Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.49024\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.49024 | −1.05376 | −0.526879 | − | 0.849940i | \(-0.676638\pi\) | ||||
−0.526879 | + | 0.849940i | \(0.676638\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.220813 | 0.110406 | ||||||||
\(5\) | −2.04744 | −0.915644 | −0.457822 | − | 0.889044i | \(-0.651370\pi\) | ||||
−0.457822 | + | 0.889044i | \(0.651370\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.65141 | 0.937417 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.05118 | 0.964868 | ||||||||
\(11\) | 1.77527 | 0.535263 | 0.267631 | − | 0.963521i | \(-0.413759\pi\) | ||||
0.267631 | + | 0.963521i | \(0.413759\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.05756 | −1.12536 | −0.562682 | − | 0.826673i | \(-0.690231\pi\) | ||||
−0.562682 | + | 0.826673i | \(0.690231\pi\) | |||||||
\(14\) | −1.49024 | −0.398283 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.39287 | −1.09822 | ||||||||
\(17\) | −7.64794 | −1.85490 | −0.927449 | − | 0.373949i | \(-0.878004\pi\) | ||||
−0.927449 | + | 0.373949i | \(0.878004\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.24885 | 0.745338 | 0.372669 | − | 0.927964i | \(-0.378443\pi\) | ||||
0.372669 | + | 0.927964i | \(0.378443\pi\) | |||||||
\(20\) | −0.452102 | −0.101093 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.64557 | −0.564037 | ||||||||
\(23\) | −6.77465 | −1.41261 | −0.706306 | − | 0.707906i | \(-0.749640\pi\) | ||||
−0.706306 | + | 0.707906i | \(0.749640\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.807977 | −0.161595 | ||||||||
\(26\) | 6.04673 | 1.18586 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.220813 | 0.0417297 | ||||||||
\(29\) | −6.90210 | −1.28169 | −0.640844 | − | 0.767671i | \(-0.721415\pi\) | ||||
−0.640844 | + | 0.767671i | \(0.721415\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.66081 | −0.298291 | −0.149145 | − | 0.988815i | \(-0.547652\pi\) | ||||
−0.149145 | + | 0.988815i | \(0.547652\pi\) | |||||||
\(32\) | 1.24359 | 0.219838 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.3973 | 1.95461 | ||||||||
\(35\) | −2.04744 | −0.346081 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.03684 | 1.48565 | 0.742824 | − | 0.669487i | \(-0.233486\pi\) | ||||
0.742824 | + | 0.669487i | \(0.233486\pi\) | |||||||
\(38\) | −4.84157 | −0.785406 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.42862 | −0.858340 | ||||||||
\(41\) | −9.40281 | −1.46847 | −0.734236 | − | 0.678894i | \(-0.762460\pi\) | ||||
−0.734236 | + | 0.678894i | \(0.762460\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.27572 | 0.347045 | 0.173522 | − | 0.984830i | \(-0.444485\pi\) | ||||
0.173522 | + | 0.984830i | \(0.444485\pi\) | |||||||
\(44\) | 0.392001 | 0.0590964 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.0958 | 1.48855 | ||||||||
\(47\) | 1.14335 | 0.166775 | 0.0833875 | − | 0.996517i | \(-0.473426\pi\) | ||||
0.0833875 | + | 0.996517i | \(0.473426\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.20408 | 0.170282 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.895961 | −0.124247 | ||||||||
\(53\) | −0.909120 | −0.124877 | −0.0624386 | − | 0.998049i | \(-0.519888\pi\) | ||||
−0.0624386 | + | 0.998049i | \(0.519888\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.63476 | −0.490110 | ||||||||
\(56\) | 2.65141 | 0.354310 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.2858 | 1.35059 | ||||||||
\(59\) | 0.510997 | 0.0665261 | 0.0332631 | − | 0.999447i | \(-0.489410\pi\) | ||||
0.0332631 | + | 0.999447i | \(0.489410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.6668 | −1.87789 | −0.938943 | − | 0.344074i | \(-0.888193\pi\) | ||||
−0.938943 | + | 0.344074i | \(0.888193\pi\) | |||||||
\(62\) | 2.47501 | 0.314326 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.93248 | 0.866560 | ||||||||
\(65\) | 8.30762 | 1.03043 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.730117 | −0.0891980 | −0.0445990 | − | 0.999005i | \(-0.514201\pi\) | ||||
−0.0445990 | + | 0.999005i | \(0.514201\pi\) | |||||||
\(68\) | −1.68876 | −0.204793 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.05118 | 0.364686 | ||||||||
\(71\) | 2.37985 | 0.282437 | 0.141218 | − | 0.989978i | \(-0.454898\pi\) | ||||
0.141218 | + | 0.989978i | \(0.454898\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.42990 | 0.401439 | 0.200720 | − | 0.979649i | \(-0.435672\pi\) | ||||
0.200720 | + | 0.979649i | \(0.435672\pi\) | |||||||
\(74\) | −13.4671 | −1.56551 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.717389 | 0.0822901 | ||||||||
\(77\) | 1.77527 | 0.202310 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.04927 | −0.793104 | −0.396552 | − | 0.918012i | \(-0.629793\pi\) | ||||
−0.396552 | + | 0.918012i | \(0.629793\pi\) | |||||||
\(80\) | 8.99415 | 1.00558 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.0124 | 1.54741 | ||||||||
\(83\) | −1.32633 | −0.145584 | −0.0727920 | − | 0.997347i | \(-0.523191\pi\) | ||||
−0.0727920 | + | 0.997347i | \(0.523191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.6587 | 1.69843 | ||||||||
\(86\) | −3.39137 | −0.365701 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.70696 | 0.501764 | ||||||||
\(89\) | 3.63475 | 0.385283 | 0.192641 | − | 0.981269i | \(-0.438295\pi\) | ||||
0.192641 | + | 0.981269i | \(0.438295\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.05756 | −0.425348 | ||||||||
\(92\) | −1.49593 | −0.155961 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.70387 | −0.175741 | ||||||||
\(95\) | −6.65185 | −0.682465 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.35645 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(98\) | −1.49024 | −0.150537 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.178412 | −0.0178412 | ||||||||
\(101\) | −1.21116 | −0.120515 | −0.0602573 | − | 0.998183i | \(-0.519192\pi\) | ||||
−0.0602573 | + | 0.998183i | \(0.519192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.69531 | −0.856774 | −0.428387 | − | 0.903595i | \(-0.640918\pi\) | ||||
−0.428387 | + | 0.903595i | \(0.640918\pi\) | |||||||
\(104\) | −10.7583 | −1.05494 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.35481 | 0.131590 | ||||||||
\(107\) | 17.3884 | 1.68100 | 0.840499 | − | 0.541813i | \(-0.182262\pi\) | ||||
0.840499 | + | 0.541813i | \(0.182262\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0624 | 1.25115 | 0.625576 | − | 0.780164i | \(-0.284864\pi\) | ||||
0.625576 | + | 0.780164i | \(0.284864\pi\) | |||||||
\(110\) | 5.41665 | 0.516458 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.39287 | −0.415087 | ||||||||
