Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80194 | −1.27416 | −0.637081 | − | 0.770797i | \(-0.719858\pi\) | ||||
−0.637081 | + | 0.770797i | \(0.719858\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.24698 | 0.623490 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | −1.80194 | −0.735638 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.35690 | 0.479735 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.80194 | −0.569823 | ||||||||
\(11\) | 1.80194 | 0.543305 | 0.271652 | − | 0.962395i | \(-0.412430\pi\) | ||||
0.271652 | + | 0.962395i | \(0.412430\pi\) | |||||||
\(12\) | 1.24698 | 0.359972 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.80194 | 0.481588 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −4.93900 | −1.23475 | ||||||||
\(17\) | −2.44504 | −0.593010 | −0.296505 | − | 0.955031i | \(-0.595821\pi\) | ||||
−0.296505 | + | 0.955031i | \(0.595821\pi\) | |||||||
\(18\) | −1.80194 | −0.424721 | ||||||||
\(19\) | 5.74094 | 1.31706 | 0.658531 | − | 0.752554i | \(-0.271178\pi\) | ||||
0.658531 | + | 0.752554i | \(0.271178\pi\) | |||||||
\(20\) | 1.24698 | 0.278833 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −3.24698 | −0.692258 | ||||||||
\(23\) | −7.04892 | −1.46980 | −0.734900 | − | 0.678175i | \(-0.762771\pi\) | ||||
−0.734900 | + | 0.678175i | \(0.762771\pi\) | |||||||
\(24\) | 1.35690 | 0.276975 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.24698 | −0.235657 | ||||||||
\(29\) | −3.15883 | −0.586581 | −0.293290 | − | 0.956023i | \(-0.594750\pi\) | ||||
−0.293290 | + | 0.956023i | \(0.594750\pi\) | |||||||
\(30\) | −1.80194 | −0.328987 | ||||||||
\(31\) | −0.445042 | −0.0799319 | −0.0399659 | − | 0.999201i | \(-0.512725\pi\) | ||||
−0.0399659 | + | 0.999201i | \(0.512725\pi\) | |||||||
\(32\) | 6.18598 | 1.09354 | ||||||||
\(33\) | 1.80194 | 0.313677 | ||||||||
\(34\) | 4.40581 | 0.755591 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 1.24698 | 0.207830 | ||||||||
\(37\) | −3.98792 | −0.655610 | −0.327805 | − | 0.944745i | \(-0.606309\pi\) | ||||
−0.327805 | + | 0.944745i | \(0.606309\pi\) | |||||||
\(38\) | −10.3448 | −1.67815 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.35690 | 0.214544 | ||||||||
\(41\) | −10.3448 | −1.61559 | −0.807794 | − | 0.589465i | \(-0.799339\pi\) | ||||
−0.807794 | + | 0.589465i | \(0.799339\pi\) | |||||||
\(42\) | 1.80194 | 0.278045 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 2.24698 | 0.338745 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 12.7017 | 1.87276 | ||||||||
\(47\) | 5.14675 | 0.750731 | 0.375365 | − | 0.926877i | \(-0.377517\pi\) | ||||
0.375365 | + | 0.926877i | \(0.377517\pi\) | |||||||
\(48\) | −4.93900 | −0.712883 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.20775 | 1.01933 | ||||||||
\(51\) | −2.44504 | −0.342374 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.92154 | 1.22547 | 0.612734 | − | 0.790289i | \(-0.290070\pi\) | ||||
0.612734 | + | 0.790289i | \(0.290070\pi\) | |||||||
\(54\) | −1.80194 | −0.245213 | ||||||||
\(55\) | 1.80194 | 0.242973 | ||||||||
\(56\) | −1.35690 | −0.181323 | ||||||||
\(57\) | 5.74094 | 0.760406 | ||||||||
\(58\) | 5.69202 | 0.747399 | ||||||||
\(59\) | −9.71379 | −1.26463 | −0.632314 | − | 0.774712i | \(-0.717895\pi\) | ||||
−0.632314 | + | 0.774712i | \(0.717895\pi\) | |||||||
\(60\) | 1.24698 | 0.160984 | ||||||||
\(61\) | −9.93900 | −1.27256 | −0.636279 | − | 0.771459i | \(-0.719527\pi\) | ||||
−0.636279 | + | 0.771459i | \(0.719527\pi\) | |||||||
\(62\) | 0.801938 | 0.101846 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −1.26875 | −0.158594 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.24698 | −0.399676 | ||||||||
\(67\) | −4.33513 | −0.529620 | −0.264810 | − | 0.964301i | \(-0.585309\pi\) | ||||
−0.264810 | + | 0.964301i | \(0.585309\pi\) | |||||||
\(68\) | −3.04892 | −0.369736 | ||||||||
\(69\) | −7.04892 | −0.848590 | ||||||||
\(70\) | 1.80194 | 0.215373 | ||||||||
\(71\) | −2.40581 | −0.285517 | −0.142759 | − | 0.989758i | \(-0.545597\pi\) | ||||
−0.142759 | + | 0.989758i | \(0.545597\pi\) | |||||||
\(72\) | 1.35690 | 0.159912 | ||||||||
\(73\) | 0.664874 | 0.0778177 | 0.0389088 | − | 0.999243i | \(-0.487612\pi\) | ||||
0.0389088 | + | 0.999243i | \(0.487612\pi\) | |||||||
\(74\) | 7.18598 | 0.835353 | ||||||||
\(75\) | −4.00000 | −0.461880 | ||||||||
\(76\) | 7.15883 | 0.821175 | ||||||||
\(77\) | −1.80194 | −0.205350 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.11960 | 0.463492 | 0.231746 | − | 0.972776i | \(-0.425556\pi\) | ||||
0.231746 | + | 0.972776i | \(0.425556\pi\) | |||||||
\(80\) | −4.93900 | −0.552197 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 18.6407 | 2.05852 | ||||||||
\(83\) | 11.0586 | 1.21384 | 0.606920 | − | 0.794763i | \(-0.292405\pi\) | ||||
0.606920 | + | 0.794763i | \(0.292405\pi\) | |||||||
\(84\) | −1.24698 | −0.136057 | ||||||||
\(85\) | −2.44504 | −0.265202 | ||||||||
\(86\) | 14.4155 | 1.55446 | ||||||||
\(87\) | −3.15883 | −0.338663 | ||||||||
\(88\) | 2.44504 | 0.260642 | ||||||||
\(89\) | 2.72587 | 0.288942 | 0.144471 | − | 0.989509i | \(-0.453852\pi\) | ||||
0.144471 | + | 0.989509i | \(0.453852\pi\) | |||||||
\(90\) | −1.80194 | −0.189941 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.78986 | −0.916406 | ||||||||
\(93\) | −0.445042 | −0.0461487 | ||||||||
\(94\) | −9.27413 | −0.956553 | ||||||||
\(95\) | 5.74094 | 0.589008 | ||||||||
\(96\) | 6.18598 | 0.631354 | ||||||||
\(97\) | −5.39373 | −0.547650 | −0.273825 | − | 0.961779i | \(-0.588289\pi\) | ||||
−0.273825 | + | 0.961779i | \(0.588289\pi\) | |||||||
\(98\) | −1.80194 | −0.182023 | ||||||||
\(99\) | 1.80194 | 0.181102 | ||||||||
\(100\) | −4.98792 | −0.498792 | ||||||||
\(101\) | −0.835790 | −0.0831642 | −0.0415821 | − | 0.999135i | \(-0.513240\pi\) | ||||
−0.0415821 | + | 0.999135i | \(0.513240\pi\) | |||||||
\(102\) | 4.40581 | 0.436241 | ||||||||
\(103\) | −16.6136 | −1.63698 | −0.818492 | − | 0.574519i | \(-0.805189\pi\) | ||||
−0.818492 | + | 0.574519i | \(0.805189\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | −16.0761 | −1.56145 | ||||||||
\(107\) | 13.0640 | 1.26294 | 0.631471 | − | 0.775399i | \(-0.282451\pi\) | ||||
0.631471 | + | 0.775399i | \(0.282451\pi\) | |||||||
\(108\) | 1.24698 | 0.119991 | ||||||||
\(109\) | −1.91185 | −0.183122 | −0.0915612 | − | 0.995799i | \(-0.529186\pi\) | ||||
−0.0915612 | + | 0.995799i | \(0.529186\pi\) | |||||||
\(110\) | −3.24698 | −0.309587 | ||||||||
\(111\) | −3.98792 | −0.378516 | ||||||||
\(112\) | 4.93900 | 0.466692 | ||||||||
\(113\) | 7.05429 | 0.663612 | 0.331806 | − | 0.943348i | \(-0.392342\pi\) | ||||
0.331806 | + | 0.943348i | \(0.392342\pi\) | |||||||
\(114\) | −10.3448 | −0.968881 | ||||||||
\(115\) | −7.04892 | −0.657315 | ||||||||
\(116\) | −3.93900 | −0.365727 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.5036 | 1.61134 | ||||||||
\(119\) | 2.44504 | 0.224137 | ||||||||
\(120\) | 1.35690 | 0.123867 | ||||||||
