Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53104 | −1.78971 | −0.894857 | − | 0.446354i | \(-0.852722\pi\) | ||||
−0.894857 | + | 0.446354i | \(0.852722\pi\) | |||||||
\(3\) | 0.289125 | 0.166926 | 0.0834632 | − | 0.996511i | \(-0.473402\pi\) | ||||
0.0834632 | + | 0.996511i | \(0.473402\pi\) | |||||||
\(4\) | 4.40615 | 2.20307 | ||||||||
\(5\) | −2.52674 | −1.12999 | −0.564996 | − | 0.825094i | \(-0.691122\pi\) | ||||
−0.564996 | + | 0.825094i | \(0.691122\pi\) | |||||||
\(6\) | −0.731786 | −0.298750 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −6.09005 | −2.15316 | ||||||||
\(9\) | −2.91641 | −0.972136 | ||||||||
\(10\) | 6.39527 | 2.02236 | ||||||||
\(11\) | 3.22310 | 0.971800 | 0.485900 | − | 0.874014i | \(-0.338492\pi\) | ||||
0.485900 | + | 0.874014i | \(0.338492\pi\) | |||||||
\(12\) | 1.27393 | 0.367751 | ||||||||
\(13\) | 0.295446 | 0.0819421 | 0.0409710 | − | 0.999160i | \(-0.486955\pi\) | ||||
0.0409710 | + | 0.999160i | \(0.486955\pi\) | |||||||
\(14\) | −2.53104 | −0.676448 | ||||||||
\(15\) | −0.730544 | −0.188626 | ||||||||
\(16\) | 6.60184 | 1.65046 | ||||||||
\(17\) | −1.30810 | −0.317261 | −0.158631 | − | 0.987338i | \(-0.550708\pi\) | ||||
−0.158631 | + | 0.987338i | \(0.550708\pi\) | |||||||
\(18\) | 7.38153 | 1.73984 | ||||||||
\(19\) | −5.37595 | −1.23333 | −0.616664 | − | 0.787227i | \(-0.711516\pi\) | ||||
−0.616664 | + | 0.787227i | \(0.711516\pi\) | |||||||
\(20\) | −11.1332 | −2.48946 | ||||||||
\(21\) | 0.289125 | 0.0630923 | ||||||||
\(22\) | −8.15777 | −1.73924 | ||||||||
\(23\) | 6.32217 | 1.31826 | 0.659131 | − | 0.752028i | \(-0.270924\pi\) | ||||
0.659131 | + | 0.752028i | \(0.270924\pi\) | |||||||
\(24\) | −1.76079 | −0.359419 | ||||||||
\(25\) | 1.38441 | 0.276882 | ||||||||
\(26\) | −0.747786 | −0.146653 | ||||||||
\(27\) | −1.71058 | −0.329202 | ||||||||
\(28\) | 4.40615 | 0.832684 | ||||||||
\(29\) | −1.72339 | −0.320026 | −0.160013 | − | 0.987115i | \(-0.551154\pi\) | ||||
−0.160013 | + | 0.987115i | \(0.551154\pi\) | |||||||
\(30\) | 1.84903 | 0.337586 | ||||||||
\(31\) | 5.03594 | 0.904481 | 0.452241 | − | 0.891896i | \(-0.350625\pi\) | ||||
0.452241 | + | 0.891896i | \(0.350625\pi\) | |||||||
\(32\) | −4.52940 | −0.800693 | ||||||||
\(33\) | 0.931878 | 0.162219 | ||||||||
\(34\) | 3.31085 | 0.567806 | ||||||||
\(35\) | −2.52674 | −0.427097 | ||||||||
\(36\) | −12.8501 | −2.14169 | ||||||||
\(37\) | −10.0376 | −1.65017 | −0.825084 | − | 0.565011i | \(-0.808872\pi\) | ||||
−0.825084 | + | 0.565011i | \(0.808872\pi\) | |||||||
\(38\) | 13.6067 | 2.20730 | ||||||||
\(39\) | 0.0854210 | 0.0136783 | ||||||||
\(40\) | 15.3880 | 2.43305 | ||||||||
\(41\) | −6.07216 | −0.948312 | −0.474156 | − | 0.880441i | \(-0.657247\pi\) | ||||
−0.474156 | + | 0.880441i | \(0.657247\pi\) | |||||||
\(42\) | −0.731786 | −0.112917 | ||||||||
\(43\) | −7.48467 | −1.14140 | −0.570701 | − | 0.821158i | \(-0.693328\pi\) | ||||
−0.570701 | + | 0.821158i | \(0.693328\pi\) | |||||||
\(44\) | 14.2014 | 2.14095 | ||||||||
\(45\) | 7.36900 | 1.09851 | ||||||||
\(46\) | −16.0016 | −2.35931 | ||||||||
\(47\) | 10.8622 | 1.58441 | 0.792206 | − | 0.610253i | \(-0.208932\pi\) | ||||
0.792206 | + | 0.610253i | \(0.208932\pi\) | |||||||
\(48\) | 1.90876 | 0.275505 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.50399 | −0.495540 | ||||||||
\(51\) | −0.378205 | −0.0529593 | ||||||||
\(52\) | 1.30178 | 0.180524 | ||||||||
\(53\) | 3.83827 | 0.527227 | 0.263613 | − | 0.964628i | \(-0.415086\pi\) | ||||
0.263613 | + | 0.964628i | \(0.415086\pi\) | |||||||
\(54\) | 4.32955 | 0.589176 | ||||||||
\(55\) | −8.14392 | −1.09813 | ||||||||
\(56\) | −6.09005 | −0.813817 | ||||||||
\(57\) | −1.55432 | −0.205875 | ||||||||
\(58\) | 4.36196 | 0.572754 | ||||||||
\(59\) | 1.17293 | 0.152703 | 0.0763514 | − | 0.997081i | \(-0.475673\pi\) | ||||
0.0763514 | + | 0.997081i | \(0.475673\pi\) | |||||||
\(60\) | −3.21888 | −0.415556 | ||||||||
\(61\) | 14.4379 | 1.84859 | 0.924293 | − | 0.381684i | \(-0.124656\pi\) | ||||
0.924293 | + | 0.381684i | \(0.124656\pi\) | |||||||
\(62\) | −12.7461 | −1.61876 | ||||||||
\(63\) | −2.91641 | −0.367433 | ||||||||
\(64\) | −1.73959 | −0.217449 | ||||||||
\(65\) | −0.746516 | −0.0925939 | ||||||||
\(66\) | −2.35862 | −0.290326 | ||||||||
\(67\) | −8.85743 | −1.08211 | −0.541054 | − | 0.840988i | \(-0.681974\pi\) | ||||
−0.541054 | + | 0.840988i | \(0.681974\pi\) | |||||||
\(68\) | −5.76369 | −0.698950 | ||||||||
\(69\) | 1.82790 | 0.220053 | ||||||||
\(70\) | 6.39527 | 0.764381 | ||||||||
\(71\) | 11.0535 | 1.31181 | 0.655907 | − | 0.754842i | \(-0.272286\pi\) | ||||
0.655907 | + | 0.754842i | \(0.272286\pi\) | |||||||
\(72\) | 17.7611 | 2.09316 | ||||||||
\(73\) | −12.7184 | −1.48858 | −0.744288 | − | 0.667859i | \(-0.767211\pi\) | ||||
−0.744288 | + | 0.667859i | \(0.767211\pi\) | |||||||
\(74\) | 25.4055 | 2.95333 | ||||||||
\(75\) | 0.400268 | 0.0462189 | ||||||||
\(76\) | −23.6872 | −2.71711 | ||||||||
\(77\) | 3.22310 | 0.367306 | ||||||||
\(78\) | −0.216204 | −0.0244802 | ||||||||
\(79\) | −13.1112 | −1.47513 | −0.737564 | − | 0.675278i | \(-0.764024\pi\) | ||||
−0.737564 | + | 0.675278i | \(0.764024\pi\) | |||||||
\(80\) | −16.6811 | −1.86501 | ||||||||
\(81\) | 8.25465 | 0.917183 | ||||||||
\(82\) | 15.3689 | 1.69721 | ||||||||
\(83\) | 1.56809 | 0.172121 | 0.0860603 | − | 0.996290i | \(-0.472572\pi\) | ||||
0.0860603 | + | 0.996290i | \(0.472572\pi\) | |||||||
\(84\) | 1.27393 | 0.138997 | ||||||||
\(85\) | 3.30523 | 0.358503 | ||||||||
\(86\) | 18.9440 | 2.04278 | ||||||||
\(87\) | −0.498275 | −0.0534207 | ||||||||
\(88\) | −19.6288 | −2.09244 | ||||||||
\(89\) | 0.986945 | 0.104616 | 0.0523080 | − | 0.998631i | \(-0.483342\pi\) | ||||
0.0523080 | + | 0.998631i | \(0.483342\pi\) | |||||||
\(90\) | −18.6512 | −1.96601 | ||||||||
\(91\) | 0.295446 | 0.0309712 | ||||||||
\(92\) | 27.8564 | 2.90423 | ||||||||
\(93\) | 1.45602 | 0.150982 | ||||||||
\(94\) | −27.4926 | −2.83564 | ||||||||
\(95\) | 13.5836 | 1.39365 | ||||||||
\(96\) | −1.30956 | −0.133657 | ||||||||
\(97\) | −1.18449 | −0.120266 | −0.0601332 | − | 0.998190i | \(-0.519153\pi\) | ||||
−0.0601332 | + | 0.998190i | \(0.519153\pi\) | |||||||
\(98\) | −2.53104 | −0.255673 | ||||||||
\(99\) | −9.39986 | −0.944721 | ||||||||
\(100\) | 6.09992 | 0.609992 | ||||||||
\(101\) | −6.41675 | −0.638490 | −0.319245 | − | 0.947672i | \(-0.603429\pi\) | ||||
−0.319245 | + | 0.947672i | \(0.603429\pi\) | |||||||
\(102\) | 0.957250 | 0.0947819 | ||||||||
\(103\) | 1.18530 | 0.116792 | 0.0583958 | − | 0.998294i | \(-0.481401\pi\) | ||||
0.0583958 | + | 0.998294i | \(0.481401\pi\) | |||||||
\(104\) | −1.79928 | −0.176434 | ||||||||
\(105\) | −0.730544 | −0.0712938 | ||||||||
\(106\) | −9.71480 | −0.943585 | ||||||||
\(107\) | 12.1543 | 1.17500 | 0.587501 | − | 0.809223i | \(-0.300112\pi\) | ||||
0.587501 | + | 0.809223i | \(0.300112\pi\) | |||||||
\(108\) | −7.53707 | −0.725255 | ||||||||
\(109\) | −3.19686 | −0.306204 | −0.153102 | − | 0.988210i | \(-0.548926\pi\) | ||||
−0.153102 | + | 0.988210i | \(0.548926\pi\) | |||||||
\(110\) | 20.6126 | 1.96533 | ||||||||
\(111\) | −2.90211 | −0.275457 | ||||||||
