Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(337,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.10 | ||
Character | \(\chi\) | \(=\) | 1183.337 |
Dual form | 1183.2.c.j.337.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.961590i | − 0.679947i | −0.940435 | − | 0.339974i | \(-0.889582\pi\) | ||||
0.940435 | − | 0.339974i | \(-0.110418\pi\) | |||||||
\(3\) | −1.98737 | −1.14741 | −0.573704 | − | 0.819063i | \(-0.694494\pi\) | ||||
−0.573704 | + | 0.819063i | \(0.694494\pi\) | |||||||
\(4\) | 1.07534 | 0.537672 | ||||||||
\(5\) | 3.39320i | 1.51749i | 0.651390 | + | 0.758743i | \(0.274186\pi\) | ||||
−0.651390 | + | 0.758743i | \(0.725814\pi\) | |||||||
\(6\) | 1.91103i | 0.780177i | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | − 2.95722i | − 1.04554i | ||||||||
\(9\) | 0.949635 | 0.316545 | ||||||||
\(10\) | 3.26287 | 1.03181 | ||||||||
\(11\) | − 4.59237i | − 1.38465i | −0.721584 | − | 0.692326i | \(-0.756586\pi\) | ||||
0.721584 | − | 0.692326i | \(-0.243414\pi\) | |||||||
\(12\) | −2.13711 | −0.616929 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.961590 | −0.256996 | ||||||||
\(15\) | − 6.74354i | − 1.74118i | ||||||||
\(16\) | −0.692948 | −0.173237 | ||||||||
\(17\) | −2.44749 | −0.593604 | −0.296802 | − | 0.954939i | \(-0.595920\pi\) | ||||
−0.296802 | + | 0.954939i | \(0.595920\pi\) | |||||||
\(18\) | − 0.913160i | − 0.215234i | ||||||||
\(19\) | 4.77408i | 1.09525i | 0.836724 | + | 0.547625i | \(0.184468\pi\) | ||||
−0.836724 | + | 0.547625i | \(0.815532\pi\) | |||||||
\(20\) | 3.64886i | 0.815910i | ||||||||
\(21\) | 1.98737i | 0.433679i | ||||||||
\(22\) | −4.41598 | −0.941491 | ||||||||
\(23\) | 4.04446 | 0.843328 | 0.421664 | − | 0.906752i | \(-0.361446\pi\) | ||||
0.421664 | + | 0.906752i | \(0.361446\pi\) | |||||||
\(24\) | 5.87709i | 1.19966i | ||||||||
\(25\) | −6.51382 | −1.30276 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.07483 | 0.784202 | ||||||||
\(28\) | − 1.07534i | − 0.203221i | ||||||||
\(29\) | −3.20889 | −0.595876 | −0.297938 | − | 0.954585i | \(-0.596299\pi\) | ||||
−0.297938 | + | 0.954585i | \(0.596299\pi\) | |||||||
\(30\) | −6.48453 | −1.18391 | ||||||||
\(31\) | − 4.83171i | − 0.867800i | −0.900961 | − | 0.433900i | \(-0.857137\pi\) | ||||
0.900961 | − | 0.433900i | \(-0.142863\pi\) | |||||||
\(32\) | − 5.24811i | − 0.927744i | ||||||||
\(33\) | 9.12674i | 1.58876i | ||||||||
\(34\) | 2.35349i | 0.403620i | ||||||||
\(35\) | 3.39320 | 0.573556 | ||||||||
\(36\) | 1.02118 | 0.170197 | ||||||||
\(37\) | − 9.61127i | − 1.58008i | −0.613053 | − | 0.790042i | \(-0.710059\pi\) | ||||
0.613053 | − | 0.790042i | \(-0.289941\pi\) | |||||||
\(38\) | 4.59071 | 0.744712 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 10.0344 | 1.58659 | ||||||||
\(41\) | − 8.99377i | − 1.40459i | −0.711885 | − | 0.702296i | \(-0.752158\pi\) | ||||
0.711885 | − | 0.702296i | \(-0.247842\pi\) | |||||||
\(42\) | 1.91103 | 0.294879 | ||||||||
\(43\) | 8.90960 | 1.35870 | 0.679351 | − | 0.733814i | \(-0.262261\pi\) | ||||
0.679351 | + | 0.733814i | \(0.262261\pi\) | |||||||
\(44\) | − 4.93838i | − 0.744489i | ||||||||
\(45\) | 3.22230i | 0.480353i | ||||||||
\(46\) | − 3.88911i | − 0.573418i | ||||||||
\(47\) | 5.37660i | 0.784258i | 0.919910 | + | 0.392129i | \(0.128261\pi\) | ||||
−0.919910 | + | 0.392129i | \(0.871739\pi\) | |||||||
\(48\) | 1.37714 | 0.198773 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 6.26362i | 0.885810i | ||||||||
\(51\) | 4.86407 | 0.681106 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.97733 | 1.37049 | 0.685246 | − | 0.728312i | \(-0.259695\pi\) | ||||
0.685246 | + | 0.728312i | \(0.259695\pi\) | |||||||
\(54\) | − 3.91832i | − 0.533216i | ||||||||
\(55\) | 15.5829 | 2.10119 | ||||||||
\(56\) | −2.95722 | −0.395175 | ||||||||
\(57\) | − 9.48786i | − 1.25670i | ||||||||
\(58\) | 3.08564i | 0.405165i | ||||||||
\(59\) | − 10.5145i | − 1.36888i | −0.729071 | − | 0.684438i | \(-0.760047\pi\) | ||||
0.729071 | − | 0.684438i | \(-0.239953\pi\) | |||||||
\(60\) | − 7.25163i | − 0.936181i | ||||||||
\(61\) | 5.29731 | 0.678252 | 0.339126 | − | 0.940741i | \(-0.389869\pi\) | ||||
0.339126 | + | 0.940741i | \(0.389869\pi\) | |||||||
\(62\) | −4.64612 | −0.590058 | ||||||||
\(63\) | − 0.949635i | − 0.119643i | ||||||||
\(64\) | −6.43243 | −0.804054 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.77619 | 1.08027 | ||||||||
\(67\) | 14.0270i | 1.71367i | 0.515588 | + | 0.856837i | \(0.327574\pi\) | ||||
−0.515588 | + | 0.856837i | \(0.672426\pi\) | |||||||
\(68\) | −2.63190 | −0.319164 | ||||||||
\(69\) | −8.03783 | −0.967641 | ||||||||
\(70\) | − 3.26287i | − 0.389988i | ||||||||
\(71\) | − 8.52794i | − 1.01208i | −0.862510 | − | 0.506040i | \(-0.831109\pi\) | ||||
0.862510 | − | 0.506040i | \(-0.168891\pi\) | |||||||
\(72\) | − 2.80828i | − 0.330959i | ||||||||
\(73\) | − 6.62822i | − 0.775775i | −0.921707 | − | 0.387887i | \(-0.873205\pi\) | ||||
0.921707 | − | 0.387887i | \(-0.126795\pi\) | |||||||
\(74\) | −9.24211 | −1.07437 | ||||||||
\(75\) | 12.9454 | 1.49480 | ||||||||
\(76\) | 5.13378i | 0.588885i | ||||||||
\(77\) | −4.59237 | −0.523350 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.98042 | −0.897867 | −0.448934 | − | 0.893565i | \(-0.648196\pi\) | ||||
−0.448934 | + | 0.893565i | \(0.648196\pi\) | |||||||
\(80\) | − 2.35131i | − 0.262885i | ||||||||
\(81\) | −10.9471 | −1.21634 | ||||||||
\(82\) | −8.64833 | −0.955048 | ||||||||
\(83\) | − 7.30165i | − 0.801460i | −0.916196 | − | 0.400730i | \(-0.868756\pi\) | ||||
0.916196 | − | 0.400730i | \(-0.131244\pi\) | |||||||
\(84\) | 2.13711i | 0.233177i | ||||||||
\(85\) | − 8.30484i | − 0.900786i | ||||||||
\(86\) | − 8.56739i | − 0.923845i | ||||||||
\(87\) | 6.37725 | 0.683713 | ||||||||
\(88\) | −13.5807 | −1.44770 | ||||||||
\(89\) | − 18.1007i | − 1.91867i | −0.282265 | − | 0.959337i | \(-0.591086\pi\) | ||||
0.282265 | − | 0.959337i | \(-0.408914\pi\) | |||||||
\(90\) | 3.09854 | 0.326614 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.34918 | 0.453434 | ||||||||
\(93\) | 9.60239i | 0.995721i | ||||||||
\(94\) | 5.17009 | 0.533254 | ||||||||
\(95\) | −16.1994 | −1.66203 | ||||||||
\(96\) | 10.4299i | 1.06450i | ||||||||
\(97\) | 6.90825i | 0.701426i | 0.936483 | + | 0.350713i | \(0.114061\pi\) | ||||
−0.936483 | + | 0.350713i | \(0.885939\pi\) | |||||||
\(98\) | 0.961590i | 0.0971353i | ||||||||
\(99\) | − 4.36108i | − 0.438305i | ||||||||
\(100\) | −7.00459 | −0.700459 | ||||||||
\(101\) | −6.10247 | −0.607218 | −0.303609 | − | 0.952797i | \(-0.598192\pi\) | ||||
−0.303609 | + | 0.952797i | \(0.598192\pi\) | |||||||
\(102\) | − 4.67725i | − 0.463116i | ||||||||
\(103\) | 3.66700 | 0.361320 | 0.180660 | − | 0.983546i | \(-0.442177\pi\) | ||||
0.180660 | + | 0.983546i | \(0.442177\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.74354 | −0.658102 | ||||||||
\(106\) | − 9.59411i | − 0.931862i | ||||||||
\(107\) | 9.82398 | 0.949720 | 0.474860 | − | 0.880061i | \(-0.342499\pi\) | ||||
0.474860 | + | 0.880061i | \(0.342499\pi\) | |||||||
\(108\) | 4.38184 | 0.421643 | ||||||||
\(109\) | 1.51609i | 0.145215i | 0.997361 | + | 0.0726074i | \(0.0231320\pi\) | ||||
−0.997361 | + | 0.0726074i | \(0.976868\pi\) | |||||||
\(110\) | − 14.9843i | − 1.42870i | ||||||||
