Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,2,Mod(1,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, 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("1617.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.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: | \(12.9118100068\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.28734\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1617.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28734 | 0.910284 | 0.455142 | − | 0.890419i | \(-0.349589\pi\) | ||||
0.455142 | + | 0.890419i | \(0.349589\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.342766 | −0.171383 | ||||||||
\(5\) | 3.91744 | 1.75193 | 0.875966 | − | 0.482373i | \(-0.160225\pi\) | ||||
0.875966 | + | 0.482373i | \(0.160225\pi\) | |||||||
\(6\) | 1.28734 | 0.525553 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.01593 | −1.06629 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 5.04306 | 1.59476 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.342766 | −0.0989482 | ||||||||
\(13\) | −3.04306 | −0.843993 | −0.421996 | − | 0.906598i | \(-0.638670\pi\) | ||||
−0.421996 | + | 0.906598i | \(0.638670\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.91744 | 1.01148 | ||||||||
\(16\) | −3.19698 | −0.799245 | ||||||||
\(17\) | 3.97287 | 0.963562 | 0.481781 | − | 0.876292i | \(-0.339990\pi\) | ||||
0.481781 | + | 0.876292i | \(0.339990\pi\) | |||||||
\(18\) | 1.28734 | 0.303428 | ||||||||
\(19\) | 7.59060 | 1.74140 | 0.870701 | − | 0.491812i | \(-0.163665\pi\) | ||||
0.870701 | + | 0.491812i | \(0.163665\pi\) | |||||||
\(20\) | −1.34277 | −0.300252 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.28734 | −0.274461 | ||||||||
\(23\) | 4.51145 | 0.940701 | 0.470351 | − | 0.882480i | \(-0.344127\pi\) | ||||
0.470351 | + | 0.882480i | \(0.344127\pi\) | |||||||
\(24\) | −3.01593 | −0.615624 | ||||||||
\(25\) | 10.3463 | 2.06926 | ||||||||
\(26\) | −3.91744 | −0.768273 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.75572 | 0.697420 | 0.348710 | − | 0.937231i | \(-0.386620\pi\) | ||||
0.348710 | + | 0.937231i | \(0.386620\pi\) | |||||||
\(30\) | 5.04306 | 0.920732 | ||||||||
\(31\) | −6.74335 | −1.21114 | −0.605571 | − | 0.795791i | \(-0.707055\pi\) | ||||
−0.605571 | + | 0.795791i | \(0.707055\pi\) | |||||||
\(32\) | 1.91627 | 0.338752 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 5.11442 | 0.877115 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.342766 | −0.0571277 | ||||||||
\(37\) | 0.342766 | 0.0563505 | 0.0281752 | − | 0.999603i | \(-0.491030\pi\) | ||||
0.0281752 | + | 0.999603i | \(0.491030\pi\) | |||||||
\(38\) | 9.77165 | 1.58517 | ||||||||
\(39\) | −3.04306 | −0.487279 | ||||||||
\(40\) | −11.8147 | −1.86807 | ||||||||
\(41\) | −2.79182 | −0.436009 | −0.218004 | − | 0.975948i | \(-0.569955\pi\) | ||||
−0.218004 | + | 0.975948i | \(0.569955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.1222 | 1.69612 | 0.848061 | − | 0.529899i | \(-0.177770\pi\) | ||||
0.848061 | + | 0.529899i | \(0.177770\pi\) | |||||||
\(44\) | 0.342766 | 0.0516740 | ||||||||
\(45\) | 3.91744 | 0.583977 | ||||||||
\(46\) | 5.80775 | 0.856305 | ||||||||
\(47\) | 1.65723 | 0.241732 | 0.120866 | − | 0.992669i | \(-0.461433\pi\) | ||||
0.120866 | + | 0.992669i | \(0.461433\pi\) | |||||||
\(48\) | −3.19698 | −0.461444 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.3192 | 1.88362 | ||||||||
\(51\) | 3.97287 | 0.556313 | ||||||||
\(52\) | 1.04306 | 0.144646 | ||||||||
\(53\) | −12.9403 | −1.77749 | −0.888745 | − | 0.458401i | \(-0.848422\pi\) | ||||
−0.888745 | + | 0.458401i | \(0.848422\pi\) | |||||||
\(54\) | 1.28734 | 0.175184 | ||||||||
\(55\) | −3.91744 | −0.528227 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.59060 | 1.00540 | ||||||||
\(58\) | 4.83488 | 0.634850 | ||||||||
\(59\) | −3.66079 | −0.476594 | −0.238297 | − | 0.971192i | \(-0.576589\pi\) | ||||
−0.238297 | + | 0.971192i | \(0.576589\pi\) | |||||||
\(60\) | −1.34277 | −0.173350 | ||||||||
\(61\) | −0.468387 | −0.0599708 | −0.0299854 | − | 0.999550i | \(-0.509546\pi\) | ||||
−0.0299854 | + | 0.999550i | \(0.509546\pi\) | |||||||
\(62\) | −8.68096 | −1.10248 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.86084 | 1.10760 | ||||||||
\(65\) | −11.9210 | −1.47862 | ||||||||
\(66\) | −1.28734 | −0.158460 | ||||||||
\(67\) | −2.57823 | −0.314981 | −0.157490 | − | 0.987521i | \(-0.550340\pi\) | ||||
−0.157490 | + | 0.987521i | \(0.550340\pi\) | |||||||
\(68\) | −1.36177 | −0.165138 | ||||||||
\(69\) | 4.51145 | 0.543114 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.00355 | −0.593813 | −0.296906 | − | 0.954907i | \(-0.595955\pi\) | ||||
−0.296906 | + | 0.954907i | \(0.595955\pi\) | |||||||
\(72\) | −3.01593 | −0.355430 | ||||||||
\(73\) | −8.73756 | −1.02265 | −0.511327 | − | 0.859386i | \(-0.670846\pi\) | ||||
−0.511327 | + | 0.859386i | \(0.670846\pi\) | |||||||
\(74\) | 0.441256 | 0.0512949 | ||||||||
\(75\) | 10.3463 | 1.19469 | ||||||||
\(76\) | −2.60180 | −0.298447 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.91744 | −0.443563 | ||||||||
\(79\) | 0.719627 | 0.0809644 | 0.0404822 | − | 0.999180i | \(-0.487111\pi\) | ||||
0.0404822 | + | 0.999180i | \(0.487111\pi\) | |||||||
\(80\) | −12.5240 | −1.40022 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.59401 | −0.396892 | ||||||||
\(83\) | −11.5976 | −1.27300 | −0.636499 | − | 0.771278i | \(-0.719618\pi\) | ||||
−0.636499 | + | 0.771278i | \(0.719618\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.5635 | 1.68810 | ||||||||
\(86\) | 14.3180 | 1.54395 | ||||||||
\(87\) | 3.75572 | 0.402656 | ||||||||
\(88\) | 3.01593 | 0.321499 | ||||||||
\(89\) | −12.3553 | −1.30966 | −0.654829 | − | 0.755777i | \(-0.727259\pi\) | ||||
−0.654829 | + | 0.755777i | \(0.727259\pi\) | |||||||
\(90\) | 5.04306 | 0.531585 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.54637 | −0.161220 | ||||||||
\(93\) | −6.74335 | −0.699253 | ||||||||
\(94\) | 2.13342 | 0.220045 | ||||||||
\(95\) | 29.7357 | 3.05082 | ||||||||
\(96\) | 1.91627 | 0.195578 | ||||||||
\(97\) | −13.1687 | −1.33708 | −0.668538 | − | 0.743678i | \(-0.733080\pi\) | ||||
−0.668538 | + | 0.743678i | \(0.733080\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −3.54637 | −0.354637 | ||||||||
\(101\) | 7.07019 | 0.703510 | 0.351755 | − | 0.936092i | \(-0.385585\pi\) | ||||
0.351755 | + | 0.936092i | \(0.385585\pi\) | |||||||
\(102\) | 5.11442 | 0.506403 | ||||||||
\(103\) | 2.33736 | 0.230307 | 0.115153 | − | 0.993348i | \(-0.463264\pi\) | ||||
0.115153 | + | 0.993348i | \(0.463264\pi\) | |||||||
\(104\) | 9.17764 | 0.899942 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.6585 | −1.61802 | ||||||||
\(107\) | −10.8532 | −1.04922 | −0.524609 | − | 0.851343i | \(-0.675788\pi\) | ||||
−0.524609 | + | 0.851343i | \(0.675788\pi\) | |||||||
\(108\) | −0.342766 | −0.0329827 | ||||||||
\(109\) | −2.19240 | −0.209994 | −0.104997 | − | 0.994473i | \(-0.533483\pi\) | ||||
−0.104997 | + | 0.994473i | \(0.533483\pi\) | |||||||
