Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, 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("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15952.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.21161\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.21161 | −1.56385 | −0.781924 | − | 0.623374i | \(-0.785761\pi\) | ||||
−0.781924 | + | 0.623374i | \(0.785761\pi\) | |||||||
\(3\) | −1.45216 | −0.838404 | −0.419202 | − | 0.907893i | \(-0.637690\pi\) | ||||
−0.419202 | + | 0.907893i | \(0.637690\pi\) | |||||||
\(4\) | 2.89124 | 1.44562 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 3.21161 | 1.31114 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.97107 | −0.696878 | ||||||||
\(9\) | −0.891236 | −0.297079 | ||||||||
\(10\) | −2.21161 | −0.699374 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −4.19853 | −1.21201 | ||||||||
\(13\) | 6.19853 | 1.71916 | 0.859582 | − | 0.510998i | \(-0.170724\pi\) | ||||
0.859582 | + | 0.510998i | \(0.170724\pi\) | |||||||
\(14\) | 2.21161 | 0.591079 | ||||||||
\(15\) | −1.45216 | −0.374946 | ||||||||
\(16\) | −1.42323 | −0.355807 | ||||||||
\(17\) | −6.75354 | −1.63797 | −0.818987 | − | 0.573812i | \(-0.805464\pi\) | ||||
−0.818987 | + | 0.573812i | \(0.805464\pi\) | |||||||
\(18\) | 1.97107 | 0.464585 | ||||||||
\(19\) | 6.55501 | 1.50382 | 0.751911 | − | 0.659265i | \(-0.229132\pi\) | ||||
0.751911 | + | 0.659265i | \(0.229132\pi\) | |||||||
\(20\) | 2.89124 | 0.646500 | ||||||||
\(21\) | 1.45216 | 0.316887 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.75946 | −0.366872 | −0.183436 | − | 0.983032i | \(-0.558722\pi\) | ||||
−0.183436 | + | 0.983032i | \(0.558722\pi\) | |||||||
\(24\) | 2.86230 | 0.584266 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −13.7088 | −2.68851 | ||||||||
\(27\) | 5.65069 | 1.08748 | ||||||||
\(28\) | −2.89124 | −0.546392 | ||||||||
\(29\) | −3.32754 | −0.617910 | −0.308955 | − | 0.951077i | \(-0.599979\pi\) | ||||
−0.308955 | + | 0.951077i | \(0.599979\pi\) | |||||||
\(30\) | 3.21161 | 0.586358 | ||||||||
\(31\) | 5.76662 | 1.03572 | 0.517858 | − | 0.855467i | \(-0.326730\pi\) | ||||
0.517858 | + | 0.855467i | \(0.326730\pi\) | |||||||
\(32\) | 7.08977 | 1.25331 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 14.9362 | 2.56154 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −2.57677 | −0.429462 | ||||||||
\(37\) | −9.70159 | −1.59493 | −0.797466 | − | 0.603364i | \(-0.793827\pi\) | ||||
−0.797466 | + | 0.603364i | \(0.793827\pi\) | |||||||
\(38\) | −14.4971 | −2.35175 | ||||||||
\(39\) | −9.00125 | −1.44135 | ||||||||
\(40\) | −1.97107 | −0.311653 | ||||||||
\(41\) | 7.98415 | 1.24691 | 0.623457 | − | 0.781857i | \(-0.285727\pi\) | ||||
0.623457 | + | 0.781857i | \(0.285727\pi\) | |||||||
\(42\) | −3.21161 | −0.495563 | ||||||||
\(43\) | 5.27837 | 0.804943 | 0.402472 | − | 0.915432i | \(-0.368151\pi\) | ||||
0.402472 | + | 0.915432i | \(0.368151\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.891236 | −0.132858 | ||||||||
\(46\) | 3.89124 | 0.573731 | ||||||||
\(47\) | −11.9493 | −1.74299 | −0.871493 | − | 0.490409i | \(-0.836848\pi\) | ||||
−0.871493 | + | 0.490409i | \(0.836848\pi\) | |||||||
\(48\) | 2.06675 | 0.298310 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.21161 | −0.312769 | ||||||||
\(51\) | 9.80721 | 1.37328 | ||||||||
\(52\) | 17.9214 | 2.48525 | ||||||||
\(53\) | 5.33623 | 0.732987 | 0.366494 | − | 0.930421i | \(-0.380558\pi\) | ||||
0.366494 | + | 0.930421i | \(0.380558\pi\) | |||||||
\(54\) | −12.4971 | −1.70065 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.97107 | 0.263395 | ||||||||
\(57\) | −9.51891 | −1.26081 | ||||||||
\(58\) | 7.35924 | 0.966316 | ||||||||
\(59\) | −14.1637 | −1.84395 | −0.921977 | − | 0.387244i | \(-0.873427\pi\) | ||||
−0.921977 | + | 0.387244i | \(0.873427\pi\) | |||||||
\(60\) | −4.19853 | −0.542028 | ||||||||
\(61\) | 10.9362 | 1.40024 | 0.700120 | − | 0.714025i | \(-0.253130\pi\) | ||||
0.700120 | + | 0.714025i | \(0.253130\pi\) | |||||||
\(62\) | −12.7535 | −1.61970 | ||||||||
\(63\) | 0.891236 | 0.112285 | ||||||||
\(64\) | −12.8334 | −1.60417 | ||||||||
\(65\) | 6.19853 | 0.768833 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.27837 | 0.889194 | 0.444597 | − | 0.895731i | \(-0.353347\pi\) | ||||
0.444597 | + | 0.895731i | \(0.353347\pi\) | |||||||
\(68\) | −19.5261 | −2.36788 | ||||||||
\(69\) | 2.55501 | 0.307587 | ||||||||
\(70\) | 2.21161 | 0.264338 | ||||||||
\(71\) | 8.82029 | 1.04678 | 0.523388 | − | 0.852094i | \(-0.324668\pi\) | ||||
0.523388 | + | 0.852094i | \(0.324668\pi\) | |||||||
\(72\) | 1.75669 | 0.207028 | ||||||||
\(73\) | 0.811402 | 0.0949674 | 0.0474837 | − | 0.998872i | \(-0.484880\pi\) | ||||
0.0474837 | + | 0.998872i | \(0.484880\pi\) | |||||||
\(74\) | 21.4562 | 2.49423 | ||||||||
\(75\) | −1.45216 | −0.167681 | ||||||||
\(76\) | 18.9521 | 2.17395 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 19.9073 | 2.25406 | ||||||||
\(79\) | −4.53199 | −0.509889 | −0.254944 | − | 0.966956i | \(-0.582057\pi\) | ||||
−0.254944 | + | 0.966956i | \(0.582057\pi\) | |||||||
\(80\) | −1.42323 | −0.159122 | ||||||||
\(81\) | −5.53199 | −0.614666 | ||||||||
\(82\) | −17.6579 | −1.94998 | ||||||||
\(83\) | −0.639032 | −0.0701429 | −0.0350715 | − | 0.999385i | \(-0.511166\pi\) | ||||
−0.0350715 | + | 0.999385i | \(0.511166\pi\) | |||||||
\(84\) | 4.19853 | 0.458097 | ||||||||
\(85\) | −6.75354 | −0.732524 | ||||||||
\(86\) | −11.6737 | −1.25881 | ||||||||
\(87\) | 4.83212 | 0.518058 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.1001 | 1.07061 | 0.535303 | − | 0.844660i | \(-0.320197\pi\) | ||||
0.535303 | + | 0.844660i | \(0.320197\pi\) | |||||||
\(90\) | 1.97107 | 0.207769 | ||||||||
\(91\) | −6.19853 | −0.649783 | ||||||||
\(92\) | −5.08700 | −0.530356 | ||||||||
\(93\) | −8.37405 | −0.868348 | ||||||||
\(94\) | 26.4272 | 2.72576 | ||||||||
\(95\) | 6.55501 | 0.672530 | ||||||||
\(96\) | −10.2955 | −1.05078 | ||||||||
\(97\) | −7.25363 | −0.736494 | −0.368247 | − | 0.929728i | \(-0.620042\pi\) | ||||
−0.368247 | + | 0.929728i | \(0.620042\pi\) | |||||||
\(98\) | −2.21161 | −0.223407 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.89124 | 0.289124 | ||||||||
\(101\) | 18.1898 | 1.80996 | 0.904979 | − | 0.425457i | \(-0.139886\pi\) | ||||
0.904979 | + | 0.425457i | \(0.139886\pi\) | |||||||
\(102\) | −21.6898 | −2.14761 | ||||||||
\(103\) | 3.79136 | 0.373574 | 0.186787 | − | 0.982400i | \(-0.440193\pi\) | ||||
0.186787 | + | 0.982400i | \(0.440193\pi\) | |||||||
\(104\) | −12.2177 | −1.19805 | ||||||||
\(105\) | 1.45216 | 0.141716 | ||||||||
\(106\) | −11.8017 | −1.14628 | ||||||||
\(107\) | −3.73644 | −0.361215 | −0.180608 | − | 0.983555i | \(-0.557806\pi\) | ||||
−0.180608 | + | 0.983555i | \(0.557806\pi\) | |||||||
\(108\) | 16.3375 | 1.57207 | ||||||||
\(109\) | −9.50708 | −0.910613 | −0.455307 | − | 0.890335i | \(-0.650470\pi\) | ||||
−0.455307 | + | 0.890335i | \(0.650470\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0883 | 1.33720 | ||||||||
