Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.a (trivial) |
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: | yes |
Analytic conductor: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 22x^{8} - 16x^{7} + 146x^{6} + 200x^{5} - 206x^{4} - 440x^{3} - 124x^{2} + 72x + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 1960) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.61569\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −0.836591 | −0.483006 | −0.241503 | − | 0.970400i | \(-0.577640\pi\) | ||||
−0.241503 | + | 0.970400i | \(0.577640\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.30012 | −0.766705 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.403442 | 0.121642 | 0.0608212 | − | 0.998149i | \(-0.480628\pi\) | ||||
0.0608212 | + | 0.998149i | \(0.480628\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.20918 | −1.72212 | −0.861058 | − | 0.508506i | \(-0.830198\pi\) | ||||
−0.861058 | + | 0.508506i | \(0.830198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.62588 | −0.636869 | −0.318435 | − | 0.947945i | \(-0.603157\pi\) | ||||
−0.318435 | + | 0.947945i | \(0.603157\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.41173 | 1.47095 | 0.735476 | − | 0.677551i | \(-0.236959\pi\) | ||||
0.735476 | + | 0.677551i | \(0.236959\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.54712 | −1.36517 | −0.682584 | − | 0.730807i | \(-0.739144\pi\) | ||||
−0.682584 | + | 0.730807i | \(0.739144\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.43403 | 0.853329 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.96279 | 0.364482 | 0.182241 | − | 0.983254i | \(-0.441665\pi\) | ||||
0.182241 | + | 0.983254i | \(0.441665\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.66707 | 0.838230 | 0.419115 | − | 0.907933i | \(-0.362340\pi\) | ||||
0.419115 | + | 0.907933i | \(0.362340\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.337516 | −0.0587541 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.44379 | 0.566155 | 0.283078 | − | 0.959097i | \(-0.408645\pi\) | ||||
0.283078 | + | 0.959097i | \(0.408645\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.19455 | 0.831793 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.68230 | 0.418905 | 0.209452 | − | 0.977819i | \(-0.432832\pi\) | ||||
0.209452 | + | 0.977819i | \(0.432832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8609 | 1.65627 | 0.828136 | − | 0.560528i | \(-0.189402\pi\) | ||||
0.828136 | + | 0.560528i | \(0.189402\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.67165 | 1.41076 | 0.705378 | − | 0.708832i | \(-0.250777\pi\) | ||||
0.705378 | + | 0.708832i | \(0.250777\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.19679 | 0.307612 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.97422 | 0.820623 | 0.410311 | − | 0.911946i | \(-0.365420\pi\) | ||||
0.410311 | + | 0.911946i | \(0.365420\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.36400 | −0.710479 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.18754 | 1.19612 | 0.598058 | − | 0.801453i | \(-0.295939\pi\) | ||||
0.598058 | + | 0.801453i | \(0.295939\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.69505 | 0.729176 | 0.364588 | − | 0.931169i | \(-0.381210\pi\) | ||||
0.364588 | + | 0.931169i | \(0.381210\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8844 | −1.45191 | −0.725957 | − | 0.687740i | \(-0.758603\pi\) | ||||
−0.725957 | + | 0.687740i | \(0.758603\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.47726 | 0.659385 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.530435 | −0.0629511 | −0.0314755 | − | 0.999505i | \(-0.510021\pi\) | ||||
−0.0314755 | + | 0.999505i | \(0.510021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.20102 | −0.959856 | −0.479928 | − | 0.877308i | \(-0.659337\pi\) | ||||
−0.479928 | + | 0.877308i | \(0.659337\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.12014 | −1.02610 | −0.513048 | − | 0.858360i | \(-0.671484\pi\) | ||||
−0.513048 | + | 0.858360i | \(0.671484\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.19087 | 0.354542 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.96013 | −0.324917 | −0.162458 | − | 0.986715i | \(-0.551942\pi\) | ||||
−0.162458 | + | 0.986715i | \(0.551942\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.64206 | −0.176047 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.8387 | −1.14890 | −0.574449 | − | 0.818540i | \(-0.694784\pi\) | ||||
−0.574449 | + | 0.818540i | \(0.694784\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.90443 | −0.404870 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5581 | 1.37661 | 0.688307 | − | 0.725419i | \(-0.258354\pi\) | ||||
0.688307 | + | 0.725419i | \(0.258354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.927964 | −0.0932639 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.56081 | −0.155306 | −0.0776531 | − | 0.996980i | \(-0.524743\pi\) | ||||
−0.0776531 | + | 0.996980i | \(0.524743\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.12354 | −0.209239 | −0.104619 | − | 0.994512i | \(-0.533362\pi\) | ||||
