Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7056,2,Mod(881,7056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7056.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7056.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(56.3424436662\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 882) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.6 | ||
Root | \(-0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7056.881 |
Dual form | 7056.2.k.d.881.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7056\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1765\) | \(4609\) | \(6175\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.765367 | 0.342282 | 0.171141 | − | 0.985247i | \(-0.445255\pi\) | ||||
0.171141 | + | 0.985247i | \(0.445255\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000i | 1.20605i | 0.797724 | + | 0.603023i | \(0.206037\pi\) | ||||
−0.797724 | + | 0.603023i | \(0.793963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.90923i | − 1.36157i | −0.732481 | − | 0.680787i | \(-0.761638\pi\) | ||||
0.732481 | − | 0.680787i | \(-0.238362\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.54328 | −1.34444 | −0.672221 | − | 0.740350i | \(-0.734660\pi\) | ||||
−0.672221 | + | 0.740350i | \(0.734660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.39104i | 1.69562i | 0.530300 | + | 0.847810i | \(0.322079\pi\) | ||||
−0.530300 | + | 0.847810i | \(0.677921\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 5.65685i | − 1.17954i | −0.807573 | − | 0.589768i | \(-0.799219\pi\) | ||||
0.807573 | − | 0.589768i | \(-0.200781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.41421 | −0.882843 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.65685i | 0.307670i | 0.988097 | + | 0.153835i | \(0.0491624\pi\) | ||||
−0.988097 | + | 0.153835i | \(0.950838\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.32957i | 0.777614i | 0.921319 | + | 0.388807i | \(0.127113\pi\) | ||||
−0.921319 | + | 0.388807i | \(0.872887\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24264 | 1.35508 | 0.677541 | − | 0.735485i | \(-0.263046\pi\) | ||||
0.677541 | + | 0.735485i | \(0.263046\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.84776 | 0.288571 | 0.144286 | − | 0.989536i | \(-0.453912\pi\) | ||||
0.144286 | + | 0.989536i | \(0.453912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.65685 | 0.252668 | 0.126334 | − | 0.991988i | \(-0.459679\pi\) | ||||
0.126334 | + | 0.991988i | \(0.459679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.39104 | −1.07809 | −0.539047 | − | 0.842276i | \(-0.681215\pi\) | ||||
−0.539047 | + | 0.842276i | \(0.681215\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 8.24264i | − 1.13221i | −0.824332 | − | 0.566107i | \(-0.808449\pi\) | ||||
0.824332 | − | 0.566107i | \(-0.191551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.06147i | 0.412808i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.32957 | 0.563662 | 0.281831 | − | 0.959464i | \(-0.409058\pi\) | ||||
0.281831 | + | 0.959464i | \(0.409058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 14.0167i | − 1.79466i | −0.441365 | − | 0.897328i | \(-0.645506\pi\) | ||||
0.441365 | − | 0.897328i | \(-0.354494\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 3.75736i | − 0.466043i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 13.6569i | − 1.62077i | −0.585897 | − | 0.810385i | \(-0.699258\pi\) | ||||
0.585897 | − | 0.810385i | \(-0.300742\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 3.82683i | − 0.447897i | −0.974601 | − | 0.223949i | \(-0.928105\pi\) | ||||
0.974601 | − | 0.223949i | \(-0.0718948\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.65685 | −0.636446 | −0.318223 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318223 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.5140 | −1.48335 | −0.741676 | − | 0.670759i | \(-0.765969\pi\) | ||||
−0.741676 | + | 0.670759i | \(0.765969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.24264 | −0.460179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.6089 | −1.97254 | −0.986270 | − | 0.165140i | \(-0.947192\pi\) | ||||
−0.986270 | + | 0.165140i | \(0.947192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.65685i | 0.580381i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.82683i | 0.388556i | 0.980946 | + | 0.194278i | \(0.0622364\pi\) | ||||
−0.980946 | + | 0.194278i | \(0.937764\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.35757 | 0.533098 | 0.266549 | − | 0.963821i | \(-0.414117\pi\) | ||||
0.266549 | + | 0.963821i | \(0.414117\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 13.5140i | − 1.33157i | −0.746143 | − | 0.665786i | \(-0.768097\pi\) | ||||