\(112\) | 1.42323 | 0.134482 | ||||||||
\(113\) | −12.8465 | −1.20849 | −0.604246 | − | 0.796797i | \(-0.706526\pi\) | ||||
−0.604246 | + | 0.796797i | \(0.706526\pi\) | |||||||
\(114\) | 21.0522 | 1.97171 | ||||||||
\(115\) | −1.75946 | −0.164070 | ||||||||
\(116\) | −9.62072 | −0.893261 | ||||||||
\(117\) | −5.52435 | −0.510727 | ||||||||
\(118\) | 31.3246 | 2.88366 | ||||||||
\(119\) | 6.75354 | 0.619096 | ||||||||
\(120\) | 2.86230 | 0.261291 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −24.1867 | −2.18976 | ||||||||
\(123\) | −11.5943 | −1.04542 | ||||||||
\(124\) | 16.6727 | 1.49725 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.97107 | −0.175597 | ||||||||
\(127\) | −10.1478 | −0.900475 | −0.450237 | − | 0.892909i | \(-0.648661\pi\) | ||||
−0.450237 | + | 0.892909i | \(0.648661\pi\) | |||||||
\(128\) | 14.2029 | 1.25537 | ||||||||
\(129\) | −7.66502 | −0.674868 | ||||||||
\(130\) | −13.7088 | −1.20234 | ||||||||
\(131\) | 4.96218 | 0.433548 | 0.216774 | − | 0.976222i | \(-0.430447\pi\) | ||||
0.216774 | + | 0.976222i | \(0.430447\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.55501 | −0.568391 | ||||||||
\(134\) | −16.0969 | −1.39056 | ||||||||
\(135\) | 5.65069 | 0.486334 | ||||||||
\(136\) | 13.3117 | 1.14147 | ||||||||
\(137\) | 2.61774 | 0.223649 | 0.111824 | − | 0.993728i | \(-0.464331\pi\) | ||||
0.111824 | + | 0.993728i | \(0.464331\pi\) | |||||||
\(138\) | −5.65069 | −0.481019 | ||||||||
\(139\) | 5.94214 | 0.504006 | 0.252003 | − | 0.967727i | \(-0.418911\pi\) | ||||
0.252003 | + | 0.967727i | \(0.418911\pi\) | |||||||
\(140\) | −2.89124 | −0.244354 | ||||||||
\(141\) | 17.3523 | 1.46133 | ||||||||
\(142\) | −19.5071 | −1.63700 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.26843 | 0.105703 | ||||||||
\(145\) | −3.32754 | −0.276338 | ||||||||
\(146\) | −1.79451 | −0.148515 | ||||||||
\(147\) | −1.45216 | −0.119772 | ||||||||
\(148\) | −28.0496 | −2.30566 | ||||||||
\(149\) | −0.686788 | −0.0562639 | −0.0281319 | − | 0.999604i | \(-0.508956\pi\) | ||||
−0.0281319 | + | 0.999604i | \(0.508956\pi\) | |||||||
\(150\) | 3.21161 | 0.262227 | ||||||||
\(151\) | −14.9751 | −1.21866 | −0.609328 | − | 0.792918i | \(-0.708561\pi\) | ||||
−0.609328 | + | 0.792918i | \(0.708561\pi\) | |||||||
\(152\) | −12.9204 | −1.04798 | ||||||||
\(153\) | 6.01900 | 0.486607 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.76662 | 0.463186 | ||||||||
\(156\) | −26.0247 | −2.08365 | ||||||||
\(157\) | 0.746374 | 0.0595671 | 0.0297836 | − | 0.999556i | \(-0.490518\pi\) | ||||
0.0297836 | + | 0.999556i | \(0.490518\pi\) | |||||||
\(158\) | 10.0230 | 0.797388 | ||||||||
\(159\) | −7.74905 | −0.614540 | ||||||||
\(160\) | 7.08977 | 0.560495 | ||||||||
\(161\) | 1.75946 | 0.138665 | ||||||||
\(162\) | 12.2346 | 0.961243 | ||||||||
\(163\) | −22.1447 | −1.73451 | −0.867253 | − | 0.497868i | \(-0.834117\pi\) | ||||
−0.867253 | + | 0.497868i | \(0.834117\pi\) | |||||||
\(164\) | 23.0841 | 1.80256 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.41329 | 0.109693 | ||||||||
\(167\) | 16.4393 | 1.27211 | 0.636055 | − | 0.771644i | \(-0.280565\pi\) | ||||
0.636055 | + | 0.771644i | \(0.280565\pi\) | |||||||
\(168\) | −2.86230 | −0.220832 | ||||||||
\(169\) | 25.4218 | 1.95552 | ||||||||
\(170\) | 14.9362 | 1.14556 | ||||||||
\(171\) | −5.84206 | −0.446753 | ||||||||
\(172\) | 15.2610 | 1.16364 | ||||||||
\(173\) | −7.23463 | −0.550039 | −0.275019 | − | 0.961439i | \(-0.588684\pi\) | ||||
−0.275019 | + | 0.961439i | \(0.588684\pi\) | |||||||
\(174\) | −10.6868 | −0.810163 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.5679 | 1.54598 | ||||||||
\(178\) | −22.3375 | −1.67426 | ||||||||
\(179\) | 1.80863 | 0.135184 | 0.0675918 | − | 0.997713i | \(-0.478468\pi\) | ||||
0.0675918 | + | 0.997713i | \(0.478468\pi\) | |||||||
\(180\) | −2.57677 | −0.192061 | ||||||||
\(181\) | −9.25363 | −0.687817 | −0.343908 | − | 0.939003i | \(-0.611751\pi\) | ||||
−0.343908 | + | 0.939003i | \(0.611751\pi\) | |||||||
\(182\) | 13.7088 | 1.01616 | ||||||||
\(183\) | −15.8811 | −1.17397 | ||||||||
\(184\) | 3.46801 | 0.255665 | ||||||||
\(185\) | −9.70159 | −0.713275 | ||||||||
\(186\) | 18.5202 | 1.35796 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −34.5483 | −2.51969 | ||||||||
\(189\) | −5.65069 | −0.411027 | ||||||||
\(190\) | −14.4971 | −1.05173 | ||||||||
\(191\) | −16.7886 | −1.21478 | −0.607390 | − | 0.794404i | \(-0.707783\pi\) | ||||
−0.607390 | + | 0.794404i | \(0.707783\pi\) | |||||||
\(192\) | 18.6361 | 1.34494 | ||||||||
\(193\) | −1.33069 | −0.0957853 | −0.0478926 | − | 0.998852i | \(-0.515251\pi\) | ||||
−0.0478926 | + | 0.998852i | \(0.515251\pi\) | |||||||
\(194\) | 16.0422 | 1.15176 | ||||||||
\(195\) | −9.00125 | −0.644593 | ||||||||
\(196\) | 2.89124 | 0.206517 | ||||||||
\(197\) | 5.59425 | 0.398574 | 0.199287 | − | 0.979941i | \(-0.436137\pi\) | ||||
0.199287 | + | 0.979941i | \(0.436137\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.05807 | 0.571221 | 0.285611 | − | 0.958346i | \(-0.407804\pi\) | ||||
0.285611 | + | 0.958346i | \(0.407804\pi\) | |||||||
\(200\) | −1.97107 | −0.139376 | ||||||||
\(201\) | −10.5693 | −0.745504 | ||||||||
\(202\) | −40.2289 | −2.83050 | ||||||||
\(203\) | 3.32754 | 0.233548 | ||||||||
\(204\) | 28.3550 | 1.98524 | ||||||||
\(205\) | 7.98415 | 0.557637 | ||||||||
\(206\) | −8.38503 | −0.584213 | ||||||||
\(207\) | 1.56809 | 0.108990 | ||||||||
\(208\) | −8.82192 | −0.611690 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.21161 | −0.221622 | ||||||||
\(211\) | −2.13350 | −0.146876 | −0.0734382 | − | 0.997300i | \(-0.523397\pi\) | ||||
−0.0734382 | + | 0.997300i | \(0.523397\pi\) | |||||||
\(212\) | 15.4283 | 1.05962 | ||||||||
\(213\) | −12.8085 | −0.877621 | ||||||||
\(214\) | 8.26356 | 0.564885 | ||||||||
\(215\) | 5.27837 | 0.359982 | ||||||||
\(216\) | −11.1379 | −0.757838 | ||||||||
\(217\) | −5.76662 | −0.391464 | ||||||||
\(218\) | 21.0260 | 1.42406 | ||||||||
\(219\) | −1.17828 | −0.0796211 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −41.8620 | −2.81595 | ||||||||
\(222\) | −31.1578 | −2.09117 | ||||||||
\(223\) | 15.5421 | 1.04078 | 0.520389 | − | 0.853929i | \(-0.325787\pi\) | ||||
0.520389 | + | 0.853929i | \(0.325787\pi\) | |||||||
\(224\) | −7.08977 | −0.473705 | ||||||||
\(225\) | −0.891236 | −0.0594157 | ||||||||
\(226\) | 28.4114 | 1.88990 | ||||||||
\(227\) | −20.5592 | −1.36456 | −0.682282 | − | 0.731089i | \(-0.739012\pi\) | ||||
−0.682282 | + | 0.731089i | \(0.739012\pi\) | |||||||
\(228\) | −27.5214 | −1.82265 | ||||||||
\(229\) | 26.3274 | 1.73976 | 0.869881 | − | 0.493262i | \(-0.164196\pi\) | ||||
0.869881 | + | 0.493262i | \(0.164196\pi\) | |||||||
\(230\) | 3.89124 | 0.256580 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.55882 | 0.430608 | ||||||||
\(233\) | −0.0808778 | −0.00529848 | −0.00264924 | − | 0.999996i | \(-0.500843\pi\) | ||||
−0.00264924 | + | 0.999996i | \(0.500843\pi\) | |||||||
\(234\) | 12.2177 | 0.798698 | ||||||||
