Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(66\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.61 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.42070 | 1.71169 | 0.855847 | − | 0.517229i | \(-0.173036\pi\) | ||||
0.855847 | + | 0.517229i | \(0.173036\pi\) | |||||||
\(3\) | −1.43320 | −0.827459 | −0.413729 | − | 0.910400i | \(-0.635774\pi\) | ||||
−0.413729 | + | 0.910400i | \(0.635774\pi\) | |||||||
\(4\) | 3.85979 | 1.92990 | ||||||||
\(5\) | −0.00337016 | −0.00150718 | −0.000753591 | − | 1.00000i | \(-0.500240\pi\) | ||||
−0.000753591 | 1.00000i | \(0.500240\pi\) | ||||||||
\(6\) | −3.46935 | −1.41636 | ||||||||
\(7\) | −4.65271 | −1.75856 | −0.879279 | − | 0.476307i | \(-0.841975\pi\) | ||||
−0.879279 | + | 0.476307i | \(0.841975\pi\) | |||||||
\(8\) | 4.50200 | 1.59170 | ||||||||
\(9\) | −0.945936 | −0.315312 | ||||||||
\(10\) | −0.00815815 | −0.00257983 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −5.53186 | −1.59691 | ||||||||
\(13\) | −3.09924 | −0.859574 | −0.429787 | − | 0.902930i | \(-0.641411\pi\) | ||||
−0.429787 | + | 0.902930i | \(0.641411\pi\) | |||||||
\(14\) | −11.2628 | −3.01011 | ||||||||
\(15\) | 0.00483012 | 0.00124713 | ||||||||
\(16\) | 3.17842 | 0.794604 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.28983 | −0.539718 | ||||||||
\(19\) | 1.66965 | 0.383045 | 0.191522 | − | 0.981488i | \(-0.438658\pi\) | ||||
0.191522 | + | 0.981488i | \(0.438658\pi\) | |||||||
\(20\) | −0.0130081 | −0.00290871 | ||||||||
\(21\) | 6.66827 | 1.45513 | ||||||||
\(22\) | −2.42070 | −0.516095 | ||||||||
\(23\) | 0.653083 | 0.136177 | 0.0680886 | − | 0.997679i | \(-0.478310\pi\) | ||||
0.0680886 | + | 0.997679i | \(0.478310\pi\) | |||||||
\(24\) | −6.45227 | −1.31706 | ||||||||
\(25\) | −4.99999 | −0.999998 | ||||||||
\(26\) | −7.50233 | −1.47133 | ||||||||
\(27\) | 5.65532 | 1.08837 | ||||||||
\(28\) | −17.9585 | −3.39384 | ||||||||
\(29\) | 6.43985 | 1.19585 | 0.597925 | − | 0.801552i | \(-0.295992\pi\) | ||||
0.597925 | + | 0.801552i | \(0.295992\pi\) | |||||||
\(30\) | 0.0116923 | 0.00213471 | ||||||||
\(31\) | −1.77371 | −0.318568 | −0.159284 | − | 0.987233i | \(-0.550918\pi\) | ||||
−0.159284 | + | 0.987233i | \(0.550918\pi\) | |||||||
\(32\) | −1.31001 | −0.231579 | ||||||||
\(33\) | 1.43320 | 0.249488 | ||||||||
\(34\) | −2.42070 | −0.415147 | ||||||||
\(35\) | 0.0156804 | 0.00265047 | ||||||||
\(36\) | −3.65112 | −0.608520 | ||||||||
\(37\) | 7.07156 | 1.16256 | 0.581279 | − | 0.813705i | \(-0.302553\pi\) | ||||
0.581279 | + | 0.813705i | \(0.302553\pi\) | |||||||
\(38\) | 4.04173 | 0.655656 | ||||||||
\(39\) | 4.44183 | 0.711262 | ||||||||
\(40\) | −0.0151725 | −0.00239898 | ||||||||
\(41\) | −3.90367 | −0.609651 | −0.304826 | − | 0.952408i | \(-0.598598\pi\) | ||||
−0.304826 | + | 0.952408i | \(0.598598\pi\) | |||||||
\(42\) | 16.1419 | 2.49075 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −3.85979 | −0.581886 | ||||||||
\(45\) | 0.00318796 | 0.000475233 0 | ||||||||
\(46\) | 1.58092 | 0.233094 | ||||||||
\(47\) | 4.49308 | 0.655384 | 0.327692 | − | 0.944785i | \(-0.393729\pi\) | ||||
0.327692 | + | 0.944785i | \(0.393729\pi\) | |||||||
\(48\) | −4.55531 | −0.657502 | ||||||||
\(49\) | 14.6477 | 2.09253 | ||||||||
\(50\) | −12.1035 | −1.71169 | ||||||||
\(51\) | 1.43320 | 0.200688 | ||||||||
\(52\) | −11.9624 | −1.65889 | ||||||||
\(53\) | 5.29549 | 0.727391 | 0.363695 | − | 0.931518i | \(-0.381515\pi\) | ||||
0.363695 | + | 0.931518i | \(0.381515\pi\) | |||||||
\(54\) | 13.6898 | 1.86295 | ||||||||
\(55\) | 0.00337016 | 0.000454432 0 | ||||||||
\(56\) | −20.9465 | −2.79910 | ||||||||
\(57\) | −2.39295 | −0.316954 | ||||||||
\(58\) | 15.5890 | 2.04693 | ||||||||
\(59\) | −3.35044 | −0.436190 | −0.218095 | − | 0.975928i | \(-0.569984\pi\) | ||||
−0.218095 | + | 0.975928i | \(0.569984\pi\) | |||||||
\(60\) | 0.0186433 | 0.00240683 | ||||||||
\(61\) | 6.18793 | 0.792283 | 0.396142 | − | 0.918189i | \(-0.370349\pi\) | ||||
0.396142 | + | 0.918189i | \(0.370349\pi\) | |||||||
\(62\) | −4.29362 | −0.545290 | ||||||||
\(63\) | 4.40116 | 0.554495 | ||||||||
\(64\) | −9.52797 | −1.19100 | ||||||||
\(65\) | 0.0104449 | 0.00129553 | ||||||||
\(66\) | 3.46935 | 0.427047 | ||||||||
\(67\) | 9.54604 | 1.16623 | 0.583117 | − | 0.812388i | \(-0.301833\pi\) | ||||
0.583117 | + | 0.812388i | \(0.301833\pi\) | |||||||
\(68\) | −3.85979 | −0.468069 | ||||||||
\(69\) | −0.935999 | −0.112681 | ||||||||
\(70\) | 0.0379575 | 0.00453679 | ||||||||
\(71\) | 16.4000 | 1.94632 | 0.973161 | − | 0.230124i | \(-0.0739131\pi\) | ||||
0.973161 | + | 0.230124i | \(0.0739131\pi\) | |||||||
\(72\) | −4.25861 | −0.501882 | ||||||||
\(73\) | 12.3859 | 1.44966 | 0.724830 | − | 0.688928i | \(-0.241918\pi\) | ||||
0.724830 | + | 0.688928i | \(0.241918\pi\) | |||||||
\(74\) | 17.1181 | 1.98994 | ||||||||
\(75\) | 7.16599 | 0.827457 | ||||||||
\(76\) | 6.44452 | 0.739237 | ||||||||
\(77\) | 4.65271 | 0.530225 | ||||||||
\(78\) | 10.7523 | 1.21746 | ||||||||
\(79\) | −3.55372 | −0.399825 | −0.199912 | − | 0.979814i | \(-0.564066\pi\) | ||||
−0.199912 | + | 0.979814i | \(0.564066\pi\) | |||||||
\(80\) | −0.0107118 | −0.00119761 | ||||||||
\(81\) | −5.26740 | −0.585266 | ||||||||
\(82\) | −9.44962 | −1.04354 | ||||||||
\(83\) | −5.51588 | −0.605447 | −0.302723 | − | 0.953078i | \(-0.597896\pi\) | ||||
−0.302723 | + | 0.953078i | \(0.597896\pi\) | |||||||
\(84\) | 25.7381 | 2.80826 | ||||||||
\(85\) | 0.00337016 | 0.000365545 0 | ||||||||
\(86\) | 2.42070 | 0.261031 | ||||||||
\(87\) | −9.22960 | −0.989517 | ||||||||
\(88\) | −4.50200 | −0.479915 | ||||||||
\(89\) | −2.24023 | −0.237464 | −0.118732 | − | 0.992926i | \(-0.537883\pi\) | ||||
−0.118732 | + | 0.992926i | \(0.537883\pi\) | |||||||
\(90\) | 0.00771709 | 0.000813453 0 | ||||||||
\(91\) | 14.4199 | 1.51161 | ||||||||
\(92\) | 2.52077 | 0.262808 | ||||||||
\(93\) | 2.54208 | 0.263602 | ||||||||
\(94\) | 10.8764 | 1.12182 | ||||||||
\(95\) | −0.00562700 | −0.000577318 0 | ||||||||
\(96\) | 1.87751 | 0.191622 | ||||||||
\(97\) | 3.26573 | 0.331584 | 0.165792 | − | 0.986161i | \(-0.446982\pi\) | ||||
0.165792 | + | 0.986161i | \(0.446982\pi\) | |||||||
\(98\) | 35.4577 | 3.58177 | ||||||||
\(99\) | 0.945936 | 0.0950701 | ||||||||
\(100\) | −19.2989 | −1.92989 | ||||||||
\(101\) | −15.2915 | −1.52156 | −0.760779 | − | 0.649011i | \(-0.775183\pi\) | ||||
−0.760779 | + | 0.649011i | \(0.775183\pi\) | |||||||
\(102\) | 3.46935 | 0.343517 | ||||||||
\(103\) | −12.7691 | −1.25818 | −0.629091 | − | 0.777332i | \(-0.716573\pi\) | ||||
−0.629091 | + | 0.777332i | \(0.716573\pi\) | |||||||
\(104\) | −13.9528 | −1.36818 | ||||||||
\(105\) | −0.0224731 | −0.00219315 | ||||||||
\(106\) | 12.8188 | 1.24507 | ||||||||
\(107\) | 4.18526 | 0.404604 | 0.202302 | − | 0.979323i | \(-0.435158\pi\) | ||||
0.202302 | + | 0.979323i | \(0.435158\pi\) | |||||||
\(108\) | 21.8284 | 2.10043 | ||||||||
\(109\) | −10.5776 | −1.01315 | −0.506576 | − | 0.862195i | \(-0.669089\pi\) | ||||
−0.506576 | + | 0.862195i | \(0.669089\pi\) | |||||||
\(110\) | 0.00815815 | 0.000777849 0 | ||||||||
\(111\) | −10.1350 | −0.961968 | ||||||||
\(112\) | −14.7883 | −1.39736 | ||||||||
\(113\) | 8.11251 | 0.763161 | 0.381580 | − | 0.924336i | \(-0.375380\pi\) | ||||