0.746143 | − | 0.665786i | \(-0.231903\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.31371i | 0.707043i | 0.935426 | + | 0.353521i | \(0.115016\pi\) | ||||
−0.935426 | + | 0.353521i | \(0.884984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.58579 | −0.247673 | −0.123837 | − | 0.992303i | \(-0.539520\pi\) | ||||
−0.123837 | + | 0.992303i | \(0.539520\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.41421i | 0.133038i | 0.997785 | + | 0.0665190i | \(0.0211893\pi\) | ||||
−0.997785 | + | 0.0665190i | \(0.978811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.32957i | − 0.403734i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.20533 | −0.644464 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.34315 | 0.207921 | 0.103960 | − | 0.994581i | \(-0.466849\pi\) | ||||
0.103960 | + | 0.994581i | \(0.466849\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.26810 | −0.110795 | −0.0553973 | − | 0.998464i | \(-0.517643\pi\) | ||||
−0.0553973 | + | 0.998464i | \(0.517643\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.3137i | 1.65008i | 0.565073 | + | 0.825041i | \(0.308848\pi\) | ||||
−0.565073 | + | 0.825041i | \(0.691152\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 22.1731i | − 1.88070i | −0.340211 | − | 0.940349i | \(-0.610498\pi\) | ||||
0.340211 | − | 0.940349i | \(-0.389502\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.6369 | 1.64212 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.26810i | 0.105310i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 10.5858i | − 0.867221i | −0.901100 | − | 0.433611i | \(-0.857239\pi\) | ||||
0.901100 | − | 0.433611i | \(-0.142761\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.6569 | −1.11138 | −0.555690 | − | 0.831390i | \(-0.687546\pi\) | ||||
−0.555690 | + | 0.831390i | \(0.687546\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.31371i | 0.266163i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 4.90923i | − 0.391799i | −0.980624 | − | 0.195899i | \(-0.937237\pi\) | ||||
0.980624 | − | 0.195899i | \(-0.0627626\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6569 | 1.38299 | 0.691496 | − | 0.722380i | \(-0.256952\pi\) | ||||
0.691496 | + | 0.722380i | \(0.256952\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.65914 | 0.670064 | 0.335032 | − | 0.942207i | \(-0.391253\pi\) | ||||
0.335032 | + | 0.942207i | \(0.391253\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1005 | −0.853885 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.3003 | −0.935172 | −0.467586 | − | 0.883948i | \(-0.654876\pi\) | ||||
−0.467586 | + | 0.883948i | \(0.654876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.3137i | 1.14460i | 0.820044 | + | 0.572300i | \(0.193949\pi\) | ||||
−0.820044 | + | 0.572300i | \(0.806051\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 9.42450i | − 0.700518i | −0.936653 | − | 0.350259i | \(-0.886094\pi\) | ||||
0.936653 | − | 0.350259i | \(-0.113906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.30864 | 0.463821 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 22.1731i | − 1.62146i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 11.3137i | − 0.818631i | −0.912393 | − | 0.409316i | \(-0.865768\pi\) | ||||
0.912393 | − | 0.409316i | \(-0.134232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.3137 | 1.39023 | 0.695116 | − | 0.718898i | \(-0.255353\pi\) | ||||
0.695116 | + | 0.718898i | \(0.255353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 5.41421i | − 0.385747i | −0.981224 | − | 0.192873i | \(-0.938219\pi\) | ||||
0.981224 | − | 0.192873i | \(-0.0617807\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.39104i | 0.523937i | 0.965076 | + | 0.261968i | \(0.0843716\pi\) | ||||
−0.965076 | + | 0.261968i | \(0.915628\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.41421 | 0.0987730 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.5641 | −2.04499 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.65685 | 0.114063 | 0.0570313 | − | 0.998372i | \(-0.481837\pi\) | ||||
0.0570313 | + | 0.998372i | \(0.481837\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.26810 | 0.0864838 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.2132i | 1.83056i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.06147i | − 0.205011i | −0.994732 | − | 0.102506i | \(-0.967314\pi\) | ||||
0.994732 | − | 0.102506i | \(-0.0326859\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.5027 | −1.75904 | −0.879522 | − | 0.475858i | \(-0.842138\pi\) | ||||
−0.879522 | + | 0.475858i | \(0.842138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.89377i | 0.521635i | 0.965388 | + | 0.260818i | \(0.0839921\pi\) | ||||
−0.965388 | + | 0.260818i | \(0.916008\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 16.6274i | − 1.08930i | −0.838664 | − | 0.544649i | \(-0.816663\pi\) | ||||
