Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 17x^{8} + 23x^{7} + 69x^{6} - 88x^{5} - 106x^{4} + 101x^{3} + 60x^{2} - 23x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-3.66000\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.24431 | 1.58697 | 0.793484 | − | 0.608591i | \(-0.208265\pi\) | ||||
0.793484 | + | 0.608591i | \(0.208265\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.03693 | 1.51847 | ||||||||
\(5\) | 1.31370 | 0.587503 | 0.293752 | − | 0.955882i | \(-0.405096\pi\) | ||||
0.293752 | + | 0.955882i | \(0.405096\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.96709 | −1.12146 | −0.560728 | − | 0.828000i | \(-0.689479\pi\) | ||||
−0.560728 | + | 0.828000i | \(0.689479\pi\) | |||||||
\(8\) | 2.32720 | 0.822788 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.94835 | 0.932349 | ||||||||
\(11\) | −1.51682 | −0.457337 | −0.228668 | − | 0.973504i | \(-0.573437\pi\) | ||||
−0.228668 | + | 0.973504i | \(0.573437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.902202 | 0.250226 | 0.125113 | − | 0.992143i | \(-0.460071\pi\) | ||||
0.125113 | + | 0.992143i | \(0.460071\pi\) | |||||||
\(14\) | −6.65908 | −1.77971 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.850911 | −0.212728 | ||||||||
\(17\) | −3.54263 | −0.859215 | −0.429607 | − | 0.903016i | \(-0.641348\pi\) | ||||
−0.429607 | + | 0.903016i | \(0.641348\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.438527 | 0.100605 | 0.0503025 | − | 0.998734i | \(-0.483981\pi\) | ||||
0.0503025 | + | 0.998734i | \(0.483981\pi\) | |||||||
\(20\) | 3.98961 | 0.892104 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.40420 | −0.725779 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.27420 | −0.654840 | ||||||||
\(26\) | 2.02482 | 0.397100 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.01086 | −1.70289 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.36633 | −0.245400 | −0.122700 | − | 0.992444i | \(-0.539155\pi\) | ||||
−0.122700 | + | 0.992444i | \(0.539155\pi\) | |||||||
\(32\) | −6.56410 | −1.16038 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.95077 | −1.36355 | ||||||||
\(35\) | −3.89786 | −0.658859 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.9378 | −1.79817 | −0.899084 | − | 0.437776i | \(-0.855766\pi\) | ||||
−0.899084 | + | 0.437776i | \(0.855766\pi\) | |||||||
\(38\) | 0.984190 | 0.159657 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.05723 | 0.483391 | ||||||||
\(41\) | −3.73744 | −0.583690 | −0.291845 | − | 0.956466i | \(-0.594269\pi\) | ||||
−0.291845 | + | 0.956466i | \(0.594269\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.23701 | −0.951135 | −0.475568 | − | 0.879679i | \(-0.657757\pi\) | ||||
−0.475568 | + | 0.879679i | \(0.657757\pi\) | |||||||
\(44\) | −4.60646 | −0.694450 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.24431 | 0.330906 | ||||||||
\(47\) | −4.40935 | −0.643170 | −0.321585 | − | 0.946881i | \(-0.604216\pi\) | ||||
−0.321585 | + | 0.946881i | \(0.604216\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.80364 | 0.257663 | ||||||||
\(50\) | −7.34832 | −1.03921 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.73993 | 0.379959 | ||||||||
\(53\) | 10.7318 | 1.47413 | 0.737065 | − | 0.675822i | \(-0.236211\pi\) | ||||
0.737065 | + | 0.675822i | \(0.236211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.99264 | −0.268687 | ||||||||
\(56\) | −6.90501 | −0.922720 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.24431 | −0.294692 | ||||||||
\(59\) | −7.80539 | −1.01618 | −0.508088 | − | 0.861305i | \(-0.669647\pi\) | ||||
−0.508088 | + | 0.861305i | \(0.669647\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.66624 | 1.10960 | 0.554799 | − | 0.831984i | \(-0.312795\pi\) | ||||
0.554799 | + | 0.831984i | \(0.312795\pi\) | |||||||
\(62\) | −3.06647 | −0.389442 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0301 | −1.62876 | ||||||||
\(65\) | 1.18522 | 0.147009 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.02600 | 0.125346 | 0.0626729 | − | 0.998034i | \(-0.480038\pi\) | ||||
0.0626729 | + | 0.998034i | \(0.480038\pi\) | |||||||
\(68\) | −10.7587 | −1.30469 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.74801 | −1.04559 | ||||||||
\(71\) | 11.2518 | 1.33535 | 0.667674 | − | 0.744454i | \(-0.267290\pi\) | ||||
0.667674 | + | 0.744454i | \(0.267290\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.88266 | −0.337390 | −0.168695 | − | 0.985668i | \(-0.553955\pi\) | ||||
−0.168695 | + | 0.985668i | \(0.553955\pi\) | |||||||
\(74\) | −24.5479 | −2.85363 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.33178 | 0.152765 | ||||||||
\(77\) | 4.50053 | 0.512883 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.1535 | 1.81741 | 0.908703 | − | 0.417443i | \(-0.137074\pi\) | ||||
0.908703 | + | 0.417443i | \(0.137074\pi\) | |||||||
\(80\) | −1.11784 | −0.124978 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.38797 | −0.926296 | ||||||||
\(83\) | −3.36143 | −0.368965 | −0.184483 | − | 0.982836i | \(-0.559061\pi\) | ||||
−0.184483 | + | 0.982836i | \(0.559061\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.65395 | −0.504792 | ||||||||
\(86\) | −13.9978 | −1.50942 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.52993 | −0.376291 | ||||||||
\(89\) | 7.47996 | 0.792874 | 0.396437 | − | 0.918062i | \(-0.370247\pi\) | ||||
0.396437 | + | 0.918062i | \(0.370247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.67692 | −0.280617 | ||||||||
\(92\) | 3.03693 | 0.316622 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.89596 | −1.02069 | ||||||||
\(95\) | 0.576092 | 0.0591057 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.6206 | −1.58603 | −0.793014 | − | 0.609203i | \(-0.791489\pi\) | ||||
−0.793014 | + | 0.609203i | \(0.791489\pi\) | |||||||
\(98\) | 4.04792 | 0.408902 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.94352 | −0.994352 | ||||||||
\(101\) | 3.63336 | 0.361533 | 0.180767 | − | 0.983526i | \(-0.442142\pi\) | ||||
0.180767 | + | 0.983526i | \(0.442142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.2810 | 1.01302 | 0.506510 | − | 0.862234i | \(-0.330935\pi\) | ||||
0.506510 | + | 0.862234i | \(0.330935\pi\) | |||||||
\(104\) | 2.09960 | 0.205883 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.0856 | 2.33940 | ||||||||
\(107\) | −7.31175 | −0.706854 | −0.353427 | − | 0.935462i | \(-0.614984\pi\) | ||||
−0.353427 | + | 0.935462i | \(0.614984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.37760 | −0.323515 | −0.161758 | − | 0.986831i | \(-0.551716\pi\) | ||||
−0.161758 | + | 0.986831i | \(0.551716\pi\) | |||||||