0.381580 | + | 0.924336i | \(0.375380\pi\) | |||||||
\(114\) | −5.79261 | −0.542528 | ||||||||
\(115\) | −0.00220100 | −0.000205244 0 | ||||||||
\(116\) | 24.8565 | 2.30787 | ||||||||
\(117\) | 2.93168 | 0.271034 | ||||||||
\(118\) | −8.11041 | −0.746624 | ||||||||
\(119\) | 4.65271 | 0.426513 | ||||||||
\(120\) | 0.0217452 | 0.00198506 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 14.9791 | 1.35615 | ||||||||
\(123\) | 5.59475 | 0.504461 | ||||||||
\(124\) | −6.84615 | −0.614803 | ||||||||
\(125\) | 0.0337016 | 0.00301436 | ||||||||
\(126\) | 10.6539 | 0.949125 | ||||||||
\(127\) | −11.6087 | −1.03010 | −0.515052 | − | 0.857159i | \(-0.672227\pi\) | ||||
−0.515052 | + | 0.857159i | \(0.672227\pi\) | |||||||
\(128\) | −20.4444 | −1.80704 | ||||||||
\(129\) | −1.43320 | −0.126186 | ||||||||
\(130\) | 0.0252841 | 0.00221756 | ||||||||
\(131\) | 22.3800 | 1.95535 | 0.977676 | − | 0.210118i | \(-0.0673847\pi\) | ||||
0.977676 | + | 0.210118i | \(0.0673847\pi\) | |||||||
\(132\) | 5.53186 | 0.481486 | ||||||||
\(133\) | −7.76841 | −0.673607 | ||||||||
\(134\) | 23.1081 | 1.99624 | ||||||||
\(135\) | −0.0190593 | −0.00164037 | ||||||||
\(136\) | −4.50200 | −0.386044 | ||||||||
\(137\) | −19.2588 | −1.64539 | −0.822694 | − | 0.568484i | \(-0.807530\pi\) | ||||
−0.822694 | + | 0.568484i | \(0.807530\pi\) | |||||||
\(138\) | −2.26577 | −0.192875 | ||||||||
\(139\) | 10.4945 | 0.890132 | 0.445066 | − | 0.895498i | \(-0.353180\pi\) | ||||
0.445066 | + | 0.895498i | \(0.353180\pi\) | |||||||
\(140\) | 0.0605230 | 0.00511513 | ||||||||
\(141\) | −6.43949 | −0.542303 | ||||||||
\(142\) | 39.6995 | 3.33151 | ||||||||
\(143\) | 3.09924 | 0.259171 | ||||||||
\(144\) | −3.00658 | −0.250548 | ||||||||
\(145\) | −0.0217033 | −0.00180236 | ||||||||
\(146\) | 29.9825 | 2.48137 | ||||||||
\(147\) | −20.9931 | −1.73148 | ||||||||
\(148\) | 27.2948 | 2.24362 | ||||||||
\(149\) | 19.5834 | 1.60434 | 0.802168 | − | 0.597098i | \(-0.203680\pi\) | ||||
0.802168 | + | 0.597098i | \(0.203680\pi\) | |||||||
\(150\) | 17.3467 | 1.41635 | ||||||||
\(151\) | 11.9601 | 0.973296 | 0.486648 | − | 0.873598i | \(-0.338220\pi\) | ||||
0.486648 | + | 0.873598i | \(0.338220\pi\) | |||||||
\(152\) | 7.51679 | 0.609692 | ||||||||
\(153\) | 0.945936 | 0.0764744 | ||||||||
\(154\) | 11.2628 | 0.907584 | ||||||||
\(155\) | 0.00597769 | 0.000480139 0 | ||||||||
\(156\) | 17.1445 | 1.37266 | ||||||||
\(157\) | −14.8675 | −1.18655 | −0.593277 | − | 0.804998i | \(-0.702166\pi\) | ||||
−0.593277 | + | 0.804998i | \(0.702166\pi\) | |||||||
\(158\) | −8.60249 | −0.684377 | ||||||||
\(159\) | −7.58949 | −0.601886 | ||||||||
\(160\) | 0.00441494 | 0.000349032 0 | ||||||||
\(161\) | −3.03861 | −0.239476 | ||||||||
\(162\) | −12.7508 | −1.00180 | ||||||||
\(163\) | −14.2584 | −1.11681 | −0.558403 | − | 0.829570i | \(-0.688586\pi\) | ||||
−0.558403 | + | 0.829570i | \(0.688586\pi\) | |||||||
\(164\) | −15.0674 | −1.17656 | ||||||||
\(165\) | −0.00483012 | −0.000376024 0 | ||||||||
\(166\) | −13.3523 | −1.03634 | ||||||||
\(167\) | −0.786164 | −0.0608352 | −0.0304176 | − | 0.999537i | \(-0.509684\pi\) | ||||
−0.0304176 | + | 0.999537i | \(0.509684\pi\) | |||||||
\(168\) | 30.0206 | 2.31614 | ||||||||
\(169\) | −3.39472 | −0.261133 | ||||||||
\(170\) | 0.00815815 | 0.000625702 0 | ||||||||
\(171\) | −1.57939 | −0.120779 | ||||||||
\(172\) | 3.85979 | 0.294306 | ||||||||
\(173\) | −8.11629 | −0.617070 | −0.308535 | − | 0.951213i | \(-0.599839\pi\) | ||||
−0.308535 | + | 0.951213i | \(0.599839\pi\) | |||||||
\(174\) | −22.3421 | −1.69375 | ||||||||
\(175\) | 23.2635 | 1.75855 | ||||||||
\(176\) | −3.17842 | −0.239582 | ||||||||
\(177\) | 4.80185 | 0.360929 | ||||||||
\(178\) | −5.42292 | −0.406465 | ||||||||
\(179\) | 20.1131 | 1.50332 | 0.751660 | − | 0.659550i | \(-0.229253\pi\) | ||||
0.751660 | + | 0.659550i | \(0.229253\pi\) | |||||||
\(180\) | 0.0123049 | 0.000917150 0 | ||||||||
\(181\) | 7.31744 | 0.543901 | 0.271950 | − | 0.962311i | \(-0.412331\pi\) | ||||
0.271950 | + | 0.962311i | \(0.412331\pi\) | |||||||
\(182\) | 34.9061 | 2.58742 | ||||||||
\(183\) | −8.86855 | −0.655582 | ||||||||
\(184\) | 2.94018 | 0.216753 | ||||||||
\(185\) | −0.0238323 | −0.00175219 | ||||||||
\(186\) | 6.15362 | 0.451205 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 17.3424 | 1.26482 | ||||||||
\(189\) | −26.3125 | −1.91396 | ||||||||
\(190\) | −0.0136213 | −0.000988192 0 | ||||||||
\(191\) | 3.70145 | 0.267828 | 0.133914 | − | 0.990993i | \(-0.457245\pi\) | ||||
0.133914 | + | 0.990993i | \(0.457245\pi\) | |||||||
\(192\) | 13.6555 | 0.985501 | ||||||||
\(193\) | −4.28658 | −0.308555 | −0.154277 | − | 0.988028i | \(-0.549305\pi\) | ||||
−0.154277 | + | 0.988028i | \(0.549305\pi\) | |||||||
\(194\) | 7.90535 | 0.567571 | ||||||||
\(195\) | −0.0149697 | −0.00107200 | ||||||||
\(196\) | 56.5371 | 4.03836 | ||||||||
\(197\) | 14.5531 | 1.03687 | 0.518433 | − | 0.855118i | \(-0.326515\pi\) | ||||
0.518433 | + | 0.855118i | \(0.326515\pi\) | |||||||
\(198\) | 2.28983 | 0.162731 | ||||||||
\(199\) | −14.2291 | −1.00867 | −0.504336 | − | 0.863507i | \(-0.668263\pi\) | ||||
−0.504336 | + | 0.863507i | \(0.668263\pi\) | |||||||
\(200\) | −22.5100 | −1.59169 | ||||||||
\(201\) | −13.6814 | −0.965011 | ||||||||
\(202\) | −37.0161 | −2.60444 | ||||||||
\(203\) | −29.9628 | −2.10297 | ||||||||
\(204\) | 5.53186 | 0.387308 | ||||||||
\(205\) | 0.0131560 | 0.000918855 0 | ||||||||
\(206\) | −30.9103 | −2.15362 | ||||||||
\(207\) | −0.617775 | −0.0429383 | ||||||||
\(208\) | −9.85067 | −0.683021 | ||||||||
\(209\) | −1.66965 | −0.115492 | ||||||||
\(210\) | −0.0544007 | −0.00375401 | ||||||||
\(211\) | 13.3185 | 0.916882 | 0.458441 | − | 0.888725i | \(-0.348408\pi\) | ||||
0.458441 | + | 0.888725i | \(0.348408\pi\) | |||||||
\(212\) | 20.4395 | 1.40379 | ||||||||
\(213\) | −23.5045 | −1.61050 | ||||||||
\(214\) | 10.1313 | 0.692559 | ||||||||
\(215\) | −0.00337016 | −0.000229843 0 | ||||||||
\(216\) | 25.4603 | 1.73235 | ||||||||
\(217\) | 8.25255 | 0.560220 | ||||||||
\(218\) | −25.6053 | −1.73421 | ||||||||
\(219\) | −17.7515 | −1.19953 | ||||||||
\(220\) | 0.0130081 | 0.000877008 0 | ||||||||
\(221\) | 3.09924 | 0.208477 | ||||||||
\(222\) | −24.5337 | −1.64660 | ||||||||
\(223\) | 12.2899 | 0.822993 | 0.411497 | − | 0.911411i | \(-0.365006\pi\) | ||||
0.411497 | + | 0.911411i | \(0.365006\pi\) | |||||||
\(224\) | 6.09509 | 0.407245 | ||||||||
\(225\) | 4.72967 | 0.315311 | ||||||||
\(226\) | 19.6380 | 1.30630 | ||||||||
\(227\) | 8.28733 | 0.550049 | 0.275025 | − | 0.961437i | \(-0.411314\pi\) | ||||
0.275025 | + | 0.961437i | \(0.411314\pi\) | |||||||
\(228\) | −9.23629 | −0.611688 | ||||||||
\(229\) | 2.24090 | 0.148083 | 0.0740413 | − | 0.997255i | \(-0.476410\pi\) | ||||
0.0740413 | + | 0.997255i | \(0.476410\pi\) | |||||||
\(230\) | −0.00532795 | −0.000351315 0 | ||||||||
\(231\) | −6.66827 | −0.438740 | ||||||||
\(232\) | 28.9922 | 1.90343 | ||||||||
\(233\) | −10.4121 | −0.682117 | −0.341058 | − | 0.940042i | \(-0.610785\pi\) | ||||
−0.341058 | + | 0.940042i | \(0.610785\pi\) | |||||||
\(234\) | 7.09672 | 0.463927 | ||||||||
\(235\) | −0.0151424 | −0.000987783 0 | ||||||||
\(236\) | −12.9320 | −0.841801 | ||||||||