0.838664 | − | 0.544649i | \(-0.183337\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.65685 | −0.369012 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.6274i | 1.46365i | 0.681495 | + | 0.731823i | \(0.261330\pi\) | ||||
−0.681495 | + | 0.731823i | \(0.738670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.11586i | 0.200710i | 0.994952 | + | 0.100355i | \(0.0319979\pi\) | ||||
−0.994952 | + | 0.100355i | \(0.968002\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.2843 | 2.30871 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.7206 | −0.739798 | −0.369899 | − | 0.929072i | \(-0.620608\pi\) | ||||
−0.369899 | + | 0.929072i | \(0.620608\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.6274 | 1.42257 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.81138 | −0.424882 | −0.212441 | − | 0.977174i | \(-0.568141\pi\) | ||||
−0.212441 | + | 0.977174i | \(0.568141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 3.31371i | − 0.204332i | −0.994767 | − | 0.102166i | \(-0.967423\pi\) | ||||
0.994767 | − | 0.102166i | \(-0.0325773\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 6.30864i | − 0.387537i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.0823 | −1.65124 | −0.825620 | − | 0.564227i | \(-0.809174\pi\) | ||||
−0.825620 | + | 0.564227i | \(0.809174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 7.39104i | − 0.448973i | −0.974477 | − | 0.224487i | \(-0.927929\pi\) | ||||
0.974477 | − | 0.224487i | \(-0.0720705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 17.6569i | − 1.06475i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.9706 | −1.26000 | −0.630000 | − | 0.776596i | \(-0.716945\pi\) | ||||
−0.630000 | + | 0.776596i | \(0.716945\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 22.0000i | − 1.31241i | −0.754583 | − | 0.656205i | \(-0.772161\pi\) | ||||
0.754583 | − | 0.656205i | \(-0.227839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.32957i | 0.257366i | 0.991686 | + | 0.128683i | \(0.0410750\pi\) | ||||
−0.991686 | + | 0.128683i | \(0.958925\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7279 | 0.807525 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.765367 | −0.0447132 | −0.0223566 | − | 0.999750i | \(-0.507117\pi\) | ||||
−0.0223566 | + | 0.999750i | \(0.507117\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.31371 | 0.192932 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.7708 | −1.60603 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 10.7279i | − 0.614279i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3.06147i | − 0.174727i | −0.996176 | − | 0.0873636i | \(-0.972156\pi\) | ||||
0.996176 | − | 0.0873636i | \(-0.0278442\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.7206 | −0.664615 | −0.332307 | − | 0.943171i | \(-0.607827\pi\) | ||||
−0.332307 | + | 0.943171i | \(0.607827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 10.5069i | − 0.593885i | −0.954895 | − | 0.296942i | \(-0.904033\pi\) | ||||
0.954895 | − | 0.296942i | \(-0.0959670\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 0.242641i | − 0.0136281i | −0.999977 | − | 0.00681403i | \(-0.997831\pi\) | ||||
0.999977 | − | 0.00681403i | \(-0.00216899\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.62742 | −0.371064 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 40.9706i | − 2.27966i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.6704i | 1.20206i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.6569 | −1.41023 | −0.705114 | − | 0.709094i | \(-0.749104\pi\) | ||||
−0.705114 | + | 0.709094i | \(0.749104\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.06147 | −0.167266 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.8995 | 1.41084 | 0.705418 | − | 0.708792i | \(-0.250759\pi\) | ||||
0.705418 | + | 0.708792i | \(0.250759\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.3183 | −0.937837 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8.68629i | − 0.466305i | −0.972440 | − | 0.233152i | \(-0.925096\pi\) | ||||
0.972440 | − | 0.233152i | \(-0.0749041\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.6913i | 1.05405i | 0.849849 | + | 0.527026i | \(0.176693\pi\) | ||||
−0.849849 | + | 0.527026i | \(0.823307\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.7933 | 1.47929 | 0.739644 | − | 0.672998i | \(-0.234994\pi\) | ||||
0.739644 | + | 0.672998i | \(0.234994\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 10.4525i | − 0.554761i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 24.0000i | − 1.26667i | −0.773877 | − | 0.633336i | \(-0.781685\pi\) | ||||