−0.104619 | + | 0.994512i | \(0.533362\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.15510 | 0.208341 | 0.104171 | − | 0.994559i | \(-0.466781\pi\) | ||||
0.104171 | + | 0.994559i | \(0.466781\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2910 | −1.08148 | −0.540742 | − | 0.841189i | \(-0.681856\pi\) | ||||
−0.540742 | + | 0.841189i | \(0.681856\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.88104 | −0.273456 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.88668 | −0.459700 | −0.229850 | − | 0.973226i | \(-0.573824\pi\) | ||||
−0.229850 | + | 0.973226i | \(0.573824\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.2818 | 1.32036 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8372 | −0.985203 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.24399 | −0.202334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.97422 | −0.885069 | −0.442535 | − | 0.896751i | \(-0.645921\pi\) | ||||
−0.442535 | + | 0.896751i | \(0.645921\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.08613 | −0.799989 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.8667 | −1.03680 | −0.518398 | − | 0.855140i | \(-0.673471\pi\) | ||||
−0.518398 | + | 0.855140i | \(0.673471\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.7167 | −1.25733 | −0.628666 | − | 0.777675i | \(-0.716399\pi\) | ||||
−0.628666 | + | 0.777675i | \(0.716399\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.80345 | −0.492242 | −0.246121 | − | 0.969239i | \(-0.579156\pi\) | ||||
−0.246121 | + | 0.969239i | \(0.579156\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.09122 | −0.681404 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.50505 | −0.209483 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.5957 | 1.19573 | 0.597865 | − | 0.801597i | \(-0.296016\pi\) | ||||
0.597865 | + | 0.801597i | \(0.296016\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.1854 | −1.72405 | −0.862024 | − | 0.506868i | \(-0.830803\pi\) | ||||
−0.862024 | + | 0.506868i | \(0.830803\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.03982 | 0.488291 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.2637 | −1.53741 | −0.768703 | − | 0.639605i | \(-0.779098\pi\) | ||||
−0.768703 | + | 0.639605i | \(0.779098\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.99798 | −0.396366 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.3427 | −1.04508 | −0.522541 | − | 0.852614i | \(-0.675016\pi\) | ||||
−0.522541 | + | 0.852614i | \(0.675016\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.3731 | 0.957459 | 0.478730 | − | 0.877962i | \(-0.341097\pi\) | ||||
0.478730 | + | 0.877962i | \(0.341097\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.5539 | 1.96569 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.7477 | −1.12779 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00524 | 0.456570 | 0.228285 | − | 0.973594i | \(-0.426688\pi\) | ||||
0.228285 | + | 0.973594i | \(0.426688\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.68622 | −0.577731 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.8069 | −0.957232 | −0.478616 | − | 0.878024i | \(-0.658861\pi\) | ||||
−0.478616 | + | 0.878024i | \(0.658861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0636 | 0.971007 | 0.485504 | − | 0.874235i | \(-0.338636\pi\) | ||||
0.485504 | + | 0.874235i | \(0.338636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.76443 | −0.352197 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.05939 | −0.0774704 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.7159 | 1.57131 | 0.785653 | − | 0.618667i | \(-0.212327\pi\) | ||||
0.785653 | + | 0.618667i | \(0.212327\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.7302 | −1.13229 | −0.566144 | − | 0.824307i | \(-0.691565\pi\) | ||||
−0.566144 | + | 0.824307i | \(0.691565\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.18536 | −0.155700 | −0.0778502 | − | 0.996965i | \(-0.524806\pi\) | ||||
−0.0778502 | + | 0.996965i | \(0.524806\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6703 | 0.969061 | 0.484530 | − | 0.874774i | \(-0.338990\pi\) | ||||
0.484530 | + | 0.874774i | \(0.338990\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.94242 | 0.701284 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.0591 | 1.04668 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.58676 | 0.178930 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.7857 | 1.63747 | 0.818737 | − | 0.574169i | \(-0.194675\pi\) | ||||
0.818737 | + | 0.574169i | \(0.194675\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.443757 | 0.0304058 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.86090 | 0.463617 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3046 | 1.09676 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1550 | −0.813961 | −0.406980 | − | 0.913437i | \(-0.633418\pi\) | ||||
−0.406980 | + | 0.913437i | \(0.633418\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.9574 | −1.92197 | −0.960986 | − | 0.276597i | \(-0.910793\pi\) | ||||
−0.960986 | + | 0.276597i | \(0.910793\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.43498 | −0.491318 | −0.245659 | − | 0.969356i | \(-0.579004\pi\) | ||||
