Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(2015,2736)]
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([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.2015");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.d (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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2015.9 | ||
Character | \(\chi\) | \(=\) | 2736.2015 |
Dual form | 2736.2.d.b.2015.16 |
$q$-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 | ||||||||
\(5\) | − 1.28244i | − 0.573524i | −0.958002 | − | 0.286762i | \(-0.907421\pi\) | ||||
0.958002 | − | 0.286762i | \(-0.0925788\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.16899i | − 1.57573i | −0.615847 | − | 0.787866i | \(-0.711186\pi\) | ||||
0.615847 | − | 0.787866i | \(-0.288814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.743817 | 0.224269 | 0.112135 | − | 0.993693i | \(-0.464231\pi\) | ||||
0.112135 | + | 0.993693i | \(0.464231\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.42357 | −1.22688 | −0.613438 | − | 0.789743i | \(-0.710214\pi\) | ||||
−0.613438 | + | 0.789743i | \(0.710214\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1.23027i | − 0.298384i | −0.988808 | − | 0.149192i | \(-0.952333\pi\) | ||||
0.988808 | − | 0.149192i | \(-0.0476673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.13146 | 1.48701 | 0.743506 | − | 0.668729i | \(-0.233161\pi\) | ||||
0.743506 | + | 0.668729i | \(0.233161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.35535 | 0.671071 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7.86993i | − 1.46141i | −0.682693 | − | 0.730705i | \(-0.739191\pi\) | ||||
0.682693 | − | 0.730705i | \(-0.260809\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.885686i | 0.159074i | 0.996832 | + | 0.0795370i | \(0.0253442\pi\) | ||||
−0.996832 | + | 0.0795370i | \(0.974656\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.34648 | −0.903719 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.287141 | 0.0472057 | 0.0236029 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236029 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 7.60097i | − 1.18707i | −0.804807 | − | 0.593536i | \(-0.797731\pi\) | ||||
0.804807 | − | 0.593536i | \(-0.202269\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.02768i | 0.766713i | 0.923600 | + | 0.383357i | \(0.125232\pi\) | ||||
−0.923600 | + | 0.383357i | \(0.874768\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.88028 | −1.44119 | −0.720593 | − | 0.693358i | \(-0.756131\pi\) | ||||
−0.720593 | + | 0.693358i | \(0.756131\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.3805 | −1.48293 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.21504i | − 1.26578i | −0.774240 | − | 0.632892i | \(-0.781868\pi\) | ||||
0.774240 | − | 0.632892i | \(-0.218132\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.953899i | − 0.128624i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.9619 | −1.42712 | −0.713560 | − | 0.700594i | \(-0.752918\pi\) | ||||
−0.713560 | + | 0.700594i | \(0.752918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2919 | −1.44578 | −0.722889 | − | 0.690964i | \(-0.757186\pi\) | ||||
−0.722889 | + | 0.690964i | \(0.757186\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.67295i | 0.703643i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.62728i | 0.931821i | 0.884832 | + | 0.465910i | \(0.154273\pi\) | ||||
−0.884832 | + | 0.465910i | \(0.845727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.47154 | −0.174640 | −0.0873198 | − | 0.996180i | \(-0.527830\pi\) | ||||
−0.0873198 | + | 0.996180i | \(0.527830\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9535 | 1.28201 | 0.641004 | − | 0.767538i | \(-0.278518\pi\) | ||||
0.641004 | + | 0.767538i | \(0.278518\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.10097i | − 0.353388i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 3.62346i | − 0.407671i | −0.979005 | − | 0.203835i | \(-0.934659\pi\) | ||||
0.979005 | − | 0.203835i | \(-0.0653407\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.21360 | −0.791795 | −0.395897 | − | 0.918295i | \(-0.629566\pi\) | ||||
−0.395897 | + | 0.918295i | \(0.629566\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.57774 | −0.171130 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.4121i | 1.42168i | 0.703352 | + | 0.710842i | \(0.251686\pi\) | ||||
−0.703352 | + | 0.710842i | \(0.748314\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.4418i | 1.93323i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.28244 | 0.131575 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.73111 | −0.784976 | −0.392488 | − | 0.919757i | \(-0.628385\pi\) | ||||
−0.392488 | + | 0.919757i | \(0.628385\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 7.71438i | − 0.767609i | −0.923414 | − | 0.383805i | \(-0.874614\pi\) | ||||
0.923414 | − | 0.383805i | \(-0.125386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.33416i | 0.821189i | 0.911818 | + | 0.410595i | \(0.134679\pi\) | ||||
