Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6046,2,Mod(1,6046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6046 = 2 \cdot 3023 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6046.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: | \(48.2775530621\) |
Analytic rank: | \(1\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.35147 | −1.93497 | −0.967487 | − | 0.252921i | \(-0.918609\pi\) | ||||
−0.967487 | + | 0.252921i | \(0.918609\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.434868 | 0.194479 | 0.0972395 | − | 0.995261i | \(-0.468999\pi\) | ||||
0.0972395 | + | 0.995261i | \(0.468999\pi\) | |||||||
\(6\) | −3.35147 | −1.36823 | ||||||||
\(7\) | 3.30614 | 1.24960 | 0.624802 | − | 0.780783i | \(-0.285180\pi\) | ||||
0.624802 | + | 0.780783i | \(0.285180\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.23237 | 2.74412 | ||||||||
\(10\) | 0.434868 | 0.137517 | ||||||||
\(11\) | −0.217260 | −0.0655065 | −0.0327533 | − | 0.999463i | \(-0.510428\pi\) | ||||
−0.0327533 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(12\) | −3.35147 | −0.967487 | ||||||||
\(13\) | −3.38686 | −0.939346 | −0.469673 | − | 0.882840i | \(-0.655628\pi\) | ||||
−0.469673 | + | 0.882840i | \(0.655628\pi\) | |||||||
\(14\) | 3.30614 | 0.883603 | ||||||||
\(15\) | −1.45745 | −0.376312 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.65181 | 1.37077 | 0.685383 | − | 0.728183i | \(-0.259635\pi\) | ||||
0.685383 | + | 0.728183i | \(0.259635\pi\) | |||||||
\(18\) | 8.23237 | 1.94039 | ||||||||
\(19\) | −2.20866 | −0.506700 | −0.253350 | − | 0.967375i | \(-0.581532\pi\) | ||||
−0.253350 | + | 0.967375i | \(0.581532\pi\) | |||||||
\(20\) | 0.434868 | 0.0972395 | ||||||||
\(21\) | −11.0804 | −2.41795 | ||||||||
\(22\) | −0.217260 | −0.0463201 | ||||||||
\(23\) | 0.600212 | 0.125153 | 0.0625765 | − | 0.998040i | \(-0.480068\pi\) | ||||
0.0625765 | + | 0.998040i | \(0.480068\pi\) | |||||||
\(24\) | −3.35147 | −0.684117 | ||||||||
\(25\) | −4.81089 | −0.962178 | ||||||||
\(26\) | −3.38686 | −0.664218 | ||||||||
\(27\) | −17.5362 | −3.37484 | ||||||||
\(28\) | 3.30614 | 0.624802 | ||||||||
\(29\) | −4.63290 | −0.860308 | −0.430154 | − | 0.902755i | \(-0.641541\pi\) | ||||
−0.430154 | + | 0.902755i | \(0.641541\pi\) | |||||||
\(30\) | −1.45745 | −0.266093 | ||||||||
\(31\) | −5.72971 | −1.02909 | −0.514543 | − | 0.857465i | \(-0.672038\pi\) | ||||
−0.514543 | + | 0.857465i | \(0.672038\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.728143 | 0.126753 | ||||||||
\(34\) | 5.65181 | 0.969278 | ||||||||
\(35\) | 1.43774 | 0.243022 | ||||||||
\(36\) | 8.23237 | 1.37206 | ||||||||
\(37\) | −9.14910 | −1.50410 | −0.752051 | − | 0.659105i | \(-0.770935\pi\) | ||||
−0.752051 | + | 0.659105i | \(0.770935\pi\) | |||||||
\(38\) | −2.20866 | −0.358291 | ||||||||
\(39\) | 11.3510 | 1.81761 | ||||||||
\(40\) | 0.434868 | 0.0687587 | ||||||||
\(41\) | 0.00426203 | 0.000665617 0 | 0.000332809 | − | 1.00000i | \(-0.499894\pi\) | ||||
0.000332809 | 1.00000i | \(0.499894\pi\) | ||||||||
\(42\) | −11.0804 | −1.70975 | ||||||||
\(43\) | −1.55279 | −0.236799 | −0.118399 | − | 0.992966i | \(-0.537776\pi\) | ||||
−0.118399 | + | 0.992966i | \(0.537776\pi\) | |||||||
\(44\) | −0.217260 | −0.0327533 | ||||||||
\(45\) | 3.58000 | 0.533675 | ||||||||
\(46\) | 0.600212 | 0.0884965 | ||||||||
\(47\) | 2.85449 | 0.416370 | 0.208185 | − | 0.978089i | \(-0.433244\pi\) | ||||
0.208185 | + | 0.978089i | \(0.433244\pi\) | |||||||
\(48\) | −3.35147 | −0.483743 | ||||||||
\(49\) | 3.93056 | 0.561509 | ||||||||
\(50\) | −4.81089 | −0.680363 | ||||||||
\(51\) | −18.9419 | −2.65240 | ||||||||
\(52\) | −3.38686 | −0.469673 | ||||||||
\(53\) | −10.1788 | −1.39817 | −0.699083 | − | 0.715041i | \(-0.746408\pi\) | ||||
−0.699083 | + | 0.715041i | \(0.746408\pi\) | |||||||
\(54\) | −17.5362 | −2.38637 | ||||||||
\(55\) | −0.0944797 | −0.0127396 | ||||||||
\(56\) | 3.30614 | 0.441802 | ||||||||
\(57\) | 7.40225 | 0.980452 | ||||||||
\(58\) | −4.63290 | −0.608330 | ||||||||
\(59\) | −7.46902 | −0.972384 | −0.486192 | − | 0.873852i | \(-0.661614\pi\) | ||||
−0.486192 | + | 0.873852i | \(0.661614\pi\) | |||||||
\(60\) | −1.45745 | −0.188156 | ||||||||
\(61\) | 8.79215 | 1.12572 | 0.562860 | − | 0.826552i | \(-0.309701\pi\) | ||||
0.562860 | + | 0.826552i | \(0.309701\pi\) | |||||||
\(62\) | −5.72971 | −0.727673 | ||||||||
\(63\) | 27.2174 | 3.42907 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.47284 | −0.182683 | ||||||||
\(66\) | 0.728143 | 0.0896282 | ||||||||
\(67\) | 2.66054 | 0.325037 | 0.162518 | − | 0.986706i | \(-0.448038\pi\) | ||||
0.162518 | + | 0.986706i | \(0.448038\pi\) | |||||||
\(68\) | 5.65181 | 0.685383 | ||||||||
\(69\) | −2.01160 | −0.242168 | ||||||||
\(70\) | 1.43774 | 0.171842 | ||||||||
\(71\) | −2.21118 | −0.262419 | −0.131210 | − | 0.991355i | \(-0.541886\pi\) | ||||
−0.131210 | + | 0.991355i | \(0.541886\pi\) | |||||||
\(72\) | 8.23237 | 0.970194 | ||||||||
\(73\) | −8.40293 | −0.983488 | −0.491744 | − | 0.870740i | \(-0.663640\pi\) | ||||
−0.491744 | + | 0.870740i | \(0.663640\pi\) | |||||||
\(74\) | −9.14910 | −1.06356 | ||||||||
\(75\) | 16.1236 | 1.86179 | ||||||||
\(76\) | −2.20866 | −0.253350 | ||||||||
\(77\) | −0.718294 | −0.0818572 | ||||||||
\(78\) | 11.3510 | 1.28524 | ||||||||
\(79\) | −4.85441 | −0.546163 | −0.273082 | − | 0.961991i | \(-0.588043\pi\) | ||||
−0.273082 | + | 0.961991i | \(0.588043\pi\) | |||||||
\(80\) | 0.434868 | 0.0486198 | ||||||||
\(81\) | 34.0748 | 3.78609 | ||||||||
\(82\) | 0.00426203 | 0.000470662 0 | ||||||||
\(83\) | −9.12566 | −1.00167 | −0.500836 | − | 0.865542i | \(-0.666974\pi\) | ||||
−0.500836 | + | 0.865542i | \(0.666974\pi\) | |||||||
\(84\) | −11.0804 | −1.20898 | ||||||||
\(85\) | 2.45779 | 0.266585 | ||||||||
\(86\) | −1.55279 | −0.167442 | ||||||||
\(87\) | 15.5270 | 1.66467 | ||||||||
\(88\) | −0.217260 | −0.0231600 | ||||||||
\(89\) | 13.1009 | 1.38869 | 0.694344 | − | 0.719643i | \(-0.255695\pi\) | ||||
0.694344 | + | 0.719643i | \(0.255695\pi\) | |||||||
\(90\) | 3.58000 | 0.377365 | ||||||||
\(91\) | −11.1974 | −1.17381 | ||||||||
\(92\) | 0.600212 | 0.0625765 | ||||||||
\(93\) | 19.2030 | 1.99125 | ||||||||
\(94\) | 2.85449 | 0.294418 | ||||||||
\(95\) | −0.960474 | −0.0985426 | ||||||||
\(96\) | −3.35147 | −0.342058 | ||||||||
\(97\) | 17.7175 | 1.79894 | 0.899471 | − | 0.436981i | \(-0.143952\pi\) | ||||
0.899471 | + | 0.436981i | \(0.143952\pi\) | |||||||
\(98\) | 3.93056 | 0.397047 | ||||||||
\(99\) | −1.78857 | −0.179758 | ||||||||
\(100\) | −4.81089 | −0.481089 | ||||||||
\(101\) | −12.2341 | −1.21734 | −0.608668 | − | 0.793425i | \(-0.708296\pi\) | ||||
−0.608668 | + | 0.793425i | \(0.708296\pi\) | |||||||
\(102\) | −18.9419 | −1.87553 | ||||||||
\(103\) | −1.99867 | −0.196935 | −0.0984676 | − | 0.995140i | \(-0.531394\pi\) | ||||
−0.0984676 | + | 0.995140i | \(0.531394\pi\) | |||||||
\(104\) | −3.38686 | −0.332109 | ||||||||
\(105\) | −4.81853 | −0.470241 | ||||||||
\(106\) | −10.1788 | −0.988652 | ||||||||
\(107\) | −9.21214 | −0.890571 | −0.445285 | − | 0.895389i | \(-0.646898\pi\) | ||||
−0.445285 | + | 0.895389i | \(0.646898\pi\) | |||||||
\(108\) | −17.5362 | −1.68742 | ||||||||