\(112\) | 6.60184 | 0.623815 | ||||||||
\(113\) | 1.38759 | 0.130533 | 0.0652667 | − | 0.997868i | \(-0.479210\pi\) | ||||
0.0652667 | + | 0.997868i | \(0.479210\pi\) | |||||||
\(114\) | 3.93405 | 0.368457 | ||||||||
\(115\) | −15.9745 | −1.48963 | ||||||||
\(116\) | −7.59351 | −0.705040 | ||||||||
\(117\) | −0.861642 | −0.0796588 | ||||||||
\(118\) | −2.96873 | −0.273294 | ||||||||
\(119\) | −1.30810 | −0.119913 | ||||||||
\(120\) | 4.44905 | 0.406140 | ||||||||
\(121\) | −0.611653 | −0.0556048 | ||||||||
\(122\) | −36.5429 | −3.30844 | ||||||||
\(123\) | −1.75561 | −0.158298 | ||||||||
\(124\) | 22.1891 | 1.99264 | ||||||||
\(125\) | 9.13565 | 0.817118 | ||||||||
\(126\) | 7.38153 | 0.657599 | ||||||||
\(127\) | −3.11282 | −0.276218 | −0.138109 | − | 0.990417i | \(-0.544102\pi\) | ||||
−0.138109 | + | 0.990417i | \(0.544102\pi\) | |||||||
\(128\) | 13.4618 | 1.18986 | ||||||||
\(129\) | −2.16401 | −0.190530 | ||||||||
\(130\) | 1.88946 | 0.165717 | ||||||||
\(131\) | −21.9862 | −1.92094 | −0.960471 | − | 0.278381i | \(-0.910202\pi\) | ||||
−0.960471 | + | 0.278381i | \(0.910202\pi\) | |||||||
\(132\) | 4.10599 | 0.357381 | ||||||||
\(133\) | −5.37595 | −0.466154 | ||||||||
\(134\) | 22.4185 | 1.93666 | ||||||||
\(135\) | 4.32219 | 0.371995 | ||||||||
\(136\) | 7.96640 | 0.683113 | ||||||||
\(137\) | −6.38763 | −0.545732 | −0.272866 | − | 0.962052i | \(-0.587972\pi\) | ||||
−0.272866 | + | 0.962052i | \(0.587972\pi\) | |||||||
\(138\) | −4.62647 | −0.393832 | ||||||||
\(139\) | −8.41355 | −0.713628 | −0.356814 | − | 0.934175i | \(-0.616137\pi\) | ||||
−0.356814 | + | 0.934175i | \(0.616137\pi\) | |||||||
\(140\) | −11.1332 | −0.940926 | ||||||||
\(141\) | 3.14053 | 0.264480 | ||||||||
\(142\) | −27.9769 | −2.34777 | ||||||||
\(143\) | 0.952252 | 0.0796313 | ||||||||
\(144\) | −19.2536 | −1.60447 | ||||||||
\(145\) | 4.35456 | 0.361626 | ||||||||
\(146\) | 32.1907 | 2.66412 | ||||||||
\(147\) | 0.289125 | 0.0238466 | ||||||||
\(148\) | −44.2270 | −3.63544 | ||||||||
\(149\) | 12.1403 | 0.994573 | 0.497287 | − | 0.867586i | \(-0.334330\pi\) | ||||
0.497287 | + | 0.867586i | \(0.334330\pi\) | |||||||
\(150\) | −1.01309 | −0.0827187 | ||||||||
\(151\) | 2.18738 | 0.178006 | 0.0890031 | − | 0.996031i | \(-0.471632\pi\) | ||||
0.0890031 | + | 0.996031i | \(0.471632\pi\) | |||||||
\(152\) | 32.7398 | 2.65555 | ||||||||
\(153\) | 3.81496 | 0.308421 | ||||||||
\(154\) | −8.15777 | −0.657372 | ||||||||
\(155\) | −12.7245 | −1.02206 | ||||||||
\(156\) | 0.376377 | 0.0301343 | ||||||||
\(157\) | 3.01375 | 0.240524 | 0.120262 | − | 0.992742i | \(-0.461627\pi\) | ||||
0.120262 | + | 0.992742i | \(0.461627\pi\) | |||||||
\(158\) | 33.1850 | 2.64005 | ||||||||
\(159\) | 1.10974 | 0.0880081 | ||||||||
\(160\) | 11.4446 | 0.904776 | ||||||||
\(161\) | 6.32217 | 0.498256 | ||||||||
\(162\) | −20.8928 | −1.64149 | ||||||||
\(163\) | 21.4132 | 1.67721 | 0.838607 | − | 0.544737i | \(-0.183371\pi\) | ||||
0.838607 | + | 0.544737i | \(0.183371\pi\) | |||||||
\(164\) | −26.7548 | −2.08920 | ||||||||
\(165\) | −2.35461 | −0.183306 | ||||||||
\(166\) | −3.96890 | −0.308047 | ||||||||
\(167\) | −16.1730 | −1.25150 | −0.625752 | − | 0.780022i | \(-0.715208\pi\) | ||||
−0.625752 | + | 0.780022i | \(0.715208\pi\) | |||||||
\(168\) | −1.76079 | −0.135848 | ||||||||
\(169\) | −12.9127 | −0.993285 | ||||||||
\(170\) | −8.36566 | −0.641617 | ||||||||
\(171\) | 15.6785 | 1.19896 | ||||||||
\(172\) | −32.9785 | −2.51459 | ||||||||
\(173\) | 2.75549 | 0.209496 | 0.104748 | − | 0.994499i | \(-0.466596\pi\) | ||||
0.104748 | + | 0.994499i | \(0.466596\pi\) | |||||||
\(174\) | 1.26115 | 0.0956078 | ||||||||
\(175\) | 1.38441 | 0.104652 | ||||||||
\(176\) | 21.2784 | 1.60392 | ||||||||
\(177\) | 0.339124 | 0.0254901 | ||||||||
\(178\) | −2.49800 | −0.187233 | ||||||||
\(179\) | 21.0117 | 1.57049 | 0.785244 | − | 0.619187i | \(-0.212538\pi\) | ||||
0.785244 | + | 0.619187i | \(0.212538\pi\) | |||||||
\(180\) | 32.4689 | 2.42009 | ||||||||
\(181\) | −0.0902325 | −0.00670693 | −0.00335347 | − | 0.999994i | \(-0.501067\pi\) | ||||
−0.00335347 | + | 0.999994i | \(0.501067\pi\) | |||||||
\(182\) | −0.747786 | −0.0554296 | ||||||||
\(183\) | 4.17436 | 0.308578 | ||||||||
\(184\) | −38.5023 | −2.83843 | ||||||||
\(185\) | 25.3623 | 1.86468 | ||||||||
\(186\) | −3.68523 | −0.270214 | ||||||||
\(187\) | −4.21614 | −0.308314 | ||||||||
\(188\) | 47.8604 | 3.49058 | ||||||||
\(189\) | −1.71058 | −0.124427 | ||||||||
\(190\) | −34.3806 | −2.49423 | ||||||||
\(191\) | −22.4058 | −1.62123 | −0.810613 | − | 0.585582i | \(-0.800866\pi\) | ||||
−0.810613 | + | 0.585582i | \(0.800866\pi\) | |||||||
\(192\) | −0.502960 | −0.0362980 | ||||||||
\(193\) | 20.6089 | 1.48346 | 0.741731 | − | 0.670698i | \(-0.234005\pi\) | ||||
0.741731 | + | 0.670698i | \(0.234005\pi\) | |||||||
\(194\) | 2.99798 | 0.215242 | ||||||||
\(195\) | −0.215836 | −0.0154564 | ||||||||
\(196\) | 4.40615 | 0.314725 | ||||||||
\(197\) | −8.09990 | −0.577094 | −0.288547 | − | 0.957466i | \(-0.593172\pi\) | ||||
−0.288547 | + | 0.957466i | \(0.593172\pi\) | |||||||
\(198\) | 23.7914 | 1.69078 | ||||||||
\(199\) | 13.8692 | 0.983164 | 0.491582 | − | 0.870831i | \(-0.336419\pi\) | ||||
0.491582 | + | 0.870831i | \(0.336419\pi\) | |||||||
\(200\) | −8.43112 | −0.596170 | ||||||||
\(201\) | −2.56091 | −0.180632 | ||||||||
\(202\) | 16.2410 | 1.14271 | ||||||||
\(203\) | −1.72339 | −0.120958 | ||||||||
\(204\) | −1.66643 | −0.116673 | ||||||||
\(205\) | 15.3428 | 1.07158 | ||||||||
\(206\) | −3.00005 | −0.209023 | ||||||||
\(207\) | −18.4380 | −1.28153 | ||||||||
\(208\) | 1.95049 | 0.135242 | ||||||||
\(209\) | −17.3272 | −1.19855 | ||||||||
\(210\) | 1.84903 | 0.127595 | ||||||||
\(211\) | −5.08346 | −0.349960 | −0.174980 | − | 0.984572i | \(-0.555986\pi\) | ||||
−0.174980 | + | 0.984572i | \(0.555986\pi\) | |||||||
\(212\) | 16.9120 | 1.16152 | ||||||||
\(213\) | 3.19586 | 0.218976 | ||||||||
\(214\) | −30.7630 | −2.10292 | ||||||||
\(215\) | 18.9118 | 1.28977 | ||||||||
\(216\) | 10.4175 | 0.708823 | ||||||||
\(217\) | 5.03594 | 0.341862 | ||||||||
\(218\) | 8.09137 | 0.548017 | ||||||||
\(219\) | −3.67721 | −0.248483 | ||||||||
\(220\) | −35.8833 | −2.41925 | ||||||||
\(221\) | −0.386474 | −0.0259970 | ||||||||
\(222\) | 7.34536 | 0.492988 | ||||||||
\(223\) | 7.85607 | 0.526082 | 0.263041 | − | 0.964785i | \(-0.415275\pi\) | ||||
0.263041 | + | 0.964785i | \(0.415275\pi\) | |||||||
\(224\) | −4.52940 | −0.302633 | ||||||||
\(225\) | −4.03750 | −0.269167 | ||||||||
\(226\) | −3.51204 | −0.233617 | ||||||||
\(227\) | 5.19582 | 0.344859 | 0.172429 | − | 0.985022i | \(-0.444838\pi\) | ||||
0.172429 | + | 0.985022i | \(0.444838\pi\) | |||||||
\(228\) | −6.84857 | −0.453558 | ||||||||
\(229\) | 24.5104 | 1.61969 | 0.809847 | − | 0.586641i | \(-0.199550\pi\) | ||||
0.809847 | + | 0.586641i | \(0.199550\pi\) | |||||||
\(230\) | 40.4320 | 2.66600 | ||||||||
\(231\) | 0.931878 | 0.0613131 | ||||||||
\(232\) | 10.4955 | 0.689065 | ||||||||
\(233\) | 4.12455 | 0.270209 | 0.135104 | − | 0.990831i | \(-0.456863\pi\) | ||||
0.135104 | + | 0.990831i | \(0.456863\pi\) | |||||||
