Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(271,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.bz (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 271.5 | ||
Character | \(\chi\) | \(=\) | 1120.271 |
Dual form | 1120.2.bz.f.591.5 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.75472 | + | 1.01309i | −1.01309 | + | 0.584908i | −0.912095 | − | 0.409979i | \(-0.865536\pi\) |
−0.100995 | + | 0.994887i | \(0.532203\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.63843 | + | 2.07739i | −0.619270 | + | 0.785178i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.552704 | − | 0.957311i | 0.184235 | − | 0.319104i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.572544 | + | 0.991675i | 0.172628 | + | 0.299001i | 0.939338 | − | 0.342993i | \(-0.111441\pi\) |
−0.766710 | + | 0.641994i | \(0.778107\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.714654 | 0.198209 | 0.0991047 | − | 0.995077i | \(-0.468402\pi\) | ||||
0.0991047 | + | 0.995077i | \(0.468402\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.02618i | 0.523158i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.98251 | + | 1.14460i | −0.480829 | + | 0.277607i | −0.720762 | − | 0.693183i | \(-0.756208\pi\) |
0.239933 | + | 0.970789i | \(0.422875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.36692 | + | 1.94389i | 0.772425 | + | 0.445960i | 0.833739 | − | 0.552159i | \(-0.186196\pi\) |
−0.0613139 | + | 0.998119i | \(0.519529\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.770420 | − | 5.30512i | 0.168119 | − | 1.15767i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00399 | − | 2.31171i | −0.834891 | − | 0.482024i | 0.0206336 | − | 0.999787i | \(-0.493432\pi\) |
−0.855524 | + | 0.517763i | \(0.826765\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.83879i | − | 0.738775i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.54366i | 0.286650i | 0.989676 | + | 0.143325i | \(0.0457794\pi\) | ||||
−0.989676 | + | 0.143325i | \(0.954221\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.590584 | − | 1.02292i | −0.106072 | − | 0.183722i | 0.808104 | − | 0.589040i | \(-0.200494\pi\) |
−0.914176 | + | 0.405318i | \(0.867161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00931 | − | 1.16008i | −0.349776 | − | 0.201943i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.979852 | + | 2.45762i | 0.165625 | + | 0.415413i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.72305 | − | 3.30420i | −0.940864 | − | 0.543208i | −0.0506326 | − | 0.998717i | \(-0.516124\pi\) |
−0.890231 | + | 0.455510i | \(0.849457\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.25402 | + | 0.724009i | −0.200804 | + | 0.115934i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9848i | 1.71555i | 0.514029 | + | 0.857773i | \(0.328152\pi\) | ||||
−0.514029 | + | 0.857773i | \(0.671848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8452 | −1.65387 | −0.826935 | − | 0.562297i | \(-0.809918\pi\) | ||||
−0.826935 | + | 0.562297i | \(0.809918\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.552704 | − | 0.957311i | −0.0823922 | − | 0.142708i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.60440 | − | 4.51095i | 0.379890 | − | 0.657989i | −0.611156 | − | 0.791510i | \(-0.709295\pi\) |
0.991046 | + | 0.133521i | \(0.0426285\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.63107 | − | 6.80732i | −0.233009 | − | 0.972474i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.31917 | − | 4.01692i | 0.324749 | − | 0.562481i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.25895 | + | 1.30420i | −0.310290 | + | 0.179146i | −0.647056 | − | 0.762442i | \(-0.724000\pi\) |
0.336766 | + | 0.941588i | \(0.390667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.14509 | 0.154404 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.87736 | −1.04338 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.5249 | + | 6.07655i | −1.37023 | + | 0.791100i | −0.990956 | − | 0.134187i | \(-0.957158\pi\) |
−0.379269 | + | 0.925286i | \(0.623824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.13513 | − | 12.3584i | 0.913559 | − | 1.58233i | 0.104563 | − | 0.994518i | \(-0.466656\pi\) |
0.808997 | − | 0.587813i | \(-0.200011\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.08314 | + | 2.71667i | 0.136462 | + | 0.342268i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.357327 | − | 0.618909i | 0.0443210 | − | 0.0767662i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.08800 | − | 7.08062i | −0.499429 | − | 0.865036i | 0.500571 | − | 0.865695i | \(-0.333123\pi\) |
−1.00000 | 0.000659524i | \(0.999790\pi\) | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.36787 | 1.12776 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 15.8551i | − | 1.88166i | −0.338881 | − | 0.940829i | \(-0.610048\pi\) | ||
0.338881 | − | 0.940829i | \(-0.389952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.71396 | + | 2.72160i | −0.551727 | + | 0.318540i | −0.749818 | − | 0.661644i | \(-0.769859\pi\) |
0.198091 | + | 0.980184i | \(0.436526\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.75472 | + | 1.01309i | 0.202618 | + | 0.116982i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.99817 | − | 0.435400i | −0.341673 | − | 0.0496184i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.20023 | − | 4.73440i | −0.922598 | − | 0.532662i | −0.0381347 | − | 0.999273i | \(-0.512142\pi\) |
−0.884463 | + | 0.466611i | \(0.845475\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.54715 | + | 9.60794i | 0.616350 | + | 1.06755i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.78987i | 0.306229i | 0.988208 | + | 0.153114i | \(0.0489303\pi\) | ||||
−0.988208 | + | 0.153114i | \(0.951070\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.28920i | 0.248299i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.56386 | − | 2.70869i | −0.167664 | − | 0.290402i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.0522 | − | 6.38097i | −1.17153 | − | 0.676382i | −0.217488 | − | 0.976063i | \(-0.569786\pi\) |
−0.954039 | + | 0.299681i | \(0.903120\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.17091 | + | 1.48461i | −0.122745 | + | 0.155630i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.07262 | + | 1.19663i | 0.214921 | + | 0.124085i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.36692 | − | 1.94389i | 0.345439 | − | 0.199439i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.18530i | 0.526487i | 0.964729 | + | 0.263244i | \(0.0847923\pi\) | ||||
−0.964729 | + | 0.263244i | \(0.915208\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.26579 | 0.127216 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.506008 | − | 0.876431i | −0.0503497 | − | 0.0872082i | 0.839752 | − | 0.542970i | \(-0.182700\pi\) |
−0.890102 | + | 0.455762i | \(0.849367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.22006 | + | 2.11321i | −0.120217 | + | 0.208221i | −0.919853 | − | 0.392263i | \(-0.871692\pi\) |
0.799636 | + | 0.600484i | \(0.205026\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.20916 | − | 3.31976i | −0.410772 | − | 0.323976i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.680251 | − | 1.17823i | 0.0657623 | − | 0.113904i | −0.831270 | − | 0.555869i | \(-0.812385\pi\) |
0.897032 | + | 0.441966i | \(0.145719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.05255 | + | 5.22649i | −0.867077 | + | 0.500607i | −0.866376 | − | 0.499393i | \(-0.833556\pi\) |
−0.000700983 | 1.00000i | \(0.500223\pi\) | ||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.3898 | 1.27091 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.83586 | −0.737135 | −0.368568 | − | 0.929601i | \(-0.620152\pi\) | ||||
