Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8619,2,Mod(1,8619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8619, 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("8619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8619 = 3 \cdot 13^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8619.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: | \(68.8230615021\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8619.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.271243 | −0.191798 | −0.0958989 | − | 0.995391i | \(-0.530573\pi\) | ||||
−0.0958989 | + | 0.995391i | \(0.530573\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.92643 | −0.963214 | ||||||||
\(5\) | 0.00688268 | 0.00307803 | 0.00153901 | − | 0.999999i | \(-0.499510\pi\) | ||||
0.00153901 | + | 0.999999i | \(0.499510\pi\) | |||||||
\(6\) | 0.271243 | 0.110734 | ||||||||
\(7\) | −0.318502 | −0.120382 | −0.0601911 | − | 0.998187i | \(-0.519171\pi\) | ||||
−0.0601911 | + | 0.998187i | \(0.519171\pi\) | |||||||
\(8\) | 1.06502 | 0.376540 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.00186688 | −0.000590359 0 | ||||||||
\(11\) | −1.42139 | −0.428566 | −0.214283 | − | 0.976772i | \(-0.568741\pi\) | ||||
−0.214283 | + | 0.976772i | \(0.568741\pi\) | |||||||
\(12\) | 1.92643 | 0.556112 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.0863913 | 0.0230891 | ||||||||
\(15\) | −0.00688268 | −0.00177710 | ||||||||
\(16\) | 3.56398 | 0.890994 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.271243 | −0.0639326 | ||||||||
\(19\) | 5.45062 | 1.25046 | 0.625229 | − | 0.780442i | \(-0.285006\pi\) | ||||
0.625229 | + | 0.780442i | \(0.285006\pi\) | |||||||
\(20\) | −0.0132590 | −0.00296480 | ||||||||
\(21\) | 0.318502 | 0.0695028 | ||||||||
\(22\) | 0.385542 | 0.0821979 | ||||||||
\(23\) | 5.80459 | 1.21034 | 0.605171 | − | 0.796096i | \(-0.293105\pi\) | ||||
0.605171 | + | 0.796096i | \(0.293105\pi\) | |||||||
\(24\) | −1.06502 | −0.217395 | ||||||||
\(25\) | −4.99995 | −0.999991 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.613570 | 0.115954 | ||||||||
\(29\) | −7.93198 | −1.47293 | −0.736466 | − | 0.676474i | \(-0.763507\pi\) | ||||
−0.736466 | + | 0.676474i | \(0.763507\pi\) | |||||||
\(30\) | 0.00186688 | 0.000340844 0 | ||||||||
\(31\) | −7.44201 | −1.33662 | −0.668312 | − | 0.743881i | \(-0.732983\pi\) | ||||
−0.668312 | + | 0.743881i | \(0.732983\pi\) | |||||||
\(32\) | −3.09674 | −0.547431 | ||||||||
\(33\) | 1.42139 | 0.247432 | ||||||||
\(34\) | 0.271243 | 0.0465178 | ||||||||
\(35\) | −0.00219214 | −0.000370540 0 | ||||||||
\(36\) | −1.92643 | −0.321071 | ||||||||
\(37\) | 5.62074 | 0.924044 | 0.462022 | − | 0.886868i | \(-0.347124\pi\) | ||||
0.462022 | + | 0.886868i | \(0.347124\pi\) | |||||||
\(38\) | −1.47844 | −0.239835 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.00733016 | 0.00115900 | ||||||||
\(41\) | −4.23517 | −0.661422 | −0.330711 | − | 0.943732i | \(-0.607289\pi\) | ||||
−0.330711 | + | 0.943732i | \(0.607289\pi\) | |||||||
\(42\) | −0.0863913 | −0.0133305 | ||||||||
\(43\) | 0.441322 | 0.0673010 | 0.0336505 | − | 0.999434i | \(-0.489287\pi\) | ||||
0.0336505 | + | 0.999434i | \(0.489287\pi\) | |||||||
\(44\) | 2.73821 | 0.412800 | ||||||||
\(45\) | 0.00688268 | 0.00102601 | ||||||||
\(46\) | −1.57446 | −0.232141 | ||||||||
\(47\) | −6.87013 | −1.00211 | −0.501055 | − | 0.865415i | \(-0.667055\pi\) | ||||
−0.501055 | + | 0.865415i | \(0.667055\pi\) | |||||||
\(48\) | −3.56398 | −0.514416 | ||||||||
\(49\) | −6.89856 | −0.985508 | ||||||||
\(50\) | 1.35620 | 0.191796 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.0316 | 1.65267 | 0.826335 | − | 0.563179i | \(-0.190422\pi\) | ||||
0.826335 | + | 0.563179i | \(0.190422\pi\) | |||||||
\(54\) | 0.271243 | 0.0369115 | ||||||||
\(55\) | −0.00978298 | −0.00131914 | ||||||||
\(56\) | −0.339209 | −0.0453287 | ||||||||
\(57\) | −5.45062 | −0.721952 | ||||||||
\(58\) | 2.15150 | 0.282505 | ||||||||
\(59\) | 9.16514 | 1.19320 | 0.596600 | − | 0.802539i | \(-0.296518\pi\) | ||||
0.596600 | + | 0.802539i | \(0.296518\pi\) | |||||||
\(60\) | 0.0132590 | 0.00171173 | ||||||||
\(61\) | 12.7980 | 1.63862 | 0.819308 | − | 0.573354i | \(-0.194358\pi\) | ||||
0.819308 | + | 0.573354i | \(0.194358\pi\) | |||||||
\(62\) | 2.01859 | 0.256362 | ||||||||
\(63\) | −0.318502 | −0.0401274 | ||||||||
\(64\) | −6.28798 | −0.785998 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.385542 | −0.0474570 | ||||||||
\(67\) | −11.9404 | −1.45876 | −0.729378 | − | 0.684111i | \(-0.760190\pi\) | ||||
−0.729378 | + | 0.684111i | \(0.760190\pi\) | |||||||
\(68\) | 1.92643 | 0.233614 | ||||||||
\(69\) | −5.80459 | −0.698791 | ||||||||
\(70\) | 0.000594604 0 | 7.10687e−5 0 | ||||||||
\(71\) | 13.0118 | 1.54422 | 0.772111 | − | 0.635488i | \(-0.219201\pi\) | ||||
0.772111 | + | 0.635488i | \(0.219201\pi\) | |||||||
\(72\) | 1.06502 | 0.125513 | ||||||||
\(73\) | 3.70014 | 0.433069 | 0.216534 | − | 0.976275i | \(-0.430525\pi\) | ||||
0.216534 | + | 0.976275i | \(0.430525\pi\) | |||||||
\(74\) | −1.52459 | −0.177230 | ||||||||
\(75\) | 4.99995 | 0.577345 | ||||||||
\(76\) | −10.5002 | −1.20446 | ||||||||
\(77\) | 0.452715 | 0.0515917 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.03937 | −0.904500 | −0.452250 | − | 0.891891i | \(-0.649379\pi\) | ||||
−0.452250 | + | 0.891891i | \(0.649379\pi\) | |||||||
\(80\) | 0.0245297 | 0.00274250 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.14876 | 0.126859 | ||||||||
\(83\) | 1.63139 | 0.179069 | 0.0895343 | − | 0.995984i | \(-0.471462\pi\) | ||||
0.0895343 | + | 0.995984i | \(0.471462\pi\) | |||||||
\(84\) | −0.613570 | −0.0669460 | ||||||||
\(85\) | −0.00688268 | −0.000746531 0 | ||||||||
\(86\) | −0.119706 | −0.0129082 | ||||||||
\(87\) | 7.93198 | 0.850398 | ||||||||
\(88\) | −1.51380 | −0.161372 | ||||||||
\(89\) | −7.33095 | −0.777080 | −0.388540 | − | 0.921432i | \(-0.627020\pi\) | ||||
−0.388540 | + | 0.921432i | \(0.627020\pi\) | |||||||
\(90\) | −0.00186688 | −0.000196786 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −11.1821 | −1.16582 | ||||||||
\(93\) | 7.44201 | 0.771701 | ||||||||
\(94\) | 1.86347 | 0.192203 | ||||||||
\(95\) | 0.0375148 | 0.00384894 | ||||||||
\(96\) | 3.09674 | 0.316059 | ||||||||
\(97\) | 6.25153 | 0.634747 | 0.317374 | − | 0.948301i | \(-0.397199\pi\) | ||||
0.317374 | + | 0.948301i | \(0.397199\pi\) | |||||||
\(98\) | 1.87119 | 0.189018 | ||||||||
\(99\) | −1.42139 | −0.142855 | ||||||||
\(100\) | 9.63204 | 0.963204 | ||||||||
\(101\) | −4.29051 | −0.426922 | −0.213461 | − | 0.976952i | \(-0.568474\pi\) | ||||
−0.213461 | + | 0.976952i | \(0.568474\pi\) | |||||||
\(102\) | −0.271243 | −0.0268571 | ||||||||
\(103\) | −13.4261 | −1.32291 | −0.661457 | − | 0.749983i | \(-0.730062\pi\) | ||||
−0.661457 | + | 0.749983i | \(0.730062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.00219214 | 0.000213931 0 | ||||||||
\(106\) | −3.26349 | −0.316978 | ||||||||
\(107\) | 16.6563 | 1.61022 | 0.805111 | − | 0.593124i | \(-0.202105\pi\) | ||||
0.805111 | + | 0.593124i | \(0.202105\pi\) | |||||||
\(108\) | 1.92643 | 0.185371 | ||||||||
\(109\) | 19.3621 | 1.85456 | 0.927278 | − | 0.374374i | \(-0.122142\pi\) | ||||