\(234\) | 2.18085 | 0.142566 | ||||||||
\(235\) | −27.4459 | −1.79037 | ||||||||
\(236\) | 5.16811 | 0.336415 | ||||||||
\(237\) | −3.79078 | −0.246238 | ||||||||
\(238\) | 3.31085 | 0.214611 | ||||||||
\(239\) | −6.63821 | −0.429390 | −0.214695 | − | 0.976681i | \(-0.568876\pi\) | ||||
−0.214695 | + | 0.976681i | \(0.568876\pi\) | |||||||
\(240\) | −4.82293 | −0.311319 | ||||||||
\(241\) | 20.3477 | 1.31071 | 0.655354 | − | 0.755322i | \(-0.272519\pi\) | ||||
0.655354 | + | 0.755322i | \(0.272519\pi\) | |||||||
\(242\) | 1.54812 | 0.0995167 | ||||||||
\(243\) | 7.51837 | 0.482304 | ||||||||
\(244\) | 63.6156 | 4.07257 | ||||||||
\(245\) | −2.52674 | −0.161427 | ||||||||
\(246\) | 4.44352 | 0.283309 | ||||||||
\(247\) | −1.58830 | −0.101061 | ||||||||
\(248\) | −30.6691 | −1.94749 | ||||||||
\(249\) | 0.453375 | 0.0287315 | ||||||||
\(250\) | −23.1227 | −1.46241 | ||||||||
\(251\) | 29.0224 | 1.83188 | 0.915940 | − | 0.401314i | \(-0.131447\pi\) | ||||
0.915940 | + | 0.401314i | \(0.131447\pi\) | |||||||
\(252\) | −12.8501 | −0.809481 | ||||||||
\(253\) | 20.3769 | 1.28109 | ||||||||
\(254\) | 7.87867 | 0.494352 | ||||||||
\(255\) | 0.955625 | 0.0598436 | ||||||||
\(256\) | −30.5931 | −1.91207 | ||||||||
\(257\) | −18.8010 | −1.17277 | −0.586387 | − | 0.810031i | \(-0.699450\pi\) | ||||
−0.586387 | + | 0.810031i | \(0.699450\pi\) | |||||||
\(258\) | 5.47718 | 0.340994 | ||||||||
\(259\) | −10.0376 | −0.623705 | ||||||||
\(260\) | −3.28926 | −0.203991 | ||||||||
\(261\) | 5.02611 | 0.311108 | ||||||||
\(262\) | 55.6478 | 3.43793 | ||||||||
\(263\) | −8.14012 | −0.501941 | −0.250971 | − | 0.967995i | \(-0.580750\pi\) | ||||
−0.250971 | + | 0.967995i | \(0.580750\pi\) | |||||||
\(264\) | −5.67518 | −0.349283 | ||||||||
\(265\) | −9.69831 | −0.595762 | ||||||||
\(266\) | 13.6067 | 0.834282 | ||||||||
\(267\) | 0.285351 | 0.0174632 | ||||||||
\(268\) | −39.0271 | −2.38396 | ||||||||
\(269\) | 6.07112 | 0.370163 | 0.185081 | − | 0.982723i | \(-0.440745\pi\) | ||||
0.185081 | + | 0.982723i | \(0.440745\pi\) | |||||||
\(270\) | −10.9396 | −0.665765 | ||||||||
\(271\) | −4.17241 | −0.253456 | −0.126728 | − | 0.991938i | \(-0.540448\pi\) | ||||
−0.126728 | + | 0.991938i | \(0.540448\pi\) | |||||||
\(272\) | −8.63587 | −0.523627 | ||||||||
\(273\) | 0.0854210 | 0.00516991 | ||||||||
\(274\) | 16.1673 | 0.976704 | ||||||||
\(275\) | 4.46209 | 0.269074 | ||||||||
\(276\) | 8.05398 | 0.484793 | ||||||||
\(277\) | 14.1861 | 0.852360 | 0.426180 | − | 0.904638i | \(-0.359859\pi\) | ||||
0.426180 | + | 0.904638i | \(0.359859\pi\) | |||||||
\(278\) | 21.2950 | 1.27719 | ||||||||
\(279\) | −14.6868 | −0.879278 | ||||||||
\(280\) | 15.3880 | 0.919606 | ||||||||
\(281\) | −26.6996 | −1.59276 | −0.796382 | − | 0.604794i | \(-0.793256\pi\) | ||||
−0.796382 | + | 0.604794i | \(0.793256\pi\) | |||||||
\(282\) | −7.94880 | −0.473344 | ||||||||
\(283\) | −8.97698 | −0.533626 | −0.266813 | − | 0.963748i | \(-0.585971\pi\) | ||||
−0.266813 | + | 0.963748i | \(0.585971\pi\) | |||||||
\(284\) | 48.7035 | 2.89002 | ||||||||
\(285\) | 3.92737 | 0.232637 | ||||||||
\(286\) | −2.41018 | −0.142517 | ||||||||
\(287\) | −6.07216 | −0.358428 | ||||||||
\(288\) | 13.2096 | 0.778382 | ||||||||
\(289\) | −15.2889 | −0.899345 | ||||||||
\(290\) | −11.0215 | −0.647207 | ||||||||
\(291\) | −0.342465 | −0.0200756 | ||||||||
\(292\) | −56.0391 | −3.27944 | ||||||||
\(293\) | 21.1130 | 1.23343 | 0.616717 | − | 0.787185i | \(-0.288462\pi\) | ||||
0.616717 | + | 0.787185i | \(0.288462\pi\) | |||||||
\(294\) | −0.731786 | −0.0426786 | ||||||||
\(295\) | −2.96369 | −0.172553 | ||||||||
\(296\) | 61.1293 | 3.55307 | ||||||||
\(297\) | −5.51337 | −0.319918 | ||||||||
\(298\) | −30.7276 | −1.78000 | ||||||||
\(299\) | 1.86786 | 0.108021 | ||||||||
\(300\) | 1.76364 | 0.101824 | ||||||||
\(301\) | −7.48467 | −0.431409 | ||||||||
\(302\) | −5.53633 | −0.318580 | ||||||||
\(303\) | −1.85524 | −0.106581 | ||||||||
\(304\) | −35.4911 | −2.03556 | ||||||||
\(305\) | −36.4808 | −2.08889 | ||||||||
\(306\) | −9.65579 | −0.551985 | ||||||||
\(307\) | 1.31237 | 0.0749010 | 0.0374505 | − | 0.999298i | \(-0.488076\pi\) | ||||
0.0374505 | + | 0.999298i | \(0.488076\pi\) | |||||||
\(308\) | 14.2014 | 0.809202 | ||||||||
\(309\) | 0.342701 | 0.0194956 | ||||||||
\(310\) | 32.2062 | 1.82919 | ||||||||
\(311\) | −5.01181 | −0.284193 | −0.142097 | − | 0.989853i | \(-0.545384\pi\) | ||||
−0.142097 | + | 0.989853i | \(0.545384\pi\) | |||||||
\(312\) | −0.520218 | −0.0294515 | ||||||||
\(313\) | 11.7713 | 0.665351 | 0.332676 | − | 0.943041i | \(-0.392049\pi\) | ||||
0.332676 | + | 0.943041i | \(0.392049\pi\) | |||||||
\(314\) | −7.62792 | −0.430469 | ||||||||
\(315\) | 7.36900 | 0.415196 | ||||||||
\(316\) | −57.7700 | −3.24981 | ||||||||
\(317\) | 5.71465 | 0.320967 | 0.160483 | − | 0.987039i | \(-0.448695\pi\) | ||||
0.160483 | + | 0.987039i | \(0.448695\pi\) | |||||||
\(318\) | −2.80879 | −0.157509 | ||||||||
\(319\) | −5.55465 | −0.311001 | ||||||||
\(320\) | 4.39550 | 0.245716 | ||||||||
\(321\) | 3.51412 | 0.196139 | ||||||||
\(322\) | −16.0016 | −0.891736 | ||||||||
\(323\) | 7.03228 | 0.391287 | ||||||||
\(324\) | 36.3712 | 2.02062 | ||||||||
\(325\) | 0.409019 | 0.0226883 | ||||||||
\(326\) | −54.1977 | −3.00173 | ||||||||
\(327\) | −0.924292 | −0.0511135 | ||||||||
\(328\) | 36.9797 | 2.04186 | ||||||||
\(329\) | 10.8622 | 0.598852 | ||||||||
\(330\) | 5.95961 | 0.328066 | ||||||||
\(331\) | −13.3725 | −0.735017 | −0.367508 | − | 0.930020i | \(-0.619789\pi\) | ||||
−0.367508 | + | 0.930020i | \(0.619789\pi\) | |||||||
\(332\) | 6.90925 | 0.379194 | ||||||||
\(333\) | 29.2736 | 1.60419 | ||||||||
\(334\) | 40.9345 | 2.23983 | ||||||||
\(335\) | 22.3804 | 1.22277 | ||||||||
\(336\) | 1.90876 | 0.104131 | ||||||||
\(337\) | −4.98328 | −0.271456 | −0.135728 | − | 0.990746i | \(-0.543337\pi\) | ||||
−0.135728 | + | 0.990746i | \(0.543337\pi\) | |||||||
\(338\) | 32.6825 | 1.77770 | ||||||||
\(339\) | 0.401187 | 0.0217895 | ||||||||
\(340\) | 14.5633 | 0.789808 | ||||||||
\(341\) | 16.2313 | 0.878975 | ||||||||
\(342\) | −39.6827 | −2.14580 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 45.5820 | 2.45762 | ||||||||
\(345\) | −4.61862 | −0.248658 | ||||||||
\(346\) | −6.97424 | −0.374938 | ||||||||
\(347\) | −36.0836 | −1.93707 | −0.968535 | − | 0.248878i | \(-0.919938\pi\) | ||||
−0.968535 | + | 0.248878i | \(0.919938\pi\) | |||||||
\(348\) | −2.19547 | −0.117690 | ||||||||
\(349\) | −18.3720 | −0.983431 | −0.491715 | − | 0.870756i | \(-0.663630\pi\) | ||||
−0.491715 | + | 0.870756i | \(0.663630\pi\) | |||||||
\(350\) | −3.50399 | −0.187296 | ||||||||
\(351\) | −0.505385 | −0.0269755 | ||||||||
\(352\) | −14.5987 | −0.778113 | ||||||||
\(353\) | −26.5619 | −1.41375 | −0.706873 | − | 0.707341i | \(-0.749895\pi\) | ||||
−0.706873 | + | 0.707341i | \(0.749895\pi\) | |||||||
\(354\) | −0.858336 | −0.0456200 | ||||||||
\(355\) | −27.9294 | −1.48234 | ||||||||
\(356\) | 4.34863 | 0.230477 | ||||||||
\(357\) | −0.378205 | −0.0200167 | ||||||||
\(358\) | −53.1814 | −2.81072 | ||||||||
\(359\) | −9.00294 | −0.475157 | −0.237579 | − | 0.971368i | \(-0.576354\pi\) | ||||