\(235\) | −11.9493 | −0.779487 | ||||||||
\(236\) | −40.9506 | −2.66565 | ||||||||
\(237\) | 6.58117 | 0.427493 | ||||||||
\(238\) | −14.9362 | −0.968172 | ||||||||
\(239\) | −6.87815 | −0.444911 | −0.222455 | − | 0.974943i | \(-0.571407\pi\) | ||||
−0.222455 | + | 0.974943i | \(0.571407\pi\) | |||||||
\(240\) | 2.06675 | 0.133408 | ||||||||
\(241\) | 9.65928 | 0.622209 | 0.311104 | − | 0.950376i | \(-0.399301\pi\) | ||||
0.311104 | + | 0.950376i | \(0.399301\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.91874 | −0.572138 | ||||||||
\(244\) | 31.6192 | 2.02421 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 25.6420 | 1.63487 | ||||||||
\(247\) | 40.6314 | 2.58532 | ||||||||
\(248\) | −11.3664 | −0.721768 | ||||||||
\(249\) | 0.927976 | 0.0588081 | ||||||||
\(250\) | −2.21161 | −0.139875 | ||||||||
\(251\) | −9.31723 | −0.588098 | −0.294049 | − | 0.955790i | \(-0.595003\pi\) | ||||
−0.294049 | + | 0.955790i | \(0.595003\pi\) | |||||||
\(252\) | 2.57677 | 0.162321 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 22.4431 | 1.40821 | ||||||||
\(255\) | 9.80721 | 0.614151 | ||||||||
\(256\) | −5.74465 | −0.359041 | ||||||||
\(257\) | −6.12624 | −0.382145 | −0.191072 | − | 0.981576i | \(-0.561196\pi\) | ||||
−0.191072 | + | 0.981576i | \(0.561196\pi\) | |||||||
\(258\) | 16.9521 | 1.05539 | ||||||||
\(259\) | 9.70159 | 0.602828 | ||||||||
\(260\) | 17.9214 | 1.11144 | ||||||||
\(261\) | 2.96563 | 0.183568 | ||||||||
\(262\) | −10.9744 | −0.678002 | ||||||||
\(263\) | 7.97384 | 0.491688 | 0.245844 | − | 0.969309i | \(-0.420935\pi\) | ||||
0.245844 | + | 0.969309i | \(0.420935\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.33623 | 0.327802 | ||||||||
\(266\) | 14.4971 | 0.888877 | ||||||||
\(267\) | −14.6669 | −0.897601 | ||||||||
\(268\) | 21.0435 | 1.28543 | ||||||||
\(269\) | −26.7084 | −1.62844 | −0.814219 | − | 0.580557i | \(-0.802835\pi\) | ||||
−0.814219 | + | 0.580557i | \(0.802835\pi\) | |||||||
\(270\) | −12.4971 | −0.760552 | ||||||||
\(271\) | 17.7706 | 1.07949 | 0.539745 | − | 0.841829i | \(-0.318521\pi\) | ||||
0.539745 | + | 0.841829i | \(0.318521\pi\) | |||||||
\(272\) | 9.61183 | 0.582803 | ||||||||
\(273\) | 9.00125 | 0.544781 | ||||||||
\(274\) | −5.78943 | −0.349752 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.38713 | 0.444653 | ||||||||
\(277\) | −30.2465 | −1.81734 | −0.908668 | − | 0.417520i | \(-0.862899\pi\) | ||||
−0.908668 | + | 0.417520i | \(0.862899\pi\) | |||||||
\(278\) | −13.1417 | −0.788188 | ||||||||
\(279\) | −5.13942 | −0.307689 | ||||||||
\(280\) | 1.97107 | 0.117794 | ||||||||
\(281\) | 26.8925 | 1.60427 | 0.802136 | − | 0.597142i | \(-0.203697\pi\) | ||||
0.802136 | + | 0.597142i | \(0.203697\pi\) | |||||||
\(282\) | −38.3766 | −2.28529 | ||||||||
\(283\) | 12.1795 | 0.723998 | 0.361999 | − | 0.932178i | \(-0.382094\pi\) | ||||
0.361999 | + | 0.932178i | \(0.382094\pi\) | |||||||
\(284\) | 25.5015 | 1.51324 | ||||||||
\(285\) | −9.51891 | −0.563852 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.98415 | −0.471290 | ||||||||
\(288\) | −6.31865 | −0.372330 | ||||||||
\(289\) | 28.6103 | 1.68296 | ||||||||
\(290\) | 7.35924 | 0.432150 | ||||||||
\(291\) | 10.5334 | 0.617480 | ||||||||
\(292\) | 2.34596 | 0.137287 | ||||||||
\(293\) | 7.02339 | 0.410311 | 0.205156 | − | 0.978729i | \(-0.434230\pi\) | ||||
0.205156 | + | 0.978729i | \(0.434230\pi\) | |||||||
\(294\) | 3.21161 | 0.187305 | ||||||||
\(295\) | −14.1637 | −0.824642 | ||||||||
\(296\) | 19.1225 | 1.11147 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.51891 | 0.0879881 | ||||||||
\(299\) | −10.9060 | −0.630713 | ||||||||
\(300\) | −4.19853 | −0.242402 | ||||||||
\(301\) | −5.27837 | −0.304240 | ||||||||
\(302\) | 33.1191 | 1.90579 | ||||||||
\(303\) | −26.4145 | −1.51748 | ||||||||
\(304\) | −9.32927 | −0.535070 | ||||||||
\(305\) | 10.9362 | 0.626206 | ||||||||
\(306\) | −13.3117 | −0.760979 | ||||||||
\(307\) | −4.02159 | −0.229524 | −0.114762 | − | 0.993393i | \(-0.536611\pi\) | ||||
−0.114762 | + | 0.993393i | \(0.536611\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.50566 | −0.313206 | ||||||||
\(310\) | −12.7535 | −0.724352 | ||||||||
\(311\) | 4.14209 | 0.234877 | 0.117438 | − | 0.993080i | \(-0.462532\pi\) | ||||
0.117438 | + | 0.993080i | \(0.462532\pi\) | |||||||
\(312\) | 17.7421 | 1.00445 | ||||||||
\(313\) | 2.35103 | 0.132888 | 0.0664441 | − | 0.997790i | \(-0.478835\pi\) | ||||
0.0664441 | + | 0.997790i | \(0.478835\pi\) | |||||||
\(314\) | −1.65069 | −0.0931539 | ||||||||
\(315\) | 0.891236 | 0.0502154 | ||||||||
\(316\) | −13.1031 | −0.737105 | ||||||||
\(317\) | −0.0198694 | −0.00111598 | −0.000557988 | − | 1.00000i | \(-0.500178\pi\) | ||||
−0.000557988 | 1.00000i | \(0.500178\pi\) | ||||||||
\(318\) | 17.1379 | 0.961046 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −12.8334 | −0.717407 | ||||||||
\(321\) | 5.42590 | 0.302844 | ||||||||
\(322\) | −3.89124 | −0.216850 | ||||||||
\(323\) | −44.2695 | −2.46322 | ||||||||
\(324\) | −15.9943 | −0.888572 | ||||||||
\(325\) | 6.19853 | 0.343833 | ||||||||
\(326\) | 48.9755 | 2.71250 | ||||||||
\(327\) | 13.8058 | 0.763462 | ||||||||
\(328\) | −15.7373 | −0.868948 | ||||||||
\(329\) | 11.9493 | 0.658786 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.11555 | 0.501036 | 0.250518 | − | 0.968112i | \(-0.419399\pi\) | ||||
0.250518 | + | 0.968112i | \(0.419399\pi\) | |||||||
\(332\) | −1.84759 | −0.101400 | ||||||||
\(333\) | 8.64641 | 0.473820 | ||||||||
\(334\) | −36.3573 | −1.98939 | ||||||||
\(335\) | 7.27837 | 0.397660 | ||||||||
\(336\) | −2.06675 | −0.112751 | ||||||||
\(337\) | 0.637610 | 0.0347328 | 0.0173664 | − | 0.999849i | \(-0.494472\pi\) | ||||
0.0173664 | + | 0.999849i | \(0.494472\pi\) | |||||||
\(338\) | −56.2232 | −3.05814 | ||||||||
\(339\) | 18.6551 | 1.01321 | ||||||||
\(340\) | −19.5261 | −1.05895 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.9204 | 0.698654 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −10.4040 | −0.560947 | ||||||||
\(345\) | 2.55501 | 0.137557 | ||||||||
\(346\) | 16.0002 | 0.860176 | ||||||||
\(347\) | 5.42620 | 0.291294 | 0.145647 | − | 0.989337i | \(-0.453474\pi\) | ||||
0.145647 | + | 0.989337i | \(0.453474\pi\) | |||||||
\(348\) | 13.9708 | 0.748914 | ||||||||
\(349\) | 20.0842 | 1.07508 | 0.537542 | − | 0.843237i | \(-0.319353\pi\) | ||||
0.537542 | + | 0.843237i | \(0.319353\pi\) | |||||||
\(350\) | 2.21161 | 0.118216 | ||||||||
\(351\) | 35.0260 | 1.86955 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0117 | 0.798990 | 0.399495 | − | 0.916735i | \(-0.369185\pi\) | ||||
0.399495 | + | 0.916735i | \(0.369185\pi\) | |||||||
\(354\) | −45.4883 | −2.41768 | ||||||||
\(355\) | 8.82029 | 0.468133 | ||||||||
\(356\) | 29.2017 | 1.54769 | ||||||||
\(357\) | −9.80721 | −0.519053 | ||||||||
\(358\) | −4.00000 | −0.211407 | ||||||||
\(359\) | −5.58968 | −0.295012 | −0.147506 | − | 0.989061i | \(-0.547125\pi\) | ||||
−0.147506 | + | 0.989061i | \(0.547125\pi\) | |||||||
\(360\) | 1.75669 | 0.0925855 | ||||||||