\(109\) | 7.79859 | 0.746969 | 0.373485 | − | 0.927636i | \(-0.378163\pi\) | ||||
0.373485 | + | 0.927636i | \(0.378163\pi\) | |||||||
\(110\) | −0.0944797 | −0.00900829 | ||||||||
\(111\) | 30.6629 | 2.91040 | ||||||||
\(112\) | 3.30614 | 0.312401 | ||||||||
\(113\) | −6.09730 | −0.573586 | −0.286793 | − | 0.957993i | \(-0.592589\pi\) | ||||
−0.286793 | + | 0.957993i | \(0.592589\pi\) | |||||||
\(114\) | 7.40225 | 0.693284 | ||||||||
\(115\) | 0.261013 | 0.0243396 | ||||||||
\(116\) | −4.63290 | −0.430154 | ||||||||
\(117\) | −27.8819 | −2.57768 | ||||||||
\(118\) | −7.46902 | −0.687579 | ||||||||
\(119\) | 18.6857 | 1.71291 | ||||||||
\(120\) | −1.45745 | −0.133046 | ||||||||
\(121\) | −10.9528 | −0.995709 | ||||||||
\(122\) | 8.79215 | 0.796004 | ||||||||
\(123\) | −0.0142841 | −0.00128795 | ||||||||
\(124\) | −5.72971 | −0.514543 | ||||||||
\(125\) | −4.26645 | −0.381602 | ||||||||
\(126\) | 27.2174 | 2.42472 | ||||||||
\(127\) | −14.9342 | −1.32520 | −0.662598 | − | 0.748976i | \(-0.730546\pi\) | ||||
−0.662598 | + | 0.748976i | \(0.730546\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.20415 | 0.458200 | ||||||||
\(130\) | −1.47284 | −0.129176 | ||||||||
\(131\) | −3.28045 | −0.286614 | −0.143307 | − | 0.989678i | \(-0.545774\pi\) | ||||
−0.143307 | + | 0.989678i | \(0.545774\pi\) | |||||||
\(132\) | 0.728143 | 0.0633767 | ||||||||
\(133\) | −7.30212 | −0.633174 | ||||||||
\(134\) | 2.66054 | 0.229836 | ||||||||
\(135\) | −7.62592 | −0.656335 | ||||||||
\(136\) | 5.65181 | 0.484639 | ||||||||
\(137\) | 21.9159 | 1.87240 | 0.936200 | − | 0.351466i | \(-0.114317\pi\) | ||||
0.936200 | + | 0.351466i | \(0.114317\pi\) | |||||||
\(138\) | −2.01160 | −0.171238 | ||||||||
\(139\) | 15.5050 | 1.31511 | 0.657557 | − | 0.753405i | \(-0.271590\pi\) | ||||
0.657557 | + | 0.753405i | \(0.271590\pi\) | |||||||
\(140\) | 1.43774 | 0.121511 | ||||||||
\(141\) | −9.56674 | −0.805665 | ||||||||
\(142\) | −2.21118 | −0.185558 | ||||||||
\(143\) | 0.735831 | 0.0615333 | ||||||||
\(144\) | 8.23237 | 0.686031 | ||||||||
\(145\) | −2.01470 | −0.167312 | ||||||||
\(146\) | −8.40293 | −0.695431 | ||||||||
\(147\) | −13.1732 | −1.08650 | ||||||||
\(148\) | −9.14910 | −0.752051 | ||||||||
\(149\) | 18.6163 | 1.52510 | 0.762551 | − | 0.646928i | \(-0.223946\pi\) | ||||
0.762551 | + | 0.646928i | \(0.223946\pi\) | |||||||
\(150\) | 16.1236 | 1.31648 | ||||||||
\(151\) | −20.3836 | −1.65880 | −0.829398 | − | 0.558658i | \(-0.811316\pi\) | ||||
−0.829398 | + | 0.558658i | \(0.811316\pi\) | |||||||
\(152\) | −2.20866 | −0.179146 | ||||||||
\(153\) | 46.5278 | 3.76155 | ||||||||
\(154\) | −0.718294 | −0.0578817 | ||||||||
\(155\) | −2.49167 | −0.200136 | ||||||||
\(156\) | 11.3510 | 0.908805 | ||||||||
\(157\) | 20.2350 | 1.61493 | 0.807466 | − | 0.589914i | \(-0.200838\pi\) | ||||
0.807466 | + | 0.589914i | \(0.200838\pi\) | |||||||
\(158\) | −4.85441 | −0.386196 | ||||||||
\(159\) | 34.1140 | 2.70541 | ||||||||
\(160\) | 0.434868 | 0.0343794 | ||||||||
\(161\) | 1.98439 | 0.156392 | ||||||||
\(162\) | 34.0748 | 2.67717 | ||||||||
\(163\) | −1.43128 | −0.112106 | −0.0560532 | − | 0.998428i | \(-0.517852\pi\) | ||||
−0.0560532 | + | 0.998428i | \(0.517852\pi\) | |||||||
\(164\) | 0.00426203 | 0.000332809 0 | ||||||||
\(165\) | 0.316646 | 0.0246509 | ||||||||
\(166\) | −9.12566 | −0.708289 | ||||||||
\(167\) | 9.12428 | 0.706058 | 0.353029 | − | 0.935612i | \(-0.385152\pi\) | ||||
0.353029 | + | 0.935612i | \(0.385152\pi\) | |||||||
\(168\) | −11.0804 | −0.854874 | ||||||||
\(169\) | −1.52917 | −0.117629 | ||||||||
\(170\) | 2.45779 | 0.188504 | ||||||||
\(171\) | −18.1825 | −1.39045 | ||||||||
\(172\) | −1.55279 | −0.118399 | ||||||||
\(173\) | 21.3312 | 1.62178 | 0.810890 | − | 0.585199i | \(-0.198984\pi\) | ||||
0.810890 | + | 0.585199i | \(0.198984\pi\) | |||||||
\(174\) | 15.5270 | 1.17710 | ||||||||
\(175\) | −15.9055 | −1.20234 | ||||||||
\(176\) | −0.217260 | −0.0163766 | ||||||||
\(177\) | 25.0322 | 1.88154 | ||||||||
\(178\) | 13.1009 | 0.981950 | ||||||||
\(179\) | −18.8002 | −1.40519 | −0.702595 | − | 0.711590i | \(-0.747975\pi\) | ||||
−0.702595 | + | 0.711590i | \(0.747975\pi\) | |||||||
\(180\) | 3.58000 | 0.266837 | ||||||||
\(181\) | −15.9940 | −1.18882 | −0.594412 | − | 0.804160i | \(-0.702615\pi\) | ||||
−0.594412 | + | 0.804160i | \(0.702615\pi\) | |||||||
\(182\) | −11.1974 | −0.830009 | ||||||||
\(183\) | −29.4667 | −2.17824 | ||||||||
\(184\) | 0.600212 | 0.0442482 | ||||||||
\(185\) | −3.97865 | −0.292516 | ||||||||
\(186\) | 19.2030 | 1.40803 | ||||||||
\(187\) | −1.22792 | −0.0897941 | ||||||||
\(188\) | 2.85449 | 0.208185 | ||||||||
\(189\) | −57.9770 | −4.21721 | ||||||||
\(190\) | −0.960474 | −0.0696801 | ||||||||
\(191\) | −6.14526 | −0.444655 | −0.222328 | − | 0.974972i | \(-0.571365\pi\) | ||||
−0.222328 | + | 0.974972i | \(0.571365\pi\) | |||||||
\(192\) | −3.35147 | −0.241872 | ||||||||
\(193\) | −20.0206 | −1.44111 | −0.720557 | − | 0.693395i | \(-0.756114\pi\) | ||||
−0.720557 | + | 0.693395i | \(0.756114\pi\) | |||||||
\(194\) | 17.7175 | 1.27204 | ||||||||
\(195\) | 4.93618 | 0.353487 | ||||||||
\(196\) | 3.93056 | 0.280754 | ||||||||
\(197\) | −12.9034 | −0.919328 | −0.459664 | − | 0.888093i | \(-0.652030\pi\) | ||||
−0.459664 | + | 0.888093i | \(0.652030\pi\) | |||||||
\(198\) | −1.78857 | −0.127108 | ||||||||
\(199\) | −10.4760 | −0.742624 | −0.371312 | − | 0.928508i | \(-0.621092\pi\) | ||||
−0.371312 | + | 0.928508i | \(0.621092\pi\) | |||||||
\(200\) | −4.81089 | −0.340181 | ||||||||
\(201\) | −8.91673 | −0.628938 | ||||||||
\(202\) | −12.2341 | −0.860786 | ||||||||
\(203\) | −15.3170 | −1.07504 | ||||||||
\(204\) | −18.9419 | −1.32620 | ||||||||
\(205\) | 0.00185342 | 0.000129449 0 | ||||||||
\(206\) | −1.99867 | −0.139254 | ||||||||
\(207\) | 4.94117 | 0.343435 | ||||||||
\(208\) | −3.38686 | −0.234837 | ||||||||
\(209\) | 0.479853 | 0.0331922 | ||||||||
\(210\) | −4.81853 | −0.332510 | ||||||||
\(211\) | −11.6433 | −0.801557 | −0.400779 | − | 0.916175i | \(-0.631260\pi\) | ||||
−0.400779 | + | 0.916175i | \(0.631260\pi\) | |||||||
\(212\) | −10.1788 | −0.699083 | ||||||||
\(213\) | 7.41073 | 0.507775 | ||||||||
\(214\) | −9.21214 | −0.629729 | ||||||||
\(215\) | −0.675261 | −0.0460524 | ||||||||
\(216\) | −17.5362 | −1.19318 | ||||||||
\(217\) | −18.9432 | −1.28595 | ||||||||
\(218\) | 7.79859 | 0.528187 | ||||||||
\(219\) | 28.1622 | 1.90302 | ||||||||
\(220\) | −0.0944797 | −0.00636982 | ||||||||
\(221\) | −19.1419 | −1.28762 | ||||||||
\(222\) | 30.6629 | 2.05796 | ||||||||
\(223\) | 5.38752 | 0.360775 | 0.180387 | − | 0.983596i | \(-0.442265\pi\) | ||||
0.180387 | + | 0.983596i | \(0.442265\pi\) | |||||||
\(224\) | 3.30614 | 0.220901 | ||||||||
\(225\) | −39.6050 | −2.64034 | ||||||||
\(226\) | −6.09730 | −0.405586 | ||||||||
\(227\) | 16.7265 | 1.11018 | 0.555090 | − | 0.831790i | \(-0.312684\pi\) | ||||
0.555090 | + | 0.831790i | \(0.312684\pi\) | |||||||
\(228\) | 7.40225 | 0.490226 | ||||||||
\(229\) | 10.2285 | 0.675915 | 0.337958 | − | 0.941161i | \(-0.390264\pi\) | ||||
0.337958 | + | 0.941161i | \(0.390264\pi\) | |||||||
\(230\) | 0.261013 | 0.0172107 | ||||||||
\(231\) | 2.40734 | 0.158391 | ||||||||
\(232\) | −4.63290 | −0.304165 | ||||||||