0.927278 | + | 0.374374i | \(0.122142\pi\) | |||||||
\(110\) | 0.00265356 | 0.000253007 0 | ||||||||
\(111\) | −5.62074 | −0.533497 | ||||||||
\(112\) | −1.13513 | −0.107260 | ||||||||
\(113\) | 6.97830 | 0.656463 | 0.328232 | − | 0.944597i | \(-0.393547\pi\) | ||||
0.328232 | + | 0.944597i | \(0.393547\pi\) | |||||||
\(114\) | 1.47844 | 0.138469 | ||||||||
\(115\) | 0.0399511 | 0.00372546 | ||||||||
\(116\) | 15.2804 | 1.41875 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.48598 | −0.228853 | ||||||||
\(119\) | 0.318502 | 0.0291970 | ||||||||
\(120\) | −0.00733016 | −0.000669149 0 | ||||||||
\(121\) | −8.97965 | −0.816331 | ||||||||
\(122\) | −3.47137 | −0.314283 | ||||||||
\(123\) | 4.23517 | 0.381872 | ||||||||
\(124\) | 14.3365 | 1.28746 | ||||||||
\(125\) | −0.0688265 | −0.00615603 | ||||||||
\(126\) | 0.0863913 | 0.00769635 | ||||||||
\(127\) | 10.5113 | 0.932725 | 0.466363 | − | 0.884594i | \(-0.345564\pi\) | ||||
0.466363 | + | 0.884594i | \(0.345564\pi\) | |||||||
\(128\) | 7.89904 | 0.698183 | ||||||||
\(129\) | −0.441322 | −0.0388563 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.4950 | −1.61592 | −0.807958 | − | 0.589240i | \(-0.799427\pi\) | ||||
−0.807958 | + | 0.589240i | \(0.799427\pi\) | |||||||
\(132\) | −2.73821 | −0.238330 | ||||||||
\(133\) | −1.73603 | −0.150533 | ||||||||
\(134\) | 3.23876 | 0.279786 | ||||||||
\(135\) | −0.00688268 | −0.000592367 0 | ||||||||
\(136\) | −1.06502 | −0.0913244 | ||||||||
\(137\) | −9.75101 | −0.833085 | −0.416543 | − | 0.909116i | \(-0.636758\pi\) | ||||
−0.416543 | + | 0.909116i | \(0.636758\pi\) | |||||||
\(138\) | 1.57446 | 0.134027 | ||||||||
\(139\) | 3.08211 | 0.261421 | 0.130711 | − | 0.991421i | \(-0.458274\pi\) | ||||
0.130711 | + | 0.991421i | \(0.458274\pi\) | |||||||
\(140\) | 0.00422301 | 0.000356909 0 | ||||||||
\(141\) | 6.87013 | 0.578569 | ||||||||
\(142\) | −3.52937 | −0.296178 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.56398 | 0.296998 | ||||||||
\(145\) | −0.0545933 | −0.00453373 | ||||||||
\(146\) | −1.00364 | −0.0830617 | ||||||||
\(147\) | 6.89856 | 0.568983 | ||||||||
\(148\) | −10.8280 | −0.890052 | ||||||||
\(149\) | 20.6199 | 1.68925 | 0.844625 | − | 0.535359i | \(-0.179823\pi\) | ||||
0.844625 | + | 0.535359i | \(0.179823\pi\) | |||||||
\(150\) | −1.35620 | −0.110733 | ||||||||
\(151\) | 23.5613 | 1.91739 | 0.958694 | − | 0.284440i | \(-0.0918075\pi\) | ||||
0.958694 | + | 0.284440i | \(0.0918075\pi\) | |||||||
\(152\) | 5.80499 | 0.470847 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −0.122796 | −0.00989518 | ||||||||
\(155\) | −0.0512210 | −0.00411417 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.92126 | 0.711994 | 0.355997 | − | 0.934487i | \(-0.384141\pi\) | ||||
0.355997 | + | 0.934487i | \(0.384141\pi\) | |||||||
\(158\) | 2.18062 | 0.173481 | ||||||||
\(159\) | −12.0316 | −0.954169 | ||||||||
\(160\) | −0.0213138 | −0.00168501 | ||||||||
\(161\) | −1.84877 | −0.145704 | ||||||||
\(162\) | −0.271243 | −0.0213109 | ||||||||
\(163\) | −9.17334 | −0.718511 | −0.359256 | − | 0.933239i | \(-0.616969\pi\) | ||||
−0.359256 | + | 0.933239i | \(0.616969\pi\) | |||||||
\(164\) | 8.15875 | 0.637091 | ||||||||
\(165\) | 0.00978298 | 0.000761604 0 | ||||||||
\(166\) | −0.442504 | −0.0343450 | ||||||||
\(167\) | −8.67286 | −0.671126 | −0.335563 | − | 0.942018i | \(-0.608927\pi\) | ||||
−0.335563 | + | 0.942018i | \(0.608927\pi\) | |||||||
\(168\) | 0.339209 | 0.0261706 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.00186688 | 0.000143183 0 | ||||||||
\(171\) | 5.45062 | 0.416819 | ||||||||
\(172\) | −0.850175 | −0.0648252 | ||||||||
\(173\) | −21.7845 | −1.65624 | −0.828121 | − | 0.560550i | \(-0.810590\pi\) | ||||
−0.828121 | + | 0.560550i | \(0.810590\pi\) | |||||||
\(174\) | −2.15150 | −0.163104 | ||||||||
\(175\) | 1.59249 | 0.120381 | ||||||||
\(176\) | −5.06581 | −0.381849 | ||||||||
\(177\) | −9.16514 | −0.688894 | ||||||||
\(178\) | 1.98847 | 0.149042 | ||||||||
\(179\) | 4.58198 | 0.342473 | 0.171236 | − | 0.985230i | \(-0.445224\pi\) | ||||
0.171236 | + | 0.985230i | \(0.445224\pi\) | |||||||
\(180\) | −0.0132590 | −0.000988266 0 | ||||||||
\(181\) | 23.9705 | 1.78172 | 0.890858 | − | 0.454281i | \(-0.150104\pi\) | ||||
0.890858 | + | 0.454281i | \(0.150104\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.7980 | −0.946055 | ||||||||
\(184\) | 6.18198 | 0.455742 | ||||||||
\(185\) | 0.0386858 | 0.00284423 | ||||||||
\(186\) | −2.01859 | −0.148010 | ||||||||
\(187\) | 1.42139 | 0.103942 | ||||||||
\(188\) | 13.2348 | 0.965247 | ||||||||
\(189\) | 0.318502 | 0.0231676 | ||||||||
\(190\) | −0.0101756 | −0.000738218 0 | ||||||||
\(191\) | 5.22989 | 0.378422 | 0.189211 | − | 0.981936i | \(-0.439407\pi\) | ||||
0.189211 | + | 0.981936i | \(0.439407\pi\) | |||||||
\(192\) | 6.28798 | 0.453796 | ||||||||
\(193\) | −15.8515 | −1.14102 | −0.570508 | − | 0.821292i | \(-0.693254\pi\) | ||||
−0.570508 | + | 0.821292i | \(0.693254\pi\) | |||||||
\(194\) | −1.69568 | −0.121743 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.2896 | 0.949255 | ||||||||
\(197\) | −4.04717 | −0.288349 | −0.144174 | − | 0.989552i | \(-0.546053\pi\) | ||||
−0.144174 | + | 0.989552i | \(0.546053\pi\) | |||||||
\(198\) | 0.385542 | 0.0273993 | ||||||||
\(199\) | −8.43818 | −0.598167 | −0.299083 | − | 0.954227i | \(-0.596681\pi\) | ||||
−0.299083 | + | 0.954227i | \(0.596681\pi\) | |||||||
\(200\) | −5.32503 | −0.376536 | ||||||||
\(201\) | 11.9404 | 0.842213 | ||||||||
\(202\) | 1.16377 | 0.0818826 | ||||||||
\(203\) | 2.52635 | 0.177315 | ||||||||
\(204\) | −1.92643 | −0.134877 | ||||||||
\(205\) | −0.0291493 | −0.00203588 | ||||||||
\(206\) | 3.64174 | 0.253732 | ||||||||
\(207\) | 5.80459 | 0.403447 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.74746 | −0.535903 | ||||||||
\(210\) | −0.000594604 0 | −4.10316e−5 0 | ||||||||
\(211\) | 9.48816 | 0.653192 | 0.326596 | − | 0.945164i | \(-0.394098\pi\) | ||||
0.326596 | + | 0.945164i | \(0.394098\pi\) | |||||||
\(212\) | −23.1780 | −1.59187 | ||||||||
\(213\) | −13.0118 | −0.891557 | ||||||||
\(214\) | −4.51790 | −0.308837 | ||||||||
\(215\) | 0.00303748 | 0.000207154 0 | ||||||||
\(216\) | −1.06502 | −0.0724652 | ||||||||
\(217\) | 2.37029 | 0.160906 | ||||||||
\(218\) | −5.25184 | −0.355700 | ||||||||
\(219\) | −3.70014 | −0.250032 | ||||||||
\(220\) | 0.0188462 | 0.00127061 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.52459 | 0.102324 | ||||||||
\(223\) | −23.1692 | −1.55153 | −0.775764 | − | 0.631024i | \(-0.782635\pi\) | ||||
−0.775764 | + | 0.631024i | \(0.782635\pi\) | |||||||
\(224\) | 0.986315 | 0.0659010 | ||||||||
\(225\) | −4.99995 | −0.333330 | ||||||||
\(226\) | −1.89281 | −0.125908 | ||||||||
\(227\) | −20.7519 | −1.37735 | −0.688677 | − | 0.725069i | \(-0.741808\pi\) | ||||
−0.688677 | + | 0.725069i | \(0.741808\pi\) | |||||||
\(228\) | 10.5002 | 0.695394 | ||||||||
\(229\) | −23.8739 | −1.57763 | −0.788816 | − | 0.614629i | \(-0.789306\pi\) | ||||
−0.788816 | + | 0.614629i | \(0.789306\pi\) | |||||||
\(230\) | −0.0108365 | −0.000714536 0 | ||||||||
\(231\) | −0.452715 | −0.0297865 | ||||||||
\(232\) | −8.44769 | −0.554618 | ||||||||
\(233\) | −15.2349 | −0.998071 | −0.499035 | − | 0.866582i | \(-0.666312\pi\) | ||||
