Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 18 x^{14} + 83 x^{13} + 112 x^{12} - 668 x^{11} - 235 x^{10} + 2648 x^{9} + \cdots - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.35655\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.35655 | −1.66633 | −0.833165 | − | 0.553024i | \(-0.813474\pi\) | ||||
−0.833165 | + | 0.553024i | \(0.813474\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.55331 | 1.77666 | ||||||||
\(5\) | −2.88159 | −1.28869 | −0.644343 | − | 0.764737i | \(-0.722869\pi\) | ||||
−0.644343 | + | 0.764737i | \(0.722869\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.66045 | −1.29417 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.79060 | 2.14738 | ||||||||
\(11\) | 2.09099 | 0.630457 | 0.315228 | − | 0.949016i | \(-0.397919\pi\) | ||||
0.315228 | + | 0.949016i | \(0.397919\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.909032 | 0.252120 | 0.126060 | − | 0.992023i | \(-0.459767\pi\) | ||||
0.126060 | + | 0.992023i | \(0.459767\pi\) | |||||||
\(14\) | 2.35655 | 0.629814 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.51941 | 0.379851 | ||||||||
\(17\) | −3.78525 | −0.918057 | −0.459028 | − | 0.888422i | \(-0.651802\pi\) | ||||
−0.459028 | + | 0.888422i | \(0.651802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.58028 | 1.73904 | 0.869518 | − | 0.493901i | \(-0.164429\pi\) | ||||
0.869518 | + | 0.493901i | \(0.164429\pi\) | |||||||
\(20\) | −10.2392 | −2.28955 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.92751 | −1.05055 | ||||||||
\(23\) | 5.96978 | 1.24478 | 0.622392 | − | 0.782705i | \(-0.286161\pi\) | ||||
0.622392 | + | 0.782705i | \(0.286161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.30355 | 0.660710 | ||||||||
\(26\) | −2.14218 | −0.420115 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.55331 | −0.671513 | ||||||||
\(29\) | 2.95240 | 0.548247 | 0.274124 | − | 0.961694i | \(-0.411612\pi\) | ||||
0.274124 | + | 0.961694i | \(0.411612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.925472 | −0.166220 | −0.0831098 | − | 0.996540i | \(-0.526485\pi\) | ||||
−0.0831098 | + | 0.996540i | \(0.526485\pi\) | |||||||
\(32\) | 3.74036 | 0.661208 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.92011 | 1.52979 | ||||||||
\(35\) | 2.88159 | 0.487077 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.864281 | −0.142087 | −0.0710435 | − | 0.997473i | \(-0.522633\pi\) | ||||
−0.0710435 | + | 0.997473i | \(0.522633\pi\) | |||||||
\(38\) | −17.8633 | −2.89781 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 10.5479 | 1.66777 | ||||||||
\(41\) | 3.36343 | 0.525280 | 0.262640 | − | 0.964894i | \(-0.415407\pi\) | ||||
0.262640 | + | 0.964894i | \(0.415407\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.26692 | 1.10819 | 0.554097 | − | 0.832452i | \(-0.313064\pi\) | ||||
0.554097 | + | 0.832452i | \(0.313064\pi\) | |||||||
\(44\) | 7.42993 | 1.12010 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.0681 | −2.07422 | ||||||||
\(47\) | −1.13179 | −0.165088 | −0.0825441 | − | 0.996587i | \(-0.526305\pi\) | ||||
−0.0825441 | + | 0.996587i | \(0.526305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −7.78497 | −1.10096 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.23007 | 0.447931 | ||||||||
\(53\) | 0.941428 | 0.129315 | 0.0646575 | − | 0.997908i | \(-0.479405\pi\) | ||||
0.0646575 | + | 0.997908i | \(0.479405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.02537 | −0.812460 | ||||||||
\(56\) | 3.66045 | 0.489149 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.95747 | −0.913561 | ||||||||
\(59\) | 4.90991 | 0.639216 | 0.319608 | − | 0.947550i | \(-0.396449\pi\) | ||||
0.319608 | + | 0.947550i | \(0.396449\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.87805 | 0.496533 | 0.248267 | − | 0.968692i | \(-0.420139\pi\) | ||||
0.248267 | + | 0.968692i | \(0.420139\pi\) | |||||||
\(62\) | 2.18092 | 0.276977 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.8531 | −1.48164 | ||||||||
\(65\) | −2.61946 | −0.324903 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.67893 | 0.327284 | 0.163642 | − | 0.986520i | \(-0.447676\pi\) | ||||
0.163642 | + | 0.986520i | \(0.447676\pi\) | |||||||
\(68\) | −13.4502 | −1.63107 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.79060 | −0.811632 | ||||||||
\(71\) | −3.06017 | −0.363175 | −0.181587 | − | 0.983375i | \(-0.558124\pi\) | ||||
−0.181587 | + | 0.983375i | \(0.558124\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.6550 | −1.59820 | −0.799098 | − | 0.601201i | \(-0.794689\pi\) | ||||
−0.799098 | + | 0.601201i | \(0.794689\pi\) | |||||||
\(74\) | 2.03672 | 0.236764 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26.9351 | 3.08967 | ||||||||
\(77\) | −2.09099 | −0.238290 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.32416 | −0.261489 | −0.130744 | − | 0.991416i | \(-0.541737\pi\) | ||||
−0.130744 | + | 0.991416i | \(0.541737\pi\) | |||||||
\(80\) | −4.37830 | −0.489509 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.92609 | −0.875290 | ||||||||
\(83\) | 9.71119 | 1.06594 | 0.532971 | − | 0.846134i | \(-0.321076\pi\) | ||||
0.532971 | + | 0.846134i | \(0.321076\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.9075 | 1.18309 | ||||||||
\(86\) | −17.1248 | −1.84662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.65397 | −0.815915 | ||||||||
\(89\) | −0.340872 | −0.0361324 | −0.0180662 | − | 0.999837i | \(-0.505751\pi\) | ||||
−0.0180662 | + | 0.999837i | \(0.505751\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.909032 | −0.0952924 | ||||||||
\(92\) | 21.2125 | 2.21155 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.66711 | 0.275091 | ||||||||
\(95\) | −21.8433 | −2.24107 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.16066 | 0.828590 | 0.414295 | − | 0.910143i | \(-0.364028\pi\) | ||||
0.414295 | + | 0.910143i | \(0.364028\pi\) | |||||||
\(98\) | −2.35655 | −0.238047 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.7386 | 1.17386 | ||||||||
\(101\) | 12.7682 | 1.27048 | 0.635241 | − | 0.772314i | \(-0.280901\pi\) | ||||
0.635241 | + | 0.772314i | \(0.280901\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.11308 | −0.503806 | −0.251903 | − | 0.967752i | \(-0.581056\pi\) | ||||
−0.251903 | + | 0.967752i | \(0.581056\pi\) | |||||||
\(104\) | −3.32747 | −0.326285 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.21852 | −0.215482 | ||||||||
\(107\) | −3.96461 | −0.383273 | −0.191637 | − | 0.981466i | \(-0.561380\pi\) | ||||
−0.191637 | + | 0.981466i | \(0.561380\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4907 | 1.19639 | 0.598195 | − | 0.801350i | \(-0.295885\pi\) | ||||