−0.368568 | + | 0.929601i | \(0.620152\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00399 | + | 2.31171i | −0.373374 | + | 0.215568i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.394992 | − | 0.684146i | 0.0365170 | − | 0.0632494i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.870430 | − | 5.99379i | 0.0797922 | − | 0.549450i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.84439 | − | 8.39073i | 0.440399 | − | 0.762793i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.1286 | − | 19.2754i | −1.00344 | − | 1.73800i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0344i | 1.06788i | 0.845522 | + | 0.533940i | \(0.179289\pi\) | ||||
−0.845522 | + | 0.533940i | \(0.820711\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.0302 | − | 10.9871i | 1.67552 | − | 0.967362i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.9090 | + | 10.3397i | 1.56471 | + | 0.903387i | 0.996769 | + | 0.0803195i | \(0.0255941\pi\) |
0.567943 | + | 0.823068i | \(0.307739\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.55470 | + | 3.80946i | −0.828498 | + | 0.330322i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.32449 | − | 1.91939i | −0.286126 | − | 0.165195i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.37459 | + | 4.11290i | 0.202875 | + | 0.351389i | 0.949453 | − | 0.313908i | \(-0.101638\pi\) |
−0.746579 | + | 0.665297i | \(0.768305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.9812i | 0.931416i | 0.884938 | + | 0.465708i | \(0.154200\pi\) | ||||
−0.884938 | + | 0.465708i | \(0.845800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.5540i | 0.888803i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.409171 | + | 0.708704i | 0.0342166 | + | 0.0592648i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.33685 | + | 0.771829i | 0.111019 | + | 0.0640969i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.75850 | + | 10.2926i | 0.804868 | + | 0.848915i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.4757 | − | 7.78020i | −1.10397 | − | 0.637379i | −0.166711 | − | 0.986006i | \(-0.553315\pi\) |
−0.937261 | + | 0.348627i | \(0.886648\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.8679 | − | 6.27460i | 0.884419 | − | 0.510620i | 0.0123061 | − | 0.999924i | \(-0.496083\pi\) |
0.872113 | + | 0.489305i | \(0.162749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.53050i | 0.204579i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.18117 | −0.0948737 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.83150 | − | 6.63634i | −0.305787 | − | 0.529638i | 0.671650 | − | 0.740869i | \(-0.265586\pi\) |
−0.977436 | + | 0.211231i | \(0.932253\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.64255 | − | 4.57704i | 0.209568 | − | 0.362983i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3626 | − | 4.53026i | 0.895498 | − | 0.357035i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0482 | − | 17.4040i | 0.787037 | − | 1.36319i | −0.140738 | − | 0.990047i | \(-0.544947\pi\) |
0.927775 | − | 0.373141i | \(-0.121719\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.00931 | + | 1.16008i | −0.156425 | + | 0.0903118i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.77446 | 0.524224 | 0.262112 | − | 0.965037i | \(-0.415581\pi\) | ||||
0.262112 | + | 0.965037i | \(0.415581\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4893 | −0.960713 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.72182 | − | 2.14880i | 0.284615 | − | 0.164322i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.70160 | + | 15.0716i | −0.661570 | + | 1.14587i | 0.318633 | + | 0.947878i | \(0.396776\pi\) |
−0.980203 | + | 0.197995i | \(0.936557\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.61829 | + | 0.380233i | 0.197924 | + | 0.0287429i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.3122 | − | 21.3253i | 0.925441 | − | 1.60291i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.66373 | + | 13.2740i | 0.572814 | + | 0.992143i | 0.996275 | + | 0.0862291i | \(0.0274817\pi\) |
−0.423461 | + | 0.905914i | \(0.639185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.10021 | −0.230437 | −0.115218 | − | 0.993340i | \(-0.536757\pi\) | ||||
−0.115218 | + | 0.993340i | \(0.536757\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.9141i | 2.13739i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.72305 | + | 3.30420i | −0.420767 | + | 0.242930i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.27014 | − | 1.31067i | −0.166009 | − | 0.0958456i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.97464 | + | 6.28960i | 0.580070 | + | 0.457501i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.6460 | − | 7.30118i | −0.915034 | − | 0.528295i | −0.0329865 | − | 0.999456i | \(-0.510502\pi\) |
−0.882047 | + | 0.471161i | \(0.843835\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.50498 | + | 14.7311i | 0.612202 | + | 1.06037i | 0.990868 | + | 0.134832i | \(0.0430494\pi\) |
−0.378666 | + | 0.925533i | \(0.623617\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.44802i | 0.103695i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.2341i | 1.08538i | 0.839932 | + | 0.542692i | \(0.182595\pi\) | ||||
−0.839932 | + | 0.542692i | \(0.817405\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.02143 | + | 13.8935i | 0.568624 | + | 0.984886i | 0.996702 | + | 0.0811444i | \(0.0258575\pi\) |
−0.428078 | + | 0.903742i | \(0.640809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.3466 | + | 8.28303i | 1.01193 | + | 0.584240i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.20677 | − | 2.52918i | −0.225071 | − | 0.177514i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.51316 | + | 5.49242i | 0.664428 | + | 0.383608i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.42605 | + | 2.55538i | −0.307632 | + | 0.177611i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.45186i | 0.307941i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.85788 | 0.403273 | 0.201637 | − | 0.979460i | \(-0.435374\pi\) | ||||
0.201637 | + | 0.979460i | \(0.435374\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.0627 | + | 27.8214i | 1.10060 | + | 1.90629i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.42258 | + | 9.39218i | −0.369817 | + | 0.640541i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.09263 | + | 0.449119i | 0.209942 | + | 0.0304882i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.51446 | − | 9.55132i | 0.372633 | − | 0.645419i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.41681 | + | 0.817994i | −0.0953048 | + | 0.0550243i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3268 | 0.825465 | 0.412732 | − | 0.910852i | \(-0.364574\pi\) | ||||
0.412732 | + | 0.910852i | \(0.364574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.10541 | −0.0736938 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.79256 | + | 3.92168i | −0.450838 | + | 0.260291i | −0.708184 | − | 0.706028i | \(-0.750485\pi\) |
0.257346 | + | 0.966319i | \(0.417152\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.70634 | − | 13.3478i | 0.509249 | − | 0.882046i | −0.490693 | − | 0.871332i | \(-0.663256\pi\) |
0.999943 | − | 0.0107133i | \(-0.00341023\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.70205 | − | 2.27341i | 0.375168 | − | 0.149579i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.62905 | + | 9.74980i | −0.368771 | + | 0.638731i | −0.989374 | − | 0.145395i | \(-0.953555\pi\) |
0.620602 | + | 0.784126i | \(0.286888\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.60440 | − | 4.51095i | −0.169892 | − | 0.294262i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.1855 | 1.24623 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.1518i | 0.915404i | 0.889106 | + | 0.457702i | \(0.151327\pi\) | ||||
−0.889106 | + | 0.457702i | \(0.848673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9056 | − | 10.3378i | 1.15340 | − | 0.665915i | 0.203685 | − | 0.979036i | \(-0.434708\pi\) |