\(110\) | −5.04306 | −0.480837 | ||||||||
\(111\) | 0.342766 | 0.0325340 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.6415 | −1.09514 | −0.547568 | − | 0.836761i | \(-0.684446\pi\) | ||||
−0.547568 | + | 0.836761i | \(0.684446\pi\) | |||||||
\(114\) | 9.77165 | 0.915199 | ||||||||
\(115\) | 17.6733 | 1.64804 | ||||||||
\(116\) | −1.28734 | −0.119526 | ||||||||
\(117\) | −3.04306 | −0.281331 | ||||||||
\(118\) | −4.71266 | −0.433836 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −11.8147 | −1.07853 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.602971 | −0.0545904 | ||||||||
\(123\) | −2.79182 | −0.251730 | ||||||||
\(124\) | 2.31139 | 0.207569 | ||||||||
\(125\) | 20.9439 | 1.87328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.41837 | 0.480802 | 0.240401 | − | 0.970674i | \(-0.422721\pi\) | ||||
0.240401 | + | 0.970674i | \(0.422721\pi\) | |||||||
\(128\) | 7.57434 | 0.669483 | ||||||||
\(129\) | 11.1222 | 0.979256 | ||||||||
\(130\) | −15.3463 | −1.34596 | ||||||||
\(131\) | −2.06595 | −0.180503 | −0.0902514 | − | 0.995919i | \(-0.528767\pi\) | ||||
−0.0902514 | + | 0.995919i | \(0.528767\pi\) | |||||||
\(132\) | 0.342766 | 0.0298340 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.31904 | −0.286722 | ||||||||
\(135\) | 3.91744 | 0.337159 | ||||||||
\(136\) | −11.9819 | −1.02744 | ||||||||
\(137\) | −4.18305 | −0.357382 | −0.178691 | − | 0.983905i | \(-0.557186\pi\) | ||||
−0.178691 | + | 0.983905i | \(0.557186\pi\) | |||||||
\(138\) | 5.80775 | 0.494388 | ||||||||
\(139\) | 3.61077 | 0.306261 | 0.153131 | − | 0.988206i | \(-0.451064\pi\) | ||||
0.153131 | + | 0.988206i | \(0.451064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.65723 | 0.139564 | ||||||||
\(142\) | −6.44126 | −0.540538 | ||||||||
\(143\) | 3.04306 | 0.254473 | ||||||||
\(144\) | −3.19698 | −0.266415 | ||||||||
\(145\) | 14.7128 | 1.22183 | ||||||||
\(146\) | −11.2482 | −0.930905 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.117489 | −0.00965752 | ||||||||
\(149\) | 13.3192 | 1.09115 | 0.545575 | − | 0.838062i | \(-0.316311\pi\) | ||||
0.545575 | + | 0.838062i | \(0.316311\pi\) | |||||||
\(150\) | 13.3192 | 1.08751 | ||||||||
\(151\) | −7.04321 | −0.573168 | −0.286584 | − | 0.958055i | \(-0.592520\pi\) | ||||
−0.286584 | + | 0.958055i | \(0.592520\pi\) | |||||||
\(152\) | −22.8927 | −1.85684 | ||||||||
\(153\) | 3.97287 | 0.321187 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −26.4167 | −2.12184 | ||||||||
\(156\) | 1.04306 | 0.0835115 | ||||||||
\(157\) | 12.7559 | 1.01803 | 0.509015 | − | 0.860758i | \(-0.330010\pi\) | ||||
0.509015 | + | 0.860758i | \(0.330010\pi\) | |||||||
\(158\) | 0.926402 | 0.0737006 | ||||||||
\(159\) | −12.9403 | −1.02623 | ||||||||
\(160\) | 7.50687 | 0.593470 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.28734 | 0.101143 | ||||||||
\(163\) | 11.4041 | 0.893241 | 0.446621 | − | 0.894723i | \(-0.352627\pi\) | ||||
0.446621 | + | 0.894723i | \(0.352627\pi\) | |||||||
\(164\) | 0.956942 | 0.0747246 | ||||||||
\(165\) | −3.91744 | −0.304972 | ||||||||
\(166\) | −14.9300 | −1.15879 | ||||||||
\(167\) | 12.1109 | 0.937167 | 0.468583 | − | 0.883419i | \(-0.344765\pi\) | ||||
0.468583 | + | 0.883419i | \(0.344765\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.73980 | −0.287677 | ||||||||
\(170\) | 20.0354 | 1.53665 | ||||||||
\(171\) | 7.59060 | 0.580468 | ||||||||
\(172\) | −3.81232 | −0.290687 | ||||||||
\(173\) | 3.64247 | 0.276932 | 0.138466 | − | 0.990367i | \(-0.455783\pi\) | ||||
0.138466 | + | 0.990367i | \(0.455783\pi\) | |||||||
\(174\) | 4.83488 | 0.366531 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.19698 | 0.240981 | ||||||||
\(177\) | −3.66079 | −0.275162 | ||||||||
\(178\) | −15.9054 | −1.19216 | ||||||||
\(179\) | 9.92640 | 0.741934 | 0.370967 | − | 0.928646i | \(-0.379026\pi\) | ||||
0.370967 | + | 0.928646i | \(0.379026\pi\) | |||||||
\(180\) | −1.34277 | −0.100084 | ||||||||
\(181\) | −8.07219 | −0.600001 | −0.300001 | − | 0.953939i | \(-0.596987\pi\) | ||||
−0.300001 | + | 0.953939i | \(0.596987\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.468387 | −0.0346241 | ||||||||
\(184\) | −13.6062 | −1.00306 | ||||||||
\(185\) | 1.34277 | 0.0987222 | ||||||||
\(186\) | −8.68096 | −0.636519 | ||||||||
\(187\) | −3.97287 | −0.290525 | ||||||||
\(188\) | −0.568044 | −0.0414289 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 38.2798 | 2.77711 | ||||||||
\(191\) | 5.58364 | 0.404018 | 0.202009 | − | 0.979384i | \(-0.435253\pi\) | ||||
0.202009 | + | 0.979384i | \(0.435253\pi\) | |||||||
\(192\) | 8.86084 | 0.639476 | ||||||||
\(193\) | 11.1338 | 0.801425 | 0.400712 | − | 0.916204i | \(-0.368763\pi\) | ||||
0.400712 | + | 0.916204i | \(0.368763\pi\) | |||||||
\(194\) | −16.9525 | −1.21712 | ||||||||
\(195\) | −11.9210 | −0.853680 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.644475 | −0.0459170 | −0.0229585 | − | 0.999736i | \(-0.507309\pi\) | ||||
−0.0229585 | + | 0.999736i | \(0.507309\pi\) | |||||||
\(198\) | −1.28734 | −0.0914870 | ||||||||
\(199\) | −25.2355 | −1.78889 | −0.894447 | − | 0.447174i | \(-0.852431\pi\) | ||||
−0.894447 | + | 0.447174i | \(0.852431\pi\) | |||||||
\(200\) | −31.2038 | −2.20644 | ||||||||
\(201\) | −2.57823 | −0.181854 | ||||||||
\(202\) | 9.10171 | 0.640394 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.36177 | −0.0953427 | ||||||||
\(205\) | −10.9368 | −0.763857 | ||||||||
\(206\) | 3.00896 | 0.209644 | ||||||||
\(207\) | 4.51145 | 0.313567 | ||||||||
\(208\) | 9.72859 | 0.674556 | ||||||||
\(209\) | −7.59060 | −0.525053 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.6357 | −1.21409 | −0.607044 | − | 0.794668i | \(-0.707645\pi\) | ||||
−0.607044 | + | 0.794668i | \(0.707645\pi\) | |||||||
\(212\) | 4.43551 | 0.304632 | ||||||||
\(213\) | −5.00355 | −0.342838 | ||||||||
\(214\) | −13.9717 | −0.955086 | ||||||||
\(215\) | 43.5706 | 2.97149 | ||||||||
\(216\) | −3.01593 | −0.205208 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.82236 | −0.191154 | ||||||||
\(219\) | −8.73756 | −0.590429 | ||||||||
\(220\) | 1.34277 | 0.0905293 | ||||||||
\(221\) | −12.0897 | −0.813239 | ||||||||
\(222\) | 0.441256 | 0.0296151 | ||||||||
\(223\) | 16.5853 | 1.11064 | 0.555318 | − | 0.831638i | \(-0.312596\pi\) | ||||
0.555318 | + | 0.831638i | \(0.312596\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.3463 | 0.689755 | ||||||||
\(226\) | −14.9865 | −0.996884 | ||||||||
\(227\) | −2.34818 | −0.155854 | −0.0779269 | − | 0.996959i | \(-0.524830\pi\) | ||||
−0.0779269 | + | 0.996959i | \(0.524830\pi\) | |||||||
\(228\) | −2.60180 | −0.172309 | ||||||||
\(229\) | −17.4504 | −1.15315 | −0.576576 | − | 0.817043i | \(-0.695612\pi\) | ||||
−0.576576 | + | 0.817043i | \(0.695612\pi\) | |||||||
\(230\) | 22.7515 | 1.50019 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.3270 | −0.743653 | ||||||||
\(233\) | −5.59060 | −0.366252 | −0.183126 | − | 0.983089i | \(-0.558622\pi\) | ||||
−0.183126 | + | 0.983089i | \(0.558622\pi\) | |||||||