\(121\) | −7.75302 | −0.704820 | ||||||||
\(122\) | 17.9095 | 1.62145 | ||||||||
\(123\) | −10.3448 | −0.932760 | ||||||||
\(124\) | −0.554958 | −0.0498367 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 1.80194 | 0.160529 | ||||||||
\(127\) | −7.69633 | −0.682939 | −0.341470 | − | 0.939893i | \(-0.610925\pi\) | ||||
−0.341470 | + | 0.939893i | \(0.610925\pi\) | |||||||
\(128\) | −10.0858 | −0.891463 | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.18598 | −0.715212 | −0.357606 | − | 0.933872i | \(-0.616407\pi\) | ||||
−0.357606 | + | 0.933872i | \(0.616407\pi\) | |||||||
\(132\) | 2.24698 | 0.195574 | ||||||||
\(133\) | −5.74094 | −0.497803 | ||||||||
\(134\) | 7.81163 | 0.674822 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −3.31767 | −0.284488 | ||||||||
\(137\) | 8.79523 | 0.751427 | 0.375714 | − | 0.926736i | \(-0.377398\pi\) | ||||
0.375714 | + | 0.926736i | \(0.377398\pi\) | |||||||
\(138\) | 12.7017 | 1.08124 | ||||||||
\(139\) | −19.4330 | −1.64828 | −0.824141 | − | 0.566385i | \(-0.808342\pi\) | ||||
−0.824141 | + | 0.566385i | \(0.808342\pi\) | |||||||
\(140\) | −1.24698 | −0.105389 | ||||||||
\(141\) | 5.14675 | 0.433435 | ||||||||
\(142\) | 4.33513 | 0.363796 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.93900 | −0.411583 | ||||||||
\(145\) | −3.15883 | −0.262327 | ||||||||
\(146\) | −1.19806 | −0.0991523 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −4.97285 | −0.408766 | ||||||||
\(149\) | −10.5090 | −0.860933 | −0.430466 | − | 0.902607i | \(-0.641651\pi\) | ||||
−0.430466 | + | 0.902607i | \(0.641651\pi\) | |||||||
\(150\) | 7.20775 | 0.588510 | ||||||||
\(151\) | 20.9758 | 1.70699 | 0.853495 | − | 0.521102i | \(-0.174479\pi\) | ||||
0.853495 | + | 0.521102i | \(0.174479\pi\) | |||||||
\(152\) | 7.78986 | 0.631841 | ||||||||
\(153\) | −2.44504 | −0.197670 | ||||||||
\(154\) | 3.24698 | 0.261649 | ||||||||
\(155\) | −0.445042 | −0.0357466 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.838773 | 0.0669414 | 0.0334707 | − | 0.999440i | \(-0.489344\pi\) | ||||
0.0334707 | + | 0.999440i | \(0.489344\pi\) | |||||||
\(158\) | −7.42327 | −0.590564 | ||||||||
\(159\) | 8.92154 | 0.707524 | ||||||||
\(160\) | 6.18598 | 0.489045 | ||||||||
\(161\) | 7.04892 | 0.555533 | ||||||||
\(162\) | −1.80194 | −0.141574 | ||||||||
\(163\) | 12.7409 | 0.997947 | 0.498974 | − | 0.866617i | \(-0.333710\pi\) | ||||
0.498974 | + | 0.866617i | \(0.333710\pi\) | |||||||
\(164\) | −12.8998 | −1.00730 | ||||||||
\(165\) | 1.80194 | 0.140281 | ||||||||
\(166\) | −19.9269 | −1.54663 | ||||||||
\(167\) | 13.5646 | 1.04966 | 0.524832 | − | 0.851206i | \(-0.324128\pi\) | ||||
0.524832 | + | 0.851206i | \(0.324128\pi\) | |||||||
\(168\) | −1.35690 | −0.104687 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.40581 | 0.337910 | ||||||||
\(171\) | 5.74094 | 0.439021 | ||||||||
\(172\) | −9.97584 | −0.760650 | ||||||||
\(173\) | 7.75733 | 0.589779 | 0.294890 | − | 0.955531i | \(-0.404717\pi\) | ||||
0.294890 | + | 0.955531i | \(0.404717\pi\) | |||||||
\(174\) | 5.69202 | 0.431511 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | −8.89977 | −0.670846 | ||||||||
\(177\) | −9.71379 | −0.730133 | ||||||||
\(178\) | −4.91185 | −0.368159 | ||||||||
\(179\) | 2.16852 | 0.162083 | 0.0810415 | − | 0.996711i | \(-0.474175\pi\) | ||||
0.0810415 | + | 0.996711i | \(0.474175\pi\) | |||||||
\(180\) | 1.24698 | 0.0929444 | ||||||||
\(181\) | −2.52781 | −0.187891 | −0.0939454 | − | 0.995577i | \(-0.529948\pi\) | ||||
−0.0939454 | + | 0.995577i | \(0.529948\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.93900 | −0.734712 | ||||||||
\(184\) | −9.56465 | −0.705115 | ||||||||
\(185\) | −3.98792 | −0.293198 | ||||||||
\(186\) | 0.801938 | 0.0588009 | ||||||||
\(187\) | −4.40581 | −0.322185 | ||||||||
\(188\) | 6.41789 | 0.468073 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −10.3448 | −0.750492 | ||||||||
\(191\) | 20.2107 | 1.46240 | 0.731199 | − | 0.682165i | \(-0.238961\pi\) | ||||
0.731199 | + | 0.682165i | \(0.238961\pi\) | |||||||
\(192\) | −1.26875 | −0.0915641 | ||||||||
\(193\) | −24.3424 | −1.75221 | −0.876103 | − | 0.482124i | \(-0.839865\pi\) | ||||
−0.876103 | + | 0.482124i | \(0.839865\pi\) | |||||||
\(194\) | 9.71917 | 0.697796 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.24698 | 0.0890700 | ||||||||
\(197\) | −1.36898 | −0.0975356 | −0.0487678 | − | 0.998810i | \(-0.515529\pi\) | ||||
−0.0487678 | + | 0.998810i | \(0.515529\pi\) | |||||||
\(198\) | −3.24698 | −0.230753 | ||||||||
\(199\) | −4.01746 | −0.284790 | −0.142395 | − | 0.989810i | \(-0.545480\pi\) | ||||
−0.142395 | + | 0.989810i | \(0.545480\pi\) | |||||||
\(200\) | −5.42758 | −0.383788 | ||||||||
\(201\) | −4.33513 | −0.305776 | ||||||||
\(202\) | 1.50604 | 0.105965 | ||||||||
\(203\) | 3.15883 | 0.221707 | ||||||||
\(204\) | −3.04892 | −0.213467 | ||||||||
\(205\) | −10.3448 | −0.722513 | ||||||||
\(206\) | 29.9366 | 2.08578 | ||||||||
\(207\) | −7.04892 | −0.489934 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.3448 | 0.715566 | ||||||||
\(210\) | 1.80194 | 0.124346 | ||||||||
\(211\) | −24.6504 | −1.69700 | −0.848502 | − | 0.529193i | \(-0.822495\pi\) | ||||
−0.848502 | + | 0.529193i | \(0.822495\pi\) | |||||||
\(212\) | 11.1250 | 0.764067 | ||||||||
\(213\) | −2.40581 | −0.164844 | ||||||||
\(214\) | −23.5405 | −1.60919 | ||||||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | 1.35690 | 0.0923251 | ||||||||
\(217\) | 0.445042 | 0.0302114 | ||||||||
\(218\) | 3.44504 | 0.233328 | ||||||||
\(219\) | 0.664874 | 0.0449280 | ||||||||
\(220\) | 2.24698 | 0.151491 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.18598 | 0.482291 | ||||||||
\(223\) | −9.41013 | −0.630149 | −0.315074 | − | 0.949067i | \(-0.602029\pi\) | ||||
−0.315074 | + | 0.949067i | \(0.602029\pi\) | |||||||
\(224\) | −6.18598 | −0.413318 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | −12.7114 | −0.845550 | ||||||||
\(227\) | 5.33513 | 0.354105 | 0.177052 | − | 0.984201i | \(-0.443344\pi\) | ||||
0.177052 | + | 0.984201i | \(0.443344\pi\) | |||||||
\(228\) | 7.15883 | 0.474105 | ||||||||
\(229\) | 9.13036 | 0.603351 | 0.301676 | − | 0.953411i | \(-0.402454\pi\) | ||||
0.301676 | + | 0.953411i | \(0.402454\pi\) | |||||||
\(230\) | 12.7017 | 0.837526 | ||||||||
\(231\) | −1.80194 | −0.118559 | ||||||||
\(232\) | −4.28621 | −0.281403 | ||||||||
\(233\) | −26.7265 | −1.75091 | −0.875454 | − | 0.483301i | \(-0.839438\pi\) | ||||
−0.875454 | + | 0.483301i | \(0.839438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.14675 | 0.335737 | ||||||||
\(236\) | −12.1129 | −0.788483 | ||||||||
\(237\) | 4.11960 | 0.267597 | ||||||||
\(238\) | −4.40581 | −0.285586 | ||||||||
\(239\) | −8.13169 | −0.525995 | −0.262998 | − | 0.964797i | \(-0.584711\pi\) | ||||
−0.262998 | + | 0.964797i | \(0.584711\pi\) | |||||||
\(240\) | −4.93900 | −0.318811 | ||||||||
\(241\) | 7.64848 | 0.492682 | 0.246341 | − | 0.969183i | \(-0.420772\pi\) | ||||
