Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(1\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.23091 | −1.28802 | −0.644009 | − | 0.765018i | \(-0.722730\pi\) | ||||
−0.644009 | + | 0.765018i | \(0.722730\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.94904 | 0.871635 | 0.435817 | − | 0.900035i | \(-0.356459\pi\) | ||||
0.435817 | + | 0.900035i | \(0.356459\pi\) | |||||||
\(6\) | 2.23091 | 0.910766 | ||||||||
\(7\) | 1.55699 | 0.588487 | 0.294244 | − | 0.955730i | \(-0.404932\pi\) | ||||
0.294244 | + | 0.955730i | \(0.404932\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.97697 | 0.658991 | ||||||||
\(10\) | −1.94904 | −0.616339 | ||||||||
\(11\) | −0.440224 | −0.132733 | −0.0663663 | − | 0.997795i | \(-0.521141\pi\) | ||||
−0.0663663 | + | 0.997795i | \(0.521141\pi\) | |||||||
\(12\) | −2.23091 | −0.644009 | ||||||||
\(13\) | −5.73346 | −1.59017 | −0.795087 | − | 0.606495i | \(-0.792575\pi\) | ||||
−0.795087 | + | 0.606495i | \(0.792575\pi\) | |||||||
\(14\) | −1.55699 | −0.416123 | ||||||||
\(15\) | −4.34813 | −1.12268 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.734051 | −0.178034 | −0.0890168 | − | 0.996030i | \(-0.528372\pi\) | ||||
−0.0890168 | + | 0.996030i | \(0.528372\pi\) | |||||||
\(18\) | −1.97697 | −0.465977 | ||||||||
\(19\) | 6.42751 | 1.47457 | 0.737285 | − | 0.675581i | \(-0.236107\pi\) | ||||
0.737285 | + | 0.675581i | \(0.236107\pi\) | |||||||
\(20\) | 1.94904 | 0.435817 | ||||||||
\(21\) | −3.47351 | −0.757982 | ||||||||
\(22\) | 0.440224 | 0.0938562 | ||||||||
\(23\) | 7.59175 | 1.58299 | 0.791495 | − | 0.611176i | \(-0.209303\pi\) | ||||
0.791495 | + | 0.611176i | \(0.209303\pi\) | |||||||
\(24\) | 2.23091 | 0.455383 | ||||||||
\(25\) | −1.20126 | −0.240253 | ||||||||
\(26\) | 5.73346 | 1.12442 | ||||||||
\(27\) | 2.28228 | 0.439226 | ||||||||
\(28\) | 1.55699 | 0.294244 | ||||||||
\(29\) | −8.95243 | −1.66242 | −0.831212 | − | 0.555955i | \(-0.812353\pi\) | ||||
−0.831212 | + | 0.555955i | \(0.812353\pi\) | |||||||
\(30\) | 4.34813 | 0.793856 | ||||||||
\(31\) | −4.51395 | −0.810729 | −0.405365 | − | 0.914155i | \(-0.632855\pi\) | ||||
−0.405365 | + | 0.914155i | \(0.632855\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.982102 | 0.170962 | ||||||||
\(34\) | 0.734051 | 0.125889 | ||||||||
\(35\) | 3.03463 | 0.512946 | ||||||||
\(36\) | 1.97697 | 0.329496 | ||||||||
\(37\) | 3.37500 | 0.554846 | 0.277423 | − | 0.960748i | \(-0.410520\pi\) | ||||
0.277423 | + | 0.960748i | \(0.410520\pi\) | |||||||
\(38\) | −6.42751 | −1.04268 | ||||||||
\(39\) | 12.7908 | 2.04817 | ||||||||
\(40\) | −1.94904 | −0.308169 | ||||||||
\(41\) | 10.4996 | 1.63977 | 0.819883 | − | 0.572531i | \(-0.194038\pi\) | ||||
0.819883 | + | 0.572531i | \(0.194038\pi\) | |||||||
\(42\) | 3.47351 | 0.535974 | ||||||||
\(43\) | −7.09790 | −1.08242 | −0.541210 | − | 0.840888i | \(-0.682033\pi\) | ||||
−0.541210 | + | 0.840888i | \(0.682033\pi\) | |||||||
\(44\) | −0.440224 | −0.0663663 | ||||||||
\(45\) | 3.85319 | 0.574400 | ||||||||
\(46\) | −7.59175 | −1.11934 | ||||||||
\(47\) | −10.1456 | −1.47989 | −0.739947 | − | 0.672666i | \(-0.765149\pi\) | ||||
−0.739947 | + | 0.672666i | \(0.765149\pi\) | |||||||
\(48\) | −2.23091 | −0.322005 | ||||||||
\(49\) | −4.57578 | −0.653683 | ||||||||
\(50\) | 1.20126 | 0.169884 | ||||||||
\(51\) | 1.63760 | 0.229310 | ||||||||
\(52\) | −5.73346 | −0.795087 | ||||||||
\(53\) | −0.00409262 | −0.000562165 0 | −0.000281082 | − | 1.00000i | \(-0.500089\pi\) | ||||
−0.000281082 | 1.00000i | \(0.500089\pi\) | ||||||||
\(54\) | −2.28228 | −0.310579 | ||||||||
\(55\) | −0.858013 | −0.115694 | ||||||||
\(56\) | −1.55699 | −0.208062 | ||||||||
\(57\) | −14.3392 | −1.89927 | ||||||||
\(58\) | 8.95243 | 1.17551 | ||||||||
\(59\) | −9.64546 | −1.25573 | −0.627866 | − | 0.778321i | \(-0.716072\pi\) | ||||
−0.627866 | + | 0.778321i | \(0.716072\pi\) | |||||||
\(60\) | −4.34813 | −0.561341 | ||||||||
\(61\) | 3.38658 | 0.433607 | 0.216803 | − | 0.976215i | \(-0.430437\pi\) | ||||
0.216803 | + | 0.976215i | \(0.430437\pi\) | |||||||
\(62\) | 4.51395 | 0.573272 | ||||||||
\(63\) | 3.07813 | 0.387808 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −11.1747 | −1.38605 | ||||||||
\(66\) | −0.982102 | −0.120888 | ||||||||
\(67\) | 5.65852 | 0.691298 | 0.345649 | − | 0.938364i | \(-0.387659\pi\) | ||||
0.345649 | + | 0.938364i | \(0.387659\pi\) | |||||||
\(68\) | −0.734051 | −0.0890168 | ||||||||
\(69\) | −16.9365 | −2.03892 | ||||||||
\(70\) | −3.03463 | −0.362708 | ||||||||
\(71\) | −16.3890 | −1.94502 | −0.972511 | − | 0.232859i | \(-0.925192\pi\) | ||||
−0.972511 | + | 0.232859i | \(0.925192\pi\) | |||||||
\(72\) | −1.97697 | −0.232989 | ||||||||
\(73\) | 12.4924 | 1.46213 | 0.731064 | − | 0.682309i | \(-0.239024\pi\) | ||||
0.731064 | + | 0.682309i | \(0.239024\pi\) | |||||||
\(74\) | −3.37500 | −0.392336 | ||||||||
\(75\) | 2.67991 | 0.309450 | ||||||||
\(76\) | 6.42751 | 0.737285 | ||||||||
\(77\) | −0.685425 | −0.0781115 | ||||||||
\(78\) | −12.7908 | −1.44828 | ||||||||
\(79\) | −8.36805 | −0.941479 | −0.470739 | − | 0.882272i | \(-0.656013\pi\) | ||||
−0.470739 | + | 0.882272i | \(0.656013\pi\) | |||||||
\(80\) | 1.94904 | 0.217909 | ||||||||
\(81\) | −11.0225 | −1.22472 | ||||||||
\(82\) | −10.4996 | −1.15949 | ||||||||
\(83\) | 8.50361 | 0.933392 | 0.466696 | − | 0.884418i | \(-0.345444\pi\) | ||||
0.466696 | + | 0.884418i | \(0.345444\pi\) | |||||||
\(84\) | −3.47351 | −0.378991 | ||||||||
\(85\) | −1.43069 | −0.155180 | ||||||||
\(86\) | 7.09790 | 0.765386 | ||||||||
\(87\) | 19.9721 | 2.14123 | ||||||||
\(88\) | 0.440224 | 0.0469281 | ||||||||
\(89\) | −3.03215 | −0.321407 | −0.160703 | − | 0.987003i | \(-0.551376\pi\) | ||||
−0.160703 | + | 0.987003i | \(0.551376\pi\) | |||||||
\(90\) | −3.85319 | −0.406162 | ||||||||
\(91\) | −8.92694 | −0.935798 | ||||||||
\(92\) | 7.59175 | 0.791495 | ||||||||
\(93\) | 10.0702 | 1.04423 | ||||||||
\(94\) | 10.1456 | 1.04644 | ||||||||
\(95\) | 12.5274 | 1.28529 | ||||||||
\(96\) | 2.23091 | 0.227692 | ||||||||
\(97\) | 16.7782 | 1.70357 | 0.851784 | − | 0.523894i | \(-0.175521\pi\) | ||||
0.851784 | + | 0.523894i | \(0.175521\pi\) | |||||||
\(98\) | 4.57578 | 0.462224 | ||||||||
\(99\) | −0.870312 | −0.0874696 | ||||||||
\(100\) | −1.20126 | −0.120126 | ||||||||
\(101\) | 17.6493 | 1.75617 | 0.878087 | − | 0.478500i | \(-0.158819\pi\) | ||||
0.878087 | + | 0.478500i | \(0.158819\pi\) | |||||||
\(102\) | −1.63760 | −0.162147 | ||||||||
\(103\) | −0.540281 | −0.0532355 | −0.0266178 | − | 0.999646i | \(-0.508474\pi\) | ||||
−0.0266178 | + | 0.999646i | \(0.508474\pi\) | |||||||
\(104\) | 5.73346 | 0.562212 | ||||||||
\(105\) | −6.77000 | −0.660684 | ||||||||
\(106\) | 0.00409262 | 0.000397511 0 | ||||||||
\(107\) | −4.36318 | −0.421804 | −0.210902 | − | 0.977507i | \(-0.567640\pi\) | ||||
−0.210902 | + | 0.977507i | \(0.567640\pi\) | |||||||
\(108\) | 2.28228 | 0.219613 | ||||||||
\(109\) | −2.93220 | −0.280854 | −0.140427 | − | 0.990091i | \(-0.544847\pi\) | ||||
−0.140427 | + | 0.990091i | \(0.544847\pi\) | |||||||
\(110\) | 0.858013 | 0.0818083 | ||||||||
\(111\) | −7.52933 | −0.714652 | ||||||||