−0.911818 | + | 0.410595i | \(0.865321\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.66786 | −0.451259 | −0.225629 | − | 0.974213i | \(-0.572444\pi\) | ||||
−0.225629 | + | 0.974213i | \(0.572444\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.10834 | 0.393507 | 0.196754 | − | 0.980453i | \(-0.436960\pi\) | ||||
0.196754 | + | 0.980453i | \(0.436960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 3.28491i | − 0.309019i | −0.987991 | − | 0.154509i | \(-0.950620\pi\) | ||||
0.987991 | − | 0.154509i | \(-0.0493796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 9.14565i | − 0.852836i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.12898 | −0.470173 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4467 | −0.949703 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 10.7152i | − 0.958398i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7389i | 1.57407i | 0.616906 | + | 0.787037i | \(0.288386\pi\) | ||||
−0.616906 | + | 0.787037i | \(0.711614\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2751 | 0.985109 | 0.492555 | − | 0.870281i | \(-0.336063\pi\) | ||||
0.492555 | + | 0.870281i | \(0.336063\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.16899 | 0.361498 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 0.233400i | − 0.0199407i | −0.999950 | − | 0.00997037i | \(-0.996826\pi\) | ||||
0.999950 | − | 0.00997037i | \(-0.00317372\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.11798i | − 0.349282i | −0.984632 | − | 0.174641i | \(-0.944123\pi\) | ||||
0.984632 | − | 0.174641i | \(-0.0558765\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.29032 | −0.275151 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.0927 | −0.838153 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.0740i | 1.31683i | 0.752655 | + | 0.658415i | \(0.228773\pi\) | ||||
−0.752655 | + | 0.658415i | \(0.771227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 17.4086i | − 1.41669i | −0.705866 | − | 0.708345i | \(-0.749442\pi\) | ||||
0.705866 | − | 0.708345i | \(-0.250558\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.13584 | 0.0912327 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.6960 | −1.25268 | −0.626340 | − | 0.779550i | \(-0.715448\pi\) | ||||
−0.626340 | + | 0.779550i | \(0.715448\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 29.7310i | − 2.34313i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.84447i | 0.771078i | 0.922691 | + | 0.385539i | \(0.125985\pi\) | ||||
−0.922691 | + | 0.385539i | \(0.874015\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.1322 | −1.09358 | −0.546790 | − | 0.837270i | \(-0.684150\pi\) | ||||
−0.546790 | + | 0.837270i | \(0.684150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.56793 | 0.505226 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 22.7579i | − 1.73025i | −0.501554 | − | 0.865126i | \(-0.667238\pi\) | ||||
0.501554 | − | 0.865126i | \(-0.332762\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 13.9884i | − 1.05743i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.64721 | 0.347349 | 0.173674 | − | 0.984803i | \(-0.444436\pi\) | ||||
0.173674 | + | 0.984803i | \(0.444436\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.4784 | −1.59647 | −0.798237 | − | 0.602344i | \(-0.794234\pi\) | ||||
−0.798237 | + | 0.602344i | \(0.794234\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 0.368241i | − 0.0270736i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 0.915095i | − 0.0669183i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.9024 | 1.36773 | 0.683864 | − | 0.729609i | \(-0.260298\pi\) | ||||
0.683864 | + | 0.729609i | \(0.260298\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.3639 | −1.10592 | −0.552960 | − | 0.833208i | \(-0.686502\pi\) | ||||
−0.552960 | + | 0.833208i | \(0.686502\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 7.50966i | − 0.535041i | −0.963552 | − | 0.267521i | \(-0.913796\pi\) | ||||
0.963552 | − | 0.267521i | \(-0.0862044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.02502i | 0.143550i | 0.997421 | + | 0.0717748i | \(0.0228663\pi\) | ||||
−0.997421 | + | 0.0717748i | \(0.977134\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −32.8097 | −2.30279 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.74777 | −0.680814 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.743817i | 0.0514509i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5645i | 0.727290i | 0.931538 | + | 0.363645i | \(0.118468\pi\) | ||||
−0.931538 | + | 0.363645i | \(0.881532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.44768 | 0.439728 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.69242 | 0.250658 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.44218i | 0.366080i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 9.26053i | − 0.620131i | −0.950715 | − | 0.310065i | \(-0.899649\pi\) | ||||
0.950715 | − | 0.310065i | \(-0.100351\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.8910 | 0.789232 | 0.394616 | − | 0.918846i | \(-0.370878\pi\) | ||||
