Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.17 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.b.2157.18 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.705440 | 0.407286 | 0.203643 | − | 0.979045i | \(-0.434722\pi\) | ||||
0.203643 | + | 0.979045i | \(0.434722\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.65594i | − | 1.18777i | −0.804549 | − | 0.593886i | \(-0.797593\pi\) | ||
0.804549 | − | 0.593886i | \(-0.202407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.50236 | −0.834118 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.54183 | + | 0.674887i | 0.982326 | + | 0.187180i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.87360i | − | 0.483762i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.198331 | −0.0481024 | −0.0240512 | − | 0.999711i | \(-0.507656\pi\) | ||||
−0.0240512 | + | 0.999711i | \(0.507656\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.34779i | 1.22687i | 0.789746 | + | 0.613434i | \(0.210212\pi\) | ||||
−0.789746 | + | 0.613434i | \(0.789788\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.705440i | 0.153940i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.13987 | 1.28025 | 0.640125 | − | 0.768270i | \(-0.278882\pi\) | ||||
0.640125 | + | 0.768270i | \(0.278882\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.05400 | −0.410800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.88158 | −0.747010 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.90461 | 0.539373 | 0.269686 | − | 0.962948i | \(-0.413080\pi\) | ||||
0.269686 | + | 0.962948i | \(0.413080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.55972i | − | 0.998555i | −0.866442 | − | 0.499277i | \(-0.833599\pi\) | ||
0.866442 | − | 0.499277i | \(-0.166401\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.705440i | 0.122801i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.65594 | 0.448935 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.81890i | 0.627824i | 0.949452 | + | 0.313912i | \(0.101640\pi\) | ||||
−0.949452 | + | 0.313912i | \(0.898360\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.49854 | + | 0.476092i | 0.400087 | + | 0.0762358i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.304576i | − | 0.0475668i | −0.999717 | − | 0.0237834i | \(-0.992429\pi\) | ||
0.999717 | − | 0.0237834i | \(-0.00757121\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.09415 | −0.319355 | −0.159677 | − | 0.987169i | \(-0.551045\pi\) | ||||
−0.159677 | + | 0.987169i | \(0.551045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.64610i | 0.990742i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.81034i | − | 0.555795i | −0.960611 | − | 0.277897i | \(-0.910363\pi\) | ||
0.960611 | − | 0.277897i | \(-0.0896375\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.139911 | −0.0195914 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.43329 | 0.608959 | 0.304479 | − | 0.952519i | \(-0.401518\pi\) | ||||
0.304479 | + | 0.952519i | \(0.401518\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.65594 | 0.358126 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.77254i | 0.499686i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.5529i | 1.89463i | 0.320309 | + | 0.947313i | \(0.396213\pi\) | ||||
−0.320309 | + | 0.947313i | \(0.603787\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.96003 | 1.27525 | 0.637626 | − | 0.770346i | \(-0.279917\pi\) | ||||
0.637626 | + | 0.770346i | \(0.279917\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.50236i | − | 0.315267i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.79246 | − | 9.40687i | 0.222327 | − | 1.16678i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.86965i | − | 0.839261i | −0.907695 | − | 0.419630i | \(-0.862160\pi\) | ||
0.907695 | − | 0.419630i | \(-0.137840\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.33130 | 0.521428 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.7769i | 1.75369i | 0.480772 | + | 0.876845i | \(0.340356\pi\) | ||||
−0.480772 | + | 0.876845i | \(0.659644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.4976i | − | 1.34570i | −0.739781 | − | 0.672848i | \(-0.765071\pi\) | ||
0.739781 | − | 0.672848i | \(-0.234929\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.44897 | −0.167313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.78198 | −0.538015 | −0.269007 | − | 0.963138i | \(-0.586696\pi\) | ||||
−0.269007 | + | 0.963138i | \(0.586696\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.76885 | 0.529872 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.0172i | 1.64836i | 0.566331 | + | 0.824178i | \(0.308363\pi\) | ||||
−0.566331 | + | 0.824178i | \(0.691637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.526755i | 0.0571346i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.04903 | 0.219679 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.28061i | − | 0.771743i | −0.922553 | − | 0.385871i | \(-0.873901\pi\) | ||
0.922553 | − | 0.385871i | \(-0.126099\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.674887 | + | 3.54183i | −0.0707474 | + | 0.371284i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 3.92204i | − | 0.406697i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.2034 | 1.45724 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.8099i | − | 1.40218i | −0.713071 | − | 0.701092i | \(-0.752696\pi\) | ||
0.713071 | − | 0.701092i | \(-0.247304\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.50236i | − | 0.251496i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0844 | 1.00344 | 0.501718 | − | 0.865031i | \(-0.332701\pi\) | ||||
0.501718 | + | 0.865031i | \(0.332701\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0334 | 1.48128 | 0.740642 | − | 0.671900i | \(-0.234521\pi\) | ||||
0.740642 | + | 0.671900i | \(0.234521\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.87360 | 0.182845 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.99038 | 0.579112 | 0.289556 | − | 0.957161i | \(-0.406492\pi\) | ||||
0.289556 | + | 0.957161i | \(0.406492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.11708i | 0.298562i | 0.988795 | + | 0.149281i | \(0.0476959\pi\) | ||||
−0.988795 | + | 0.149281i | \(0.952304\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.69401i | 0.255704i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.77719 | −0.731616 | −0.365808 | − | 0.930690i | \(-0.619207\pi\) | ||||