−0.499035 | + | 0.866582i | \(0.666312\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0472849 | −0.00308452 | ||||||||
\(236\) | −17.6560 | −1.14931 | ||||||||
\(237\) | 8.03937 | 0.522213 | ||||||||
\(238\) | −0.0863913 | −0.00559992 | ||||||||
\(239\) | −22.2874 | −1.44165 | −0.720826 | − | 0.693116i | \(-0.756237\pi\) | ||||
−0.720826 | + | 0.693116i | \(0.756237\pi\) | |||||||
\(240\) | −0.0245297 | −0.00158339 | ||||||||
\(241\) | 10.8332 | 0.697831 | 0.348915 | − | 0.937154i | \(-0.386550\pi\) | ||||
0.348915 | + | 0.937154i | \(0.386550\pi\) | |||||||
\(242\) | 2.43567 | 0.156571 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −24.6544 | −1.57834 | ||||||||
\(245\) | −0.0474805 | −0.00303342 | ||||||||
\(246\) | −1.14876 | −0.0732423 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.92586 | −0.503293 | ||||||||
\(249\) | −1.63139 | −0.103385 | ||||||||
\(250\) | 0.0186687 | 0.00118071 | ||||||||
\(251\) | 2.68284 | 0.169339 | 0.0846696 | − | 0.996409i | \(-0.473017\pi\) | ||||
0.0846696 | + | 0.996409i | \(0.473017\pi\) | |||||||
\(252\) | 0.613570 | 0.0386513 | ||||||||
\(253\) | −8.25060 | −0.518711 | ||||||||
\(254\) | −2.85111 | −0.178895 | ||||||||
\(255\) | 0.00688268 | 0.000431010 0 | ||||||||
\(256\) | 10.4334 | 0.652088 | ||||||||
\(257\) | −2.75207 | −0.171669 | −0.0858346 | − | 0.996309i | \(-0.527356\pi\) | ||||
−0.0858346 | + | 0.996309i | \(0.527356\pi\) | |||||||
\(258\) | 0.119706 | 0.00745254 | ||||||||
\(259\) | −1.79022 | −0.111239 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.93198 | −0.490978 | ||||||||
\(262\) | 5.01664 | 0.309929 | ||||||||
\(263\) | 27.9696 | 1.72468 | 0.862339 | − | 0.506332i | \(-0.168999\pi\) | ||||
0.862339 | + | 0.506332i | \(0.168999\pi\) | |||||||
\(264\) | 1.51380 | 0.0931682 | ||||||||
\(265\) | 0.0828097 | 0.00508696 | ||||||||
\(266\) | 0.470886 | 0.0288719 | ||||||||
\(267\) | 7.33095 | 0.448647 | ||||||||
\(268\) | 23.0024 | 1.40509 | ||||||||
\(269\) | 5.91910 | 0.360894 | 0.180447 | − | 0.983585i | \(-0.442246\pi\) | ||||
0.180447 | + | 0.983585i | \(0.442246\pi\) | |||||||
\(270\) | 0.00186688 | 0.000113615 0 | ||||||||
\(271\) | −12.5645 | −0.763240 | −0.381620 | − | 0.924319i | \(-0.624634\pi\) | ||||
−0.381620 | + | 0.924319i | \(0.624634\pi\) | |||||||
\(272\) | −3.56398 | −0.216098 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.64489 | 0.159784 | ||||||||
\(275\) | 7.10689 | 0.428562 | ||||||||
\(276\) | 11.1821 | 0.673085 | ||||||||
\(277\) | 5.83069 | 0.350332 | 0.175166 | − | 0.984539i | \(-0.443954\pi\) | ||||
0.175166 | + | 0.984539i | \(0.443954\pi\) | |||||||
\(278\) | −0.836002 | −0.0501400 | ||||||||
\(279\) | −7.44201 | −0.445542 | ||||||||
\(280\) | −0.00233467 | −0.000139523 0 | ||||||||
\(281\) | −4.16768 | −0.248623 | −0.124311 | − | 0.992243i | \(-0.539672\pi\) | ||||
−0.124311 | + | 0.992243i | \(0.539672\pi\) | |||||||
\(282\) | −1.86347 | −0.110968 | ||||||||
\(283\) | −17.8601 | −1.06167 | −0.530837 | − | 0.847474i | \(-0.678123\pi\) | ||||
−0.530837 | + | 0.847474i | \(0.678123\pi\) | |||||||
\(284\) | −25.0664 | −1.48742 | ||||||||
\(285\) | −0.0375148 | −0.00222219 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.34891 | 0.0796236 | ||||||||
\(288\) | −3.09674 | −0.182477 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.0148080 | 0.000869559 0 | ||||||||
\(291\) | −6.25153 | −0.366471 | ||||||||
\(292\) | −7.12806 | −0.417138 | ||||||||
\(293\) | 10.4494 | 0.610459 | 0.305229 | − | 0.952279i | \(-0.401267\pi\) | ||||
0.305229 | + | 0.952279i | \(0.401267\pi\) | |||||||
\(294\) | −1.87119 | −0.109130 | ||||||||
\(295\) | 0.0630807 | 0.00367270 | ||||||||
\(296\) | 5.98618 | 0.347940 | ||||||||
\(297\) | 1.42139 | 0.0824775 | ||||||||
\(298\) | −5.59301 | −0.323994 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −9.63204 | −0.556106 | ||||||||
\(301\) | −0.140562 | −0.00810185 | ||||||||
\(302\) | −6.39083 | −0.367751 | ||||||||
\(303\) | 4.29051 | 0.246483 | ||||||||
\(304\) | 19.4259 | 1.11415 | ||||||||
\(305\) | 0.0880845 | 0.00504370 | ||||||||
\(306\) | 0.271243 | 0.0155059 | ||||||||
\(307\) | −28.2902 | −1.61461 | −0.807304 | − | 0.590135i | \(-0.799074\pi\) | ||||
−0.807304 | + | 0.590135i | \(0.799074\pi\) | |||||||
\(308\) | −0.872123 | −0.0496938 | ||||||||
\(309\) | 13.4261 | 0.763785 | ||||||||
\(310\) | 0.0138933 | 0.000789088 0 | ||||||||
\(311\) | 22.6949 | 1.28691 | 0.643456 | − | 0.765483i | \(-0.277500\pi\) | ||||
0.643456 | + | 0.765483i | \(0.277500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.794040 | 0.0448818 | 0.0224409 | − | 0.999748i | \(-0.492856\pi\) | ||||
0.0224409 | + | 0.999748i | \(0.492856\pi\) | |||||||
\(314\) | −2.41983 | −0.136559 | ||||||||
\(315\) | −0.00219214 | −0.000123513 0 | ||||||||
\(316\) | 15.4873 | 0.871227 | ||||||||
\(317\) | −32.7911 | −1.84173 | −0.920867 | − | 0.389877i | \(-0.872518\pi\) | ||||
−0.920867 | + | 0.389877i | \(0.872518\pi\) | |||||||
\(318\) | 3.26349 | 0.183007 | ||||||||
\(319\) | 11.2745 | 0.631248 | ||||||||
\(320\) | −0.0432782 | −0.00241932 | ||||||||
\(321\) | −16.6563 | −0.929663 | ||||||||
\(322\) | 0.501467 | 0.0279456 | ||||||||
\(323\) | −5.45062 | −0.303280 | ||||||||
\(324\) | −1.92643 | −0.107024 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.48820 | 0.137809 | ||||||||
\(327\) | −19.3621 | −1.07073 | ||||||||
\(328\) | −4.51052 | −0.249052 | ||||||||
\(329\) | 2.18815 | 0.120636 | ||||||||
\(330\) | −0.00265356 | −0.000146074 0 | ||||||||
\(331\) | −7.77000 | −0.427078 | −0.213539 | − | 0.976935i | \(-0.568499\pi\) | ||||
−0.213539 | + | 0.976935i | \(0.568499\pi\) | |||||||
\(332\) | −3.14276 | −0.172481 | ||||||||
\(333\) | 5.62074 | 0.308015 | ||||||||
\(334\) | 2.35245 | 0.128720 | ||||||||
\(335\) | −0.0821821 | −0.00449009 | ||||||||
\(336\) | 1.13513 | 0.0619265 | ||||||||
\(337\) | −24.3752 | −1.32780 | −0.663902 | − | 0.747820i | \(-0.731101\pi\) | ||||
−0.663902 | + | 0.747820i | \(0.731101\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.97830 | −0.379009 | ||||||||
\(340\) | 0.0132590 | 0.000719069 0 | ||||||||
\(341\) | 10.5780 | 0.572831 | ||||||||
\(342\) | −1.47844 | −0.0799450 | ||||||||
\(343\) | 4.42671 | 0.239020 | ||||||||
\(344\) | 0.470015 | 0.0253415 | ||||||||
\(345\) | −0.0399511 | −0.00215090 | ||||||||
\(346\) | 5.90888 | 0.317663 | ||||||||
\(347\) | −5.88456 | −0.315900 | −0.157950 | − | 0.987447i | \(-0.550488\pi\) | ||||
−0.157950 | + | 0.987447i | \(0.550488\pi\) | |||||||
\(348\) | −15.2804 | −0.819115 | ||||||||
\(349\) | −11.5578 | −0.618673 | −0.309337 | − | 0.950953i | \(-0.600107\pi\) | ||||
−0.309337 | + | 0.950953i | \(0.600107\pi\) | |||||||
\(350\) | −0.431953 | −0.0230888 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.40167 | 0.234610 | ||||||||
\(353\) | 22.4803 | 1.19651 | 0.598253 | − | 0.801308i | \(-0.295862\pi\) | ||||
0.598253 | + | 0.801308i | \(0.295862\pi\) | |||||||
\(354\) | 2.48598 | 0.132128 | ||||||||
\(355\) | 0.0895563 | 0.00475316 | ||||||||
\(356\) | 14.1225 | 0.748494 | ||||||||
\(357\) | −0.318502 | −0.0168569 | ||||||||
\(358\) | −1.24283 | −0.0656855 | ||||||||
\(359\) | −24.5967 | −1.29816 | −0.649082 | − | 0.760719i | \(-0.724847\pi\) | ||||
