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: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.661934\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.661934 | 0.468058 | 0.234029 | − | 0.972230i | \(-0.424809\pi\) | ||||
0.234029 | + | 0.972230i | \(0.424809\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.56184 | −0.780922 | ||||||||
\(5\) | 1.16115 | 0.519284 | 0.259642 | − | 0.965705i | \(-0.416395\pi\) | ||||
0.259642 | + | 0.965705i | \(0.416395\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.80000 | 1.81423 | 0.907115 | − | 0.420884i | \(-0.138280\pi\) | ||||
0.907115 | + | 0.420884i | \(0.138280\pi\) | |||||||
\(8\) | −2.35770 | −0.833574 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.768607 | 0.243055 | ||||||||
\(11\) | 0.481747 | 0.145252 | 0.0726260 | − | 0.997359i | \(-0.476862\pi\) | ||||
0.0726260 | + | 0.997359i | \(0.476862\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.88315 | −1.07699 | −0.538497 | − | 0.842628i | \(-0.681008\pi\) | ||||
−0.538497 | + | 0.842628i | \(0.681008\pi\) | |||||||
\(14\) | 3.17728 | 0.849164 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.56304 | 0.390761 | ||||||||
\(17\) | −7.41544 | −1.79851 | −0.899254 | − | 0.437427i | \(-0.855890\pi\) | ||||
−0.899254 | + | 0.437427i | \(0.855890\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.27098 | 0.979829 | 0.489914 | − | 0.871771i | \(-0.337028\pi\) | ||||
0.489914 | + | 0.871771i | \(0.337028\pi\) | |||||||
\(20\) | −1.81354 | −0.405521 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.318884 | 0.0679864 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.65172 | −0.730344 | ||||||||
\(26\) | −2.57039 | −0.504095 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.49685 | −1.41677 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.692651 | −0.124404 | −0.0622019 | − | 0.998064i | \(-0.519812\pi\) | ||||
−0.0622019 | + | 0.998064i | \(0.519812\pi\) | |||||||
\(32\) | 5.75004 | 1.01647 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.90853 | −0.841805 | ||||||||
\(35\) | 5.57354 | 0.942101 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.71364 | −0.939317 | −0.469658 | − | 0.882848i | \(-0.655623\pi\) | ||||
−0.469658 | + | 0.882848i | \(0.655623\pi\) | |||||||
\(38\) | 2.82710 | 0.458616 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.73766 | −0.432862 | ||||||||
\(41\) | −6.42272 | −1.00306 | −0.501530 | − | 0.865140i | \(-0.667229\pi\) | ||||
−0.501530 | + | 0.865140i | \(0.667229\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.76031 | −1.33593 | −0.667967 | − | 0.744191i | \(-0.732835\pi\) | ||||
−0.667967 | + | 0.744191i | \(0.732835\pi\) | |||||||
\(44\) | −0.752413 | −0.113431 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.661934 | −0.0975968 | ||||||||
\(47\) | −0.616265 | −0.0898915 | −0.0449457 | − | 0.998989i | \(-0.514311\pi\) | ||||
−0.0449457 | + | 0.998989i | \(0.514311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.0400 | 2.29143 | ||||||||
\(50\) | −2.41720 | −0.341843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.06488 | 0.841048 | ||||||||
\(53\) | −6.31136 | −0.866932 | −0.433466 | − | 0.901170i | \(-0.642710\pi\) | ||||
−0.433466 | + | 0.901170i | \(0.642710\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.559383 | 0.0754271 | ||||||||
\(56\) | −11.3170 | −1.51229 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.661934 | 0.0869161 | ||||||||
\(59\) | −1.01528 | −0.132178 | −0.0660889 | − | 0.997814i | \(-0.521052\pi\) | ||||
−0.0660889 | + | 0.997814i | \(0.521052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.33953 | −0.811693 | −0.405847 | − | 0.913941i | \(-0.633023\pi\) | ||||
−0.405847 | + | 0.913941i | \(0.633023\pi\) | |||||||
\(62\) | −0.458489 | −0.0582282 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.680055 | 0.0850069 | ||||||||
\(65\) | −4.50894 | −0.559266 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6618 | −1.42472 | −0.712360 | − | 0.701814i | \(-0.752374\pi\) | ||||
−0.712360 | + | 0.701814i | \(0.752374\pi\) | |||||||
\(68\) | 11.5818 | 1.40449 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.68932 | 0.440958 | ||||||||
\(71\) | −6.45040 | −0.765522 | −0.382761 | − | 0.923847i | \(-0.625027\pi\) | ||||
−0.382761 | + | 0.923847i | \(0.625027\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7390 | 1.72507 | 0.862533 | − | 0.506000i | \(-0.168876\pi\) | ||||
0.862533 | + | 0.506000i | \(0.168876\pi\) | |||||||
\(74\) | −3.78205 | −0.439654 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.67060 | −0.765170 | ||||||||
\(77\) | 2.31238 | 0.263521 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.44072 | −0.274602 | −0.137301 | − | 0.990529i | \(-0.543843\pi\) | ||||
−0.137301 | + | 0.990529i | \(0.543843\pi\) | |||||||
\(80\) | 1.81494 | 0.202916 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.25142 | −0.469490 | ||||||||
\(83\) | −11.5245 | −1.26498 | −0.632488 | − | 0.774570i | \(-0.717966\pi\) | ||||
−0.632488 | + | 0.774570i | \(0.717966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.61047 | −0.933937 | ||||||||
\(86\) | −5.79874 | −0.625294 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.13582 | −0.121078 | ||||||||
\(89\) | −1.71946 | −0.182262 | −0.0911310 | − | 0.995839i | \(-0.529048\pi\) | ||||
−0.0911310 | + | 0.995839i | \(0.529048\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.6391 | −1.95391 | ||||||||
\(92\) | 1.56184 | 0.162833 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.407926 | −0.0420744 | ||||||||
\(95\) | 4.95926 | 0.508810 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.96175 | 0.402255 | 0.201127 | − | 0.979565i | \(-0.435540\pi\) | ||||
0.201127 | + | 0.979565i | \(0.435540\pi\) | |||||||
\(98\) | 10.6174 | 1.07252 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.70342 | 0.570342 | ||||||||
\(101\) | 18.2587 | 1.81681 | 0.908407 | − | 0.418088i | \(-0.137300\pi\) | ||||
0.908407 | + | 0.418088i | \(0.137300\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.17157 | 0.903702 | 0.451851 | − | 0.892094i | \(-0.350764\pi\) | ||||
0.451851 | + | 0.892094i | \(0.350764\pi\) | |||||||
\(104\) | 9.15533 | 0.897754 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.17770 | −0.405774 | ||||||||
\(107\) | −9.32854 | −0.901824 | −0.450912 | − | 0.892569i | \(-0.648901\pi\) | ||||
−0.450912 | + | 0.892569i | \(0.648901\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.1548 | 1.64313 | 0.821566 | − | 0.570114i | \(-0.193101\pi\) | ||||
0.821566 | + | 0.570114i | \(0.193101\pi\) | |||||||
\(110\) | 0.370274 | 0.0353042 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.50261 | 0.708930 | ||||||||