−0.365808 | + | 0.930690i | \(0.619207\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 16.3071i | − | 1.52064i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.86290 | − | 1.68881i | −0.819376 | − | 0.156130i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.198331i | − | 0.0181810i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 0.214860i | − | 0.0193733i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 7.82438i | − | 0.699834i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8017 | 1.75712 | 0.878560 | − | 0.477632i | \(-0.158505\pi\) | ||||
0.878560 | + | 0.477632i | \(0.158505\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.47729 | −0.130069 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.57293 | 0.486909 | 0.243454 | − | 0.969912i | \(-0.421719\pi\) | ||||
0.243454 | + | 0.969912i | \(0.421719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.34779 | −0.463712 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.3092i | 0.887277i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.9336i | − | 1.10500i | −0.833514 | − | 0.552498i | \(-0.813675\pi\) | ||
0.833514 | − | 0.552498i | \(-0.186325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.2437 | 1.63223 | 0.816113 | − | 0.577893i | \(-0.196125\pi\) | ||||
0.816113 | + | 0.577893i | \(0.196125\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 2.68796i | − | 0.226367i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.674887 | + | 3.54183i | −0.0564369 | + | 0.296182i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.71447i | − | 0.640652i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.705440 | −0.0581837 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.62913i | 0.461157i | 0.973054 | + | 0.230578i | \(0.0740618\pi\) | ||||
−0.973054 | + | 0.230578i | \(0.925938\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.7528i | − | 1.28195i | −0.767563 | − | 0.640974i | \(-0.778531\pi\) | ||
0.767563 | − | 0.640974i | \(-0.221469\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.496295 | 0.0401231 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.7663 | −1.18605 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.5648 | −1.40182 | −0.700912 | − | 0.713248i | \(-0.747223\pi\) | ||||
−0.700912 | + | 0.713248i | \(0.747223\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.12741 | 0.248020 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.13987i | 0.483889i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.54171i | − | 0.277409i | −0.990334 | − | 0.138704i | \(-0.955706\pi\) | ||
0.990334 | − | 0.138704i | \(-0.0442937\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.87360 | 0.145860 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.04934i | 0.700259i | 0.936701 | + | 0.350130i | \(0.113862\pi\) | ||||
−0.936701 | + | 0.350130i | \(0.886138\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0891 | + | 4.78067i | 0.929927 | + | 0.367744i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 13.3821i | − | 1.02335i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.0848 | 1.45099 | 0.725495 | − | 0.688227i | \(-0.241611\pi\) | ||||
0.725495 | + | 0.688227i | \(0.241611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.05400i | − | 0.155268i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.2662i | 0.771654i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.6188 | −1.69061 | −0.845303 | − | 0.534287i | \(-0.820580\pi\) | ||||
−0.845303 | + | 0.534287i | \(0.820580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4861 | 1.29973 | 0.649866 | − | 0.760049i | \(-0.274825\pi\) | ||||
0.649866 | + | 0.760049i | \(0.274825\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.02620 | 0.519392 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.1428 | 0.745711 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.198331i | − | 0.0145034i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 3.88158i | − | 0.282343i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6134 | 0.985028 | 0.492514 | − | 0.870305i | \(-0.336078\pi\) | ||||
0.492514 | + | 0.870305i | \(0.336078\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.46264i | 0.393209i | 0.980483 | + | 0.196605i | \(0.0629915\pi\) | ||||
−0.980483 | + | 0.196605i | \(0.937008\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.26447 | − | 6.63598i | 0.0905507 | − | 0.475212i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.67116i | 0.261560i | 0.991411 | + | 0.130780i | \(0.0417481\pi\) | ||||
−0.991411 | + | 0.130780i | \(0.958252\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.9167 | −1.27008 | −0.635042 | − | 0.772478i | \(-0.719017\pi\) | ||||
−0.635042 | + | 0.772478i | \(0.719017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 4.84612i | − | 0.341819i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.90461i | 0.203864i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.808935 | −0.0564985 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.3641 | −1.06788 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.34779 | −0.369915 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.3108 | 1.74247 | 0.871233 | − | 0.490869i | \(-0.163321\pi\) | ||||
0.871233 | + | 0.490869i | \(0.163321\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.4242i | 0.714253i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.56193i | 0.379320i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.55972 | 0.377418 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 8.11088i | − | 0.548083i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.702454 | − | 0.133851i | −0.0472522 | − | 0.00900380i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.91130i | 0.462815i | 0.972857 | + | 0.231408i | \(0.0743331\pi\) | ||||
−0.972857 | + | 0.231408i | \(0.925667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.13984 | 0.342656 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 23.8006i | − | 1.57970i | −0.613300 | − | 0.789850i | \(-0.710158\pi\) | ||
0.613300 | − | 0.789850i | \(-0.289842\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 27.8953i | − | 1.84338i | −0.387931 | − | 0.921688i | \(-0.626810\pi\) | ||
0.387931 | − | 0.921688i | \(-0.373190\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.705440 | −0.0464145 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.570395 | −0.0373678 | −0.0186839 | − | 0.999825i | \(-0.505948\pi\) | ||||
−0.0186839 | + | 0.999825i | \(0.505948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1200 | −0.660157 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.37340 | −0.219126 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.4981i | − | 0.679068i | −0.940594 | − | 0.339534i | \(-0.889731\pi\) | ||