−0.649082 | + | 0.760719i | \(0.724847\pi\) | |||||||
\(360\) | 0.00733016 | 0.000386333 0 | ||||||||
\(361\) | 10.7092 | 0.563644 | ||||||||
\(362\) | −6.50184 | −0.341729 | ||||||||
\(363\) | 8.97965 | 0.471309 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0254669 | 0.00133300 | ||||||||
\(366\) | 3.47137 | 0.181451 | ||||||||
\(367\) | −6.84500 | −0.357306 | −0.178653 | − | 0.983912i | \(-0.557174\pi\) | ||||
−0.178653 | + | 0.983912i | \(0.557174\pi\) | |||||||
\(368\) | 20.6874 | 1.07841 | ||||||||
\(369\) | −4.23517 | −0.220474 | ||||||||
\(370\) | −0.0104932 | −0.000545518 0 | ||||||||
\(371\) | −3.83209 | −0.198952 | ||||||||
\(372\) | −14.3365 | −0.743313 | ||||||||
\(373\) | 23.4415 | 1.21375 | 0.606876 | − | 0.794796i | \(-0.292422\pi\) | ||||
0.606876 | + | 0.794796i | \(0.292422\pi\) | |||||||
\(374\) | −0.385542 | −0.0199359 | ||||||||
\(375\) | 0.0688265 | 0.00355418 | ||||||||
\(376\) | −7.31679 | −0.377335 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.0863913 | −0.00444349 | ||||||||
\(379\) | −28.2309 | −1.45013 | −0.725063 | − | 0.688683i | \(-0.758189\pi\) | ||||
−0.725063 | + | 0.688683i | \(0.758189\pi\) | |||||||
\(380\) | −0.0722696 | −0.00370735 | ||||||||
\(381\) | −10.5113 | −0.538509 | ||||||||
\(382\) | −1.41857 | −0.0725804 | ||||||||
\(383\) | 20.2683 | 1.03566 | 0.517830 | − | 0.855483i | \(-0.326740\pi\) | ||||
0.517830 | + | 0.855483i | \(0.326740\pi\) | |||||||
\(384\) | −7.89904 | −0.403096 | ||||||||
\(385\) | 0.00311589 | 0.000158801 0 | ||||||||
\(386\) | 4.29961 | 0.218844 | ||||||||
\(387\) | 0.441322 | 0.0224337 | ||||||||
\(388\) | −12.0431 | −0.611397 | ||||||||
\(389\) | 31.4421 | 1.59418 | 0.797088 | − | 0.603864i | \(-0.206373\pi\) | ||||
0.797088 | + | 0.603864i | \(0.206373\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.80459 | −0.293551 | ||||||||
\(392\) | −7.34707 | −0.371083 | ||||||||
\(393\) | 18.4950 | 0.932949 | ||||||||
\(394\) | 1.09777 | 0.0553046 | ||||||||
\(395\) | −0.0553324 | −0.00278408 | ||||||||
\(396\) | 2.73821 | 0.137600 | ||||||||
\(397\) | −17.4925 | −0.877925 | −0.438963 | − | 0.898505i | \(-0.644654\pi\) | ||||
−0.438963 | + | 0.898505i | \(0.644654\pi\) | |||||||
\(398\) | 2.28880 | 0.114727 | ||||||||
\(399\) | 1.73603 | 0.0869102 | ||||||||
\(400\) | −17.8197 | −0.890986 | ||||||||
\(401\) | −29.9104 | −1.49365 | −0.746826 | − | 0.665020i | \(-0.768423\pi\) | ||||
−0.746826 | + | 0.665020i | \(0.768423\pi\) | |||||||
\(402\) | −3.23876 | −0.161535 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8.26535 | 0.411217 | ||||||||
\(405\) | 0.00688268 | 0.000342003 0 | ||||||||
\(406\) | −0.685255 | −0.0340086 | ||||||||
\(407\) | −7.98927 | −0.396014 | ||||||||
\(408\) | 1.06502 | 0.0527261 | ||||||||
\(409\) | 0.625173 | 0.0309128 | 0.0154564 | − | 0.999881i | \(-0.495080\pi\) | ||||
0.0154564 | + | 0.999881i | \(0.495080\pi\) | |||||||
\(410\) | 0.00790655 | 0.000390476 0 | ||||||||
\(411\) | 9.75101 | 0.480982 | ||||||||
\(412\) | 25.8644 | 1.27425 | ||||||||
\(413\) | −2.91911 | −0.143640 | ||||||||
\(414\) | −1.57446 | −0.0773802 | ||||||||
\(415\) | 0.0112283 | 0.000551178 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.08211 | −0.150932 | ||||||||
\(418\) | 2.10144 | 0.102785 | ||||||||
\(419\) | 16.0459 | 0.783892 | 0.391946 | − | 0.919988i | \(-0.371802\pi\) | ||||
0.391946 | + | 0.919988i | \(0.371802\pi\) | |||||||
\(420\) | −0.00422301 | −0.000206062 0 | ||||||||
\(421\) | 0.622631 | 0.0303452 | 0.0151726 | − | 0.999885i | \(-0.495170\pi\) | ||||
0.0151726 | + | 0.999885i | \(0.495170\pi\) | |||||||
\(422\) | −2.57360 | −0.125281 | ||||||||
\(423\) | −6.87013 | −0.334037 | ||||||||
\(424\) | 12.8139 | 0.622296 | ||||||||
\(425\) | 4.99995 | 0.242533 | ||||||||
\(426\) | 3.52937 | 0.170999 | ||||||||
\(427\) | −4.07618 | −0.197260 | ||||||||
\(428\) | −32.0871 | −1.55099 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.000823895 0 | −3.97317e−5 0 | ||||||||
\(431\) | −2.95119 | −0.142154 | −0.0710768 | − | 0.997471i | \(-0.522644\pi\) | ||||
−0.0710768 | + | 0.997471i | \(0.522644\pi\) | |||||||
\(432\) | −3.56398 | −0.171472 | ||||||||
\(433\) | 8.33543 | 0.400575 | 0.200288 | − | 0.979737i | \(-0.435812\pi\) | ||||
0.200288 | + | 0.979737i | \(0.435812\pi\) | |||||||
\(434\) | −0.642925 | −0.0308614 | ||||||||
\(435\) | 0.0545933 | 0.00261755 | ||||||||
\(436\) | −37.2997 | −1.78633 | ||||||||
\(437\) | 31.6386 | 1.51348 | ||||||||
\(438\) | 1.00364 | 0.0479557 | ||||||||
\(439\) | −31.8986 | −1.52244 | −0.761219 | − | 0.648494i | \(-0.775399\pi\) | ||||
−0.761219 | + | 0.648494i | \(0.775399\pi\) | |||||||
\(440\) | −0.0104190 | −0.000496708 0 | ||||||||
\(441\) | −6.89856 | −0.328503 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.7556 | −0.653548 | −0.326774 | − | 0.945103i | \(-0.605962\pi\) | ||||
−0.326774 | + | 0.945103i | \(0.605962\pi\) | |||||||
\(444\) | 10.8280 | 0.513872 | ||||||||
\(445\) | −0.0504566 | −0.00239187 | ||||||||
\(446\) | 6.28449 | 0.297579 | ||||||||
\(447\) | −20.6199 | −0.975289 | ||||||||
\(448\) | 2.00273 | 0.0946203 | ||||||||
\(449\) | −22.1259 | −1.04419 | −0.522094 | − | 0.852888i | \(-0.674849\pi\) | ||||
−0.522094 | + | 0.852888i | \(0.674849\pi\) | |||||||
\(450\) | 1.35620 | 0.0639320 | ||||||||
\(451\) | 6.01983 | 0.283463 | ||||||||
\(452\) | −13.4432 | −0.632314 | ||||||||
\(453\) | −23.5613 | −1.10700 | ||||||||
\(454\) | 5.62881 | 0.264173 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.80499 | −0.271844 | ||||||||
\(457\) | −13.3415 | −0.624088 | −0.312044 | − | 0.950068i | \(-0.601014\pi\) | ||||
−0.312044 | + | 0.950068i | \(0.601014\pi\) | |||||||
\(458\) | 6.47563 | 0.302586 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −0.0769630 | −0.00358842 | ||||||||
\(461\) | −2.20411 | −0.102656 | −0.0513279 | − | 0.998682i | \(-0.516345\pi\) | ||||
−0.0513279 | + | 0.998682i | \(0.516345\pi\) | |||||||
\(462\) | 0.122796 | 0.00571298 | ||||||||
\(463\) | 0.0836288 | 0.00388656 | 0.00194328 | − | 0.999998i | \(-0.499381\pi\) | ||||
0.00194328 | + | 0.999998i | \(0.499381\pi\) | |||||||
\(464\) | −28.2694 | −1.31237 | ||||||||
\(465\) | 0.0512210 | 0.00237532 | ||||||||
\(466\) | 4.13236 | 0.191428 | ||||||||
\(467\) | 19.3109 | 0.893602 | 0.446801 | − | 0.894633i | \(-0.352563\pi\) | ||||
0.446801 | + | 0.894633i | \(0.352563\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.80305 | 0.175608 | ||||||||
\(470\) | 0.0128257 | 0.000591605 0 | ||||||||
\(471\) | −8.92126 | −0.411070 | ||||||||
\(472\) | 9.76102 | 0.449287 | ||||||||
\(473\) | −0.627292 | −0.0288429 | ||||||||
\(474\) | −2.18062 | −0.100159 | ||||||||
\(475\) | −27.2528 | −1.25045 | ||||||||
\(476\) | −0.613570 | −0.0281229 | ||||||||
\(477\) | 12.0316 | 0.550890 | ||||||||
\(478\) | 6.04530 | 0.276506 | ||||||||
\(479\) | 10.7890 | 0.492962 | 0.246481 | − | 0.969148i | \(-0.420726\pi\) | ||||
0.246481 | + | 0.969148i | \(0.420726\pi\) | |||||||
\(480\) | 0.0213138 | 0.000972839 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2.93844 | −0.133842 | ||||||||
\(483\) | 1.84877 | 0.0841220 | ||||||||
\(484\) | 17.2986 | 0.786302 | ||||||||
\(485\) | 0.0430273 | 0.00195377 | ||||||||
