Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [243,2,Mod(1,243)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(243, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("243.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 243 = 3^{5} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 243.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: | \(1.94036476912\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
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 | 1.1 | ||
Root | \(-1.53209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 243.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53209 | −1.79046 | −0.895229 | − | 0.445607i | \(-0.852988\pi\) | ||||
−0.895229 | + | 0.445607i | \(0.852988\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.41147 | 2.20574 | ||||||||
\(5\) | −0.467911 | −0.209256 | −0.104628 | − | 0.994511i | \(-0.533365\pi\) | ||||
−0.104628 | + | 0.994511i | \(0.533365\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.22668 | −1.21957 | −0.609786 | − | 0.792566i | \(-0.708744\pi\) | ||||
−0.609786 | + | 0.792566i | \(0.708744\pi\) | |||||||
\(8\) | −6.10607 | −2.15882 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.18479 | 0.374664 | ||||||||
\(11\) | 3.10607 | 0.936514 | 0.468257 | − | 0.883592i | \(-0.344882\pi\) | ||||
0.468257 | + | 0.883592i | \(0.344882\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.18479 | −0.605952 | −0.302976 | − | 0.952998i | \(-0.597980\pi\) | ||||
−0.302976 | + | 0.952998i | \(0.597980\pi\) | |||||||
\(14\) | 8.17024 | 2.18359 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.63816 | 1.65954 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0418891 | 0.00961001 | 0.00480501 | − | 0.999988i | \(-0.498471\pi\) | ||||
0.00480501 | + | 0.999988i | \(0.498471\pi\) | |||||||
\(20\) | −2.06418 | −0.461564 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.86484 | −1.67679 | ||||||||
\(23\) | −6.10607 | −1.27320 | −0.636601 | − | 0.771193i | \(-0.719660\pi\) | ||||
−0.636601 | + | 0.771193i | \(0.719660\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.78106 | −0.956212 | ||||||||
\(26\) | 5.53209 | 1.08493 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −14.2344 | −2.69005 | ||||||||
\(29\) | −6.57398 | −1.22076 | −0.610379 | − | 0.792110i | \(-0.708983\pi\) | ||||
−0.610379 | + | 0.792110i | \(0.708983\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.22668 | −1.11835 | −0.559173 | − | 0.829051i | \(-0.688881\pi\) | ||||
−0.559173 | + | 0.829051i | \(0.688881\pi\) | |||||||
\(32\) | −4.59627 | −0.812513 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.59627 | 1.30275 | ||||||||
\(35\) | 1.50980 | 0.255203 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.59627 | 0.591223 | 0.295611 | − | 0.955308i | \(-0.404477\pi\) | ||||
0.295611 | + | 0.955308i | \(0.404477\pi\) | |||||||
\(38\) | −0.106067 | −0.0172063 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.85710 | 0.451747 | ||||||||
\(41\) | −7.70233 | −1.20290 | −0.601451 | − | 0.798910i | \(-0.705411\pi\) | ||||
−0.601451 | + | 0.798910i | \(0.705411\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.588526 | −0.0897494 | −0.0448747 | − | 0.998993i | \(-0.514289\pi\) | ||||
−0.0448747 | + | 0.998993i | \(0.514289\pi\) | |||||||
\(44\) | 13.7023 | 2.06570 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15.4611 | 2.27962 | ||||||||
\(47\) | 9.66044 | 1.40912 | 0.704560 | − | 0.709644i | \(-0.251144\pi\) | ||||
0.704560 | + | 0.709644i | \(0.251144\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.41147 | 0.487353 | ||||||||
\(50\) | 12.1061 | 1.71206 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.63816 | −1.33657 | ||||||||
\(53\) | −4.95811 | −0.681049 | −0.340524 | − | 0.940236i | \(-0.610605\pi\) | ||||
−0.340524 | + | 0.940236i | \(0.610605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.45336 | −0.195971 | ||||||||
\(56\) | 19.7023 | 2.63284 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 16.6459 | 2.18571 | ||||||||
\(59\) | 8.53209 | 1.11078 | 0.555392 | − | 0.831589i | \(-0.312568\pi\) | ||||
0.555392 | + | 0.831589i | \(0.312568\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.26857 | −0.162424 | −0.0812119 | − | 0.996697i | \(-0.525879\pi\) | ||||
−0.0812119 | + | 0.996697i | \(0.525879\pi\) | |||||||
\(62\) | 15.7665 | 2.00235 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.63816 | −0.204769 | ||||||||
\(65\) | 1.02229 | 0.126799 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0077 | 1.22264 | 0.611320 | − | 0.791383i | \(-0.290639\pi\) | ||||
0.611320 | + | 0.791383i | \(0.290639\pi\) | |||||||
\(68\) | −13.2344 | −1.60491 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.82295 | −0.456930 | ||||||||
\(71\) | −11.8307 | −1.40404 | −0.702022 | − | 0.712155i | \(-0.747719\pi\) | ||||
−0.702022 | + | 0.712155i | \(0.747719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.23442 | −0.963766 | −0.481883 | − | 0.876236i | \(-0.660047\pi\) | ||||
−0.481883 | + | 0.876236i | \(0.660047\pi\) | |||||||
\(74\) | −9.10607 | −1.05856 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.184793 | 0.0211972 | ||||||||
\(77\) | −10.0223 | −1.14215 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0496 | 1.24318 | 0.621590 | − | 0.783343i | \(-0.286487\pi\) | ||||
0.621590 | + | 0.783343i | \(0.286487\pi\) | |||||||
\(80\) | −3.10607 | −0.347269 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 19.5030 | 2.15375 | ||||||||
\(83\) | 1.50980 | 0.165722 | 0.0828610 | − | 0.996561i | \(-0.473594\pi\) | ||||
0.0828610 | + | 0.996561i | \(0.473594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.40373 | 0.152256 | ||||||||
\(86\) | 1.49020 | 0.160692 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −18.9659 | −2.02177 | ||||||||
\(89\) | 15.8726 | 1.68249 | 0.841245 | − | 0.540654i | \(-0.181823\pi\) | ||||
0.841245 | + | 0.540654i | \(0.181823\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.04963 | 0.739002 | ||||||||
\(92\) | −26.9368 | −2.80835 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −24.4611 | −2.52297 | ||||||||
\(95\) | −0.0196004 | −0.00201095 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.6459 | 1.89320 | 0.946602 | − | 0.322405i | \(-0.104491\pi\) | ||||
0.946602 | + | 0.322405i | \(0.104491\pi\) | |||||||
\(98\) | −8.63816 | −0.872585 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −21.0915 | −2.10915 | ||||||||
\(101\) | −9.08647 | −0.904137 | −0.452069 | − | 0.891983i | \(-0.649314\pi\) | ||||
−0.452069 | + | 0.891983i | \(0.649314\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.260830 | 0.0257003 | 0.0128502 | − | 0.999917i | \(-0.495910\pi\) | ||||
0.0128502 | + | 0.999917i | \(0.495910\pi\) | |||||||
\(104\) | 13.3405 | 1.30814 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.5544 | 1.21939 | ||||||||
\(107\) | −4.04189 | −0.390744 | −0.195372 | − | 0.980729i | \(-0.562591\pi\) | ||||