−0.245659 | + | 0.969356i | \(0.579004\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.6389 | −1.09005 | −0.545024 | − | 0.838420i | \(-0.683480\pi\) | ||||
−0.545024 | + | 0.838420i | \(0.683480\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.62983 | 0.495611 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.80387 | −0.246052 | −0.123026 | − | 0.992403i | \(-0.539260\pi\) | ||||
−0.123026 | + | 0.992403i | \(0.539260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4275 | 0.864940 | 0.432470 | − | 0.901648i | \(-0.357642\pi\) | ||||
0.432470 | + | 0.901648i | \(0.357642\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.9715 | −1.02458 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −39.8116 | −2.53315 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.47642 | 0.156937 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.2130 | −0.960238 | −0.480119 | − | 0.877203i | \(-0.659407\pi\) | ||||
−0.480119 | + | 0.877203i | \(0.659407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.64138 | −0.166062 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.75756 | −0.109634 | −0.0548168 | − | 0.998496i | \(-0.517457\pi\) | ||||
−0.0548168 | + | 0.998496i | \(0.517457\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.51465 | −0.279450 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.7280 | 0.661516 | 0.330758 | − | 0.943716i | \(-0.392696\pi\) | ||||
0.330758 | + | 0.943716i | \(0.392696\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.06755 | 0.554925 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.38628 | −0.572292 | −0.286146 | − | 0.958186i | \(-0.592374\pi\) | ||||
−0.286146 | + | 0.958186i | \(0.592374\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.23762 | −0.318163 | −0.159081 | − | 0.987265i | \(-0.550853\pi\) | ||||
−0.159081 | + | 0.987265i | \(0.550853\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2871 | −0.978597 | −0.489299 | − | 0.872116i | \(-0.662747\pi\) | ||||
−0.489299 | + | 0.872116i | \(0.662747\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.7348 | −0.642675 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.49547 | 0.208522 | 0.104261 | − | 0.994550i | \(-0.466752\pi\) | ||||
0.104261 | + | 0.994550i | \(0.466752\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.6600 | −0.812006 | −0.406003 | − | 0.913872i | \(-0.633078\pi\) | ||||
−0.406003 | + | 0.913872i | \(0.633078\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.1048 | −0.594398 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.3426 | −0.664913 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.5720 | 1.78604 | 0.893019 | − | 0.450020i | \(-0.148583\pi\) | ||||
0.893019 | + | 0.450020i | \(0.148583\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.78888 | 0.103801 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 40.6522 | 2.35098 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.30576 | 0.0750139 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3514 | −0.590786 | −0.295393 | − | 0.955376i | \(-0.595451\pi\) | ||||
−0.295393 | + | 0.955376i | \(0.595451\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.77654 | 0.101064 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.8740 | 0.730020 | 0.365010 | − | 0.931004i | \(-0.381066\pi\) | ||||
0.365010 | + | 0.931004i | \(0.381066\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.37734 | 0.360469 | 0.180234 | − | 0.983624i | \(-0.442314\pi\) | ||||
0.180234 | + | 0.983624i | \(0.442314\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.5333 | −1.82725 | −0.913626 | − | 0.406556i | \(-0.866730\pi\) | ||||
−0.913626 | + | 0.406556i | \(0.866730\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.791875 | 0.0443365 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.80294 | −0.100630 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.8364 | −0.936804 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.44597 | 0.522363 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.3687 | −1.77914 | −0.889572 | − | 0.456794i | \(-0.848997\pi\) | ||||
−0.889572 | + | 0.456794i | \(0.848997\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.92111 | −0.434074 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.17626 | 0.227496 | 0.113748 | − | 0.993510i | \(-0.463714\pi\) | ||||
0.113748 | + | 0.993510i | \(0.463714\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.08815 | 0.222038 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.88289 | 0.101964 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.8062 | −1.49272 | −0.746358 | − | 0.665545i | \(-0.768199\pi\) | ||||
−0.746358 | + | 0.665545i | \(0.768199\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.4108 | 1.78844 | 0.894219 | − | 0.447629i | \(-0.147732\pi\) | ||||
0.894219 | + | 0.447629i | \(0.147732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.5317 | −1.46953 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6932 | 0.569142 | 0.284571 | − | 0.958655i | \(-0.408149\pi\) | ||||