\(113\) | −8.38650 | −0.788936 | −0.394468 | − | 0.918910i | \(-0.629071\pi\) | ||||
−0.394468 | + | 0.918910i | \(0.629071\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.16115 | −0.108278 | ||||||||
\(116\) | −1.56184 | −0.145014 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.672045 | −0.0618668 | ||||||||
\(119\) | −35.5941 | −3.26290 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7679 | −0.978902 | ||||||||
\(122\) | −4.19634 | −0.379919 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.08181 | 0.0971497 | ||||||||
\(125\) | −10.0460 | −0.898540 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.39321 | 0.833513 | 0.416757 | − | 0.909018i | \(-0.363167\pi\) | ||||
0.416757 | + | 0.909018i | \(0.363167\pi\) | |||||||
\(128\) | −11.0499 | −0.976685 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.98462 | −0.261769 | ||||||||
\(131\) | 17.8413 | 1.55881 | 0.779403 | − | 0.626523i | \(-0.215523\pi\) | ||||
0.779403 | + | 0.626523i | \(0.215523\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.5007 | 1.77763 | ||||||||
\(134\) | −7.71936 | −0.666851 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.4834 | 1.49919 | ||||||||
\(137\) | −6.50179 | −0.555485 | −0.277743 | − | 0.960656i | \(-0.589586\pi\) | ||||
−0.277743 | + | 0.960656i | \(0.589586\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.92280 | 0.756822 | 0.378411 | − | 0.925638i | \(-0.376471\pi\) | ||||
0.378411 | + | 0.925638i | \(0.376471\pi\) | |||||||
\(140\) | −8.70500 | −0.735707 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.26974 | −0.358308 | ||||||||
\(143\) | −1.87070 | −0.156436 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.16115 | 0.0964287 | ||||||||
\(146\) | 9.75622 | 0.807431 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.92382 | 0.733533 | ||||||||
\(149\) | −12.3725 | −1.01359 | −0.506797 | − | 0.862065i | \(-0.669171\pi\) | ||||
−0.506797 | + | 0.862065i | \(0.669171\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.18528 | −0.177836 | −0.0889180 | − | 0.996039i | \(-0.528341\pi\) | ||||
−0.0889180 | + | 0.996039i | \(0.528341\pi\) | |||||||
\(152\) | −10.0697 | −0.816760 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.53064 | 0.123343 | ||||||||
\(155\) | −0.804275 | −0.0646009 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.9914 | 1.19645 | 0.598224 | − | 0.801329i | \(-0.295873\pi\) | ||||
0.598224 | + | 0.801329i | \(0.295873\pi\) | |||||||
\(158\) | −1.61559 | −0.128530 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.67669 | 0.527838 | ||||||||
\(161\) | −4.80000 | −0.378293 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.88481 | −0.695912 | −0.347956 | − | 0.937511i | \(-0.613124\pi\) | ||||
−0.347956 | + | 0.937511i | \(0.613124\pi\) | |||||||
\(164\) | 10.0313 | 0.783312 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.62844 | −0.592081 | ||||||||
\(167\) | −2.40802 | −0.186338 | −0.0931692 | − | 0.995650i | \(-0.529700\pi\) | ||||
−0.0931692 | + | 0.995650i | \(0.529700\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.07889 | 0.159915 | ||||||||
\(170\) | −5.69956 | −0.437136 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.6822 | 1.04326 | ||||||||
\(173\) | −18.9340 | −1.43952 | −0.719762 | − | 0.694221i | \(-0.755749\pi\) | ||||
−0.719762 | + | 0.694221i | \(0.755749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.5283 | −1.32501 | ||||||||
\(176\) | 0.752991 | 0.0567589 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.13817 | −0.0853091 | ||||||||
\(179\) | 3.18736 | 0.238235 | 0.119117 | − | 0.992880i | \(-0.461994\pi\) | ||||
0.119117 | + | 0.992880i | \(0.461994\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.2936 | 0.988109 | 0.494054 | − | 0.869431i | \(-0.335514\pi\) | ||||
0.494054 | + | 0.869431i | \(0.335514\pi\) | |||||||
\(182\) | −12.3379 | −0.914544 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.35770 | 0.173812 | ||||||||
\(185\) | −6.63442 | −0.487772 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.57236 | −0.261237 | ||||||||
\(188\) | 0.962510 | 0.0701982 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.28270 | 0.238152 | ||||||||
\(191\) | −21.5092 | −1.55635 | −0.778177 | − | 0.628045i | \(-0.783855\pi\) | ||||
−0.778177 | + | 0.628045i | \(0.783855\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.35343 | −0.169403 | −0.0847017 | − | 0.996406i | \(-0.526994\pi\) | ||||
−0.0847017 | + | 0.996406i | \(0.526994\pi\) | |||||||
\(194\) | 2.62241 | 0.188278 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −25.0520 | −1.78943 | ||||||||
\(197\) | −0.766029 | −0.0545773 | −0.0272886 | − | 0.999628i | \(-0.508687\pi\) | ||||
−0.0272886 | + | 0.999628i | \(0.508687\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.77290 | 0.692783 | 0.346391 | − | 0.938090i | \(-0.387407\pi\) | ||||
0.346391 | + | 0.938090i | \(0.387407\pi\) | |||||||
\(200\) | 8.60967 | 0.608796 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0861 | 0.850373 | ||||||||
\(203\) | 4.80000 | 0.336894 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.45778 | −0.520874 | ||||||||
\(206\) | 6.07097 | 0.422984 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.06954 | −0.420847 | ||||||||
\(209\) | 2.05753 | 0.142322 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.5678 | −1.48479 | −0.742395 | − | 0.669963i | \(-0.766310\pi\) | ||||
−0.742395 | + | 0.669963i | \(0.766310\pi\) | |||||||
\(212\) | 9.85736 | 0.677007 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.17487 | −0.422105 | ||||||||
\(215\) | −10.1721 | −0.693730 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.32472 | −0.225697 | ||||||||
\(218\) | 11.3553 | 0.769080 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.873668 | −0.0589027 | ||||||||
\(221\) | 28.7953 | 1.93698 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.944373 | −0.0632399 | −0.0316199 | − | 0.999500i | \(-0.510067\pi\) | ||||
−0.0316199 | + | 0.999500i | \(0.510067\pi\) | |||||||
\(224\) | 27.6002 | 1.84412 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.55131 | −0.369268 | ||||||||
\(227\) | −20.2556 | −1.34441 | −0.672204 | − | 0.740366i | \(-0.734652\pi\) | ||||
−0.672204 | + | 0.740366i | \(0.734652\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.15599 | 0.274635 | 0.137318 | − | 0.990527i | \(-0.456152\pi\) | ||||
0.137318 | + | 0.990527i | \(0.456152\pi\) | |||||||
\(230\) | −0.768607 | −0.0506805 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.35770 | −0.154791 | ||||||||
\(233\) | 13.3848 | 0.876866 | 0.438433 | − | 0.898764i | \(-0.355534\pi\) | ||||