−0.195372 | + | 0.980729i | \(0.562591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.40373 | −0.517584 | −0.258792 | − | 0.965933i | \(-0.583324\pi\) | ||||
−0.258792 | + | 0.965933i | \(0.583324\pi\) | |||||||
\(110\) | 3.68004 | 0.350879 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −21.4192 | −2.02393 | ||||||||
\(113\) | −1.38413 | −0.130208 | −0.0651041 | − | 0.997878i | \(-0.520738\pi\) | ||||
−0.0651041 | + | 0.997878i | \(0.520738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.85710 | 0.266426 | ||||||||
\(116\) | −29.0009 | −2.69267 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −21.6040 | −1.98881 | ||||||||
\(119\) | 9.68004 | 0.887368 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.35235 | −0.122941 | ||||||||
\(122\) | 3.21213 | 0.290813 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −27.4688 | −2.46678 | ||||||||
\(125\) | 4.57667 | 0.409349 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.63816 | −0.589041 | −0.294521 | − | 0.955645i | \(-0.595160\pi\) | ||||
−0.294521 | + | 0.955645i | \(0.595160\pi\) | |||||||
\(128\) | 13.3405 | 1.17914 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.58853 | −0.227029 | ||||||||
\(131\) | 12.6408 | 1.10444 | 0.552218 | − | 0.833700i | \(-0.313782\pi\) | ||||
0.552218 | + | 0.833700i | \(0.313782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.135163 | −0.0117201 | ||||||||
\(134\) | −25.3405 | −2.18908 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 18.3182 | 1.57077 | ||||||||
\(137\) | −10.6159 | −0.906975 | −0.453487 | − | 0.891263i | \(-0.649820\pi\) | ||||
−0.453487 | + | 0.891263i | \(0.649820\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.46110 | −0.632843 | −0.316421 | − | 0.948619i | \(-0.602481\pi\) | ||||
−0.316421 | + | 0.948619i | \(0.602481\pi\) | |||||||
\(140\) | 6.66044 | 0.562910 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 29.9564 | 2.51388 | ||||||||
\(143\) | −6.78611 | −0.567483 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.07604 | 0.255451 | ||||||||
\(146\) | 20.8503 | 1.72558 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.8648 | 1.30408 | ||||||||
\(149\) | 4.25402 | 0.348503 | 0.174252 | − | 0.984701i | \(-0.444249\pi\) | ||||
0.174252 | + | 0.984701i | \(0.444249\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.135163 | 0.0109994 | 0.00549969 | − | 0.999985i | \(-0.498249\pi\) | ||||
0.00549969 | + | 0.999985i | \(0.498249\pi\) | |||||||
\(152\) | −0.255777 | −0.0207463 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 25.3773 | 2.04496 | ||||||||
\(155\) | 2.91353 | 0.234021 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.3259 | 1.06353 | 0.531763 | − | 0.846893i | \(-0.321530\pi\) | ||||
0.531763 | + | 0.846893i | \(0.321530\pi\) | |||||||
\(158\) | −27.9786 | −2.22586 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.15064 | 0.170023 | ||||||||
\(161\) | 19.7023 | 1.55276 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.76382 | −0.764762 | −0.382381 | − | 0.924005i | \(-0.624896\pi\) | ||||
−0.382381 | + | 0.924005i | \(0.624896\pi\) | |||||||
\(164\) | −33.9786 | −2.65329 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.82295 | −0.296718 | ||||||||
\(167\) | 3.57398 | 0.276563 | 0.138281 | − | 0.990393i | \(-0.455842\pi\) | ||||
0.138281 | + | 0.990393i | \(0.455842\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.22668 | −0.632822 | ||||||||
\(170\) | −3.55438 | −0.272608 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.59627 | −0.197963 | ||||||||
\(173\) | −18.7665 | −1.42679 | −0.713396 | − | 0.700761i | \(-0.752844\pi\) | ||||
−0.713396 | + | 0.700761i | \(0.752844\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.4270 | 1.16617 | ||||||||
\(176\) | 20.6186 | 1.55418 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −40.1908 | −3.01243 | ||||||||
\(179\) | 5.08378 | 0.379979 | 0.189990 | − | 0.981786i | \(-0.439155\pi\) | ||||
0.189990 | + | 0.981786i | \(0.439155\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.15064 | 0.531503 | 0.265752 | − | 0.964042i | \(-0.414380\pi\) | ||||
0.265752 | + | 0.964042i | \(0.414380\pi\) | |||||||
\(182\) | −17.8503 | −1.32315 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 37.2841 | 2.74862 | ||||||||
\(185\) | −1.68273 | −0.123717 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.31820 | −0.681414 | ||||||||
\(188\) | 42.6168 | 3.10815 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0496299 | 0.00360053 | ||||||||
\(191\) | 10.5098 | 0.760462 | 0.380231 | − | 0.924891i | \(-0.375844\pi\) | ||||
0.380231 | + | 0.924891i | \(0.375844\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.1429 | −0.730102 | −0.365051 | − | 0.930987i | \(-0.618948\pi\) | ||||
−0.365051 | + | 0.930987i | \(0.618948\pi\) | |||||||
\(194\) | −47.2131 | −3.38970 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.0496 | 1.07497 | ||||||||
\(197\) | −14.0838 | −1.00343 | −0.501714 | − | 0.865034i | \(-0.667297\pi\) | ||||
−0.501714 | + | 0.865034i | \(0.667297\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.2763 | 0.728468 | 0.364234 | − | 0.931307i | \(-0.381331\pi\) | ||||
0.364234 | + | 0.931307i | \(0.381331\pi\) | |||||||
\(200\) | 29.1935 | 2.06429 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 23.0077 | 1.61882 | ||||||||
\(203\) | 21.2121 | 1.48880 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.60401 | 0.251715 | ||||||||
\(206\) | −0.660444 | −0.0460153 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.5030 | −1.00560 | ||||||||
\(209\) | 0.130110 | 0.00899991 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.14290 | −0.491738 | −0.245869 | − | 0.969303i | \(-0.579073\pi\) | ||||
−0.245869 | + | 0.969303i | \(0.579073\pi\) | |||||||
\(212\) | −21.8726 | −1.50221 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.2344 | 0.699611 | ||||||||
\(215\) | 0.275378 | 0.0187806 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.0915 | 1.36390 | ||||||||
\(218\) | 13.6827 | 0.926712 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.41147 | −0.432261 | ||||||||
\(221\) | 6.55438 | 0.440895 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.3354 | −0.692112 | −0.346056 | − | 0.938214i | \(-0.612479\pi\) | ||||
−0.346056 | + | 0.938214i | \(0.612479\pi\) | |||||||
\(224\) | 14.8307 | 0.990917 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.50475 | 0.233132 | ||||||||
\(227\) | 13.0223 | 0.864320 | 0.432160 | − | 0.901797i | \(-0.357752\pi\) | ||||
0.432160 | + | 0.901797i | \(0.357752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.0993 | −1.85685 | −0.928426 | − | 0.371518i | \(-0.878837\pi\) | ||||
−0.928426 | + | 0.371518i | \(0.878837\pi\) | |||||||
\(230\) | −7.23442 | −0.477024 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 40.1411 | 2.63540 | ||||||||
\(233\) | 13.9145 | 0.911567 | 0.455784 | − | 0.890091i | \(-0.349359\pi\) | ||||
0.455784 | + | 0.890091i | \(0.349359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.52023 | −0.294867 | ||||||||
