Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3744,2,Mod(1,3744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3744, 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("3744.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3744.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: | \(29.8959905168\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3744.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.03528 | −0.462990 | −0.231495 | − | 0.972836i | \(-0.574362\pi\) | ||||
−0.231495 | + | 0.972836i | \(0.574362\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.86370 | 1.46034 | 0.730171 | − | 0.683264i | \(-0.239440\pi\) | ||||
0.730171 | + | 0.683264i | \(0.239440\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.46410 | 0.441443 | 0.220722 | − | 0.975337i | \(-0.429159\pi\) | ||||
0.220722 | + | 0.975337i | \(0.429159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.65685 | −1.37199 | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||||
−0.685994 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.79315 | −0.411377 | −0.205689 | − | 0.978618i | \(-0.565943\pi\) | ||||
−0.205689 | + | 0.978618i | \(0.565943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.92820 | −1.44463 | −0.722315 | − | 0.691564i | \(-0.756922\pi\) | ||||
−0.722315 | + | 0.691564i | \(0.756922\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.92820 | −0.785641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.07055 | −0.384492 | −0.192246 | − | 0.981347i | \(-0.561577\pi\) | ||||
−0.192246 | + | 0.981347i | \(0.561577\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.86370 | 0.693942 | 0.346971 | − | 0.937876i | \(-0.387210\pi\) | ||||
0.346971 | + | 0.937876i | \(0.387210\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | −0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.03528 | 0.161683 | 0.0808415 | − | 0.996727i | \(-0.474239\pi\) | ||||
0.0808415 | + | 0.996727i | \(0.474239\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.65685 | −0.862662 | −0.431331 | − | 0.902194i | \(-0.641956\pi\) | ||||
−0.431331 | + | 0.902194i | \(0.641956\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.53590 | −0.369899 | −0.184949 | − | 0.982748i | \(-0.559212\pi\) | ||||
−0.184949 | + | 0.982748i | \(0.559212\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.92820 | 1.13260 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.65685 | −0.777029 | −0.388514 | − | 0.921443i | \(-0.627012\pi\) | ||||
−0.388514 | + | 0.921443i | \(0.627012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.51575 | −0.204384 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.46410 | −1.23212 | −0.616061 | − | 0.787699i | \(-0.711272\pi\) | ||||
−0.616061 | + | 0.787699i | \(0.711272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.92820 | −1.14314 | −0.571570 | − | 0.820554i | \(-0.693665\pi\) | ||||
−0.571570 | + | 0.820554i | \(0.693665\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.03528 | 0.128410 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.79315 | 0.219068 | 0.109534 | − | 0.993983i | \(-0.465064\pi\) | ||||
0.109534 | + | 0.993983i | \(0.465064\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.53590 | −0.300956 | −0.150478 | − | 0.988613i | \(-0.548081\pi\) | ||||
−0.150478 | + | 0.988613i | \(0.548081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.8564 | 1.38769 | 0.693844 | − | 0.720126i | \(-0.255916\pi\) | ||||
0.693844 | + | 0.720126i | \(0.255916\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65685 | 0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.53590 | −0.717408 | −0.358704 | − | 0.933451i | \(-0.616781\pi\) | ||||
−0.358704 | + | 0.933451i | \(0.616781\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.85641 | 0.635216 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.4195 | 1.52847 | 0.764234 | − | 0.644939i | \(-0.223117\pi\) | ||||
0.764234 | + | 0.644939i | \(0.223117\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.86370 | −0.405026 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.85641 | 0.190463 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.72741 | −0.768906 | −0.384453 | − | 0.923145i | \(-0.625610\pi\) | ||||
−0.384453 | + | 0.923145i | \(0.625610\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9706 | 1.67216 | 0.836080 | − | 0.548608i | \(-0.184842\pi\) | ||||
0.836080 | + | 0.548608i | \(0.184842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.92820 | −0.669775 | −0.334887 | − | 0.942258i | \(-0.608698\pi\) | ||||
−0.334887 | + | 0.942258i | \(0.608698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.00000 | −0.574696 | −0.287348 | − | 0.957826i | \(-0.592774\pi\) | ||||