\(233\) | 12.9318 | 0.847190 | 0.423595 | − | 0.905852i | \(-0.360768\pi\) | ||||
0.423595 | + | 0.905852i | \(0.360768\pi\) | |||||||
\(234\) | −27.8819 | −1.82270 | ||||||||
\(235\) | 1.24133 | 0.0809752 | ||||||||
\(236\) | −7.46902 | −0.486192 | ||||||||
\(237\) | 16.2694 | 1.05681 | ||||||||
\(238\) | 18.6857 | 1.21121 | ||||||||
\(239\) | −8.86048 | −0.573137 | −0.286568 | − | 0.958060i | \(-0.592515\pi\) | ||||
−0.286568 | + | 0.958060i | \(0.592515\pi\) | |||||||
\(240\) | −1.45745 | −0.0940780 | ||||||||
\(241\) | −19.5027 | −1.25628 | −0.628139 | − | 0.778101i | \(-0.716183\pi\) | ||||
−0.628139 | + | 0.778101i | \(0.716183\pi\) | |||||||
\(242\) | −10.9528 | −0.704073 | ||||||||
\(243\) | −61.5925 | −3.95116 | ||||||||
\(244\) | 8.79215 | 0.562860 | ||||||||
\(245\) | 1.70928 | 0.109202 | ||||||||
\(246\) | −0.0142841 | −0.000910719 0 | ||||||||
\(247\) | 7.48041 | 0.475967 | ||||||||
\(248\) | −5.72971 | −0.363837 | ||||||||
\(249\) | 30.5844 | 1.93821 | ||||||||
\(250\) | −4.26645 | −0.269834 | ||||||||
\(251\) | −15.5243 | −0.979887 | −0.489944 | − | 0.871754i | \(-0.662983\pi\) | ||||
−0.489944 | + | 0.871754i | \(0.662983\pi\) | |||||||
\(252\) | 27.2174 | 1.71453 | ||||||||
\(253\) | −0.130402 | −0.00819833 | ||||||||
\(254\) | −14.9342 | −0.937054 | ||||||||
\(255\) | −8.23723 | −0.515835 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.2727 | −0.890307 | −0.445153 | − | 0.895454i | \(-0.646851\pi\) | ||||
−0.445153 | + | 0.895454i | \(0.646851\pi\) | |||||||
\(258\) | 5.20415 | 0.323996 | ||||||||
\(259\) | −30.2482 | −1.87953 | ||||||||
\(260\) | −1.47284 | −0.0913416 | ||||||||
\(261\) | −38.1398 | −2.36079 | ||||||||
\(262\) | −3.28045 | −0.202667 | ||||||||
\(263\) | −14.4433 | −0.890613 | −0.445306 | − | 0.895378i | \(-0.646905\pi\) | ||||
−0.445306 | + | 0.895378i | \(0.646905\pi\) | |||||||
\(264\) | 0.728143 | 0.0448141 | ||||||||
\(265\) | −4.42644 | −0.271914 | ||||||||
\(266\) | −7.30212 | −0.447722 | ||||||||
\(267\) | −43.9072 | −2.68707 | ||||||||
\(268\) | 2.66054 | 0.162518 | ||||||||
\(269\) | 17.1774 | 1.04733 | 0.523663 | − | 0.851926i | \(-0.324565\pi\) | ||||
0.523663 | + | 0.851926i | \(0.324565\pi\) | |||||||
\(270\) | −7.62592 | −0.464099 | ||||||||
\(271\) | 18.4436 | 1.12037 | 0.560185 | − | 0.828368i | \(-0.310730\pi\) | ||||
0.560185 | + | 0.828368i | \(0.310730\pi\) | |||||||
\(272\) | 5.65181 | 0.342691 | ||||||||
\(273\) | 37.5279 | 2.27129 | ||||||||
\(274\) | 21.9159 | 1.32399 | ||||||||
\(275\) | 1.04522 | 0.0630289 | ||||||||
\(276\) | −2.01160 | −0.121084 | ||||||||
\(277\) | −29.9926 | −1.80208 | −0.901039 | − | 0.433738i | \(-0.857194\pi\) | ||||
−0.901039 | + | 0.433738i | \(0.857194\pi\) | |||||||
\(278\) | 15.5050 | 0.929926 | ||||||||
\(279\) | −47.1691 | −2.82394 | ||||||||
\(280\) | 1.43774 | 0.0859211 | ||||||||
\(281\) | 2.45136 | 0.146236 | 0.0731179 | − | 0.997323i | \(-0.476705\pi\) | ||||
0.0731179 | + | 0.997323i | \(0.476705\pi\) | |||||||
\(282\) | −9.56674 | −0.569691 | ||||||||
\(283\) | −6.68694 | −0.397498 | −0.198749 | − | 0.980050i | \(-0.563688\pi\) | ||||
−0.198749 | + | 0.980050i | \(0.563688\pi\) | |||||||
\(284\) | −2.21118 | −0.131210 | ||||||||
\(285\) | 3.21900 | 0.190677 | ||||||||
\(286\) | 0.735831 | 0.0435106 | ||||||||
\(287\) | 0.0140909 | 0.000831757 0 | ||||||||
\(288\) | 8.23237 | 0.485097 | ||||||||
\(289\) | 14.9430 | 0.878998 | ||||||||
\(290\) | −2.01470 | −0.118307 | ||||||||
\(291\) | −59.3798 | −3.48091 | ||||||||
\(292\) | −8.40293 | −0.491744 | ||||||||
\(293\) | −1.60411 | −0.0937132 | −0.0468566 | − | 0.998902i | \(-0.514920\pi\) | ||||
−0.0468566 | + | 0.998902i | \(0.514920\pi\) | |||||||
\(294\) | −13.1732 | −0.768275 | ||||||||
\(295\) | −3.24804 | −0.189108 | ||||||||
\(296\) | −9.14910 | −0.531780 | ||||||||
\(297\) | 3.80991 | 0.221074 | ||||||||
\(298\) | 18.6163 | 1.07841 | ||||||||
\(299\) | −2.03284 | −0.117562 | ||||||||
\(300\) | 16.1236 | 0.930895 | ||||||||
\(301\) | −5.13376 | −0.295905 | ||||||||
\(302\) | −20.3836 | −1.17295 | ||||||||
\(303\) | 41.0022 | 2.35551 | ||||||||
\(304\) | −2.20866 | −0.126675 | ||||||||
\(305\) | 3.82343 | 0.218929 | ||||||||
\(306\) | 46.5278 | 2.65982 | ||||||||
\(307\) | −28.5303 | −1.62831 | −0.814154 | − | 0.580648i | \(-0.802799\pi\) | ||||
−0.814154 | + | 0.580648i | \(0.802799\pi\) | |||||||
\(308\) | −0.718294 | −0.0409286 | ||||||||
\(309\) | 6.69850 | 0.381064 | ||||||||
\(310\) | −2.49167 | −0.141517 | ||||||||
\(311\) | 5.86377 | 0.332504 | 0.166252 | − | 0.986083i | \(-0.446834\pi\) | ||||
0.166252 | + | 0.986083i | \(0.446834\pi\) | |||||||
\(312\) | 11.3510 | 0.642622 | ||||||||
\(313\) | −9.05604 | −0.511878 | −0.255939 | − | 0.966693i | \(-0.582385\pi\) | ||||
−0.255939 | + | 0.966693i | \(0.582385\pi\) | |||||||
\(314\) | 20.2350 | 1.14193 | ||||||||
\(315\) | 11.8360 | 0.666882 | ||||||||
\(316\) | −4.85441 | −0.273082 | ||||||||
\(317\) | 12.6046 | 0.707946 | 0.353973 | − | 0.935256i | \(-0.384830\pi\) | ||||
0.353973 | + | 0.935256i | \(0.384830\pi\) | |||||||
\(318\) | 34.1140 | 1.91302 | ||||||||
\(319\) | 1.00655 | 0.0563558 | ||||||||
\(320\) | 0.434868 | 0.0243099 | ||||||||
\(321\) | 30.8742 | 1.72323 | ||||||||
\(322\) | 1.98439 | 0.110585 | ||||||||
\(323\) | −12.4829 | −0.694567 | ||||||||
\(324\) | 34.0748 | 1.89305 | ||||||||
\(325\) | 16.2938 | 0.903818 | ||||||||
\(326\) | −1.43128 | −0.0792711 | ||||||||
\(327\) | −26.1368 | −1.44537 | ||||||||
\(328\) | 0.00426203 | 0.000235331 0 | ||||||||
\(329\) | 9.43734 | 0.520297 | ||||||||
\(330\) | 0.316646 | 0.0174308 | ||||||||
\(331\) | 20.0210 | 1.10045 | 0.550227 | − | 0.835015i | \(-0.314541\pi\) | ||||
0.550227 | + | 0.835015i | \(0.314541\pi\) | |||||||
\(332\) | −9.12566 | −0.500836 | ||||||||
\(333\) | −75.3188 | −4.12744 | ||||||||
\(334\) | 9.12428 | 0.499258 | ||||||||
\(335\) | 1.15698 | 0.0632128 | ||||||||
\(336\) | −11.0804 | −0.604488 | ||||||||
\(337\) | 22.6253 | 1.23248 | 0.616239 | − | 0.787559i | \(-0.288656\pi\) | ||||
0.616239 | + | 0.787559i | \(0.288656\pi\) | |||||||
\(338\) | −1.52917 | −0.0831760 | ||||||||
\(339\) | 20.4349 | 1.10987 | ||||||||
\(340\) | 2.45779 | 0.133293 | ||||||||
\(341\) | 1.24484 | 0.0674118 | ||||||||
\(342\) | −18.1825 | −0.983195 | ||||||||
\(343\) | −10.1480 | −0.547940 | ||||||||
\(344\) | −1.55279 | −0.0837211 | ||||||||
\(345\) | −0.874779 | −0.0470965 | ||||||||
\(346\) | 21.3312 | 1.14677 | ||||||||
\(347\) | −11.6323 | −0.624456 | −0.312228 | − | 0.950007i | \(-0.601075\pi\) | ||||
−0.312228 | + | 0.950007i | \(0.601075\pi\) | |||||||
\(348\) | 15.5270 | 0.832337 | ||||||||
\(349\) | 10.1951 | 0.545731 | 0.272866 | − | 0.962052i | \(-0.412029\pi\) | ||||
0.272866 | + | 0.962052i | \(0.412029\pi\) | |||||||
\(350\) | −15.9055 | −0.850183 | ||||||||
\(351\) | 59.3925 | 3.17014 | ||||||||
\(352\) | −0.217260 | −0.0115800 | ||||||||
\(353\) | −7.96016 | −0.423677 | −0.211838 | − | 0.977305i | \(-0.567945\pi\) | ||||
−0.211838 | + | 0.977305i | \(0.567945\pi\) | |||||||
\(354\) | 25.0322 | 1.33045 | ||||||||
\(355\) | −0.961574 | −0.0510351 | ||||||||
\(356\) | 13.1009 | 0.694344 | ||||||||
\(357\) | −62.6245 | −3.31444 | ||||||||