\(236\) | 37.6391 | 2.45010 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −24.5107 | −1.58879 | ||||||||
\(239\) | 15.0196 | 0.971537 | 0.485769 | − | 0.874087i | \(-0.338540\pi\) | ||||
0.485769 | + | 0.874087i | \(0.338540\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9736 | −0.835703 | −0.417851 | − | 0.908515i | \(-0.637217\pi\) | ||||
−0.417851 | + | 0.908515i | \(0.637217\pi\) | |||||||
\(242\) | 3.42427 | 0.220120 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.59627 | −0.358264 | ||||||||
\(245\) | −1.59627 | −0.101982 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0915189 | −0.00582321 | ||||||||
\(248\) | 38.0205 | 2.41431 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.5885 | −0.732923 | ||||||||
\(251\) | −0.872578 | −0.0550766 | −0.0275383 | − | 0.999621i | \(-0.508767\pi\) | ||||
−0.0275383 | + | 0.999621i | \(0.508767\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.9659 | −1.19237 | ||||||||
\(254\) | 16.8084 | 1.05465 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30.5030 | −1.90644 | ||||||||
\(257\) | −4.57667 | −0.285485 | −0.142742 | − | 0.989760i | \(-0.545592\pi\) | ||||
−0.142742 | + | 0.989760i | \(0.545592\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.6040 | −0.721038 | ||||||||
\(260\) | 4.50980 | 0.279686 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −32.0077 | −1.97744 | ||||||||
\(263\) | −4.29767 | −0.265005 | −0.132503 | − | 0.991183i | \(-0.542301\pi\) | ||||
−0.132503 | + | 0.991183i | \(0.542301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.31996 | 0.142514 | ||||||||
\(266\) | 0.342244 | 0.0209843 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 44.1489 | 2.69682 | ||||||||
\(269\) | −12.1257 | −0.739315 | −0.369657 | − | 0.929168i | \(-0.620525\pi\) | ||||
−0.369657 | + | 0.929168i | \(0.620525\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.319955 | −0.0194359 | −0.00971795 | − | 0.999953i | \(-0.503093\pi\) | ||||
−0.00971795 | + | 0.999953i | \(0.503093\pi\) | |||||||
\(272\) | −19.9145 | −1.20749 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 26.8803 | 1.62390 | ||||||||
\(275\) | −14.8503 | −0.895506 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.8212 | −1.61153 | −0.805765 | − | 0.592236i | \(-0.798245\pi\) | ||||
−0.805765 | + | 0.592236i | \(0.798245\pi\) | |||||||
\(278\) | 18.8922 | 1.13308 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.21894 | −0.550937 | ||||||||
\(281\) | −26.6810 | −1.59165 | −0.795827 | − | 0.605524i | \(-0.792963\pi\) | ||||
−0.795827 | + | 0.605524i | \(0.792963\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.29355 | −0.552444 | −0.276222 | − | 0.961094i | \(-0.589083\pi\) | ||||
−0.276222 | + | 0.961094i | \(0.589083\pi\) | |||||||
\(284\) | −52.1908 | −3.09695 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.1830 | 1.01605 | ||||||||
\(287\) | 24.8530 | 1.46702 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | −7.78880 | −0.457374 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −36.3259 | −2.12581 | ||||||||
\(293\) | 19.6391 | 1.14733 | 0.573664 | − | 0.819091i | \(-0.305522\pi\) | ||||
0.573664 | + | 0.819091i | \(0.305522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.99226 | −0.232438 | ||||||||
\(296\) | −21.9590 | −1.27634 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.7716 | −0.623980 | ||||||||
\(299\) | 13.3405 | 0.771500 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.89899 | 0.109456 | ||||||||
\(302\) | −0.342244 | −0.0196939 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.278066 | 0.0159482 | ||||||||
\(305\) | 0.593578 | 0.0339882 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.3432 | 1.61763 | 0.808815 | − | 0.588063i | \(-0.200109\pi\) | ||||
0.808815 | + | 0.588063i | \(0.200109\pi\) | |||||||
\(308\) | −44.2131 | −2.51927 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.37733 | −0.419004 | ||||||||
\(311\) | 2.04458 | 0.115937 | 0.0579687 | − | 0.998318i | \(-0.481538\pi\) | ||||
0.0579687 | + | 0.998318i | \(0.481538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.41147 | 0.475445 | 0.237722 | − | 0.971333i | \(-0.423599\pi\) | ||||
0.237722 | + | 0.971333i | \(0.423599\pi\) | |||||||
\(314\) | −33.7425 | −1.90420 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 48.7452 | 2.74213 | ||||||||
\(317\) | −31.1284 | −1.74834 | −0.874171 | − | 0.485618i | \(-0.838595\pi\) | ||||
−0.874171 | + | 0.485618i | \(0.838595\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.4192 | −1.14326 | ||||||||
\(320\) | 0.766511 | 0.0428493 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −49.8881 | −2.78015 | ||||||||
\(323\) | −0.125667 | −0.00699231 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.4456 | 0.579419 | ||||||||
\(326\) | 24.7229 | 1.36927 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 47.0310 | 2.59685 | ||||||||
\(329\) | −31.1712 | −1.71852 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.0310 | 1.70562 | 0.852808 | − | 0.522225i | \(-0.174898\pi\) | ||||
0.852808 | + | 0.522225i | \(0.174898\pi\) | |||||||
\(332\) | 6.66044 | 0.365539 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.04963 | −0.495174 | ||||||||
\(335\) | −4.68273 | −0.255845 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.7297 | 1.29264 | 0.646319 | − | 0.763067i | \(-0.276308\pi\) | ||||
0.646319 | + | 0.763067i | \(0.276308\pi\) | |||||||
\(338\) | 20.8307 | 1.13304 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.19253 | 0.335837 | ||||||||
\(341\) | −19.3405 | −1.04735 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.5790 | 0.625209 | ||||||||
\(344\) | 3.59358 | 0.193753 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 47.5185 | 2.55461 | ||||||||
\(347\) | 1.80840 | 0.0970800 | 0.0485400 | − | 0.998821i | \(-0.484543\pi\) | ||||
0.0485400 | + | 0.998821i | \(0.484543\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.2608 | 0.816893 | 0.408447 | − | 0.912782i | \(-0.366071\pi\) | ||||
0.408447 | + | 0.912782i | \(0.366071\pi\) | |||||||
\(350\) | −39.0624 | −2.08797 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14.2763 | −0.760930 | ||||||||
\(353\) | 32.3824 | 1.72354 | 0.861770 | − | 0.507299i | \(-0.169356\pi\) | ||||
0.861770 | + | 0.507299i | \(0.169356\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.53571 | 0.293805 | ||||||||
\(356\) | 70.0215 | 3.71113 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.8726 | −0.680337 | ||||||||
\(359\) | 1.91447 | 0.101042 | 0.0505209 | − | 0.998723i | \(-0.483912\pi\) | ||||
0.0505209 | + | 0.998723i | \(0.483912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9982 | −0.999908 | ||||||||
\(362\) | −18.1061 | −0.951634 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 31.0993 | 1.63004 | ||||||||
\(365\) | 3.85298 | 0.201674 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.8648 | −1.40233 | −0.701167 | − | 0.712998i | \(-0.747337\pi\) | ||||
