Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.233489.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + x^{2} + 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.16000\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35647 | 0.959166 | 0.479583 | − | 0.877496i | \(-0.340788\pi\) | ||||
0.479583 | + | 0.877496i | \(0.340788\pi\) | |||||||
\(3\) | −2.22790 | −1.28628 | −0.643139 | − | 0.765749i | \(-0.722368\pi\) | ||||
−0.643139 | + | 0.765749i | \(0.722368\pi\) | |||||||
\(4\) | −0.160001 | −0.0800004 | ||||||||
\(5\) | 2.22790 | 0.996347 | 0.498173 | − | 0.867077i | \(-0.334004\pi\) | ||||
0.498173 | + | 0.867077i | \(0.334004\pi\) | |||||||
\(6\) | −3.02207 | −1.23375 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.92997 | −1.03590 | ||||||||
\(9\) | 1.96354 | 0.654512 | ||||||||
\(10\) | 3.02207 | 0.955662 | ||||||||
\(11\) | −1.12857 | −0.340276 | −0.170138 | − | 0.985420i | \(-0.554421\pi\) | ||||
−0.170138 | + | 0.985420i | \(0.554421\pi\) | |||||||
\(12\) | 0.356466 | 0.102903 | ||||||||
\(13\) | 2.22790 | 0.617908 | 0.308954 | − | 0.951077i | \(-0.400021\pi\) | ||||
0.308954 | + | 0.951077i | \(0.400021\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.96354 | −1.28158 | ||||||||
\(16\) | −3.65440 | −0.913600 | ||||||||
\(17\) | 4.05350 | 0.983119 | 0.491560 | − | 0.870844i | \(-0.336427\pi\) | ||||
0.491560 | + | 0.870844i | \(0.336427\pi\) | |||||||
\(18\) | 2.66347 | 0.627786 | ||||||||
\(19\) | −3.61580 | −0.829521 | −0.414761 | − | 0.909931i | \(-0.636135\pi\) | ||||
−0.414761 | + | 0.909931i | \(0.636135\pi\) | |||||||
\(20\) | −0.356466 | −0.0797082 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.53086 | −0.326381 | ||||||||
\(23\) | −2.68583 | −0.560035 | −0.280017 | − | 0.959995i | \(-0.590340\pi\) | ||||
−0.280017 | + | 0.959995i | \(0.590340\pi\) | |||||||
\(24\) | 6.52767 | 1.33246 | ||||||||
\(25\) | −0.0364641 | −0.00729282 | ||||||||
\(26\) | 3.02207 | 0.592677 | ||||||||
\(27\) | 2.30914 | 0.444394 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.72230 | −0.691213 | −0.345607 | − | 0.938380i | \(-0.612327\pi\) | ||||
−0.345607 | + | 0.938380i | \(0.612327\pi\) | |||||||
\(30\) | −6.73287 | −1.22925 | ||||||||
\(31\) | 0.345260 | 0.0620106 | 0.0310053 | − | 0.999519i | \(-0.490129\pi\) | ||||
0.0310053 | + | 0.999519i | \(0.490129\pi\) | |||||||
\(32\) | 0.902868 | 0.159606 | ||||||||
\(33\) | 2.51433 | 0.437689 | ||||||||
\(34\) | 5.49844 | 0.942974 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.314167 | −0.0523612 | ||||||||
\(37\) | 3.34930 | 0.550622 | 0.275311 | − | 0.961355i | \(-0.411219\pi\) | ||||
0.275311 | + | 0.961355i | \(0.411219\pi\) | |||||||
\(38\) | −4.90471 | −0.795649 | ||||||||
\(39\) | −4.96354 | −0.794802 | ||||||||
\(40\) | −6.52767 | −1.03212 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.6805 | −1.93376 | −0.966880 | − | 0.255232i | \(-0.917848\pi\) | ||||
−0.966880 | + | 0.255232i | \(0.917848\pi\) | |||||||
\(44\) | 0.180572 | 0.0272222 | ||||||||
\(45\) | 4.37456 | 0.652121 | ||||||||
\(46\) | −3.64324 | −0.537166 | ||||||||
\(47\) | −7.31284 | −1.06669 | −0.533344 | − | 0.845899i | \(-0.679065\pi\) | ||||
−0.533344 | + | 0.845899i | \(0.679065\pi\) | |||||||
\(48\) | 8.14163 | 1.17514 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.0494623 | −0.00699502 | ||||||||
\(51\) | −9.03080 | −1.26456 | ||||||||
\(52\) | −0.356466 | −0.0494329 | ||||||||
\(53\) | −8.35617 | −1.14781 | −0.573904 | − | 0.818922i | \(-0.694572\pi\) | ||||
−0.573904 | + | 0.818922i | \(0.694572\pi\) | |||||||
\(54\) | 3.13227 | 0.426247 | ||||||||
\(55\) | −2.51433 | −0.339032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.05564 | 1.06700 | ||||||||
\(58\) | −5.04917 | −0.662988 | ||||||||
\(59\) | −5.22500 | −0.680238 | −0.340119 | − | 0.940382i | \(-0.610467\pi\) | ||||
−0.340119 | + | 0.940382i | \(0.610467\pi\) | |||||||
\(60\) | 0.794170 | 0.102527 | ||||||||
\(61\) | 5.60864 | 0.718112 | 0.359056 | − | 0.933316i | \(-0.383099\pi\) | ||||
0.359056 | + | 0.933316i | \(0.383099\pi\) | |||||||
\(62\) | 0.468334 | 0.0594785 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.53351 | 1.06669 | ||||||||
\(65\) | 4.96354 | 0.615651 | ||||||||
\(66\) | 3.41061 | 0.419816 | ||||||||
\(67\) | −8.83249 | −1.07906 | −0.539530 | − | 0.841966i | \(-0.681398\pi\) | ||||
−0.539530 | + | 0.841966i | \(0.681398\pi\) | |||||||
\(68\) | −0.648564 | −0.0786499 | ||||||||
\(69\) | 5.98377 | 0.720361 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.92933 | 1.17839 | 0.589197 | − | 0.807989i | \(-0.299444\pi\) | ||||
0.589197 | + | 0.807989i | \(0.299444\pi\) | |||||||
\(72\) | −5.75310 | −0.678009 | ||||||||
\(73\) | 0.815796 | 0.0954817 | 0.0477408 | − | 0.998860i | \(-0.484798\pi\) | ||||
0.0477408 | + | 0.998860i | \(0.484798\pi\) | |||||||
\(74\) | 4.54321 | 0.528138 | ||||||||
\(75\) | 0.0812383 | 0.00938059 | ||||||||
\(76\) | 0.578531 | 0.0663620 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.73287 | −0.762347 | ||||||||
\(79\) | −8.84184 | −0.994785 | −0.497392 | − | 0.867526i | \(-0.665709\pi\) | ||||
−0.497392 | + | 0.867526i | \(0.665709\pi\) | |||||||
\(80\) | −8.14163 | −0.910262 | ||||||||
\(81\) | −11.0351 | −1.22613 | ||||||||
\(82\) | −1.35647 | −0.149797 | ||||||||
\(83\) | −7.48907 | −0.822033 | −0.411016 | − | 0.911628i | \(-0.634826\pi\) | ||||
−0.411016 | + | 0.911628i | \(0.634826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.03080 | 0.979528 | ||||||||
\(86\) | −17.2007 | −1.85480 | ||||||||
\(87\) | 8.29290 | 0.889093 | ||||||||
\(88\) | 3.30666 | 0.352491 | ||||||||
\(89\) | −15.7637 | −1.67095 | −0.835473 | − | 0.549532i | \(-0.814806\pi\) | ||||
−0.835473 | + | 0.549532i | \(0.814806\pi\) | |||||||
\(90\) | 5.93394 | 0.625492 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.429735 | 0.0448030 | ||||||||
\(93\) | −0.769205 | −0.0797629 | ||||||||
\(94\) | −9.91961 | −1.02313 | ||||||||
\(95\) | −8.05564 | −0.826491 | ||||||||
\(96\) | −2.01150 | −0.205298 | ||||||||
\(97\) | −2.10829 | −0.214064 | −0.107032 | − | 0.994256i | \(-0.534135\pi\) | ||||
−0.107032 | + | 0.994256i | \(0.534135\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.21598 | −0.222714 | ||||||||
\(100\) | 0.00583428 | 0.000583428 0 | ||||||||
\(101\) | 7.84179 | 0.780287 | 0.390144 | − | 0.920754i | \(-0.372425\pi\) | ||||
0.390144 | + | 0.920754i | \(0.372425\pi\) | |||||||
\(102\) | −12.2500 | −1.21293 | ||||||||
\(103\) | −6.90910 | −0.680774 | −0.340387 | − | 0.940285i | \(-0.610558\pi\) | ||||
−0.340387 | + | 0.940285i | \(0.610558\pi\) | |||||||
\(104\) | −6.52767 | −0.640091 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.3349 | −1.10094 | ||||||||
\(107\) | 19.5675 | 1.89167 | 0.945833 | − | 0.324654i | \(-0.105248\pi\) | ||||
0.945833 | + | 0.324654i | \(0.105248\pi\) | |||||||
\(108\) | −0.369464 | −0.0355517 | ||||||||
\(109\) | 3.92210 | 0.375669 | 0.187835 | − | 0.982201i | \(-0.439853\pi\) | ||||
0.187835 | + | 0.982201i | \(0.439853\pi\) | |||||||