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.0411 | 1.79124 | 0.895619 | − | 0.444823i | \(-0.146733\pi\) | ||||
0.895619 | + | 0.444823i | \(0.146733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.17260 | 0.668849 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21.8564 | −2.00357 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85641 | −0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.24316 | 0.826733 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8685 | −1.05316 | −0.526580 | − | 0.850126i | \(-0.676526\pi\) | ||||
−0.526580 | + | 0.850126i | \(0.676526\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.9282 | −1.30428 | −0.652142 | − | 0.758097i | \(-0.726129\pi\) | ||||
−0.652142 | + | 0.758097i | \(0.726129\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.92820 | −0.600751 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.17638 | 0.442248 | 0.221124 | − | 0.975246i | \(-0.429027\pi\) | ||||
0.221124 | + | 0.975246i | \(0.429027\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3843 | −1.13524 | −0.567619 | − | 0.823291i | \(-0.692135\pi\) | ||||
−0.567619 | + | 0.823291i | \(0.692135\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.46410 | −0.122434 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.14359 | 0.178016 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.6312 | 1.69017 | 0.845087 | − | 0.534629i | \(-0.179549\pi\) | ||||
0.845087 | + | 0.534629i | \(0.179549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00481 | −0.651422 | −0.325711 | − | 0.945469i | \(-0.605604\pi\) | ||||
−0.325711 | + | 0.945469i | \(0.605604\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.07180 | −0.245156 | −0.122578 | − | 0.992459i | \(-0.539116\pi\) | ||||
−0.122578 | + | 0.992459i | \(0.539116\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −26.7685 | −2.10966 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.3891 | 1.67532 | 0.837661 | − | 0.546191i | \(-0.183923\pi\) | ||||
0.837661 | + | 0.546191i | \(0.183923\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.53590 | −0.196234 | −0.0981169 | − | 0.995175i | \(-0.531282\pi\) | ||||
−0.0981169 | + | 0.995175i | \(0.531282\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.1822 | −1.76251 | −0.881256 | − | 0.472640i | \(-0.843301\pi\) | ||||
−0.881256 | + | 0.472640i | \(0.843301\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.1774 | −1.14730 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.85641 | 0.736702 | 0.368351 | − | 0.929687i | \(-0.379922\pi\) | ||||
0.368351 | + | 0.929687i | \(0.379922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.7846 | −1.39625 | −0.698125 | − | 0.715976i | \(-0.745982\pi\) | ||||
−0.698125 | + | 0.715976i | \(0.745982\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.07055 | 0.152230 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.28221 | −0.605655 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0000 | −1.44715 | −0.723575 | − | 0.690246i | \(-0.757502\pi\) | ||||
−0.723575 | + | 0.690246i | \(0.757502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0000 | 0.719816 | 0.359908 | − | 0.932988i | \(-0.382808\pi\) | ||||
0.359908 | + | 0.932988i | \(0.382808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.10583 | 0.221281 | 0.110641 | − | 0.993860i | \(-0.464710\pi\) | ||||
0.110641 | + | 0.993860i | \(0.464710\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.58630 | −0.254226 | −0.127113 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127113 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.00000 | −0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.07180 | −0.0748575 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.62536 | −0.181600 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.14110 | 0.285085 | 0.142543 | − | 0.989789i | \(-0.454472\pi\) | ||||
0.142543 | + | 0.989789i | \(0.454472\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.85641 | 0.399404 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.9282 | 1.01339 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.65685 | 0.380521 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.7322 | −1.05351 | −0.526754 | − | 0.850018i | \(-0.676591\pi\) | ||||
−0.526754 | + | 0.850018i | \(0.676591\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.46410 | −0.628154 | −0.314077 | − | 0.949397i | \(-0.601695\pi\) | ||||
−0.314077 | + | 0.949397i | \(0.601695\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.3843 | −0.876832 | −0.438416 | − | 0.898772i | \(-0.644460\pi\) | ||||
−0.438416 | + | 0.898772i | \(0.644460\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.62536 | 0.171259 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.3923 | −1.57781 | −0.788904 | − | 0.614517i | \(-0.789351\pi\) | ||||