\(486\) | 0.271243 | 0.0123038 | ||||||||
\(487\) | 11.4032 | 0.516727 | 0.258363 | − | 0.966048i | \(-0.416817\pi\) | ||||
0.258363 | + | 0.966048i | \(0.416817\pi\) | |||||||
\(488\) | 13.6301 | 0.617004 | ||||||||
\(489\) | 9.17334 | 0.414833 | ||||||||
\(490\) | 0.0128788 | 0.000581803 0 | ||||||||
\(491\) | 36.3438 | 1.64017 | 0.820086 | − | 0.572240i | \(-0.193925\pi\) | ||||
0.820086 | + | 0.572240i | \(0.193925\pi\) | |||||||
\(492\) | −8.15875 | −0.367825 | ||||||||
\(493\) | 7.93198 | 0.357239 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.00978298 | −0.000439712 0 | ||||||||
\(496\) | −26.5232 | −1.19092 | ||||||||
\(497\) | −4.14429 | −0.185897 | ||||||||
\(498\) | 0.442504 | 0.0198291 | ||||||||
\(499\) | 22.4463 | 1.00483 | 0.502417 | − | 0.864625i | \(-0.332444\pi\) | ||||
0.502417 | + | 0.864625i | \(0.332444\pi\) | |||||||
\(500\) | 0.132589 | 0.00592957 | ||||||||
\(501\) | 8.67286 | 0.387475 | ||||||||
\(502\) | −0.727700 | −0.0324789 | ||||||||
\(503\) | −10.3409 | −0.461080 | −0.230540 | − | 0.973063i | \(-0.574049\pi\) | ||||
−0.230540 | + | 0.973063i | \(0.574049\pi\) | |||||||
\(504\) | −0.339209 | −0.0151096 | ||||||||
\(505\) | −0.0295302 | −0.00131408 | ||||||||
\(506\) | 2.23792 | 0.0994875 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20.2492 | −0.898414 | ||||||||
\(509\) | −25.6559 | −1.13718 | −0.568590 | − | 0.822621i | \(-0.692511\pi\) | ||||
−0.568590 | + | 0.822621i | \(0.692511\pi\) | |||||||
\(510\) | −0.00186688 | −8.26668e−5 0 | ||||||||
\(511\) | −1.17850 | −0.0521338 | ||||||||
\(512\) | −18.6281 | −0.823252 | ||||||||
\(513\) | −5.45062 | −0.240651 | ||||||||
\(514\) | 0.746479 | 0.0329258 | ||||||||
\(515\) | −0.0924076 | −0.00407197 | ||||||||
\(516\) | 0.850175 | 0.0374269 | ||||||||
\(517\) | 9.76514 | 0.429470 | ||||||||
\(518\) | 0.485583 | 0.0213353 | ||||||||
\(519\) | 21.7845 | 0.956231 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.8613 | −1.26444 | −0.632218 | − | 0.774790i | \(-0.717855\pi\) | ||||
−0.632218 | + | 0.774790i | \(0.717855\pi\) | |||||||
\(522\) | 2.15150 | 0.0941684 | ||||||||
\(523\) | 29.4307 | 1.28691 | 0.643457 | − | 0.765483i | \(-0.277500\pi\) | ||||
0.643457 | + | 0.765483i | \(0.277500\pi\) | |||||||
\(524\) | 35.6293 | 1.55647 | ||||||||
\(525\) | −1.59249 | −0.0695021 | ||||||||
\(526\) | −7.58655 | −0.330789 | ||||||||
\(527\) | 7.44201 | 0.324179 | ||||||||
\(528\) | 5.06581 | 0.220461 | ||||||||
\(529\) | 10.6933 | 0.464926 | ||||||||
\(530\) | −0.0224616 | −0.000975668 0 | ||||||||
\(531\) | 9.16514 | 0.397733 | ||||||||
\(532\) | 3.34434 | 0.144995 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.98847 | −0.0860495 | ||||||||
\(535\) | 0.114640 | 0.00495631 | ||||||||
\(536\) | −12.7167 | −0.549280 | ||||||||
\(537\) | −4.58198 | −0.197727 | ||||||||
\(538\) | −1.60551 | −0.0692186 | ||||||||
\(539\) | 9.80555 | 0.422355 | ||||||||
\(540\) | 0.0132590 | 0.000570576 0 | ||||||||
\(541\) | −15.6430 | −0.672546 | −0.336273 | − | 0.941765i | \(-0.609166\pi\) | ||||
−0.336273 | + | 0.941765i | \(0.609166\pi\) | |||||||
\(542\) | 3.40804 | 0.146388 | ||||||||
\(543\) | −23.9705 | −1.02867 | ||||||||
\(544\) | 3.09674 | 0.132771 | ||||||||
\(545\) | 0.133263 | 0.00570837 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.3593 | 0.956014 | 0.478007 | − | 0.878356i | \(-0.341359\pi\) | ||||
0.478007 | + | 0.878356i | \(0.341359\pi\) | |||||||
\(548\) | 18.7846 | 0.802439 | ||||||||
\(549\) | 12.7980 | 0.546205 | ||||||||
\(550\) | −1.92769 | −0.0821972 | ||||||||
\(551\) | −43.2342 | −1.84184 | ||||||||
\(552\) | −6.18198 | −0.263123 | ||||||||
\(553\) | 2.56055 | 0.108886 | ||||||||
\(554\) | −1.58153 | −0.0671929 | ||||||||
\(555\) | −0.0386858 | −0.00164212 | ||||||||
\(556\) | −5.93747 | −0.251805 | ||||||||
\(557\) | 14.5131 | 0.614941 | 0.307470 | − | 0.951558i | \(-0.400517\pi\) | ||||
0.307470 | + | 0.951558i | \(0.400517\pi\) | |||||||
\(558\) | 2.01859 | 0.0854539 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.00781275 | −0.000330149 0 | ||||||||
\(561\) | −1.42139 | −0.0600112 | ||||||||
\(562\) | 1.13045 | 0.0476853 | ||||||||
\(563\) | −3.83294 | −0.161539 | −0.0807697 | − | 0.996733i | \(-0.525738\pi\) | ||||
−0.0807697 | + | 0.996733i | \(0.525738\pi\) | |||||||
\(564\) | −13.2348 | −0.557285 | ||||||||
\(565\) | 0.0480294 | 0.00202061 | ||||||||
\(566\) | 4.84444 | 0.203627 | ||||||||
\(567\) | −0.318502 | −0.0133758 | ||||||||
\(568\) | 13.8578 | 0.581461 | ||||||||
\(569\) | −36.7941 | −1.54249 | −0.771245 | − | 0.636538i | \(-0.780366\pi\) | ||||
−0.771245 | + | 0.636538i | \(0.780366\pi\) | |||||||
\(570\) | 0.0101756 | 0.000426211 0 | ||||||||
\(571\) | −30.2379 | −1.26542 | −0.632709 | − | 0.774390i | \(-0.718057\pi\) | ||||
−0.632709 | + | 0.774390i | \(0.718057\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.22989 | −0.218482 | ||||||||
\(574\) | −0.365882 | −0.0152716 | ||||||||
\(575\) | −29.0227 | −1.21033 | ||||||||
\(576\) | −6.28798 | −0.261999 | ||||||||
\(577\) | −44.3418 | −1.84597 | −0.922987 | − | 0.384832i | \(-0.874260\pi\) | ||||
−0.922987 | + | 0.384832i | \(0.874260\pi\) | |||||||
\(578\) | −0.271243 | −0.0112822 | ||||||||
\(579\) | 15.8515 | 0.658766 | ||||||||
\(580\) | 0.105170 | 0.00436695 | ||||||||
\(581\) | −0.519601 | −0.0215567 | ||||||||
\(582\) | 1.69568 | 0.0702884 | ||||||||
\(583\) | −17.1016 | −0.708277 | ||||||||
\(584\) | 3.94071 | 0.163068 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.83432 | −0.117085 | ||||||||
\(587\) | 30.0522 | 1.24039 | 0.620194 | − | 0.784449i | \(-0.287054\pi\) | ||||
0.620194 | + | 0.784449i | \(0.287054\pi\) | |||||||
\(588\) | −13.2896 | −0.548053 | ||||||||
\(589\) | −40.5636 | −1.67139 | ||||||||
\(590\) | −0.0171102 | −0.000704416 0 | ||||||||
\(591\) | 4.04717 | 0.166478 | ||||||||
\(592\) | 20.0322 | 0.823318 | ||||||||
\(593\) | −12.4463 | −0.511107 | −0.255554 | − | 0.966795i | \(-0.582258\pi\) | ||||
−0.255554 | + | 0.966795i | \(0.582258\pi\) | |||||||
\(594\) | −0.385542 | −0.0158190 | ||||||||
\(595\) | 0.00219214 | 8.98691e−5 0 | ||||||||
\(596\) | −39.7228 | −1.62711 | ||||||||
\(597\) | 8.43818 | 0.345352 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.956746 | −0.0390916 | −0.0195458 | − | 0.999809i | \(-0.506222\pi\) | ||||
−0.0195458 | + | 0.999809i | \(0.506222\pi\) | |||||||
\(600\) | 5.32503 | 0.217393 | ||||||||
\(601\) | −14.1641 | −0.577765 | −0.288882 | − | 0.957365i | \(-0.593284\pi\) | ||||
−0.288882 | + | 0.957365i | \(0.593284\pi\) | |||||||
\(602\) | 0.0381264 | 0.00155392 | ||||||||
\(603\) | −11.9404 | −0.486252 | ||||||||
\(604\) | −45.3890 | −1.84685 | ||||||||
\(605\) | −0.0618040 | −0.00251269 | ||||||||
\(606\) | −1.16377 | −0.0472749 | ||||||||
\(607\) | 1.86891 | 0.0758568 | 0.0379284 | − | 0.999280i | \(-0.487924\pi\) | ||||
0.0379284 | + | 0.999280i | \(0.487924\pi\) | |||||||
\(608\) | −16.8791 | −0.684539 | ||||||||
\(609\) | −2.52635 | −0.102373 | ||||||||
\(610\) | −0.0238923 | −0.000967371 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.92643 | 0.0778712 | ||||||||
\(613\) | −3.87460 | −0.156493 | −0.0782467 | − | 0.996934i | \(-0.524932\pi\) | ||||
−0.0782467 | + | 0.996934i | \(0.524932\pi\) | |||||||
