Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2793,2,Mod(1,2793)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2793, 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("2793.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2793 = 3 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2793.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: | \(22.3022172845\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1240016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 8x^{3} + 2x^{2} + 16x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 399) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.77304\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2793.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.91670 | 1.35531 | 0.677656 | − | 0.735379i | \(-0.262996\pi\) | ||||
0.677656 | + | 0.735379i | \(0.262996\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.67374 | 0.836870 | ||||||||
\(5\) | −2.54204 | −1.13684 | −0.568418 | − | 0.822740i | \(-0.692444\pi\) | ||||
−0.568418 | + | 0.822740i | \(0.692444\pi\) | |||||||
\(6\) | −1.91670 | −0.782490 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.625344 | −0.221092 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.87234 | −1.54077 | ||||||||
\(11\) | −5.54608 | −1.67220 | −0.836102 | − | 0.548574i | \(-0.815171\pi\) | ||||
−0.836102 | + | 0.548574i | \(0.815171\pi\) | |||||||
\(12\) | −1.67374 | −0.483167 | ||||||||
\(13\) | 1.83340 | 0.508494 | 0.254247 | − | 0.967139i | \(-0.418172\pi\) | ||||
0.254247 | + | 0.967139i | \(0.418172\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.54204 | 0.656353 | ||||||||
\(16\) | −4.54608 | −1.13652 | ||||||||
\(17\) | 3.88952 | 0.943348 | 0.471674 | − | 0.881773i | \(-0.343650\pi\) | ||||
0.471674 | + | 0.881773i | \(0.343650\pi\) | |||||||
\(18\) | 1.91670 | 0.451771 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −4.25472 | −0.951384 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.6302 | −2.26636 | ||||||||
\(23\) | 5.54608 | 1.15644 | 0.578218 | − | 0.815882i | \(-0.303748\pi\) | ||||
0.578218 | + | 0.815882i | \(0.303748\pi\) | |||||||
\(24\) | 0.625344 | 0.127648 | ||||||||
\(25\) | 1.46199 | 0.292397 | ||||||||
\(26\) | 3.51408 | 0.689167 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.08812 | 1.50193 | 0.750963 | − | 0.660344i | \(-0.229590\pi\) | ||||
0.750963 | + | 0.660344i | \(0.229590\pi\) | |||||||
\(30\) | 4.87234 | 0.889563 | ||||||||
\(31\) | 3.54608 | 0.636894 | 0.318447 | − | 0.947941i | \(-0.396839\pi\) | ||||
0.318447 | + | 0.947941i | \(0.396839\pi\) | |||||||
\(32\) | −7.46278 | −1.31924 | ||||||||
\(33\) | 5.54608 | 0.965448 | ||||||||
\(34\) | 7.45505 | 1.27853 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.67374 | 0.278957 | ||||||||
\(37\) | 5.73661 | 0.943093 | 0.471546 | − | 0.881841i | \(-0.343696\pi\) | ||||
0.471546 | + | 0.881841i | \(0.343696\pi\) | |||||||
\(38\) | −1.91670 | −0.310930 | ||||||||
\(39\) | −1.83340 | −0.293579 | ||||||||
\(40\) | 1.58965 | 0.251346 | ||||||||
\(41\) | 2.48592 | 0.388236 | 0.194118 | − | 0.980978i | \(-0.437816\pi\) | ||||
0.194118 | + | 0.980978i | \(0.437816\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.80947 | 0.580938 | 0.290469 | − | 0.956884i | \(-0.406189\pi\) | ||||