−0.788904 | + | 0.614517i | \(0.789351\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.20788 | −0.524382 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.79315 | 0.114095 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.7846 | −1.05944 | −0.529718 | − | 0.848174i | \(-0.677702\pi\) | ||||
−0.529718 | + | 0.848174i | \(0.677702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.1436 | −0.637722 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.5254 | −1.09320 | −0.546601 | − | 0.837393i | \(-0.684079\pi\) | ||||
−0.546601 | + | 0.837393i | \(0.684079\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.72741 | −0.480158 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.9282 | 0.673862 | 0.336931 | − | 0.941529i | \(-0.390611\pi\) | ||||
0.336931 | + | 0.941529i | \(0.390611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.85641 | 0.359756 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.3843 | 0.816053 | 0.408026 | − | 0.912970i | \(-0.366217\pi\) | ||||
0.408026 | + | 0.912970i | \(0.366217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.41851 | −0.268405 | −0.134203 | − | 0.990954i | \(-0.542847\pi\) | ||||
−0.134203 | + | 0.990954i | \(0.542847\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.75129 | −0.346816 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.4195 | −0.860197 | −0.430099 | − | 0.902782i | \(-0.641521\pi\) | ||||
−0.430099 | + | 0.902782i | \(0.641521\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9000 | 0.885714 | 0.442857 | − | 0.896592i | \(-0.353965\pi\) | ||||
0.442857 | + | 0.896592i | \(0.353965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | 0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.3490 | 0.721435 | 0.360718 | − | 0.932675i | \(-0.382532\pi\) | ||||
0.360718 | + | 0.932675i | \(0.382532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.79796 | 0.570459 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.92820 | 0.400668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.8564 | −1.25978 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.24316 | 0.529262 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.8028 | 1.01606 | 0.508029 | − | 0.861340i | \(-0.330374\pi\) | ||||
0.508029 | + | 0.861340i | \(0.330374\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.92820 | −0.392862 | −0.196431 | − | 0.980518i | \(-0.562935\pi\) | ||||
−0.196431 | + | 0.980518i | \(0.562935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.85641 | 0.444070 | 0.222035 | − | 0.975039i | \(-0.428730\pi\) | ||||
0.222035 | + | 0.975039i | \(0.428730\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.9449 | −1.79420 | −0.897102 | − | 0.441823i | \(-0.854332\pi\) | ||||
−0.897102 | + | 0.441823i | \(0.854332\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.03150 | −0.169731 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.1436 | 0.564405 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.92820 | 0.217898 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.79796 | −0.540179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.96575 | 0.492802 | 0.246401 | − | 0.969168i | \(-0.420752\pi\) | ||||
0.246401 | + | 0.969168i | \(0.420752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.85641 | −0.101426 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.8564 | 1.51744 | 0.758718 | − | 0.651420i | \(-0.225826\pi\) | ||||
0.758718 | + | 0.651420i | \(0.225826\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.65685 | 0.306336 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.58630 | 0.193642 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.0000 | −1.28839 | −0.644194 | − | 0.764862i | \(-0.722807\pi\) | ||||
−0.644194 | + | 0.764862i | \(0.722807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.24693 | −0.385715 | −0.192858 | − | 0.981227i | \(-0.561776\pi\) | ||||
−0.192858 | + | 0.981227i | \(0.561776\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.62536 | 0.139339 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.46410 | 0.288384 | 0.144192 | − | 0.989550i | \(-0.453942\pi\) | ||||
0.144192 | + | 0.989550i | \(0.453942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7846 | −0.830769 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.2747 | −0.642485 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.21166 | 0.324246 | 0.162123 | − | 0.986771i | \(-0.448166\pi\) | ||||
0.162123 | + | 0.986771i | \(0.448166\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.8564 | −1.13473 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.07055 | 0.106639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.52056 | 0.489038 | 0.244519 | − | 0.969644i | \(-0.421370\pi\) | ||||