\(111\) | 19.1011i | 1.81300i | ||||||||
\(112\) | 0.692948i | 0.0654774i | ||||||||
\(113\) | 10.7558 | 1.01182 | 0.505908 | − | 0.862587i | \(-0.331158\pi\) | ||||
0.505908 | + | 0.862587i | \(0.331158\pi\) | |||||||
\(114\) | −9.12344 | −0.854488 | ||||||||
\(115\) | 13.7237i | 1.27974i | ||||||||
\(116\) | −3.45066 | −0.320386 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.1107 | −0.930764 | ||||||||
\(119\) | 2.44749i | 0.224361i | ||||||||
\(120\) | −19.9421 | −1.82046 | ||||||||
\(121\) | −10.0899 | −0.917264 | ||||||||
\(122\) | − 5.09385i | − 0.461175i | ||||||||
\(123\) | 17.8739i | 1.61164i | ||||||||
\(124\) | − 5.19575i | − 0.466592i | ||||||||
\(125\) | − 5.13668i | − 0.459439i | ||||||||
\(126\) | −0.913160 | −0.0813508 | ||||||||
\(127\) | 11.0034 | 0.976390 | 0.488195 | − | 0.872735i | \(-0.337655\pi\) | ||||
0.488195 | + | 0.872735i | \(0.337655\pi\) | |||||||
\(128\) | − 4.31086i | − 0.381030i | ||||||||
\(129\) | −17.7067 | −1.55899 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.69627 | −0.672426 | −0.336213 | − | 0.941786i | \(-0.609146\pi\) | ||||
−0.336213 | + | 0.941786i | \(0.609146\pi\) | |||||||
\(132\) | 9.81439i | 0.854233i | ||||||||
\(133\) | 4.77408 | 0.413965 | ||||||||
\(134\) | 13.4883 | 1.16521 | ||||||||
\(135\) | 13.8267i | 1.19001i | ||||||||
\(136\) | 7.23778i | 0.620634i | ||||||||
\(137\) | − 2.91596i | − 0.249128i | −0.992212 | − | 0.124564i | \(-0.960247\pi\) | ||||
0.992212 | − | 0.124564i | \(-0.0397532\pi\) | |||||||
\(138\) | 7.72910i | 0.657945i | ||||||||
\(139\) | 7.38529 | 0.626412 | 0.313206 | − | 0.949685i | \(-0.398597\pi\) | ||||
0.313206 | + | 0.949685i | \(0.398597\pi\) | |||||||
\(140\) | 3.64886 | 0.308385 | ||||||||
\(141\) | − 10.6853i | − 0.899864i | ||||||||
\(142\) | −8.20039 | −0.688161 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.658048 | −0.0548373 | ||||||||
\(145\) | − 10.8884i | − 0.904234i | ||||||||
\(146\) | −6.37363 | −0.527486 | ||||||||
\(147\) | 1.98737 | 0.163915 | ||||||||
\(148\) | − 10.3354i | − 0.849567i | ||||||||
\(149\) | − 5.62392i | − 0.460730i | −0.973104 | − | 0.230365i | \(-0.926008\pi\) | ||||
0.973104 | − | 0.230365i | \(-0.0739919\pi\) | |||||||
\(150\) | − 12.4481i | − 1.01639i | ||||||||
\(151\) | 8.87295i | 0.722071i | 0.932552 | + | 0.361035i | \(0.117577\pi\) | ||||
−0.932552 | + | 0.361035i | \(0.882423\pi\) | |||||||
\(152\) | 14.1180 | 1.14512 | ||||||||
\(153\) | −2.32423 | −0.187903 | ||||||||
\(154\) | 4.41598i | 0.355850i | ||||||||
\(155\) | 16.3950 | 1.31687 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.7335 | −1.17586 | −0.587929 | − | 0.808913i | \(-0.700056\pi\) | ||||
−0.587929 | + | 0.808913i | \(0.700056\pi\) | |||||||
\(158\) | 7.67389i | 0.610502i | ||||||||
\(159\) | −19.8286 | −1.57251 | ||||||||
\(160\) | 17.8079 | 1.40784 | ||||||||
\(161\) | − 4.04446i | − 0.318748i | ||||||||
\(162\) | 10.5266i | 0.827050i | ||||||||
\(163\) | − 17.4467i | − 1.36653i | −0.730170 | − | 0.683265i | \(-0.760559\pi\) | ||||
0.730170 | − | 0.683265i | \(-0.239441\pi\) | |||||||
\(164\) | − 9.67140i | − 0.755209i | ||||||||
\(165\) | −30.9689 | −2.41092 | ||||||||
\(166\) | −7.02120 | −0.544951 | ||||||||
\(167\) | 12.3209i | 0.953422i | 0.879060 | + | 0.476711i | \(0.158171\pi\) | ||||
−0.879060 | + | 0.476711i | \(0.841829\pi\) | |||||||
\(168\) | 5.87709 | 0.453427 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −7.98585 | −0.612487 | ||||||||
\(171\) | 4.53364i | 0.346696i | ||||||||
\(172\) | 9.58089 | 0.730536 | ||||||||
\(173\) | −0.540871 | −0.0411217 | −0.0205608 | − | 0.999789i | \(-0.506545\pi\) | ||||
−0.0205608 | + | 0.999789i | \(0.506545\pi\) | |||||||
\(174\) | − 6.13231i | − 0.464889i | ||||||||
\(175\) | 6.51382i | 0.492398i | ||||||||
\(176\) | 3.18228i | 0.239873i | ||||||||
\(177\) | 20.8963i | 1.57066i | ||||||||
\(178\) | −17.4055 | −1.30460 | ||||||||
\(179\) | −13.6466 | −1.02000 | −0.509999 | − | 0.860175i | \(-0.670354\pi\) | ||||
−0.509999 | + | 0.860175i | \(0.670354\pi\) | |||||||
\(180\) | 3.46509i | 0.258272i | ||||||||
\(181\) | −1.83569 | −0.136446 | −0.0682230 | − | 0.997670i | \(-0.521733\pi\) | ||||
−0.0682230 | + | 0.997670i | \(0.521733\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.5277 | −0.778231 | ||||||||
\(184\) | − 11.9604i | − 0.881729i | ||||||||
\(185\) | 32.6130 | 2.39775 | ||||||||
\(186\) | 9.23356 | 0.677038 | ||||||||
\(187\) | 11.2398i | 0.821936i | ||||||||
\(188\) | 5.78169i | 0.421673i | ||||||||
\(189\) | − 4.07483i | − 0.296400i | ||||||||
\(190\) | 15.5772i | 1.13009i | ||||||||
\(191\) | −10.1490 | −0.734356 | −0.367178 | − | 0.930151i | \(-0.619676\pi\) | ||||
−0.367178 | + | 0.930151i | \(0.619676\pi\) | |||||||
\(192\) | 12.7836 | 0.922577 | ||||||||
\(193\) | 4.66529i | 0.335815i | 0.985803 | + | 0.167908i | \(0.0537010\pi\) | ||||
−0.985803 | + | 0.167908i | \(0.946299\pi\) | |||||||
\(194\) | 6.64291 | 0.476933 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.07534 | −0.0768103 | ||||||||
\(197\) | 9.10037i | 0.648375i | 0.945993 | + | 0.324187i | \(0.105091\pi\) | ||||
−0.945993 | + | 0.324187i | \(0.894909\pi\) | |||||||
\(198\) | −4.19357 | −0.298024 | ||||||||
\(199\) | 13.4461 | 0.953168 | 0.476584 | − | 0.879129i | \(-0.341875\pi\) | ||||
0.476584 | + | 0.879129i | \(0.341875\pi\) | |||||||
\(200\) | 19.2628i | 1.36209i | ||||||||
\(201\) | − 27.8769i | − 1.96628i | ||||||||
\(202\) | 5.86808i | 0.412876i | ||||||||
\(203\) | 3.20889i | 0.225220i | ||||||||
\(204\) | 5.23055 | 0.366212 | ||||||||
\(205\) | 30.5177 | 2.13145 | ||||||||
\(206\) | − 3.52615i | − 0.245678i | ||||||||
\(207\) | 3.84076 | 0.266951 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.9244 | 1.51654 | ||||||||
\(210\) | 6.48453i | 0.447475i | ||||||||
\(211\) | 11.9909 | 0.825490 | 0.412745 | − | 0.910847i | \(-0.364570\pi\) | ||||
0.412745 | + | 0.910847i | \(0.364570\pi\) | |||||||
\(212\) | 10.7291 | 0.736875 | ||||||||
\(213\) | 16.9482i | 1.16127i | ||||||||
\(214\) | − 9.44664i | − 0.645759i | ||||||||
\(215\) | 30.2321i | 2.06181i | ||||||||
\(216\) | − 12.0502i | − 0.819911i | ||||||||
\(217\) | −4.83171 | −0.327998 | ||||||||
\(218\) | 1.45785 | 0.0987384 | ||||||||
\(219\) | 13.1727i | 0.890130i | ||||||||
\(220\) | 16.7569 | 1.12975 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 18.3675 | 1.23274 | ||||||||
\(223\) | − 2.54948i | − 0.170726i | −0.996350 | − | 0.0853629i | \(-0.972795\pi\) | ||||
0.996350 | − | 0.0853629i | \(-0.0272050\pi\) | |||||||
\(224\) | −5.24811 | −0.350654 | ||||||||
\(225\) | −6.18575 | −0.412383 | ||||||||
\(226\) | − 10.3426i | − 0.687981i | ||||||||
\(227\) | − 8.99748i | − 0.597184i | −0.954381 | − | 0.298592i | \(-0.903483\pi\) | ||||
0.954381 | − | 0.298592i | \(-0.0965169\pi\) | |||||||
\(228\) | − 10.2027i | − 0.675691i | ||||||||
\(229\) | − 7.21104i | − 0.476519i | −0.971202 | − | 0.238259i | \(-0.923423\pi\) | ||||
0.971202 | − | 0.238259i | \(-0.0765769\pi\) | |||||||
\(230\) | 13.1965 | 0.870154 | ||||||||
\(231\) | 9.12674 | 0.600496 | ||||||||
\(232\) | 9.48941i | 0.623010i | ||||||||
\(233\) | −13.1933 | −0.864323 | −0.432162 | − | 0.901796i | \(-0.642249\pi\) | ||||
−0.432162 | + | 0.901796i | \(0.642249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.2439 | −1.19010 | ||||||||