0.394616 | + | 0.918846i | \(0.370878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.03944 | 0.531261 | 0.265631 | − | 0.964075i | \(-0.414420\pi\) | ||||
0.265631 | + | 0.964075i | \(0.414420\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 24.2635i | − 1.58956i | −0.606900 | − | 0.794778i | \(-0.707587\pi\) | ||||
0.606900 | − | 0.794778i | \(-0.292413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.6708i | 0.826555i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.4847 | 1.45442 | 0.727208 | − | 0.686417i | \(-0.240818\pi\) | ||||
0.727208 | + | 0.686417i | \(0.240818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5412 | 1.25876 | 0.629379 | − | 0.777099i | \(-0.283309\pi\) | ||||
0.629379 | + | 0.777099i | \(0.283309\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.3124i | 0.850496i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.42357i | − 0.281465i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.73713 | 0.109646 | 0.0548232 | − | 0.998496i | \(-0.482540\pi\) | ||||
0.0548232 | + | 0.998496i | \(0.482540\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.30450 | 0.333491 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 28.8546i | − 1.79990i | −0.435994 | − | 0.899949i | \(-0.643603\pi\) | ||||
0.435994 | − | 0.899949i | \(-0.356397\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.19709i | − 0.0743836i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.4759 | 0.830960 | 0.415480 | − | 0.909602i | \(-0.363614\pi\) | ||||
0.415480 | + | 0.909602i | \(0.363614\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.8177 | −0.725956 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 0.894031i | − 0.0545100i | −0.999629 | − | 0.0272550i | \(-0.991323\pi\) | ||||
0.999629 | − | 0.0272550i | \(-0.00867662\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 24.6977i | − 1.50028i | −0.661280 | − | 0.750139i | \(-0.729986\pi\) | ||||
0.661280 | − | 0.750139i | \(-0.270014\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.49577 | 0.150500 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.3676 | 1.34394 | 0.671971 | − | 0.740578i | \(-0.265448\pi\) | ||||
0.671971 | + | 0.740578i | \(0.265448\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 6.64344i | − 0.396314i | −0.980170 | − | 0.198157i | \(-0.936504\pi\) | ||||
0.980170 | − | 0.198157i | \(-0.0634957\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.47351i | 0.206479i | 0.994657 | + | 0.103239i | \(0.0329208\pi\) | ||||
−0.994657 | + | 0.103239i | \(0.967079\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −31.6884 | −1.87051 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.4864 | 0.910967 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.5716i | 1.37707i | 0.725204 | + | 0.688534i | \(0.241745\pi\) | ||||
−0.725204 | + | 0.688534i | \(0.758255\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.0580i | 0.818487i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.5465 | −1.82438 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.9604 | 1.20813 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.4811i | 0.829188i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.2077i | 0.696728i | 0.937359 | + | 0.348364i | \(0.113263\pi\) | ||||
−0.937359 | + | 0.348364i | \(0.886737\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.4706 | 0.990665 | 0.495333 | − | 0.868703i | \(-0.335046\pi\) | ||||
0.495333 | + | 0.868703i | \(0.335046\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.55101 | −0.144191 | −0.0720957 | − | 0.997398i | \(-0.522969\pi\) | ||||
−0.0720957 | + | 0.997398i | \(0.522969\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.4886i | 0.757595i | 0.925480 | + | 0.378798i | \(0.123662\pi\) | ||||
−0.925480 | + | 0.378798i | \(0.876338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 5.85379i | − 0.327749i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.23027 | 0.0684540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.8426 | −0.823321 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 41.1908i | 2.27092i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 31.6269i | − 1.73837i | −0.494484 | − | 0.869187i | \(-0.664643\pi\) | ||||
0.494484 | − | 0.869187i | \(-0.335357\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.78151 | 0.534421 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.92289 | −0.540534 | −0.270267 | − | 0.962785i | \(-0.587112\pi\) | ||||
−0.270267 | + | 0.962785i | \(0.587112\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.658788i | 0.0356754i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.0933i | 0.760969i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.9484 | −0.748791 | −0.374395 | − | 0.927269i | \(-0.622150\pi\) | ||||
−0.374395 | + | 0.927269i | \(0.622150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.9967 | 0.588638 | 0.294319 | − | 0.955707i | \(-0.404907\pi\) | ||||
0.294319 | + | 0.955707i | \(0.404907\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 23.7735i | − 1.26534i | −0.774423 | − | 0.632669i | \(-0.781960\pi\) | ||||