−0.701167 | + | 0.712998i | \(0.747337\pi\) | |||||||
\(368\) | −40.5330 | −2.11293 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.26083 | 0.221510 | ||||||||
\(371\) | 15.9982 | 0.830588 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.8402 | 0.768396 | 0.384198 | − | 0.923251i | \(-0.374478\pi\) | ||||
0.384198 | + | 0.923251i | \(0.374478\pi\) | |||||||
\(374\) | 23.5945 | 1.22004 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −58.9873 | −3.04204 | ||||||||
\(377\) | 14.3628 | 0.739721 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.7870 | −1.73552 | −0.867762 | − | 0.496980i | \(-0.834442\pi\) | ||||
−0.867762 | + | 0.496980i | \(0.834442\pi\) | |||||||
\(380\) | −0.0864665 | −0.00443564 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26.6117 | −1.36158 | ||||||||
\(383\) | 9.27900 | 0.474135 | 0.237067 | − | 0.971493i | \(-0.423814\pi\) | ||||
0.237067 | + | 0.971493i | \(0.423814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.68954 | 0.239001 | ||||||||
\(386\) | 25.6827 | 1.30722 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 82.2559 | 4.17591 | ||||||||
\(389\) | 15.9786 | 0.810149 | 0.405075 | − | 0.914284i | \(-0.367245\pi\) | ||||
0.405075 | + | 0.914284i | \(0.367245\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.3182 | 0.926391 | ||||||||
\(392\) | −20.8307 | −1.05211 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 35.6614 | 1.79659 | ||||||||
\(395\) | −5.17024 | −0.260143 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.7050 | 0.988967 | 0.494483 | − | 0.869187i | \(-0.335357\pi\) | ||||
0.494483 | + | 0.869187i | \(0.335357\pi\) | |||||||
\(398\) | −26.0205 | −1.30429 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −31.7374 | −1.58687 | ||||||||
\(401\) | −1.14796 | −0.0573262 | −0.0286631 | − | 0.999589i | \(-0.509125\pi\) | ||||
−0.0286631 | + | 0.999589i | \(0.509125\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.6040 | 0.677664 | ||||||||
\(404\) | −40.0847 | −1.99429 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −53.7110 | −2.66563 | ||||||||
\(407\) | 11.1702 | 0.553688 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.10101 | −0.153335 | −0.0766676 | − | 0.997057i | \(-0.524428\pi\) | ||||
−0.0766676 | + | 0.997057i | \(0.524428\pi\) | |||||||
\(410\) | −9.12567 | −0.450685 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.15064 | 0.0566882 | ||||||||
\(413\) | −27.5303 | −1.35468 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.706452 | −0.0346784 | ||||||||
\(416\) | 10.0419 | 0.492344 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.329451 | −0.0161140 | ||||||||
\(419\) | −35.4492 | −1.73181 | −0.865904 | − | 0.500209i | \(-0.833256\pi\) | ||||
−0.865904 | + | 0.500209i | \(0.833256\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.21719 | 0.449218 | 0.224609 | − | 0.974449i | \(-0.427889\pi\) | ||||
0.224609 | + | 0.974449i | \(0.427889\pi\) | |||||||
\(422\) | 18.0865 | 0.880435 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 30.2746 | 1.47026 | ||||||||
\(425\) | 14.3432 | 0.695746 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.09327 | 0.198087 | ||||||||
\(428\) | −17.8307 | −0.861879 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.697281 | −0.0336259 | ||||||||
\(431\) | −11.5794 | −0.557758 | −0.278879 | − | 0.960326i | \(-0.589963\pi\) | ||||
−0.278879 | + | 0.960326i | \(0.589963\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.06511 | 0.291471 | 0.145735 | − | 0.989324i | \(-0.453445\pi\) | ||||
0.145735 | + | 0.989324i | \(0.453445\pi\) | |||||||
\(434\) | −50.8735 | −2.44201 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.8384 | −1.14165 | ||||||||
\(437\) | −0.255777 | −0.0122355 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.0060 | 1.38438 | 0.692190 | − | 0.721715i | \(-0.256646\pi\) | ||||
0.692190 | + | 0.721715i | \(0.256646\pi\) | |||||||
\(440\) | 8.87433 | 0.423067 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.5963 | −0.789404 | ||||||||
\(443\) | −30.8922 | −1.46773 | −0.733866 | − | 0.679294i | \(-0.762286\pi\) | ||||
−0.733866 | + | 0.679294i | \(0.762286\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.42696 | −0.352071 | ||||||||
\(446\) | 26.1702 | 1.23920 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.28581 | 0.249731 | ||||||||
\(449\) | 39.0820 | 1.84439 | 0.922197 | − | 0.386720i | \(-0.126392\pi\) | ||||
0.922197 | + | 0.386720i | \(0.126392\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.9240 | −1.12654 | ||||||||
\(452\) | −6.10607 | −0.287205 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −32.9736 | −1.54753 | ||||||||
\(455\) | −3.29860 | −0.154641 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.50475 | −0.0703891 | −0.0351946 | − | 0.999380i | \(-0.511205\pi\) | ||||
−0.0351946 | + | 0.999380i | \(0.511205\pi\) | |||||||
\(458\) | 71.1498 | 3.32461 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.6040 | 0.587665 | ||||||||
\(461\) | −26.2371 | −1.22198 | −0.610992 | − | 0.791637i | \(-0.709229\pi\) | ||||
−0.610992 | + | 0.791637i | \(0.709229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.75641 | 0.313997 | 0.156998 | − | 0.987599i | \(-0.449818\pi\) | ||||
0.156998 | + | 0.987599i | \(0.449818\pi\) | |||||||
\(464\) | −43.6391 | −2.02589 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.2327 | −1.63212 | ||||||||
\(467\) | −33.7469 | −1.56162 | −0.780810 | − | 0.624768i | \(-0.785194\pi\) | ||||
−0.780810 | + | 0.624768i | \(0.785194\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.2918 | −1.49110 | ||||||||
\(470\) | 11.4456 | 0.527947 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −52.0975 | −2.39798 | ||||||||
\(473\) | −1.82800 | −0.0840516 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.200274 | −0.00918921 | ||||||||
\(476\) | 42.7033 | 1.95730 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −38.0310 | −1.73950 | ||||||||
\(479\) | −11.1266 | −0.508387 | −0.254194 | − | 0.967153i | \(-0.581810\pi\) | ||||
−0.254194 | + | 0.967153i | \(0.581810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.85710 | −0.358253 | ||||||||
\(482\) | 32.8503 | 1.49629 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.96585 | −0.271175 | ||||||||
\(485\) | −8.72462 | −0.396165 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.74691 | −0.215103 | −0.107552 | − | 0.994200i | \(-0.534301\pi\) | ||||
−0.107552 | + | 0.994200i | \(0.534301\pi\) | |||||||
\(488\) | 7.74598 | 0.350644 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.04189 | 0.182594 | ||||||||
\(491\) | −22.3405 | −1.00821 | −0.504106 | − | 0.863642i | \(-0.668178\pi\) | ||||
−0.504106 | + | 0.863642i | \(0.668178\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.7219 | 0.888231 | ||||||||
\(494\) | 0.231734 | 0.0104262 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −41.3337 | −1.85594 | ||||||||