\(110\) | −4.47210 | −0.426398 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.52473 | 0.238565 | ||||||||
\(113\) | 2.02102 | 0.190122 | 0.0950610 | − | 0.995471i | \(-0.469695\pi\) | ||||
0.0950610 | + | 0.995471i | \(0.469695\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.31370 | 0.122503 | ||||||||
\(116\) | −3.03693 | −0.281972 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.5177 | −1.61264 | ||||||||
\(119\) | 10.5113 | 0.963571 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.69927 | −0.790843 | ||||||||
\(122\) | 19.4497 | 1.76090 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.14945 | −0.372632 | ||||||||
\(125\) | −10.8698 | −0.972224 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.41766 | 0.214533 | 0.107266 | − | 0.994230i | \(-0.465790\pi\) | ||||
0.107266 | + | 0.994230i | \(0.465790\pi\) | |||||||
\(128\) | −16.1153 | −1.42441 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.66000 | 0.233298 | ||||||||
\(131\) | −3.99026 | −0.348630 | −0.174315 | − | 0.984690i | \(-0.555771\pi\) | ||||
−0.174315 | + | 0.984690i | \(0.555771\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.30115 | −0.112824 | ||||||||
\(134\) | 2.30266 | 0.198920 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.24440 | −0.706951 | ||||||||
\(137\) | −6.48948 | −0.554434 | −0.277217 | − | 0.960807i | \(-0.589412\pi\) | ||||
−0.277217 | + | 0.960807i | \(0.589412\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.9540 | −1.60766 | −0.803830 | − | 0.594859i | \(-0.797208\pi\) | ||||
−0.803830 | + | 0.594859i | \(0.797208\pi\) | |||||||
\(140\) | −11.8375 | −1.00045 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.2526 | 2.11915 | ||||||||
\(143\) | −1.36847 | −0.114438 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.31370 | −0.109097 | ||||||||
\(146\) | −6.46958 | −0.535427 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −33.2174 | −2.73046 | ||||||||
\(149\) | −22.8616 | −1.87290 | −0.936448 | − | 0.350807i | \(-0.885907\pi\) | ||||
−0.936448 | + | 0.350807i | \(0.885907\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8032 | 1.36743 | 0.683714 | − | 0.729750i | \(-0.260364\pi\) | ||||
0.683714 | + | 0.729750i | \(0.260364\pi\) | |||||||
\(152\) | 1.02054 | 0.0827765 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.1006 | 0.813929 | ||||||||
\(155\) | −1.79495 | −0.144174 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.66486 | 0.372296 | 0.186148 | − | 0.982522i | \(-0.440400\pi\) | ||||
0.186148 | + | 0.982522i | \(0.440400\pi\) | |||||||
\(158\) | 36.2534 | 2.88416 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.62324 | −0.681727 | ||||||||
\(161\) | −2.96709 | −0.233840 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.11817 | −0.479212 | −0.239606 | − | 0.970870i | \(-0.577018\pi\) | ||||
−0.239606 | + | 0.970870i | \(0.577018\pi\) | |||||||
\(164\) | −11.3503 | −0.886312 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.54410 | −0.585536 | ||||||||
\(167\) | −5.11459 | −0.395779 | −0.197889 | − | 0.980224i | \(-0.563409\pi\) | ||||
−0.197889 | + | 0.980224i | \(0.563409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1860 | −0.937387 | ||||||||
\(170\) | −10.4449 | −0.801088 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −18.9414 | −1.44427 | ||||||||
\(173\) | −10.5173 | −0.799614 | −0.399807 | − | 0.916599i | \(-0.630923\pi\) | ||||
−0.399807 | + | 0.916599i | \(0.630923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.71485 | 0.734374 | ||||||||
\(176\) | 1.29068 | 0.0972883 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.7873 | 1.25826 | ||||||||
\(179\) | −10.1812 | −0.760981 | −0.380491 | − | 0.924785i | \(-0.624245\pi\) | ||||
−0.380491 | + | 0.924785i | \(0.624245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.6445 | 1.60882 | 0.804412 | − | 0.594072i | \(-0.202481\pi\) | ||||
0.804412 | + | 0.594072i | \(0.202481\pi\) | |||||||
\(182\) | −6.00784 | −0.445330 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.32720 | 0.171563 | ||||||||
\(185\) | −14.3690 | −1.05643 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.37352 | 0.392951 | ||||||||
\(188\) | −13.3909 | −0.976632 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.29293 | 0.0937989 | ||||||||
\(191\) | −17.2119 | −1.24541 | −0.622705 | − | 0.782457i | \(-0.713966\pi\) | ||||
−0.622705 | + | 0.782457i | \(0.713966\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.97678 | −0.574181 | −0.287090 | − | 0.957903i | \(-0.592688\pi\) | ||||
−0.287090 | + | 0.957903i | \(0.592688\pi\) | |||||||
\(194\) | −35.0574 | −2.51698 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.47752 | 0.391252 | ||||||||
\(197\) | −5.13962 | −0.366183 | −0.183092 | − | 0.983096i | \(-0.558610\pi\) | ||||
−0.183092 | + | 0.983096i | \(0.558610\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.9501 | 1.55600 | 0.777999 | − | 0.628265i | \(-0.216235\pi\) | ||||
0.777999 | + | 0.628265i | \(0.216235\pi\) | |||||||
\(200\) | −7.61970 | −0.538794 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.15440 | 0.573741 | ||||||||
\(203\) | 2.96709 | 0.208249 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.90986 | −0.342920 | ||||||||
\(206\) | 23.0738 | 1.60763 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.767694 | −0.0532300 | ||||||||
\(209\) | −0.665164 | −0.0460104 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.00040 | 0.481927 | 0.240964 | − | 0.970534i | \(-0.422537\pi\) | ||||
0.240964 | + | 0.970534i | \(0.422537\pi\) | |||||||
\(212\) | 32.5918 | 2.23841 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.4098 | −1.12175 | ||||||||
\(215\) | −8.19355 | −0.558795 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.05403 | 0.275206 | ||||||||
\(218\) | −7.58038 | −0.513408 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.05150 | −0.407992 | ||||||||
\(221\) | −3.19617 | −0.214998 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.3205 | 1.29380 | 0.646899 | − | 0.762575i | \(-0.276065\pi\) | ||||
0.646899 | + | 0.762575i | \(0.276065\pi\) | |||||||
\(224\) | 19.4763 | 1.30131 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.53581 | 0.301717 | ||||||||
\(227\) | 4.35027 | 0.288738 | 0.144369 | − | 0.989524i | \(-0.453885\pi\) | ||||
0.144369 | + | 0.989524i | \(0.453885\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.2691 | 0.942927 | 0.471464 | − | 0.881886i | \(-0.343726\pi\) | ||||
0.471464 | + | 0.881886i | \(0.343726\pi\) | |||||||
\(230\) | 2.94835 | 0.194408 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.32720 | −0.152788 | ||||||||
\(233\) | −1.10104 | −0.0721315 | −0.0360657 | − | 0.999349i | \(-0.511483\pi\) | ||||