\(113\) | 12.6936 | 1.19411 | 0.597057 | − | 0.802199i | \(-0.296337\pi\) | ||||
0.597057 | + | 0.802199i | \(0.296337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.8707 | 1.29345 | ||||||||
\(116\) | −1.52407 | −0.141506 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.761508 | −0.0701025 | ||||||||
\(119\) | −7.64794 | −0.701086 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.84843 | −0.713494 | ||||||||
\(122\) | 21.8570 | 1.97884 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.366729 | −0.0329332 | ||||||||
\(125\) | 11.8915 | 1.06361 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −12.8182 | −1.13298 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.3803 | −1.08583 | ||||||||
\(131\) | 10.1857 | 0.889928 | 0.444964 | − | 0.895548i | \(-0.353216\pi\) | ||||
0.444964 | + | 0.895548i | \(0.353216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.24885 | 0.281711 | ||||||||
\(134\) | 1.08805 | 0.0939931 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.2779 | −1.73881 | ||||||||
\(137\) | −5.48349 | −0.468486 | −0.234243 | − | 0.972178i | \(-0.575261\pi\) | ||||
−0.234243 | + | 0.972178i | \(0.575261\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.95792 | −0.844620 | −0.422310 | − | 0.906451i | \(-0.638781\pi\) | ||||
−0.422310 | + | 0.906451i | \(0.638781\pi\) | |||||||
\(140\) | −0.452102 | −0.0382096 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.54655 | −0.297620 | ||||||||
\(143\) | −7.20324 | −0.602366 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.1317 | 1.17357 | ||||||||
\(146\) | −5.11137 | −0.423020 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.99545 | 0.164025 | ||||||||
\(149\) | 4.47456 | 0.366571 | 0.183285 | − | 0.983060i | \(-0.441327\pi\) | ||||
0.183285 | + | 0.983060i | \(0.441327\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0817 | −1.14595 | −0.572977 | − | 0.819571i | \(-0.694212\pi\) | ||||
−0.572977 | + | 0.819571i | \(0.694212\pi\) | |||||||
\(152\) | 8.61406 | 0.698693 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.64557 | −0.213186 | ||||||||
\(155\) | 3.40042 | 0.273128 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.58675 | −0.445871 | −0.222936 | − | 0.974833i | \(-0.571564\pi\) | ||||
−0.222936 | + | 0.974833i | \(0.571564\pi\) | |||||||
\(158\) | 10.5051 | 0.835740 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.54619 | −0.201294 | ||||||||
\(161\) | −6.77465 | −0.533917 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.1815 | −0.954127 | −0.477064 | − | 0.878869i | \(-0.658299\pi\) | ||||
−0.477064 | + | 0.878869i | \(0.658299\pi\) | |||||||
\(164\) | −2.07626 | −0.162129 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.97655 | 0.153410 | ||||||||
\(167\) | −6.23754 | −0.482676 | −0.241338 | − | 0.970441i | \(-0.577586\pi\) | ||||
−0.241338 | + | 0.970441i | \(0.577586\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.46378 | 0.266445 | ||||||||
\(170\) | −23.3353 | −1.78973 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.502509 | 0.0383159 | ||||||||
\(173\) | 13.5405 | 1.02946 | 0.514731 | − | 0.857352i | \(-0.327892\pi\) | ||||
0.514731 | + | 0.857352i | \(0.327892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.807977 | −0.0610773 | ||||||||
\(176\) | −7.79851 | −0.587834 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.41664 | −0.405995 | ||||||||
\(179\) | −10.0729 | −0.752887 | −0.376443 | − | 0.926440i | \(-0.622853\pi\) | ||||
−0.376443 | + | 0.926440i | \(0.622853\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.0581 | 1.11926 | 0.559630 | − | 0.828742i | \(-0.310943\pi\) | ||||
0.559630 | + | 0.828742i | \(0.310943\pi\) | |||||||
\(182\) | 6.04673 | 0.448214 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.9624 | −1.32421 | ||||||||
\(185\) | −18.5024 | −1.36032 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.5771 | −0.992858 | ||||||||
\(188\) | 0.252467 | 0.0184130 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.91284 | 0.719153 | ||||||||
\(191\) | −4.76684 | −0.344916 | −0.172458 | − | 0.985017i | \(-0.555171\pi\) | ||||
−0.172458 | + | 0.985017i | \(0.555171\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.71655 | −0.555449 | −0.277725 | − | 0.960661i | \(-0.589580\pi\) | ||||
−0.277725 | + | 0.960661i | \(0.589580\pi\) | |||||||
\(194\) | 13.9434 | 1.00107 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.220813 | 0.0157723 | ||||||||
\(197\) | 2.00654 | 0.142960 | 0.0714799 | − | 0.997442i | \(-0.477228\pi\) | ||||
0.0714799 | + | 0.997442i | \(0.477228\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5326 | 0.817525 | 0.408762 | − | 0.912641i | \(-0.365960\pi\) | ||||
0.408762 | + | 0.912641i | \(0.365960\pi\) | |||||||
\(200\) | −2.14228 | −0.151482 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.80491 | 0.126993 | ||||||||
\(203\) | −6.90210 | −0.484432 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.2517 | 1.34460 | ||||||||
\(206\) | 12.9581 | 0.902833 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.8243 | 1.23589 | ||||||||
\(209\) | 5.76758 | 0.398952 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.5078 | 1.41181 | 0.705906 | − | 0.708306i | \(-0.250540\pi\) | ||||
0.705906 | + | 0.708306i | \(0.250540\pi\) | |||||||
\(212\) | −0.200745 | −0.0137872 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −25.9129 | −1.77137 | ||||||||
\(215\) | −4.65942 | −0.317769 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.66081 | −0.112743 | ||||||||
\(218\) | −19.4661 | −1.31841 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.802600 | −0.0541113 | ||||||||
\(221\) | 31.0320 | 2.08744 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.44549 | −0.0967969 | −0.0483985 | − | 0.998828i | \(-0.515412\pi\) | ||||
−0.0483985 | + | 0.998828i | \(0.515412\pi\) | |||||||
\(224\) | 1.24359 | 0.0830911 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.9165 | −1.25831 | ||||||||
\(227\) | −23.4362 | −1.55551 | −0.777757 | − | 0.628565i | \(-0.783643\pi\) | ||||
−0.777757 | + | 0.628565i | \(0.783643\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.5045 | 1.15673 | 0.578364 | − | 0.815779i | \(-0.303691\pi\) | ||||
0.578364 | + | 0.815779i | \(0.303691\pi\) | |||||||
\(230\) | −20.6707 | −1.36298 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.3003 | −1.20147 | ||||||||
\(233\) | −24.5272 | −1.60683 | −0.803415 | − | 0.595419i | \(-0.796986\pi\) | ||||
−0.803415 | + | 0.595419i | \(0.796986\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.34095 | −0.152707 | ||||||||