\(237\) | 5.09319 | 0.330838 | ||||||||
\(238\) | 11.2628 | 0.730060 | ||||||||
\(239\) | 18.9236 | 1.22406 | 0.612032 | − | 0.790833i | \(-0.290352\pi\) | ||||
0.612032 | + | 0.790833i | \(0.290352\pi\) | |||||||
\(240\) | 0.0153521 | 0.000990976 0 | ||||||||
\(241\) | 12.7638 | 0.822192 | 0.411096 | − | 0.911592i | \(-0.365146\pi\) | ||||
0.411096 | + | 0.911592i | \(0.365146\pi\) | |||||||
\(242\) | 2.42070 | 0.155609 | ||||||||
\(243\) | −9.41672 | −0.604083 | ||||||||
\(244\) | 23.8841 | 1.52902 | ||||||||
\(245\) | −0.0493651 | −0.00315382 | ||||||||
\(246\) | 13.5432 | 0.863483 | ||||||||
\(247\) | −5.17465 | −0.329255 | ||||||||
\(248\) | −7.98525 | −0.507064 | ||||||||
\(249\) | 7.90537 | 0.500982 | ||||||||
\(250\) | 0.0815814 | 0.00515966 | ||||||||
\(251\) | 12.0641 | 0.761479 | 0.380739 | − | 0.924682i | \(-0.375669\pi\) | ||||
0.380739 | + | 0.924682i | \(0.375669\pi\) | |||||||
\(252\) | 16.9876 | 1.07012 | ||||||||
\(253\) | −0.653083 | −0.0410590 | ||||||||
\(254\) | −28.1011 | −1.76322 | ||||||||
\(255\) | −0.00483012 | −0.000302474 0 | ||||||||
\(256\) | −30.4337 | −1.90211 | ||||||||
\(257\) | −7.07338 | −0.441225 | −0.220613 | − | 0.975362i | \(-0.570806\pi\) | ||||
−0.220613 | + | 0.975362i | \(0.570806\pi\) | |||||||
\(258\) | −3.46935 | −0.215992 | ||||||||
\(259\) | −32.9019 | −2.04443 | ||||||||
\(260\) | 0.0403153 | 0.00250025 | ||||||||
\(261\) | −6.09169 | −0.377066 | ||||||||
\(262\) | 54.1754 | 3.34696 | ||||||||
\(263\) | 5.45141 | 0.336148 | 0.168074 | − | 0.985774i | \(-0.446245\pi\) | ||||
0.168074 | + | 0.985774i | \(0.446245\pi\) | |||||||
\(264\) | 6.45227 | 0.397110 | ||||||||
\(265\) | −0.0178466 | −0.00109631 | ||||||||
\(266\) | −18.8050 | −1.15301 | ||||||||
\(267\) | 3.21070 | 0.196491 | ||||||||
\(268\) | 36.8457 | 2.25071 | ||||||||
\(269\) | −0.556012 | −0.0339006 | −0.0169503 | − | 0.999856i | \(-0.505396\pi\) | ||||
−0.0169503 | + | 0.999856i | \(0.505396\pi\) | |||||||
\(270\) | −0.0461369 | −0.00280781 | ||||||||
\(271\) | 3.62552 | 0.220234 | 0.110117 | − | 0.993919i | \(-0.464877\pi\) | ||||
0.110117 | + | 0.993919i | \(0.464877\pi\) | |||||||
\(272\) | −3.17842 | −0.192720 | ||||||||
\(273\) | −20.6665 | −1.25080 | ||||||||
\(274\) | −46.6198 | −2.81640 | ||||||||
\(275\) | 4.99999 | 0.301511 | ||||||||
\(276\) | −3.61276 | −0.217463 | ||||||||
\(277\) | 17.8843 | 1.07457 | 0.537283 | − | 0.843402i | \(-0.319451\pi\) | ||||
0.537283 | + | 0.843402i | \(0.319451\pi\) | |||||||
\(278\) | 25.4041 | 1.52363 | ||||||||
\(279\) | 1.67782 | 0.100448 | ||||||||
\(280\) | 0.0705931 | 0.00421875 | ||||||||
\(281\) | −32.9929 | −1.96819 | −0.984096 | − | 0.177640i | \(-0.943154\pi\) | ||||
−0.984096 | + | 0.177640i | \(0.943154\pi\) | |||||||
\(282\) | −15.5881 | −0.928257 | ||||||||
\(283\) | 6.13948 | 0.364954 | 0.182477 | − | 0.983210i | \(-0.441588\pi\) | ||||
0.182477 | + | 0.983210i | \(0.441588\pi\) | |||||||
\(284\) | 63.3006 | 3.75620 | ||||||||
\(285\) | 0.00806462 | 0.000477707 0 | ||||||||
\(286\) | 7.50233 | 0.443622 | ||||||||
\(287\) | 18.1626 | 1.07211 | ||||||||
\(288\) | 1.23918 | 0.0730196 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.0525373 | −0.00308510 | ||||||||
\(291\) | −4.68044 | −0.274372 | ||||||||
\(292\) | 47.8070 | 2.79769 | ||||||||
\(293\) | 6.09142 | 0.355864 | 0.177932 | − | 0.984043i | \(-0.443059\pi\) | ||||
0.177932 | + | 0.984043i | \(0.443059\pi\) | |||||||
\(294\) | −50.8180 | −2.96377 | ||||||||
\(295\) | 0.0112915 | 0.000657417 0 | ||||||||
\(296\) | 31.8362 | 1.85044 | ||||||||
\(297\) | −5.65532 | −0.328155 | ||||||||
\(298\) | 47.4056 | 2.74613 | ||||||||
\(299\) | −2.02406 | −0.117054 | ||||||||
\(300\) | 27.6592 | 1.59691 | ||||||||
\(301\) | −4.65271 | −0.268178 | ||||||||
\(302\) | 28.9517 | 1.66598 | ||||||||
\(303\) | 21.9157 | 1.25903 | ||||||||
\(304\) | 5.30686 | 0.304369 | ||||||||
\(305\) | −0.0208543 | −0.00119412 | ||||||||
\(306\) | 2.28983 | 0.130901 | ||||||||
\(307\) | 18.0884 | 1.03236 | 0.516180 | − | 0.856480i | \(-0.327353\pi\) | ||||
0.516180 | + | 0.856480i | \(0.327353\pi\) | |||||||
\(308\) | 17.9585 | 1.02328 | ||||||||
\(309\) | 18.3007 | 1.04109 | ||||||||
\(310\) | 0.0144702 | 0.000821852 0 | ||||||||
\(311\) | 13.9496 | 0.791009 | 0.395505 | − | 0.918464i | \(-0.370570\pi\) | ||||
0.395505 | + | 0.918464i | \(0.370570\pi\) | |||||||
\(312\) | 19.9971 | 1.13211 | ||||||||
\(313\) | 12.2987 | 0.695161 | 0.347581 | − | 0.937650i | \(-0.387003\pi\) | ||||
0.347581 | + | 0.937650i | \(0.387003\pi\) | |||||||
\(314\) | −35.9897 | −2.03102 | ||||||||
\(315\) | −0.0148326 | −0.000835724 0 | ||||||||
\(316\) | −13.7166 | −0.771620 | ||||||||
\(317\) | −33.7606 | −1.89618 | −0.948092 | − | 0.317995i | \(-0.896990\pi\) | ||||
−0.948092 | + | 0.317995i | \(0.896990\pi\) | |||||||
\(318\) | −18.3719 | −1.03024 | ||||||||
\(319\) | −6.43985 | −0.360562 | ||||||||
\(320\) | 0.0321108 | 0.00179505 | ||||||||
\(321\) | −5.99832 | −0.334793 | ||||||||
\(322\) | −7.35555 | −0.409909 | ||||||||
\(323\) | −1.66965 | −0.0929020 | ||||||||
\(324\) | −20.3311 | −1.12950 | ||||||||
\(325\) | 15.4962 | 0.859572 | ||||||||
\(326\) | −34.5154 | −1.91163 | ||||||||
\(327\) | 15.1599 | 0.838342 | ||||||||
\(328\) | −17.5743 | −0.970381 | ||||||||
\(329\) | −20.9050 | −1.15253 | ||||||||
\(330\) | −0.0116923 | −0.000643638 0 | ||||||||
\(331\) | −12.7011 | −0.698117 | −0.349058 | − | 0.937101i | \(-0.613498\pi\) | ||||
−0.349058 | + | 0.937101i | \(0.613498\pi\) | |||||||
\(332\) | −21.2902 | −1.16845 | ||||||||
\(333\) | −6.68924 | −0.366568 | ||||||||
\(334\) | −1.90307 | −0.104131 | ||||||||
\(335\) | −0.0321717 | −0.00175773 | ||||||||
\(336\) | 21.1945 | 1.15626 | ||||||||
\(337\) | 9.24386 | 0.503545 | 0.251772 | − | 0.967786i | \(-0.418987\pi\) | ||||
0.251772 | + | 0.967786i | \(0.418987\pi\) | |||||||
\(338\) | −8.21761 | −0.446979 | ||||||||
\(339\) | −11.6269 | −0.631484 | ||||||||
\(340\) | 0.0130081 | 0.000705465 0 | ||||||||
\(341\) | 1.77371 | 0.0960517 | ||||||||
\(342\) | −3.82322 | −0.206736 | ||||||||
\(343\) | −35.5825 | −1.92128 | ||||||||
\(344\) | 4.50200 | 0.242732 | ||||||||
\(345\) | 0.00315447 | 0.000169831 0 | ||||||||
\(346\) | −19.6471 | −1.05623 | ||||||||
\(347\) | −9.47927 | −0.508874 | −0.254437 | − | 0.967089i | \(-0.581890\pi\) | ||||
−0.254437 | + | 0.967089i | \(0.581890\pi\) | |||||||
\(348\) | −35.6243 | −1.90967 | ||||||||
\(349\) | 18.7488 | 1.00360 | 0.501799 | − | 0.864984i | \(-0.332672\pi\) | ||||
0.501799 | + | 0.864984i | \(0.332672\pi\) | |||||||
\(350\) | 56.3140 | 3.01011 | ||||||||
\(351\) | −17.5272 | −0.935531 | ||||||||
\(352\) | 1.31001 | 0.0698237 | ||||||||
\(353\) | −17.3687 | −0.924443 | −0.462222 | − | 0.886764i | \(-0.652948\pi\) | ||||
−0.462222 | + | 0.886764i | \(0.652948\pi\) | |||||||
\(354\) | 11.6238 | 0.617800 | ||||||||
\(355\) | −0.0552707 | −0.00293346 | ||||||||
\(356\) | −8.64681 | −0.458280 | ||||||||
\(357\) | −6.66827 | −0.352922 | ||||||||
\(358\) | 48.6877 | 2.57323 | ||||||||
\(359\) | −9.93520 | −0.524360 | −0.262180 | − | 0.965019i | \(-0.584441\pi\) | ||||
−0.262180 | + | 0.965019i | \(0.584441\pi\) | |||||||
\(360\) | 0.0143522 | 0.000756427 0 | ||||||||
\(361\) | −16.2123 | −0.853277 | ||||||||
