Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(0\) |
Dimension: | \(156\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53163 | −1.79013 | −0.895067 | − | 0.445933i | \(-0.852872\pi\) | ||||
−0.895067 | + | 0.445933i | \(0.852872\pi\) | |||||||
\(3\) | −1.76740 | −1.02041 | −0.510205 | − | 0.860053i | \(-0.670431\pi\) | ||||
−0.510205 | + | 0.860053i | \(0.670431\pi\) | |||||||
\(4\) | 4.40915 | 2.20458 | ||||||||
\(5\) | 3.70059 | 1.65495 | 0.827476 | − | 0.561501i | \(-0.189776\pi\) | ||||
0.827476 | + | 0.561501i | \(0.189776\pi\) | |||||||
\(6\) | 4.47441 | 1.82667 | ||||||||
\(7\) | 1.97275 | 0.745629 | 0.372815 | − | 0.927906i | \(-0.378393\pi\) | ||||
0.372815 | + | 0.927906i | \(0.378393\pi\) | |||||||
\(8\) | −6.09908 | −2.15635 | ||||||||
\(9\) | 0.123713 | 0.0412378 | ||||||||
\(10\) | −9.36852 | −2.96258 | ||||||||
\(11\) | 0.845819 | 0.255024 | 0.127512 | − | 0.991837i | \(-0.459301\pi\) | ||||
0.127512 | + | 0.991837i | \(0.459301\pi\) | |||||||
\(12\) | −7.79275 | −2.24957 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −4.99427 | −1.33478 | ||||||||
\(15\) | −6.54043 | −1.68873 | ||||||||
\(16\) | 6.62232 | 1.65558 | ||||||||
\(17\) | −1.87515 | −0.454791 | −0.227396 | − | 0.973802i | \(-0.573021\pi\) | ||||
−0.227396 | + | 0.973802i | \(0.573021\pi\) | |||||||
\(18\) | −0.313196 | −0.0738211 | ||||||||
\(19\) | 0.327217 | 0.0750688 | 0.0375344 | − | 0.999295i | \(-0.488050\pi\) | ||||
0.0375344 | + | 0.999295i | \(0.488050\pi\) | |||||||
\(20\) | 16.3164 | 3.64847 | ||||||||
\(21\) | −3.48664 | −0.760848 | ||||||||
\(22\) | −2.14130 | −0.456527 | ||||||||
\(23\) | 4.68118 | 0.976093 | 0.488047 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488047 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(24\) | 10.7795 | 2.20036 | ||||||||
\(25\) | 8.69433 | 1.73887 | ||||||||
\(26\) | 2.53163 | 0.496494 | ||||||||
\(27\) | 5.08356 | 0.978331 | ||||||||
\(28\) | 8.69816 | 1.64380 | ||||||||
\(29\) | 5.72085 | 1.06233 | 0.531167 | − | 0.847267i | \(-0.321754\pi\) | ||||
0.531167 | + | 0.847267i | \(0.321754\pi\) | |||||||
\(30\) | 16.5579 | 3.02305 | ||||||||
\(31\) | 4.15100 | 0.745542 | 0.372771 | − | 0.927923i | \(-0.378408\pi\) | ||||
0.372771 | + | 0.927923i | \(0.378408\pi\) | |||||||
\(32\) | −4.56710 | −0.807358 | ||||||||
\(33\) | −1.49490 | −0.260229 | ||||||||
\(34\) | 4.74719 | 0.814137 | ||||||||
\(35\) | 7.30033 | 1.23398 | ||||||||
\(36\) | 0.545471 | 0.0909118 | ||||||||
\(37\) | 4.26358 | 0.700928 | 0.350464 | − | 0.936576i | \(-0.386024\pi\) | ||||
0.350464 | + | 0.936576i | \(0.386024\pi\) | |||||||
\(38\) | −0.828394 | −0.134383 | ||||||||
\(39\) | 1.76740 | 0.283011 | ||||||||
\(40\) | −22.5702 | −3.56866 | ||||||||
\(41\) | −6.77134 | −1.05750 | −0.528752 | − | 0.848776i | \(-0.677340\pi\) | ||||
−0.528752 | + | 0.848776i | \(0.677340\pi\) | |||||||
\(42\) | 8.82690 | 1.36202 | ||||||||
\(43\) | −8.94374 | −1.36391 | −0.681954 | − | 0.731395i | \(-0.738870\pi\) | ||||
−0.681954 | + | 0.731395i | \(0.738870\pi\) | |||||||
\(44\) | 3.72934 | 0.562220 | ||||||||
\(45\) | 0.457812 | 0.0682466 | ||||||||
\(46\) | −11.8510 | −1.74734 | ||||||||
\(47\) | 3.76653 | 0.549405 | 0.274702 | − | 0.961529i | \(-0.411421\pi\) | ||||
0.274702 | + | 0.961529i | \(0.411421\pi\) | |||||||
\(48\) | −11.7043 | −1.68937 | ||||||||
\(49\) | −3.10826 | −0.444037 | ||||||||
\(50\) | −22.0108 | −3.11280 | ||||||||
\(51\) | 3.31415 | 0.464074 | ||||||||
\(52\) | −4.40915 | −0.611439 | ||||||||
\(53\) | −3.11599 | −0.428015 | −0.214007 | − | 0.976832i | \(-0.568652\pi\) | ||||
−0.214007 | + | 0.976832i | \(0.568652\pi\) | |||||||
\(54\) | −12.8697 | −1.75134 | ||||||||
\(55\) | 3.13002 | 0.422052 | ||||||||
\(56\) | −12.0320 | −1.60784 | ||||||||
\(57\) | −0.578325 | −0.0766010 | ||||||||
\(58\) | −14.4831 | −1.90172 | ||||||||
\(59\) | 4.25737 | 0.554262 | 0.277131 | − | 0.960832i | \(-0.410616\pi\) | ||||
0.277131 | + | 0.960832i | \(0.410616\pi\) | |||||||
\(60\) | −28.8377 | −3.72294 | ||||||||
\(61\) | 13.3881 | 1.71417 | 0.857083 | − | 0.515179i | \(-0.172275\pi\) | ||||
0.857083 | + | 0.515179i | \(0.172275\pi\) | |||||||
\(62\) | −10.5088 | −1.33462 | ||||||||
\(63\) | 0.244056 | 0.0307481 | ||||||||
\(64\) | −1.68242 | −0.210303 | ||||||||
\(65\) | −3.70059 | −0.459001 | ||||||||
\(66\) | 3.78454 | 0.465845 | ||||||||
\(67\) | 8.99342 | 1.09872 | 0.549361 | − | 0.835585i | \(-0.314871\pi\) | ||||
0.549361 | + | 0.835585i | \(0.314871\pi\) | |||||||
\(68\) | −8.26783 | −1.00262 | ||||||||
\(69\) | −8.27353 | −0.996016 | ||||||||
\(70\) | −18.4817 | −2.20899 | ||||||||
\(71\) | −11.6754 | −1.38561 | −0.692805 | − | 0.721125i | \(-0.743625\pi\) | ||||
−0.692805 | + | 0.721125i | \(0.743625\pi\) | |||||||
\(72\) | −0.754538 | −0.0889232 | ||||||||
\(73\) | 6.09426 | 0.713279 | 0.356639 | − | 0.934242i | \(-0.383922\pi\) | ||||
0.356639 | + | 0.934242i | \(0.383922\pi\) | |||||||
\(74\) | −10.7938 | −1.25475 | ||||||||
\(75\) | −15.3664 | −1.77436 | ||||||||
\(76\) | 1.44275 | 0.165495 | ||||||||
\(77\) | 1.66859 | 0.190153 | ||||||||
\(78\) | −4.47441 | −0.506627 | ||||||||
\(79\) | −4.87010 | −0.547929 | −0.273964 | − | 0.961740i | \(-0.588335\pi\) | ||||
−0.273964 | + | 0.961740i | \(0.588335\pi\) | |||||||
\(80\) | 24.5065 | 2.73991 | ||||||||
\(81\) | −9.35584 | −1.03954 | ||||||||
\(82\) | 17.1425 | 1.89307 | ||||||||
\(83\) | 14.6972 | 1.61323 | 0.806615 | − | 0.591077i | \(-0.201297\pi\) | ||||
0.806615 | + | 0.591077i | \(0.201297\pi\) | |||||||
\(84\) | −15.3731 | −1.67735 | ||||||||
\(85\) | −6.93916 | −0.752658 | ||||||||
\(86\) | 22.6422 | 2.44158 | ||||||||
\(87\) | −10.1110 | −1.08402 | ||||||||
\(88\) | −5.15872 | −0.549921 | ||||||||
\(89\) | −6.08270 | −0.644765 | −0.322383 | − | 0.946609i | \(-0.604484\pi\) | ||||
−0.322383 | + | 0.946609i | \(0.604484\pi\) | |||||||
\(90\) | −1.15901 | −0.122170 | ||||||||
\(91\) | −1.97275 | −0.206800 | ||||||||
\(92\) | 20.6400 | 2.15187 | ||||||||
\(93\) | −7.33650 | −0.760759 | ||||||||
\(94\) | −9.53546 | −0.983508 | ||||||||
\(95\) | 1.21090 | 0.124235 | ||||||||
\(96\) | 8.07191 | 0.823836 | ||||||||
\(97\) | −5.79937 | −0.588837 | −0.294419 | − | 0.955677i | \(-0.595126\pi\) | ||||
−0.294419 | + | 0.955677i | \(0.595126\pi\) | |||||||
\(98\) | 7.86896 | 0.794885 | ||||||||
\(99\) | 0.104639 | 0.0105166 | ||||||||
\(100\) | 38.3346 | 3.83346 | ||||||||
\(101\) | −2.64341 | −0.263029 | −0.131515 | − | 0.991314i | \(-0.541984\pi\) | ||||
−0.131515 | + | 0.991314i | \(0.541984\pi\) | |||||||
\(102\) | −8.39020 | −0.830754 | ||||||||
\(103\) | −6.85005 | −0.674955 | −0.337478 | − | 0.941334i | \(-0.609574\pi\) | ||||
−0.337478 | + | 0.941334i | \(0.609574\pi\) | |||||||
\(104\) | 6.09908 | 0.598064 | ||||||||
\(105\) | −12.9026 | −1.25917 | ||||||||
\(106\) | 7.88854 | 0.766203 | ||||||||
\(107\) | 3.20026 | 0.309381 | 0.154690 | − | 0.987963i | \(-0.450562\pi\) | ||||
0.154690 | + | 0.987963i | \(0.450562\pi\) | |||||||
\(108\) | 22.4142 | 2.15681 | ||||||||
\(109\) | 4.47884 | 0.428995 | 0.214498 | − | 0.976725i | \(-0.431189\pi\) | ||||
0.214498 | + | 0.976725i | \(0.431189\pi\) | |||||||
