Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9675,2,Mod(1,9675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9675 = 3^{2} \cdot 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9675.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: | \(77.2552639556\) |
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: | \( x^{10} - 13x^{8} + 58x^{6} - 103x^{4} + 65x^{2} - 13 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.643165\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.643165 | 0.454786 | 0.227393 | − | 0.973803i | \(-0.426980\pi\) | ||||
0.227393 | + | 0.973803i | \(0.426980\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.58634 | −0.793170 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.33434 | −0.504334 | −0.252167 | − | 0.967684i | \(-0.581143\pi\) | ||||
−0.252167 | + | 0.967684i | \(0.581143\pi\) | |||||||
\(8\) | −2.30661 | −0.815509 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.30661 | 0.695468 | 0.347734 | − | 0.937593i | \(-0.386951\pi\) | ||||
0.347734 | + | 0.937593i | \(0.386951\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.25200 | −0.347241 | −0.173621 | − | 0.984813i | \(-0.555547\pi\) | ||||
−0.173621 | + | 0.984813i | \(0.555547\pi\) | |||||||
\(14\) | −0.858202 | −0.229364 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.68915 | 0.422288 | ||||||||
\(17\) | 3.88304 | 0.941776 | 0.470888 | − | 0.882193i | \(-0.343934\pi\) | ||||
0.470888 | + | 0.882193i | \(0.343934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.02349 | 0.693637 | 0.346818 | − | 0.937932i | \(-0.387262\pi\) | ||||
0.346818 | + | 0.937932i | \(0.387262\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.48353 | 0.316289 | ||||||||
\(23\) | −5.45053 | −1.13651 | −0.568257 | − | 0.822851i | \(-0.692382\pi\) | ||||
−0.568257 | + | 0.822851i | \(0.692382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.805240 | −0.157921 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.11672 | 0.400022 | ||||||||
\(29\) | −5.11641 | −0.950094 | −0.475047 | − | 0.879961i | \(-0.657569\pi\) | ||||
−0.475047 | + | 0.879961i | \(0.657569\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.24302 | −1.48049 | −0.740245 | − | 0.672337i | \(-0.765291\pi\) | ||||
−0.740245 | + | 0.672337i | \(0.765291\pi\) | |||||||
\(32\) | 5.69962 | 1.00756 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.49744 | 0.428307 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.59592 | 0.919964 | 0.459982 | − | 0.887928i | \(-0.347856\pi\) | ||||
0.459982 | + | 0.887928i | \(0.347856\pi\) | |||||||
\(38\) | 1.94460 | 0.315456 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.75897 | 1.05557 | 0.527787 | − | 0.849377i | \(-0.323022\pi\) | ||||
0.527787 | + | 0.849377i | \(0.323022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −3.65906 | −0.551624 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.50559 | −0.516871 | ||||||||
\(47\) | −3.52804 | −0.514617 | −0.257309 | − | 0.966329i | \(-0.582836\pi\) | ||||
−0.257309 | + | 0.966329i | \(0.582836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.21953 | −0.745647 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.98609 | 0.275421 | ||||||||
\(53\) | 4.31733 | 0.593032 | 0.296516 | − | 0.955028i | \(-0.404175\pi\) | ||||
0.296516 | + | 0.955028i | \(0.404175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.07780 | 0.411289 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.29069 | −0.432089 | ||||||||
\(59\) | −6.05267 | −0.787991 | −0.393995 | − | 0.919112i | \(-0.628907\pi\) | ||||
−0.393995 | + | 0.919112i | \(0.628907\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0482823 | 0.00618191 | 0.00309095 | − | 0.999995i | \(-0.499016\pi\) | ||||
0.00309095 | + | 0.999995i | \(0.499016\pi\) | |||||||
\(62\) | −5.30162 | −0.673307 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.287490 | 0.0359362 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7760 | 1.31649 | 0.658246 | − | 0.752803i | \(-0.271299\pi\) | ||||
0.658246 | + | 0.752803i | \(0.271299\pi\) | |||||||
\(68\) | −6.15982 | −0.746988 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.57072 | −1.13584 | −0.567918 | − | 0.823085i | \(-0.692251\pi\) | ||||
−0.567918 | + | 0.823085i | \(0.692251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.93217 | −1.04543 | −0.522716 | − | 0.852507i | \(-0.675081\pi\) | ||||
−0.522716 | + | 0.852507i | \(0.675081\pi\) | |||||||
\(74\) | 3.59910 | 0.418387 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.79629 | −0.550172 | ||||||||
\(77\) | −3.07780 | −0.350748 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3473 | 1.16416 | 0.582079 | − | 0.813132i | \(-0.302239\pi\) | ||||
0.582079 | + | 0.813132i | \(0.302239\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.34713 | 0.480060 | ||||||||
\(83\) | 13.3799 | 1.46864 | 0.734319 | − | 0.678805i | \(-0.237502\pi\) | ||||
0.734319 | + | 0.678805i | \(0.237502\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.643165 | 0.0693542 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.32043 | −0.567160 | ||||||||
\(89\) | 8.70358 | 0.922577 | 0.461289 | − | 0.887250i | \(-0.347387\pi\) | ||||
0.461289 | + | 0.887250i | \(0.347387\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.67059 | 0.175126 | ||||||||
\(92\) | 8.64640 | 0.901449 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.26911 | −0.234041 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0546 | 1.63010 | 0.815051 | − | 0.579389i | \(-0.196709\pi\) | ||||
0.815051 | + | 0.579389i | \(0.196709\pi\) | |||||||
\(98\) | −3.35702 | −0.339110 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.4555 | −1.53788 | −0.768942 | − | 0.639318i | \(-0.779217\pi\) | ||||
−0.768942 | + | 0.639318i | \(0.779217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.77773 | 0.569296 | 0.284648 | − | 0.958632i | \(-0.408123\pi\) | ||||
0.284648 | + | 0.958632i | \(0.408123\pi\) | |||||||
\(104\) | 2.88786 | 0.283178 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.77676 | 0.269703 | ||||||||