\(497\) | 38.1739 | 1.71233 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.4611 | −0.468303 | −0.234152 | − | 0.972200i | \(-0.575231\pi\) | ||||
−0.234152 | + | 0.972200i | \(0.575231\pi\) | |||||||
\(500\) | 20.1898 | 0.902917 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.20945 | 0.0986124 | ||||||||
\(503\) | −25.0419 | −1.11656 | −0.558281 | − | 0.829652i | \(-0.688539\pi\) | ||||
−0.558281 | + | 0.829652i | \(0.688539\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.25166 | 0.189196 | ||||||||
\(506\) | 48.0232 | 2.13489 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −29.2841 | −1.29927 | ||||||||
\(509\) | −18.0624 | −0.800603 | −0.400301 | − | 0.916384i | \(-0.631095\pi\) | ||||
−0.400301 | + | 0.916384i | \(0.631095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.5699 | 1.17538 | ||||||||
\(512\) | 50.5553 | 2.23425 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.5885 | 0.511148 | ||||||||
\(515\) | −0.122045 | −0.00537795 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.0060 | 1.31966 | ||||||||
\(518\) | 29.3824 | 1.29099 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.24216 | −0.273737 | ||||||||
\(521\) | 25.9581 | 1.13725 | 0.568623 | − | 0.822598i | \(-0.307476\pi\) | ||||
0.568623 | + | 0.822598i | \(0.307476\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.5945 | 1.11917 | 0.559585 | − | 0.828773i | \(-0.310961\pi\) | ||||
0.559585 | + | 0.828773i | \(0.310961\pi\) | |||||||
\(524\) | 55.7648 | 2.43609 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.8821 | 0.474481 | ||||||||
\(527\) | 18.6800 | 0.813716 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.2841 | 0.621046 | ||||||||
\(530\) | −5.87433 | −0.255165 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.596267 | −0.0258514 | ||||||||
\(533\) | 16.8280 | 0.728902 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.89124 | 0.0817656 | ||||||||
\(536\) | −61.1079 | −2.63946 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.7033 | 1.32371 | ||||||||
\(539\) | 10.5963 | 0.456414 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.8476 | 1.19726 | 0.598631 | − | 0.801025i | \(-0.295712\pi\) | ||||
0.598631 | + | 0.801025i | \(0.295712\pi\) | |||||||
\(542\) | 0.810155 | 0.0347991 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.7888 | 0.591190 | ||||||||
\(545\) | 2.52847 | 0.108308 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.90848 | −0.252628 | −0.126314 | − | 0.991990i | \(-0.540315\pi\) | ||||
−0.126314 | + | 0.991990i | \(0.540315\pi\) | |||||||
\(548\) | −46.8316 | −2.00055 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 37.6023 | 1.60337 | ||||||||
\(551\) | −0.275378 | −0.0117315 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.6536 | −1.51615 | ||||||||
\(554\) | 67.9136 | 2.88537 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −32.9145 | −1.39588 | ||||||||
\(557\) | −26.7050 | −1.13153 | −0.565764 | − | 0.824567i | \(-0.691419\pi\) | ||||
−0.565764 | + | 0.824567i | \(0.691419\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.28581 | 0.0543838 | ||||||||
\(560\) | 10.0223 | 0.423519 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 67.5586 | 2.84979 | ||||||||
\(563\) | −36.0624 | −1.51985 | −0.759925 | − | 0.650011i | \(-0.774764\pi\) | ||||
−0.759925 | + | 0.650011i | \(0.774764\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.647651 | 0.0272469 | ||||||||
\(566\) | 23.5321 | 0.989127 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 72.2390 | 3.03108 | ||||||||
\(569\) | 9.04727 | 0.379281 | 0.189641 | − | 0.981854i | \(-0.439268\pi\) | ||||
0.189641 | + | 0.981854i | \(0.439268\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.5790 | 1.27969 | 0.639846 | − | 0.768503i | \(-0.278998\pi\) | ||||
0.639846 | + | 0.768503i | \(0.278998\pi\) | |||||||
\(572\) | −29.9368 | −1.25172 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −62.9299 | −2.62665 | ||||||||
\(575\) | 29.1935 | 1.21745 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.1489 | −1.04696 | −0.523481 | − | 0.852037i | \(-0.675367\pi\) | ||||
−0.523481 | + | 0.852037i | \(0.675367\pi\) | |||||||
\(578\) | 20.2567 | 0.842568 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.5699 | 0.563458 | ||||||||
\(581\) | −4.87164 | −0.202110 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.4002 | −0.637812 | ||||||||
\(584\) | 50.2799 | 2.08060 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −49.7279 | −2.05424 | ||||||||
\(587\) | −20.8735 | −0.861542 | −0.430771 | − | 0.902461i | \(-0.641758\pi\) | ||||
−0.430771 | + | 0.902461i | \(0.641758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.260830 | −0.0107473 | ||||||||
\(590\) | 10.1088 | 0.416171 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.8726 | 0.981157 | ||||||||
\(593\) | −15.6212 | −0.641488 | −0.320744 | − | 0.947166i | \(-0.603933\pi\) | ||||
−0.320744 | + | 0.947166i | \(0.603933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.52940 | −0.185687 | ||||||||
\(596\) | 18.7665 | 0.768706 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −33.7793 | −1.38134 | ||||||||
\(599\) | 0.448311 | 0.0183175 | 0.00915874 | − | 0.999958i | \(-0.497085\pi\) | ||||
0.00915874 | + | 0.999958i | \(0.497085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.6723 | −0.720868 | −0.360434 | − | 0.932785i | \(-0.617371\pi\) | ||||
−0.360434 | + | 0.932785i | \(0.617371\pi\) | |||||||
\(602\) | −4.80840 | −0.195976 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.596267 | 0.0242617 | ||||||||
\(605\) | 0.632779 | 0.0257261 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.1985 | 1.06337 | 0.531683 | − | 0.846944i | \(-0.321560\pi\) | ||||
0.531683 | + | 0.846944i | \(0.321560\pi\) | |||||||
\(608\) | −0.192533 | −0.00780826 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.50299 | −0.0608544 | ||||||||
\(611\) | −21.1061 | −0.853860 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.5544 | 0.587846 | 0.293923 | − | 0.955829i | \(-0.405039\pi\) | ||||
0.293923 | + | 0.955829i | \(0.405039\pi\) | |||||||
\(614\) | −71.7674 | −2.89630 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 61.1968 | 2.46569 | ||||||||
\(617\) | −14.0205 | −0.564445 | −0.282223 | − | 0.959349i | \(-0.591072\pi\) | ||||
−0.282223 | + | 0.959349i | \(0.591072\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.7124 | −1.27463 | −0.637315 | − | 0.770603i | \(-0.719955\pi\) | ||||
−0.637315 | + | 0.770603i | \(0.719955\pi\) | |||||||
\(620\) | 12.8530 | 0.516188 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.17705 | −0.207581 | ||||||||
\(623\) | −51.2158 | −2.05192 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7638 | 0.870553 | ||||||||
\(626\) | −21.2986 | −0.851263 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 58.7870 | 2.34586 | ||||||||
\(629\) | −10.7888 | −0.430178 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.5758 | −1.53568 | −0.767840 | − | 0.640642i | \(-0.778668\pi\) | ||||