\(234\) | −3.91744 | −0.256091 | ||||||||
\(235\) | 6.49211 | 0.423499 | ||||||||
\(236\) | 1.25480 | 0.0816802 | ||||||||
\(237\) | 0.719627 | 0.0467448 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.8147 | 1.15234 | 0.576169 | − | 0.817331i | \(-0.304547\pi\) | ||||
0.576169 | + | 0.817331i | \(0.304547\pi\) | |||||||
\(240\) | −12.5240 | −0.808418 | ||||||||
\(241\) | 2.98422 | 0.192230 | 0.0961152 | − | 0.995370i | \(-0.469358\pi\) | ||||
0.0961152 | + | 0.995370i | \(0.469358\pi\) | |||||||
\(242\) | 1.28734 | 0.0827531 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.160547 | 0.0102780 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.59401 | −0.229146 | ||||||||
\(247\) | −23.0986 | −1.46973 | ||||||||
\(248\) | 20.3375 | 1.29143 | ||||||||
\(249\) | −11.5976 | −0.734966 | ||||||||
\(250\) | 26.9618 | 1.70521 | ||||||||
\(251\) | 25.0829 | 1.58322 | 0.791608 | − | 0.611029i | \(-0.209244\pi\) | ||||
0.791608 | + | 0.611029i | \(0.209244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.51145 | −0.283632 | ||||||||
\(254\) | 6.97526 | 0.437666 | ||||||||
\(255\) | 15.5635 | 0.974622 | ||||||||
\(256\) | −7.97096 | −0.498185 | ||||||||
\(257\) | −22.5570 | −1.40707 | −0.703535 | − | 0.710661i | \(-0.748396\pi\) | ||||
−0.703535 | + | 0.710661i | \(0.748396\pi\) | |||||||
\(258\) | 14.3180 | 0.891401 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.08612 | 0.253410 | ||||||||
\(261\) | 3.75572 | 0.232473 | ||||||||
\(262\) | −2.65957 | −0.164309 | ||||||||
\(263\) | 25.7559 | 1.58817 | 0.794087 | − | 0.607803i | \(-0.207949\pi\) | ||||
0.794087 | + | 0.607803i | \(0.207949\pi\) | |||||||
\(264\) | 3.01593 | 0.185617 | ||||||||
\(265\) | −50.6929 | −3.11404 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.3553 | −0.756131 | ||||||||
\(268\) | 0.883730 | 0.0539824 | ||||||||
\(269\) | −20.6962 | −1.26187 | −0.630935 | − | 0.775836i | \(-0.717328\pi\) | ||||
−0.630935 | + | 0.775836i | \(0.717328\pi\) | |||||||
\(270\) | 5.04306 | 0.306911 | ||||||||
\(271\) | 3.06780 | 0.186356 | 0.0931779 | − | 0.995649i | \(-0.470297\pi\) | ||||
0.0931779 | + | 0.995649i | \(0.470297\pi\) | |||||||
\(272\) | −12.7012 | −0.770122 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.38499 | −0.325319 | ||||||||
\(275\) | −10.3463 | −0.623907 | ||||||||
\(276\) | −1.54637 | −0.0930807 | ||||||||
\(277\) | −6.68553 | −0.401695 | −0.200847 | − | 0.979623i | \(-0.564370\pi\) | ||||
−0.200847 | + | 0.979623i | \(0.564370\pi\) | |||||||
\(278\) | 4.64827 | 0.278785 | ||||||||
\(279\) | −6.74335 | −0.403714 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.11286 | 0.185698 | 0.0928489 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928489 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(282\) | 2.13342 | 0.127043 | ||||||||
\(283\) | −22.3599 | −1.32916 | −0.664578 | − | 0.747219i | \(-0.731389\pi\) | ||||
−0.664578 | + | 0.747219i | \(0.731389\pi\) | |||||||
\(284\) | 1.71505 | 0.101770 | ||||||||
\(285\) | 29.7357 | 1.76139 | ||||||||
\(286\) | 3.91744 | 0.231643 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.91627 | 0.112917 | ||||||||
\(289\) | −1.21631 | −0.0715479 | ||||||||
\(290\) | 18.9403 | 1.11221 | ||||||||
\(291\) | −13.1687 | −0.771962 | ||||||||
\(292\) | 2.99494 | 0.175266 | ||||||||
\(293\) | 10.6291 | 0.620958 | 0.310479 | − | 0.950580i | \(-0.399511\pi\) | ||||
0.310479 | + | 0.950580i | \(0.399511\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.3409 | −0.834960 | ||||||||
\(296\) | −1.03376 | −0.0600860 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 17.1463 | 0.993257 | ||||||||
\(299\) | −13.7286 | −0.793945 | ||||||||
\(300\) | −3.54637 | −0.204750 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.06697 | −0.521746 | ||||||||
\(303\) | 7.07019 | 0.406172 | ||||||||
\(304\) | −24.2670 | −1.39181 | ||||||||
\(305\) | −1.83488 | −0.105065 | ||||||||
\(306\) | 5.11442 | 0.292372 | ||||||||
\(307\) | −18.5229 | −1.05716 | −0.528580 | − | 0.848883i | \(-0.677275\pi\) | ||||
−0.528580 | + | 0.848883i | \(0.677275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.33736 | 0.132968 | ||||||||
\(310\) | −34.0071 | −1.93147 | ||||||||
\(311\) | −19.8438 | −1.12524 | −0.562620 | − | 0.826715i | \(-0.690207\pi\) | ||||
−0.562620 | + | 0.826715i | \(0.690207\pi\) | |||||||
\(312\) | 9.17764 | 0.519582 | ||||||||
\(313\) | −21.1144 | −1.19346 | −0.596729 | − | 0.802443i | \(-0.703533\pi\) | ||||
−0.596729 | + | 0.802443i | \(0.703533\pi\) | |||||||
\(314\) | 16.4211 | 0.926696 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.246664 | −0.0138759 | ||||||||
\(317\) | −15.8066 | −0.887786 | −0.443893 | − | 0.896080i | \(-0.646403\pi\) | ||||
−0.443893 | + | 0.896080i | \(0.646403\pi\) | |||||||
\(318\) | −16.6585 | −0.934165 | ||||||||
\(319\) | −3.75572 | −0.210280 | ||||||||
\(320\) | 34.7118 | 1.94045 | ||||||||
\(321\) | −10.8532 | −0.605766 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.1565 | 1.67795 | ||||||||
\(324\) | −0.342766 | −0.0190426 | ||||||||
\(325\) | −31.4845 | −1.74644 | ||||||||
\(326\) | 14.6810 | 0.813103 | ||||||||
\(327\) | −2.19240 | −0.121240 | ||||||||
\(328\) | 8.41992 | 0.464912 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −5.04306 | −0.277611 | ||||||||
\(331\) | −9.16327 | −0.503659 | −0.251829 | − | 0.967772i | \(-0.581032\pi\) | ||||
−0.251829 | + | 0.967772i | \(0.581032\pi\) | |||||||
\(332\) | 3.97526 | 0.218170 | ||||||||
\(333\) | 0.342766 | 0.0187835 | ||||||||
\(334\) | 15.5907 | 0.853088 | ||||||||
\(335\) | −10.1000 | −0.551824 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.7174 | −0.692760 | −0.346380 | − | 0.938094i | \(-0.612589\pi\) | ||||
−0.346380 | + | 0.938094i | \(0.612589\pi\) | |||||||
\(338\) | −4.81437 | −0.261867 | ||||||||
\(339\) | −11.6415 | −0.632277 | ||||||||
\(340\) | −5.33464 | −0.289311 | ||||||||
\(341\) | 6.74335 | 0.365173 | ||||||||
\(342\) | 9.77165 | 0.528390 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −33.5438 | −1.80856 | ||||||||
\(345\) | 17.6733 | 0.951499 | ||||||||
\(346\) | 4.68909 | 0.252087 | ||||||||
\(347\) | 2.54739 | 0.136751 | 0.0683756 | − | 0.997660i | \(-0.478218\pi\) | ||||
0.0683756 | + | 0.997660i | \(0.478218\pi\) | |||||||
\(348\) | −1.28734 | −0.0690084 | ||||||||
\(349\) | −25.0183 | −1.33920 | −0.669600 | − | 0.742722i | \(-0.733534\pi\) | ||||
−0.669600 | + | 0.742722i | \(0.733534\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.04306 | −0.162426 | ||||||||
\(352\) | −1.91627 | −0.102138 | ||||||||
\(353\) | −11.4289 | −0.608298 | −0.304149 | − | 0.952624i | \(-0.598372\pi\) | ||||
−0.304149 | + | 0.952624i | \(0.598372\pi\) | |||||||
\(354\) | −4.71266 | −0.250475 | ||||||||
\(355\) | −19.6011 | −1.04032 | ||||||||
\(356\) | 4.23498 | 0.224453 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.7786 | 0.675371 | ||||||||
\(359\) | 29.9622 | 1.58134 | 0.790672 | − | 0.612240i | \(-0.209731\pi\) | ||||
0.790672 | + | 0.612240i | \(0.209731\pi\) | |||||||
\(360\) | −11.8147 | −0.622690 | ||||||||