0.438433 | + | 0.898764i | \(0.355534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.715579 | −0.0466792 | ||||||||
\(236\) | 1.58570 | 0.103220 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −23.5609 | −1.52723 | ||||||||
\(239\) | 22.7219 | 1.46976 | 0.734878 | − | 0.678199i | \(-0.237239\pi\) | ||||
0.734878 | + | 0.678199i | \(0.237239\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.27597 | 0.275440 | 0.137720 | − | 0.990471i | \(-0.456023\pi\) | ||||
0.137720 | + | 0.990471i | \(0.456023\pi\) | |||||||
\(242\) | −7.12765 | −0.458183 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.90135 | 0.633869 | ||||||||
\(245\) | 18.6249 | 1.18990 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.5849 | −1.05527 | ||||||||
\(248\) | 1.63307 | 0.103700 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.64978 | −0.420569 | ||||||||
\(251\) | −18.8353 | −1.18887 | −0.594437 | − | 0.804142i | \(-0.702625\pi\) | ||||
−0.594437 | + | 0.804142i | \(0.702625\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.481747 | −0.0302872 | ||||||||
\(254\) | 6.21768 | 0.390132 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.67443 | −0.542152 | ||||||||
\(257\) | 9.25845 | 0.577526 | 0.288763 | − | 0.957401i | \(-0.406756\pi\) | ||||
0.288763 | + | 0.957401i | \(0.406756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.4255 | −1.70414 | ||||||||
\(260\) | 7.04227 | 0.436743 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.8098 | 0.729611 | ||||||||
\(263\) | −19.7994 | −1.22089 | −0.610443 | − | 0.792060i | \(-0.709008\pi\) | ||||
−0.610443 | + | 0.792060i | \(0.709008\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.32847 | −0.450184 | ||||||||
\(266\) | 13.5701 | 0.832035 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18.2140 | 1.11259 | ||||||||
\(269\) | 6.41447 | 0.391097 | 0.195548 | − | 0.980694i | \(-0.437351\pi\) | ||||
0.195548 | + | 0.980694i | \(0.437351\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0813137 | 0.00493946 | 0.00246973 | − | 0.999997i | \(-0.499214\pi\) | ||||
0.00246973 | + | 0.999997i | \(0.499214\pi\) | |||||||
\(272\) | −11.5907 | −0.702787 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.30375 | −0.259999 | ||||||||
\(275\) | −1.75920 | −0.106084 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.2170 | −1.93573 | −0.967866 | − | 0.251465i | \(-0.919088\pi\) | ||||
−0.967866 | + | 0.251465i | \(0.919088\pi\) | |||||||
\(278\) | 5.90630 | 0.354236 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13.1408 | −0.785311 | ||||||||
\(281\) | 20.6489 | 1.23181 | 0.615906 | − | 0.787820i | \(-0.288790\pi\) | ||||
0.615906 | + | 0.787820i | \(0.288790\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.0893 | −1.25363 | −0.626813 | − | 0.779170i | \(-0.715641\pi\) | ||||
−0.626813 | + | 0.779170i | \(0.715641\pi\) | |||||||
\(284\) | 10.0745 | 0.597813 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.23828 | −0.0732208 | ||||||||
\(287\) | −30.8291 | −1.81978 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.9887 | 2.23463 | ||||||||
\(290\) | 0.768607 | 0.0451342 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −23.0200 | −1.34714 | ||||||||
\(293\) | −19.7744 | −1.15523 | −0.577615 | − | 0.816309i | \(-0.696017\pi\) | ||||
−0.577615 | + | 0.816309i | \(0.696017\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.17889 | −0.0686378 | ||||||||
\(296\) | 13.4711 | 0.782990 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.18977 | −0.474420 | ||||||||
\(299\) | 3.88315 | 0.224569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.0495 | −2.42369 | ||||||||
\(302\) | −1.44651 | −0.0832375 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.67572 | 0.382879 | ||||||||
\(305\) | −7.36117 | −0.421499 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.8499 | 0.904601 | 0.452300 | − | 0.891866i | \(-0.350603\pi\) | ||||
0.452300 | + | 0.891866i | \(0.350603\pi\) | |||||||
\(308\) | −3.61158 | −0.205789 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.532377 | −0.0302370 | ||||||||
\(311\) | −6.50938 | −0.369113 | −0.184557 | − | 0.982822i | \(-0.559085\pi\) | ||||
−0.184557 | + | 0.982822i | \(0.559085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.9378 | −1.69218 | −0.846092 | − | 0.533038i | \(-0.821050\pi\) | ||||
−0.846092 | + | 0.533038i | \(0.821050\pi\) | |||||||
\(314\) | 9.92334 | 0.560007 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.81202 | 0.214443 | ||||||||
\(317\) | −17.5373 | −0.984993 | −0.492497 | − | 0.870314i | \(-0.663916\pi\) | ||||
−0.492497 | + | 0.870314i | \(0.663916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.481747 | 0.0269726 | ||||||||
\(320\) | 0.789649 | 0.0441427 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.17728 | −0.177063 | ||||||||
\(323\) | −31.6711 | −1.76223 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.1802 | 0.786575 | ||||||||
\(326\) | −5.88116 | −0.325727 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.1429 | 0.836126 | ||||||||
\(329\) | −2.95807 | −0.163084 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.82327 | 0.265111 | 0.132556 | − | 0.991176i | \(-0.457682\pi\) | ||||
0.132556 | + | 0.991176i | \(0.457682\pi\) | |||||||
\(332\) | 17.9994 | 0.987847 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.59395 | −0.0872171 | ||||||||
\(335\) | −13.5412 | −0.739835 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.34820 | 0.291335 | 0.145667 | − | 0.989334i | \(-0.453467\pi\) | ||||
0.145667 | + | 0.989334i | \(0.453467\pi\) | |||||||
\(338\) | 1.37609 | 0.0748492 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13.4482 | 0.729332 | ||||||||
\(341\) | −0.333682 | −0.0180699 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 43.3920 | 2.34295 | ||||||||
\(344\) | 20.6542 | 1.11360 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.5330 | −0.673780 | ||||||||
\(347\) | −12.8945 | −0.692211 | −0.346106 | − | 0.938196i | \(-0.612496\pi\) | ||||
−0.346106 | + | 0.938196i | \(0.612496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.2259 | 0.761496 | 0.380748 | − | 0.924679i | \(-0.375667\pi\) | ||||
0.380748 | + | 0.924679i | \(0.375667\pi\) | |||||||
\(350\) | −11.6025 | −0.620182 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.77006 | 0.147645 | ||||||||
\(353\) | 27.1279 | 1.44387 | 0.721936 | − | 0.691960i | \(-0.243252\pi\) | ||||
0.721936 | + | 0.691960i | \(0.243252\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.48991 | −0.397523 | ||||||||
\(356\) | 2.68552 | 0.142332 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.10982 | 0.111508 | ||||||||
\(359\) | −33.1581 | −1.75002 | −0.875010 | − | 0.484105i | \(-0.839145\pi\) | ||||