\(110\) | −7.92407 | −0.755530 | ||||||||
\(111\) | −7.53546 | −0.715234 | ||||||||
\(112\) | 13.0642 | 1.23445 | ||||||||
\(113\) | 10.6855 | 1.00521 | 0.502606 | − | 0.864516i | \(-0.332375\pi\) | ||||
0.502606 | + | 0.864516i | \(0.332375\pi\) | |||||||
\(114\) | 1.46411 | 0.137126 | ||||||||
\(115\) | 17.3231 | 1.61539 | ||||||||
\(116\) | 25.2241 | 2.34200 | ||||||||
\(117\) | −0.123713 | −0.0114373 | ||||||||
\(118\) | −10.7781 | −0.992203 | ||||||||
\(119\) | −3.69921 | −0.339106 | ||||||||
\(120\) | 39.8906 | 3.64150 | ||||||||
\(121\) | −10.2846 | −0.934963 | ||||||||
\(122\) | −33.8936 | −3.06858 | ||||||||
\(123\) | 11.9677 | 1.07909 | ||||||||
\(124\) | 18.3024 | 1.64361 | ||||||||
\(125\) | 13.6712 | 1.22279 | ||||||||
\(126\) | −0.617858 | −0.0550432 | ||||||||
\(127\) | −6.13172 | −0.544102 | −0.272051 | − | 0.962283i | \(-0.587702\pi\) | ||||
−0.272051 | + | 0.962283i | \(0.587702\pi\) | |||||||
\(128\) | 13.3935 | 1.18383 | ||||||||
\(129\) | 15.8072 | 1.39175 | ||||||||
\(130\) | 9.36852 | 0.821673 | ||||||||
\(131\) | 7.49401 | 0.654755 | 0.327377 | − | 0.944894i | \(-0.393835\pi\) | ||||
0.327377 | + | 0.944894i | \(0.393835\pi\) | |||||||
\(132\) | −6.59125 | −0.573695 | ||||||||
\(133\) | 0.645518 | 0.0559735 | ||||||||
\(134\) | −22.7680 | −1.96686 | ||||||||
\(135\) | 18.8121 | 1.61909 | ||||||||
\(136\) | 11.4367 | 0.980690 | ||||||||
\(137\) | −2.80027 | −0.239243 | −0.119622 | − | 0.992820i | \(-0.538168\pi\) | ||||
−0.119622 | + | 0.992820i | \(0.538168\pi\) | |||||||
\(138\) | 20.9455 | 1.78300 | ||||||||
\(139\) | 18.9934 | 1.61100 | 0.805499 | − | 0.592597i | \(-0.201898\pi\) | ||||
0.805499 | + | 0.592597i | \(0.201898\pi\) | |||||||
\(140\) | 32.1883 | 2.72041 | ||||||||
\(141\) | −6.65698 | −0.560619 | ||||||||
\(142\) | 29.5577 | 2.48043 | ||||||||
\(143\) | −0.845819 | −0.0707309 | ||||||||
\(144\) | 0.819270 | 0.0682725 | ||||||||
\(145\) | 21.1705 | 1.75811 | ||||||||
\(146\) | −15.4284 | −1.27686 | ||||||||
\(147\) | 5.49354 | 0.453100 | ||||||||
\(148\) | 18.7988 | 1.54525 | ||||||||
\(149\) | −7.67291 | −0.628589 | −0.314295 | − | 0.949325i | \(-0.601768\pi\) | ||||
−0.314295 | + | 0.949325i | \(0.601768\pi\) | |||||||
\(150\) | 38.9020 | 3.17634 | ||||||||
\(151\) | −6.81345 | −0.554471 | −0.277235 | − | 0.960802i | \(-0.589418\pi\) | ||||
−0.277235 | + | 0.960802i | \(0.589418\pi\) | |||||||
\(152\) | −1.99573 | −0.161875 | ||||||||
\(153\) | −0.231981 | −0.0187546 | ||||||||
\(154\) | −4.22425 | −0.340400 | ||||||||
\(155\) | 15.3611 | 1.23384 | ||||||||
\(156\) | 7.79275 | 0.623919 | ||||||||
\(157\) | 19.1957 | 1.53199 | 0.765993 | − | 0.642848i | \(-0.222248\pi\) | ||||
0.765993 | + | 0.642848i | \(0.222248\pi\) | |||||||
\(158\) | 12.3293 | 0.980866 | ||||||||
\(159\) | 5.50722 | 0.436751 | ||||||||
\(160\) | −16.9010 | −1.33614 | ||||||||
\(161\) | 9.23480 | 0.727804 | ||||||||
\(162\) | 23.6855 | 1.86091 | ||||||||
\(163\) | 20.0771 | 1.57256 | 0.786282 | − | 0.617868i | \(-0.212003\pi\) | ||||
0.786282 | + | 0.617868i | \(0.212003\pi\) | |||||||
\(164\) | −29.8559 | −2.33135 | ||||||||
\(165\) | −5.53201 | −0.430667 | ||||||||
\(166\) | −37.2080 | −2.88790 | ||||||||
\(167\) | −19.3301 | −1.49581 | −0.747906 | − | 0.663805i | \(-0.768940\pi\) | ||||
−0.747906 | + | 0.663805i | \(0.768940\pi\) | |||||||
\(168\) | 21.2653 | 1.64066 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 17.5674 | 1.34736 | ||||||||
\(171\) | 0.0404812 | 0.00309567 | ||||||||
\(172\) | −39.4343 | −3.00684 | ||||||||
\(173\) | 14.8091 | 1.12591 | 0.562957 | − | 0.826486i | \(-0.309663\pi\) | ||||
0.562957 | + | 0.826486i | \(0.309663\pi\) | |||||||
\(174\) | 25.5974 | 1.94054 | ||||||||
\(175\) | 17.1517 | 1.29655 | ||||||||
\(176\) | 5.60128 | 0.422213 | ||||||||
\(177\) | −7.52448 | −0.565575 | ||||||||
\(178\) | 15.3992 | 1.15422 | ||||||||
\(179\) | 6.59466 | 0.492908 | 0.246454 | − | 0.969154i | \(-0.420735\pi\) | ||||
0.246454 | + | 0.969154i | \(0.420735\pi\) | |||||||
\(180\) | 2.01856 | 0.150455 | ||||||||
\(181\) | 6.43405 | 0.478239 | 0.239119 | − | 0.970990i | \(-0.423141\pi\) | ||||
0.239119 | + | 0.970990i | \(0.423141\pi\) | |||||||
\(182\) | 4.99427 | 0.370200 | ||||||||
\(183\) | −23.6621 | −1.74915 | ||||||||
\(184\) | −28.5509 | −2.10480 | ||||||||
\(185\) | 15.7777 | 1.16000 | ||||||||
\(186\) | 18.5733 | 1.36186 | ||||||||
\(187\) | −1.58604 | −0.115983 | ||||||||
\(188\) | 16.6072 | 1.21121 | ||||||||
\(189\) | 10.0286 | 0.729473 | ||||||||
\(190\) | −3.06554 | −0.222398 | ||||||||
\(191\) | 22.5531 | 1.63188 | 0.815941 | − | 0.578135i | \(-0.196219\pi\) | ||||
0.815941 | + | 0.578135i | \(0.196219\pi\) | |||||||
\(192\) | 2.97352 | 0.214595 | ||||||||
\(193\) | −0.426356 | −0.0306898 | −0.0153449 | − | 0.999882i | \(-0.504885\pi\) | ||||
−0.0153449 | + | 0.999882i | \(0.504885\pi\) | |||||||
\(194\) | 14.6819 | 1.05410 | ||||||||
\(195\) | 6.54043 | 0.468370 | ||||||||
\(196\) | −13.7048 | −0.978913 | ||||||||
\(197\) | 3.79037 | 0.270053 | 0.135026 | − | 0.990842i | \(-0.456888\pi\) | ||||
0.135026 | + | 0.990842i | \(0.456888\pi\) | |||||||
\(198\) | −0.264907 | −0.0188262 | ||||||||
\(199\) | −25.2238 | −1.78807 | −0.894035 | − | 0.447996i | \(-0.852138\pi\) | ||||
−0.894035 | + | 0.447996i | \(0.852138\pi\) | |||||||
\(200\) | −53.0275 | −3.74961 | ||||||||
\(201\) | −15.8950 | −1.12115 | ||||||||
\(202\) | 6.69214 | 0.470858 | ||||||||
\(203\) | 11.2858 | 0.792108 | ||||||||
\(204\) | 14.6126 | 1.02309 | ||||||||
\(205\) | −25.0579 | −1.75012 | ||||||||
\(206\) | 17.3418 | 1.20826 | ||||||||
\(207\) | 0.579124 | 0.0402519 | ||||||||
\(208\) | −6.62232 | −0.459175 | ||||||||
\(209\) | 0.276767 | 0.0191444 | ||||||||
\(210\) | 32.6647 | 2.25408 | ||||||||
\(211\) | −13.6111 | −0.937024 | −0.468512 | − | 0.883457i | \(-0.655210\pi\) | ||||
−0.468512 | + | 0.883457i | \(0.655210\pi\) | |||||||
\(212\) | −13.7389 | −0.943591 | ||||||||
\(213\) | 20.6351 | 1.41389 | ||||||||
\(214\) | −8.10187 | −0.553832 | ||||||||
\(215\) | −33.0971 | −2.25720 | ||||||||
\(216\) | −31.0050 | −2.10963 | ||||||||
\(217\) | 8.18890 | 0.555898 | ||||||||
\(218\) | −11.3388 | −0.767959 | ||||||||
\(219\) | −10.7710 | −0.727837 | ||||||||
\(220\) | 13.8008 | 0.930447 | ||||||||
\(221\) | 1.87515 | 0.126136 | ||||||||
\(222\) | 19.0770 | 1.28036 | ||||||||
\(223\) | −28.8573 | −1.93243 | −0.966215 | − | 0.257736i | \(-0.917023\pi\) | ||||
−0.966215 | + | 0.257736i | \(0.917023\pi\) | |||||||
\(224\) | −9.00976 | −0.601990 | ||||||||
\(225\) | 1.07561 | 0.0717070 | ||||||||
\(226\) | −27.0519 | −1.79946 | ||||||||
\(227\) | −10.0709 | −0.668429 | −0.334214 | − | 0.942497i | \(-0.608471\pi\) | ||||
−0.334214 | + | 0.942497i | \(0.608471\pi\) | |||||||
\(228\) | −2.54992 | −0.168873 | ||||||||
\(229\) | −21.2559 | −1.40463 | −0.702315 | − | 0.711866i | \(-0.747850\pi\) | ||||
−0.702315 | + | 0.711866i | \(0.747850\pi\) | |||||||
\(230\) | −43.8557 | −2.89176 | ||||||||
\(231\) | −2.94907 | −0.194035 | ||||||||
\(232\) | −34.8919 | −2.29077 | ||||||||
\(233\) | 20.4561 | 1.34012 | 0.670061 | − | 0.742306i | \(-0.266268\pi\) | ||||
