Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(214,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.s (of order \(16\), degree \(8\), 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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{16})\) |
Coefficient field: | 16.0.3289935900927224469054816256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10319x^{8} + 214358881 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{16}]$ |
Embedding invariants
Embedding label | 386.1 | ||
Root | \(-0.792772 - 3.22048i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.386 |
Dual form | 731.2.s.a.214.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{13}{16}\right)\) | \(-1\) |
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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(3\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(4\) | −1.41421 | + | 1.41421i | −0.707107 | + | 0.707107i | ||||
\(5\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.14805 | − | 2.77164i | 0.382683 | − | 0.923880i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.165842 | + | 0.248200i | −0.0500032 | + | 0.0748351i | −0.855629 | − | 0.517590i | \(-0.826829\pi\) |
0.805626 | + | 0.592425i | \(0.201829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.77872 | − | 4.77872i | −1.32538 | − | 1.32538i | −0.909353 | − | 0.416025i | \(-0.863423\pi\) |
−0.416025 | − | 0.909353i | \(-0.636577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | − | 4.00000i | − | 1.00000i | ||||||
\(17\) | 3.56441 | − | 2.07243i | 0.864496 | − | 0.502639i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.86853 | + | 5.25759i | 1.64070 | + | 1.09628i | 0.910902 | + | 0.412622i | \(0.135387\pi\) |
0.729800 | + | 0.683660i | \(0.239613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.61940 | + | 1.91342i | 0.923880 | + | 0.382683i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.59764 | − | 3.88764i | −0.466550 | − | 0.698241i | 0.521349 | − | 0.853344i | \(-0.325429\pi\) |
−0.987898 | + | 0.155103i | \(0.950429\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.29610 | + | 5.54328i | 0.382683 | + | 0.923880i | ||||
\(37\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.3414 | − | 2.25594i | 1.77123 | − | 0.352319i | 0.801781 | − | 0.597619i | \(-0.203886\pi\) |
0.969447 | + | 0.245299i | \(0.0788863\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.50942 | − | 6.05828i | 0.382683 | − | 0.923880i | ||||
\(44\) | −0.116472 | − | 0.585544i | −0.0175588 | − | 0.0882740i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.48531 | − | 7.48531i | −1.09185 | − | 1.09185i | −0.995332 | − | 0.0965136i | \(-0.969231\pi\) |
−0.0965136 | − | 0.995332i | \(-0.530769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.46716 | − | 2.67878i | 0.923880 | − | 0.382683i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.5163 | 1.87437 | ||||||||
\(53\) | −3.63588 | − | 8.77779i | −0.499426 | − | 1.20572i | −0.949793 | − | 0.312878i | \(-0.898707\pi\) |
0.450367 | − | 0.892844i | \(-0.351293\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.4652 | − | 4.74906i | −1.49265 | − | 0.618274i | −0.520756 | − | 0.853706i | \(-0.674350\pi\) |
−0.971891 | + | 0.235431i | \(0.924350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.65685 | + | 5.65685i | 0.707107 | + | 0.707107i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7985i | 1.44142i | 0.693236 | + | 0.720710i | \(0.256184\pi\) | ||||
−0.693236 | + | 0.720710i | \(0.743816\pi\) | |||||||
\(68\) | −2.10997 | + | 7.97170i | −0.255872 | + | 0.966711i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.35438 | + | 3.52358i | −0.264889 | + | 0.396434i | −0.939942 | − | 0.341335i | \(-0.889121\pi\) |
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.36396 | − | 6.36396i | −0.707107 | − | 0.707107i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.05828 | + | 2.50942i | −0.664983 | + | 0.275445i | −0.689534 | − | 0.724254i | \(-0.742184\pi\) |
0.0245507 | + | 0.999699i | \(0.492184\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −18.5631 | + | 3.69244i | −1.93534 | + | 0.384963i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.08269 | − | 15.4977i | 0.313000 | − | 1.57356i | −0.429093 | − | 0.903260i | \(-0.641167\pi\) |