\(236\) | − 11.3067i | − 0.736007i | ||||||||
\(237\) | 15.8600 | 1.03022 | ||||||||
\(238\) | 2.35349 | 0.152554 | ||||||||
\(239\) | 15.9833i | 1.03387i | 0.856024 | + | 0.516936i | \(0.172927\pi\) | ||||
−0.856024 | + | 0.516936i | \(0.827073\pi\) | |||||||
\(240\) | 4.67292i | 0.301636i | ||||||||
\(241\) | 25.1342i | 1.61903i | 0.587096 | + | 0.809517i | \(0.300271\pi\) | ||||
−0.587096 | + | 0.809517i | \(0.699729\pi\) | |||||||
\(242\) | 9.70235i | 0.623691i | ||||||||
\(243\) | 9.53143 | 0.611442 | ||||||||
\(244\) | 5.69643 | 0.364677 | ||||||||
\(245\) | − 3.39320i | − 0.216784i | ||||||||
\(246\) | 17.1874 | 1.09583 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −14.2884 | −0.907316 | ||||||||
\(249\) | 14.5111i | 0.919602i | ||||||||
\(250\) | −4.93939 | −0.312394 | ||||||||
\(251\) | 2.94037 | 0.185594 | 0.0927972 | − | 0.995685i | \(-0.470419\pi\) | ||||
0.0927972 | + | 0.995685i | \(0.470419\pi\) | |||||||
\(252\) | − 1.02118i | − 0.0643286i | ||||||||
\(253\) | − 18.5737i | − 1.16772i | ||||||||
\(254\) | − 10.5807i | − 0.663894i | ||||||||
\(255\) | 16.5048i | 1.03357i | ||||||||
\(256\) | −17.0101 | −1.06313 | ||||||||
\(257\) | −18.5537 | −1.15735 | −0.578675 | − | 0.815559i | \(-0.696430\pi\) | ||||
−0.578675 | + | 0.815559i | \(0.696430\pi\) | |||||||
\(258\) | 17.0266i | 1.06003i | ||||||||
\(259\) | −9.61127 | −0.597216 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.04728 | −0.188622 | ||||||||
\(262\) | 7.40066i | 0.457214i | ||||||||
\(263\) | −10.3996 | −0.641269 | −0.320634 | − | 0.947203i | \(-0.603896\pi\) | ||||
−0.320634 | + | 0.947203i | \(0.603896\pi\) | |||||||
\(264\) | 26.9898 | 1.66111 | ||||||||
\(265\) | 33.8551i | 2.07970i | ||||||||
\(266\) | − 4.59071i | − 0.281475i | ||||||||
\(267\) | 35.9728i | 2.20150i | ||||||||
\(268\) | 15.0839i | 0.921394i | ||||||||
\(269\) | 2.74007 | 0.167065 | 0.0835324 | − | 0.996505i | \(-0.473380\pi\) | ||||
0.0835324 | + | 0.996505i | \(0.473380\pi\) | |||||||
\(270\) | 13.2956 | 0.809147 | ||||||||
\(271\) | 11.0867i | 0.673469i | 0.941600 | + | 0.336735i | \(0.109323\pi\) | ||||
−0.941600 | + | 0.336735i | \(0.890677\pi\) | |||||||
\(272\) | 1.69599 | 0.102834 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.80396 | −0.169394 | ||||||||
\(275\) | 29.9139i | 1.80387i | ||||||||
\(276\) | −8.64343 | −0.520273 | ||||||||
\(277\) | −9.14278 | −0.549336 | −0.274668 | − | 0.961539i | \(-0.588568\pi\) | ||||
−0.274668 | + | 0.961539i | \(0.588568\pi\) | |||||||
\(278\) | − 7.10163i | − 0.425927i | ||||||||
\(279\) | − 4.58836i | − 0.274698i | ||||||||
\(280\) | − 10.0344i | − 0.599673i | ||||||||
\(281\) | − 0.571443i | − 0.0340895i | −0.999855 | − | 0.0170447i | \(-0.994574\pi\) | ||||
0.999855 | − | 0.0170447i | \(-0.00542577\pi\) | |||||||
\(282\) | −10.2749 | −0.611860 | ||||||||
\(283\) | −18.7911 | −1.11701 | −0.558506 | − | 0.829500i | \(-0.688625\pi\) | ||||
−0.558506 | + | 0.829500i | \(0.688625\pi\) | |||||||
\(284\) | − 9.17047i | − 0.544167i | ||||||||
\(285\) | 32.1942 | 1.90702 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.99377 | −0.530886 | ||||||||
\(288\) | − 4.98379i | − 0.293673i | ||||||||
\(289\) | −11.0098 | −0.647634 | ||||||||
\(290\) | −10.4702 | −0.614831 | ||||||||
\(291\) | − 13.7292i | − 0.804822i | ||||||||
\(292\) | − 7.12762i | − 0.417112i | ||||||||
\(293\) | − 9.39283i | − 0.548735i | −0.961625 | − | 0.274368i | \(-0.911532\pi\) | ||||
0.961625 | − | 0.274368i | \(-0.0884685\pi\) | |||||||
\(294\) | − 1.91103i | − 0.111454i | ||||||||
\(295\) | 35.6780 | 2.07725 | ||||||||
\(296\) | −28.4227 | −1.65203 | ||||||||
\(297\) | − 18.7131i | − 1.08585i | ||||||||
\(298\) | −5.40791 | −0.313272 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 13.9207 | 0.803713 | ||||||||
\(301\) | − 8.90960i | − 0.513541i | ||||||||
\(302\) | 8.53215 | 0.490970 | ||||||||
\(303\) | 12.1279 | 0.696727 | ||||||||
\(304\) | − 3.30819i | − 0.189738i | ||||||||
\(305\) | 17.9749i | 1.02924i | ||||||||
\(306\) | 2.23495i | 0.127764i | ||||||||
\(307\) | 1.39399i | 0.0795591i | 0.999208 | + | 0.0397796i | \(0.0126656\pi\) | ||||
−0.999208 | + | 0.0397796i | \(0.987334\pi\) | |||||||
\(308\) | −4.93838 | −0.281390 | ||||||||
\(309\) | −7.28767 | −0.414581 | ||||||||
\(310\) | − 15.7652i | − 0.895405i | ||||||||
\(311\) | 10.0430 | 0.569486 | 0.284743 | − | 0.958604i | \(-0.408092\pi\) | ||||
0.284743 | + | 0.958604i | \(0.408092\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.0874 | 1.64411 | 0.822057 | − | 0.569405i | \(-0.192826\pi\) | ||||
0.822057 | + | 0.569405i | \(0.192826\pi\) | |||||||
\(314\) | 14.1675i | 0.799521i | ||||||||
\(315\) | 3.22230 | 0.181556 | ||||||||
\(316\) | −8.58169 | −0.482758 | ||||||||
\(317\) | 4.50428i | 0.252986i | 0.991968 | + | 0.126493i | \(0.0403721\pi\) | ||||
−0.991968 | + | 0.126493i | \(0.959628\pi\) | |||||||
\(318\) | 19.0670i | 1.06923i | ||||||||
\(319\) | 14.7364i | 0.825082i | ||||||||
\(320\) | − 21.8265i | − 1.22014i | ||||||||
\(321\) | −19.5239 | −1.08972 | ||||||||
\(322\) | −3.88911 | −0.216732 | ||||||||
\(323\) | − 11.6845i | − 0.650145i | ||||||||
\(324\) | −11.7719 | −0.653994 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.7766 | −0.929168 | ||||||||
\(327\) | − 3.01302i | − 0.166621i | ||||||||
\(328\) | −26.5966 | −1.46855 | ||||||||
\(329\) | 5.37660 | 0.296422 | ||||||||
\(330\) | 29.7794i | 1.63930i | ||||||||
\(331\) | 14.2992i | 0.785953i | 0.919549 | + | 0.392976i | \(0.128555\pi\) | ||||
−0.919549 | + | 0.392976i | \(0.871445\pi\) | |||||||
\(332\) | − 7.85179i | − 0.430923i | ||||||||
\(333\) | − 9.12721i | − 0.500168i | ||||||||
\(334\) | 11.8477 | 0.648277 | ||||||||
\(335\) | −47.5965 | −2.60048 | ||||||||
\(336\) | − 1.37714i | − 0.0751293i | ||||||||
\(337\) | −28.4506 | −1.54981 | −0.774903 | − | 0.632081i | \(-0.782201\pi\) | ||||
−0.774903 | + | 0.632081i | \(0.782201\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.3756 | −1.16097 | ||||||||
\(340\) | − 8.93056i | − 0.484327i | ||||||||
\(341\) | −22.1890 | −1.20160 | ||||||||
\(342\) | 4.35950 | 0.235735 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | − 26.3477i | − 1.42057i | ||||||||
\(345\) | − 27.2740i | − 1.46838i | ||||||||
\(346\) | 0.520097i | 0.0279606i | ||||||||
\(347\) | 27.4960 | 1.47606 | 0.738032 | − | 0.674766i | \(-0.235755\pi\) | ||||
0.738032 | + | 0.674766i | \(0.235755\pi\) | |||||||
\(348\) | 6.85774 | 0.367614 | ||||||||
\(349\) | 22.0281i | 1.17914i | 0.807718 | + | 0.589570i | \(0.200703\pi\) | ||||
−0.807718 | + | 0.589570i | \(0.799297\pi\) | |||||||
\(350\) | 6.26362 | 0.334805 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −24.1013 | −1.28460 | ||||||||
\(353\) | 1.60451i | 0.0853993i | 0.999088 | + | 0.0426996i | \(0.0135958\pi\) | ||||
−0.999088 | + | 0.0426996i | \(0.986404\pi\) | |||||||
\(354\) | 20.0937 | 1.06797 | ||||||||
\(355\) | 28.9370 | 1.53582 | ||||||||
\(356\) | − 19.4645i | − 1.03162i | ||||||||
\(357\) | − 4.86407i | − 0.257434i | ||||||||
\(358\) | 13.1225i | 0.693545i | ||||||||
\(359\) | − 21.4030i | − 1.12961i | −0.825225 | − | 0.564804i | \(-0.808952\pi\) | ||||
0.825225 | − | 0.564804i | \(-0.191048\pi\) | |||||||
\(360\) | 9.52907 | 0.502226 | ||||||||
\(361\) | −3.79185 | −0.199571 | ||||||||