0.670061 | + | 0.742306i | \(0.266268\pi\) | |||||||
\(234\) | 0.313196 | 0.0204743 | ||||||||
\(235\) | 13.9384 | 0.909239 | ||||||||
\(236\) | 18.7714 | 1.22191 | ||||||||
\(237\) | 8.60743 | 0.559112 | ||||||||
\(238\) | 9.36503 | 0.607044 | ||||||||
\(239\) | −18.2924 | −1.18324 | −0.591619 | − | 0.806217i | \(-0.701511\pi\) | ||||
−0.591619 | + | 0.806217i | \(0.701511\pi\) | |||||||
\(240\) | −43.3128 | −2.79583 | ||||||||
\(241\) | 21.1221 | 1.36059 | 0.680296 | − | 0.732937i | \(-0.261851\pi\) | ||||
0.680296 | + | 0.732937i | \(0.261851\pi\) | |||||||
\(242\) | 26.0368 | 1.67371 | ||||||||
\(243\) | 1.28486 | 0.0824237 | ||||||||
\(244\) | 59.0300 | 3.77901 | ||||||||
\(245\) | −11.5024 | −0.734859 | ||||||||
\(246\) | −30.2977 | −1.93171 | ||||||||
\(247\) | −0.327217 | −0.0208204 | ||||||||
\(248\) | −25.3173 | −1.60765 | ||||||||
\(249\) | −25.9759 | −1.64616 | ||||||||
\(250\) | −34.6104 | −2.18896 | ||||||||
\(251\) | 4.36988 | 0.275824 | 0.137912 | − | 0.990444i | \(-0.455961\pi\) | ||||
0.137912 | + | 0.990444i | \(0.455961\pi\) | |||||||
\(252\) | 1.07608 | 0.0677866 | ||||||||
\(253\) | 3.95943 | 0.248927 | ||||||||
\(254\) | 15.5232 | 0.974015 | ||||||||
\(255\) | 12.2643 | 0.768020 | ||||||||
\(256\) | −30.5425 | −1.90891 | ||||||||
\(257\) | −15.5231 | −0.968304 | −0.484152 | − | 0.874984i | \(-0.660872\pi\) | ||||
−0.484152 | + | 0.874984i | \(0.660872\pi\) | |||||||
\(258\) | −40.0180 | −2.49141 | ||||||||
\(259\) | 8.41097 | 0.522632 | ||||||||
\(260\) | −16.3164 | −1.01190 | ||||||||
\(261\) | 0.707745 | 0.0438083 | ||||||||
\(262\) | −18.9721 | −1.17210 | ||||||||
\(263\) | 31.5687 | 1.94661 | 0.973305 | − | 0.229516i | \(-0.0737144\pi\) | ||||
0.973305 | + | 0.229516i | \(0.0737144\pi\) | |||||||
\(264\) | 9.11754 | 0.561146 | ||||||||
\(265\) | −11.5310 | −0.708344 | ||||||||
\(266\) | −1.63421 | −0.100200 | ||||||||
\(267\) | 10.7506 | 0.657925 | ||||||||
\(268\) | 39.6534 | 2.42221 | ||||||||
\(269\) | 29.2400 | 1.78279 | 0.891397 | − | 0.453222i | \(-0.149726\pi\) | ||||
0.891397 | + | 0.453222i | \(0.149726\pi\) | |||||||
\(270\) | −47.6254 | −2.89839 | ||||||||
\(271\) | −8.99741 | −0.546554 | −0.273277 | − | 0.961935i | \(-0.588108\pi\) | ||||
−0.273277 | + | 0.961935i | \(0.588108\pi\) | |||||||
\(272\) | −12.4179 | −0.752944 | ||||||||
\(273\) | 3.48664 | 0.211021 | ||||||||
\(274\) | 7.08925 | 0.428277 | ||||||||
\(275\) | 7.35383 | 0.443453 | ||||||||
\(276\) | −36.4793 | −2.19579 | ||||||||
\(277\) | −5.43648 | −0.326646 | −0.163323 | − | 0.986573i | \(-0.552221\pi\) | ||||
−0.163323 | + | 0.986573i | \(0.552221\pi\) | |||||||
\(278\) | −48.0842 | −2.88390 | ||||||||
\(279\) | 0.513535 | 0.0307445 | ||||||||
\(280\) | −44.5253 | −2.66090 | ||||||||
\(281\) | 22.1044 | 1.31864 | 0.659319 | − | 0.751863i | \(-0.270845\pi\) | ||||
0.659319 | + | 0.751863i | \(0.270845\pi\) | |||||||
\(282\) | 16.8530 | 1.00358 | ||||||||
\(283\) | −19.0897 | −1.13477 | −0.567384 | − | 0.823454i | \(-0.692044\pi\) | ||||
−0.567384 | + | 0.823454i | \(0.692044\pi\) | |||||||
\(284\) | −51.4784 | −3.05468 | ||||||||
\(285\) | −2.14014 | −0.126771 | ||||||||
\(286\) | 2.14130 | 0.126618 | ||||||||
\(287\) | −13.3582 | −0.788507 | ||||||||
\(288\) | −0.565012 | −0.0332936 | ||||||||
\(289\) | −13.4838 | −0.793165 | ||||||||
\(290\) | −53.5958 | −3.14726 | ||||||||
\(291\) | 10.2498 | 0.600856 | ||||||||
\(292\) | 26.8705 | 1.57248 | ||||||||
\(293\) | −1.77125 | −0.103477 | −0.0517387 | − | 0.998661i | \(-0.516476\pi\) | ||||
−0.0517387 | + | 0.998661i | \(0.516476\pi\) | |||||||
\(294\) | −13.9076 | −0.811109 | ||||||||
\(295\) | 15.7548 | 0.917277 | ||||||||
\(296\) | −26.0039 | −1.51145 | ||||||||
\(297\) | 4.29977 | 0.249498 | ||||||||
\(298\) | 19.4250 | 1.12526 | ||||||||
\(299\) | −4.68118 | −0.270720 | ||||||||
\(300\) | −67.7528 | −3.91171 | ||||||||
\(301\) | −17.6438 | −1.01697 | ||||||||
\(302\) | 17.2491 | 0.992577 | ||||||||
\(303\) | 4.67197 | 0.268398 | ||||||||
\(304\) | 2.16694 | 0.124283 | ||||||||
\(305\) | 49.5437 | 2.83686 | ||||||||
\(306\) | 0.587291 | 0.0335732 | ||||||||
\(307\) | −23.2120 | −1.32478 | −0.662390 | − | 0.749160i | \(-0.730458\pi\) | ||||
−0.662390 | + | 0.749160i | \(0.730458\pi\) | |||||||
\(308\) | 7.35706 | 0.419208 | ||||||||
\(309\) | 12.1068 | 0.688731 | ||||||||
\(310\) | −38.8888 | −2.20873 | ||||||||
\(311\) | 15.8763 | 0.900262 | 0.450131 | − | 0.892962i | \(-0.351377\pi\) | ||||
0.450131 | + | 0.892962i | \(0.351377\pi\) | |||||||
\(312\) | −10.7795 | −0.610271 | ||||||||
\(313\) | 11.3353 | 0.640707 | 0.320353 | − | 0.947298i | \(-0.396198\pi\) | ||||
0.320353 | + | 0.947298i | \(0.396198\pi\) | |||||||
\(314\) | −48.5965 | −2.74246 | ||||||||
\(315\) | 0.903148 | 0.0508866 | ||||||||
\(316\) | −21.4730 | −1.20795 | ||||||||
\(317\) | 18.6812 | 1.04924 | 0.524620 | − | 0.851337i | \(-0.324207\pi\) | ||||
0.524620 | + | 0.851337i | \(0.324207\pi\) | |||||||
\(318\) | −13.9422 | −0.781842 | ||||||||
\(319\) | 4.83880 | 0.270921 | ||||||||
\(320\) | −6.22595 | −0.348041 | ||||||||
\(321\) | −5.65614 | −0.315695 | ||||||||
\(322\) | −23.3791 | −1.30287 | ||||||||
\(323\) | −0.613583 | −0.0341407 | ||||||||
\(324\) | −41.2513 | −2.29174 | ||||||||
\(325\) | −8.69433 | −0.482275 | ||||||||
\(326\) | −50.8279 | −2.81510 | ||||||||
\(327\) | −7.91592 | −0.437751 | ||||||||
\(328\) | 41.2989 | 2.28035 | ||||||||
\(329\) | 7.43042 | 0.409653 | ||||||||
\(330\) | 14.0050 | 0.770951 | ||||||||
\(331\) | 14.4353 | 0.793437 | 0.396718 | − | 0.917940i | \(-0.370149\pi\) | ||||
0.396718 | + | 0.917940i | \(0.370149\pi\) | |||||||
\(332\) | 64.8023 | 3.55649 | ||||||||
\(333\) | 0.527461 | 0.0289047 | ||||||||
\(334\) | 48.9368 | 2.67770 | ||||||||
\(335\) | 33.2809 | 1.81833 | ||||||||
\(336\) | −23.0897 | −1.25965 | ||||||||
\(337\) | 24.4803 | 1.33352 | 0.666762 | − | 0.745270i | \(-0.267680\pi\) | ||||
0.666762 | + | 0.745270i | \(0.267680\pi\) | |||||||
\(338\) | −2.53163 | −0.137703 | ||||||||
\(339\) | −18.8857 | −1.02573 | ||||||||
\(340\) | −30.5958 | −1.65929 | ||||||||
\(341\) | 3.51100 | 0.190131 | ||||||||
\(342\) | −0.102483 | −0.00554167 | ||||||||
\(343\) | −19.9411 | −1.07672 | ||||||||
\(344\) | 54.5486 | 2.94107 | ||||||||
\(345\) | −30.6169 | −1.64836 | ||||||||
\(346\) | −37.4912 | −2.01554 | ||||||||
\(347\) | −9.04071 | −0.485331 | −0.242665 | − | 0.970110i | \(-0.578022\pi\) | ||||
−0.242665 | + | 0.970110i | \(0.578022\pi\) | |||||||
\(348\) | −44.5811 | −2.38980 | ||||||||
\(349\) | 6.41330 | 0.343296 | 0.171648 | − | 0.985158i | \(-0.445091\pi\) | ||||
0.171648 | + | 0.985158i | \(0.445091\pi\) | |||||||
\(350\) | −43.4219 | −2.32100 | ||||||||
\(351\) | −5.08356 | −0.271340 | ||||||||
\(352\) | −3.86294 | −0.205896 | ||||||||
\(353\) | 17.1077 | 0.910550 | 0.455275 | − | 0.890351i | \(-0.349541\pi\) | ||||
0.455275 | + | 0.890351i | \(0.349541\pi\) | |||||||
\(354\) | 19.0492 | 1.01245 | ||||||||
\(355\) | −43.2057 | −2.29312 | ||||||||
\(356\) | −26.8196 | −1.42143 | ||||||||
\(357\) | 6.53799 | 0.346027 | ||||||||
\(358\) | −16.6952 | −0.882371 | ||||||||