\(236\) | 0.112835 | 0.00734491 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.3973 | 0.738775 | ||||||||
\(239\) | −12.9074 | −0.834908 | −0.417454 | − | 0.908698i | \(-0.637077\pi\) | ||||
−0.417454 | + | 0.908698i | \(0.637077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.5870 | −1.13288 | −0.566440 | − | 0.824103i | \(-0.691680\pi\) | ||||
−0.566440 | + | 0.824103i | \(0.691680\pi\) | |||||||
\(242\) | 11.6960 | 0.751850 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.23861 | −0.207330 | ||||||||
\(245\) | −2.04744 | −0.130806 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1824 | −0.838777 | ||||||||
\(248\) | −4.40350 | −0.279623 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −17.7212 | −1.12079 | ||||||||
\(251\) | −10.2258 | −0.645445 | −0.322722 | − | 0.946494i | \(-0.604598\pi\) | ||||
−0.322722 | + | 0.946494i | \(0.604598\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0268 | −0.756119 | ||||||||
\(254\) | −1.49024 | −0.0935059 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.23728 | 0.327330 | ||||||||
\(257\) | −13.1251 | −0.818723 | −0.409361 | − | 0.912372i | \(-0.634248\pi\) | ||||
−0.409361 | + | 0.912372i | \(0.634248\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.03684 | 0.561522 | ||||||||
\(260\) | 1.83443 | 0.113766 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.1791 | −0.937769 | ||||||||
\(263\) | 6.65987 | 0.410665 | 0.205333 | − | 0.978692i | \(-0.434172\pi\) | ||||
0.205333 | + | 0.978692i | \(0.434172\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.86137 | 0.114343 | ||||||||
\(266\) | −4.84157 | −0.296856 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.161219 | −0.00984802 | ||||||||
\(269\) | −7.74043 | −0.471942 | −0.235971 | − | 0.971760i | \(-0.575827\pi\) | ||||
−0.235971 | + | 0.971760i | \(0.575827\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.03897 | 0.366842 | 0.183421 | − | 0.983034i | \(-0.441283\pi\) | ||||
0.183421 | + | 0.983034i | \(0.441283\pi\) | |||||||
\(272\) | 33.5964 | 2.03708 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.17171 | 0.493671 | ||||||||
\(275\) | −1.43437 | −0.0864959 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.9334 | −1.37794 | −0.688968 | − | 0.724792i | \(-0.741936\pi\) | ||||
−0.688968 | + | 0.724792i | \(0.741936\pi\) | |||||||
\(278\) | 14.8397 | 0.890025 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.42862 | −0.324422 | ||||||||
\(281\) | 25.2804 | 1.50810 | 0.754052 | − | 0.656814i | \(-0.228096\pi\) | ||||
0.754052 | + | 0.656814i | \(0.228096\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0595 | −0.776308 | −0.388154 | − | 0.921594i | \(-0.626887\pi\) | ||||
−0.388154 | + | 0.921594i | \(0.626887\pi\) | |||||||
\(284\) | 0.525502 | 0.0311828 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.7346 | 0.634748 | ||||||||
\(287\) | −9.40281 | −0.555030 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.4910 | 2.44065 | ||||||||
\(290\) | −21.0595 | −1.23666 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.757366 | 0.0443215 | ||||||||
\(293\) | 3.00348 | 0.175465 | 0.0877327 | − | 0.996144i | \(-0.472038\pi\) | ||||
0.0877327 | + | 0.996144i | \(0.472038\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.04624 | −0.0609143 | ||||||||
\(296\) | 23.9604 | 1.39267 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.66817 | −0.386277 | ||||||||
\(299\) | 27.4885 | 1.58970 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.27572 | 0.131171 | ||||||||
\(302\) | 20.9851 | 1.20756 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.2718 | −0.818543 | ||||||||
\(305\) | 30.0293 | 1.71947 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.33304 | 0.133153 | 0.0665767 | − | 0.997781i | \(-0.478792\pi\) | ||||
0.0665767 | + | 0.997781i | \(0.478792\pi\) | |||||||
\(308\) | 0.392001 | 0.0223363 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.06744 | −0.287811 | ||||||||
\(311\) | 0.675512 | 0.0383047 | 0.0191524 | − | 0.999817i | \(-0.493903\pi\) | ||||
0.0191524 | + | 0.999817i | \(0.493903\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.63228 | −0.374879 | −0.187439 | − | 0.982276i | \(-0.560019\pi\) | ||||
−0.187439 | + | 0.982276i | \(0.560019\pi\) | |||||||
\(314\) | 8.32560 | 0.469841 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.55657 | −0.0875638 | ||||||||
\(317\) | 4.68652 | 0.263221 | 0.131611 | − | 0.991301i | \(-0.457985\pi\) | ||||
0.131611 | + | 0.991301i | \(0.457985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.2531 | −0.686039 | ||||||||
\(320\) | −14.1939 | −0.793461 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.0958 | 0.562620 | ||||||||
\(323\) | −24.8471 | −1.38253 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.27841 | 0.181854 | ||||||||
\(326\) | 18.1533 | 1.00542 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −24.9308 | −1.37657 | ||||||||
\(329\) | 1.14335 | 0.0630350 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.07509 | −0.333917 | −0.166959 | − | 0.985964i | \(-0.553395\pi\) | ||||
−0.166959 | + | 0.985964i | \(0.553395\pi\) | |||||||
\(332\) | −0.292871 | −0.0160734 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.29543 | 0.508623 | ||||||||
\(335\) | 1.49487 | 0.0816736 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.31829 | 0.289706 | 0.144853 | − | 0.989453i | \(-0.453729\pi\) | ||||
0.144853 | + | 0.989453i | \(0.453729\pi\) | |||||||
\(338\) | −5.16187 | −0.280769 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.45765 | 0.187517 | ||||||||
\(341\) | −2.94838 | −0.159664 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 6.03389 | 0.325325 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.1785 | −1.08480 | ||||||||
\(347\) | 14.5110 | 0.778993 | 0.389496 | − | 0.921028i | \(-0.372649\pi\) | ||||
0.389496 | + | 0.921028i | \(0.372649\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.6940 | 1.05419 | 0.527097 | − | 0.849805i | \(-0.323281\pi\) | ||||
0.527097 | + | 0.849805i | \(0.323281\pi\) | |||||||
\(350\) | 1.20408 | 0.0643607 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.20771 | 0.117671 | ||||||||
\(353\) | −17.7743 | −0.946033 | −0.473016 | − | 0.881054i | \(-0.656835\pi\) | ||||
−0.473016 | + | 0.881054i | \(0.656835\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.87262 | −0.258612 | ||||||||
\(356\) | 0.802599 | 0.0425376 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.0111 | 0.793360 | ||||||||
\(359\) | 14.7077 | 0.776245 | 0.388123 | − | 0.921608i | \(-0.373124\pi\) | ||||
0.388123 | + | 0.921608i | \(0.373124\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.44494 | −0.444471 | ||||||||