\(362\) | 1.76518i | 0.0927761i | ||||||||
\(363\) | 20.0524 | 1.05248 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.4909 | 1.17723 | ||||||||
\(366\) | 10.1234i | 0.529156i | ||||||||
\(367\) | −17.8326 | −0.930856 | −0.465428 | − | 0.885086i | \(-0.654100\pi\) | ||||
−0.465428 | + | 0.885086i | \(0.654100\pi\) | |||||||
\(368\) | −2.80260 | −0.146096 | ||||||||
\(369\) | − 8.54081i | − 0.444617i | ||||||||
\(370\) | − 31.3603i | − 1.63035i | ||||||||
\(371\) | − 9.97733i | − 0.517997i | ||||||||
\(372\) | 10.3259i | 0.535371i | ||||||||
\(373\) | 25.9981 | 1.34613 | 0.673066 | − | 0.739582i | \(-0.264977\pi\) | ||||
0.673066 | + | 0.739582i | \(0.264977\pi\) | |||||||
\(374\) | 10.8081 | 0.558873 | ||||||||
\(375\) | 10.2085i | 0.527164i | ||||||||
\(376\) | 15.8998 | 0.819969 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.91832 | −0.201537 | ||||||||
\(379\) | − 23.0715i | − 1.18510i | −0.805532 | − | 0.592552i | \(-0.798120\pi\) | ||||
0.805532 | − | 0.592552i | \(-0.201880\pi\) | |||||||
\(380\) | −17.4199 | −0.893624 | ||||||||
\(381\) | −21.8677 | −1.12032 | ||||||||
\(382\) | 9.75919i | 0.499323i | ||||||||
\(383\) | − 7.91174i | − 0.404271i | −0.979358 | − | 0.202136i | \(-0.935212\pi\) | ||||
0.979358 | − | 0.202136i | \(-0.0647882\pi\) | |||||||
\(384\) | 8.56727i | 0.437197i | ||||||||
\(385\) | − 15.5829i | − 0.794176i | ||||||||
\(386\) | 4.48610 | 0.228336 | ||||||||
\(387\) | 8.46087 | 0.430090 | ||||||||
\(388\) | 7.42874i | 0.377137i | ||||||||
\(389\) | 6.69526 | 0.339463 | 0.169732 | − | 0.985490i | \(-0.445710\pi\) | ||||
0.169732 | + | 0.985490i | \(0.445710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.89878 | −0.500603 | ||||||||
\(392\) | 2.95722i | 0.149362i | ||||||||
\(393\) | 15.2953 | 0.771547 | ||||||||
\(394\) | 8.75083 | 0.440861 | ||||||||
\(395\) | − 27.0792i | − 1.36250i | ||||||||
\(396\) | − 4.68966i | − 0.235664i | ||||||||
\(397\) | 38.8307i | 1.94886i | 0.224698 | + | 0.974428i | \(0.427860\pi\) | ||||
−0.224698 | + | 0.974428i | \(0.572140\pi\) | |||||||
\(398\) | − 12.9296i | − 0.648104i | ||||||||
\(399\) | −9.48786 | −0.474987 | ||||||||
\(400\) | 4.51374 | 0.225687 | ||||||||
\(401\) | 25.5291i | 1.27486i | 0.770508 | + | 0.637431i | \(0.220003\pi\) | ||||
−0.770508 | + | 0.637431i | \(0.779997\pi\) | |||||||
\(402\) | −26.8061 | −1.33697 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.56225 | −0.326484 | ||||||||
\(405\) | − 37.1457i | − 1.84579i | ||||||||
\(406\) | 3.08564 | 0.153138 | ||||||||
\(407\) | −44.1386 | −2.18787 | ||||||||
\(408\) | − 14.3841i | − 0.712121i | ||||||||
\(409\) | 11.0908i | 0.548402i | 0.961672 | + | 0.274201i | \(0.0884134\pi\) | ||||
−0.961672 | + | 0.274201i | \(0.911587\pi\) | |||||||
\(410\) | − 29.3455i | − 1.44927i | ||||||||
\(411\) | 5.79510i | 0.285851i | ||||||||
\(412\) | 3.94328 | 0.194272 | ||||||||
\(413\) | −10.5145 | −0.517387 | ||||||||
\(414\) | − 3.69324i | − 0.181513i | ||||||||
\(415\) | 24.7760 | 1.21620 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.6773 | −0.718751 | ||||||||
\(418\) | − 21.0823i | − 1.03117i | ||||||||
\(419\) | −14.9846 | −0.732044 | −0.366022 | − | 0.930606i | \(-0.619281\pi\) | ||||
−0.366022 | + | 0.930606i | \(0.619281\pi\) | |||||||
\(420\) | −7.25163 | −0.353843 | ||||||||
\(421\) | 13.0941i | 0.638166i | 0.947727 | + | 0.319083i | \(0.103375\pi\) | ||||
−0.947727 | + | 0.319083i | \(0.896625\pi\) | |||||||
\(422\) | − 11.5304i | − 0.561289i | ||||||||
\(423\) | 5.10581i | 0.248253i | ||||||||
\(424\) | − 29.5052i | − 1.43290i | ||||||||
\(425\) | 15.9425 | 0.773326 | ||||||||
\(426\) | 16.2972 | 0.789602 | ||||||||
\(427\) | − 5.29731i | − 0.256355i | ||||||||
\(428\) | 10.5642 | 0.510638 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 29.0709 | 1.40192 | ||||||||
\(431\) | 25.1962i | 1.21366i | 0.794832 | + | 0.606829i | \(0.207559\pi\) | ||||
−0.794832 | + | 0.606829i | \(0.792441\pi\) | |||||||
\(432\) | −2.82365 | −0.135853 | ||||||||
\(433\) | 20.0880 | 0.965369 | 0.482684 | − | 0.875794i | \(-0.339662\pi\) | ||||
0.482684 | + | 0.875794i | \(0.339662\pi\) | |||||||
\(434\) | 4.64612i | 0.223021i | ||||||||
\(435\) | 21.6393i | 1.03753i | ||||||||
\(436\) | 1.63031i | 0.0780779i | ||||||||
\(437\) | 19.3086i | 0.923654i | ||||||||
\(438\) | 12.6668 | 0.605241 | ||||||||
\(439\) | 29.7431 | 1.41956 | 0.709779 | − | 0.704424i | \(-0.248795\pi\) | ||||
0.709779 | + | 0.704424i | \(0.248795\pi\) | |||||||
\(440\) | − 46.0819i | − 2.19687i | ||||||||
\(441\) | −0.949635 | −0.0452207 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.81064 | −0.228560 | −0.114280 | − | 0.993449i | \(-0.536456\pi\) | ||||
−0.114280 | + | 0.993449i | \(0.536456\pi\) | |||||||
\(444\) | 20.5403i | 0.974800i | ||||||||
\(445\) | 61.4194 | 2.91156 | ||||||||
\(446\) | −2.45156 | −0.116085 | ||||||||
\(447\) | 11.1768i | 0.528645i | ||||||||
\(448\) | 6.43243i | 0.303904i | ||||||||
\(449\) | − 19.5128i | − 0.920866i | −0.887695 | − | 0.460433i | \(-0.847694\pi\) | ||||
0.887695 | − | 0.460433i | \(-0.152306\pi\) | |||||||
\(450\) | 5.94816i | 0.280399i | ||||||||
\(451\) | −41.3028 | −1.94487 | ||||||||
\(452\) | 11.5661 | 0.544025 | ||||||||
\(453\) | − 17.6338i | − 0.828510i | ||||||||
\(454\) | −8.65189 | −0.406053 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −28.0577 | −1.31392 | ||||||||
\(457\) | 4.96981i | 0.232478i | 0.993221 | + | 0.116239i | \(0.0370839\pi\) | ||||
−0.993221 | + | 0.116239i | \(0.962916\pi\) | |||||||
\(458\) | −6.93407 | −0.324008 | ||||||||
\(459\) | −9.97312 | −0.465505 | ||||||||
\(460\) | 14.7577i | 0.688079i | ||||||||
\(461\) | − 4.13305i | − 0.192495i | −0.995357 | − | 0.0962476i | \(-0.969316\pi\) | ||||
0.995357 | − | 0.0962476i | \(-0.0306841\pi\) | |||||||
\(462\) | − 8.77619i | − 0.408305i | ||||||||
\(463\) | 24.3782i | 1.13295i | 0.824079 | + | 0.566475i | \(0.191693\pi\) | ||||
−0.824079 | + | 0.566475i | \(0.808307\pi\) | |||||||
\(464\) | 2.22360 | 0.103228 | ||||||||
\(465\) | −32.5828 | −1.51099 | ||||||||
\(466\) | 12.6866i | 0.587694i | ||||||||
\(467\) | −16.1866 | −0.749028 | −0.374514 | − | 0.927221i | \(-0.622190\pi\) | ||||
−0.374514 | + | 0.927221i | \(0.622190\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.0270 | 0.647708 | ||||||||
\(470\) | 17.5431i | 0.809205i | ||||||||
\(471\) | 29.2808 | 1.34919 | ||||||||
\(472\) | −31.0938 | −1.43121 | ||||||||
\(473\) | − 40.9162i | − 1.88133i | ||||||||
\(474\) | − 15.2509i | − 0.700495i | ||||||||
\(475\) | − 31.0975i | − 1.42685i | ||||||||
\(476\) | 2.63190i | 0.120633i | ||||||||
\(477\) | 9.47483 | 0.433823 | ||||||||
\(478\) | 15.3694 | 0.702978 | ||||||||
\(479\) | 3.89449i | 0.177944i | 0.996034 | + | 0.0889719i | \(0.0283581\pi\) | ||||
−0.996034 | + | 0.0889719i | \(0.971642\pi\) | |||||||
\(480\) | −35.3909 | −1.61536 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 24.1688 | 1.10086 | ||||||||
\(483\) | 8.03783i | 0.365734i | ||||||||
\(484\) | −10.8501 | −0.493187 | ||||||||
\(485\) | −23.4411 | −1.06440 | ||||||||
\(486\) | − 9.16533i | − 0.415748i | ||||||||
\(487\) | 18.1062i | 0.820470i | 0.911980 | + | 0.410235i | \(0.134553\pi\) | ||||
−0.911980 | + | 0.410235i | \(0.865447\pi\) | |||||||
\(488\) | − 15.6653i | − 0.709136i | ||||||||