\(614\) | 7.67353 | 0.309678 | ||||||||
\(615\) | 0.0291493 | 0.00117541 | ||||||||
\(616\) | 0.482149 | 0.0194263 | ||||||||
\(617\) | −27.9349 | −1.12462 | −0.562309 | − | 0.826927i | \(-0.690087\pi\) | ||||
−0.562309 | + | 0.826927i | \(0.690087\pi\) | |||||||
\(618\) | −3.64174 | −0.146492 | ||||||||
\(619\) | 18.0563 | 0.725746 | 0.362873 | − | 0.931839i | \(-0.381796\pi\) | ||||
0.362873 | + | 0.931839i | \(0.381796\pi\) | |||||||
\(620\) | 0.0986735 | 0.00396282 | ||||||||
\(621\) | −5.80459 | −0.232930 | ||||||||
\(622\) | −6.15585 | −0.246827 | ||||||||
\(623\) | 2.33492 | 0.0935466 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9993 | 0.999972 | ||||||||
\(626\) | −0.215378 | −0.00860823 | ||||||||
\(627\) | 7.74746 | 0.309404 | ||||||||
\(628\) | −17.1862 | −0.685802 | ||||||||
\(629\) | −5.62074 | −0.224114 | ||||||||
\(630\) | 0.000594604 0 | 2.36896e−5 0 | ||||||||
\(631\) | −4.46422 | −0.177718 | −0.0888588 | − | 0.996044i | \(-0.528322\pi\) | ||||
−0.0888588 | + | 0.996044i | \(0.528322\pi\) | |||||||
\(632\) | −8.56206 | −0.340580 | ||||||||
\(633\) | −9.48816 | −0.377120 | ||||||||
\(634\) | 8.89437 | 0.353240 | ||||||||
\(635\) | 0.0723457 | 0.00287095 | ||||||||
\(636\) | 23.1780 | 0.919069 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.05812 | −0.121072 | ||||||||
\(639\) | 13.0118 | 0.514741 | ||||||||
\(640\) | 0.0543666 | 0.00214903 | ||||||||
\(641\) | −11.5138 | −0.454768 | −0.227384 | − | 0.973805i | \(-0.573017\pi\) | ||||
−0.227384 | + | 0.973805i | \(0.573017\pi\) | |||||||
\(642\) | 4.51790 | 0.178307 | ||||||||
\(643\) | −26.5641 | −1.04759 | −0.523794 | − | 0.851845i | \(-0.675484\pi\) | ||||
−0.523794 | + | 0.851845i | \(0.675484\pi\) | |||||||
\(644\) | 3.56153 | 0.140344 | ||||||||
\(645\) | −0.00303748 | −0.000119601 0 | ||||||||
\(646\) | 1.47844 | 0.0581685 | ||||||||
\(647\) | −5.12374 | −0.201435 | −0.100718 | − | 0.994915i | \(-0.532114\pi\) | ||||
−0.100718 | + | 0.994915i | \(0.532114\pi\) | |||||||
\(648\) | 1.06502 | 0.0418378 | ||||||||
\(649\) | −13.0273 | −0.511365 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.37029 | −0.0928991 | ||||||||
\(652\) | 17.6718 | 0.692080 | ||||||||
\(653\) | −19.6655 | −0.769572 | −0.384786 | − | 0.923006i | \(-0.625725\pi\) | ||||
−0.384786 | + | 0.923006i | \(0.625725\pi\) | |||||||
\(654\) | 5.25184 | 0.205363 | ||||||||
\(655\) | −0.127295 | −0.00497383 | ||||||||
\(656\) | −15.0940 | −0.589323 | ||||||||
\(657\) | 3.70014 | 0.144356 | ||||||||
\(658\) | −0.593519 | −0.0231378 | ||||||||
\(659\) | 2.21540 | 0.0862999 | 0.0431499 | − | 0.999069i | \(-0.486261\pi\) | ||||
0.0431499 | + | 0.999069i | \(0.486261\pi\) | |||||||
\(660\) | −0.0188462 | −0.000733587 0 | ||||||||
\(661\) | 19.9744 | 0.776916 | 0.388458 | − | 0.921466i | \(-0.373008\pi\) | ||||
0.388458 | + | 0.921466i | \(0.373008\pi\) | |||||||
\(662\) | 2.10756 | 0.0819126 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.73746 | 0.0674265 | ||||||||
\(665\) | −0.0119485 | −0.000463344 0 | ||||||||
\(666\) | −1.52459 | −0.0590765 | ||||||||
\(667\) | −46.0419 | −1.78275 | ||||||||
\(668\) | 16.7076 | 0.646437 | ||||||||
\(669\) | 23.1692 | 0.895775 | ||||||||
\(670\) | 0.0222913 | 0.000861189 0 | ||||||||
\(671\) | −18.1910 | −0.702255 | ||||||||
\(672\) | −0.986315 | −0.0380479 | ||||||||
\(673\) | −26.9075 | −1.03721 | −0.518603 | − | 0.855015i | \(-0.673548\pi\) | ||||
−0.518603 | + | 0.855015i | \(0.673548\pi\) | |||||||
\(674\) | 6.61161 | 0.254670 | ||||||||
\(675\) | 4.99995 | 0.192448 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.71905 | 0.258234 | 0.129117 | − | 0.991629i | \(-0.458786\pi\) | ||||
0.129117 | + | 0.991629i | \(0.458786\pi\) | |||||||
\(678\) | 1.89281 | 0.0726931 | ||||||||
\(679\) | −1.99112 | −0.0764123 | ||||||||
\(680\) | −0.00733016 | −0.000281099 0 | ||||||||
\(681\) | 20.7519 | 0.795215 | ||||||||
\(682\) | −2.86921 | −0.109868 | ||||||||
\(683\) | −25.1476 | −0.962248 | −0.481124 | − | 0.876653i | \(-0.659771\pi\) | ||||
−0.481124 | + | 0.876653i | \(0.659771\pi\) | |||||||
\(684\) | −10.5002 | −0.401486 | ||||||||
\(685\) | −0.0671131 | −0.00256426 | ||||||||
\(686\) | −1.20071 | −0.0458435 | ||||||||
\(687\) | 23.8739 | 0.910847 | ||||||||
\(688\) | 1.57286 | 0.0599648 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.0108365 | 0.000412537 0 | ||||||||
\(691\) | −24.6761 | −0.938725 | −0.469362 | − | 0.883006i | \(-0.655516\pi\) | ||||
−0.469362 | + | 0.883006i | \(0.655516\pi\) | |||||||
\(692\) | 41.9662 | 1.59531 | ||||||||
\(693\) | 0.452715 | 0.0171972 | ||||||||
\(694\) | 1.59615 | 0.0605889 | ||||||||
\(695\) | 0.0212132 | 0.000804662 0 | ||||||||
\(696\) | 8.44769 | 0.320209 | ||||||||
\(697\) | 4.23517 | 0.160419 | ||||||||
\(698\) | 3.13497 | 0.118660 | ||||||||
\(699\) | 15.2349 | 0.576236 | ||||||||
\(700\) | −3.06782 | −0.115953 | ||||||||
\(701\) | −41.8636 | −1.58116 | −0.790582 | − | 0.612356i | \(-0.790222\pi\) | ||||
−0.790582 | + | 0.612356i | \(0.790222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.6365 | 1.15548 | ||||||||
\(704\) | 8.93769 | 0.336852 | ||||||||
\(705\) | 0.0472849 | 0.00178085 | ||||||||
\(706\) | −6.09762 | −0.229487 | ||||||||
\(707\) | 1.36653 | 0.0513938 | ||||||||
\(708\) | 17.6560 | 0.663552 | ||||||||
\(709\) | −28.5207 | −1.07112 | −0.535559 | − | 0.844498i | \(-0.679899\pi\) | ||||
−0.535559 | + | 0.844498i | \(0.679899\pi\) | |||||||
\(710\) | −0.0242915 | −0.000911645 0 | ||||||||
\(711\) | −8.03937 | −0.301500 | ||||||||
\(712\) | −7.80758 | −0.292602 | ||||||||
\(713\) | −43.1978 | −1.61777 | ||||||||
\(714\) | 0.0863913 | 0.00323311 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.82684 | −0.329875 | ||||||||
\(717\) | 22.2874 | 0.832338 | ||||||||
\(718\) | 6.67168 | 0.248985 | ||||||||
\(719\) | −11.7552 | −0.438394 | −0.219197 | − | 0.975681i | \(-0.570344\pi\) | ||||
−0.219197 | + | 0.975681i | \(0.570344\pi\) | |||||||
\(720\) | 0.0245297 | 0.000914168 0 | ||||||||
\(721\) | 4.27624 | 0.159255 | ||||||||
\(722\) | −2.90480 | −0.108106 | ||||||||
\(723\) | −10.8332 | −0.402893 | ||||||||
\(724\) | −46.1775 | −1.71617 | ||||||||
\(725\) | 39.6595 | 1.47292 | ||||||||
\(726\) | −2.43567 | −0.0903960 | ||||||||
\(727\) | −43.6953 | −1.62057 | −0.810284 | − | 0.586038i | \(-0.800687\pi\) | ||||
−0.810284 | + | 0.586038i | \(0.800687\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.00690772 | −0.000255666 0 | ||||||||
\(731\) | −0.441322 | −0.0163229 | ||||||||
\(732\) | 24.6544 | 0.911253 | ||||||||
\(733\) | −21.3248 | −0.787650 | −0.393825 | − | 0.919185i | \(-0.628848\pi\) | ||||
−0.393825 | + | 0.919185i | \(0.628848\pi\) | |||||||
\(734\) | 1.85666 | 0.0685305 | ||||||||
\(735\) | 0.0474805 | 0.00175135 | ||||||||
\(736\) | −17.9753 | −0.662578 | ||||||||
\(737\) | 16.9720 | 0.625173 | ||||||||
\(738\) | 1.14876 | 0.0422864 | ||||||||
\(739\) | −0.819899 | −0.0301605 | −0.0150802 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150802 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(740\) | −0.0745253 | −0.00273960 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.03943 | 0.0381586 | ||||||||