\(361\) | 38.6172 | 2.03248 | ||||||||
\(362\) | −10.3916 | −0.546171 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.2288 | −1.79162 | ||||||||
\(366\) | −0.602971 | −0.0315178 | ||||||||
\(367\) | −14.4626 | −0.754941 | −0.377471 | − | 0.926022i | \(-0.623206\pi\) | ||||
−0.377471 | + | 0.926022i | \(0.623206\pi\) | |||||||
\(368\) | −14.4230 | −0.751850 | ||||||||
\(369\) | −2.79182 | −0.145336 | ||||||||
\(370\) | 1.72859 | 0.0898652 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.31139 | 0.119840 | ||||||||
\(373\) | 30.1452 | 1.56086 | 0.780431 | − | 0.625242i | \(-0.215000\pi\) | ||||
0.780431 | + | 0.625242i | \(0.215000\pi\) | |||||||
\(374\) | −5.11442 | −0.264460 | ||||||||
\(375\) | 20.9439 | 1.08154 | ||||||||
\(376\) | −4.99810 | −0.257757 | ||||||||
\(377\) | −11.4289 | −0.588617 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.7452 | −0.603311 | −0.301655 | − | 0.953417i | \(-0.597539\pi\) | ||||
−0.301655 | + | 0.953417i | \(0.597539\pi\) | |||||||
\(380\) | −10.1924 | −0.522859 | ||||||||
\(381\) | 5.41837 | 0.277591 | ||||||||
\(382\) | 7.18801 | 0.367771 | ||||||||
\(383\) | 27.9371 | 1.42752 | 0.713759 | − | 0.700392i | \(-0.246991\pi\) | ||||
0.713759 | + | 0.700392i | \(0.246991\pi\) | |||||||
\(384\) | 7.57434 | 0.386526 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.3329 | 0.729524 | ||||||||
\(387\) | 11.1222 | 0.565374 | ||||||||
\(388\) | 4.51378 | 0.229153 | ||||||||
\(389\) | −15.7579 | −0.798958 | −0.399479 | − | 0.916742i | \(-0.630809\pi\) | ||||
−0.399479 | + | 0.916742i | \(0.630809\pi\) | |||||||
\(390\) | −15.3463 | −0.777091 | ||||||||
\(391\) | 17.9234 | 0.906424 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.06595 | −0.104213 | ||||||||
\(394\) | −0.829656 | −0.0417975 | ||||||||
\(395\) | 2.81910 | 0.141844 | ||||||||
\(396\) | 0.342766 | 0.0172247 | ||||||||
\(397\) | 12.8089 | 0.642861 | 0.321430 | − | 0.946933i | \(-0.395836\pi\) | ||||
0.321430 | + | 0.946933i | \(0.395836\pi\) | |||||||
\(398\) | −32.4865 | −1.62840 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −33.0770 | −1.65385 | ||||||||
\(401\) | −10.9807 | −0.548348 | −0.274174 | − | 0.961680i | \(-0.588404\pi\) | ||||
−0.274174 | + | 0.961680i | \(0.588404\pi\) | |||||||
\(402\) | −3.31904 | −0.165539 | ||||||||
\(403\) | 20.5204 | 1.02219 | ||||||||
\(404\) | −2.42342 | −0.120570 | ||||||||
\(405\) | 3.91744 | 0.194659 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.342766 | −0.0169903 | ||||||||
\(408\) | −11.9819 | −0.593192 | ||||||||
\(409\) | 18.0256 | 0.891309 | 0.445655 | − | 0.895205i | \(-0.352971\pi\) | ||||
0.445655 | + | 0.895205i | \(0.352971\pi\) | |||||||
\(410\) | −14.0793 | −0.695327 | ||||||||
\(411\) | −4.18305 | −0.206335 | ||||||||
\(412\) | −0.801168 | −0.0394707 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.80775 | 0.285435 | ||||||||
\(415\) | −45.4327 | −2.23021 | ||||||||
\(416\) | −5.83132 | −0.285904 | ||||||||
\(417\) | 3.61077 | 0.176820 | ||||||||
\(418\) | −9.77165 | −0.477947 | ||||||||
\(419\) | 11.8542 | 0.579116 | 0.289558 | − | 0.957160i | \(-0.406492\pi\) | ||||
0.289558 | + | 0.957160i | \(0.406492\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4890 | 1.29100 | 0.645498 | − | 0.763762i | \(-0.276650\pi\) | ||||
0.645498 | + | 0.763762i | \(0.276650\pi\) | |||||||
\(422\) | −22.7030 | −1.10517 | ||||||||
\(423\) | 1.65723 | 0.0805775 | ||||||||
\(424\) | 39.0271 | 1.89532 | ||||||||
\(425\) | 41.1046 | 1.99386 | ||||||||
\(426\) | −6.44126 | −0.312080 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.72011 | 0.179818 | ||||||||
\(429\) | 3.04306 | 0.146920 | ||||||||
\(430\) | 56.0900 | 2.70490 | ||||||||
\(431\) | −2.17681 | −0.104853 | −0.0524266 | − | 0.998625i | \(-0.516696\pi\) | ||||
−0.0524266 | + | 0.998625i | \(0.516696\pi\) | |||||||
\(432\) | −3.19698 | −0.153815 | ||||||||
\(433\) | −16.4831 | −0.792129 | −0.396065 | − | 0.918223i | \(-0.629624\pi\) | ||||
−0.396065 | + | 0.918223i | \(0.629624\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.7128 | 0.705425 | ||||||||
\(436\) | 0.751482 | 0.0359895 | ||||||||
\(437\) | 34.2446 | 1.63814 | ||||||||
\(438\) | −11.2482 | −0.537458 | ||||||||
\(439\) | −0.753000 | −0.0359387 | −0.0179694 | − | 0.999839i | \(-0.505720\pi\) | ||||
−0.0179694 | + | 0.999839i | \(0.505720\pi\) | |||||||
\(440\) | 11.8147 | 0.563244 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.5635 | −0.740279 | ||||||||
\(443\) | 40.0619 | 1.90340 | 0.951698 | − | 0.307035i | \(-0.0993370\pi\) | ||||
0.951698 | + | 0.307035i | \(0.0993370\pi\) | |||||||
\(444\) | −0.117489 | −0.00557577 | ||||||||
\(445\) | −48.4011 | −2.29443 | ||||||||
\(446\) | 21.3509 | 1.01099 | ||||||||
\(447\) | 13.3192 | 0.629976 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.71924 | −0.364294 | −0.182147 | − | 0.983271i | \(-0.558305\pi\) | ||||
−0.182147 | + | 0.983271i | \(0.558305\pi\) | |||||||
\(450\) | 13.3192 | 0.627873 | ||||||||
\(451\) | 2.79182 | 0.131462 | ||||||||
\(452\) | 3.99030 | 0.187688 | ||||||||
\(453\) | −7.04321 | −0.330919 | ||||||||
\(454\) | −3.02289 | −0.141871 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −22.8927 | −1.07205 | ||||||||
\(457\) | 26.3646 | 1.23329 | 0.616643 | − | 0.787243i | \(-0.288492\pi\) | ||||
0.616643 | + | 0.787243i | \(0.288492\pi\) | |||||||
\(458\) | −22.4645 | −1.04970 | ||||||||
\(459\) | 3.97287 | 0.185438 | ||||||||
\(460\) | −6.05782 | −0.282447 | ||||||||
\(461\) | 12.4685 | 0.580718 | 0.290359 | − | 0.956918i | \(-0.406225\pi\) | ||||
0.290359 | + | 0.956918i | \(0.406225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.7630 | 1.75499 | 0.877497 | − | 0.479582i | \(-0.159212\pi\) | ||||
0.877497 | + | 0.479582i | \(0.159212\pi\) | |||||||
\(464\) | −12.0070 | −0.557409 | ||||||||
\(465\) | −26.4167 | −1.22504 | ||||||||
\(466\) | −7.19698 | −0.333394 | ||||||||
\(467\) | 22.0208 | 1.01900 | 0.509502 | − | 0.860470i | \(-0.329830\pi\) | ||||
0.509502 | + | 0.860470i | \(0.329830\pi\) | |||||||
\(468\) | 1.04306 | 0.0482154 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.35753 | 0.385504 | ||||||||
\(471\) | 12.7559 | 0.587759 | ||||||||
\(472\) | 11.0407 | 0.508188 | ||||||||
\(473\) | −11.1222 | −0.511400 | ||||||||
\(474\) | 0.926402 | 0.0425511 | ||||||||
\(475\) | 78.5348 | 3.60342 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.9403 | −0.592497 | ||||||||
\(478\) | 22.9335 | 1.04895 | ||||||||
\(479\) | −9.44803 | −0.431692 | −0.215846 | − | 0.976427i | \(-0.569251\pi\) | ||||
−0.215846 | + | 0.976427i | \(0.569251\pi\) | |||||||
\(480\) | 7.50687 | 0.342640 | ||||||||
\(481\) | −1.04306 | −0.0475594 | ||||||||
\(482\) | 3.84169 | 0.174984 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.342766 | −0.0155803 | ||||||||
\(485\) | −51.5875 | −2.34247 | ||||||||
\(486\) | 1.28734 | 0.0583947 | ||||||||
\(487\) | 40.2341 | 1.82318 | 0.911589 | − | 0.411102i | \(-0.134856\pi\) | ||||
0.911589 | + | 0.411102i | \(0.134856\pi\) | |||||||
\(488\) | 1.41262 | 0.0639463 | ||||||||