0.246341 | + | 0.969183i | \(0.420772\pi\) | |||||||
\(242\) | 13.9705 | 0.898055 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −12.3937 | −0.793427 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 18.6407 | 1.18849 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.603875 | −0.0383461 | ||||||||
\(249\) | 11.0586 | 0.700811 | ||||||||
\(250\) | 16.2174 | 1.02568 | ||||||||
\(251\) | −8.24459 | −0.520394 | −0.260197 | − | 0.965556i | \(-0.583787\pi\) | ||||
−0.260197 | + | 0.965556i | \(0.583787\pi\) | |||||||
\(252\) | −1.24698 | −0.0785523 | ||||||||
\(253\) | −12.7017 | −0.798550 | ||||||||
\(254\) | 13.8683 | 0.870175 | ||||||||
\(255\) | −2.44504 | −0.153114 | ||||||||
\(256\) | 20.7114 | 1.29446 | ||||||||
\(257\) | 24.6329 | 1.53656 | 0.768280 | − | 0.640114i | \(-0.221113\pi\) | ||||
0.768280 | + | 0.640114i | \(0.221113\pi\) | |||||||
\(258\) | 14.4155 | 0.897470 | ||||||||
\(259\) | 3.98792 | 0.247797 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.15883 | −0.195527 | ||||||||
\(262\) | 14.7506 | 0.911297 | ||||||||
\(263\) | 17.1588 | 1.05806 | 0.529030 | − | 0.848603i | \(-0.322556\pi\) | ||||
0.529030 | + | 0.848603i | \(0.322556\pi\) | |||||||
\(264\) | 2.44504 | 0.150482 | ||||||||
\(265\) | 8.92154 | 0.548046 | ||||||||
\(266\) | 10.3448 | 0.634281 | ||||||||
\(267\) | 2.72587 | 0.166821 | ||||||||
\(268\) | −5.40581 | −0.330213 | ||||||||
\(269\) | −7.08708 | −0.432107 | −0.216053 | − | 0.976382i | \(-0.569319\pi\) | ||||
−0.216053 | + | 0.976382i | \(0.569319\pi\) | |||||||
\(270\) | −1.80194 | −0.109662 | ||||||||
\(271\) | −24.5483 | −1.49120 | −0.745600 | − | 0.666394i | \(-0.767837\pi\) | ||||
−0.745600 | + | 0.666394i | \(0.767837\pi\) | |||||||
\(272\) | 12.0761 | 0.732219 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.8485 | −0.957441 | ||||||||
\(275\) | −7.20775 | −0.434644 | ||||||||
\(276\) | −8.78986 | −0.529087 | ||||||||
\(277\) | 33.0810 | 1.98764 | 0.993821 | − | 0.110992i | \(-0.0354027\pi\) | ||||
0.993821 | + | 0.110992i | \(0.0354027\pi\) | |||||||
\(278\) | 35.0170 | 2.10018 | ||||||||
\(279\) | −0.445042 | −0.0266440 | ||||||||
\(280\) | −1.35690 | −0.0810900 | ||||||||
\(281\) | −26.3163 | −1.56990 | −0.784951 | − | 0.619558i | \(-0.787312\pi\) | ||||
−0.784951 | + | 0.619558i | \(0.787312\pi\) | |||||||
\(282\) | −9.27413 | −0.552266 | ||||||||
\(283\) | 31.7778 | 1.88899 | 0.944496 | − | 0.328522i | \(-0.106551\pi\) | ||||
0.944496 | + | 0.328522i | \(0.106551\pi\) | |||||||
\(284\) | −3.00000 | −0.178017 | ||||||||
\(285\) | 5.74094 | 0.340064 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3448 | 0.610635 | ||||||||
\(288\) | 6.18598 | 0.364512 | ||||||||
\(289\) | −11.0218 | −0.648339 | ||||||||
\(290\) | 5.69202 | 0.334247 | ||||||||
\(291\) | −5.39373 | −0.316186 | ||||||||
\(292\) | 0.829085 | 0.0485185 | ||||||||
\(293\) | 12.8616 | 0.751383 | 0.375692 | − | 0.926745i | \(-0.377405\pi\) | ||||
0.375692 | + | 0.926745i | \(0.377405\pi\) | |||||||
\(294\) | −1.80194 | −0.105091 | ||||||||
\(295\) | −9.71379 | −0.565559 | ||||||||
\(296\) | −5.41119 | −0.314519 | ||||||||
\(297\) | 1.80194 | 0.104559 | ||||||||
\(298\) | 18.9366 | 1.09697 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.98792 | −0.287978 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | −37.7972 | −2.17498 | ||||||||
\(303\) | −0.835790 | −0.0480149 | ||||||||
\(304\) | −28.3545 | −1.62624 | ||||||||
\(305\) | −9.93900 | −0.569106 | ||||||||
\(306\) | 4.40581 | 0.251864 | ||||||||
\(307\) | −29.5937 | −1.68900 | −0.844501 | − | 0.535554i | \(-0.820103\pi\) | ||||
−0.844501 | + | 0.535554i | \(0.820103\pi\) | |||||||
\(308\) | −2.24698 | −0.128034 | ||||||||
\(309\) | −16.6136 | −0.945113 | ||||||||
\(310\) | 0.801938 | 0.0455470 | ||||||||
\(311\) | −8.55794 | −0.485276 | −0.242638 | − | 0.970117i | \(-0.578013\pi\) | ||||
−0.242638 | + | 0.970117i | \(0.578013\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.3569 | −0.924546 | −0.462273 | − | 0.886738i | \(-0.652966\pi\) | ||||
−0.462273 | + | 0.886738i | \(0.652966\pi\) | |||||||
\(314\) | −1.51142 | −0.0852942 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 5.13706 | 0.288982 | ||||||||
\(317\) | 28.3545 | 1.59255 | 0.796274 | − | 0.604936i | \(-0.206801\pi\) | ||||
0.796274 | + | 0.604936i | \(0.206801\pi\) | |||||||
\(318\) | −16.0761 | −0.901501 | ||||||||
\(319\) | −5.69202 | −0.318692 | ||||||||
\(320\) | −1.26875 | −0.0709253 | ||||||||
\(321\) | 13.0640 | 0.729160 | ||||||||
\(322\) | −12.7017 | −0.707839 | ||||||||
\(323\) | −14.0368 | −0.781030 | ||||||||
\(324\) | 1.24698 | 0.0692766 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.9584 | −1.27155 | ||||||||
\(327\) | −1.91185 | −0.105726 | ||||||||
\(328\) | −14.0368 | −0.775055 | ||||||||
\(329\) | −5.14675 | −0.283750 | ||||||||
\(330\) | −3.24698 | −0.178740 | ||||||||
\(331\) | −11.3894 | −0.626019 | −0.313010 | − | 0.949750i | \(-0.601337\pi\) | ||||
−0.313010 | + | 0.949750i | \(0.601337\pi\) | |||||||
\(332\) | 13.7899 | 0.756817 | ||||||||
\(333\) | −3.98792 | −0.218537 | ||||||||
\(334\) | −24.4426 | −1.33744 | ||||||||
\(335\) | −4.33513 | −0.236853 | ||||||||
\(336\) | 4.93900 | 0.269445 | ||||||||
\(337\) | −7.64609 | −0.416509 | −0.208254 | − | 0.978075i | \(-0.566778\pi\) | ||||
−0.208254 | + | 0.978075i | \(0.566778\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.05429 | 0.383137 | ||||||||
\(340\) | −3.04892 | −0.165351 | ||||||||
\(341\) | −0.801938 | −0.0434274 | ||||||||
\(342\) | −10.3448 | −0.559383 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −10.8552 | −0.585271 | ||||||||
\(345\) | −7.04892 | −0.379501 | ||||||||
\(346\) | −13.9782 | −0.751474 | ||||||||
\(347\) | 14.4668 | 0.776619 | 0.388310 | − | 0.921529i | \(-0.373059\pi\) | ||||
0.388310 | + | 0.921529i | \(0.373059\pi\) | |||||||
\(348\) | −3.93900 | −0.211153 | ||||||||
\(349\) | −17.0519 | −0.912767 | −0.456384 | − | 0.889783i | \(-0.650856\pi\) | ||||
−0.456384 | + | 0.889783i | \(0.650856\pi\) | |||||||
\(350\) | −7.20775 | −0.385270 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.1468 | 0.594124 | ||||||||
\(353\) | 21.0151 | 1.11852 | 0.559260 | − | 0.828993i | \(-0.311086\pi\) | ||||
0.559260 | + | 0.828993i | \(0.311086\pi\) | |||||||
\(354\) | 17.5036 | 0.930308 | ||||||||
\(355\) | −2.40581 | −0.127687 | ||||||||
\(356\) | 3.39911 | 0.180152 | ||||||||
\(357\) | 2.44504 | 0.129405 | ||||||||
\(358\) | −3.90754 | −0.206520 | ||||||||
\(359\) | −16.3424 | −0.862520 | −0.431260 | − | 0.902228i | \(-0.641931\pi\) | ||||
−0.431260 | + | 0.902228i | \(0.641931\pi\) | |||||||
\(360\) | 1.35690 | 0.0715147 | ||||||||
\(361\) | 13.9584 | 0.734651 | ||||||||
\(362\) | 4.55496 | 0.239403 | ||||||||
\(363\) | −7.75302 | −0.406928 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.664874 | 0.0348011 | ||||||||
\(366\) | 17.9095 | 0.936143 | ||||||||
\(367\) | −34.4209 | −1.79676 | −0.898378 | − | 0.439224i | \(-0.855253\pi\) | ||||