0.940594 | − | 0.339534i | \(-0.110269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.27105i | 0.146291i | 0.997321 | + | 0.0731457i | \(0.0233038\pi\) | ||||
−0.997321 | + | 0.0731457i | \(0.976696\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.0089 | 0.962819 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.65594i | 0.169682i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.60916 | + | 18.9409i | −0.229645 | + | 1.20518i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.5938i | 0.671352i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0831 | −0.952036 | −0.476018 | − | 0.879436i | \(-0.657920\pi\) | ||||
−0.476018 | + | 0.879436i | \(0.657920\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.13987i | 0.386010i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.371594i | 0.0232701i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.4790 | −1.65172 | −0.825859 | − | 0.563877i | \(-0.809309\pi\) | ||||
−0.825859 | + | 0.563877i | \(0.809309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.81890 | −0.237295 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.26837 | −0.449901 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.1052 | −0.808103 | −0.404052 | − | 0.914736i | \(-0.632398\pi\) | ||||
−0.404052 | + | 0.914736i | \(0.632398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 11.7745i | − | 0.723303i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.13603i | − | 0.314320i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.8567 | −0.722914 | −0.361457 | − | 0.932389i | \(-0.617720\pi\) | ||||
−0.361457 | + | 0.932389i | \(0.617720\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.1867i | − | 1.34775i | −0.738847 | − | 0.673873i | \(-0.764629\pi\) | ||
0.738847 | − | 0.673873i | \(-0.235371\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.476092 | + | 2.49854i | −0.0288144 | + | 0.151219i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.05400i | − | 0.123861i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.53738 | −0.212541 | −0.106270 | − | 0.994337i | \(-0.533891\pi\) | ||||
−0.106270 | + | 0.994337i | \(0.533891\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.9124i | 0.832913i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.06393i | 0.302089i | 0.988527 | + | 0.151044i | \(0.0482636\pi\) | ||||
−0.988527 | + | 0.151044i | \(0.951736\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.366079 | 0.0217612 | 0.0108806 | − | 0.999941i | \(-0.496537\pi\) | ||||
0.0108806 | + | 0.999941i | \(0.496537\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.0196 | 0.593512 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.304576 | 0.0179786 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9607 | −0.997686 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 9.74205i | − | 0.571089i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.8379i | 0.866842i | 0.901192 | + | 0.433421i | \(0.142694\pi\) | ||||
−0.901192 | + | 0.433421i | \(0.857306\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.6516 | 2.25038 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.88158i | − | 0.225232i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.7463 | + | 4.14372i | 1.25762 | + | 0.239637i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.09415i | − | 0.120705i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.11395 | 0.408686 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 26.4532i | − | 1.51471i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.7430i | 0.898503i | 0.893405 | + | 0.449251i | \(0.148309\pi\) | ||||
−0.893405 | + | 0.449251i | \(0.851691\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.6051 | 0.603306 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3495 | 0.927097 | 0.463549 | − | 0.886071i | \(-0.346576\pi\) | ||||
0.463549 | + | 0.886071i | \(0.346576\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.9006 | 1.12485 | 0.562424 | − | 0.826849i | \(-0.309869\pi\) | ||||
0.562424 | + | 0.826849i | \(0.309869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.64610 | −0.374465 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.86991i | − | 0.105024i | −0.998620 | − | 0.0525122i | \(-0.983277\pi\) | ||
0.998620 | − | 0.0525122i | \(-0.0167228\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.90461i | 0.162627i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.22585 | 0.235864 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.06063i | − | 0.0590152i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.27492 | − | 1.38622i | −0.403540 | − | 0.0768937i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.19891i | 0.121600i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.81034 | 0.210071 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.4955i | 0.961641i | 0.876819 | + | 0.480821i | \(0.159661\pi\) | ||||
−0.876819 | + | 0.480821i | \(0.840339\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 9.55625i | − | 0.523679i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.2453 | −0.996850 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.2181 | −0.611091 | −0.305545 | − | 0.952178i | \(-0.598839\pi\) | ||||
−0.305545 | + | 0.952178i | \(0.598839\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.48633 | −0.297977 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.55972 | 0.301076 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 11.5037i | − | 0.619337i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.5357 | −1.58556 | −0.792780 | − | 0.609508i | \(-0.791367\pi\) | ||||
−0.792780 | + | 0.609508i | \(0.791367\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 21.0977i | − | 1.12933i | −0.825319 | − | 0.564667i | \(-0.809005\pi\) | ||
0.825319 | − | 0.564667i | \(-0.190995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.7479 | − | 2.61963i | −0.733807 | − | 0.139825i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.3734i | 0.977916i | 0.872307 | + | 0.488958i | \(0.162623\pi\) | ||||
−0.872307 | + | 0.488958i | \(0.837377\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.2464 | 2.08298 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.139911i | − | 0.00740485i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.68579i | 0.141750i | 0.997485 | + | 0.0708752i | \(0.0225792\pi\) | ||||
−0.997485 | + | 0.0708752i | \(0.977421\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.59889 | −0.505205 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.705440 | −0.0370260 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.5370 | −1.59838 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0522 | 0.837920 | 0.418960 | − | 0.908005i | \(-0.362395\pi\) | ||||