\(107\) | 9.85293 | 0.952519 | 0.476259 | − | 0.879305i | \(-0.341992\pi\) | ||||
0.476259 | + | 0.879305i | \(0.341992\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.9246 | 1.52530 | 0.762651 | − | 0.646810i | \(-0.223897\pi\) | ||||
0.762651 | + | 0.646810i | \(0.223897\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.25390 | −0.212974 | ||||||||
\(113\) | −5.87866 | −0.553018 | −0.276509 | − | 0.961011i | \(-0.589178\pi\) | ||||
−0.276509 | + | 0.961011i | \(0.589178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.11636 | 0.753585 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.89287 | −0.358367 | ||||||||
\(119\) | −5.18131 | −0.474970 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.67957 | −0.516324 | ||||||||
\(122\) | 0.0310534 | 0.00281145 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.0762 | 1.17428 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.6041 | −1.11843 | −0.559215 | − | 0.829023i | \(-0.688897\pi\) | ||||
−0.559215 | + | 0.829023i | \(0.688897\pi\) | |||||||
\(128\) | −11.2143 | −0.991216 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2030 | 0.891440 | 0.445720 | − | 0.895172i | \(-0.352948\pi\) | ||||
0.445720 | + | 0.895172i | \(0.352948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.03437 | −0.349825 | ||||||||
\(134\) | 6.93071 | 0.598722 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.95665 | −0.768027 | ||||||||
\(137\) | −18.8663 | −1.61185 | −0.805927 | − | 0.592015i | \(-0.798333\pi\) | ||||
−0.805927 | + | 0.592015i | \(0.798333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.6952 | −1.07679 | −0.538397 | − | 0.842692i | \(-0.680970\pi\) | ||||
−0.538397 | + | 0.842692i | \(0.680970\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.15555 | −0.516562 | ||||||||
\(143\) | −2.88786 | −0.241495 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.74486 | −0.475448 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.87703 | −0.729688 | ||||||||
\(149\) | −19.1204 | −1.56640 | −0.783201 | − | 0.621768i | \(-0.786415\pi\) | ||||
−0.783201 | + | 0.621768i | \(0.786415\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.321731 | −0.0261821 | −0.0130910 | − | 0.999914i | \(-0.504167\pi\) | ||||
−0.0130910 | + | 0.999914i | \(0.504167\pi\) | |||||||
\(152\) | −6.97401 | −0.565667 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.97953 | −0.159515 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.59895 | 0.766080 | 0.383040 | − | 0.923732i | \(-0.374877\pi\) | ||||
0.383040 | + | 0.923732i | \(0.374877\pi\) | |||||||
\(158\) | 6.65500 | 0.529443 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.27288 | 0.573183 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.53674 | −0.746976 | −0.373488 | − | 0.927635i | \(-0.621838\pi\) | ||||
−0.373488 | + | 0.927635i | \(0.621838\pi\) | |||||||
\(164\) | −10.7220 | −0.837249 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.60549 | 0.667916 | ||||||||
\(167\) | −9.36567 | −0.724738 | −0.362369 | − | 0.932035i | \(-0.618032\pi\) | ||||
−0.362369 | + | 0.932035i | \(0.618032\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4325 | −0.879423 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.58634 | −0.120957 | ||||||||
\(173\) | −11.0791 | −0.842327 | −0.421164 | − | 0.906985i | \(-0.638378\pi\) | ||||
−0.421164 | + | 0.906985i | \(0.638378\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.89621 | 0.293688 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.59783 | 0.419575 | ||||||||
\(179\) | 17.6771 | 1.32125 | 0.660625 | − | 0.750716i | \(-0.270291\pi\) | ||||
0.660625 | + | 0.750716i | \(0.270291\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.6919 | −0.869050 | −0.434525 | − | 0.900660i | \(-0.643084\pi\) | ||||
−0.434525 | + | 0.900660i | \(0.643084\pi\) | |||||||
\(182\) | 1.07447 | 0.0796447 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.5722 | 0.926838 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.95665 | 0.654975 | ||||||||
\(188\) | 5.59667 | 0.408179 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.5290 | 1.48542 | 0.742712 | − | 0.669611i | \(-0.233539\pi\) | ||||
0.742712 | + | 0.669611i | \(0.233539\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.9974 | −1.07954 | −0.539768 | − | 0.841814i | \(-0.681488\pi\) | ||||
−0.539768 | + | 0.841814i | \(0.681488\pi\) | |||||||
\(194\) | 10.3258 | 0.741348 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.27995 | 0.591425 | ||||||||
\(197\) | 7.33128 | 0.522332 | 0.261166 | − | 0.965294i | \(-0.415893\pi\) | ||||
0.261166 | + | 0.965294i | \(0.415893\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3706 | −0.735154 | −0.367577 | − | 0.929993i | \(-0.619813\pi\) | ||||
−0.367577 | + | 0.929993i | \(0.619813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.94046 | −0.699408 | ||||||||
\(203\) | 6.82704 | 0.479164 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.71603 | 0.258908 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.11481 | −0.146636 | ||||||||
\(209\) | 6.97401 | 0.482402 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.90388 | −0.612968 | −0.306484 | − | 0.951876i | \(-0.599153\pi\) | ||||
−0.306484 | + | 0.951876i | \(0.599153\pi\) | |||||||
\(212\) | −6.84876 | −0.470375 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.33706 | 0.433192 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.9990 | 0.746662 | ||||||||
\(218\) | 10.2422 | 0.693687 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.86156 | −0.327024 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3669 | 0.895115 | 0.447557 | − | 0.894255i | \(-0.352294\pi\) | ||||
0.447557 | + | 0.894255i | \(0.352294\pi\) | |||||||
\(224\) | −7.60524 | −0.508146 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.78095 | −0.251505 | ||||||||
\(227\) | 10.8891 | 0.722737 | 0.361369 | − | 0.932423i | \(-0.382310\pi\) | ||||
0.361369 | + | 0.932423i | \(0.382310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.1384 | −1.33079 | −0.665393 | − | 0.746494i | \(-0.731736\pi\) | ||||