\(361\) | 23.9681 | 1.26148 | ||||||||
\(362\) | 20.4654 | 1.07564 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.9214 | −0.939338 | ||||||||
\(365\) | 0.811402 | 0.0424707 | ||||||||
\(366\) | 35.1229 | 1.83590 | ||||||||
\(367\) | 26.4503 | 1.38069 | 0.690346 | − | 0.723479i | \(-0.257458\pi\) | ||||
0.690346 | + | 0.723479i | \(0.257458\pi\) | |||||||
\(368\) | 2.50411 | 0.130536 | ||||||||
\(369\) | −7.11576 | −0.370432 | ||||||||
\(370\) | 21.4562 | 1.11545 | ||||||||
\(371\) | −5.33623 | −0.277043 | ||||||||
\(372\) | −24.2113 | −1.25530 | ||||||||
\(373\) | 21.7595 | 1.12666 | 0.563331 | − | 0.826231i | \(-0.309520\pi\) | ||||
0.563331 | + | 0.826231i | \(0.309520\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.45216 | −0.0749891 | ||||||||
\(376\) | 23.5529 | 1.21465 | ||||||||
\(377\) | −20.6259 | −1.06229 | ||||||||
\(378\) | 12.4971 | 0.642784 | ||||||||
\(379\) | 4.28972 | 0.220348 | 0.110174 | − | 0.993912i | \(-0.464859\pi\) | ||||
0.110174 | + | 0.993912i | \(0.464859\pi\) | |||||||
\(380\) | 18.9521 | 0.972221 | ||||||||
\(381\) | 14.7363 | 0.754962 | ||||||||
\(382\) | 37.1299 | 1.89973 | ||||||||
\(383\) | 17.8319 | 0.911165 | 0.455583 | − | 0.890193i | \(-0.349431\pi\) | ||||
0.455583 | + | 0.890193i | \(0.349431\pi\) | |||||||
\(384\) | −20.6249 | −1.05251 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.94298 | 0.149793 | ||||||||
\(387\) | −4.70427 | −0.239131 | ||||||||
\(388\) | −20.9719 | −1.06469 | ||||||||
\(389\) | 26.6694 | 1.35219 | 0.676097 | − | 0.736813i | \(-0.263670\pi\) | ||||
0.676097 | + | 0.736813i | \(0.263670\pi\) | |||||||
\(390\) | 19.9073 | 1.00804 | ||||||||
\(391\) | 11.8826 | 0.600927 | ||||||||
\(392\) | −1.97107 | −0.0995540 | ||||||||
\(393\) | −7.20587 | −0.363488 | ||||||||
\(394\) | −12.3723 | −0.623309 | ||||||||
\(395\) | −4.53199 | −0.228029 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.514512 | −0.0258226 | −0.0129113 | − | 0.999917i | \(-0.504110\pi\) | ||||
−0.0129113 | + | 0.999917i | \(0.504110\pi\) | |||||||
\(398\) | −17.8213 | −0.893303 | ||||||||
\(399\) | 9.51891 | 0.476542 | ||||||||
\(400\) | −1.42323 | −0.0711614 | ||||||||
\(401\) | 5.03437 | 0.251405 | 0.125702 | − | 0.992068i | \(-0.459882\pi\) | ||||
0.125702 | + | 0.992068i | \(0.459882\pi\) | |||||||
\(402\) | 23.3753 | 1.16585 | ||||||||
\(403\) | 35.7446 | 1.78056 | ||||||||
\(404\) | 52.5911 | 2.61651 | ||||||||
\(405\) | −5.53199 | −0.274887 | ||||||||
\(406\) | −7.35924 | −0.365233 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −19.3307 | −0.957012 | ||||||||
\(409\) | 25.4435 | 1.25810 | 0.629049 | − | 0.777365i | \(-0.283444\pi\) | ||||
0.629049 | + | 0.777365i | \(0.283444\pi\) | |||||||
\(410\) | −17.6579 | −0.872059 | ||||||||
\(411\) | −3.80137 | −0.187508 | ||||||||
\(412\) | 10.9617 | 0.540045 | ||||||||
\(413\) | 14.1637 | 0.696949 | ||||||||
\(414\) | −3.46801 | −0.170443 | ||||||||
\(415\) | −0.639032 | −0.0313689 | ||||||||
\(416\) | 43.9462 | 2.15464 | ||||||||
\(417\) | −8.62893 | −0.422560 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.24961 | −0.158754 | −0.0793768 | − | 0.996845i | \(-0.525293\pi\) | ||||
−0.0793768 | + | 0.996845i | \(0.525293\pi\) | |||||||
\(420\) | 4.19853 | 0.204867 | ||||||||
\(421\) | 36.8737 | 1.79711 | 0.898557 | − | 0.438857i | \(-0.144616\pi\) | ||||
0.898557 | + | 0.438857i | \(0.144616\pi\) | |||||||
\(422\) | 4.71849 | 0.229692 | ||||||||
\(423\) | 10.6496 | 0.517804 | ||||||||
\(424\) | −10.5181 | −0.510803 | ||||||||
\(425\) | −6.75354 | −0.327595 | ||||||||
\(426\) | 28.3274 | 1.37247 | ||||||||
\(427\) | −10.9362 | −0.529241 | ||||||||
\(428\) | −10.8029 | −0.522179 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.6737 | −0.562956 | ||||||||
\(431\) | −2.29459 | −0.110527 | −0.0552633 | − | 0.998472i | \(-0.517600\pi\) | ||||
−0.0552633 | + | 0.998472i | \(0.517600\pi\) | |||||||
\(432\) | −8.04222 | −0.386931 | ||||||||
\(433\) | 19.3213 | 0.928520 | 0.464260 | − | 0.885699i | \(-0.346320\pi\) | ||||
0.464260 | + | 0.885699i | \(0.346320\pi\) | |||||||
\(434\) | 12.7535 | 0.612190 | ||||||||
\(435\) | 4.83212 | 0.231683 | ||||||||
\(436\) | −27.4872 | −1.31640 | ||||||||
\(437\) | −11.5332 | −0.551710 | ||||||||
\(438\) | 2.60591 | 0.124515 | ||||||||
\(439\) | 21.4610 | 1.02428 | 0.512140 | − | 0.858902i | \(-0.328853\pi\) | ||||
0.512140 | + | 0.858902i | \(0.328853\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.891236 | −0.0424398 | ||||||||
\(442\) | 92.5827 | 4.40371 | ||||||||
\(443\) | 25.8000 | 1.22579 | 0.612896 | − | 0.790163i | \(-0.290004\pi\) | ||||
0.612896 | + | 0.790163i | \(0.290004\pi\) | |||||||
\(444\) | 40.7325 | 1.93308 | ||||||||
\(445\) | 10.1001 | 0.478790 | ||||||||
\(446\) | −34.3732 | −1.62762 | ||||||||
\(447\) | 0.997326 | 0.0471719 | ||||||||
\(448\) | 12.8334 | 0.606320 | ||||||||
\(449\) | 18.5408 | 0.874994 | 0.437497 | − | 0.899220i | \(-0.355865\pi\) | ||||
0.437497 | + | 0.899220i | \(0.355865\pi\) | |||||||
\(450\) | 1.97107 | 0.0929171 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −37.1421 | −1.74702 | ||||||||
\(453\) | 21.7462 | 1.02173 | ||||||||
\(454\) | 45.4691 | 2.13397 | ||||||||
\(455\) | −6.19853 | −0.290592 | ||||||||
\(456\) | 18.7624 | 0.878631 | ||||||||
\(457\) | 10.9155 | 0.510606 | 0.255303 | − | 0.966861i | \(-0.417825\pi\) | ||||
0.255303 | + | 0.966861i | \(0.417825\pi\) | |||||||
\(458\) | −58.2260 | −2.72072 | ||||||||
\(459\) | −38.1622 | −1.78126 | ||||||||
\(460\) | −5.08700 | −0.237183 | ||||||||
\(461\) | 20.2160 | 0.941554 | 0.470777 | − | 0.882252i | \(-0.343974\pi\) | ||||
0.470777 | + | 0.882252i | \(0.343974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.5425 | 1.51238 | 0.756189 | − | 0.654353i | \(-0.227059\pi\) | ||||
0.756189 | + | 0.654353i | \(0.227059\pi\) | |||||||
\(464\) | 4.73585 | 0.219856 | ||||||||
\(465\) | −8.37405 | −0.388337 | ||||||||
\(466\) | 0.178870 | 0.00828601 | ||||||||
\(467\) | 30.5276 | 1.41265 | 0.706325 | − | 0.707888i | \(-0.250352\pi\) | ||||
0.706325 | + | 0.707888i | \(0.250352\pi\) | |||||||
\(468\) | −15.9722 | −0.738316 | ||||||||
\(469\) | −7.27837 | −0.336084 | ||||||||
\(470\) | 26.4272 | 1.21900 | ||||||||
\(471\) | −1.08385 | −0.0499413 | ||||||||
\(472\) | 27.9176 | 1.28501 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −14.5550 | −0.668534 | ||||||||
\(475\) | 6.55501 | 0.300764 | ||||||||
\(476\) | 19.5261 | 0.894976 | ||||||||
\(477\) | −4.75584 | −0.217755 | ||||||||
\(478\) | 15.2118 | 0.695773 | ||||||||
\(479\) | −13.0560 | −0.596542 | −0.298271 | − | 0.954481i | \(-0.596410\pi\) | ||||
−0.298271 | + | 0.954481i | \(0.596410\pi\) | |||||||
\(480\) | −10.2955 | −0.469922 | ||||||||
\(481\) | −60.1356 | −2.74195 | ||||||||
\(482\) | −21.3626 | −0.973040 | ||||||||
\(483\) | −2.55501 | −0.116257 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.25363 | −0.329370 | ||||||||
\(486\) | 19.7248 | 0.894736 | ||||||||
\(487\) | 2.07534 | 0.0940427 | 0.0470213 | − | 0.998894i | \(-0.485027\pi\) | ||||