−0.767840 | + | 0.640642i | \(0.778668\pi\) | |||||||
\(632\) | −67.4698 | −2.68380 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 78.8198 | 3.13033 | ||||||||
\(635\) | 3.10607 | 0.123261 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.45336 | −0.295313 | ||||||||
\(638\) | 51.7033 | 2.04695 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.24216 | −0.246743 | ||||||||
\(641\) | 30.6168 | 1.20929 | 0.604645 | − | 0.796495i | \(-0.293315\pi\) | ||||
0.604645 | + | 0.796495i | \(0.293315\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.2249 | −1.34970 | −0.674850 | − | 0.737955i | \(-0.735792\pi\) | ||||
−0.674850 | + | 0.737955i | \(0.735792\pi\) | |||||||
\(644\) | 86.9163 | 3.42498 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.318201 | 0.0125194 | ||||||||
\(647\) | 12.8726 | 0.506073 | 0.253037 | − | 0.967457i | \(-0.418571\pi\) | ||||
0.253037 | + | 0.967457i | \(0.418571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.5012 | 1.04026 | ||||||||
\(650\) | −26.4492 | −1.03742 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43.0729 | −1.68686 | ||||||||
\(653\) | 11.3191 | 0.442952 | 0.221476 | − | 0.975166i | \(-0.428913\pi\) | ||||
0.221476 | + | 0.975166i | \(0.428913\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.91479 | −0.231110 | ||||||||
\(656\) | −51.1293 | −1.99626 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 78.9282 | 3.07694 | ||||||||
\(659\) | 13.7692 | 0.536372 | 0.268186 | − | 0.963367i | \(-0.413576\pi\) | ||||
0.268186 | + | 0.963367i | \(0.413576\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.2668 | −0.788288 | −0.394144 | − | 0.919049i | \(-0.628959\pi\) | ||||
−0.394144 | + | 0.919049i | \(0.628959\pi\) | |||||||
\(662\) | −78.5732 | −3.05383 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.21894 | −0.357764 | ||||||||
\(665\) | 0.0632441 | 0.00245250 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.1411 | 1.55427 | ||||||||
\(668\) | 15.7665 | 0.610025 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.8571 | 0.458080 | ||||||||
\(671\) | −3.94027 | −0.152112 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.5449 | −1.17742 | −0.588709 | − | 0.808345i | \(-0.700364\pi\) | ||||
−0.588709 | + | 0.808345i | \(0.700364\pi\) | |||||||
\(674\) | −60.0856 | −2.31441 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −36.2918 | −1.39584 | ||||||||
\(677\) | 3.71925 | 0.142942 | 0.0714711 | − | 0.997443i | \(-0.477231\pi\) | ||||
0.0714711 | + | 0.997443i | \(0.477231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −60.1644 | −2.30890 | ||||||||
\(680\) | −8.57129 | −0.328694 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 48.9718 | 1.87523 | ||||||||
\(683\) | 21.7469 | 0.832122 | 0.416061 | − | 0.909337i | \(-0.363410\pi\) | ||||
0.416061 | + | 0.909337i | \(0.363410\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.96728 | 0.189790 | ||||||||
\(686\) | −29.3191 | −1.11941 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.90673 | −0.148943 | ||||||||
\(689\) | 10.8324 | 0.412683 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.5948 | −1.43017 | −0.715087 | − | 0.699035i | \(-0.753613\pi\) | ||||
−0.715087 | + | 0.699035i | \(0.753613\pi\) | |||||||
\(692\) | −82.7880 | −3.14713 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.57903 | −0.173818 | ||||||||
\(695\) | 3.49113 | 0.132426 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.1070 | 0.875240 | ||||||||
\(698\) | −38.6418 | −1.46261 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 68.0556 | 2.57226 | ||||||||
\(701\) | −23.3351 | −0.881355 | −0.440678 | − | 0.897665i | \(-0.645262\pi\) | ||||
−0.440678 | + | 0.897665i | \(0.645262\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.150644 | 0.00568166 | ||||||||
\(704\) | −5.08822 | −0.191770 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −81.9951 | −3.08592 | ||||||||
\(707\) | 29.3191 | 1.10266 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.57903 | 0.247081 | 0.123540 | − | 0.992340i | \(-0.460575\pi\) | ||||
0.123540 | + | 0.992340i | \(0.460575\pi\) | |||||||
\(710\) | −14.0169 | −0.526045 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −96.9190 | −3.63219 | ||||||||
\(713\) | 38.0205 | 1.42388 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.17530 | 0.118749 | ||||||||
\(716\) | 22.4270 | 0.838135 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.84760 | −0.180911 | ||||||||
\(719\) | 16.8324 | 0.627744 | 0.313872 | − | 0.949465i | \(-0.398374\pi\) | ||||
0.313872 | + | 0.949465i | \(0.398374\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.841615 | −0.0313434 | ||||||||
\(722\) | 48.1052 | 1.79029 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 31.5449 | 1.17236 | ||||||||
\(725\) | 31.4306 | 1.16730 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.5621 | 0.948046 | 0.474023 | − | 0.880512i | \(-0.342801\pi\) | ||||
0.474023 | + | 0.880512i | \(0.342801\pi\) | |||||||
\(728\) | −43.0455 | −1.59537 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.75608 | −0.361089 | ||||||||
\(731\) | 1.76558 | 0.0653022 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7980 | −0.546576 | −0.273288 | − | 0.961932i | \(-0.588111\pi\) | ||||
−0.273288 | + | 0.961932i | \(0.588111\pi\) | |||||||
\(734\) | 68.0242 | 2.51082 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.0651 | 1.03449 | ||||||||
\(737\) | 31.0847 | 1.14502 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.19078 | 0.338088 | 0.169044 | − | 0.985608i | \(-0.445932\pi\) | ||||
0.169044 | + | 0.985608i | \(0.445932\pi\) | |||||||
\(740\) | −7.42333 | −0.272887 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −40.5090 | −1.48713 | ||||||||
\(743\) | −44.4492 | −1.63068 | −0.815342 | − | 0.578979i | \(-0.803451\pi\) | ||||
−0.815342 | + | 0.578979i | \(0.803451\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.99050 | −0.0729264 | ||||||||
\(746\) | −37.5767 | −1.37578 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −41.1070 | −1.50302 | ||||||||
\(749\) | 13.0419 | 0.476540 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.8060 | −1.30658 | −0.653290 | − | 0.757107i | \(-0.726612\pi\) | ||||
−0.653290 | + | 0.757107i | \(0.726612\pi\) | |||||||
\(752\) | 64.1275 | 2.33849 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −36.3678 | −1.32444 | ||||||||
\(755\) | −0.0632441 | −0.00230169 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.8976 | −1.66818 | −0.834088 | − | 0.551632i | \(-0.814005\pi\) | ||||
−0.834088 | + | 0.551632i | \(0.814005\pi\) | |||||||
\(758\) | 85.5518 | 3.10738 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.119681 | 0.00434129 | ||||||||
\(761\) | 37.1952 | 1.34833 | 0.674163 | − | 0.738583i | \(-0.264505\pi\) | ||||
0.674163 | + | 0.738583i | \(0.264505\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.4361 | 0.631230 | ||||||||
\(764\) | 46.3637 | 1.67738 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.4953 | −0.848918 | ||||||||