\(489\) | 34.6730i | 1.56797i | ||||||||
\(490\) | −3.26287 | −0.147401 | ||||||||
\(491\) | 15.5669 | 0.702524 | 0.351262 | − | 0.936277i | \(-0.385753\pi\) | ||||
0.351262 | + | 0.936277i | \(0.385753\pi\) | |||||||
\(492\) | 19.2206i | 0.866533i | ||||||||
\(493\) | 7.85374 | 0.353715 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.7980 | 0.665122 | ||||||||
\(496\) | 3.34812i | 0.150335i | ||||||||
\(497\) | −8.52794 | −0.382530 | ||||||||
\(498\) | 13.9537 | 0.625281 | ||||||||
\(499\) | − 23.4892i | − 1.05152i | −0.850632 | − | 0.525761i | \(-0.823781\pi\) | ||||
0.850632 | − | 0.525761i | \(-0.176219\pi\) | |||||||
\(500\) | − 5.52370i | − 0.247027i | ||||||||
\(501\) | − 24.4862i | − 1.09396i | ||||||||
\(502\) | − 2.82743i | − 0.126194i | ||||||||
\(503\) | −15.2579 | −0.680317 | −0.340159 | − | 0.940368i | \(-0.610481\pi\) | ||||
−0.340159 | + | 0.940368i | \(0.610481\pi\) | |||||||
\(504\) | −2.80828 | −0.125091 | ||||||||
\(505\) | − 20.7069i | − 0.921445i | ||||||||
\(506\) | −17.8603 | −0.793985 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.8324 | 0.524978 | ||||||||
\(509\) | − 41.2509i | − 1.82842i | −0.405246 | − | 0.914208i | \(-0.632814\pi\) | ||||
0.405246 | − | 0.914208i | \(-0.367186\pi\) | |||||||
\(510\) | 15.8708 | 0.702772 | ||||||||
\(511\) | −6.62822 | −0.293215 | ||||||||
\(512\) | 7.73507i | 0.341845i | ||||||||
\(513\) | 19.4536i | 0.858896i | ||||||||
\(514\) | 17.8411i | 0.786936i | ||||||||
\(515\) | 12.4429i | 0.548298i | ||||||||
\(516\) | −19.0408 | −0.838223 | ||||||||
\(517\) | 24.6914 | 1.08592 | ||||||||
\(518\) | 9.24211i | 0.406075i | ||||||||
\(519\) | 1.07491 | 0.0471834 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.5558 | −0.856756 | −0.428378 | − | 0.903600i | \(-0.640915\pi\) | ||||
−0.428378 | + | 0.903600i | \(0.640915\pi\) | |||||||
\(522\) | 2.93023i | 0.128253i | ||||||||
\(523\) | −16.4130 | −0.717689 | −0.358845 | − | 0.933397i | \(-0.616829\pi\) | ||||
−0.358845 | + | 0.933397i | \(0.616829\pi\) | |||||||
\(524\) | −8.27613 | −0.361545 | ||||||||
\(525\) | − 12.9454i | − 0.564982i | ||||||||
\(526\) | 10.0002i | 0.436029i | ||||||||
\(527\) | 11.8256i | 0.515130i | ||||||||
\(528\) | − 6.32436i | − 0.275232i | ||||||||
\(529\) | −6.64237 | −0.288799 | ||||||||
\(530\) | 32.5547 | 1.41409 | ||||||||
\(531\) | − 9.98498i | − 0.433311i | ||||||||
\(532\) | 5.13378 | 0.222578 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 34.5911 | 1.49690 | ||||||||
\(535\) | 33.3347i | 1.44119i | ||||||||
\(536\) | 41.4810 | 1.79171 | ||||||||
\(537\) | 27.1209 | 1.17035 | ||||||||
\(538\) | − 2.63482i | − 0.113595i | ||||||||
\(539\) | 4.59237i | 0.197808i | ||||||||
\(540\) | 14.8685i | 0.639838i | ||||||||
\(541\) | − 33.7185i | − 1.44967i | −0.688922 | − | 0.724836i | \(-0.741916\pi\) | ||||
0.688922 | − | 0.724836i | \(-0.258084\pi\) | |||||||
\(542\) | 10.6609 | 0.457923 | ||||||||
\(543\) | 3.64820 | 0.156559 | ||||||||
\(544\) | 12.8447i | 0.550713i | ||||||||
\(545\) | −5.14439 | −0.220361 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.0637 | 1.71300 | 0.856501 | − | 0.516145i | \(-0.172634\pi\) | ||||
0.856501 | + | 0.516145i | \(0.172634\pi\) | |||||||
\(548\) | − 3.13566i | − 0.133949i | ||||||||
\(549\) | 5.03052 | 0.214697 | ||||||||
\(550\) | 28.7649 | 1.22654 | ||||||||
\(551\) | − 15.3195i | − 0.652633i | ||||||||
\(552\) | 23.7696i | 1.01170i | ||||||||
\(553\) | 7.98042i | 0.339362i | ||||||||
\(554\) | 8.79161i | 0.373520i | ||||||||
\(555\) | −64.8140 | −2.75120 | ||||||||
\(556\) | 7.94173 | 0.336804 | ||||||||
\(557\) | 6.26450i | 0.265435i | 0.991154 | + | 0.132718i | \(0.0423703\pi\) | ||||
−0.991154 | + | 0.132718i | \(0.957630\pi\) | |||||||
\(558\) | −4.41212 | −0.186780 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.35131 | −0.0993611 | ||||||||
\(561\) | − 22.3376i | − 0.943096i | ||||||||
\(562\) | −0.549494 | −0.0231790 | ||||||||
\(563\) | 18.9876 | 0.800231 | 0.400115 | − | 0.916465i | \(-0.368970\pi\) | ||||
0.400115 | + | 0.916465i | \(0.368970\pi\) | |||||||
\(564\) | − 11.4904i | − 0.483831i | ||||||||
\(565\) | 36.4964i | 1.53542i | ||||||||
\(566\) | 18.0693i | 0.759510i | ||||||||
\(567\) | 10.9471i | 0.459735i | ||||||||
\(568\) | −25.2190 | −1.05817 | ||||||||
\(569\) | −40.9151 | −1.71525 | −0.857626 | − | 0.514274i | \(-0.828061\pi\) | ||||
−0.857626 | + | 0.514274i | \(0.828061\pi\) | |||||||
\(570\) | − 30.9577i | − 1.29667i | ||||||||
\(571\) | 18.9901 | 0.794713 | 0.397356 | − | 0.917664i | \(-0.369928\pi\) | ||||
0.397356 | + | 0.917664i | \(0.369928\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.1698 | 0.842606 | ||||||||
\(574\) | 8.64833i | 0.360974i | ||||||||
\(575\) | −26.3448 | −1.09866 | ||||||||
\(576\) | −6.10846 | −0.254519 | ||||||||
\(577\) | 6.42794i | 0.267599i | 0.991008 | + | 0.133799i | \(0.0427177\pi\) | ||||
−0.991008 | + | 0.133799i | \(0.957282\pi\) | |||||||
\(578\) | 10.5869i | 0.440357i | ||||||||
\(579\) | − 9.27166i | − 0.385317i | ||||||||
\(580\) | − 11.7088i | − 0.486181i | ||||||||
\(581\) | −7.30165 | −0.302924 | ||||||||
\(582\) | −13.2019 | −0.547237 | ||||||||
\(583\) | − 45.8196i | − 1.89766i | ||||||||
\(584\) | −19.6011 | −0.811100 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.03206 | −0.373111 | ||||||||
\(587\) | 10.4081i | 0.429588i | 0.976659 | + | 0.214794i | \(0.0689079\pi\) | ||||
−0.976659 | + | 0.214794i | \(0.931092\pi\) | |||||||
\(588\) | 2.13711 | 0.0881327 | ||||||||
\(589\) | 23.0670 | 0.950458 | ||||||||
\(590\) | − 34.3076i | − 1.41242i | ||||||||
\(591\) | − 18.0858i | − 0.743950i | ||||||||
\(592\) | 6.66011i | 0.273729i | ||||||||
\(593\) | 16.2341i | 0.666654i | 0.942811 | + | 0.333327i | \(0.108171\pi\) | ||||
−0.942811 | + | 0.333327i | \(0.891829\pi\) | |||||||
\(594\) | −17.9944 | −0.738319 | ||||||||
\(595\) | −8.30484 | −0.340465 | ||||||||
\(596\) | − 6.04765i | − 0.247721i | ||||||||
\(597\) | −26.7223 | −1.09367 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.84879 | 0.198116 | 0.0990580 | − | 0.995082i | \(-0.468417\pi\) | ||||
0.0990580 | + | 0.995082i | \(0.468417\pi\) | |||||||
\(600\) | − 38.2823i | − 1.56287i | ||||||||
\(601\) | −35.9758 | −1.46748 | −0.733742 | − | 0.679428i | \(-0.762228\pi\) | ||||
−0.733742 | + | 0.679428i | \(0.762228\pi\) | |||||||
\(602\) | −8.56739 | −0.349181 | ||||||||
\(603\) | 13.3206i | 0.542455i | ||||||||
\(604\) | 9.54148i | 0.388237i | ||||||||
\(605\) | − 34.2371i | − 1.39193i | ||||||||
\(606\) | − 11.6620i | − 0.473738i | ||||||||
\(607\) | 28.7089 | 1.16526 | 0.582629 | − | 0.812738i | \(-0.302024\pi\) | ||||
0.582629 | + | 0.812738i | \(0.302024\pi\) | |||||||
\(608\) | 25.0549 | 1.01611 | ||||||||
\(609\) | − 6.37725i | − 0.258419i | ||||||||
\(610\) | 17.2844 | 0.699827 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.49934 | −0.101030 | ||||||||
\(613\) | − 37.1913i | − 1.50214i | −0.660221 | − | 0.751071i | \(-0.729538\pi\) | ||||
0.660221 | − | 0.751071i | \(-0.270462\pi\) | |||||||
\(614\) | 1.34045 | 0.0540960 | ||||||||
\(615\) | −60.6499 | −2.44564 | ||||||||
\(616\) | 13.5807i | 0.547181i | ||||||||
\(617\) | − 0.556995i | − 0.0224238i | −0.999937 | − | 0.0112119i | \(-0.996431\pi\) | ||||
0.999937 | − | 0.0112119i | \(-0.00356893\pi\) | |||||||