0.290469 | + | 0.956884i | \(0.406189\pi\) | |||||||
\(44\) | −9.28268 | −1.39942 | ||||||||
\(45\) | −2.54204 | −0.378946 | ||||||||
\(46\) | 10.6302 | 1.56733 | ||||||||
\(47\) | 2.99597 | 0.437007 | 0.218503 | − | 0.975836i | \(-0.429883\pi\) | ||||
0.218503 | + | 0.975836i | \(0.429883\pi\) | |||||||
\(48\) | 4.54608 | 0.656169 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.80219 | 0.396290 | ||||||||
\(51\) | −3.88952 | −0.544642 | ||||||||
\(52\) | 3.06863 | 0.425543 | ||||||||
\(53\) | −3.31529 | −0.455390 | −0.227695 | − | 0.973732i | \(-0.573119\pi\) | ||||
−0.227695 | + | 0.973732i | \(0.573119\pi\) | |||||||
\(54\) | −1.91670 | −0.260830 | ||||||||
\(55\) | 14.0984 | 1.90102 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 15.5025 | 2.03558 | ||||||||
\(59\) | 11.0922 | 1.44408 | 0.722038 | − | 0.691854i | \(-0.243206\pi\) | ||||
0.722038 | + | 0.691854i | \(0.243206\pi\) | |||||||
\(60\) | 4.25472 | 0.549282 | ||||||||
\(61\) | −8.43157 | −1.07955 | −0.539776 | − | 0.841809i | \(-0.681491\pi\) | ||||
−0.539776 | + | 0.841809i | \(0.681491\pi\) | |||||||
\(62\) | 6.79676 | 0.863190 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.21175 | −0.651469 | ||||||||
\(65\) | −4.66058 | −0.578074 | ||||||||
\(66\) | 10.6302 | 1.30848 | ||||||||
\(67\) | −6.14424 | −0.750639 | −0.375319 | − | 0.926896i | \(-0.622467\pi\) | ||||
−0.375319 | + | 0.926896i | \(0.622467\pi\) | |||||||
\(68\) | 6.51005 | 0.789459 | ||||||||
\(69\) | −5.54608 | −0.667669 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.18491 | 0.971370 | 0.485685 | − | 0.874134i | \(-0.338570\pi\) | ||||
0.485685 | + | 0.874134i | \(0.338570\pi\) | |||||||
\(72\) | −0.625344 | −0.0736975 | ||||||||
\(73\) | −8.31932 | −0.973703 | −0.486851 | − | 0.873485i | \(-0.661855\pi\) | ||||
−0.486851 | + | 0.873485i | \(0.661855\pi\) | |||||||
\(74\) | 10.9954 | 1.27818 | ||||||||
\(75\) | −1.46199 | −0.168816 | ||||||||
\(76\) | −1.67374 | −0.191991 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.51408 | −0.397891 | ||||||||
\(79\) | −4.79676 | −0.539678 | −0.269839 | − | 0.962905i | \(-0.586970\pi\) | ||||
−0.269839 | + | 0.962905i | \(0.586970\pi\) | |||||||
\(80\) | 11.5563 | 1.29204 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.76477 | 0.526180 | ||||||||
\(83\) | 15.3234 | 1.68196 | 0.840978 | − | 0.541069i | \(-0.181980\pi\) | ||||
0.840978 | + | 0.541069i | \(0.181980\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.88734 | −1.07243 | ||||||||
\(86\) | 7.30160 | 0.787352 | ||||||||
\(87\) | −8.08812 | −0.867137 | ||||||||
\(88\) | 3.46820 | 0.369712 | ||||||||
\(89\) | 12.6541 | 1.34133 | 0.670666 | − | 0.741760i | \(-0.266008\pi\) | ||||
0.670666 | + | 0.741760i | \(0.266008\pi\) | |||||||
\(90\) | −4.87234 | −0.513589 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.28268 | 0.967787 | ||||||||
\(93\) | −3.54608 | −0.367711 | ||||||||
\(94\) | 5.74237 | 0.592281 | ||||||||
\(95\) | 2.54204 | 0.260808 | ||||||||
\(96\) | 7.46278 | 0.761666 | ||||||||
\(97\) | −15.1241 | −1.53562 | −0.767812 | − | 0.640675i | \(-0.778655\pi\) | ||||
−0.767812 | + | 0.640675i | \(0.778655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.54608 | −0.557402 | ||||||||
\(100\) | 2.44699 | 0.244699 | ||||||||