0.949713 | + | 0.313121i | \(0.101375\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.49397 | − | 5.48135i | −0.609038 | − | 0.351628i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.71085 | − | 1.99112i | −0.428740 | − | 0.127208i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.40619 | + | 1.38921i | 0.153102 | + | 0.0883935i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.82640 | − | 4.89546i | −0.179116 | − | 0.310237i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.1277i | 0.828616i | 0.910137 | + | 0.414308i | \(0.135976\pi\) | ||||
−0.910137 | + | 0.414308i | \(0.864024\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.29421i | − | 0.332844i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.31917 | − | 4.01692i | −0.145232 | − | 0.251549i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6932 | + | 10.2152i | 1.10367 | + | 0.637205i | 0.937183 | − | 0.348839i | \(-0.113424\pi\) |
0.166488 | + | 0.986043i | \(0.446757\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.2409 | − | 6.47526i | 1.00916 | − | 0.402353i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.47776 | + | 0.853186i | 0.0914711 | + | 0.0528109i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.1210 | + | 15.6583i | −1.67235 | + | 0.965532i | −0.706034 | + | 0.708178i | \(0.749517\pi\) |
−0.966317 | + | 0.257355i | \(0.917149\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.60841i | 0.160233i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.8580 | 1.58248 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.435079 | + | 0.753580i | 0.0265273 | + | 0.0459466i | 0.878984 | − | 0.476851i | \(-0.158222\pi\) |
−0.852457 | + | 0.522797i | \(0.824888\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.6655 | + | 27.1335i | −0.951614 | + | 1.64824i | −0.209682 | + | 0.977770i | \(0.567243\pi\) |
−0.741932 | + | 0.670475i | \(0.766090\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.550584 | − | 3.79133i | 0.0333229 | − | 0.229462i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.572544 | − | 0.991675i | 0.0345257 | − | 0.0598002i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.3707 | − | 14.0705i | 1.46430 | − | 0.845412i | 0.465091 | − | 0.885263i | \(-0.346022\pi\) |
0.999206 | + | 0.0398511i | \(0.0126883\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.30567 | −0.0781685 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.1338 | −1.32039 | −0.660195 | − | 0.751094i | \(-0.729527\pi\) | ||||
−0.660195 | + | 0.751094i | \(0.729527\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.28363 | − | 1.31845i | 0.135748 | − | 0.0783739i | −0.430588 | − | 0.902548i | \(-0.641694\pi\) |
0.566336 | + | 0.824175i | \(0.308361\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.93868 | + | 6.82199i | −0.233307 | + | 0.404100i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.8198 | − | 17.9980i | −1.34701 | − | 1.06239i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.87977 | + | 10.1841i | −0.345869 | + | 0.599063i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.25318 | − | 9.09877i | −0.307947 | − | 0.533379i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.78791 | 0.571816 | 0.285908 | − | 0.958257i | \(-0.407705\pi\) | ||||
0.285908 | + | 0.958257i | \(0.407705\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1531i | 0.707581i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.80683 | − | 2.19787i | 0.220894 | − | 0.127533i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.86147 | − | 1.65207i | −0.165483 | − | 0.0955418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.7691 | − | 22.5296i | 1.02419 | − | 1.29858i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.77581 | + | 1.02526i | 0.102017 | + | 0.0588998i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.13513 | − | 12.3584i | −0.408556 | − | 0.707640i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.6770i | 0.609367i | 0.952454 | + | 0.304683i | \(0.0985506\pi\) | ||||
−0.952454 | + | 0.304683i | \(0.901449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.94414i | − | 0.281262i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.23321 | − | 7.33214i | −0.240043 | − | 0.415767i | 0.720683 | − | 0.693265i | \(-0.243828\pi\) |
−0.960726 | + | 0.277497i | \(0.910495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.2436 | − | 11.6877i | −1.14424 | − | 0.660626i | −0.196761 | − | 0.980452i | \(-0.563042\pi\) |
−0.947476 | + | 0.319826i | \(0.896376\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.89427 | + | 0.420312i | 0.163074 | + | 0.0236819i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0950 | − | 6.40571i | −0.623158 | − | 0.359780i | 0.154940 | − | 0.987924i | \(-0.450482\pi\) |
−0.778097 | + | 0.628144i | \(0.783815\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.53081 | + | 0.883811i | −0.0857087 | + | 0.0494839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.75662i | 0.153860i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.89994 | −0.495206 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.357327 | − | 0.618909i | −0.0198209 | − | 0.0343309i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.5898 | − | 18.3421i | 0.585618 | − | 1.01432i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.10384 | + | 12.8012i | 0.281384 | + | 0.705754i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1099 | − | 19.2429i | 0.610656 | − | 1.05769i | −0.380474 | − | 0.924792i | \(-0.624239\pi\) |
0.991130 | − | 0.132896i | \(-0.0424275\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.32630 | + | 3.65249i | −0.346679 | + | 0.200155i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.17600 | −0.446703 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.9570 | 0.814761 | 0.407381 | − | 0.913258i | \(-0.366442\pi\) | ||||
0.407381 | + | 0.913258i | \(0.366442\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.7498 | − | 7.93843i | 0.746785 | − | 0.431156i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.676270 | − | 1.17133i | 0.0366221 | − | 0.0634313i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8138 | + | 7.76500i | 0.907861 | + | 0.419270i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.68394 | − | 8.11282i | 0.252175 | − | 0.436779i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.51734 | − | 14.7525i | −0.457235 | − | 0.791954i | 0.541579 | − | 0.840650i | \(-0.317827\pi\) |
−0.998814 | + | 0.0486962i | \(0.984493\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.40440 | −0.0751760 | −0.0375880 | − | 0.999293i | \(-0.511967\pi\) | ||||
−0.0375880 | + | 0.999293i | \(0.511967\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.74340i | − | 0.146432i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.0830 | − | 6.39876i | 0.589887 | − | 0.340572i | −0.175166 | − | 0.984539i | \(-0.556046\pi\) |
0.765053 | + | 0.643967i | \(0.222713\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7310 | − | 7.92757i | −0.728763 | − | 0.420752i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.54489 | + | 11.3993i | 0.240541 | + | 0.603313i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.28987 | + | 3.05411i | 0.279189 | + | 0.161190i | 0.633056 | − | 0.774106i | \(-0.281800\pi\) |
−0.353867 | + | 0.935296i | \(0.615134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.94255 | − | 3.36460i | −0.102240 | − | 0.177084i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.6312i | 1.03037i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.44321i | 0.284910i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.55727 | − | 7.89342i | −0.237888 | − | 0.412033i | 0.722220 | − | 0.691663i | \(-0.243122\pi\) |