−0.665393 | + | 0.746494i | \(0.731736\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.8015 | 0.774809 | ||||||||
\(233\) | −22.3394 | −1.46350 | −0.731751 | − | 0.681572i | \(-0.761296\pi\) | ||||
−0.731751 | + | 0.681572i | \(0.761296\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.60159 | 0.625010 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.33243 | −0.216010 | ||||||||
\(239\) | −15.0681 | −0.974671 | −0.487336 | − | 0.873215i | \(-0.662031\pi\) | ||||
−0.487336 | + | 0.873215i | \(0.662031\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.3511 | −1.89067 | −0.945335 | − | 0.326102i | \(-0.894265\pi\) | ||||
−0.945335 | + | 0.326102i | \(0.894265\pi\) | |||||||
\(242\) | −3.65290 | −0.234817 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.0765920 | −0.00490330 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.78540 | −0.240859 | ||||||||
\(248\) | 19.0134 | 1.20735 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.31265 | −0.398451 | −0.199225 | − | 0.979954i | \(-0.563843\pi\) | ||||
−0.199225 | + | 0.979954i | \(0.563843\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.5722 | −0.790410 | ||||||||
\(254\) | −8.10649 | −0.508646 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.78764 | −0.486727 | ||||||||
\(257\) | −10.6569 | −0.664762 | −0.332381 | − | 0.943145i | \(-0.607852\pi\) | ||||
−0.332381 | + | 0.943145i | \(0.607852\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.46688 | −0.463969 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.56221 | 0.405414 | ||||||||
\(263\) | −14.0338 | −0.865361 | −0.432680 | − | 0.901547i | \(-0.642432\pi\) | ||||
−0.432680 | + | 0.901547i | \(0.642432\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.59477 | −0.159095 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17.0943 | −1.04420 | ||||||||
\(269\) | −5.62958 | −0.343242 | −0.171621 | − | 0.985163i | \(-0.554900\pi\) | ||||
−0.171621 | + | 0.985163i | \(0.554900\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5540 | −0.944839 | −0.472419 | − | 0.881374i | \(-0.656619\pi\) | ||||
−0.472419 | + | 0.881374i | \(0.656619\pi\) | |||||||
\(272\) | 6.55904 | 0.397700 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.1341 | −0.733049 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.94356 | 0.236946 | 0.118473 | − | 0.992957i | \(-0.462200\pi\) | ||||
0.118473 | + | 0.992957i | \(0.462200\pi\) | |||||||
\(278\) | −8.16511 | −0.489711 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.1731 | 1.32274 | 0.661368 | − | 0.750062i | \(-0.269976\pi\) | ||||
0.661368 | + | 0.750062i | \(0.269976\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.17588 | −0.367118 | −0.183559 | − | 0.983009i | \(-0.558762\pi\) | ||||
−0.183559 | + | 0.983009i | \(0.558762\pi\) | |||||||
\(284\) | 15.1824 | 0.900910 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.85737 | −0.109829 | ||||||||
\(287\) | −9.01878 | −0.532362 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.92198 | −0.113058 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.1695 | 0.829205 | ||||||||
\(293\) | −23.4684 | −1.37104 | −0.685518 | − | 0.728056i | \(-0.740424\pi\) | ||||
−0.685518 | + | 0.728056i | \(0.740424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.9076 | −0.750239 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.2976 | −0.712378 | ||||||||
\(299\) | 6.82405 | 0.394645 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.33434 | −0.0769102 | ||||||||
\(302\) | −0.206926 | −0.0119072 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.10713 | 0.292914 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.19283 | −0.125152 | −0.0625758 | − | 0.998040i | \(-0.519932\pi\) | ||||
−0.0625758 | + | 0.998040i | \(0.519932\pi\) | |||||||
\(308\) | 4.88244 | 0.278203 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.67149 | −0.491715 | −0.245858 | − | 0.969306i | \(-0.579070\pi\) | ||||
−0.245858 | + | 0.969306i | \(0.579070\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.8927 | −1.23745 | −0.618723 | − | 0.785609i | \(-0.712350\pi\) | ||||
−0.618723 | + | 0.785609i | \(0.712350\pi\) | |||||||
\(314\) | 6.17371 | 0.348402 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.4143 | −0.923375 | ||||||||
\(317\) | −16.4418 | −0.923462 | −0.461731 | − | 0.887020i | \(-0.652772\pi\) | ||||
−0.461731 | + | 0.887020i | \(0.652772\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.8015 | −0.660760 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.67766 | 0.260676 | ||||||||
\(323\) | 11.7404 | 0.653251 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.13370 | −0.339714 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.5903 | −0.860830 | ||||||||
\(329\) | 4.70761 | 0.259539 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.831494 | −0.0457030 | −0.0228515 | − | 0.999739i | \(-0.507274\pi\) | ||||
−0.0228515 | + | 0.999739i | \(0.507274\pi\) | |||||||
\(332\) | −21.2251 | −1.16488 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.02367 | −0.329601 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.8853 | 1.02875 | 0.514375 | − | 0.857566i | \(-0.328024\pi\) | ||||
0.514375 | + | 0.857566i | \(0.328024\pi\) | |||||||
\(338\) | −7.35298 | −0.399950 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.0134 | −1.02963 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.3050 | 0.880389 | ||||||||
\(344\) | −2.30661 | −0.124364 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.12568 | −0.383079 | ||||||||
\(347\) | 3.17303 | 0.170337 | 0.0851687 | − | 0.996367i | \(-0.472857\pi\) | ||||
0.0851687 | + | 0.996367i | \(0.472857\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.10505 | −0.487382 | −0.243691 | − | 0.969853i | \(-0.578358\pi\) | ||||
−0.243691 | + | 0.969853i | \(0.578358\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.1468 | 0.700725 | ||||||||
\(353\) | −21.1860 | −1.12762 | −0.563809 | − | 0.825905i | \(-0.690665\pi\) | ||||