−0.875010 | + | 0.484105i | \(0.839145\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.758770 | −0.0399352 | ||||||||
\(362\) | 8.79951 | 0.462492 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 29.1114 | 1.52585 | ||||||||
\(365\) | 17.1142 | 0.895800 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.4982 | −1.43539 | −0.717697 | − | 0.696355i | \(-0.754804\pi\) | ||||
−0.717697 | + | 0.696355i | \(0.754804\pi\) | |||||||
\(368\) | −1.56304 | −0.0814793 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.39155 | −0.228306 | ||||||||
\(371\) | −30.2945 | −1.57281 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.8037 | 0.870062 | 0.435031 | − | 0.900416i | \(-0.356737\pi\) | ||||
0.435031 | + | 0.900416i | \(0.356737\pi\) | |||||||
\(374\) | −2.36467 | −0.122274 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.45297 | 0.0749312 | ||||||||
\(377\) | −3.88315 | −0.199993 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.0834 | 1.39118 | 0.695591 | − | 0.718438i | \(-0.255143\pi\) | ||||
0.695591 | + | 0.718438i | \(0.255143\pi\) | |||||||
\(380\) | −7.74560 | −0.397341 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.2377 | −0.728463 | ||||||||
\(383\) | 17.5873 | 0.898667 | 0.449334 | − | 0.893364i | \(-0.351661\pi\) | ||||
0.449334 | + | 0.893364i | \(0.351661\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.68504 | 0.136842 | ||||||||
\(386\) | −1.55781 | −0.0792906 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.18763 | −0.314129 | ||||||||
\(389\) | −6.36584 | −0.322761 | −0.161380 | − | 0.986892i | \(-0.551595\pi\) | ||||
−0.161380 | + | 0.986892i | \(0.551595\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.41544 | 0.375015 | ||||||||
\(392\) | −37.8176 | −1.91008 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.507060 | −0.0255453 | ||||||||
\(395\) | −2.83405 | −0.142597 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.1969 | −0.712520 | −0.356260 | − | 0.934387i | \(-0.615948\pi\) | ||||
−0.356260 | + | 0.934387i | \(0.615948\pi\) | |||||||
\(398\) | 6.46901 | 0.324262 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.70780 | −0.285390 | ||||||||
\(401\) | −4.07996 | −0.203743 | −0.101872 | − | 0.994798i | \(-0.532483\pi\) | ||||
−0.101872 | + | 0.994798i | \(0.532483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.68967 | 0.133982 | ||||||||
\(404\) | −28.5173 | −1.41879 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.17728 | 0.157686 | ||||||||
\(407\) | −2.75253 | −0.136438 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.77817 | −0.0879247 | −0.0439624 | − | 0.999033i | \(-0.513998\pi\) | ||||
−0.0439624 | + | 0.999033i | \(0.513998\pi\) | |||||||
\(410\) | −4.93655 | −0.243799 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.3246 | −0.705720 | ||||||||
\(413\) | −4.87333 | −0.239801 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.3817 | −0.656882 | ||||||||
\(416\) | −22.3283 | −1.09473 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.36195 | 0.0666150 | ||||||||
\(419\) | 12.4164 | 0.606578 | 0.303289 | − | 0.952899i | \(-0.401915\pi\) | ||||
0.303289 | + | 0.952899i | \(0.401915\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.1062 | 1.90592 | 0.952960 | − | 0.303096i | \(-0.0980202\pi\) | ||||
0.952960 | + | 0.303096i | \(0.0980202\pi\) | |||||||
\(422\) | −14.2765 | −0.694967 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.8803 | 0.722653 | ||||||||
\(425\) | 27.0791 | 1.31353 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.4297 | −1.47260 | ||||||||
\(428\) | 14.5697 | 0.704254 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.73324 | −0.324706 | ||||||||
\(431\) | 25.8815 | 1.24667 | 0.623333 | − | 0.781957i | \(-0.285778\pi\) | ||||
0.623333 | + | 0.781957i | \(0.285778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.2711 | −1.21445 | −0.607226 | − | 0.794529i | \(-0.707718\pi\) | ||||
−0.607226 | + | 0.794529i | \(0.707718\pi\) | |||||||
\(434\) | −2.20075 | −0.105639 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −26.7931 | −1.28316 | ||||||||
\(437\) | −4.27098 | −0.204308 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.3513 | −1.92586 | −0.962931 | − | 0.269749i | \(-0.913059\pi\) | ||||
−0.962931 | + | 0.269749i | \(0.913059\pi\) | |||||||
\(440\) | −1.31886 | −0.0628741 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.0606 | 0.906619 | ||||||||
\(443\) | −12.7973 | −0.608018 | −0.304009 | − | 0.952669i | \(-0.598325\pi\) | ||||
−0.304009 | + | 0.952669i | \(0.598325\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.99656 | −0.0946458 | ||||||||
\(446\) | −0.625112 | −0.0295999 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.26426 | 0.154222 | ||||||||
\(449\) | −6.34149 | −0.299274 | −0.149637 | − | 0.988741i | \(-0.547810\pi\) | ||||
−0.149637 | + | 0.988741i | \(0.547810\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.09413 | −0.145697 | ||||||||
\(452\) | 13.0984 | 0.616097 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.4078 | −0.629261 | ||||||||
\(455\) | −21.6429 | −1.01464 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.4505 | −1.56475 | −0.782375 | − | 0.622808i | \(-0.785992\pi\) | ||||
−0.782375 | + | 0.622808i | \(0.785992\pi\) | |||||||
\(458\) | 2.75099 | 0.128545 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.81354 | 0.0845569 | ||||||||
\(461\) | −5.42683 | −0.252753 | −0.126376 | − | 0.991982i | \(-0.540335\pi\) | ||||
−0.126376 | + | 0.991982i | \(0.540335\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6646 | 0.495624 | 0.247812 | − | 0.968808i | \(-0.420289\pi\) | ||||
0.247812 | + | 0.968808i | \(0.420289\pi\) | |||||||
\(464\) | 1.56304 | 0.0725625 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.85984 | 0.410424 | ||||||||
\(467\) | −10.6209 | −0.491479 | −0.245739 | − | 0.969336i | \(-0.579031\pi\) | ||||
−0.245739 | + | 0.969336i | \(0.579031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −55.9768 | −2.58477 | ||||||||
\(470\) | −0.473666 | −0.0218486 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.39372 | 0.110180 | ||||||||
\(473\) | −4.22025 | −0.194047 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.5964 | −0.715612 | ||||||||
\(476\) | 55.5924 | 2.54807 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.0404 | 0.687931 | ||||||||
\(479\) | −17.4622 | −0.797867 | −0.398934 | − | 0.916980i | \(-0.630620\pi\) | ||||
−0.398934 | + | 0.916980i | \(0.630620\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.1870 | 1.01164 | ||||||||
\(482\) | 2.83041 | 0.128922 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.8178 | 0.764446 | ||||||||