\(110\) | −3.41061 | −0.325188 | ||||||||
\(111\) | −7.46191 | −0.708253 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.10800 | −0.480520 | −0.240260 | − | 0.970709i | \(-0.577233\pi\) | ||||
−0.240260 | + | 0.970709i | \(0.577233\pi\) | |||||||
\(114\) | 10.9272 | 1.02343 | ||||||||
\(115\) | −5.98377 | −0.557989 | ||||||||
\(116\) | 0.595570 | 0.0552973 | ||||||||
\(117\) | 4.37456 | 0.404428 | ||||||||
\(118\) | −7.08754 | −0.652461 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 14.5430 | 1.32759 | ||||||||
\(121\) | −9.72634 | −0.884213 | ||||||||
\(122\) | 7.60792 | 0.688789 | ||||||||
\(123\) | 2.22790 | 0.200883 | ||||||||
\(124\) | −0.0552419 | −0.00496087 | ||||||||
\(125\) | −11.2207 | −1.00361 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.3732 | −1.71909 | −0.859547 | − | 0.511056i | \(-0.829254\pi\) | ||||
−0.859547 | + | 0.511056i | \(0.829254\pi\) | |||||||
\(128\) | 9.76967 | 0.863525 | ||||||||
\(129\) | 28.2509 | 2.48735 | ||||||||
\(130\) | 6.73287 | 0.590511 | ||||||||
\(131\) | −0.309091 | −0.0270054 | −0.0135027 | − | 0.999909i | \(-0.504298\pi\) | ||||
−0.0135027 | + | 0.999909i | \(0.504298\pi\) | |||||||
\(132\) | −0.402295 | −0.0350153 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.9810 | −1.03500 | ||||||||
\(135\) | 5.14453 | 0.442770 | ||||||||
\(136\) | −11.8766 | −1.01841 | ||||||||
\(137\) | −17.3675 | −1.48381 | −0.741905 | − | 0.670505i | \(-0.766077\pi\) | ||||
−0.741905 | + | 0.670505i | \(0.766077\pi\) | |||||||
\(138\) | 8.11677 | 0.690946 | ||||||||
\(139\) | −15.1514 | −1.28512 | −0.642562 | − | 0.766233i | \(-0.722129\pi\) | ||||
−0.642562 | + | 0.766233i | \(0.722129\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.2923 | 1.37206 | ||||||||
\(142\) | 13.4688 | 1.13028 | ||||||||
\(143\) | −2.51433 | −0.210259 | ||||||||
\(144\) | −7.17554 | −0.597962 | ||||||||
\(145\) | −8.29290 | −0.688688 | ||||||||
\(146\) | 1.10660 | 0.0915828 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.535891 | −0.0440500 | ||||||||
\(149\) | −10.4934 | −0.859654 | −0.429827 | − | 0.902911i | \(-0.641425\pi\) | ||||
−0.429827 | + | 0.902911i | \(0.641425\pi\) | |||||||
\(150\) | 0.110197 | 0.00899755 | ||||||||
\(151\) | −5.11950 | −0.416619 | −0.208309 | − | 0.978063i | \(-0.566796\pi\) | ||||
−0.208309 | + | 0.978063i | \(0.566796\pi\) | |||||||
\(152\) | 10.5942 | 0.859301 | ||||||||
\(153\) | 7.95920 | 0.643463 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.769205 | 0.0617841 | ||||||||
\(156\) | 0.794170 | 0.0635845 | ||||||||
\(157\) | 15.0958 | 1.20478 | 0.602388 | − | 0.798203i | \(-0.294216\pi\) | ||||
0.602388 | + | 0.798203i | \(0.294216\pi\) | |||||||
\(158\) | −11.9937 | −0.954164 | ||||||||
\(159\) | 18.6167 | 1.47640 | ||||||||
\(160\) | 2.01150 | 0.159023 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −14.9688 | −1.17606 | ||||||||
\(163\) | 7.61624 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(164\) | 0.160001 | 0.0124940 | ||||||||
\(165\) | 5.60168 | 0.436090 | ||||||||
\(166\) | −10.1587 | −0.788466 | ||||||||
\(167\) | 8.24963 | 0.638375 | 0.319188 | − | 0.947692i | \(-0.396590\pi\) | ||||
0.319188 | + | 0.947692i | \(0.396590\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.03646 | −0.618190 | ||||||||
\(170\) | 12.2500 | 0.939530 | ||||||||
\(171\) | −7.09975 | −0.542932 | ||||||||
\(172\) | 2.02889 | 0.154702 | ||||||||
\(173\) | −23.7381 | −1.80477 | −0.902386 | − | 0.430929i | \(-0.858186\pi\) | ||||
−0.902386 | + | 0.430929i | \(0.858186\pi\) | |||||||
\(174\) | 11.2490 | 0.852787 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.12423 | 0.310876 | ||||||||
\(177\) | 11.6408 | 0.874975 | ||||||||
\(178\) | −21.3829 | −1.60271 | ||||||||
\(179\) | 11.4555 | 0.856221 | 0.428111 | − | 0.903726i | \(-0.359179\pi\) | ||||
0.428111 | + | 0.903726i | \(0.359179\pi\) | |||||||
\(180\) | −0.699933 | −0.0521699 | ||||||||
\(181\) | 17.7517 | 1.31948 | 0.659738 | − | 0.751495i | \(-0.270667\pi\) | ||||
0.659738 | + | 0.751495i | \(0.270667\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.4955 | −0.923692 | ||||||||
\(184\) | 7.86940 | 0.580140 | ||||||||
\(185\) | 7.46191 | 0.548610 | ||||||||
\(186\) | −1.04340 | −0.0765059 | ||||||||
\(187\) | −4.57465 | −0.334531 | ||||||||
\(188\) | 1.17006 | 0.0853354 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.9272 | −0.792742 | ||||||||
\(191\) | 16.4578 | 1.19085 | 0.595423 | − | 0.803413i | \(-0.296985\pi\) | ||||
0.595423 | + | 0.803413i | \(0.296985\pi\) | |||||||
\(192\) | −19.0118 | −1.37206 | ||||||||
\(193\) | 19.7096 | 1.41873 | 0.709365 | − | 0.704842i | \(-0.248982\pi\) | ||||
0.709365 | + | 0.704842i | \(0.248982\pi\) | |||||||
\(194\) | −2.85982 | −0.205323 | ||||||||
\(195\) | −11.0583 | −0.791898 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.9492 | 0.922592 | 0.461296 | − | 0.887246i | \(-0.347385\pi\) | ||||
0.461296 | + | 0.887246i | \(0.347385\pi\) | |||||||
\(198\) | −3.00590 | −0.213620 | ||||||||
\(199\) | 25.7131 | 1.82276 | 0.911378 | − | 0.411570i | \(-0.135019\pi\) | ||||
0.911378 | + | 0.411570i | \(0.135019\pi\) | |||||||
\(200\) | 0.106839 | 0.00755463 | ||||||||
\(201\) | 19.6779 | 1.38797 | ||||||||
\(202\) | 10.6371 | 0.748425 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.44494 | 0.101166 | ||||||||
\(205\) | −2.22790 | −0.155603 | ||||||||
\(206\) | −9.37196 | −0.652975 | ||||||||
\(207\) | −5.27373 | −0.366549 | ||||||||
\(208\) | −8.14163 | −0.564521 | ||||||||
\(209\) | 4.08067 | 0.282266 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.4799 | 0.927993 | 0.463996 | − | 0.885837i | \(-0.346415\pi\) | ||||
0.463996 | + | 0.885837i | \(0.346415\pi\) | |||||||
\(212\) | 1.33699 | 0.0918251 | ||||||||
\(213\) | −22.1216 | −1.51574 | ||||||||
\(214\) | 26.5427 | 1.81442 | ||||||||
\(215\) | −28.2509 | −1.92670 | ||||||||
\(216\) | −6.76570 | −0.460347 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.32019 | 0.360329 | ||||||||
\(219\) | −1.81751 | −0.122816 | ||||||||
\(220\) | 0.402295 | 0.0271227 | ||||||||
\(221\) | 9.03080 | 0.607477 | ||||||||
\(222\) | −10.1218 | −0.679332 | ||||||||
\(223\) | −2.59701 | −0.173909 | −0.0869544 | − | 0.996212i | \(-0.527713\pi\) | ||||
−0.0869544 | + | 0.996212i | \(0.527713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0715986 | −0.00477324 | ||||||||
\(226\) | −6.92882 | −0.460898 | ||||||||
\(227\) | −10.1112 | −0.671102 | −0.335551 | − | 0.942022i | \(-0.608923\pi\) | ||||
−0.335551 | + | 0.942022i | \(0.608923\pi\) | |||||||
\(228\) | −1.28891 | −0.0853601 | ||||||||
\(229\) | −13.5898 | −0.898042 | −0.449021 | − | 0.893521i | \(-0.648227\pi\) | ||||
−0.449021 | + | 0.893521i | \(0.648227\pi\) | |||||||
\(230\) | −8.11677 | −0.535204 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.9062 | 0.716028 | ||||||||
\(233\) | 9.26227 | 0.606792 | 0.303396 | − | 0.952865i | \(-0.401880\pi\) | ||||
0.303396 | + | 0.952865i | \(0.401880\pi\) | |||||||
\(234\) | 5.93394 | 0.387914 | ||||||||