\(362\) | 17.7133 | 0.930992 | ||||||||
\(363\) | −1.43320 | −0.0752235 | ||||||||
\(364\) | 55.6576 | 2.91725 | ||||||||
\(365\) | −0.0417425 | −0.00218490 | ||||||||
\(366\) | −21.4681 | −1.12216 | ||||||||
\(367\) | −32.3738 | −1.68990 | −0.844950 | − | 0.534845i | \(-0.820370\pi\) | ||||
−0.844950 | + | 0.534845i | \(0.820370\pi\) | |||||||
\(368\) | 2.07577 | 0.108207 | ||||||||
\(369\) | 3.69262 | 0.192230 | ||||||||
\(370\) | −0.0576909 | −0.00299921 | ||||||||
\(371\) | −24.6384 | −1.27916 | ||||||||
\(372\) | 9.81191 | 0.508724 | ||||||||
\(373\) | 32.4726 | 1.68137 | 0.840683 | − | 0.541528i | \(-0.182154\pi\) | ||||
0.840683 | + | 0.541528i | \(0.182154\pi\) | |||||||
\(374\) | 2.42070 | 0.125171 | ||||||||
\(375\) | −0.0483011 | −0.00249426 | ||||||||
\(376\) | 20.2279 | 1.04317 | ||||||||
\(377\) | −19.9586 | −1.02792 | ||||||||
\(378\) | −63.6948 | −3.27611 | ||||||||
\(379\) | 22.1365 | 1.13708 | 0.568538 | − | 0.822657i | \(-0.307509\pi\) | ||||
0.568538 | + | 0.822657i | \(0.307509\pi\) | |||||||
\(380\) | −0.0217191 | −0.00111416 | ||||||||
\(381\) | 16.6376 | 0.852368 | ||||||||
\(382\) | 8.96010 | 0.458439 | ||||||||
\(383\) | 3.88010 | 0.198264 | 0.0991320 | − | 0.995074i | \(-0.468393\pi\) | ||||
0.0991320 | + | 0.995074i | \(0.468393\pi\) | |||||||
\(384\) | 29.3009 | 1.49525 | ||||||||
\(385\) | −0.0156804 | −0.000799146 0 | ||||||||
\(386\) | −10.3765 | −0.528151 | ||||||||
\(387\) | −0.945936 | −0.0480846 | ||||||||
\(388\) | 12.6050 | 0.639923 | ||||||||
\(389\) | 10.2080 | 0.517568 | 0.258784 | − | 0.965935i | \(-0.416678\pi\) | ||||
0.258784 | + | 0.965935i | \(0.416678\pi\) | |||||||
\(390\) | −0.0362371 | −0.00183494 | ||||||||
\(391\) | −0.653083 | −0.0330278 | ||||||||
\(392\) | 65.9440 | 3.33067 | ||||||||
\(393\) | −32.0751 | −1.61797 | ||||||||
\(394\) | 35.2287 | 1.77480 | ||||||||
\(395\) | 0.0119766 | 0.000602608 0 | ||||||||
\(396\) | 3.65112 | 0.183476 | ||||||||
\(397\) | −26.7403 | −1.34206 | −0.671029 | − | 0.741432i | \(-0.734147\pi\) | ||||
−0.671029 | + | 0.741432i | \(0.734147\pi\) | |||||||
\(398\) | −34.4444 | −1.72654 | ||||||||
\(399\) | 11.1337 | 0.557382 | ||||||||
\(400\) | −15.8921 | −0.794603 | ||||||||
\(401\) | −34.9763 | −1.74663 | −0.873317 | − | 0.487153i | \(-0.838035\pi\) | ||||
−0.873317 | + | 0.487153i | \(0.838035\pi\) | |||||||
\(402\) | −33.1185 | −1.65180 | ||||||||
\(403\) | 5.49715 | 0.273832 | ||||||||
\(404\) | −59.0219 | −2.93645 | ||||||||
\(405\) | 0.0177520 | 0.000882103 0 | ||||||||
\(406\) | −72.5309 | −3.59965 | ||||||||
\(407\) | −7.07156 | −0.350524 | ||||||||
\(408\) | 6.45227 | 0.319435 | ||||||||
\(409\) | −28.6961 | −1.41893 | −0.709466 | − | 0.704739i | \(-0.751064\pi\) | ||||
−0.709466 | + | 0.704739i | \(0.751064\pi\) | |||||||
\(410\) | 0.0318468 | 0.00157280 | ||||||||
\(411\) | 27.6017 | 1.36149 | ||||||||
\(412\) | −49.2863 | −2.42816 | ||||||||
\(413\) | 15.5886 | 0.767065 | ||||||||
\(414\) | −1.49545 | −0.0734973 | ||||||||
\(415\) | 0.0185894 | 0.000912518 0 | ||||||||
\(416\) | 4.06003 | 0.199059 | ||||||||
\(417\) | −15.0407 | −0.736548 | ||||||||
\(418\) | −4.04173 | −0.197688 | ||||||||
\(419\) | −20.2516 | −0.989355 | −0.494677 | − | 0.869077i | \(-0.664714\pi\) | ||||
−0.494677 | + | 0.869077i | \(0.664714\pi\) | |||||||
\(420\) | −0.0867416 | −0.00423256 | ||||||||
\(421\) | 18.2477 | 0.889340 | 0.444670 | − | 0.895694i | \(-0.353321\pi\) | ||||
0.444670 | + | 0.895694i | \(0.353321\pi\) | |||||||
\(422\) | 32.2401 | 1.56942 | ||||||||
\(423\) | −4.25017 | −0.206650 | ||||||||
\(424\) | 23.8403 | 1.15779 | ||||||||
\(425\) | 4.99999 | 0.242535 | ||||||||
\(426\) | −56.8974 | −2.75669 | ||||||||
\(427\) | −28.7906 | −1.39328 | ||||||||
\(428\) | 16.1542 | 0.780845 | ||||||||
\(429\) | −4.44183 | −0.214454 | ||||||||
\(430\) | −0.00815815 | −0.000393421 0 | ||||||||
\(431\) | −12.3184 | −0.593358 | −0.296679 | − | 0.954977i | \(-0.595879\pi\) | ||||
−0.296679 | + | 0.954977i | \(0.595879\pi\) | |||||||
\(432\) | 17.9750 | 0.864821 | ||||||||
\(433\) | 35.0052 | 1.68224 | 0.841121 | − | 0.540847i | \(-0.181896\pi\) | ||||
0.841121 | + | 0.540847i | \(0.181896\pi\) | |||||||
\(434\) | 19.9770 | 0.958925 | ||||||||
\(435\) | 0.0311052 | 0.00149138 | ||||||||
\(436\) | −40.8274 | −1.95528 | ||||||||
\(437\) | 1.09042 | 0.0521620 | ||||||||
\(438\) | −42.9710 | −2.05323 | ||||||||
\(439\) | −18.4200 | −0.879136 | −0.439568 | − | 0.898209i | \(-0.644869\pi\) | ||||
−0.439568 | + | 0.898209i | \(0.644869\pi\) | |||||||
\(440\) | 0.0151725 | 0.000723319 0 | ||||||||
\(441\) | −13.8558 | −0.659799 | ||||||||
\(442\) | 7.50233 | 0.356849 | ||||||||
\(443\) | −16.7861 | −0.797532 | −0.398766 | − | 0.917053i | \(-0.630562\pi\) | ||||
−0.398766 | + | 0.917053i | \(0.630562\pi\) | |||||||
\(444\) | −39.1189 | −1.85650 | ||||||||
\(445\) | 0.00754993 | 0.000357901 0 | ||||||||
\(446\) | 29.7502 | 1.40871 | ||||||||
\(447\) | −28.0670 | −1.32752 | ||||||||
\(448\) | 44.3309 | 2.09444 | ||||||||
\(449\) | 4.12689 | 0.194760 | 0.0973799 | − | 0.995247i | \(-0.468954\pi\) | ||||
0.0973799 | + | 0.995247i | \(0.468954\pi\) | |||||||
\(450\) | 11.4491 | 0.539716 | ||||||||
\(451\) | 3.90367 | 0.183817 | ||||||||
\(452\) | 31.3126 | 1.47282 | ||||||||
\(453\) | −17.1412 | −0.805362 | ||||||||
\(454\) | 20.0611 | 0.941516 | ||||||||
\(455\) | −0.0485972 | −0.00227827 | ||||||||
\(456\) | −10.7731 | −0.504495 | ||||||||
\(457\) | 30.9452 | 1.44756 | 0.723778 | − | 0.690033i | \(-0.242404\pi\) | ||||
0.723778 | + | 0.690033i | \(0.242404\pi\) | |||||||
\(458\) | 5.42454 | 0.253472 | ||||||||
\(459\) | −5.65532 | −0.263968 | ||||||||
\(460\) | −0.00849539 | −0.000396099 0 | ||||||||
\(461\) | 11.3266 | 0.527531 | 0.263765 | − | 0.964587i | \(-0.415036\pi\) | ||||
0.263765 | + | 0.964587i | \(0.415036\pi\) | |||||||
\(462\) | −16.1419 | −0.750988 | ||||||||
\(463\) | 18.4214 | 0.856117 | 0.428058 | − | 0.903751i | \(-0.359198\pi\) | ||||
0.428058 | + | 0.903751i | \(0.359198\pi\) | |||||||
\(464\) | 20.4685 | 0.950228 | ||||||||
\(465\) | −0.00856722 | −0.000397295 0 | ||||||||
\(466\) | −25.2045 | −1.16758 | ||||||||
\(467\) | −19.0954 | −0.883630 | −0.441815 | − | 0.897106i | \(-0.645665\pi\) | ||||
−0.441815 | + | 0.897106i | \(0.645665\pi\) | |||||||
\(468\) | 11.3157 | 0.523068 | ||||||||
\(469\) | −44.4149 | −2.05089 | ||||||||
\(470\) | −0.0366553 | −0.00169078 | ||||||||
\(471\) | 21.3081 | 0.981825 | ||||||||
\(472\) | −15.0837 | −0.694283 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 12.3291 | 0.566294 | ||||||||
\(475\) | −8.34825 | −0.383044 | ||||||||
\(476\) | 17.9585 | 0.823126 | ||||||||
\(477\) | −5.00919 | −0.229355 | ||||||||
\(478\) | 45.8083 | 2.09522 | ||||||||
\(479\) | 2.98698 | 0.136479 | 0.0682393 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682393 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(480\) | −0.00632750 | −0.000288809 0 | ||||||||
\(481\) | −21.9164 | −0.999304 | ||||||||
\(482\) | 30.8975 | 1.40734 | ||||||||
\(483\) | 4.35493 | 0.198156 | ||||||||
\(484\) | 3.85979 | 0.175445 | ||||||||
\(485\) | −0.0110060 | −0.000499758 0 | ||||||||
\(486\) | −22.7951 | −1.03400 | ||||||||