\(743\) | −20.6398 | −0.757200 | −0.378600 | − | 0.925560i | \(-0.623594\pi\) | ||||
−0.378600 | + | 0.925560i | \(0.623594\pi\) | |||||||
\(744\) | 7.92586 | 0.290576 | ||||||||
\(745\) | 0.141920 | 0.00519956 | ||||||||
\(746\) | −6.35833 | −0.232795 | ||||||||
\(747\) | 1.63139 | 0.0596895 | ||||||||
\(748\) | −2.73821 | −0.100119 | ||||||||
\(749\) | −5.30505 | −0.193842 | ||||||||
\(750\) | −0.0186687 | −0.000681684 0 | ||||||||
\(751\) | −4.66362 | −0.170178 | −0.0850890 | − | 0.996373i | \(-0.527117\pi\) | ||||
−0.0850890 | + | 0.996373i | \(0.527117\pi\) | |||||||
\(752\) | −24.4850 | −0.892875 | ||||||||
\(753\) | −2.68284 | −0.0977680 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.162165 | 0.00590177 | ||||||||
\(756\) | −0.613570 | −0.0223153 | ||||||||
\(757\) | −16.0586 | −0.583659 | −0.291829 | − | 0.956470i | \(-0.594264\pi\) | ||||
−0.291829 | + | 0.956470i | \(0.594264\pi\) | |||||||
\(758\) | 7.65744 | 0.278131 | ||||||||
\(759\) | 8.25060 | 0.299478 | ||||||||
\(760\) | 0.0399539 | 0.00144928 | ||||||||
\(761\) | 11.8240 | 0.428621 | 0.214310 | − | 0.976766i | \(-0.431250\pi\) | ||||
0.214310 | + | 0.976766i | \(0.431250\pi\) | |||||||
\(762\) | 2.85111 | 0.103285 | ||||||||
\(763\) | −6.16687 | −0.223256 | ||||||||
\(764\) | −10.0750 | −0.364501 | ||||||||
\(765\) | −0.00688268 | −0.000248844 0 | ||||||||
\(766\) | −5.49763 | −0.198637 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −10.4334 | −0.376483 | ||||||||
\(769\) | −29.2725 | −1.05559 | −0.527797 | − | 0.849370i | \(-0.676982\pi\) | ||||
−0.527797 | + | 0.849370i | \(0.676982\pi\) | |||||||
\(770\) | −0.000845165 0 | −3.04576e−5 0 | ||||||||
\(771\) | 2.75207 | 0.0991133 | ||||||||
\(772\) | 30.5368 | 1.09904 | ||||||||
\(773\) | 17.3025 | 0.622326 | 0.311163 | − | 0.950357i | \(-0.399281\pi\) | ||||
0.311163 | + | 0.950357i | \(0.399281\pi\) | |||||||
\(774\) | −0.119706 | −0.00430273 | ||||||||
\(775\) | 37.2097 | 1.33661 | ||||||||
\(776\) | 6.65798 | 0.239008 | ||||||||
\(777\) | 1.79022 | 0.0642236 | ||||||||
\(778\) | −8.52844 | −0.305759 | ||||||||
\(779\) | −23.0843 | −0.827081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.4949 | −0.661801 | ||||||||
\(782\) | 1.57446 | 0.0563024 | ||||||||
\(783\) | 7.93198 | 0.283466 | ||||||||
\(784\) | −24.5863 | −0.878082 | ||||||||
\(785\) | 0.0614022 | 0.00219154 | ||||||||
\(786\) | −5.01664 | −0.178938 | ||||||||
\(787\) | −31.4636 | −1.12156 | −0.560778 | − | 0.827966i | \(-0.689498\pi\) | ||||
−0.560778 | + | 0.827966i | \(0.689498\pi\) | |||||||
\(788\) | 7.79657 | 0.277741 | ||||||||
\(789\) | −27.9696 | −0.995743 | ||||||||
\(790\) | 0.0150085 | 0.000533980 0 | ||||||||
\(791\) | −2.22260 | −0.0790265 | ||||||||
\(792\) | −1.51380 | −0.0537907 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 4.74473 | 0.168384 | ||||||||
\(795\) | −0.0828097 | −0.00293696 | ||||||||
\(796\) | 16.2555 | 0.576162 | ||||||||
\(797\) | −1.23443 | −0.0437259 | −0.0218630 | − | 0.999761i | \(-0.506960\pi\) | ||||
−0.0218630 | + | 0.999761i | \(0.506960\pi\) | |||||||
\(798\) | −0.470886 | −0.0166692 | ||||||||
\(799\) | 6.87013 | 0.243048 | ||||||||
\(800\) | 15.4835 | 0.547425 | ||||||||
\(801\) | −7.33095 | −0.259027 | ||||||||
\(802\) | 8.11297 | 0.286479 | ||||||||
\(803\) | −5.25935 | −0.185598 | ||||||||
\(804\) | −23.0024 | −0.811231 | ||||||||
\(805\) | −0.0127245 | −0.000448480 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.91910 | −0.208362 | ||||||||
\(808\) | −4.56946 | −0.160753 | ||||||||
\(809\) | 48.7732 | 1.71477 | 0.857387 | − | 0.514672i | \(-0.172086\pi\) | ||||
0.857387 | + | 0.514672i | \(0.172086\pi\) | |||||||
\(810\) | −0.00186688 | −6.55954e−5 0 | ||||||||
\(811\) | −52.7478 | −1.85223 | −0.926113 | − | 0.377246i | \(-0.876871\pi\) | ||||
−0.926113 | + | 0.377246i | \(0.876871\pi\) | |||||||
\(812\) | −4.86683 | −0.170792 | ||||||||
\(813\) | 12.5645 | 0.440657 | ||||||||
\(814\) | 2.16703 | 0.0759545 | ||||||||
\(815\) | −0.0631371 | −0.00221160 | ||||||||
\(816\) | 3.56398 | 0.124764 | ||||||||
\(817\) | 2.40548 | 0.0841570 | ||||||||
\(818\) | −0.169574 | −0.00592901 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0561540 | 0.00196098 | ||||||||
\(821\) | 5.68088 | 0.198264 | 0.0991320 | − | 0.995074i | \(-0.468393\pi\) | ||||
0.0991320 | + | 0.995074i | \(0.468393\pi\) | |||||||
\(822\) | −2.64489 | −0.0922513 | ||||||||
\(823\) | 29.2354 | 1.01908 | 0.509541 | − | 0.860447i | \(-0.329815\pi\) | ||||
0.509541 | + | 0.860447i | \(0.329815\pi\) | |||||||
\(824\) | −14.2990 | −0.498130 | ||||||||
\(825\) | −7.10689 | −0.247430 | ||||||||
\(826\) | 0.791789 | 0.0275499 | ||||||||
\(827\) | 13.3881 | 0.465549 | 0.232774 | − | 0.972531i | \(-0.425220\pi\) | ||||
0.232774 | + | 0.972531i | \(0.425220\pi\) | |||||||
\(828\) | −11.1821 | −0.388606 | ||||||||
\(829\) | −16.5426 | −0.574548 | −0.287274 | − | 0.957848i | \(-0.592749\pi\) | ||||
−0.287274 | + | 0.957848i | \(0.592749\pi\) | |||||||
\(830\) | −0.00304561 | −0.000105715 0 | ||||||||
\(831\) | −5.83069 | −0.202264 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.89856 | 0.239021 | ||||||||
\(834\) | 0.836002 | 0.0289484 | ||||||||
\(835\) | −0.0596925 | −0.00206574 | ||||||||
\(836\) | 14.9249 | 0.516189 | ||||||||
\(837\) | 7.44201 | 0.257234 | ||||||||
\(838\) | −4.35233 | −0.150349 | ||||||||
\(839\) | 41.6911 | 1.43933 | 0.719667 | − | 0.694319i | \(-0.244294\pi\) | ||||
0.719667 | + | 0.694319i | \(0.244294\pi\) | |||||||
\(840\) | 0.00233467 | 8.05537e−5 0 | ||||||||
\(841\) | 33.9164 | 1.16953 | ||||||||
\(842\) | −0.168884 | −0.00582013 | ||||||||
\(843\) | 4.16768 | 0.143542 | ||||||||
\(844\) | −18.2782 | −0.629163 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.86347 | 0.0640675 | ||||||||
\(847\) | 2.86003 | 0.0982719 | ||||||||
\(848\) | 42.8804 | 1.47252 | ||||||||
\(849\) | 17.8601 | 0.612958 | ||||||||
\(850\) | −1.35620 | −0.0465173 | ||||||||
\(851\) | 32.6261 | 1.11841 | ||||||||
\(852\) | 25.0664 | 0.858760 | ||||||||
\(853\) | −28.6964 | −0.982548 | −0.491274 | − | 0.871005i | \(-0.663469\pi\) | ||||
−0.491274 | + | 0.871005i | \(0.663469\pi\) | |||||||
\(854\) | 1.10564 | 0.0378341 | ||||||||
\(855\) | 0.0375148 | 0.00128298 | ||||||||
\(856\) | 17.7392 | 0.606313 | ||||||||
\(857\) | 16.7513 | 0.572213 | 0.286107 | − | 0.958198i | \(-0.407639\pi\) | ||||
0.286107 | + | 0.958198i | \(0.407639\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.12064 | −0.174714 | −0.0873571 | − | 0.996177i | \(-0.527842\pi\) | ||||
−0.0873571 | + | 0.996177i | \(0.527842\pi\) | |||||||
\(860\) | −0.00585148 | −0.000199534 0 | ||||||||
\(861\) | −1.34891 | −0.0459707 | ||||||||
\(862\) | 0.800489 | 0.0272648 | ||||||||
\(863\) | 36.6991 | 1.24925 | 0.624626 | − | 0.780924i | \(-0.285251\pi\) | ||||
0.624626 | + | 0.780924i | \(0.285251\pi\) | |||||||
\(864\) | 3.09674 | 0.105353 | ||||||||
\(865\) | −0.149935 | −0.00509796 | ||||||||
\(866\) | −2.26093 | −0.0768294 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −4.56620 | −0.154987 | ||||||||
\(869\) | 11.4271 | 0.387638 | ||||||||
\(870\) | −0.0148080 | −0.000502040 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 20.6210 | 0.698314 | ||||||||
\(873\) | 6.25153 | 0.211582 | ||||||||