\(235\) | −16.2923 | −1.06279 | ||||||||
\(236\) | 0.836005 | 0.0544193 | ||||||||
\(237\) | 19.6987 | 1.27957 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5580 | −0.682942 | −0.341471 | − | 0.939892i | \(-0.610925\pi\) | ||||
−0.341471 | + | 0.939892i | \(0.610925\pi\) | |||||||
\(240\) | 18.1387 | 1.17085 | ||||||||
\(241\) | 9.01525 | 0.580723 | 0.290362 | − | 0.956917i | \(-0.406224\pi\) | ||||
0.290362 | + | 0.956917i | \(0.406224\pi\) | |||||||
\(242\) | −13.1934 | −0.848107 | ||||||||
\(243\) | 17.6578 | 1.13275 | ||||||||
\(244\) | −0.897386 | −0.0574493 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.02207 | 0.192680 | ||||||||
\(247\) | −8.05564 | −0.512568 | ||||||||
\(248\) | −1.01160 | −0.0642368 | ||||||||
\(249\) | 16.6849 | 1.05736 | ||||||||
\(250\) | −15.2205 | −0.962632 | ||||||||
\(251\) | 21.2912 | 1.34389 | 0.671945 | − | 0.740601i | \(-0.265459\pi\) | ||||
0.671945 | + | 0.740601i | \(0.265459\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.03114 | 0.190566 | ||||||||
\(254\) | −26.2791 | −1.64890 | ||||||||
\(255\) | −20.1197 | −1.25995 | ||||||||
\(256\) | −3.81479 | −0.238424 | ||||||||
\(257\) | 8.45793 | 0.527591 | 0.263796 | − | 0.964579i | \(-0.415026\pi\) | ||||
0.263796 | + | 0.964579i | \(0.415026\pi\) | |||||||
\(258\) | 38.3214 | 2.38578 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.794170 | −0.0492523 | ||||||||
\(261\) | −7.30886 | −0.452407 | ||||||||
\(262\) | −0.419271 | −0.0259026 | ||||||||
\(263\) | −2.72257 | −0.167881 | −0.0839405 | − | 0.996471i | \(-0.526751\pi\) | ||||
−0.0839405 | + | 0.996471i | \(0.526751\pi\) | |||||||
\(264\) | −7.36691 | −0.453402 | ||||||||
\(265\) | −18.6167 | −1.14362 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.1199 | 2.14930 | ||||||||
\(268\) | 1.41321 | 0.0863253 | ||||||||
\(269\) | 29.5788 | 1.80345 | 0.901726 | − | 0.432309i | \(-0.142301\pi\) | ||||
0.901726 | + | 0.432309i | \(0.142301\pi\) | |||||||
\(270\) | 6.97837 | 0.424690 | ||||||||
\(271\) | 8.11601 | 0.493013 | 0.246506 | − | 0.969141i | \(-0.420717\pi\) | ||||
0.246506 | + | 0.969141i | \(0.420717\pi\) | |||||||
\(272\) | −14.8131 | −0.898177 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.5585 | −1.42322 | ||||||||
\(275\) | 0.0411521 | 0.00248157 | ||||||||
\(276\) | −0.957407 | −0.0576291 | ||||||||
\(277\) | −1.09394 | −0.0657286 | −0.0328643 | − | 0.999460i | \(-0.510463\pi\) | ||||
−0.0328643 | + | 0.999460i | \(0.510463\pi\) | |||||||
\(278\) | −20.5523 | −1.23265 | ||||||||
\(279\) | 0.677931 | 0.0405867 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.95015 | 0.474266 | 0.237133 | − | 0.971477i | \(-0.423792\pi\) | ||||
0.237133 | + | 0.971477i | \(0.423792\pi\) | |||||||
\(282\) | 22.0999 | 1.31603 | ||||||||
\(283\) | −27.6594 | −1.64418 | −0.822089 | − | 0.569358i | \(-0.807192\pi\) | ||||
−0.822089 | + | 0.569358i | \(0.807192\pi\) | |||||||
\(284\) | −1.58870 | −0.0942721 | ||||||||
\(285\) | 17.9472 | 1.06310 | ||||||||
\(286\) | −3.41061 | −0.201673 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.77281 | 0.104464 | ||||||||
\(289\) | −0.569108 | −0.0334769 | ||||||||
\(290\) | −11.2490 | −0.660566 | ||||||||
\(291\) | 4.69706 | 0.275346 | ||||||||
\(292\) | −0.130528 | −0.00763857 | ||||||||
\(293\) | −9.57574 | −0.559421 | −0.279710 | − | 0.960084i | \(-0.590238\pi\) | ||||
−0.279710 | + | 0.960084i | \(0.590238\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.6408 | −0.677753 | ||||||||
\(296\) | −9.81334 | −0.570389 | ||||||||
\(297\) | −2.60601 | −0.151216 | ||||||||
\(298\) | −14.2339 | −0.824551 | ||||||||
\(299\) | −5.98377 | −0.346050 | ||||||||
\(300\) | −0.0129982 | −0.000750451 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.94442 | −0.399606 | ||||||||
\(303\) | −17.4707 | −1.00367 | ||||||||
\(304\) | 13.2136 | 0.757850 | ||||||||
\(305\) | 12.4955 | 0.715489 | ||||||||
\(306\) | 10.7964 | 0.617188 | ||||||||
\(307\) | 8.24141 | 0.470362 | 0.235181 | − | 0.971952i | \(-0.424432\pi\) | ||||
0.235181 | + | 0.971952i | \(0.424432\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.3928 | 0.875665 | ||||||||
\(310\) | 1.04340 | 0.0592612 | ||||||||
\(311\) | −11.6642 | −0.661418 | −0.330709 | − | 0.943733i | \(-0.607288\pi\) | ||||
−0.330709 | + | 0.943733i | \(0.607288\pi\) | |||||||
\(312\) | 14.5430 | 0.823335 | ||||||||
\(313\) | 30.6181 | 1.73064 | 0.865319 | − | 0.501222i | \(-0.167116\pi\) | ||||
0.865319 | + | 0.501222i | \(0.167116\pi\) | |||||||
\(314\) | 20.4769 | 1.15558 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.41470 | 0.0795832 | ||||||||
\(317\) | −20.8117 | −1.16890 | −0.584450 | − | 0.811430i | \(-0.698690\pi\) | ||||
−0.584450 | + | 0.811430i | \(0.698690\pi\) | |||||||
\(318\) | 25.2529 | 1.41611 | ||||||||
\(319\) | 4.20086 | 0.235203 | ||||||||
\(320\) | 19.0118 | 1.06279 | ||||||||
\(321\) | −43.5945 | −2.43321 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.6567 | −0.815518 | ||||||||
\(324\) | 1.76563 | 0.0980906 | ||||||||
\(325\) | −0.0812383 | −0.00450629 | ||||||||
\(326\) | 10.3312 | 0.572191 | ||||||||
\(327\) | −8.73804 | −0.483215 | ||||||||
\(328\) | 2.92997 | 0.161780 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.59849 | 0.418283 | ||||||||
\(331\) | −0.667000 | −0.0366616 | −0.0183308 | − | 0.999832i | \(-0.505835\pi\) | ||||
−0.0183308 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(332\) | 1.19826 | 0.0657629 | ||||||||
\(333\) | 6.57647 | 0.360389 | ||||||||
\(334\) | 11.1903 | 0.612308 | ||||||||
\(335\) | −19.6779 | −1.07512 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.0671610 | 0.00365849 | 0.00182925 | − | 0.999998i | \(-0.499418\pi\) | ||||
0.00182925 | + | 0.999998i | \(0.499418\pi\) | |||||||
\(338\) | −10.9012 | −0.592946 | ||||||||
\(339\) | 11.3801 | 0.618082 | ||||||||
\(340\) | −1.44494 | −0.0783626 | ||||||||
\(341\) | −0.389649 | −0.0211007 | ||||||||
\(342\) | −9.63057 | −0.520762 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 37.1535 | 2.00318 | ||||||||
\(345\) | 13.3312 | 0.717729 | ||||||||
\(346\) | −32.1999 | −1.73108 | ||||||||
\(347\) | 28.5133 | 1.53068 | 0.765338 | − | 0.643628i | \(-0.222572\pi\) | ||||
0.765338 | + | 0.643628i | \(0.222572\pi\) | |||||||
\(348\) | −1.32687 | −0.0711278 | ||||||||
\(349\) | 30.8596 | 1.65188 | 0.825938 | − | 0.563761i | \(-0.190646\pi\) | ||||
0.825938 | + | 0.563761i | \(0.190646\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.14453 | 0.274595 | ||||||||
\(352\) | −1.01895 | −0.0543100 | ||||||||
\(353\) | 18.8658 | 1.00413 | 0.502064 | − | 0.864831i | \(-0.332574\pi\) | ||||
0.502064 | + | 0.864831i | \(0.332574\pi\) | |||||||
\(354\) | 15.7903 | 0.839246 | ||||||||
\(355\) | 22.1216 | 1.17409 | ||||||||
\(356\) | 2.52220 | 0.133676 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.5389 | 0.821258 | ||||||||
\(359\) | −0.647576 | −0.0341777 | −0.0170889 | − | 0.999854i | \(-0.505440\pi\) | ||||
−0.0170889 | + | 0.999854i | \(0.505440\pi\) | |||||||