\(359\) | −12.5004 | −0.659744 | −0.329872 | − | 0.944026i | \(-0.607006\pi\) | ||||
−0.329872 | + | 0.944026i | \(0.607006\pi\) | |||||||
\(360\) | −2.79223 | −0.147164 | ||||||||
\(361\) | −18.8929 | −0.994365 | ||||||||
\(362\) | −16.2886 | −0.856111 | ||||||||
\(363\) | 18.1770 | 0.954046 | ||||||||
\(364\) | −8.69816 | −0.455907 | ||||||||
\(365\) | 22.5523 | 1.18044 | ||||||||
\(366\) | 59.9037 | 3.13122 | ||||||||
\(367\) | 5.28804 | 0.276033 | 0.138017 | − | 0.990430i | \(-0.455927\pi\) | ||||
0.138017 | + | 0.990430i | \(0.455927\pi\) | |||||||
\(368\) | 31.0003 | 1.61600 | ||||||||
\(369\) | −0.837705 | −0.0436092 | ||||||||
\(370\) | −39.9434 | −2.07656 | ||||||||
\(371\) | −6.14708 | −0.319140 | ||||||||
\(372\) | −32.3477 | −1.67715 | ||||||||
\(373\) | 9.74580 | 0.504618 | 0.252309 | − | 0.967647i | \(-0.418810\pi\) | ||||
0.252309 | + | 0.967647i | \(0.418810\pi\) | |||||||
\(374\) | 4.01526 | 0.207624 | ||||||||
\(375\) | −24.1625 | −1.24775 | ||||||||
\(376\) | −22.9724 | −1.18471 | ||||||||
\(377\) | −5.72085 | −0.294639 | ||||||||
\(378\) | −25.3887 | −1.30585 | ||||||||
\(379\) | 18.2863 | 0.939302 | 0.469651 | − | 0.882852i | \(-0.344380\pi\) | ||||
0.469651 | + | 0.882852i | \(0.344380\pi\) | |||||||
\(380\) | 5.33903 | 0.273886 | ||||||||
\(381\) | 10.8372 | 0.555208 | ||||||||
\(382\) | −57.0960 | −2.92129 | ||||||||
\(383\) | −1.39836 | −0.0714527 | −0.0357263 | − | 0.999362i | \(-0.511374\pi\) | ||||
−0.0357263 | + | 0.999362i | \(0.511374\pi\) | |||||||
\(384\) | −23.6717 | −1.20799 | ||||||||
\(385\) | 6.17476 | 0.314695 | ||||||||
\(386\) | 1.07938 | 0.0549388 | ||||||||
\(387\) | −1.10646 | −0.0562445 | ||||||||
\(388\) | −25.5703 | −1.29814 | ||||||||
\(389\) | 2.10373 | 0.106663 | 0.0533316 | − | 0.998577i | \(-0.483016\pi\) | ||||
0.0533316 | + | 0.998577i | \(0.483016\pi\) | |||||||
\(390\) | −16.5579 | −0.838444 | ||||||||
\(391\) | −8.77792 | −0.443919 | ||||||||
\(392\) | 18.9575 | 0.957499 | ||||||||
\(393\) | −13.2449 | −0.668119 | ||||||||
\(394\) | −9.59583 | −0.483431 | ||||||||
\(395\) | −18.0222 | −0.906796 | ||||||||
\(396\) | 0.461370 | 0.0231847 | ||||||||
\(397\) | 16.2526 | 0.815696 | 0.407848 | − | 0.913050i | \(-0.366279\pi\) | ||||
0.407848 | + | 0.913050i | \(0.366279\pi\) | |||||||
\(398\) | 63.8575 | 3.20088 | ||||||||
\(399\) | −1.14089 | −0.0571160 | ||||||||
\(400\) | 57.5767 | 2.87883 | ||||||||
\(401\) | 16.1249 | 0.805238 | 0.402619 | − | 0.915368i | \(-0.368100\pi\) | ||||
0.402619 | + | 0.915368i | \(0.368100\pi\) | |||||||
\(402\) | 40.2403 | 2.00700 | ||||||||
\(403\) | −4.15100 | −0.206776 | ||||||||
\(404\) | −11.6552 | −0.579868 | ||||||||
\(405\) | −34.6221 | −1.72038 | ||||||||
\(406\) | −28.5715 | −1.41798 | ||||||||
\(407\) | 3.60621 | 0.178753 | ||||||||
\(408\) | −20.2133 | −1.00071 | ||||||||
\(409\) | −4.21776 | −0.208555 | −0.104277 | − | 0.994548i | \(-0.533253\pi\) | ||||
−0.104277 | + | 0.994548i | \(0.533253\pi\) | |||||||
\(410\) | 63.4374 | 3.13295 | ||||||||
\(411\) | 4.94921 | 0.244126 | ||||||||
\(412\) | −30.2029 | −1.48799 | ||||||||
\(413\) | 8.39872 | 0.413274 | ||||||||
\(414\) | −1.46613 | −0.0720563 | ||||||||
\(415\) | 54.3884 | 2.66982 | ||||||||
\(416\) | 4.56710 | 0.223921 | ||||||||
\(417\) | −33.5690 | −1.64388 | ||||||||
\(418\) | −0.700671 | −0.0342709 | ||||||||
\(419\) | −5.29424 | −0.258640 | −0.129320 | − | 0.991603i | \(-0.541280\pi\) | ||||
−0.129320 | + | 0.991603i | \(0.541280\pi\) | |||||||
\(420\) | −56.8897 | −2.77593 | ||||||||
\(421\) | −11.9428 | −0.582054 | −0.291027 | − | 0.956715i | \(-0.593997\pi\) | ||||
−0.291027 | + | 0.956715i | \(0.593997\pi\) | |||||||
\(422\) | 34.4582 | 1.67740 | ||||||||
\(423\) | 0.465970 | 0.0226562 | ||||||||
\(424\) | 19.0047 | 0.922950 | ||||||||
\(425\) | −16.3032 | −0.790821 | ||||||||
\(426\) | −52.2404 | −2.53105 | ||||||||
\(427\) | 26.4113 | 1.27813 | ||||||||
\(428\) | 14.1104 | 0.682053 | ||||||||
\(429\) | 1.49490 | 0.0721746 | ||||||||
\(430\) | 83.7896 | 4.04069 | ||||||||
\(431\) | −41.0400 | −1.97683 | −0.988414 | − | 0.151785i | \(-0.951498\pi\) | ||||
−0.988414 | + | 0.151785i | \(0.951498\pi\) | |||||||
\(432\) | 33.6650 | 1.61971 | ||||||||
\(433\) | 13.3033 | 0.639318 | 0.319659 | − | 0.947533i | \(-0.396432\pi\) | ||||
0.319659 | + | 0.947533i | \(0.396432\pi\) | |||||||
\(434\) | −20.7313 | −0.995132 | ||||||||
\(435\) | −37.4168 | −1.79400 | ||||||||
\(436\) | 19.7479 | 0.945753 | ||||||||
\(437\) | 1.53176 | 0.0732742 | ||||||||
\(438\) | 27.2682 | 1.30293 | ||||||||
\(439\) | −21.4829 | −1.02532 | −0.512661 | − | 0.858591i | \(-0.671340\pi\) | ||||
−0.512661 | + | 0.858591i | \(0.671340\pi\) | |||||||
\(440\) | −19.0903 | −0.910094 | ||||||||
\(441\) | −0.384533 | −0.0183111 | ||||||||
\(442\) | −4.74719 | −0.225801 | ||||||||
\(443\) | 24.3508 | 1.15694 | 0.578472 | − | 0.815702i | \(-0.303649\pi\) | ||||
0.578472 | + | 0.815702i | \(0.303649\pi\) | |||||||
\(444\) | −33.2250 | −1.57679 | ||||||||
\(445\) | −22.5096 | −1.06706 | ||||||||
\(446\) | 73.0561 | 3.45931 | ||||||||
\(447\) | 13.5611 | 0.641419 | ||||||||
\(448\) | −3.31900 | −0.156808 | ||||||||
\(449\) | −12.5155 | −0.590643 | −0.295321 | − | 0.955398i | \(-0.595427\pi\) | ||||
−0.295321 | + | 0.955398i | \(0.595427\pi\) | |||||||
\(450\) | −2.72303 | −0.128365 | ||||||||
\(451\) | −5.72732 | −0.269689 | ||||||||
\(452\) | 47.1142 | 2.21607 | ||||||||
\(453\) | 12.0421 | 0.565788 | ||||||||
\(454\) | 25.4958 | 1.19658 | ||||||||
\(455\) | −7.30033 | −0.342245 | ||||||||
\(456\) | 3.52725 | 0.165179 | ||||||||
\(457\) | −2.49060 | −0.116505 | −0.0582526 | − | 0.998302i | \(-0.518553\pi\) | ||||
−0.0582526 | + | 0.998302i | \(0.518553\pi\) | |||||||
\(458\) | 53.8121 | 2.51447 | ||||||||
\(459\) | −9.53245 | −0.444936 | ||||||||
\(460\) | 76.3802 | 3.56125 | ||||||||
\(461\) | −25.4156 | −1.18372 | −0.591861 | − | 0.806040i | \(-0.701607\pi\) | ||||
−0.591861 | + | 0.806040i | \(0.701607\pi\) | |||||||
\(462\) | 7.46595 | 0.347348 | ||||||||
\(463\) | 23.4758 | 1.09101 | 0.545506 | − | 0.838107i | \(-0.316338\pi\) | ||||
0.545506 | + | 0.838107i | \(0.316338\pi\) | |||||||
\(464\) | 37.8853 | 1.75878 | ||||||||
\(465\) | −27.1493 | −1.25902 | ||||||||
\(466\) | −51.7872 | −2.39900 | ||||||||
\(467\) | 33.0851 | 1.53100 | 0.765498 | − | 0.643438i | \(-0.222493\pi\) | ||||
0.765498 | + | 0.643438i | \(0.222493\pi\) | |||||||
\(468\) | −0.545471 | −0.0252144 | ||||||||
\(469\) | 17.7418 | 0.819239 | ||||||||
\(470\) | −35.2868 | −1.62766 | ||||||||
\(471\) | −33.9266 | −1.56326 | ||||||||
\(472\) | −25.9660 | −1.19518 | ||||||||
\(473\) | −7.56478 | −0.347829 | ||||||||
\(474\) | −21.7908 | −1.00089 | ||||||||
\(475\) | 2.84494 | 0.130535 | ||||||||
\(476\) | −16.3104 | −0.747585 | ||||||||
\(477\) | −0.385490 | −0.0176504 | ||||||||
\(478\) | 46.3097 | 2.11816 | ||||||||
\(479\) | −3.88622 | −0.177566 | −0.0887831 | − | 0.996051i | \(-0.528298\pi\) | ||||
−0.0887831 | + | 0.996051i | \(0.528298\pi\) | |||||||
\(480\) | 29.8708 | 1.36341 | ||||||||
\(481\) | −4.26358 | −0.194402 | ||||||||
\(482\) | −53.4733 | −2.43564 | ||||||||
\(483\) | −16.3216 | −0.742659 | ||||||||