0.742093 | − | 0.670297i | \(-0.233833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.497526 | + | 0.744600i | 0.0500032 | + | 0.0748351i | ||||
\(100\) | −9.23880 | + | 3.82683i | −0.923880 | + | 0.382683i | ||||
\(101\) | − | 1.21270i | − | 0.120668i | −0.998178 | − | 0.0603342i | \(-0.980783\pi\) | ||
0.998178 | − | 0.0603342i | \(-0.0192166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.90887 | 0.286620 | 0.143310 | − | 0.989678i | \(-0.454225\pi\) | ||||
0.143310 | + | 0.989678i | \(0.454225\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.6772 | + | 3.11839i | 1.51557 | + | 0.301466i | 0.881640 | − | 0.471923i | \(-0.156440\pi\) |
0.633932 | + | 0.773389i | \(0.281440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.2630 | + | 4.03056i | −1.94084 | + | 0.386057i | −0.942133 | + | 0.335239i | \(0.891183\pi\) |
−0.998708 | + | 0.0508181i | \(0.983817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.7311 | + | 7.75867i | −1.73169 | + | 0.717290i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.17542 | + | 10.0804i | 0.379583 | + | 0.916396i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.17157 | + | 1.82434i | 0.823631 | + | 0.163830i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.6805 | + | 8.56613i | 1.83509 | + | 0.760121i | 0.962276 | + | 0.272075i | \(0.0877098\pi\) |
0.872818 | + | 0.488046i | \(0.162290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0999825 | − | 0.0668062i | 0.00848041 | − | 0.00566643i | −0.551323 | − | 0.834292i | \(-0.685877\pi\) |
0.559803 | + | 0.828626i | \(0.310877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.97859 | − | 0.393566i | 0.165458 | − | 0.0329116i | ||||
\(144\) | −11.0866 | − | 4.59220i | −0.923880 | − | 0.382683i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.65191 | − | 12.2585i | −0.133549 | − | 0.991042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(164\) | −12.8488 | + | 19.2295i | −1.00332 | + | 1.50157i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.28278 | − | 9.40284i | −0.486176 | − | 0.727613i | 0.504566 | − | 0.863373i | \(-0.331653\pi\) |
−0.990742 | + | 0.135760i | \(0.956653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.6723i | 2.51326i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.01885 | + | 12.1166i | 0.382683 | + | 0.923880i | ||||
\(173\) | −21.0658 | + | 14.0757i | −1.60160 | + | 1.07016i | −0.651300 | + | 0.758820i | \(0.725776\pi\) |
−0.950300 | + | 0.311335i | \(0.899224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.992800 | + | 0.663368i | 0.0748351 | + | 0.0500032i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.32439 | − | 7.96852i | 0.395759 | − | 0.592295i | −0.579062 | − | 0.815283i | \(-0.696581\pi\) |
0.974821 | + | 0.222988i | \(0.0715812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0767508 | + | 1.22838i | −0.00561258 | + | 0.0898282i | ||||
\(188\) | 21.1717 | 1.54410 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.6371 | − | 10.4484i | −1.12558 | − | 0.752090i | −0.153831 | − | 0.988097i | \(-0.549161\pi\) |
−0.971751 | + | 0.236007i | \(0.924161\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.35757 | + | 12.9343i | −0.382683 | + | 0.923880i | ||||
\(197\) | −5.33864 | − | 26.8391i | −0.380362 | − | 1.91221i | −0.408822 | − | 0.912614i | \(-0.634060\pi\) |
0.0284595 | − | 0.999595i | \(-0.490940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 23.6056 | − | 15.7728i | 1.64070 | − | 1.09628i | ||||
\(208\) | −19.1149 | + | 19.1149i | −1.32538 | + | 1.32538i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(212\) | 17.5556 | + | 7.27176i | 1.20572 | + | 0.499426i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.9369 | − | 7.12974i | −1.81197 | − | 0.479598i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.6066 | − | 10.6066i | 0.707107 | − | 0.707107i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.65964 | + | 3.58694i | 0.572245 | + | 0.237032i | 0.649992 | − | 0.759941i | \(-0.274772\pi\) |