0.244519 | + | 0.969644i | \(0.421370\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.53590 | 0.129578 | 0.0647892 | − | 0.997899i | \(-0.479363\pi\) | ||||
0.0647892 | + | 0.997899i | \(0.479363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.85641 | −0.298470 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.4548 | 0.783590 | 0.391795 | − | 0.920053i | \(-0.371854\pi\) | ||||
0.391795 | + | 0.920053i | \(0.371854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.1918 | 1.98202 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.8564 | −1.59883 | −0.799414 | − | 0.600781i | \(-0.794856\pi\) | ||||
−0.799414 | + | 0.600781i | \(0.794856\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.5921 | 1.07826 | 0.539130 | − | 0.842223i | \(-0.318753\pi\) | ||||
0.539130 | + | 0.842223i | \(0.318753\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.86370 | −0.192465 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.92820 | −0.145146 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.143594 | 0.00710024 | 0.00355012 | − | 0.999994i | \(-0.498870\pi\) | ||||
0.00355012 | + | 0.999994i | \(0.498870\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.5665 | −1.79932 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.76646 | 0.332152 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.7846 | 1.40622 | 0.703110 | − | 0.711081i | \(-0.251794\pi\) | ||||
0.703110 | + | 0.711081i | \(0.251794\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.7128 | 1.83801 | 0.919005 | − | 0.394246i | \(-0.128994\pi\) | ||||
0.919005 | + | 0.394246i | \(0.128994\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.2213 | 1.07789 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.4959 | −1.66937 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.392305 | 0.0188967 | 0.00944833 | − | 0.999955i | \(-0.496992\pi\) | ||||
0.00944833 | + | 0.999955i | \(0.496992\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.9282 | 0.813518 | 0.406759 | − | 0.913536i | \(-0.366659\pi\) | ||||
0.406759 | + | 0.913536i | \(0.366659\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.4233 | 0.594288 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.7076 | −1.94287 | −0.971434 | − | 0.237312i | \(-0.923734\pi\) | ||||
−0.971434 | + | 0.237312i | \(0.923734\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.6410 | 1.64584 | 0.822922 | − | 0.568154i | \(-0.192342\pi\) | ||||
0.822922 | + | 0.568154i | \(0.192342\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.9282 | −0.707665 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.8744 | 1.40986 | 0.704929 | − | 0.709278i | \(-0.250979\pi\) | ||||
0.704929 | + | 0.709278i | \(0.250979\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.51575 | 0.0713739 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.00000 | 0.187523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.00000 | −0.0935561 | −0.0467780 | − | 0.998905i | \(-0.514895\pi\) | ||||
−0.0467780 | + | 0.998905i | \(0.514895\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.1881 | 1.91832 | 0.959160 | − | 0.282866i | \(-0.0912850\pi\) | ||||
0.959160 | + | 0.282866i | \(0.0912850\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.0459 | −1.25693 | −0.628465 | − | 0.777838i | \(-0.716317\pi\) | ||||
−0.628465 | + | 0.777838i | \(0.716317\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.9282 | 1.61628 | 0.808142 | − | 0.588987i | \(-0.200473\pi\) | ||||
0.808142 | + | 0.588987i | \(0.200473\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.92820 | 0.319915 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.28221 | −0.380816 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.04386 | 0.323195 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.5359 | 0.846927 | 0.423463 | − | 0.905913i | \(-0.360814\pi\) | ||||
0.423463 | + | 0.905913i | \(0.360814\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.21166 | −0.282057 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.3185 | 0.875406 | 0.437703 | − | 0.899120i | \(-0.355792\pi\) | ||||
0.437703 | + | 0.899120i | \(0.355792\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.7846 | 0.757479 | 0.378739 | − | 0.925503i | \(-0.376358\pi\) | ||||
0.378739 | + | 0.925503i | \(0.376358\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.7128 | 0.527519 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.79796 | −0.439499 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.2576 | −1.48881 | −0.744407 | − | 0.667726i | \(-0.767268\pi\) | ||||
−0.744407 | + | 0.667726i | \(0.767268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.9282 | −0.487264 | −0.243632 | − | 0.969868i | \(-0.578339\pi\) | ||||