0.284571 | + | 0.958655i | \(0.408149\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.0636 | −1.79781 | −0.898903 | − | 0.438148i | \(-0.855635\pi\) | ||||
−0.898903 | + | 0.438148i | \(0.855635\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.1103 | 1.16370 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.06634 | 0.475859 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.0564 | −0.994735 | −0.497367 | − | 0.867540i | \(-0.665700\pi\) | ||||
−0.497367 | + | 0.867540i | \(0.665700\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.16960 | −0.321176 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.4787 | 1.52635 | 0.763175 | − | 0.646192i | \(-0.223639\pi\) | ||||
0.763175 | + | 0.646192i | \(0.223639\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.1873 | −0.627680 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.7211 | −1.42394 | −0.711970 | − | 0.702210i | \(-0.752197\pi\) | ||||
−0.711970 | + | 0.702210i | \(0.752197\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.34435 | 0.427494 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.8299 | 1.42204 | 0.711020 | − | 0.703172i | \(-0.248234\pi\) | ||||
0.711020 | + | 0.703172i | \(0.248234\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.9813 | −1.26987 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.7590 | 1.81305 | 0.906527 | − | 0.422148i | \(-0.138724\pi\) | ||||
0.906527 | + | 0.422148i | \(0.138724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.1919 | 0.869433 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.92755 | 0.500779 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5015 | 0.677620 | 0.338810 | − | 0.940855i | \(-0.389976\pi\) | ||||
0.338810 | + | 0.940855i | \(0.389976\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.97476 | 0.498115 | 0.249058 | − | 0.968489i | \(-0.419879\pi\) | ||||
0.249058 | + | 0.968489i | \(0.419879\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.9787 | −1.44353 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.38937 | 0.0688685 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.03254 | 0.248843 | 0.124422 | − | 0.992229i | \(-0.460292\pi\) | ||||
0.124422 | + | 0.992229i | \(0.460292\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.3119 | 0.607299 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.85511 | 0.237756 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.23209 | 0.157898 | 0.0789491 | − | 0.996879i | \(-0.474844\pi\) | ||||
0.0789491 | + | 0.996879i | \(0.474844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3052 | 0.892142 | 0.446071 | − | 0.894998i | \(-0.352823\pi\) | ||||
0.446071 | + | 0.894998i | \(0.352823\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.2459 | −1.08163 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.09570 | 0.101181 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.87077 | 0.330953 | 0.165477 | − | 0.986214i | \(-0.447084\pi\) | ||||
0.165477 | + | 0.986214i | \(0.447084\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.2716 | 1.21447 | 0.607237 | − | 0.794521i | \(-0.292278\pi\) | ||||
0.607237 | + | 0.794521i | \(0.292278\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −41.9783 | −2.00810 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.63193 | −0.364252 | −0.182126 | − | 0.983275i | \(-0.558298\pi\) | ||||
−0.182126 | + | 0.983275i | \(0.558298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.03640 | 0.334309 | 0.167155 | − | 0.985931i | \(-0.446542\pi\) | ||||
0.167155 | + | 0.985931i | \(0.446542\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.2107 | −0.577545 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.1384 | −0.997582 | −0.498791 | − | 0.866722i | \(-0.666222\pi\) | ||||
−0.498791 | + | 0.866722i | \(0.666222\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.08215 | 0.0509566 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.7236 | 0.832726 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.7942 | −1.30016 | −0.650080 | − | 0.759866i | \(-0.725265\pi\) | ||||
−0.650080 | + | 0.759866i | \(0.725265\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.6432 | −0.543459 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.74916 | −0.407489 | −0.203744 | − | 0.979024i | \(-0.565311\pi\) | ||||
−0.203744 | + | 0.979024i | \(0.565311\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.1551 | −1.02963 | −0.514817 | − | 0.857300i | \(-0.672140\pi\) | ||||
−0.514817 | + | 0.857300i | \(0.672140\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.90576 | −0.365835 | −0.182918 | − | 0.983128i | \(-0.558554\pi\) | ||||
−0.182918 | + | 0.983128i | \(0.558554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.1158 | 0.742577 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.38175 | 0.201473 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.7414 | −0.629175 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.8720 | 0.816594 | 0.408297 | − | 0.912849i | \(-0.366123\pi\) | ||||
0.408297 | + | 0.912849i | \(0.366123\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.3831 | −0.974986 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.28891 | 0.375606 | 0.187803 | − | 0.982207i | \(-0.439863\pi\) | ||||