−0.563809 | + | 0.825905i | \(0.690665\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −13.8068 | −0.731760 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.3693 | 0.600886 | ||||||||
\(359\) | −33.8868 | −1.78848 | −0.894238 | − | 0.447591i | \(-0.852282\pi\) | ||||
−0.894238 | + | 0.447591i | \(0.852282\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.85849 | −0.518868 | ||||||||
\(362\) | −7.51980 | −0.395232 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.65013 | −0.138904 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.2326 | −1.00393 | −0.501966 | − | 0.864887i | \(-0.667390\pi\) | ||||
−0.501966 | + | 0.864887i | \(0.667390\pi\) | |||||||
\(368\) | −9.20677 | −0.479936 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.76080 | −0.299086 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.8910 | 1.23703 | 0.618516 | − | 0.785772i | \(-0.287734\pi\) | ||||
0.618516 | + | 0.785772i | \(0.287734\pi\) | |||||||
\(374\) | 5.76060 | 0.297874 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.13780 | 0.419675 | ||||||||
\(377\) | 6.40573 | 0.329912 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.6048 | −1.46933 | −0.734666 | − | 0.678429i | \(-0.762661\pi\) | ||||
−0.734666 | + | 0.678429i | \(0.762661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.2035 | 0.675550 | ||||||||
\(383\) | 11.2121 | 0.572910 | 0.286455 | − | 0.958094i | \(-0.407523\pi\) | ||||
0.286455 | + | 0.958094i | \(0.407523\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.64580 | −0.490958 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −25.4681 | −1.29295 | ||||||||
\(389\) | −10.2641 | −0.520410 | −0.260205 | − | 0.965553i | \(-0.583790\pi\) | ||||
−0.260205 | + | 0.965553i | \(0.583790\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.1647 | −1.07034 | ||||||||
\(392\) | 12.0394 | 0.608082 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.71522 | 0.237549 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.52302 | −0.477947 | −0.238973 | − | 0.971026i | \(-0.576811\pi\) | ||||
−0.238973 | + | 0.971026i | \(0.576811\pi\) | |||||||
\(398\) | −6.67002 | −0.334338 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.5099 | 0.724592 | 0.362296 | − | 0.932063i | \(-0.381993\pi\) | ||||
0.362296 | + | 0.932063i | \(0.381993\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.3202 | 0.514088 | ||||||||
\(404\) | 24.5177 | 1.21980 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.39091 | 0.217917 | ||||||||
\(407\) | 12.9076 | 0.639806 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.1375 | −1.09463 | −0.547313 | − | 0.836928i | \(-0.684349\pi\) | ||||
−0.547313 | + | 0.836928i | \(0.684349\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.16544 | −0.451549 | ||||||||
\(413\) | 8.07634 | 0.397411 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.13590 | −0.349866 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.48544 | 0.219390 | ||||||||
\(419\) | −18.0673 | −0.882646 | −0.441323 | − | 0.897348i | \(-0.645491\pi\) | ||||
−0.441323 | + | 0.897348i | \(0.645491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.48989 | 0.170087 | 0.0850435 | − | 0.996377i | \(-0.472897\pi\) | ||||
0.0850435 | + | 0.996377i | \(0.472897\pi\) | |||||||
\(422\) | −5.72666 | −0.278769 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.95839 | −0.483622 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0644250 | −0.00311775 | ||||||||
\(428\) | −15.6301 | −0.755509 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.6312 | 0.560257 | 0.280129 | − | 0.959963i | \(-0.409623\pi\) | ||||
0.280129 | + | 0.959963i | \(0.409623\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.996806 | 0.0479035 | 0.0239517 | − | 0.999713i | \(-0.492375\pi\) | ||||
0.0239517 | + | 0.999713i | \(0.492375\pi\) | |||||||
\(434\) | 7.07418 | 0.339571 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −25.2619 | −1.20982 | ||||||||
\(437\) | −16.4797 | −0.788329 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.98670 | −0.381185 | −0.190592 | − | 0.981669i | \(-0.561041\pi\) | ||||
−0.190592 | + | 0.981669i | \(0.561041\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.12678 | −0.148726 | ||||||||
\(443\) | −3.28658 | −0.156150 | −0.0780750 | − | 0.996947i | \(-0.524877\pi\) | ||||
−0.0780750 | + | 0.996947i | \(0.524877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.59713 | 0.407086 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.383610 | −0.0181239 | ||||||||
\(449\) | 16.0435 | 0.757139 | 0.378570 | − | 0.925573i | \(-0.376416\pi\) | ||||
0.378570 | + | 0.925573i | \(0.376416\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.5903 | 0.734118 | ||||||||
\(452\) | 9.32555 | 0.438637 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.00350 | 0.328691 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.20719 | −0.243582 | −0.121791 | − | 0.992556i | \(-0.538864\pi\) | ||||
−0.121791 | + | 0.992556i | \(0.538864\pi\) | |||||||
\(458\) | −12.9523 | −0.605223 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.8040 | 1.80728 | 0.903641 | − | 0.428290i | \(-0.140884\pi\) | ||||
0.903641 | + | 0.428290i | \(0.140884\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.9251 | −1.71605 | −0.858027 | − | 0.513605i | \(-0.828310\pi\) | ||||
−0.858027 | + | 0.513605i | \(0.828310\pi\) | |||||||
\(464\) | −8.64239 | −0.401213 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.3679 | −0.665580 | ||||||||
\(467\) | 36.5217 | 1.69002 | 0.845011 | − | 0.534749i | \(-0.179594\pi\) | ||||
0.845011 | + | 0.534749i | \(0.179594\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.3788 | −0.663952 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.9611 | 0.642613 | ||||||||
\(473\) | 2.30661 | 0.106058 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.21931 | 0.376732 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.69124 | −0.443267 | ||||||||
\(479\) | 5.12380 | 0.234113 | 0.117056 | − | 0.993125i | \(-0.462654\pi\) | ||||
0.117056 | + | 0.993125i | \(0.462654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.00608 | −0.319450 | ||||||||