\(485\) | 4.60020 | 0.208884 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.98493 | 0.180575 | 0.0902873 | − | 0.995916i | \(-0.471221\pi\) | ||||
0.0902873 | + | 0.995916i | \(0.471221\pi\) | |||||||
\(488\) | 14.9467 | 0.676606 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.3285 | 0.556943 | ||||||||
\(491\) | −14.1616 | −0.639103 | −0.319552 | − | 0.947569i | \(-0.603532\pi\) | ||||
−0.319552 | + | 0.947569i | \(0.603532\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.41544 | −0.333974 | ||||||||
\(494\) | −10.9781 | −0.493927 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.08264 | −0.0486122 | ||||||||
\(497\) | −30.9619 | −1.38883 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.75546 | −0.168117 | −0.0840587 | − | 0.996461i | \(-0.526788\pi\) | ||||
−0.0840587 | + | 0.996461i | \(0.526788\pi\) | |||||||
\(500\) | 15.6903 | 0.701690 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.4677 | −0.556462 | ||||||||
\(503\) | 21.1293 | 0.942110 | 0.471055 | − | 0.882104i | \(-0.343873\pi\) | ||||
0.471055 | + | 0.882104i | \(0.343873\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.2012 | 0.943442 | ||||||||
\(506\) | −0.318884 | −0.0141761 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.6707 | −0.650909 | ||||||||
\(509\) | 3.59910 | 0.159527 | 0.0797637 | − | 0.996814i | \(-0.474583\pi\) | ||||
0.0797637 | + | 0.996814i | \(0.474583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 70.7471 | 3.12967 | ||||||||
\(512\) | 16.3580 | 0.722927 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.12848 | 0.270316 | ||||||||
\(515\) | 10.6496 | 0.469278 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.296884 | −0.0130569 | ||||||||
\(518\) | −18.1538 | −0.797634 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.6308 | 0.466189 | ||||||||
\(521\) | 3.83170 | 0.167870 | 0.0839349 | − | 0.996471i | \(-0.473251\pi\) | ||||
0.0839349 | + | 0.996471i | \(0.473251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.0646 | 1.83936 | 0.919678 | − | 0.392674i | \(-0.128450\pi\) | ||||
0.919678 | + | 0.392674i | \(0.128450\pi\) | |||||||
\(524\) | −27.8654 | −1.21731 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.1059 | −0.571445 | ||||||||
\(527\) | 5.13631 | 0.223741 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.85096 | −0.210712 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −32.0189 | −1.38819 | ||||||||
\(533\) | 24.9404 | 1.08029 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.8319 | −0.468303 | ||||||||
\(536\) | 27.4952 | 1.18761 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.24595 | 0.183056 | ||||||||
\(539\) | 7.72721 | 0.332835 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.9360 | 1.41603 | 0.708015 | − | 0.706197i | \(-0.249591\pi\) | ||||
0.708015 | + | 0.706197i | \(0.249591\pi\) | |||||||
\(542\) | 0.0538243 | 0.00231195 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −42.6391 | −1.82813 | ||||||||
\(545\) | 19.9194 | 0.853252 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.89683 | −0.0811024 | −0.0405512 | − | 0.999177i | \(-0.512911\pi\) | ||||
−0.0405512 | + | 0.999177i | \(0.512911\pi\) | |||||||
\(548\) | 10.1548 | 0.433791 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.16448 | −0.0496534 | ||||||||
\(551\) | 4.27098 | 0.181950 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.7154 | −0.498191 | ||||||||
\(554\) | −21.3255 | −0.906035 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.9360 | −0.591019 | ||||||||
\(557\) | −6.32207 | −0.267875 | −0.133937 | − | 0.990990i | \(-0.542762\pi\) | ||||
−0.133937 | + | 0.990990i | \(0.542762\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.0176 | 1.43879 | ||||||||
\(560\) | 8.71170 | 0.368136 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.6682 | 0.576559 | ||||||||
\(563\) | −35.8000 | −1.50879 | −0.754395 | − | 0.656420i | \(-0.772070\pi\) | ||||
−0.754395 | + | 0.656420i | \(0.772070\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.73803 | −0.409682 | ||||||||
\(566\) | −13.9597 | −0.586769 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.2081 | 0.638119 | ||||||||
\(569\) | −6.27427 | −0.263031 | −0.131515 | − | 0.991314i | \(-0.541984\pi\) | ||||
−0.131515 | + | 0.991314i | \(0.541984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.0402 | 0.713109 | 0.356555 | − | 0.934274i | \(-0.383951\pi\) | ||||
0.356555 | + | 0.934274i | \(0.383951\pi\) | |||||||
\(572\) | 2.92174 | 0.122164 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −20.4068 | −0.851763 | ||||||||
\(575\) | 3.65172 | 0.152287 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.1392 | −1.54613 | −0.773063 | − | 0.634329i | \(-0.781277\pi\) | ||||
−0.773063 | + | 0.634329i | \(0.781277\pi\) | |||||||
\(578\) | 25.1460 | 1.04594 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.81354 | −0.0753033 | ||||||||
\(581\) | −55.3175 | −2.29496 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.04048 | −0.125924 | ||||||||
\(584\) | −34.7501 | −1.43797 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.0893 | −0.540714 | ||||||||
\(587\) | −5.01609 | −0.207036 | −0.103518 | − | 0.994628i | \(-0.533010\pi\) | ||||
−0.103518 | + | 0.994628i | \(0.533010\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.95830 | −0.121894 | ||||||||
\(590\) | −0.780349 | −0.0321265 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.93068 | −0.367049 | ||||||||
\(593\) | −0.761753 | −0.0312815 | −0.0156407 | − | 0.999878i | \(-0.504979\pi\) | ||||
−0.0156407 | + | 0.999878i | \(0.504979\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −41.3303 | −1.69438 | ||||||||
\(596\) | 19.3239 | 0.791538 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.57039 | 0.105111 | ||||||||
\(599\) | −14.8728 | −0.607688 | −0.303844 | − | 0.952722i | \(-0.598270\pi\) | ||||
−0.303844 | + | 0.952722i | \(0.598270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.810605 | 0.0330653 | 0.0165326 | − | 0.999863i | \(-0.494737\pi\) | ||||
0.0165326 | + | 0.999863i | \(0.494737\pi\) | |||||||
\(602\) | −27.8340 | −1.13443 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.41307 | 0.138876 | ||||||||
\(605\) | −12.5032 | −0.508328 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.0304 | 0.528888 | 0.264444 | − | 0.964401i | \(-0.414812\pi\) | ||||
0.264444 | + | 0.964401i | \(0.414812\pi\) | |||||||
\(608\) | 24.5583 | 0.995970 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.87261 | −0.197286 | ||||||||
\(611\) | 2.39305 | 0.0968125 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.4250 | −1.83470 | −0.917350 | − | 0.398082i | \(-0.869676\pi\) | ||||