0.187803 | + | 0.982207i | \(0.439863\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.1624 | 0.504781 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.7385 | −0.935916 | −0.467958 | − | 0.883751i | \(-0.655010\pi\) | ||||
−0.467958 | + | 0.883751i | \(0.655010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.15406 | −0.232127 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.2935 | 1.31136 | 0.655678 | − | 0.755041i | \(-0.272383\pi\) | ||||
0.655678 | + | 0.755041i | \(0.272383\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.3512 | −0.462459 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.3632 | 1.39841 | 0.699207 | − | 0.714919i | \(-0.253536\pi\) | ||||
0.699207 | + | 0.714919i | \(0.253536\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.3782 | −0.949439 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.18921 | −0.274332 | −0.137166 | − | 0.990548i | \(-0.543799\pi\) | ||||
−0.137166 | + | 0.990548i | \(0.543799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 28.4298 | 1.25521 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.90196 | 0.171608 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.02394 | −0.220526 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.3709 | −1.59344 | −0.796720 | − | 0.604349i | \(-0.793433\pi\) | ||||
−0.796720 | + | 0.604349i | \(0.793433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.7114 | 1.08055 | 0.540276 | − | 0.841488i | \(-0.318320\pi\) | ||||
0.540276 | + | 0.841488i | \(0.318320\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.2552 | −0.533843 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.8647 | 0.863683 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.1324 | −0.917068 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.6549 | −0.721403 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.7141 | 0.462349 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.8192 | 0.895088 | 0.447544 | − | 0.894262i | \(-0.352299\pi\) | ||||
0.447544 | + | 0.894262i | \(0.352299\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.9289 | −0.469002 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.09203 | −0.132206 | −0.0661028 | − | 0.997813i | \(-0.521057\pi\) | ||||
−0.0661028 | + | 0.997813i | \(0.521057\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.0993 | −0.559063 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.5849 | 0.536135 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.23109 | −0.221648 | −0.110824 | − | 0.993840i | \(-0.535349\pi\) | ||||
−0.110824 | + | 0.993840i | \(0.535349\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −67.4373 | −2.85229 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.886277 | 0.0374187 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.260526 | 0.0109799 | 0.00548994 | − | 0.999985i | \(-0.498252\pi\) | ||||
0.00548994 | + | 0.999985i | \(0.498252\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.5445 | 1.28049 | 0.640245 | − | 0.768171i | \(-0.278833\pi\) | ||||
0.640245 | + | 0.768171i | \(0.278833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.45361 | 0.353773 | 0.176886 | − | 0.984231i | \(-0.443398\pi\) | ||||
0.176886 | + | 0.984231i | \(0.443398\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.1673 | −0.758951 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6074 | −0.483220 | −0.241610 | − | 0.970373i | \(-0.577676\pi\) | ||||
−0.241610 | + | 0.970373i | \(0.577676\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.1598 | 0.546902 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.41026 | 0.0998226 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.5957 | 1.22155 | 0.610774 | − | 0.791805i | \(-0.290859\pi\) | ||||
0.610774 | + | 0.791805i | \(0.290859\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.9240 | 1.23300 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.82825 | 0.0752043 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.4394 | 1.41426 | 0.707128 | − | 0.707085i | \(-0.249990\pi\) | ||||
0.707128 | + | 0.707085i | \(0.249990\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.4364 | −0.468062 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.6107 | −1.20986 | −0.604931 | − | 0.796278i | \(-0.706799\pi\) | ||||
−0.604931 | + | 0.796278i | \(0.706799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.91726 | −0.0782068 | −0.0391034 | − | 0.999235i | \(-0.512450\pi\) | ||||
−0.0391034 | + | 0.999235i | \(0.512450\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.3356 | 1.11319 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.6190 | 1.40514 | 0.702571 | − | 0.711614i | \(-0.252035\pi\) | ||||
0.702571 | + | 0.711614i | \(0.252035\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −60.0530 | −2.42949 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.9758 | −1.61461 | −0.807303 | − | 0.590137i | \(-0.799074\pi\) | ||||
−0.807303 | + | 0.590137i | \(0.799074\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.8372 | 1.80508 | 0.902539 | − | 0.430609i | \(-0.141701\pi\) | ||||