−0.237579 | + | 0.971368i | \(0.576354\pi\) | |||||||
\(360\) | −44.8775 | −2.36525 | ||||||||
\(361\) | 9.90082 | 0.521096 | ||||||||
\(362\) | 0.228382 | 0.0120035 | ||||||||
\(363\) | −0.176844 | −0.00928192 | ||||||||
\(364\) | 1.30178 | 0.0682318 | ||||||||
\(365\) | 32.1361 | 1.68208 | ||||||||
\(366\) | −10.5655 | −0.552266 | ||||||||
\(367\) | 13.8384 | 0.722357 | 0.361179 | − | 0.932497i | \(-0.382374\pi\) | ||||
0.361179 | + | 0.932497i | \(0.382374\pi\) | |||||||
\(368\) | 41.7379 | 2.17574 | ||||||||
\(369\) | 17.7089 | 0.921888 | ||||||||
\(370\) | −64.1930 | −3.33723 | ||||||||
\(371\) | 3.83827 | 0.199273 | ||||||||
\(372\) | 6.41542 | 0.332624 | ||||||||
\(373\) | 34.3713 | 1.77968 | 0.889840 | − | 0.456272i | \(-0.150816\pi\) | ||||
0.889840 | + | 0.456272i | \(0.150816\pi\) | |||||||
\(374\) | 10.6712 | 0.551794 | ||||||||
\(375\) | 2.64135 | 0.136399 | ||||||||
\(376\) | −66.1512 | −3.41149 | ||||||||
\(377\) | −0.509169 | −0.0262236 | ||||||||
\(378\) | 4.32955 | 0.222688 | ||||||||
\(379\) | −8.74453 | −0.449176 | −0.224588 | − | 0.974454i | \(-0.572104\pi\) | ||||
−0.224588 | + | 0.974454i | \(0.572104\pi\) | |||||||
\(380\) | 59.8514 | 3.07031 | ||||||||
\(381\) | −0.899996 | −0.0461082 | ||||||||
\(382\) | 56.7099 | 2.90153 | ||||||||
\(383\) | 15.1599 | 0.774635 | 0.387317 | − | 0.921946i | \(-0.373402\pi\) | ||||
0.387317 | + | 0.921946i | \(0.373402\pi\) | |||||||
\(384\) | 3.89214 | 0.198620 | ||||||||
\(385\) | −8.14392 | −0.415053 | ||||||||
\(386\) | −52.1619 | −2.65497 | ||||||||
\(387\) | 21.8283 | 1.10960 | ||||||||
\(388\) | −5.21902 | −0.264956 | ||||||||
\(389\) | 14.8276 | 0.751788 | 0.375894 | − | 0.926663i | \(-0.377336\pi\) | ||||
0.375894 | + | 0.926663i | \(0.377336\pi\) | |||||||
\(390\) | 0.546290 | 0.0276625 | ||||||||
\(391\) | −8.27003 | −0.418234 | ||||||||
\(392\) | −6.09005 | −0.307594 | ||||||||
\(393\) | −6.35676 | −0.320656 | ||||||||
\(394\) | 20.5011 | 1.03283 | ||||||||
\(395\) | 33.1286 | 1.66688 | ||||||||
\(396\) | −41.4172 | −2.08129 | ||||||||
\(397\) | 16.8209 | 0.844215 | 0.422108 | − | 0.906546i | \(-0.361290\pi\) | ||||
0.422108 | + | 0.906546i | \(0.361290\pi\) | |||||||
\(398\) | −35.1036 | −1.75958 | ||||||||
\(399\) | −1.55432 | −0.0778134 | ||||||||
\(400\) | 9.13965 | 0.456983 | ||||||||
\(401\) | −18.1018 | −0.903958 | −0.451979 | − | 0.892029i | \(-0.649282\pi\) | ||||
−0.451979 | + | 0.892029i | \(0.649282\pi\) | |||||||
\(402\) | 6.48174 | 0.323280 | ||||||||
\(403\) | 1.48785 | 0.0741151 | ||||||||
\(404\) | −28.2731 | −1.40664 | ||||||||
\(405\) | −20.8573 | −1.03641 | ||||||||
\(406\) | 4.36196 | 0.216481 | ||||||||
\(407\) | −32.3521 | −1.60363 | ||||||||
\(408\) | 2.30329 | 0.114030 | ||||||||
\(409\) | −1.37063 | −0.0677731 | −0.0338865 | − | 0.999426i | \(-0.510788\pi\) | ||||
−0.0338865 | + | 0.999426i | \(0.510788\pi\) | |||||||
\(410\) | −38.8331 | −1.91783 | ||||||||
\(411\) | −1.84682 | −0.0910971 | ||||||||
\(412\) | 5.22263 | 0.257300 | ||||||||
\(413\) | 1.17293 | 0.0577162 | ||||||||
\(414\) | 46.6673 | 2.29357 | ||||||||
\(415\) | −3.96216 | −0.194495 | ||||||||
\(416\) | −1.33820 | −0.0656104 | ||||||||
\(417\) | −2.43257 | −0.119123 | ||||||||
\(418\) | 43.8558 | 2.14506 | ||||||||
\(419\) | 20.8605 | 1.01910 | 0.509552 | − | 0.860440i | \(-0.329811\pi\) | ||||
0.509552 | + | 0.860440i | \(0.329811\pi\) | |||||||
\(420\) | −3.21888 | −0.157065 | ||||||||
\(421\) | −11.7759 | −0.573921 | −0.286960 | − | 0.957942i | \(-0.592645\pi\) | ||||
−0.286960 | + | 0.957942i | \(0.592645\pi\) | |||||||
\(422\) | 12.8664 | 0.626328 | ||||||||
\(423\) | −31.6786 | −1.54026 | ||||||||
\(424\) | −23.3752 | −1.13520 | ||||||||
\(425\) | −1.81095 | −0.0878439 | ||||||||
\(426\) | −8.08883 | −0.391905 | ||||||||
\(427\) | 14.4379 | 0.698700 | ||||||||
\(428\) | 53.5537 | 2.58862 | ||||||||
\(429\) | 0.275320 | 0.0132926 | ||||||||
\(430\) | −47.8665 | −2.30833 | ||||||||
\(431\) | −7.08570 | −0.341306 | −0.170653 | − | 0.985331i | \(-0.554588\pi\) | ||||
−0.170653 | + | 0.985331i | \(0.554588\pi\) | |||||||
\(432\) | −11.2930 | −0.543334 | ||||||||
\(433\) | 6.21534 | 0.298690 | 0.149345 | − | 0.988785i | \(-0.452283\pi\) | ||||
0.149345 | + | 0.988785i | \(0.452283\pi\) | |||||||
\(434\) | −12.7461 | −0.611835 | ||||||||
\(435\) | 1.25901 | 0.0603650 | ||||||||
\(436\) | −14.0858 | −0.674589 | ||||||||
\(437\) | −33.9876 | −1.62585 | ||||||||
\(438\) | 9.30715 | 0.444713 | ||||||||
\(439\) | 10.9523 | 0.522723 | 0.261362 | − | 0.965241i | \(-0.415828\pi\) | ||||
0.261362 | + | 0.965241i | \(0.415828\pi\) | |||||||
\(440\) | 49.5969 | 2.36444 | ||||||||
\(441\) | −2.91641 | −0.138877 | ||||||||
\(442\) | 0.978179 | 0.0465272 | ||||||||
\(443\) | −5.51650 | −0.262097 | −0.131048 | − | 0.991376i | \(-0.541834\pi\) | ||||
−0.131048 | + | 0.991376i | \(0.541834\pi\) | |||||||
\(444\) | −12.7871 | −0.606851 | ||||||||
\(445\) | −2.49375 | −0.118215 | ||||||||
\(446\) | −19.8840 | −0.941535 | ||||||||
\(447\) | 3.51007 | 0.166021 | ||||||||
\(448\) | −1.73959 | −0.0821881 | ||||||||
\(449\) | 22.4565 | 1.05979 | 0.529895 | − | 0.848063i | \(-0.322231\pi\) | ||||
0.529895 | + | 0.848063i | \(0.322231\pi\) | |||||||
\(450\) | 10.2191 | 0.481732 | ||||||||
\(451\) | −19.5711 | −0.921569 | ||||||||
\(452\) | 6.11392 | 0.287575 | ||||||||
\(453\) | 0.632426 | 0.0297140 | ||||||||
\(454\) | −13.1508 | −0.617199 | ||||||||
\(455\) | −0.746516 | −0.0349972 | ||||||||
\(456\) | 9.46589 | 0.443281 | ||||||||
\(457\) | 39.0414 | 1.82628 | 0.913139 | − | 0.407648i | \(-0.133651\pi\) | ||||
0.913139 | + | 0.407648i | \(0.133651\pi\) | |||||||
\(458\) | −62.0368 | −2.89879 | ||||||||
\(459\) | 2.23761 | 0.104443 | ||||||||
\(460\) | −70.3858 | −3.28176 | ||||||||
\(461\) | 17.0595 | 0.794542 | 0.397271 | − | 0.917701i | \(-0.369957\pi\) | ||||
0.397271 | + | 0.917701i | \(0.369957\pi\) | |||||||
\(462\) | −2.35862 | −0.109733 | ||||||||
\(463\) | 30.2558 | 1.40611 | 0.703054 | − | 0.711136i | \(-0.251819\pi\) | ||||
0.703054 | + | 0.711136i | \(0.251819\pi\) | |||||||
\(464\) | −11.3775 | −0.528189 | ||||||||
\(465\) | −3.67897 | −0.170608 | ||||||||
\(466\) | −10.4394 | −0.483596 | ||||||||
\(467\) | 6.28049 | 0.290627 | 0.145313 | − | 0.989386i | \(-0.453581\pi\) | ||||
0.145313 | + | 0.989386i | \(0.453581\pi\) | |||||||
\(468\) | −3.79652 | −0.175494 | ||||||||
\(469\) | −8.85743 | −0.408998 | ||||||||
\(470\) | 69.4666 | 3.20426 | ||||||||
\(471\) | 0.871352 | 0.0401498 | ||||||||
\(472\) | −7.14321 | −0.328793 | ||||||||
\(473\) | −24.1238 | −1.10921 | ||||||||
\(474\) | 9.59461 | 0.440695 | ||||||||
\(475\) | −7.44252 | −0.341486 | ||||||||
\(476\) | −5.76369 | −0.264178 | ||||||||
\(477\) | −11.1940 | −0.512536 | ||||||||
\(478\) | 16.8016 | 0.768485 | ||||||||
\(479\) | 5.01403 | 0.229097 | 0.114548 | − | 0.993418i | \(-0.463458\pi\) | ||||
0.114548 | + | 0.993418i | \(0.463458\pi\) | |||||||
\(480\) | 3.30893 | 0.151031 | ||||||||
\(481\) | −2.96556 | −0.135218 | ||||||||
\(482\) | −51.5007 | −2.34579 | ||||||||
\(483\) | 1.82790 | 0.0831722 | ||||||||