\(360\) | −12.8173 | −0.675532 | ||||||||
\(361\) | −5.92599 | −0.311894 | ||||||||
\(362\) | 24.0796 | 1.26560 | ||||||||
\(363\) | 21.6693 | 1.13734 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.81751 | 0.0951329 | ||||||||
\(366\) | −16.9497 | −0.885974 | ||||||||
\(367\) | −10.1637 | −0.530539 | −0.265269 | − | 0.964174i | \(-0.585461\pi\) | ||||
−0.265269 | + | 0.964174i | \(0.585461\pi\) | |||||||
\(368\) | 9.81510 | 0.511648 | ||||||||
\(369\) | −1.96354 | −0.102218 | ||||||||
\(370\) | 10.1218 | 0.526208 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.123073 | 0.00638106 | ||||||||
\(373\) | 6.96897 | 0.360840 | 0.180420 | − | 0.983590i | \(-0.442254\pi\) | ||||
0.180420 | + | 0.983590i | \(0.442254\pi\) | |||||||
\(374\) | −6.20535 | −0.320871 | ||||||||
\(375\) | 24.9987 | 1.29093 | ||||||||
\(376\) | 21.4264 | 1.10498 | ||||||||
\(377\) | −8.29290 | −0.427106 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.4593 | −1.87279 | −0.936394 | − | 0.350950i | \(-0.885859\pi\) | ||||
−0.936394 | + | 0.350950i | \(0.885859\pi\) | |||||||
\(380\) | 1.28891 | 0.0661196 | ||||||||
\(381\) | 43.1616 | 2.21123 | ||||||||
\(382\) | 22.3245 | 1.14222 | ||||||||
\(383\) | −20.1784 | −1.03107 | −0.515534 | − | 0.856869i | \(-0.672407\pi\) | ||||
−0.515534 | + | 0.856869i | \(0.672407\pi\) | |||||||
\(384\) | −21.7658 | −1.11073 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.7354 | 1.36080 | ||||||||
\(387\) | −24.8986 | −1.26567 | ||||||||
\(388\) | 0.337328 | 0.0171252 | ||||||||
\(389\) | −18.2388 | −0.924745 | −0.462373 | − | 0.886686i | \(-0.653002\pi\) | ||||
−0.462373 | + | 0.886686i | \(0.653002\pi\) | |||||||
\(390\) | −15.0001 | −0.759562 | ||||||||
\(391\) | −10.8870 | −0.550581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.688623 | 0.0347364 | ||||||||
\(394\) | 17.5651 | 0.884919 | ||||||||
\(395\) | −19.6987 | −0.991151 | ||||||||
\(396\) | 0.354559 | 0.0178172 | ||||||||
\(397\) | 37.6739 | 1.89080 | 0.945400 | − | 0.325912i | \(-0.105671\pi\) | ||||
0.945400 | + | 0.325912i | \(0.105671\pi\) | |||||||
\(398\) | 34.8790 | 1.74833 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.133254 | 0.00666272 | ||||||||
\(401\) | −25.6232 | −1.27956 | −0.639780 | − | 0.768558i | \(-0.720975\pi\) | ||||
−0.639780 | + | 0.768558i | \(0.720975\pi\) | |||||||
\(402\) | 26.6924 | 1.33130 | ||||||||
\(403\) | 0.769205 | 0.0383168 | ||||||||
\(404\) | −1.25469 | −0.0624233 | ||||||||
\(405\) | −24.5852 | −1.22165 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.77991 | −0.187363 | ||||||||
\(408\) | 26.4599 | 1.30996 | ||||||||
\(409\) | −4.09136 | −0.202305 | −0.101152 | − | 0.994871i | \(-0.532253\pi\) | ||||
−0.101152 | + | 0.994871i | \(0.532253\pi\) | |||||||
\(410\) | −3.02207 | −0.149249 | ||||||||
\(411\) | 38.6931 | 1.90859 | ||||||||
\(412\) | 1.10546 | 0.0544622 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.15363 | −0.351582 | ||||||||
\(415\) | −16.6849 | −0.819030 | ||||||||
\(416\) | 2.01150 | 0.0986219 | ||||||||
\(417\) | 33.7558 | 1.65303 | ||||||||
\(418\) | 5.53529 | 0.270740 | ||||||||
\(419\) | −33.7334 | −1.64798 | −0.823992 | − | 0.566602i | \(-0.808258\pi\) | ||||
−0.823992 | + | 0.566602i | \(0.808258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.804296 | 0.0391990 | 0.0195995 | − | 0.999808i | \(-0.493761\pi\) | ||||
0.0195995 | + | 0.999808i | \(0.493761\pi\) | |||||||
\(422\) | 18.2850 | 0.890099 | ||||||||
\(423\) | −14.3590 | −0.698159 | ||||||||
\(424\) | 24.4833 | 1.18901 | ||||||||
\(425\) | −0.147807 | −0.00716971 | ||||||||
\(426\) | −30.0071 | −1.45385 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.13082 | −0.151334 | ||||||||
\(429\) | 5.60168 | 0.270452 | ||||||||
\(430\) | −38.3214 | −1.84802 | ||||||||
\(431\) | −39.8279 | −1.91844 | −0.959221 | − | 0.282656i | \(-0.908785\pi\) | ||||
−0.959221 | + | 0.282656i | \(0.908785\pi\) | |||||||
\(432\) | −8.43851 | −0.405998 | ||||||||
\(433\) | −6.07965 | −0.292169 | −0.146085 | − | 0.989272i | \(-0.546667\pi\) | ||||
−0.146085 | + | 0.989272i | \(0.546667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.4758 | 0.885845 | ||||||||
\(436\) | −0.627539 | −0.0300537 | ||||||||
\(437\) | 9.71143 | 0.464561 | ||||||||
\(438\) | −2.46539 | −0.117801 | ||||||||
\(439\) | 40.0899 | 1.91339 | 0.956694 | − | 0.291094i | \(-0.0940194\pi\) | ||||
0.956694 | + | 0.291094i | \(0.0940194\pi\) | |||||||
\(440\) | 7.36691 | 0.351204 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.2500 | 0.582672 | ||||||||
\(443\) | 18.0821 | 0.859106 | 0.429553 | − | 0.903042i | \(-0.358671\pi\) | ||||
0.429553 | + | 0.903042i | \(0.358671\pi\) | |||||||
\(444\) | 1.19391 | 0.0566605 | ||||||||
\(445\) | −35.1199 | −1.66484 | ||||||||
\(446\) | −3.52276 | −0.166807 | ||||||||
\(447\) | 23.3783 | 1.10575 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.4042 | −0.538200 | −0.269100 | − | 0.963112i | \(-0.586726\pi\) | ||||
−0.269100 | + | 0.963112i | \(0.586726\pi\) | |||||||
\(450\) | −0.0971210 | −0.00457833 | ||||||||
\(451\) | 1.12857 | 0.0531421 | ||||||||
\(452\) | 0.817283 | 0.0384418 | ||||||||
\(453\) | 11.4057 | 0.535888 | ||||||||
\(454\) | −13.7155 | −0.643698 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −23.6028 | −1.10530 | ||||||||
\(457\) | 28.1756 | 1.31800 | 0.658999 | − | 0.752144i | \(-0.270980\pi\) | ||||
0.658999 | + | 0.752144i | \(0.270980\pi\) | |||||||
\(458\) | −18.4341 | −0.861371 | ||||||||
\(459\) | 9.36010 | 0.436892 | ||||||||
\(460\) | 0.957407 | 0.0446393 | ||||||||
\(461\) | 29.6306 | 1.38003 | 0.690017 | − | 0.723793i | \(-0.257603\pi\) | ||||
0.690017 | + | 0.723793i | \(0.257603\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.1404 | 1.35427 | 0.677135 | − | 0.735859i | \(-0.263221\pi\) | ||||
0.677135 | + | 0.735859i | \(0.263221\pi\) | |||||||
\(464\) | 13.6028 | 0.631492 | ||||||||
\(465\) | −1.71371 | −0.0794715 | ||||||||
\(466\) | 12.5640 | 0.582014 | ||||||||
\(467\) | 15.8591 | 0.733871 | 0.366936 | − | 0.930246i | \(-0.380407\pi\) | ||||
0.366936 | + | 0.930246i | \(0.380407\pi\) | |||||||
\(468\) | −0.699933 | −0.0323544 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −22.0999 | −1.01939 | ||||||||
\(471\) | −33.6319 | −1.54968 | ||||||||
\(472\) | 15.3091 | 0.704658 | ||||||||
\(473\) | 14.3108 | 0.658011 | ||||||||
\(474\) | 26.7206 | 1.22732 | ||||||||
\(475\) | 0.131847 | 0.00604955 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.4076 | −0.751254 | ||||||||
\(478\) | −14.3216 | −0.655055 | ||||||||
\(479\) | 3.67832 | 0.168067 | 0.0840333 | − | 0.996463i | \(-0.473220\pi\) | ||||
0.0840333 | + | 0.996463i | \(0.473220\pi\) | |||||||
\(480\) | −4.48142 | −0.204548 | ||||||||
\(481\) | 7.46191 | 0.340234 | ||||||||
\(482\) | 12.2289 | 0.557010 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.55622 | 0.0707374 | ||||||||
\(485\) | −4.69706 | −0.213282 | ||||||||
\(486\) | 23.9521 | 1.08649 | ||||||||
\(487\) | 28.9815 | 1.31328 | 0.656638 | − | 0.754205i | \(-0.271978\pi\) | ||||