\(112\) | 1.55699 | 0.147122 | ||||||||
\(113\) | −4.52487 | −0.425664 | −0.212832 | − | 0.977089i | \(-0.568269\pi\) | ||||
−0.212832 | + | 0.977089i | \(0.568269\pi\) | |||||||
\(114\) | 14.3392 | 1.34299 | ||||||||
\(115\) | 14.7966 | 1.37979 | ||||||||
\(116\) | −8.95243 | −0.831212 | ||||||||
\(117\) | −11.3349 | −1.04791 | ||||||||
\(118\) | 9.64546 | 0.887937 | ||||||||
\(119\) | −1.14291 | −0.104770 | ||||||||
\(120\) | 4.34813 | 0.396928 | ||||||||
\(121\) | −10.8062 | −0.982382 | ||||||||
\(122\) | −3.38658 | −0.306606 | ||||||||
\(123\) | −23.4237 | −2.11205 | ||||||||
\(124\) | −4.51395 | −0.405365 | ||||||||
\(125\) | −12.0865 | −1.08105 | ||||||||
\(126\) | −3.07813 | −0.274222 | ||||||||
\(127\) | −16.3837 | −1.45382 | −0.726911 | − | 0.686732i | \(-0.759045\pi\) | ||||
−0.726911 | + | 0.686732i | \(0.759045\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 15.8348 | 1.39418 | ||||||||
\(130\) | 11.1747 | 0.980087 | ||||||||
\(131\) | −1.43967 | −0.125784 | −0.0628921 | − | 0.998020i | \(-0.520032\pi\) | ||||
−0.0628921 | + | 0.998020i | \(0.520032\pi\) | |||||||
\(132\) | 0.982102 | 0.0854810 | ||||||||
\(133\) | 10.0076 | 0.867766 | ||||||||
\(134\) | −5.65852 | −0.488822 | ||||||||
\(135\) | 4.44825 | 0.382844 | ||||||||
\(136\) | 0.734051 | 0.0629444 | ||||||||
\(137\) | 9.63273 | 0.822980 | 0.411490 | − | 0.911414i | \(-0.365009\pi\) | ||||
0.411490 | + | 0.911414i | \(0.365009\pi\) | |||||||
\(138\) | 16.9365 | 1.44173 | ||||||||
\(139\) | −3.04315 | −0.258117 | −0.129059 | − | 0.991637i | \(-0.541196\pi\) | ||||
−0.129059 | + | 0.991637i | \(0.541196\pi\) | |||||||
\(140\) | 3.03463 | 0.256473 | ||||||||
\(141\) | 22.6340 | 1.90613 | ||||||||
\(142\) | 16.3890 | 1.37534 | ||||||||
\(143\) | 2.52401 | 0.211068 | ||||||||
\(144\) | 1.97697 | 0.164748 | ||||||||
\(145\) | −17.4486 | −1.44903 | ||||||||
\(146\) | −12.4924 | −1.03388 | ||||||||
\(147\) | 10.2082 | 0.841955 | ||||||||
\(148\) | 3.37500 | 0.277423 | ||||||||
\(149\) | 5.79400 | 0.474663 | 0.237331 | − | 0.971429i | \(-0.423727\pi\) | ||||
0.237331 | + | 0.971429i | \(0.423727\pi\) | |||||||
\(150\) | −2.67991 | −0.218814 | ||||||||
\(151\) | −9.39394 | −0.764468 | −0.382234 | − | 0.924066i | \(-0.624845\pi\) | ||||
−0.382234 | + | 0.924066i | \(0.624845\pi\) | |||||||
\(152\) | −6.42751 | −0.521340 | ||||||||
\(153\) | −1.45120 | −0.117323 | ||||||||
\(154\) | 0.685425 | 0.0552332 | ||||||||
\(155\) | −8.79785 | −0.706660 | ||||||||
\(156\) | 12.7908 | 1.02409 | ||||||||
\(157\) | −0.880167 | −0.0702450 | −0.0351225 | − | 0.999383i | \(-0.511182\pi\) | ||||
−0.0351225 | + | 0.999383i | \(0.511182\pi\) | |||||||
\(158\) | 8.36805 | 0.665726 | ||||||||
\(159\) | 0.00913028 | 0.000724079 0 | ||||||||
\(160\) | −1.94904 | −0.154085 | ||||||||
\(161\) | 11.8203 | 0.931569 | ||||||||
\(162\) | 11.0225 | 0.866009 | ||||||||
\(163\) | 22.9288 | 1.79592 | 0.897960 | − | 0.440076i | \(-0.145049\pi\) | ||||
0.897960 | + | 0.440076i | \(0.145049\pi\) | |||||||
\(164\) | 10.4996 | 0.819883 | ||||||||
\(165\) | 1.91415 | 0.149017 | ||||||||
\(166\) | −8.50361 | −0.660008 | ||||||||
\(167\) | −3.44539 | −0.266613 | −0.133306 | − | 0.991075i | \(-0.542559\pi\) | ||||
−0.133306 | + | 0.991075i | \(0.542559\pi\) | |||||||
\(168\) | 3.47351 | 0.267987 | ||||||||
\(169\) | 19.8725 | 1.52866 | ||||||||
\(170\) | 1.43069 | 0.109729 | ||||||||
\(171\) | 12.7070 | 0.971729 | ||||||||
\(172\) | −7.09790 | −0.541210 | ||||||||
\(173\) | 10.7624 | 0.818249 | 0.409125 | − | 0.912479i | \(-0.365834\pi\) | ||||
0.409125 | + | 0.912479i | \(0.365834\pi\) | |||||||
\(174\) | −19.9721 | −1.51408 | ||||||||
\(175\) | −1.87035 | −0.141386 | ||||||||
\(176\) | −0.440224 | −0.0331832 | ||||||||
\(177\) | 21.5182 | 1.61741 | ||||||||
\(178\) | 3.03215 | 0.227269 | ||||||||
\(179\) | 25.1072 | 1.87660 | 0.938300 | − | 0.345823i | \(-0.112400\pi\) | ||||
0.938300 | + | 0.345823i | \(0.112400\pi\) | |||||||
\(180\) | 3.85319 | 0.287200 | ||||||||
\(181\) | −21.5432 | −1.60129 | −0.800645 | − | 0.599139i | \(-0.795510\pi\) | ||||
−0.800645 | + | 0.599139i | \(0.795510\pi\) | |||||||
\(182\) | 8.92694 | 0.661709 | ||||||||
\(183\) | −7.55516 | −0.558494 | ||||||||
\(184\) | −7.59175 | −0.559671 | ||||||||
\(185\) | 6.57799 | 0.483624 | ||||||||
\(186\) | −10.0702 | −0.738385 | ||||||||
\(187\) | 0.323147 | 0.0236309 | ||||||||
\(188\) | −10.1456 | −0.739947 | ||||||||
\(189\) | 3.55350 | 0.258479 | ||||||||
\(190\) | −12.5274 | −0.908836 | ||||||||
\(191\) | −17.7850 | −1.28688 | −0.643440 | − | 0.765497i | \(-0.722493\pi\) | ||||
−0.643440 | + | 0.765497i | \(0.722493\pi\) | |||||||
\(192\) | −2.23091 | −0.161002 | ||||||||
\(193\) | −20.1608 | −1.45121 | −0.725603 | − | 0.688114i | \(-0.758439\pi\) | ||||
−0.725603 | + | 0.688114i | \(0.758439\pi\) | |||||||
\(194\) | −16.7782 | −1.20460 | ||||||||
\(195\) | 24.9298 | 1.78526 | ||||||||
\(196\) | −4.57578 | −0.326841 | ||||||||
\(197\) | −2.10006 | −0.149623 | −0.0748114 | − | 0.997198i | \(-0.523835\pi\) | ||||
−0.0748114 | + | 0.997198i | \(0.523835\pi\) | |||||||
\(198\) | 0.870312 | 0.0618504 | ||||||||
\(199\) | 2.62596 | 0.186149 | 0.0930747 | − | 0.995659i | \(-0.470330\pi\) | ||||
0.0930747 | + | 0.995659i | \(0.470330\pi\) | |||||||
\(200\) | 1.20126 | 0.0849421 | ||||||||
\(201\) | −12.6237 | −0.890405 | ||||||||
\(202\) | −17.6493 | −1.24180 | ||||||||
\(203\) | −13.9389 | −0.978316 | ||||||||
\(204\) | 1.63760 | 0.114655 | ||||||||
\(205\) | 20.4641 | 1.42928 | ||||||||
\(206\) | 0.540281 | 0.0376432 | ||||||||
\(207\) | 15.0087 | 1.04318 | ||||||||
\(208\) | −5.73346 | −0.397544 | ||||||||
\(209\) | −2.82955 | −0.195724 | ||||||||
\(210\) | 6.77000 | 0.467174 | ||||||||
\(211\) | −3.83782 | −0.264206 | −0.132103 | − | 0.991236i | \(-0.542173\pi\) | ||||
−0.132103 | + | 0.991236i | \(0.542173\pi\) | |||||||
\(212\) | −0.00409262 | −0.000281082 0 | ||||||||
\(213\) | 36.5625 | 2.50522 | ||||||||
\(214\) | 4.36318 | 0.298261 | ||||||||
\(215\) | −13.8341 | −0.943474 | ||||||||
\(216\) | −2.28228 | −0.155290 | ||||||||
\(217\) | −7.02818 | −0.477104 | ||||||||
\(218\) | 2.93220 | 0.198594 | ||||||||
\(219\) | −27.8695 | −1.88325 | ||||||||
\(220\) | −0.858013 | −0.0578472 | ||||||||
\(221\) | 4.20865 | 0.283104 | ||||||||
\(222\) | 7.52933 | 0.505336 | ||||||||
\(223\) | −14.2152 | −0.951922 | −0.475961 | − | 0.879466i | \(-0.657900\pi\) | ||||
−0.475961 | + | 0.879466i | \(0.657900\pi\) | |||||||
\(224\) | −1.55699 | −0.104031 | ||||||||
\(225\) | −2.37486 | −0.158324 | ||||||||
\(226\) | 4.52487 | 0.300990 | ||||||||
\(227\) | 7.70742 | 0.511559 | 0.255780 | − | 0.966735i | \(-0.417668\pi\) | ||||
0.255780 | + | 0.966735i | \(0.417668\pi\) | |||||||
\(228\) | −14.3392 | −0.949637 | ||||||||
\(229\) | −12.7734 | −0.844090 | −0.422045 | − | 0.906575i | \(-0.638688\pi\) | ||||
−0.422045 | + | 0.906575i | \(0.638688\pi\) | |||||||
\(230\) | −14.7966 | −0.975658 | ||||||||
\(231\) | 1.52912 | 0.100609 | ||||||||
\(232\) | 8.95243 | 0.587756 | ||||||||
\(233\) | −7.97890 | −0.522715 | −0.261358 | − | 0.965242i | \(-0.584170\pi\) | ||||
−0.261358 | + | 0.965242i | \(0.584170\pi\) | |||||||