0.598195 | + | 0.801350i | \(0.295885\pi\) | |||||||
\(110\) | 14.1991 | 1.35383 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.51941 | −0.143570 | ||||||||
\(113\) | −0.691741 | −0.0650736 | −0.0325368 | − | 0.999471i | \(-0.510359\pi\) | ||||
−0.0325368 | + | 0.999471i | \(0.510359\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.2024 | −1.60414 | ||||||||
\(116\) | 10.4908 | 0.974047 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.5704 | −1.06514 | ||||||||
\(119\) | 3.78525 | 0.346993 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.62777 | −0.602524 | ||||||||
\(122\) | −9.13881 | −0.827389 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.28849 | −0.295315 | ||||||||
\(125\) | 4.88847 | 0.437238 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 20.4518 | 1.80770 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.17287 | 0.541396 | ||||||||
\(131\) | −2.30452 | −0.201347 | −0.100673 | − | 0.994920i | \(-0.532100\pi\) | ||||
−0.100673 | + | 0.994920i | \(0.532100\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.58028 | −0.657294 | ||||||||
\(134\) | −6.31303 | −0.545363 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.8557 | 1.18812 | ||||||||
\(137\) | −6.70881 | −0.573172 | −0.286586 | − | 0.958054i | \(-0.592520\pi\) | ||||
−0.286586 | + | 0.958054i | \(0.592520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3703 | −0.879600 | −0.439800 | − | 0.898096i | \(-0.644951\pi\) | ||||
−0.439800 | + | 0.898096i | \(0.644951\pi\) | |||||||
\(140\) | 10.2392 | 0.865369 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.21142 | 0.605169 | ||||||||
\(143\) | 1.90077 | 0.158951 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.50761 | −0.706518 | ||||||||
\(146\) | 32.1786 | 2.66312 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.07106 | −0.252440 | ||||||||
\(149\) | −11.5293 | −0.944518 | −0.472259 | − | 0.881460i | \(-0.656561\pi\) | ||||
−0.472259 | + | 0.881460i | \(0.656561\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.4583 | −1.74625 | −0.873126 | − | 0.487494i | \(-0.837911\pi\) | ||||
−0.873126 | + | 0.487494i | \(0.837911\pi\) | |||||||
\(152\) | −27.7473 | −2.25060 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.92751 | 0.397070 | ||||||||
\(155\) | 2.66683 | 0.214205 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.67835 | 0.213756 | 0.106878 | − | 0.994272i | \(-0.465915\pi\) | ||||
0.106878 | + | 0.994272i | \(0.465915\pi\) | |||||||
\(158\) | 5.47699 | 0.435726 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.7782 | −0.852089 | ||||||||
\(161\) | −5.96978 | −0.470484 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.3157 | −1.51292 | −0.756460 | − | 0.654040i | \(-0.773073\pi\) | ||||
−0.756460 | + | 0.654040i | \(0.773073\pi\) | |||||||
\(164\) | 11.9513 | 0.933242 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.8849 | −1.77621 | ||||||||
\(167\) | −0.608353 | −0.0470758 | −0.0235379 | − | 0.999723i | \(-0.507493\pi\) | ||||
−0.0235379 | + | 0.999723i | \(0.507493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1737 | −0.936435 | ||||||||
\(170\) | −25.7041 | −1.97141 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 25.8216 | 1.96888 | ||||||||
\(173\) | 8.03576 | 0.610948 | 0.305474 | − | 0.952200i | \(-0.401185\pi\) | ||||
0.305474 | + | 0.952200i | \(0.401185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.30355 | −0.249725 | ||||||||
\(176\) | 3.17706 | 0.239480 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.803281 | 0.0602085 | ||||||||
\(179\) | 17.4649 | 1.30539 | 0.652694 | − | 0.757622i | \(-0.273639\pi\) | ||||
0.652694 | + | 0.757622i | \(0.273639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.2958 | 1.58290 | 0.791452 | − | 0.611231i | \(-0.209326\pi\) | ||||
0.791452 | + | 0.611231i | \(0.209326\pi\) | |||||||
\(182\) | 2.14218 | 0.158789 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −21.8521 | −1.61096 | ||||||||
\(185\) | 2.49050 | 0.183105 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.91490 | −0.578795 | ||||||||
\(188\) | −4.02160 | −0.293305 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 51.4747 | 3.73436 | ||||||||
\(191\) | −17.5241 | −1.26800 | −0.634001 | − | 0.773333i | \(-0.718588\pi\) | ||||
−0.634001 | + | 0.773333i | \(0.718588\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.80348 | −0.561707 | −0.280853 | − | 0.959751i | \(-0.590617\pi\) | ||||
−0.280853 | + | 0.959751i | \(0.590617\pi\) | |||||||
\(194\) | −19.2310 | −1.38070 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.55331 | 0.253808 | ||||||||
\(197\) | −4.86752 | −0.346796 | −0.173398 | − | 0.984852i | \(-0.555475\pi\) | ||||
−0.173398 | + | 0.984852i | \(0.555475\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.9314 | 1.41290 | 0.706449 | − | 0.707764i | \(-0.250296\pi\) | ||||
0.706449 | + | 0.707764i | \(0.250296\pi\) | |||||||
\(200\) | −12.0925 | −0.855069 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −30.0888 | −2.11704 | ||||||||
\(203\) | −2.95240 | −0.207218 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.69203 | −0.676921 | ||||||||
\(206\) | 12.0492 | 0.839508 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.38119 | 0.0957681 | ||||||||
\(209\) | 15.8503 | 1.09639 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.58891 | −0.522442 | −0.261221 | − | 0.965279i | \(-0.584125\pi\) | ||||
−0.261221 | + | 0.965279i | \(0.584125\pi\) | |||||||
\(212\) | 3.34519 | 0.229748 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.34279 | 0.638660 | ||||||||
\(215\) | −20.9403 | −1.42811 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.925472 | 0.0628251 | ||||||||
\(218\) | −29.4349 | −1.99358 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −21.4100 | −1.44346 | ||||||||
\(221\) | −3.44091 | −0.231461 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.0673464 | −0.00450985 | −0.00225493 | − | 0.999997i | \(-0.500718\pi\) | ||||
−0.00225493 | + | 0.999997i | \(0.500718\pi\) | |||||||
\(224\) | −3.74036 | −0.249913 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.63012 | 0.108434 | ||||||||
\(227\) | 16.9576 | 1.12552 | 0.562758 | − | 0.826622i | \(-0.309740\pi\) | ||||
0.562758 | + | 0.826622i | \(0.309740\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.3712 | 1.74266 | 0.871329 | − | 0.490698i | \(-0.163258\pi\) | ||||
0.871329 | + | 0.490698i | \(0.163258\pi\) | |||||||
\(230\) | 40.5384 | 2.67302 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.8071 | −0.709523 | ||||||||
\(233\) | −30.1882 | −1.97769 | −0.988846 | − | 0.148943i | \(-0.952413\pi\) | ||||