−0.0777462 | + | 0.996973i | \(0.524772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22.9305 | − | 9.49811i | 1.49265 | − | 0.618274i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5254 | −0.680830 | −0.340415 | − | 0.940275i | \(-0.610568\pi\) | ||||
−0.340415 | + | 0.940275i | \(0.610568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.2213 | + | 12.2213i | 0.771400 | + | 0.771400i | 0.978351 | − | 0.206951i | \(-0.0663540\pi\) |
−0.206951 | + | 0.978351i | \(0.566354\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.60986 | + | 1.08104i | −0.164081 | + | 0.0679645i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.0000 | −1.00000 | ||||||||
\(257\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.6856 | − | 16.6856i | −1.01924 | − | 1.01924i | ||||
\(269\) | 10.5820 | + | 15.8370i | 0.645195 | + | 0.965602i | 0.999535 | + | 0.0304855i | \(0.00970535\pi\) |
−0.354341 | + | 0.935116i | \(0.615295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3188i | 0.930548i | 0.885167 | + | 0.465274i | \(0.154044\pi\) | ||||
−0.885167 | + | 0.465274i | \(0.845956\pi\) | |||||||
\(272\) | −8.28973 | − | 14.2576i | −0.502639 | − | 0.864496i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.24100 | + | 0.829209i | −0.0748351 | + | 0.0500032i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.7574 | + | 2.73651i | −0.823631 | + | 0.163830i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.6171 | + | 30.4605i | −0.752676 | + | 1.81712i | −0.208792 | + | 0.977960i | \(0.566953\pi\) |
−0.543884 | + | 0.839161i | \(0.683047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.6923 | + | 27.9750i | −1.11114 | + | 1.66294i | −0.555409 | + | 0.831578i | \(0.687438\pi\) |
−0.555732 | + | 0.831362i | \(0.687562\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.41004 | − | 14.7740i | 0.494708 | − | 0.869059i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.11488 | + | 2.11488i | −0.123552 | + | 0.123552i | −0.766179 | − | 0.642627i | \(-0.777845\pi\) |
0.642627 | + | 0.766179i | \(0.277845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.4770 | − | 62.7260i | −0.721563 | − | 3.62754i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.3208 | 1.95879 | 0.979395 | − | 0.201954i | \(-0.0647291\pi\) | ||||
0.979395 | + | 0.201954i | \(0.0647291\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.6541 | + | 3.90944i | 1.11448 | + | 0.221684i | 0.717784 | − | 0.696265i | \(-0.245156\pi\) |
0.396697 | + | 0.917950i | \(0.370156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.65350 | − | 8.31270i | −0.0930166 | − | 0.467626i | ||||
\(317\) | 18.3606 | − | 27.4786i | 1.03123 | − | 1.54335i | 0.206005 | − | 0.978551i | \(-0.433954\pi\) |
0.825228 | − | 0.564799i | \(-0.191046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 18.0000 | 1.00000 | ||||||||
\(325\) | −12.9311 | − | 31.2185i | −0.717290 | − | 1.73169i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(332\) | 5.01885 | − | 12.1166i | 0.275445 | − | 0.664983i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.0240 | + | 28.4714i | 1.03630 | + | 1.55093i | 0.818138 | + | 0.575022i | \(0.195006\pi\) |
0.218163 | + | 0.975912i | \(0.429994\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.39571 | 0.0755819 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.7787 | − | 21.7787i | −1.15916 | − | 1.15916i | −0.984656 | − | 0.174509i | \(-0.944166\pi\) |
−0.174509 | − | 0.984656i | \(-0.555834\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.73079 | − | 9.00692i | −0.196903 | − | 0.475367i | 0.794330 | − | 0.607486i | \(-0.207822\pi\) |
−0.991234 | + | 0.132119i | \(0.957822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4350 | + | 13.4350i | −0.707107 | + | 0.707107i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.38915 | + | 32.1204i | 0.333511 | + | 1.67667i | 0.675806 | + | 0.737079i | \(0.263796\pi\) |
−0.342296 | + | 0.939592i | \(0.611204\pi\) | |||||||
\(368\) | 21.0303 | − | 31.4741i | 1.09628 | − | 1.64070i | ||||
\(369\) | 6.76783 | − | 34.0242i | 0.352319 | − | 1.77123i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.1805 | + | 7.59458i | 1.96120 | + | 0.390107i | 0.984383 | + | 0.176042i | \(0.0563295\pi\) |