0.774423 | − | 0.632669i | \(-0.218040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.88716i | 0.100160i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.3019 | 0.702050 | 0.351025 | − | 0.936366i | \(-0.385833\pi\) | ||||
0.351025 | + | 0.936366i | \(0.385833\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 14.0472i | − 0.735262i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.71599i | 0.507170i | 0.967313 | + | 0.253585i | \(0.0816098\pi\) | ||||
−0.967313 | + | 0.253585i | \(0.918390\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −38.4174 | −1.99453 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.4428 | 1.05849 | 0.529245 | − | 0.848469i | \(-0.322475\pi\) | ||||
0.529245 | + | 0.848469i | \(0.322475\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.8132i | 1.79297i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 12.3290i | − 0.633297i | −0.948543 | − | 0.316649i | \(-0.897442\pi\) | ||||
0.948543 | − | 0.316649i | \(-0.102558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.32251 | −0.169772 | −0.0848861 | − | 0.996391i | \(-0.527053\pi\) | ||||
−0.0848861 | + | 0.996391i | \(0.527053\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.97680 | −0.202676 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.93846i | 0.301092i | 0.988603 | + | 0.150546i | \(0.0481032\pi\) | ||||
−0.988603 | + | 0.150546i | \(0.951897\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 8.77361i | − 0.443701i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.64686 | −0.233809 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.14026 | −0.257982 | −0.128991 | − | 0.991646i | \(-0.541174\pi\) | ||||
−0.128991 | + | 0.991646i | \(0.541174\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.4755i | 0.523121i | 0.965187 | + | 0.261561i | \(0.0842371\pi\) | ||||
−0.965187 | + | 0.261561i | \(0.915763\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3.91789i | − 0.195164i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.213580 | 0.0105868 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.282636 | −0.0139755 | −0.00698773 | − | 0.999976i | \(-0.502224\pi\) | ||||
−0.00698773 | + | 0.999976i | \(0.502224\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.7002i | 2.24876i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.25099i | 0.454113i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.7445 | 1.30655 | 0.653277 | − | 0.757119i | \(-0.273394\pi\) | ||||
0.653277 | + | 0.757119i | \(0.273394\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.6874 | 0.618346 | 0.309173 | − | 0.951006i | \(-0.399948\pi\) | ||||
0.309173 | + | 0.951006i | \(0.399948\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 4.12799i | − 0.200237i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 47.0758i | 2.27816i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.8802 | 1.63195 | 0.815975 | − | 0.578087i | \(-0.196201\pi\) | ||||
0.815975 | + | 0.578087i | \(0.196201\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1806 | −0.969818 | −0.484909 | − | 0.874565i | \(-0.661147\pi\) | ||||
−0.484909 | + | 0.874565i | \(0.661147\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.13146i | 0.341144i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3057i | 1.01687i | 0.861101 | + | 0.508434i | \(0.169775\pi\) | ||||
−0.861101 | + | 0.508434i | \(0.830225\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.6164 | −1.54965 | −0.774827 | − | 0.632174i | \(-0.782163\pi\) | ||||
−0.774827 | + | 0.632174i | \(0.782163\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.2002 | 0.815369 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 11.4787i | − 0.541713i | −0.962620 | − | 0.270857i | \(-0.912693\pi\) | ||||
0.962620 | − | 0.270857i | \(-0.0873069\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 5.65373i | − 0.266224i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.6505 | 1.10875 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.2828 | 1.08912 | 0.544561 | − | 0.838721i | \(-0.316696\pi\) | ||||
0.544561 | + | 0.838721i | \(0.316696\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 8.56760i | − 0.399033i | −0.979894 | − | 0.199516i | \(-0.936063\pi\) | ||||
0.979894 | − | 0.199516i | \(-0.0639371\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 37.6104i | − 1.74790i | −0.486012 | − | 0.873952i | \(-0.661549\pi\) | ||||
0.486012 | − | 0.873952i | \(-0.338451\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.1560 | −1.48800 | −0.744000 | − | 0.668180i | \(-0.767074\pi\) | ||||
−0.744000 | + | 0.668180i | \(0.767074\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.7981 | 1.46830 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.73967i | 0.171950i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.35535i | 0.153954i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.7819 | 1.36077 | 0.680385 | − | 0.732855i | \(-0.261813\pi\) | ||||