−0.0360657 | + | 0.999349i | \(0.511483\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.79256 | −0.377865 | ||||||||
\(236\) | −23.7044 | −1.54303 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.5907 | 1.52916 | ||||||||
\(239\) | −3.57602 | −0.231314 | −0.115657 | − | 0.993289i | \(-0.536897\pi\) | ||||
−0.115657 | + | 0.993289i | \(0.536897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.8181 | 1.53426 | 0.767130 | − | 0.641492i | \(-0.221684\pi\) | ||||
0.767130 | + | 0.641492i | \(0.221684\pi\) | |||||||
\(242\) | −19.5239 | −1.25504 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 26.3188 | 1.68489 | ||||||||
\(245\) | 2.36943 | 0.151378 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.395640 | 0.0251740 | ||||||||
\(248\) | −3.17972 | −0.201912 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −24.3952 | −1.54289 | ||||||||
\(251\) | 11.0028 | 0.694489 | 0.347245 | − | 0.937775i | \(-0.387117\pi\) | ||||
0.347245 | + | 0.937775i | \(0.387117\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.51682 | −0.0953614 | ||||||||
\(254\) | 5.42599 | 0.340457 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.1076 | −0.631727 | ||||||||
\(257\) | −22.5544 | −1.40691 | −0.703453 | − | 0.710742i | \(-0.748360\pi\) | ||||
−0.703453 | + | 0.710742i | \(0.748360\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.4536 | 2.01657 | ||||||||
\(260\) | 3.59943 | 0.223227 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8.95538 | −0.553265 | ||||||||
\(263\) | −10.0124 | −0.617390 | −0.308695 | − | 0.951161i | \(-0.599892\pi\) | ||||
−0.308695 | + | 0.951161i | \(0.599892\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.0984 | 0.866056 | ||||||||
\(266\) | −2.92018 | −0.179048 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.11589 | 0.190333 | ||||||||
\(269\) | 12.9882 | 0.791902 | 0.395951 | − | 0.918272i | \(-0.370415\pi\) | ||||
0.395951 | + | 0.918272i | \(0.370415\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.5385 | 0.943894 | 0.471947 | − | 0.881627i | \(-0.343551\pi\) | ||||
0.471947 | + | 0.881627i | \(0.343551\pi\) | |||||||
\(272\) | 3.01447 | 0.182779 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.5644 | −0.879868 | ||||||||
\(275\) | 4.96635 | 0.299482 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.5683 | 1.05557 | 0.527787 | − | 0.849377i | \(-0.323022\pi\) | ||||
0.527787 | + | 0.849377i | \(0.323022\pi\) | |||||||
\(278\) | −42.5387 | −2.55130 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.07109 | −0.542101 | ||||||||
\(281\) | 13.1371 | 0.783693 | 0.391846 | − | 0.920031i | \(-0.371836\pi\) | ||||
0.391846 | + | 0.920031i | \(0.371836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.30957 | −0.434509 | −0.217254 | − | 0.976115i | \(-0.569710\pi\) | ||||
−0.217254 | + | 0.976115i | \(0.569710\pi\) | |||||||
\(284\) | 34.1710 | 2.02768 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.07128 | −0.181609 | ||||||||
\(287\) | 11.0893 | 0.654582 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.44975 | −0.261750 | ||||||||
\(290\) | −2.94835 | −0.173133 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.75444 | −0.512315 | ||||||||
\(293\) | 8.00780 | 0.467821 | 0.233910 | − | 0.972258i | \(-0.424848\pi\) | ||||
0.233910 | + | 0.972258i | \(0.424848\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.2539 | −0.597007 | ||||||||
\(296\) | −25.4545 | −1.47951 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −51.3085 | −2.97222 | ||||||||
\(299\) | 0.902202 | 0.0521757 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.5058 | 1.06666 | ||||||||
\(302\) | 37.7117 | 2.17006 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.373147 | −0.0214015 | ||||||||
\(305\) | 11.3848 | 0.651893 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.5296 | −1.74242 | −0.871208 | − | 0.490915i | \(-0.836663\pi\) | ||||
−0.871208 | + | 0.490915i | \(0.836663\pi\) | |||||||
\(308\) | 13.6678 | 0.778795 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.02842 | −0.228799 | ||||||||
\(311\) | −26.8315 | −1.52148 | −0.760738 | − | 0.649060i | \(-0.775163\pi\) | ||||
−0.760738 | + | 0.649060i | \(0.775163\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.67441 | 0.433783 | 0.216892 | − | 0.976196i | \(-0.430408\pi\) | ||||
0.216892 | + | 0.976196i | \(0.430408\pi\) | |||||||
\(314\) | 10.4694 | 0.590822 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 49.0569 | 2.75967 | ||||||||
\(317\) | 11.3137 | 0.635441 | 0.317721 | − | 0.948184i | \(-0.397083\pi\) | ||||
0.317721 | + | 0.948184i | \(0.397083\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.51682 | 0.0849253 | ||||||||
\(320\) | −17.1176 | −0.956901 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.65908 | −0.371096 | ||||||||
\(323\) | −1.55354 | −0.0864412 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.95399 | −0.163858 | ||||||||
\(326\) | −13.7311 | −0.760493 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.69775 | −0.480253 | ||||||||
\(329\) | 13.0830 | 0.721287 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.5401 | 1.89849 | 0.949247 | − | 0.314531i | \(-0.101847\pi\) | ||||
0.949247 | + | 0.314531i | \(0.101847\pi\) | |||||||
\(332\) | −10.2084 | −0.560261 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.4787 | −0.628088 | ||||||||
\(335\) | 1.34785 | 0.0736411 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.5432 | 1.22801 | 0.614004 | − | 0.789303i | \(-0.289558\pi\) | ||||
0.614004 | + | 0.789303i | \(0.289558\pi\) | |||||||
\(338\) | −27.3492 | −1.48760 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.1337 | −0.766509 | ||||||||
\(341\) | 2.07247 | 0.112231 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4181 | 0.832498 | ||||||||
\(344\) | −14.5147 | −0.782583 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.6041 | −1.26896 | ||||||||
\(347\) | −15.7661 | −0.846367 | −0.423184 | − | 0.906044i | \(-0.639087\pi\) | ||||
−0.423184 | + | 0.906044i | \(0.639087\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.6754 | −0.999673 | −0.499836 | − | 0.866120i | \(-0.666607\pi\) | ||||
−0.499836 | + | 0.866120i | \(0.666607\pi\) | |||||||
\(350\) | 21.8031 | 1.16543 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.95653 | 0.530685 | ||||||||
\(353\) | 22.1152 | 1.17708 | 0.588538 | − | 0.808470i | \(-0.299704\pi\) | ||||
0.588538 | + | 0.808470i | \(0.299704\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.7815 | 0.784521 | ||||||||
\(356\) | 22.7161 | 1.20395 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.8499 | −1.20765 | ||||||||
\(359\) | 31.7410 | 1.67523 | 0.837613 | − | 0.546264i | \(-0.183951\pi\) | ||||