\(358\) | −18.8002 | −0.993619 | ||||||||
\(359\) | −13.0352 | −0.687971 | −0.343985 | − | 0.938975i | \(-0.611777\pi\) | ||||
−0.343985 | + | 0.938975i | \(0.611777\pi\) | |||||||
\(360\) | 3.58000 | 0.188682 | ||||||||
\(361\) | −14.1218 | −0.743255 | ||||||||
\(362\) | −15.9940 | −0.840626 | ||||||||
\(363\) | 36.7080 | 1.92667 | ||||||||
\(364\) | −11.1974 | −0.586905 | ||||||||
\(365\) | −3.65417 | −0.191268 | ||||||||
\(366\) | −29.4667 | −1.54025 | ||||||||
\(367\) | −21.3991 | −1.11702 | −0.558511 | − | 0.829497i | \(-0.688627\pi\) | ||||
−0.558511 | + | 0.829497i | \(0.688627\pi\) | |||||||
\(368\) | 0.600212 | 0.0312882 | ||||||||
\(369\) | 0.0350866 | 0.00182654 | ||||||||
\(370\) | −3.97865 | −0.206840 | ||||||||
\(371\) | −33.6525 | −1.74715 | ||||||||
\(372\) | 19.2030 | 0.995627 | ||||||||
\(373\) | 28.2030 | 1.46029 | 0.730147 | − | 0.683290i | \(-0.239451\pi\) | ||||
0.730147 | + | 0.683290i | \(0.239451\pi\) | |||||||
\(374\) | −1.22792 | −0.0634940 | ||||||||
\(375\) | 14.2989 | 0.738391 | ||||||||
\(376\) | 2.85449 | 0.147209 | ||||||||
\(377\) | 15.6910 | 0.808128 | ||||||||
\(378\) | −57.9770 | −2.98201 | ||||||||
\(379\) | 14.0002 | 0.719143 | 0.359572 | − | 0.933117i | \(-0.382923\pi\) | ||||
0.359572 | + | 0.933117i | \(0.382923\pi\) | |||||||
\(380\) | −0.960474 | −0.0492713 | ||||||||
\(381\) | 50.0515 | 2.56422 | ||||||||
\(382\) | −6.14526 | −0.314419 | ||||||||
\(383\) | 30.1483 | 1.54051 | 0.770253 | − | 0.637738i | \(-0.220130\pi\) | ||||
0.770253 | + | 0.637738i | \(0.220130\pi\) | |||||||
\(384\) | −3.35147 | −0.171029 | ||||||||
\(385\) | −0.312363 | −0.0159195 | ||||||||
\(386\) | −20.0206 | −1.01902 | ||||||||
\(387\) | −12.7832 | −0.649806 | ||||||||
\(388\) | 17.7175 | 0.899471 | ||||||||
\(389\) | −21.1708 | −1.07340 | −0.536702 | − | 0.843772i | \(-0.680330\pi\) | ||||
−0.536702 | + | 0.843772i | \(0.680330\pi\) | |||||||
\(390\) | 4.93618 | 0.249953 | ||||||||
\(391\) | 3.39229 | 0.171555 | ||||||||
\(392\) | 3.93056 | 0.198523 | ||||||||
\(393\) | 10.9943 | 0.554590 | ||||||||
\(394\) | −12.9034 | −0.650063 | ||||||||
\(395\) | −2.11103 | −0.106217 | ||||||||
\(396\) | −1.78857 | −0.0898790 | ||||||||
\(397\) | −5.71182 | −0.286668 | −0.143334 | − | 0.989674i | \(-0.545782\pi\) | ||||
−0.143334 | + | 0.989674i | \(0.545782\pi\) | |||||||
\(398\) | −10.4760 | −0.525114 | ||||||||
\(399\) | 24.4729 | 1.22518 | ||||||||
\(400\) | −4.81089 | −0.240544 | ||||||||
\(401\) | 15.4069 | 0.769384 | 0.384692 | − | 0.923045i | \(-0.374308\pi\) | ||||
0.384692 | + | 0.923045i | \(0.374308\pi\) | |||||||
\(402\) | −8.91673 | −0.444726 | ||||||||
\(403\) | 19.4057 | 0.966668 | ||||||||
\(404\) | −12.2341 | −0.608668 | ||||||||
\(405\) | 14.8181 | 0.736316 | ||||||||
\(406\) | −15.3170 | −0.760171 | ||||||||
\(407\) | 1.98774 | 0.0985285 | ||||||||
\(408\) | −18.9419 | −0.937763 | ||||||||
\(409\) | 17.1086 | 0.845968 | 0.422984 | − | 0.906137i | \(-0.360983\pi\) | ||||
0.422984 | + | 0.906137i | \(0.360983\pi\) | |||||||
\(410\) | 0.00185342 | 9.15340e−5 0 | ||||||||
\(411\) | −73.4505 | −3.62305 | ||||||||
\(412\) | −1.99867 | −0.0984676 | ||||||||
\(413\) | −24.6936 | −1.21509 | ||||||||
\(414\) | 4.94117 | 0.242845 | ||||||||
\(415\) | −3.96846 | −0.194804 | ||||||||
\(416\) | −3.38686 | −0.166055 | ||||||||
\(417\) | −51.9645 | −2.54471 | ||||||||
\(418\) | 0.479853 | 0.0234704 | ||||||||
\(419\) | 11.2794 | 0.551035 | 0.275518 | − | 0.961296i | \(-0.411151\pi\) | ||||
0.275518 | + | 0.961296i | \(0.411151\pi\) | |||||||
\(420\) | −4.81853 | −0.235120 | ||||||||
\(421\) | 10.2858 | 0.501298 | 0.250649 | − | 0.968078i | \(-0.419356\pi\) | ||||
0.250649 | + | 0.968078i | \(0.419356\pi\) | |||||||
\(422\) | −11.6433 | −0.566786 | ||||||||
\(423\) | 23.4992 | 1.14257 | ||||||||
\(424\) | −10.1788 | −0.494326 | ||||||||
\(425\) | −27.1902 | −1.31892 | ||||||||
\(426\) | 7.41073 | 0.359051 | ||||||||
\(427\) | 29.0681 | 1.40670 | ||||||||
\(428\) | −9.21214 | −0.445285 | ||||||||
\(429\) | −2.46612 | −0.119065 | ||||||||
\(430\) | −0.675261 | −0.0325640 | ||||||||
\(431\) | 0.224416 | 0.0108098 | 0.00540488 | − | 0.999985i | \(-0.498280\pi\) | ||||
0.00540488 | + | 0.999985i | \(0.498280\pi\) | |||||||
\(432\) | −17.5362 | −0.843709 | ||||||||
\(433\) | 19.0708 | 0.916483 | 0.458242 | − | 0.888828i | \(-0.348479\pi\) | ||||
0.458242 | + | 0.888828i | \(0.348479\pi\) | |||||||
\(434\) | −18.9432 | −0.909303 | ||||||||
\(435\) | 6.75222 | 0.323744 | ||||||||
\(436\) | 7.79859 | 0.373485 | ||||||||
\(437\) | −1.32566 | −0.0634150 | ||||||||
\(438\) | 28.1622 | 1.34564 | ||||||||
\(439\) | −39.6835 | −1.89399 | −0.946994 | − | 0.321251i | \(-0.895897\pi\) | ||||
−0.946994 | + | 0.321251i | \(0.895897\pi\) | |||||||
\(440\) | −0.0944797 | −0.00450414 | ||||||||
\(441\) | 32.3578 | 1.54085 | ||||||||
\(442\) | −19.1419 | −0.910487 | ||||||||
\(443\) | 8.94594 | 0.425035 | 0.212517 | − | 0.977157i | \(-0.431834\pi\) | ||||
0.212517 | + | 0.977157i | \(0.431834\pi\) | |||||||
\(444\) | 30.6629 | 1.45520 | ||||||||
\(445\) | 5.69715 | 0.270071 | ||||||||
\(446\) | 5.38752 | 0.255106 | ||||||||
\(447\) | −62.3919 | −2.95103 | ||||||||
\(448\) | 3.30614 | 0.156200 | ||||||||
\(449\) | −23.2518 | −1.09732 | −0.548660 | − | 0.836046i | \(-0.684862\pi\) | ||||
−0.548660 | + | 0.836046i | \(0.684862\pi\) | |||||||
\(450\) | −39.6050 | −1.86700 | ||||||||
\(451\) | −0.000925971 0 | −4.36022e−5 0 | ||||||||
\(452\) | −6.09730 | −0.286793 | ||||||||
\(453\) | 68.3152 | 3.20973 | ||||||||
\(454\) | 16.7265 | 0.785016 | ||||||||
\(455\) | −4.86941 | −0.228281 | ||||||||
\(456\) | 7.40225 | 0.346642 | ||||||||
\(457\) | 20.4390 | 0.956095 | 0.478048 | − | 0.878334i | \(-0.341345\pi\) | ||||
0.478048 | + | 0.878334i | \(0.341345\pi\) | |||||||
\(458\) | 10.2285 | 0.477944 | ||||||||
\(459\) | −99.1111 | −4.62611 | ||||||||
\(460\) | 0.261013 | 0.0121698 | ||||||||
\(461\) | −20.1844 | −0.940080 | −0.470040 | − | 0.882645i | \(-0.655761\pi\) | ||||
−0.470040 | + | 0.882645i | \(0.655761\pi\) | |||||||
\(462\) | 2.40734 | 0.112000 | ||||||||
\(463\) | −30.3322 | −1.40966 | −0.704829 | − | 0.709378i | \(-0.748976\pi\) | ||||
−0.704829 | + | 0.709378i | \(0.748976\pi\) | |||||||
\(464\) | −4.63290 | −0.215077 | ||||||||
\(465\) | 8.35076 | 0.387257 | ||||||||
\(466\) | 12.9318 | 0.599054 | ||||||||
\(467\) | −9.47525 | −0.438462 | −0.219231 | − | 0.975673i | \(-0.570355\pi\) | ||||
−0.219231 | + | 0.975673i | \(0.570355\pi\) | |||||||
\(468\) | −27.8819 | −1.28884 | ||||||||
\(469\) | 8.79612 | 0.406167 | ||||||||
\(470\) | 1.24133 | 0.0572581 | ||||||||
\(471\) | −67.8172 | −3.12485 | ||||||||
\(472\) | −7.46902 | −0.343790 | ||||||||
\(473\) | 0.337361 | 0.0155119 | ||||||||
\(474\) | 16.2694 | 0.747279 | ||||||||
\(475\) | 10.6256 | 0.487536 | ||||||||
\(476\) | 18.6857 | 0.856457 | ||||||||
\(477\) | −83.7957 | −3.83674 | ||||||||
\(478\) | −8.86048 | −0.405269 | ||||||||
\(479\) | 12.5310 | 0.572555 | 0.286278 | − | 0.958147i | \(-0.407582\pi\) | ||||
0.286278 | + | 0.958147i | \(0.407582\pi\) | |||||||
\(480\) | −1.45745 | −0.0665232 | ||||||||
\(481\) | 30.9867 | 1.41287 | ||||||||
\(482\) | −19.5027 | −0.888323 | ||||||||
\(483\) | −6.65062 | −0.302613 | ||||||||