−0.917350 | + | 0.398082i | \(0.869676\pi\) | |||||||
\(614\) | 10.4916 | 0.423405 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.45192 | −0.219664 | ||||||||
\(617\) | 18.6626 | 0.751326 | 0.375663 | − | 0.926756i | \(-0.377415\pi\) | ||||
0.375663 | + | 0.926756i | \(0.377415\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.2424 | 1.01458 | 0.507289 | − | 0.861776i | \(-0.330648\pi\) | ||||
0.507289 | + | 0.861776i | \(0.330648\pi\) | |||||||
\(620\) | 1.25615 | 0.0504483 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.30878 | −0.172766 | ||||||||
\(623\) | −8.25339 | −0.330665 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.59365 | 0.263746 | ||||||||
\(626\) | −19.8168 | −0.792039 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.4143 | −0.934332 | ||||||||
\(629\) | 42.3691 | 1.68937 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.64426 | 0.304313 | 0.152157 | − | 0.988356i | \(-0.451378\pi\) | ||||
0.152157 | + | 0.988356i | \(0.451378\pi\) | |||||||
\(632\) | 5.75449 | 0.228901 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.6085 | −0.461034 | ||||||||
\(635\) | 10.9070 | 0.432830 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −62.2858 | −2.46785 | ||||||||
\(638\) | 0.318884 | 0.0126247 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12.8307 | −0.507177 | ||||||||
\(641\) | −27.0958 | −1.07022 | −0.535110 | − | 0.844783i | \(-0.679730\pi\) | ||||
−0.535110 | + | 0.844783i | \(0.679730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.6696 | 0.617949 | 0.308974 | − | 0.951070i | \(-0.400014\pi\) | ||||
0.308974 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(644\) | 7.49685 | 0.295417 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.9642 | −0.824825 | ||||||||
\(647\) | 28.0698 | 1.10354 | 0.551769 | − | 0.833997i | \(-0.313953\pi\) | ||||
0.551769 | + | 0.833997i | \(0.313953\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.489106 | −0.0191991 | ||||||||
\(650\) | 9.38634 | 0.368163 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.8767 | 0.543453 | ||||||||
\(653\) | 4.85411 | 0.189956 | 0.0949780 | − | 0.995479i | \(-0.469722\pi\) | ||||
0.0949780 | + | 0.995479i | \(0.469722\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.7166 | 0.809463 | ||||||||
\(656\) | −10.0390 | −0.391957 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.95805 | −0.0763326 | ||||||||
\(659\) | 2.91789 | 0.113665 | 0.0568324 | − | 0.998384i | \(-0.481900\pi\) | ||||
0.0568324 | + | 0.998384i | \(0.481900\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.93405 | 0.230808 | 0.115404 | − | 0.993319i | \(-0.463184\pi\) | ||||
0.115404 | + | 0.993319i | \(0.463184\pi\) | |||||||
\(662\) | 3.19269 | 0.124087 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27.1713 | 1.05445 | ||||||||
\(665\) | 23.8045 | 0.923098 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 3.76096 | 0.145516 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.96337 | −0.346285 | ||||||||
\(671\) | −3.05405 | −0.117900 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.3141 | 1.01434 | 0.507168 | − | 0.861847i | \(-0.330693\pi\) | ||||
0.507168 | + | 0.861847i | \(0.330693\pi\) | |||||||
\(674\) | 3.54015 | 0.136362 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.24690 | −0.124881 | ||||||||
\(677\) | −5.30262 | −0.203796 | −0.101898 | − | 0.994795i | \(-0.532492\pi\) | ||||
−0.101898 | + | 0.994795i | \(0.532492\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.0164 | 0.729782 | ||||||||
\(680\) | 20.3009 | 0.778506 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.220875 | −0.00845776 | ||||||||
\(683\) | 45.1373 | 1.72713 | 0.863566 | − | 0.504236i | \(-0.168226\pi\) | ||||
0.863566 | + | 0.504236i | \(0.168226\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.54958 | −0.288455 | ||||||||
\(686\) | 28.7226 | 1.09663 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.6928 | −0.522031 | ||||||||
\(689\) | 24.5080 | 0.933680 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.14576 | −0.157712 | −0.0788561 | − | 0.996886i | \(-0.525127\pi\) | ||||
−0.0788561 | + | 0.996886i | \(0.525127\pi\) | |||||||
\(692\) | 29.5719 | 1.12416 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.53528 | −0.323995 | ||||||||
\(695\) | 10.3608 | 0.393006 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 47.6273 | 1.80401 | ||||||||
\(698\) | 9.41661 | 0.356424 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 27.3764 | 1.03473 | ||||||||
\(701\) | −2.99761 | −0.113218 | −0.0566091 | − | 0.998396i | \(-0.518029\pi\) | ||||
−0.0566091 | + | 0.998396i | \(0.518029\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.4028 | −0.920370 | ||||||||
\(704\) | 0.327614 | 0.0123474 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.9569 | 0.675816 | ||||||||
\(707\) | 87.6420 | 3.29612 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 50.3931 | 1.89255 | 0.946277 | − | 0.323357i | \(-0.104811\pi\) | ||||
0.946277 | + | 0.323357i | \(0.104811\pi\) | |||||||
\(710\) | −4.95783 | −0.186064 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.05397 | 0.151929 | ||||||||
\(713\) | 0.692651 | 0.0259400 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.17217 | −0.0812345 | ||||||||
\(716\) | −4.97816 | −0.186043 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.9485 | −0.819110 | ||||||||
\(719\) | −1.37707 | −0.0513561 | −0.0256781 | − | 0.999670i | \(-0.508174\pi\) | ||||
−0.0256781 | + | 0.999670i | \(0.508174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.0235 | 1.63952 | ||||||||
\(722\) | −0.502255 | −0.0186920 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.7626 | −0.771636 | ||||||||
\(725\) | −3.65172 | −0.135621 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.89494 | 0.107367 | 0.0536836 | − | 0.998558i | \(-0.482904\pi\) | ||||
0.0536836 | + | 0.998558i | \(0.482904\pi\) | |||||||
\(728\) | 43.9456 | 1.62873 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.3285 | 0.419286 | ||||||||
\(731\) | 64.9615 | 2.40269 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.9159 | 0.957227 | 0.478613 | − | 0.878026i | \(-0.341140\pi\) | ||||
0.478613 | + | 0.878026i | \(0.341140\pi\) | |||||||
\(734\) | −18.2020 | −0.671848 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.75004 | −0.211949 | ||||||||
\(737\) | −5.61805 | −0.206944 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.34877 | 0.0864010 | 0.0432005 | − | 0.999066i | \(-0.486245\pi\) | ||||
0.0432005 | + | 0.999066i | \(0.486245\pi\) | |||||||
\(740\) | 10.3619 | 0.380912 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.0530 | −0.736168 | ||||||||