0.773877 | − | 0.633336i | \(-0.218315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.6274 | −1.87513 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2.92893i | − 0.153307i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 23.9665i | − 1.25104i | −0.780208 | − | 0.625520i | \(-0.784887\pi\) | ||||
0.780208 | − | 0.625520i | \(-0.215113\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.65685 | 0.0857887 | 0.0428943 | − | 0.999080i | \(-0.486342\pi\) | ||||
0.0428943 | + | 0.999080i | \(0.486342\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.13387 | 0.418916 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.2843 | 1.24740 | 0.623700 | − | 0.781664i | \(-0.285629\pi\) | ||||
0.623700 | + | 0.781664i | \(0.285629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −38.7485 | −1.97996 | −0.989979 | − | 0.141214i | \(-0.954900\pi\) | ||||
−0.989979 | + | 0.141214i | \(0.954900\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.3431i | 0.727226i | 0.931550 | + | 0.363613i | \(0.118457\pi\) | ||||
−0.931550 | + | 0.363613i | \(0.881543\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.3575i | 1.58582i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.32957 | −0.217844 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 18.6089i | − 0.933954i | −0.884269 | − | 0.466977i | \(-0.845343\pi\) | ||||
0.884269 | − | 0.466977i | \(-0.154657\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 14.0000i | − 0.699127i | −0.936913 | − | 0.349563i | \(-0.886330\pi\) | ||||
0.936913 | − | 0.349563i | \(-0.113670\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.2548 | 1.05878 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.9706i | 1.63429i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0112i | 0.643364i | 0.946848 | + | 0.321682i | \(0.104248\pi\) | ||||
−0.946848 | + | 0.321682i | \(0.895752\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.3431 | −0.507725 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.5641 | −1.44430 | −0.722151 | − | 0.691735i | \(-0.756847\pi\) | ||||
−0.722151 | + | 0.691735i | \(0.756847\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.65685 | −0.0807501 | −0.0403751 | − | 0.999185i | \(-0.512855\pi\) | ||||
−0.0403751 | + | 0.999185i | \(0.512855\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.4692 | 1.18693 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.3137i | 1.31566i | 0.753169 | + | 0.657828i | \(0.228524\pi\) | ||||
−0.753169 | + | 0.657828i | \(0.771476\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 31.8602i | − 1.53111i | −0.643373 | − | 0.765553i | \(-0.722466\pi\) | ||||
0.643373 | − | 0.765553i | \(-0.277534\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 41.8100 | 2.00004 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.7821i | 0.705510i | 0.935716 | + | 0.352755i | \(0.114755\pi\) | ||||
−0.935716 | + | 0.352755i | \(0.885245\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.34315i | 0.301372i | 0.988582 | + | 0.150686i | \(0.0481482\pi\) | ||||
−0.988582 | + | 0.150686i | \(0.951852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.2426 | −0.675166 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.5563i | 1.11169i | 0.831285 | + | 0.555846i | \(0.187606\pi\) | ||||
−0.831285 | + | 0.555846i | \(0.812394\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.39104i | 0.348030i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.0000 | 1.21623 | 0.608114 | − | 0.793849i | \(-0.291926\pi\) | ||||
0.608114 | + | 0.793849i | \(0.291926\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.48181 | 0.115589 | 0.0577947 | − | 0.998328i | \(-0.481593\pi\) | ||||
0.0577947 | + | 0.998328i | \(0.481593\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.6569 | −1.37827 | −0.689135 | − | 0.724633i | \(-0.742010\pi\) | ||||
−0.689135 | + | 0.724633i | \(0.742010\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.5140 | −0.625352 | −0.312676 | − | 0.949860i | \(-0.601225\pi\) | ||||
−0.312676 | + | 0.949860i | \(0.601225\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.62742i | 0.304729i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 32.6256i | − 1.49697i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.0502 | 0.733351 | 0.366676 | − | 0.930349i | \(-0.380496\pi\) | ||||
0.366676 | + | 0.930349i | \(0.380496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 40.4650i | − 1.84504i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.92893i | 0.132996i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.3137 | −0.512673 | −0.256337 | − | 0.966588i | \(-0.582516\pi\) | ||||
−0.256337 | + | 0.966588i | \(0.582516\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 12.9706i | − 0.585353i | −0.956211 | − | 0.292677i | \(-0.905454\pi\) | ||||