−0.898378 | + | 0.439224i | \(0.855253\pi\) | |||||||
\(368\) | 34.8146 | 1.81484 | ||||||||
\(369\) | −10.3448 | −0.538530 | ||||||||
\(370\) | 7.18598 | 0.373581 | ||||||||
\(371\) | −8.92154 | −0.463183 | ||||||||
\(372\) | −0.554958 | −0.0287732 | ||||||||
\(373\) | 1.35391 | 0.0701029 | 0.0350515 | − | 0.999386i | \(-0.488840\pi\) | ||||
0.0350515 | + | 0.999386i | \(0.488840\pi\) | |||||||
\(374\) | 7.93900 | 0.410516 | ||||||||
\(375\) | −9.00000 | −0.464758 | ||||||||
\(376\) | 6.98361 | 0.360152 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.80194 | 0.0926817 | ||||||||
\(379\) | 30.7590 | 1.57998 | 0.789992 | − | 0.613118i | \(-0.210085\pi\) | ||||
0.789992 | + | 0.613118i | \(0.210085\pi\) | |||||||
\(380\) | 7.15883 | 0.367240 | ||||||||
\(381\) | −7.69633 | −0.394295 | ||||||||
\(382\) | −36.4185 | −1.86333 | ||||||||
\(383\) | −31.6582 | −1.61766 | −0.808828 | − | 0.588045i | \(-0.799898\pi\) | ||||
−0.808828 | + | 0.588045i | \(0.799898\pi\) | |||||||
\(384\) | −10.0858 | −0.514686 | ||||||||
\(385\) | −1.80194 | −0.0918353 | ||||||||
\(386\) | 43.8635 | 2.23259 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | −6.72587 | −0.341454 | ||||||||
\(389\) | −19.0495 | −0.965848 | −0.482924 | − | 0.875662i | \(-0.660425\pi\) | ||||
−0.482924 | + | 0.875662i | \(0.660425\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.2349 | 0.871606 | ||||||||
\(392\) | 1.35690 | 0.0685336 | ||||||||
\(393\) | −8.18598 | −0.412928 | ||||||||
\(394\) | 2.46681 | 0.124276 | ||||||||
\(395\) | 4.11960 | 0.207280 | ||||||||
\(396\) | 2.24698 | 0.112915 | ||||||||
\(397\) | 6.37435 | 0.319920 | 0.159960 | − | 0.987124i | \(-0.448864\pi\) | ||||
0.159960 | + | 0.987124i | \(0.448864\pi\) | |||||||
\(398\) | 7.23921 | 0.362869 | ||||||||
\(399\) | −5.74094 | −0.287406 | ||||||||
\(400\) | 19.7560 | 0.987800 | ||||||||
\(401\) | −20.7754 | −1.03747 | −0.518737 | − | 0.854934i | \(-0.673597\pi\) | ||||
−0.518737 | + | 0.854934i | \(0.673597\pi\) | |||||||
\(402\) | 7.81163 | 0.389609 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.04221 | −0.0518520 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −5.69202 | −0.282490 | ||||||||
\(407\) | −7.18598 | −0.356196 | ||||||||
\(408\) | −3.31767 | −0.164249 | ||||||||
\(409\) | 5.48725 | 0.271327 | 0.135664 | − | 0.990755i | \(-0.456683\pi\) | ||||
0.135664 | + | 0.990755i | \(0.456683\pi\) | |||||||
\(410\) | 18.6407 | 0.920599 | ||||||||
\(411\) | 8.79523 | 0.433837 | ||||||||
\(412\) | −20.7168 | −1.02064 | ||||||||
\(413\) | 9.71379 | 0.477984 | ||||||||
\(414\) | 12.7017 | 0.624255 | ||||||||
\(415\) | 11.0586 | 0.542846 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.4330 | −0.951636 | ||||||||
\(418\) | −18.6407 | −0.911747 | ||||||||
\(419\) | −14.7259 | −0.719406 | −0.359703 | − | 0.933067i | \(-0.617122\pi\) | ||||
−0.359703 | + | 0.933067i | \(0.617122\pi\) | |||||||
\(420\) | −1.24698 | −0.0608464 | ||||||||
\(421\) | 1.64071 | 0.0799634 | 0.0399817 | − | 0.999200i | \(-0.487270\pi\) | ||||
0.0399817 | + | 0.999200i | \(0.487270\pi\) | |||||||
\(422\) | 44.4185 | 2.16226 | ||||||||
\(423\) | 5.14675 | 0.250244 | ||||||||
\(424\) | 12.1056 | 0.587900 | ||||||||
\(425\) | 9.78017 | 0.474408 | ||||||||
\(426\) | 4.33513 | 0.210038 | ||||||||
\(427\) | 9.93900 | 0.480982 | ||||||||
\(428\) | 16.2905 | 0.787432 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.4155 | 0.695177 | ||||||||
\(431\) | 6.94331 | 0.334448 | 0.167224 | − | 0.985919i | \(-0.446520\pi\) | ||||
0.167224 | + | 0.985919i | \(0.446520\pi\) | |||||||
\(432\) | −4.93900 | −0.237628 | ||||||||
\(433\) | −36.1909 | −1.73922 | −0.869611 | − | 0.493737i | \(-0.835631\pi\) | ||||
−0.869611 | + | 0.493737i | \(0.835631\pi\) | |||||||
\(434\) | −0.801938 | −0.0384942 | ||||||||
\(435\) | −3.15883 | −0.151454 | ||||||||
\(436\) | −2.38404 | −0.114175 | ||||||||
\(437\) | −40.4674 | −1.93582 | ||||||||
\(438\) | −1.19806 | −0.0572456 | ||||||||
\(439\) | 8.76032 | 0.418107 | 0.209054 | − | 0.977904i | \(-0.432962\pi\) | ||||
0.209054 | + | 0.977904i | \(0.432962\pi\) | |||||||
\(440\) | 2.44504 | 0.116563 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.4577 | −0.876952 | −0.438476 | − | 0.898743i | \(-0.644482\pi\) | ||||
−0.438476 | + | 0.898743i | \(0.644482\pi\) | |||||||
\(444\) | −4.97285 | −0.236001 | ||||||||
\(445\) | 2.72587 | 0.129219 | ||||||||
\(446\) | 16.9565 | 0.802912 | ||||||||
\(447\) | −10.5090 | −0.497060 | ||||||||
\(448\) | 1.26875 | 0.0599428 | ||||||||
\(449\) | −34.7952 | −1.64209 | −0.821044 | − | 0.570865i | \(-0.806608\pi\) | ||||
−0.821044 | + | 0.570865i | \(0.806608\pi\) | |||||||
\(450\) | 7.20775 | 0.339777 | ||||||||
\(451\) | −18.6407 | −0.877757 | ||||||||
\(452\) | 8.79656 | 0.413755 | ||||||||
\(453\) | 20.9758 | 0.985531 | ||||||||
\(454\) | −9.61356 | −0.451187 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.78986 | 0.364793 | ||||||||
\(457\) | −23.2664 | −1.08835 | −0.544177 | − | 0.838970i | \(-0.683158\pi\) | ||||
−0.544177 | + | 0.838970i | \(0.683158\pi\) | |||||||
\(458\) | −16.4523 | −0.768767 | ||||||||
\(459\) | −2.44504 | −0.114125 | ||||||||
\(460\) | −8.78986 | −0.409829 | ||||||||
\(461\) | 32.8702 | 1.53092 | 0.765460 | − | 0.643484i | \(-0.222512\pi\) | ||||
0.765460 | + | 0.643484i | \(0.222512\pi\) | |||||||
\(462\) | 3.24698 | 0.151063 | ||||||||
\(463\) | −22.6015 | −1.05038 | −0.525190 | − | 0.850985i | \(-0.676006\pi\) | ||||
−0.525190 | + | 0.850985i | \(0.676006\pi\) | |||||||
\(464\) | 15.6015 | 0.724281 | ||||||||
\(465\) | −0.445042 | −0.0206383 | ||||||||
\(466\) | 48.1594 | 2.23094 | ||||||||
\(467\) | −12.4886 | −0.577903 | −0.288951 | − | 0.957344i | \(-0.593307\pi\) | ||||
−0.288951 | + | 0.957344i | \(0.593307\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.33513 | 0.200178 | ||||||||
\(470\) | −9.27413 | −0.427784 | ||||||||
\(471\) | 0.838773 | 0.0386486 | ||||||||
\(472\) | −13.1806 | −0.606686 | ||||||||
\(473\) | −14.4155 | −0.662825 | ||||||||
\(474\) | −7.42327 | −0.340962 | ||||||||
\(475\) | −22.9638 | −1.05365 | ||||||||
\(476\) | 3.04892 | 0.139747 | ||||||||
\(477\) | 8.92154 | 0.408489 | ||||||||
\(478\) | 14.6528 | 0.670203 | ||||||||
\(479\) | 13.5536 | 0.619281 | 0.309641 | − | 0.950854i | \(-0.399791\pi\) | ||||
0.309641 | + | 0.950854i | \(0.399791\pi\) | |||||||
\(480\) | 6.18598 | 0.282350 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −13.7821 | −0.627757 | ||||||||
\(483\) | 7.04892 | 0.320737 | ||||||||
\(484\) | −9.66786 | −0.439448 | ||||||||
\(485\) | −5.39373 | −0.244917 | ||||||||
\(486\) | −1.80194 | −0.0817376 | ||||||||
\(487\) | −14.9414 | −0.677059 | −0.338530 | − | 0.940956i | \(-0.609930\pi\) | ||||
−0.338530 | + | 0.940956i | \(0.609930\pi\) | |||||||
\(488\) | −13.4862 | −0.610491 | ||||||||
\(489\) | 12.7409 | 0.576165 | ||||||||
\(490\) | −1.80194 | −0.0814032 | ||||||||
\(491\) | 27.4862 | 1.24043 | 0.620217 | − | 0.784430i | \(-0.287044\pi\) | ||||