\(489\) | 11.4041 | 0.515713 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2964 | 0.915966 | 0.457983 | − | 0.888961i | \(-0.348572\pi\) | ||||
0.457983 | + | 0.888961i | \(0.348572\pi\) | |||||||
\(492\) | 0.956942 | 0.0431423 | ||||||||
\(493\) | 14.9210 | 0.672008 | ||||||||
\(494\) | −29.7357 | −1.33787 | ||||||||
\(495\) | −3.91744 | −0.176076 | ||||||||
\(496\) | 21.5583 | 0.967998 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.9300 | −0.669027 | ||||||||
\(499\) | 36.2954 | 1.62481 | 0.812403 | − | 0.583096i | \(-0.198159\pi\) | ||||
0.812403 | + | 0.583096i | \(0.198159\pi\) | |||||||
\(500\) | −7.17886 | −0.321048 | ||||||||
\(501\) | 12.1109 | 0.541073 | ||||||||
\(502\) | 32.2901 | 1.44118 | ||||||||
\(503\) | −27.6923 | −1.23474 | −0.617368 | − | 0.786674i | \(-0.711801\pi\) | ||||
−0.617368 | + | 0.786674i | \(0.711801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.6970 | 1.23250 | ||||||||
\(506\) | −5.80775 | −0.258186 | ||||||||
\(507\) | −3.73980 | −0.166090 | ||||||||
\(508\) | −1.85723 | −0.0824014 | ||||||||
\(509\) | 9.08797 | 0.402817 | 0.201409 | − | 0.979507i | \(-0.435448\pi\) | ||||
0.201409 | + | 0.979507i | \(0.435448\pi\) | |||||||
\(510\) | 20.0354 | 0.887183 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −25.4100 | −1.12297 | ||||||||
\(513\) | 7.59060 | 0.335133 | ||||||||
\(514\) | −29.0385 | −1.28083 | ||||||||
\(515\) | 9.15645 | 0.403482 | ||||||||
\(516\) | −3.81232 | −0.167828 | ||||||||
\(517\) | −1.65723 | −0.0728850 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.64247 | 0.159887 | ||||||||
\(520\) | 35.9528 | 1.57664 | ||||||||
\(521\) | 38.8510 | 1.70209 | 0.851046 | − | 0.525092i | \(-0.175969\pi\) | ||||
0.851046 | + | 0.525092i | \(0.175969\pi\) | |||||||
\(522\) | 4.83488 | 0.211617 | ||||||||
\(523\) | −21.5001 | −0.940132 | −0.470066 | − | 0.882631i | \(-0.655770\pi\) | ||||
−0.470066 | + | 0.882631i | \(0.655770\pi\) | |||||||
\(524\) | 0.708138 | 0.0309352 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.1565 | 1.44569 | ||||||||
\(527\) | −26.7904 | −1.16701 | ||||||||
\(528\) | 3.19698 | 0.139131 | ||||||||
\(529\) | −2.64686 | −0.115081 | ||||||||
\(530\) | −65.2588 | −2.83466 | ||||||||
\(531\) | −3.66079 | −0.158865 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.49566 | 0.367988 | ||||||||
\(534\) | −15.9054 | −0.688294 | ||||||||
\(535\) | −42.5167 | −1.83816 | ||||||||
\(536\) | 7.77574 | 0.335861 | ||||||||
\(537\) | 9.92640 | 0.428356 | ||||||||
\(538\) | −26.6430 | −1.14866 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.34277 | −0.0577835 | ||||||||
\(541\) | −29.8940 | −1.28524 | −0.642622 | − | 0.766183i | \(-0.722153\pi\) | ||||
−0.642622 | + | 0.766183i | \(0.722153\pi\) | |||||||
\(542\) | 3.94929 | 0.169637 | ||||||||
\(543\) | −8.07219 | −0.346411 | ||||||||
\(544\) | 7.61309 | 0.326408 | ||||||||
\(545\) | −8.58860 | −0.367895 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.9072 | −1.36425 | −0.682127 | − | 0.731234i | \(-0.738945\pi\) | ||||
−0.682127 | + | 0.731234i | \(0.738945\pi\) | |||||||
\(548\) | 1.43381 | 0.0612493 | ||||||||
\(549\) | −0.468387 | −0.0199903 | ||||||||
\(550\) | −13.3192 | −0.567932 | ||||||||
\(551\) | 28.5082 | 1.21449 | ||||||||
\(552\) | −13.6062 | −0.579118 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.60653 | −0.365656 | ||||||||
\(555\) | 1.34277 | 0.0569973 | ||||||||
\(556\) | −1.23765 | −0.0524880 | ||||||||
\(557\) | −14.6089 | −0.619000 | −0.309500 | − | 0.950900i | \(-0.600162\pi\) | ||||
−0.309500 | + | 0.950900i | \(0.600162\pi\) | |||||||
\(558\) | −8.68096 | −0.367494 | ||||||||
\(559\) | −33.8455 | −1.43151 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.97287 | −0.167735 | ||||||||
\(562\) | 4.00730 | 0.169038 | ||||||||
\(563\) | −8.48231 | −0.357487 | −0.178743 | − | 0.983896i | \(-0.557203\pi\) | ||||
−0.178743 | + | 0.983896i | \(0.557203\pi\) | |||||||
\(564\) | −0.568044 | −0.0239190 | ||||||||
\(565\) | −45.6047 | −1.91860 | ||||||||
\(566\) | −28.7847 | −1.20991 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.0904 | 0.633177 | ||||||||
\(569\) | 20.7058 | 0.868034 | 0.434017 | − | 0.900905i | \(-0.357096\pi\) | ||||
0.434017 | + | 0.900905i | \(0.357096\pi\) | |||||||
\(570\) | 38.2798 | 1.60337 | ||||||||
\(571\) | 1.00882 | 0.0422177 | 0.0211088 | − | 0.999777i | \(-0.493280\pi\) | ||||
0.0211088 | + | 0.999777i | \(0.493280\pi\) | |||||||
\(572\) | −1.04306 | −0.0436125 | ||||||||
\(573\) | 5.58364 | 0.233260 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 46.6769 | 1.94656 | ||||||||
\(576\) | 8.86084 | 0.369202 | ||||||||
\(577\) | −38.3851 | −1.59799 | −0.798996 | − | 0.601336i | \(-0.794635\pi\) | ||||
−0.798996 | + | 0.601336i | \(0.794635\pi\) | |||||||
\(578\) | −1.56580 | −0.0651289 | ||||||||
\(579\) | 11.1338 | 0.462703 | ||||||||
\(580\) | −5.04306 | −0.209402 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −16.9525 | −0.702704 | ||||||||
\(583\) | 12.9403 | 0.535934 | ||||||||
\(584\) | 26.3518 | 1.09045 | ||||||||
\(585\) | −11.9210 | −0.492872 | ||||||||
\(586\) | 13.6832 | 0.565248 | ||||||||
\(587\) | 3.95733 | 0.163336 | 0.0816682 | − | 0.996660i | \(-0.473975\pi\) | ||||
0.0816682 | + | 0.996660i | \(0.473975\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51.1861 | −2.10909 | ||||||||
\(590\) | −18.4616 | −0.760051 | ||||||||
\(591\) | −0.644475 | −0.0265102 | ||||||||
\(592\) | −1.09582 | −0.0450378 | ||||||||
\(593\) | 8.50263 | 0.349161 | 0.174581 | − | 0.984643i | \(-0.444143\pi\) | ||||
0.174581 | + | 0.984643i | \(0.444143\pi\) | |||||||
\(594\) | −1.28734 | −0.0528200 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.56537 | −0.187005 | ||||||||
\(597\) | −25.2355 | −1.03282 | ||||||||
\(598\) | −17.6733 | −0.722715 | ||||||||
\(599\) | −6.96152 | −0.284440 | −0.142220 | − | 0.989835i | \(-0.545424\pi\) | ||||
−0.142220 | + | 0.989835i | \(0.545424\pi\) | |||||||
\(600\) | −31.2038 | −1.27389 | ||||||||
\(601\) | 31.8738 | 1.30016 | 0.650081 | − | 0.759865i | \(-0.274735\pi\) | ||||
0.650081 | + | 0.759865i | \(0.274735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.57823 | −0.104994 | ||||||||
\(604\) | 2.41417 | 0.0982314 | ||||||||
\(605\) | 3.91744 | 0.159267 | ||||||||
\(606\) | 9.10171 | 0.369732 | ||||||||
\(607\) | 3.34408 | 0.135732 | 0.0678660 | − | 0.997694i | \(-0.478381\pi\) | ||||
0.0678660 | + | 0.997694i | \(0.478381\pi\) | |||||||
\(608\) | 14.5456 | 0.589903 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.36210 | −0.0956387 | ||||||||
\(611\) | −5.04306 | −0.204020 | ||||||||
\(612\) | −1.36177 | −0.0550461 | ||||||||
\(613\) | −4.22650 | −0.170707 | −0.0853533 | − | 0.996351i | \(-0.527202\pi\) | ||||
−0.0853533 | + | 0.996351i | \(0.527202\pi\) | |||||||
\(614\) | −23.8452 | −0.962316 | ||||||||
\(615\) | −10.9368 | −0.441013 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.91266 | 0.157518 | 0.0787590 | − | 0.996894i | \(-0.474904\pi\) | ||||
0.0787590 | + | 0.996894i | \(0.474904\pi\) | |||||||