−0.988846 | + | 0.148943i | \(0.952413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.26135 | 0.212747 | ||||||||
\(236\) | 17.4465 | 1.13567 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.92011 | −0.578205 | ||||||||
\(239\) | 0.635680 | 0.0411188 | 0.0205594 | − | 0.999789i | \(-0.493455\pi\) | ||||
0.0205594 | + | 0.999789i | \(0.493455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1376 | 0.910683 | 0.455341 | − | 0.890317i | \(-0.349517\pi\) | ||||
0.455341 | + | 0.890317i | \(0.349517\pi\) | |||||||
\(242\) | 15.6186 | 1.00400 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.7799 | 0.882169 | ||||||||
\(245\) | −2.88159 | −0.184098 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.89072 | 0.438446 | ||||||||
\(248\) | 3.38765 | 0.215116 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.5199 | −0.728582 | ||||||||
\(251\) | 12.8099 | 0.808557 | 0.404278 | − | 0.914636i | \(-0.367523\pi\) | ||||
0.404278 | + | 0.914636i | \(0.367523\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.4827 | 0.784783 | ||||||||
\(254\) | 2.35655 | 0.147863 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −24.4893 | −1.53058 | ||||||||
\(257\) | −10.5321 | −0.656976 | −0.328488 | − | 0.944508i | \(-0.606539\pi\) | ||||
−0.328488 | + | 0.944508i | \(0.606539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.864281 | 0.0537038 | ||||||||
\(260\) | −9.30774 | −0.577242 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.43071 | 0.335510 | ||||||||
\(263\) | −9.93958 | −0.612901 | −0.306450 | − | 0.951887i | \(-0.599141\pi\) | ||||
−0.306450 | + | 0.951887i | \(0.599141\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.71281 | −0.166646 | ||||||||
\(266\) | 17.8633 | 1.09527 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.51909 | 0.581471 | ||||||||
\(269\) | 12.5316 | 0.764062 | 0.382031 | − | 0.924149i | \(-0.375225\pi\) | ||||
0.382031 | + | 0.924149i | \(0.375225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.23955 | −0.500517 | −0.250259 | − | 0.968179i | \(-0.580516\pi\) | ||||
−0.250259 | + | 0.968179i | \(0.580516\pi\) | |||||||
\(272\) | −5.75132 | −0.348725 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.8096 | 0.955094 | ||||||||
\(275\) | 6.90769 | 0.416549 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.9032 | 0.895444 | 0.447722 | − | 0.894173i | \(-0.352235\pi\) | ||||
0.447722 | + | 0.894173i | \(0.352235\pi\) | |||||||
\(278\) | 24.4382 | 1.46570 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.5479 | −0.630359 | ||||||||
\(281\) | 28.8176 | 1.71911 | 0.859557 | − | 0.511039i | \(-0.170739\pi\) | ||||
0.859557 | + | 0.511039i | \(0.170739\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.9980 | −1.72375 | −0.861875 | − | 0.507121i | \(-0.830710\pi\) | ||||
−0.861875 | + | 0.507121i | \(0.830710\pi\) | |||||||
\(284\) | −10.8737 | −0.645237 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.47926 | −0.264864 | ||||||||
\(287\) | −3.36343 | −0.198537 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.67192 | −0.157172 | ||||||||
\(290\) | 20.0486 | 1.17729 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −48.5204 | −2.83944 | ||||||||
\(293\) | −18.0306 | −1.05336 | −0.526678 | − | 0.850065i | \(-0.676563\pi\) | ||||
−0.526678 | + | 0.850065i | \(0.676563\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.1483 | −0.823748 | ||||||||
\(296\) | 3.16366 | 0.183884 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.1694 | 1.57388 | ||||||||
\(299\) | 5.42672 | 0.313835 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.26692 | −0.418858 | ||||||||
\(302\) | 50.5675 | 2.90983 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.5175 | 0.660575 | ||||||||
\(305\) | −11.1749 | −0.639875 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.156981 | −0.00895936 | −0.00447968 | − | 0.999990i | \(-0.501426\pi\) | ||||
−0.00447968 | + | 0.999990i | \(0.501426\pi\) | |||||||
\(308\) | −7.42993 | −0.423360 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.28451 | −0.356936 | ||||||||
\(311\) | 3.98103 | 0.225743 | 0.112872 | − | 0.993610i | \(-0.463995\pi\) | ||||
0.112872 | + | 0.993610i | \(0.463995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.93875 | 0.335678 | 0.167839 | − | 0.985814i | \(-0.446321\pi\) | ||||
0.167839 | + | 0.985814i | \(0.446321\pi\) | |||||||
\(314\) | −6.31166 | −0.356188 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.25847 | −0.464575 | ||||||||
\(317\) | −2.42916 | −0.136435 | −0.0682177 | − | 0.997670i | \(-0.521731\pi\) | ||||
−0.0682177 | + | 0.997670i | \(0.521731\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.17344 | 0.345646 | ||||||||
\(320\) | 34.1559 | 1.90937 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.0681 | 0.783982 | ||||||||
\(323\) | −28.6932 | −1.59653 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00303 | 0.166578 | ||||||||
\(326\) | 45.5183 | 2.52103 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.3117 | −0.679800 | ||||||||
\(329\) | 1.13179 | 0.0623975 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.0202 | 1.26531 | 0.632653 | − | 0.774436i | \(-0.281966\pi\) | ||||
0.632653 | + | 0.774436i | \(0.281966\pi\) | |||||||
\(332\) | 34.5069 | 1.89381 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.43361 | 0.0784438 | ||||||||
\(335\) | −7.71959 | −0.421766 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.2748 | 0.723122 | 0.361561 | − | 0.932348i | \(-0.382244\pi\) | ||||
0.361561 | + | 0.932348i | \(0.382244\pi\) | |||||||
\(338\) | 28.6878 | 1.56041 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 38.7578 | 2.10194 | ||||||||
\(341\) | −1.93515 | −0.104794 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −26.6002 | −1.43419 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.9366 | −1.01804 | ||||||||
\(347\) | −21.0772 | −1.13148 | −0.565742 | − | 0.824582i | \(-0.691410\pi\) | ||||
−0.565742 | + | 0.824582i | \(0.691410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.8288 | 1.16847 | 0.584234 | − | 0.811585i | \(-0.301395\pi\) | ||||
0.584234 | + | 0.811585i | \(0.301395\pi\) | |||||||
\(350\) | 7.78497 | 0.416124 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.82105 | 0.416863 | ||||||||
\(353\) | −0.580410 | −0.0308921 | −0.0154461 | − | 0.999881i | \(-0.504917\pi\) | ||||
−0.0154461 | + | 0.999881i | \(0.504917\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.81814 | 0.468018 | ||||||||
\(356\) | −1.21123 | −0.0641948 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −41.1568 | −2.17521 | ||||||||
\(359\) | −23.8413 | −1.25830 | −0.629148 | − | 0.777286i | \(-0.716596\pi\) | ||||