\(484\) | −10.9528 | −0.497854 | ||||||||
\(485\) | 7.70479 | 0.349856 | ||||||||
\(486\) | −61.5925 | −2.79389 | ||||||||
\(487\) | −0.847982 | −0.0384257 | −0.0192129 | − | 0.999815i | \(-0.506116\pi\) | ||||
−0.0192129 | + | 0.999815i | \(0.506116\pi\) | |||||||
\(488\) | 8.79215 | 0.398002 | ||||||||
\(489\) | 4.79689 | 0.216923 | ||||||||
\(490\) | 1.70928 | 0.0772172 | ||||||||
\(491\) | 22.6153 | 1.02061 | 0.510307 | − | 0.859993i | \(-0.329532\pi\) | ||||
0.510307 | + | 0.859993i | \(0.329532\pi\) | |||||||
\(492\) | −0.0142841 | −0.000643976 0 | ||||||||
\(493\) | −26.1843 | −1.17928 | ||||||||
\(494\) | 7.48041 | 0.336559 | ||||||||
\(495\) | −0.777792 | −0.0349592 | ||||||||
\(496\) | −5.72971 | −0.257271 | ||||||||
\(497\) | −7.31049 | −0.327920 | ||||||||
\(498\) | 30.5844 | 1.37052 | ||||||||
\(499\) | −18.9290 | −0.847379 | −0.423690 | − | 0.905807i | \(-0.639265\pi\) | ||||
−0.423690 | + | 0.905807i | \(0.639265\pi\) | |||||||
\(500\) | −4.26645 | −0.190801 | ||||||||
\(501\) | −30.5798 | −1.36620 | ||||||||
\(502\) | −15.5243 | −0.692885 | ||||||||
\(503\) | 4.79194 | 0.213662 | 0.106831 | − | 0.994277i | \(-0.465930\pi\) | ||||
0.106831 | + | 0.994277i | \(0.465930\pi\) | |||||||
\(504\) | 27.2174 | 1.21236 | ||||||||
\(505\) | −5.32021 | −0.236746 | ||||||||
\(506\) | −0.130402 | −0.00579709 | ||||||||
\(507\) | 5.12498 | 0.227608 | ||||||||
\(508\) | −14.9342 | −0.662598 | ||||||||
\(509\) | −11.6694 | −0.517237 | −0.258619 | − | 0.965979i | \(-0.583267\pi\) | ||||
−0.258619 | + | 0.965979i | \(0.583267\pi\) | |||||||
\(510\) | −8.23723 | −0.364751 | ||||||||
\(511\) | −27.7813 | −1.22897 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 38.7313 | 1.71003 | ||||||||
\(514\) | −14.2727 | −0.629542 | ||||||||
\(515\) | −0.869160 | −0.0382998 | ||||||||
\(516\) | 5.20415 | 0.229100 | ||||||||
\(517\) | −0.620167 | −0.0272749 | ||||||||
\(518\) | −30.2482 | −1.32903 | ||||||||
\(519\) | −71.4909 | −3.13810 | ||||||||
\(520\) | −1.47284 | −0.0645882 | ||||||||
\(521\) | −30.3473 | −1.32954 | −0.664770 | − | 0.747048i | \(-0.731470\pi\) | ||||
−0.664770 | + | 0.747048i | \(0.731470\pi\) | |||||||
\(522\) | −38.1398 | −1.66933 | ||||||||
\(523\) | 17.0560 | 0.745808 | 0.372904 | − | 0.927870i | \(-0.378362\pi\) | ||||
0.372904 | + | 0.927870i | \(0.378362\pi\) | |||||||
\(524\) | −3.28045 | −0.143307 | ||||||||
\(525\) | 53.3068 | 2.32650 | ||||||||
\(526\) | −14.4433 | −0.629758 | ||||||||
\(527\) | −32.3832 | −1.41064 | ||||||||
\(528\) | 0.728143 | 0.0316883 | ||||||||
\(529\) | −22.6397 | −0.984337 | ||||||||
\(530\) | −4.42644 | −0.192272 | ||||||||
\(531\) | −61.4878 | −2.66834 | ||||||||
\(532\) | −7.30212 | −0.316587 | ||||||||
\(533\) | −0.0144349 | −0.000625245 0 | ||||||||
\(534\) | −43.9072 | −1.90005 | ||||||||
\(535\) | −4.00607 | −0.173197 | ||||||||
\(536\) | 2.66054 | 0.114918 | ||||||||
\(537\) | 63.0082 | 2.71901 | ||||||||
\(538\) | 17.1774 | 0.740571 | ||||||||
\(539\) | −0.853956 | −0.0367825 | ||||||||
\(540\) | −7.62592 | −0.328167 | ||||||||
\(541\) | −21.9122 | −0.942077 | −0.471039 | − | 0.882113i | \(-0.656121\pi\) | ||||
−0.471039 | + | 0.882113i | \(0.656121\pi\) | |||||||
\(542\) | 18.4436 | 0.792221 | ||||||||
\(543\) | 53.6035 | 2.30034 | ||||||||
\(544\) | 5.65181 | 0.242319 | ||||||||
\(545\) | 3.39136 | 0.145270 | ||||||||
\(546\) | 37.5279 | 1.60605 | ||||||||
\(547\) | 41.8157 | 1.78791 | 0.893956 | − | 0.448155i | \(-0.147919\pi\) | ||||
0.893956 | + | 0.448155i | \(0.147919\pi\) | |||||||
\(548\) | 21.9159 | 0.936200 | ||||||||
\(549\) | 72.3802 | 3.08911 | ||||||||
\(550\) | 1.04522 | 0.0445682 | ||||||||
\(551\) | 10.2325 | 0.435918 | ||||||||
\(552\) | −2.01160 | −0.0856192 | ||||||||
\(553\) | −16.0493 | −0.682488 | ||||||||
\(554\) | −29.9926 | −1.27426 | ||||||||
\(555\) | 13.3343 | 0.566011 | ||||||||
\(556\) | 15.5050 | 0.657557 | ||||||||
\(557\) | 4.41538 | 0.187086 | 0.0935429 | − | 0.995615i | \(-0.470181\pi\) | ||||
0.0935429 | + | 0.995615i | \(0.470181\pi\) | |||||||
\(558\) | −47.1691 | −1.99683 | ||||||||
\(559\) | 5.25910 | 0.222436 | ||||||||
\(560\) | 1.43774 | 0.0607554 | ||||||||
\(561\) | 4.11533 | 0.173749 | ||||||||
\(562\) | 2.45136 | 0.103404 | ||||||||
\(563\) | −20.4225 | −0.860707 | −0.430353 | − | 0.902661i | \(-0.641611\pi\) | ||||
−0.430353 | + | 0.902661i | \(0.641611\pi\) | |||||||
\(564\) | −9.56674 | −0.402832 | ||||||||
\(565\) | −2.65152 | −0.111550 | ||||||||
\(566\) | −6.68694 | −0.281073 | ||||||||
\(567\) | 112.656 | 4.73112 | ||||||||
\(568\) | −2.21118 | −0.0927792 | ||||||||
\(569\) | 20.8290 | 0.873198 | 0.436599 | − | 0.899656i | \(-0.356183\pi\) | ||||
0.436599 | + | 0.899656i | \(0.356183\pi\) | |||||||
\(570\) | 3.21900 | 0.134829 | ||||||||
\(571\) | 4.49847 | 0.188255 | 0.0941276 | − | 0.995560i | \(-0.469994\pi\) | ||||
0.0941276 | + | 0.995560i | \(0.469994\pi\) | |||||||
\(572\) | 0.735831 | 0.0307666 | ||||||||
\(573\) | 20.5957 | 0.860396 | ||||||||
\(574\) | 0.0140909 | 0.000588141 0 | ||||||||
\(575\) | −2.88756 | −0.120419 | ||||||||
\(576\) | 8.23237 | 0.343016 | ||||||||
\(577\) | −10.8655 | −0.452335 | −0.226168 | − | 0.974088i | \(-0.572620\pi\) | ||||
−0.226168 | + | 0.974088i | \(0.572620\pi\) | |||||||
\(578\) | 14.9430 | 0.621546 | ||||||||
\(579\) | 67.0985 | 2.78852 | ||||||||
\(580\) | −2.01470 | −0.0836560 | ||||||||
\(581\) | −30.1707 | −1.25169 | ||||||||
\(582\) | −59.3798 | −2.46137 | ||||||||
\(583\) | 2.21145 | 0.0915889 | ||||||||
\(584\) | −8.40293 | −0.347716 | ||||||||
\(585\) | −12.1250 | −0.501305 | ||||||||
\(586\) | −1.60411 | −0.0662652 | ||||||||
\(587\) | 12.1632 | 0.502031 | 0.251015 | − | 0.967983i | \(-0.419236\pi\) | ||||
0.251015 | + | 0.967983i | \(0.419236\pi\) | |||||||
\(588\) | −13.1732 | −0.543252 | ||||||||
\(589\) | 12.6549 | 0.521438 | ||||||||
\(590\) | −3.24804 | −0.133720 | ||||||||
\(591\) | 43.2453 | 1.77887 | ||||||||
\(592\) | −9.14910 | −0.376026 | ||||||||
\(593\) | 15.3029 | 0.628416 | 0.314208 | − | 0.949354i | \(-0.398261\pi\) | ||||
0.314208 | + | 0.949354i | \(0.398261\pi\) | |||||||
\(594\) | 3.80991 | 0.156323 | ||||||||
\(595\) | 8.12581 | 0.333126 | ||||||||
\(596\) | 18.6163 | 0.762551 | ||||||||
\(597\) | 35.1100 | 1.43696 | ||||||||
\(598\) | −2.03284 | −0.0831288 | ||||||||
\(599\) | −28.3164 | −1.15697 | −0.578487 | − | 0.815691i | \(-0.696357\pi\) | ||||
−0.578487 | + | 0.815691i | \(0.696357\pi\) | |||||||
\(600\) | 16.1236 | 0.658242 | ||||||||
\(601\) | 11.1384 | 0.454344 | 0.227172 | − | 0.973855i | \(-0.427052\pi\) | ||||
0.227172 | + | 0.973855i | \(0.427052\pi\) | |||||||
\(602\) | −5.13376 | −0.209236 | ||||||||
\(603\) | 21.9026 | 0.891941 | ||||||||
\(604\) | −20.3836 | −0.829398 | ||||||||
\(605\) | −4.76302 | −0.193645 | ||||||||
\(606\) | 41.0022 | 1.66560 | ||||||||
\(607\) | 3.03254 | 0.123087 | 0.0615436 | − | 0.998104i | \(-0.480398\pi\) | ||||
0.0615436 | + | 0.998104i | \(0.480398\pi\) | |||||||
\(608\) | −2.20866 | −0.0895728 | ||||||||
\(609\) | 51.3346 | 2.08018 | ||||||||
\(610\) | 3.82343 | 0.154806 | ||||||||
\(611\) | −9.66775 | −0.391115 | ||||||||
\(612\) | 46.5278 | 1.88078 | ||||||||
\(613\) | 28.0600 | 1.13333 | 0.566667 | − | 0.823947i | \(-0.308233\pi\) | ||||