\(234\) | 11.3349 | 0.740985 | ||||||||
\(235\) | −19.7742 | −1.28993 | ||||||||
\(236\) | −9.64546 | −0.627866 | ||||||||
\(237\) | 18.6684 | 1.21264 | ||||||||
\(238\) | 1.14291 | 0.0740839 | ||||||||
\(239\) | −8.65986 | −0.560160 | −0.280080 | − | 0.959977i | \(-0.590361\pi\) | ||||
−0.280080 | + | 0.959977i | \(0.590361\pi\) | |||||||
\(240\) | −4.34813 | −0.280670 | ||||||||
\(241\) | −13.0891 | −0.843144 | −0.421572 | − | 0.906795i | \(-0.638521\pi\) | ||||
−0.421572 | + | 0.906795i | \(0.638521\pi\) | |||||||
\(242\) | 10.8062 | 0.694649 | ||||||||
\(243\) | 17.7434 | 1.13824 | ||||||||
\(244\) | 3.38658 | 0.216803 | ||||||||
\(245\) | −8.91835 | −0.569773 | ||||||||
\(246\) | 23.4237 | 1.49344 | ||||||||
\(247\) | −36.8518 | −2.34483 | ||||||||
\(248\) | 4.51395 | 0.286636 | ||||||||
\(249\) | −18.9708 | −1.20223 | ||||||||
\(250\) | 12.0865 | 0.764416 | ||||||||
\(251\) | −0.752494 | −0.0474970 | −0.0237485 | − | 0.999718i | \(-0.507560\pi\) | ||||
−0.0237485 | + | 0.999718i | \(0.507560\pi\) | |||||||
\(252\) | 3.07813 | 0.193904 | ||||||||
\(253\) | −3.34207 | −0.210114 | ||||||||
\(254\) | 16.3837 | 1.02801 | ||||||||
\(255\) | 3.19175 | 0.199875 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.8740 | 1.05257 | 0.526287 | − | 0.850307i | \(-0.323584\pi\) | ||||
0.526287 | + | 0.850307i | \(0.323584\pi\) | |||||||
\(258\) | −15.8348 | −0.985831 | ||||||||
\(259\) | 5.25484 | 0.326520 | ||||||||
\(260\) | −11.1747 | −0.693026 | ||||||||
\(261\) | −17.6987 | −1.09552 | ||||||||
\(262\) | 1.43967 | 0.0889429 | ||||||||
\(263\) | −7.34698 | −0.453034 | −0.226517 | − | 0.974007i | \(-0.572734\pi\) | ||||
−0.226517 | + | 0.974007i | \(0.572734\pi\) | |||||||
\(264\) | −0.982102 | −0.0604442 | ||||||||
\(265\) | −0.00797666 | −0.000490002 0 | ||||||||
\(266\) | −10.0076 | −0.613603 | ||||||||
\(267\) | 6.76446 | 0.413978 | ||||||||
\(268\) | 5.65852 | 0.345649 | ||||||||
\(269\) | −10.0737 | −0.614202 | −0.307101 | − | 0.951677i | \(-0.599359\pi\) | ||||
−0.307101 | + | 0.951677i | \(0.599359\pi\) | |||||||
\(270\) | −4.44825 | −0.270712 | ||||||||
\(271\) | −28.5181 | −1.73235 | −0.866175 | − | 0.499740i | \(-0.833429\pi\) | ||||
−0.866175 | + | 0.499740i | \(0.833429\pi\) | |||||||
\(272\) | −0.734051 | −0.0445084 | ||||||||
\(273\) | 19.9152 | 1.20532 | ||||||||
\(274\) | −9.63273 | −0.581935 | ||||||||
\(275\) | 0.528825 | 0.0318894 | ||||||||
\(276\) | −16.9365 | −1.01946 | ||||||||
\(277\) | 13.4506 | 0.808166 | 0.404083 | − | 0.914722i | \(-0.367591\pi\) | ||||
0.404083 | + | 0.914722i | \(0.367591\pi\) | |||||||
\(278\) | 3.04315 | 0.182516 | ||||||||
\(279\) | −8.92396 | −0.534263 | ||||||||
\(280\) | −3.03463 | −0.181354 | ||||||||
\(281\) | 20.3270 | 1.21261 | 0.606305 | − | 0.795232i | \(-0.292651\pi\) | ||||
0.606305 | + | 0.795232i | \(0.292651\pi\) | |||||||
\(282\) | −22.6340 | −1.34784 | ||||||||
\(283\) | −13.6527 | −0.811568 | −0.405784 | − | 0.913969i | \(-0.633001\pi\) | ||||
−0.405784 | + | 0.913969i | \(0.633001\pi\) | |||||||
\(284\) | −16.3890 | −0.972511 | ||||||||
\(285\) | −27.9476 | −1.65547 | ||||||||
\(286\) | −2.52401 | −0.149248 | ||||||||
\(287\) | 16.3478 | 0.964981 | ||||||||
\(288\) | −1.97697 | −0.116494 | ||||||||
\(289\) | −16.4612 | −0.968304 | ||||||||
\(290\) | 17.4486 | 1.02462 | ||||||||
\(291\) | −37.4307 | −2.19423 | ||||||||
\(292\) | 12.4924 | 0.731064 | ||||||||
\(293\) | −29.9923 | −1.75217 | −0.876084 | − | 0.482158i | \(-0.839853\pi\) | ||||
−0.876084 | + | 0.482158i | \(0.839853\pi\) | |||||||
\(294\) | −10.2082 | −0.595352 | ||||||||
\(295\) | −18.7993 | −1.09454 | ||||||||
\(296\) | −3.37500 | −0.196168 | ||||||||
\(297\) | −1.00472 | −0.0582996 | ||||||||
\(298\) | −5.79400 | −0.335637 | ||||||||
\(299\) | −43.5270 | −2.51723 | ||||||||
\(300\) | 2.67991 | 0.154725 | ||||||||
\(301\) | −11.0514 | −0.636990 | ||||||||
\(302\) | 9.39394 | 0.540561 | ||||||||
\(303\) | −39.3741 | −2.26199 | ||||||||
\(304\) | 6.42751 | 0.368643 | ||||||||
\(305\) | 6.60056 | 0.377947 | ||||||||
\(306\) | 1.45120 | 0.0829596 | ||||||||
\(307\) | −21.1556 | −1.20741 | −0.603707 | − | 0.797206i | \(-0.706310\pi\) | ||||
−0.603707 | + | 0.797206i | \(0.706310\pi\) | |||||||
\(308\) | −0.685425 | −0.0390557 | ||||||||
\(309\) | 1.20532 | 0.0685683 | ||||||||
\(310\) | 8.79785 | 0.499684 | ||||||||
\(311\) | −10.5951 | −0.600794 | −0.300397 | − | 0.953814i | \(-0.597119\pi\) | ||||
−0.300397 | + | 0.953814i | \(0.597119\pi\) | |||||||
\(312\) | −12.7908 | −0.724139 | ||||||||
\(313\) | 16.6891 | 0.943324 | 0.471662 | − | 0.881779i | \(-0.343654\pi\) | ||||
0.471662 | + | 0.881779i | \(0.343654\pi\) | |||||||
\(314\) | 0.880167 | 0.0496707 | ||||||||
\(315\) | 5.99938 | 0.338027 | ||||||||
\(316\) | −8.36805 | −0.470739 | ||||||||
\(317\) | −21.1420 | −1.18745 | −0.593725 | − | 0.804668i | \(-0.702343\pi\) | ||||
−0.593725 | + | 0.804668i | \(0.702343\pi\) | |||||||
\(318\) | −0.00913028 | −0.000512001 0 | ||||||||
\(319\) | 3.94108 | 0.220658 | ||||||||
\(320\) | 1.94904 | 0.108954 | ||||||||
\(321\) | 9.73387 | 0.543292 | ||||||||
\(322\) | −11.8203 | −0.658719 | ||||||||
\(323\) | −4.71812 | −0.262523 | ||||||||
\(324\) | −11.0225 | −0.612361 | ||||||||
\(325\) | 6.88739 | 0.382044 | ||||||||
\(326\) | −22.9288 | −1.26991 | ||||||||
\(327\) | 6.54148 | 0.361745 | ||||||||
\(328\) | −10.4996 | −0.579745 | ||||||||
\(329\) | −15.7967 | −0.870898 | ||||||||
\(330\) | −1.91415 | −0.105371 | ||||||||
\(331\) | −33.7844 | −1.85696 | −0.928478 | − | 0.371388i | \(-0.878882\pi\) | ||||
−0.928478 | + | 0.371388i | \(0.878882\pi\) | |||||||
\(332\) | 8.50361 | 0.466696 | ||||||||
\(333\) | 6.67228 | 0.365639 | ||||||||
\(334\) | 3.44539 | 0.188524 | ||||||||
\(335\) | 11.0287 | 0.602560 | ||||||||
\(336\) | −3.47351 | −0.189496 | ||||||||
\(337\) | −5.38261 | −0.293210 | −0.146605 | − | 0.989195i | \(-0.546835\pi\) | ||||
−0.146605 | + | 0.989195i | \(0.546835\pi\) | |||||||
\(338\) | −19.8725 | −1.08092 | ||||||||
\(339\) | 10.0946 | 0.548263 | ||||||||
\(340\) | −1.43069 | −0.0775901 | ||||||||
\(341\) | 1.98715 | 0.107610 | ||||||||
\(342\) | −12.7070 | −0.687116 | ||||||||
\(343\) | −18.0234 | −0.973171 | ||||||||
\(344\) | 7.09790 | 0.382693 | ||||||||
\(345\) | −33.0099 | −1.77719 | ||||||||
\(346\) | −10.7624 | −0.578589 | ||||||||
\(347\) | −1.75005 | −0.0939474 | −0.0469737 | − | 0.998896i | \(-0.514958\pi\) | ||||
−0.0469737 | + | 0.998896i | \(0.514958\pi\) | |||||||
\(348\) | 19.9721 | 1.07062 | ||||||||
\(349\) | 18.3326 | 0.981320 | 0.490660 | − | 0.871351i | \(-0.336756\pi\) | ||||
0.490660 | + | 0.871351i | \(0.336756\pi\) | |||||||
\(350\) | 1.87035 | 0.0999747 | ||||||||
\(351\) | −13.0854 | −0.698446 | ||||||||
\(352\) | 0.440224 | 0.0234640 | ||||||||
\(353\) | 26.0465 | 1.38632 | 0.693159 | − | 0.720785i | \(-0.256219\pi\) | ||||
0.693159 | + | 0.720785i | \(0.256219\pi\) | |||||||
\(354\) | −21.5182 | −1.14368 | ||||||||
\(355\) | −31.9428 | −1.69535 | ||||||||
\(356\) | −3.03215 | −0.160703 | ||||||||
\(357\) | 2.54973 | 0.134946 | ||||||||
\(358\) | −25.1072 | −1.32696 | ||||||||
\(359\) | 0.941185 | 0.0496739 | 0.0248369 | − | 0.999692i | \(-0.492093\pi\) | ||||