0.0470213 | + | 0.998894i | \(0.485027\pi\) | |||||||
\(488\) | −21.5561 | −0.975797 | ||||||||
\(489\) | 32.1576 | 1.45422 | ||||||||
\(490\) | −2.21161 | −0.0999105 | ||||||||
\(491\) | −24.4163 | −1.10189 | −0.550945 | − | 0.834541i | \(-0.685733\pi\) | ||||
−0.550945 | + | 0.834541i | \(0.685733\pi\) | |||||||
\(492\) | −33.5217 | −1.51128 | ||||||||
\(493\) | 22.4727 | 1.01212 | ||||||||
\(494\) | −89.8610 | −4.04304 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.20722 | −0.368515 | ||||||||
\(497\) | −8.82029 | −0.395644 | ||||||||
\(498\) | −2.05233 | −0.0919669 | ||||||||
\(499\) | 4.60906 | 0.206330 | 0.103165 | − | 0.994664i | \(-0.467103\pi\) | ||||
0.103165 | + | 0.994664i | \(0.467103\pi\) | |||||||
\(500\) | 2.89124 | 0.129300 | ||||||||
\(501\) | −23.8724 | −1.06654 | ||||||||
\(502\) | 20.6061 | 0.919696 | ||||||||
\(503\) | −30.2653 | −1.34946 | −0.674731 | − | 0.738064i | \(-0.735740\pi\) | ||||
−0.674731 | + | 0.738064i | \(0.735740\pi\) | |||||||
\(504\) | −1.75669 | −0.0782491 | ||||||||
\(505\) | 18.1898 | 0.809438 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −36.9165 | −1.63952 | ||||||||
\(508\) | −29.3398 | −1.30174 | ||||||||
\(509\) | −5.34741 | −0.237020 | −0.118510 | − | 0.992953i | \(-0.537812\pi\) | ||||
−0.118510 | + | 0.992953i | \(0.537812\pi\) | |||||||
\(510\) | −21.6898 | −0.960439 | ||||||||
\(511\) | −0.811402 | −0.0358943 | ||||||||
\(512\) | −15.7009 | −0.693889 | ||||||||
\(513\) | 37.0403 | 1.63537 | ||||||||
\(514\) | 13.5489 | 0.597616 | ||||||||
\(515\) | 3.79136 | 0.167067 | ||||||||
\(516\) | −22.1614 | −0.975601 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −21.4562 | −0.942730 | ||||||||
\(519\) | 10.5058 | 0.461155 | ||||||||
\(520\) | −12.2177 | −0.535783 | ||||||||
\(521\) | 15.8247 | 0.693292 | 0.346646 | − | 0.937996i | \(-0.387320\pi\) | ||||
0.346646 | + | 0.937996i | \(0.387320\pi\) | |||||||
\(522\) | −6.55882 | −0.287072 | ||||||||
\(523\) | −36.1406 | −1.58032 | −0.790159 | − | 0.612902i | \(-0.790002\pi\) | ||||
−0.790159 | + | 0.612902i | \(0.790002\pi\) | |||||||
\(524\) | 14.3468 | 0.626744 | ||||||||
\(525\) | 1.45216 | 0.0633774 | ||||||||
\(526\) | −17.6350 | −0.768925 | ||||||||
\(527\) | −38.9451 | −1.69648 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.9043 | −0.865405 | ||||||||
\(530\) | −11.8017 | −0.512632 | ||||||||
\(531\) | 12.6232 | 0.547799 | ||||||||
\(532\) | −18.9521 | −0.821677 | ||||||||
\(533\) | 49.4900 | 2.14365 | ||||||||
\(534\) | 32.4376 | 1.40371 | ||||||||
\(535\) | −3.73644 | −0.161540 | ||||||||
\(536\) | −14.3462 | −0.619660 | ||||||||
\(537\) | −2.62642 | −0.113339 | ||||||||
\(538\) | 59.0686 | 2.54663 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16.3375 | 0.703053 | ||||||||
\(541\) | 19.5594 | 0.840925 | 0.420462 | − | 0.907310i | \(-0.361868\pi\) | ||||
0.420462 | + | 0.907310i | \(0.361868\pi\) | |||||||
\(542\) | −39.3018 | −1.68816 | ||||||||
\(543\) | 13.4377 | 0.576668 | ||||||||
\(544\) | −47.8810 | −2.05288 | ||||||||
\(545\) | −9.50708 | −0.407239 | ||||||||
\(546\) | −19.9073 | −0.851953 | ||||||||
\(547\) | 24.1043 | 1.03063 | 0.515313 | − | 0.857002i | \(-0.327676\pi\) | ||||
0.515313 | + | 0.857002i | \(0.327676\pi\) | |||||||
\(548\) | 7.56850 | 0.323310 | ||||||||
\(549\) | −9.74675 | −0.415981 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.8121 | −0.929226 | ||||||||
\(552\) | −5.03610 | −0.214351 | ||||||||
\(553\) | 4.53199 | 0.192720 | ||||||||
\(554\) | 66.8936 | 2.84204 | ||||||||
\(555\) | 14.0883 | 0.598013 | ||||||||
\(556\) | 17.1801 | 0.728599 | ||||||||
\(557\) | 33.6176 | 1.42442 | 0.712211 | − | 0.701965i | \(-0.247694\pi\) | ||||
0.712211 | + | 0.701965i | \(0.247694\pi\) | |||||||
\(558\) | 11.3664 | 0.481179 | ||||||||
\(559\) | 32.7181 | 1.38383 | ||||||||
\(560\) | 1.42323 | 0.0601423 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −59.4758 | −2.50884 | ||||||||
\(563\) | −10.5711 | −0.445517 | −0.222759 | − | 0.974874i | \(-0.571506\pi\) | ||||
−0.222759 | + | 0.974874i | \(0.571506\pi\) | |||||||
\(564\) | 50.1695 | 2.11252 | ||||||||
\(565\) | −12.8465 | −0.540454 | ||||||||
\(566\) | −26.9364 | −1.13222 | ||||||||
\(567\) | 5.53199 | 0.232322 | ||||||||
\(568\) | −17.3854 | −0.729475 | ||||||||
\(569\) | 31.6316 | 1.32607 | 0.663033 | − | 0.748590i | \(-0.269269\pi\) | ||||
0.663033 | + | 0.748590i | \(0.269269\pi\) | |||||||
\(570\) | 21.0522 | 0.881778 | ||||||||
\(571\) | −13.9160 | −0.582365 | −0.291183 | − | 0.956667i | \(-0.594049\pi\) | ||||
−0.291183 | + | 0.956667i | \(0.594049\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.3797 | 1.01848 | ||||||||
\(574\) | 17.6579 | 0.737025 | ||||||||
\(575\) | −1.75946 | −0.0733744 | ||||||||
\(576\) | 11.4376 | 0.476565 | ||||||||
\(577\) | 45.7055 | 1.90275 | 0.951373 | − | 0.308042i | \(-0.0996736\pi\) | ||||
0.951373 | + | 0.308042i | \(0.0996736\pi\) | |||||||
\(578\) | −63.2750 | −2.63189 | ||||||||
\(579\) | 1.93237 | 0.0803068 | ||||||||
\(580\) | −9.62072 | −0.399478 | ||||||||
\(581\) | 0.639032 | 0.0265115 | ||||||||
\(582\) | −23.2958 | −0.965644 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.59933 | −0.0661807 | ||||||||
\(585\) | −5.52435 | −0.228404 | ||||||||
\(586\) | −15.5330 | −0.641664 | ||||||||
\(587\) | 12.8553 | 0.530597 | 0.265298 | − | 0.964166i | \(-0.414530\pi\) | ||||
0.265298 | + | 0.964166i | \(0.414530\pi\) | |||||||
\(588\) | −4.19853 | −0.173145 | ||||||||
\(589\) | 37.8003 | 1.55753 | ||||||||
\(590\) | 31.3246 | 1.28961 | ||||||||
\(591\) | −8.12374 | −0.334166 | ||||||||
\(592\) | 13.8076 | 0.567488 | ||||||||
\(593\) | 15.4564 | 0.634718 | 0.317359 | − | 0.948306i | \(-0.397204\pi\) | ||||
0.317359 | + | 0.948306i | \(0.397204\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.75354 | 0.276868 | ||||||||
\(596\) | −1.98567 | −0.0813361 | ||||||||
\(597\) | −11.7016 | −0.478914 | ||||||||
\(598\) | 24.1200 | 0.986338 | ||||||||
\(599\) | −34.2496 | −1.39940 | −0.699701 | − | 0.714436i | \(-0.746684\pi\) | ||||
−0.699701 | + | 0.714436i | \(0.746684\pi\) | |||||||
\(600\) | 2.86230 | 0.116853 | ||||||||
\(601\) | −25.5119 | −1.04065 | −0.520325 | − | 0.853968i | \(-0.674189\pi\) | ||||
−0.520325 | + | 0.853968i | \(0.674189\pi\) | |||||||
\(602\) | 11.6737 | 0.475785 | ||||||||
\(603\) | −6.48674 | −0.264160 | ||||||||
\(604\) | −43.2965 | −1.76171 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 58.4188 | 2.37310 | ||||||||
\(607\) | 1.52063 | 0.0617206 | 0.0308603 | − | 0.999524i | \(-0.490175\pi\) | ||||
0.0308603 | + | 0.999524i | \(0.490175\pi\) | |||||||
\(608\) | 46.4735 | 1.88475 | ||||||||
\(609\) | −4.83212 | −0.195807 | ||||||||
\(610\) | −24.1867 | −0.979291 | ||||||||
\(611\) | −74.0682 | −2.99648 | ||||||||
\(612\) | 17.4023 | 0.703448 | ||||||||
\(613\) | 41.1735 | 1.66298 | 0.831492 | − | 0.555537i | \(-0.187487\pi\) | ||||
0.831492 | + | 0.555537i | \(0.187487\pi\) | |||||||
\(614\) | 8.89421 | 0.358941 | ||||||||