0.620217 | + | 0.784430i | \(0.287044\pi\) | |||||||
\(492\) | −12.8998 | −0.581567 | ||||||||
\(493\) | 7.72348 | 0.347848 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.80194 | 0.0809911 | ||||||||
\(496\) | 2.19806 | 0.0986959 | ||||||||
\(497\) | 2.40581 | 0.107915 | ||||||||
\(498\) | −19.9269 | −0.892947 | ||||||||
\(499\) | −17.8756 | −0.800222 | −0.400111 | − | 0.916467i | \(-0.631028\pi\) | ||||
−0.400111 | + | 0.916467i | \(0.631028\pi\) | |||||||
\(500\) | −11.2228 | −0.501900 | ||||||||
\(501\) | 13.5646 | 0.606024 | ||||||||
\(502\) | 14.8562 | 0.663066 | ||||||||
\(503\) | −37.6510 | −1.67877 | −0.839387 | − | 0.543534i | \(-0.817086\pi\) | ||||
−0.839387 | + | 0.543534i | \(0.817086\pi\) | |||||||
\(504\) | −1.35690 | −0.0604409 | ||||||||
\(505\) | −0.835790 | −0.0371921 | ||||||||
\(506\) | 22.8877 | 1.01748 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.59717 | −0.425806 | ||||||||
\(509\) | −0.552565 | −0.0244920 | −0.0122460 | − | 0.999925i | \(-0.503898\pi\) | ||||
−0.0122460 | + | 0.999925i | \(0.503898\pi\) | |||||||
\(510\) | 4.40581 | 0.195093 | ||||||||
\(511\) | −0.664874 | −0.0294123 | ||||||||
\(512\) | −17.1491 | −0.757892 | ||||||||
\(513\) | 5.74094 | 0.253469 | ||||||||
\(514\) | −44.3870 | −1.95783 | ||||||||
\(515\) | −16.6136 | −0.732081 | ||||||||
\(516\) | −9.97584 | −0.439162 | ||||||||
\(517\) | 9.27413 | 0.407876 | ||||||||
\(518\) | −7.18598 | −0.315734 | ||||||||
\(519\) | 7.75733 | 0.340509 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.0127 | −1.13964 | −0.569818 | − | 0.821771i | \(-0.692986\pi\) | ||||
−0.569818 | + | 0.821771i | \(0.692986\pi\) | |||||||
\(522\) | 5.69202 | 0.249133 | ||||||||
\(523\) | 41.0428 | 1.79468 | 0.897338 | − | 0.441343i | \(-0.145498\pi\) | ||||
0.897338 | + | 0.441343i | \(0.145498\pi\) | |||||||
\(524\) | −10.2078 | −0.445928 | ||||||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | −30.9191 | −1.34814 | ||||||||
\(527\) | 1.08815 | 0.0474004 | ||||||||
\(528\) | −8.89977 | −0.387313 | ||||||||
\(529\) | 26.6872 | 1.16031 | ||||||||
\(530\) | −16.0761 | −0.698300 | ||||||||
\(531\) | −9.71379 | −0.421543 | ||||||||
\(532\) | −7.15883 | −0.310375 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −4.91185 | −0.212557 | ||||||||
\(535\) | 13.0640 | 0.564805 | ||||||||
\(536\) | −5.88231 | −0.254077 | ||||||||
\(537\) | 2.16852 | 0.0935786 | ||||||||
\(538\) | 12.7705 | 0.550574 | ||||||||
\(539\) | 1.80194 | 0.0776150 | ||||||||
\(540\) | 1.24698 | 0.0536615 | ||||||||
\(541\) | 33.2664 | 1.43023 | 0.715116 | − | 0.699006i | \(-0.246374\pi\) | ||||
0.715116 | + | 0.699006i | \(0.246374\pi\) | |||||||
\(542\) | 44.2344 | 1.90003 | ||||||||
\(543\) | −2.52781 | −0.108479 | ||||||||
\(544\) | −15.1250 | −0.648478 | ||||||||
\(545\) | −1.91185 | −0.0818948 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.4808 | −1.68808 | −0.844039 | − | 0.536282i | \(-0.819828\pi\) | ||||
−0.844039 | + | 0.536282i | \(0.819828\pi\) | |||||||
\(548\) | 10.9675 | 0.468507 | ||||||||
\(549\) | −9.93900 | −0.424186 | ||||||||
\(550\) | 12.9879 | 0.553807 | ||||||||
\(551\) | −18.1347 | −0.772563 | ||||||||
\(552\) | −9.56465 | −0.407098 | ||||||||
\(553\) | −4.11960 | −0.175183 | ||||||||
\(554\) | −59.6098 | −2.53258 | ||||||||
\(555\) | −3.98792 | −0.169278 | ||||||||
\(556\) | −24.2325 | −1.02769 | ||||||||
\(557\) | −33.4446 | −1.41709 | −0.708546 | − | 0.705665i | \(-0.750648\pi\) | ||||
−0.708546 | + | 0.705665i | \(0.750648\pi\) | |||||||
\(558\) | 0.801938 | 0.0339487 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.93900 | 0.208711 | ||||||||
\(561\) | −4.40581 | −0.186014 | ||||||||
\(562\) | 47.4204 | 2.00031 | ||||||||
\(563\) | −32.4674 | −1.36834 | −0.684169 | − | 0.729324i | \(-0.739835\pi\) | ||||
−0.684169 | + | 0.729324i | \(0.739835\pi\) | |||||||
\(564\) | 6.41789 | 0.270242 | ||||||||
\(565\) | 7.05429 | 0.296776 | ||||||||
\(566\) | −57.2616 | −2.40688 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −3.26444 | −0.136973 | ||||||||
\(569\) | 17.7506 | 0.744145 | 0.372073 | − | 0.928204i | \(-0.378647\pi\) | ||||
0.372073 | + | 0.928204i | \(0.378647\pi\) | |||||||
\(570\) | −10.3448 | −0.433297 | ||||||||
\(571\) | 33.1336 | 1.38660 | 0.693299 | − | 0.720650i | \(-0.256156\pi\) | ||||
0.693299 | + | 0.720650i | \(0.256156\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.2107 | 0.844316 | ||||||||
\(574\) | −18.6407 | −0.778048 | ||||||||
\(575\) | 28.1957 | 1.17584 | ||||||||
\(576\) | −1.26875 | −0.0528646 | ||||||||
\(577\) | 9.76702 | 0.406606 | 0.203303 | − | 0.979116i | \(-0.434832\pi\) | ||||
0.203303 | + | 0.979116i | \(0.434832\pi\) | |||||||
\(578\) | 19.8605 | 0.826090 | ||||||||
\(579\) | −24.3424 | −1.01164 | ||||||||
\(580\) | −3.93900 | −0.163558 | ||||||||
\(581\) | −11.0586 | −0.458788 | ||||||||
\(582\) | 9.71917 | 0.402872 | ||||||||
\(583\) | 16.0761 | 0.665803 | ||||||||
\(584\) | 0.902165 | 0.0373319 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.1758 | −0.957384 | ||||||||
\(587\) | −7.43488 | −0.306870 | −0.153435 | − | 0.988159i | \(-0.549034\pi\) | ||||
−0.153435 | + | 0.988159i | \(0.549034\pi\) | |||||||
\(588\) | 1.24698 | 0.0514246 | ||||||||
\(589\) | −2.55496 | −0.105275 | ||||||||
\(590\) | 17.5036 | 0.720614 | ||||||||
\(591\) | −1.36898 | −0.0563122 | ||||||||
\(592\) | 19.6963 | 0.809514 | ||||||||
\(593\) | 42.9366 | 1.76320 | 0.881598 | − | 0.472002i | \(-0.156468\pi\) | ||||
0.881598 | + | 0.472002i | \(0.156468\pi\) | |||||||
\(594\) | −3.24698 | −0.133225 | ||||||||
\(595\) | 2.44504 | 0.100237 | ||||||||
\(596\) | −13.1045 | −0.536783 | ||||||||
\(597\) | −4.01746 | −0.164424 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.0151 | −0.858652 | −0.429326 | − | 0.903150i | \(-0.641249\pi\) | ||||
−0.429326 | + | 0.903150i | \(0.641249\pi\) | |||||||
\(600\) | −5.42758 | −0.221580 | ||||||||
\(601\) | −3.18837 | −0.130056 | −0.0650282 | − | 0.997883i | \(-0.520714\pi\) | ||||
−0.0650282 | + | 0.997883i | \(0.520714\pi\) | |||||||
\(602\) | −14.4155 | −0.587532 | ||||||||
\(603\) | −4.33513 | −0.176540 | ||||||||
\(604\) | 26.1564 | 1.06429 | ||||||||
\(605\) | −7.75302 | −0.315205 | ||||||||
\(606\) | 1.50604 | 0.0611787 | ||||||||
\(607\) | −36.6491 | −1.48754 | −0.743770 | − | 0.668436i | \(-0.766964\pi\) | ||||
−0.743770 | + | 0.668436i | \(0.766964\pi\) | |||||||
\(608\) | 35.5133 | 1.44026 | ||||||||
\(609\) | 3.15883 | 0.128002 | ||||||||
\(610\) | 17.9095 | 0.725133 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.04892 | −0.123245 | ||||||||
\(613\) | 13.9433 | 0.563165 | 0.281583 | − | 0.959537i | \(-0.409141\pi\) | ||||
0.281583 | + | 0.959537i | \(0.409141\pi\) | |||||||
\(614\) | 53.3260 | 2.15206 | ||||||||
\(615\) | −10.3448 | −0.417143 | ||||||||
\(616\) | −2.44504 | −0.0985135 | ||||||||
\(617\) | −14.3026 | −0.575801 | −0.287901 | − | 0.957660i | \(-0.592957\pi\) | ||||