\(484\) | −2.69503 | −0.122502 | ||||||||
\(485\) | 2.99289 | 0.135900 | ||||||||
\(486\) | −19.0293 | −0.863185 | ||||||||
\(487\) | −8.45019 | −0.382915 | −0.191457 | − | 0.981501i | \(-0.561321\pi\) | ||||
−0.191457 | + | 0.981501i | \(0.561321\pi\) | |||||||
\(488\) | −87.9276 | −3.98029 | ||||||||
\(489\) | 6.19110 | 0.279971 | ||||||||
\(490\) | 6.39527 | 0.288909 | ||||||||
\(491\) | −14.0934 | −0.636026 | −0.318013 | − | 0.948086i | \(-0.603016\pi\) | ||||
−0.318013 | + | 0.948086i | \(0.603016\pi\) | |||||||
\(492\) | −7.73549 | −0.348743 | ||||||||
\(493\) | 2.25437 | 0.101532 | ||||||||
\(494\) | 4.02006 | 0.180871 | ||||||||
\(495\) | 23.7510 | 1.06753 | ||||||||
\(496\) | 33.2465 | 1.49281 | ||||||||
\(497\) | 11.0535 | 0.495819 | ||||||||
\(498\) | −1.14751 | −0.0514211 | ||||||||
\(499\) | −6.62850 | −0.296732 | −0.148366 | − | 0.988932i | \(-0.547401\pi\) | ||||
−0.148366 | + | 0.988932i | \(0.547401\pi\) | |||||||
\(500\) | 40.2530 | 1.80017 | ||||||||
\(501\) | −4.67602 | −0.208909 | ||||||||
\(502\) | −73.4569 | −3.27854 | ||||||||
\(503\) | 38.1438 | 1.70075 | 0.850374 | − | 0.526179i | \(-0.176376\pi\) | ||||
0.850374 | + | 0.526179i | \(0.176376\pi\) | |||||||
\(504\) | 17.7611 | 0.791140 | ||||||||
\(505\) | 16.2135 | 0.721489 | ||||||||
\(506\) | −51.5748 | −2.29278 | ||||||||
\(507\) | −3.73339 | −0.165806 | ||||||||
\(508\) | −13.7156 | −0.608530 | ||||||||
\(509\) | 25.0132 | 1.10869 | 0.554346 | − | 0.832287i | \(-0.312969\pi\) | ||||
0.554346 | + | 0.832287i | \(0.312969\pi\) | |||||||
\(510\) | −2.41872 | −0.107103 | ||||||||
\(511\) | −12.7184 | −0.562629 | ||||||||
\(512\) | 50.5086 | 2.23219 | ||||||||
\(513\) | 9.19600 | 0.406013 | ||||||||
\(514\) | 47.5860 | 2.09893 | ||||||||
\(515\) | −2.99496 | −0.131974 | ||||||||
\(516\) | −9.53493 | −0.419752 | ||||||||
\(517\) | 35.0099 | 1.53973 | ||||||||
\(518\) | 25.4055 | 1.11625 | ||||||||
\(519\) | 0.796681 | 0.0349704 | ||||||||
\(520\) | 4.54632 | 0.199369 | ||||||||
\(521\) | −20.8270 | −0.912448 | −0.456224 | − | 0.889865i | \(-0.650799\pi\) | ||||
−0.456224 | + | 0.889865i | \(0.650799\pi\) | |||||||
\(522\) | −12.7213 | −0.556795 | ||||||||
\(523\) | −29.2822 | −1.28042 | −0.640211 | − | 0.768199i | \(-0.721153\pi\) | ||||
−0.640211 | + | 0.768199i | \(0.721153\pi\) | |||||||
\(524\) | −96.8744 | −4.23198 | ||||||||
\(525\) | 0.400268 | 0.0174691 | ||||||||
\(526\) | 20.6029 | 0.898331 | ||||||||
\(527\) | −6.58752 | −0.286957 | ||||||||
\(528\) | 6.15211 | 0.267736 | ||||||||
\(529\) | 16.9698 | 0.737817 | ||||||||
\(530\) | 24.5468 | 1.06624 | ||||||||
\(531\) | −3.42075 | −0.148448 | ||||||||
\(532\) | −23.6872 | −1.02697 | ||||||||
\(533\) | −1.79400 | −0.0777066 | ||||||||
\(534\) | −0.722233 | −0.0312541 | ||||||||
\(535\) | −30.7108 | −1.32774 | ||||||||
\(536\) | 53.9422 | 2.32995 | ||||||||
\(537\) | 6.07501 | 0.262156 | ||||||||
\(538\) | −15.3662 | −0.662485 | ||||||||
\(539\) | 3.22310 | 0.138829 | ||||||||
\(540\) | 19.0442 | 0.819533 | ||||||||
\(541\) | 23.3158 | 1.00242 | 0.501212 | − | 0.865324i | \(-0.332888\pi\) | ||||
0.501212 | + | 0.865324i | \(0.332888\pi\) | |||||||
\(542\) | 10.5605 | 0.453613 | ||||||||
\(543\) | −0.0260885 | −0.00111956 | ||||||||
\(544\) | 5.92492 | 0.254029 | ||||||||
\(545\) | 8.07763 | 0.346008 | ||||||||
\(546\) | −0.216204 | −0.00925266 | ||||||||
\(547\) | −24.3738 | −1.04215 | −0.521073 | − | 0.853512i | \(-0.674468\pi\) | ||||
−0.521073 | + | 0.853512i | \(0.674468\pi\) | |||||||
\(548\) | −28.1448 | −1.20229 | ||||||||
\(549\) | −42.1068 | −1.79708 | ||||||||
\(550\) | −11.2937 | −0.481565 | ||||||||
\(551\) | 9.26486 | 0.394696 | ||||||||
\(552\) | −11.1320 | −0.473808 | ||||||||
\(553\) | −13.1112 | −0.557546 | ||||||||
\(554\) | −35.9055 | −1.52548 | ||||||||
\(555\) | 7.33289 | 0.311264 | ||||||||
\(556\) | −37.0713 | −1.57218 | ||||||||
\(557\) | 28.2930 | 1.19881 | 0.599407 | − | 0.800445i | \(-0.295403\pi\) | ||||
0.599407 | + | 0.800445i | \(0.295403\pi\) | |||||||
\(558\) | 37.1729 | 1.57366 | ||||||||
\(559\) | −2.21132 | −0.0935288 | ||||||||
\(560\) | −16.6811 | −0.704906 | ||||||||
\(561\) | −1.21899 | −0.0514658 | ||||||||
\(562\) | 67.5777 | 2.85059 | ||||||||
\(563\) | 45.8567 | 1.93263 | 0.966315 | − | 0.257364i | \(-0.0828538\pi\) | ||||
0.966315 | + | 0.257364i | \(0.0828538\pi\) | |||||||
\(564\) | 13.8376 | 0.582670 | ||||||||
\(565\) | −3.50607 | −0.147502 | ||||||||
\(566\) | 22.7211 | 0.955038 | ||||||||
\(567\) | 8.25465 | 0.346663 | ||||||||
\(568\) | −67.3166 | −2.82454 | ||||||||
\(569\) | 40.2347 | 1.68673 | 0.843363 | − | 0.537344i | \(-0.180572\pi\) | ||||
0.843363 | + | 0.537344i | \(0.180572\pi\) | |||||||
\(570\) | −9.94031 | −0.416354 | ||||||||
\(571\) | 31.9257 | 1.33605 | 0.668025 | − | 0.744139i | \(-0.267140\pi\) | ||||
0.668025 | + | 0.744139i | \(0.267140\pi\) | |||||||
\(572\) | 4.19576 | 0.175434 | ||||||||
\(573\) | −6.47808 | −0.270626 | ||||||||
\(574\) | 15.3689 | 0.641484 | ||||||||
\(575\) | 8.75247 | 0.365003 | ||||||||
\(576\) | 5.07337 | 0.211390 | ||||||||
\(577\) | 5.13806 | 0.213900 | 0.106950 | − | 0.994264i | \(-0.465891\pi\) | ||||
0.106950 | + | 0.994264i | \(0.465891\pi\) | |||||||
\(578\) | 38.6967 | 1.60957 | ||||||||
\(579\) | 5.95855 | 0.247629 | ||||||||
\(580\) | 19.1868 | 0.796689 | ||||||||
\(581\) | 1.56809 | 0.0650555 | ||||||||
\(582\) | 0.866790 | 0.0359296 | ||||||||
\(583\) | 12.3711 | 0.512359 | ||||||||
\(584\) | 77.4556 | 3.20514 | ||||||||
\(585\) | 2.17714 | 0.0900138 | ||||||||
\(586\) | −53.4377 | −2.20749 | ||||||||
\(587\) | −17.6558 | −0.728734 | −0.364367 | − | 0.931255i | \(-0.618715\pi\) | ||||
−0.364367 | + | 0.931255i | \(0.618715\pi\) | |||||||
\(588\) | 1.27393 | 0.0525359 | ||||||||
\(589\) | −27.0730 | −1.11552 | ||||||||
\(590\) | 7.50122 | 0.308820 | ||||||||
\(591\) | −2.34188 | −0.0963323 | ||||||||
\(592\) | −66.2664 | −2.72353 | ||||||||
\(593\) | 22.5350 | 0.925402 | 0.462701 | − | 0.886514i | \(-0.346880\pi\) | ||||
0.462701 | + | 0.886514i | \(0.346880\pi\) | |||||||
\(594\) | 13.9545 | 0.572562 | ||||||||
\(595\) | 3.30523 | 0.135501 | ||||||||
\(596\) | 53.4920 | 2.19112 | ||||||||
\(597\) | 4.00994 | 0.164116 | ||||||||
\(598\) | −4.72762 | −0.193327 | ||||||||
\(599\) | 21.5029 | 0.878585 | 0.439293 | − | 0.898344i | \(-0.355229\pi\) | ||||
0.439293 | + | 0.898344i | \(0.355229\pi\) | |||||||
\(600\) | −2.43765 | −0.0995166 | ||||||||
\(601\) | 6.88847 | 0.280986 | 0.140493 | − | 0.990082i | \(-0.455131\pi\) | ||||
0.140493 | + | 0.990082i | \(0.455131\pi\) | |||||||
\(602\) | 18.9440 | 0.772099 | ||||||||
\(603\) | 25.8319 | 1.05195 | ||||||||
\(604\) | 9.63791 | 0.392161 | ||||||||
\(605\) | 1.54549 | 0.0628330 | ||||||||
\(606\) | 4.69569 | 0.190749 | ||||||||
\(607\) | −7.80968 | −0.316985 | −0.158493 | − | 0.987360i | \(-0.550663\pi\) | ||||
−0.158493 | + | 0.987360i | \(0.550663\pi\) | |||||||
\(608\) | 24.3498 | 0.987516 | ||||||||
\(609\) | −0.498275 | −0.0201911 | ||||||||
\(610\) | 92.3343 | 3.73851 | ||||||||
\(611\) | 3.20919 | 0.129830 | ||||||||
\(612\) | 16.8093 | 0.679474 | ||||||||
\(613\) | −10.1103 | −0.408353 | −0.204176 | − | 0.978934i | \(-0.565452\pi\) | ||||