0.680385 | + | 0.732855i | \(0.261813\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.27019 | −0.0579156 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.91467i | 0.450202i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1.60249i | − 0.0726158i | −0.999341 | − | 0.0363079i | \(-0.988440\pi\) | ||||
0.999341 | − | 0.0363079i | \(-0.0115597\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.26773 | −0.0572117 | −0.0286058 | − | 0.999591i | \(-0.509107\pi\) | ||||
−0.0286058 | + | 0.999591i | \(0.509107\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.68214 | −0.436061 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.13484i | 0.275185i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 0.186383i | − 0.00834367i | −0.999991 | − | 0.00417183i | \(-0.998672\pi\) | ||||
0.999991 | − | 0.00417183i | \(-0.00132794\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.6715 | 1.14464 | 0.572318 | − | 0.820031i | \(-0.306044\pi\) | ||||
0.572318 | + | 0.820031i | \(0.306044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.89321 | −0.440242 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 37.1654i | − 1.64733i | −0.567078 | − | 0.823664i | \(-0.691926\pi\) | ||||
0.567078 | − | 0.823664i | \(-0.308074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 45.6650i | − 2.02010i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.6880 | 0.470972 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.34912 | −0.323214 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 17.6596i | − 0.773683i | −0.922146 | − | 0.386841i | \(-0.873566\pi\) | ||||
0.922146 | − | 0.386841i | \(-0.126434\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.89269i | 0.257669i | 0.991666 | + | 0.128835i | \(0.0411236\pi\) | ||||
−0.991666 | + | 0.128835i | \(0.958876\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.08963 | 0.0474651 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.8577 | 1.21120 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.6234i | 1.45639i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.98623i | 0.258808i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.72120 | −0.332576 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.7900 | −1.75370 | −0.876849 | − | 0.480767i | \(-0.840358\pi\) | ||||
−0.876849 | + | 0.480767i | \(0.840358\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 5.26869i | − 0.225686i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 7.95762i | − 0.340243i | −0.985423 | − | 0.170122i | \(-0.945584\pi\) | ||||
0.985423 | − | 0.170122i | \(-0.0544161\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.86993 | 0.335270 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.1062 | −0.642380 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.1166i | 0.598138i | 0.954232 | + | 0.299069i | \(0.0966760\pi\) | ||||
−0.954232 | + | 0.299069i | \(0.903324\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 22.2403i | − 0.940663i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.8435 | 1.08917 | 0.544587 | − | 0.838704i | \(-0.316686\pi\) | ||||
0.544587 | + | 0.838704i | \(0.316686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.21270 | −0.177229 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.8478i | 1.46090i | 0.682968 | + | 0.730449i | \(0.260689\pi\) | ||||
−0.682968 | + | 0.730449i | \(0.739311\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.32290i | 0.180908i | 0.995901 | + | 0.0904538i | \(0.0288317\pi\) | ||||
−0.995901 | + | 0.0904538i | \(0.971168\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.9286 | 0.997890 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.93312 | −0.413521 | −0.206761 | − | 0.978392i | \(-0.566292\pi\) | ||||
−0.206761 | + | 0.978392i | \(0.566292\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.0734i | 1.24766i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 6.85430i | − 0.283876i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 43.4288 | 1.79250 | 0.896249 | − | 0.443551i | \(-0.146281\pi\) | ||||
0.896249 | + | 0.443551i | \(0.146281\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.885686 | −0.0364941 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.1735i | 1.64973i | 0.565331 | + | 0.824864i | \(0.308748\pi\) | ||||
−0.565331 | + | 0.824864i | \(0.691252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.57760i | 0.269655i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.45838 | −0.386459 | −0.193229 | − | 0.981154i | \(-0.561896\pi\) | ||||
−0.193229 | + | 0.981154i | \(0.561896\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.6402 | 1.41300 | 0.706501 | − | 0.707712i | \(-0.250272\pi\) | ||||
0.706501 | + | 0.707712i | \(0.250272\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.3973i | 0.544677i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 41.8946i | − 1.70045i | −0.526419 | − | 0.850225i | \(-0.676466\pi\) | ||||
0.526419 | − | 0.850225i | \(-0.323534\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 43.7061 | 1.76816 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.25774 | 0.0507997 | 0.0253999 | − | 0.999677i | \(-0.491914\pi\) | ||||