−0.287901 | + | 0.957660i | \(0.592957\pi\) | |||||||
\(618\) | 29.9366 | 1.20423 | ||||||||
\(619\) | 10.5690 | 0.424802 | 0.212401 | − | 0.977183i | \(-0.431872\pi\) | ||||
0.212401 | + | 0.977183i | \(0.431872\pi\) | |||||||
\(620\) | −0.554958 | −0.0222877 | ||||||||
\(621\) | −7.04892 | −0.282863 | ||||||||
\(622\) | 15.4209 | 0.618321 | ||||||||
\(623\) | −2.72587 | −0.109210 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 29.4741 | 1.17802 | ||||||||
\(627\) | 10.3448 | 0.413132 | ||||||||
\(628\) | 1.04593 | 0.0417373 | ||||||||
\(629\) | 9.75063 | 0.388783 | ||||||||
\(630\) | 1.80194 | 0.0717909 | ||||||||
\(631\) | 26.6614 | 1.06137 | 0.530687 | − | 0.847568i | \(-0.321934\pi\) | ||||
0.530687 | + | 0.847568i | \(0.321934\pi\) | |||||||
\(632\) | 5.58987 | 0.222353 | ||||||||
\(633\) | −24.6504 | −0.979765 | ||||||||
\(634\) | −51.0930 | −2.02916 | ||||||||
\(635\) | −7.69633 | −0.305420 | ||||||||
\(636\) | 11.1250 | 0.441134 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.2567 | 0.406065 | ||||||||
\(639\) | −2.40581 | −0.0951725 | ||||||||
\(640\) | −10.0858 | −0.398674 | ||||||||
\(641\) | 35.0291 | 1.38356 | 0.691782 | − | 0.722106i | \(-0.256826\pi\) | ||||
0.691782 | + | 0.722106i | \(0.256826\pi\) | |||||||
\(642\) | −23.5405 | −0.929069 | ||||||||
\(643\) | −3.53558 | −0.139430 | −0.0697148 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697148 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(644\) | 8.78986 | 0.346369 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 25.2935 | 0.995160 | ||||||||
\(647\) | 8.69309 | 0.341760 | 0.170880 | − | 0.985292i | \(-0.445339\pi\) | ||||
0.170880 | + | 0.985292i | \(0.445339\pi\) | |||||||
\(648\) | 1.35690 | 0.0533039 | ||||||||
\(649\) | −17.5036 | −0.687078 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.445042 | 0.0174426 | ||||||||
\(652\) | 15.8877 | 0.622210 | ||||||||
\(653\) | −4.93123 | −0.192974 | −0.0964870 | − | 0.995334i | \(-0.530761\pi\) | ||||
−0.0964870 | + | 0.995334i | \(0.530761\pi\) | |||||||
\(654\) | 3.44504 | 0.134712 | ||||||||
\(655\) | −8.18598 | −0.319853 | ||||||||
\(656\) | 51.0930 | 1.99485 | ||||||||
\(657\) | 0.664874 | 0.0259392 | ||||||||
\(658\) | 9.27413 | 0.361543 | ||||||||
\(659\) | −25.6571 | −0.999459 | −0.499729 | − | 0.866182i | \(-0.666567\pi\) | ||||
−0.499729 | + | 0.866182i | \(0.666567\pi\) | |||||||
\(660\) | 2.24698 | 0.0874636 | ||||||||
\(661\) | 4.18359 | 0.162723 | 0.0813614 | − | 0.996685i | \(-0.474073\pi\) | ||||
0.0813614 | + | 0.996685i | \(0.474073\pi\) | |||||||
\(662\) | 20.5230 | 0.797650 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.0054 | 0.582322 | ||||||||
\(665\) | −5.74094 | −0.222624 | ||||||||
\(666\) | 7.18598 | 0.278451 | ||||||||
\(667\) | 22.2664 | 0.862157 | ||||||||
\(668\) | 16.9148 | 0.654455 | ||||||||
\(669\) | −9.41013 | −0.363816 | ||||||||
\(670\) | 7.81163 | 0.301789 | ||||||||
\(671\) | −17.9095 | −0.691387 | ||||||||
\(672\) | −6.18598 | −0.238629 | ||||||||
\(673\) | 15.2946 | 0.589562 | 0.294781 | − | 0.955565i | \(-0.404753\pi\) | ||||
0.294781 | + | 0.955565i | \(0.404753\pi\) | |||||||
\(674\) | 13.7778 | 0.530700 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.4547 | 1.09360 | 0.546802 | − | 0.837262i | \(-0.315845\pi\) | ||||
0.546802 | + | 0.837262i | \(0.315845\pi\) | |||||||
\(678\) | −12.7114 | −0.488178 | ||||||||
\(679\) | 5.39373 | 0.206992 | ||||||||
\(680\) | −3.31767 | −0.127227 | ||||||||
\(681\) | 5.33513 | 0.204442 | ||||||||
\(682\) | 1.44504 | 0.0553335 | ||||||||
\(683\) | 50.4844 | 1.93173 | 0.965866 | − | 0.259043i | \(-0.0834072\pi\) | ||||
0.965866 | + | 0.259043i | \(0.0834072\pi\) | |||||||
\(684\) | 7.15883 | 0.273725 | ||||||||
\(685\) | 8.79523 | 0.336049 | ||||||||
\(686\) | 1.80194 | 0.0687983 | ||||||||
\(687\) | 9.13036 | 0.348345 | ||||||||
\(688\) | 39.5120 | 1.50638 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 12.7017 | 0.483546 | ||||||||
\(691\) | 39.9845 | 1.52108 | 0.760540 | − | 0.649291i | \(-0.224934\pi\) | ||||
0.760540 | + | 0.649291i | \(0.224934\pi\) | |||||||
\(692\) | 9.67324 | 0.367721 | ||||||||
\(693\) | −1.80194 | −0.0684500 | ||||||||
\(694\) | −26.0683 | −0.989539 | ||||||||
\(695\) | −19.4330 | −0.737134 | ||||||||
\(696\) | −4.28621 | −0.162468 | ||||||||
\(697\) | 25.2935 | 0.958060 | ||||||||
\(698\) | 30.7265 | 1.16301 | ||||||||
\(699\) | −26.7265 | −1.01089 | ||||||||
\(700\) | 4.98792 | 0.188526 | ||||||||
\(701\) | −7.83984 | −0.296107 | −0.148053 | − | 0.988979i | \(-0.547301\pi\) | ||||
−0.148053 | + | 0.988979i | \(0.547301\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.8944 | −0.863478 | ||||||||
\(704\) | −2.28621 | −0.0861647 | ||||||||
\(705\) | 5.14675 | 0.193838 | ||||||||
\(706\) | −37.8678 | −1.42517 | ||||||||
\(707\) | 0.835790 | 0.0314331 | ||||||||
\(708\) | −12.1129 | −0.455231 | ||||||||
\(709\) | 30.4631 | 1.14407 | 0.572033 | − | 0.820231i | \(-0.306155\pi\) | ||||
0.572033 | + | 0.820231i | \(0.306155\pi\) | |||||||
\(710\) | 4.33513 | 0.162694 | ||||||||
\(711\) | 4.11960 | 0.154497 | ||||||||
\(712\) | 3.69873 | 0.138616 | ||||||||
\(713\) | 3.13706 | 0.117484 | ||||||||
\(714\) | −4.40581 | −0.164883 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.70410 | 0.101057 | ||||||||
\(717\) | −8.13169 | −0.303683 | ||||||||
\(718\) | 29.4480 | 1.09899 | ||||||||
\(719\) | −7.19673 | −0.268393 | −0.134196 | − | 0.990955i | \(-0.542845\pi\) | ||||
−0.134196 | + | 0.990955i | \(0.542845\pi\) | |||||||
\(720\) | −4.93900 | −0.184066 | ||||||||
\(721\) | 16.6136 | 0.618721 | ||||||||
\(722\) | −25.1521 | −0.936065 | ||||||||
\(723\) | 7.64848 | 0.284450 | ||||||||
\(724\) | −3.15213 | −0.117148 | ||||||||
\(725\) | 12.6353 | 0.469265 | ||||||||
\(726\) | 13.9705 | 0.518492 | ||||||||
\(727\) | −10.8304 | −0.401678 | −0.200839 | − | 0.979624i | \(-0.564367\pi\) | ||||
−0.200839 | + | 0.979624i | \(0.564367\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.19806 | −0.0443423 | ||||||||
\(731\) | 19.5603 | 0.723465 | ||||||||
\(732\) | −12.3937 | −0.458086 | ||||||||
\(733\) | 37.3569 | 1.37981 | 0.689904 | − | 0.723901i | \(-0.257653\pi\) | ||||
0.689904 | + | 0.723901i | \(0.257653\pi\) | |||||||
\(734\) | 62.0243 | 2.28936 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | −43.6045 | −1.60728 | ||||||||
\(737\) | −7.81163 | −0.287745 | ||||||||
\(738\) | 18.6407 | 0.686174 | ||||||||
\(739\) | −22.5515 | −0.829570 | −0.414785 | − | 0.909919i | \(-0.636143\pi\) | ||||
−0.414785 | + | 0.909919i | \(0.636143\pi\) | |||||||
\(740\) | −4.97285 | −0.182806 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.0761 | 0.590171 | ||||||||
\(743\) | 12.6568 | 0.464334 | 0.232167 | − | 0.972676i | \(-0.425418\pi\) | ||||
0.232167 | + | 0.972676i | \(0.425418\pi\) | |||||||
\(744\) | −0.603875 | −0.0221391 | ||||||||
\(745\) | −10.5090 | −0.385021 | ||||||||
\(746\) | −2.43967 | −0.0893225 | ||||||||
\(747\) | 11.0586 | 0.404613 | ||||||||