\(484\) | −45.3463 | −2.06120 | ||||||||
\(485\) | −21.4611 | −0.974497 | ||||||||
\(486\) | −3.25279 | −0.147549 | ||||||||
\(487\) | −9.32802 | −0.422693 | −0.211347 | − | 0.977411i | \(-0.567785\pi\) | ||||
−0.211347 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(488\) | −81.6549 | −3.69634 | ||||||||
\(489\) | −35.4844 | −1.60466 | ||||||||
\(490\) | 29.1198 | 1.31550 | ||||||||
\(491\) | −16.5907 | −0.748730 | −0.374365 | − | 0.927281i | \(-0.622139\pi\) | ||||
−0.374365 | + | 0.927281i | \(0.622139\pi\) | |||||||
\(492\) | 52.7673 | 2.37893 | ||||||||
\(493\) | −10.7275 | −0.483140 | ||||||||
\(494\) | 0.828394 | 0.0372712 | ||||||||
\(495\) | 0.387226 | 0.0174045 | ||||||||
\(496\) | 27.4893 | 1.23431 | ||||||||
\(497\) | −23.0326 | −1.03315 | ||||||||
\(498\) | 65.7614 | 2.94684 | ||||||||
\(499\) | −6.37068 | −0.285191 | −0.142595 | − | 0.989781i | \(-0.545545\pi\) | ||||
−0.142595 | + | 0.989781i | \(0.545545\pi\) | |||||||
\(500\) | 60.2784 | 2.69573 | ||||||||
\(501\) | 34.1641 | 1.52634 | ||||||||
\(502\) | −11.0629 | −0.493762 | ||||||||
\(503\) | 21.8938 | 0.976196 | 0.488098 | − | 0.872789i | \(-0.337691\pi\) | ||||
0.488098 | + | 0.872789i | \(0.337691\pi\) | |||||||
\(504\) | −1.48852 | −0.0663037 | ||||||||
\(505\) | −9.78217 | −0.435301 | ||||||||
\(506\) | −10.0238 | −0.445613 | ||||||||
\(507\) | −1.76740 | −0.0784931 | ||||||||
\(508\) | −27.0357 | −1.19951 | ||||||||
\(509\) | 3.72354 | 0.165043 | 0.0825216 | − | 0.996589i | \(-0.473703\pi\) | ||||
0.0825216 | + | 0.996589i | \(0.473703\pi\) | |||||||
\(510\) | −31.0487 | −1.37486 | ||||||||
\(511\) | 12.0224 | 0.531842 | ||||||||
\(512\) | 50.5354 | 2.23337 | ||||||||
\(513\) | 1.66343 | 0.0734422 | ||||||||
\(514\) | 39.2987 | 1.73339 | ||||||||
\(515\) | −25.3492 | −1.11702 | ||||||||
\(516\) | 69.6963 | 3.06821 | ||||||||
\(517\) | 3.18580 | 0.140111 | ||||||||
\(518\) | −21.2935 | −0.935582 | ||||||||
\(519\) | −26.1736 | −1.14890 | ||||||||
\(520\) | 22.5702 | 0.989768 | ||||||||
\(521\) | 23.3076 | 1.02113 | 0.510563 | − | 0.859840i | \(-0.329437\pi\) | ||||
0.510563 | + | 0.859840i | \(0.329437\pi\) | |||||||
\(522\) | −1.79175 | −0.0784227 | ||||||||
\(523\) | −41.9169 | −1.83290 | −0.916449 | − | 0.400151i | \(-0.868958\pi\) | ||||
−0.916449 | + | 0.400151i | \(0.868958\pi\) | |||||||
\(524\) | 33.0422 | 1.44346 | ||||||||
\(525\) | −30.3141 | −1.32301 | ||||||||
\(526\) | −79.9203 | −3.48469 | ||||||||
\(527\) | −7.78377 | −0.339066 | ||||||||
\(528\) | −9.89973 | −0.430830 | ||||||||
\(529\) | −1.08657 | −0.0472420 | ||||||||
\(530\) | 29.1922 | 1.26803 | ||||||||
\(531\) | 0.526693 | 0.0228565 | ||||||||
\(532\) | 2.84619 | 0.123398 | ||||||||
\(533\) | 6.77134 | 0.293299 | ||||||||
\(534\) | −27.2165 | −1.17777 | ||||||||
\(535\) | 11.8428 | 0.512010 | ||||||||
\(536\) | −54.8516 | −2.36923 | ||||||||
\(537\) | −11.6554 | −0.502969 | ||||||||
\(538\) | −74.0249 | −3.19144 | ||||||||
\(539\) | −2.62902 | −0.113240 | ||||||||
\(540\) | 82.9456 | 3.56941 | ||||||||
\(541\) | 35.8528 | 1.54143 | 0.770717 | − | 0.637178i | \(-0.219898\pi\) | ||||
0.770717 | + | 0.637178i | \(0.219898\pi\) | |||||||
\(542\) | 22.7781 | 0.978404 | ||||||||
\(543\) | −11.3716 | −0.488000 | ||||||||
\(544\) | 8.56402 | 0.367179 | ||||||||
\(545\) | 16.5743 | 0.709967 | ||||||||
\(546\) | −8.82690 | −0.377756 | ||||||||
\(547\) | 35.5768 | 1.52115 | 0.760577 | − | 0.649248i | \(-0.224916\pi\) | ||||
0.760577 | + | 0.649248i | \(0.224916\pi\) | |||||||
\(548\) | −12.3468 | −0.527430 | ||||||||
\(549\) | 1.65628 | 0.0706884 | ||||||||
\(550\) | −18.6172 | −0.793839 | ||||||||
\(551\) | 1.87196 | 0.0797482 | ||||||||
\(552\) | 50.4610 | 2.14776 | ||||||||
\(553\) | −9.60749 | −0.408552 | ||||||||
\(554\) | 13.7632 | 0.584741 | ||||||||
\(555\) | −27.8856 | −1.18368 | ||||||||
\(556\) | 83.7447 | 3.55157 | ||||||||
\(557\) | 7.82800 | 0.331683 | 0.165841 | − | 0.986152i | \(-0.446966\pi\) | ||||
0.165841 | + | 0.986152i | \(0.446966\pi\) | |||||||
\(558\) | −1.30008 | −0.0550368 | ||||||||
\(559\) | 8.94374 | 0.378280 | ||||||||
\(560\) | 48.3451 | 2.04296 | ||||||||
\(561\) | 2.80317 | 0.118350 | ||||||||
\(562\) | −55.9602 | −2.36054 | ||||||||
\(563\) | 18.3991 | 0.775431 | 0.387716 | − | 0.921779i | \(-0.373264\pi\) | ||||
0.387716 | + | 0.921779i | \(0.373264\pi\) | |||||||
\(564\) | −29.3516 | −1.23593 | ||||||||
\(565\) | 39.5428 | 1.66358 | ||||||||
\(566\) | 48.3282 | 2.03138 | ||||||||
\(567\) | −18.4567 | −0.775110 | ||||||||
\(568\) | 71.2090 | 2.98786 | ||||||||
\(569\) | −26.6254 | −1.11619 | −0.558097 | − | 0.829776i | \(-0.688468\pi\) | ||||
−0.558097 | + | 0.829776i | \(0.688468\pi\) | |||||||
\(570\) | 5.41805 | 0.226937 | ||||||||
\(571\) | −23.1096 | −0.967107 | −0.483553 | − | 0.875315i | \(-0.660654\pi\) | ||||
−0.483553 | + | 0.875315i | \(0.660654\pi\) | |||||||
\(572\) | −3.72934 | −0.155932 | ||||||||
\(573\) | −39.8603 | −1.66519 | ||||||||
\(574\) | 33.8179 | 1.41153 | ||||||||
\(575\) | 40.6997 | 1.69730 | ||||||||
\(576\) | −0.208138 | −0.00867243 | ||||||||
\(577\) | 41.4684 | 1.72635 | 0.863177 | − | 0.504902i | \(-0.168471\pi\) | ||||
0.863177 | + | 0.504902i | \(0.168471\pi\) | |||||||
\(578\) | 34.1360 | 1.41987 | ||||||||
\(579\) | 0.753542 | 0.0313162 | ||||||||
\(580\) | 93.3439 | 3.87589 | ||||||||
\(581\) | 28.9940 | 1.20287 | ||||||||
\(582\) | −25.9488 | −1.07561 | ||||||||
\(583\) | −2.63557 | −0.109154 | ||||||||
\(584\) | −37.1694 | −1.53808 | ||||||||
\(585\) | −0.457812 | −0.0189282 | ||||||||
\(586\) | 4.48415 | 0.185238 | ||||||||
\(587\) | −17.4452 | −0.720039 | −0.360019 | − | 0.932945i | \(-0.617230\pi\) | ||||
−0.360019 | + | 0.932945i | \(0.617230\pi\) | |||||||
\(588\) | 24.2219 | 0.998893 | ||||||||
\(589\) | 1.35828 | 0.0559670 | ||||||||
\(590\) | −39.8852 | −1.64205 | ||||||||
\(591\) | −6.69912 | −0.275565 | ||||||||
\(592\) | 28.2348 | 1.16044 | ||||||||
\(593\) | −26.2024 | −1.07600 | −0.538001 | − | 0.842944i | \(-0.680820\pi\) | ||||
−0.538001 | + | 0.842944i | \(0.680820\pi\) | |||||||
\(594\) | −10.8854 | −0.446634 | ||||||||
\(595\) | −13.6892 | −0.561204 | ||||||||
\(596\) | −33.8310 | −1.38577 | ||||||||
\(597\) | 44.5807 | 1.82457 | ||||||||
\(598\) | 11.8510 | 0.484624 | ||||||||
\(599\) | −27.6202 | −1.12853 | −0.564265 | − | 0.825594i | \(-0.690840\pi\) | ||||
−0.564265 | + | 0.825594i | \(0.690840\pi\) | |||||||
\(600\) | 93.7209 | 3.82614 | ||||||||
\(601\) | −21.7782 | −0.888352 | −0.444176 | − | 0.895939i | \(-0.646504\pi\) | ||||
−0.444176 | + | 0.895939i | \(0.646504\pi\) | |||||||
\(602\) | 44.6675 | 1.82051 | ||||||||
\(603\) | 1.11261 | 0.0453088 | ||||||||
\(604\) | −30.0416 | −1.22237 | ||||||||
\(605\) | −38.0590 | −1.54732 | ||||||||
\(606\) | −11.8277 | −0.480468 | ||||||||
\(607\) | −23.6448 | −0.959711 | −0.479855 | − | 0.877348i | \(-0.659311\pi\) | ||||
−0.479855 | + | 0.877348i | \(0.659311\pi\) | |||||||
\(608\) | −1.49444 | −0.0606074 | ||||||||
\(609\) | −19.9466 | −0.808275 | ||||||||
\(610\) | −125.426 | −5.07836 | ||||||||
\(611\) | −3.76653 | −0.152378 | ||||||||
\(612\) | −1.02284 | −0.0413459 | ||||||||