−0.629148 | + | 0.777286i | \(0.716596\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.4607 | 2.02425 | ||||||||
\(362\) | −50.1845 | −2.63764 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.23007 | −0.169302 | ||||||||
\(365\) | 39.3480 | 2.05957 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.13290 | 0.0591367 | 0.0295683 | − | 0.999563i | \(-0.490587\pi\) | ||||
0.0295683 | + | 0.999563i | \(0.490587\pi\) | |||||||
\(368\) | 9.07051 | 0.472833 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.86899 | −0.305114 | ||||||||
\(371\) | −0.941428 | −0.0488765 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.250885 | −0.0129903 | −0.00649515 | − | 0.999979i | \(-0.502067\pi\) | ||||
−0.00649515 | + | 0.999979i | \(0.502067\pi\) | |||||||
\(374\) | 18.6518 | 0.964464 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.14286 | 0.213652 | ||||||||
\(377\) | 2.68383 | 0.138224 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.7844 | −1.06762 | −0.533812 | − | 0.845603i | \(-0.679241\pi\) | ||||
−0.533812 | + | 0.845603i | \(0.679241\pi\) | |||||||
\(380\) | −77.6159 | −3.98161 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 41.2964 | 2.11291 | ||||||||
\(383\) | −13.1231 | −0.670559 | −0.335280 | − | 0.942119i | \(-0.608831\pi\) | ||||
−0.335280 | + | 0.942119i | \(0.608831\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.02537 | 0.307081 | ||||||||
\(386\) | 18.3893 | 0.935989 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28.9974 | 1.47212 | ||||||||
\(389\) | 1.05720 | 0.0536019 | 0.0268010 | − | 0.999641i | \(-0.491468\pi\) | ||||
0.0268010 | + | 0.999641i | \(0.491468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.5971 | −1.14278 | ||||||||
\(392\) | −3.66045 | −0.184881 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.4705 | 0.577877 | ||||||||
\(395\) | 6.69728 | 0.336977 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.516619 | −0.0259284 | −0.0129642 | − | 0.999916i | \(-0.504127\pi\) | ||||
−0.0129642 | + | 0.999916i | \(0.504127\pi\) | |||||||
\(398\) | −46.9692 | −2.35435 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.01943 | 0.250972 | ||||||||
\(401\) | −15.0413 | −0.751127 | −0.375564 | − | 0.926797i | \(-0.622551\pi\) | ||||
−0.375564 | + | 0.926797i | \(0.622551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.841283 | −0.0419073 | ||||||||
\(404\) | 45.3693 | 2.25721 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.95747 | 0.345294 | ||||||||
\(407\) | −1.80720 | −0.0895797 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.70715 | −0.381094 | −0.190547 | − | 0.981678i | \(-0.561026\pi\) | ||||
−0.190547 | + | 0.981678i | \(0.561026\pi\) | |||||||
\(410\) | 22.8397 | 1.12797 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.1684 | −0.895091 | ||||||||
\(413\) | −4.90991 | −0.241601 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.9836 | −1.37366 | ||||||||
\(416\) | 3.40010 | 0.166704 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −37.3519 | −1.82694 | ||||||||
\(419\) | 28.0313 | 1.36942 | 0.684710 | − | 0.728815i | \(-0.259929\pi\) | ||||
0.684710 | + | 0.728815i | \(0.259929\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.9491 | 1.55711 | 0.778553 | − | 0.627579i | \(-0.215954\pi\) | ||||
0.778553 | + | 0.627579i | \(0.215954\pi\) | |||||||
\(422\) | 17.8836 | 0.870561 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.44605 | −0.167355 | ||||||||
\(425\) | −12.5048 | −0.606570 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.87805 | −0.187672 | ||||||||
\(428\) | −14.0875 | −0.680945 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 49.3467 | 2.37971 | ||||||||
\(431\) | 29.7065 | 1.43091 | 0.715455 | − | 0.698659i | \(-0.246219\pi\) | ||||
0.715455 | + | 0.698659i | \(0.246219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.61337 | 0.413932 | 0.206966 | − | 0.978348i | \(-0.433641\pi\) | ||||
0.206966 | + | 0.978348i | \(0.433641\pi\) | |||||||
\(434\) | −2.18092 | −0.104687 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 44.3833 | 2.12557 | ||||||||
\(437\) | 45.2526 | 2.16473 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.77586 | −0.323394 | −0.161697 | − | 0.986840i | \(-0.551697\pi\) | ||||
−0.161697 | + | 0.986840i | \(0.551697\pi\) | |||||||
\(440\) | 22.0556 | 1.05146 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.10866 | 0.385690 | ||||||||
\(443\) | 20.9325 | 0.994532 | 0.497266 | − | 0.867598i | \(-0.334337\pi\) | ||||
0.497266 | + | 0.867598i | \(0.334337\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.982253 | 0.0465633 | ||||||||
\(446\) | 0.158705 | 0.00751490 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11.8531 | 0.560008 | ||||||||
\(449\) | −32.9230 | −1.55373 | −0.776865 | − | 0.629667i | \(-0.783191\pi\) | ||||
−0.776865 | + | 0.629667i | \(0.783191\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.03290 | 0.331166 | ||||||||
\(452\) | −2.45797 | −0.115613 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −39.9614 | −1.87548 | ||||||||
\(455\) | 2.61946 | 0.122802 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.6965 | 0.968140 | 0.484070 | − | 0.875029i | \(-0.339158\pi\) | ||||
0.484070 | + | 0.875029i | \(0.339158\pi\) | |||||||
\(458\) | −62.1450 | −2.90385 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −61.1257 | −2.85000 | ||||||||
\(461\) | −3.86099 | −0.179824 | −0.0899122 | − | 0.995950i | \(-0.528659\pi\) | ||||
−0.0899122 | + | 0.995950i | \(0.528659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.29039 | −0.292339 | −0.146170 | − | 0.989260i | \(-0.546695\pi\) | ||||
−0.146170 | + | 0.989260i | \(0.546695\pi\) | |||||||
\(464\) | 4.48589 | 0.208252 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 71.1398 | 3.29549 | ||||||||
\(467\) | −11.6118 | −0.537331 | −0.268665 | − | 0.963234i | \(-0.586583\pi\) | ||||
−0.268665 | + | 0.963234i | \(0.586583\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.67893 | −0.123702 | ||||||||
\(470\) | −7.68552 | −0.354506 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17.9725 | −0.827252 | ||||||||
\(473\) | 15.1950 | 0.698669 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.0419 | 1.14900 | ||||||||
\(476\) | 13.4502 | 0.616487 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.49801 | −0.0685174 | ||||||||
\(479\) | 36.5063 | 1.66801 | 0.834007 | − | 0.551754i | \(-0.186041\pi\) | ||||
0.834007 | + | 0.551754i | \(0.186041\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.785659 | −0.0358230 | ||||||||
\(482\) | −33.3159 | −1.51750 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −23.5505 | −1.07048 | ||||||||