0.976819 | + | 0.214065i | \(0.0686705\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.9104 | − | 13.9104i | −0.707107 | − | 0.707107i | ||||
\(388\) | 17.5575 | + | 26.2767i | 0.891349 | + | 1.33400i | ||||
\(389\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.9427 | + | 2.43319i | 1.96942 | + | 0.123051i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.75663 | − | 0.349416i | −0.0882740 | − | 0.0175588i | ||||
\(397\) | 28.7196 | + | 19.1898i | 1.44139 | + | 0.963109i | 0.997760 | + | 0.0669005i | \(0.0213110\pi\) |
0.443634 | + | 0.896208i | \(0.353689\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.65367 | − | 18.4776i | 0.382683 | − | 0.923880i | ||||
\(401\) | −7.14894 | − | 35.9402i | −0.357001 | − | 1.79477i | −0.574283 | − | 0.818657i | \(-0.694719\pi\) |
0.217281 | − | 0.976109i | \(-0.430281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.16456 | + | 30.9913i | −0.307079 | + | 1.54379i | ||||
\(404\) | 1.71502 | + | 1.71502i | 0.0853254 | + | 0.0853254i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.11377 | + | 4.11377i | −0.202671 | + | 0.202671i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −29.3401 | + | 12.1531i | −1.42656 | + | 0.590902i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.4309 | − | 2.75319i | 0.991042 | − | 0.133549i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.5810 | + | 17.7608i | −1.28484 | + | 0.858502i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.3742 | + | 20.9635i | 1.51124 | + | 1.00978i | 0.987450 | + | 0.157930i | \(0.0504821\pi\) |
0.523789 | + | 0.851848i | \(0.324518\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.9561 | − | 34.3562i | 1.09940 | − | 1.64537i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.0289 | − | 26.9822i | −0.860473 | − | 1.28779i | −0.956299 | − | 0.292391i | \(-0.905549\pi\) |
0.0958262 | − | 0.995398i | \(-0.469451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 21.0000i | − | 1.00000i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.5579 | 1.78443 | 0.892215 | − | 0.451612i | \(-0.149151\pi\) | ||||
0.892215 | + | 0.451612i | \(0.149151\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.32095 | + | 3.18906i | −0.0622012 | + | 0.150167i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0377 | + | 24.2331i | 0.467502 | + | 1.12865i | 0.965250 | + | 0.261328i | \(0.0841604\pi\) |
−0.497748 | + | 0.867322i | \(0.665840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(468\) | 15.5173 | − | 37.4622i | 0.717290 | − | 1.73169i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.08750 | + | 1.62756i | 0.0500032 | + | 0.0748351i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.5030 | −1.30506 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.9678 | + | 19.3556i | −1.32357 | + | 0.884382i | −0.998127 | − | 0.0611793i | \(-0.980514\pi\) |
−0.325444 | + | 0.945561i | \(0.605514\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20.1607 | − | 8.35084i | −0.916396 | − | 0.379583i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.2710 | − | 28.8410i | 0.873251 | − | 1.30691i | −0.0775113 | − | 0.996991i | \(-0.524697\pi\) |
0.950762 | − | 0.309921i | \(-0.100303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.5506 | + | 10.3906i | −0.698241 | + | 0.466550i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −41.3609 | + | 17.1323i | −1.83509 | + | 0.760121i | ||||
\(509\) | − | 16.0932i | − | 0.713316i | −0.934235 | − | 0.356658i | \(-0.883916\pi\) | ||
0.934235 | − | 0.356658i | \(-0.116084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.09923 | − | 0.616476i | 0.136304 | − | 0.0271126i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.3159 | − | 8.47372i | −0.754294 | − | 0.369121i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.4699 | + | 61.4898i | 1.10739 | + | 2.67347i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.3253 | + | 26.3253i | −1.14242 | + | 1.14242i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −64.9778 | − | 43.4168i | −2.81450 | − | 1.88059i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.407651 | + | 2.04940i | −0.0175588 | + | 0.0882740i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.12397 | − | 7.66857i | −0.220297 | − | 0.329698i | 0.704816 | − | 0.709390i | \(-0.251030\pi\) |