0.0253999 | + | 0.999677i | \(0.491914\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 8.12508i | − 0.327103i | −0.986535 | − | 0.163552i | \(-0.947705\pi\) | ||||
0.986535 | − | 0.163552i | \(-0.0522951\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.9388i | 0.881794i | 0.897558 | + | 0.440897i | \(0.145340\pi\) | ||||
−0.897558 | + | 0.440897i | \(0.854660\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 55.9151 | 2.24019 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.03516 | 0.121407 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 0.353261i | − 0.0140854i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 18.9260i | − 0.753434i | −0.926328 | − | 0.376717i | \(-0.877053\pi\) | ||||
0.926328 | − | 0.376717i | \(-0.122947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.7491 | 0.902769 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 45.9189 | 1.81937 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.6972i | 0.935983i | 0.883733 | + | 0.467991i | \(0.155022\pi\) | ||||
−0.883733 | + | 0.467991i | \(0.844978\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.9864i | 0.433261i | 0.976254 | + | 0.216630i | \(0.0695066\pi\) | ||||
−0.976254 | + | 0.216630i | \(0.930493\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.8804 | −1.17472 | −0.587360 | − | 0.809326i | \(-0.699833\pi\) | ||||
−0.587360 | + | 0.809326i | \(0.699833\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.15365 | −0.320059 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.69439i | 0.105440i | 0.998609 | + | 0.0527199i | \(0.0167890\pi\) | ||||
−0.998609 | + | 0.0527199i | \(0.983211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 14.4596i | − 0.564983i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.6546 | −1.38890 | −0.694452 | − | 0.719539i | \(-0.744353\pi\) | ||||
−0.694452 | + | 0.719539i | \(0.744353\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6821 | −0.609963 | −0.304982 | − | 0.952358i | \(-0.598650\pi\) | ||||
−0.304982 | + | 0.952358i | \(0.598650\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 5.34648i | − 0.207327i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 56.1241i | − 2.17313i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.39909 | −0.324243 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0739 | 0.850886 | 0.425443 | − | 0.904985i | \(-0.360118\pi\) | ||||
0.425443 | + | 0.904985i | \(0.360118\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 27.1750i | − 1.04442i | −0.852817 | − | 0.522209i | \(-0.825108\pi\) | ||||
0.852817 | − | 0.522209i | \(-0.174892\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.2310i | 1.23691i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.4504 | −0.438137 | −0.219069 | − | 0.975709i | \(-0.570302\pi\) | ||||
−0.219069 | + | 0.975709i | \(0.570302\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.299321 | −0.0114365 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.7633i | 1.55296i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.60749i | 0.0611518i | 0.999532 | + | 0.0305759i | \(0.00973412\pi\) | ||||
−0.999532 | + | 0.0305759i | \(0.990266\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.28105 | −0.200322 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.35124 | −0.354204 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 20.4400i | − 0.772008i | −0.922497 | − | 0.386004i | \(-0.873855\pi\) | ||||
0.922497 | − | 0.386004i | \(-0.126145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.287141i | 0.0108297i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32.1612 | −1.20955 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.6945 | 1.37809 | 0.689046 | − | 0.724718i | \(-0.258030\pi\) | ||||
0.689046 | + | 0.724718i | \(0.258030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.31624i | 0.236545i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.21963i | 0.157805i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.7366 | 0.586878 | 0.293439 | − | 0.955978i | \(-0.405200\pi\) | ||||
0.293439 | + | 0.955978i | \(0.405200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.7451 | 1.29397 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 26.4064i | − 0.980709i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 10.6478i | − 0.394906i | −0.980312 | − | 0.197453i | \(-0.936733\pi\) | ||||
0.980312 | − | 0.197453i | \(-0.0632670\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.18539 | 0.228775 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.7388 | 0.876811 | 0.438406 | − | 0.898777i | \(-0.355543\pi\) | ||||
0.438406 | + | 0.898777i | \(0.355543\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.67330i | 0.208979i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 40.5762i | − 1.49262i | −0.665598 | − | 0.746310i | \(-0.731824\pi\) | ||||
0.665598 | − | 0.746310i | \(-0.268176\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.2145 | −0.558164 | −0.279082 | − | 0.960267i | \(-0.590030\pi\) | ||||