0.656638 | + | 0.754205i | \(0.271978\pi\) | |||||||
\(488\) | −16.4331 | −0.743892 | ||||||||
\(489\) | −16.9682 | −0.767330 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.5204 | −1.78353 | −0.891766 | − | 0.452496i | \(-0.850534\pi\) | ||||
−0.891766 | + | 0.452496i | \(0.850534\pi\) | |||||||
\(492\) | −0.356466 | −0.0160707 | ||||||||
\(493\) | −15.0883 | −0.679545 | ||||||||
\(494\) | −10.9272 | −0.491638 | ||||||||
\(495\) | −4.93698 | −0.221901 | ||||||||
\(496\) | −1.26172 | −0.0566528 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 22.6325 | 1.01419 | ||||||||
\(499\) | 5.38189 | 0.240927 | 0.120463 | − | 0.992718i | \(-0.461562\pi\) | ||||
0.120463 | + | 0.992718i | \(0.461562\pi\) | |||||||
\(500\) | 1.79533 | 0.0802895 | ||||||||
\(501\) | −18.3793 | −0.821128 | ||||||||
\(502\) | 28.8808 | 1.28901 | ||||||||
\(503\) | 3.46954 | 0.154699 | 0.0773495 | − | 0.997004i | \(-0.475354\pi\) | ||||
0.0773495 | + | 0.997004i | \(0.475354\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.4707 | 0.777437 | ||||||||
\(506\) | 4.11164 | 0.182785 | ||||||||
\(507\) | 17.9044 | 0.795164 | ||||||||
\(508\) | 3.09973 | 0.137528 | ||||||||
\(509\) | −33.7241 | −1.49479 | −0.747397 | − | 0.664378i | \(-0.768696\pi\) | ||||
−0.747397 | + | 0.664378i | \(0.768696\pi\) | |||||||
\(510\) | −27.2917 | −1.20850 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −24.7140 | −1.09221 | ||||||||
\(513\) | −8.34938 | −0.368634 | ||||||||
\(514\) | 11.4729 | 0.506048 | ||||||||
\(515\) | −15.3928 | −0.678287 | ||||||||
\(516\) | −4.52017 | −0.198989 | ||||||||
\(517\) | 8.25302 | 0.362967 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 52.8860 | 2.32144 | ||||||||
\(520\) | −14.5430 | −0.637753 | ||||||||
\(521\) | 8.34928 | 0.365789 | 0.182894 | − | 0.983133i | \(-0.441453\pi\) | ||||
0.182894 | + | 0.983133i | \(0.441453\pi\) | |||||||
\(522\) | −9.91422 | −0.433934 | ||||||||
\(523\) | −12.9946 | −0.568215 | −0.284107 | − | 0.958792i | \(-0.591697\pi\) | ||||
−0.284107 | + | 0.958792i | \(0.591697\pi\) | |||||||
\(524\) | 0.0494548 | 0.00216044 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.69307 | −0.161026 | ||||||||
\(527\) | 1.39951 | 0.0609638 | ||||||||
\(528\) | −9.18837 | −0.399873 | ||||||||
\(529\) | −15.7863 | −0.686361 | ||||||||
\(530\) | −25.2529 | −1.09692 | ||||||||
\(531\) | −10.2595 | −0.445224 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.22790 | −0.0965010 | ||||||||
\(534\) | 47.6389 | 2.06154 | ||||||||
\(535\) | 43.5945 | 1.88476 | ||||||||
\(536\) | 25.8789 | 1.11780 | ||||||||
\(537\) | −25.5216 | −1.10134 | ||||||||
\(538\) | 40.1226 | 1.72981 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.823128 | −0.0354218 | ||||||||
\(541\) | −35.8515 | −1.54137 | −0.770687 | − | 0.637214i | \(-0.780087\pi\) | ||||
−0.770687 | + | 0.637214i | \(0.780087\pi\) | |||||||
\(542\) | 11.0091 | 0.472881 | ||||||||
\(543\) | −39.5491 | −1.69721 | ||||||||
\(544\) | 3.65978 | 0.156912 | ||||||||
\(545\) | 8.73804 | 0.374297 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.4317 | −1.60046 | −0.800232 | − | 0.599691i | \(-0.795290\pi\) | ||||
−0.800232 | + | 0.599691i | \(0.795290\pi\) | |||||||
\(548\) | 2.77882 | 0.118705 | ||||||||
\(549\) | 11.0128 | 0.470013 | ||||||||
\(550\) | 0.0558215 | 0.00238024 | ||||||||
\(551\) | 13.4591 | 0.573376 | ||||||||
\(552\) | −17.5322 | −0.746221 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.48389 | −0.0630447 | ||||||||
\(555\) | −16.6244 | −0.705666 | ||||||||
\(556\) | 2.42424 | 0.102810 | ||||||||
\(557\) | −14.4468 | −0.612131 | −0.306066 | − | 0.952010i | \(-0.599013\pi\) | ||||
−0.306066 | + | 0.952010i | \(0.599013\pi\) | |||||||
\(558\) | 0.919590 | 0.0389294 | ||||||||
\(559\) | −28.2509 | −1.19489 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.1919 | 0.430300 | ||||||||
\(562\) | 10.7841 | 0.454900 | ||||||||
\(563\) | −5.73581 | −0.241736 | −0.120868 | − | 0.992669i | \(-0.538568\pi\) | ||||
−0.120868 | + | 0.992669i | \(0.538568\pi\) | |||||||
\(564\) | −2.60678 | −0.109765 | ||||||||
\(565\) | −11.3801 | −0.478764 | ||||||||
\(566\) | −37.5190 | −1.57704 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −29.0926 | −1.22070 | ||||||||
\(569\) | 11.7364 | 0.492017 | 0.246009 | − | 0.969268i | \(-0.420881\pi\) | ||||
0.246009 | + | 0.969268i | \(0.420881\pi\) | |||||||
\(570\) | 24.3447 | 1.01969 | ||||||||
\(571\) | 7.16254 | 0.299743 | 0.149872 | − | 0.988705i | \(-0.452114\pi\) | ||||
0.149872 | + | 0.988705i | \(0.452114\pi\) | |||||||
\(572\) | 0.402295 | 0.0168208 | ||||||||
\(573\) | −36.6663 | −1.53176 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0979365 | 0.00408423 | ||||||||
\(576\) | 16.7558 | 0.698160 | ||||||||
\(577\) | −29.0407 | −1.20898 | −0.604491 | − | 0.796612i | \(-0.706623\pi\) | ||||
−0.604491 | + | 0.796612i | \(0.706623\pi\) | |||||||
\(578\) | −0.771975 | −0.0321099 | ||||||||
\(579\) | −43.9110 | −1.82488 | ||||||||
\(580\) | 1.32687 | 0.0550953 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 6.37140 | 0.264103 | ||||||||
\(583\) | 9.43049 | 0.390571 | ||||||||
\(584\) | −2.39025 | −0.0989094 | ||||||||
\(585\) | 9.74608 | 0.402951 | ||||||||
\(586\) | −12.9892 | −0.536577 | ||||||||
\(587\) | 8.38291 | 0.346000 | 0.173000 | − | 0.984922i | \(-0.444654\pi\) | ||||
0.173000 | + | 0.984922i | \(0.444654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.24839 | −0.0514391 | ||||||||
\(590\) | −15.7903 | −0.650077 | ||||||||
\(591\) | −28.8495 | −1.18671 | ||||||||
\(592\) | −12.2397 | −0.503048 | ||||||||
\(593\) | 2.29106 | 0.0940824 | 0.0470412 | − | 0.998893i | \(-0.485021\pi\) | ||||
0.0470412 | + | 0.998893i | \(0.485021\pi\) | |||||||
\(594\) | −3.53497 | −0.145042 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.67895 | 0.0687726 | ||||||||
\(597\) | −57.2863 | −2.34457 | ||||||||
\(598\) | −8.11677 | −0.331919 | ||||||||
\(599\) | 6.77016 | 0.276621 | 0.138311 | − | 0.990389i | \(-0.455833\pi\) | ||||
0.138311 | + | 0.990389i | \(0.455833\pi\) | |||||||
\(600\) | −0.238026 | −0.00971736 | ||||||||
\(601\) | −41.3732 | −1.68765 | −0.843824 | − | 0.536619i | \(-0.819701\pi\) | ||||
−0.843824 | + | 0.536619i | \(0.819701\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.3429 | −0.706258 | ||||||||
\(604\) | 0.819123 | 0.0333297 | ||||||||
\(605\) | −21.6693 | −0.880982 | ||||||||
\(606\) | −23.6984 | −0.962683 | ||||||||
\(607\) | −17.5678 | −0.713056 | −0.356528 | − | 0.934285i | \(-0.616040\pi\) | ||||
−0.356528 | + | 0.934285i | \(0.616040\pi\) | |||||||
\(608\) | −3.26459 | −0.132397 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.9497 | 0.686273 | ||||||||
\(611\) | −16.2923 | −0.659115 | ||||||||
\(612\) | −1.27348 | −0.0514773 | ||||||||
\(613\) | −15.5816 | −0.629333 | −0.314666 | − | 0.949202i | \(-0.601893\pi\) | ||||
−0.314666 | + | 0.949202i | \(0.601893\pi\) | |||||||
\(614\) | 11.1792 | 0.451155 | ||||||||