\(482\) | −18.8776 | −0.859850 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.00972 | 0.409533 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.9905 | 0.498029 | 0.249014 | − | 0.968500i | \(-0.419893\pi\) | ||||
0.249014 | + | 0.968500i | \(0.419893\pi\) | |||||||
\(488\) | −0.111368 | −0.00504140 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.5018 | −1.24114 | −0.620568 | − | 0.784152i | \(-0.713098\pi\) | ||||
−0.620568 | + | 0.784152i | \(0.713098\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.8672 | −0.894776 | ||||||||
\(494\) | −2.43464 | −0.109540 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.9237 | −0.625193 | ||||||||
\(497\) | 12.7706 | 0.572841 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.8799 | 0.621348 | 0.310674 | − | 0.950517i | \(-0.399445\pi\) | ||||
0.310674 | + | 0.950517i | \(0.399445\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.06007 | −0.181210 | ||||||||
\(503\) | 32.2039 | 1.43590 | 0.717951 | − | 0.696094i | \(-0.245080\pi\) | ||||
0.717951 | + | 0.696094i | \(0.245080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.08602 | −0.359467 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.9943 | 0.887104 | ||||||||
\(509\) | 30.1266 | 1.33534 | 0.667668 | − | 0.744459i | \(-0.267293\pi\) | ||||
0.667668 | + | 0.744459i | \(0.267293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9186 | 0.527247 | ||||||||
\(512\) | 17.4199 | 0.769859 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.85417 | −0.302324 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.13780 | −0.357900 | ||||||||
\(518\) | −4.80243 | −0.211007 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.1821 | 0.665141 | 0.332570 | − | 0.943078i | \(-0.392084\pi\) | ||||
0.332570 | + | 0.943078i | \(0.392084\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.1021 | 1.62236 | 0.811180 | − | 0.584797i | \(-0.198826\pi\) | ||||
0.811180 | + | 0.584797i | \(0.198826\pi\) | |||||||
\(524\) | −16.1854 | −0.707063 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.02604 | −0.393554 | ||||||||
\(527\) | −32.0080 | −1.39429 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.70832 | 0.291666 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.39989 | 0.277470 | ||||||||
\(533\) | −8.46221 | −0.366539 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −24.8559 | −1.07361 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.62075 | −0.156101 | ||||||||
\(539\) | −12.0394 | −0.518574 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.0878 | −0.562687 | −0.281344 | − | 0.959607i | \(-0.590780\pi\) | ||||
−0.281344 | + | 0.959607i | \(0.590780\pi\) | |||||||
\(542\) | −10.0038 | −0.429699 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.1319 | 0.948895 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.7783 | 1.27323 | 0.636614 | − | 0.771183i | \(-0.280334\pi\) | ||||
0.636614 | + | 0.771183i | \(0.280334\pi\) | |||||||
\(548\) | 29.9283 | 1.27847 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.4694 | −0.659020 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.8068 | −0.587125 | ||||||||
\(554\) | 2.53636 | 0.107760 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.1389 | 0.854080 | ||||||||
\(557\) | 31.3627 | 1.32888 | 0.664440 | − | 0.747341i | \(-0.268670\pi\) | ||||
0.664440 | + | 0.747341i | \(0.268670\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.25200 | −0.0529538 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.2609 | 0.601562 | ||||||||
\(563\) | −20.2672 | −0.854159 | −0.427079 | − | 0.904214i | \(-0.640457\pi\) | ||||
−0.427079 | + | 0.904214i | \(0.640457\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.97211 | −0.166960 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22.0759 | 0.926284 | ||||||||
\(569\) | −26.9433 | −1.12952 | −0.564761 | − | 0.825254i | \(-0.691032\pi\) | ||||
−0.564761 | + | 0.825254i | \(0.691032\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.0542 | −0.881089 | −0.440545 | − | 0.897731i | \(-0.645215\pi\) | ||||
−0.440545 | + | 0.897731i | \(0.645215\pi\) | |||||||
\(572\) | 4.58113 | 0.191547 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.80056 | −0.242111 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.3849 | −1.63961 | −0.819807 | − | 0.572639i | \(-0.805920\pi\) | ||||
−0.819807 | + | 0.572639i | \(0.805920\pi\) | |||||||
\(578\) | −1.23615 | −0.0514170 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.8534 | −0.740684 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.95839 | 0.412435 | ||||||||
\(584\) | 20.6030 | 0.852559 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.0940 | −0.623528 | ||||||||
\(587\) | 43.9502 | 1.81402 | 0.907010 | − | 0.421109i | \(-0.138359\pi\) | ||||
0.907010 | + | 0.421109i | \(0.138359\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.9227 | −1.02692 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.45236 | 0.388490 | ||||||||
\(593\) | 37.1270 | 1.52462 | 0.762312 | − | 0.647210i | \(-0.224064\pi\) | ||||
0.762312 | + | 0.647210i | \(0.224064\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 30.3314 | 1.24242 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.38899 | 0.179479 | ||||||||
\(599\) | −14.3002 | −0.584292 | −0.292146 | − | 0.956374i | \(-0.594369\pi\) | ||||
−0.292146 | + | 0.956374i | \(0.594369\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.3855 | −1.32103 | −0.660515 | − | 0.750812i | \(-0.729662\pi\) | ||||
−0.660515 | + | 0.750812i | \(0.729662\pi\) | |||||||
\(602\) | −0.858202 | −0.0349777 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.510374 | 0.0207668 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.6944 | −0.637017 | −0.318509 | − | 0.947920i | \(-0.603182\pi\) | ||||
−0.318509 | + | 0.947920i | \(0.603182\pi\) | |||||||
\(608\) | 17.2327 | 0.698880 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.41709 | 0.178696 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.07911 | 0.164754 | 0.0823769 | − | 0.996601i | \(-0.473749\pi\) | ||||