\(101\) | −14.9817 | −1.49073 | −0.745366 | − | 0.666655i | \(-0.767725\pi\) | ||||
−0.745366 | + | 0.666655i | \(0.767725\pi\) | |||||||
\(102\) | −7.45505 | −0.738160 | ||||||||
\(103\) | −6.36176 | −0.626843 | −0.313421 | − | 0.949614i | \(-0.601475\pi\) | ||||
−0.313421 | + | 0.949614i | \(0.601475\pi\) | |||||||
\(104\) | −1.14651 | −0.112424 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.35442 | −0.617196 | ||||||||
\(107\) | 17.9296 | 1.73332 | 0.866659 | − | 0.498901i | \(-0.166263\pi\) | ||||
0.866659 | + | 0.498901i | \(0.166263\pi\) | |||||||
\(108\) | −1.67374 | −0.161056 | ||||||||
\(109\) | −4.00806 | −0.383903 | −0.191951 | − | 0.981404i | \(-0.561482\pi\) | ||||
−0.191951 | + | 0.981404i | \(0.561482\pi\) | |||||||
\(110\) | 27.0223 | 2.57648 | ||||||||
\(111\) | −5.73661 | −0.544495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.96781 | 0.185116 | 0.0925581 | − | 0.995707i | \(-0.470496\pi\) | ||||
0.0925581 | + | 0.995707i | \(0.470496\pi\) | |||||||
\(114\) | 1.91670 | 0.179515 | ||||||||
\(115\) | −14.0984 | −1.31468 | ||||||||
\(116\) | 13.5374 | 1.25692 | ||||||||
\(117\) | 1.83340 | 0.169498 | ||||||||
\(118\) | 21.2603 | 1.95717 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.58965 | −0.145115 | ||||||||
\(121\) | 19.7590 | 1.79627 | ||||||||
\(122\) | −16.1608 | −1.46313 | ||||||||
\(123\) | −2.48592 | −0.224148 | ||||||||
\(124\) | 5.93521 | 0.532997 | ||||||||
\(125\) | 8.99378 | 0.804428 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.44928 | 0.661017 | 0.330509 | − | 0.943803i | \(-0.392780\pi\) | ||||
0.330509 | + | 0.943803i | \(0.392780\pi\) | |||||||
\(128\) | 4.93619 | 0.436301 | ||||||||
\(129\) | −3.80947 | −0.335405 | ||||||||
\(130\) | −8.93294 | −0.783471 | ||||||||
\(131\) | 15.4356 | 1.34861 | 0.674307 | − | 0.738451i | \(-0.264442\pi\) | ||||
0.674307 | + | 0.738451i | \(0.264442\pi\) | |||||||
\(132\) | 9.28268 | 0.807954 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.7767 | −1.01735 | ||||||||
\(135\) | 2.54204 | 0.218784 | ||||||||
\(136\) | −2.43229 | −0.208567 | ||||||||
\(137\) | −15.4539 | −1.32032 | −0.660158 | − | 0.751127i | \(-0.729511\pi\) | ||||
−0.660158 | + | 0.751127i | \(0.729511\pi\) | |||||||
\(138\) | −10.6302 | −0.904900 | ||||||||
\(139\) | 10.3193 | 0.875273 | 0.437637 | − | 0.899152i | \(-0.355816\pi\) | ||||
0.437637 | + | 0.899152i | \(0.355816\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.99597 | −0.252306 | ||||||||
\(142\) | 15.6880 | 1.31651 | ||||||||
\(143\) | −10.1682 | −0.850306 | ||||||||
\(144\) | −4.54608 | −0.378840 | ||||||||
\(145\) | −20.5604 | −1.70744 | ||||||||
\(146\) | −15.9456 | −1.31967 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.60159 | 0.789246 | ||||||||
\(149\) | 12.0081 | 0.983739 | 0.491869 | − | 0.870669i | \(-0.336314\pi\) | ||||
0.491869 | + | 0.870669i | \(0.336314\pi\) | |||||||
\(150\) | −2.80219 | −0.228798 | ||||||||
\(151\) | 19.0463 | 1.54996 | 0.774982 | − | 0.631983i | \(-0.217759\pi\) | ||||
0.774982 | + | 0.631983i | \(0.217759\pi\) | |||||||
\(152\) | 0.625344 | 0.0507221 | ||||||||
\(153\) | 3.88952 | 0.314449 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.01428 | −0.724044 | ||||||||
\(156\) | −3.06863 | −0.245687 | ||||||||