0.418960 | + | 0.908005i | \(0.362395\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.762158i | 0.0396764i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.43329i | 0.230165i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.9851 | −1.39723 | −0.698617 | − | 0.715496i | \(-0.746201\pi\) | ||||
−0.698617 | + | 0.715496i | \(0.746201\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 5.51963i | − | 0.285032i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2876 | + | 1.96029i | 0.529840 | + | 0.100960i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.0542i | 0.721917i | 0.932582 | + | 0.360959i | \(0.117550\pi\) | ||||
−0.932582 | + | 0.360959i | \(0.882450\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.9689 | 0.715650 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.4515i | 1.76039i | 0.474611 | + | 0.880196i | \(0.342589\pi\) | ||||
−0.474611 | + | 0.880196i | \(0.657411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.65594i | 0.135359i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.24030 | 0.266380 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.3692 | 1.13416 | 0.567082 | − | 0.823661i | \(-0.308072\pi\) | ||||
0.567082 | + | 0.823661i | \(0.308072\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.21773 | −0.0615831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.93136 | 0.198311 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.7006i | 0.639038i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.67112i | 0.234437i | 0.993106 | + | 0.117218i | \(0.0373978\pi\) | ||||
−0.993106 | + | 0.117218i | \(0.962602\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.77254 | −0.188863 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.8732i | 1.49179i | 0.666061 | + | 0.745897i | \(0.267979\pi\) | ||||
−0.666061 | + | 0.745897i | \(0.732021\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.75218 | − | 19.6916i | 0.186910 | − | 0.980906i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 12.6658i | − | 0.629366i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.81890 | −0.189296 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.9253i | 1.47971i | 0.672767 | + | 0.739855i | \(0.265106\pi\) | ||||
−0.672767 | + | 0.739855i | \(0.734894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 9.12391i | − | 0.450049i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.5529 | −0.716101 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 39.8849 | 1.95787 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.5752 | 0.664782 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.6971 | 0.815709 | 0.407855 | − | 0.913047i | \(-0.366277\pi\) | ||||
0.407855 | + | 0.913047i | \(0.366277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.4641i | 0.753676i | 0.926279 | + | 0.376838i | \(0.122989\pi\) | ||||
−0.926279 | + | 0.376838i | \(0.877011\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.53481i | 0.463598i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.407373 | 0.0197605 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.96003i | 0.482000i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.476092 | + | 2.49854i | −0.0229860 | + | 0.120631i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.9153i | − | 0.525772i | −0.964827 | − | 0.262886i | \(-0.915326\pi\) | ||
0.964827 | − | 0.262886i | \(-0.0846744\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.6461 | 1.23247 | 0.616237 | − | 0.787561i | \(-0.288656\pi\) | ||||
0.616237 | + | 0.787561i | \(0.288656\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 5.44209i | − | 0.260928i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.8347i | 1.57070i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.9269 | −0.855606 | −0.427803 | − | 0.903872i | \(-0.640712\pi\) | ||||
−0.427803 | + | 0.903872i | \(0.640712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.50236 | 0.119160 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.2777 | −1.24849 | −0.624245 | − | 0.781229i | \(-0.714593\pi\) | ||||
−0.624245 | + | 0.781229i | \(0.714593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.3368 | −0.916654 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.97101i | 0.187822i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.1211i | 0.902382i | 0.892427 | + | 0.451191i | \(0.149001\pi\) | ||||
−0.892427 | + | 0.451191i | \(0.850999\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.304576 | 0.0143419 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 11.1127i | − | 0.522119i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.40687 | + | 1.79246i | 0.441001 | + | 0.0840318i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.77591i | 0.223408i | 0.993742 | + | 0.111704i | \(0.0356308\pi\) | ||||
−0.993742 | + | 0.111704i | \(0.964369\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.769838 | 0.0359330 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.5341i | 1.09609i | 0.836448 | + | 0.548046i | \(0.184628\pi\) | ||||
−0.836448 | + | 0.548046i | \(0.815372\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.55074i | − | 0.211491i | −0.994393 | − | 0.105745i | \(-0.966277\pi\) | ||
0.994393 | − | 0.105745i | \(-0.0337229\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.4167 | −0.483063 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.5871 | 1.18403 | 0.592016 | − | 0.805926i | \(-0.298332\pi\) | ||||
0.592016 | + | 0.805926i | \(0.298332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.86965 | 0.317211 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.3909 | −0.570943 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.09415i | − | 0.0962890i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 10.9844i | − | 0.503998i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.0937 | −0.507943 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.5055i | 0.754154i | 0.926182 | + | 0.377077i | \(0.123071\pi\) | ||||
−0.926182 | + | 0.377077i | \(0.876929\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.57733 | + | 13.5259i | −0.117516 | + | 0.616727i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.33130i | 0.197081i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −36.6782 | −1.66547 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.40067i | − | 0.425985i | −0.977054 | − | 0.212992i | \(-0.931679\pi\) | ||
0.977054 | − | 0.212992i | \(-0.0683210\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.49847i | − | 0.112985i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.1695 | 1.58718 | 0.793589 | − | 0.608454i | \(-0.208210\pi\) | ||||