\(615\) | 4.96354 | 0.200149 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.07666 | 0.123862 | 0.0619309 | − | 0.998080i | \(-0.480274\pi\) | ||||
0.0619309 | + | 0.998080i | \(0.480274\pi\) | |||||||
\(618\) | 20.8798 | 0.839908 | ||||||||
\(619\) | −46.9740 | −1.88804 | −0.944021 | − | 0.329885i | \(-0.892990\pi\) | ||||
−0.944021 | + | 0.329885i | \(0.892990\pi\) | |||||||
\(620\) | −0.123073 | −0.00494275 | ||||||||
\(621\) | −6.20196 | −0.248876 | ||||||||
\(622\) | −15.8221 | −0.634409 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 18.1387 | 0.726131 | ||||||||
\(625\) | −24.8163 | −0.992654 | ||||||||
\(626\) | 41.5324 | 1.65997 | ||||||||
\(627\) | −9.09132 | −0.363072 | ||||||||
\(628\) | −2.41534 | −0.0963826 | ||||||||
\(629\) | 13.5764 | 0.541327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.85357 | 0.193218 | 0.0966089 | − | 0.995322i | \(-0.469200\pi\) | ||||
0.0966089 | + | 0.995322i | \(0.469200\pi\) | |||||||
\(632\) | 25.9063 | 1.03050 | ||||||||
\(633\) | −30.0318 | −1.19366 | ||||||||
\(634\) | −28.2303 | −1.12117 | ||||||||
\(635\) | −43.1616 | −1.71281 | ||||||||
\(636\) | −2.97869 | −0.118113 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.69832 | 0.225599 | ||||||||
\(639\) | 19.4966 | 0.771274 | ||||||||
\(640\) | 21.7658 | 0.860371 | ||||||||
\(641\) | −9.57828 | −0.378319 | −0.189160 | − | 0.981946i | \(-0.560576\pi\) | ||||
−0.189160 | + | 0.981946i | \(0.560576\pi\) | |||||||
\(642\) | −59.1345 | −2.33385 | ||||||||
\(643\) | 8.31243 | 0.327810 | 0.163905 | − | 0.986476i | \(-0.447591\pi\) | ||||
0.163905 | + | 0.986476i | \(0.447591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 62.9402 | 2.47827 | ||||||||
\(646\) | −19.8813 | −0.782217 | ||||||||
\(647\) | 20.3902 | 0.801620 | 0.400810 | − | 0.916161i | \(-0.368729\pi\) | ||||
0.400810 | + | 0.916161i | \(0.368729\pi\) | |||||||
\(648\) | 32.3326 | 1.27014 | ||||||||
\(649\) | 5.89676 | 0.231468 | ||||||||
\(650\) | −0.110197 | −0.00432228 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.21860 | −0.0477243 | ||||||||
\(653\) | 15.6258 | 0.611484 | 0.305742 | − | 0.952114i | \(-0.401095\pi\) | ||||
0.305742 | + | 0.952114i | \(0.401095\pi\) | |||||||
\(654\) | −11.8529 | −0.463483 | ||||||||
\(655\) | −0.688623 | −0.0269067 | ||||||||
\(656\) | 3.65440 | 0.142680 | ||||||||
\(657\) | 1.60184 | 0.0624939 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.6929 | 0.767127 | 0.383564 | − | 0.923514i | \(-0.374697\pi\) | ||||
0.383564 | + | 0.923514i | \(0.374697\pi\) | |||||||
\(660\) | −0.896273 | −0.0348874 | ||||||||
\(661\) | −32.8527 | −1.27782 | −0.638910 | − | 0.769281i | \(-0.720614\pi\) | ||||
−0.638910 | + | 0.769281i | \(0.720614\pi\) | |||||||
\(662\) | −0.904763 | −0.0351646 | ||||||||
\(663\) | −20.1197 | −0.781385 | ||||||||
\(664\) | 21.9427 | 0.851543 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.92076 | 0.345673 | ||||||||
\(667\) | 9.99747 | 0.387103 | ||||||||
\(668\) | −1.31995 | −0.0510703 | ||||||||
\(669\) | 5.78588 | 0.223695 | ||||||||
\(670\) | −26.6924 | −1.03122 | ||||||||
\(671\) | −6.32972 | −0.244356 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.56402 | −0.0988358 | −0.0494179 | − | 0.998778i | \(-0.515737\pi\) | ||||
−0.0494179 | + | 0.998778i | \(0.515737\pi\) | |||||||
\(674\) | 0.0911016 | 0.00350910 | ||||||||
\(675\) | −0.0842006 | −0.00324088 | ||||||||
\(676\) | 1.28584 | 0.0494554 | ||||||||
\(677\) | 22.7084 | 0.872753 | 0.436377 | − | 0.899764i | \(-0.356262\pi\) | ||||
0.436377 | + | 0.899764i | \(0.356262\pi\) | |||||||
\(678\) | 15.4367 | 0.592844 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −26.4599 | −1.01469 | ||||||||
\(681\) | 22.5267 | 0.863224 | ||||||||
\(682\) | −0.528546 | −0.0202391 | ||||||||
\(683\) | 39.4613 | 1.50994 | 0.754972 | − | 0.655757i | \(-0.227650\pi\) | ||||
0.754972 | + | 0.655757i | \(0.227650\pi\) | |||||||
\(684\) | 1.13597 | 0.0434347 | ||||||||
\(685\) | −38.6931 | −1.47839 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.2768 | 1.15513 | ||||||||
\(688\) | 46.3396 | 1.76668 | ||||||||
\(689\) | −18.6167 | −0.709240 | ||||||||
\(690\) | 18.0834 | 0.688421 | ||||||||
\(691\) | 25.5873 | 0.973387 | 0.486694 | − | 0.873573i | \(-0.338203\pi\) | ||||
0.486694 | + | 0.873573i | \(0.338203\pi\) | |||||||
\(692\) | 3.79811 | 0.144382 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.6774 | 1.46817 | ||||||||
\(695\) | −33.7558 | −1.28043 | ||||||||
\(696\) | −24.2979 | −0.921011 | ||||||||
\(697\) | −4.05350 | −0.153537 | ||||||||
\(698\) | 41.8600 | 1.58442 | ||||||||
\(699\) | −20.6354 | −0.780503 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.4667 | −1.07517 | −0.537586 | − | 0.843209i | \(-0.680664\pi\) | ||||
−0.537586 | + | 0.843209i | \(0.680664\pi\) | |||||||
\(702\) | 6.97837 | 0.263382 | ||||||||
\(703\) | −12.1104 | −0.456753 | ||||||||
\(704\) | −9.63063 | −0.362968 | ||||||||
\(705\) | 36.2975 | 1.36704 | ||||||||
\(706\) | 25.5909 | 0.963125 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.86253 | −0.0699983 | ||||||||
\(709\) | −18.5889 | −0.698121 | −0.349061 | − | 0.937100i | \(-0.613499\pi\) | ||||
−0.349061 | + | 0.937100i | \(0.613499\pi\) | |||||||
\(710\) | 30.0071 | 1.12615 | ||||||||
\(711\) | −17.3613 | −0.651098 | ||||||||
\(712\) | 46.1870 | 1.73093 | ||||||||
\(713\) | −0.927312 | −0.0347281 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.60168 | −0.209491 | ||||||||
\(716\) | −1.83288 | −0.0684980 | ||||||||
\(717\) | 23.5222 | 0.878454 | ||||||||
\(718\) | −0.878414 | −0.0327821 | ||||||||
\(719\) | 16.6258 | 0.620039 | 0.310020 | − | 0.950730i | \(-0.399664\pi\) | ||||
0.310020 | + | 0.950730i | \(0.399664\pi\) | |||||||
\(720\) | −15.9864 | −0.595777 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.03841 | −0.299158 | ||||||||
\(723\) | −20.0851 | −0.746972 | ||||||||
\(724\) | −2.84029 | −0.105559 | ||||||||
\(725\) | 0.135730 | 0.00504089 | ||||||||
\(726\) | 29.3937 | 1.09090 | ||||||||
\(727\) | −13.5357 | −0.502010 | −0.251005 | − | 0.967986i | \(-0.580761\pi\) | ||||
−0.251005 | + | 0.967986i | \(0.580761\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.23430 | −0.230900 | ||||||||
\(730\) | 2.46539 | 0.0912482 | ||||||||
\(731\) | −51.4005 | −1.90112 | ||||||||
\(732\) | 1.99929 | 0.0738957 | ||||||||
\(733\) | 3.69061 | 0.136316 | 0.0681579 | − | 0.997675i | \(-0.478288\pi\) | ||||
0.0681579 | + | 0.997675i | \(0.478288\pi\) | |||||||
\(734\) | −13.7867 | −0.508875 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.42495 | −0.0893850 | ||||||||
\(737\) | 9.96805 | 0.367178 | ||||||||
\(738\) | −2.66347 | −0.0980437 | ||||||||
\(739\) | 30.2567 | 1.11301 | 0.556505 | − | 0.830844i | \(-0.312142\pi\) | ||||
0.556505 | + | 0.830844i | \(0.312142\pi\) | |||||||
\(740\) | −1.19391 | −0.0438890 | ||||||||
\(741\) | 17.9472 | 0.659305 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.1181 | −1.54516 | −0.772581 | − | 0.634917i | \(-0.781034\pi\) | ||||
−0.772581 | + | 0.634917i | \(0.781034\pi\) | |||||||
\(744\) | 2.25375 | 0.0826264 | ||||||||