0.0823769 | + | 0.996601i | \(0.473749\pi\) | |||||||
\(614\) | −1.41035 | −0.0569172 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.09928 | 0.286038 | ||||||||
\(617\) | 24.4536 | 0.984465 | 0.492232 | − | 0.870464i | \(-0.336181\pi\) | ||||
0.492232 | + | 0.870464i | \(0.336181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.5505 | 1.02696 | 0.513480 | − | 0.858101i | \(-0.328356\pi\) | ||||
0.513480 | + | 0.858101i | \(0.328356\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.57720 | −0.223625 | ||||||||
\(623\) | −11.6135 | −0.465287 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.0806 | −0.562774 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.2272 | −0.607631 | ||||||||
\(629\) | 21.7292 | 0.866400 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −48.8985 | −1.94662 | −0.973309 | − | 0.229499i | \(-0.926291\pi\) | ||||
−0.973309 | + | 0.229499i | \(0.926291\pi\) | |||||||
\(632\) | −23.8671 | −0.949381 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.5748 | −0.419978 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.53484 | 0.258920 | ||||||||
\(638\) | −7.59034 | −0.300504 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.53179 | 0.218492 | 0.109246 | − | 0.994015i | \(-0.465156\pi\) | ||||
0.109246 | + | 0.994015i | \(0.465156\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1529 | −0.400389 | −0.200195 | − | 0.979756i | \(-0.564157\pi\) | ||||
−0.200195 | + | 0.979756i | \(0.564157\pi\) | |||||||
\(644\) | −11.5373 | −0.454631 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.55098 | 0.297089 | ||||||||
\(647\) | 21.6339 | 0.850516 | 0.425258 | − | 0.905072i | \(-0.360183\pi\) | ||||
0.425258 | + | 0.905072i | \(0.360183\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.9611 | −0.548023 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.1285 | 0.592478 | ||||||||
\(653\) | 38.5870 | 1.51003 | 0.755013 | − | 0.655710i | \(-0.227630\pi\) | ||||
0.755013 | + | 0.655710i | \(0.227630\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.4169 | 0.445756 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.02777 | 0.118035 | ||||||||
\(659\) | 2.07264 | 0.0807384 | 0.0403692 | − | 0.999185i | \(-0.487147\pi\) | ||||
0.0403692 | + | 0.999185i | \(0.487147\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.02218 | 0.0397582 | 0.0198791 | − | 0.999802i | \(-0.493672\pi\) | ||||
0.0198791 | + | 0.999802i | \(0.493672\pi\) | |||||||
\(662\) | −0.534787 | −0.0207851 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −30.8622 | −1.19769 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.8872 | 1.07980 | ||||||||
\(668\) | 14.8571 | 0.574840 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.111368 | 0.00429932 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.89719 | −0.150226 | −0.0751128 | − | 0.997175i | \(-0.523932\pi\) | ||||
−0.0751128 | + | 0.997175i | \(0.523932\pi\) | |||||||
\(674\) | 12.1464 | 0.467861 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.1358 | 0.697532 | ||||||||
\(677\) | −32.8769 | −1.26356 | −0.631781 | − | 0.775147i | \(-0.717676\pi\) | ||||
−0.631781 | + | 0.775147i | \(0.717676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.4224 | −0.822116 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.2288 | −0.468263 | ||||||||
\(683\) | −2.95808 | −0.113188 | −0.0565939 | − | 0.998397i | \(-0.518024\pi\) | ||||
−0.0565939 | + | 0.998397i | \(0.518024\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.4868 | 0.400389 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.68915 | 0.0643983 | ||||||||
\(689\) | −5.40529 | −0.205925 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.9757 | −0.493618 | −0.246809 | − | 0.969064i | \(-0.579382\pi\) | ||||
−0.246809 | + | 0.969064i | \(0.579382\pi\) | |||||||
\(692\) | 17.5752 | 0.668108 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.04078 | 0.0774671 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.2454 | 0.994115 | ||||||||
\(698\) | −5.85604 | −0.221655 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.2621 | 1.36960 | 0.684801 | − | 0.728731i | \(-0.259889\pi\) | ||||
0.684801 | + | 0.728731i | \(0.259889\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9192 | 0.638121 | ||||||||
\(704\) | 0.663126 | 0.0249925 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.6261 | −0.512825 | ||||||||
\(707\) | 20.6230 | 0.775607 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.1008 | −0.905126 | −0.452563 | − | 0.891732i | \(-0.649490\pi\) | ||||
−0.452563 | + | 0.891732i | \(0.649490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20.0757 | −0.752370 | ||||||||
\(713\) | 44.9289 | 1.68260 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −28.0419 | −1.04797 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.7948 | −0.813374 | ||||||||
\(719\) | −29.8002 | −1.11136 | −0.555681 | − | 0.831396i | \(-0.687542\pi\) | ||||
−0.555681 | + | 0.831396i | \(0.687542\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.70947 | −0.287115 | ||||||||
\(722\) | −6.34063 | −0.235974 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.5473 | 0.689304 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.8763 | −0.922611 | −0.461306 | − | 0.887241i | \(-0.652619\pi\) | ||||
−0.461306 | + | 0.887241i | \(0.652619\pi\) | |||||||
\(728\) | −3.85340 | −0.142816 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.88304 | 0.143620 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.6472 | −0.873430 | −0.436715 | − | 0.899600i | \(-0.643858\pi\) | ||||
−0.436715 | + | 0.899600i | \(0.643858\pi\) | |||||||
\(734\) | −12.3697 | −0.456575 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −31.0659 | −1.14511 | ||||||||
\(737\) | 24.8559 | 0.915578 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.3165 | 1.29914 | 0.649569 | − | 0.760302i | \(-0.274949\pi\) | ||||
0.649569 | + | 0.760302i | \(0.274949\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.70514 | −0.136020 | ||||||||
\(743\) | 27.9426 | 1.02511 | 0.512556 | − | 0.858654i | \(-0.328699\pi\) | ||||