0.793589 | + | 0.608454i | \(0.208210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.576075 | −0.0259451 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.64610 | −0.298720 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.7769 | −0.662833 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.4953i | − | 0.738432i | −0.929344 | − | 0.369216i | \(-0.879626\pi\) | ||
0.929344 | − | 0.369216i | \(-0.120374\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.38376i | 0.285206i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.6269 | 0.830532 | 0.415266 | − | 0.909700i | \(-0.363689\pi\) | ||||
0.415266 | + | 0.909700i | \(0.363689\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 26.7836i | − | 1.19185i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.52810 | + | 3.37247i | 0.378746 | + | 0.149777i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 4.45845i | − | 0.197617i | −0.995106 | − | 0.0988086i | \(-0.968497\pi\) | ||
0.995106 | − | 0.0988086i | \(-0.0315032\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.4976 | 0.508625 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 20.7579i | − | 0.916483i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 39.9277i | − | 1.75943i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.81034 | 0.167578 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.4632 | 0.590968 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.3517 | 1.59260 | 0.796298 | − | 0.604905i | \(-0.206789\pi\) | ||||
0.796298 | + | 0.604905i | \(0.206789\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.2262 | −1.32170 | −0.660849 | − | 0.750519i | \(-0.729804\pi\) | ||||
−0.660849 | + | 0.750519i | \(0.729804\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.44897i | − | 0.0632384i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.10267i | 0.0480328i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.6980 | 0.639042 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 36.4165i | − | 1.58034i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.205555 | − | 1.07876i | 0.00890356 | − | 0.0467261i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 15.9101i | − | 0.687852i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.9562 | −0.688560 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.00000i | − | 0.0430730i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 5.08391i | − | 0.218574i | −0.994010 | − | 0.109287i | \(-0.965143\pi\) | ||
0.994010 | − | 0.109287i | \(-0.0348568\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.3354 | 0.529362 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.27876 | 0.354623 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.4442 | −1.34446 | −0.672228 | − | 0.740344i | \(-0.734663\pi\) | ||||
−0.672228 | + | 0.740344i | \(0.734663\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.9235 | −1.06371 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.5333i | 0.661739i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.78198i | − | 0.203350i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.15511 | 0.303717 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15.5675i | − | 0.659618i | −0.944048 | − | 0.329809i | \(-0.893016\pi\) | ||
0.944048 | − | 0.329809i | \(-0.106984\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.41711 | − | 1.41331i | −0.313710 | − | 0.0597768i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 0.139911i | − | 0.00590703i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.5965 | 0.868038 | 0.434019 | − | 0.900904i | \(-0.357095\pi\) | ||||
0.434019 | + | 0.900904i | \(0.357095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.6557i | 0.868993i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.76885i | 0.200273i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.21354 | 0.344329 | 0.172165 | − | 0.985068i | \(-0.444924\pi\) | ||||
0.172165 | + | 0.985068i | \(0.444924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.26806 | −0.220461 | −0.110231 | − | 0.993906i | \(-0.535159\pi\) | ||||
−0.110231 | + | 0.993906i | \(0.535159\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.60340 | 0.401188 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.6113 | −0.525928 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.6436i | 1.19245i | 0.802817 | + | 0.596225i | \(0.203333\pi\) | ||||
−0.802817 | + | 0.596225i | \(0.796667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.85356i | 0.160149i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0172 | −0.623020 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.43329i | 0.183608i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.48537 | + | 23.5393i | −0.185447 | + | 0.973231i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.8645i | 1.35646i | 0.734848 | + | 0.678232i | \(0.237253\pi\) | ||||
−0.734848 | + | 0.678232i | \(0.762747\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.7322 | 1.22509 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.58978i | 0.106530i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.6661i | − | 0.766523i | −0.923640 | − | 0.383262i | \(-0.874801\pi\) | ||
0.923640 | − | 0.383262i | \(-0.125199\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.526755 | −0.0215948 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.6392 | −0.517287 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.46110 | −0.263993 | −0.131997 | − | 0.991250i | \(-0.542139\pi\) | ||||
−0.131997 | + | 0.991250i | \(0.542139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.2597 | −1.19353 | −0.596765 | − | 0.802416i | \(-0.703547\pi\) | ||||
−0.596765 | + | 0.802416i | \(0.703547\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.1903i | 0.700043i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.65594i | 0.107979i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.7736 | −1.00553 | −0.502765 | − | 0.864423i | \(-0.667684\pi\) | ||||
−0.502765 | + | 0.864423i | \(0.667684\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.04903i | 0.0830308i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.57155 | − | 13.4955i | 0.104034 | − | 0.545971i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 29.4688i | − | 1.19023i | −0.803639 | − | 0.595117i | \(-0.797106\pi\) | ||
0.803639 | − | 0.595117i | \(-0.202894\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.570655 | −0.0230110 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.8453i | 0.517134i | 0.965993 | + | 0.258567i | \(0.0832502\pi\) | ||||