\(748\) | −5.49396 | −0.200879 | ||||||||
\(749\) | −13.0640 | −0.477348 | ||||||||
\(750\) | 16.2174 | 0.592177 | ||||||||
\(751\) | −2.04892 | −0.0747661 | −0.0373830 | − | 0.999301i | \(-0.511902\pi\) | ||||
−0.0373830 | + | 0.999301i | \(0.511902\pi\) | |||||||
\(752\) | −25.4198 | −0.926965 | ||||||||
\(753\) | −8.24459 | −0.300449 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.9758 | 0.763389 | ||||||||
\(756\) | −1.24698 | −0.0453522 | ||||||||
\(757\) | −9.19460 | −0.334184 | −0.167092 | − | 0.985941i | \(-0.553438\pi\) | ||||
−0.167092 | + | 0.985941i | \(0.553438\pi\) | |||||||
\(758\) | −55.4258 | −2.01316 | ||||||||
\(759\) | −12.7017 | −0.461043 | ||||||||
\(760\) | 7.78986 | 0.282568 | ||||||||
\(761\) | 19.7095 | 0.714468 | 0.357234 | − | 0.934015i | \(-0.383720\pi\) | ||||
0.357234 | + | 0.934015i | \(0.383720\pi\) | |||||||
\(762\) | 13.8683 | 0.502396 | ||||||||
\(763\) | 1.91185 | 0.0692138 | ||||||||
\(764\) | 25.2024 | 0.911790 | ||||||||
\(765\) | −2.44504 | −0.0884007 | ||||||||
\(766\) | 57.0461 | 2.06116 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 20.7114 | 0.747358 | ||||||||
\(769\) | −2.24996 | −0.0811358 | −0.0405679 | − | 0.999177i | \(-0.512917\pi\) | ||||
−0.0405679 | + | 0.999177i | \(0.512917\pi\) | |||||||
\(770\) | 3.24698 | 0.117013 | ||||||||
\(771\) | 24.6329 | 0.887134 | ||||||||
\(772\) | −30.3545 | −1.09248 | ||||||||
\(773\) | 41.3080 | 1.48574 | 0.742872 | − | 0.669433i | \(-0.233463\pi\) | ||||
0.742872 | + | 0.669433i | \(0.233463\pi\) | |||||||
\(774\) | 14.4155 | 0.518155 | ||||||||
\(775\) | 1.78017 | 0.0639455 | ||||||||
\(776\) | −7.31873 | −0.262727 | ||||||||
\(777\) | 3.98792 | 0.143066 | ||||||||
\(778\) | 34.3260 | 1.23065 | ||||||||
\(779\) | −59.3889 | −2.12783 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.33513 | −0.155123 | ||||||||
\(782\) | −31.0562 | −1.11057 | ||||||||
\(783\) | −3.15883 | −0.112888 | ||||||||
\(784\) | −4.93900 | −0.176393 | ||||||||
\(785\) | 0.838773 | 0.0299371 | ||||||||
\(786\) | 14.7506 | 0.526137 | ||||||||
\(787\) | −38.1702 | −1.36062 | −0.680310 | − | 0.732925i | \(-0.738155\pi\) | ||||
−0.680310 | + | 0.732925i | \(0.738155\pi\) | |||||||
\(788\) | −1.70709 | −0.0608125 | ||||||||
\(789\) | 17.1588 | 0.610871 | ||||||||
\(790\) | −7.42327 | −0.264108 | ||||||||
\(791\) | −7.05429 | −0.250822 | ||||||||
\(792\) | 2.44504 | 0.0868808 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −11.4862 | −0.407630 | ||||||||
\(795\) | 8.92154 | 0.316415 | ||||||||
\(796\) | −5.00969 | −0.177564 | ||||||||
\(797\) | 49.7265 | 1.76140 | 0.880701 | − | 0.473673i | \(-0.157072\pi\) | ||||
0.880701 | + | 0.473673i | \(0.157072\pi\) | |||||||
\(798\) | 10.3448 | 0.366202 | ||||||||
\(799\) | −12.5840 | −0.445191 | ||||||||
\(800\) | −24.7439 | −0.874830 | ||||||||
\(801\) | 2.72587 | 0.0963140 | ||||||||
\(802\) | 37.4359 | 1.32191 | ||||||||
\(803\) | 1.19806 | 0.0422787 | ||||||||
\(804\) | −5.40581 | −0.190648 | ||||||||
\(805\) | 7.04892 | 0.248442 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.08708 | −0.249477 | ||||||||
\(808\) | −1.13408 | −0.0398968 | ||||||||
\(809\) | 50.9111 | 1.78994 | 0.894970 | − | 0.446127i | \(-0.147197\pi\) | ||||
0.894970 | + | 0.446127i | \(0.147197\pi\) | |||||||
\(810\) | −1.80194 | −0.0633136 | ||||||||
\(811\) | 35.8106 | 1.25748 | 0.628739 | − | 0.777616i | \(-0.283571\pi\) | ||||
0.628739 | + | 0.777616i | \(0.283571\pi\) | |||||||
\(812\) | 3.93900 | 0.138232 | ||||||||
\(813\) | −24.5483 | −0.860945 | ||||||||
\(814\) | 12.9487 | 0.453851 | ||||||||
\(815\) | 12.7409 | 0.446296 | ||||||||
\(816\) | 12.0761 | 0.422747 | ||||||||
\(817\) | −45.9275 | −1.60680 | ||||||||
\(818\) | −9.88769 | −0.345715 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.8998 | −0.450480 | ||||||||
\(821\) | −16.2457 | −0.566977 | −0.283489 | − | 0.958976i | \(-0.591492\pi\) | ||||
−0.283489 | + | 0.958976i | \(0.591492\pi\) | |||||||
\(822\) | −15.8485 | −0.552779 | ||||||||
\(823\) | −39.5120 | −1.37730 | −0.688651 | − | 0.725093i | \(-0.741797\pi\) | ||||
−0.688651 | + | 0.725093i | \(0.741797\pi\) | |||||||
\(824\) | −22.5429 | −0.785318 | ||||||||
\(825\) | −7.20775 | −0.250942 | ||||||||
\(826\) | −17.5036 | −0.609030 | ||||||||
\(827\) | 22.8377 | 0.794145 | 0.397072 | − | 0.917787i | \(-0.370026\pi\) | ||||
0.397072 | + | 0.917787i | \(0.370026\pi\) | |||||||
\(828\) | −8.78986 | −0.305469 | ||||||||
\(829\) | −24.1823 | −0.839885 | −0.419942 | − | 0.907551i | \(-0.637950\pi\) | ||||
−0.419942 | + | 0.907551i | \(0.637950\pi\) | |||||||
\(830\) | −19.9269 | −0.691673 | ||||||||
\(831\) | 33.0810 | 1.14757 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.44504 | −0.0847157 | ||||||||
\(834\) | 35.0170 | 1.21254 | ||||||||
\(835\) | 13.5646 | 0.469424 | ||||||||
\(836\) | 12.8998 | 0.446148 | ||||||||
\(837\) | −0.445042 | −0.0153829 | ||||||||
\(838\) | 26.5351 | 0.916640 | ||||||||
\(839\) | 5.10082 | 0.176100 | 0.0880499 | − | 0.996116i | \(-0.471937\pi\) | ||||
0.0880499 | + | 0.996116i | \(0.471937\pi\) | |||||||
\(840\) | −1.35690 | −0.0468174 | ||||||||
\(841\) | −19.0218 | −0.655923 | ||||||||
\(842\) | −2.95646 | −0.101886 | ||||||||
\(843\) | −26.3163 | −0.906383 | ||||||||
\(844\) | −30.7385 | −1.05806 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.27413 | −0.318851 | ||||||||
\(847\) | 7.75302 | 0.266397 | ||||||||
\(848\) | −44.0635 | −1.51315 | ||||||||
\(849\) | 31.7778 | 1.09061 | ||||||||
\(850\) | −17.6233 | −0.604473 | ||||||||
\(851\) | 28.1105 | 0.963616 | ||||||||
\(852\) | −3.00000 | −0.102778 | ||||||||
\(853\) | 43.0170 | 1.47287 | 0.736437 | − | 0.676506i | \(-0.236507\pi\) | ||||
0.736437 | + | 0.676506i | \(0.236507\pi\) | |||||||
\(854\) | −17.9095 | −0.612849 | ||||||||
\(855\) | 5.74094 | 0.196336 | ||||||||
\(856\) | 17.7265 | 0.605878 | ||||||||
\(857\) | −0.479485 | −0.0163789 | −0.00818944 | − | 0.999966i | \(-0.502607\pi\) | ||||
−0.00818944 | + | 0.999966i | \(0.502607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.9627 | −0.817596 | −0.408798 | − | 0.912625i | \(-0.634052\pi\) | ||||
−0.408798 | + | 0.912625i | \(0.634052\pi\) | |||||||
\(860\) | −9.97584 | −0.340173 | ||||||||
\(861\) | 10.3448 | 0.352550 | ||||||||
\(862\) | −12.5114 | −0.426141 | ||||||||
\(863\) | −6.91590 | −0.235420 | −0.117710 | − | 0.993048i | \(-0.537555\pi\) | ||||
−0.117710 | + | 0.993048i | \(0.537555\pi\) | |||||||
\(864\) | 6.18598 | 0.210451 | ||||||||
\(865\) | 7.75733 | 0.263757 | ||||||||
\(866\) | 65.2137 | 2.21605 | ||||||||
\(867\) | −11.0218 | −0.374319 | ||||||||
\(868\) | 0.554958 | 0.0188365 | ||||||||
\(869\) | 7.42327 | 0.251817 | ||||||||
\(870\) | 5.69202 | 0.192978 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2.59419 | −0.0878502 | ||||||||
\(873\) | −5.39373 | −0.182550 | ||||||||
\(874\) | 72.9197 | 2.46655 | ||||||||
\(875\) | 9.00000 | 0.304256 | ||||||||
\(876\) | 0.829085 | 0.0280122 | ||||||||