\(743\) | −19.1323 | −0.701895 | −0.350947 | − | 0.936395i | \(-0.614140\pi\) | ||||
−0.350947 | + | 0.936395i | \(0.614140\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.3664 | −0.526343 | ||||||||
\(746\) | 11.1229 | 0.407239 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.57947 | 0.204006 | ||||||||
\(749\) | −44.7770 | −1.63611 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.4428 | 1.87717 | 0.938587 | − | 0.345043i | \(-0.112136\pi\) | ||||
0.938587 | + | 0.345043i | \(0.112136\pi\) | |||||||
\(752\) | −0.963250 | −0.0351261 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.57039 | −0.0936081 | ||||||||
\(755\) | −2.53745 | −0.0923474 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.1639 | −1.53247 | −0.766236 | − | 0.642560i | \(-0.777872\pi\) | ||||
−0.766236 | + | 0.642560i | \(0.777872\pi\) | |||||||
\(758\) | 17.9274 | 0.651153 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.6925 | −0.424131 | ||||||||
\(761\) | 11.1416 | 0.403884 | 0.201942 | − | 0.979397i | \(-0.435275\pi\) | ||||
0.201942 | + | 0.979397i | \(0.435275\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 82.3430 | 2.98102 | ||||||||
\(764\) | 33.5941 | 1.21539 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.6416 | 0.420628 | ||||||||
\(767\) | 3.94247 | 0.142355 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.0823 | −0.940551 | −0.470275 | − | 0.882520i | \(-0.655845\pi\) | ||||
−0.470275 | + | 0.882520i | \(0.655845\pi\) | |||||||
\(770\) | 1.77732 | 0.0640500 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.67569 | 0.132291 | ||||||||
\(773\) | 29.4575 | 1.05951 | 0.529756 | − | 0.848150i | \(-0.322284\pi\) | ||||
0.529756 | + | 0.848150i | \(0.322284\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.52937 | 0.0908575 | ||||||||
\(776\) | −9.34063 | −0.335309 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.21376 | −0.151071 | ||||||||
\(779\) | −27.4313 | −0.982828 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.10746 | −0.111194 | ||||||||
\(782\) | 4.90853 | 0.175529 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25.0712 | 0.895401 | ||||||||
\(785\) | 17.4074 | 0.621297 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.08437 | 0.252530 | 0.126265 | − | 0.991997i | \(-0.459701\pi\) | ||||
0.126265 | + | 0.991997i | \(0.459701\pi\) | |||||||
\(788\) | 1.19642 | 0.0426206 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.87595 | −0.0667434 | ||||||||
\(791\) | −40.2552 | −1.43131 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.6174 | 0.874188 | ||||||||
\(794\) | −9.39738 | −0.333501 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.2638 | −0.541009 | ||||||||
\(797\) | −37.8352 | −1.34019 | −0.670096 | − | 0.742275i | \(-0.733747\pi\) | ||||
−0.670096 | + | 0.742275i | \(0.733747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.56987 | 0.161671 | ||||||||
\(800\) | −20.9975 | −0.742375 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.70066 | −0.0953637 | ||||||||
\(803\) | 7.10045 | 0.250570 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.57354 | −0.196442 | ||||||||
\(806\) | 1.78038 | 0.0627113 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −43.0487 | −1.51445 | ||||||||
\(809\) | 45.3863 | 1.59570 | 0.797849 | − | 0.602858i | \(-0.205971\pi\) | ||||
0.797849 | + | 0.602858i | \(0.205971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.1196 | −1.51413 | −0.757067 | − | 0.653337i | \(-0.773368\pi\) | ||||
−0.757067 | + | 0.653337i | \(0.773368\pi\) | |||||||
\(812\) | −7.49685 | −0.263088 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.82199 | −0.0638607 | ||||||||
\(815\) | −10.3166 | −0.361376 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.4151 | −1.30899 | ||||||||
\(818\) | −1.17703 | −0.0411538 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.6479 | 0.406762 | ||||||||
\(821\) | 41.4654 | 1.44715 | 0.723576 | − | 0.690245i | \(-0.242497\pi\) | ||||
0.723576 | + | 0.690245i | \(0.242497\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.5317 | 1.06427 | 0.532134 | − | 0.846660i | \(-0.321390\pi\) | ||||
0.532134 | + | 0.846660i | \(0.321390\pi\) | |||||||
\(824\) | −21.6238 | −0.753302 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.22582 | −0.112241 | ||||||||
\(827\) | −53.7558 | −1.86927 | −0.934637 | − | 0.355604i | \(-0.884275\pi\) | ||||
−0.934637 | + | 0.355604i | \(0.884275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.5801 | −0.923164 | −0.461582 | − | 0.887098i | \(-0.652718\pi\) | ||||
−0.461582 | + | 0.887098i | \(0.652718\pi\) | |||||||
\(830\) | −8.85780 | −0.307459 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.64076 | −0.0915518 | ||||||||
\(833\) | −118.944 | −4.12115 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.79609 | −0.0967626 | ||||||||
\(836\) | −3.21354 | −0.111143 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.21880 | 0.283914 | ||||||||
\(839\) | 24.9153 | 0.860172 | 0.430086 | − | 0.902788i | \(-0.358483\pi\) | ||||
0.430086 | + | 0.902788i | \(0.358483\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 25.8857 | 0.892081 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 33.6856 | 1.15950 | ||||||||
\(845\) | 2.41391 | 0.0830411 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −51.6860 | −1.77595 | ||||||||
\(848\) | −9.86494 | −0.338763 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.9246 | 0.614807 | ||||||||
\(851\) | 5.71364 | 0.195861 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.6402 | 1.28878 | 0.644388 | − | 0.764699i | \(-0.277112\pi\) | ||||
0.644388 | + | 0.764699i | \(0.277112\pi\) | |||||||
\(854\) | −20.1425 | −0.689260 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.9939 | 0.751737 | ||||||||
\(857\) | 34.1351 | 1.16603 | 0.583017 | − | 0.812460i | \(-0.301872\pi\) | ||||
0.583017 | + | 0.812460i | \(0.301872\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.59289 | −0.259066 | −0.129533 | − | 0.991575i | \(-0.541348\pi\) | ||||
−0.129533 | + | 0.991575i | \(0.541348\pi\) | |||||||
\(860\) | 15.8872 | 0.541749 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.1318 | 0.583512 | ||||||||
\(863\) | −12.6678 | −0.431218 | −0.215609 | − | 0.976480i | \(-0.569174\pi\) | ||||
−0.215609 | + | 0.976480i | \(0.569174\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.9853 | −0.747522 | ||||||||
\(866\) | −16.7278 | −0.568434 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.19270 | 0.176252 | ||||||||
\(869\) | −1.17581 | −0.0398865 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.2847 | 1.53441 | ||||||||
\(872\) | −40.4459 | −1.36967 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.82710 | −0.0956281 | ||||||||