\(485\) | −23.5157 | −1.06779 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.8621 | 0.854723 | 0.427361 | − | 0.904081i | \(-0.359443\pi\) | ||||
0.427361 | + | 0.904081i | \(0.359443\pi\) | |||||||
\(488\) | −14.1954 | −0.642597 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.79060 | 0.306768 | ||||||||
\(491\) | −3.22865 | −0.145707 | −0.0728535 | − | 0.997343i | \(-0.523211\pi\) | ||||
−0.0728535 | + | 0.997343i | \(0.523211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.1756 | −0.503322 | ||||||||
\(494\) | −16.2383 | −0.730596 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.40617 | −0.0631387 | ||||||||
\(497\) | 3.06017 | 0.137267 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.1242 | −1.25901 | −0.629506 | − | 0.776996i | \(-0.716743\pi\) | ||||
−0.629506 | + | 0.776996i | \(0.716743\pi\) | |||||||
\(500\) | 17.3702 | 0.776821 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.1872 | −1.34732 | ||||||||
\(503\) | 26.7342 | 1.19202 | 0.596010 | − | 0.802977i | \(-0.296752\pi\) | ||||
0.596010 | + | 0.802977i | \(0.296752\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.7926 | −1.63725 | ||||||||
\(506\) | −29.4162 | −1.30771 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.55331 | −0.157653 | ||||||||
\(509\) | −34.2422 | −1.51776 | −0.758879 | − | 0.651232i | \(-0.774252\pi\) | ||||
−0.758879 | + | 0.651232i | \(0.774252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.6550 | 0.604061 | ||||||||
\(512\) | 16.8065 | 0.742751 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.8194 | 1.09474 | ||||||||
\(515\) | 14.7338 | 0.649248 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.36655 | −0.104081 | ||||||||
\(518\) | −2.03672 | −0.0894883 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.58839 | 0.420479 | ||||||||
\(521\) | 7.34862 | 0.321949 | 0.160974 | − | 0.986959i | \(-0.448536\pi\) | ||||
0.160974 | + | 0.986959i | \(0.448536\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.84572 | 0.0807077 | 0.0403538 | − | 0.999185i | \(-0.487151\pi\) | ||||
0.0403538 | + | 0.999185i | \(0.487151\pi\) | |||||||
\(524\) | −8.18868 | −0.357724 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.4231 | 1.02129 | ||||||||
\(527\) | 3.50314 | 0.152599 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.6383 | 0.549490 | ||||||||
\(530\) | 6.39286 | 0.277688 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −26.9351 | −1.16779 | ||||||||
\(533\) | 3.05747 | 0.132434 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4244 | 0.493919 | ||||||||
\(536\) | −9.80611 | −0.423560 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.5312 | −1.27318 | ||||||||
\(539\) | 2.09099 | 0.0900652 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.2748 | −0.441750 | −0.220875 | − | 0.975302i | \(-0.570891\pi\) | ||||
−0.220875 | + | 0.975302i | \(0.570891\pi\) | |||||||
\(542\) | 19.4169 | 0.834027 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.1582 | −0.607027 | ||||||||
\(545\) | −35.9930 | −1.54177 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.1107 | −1.62950 | −0.814748 | − | 0.579816i | \(-0.803125\pi\) | ||||
−0.814748 | + | 0.579816i | \(0.803125\pi\) | |||||||
\(548\) | −23.8385 | −1.01833 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.2783 | −0.694109 | ||||||||
\(551\) | 22.3800 | 0.953422 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.32416 | 0.0988334 | ||||||||
\(554\) | −35.1200 | −1.49211 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −36.8490 | −1.56275 | ||||||||
\(557\) | 2.06112 | 0.0873325 | 0.0436663 | − | 0.999046i | \(-0.486096\pi\) | ||||
0.0436663 | + | 0.999046i | \(0.486096\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.60586 | 0.279398 | ||||||||
\(560\) | 4.37830 | 0.185017 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −67.9101 | −2.86461 | ||||||||
\(563\) | −3.75432 | −0.158226 | −0.0791129 | − | 0.996866i | \(-0.525209\pi\) | ||||
−0.0791129 | + | 0.996866i | \(0.525209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.99331 | 0.0838594 | ||||||||
\(566\) | 68.3351 | 2.87234 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.2016 | 0.470009 | ||||||||
\(569\) | 6.62415 | 0.277699 | 0.138849 | − | 0.990314i | \(-0.455660\pi\) | ||||
0.138849 | + | 0.990314i | \(0.455660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.6145 | 0.569748 | 0.284874 | − | 0.958565i | \(-0.408048\pi\) | ||||
0.284874 | + | 0.958565i | \(0.408048\pi\) | |||||||
\(572\) | 6.75405 | 0.282401 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.92609 | 0.330829 | ||||||||
\(575\) | 19.7215 | 0.822442 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.7697 | −0.614870 | −0.307435 | − | 0.951569i | \(-0.599471\pi\) | ||||
−0.307435 | + | 0.951569i | \(0.599471\pi\) | |||||||
\(578\) | 6.29650 | 0.261900 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −30.2302 | −1.25524 | ||||||||
\(581\) | −9.71119 | −0.402888 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.96851 | 0.0815275 | ||||||||
\(584\) | 49.9834 | 2.06833 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.4899 | 1.75524 | ||||||||
\(587\) | 4.82816 | 0.199279 | 0.0996396 | − | 0.995024i | \(-0.468231\pi\) | ||||
0.0996396 | + | 0.995024i | \(0.468231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.01534 | −0.289062 | ||||||||
\(590\) | 33.3412 | 1.37264 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.31319 | −0.0539719 | ||||||||
\(593\) | 4.10629 | 0.168625 | 0.0843126 | − | 0.996439i | \(-0.473131\pi\) | ||||
0.0843126 | + | 0.996439i | \(0.473131\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.9075 | −0.447165 | ||||||||
\(596\) | −40.9673 | −1.67808 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.7883 | −0.522953 | ||||||||
\(599\) | −2.52365 | −0.103114 | −0.0515568 | − | 0.998670i | \(-0.516418\pi\) | ||||
−0.0515568 | + | 0.998670i | \(0.516418\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.8188 | −1.21633 | −0.608167 | − | 0.793809i | \(-0.708095\pi\) | ||||
−0.608167 | + | 0.793809i | \(0.708095\pi\) | |||||||
\(602\) | 17.1248 | 0.697956 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −76.2481 | −3.10249 | ||||||||
\(605\) | 19.0985 | 0.776464 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.7270 | 1.24717 | 0.623585 | − | 0.781756i | \(-0.285676\pi\) | ||||
0.623585 | + | 0.781756i | \(0.285676\pi\) | |||||||
\(608\) | 28.3530 | 1.14987 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.3343 | 1.06624 | ||||||||
\(611\) | −1.02883 | −0.0416220 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.99195 | −0.242013 | −0.121006 | − | 0.992652i | \(-0.538612\pi\) | ||||