−0.960108 | + | 0.279630i | \(0.909788\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.5159 | + | 6.07137i | 0.547437 | + | 0.316063i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.991802 | − | 6.82956i | 0.0514918 | − | 0.354573i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.9065 | − | 11.4930i | −1.03072 | − | 0.595086i | −0.113529 | − | 0.993535i | \(-0.536215\pi\) |
−0.917191 | + | 0.398448i | \(0.869549\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.75472 | − | 1.01309i | 0.0906135 | − | 0.0523158i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.10318i | 0.0568167i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.0966 | −0.929562 | −0.464781 | − | 0.885426i | \(-0.653867\pi\) | ||||
−0.464781 | + | 0.885426i | \(0.653867\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.1919 | − | 21.1170i | −0.624612 | − | 1.08186i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.7474 | − | 18.6150i | 0.549165 | − | 0.951182i | −0.449167 | − | 0.893448i | \(-0.648279\pi\) |
0.998332 | − | 0.0577341i | \(-0.0183876\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.87615 | + | 2.37879i | −0.0956175 | + | 0.121234i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.99416 | + | 10.3822i | −0.304700 | + | 0.527756i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.38186 | + | 1.37517i | −0.120765 | + | 0.0697238i | −0.559166 | − | 0.829056i | \(-0.688878\pi\) |
0.438401 | + | 0.898780i | \(0.355545\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.5839 | 0.535253 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −41.9004 | −2.11359 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.20023 | + | 4.73440i | −0.412598 | + | 0.238214i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.62990 | + | 13.2154i | −0.382934 | + | 0.663260i | −0.991480 | − | 0.130258i | \(-0.958420\pi\) |
0.608547 | + | 0.793518i | \(0.291753\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.9065 | − | 16.3643i | 0.646135 | − | 0.819241i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.15899 | − | 7.20358i | 0.207690 | − | 0.359729i | −0.743297 | − | 0.668962i | \(-0.766739\pi\) |
0.950986 | + | 0.309233i | \(0.100072\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.422063 | − | 0.731035i | −0.0210245 | − | 0.0364154i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.0943 | 0.551280 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.56720i | − | 0.375092i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.3269 | − | 13.4678i | 1.15344 | − | 0.665941i | 0.203719 | − | 0.979029i | \(-0.434697\pi\) |
0.949724 | + | 0.313089i | \(0.101364\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.33349 | − | 4.81134i | −0.411061 | − | 0.237326i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.62101 | − | 31.8203i | 0.227385 | − | 1.56578i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.41610 | + | 1.39494i | 0.118602 | + | 0.0684748i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.1250 | − | 19.2690i | −0.544793 | − | 0.943608i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 8.97603i | − | 0.438508i | −0.975668 | − | 0.219254i | \(-0.929638\pi\) | ||
0.975668 | − | 0.219254i | \(-0.0703623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4720i | 0.656583i | 0.944576 | + | 0.328292i | \(0.106473\pi\) | ||||
−0.944576 | + | 0.328292i | \(0.893527\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.87892 | − | 4.98643i | −0.139978 | − | 0.242449i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.98251 | + | 1.14460i | 0.0961658 | + | 0.0555213i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.9827 | + | 35.0708i | 0.676672 | + | 1.69720i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.43596 | − | 0.829054i | −0.0693290 | − | 0.0400271i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.5363 | + | 11.8567i | −0.989200 | + | 0.571115i | −0.905035 | − | 0.425337i | \(-0.860156\pi\) |
−0.0841648 | + | 0.996452i | \(0.526822\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 18.5650i | − | 0.892178i | −0.894989 | − | 0.446089i | \(-0.852817\pi\) | ||
0.894989 | − | 0.446089i | \(-0.147183\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.12773 | −0.149963 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.98743 | − | 15.5667i | −0.429927 | − | 0.744656i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.44704 | − | 5.97045i | 0.164518 | − | 0.284954i | −0.771966 | − | 0.635664i | \(-0.780726\pi\) |
0.936484 | + | 0.350710i | \(0.114060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.41822 | − | 2.20100i | −0.353249 | − | 0.104809i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.1129 | + | 24.4443i | −0.670525 | + | 1.16138i | 0.307230 | + | 0.951635i | \(0.400598\pi\) |
−0.977755 | + | 0.209749i | \(0.932735\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.0522 | + | 6.38097i | −0.523923 | + | 0.302487i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31.5282 | 1.49123 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.93651 | 0.0913896 | 0.0456948 | − | 0.998955i | \(-0.485450\pi\) | ||||
0.0456948 | + | 0.998955i | \(0.485450\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8934 | + | 6.28930i | −0.512950 | + | 0.296152i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.7135 | + | 22.0204i | −0.597331 | + | 1.03461i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.700255 | + | 1.75635i | 0.0328285 | + | 0.0823389i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3752 | + | 30.0948i | −0.812779 | + | 1.40777i | 0.0981335 | + | 0.995173i | \(0.468713\pi\) |
−0.910912 | + | 0.412601i | \(0.864621\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.39388 | + | 7.61043i | 0.205089 | + | 0.355224i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.3117 | −1.36518 | −0.682590 | − | 0.730802i | \(-0.739146\pi\) | ||||
−0.682590 | + | 0.730802i | \(0.739146\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.47208i | 0.440205i | 0.975477 | + | 0.220102i | \(0.0706391\pi\) | ||||
−0.975477 | + | 0.220102i | \(0.929361\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.07262 | − | 1.19663i | 0.0961156 | − | 0.0554924i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.2422 | − | 6.49066i | −0.520225 | − | 0.300352i | 0.216802 | − | 0.976216i | \(-0.430437\pi\) |
−0.737027 | + | 0.675864i | \(0.763771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.4071 | + | 3.10878i | 0.988489 | + | 0.143550i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.4464 | + | 7.76330i | 0.619579 | + | 0.357714i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.20932 | − | 10.7549i | −0.285505 | − | 0.494509i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.88779i | − | 0.178384i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.88335i | 0.132020i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.96246 | + | 17.2555i | 0.455197 | + | 0.788424i | 0.998699 | − | 0.0509837i | \(-0.0162357\pi\) |
−0.543503 | + | 0.839407i | \(0.682902\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.09000 | − | 2.36136i | −0.186488 | − | 0.107669i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.3486 | + | 19.4607i | −0.698388 | + | 0.885492i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.49060 | + | 2.59265i | 0.203908 | + | 0.117726i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.4025 | − | 13.5114i | 1.06047 | − | 0.612261i | 0.134906 | − | 0.990858i | \(-0.456927\pi\) |
0.925562 | + | 0.378597i | \(0.123593\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.7190i | 1.84138i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.454409 | −0.0205072 | −0.0102536 | − | 0.999947i | \(-0.503264\pi\) | ||||