\(767\) | −18.6408 | −0.673082 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.3337 | −1.38235 | −0.691174 | − | 0.722688i | \(-0.742906\pi\) | ||||
−0.691174 | + | 0.722688i | \(0.742906\pi\) | |||||||
\(770\) | −11.8743 | −0.427921 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −44.7452 | −1.61041 | ||||||||
\(773\) | −52.8272 | −1.90006 | −0.950031 | − | 0.312156i | \(-0.898949\pi\) | ||||
−0.950031 | + | 0.312156i | \(0.898949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.7701 | 1.06937 | ||||||||
\(776\) | −113.853 | −4.08709 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −40.4593 | −1.45054 | ||||||||
\(779\) | −0.322644 | −0.0115599 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.7469 | −1.31491 | ||||||||
\(782\) | −46.3833 | −1.65866 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.6459 | 0.808782 | ||||||||
\(785\) | −6.23536 | −0.222549 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.2404 | 1.61265 | 0.806323 | − | 0.591475i | \(-0.201454\pi\) | ||||
0.806323 | + | 0.591475i | \(0.201454\pi\) | |||||||
\(788\) | −62.1302 | −2.21330 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.0915 | 0.465775 | ||||||||
\(791\) | 4.46616 | 0.158798 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.77156 | 0.0984211 | ||||||||
\(794\) | −49.8949 | −1.77070 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.3337 | 1.60681 | ||||||||
\(797\) | 16.9189 | 0.599299 | 0.299649 | − | 0.954049i | \(-0.403130\pi\) | ||||
0.299649 | + | 0.954049i | \(0.403130\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.9813 | −1.02529 | ||||||||
\(800\) | 21.9750 | 0.776934 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.90673 | 0.102640 | ||||||||
\(803\) | −25.5767 | −0.902581 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.21894 | −0.324925 | ||||||||
\(806\) | −34.4466 | −1.21333 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 55.4826 | 1.95187 | ||||||||
\(809\) | 34.9145 | 1.22753 | 0.613764 | − | 0.789490i | \(-0.289655\pi\) | ||||
0.613764 | + | 0.789490i | \(0.289655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.0419 | 0.633536 | 0.316768 | − | 0.948503i | \(-0.397402\pi\) | ||||
0.316768 | + | 0.948503i | \(0.397402\pi\) | |||||||
\(812\) | 93.5768 | 3.28390 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −28.2841 | −0.991356 | ||||||||
\(815\) | 4.56860 | 0.160031 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.0246528 | −0.000862492 0 | ||||||||
\(818\) | 7.85204 | 0.274540 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.8990 | 0.555217 | ||||||||
\(821\) | −40.6391 | −1.41831 | −0.709157 | − | 0.705051i | \(-0.750924\pi\) | ||||
−0.709157 | + | 0.705051i | \(0.750924\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.0496 | 0.908033 | 0.454017 | − | 0.890993i | \(-0.349991\pi\) | ||||
0.454017 | + | 0.890993i | \(0.349991\pi\) | |||||||
\(824\) | −1.59264 | −0.0554824 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 69.7093 | 2.42550 | ||||||||
\(827\) | 37.6195 | 1.30816 | 0.654079 | − | 0.756426i | \(-0.273056\pi\) | ||||
0.654079 | + | 0.756426i | \(0.273056\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.0215 | −1.21635 | −0.608173 | − | 0.793805i | \(-0.708097\pi\) | ||||
−0.608173 | + | 0.793805i | \(0.708097\pi\) | |||||||
\(830\) | 1.78880 | 0.0620902 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.57903 | 0.124081 | ||||||||
\(833\) | −10.2344 | −0.354602 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.67230 | −0.0578725 | ||||||||
\(836\) | 0.573978 | 0.0198514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 89.7606 | 3.10073 | ||||||||
\(839\) | −26.6141 | −0.918821 | −0.459411 | − | 0.888224i | \(-0.651939\pi\) | ||||
−0.459411 | + | 0.888224i | \(0.651939\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2172 | 0.490248 | ||||||||
\(842\) | −23.3387 | −0.804306 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −31.5107 | −1.08464 | ||||||||
\(845\) | 3.84936 | 0.132422 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.36360 | 0.149935 | ||||||||
\(848\) | −32.9127 | −1.13023 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −36.3182 | −1.24570 | ||||||||
\(851\) | −21.9590 | −0.752746 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.45512 | 0.0840616 | 0.0420308 | − | 0.999116i | \(-0.486617\pi\) | ||||
0.0420308 | + | 0.999116i | \(0.486617\pi\) | |||||||
\(854\) | −10.3645 | −0.354667 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.6800 | 0.843547 | ||||||||
\(857\) | 9.82976 | 0.335778 | 0.167889 | − | 0.985806i | \(-0.446305\pi\) | ||||
0.167889 | + | 0.985806i | \(0.446305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.81696 | 0.300831 | 0.150415 | − | 0.988623i | \(-0.451939\pi\) | ||||
0.150415 | + | 0.988623i | \(0.451939\pi\) | |||||||
\(860\) | 1.21482 | 0.0414251 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.3200 | 0.998642 | ||||||||
\(863\) | 6.62124 | 0.225390 | 0.112695 | − | 0.993630i | \(-0.464052\pi\) | ||||
0.112695 | + | 0.993630i | \(0.464052\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.78106 | 0.298565 | ||||||||
\(866\) | −15.3574 | −0.521866 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 88.6332 | 3.00841 | ||||||||
\(869\) | 34.3209 | 1.16426 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.8648 | −0.740862 | ||||||||
\(872\) | 32.9956 | 1.11737 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.647651 | 0.0219071 | ||||||||
\(875\) | −14.7674 | −0.499231 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.07604 | −0.137638 | −0.0688190 | − | 0.997629i | \(-0.521923\pi\) | ||||
−0.0688190 | + | 0.997629i | \(0.521923\pi\) | |||||||
\(878\) | −73.4457 | −2.47867 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.64765 | −0.325222 | ||||||||
\(881\) | −9.25133 | −0.311685 | −0.155843 | − | 0.987782i | \(-0.549809\pi\) | ||||
−0.155843 | + | 0.987782i | \(0.549809\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.7701 | −1.27107 | −0.635533 | − | 0.772074i | \(-0.719220\pi\) | ||||
−0.635533 | + | 0.772074i | \(0.719220\pi\) | |||||||
\(884\) | 28.9145 | 0.972499 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 78.2217 | 2.62791 | ||||||||
\(887\) | −18.9786 | −0.637241 | −0.318620 | − | 0.947882i | \(-0.603219\pi\) | ||||
−0.318620 | + | 0.947882i | \(0.603219\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.4192 | 0.718377 | ||||||||
\(890\) | 18.8057 | 0.630369 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −45.5945 | −1.52662 | ||||||||
\(893\) | 0.404667 | 0.0135417 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.37876 | −0.0795131 | ||||||||
\(896\) | −43.0455 | −1.43805 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −98.9592 | −3.30231 | ||||||||
\(899\) | 40.9341 | 1.36523 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.8743 | 0.495536 | ||||||||
\(902\) | 60.5776 | 2.01701 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.45161 | 0.281096 | ||||||||