−0.121006 | + | 0.992652i | \(0.538612\pi\) | |||||||
\(614\) | 0.369932 | 0.0149292 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.65397 | 0.308387 | ||||||||
\(617\) | 36.8789 | 1.48469 | 0.742345 | − | 0.670018i | \(-0.233713\pi\) | ||||
0.742345 | + | 0.670018i | \(0.233713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.4588 | 0.822308 | 0.411154 | − | 0.911566i | \(-0.365126\pi\) | ||||
0.411154 | + | 0.911566i | \(0.365126\pi\) | |||||||
\(620\) | 9.47608 | 0.380568 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.38148 | −0.376163 | ||||||||
\(623\) | 0.340872 | 0.0136568 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6043 | −1.22417 | ||||||||
\(626\) | −13.9949 | −0.559350 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.51702 | 0.379771 | ||||||||
\(629\) | 3.27152 | 0.130444 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4014 | 0.493692 | 0.246846 | − | 0.969055i | \(-0.420606\pi\) | ||||
0.246846 | + | 0.969055i | \(0.420606\pi\) | |||||||
\(632\) | 8.50748 | 0.338410 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.72443 | 0.227346 | ||||||||
\(635\) | 2.88159 | 0.114352 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.909032 | 0.0360171 | ||||||||
\(638\) | −14.5480 | −0.575961 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −58.9336 | −2.32955 | ||||||||
\(641\) | −5.76037 | −0.227521 | −0.113761 | − | 0.993508i | \(-0.536290\pi\) | ||||
−0.113761 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.93658 | −0.273552 | −0.136776 | − | 0.990602i | \(-0.543674\pi\) | ||||
−0.136776 | + | 0.990602i | \(0.543674\pi\) | |||||||
\(644\) | −21.2125 | −0.835889 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 67.6170 | 2.66035 | ||||||||
\(647\) | −33.1829 | −1.30456 | −0.652278 | − | 0.757980i | \(-0.726186\pi\) | ||||
−0.652278 | + | 0.757980i | \(0.726186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2666 | 0.402998 | ||||||||
\(650\) | −7.07679 | −0.277574 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −68.6346 | −2.68794 | ||||||||
\(653\) | 46.9289 | 1.83647 | 0.918235 | − | 0.396035i | \(-0.129614\pi\) | ||||
0.918235 | + | 0.396035i | \(0.129614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.64068 | 0.259473 | ||||||||
\(656\) | 5.11042 | 0.199528 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.66711 | −0.103975 | ||||||||
\(659\) | 15.8666 | 0.618076 | 0.309038 | − | 0.951050i | \(-0.399993\pi\) | ||||
0.309038 | + | 0.951050i | \(0.399993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.41844 | 0.288544 | 0.144272 | − | 0.989538i | \(-0.453916\pi\) | ||||
0.144272 | + | 0.989538i | \(0.453916\pi\) | |||||||
\(662\) | −54.2482 | −2.10842 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −35.5473 | −1.37950 | ||||||||
\(665\) | 21.8433 | 0.847045 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.6252 | 0.682450 | ||||||||
\(668\) | −2.16167 | −0.0836375 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.1916 | 0.702801 | ||||||||
\(671\) | 8.10896 | 0.313043 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.1749 | 0.816232 | 0.408116 | − | 0.912930i | \(-0.366186\pi\) | ||||
0.408116 | + | 0.912930i | \(0.366186\pi\) | |||||||
\(674\) | −31.2826 | −1.20496 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −43.2568 | −1.66372 | ||||||||
\(677\) | 6.57777 | 0.252804 | 0.126402 | − | 0.991979i | \(-0.459657\pi\) | ||||
0.126402 | + | 0.991979i | \(0.459657\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.16066 | −0.313177 | ||||||||
\(680\) | −39.9265 | −1.53111 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.56027 | 0.174622 | ||||||||
\(683\) | −19.3432 | −0.740145 | −0.370073 | − | 0.929003i | \(-0.620667\pi\) | ||||
−0.370073 | + | 0.929003i | \(0.620667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3320 | 0.738639 | ||||||||
\(686\) | 2.35655 | 0.0899734 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.0414 | 0.420949 | ||||||||
\(689\) | 0.855788 | 0.0326029 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.3865 | −1.00379 | −0.501895 | − | 0.864929i | \(-0.667364\pi\) | ||||
−0.501895 | + | 0.864929i | \(0.667364\pi\) | |||||||
\(692\) | 28.5536 | 1.08544 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 49.6694 | 1.88543 | ||||||||
\(695\) | 29.8830 | 1.13353 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.7314 | −0.482237 | ||||||||
\(698\) | −51.4405 | −1.94705 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.7386 | −0.443676 | ||||||||
\(701\) | −17.6124 | −0.665210 | −0.332605 | − | 0.943066i | \(-0.607928\pi\) | ||||
−0.332605 | + | 0.943066i | \(0.607928\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.55150 | −0.247094 | ||||||||
\(704\) | −24.7848 | −0.934111 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.36776 | 0.0514765 | ||||||||
\(707\) | −12.7682 | −0.480197 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 48.0398 | 1.80417 | 0.902086 | − | 0.431557i | \(-0.142036\pi\) | ||||
0.902086 | + | 0.431557i | \(0.142036\pi\) | |||||||
\(710\) | −20.7804 | −0.779873 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.24775 | 0.0467613 | ||||||||
\(713\) | −5.52486 | −0.206908 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.47725 | −0.204838 | ||||||||
\(716\) | 62.0582 | 2.31922 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 56.1831 | 2.09674 | ||||||||
\(719\) | −45.6237 | −1.70148 | −0.850739 | − | 0.525589i | \(-0.823845\pi\) | ||||
−0.850739 | + | 0.525589i | \(0.823845\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.11308 | 0.190421 | ||||||||
\(722\) | −90.6345 | −3.37307 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 75.6706 | 2.81228 | ||||||||
\(725\) | 9.75341 | 0.362233 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.30019 | −0.196573 | −0.0982867 | − | 0.995158i | \(-0.531336\pi\) | ||||
−0.0982867 | + | 0.995158i | \(0.531336\pi\) | |||||||
\(728\) | 3.32747 | 0.123324 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −92.7255 | −3.43193 | ||||||||
\(731\) | −27.5071 | −1.01739 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.30042 | −0.306583 | −0.153292 | − | 0.988181i | \(-0.548987\pi\) | ||||
−0.153292 | + | 0.988181i | \(0.548987\pi\) | |||||||
\(734\) | −2.66972 | −0.0985412 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.3291 | 0.823062 | ||||||||
\(737\) | 5.60162 | 0.206338 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.5316 | 1.04955 | 0.524775 | − | 0.851241i | \(-0.324149\pi\) | ||||
0.524775 | + | 0.851241i | \(0.324149\pi\) | |||||||
\(740\) | 8.84954 | 0.325315 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.21852 | 0.0814444 | ||||||||