0.837613 | + | 0.546264i | \(0.183951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8077 | −0.989879 | ||||||||
\(362\) | 48.5770 | 2.55315 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.12961 | −0.426108 | ||||||||
\(365\) | −3.78694 | −0.198218 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.88341 | 0.411511 | 0.205755 | − | 0.978603i | \(-0.434035\pi\) | ||||
0.205755 | + | 0.978603i | \(0.434035\pi\) | |||||||
\(368\) | −0.850911 | −0.0443568 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −32.2485 | −1.67652 | ||||||||
\(371\) | −31.8423 | −1.65317 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.3349 | −1.00112 | −0.500561 | − | 0.865701i | \(-0.666873\pi\) | ||||
−0.500561 | + | 0.865701i | \(0.666873\pi\) | |||||||
\(374\) | 12.0598 | 0.623600 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.2614 | −0.529193 | ||||||||
\(377\) | −0.902202 | −0.0464658 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.7522 | −0.706405 | −0.353202 | − | 0.935547i | \(-0.614907\pi\) | ||||
−0.353202 | + | 0.935547i | \(0.614907\pi\) | |||||||
\(380\) | 1.74955 | 0.0897500 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −38.6289 | −1.97642 | ||||||||
\(383\) | −9.78378 | −0.499928 | −0.249964 | − | 0.968255i | \(-0.580419\pi\) | ||||
−0.249964 | + | 0.968255i | \(0.580419\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.91234 | 0.301321 | ||||||||
\(386\) | −17.9024 | −0.911206 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −47.4386 | −2.40833 | ||||||||
\(389\) | −20.3246 | −1.03050 | −0.515250 | − | 0.857040i | \(-0.672301\pi\) | ||||
−0.515250 | + | 0.857040i | \(0.672301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.54263 | −0.179159 | ||||||||
\(392\) | 4.19742 | 0.212002 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11.5349 | −0.581120 | ||||||||
\(395\) | 21.2208 | 1.06773 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.0836 | −0.757024 | −0.378512 | − | 0.925596i | \(-0.623564\pi\) | ||||
−0.378512 | + | 0.925596i | \(0.623564\pi\) | |||||||
\(398\) | 49.2628 | 2.46932 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.78605 | 0.139303 | ||||||||
\(401\) | −31.7667 | −1.58635 | −0.793176 | − | 0.608993i | \(-0.791574\pi\) | ||||
−0.793176 | + | 0.608993i | \(0.791574\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.23271 | −0.0614055 | ||||||||
\(404\) | 11.0343 | 0.548976 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.65908 | 0.330484 | ||||||||
\(407\) | 16.5907 | 0.822369 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.67330 | −0.132186 | −0.0660931 | − | 0.997813i | \(-0.521053\pi\) | ||||
−0.0660931 | + | 0.997813i | \(0.521053\pi\) | |||||||
\(410\) | −11.0193 | −0.544202 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 31.2228 | 1.53824 | ||||||||
\(413\) | 23.1593 | 1.13960 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.41591 | −0.216768 | ||||||||
\(416\) | −5.92215 | −0.290357 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.49283 | −0.0730169 | ||||||||
\(419\) | −28.1776 | −1.37657 | −0.688284 | − | 0.725442i | \(-0.741636\pi\) | ||||
−0.688284 | + | 0.725442i | \(0.741636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.5851 | 1.34441 | 0.672207 | − | 0.740363i | \(-0.265346\pi\) | ||||
0.672207 | + | 0.740363i | \(0.265346\pi\) | |||||||
\(422\) | 15.7111 | 0.764803 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 24.9751 | 1.21290 | ||||||||
\(425\) | 11.5993 | 0.562648 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.7135 | −1.24437 | ||||||||
\(428\) | −22.2053 | −1.07333 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.3889 | −0.886790 | ||||||||
\(431\) | −5.24056 | −0.252429 | −0.126215 | − | 0.992003i | \(-0.540283\pi\) | ||||
−0.126215 | + | 0.992003i | \(0.540283\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.8854 | −1.05174 | −0.525872 | − | 0.850564i | \(-0.676261\pi\) | ||||
−0.525872 | + | 0.850564i | \(0.676261\pi\) | |||||||
\(434\) | 9.09851 | 0.436742 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.2575 | −0.491247 | ||||||||
\(437\) | 0.438527 | 0.0209776 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.9271 | −0.664702 | −0.332351 | − | 0.943156i | \(-0.607842\pi\) | ||||
−0.332351 | + | 0.943156i | \(0.607842\pi\) | |||||||
\(440\) | −4.63726 | −0.221072 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.17320 | −0.341194 | ||||||||
\(443\) | 27.5227 | 1.30764 | 0.653821 | − | 0.756649i | \(-0.273165\pi\) | ||||
0.653821 | + | 0.756649i | \(0.273165\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.82640 | 0.465816 | ||||||||
\(446\) | 43.3613 | 2.05322 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 38.6614 | 1.82658 | ||||||||
\(449\) | −35.1874 | −1.66060 | −0.830298 | − | 0.557320i | \(-0.811830\pi\) | ||||
−0.830298 | + | 0.557320i | \(0.811830\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.66900 | 0.266943 | ||||||||
\(452\) | 6.13771 | 0.288694 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.76336 | 0.458217 | ||||||||
\(455\) | −3.51666 | −0.164864 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.3507 | −0.858409 | −0.429205 | − | 0.903207i | \(-0.641206\pi\) | ||||
−0.429205 | + | 0.903207i | \(0.641206\pi\) | |||||||
\(458\) | 32.0242 | 1.49639 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.98961 | 0.186016 | ||||||||
\(461\) | 24.7369 | 1.15211 | 0.576056 | − | 0.817410i | \(-0.304591\pi\) | ||||
0.576056 | + | 0.817410i | \(0.304591\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6364 | 0.587264 | 0.293632 | − | 0.955919i | \(-0.405136\pi\) | ||||
0.293632 | + | 0.955919i | \(0.405136\pi\) | |||||||
\(464\) | 0.850911 | 0.0395026 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.47107 | −0.114470 | ||||||||
\(467\) | 20.5427 | 0.950603 | 0.475301 | − | 0.879823i | \(-0.342339\pi\) | ||||
0.475301 | + | 0.879823i | \(0.342339\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.04424 | −0.140570 | ||||||||
\(470\) | −13.0003 | −0.599659 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.1647 | −0.836097 | ||||||||
\(473\) | 9.46039 | 0.434989 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.43582 | −0.0658801 | ||||||||
\(476\) | 31.9222 | 1.46315 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.02570 | −0.367087 | ||||||||
\(479\) | 14.3319 | 0.654842 | 0.327421 | − | 0.944879i | \(-0.393821\pi\) | ||||
0.327421 | + | 0.944879i | \(0.393821\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.86814 | −0.449948 | ||||||||
\(482\) | 53.4553 | 2.43482 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.4191 | −1.20087 | ||||||||