\(613\) | 15.0643 | 0.608440 | 0.304220 | − | 0.952602i | \(-0.401604\pi\) | ||||
0.304220 | + | 0.952602i | \(0.401604\pi\) | |||||||
\(614\) | 58.7642 | 2.37153 | ||||||||
\(615\) | 44.2874 | 1.78584 | ||||||||
\(616\) | −10.1769 | −0.410038 | ||||||||
\(617\) | 34.6714 | 1.39582 | 0.697909 | − | 0.716186i | \(-0.254114\pi\) | ||||
0.697909 | + | 0.716186i | \(0.254114\pi\) | |||||||
\(618\) | −30.6499 | −1.23292 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 67.7297 | 2.72009 | ||||||||
\(621\) | 23.7970 | 0.954942 | ||||||||
\(622\) | −40.1929 | −1.61159 | ||||||||
\(623\) | −11.9997 | −0.480756 | ||||||||
\(624\) | 11.7043 | 0.468548 | ||||||||
\(625\) | 7.11978 | 0.284791 | ||||||||
\(626\) | −28.6967 | −1.14695 | ||||||||
\(627\) | −0.489158 | −0.0195351 | ||||||||
\(628\) | 84.6369 | 3.37738 | ||||||||
\(629\) | −7.99486 | −0.318776 | ||||||||
\(630\) | −2.28644 | −0.0910939 | ||||||||
\(631\) | −11.8685 | −0.472477 | −0.236238 | − | 0.971695i | \(-0.575915\pi\) | ||||
−0.236238 | + | 0.971695i | \(0.575915\pi\) | |||||||
\(632\) | 29.7031 | 1.18153 | ||||||||
\(633\) | 24.0562 | 0.956150 | ||||||||
\(634\) | −47.2938 | −1.87828 | ||||||||
\(635\) | −22.6910 | −0.900463 | ||||||||
\(636\) | 24.2822 | 0.962850 | ||||||||
\(637\) | 3.10826 | 0.123154 | ||||||||
\(638\) | −12.2500 | −0.484984 | ||||||||
\(639\) | −1.44440 | −0.0571395 | ||||||||
\(640\) | 49.5637 | 1.95918 | ||||||||
\(641\) | 4.74522 | 0.187425 | 0.0937124 | − | 0.995599i | \(-0.470127\pi\) | ||||
0.0937124 | + | 0.995599i | \(0.470127\pi\) | |||||||
\(642\) | 14.3193 | 0.565136 | ||||||||
\(643\) | −10.9002 | −0.429861 | −0.214931 | − | 0.976629i | \(-0.568953\pi\) | ||||
−0.214931 | + | 0.976629i | \(0.568953\pi\) | |||||||
\(644\) | 40.7176 | 1.60450 | ||||||||
\(645\) | 58.4959 | 2.30327 | ||||||||
\(646\) | 1.55336 | 0.0611163 | ||||||||
\(647\) | 31.6637 | 1.24483 | 0.622414 | − | 0.782689i | \(-0.286152\pi\) | ||||
0.622414 | + | 0.782689i | \(0.286152\pi\) | |||||||
\(648\) | 57.0620 | 2.24161 | ||||||||
\(649\) | 3.60096 | 0.141350 | ||||||||
\(650\) | 22.0108 | 0.863336 | ||||||||
\(651\) | −14.4731 | −0.567245 | ||||||||
\(652\) | 88.5232 | 3.46684 | ||||||||
\(653\) | −14.8689 | −0.581867 | −0.290933 | − | 0.956743i | \(-0.593966\pi\) | ||||
−0.290933 | + | 0.956743i | \(0.593966\pi\) | |||||||
\(654\) | 20.0402 | 0.783633 | ||||||||
\(655\) | 27.7322 | 1.08359 | ||||||||
\(656\) | −44.8420 | −1.75078 | ||||||||
\(657\) | 0.753941 | 0.0294140 | ||||||||
\(658\) | −18.8111 | −0.733333 | ||||||||
\(659\) | −42.1798 | −1.64309 | −0.821546 | − | 0.570142i | \(-0.806888\pi\) | ||||
−0.821546 | + | 0.570142i | \(0.806888\pi\) | |||||||
\(660\) | −24.3915 | −0.949438 | ||||||||
\(661\) | −12.4500 | −0.484250 | −0.242125 | − | 0.970245i | \(-0.577844\pi\) | ||||
−0.242125 | + | 0.970245i | \(0.577844\pi\) | |||||||
\(662\) | −36.5449 | −1.42036 | ||||||||
\(663\) | −3.31415 | −0.128711 | ||||||||
\(664\) | −89.6396 | −3.47869 | ||||||||
\(665\) | 2.38880 | 0.0926335 | ||||||||
\(666\) | −1.33534 | −0.0517433 | ||||||||
\(667\) | 26.7803 | 1.03694 | ||||||||
\(668\) | −85.2295 | −3.29763 | ||||||||
\(669\) | 51.0026 | 1.97187 | ||||||||
\(670\) | −84.2550 | −3.25505 | ||||||||
\(671\) | 11.3239 | 0.437153 | ||||||||
\(672\) | 15.9239 | 0.614277 | ||||||||
\(673\) | −15.4851 | −0.596906 | −0.298453 | − | 0.954424i | \(-0.596471\pi\) | ||||
−0.298453 | + | 0.954424i | \(0.596471\pi\) | |||||||
\(674\) | −61.9750 | −2.38719 | ||||||||
\(675\) | 44.1981 | 1.70119 | ||||||||
\(676\) | 4.40915 | 0.169583 | ||||||||
\(677\) | −30.1595 | −1.15912 | −0.579562 | − | 0.814928i | \(-0.696776\pi\) | ||||
−0.579562 | + | 0.814928i | \(0.696776\pi\) | |||||||
\(678\) | 47.8115 | 1.83619 | ||||||||
\(679\) | −11.4407 | −0.439054 | ||||||||
\(680\) | 42.3225 | 1.62300 | ||||||||
\(681\) | 17.7993 | 0.682072 | ||||||||
\(682\) | −8.88855 | −0.340360 | ||||||||
\(683\) | 1.57949 | 0.0604374 | 0.0302187 | − | 0.999543i | \(-0.490380\pi\) | ||||
0.0302187 | + | 0.999543i | \(0.490380\pi\) | |||||||
\(684\) | 0.178488 | 0.00682465 | ||||||||
\(685\) | −10.3626 | −0.395936 | ||||||||
\(686\) | 50.4834 | 1.92747 | ||||||||
\(687\) | 37.5677 | 1.43330 | ||||||||
\(688\) | −59.2283 | −2.25806 | ||||||||
\(689\) | 3.11599 | 0.118710 | ||||||||
\(690\) | 77.5107 | 2.95078 | ||||||||
\(691\) | −5.28678 | −0.201118 | −0.100559 | − | 0.994931i | \(-0.532063\pi\) | ||||
−0.100559 | + | 0.994931i | \(0.532063\pi\) | |||||||
\(692\) | 65.2956 | 2.48217 | ||||||||
\(693\) | 0.206427 | 0.00784150 | ||||||||
\(694\) | 22.8877 | 0.868807 | ||||||||
\(695\) | 70.2866 | 2.66612 | ||||||||
\(696\) | 61.6681 | 2.33752 | ||||||||
\(697\) | 12.6973 | 0.480944 | ||||||||
\(698\) | −16.2361 | −0.614546 | ||||||||
\(699\) | −36.1541 | −1.36747 | ||||||||
\(700\) | 75.6247 | 2.85834 | ||||||||
\(701\) | 0.265272 | 0.0100192 | 0.00500958 | − | 0.999987i | \(-0.498405\pi\) | ||||
0.00500958 | + | 0.999987i | \(0.498405\pi\) | |||||||
\(702\) | 12.8697 | 0.485735 | ||||||||
\(703\) | 1.39512 | 0.0526178 | ||||||||
\(704\) | −1.42303 | −0.0536323 | ||||||||
\(705\) | −24.6347 | −0.927797 | ||||||||
\(706\) | −43.3103 | −1.63001 | ||||||||
\(707\) | −5.21479 | −0.196122 | ||||||||
\(708\) | −33.1766 | −1.24685 | ||||||||
\(709\) | 1.61232 | 0.0605520 | 0.0302760 | − | 0.999542i | \(-0.490361\pi\) | ||||
0.0302760 | + | 0.999542i | \(0.490361\pi\) | |||||||
\(710\) | 109.381 | 4.10499 | ||||||||
\(711\) | −0.602496 | −0.0225954 | ||||||||
\(712\) | 37.0989 | 1.39034 | ||||||||
\(713\) | 19.4316 | 0.727719 | ||||||||
\(714\) | −16.5518 | −0.619435 | ||||||||
\(715\) | −3.13002 | −0.117056 | ||||||||
\(716\) | 29.0769 | 1.08665 | ||||||||
\(717\) | 32.3301 | 1.20739 | ||||||||
\(718\) | 31.6463 | 1.18103 | ||||||||
\(719\) | −24.2792 | −0.905462 | −0.452731 | − | 0.891647i | \(-0.649550\pi\) | ||||
−0.452731 | + | 0.891647i | \(0.649550\pi\) | |||||||
\(720\) | 3.03178 | 0.112988 | ||||||||
\(721\) | −13.5134 | −0.503266 | ||||||||
\(722\) | 47.8299 | 1.78005 | ||||||||
\(723\) | −37.3312 | −1.38836 | ||||||||
\(724\) | 28.3687 | 1.05431 | ||||||||
\(725\) | 49.7389 | 1.84726 | ||||||||
\(726\) | −46.0175 | −1.70787 | ||||||||
\(727\) | −28.8320 | −1.06932 | −0.534660 | − | 0.845067i | \(-0.679560\pi\) | ||||
−0.534660 | + | 0.845067i | \(0.679560\pi\) | |||||||
\(728\) | 12.0320 | 0.445934 | ||||||||
\(729\) | 25.7966 | 0.955431 | ||||||||
\(730\) | −57.0941 | −2.11315 | ||||||||
\(731\) | 16.7709 | 0.620293 | ||||||||
\(732\) | −104.330 | −3.85614 | ||||||||
\(733\) | −30.4058 | −1.12306 | −0.561532 | − | 0.827455i | \(-0.689788\pi\) | ||||
−0.561532 | + | 0.827455i | \(0.689788\pi\) | |||||||
\(734\) | −13.3874 | −0.494136 | ||||||||
\(735\) | 20.3293 | 0.749858 | ||||||||
\(736\) | −21.3794 | −0.788056 | ||||||||
\(737\) | 7.60680 | 0.280200 | ||||||||
\(738\) | 2.12076 | 0.0780662 | ||||||||
\(739\) | 21.7593 | 0.800429 | 0.400215 | − | 0.916421i | \(-0.368936\pi\) | ||||
0.400215 | + | 0.916421i | \(0.368936\pi\) | |||||||
\(740\) | 69.5664 | 2.55731 | ||||||||
\(741\) | 0.578325 | 0.0212453 | ||||||||
\(742\) | 15.5621 | 0.571304 | ||||||||