−0.965993 | + | 0.258567i | \(0.916750\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.2058i | 1.29446i | 0.762295 | + | 0.647230i | \(0.224073\pi\) | ||||
−0.762295 | + | 0.647230i | \(0.775927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.8324 | −0.956360 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.28061 | 0.291691 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0511 | −1.24204 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.77254 | −0.150661 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 0.757407i | − | 0.0301998i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.1313i | 0.482940i | 0.970408 | + | 0.241470i | \(0.0776296\pi\) | ||||
−0.970408 | + | 0.241470i | \(0.922370\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.8552 | 0.709682 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 52.5922i | − | 2.08706i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.54183 | − | 0.674887i | −0.140332 | − | 0.0267400i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 36.9770i | − | 1.46279i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.3335 | −1.55358 | −0.776789 | − | 0.629761i | \(-0.783153\pi\) | ||||
−0.776789 | + | 0.629761i | \(0.783153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 33.0164i | − | 1.30204i | −0.759061 | − | 0.651020i | \(-0.774341\pi\) | ||
0.759061 | − | 0.651020i | \(-0.225659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.92360i | 0.154492i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.6704 | −1.36303 | −0.681517 | − | 0.731803i | \(-0.738679\pi\) | ||||
−0.681517 | + | 0.731803i | \(0.738679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.5529 | −0.571251 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.92204 | 0.153717 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.40662 | 0.133311 | 0.0666557 | − | 0.997776i | \(-0.478767\pi\) | ||||
0.0666557 | + | 0.997776i | \(0.478767\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 14.8013i | − | 0.578336i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.7711i | 1.12247i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.2434 | 0.983342 | 0.491671 | − | 0.870781i | \(-0.336386\pi\) | ||||
0.491671 | + | 0.870781i | \(0.336386\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.2666i | 1.68288i | 0.540354 | + | 0.841438i | \(0.318290\pi\) | ||||
−0.540354 | + | 0.841438i | \(0.681710\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.495539 | − | 0.0944239i | −0.0192451 | − | 0.00366712i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.2034i | 0.550784i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.8339 | 0.690533 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.87551i | 0.188498i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.96003i | 0.384503i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.5991 | −1.06387 | −0.531934 | − | 0.846786i | \(-0.678534\pi\) | ||||
−0.531934 | + | 0.846786i | \(0.678534\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.97277 | 0.306872 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.2797 | −1.81711 | −0.908554 | − | 0.417768i | \(-0.862813\pi\) | ||||
−0.908554 | + | 0.417768i | \(0.862813\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8099 | 0.529976 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 16.7899i | − | 0.643389i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 25.2893i | − | 0.967670i | −0.875159 | − | 0.483835i | \(-0.839243\pi\) | ||
0.875159 | − | 0.483835i | \(-0.160757\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.3510 | −1.31248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 19.6785i | − | 0.750781i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.7019 | + | 2.99197i | 0.598196 | + | 0.113985i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.5772i | 1.12517i | 0.826740 | + | 0.562584i | \(0.190193\pi\) | ||||
−0.826740 | + | 0.562584i | \(0.809807\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.50236 | 0.0950566 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 51.1099i | − | 1.93871i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0604069i | 0.00228808i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.402379 | −0.0152194 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.2769 | −1.33239 | −0.666196 | − | 0.745777i | \(-0.732079\pi\) | ||||
−0.666196 | + | 0.745777i | \(0.732079\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.4227 | −0.770257 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.13906 | −0.268872 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0844i | 0.379264i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 15.6266i | − | 0.586870i | −0.955979 | − | 0.293435i | \(-0.905202\pi\) | ||
0.955979 | − | 0.293435i | \(-0.0947984\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.9662 | 0.448768 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 34.1359i | − | 1.27840i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.40687 | + | 1.79246i | 0.351797 | + | 0.0670341i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 7.40581i | − | 0.276575i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.4518 | −0.762722 | −0.381361 | − | 0.924426i | \(-0.624545\pi\) | ||||
−0.381361 | + | 0.924426i | \(0.624545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0334i | 0.559873i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.60209i | 0.0595824i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.96608 | −0.221575 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2659 | −0.677444 | −0.338722 | − | 0.940887i | \(-0.609995\pi\) | ||||
−0.338722 | + | 0.940887i | \(0.609995\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.71869 | −0.137729 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.415335 | 0.0153617 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.8353i | 0.769569i | 0.923006 | + | 0.384785i | \(0.125724\pi\) | ||||
−0.923006 | + | 0.384785i | \(0.874276\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.87360i | 0.0691089i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.86965 | 0.253047 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 46.7097i | − | 1.71824i | −0.511772 | − | 0.859122i | \(-0.671011\pi\) | ||
0.511772 | − | 0.859122i | \(-0.328989\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.54604 | + | 13.3617i | −0.0935312 | + | 0.490854i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.7362i | 0.540620i | 0.962773 | + | 0.270310i | \(0.0871261\pi\) | ||||