\(485\) | −20.5207 | −0.931797 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.62111 | −0.300031 | −0.150016 | − | 0.988684i | \(-0.547932\pi\) | ||||
−0.150016 | + | 0.988684i | \(0.547932\pi\) | |||||||
\(488\) | 20.1680 | 0.912964 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.31775 | 0.240231 | ||||||||
\(491\) | 16.2298 | 0.732440 | 0.366220 | − | 0.930528i | \(-0.380652\pi\) | ||||
0.366220 | + | 0.930528i | \(0.380652\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.54263 | 0.159552 | ||||||||
\(494\) | 0.887939 | 0.0399503 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.16263 | 0.0522035 | ||||||||
\(497\) | −33.3852 | −1.49753 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.1031 | −0.497043 | −0.248521 | − | 0.968626i | \(-0.579945\pi\) | ||||
−0.248521 | + | 0.968626i | \(0.579945\pi\) | |||||||
\(500\) | −33.0108 | −1.47629 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.6937 | 1.10213 | ||||||||
\(503\) | −7.73894 | −0.345062 | −0.172531 | − | 0.985004i | \(-0.555195\pi\) | ||||
−0.172531 | + | 0.985004i | \(0.555195\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.77314 | 0.212402 | ||||||||
\(506\) | −3.40420 | −0.151335 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.34227 | 0.325761 | ||||||||
\(509\) | −12.1628 | −0.539105 | −0.269553 | − | 0.962986i | \(-0.586876\pi\) | ||||
−0.269553 | + | 0.962986i | \(0.586876\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.55312 | 0.378368 | ||||||||
\(512\) | 9.54594 | 0.421875 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −50.6191 | −2.23271 | ||||||||
\(515\) | 13.5062 | 0.595152 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.68817 | 0.294146 | ||||||||
\(518\) | 72.8359 | 3.20022 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.75824 | 0.120957 | ||||||||
\(521\) | 19.3594 | 0.848152 | 0.424076 | − | 0.905627i | \(-0.360599\pi\) | ||||
0.424076 | + | 0.905627i | \(0.360599\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.25739 | 0.186163 | 0.0930814 | − | 0.995659i | \(-0.470328\pi\) | ||||
0.0930814 | + | 0.995659i | \(0.470328\pi\) | |||||||
\(524\) | −12.1181 | −0.529383 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.4709 | −0.979777 | ||||||||
\(527\) | 4.84041 | 0.210852 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 31.6411 | 1.37440 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.95150 | −0.171319 | ||||||||
\(533\) | −3.37192 | −0.146054 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.60543 | −0.415279 | ||||||||
\(536\) | 2.38770 | 0.103133 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 29.1495 | 1.25672 | ||||||||
\(539\) | −2.73579 | −0.117839 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.3992 | 0.705057 | 0.352528 | − | 0.935801i | \(-0.385322\pi\) | ||||
0.352528 | + | 0.935801i | \(0.385322\pi\) | |||||||
\(542\) | 34.8731 | 1.49793 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 23.2542 | 0.997016 | ||||||||
\(545\) | −4.43714 | −0.190066 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.7707 | −0.717065 | −0.358533 | − | 0.933517i | \(-0.616723\pi\) | ||||
−0.358533 | + | 0.933517i | \(0.616723\pi\) | |||||||
\(548\) | −19.7081 | −0.841889 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.1460 | 0.475269 | ||||||||
\(551\) | −0.438527 | −0.0186819 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −47.9288 | −2.03814 | ||||||||
\(554\) | 39.4286 | 1.67516 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −57.5621 | −2.44118 | ||||||||
\(557\) | −36.1688 | −1.53252 | −0.766261 | − | 0.642530i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642530i | \(0.777885\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.62705 | −0.237999 | ||||||||
\(560\) | 3.31674 | 0.140158 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 29.4837 | 1.24370 | ||||||||
\(563\) | −15.4439 | −0.650883 | −0.325441 | − | 0.945562i | \(-0.605513\pi\) | ||||
−0.325441 | + | 0.945562i | \(0.605513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.65501 | 0.111697 | ||||||||
\(566\) | −16.4049 | −0.689551 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 26.1852 | 1.09871 | ||||||||
\(569\) | 18.1051 | 0.759007 | 0.379503 | − | 0.925190i | \(-0.376095\pi\) | ||||
0.379503 | + | 0.925190i | \(0.376095\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.4246 | 1.69171 | 0.845857 | − | 0.533409i | \(-0.179089\pi\) | ||||
0.845857 | + | 0.533409i | \(0.179089\pi\) | |||||||
\(572\) | −4.15596 | −0.173769 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.8879 | 1.03880 | ||||||||
\(575\) | −3.27420 | −0.136544 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.89094 | −0.245243 | −0.122621 | − | 0.992454i | \(-0.539130\pi\) | ||||
−0.122621 | + | 0.992454i | \(0.539130\pi\) | |||||||
\(578\) | −9.98663 | −0.415389 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.98961 | −0.165660 | ||||||||
\(581\) | 9.97368 | 0.413778 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.2782 | −0.674174 | ||||||||
\(584\) | −6.70851 | −0.277600 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.9720 | 0.742416 | ||||||||
\(587\) | 13.3990 | 0.553036 | 0.276518 | − | 0.961009i | \(-0.410819\pi\) | ||||
0.276518 | + | 0.961009i | \(0.410819\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.599173 | −0.0246885 | ||||||||
\(590\) | −23.0130 | −0.947430 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.30713 | 0.382521 | ||||||||
\(593\) | −7.11166 | −0.292041 | −0.146020 | − | 0.989282i | \(-0.546647\pi\) | ||||
−0.146020 | + | 0.989282i | \(0.546647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.8087 | 0.566101 | ||||||||
\(596\) | −69.4291 | −2.84393 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.02482 | 0.0828011 | ||||||||
\(599\) | −0.867674 | −0.0354522 | −0.0177261 | − | 0.999843i | \(-0.505643\pi\) | ||||
−0.0177261 | + | 0.999843i | \(0.505643\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.04317 | 0.0833424 | 0.0416712 | − | 0.999131i | \(-0.486732\pi\) | ||||
0.0416712 | + | 0.999131i | \(0.486732\pi\) | |||||||
\(602\) | 41.5327 | 1.69275 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 51.0302 | 2.07639 | ||||||||
\(605\) | −11.4282 | −0.464623 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.7094 | 1.85529 | 0.927644 | − | 0.373465i | \(-0.121830\pi\) | ||||
0.927644 | + | 0.373465i | \(0.121830\pi\) | |||||||
\(608\) | −2.87853 | −0.116740 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.5511 | 1.03453 | ||||||||
\(611\) | −3.97813 | −0.160938 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0161 | 0.848831 | 0.424416 | − | 0.905467i | \(-0.360480\pi\) | ||||