\(743\) | −16.8152 | −0.616891 | −0.308446 | − | 0.951242i | \(-0.599809\pi\) | ||||
−0.308446 | + | 0.951242i | \(0.599809\pi\) | |||||||
\(744\) | 44.7459 | 1.64047 | ||||||||
\(745\) | −28.3943 | −1.04029 | ||||||||
\(746\) | −24.6728 | −0.903334 | ||||||||
\(747\) | 1.81824 | 0.0665260 | ||||||||
\(748\) | −6.99309 | −0.255693 | ||||||||
\(749\) | 6.31331 | 0.230683 | ||||||||
\(750\) | 61.1706 | 2.23363 | ||||||||
\(751\) | 47.0763 | 1.71784 | 0.858919 | − | 0.512111i | \(-0.171136\pi\) | ||||
0.858919 | + | 0.512111i | \(0.171136\pi\) | |||||||
\(752\) | 24.9432 | 0.909584 | ||||||||
\(753\) | −7.72334 | −0.281454 | ||||||||
\(754\) | 14.4831 | 0.527442 | ||||||||
\(755\) | −25.2138 | −0.917623 | ||||||||
\(756\) | 44.2176 | 1.60818 | ||||||||
\(757\) | −5.47143 | −0.198863 | −0.0994313 | − | 0.995044i | \(-0.531702\pi\) | ||||
−0.0994313 | + | 0.995044i | \(0.531702\pi\) | |||||||
\(758\) | −46.2941 | −1.68148 | ||||||||
\(759\) | −6.99791 | −0.254008 | ||||||||
\(760\) | −7.38536 | −0.267895 | ||||||||
\(761\) | 47.4111 | 1.71865 | 0.859326 | − | 0.511429i | \(-0.170884\pi\) | ||||
0.859326 | + | 0.511429i | \(0.170884\pi\) | |||||||
\(762\) | −27.4358 | −0.993895 | ||||||||
\(763\) | 8.83564 | 0.319872 | ||||||||
\(764\) | 99.4399 | 3.59761 | ||||||||
\(765\) | −0.858467 | −0.0310379 | ||||||||
\(766\) | 3.54012 | 0.127910 | ||||||||
\(767\) | −4.25737 | −0.153725 | ||||||||
\(768\) | 53.9809 | 1.94787 | ||||||||
\(769\) | 15.2573 | 0.550192 | 0.275096 | − | 0.961417i | \(-0.411290\pi\) | ||||
0.275096 | + | 0.961417i | \(0.411290\pi\) | |||||||
\(770\) | −15.6322 | −0.563345 | ||||||||
\(771\) | 27.4356 | 0.988068 | ||||||||
\(772\) | −1.87987 | −0.0676579 | ||||||||
\(773\) | 16.1020 | 0.579149 | 0.289575 | − | 0.957155i | \(-0.406486\pi\) | ||||
0.289575 | + | 0.957155i | \(0.406486\pi\) | |||||||
\(774\) | 2.80115 | 0.100685 | ||||||||
\(775\) | 36.0902 | 1.29640 | ||||||||
\(776\) | 35.3709 | 1.26974 | ||||||||
\(777\) | −14.8656 | −0.533300 | ||||||||
\(778\) | −5.32586 | −0.190941 | ||||||||
\(779\) | −2.21570 | −0.0793857 | ||||||||
\(780\) | 28.8377 | 1.03256 | ||||||||
\(781\) | −9.87524 | −0.353364 | ||||||||
\(782\) | 22.2225 | 0.794673 | ||||||||
\(783\) | 29.0822 | 1.03931 | ||||||||
\(784\) | −20.5839 | −0.735139 | ||||||||
\(785\) | 71.0355 | 2.53536 | ||||||||
\(786\) | 33.5313 | 1.19602 | ||||||||
\(787\) | −3.75967 | −0.134018 | −0.0670089 | − | 0.997752i | \(-0.521346\pi\) | ||||
−0.0670089 | + | 0.997752i | \(0.521346\pi\) | |||||||
\(788\) | 16.7123 | 0.595352 | ||||||||
\(789\) | −55.7946 | −1.98634 | ||||||||
\(790\) | 45.6256 | 1.62329 | ||||||||
\(791\) | 21.0799 | 0.749515 | ||||||||
\(792\) | −0.638203 | −0.0226775 | ||||||||
\(793\) | −13.3881 | −0.475424 | ||||||||
\(794\) | −41.1456 | −1.46020 | ||||||||
\(795\) | 20.3799 | 0.722801 | ||||||||
\(796\) | −111.216 | −3.94194 | ||||||||
\(797\) | 42.6233 | 1.50980 | 0.754898 | − | 0.655842i | \(-0.227686\pi\) | ||||
0.754898 | + | 0.655842i | \(0.227686\pi\) | |||||||
\(798\) | 2.88831 | 0.102245 | ||||||||
\(799\) | −7.06282 | −0.249865 | ||||||||
\(800\) | −39.7079 | −1.40389 | ||||||||
\(801\) | −0.752512 | −0.0265887 | ||||||||
\(802\) | −40.8223 | −1.44148 | ||||||||
\(803\) | 5.15464 | 0.181903 | ||||||||
\(804\) | −70.0835 | −2.47165 | ||||||||
\(805\) | 34.1742 | 1.20448 | ||||||||
\(806\) | 10.5088 | 0.370157 | ||||||||
\(807\) | −51.6789 | −1.81918 | ||||||||
\(808\) | 16.1224 | 0.567184 | ||||||||
\(809\) | 40.4062 | 1.42061 | 0.710303 | − | 0.703896i | \(-0.248558\pi\) | ||||
0.710303 | + | 0.703896i | \(0.248558\pi\) | |||||||
\(810\) | 87.6503 | 3.07972 | ||||||||
\(811\) | 49.2665 | 1.72998 | 0.864990 | − | 0.501789i | \(-0.167325\pi\) | ||||
0.864990 | + | 0.501789i | \(0.167325\pi\) | |||||||
\(812\) | 49.7608 | 1.74626 | ||||||||
\(813\) | 15.9020 | 0.557709 | ||||||||
\(814\) | −9.12960 | −0.319992 | ||||||||
\(815\) | 74.2972 | 2.60252 | ||||||||
\(816\) | 21.9474 | 0.768312 | ||||||||
\(817\) | −2.92655 | −0.102387 | ||||||||
\(818\) | 10.6778 | 0.373341 | ||||||||
\(819\) | −0.244056 | −0.00852799 | ||||||||
\(820\) | −110.484 | −3.85827 | ||||||||
\(821\) | 32.9830 | 1.15111 | 0.575557 | − | 0.817762i | \(-0.304785\pi\) | ||||
0.575557 | + | 0.817762i | \(0.304785\pi\) | |||||||
\(822\) | −12.5296 | −0.437019 | ||||||||
\(823\) | −5.30776 | −0.185017 | −0.0925085 | − | 0.995712i | \(-0.529489\pi\) | ||||
−0.0925085 | + | 0.995712i | \(0.529489\pi\) | |||||||
\(824\) | 41.7790 | 1.45544 | ||||||||
\(825\) | −12.9972 | −0.452504 | ||||||||
\(826\) | −21.2625 | −0.739816 | ||||||||
\(827\) | 50.0827 | 1.74154 | 0.870772 | − | 0.491687i | \(-0.163619\pi\) | ||||
0.870772 | + | 0.491687i | \(0.163619\pi\) | |||||||
\(828\) | 2.55345 | 0.0887384 | ||||||||
\(829\) | −43.5847 | −1.51376 | −0.756880 | − | 0.653554i | \(-0.773277\pi\) | ||||
−0.756880 | + | 0.653554i | \(0.773277\pi\) | |||||||
\(830\) | −137.691 | −4.77933 | ||||||||
\(831\) | 9.60845 | 0.333314 | ||||||||
\(832\) | 1.68242 | 0.0583276 | ||||||||
\(833\) | 5.82846 | 0.201944 | ||||||||
\(834\) | 84.9842 | 2.94276 | ||||||||
\(835\) | −71.5328 | −2.47550 | ||||||||
\(836\) | 1.22031 | 0.0422052 | ||||||||
\(837\) | 21.1019 | 0.729387 | ||||||||
\(838\) | 13.4031 | 0.463001 | ||||||||
\(839\) | −15.8576 | −0.547467 | −0.273733 | − | 0.961806i | \(-0.588259\pi\) | ||||
−0.273733 | + | 0.961806i | \(0.588259\pi\) | |||||||
\(840\) | 78.6942 | 2.71521 | ||||||||
\(841\) | 3.72807 | 0.128554 | ||||||||
\(842\) | 30.2346 | 1.04195 | ||||||||
\(843\) | −39.0674 | −1.34555 | ||||||||
\(844\) | −60.0133 | −2.06574 | ||||||||
\(845\) | 3.70059 | 0.127304 | ||||||||
\(846\) | −1.17966 | −0.0405577 | ||||||||
\(847\) | −20.2889 | −0.697136 | ||||||||
\(848\) | −20.6351 | −0.708613 | ||||||||
\(849\) | 33.7393 | 1.15793 | ||||||||
\(850\) | 41.2737 | 1.41568 | ||||||||
\(851\) | 19.9586 | 0.684171 | ||||||||
\(852\) | 90.9832 | 3.11703 | ||||||||
\(853\) | −11.2327 | −0.384600 | −0.192300 | − | 0.981336i | \(-0.561595\pi\) | ||||
−0.192300 | + | 0.981336i | \(0.561595\pi\) | |||||||
\(854\) | −66.8636 | −2.28803 | ||||||||
\(855\) | 0.149804 | 0.00512319 | ||||||||
\(856\) | −19.5186 | −0.667133 | ||||||||
\(857\) | −33.2638 | −1.13627 | −0.568135 | − | 0.822936i | \(-0.692335\pi\) | ||||
−0.568135 | + | 0.822936i | \(0.692335\pi\) | |||||||
\(858\) | −3.78454 | −0.129202 | ||||||||
\(859\) | −48.2838 | −1.64742 | −0.823710 | − | 0.567011i | \(-0.808100\pi\) | ||||
−0.823710 | + | 0.567011i | \(0.808100\pi\) | |||||||
\(860\) | −145.930 | −4.97617 | ||||||||
\(861\) | 23.6092 | 0.804601 | ||||||||
\(862\) | 103.898 | 3.53878 | ||||||||
\(863\) | 7.07146 | 0.240715 | 0.120358 | − | 0.992731i | \(-0.461596\pi\) | ||||
0.120358 | + | 0.992731i | \(0.461596\pi\) | |||||||
\(864\) | −23.2171 | −0.789863 | ||||||||
\(865\) | 54.8023 | 1.86334 | ||||||||
\(866\) | −33.6792 | −1.14446 | ||||||||
\(867\) | 23.8313 | 0.809354 | ||||||||
\(868\) | 36.1061 | 1.22552 | ||||||||
\(869\) | −4.11922 | −0.139735 | ||||||||
\(870\) | 94.7254 | 3.21149 | ||||||||
\(871\) | −8.99342 | −0.304730 | ||||||||