−0.0102536 | + | 0.999947i | \(0.503264\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.76687 | − | 3.06031i | −0.0795760 | − | 0.137830i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.632894 | − | 1.09620i | 0.0284465 | − | 0.0492707i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.9372 | + | 25.9776i | 1.47744 | + | 1.16525i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.29223 | − | 7.43436i | 0.192147 | − | 0.332808i | −0.753815 | − | 0.657087i | \(-0.771788\pi\) |
0.945961 | + | 0.324279i | \(0.105122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.8873 | + | 6.86314i | −0.531086 | + | 0.306623i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −43.3946 | −1.93487 | −0.967434 | − | 0.253123i | \(-0.918542\pi\) | ||||
−0.967434 | + | 0.253123i | \(0.918542\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.01202 | −0.0450341 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.9152 | − | 12.6528i | 0.973289 | − | 0.561929i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.5209 | + | 19.9548i | −0.510654 | + | 0.884479i | 0.489270 | + | 0.872133i | \(0.337263\pi\) |
−0.999924 | + | 0.0123465i | \(0.996070\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.06969 | − | 14.2519i | 0.0915575 | − | 0.630466i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.46219 | − | 12.9249i | 0.329464 | − | 0.570648i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.22006 | + | 2.11321i | 0.0537625 | + | 0.0931193i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.96452 | 0.262319 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 35.2620i | − | 1.54783i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.5041 | + | 21.0756i | −1.59927 | + | 0.923340i | −0.607644 | + | 0.794209i | \(0.707885\pi\) |
−0.991628 | + | 0.129130i | \(0.958781\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.61525 | + | 5.55137i | 0.420445 | + | 0.242744i | 0.695268 | − | 0.718751i | \(-0.255286\pi\) |
−0.274822 | + | 0.961495i | \(0.588619\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.97958 | + | 1.98536i | −0.217327 | + | 0.0866481i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.34167 | + | 1.35197i | 0.102005 | + | 0.0588926i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.812016 | − | 1.40645i | −0.0353051 | − | 0.0611501i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.4341i | 0.582992i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.85037i | 0.340037i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.680251 | − | 1.17823i | −0.0294098 | − | 0.0509393i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.8955 | − | 15.5281i | −1.16063 | − | 0.670087i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.81679 | − | 5.51497i | 0.250547 | − | 0.237547i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.7744 | + | 12.5715i | 0.936156 | + | 0.540490i | 0.888753 | − | 0.458386i | \(-0.151572\pi\) |
0.0474025 | + | 0.998876i | \(0.484906\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.44001 | − | 3.14079i | 0.233453 | − | 0.134784i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.4530i | 0.447756i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.35086 | −0.186030 | −0.0930148 | − | 0.995665i | \(-0.529650\pi\) | ||||
−0.0930148 | + | 0.995665i | \(0.529650\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.88722 | − | 13.6611i | −0.336619 | − | 0.583040i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.00071 | + | 5.19738i | −0.127834 | + | 0.221416i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.2707 | − | 9.27803i | 0.989571 | − | 0.394542i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.69491 | − | 11.5959i | 0.284183 | − | 0.492220i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.5821 | − | 13.0378i | 0.956833 | − | 0.552428i | 0.0616365 | − | 0.998099i | \(-0.480368\pi\) |
0.895197 | + | 0.445671i | \(0.147035\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.75053 | −0.327813 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.31130 | 0.224243 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.6768 | − | 9.05099i | 0.660697 | − | 0.381454i | −0.131845 | − | 0.991270i | \(-0.542090\pi\) |
0.792542 | + | 0.609817i | \(0.208757\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.91793 | + | 6.78605i | −0.164828 | + | 0.285491i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.0480 | − | 4.21842i | −1.21990 | − | 0.177157i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.4224 | + | 21.5163i | −0.520776 | + | 0.902010i | 0.478932 | + | 0.877852i | \(0.341024\pi\) |
−0.999708 | + | 0.0241585i | \(0.992309\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.25668 | + | 3.90869i | 0.0944392 | + | 0.163574i | 0.909374 | − | 0.415979i | \(-0.136561\pi\) |
−0.814935 | + | 0.579552i | \(0.803228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.5870 | 1.23602 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.62342i | 0.192810i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.3993 | + | 11.7776i | −0.849235 | + | 0.490306i | −0.860393 | − | 0.509632i | \(-0.829782\pi\) |
0.0111579 | + | 0.999938i | \(0.496448\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.8478 | − | 17.2326i | −1.24043 | − | 0.716164i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.79565 | − | 4.57103i | −0.240444 | − | 0.189638i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.58669 | − | 1.49343i | −0.107130 | − | 0.0618514i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.394992 | − | 0.684146i | −0.0163309 | − | 0.0282860i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 3.48482i | − | 0.143834i | −0.997411 | − | 0.0719170i | \(-0.977088\pi\) | ||
0.997411 | − | 0.0719170i | \(-0.0229117\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.59213i | − | 0.189215i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.4335 | − | 26.7316i | −0.634850 | − | 1.09959i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.4527 | − | 6.61223i | −0.470307 | − | 0.271532i | 0.246061 | − | 0.969254i | \(-0.420864\pi\) |
−0.716368 | + | 0.697722i | \(0.754197\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.75556 | − | 3.75071i | −0.194959 | − | 0.153764i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.1508 | − | 16.2529i | −1.15214 | − | 0.665186i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0329 | + | 6.94719i | −0.491650 | + | 0.283855i | −0.725259 | − | 0.688476i | \(-0.758280\pi\) |
0.233608 | + | 0.972331i | \(0.424947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 18.8327i | − | 0.768200i | −0.923291 | − | 0.384100i | \(-0.874512\pi\) | ||
0.923291 | − | 0.384100i | \(-0.125488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.03781 | −0.368048 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.84439 | − | 8.39073i | −0.196952 | − | 0.341132i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.1505 | + | 21.0453i | −0.493175 | + | 0.854204i | −0.999969 | − | 0.00786319i | \(-0.997497\pi\) |
0.506794 | + | 0.862067i | \(0.330830\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.18929 | + | 1.18927i | 0.331847 | + | 0.0481915i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.86124 | − | 3.22377i | 0.0752978 | − | 0.130420i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.2648 | + | 9.39048i | −0.656929 | + | 0.379278i | −0.791106 | − | 0.611679i | \(-0.790494\pi\) |
0.134177 | + | 0.990957i | \(0.457161\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.2573 | −0.897500 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.0641 | 1.04930 | 0.524651 | − | 0.851317i | \(-0.324196\pi\) | ||||
0.524651 | + | 0.851317i | \(0.324196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.7007 | − | 11.9515i | 0.832030 | − | 0.480373i | −0.0225171 | − | 0.999746i | \(-0.507168\pi\) |