0.424416 | + | 0.905467i | \(0.360480\pi\) | |||||||
\(614\) | −68.5179 | −2.76516 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.4736 | 0.421994 | ||||||||
\(617\) | 16.5056 | 0.664489 | 0.332244 | − | 0.943193i | \(-0.392194\pi\) | ||||
0.332244 | + | 0.943193i | \(0.392194\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.3608 | 1.22030 | 0.610152 | − | 0.792284i | \(-0.291108\pi\) | ||||
0.610152 | + | 0.792284i | \(0.291108\pi\) | |||||||
\(620\) | −5.45113 | −0.218923 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −60.2182 | −2.41453 | ||||||||
\(623\) | −22.1937 | −0.889173 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.09137 | 0.0836548 | ||||||||
\(626\) | 17.2238 | 0.688400 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.1669 | 0.565319 | ||||||||
\(629\) | 38.7487 | 1.54501 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.182379 | 0.00726040 | 0.00363020 | − | 0.999993i | \(-0.498844\pi\) | ||||
0.00363020 | + | 0.999993i | \(0.498844\pi\) | |||||||
\(632\) | 37.5923 | 1.49534 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.3915 | 1.00842 | ||||||||
\(635\) | 3.17608 | 0.126039 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.62725 | 0.0644738 | ||||||||
\(638\) | 3.40420 | 0.134774 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.1706 | −0.836843 | ||||||||
\(641\) | 7.86588 | 0.310684 | 0.155342 | − | 0.987861i | \(-0.450352\pi\) | ||||
0.155342 | + | 0.987861i | \(0.450352\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.3455 | 0.447423 | 0.223711 | − | 0.974655i | \(-0.428183\pi\) | ||||
0.223711 | + | 0.974655i | \(0.428183\pi\) | |||||||
\(644\) | −9.01086 | −0.355077 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.48663 | −0.137179 | ||||||||
\(647\) | −22.3414 | −0.878330 | −0.439165 | − | 0.898406i | \(-0.644726\pi\) | ||||
−0.439165 | + | 0.898406i | \(0.644726\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.8393 | 0.464735 | ||||||||
\(650\) | −6.62967 | −0.260037 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.5804 | −0.727667 | ||||||||
\(653\) | −39.1961 | −1.53386 | −0.766931 | − | 0.641729i | \(-0.778217\pi\) | ||||
−0.766931 | + | 0.641729i | \(0.778217\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.24199 | −0.204821 | ||||||||
\(656\) | 3.18023 | 0.124167 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 29.3622 | 1.14466 | ||||||||
\(659\) | 15.0318 | 0.585557 | 0.292778 | − | 0.956180i | \(-0.405420\pi\) | ||||
0.292778 | + | 0.956180i | \(0.405420\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.2171 | −1.52537 | −0.762685 | − | 0.646770i | \(-0.776119\pi\) | ||||
−0.762685 | + | 0.646770i | \(0.776119\pi\) | |||||||
\(662\) | 77.5187 | 3.01285 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.82271 | −0.303580 | ||||||||
\(665\) | −1.70932 | −0.0662845 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −15.5327 | −0.600976 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.02500 | 0.116866 | ||||||||
\(671\) | −13.1451 | −0.507460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.9758 | 0.461635 | 0.230818 | − | 0.972997i | \(-0.425860\pi\) | ||||
0.230818 | + | 0.972997i | \(0.425860\pi\) | |||||||
\(674\) | 50.5941 | 1.94881 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −37.0081 | −1.42339 | ||||||||
\(677\) | −22.1732 | −0.852185 | −0.426093 | − | 0.904680i | \(-0.640110\pi\) | ||||
−0.426093 | + | 0.904680i | \(0.640110\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 46.3477 | 1.77866 | ||||||||
\(680\) | −10.8306 | −0.415336 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.65127 | 0.178106 | ||||||||
\(683\) | 3.66223 | 0.140131 | 0.0700657 | − | 0.997542i | \(-0.477679\pi\) | ||||
0.0700657 | + | 0.997542i | \(0.477679\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.52522 | −0.325732 | ||||||||
\(686\) | 34.6030 | 1.32115 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.30715 | 0.202333 | ||||||||
\(689\) | 9.68228 | 0.368865 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.7825 | 0.562354 | 0.281177 | − | 0.959656i | \(-0.409275\pi\) | ||||
0.281177 | + | 0.959656i | \(0.409275\pi\) | |||||||
\(692\) | −31.9403 | −1.21419 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −35.3840 | −1.34316 | ||||||||
\(695\) | −24.8999 | −0.944505 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.2404 | 0.501515 | ||||||||
\(698\) | −41.9135 | −1.58645 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 29.5033 | 1.11512 | ||||||||
\(701\) | −19.8395 | −0.749328 | −0.374664 | − | 0.927161i | \(-0.622242\pi\) | ||||
−0.374664 | + | 0.927161i | \(0.622242\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.79653 | −0.180905 | ||||||||
\(704\) | 19.7642 | 0.744891 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 49.6335 | 1.86798 | ||||||||
\(707\) | −10.7805 | −0.405443 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.7266 | 0.665735 | 0.332868 | − | 0.942974i | \(-0.391984\pi\) | ||||
0.332868 | + | 0.942974i | \(0.391984\pi\) | |||||||
\(710\) | 33.1743 | 1.24501 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.4073 | 0.652367 | ||||||||
\(713\) | −1.36633 | −0.0511695 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.79776 | −0.0672325 | ||||||||
\(716\) | −30.9197 | −1.15552 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 71.2367 | 2.65853 | ||||||||
\(719\) | −18.0624 | −0.673612 | −0.336806 | − | 0.941574i | \(-0.609347\pi\) | ||||
−0.336806 | + | 0.941574i | \(0.609347\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.5048 | −1.13606 | ||||||||
\(722\) | −42.2103 | −1.57091 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 65.7329 | 2.44294 | ||||||||
\(725\) | 3.27420 | 0.121601 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.3044 | −0.753048 | −0.376524 | − | 0.926407i | \(-0.622881\pi\) | ||||
−0.376524 | + | 0.926407i | \(0.622881\pi\) | |||||||
\(728\) | −6.22971 | −0.230888 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.49908 | −0.314565 | ||||||||
\(731\) | 22.0954 | 0.817229 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.63182 | −0.244952 | −0.122476 | − | 0.992471i | \(-0.539083\pi\) | ||||
−0.122476 | + | 0.992471i | \(0.539083\pi\) | |||||||
\(734\) | 17.6928 | 0.653054 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.56410 | −0.241956 | ||||||||
\(737\) | −1.55625 | −0.0573253 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.4937 | 0.974588 | 0.487294 | − | 0.873238i | \(-0.337984\pi\) | ||||
0.487294 | + | 0.873238i | \(0.337984\pi\) | |||||||
\(740\) | −43.6377 | −1.60415 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −71.4641 | −2.62353 | ||||||||