\(487\) | 30.5470 | 1.38421 | 0.692107 | − | 0.721795i | \(-0.256682\pi\) | ||||
0.692107 | + | 0.721795i | \(0.256682\pi\) | |||||||
\(488\) | 27.8581 | 1.26108 | ||||||||
\(489\) | 20.4352 | 0.924112 | ||||||||
\(490\) | −0.119498 | −0.00539838 | ||||||||
\(491\) | 12.7753 | 0.576539 | 0.288270 | − | 0.957549i | \(-0.406920\pi\) | ||||
0.288270 | + | 0.957549i | \(0.406920\pi\) | |||||||
\(492\) | 21.5946 | 0.973558 | ||||||||
\(493\) | −6.43985 | −0.290036 | ||||||||
\(494\) | −12.5263 | −0.563584 | ||||||||
\(495\) | −0.00318796 | −0.000143288 0 | ||||||||
\(496\) | −5.63759 | −0.253135 | ||||||||
\(497\) | −76.3045 | −3.42272 | ||||||||
\(498\) | 19.1365 | 0.857528 | ||||||||
\(499\) | 13.8077 | 0.618115 | 0.309058 | − | 0.951043i | \(-0.399986\pi\) | ||||
0.309058 | + | 0.951043i | \(0.399986\pi\) | |||||||
\(500\) | 0.130081 | 0.00581740 | ||||||||
\(501\) | 1.12673 | 0.0503386 | ||||||||
\(502\) | 29.2036 | 1.30342 | ||||||||
\(503\) | 9.87009 | 0.440086 | 0.220043 | − | 0.975490i | \(-0.429380\pi\) | ||||
0.220043 | + | 0.975490i | \(0.429380\pi\) | |||||||
\(504\) | 19.8141 | 0.882588 | ||||||||
\(505\) | 0.0515347 | 0.00229326 | ||||||||
\(506\) | −1.58092 | −0.0702804 | ||||||||
\(507\) | 4.86532 | 0.216076 | ||||||||
\(508\) | −44.8071 | −1.98799 | ||||||||
\(509\) | 34.2672 | 1.51887 | 0.759434 | − | 0.650585i | \(-0.225476\pi\) | ||||
0.759434 | + | 0.650585i | \(0.225476\pi\) | |||||||
\(510\) | −0.0116923 | −0.000517742 0 | ||||||||
\(511\) | −57.6280 | −2.54931 | ||||||||
\(512\) | −32.7822 | −1.44878 | ||||||||
\(513\) | 9.44242 | 0.416893 | ||||||||
\(514\) | −17.1225 | −0.755242 | ||||||||
\(515\) | 0.0430341 | 0.00189631 | ||||||||
\(516\) | −5.53186 | −0.243526 | ||||||||
\(517\) | −4.49308 | −0.197606 | ||||||||
\(518\) | −79.6457 | −3.49943 | ||||||||
\(519\) | 11.6323 | 0.510600 | ||||||||
\(520\) | 0.0470231 | 0.00206210 | ||||||||
\(521\) | 33.3367 | 1.46051 | 0.730254 | − | 0.683176i | \(-0.239402\pi\) | ||||
0.730254 | + | 0.683176i | \(0.239402\pi\) | |||||||
\(522\) | −14.7462 | −0.645422 | ||||||||
\(523\) | 11.5885 | 0.506731 | 0.253366 | − | 0.967371i | \(-0.418462\pi\) | ||||
0.253366 | + | 0.967371i | \(0.418462\pi\) | |||||||
\(524\) | 86.3823 | 3.77363 | ||||||||
\(525\) | −33.3412 | −1.45513 | ||||||||
\(526\) | 13.1962 | 0.575383 | ||||||||
\(527\) | 1.77371 | 0.0772640 | ||||||||
\(528\) | 4.55531 | 0.198244 | ||||||||
\(529\) | −22.5735 | −0.981456 | ||||||||
\(530\) | −0.0432014 | −0.00187655 | ||||||||
\(531\) | 3.16930 | 0.137536 | ||||||||
\(532\) | −29.9845 | −1.29999 | ||||||||
\(533\) | 12.0984 | 0.524040 | ||||||||
\(534\) | 7.77213 | 0.336333 | ||||||||
\(535\) | −0.0141050 | −0.000609812 0 | ||||||||
\(536\) | 42.9763 | 1.85629 | ||||||||
\(537\) | −28.8261 | −1.24394 | ||||||||
\(538\) | −1.34594 | −0.0580275 | ||||||||
\(539\) | −14.6477 | −0.630921 | ||||||||
\(540\) | −0.0735651 | −0.00316574 | ||||||||
\(541\) | −28.1828 | −1.21167 | −0.605836 | − | 0.795590i | \(-0.707161\pi\) | ||||
−0.605836 | + | 0.795590i | \(0.707161\pi\) | |||||||
\(542\) | 8.77629 | 0.376974 | ||||||||
\(543\) | −10.4874 | −0.450055 | ||||||||
\(544\) | 1.31001 | 0.0561662 | ||||||||
\(545\) | 0.0356483 | 0.00152700 | ||||||||
\(546\) | −50.0275 | −2.14098 | ||||||||
\(547\) | 38.3248 | 1.63865 | 0.819325 | − | 0.573329i | \(-0.194348\pi\) | ||||
0.819325 | + | 0.573329i | \(0.194348\pi\) | |||||||
\(548\) | −74.3349 | −3.17543 | ||||||||
\(549\) | −5.85339 | −0.249816 | ||||||||
\(550\) | 12.1035 | 0.516094 | ||||||||
\(551\) | 10.7523 | 0.458064 | ||||||||
\(552\) | −4.21387 | −0.179354 | ||||||||
\(553\) | 16.5344 | 0.703115 | ||||||||
\(554\) | 43.2927 | 1.83933 | ||||||||
\(555\) | 0.0341565 | 0.00144986 | ||||||||
\(556\) | 40.5066 | 1.71786 | ||||||||
\(557\) | 5.60272 | 0.237395 | 0.118697 | − | 0.992930i | \(-0.462128\pi\) | ||||
0.118697 | + | 0.992930i | \(0.462128\pi\) | |||||||
\(558\) | 4.06149 | 0.171937 | ||||||||
\(559\) | −3.09924 | −0.131084 | ||||||||
\(560\) | 0.0498388 | 0.00210607 | ||||||||
\(561\) | −1.43320 | −0.0605098 | ||||||||
\(562\) | −79.8659 | −3.36894 | ||||||||
\(563\) | 17.7650 | 0.748706 | 0.374353 | − | 0.927286i | \(-0.377865\pi\) | ||||
0.374353 | + | 0.927286i | \(0.377865\pi\) | |||||||
\(564\) | −24.8551 | −1.04659 | ||||||||
\(565\) | −0.0273405 | −0.00115022 | ||||||||
\(566\) | 14.8618 | 0.624690 | ||||||||
\(567\) | 24.5077 | 1.02923 | ||||||||
\(568\) | 73.8329 | 3.09796 | ||||||||
\(569\) | 37.6858 | 1.57987 | 0.789936 | − | 0.613189i | \(-0.210114\pi\) | ||||
0.789936 | + | 0.613189i | \(0.210114\pi\) | |||||||
\(570\) | 0.0195220 | 0.000817688 0 | ||||||||
\(571\) | 41.7821 | 1.74852 | 0.874262 | − | 0.485454i | \(-0.161346\pi\) | ||||
0.874262 | + | 0.485454i | \(0.161346\pi\) | |||||||
\(572\) | 11.9624 | 0.500174 | ||||||||
\(573\) | −5.30492 | −0.221616 | ||||||||
\(574\) | 43.9663 | 1.83512 | ||||||||
\(575\) | −3.26541 | −0.136177 | ||||||||
\(576\) | 9.01285 | 0.375536 | ||||||||
\(577\) | −26.7934 | −1.11542 | −0.557711 | − | 0.830035i | \(-0.688320\pi\) | ||||
−0.557711 | + | 0.830035i | \(0.688320\pi\) | |||||||
\(578\) | 2.42070 | 0.100688 | ||||||||
\(579\) | 6.14353 | 0.255316 | ||||||||
\(580\) | −0.0837704 | −0.00347838 | ||||||||
\(581\) | 25.6638 | 1.06471 | ||||||||
\(582\) | −11.3299 | −0.469641 | ||||||||
\(583\) | −5.29549 | −0.219317 | ||||||||
\(584\) | 55.7613 | 2.30742 | ||||||||
\(585\) | −0.00988024 | −0.000408498 0 | ||||||||
\(586\) | 14.7455 | 0.609131 | ||||||||
\(587\) | 38.8365 | 1.60295 | 0.801477 | − | 0.598026i | \(-0.204048\pi\) | ||||
0.801477 | + | 0.598026i | \(0.204048\pi\) | |||||||
\(588\) | −81.0290 | −3.34158 | ||||||||
\(589\) | −2.96148 | −0.122026 | ||||||||
\(590\) | 0.0273334 | 0.00112530 | ||||||||
\(591\) | −20.8575 | −0.857964 | ||||||||
\(592\) | 22.4764 | 0.923773 | ||||||||
\(593\) | −17.5814 | −0.721983 | −0.360991 | − | 0.932569i | \(-0.617562\pi\) | ||||
−0.360991 | + | 0.932569i | \(0.617562\pi\) | |||||||
\(594\) | −13.6898 | −0.561701 | ||||||||
\(595\) | −0.0156804 | −0.000642833 0 | ||||||||
\(596\) | 75.5880 | 3.09620 | ||||||||
\(597\) | 20.3931 | 0.834635 | ||||||||
\(598\) | −4.89964 | −0.200361 | ||||||||
\(599\) | 30.7979 | 1.25837 | 0.629185 | − | 0.777256i | \(-0.283389\pi\) | ||||
0.629185 | + | 0.777256i | \(0.283389\pi\) | |||||||
\(600\) | 32.2613 | 1.31706 | ||||||||
\(601\) | −0.256449 | −0.0104608 | −0.00523038 | − | 0.999986i | \(-0.501665\pi\) | ||||
−0.00523038 | + | 0.999986i | \(0.501665\pi\) | |||||||
\(602\) | −11.2628 | −0.459038 | ||||||||
\(603\) | −9.02994 | −0.367728 | ||||||||
\(604\) | 46.1633 | 1.87836 | ||||||||
\(605\) | −0.00337016 | −0.000137017 0 | ||||||||
\(606\) | 53.0515 | 2.15507 | ||||||||
\(607\) | −10.4276 | −0.423242 | −0.211621 | − | 0.977352i | \(-0.567874\pi\) | ||||
−0.211621 | + | 0.977352i | \(0.567874\pi\) | |||||||
\(608\) | −2.18726 | −0.0887051 | ||||||||
\(609\) | 42.9426 | 1.74012 | ||||||||
\(610\) | −0.0504821 | −0.00204396 | ||||||||
\(611\) | −13.9251 | −0.563351 | ||||||||
\(612\) | 3.65112 | 0.147588 | ||||||||
\(613\) | 27.9080 | 1.12719 | 0.563596 | − | 0.826050i | \(-0.309417\pi\) | ||||
0.563596 | + | 0.826050i | \(0.309417\pi\) | |||||||
\(614\) | 43.7866 | 1.76709 | ||||||||