0.512556 | + | 0.858654i | \(0.328699\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.3659 | 0.562585 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.2083 | −0.519507 | ||||||||
\(749\) | −13.1472 | −0.480387 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7598 | 0.429121 | 0.214561 | − | 0.976711i | \(-0.431168\pi\) | ||||
0.214561 | + | 0.976711i | \(0.431168\pi\) | |||||||
\(752\) | −5.95939 | −0.217317 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.11994 | 0.150039 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.4192 | −0.814839 | −0.407420 | − | 0.913241i | \(-0.633571\pi\) | ||||
−0.407420 | + | 0.913241i | \(0.633571\pi\) | |||||||
\(758\) | −18.3976 | −0.668232 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.9155 | 1.15694 | 0.578469 | − | 0.815704i | \(-0.303650\pi\) | ||||
0.578469 | + | 0.815704i | \(0.303650\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.2489 | −0.769262 | ||||||||
\(764\) | −32.5659 | −1.17819 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.21121 | 0.260552 | ||||||||
\(767\) | 7.57793 | 0.273623 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.5867 | −1.35541 | −0.677706 | − | 0.735333i | \(-0.737026\pi\) | ||||
−0.677706 | + | 0.735333i | \(0.737026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.7910 | 0.856256 | ||||||||
\(773\) | 11.3390 | 0.407836 | 0.203918 | − | 0.978988i | \(-0.434632\pi\) | ||||
0.203918 | + | 0.978988i | \(0.434632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −37.0318 | −1.32936 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.60150 | −0.236675 | ||||||||
\(779\) | 20.4357 | 0.732185 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.0759 | −0.789937 | ||||||||
\(782\) | −13.6124 | −0.486777 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.81657 | −0.314878 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7368 | 0.454017 | 0.227008 | − | 0.973893i | \(-0.427106\pi\) | ||||
0.227008 | + | 0.973893i | \(0.427106\pi\) | |||||||
\(788\) | −11.6299 | −0.414298 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.84415 | 0.278906 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0604492 | −0.00214662 | ||||||||
\(794\) | −6.12487 | −0.217363 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.4513 | 0.583102 | ||||||||
\(797\) | −7.51825 | −0.266310 | −0.133155 | − | 0.991095i | \(-0.542511\pi\) | ||||
−0.133155 | + | 0.991095i | \(0.542511\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.6995 | −0.484654 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.33229 | 0.329534 | ||||||||
\(803\) | −20.6030 | −0.727065 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.63761 | 0.233800 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 35.6499 | 1.25416 | ||||||||
\(809\) | 10.3706 | 0.364611 | 0.182306 | − | 0.983242i | \(-0.441644\pi\) | ||||
0.182306 | + | 0.983242i | \(0.441644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.8669 | −0.557163 | −0.278582 | − | 0.960413i | \(-0.589864\pi\) | ||||
−0.278582 | + | 0.960413i | \(0.589864\pi\) | |||||||
\(812\) | −10.8300 | −0.380059 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.30171 | 0.290975 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.02349 | 0.105779 | ||||||||
\(818\) | −14.2380 | −0.497821 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.7878 | −1.42350 | −0.711752 | − | 0.702431i | \(-0.752098\pi\) | ||||
−0.711752 | + | 0.702431i | \(0.752098\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.33164 | 0.290423 | 0.145211 | − | 0.989401i | \(-0.453614\pi\) | ||||
0.145211 | + | 0.989401i | \(0.453614\pi\) | |||||||
\(824\) | −13.3269 | −0.464266 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.19441 | 0.180737 | ||||||||
\(827\) | −23.5733 | −0.819725 | −0.409862 | − | 0.912147i | \(-0.634423\pi\) | ||||
−0.409862 | + | 0.912147i | \(0.634423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.2563 | −0.599337 | −0.299668 | − | 0.954043i | \(-0.596876\pi\) | ||||
−0.299668 | + | 0.954043i | \(0.596876\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.359936 | −0.0124786 | ||||||||
\(833\) | −20.2677 | −0.702233 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11.0631 | −0.382627 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.6203 | −0.401415 | ||||||||
\(839\) | 51.0992 | 1.76414 | 0.882070 | − | 0.471118i | \(-0.156149\pi\) | ||||
0.882070 | + | 0.471118i | \(0.156149\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.82234 | −0.0973221 | ||||||||
\(842\) | 2.24458 | 0.0773532 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.1246 | 0.486188 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.57848 | 0.260400 | ||||||||
\(848\) | 7.29263 | 0.250430 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.5008 | −1.04555 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.5197 | 1.55857 | 0.779283 | − | 0.626672i | \(-0.215584\pi\) | ||||
0.779283 | + | 0.626672i | \(0.215584\pi\) | |||||||
\(854\) | −0.0414359 | −0.00141791 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.7268 | −0.776787 | ||||||||
\(857\) | −13.4209 | −0.458448 | −0.229224 | − | 0.973374i | \(-0.573619\pi\) | ||||
−0.229224 | + | 0.973374i | \(0.573619\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.29696 | −0.146610 | −0.0733051 | − | 0.997310i | \(-0.523355\pi\) | ||||
−0.0733051 | + | 0.997310i | \(0.523355\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.48080 | 0.254797 | ||||||||
\(863\) | −41.5929 | −1.41584 | −0.707920 | − | 0.706293i | \(-0.750366\pi\) | ||||
−0.707920 | + | 0.706293i | \(0.750366\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.641111 | 0.0217858 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −17.4482 | −0.592229 | ||||||||
\(869\) | 23.8671 | 0.809635 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.4915 | −0.457141 | ||||||||
\(872\) | −36.7319 | −1.24390 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.5991 | −0.358521 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.9754 | 1.11350 | 0.556751 | − | 0.830680i | \(-0.312048\pi\) | ||||