\(743\) | 41.8653 | 1.53589 | 0.767945 | − | 0.640516i | \(-0.221279\pi\) | ||||
0.767945 | + | 0.640516i | \(0.221279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.0332 | −1.10033 | ||||||||
\(746\) | −43.3935 | −1.58875 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.3190 | 0.596682 | ||||||||
\(749\) | 21.6946 | 0.792705 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.9711 | −0.509811 | −0.254905 | − | 0.966966i | \(-0.582044\pi\) | ||||
−0.254905 | + | 0.966966i | \(0.582044\pi\) | |||||||
\(752\) | 3.75197 | 0.136820 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.02482 | −0.0737397 | ||||||||
\(755\) | 22.0744 | 0.803368 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.79857 | 0.0653703 | 0.0326852 | − | 0.999466i | \(-0.489594\pi\) | ||||
0.0326852 | + | 0.999466i | \(0.489594\pi\) | |||||||
\(758\) | −30.8643 | −1.12104 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.34068 | 0.0486315 | ||||||||
\(761\) | 22.2173 | 0.805378 | 0.402689 | − | 0.915337i | \(-0.368076\pi\) | ||||
0.402689 | + | 0.915337i | \(0.368076\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0216 | 0.362808 | ||||||||
\(764\) | −52.2714 | −1.89111 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.9578 | −0.793369 | ||||||||
\(767\) | −7.04204 | −0.254273 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.3008 | −1.48934 | −0.744672 | − | 0.667431i | \(-0.767394\pi\) | ||||
−0.744672 | + | 0.667431i | \(0.767394\pi\) | |||||||
\(770\) | 13.2691 | 0.478186 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24.2249 | −0.871874 | ||||||||
\(773\) | 19.5525 | 0.703254 | 0.351627 | − | 0.936140i | \(-0.385629\pi\) | ||||
0.351627 | + | 0.936140i | \(0.385629\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.47364 | 0.160698 | ||||||||
\(776\) | −36.3521 | −1.30497 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −45.6148 | −1.63537 | ||||||||
\(779\) | −1.63897 | −0.0587221 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0670 | −0.610704 | ||||||||
\(782\) | −7.95077 | −0.284319 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.53474 | −0.0548120 | ||||||||
\(785\) | 6.12821 | 0.218725 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.6255 | 0.485695 | 0.242848 | − | 0.970064i | \(-0.421919\pi\) | ||||
0.242848 | + | 0.970064i | \(0.421919\pi\) | |||||||
\(788\) | −15.6087 | −0.556036 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 47.6260 | 1.69446 | ||||||||
\(791\) | −5.99656 | −0.213213 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.81870 | 0.277650 | ||||||||
\(794\) | −33.8523 | −1.20137 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 66.6608 | 2.36273 | ||||||||
\(797\) | −14.3368 | −0.507836 | −0.253918 | − | 0.967226i | \(-0.581719\pi\) | ||||
−0.253918 | + | 0.967226i | \(0.581719\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.6207 | 0.552621 | ||||||||
\(800\) | 21.4922 | 0.759863 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −71.2943 | −2.51749 | ||||||||
\(803\) | 4.37246 | 0.154301 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.89786 | −0.137382 | ||||||||
\(806\) | −2.76658 | −0.0974486 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.45555 | 0.297465 | ||||||||
\(809\) | 45.8588 | 1.61231 | 0.806155 | − | 0.591705i | \(-0.201545\pi\) | ||||
0.806155 | + | 0.591705i | \(0.201545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.4624 | 0.472728 | 0.236364 | − | 0.971665i | \(-0.424044\pi\) | ||||
0.236364 | + | 0.971665i | \(0.424044\pi\) | |||||||
\(812\) | 9.01086 | 0.316219 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 37.2346 | 1.30507 | ||||||||
\(815\) | −8.03742 | −0.281539 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.73510 | −0.0956889 | ||||||||
\(818\) | −5.99972 | −0.209775 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.9109 | −0.520712 | ||||||||
\(821\) | −48.9229 | −1.70742 | −0.853711 | − | 0.520748i | \(-0.825653\pi\) | ||||
−0.853711 | + | 0.520748i | \(0.825653\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.18455 | 0.215580 | 0.107790 | − | 0.994174i | \(-0.465623\pi\) | ||||
0.107790 | + | 0.994174i | \(0.465623\pi\) | |||||||
\(824\) | 23.9260 | 0.833500 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 51.9767 | 1.80850 | ||||||||
\(827\) | 21.6665 | 0.753417 | 0.376709 | − | 0.926332i | \(-0.377056\pi\) | ||||
0.376709 | + | 0.926332i | \(0.377056\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.9818 | −1.80540 | −0.902702 | − | 0.430267i | \(-0.858420\pi\) | ||||
−0.902702 | + | 0.430267i | \(0.858420\pi\) | |||||||
\(830\) | −9.91066 | −0.344004 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.7558 | −0.407557 | ||||||||
\(833\) | −6.38963 | −0.221387 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.71902 | −0.232521 | ||||||||
\(836\) | −2.02006 | −0.0698652 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −63.2394 | −2.18457 | ||||||||
\(839\) | 29.1361 | 1.00589 | 0.502946 | − | 0.864318i | \(-0.332250\pi\) | ||||
0.502946 | + | 0.864318i | \(0.332250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 61.9095 | 2.13354 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 21.2597 | 0.731790 | ||||||||
\(845\) | −16.0088 | −0.550718 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.8115 | 0.886895 | ||||||||
\(848\) | −9.13183 | −0.313588 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.0324 | 0.892904 | ||||||||
\(851\) | −10.9378 | −0.374944 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.26515 | −0.214515 | −0.107257 | − | 0.994231i | \(-0.534207\pi\) | ||||
−0.107257 | + | 0.994231i | \(0.534207\pi\) | |||||||
\(854\) | −57.7092 | −1.97477 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.0159 | −0.581591 | ||||||||
\(857\) | −32.0046 | −1.09326 | −0.546628 | − | 0.837376i | \(-0.684089\pi\) | ||||
−0.546628 | + | 0.837376i | \(0.684089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.27931 | −0.0777690 | −0.0388845 | − | 0.999244i | \(-0.512380\pi\) | ||||
−0.0388845 | + | 0.999244i | \(0.512380\pi\) | |||||||
\(860\) | −24.8832 | −0.848511 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.7615 | −0.400597 | ||||||||
\(863\) | −23.3854 | −0.796048 | −0.398024 | − | 0.917375i | \(-0.630304\pi\) | ||||
−0.398024 | + | 0.917375i | \(0.630304\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.8165 | −0.469776 | ||||||||
\(866\) | −49.1176 | −1.66908 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.3118 | 0.417890 | ||||||||
\(869\) | −24.5018 | −0.831167 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.925659 | 0.0313648 | ||||||||