−0.925113 | + | 0.379693i | \(0.876030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.8915 | − | 23.9819i | 1.53461 | − | 1.02539i | 0.553293 | − | 0.832987i | \(-0.313371\pi\) |
0.981315 | − | 0.192406i | \(-0.0616291\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0469184 | + | 0.235875i | −0.00198978 | + | 0.0100033i | ||||
\(557\) | 19.6071 | + | 19.6071i | 0.830780 | + | 0.830780i | 0.987623 | − | 0.156844i | \(-0.0501319\pi\) |
−0.156844 | + | 0.987623i | \(0.550132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.9427 | + | 16.9590i | −1.73169 | + | 0.717290i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.6567 | − | 37.7986i | −0.659851 | − | 1.59302i | −0.798033 | − | 0.602614i | \(-0.794126\pi\) |
0.138182 | − | 0.990407i | \(-0.455874\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.4943 | − | 8.90324i | −0.901088 | − | 0.373243i | −0.116450 | − | 0.993197i | \(-0.537151\pi\) |
−0.784639 | + | 0.619953i | \(0.787151\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(572\) | −2.24156 | + | 3.35473i | −0.0937244 | + | 0.140268i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.2879 | + | 39.3427i | 1.09628 | + | 1.64070i | ||||
\(576\) | 22.1731 | − | 9.18440i | 0.923880 | − | 0.382683i | ||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.78163 | + | 0.553300i | 0.115203 | + | 0.0229154i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.4577 | + | 32.4577i | −1.32618 | + | 1.32618i | −0.417514 | + | 0.908671i | \(0.637098\pi\) |
−0.908671 | + | 0.417514i | \(0.862902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.7013 | + | 13.5453i | 1.33170 | + | 0.551608i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 71.5404i | 2.89422i | ||||||||
\(612\) | 19.6723 | + | 15.0000i | 0.795206 | + | 0.606339i | ||||
\(613\) | 8.16043 | 0.329597 | 0.164798 | − | 0.986327i | \(-0.447303\pi\) | ||||
0.164798 | + | 0.986327i | \(0.447303\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.51744 | + | 1.89314i | 0.383158 | + | 0.0762148i | 0.382911 | − | 0.923785i | \(-0.374922\pi\) |
0.000246592 | 1.00000i | \(0.499922\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.2899 | + | 9.20763i | −1.86055 | + | 0.370086i | −0.992075 | − | 0.125649i | \(-0.959899\pi\) |
−0.868474 | + | 0.495735i | \(0.834899\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.6777 | + | 17.6777i | 0.707107 | + | 0.707107i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −43.7059 | − | 18.1036i | −1.73169 | − | 0.717290i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.0519 | + | 41.9827i | 1.10626 | + | 1.65563i | 0.630978 | + | 0.775800i | \(0.282654\pi\) |
0.475281 | + | 0.879834i | \(0.342346\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.08013 | − | 2.05808i | 0.120906 | − | 0.0807866i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.02377 | − | 45.3656i | −0.352319 | − | 1.77123i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.60446 | − | 2.60446i | −0.101455 | − | 0.101455i | 0.654557 | − | 0.756013i | \(-0.272855\pi\) |
−0.756013 | + | 0.654557i | \(0.772855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.05828 | + | 2.50942i | −0.235640 | + | 0.0976052i | −0.497379 | − | 0.867533i | \(-0.665704\pi\) |
0.261739 | + | 0.965139i | \(0.415704\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 22.1828 | + | 4.41243i | 0.858279 | + | 0.170722i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −46.2056 | − | 46.2056i | −1.77714 | − | 1.77714i | ||||
\(677\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.1855 | − | 13.4875i | 0.772378 | − | 0.516086i | −0.105819 | − | 0.994385i | \(-0.533747\pi\) |
0.878197 | + | 0.478299i | \(0.158747\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.2331 | − | 10.0377i | −0.923880 | − | 0.382683i | ||||
\(689\) | −24.5717 | + | 59.3214i | −0.936109 | + | 2.25997i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(692\) | 9.88545 | − | 49.6975i | 0.375788 | − | 1.88922i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.7501 | − | 31.5454i | 1.35413 | − | 1.19487i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.1149 | + | 36.1149i | −1.36404 | + | 1.36404i | −0.495342 | + | 0.868698i | \(0.664957\pi\) |