\(618\) | 3.00896 | 0.121038 | ||||||||
\(619\) | 1.73839 | 0.0698717 | 0.0349359 | − | 0.999390i | \(-0.488877\pi\) | ||||
0.0349359 | + | 0.999390i | \(0.488877\pi\) | |||||||
\(620\) | 9.05474 | 0.363647 | ||||||||
\(621\) | 4.51145 | 0.181038 | ||||||||
\(622\) | −25.5457 | −1.02429 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.72859 | 0.389455 | ||||||||
\(625\) | 30.3148 | 1.21259 | ||||||||
\(626\) | −27.1813 | −1.08639 | ||||||||
\(627\) | −7.59060 | −0.303139 | ||||||||
\(628\) | −4.37228 | −0.174473 | ||||||||
\(629\) | 1.36177 | 0.0542972 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.3994 | −0.533420 | −0.266710 | − | 0.963777i | \(-0.585937\pi\) | ||||
−0.266710 | + | 0.963777i | \(0.585937\pi\) | |||||||
\(632\) | −2.17034 | −0.0863316 | ||||||||
\(633\) | −17.6357 | −0.700954 | ||||||||
\(634\) | −20.3484 | −0.808137 | ||||||||
\(635\) | 21.2261 | 0.842332 | ||||||||
\(636\) | 4.43551 | 0.175879 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.83488 | −0.191415 | ||||||||
\(639\) | −5.00355 | −0.197938 | ||||||||
\(640\) | 29.6720 | 1.17289 | ||||||||
\(641\) | 10.7820 | 0.425864 | 0.212932 | − | 0.977067i | \(-0.431699\pi\) | ||||
0.212932 | + | 0.977067i | \(0.431699\pi\) | |||||||
\(642\) | −13.9717 | −0.551419 | ||||||||
\(643\) | 30.1180 | 1.18774 | 0.593868 | − | 0.804562i | \(-0.297600\pi\) | ||||
0.593868 | + | 0.804562i | \(0.297600\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 43.5706 | 1.71559 | ||||||||
\(646\) | 38.8215 | 1.52741 | ||||||||
\(647\) | −12.6469 | −0.497199 | −0.248600 | − | 0.968606i | \(-0.579970\pi\) | ||||
−0.248600 | + | 0.968606i | \(0.579970\pi\) | |||||||
\(648\) | −3.01593 | −0.118477 | ||||||||
\(649\) | 3.66079 | 0.143699 | ||||||||
\(650\) | −40.5311 | −1.58976 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.90896 | −0.153087 | ||||||||
\(653\) | 1.50229 | 0.0587892 | 0.0293946 | − | 0.999568i | \(-0.490642\pi\) | ||||
0.0293946 | + | 0.999568i | \(0.490642\pi\) | |||||||
\(654\) | −2.82236 | −0.110363 | ||||||||
\(655\) | −8.09323 | −0.316229 | ||||||||
\(656\) | 8.92538 | 0.348478 | ||||||||
\(657\) | −8.73756 | −0.340885 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.4079 | −0.561251 | −0.280626 | − | 0.959817i | \(-0.590542\pi\) | ||||
−0.280626 | + | 0.959817i | \(0.590542\pi\) | |||||||
\(660\) | 1.34277 | 0.0522671 | ||||||||
\(661\) | −16.7854 | −0.652876 | −0.326438 | − | 0.945219i | \(-0.605848\pi\) | ||||
−0.326438 | + | 0.945219i | \(0.605848\pi\) | |||||||
\(662\) | −11.7962 | −0.458473 | ||||||||
\(663\) | −12.0897 | −0.469524 | ||||||||
\(664\) | 34.9774 | 1.35739 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.441256 | 0.0170983 | ||||||||
\(667\) | 16.9437 | 0.656064 | ||||||||
\(668\) | −4.15120 | −0.160615 | ||||||||
\(669\) | 16.5853 | 0.641226 | ||||||||
\(670\) | −13.0021 | −0.502317 | ||||||||
\(671\) | 0.468387 | 0.0180819 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.1663 | −1.85667 | −0.928337 | − | 0.371740i | \(-0.878761\pi\) | ||||
−0.928337 | + | 0.371740i | \(0.878761\pi\) | |||||||
\(674\) | −16.3715 | −0.630608 | ||||||||
\(675\) | 10.3463 | 0.398230 | ||||||||
\(676\) | 1.28188 | 0.0493029 | ||||||||
\(677\) | −11.7148 | −0.450237 | −0.225118 | − | 0.974331i | \(-0.572277\pi\) | ||||
−0.225118 | + | 0.974331i | \(0.572277\pi\) | |||||||
\(678\) | −14.9865 | −0.575552 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −46.9383 | −1.80000 | ||||||||
\(681\) | −2.34818 | −0.0899823 | ||||||||
\(682\) | 8.68096 | 0.332411 | ||||||||
\(683\) | 11.4199 | 0.436971 | 0.218486 | − | 0.975840i | \(-0.429888\pi\) | ||||
0.218486 | + | 0.975840i | \(0.429888\pi\) | |||||||
\(684\) | −2.60180 | −0.0994824 | ||||||||
\(685\) | −16.3868 | −0.626109 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.4504 | −0.665773 | ||||||||
\(688\) | −35.5575 | −1.35562 | ||||||||
\(689\) | 39.3782 | 1.50019 | ||||||||
\(690\) | 22.7515 | 0.866134 | ||||||||
\(691\) | −22.9191 | −0.871885 | −0.435943 | − | 0.899974i | \(-0.643585\pi\) | ||||
−0.435943 | + | 0.899974i | \(0.643585\pi\) | |||||||
\(692\) | −1.24852 | −0.0474615 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.27935 | 0.124482 | ||||||||
\(695\) | 14.1450 | 0.536549 | ||||||||
\(696\) | −11.3270 | −0.429348 | ||||||||
\(697\) | −11.0915 | −0.420122 | ||||||||
\(698\) | −32.2070 | −1.21905 | ||||||||
\(699\) | −5.59060 | −0.211456 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.3982 | 0.959277 | 0.479638 | − | 0.877466i | \(-0.340768\pi\) | ||||
0.479638 | + | 0.877466i | \(0.340768\pi\) | |||||||
\(702\) | −3.91744 | −0.147854 | ||||||||
\(703\) | 2.60180 | 0.0981289 | ||||||||
\(704\) | −8.86084 | −0.333955 | ||||||||
\(705\) | 6.49211 | 0.244507 | ||||||||
\(706\) | −14.7128 | −0.553724 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.25480 | 0.0471581 | ||||||||
\(709\) | −16.5011 | −0.619711 | −0.309855 | − | 0.950784i | \(-0.600281\pi\) | ||||
−0.309855 | + | 0.950784i | \(0.600281\pi\) | |||||||
\(710\) | −25.2332 | −0.946986 | ||||||||
\(711\) | 0.719627 | 0.0269881 | ||||||||
\(712\) | 37.2626 | 1.39648 | ||||||||
\(713\) | −30.4223 | −1.13932 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.9210 | 0.445820 | ||||||||
\(716\) | −3.40244 | −0.127155 | ||||||||
\(717\) | 17.8147 | 0.665302 | ||||||||
\(718\) | 38.5714 | 1.43947 | ||||||||
\(719\) | −35.8298 | −1.33622 | −0.668112 | − | 0.744060i | \(-0.732897\pi\) | ||||
−0.668112 | + | 0.744060i | \(0.732897\pi\) | |||||||
\(720\) | −12.5240 | −0.466741 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 49.7133 | 1.85014 | ||||||||
\(723\) | 2.98422 | 0.110984 | ||||||||
\(724\) | 2.76688 | 0.102830 | ||||||||
\(725\) | 38.8579 | 1.44315 | ||||||||
\(726\) | 1.28734 | 0.0477775 | ||||||||
\(727\) | −18.7401 | −0.695031 | −0.347516 | − | 0.937674i | \(-0.612975\pi\) | ||||
−0.347516 | + | 0.937674i | \(0.612975\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −44.0640 | −1.63088 | ||||||||
\(731\) | 44.1871 | 1.63432 | ||||||||
\(732\) | 0.160547 | 0.00593400 | ||||||||
\(733\) | 47.8079 | 1.76582 | 0.882912 | − | 0.469538i | \(-0.155579\pi\) | ||||
0.882912 | + | 0.469538i | \(0.155579\pi\) | |||||||
\(734\) | −18.6182 | −0.687211 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.64515 | 0.318664 | ||||||||
\(737\) | 2.57823 | 0.0949702 | ||||||||
\(738\) | −3.59401 | −0.132297 | ||||||||
\(739\) | −12.1402 | −0.446584 | −0.223292 | − | 0.974752i | \(-0.571680\pi\) | ||||
−0.223292 | + | 0.974752i | \(0.571680\pi\) | |||||||
\(740\) | −0.460255 | −0.0169193 | ||||||||
\(741\) | −23.0986 | −0.848550 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.9615 | 1.13587 | 0.567934 | − | 0.823074i | \(-0.307743\pi\) | ||||
0.567934 | + | 0.823074i | \(0.307743\pi\) | |||||||
\(744\) | 20.3375 | 0.745607 | ||||||||
\(745\) | 52.1771 | 1.91162 | ||||||||
\(746\) | 38.8071 | 1.42083 | ||||||||
\(747\) | −11.5976 | −0.424333 | ||||||||
\(748\) | 1.36177 | 0.0497911 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 26.9618 | 0.984506 | ||||||||