0.902539 | + | 0.430609i | \(0.141701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.6368 | −1.27159 | −0.635796 | − | 0.771858i | \(-0.719328\pi\) | ||||
−0.635796 | + | 0.771858i | \(0.719328\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −29.0301 | −1.16494 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.16406 | −0.0864244 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.04297 | −0.360567 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.14722 | 0.284526 | 0.142263 | − | 0.989829i | \(-0.454562\pi\) | ||||
0.142263 | + | 0.989829i | \(0.454562\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.8989 | −0.790910 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.22006 | 0.0482649 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.9734 | −1.18388 | −0.591938 | − | 0.805983i | \(-0.701637\pi\) | ||||
−0.591938 | + | 0.805983i | \(0.701637\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.1717 | −0.637750 | −0.318875 | − | 0.947797i | \(-0.603305\pi\) | ||||
−0.318875 | + | 0.947797i | \(0.603305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.3068 | −0.562460 | −0.281230 | − | 0.959640i | \(-0.590742\pi\) | ||||
−0.281230 | + | 0.959640i | \(0.590742\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.70664 | 0.145499 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.7309 | −1.28086 | −0.640429 | − | 0.768018i | \(-0.721243\pi\) | ||||
−0.640429 | + | 0.768018i | \(0.721243\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.8633 | 0.735927 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.326169 | −0.0127057 | −0.00635287 | − | 0.999980i | \(-0.502022\pi\) | ||||
−0.00635287 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.2200 | −0.825361 | −0.412680 | − | 0.910876i | \(-0.635407\pi\) | ||||
−0.412680 | + | 0.910876i | \(0.635407\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.6403 | −0.529743 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.8506 | −0.497579 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.1688 | 0.393148 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.29762 | 0.0886988 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.9064 | −0.613146 | −0.306573 | − | 0.951847i | \(-0.599182\pi\) | ||||
−0.306573 | + | 0.951847i | \(0.599182\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.5811 | −1.29063 | −0.645314 | − | 0.763917i | \(-0.723273\pi\) | ||||
−0.645314 | + | 0.763917i | \(0.723273\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.2255 | 0.928324 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.7281 | 1.52015 | 0.760076 | − | 0.649834i | \(-0.225162\pi\) | ||||
0.760076 | + | 0.649834i | \(0.225162\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.22004 | 0.237309 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37.0950 | −1.41321 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.8959 | 1.40358 | 0.701792 | − | 0.712382i | \(-0.252383\pi\) | ||||
0.701792 | + | 0.712382i | \(0.252383\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.04340 | −0.266788 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.9199 | 0.526500 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.0237 | 0.416358 | 0.208179 | − | 0.978091i | \(-0.433246\pi\) | ||||
0.208179 | + | 0.978091i | \(0.433246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.0806 | 0.832787 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.55854 | −0.246311 | −0.123156 | − | 0.992387i | \(-0.539301\pi\) | ||||
−0.123156 | + | 0.992387i | \(0.539301\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.9774 | 0.786713 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.5558 | −1.14432 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.18229 | 0.118845 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −49.4169 | −1.84294 | −0.921470 | − | 0.388450i | \(-0.873010\pi\) | ||||
−0.921470 | + | 0.388450i | \(0.873010\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.2333 | −0.417771 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.05602 | −0.335869 | −0.167935 | − | 0.985798i | \(-0.553710\pi\) | ||||
−0.167935 | + | 0.985798i | \(0.553710\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.78904 | 0.140335 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.5194 | −1.05483 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.9803 | −1.36590 | −0.682949 | − | 0.730466i | \(-0.739303\pi\) | ||||
−0.682949 | + | 0.730466i | \(0.739303\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.79469 | −0.176615 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.0463 | −1.76741 | −0.883707 | − | 0.468041i | \(-0.844960\pi\) | ||||
−0.883707 | + | 0.468041i | \(0.844960\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.3060 | 1.22353 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.9706 | 1.64981 | 0.824906 | − | 0.565270i | \(-0.191228\pi\) | ||||
0.824906 | + | 0.565270i | \(0.191228\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.80864 | 0.249115 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.6670 | 1.48396 | 0.741979 | − | 0.670423i | \(-0.233887\pi\) | ||||