\(615\) | −11.5943 | −0.467525 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.9037 | 1.72724 | 0.863618 | − | 0.504146i | \(-0.168193\pi\) | ||||
0.863618 | + | 0.504146i | \(0.168193\pi\) | |||||||
\(618\) | 12.1764 | 0.489806 | ||||||||
\(619\) | −41.9939 | −1.68788 | −0.843939 | − | 0.536439i | \(-0.819769\pi\) | ||||
−0.843939 | + | 0.536439i | \(0.819769\pi\) | |||||||
\(620\) | 16.6727 | 0.669590 | ||||||||
\(621\) | −9.94214 | −0.398964 | ||||||||
\(622\) | −9.16071 | −0.367311 | ||||||||
\(623\) | −10.1001 | −0.404651 | ||||||||
\(624\) | 12.8108 | 0.512844 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.19958 | −0.207817 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.15794 | 0.0861113 | ||||||||
\(629\) | 65.5201 | 2.61246 | ||||||||
\(630\) | −1.97107 | −0.0785293 | ||||||||
\(631\) | 0.0696914 | 0.00277437 | 0.00138719 | − | 0.999999i | \(-0.499558\pi\) | ||||
0.00138719 | + | 0.999999i | \(0.499558\pi\) | |||||||
\(632\) | 8.93287 | 0.355330 | ||||||||
\(633\) | 3.09819 | 0.123142 | ||||||||
\(634\) | 0.0439434 | 0.00174522 | ||||||||
\(635\) | −10.1478 | −0.402705 | ||||||||
\(636\) | −22.4043 | −0.888389 | ||||||||
\(637\) | 6.19853 | 0.245595 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.86096 | −0.310975 | ||||||||
\(640\) | 14.2029 | 0.561420 | ||||||||
\(641\) | −9.52913 | −0.376378 | −0.188189 | − | 0.982133i | \(-0.560262\pi\) | ||||
−0.188189 | + | 0.982133i | \(0.560262\pi\) | |||||||
\(642\) | −12.0000 | −0.473602 | ||||||||
\(643\) | −33.6596 | −1.32740 | −0.663702 | − | 0.747997i | \(-0.731016\pi\) | ||||
−0.663702 | + | 0.747997i | \(0.731016\pi\) | |||||||
\(644\) | 5.08700 | 0.200456 | ||||||||
\(645\) | −7.66502 | −0.301810 | ||||||||
\(646\) | 97.9071 | 3.85210 | ||||||||
\(647\) | 45.7694 | 1.79938 | 0.899691 | − | 0.436528i | \(-0.143792\pi\) | ||||
0.899691 | + | 0.436528i | \(0.143792\pi\) | |||||||
\(648\) | 10.9039 | 0.428347 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −13.7088 | −0.537702 | ||||||||
\(651\) | 8.37405 | 0.328205 | ||||||||
\(652\) | −64.0255 | −2.50743 | ||||||||
\(653\) | 10.7743 | 0.421629 | 0.210815 | − | 0.977526i | \(-0.432388\pi\) | ||||
0.210815 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(654\) | −30.5331 | −1.19394 | ||||||||
\(655\) | 4.96218 | 0.193888 | ||||||||
\(656\) | −11.3633 | −0.443661 | ||||||||
\(657\) | −0.723151 | −0.0282128 | ||||||||
\(658\) | −26.4272 | −1.03024 | ||||||||
\(659\) | 16.8298 | 0.655594 | 0.327797 | − | 0.944748i | \(-0.393694\pi\) | ||||
0.327797 | + | 0.944748i | \(0.393694\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.3814 | −1.18170 | −0.590850 | − | 0.806781i | \(-0.701208\pi\) | ||||
−0.590850 | + | 0.806781i | \(0.701208\pi\) | |||||||
\(662\) | −20.1601 | −0.783544 | ||||||||
\(663\) | 60.7903 | 2.36090 | ||||||||
\(664\) | 1.25958 | 0.0488811 | ||||||||
\(665\) | −6.55501 | −0.254192 | ||||||||
\(666\) | −19.1225 | −0.740982 | ||||||||
\(667\) | 5.85467 | 0.226694 | ||||||||
\(668\) | 47.5298 | 1.83898 | ||||||||
\(669\) | −22.5696 | −0.872593 | ||||||||
\(670\) | −16.0969 | −0.621879 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 10.2955 | 0.397156 | ||||||||
\(673\) | 17.0093 | 0.655659 | 0.327830 | − | 0.944737i | \(-0.393683\pi\) | ||||
0.327830 | + | 0.944737i | \(0.393683\pi\) | |||||||
\(674\) | −1.41015 | −0.0543168 | ||||||||
\(675\) | 5.65069 | 0.217495 | ||||||||
\(676\) | 73.5004 | 2.82694 | ||||||||
\(677\) | −11.5295 | −0.443116 | −0.221558 | − | 0.975147i | \(-0.571114\pi\) | ||||
−0.221558 | + | 0.975147i | \(0.571114\pi\) | |||||||
\(678\) | −41.2579 | −1.58450 | ||||||||
\(679\) | 7.25363 | 0.278369 | ||||||||
\(680\) | 13.3117 | 0.510480 | ||||||||
\(681\) | 29.8553 | 1.14406 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.61429 | −0.176561 | −0.0882805 | − | 0.996096i | \(-0.528137\pi\) | ||||
−0.0882805 | + | 0.996096i | \(0.528137\pi\) | |||||||
\(684\) | −16.8908 | −0.645834 | ||||||||
\(685\) | 2.61774 | 0.100019 | ||||||||
\(686\) | 2.21161 | 0.0844398 | ||||||||
\(687\) | −38.2315 | −1.45862 | ||||||||
\(688\) | −7.51232 | −0.286404 | ||||||||
\(689\) | 33.0768 | 1.26012 | ||||||||
\(690\) | −5.65069 | −0.215118 | ||||||||
\(691\) | −16.3453 | −0.621804 | −0.310902 | − | 0.950442i | \(-0.600631\pi\) | ||||
−0.310902 | + | 0.950442i | \(0.600631\pi\) | |||||||
\(692\) | −20.9170 | −0.795146 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0007 | −0.455539 | ||||||||
\(695\) | 5.94214 | 0.225398 | ||||||||
\(696\) | −9.52445 | −0.361023 | ||||||||
\(697\) | −53.9213 | −2.04241 | ||||||||
\(698\) | −44.4186 | −1.68127 | ||||||||
\(699\) | 0.117447 | 0.00444227 | ||||||||
\(700\) | −2.89124 | −0.109278 | ||||||||
\(701\) | 21.3419 | 0.806072 | 0.403036 | − | 0.915184i | \(-0.367955\pi\) | ||||
0.403036 | + | 0.915184i | \(0.367955\pi\) | |||||||
\(702\) | −77.4640 | −2.92369 | ||||||||
\(703\) | −63.5940 | −2.39849 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.3523 | 0.653525 | ||||||||
\(706\) | −33.2000 | −1.24950 | ||||||||
\(707\) | −18.1898 | −0.684100 | ||||||||
\(708\) | 59.4667 | 2.23490 | ||||||||
\(709\) | 17.1857 | 0.645421 | 0.322710 | − | 0.946498i | \(-0.395406\pi\) | ||||
0.322710 | + | 0.946498i | \(0.395406\pi\) | |||||||
\(710\) | −19.5071 | −0.732088 | ||||||||
\(711\) | 4.03907 | 0.151477 | ||||||||
\(712\) | −19.9080 | −0.746082 | ||||||||
\(713\) | −10.1461 | −0.379975 | ||||||||
\(714\) | 21.6898 | 0.811719 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.22919 | 0.195424 | ||||||||
\(717\) | 9.98817 | 0.373015 | ||||||||
\(718\) | 12.3622 | 0.461354 | ||||||||
\(719\) | −19.5770 | −0.730098 | −0.365049 | − | 0.930988i | \(-0.618948\pi\) | ||||
−0.365049 | + | 0.930988i | \(0.618948\pi\) | |||||||
\(720\) | 1.26843 | 0.0472716 | ||||||||
\(721\) | −3.79136 | −0.141198 | ||||||||
\(722\) | −53.0082 | −1.97276 | ||||||||
\(723\) | −14.0268 | −0.521663 | ||||||||
\(724\) | −26.7544 | −0.994320 | ||||||||
\(725\) | −3.32754 | −0.123582 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.7261 | −0.768687 | −0.384344 | − | 0.923190i | \(-0.625572\pi\) | ||||
−0.384344 | + | 0.923190i | \(0.625572\pi\) | |||||||
\(728\) | 12.2177 | 0.452819 | ||||||||
\(729\) | 29.5474 | 1.09435 | ||||||||
\(730\) | −1.79451 | −0.0664177 | ||||||||
\(731\) | −35.6477 | −1.31848 | ||||||||
\(732\) | −45.9161 | −1.69711 | ||||||||
\(733\) | −10.2931 | −0.380183 | −0.190092 | − | 0.981766i | \(-0.560879\pi\) | ||||
−0.190092 | + | 0.981766i | \(0.560879\pi\) | |||||||
\(734\) | −58.4978 | −2.15919 | ||||||||
\(735\) | −1.45216 | −0.0535637 | ||||||||
\(736\) | −12.4741 | −0.459803 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 15.7373 | 0.579298 | ||||||||
\(739\) | −14.2200 | −0.523092 | −0.261546 | − | 0.965191i | \(-0.584232\pi\) | ||||
−0.261546 | + | 0.965191i | \(0.584232\pi\) | |||||||
\(740\) | −28.0496 | −1.03112 | ||||||||
\(741\) | −59.0033 | −2.16754 | ||||||||
\(742\) | 11.8017 | 0.433253 | ||||||||
\(743\) | 1.42306 | 0.0522069 | 0.0261034 | − | 0.999659i | \(-0.491690\pi\) | ||||