−0.279082 | + | 0.960267i | \(0.590030\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.6139 | 0.755233 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.4603i | 0.711063i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.5365i | 1.62516i | 0.582851 | + | 0.812579i | \(0.301937\pi\) | ||||
−0.582851 | + | 0.812579i | \(0.698063\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.3254 | −0.812505 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.7119 | −1.29797 | −0.648986 | − | 0.760800i | \(-0.724807\pi\) | ||||
−0.648986 | + | 0.760800i | \(0.724807\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 16.3436i | − 0.592456i | −0.955117 | − | 0.296228i | \(-0.904271\pi\) | ||||
0.955117 | − | 0.296228i | \(-0.0957288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 17.1276i | − 0.620062i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 48.4907 | 1.75090 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.4698 | 0.485734 | 0.242867 | − | 0.970060i | \(-0.421912\pi\) | ||||
0.242867 | + | 0.970060i | \(0.421912\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.9105i | 1.07580i | 0.843007 | + | 0.537902i | \(0.180783\pi\) | ||||
−0.843007 | + | 0.537902i | \(0.819217\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.97179i | 0.106750i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.60097 | 0.272333 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.09456 | −0.0391663 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.1292i | 0.718441i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3674i | 0.476497i | 0.971204 | + | 0.238248i | \(0.0765732\pi\) | ||||
−0.971204 | + | 0.238248i | \(0.923427\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.6948 | −0.486930 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.9504 | 1.77379 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 21.9906i | − 0.778946i | −0.921038 | − | 0.389473i | \(-0.872657\pi\) | ||||
0.921038 | − | 0.389473i | \(-0.127343\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.1554i | 0.430027i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.14738 | 0.287515 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −38.1282 | −1.34384 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.79728i | 0.0983471i | 0.998790 | + | 0.0491736i | \(0.0156587\pi\) | ||||
−0.998790 | + | 0.0491736i | \(0.984341\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9149i | 0.734423i | 0.930138 | + | 0.367211i | \(0.119687\pi\) | ||||
−0.930138 | + | 0.367211i | \(0.880313\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.6249 | 0.442232 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.02768 | −0.175896 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 14.3274i | − 0.500031i | −0.968242 | − | 0.250015i | \(-0.919564\pi\) | ||||
0.968242 | − | 0.250015i | \(-0.0804357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.9377i | 0.799557i | 0.916612 | + | 0.399778i | \(0.130913\pi\) | ||||
−0.916612 | + | 0.399778i | \(0.869087\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.0384 | −1.63568 | −0.817842 | − | 0.575442i | \(-0.804830\pi\) | ||||
−0.817842 | + | 0.575442i | \(0.804830\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.4073 | −1.05609 | −0.528044 | − | 0.849217i | \(-0.677075\pi\) | ||||
−0.528044 | + | 0.849217i | \(0.677075\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.7708i | 0.442483i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.1236i | 0.627194i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.3644 | −1.11734 | −0.558672 | − | 0.829389i | \(-0.688689\pi\) | ||||
−0.558672 | + | 0.829389i | \(0.688689\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −32.9359 | −1.13572 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 8.42297i | − 0.289759i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 43.5524i | 1.49648i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.04774 | 0.0701955 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.4556 | 0.426472 | 0.213236 | − | 0.977001i | \(-0.431600\pi\) | ||||
0.213236 | + | 0.977001i | \(0.431600\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.98270i | 0.0677278i | 0.999426 | + | 0.0338639i | \(0.0107813\pi\) | ||||
−0.999426 | + | 0.0338639i | \(0.989219\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.4260i | 1.54992i | 0.632013 | + | 0.774958i | \(0.282229\pi\) | ||||
−0.632013 | + | 0.774958i | \(0.717771\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.2358 | −0.416512 | −0.208256 | − | 0.978074i | \(-0.566779\pi\) | ||||
−0.208256 | + | 0.978074i | \(0.566779\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.1856 | −0.992341 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2.69519i | − 0.0914280i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 33.7398i | − 1.14323i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −44.6717 | −1.51018 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.2691 | 0.684438 | 0.342219 | − | 0.939620i | \(-0.388822\pi\) | ||||