−0.243632 | + | 0.969868i | \(0.578339\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.00000 | 0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.5606 | 0.822686 | 0.411343 | − | 0.911481i | \(-0.365060\pi\) | ||||
0.411343 | + | 0.911481i | \(0.365060\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 45.8096 | 2.02650 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.5692 | −0.774192 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.71281 | −0.163289 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.554803 | −0.0243064 | −0.0121532 | − | 0.999926i | \(-0.503869\pi\) | ||||
−0.0121532 | + | 0.999926i | \(0.503869\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.5254 | 0.766331 | 0.383165 | − | 0.923680i | \(-0.374834\pi\) | ||||
0.383165 | + | 0.923680i | \(0.374834\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.8564 | −0.952080 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0000 | 1.08696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.03528 | −0.0448428 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.17260 | 0.310099 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.6077 | 0.499979 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.8564 | −1.19764 | −0.598820 | − | 0.800883i | \(-0.704364\pi\) | ||||
−0.598820 | + | 0.800883i | \(0.704364\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.21166 | 0.266078 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.1528 | −1.71681 | −0.858405 | − | 0.512973i | \(-0.828544\pi\) | ||||
−0.858405 | + | 0.512973i | \(0.828544\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.71281 | 0.158171 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.8038 | 1.17808 | 0.589042 | − | 0.808102i | \(-0.299505\pi\) | ||||
0.589042 | + | 0.808102i | \(0.299505\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.65685 | 0.239259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.85641 | −0.0782382 | −0.0391191 | − | 0.999235i | \(-0.512455\pi\) | ||||
−0.0391191 | + | 0.999235i | \(0.512455\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.7128 | −0.829324 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.8076 | 1.08191 | 0.540955 | − | 0.841052i | \(-0.318063\pi\) | ||||
0.540955 | + | 0.841052i | \(0.318063\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.8096 | −1.91707 | −0.958537 | − | 0.284969i | \(-0.908017\pi\) | ||||
−0.958537 | + | 0.284969i | \(0.908017\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.2154 | 1.13496 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.8564 | −0.493589 | −0.246794 | − | 0.969068i | \(-0.579377\pi\) | ||||
−0.246794 | + | 0.969068i | \(0.579377\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.2528 | −1.04766 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.28221 | −0.343014 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.3923 | −1.17188 | −0.585938 | − | 0.810356i | \(-0.699274\pi\) | ||||
−0.585938 | + | 0.810356i | \(0.699274\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.92820 | −0.285472 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.20788 | −0.337057 | −0.168529 | − | 0.985697i | \(-0.553902\pi\) | ||||
−0.168529 | + | 0.985697i | \(0.553902\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.6274 | 0.927634 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.92820 | −0.119643 | −0.0598216 | − | 0.998209i | \(-0.519053\pi\) | ||||
−0.0598216 | + | 0.998209i | \(0.519053\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.14359 | −0.332184 | −0.166092 | − | 0.986110i | \(-0.553115\pi\) | ||||
−0.166092 | + | 0.986110i | \(0.553115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.16883 | 0.372766 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.0117 | 1.46167 | 0.730834 | − | 0.682555i | \(-0.239131\pi\) | ||||
0.730834 | + | 0.682555i | \(0.239131\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.53590 | 0.102591 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.8564 | 0.478876 | 0.239438 | − | 0.970912i | \(-0.423037\pi\) | ||||
0.239438 | + | 0.970912i | \(0.423037\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.5606 | −0.747223 | −0.373612 | − | 0.927585i | \(-0.621881\pi\) | ||||
−0.373612 | + | 0.927585i | \(0.621881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.1480 | 1.29214 | 0.646068 | − | 0.763280i | \(-0.276412\pi\) | ||||
0.646068 | + | 0.763280i | \(0.276412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 55.7128 | 2.23209 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.3137 | 0.451107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.9459 | −1.66984 | −0.834921 | − | 0.550370i | \(-0.814487\pi\) | ||||