0.956211 | − | 0.292677i | \(-0.0945460\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 9.18440i | − 0.413645i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.6569 | −0.790429 | −0.395215 | − | 0.918589i | \(-0.629330\pi\) | ||||
−0.395215 | + | 0.918589i | \(0.629330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.9665 | −1.06861 | −0.534306 | − | 0.845291i | \(-0.679427\pi\) | ||||
−0.534306 | + | 0.845291i | \(0.679427\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.10051 | 0.182470 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.0543929 | 0.00241093 | 0.00120546 | − | 0.999999i | \(-0.499616\pi\) | ||||
0.00120546 | + | 0.999999i | \(0.499616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 10.3431i | − 0.455773i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 29.5641i | − 1.30023i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.5474 | −0.681146 | −0.340573 | − | 0.940218i | \(-0.610621\pi\) | ||||
−0.340573 | + | 0.940218i | \(0.610621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.53620i | 0.110900i | 0.998461 | + | 0.0554502i | \(0.0176594\pi\) | ||||
−0.998461 | + | 0.0554502i | \(0.982341\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 24.0000i | − 1.04546i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00000 | −0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 9.07107i | − 0.392912i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.59767i | 0.242008i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.6274 | −0.886842 | −0.443421 | − | 0.896313i | \(-0.646235\pi\) | ||||
−0.443421 | + | 0.896313i | \(0.646235\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.97908 | −0.0847743 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | −0.171028 | −0.0855138 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855138 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.2459 | −0.521692 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.72792i | 0.369814i | 0.982756 | + | 0.184907i | \(0.0591984\pi\) | ||||
−0.982756 | + | 0.184907i | \(0.940802\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 8.13387i | − 0.344026i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.7821 | −0.622990 | −0.311495 | − | 0.950248i | \(-0.600830\pi\) | ||||
−0.311495 | + | 0.950248i | \(0.600830\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.08239i | 0.0455366i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.9411i | 1.75826i | 0.476579 | + | 0.879132i | \(0.341877\pi\) | ||||
−0.476579 | + | 0.879132i | \(0.658123\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.6274 | 1.11432 | 0.557161 | − | 0.830404i | \(-0.311890\pi\) | ||||
0.557161 | + | 0.830404i | \(0.311890\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.9706i | 1.04134i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.88830i | 0.286764i | 0.989667 | + | 0.143382i | \(0.0457977\pi\) | ||||
−0.989667 | + | 0.143382i | \(0.954202\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.9706 | 1.36550 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.26810 | −0.0523401 | −0.0261701 | − | 0.999658i | \(-0.508331\pi\) | ||||
−0.0261701 | + | 0.999658i | \(0.508331\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.0000 | −1.31854 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.5069 | −0.431467 | −0.215733 | − | 0.976452i | \(-0.569214\pi\) | ||||
−0.215733 | + | 0.976452i | \(0.569214\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.6569i | 1.53862i | 0.638877 | + | 0.769309i | \(0.279399\pi\) | ||||
−0.638877 | + | 0.769309i | \(0.720601\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 5.54328i | − 0.226115i | −0.993588 | − | 0.113057i | \(-0.963936\pi\) | ||||
0.993588 | − | 0.113057i | \(-0.0360644\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.82683 | −0.155583 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 9.92724i | − 0.402934i | −0.979495 | − | 0.201467i | \(-0.935429\pi\) | ||||
0.979495 | − | 0.201467i | \(-0.0645709\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.2843i | 1.46790i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.2132 | 1.34147 | 0.670734 | − | 0.741698i | \(-0.265979\pi\) | ||||
0.670734 | + | 0.741698i | \(0.265979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 16.0000i | − 0.644136i | −0.946717 | − | 0.322068i | \(-0.895622\pi\) | ||||
0.946717 | − | 0.322068i | \(-0.104378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 46.1396i | − 1.85451i | −0.374435 | − | 0.927253i | \(-0.622163\pi\) | ||||
0.374435 | − | 0.927253i | \(-0.377837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.5563 | 0.662254 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −45.6912 | −1.82183 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.9411 | −1.66965 | −0.834825 | − | 0.550516i | \(-0.814431\pi\) | ||||