\(872\) | −27.3168 | −0.925065 | ||||||||
\(873\) | −0.717460 | −0.0242823 | ||||||||
\(874\) | −3.87786 | −0.131171 | ||||||||
\(875\) | 26.9699 | 0.911748 | ||||||||
\(876\) | −47.4910 | −1.60457 | ||||||||
\(877\) | −28.3640 | −0.957786 | −0.478893 | − | 0.877873i | \(-0.658962\pi\) | ||||
−0.478893 | + | 0.877873i | \(0.658962\pi\) | |||||||
\(878\) | 54.3867 | 1.83546 | ||||||||
\(879\) | 3.13051 | 0.105589 | ||||||||
\(880\) | 20.7280 | 0.698742 | ||||||||
\(881\) | 47.4819 | 1.59971 | 0.799853 | − | 0.600196i | \(-0.204911\pi\) | ||||
0.799853 | + | 0.600196i | \(0.204911\pi\) | |||||||
\(882\) | 0.973495 | 0.0327793 | ||||||||
\(883\) | 47.4445 | 1.59663 | 0.798317 | − | 0.602237i | \(-0.205724\pi\) | ||||
0.798317 | + | 0.602237i | \(0.205724\pi\) | |||||||
\(884\) | 8.26783 | 0.278077 | ||||||||
\(885\) | −27.8450 | −0.935999 | ||||||||
\(886\) | −61.6473 | −2.07108 | ||||||||
\(887\) | −5.05011 | −0.169566 | −0.0847830 | − | 0.996399i | \(-0.527020\pi\) | ||||
−0.0847830 | + | 0.996399i | \(0.527020\pi\) | |||||||
\(888\) | 45.9594 | 1.54230 | ||||||||
\(889\) | −12.0964 | −0.405699 | ||||||||
\(890\) | 56.9859 | 1.91017 | ||||||||
\(891\) | −7.91334 | −0.265107 | ||||||||
\(892\) | −127.236 | −4.26019 | ||||||||
\(893\) | 1.23247 | 0.0412432 | ||||||||
\(894\) | −34.3318 | −1.14823 | ||||||||
\(895\) | 24.4041 | 0.815739 | ||||||||
\(896\) | 26.4220 | 0.882697 | ||||||||
\(897\) | 8.27353 | 0.276245 | ||||||||
\(898\) | 31.6846 | 1.05733 | ||||||||
\(899\) | 23.7473 | 0.792015 | ||||||||
\(900\) | 4.74251 | 0.158084 | ||||||||
\(901\) | 5.84296 | 0.194657 | ||||||||
\(902\) | 14.4995 | 0.482779 | ||||||||
\(903\) | 31.1836 | 1.03773 | ||||||||
\(904\) | −65.1720 | −2.16759 | ||||||||
\(905\) | 23.8097 | 0.791462 | ||||||||
\(906\) | −30.4862 | −1.01284 | ||||||||
\(907\) | 1.10870 | 0.0368138 | 0.0184069 | − | 0.999831i | \(-0.494141\pi\) | ||||
0.0184069 | + | 0.999831i | \(0.494141\pi\) | |||||||
\(908\) | −44.4041 | −1.47360 | ||||||||
\(909\) | −0.327025 | −0.0108467 | ||||||||
\(910\) | 18.4817 | 0.612664 | ||||||||
\(911\) | 37.0396 | 1.22718 | 0.613588 | − | 0.789626i | \(-0.289726\pi\) | ||||
0.613588 | + | 0.789626i | \(0.289726\pi\) | |||||||
\(912\) | −3.82986 | −0.126819 | ||||||||
\(913\) | 12.4312 | 0.411412 | ||||||||
\(914\) | 6.30527 | 0.208560 | ||||||||
\(915\) | −87.5636 | −2.89476 | ||||||||
\(916\) | −93.7205 | −3.09661 | ||||||||
\(917\) | 14.7838 | 0.488204 | ||||||||
\(918\) | 24.1326 | 0.796495 | ||||||||
\(919\) | −28.7166 | −0.947274 | −0.473637 | − | 0.880720i | \(-0.657059\pi\) | ||||
−0.473637 | + | 0.880720i | \(0.657059\pi\) | |||||||
\(920\) | −105.655 | −3.48334 | ||||||||
\(921\) | 41.0250 | 1.35182 | ||||||||
\(922\) | 64.3429 | 2.11902 | ||||||||
\(923\) | 11.6754 | 0.384299 | ||||||||
\(924\) | −13.0029 | −0.427764 | ||||||||
\(925\) | 37.0690 | 1.21882 | ||||||||
\(926\) | −59.4320 | −1.95306 | ||||||||
\(927\) | −0.847442 | −0.0278336 | ||||||||
\(928\) | −26.1277 | −0.857684 | ||||||||
\(929\) | 50.2654 | 1.64916 | 0.824578 | − | 0.565749i | \(-0.191413\pi\) | ||||
0.824578 | + | 0.565749i | \(0.191413\pi\) | |||||||
\(930\) | 68.7321 | 2.25381 | ||||||||
\(931\) | −1.01708 | −0.0333333 | ||||||||
\(932\) | 90.1939 | 2.95440 | ||||||||
\(933\) | −28.0598 | −0.918637 | ||||||||
\(934\) | −83.7593 | −2.74069 | ||||||||
\(935\) | −5.86927 | −0.191946 | ||||||||
\(936\) | 0.754538 | 0.0246629 | ||||||||
\(937\) | −29.6688 | −0.969239 | −0.484619 | − | 0.874725i | \(-0.661042\pi\) | ||||
−0.484619 | + | 0.874725i | \(0.661042\pi\) | |||||||
\(938\) | −44.9156 | −1.46655 | ||||||||
\(939\) | −20.0340 | −0.653784 | ||||||||
\(940\) | 61.4564 | 2.00449 | ||||||||
\(941\) | 16.9290 | 0.551870 | 0.275935 | − | 0.961176i | \(-0.411013\pi\) | ||||
0.275935 | + | 0.961176i | \(0.411013\pi\) | |||||||
\(942\) | 85.8896 | 2.79844 | ||||||||
\(943\) | −31.6978 | −1.03222 | ||||||||
\(944\) | 28.1937 | 0.917625 | ||||||||
\(945\) | 37.1117 | 1.20724 | ||||||||
\(946\) | 19.1512 | 0.622660 | ||||||||
\(947\) | −14.1617 | −0.460193 | −0.230097 | − | 0.973168i | \(-0.573904\pi\) | ||||
−0.230097 | + | 0.973168i | \(0.573904\pi\) | |||||||
\(948\) | 37.9515 | 1.23261 | ||||||||
\(949\) | −6.09426 | −0.197828 | ||||||||
\(950\) | −7.20233 | −0.233675 | ||||||||
\(951\) | −33.0172 | −1.07066 | ||||||||
\(952\) | 22.5618 | 0.731231 | ||||||||
\(953\) | 1.75447 | 0.0568327 | 0.0284164 | − | 0.999596i | \(-0.490954\pi\) | ||||
0.0284164 | + | 0.999596i | \(0.490954\pi\) | |||||||
\(954\) | 0.975918 | 0.0315965 | ||||||||
\(955\) | 83.4595 | 2.70069 | ||||||||
\(956\) | −80.6541 | −2.60854 | ||||||||
\(957\) | −8.55211 | −0.276450 | ||||||||
\(958\) | 9.83848 | 0.317867 | ||||||||
\(959\) | −5.52423 | −0.178387 | ||||||||
\(960\) | 11.0038 | 0.355145 | ||||||||
\(961\) | −13.7692 | −0.444166 | ||||||||
\(962\) | 10.7938 | 0.348006 | ||||||||
\(963\) | 0.395914 | 0.0127582 | ||||||||
\(964\) | 93.1305 | 2.99953 | ||||||||
\(965\) | −1.57777 | −0.0507901 | ||||||||
\(966\) | 41.3203 | 1.32946 | ||||||||
\(967\) | 46.3117 | 1.48928 | 0.744642 | − | 0.667464i | \(-0.232620\pi\) | ||||
0.744642 | + | 0.667464i | \(0.232620\pi\) | |||||||
\(968\) | 62.7266 | 2.01611 | ||||||||
\(969\) | 1.08445 | 0.0348375 | ||||||||
\(970\) | 54.3315 | 1.74448 | ||||||||
\(971\) | −6.42833 | −0.206295 | −0.103147 | − | 0.994666i | \(-0.532891\pi\) | ||||
−0.103147 | + | 0.994666i | \(0.532891\pi\) | |||||||
\(972\) | 5.66514 | 0.181709 | ||||||||
\(973\) | 37.4692 | 1.20121 | ||||||||
\(974\) | 23.6151 | 0.756677 | ||||||||
\(975\) | 15.3664 | 0.492118 | ||||||||
\(976\) | 88.6601 | 2.83794 | ||||||||
\(977\) | 38.3288 | 1.22625 | 0.613124 | − | 0.789987i | \(-0.289913\pi\) | ||||
0.613124 | + | 0.789987i | \(0.289913\pi\) | |||||||
\(978\) | 89.8334 | 2.87256 | ||||||||
\(979\) | −5.14486 | −0.164431 | ||||||||
\(980\) | −50.7157 | −1.62005 | ||||||||
\(981\) | 0.554093 | 0.0176908 | ||||||||
\(982\) | 42.0016 | 1.34033 | ||||||||
\(983\) | −18.3481 | −0.585214 | −0.292607 | − | 0.956233i | \(-0.594523\pi\) | ||||
−0.292607 | + | 0.956233i | \(0.594523\pi\) | |||||||
\(984\) | −72.9919 | −2.32690 | ||||||||
\(985\) | 14.0266 | 0.446925 | ||||||||
\(986\) | 27.1580 | 0.864886 | ||||||||
\(987\) | −13.1326 | −0.418014 | ||||||||
\(988\) | −1.44275 | −0.0459001 | ||||||||
\(989\) | −41.8673 | −1.33130 | ||||||||
\(990\) | −0.980313 | −0.0311564 | ||||||||
\(991\) | −27.2405 | −0.865324 | −0.432662 | − | 0.901556i | \(-0.642426\pi\) | ||||
−0.432662 | + | 0.901556i | \(0.642426\pi\) | |||||||
\(992\) | −18.9581 | −0.601919 | ||||||||
\(993\) | −25.5130 | −0.809631 | ||||||||
\(994\) | 58.3100 | 1.84948 | ||||||||
\(995\) | −93.3430 | −2.95917 | ||||||||
\(996\) | −114.532 | −3.62908 | ||||||||
\(997\) | 19.7638 | 0.625926 | 0.312963 | − | 0.949765i | \(-0.398678\pi\) | ||||
0.312963 | + | 0.949765i | \(0.398678\pi\) | |||||||
\(998\) | 16.1282 | 0.510530 | ||||||||
\(999\) | 21.6741 | 0.685739 |
(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 | 8047.2.a.d.1.7 | ✓ | 156 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.d.1.7 | ✓ | 156 | 1.1 | even | 1 | trivial |