−0.868698 | + | 0.495342i | \(0.835043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.34217 | + | 0.465887i | −0.0882740 | + | 0.0175588i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.91327 | + | 34.7554i | −0.259633 | + | 1.30526i | 0.602311 | + | 0.798262i | \(0.294247\pi\) |
−0.861944 | + | 0.507003i | \(0.830753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.06315 | + | 10.5708i | 0.264889 | + | 0.396434i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 44.2473i | − | 1.65708i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.66595 | + | 0.530291i | 0.0994233 | + | 0.0197765i | 0.244551 | − | 0.969636i | \(-0.421359\pi\) |
−0.145128 | + | 0.989413i | \(0.546359\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.73936 | + | 18.7990i | 0.138972 | + | 0.698660i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.9447 | + | 10.3325i | −0.923880 | + | 0.382683i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.61077 | − | 26.7948i | −0.133549 | − | 0.991042i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.92840 | − | 1.95669i | −0.107869 | − | 0.0720756i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.6723i | 0.719772i | ||||||||
\(748\) | −1.62865 | − | 1.84574i | −0.0595495 | − | 0.0674868i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(752\) | −29.9413 | + | 29.9413i | −1.09185 | + | 1.09185i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.0947 | + | 77.4836i | 1.15887 | + | 2.79777i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.1416 | + | 39.1416i | −1.41148 | + | 1.41148i | −0.661812 | + | 0.749670i | \(0.730212\pi\) |
−0.749670 | + | 0.661812i | \(0.769788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 36.8904 | − | 7.33796i | 1.32771 | − | 0.264099i | ||||
\(773\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.56085 | − | 22.9289i | −0.163830 | − | 0.823631i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.7151 | − | 25.8686i | −0.382683 | − | 0.923880i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.9493 | + | 6.15620i | 1.10322 | + | 0.219445i | 0.712923 | − | 0.701242i | \(-0.247371\pi\) |
0.390301 | + | 0.920687i | \(0.372371\pi\) | |||||||
\(788\) | 45.5062 | + | 30.4063i | 1.62109 | + | 1.08318i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51.9513 | − | 21.5189i | 1.84021 | − | 0.762240i | 0.885545 | − | 0.464553i | \(-0.153785\pi\) |
0.954664 | − | 0.297687i | \(-0.0962151\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.1935 | − | 11.1679i | −1.49270 | − | 0.395093i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.25455 | + | 46.5258i | 0.325373 | + | 1.63576i | 0.703993 | + | 0.710207i | \(0.251399\pi\) |
−0.378620 | + | 0.925552i | \(0.623601\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.12766 | + | 0.224306i | 0.0393556 | + | 0.00782832i | 0.214729 | − | 0.976674i | \(-0.431113\pi\) |
−0.175373 | + | 0.984502i | \(0.556113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.7115 | + | 5.11433i | −0.896246 | + | 0.178274i | −0.621659 | − | 0.783288i | \(-0.713541\pi\) |
−0.274587 | + | 0.961562i | \(0.588541\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.3431 | + | 34.9355i | −0.811721 | + | 1.21483i | 0.161935 | + | 0.986801i | \(0.448227\pi\) |
−0.973655 | + | 0.228024i | \(0.926773\pi\) | |||||||
\(828\) | −11.0773 | + | 55.6894i | −0.384963 | + | 1.93534i | ||||
\(829\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 54.0650i | − | 1.87437i | ||||||
\(833\) | 17.5000 | − | 22.9510i | 0.606339 | − | 0.795206i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7925 | − | 11.0978i | −0.923880 | − | 0.382683i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −35.1112 | + | 14.5435i | −1.20572 | + | 0.499426i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.1112 | − | 31.4787i | 1.61306 | − | 1.07781i | 0.671475 | − | 0.741027i | \(-0.265661\pi\) |
0.941582 | − | 0.336784i | \(-0.109339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.0481 | + | 6.97151i | −1.19722 | + | 0.238142i | −0.753150 | − | 0.657849i | \(-0.771466\pi\) |