0.741979 | + | 0.670423i | \(0.233887\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.7271 | 0.463801 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.2736 | −1.17301 | −0.586503 | − | 0.809947i | \(-0.699496\pi\) | ||||
−0.586503 | + | 0.809947i | \(0.699496\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.20976 | 0.0802092 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.7233 | −0.606217 | −0.303109 | − | 0.952956i | \(-0.598025\pi\) | ||||
−0.303109 | + | 0.952956i | \(0.598025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −57.0471 | −2.05985 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.7197 | 1.39627 | 0.698134 | − | 0.715967i | \(-0.254014\pi\) | ||||
0.698134 | + | 0.715967i | \(0.254014\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.47036 | 0.0529537 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.4246 | −1.16623 | −0.583116 | − | 0.812389i | \(-0.698167\pi\) | ||||
−0.583116 | + | 0.812389i | \(0.698167\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.1982 | 0.616189 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.214000 | −0.00765752 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.70309 | 0.311023 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.1453 | 0.539871 | 0.269935 | − | 0.962878i | \(-0.412998\pi\) | ||||
0.269935 | + | 0.962878i | \(0.412998\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.97495 | −0.319517 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.3616 | −1.25573 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.0776 | −0.427810 | −0.213905 | − | 0.976854i | \(-0.568618\pi\) | ||||
−0.213905 | + | 0.976854i | \(0.568618\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.3966 | −0.898467 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.9302 | 0.880867 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.30864 | −0.116759 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.85248 | 0.276420 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.9340 | 1.54464 | 0.772318 | − | 0.635236i | \(-0.219097\pi\) | ||||
0.772318 | + | 0.635236i | \(0.219097\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.1167 | −1.30334 | −0.651671 | − | 0.758501i | \(-0.725932\pi\) | ||||
−0.651671 | + | 0.758501i | \(0.725932\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.38175 | 0.153675 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 69.6371 | 2.43630 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.3112 | −0.848468 | −0.424234 | − | 0.905553i | \(-0.639457\pi\) | ||||
−0.424234 | + | 0.905553i | \(0.639457\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.0685 | −0.490397 | −0.245198 | − | 0.969473i | \(-0.578853\pi\) | ||||
−0.245198 | + | 0.969473i | \(0.578853\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.8782 | −0.795554 | −0.397777 | − | 0.917482i | \(-0.630218\pi\) | ||||
−0.397777 | + | 0.917482i | \(0.630218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0626 | 0.349488 | 0.174744 | − | 0.984614i | \(-0.444090\pi\) | ||||
0.174744 | + | 0.984614i | \(0.444090\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.6257 | 0.472669 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.6939 | 0.715286 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.3245 | −1.70287 | −0.851436 | − | 0.524459i | \(-0.824268\pi\) | ||||
−0.851436 | + | 0.524459i | \(0.824268\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.1474 | −0.867153 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.92428 | −0.100718 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.4279 | 0.392204 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.5469 | −0.772897 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.3633 | −0.834185 | −0.417092 | − | 0.908864i | \(-0.636951\pi\) | ||||
−0.417092 | + | 0.908864i | \(0.636951\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.6446 | −1.28591 | −0.642957 | − | 0.765902i | \(-0.722293\pi\) | ||||
−0.642957 | + | 0.765902i | \(0.722293\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.4954 | −0.358098 | −0.179049 | − | 0.983840i | \(-0.557302\pi\) | ||||
−0.179049 | + | 0.983840i | \(0.557302\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.9271 | −1.12085 | −0.560426 | − | 0.828205i | \(-0.689363\pi\) | ||||
−0.560426 | + | 0.828205i | \(0.689363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.45355 | 0.287098 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.67945 | −0.124817 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 73.7926 | 2.50037 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.1851 | −1.05546 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.2674 | 0.481774 | 0.240887 | − | 0.970553i | \(-0.422562\pi\) | ||||
0.240887 | + | 0.970553i | \(0.422562\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.5763 | −0.862667 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.9553 | 0.537547 | 0.268774 | − | 0.963203i | \(-0.413382\pi\) | ||||
0.268774 | + | 0.963203i | \(0.413382\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.32356 | −0.179152 | −0.0895760 | − | 0.995980i | \(-0.528551\pi\) | ||||