0.342219 | + | 0.939620i | \(0.388822\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.60011i | 0.222363i | 0.993800 | + | 0.111182i | \(0.0354636\pi\) | ||||
−0.993800 | + | 0.111182i | \(0.964536\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 58.0485i | − 1.95349i | −0.214410 | − | 0.976744i | \(-0.568783\pi\) | ||||
0.214410 | − | 0.976744i | \(-0.431217\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.3048 | −1.52119 | −0.760594 | − | 0.649228i | \(-0.775092\pi\) | ||||
−0.760594 | + | 0.649228i | \(0.775092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 73.9534 | 2.48032 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 9.88028i | − 0.330631i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 5.95976i | − 0.199213i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.97029 | 0.232472 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.3370 | −0.377690 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.5447i | 0.915615i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.5782i | 0.948924i | 0.880276 | + | 0.474462i | \(0.157357\pi\) | ||||
−0.880276 | + | 0.474462i | \(0.842643\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.45969 | −0.0483618 | −0.0241809 | − | 0.999708i | \(-0.507698\pi\) | ||||
−0.0241809 | + | 0.999708i | \(0.507698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.36559 | −0.177575 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 47.0058i | − 1.55227i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 57.9682i | − 1.91219i | −0.293049 | − | 0.956097i | \(-0.594670\pi\) | ||||
0.293049 | − | 0.956097i | \(-0.405330\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.50945 | 0.214261 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.963460 | 0.0316784 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 35.4982i | − 1.16466i | −0.812953 | − | 0.582329i | \(-0.802141\pi\) | ||||
0.812953 | − | 0.582329i | \(-0.197859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 10.3805i | − 0.340208i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.17355 | −0.0383793 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.78900 | 0.189118 | 0.0945592 | − | 0.995519i | \(-0.469856\pi\) | ||||
0.0945592 | + | 0.995519i | \(0.469856\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.8831i | 1.75654i | 0.478165 | + | 0.878270i | \(0.341302\pi\) | ||||
−0.478165 | + | 0.878270i | \(0.658698\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 54.2060i | − 1.76519i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.7495 | −0.544287 | −0.272143 | − | 0.962257i | \(-0.587733\pi\) | ||||
−0.272143 | + | 0.962257i | \(0.587733\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.4534 | −1.57286 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.25135i | 0.267288i | 0.991029 | + | 0.133644i | \(0.0426678\pi\) | ||||
−0.991029 | + | 0.133644i | \(0.957332\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 24.2411i | − 0.784425i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.973045 | −0.0314212 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.2156 | 0.974695 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.7033i | 0.634271i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.9341i | 1.15556i | 0.816192 | + | 0.577781i | \(0.196081\pi\) | ||||
−0.816192 | + | 0.577781i | \(0.803919\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.0795 | 0.355557 | 0.177779 | − | 0.984070i | \(-0.443109\pi\) | ||||
0.177779 | + | 0.984070i | \(0.443109\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.1678 | −0.550375 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 12.6243i | − 0.403888i | −0.979397 | − | 0.201944i | \(-0.935274\pi\) | ||||
0.979397 | − | 0.201944i | \(-0.0647259\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.97617i | 0.318840i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.3442 | −0.521300 | −0.260650 | − | 0.965433i | \(-0.583937\pi\) | ||||
−0.260650 | + | 0.965433i | \(0.583937\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.63068 | −0.306859 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.8547i | 1.14011i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.4374i | 0.712748i | 0.934343 | + | 0.356374i | \(0.115987\pi\) | ||||
−0.934343 | + | 0.356374i | \(0.884013\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.59696 | 0.0823291 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.8152 | 1.86270 | 0.931349 | − | 0.364129i | \(-0.118633\pi\) | ||||
0.931349 | + | 0.364129i | \(0.118633\pi\) | |||||||
\(998\) | 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.d.b.2015.9 | ✓ | 24 | |
3.2 | odd | 2 | inner | 2736.2.d.b.2015.15 | yes | 24 | |
4.3 | odd | 2 | inner | 2736.2.d.b.2015.10 | yes | 24 | |
12.11 | even | 2 | inner | 2736.2.d.b.2015.16 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.d.b.2015.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2736.2.d.b.2015.10 | yes | 24 | 4.3 | odd | 2 | inner | |
2736.2.d.b.2015.15 | yes | 24 | 3.2 | odd | 2 | inner | |
2736.2.d.b.2015.16 | yes | 24 | 12.11 | even | 2 | inner |