−0.444072 | + | 0.895991i | \(0.646466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.484098 | − | 1.16872i | −0.0164219 | − | 0.0396460i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.3819 | − | 56.3819i | 1.91043 | − | 1.91043i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.4151 | − | 26.3363i | −1.33400 | − | 0.891349i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.58557 | − | 28.0806i | −0.188611 | − | 0.948214i | −0.952887 | − | 0.303324i | \(-0.901903\pi\) |
0.764276 | − | 0.644889i | \(-0.223097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.96791 | − | 14.9180i | −0.335827 | − | 0.502601i | 0.624670 | − | 0.780889i | \(-0.285233\pi\) |
−0.960498 | + | 0.278287i | \(0.910233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.7815i | 1.23780i | 0.785471 | + | 0.618899i | \(0.212421\pi\) | ||||
−0.785471 | + | 0.618899i | \(0.787579\pi\) | |||||||
\(884\) | 48.1775 | − | 28.0115i | 1.62038 | − | 0.942130i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.63495 | − | 0.524123i | 0.0882740 | − | 0.0175588i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 30.0000i | 1.00000i | ||||||||
\(901\) | −31.1511 | − | 23.7525i | −1.03780 | − | 0.791311i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.7591 | − | 29.2389i | −1.45300 | − | 0.970861i | −0.996712 | − | 0.0810272i | \(-0.974180\pi\) |
−0.456284 | − | 0.889834i | \(-0.650820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.36117 | − | 1.39224i | −0.111483 | − | 0.0461778i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.381879 | − | 1.91983i | 0.0126383 | − | 0.0635372i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.3193 | + | 7.17388i | −0.572245 | + | 0.237032i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.7872 | −1.08155 | −0.540775 | − | 0.841167i | \(-0.681869\pi\) | ||||
−0.540775 | + | 0.841167i | \(0.681869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.33953 | − | 8.06234i | 0.109685 | − | 0.264802i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.1427 | − | 26.1543i | −1.27602 | − | 0.852606i | −0.281744 | − | 0.959490i | \(-0.590913\pi\) |
−0.994272 | + | 0.106883i | \(0.965913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 101.101 | + | 41.8774i | 3.29230 | + | 1.36372i | ||||
\(944\) | −18.9962 | + | 45.8609i | −0.618274 | + | 1.49265i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.09797 | − | 30.6565i | 0.198157 | − | 0.996204i | −0.745808 | − | 0.666160i | \(-0.767937\pi\) |
0.943966 | − | 0.330044i | \(-0.107063\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.8851 | − | 14.8851i | 0.481419 | − | 0.481419i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.49716 | − | 8.44289i | 0.112812 | − | 0.272351i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.6412 | − | 39.8714i | 0.858502 | − | 1.28484i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.6920 | − | 10.6420i | 0.826201 | − | 0.342223i | 0.0708031 | − | 0.997490i | \(-0.477444\pi\) |
0.755397 | + | 0.655267i | \(0.227444\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.46955 | + | 13.2047i | 0.175526 | + | 0.423757i | 0.987019 | − | 0.160605i | \(-0.0513446\pi\) |
−0.811493 | + | 0.584363i | \(0.801345\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.4663 | − | 20.0754i | −1.55057 | − | 0.642268i | −0.567153 | − | 0.823612i | \(-0.691955\pi\) |
−0.983420 | + | 0.181344i | \(0.941955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.0917 | + | 60.7889i | −0.386057 | + | 1.94084i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51.5974 | − | 34.4763i | 1.64070 | − | 1.09628i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 731.2.s.a.386.1 | yes | 16 | |
17.10 | odd | 16 | inner | 731.2.s.a.214.1 | ✓ | 16 | |
43.42 | odd | 2 | CM | 731.2.s.a.386.1 | yes | 16 | |
731.214 | even | 16 | inner | 731.2.s.a.214.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.s.a.214.1 | ✓ | 16 | 17.10 | odd | 16 | inner | |
731.2.s.a.214.1 | ✓ | 16 | 731.214 | even | 16 | inner | |
731.2.s.a.386.1 | yes | 16 | 1.1 | even | 1 | trivial | |
731.2.s.a.386.1 | yes | 16 | 43.42 | odd | 2 | CM |