−0.0895760 | + | 0.995980i | \(0.528551\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.9406 | −1.34107 | −0.670536 | − | 0.741877i | \(-0.733936\pi\) | ||||
−0.670536 | + | 0.741877i | \(0.733936\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.28733 | 0.0431273 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 62.0120 | 2.07515 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34.0093 | −1.13554 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.16050 | 0.305520 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.6876 | −0.522629 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.9996 | 0.863301 | 0.431650 | − | 0.902041i | \(-0.357931\pi\) | ||||
0.431650 | + | 0.902041i | \(0.357931\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.59004 | 0.119074 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.5747 | −0.814196 | −0.407098 | − | 0.913385i | \(-0.633459\pi\) | ||||
−0.407098 | + | 0.913385i | \(0.633459\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.19424 | −0.0395237 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.92702 | −0.0635666 | −0.0317833 | − | 0.999495i | \(-0.510119\pi\) | ||||
−0.0317833 | + | 0.999495i | \(0.510119\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.65990 | 0.285353 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.29357 | 0.108409 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.88439 | 0.160424 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.5639 | 0.445017 | 0.222509 | − | 0.974931i | \(-0.428575\pi\) | ||||
0.222509 | + | 0.974931i | \(0.428575\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.7703 | −0.352604 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.8976 | 1.04205 | 0.521025 | − | 0.853541i | \(-0.325550\pi\) | ||||
0.521025 | + | 0.853541i | \(0.325550\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.33523 | −0.174109 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.46416 | −0.243325 | −0.121662 | − | 0.992572i | \(-0.538822\pi\) | ||||
−0.121662 | + | 0.992572i | \(0.538822\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.5613 | −0.571876 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.0934 | 1.20537 | 0.602686 | − | 0.797978i | \(-0.294097\pi\) | ||||
0.602686 | + | 0.797978i | \(0.294097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.9216 | 1.65299 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.2171 | 0.882574 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.1489 | 0.393542 | 0.196771 | − | 0.980449i | \(-0.436954\pi\) | ||||
0.196771 | + | 0.980449i | \(0.436954\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.662476 | −0.0214148 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.21848 | −0.297370 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.95698 | −0.159736 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.16851 | −0.166208 | −0.0831040 | − | 0.996541i | \(-0.526483\pi\) | ||||
−0.0831040 | + | 0.996541i | \(0.526483\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.0852 | 0.452482 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.3784 | −0.846523 | −0.423261 | − | 0.906008i | \(-0.639115\pi\) | ||||
−0.423261 | + | 0.906008i | \(0.639115\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.2923 | −1.28906 | −0.644532 | − | 0.764577i | \(-0.722948\pi\) | ||||
−0.644532 | + | 0.764577i | \(0.722948\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.37279 | −0.139755 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.9706 | 0.829179 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.3832 | 0.458751 | 0.229376 | − | 0.973338i | \(-0.426332\pi\) | ||||
0.229376 | + | 0.973338i | \(0.426332\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −71.1076 | −2.26109 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.09085 | 0.0664181 | 0.0332090 | − | 0.999448i | \(-0.489427\pi\) | ||||
0.0332090 | + | 0.999448i | \(0.489427\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.0794 | 0.859338 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.4579 | 0.901270 | 0.450635 | − | 0.892708i | \(-0.351198\pi\) | ||||
0.450635 | + | 0.892708i | \(0.351198\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.2699 | 0.483117 |
(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 | 9800.2.a.db.1.5 | 10 | ||
5.2 | odd | 4 | 1960.2.g.g.1569.12 | yes | 20 | ||
5.3 | odd | 4 | 1960.2.g.g.1569.10 | yes | 20 | ||
5.4 | even | 2 | 9800.2.a.dc.1.6 | 10 | |||
7.6 | odd | 2 | inner | 9800.2.a.db.1.6 | 10 | ||
35.13 | even | 4 | 1960.2.g.g.1569.11 | yes | 20 | ||
35.27 | even | 4 | 1960.2.g.g.1569.9 | ✓ | 20 | ||
35.34 | odd | 2 | 9800.2.a.dc.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.g.g.1569.9 | ✓ | 20 | 35.27 | even | 4 | ||
1960.2.g.g.1569.10 | yes | 20 | 5.3 | odd | 4 | ||
1960.2.g.g.1569.11 | yes | 20 | 35.13 | even | 4 | ||
1960.2.g.g.1569.12 | yes | 20 | 5.2 | odd | 4 | ||
9800.2.a.db.1.5 | 10 | 1.1 | even | 1 | trivial | ||
9800.2.a.db.1.6 | 10 | 7.6 | odd | 2 | inner | ||
9800.2.a.dc.1.5 | 10 | 35.34 | odd | 2 | |||
9800.2.a.dc.1.6 | 10 | 5.4 | even | 2 |