\(362\) | −22.4402 | −1.17943 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.895961 | −0.0469611 | ||||||||
\(365\) | −7.02252 | −0.367576 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.9272 | −0.726995 | −0.363498 | − | 0.931595i | \(-0.618417\pi\) | ||||
−0.363498 | + | 0.931595i | \(0.618417\pi\) | |||||||
\(368\) | 29.7601 | 1.55135 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 27.5730 | 1.43345 | ||||||||
\(371\) | −0.909120 | −0.0471991 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.6120 | 1.53325 | 0.766627 | − | 0.642093i | \(-0.221934\pi\) | ||||
0.766627 | + | 0.642093i | \(0.221934\pi\) | |||||||
\(374\) | 20.2332 | 1.04623 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.03150 | 0.156338 | ||||||||
\(377\) | 28.0057 | 1.44237 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.3108 | −0.837829 | −0.418914 | − | 0.908026i | \(-0.637589\pi\) | ||||
−0.418914 | + | 0.908026i | \(0.637589\pi\) | |||||||
\(380\) | −1.46881 | −0.0753485 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.10373 | 0.363458 | ||||||||
\(383\) | 30.7897 | 1.57328 | 0.786640 | − | 0.617412i | \(-0.211819\pi\) | ||||
0.786640 | + | 0.617412i | \(0.211819\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.63476 | −0.185244 | ||||||||
\(386\) | 11.4995 | 0.585309 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.06602 | −0.104886 | ||||||||
\(389\) | −3.20667 | −0.162585 | −0.0812923 | − | 0.996690i | \(-0.525905\pi\) | ||||
−0.0812923 | + | 0.996690i | \(0.525905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 51.8121 | 2.62025 | ||||||||
\(392\) | 2.65141 | 0.133917 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.99022 | −0.150645 | ||||||||
\(395\) | 14.4330 | 0.726202 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.4082 | 1.72690 | 0.863449 | − | 0.504435i | \(-0.168299\pi\) | ||||
0.863449 | + | 0.504435i | \(0.168299\pi\) | |||||||
\(398\) | −17.1863 | −0.861474 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.54933 | 0.177467 | ||||||||
\(401\) | 6.69898 | 0.334531 | 0.167266 | − | 0.985912i | \(-0.446506\pi\) | ||||
0.167266 | + | 0.985912i | \(0.446506\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.73884 | 0.335686 | ||||||||
\(404\) | −0.267439 | −0.0133056 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.2858 | 0.510474 | ||||||||
\(407\) | 16.0428 | 0.795212 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.8318 | −1.42564 | −0.712820 | − | 0.701347i | \(-0.752582\pi\) | ||||
−0.712820 | + | 0.701347i | \(0.752582\pi\) | |||||||
\(410\) | −28.6897 | −1.41688 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.92003 | −0.0945933 | ||||||||
\(413\) | 0.510997 | 0.0251445 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.71559 | 0.133303 | ||||||||
\(416\) | −5.04595 | −0.247398 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.59507 | −0.420399 | ||||||||
\(419\) | −26.8706 | −1.31272 | −0.656358 | − | 0.754450i | \(-0.727904\pi\) | ||||
−0.656358 | + | 0.754450i | \(0.727904\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.8612 | 1.74777 | 0.873884 | − | 0.486135i | \(-0.161594\pi\) | ||||
0.873884 | + | 0.486135i | \(0.161594\pi\) | |||||||
\(422\) | −30.5615 | −1.48771 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.41045 | −0.117062 | ||||||||
\(425\) | 6.17936 | 0.299743 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.6668 | −0.709774 | ||||||||
\(428\) | 3.83958 | 0.185593 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.94364 | 0.334852 | ||||||||
\(431\) | 25.9119 | 1.24813 | 0.624066 | − | 0.781372i | \(-0.285480\pi\) | ||||
0.624066 | + | 0.781372i | \(0.285480\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.2601 | 0.829468 | 0.414734 | − | 0.909943i | \(-0.363875\pi\) | ||||
0.414734 | + | 0.909943i | \(0.363875\pi\) | |||||||
\(434\) | 2.47501 | 0.118804 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.88434 | 0.138135 | ||||||||
\(437\) | −22.0099 | −1.05287 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.7590 | 1.56350 | 0.781752 | − | 0.623590i | \(-0.214327\pi\) | ||||
0.781752 | + | 0.623590i | \(0.214327\pi\) | |||||||
\(440\) | −9.63724 | −0.459438 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −46.2451 | −2.19965 | ||||||||
\(443\) | 25.1899 | 1.19681 | 0.598404 | − | 0.801195i | \(-0.295802\pi\) | ||||
0.598404 | + | 0.801195i | \(0.295802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.44194 | −0.352782 | ||||||||
\(446\) | 2.15412 | 0.102001 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.93248 | 0.327529 | ||||||||
\(449\) | 38.5015 | 1.81700 | 0.908500 | − | 0.417885i | \(-0.137229\pi\) | ||||
0.908500 | + | 0.417885i | \(0.137229\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.6925 | −0.786018 | ||||||||
\(452\) | 2.80291 | 0.131838 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 34.9255 | 1.63914 | ||||||||
\(455\) | 8.30762 | 0.389467 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.8848 | −1.11729 | −0.558643 | − | 0.829408i | \(-0.688678\pi\) | ||||
−0.558643 | + | 0.829408i | \(0.688678\pi\) | |||||||
\(458\) | −26.0859 | −1.21891 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.06283 | 0.142805 | ||||||||
\(461\) | 22.5033 | 1.04808 | 0.524041 | − | 0.851693i | \(-0.324424\pi\) | ||||
0.524041 | + | 0.851693i | \(0.324424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.25600 | −0.337215 | −0.168607 | − | 0.985683i | \(-0.553927\pi\) | ||||
−0.168607 | + | 0.985683i | \(0.553927\pi\) | |||||||
\(464\) | 30.3200 | 1.40757 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 36.5514 | 1.69321 | ||||||||
\(467\) | 3.02312 | 0.139893 | 0.0699465 | − | 0.997551i | \(-0.477717\pi\) | ||||
0.0699465 | + | 0.997551i | \(0.477717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.730117 | −0.0337137 | ||||||||
\(470\) | 3.48857 | 0.160916 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.35486 | 0.0623627 | ||||||||
\(473\) | 4.04001 | 0.185760 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.62500 | −0.120443 | ||||||||
\(476\) | −1.68876 | −0.0774043 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.2351 | 0.879791 | ||||||||
\(479\) | −12.8660 | −0.587862 | −0.293931 | − | 0.955827i | \(-0.594964\pi\) | ||||
−0.293931 | + | 0.955827i | \(0.594964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.6675 | −1.67189 | ||||||||
\(482\) | 26.2089 | 1.19378 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.73303 | −0.0787743 | ||||||||
\(485\) | 19.1568 | 0.869866 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.6527 | −1.75152 | −0.875761 | − | 0.482745i | \(-0.839640\pi\) | ||||