−0.962773 | + | 0.270310i | \(0.912874\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.9506 | 0.547749 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 37.5785i | − | 1.37492i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.99038i | 0.218884i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.8710 | 1.09001 | 0.545004 | − | 0.838433i | \(-0.316528\pi\) | ||||
0.545004 | + | 0.838433i | \(0.316528\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.6402 | −0.387750 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41.8385 | −1.52266 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.1350 | −0.659129 | −0.329564 | − | 0.944133i | \(-0.606902\pi\) | ||||
−0.329564 | + | 0.944133i | \(0.606902\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.33130i | 0.157216i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.35917i | − | 0.121770i | −0.998145 | − | 0.0608850i | \(-0.980608\pi\) | ||
0.998145 | − | 0.0608850i | \(-0.0193923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.11708 | −0.112846 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 1.31813i | − | 0.0476570i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.82157 | + | 51.5438i | −0.354636 | + | 1.86114i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.8495i | 0.787914i | 0.919129 | + | 0.393957i | \(0.128894\pi\) | ||||
−0.919129 | + | 0.393957i | \(0.871106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.6794 | −0.672721 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 30.6298i | − | 1.10168i | −0.834611 | − | 0.550839i | \(-0.814308\pi\) | ||
0.834611 | − | 0.550839i | \(-0.185692\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.4197i | 0.410207i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.69401 | −0.0966469 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.62881 | 0.0583582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.7769 | −0.528758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.2745 | −0.402917 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.6510i | 1.66505i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.7694i | 0.775995i | 0.921660 | + | 0.387997i | \(0.126833\pi\) | ||||
−0.921660 | + | 0.387997i | \(0.873167\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.24495 | −0.329129 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.77719i | − | 0.276525i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.2767 | + | 6.72190i | 1.25271 | + | 0.238702i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 8.30622i | − | 0.294591i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.37738 | 0.0842113 | 0.0421056 | − | 0.999113i | \(-0.486593\pi\) | ||||
0.0421056 | + | 0.999113i | \(0.486593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.755708i | 0.0267350i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.2187i | 0.643725i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.4976 | 0.405742 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.3071 | 0.574750 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.36416 | −0.294432 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.24207 | −0.324934 | −0.162467 | − | 0.986714i | \(-0.551945\pi\) | ||||
−0.162467 | + | 0.986714i | \(0.551945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24.0516i | − | 0.844567i | −0.906464 | − | 0.422284i | \(-0.861229\pi\) | ||
0.906464 | − | 0.422284i | \(-0.138771\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 15.6514i | − | 0.548918i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.40657 | −0.329498 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 11.1991i | − | 0.391806i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.68881 | − | 8.86290i | 0.0590117 | − | 0.309695i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.30719i | 0.115422i | 0.998333 | + | 0.0577109i | \(0.0183802\pi\) | ||||
−0.998333 | + | 0.0577109i | \(0.981620\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.1081 | 1.60723 | 0.803613 | − | 0.595152i | \(-0.202908\pi\) | ||||
0.803613 | + | 0.595152i | \(0.202908\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.44897i | − | 0.0504468i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 40.8890i | − | 1.42185i | −0.703268 | − | 0.710925i | \(-0.748277\pi\) | ||
0.703268 | − | 0.710925i | \(-0.251723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.6020 | −1.75748 | −0.878740 | − | 0.477301i | \(-0.841615\pi\) | ||||
−0.878740 | + | 0.477301i | \(0.841615\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.49541 | −0.0865649 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.198331 | 0.00687177 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.0345 | 0.831748 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.5805i | 0.745931i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 10.4839i | − | 0.361945i | −0.983488 | − | 0.180972i | \(-0.942076\pi\) | ||
0.983488 | − | 0.180972i | \(-0.0579244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5632 | −0.709077 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.57229i | 0.123036i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6972 | − | 32.1078i | 0.436795 | − | 1.10454i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.258247 | 0.00886301 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.4476i | 0.803772i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 20.9651i | − | 0.717832i | −0.933370 | − | 0.358916i | \(-0.883146\pi\) | ||
0.933370 | − | 0.358916i | \(-0.116854\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −35.5420 | −1.21551 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.6410 | 0.841721 | 0.420861 | − | 0.907125i | \(-0.361728\pi\) | ||||
0.420861 | + | 0.907125i | \(0.361728\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.6433 | 1.59145 | 0.795724 | − | 0.605659i | \(-0.207091\pi\) | ||||
0.795724 | + | 0.605659i | \(0.207091\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.214860 | 0.00732241 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.4036i | 1.17111i | 0.810632 | + | 0.585555i | \(0.199124\pi\) | ||||
−0.810632 | + | 0.585555i | \(0.800876\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 50.6880i | − | 1.72345i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.9647 | −0.406343 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.78198i | − | 0.162218i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.63624 | − | 24.3311i | 0.157093 | − | 0.824427i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 34.5573i | 1.16959i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.82438 | 0.264512 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.57270i | 0.0531064i | 0.999647 | + | 0.0265532i | \(0.00845313\pi\) | ||||