\(615\) | −0.0188552 | −0.000760315 0 | ||||||||
\(616\) | 20.9465 | 0.843959 | ||||||||
\(617\) | 34.6786 | 1.39611 | 0.698055 | − | 0.716044i | \(-0.254049\pi\) | ||||
0.698055 | + | 0.716044i | \(0.254049\pi\) | |||||||
\(618\) | 44.3006 | 1.78203 | ||||||||
\(619\) | 7.99806 | 0.321469 | 0.160735 | − | 0.986998i | \(-0.448614\pi\) | ||||
0.160735 | + | 0.986998i | \(0.448614\pi\) | |||||||
\(620\) | 0.0230726 | 0.000926619 0 | ||||||||
\(621\) | 3.69339 | 0.148211 | ||||||||
\(622\) | 33.7678 | 1.35397 | ||||||||
\(623\) | 10.4231 | 0.417594 | ||||||||
\(624\) | 14.1180 | 0.565172 | ||||||||
\(625\) | 24.9998 | 0.999993 | ||||||||
\(626\) | 29.7714 | 1.18990 | ||||||||
\(627\) | 2.39295 | 0.0955652 | ||||||||
\(628\) | −57.3854 | −2.28993 | ||||||||
\(629\) | −7.07156 | −0.281962 | ||||||||
\(630\) | −0.0359054 | −0.00143050 | ||||||||
\(631\) | −13.0325 | −0.518817 | −0.259409 | − | 0.965768i | \(-0.583528\pi\) | ||||
−0.259409 | + | 0.965768i | \(0.583528\pi\) | |||||||
\(632\) | −15.9989 | −0.636400 | ||||||||
\(633\) | −19.0881 | −0.758682 | ||||||||
\(634\) | −81.7243 | −3.24569 | ||||||||
\(635\) | 0.0391231 | 0.00155255 | ||||||||
\(636\) | −29.2939 | −1.16158 | ||||||||
\(637\) | −45.3967 | −1.79868 | ||||||||
\(638\) | −15.5890 | −0.617173 | ||||||||
\(639\) | −15.5134 | −0.613699 | ||||||||
\(640\) | 0.0689008 | 0.00272354 | ||||||||
\(641\) | −13.1262 | −0.518455 | −0.259227 | − | 0.965816i | \(-0.583468\pi\) | ||||
−0.259227 | + | 0.965816i | \(0.583468\pi\) | |||||||
\(642\) | −14.5201 | −0.573064 | ||||||||
\(643\) | 3.02639 | 0.119349 | 0.0596747 | − | 0.998218i | \(-0.480994\pi\) | ||||
0.0596747 | + | 0.998218i | \(0.480994\pi\) | |||||||
\(644\) | −11.7284 | −0.462163 | ||||||||
\(645\) | 0.00483012 | 0.000190186 0 | ||||||||
\(646\) | −4.04173 | −0.159020 | ||||||||
\(647\) | −35.3023 | −1.38788 | −0.693939 | − | 0.720034i | \(-0.744126\pi\) | ||||
−0.693939 | + | 0.720034i | \(0.744126\pi\) | |||||||
\(648\) | −23.7138 | −0.931568 | ||||||||
\(649\) | 3.35044 | 0.131516 | ||||||||
\(650\) | 37.5116 | 1.47132 | ||||||||
\(651\) | −11.8276 | −0.463559 | ||||||||
\(652\) | −55.0346 | −2.15532 | ||||||||
\(653\) | 30.3200 | 1.18651 | 0.593257 | − | 0.805013i | \(-0.297842\pi\) | ||||
0.593257 | + | 0.805013i | \(0.297842\pi\) | |||||||
\(654\) | 36.6975 | 1.43498 | ||||||||
\(655\) | −0.0754243 | −0.00294707 | ||||||||
\(656\) | −12.4075 | −0.484431 | ||||||||
\(657\) | −11.7163 | −0.457095 | ||||||||
\(658\) | −50.6048 | −1.97278 | ||||||||
\(659\) | −23.3034 | −0.907771 | −0.453886 | − | 0.891060i | \(-0.649963\pi\) | ||||
−0.453886 | + | 0.891060i | \(0.649963\pi\) | |||||||
\(660\) | −0.0186433 | −0.000725688 0 | ||||||||
\(661\) | 34.6028 | 1.34589 | 0.672946 | − | 0.739692i | \(-0.265029\pi\) | ||||
0.672946 | + | 0.739692i | \(0.265029\pi\) | |||||||
\(662\) | −30.7456 | −1.19496 | ||||||||
\(663\) | −4.44183 | −0.172506 | ||||||||
\(664\) | −24.8325 | −0.963689 | ||||||||
\(665\) | 0.0261808 | 0.00101525 | ||||||||
\(666\) | −16.1927 | −0.627453 | ||||||||
\(667\) | 4.20576 | 0.162848 | ||||||||
\(668\) | −3.03443 | −0.117406 | ||||||||
\(669\) | −17.6139 | −0.680993 | ||||||||
\(670\) | −0.0778780 | −0.00300869 | ||||||||
\(671\) | −6.18793 | −0.238882 | ||||||||
\(672\) | −8.73548 | −0.336979 | ||||||||
\(673\) | 22.7540 | 0.877101 | 0.438551 | − | 0.898706i | \(-0.355492\pi\) | ||||
0.438551 | + | 0.898706i | \(0.355492\pi\) | |||||||
\(674\) | 22.3766 | 0.861915 | ||||||||
\(675\) | −28.2765 | −1.08836 | ||||||||
\(676\) | −13.1029 | −0.503959 | ||||||||
\(677\) | −4.19826 | −0.161352 | −0.0806761 | − | 0.996740i | \(-0.525708\pi\) | ||||
−0.0806761 | + | 0.996740i | \(0.525708\pi\) | |||||||
\(678\) | −28.1451 | −1.08091 | ||||||||
\(679\) | −15.1945 | −0.583110 | ||||||||
\(680\) | 0.0151725 | 0.000581838 0 | ||||||||
\(681\) | −11.8774 | −0.455143 | ||||||||
\(682\) | 4.29362 | 0.164411 | ||||||||
\(683\) | 14.5718 | 0.557574 | 0.278787 | − | 0.960353i | \(-0.410068\pi\) | ||||
0.278787 | + | 0.960353i | \(0.410068\pi\) | |||||||
\(684\) | −6.09610 | −0.233090 | ||||||||
\(685\) | 0.0649052 | 0.00247990 | ||||||||
\(686\) | −86.1346 | −3.28864 | ||||||||
\(687\) | −3.21166 | −0.122532 | ||||||||
\(688\) | 3.17842 | 0.121176 | ||||||||
\(689\) | −16.4120 | −0.625246 | ||||||||
\(690\) | 0.00763602 | 0.000290698 0 | ||||||||
\(691\) | 35.5067 | 1.35074 | 0.675369 | − | 0.737480i | \(-0.263984\pi\) | ||||
0.675369 | + | 0.737480i | \(0.263984\pi\) | |||||||
\(692\) | −31.3272 | −1.19088 | ||||||||
\(693\) | −4.40116 | −0.167186 | ||||||||
\(694\) | −22.9465 | −0.871036 | ||||||||
\(695\) | −0.0353682 | −0.00134159 | ||||||||
\(696\) | −41.5517 | −1.57501 | ||||||||
\(697\) | 3.90367 | 0.147862 | ||||||||
\(698\) | 45.3852 | 1.71785 | ||||||||
\(699\) | 14.9226 | 0.564424 | ||||||||
\(700\) | 89.7923 | 3.39383 | ||||||||
\(701\) | −14.5349 | −0.548974 | −0.274487 | − | 0.961591i | \(-0.588508\pi\) | ||||
−0.274487 | + | 0.961591i | \(0.588508\pi\) | |||||||
\(702\) | −42.4281 | −1.60134 | ||||||||
\(703\) | 11.8071 | 0.445312 | ||||||||
\(704\) | 9.52797 | 0.359099 | ||||||||
\(705\) | 0.0217021 | 0.000817349 0 | ||||||||
\(706\) | −42.0445 | −1.58236 | ||||||||
\(707\) | 71.1468 | 2.67575 | ||||||||
\(708\) | 18.5341 | 0.696556 | ||||||||
\(709\) | 10.9317 | 0.410548 | 0.205274 | − | 0.978705i | \(-0.434191\pi\) | ||||
0.205274 | + | 0.978705i | \(0.434191\pi\) | |||||||
\(710\) | −0.133794 | −0.00502119 | ||||||||
\(711\) | 3.36159 | 0.126069 | ||||||||
\(712\) | −10.0855 | −0.377971 | ||||||||
\(713\) | −1.15838 | −0.0433817 | ||||||||
\(714\) | −16.1419 | −0.604095 | ||||||||
\(715\) | −0.0104449 | −0.000390618 0 | ||||||||
\(716\) | 77.6323 | 2.90125 | ||||||||
\(717\) | −27.1213 | −1.01286 | ||||||||
\(718\) | −24.0502 | −0.897544 | ||||||||
\(719\) | −47.8088 | −1.78297 | −0.891484 | − | 0.453051i | \(-0.850335\pi\) | ||||
−0.891484 | + | 0.453051i | \(0.850335\pi\) | |||||||
\(720\) | 0.0101327 | 0.000377622 0 | ||||||||
\(721\) | 59.4111 | 2.21259 | ||||||||
\(722\) | −39.2450 | −1.46055 | ||||||||
\(723\) | −18.2932 | −0.680330 | ||||||||
\(724\) | 28.2438 | 1.04967 | ||||||||
\(725\) | −32.1992 | −1.19585 | ||||||||
\(726\) | −3.46935 | −0.128760 | ||||||||
\(727\) | 6.58111 | 0.244080 | 0.122040 | − | 0.992525i | \(-0.461056\pi\) | ||||
0.122040 | + | 0.992525i | \(0.461056\pi\) | |||||||
\(728\) | 64.9182 | 2.40603 | ||||||||
\(729\) | 29.2982 | 1.08512 | ||||||||
\(730\) | −0.101046 | −0.00373988 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | −34.2308 | −1.26521 | ||||||||
\(733\) | −11.8219 | −0.436653 | −0.218326 | − | 0.975876i | \(-0.570060\pi\) | ||||
−0.218326 | + | 0.975876i | \(0.570060\pi\) | |||||||
\(734\) | −78.3674 | −2.89259 | ||||||||
\(735\) | 0.0707501 | 0.00260966 | ||||||||
\(736\) | −0.855544 | −0.0315358 | ||||||||
\(737\) | −9.54604 | −0.351633 | ||||||||
\(738\) | 8.93874 | 0.329039 | ||||||||
\(739\) | 31.6473 | 1.16417 | 0.582083 | − | 0.813130i | \(-0.302238\pi\) | ||||
0.582083 | + | 0.813130i | \(0.302238\pi\) | |||||||
\(740\) | −0.0919877 | −0.00338154 | ||||||||
\(741\) | 7.41632 | 0.272445 | ||||||||
\(742\) | −59.6421 | −2.18953 | ||||||||
\(743\) | −16.9663 | −0.622435 | −0.311217 | − | 0.950339i | \(-0.600737\pi\) | ||||