\(745\) | −23.3783 | −0.856513 | ||||||||
\(746\) | 9.45317 | 0.346105 | ||||||||
\(747\) | −14.7051 | −0.538030 | ||||||||
\(748\) | 0.731947 | 0.0267626 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 33.9098 | 1.23821 | ||||||||
\(751\) | −19.2262 | −0.701573 | −0.350786 | − | 0.936456i | \(-0.614086\pi\) | ||||
−0.350786 | + | 0.936456i | \(0.614086\pi\) | |||||||
\(752\) | 26.7240 | 0.974525 | ||||||||
\(753\) | −47.4347 | −1.72862 | ||||||||
\(754\) | −11.2490 | −0.409666 | ||||||||
\(755\) | −11.4057 | −0.415097 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.23128 | 0.226480 | 0.113240 | − | 0.993568i | \(-0.463877\pi\) | ||||
0.113240 | + | 0.993568i | \(0.463877\pi\) | |||||||
\(758\) | −49.4558 | −1.79631 | ||||||||
\(759\) | −6.75308 | −0.245121 | ||||||||
\(760\) | 23.6028 | 0.856162 | ||||||||
\(761\) | −28.5205 | −1.03387 | −0.516933 | − | 0.856026i | \(-0.672927\pi\) | ||||
−0.516933 | + | 0.856026i | \(0.672927\pi\) | |||||||
\(762\) | 58.5472 | 2.12094 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.63326 | −0.0952681 | ||||||||
\(765\) | 17.7323 | 0.641113 | ||||||||
\(766\) | −27.3713 | −0.988966 | ||||||||
\(767\) | −11.6408 | −0.420324 | ||||||||
\(768\) | 8.49896 | 0.306680 | ||||||||
\(769\) | 13.9303 | 0.502340 | 0.251170 | − | 0.967943i | \(-0.419185\pi\) | ||||
0.251170 | + | 0.967943i | \(0.419185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.8434 | −0.678629 | ||||||||
\(772\) | −3.15355 | −0.113499 | ||||||||
\(773\) | 39.7945 | 1.43131 | 0.715654 | − | 0.698455i | \(-0.246129\pi\) | ||||
0.715654 | + | 0.698455i | \(0.246129\pi\) | |||||||
\(774\) | −33.7741 | −1.21399 | ||||||||
\(775\) | −0.0125896 | −0.000452232 0 | ||||||||
\(776\) | 6.17722 | 0.221749 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.7403 | −0.886984 | ||||||||
\(779\) | 3.61580 | 0.129549 | ||||||||
\(780\) | 1.76933 | 0.0633522 | ||||||||
\(781\) | −11.2059 | −0.400979 | ||||||||
\(782\) | −14.7679 | −0.528099 | ||||||||
\(783\) | −8.59530 | −0.307171 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.6319 | 1.20038 | ||||||||
\(786\) | 0.934093 | 0.0333180 | ||||||||
\(787\) | −22.0699 | −0.786708 | −0.393354 | − | 0.919387i | \(-0.628685\pi\) | ||||
−0.393354 | + | 0.919387i | \(0.628685\pi\) | |||||||
\(788\) | −2.07188 | −0.0738077 | ||||||||
\(789\) | 6.06561 | 0.215942 | ||||||||
\(790\) | −26.7206 | −0.950678 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.49275 | 0.230710 | ||||||||
\(793\) | 12.4955 | 0.443727 | ||||||||
\(794\) | 51.1034 | 1.81359 | ||||||||
\(795\) | 41.4762 | 1.47101 | ||||||||
\(796\) | −4.11412 | −0.145821 | ||||||||
\(797\) | 13.9948 | 0.495720 | 0.247860 | − | 0.968796i | \(-0.420273\pi\) | ||||
0.247860 | + | 0.968796i | \(0.420273\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.6426 | −1.04868 | ||||||||
\(800\) | −0.0329223 | −0.00116398 | ||||||||
\(801\) | −30.9525 | −1.09365 | ||||||||
\(802\) | −34.7570 | −1.22731 | ||||||||
\(803\) | −0.920679 | −0.0324901 | ||||||||
\(804\) | −3.14848 | −0.111038 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.04340 | 0.0367522 | ||||||||
\(807\) | −65.8986 | −2.31974 | ||||||||
\(808\) | −22.9762 | −0.808300 | ||||||||
\(809\) | −5.29163 | −0.186044 | −0.0930219 | − | 0.995664i | \(-0.529653\pi\) | ||||
−0.0930219 | + | 0.995664i | \(0.529653\pi\) | |||||||
\(810\) | −33.3489 | −1.17176 | ||||||||
\(811\) | −19.4147 | −0.681744 | −0.340872 | − | 0.940110i | \(-0.610722\pi\) | ||||
−0.340872 | + | 0.940110i | \(0.610722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.0817 | −0.634151 | ||||||||
\(814\) | −5.12732 | −0.179712 | ||||||||
\(815\) | 16.9682 | 0.594371 | ||||||||
\(816\) | 33.0021 | 1.15531 | ||||||||
\(817\) | 45.8502 | 1.60409 | ||||||||
\(818\) | −5.54979 | −0.194044 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.356466 | 0.0124483 | ||||||||
\(821\) | −3.44679 | −0.120294 | −0.0601470 | − | 0.998190i | \(-0.519157\pi\) | ||||
−0.0601470 | + | 0.998190i | \(0.519157\pi\) | |||||||
\(822\) | 52.4859 | 1.83066 | ||||||||
\(823\) | 39.7137 | 1.38433 | 0.692166 | − | 0.721738i | \(-0.256657\pi\) | ||||
0.692166 | + | 0.721738i | \(0.256657\pi\) | |||||||
\(824\) | 20.2434 | 0.705214 | ||||||||
\(825\) | −0.0916828 | −0.00319199 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.66589 | 0.127475 | 0.0637377 | − | 0.997967i | \(-0.479698\pi\) | ||||
0.0637377 | + | 0.997967i | \(0.479698\pi\) | |||||||
\(828\) | 0.843801 | 0.0293241 | ||||||||
\(829\) | 5.76355 | 0.200176 | 0.100088 | − | 0.994979i | \(-0.468088\pi\) | ||||
0.100088 | + | 0.994979i | \(0.468088\pi\) | |||||||
\(830\) | −22.6325 | −0.785585 | ||||||||
\(831\) | 2.43719 | 0.0845453 | ||||||||
\(832\) | 19.0118 | 0.659115 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 45.7886 | 1.58553 | ||||||||
\(835\) | 18.3793 | 0.636043 | ||||||||
\(836\) | −0.652910 | −0.0225814 | ||||||||
\(837\) | 0.797254 | 0.0275571 | ||||||||
\(838\) | −45.7582 | −1.58069 | ||||||||
\(839\) | 2.49460 | 0.0861232 | 0.0430616 | − | 0.999072i | \(-0.486289\pi\) | ||||
0.0430616 | + | 0.999072i | \(0.486289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.1445 | −0.522224 | ||||||||
\(842\) | 1.09100 | 0.0375983 | ||||||||
\(843\) | −17.7121 | −0.610038 | ||||||||
\(844\) | −2.15679 | −0.0742398 | ||||||||
\(845\) | −17.9044 | −0.615931 | ||||||||
\(846\) | −19.4775 | −0.669651 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 30.5368 | 1.04864 | ||||||||
\(849\) | 61.6223 | 2.11487 | ||||||||
\(850\) | −0.200496 | −0.00687694 | ||||||||
\(851\) | −8.99566 | −0.308367 | ||||||||
\(852\) | 3.53947 | 0.121260 | ||||||||
\(853\) | 34.6227 | 1.18546 | 0.592729 | − | 0.805402i | \(-0.298051\pi\) | ||||
0.592729 | + | 0.805402i | \(0.298051\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.8175 | −0.540948 | ||||||||
\(856\) | −57.3323 | −1.95958 | ||||||||
\(857\) | 2.42362 | 0.0827891 | 0.0413946 | − | 0.999143i | \(-0.486820\pi\) | ||||
0.0413946 | + | 0.999143i | \(0.486820\pi\) | |||||||
\(858\) | 7.59849 | 0.259408 | ||||||||
\(859\) | −42.1876 | −1.43942 | −0.719711 | − | 0.694274i | \(-0.755726\pi\) | ||||
−0.719711 | + | 0.694274i | \(0.755726\pi\) | |||||||
\(860\) | 4.52017 | 0.154136 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −54.0252 | −1.84011 | ||||||||
\(863\) | 50.2649 | 1.71104 | 0.855519 | − | 0.517771i | \(-0.173238\pi\) | ||||
0.855519 | + | 0.517771i | \(0.173238\pi\) | |||||||
\(864\) | 2.08485 | 0.0709279 | ||||||||
\(865\) | −52.8860 | −1.79818 | ||||||||
\(866\) | −8.24684 | −0.280239 | ||||||||
\(867\) | 1.26791 | 0.0430606 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.97860 | 0.338501 | ||||||||
\(870\) | 25.0617 | 0.849672 | ||||||||
\(871\) | −19.6779 | −0.666760 | ||||||||
\(872\) | −11.4916 | −0.389155 | ||||||||
\(873\) | −4.13970 | −0.140108 | ||||||||
\(874\) | 13.1732 | 0.445591 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.290803 | 0.00982533 | ||||||||