−0.204176 | + | 0.978934i | \(0.565452\pi\) | |||||||
\(614\) | −3.32166 | −0.134051 | ||||||||
\(615\) | 4.43598 | 0.178876 | ||||||||
\(616\) | −19.6288 | −0.790867 | ||||||||
\(617\) | −30.6342 | −1.23329 | −0.616643 | − | 0.787243i | \(-0.711508\pi\) | ||||
−0.616643 | + | 0.787243i | \(0.711508\pi\) | |||||||
\(618\) | −0.867390 | −0.0348915 | ||||||||
\(619\) | 25.4695 | 1.02370 | 0.511852 | − | 0.859074i | \(-0.328960\pi\) | ||||
0.511852 | + | 0.859074i | \(0.328960\pi\) | |||||||
\(620\) | −56.0660 | −2.25167 | ||||||||
\(621\) | −10.8146 | −0.433974 | ||||||||
\(622\) | 12.6851 | 0.508625 | ||||||||
\(623\) | 0.986945 | 0.0395411 | ||||||||
\(624\) | 0.563935 | 0.0225755 | ||||||||
\(625\) | −30.0055 | −1.20022 | ||||||||
\(626\) | −29.7935 | −1.19079 | ||||||||
\(627\) | −5.00973 | −0.200069 | ||||||||
\(628\) | 13.2790 | 0.529892 | ||||||||
\(629\) | 13.1302 | 0.523534 | ||||||||
\(630\) | −18.6512 | −0.743082 | ||||||||
\(631\) | −3.20776 | −0.127699 | −0.0638495 | − | 0.997960i | \(-0.520338\pi\) | ||||
−0.0638495 | + | 0.997960i | \(0.520338\pi\) | |||||||
\(632\) | 79.8479 | 3.17618 | ||||||||
\(633\) | −1.46976 | −0.0584176 | ||||||||
\(634\) | −14.4640 | −0.574439 | ||||||||
\(635\) | 7.86529 | 0.312125 | ||||||||
\(636\) | 4.88968 | 0.193888 | ||||||||
\(637\) | 0.295446 | 0.0117060 | ||||||||
\(638\) | 14.0590 | 0.556602 | ||||||||
\(639\) | −32.2366 | −1.27526 | ||||||||
\(640\) | −34.0144 | −1.34454 | ||||||||
\(641\) | 37.3692 | 1.47599 | 0.737997 | − | 0.674804i | \(-0.235772\pi\) | ||||
0.737997 | + | 0.674804i | \(0.235772\pi\) | |||||||
\(642\) | −8.89436 | −0.351033 | ||||||||
\(643\) | 34.5691 | 1.36327 | 0.681636 | − | 0.731692i | \(-0.261269\pi\) | ||||
0.681636 | + | 0.731692i | \(0.261269\pi\) | |||||||
\(644\) | 27.8564 | 1.09770 | ||||||||
\(645\) | 5.46788 | 0.215297 | ||||||||
\(646\) | −17.7990 | −0.700291 | ||||||||
\(647\) | 39.5573 | 1.55516 | 0.777579 | − | 0.628785i | \(-0.216447\pi\) | ||||
0.777579 | + | 0.628785i | \(0.216447\pi\) | |||||||
\(648\) | −50.2712 | −1.97484 | ||||||||
\(649\) | 3.78047 | 0.148397 | ||||||||
\(650\) | −1.03524 | −0.0406055 | ||||||||
\(651\) | 1.45602 | 0.0570658 | ||||||||
\(652\) | 94.3499 | 3.69503 | ||||||||
\(653\) | 47.7365 | 1.86807 | 0.934036 | − | 0.357178i | \(-0.116261\pi\) | ||||
0.934036 | + | 0.357178i | \(0.116261\pi\) | |||||||
\(654\) | 2.33942 | 0.0914785 | ||||||||
\(655\) | 55.5533 | 2.17065 | ||||||||
\(656\) | −40.0874 | −1.56515 | ||||||||
\(657\) | 37.0920 | 1.44710 | ||||||||
\(658\) | −27.4926 | −1.07177 | ||||||||
\(659\) | −49.4866 | −1.92772 | −0.963862 | − | 0.266402i | \(-0.914165\pi\) | ||||
−0.963862 | + | 0.266402i | \(0.914165\pi\) | |||||||
\(660\) | −10.3748 | −0.403837 | ||||||||
\(661\) | 44.6284 | 1.73584 | 0.867922 | − | 0.496700i | \(-0.165455\pi\) | ||||
0.867922 | + | 0.496700i | \(0.165455\pi\) | |||||||
\(662\) | 33.8462 | 1.31547 | ||||||||
\(663\) | −0.111739 | −0.00433959 | ||||||||
\(664\) | −9.54976 | −0.370603 | ||||||||
\(665\) | 13.5836 | 0.526750 | ||||||||
\(666\) | −74.0927 | −2.87103 | ||||||||
\(667\) | −10.8956 | −0.421878 | ||||||||
\(668\) | −71.2606 | −2.75716 | ||||||||
\(669\) | 2.27139 | 0.0878169 | ||||||||
\(670\) | −56.6456 | −2.18841 | ||||||||
\(671\) | 46.5348 | 1.79646 | ||||||||
\(672\) | −1.30956 | −0.0505175 | ||||||||
\(673\) | 35.5597 | 1.37072 | 0.685362 | − | 0.728202i | \(-0.259644\pi\) | ||||
0.685362 | + | 0.728202i | \(0.259644\pi\) | |||||||
\(674\) | 12.6129 | 0.485829 | ||||||||
\(675\) | −2.36815 | −0.0911500 | ||||||||
\(676\) | −56.8953 | −2.18828 | ||||||||
\(677\) | 47.1000 | 1.81020 | 0.905101 | − | 0.425197i | \(-0.139795\pi\) | ||||
0.905101 | + | 0.425197i | \(0.139795\pi\) | |||||||
\(678\) | −1.01542 | −0.0389969 | ||||||||
\(679\) | −1.18449 | −0.0454564 | ||||||||
\(680\) | −20.1290 | −0.771912 | ||||||||
\(681\) | 1.50224 | 0.0575661 | ||||||||
\(682\) | −41.0821 | −1.57311 | ||||||||
\(683\) | 31.7202 | 1.21374 | 0.606870 | − | 0.794801i | \(-0.292425\pi\) | ||||
0.606870 | + | 0.794801i | \(0.292425\pi\) | |||||||
\(684\) | 69.0816 | 2.64140 | ||||||||
\(685\) | 16.1399 | 0.616673 | ||||||||
\(686\) | −2.53104 | −0.0966354 | ||||||||
\(687\) | 7.08658 | 0.270370 | ||||||||
\(688\) | −49.4126 | −1.88384 | ||||||||
\(689\) | 1.13400 | 0.0432021 | ||||||||
\(690\) | 11.6899 | 0.445027 | ||||||||
\(691\) | −11.8878 | −0.452233 | −0.226116 | − | 0.974100i | \(-0.572603\pi\) | ||||
−0.226116 | + | 0.974100i | \(0.572603\pi\) | |||||||
\(692\) | 12.1411 | 0.461535 | ||||||||
\(693\) | −9.39986 | −0.357071 | ||||||||
\(694\) | 91.3290 | 3.46680 | ||||||||
\(695\) | 21.2589 | 0.806394 | ||||||||
\(696\) | 3.03452 | 0.115023 | ||||||||
\(697\) | 7.94300 | 0.300862 | ||||||||
\(698\) | 46.5002 | 1.76006 | ||||||||
\(699\) | 1.19251 | 0.0451050 | ||||||||
\(700\) | 6.09992 | 0.230555 | ||||||||
\(701\) | 33.1635 | 1.25257 | 0.626285 | − | 0.779594i | \(-0.284575\pi\) | ||||
0.626285 | + | 0.779594i | \(0.284575\pi\) | |||||||
\(702\) | 1.27915 | 0.0482783 | ||||||||
\(703\) | 53.9615 | 2.03520 | ||||||||
\(704\) | −5.60688 | −0.211317 | ||||||||
\(705\) | −7.93530 | −0.298861 | ||||||||
\(706\) | 67.2290 | 2.53020 | ||||||||
\(707\) | −6.41675 | −0.241327 | ||||||||
\(708\) | 1.49423 | 0.0561566 | ||||||||
\(709\) | −8.84896 | −0.332330 | −0.166165 | − | 0.986098i | \(-0.553138\pi\) | ||||
−0.166165 | + | 0.986098i | \(0.553138\pi\) | |||||||
\(710\) | 70.6904 | 2.65296 | ||||||||
\(711\) | 38.2376 | 1.43402 | ||||||||
\(712\) | −6.01054 | −0.225255 | ||||||||
\(713\) | 31.8380 | 1.19234 | ||||||||
\(714\) | 0.957250 | 0.0358242 | ||||||||
\(715\) | −2.40609 | −0.0899827 | ||||||||
\(716\) | 92.5806 | 3.45990 | ||||||||
\(717\) | −1.91927 | −0.0716766 | ||||||||
\(718\) | 22.7868 | 0.850395 | ||||||||
\(719\) | −48.6385 | −1.81391 | −0.906956 | − | 0.421226i | \(-0.861600\pi\) | ||||
−0.906956 | + | 0.421226i | \(0.861600\pi\) | |||||||
\(720\) | 48.6489 | 1.81304 | ||||||||
\(721\) | 1.18530 | 0.0441431 | ||||||||
\(722\) | −25.0593 | −0.932612 | ||||||||
\(723\) | 5.88302 | 0.218792 | ||||||||
\(724\) | −0.397578 | −0.0147759 | ||||||||
\(725\) | −2.38588 | −0.0886093 | ||||||||
\(726\) | 0.447599 | 0.0166120 | ||||||||
\(727\) | 38.1262 | 1.41402 | 0.707012 | − | 0.707202i | \(-0.250043\pi\) | ||||
0.707012 | + | 0.707202i | \(0.250043\pi\) | |||||||
\(728\) | −1.79928 | −0.0666858 | ||||||||
\(729\) | −22.5902 | −0.836674 | ||||||||
\(730\) | −81.3376 | −3.01044 | ||||||||
\(731\) | 9.79070 | 0.362122 | ||||||||
\(732\) | 18.3929 | 0.679820 | ||||||||
\(733\) | 10.4874 | 0.387360 | 0.193680 | − | 0.981065i | \(-0.437958\pi\) | ||||
0.193680 | + | 0.981065i | \(0.437958\pi\) | |||||||
\(734\) | −35.0254 | −1.29281 | ||||||||
\(735\) | −0.730544 | −0.0269465 | ||||||||
\(736\) | −28.6356 | −1.05552 | ||||||||
\(737\) | −28.5483 | −1.05159 | ||||||||
\(738\) | −44.8218 | −1.64991 | ||||||||
\(739\) | −51.2896 | −1.88672 | −0.943359 | − | 0.331773i | \(-0.892353\pi\) | ||||
−0.943359 | + | 0.331773i | \(0.892353\pi\) | |||||||
\(740\) | 111.750 | 4.10802 | ||||||||