0.566667 | + | 0.823947i | \(0.308233\pi\) | |||||||
\(614\) | −28.5303 | −1.15139 | ||||||||
\(615\) | −0.00621169 | −0.000250480 0 | ||||||||
\(616\) | −0.718294 | −0.0289409 | ||||||||
\(617\) | −18.0963 | −0.728528 | −0.364264 | − | 0.931296i | \(-0.618679\pi\) | ||||
−0.364264 | + | 0.931296i | \(0.618679\pi\) | |||||||
\(618\) | 6.69850 | 0.269453 | ||||||||
\(619\) | −5.14305 | −0.206717 | −0.103358 | − | 0.994644i | \(-0.532959\pi\) | ||||
−0.103358 | + | 0.994644i | \(0.532959\pi\) | |||||||
\(620\) | −2.49167 | −0.100068 | ||||||||
\(621\) | −10.5254 | −0.422370 | ||||||||
\(622\) | 5.86377 | 0.235116 | ||||||||
\(623\) | 43.3132 | 1.73531 | ||||||||
\(624\) | 11.3510 | 0.454403 | ||||||||
\(625\) | 22.1991 | 0.887964 | ||||||||
\(626\) | −9.05604 | −0.361952 | ||||||||
\(627\) | −1.60822 | −0.0642260 | ||||||||
\(628\) | 20.2350 | 0.807466 | ||||||||
\(629\) | −51.7090 | −2.06177 | ||||||||
\(630\) | 11.8360 | 0.471557 | ||||||||
\(631\) | −34.0365 | −1.35497 | −0.677486 | − | 0.735536i | \(-0.736930\pi\) | ||||
−0.677486 | + | 0.735536i | \(0.736930\pi\) | |||||||
\(632\) | −4.85441 | −0.193098 | ||||||||
\(633\) | 39.0222 | 1.55099 | ||||||||
\(634\) | 12.6046 | 0.500594 | ||||||||
\(635\) | −6.49441 | −0.257723 | ||||||||
\(636\) | 34.1140 | 1.35271 | ||||||||
\(637\) | −13.3123 | −0.527451 | ||||||||
\(638\) | 1.00655 | 0.0398496 | ||||||||
\(639\) | −18.2033 | −0.720111 | ||||||||
\(640\) | 0.434868 | 0.0171897 | ||||||||
\(641\) | −1.45353 | −0.0574110 | −0.0287055 | − | 0.999588i | \(-0.509139\pi\) | ||||
−0.0287055 | + | 0.999588i | \(0.509139\pi\) | |||||||
\(642\) | 30.8742 | 1.21851 | ||||||||
\(643\) | 1.37521 | 0.0542330 | 0.0271165 | − | 0.999632i | \(-0.491367\pi\) | ||||
0.0271165 | + | 0.999632i | \(0.491367\pi\) | |||||||
\(644\) | 1.98439 | 0.0781958 | ||||||||
\(645\) | 2.26312 | 0.0891103 | ||||||||
\(646\) | −12.4829 | −0.491133 | ||||||||
\(647\) | −8.41504 | −0.330829 | −0.165415 | − | 0.986224i | \(-0.552896\pi\) | ||||
−0.165415 | + | 0.986224i | \(0.552896\pi\) | |||||||
\(648\) | 34.0748 | 1.33859 | ||||||||
\(649\) | 1.62272 | 0.0636975 | ||||||||
\(650\) | 16.2938 | 0.639096 | ||||||||
\(651\) | 63.4877 | 2.48828 | ||||||||
\(652\) | −1.43128 | −0.0560532 | ||||||||
\(653\) | −37.3567 | −1.46188 | −0.730940 | − | 0.682442i | \(-0.760918\pi\) | ||||
−0.730940 | + | 0.682442i | \(0.760918\pi\) | |||||||
\(654\) | −26.1368 | −1.02203 | ||||||||
\(655\) | −1.42656 | −0.0557404 | ||||||||
\(656\) | 0.00426203 | 0.000166404 0 | ||||||||
\(657\) | −69.1760 | −2.69881 | ||||||||
\(658\) | 9.43734 | 0.367906 | ||||||||
\(659\) | 24.6868 | 0.961661 | 0.480831 | − | 0.876814i | \(-0.340335\pi\) | ||||
0.480831 | + | 0.876814i | \(0.340335\pi\) | |||||||
\(660\) | 0.316646 | 0.0123254 | ||||||||
\(661\) | 3.10382 | 0.120725 | 0.0603623 | − | 0.998177i | \(-0.480774\pi\) | ||||
0.0603623 | + | 0.998177i | \(0.480774\pi\) | |||||||
\(662\) | 20.0210 | 0.778138 | ||||||||
\(663\) | 64.1536 | 2.49152 | ||||||||
\(664\) | −9.12566 | −0.354144 | ||||||||
\(665\) | −3.17546 | −0.123139 | ||||||||
\(666\) | −75.3188 | −2.91854 | ||||||||
\(667\) | −2.78073 | −0.107670 | ||||||||
\(668\) | 9.12428 | 0.353029 | ||||||||
\(669\) | −18.0561 | −0.698090 | ||||||||
\(670\) | 1.15698 | 0.0446982 | ||||||||
\(671\) | −1.91019 | −0.0737419 | ||||||||
\(672\) | −11.0804 | −0.427437 | ||||||||
\(673\) | 25.1937 | 0.971145 | 0.485573 | − | 0.874196i | \(-0.338611\pi\) | ||||
0.485573 | + | 0.874196i | \(0.338611\pi\) | |||||||
\(674\) | 22.6253 | 0.871493 | ||||||||
\(675\) | 84.3645 | 3.24719 | ||||||||
\(676\) | −1.52917 | −0.0588143 | ||||||||
\(677\) | 13.6488 | 0.524566 | 0.262283 | − | 0.964991i | \(-0.415525\pi\) | ||||
0.262283 | + | 0.964991i | \(0.415525\pi\) | |||||||
\(678\) | 20.4349 | 0.784799 | ||||||||
\(679\) | 58.5766 | 2.24796 | ||||||||
\(680\) | 2.45779 | 0.0942521 | ||||||||
\(681\) | −56.0586 | −2.14817 | ||||||||
\(682\) | 1.24484 | 0.0476673 | ||||||||
\(683\) | 24.2634 | 0.928413 | 0.464207 | − | 0.885727i | \(-0.346339\pi\) | ||||
0.464207 | + | 0.885727i | \(0.346339\pi\) | |||||||
\(684\) | −18.1825 | −0.695224 | ||||||||
\(685\) | 9.53053 | 0.364143 | ||||||||
\(686\) | −10.1480 | −0.387452 | ||||||||
\(687\) | −34.2804 | −1.30788 | ||||||||
\(688\) | −1.55279 | −0.0591997 | ||||||||
\(689\) | 34.4742 | 1.31336 | ||||||||
\(690\) | −0.874779 | −0.0333023 | ||||||||
\(691\) | 21.3447 | 0.811992 | 0.405996 | − | 0.913875i | \(-0.366925\pi\) | ||||
0.405996 | + | 0.913875i | \(0.366925\pi\) | |||||||
\(692\) | 21.3312 | 0.810890 | ||||||||
\(693\) | −5.91326 | −0.224626 | ||||||||
\(694\) | −11.6323 | −0.441557 | ||||||||
\(695\) | 6.74262 | 0.255762 | ||||||||
\(696\) | 15.5270 | 0.588551 | ||||||||
\(697\) | 0.0240882 | 0.000912405 0 | ||||||||
\(698\) | 10.1951 | 0.385890 | ||||||||
\(699\) | −43.3406 | −1.63929 | ||||||||
\(700\) | −15.9055 | −0.601170 | ||||||||
\(701\) | 0.169561 | 0.00640425 | 0.00320212 | − | 0.999995i | \(-0.498981\pi\) | ||||
0.00320212 | + | 0.999995i | \(0.498981\pi\) | |||||||
\(702\) | 59.3925 | 2.24163 | ||||||||
\(703\) | 20.2072 | 0.762129 | ||||||||
\(704\) | −0.217260 | −0.00818831 | ||||||||
\(705\) | −4.16027 | −0.156685 | ||||||||
\(706\) | −7.96016 | −0.299585 | ||||||||
\(707\) | −40.4475 | −1.52119 | ||||||||
\(708\) | 25.0322 | 0.940769 | ||||||||
\(709\) | −6.51741 | −0.244766 | −0.122383 | − | 0.992483i | \(-0.539054\pi\) | ||||
−0.122383 | + | 0.992483i | \(0.539054\pi\) | |||||||
\(710\) | −0.961574 | −0.0360872 | ||||||||
\(711\) | −39.9633 | −1.49874 | ||||||||
\(712\) | 13.1009 | 0.490975 | ||||||||
\(713\) | −3.43904 | −0.128793 | ||||||||
\(714\) | −62.6245 | −2.34366 | ||||||||
\(715\) | 0.319990 | 0.0119669 | ||||||||
\(716\) | −18.8002 | −0.702595 | ||||||||
\(717\) | 29.6957 | 1.10901 | ||||||||
\(718\) | −13.0352 | −0.486469 | ||||||||
\(719\) | −17.0819 | −0.637047 | −0.318523 | − | 0.947915i | \(-0.603187\pi\) | ||||
−0.318523 | + | 0.947915i | \(0.603187\pi\) | |||||||
\(720\) | 3.58000 | 0.133419 | ||||||||
\(721\) | −6.60790 | −0.246091 | ||||||||
\(722\) | −14.1218 | −0.525561 | ||||||||
\(723\) | 65.3627 | 2.43087 | ||||||||
\(724\) | −15.9940 | −0.594412 | ||||||||
\(725\) | 22.2884 | 0.827770 | ||||||||
\(726\) | 36.7080 | 1.36236 | ||||||||
\(727\) | 33.6111 | 1.24657 | 0.623283 | − | 0.781996i | \(-0.285798\pi\) | ||||
0.623283 | + | 0.781996i | \(0.285798\pi\) | |||||||
\(728\) | −11.1974 | −0.415005 | ||||||||
\(729\) | 104.201 | 3.85929 | ||||||||
\(730\) | −3.65417 | −0.135247 | ||||||||
\(731\) | −8.77610 | −0.324596 | ||||||||
\(732\) | −29.4667 | −1.08912 | ||||||||
\(733\) | −38.8574 | −1.43523 | −0.717615 | − | 0.696440i | \(-0.754766\pi\) | ||||
−0.717615 | + | 0.696440i | \(0.754766\pi\) | |||||||
\(734\) | −21.3991 | −0.789854 | ||||||||
\(735\) | −5.72859 | −0.211302 | ||||||||
\(736\) | 0.600212 | 0.0221241 | ||||||||
\(737\) | −0.578030 | −0.0212920 | ||||||||
\(738\) | 0.0350866 | 0.00129156 | ||||||||
\(739\) | 40.0712 | 1.47404 | 0.737022 | − | 0.675868i | \(-0.236231\pi\) | ||||
0.737022 | + | 0.675868i | \(0.236231\pi\) | |||||||
\(740\) | −3.97865 | −0.146258 | ||||||||
\(741\) | −25.0704 | −0.920984 | ||||||||