0.0261034 | + | 0.999659i | \(0.491690\pi\) | |||||||
\(744\) | 16.5058 | 0.605133 | ||||||||
\(745\) | −0.686788 | −0.0251620 | ||||||||
\(746\) | −48.1235 | −1.76193 | ||||||||
\(747\) | 0.569528 | 0.0208380 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.73644 | 0.136527 | ||||||||
\(750\) | 3.21161 | 0.117272 | ||||||||
\(751\) | −17.8201 | −0.650265 | −0.325133 | − | 0.945668i | \(-0.605409\pi\) | ||||
−0.325133 | + | 0.945668i | \(0.605409\pi\) | |||||||
\(752\) | 17.0066 | 0.620166 | ||||||||
\(753\) | 13.5301 | 0.493064 | ||||||||
\(754\) | 45.6165 | 1.66126 | ||||||||
\(755\) | −14.9751 | −0.544999 | ||||||||
\(756\) | −16.3375 | −0.594188 | ||||||||
\(757\) | −22.5791 | −0.820652 | −0.410326 | − | 0.911939i | \(-0.634585\pi\) | ||||
−0.410326 | + | 0.911939i | \(0.634585\pi\) | |||||||
\(758\) | −9.48721 | −0.344591 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.9204 | −0.468671 | ||||||||
\(761\) | −13.6408 | −0.494478 | −0.247239 | − | 0.968954i | \(-0.579523\pi\) | ||||
−0.247239 | + | 0.968954i | \(0.579523\pi\) | |||||||
\(762\) | −32.5909 | −1.18064 | ||||||||
\(763\) | 9.50708 | 0.344179 | ||||||||
\(764\) | −48.5398 | −1.75611 | ||||||||
\(765\) | 6.01900 | 0.217617 | ||||||||
\(766\) | −39.4372 | −1.42492 | ||||||||
\(767\) | −87.7941 | −3.17006 | ||||||||
\(768\) | 8.34214 | 0.301021 | ||||||||
\(769\) | −20.8163 | −0.750654 | −0.375327 | − | 0.926892i | \(-0.622470\pi\) | ||||
−0.375327 | + | 0.926892i | \(0.622470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.89628 | 0.320392 | ||||||||
\(772\) | −3.84734 | −0.138469 | ||||||||
\(773\) | 9.30561 | 0.334699 | 0.167350 | − | 0.985898i | \(-0.446479\pi\) | ||||
0.167350 | + | 0.985898i | \(0.446479\pi\) | |||||||
\(774\) | 10.4040 | 0.373965 | ||||||||
\(775\) | 5.76662 | 0.207143 | ||||||||
\(776\) | 14.2974 | 0.513247 | ||||||||
\(777\) | −14.0883 | −0.505413 | ||||||||
\(778\) | −58.9825 | −2.11462 | ||||||||
\(779\) | 52.3362 | 1.87514 | ||||||||
\(780\) | −26.0247 | −0.931835 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −26.2796 | −0.939757 | ||||||||
\(783\) | −18.8029 | −0.671962 | ||||||||
\(784\) | −1.42323 | −0.0508296 | ||||||||
\(785\) | 0.746374 | 0.0266392 | ||||||||
\(786\) | 15.9366 | 0.568440 | ||||||||
\(787\) | 15.0205 | 0.535421 | 0.267711 | − | 0.963499i | \(-0.413733\pi\) | ||||
0.267711 | + | 0.963499i | \(0.413733\pi\) | |||||||
\(788\) | 16.1743 | 0.576186 | ||||||||
\(789\) | −11.5793 | −0.412233 | ||||||||
\(790\) | 10.0230 | 0.356603 | ||||||||
\(791\) | 12.8465 | 0.456767 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 67.7885 | 2.40724 | ||||||||
\(794\) | 1.13790 | 0.0403826 | ||||||||
\(795\) | −7.74905 | −0.274830 | ||||||||
\(796\) | 23.2978 | 0.825768 | ||||||||
\(797\) | −40.8706 | −1.44771 | −0.723855 | − | 0.689953i | \(-0.757631\pi\) | ||||
−0.723855 | + | 0.689953i | \(0.757631\pi\) | |||||||
\(798\) | −21.0522 | −0.745238 | ||||||||
\(799\) | 80.7001 | 2.85496 | ||||||||
\(800\) | 7.08977 | 0.250661 | ||||||||
\(801\) | −9.00155 | −0.318054 | ||||||||
\(802\) | −11.1341 | −0.393158 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −30.5585 | −1.07771 | ||||||||
\(805\) | 1.75946 | 0.0620127 | ||||||||
\(806\) | −79.0532 | −2.78453 | ||||||||
\(807\) | 38.7848 | 1.36529 | ||||||||
\(808\) | −35.8535 | −1.26132 | ||||||||
\(809\) | 16.2670 | 0.571918 | 0.285959 | − | 0.958242i | \(-0.407688\pi\) | ||||
0.285959 | + | 0.958242i | \(0.407688\pi\) | |||||||
\(810\) | 12.2346 | 0.429881 | ||||||||
\(811\) | 25.1784 | 0.884133 | 0.442067 | − | 0.896982i | \(-0.354245\pi\) | ||||
0.442067 | + | 0.896982i | \(0.354245\pi\) | |||||||
\(812\) | 9.62072 | 0.337621 | ||||||||
\(813\) | −25.8058 | −0.905049 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.1447 | −0.775695 | ||||||||
\(816\) | −13.9579 | −0.488624 | ||||||||
\(817\) | 34.5997 | 1.21049 | ||||||||
\(818\) | −56.2711 | −1.96747 | ||||||||
\(819\) | 5.52435 | 0.193037 | ||||||||
\(820\) | 23.0841 | 0.806130 | ||||||||
\(821\) | −24.5153 | −0.855590 | −0.427795 | − | 0.903876i | \(-0.640709\pi\) | ||||
−0.427795 | + | 0.903876i | \(0.640709\pi\) | |||||||
\(822\) | 8.40717 | 0.293234 | ||||||||
\(823\) | −9.15460 | −0.319109 | −0.159555 | − | 0.987189i | \(-0.551006\pi\) | ||||
−0.159555 | + | 0.987189i | \(0.551006\pi\) | |||||||
\(824\) | −7.47304 | −0.260336 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −31.3246 | −1.08992 | ||||||||
\(827\) | −24.3588 | −0.847037 | −0.423519 | − | 0.905887i | \(-0.639205\pi\) | ||||
−0.423519 | + | 0.905887i | \(0.639205\pi\) | |||||||
\(828\) | 4.53372 | 0.157558 | ||||||||
\(829\) | −15.1100 | −0.524793 | −0.262396 | − | 0.964960i | \(-0.584513\pi\) | ||||
−0.262396 | + | 0.964960i | \(0.584513\pi\) | |||||||
\(830\) | 1.41329 | 0.0490561 | ||||||||
\(831\) | 43.9227 | 1.52366 | ||||||||
\(832\) | −79.5481 | −2.75783 | ||||||||
\(833\) | −6.75354 | −0.233996 | ||||||||
\(834\) | 19.0839 | 0.660820 | ||||||||
\(835\) | 16.4393 | 0.568905 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.5854 | 1.12632 | ||||||||
\(838\) | 7.18687 | 0.248266 | ||||||||
\(839\) | 0.170947 | 0.00590175 | 0.00295087 | − | 0.999996i | \(-0.499061\pi\) | ||||
0.00295087 | + | 0.999996i | \(0.499061\pi\) | |||||||
\(840\) | −2.86230 | −0.0987589 | ||||||||
\(841\) | −17.9274 | −0.618188 | ||||||||
\(842\) | −81.5504 | −2.81041 | ||||||||
\(843\) | −39.0522 | −1.34503 | ||||||||
\(844\) | −6.16846 | −0.212327 | ||||||||
\(845\) | 25.4218 | 0.874537 | ||||||||
\(846\) | −23.5529 | −0.809766 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.59467 | −0.260802 | ||||||||
\(849\) | −17.6866 | −0.607003 | ||||||||
\(850\) | 14.9362 | 0.512308 | ||||||||
\(851\) | 17.0695 | 0.585136 | ||||||||
\(852\) | −37.0323 | −1.26871 | ||||||||
\(853\) | 39.4944 | 1.35226 | 0.676131 | − | 0.736782i | \(-0.263655\pi\) | ||||
0.676131 | + | 0.736782i | \(0.263655\pi\) | |||||||
\(854\) | 24.1867 | 0.827652 | ||||||||
\(855\) | −5.84206 | −0.199794 | ||||||||
\(856\) | 7.36478 | 0.251723 | ||||||||
\(857\) | 32.2687 | 1.10228 | 0.551138 | − | 0.834414i | \(-0.314194\pi\) | ||||
0.551138 | + | 0.834414i | \(0.314194\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.6791 | 0.603205 | 0.301602 | − | 0.953434i | \(-0.402478\pi\) | ||||
0.301602 | + | 0.953434i | \(0.402478\pi\) | |||||||
\(860\) | 15.2610 | 0.520396 | ||||||||
\(861\) | 11.5943 | 0.395131 | ||||||||
\(862\) | 5.07476 | 0.172847 | ||||||||
\(863\) | −27.6057 | −0.939710 | −0.469855 | − | 0.882744i | \(-0.655694\pi\) | ||||
−0.469855 | + | 0.882744i | \(0.655694\pi\) | |||||||
\(864\) | 40.0621 | 1.36294 | ||||||||
\(865\) | −7.23463 | −0.245985 | ||||||||
\(866\) | −42.7311 | −1.45206 | ||||||||
\(867\) | −41.5467 | −1.41100 | ||||||||
\(868\) | −16.6727 | −0.565907 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −10.6868 | −0.362316 | ||||||||
\(871\) | 45.1152 | 1.52867 | ||||||||
\(872\) | 18.7391 | 0.634586 | ||||||||
\(873\) | 6.46469 | 0.218797 | ||||||||