0.854547 | + | 0.519374i | \(0.173835\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.87415 | + | 15.3705i | −0.356107 | + | 0.616796i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.3640 | − | 12.5048i | 1.25657 | − | 0.500995i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.51013 | − | 7.81178i | −0.180117 | − | 0.311972i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.1280 | 0.603192 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 29.3239i | − | 1.16736i | −0.811982 | − | 0.583682i | \(-0.801611\pi\) | ||
0.811982 | − | 0.583682i | \(-0.198389\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.2790 | + | 5.93457i | −0.408552 | + | 0.235878i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.4221 | + | 6.01720i | 0.413588 | + | 0.238785i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.16565 | − | 4.86488i | −0.0461847 | − | 0.192754i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.1783 | − | 8.76320i | −0.600444 | − | 0.346667i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.35512 | + | 4.07919i | 0.0930217 | + | 0.161118i | 0.908781 | − | 0.417273i | \(-0.137014\pi\) |
−0.815760 | + | 0.578391i | \(0.803681\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.22266i | − | 0.127089i | −0.997979 | − | 0.0635446i | \(-0.979759\pi\) | ||
0.997979 | − | 0.0635446i | \(-0.0202405\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 21.9742i | − | 0.865235i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.242759 | + | 0.420471i | 0.00954385 | + | 0.0165304i | 0.870758 | − | 0.491712i | \(-0.163629\pi\) |
−0.861214 | + | 0.508242i | \(0.830295\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0519 | − | 6.95818i | −0.473079 | − | 0.273133i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.88172 | + | 2.34504i | −0.230523 | + | 0.0919093i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.25225 | + | 2.45504i | 0.166403 | + | 0.0960730i | 0.580889 | − | 0.813983i | \(-0.302705\pi\) |
−0.414485 | + | 0.910056i | \(0.636038\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.9090 | − | 10.3397i | 0.699761 | − | 0.404007i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.01696i | 0.234744i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −50.3794 | −1.96250 | −0.981252 | − | 0.192729i | \(-0.938266\pi\) | ||||
−0.981252 | + | 0.192729i | \(0.938266\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.39100 | + | 4.14133i | 0.0929991 | + | 0.161079i | 0.908772 | − | 0.417294i | \(-0.137021\pi\) |
−0.815773 | + | 0.578373i | \(0.803688\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.65740 | − | 2.87071i | 0.0643683 | − | 0.111489i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.47826 | + | 10.1793i | −0.0573246 | + | 0.394738i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.56849 | − | 6.18080i | 0.138172 | − | 0.239321i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.6302 | + | 12.4882i | −0.836270 | + | 0.482821i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.3407 | 0.630825 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.2854 | 1.05177 | 0.525887 | − | 0.850555i | \(-0.323734\pi\) | ||||
0.525887 | + | 0.850555i | \(0.323734\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.32449 | + | 1.91939i | −0.127960 | + | 0.0738775i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.2029 | − | 36.7245i | 0.814893 | − | 1.41144i | −0.0945112 | − | 0.995524i | \(-0.530129\pi\) |
0.909405 | − | 0.415913i | \(-0.136538\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7719 | − | 8.49577i | −0.413386 | − | 0.326038i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.94604 | − | 13.7629i | 0.304493 | − | 0.527397i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.2969 | + | 38.6193i | 0.853165 | + | 1.47773i | 0.878337 | + | 0.478042i | \(0.158653\pi\) |
−0.0251714 | + | 0.999683i | \(0.508013\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.74917 | 0.181457 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.2289i | 1.19146i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.61437 | + | 0.932055i | −0.0615025 | + | 0.0355085i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.71156 | − | 1.56552i | −0.103152 | − | 0.0595551i | 0.447536 | − | 0.894266i | \(-0.352302\pi\) |
−0.550689 | + | 0.834711i | \(0.685635\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.07391 | + | 2.62953i | −0.0787814 | + | 0.0998876i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.51003 | + | 5.49062i | 0.360736 | + | 0.208271i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.5733 | − | 21.7776i | −0.476247 | − | 0.824884i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 22.8110i | − | 0.862789i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 0.816220i | − | 0.0308282i | −0.999881 | − | 0.0154141i | \(-0.995093\pi\) | ||
0.999881 | − | 0.0154141i | \(-0.00490665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.8460 | − | 22.2500i | −0.484498 | − | 0.839175i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.13999 | + | 5.27698i | 0.344232 | + | 0.198742i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.64975 | + | 0.384801i | 0.0996540 | + | 0.0144719i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.7963 | − | 14.8935i | −0.968799 | − | 0.559336i | −0.0699290 | − | 0.997552i | \(-0.522277\pi\) |
−0.898870 | + | 0.438216i | \(0.855611\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.06459 | + | 5.23345i | −0.339949 | + | 0.196270i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.46103i | 0.204517i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.818341 | 0.0306042 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.3370 | − | 24.8325i | −0.535427 | − | 0.927386i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.37920 | − | 4.12090i | 0.0887293 | − | 0.153684i | −0.818245 | − | 0.574870i | \(-0.805053\pi\) |
0.906974 | + | 0.421186i | \(0.138386\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.39096 | − | 5.99691i | −0.0890442 | − | 0.223336i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.9462 | + | 36.2799i | −0.778998 | + | 1.34926i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.33685 | − | 0.771829i | 0.0496492 | − | 0.0286650i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0543 | 0.521246 | 0.260623 | − | 0.965441i | \(-0.416072\pi\) | ||||
0.260623 | + | 0.965441i | \(0.416072\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.0705 | −0.410019 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.5006 | − | 12.4134i | 0.795229 | − | 0.459125i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.785118 | + | 1.35986i | −0.0289990 | + | 0.0502277i | −0.880161 | − | 0.474676i | \(-0.842565\pi\) |
0.851162 | + | 0.524904i | \(0.175899\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.7929 | − | 3.30483i | 0.508757 | − | 0.121901i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.68112 | − | 8.10793i | 0.172431 | − | 0.298660i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.63252 | + | 6.29171i | 0.133625 | + | 0.231444i | 0.925071 | − | 0.379794i | \(-0.124005\pi\) |
−0.791447 | + | 0.611238i | \(0.790672\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.62959 | −0.206808 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 0.694046i | − | 0.0254621i | −0.999919 | − | 0.0127310i | \(-0.995947\pi\) | ||
0.999919 | − | 0.0127310i | \(-0.00405253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.4757 | + | 7.78020i | −0.493711 | + | 0.285044i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.67078 | + | 1.54197i | 0.0977187 | + | 0.0564179i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.33309 | + | 3.34359i | 0.0487100 | + | 0.122172i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.2883 | + | 8.24935i | 0.521387 | + | 0.301023i | 0.737502 | − | 0.675345i | \(-0.236005\pi\) |