0.0248369 | + | 0.999692i | \(0.492093\pi\) | |||||||
\(360\) | −3.85319 | −0.203081 | ||||||||
\(361\) | 22.3128 | 1.17436 | ||||||||
\(362\) | 21.5432 | 1.13228 | ||||||||
\(363\) | 24.1077 | 1.26533 | ||||||||
\(364\) | −8.92694 | −0.467899 | ||||||||
\(365\) | 24.3482 | 1.27444 | ||||||||
\(366\) | 7.55516 | 0.394915 | ||||||||
\(367\) | −23.6295 | −1.23345 | −0.616725 | − | 0.787178i | \(-0.711541\pi\) | ||||
−0.616725 | + | 0.787178i | \(0.711541\pi\) | |||||||
\(368\) | 7.59175 | 0.395747 | ||||||||
\(369\) | 20.7575 | 1.08059 | ||||||||
\(370\) | −6.57799 | −0.341974 | ||||||||
\(371\) | −0.00637217 | −0.000330827 0 | ||||||||
\(372\) | 10.0702 | 0.522117 | ||||||||
\(373\) | −5.77445 | −0.298990 | −0.149495 | − | 0.988762i | \(-0.547765\pi\) | ||||
−0.149495 | + | 0.988762i | \(0.547765\pi\) | |||||||
\(374\) | −0.323147 | −0.0167095 | ||||||||
\(375\) | 26.9639 | 1.39241 | ||||||||
\(376\) | 10.1456 | 0.523221 | ||||||||
\(377\) | 51.3284 | 2.64355 | ||||||||
\(378\) | −3.55350 | −0.182772 | ||||||||
\(379\) | 27.9068 | 1.43347 | 0.716737 | − | 0.697343i | \(-0.245635\pi\) | ||||
0.716737 | + | 0.697343i | \(0.245635\pi\) | |||||||
\(380\) | 12.5274 | 0.642644 | ||||||||
\(381\) | 36.5507 | 1.87255 | ||||||||
\(382\) | 17.7850 | 0.909961 | ||||||||
\(383\) | −17.7600 | −0.907496 | −0.453748 | − | 0.891130i | \(-0.649913\pi\) | ||||
−0.453748 | + | 0.891130i | \(0.649913\pi\) | |||||||
\(384\) | 2.23091 | 0.113846 | ||||||||
\(385\) | −1.33592 | −0.0680847 | ||||||||
\(386\) | 20.1608 | 1.02616 | ||||||||
\(387\) | −14.0324 | −0.713305 | ||||||||
\(388\) | 16.7782 | 0.851784 | ||||||||
\(389\) | 7.81152 | 0.396060 | 0.198030 | − | 0.980196i | \(-0.436546\pi\) | ||||
0.198030 | + | 0.980196i | \(0.436546\pi\) | |||||||
\(390\) | −24.9298 | −1.26237 | ||||||||
\(391\) | −5.57273 | −0.281825 | ||||||||
\(392\) | 4.57578 | 0.231112 | ||||||||
\(393\) | 3.21177 | 0.162012 | ||||||||
\(394\) | 2.10006 | 0.105799 | ||||||||
\(395\) | −16.3096 | −0.820626 | ||||||||
\(396\) | −0.870312 | −0.0437348 | ||||||||
\(397\) | −2.81916 | −0.141490 | −0.0707449 | − | 0.997494i | \(-0.522538\pi\) | ||||
−0.0707449 | + | 0.997494i | \(0.522538\pi\) | |||||||
\(398\) | −2.62596 | −0.131627 | ||||||||
\(399\) | −22.3260 | −1.11770 | ||||||||
\(400\) | −1.20126 | −0.0600631 | ||||||||
\(401\) | −3.65545 | −0.182545 | −0.0912723 | − | 0.995826i | \(-0.529093\pi\) | ||||
−0.0912723 | + | 0.995826i | \(0.529093\pi\) | |||||||
\(402\) | 12.6237 | 0.629611 | ||||||||
\(403\) | 25.8805 | 1.28920 | ||||||||
\(404\) | 17.6493 | 0.878087 | ||||||||
\(405\) | −21.4832 | −1.06751 | ||||||||
\(406\) | 13.9389 | 0.691774 | ||||||||
\(407\) | −1.48576 | −0.0736462 | ||||||||
\(408\) | −1.63760 | −0.0810735 | ||||||||
\(409\) | −23.6464 | −1.16924 | −0.584619 | − | 0.811308i | \(-0.698756\pi\) | ||||
−0.584619 | + | 0.811308i | \(0.698756\pi\) | |||||||
\(410\) | −20.4641 | −1.01065 | ||||||||
\(411\) | −21.4898 | −1.06001 | ||||||||
\(412\) | −0.540281 | −0.0266178 | ||||||||
\(413\) | −15.0179 | −0.738983 | ||||||||
\(414\) | −15.0087 | −0.737637 | ||||||||
\(415\) | 16.5738 | 0.813577 | ||||||||
\(416\) | 5.73346 | 0.281106 | ||||||||
\(417\) | 6.78901 | 0.332459 | ||||||||
\(418\) | 2.82955 | 0.138398 | ||||||||
\(419\) | −20.9633 | −1.02412 | −0.512061 | − | 0.858949i | \(-0.671118\pi\) | ||||
−0.512061 | + | 0.858949i | \(0.671118\pi\) | |||||||
\(420\) | −6.77000 | −0.330342 | ||||||||
\(421\) | 4.81889 | 0.234859 | 0.117429 | − | 0.993081i | \(-0.462535\pi\) | ||||
0.117429 | + | 0.993081i | \(0.462535\pi\) | |||||||
\(422\) | 3.83782 | 0.186822 | ||||||||
\(423\) | −20.0577 | −0.975236 | ||||||||
\(424\) | 0.00409262 | 0.000198755 0 | ||||||||
\(425\) | 0.881788 | 0.0427730 | ||||||||
\(426\) | −36.5625 | −1.77146 | ||||||||
\(427\) | 5.27287 | 0.255172 | ||||||||
\(428\) | −4.36318 | −0.210902 | ||||||||
\(429\) | −5.63084 | −0.271860 | ||||||||
\(430\) | 13.8341 | 0.667137 | ||||||||
\(431\) | −37.9963 | −1.83022 | −0.915109 | − | 0.403207i | \(-0.867896\pi\) | ||||
−0.915109 | + | 0.403207i | \(0.867896\pi\) | |||||||
\(432\) | 2.28228 | 0.109806 | ||||||||
\(433\) | −8.67778 | −0.417027 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(434\) | 7.02818 | 0.337363 | ||||||||
\(435\) | 38.9263 | 1.86637 | ||||||||
\(436\) | −2.93220 | −0.140427 | ||||||||
\(437\) | 48.7960 | 2.33423 | ||||||||
\(438\) | 27.8695 | 1.33166 | ||||||||
\(439\) | −18.2631 | −0.871651 | −0.435826 | − | 0.900031i | \(-0.643544\pi\) | ||||
−0.435826 | + | 0.900031i | \(0.643544\pi\) | |||||||
\(440\) | 0.858013 | 0.0409042 | ||||||||
\(441\) | −9.04619 | −0.430771 | ||||||||
\(442\) | −4.20865 | −0.200185 | ||||||||
\(443\) | 23.0656 | 1.09588 | 0.547941 | − | 0.836517i | \(-0.315412\pi\) | ||||
0.547941 | + | 0.836517i | \(0.315412\pi\) | |||||||
\(444\) | −7.52933 | −0.357326 | ||||||||
\(445\) | −5.90976 | −0.280149 | ||||||||
\(446\) | 14.2152 | 0.673111 | ||||||||
\(447\) | −12.9259 | −0.611374 | ||||||||
\(448\) | 1.55699 | 0.0735609 | ||||||||
\(449\) | 23.0115 | 1.08598 | 0.542990 | − | 0.839739i | \(-0.317292\pi\) | ||||
0.542990 | + | 0.839739i | \(0.317292\pi\) | |||||||
\(450\) | 2.37486 | 0.111952 | ||||||||
\(451\) | −4.62219 | −0.217650 | ||||||||
\(452\) | −4.52487 | −0.212832 | ||||||||
\(453\) | 20.9571 | 0.984649 | ||||||||
\(454\) | −7.70742 | −0.361727 | ||||||||
\(455\) | −17.3989 | −0.815674 | ||||||||
\(456\) | 14.3392 | 0.671495 | ||||||||
\(457\) | 11.0924 | 0.518879 | 0.259439 | − | 0.965759i | \(-0.416462\pi\) | ||||
0.259439 | + | 0.965759i | \(0.416462\pi\) | |||||||
\(458\) | 12.7734 | 0.596862 | ||||||||
\(459\) | −1.67531 | −0.0781969 | ||||||||
\(460\) | 14.7966 | 0.689894 | ||||||||
\(461\) | −35.2780 | −1.64306 | −0.821530 | − | 0.570166i | \(-0.806879\pi\) | ||||
−0.821530 | + | 0.570166i | \(0.806879\pi\) | |||||||
\(462\) | −1.52912 | −0.0711413 | ||||||||
\(463\) | −18.6447 | −0.866491 | −0.433245 | − | 0.901276i | \(-0.642632\pi\) | ||||
−0.433245 | + | 0.901276i | \(0.642632\pi\) | |||||||
\(464\) | −8.95243 | −0.415606 | ||||||||
\(465\) | 19.6272 | 0.910191 | ||||||||
\(466\) | 7.97890 | 0.369616 | ||||||||
\(467\) | 19.8755 | 0.919731 | 0.459865 | − | 0.887989i | \(-0.347898\pi\) | ||||
0.459865 | + | 0.887989i | \(0.347898\pi\) | |||||||
\(468\) | −11.3349 | −0.523956 | ||||||||
\(469\) | 8.81026 | 0.406820 | ||||||||
\(470\) | 19.7742 | 0.912116 | ||||||||
\(471\) | 1.96358 | 0.0904768 | ||||||||
\(472\) | 9.64546 | 0.443968 | ||||||||
\(473\) | 3.12467 | 0.143672 | ||||||||
\(474\) | −18.6684 | −0.857467 | ||||||||
\(475\) | −7.72112 | −0.354269 | ||||||||
\(476\) | −1.14291 | −0.0523852 | ||||||||
\(477\) | −0.00809100 | −0.000370462 0 | ||||||||
\(478\) | 8.65986 | 0.396093 | ||||||||
\(479\) | 33.1663 | 1.51541 | 0.757703 | − | 0.652599i | \(-0.226321\pi\) | ||||
0.757703 | + | 0.652599i | \(0.226321\pi\) | |||||||
\(480\) | 4.34813 | 0.198464 | ||||||||
\(481\) | −19.3504 | −0.882303 | ||||||||
\(482\) | 13.0891 | 0.596193 | ||||||||
\(483\) | −26.3700 | −1.19988 | ||||||||
\(484\) | −10.8062 | −0.491191 | ||||||||
\(485\) | 32.7013 | 1.48489 | ||||||||
\(486\) | −17.7434 | −0.804856 | ||||||||