\(877\) | 32.5153 | 1.09796 | 0.548981 | − | 0.835835i | \(-0.315016\pi\) | ||||
0.548981 | + | 0.835835i | \(0.315016\pi\) | |||||||
\(878\) | −15.7855 | −0.532736 | ||||||||
\(879\) | 12.8616 | 0.433811 | ||||||||
\(880\) | −8.89977 | −0.300011 | ||||||||
\(881\) | −49.0350 | −1.65203 | −0.826016 | − | 0.563646i | \(-0.809398\pi\) | ||||
−0.826016 | + | 0.563646i | \(0.809398\pi\) | |||||||
\(882\) | −1.80194 | −0.0606744 | ||||||||
\(883\) | 22.5190 | 0.757824 | 0.378912 | − | 0.925433i | \(-0.376298\pi\) | ||||
0.378912 | + | 0.925433i | \(0.376298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.71379 | −0.326526 | ||||||||
\(886\) | 33.2597 | 1.11738 | ||||||||
\(887\) | 55.5889 | 1.86649 | 0.933247 | − | 0.359236i | \(-0.116963\pi\) | ||||
0.933247 | + | 0.359236i | \(0.116963\pi\) | |||||||
\(888\) | −5.41119 | −0.181588 | ||||||||
\(889\) | 7.69633 | 0.258127 | ||||||||
\(890\) | −4.91185 | −0.164646 | ||||||||
\(891\) | 1.80194 | 0.0603672 | ||||||||
\(892\) | −11.7342 | −0.392891 | ||||||||
\(893\) | 29.5472 | 0.988759 | ||||||||
\(894\) | 18.9366 | 0.633335 | ||||||||
\(895\) | 2.16852 | 0.0724857 | ||||||||
\(896\) | 10.0858 | 0.336941 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 62.6988 | 2.09229 | ||||||||
\(899\) | 1.40581 | 0.0468865 | ||||||||
\(900\) | −4.98792 | −0.166264 | ||||||||
\(901\) | −21.8135 | −0.726715 | ||||||||
\(902\) | 33.5894 | 1.11840 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | 9.57194 | 0.318358 | ||||||||
\(905\) | −2.52781 | −0.0840273 | ||||||||
\(906\) | −37.7972 | −1.25573 | ||||||||
\(907\) | −0.801938 | −0.0266279 | −0.0133140 | − | 0.999911i | \(-0.504238\pi\) | ||||
−0.0133140 | + | 0.999911i | \(0.504238\pi\) | |||||||
\(908\) | 6.65279 | 0.220781 | ||||||||
\(909\) | −0.835790 | −0.0277214 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.2131 | 0.371507 | 0.185754 | − | 0.982596i | \(-0.440527\pi\) | ||||
0.185754 | + | 0.982596i | \(0.440527\pi\) | |||||||
\(912\) | −28.3545 | −0.938911 | ||||||||
\(913\) | 19.9269 | 0.659485 | ||||||||
\(914\) | 41.9245 | 1.38674 | ||||||||
\(915\) | −9.93900 | −0.328573 | ||||||||
\(916\) | 11.3854 | 0.376183 | ||||||||
\(917\) | 8.18598 | 0.270325 | ||||||||
\(918\) | 4.40581 | 0.145414 | ||||||||
\(919\) | −15.1226 | −0.498848 | −0.249424 | − | 0.968394i | \(-0.580241\pi\) | ||||
−0.249424 | + | 0.968394i | \(0.580241\pi\) | |||||||
\(920\) | −9.56465 | −0.315337 | ||||||||
\(921\) | −29.5937 | −0.975146 | ||||||||
\(922\) | −59.2301 | −1.95064 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.24698 | −0.0739202 | ||||||||
\(925\) | 15.9517 | 0.524488 | ||||||||
\(926\) | 40.7265 | 1.33835 | ||||||||
\(927\) | −16.6136 | −0.545661 | ||||||||
\(928\) | −19.5405 | −0.641448 | ||||||||
\(929\) | 17.7573 | 0.582599 | 0.291300 | − | 0.956632i | \(-0.405912\pi\) | ||||
0.291300 | + | 0.956632i | \(0.405912\pi\) | |||||||
\(930\) | 0.801938 | 0.0262966 | ||||||||
\(931\) | 5.74094 | 0.188152 | ||||||||
\(932\) | −33.3274 | −1.09167 | ||||||||
\(933\) | −8.55794 | −0.280174 | ||||||||
\(934\) | 22.5036 | 0.736342 | ||||||||
\(935\) | −4.40581 | −0.144085 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.0170 | −1.50331 | −0.751655 | − | 0.659557i | \(-0.770744\pi\) | ||||
−0.751655 | + | 0.659557i | \(0.770744\pi\) | |||||||
\(938\) | −7.81163 | −0.255059 | ||||||||
\(939\) | −16.3569 | −0.533787 | ||||||||
\(940\) | 6.41789 | 0.209329 | ||||||||
\(941\) | −13.9685 | −0.455361 | −0.227681 | − | 0.973736i | \(-0.573114\pi\) | ||||
−0.227681 | + | 0.973736i | \(0.573114\pi\) | |||||||
\(942\) | −1.51142 | −0.0492446 | ||||||||
\(943\) | 72.9197 | 2.37459 | ||||||||
\(944\) | 47.9764 | 1.56150 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | 25.9758 | 0.844547 | ||||||||
\(947\) | −0.994623 | −0.0323209 | −0.0161605 | − | 0.999869i | \(-0.505144\pi\) | ||||
−0.0161605 | + | 0.999869i | \(0.505144\pi\) | |||||||
\(948\) | 5.13706 | 0.166844 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 41.3793 | 1.34252 | ||||||||
\(951\) | 28.3545 | 0.919458 | ||||||||
\(952\) | 3.31767 | 0.107526 | ||||||||
\(953\) | 23.5937 | 0.764275 | 0.382138 | − | 0.924105i | \(-0.375188\pi\) | ||||
0.382138 | + | 0.924105i | \(0.375188\pi\) | |||||||
\(954\) | −16.0761 | −0.520482 | ||||||||
\(955\) | 20.2107 | 0.654004 | ||||||||
\(956\) | −10.1400 | −0.327953 | ||||||||
\(957\) | −5.69202 | −0.183997 | ||||||||
\(958\) | −24.4228 | −0.789065 | ||||||||
\(959\) | −8.79523 | −0.284013 | ||||||||
\(960\) | −1.26875 | −0.0409487 | ||||||||
\(961\) | −30.8019 | −0.993611 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.0640 | 0.420981 | ||||||||
\(964\) | 9.53750 | 0.307182 | ||||||||
\(965\) | −24.3424 | −0.783610 | ||||||||
\(966\) | −12.7017 | −0.408671 | ||||||||
\(967\) | 50.4228 | 1.62149 | 0.810744 | − | 0.585401i | \(-0.199063\pi\) | ||||
0.810744 | + | 0.585401i | \(0.199063\pi\) | |||||||
\(968\) | −10.5200 | −0.338127 | ||||||||
\(969\) | −14.0368 | −0.450928 | ||||||||
\(970\) | 9.71917 | 0.312064 | ||||||||
\(971\) | 1.06770 | 0.0342642 | 0.0171321 | − | 0.999853i | \(-0.494546\pi\) | ||||
0.0171321 | + | 0.999853i | \(0.494546\pi\) | |||||||
\(972\) | 1.24698 | 0.0399969 | ||||||||
\(973\) | 19.4330 | 0.622992 | ||||||||
\(974\) | 26.9235 | 0.862683 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 49.0887 | 1.57129 | ||||||||
\(977\) | 4.03444 | 0.129073 | 0.0645366 | − | 0.997915i | \(-0.479443\pi\) | ||||
0.0645366 | + | 0.997915i | \(0.479443\pi\) | |||||||
\(978\) | −22.9584 | −0.734128 | ||||||||
\(979\) | 4.91185 | 0.156984 | ||||||||
\(980\) | 1.24698 | 0.0398333 | ||||||||
\(981\) | −1.91185 | −0.0610408 | ||||||||
\(982\) | −49.5284 | −1.58051 | ||||||||
\(983\) | −33.6534 | −1.07338 | −0.536688 | − | 0.843781i | \(-0.680325\pi\) | ||||
−0.536688 | + | 0.843781i | \(0.680325\pi\) | |||||||
\(984\) | −14.0368 | −0.447478 | ||||||||
\(985\) | −1.36898 | −0.0436192 | ||||||||
\(986\) | −13.9172 | −0.443215 | ||||||||
\(987\) | −5.14675 | −0.163823 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56.3913 | 1.79314 | ||||||||
\(990\) | −3.24698 | −0.103196 | ||||||||
\(991\) | 33.3739 | 1.06016 | 0.530078 | − | 0.847949i | \(-0.322163\pi\) | ||||
0.530078 | + | 0.847949i | \(0.322163\pi\) | |||||||
\(992\) | −2.75302 | −0.0874085 | ||||||||
\(993\) | −11.3894 | −0.361432 | ||||||||
\(994\) | −4.33513 | −0.137502 | ||||||||
\(995\) | −4.01746 | −0.127362 | ||||||||
\(996\) | 13.7899 | 0.436948 | ||||||||
\(997\) | 54.4172 | 1.72341 | 0.861704 | − | 0.507411i | \(-0.169397\pi\) | ||||
0.861704 | + | 0.507411i | \(0.169397\pi\) | |||||||
\(998\) | 32.2107 | 1.01961 | ||||||||
\(999\) | −3.98792 | −0.126172 |
(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 | 3549.2.a.j.1.1 | ✓ | 3 | |
13.12 | even | 2 | 3549.2.a.p.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.j.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3549.2.a.p.1.3 | yes | 3 | 13.12 | even | 2 |