\(618\) | 7.00776i | 0.281893i | ||||||||
\(619\) | 12.4079i | 0.498715i | 0.968411 | + | 0.249358i | \(0.0802195\pi\) | ||||
−0.968411 | + | 0.249358i | \(0.919781\pi\) | |||||||
\(620\) | 17.6302 | 0.708047 | ||||||||
\(621\) | 16.4805 | 0.661339 | ||||||||
\(622\) | − 9.65725i | − 0.387220i | ||||||||
\(623\) | −18.1007 | −0.725190 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.1393 | −0.605571 | ||||||||
\(626\) | − 27.9701i | − 1.11791i | ||||||||
\(627\) | −43.5718 | −1.74009 | ||||||||
\(628\) | −15.8435 | −0.632226 | ||||||||
\(629\) | 23.5235i | 0.937945i | ||||||||
\(630\) | − 3.09854i | − 0.123449i | ||||||||
\(631\) | 10.5304i | 0.419208i | 0.977786 | + | 0.209604i | \(0.0672174\pi\) | ||||
−0.977786 | + | 0.209604i | \(0.932783\pi\) | |||||||
\(632\) | 23.5999i | 0.938752i | ||||||||
\(633\) | −23.8304 | −0.947174 | ||||||||
\(634\) | 4.33127 | 0.172017 | ||||||||
\(635\) | 37.3366i | 1.48166i | ||||||||
\(636\) | −21.3226 | −0.845496 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.1704 | 0.561012 | ||||||||
\(639\) | − 8.09844i | − 0.320369i | ||||||||
\(640\) | 14.6276 | 0.578207 | ||||||||
\(641\) | −17.8975 | −0.706910 | −0.353455 | − | 0.935452i | \(-0.614993\pi\) | ||||
−0.353455 | + | 0.935452i | \(0.614993\pi\) | |||||||
\(642\) | 18.7740i | 0.740949i | ||||||||
\(643\) | − 11.7963i | − 0.465202i | −0.972572 | − | 0.232601i | \(-0.925276\pi\) | ||||
0.972572 | − | 0.232601i | \(-0.0747236\pi\) | |||||||
\(644\) | − 4.34918i | − 0.171382i | ||||||||
\(645\) | − 60.0823i | − 2.36574i | ||||||||
\(646\) | −11.2357 | −0.442064 | ||||||||
\(647\) | −4.52415 | −0.177863 | −0.0889313 | − | 0.996038i | \(-0.528345\pi\) | ||||
−0.0889313 | + | 0.996038i | \(0.528345\pi\) | |||||||
\(648\) | 32.3730i | 1.27173i | ||||||||
\(649\) | −48.2867 | −1.89542 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.60239 | 0.376347 | ||||||||
\(652\) | − 18.7612i | − 0.734745i | ||||||||
\(653\) | 46.9198 | 1.83611 | 0.918057 | − | 0.396448i | \(-0.129757\pi\) | ||||
0.918057 | + | 0.396448i | \(0.129757\pi\) | |||||||
\(654\) | −2.89730 | −0.113293 | ||||||||
\(655\) | − 26.1150i | − 1.02040i | ||||||||
\(656\) | 6.23222i | 0.243327i | ||||||||
\(657\) | − 6.29439i | − 0.245568i | ||||||||
\(658\) | − 5.17009i | − 0.201551i | ||||||||
\(659\) | −39.3468 | −1.53273 | −0.766366 | − | 0.642404i | \(-0.777937\pi\) | ||||
−0.766366 | + | 0.642404i | \(0.777937\pi\) | |||||||
\(660\) | −33.3022 | −1.29629 | ||||||||
\(661\) | − 23.0664i | − 0.897179i | −0.893738 | − | 0.448590i | \(-0.851926\pi\) | ||||
0.893738 | − | 0.448590i | \(-0.148074\pi\) | |||||||
\(662\) | 13.7499 | 0.534406 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.5926 | −0.837955 | ||||||||
\(665\) | 16.1994i | 0.628187i | ||||||||
\(666\) | −8.77663 | −0.340088 | ||||||||
\(667\) | −12.9782 | −0.502519 | ||||||||
\(668\) | 13.2492i | 0.512628i | ||||||||
\(669\) | 5.06676i | 0.195892i | ||||||||
\(670\) | 45.7684i | 1.76819i | ||||||||
\(671\) | − 24.3272i | − 0.939143i | ||||||||
\(672\) | 10.4299 | 0.402343 | ||||||||
\(673\) | 15.7225 | 0.606057 | 0.303028 | − | 0.952981i | \(-0.402002\pi\) | ||||
0.303028 | + | 0.952981i | \(0.402002\pi\) | |||||||
\(674\) | 27.3579i | 1.05379i | ||||||||
\(675\) | −26.5427 | −1.02163 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.59613 | 0.0613443 | 0.0306721 | − | 0.999529i | \(-0.490235\pi\) | ||||
0.0306721 | + | 0.999529i | \(0.490235\pi\) | |||||||
\(678\) | 20.5546i | 0.789395i | ||||||||
\(679\) | 6.90825 | 0.265114 | ||||||||
\(680\) | −24.5592 | −0.941804 | ||||||||
\(681\) | 17.8813i | 0.685213i | ||||||||
\(682\) | 21.3367i | 0.817026i | ||||||||
\(683\) | − 18.4740i | − 0.706889i | −0.935455 | − | 0.353445i | \(-0.885010\pi\) | ||||
0.935455 | − | 0.353445i | \(-0.114990\pi\) | |||||||
\(684\) | 4.87522i | 0.186409i | ||||||||
\(685\) | 9.89445 | 0.378048 | ||||||||
\(686\) | 0.961590 | 0.0367137 | ||||||||
\(687\) | 14.3310i | 0.546762i | ||||||||
\(688\) | −6.17389 | −0.235377 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −26.2264 | −0.998422 | ||||||||
\(691\) | 26.1768i | 0.995813i | 0.867231 | + | 0.497906i | \(0.165898\pi\) | ||||
−0.867231 | + | 0.497906i | \(0.834102\pi\) | |||||||
\(692\) | −0.581623 | −0.0221100 | ||||||||
\(693\) | −4.36108 | −0.165664 | ||||||||
\(694\) | − 26.4399i | − 1.00365i | ||||||||
\(695\) | 25.0598i | 0.950572i | ||||||||
\(696\) | − 18.8590i | − 0.714847i | ||||||||
\(697\) | 22.0122i | 0.833772i | ||||||||
\(698\) | 21.1820 | 0.801752 | ||||||||
\(699\) | 26.2200 | 0.991731 | ||||||||
\(700\) | 7.00459i | 0.264749i | ||||||||
\(701\) | 2.16383 | 0.0817267 | 0.0408634 | − | 0.999165i | \(-0.486989\pi\) | ||||
0.0408634 | + | 0.999165i | \(0.486989\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45.8850 | 1.73059 | ||||||||
\(704\) | 29.5401i | 1.11334i | ||||||||
\(705\) | 36.2573 | 1.36553 | ||||||||
\(706\) | 1.54288 | 0.0580670 | ||||||||
\(707\) | 6.10247i | 0.229507i | ||||||||
\(708\) | 22.4707i | 0.844500i | ||||||||
\(709\) | − 34.7042i | − 1.30334i | −0.758501 | − | 0.651672i | \(-0.774068\pi\) | ||||
0.758501 | − | 0.651672i | \(-0.225932\pi\) | |||||||
\(710\) | − 27.8256i | − 1.04427i | ||||||||
\(711\) | −7.57849 | −0.284215 | ||||||||
\(712\) | −53.5279 | −2.00604 | ||||||||
\(713\) | − 19.5416i | − 0.731840i | ||||||||
\(714\) | −4.67725 | −0.175042 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.6748 | −0.548424 | ||||||||
\(717\) | − 31.7647i | − 1.18627i | ||||||||
\(718\) | −20.5809 | −0.768074 | ||||||||
\(719\) | −0.969723 | −0.0361646 | −0.0180823 | − | 0.999837i | \(-0.505756\pi\) | ||||
−0.0180823 | + | 0.999837i | \(0.505756\pi\) | |||||||
\(720\) | − 2.23289i | − 0.0832149i | ||||||||
\(721\) | − 3.66700i | − 0.136566i | ||||||||
\(722\) | 3.64621i | 0.135698i | ||||||||
\(723\) | − 49.9509i | − 1.85769i | ||||||||
\(724\) | −1.97400 | −0.0733632 | ||||||||
\(725\) | 20.9021 | 0.776286 | ||||||||
\(726\) | − 19.2822i | − 0.715628i | ||||||||
\(727\) | 17.0417 | 0.632040 | 0.316020 | − | 0.948752i | \(-0.397653\pi\) | ||||
0.316020 | + | 0.948752i | \(0.397653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.8988 | 0.514771 | ||||||||
\(730\) | − 21.6270i | − 0.800452i | ||||||||
\(731\) | −21.8062 | −0.806531 | ||||||||
\(732\) | −11.3209 | −0.418433 | ||||||||
\(733\) | 13.5638i | 0.500989i | 0.968118 | + | 0.250494i | \(0.0805932\pi\) | ||||
−0.968118 | + | 0.250494i | \(0.919407\pi\) | |||||||
\(734\) | 17.1477i | 0.632933i | ||||||||
\(735\) | 6.74354i | 0.248739i | ||||||||
\(736\) | − 21.2258i | − 0.782392i | ||||||||
\(737\) | 64.4173 | 2.37284 | ||||||||
\(738\) | −8.21276 | −0.302316 | ||||||||
\(739\) | 25.5091i | 0.938366i | 0.883101 | + | 0.469183i | \(0.155452\pi\) | ||||
−0.883101 | + | 0.469183i | \(0.844548\pi\) | |||||||
\(740\) | 35.0702 | 1.28921 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.59411 | −0.352211 | ||||||||
\(743\) | 20.1185i | 0.738078i | 0.929414 | + | 0.369039i | \(0.120313\pi\) | ||||
−0.929414 | + | 0.369039i | \(0.879687\pi\) | |||||||
\(744\) | 28.3964 | 1.04106 | ||||||||
\(745\) | 19.0831 | 0.699150 | ||||||||
\(746\) | − 24.9996i | − 0.915299i | ||||||||
\(747\) | − 6.93391i | − 0.253698i | ||||||||
\(748\) | 12.0867i | 0.441932i | ||||||||