\(742\) | −33.6525 | −1.23542 | ||||||||
\(743\) | −51.6743 | −1.89575 | −0.947874 | − | 0.318647i | \(-0.896772\pi\) | ||||
−0.947874 | + | 0.318647i | \(0.896772\pi\) | |||||||
\(744\) | 19.2030 | 0.704015 | ||||||||
\(745\) | 8.09562 | 0.296600 | ||||||||
\(746\) | 28.2030 | 1.03258 | ||||||||
\(747\) | −75.1259 | −2.74871 | ||||||||
\(748\) | −1.22792 | −0.0448970 | ||||||||
\(749\) | −30.4566 | −1.11286 | ||||||||
\(750\) | 14.2989 | 0.522121 | ||||||||
\(751\) | 13.5297 | 0.493705 | 0.246852 | − | 0.969053i | \(-0.420604\pi\) | ||||
0.246852 | + | 0.969053i | \(0.420604\pi\) | |||||||
\(752\) | 2.85449 | 0.104092 | ||||||||
\(753\) | 52.0294 | 1.89606 | ||||||||
\(754\) | 15.6910 | 0.571432 | ||||||||
\(755\) | −8.86419 | −0.322601 | ||||||||
\(756\) | −57.9770 | −2.10860 | ||||||||
\(757\) | 21.7540 | 0.790661 | 0.395331 | − | 0.918539i | \(-0.370630\pi\) | ||||
0.395331 | + | 0.918539i | \(0.370630\pi\) | |||||||
\(758\) | 14.0002 | 0.508511 | ||||||||
\(759\) | 0.437040 | 0.0158636 | ||||||||
\(760\) | −0.960474 | −0.0348401 | ||||||||
\(761\) | −0.211788 | −0.00767729 | −0.00383865 | − | 0.999993i | \(-0.501222\pi\) | ||||
−0.00383865 | + | 0.999993i | \(0.501222\pi\) | |||||||
\(762\) | 50.0515 | 1.81318 | ||||||||
\(763\) | 25.7832 | 0.933415 | ||||||||
\(764\) | −6.14526 | −0.222328 | ||||||||
\(765\) | 20.2335 | 0.731543 | ||||||||
\(766\) | 30.1483 | 1.08930 | ||||||||
\(767\) | 25.2965 | 0.913405 | ||||||||
\(768\) | −3.35147 | −0.120936 | ||||||||
\(769\) | 13.0480 | 0.470522 | 0.235261 | − | 0.971932i | \(-0.424406\pi\) | ||||
0.235261 | + | 0.971932i | \(0.424406\pi\) | |||||||
\(770\) | −0.312363 | −0.0112568 | ||||||||
\(771\) | 47.8346 | 1.72272 | ||||||||
\(772\) | −20.0206 | −0.720557 | ||||||||
\(773\) | −2.11599 | −0.0761070 | −0.0380535 | − | 0.999276i | \(-0.512116\pi\) | ||||
−0.0380535 | + | 0.999276i | \(0.512116\pi\) | |||||||
\(774\) | −12.7832 | −0.459482 | ||||||||
\(775\) | 27.5650 | 0.990163 | ||||||||
\(776\) | 17.7175 | 0.636022 | ||||||||
\(777\) | 101.376 | 3.63684 | ||||||||
\(778\) | −21.1708 | −0.759011 | ||||||||
\(779\) | −0.00941335 | −0.000337268 0 | ||||||||
\(780\) | 4.93618 | 0.176744 | ||||||||
\(781\) | 0.480403 | 0.0171902 | ||||||||
\(782\) | 3.39229 | 0.121308 | ||||||||
\(783\) | 81.2433 | 2.90340 | ||||||||
\(784\) | 3.93056 | 0.140377 | ||||||||
\(785\) | 8.79958 | 0.314070 | ||||||||
\(786\) | 10.9943 | 0.392155 | ||||||||
\(787\) | −21.3347 | −0.760500 | −0.380250 | − | 0.924884i | \(-0.624162\pi\) | ||||
−0.380250 | + | 0.924884i | \(0.624162\pi\) | |||||||
\(788\) | −12.9034 | −0.459664 | ||||||||
\(789\) | 48.4064 | 1.72331 | ||||||||
\(790\) | −2.11103 | −0.0751070 | ||||||||
\(791\) | −20.1585 | −0.716755 | ||||||||
\(792\) | −1.78857 | −0.0635540 | ||||||||
\(793\) | −29.7778 | −1.05744 | ||||||||
\(794\) | −5.71182 | −0.202705 | ||||||||
\(795\) | 14.8351 | 0.526146 | ||||||||
\(796\) | −10.4760 | −0.371312 | ||||||||
\(797\) | 15.6134 | 0.553054 | 0.276527 | − | 0.961006i | \(-0.410816\pi\) | ||||
0.276527 | + | 0.961006i | \(0.410816\pi\) | |||||||
\(798\) | 24.4729 | 0.866330 | ||||||||
\(799\) | 16.1330 | 0.570745 | ||||||||
\(800\) | −4.81089 | −0.170091 | ||||||||
\(801\) | 107.851 | 3.81073 | ||||||||
\(802\) | 15.4069 | 0.544036 | ||||||||
\(803\) | 1.82562 | 0.0644249 | ||||||||
\(804\) | −8.91673 | −0.314469 | ||||||||
\(805\) | 0.862947 | 0.0304149 | ||||||||
\(806\) | 19.4057 | 0.683537 | ||||||||
\(807\) | −57.5697 | −2.02655 | ||||||||
\(808\) | −12.2341 | −0.430393 | ||||||||
\(809\) | 34.6120 | 1.21689 | 0.608446 | − | 0.793595i | \(-0.291793\pi\) | ||||
0.608446 | + | 0.793595i | \(0.291793\pi\) | |||||||
\(810\) | 14.8181 | 0.520654 | ||||||||
\(811\) | 27.7945 | 0.975997 | 0.487998 | − | 0.872845i | \(-0.337727\pi\) | ||||
0.487998 | + | 0.872845i | \(0.337727\pi\) | |||||||
\(812\) | −15.3170 | −0.537522 | ||||||||
\(813\) | −61.8132 | −2.16789 | ||||||||
\(814\) | 1.98774 | 0.0696701 | ||||||||
\(815\) | −0.622417 | −0.0218023 | ||||||||
\(816\) | −18.9419 | −0.663099 | ||||||||
\(817\) | 3.42959 | 0.119986 | ||||||||
\(818\) | 17.1086 | 0.598189 | ||||||||
\(819\) | −92.1815 | −3.22108 | ||||||||
\(820\) | 0.00185342 | 6.47243e−5 0 | ||||||||
\(821\) | 54.8556 | 1.91447 | 0.957236 | − | 0.289307i | \(-0.0934247\pi\) | ||||
0.957236 | + | 0.289307i | \(0.0934247\pi\) | |||||||
\(822\) | −73.4505 | −2.56188 | ||||||||
\(823\) | 2.80963 | 0.0979374 | 0.0489687 | − | 0.998800i | \(-0.484407\pi\) | ||||
0.0489687 | + | 0.998800i | \(0.484407\pi\) | |||||||
\(824\) | −1.99867 | −0.0696271 | ||||||||
\(825\) | −3.50301 | −0.121959 | ||||||||
\(826\) | −24.6936 | −0.859201 | ||||||||
\(827\) | −43.2228 | −1.50300 | −0.751502 | − | 0.659731i | \(-0.770670\pi\) | ||||
−0.751502 | + | 0.659731i | \(0.770670\pi\) | |||||||
\(828\) | 4.94117 | 0.171718 | ||||||||
\(829\) | 2.97614 | 0.103366 | 0.0516828 | − | 0.998664i | \(-0.483542\pi\) | ||||
0.0516828 | + | 0.998664i | \(0.483542\pi\) | |||||||
\(830\) | −3.96846 | −0.137747 | ||||||||
\(831\) | 100.519 | 3.48697 | ||||||||
\(832\) | −3.38686 | −0.117418 | ||||||||
\(833\) | 22.2148 | 0.769697 | ||||||||
\(834\) | −51.9645 | −1.79938 | ||||||||
\(835\) | 3.96786 | 0.137313 | ||||||||
\(836\) | 0.479853 | 0.0165961 | ||||||||
\(837\) | 100.477 | 3.47299 | ||||||||
\(838\) | 11.2794 | 0.389641 | ||||||||
\(839\) | −39.3598 | −1.35885 | −0.679425 | − | 0.733745i | \(-0.737771\pi\) | ||||
−0.679425 | + | 0.733745i | \(0.737771\pi\) | |||||||
\(840\) | −4.81853 | −0.166255 | ||||||||
\(841\) | −7.53621 | −0.259869 | ||||||||
\(842\) | 10.2858 | 0.354471 | ||||||||
\(843\) | −8.21567 | −0.282963 | ||||||||
\(844\) | −11.6433 | −0.400779 | ||||||||
\(845\) | −0.664988 | −0.0228763 | ||||||||
\(846\) | 23.4992 | 0.807919 | ||||||||
\(847\) | −36.2115 | −1.24424 | ||||||||
\(848\) | −10.1788 | −0.349541 | ||||||||
\(849\) | 22.4111 | 0.769147 | ||||||||
\(850\) | −27.1902 | −0.932617 | ||||||||
\(851\) | −5.49140 | −0.188243 | ||||||||
\(852\) | 7.41073 | 0.253887 | ||||||||
\(853\) | −9.30954 | −0.318753 | −0.159376 | − | 0.987218i | \(-0.550948\pi\) | ||||
−0.159376 | + | 0.987218i | \(0.550948\pi\) | |||||||
\(854\) | 29.0681 | 0.994689 | ||||||||
\(855\) | −7.90698 | −0.270413 | ||||||||
\(856\) | −9.21214 | −0.314864 | ||||||||
\(857\) | 34.5400 | 1.17986 | 0.589932 | − | 0.807453i | \(-0.299155\pi\) | ||||
0.589932 | + | 0.807453i | \(0.299155\pi\) | |||||||
\(858\) | −2.46612 | −0.0841919 | ||||||||
\(859\) | 33.1808 | 1.13211 | 0.566056 | − | 0.824367i | \(-0.308468\pi\) | ||||
0.566056 | + | 0.824367i | \(0.308468\pi\) | |||||||
\(860\) | −0.675261 | −0.0230262 | ||||||||
\(861\) | −0.0472252 | −0.00160943 | ||||||||
\(862\) | 0.224416 | 0.00764365 | ||||||||
\(863\) | −53.1590 | −1.80955 | −0.904777 | − | 0.425886i | \(-0.859962\pi\) | ||||
−0.904777 | + | 0.425886i | \(0.859962\pi\) | |||||||
\(864\) | −17.5362 | −0.596592 | ||||||||
\(865\) | 9.27625 | 0.315402 | ||||||||
\(866\) | 19.0708 | 0.648051 | ||||||||
\(867\) | −50.0810 | −1.70084 | ||||||||
\(868\) | −18.9432 | −0.642974 | ||||||||
\(869\) | 1.05467 | 0.0357773 | ||||||||
\(870\) | 6.75222 | 0.228922 | ||||||||
\(871\) | −9.01088 | −0.305322 | ||||||||