\(751\) | −32.0437 | −1.16929 | −0.584646 | − | 0.811288i | \(-0.698767\pi\) | ||||
−0.584646 | + | 0.811288i | \(0.698767\pi\) | |||||||
\(752\) | −5.29814 | −0.193203 | ||||||||
\(753\) | 25.0829 | 0.914070 | ||||||||
\(754\) | −14.7128 | −0.535809 | ||||||||
\(755\) | −27.5913 | −1.00415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.5209 | 1.18199 | 0.590996 | − | 0.806675i | \(-0.298735\pi\) | ||||
0.590996 | + | 0.806675i | \(0.298735\pi\) | |||||||
\(758\) | −15.1200 | −0.549184 | ||||||||
\(759\) | −4.51145 | −0.163755 | ||||||||
\(760\) | −89.6807 | −3.25306 | ||||||||
\(761\) | −2.46361 | −0.0893059 | −0.0446530 | − | 0.999003i | \(-0.514218\pi\) | ||||
−0.0446530 | + | 0.999003i | \(0.514218\pi\) | |||||||
\(762\) | 6.97526 | 0.252687 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.91388 | −0.0692419 | ||||||||
\(765\) | 15.5635 | 0.562698 | ||||||||
\(766\) | 35.9644 | 1.29945 | ||||||||
\(767\) | 11.1400 | 0.402242 | ||||||||
\(768\) | −7.97096 | −0.287627 | ||||||||
\(769\) | 49.0232 | 1.76782 | 0.883911 | − | 0.467656i | \(-0.154901\pi\) | ||||
0.883911 | + | 0.467656i | \(0.154901\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.5570 | −0.812372 | ||||||||
\(772\) | −3.81628 | −0.137351 | ||||||||
\(773\) | 0.416364 | 0.0149756 | 0.00748779 | − | 0.999972i | \(-0.497617\pi\) | ||||
0.00748779 | + | 0.999972i | \(0.497617\pi\) | |||||||
\(774\) | 14.3180 | 0.514651 | ||||||||
\(775\) | −69.7689 | −2.50617 | ||||||||
\(776\) | 39.7158 | 1.42571 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.2857 | −0.727278 | ||||||||
\(779\) | −21.1916 | −0.759267 | ||||||||
\(780\) | 4.08612 | 0.146306 | ||||||||
\(781\) | 5.00355 | 0.179041 | ||||||||
\(782\) | 23.0734 | 0.825103 | ||||||||
\(783\) | 3.75572 | 0.134219 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 49.9703 | 1.78352 | ||||||||
\(786\) | −2.65957 | −0.0948637 | ||||||||
\(787\) | 4.83064 | 0.172194 | 0.0860968 | − | 0.996287i | \(-0.472561\pi\) | ||||
0.0860968 | + | 0.996287i | \(0.472561\pi\) | |||||||
\(788\) | 0.220905 | 0.00786940 | ||||||||
\(789\) | 25.7559 | 0.916933 | ||||||||
\(790\) | 3.62912 | 0.129118 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.01593 | 0.107166 | ||||||||
\(793\) | 1.42533 | 0.0506149 | ||||||||
\(794\) | 16.4894 | 0.585186 | ||||||||
\(795\) | −50.6929 | −1.79789 | ||||||||
\(796\) | 8.64987 | 0.306587 | ||||||||
\(797\) | 43.5752 | 1.54351 | 0.771756 | − | 0.635919i | \(-0.219379\pi\) | ||||
0.771756 | + | 0.635919i | \(0.219379\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.58397 | 0.232924 | ||||||||
\(800\) | 19.8263 | 0.700967 | ||||||||
\(801\) | −12.3553 | −0.436553 | ||||||||
\(802\) | −14.1358 | −0.499153 | ||||||||
\(803\) | 8.73756 | 0.308342 | ||||||||
\(804\) | 0.883730 | 0.0311667 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.4167 | 0.930487 | ||||||||
\(807\) | −20.6962 | −0.728541 | ||||||||
\(808\) | −21.3232 | −0.750147 | ||||||||
\(809\) | −18.7352 | −0.658695 | −0.329348 | − | 0.944209i | \(-0.606829\pi\) | ||||
−0.329348 | + | 0.944209i | \(0.606829\pi\) | |||||||
\(810\) | 5.04306 | 0.177195 | ||||||||
\(811\) | −4.64229 | −0.163013 | −0.0815063 | − | 0.996673i | \(-0.525973\pi\) | ||||
−0.0815063 | + | 0.996673i | \(0.525973\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.06780 | 0.107593 | ||||||||
\(814\) | −0.441256 | −0.0154660 | ||||||||
\(815\) | 44.6750 | 1.56490 | ||||||||
\(816\) | −12.7012 | −0.444630 | ||||||||
\(817\) | 84.4243 | 2.95363 | ||||||||
\(818\) | 23.2050 | 0.811344 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.74876 | 0.130912 | ||||||||
\(821\) | 17.9116 | 0.625121 | 0.312560 | − | 0.949898i | \(-0.398813\pi\) | ||||
0.312560 | + | 0.949898i | \(0.398813\pi\) | |||||||
\(822\) | −5.38499 | −0.187823 | ||||||||
\(823\) | −27.5943 | −0.961877 | −0.480938 | − | 0.876754i | \(-0.659704\pi\) | ||||
−0.480938 | + | 0.876754i | \(0.659704\pi\) | |||||||
\(824\) | −7.04930 | −0.245574 | ||||||||
\(825\) | −10.3463 | −0.360213 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.2202 | 0.946538 | 0.473269 | − | 0.880918i | \(-0.343074\pi\) | ||||
0.473269 | + | 0.880918i | \(0.343074\pi\) | |||||||
\(828\) | −1.54637 | −0.0537401 | ||||||||
\(829\) | 19.4199 | 0.674482 | 0.337241 | − | 0.941418i | \(-0.390506\pi\) | ||||
0.337241 | + | 0.941418i | \(0.390506\pi\) | |||||||
\(830\) | −58.4872 | −2.03012 | ||||||||
\(831\) | −6.68553 | −0.231919 | ||||||||
\(832\) | −26.9641 | −0.934810 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.64827 | 0.160956 | ||||||||
\(835\) | 47.4435 | 1.64185 | ||||||||
\(836\) | 2.60180 | 0.0899852 | ||||||||
\(837\) | −6.74335 | −0.233084 | ||||||||
\(838\) | 15.2604 | 0.527160 | ||||||||
\(839\) | 42.1143 | 1.45395 | 0.726973 | − | 0.686666i | \(-0.240927\pi\) | ||||
0.726973 | + | 0.686666i | \(0.240927\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.8945 | −0.513605 | ||||||||
\(842\) | 34.1003 | 1.17517 | ||||||||
\(843\) | 3.11286 | 0.107213 | ||||||||
\(844\) | 6.04491 | 0.208074 | ||||||||
\(845\) | −14.6504 | −0.503990 | ||||||||
\(846\) | 2.13342 | 0.0733484 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 41.3699 | 1.42065 | ||||||||
\(849\) | −22.3599 | −0.767388 | ||||||||
\(850\) | 52.9154 | 1.81498 | ||||||||
\(851\) | 1.54637 | 0.0530090 | ||||||||
\(852\) | 1.71505 | 0.0587567 | ||||||||
\(853\) | −53.7179 | −1.83926 | −0.919632 | − | 0.392780i | \(-0.871513\pi\) | ||||
−0.919632 | + | 0.392780i | \(0.871513\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.7357 | 1.01694 | ||||||||
\(856\) | 32.7324 | 1.11877 | ||||||||
\(857\) | −6.96848 | −0.238039 | −0.119019 | − | 0.992892i | \(-0.537975\pi\) | ||||
−0.119019 | + | 0.992892i | \(0.537975\pi\) | |||||||
\(858\) | 3.91744 | 0.133739 | ||||||||
\(859\) | −33.6294 | −1.14742 | −0.573710 | − | 0.819058i | \(-0.694497\pi\) | ||||
−0.573710 | + | 0.819058i | \(0.694497\pi\) | |||||||
\(860\) | −14.9345 | −0.509263 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.80229 | −0.0954462 | ||||||||
\(863\) | 44.0972 | 1.50109 | 0.750544 | − | 0.660821i | \(-0.229792\pi\) | ||||
0.750544 | + | 0.660821i | \(0.229792\pi\) | |||||||
\(864\) | 1.91627 | 0.0651928 | ||||||||
\(865\) | 14.2692 | 0.485166 | ||||||||
\(866\) | −21.2193 | −0.721063 | ||||||||
\(867\) | −1.21631 | −0.0413082 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.719627 | −0.0244117 | ||||||||
\(870\) | 18.9403 | 0.642137 | ||||||||
\(871\) | 7.84569 | 0.265841 | ||||||||
\(872\) | 6.61212 | 0.223915 | ||||||||
\(873\) | −13.1687 | −0.445692 | ||||||||
\(874\) | 44.0843 | 1.49117 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.99494 | 0.101190 | ||||||||
\(877\) | 10.1450 | 0.342571 | 0.171285 | − | 0.985221i | \(-0.445208\pi\) | ||||
0.171285 | + | 0.985221i | \(0.445208\pi\) | |||||||
\(878\) | −0.969364 | −0.0327145 | ||||||||
\(879\) | 10.6291 | 0.358510 | ||||||||
\(880\) | 12.5240 | 0.422183 | ||||||||
\(881\) | 32.4394 | 1.09291 | 0.546455 | − | 0.837489i | \(-0.315977\pi\) | ||||