\(749\) | − 9.82398i | − 0.358960i | ||||||||
\(750\) | 9.81638 | 0.358444 | ||||||||
\(751\) | 50.7696 | 1.85261 | 0.926305 | − | 0.376774i | \(-0.122967\pi\) | ||||
0.926305 | + | 0.376774i | \(0.122967\pi\) | |||||||
\(752\) | − 3.72570i | − 0.135862i | ||||||||
\(753\) | −5.84360 | −0.212953 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.1077 | −1.09573 | ||||||||
\(756\) | − 4.38184i | − 0.159366i | ||||||||
\(757\) | 5.42838 | 0.197298 | 0.0986490 | − | 0.995122i | \(-0.468548\pi\) | ||||
0.0986490 | + | 0.995122i | \(0.468548\pi\) | |||||||
\(758\) | −22.1854 | −0.805808 | ||||||||
\(759\) | 36.9127i | 1.33985i | ||||||||
\(760\) | 47.9053i | 1.73771i | ||||||||
\(761\) | 29.3194i | 1.06283i | 0.847112 | + | 0.531414i | \(0.178339\pi\) | ||||
−0.847112 | + | 0.531414i | \(0.821661\pi\) | |||||||
\(762\) | 21.0278i | 0.761757i | ||||||||
\(763\) | 1.51609 | 0.0548860 | ||||||||
\(764\) | −10.9137 | −0.394843 | ||||||||
\(765\) | − 7.88657i | − 0.285139i | ||||||||
\(766\) | −7.60786 | −0.274883 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 33.8054 | 1.21985 | ||||||||
\(769\) | − 46.5006i | − 1.67686i | −0.545013 | − | 0.838428i | \(-0.683475\pi\) | ||||
0.545013 | − | 0.838428i | \(-0.316525\pi\) | |||||||
\(770\) | −14.9843 | −0.539997 | ||||||||
\(771\) | 36.8731 | 1.32795 | ||||||||
\(772\) | 5.01679i | 0.180558i | ||||||||
\(773\) | − 15.5317i | − 0.558637i | −0.960198 | − | 0.279319i | \(-0.909891\pi\) | ||||
0.960198 | − | 0.279319i | \(-0.0901085\pi\) | |||||||
\(774\) | − 8.13590i | − 0.292439i | ||||||||
\(775\) | 31.4729i | 1.13054i | ||||||||
\(776\) | 20.4292 | 0.733366 | ||||||||
\(777\) | 19.1011 | 0.685250 | ||||||||
\(778\) | − 6.43810i | − 0.230817i | ||||||||
\(779\) | 42.9370 | 1.53838 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.1635 | −1.40138 | ||||||||
\(782\) | 9.51857i | 0.340384i | ||||||||
\(783\) | −13.0757 | −0.467287 | ||||||||
\(784\) | 0.692948 | 0.0247481 | ||||||||
\(785\) | − 49.9936i | − 1.78435i | ||||||||
\(786\) | − 14.7078i | − 0.524611i | ||||||||
\(787\) | − 33.9561i | − 1.21040i | −0.796072 | − | 0.605202i | \(-0.793092\pi\) | ||||
0.796072 | − | 0.605202i | \(-0.206908\pi\) | |||||||
\(788\) | 9.78603i | 0.348613i | ||||||||
\(789\) | 20.6679 | 0.735797 | ||||||||
\(790\) | −26.0391 | −0.926428 | ||||||||
\(791\) | − 10.7558i | − 0.382430i | ||||||||
\(792\) | −12.8967 | −0.458264 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 37.3392 | 1.32512 | ||||||||
\(795\) | − 67.2826i | − 2.38627i | ||||||||
\(796\) | 14.4592 | 0.512492 | ||||||||
\(797\) | −5.90891 | −0.209304 | −0.104652 | − | 0.994509i | \(-0.533373\pi\) | ||||
−0.104652 | + | 0.994509i | \(0.533373\pi\) | |||||||
\(798\) | 9.12344i | 0.322966i | ||||||||
\(799\) | − 13.1592i | − 0.465539i | ||||||||
\(800\) | 34.1852i | 1.20863i | ||||||||
\(801\) | − 17.1891i | − 0.607347i | ||||||||
\(802\) | 24.5485 | 0.866838 | ||||||||
\(803\) | −30.4393 | −1.07418 | ||||||||
\(804\) | − 29.9772i | − 1.05722i | ||||||||
\(805\) | 13.7237 | 0.483695 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.44552 | −0.191691 | ||||||||
\(808\) | 18.0464i | 0.634868i | ||||||||
\(809\) | −30.4401 | −1.07022 | −0.535109 | − | 0.844783i | \(-0.679730\pi\) | ||||
−0.535109 | + | 0.844783i | \(0.679730\pi\) | |||||||
\(810\) | −35.7190 | −1.25504 | ||||||||
\(811\) | − 21.9976i | − 0.772442i | −0.922406 | − | 0.386221i | \(-0.873780\pi\) | ||||
0.922406 | − | 0.386221i | \(-0.126220\pi\) | |||||||
\(812\) | 3.45066i | 0.121095i | ||||||||
\(813\) | − 22.0334i | − 0.772744i | ||||||||
\(814\) | 42.4432i | 1.48763i | ||||||||
\(815\) | 59.2001 | 2.07369 | ||||||||
\(816\) | −3.37055 | −0.117993 | ||||||||
\(817\) | 42.5352i | 1.48812i | ||||||||
\(818\) | 10.6648 | 0.372885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 32.8170 | 1.14602 | ||||||||
\(821\) | − 0.557598i | − 0.0194603i | −0.999953 | − | 0.00973015i | \(-0.996903\pi\) | ||||
0.999953 | − | 0.00973015i | \(-0.00309725\pi\) | |||||||
\(822\) | 5.57251 | 0.194364 | ||||||||
\(823\) | −9.50436 | −0.331301 | −0.165651 | − | 0.986185i | \(-0.552972\pi\) | ||||
−0.165651 | + | 0.986185i | \(0.552972\pi\) | |||||||
\(824\) | − 10.8441i | − 0.377773i | ||||||||
\(825\) | − 59.4499i | − 2.06978i | ||||||||
\(826\) | 10.1107i | 0.351796i | ||||||||
\(827\) | − 40.7855i | − 1.41825i | −0.705083 | − | 0.709125i | \(-0.749090\pi\) | ||||
0.705083 | − | 0.709125i | \(-0.250910\pi\) | |||||||
\(828\) | 4.13014 | 0.143532 | ||||||||
\(829\) | −2.74011 | −0.0951679 | −0.0475839 | − | 0.998867i | \(-0.515152\pi\) | ||||
−0.0475839 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(830\) | − 23.8243i | − 0.826955i | ||||||||
\(831\) | 18.1701 | 0.630313 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.44749 | 0.0848006 | ||||||||
\(834\) | 14.1136i | 0.488712i | ||||||||
\(835\) | −41.8074 | −1.44680 | ||||||||
\(836\) | 23.5762 | 0.815401 | ||||||||
\(837\) | − 19.6884i | − 0.680530i | ||||||||
\(838\) | 14.4090i | 0.497751i | ||||||||
\(839\) | − 4.66572i | − 0.161078i | −0.996751 | − | 0.0805392i | \(-0.974336\pi\) | ||||
0.996751 | − | 0.0805392i | \(-0.0256642\pi\) | |||||||
\(840\) | 19.9421i | 0.688070i | ||||||||
\(841\) | −18.7030 | −0.644931 | ||||||||
\(842\) | 12.5911 | 0.433919 | ||||||||
\(843\) | 1.13567i | 0.0391145i | ||||||||
\(844\) | 12.8944 | 0.443843 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.90970 | 0.168799 | ||||||||
\(847\) | 10.0899i | 0.346693i | ||||||||
\(848\) | −6.91377 | −0.237420 | ||||||||
\(849\) | 37.3448 | 1.28167 | ||||||||
\(850\) | − 15.3302i | − 0.525821i | ||||||||
\(851\) | − 38.8724i | − 1.33253i | ||||||||
\(852\) | 18.2251i | 0.624382i | ||||||||
\(853\) | 25.2886i | 0.865864i | 0.901427 | + | 0.432932i | \(0.142521\pi\) | ||||
−0.901427 | + | 0.432932i | \(0.857479\pi\) | |||||||
\(854\) | −5.09385 | −0.174308 | ||||||||
\(855\) | −15.3835 | −0.526106 | ||||||||
\(856\) | − 29.0517i | − 0.992966i | ||||||||
\(857\) | −9.30340 | −0.317798 | −0.158899 | − | 0.987295i | \(-0.550794\pi\) | ||||
−0.158899 | + | 0.987295i | \(0.550794\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.4360 | 1.44790 | 0.723949 | − | 0.689854i | \(-0.242325\pi\) | ||||
0.723949 | + | 0.689854i | \(0.242325\pi\) | |||||||
\(860\) | 32.5099i | 1.10858i | ||||||||
\(861\) | 17.8739 | 0.609142 | ||||||||
\(862\) | 24.2284 | 0.825223 | ||||||||
\(863\) | 17.0172i | 0.579273i | 0.957137 | + | 0.289636i | \(0.0935344\pi\) | ||||
−0.957137 | + | 0.289636i | \(0.906466\pi\) | |||||||
\(864\) | − 21.3852i | − 0.727538i | ||||||||
\(865\) | − 1.83529i | − 0.0624016i | ||||||||
\(866\) | − 19.3165i | − 0.656400i | ||||||||
\(867\) | 21.8805 | 0.743100 | ||||||||
\(868\) | −5.19575 | −0.176355 | ||||||||
\(869\) | 36.6491i | 1.24323i | ||||||||
\(870\) | 20.8082 | 0.705462 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.48340 | 0.151827 | ||||||||
\(873\) | 6.56032i | 0.222033i | ||||||||
\(874\) | 18.5669 | 0.628036 | ||||||||
\(875\) | −5.13668 | −0.173652 | ||||||||
\(876\) | 14.1652i | 0.478598i | ||||||||
\(877\) | − 39.3974i | − 1.33035i | −0.746685 | − | 0.665177i | \(-0.768356\pi\) | ||||
0.746685 | − | 0.665177i | \(-0.231644\pi\) | |||||||
\(878\) | − 28.6006i | − 0.965225i | ||||||||
\(879\) | 18.6670i | 0.629623i | ||||||||