\(487\) | 9.28333 | 0.420668 | 0.210334 | − | 0.977630i | \(-0.432545\pi\) | ||||
0.210334 | + | 0.977630i | \(0.432545\pi\) | |||||||
\(488\) | −3.38658 | −0.153303 | ||||||||
\(489\) | −51.1521 | −2.31318 | ||||||||
\(490\) | 8.91835 | 0.402890 | ||||||||
\(491\) | −6.84627 | −0.308968 | −0.154484 | − | 0.987995i | \(-0.549372\pi\) | ||||
−0.154484 | + | 0.987995i | \(0.549372\pi\) | |||||||
\(492\) | −23.4237 | −1.05602 | ||||||||
\(493\) | 6.57154 | 0.295967 | ||||||||
\(494\) | 36.8518 | 1.65804 | ||||||||
\(495\) | −1.69627 | −0.0762416 | ||||||||
\(496\) | −4.51395 | −0.202682 | ||||||||
\(497\) | −25.5176 | −1.14462 | ||||||||
\(498\) | 18.9708 | 0.850102 | ||||||||
\(499\) | 9.43753 | 0.422482 | 0.211241 | − | 0.977434i | \(-0.432250\pi\) | ||||
0.211241 | + | 0.977434i | \(0.432250\pi\) | |||||||
\(500\) | −12.0865 | −0.540524 | ||||||||
\(501\) | 7.68638 | 0.343402 | ||||||||
\(502\) | 0.752494 | 0.0335854 | ||||||||
\(503\) | −17.3061 | −0.771641 | −0.385820 | − | 0.922574i | \(-0.626082\pi\) | ||||
−0.385820 | + | 0.922574i | \(0.626082\pi\) | |||||||
\(504\) | −3.07813 | −0.137111 | ||||||||
\(505\) | 34.3992 | 1.53074 | ||||||||
\(506\) | 3.34207 | 0.148573 | ||||||||
\(507\) | −44.3339 | −1.96894 | ||||||||
\(508\) | −16.3837 | −0.726911 | ||||||||
\(509\) | −31.5887 | −1.40015 | −0.700073 | − | 0.714071i | \(-0.746849\pi\) | ||||
−0.700073 | + | 0.714071i | \(0.746849\pi\) | |||||||
\(510\) | −3.19175 | −0.141333 | ||||||||
\(511\) | 19.4506 | 0.860444 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 14.6694 | 0.647670 | ||||||||
\(514\) | −16.8740 | −0.744282 | ||||||||
\(515\) | −1.05303 | −0.0464019 | ||||||||
\(516\) | 15.8348 | 0.697088 | ||||||||
\(517\) | 4.46636 | 0.196430 | ||||||||
\(518\) | −5.25484 | −0.230885 | ||||||||
\(519\) | −24.0099 | −1.05392 | ||||||||
\(520\) | 11.1747 | 0.490043 | ||||||||
\(521\) | 8.00837 | 0.350853 | 0.175427 | − | 0.984493i | \(-0.443870\pi\) | ||||
0.175427 | + | 0.984493i | \(0.443870\pi\) | |||||||
\(522\) | 17.6987 | 0.774652 | ||||||||
\(523\) | −38.2521 | −1.67265 | −0.836325 | − | 0.548235i | \(-0.815300\pi\) | ||||
−0.836325 | + | 0.548235i | \(0.815300\pi\) | |||||||
\(524\) | −1.43967 | −0.0628921 | ||||||||
\(525\) | 4.17260 | 0.182107 | ||||||||
\(526\) | 7.34698 | 0.320344 | ||||||||
\(527\) | 3.31347 | 0.144337 | ||||||||
\(528\) | 0.982102 | 0.0427405 | ||||||||
\(529\) | 34.6346 | 1.50585 | ||||||||
\(530\) | 0.00797666 | 0.000346484 0 | ||||||||
\(531\) | −19.0688 | −0.827517 | ||||||||
\(532\) | 10.0076 | 0.433883 | ||||||||
\(533\) | −60.1991 | −2.60751 | ||||||||
\(534\) | −6.76446 | −0.292727 | ||||||||
\(535\) | −8.50399 | −0.367660 | ||||||||
\(536\) | −5.65852 | −0.244411 | ||||||||
\(537\) | −56.0120 | −2.41709 | ||||||||
\(538\) | 10.0737 | 0.434306 | ||||||||
\(539\) | 2.01437 | 0.0867651 | ||||||||
\(540\) | 4.44825 | 0.191422 | ||||||||
\(541\) | 5.77632 | 0.248343 | 0.124172 | − | 0.992261i | \(-0.460373\pi\) | ||||
0.124172 | + | 0.992261i | \(0.460373\pi\) | |||||||
\(542\) | 28.5181 | 1.22496 | ||||||||
\(543\) | 48.0609 | 2.06249 | ||||||||
\(544\) | 0.734051 | 0.0314722 | ||||||||
\(545\) | −5.71496 | −0.244802 | ||||||||
\(546\) | −19.9152 | −0.852293 | ||||||||
\(547\) | 21.4907 | 0.918878 | 0.459439 | − | 0.888209i | \(-0.348051\pi\) | ||||
0.459439 | + | 0.888209i | \(0.348051\pi\) | |||||||
\(548\) | 9.63273 | 0.411490 | ||||||||
\(549\) | 6.69517 | 0.285743 | ||||||||
\(550\) | −0.528825 | −0.0225492 | ||||||||
\(551\) | −57.5418 | −2.45136 | ||||||||
\(552\) | 16.9365 | 0.720867 | ||||||||
\(553\) | −13.0290 | −0.554048 | ||||||||
\(554\) | −13.4506 | −0.571460 | ||||||||
\(555\) | −14.6749 | −0.622916 | ||||||||
\(556\) | −3.04315 | −0.129059 | ||||||||
\(557\) | −2.53863 | −0.107565 | −0.0537827 | − | 0.998553i | \(-0.517128\pi\) | ||||
−0.0537827 | + | 0.998553i | \(0.517128\pi\) | |||||||
\(558\) | 8.92396 | 0.377781 | ||||||||
\(559\) | 40.6955 | 1.72124 | ||||||||
\(560\) | 3.03463 | 0.128237 | ||||||||
\(561\) | −0.720913 | −0.0304370 | ||||||||
\(562\) | −20.3270 | −0.857445 | ||||||||
\(563\) | −16.4735 | −0.694274 | −0.347137 | − | 0.937814i | \(-0.612846\pi\) | ||||
−0.347137 | + | 0.937814i | \(0.612846\pi\) | |||||||
\(564\) | 22.6340 | 0.953065 | ||||||||
\(565\) | −8.81913 | −0.371023 | ||||||||
\(566\) | 13.6527 | 0.573865 | ||||||||
\(567\) | −17.1619 | −0.720733 | ||||||||
\(568\) | 16.3890 | 0.687669 | ||||||||
\(569\) | 30.6335 | 1.28422 | 0.642112 | − | 0.766611i | \(-0.278058\pi\) | ||||
0.642112 | + | 0.766611i | \(0.278058\pi\) | |||||||
\(570\) | 27.9476 | 1.17060 | ||||||||
\(571\) | −7.84295 | −0.328217 | −0.164109 | − | 0.986442i | \(-0.552475\pi\) | ||||
−0.164109 | + | 0.986442i | \(0.552475\pi\) | |||||||
\(572\) | 2.52401 | 0.105534 | ||||||||
\(573\) | 39.6769 | 1.65752 | ||||||||
\(574\) | −16.3478 | −0.682345 | ||||||||
\(575\) | −9.11968 | −0.380317 | ||||||||
\(576\) | 1.97697 | 0.0823739 | ||||||||
\(577\) | −22.6644 | −0.943532 | −0.471766 | − | 0.881724i | \(-0.656383\pi\) | ||||
−0.471766 | + | 0.881724i | \(0.656383\pi\) | |||||||
\(578\) | 16.4612 | 0.684694 | ||||||||
\(579\) | 44.9770 | 1.86918 | ||||||||
\(580\) | −17.4486 | −0.724514 | ||||||||
\(581\) | 13.2400 | 0.549289 | ||||||||
\(582\) | 37.4307 | 1.55155 | ||||||||
\(583\) | 0.00180167 | 7.46176e−5 0 | ||||||||
\(584\) | −12.4924 | −0.516941 | ||||||||
\(585\) | −22.0921 | −0.913396 | ||||||||
\(586\) | 29.9923 | 1.23897 | ||||||||
\(587\) | 26.0059 | 1.07338 | 0.536690 | − | 0.843780i | \(-0.319675\pi\) | ||||
0.536690 | + | 0.843780i | \(0.319675\pi\) | |||||||
\(588\) | 10.2082 | 0.420978 | ||||||||
\(589\) | −29.0134 | −1.19548 | ||||||||
\(590\) | 18.7993 | 0.773957 | ||||||||
\(591\) | 4.68504 | 0.192717 | ||||||||
\(592\) | 3.37500 | 0.138712 | ||||||||
\(593\) | −15.6415 | −0.642321 | −0.321160 | − | 0.947025i | \(-0.604073\pi\) | ||||
−0.321160 | + | 0.947025i | \(0.604073\pi\) | |||||||
\(594\) | 1.00472 | 0.0412240 | ||||||||
\(595\) | −2.22757 | −0.0913216 | ||||||||
\(596\) | 5.79400 | 0.237331 | ||||||||
\(597\) | −5.85829 | −0.239764 | ||||||||
\(598\) | 43.5270 | 1.77995 | ||||||||
\(599\) | 40.7617 | 1.66548 | 0.832739 | − | 0.553665i | \(-0.186771\pi\) | ||||
0.832739 | + | 0.553665i | \(0.186771\pi\) | |||||||
\(600\) | −2.67991 | −0.109407 | ||||||||
\(601\) | −19.6906 | −0.803197 | −0.401598 | − | 0.915816i | \(-0.631545\pi\) | ||||
−0.401598 | + | 0.915816i | \(0.631545\pi\) | |||||||
\(602\) | 11.0514 | 0.450420 | ||||||||
\(603\) | 11.1867 | 0.455559 | ||||||||
\(604\) | −9.39394 | −0.382234 | ||||||||
\(605\) | −21.0617 | −0.856279 | ||||||||
\(606\) | 39.3741 | 1.59947 | ||||||||
\(607\) | 12.1307 | 0.492371 | 0.246185 | − | 0.969223i | \(-0.420823\pi\) | ||||
0.246185 | + | 0.969223i | \(0.420823\pi\) | |||||||
\(608\) | −6.42751 | −0.260670 | ||||||||
\(609\) | 31.0964 | 1.26009 | ||||||||
\(610\) | −6.60056 | −0.267249 | ||||||||
\(611\) | 58.1696 | 2.35329 | ||||||||
\(612\) | −1.45120 | −0.0586613 | ||||||||
\(613\) | −19.5832 | −0.790958 | −0.395479 | − | 0.918475i | \(-0.629421\pi\) | ||||
−0.395479 | + | 0.918475i | \(0.629421\pi\) | |||||||