−0.875761 | + | 0.482745i | \(0.839640\pi\) | |||||||
\(488\) | −38.8876 | −1.76036 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.05118 | 0.137838 | ||||||||
\(491\) | 17.5142 | 0.790404 | 0.395202 | − | 0.918594i | \(-0.370675\pi\) | ||||
0.395202 | + | 0.918594i | \(0.370675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.7869 | 2.37740 | ||||||||
\(494\) | 19.6450 | 0.883868 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.29573 | 0.327588 | ||||||||
\(497\) | 2.37985 | 0.106751 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.34272 | 0.373471 | 0.186736 | − | 0.982410i | \(-0.440209\pi\) | ||||
0.186736 | + | 0.982410i | \(0.440209\pi\) | |||||||
\(500\) | 2.62580 | 0.117429 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.2388 | 0.680143 | ||||||||
\(503\) | 20.6604 | 0.921203 | 0.460602 | − | 0.887607i | \(-0.347634\pi\) | ||||
0.460602 | + | 0.887607i | \(0.347634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.47977 | 0.110349 | ||||||||
\(506\) | 17.9228 | 0.796766 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.220813 | 0.00979698 | ||||||||
\(509\) | 23.3833 | 1.03644 | 0.518222 | − | 0.855246i | \(-0.326594\pi\) | ||||
0.518222 | + | 0.855246i | \(0.326594\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.42990 | 0.151730 | ||||||||
\(512\) | 17.8317 | 0.788056 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19.5596 | 0.862736 | ||||||||
\(515\) | 17.8031 | 0.784500 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.02975 | 0.0892684 | ||||||||
\(518\) | −13.4671 | −0.591708 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 22.0269 | 0.965946 | ||||||||
\(521\) | −17.6114 | −0.771568 | −0.385784 | − | 0.922589i | \(-0.626069\pi\) | ||||
−0.385784 | + | 0.922589i | \(0.626069\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.6248 | −1.16422 | −0.582110 | − | 0.813110i | \(-0.697773\pi\) | ||||
−0.582110 | + | 0.813110i | \(0.697773\pi\) | |||||||
\(524\) | 2.24913 | 0.0982538 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.92481 | −0.432742 | ||||||||
\(527\) | 12.7018 | 0.553299 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8959 | 0.995474 | ||||||||
\(530\) | −2.77389 | −0.120490 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.717389 | 0.0311027 | ||||||||
\(533\) | 38.1525 | 1.65257 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.6017 | −1.53920 | ||||||||
\(536\) | −1.93584 | −0.0836157 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.5351 | 0.497313 | ||||||||
\(539\) | 1.77527 | 0.0764661 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.4985 | 1.18225 | 0.591126 | − | 0.806579i | \(-0.298684\pi\) | ||||
0.591126 | + | 0.806579i | \(0.298684\pi\) | |||||||
\(542\) | −8.99952 | −0.386562 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.51094 | −0.407778 | ||||||||
\(545\) | −26.7445 | −1.14561 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0299 | 0.428846 | 0.214423 | − | 0.976741i | \(-0.431213\pi\) | ||||
0.214423 | + | 0.976741i | \(0.431213\pi\) | |||||||
\(548\) | −1.21082 | −0.0517239 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.13756 | 0.0911458 | ||||||||
\(551\) | −22.4239 | −0.955291 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.04927 | −0.299765 | ||||||||
\(554\) | 34.1763 | 1.45201 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.19884 | −0.0932514 | ||||||||
\(557\) | 32.2636 | 1.36705 | 0.683527 | − | 0.729925i | \(-0.260445\pi\) | ||||
0.683527 | + | 0.729925i | \(0.260445\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.23388 | −0.390552 | ||||||||
\(560\) | 8.99415 | 0.380072 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −37.6739 | −1.58918 | ||||||||
\(563\) | −5.87677 | −0.247676 | −0.123838 | − | 0.992302i | \(-0.539520\pi\) | ||||
−0.123838 | + | 0.992302i | \(0.539520\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.9894 | −1.09338 | ||||||||
\(566\) | 19.4618 | 0.818041 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.30998 | 0.264761 | ||||||||
\(569\) | 33.2432 | 1.39363 | 0.696813 | − | 0.717253i | \(-0.254601\pi\) | ||||
0.696813 | + | 0.717253i | \(0.254601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.6479 | 1.82661 | 0.913305 | − | 0.407277i | \(-0.133522\pi\) | ||||
0.913305 | + | 0.407277i | \(0.133522\pi\) | |||||||
\(572\) | −1.59057 | −0.0665050 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.0124 | 0.584868 | ||||||||
\(575\) | 5.47376 | 0.228272 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.2681 | −0.469099 | −0.234549 | − | 0.972104i | \(-0.575361\pi\) | ||||
−0.234549 | + | 0.972104i | \(0.575361\pi\) | |||||||
\(578\) | −61.8316 | −2.57185 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.12045 | 0.129570 | ||||||||
\(581\) | −1.32633 | −0.0550256 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.61393 | −0.0668421 | ||||||||
\(584\) | 9.09409 | 0.376316 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.47591 | −0.184898 | ||||||||
\(587\) | 11.3396 | 0.468037 | 0.234018 | − | 0.972232i | \(-0.424812\pi\) | ||||
0.234018 | + | 0.972232i | \(0.424812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.39574 | −0.222328 | ||||||||
\(590\) | 1.55914 | 0.0641889 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −39.6976 | −1.63156 | ||||||||
\(593\) | −12.6697 | −0.520283 | −0.260141 | − | 0.965571i | \(-0.583769\pi\) | ||||
−0.260141 | + | 0.965571i | \(0.583769\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.6587 | 0.641945 | ||||||||
\(596\) | 0.988041 | 0.0404717 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −40.9645 | −1.67516 | ||||||||
\(599\) | −11.1486 | −0.455520 | −0.227760 | − | 0.973717i | \(-0.573140\pi\) | ||||
−0.227760 | + | 0.973717i | \(0.573140\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.8081 | 1.46064 | 0.730322 | − | 0.683104i | \(-0.239370\pi\) | ||||
0.730322 | + | 0.683104i | \(0.239370\pi\) | |||||||
\(602\) | −3.39137 | −0.138222 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.10942 | −0.126521 | ||||||||
\(605\) | 16.0692 | 0.653307 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.95533 | −0.241719 | −0.120860 | − | 0.992670i | \(-0.538565\pi\) | ||||
−0.120860 | + | 0.992670i | \(0.538565\pi\) | |||||||
\(608\) | 4.04026 | 0.163854 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −44.7509 | −1.81191 | ||||||||
\(611\) | −4.63922 | −0.187683 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0813 | 0.689908 | 0.344954 | − | 0.938620i | \(-0.387894\pi\) | ||||
0.344954 | + | 0.938620i | \(0.387894\pi\) | |||||||
\(614\) | −3.47678 | −0.140311 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.70696 | 0.189649 | ||||||||