\(880\) | −10.7981 | −0.364004 | ||||||||
\(881\) | −9.92005 | −0.334215 | −0.167107 | − | 0.985939i | \(-0.553443\pi\) | ||||
−0.167107 | + | 0.985939i | \(0.553443\pi\) | |||||||
\(882\) | 0.913160i | 0.0307477i | ||||||||
\(883\) | 18.9158 | 0.636568 | 0.318284 | − | 0.947995i | \(-0.396894\pi\) | ||||
0.318284 | + | 0.947995i | \(0.396894\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −70.9053 | −2.38345 | ||||||||
\(886\) | 4.62586i | 0.155409i | ||||||||
\(887\) | 24.2260 | 0.813431 | 0.406715 | − | 0.913555i | \(-0.366674\pi\) | ||||
0.406715 | + | 0.913555i | \(0.366674\pi\) | |||||||
\(888\) | 56.4863 | 1.89556 | ||||||||
\(889\) | − 11.0034i | − 0.369041i | ||||||||
\(890\) | − 59.0603i | − 1.97971i | ||||||||
\(891\) | 50.2732i | 1.68421i | ||||||||
\(892\) | − 2.74157i | − 0.0917945i | ||||||||
\(893\) | −25.6683 | −0.858958 | ||||||||
\(894\) | 10.7475 | 0.359450 | ||||||||
\(895\) | − 46.3058i | − 1.54783i | ||||||||
\(896\) | −4.31086 | −0.144016 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.7633 | −0.626140 | ||||||||
\(899\) | 15.5044i | 0.517102i | ||||||||
\(900\) | −6.65181 | −0.221727 | ||||||||
\(901\) | −24.4195 | −0.813530 | ||||||||
\(902\) | 39.7164i | 1.32241i | ||||||||
\(903\) | 17.7067i | 0.589241i | ||||||||
\(904\) | − 31.8071i | − 1.05789i | ||||||||
\(905\) | − 6.22888i | − 0.207055i | ||||||||
\(906\) | −16.9565 | −0.563343 | ||||||||
\(907\) | 20.0403 | 0.665427 | 0.332714 | − | 0.943028i | \(-0.392036\pi\) | ||||
0.332714 | + | 0.943028i | \(0.392036\pi\) | |||||||
\(908\) | − 9.67539i | − 0.321089i | ||||||||
\(909\) | −5.79512 | −0.192212 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.5680 | 1.07903 | 0.539514 | − | 0.841977i | \(-0.318608\pi\) | ||||
0.539514 | + | 0.841977i | \(0.318608\pi\) | |||||||
\(912\) | 6.57459i | 0.217707i | ||||||||
\(913\) | −33.5319 | −1.10974 | ||||||||
\(914\) | 4.77892 | 0.158073 | ||||||||
\(915\) | − 35.7227i | − 1.18095i | ||||||||
\(916\) | − 7.75435i | − 0.256211i | ||||||||
\(917\) | 7.69627i | 0.254153i | ||||||||
\(918\) | 9.59006i | 0.316519i | ||||||||
\(919\) | −43.7858 | −1.44436 | −0.722181 | − | 0.691705i | \(-0.756860\pi\) | ||||
−0.722181 | + | 0.691705i | \(0.756860\pi\) | |||||||
\(920\) | 40.5839 | 1.33801 | ||||||||
\(921\) | − 2.77037i | − 0.0912868i | ||||||||
\(922\) | −3.97430 | −0.130887 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 9.81439 | 0.322870 | ||||||||
\(925\) | 62.6061i | 2.05848i | ||||||||
\(926\) | 23.4418 | 0.770346 | ||||||||
\(927\) | 3.48231 | 0.114374 | ||||||||
\(928\) | 16.8406i | 0.552821i | ||||||||
\(929\) | − 47.7826i | − 1.56770i | −0.620953 | − | 0.783848i | \(-0.713254\pi\) | ||||
0.620953 | − | 0.783848i | \(-0.286746\pi\) | |||||||
\(930\) | 31.3313i | 1.02740i | ||||||||
\(931\) | − 4.77408i | − 0.156464i | ||||||||
\(932\) | −14.1874 | −0.464722 | ||||||||
\(933\) | −19.9591 | −0.653433 | ||||||||
\(934\) | 15.5649i | 0.509299i | ||||||||
\(935\) | −38.1389 | −1.24728 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.7762 | −0.613393 | −0.306696 | − | 0.951807i | \(-0.599224\pi\) | ||||
−0.306696 | + | 0.951807i | \(0.599224\pi\) | |||||||
\(938\) | − 13.4883i | − 0.440407i | ||||||||
\(939\) | −57.8073 | −1.88647 | ||||||||
\(940\) | −19.6184 | −0.639883 | ||||||||
\(941\) | − 41.5379i | − 1.35410i | −0.735938 | − | 0.677049i | \(-0.763259\pi\) | ||||
0.735938 | − | 0.677049i | \(-0.236741\pi\) | |||||||
\(942\) | − 28.1561i | − 0.917377i | ||||||||
\(943\) | − 36.3749i | − 1.18453i | ||||||||
\(944\) | 7.28603i | 0.237140i | ||||||||
\(945\) | 13.8267 | 0.449783 | ||||||||
\(946\) | −39.3447 | −1.27921 | ||||||||
\(947\) | 33.6878i | 1.09471i | 0.836902 | + | 0.547353i | \(0.184364\pi\) | ||||
−0.836902 | + | 0.547353i | \(0.815636\pi\) | |||||||
\(948\) | 17.0550 | 0.553920 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −29.9030 | −0.970183 | ||||||||
\(951\) | − 8.95167i | − 0.290278i | ||||||||
\(952\) | 7.23778 | 0.234578 | ||||||||
\(953\) | 30.0769 | 0.974286 | 0.487143 | − | 0.873322i | \(-0.338039\pi\) | ||||
0.487143 | + | 0.873322i | \(0.338039\pi\) | |||||||
\(954\) | − 9.11090i | − 0.294976i | ||||||||
\(955\) | − 34.4376i | − 1.11438i | ||||||||
\(956\) | 17.1875i | 0.555884i | ||||||||
\(957\) | − 29.2867i | − 0.946706i | ||||||||
\(958\) | 3.74490 | 0.120992 | ||||||||
\(959\) | −2.91596 | −0.0941614 | ||||||||
\(960\) | 43.3774i | 1.40000i | ||||||||
\(961\) | 7.65460 | 0.246922 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.32919 | 0.300629 | ||||||||
\(964\) | 27.0279i | 0.870510i | ||||||||
\(965\) | −15.8303 | −0.509595 | ||||||||
\(966\) | 7.72910 | 0.248680 | ||||||||
\(967\) | − 0.586833i | − 0.0188713i | −0.999955 | − | 0.00943564i | \(-0.996996\pi\) | ||||
0.999955 | − | 0.00943564i | \(-0.00300350\pi\) | |||||||
\(968\) | 29.8381i | 0.959032i | ||||||||
\(969\) | 23.2215i | 0.745981i | ||||||||
\(970\) | 22.5407i | 0.723739i | ||||||||
\(971\) | 6.42217 | 0.206097 | 0.103049 | − | 0.994676i | \(-0.467140\pi\) | ||||
0.103049 | + | 0.994676i | \(0.467140\pi\) | |||||||
\(972\) | 10.2496 | 0.328755 | ||||||||
\(973\) | − 7.38529i | − 0.236762i | ||||||||
\(974\) | 17.4107 | 0.557876 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.67076 | −0.117498 | ||||||||
\(977\) | − 29.2836i | − 0.936867i | −0.883499 | − | 0.468433i | \(-0.844819\pi\) | ||||
0.883499 | − | 0.468433i | \(-0.155181\pi\) | |||||||
\(978\) | 33.3412 | 1.06614 | ||||||||
\(979\) | −83.1253 | −2.65670 | ||||||||
\(980\) | − 3.64886i | − 0.116559i | ||||||||
\(981\) | 1.43973i | 0.0459670i | ||||||||
\(982\) | − 14.9690i | − 0.477679i | ||||||||
\(983\) | 39.4156i | 1.25716i | 0.777745 | + | 0.628581i | \(0.216364\pi\) | ||||
−0.777745 | + | 0.628581i | \(0.783636\pi\) | |||||||
\(984\) | 52.8572 | 1.68503 | ||||||||
\(985\) | −30.8794 | −0.983899 | ||||||||
\(986\) | − 7.55209i | − 0.240507i | ||||||||
\(987\) | −10.6853 | −0.340116 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.0345 | 1.14583 | ||||||||
\(990\) | − 14.2296i | − 0.452248i | ||||||||
\(991\) | 24.3027 | 0.772000 | 0.386000 | − | 0.922499i | \(-0.373856\pi\) | ||||
0.386000 | + | 0.922499i | \(0.373856\pi\) | |||||||
\(992\) | −25.3573 | −0.805096 | ||||||||
\(993\) | − 28.4177i | − 0.901809i | ||||||||
\(994\) | 8.20039i | 0.260100i | ||||||||
\(995\) | 45.6253i | 1.44642i | ||||||||
\(996\) | 15.6044i | 0.494444i | ||||||||
\(997\) | −46.4460 | −1.47096 | −0.735479 | − | 0.677547i | \(-0.763043\pi\) | ||||
−0.735479 | + | 0.677547i | \(0.763043\pi\) | |||||||
\(998\) | −22.5870 | −0.714980 | ||||||||
\(999\) | − 39.1643i | − 1.23910i |
(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 | 1183.2.c.j.337.10 | 24 | ||
13.5 | odd | 4 | 1183.2.a.r.1.5 | yes | 12 | ||
13.8 | odd | 4 | 1183.2.a.q.1.8 | ✓ | 12 | ||
13.12 | even | 2 | inner | 1183.2.c.j.337.15 | 24 | ||
91.34 | even | 4 | 8281.2.a.cn.1.8 | 12 | |||
91.83 | even | 4 | 8281.2.a.cq.1.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.q.1.8 | ✓ | 12 | 13.8 | odd | 4 | ||
1183.2.a.r.1.5 | yes | 12 | 13.5 | odd | 4 | ||
1183.2.c.j.337.10 | 24 | 1.1 | even | 1 | trivial | ||
1183.2.c.j.337.15 | 24 | 13.12 | even | 2 | inner | ||
8281.2.a.cn.1.8 | 12 | 91.34 | even | 4 | |||
8281.2.a.cq.1.5 | 12 | 91.83 | even | 4 |