\(614\) | 21.1556 | 0.853770 | ||||||||
\(615\) | −45.6537 | −1.84094 | ||||||||
\(616\) | 0.685425 | 0.0276166 | ||||||||
\(617\) | −47.2394 | −1.90179 | −0.950893 | − | 0.309519i | \(-0.899832\pi\) | ||||
−0.950893 | + | 0.309519i | \(0.899832\pi\) | |||||||
\(618\) | −1.20532 | −0.0484851 | ||||||||
\(619\) | 41.9874 | 1.68762 | 0.843809 | − | 0.536644i | \(-0.180308\pi\) | ||||
0.843809 | + | 0.536644i | \(0.180308\pi\) | |||||||
\(620\) | −8.79785 | −0.353330 | ||||||||
\(621\) | 17.3265 | 0.695290 | ||||||||
\(622\) | 10.5951 | 0.424825 | ||||||||
\(623\) | −4.72102 | −0.189144 | ||||||||
\(624\) | 12.7908 | 0.512044 | ||||||||
\(625\) | −17.5507 | −0.702026 | ||||||||
\(626\) | −16.6891 | −0.667031 | ||||||||
\(627\) | 6.31247 | 0.252096 | ||||||||
\(628\) | −0.880167 | −0.0351225 | ||||||||
\(629\) | −2.47742 | −0.0987813 | ||||||||
\(630\) | −5.99938 | −0.239021 | ||||||||
\(631\) | −23.8201 | −0.948265 | −0.474132 | − | 0.880454i | \(-0.657238\pi\) | ||||
−0.474132 | + | 0.880454i | \(0.657238\pi\) | |||||||
\(632\) | 8.36805 | 0.332863 | ||||||||
\(633\) | 8.56184 | 0.340302 | ||||||||
\(634\) | 21.1420 | 0.839654 | ||||||||
\(635\) | −31.9325 | −1.26720 | ||||||||
\(636\) | 0.00913028 | 0.000362039 0 | ||||||||
\(637\) | 26.2350 | 1.03947 | ||||||||
\(638\) | −3.94108 | −0.156029 | ||||||||
\(639\) | −32.4007 | −1.28175 | ||||||||
\(640\) | −1.94904 | −0.0770424 | ||||||||
\(641\) | −32.3939 | −1.27948 | −0.639742 | − | 0.768590i | \(-0.720959\pi\) | ||||
−0.639742 | + | 0.768590i | \(0.720959\pi\) | |||||||
\(642\) | −9.73387 | −0.384165 | ||||||||
\(643\) | −7.72057 | −0.304470 | −0.152235 | − | 0.988344i | \(-0.548647\pi\) | ||||
−0.152235 | + | 0.988344i | \(0.548647\pi\) | |||||||
\(644\) | 11.8203 | 0.465784 | ||||||||
\(645\) | 30.8626 | 1.21521 | ||||||||
\(646\) | 4.71812 | 0.185632 | ||||||||
\(647\) | −46.7724 | −1.83881 | −0.919406 | − | 0.393309i | \(-0.871330\pi\) | ||||
−0.919406 | + | 0.393309i | \(0.871330\pi\) | |||||||
\(648\) | 11.0225 | 0.433005 | ||||||||
\(649\) | 4.24617 | 0.166677 | ||||||||
\(650\) | −6.88739 | −0.270146 | ||||||||
\(651\) | 15.6793 | 0.614519 | ||||||||
\(652\) | 22.9288 | 0.897960 | ||||||||
\(653\) | 35.5160 | 1.38985 | 0.694924 | − | 0.719083i | \(-0.255438\pi\) | ||||
0.694924 | + | 0.719083i | \(0.255438\pi\) | |||||||
\(654\) | −6.54148 | −0.255792 | ||||||||
\(655\) | −2.80596 | −0.109638 | ||||||||
\(656\) | 10.4996 | 0.409941 | ||||||||
\(657\) | 24.6972 | 0.963530 | ||||||||
\(658\) | 15.7967 | 0.615818 | ||||||||
\(659\) | −12.7899 | −0.498224 | −0.249112 | − | 0.968475i | \(-0.580139\pi\) | ||||
−0.249112 | + | 0.968475i | \(0.580139\pi\) | |||||||
\(660\) | 1.91415 | 0.0745083 | ||||||||
\(661\) | −44.0998 | −1.71529 | −0.857643 | − | 0.514246i | \(-0.828072\pi\) | ||||
−0.857643 | + | 0.514246i | \(0.828072\pi\) | |||||||
\(662\) | 33.7844 | 1.31307 | ||||||||
\(663\) | −9.38913 | −0.364644 | ||||||||
\(664\) | −8.50361 | −0.330004 | ||||||||
\(665\) | 19.5051 | 0.756375 | ||||||||
\(666\) | −6.67228 | −0.258546 | ||||||||
\(667\) | −67.9646 | −2.63160 | ||||||||
\(668\) | −3.44539 | −0.133306 | ||||||||
\(669\) | 31.7129 | 1.22609 | ||||||||
\(670\) | −11.0287 | −0.426074 | ||||||||
\(671\) | −1.49085 | −0.0575538 | ||||||||
\(672\) | 3.47351 | 0.133994 | ||||||||
\(673\) | 21.5334 | 0.830050 | 0.415025 | − | 0.909810i | \(-0.363773\pi\) | ||||
0.415025 | + | 0.909810i | \(0.363773\pi\) | |||||||
\(674\) | 5.38261 | 0.207330 | ||||||||
\(675\) | −2.74162 | −0.105525 | ||||||||
\(676\) | 19.8725 | 0.764328 | ||||||||
\(677\) | 12.2531 | 0.470924 | 0.235462 | − | 0.971884i | \(-0.424340\pi\) | ||||
0.235462 | + | 0.971884i | \(0.424340\pi\) | |||||||
\(678\) | −10.0946 | −0.387680 | ||||||||
\(679\) | 26.1235 | 1.00253 | ||||||||
\(680\) | 1.43069 | 0.0548645 | ||||||||
\(681\) | −17.1946 | −0.658897 | ||||||||
\(682\) | −1.98715 | −0.0760920 | ||||||||
\(683\) | 34.1387 | 1.30628 | 0.653141 | − | 0.757237i | \(-0.273451\pi\) | ||||
0.653141 | + | 0.757237i | \(0.273451\pi\) | |||||||
\(684\) | 12.7070 | 0.485865 | ||||||||
\(685\) | 18.7745 | 0.717338 | ||||||||
\(686\) | 18.0234 | 0.688136 | ||||||||
\(687\) | 28.4964 | 1.08720 | ||||||||
\(688\) | −7.09790 | −0.270605 | ||||||||
\(689\) | 0.0234649 | 0.000893940 0 | ||||||||
\(690\) | 33.0099 | 1.25667 | ||||||||
\(691\) | 29.0781 | 1.10618 | 0.553091 | − | 0.833121i | \(-0.313448\pi\) | ||||
0.553091 | + | 0.833121i | \(0.313448\pi\) | |||||||
\(692\) | 10.7624 | 0.409125 | ||||||||
\(693\) | −1.35507 | −0.0514748 | ||||||||
\(694\) | 1.75005 | 0.0664309 | ||||||||
\(695\) | −5.93122 | −0.224984 | ||||||||
\(696\) | −19.9721 | −0.757040 | ||||||||
\(697\) | −7.70726 | −0.291933 | ||||||||
\(698\) | −18.3326 | −0.693898 | ||||||||
\(699\) | 17.8002 | 0.673267 | ||||||||
\(700\) | −1.87035 | −0.0706928 | ||||||||
\(701\) | −28.4110 | −1.07307 | −0.536533 | − | 0.843879i | \(-0.680266\pi\) | ||||
−0.536533 | + | 0.843879i | \(0.680266\pi\) | |||||||
\(702\) | 13.0854 | 0.493876 | ||||||||
\(703\) | 21.6928 | 0.818161 | ||||||||
\(704\) | −0.440224 | −0.0165916 | ||||||||
\(705\) | 44.1145 | 1.66145 | ||||||||
\(706\) | −26.0465 | −0.980274 | ||||||||
\(707\) | 27.4799 | 1.03349 | ||||||||
\(708\) | 21.5182 | 0.808703 | ||||||||
\(709\) | 13.0845 | 0.491400 | 0.245700 | − | 0.969346i | \(-0.420982\pi\) | ||||
0.245700 | + | 0.969346i | \(0.420982\pi\) | |||||||
\(710\) | 31.9428 | 1.19879 | ||||||||
\(711\) | −16.5434 | −0.620426 | ||||||||
\(712\) | 3.03215 | 0.113635 | ||||||||
\(713\) | −34.2688 | −1.28338 | ||||||||
\(714\) | −2.54973 | −0.0954214 | ||||||||
\(715\) | 4.91938 | 0.183974 | ||||||||
\(716\) | 25.1072 | 0.938300 | ||||||||
\(717\) | 19.3194 | 0.721496 | ||||||||
\(718\) | −0.941185 | −0.0351247 | ||||||||
\(719\) | −8.91601 | −0.332511 | −0.166256 | − | 0.986083i | \(-0.553168\pi\) | ||||
−0.166256 | + | 0.986083i | \(0.553168\pi\) | |||||||
\(720\) | 3.85319 | 0.143600 | ||||||||
\(721\) | −0.841213 | −0.0313284 | ||||||||
\(722\) | −22.3128 | −0.830398 | ||||||||
\(723\) | 29.2007 | 1.08598 | ||||||||
\(724\) | −21.5432 | −0.800645 | ||||||||
\(725\) | 10.7542 | 0.399402 | ||||||||
\(726\) | −24.1077 | −0.894721 | ||||||||
\(727\) | −19.8521 | −0.736274 | −0.368137 | − | 0.929771i | \(-0.620004\pi\) | ||||
−0.368137 | + | 0.929771i | \(0.620004\pi\) | |||||||
\(728\) | 8.92694 | 0.330854 | ||||||||
\(729\) | −6.51645 | −0.241350 | ||||||||
\(730\) | −24.3482 | −0.901167 | ||||||||
\(731\) | 5.21022 | 0.192707 | ||||||||
\(732\) | −7.55516 | −0.279247 | ||||||||
\(733\) | −16.3650 | −0.604454 | −0.302227 | − | 0.953236i | \(-0.597730\pi\) | ||||
−0.302227 | + | 0.953236i | \(0.597730\pi\) | |||||||
\(734\) | 23.6295 | 0.872181 | ||||||||
\(735\) | 19.8961 | 0.733878 | ||||||||
\(736\) | −7.59175 | −0.279836 | ||||||||
\(737\) | −2.49102 | −0.0917578 | ||||||||
\(738\) | −20.7575 | −0.764093 | ||||||||
\(739\) | 7.64397 | 0.281188 | 0.140594 | − | 0.990067i | \(-0.455099\pi\) | ||||
0.140594 | + | 0.990067i | \(0.455099\pi\) | |||||||
\(740\) | 6.57799 | 0.241812 | ||||||||
\(741\) | 82.2132 | 3.02018 | ||||||||
\(742\) | 0.00637217 | 0.000233930 0 | ||||||||