−0.216115 | + | 0.976368i | \(0.569339\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.2996 | − | 23.0356i | −0.484664 | − | 0.839463i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 12.5492i | − | 0.456712i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.3048i | 1.64663i | 0.567583 | + | 0.823316i | \(0.307879\pi\) | ||||
−0.567583 | + | 0.823316i | \(0.692121\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.36352 | + | 9.28988i | 0.194683 | + | 0.337201i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.16297 | + | 2.40349i | 0.150907 | + | 0.0871265i | 0.573552 | − | 0.819169i | \(-0.305565\pi\) |
−0.422645 | + | 0.906295i | \(0.638898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.97457 | − | 27.3689i | 0.143889 | − | 0.990820i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.19148 | + | 1.26525i | 0.0792331 | + | 0.0457453i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.52166 | + | 4.34263i | −0.271592 | + | 0.156803i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.47427i | − | 0.197407i | −0.995117 | − | 0.0987035i | \(-0.968530\pi\) | ||
0.995117 | − | 0.0987035i | \(-0.0314695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.3955 | −1.49082 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.14164 | + | 12.3697i | 0.256867 | + | 0.444906i | 0.965401 | − | 0.260770i | \(-0.0839765\pi\) |
−0.708534 | + | 0.705677i | \(0.750643\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.590584 | + | 1.02292i | −0.0212144 | + | 0.0367444i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.9384 | + | 27.8158i | −0.787034 | + | 0.997888i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.3534 | + | 36.9851i | −0.765064 | + | 1.32513i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.7231 | − | 9.07776i | 0.562618 | − | 0.324828i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.92577 | 0.211770 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.66299 | −0.273504 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.3383 | + | 5.96882i | −0.368521 | + | 0.212765i | −0.672812 | − | 0.739814i | \(-0.734914\pi\) |
0.304291 | + | 0.952579i | \(0.401580\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.7266 | − | 54.9520i | 1.12950 | − | 1.95634i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.8385 | − | 16.2781i | 0.456486 | − | 0.578783i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.09915 | − | 8.83199i | 0.181076 | − | 0.313633i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.64255 | − | 4.57704i | −0.0937217 | − | 0.162331i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.5344 | −1.57749 | −0.788745 | − | 0.614720i | \(-0.789269\pi\) | ||||
−0.788745 | + | 0.614720i | \(0.789269\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.9240i | 0.421840i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.2172 | + | 7.05358i | −0.431672 | + | 0.249226i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.39789 | − | 3.11647i | −0.190487 | − | 0.109978i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.75797 | − | 12.1054i | 0.0619604 | − | 0.426660i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.52689 | − | 0.881550i | −0.0537490 | − | 0.0310320i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.90901 | + | 15.4309i | 0.313224 | + | 0.542520i | 0.979058 | − | 0.203579i | \(-0.0652575\pi\) |
−0.665834 | + | 0.746100i | \(0.731924\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.8733i | 1.36503i | 0.730873 | + | 0.682513i | \(0.239113\pi\) | ||||
−0.730873 | + | 0.682513i | \(0.760887\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 63.4825i | − | 2.22643i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.0482 | − | 17.4040i | −0.351974 | − | 0.609636i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.5148 | − | 21.0818i | −1.27749 | − | 0.737560i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.774068 | + | 1.94148i | 0.0270481 | + | 0.0678408i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.4121 | + | 7.16612i | 0.433185 | + | 0.250099i | 0.700703 | − | 0.713454i | \(-0.252870\pi\) |
−0.267518 | + | 0.963553i | \(0.586203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.71650 | − | 5.03248i | 0.303838 | − | 0.175421i | −0.340328 | − | 0.940307i | \(-0.610538\pi\) |
0.644166 | + | 0.764886i | \(0.277205\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.32015i | 0.0807774i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.0985 | −1.15095 | −0.575475 | − | 0.817820i | \(-0.695183\pi\) | ||||
−0.575475 | + | 0.817820i | \(0.695183\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.9412 | + | 34.5392i | 0.692586 | + | 1.19959i | 0.970988 | + | 0.239130i | \(0.0768622\pi\) |
−0.278401 | + | 0.960465i | \(0.589804\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.5093 | + | 49.3795i | −0.988976 | + | 1.71296i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.0253 | + | 11.6287i | 0.382003 | + | 0.402909i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.38723 | − | 5.86686i | 0.117220 | − | 0.203031i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.92678 | + | 2.26712i | −0.135729 | + | 0.0783633i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.19183 | 0.317337 | 0.158669 | − | 0.987332i | \(-0.449280\pi\) | ||||
0.158669 | + | 0.987332i | \(0.449280\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.6171 | 0.917832 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.8387 | − | 22.4235i | 1.33768 | − | 0.772307i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.24463 | + | 10.8160i | −0.214822 | + | 0.372083i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.49356 | + | 23.8113i | 0.326203 | + | 0.818167i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.67142 | + | 4.62704i | −0.0916830 | + | 0.158800i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.2767 | + | 26.4600i | 0.523679 | + | 0.907038i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.3596 | 0.765577 | 0.382788 | − | 0.923836i | \(-0.374964\pi\) | ||||
0.382788 | + | 0.923836i | \(0.374964\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4.29759i | − | 0.146975i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.08869 | − | 1.20591i | 0.0713485 | − | 0.0411930i | −0.463901 | − | 0.885887i | \(-0.653551\pi\) |
0.535250 | + | 0.844694i | \(0.320217\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.5635 | − | 17.6459i | −1.04281 | − | 0.602069i | −0.122185 | − | 0.992507i | \(-0.538990\pi\) |
−0.920629 | + | 0.390438i | \(0.872324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 58.2759 | + | 8.46295i | 1.98604 | + | 0.288417i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.8260 | − | 11.4466i | −0.674886 | − | 0.389645i | 0.123040 | − | 0.992402i | \(-0.460736\pi\) |
−0.797925 | + | 0.602756i | \(0.794069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.70160 | + | 15.0716i | 0.295863 | + | 0.512450i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 23.8270i | − | 0.809206i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 10.8426i | − | 0.367810i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.92151 | − | 5.06020i | −0.0989915 | − | 0.171458i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.96395 | + | 2.86594i | 0.168004 | + | 0.0969972i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.63843 | − | 2.07739i | 0.0553892 | − | 0.0702285i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.7590 | + | 21.8002i | 1.27503 | + | 0.736140i | 0.975931 | − | 0.218082i | \(-0.0699799\pi\) |
0.299101 | + | 0.954221i | \(0.403313\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.1751 | + | 9.91604i | −0.579301 | + | 0.334460i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.79085i | − | 0.195099i | −0.995231 | − | 0.0975494i | \(-0.968900\pi\) | ||