\(905\) | −3.34587 | −0.111220 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.64590 | 0.320287 | 0.160143 | − | 0.987094i | \(-0.448804\pi\) | ||||
0.160143 | + | 0.987094i | \(0.448804\pi\) | |||||||
\(908\) | 57.4475 | 1.90646 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.35235 | 0.276878 | ||||||||
\(911\) | 6.53478 | 0.216507 | 0.108253 | − | 0.994123i | \(-0.465474\pi\) | ||||
0.108253 | + | 0.994123i | \(0.465474\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.68954 | 0.155201 | ||||||||
\(914\) | 3.81016 | 0.126029 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −123.959 | −4.09573 | ||||||||
\(917\) | −40.7880 | −1.34694 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.89124 | 0.128360 | 0.0641802 | − | 0.997938i | \(-0.479557\pi\) | ||||
0.0641802 | + | 0.997938i | \(0.479557\pi\) | |||||||
\(920\) | −17.4456 | −0.575165 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 66.4347 | 2.18791 | ||||||||
\(923\) | 25.8476 | 0.850784 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.1940 | −0.565334 | ||||||||
\(926\) | −17.1078 | −0.562198 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 30.2158 | 0.991881 | ||||||||
\(929\) | 39.8530 | 1.30753 | 0.653767 | − | 0.756696i | \(-0.273188\pi\) | ||||
0.653767 | + | 0.756696i | \(0.273188\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.142903 | 0.00468347 | ||||||||
\(932\) | 61.3833 | 2.01068 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 85.4502 | 2.79602 | ||||||||
\(935\) | 4.36009 | 0.142590 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.0651 | 1.08019 | 0.540095 | − | 0.841604i | \(-0.318388\pi\) | ||||
0.540095 | + | 0.841604i | \(0.318388\pi\) | |||||||
\(938\) | 81.7657 | 2.66974 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.9409 | −0.650400 | ||||||||
\(941\) | 53.8066 | 1.75405 | 0.877023 | − | 0.480448i | \(-0.159526\pi\) | ||||
0.877023 | + | 0.480448i | \(0.159526\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47.0310 | 1.53154 | ||||||||
\(944\) | 56.6373 | 1.84339 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.62866 | 0.150491 | ||||||||
\(947\) | −42.2354 | −1.37246 | −0.686232 | − | 0.727382i | \(-0.740737\pi\) | ||||
−0.686232 | + | 0.727382i | \(0.740737\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.9905 | 0.583996 | ||||||||
\(950\) | 0.507112 | 0.0164529 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −59.1070 | −1.91567 | ||||||||
\(953\) | −24.5776 | −0.796147 | −0.398073 | − | 0.917354i | \(-0.630321\pi\) | ||||
−0.398073 | + | 0.917354i | \(0.630321\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.91765 | −0.159131 | ||||||||
\(956\) | 66.2586 | 2.14296 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.1735 | 0.910246 | ||||||||
\(959\) | 34.2540 | 1.10612 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.77156 | 0.250696 | ||||||||
\(962\) | 19.8949 | 0.641436 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −57.2327 | −1.84334 | ||||||||
\(965\) | 4.74598 | 0.152778 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.47203 | 0.143811 | 0.0719054 | − | 0.997411i | \(-0.477092\pi\) | ||||
0.0719054 | + | 0.997411i | \(0.477092\pi\) | |||||||
\(968\) | 8.25753 | 0.265407 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.0915 | 0.709316 | ||||||||
\(971\) | 4.61949 | 0.148246 | 0.0741232 | − | 0.997249i | \(-0.476384\pi\) | ||||
0.0741232 | + | 0.997249i | \(0.476384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.0746 | 0.771796 | ||||||||
\(974\) | 12.0196 | 0.385133 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.42097 | −0.269549 | ||||||||
\(977\) | 11.2808 | 0.360903 | 0.180452 | − | 0.983584i | \(-0.442244\pi\) | ||||
0.180452 | + | 0.983584i | \(0.442244\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.3013 | 1.57568 | ||||||||
\(980\) | −7.04189 | −0.224945 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 56.5681 | 1.80516 | ||||||||
\(983\) | 17.0642 | 0.544263 | 0.272131 | − | 0.962260i | \(-0.412271\pi\) | ||||
0.272131 | + | 0.962260i | \(0.412271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.58996 | 0.209973 | ||||||||
\(986\) | −49.9377 | −1.59034 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.403733 | −0.0128445 | ||||||||
\(989\) | 3.59358 | 0.114269 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000 | 0.0635321 | 0.0317660 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317660 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(992\) | 28.6195 | 0.908670 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −96.6596 | −3.06586 | ||||||||
\(995\) | −4.80840 | −0.152437 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.3847 | 0.708932 | 0.354466 | − | 0.935069i | \(-0.384663\pi\) | ||||
0.354466 | + | 0.935069i | \(0.384663\pi\) | |||||||
\(998\) | 26.4884 | 0.838477 | ||||||||
\(999\) | 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 | 243.2.a.e.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 243.2.a.f.1.3 | yes | 3 | ||
4.3 | odd | 2 | 3888.2.a.bd.1.3 | 3 | |||
5.4 | even | 2 | 6075.2.a.bv.1.3 | 3 | |||
9.2 | odd | 6 | 243.2.c.e.82.1 | 6 | |||
9.4 | even | 3 | 243.2.c.f.163.3 | 6 | |||
9.5 | odd | 6 | 243.2.c.e.163.1 | 6 | |||
9.7 | even | 3 | 243.2.c.f.82.3 | 6 | |||
12.11 | even | 2 | 3888.2.a.bk.1.1 | 3 | |||
15.14 | odd | 2 | 6075.2.a.bq.1.1 | 3 | |||
27.2 | odd | 18 | 729.2.e.c.568.1 | 6 | |||
27.4 | even | 9 | 729.2.e.a.406.1 | 6 | |||
27.5 | odd | 18 | 729.2.e.b.649.1 | 6 | |||
27.7 | even | 9 | 729.2.e.a.325.1 | 6 | |||
27.11 | odd | 18 | 729.2.e.b.82.1 | 6 | |||
27.13 | even | 9 | 729.2.e.h.163.1 | 6 | |||
27.14 | odd | 18 | 729.2.e.c.163.1 | 6 | |||
27.16 | even | 9 | 729.2.e.g.82.1 | 6 | |||
27.20 | odd | 18 | 729.2.e.i.325.1 | 6 | |||
27.22 | even | 9 | 729.2.e.g.649.1 | 6 | |||
27.23 | odd | 18 | 729.2.e.i.406.1 | 6 | |||
27.25 | even | 9 | 729.2.e.h.568.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
243.2.a.e.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
243.2.a.f.1.3 | yes | 3 | 3.2 | odd | 2 | ||
243.2.c.e.82.1 | 6 | 9.2 | odd | 6 | |||
243.2.c.e.163.1 | 6 | 9.5 | odd | 6 | |||
243.2.c.f.82.3 | 6 | 9.7 | even | 3 | |||
243.2.c.f.163.3 | 6 | 9.4 | even | 3 | |||
729.2.e.a.325.1 | 6 | 27.7 | even | 9 | |||
729.2.e.a.406.1 | 6 | 27.4 | even | 9 | |||
729.2.e.b.82.1 | 6 | 27.11 | odd | 18 | |||
729.2.e.b.649.1 | 6 | 27.5 | odd | 18 | |||
729.2.e.c.163.1 | 6 | 27.14 | odd | 18 | |||
729.2.e.c.568.1 | 6 | 27.2 | odd | 18 | |||
729.2.e.g.82.1 | 6 | 27.16 | even | 9 | |||
729.2.e.g.649.1 | 6 | 27.22 | even | 9 | |||
729.2.e.h.163.1 | 6 | 27.13 | even | 9 | |||
729.2.e.h.568.1 | 6 | 27.25 | even | 9 | |||
729.2.e.i.325.1 | 6 | 27.20 | odd | 18 | |||
729.2.e.i.406.1 | 6 | 27.23 | odd | 18 | |||
3888.2.a.bd.1.3 | 3 | 4.3 | odd | 2 | |||
3888.2.a.bk.1.1 | 3 | 12.11 | even | 2 | |||
6075.2.a.bq.1.1 | 3 | 15.14 | odd | 2 | |||
6075.2.a.bv.1.3 | 3 | 5.4 | even | 2 |