\(743\) | 43.7311 | 1.60434 | 0.802169 | − | 0.597097i | \(-0.203679\pi\) | ||||
0.802169 | + | 0.597097i | \(0.203679\pi\) | |||||||
\(744\) | −10.0702 | −0.369193 | ||||||||
\(745\) | 11.2927 | 0.413733 | ||||||||
\(746\) | 5.77445 | 0.211418 | ||||||||
\(747\) | 16.8114 | 0.615097 | ||||||||
\(748\) | 0.323147 | 0.0118154 | ||||||||
\(749\) | −6.79343 | −0.248227 | ||||||||
\(750\) | −26.9639 | −0.984582 | ||||||||
\(751\) | 19.5508 | 0.713418 | 0.356709 | − | 0.934216i | \(-0.383899\pi\) | ||||
0.356709 | + | 0.934216i | \(0.383899\pi\) | |||||||
\(752\) | −10.1456 | −0.369973 | ||||||||
\(753\) | 1.67875 | 0.0611770 | ||||||||
\(754\) | −51.3284 | −1.86927 | ||||||||
\(755\) | −18.3091 | −0.666337 | ||||||||
\(756\) | 3.55350 | 0.129239 | ||||||||
\(757\) | −43.6472 | −1.58638 | −0.793192 | − | 0.608972i | \(-0.791582\pi\) | ||||
−0.793192 | + | 0.608972i | \(0.791582\pi\) | |||||||
\(758\) | −27.9068 | −1.01362 | ||||||||
\(759\) | 7.45587 | 0.270631 | ||||||||
\(760\) | −12.5274 | −0.454418 | ||||||||
\(761\) | −15.4617 | −0.560487 | −0.280243 | − | 0.959929i | \(-0.590415\pi\) | ||||
−0.280243 | + | 0.959929i | \(0.590415\pi\) | |||||||
\(762\) | −36.5507 | −1.32409 | ||||||||
\(763\) | −4.56541 | −0.165279 | ||||||||
\(764\) | −17.7850 | −0.643440 | ||||||||
\(765\) | −2.82844 | −0.102262 | ||||||||
\(766\) | 17.7600 | 0.641696 | ||||||||
\(767\) | 55.3019 | 1.99683 | ||||||||
\(768\) | −2.23091 | −0.0805011 | ||||||||
\(769\) | −29.3228 | −1.05741 | −0.528704 | − | 0.848806i | \(-0.677322\pi\) | ||||
−0.528704 | + | 0.848806i | \(0.677322\pi\) | |||||||
\(770\) | 1.33592 | 0.0481431 | ||||||||
\(771\) | −37.6445 | −1.35573 | ||||||||
\(772\) | −20.1608 | −0.725603 | ||||||||
\(773\) | 53.2951 | 1.91689 | 0.958446 | − | 0.285275i | \(-0.0920848\pi\) | ||||
0.958446 | + | 0.285275i | \(0.0920848\pi\) | |||||||
\(774\) | 14.0324 | 0.504383 | ||||||||
\(775\) | 5.42244 | 0.194780 | ||||||||
\(776\) | −16.7782 | −0.602302 | ||||||||
\(777\) | −11.7231 | −0.420564 | ||||||||
\(778\) | −7.81152 | −0.280057 | ||||||||
\(779\) | 67.4864 | 2.41795 | ||||||||
\(780\) | 24.9298 | 0.892630 | ||||||||
\(781\) | 7.21486 | 0.258168 | ||||||||
\(782\) | 5.57273 | 0.199280 | ||||||||
\(783\) | −20.4320 | −0.730180 | ||||||||
\(784\) | −4.57578 | −0.163421 | ||||||||
\(785\) | −1.71548 | −0.0612280 | ||||||||
\(786\) | −3.21177 | −0.114560 | ||||||||
\(787\) | −32.5507 | −1.16031 | −0.580153 | − | 0.814507i | \(-0.697007\pi\) | ||||
−0.580153 | + | 0.814507i | \(0.697007\pi\) | |||||||
\(788\) | −2.10006 | −0.0748114 | ||||||||
\(789\) | 16.3905 | 0.583517 | ||||||||
\(790\) | 16.3096 | 0.580270 | ||||||||
\(791\) | −7.04518 | −0.250498 | ||||||||
\(792\) | 0.870312 | 0.0309252 | ||||||||
\(793\) | −19.4168 | −0.689511 | ||||||||
\(794\) | 2.81916 | 0.100048 | ||||||||
\(795\) | 0.0177952 | 0.000631132 0 | ||||||||
\(796\) | 2.62596 | 0.0930747 | ||||||||
\(797\) | −30.4445 | −1.07840 | −0.539200 | − | 0.842178i | \(-0.681273\pi\) | ||||
−0.539200 | + | 0.842178i | \(0.681273\pi\) | |||||||
\(798\) | 22.3260 | 0.790332 | ||||||||
\(799\) | 7.44742 | 0.263471 | ||||||||
\(800\) | 1.20126 | 0.0424710 | ||||||||
\(801\) | −5.99447 | −0.211804 | ||||||||
\(802\) | 3.65545 | 0.129079 | ||||||||
\(803\) | −5.49947 | −0.194072 | ||||||||
\(804\) | −12.6237 | −0.445202 | ||||||||
\(805\) | 23.0381 | 0.811988 | ||||||||
\(806\) | −25.8805 | −0.911603 | ||||||||
\(807\) | 22.4735 | 0.791103 | ||||||||
\(808\) | −17.6493 | −0.620902 | ||||||||
\(809\) | −15.4266 | −0.542371 | −0.271186 | − | 0.962527i | \(-0.587416\pi\) | ||||
−0.271186 | + | 0.962527i | \(0.587416\pi\) | |||||||
\(810\) | 21.4832 | 0.754844 | ||||||||
\(811\) | −10.0002 | −0.351154 | −0.175577 | − | 0.984466i | \(-0.556179\pi\) | ||||
−0.175577 | + | 0.984466i | \(0.556179\pi\) | |||||||
\(812\) | −13.9389 | −0.489158 | ||||||||
\(813\) | 63.6214 | 2.23130 | ||||||||
\(814\) | 1.48576 | 0.0520758 | ||||||||
\(815\) | 44.6890 | 1.56539 | ||||||||
\(816\) | 1.63760 | 0.0573276 | ||||||||
\(817\) | −45.6218 | −1.59610 | ||||||||
\(818\) | 23.6464 | 0.826775 | ||||||||
\(819\) | −17.6483 | −0.616682 | ||||||||
\(820\) | 20.4641 | 0.714639 | ||||||||
\(821\) | 5.43781 | 0.189781 | 0.0948904 | − | 0.995488i | \(-0.469750\pi\) | ||||
0.0948904 | + | 0.995488i | \(0.469750\pi\) | |||||||
\(822\) | 21.4898 | 0.749542 | ||||||||
\(823\) | −28.8032 | −1.00402 | −0.502008 | − | 0.864863i | \(-0.667405\pi\) | ||||
−0.502008 | + | 0.864863i | \(0.667405\pi\) | |||||||
\(824\) | 0.540281 | 0.0188216 | ||||||||
\(825\) | −1.17976 | −0.0410741 | ||||||||
\(826\) | 15.0179 | 0.522540 | ||||||||
\(827\) | 26.4130 | 0.918468 | 0.459234 | − | 0.888315i | \(-0.348124\pi\) | ||||
0.459234 | + | 0.888315i | \(0.348124\pi\) | |||||||
\(828\) | 15.0087 | 0.521588 | ||||||||
\(829\) | −12.4596 | −0.432738 | −0.216369 | − | 0.976312i | \(-0.569421\pi\) | ||||
−0.216369 | + | 0.976312i | \(0.569421\pi\) | |||||||
\(830\) | −16.5738 | −0.575286 | ||||||||
\(831\) | −30.0071 | −1.04093 | ||||||||
\(832\) | −5.73346 | −0.198772 | ||||||||
\(833\) | 3.35886 | 0.116377 | ||||||||
\(834\) | −6.78901 | −0.235084 | ||||||||
\(835\) | −6.71519 | −0.232389 | ||||||||
\(836\) | −2.82955 | −0.0978619 | ||||||||
\(837\) | −10.3021 | −0.356093 | ||||||||
\(838\) | 20.9633 | 0.724164 | ||||||||
\(839\) | 45.5511 | 1.57260 | 0.786299 | − | 0.617846i | \(-0.211995\pi\) | ||||
0.786299 | + | 0.617846i | \(0.211995\pi\) | |||||||
\(840\) | 6.77000 | 0.233587 | ||||||||
\(841\) | 51.1460 | 1.76366 | ||||||||
\(842\) | −4.81889 | −0.166070 | ||||||||
\(843\) | −45.3479 | −1.56186 | ||||||||
\(844\) | −3.83782 | −0.132103 | ||||||||
\(845\) | 38.7323 | 1.33243 | ||||||||
\(846\) | 20.0577 | 0.689596 | ||||||||
\(847\) | −16.8252 | −0.578119 | ||||||||
\(848\) | −0.00409262 | −0.000140541 0 | ||||||||
\(849\) | 30.4579 | 1.04531 | ||||||||
\(850\) | −0.881788 | −0.0302451 | ||||||||
\(851\) | 25.6221 | 0.878316 | ||||||||
\(852\) | 36.5625 | 1.25261 | ||||||||
\(853\) | 24.1539 | 0.827014 | 0.413507 | − | 0.910501i | \(-0.364304\pi\) | ||||
0.413507 | + | 0.910501i | \(0.364304\pi\) | |||||||
\(854\) | −5.27287 | −0.180434 | ||||||||
\(855\) | 24.7664 | 0.846993 | ||||||||
\(856\) | 4.36318 | 0.149130 | ||||||||
\(857\) | 15.6571 | 0.534836 | 0.267418 | − | 0.963581i | \(-0.413830\pi\) | ||||
0.267418 | + | 0.963581i | \(0.413830\pi\) | |||||||
\(858\) | 5.63084 | 0.192234 | ||||||||
\(859\) | −36.3757 | −1.24112 | −0.620562 | − | 0.784158i | \(-0.713095\pi\) | ||||
−0.620562 | + | 0.784158i | \(0.713095\pi\) | |||||||
\(860\) | −13.8341 | −0.471737 | ||||||||
\(861\) | −36.4706 | −1.24291 | ||||||||
\(862\) | 37.9963 | 1.29416 | ||||||||
\(863\) | 27.9874 | 0.952703 | 0.476352 | − | 0.879255i | \(-0.341959\pi\) | ||||
0.476352 | + | 0.879255i | \(0.341959\pi\) | |||||||
\(864\) | −2.28228 | −0.0776449 | ||||||||
\(865\) | 20.9763 | 0.713214 | ||||||||
\(866\) | 8.67778 | 0.294883 | ||||||||
\(867\) | 36.7234 | 1.24719 | ||||||||
\(868\) | −7.02818 | −0.238552 | ||||||||
\(869\) | 3.68382 | 0.124965 | ||||||||
\(870\) | −38.9263 | −1.31973 | ||||||||
\(871\) | −32.4429 | −1.09928 | ||||||||