−0.311217 | + | 0.950339i | \(0.600737\pi\) | |||||||
\(744\) | 11.4445 | 0.419574 | ||||||||
\(745\) | −0.0659993 | −0.00241803 | ||||||||
\(746\) | 78.6064 | 2.87798 | ||||||||
\(747\) | 5.21767 | 0.190905 | ||||||||
\(748\) | 3.85979 | 0.141128 | ||||||||
\(749\) | −19.4728 | −0.711521 | ||||||||
\(750\) | −0.116923 | −0.00426941 | ||||||||
\(751\) | −33.3407 | −1.21662 | −0.608310 | − | 0.793699i | \(-0.708152\pi\) | ||||
−0.608310 | + | 0.793699i | \(0.708152\pi\) | |||||||
\(752\) | 14.2809 | 0.520771 | ||||||||
\(753\) | −17.2903 | −0.630092 | ||||||||
\(754\) | −48.3139 | −1.75949 | ||||||||
\(755\) | −0.0403073 | −0.00146693 | ||||||||
\(756\) | −101.561 | −3.69374 | ||||||||
\(757\) | 29.2280 | 1.06231 | 0.531154 | − | 0.847275i | \(-0.321758\pi\) | ||||
0.531154 | + | 0.847275i | \(0.321758\pi\) | |||||||
\(758\) | 53.5858 | 1.94632 | ||||||||
\(759\) | 0.935999 | 0.0339746 | ||||||||
\(760\) | −0.0253328 | −0.000918917 0 | ||||||||
\(761\) | −1.57659 | −0.0571512 | −0.0285756 | − | 0.999592i | \(-0.509097\pi\) | ||||
−0.0285756 | + | 0.999592i | \(0.509097\pi\) | |||||||
\(762\) | 40.2746 | 1.45899 | ||||||||
\(763\) | 49.2146 | 1.78169 | ||||||||
\(764\) | 14.2868 | 0.516879 | ||||||||
\(765\) | −0.00318796 | −0.000115261 0 | ||||||||
\(766\) | 9.39257 | 0.339367 | ||||||||
\(767\) | 10.3838 | 0.374937 | ||||||||
\(768\) | 43.6176 | 1.57392 | ||||||||
\(769\) | −17.5026 | −0.631159 | −0.315580 | − | 0.948899i | \(-0.602199\pi\) | ||||
−0.315580 | + | 0.948899i | \(0.602199\pi\) | |||||||
\(770\) | −0.0379575 | −0.00136789 | ||||||||
\(771\) | 10.1376 | 0.365096 | ||||||||
\(772\) | −16.5453 | −0.595479 | ||||||||
\(773\) | −33.3925 | −1.20105 | −0.600523 | − | 0.799607i | \(-0.705041\pi\) | ||||
−0.600523 | + | 0.799607i | \(0.705041\pi\) | |||||||
\(774\) | −2.28983 | −0.0823062 | ||||||||
\(775\) | 8.86853 | 0.318567 | ||||||||
\(776\) | 14.7023 | 0.527782 | ||||||||
\(777\) | 47.1550 | 1.69168 | ||||||||
\(778\) | 24.7106 | 0.885919 | ||||||||
\(779\) | −6.51778 | −0.233524 | ||||||||
\(780\) | −0.0577799 | −0.00206885 | ||||||||
\(781\) | −16.4000 | −0.586838 | ||||||||
\(782\) | −1.58092 | −0.0565335 | ||||||||
\(783\) | 36.4194 | 1.30152 | ||||||||
\(784\) | 46.5565 | 1.66273 | ||||||||
\(785\) | 0.0501058 | 0.00178835 | ||||||||
\(786\) | −77.6442 | −2.76948 | ||||||||
\(787\) | 42.3363 | 1.50913 | 0.754563 | − | 0.656227i | \(-0.227849\pi\) | ||||
0.754563 | + | 0.656227i | \(0.227849\pi\) | |||||||
\(788\) | 56.1720 | 2.00105 | ||||||||
\(789\) | −7.81296 | −0.278149 | ||||||||
\(790\) | 0.0289918 | 0.00103148 | ||||||||
\(791\) | −37.7452 | −1.34206 | ||||||||
\(792\) | 4.25861 | 0.151323 | ||||||||
\(793\) | −19.1779 | −0.681026 | ||||||||
\(794\) | −64.7303 | −2.29719 | ||||||||
\(795\) | 0.0255778 | 0.000907152 0 | ||||||||
\(796\) | −54.9213 | −1.94663 | ||||||||
\(797\) | 48.0573 | 1.70228 | 0.851138 | − | 0.524942i | \(-0.175913\pi\) | ||||
0.851138 | + | 0.524942i | \(0.175913\pi\) | |||||||
\(798\) | 26.9513 | 0.954067 | ||||||||
\(799\) | −4.49308 | −0.158954 | ||||||||
\(800\) | 6.55003 | 0.231578 | ||||||||
\(801\) | 2.11911 | 0.0748751 | ||||||||
\(802\) | −84.6672 | −2.98970 | ||||||||
\(803\) | −12.3859 | −0.437089 | ||||||||
\(804\) | −52.8073 | −1.86237 | ||||||||
\(805\) | 0.0102406 | 0.000360933 0 | ||||||||
\(806\) | 13.3069 | 0.468717 | ||||||||
\(807\) | 0.796876 | 0.0280514 | ||||||||
\(808\) | −68.8422 | −2.42186 | ||||||||
\(809\) | 15.3168 | 0.538512 | 0.269256 | − | 0.963069i | \(-0.413222\pi\) | ||||
0.269256 | + | 0.963069i | \(0.413222\pi\) | |||||||
\(810\) | 0.0429722 | 0.00150989 | ||||||||
\(811\) | 30.8082 | 1.08182 | 0.540911 | − | 0.841080i | \(-0.318079\pi\) | ||||
0.540911 | + | 0.841080i | \(0.318079\pi\) | |||||||
\(812\) | −115.650 | −4.05852 | ||||||||
\(813\) | −5.19609 | −0.182235 | ||||||||
\(814\) | −17.1181 | −0.599990 | ||||||||
\(815\) | 0.0480532 | 0.00168323 | ||||||||
\(816\) | 4.55531 | 0.159468 | ||||||||
\(817\) | 1.66965 | 0.0584138 | ||||||||
\(818\) | −69.4648 | −2.42878 | ||||||||
\(819\) | −13.6403 | −0.476629 | ||||||||
\(820\) | 0.0507795 | 0.00177330 | ||||||||
\(821\) | 33.1298 | 1.15624 | 0.578118 | − | 0.815953i | \(-0.303787\pi\) | ||||
0.578118 | + | 0.815953i | \(0.303787\pi\) | |||||||
\(822\) | 66.8155 | 2.33046 | ||||||||
\(823\) | −27.0510 | −0.942937 | −0.471468 | − | 0.881883i | \(-0.656276\pi\) | ||||
−0.471468 | + | 0.881883i | \(0.656276\pi\) | |||||||
\(824\) | −57.4867 | −2.00265 | ||||||||
\(825\) | −7.16599 | −0.249488 | ||||||||
\(826\) | 37.7354 | 1.31298 | ||||||||
\(827\) | 13.6442 | 0.474454 | 0.237227 | − | 0.971454i | \(-0.423762\pi\) | ||||
0.237227 | + | 0.971454i | \(0.423762\pi\) | |||||||
\(828\) | −2.38448 | −0.0828665 | ||||||||
\(829\) | 0.905397 | 0.0314457 | 0.0157229 | − | 0.999876i | \(-0.494995\pi\) | ||||
0.0157229 | + | 0.999876i | \(0.494995\pi\) | |||||||
\(830\) | 0.0449994 | 0.00156195 | ||||||||
\(831\) | −25.6319 | −0.889159 | ||||||||
\(832\) | 29.5295 | 1.02375 | ||||||||
\(833\) | −14.6477 | −0.507513 | ||||||||
\(834\) | −36.4091 | −1.26074 | ||||||||
\(835\) | 0.00264950 | 9.16897e−5 0 | ||||||||
\(836\) | −6.44452 | −0.222888 | ||||||||
\(837\) | −10.0309 | −0.346718 | ||||||||
\(838\) | −49.0230 | −1.69347 | ||||||||
\(839\) | −51.9197 | −1.79247 | −0.896233 | − | 0.443583i | \(-0.853707\pi\) | ||||
−0.896233 | + | 0.443583i | \(0.853707\pi\) | |||||||
\(840\) | −0.101174 | −0.00349084 | ||||||||
\(841\) | 12.4717 | 0.430058 | ||||||||
\(842\) | 44.1723 | 1.52228 | ||||||||
\(843\) | 47.2854 | 1.62860 | ||||||||
\(844\) | 51.4066 | 1.76949 | ||||||||
\(845\) | 0.0114408 | 0.000393574 0 | ||||||||
\(846\) | −10.2884 | −0.353722 | ||||||||
\(847\) | −4.65271 | −0.159869 | ||||||||
\(848\) | 16.8313 | 0.577988 | ||||||||
\(849\) | −8.79910 | −0.301984 | ||||||||
\(850\) | 12.1035 | 0.415146 | ||||||||
\(851\) | 4.61832 | 0.158314 | ||||||||
\(852\) | −90.7225 | −3.10810 | ||||||||
\(853\) | 12.9546 | 0.443558 | 0.221779 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221779 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(854\) | −69.6935 | −2.38486 | ||||||||
\(855\) | 0.00532278 | 0.000182035 0 | ||||||||
\(856\) | 18.8421 | 0.644008 | ||||||||
\(857\) | −28.7265 | −0.981278 | −0.490639 | − | 0.871363i | \(-0.663237\pi\) | ||||
−0.490639 | + | 0.871363i | \(0.663237\pi\) | |||||||
\(858\) | −10.7523 | −0.367079 | ||||||||
\(859\) | −42.5297 | −1.45110 | −0.725548 | − | 0.688172i | \(-0.758413\pi\) | ||||
−0.725548 | + | 0.688172i | \(0.758413\pi\) | |||||||
\(860\) | −0.0130081 | −0.000443573 0 | ||||||||
\(861\) | −26.0307 | −0.887125 | ||||||||
\(862\) | −29.8193 | −1.01565 | ||||||||
\(863\) | 35.7652 | 1.21746 | 0.608730 | − | 0.793377i | \(-0.291679\pi\) | ||||
0.608730 | + | 0.793377i | \(0.291679\pi\) | |||||||
\(864\) | −7.40852 | −0.252043 | ||||||||
\(865\) | 0.0273532 | 0.000930036 0 | ||||||||
\(866\) | 84.7371 | 2.87948 | ||||||||
\(867\) | −1.43320 | −0.0486740 | ||||||||
\(868\) | 31.8531 | 1.08117 | ||||||||
\(869\) | 3.55372 | 0.120552 | ||||||||
\(870\) | 0.0752965 | 0.00255279 | ||||||||
\(871\) | −29.5854 | −1.00246 | ||||||||
\(872\) | −47.6205 | −1.61263 | ||||||||