−0.834825 | + | 0.550516i | \(0.814431\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.79337 | 0.0711676 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000i | 0.0789953i | 0.999220 | + | 0.0394976i | \(0.0125758\pi\) | ||||
−0.999220 | + | 0.0394976i | \(0.987424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.1116i | 0.753690i | 0.926276 | + | 0.376845i | \(0.122991\pi\) | ||||
−0.926276 | + | 0.376845i | \(0.877009\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.1509 | 1.30330 | 0.651648 | − | 0.758522i | \(-0.274078\pi\) | ||||
0.651648 | + | 0.758522i | \(0.274078\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.3183i | 0.679802i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 14.3431i | − 0.561291i | −0.959812 | − | 0.280645i | \(-0.909452\pi\) | ||||
0.959812 | − | 0.280645i | \(-0.0905485\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.970563 | −0.0379230 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 20.0000i | − 0.779089i | −0.921008 | − | 0.389545i | \(-0.872632\pi\) | ||||
0.921008 | − | 0.389545i | \(-0.127368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 28.2417i | − 1.09847i | −0.835667 | − | 0.549236i | \(-0.814919\pi\) | ||||
0.835667 | − | 0.549236i | \(-0.185081\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.37258 | 0.362908 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.0668 | 2.16444 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.8701 | −0.727387 | −0.363694 | − | 0.931519i | \(-0.618484\pi\) | ||||
−0.363694 | + | 0.931519i | \(0.618484\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.87285 | −0.379444 | −0.189722 | − | 0.981838i | \(-0.560759\pi\) | ||||
−0.189722 | + | 0.981838i | \(0.560759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.97056i | 0.190193i | 0.995468 | + | 0.0950966i | \(0.0303160\pi\) | ||||
−0.995468 | + | 0.0950966i | \(0.969684\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.7821i | 0.564794i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.4650 | −1.54159 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 15.3073i | − 0.582319i | −0.956675 | − | 0.291159i | \(-0.905959\pi\) | ||||
0.956675 | − | 0.291159i | \(-0.0940410\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 16.9706i | − 0.643730i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.2426 | −0.387968 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 2.00000i | − 0.0755390i | −0.999286 | − | 0.0377695i | \(-0.987975\pi\) | ||||
0.999286 | − | 0.0377695i | \(-0.0120253\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 60.9217i | 2.29770i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.5269 | 1.07135 | 0.535675 | − | 0.844424i | \(-0.320057\pi\) | ||||
0.535675 | + | 0.844424i | \(0.320057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.4917 | 0.917223 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0294 | 0.562069 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.0781 | 1.60654 | 0.803271 | − | 0.595613i | \(-0.203091\pi\) | ||||
0.803271 | + | 0.595613i | \(0.203091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 7.31371i | − 0.271624i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 0.525265i | − 0.0194810i | −0.999953 | − | 0.00974050i | \(-0.996899\pi\) | ||||
0.999953 | − | 0.00974050i | \(-0.00310055\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.18440 | −0.339697 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.1396i | 0.743875i | 0.928258 | + | 0.371937i | \(0.121306\pi\) | ||||
−0.928258 | + | 0.371937i | \(0.878694\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 16.0000i | − 0.589368i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.9411 | −1.39569 | −0.697843 | − | 0.716250i | \(-0.745857\pi\) | ||||
−0.697843 | + | 0.716250i | \(0.745857\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 27.3137i | − 1.00204i | −0.865435 | − | 0.501021i | \(-0.832958\pi\) | ||||
0.865435 | − | 0.501021i | \(-0.167042\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 8.10201i | − 0.296835i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.3431 | 0.961275 | 0.480638 | − | 0.876919i | \(-0.340405\pi\) | ||||
0.480638 | + | 0.876919i | \(0.340405\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.4525 | −0.380406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.5563 | 0.710788 | 0.355394 | − | 0.934717i | \(-0.384347\pi\) | ||||
0.355394 | + | 0.934717i | \(0.384347\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.1396 | −0.730061 | −0.365031 | − | 0.930995i | \(-0.618942\pi\) | ||||
−0.365031 | + | 0.930995i | \(0.618942\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 21.2548i | − 0.767468i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.2680i | 0.983311i | 0.870790 | + | 0.491655i | \(0.163608\pi\) | ||||