0.556751 | + | 0.830680i | \(0.312048\pi\) | |||||||
\(878\) | −5.13677 | −0.173357 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.2769 | 1.05375 | 0.526873 | − | 0.849944i | \(-0.323364\pi\) | ||||
0.526873 | + | 0.849944i | \(0.323364\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.2793 | 1.11994 | 0.559969 | − | 0.828513i | \(-0.310813\pi\) | ||||
0.559969 | + | 0.828513i | \(0.310813\pi\) | |||||||
\(884\) | 7.71208 | 0.259385 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.11381 | −0.0710149 | ||||||||
\(887\) | −25.8681 | −0.868567 | −0.434283 | − | 0.900776i | \(-0.642998\pi\) | ||||
−0.434283 | + | 0.900776i | \(0.642998\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.8181 | 0.564062 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21.2045 | −0.709978 | ||||||||
\(893\) | −10.6670 | −0.356958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 14.9638 | 0.499904 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.3186 | 0.344336 | ||||||||
\(899\) | 42.1747 | 1.40660 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.7644 | 0.558503 | ||||||||
\(902\) | 10.0271 | 0.333867 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.5598 | 0.450991 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.2479 | −1.46923 | −0.734613 | − | 0.678486i | \(-0.762636\pi\) | ||||
−0.734613 | + | 0.678486i | \(0.762636\pi\) | |||||||
\(908\) | −17.2739 | −0.573253 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.8278 | 0.855715 | 0.427857 | − | 0.903846i | \(-0.359269\pi\) | ||||
0.427857 | + | 0.903846i | \(0.359269\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.8622 | 1.02139 | ||||||||
\(914\) | −3.34908 | −0.110778 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 31.9464 | 1.05554 | ||||||||
\(917\) | −13.6143 | −0.449583 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.5667 | −1.40415 | −0.702073 | − | 0.712105i | \(-0.747742\pi\) | ||||
−0.702073 | + | 0.712105i | \(0.747742\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.9574 | 0.821927 | ||||||||
\(923\) | 11.9825 | 0.394409 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23.7489 | −0.780437 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.1616 | −0.957275 | ||||||||
\(929\) | −36.7900 | −1.20704 | −0.603520 | − | 0.797348i | \(-0.706236\pi\) | ||||
−0.603520 | + | 0.797348i | \(0.706236\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.7812 | −0.517208 | ||||||||
\(932\) | 35.4378 | 1.16080 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.4895 | 0.768599 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.0303 | −0.752368 | −0.376184 | − | 0.926545i | \(-0.622764\pi\) | ||||
−0.376184 | + | 0.926545i | \(0.622764\pi\) | |||||||
\(938\) | −9.24794 | −0.301956 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.13277 | −0.297720 | −0.148860 | − | 0.988858i | \(-0.547560\pi\) | ||||
−0.148860 | + | 0.988858i | \(0.547560\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.8400 | −1.19968 | ||||||||
\(944\) | −10.2239 | −0.332759 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.48353 | 0.0482337 | ||||||||
\(947\) | −37.2639 | −1.21091 | −0.605457 | − | 0.795878i | \(-0.707010\pi\) | ||||
−0.605457 | + | 0.795878i | \(0.707010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.1831 | 0.363017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.9512 | 0.387342 | ||||||||
\(953\) | 39.7614 | 1.28800 | 0.643999 | − | 0.765026i | \(-0.277274\pi\) | ||||
0.643999 | + | 0.765026i | \(0.277274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 23.9030 | 0.773080 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.29545 | 0.106471 | ||||||||
\(959\) | 25.1741 | 0.812913 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.9474 | 1.19185 | ||||||||
\(962\) | −4.50606 | −0.145281 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 46.5608 | 1.49962 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.01815 | 0.0648993 | 0.0324497 | − | 0.999473i | \(-0.489669\pi\) | ||||
0.0324497 | + | 0.999473i | \(0.489669\pi\) | |||||||
\(968\) | 13.1005 | 0.421067 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.09972 | 0.163658 | 0.0818289 | − | 0.996646i | \(-0.473924\pi\) | ||||
0.0818289 | + | 0.996646i | \(0.473924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.9397 | 0.543063 | ||||||||
\(974\) | 7.06872 | 0.226496 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.0815560 | 0.00261054 | ||||||||
\(977\) | 5.90918 | 0.189051 | 0.0945257 | − | 0.995522i | \(-0.469867\pi\) | ||||
0.0945257 | + | 0.995522i | \(0.469867\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0757 | 0.641623 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.6882 | −0.564452 | ||||||||
\(983\) | −9.96798 | −0.317929 | −0.158965 | − | 0.987284i | \(-0.550816\pi\) | ||||
−0.158965 | + | 0.987284i | \(0.550816\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.7779 | −0.406931 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.00493 | 0.191042 | ||||||||
\(989\) | −5.45053 | −0.173317 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.26844 | −0.0402933 | −0.0201467 | − | 0.999797i | \(-0.506413\pi\) | ||||
−0.0201467 | + | 0.999797i | \(0.506413\pi\) | |||||||
\(992\) | −46.9821 | −1.49168 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.21361 | 0.260520 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.0616 | 0.635358 | 0.317679 | − | 0.948198i | \(-0.397096\pi\) | ||||
0.317679 | + | 0.948198i | \(0.397096\pi\) | |||||||
\(998\) | 8.92703 | 0.282580 | ||||||||
\(999\) | 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 | 9675.2.a.cv.1.6 | yes | 10 | |
3.2 | odd | 2 | inner | 9675.2.a.cv.1.5 | ✓ | 10 | |
5.4 | even | 2 | 9675.2.a.cw.1.5 | yes | 10 | ||
15.14 | odd | 2 | 9675.2.a.cw.1.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9675.2.a.cv.1.5 | ✓ | 10 | 3.2 | odd | 2 | inner | |
9675.2.a.cv.1.6 | yes | 10 | 1.1 | even | 1 | trivial | |
9675.2.a.cw.1.5 | yes | 10 | 5.4 | even | 2 | ||
9675.2.a.cw.1.6 | yes | 10 | 15.14 | odd | 2 |