\(743\) | 7.19884 | 0.264100 | 0.132050 | − | 0.991243i | \(-0.457844\pi\) | ||||
0.132050 | + | 0.991243i | \(0.457844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.2227 | 1.21719 | ||||||||
\(746\) | 0.591221 | 0.0216461 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −28.1241 | −1.02832 | ||||||||
\(749\) | 3.96461 | 0.144864 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.8207 | 0.942211 | 0.471106 | − | 0.882077i | \(-0.343855\pi\) | ||||
0.471106 | + | 0.882077i | \(0.343855\pi\) | |||||||
\(752\) | −1.71964 | −0.0627090 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.32456 | −0.230327 | ||||||||
\(755\) | 61.8340 | 2.25037 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.3933 | 0.668516 | 0.334258 | − | 0.942482i | \(-0.391514\pi\) | ||||
0.334258 | + | 0.942482i | \(0.391514\pi\) | |||||||
\(758\) | 48.9795 | 1.77902 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 79.9562 | 2.90032 | ||||||||
\(761\) | −54.4345 | −1.97325 | −0.986625 | − | 0.163009i | \(-0.947880\pi\) | ||||
−0.986625 | + | 0.163009i | \(0.947880\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.4907 | −0.452193 | ||||||||
\(764\) | −62.2687 | −2.25280 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.9252 | 1.11737 | ||||||||
\(767\) | 4.46327 | 0.161159 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.3709 | 1.38369 | 0.691845 | − | 0.722046i | \(-0.256798\pi\) | ||||
0.691845 | + | 0.722046i | \(0.256798\pi\) | |||||||
\(770\) | −14.1991 | −0.511699 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27.7282 | −0.997960 | ||||||||
\(773\) | −11.0889 | −0.398841 | −0.199421 | − | 0.979914i | \(-0.563906\pi\) | ||||
−0.199421 | + | 0.979914i | \(0.563906\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.05734 | −0.109823 | ||||||||
\(776\) | −29.8717 | −1.07233 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.49133 | −0.0893185 | ||||||||
\(779\) | 25.4958 | 0.913481 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.39877 | −0.228966 | ||||||||
\(782\) | 53.2511 | 1.90425 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.51941 | 0.0542645 | ||||||||
\(785\) | −7.71791 | −0.275464 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.1820 | −0.541179 | −0.270589 | − | 0.962695i | \(-0.587219\pi\) | ||||
−0.270589 | + | 0.962695i | \(0.587219\pi\) | |||||||
\(788\) | −17.2958 | −0.616138 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.7824 | −0.561514 | ||||||||
\(791\) | 0.691741 | 0.0245955 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.52527 | 0.125186 | ||||||||
\(794\) | 1.21744 | 0.0432052 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 70.8224 | 2.51023 | ||||||||
\(797\) | 42.0898 | 1.49090 | 0.745449 | − | 0.666563i | \(-0.232235\pi\) | ||||
0.745449 | + | 0.666563i | \(0.232235\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.28409 | 0.151560 | ||||||||
\(800\) | 12.3565 | 0.436867 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 35.4455 | 1.25163 | ||||||||
\(803\) | −28.5524 | −1.00759 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.2024 | 0.606307 | ||||||||
\(806\) | 1.98252 | 0.0698314 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −46.7373 | −1.64421 | ||||||||
\(809\) | −35.4386 | −1.24595 | −0.622977 | − | 0.782240i | \(-0.714077\pi\) | ||||
−0.622977 | + | 0.782240i | \(0.714077\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.0006 | 0.632087 | 0.316044 | − | 0.948745i | \(-0.397645\pi\) | ||||
0.316044 | + | 0.948745i | \(0.397645\pi\) | |||||||
\(812\) | −10.4908 | −0.368155 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.25876 | 0.149269 | ||||||||
\(815\) | 55.6598 | 1.94968 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55.0853 | 1.92719 | ||||||||
\(818\) | 18.1623 | 0.635028 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −34.4388 | −1.20266 | ||||||||
\(821\) | 21.1160 | 0.736955 | 0.368477 | − | 0.929637i | \(-0.379879\pi\) | ||||
0.368477 | + | 0.929637i | \(0.379879\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.8585 | 1.21509 | 0.607545 | − | 0.794285i | \(-0.292154\pi\) | ||||
0.607545 | + | 0.794285i | \(0.292154\pi\) | |||||||
\(824\) | 18.7162 | 0.652009 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.5704 | 0.402587 | ||||||||
\(827\) | −15.8606 | −0.551527 | −0.275764 | − | 0.961225i | \(-0.588931\pi\) | ||||
−0.275764 | + | 0.961225i | \(0.588931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.1365 | 0.560445 | 0.280223 | − | 0.959935i | \(-0.409592\pi\) | ||||
0.280223 | + | 0.959935i | \(0.409592\pi\) | |||||||
\(830\) | 65.9448 | 2.28898 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.7749 | −0.373552 | ||||||||
\(833\) | −3.78525 | −0.131151 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.75302 | 0.0606659 | ||||||||
\(836\) | 56.3210 | 1.94790 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −66.0572 | −2.28191 | ||||||||
\(839\) | 39.0471 | 1.34806 | 0.674028 | − | 0.738705i | \(-0.264563\pi\) | ||||
0.674028 | + | 0.738705i | \(0.264563\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.2833 | −0.699425 | ||||||||
\(842\) | −75.2897 | −2.59465 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −26.9658 | −0.928200 | ||||||||
\(845\) | 35.0795 | 1.20677 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.62777 | 0.227733 | ||||||||
\(848\) | 1.43041 | 0.0491205 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 29.4680 | 1.01075 | ||||||||
\(851\) | −5.15957 | −0.176868 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.6231 | 1.21971 | 0.609856 | − | 0.792512i | \(-0.291227\pi\) | ||||
0.609856 | + | 0.792512i | \(0.291227\pi\) | |||||||
\(854\) | 9.13881 | 0.312723 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.5123 | 0.496019 | ||||||||
\(857\) | −6.14909 | −0.210049 | −0.105025 | − | 0.994470i | \(-0.533492\pi\) | ||||
−0.105025 | + | 0.994470i | \(0.533492\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.17991 | −0.0743775 | −0.0371888 | − | 0.999308i | \(-0.511840\pi\) | ||||
−0.0371888 | + | 0.999308i | \(0.511840\pi\) | |||||||
\(860\) | −74.4073 | −2.53727 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −70.0047 | −2.38437 | ||||||||
\(863\) | 14.2536 | 0.485198 | 0.242599 | − | 0.970127i | \(-0.422000\pi\) | ||||
0.242599 | + | 0.970127i | \(0.422000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.1558 | −0.787319 | ||||||||
\(866\) | −20.2978 | −0.689747 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.28849 | 0.111619 | ||||||||
\(869\) | −4.85979 | −0.164857 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.43524 | 0.0825148 | ||||||||