\(873\) | −3.08917 | −0.104553 | ||||||||
\(874\) | 2.63959 | 0.0892854 | ||||||||
\(875\) | −0.156804 | −0.00530093 | ||||||||
\(876\) | −68.5170 | −2.31498 | ||||||||
\(877\) | −41.1818 | −1.39061 | −0.695305 | − | 0.718715i | \(-0.744731\pi\) | ||||
−0.695305 | + | 0.718715i | \(0.744731\pi\) | |||||||
\(878\) | −44.5892 | −1.50481 | ||||||||
\(879\) | −8.73022 | −0.294463 | ||||||||
\(880\) | 0.0107118 | 0.000361094 0 | ||||||||
\(881\) | −6.97043 | −0.234840 | −0.117420 | − | 0.993082i | \(-0.537462\pi\) | ||||
−0.117420 | + | 0.993082i | \(0.537462\pi\) | |||||||
\(882\) | −33.5407 | −1.12937 | ||||||||
\(883\) | 2.80643 | 0.0944440 | 0.0472220 | − | 0.998884i | \(-0.484963\pi\) | ||||
0.0472220 | + | 0.998884i | \(0.484963\pi\) | |||||||
\(884\) | 11.9624 | 0.402340 | ||||||||
\(885\) | −0.0161830 | −0.000543986 0 | ||||||||
\(886\) | −40.6342 | −1.36513 | ||||||||
\(887\) | −8.02323 | −0.269394 | −0.134697 | − | 0.990887i | \(-0.543006\pi\) | ||||
−0.134697 | + | 0.990887i | \(0.543006\pi\) | |||||||
\(888\) | −45.6276 | −1.53116 | ||||||||
\(889\) | 54.0118 | 1.81150 | ||||||||
\(890\) | 0.0182761 | 0.000612617 0 | ||||||||
\(891\) | 5.26740 | 0.176464 | ||||||||
\(892\) | 47.4365 | 1.58829 | ||||||||
\(893\) | 7.50190 | 0.251041 | ||||||||
\(894\) | −67.9417 | −2.27231 | ||||||||
\(895\) | −0.0677843 | −0.00226578 | ||||||||
\(896\) | 95.1216 | 3.17779 | ||||||||
\(897\) | 2.90088 | 0.0968577 | ||||||||
\(898\) | 9.98996 | 0.333369 | ||||||||
\(899\) | −11.4224 | −0.380959 | ||||||||
\(900\) | 18.2555 | 0.608518 | ||||||||
\(901\) | −5.29549 | −0.176418 | ||||||||
\(902\) | 9.44962 | 0.314638 | ||||||||
\(903\) | 6.66827 | 0.221906 | ||||||||
\(904\) | 36.5226 | 1.21472 | ||||||||
\(905\) | −0.0246609 | −0.000819757 0 | ||||||||
\(906\) | −41.4936 | −1.37853 | ||||||||
\(907\) | 31.9899 | 1.06221 | 0.531104 | − | 0.847307i | \(-0.321778\pi\) | ||||
0.531104 | + | 0.847307i | \(0.321778\pi\) | |||||||
\(908\) | 31.9874 | 1.06154 | ||||||||
\(909\) | 14.4648 | 0.479766 | ||||||||
\(910\) | −0.117639 | −0.00389971 | ||||||||
\(911\) | −9.95945 | −0.329971 | −0.164986 | − | 0.986296i | \(-0.552758\pi\) | ||||
−0.164986 | + | 0.986296i | \(0.552758\pi\) | |||||||
\(912\) | −7.60579 | −0.251853 | ||||||||
\(913\) | 5.51588 | 0.182549 | ||||||||
\(914\) | 74.9091 | 2.47777 | ||||||||
\(915\) | 0.0298884 | 0.000988081 0 | ||||||||
\(916\) | 8.64940 | 0.285784 | ||||||||
\(917\) | −104.128 | −3.43860 | ||||||||
\(918\) | −13.6898 | −0.451832 | ||||||||
\(919\) | 37.7441 | 1.24506 | 0.622531 | − | 0.782595i | \(-0.286104\pi\) | ||||
0.622531 | + | 0.782595i | \(0.286104\pi\) | |||||||
\(920\) | −0.00990889 | −0.000326686 0 | ||||||||
\(921\) | −25.9243 | −0.854236 | ||||||||
\(922\) | 27.4182 | 0.902971 | ||||||||
\(923\) | −50.8275 | −1.67301 | ||||||||
\(924\) | −25.7381 | −0.846722 | ||||||||
\(925\) | −35.3577 | −1.16255 | ||||||||
\(926\) | 44.5928 | 1.46541 | ||||||||
\(927\) | 12.0788 | 0.396720 | ||||||||
\(928\) | −8.43626 | −0.276934 | ||||||||
\(929\) | −27.1521 | −0.890830 | −0.445415 | − | 0.895324i | \(-0.646944\pi\) | ||||
−0.445415 | + | 0.895324i | \(0.646944\pi\) | |||||||
\(930\) | −0.0207387 | −0.000680048 0 | ||||||||
\(931\) | 24.4566 | 0.801532 | ||||||||
\(932\) | −40.1884 | −1.31642 | ||||||||
\(933\) | −19.9926 | −0.654527 | ||||||||
\(934\) | −46.2243 | −1.51250 | ||||||||
\(935\) | −0.00337016 | −0.000110216 0 | ||||||||
\(936\) | 13.1984 | 0.431404 | ||||||||
\(937\) | −18.1323 | −0.592357 | −0.296179 | − | 0.955133i | \(-0.595712\pi\) | ||||
−0.296179 | + | 0.955133i | \(0.595712\pi\) | |||||||
\(938\) | −107.515 | −3.51050 | ||||||||
\(939\) | −17.6264 | −0.575217 | ||||||||
\(940\) | −0.0584466 | −0.00190632 | ||||||||
\(941\) | −22.8385 | −0.744512 | −0.372256 | − | 0.928130i | \(-0.621416\pi\) | ||||
−0.372256 | + | 0.928130i | \(0.621416\pi\) | |||||||
\(942\) | 51.5805 | 1.68058 | ||||||||
\(943\) | −2.54942 | −0.0830206 | ||||||||
\(944\) | −10.6491 | −0.346598 | ||||||||
\(945\) | 0.0886775 | 0.00288468 | ||||||||
\(946\) | −2.42070 | −0.0787038 | ||||||||
\(947\) | −12.0461 | −0.391446 | −0.195723 | − | 0.980659i | \(-0.562705\pi\) | ||||
−0.195723 | + | 0.980659i | \(0.562705\pi\) | |||||||
\(948\) | 19.6587 | 0.638484 | ||||||||
\(949\) | −38.3868 | −1.24609 | ||||||||
\(950\) | −20.2086 | −0.655654 | ||||||||
\(951\) | 48.3857 | 1.56901 | ||||||||
\(952\) | 20.9465 | 0.678880 | ||||||||
\(953\) | −2.81368 | −0.0911440 | −0.0455720 | − | 0.998961i | \(-0.514511\pi\) | ||||
−0.0455720 | + | 0.998961i | \(0.514511\pi\) | |||||||
\(954\) | −12.1258 | −0.392586 | ||||||||
\(955\) | −0.0124745 | −0.000403665 0 | ||||||||
\(956\) | 73.0411 | 2.36232 | ||||||||
\(957\) | 9.22960 | 0.298351 | ||||||||
\(958\) | 7.23059 | 0.233610 | ||||||||
\(959\) | 89.6055 | 2.89351 | ||||||||
\(960\) | −0.0460212 | −0.00148533 | ||||||||
\(961\) | −27.8540 | −0.898515 | ||||||||
\(962\) | −53.0532 | −1.71050 | ||||||||
\(963\) | −3.95899 | −0.127577 | ||||||||
\(964\) | 49.2658 | 1.58675 | ||||||||
\(965\) | 0.0144465 | 0.000465048 0 | ||||||||
\(966\) | 10.5420 | 0.339183 | ||||||||
\(967\) | −29.9527 | −0.963213 | −0.481607 | − | 0.876388i | \(-0.659947\pi\) | ||||
−0.481607 | + | 0.876388i | \(0.659947\pi\) | |||||||
\(968\) | 4.50200 | 0.144700 | ||||||||
\(969\) | 2.39295 | 0.0768726 | ||||||||
\(970\) | −0.0266423 | −0.000855433 0 | ||||||||
\(971\) | 31.9834 | 1.02640 | 0.513198 | − | 0.858270i | \(-0.328461\pi\) | ||||
0.513198 | + | 0.858270i | \(0.328461\pi\) | |||||||
\(972\) | −36.3466 | −1.16582 | ||||||||
\(973\) | −48.8279 | −1.56535 | ||||||||
\(974\) | 73.9450 | 2.36935 | ||||||||
\(975\) | −22.2091 | −0.711260 | ||||||||
\(976\) | 19.6678 | 0.629552 | ||||||||
\(977\) | −47.4165 | −1.51699 | −0.758495 | − | 0.651679i | \(-0.774065\pi\) | ||||
−0.758495 | + | 0.651679i | \(0.774065\pi\) | |||||||
\(978\) | 49.4675 | 1.58180 | ||||||||
\(979\) | 2.24023 | 0.0715980 | ||||||||
\(980\) | −0.190539 | −0.00608655 | ||||||||
\(981\) | 10.0058 | 0.319459 | ||||||||
\(982\) | 30.9251 | 0.986859 | ||||||||
\(983\) | 31.6488 | 1.00944 | 0.504719 | − | 0.863283i | \(-0.331596\pi\) | ||||
0.504719 | + | 0.863283i | \(0.331596\pi\) | |||||||
\(984\) | 25.1876 | 0.802950 | ||||||||
\(985\) | −0.0490463 | −0.00156275 | ||||||||
\(986\) | −15.5890 | −0.496453 | ||||||||
\(987\) | 29.9611 | 0.953672 | ||||||||
\(988\) | −19.9731 | −0.635429 | ||||||||
\(989\) | 0.653083 | 0.0207668 | ||||||||
\(990\) | −0.00771709 | −0.000245265 0 | ||||||||
\(991\) | 35.2906 | 1.12104 | 0.560522 | − | 0.828140i | \(-0.310601\pi\) | ||||
0.560522 | + | 0.828140i | \(0.310601\pi\) | |||||||
\(992\) | 2.32357 | 0.0737736 | ||||||||
\(993\) | 18.2032 | 0.577663 | ||||||||
\(994\) | −184.710 | −5.85865 | ||||||||
\(995\) | 0.0479543 | 0.00152025 | ||||||||
\(996\) | 30.5131 | 0.966844 | ||||||||
\(997\) | 60.2902 | 1.90941 | 0.954704 | − | 0.297557i | \(-0.0961717\pi\) | ||||
0.954704 | + | 0.297557i | \(0.0961717\pi\) | |||||||
\(998\) | 33.4242 | 1.05802 | ||||||||
\(999\) | 39.9919 | 1.26529 |
(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 | 8041.2.a.e.1.61 | ✓ | 66 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.e.1.61 | ✓ | 66 | 1.1 | even | 1 | trivial |