\(741\) | −0.459219 | −0.0168698 | ||||||||
\(742\) | −9.71480 | −0.356642 | ||||||||
\(743\) | −6.44101 | −0.236298 | −0.118149 | − | 0.992996i | \(-0.537696\pi\) | ||||
−0.118149 | + | 0.992996i | \(0.537696\pi\) | |||||||
\(744\) | −8.86721 | −0.325088 | ||||||||
\(745\) | −30.6754 | −1.12386 | ||||||||
\(746\) | −86.9951 | −3.18512 | ||||||||
\(747\) | −4.57320 | −0.167325 | ||||||||
\(748\) | −18.5769 | −0.679239 | ||||||||
\(749\) | 12.1543 | 0.444109 | ||||||||
\(750\) | −6.68534 | −0.244114 | ||||||||
\(751\) | 23.0230 | 0.840120 | 0.420060 | − | 0.907496i | \(-0.362009\pi\) | ||||
0.420060 | + | 0.907496i | \(0.362009\pi\) | |||||||
\(752\) | 71.7104 | 2.61501 | ||||||||
\(753\) | 8.39112 | 0.305789 | ||||||||
\(754\) | 1.28873 | 0.0469327 | ||||||||
\(755\) | −5.52693 | −0.201146 | ||||||||
\(756\) | −7.53707 | −0.274121 | ||||||||
\(757\) | −22.1852 | −0.806333 | −0.403167 | − | 0.915127i | \(-0.632090\pi\) | ||||
−0.403167 | + | 0.915127i | \(0.632090\pi\) | |||||||
\(758\) | 22.1327 | 0.803897 | ||||||||
\(759\) | 5.89149 | 0.213847 | ||||||||
\(760\) | −82.7249 | −3.00075 | ||||||||
\(761\) | −36.3675 | −1.31832 | −0.659161 | − | 0.752002i | \(-0.729088\pi\) | ||||
−0.659161 | + | 0.752002i | \(0.729088\pi\) | |||||||
\(762\) | 2.27792 | 0.0825204 | ||||||||
\(763\) | −3.19686 | −0.115734 | ||||||||
\(764\) | −98.7232 | −3.57168 | ||||||||
\(765\) | −9.63940 | −0.348513 | ||||||||
\(766\) | −38.3703 | −1.38637 | ||||||||
\(767\) | 0.346539 | 0.0125128 | ||||||||
\(768\) | −8.84523 | −0.319175 | ||||||||
\(769\) | 7.87740 | 0.284066 | 0.142033 | − | 0.989862i | \(-0.454636\pi\) | ||||
0.142033 | + | 0.989862i | \(0.454636\pi\) | |||||||
\(770\) | 20.6126 | 0.742825 | ||||||||
\(771\) | −5.43584 | −0.195767 | ||||||||
\(772\) | 90.8059 | 3.26817 | ||||||||
\(773\) | 43.2792 | 1.55665 | 0.778323 | − | 0.627864i | \(-0.216071\pi\) | ||||
0.778323 | + | 0.627864i | \(0.216071\pi\) | |||||||
\(774\) | −55.2483 | −1.98586 | ||||||||
\(775\) | 6.97181 | 0.250435 | ||||||||
\(776\) | 7.21357 | 0.258952 | ||||||||
\(777\) | −2.90211 | −0.104113 | ||||||||
\(778\) | −37.5291 | −1.34548 | ||||||||
\(779\) | 32.6436 | 1.16958 | ||||||||
\(780\) | −0.951007 | −0.0340515 | ||||||||
\(781\) | 35.6266 | 1.27482 | ||||||||
\(782\) | 20.9318 | 0.748518 | ||||||||
\(783\) | 2.94800 | 0.105353 | ||||||||
\(784\) | 6.60184 | 0.235780 | ||||||||
\(785\) | −7.61497 | −0.271790 | ||||||||
\(786\) | 16.0892 | 0.573882 | ||||||||
\(787\) | 9.95463 | 0.354844 | 0.177422 | − | 0.984135i | \(-0.443224\pi\) | ||||
0.177422 | + | 0.984135i | \(0.443224\pi\) | |||||||
\(788\) | −35.6894 | −1.27138 | ||||||||
\(789\) | −2.35351 | −0.0837873 | ||||||||
\(790\) | −83.8498 | −2.98324 | ||||||||
\(791\) | 1.38759 | 0.0493370 | ||||||||
\(792\) | 57.2456 | 2.03413 | ||||||||
\(793\) | 4.26563 | 0.151477 | ||||||||
\(794\) | −42.5742 | −1.51090 | ||||||||
\(795\) | −2.80402 | −0.0994485 | ||||||||
\(796\) | 61.1099 | 2.16598 | ||||||||
\(797\) | 10.5031 | 0.372037 | 0.186019 | − | 0.982546i | \(-0.440442\pi\) | ||||
0.186019 | + | 0.982546i | \(0.440442\pi\) | |||||||
\(798\) | 3.93405 | 0.139264 | ||||||||
\(799\) | −14.2088 | −0.502673 | ||||||||
\(800\) | −6.27055 | −0.221697 | ||||||||
\(801\) | −2.87833 | −0.101701 | ||||||||
\(802\) | 45.8162 | 1.61783 | ||||||||
\(803\) | −40.9926 | −1.44660 | ||||||||
\(804\) | −11.2837 | −0.397946 | ||||||||
\(805\) | −15.9745 | −0.563026 | ||||||||
\(806\) | −3.76580 | −0.132645 | ||||||||
\(807\) | 1.75531 | 0.0617900 | ||||||||
\(808\) | 39.0783 | 1.37477 | ||||||||
\(809\) | −4.58616 | −0.161241 | −0.0806204 | − | 0.996745i | \(-0.525690\pi\) | ||||
−0.0806204 | + | 0.996745i | \(0.525690\pi\) | |||||||
\(810\) | 52.7907 | 1.85488 | ||||||||
\(811\) | 31.9442 | 1.12171 | 0.560856 | − | 0.827913i | \(-0.310472\pi\) | ||||
0.560856 | + | 0.827913i | \(0.310472\pi\) | |||||||
\(812\) | −7.59351 | −0.266480 | ||||||||
\(813\) | −1.20635 | −0.0423085 | ||||||||
\(814\) | 81.8843 | 2.87004 | ||||||||
\(815\) | −54.1057 | −1.89524 | ||||||||
\(816\) | −2.49685 | −0.0874071 | ||||||||
\(817\) | 40.2372 | 1.40772 | ||||||||
\(818\) | 3.46910 | 0.121294 | ||||||||
\(819\) | −0.861642 | −0.0301082 | ||||||||
\(820\) | 67.6025 | 2.36078 | ||||||||
\(821\) | −10.6343 | −0.371139 | −0.185570 | − | 0.982631i | \(-0.559413\pi\) | ||||
−0.185570 | + | 0.982631i | \(0.559413\pi\) | |||||||
\(822\) | 4.67438 | 0.163038 | ||||||||
\(823\) | 19.2072 | 0.669520 | 0.334760 | − | 0.942303i | \(-0.391345\pi\) | ||||
0.334760 | + | 0.942303i | \(0.391345\pi\) | |||||||
\(824\) | −7.21856 | −0.251470 | ||||||||
\(825\) | 1.29010 | 0.0449156 | ||||||||
\(826\) | −2.96873 | −0.103295 | ||||||||
\(827\) | 55.5387 | 1.93127 | 0.965635 | − | 0.259902i | \(-0.0836902\pi\) | ||||
0.965635 | + | 0.259902i | \(0.0836902\pi\) | |||||||
\(828\) | −81.2406 | −2.82331 | ||||||||
\(829\) | 28.2653 | 0.981693 | 0.490846 | − | 0.871246i | \(-0.336688\pi\) | ||||
0.490846 | + | 0.871246i | \(0.336688\pi\) | |||||||
\(830\) | 10.0284 | 0.348090 | ||||||||
\(831\) | 4.10156 | 0.142281 | ||||||||
\(832\) | −0.513957 | −0.0178182 | ||||||||
\(833\) | −1.30810 | −0.0453230 | ||||||||
\(834\) | 6.15692 | 0.213197 | ||||||||
\(835\) | 40.8650 | 1.41419 | ||||||||
\(836\) | −76.3462 | −2.64049 | ||||||||
\(837\) | −8.61439 | −0.297757 | ||||||||
\(838\) | −52.7988 | −1.82390 | ||||||||
\(839\) | 11.8970 | 0.410730 | 0.205365 | − | 0.978685i | \(-0.434162\pi\) | ||||
0.205365 | + | 0.978685i | \(0.434162\pi\) | |||||||
\(840\) | 4.44905 | 0.153507 | ||||||||
\(841\) | −26.0299 | −0.897584 | ||||||||
\(842\) | 29.8052 | 1.02715 | ||||||||
\(843\) | −7.71952 | −0.265875 | ||||||||
\(844\) | −22.3985 | −0.770987 | ||||||||
\(845\) | 32.6271 | 1.12240 | ||||||||
\(846\) | 80.1796 | 2.75663 | ||||||||
\(847\) | −0.611653 | −0.0210166 | ||||||||
\(848\) | 25.3396 | 0.870167 | ||||||||
\(849\) | −2.59547 | −0.0890763 | ||||||||
\(850\) | 4.58358 | 0.157215 | ||||||||
\(851\) | −63.4592 | −2.17535 | ||||||||
\(852\) | 14.0814 | 0.482421 | ||||||||
\(853\) | −18.6623 | −0.638986 | −0.319493 | − | 0.947589i | \(-0.603513\pi\) | ||||
−0.319493 | + | 0.947589i | \(0.603513\pi\) | |||||||
\(854\) | −36.5429 | −1.25047 | ||||||||
\(855\) | −39.6154 | −1.35482 | ||||||||
\(856\) | −74.0204 | −2.52996 | ||||||||
\(857\) | 1.59377 | 0.0544420 | 0.0272210 | − | 0.999629i | \(-0.491334\pi\) | ||||
0.0272210 | + | 0.999629i | \(0.491334\pi\) | |||||||
\(858\) | −0.696845 | −0.0237899 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | 83.3282 | 2.84147 | ||||||||
\(861\) | −1.75561 | −0.0598311 | ||||||||
\(862\) | 17.9342 | 0.610840 | ||||||||
\(863\) | 12.1094 | 0.412210 | 0.206105 | − | 0.978530i | \(-0.433921\pi\) | ||||
0.206105 | + | 0.978530i | \(0.433921\pi\) | |||||||
\(864\) | 7.74791 | 0.263589 | ||||||||
\(865\) | −6.96240 | −0.236729 | ||||||||
\(866\) | −15.7313 | −0.534570 | ||||||||
\(867\) | −4.42040 | −0.150125 | ||||||||
\(868\) | 22.1891 | 0.753147 | ||||||||
\(869\) | −42.2587 | −1.43353 | ||||||||
\(870\) | −3.18661 | −0.108036 | ||||||||
\(871\) | −2.61690 | −0.0886701 | ||||||||
\(872\) | 19.4690 | 0.659304 | ||||||||