0.546455 | + | 0.837489i | \(0.315977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.0795 | 0.843992 | 0.421996 | − | 0.906598i | \(-0.361330\pi\) | ||||
0.421996 | + | 0.906598i | \(0.361330\pi\) | |||||||
\(884\) | 4.14393 | 0.139376 | ||||||||
\(885\) | −14.3409 | −0.482064 | ||||||||
\(886\) | 51.5731 | 1.73263 | ||||||||
\(887\) | −52.6253 | −1.76699 | −0.883493 | − | 0.468445i | \(-0.844814\pi\) | ||||
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(888\) | −1.03376 | −0.0346907 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −62.3084 | −2.08858 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −5.68490 | −0.190344 | ||||||||
\(893\) | 12.5794 | 0.420953 | ||||||||
\(894\) | 17.1463 | 0.573457 | ||||||||
\(895\) | 38.8861 | 1.29982 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.7286 | −0.458384 | ||||||||
\(898\) | −9.93726 | −0.331611 | ||||||||
\(899\) | −25.3262 | −0.844675 | ||||||||
\(900\) | −3.54637 | −0.118212 | ||||||||
\(901\) | −51.4102 | −1.71272 | ||||||||
\(902\) | 3.59401 | 0.119667 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35.1098 | 1.16773 | ||||||||
\(905\) | −31.6223 | −1.05116 | ||||||||
\(906\) | −9.06697 | −0.301230 | ||||||||
\(907\) | −36.3628 | −1.20741 | −0.603704 | − | 0.797208i | \(-0.706309\pi\) | ||||
−0.603704 | + | 0.797208i | \(0.706309\pi\) | |||||||
\(908\) | 0.804876 | 0.0267107 | ||||||||
\(909\) | 7.07019 | 0.234503 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.4516 | −0.478802 | −0.239401 | − | 0.970921i | \(-0.576951\pi\) | ||||
−0.239401 | + | 0.970921i | \(0.576951\pi\) | |||||||
\(912\) | −24.2670 | −0.803560 | ||||||||
\(913\) | 11.5976 | 0.383823 | ||||||||
\(914\) | 33.9401 | 1.12264 | ||||||||
\(915\) | −1.83488 | −0.0606591 | ||||||||
\(916\) | 5.98140 | 0.197631 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.11442 | 0.168801 | ||||||||
\(919\) | 45.6611 | 1.50622 | 0.753111 | − | 0.657894i | \(-0.228552\pi\) | ||||
0.753111 | + | 0.657894i | \(0.228552\pi\) | |||||||
\(920\) | −53.3014 | −1.75730 | ||||||||
\(921\) | −18.5229 | −0.610352 | ||||||||
\(922\) | 16.0512 | 0.528618 | ||||||||
\(923\) | 15.2261 | 0.501174 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.54637 | 0.116604 | ||||||||
\(926\) | 48.6136 | 1.59754 | ||||||||
\(927\) | 2.33736 | 0.0767689 | ||||||||
\(928\) | 7.19698 | 0.236252 | ||||||||
\(929\) | −45.3661 | −1.48841 | −0.744207 | − | 0.667949i | \(-0.767173\pi\) | ||||
−0.744207 | + | 0.667949i | \(0.767173\pi\) | |||||||
\(930\) | −34.0071 | −1.11514 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.91627 | 0.0627695 | ||||||||
\(933\) | −19.8438 | −0.649658 | ||||||||
\(934\) | 28.3482 | 0.927582 | ||||||||
\(935\) | −15.5635 | −0.508980 | ||||||||
\(936\) | 9.17764 | 0.299981 | ||||||||
\(937\) | 14.7757 | 0.482699 | 0.241350 | − | 0.970438i | \(-0.422410\pi\) | ||||
0.241350 | + | 0.970438i | \(0.422410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.1144 | −0.689043 | ||||||||
\(940\) | −2.22528 | −0.0725806 | ||||||||
\(941\) | −15.9211 | −0.519014 | −0.259507 | − | 0.965741i | \(-0.583560\pi\) | ||||
−0.259507 | + | 0.965741i | \(0.583560\pi\) | |||||||
\(942\) | 16.4211 | 0.535028 | ||||||||
\(943\) | −12.5951 | −0.410154 | ||||||||
\(944\) | 11.7035 | 0.380915 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.3180 | −0.465519 | ||||||||
\(947\) | 24.3584 | 0.791540 | 0.395770 | − | 0.918350i | \(-0.370478\pi\) | ||||
0.395770 | + | 0.918350i | \(0.370478\pi\) | |||||||
\(948\) | −0.246664 | −0.00801128 | ||||||||
\(949\) | 26.5889 | 0.863112 | ||||||||
\(950\) | 101.101 | 3.28014 | ||||||||
\(951\) | −15.8066 | −0.512563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.2682 | −1.53117 | −0.765583 | − | 0.643337i | \(-0.777550\pi\) | ||||
−0.765583 | + | 0.643337i | \(0.777550\pi\) | |||||||
\(954\) | −16.6585 | −0.539340 | ||||||||
\(955\) | 21.8735 | 0.707811 | ||||||||
\(956\) | −6.10628 | −0.197491 | ||||||||
\(957\) | −3.75572 | −0.121405 | ||||||||
\(958\) | −12.1628 | −0.392962 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 34.7118 | 1.12032 | ||||||||
\(961\) | 14.4728 | 0.466864 | ||||||||
\(962\) | −1.34277 | −0.0432925 | ||||||||
\(963\) | −10.8532 | −0.349739 | ||||||||
\(964\) | −1.02289 | −0.0329451 | ||||||||
\(965\) | 43.6158 | 1.40404 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.7062 | 1.21255 | 0.606275 | − | 0.795255i | \(-0.292663\pi\) | ||||
0.606275 | + | 0.795255i | \(0.292663\pi\) | |||||||
\(968\) | −3.01593 | −0.0969356 | ||||||||
\(969\) | 30.1565 | 0.968765 | ||||||||
\(970\) | −66.4104 | −2.13231 | ||||||||
\(971\) | 1.99152 | 0.0639109 | 0.0319554 | − | 0.999489i | \(-0.489827\pi\) | ||||
0.0319554 | + | 0.999489i | \(0.489827\pi\) | |||||||
\(972\) | −0.342766 | −0.0109942 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 51.7947 | 1.65961 | ||||||||
\(975\) | −31.4845 | −1.00831 | ||||||||
\(976\) | 1.49742 | 0.0479313 | ||||||||
\(977\) | −27.2601 | −0.872126 | −0.436063 | − | 0.899916i | \(-0.643628\pi\) | ||||
−0.436063 | + | 0.899916i | \(0.643628\pi\) | |||||||
\(978\) | 14.6810 | 0.469445 | ||||||||
\(979\) | 12.3553 | 0.394877 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.19240 | −0.0699980 | ||||||||
\(982\) | 26.1283 | 0.833789 | ||||||||
\(983\) | 10.1422 | 0.323487 | 0.161744 | − | 0.986833i | \(-0.448288\pi\) | ||||
0.161744 | + | 0.986833i | \(0.448288\pi\) | |||||||
\(984\) | 8.41992 | 0.268417 | ||||||||
\(985\) | −2.52469 | −0.0804434 | ||||||||
\(986\) | 19.2083 | 0.611718 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.91744 | 0.251887 | ||||||||
\(989\) | 50.1773 | 1.59554 | ||||||||
\(990\) | −5.04306 | −0.160279 | ||||||||
\(991\) | 22.1404 | 0.703312 | 0.351656 | − | 0.936129i | \(-0.385619\pi\) | ||||
0.351656 | + | 0.936129i | \(0.385619\pi\) | |||||||
\(992\) | −12.9221 | −0.410276 | ||||||||
\(993\) | −9.16327 | −0.290788 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −98.8584 | −3.13402 | ||||||||
\(996\) | 3.97526 | 0.125961 | ||||||||
\(997\) | 48.8984 | 1.54863 | 0.774314 | − | 0.632802i | \(-0.218095\pi\) | ||||
0.774314 | + | 0.632802i | \(0.218095\pi\) | |||||||
\(998\) | 46.7244 | 1.47904 | ||||||||
\(999\) | 0.342766 | 0.0108447 |
(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 | 1617.2.a.z.1.3 | 4 | ||
3.2 | odd | 2 | 4851.2.a.bt.1.2 | 4 | |||
7.2 | even | 3 | 231.2.i.e.67.2 | ✓ | 8 | ||
7.4 | even | 3 | 231.2.i.e.100.2 | yes | 8 | ||
7.6 | odd | 2 | 1617.2.a.x.1.3 | 4 | |||
21.2 | odd | 6 | 693.2.i.i.298.3 | 8 | |||
21.11 | odd | 6 | 693.2.i.i.100.3 | 8 | |||
21.20 | even | 2 | 4851.2.a.bu.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.i.e.67.2 | ✓ | 8 | 7.2 | even | 3 | ||
231.2.i.e.100.2 | yes | 8 | 7.4 | even | 3 | ||
693.2.i.i.100.3 | 8 | 21.11 | odd | 6 | |||
693.2.i.i.298.3 | 8 | 21.2 | odd | 6 | |||
1617.2.a.x.1.3 | 4 | 7.6 | odd | 2 | |||
1617.2.a.z.1.3 | 4 | 1.1 | even | 1 | trivial | ||
4851.2.a.bt.1.2 | 4 | 3.2 | odd | 2 | |||
4851.2.a.bu.1.2 | 4 | 21.20 | even | 2 |