\(872\) | −7.86033 | −0.266185 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.984190 | 0.0332907 | ||||||||
\(875\) | 32.2517 | 1.09031 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.0607 | −1.25145 | −0.625725 | − | 0.780044i | \(-0.715197\pi\) | ||||
−0.625725 | + | 0.780044i | \(0.715197\pi\) | |||||||
\(878\) | −31.2566 | −1.05486 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.69556 | 0.0571572 | ||||||||
\(881\) | −20.0136 | −0.674274 | −0.337137 | − | 0.941456i | \(-0.609459\pi\) | ||||
−0.337137 | + | 0.941456i | \(0.609459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.4866 | 1.09326 | 0.546631 | − | 0.837374i | \(-0.315910\pi\) | ||||
0.546631 | + | 0.837374i | \(0.315910\pi\) | |||||||
\(884\) | −9.70655 | −0.326467 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 61.7695 | 2.07519 | ||||||||
\(887\) | −19.3042 | −0.648170 | −0.324085 | − | 0.946028i | \(-0.605056\pi\) | ||||
−0.324085 | + | 0.946028i | \(0.605056\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.17343 | −0.240589 | ||||||||
\(890\) | 22.0535 | 0.739235 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 58.6751 | 1.96459 | ||||||||
\(893\) | −1.93362 | −0.0647061 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.3751 | −0.447079 | ||||||||
\(896\) | 47.8156 | 1.59741 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −78.9715 | −2.63531 | ||||||||
\(899\) | 1.36633 | 0.0455697 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.0189 | −1.26659 | ||||||||
\(902\) | 12.7230 | 0.423630 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.70332 | 0.156430 | ||||||||
\(905\) | 28.4343 | 0.945189 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.6991 | −0.355259 | −0.177629 | − | 0.984097i | \(-0.556843\pi\) | ||||
−0.177629 | + | 0.984097i | \(0.556843\pi\) | |||||||
\(908\) | 13.2115 | 0.438438 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.89248 | −0.261633 | ||||||||
\(911\) | −30.1038 | −0.997384 | −0.498692 | − | 0.866779i | \(-0.666186\pi\) | ||||
−0.498692 | + | 0.866779i | \(0.666186\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.09867 | 0.168741 | ||||||||
\(914\) | −41.1847 | −1.36227 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 43.3342 | 1.43180 | ||||||||
\(917\) | 11.8395 | 0.390973 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.97055 | 0.262924 | 0.131462 | − | 0.991321i | \(-0.458033\pi\) | ||||
0.131462 | + | 0.991321i | \(0.458033\pi\) | |||||||
\(920\) | 3.05723 | 0.100794 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 55.5173 | 1.82837 | ||||||||
\(923\) | 10.1514 | 0.334138 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.8126 | 1.17751 | ||||||||
\(926\) | 28.3600 | 0.931969 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.56410 | 0.215477 | ||||||||
\(929\) | −45.5813 | −1.49548 | −0.747738 | − | 0.663994i | \(-0.768860\pi\) | ||||
−0.747738 | + | 0.663994i | \(0.768860\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.790944 | 0.0259221 | ||||||||
\(932\) | −3.34378 | −0.109529 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 46.1042 | 1.50858 | ||||||||
\(935\) | 7.05918 | 0.230860 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.9955 | 1.40460 | 0.702301 | − | 0.711880i | \(-0.252156\pi\) | ||||
0.702301 | + | 0.711880i | \(0.252156\pi\) | |||||||
\(938\) | −6.83221 | −0.223080 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −17.5916 | −0.573775 | ||||||||
\(941\) | 22.3893 | 0.729870 | 0.364935 | − | 0.931033i | \(-0.381091\pi\) | ||||
0.364935 | + | 0.931033i | \(0.381091\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.73744 | −0.121708 | ||||||||
\(944\) | 6.64170 | 0.216169 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.2321 | 0.690314 | ||||||||
\(947\) | 14.3161 | 0.465211 | 0.232605 | − | 0.972571i | \(-0.425275\pi\) | ||||
0.232605 | + | 0.972571i | \(0.425275\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.60074 | −0.0844237 | ||||||||
\(950\) | −3.22243 | −0.104550 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 24.4619 | 0.792815 | ||||||||
\(953\) | −46.4935 | −1.50607 | −0.753036 | − | 0.657979i | \(-0.771411\pi\) | ||||
−0.753036 | + | 0.657979i | \(0.771411\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.6112 | −0.731682 | ||||||||
\(956\) | −10.8601 | −0.351242 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32.1653 | 1.03921 | ||||||||
\(959\) | 19.2549 | 0.621773 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1331 | −0.939779 | ||||||||
\(962\) | −22.1472 | −0.714053 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 72.3340 | 2.32972 | ||||||||
\(965\) | −10.4791 | −0.337333 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.58785 | −0.211851 | −0.105926 | − | 0.994374i | \(-0.533781\pi\) | ||||
−0.105926 | + | 0.994374i | \(0.533781\pi\) | |||||||
\(968\) | −20.2449 | −0.650696 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −46.0548 | −1.47873 | ||||||||
\(971\) | −7.43166 | −0.238493 | −0.119247 | − | 0.992865i | \(-0.538048\pi\) | ||||
−0.119247 | + | 0.992865i | \(0.538048\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 56.2383 | 1.80292 | ||||||||
\(974\) | −14.8598 | −0.476140 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.37420 | −0.236042 | ||||||||
\(977\) | −36.1933 | −1.15793 | −0.578963 | − | 0.815354i | \(-0.696542\pi\) | ||||
−0.578963 | + | 0.815354i | \(0.696542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.3457 | −0.362610 | ||||||||
\(980\) | 7.19581 | 0.229862 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.4247 | 1.16236 | ||||||||
\(983\) | −25.3261 | −0.807779 | −0.403889 | − | 0.914808i | \(-0.632342\pi\) | ||||
−0.403889 | + | 0.914808i | \(0.632342\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.75191 | −0.215134 | ||||||||
\(986\) | 7.95077 | 0.253204 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.20153 | 0.0382258 | ||||||||
\(989\) | −6.23701 | −0.198325 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.1884 | −0.736603 | −0.368302 | − | 0.929706i | \(-0.620061\pi\) | ||||
−0.368302 | + | 0.929706i | \(0.620061\pi\) | |||||||
\(992\) | 8.96874 | 0.284758 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −74.9268 | −2.37654 | ||||||||
\(995\) | 28.8357 | 0.914154 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.28351 | 0.230671 | 0.115336 | − | 0.993327i | \(-0.463206\pi\) | ||||
0.115336 | + | 0.993327i | \(0.463206\pi\) | |||||||
\(998\) | −24.9188 | −0.788791 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.k.1.9 | 10 | ||
3.2 | odd | 2 | 2001.2.a.k.1.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.k.1.2 | ✓ | 10 | 3.2 | odd | 2 | ||
6003.2.a.k.1.9 | 10 | 1.1 | even | 1 | trivial |