\(874\) | −8.58175 | −0.290282 | ||||||||
\(875\) | 0.0219213 | 0.000741076 0 | ||||||||
\(876\) | 7.12806 | 0.240835 | ||||||||
\(877\) | −36.5447 | −1.23403 | −0.617013 | − | 0.786953i | \(-0.711657\pi\) | ||||
−0.617013 | + | 0.786953i | \(0.711657\pi\) | |||||||
\(878\) | 8.65228 | 0.292000 | ||||||||
\(879\) | −10.4494 | −0.352448 | ||||||||
\(880\) | −0.0348663 | −0.00117534 | ||||||||
\(881\) | 49.7618 | 1.67652 | 0.838259 | − | 0.545273i | \(-0.183574\pi\) | ||||
0.838259 | + | 0.545273i | \(0.183574\pi\) | |||||||
\(882\) | 1.87119 | 0.0630061 | ||||||||
\(883\) | 23.0084 | 0.774293 | 0.387146 | − | 0.922018i | \(-0.373461\pi\) | ||||
0.387146 | + | 0.922018i | \(0.373461\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0630807 | −0.00212044 | ||||||||
\(886\) | 3.73111 | 0.125349 | ||||||||
\(887\) | −3.98116 | −0.133674 | −0.0668372 | − | 0.997764i | \(-0.521291\pi\) | ||||
−0.0668372 | + | 0.997764i | \(0.521291\pi\) | |||||||
\(888\) | −5.98618 | −0.200883 | ||||||||
\(889\) | −3.34786 | −0.112284 | ||||||||
\(890\) | 0.0136860 | 0.000458756 0 | ||||||||
\(891\) | −1.42139 | −0.0476184 | ||||||||
\(892\) | 44.6339 | 1.49445 | ||||||||
\(893\) | −37.4464 | −1.25310 | ||||||||
\(894\) | 5.59301 | 0.187058 | ||||||||
\(895\) | 0.0315363 | 0.00105414 | ||||||||
\(896\) | −2.51586 | −0.0840489 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.00151 | 0.200273 | ||||||||
\(899\) | 59.0299 | 1.96876 | ||||||||
\(900\) | 9.63204 | 0.321068 | ||||||||
\(901\) | −12.0316 | −0.400831 | ||||||||
\(902\) | −1.63284 | −0.0543676 | ||||||||
\(903\) | 0.140562 | 0.00467761 | ||||||||
\(904\) | 7.43200 | 0.247185 | ||||||||
\(905\) | 0.164982 | 0.00548417 | ||||||||
\(906\) | 6.39083 | 0.212321 | ||||||||
\(907\) | 34.6173 | 1.14945 | 0.574725 | − | 0.818347i | \(-0.305109\pi\) | ||||
0.574725 | + | 0.818347i | \(0.305109\pi\) | |||||||
\(908\) | 39.9771 | 1.32669 | ||||||||
\(909\) | −4.29051 | −0.142307 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.42533 | −0.312275 | −0.156138 | − | 0.987735i | \(-0.549904\pi\) | ||||
−0.156138 | + | 0.987735i | \(0.549904\pi\) | |||||||
\(912\) | −19.4259 | −0.643255 | ||||||||
\(913\) | −2.31885 | −0.0767426 | ||||||||
\(914\) | 3.61878 | 0.119699 | ||||||||
\(915\) | −0.0880845 | −0.00291198 | ||||||||
\(916\) | 45.9914 | 1.51960 | ||||||||
\(917\) | 5.89069 | 0.194528 | ||||||||
\(918\) | −0.271243 | −0.00895235 | ||||||||
\(919\) | 9.82367 | 0.324053 | 0.162026 | − | 0.986786i | \(-0.448197\pi\) | ||||
0.162026 | + | 0.986786i | \(0.448197\pi\) | |||||||
\(920\) | 0.0425486 | 0.00140279 | ||||||||
\(921\) | 28.2902 | 0.932195 | ||||||||
\(922\) | 0.597850 | 0.0196892 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.872123 | 0.0286908 | ||||||||
\(925\) | −28.1034 | −0.924036 | ||||||||
\(926\) | −0.0226837 | −0.000745433 0 | ||||||||
\(927\) | −13.4261 | −0.440971 | ||||||||
\(928\) | 24.5633 | 0.806328 | ||||||||
\(929\) | −2.72942 | −0.0895494 | −0.0447747 | − | 0.998997i | \(-0.514257\pi\) | ||||
−0.0447747 | + | 0.998997i | \(0.514257\pi\) | |||||||
\(930\) | −0.0138933 | −0.000455580 0 | ||||||||
\(931\) | −37.6014 | −1.23234 | ||||||||
\(932\) | 29.3489 | 0.961355 | ||||||||
\(933\) | −22.6949 | −0.742999 | ||||||||
\(934\) | −5.23795 | −0.171391 | ||||||||
\(935\) | 0.00978298 | 0.000319938 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −57.1445 | −1.86683 | −0.933414 | − | 0.358801i | \(-0.883186\pi\) | ||||
−0.933414 | + | 0.358801i | \(0.883186\pi\) | |||||||
\(938\) | −1.03155 | −0.0336813 | ||||||||
\(939\) | −0.794040 | −0.0259125 | ||||||||
\(940\) | 0.0910908 | 0.00297106 | ||||||||
\(941\) | −29.5157 | −0.962184 | −0.481092 | − | 0.876670i | \(-0.659760\pi\) | ||||
−0.481092 | + | 0.876670i | \(0.659760\pi\) | |||||||
\(942\) | 2.41983 | 0.0788423 | ||||||||
\(943\) | −24.5834 | −0.800547 | ||||||||
\(944\) | 32.6644 | 1.06313 | ||||||||
\(945\) | 0.00219214 | 7.13105e−5 0 | ||||||||
\(946\) | 0.170148 | 0.00553200 | ||||||||
\(947\) | 42.7602 | 1.38952 | 0.694760 | − | 0.719242i | \(-0.255511\pi\) | ||||
0.694760 | + | 0.719242i | \(0.255511\pi\) | |||||||
\(948\) | −15.4873 | −0.503003 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.39214 | 0.239833 | ||||||||
\(951\) | 32.7911 | 1.06333 | ||||||||
\(952\) | 0.339209 | 0.0109938 | ||||||||
\(953\) | −16.1738 | −0.523921 | −0.261960 | − | 0.965079i | \(-0.584369\pi\) | ||||
−0.261960 | + | 0.965079i | \(0.584369\pi\) | |||||||
\(954\) | −3.26349 | −0.105659 | ||||||||
\(955\) | 0.0359957 | 0.00116479 | ||||||||
\(956\) | 42.9351 | 1.38862 | ||||||||
\(957\) | −11.2745 | −0.364451 | ||||||||
\(958\) | −2.92644 | −0.0945491 | ||||||||
\(959\) | 3.10571 | 0.100289 | ||||||||
\(960\) | 0.0432782 | 0.00139680 | ||||||||
\(961\) | 24.3835 | 0.786565 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.6563 | 0.536741 | ||||||||
\(964\) | −20.8695 | −0.672160 | ||||||||
\(965\) | −0.109101 | −0.00351208 | ||||||||
\(966\) | −0.501467 | −0.0161344 | ||||||||
\(967\) | 57.2411 | 1.84075 | 0.920375 | − | 0.391037i | \(-0.127884\pi\) | ||||
0.920375 | + | 0.391037i | \(0.127884\pi\) | |||||||
\(968\) | −9.56347 | −0.307381 | ||||||||
\(969\) | 5.45062 | 0.175099 | ||||||||
\(970\) | −0.0116709 | −0.000374729 0 | ||||||||
\(971\) | −40.9123 | −1.31294 | −0.656470 | − | 0.754352i | \(-0.727951\pi\) | ||||
−0.656470 | + | 0.754352i | \(0.727951\pi\) | |||||||
\(972\) | 1.92643 | 0.0617902 | ||||||||
\(973\) | −0.981658 | −0.0314705 | ||||||||
\(974\) | −3.09303 | −0.0991070 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 45.6118 | 1.46000 | ||||||||
\(977\) | −21.1028 | −0.675138 | −0.337569 | − | 0.941301i | \(-0.609605\pi\) | ||||
−0.337569 | + | 0.941301i | \(0.609605\pi\) | |||||||
\(978\) | −2.48820 | −0.0795640 | ||||||||
\(979\) | 10.4202 | 0.333030 | ||||||||
\(980\) | 0.0914678 | 0.00292183 | ||||||||
\(981\) | 19.3621 | 0.618185 | ||||||||
\(982\) | −9.85800 | −0.314581 | ||||||||
\(983\) | 32.9357 | 1.05049 | 0.525244 | − | 0.850952i | \(-0.323974\pi\) | ||||
0.525244 | + | 0.850952i | \(0.323974\pi\) | |||||||
\(984\) | 4.51052 | 0.143790 | ||||||||
\(985\) | −0.0278553 | −0.000887545 0 | ||||||||
\(986\) | −2.15150 | −0.0685176 | ||||||||
\(987\) | −2.18815 | −0.0696495 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.56170 | 0.0814572 | ||||||||
\(990\) | 0.00265356 | 8.43358e−5 0 | ||||||||
\(991\) | −51.0240 | −1.62083 | −0.810415 | − | 0.585856i | \(-0.800759\pi\) | ||||
−0.810415 | + | 0.585856i | \(0.800759\pi\) | |||||||
\(992\) | 23.0459 | 0.731709 | ||||||||
\(993\) | 7.77000 | 0.246574 | ||||||||
\(994\) | 1.12411 | 0.0356546 | ||||||||
\(995\) | −0.0580773 | −0.00184117 | ||||||||
\(996\) | 3.14276 | 0.0995821 | ||||||||
\(997\) | 36.1921 | 1.14622 | 0.573108 | − | 0.819480i | \(-0.305738\pi\) | ||||
0.573108 | + | 0.819480i | \(0.305738\pi\) | |||||||
\(998\) | −6.08840 | −0.192725 | ||||||||
\(999\) | −5.62074 | −0.177832 |
(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 | 8619.2.a.bw.1.11 | yes | 24 | |
13.12 | even | 2 | 8619.2.a.bt.1.14 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8619.2.a.bt.1.14 | ✓ | 24 | 13.12 | even | 2 | ||
8619.2.a.bw.1.11 | yes | 24 | 1.1 | even | 1 | trivial |