\(877\) | 10.6100 | 0.358275 | 0.179137 | − | 0.983824i | \(-0.442669\pi\) | ||||
0.179137 | + | 0.983824i | \(0.442669\pi\) | |||||||
\(878\) | 54.3806 | 1.83526 | ||||||||
\(879\) | 21.3338 | 0.719571 | ||||||||
\(880\) | 9.18837 | 0.309740 | ||||||||
\(881\) | 2.45538 | 0.0827238 | 0.0413619 | − | 0.999144i | \(-0.486830\pi\) | ||||
0.0413619 | + | 0.999144i | \(0.486830\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.5296 | −1.59950 | −0.799750 | − | 0.600333i | \(-0.795035\pi\) | ||||
−0.799750 | + | 0.600333i | \(0.795035\pi\) | |||||||
\(884\) | −1.44494 | −0.0485984 | ||||||||
\(885\) | 25.9345 | 0.871779 | ||||||||
\(886\) | 24.5277 | 0.824025 | ||||||||
\(887\) | −4.34818 | −0.145998 | −0.0729988 | − | 0.997332i | \(-0.523257\pi\) | ||||
−0.0729988 | + | 0.997332i | \(0.523257\pi\) | |||||||
\(888\) | 21.8631 | 0.733679 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −47.6389 | −1.59686 | ||||||||
\(891\) | 12.4539 | 0.417221 | ||||||||
\(892\) | 0.415524 | 0.0139128 | ||||||||
\(893\) | 26.4418 | 0.884840 | ||||||||
\(894\) | 31.7118 | 1.06060 | ||||||||
\(895\) | 25.5216 | 0.853093 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.3312 | 0.445117 | ||||||||
\(898\) | −15.4695 | −0.516223 | ||||||||
\(899\) | −1.28516 | −0.0428625 | ||||||||
\(900\) | 0.0114558 | 0.000381861 0 | ||||||||
\(901\) | −33.8718 | −1.12843 | ||||||||
\(902\) | 1.53086 | 0.0509721 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.9663 | 0.497770 | ||||||||
\(905\) | 39.5491 | 1.31466 | ||||||||
\(906\) | 15.4715 | 0.514005 | ||||||||
\(907\) | 12.9887 | 0.431282 | 0.215641 | − | 0.976473i | \(-0.430816\pi\) | ||||
0.215641 | + | 0.976473i | \(0.430816\pi\) | |||||||
\(908\) | 1.61780 | 0.0536884 | ||||||||
\(909\) | 15.3976 | 0.510707 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.4395 | −0.511535 | −0.255767 | − | 0.966738i | \(-0.582328\pi\) | ||||
−0.255767 | + | 0.966738i | \(0.582328\pi\) | |||||||
\(912\) | −29.4385 | −0.974806 | ||||||||
\(913\) | 8.45192 | 0.279718 | ||||||||
\(914\) | 38.2192 | 1.26418 | ||||||||
\(915\) | −27.8387 | −0.920318 | ||||||||
\(916\) | 2.17438 | 0.0718437 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12.6967 | 0.419052 | ||||||||
\(919\) | 40.2229 | 1.32683 | 0.663415 | − | 0.748252i | \(-0.269106\pi\) | ||||
0.663415 | + | 0.748252i | \(0.269106\pi\) | |||||||
\(920\) | 17.5322 | 0.578021 | ||||||||
\(921\) | −18.3610 | −0.605016 | ||||||||
\(922\) | 40.1929 | 1.32368 | ||||||||
\(923\) | 22.1216 | 0.728140 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.122129 | −0.00401559 | ||||||||
\(926\) | 39.5280 | 1.29897 | ||||||||
\(927\) | −13.5663 | −0.445575 | ||||||||
\(928\) | −3.36074 | −0.110322 | ||||||||
\(929\) | 13.5103 | 0.443258 | 0.221629 | − | 0.975131i | \(-0.428863\pi\) | ||||
0.221629 | + | 0.975131i | \(0.428863\pi\) | |||||||
\(930\) | −2.32459 | −0.0762264 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.48197 | −0.0485436 | ||||||||
\(933\) | 25.9867 | 0.850767 | ||||||||
\(934\) | 21.5123 | 0.703905 | ||||||||
\(935\) | −10.1919 | −0.333309 | ||||||||
\(936\) | −12.8173 | −0.418947 | ||||||||
\(937\) | −35.6590 | −1.16493 | −0.582465 | − | 0.812856i | \(-0.697912\pi\) | ||||
−0.582465 | + | 0.812856i | \(0.697912\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −68.2141 | −2.22608 | ||||||||
\(940\) | 2.60678 | 0.0850237 | ||||||||
\(941\) | −13.8134 | −0.450305 | −0.225153 | − | 0.974323i | \(-0.572288\pi\) | ||||
−0.225153 | + | 0.974323i | \(0.572288\pi\) | |||||||
\(942\) | −45.6206 | −1.48640 | ||||||||
\(943\) | 2.68583 | 0.0874627 | ||||||||
\(944\) | 19.0942 | 0.621465 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.4121 | 0.631142 | ||||||||
\(947\) | 53.4437 | 1.73669 | 0.868343 | − | 0.495965i | \(-0.165185\pi\) | ||||
0.868343 | + | 0.495965i | \(0.165185\pi\) | |||||||
\(948\) | −3.15181 | −0.102366 | ||||||||
\(949\) | 1.81751 | 0.0589989 | ||||||||
\(950\) | 0.178846 | 0.00580252 | ||||||||
\(951\) | 46.3663 | 1.50353 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.4781 | 1.40840 | 0.704198 | − | 0.710004i | \(-0.251307\pi\) | ||||
0.704198 | + | 0.710004i | \(0.251307\pi\) | |||||||
\(954\) | −22.2564 | −0.720578 | ||||||||
\(955\) | 36.6663 | 1.18649 | ||||||||
\(956\) | 1.68929 | 0.0546356 | ||||||||
\(957\) | −9.35909 | −0.302536 | ||||||||
\(958\) | 4.98951 | 0.161204 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −42.3564 | −1.36705 | ||||||||
\(961\) | −30.8808 | −0.996155 | ||||||||
\(962\) | 10.1218 | 0.326341 | ||||||||
\(963\) | 38.4216 | 1.23812 | ||||||||
\(964\) | −1.44245 | −0.0464581 | ||||||||
\(965\) | 43.9110 | 1.41355 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −60.5248 | −1.94635 | −0.973173 | − | 0.230075i | \(-0.926103\pi\) | ||||
−0.973173 | + | 0.230075i | \(0.926103\pi\) | |||||||
\(968\) | 28.4978 | 0.915956 | ||||||||
\(969\) | 32.6536 | 1.04898 | ||||||||
\(970\) | −6.37140 | −0.204573 | ||||||||
\(971\) | 16.3175 | 0.523653 | 0.261826 | − | 0.965115i | \(-0.415675\pi\) | ||||
0.261826 | + | 0.965115i | \(0.415675\pi\) | |||||||
\(972\) | −2.82526 | −0.0906201 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 39.3124 | 1.25965 | ||||||||
\(975\) | 0.180991 | 0.00579635 | ||||||||
\(976\) | −20.4962 | −0.656067 | ||||||||
\(977\) | −14.1551 | −0.452862 | −0.226431 | − | 0.974027i | \(-0.572706\pi\) | ||||
−0.226431 | + | 0.974027i | \(0.572706\pi\) | |||||||
\(978\) | −23.0168 | −0.735997 | ||||||||
\(979\) | 17.7903 | 0.568582 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.70118 | 0.245880 | ||||||||
\(982\) | −53.6081 | −1.71070 | ||||||||
\(983\) | 25.3167 | 0.807476 | 0.403738 | − | 0.914875i | \(-0.367711\pi\) | ||||
0.403738 | + | 0.914875i | \(0.367711\pi\) | |||||||
\(984\) | −6.52767 | −0.208095 | ||||||||
\(985\) | 28.8495 | 0.919222 | ||||||||
\(986\) | −20.4668 | −0.651796 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.28891 | 0.0410056 | ||||||||
\(989\) | 34.0577 | 1.08297 | ||||||||
\(990\) | −6.69685 | −0.212840 | ||||||||
\(991\) | −35.8520 | −1.13887 | −0.569437 | − | 0.822035i | \(-0.692839\pi\) | ||||
−0.569437 | + | 0.822035i | \(0.692839\pi\) | |||||||
\(992\) | 0.311725 | 0.00989727 | ||||||||
\(993\) | 1.48601 | 0.0471571 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 57.2863 | 1.81610 | ||||||||
\(996\) | −2.66960 | −0.0845894 | ||||||||
\(997\) | 23.4249 | 0.741873 | 0.370937 | − | 0.928658i | \(-0.379037\pi\) | ||||
0.370937 | + | 0.928658i | \(0.379037\pi\) | |||||||
\(998\) | 7.30035 | 0.231089 | ||||||||
\(999\) | 7.73400 | 0.244693 |
(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 | 2009.2.a.l.1.4 | 5 | ||
7.2 | even | 3 | 287.2.e.c.165.2 | ✓ | 10 | ||
7.4 | even | 3 | 287.2.e.c.247.2 | yes | 10 | ||
7.6 | odd | 2 | 2009.2.a.m.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.c.165.2 | ✓ | 10 | 7.2 | even | 3 | ||
287.2.e.c.247.2 | yes | 10 | 7.4 | even | 3 | ||
2009.2.a.l.1.4 | 5 | 1.1 | even | 1 | trivial | ||
2009.2.a.m.1.4 | 5 | 7.6 | odd | 2 |