\(872\) | 2.93220 | 0.0992968 | ||||||||
\(873\) | 33.1700 | 1.12264 | ||||||||
\(874\) | −48.7960 | −1.65055 | ||||||||
\(875\) | −18.8185 | −0.636183 | ||||||||
\(876\) | −27.8695 | −0.941624 | ||||||||
\(877\) | −0.0316773 | −0.00106967 | −0.000534834 | − | 1.00000i | \(-0.500170\pi\) | ||||
−0.000534834 | 1.00000i | \(0.500170\pi\) | ||||||||
\(878\) | 18.2631 | 0.616350 | ||||||||
\(879\) | 66.9102 | 2.25682 | ||||||||
\(880\) | −0.858013 | −0.0289236 | ||||||||
\(881\) | 29.5166 | 0.994440 | 0.497220 | − | 0.867625i | \(-0.334354\pi\) | ||||
0.497220 | + | 0.867625i | \(0.334354\pi\) | |||||||
\(882\) | 9.04619 | 0.304601 | ||||||||
\(883\) | −21.2466 | −0.715004 | −0.357502 | − | 0.933912i | \(-0.616372\pi\) | ||||
−0.357502 | + | 0.933912i | \(0.616372\pi\) | |||||||
\(884\) | 4.20865 | 0.141552 | ||||||||
\(885\) | 41.9397 | 1.40979 | ||||||||
\(886\) | −23.0656 | −0.774906 | ||||||||
\(887\) | 55.9524 | 1.87870 | 0.939349 | − | 0.342963i | \(-0.111431\pi\) | ||||
0.939349 | + | 0.342963i | \(0.111431\pi\) | |||||||
\(888\) | 7.52933 | 0.252668 | ||||||||
\(889\) | −25.5093 | −0.855556 | ||||||||
\(890\) | 5.90976 | 0.198096 | ||||||||
\(891\) | 4.85237 | 0.162561 | ||||||||
\(892\) | −14.2152 | −0.475961 | ||||||||
\(893\) | −65.2111 | −2.18221 | ||||||||
\(894\) | 12.9259 | 0.432307 | ||||||||
\(895\) | 48.9348 | 1.63571 | ||||||||
\(896\) | −1.55699 | −0.0520154 | ||||||||
\(897\) | 97.1049 | 3.24224 | ||||||||
\(898\) | −23.0115 | −0.767904 | ||||||||
\(899\) | 40.4108 | 1.34778 | ||||||||
\(900\) | −2.37486 | −0.0791621 | ||||||||
\(901\) | 0.00300419 | 0.000100084 0 | ||||||||
\(902\) | 4.62219 | 0.153902 | ||||||||
\(903\) | 24.6546 | 0.820455 | ||||||||
\(904\) | 4.52487 | 0.150495 | ||||||||
\(905\) | −41.9884 | −1.39574 | ||||||||
\(906\) | −20.9571 | −0.696252 | ||||||||
\(907\) | −16.7072 | −0.554754 | −0.277377 | − | 0.960761i | \(-0.589465\pi\) | ||||
−0.277377 | + | 0.960761i | \(0.589465\pi\) | |||||||
\(908\) | 7.70742 | 0.255780 | ||||||||
\(909\) | 34.8923 | 1.15730 | ||||||||
\(910\) | 17.3989 | 0.576769 | ||||||||
\(911\) | −5.37099 | −0.177949 | −0.0889745 | − | 0.996034i | \(-0.528359\pi\) | ||||
−0.0889745 | + | 0.996034i | \(0.528359\pi\) | |||||||
\(912\) | −14.3392 | −0.474819 | ||||||||
\(913\) | −3.74349 | −0.123892 | ||||||||
\(914\) | −11.0924 | −0.366903 | ||||||||
\(915\) | −14.7253 | −0.486803 | ||||||||
\(916\) | −12.7734 | −0.422045 | ||||||||
\(917\) | −2.24155 | −0.0740224 | ||||||||
\(918\) | 1.67531 | 0.0552936 | ||||||||
\(919\) | −42.9358 | −1.41632 | −0.708161 | − | 0.706051i | \(-0.750475\pi\) | ||||
−0.708161 | + | 0.706051i | \(0.750475\pi\) | |||||||
\(920\) | −14.7966 | −0.487829 | ||||||||
\(921\) | 47.1963 | 1.55517 | ||||||||
\(922\) | 35.2780 | 1.16182 | ||||||||
\(923\) | 93.9659 | 3.09292 | ||||||||
\(924\) | 1.52912 | 0.0503045 | ||||||||
\(925\) | −4.05426 | −0.133303 | ||||||||
\(926\) | 18.6447 | 0.612701 | ||||||||
\(927\) | −1.06812 | −0.0350817 | ||||||||
\(928\) | 8.95243 | 0.293878 | ||||||||
\(929\) | 9.93544 | 0.325971 | 0.162986 | − | 0.986628i | \(-0.447888\pi\) | ||||
0.162986 | + | 0.986628i | \(0.447888\pi\) | |||||||
\(930\) | −19.6272 | −0.643602 | ||||||||
\(931\) | −29.4108 | −0.963902 | ||||||||
\(932\) | −7.97890 | −0.261358 | ||||||||
\(933\) | 23.6368 | 0.773833 | ||||||||
\(934\) | −19.8755 | −0.650348 | ||||||||
\(935\) | 0.629825 | 0.0205975 | ||||||||
\(936\) | 11.3349 | 0.370493 | ||||||||
\(937\) | −4.70578 | −0.153731 | −0.0768655 | − | 0.997041i | \(-0.524491\pi\) | ||||
−0.0768655 | + | 0.997041i | \(0.524491\pi\) | |||||||
\(938\) | −8.81026 | −0.287665 | ||||||||
\(939\) | −37.2319 | −1.21502 | ||||||||
\(940\) | −19.7742 | −0.644963 | ||||||||
\(941\) | 25.6757 | 0.837005 | 0.418503 | − | 0.908216i | \(-0.362555\pi\) | ||||
0.418503 | + | 0.908216i | \(0.362555\pi\) | |||||||
\(942\) | −1.96358 | −0.0639768 | ||||||||
\(943\) | 79.7105 | 2.59573 | ||||||||
\(944\) | −9.64546 | −0.313933 | ||||||||
\(945\) | 6.92589 | 0.225299 | ||||||||
\(946\) | −3.12467 | −0.101592 | ||||||||
\(947\) | −11.2389 | −0.365215 | −0.182607 | − | 0.983186i | \(-0.558454\pi\) | ||||
−0.182607 | + | 0.983186i | \(0.558454\pi\) | |||||||
\(948\) | 18.6684 | 0.606321 | ||||||||
\(949\) | −71.6248 | −2.32504 | ||||||||
\(950\) | 7.72112 | 0.250506 | ||||||||
\(951\) | 47.1659 | 1.52946 | ||||||||
\(952\) | 1.14291 | 0.0370420 | ||||||||
\(953\) | 36.7864 | 1.19163 | 0.595814 | − | 0.803123i | \(-0.296830\pi\) | ||||
0.595814 | + | 0.803123i | \(0.296830\pi\) | |||||||
\(954\) | 0.00809100 | 0.000261956 0 | ||||||||
\(955\) | −34.6636 | −1.12169 | ||||||||
\(956\) | −8.65986 | −0.280080 | ||||||||
\(957\) | −8.79221 | −0.284212 | ||||||||
\(958\) | −33.1663 | −1.07155 | ||||||||
\(959\) | 14.9981 | 0.484313 | ||||||||
\(960\) | −4.34813 | −0.140335 | ||||||||
\(961\) | −10.6242 | −0.342718 | ||||||||
\(962\) | 19.3504 | 0.623882 | ||||||||
\(963\) | −8.62589 | −0.277965 | ||||||||
\(964\) | −13.0891 | −0.421572 | ||||||||
\(965\) | −39.2941 | −1.26492 | ||||||||
\(966\) | 26.3700 | 0.848442 | ||||||||
\(967\) | −36.4809 | −1.17315 | −0.586574 | − | 0.809896i | \(-0.699524\pi\) | ||||
−0.586574 | + | 0.809896i | \(0.699524\pi\) | |||||||
\(968\) | 10.8062 | 0.347325 | ||||||||
\(969\) | 10.5257 | 0.338135 | ||||||||
\(970\) | −32.7013 | −1.04997 | ||||||||
\(971\) | −53.8830 | −1.72919 | −0.864594 | − | 0.502471i | \(-0.832424\pi\) | ||||
−0.864594 | + | 0.502471i | \(0.832424\pi\) | |||||||
\(972\) | 17.7434 | 0.569119 | ||||||||
\(973\) | −4.73816 | −0.151899 | ||||||||
\(974\) | −9.28333 | −0.297457 | ||||||||
\(975\) | −15.3652 | −0.492079 | ||||||||
\(976\) | 3.38658 | 0.108402 | ||||||||
\(977\) | 7.10952 | 0.227454 | 0.113727 | − | 0.993512i | \(-0.463721\pi\) | ||||
0.113727 | + | 0.993512i | \(0.463721\pi\) | |||||||
\(978\) | 51.1521 | 1.63566 | ||||||||
\(979\) | 1.33483 | 0.0426612 | ||||||||
\(980\) | −8.91835 | −0.284886 | ||||||||
\(981\) | −5.79688 | −0.185080 | ||||||||
\(982\) | 6.84627 | 0.218473 | ||||||||
\(983\) | −41.6492 | −1.32840 | −0.664202 | − | 0.747553i | \(-0.731228\pi\) | ||||
−0.664202 | + | 0.747553i | \(0.731228\pi\) | |||||||
\(984\) | 23.4237 | 0.746722 | ||||||||
\(985\) | −4.09308 | −0.130417 | ||||||||
\(986\) | −6.57154 | −0.209281 | ||||||||
\(987\) | 35.2410 | 1.12173 | ||||||||
\(988\) | −36.8518 | −1.17241 | ||||||||
\(989\) | −53.8855 | −1.71346 | ||||||||
\(990\) | 1.69627 | 0.0539109 | ||||||||
\(991\) | −21.4172 | −0.680339 | −0.340169 | − | 0.940364i | \(-0.610484\pi\) | ||||
−0.340169 | + | 0.940364i | \(0.610484\pi\) | |||||||
\(992\) | 4.51395 | 0.143318 | ||||||||
\(993\) | 75.3700 | 2.39179 | ||||||||
\(994\) | 25.5176 | 0.809369 | ||||||||
\(995\) | 5.11809 | 0.162254 | ||||||||
\(996\) | −18.9708 | −0.601113 | ||||||||
\(997\) | 14.7933 | 0.468510 | 0.234255 | − | 0.972175i | \(-0.424735\pi\) | ||||
0.234255 | + | 0.972175i | \(0.424735\pi\) | |||||||
\(998\) | −9.43753 | −0.298740 | ||||||||
\(999\) | 7.70271 | 0.243703 |
(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 | 4034.2.a.b.1.6 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.b.1.6 | ✓ | 35 | 1.1 | even | 1 | trivial |