−0.999647 | + | 0.0265532i | \(0.991547\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.4673i | 0.353052i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.18142 | −0.208257 | −0.104129 | − | 0.994564i | \(-0.533205\pi\) | ||||
−0.104129 | + | 0.994564i | \(0.533205\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.8498 | 1.34105 | 0.670527 | − | 0.741885i | \(-0.266068\pi\) | ||||
0.670527 | + | 0.741885i | \(0.266068\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27.2664 | 0.916549 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.1687 | −0.710776 | −0.355388 | − | 0.934719i | \(-0.615651\pi\) | ||||
−0.355388 | + | 0.934719i | \(0.615651\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.8017i | 0.664129i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.76885i | 0.159762i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.3769 | 0.681886 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 60.0740i | 2.00805i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.3407 | + | 2.92314i | 0.512212 | + | 0.0976009i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 16.1488i | − | 0.538593i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.879258 | −0.0292923 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.47729i | − | 0.0491613i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 46.4420i | − | 1.54378i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.3216 | 1.10643 | 0.553213 | − | 0.833040i | \(-0.313401\pi\) | ||||
0.553213 | + | 0.833040i | \(0.313401\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −25.2348 | −0.836985 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.98570 | 0.231447 | 0.115723 | − | 0.993281i | \(-0.463081\pi\) | ||||
0.115723 | + | 0.993281i | \(0.463081\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.0172 | −0.496998 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 18.6611i | − | 0.616919i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.57293i | 0.184034i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.4737 | −0.378481 | −0.189240 | − | 0.981931i | \(-0.560603\pi\) | ||||
−0.189240 | + | 0.981931i | \(0.560603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.1058i | 0.365947i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.97272 | + | 52.3371i | −0.328256 | + | 1.72270i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 7.84404i | − | 0.257910i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37.6189 | −1.23557 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.6879i | 1.00684i | 0.864043 | + | 0.503418i | \(0.167924\pi\) | ||||
−0.864043 | + | 0.503418i | \(0.832076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 5.34779i | − | 0.175267i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.5336 | 0.377594 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.526755 | −0.0172267 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.3527 | −0.893574 | −0.446787 | − | 0.894640i | \(-0.647432\pi\) | ||||
−0.446787 | + | 0.894640i | \(0.647432\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0387 | 0.458134 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.9241i | 0.421312i | 0.977560 | + | 0.210656i | \(0.0675600\pi\) | ||||
−0.977560 | + | 0.210656i | \(0.932440\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.87006i | − | 0.0608975i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.3092 | −0.335359 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 20.5595i | − | 0.668093i | −0.942557 | − | 0.334046i | \(-0.891586\pi\) | ||
0.942557 | − | 0.334046i | \(-0.108414\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.75960 | − | 40.7226i | 0.251887 | − | 1.32191i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.31911i | − | 0.0427749i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.2123 | −0.427988 | −0.213994 | − | 0.976835i | \(-0.568647\pi\) | ||||
−0.213994 | + | 0.976835i | \(0.568647\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 36.1562i | − | 1.16999i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.04903i | 0.0662357i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.9336 | 0.417649 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.0895349 | 0.00288822 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.9901 | −0.483048 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.5084 | 0.467043 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.0154i | − | 1.28681i | −0.765526 | − | 0.643405i | \(-0.777521\pi\) | ||
0.765526 | − | 0.643405i | \(-0.222479\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 0.748213i | − | 0.0240361i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.6080 | −0.693435 | −0.346717 | − | 0.937970i | \(-0.612704\pi\) | ||||
−0.346717 | + | 0.937970i | \(0.612704\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.2437i | 0.616923i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.13201 | − | 0.977895i | −0.164356 | − | 0.0313177i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 54.7924i | − | 1.75296i | −0.481434 | − | 0.876482i | \(-0.659884\pi\) | ||
0.481434 | − | 0.876482i | \(-0.340116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.28061 | 0.232689 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 7.80003i | − | 0.249036i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 30.4918i | − | 0.972538i | −0.873809 | − | 0.486269i | \(-0.838358\pi\) | ||
0.873809 | − | 0.486269i | \(-0.161642\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.75038 | 0.310673 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.68796 | 0.0855587 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.8578 | −0.408854 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.46454 | 0.300651 | 0.150326 | − | 0.988637i | \(-0.451968\pi\) | ||||
0.150326 | + | 0.988637i | \(0.451968\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.3420i | 0.391663i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 47.5857i | 1.50857i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.85518 | −0.122095 | −0.0610473 | − | 0.998135i | \(-0.519444\pi\) | ||||
−0.0610473 | + | 0.998135i | \(0.519444\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 14.8234i | − | 0.468991i |
(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 | 4004.2.m.b.2157.17 | ✓ | 30 | |
13.12 | even | 2 | inner | 4004.2.m.b.2157.18 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.b.2157.17 | ✓ | 30 | 1.1 | even | 1 | trivial | |
4004.2.m.b.2157.18 | yes | 30 | 13.12 | even | 2 | inner |