−0.834921 | + | 0.550370i | \(0.814487\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.2872 | 0.487602 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.92820 | −0.314127 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8295 | −0.506733 | −0.253367 | − | 0.967370i | \(-0.581538\pi\) | ||||
−0.253367 | + | 0.967370i | \(0.581538\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.79315 | 0.0707150 | 0.0353575 | − | 0.999375i | \(-0.488743\pi\) | ||||
0.0353575 | + | 0.999375i | \(0.488743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.8564 | 1.80280 | 0.901401 | − | 0.432986i | \(-0.142540\pi\) | ||||
0.901401 | + | 0.432986i | \(0.142540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8564 | −0.543912 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.4158 | −0.642398 | −0.321199 | − | 0.947012i | \(-0.604086\pi\) | ||||
−0.321199 | + | 0.947012i | \(0.604086\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.4548 | 0.603870 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.1436 | −0.395138 | −0.197569 | − | 0.980289i | \(-0.563305\pi\) | ||||
−0.197569 | + | 0.980289i | \(0.563305\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.8564 | 0.461161 | 0.230580 | − | 0.973053i | \(-0.425938\pi\) | ||||
0.230580 | + | 0.973053i | \(0.425938\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.17260 | 0.278142 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.3452 | 0.555449 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0718 | −0.504631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.0718 | −0.580975 | −0.290488 | − | 0.956879i | \(-0.593817\pi\) | ||||
−0.290488 | + | 0.956879i | \(0.593817\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.9706 | 0.652232 | 0.326116 | − | 0.945330i | \(-0.394260\pi\) | ||||
0.326116 | + | 0.945330i | \(0.394260\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.1822 | 0.889652 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.1769 | 1.72865 | 0.864323 | − | 0.502937i | \(-0.167747\pi\) | ||||
0.864323 | + | 0.502937i | \(0.167747\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.35898 | −0.204756 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.65685 | 0.215509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.1165 | −1.10764 | −0.553821 | − | 0.832635i | \(-0.686831\pi\) | ||||
−0.553821 | + | 0.832635i | \(0.686831\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.8564 | 0.525603 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.85641 | −0.221827 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.5959 | −0.740128 | −0.370064 | − | 0.929006i | \(-0.620664\pi\) | ||||
−0.370064 | + | 0.929006i | \(0.620664\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.58630 | 0.135260 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.8564 | −1.12287 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.7128 | −0.665219 | −0.332609 | − | 0.943065i | \(-0.607929\pi\) | ||||
−0.332609 | + | 0.943065i | \(0.607929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.7685 | −1.00249 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.51575 | 0.0566858 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.7846 | 1.67018 | 0.835092 | − | 0.550110i | \(-0.185414\pi\) | ||||
0.835092 | + | 0.550110i | \(0.185414\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 65.5692 | 2.44193 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.13355 | 0.302072 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.72741 | −0.286594 | −0.143297 | − | 0.989680i | \(-0.545770\pi\) | ||||
−0.143297 | + | 0.989680i | \(0.545770\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32.0000 | 1.18356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.7128 | −0.654238 | −0.327119 | − | 0.944983i | \(-0.606078\pi\) | ||||
−0.327119 | + | 0.944983i | \(0.606078\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.62536 | 0.0967062 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.2165 | −0.522961 | −0.261481 | − | 0.965209i | \(-0.584211\pi\) | ||||
−0.261481 | + | 0.965209i | \(0.584211\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.2487 | −1.10972 | −0.554859 | − | 0.831945i | \(-0.687228\pi\) | ||||
−0.554859 | + | 0.831945i | \(0.687228\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.3590 | −0.782533 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.7685 | −0.978100 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.76646 | −0.246912 | −0.123456 | − | 0.992350i | \(-0.539398\pi\) | ||||
−0.123456 | + | 0.992350i | \(0.539398\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.28719 | 0.301602 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.6410 | 1.04098 | 0.520488 | − | 0.853869i | \(-0.325750\pi\) | ||||
0.520488 | + | 0.853869i | \(0.325750\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.4510 | −0.632600 | −0.316300 | − | 0.948659i | \(-0.602441\pi\) | ||||