\(872\) | −45.7216 | −1.54833 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −106.640 | −3.60715 | ||||||||
\(875\) | −4.88847 | −0.165260 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.8181 | 1.54717 | 0.773584 | − | 0.633694i | \(-0.218462\pi\) | ||||
0.773584 | + | 0.633694i | \(0.218462\pi\) | |||||||
\(878\) | 15.9676 | 0.538882 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.15497 | −0.308614 | ||||||||
\(881\) | 53.7021 | 1.80927 | 0.904634 | − | 0.426189i | \(-0.140144\pi\) | ||||
0.904634 | + | 0.426189i | \(0.140144\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.3029 | 0.784205 | 0.392103 | − | 0.919922i | \(-0.371748\pi\) | ||||
0.392103 | + | 0.919922i | \(0.371748\pi\) | |||||||
\(884\) | −12.2266 | −0.411226 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −49.3284 | −1.65722 | ||||||||
\(887\) | 9.22062 | 0.309598 | 0.154799 | − | 0.987946i | \(-0.450527\pi\) | ||||
0.154799 | + | 0.987946i | \(0.450527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −2.31473 | −0.0775898 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.239303 | −0.00801245 | ||||||||
\(893\) | −8.57927 | −0.287094 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −50.3266 | −1.68223 | ||||||||
\(896\) | −20.4518 | −0.683245 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 77.5845 | 2.58903 | ||||||||
\(899\) | −2.73236 | −0.0911295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.56354 | −0.118719 | ||||||||
\(902\) | −16.5734 | −0.551833 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.53209 | 0.0842160 | ||||||||
\(905\) | −61.3657 | −2.03987 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.5765 | 1.51334 | 0.756672 | − | 0.653795i | \(-0.226824\pi\) | ||||
0.756672 | + | 0.653795i | \(0.226824\pi\) | |||||||
\(908\) | 60.2557 | 1.99966 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.17287 | −0.204629 | ||||||||
\(911\) | 8.51625 | 0.282156 | 0.141078 | − | 0.989998i | \(-0.454943\pi\) | ||||
0.141078 | + | 0.989998i | \(0.454943\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.3060 | 0.672030 | ||||||||
\(914\) | −48.7722 | −1.61324 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 93.7052 | 3.09611 | ||||||||
\(917\) | 2.30452 | 0.0761019 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.8342 | 1.54492 | 0.772458 | − | 0.635066i | \(-0.219027\pi\) | ||||
0.772458 | + | 0.635066i | \(0.219027\pi\) | |||||||
\(920\) | 62.9688 | 2.07602 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.09861 | 0.299647 | ||||||||
\(923\) | −2.78179 | −0.0915637 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.85520 | −0.0938783 | ||||||||
\(926\) | 14.8236 | 0.487133 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.0430 | 0.362506 | ||||||||
\(929\) | 35.8706 | 1.17688 | 0.588438 | − | 0.808542i | \(-0.299743\pi\) | ||||
0.588438 | + | 0.808542i | \(0.299743\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.58028 | 0.248434 | ||||||||
\(932\) | −107.268 | −3.51368 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.3638 | 0.895370 | ||||||||
\(935\) | 22.8075 | 0.745885 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.9419 | 1.23951 | 0.619753 | − | 0.784797i | \(-0.287233\pi\) | ||||
0.619753 | + | 0.784797i | \(0.287233\pi\) | |||||||
\(938\) | 6.31303 | 0.206128 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.5886 | 0.377978 | ||||||||
\(941\) | 40.0327 | 1.30503 | 0.652515 | − | 0.757776i | \(-0.273714\pi\) | ||||
0.652515 | + | 0.757776i | \(0.273714\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.0790 | 0.653861 | ||||||||
\(944\) | 7.46014 | 0.242807 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35.8078 | −1.16421 | ||||||||
\(947\) | 42.7394 | 1.38884 | 0.694422 | − | 0.719568i | \(-0.255660\pi\) | ||||
0.694422 | + | 0.719568i | \(0.255660\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.4128 | −0.402937 | ||||||||
\(950\) | −59.0123 | −1.91461 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.8557 | −0.449066 | ||||||||
\(953\) | −43.9497 | −1.42367 | −0.711835 | − | 0.702347i | \(-0.752135\pi\) | ||||
−0.711835 | + | 0.702347i | \(0.752135\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.4973 | 1.63405 | ||||||||
\(956\) | 2.25877 | 0.0730539 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −86.0287 | −2.77946 | ||||||||
\(959\) | 6.70881 | 0.216639 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1435 | −0.972371 | ||||||||
\(962\) | 1.85144 | 0.0596929 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 50.2353 | 1.61797 | ||||||||
\(965\) | 22.4864 | 0.723863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3318 | 1.03972 | 0.519860 | − | 0.854251i | \(-0.325984\pi\) | ||||
0.519860 | + | 0.854251i | \(0.325984\pi\) | |||||||
\(968\) | 24.2606 | 0.779766 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 55.4158 | 1.77929 | ||||||||
\(971\) | 33.1010 | 1.06226 | 0.531131 | − | 0.847290i | \(-0.321767\pi\) | ||||
0.531131 | + | 0.847290i | \(0.321767\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.3703 | 0.332458 | ||||||||
\(974\) | −44.4494 | −1.42425 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.89233 | 0.188609 | ||||||||
\(977\) | 26.3507 | 0.843033 | 0.421516 | − | 0.906821i | \(-0.361498\pi\) | ||||
0.421516 | + | 0.906821i | \(0.361498\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.712760 | −0.0227799 | ||||||||
\(980\) | −10.2392 | −0.327079 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.60847 | 0.242796 | ||||||||
\(983\) | −20.5951 | −0.656883 | −0.328442 | − | 0.944524i | \(-0.606523\pi\) | ||||
−0.328442 | + | 0.944524i | \(0.606523\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.0262 | 0.446911 | ||||||||
\(986\) | 26.3357 | 0.838701 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.4849 | 0.778968 | ||||||||
\(989\) | 43.3819 | 1.37946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.2387 | −0.484074 | −0.242037 | − | 0.970267i | \(-0.577815\pi\) | ||||
−0.242037 | + | 0.970267i | \(0.577815\pi\) | |||||||
\(992\) | −3.46160 | −0.109906 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.21142 | −0.228733 | ||||||||
\(995\) | −57.4340 | −1.82078 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.6942 | 0.972096 | 0.486048 | − | 0.873932i | \(-0.338438\pi\) | ||||
0.486048 | + | 0.873932i | \(0.338438\pi\) | |||||||
\(998\) | 66.2759 | 2.09793 | ||||||||
\(999\) | 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 | 8001.2.a.s.1.4 | 16 | ||
3.2 | odd | 2 | 2667.2.a.n.1.13 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.n.1.13 | ✓ | 16 | 3.2 | odd | 2 | ||
8001.2.a.s.1.4 | 16 | 1.1 | even | 1 | trivial |