\(617\) | −23.2365 | −0.935465 | −0.467732 | − | 0.883870i | \(-0.654929\pi\) | ||||
−0.467732 | + | 0.883870i | \(0.654929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −48.1408 | −1.93494 | −0.967470 | − | 0.252984i | \(-0.918588\pi\) | ||||
−0.967470 | + | 0.252984i | \(0.918588\pi\) | |||||||
\(620\) | 0.750856 | 0.0301551 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.00667 | −0.0403639 | ||||||||
\(623\) | 3.63475 | 0.145623 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.3073 | −0.812292 | ||||||||
\(626\) | 9.88369 | 0.395032 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.23363 | −0.0492270 | ||||||||
\(629\) | −69.1132 | −2.75573 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0853 | −0.719963 | −0.359982 | − | 0.932959i | \(-0.617217\pi\) | ||||
−0.359982 | + | 0.932959i | \(0.617217\pi\) | |||||||
\(632\) | −18.6905 | −0.743469 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.98403 | −0.277371 | ||||||||
\(635\) | −2.04744 | −0.0812503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.05756 | −0.160766 | ||||||||
\(638\) | 18.2600 | 0.722920 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 26.2446 | 1.03741 | ||||||||
\(641\) | 12.7420 | 0.503280 | 0.251640 | − | 0.967821i | \(-0.419030\pi\) | ||||
0.251640 | + | 0.967821i | \(0.419030\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.19773 | −0.165542 | −0.0827712 | − | 0.996569i | \(-0.526377\pi\) | ||||
−0.0827712 | + | 0.996569i | \(0.526377\pi\) | |||||||
\(644\) | −1.49593 | −0.0589479 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 37.0281 | 1.45685 | ||||||||
\(647\) | 21.9409 | 0.862587 | 0.431293 | − | 0.902212i | \(-0.358057\pi\) | ||||
0.431293 | + | 0.902212i | \(0.358057\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.907155 | 0.0356090 | ||||||||
\(650\) | −4.88562 | −0.191630 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.68983 | −0.105342 | ||||||||
\(653\) | 1.77511 | 0.0694654 | 0.0347327 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347327 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.8546 | −0.814858 | ||||||||
\(656\) | 41.3053 | 1.61270 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.70387 | −0.0664237 | ||||||||
\(659\) | 14.8065 | 0.576780 | 0.288390 | − | 0.957513i | \(-0.406880\pi\) | ||||
0.288390 | + | 0.957513i | \(0.406880\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.5004 | −0.875164 | −0.437582 | − | 0.899179i | \(-0.644165\pi\) | ||||
−0.437582 | + | 0.899179i | \(0.644165\pi\) | |||||||
\(662\) | 9.05334 | 0.351868 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.51666 | −0.136473 | ||||||||
\(665\) | −6.65185 | −0.257947 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46.7593 | 1.81053 | ||||||||
\(668\) | −1.37733 | −0.0532905 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.22772 | −0.0860643 | ||||||||
\(671\) | −26.0374 | −1.00516 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.2028 | 1.24133 | 0.620663 | − | 0.784077i | \(-0.286864\pi\) | ||||
0.620663 | + | 0.784077i | \(0.286864\pi\) | |||||||
\(674\) | −7.92553 | −0.305280 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.764848 | 0.0294172 | ||||||||
\(677\) | −38.5853 | −1.48296 | −0.741478 | − | 0.670978i | \(-0.765875\pi\) | ||||
−0.741478 | + | 0.670978i | \(0.765875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.35645 | −0.359068 | ||||||||
\(680\) | 41.5178 | 1.59213 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.39380 | 0.168247 | ||||||||
\(683\) | −37.7291 | −1.44366 | −0.721831 | − | 0.692069i | \(-0.756699\pi\) | ||||
−0.721831 | + | 0.692069i | \(0.756699\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.2271 | 0.428967 | ||||||||
\(686\) | −1.49024 | −0.0568976 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.99695 | −0.381130 | ||||||||
\(689\) | 3.68881 | 0.140532 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.9255 | 1.55688 | 0.778439 | − | 0.627720i | \(-0.216012\pi\) | ||||
0.778439 | + | 0.627720i | \(0.216012\pi\) | |||||||
\(692\) | 2.98991 | 0.113659 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.6249 | −0.820870 | ||||||||
\(695\) | 20.3883 | 0.773372 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 71.9122 | 2.72387 | ||||||||
\(698\) | −29.3487 | −1.11087 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.178412 | −0.00674332 | ||||||||
\(701\) | −18.9250 | −0.714788 | −0.357394 | − | 0.933954i | \(-0.616335\pi\) | ||||
−0.357394 | + | 0.933954i | \(0.616335\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.3594 | 1.10731 | ||||||||
\(704\) | 12.3070 | 0.463837 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.4880 | 0.996890 | ||||||||
\(707\) | −1.21116 | −0.0455502 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.73734 | −0.365693 | −0.182847 | − | 0.983141i | \(-0.558531\pi\) | ||||
−0.182847 | + | 0.983141i | \(0.558531\pi\) | |||||||
\(710\) | 7.26136 | 0.272514 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.63722 | 0.361170 | ||||||||
\(713\) | 11.2514 | 0.421369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.7482 | 0.551553 | ||||||||
\(716\) | −2.22423 | −0.0831235 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.9181 | −0.817975 | ||||||||
\(719\) | 33.4897 | 1.24896 | 0.624478 | − | 0.781042i | \(-0.285312\pi\) | ||||
0.624478 | + | 0.781042i | \(0.285312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.69531 | −0.323830 | ||||||||
\(722\) | 12.5850 | 0.468365 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.32502 | 0.123574 | ||||||||
\(725\) | 5.57673 | 0.207115 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.63222 | 0.283063 | 0.141532 | − | 0.989934i | \(-0.454797\pi\) | ||||
0.141532 | + | 0.989934i | \(0.454797\pi\) | |||||||
\(728\) | −10.7583 | −0.398728 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.4652 | 0.387336 | ||||||||
\(731\) | −17.4046 | −0.643733 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.0907 | 1.51772 | 0.758859 | − | 0.651254i | \(-0.225757\pi\) | ||||
0.758859 | + | 0.651254i | \(0.225757\pi\) | |||||||
\(734\) | 20.7549 | 0.766077 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.42491 | −0.310546 | ||||||||
\(737\) | −1.29615 | −0.0477443 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.6018 | −1.49356 | −0.746781 | − | 0.665070i | \(-0.768402\pi\) | ||||
−0.746781 | + | 0.665070i | \(0.768402\pi\) | |||||||
\(740\) | −4.08557 | −0.150189 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.35481 | 0.0497365 | ||||||||
\(743\) | 18.3986 | 0.674977 | 0.337489 | − | 0.941330i | \(-0.390423\pi\) | ||||