−0.870790 | + | 0.491655i | \(0.836392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.71353 | 0.313404 | 0.156702 | − | 0.987646i | \(-0.449914\pi\) | ||||
0.156702 | + | 0.987646i | \(0.449914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 19.1116i | − 0.686510i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.6569i | 0.489308i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 54.6274 | 1.95472 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 3.75736i | − 0.134106i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 9.92724i | − 0.353868i | −0.984223 | − | 0.176934i | \(-0.943382\pi\) | ||||
0.984223 | − | 0.176934i | \(-0.0566179\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.8112 | −2.44356 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.88830 | 0.243996 | 0.121998 | − | 0.992530i | \(-0.461070\pi\) | ||||
0.121998 | + | 0.992530i | \(0.461070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.9706 | 1.44943 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.3073 | 0.540184 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.2721i | 0.396305i | 0.980171 | + | 0.198153i | \(0.0634942\pi\) | ||||
−0.980171 | + | 0.198153i | \(0.936506\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 22.6984i | − 0.797048i | −0.917158 | − | 0.398524i | \(-0.869523\pi\) | ||||
0.917158 | − | 0.398524i | \(-0.130477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.5140 | 0.473374 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.2459i | 0.428429i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 39.3553i | − 1.37351i | −0.726889 | − | 0.686755i | \(-0.759034\pi\) | ||||
0.726889 | − | 0.686755i | \(-0.240966\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.6569 | −1.03377 | −0.516886 | − | 0.856054i | \(-0.672909\pi\) | ||||
−0.516886 | + | 0.856054i | \(0.672909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 11.0294i | − 0.383531i | −0.981441 | − | 0.191766i | \(-0.938579\pi\) | ||||
0.981441 | − | 0.191766i | \(-0.0614213\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.60474i | 0.298855i | 0.988773 | + | 0.149428i | \(0.0477431\pi\) | ||||
−0.988773 | + | 0.149428i | \(0.952257\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.62742 | 0.229351 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.4692 | 1.74239 | 0.871194 | − | 0.490938i | \(-0.163346\pi\) | ||||
0.871194 | + | 0.490938i | \(0.163346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.2548 | 0.905339 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.49596 | −0.292270 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 46.6274i | − 1.59837i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.5098i | 1.01039i | 0.863004 | + | 0.505197i | \(0.168580\pi\) | ||||
−0.863004 | + | 0.505197i | \(0.831420\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.5474 | 0.531090 | 0.265545 | − | 0.964098i | \(-0.414448\pi\) | ||||
0.265545 | + | 0.964098i | \(0.414448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.5419i | 1.38327i | 0.722246 | + | 0.691636i | \(0.243110\pi\) | ||||
−0.722246 | + | 0.691636i | \(0.756890\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 28.2843i | − 0.962808i | −0.876499 | − | 0.481404i | \(-0.840127\pi\) | ||||
0.876499 | − | 0.481404i | \(-0.159873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.41421 | −0.320093 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 22.6274i | − 0.767583i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.6369i | 0.665371i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.58579 | −0.0873158 | −0.0436579 | − | 0.999047i | \(-0.513901\pi\) | ||||
−0.0436579 | + | 0.999047i | \(0.513901\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.2166 | 0.681113 | 0.340557 | − | 0.940224i | \(-0.389384\pi\) | ||||
0.340557 | + | 0.940224i | \(0.389384\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.2548 | 1.92678 | 0.963389 | − | 0.268106i | \(-0.0863979\pi\) | ||||
0.963389 | + | 0.268106i | \(0.0863979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.2346 | 0.847294 | 0.423647 | − | 0.905827i | \(-0.360750\pi\) | ||||
0.423647 | + | 0.905827i | \(0.360750\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 54.6274i | − 1.82804i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.7206i | 0.391777i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.17346 | −0.239248 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.6912i | 1.52220i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 7.21320i | − 0.239775i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.0000 | −0.398453 | −0.199227 | − | 0.979953i | \(-0.563843\pi\) | ||||