−0.316300 | + | 0.948659i | \(0.602441\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.1822 | −0.839253 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.46410 | 0.341729 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.7128 | 0.782984 | 0.391492 | − | 0.920181i | \(-0.371959\pi\) | ||||
0.391492 | + | 0.920181i | \(0.371959\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.2196 | −1.59047 | −0.795233 | − | 0.606303i | \(-0.792652\pi\) | ||||
−0.795233 | + | 0.606303i | \(0.792652\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.1774 | −0.545189 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.85641 | −0.0665127 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.71281 | −0.132855 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.18016 | 0.113505 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.1165 | 1.03789 | 0.518945 | − | 0.854808i | \(-0.326325\pi\) | ||||
0.518945 | + | 0.854808i | \(0.326325\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 73.5692 | 2.61582 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.92820 | 0.317050 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.4233 | −0.440056 | −0.220028 | − | 0.975494i | \(-0.570615\pi\) | ||||
−0.220028 | + | 0.975494i | \(0.570615\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.3452 | 0.507497 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.3590 | 0.612585 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.7128 | 0.976748 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.554803 | 0.0195058 | 0.00975291 | − | 0.999952i | \(-0.496896\pi\) | ||||
0.00975291 | + | 0.999952i | \(0.496896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.2795 | −0.712108 | −0.356054 | − | 0.934465i | \(-0.615878\pi\) | ||||
−0.356054 | + | 0.934465i | \(0.615878\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.1436 | −0.775656 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.1436 | 0.354879 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.2784 | −0.358720 | −0.179360 | − | 0.983784i | \(-0.557403\pi\) | ||||
−0.179360 | + | 0.983784i | \(0.557403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.7391 | −1.52465 | −0.762324 | − | 0.647195i | \(-0.775942\pi\) | ||||
−0.762324 | + | 0.647195i | \(0.775942\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.0333 | 1.77460 | 0.887301 | − | 0.461190i | \(-0.152577\pi\) | ||||
0.887301 | + | 0.461190i | \(0.152577\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.78461 | 0.235639 | 0.117820 | − | 0.993035i | \(-0.462410\pi\) | ||||
0.117820 | + | 0.993035i | \(0.462410\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44.8487 | −1.55392 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.62536 | 0.0908542 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.3205 | −0.667018 | −0.333509 | − | 0.942747i | \(-0.608233\pi\) | ||||
−0.333509 | + | 0.942747i | \(0.608233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.7128 | −0.852166 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.03528 | −0.0356146 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.2185 | −1.17576 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.8564 | 0.474991 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.7128 | 1.42822 | 0.714110 | − | 0.700034i | \(-0.246832\pi\) | ||||
0.714110 | + | 0.700034i | \(0.246832\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.6980 | 0.843667 | 0.421833 | − | 0.906673i | \(-0.361387\pi\) | ||||
0.421833 | + | 0.906673i | \(0.361387\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.9411 | 1.15806 | 0.579028 | − | 0.815308i | \(-0.303432\pi\) | ||||
0.579028 | + | 0.815308i | \(0.303432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.1769 | −0.584709 | −0.292354 | − | 0.956310i | \(-0.594439\pi\) | ||||
−0.292354 | + | 0.956310i | \(0.594439\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0000 | 0.816024 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.79315 | −0.0607586 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.7128 | 1.20731 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.0000 | −0.877958 | −0.438979 | − | 0.898497i | \(-0.644660\pi\) | ||||
−0.438979 | + | 0.898497i | \(0.644660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.4158 | −0.553061 | −0.276531 | − | 0.961005i | \(-0.589185\pi\) | ||||
−0.276531 | + | 0.961005i | \(0.589185\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8685 | −0.399407 | −0.199704 | − | 0.979856i | \(-0.563998\pi\) | ||||
−0.199704 | + | 0.979856i | \(0.563998\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.1436 | 0.743509 | 0.371755 | − | 0.928331i | \(-0.378756\pi\) | ||||