0.337489 | + | 0.941330i | \(0.390423\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.16141 | −0.335648 | ||||||||
\(746\) | −44.1290 | −1.61568 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.99800 | −0.109618 | ||||||||
\(749\) | 17.3884 | 0.635358 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.7553 | 1.19526 | 0.597630 | − | 0.801772i | \(-0.296109\pi\) | ||||
0.597630 | + | 0.801772i | \(0.296109\pi\) | |||||||
\(752\) | −5.02259 | −0.183155 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −41.7351 | −1.51990 | ||||||||
\(755\) | 28.8315 | 1.04929 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.5385 | −1.69147 | −0.845735 | − | 0.533604i | \(-0.820837\pi\) | ||||
−0.845735 | + | 0.533604i | \(0.820837\pi\) | |||||||
\(758\) | 24.3070 | 0.882869 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.6368 | −0.639754 | ||||||||
\(761\) | 11.4405 | 0.414718 | 0.207359 | − | 0.978265i | \(-0.433513\pi\) | ||||
0.207359 | + | 0.978265i | \(0.433513\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.0624 | 0.472891 | ||||||||
\(764\) | −1.05258 | −0.0380810 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −45.8840 | −1.65786 | ||||||||
\(767\) | −2.07340 | −0.0748662 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.29466 | −0.0466867 | −0.0233434 | − | 0.999728i | \(-0.507431\pi\) | ||||
−0.0233434 | + | 0.999728i | \(0.507431\pi\) | |||||||
\(770\) | 5.41665 | 0.195203 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.70391 | −0.0613251 | ||||||||
\(773\) | −34.0700 | −1.22541 | −0.612706 | − | 0.790311i | \(-0.709919\pi\) | ||||
−0.612706 | + | 0.790311i | \(0.709919\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.34190 | 0.0482024 | ||||||||
\(776\) | −24.8078 | −0.890549 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.77870 | 0.171325 | ||||||||
\(779\) | −30.5484 | −1.09451 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.22487 | 0.151178 | ||||||||
\(782\) | −77.2125 | −2.76111 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.39287 | −0.156888 | ||||||||
\(785\) | 11.4386 | 0.408260 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.5028 | 1.19424 | 0.597122 | − | 0.802150i | \(-0.296311\pi\) | ||||
0.597122 | + | 0.802150i | \(0.296311\pi\) | |||||||
\(788\) | 0.443069 | 0.0157837 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.5086 | −0.765241 | ||||||||
\(791\) | 12.6936 | 0.451333 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 59.5112 | 2.11330 | ||||||||
\(794\) | −51.2765 | −1.81973 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.54655 | 0.0902600 | ||||||||
\(797\) | −19.4492 | −0.688927 | −0.344464 | − | 0.938800i | \(-0.611939\pi\) | ||||
−0.344464 | + | 0.938800i | \(0.611939\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.74429 | −0.309351 | ||||||||
\(800\) | −1.00479 | −0.0355249 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.98309 | −0.352515 | ||||||||
\(803\) | 6.08898 | 0.214876 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.8707 | 0.488878 | ||||||||
\(806\) | −10.0425 | −0.353732 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.21128 | −0.112972 | ||||||||
\(809\) | 16.3351 | 0.574311 | 0.287156 | − | 0.957884i | \(-0.407290\pi\) | ||||
0.287156 | + | 0.957884i | \(0.407290\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.0347 | −1.12489 | −0.562445 | − | 0.826835i | \(-0.690139\pi\) | ||||
−0.562445 | + | 0.826835i | \(0.690139\pi\) | |||||||
\(812\) | −1.52407 | −0.0534844 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −23.9076 | −0.837961 | ||||||||
\(815\) | 24.9409 | 0.873641 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.39350 | 0.258666 | ||||||||
\(818\) | 42.9663 | 1.50228 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.25103 | 0.148452 | ||||||||
\(821\) | −21.7526 | −0.759171 | −0.379586 | − | 0.925157i | \(-0.623933\pi\) | ||||
−0.379586 | + | 0.925157i | \(0.623933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.0673 | −0.664643 | −0.332322 | − | 0.943166i | \(-0.607832\pi\) | ||||
−0.332322 | + | 0.943166i | \(0.607832\pi\) | |||||||
\(824\) | −23.0549 | −0.803154 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.761508 | −0.0264962 | ||||||||
\(827\) | −16.0124 | −0.556807 | −0.278403 | − | 0.960464i | \(-0.589805\pi\) | ||||
−0.278403 | + | 0.960464i | \(0.589805\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.10746 | 0.281584 | 0.140792 | − | 0.990039i | \(-0.455035\pi\) | ||||
0.140792 | + | 0.990039i | \(0.455035\pi\) | |||||||
\(830\) | −4.04688 | −0.140469 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −28.1290 | −0.975196 | ||||||||
\(833\) | −7.64794 | −0.264986 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.7710 | 0.441959 | ||||||||
\(836\) | 1.27356 | 0.0440468 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 40.0436 | 1.38328 | ||||||||
\(839\) | −13.7923 | −0.476161 | −0.238081 | − | 0.971245i | \(-0.576518\pi\) | ||||
−0.238081 | + | 0.971245i | \(0.576518\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.6389 | 0.642722 | ||||||||
\(842\) | −53.4418 | −1.84172 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.52837 | 0.155873 | ||||||||
\(845\) | −7.09190 | −0.243969 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.84843 | −0.269675 | ||||||||
\(848\) | 3.99364 | 0.137142 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.20872 | −0.315857 | ||||||||
\(851\) | −61.2214 | −2.09864 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.711300 | 0.0243545 | 0.0121772 | − | 0.999926i | \(-0.496124\pi\) | ||||
0.0121772 | + | 0.999926i | \(0.496124\pi\) | |||||||
\(854\) | 21.8570 | 0.747930 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 46.1038 | 1.57580 | ||||||||
\(857\) | 7.40150 | 0.252831 | 0.126415 | − | 0.991977i | \(-0.459653\pi\) | ||||
0.126415 | + | 0.991977i | \(0.459653\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.0089 | −0.580335 | −0.290167 | − | 0.956976i | \(-0.593711\pi\) | ||||
−0.290167 | + | 0.956976i | \(0.593711\pi\) | |||||||
\(860\) | −1.02886 | −0.0350838 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −38.6149 | −1.31523 | ||||||||
\(863\) | −18.4171 | −0.626927 | −0.313464 | − | 0.949600i | \(-0.601489\pi\) | ||||
−0.313464 | + | 0.949600i | \(0.601489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.7233 | −0.942621 | ||||||||
\(866\) | −25.7217 | −0.874059 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.366729 | −0.0124476 | ||||||||
\(869\) | −12.5143 | −0.424519 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.96249 | 0.100380 | ||||||||