−0.199227 | + | 0.979953i | \(0.563843\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 14.6274i | − 0.484628i | −0.970198 | − | 0.242314i | \(-0.922094\pi\) | ||||
0.970198 | − | 0.242314i | \(-0.0779064\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 54.0559i | − 1.78899i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.9117 | −1.67942 | −0.839711 | − | 0.543034i | \(-0.817276\pi\) | ||||
−0.839711 | + | 0.543034i | \(0.817276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −67.0446 | −2.20680 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.3848 | −1.19632 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.3240 | −0.962091 | −0.481045 | − | 0.876696i | \(-0.659743\pi\) | ||||
−0.481045 | + | 0.876696i | \(0.659743\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 16.9706i | − 0.554997i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.3253i | 0.664000i | 0.943279 | + | 0.332000i | \(0.107723\pi\) | ||||
−0.943279 | + | 0.332000i | \(0.892277\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.3504 | −0.924198 | −0.462099 | − | 0.886828i | \(-0.652903\pi\) | ||||
−0.462099 | + | 0.886828i | \(0.652903\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 10.4525i | − 0.340380i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 58.6274i | 1.90514i | 0.304327 | + | 0.952568i | \(0.401568\pi\) | ||||
−0.304327 | + | 0.952568i | \(0.598432\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.7868 | −0.609845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.1005i | 0.975051i | 0.873109 | + | 0.487526i | \(0.162100\pi\) | ||||
−0.873109 | + | 0.487526i | \(0.837900\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 8.65914i | − 0.280203i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2548 | 0.395317 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.7821 | 0.475852 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.9706 | −0.545737 | −0.272868 | − | 0.962051i | \(-0.587972\pi\) | ||||
−0.272868 | + | 0.962051i | \(0.587972\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.4804 | 1.20280 | 0.601402 | − | 0.798946i | \(-0.294609\pi\) | ||||
0.601402 | + | 0.798946i | \(0.294609\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 25.9411i | − 0.829930i | −0.909837 | − | 0.414965i | \(-0.863794\pi\) | ||||
0.909837 | − | 0.414965i | \(-0.136206\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 74.4356i | − 2.37897i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.0392 | 0.447782 | 0.223891 | − | 0.974614i | \(-0.428124\pi\) | ||||
0.223891 | + | 0.974614i | \(0.428124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 4.14386i | − 0.132034i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 9.37258i | − 0.298031i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.6863 | −0.402993 | −0.201497 | − | 0.979489i | \(-0.564581\pi\) | ||||
−0.201497 | + | 0.979489i | \(0.564581\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.65685i | 0.179334i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.7779i | 0.974744i | 0.873194 | + | 0.487372i | \(0.162044\pi\) | ||||
−0.873194 | + | 0.487372i | \(0.837956\pi\) | |||||||
\(998\) | 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 | 7056.2.k.d.881.6 | 8 | ||
3.2 | odd | 2 | inner | 7056.2.k.d.881.3 | 8 | ||
4.3 | odd | 2 | 882.2.d.b.881.7 | yes | 8 | ||
7.6 | odd | 2 | inner | 7056.2.k.d.881.4 | 8 | ||
12.11 | even | 2 | 882.2.d.b.881.2 | ✓ | 8 | ||
21.20 | even | 2 | inner | 7056.2.k.d.881.5 | 8 | ||
28.3 | even | 6 | 882.2.k.b.215.3 | 16 | |||
28.11 | odd | 6 | 882.2.k.b.215.2 | 16 | |||
28.19 | even | 6 | 882.2.k.b.521.7 | 16 | |||
28.23 | odd | 6 | 882.2.k.b.521.6 | 16 | |||
28.27 | even | 2 | 882.2.d.b.881.6 | yes | 8 | ||
84.11 | even | 6 | 882.2.k.b.215.7 | 16 | |||
84.23 | even | 6 | 882.2.k.b.521.3 | 16 | |||
84.47 | odd | 6 | 882.2.k.b.521.2 | 16 | |||
84.59 | odd | 6 | 882.2.k.b.215.6 | 16 | |||
84.83 | odd | 2 | 882.2.d.b.881.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.d.b.881.2 | ✓ | 8 | 12.11 | even | 2 | ||
882.2.d.b.881.3 | yes | 8 | 84.83 | odd | 2 | ||
882.2.d.b.881.6 | yes | 8 | 28.27 | even | 2 | ||
882.2.d.b.881.7 | yes | 8 | 4.3 | odd | 2 | ||
882.2.k.b.215.2 | 16 | 28.11 | odd | 6 | |||
882.2.k.b.215.3 | 16 | 28.3 | even | 6 | |||
882.2.k.b.215.6 | 16 | 84.59 | odd | 6 | |||
882.2.k.b.215.7 | 16 | 84.11 | even | 6 | |||
882.2.k.b.521.2 | 16 | 84.47 | odd | 6 | |||
882.2.k.b.521.3 | 16 | 84.23 | even | 6 | |||
882.2.k.b.521.6 | 16 | 28.23 | odd | 6 | |||
882.2.k.b.521.7 | 16 | 28.19 | even | 6 | |||
7056.2.k.d.881.3 | 8 | 3.2 | odd | 2 | inner | ||
7056.2.k.d.881.4 | 8 | 7.6 | odd | 2 | inner | ||
7056.2.k.d.881.5 | 8 | 21.20 | even | 2 | inner | ||
7056.2.k.d.881.6 | 8 | 1.1 | even | 1 | trivial |