\(875\) | −48.2207 | −1.63016 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.7555 | 1.68012 | 0.840061 | − | 0.542492i | \(-0.182519\pi\) | ||||
0.840061 | + | 0.542492i | \(0.182519\pi\) | |||||||
\(878\) | −26.7099 | −0.901414 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.874340 | 0.0294740 | ||||||||
\(881\) | 18.2360 | 0.614386 | 0.307193 | − | 0.951647i | \(-0.400610\pi\) | ||||
0.307193 | + | 0.951647i | \(0.400610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.6184 | 0.761170 | 0.380585 | − | 0.924746i | \(-0.375723\pi\) | ||||
0.380585 | + | 0.924746i | \(0.375723\pi\) | |||||||
\(884\) | −44.9737 | −1.51263 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.47096 | −0.284587 | ||||||||
\(887\) | 18.8293 | 0.632227 | 0.316113 | − | 0.948721i | \(-0.397622\pi\) | ||||
0.316113 | + | 0.948721i | \(0.397622\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.0874 | 1.51218 | ||||||||
\(890\) | −1.32159 | −0.0442997 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.47496 | 0.0493854 | ||||||||
\(893\) | −2.63205 | −0.0880783 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.70102 | 0.123712 | ||||||||
\(896\) | −53.0396 | −1.77193 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.19765 | −0.140077 | ||||||||
\(899\) | −0.692651 | −0.0231012 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.8015 | 1.55918 | ||||||||
\(902\) | −2.04811 | −0.0681944 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.7729 | 0.657637 | ||||||||
\(905\) | 15.4360 | 0.513109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.9004 | −1.49089 | −0.745446 | − | 0.666566i | \(-0.767764\pi\) | ||||
−0.745446 | + | 0.666566i | \(0.767764\pi\) | |||||||
\(908\) | 31.6360 | 1.04988 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14.3262 | −0.474908 | ||||||||
\(911\) | −16.6245 | −0.550795 | −0.275398 | − | 0.961330i | \(-0.588809\pi\) | ||||
−0.275398 | + | 0.961330i | \(0.588809\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.55188 | −0.183740 | ||||||||
\(914\) | −22.1420 | −0.732393 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.49100 | −0.214469 | ||||||||
\(917\) | 85.6385 | 2.82803 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.1293 | 1.78556 | 0.892781 | − | 0.450492i | \(-0.148751\pi\) | ||||
0.892781 | + | 0.450492i | \(0.148751\pi\) | |||||||
\(920\) | 2.73766 | 0.0902580 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.59220 | −0.118303 | ||||||||
\(923\) | 25.0479 | 0.824462 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.8646 | 0.686024 | ||||||||
\(926\) | 7.05923 | 0.231981 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.75004 | 0.188754 | ||||||||
\(929\) | −56.9814 | −1.86950 | −0.934749 | − | 0.355309i | \(-0.884376\pi\) | ||||
−0.934749 | + | 0.355309i | \(0.884376\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 68.5064 | 2.24521 | ||||||||
\(932\) | −20.9049 | −0.684764 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.03036 | −0.230040 | ||||||||
\(935\) | −4.14807 | −0.135656 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.24635 | 0.0733850 | 0.0366925 | − | 0.999327i | \(-0.488318\pi\) | ||||
0.0366925 | + | 0.999327i | \(0.488318\pi\) | |||||||
\(938\) | −37.0529 | −1.20982 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.11762 | 0.0364528 | ||||||||
\(941\) | −3.37208 | −0.109927 | −0.0549634 | − | 0.998488i | \(-0.517504\pi\) | ||||
−0.0549634 | + | 0.998488i | \(0.517504\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.42272 | 0.209153 | ||||||||
\(944\) | −1.58692 | −0.0516499 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.79352 | −0.0908253 | ||||||||
\(947\) | 54.2976 | 1.76444 | 0.882218 | − | 0.470842i | \(-0.156050\pi\) | ||||
0.882218 | + | 0.470842i | \(0.156050\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57.2337 | −1.85789 | ||||||||
\(950\) | −10.3238 | −0.334948 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 83.9203 | 2.71987 | ||||||||
\(953\) | 46.6397 | 1.51081 | 0.755405 | − | 0.655258i | \(-0.227440\pi\) | ||||
0.755405 | + | 0.655258i | \(0.227440\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.9756 | −0.808190 | ||||||||
\(956\) | −35.4880 | −1.14777 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.5588 | −0.373448 | ||||||||
\(959\) | −31.2086 | −1.00778 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5202 | −0.984524 | ||||||||
\(962\) | 14.6863 | 0.473505 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.67840 | −0.215097 | ||||||||
\(965\) | −2.73269 | −0.0879685 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.1471 | −1.09810 | −0.549048 | − | 0.835791i | \(-0.685010\pi\) | ||||
−0.549048 | + | 0.835791i | \(0.685010\pi\) | |||||||
\(968\) | 25.3876 | 0.815987 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.04503 | 0.0977700 | ||||||||
\(971\) | 24.8313 | 0.796873 | 0.398437 | − | 0.917196i | \(-0.369553\pi\) | ||||
0.398437 | + | 0.917196i | \(0.369553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.8294 | 1.37305 | ||||||||
\(974\) | 2.63776 | 0.0845193 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.90896 | −0.317178 | ||||||||
\(977\) | 60.2384 | 1.92720 | 0.963598 | − | 0.267355i | \(-0.0861495\pi\) | ||||
0.963598 | + | 0.267355i | \(0.0861495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.828342 | −0.0264739 | ||||||||
\(980\) | −29.0892 | −0.929221 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.37403 | −0.299137 | ||||||||
\(983\) | 53.8499 | 1.71754 | 0.858772 | − | 0.512357i | \(-0.171228\pi\) | ||||
0.858772 | + | 0.512357i | \(0.171228\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.889478 | −0.0283411 | ||||||||
\(986\) | −4.90853 | −0.156319 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25.9030 | 0.824083 | ||||||||
\(989\) | 8.76031 | 0.278562 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.34232 | 0.296769 | 0.148384 | − | 0.988930i | \(-0.452593\pi\) | ||||
0.148384 | + | 0.988930i | \(0.452593\pi\) | |||||||
\(992\) | −3.98277 | −0.126453 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.4947 | −0.650053 | ||||||||
\(995\) | 11.3479 | 0.359751 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.9157 | −1.58085 | −0.790423 | − | 0.612562i | \(-0.790139\pi\) | ||||
−0.790423 | + | 0.612562i | \(0.790139\pi\) | |||||||
\(998\) | −2.48586 | −0.0786886 | ||||||||
\(999\) | 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.m.1.7 | 11 | ||
3.2 | odd | 2 | 2001.2.a.l.1.5 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.l.1.5 | ✓ | 11 | 3.2 | odd | 2 | ||
6003.2.a.m.1.7 | 11 | 1.1 | even | 1 | trivial |