0.995231 | − | 0.0975494i | \(-0.0311004\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0070 | 0.673288 | 0.336644 | − | 0.941632i | \(-0.390708\pi\) | ||||
0.336644 | + | 0.941632i | \(0.390708\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.3122 | − | 21.3253i | −0.413870 | − | 0.716844i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.86765 | + | 11.8951i | −0.230593 | + | 0.399399i | −0.957983 | − | 0.286826i | \(-0.907400\pi\) |
0.727390 | + | 0.686225i | \(0.240733\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.0001 | − | 19.7176i | −0.838476 | − | 0.661306i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.35197 | + | 11.0019i | −0.212799 | + | 0.368579i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.5376 | − | 10.1253i | 0.586873 | − | 0.338832i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.3275 | 0.512341 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.69479 | 0.223533 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.57904 | − | 0.911659i | 0.0526639 | − | 0.0304055i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.98559 | − | 5.17119i | 0.0994644 | − | 0.172277i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.35533 | + | 57.5348i | −0.278048 | + | 1.91464i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.55010 | + | 2.68486i | −0.0515272 | + | 0.0892478i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.55400 | + | 6.15571i | 0.118009 | + | 0.204397i | 0.918978 | − | 0.394308i | \(-0.129016\pi\) |
−0.800970 | + | 0.598705i | \(0.795682\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.11869 | −0.0371046 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.1201i | 0.434690i | 0.976095 | + | 0.217345i | \(0.0697397\pi\) | ||||
−0.976095 | + | 0.217345i | \(0.930260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.76665 | + | 1.59732i | −0.0915627 | + | 0.0528637i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25.0404 | + | 14.4571i | 0.827809 | + | 0.477936i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −50.8223 | + | 20.2628i | −1.67830 | + | 0.669137i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.7519 | − | 13.7132i | −0.783502 | − | 0.452355i | 0.0541677 | − | 0.998532i | \(-0.482749\pi\) |
−0.837670 | + | 0.546176i | \(0.816083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.8167 | − | 18.7351i | −0.356423 | − | 0.617343i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 11.3309i | − | 0.372963i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.60841i | 0.217283i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.34867 | + | 2.33596i | 0.0442961 | + | 0.0767231i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.4779 | + | 6.04939i | 0.343767 | + | 0.198474i | 0.661937 | − | 0.749560i | \(-0.269735\pi\) |
−0.318169 | + | 0.948034i | \(0.603068\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.74104 | − | 26.0903i | 0.253702 | − | 0.855077i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.8562 | + | 8.57725i | 0.486371 | + | 0.280807i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.27014 | + | 1.31067i | −0.0742417 | + | 0.0428634i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 50.1666i | − | 1.63887i | −0.573171 | − | 0.819435i | \(-0.694287\pi\) | ||
0.573171 | − | 0.819435i | \(-0.305713\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 47.3626 | 1.54562 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.2678 | − | 36.8369i | −0.693311 | − | 1.20085i | −0.970747 | − | 0.240106i | \(-0.922818\pi\) |
0.277436 | − | 0.960744i | \(-0.410515\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3938 | − | 43.9833i | 0.826935 | − | 1.43229i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.43427 | − | 3.76144i | 0.306897 | − | 0.122360i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.96280 | − | 13.7920i | 0.258756 | − | 0.448179i | −0.707153 | − | 0.707061i | \(-0.750021\pi\) |
0.965909 | + | 0.258882i | \(0.0833540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.36885 | + | 1.94501i | −0.109357 | + | 0.0631375i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.9582 | 0.841754 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.6348 | 1.02475 | 0.512375 | − | 0.858762i | \(-0.328766\pi\) | ||||
0.512375 | + | 0.858762i | \(0.328766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.6460 | + | 7.30118i | −0.409216 | + | 0.236261i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.79076 | − | 3.10169i | 0.0578871 | − | 0.100263i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.4347 | − | 1.80579i | −0.401537 | − | 0.0583120i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8024 | − | 25.6385i | 0.477497 | − | 0.827050i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.751954 | − | 1.30242i | −0.0242314 | − | 0.0419700i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.0100 | 0.547570 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.06338i | 0.291459i | 0.989324 | + | 0.145729i | \(0.0465529\pi\) | ||||
−0.989324 | + | 0.145729i | \(0.953447\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.6169 | − | 9.01644i | 0.501688 | − | 0.289650i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.3233 | + | 24.4354i | 1.35822 | + | 0.784168i | 0.989384 | − | 0.145327i | \(-0.0464234\pi\) |
0.368835 | + | 0.929495i | \(0.379757\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.8123 | − | 17.9920i | −0.731327 | − | 0.576798i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.25402 | + | 0.724009i | 0.0401608 | + | 0.0231869i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.3107 | − | 26.5188i | −0.489831 | − | 0.848413i | 0.510100 | − | 0.860115i | \(-0.329608\pi\) |
−0.999932 | + | 0.0117023i | \(0.996275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 14.6135i | − | 0.467051i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.5548i | 0.368917i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.15271 | + | 15.8530i | 0.291926 | + | 0.505631i | 0.974265 | − | 0.225405i | \(-0.0723705\pi\) |
−0.682339 | + | 0.731036i | \(0.739037\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.1931 | + | 7.61705i | 0.420367 | + | 0.242699i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.9246 | − | 17.2920i | −0.697869 | − | 0.550409i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.4239 | + | 25.0708i | 1.38080 | + | 0.797206i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.4098 | + | 19.2891i | −1.06130 | + | 0.612740i | −0.925791 | − | 0.378037i | \(-0.876599\pi\) |
−0.135506 | + | 0.990777i | \(0.543266\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.0214i | 1.42871i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0429 | 0.508593 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.5501 | + | 47.7182i | 0.872522 | + | 1.51125i | 0.859379 | + | 0.511338i | \(0.170850\pi\) |
0.0131423 | + | 0.999914i | \(0.495817\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.6841 | + | 21.9696i | −0.401308 | + | 0.695086i |
(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 | 1120.2.bz.f.271.5 | 24 | ||
4.3 | odd | 2 | 280.2.bj.e.131.7 | ✓ | 24 | ||
7.3 | odd | 6 | 1120.2.bz.e.591.5 | 24 | |||
8.3 | odd | 2 | 1120.2.bz.e.271.5 | 24 | |||
8.5 | even | 2 | 280.2.bj.f.131.11 | yes | 24 | ||
28.3 | even | 6 | 280.2.bj.f.171.11 | yes | 24 | ||
56.3 | even | 6 | inner | 1120.2.bz.f.591.5 | 24 | ||
56.45 | odd | 6 | 280.2.bj.e.171.7 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bj.e.131.7 | ✓ | 24 | 4.3 | odd | 2 | ||
280.2.bj.e.171.7 | yes | 24 | 56.45 | odd | 6 | ||
280.2.bj.f.131.11 | yes | 24 | 8.5 | even | 2 | ||
280.2.bj.f.171.11 | yes | 24 | 28.3 | even | 6 | ||
1120.2.bz.e.271.5 | 24 | 8.3 | odd | 2 | |||
1120.2.bz.e.591.5 | 24 | 7.3 | odd | 6 | |||
1120.2.bz.f.271.5 | 24 | 1.1 | even | 1 | trivial | ||
1120.2.bz.f.591.5 | 24 | 56.3 | even | 6 | inner |