0.371755 | + | 0.928331i | \(0.378756\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.8564 | −1.53797 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.54725 | 0.152168 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.2041 | −0.341086 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0000 | 1.06607 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.4473 | 0.646449 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.0096 | 0.531591 | 0.265795 | − | 0.964029i | \(-0.414365\pi\) | ||||
0.265795 | + | 0.964029i | \(0.414365\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.7128 | −0.520589 | −0.260294 | − | 0.965529i | \(-0.583820\pi\) | ||||
−0.260294 | + | 0.965529i | \(0.583820\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.56922 | −0.316695 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −57.6781 | −1.90470 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.9096 | −1.01961 | −0.509807 | − | 0.860289i | \(-0.670283\pi\) | ||||
−0.509807 | + | 0.860289i | \(0.670283\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.53590 | 0.0834701 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.85641 | 0.258317 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.1175 | 1.28340 | 0.641702 | − | 0.766954i | \(-0.278229\pi\) | ||||
0.641702 | + | 0.766954i | \(0.278229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.2165 | −0.465926 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.57437 | 0.280412 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.6410 | −1.58903 | −0.794516 | − | 0.607243i | \(-0.792276\pi\) | ||||
−0.794516 | + | 0.607243i | \(0.792276\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.31749 | 0.303741 | 0.151871 | − | 0.988400i | \(-0.451470\pi\) | ||||
0.151871 | + | 0.988400i | \(0.451470\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.17260 | −0.233572 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.2487 | 1.11293 | 0.556467 | − | 0.830870i | \(-0.312157\pi\) | ||||
0.556467 | + | 0.830870i | \(0.312157\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.8564 | −0.384875 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.4665 | 1.66716 | 0.833582 | − | 0.552396i | \(-0.186286\pi\) | ||||
0.833582 | + | 0.552396i | \(0.186286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.7055 | 0.670015 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.0000 | 0.645834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.0718 | −0.518445 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.3528 | −0.333267 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.1774 | 0.488073 | 0.244036 | − | 0.969766i | \(-0.421528\pi\) | ||||
0.244036 | + | 0.969766i | \(0.421528\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.7128 | −1.40281 | −0.701405 | − | 0.712762i | \(-0.747444\pi\) | ||||
−0.701405 | + | 0.712762i | \(0.747444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.7128 | −1.65784 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.4586 | −0.430578 | −0.215289 | − | 0.976550i | \(-0.569069\pi\) | ||||
−0.215289 | + | 0.976550i | \(0.569069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.1117 | 0.674732 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.3923 | 1.03315 | 0.516577 | − | 0.856241i | \(-0.327206\pi\) | ||||
0.516577 | + | 0.856241i | \(0.327206\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.21539 | −0.102451 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39.1918 | 1.24623 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.3843 | 0.425165 | 0.212583 | − | 0.977143i | \(-0.431813\pi\) | ||||
0.212583 | + | 0.977143i | \(0.431813\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.71281 | 0.117704 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.7128 | −0.434289 | −0.217145 | − | 0.976139i | \(-0.569674\pi\) | ||||
−0.217145 | + | 0.976139i | \(0.569674\pi\) | |||||||
\(998\) | 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 | 3744.2.a.bc.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 3744.2.a.bd.1.3 | yes | 4 | ||
4.3 | odd | 2 | 3744.2.a.bd.1.2 | yes | 4 | ||
8.3 | odd | 2 | 7488.2.a.db.1.3 | 4 | |||
8.5 | even | 2 | 7488.2.a.dc.1.3 | 4 | |||
12.11 | even | 2 | inner | 3744.2.a.bc.1.3 | yes | 4 | |
24.5 | odd | 2 | 7488.2.a.db.1.2 | 4 | |||
24.11 | even | 2 | 7488.2.a.dc.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3744.2.a.bc.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3744.2.a.bc.1.3 | yes | 4 | 12.11 | even | 2 | inner | |
3744.2.a.bd.1.2 | yes | 4 | 4.3 | odd | 2 | ||
3744.2.a.bd.1.3 | yes | 4 | 3.2 | odd | 2 | ||
7488.2.a.db.1.2 | 4 | 24.5 | odd | 2 | |||
7488.2.a.db.1.3 | 4 | 8.3 | odd | 2 | |||
7488.2.a.dc.1.2 | 4 | 24.11 | even | 2 | |||
7488.2.a.dc.1.3 | 4 | 8.5 | even | 2 |