\(872\) | 34.6338 | 1.17285 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.7999 | 1.10947 | ||||||||
\(875\) | 11.8915 | 0.402006 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.4975 | 0.388242 | 0.194121 | − | 0.980978i | \(-0.437815\pi\) | ||||
0.194121 | + | 0.980978i | \(0.437815\pi\) | |||||||
\(878\) | −48.8188 | −1.64755 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 15.9670 | 0.538247 | ||||||||
\(881\) | −25.7078 | −0.866119 | −0.433060 | − | 0.901365i | \(-0.642566\pi\) | ||||
−0.433060 | + | 0.901365i | \(0.642566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.3302 | −1.66009 | −0.830047 | − | 0.557693i | \(-0.811687\pi\) | ||||
−0.830047 | + | 0.557693i | \(0.811687\pi\) | |||||||
\(884\) | 6.85226 | 0.230466 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −37.5390 | −1.26115 | ||||||||
\(887\) | 9.71012 | 0.326034 | 0.163017 | − | 0.986623i | \(-0.447877\pi\) | ||||
0.163017 | + | 0.986623i | \(0.447877\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 11.0903 | 0.371747 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.319182 | −0.0106870 | ||||||||
\(893\) | 3.71458 | 0.124304 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.6238 | 0.689376 | ||||||||
\(896\) | −12.8182 | −0.428227 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −57.3765 | −1.91468 | ||||||||
\(899\) | 11.4631 | 0.382315 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.95290 | 0.231635 | ||||||||
\(902\) | 24.8758 | 0.828273 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 33.6560 | 1.11938 | ||||||||
\(905\) | −30.8306 | −1.02484 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.87266 | 0.294612 | 0.147306 | − | 0.989091i | \(-0.452940\pi\) | ||||
0.147306 | + | 0.989091i | \(0.452940\pi\) | |||||||
\(908\) | −5.17501 | −0.171739 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.3803 | −0.410404 | ||||||||
\(911\) | 16.3270 | 0.540938 | 0.270469 | − | 0.962729i | \(-0.412821\pi\) | ||||
0.270469 | + | 0.962729i | \(0.412821\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.35459 | −0.0779257 | ||||||||
\(914\) | 35.5941 | 1.17735 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.86521 | 0.127710 | ||||||||
\(917\) | 10.1857 | 0.336361 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0448 | −0.925111 | −0.462556 | − | 0.886590i | \(-0.653067\pi\) | ||||
−0.462556 | + | 0.886590i | \(0.653067\pi\) | |||||||
\(920\) | 36.7770 | 1.21250 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33.5353 | −1.10442 | ||||||||
\(923\) | −9.65640 | −0.317844 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.30156 | −0.240074 | ||||||||
\(926\) | 10.8132 | 0.355343 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.58340 | −0.281764 | ||||||||
\(929\) | 50.8036 | 1.66681 | 0.833406 | − | 0.552662i | \(-0.186388\pi\) | ||||
0.833406 | + | 0.552662i | \(0.186388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.24885 | 0.106477 | ||||||||
\(932\) | −5.41592 | −0.177404 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.50516 | −0.147413 | ||||||||
\(935\) | 27.7984 | 0.909105 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.2345 | 0.987719 | 0.493860 | − | 0.869542i | \(-0.335586\pi\) | ||||
0.493860 | + | 0.869542i | \(0.335586\pi\) | |||||||
\(938\) | 1.08805 | 0.0355261 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.516911 | −0.0168598 | ||||||||
\(941\) | −22.7086 | −0.740280 | −0.370140 | − | 0.928976i | \(-0.620690\pi\) | ||||
−0.370140 | + | 0.928976i | \(0.620690\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 63.7008 | 2.07438 | ||||||||
\(944\) | −2.24474 | −0.0730601 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.02059 | −0.195746 | ||||||||
\(947\) | −48.8988 | −1.58900 | −0.794499 | − | 0.607265i | \(-0.792267\pi\) | ||||
−0.794499 | + | 0.607265i | \(0.792267\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.9170 | −0.451766 | ||||||||
\(950\) | 3.91188 | 0.126918 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −20.2779 | −0.657210 | ||||||||
\(953\) | 43.4704 | 1.40814 | 0.704072 | − | 0.710129i | \(-0.251363\pi\) | ||||
0.704072 | + | 0.710129i | \(0.251363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.75983 | 0.315821 | ||||||||
\(956\) | −2.85011 | −0.0921792 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.1734 | 0.619464 | ||||||||
\(959\) | −5.48349 | −0.177071 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2417 | −0.911023 | ||||||||
\(962\) | 54.6434 | 1.76177 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.88344 | −0.125077 | ||||||||
\(965\) | 15.7992 | 0.508594 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.76371 | 0.185348 | 0.0926742 | − | 0.995696i | \(-0.470458\pi\) | ||||
0.0926742 | + | 0.995696i | \(0.470458\pi\) | |||||||
\(968\) | −20.8094 | −0.668841 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −28.5482 | −0.916628 | ||||||||
\(971\) | −42.8223 | −1.37423 | −0.687117 | − | 0.726547i | \(-0.741124\pi\) | ||||
−0.687117 | + | 0.726547i | \(0.741124\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.95792 | −0.319236 | ||||||||
\(974\) | 57.6018 | 1.84568 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 64.4291 | 2.06232 | ||||||||
\(977\) | 35.6861 | 1.14170 | 0.570850 | − | 0.821054i | \(-0.306614\pi\) | ||||
0.570850 | + | 0.821054i | \(0.306614\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.45264 | 0.206227 | ||||||||
\(980\) | −0.452102 | −0.0144419 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.1003 | −0.832895 | ||||||||
\(983\) | −15.2090 | −0.485092 | −0.242546 | − | 0.970140i | \(-0.577983\pi\) | ||||
−0.242546 | + | 0.970140i | \(0.577983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.10827 | −0.130900 | ||||||||
\(986\) | −78.6650 | −2.50521 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.91085 | −0.0926063 | ||||||||
\(989\) | −15.4172 | −0.490240 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7220 | −0.404126 | −0.202063 | − | 0.979373i | \(-0.564765\pi\) | ||||
−0.202063 | + | 0.979373i | \(0.564765\pi\) | |||||||
\(992\) | −2.06538 | −0.0655757 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.54655 | −0.112490 | ||||||||
\(995\) | −23.6124 | −0.748562 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.9043 | −0.503695 | −0.251847 | − | 0.967767i | \(-0.581038\pi\) | ||||
−0.251847 | + | 0.967767i | \(0.581038\pi\) | |||||||
\(998\) | −12.4326 | −0.393549 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.v.1.6 | 19 | ||
3.2 | odd | 2 | 2667.2.a.q.1.14 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.q.1.14 | ✓ | 19 | 3.2 | odd | 2 | ||
8001.2.a.v.1.6 | 19 | 1.1 | even | 1 | trivial |