\(874\) | 25.5071 | 0.862790 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −3.40670 | −0.115102 | ||||||||
\(877\) | −3.64582 | −0.123111 | −0.0615553 | − | 0.998104i | \(-0.519606\pi\) | ||||
−0.0615553 | + | 0.998104i | \(0.519606\pi\) | |||||||
\(878\) | −47.4636 | −1.60182 | ||||||||
\(879\) | −10.1991 | −0.344006 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.0883 | −0.811554 | −0.405777 | − | 0.913972i | \(-0.632999\pi\) | ||||
−0.405777 | + | 0.913972i | \(0.632999\pi\) | |||||||
\(882\) | 1.97107 | 0.0663693 | ||||||||
\(883\) | 8.40021 | 0.282690 | 0.141345 | − | 0.989960i | \(-0.454857\pi\) | ||||
0.141345 | + | 0.989960i | \(0.454857\pi\) | |||||||
\(884\) | −121.033 | −4.07078 | ||||||||
\(885\) | 20.5679 | 0.691383 | ||||||||
\(886\) | −57.0595 | −1.91695 | ||||||||
\(887\) | 48.8895 | 1.64155 | 0.820774 | − | 0.571254i | \(-0.193543\pi\) | ||||
0.820774 | + | 0.571254i | \(0.193543\pi\) | |||||||
\(888\) | −27.7689 | −0.931864 | ||||||||
\(889\) | 10.1478 | 0.340348 | ||||||||
\(890\) | −22.3375 | −0.748754 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 44.9360 | 1.50457 | ||||||||
\(893\) | −78.3278 | −2.62114 | ||||||||
\(894\) | −2.20570 | −0.0737696 | ||||||||
\(895\) | 1.80863 | 0.0604560 | ||||||||
\(896\) | −14.2029 | −0.474487 | ||||||||
\(897\) | 15.8373 | 0.528792 | ||||||||
\(898\) | −41.0051 | −1.36836 | ||||||||
\(899\) | −19.1887 | −0.639979 | ||||||||
\(900\) | −2.57677 | −0.0858924 | ||||||||
\(901\) | −36.0384 | −1.20061 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.66502 | 0.255076 | ||||||||
\(904\) | 25.3213 | 0.842172 | ||||||||
\(905\) | −9.25363 | −0.307601 | ||||||||
\(906\) | −48.0942 | −1.59782 | ||||||||
\(907\) | 9.06429 | 0.300975 | 0.150487 | − | 0.988612i | \(-0.451916\pi\) | ||||
0.150487 | + | 0.988612i | \(0.451916\pi\) | |||||||
\(908\) | −59.4416 | −1.97264 | ||||||||
\(909\) | −16.2114 | −0.537700 | ||||||||
\(910\) | 13.7088 | 0.454441 | ||||||||
\(911\) | 38.1305 | 1.26332 | 0.631659 | − | 0.775246i | \(-0.282374\pi\) | ||||
0.631659 | + | 0.775246i | \(0.282374\pi\) | |||||||
\(912\) | 13.5476 | 0.448605 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −24.1409 | −0.798509 | ||||||||
\(915\) | −15.8811 | −0.525014 | ||||||||
\(916\) | 76.1186 | 2.51503 | ||||||||
\(917\) | −4.96218 | −0.163866 | ||||||||
\(918\) | 84.4000 | 2.78561 | ||||||||
\(919\) | −28.5711 | −0.942472 | −0.471236 | − | 0.882007i | \(-0.656192\pi\) | ||||
−0.471236 | + | 0.882007i | \(0.656192\pi\) | |||||||
\(920\) | 3.46801 | 0.114337 | ||||||||
\(921\) | 5.83999 | 0.192434 | ||||||||
\(922\) | −44.7100 | −1.47245 | ||||||||
\(923\) | 54.6729 | 1.79958 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.70159 | −0.318986 | ||||||||
\(926\) | −71.9715 | −2.36513 | ||||||||
\(927\) | −3.37900 | −0.110981 | ||||||||
\(928\) | −23.5915 | −0.774430 | ||||||||
\(929\) | −7.79299 | −0.255680 | −0.127840 | − | 0.991795i | \(-0.540804\pi\) | ||||
−0.127840 | + | 0.991795i | \(0.540804\pi\) | |||||||
\(930\) | 18.5202 | 0.607300 | ||||||||
\(931\) | 6.55501 | 0.214832 | ||||||||
\(932\) | −0.233837 | −0.00765958 | ||||||||
\(933\) | −6.01498 | −0.196921 | ||||||||
\(934\) | −67.5153 | −2.20917 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.8889 | 0.355914 | ||||||||
\(937\) | 0.427891 | 0.0139786 | 0.00698929 | − | 0.999976i | \(-0.497775\pi\) | ||||
0.00698929 | + | 0.999976i | \(0.497775\pi\) | |||||||
\(938\) | 16.0969 | 0.525584 | ||||||||
\(939\) | −3.41407 | −0.111414 | ||||||||
\(940\) | −34.5483 | −1.12684 | ||||||||
\(941\) | 50.7330 | 1.65385 | 0.826925 | − | 0.562313i | \(-0.190088\pi\) | ||||
0.826925 | + | 0.562313i | \(0.190088\pi\) | |||||||
\(942\) | 2.39706 | 0.0781006 | ||||||||
\(943\) | −14.0478 | −0.457458 | ||||||||
\(944\) | 20.1582 | 0.656092 | ||||||||
\(945\) | −5.65069 | −0.183817 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.7388 | −0.771408 | −0.385704 | − | 0.922623i | \(-0.626041\pi\) | ||||
−0.385704 | + | 0.922623i | \(0.626041\pi\) | |||||||
\(948\) | 19.0277 | 0.617991 | ||||||||
\(949\) | 5.02950 | 0.163265 | ||||||||
\(950\) | −14.4971 | −0.470350 | ||||||||
\(951\) | 0.0288535 | 0.000935639 0 | ||||||||
\(952\) | −13.3117 | −0.431435 | ||||||||
\(953\) | 4.55359 | 0.147505 | 0.0737525 | − | 0.997277i | \(-0.476503\pi\) | ||||
0.0737525 | + | 0.997277i | \(0.476503\pi\) | |||||||
\(954\) | 10.5181 | 0.340535 | ||||||||
\(955\) | −16.7886 | −0.543266 | ||||||||
\(956\) | −19.8864 | −0.643171 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.8748 | 0.932901 | ||||||||
\(959\) | −2.61774 | −0.0845312 | ||||||||
\(960\) | 18.6361 | 0.601477 | ||||||||
\(961\) | 2.25393 | 0.0727073 | ||||||||
\(962\) | 132.997 | 4.28799 | ||||||||
\(963\) | 3.33005 | 0.107309 | ||||||||
\(964\) | 27.9273 | 0.899476 | ||||||||
\(965\) | −1.33069 | −0.0428365 | ||||||||
\(966\) | 5.65069 | 0.181808 | ||||||||
\(967\) | 38.9252 | 1.25175 | 0.625876 | − | 0.779923i | \(-0.284742\pi\) | ||||
0.625876 | + | 0.779923i | \(0.284742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 64.2863 | 2.06518 | ||||||||
\(970\) | 16.0422 | 0.515085 | ||||||||
\(971\) | 6.67820 | 0.214314 | 0.107157 | − | 0.994242i | \(-0.465825\pi\) | ||||
0.107157 | + | 0.994242i | \(0.465825\pi\) | |||||||
\(972\) | −25.7862 | −0.827092 | ||||||||
\(973\) | −5.94214 | −0.190496 | ||||||||
\(974\) | −4.58985 | −0.147068 | ||||||||
\(975\) | −9.00125 | −0.288271 | ||||||||
\(976\) | −15.5647 | −0.498215 | ||||||||
\(977\) | 34.5917 | 1.10669 | 0.553343 | − | 0.832953i | \(-0.313352\pi\) | ||||
0.553343 | + | 0.832953i | \(0.313352\pi\) | |||||||
\(978\) | −71.1202 | −2.27417 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.89124 | 0.0923571 | ||||||||
\(981\) | 8.47305 | 0.270524 | ||||||||
\(982\) | 53.9994 | 1.72319 | ||||||||
\(983\) | −6.03257 | −0.192409 | −0.0962046 | − | 0.995362i | \(-0.530670\pi\) | ||||
−0.0962046 | + | 0.995362i | \(0.530670\pi\) | |||||||
\(984\) | 22.8531 | 0.728529 | ||||||||
\(985\) | 5.59425 | 0.178248 | ||||||||
\(986\) | −49.7010 | −1.58280 | ||||||||
\(987\) | −17.3523 | −0.552329 | ||||||||
\(988\) | 117.475 | 3.73738 | ||||||||
\(989\) | −9.28705 | −0.295311 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.1912 | 0.419032 | 0.209516 | − | 0.977805i | \(-0.432811\pi\) | ||||
0.209516 | + | 0.977805i | \(0.432811\pi\) | |||||||
\(992\) | 40.8840 | 1.29807 | ||||||||
\(993\) | −13.2372 | −0.420071 | ||||||||
\(994\) | 19.5071 | 0.618727 | ||||||||
\(995\) | 8.05807 | 0.255458 | ||||||||
\(996\) | 2.68300 | 0.0850141 | ||||||||
\(997\) | 2.69777 | 0.0854392 | 0.0427196 | − | 0.999087i | \(-0.486398\pi\) | ||||
0.0427196 | + | 0.999087i | \(0.486398\pi\) | |||||||
\(998\) | −10.1935 | −0.322668 | ||||||||
\(999\) | −54.8207 | −1.73445 |
(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 | 4235.2.a.v.1.1 | yes | 4 | |
11.10 | odd | 2 | 4235.2.a.u.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.u.1.4 | ✓ | 4 | 11.10 | odd | 2 | ||
4235.2.a.v.1.1 | yes | 4 | 1.1 | even | 1 | trivial |