\(873\) | 3.45444 | 0.116915 | ||||||||
\(874\) | 86.0240 | 2.90980 | ||||||||
\(875\) | 9.13565 | 0.308841 | ||||||||
\(876\) | −16.2023 | −0.547426 | ||||||||
\(877\) | −14.7202 | −0.497065 | −0.248532 | − | 0.968624i | \(-0.579948\pi\) | ||||
−0.248532 | + | 0.968624i | \(0.579948\pi\) | |||||||
\(878\) | −27.7206 | −0.935525 | ||||||||
\(879\) | 6.10429 | 0.205893 | ||||||||
\(880\) | −53.7649 | −1.81241 | ||||||||
\(881\) | −11.7035 | −0.394301 | −0.197151 | − | 0.980373i | \(-0.563169\pi\) | ||||
−0.197151 | + | 0.980373i | \(0.563169\pi\) | |||||||
\(882\) | 7.38153 | 0.248549 | ||||||||
\(883\) | −8.03627 | −0.270442 | −0.135221 | − | 0.990815i | \(-0.543174\pi\) | ||||
−0.135221 | + | 0.990815i | \(0.543174\pi\) | |||||||
\(884\) | −1.70286 | −0.0572734 | ||||||||
\(885\) | −0.856878 | −0.0288036 | ||||||||
\(886\) | 13.9625 | 0.469078 | ||||||||
\(887\) | 42.5424 | 1.42843 | 0.714217 | − | 0.699925i | \(-0.246783\pi\) | ||||
0.714217 | + | 0.699925i | \(0.246783\pi\) | |||||||
\(888\) | 17.6740 | 0.593101 | ||||||||
\(889\) | −3.11282 | −0.104401 | ||||||||
\(890\) | 6.31178 | 0.211571 | ||||||||
\(891\) | 26.6055 | 0.891319 | ||||||||
\(892\) | 34.6150 | 1.15900 | ||||||||
\(893\) | −58.3946 | −1.95410 | ||||||||
\(894\) | −8.88411 | −0.297129 | ||||||||
\(895\) | −53.0911 | −1.77464 | ||||||||
\(896\) | 13.4618 | 0.449727 | ||||||||
\(897\) | 0.540045 | 0.0180316 | ||||||||
\(898\) | −56.8383 | −1.89672 | ||||||||
\(899\) | −8.67889 | −0.289457 | ||||||||
\(900\) | −17.7898 | −0.592995 | ||||||||
\(901\) | −5.02085 | −0.167269 | ||||||||
\(902\) | 49.5353 | 1.64934 | ||||||||
\(903\) | −2.16401 | −0.0720136 | ||||||||
\(904\) | −8.45048 | −0.281059 | ||||||||
\(905\) | 0.227994 | 0.00757878 | ||||||||
\(906\) | −1.60069 | −0.0531795 | ||||||||
\(907\) | 5.90337 | 0.196018 | 0.0980091 | − | 0.995186i | \(-0.468753\pi\) | ||||
0.0980091 | + | 0.995186i | \(0.468753\pi\) | |||||||
\(908\) | 22.8936 | 0.759750 | ||||||||
\(909\) | 18.7139 | 0.620699 | ||||||||
\(910\) | 1.88946 | 0.0626350 | ||||||||
\(911\) | −10.0983 | −0.334571 | −0.167285 | − | 0.985908i | \(-0.553500\pi\) | ||||
−0.167285 | + | 0.985908i | \(0.553500\pi\) | |||||||
\(912\) | −10.2614 | −0.339788 | ||||||||
\(913\) | 5.05412 | 0.167267 | ||||||||
\(914\) | −98.8151 | −3.26851 | ||||||||
\(915\) | −10.5475 | −0.348690 | ||||||||
\(916\) | 107.997 | 3.56831 | ||||||||
\(917\) | −21.9862 | −0.726048 | ||||||||
\(918\) | −5.66348 | −0.186923 | ||||||||
\(919\) | −51.8165 | −1.70927 | −0.854634 | − | 0.519231i | \(-0.826218\pi\) | ||||
−0.854634 | + | 0.519231i | \(0.826218\pi\) | |||||||
\(920\) | 97.2852 | 3.20740 | ||||||||
\(921\) | 0.379440 | 0.0125030 | ||||||||
\(922\) | −43.1783 | −1.42200 | ||||||||
\(923\) | 3.26573 | 0.107493 | ||||||||
\(924\) | 4.10599 | 0.135077 | ||||||||
\(925\) | −13.8961 | −0.456902 | ||||||||
\(926\) | −76.5786 | −2.51653 | ||||||||
\(927\) | −3.45683 | −0.113537 | ||||||||
\(928\) | 7.80593 | 0.256242 | ||||||||
\(929\) | −45.3911 | −1.48923 | −0.744616 | − | 0.667493i | \(-0.767367\pi\) | ||||
−0.744616 | + | 0.667493i | \(0.767367\pi\) | |||||||
\(930\) | 9.31162 | 0.305340 | ||||||||
\(931\) | −5.37595 | −0.176190 | ||||||||
\(932\) | 18.1734 | 0.595289 | ||||||||
\(933\) | −1.44904 | −0.0474394 | ||||||||
\(934\) | −15.8962 | −0.520138 | ||||||||
\(935\) | 10.6531 | 0.348393 | ||||||||
\(936\) | 5.24744 | 0.171518 | ||||||||
\(937\) | 43.2934 | 1.41433 | 0.707167 | − | 0.707047i | \(-0.249973\pi\) | ||||
0.707167 | + | 0.707047i | \(0.249973\pi\) | |||||||
\(938\) | 22.4185 | 0.731989 | ||||||||
\(939\) | 3.40337 | 0.111065 | ||||||||
\(940\) | −120.931 | −3.94433 | ||||||||
\(941\) | 33.2694 | 1.08455 | 0.542276 | − | 0.840200i | \(-0.317563\pi\) | ||||
0.542276 | + | 0.840200i | \(0.317563\pi\) | |||||||
\(942\) | −2.20542 | −0.0718566 | ||||||||
\(943\) | −38.3892 | −1.25012 | ||||||||
\(944\) | 7.74351 | 0.252030 | ||||||||
\(945\) | 4.32219 | 0.140601 | ||||||||
\(946\) | 61.0582 | 1.98517 | ||||||||
\(947\) | 58.9688 | 1.91623 | 0.958114 | − | 0.286388i | \(-0.0924547\pi\) | ||||
0.958114 | + | 0.286388i | \(0.0924547\pi\) | |||||||
\(948\) | −16.7027 | −0.542480 | ||||||||
\(949\) | −3.75760 | −0.121977 | ||||||||
\(950\) | 18.8373 | 0.611162 | ||||||||
\(951\) | 1.65225 | 0.0535778 | ||||||||
\(952\) | 7.96640 | 0.258192 | ||||||||
\(953\) | −18.5706 | −0.601560 | −0.300780 | − | 0.953694i | \(-0.597247\pi\) | ||||
−0.300780 | + | 0.953694i | \(0.597247\pi\) | |||||||
\(954\) | 28.3323 | 0.917293 | ||||||||
\(955\) | 56.6136 | 1.83197 | ||||||||
\(956\) | −29.2489 | −0.945978 | ||||||||
\(957\) | −1.60599 | −0.0519143 | ||||||||
\(958\) | −12.6907 | −0.410017 | ||||||||
\(959\) | −6.38763 | −0.206267 | ||||||||
\(960\) | 1.27085 | 0.0410165 | ||||||||
\(961\) | −5.63932 | −0.181913 | ||||||||
\(962\) | 7.50595 | 0.242002 | ||||||||
\(963\) | −35.4469 | −1.14226 | ||||||||
\(964\) | 89.6548 | 2.88759 | ||||||||
\(965\) | −52.0733 | −1.67630 | ||||||||
\(966\) | −4.62647 | −0.148854 | ||||||||
\(967\) | 5.30714 | 0.170666 | 0.0853330 | − | 0.996352i | \(-0.472805\pi\) | ||||
0.0853330 | + | 0.996352i | \(0.472805\pi\) | |||||||
\(968\) | 3.72500 | 0.119726 | ||||||||
\(969\) | 2.03321 | 0.0653161 | ||||||||
\(970\) | −7.57511 | −0.243222 | ||||||||
\(971\) | −22.3661 | −0.717763 | −0.358881 | − | 0.933383i | \(-0.616842\pi\) | ||||
−0.358881 | + | 0.933383i | \(0.616842\pi\) | |||||||
\(972\) | 33.1270 | 1.06255 | ||||||||
\(973\) | −8.41355 | −0.269726 | ||||||||
\(974\) | 21.3877 | 0.685308 | ||||||||
\(975\) | 0.118258 | 0.00378728 | ||||||||
\(976\) | 95.3168 | 3.05102 | ||||||||
\(977\) | 35.4689 | 1.13475 | 0.567375 | − | 0.823459i | \(-0.307959\pi\) | ||||
0.567375 | + | 0.823459i | \(0.307959\pi\) | |||||||
\(978\) | −15.6699 | −0.501068 | ||||||||
\(979\) | 3.18102 | 0.101666 | ||||||||
\(980\) | −11.1332 | −0.355637 | ||||||||
\(981\) | 9.32334 | 0.297671 | ||||||||
\(982\) | 35.6709 | 1.13830 | ||||||||
\(983\) | −2.38518 | −0.0760753 | −0.0380377 | − | 0.999276i | \(-0.512111\pi\) | ||||
−0.0380377 | + | 0.999276i | \(0.512111\pi\) | |||||||
\(984\) | 10.6918 | 0.340841 | ||||||||
\(985\) | 20.4663 | 0.652112 | ||||||||
\(986\) | −5.70589 | −0.181713 | ||||||||
\(987\) | 3.14053 | 0.0999642 | ||||||||
\(988\) | −6.99830 | −0.222646 | ||||||||
\(989\) | −47.3193 | −1.50467 | ||||||||
\(990\) | −60.1146 | −1.91057 | ||||||||
\(991\) | −35.2261 | −1.11899 | −0.559497 | − | 0.828833i | \(-0.689005\pi\) | ||||
−0.559497 | + | 0.828833i | \(0.689005\pi\) | |||||||
\(992\) | −22.8098 | −0.724212 | ||||||||
\(993\) | −3.86631 | −0.122694 | ||||||||
\(994\) | −27.9769 | −0.887374 | ||||||||
\(995\) | −35.0439 | −1.11097 | ||||||||
\(996\) | 1.99764 | 0.0632976 | ||||||||
\(997\) | 3.91260 | 0.123913 | 0.0619567 | − | 0.998079i | \(-0.480266\pi\) | ||||
0.0619567 | + | 0.998079i | \(0.480266\pi\) | |||||||
\(998\) | 16.7770 | 0.531066 | ||||||||
\(999\) | 17.1701 | 0.543238 |
(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 | 6013.2.a.e.1.6 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.e.1.6 | ✓ | 109 | 1.1 | even | 1 | trivial |