\(872\) | 7.79859 | 0.264093 | ||||||||
\(873\) | 145.857 | 4.93652 | ||||||||
\(874\) | −1.32566 | −0.0448412 | ||||||||
\(875\) | −14.1055 | −0.476852 | ||||||||
\(876\) | 28.1622 | 0.951512 | ||||||||
\(877\) | 42.7438 | 1.44335 | 0.721677 | − | 0.692230i | \(-0.243371\pi\) | ||||
0.721677 | + | 0.692230i | \(0.243371\pi\) | |||||||
\(878\) | −39.6835 | −1.33925 | ||||||||
\(879\) | 5.37613 | 0.181333 | ||||||||
\(880\) | −0.0944797 | −0.00318491 | ||||||||
\(881\) | −1.21105 | −0.0408012 | −0.0204006 | − | 0.999792i | \(-0.506494\pi\) | ||||
−0.0204006 | + | 0.999792i | \(0.506494\pi\) | |||||||
\(882\) | 32.3578 | 1.08955 | ||||||||
\(883\) | 26.7723 | 0.900961 | 0.450480 | − | 0.892786i | \(-0.351253\pi\) | ||||
0.450480 | + | 0.892786i | \(0.351253\pi\) | |||||||
\(884\) | −19.1419 | −0.643812 | ||||||||
\(885\) | 10.8857 | 0.365920 | ||||||||
\(886\) | 8.94594 | 0.300545 | ||||||||
\(887\) | −40.2904 | −1.35282 | −0.676410 | − | 0.736526i | \(-0.736465\pi\) | ||||
−0.676410 | + | 0.736526i | \(0.736465\pi\) | |||||||
\(888\) | 30.6629 | 1.02898 | ||||||||
\(889\) | −49.3745 | −1.65597 | ||||||||
\(890\) | 5.69715 | 0.190969 | ||||||||
\(891\) | −7.40312 | −0.248014 | ||||||||
\(892\) | 5.38752 | 0.180387 | ||||||||
\(893\) | −6.30458 | −0.210975 | ||||||||
\(894\) | −62.3919 | −2.08670 | ||||||||
\(895\) | −8.17559 | −0.273280 | ||||||||
\(896\) | 3.30614 | 0.110450 | ||||||||
\(897\) | 6.81299 | 0.227479 | ||||||||
\(898\) | −23.2518 | −0.775922 | ||||||||
\(899\) | 26.5452 | 0.885331 | ||||||||
\(900\) | −39.6050 | −1.32017 | ||||||||
\(901\) | −57.5286 | −1.91656 | ||||||||
\(902\) | −0.000925971 0 | −3.08314e−5 0 | ||||||||
\(903\) | 17.2056 | 0.572568 | ||||||||
\(904\) | −6.09730 | −0.202793 | ||||||||
\(905\) | −6.95528 | −0.231201 | ||||||||
\(906\) | 68.3152 | 2.26962 | ||||||||
\(907\) | −9.64937 | −0.320402 | −0.160201 | − | 0.987084i | \(-0.551214\pi\) | ||||
−0.160201 | + | 0.987084i | \(0.551214\pi\) | |||||||
\(908\) | 16.7265 | 0.555090 | ||||||||
\(909\) | −100.715 | −3.34052 | ||||||||
\(910\) | −4.86941 | −0.161419 | ||||||||
\(911\) | −34.3560 | −1.13827 | −0.569133 | − | 0.822246i | \(-0.692721\pi\) | ||||
−0.569133 | + | 0.822246i | \(0.692721\pi\) | |||||||
\(912\) | 7.40225 | 0.245113 | ||||||||
\(913\) | 1.98265 | 0.0656160 | ||||||||
\(914\) | 20.4390 | 0.676061 | ||||||||
\(915\) | −12.8141 | −0.423622 | ||||||||
\(916\) | 10.2285 | 0.337958 | ||||||||
\(917\) | −10.8456 | −0.358154 | ||||||||
\(918\) | −99.1111 | −3.27115 | ||||||||
\(919\) | 56.4235 | 1.86124 | 0.930620 | − | 0.365988i | \(-0.119269\pi\) | ||||
0.930620 | + | 0.365988i | \(0.119269\pi\) | |||||||
\(920\) | 0.261013 | 0.00860535 | ||||||||
\(921\) | 95.6185 | 3.15074 | ||||||||
\(922\) | −20.1844 | −0.664737 | ||||||||
\(923\) | 7.48897 | 0.246503 | ||||||||
\(924\) | 2.40734 | 0.0791957 | ||||||||
\(925\) | 44.0153 | 1.44721 | ||||||||
\(926\) | −30.3322 | −0.996778 | ||||||||
\(927\) | −16.4538 | −0.540415 | ||||||||
\(928\) | −4.63290 | −0.152082 | ||||||||
\(929\) | −9.41055 | −0.308750 | −0.154375 | − | 0.988012i | \(-0.549336\pi\) | ||||
−0.154375 | + | 0.988012i | \(0.549336\pi\) | |||||||
\(930\) | 8.35076 | 0.273832 | ||||||||
\(931\) | −8.68125 | −0.284517 | ||||||||
\(932\) | 12.9318 | 0.423595 | ||||||||
\(933\) | −19.6523 | −0.643386 | ||||||||
\(934\) | −9.47525 | −0.310040 | ||||||||
\(935\) | −0.533981 | −0.0174631 | ||||||||
\(936\) | −27.8819 | −0.911349 | ||||||||
\(937\) | −4.82246 | −0.157543 | −0.0787714 | − | 0.996893i | \(-0.525100\pi\) | ||||
−0.0787714 | + | 0.996893i | \(0.525100\pi\) | |||||||
\(938\) | 8.79612 | 0.287203 | ||||||||
\(939\) | 30.3511 | 0.990470 | ||||||||
\(940\) | 1.24133 | 0.0404876 | ||||||||
\(941\) | 25.9614 | 0.846319 | 0.423159 | − | 0.906055i | \(-0.360921\pi\) | ||||
0.423159 | + | 0.906055i | \(0.360921\pi\) | |||||||
\(942\) | −67.8172 | −2.20960 | ||||||||
\(943\) | 0.00255812 | 8.33039e−5 0 | ||||||||
\(944\) | −7.46902 | −0.243096 | ||||||||
\(945\) | −25.2124 | −0.820158 | ||||||||
\(946\) | 0.337361 | 0.0109686 | ||||||||
\(947\) | 0.571460 | 0.0185700 | 0.00928498 | − | 0.999957i | \(-0.497044\pi\) | ||||
0.00928498 | + | 0.999957i | \(0.497044\pi\) | |||||||
\(948\) | 16.2694 | 0.528406 | ||||||||
\(949\) | 28.4595 | 0.923836 | ||||||||
\(950\) | 10.6256 | 0.344740 | ||||||||
\(951\) | −42.2441 | −1.36986 | ||||||||
\(952\) | 18.6857 | 0.605606 | ||||||||
\(953\) | −35.9909 | −1.16586 | −0.582929 | − | 0.812523i | \(-0.698094\pi\) | ||||
−0.582929 | + | 0.812523i | \(0.698094\pi\) | |||||||
\(954\) | −83.7957 | −2.71298 | ||||||||
\(955\) | −2.67238 | −0.0864761 | ||||||||
\(956\) | −8.86048 | −0.286568 | ||||||||
\(957\) | −3.37341 | −0.109047 | ||||||||
\(958\) | 12.5310 | 0.404858 | ||||||||
\(959\) | 72.4570 | 2.33976 | ||||||||
\(960\) | −1.45745 | −0.0470390 | ||||||||
\(961\) | 1.82953 | 0.0590172 | ||||||||
\(962\) | 30.9867 | 0.999052 | ||||||||
\(963\) | −75.8377 | −2.44384 | ||||||||
\(964\) | −19.5027 | −0.628139 | ||||||||
\(965\) | −8.70633 | −0.280267 | ||||||||
\(966\) | −6.65062 | −0.213980 | ||||||||
\(967\) | −8.34128 | −0.268238 | −0.134119 | − | 0.990965i | \(-0.542820\pi\) | ||||
−0.134119 | + | 0.990965i | \(0.542820\pi\) | |||||||
\(968\) | −10.9528 | −0.352036 | ||||||||
\(969\) | 41.8361 | 1.34397 | ||||||||
\(970\) | 7.70479 | 0.247386 | ||||||||
\(971\) | −26.8460 | −0.861531 | −0.430765 | − | 0.902464i | \(-0.641756\pi\) | ||||
−0.430765 | + | 0.902464i | \(0.641756\pi\) | |||||||
\(972\) | −61.5925 | −1.97558 | ||||||||
\(973\) | 51.2616 | 1.64337 | ||||||||
\(974\) | −0.847982 | −0.0271711 | ||||||||
\(975\) | −54.6083 | −1.74886 | ||||||||
\(976\) | 8.79215 | 0.281430 | ||||||||
\(977\) | 35.5455 | 1.13720 | 0.568600 | − | 0.822614i | \(-0.307485\pi\) | ||||
0.568600 | + | 0.822614i | \(0.307485\pi\) | |||||||
\(978\) | 4.79689 | 0.153388 | ||||||||
\(979\) | −2.84630 | −0.0909681 | ||||||||
\(980\) | 1.70928 | 0.0546008 | ||||||||
\(981\) | 64.2009 | 2.04978 | ||||||||
\(982\) | 22.6153 | 0.721683 | ||||||||
\(983\) | −39.2267 | −1.25114 | −0.625569 | − | 0.780169i | \(-0.715133\pi\) | ||||
−0.625569 | + | 0.780169i | \(0.715133\pi\) | |||||||
\(984\) | −0.0142841 | −0.000455360 0 | ||||||||
\(985\) | −5.61127 | −0.178790 | ||||||||
\(986\) | −26.1843 | −0.833878 | ||||||||
\(987\) | −31.6290 | −1.00676 | ||||||||
\(988\) | 7.48041 | 0.237983 | ||||||||
\(989\) | −0.932007 | −0.0296361 | ||||||||
\(990\) | −0.777792 | −0.0247199 | ||||||||
\(991\) | 62.8115 | 1.99527 | 0.997636 | − | 0.0687227i | \(-0.0218924\pi\) | ||||
0.997636 | + | 0.0687227i | \(0.0218924\pi\) | |||||||
\(992\) | −5.72971 | −0.181918 | ||||||||
\(993\) | −67.0998 | −2.12935 | ||||||||
\(994\) | −7.31049 | −0.231875 | ||||||||
\(995\) | −4.55568 | −0.144425 | ||||||||
\(996\) | 30.5844 | 0.969104 | ||||||||
\(997\) | −3.46020 | −0.109586 | −0.0547928 | − | 0.998498i | \(-0.517450\pi\) | ||||
−0.0547928 | + | 0.998498i | \(0.517450\pi\) | |||||||
\(998\) | −18.9290 | −0.599188 | ||||||||
\(999\) | 160.440 | 5.07610 |
(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 | 6046.2.a.e.1.1 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6046.2.a.e.1.1 | ✓ | 56 | 1.1 | even | 1 | trivial |