\(157\) | −5.93019 | −0.473281 | −0.236640 | − | 0.971597i | \(-0.576046\pi\) | ||||
−0.236640 | + | 0.971597i | \(0.576046\pi\) | |||||||
\(158\) | −9.19396 | −0.731432 | ||||||||
\(159\) | 3.31529 | 0.262920 | ||||||||
\(160\) | 18.9707 | 1.49977 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.91670 | 0.150590 | ||||||||
\(163\) | −2.31084 | −0.180999 | −0.0904995 | − | 0.995896i | \(-0.528846\pi\) | ||||
−0.0904995 | + | 0.995896i | \(0.528846\pi\) | |||||||
\(164\) | 4.16078 | 0.324903 | ||||||||
\(165\) | −14.0984 | −1.09756 | ||||||||
\(166\) | 29.3703 | 2.27958 | ||||||||
\(167\) | 9.41729 | 0.728732 | 0.364366 | − | 0.931256i | \(-0.381286\pi\) | ||||
0.364366 | + | 0.931256i | \(0.381286\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.63864 | −0.741434 | ||||||||
\(170\) | −18.9511 | −1.45348 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 6.37605 | 0.486170 | ||||||||
\(173\) | 13.5781 | 1.03232 | 0.516161 | − | 0.856492i | \(-0.327361\pi\) | ||||
0.516161 | + | 0.856492i | \(0.327361\pi\) | |||||||
\(174\) | −15.5025 | −1.17524 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.2129 | 1.90049 | ||||||||
\(177\) | −11.0922 | −0.833737 | ||||||||
\(178\) | 24.2541 | 1.81792 | ||||||||
\(179\) | 1.55976 | 0.116582 | 0.0582910 | − | 0.998300i | \(-0.481435\pi\) | ||||
0.0582910 | + | 0.998300i | \(0.481435\pi\) | |||||||
\(180\) | −4.25472 | −0.317128 | ||||||||
\(181\) | −18.5334 | −1.37757 | −0.688787 | − | 0.724963i | \(-0.741857\pi\) | ||||
−0.688787 | + | 0.724963i | \(0.741857\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.43157 | 0.623279 | ||||||||
\(184\) | −3.46820 | −0.255679 | ||||||||
\(185\) | −14.5827 | −1.07214 | ||||||||
\(186\) | −6.79676 | −0.498363 | ||||||||
\(187\) | −21.5716 | −1.57747 | ||||||||
\(188\) | 5.01447 | 0.365718 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.87234 | 0.353476 | ||||||||
\(191\) | −23.3811 | −1.69179 | −0.845897 | − | 0.533347i | \(-0.820934\pi\) | ||||
−0.845897 | + | 0.533347i | \(0.820934\pi\) | |||||||
\(192\) | 5.21175 | 0.376126 | ||||||||
\(193\) | 16.8288 | 1.21136 | 0.605680 | − | 0.795708i | \(-0.292901\pi\) | ||||
0.605680 | + | 0.795708i | \(0.292901\pi\) | |||||||
\(194\) | −28.9885 | −2.08125 | ||||||||
\(195\) | 4.66058 | 0.333751 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.1207 | −1.64728 | −0.823641 | − | 0.567111i | \(-0.808061\pi\) | ||||
−0.823641 | + | 0.567111i | \(0.808061\pi\) | |||||||
\(198\) | −10.6302 | −0.755453 | ||||||||
\(199\) | −12.1762 | −0.863151 | −0.431575 | − | 0.902077i | \(-0.642042\pi\) | ||||
−0.431575 | + | 0.902077i | \(0.642042\pi\) | |||||||
\(200\) | −0.914245 | −0.0646469 | ||||||||
\(201\) | 6.14424 | 0.433381 | ||||||||
\(202\) | −28.7154 | −2.02041 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.51005 | −0.455794 | ||||||||
\(205\) | −6.31932 | −0.441361 | ||||||||
\(206\) | −12.1936 | −0.849567 | ||||||||
\(207\) | 5.54608 | 0.385479 | ||||||||
\(208\) | −8.33478 | −0.577913 | ||||||||
\(209\) | 5.54608 | 0.383630 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.95597 | −0.478869 | −0.239434 | − | 0.970913i | \(-0.576962\pi\) | ||||
−0.239434 | + | 0.970913i | \(0.576962\pi\) | |||||||
\(212\) | −5.54893 | −0.381102 | ||||||||
\(213\) | −8.18491 | −0.560821 | ||||||||
\(214\) | 34.3656 | 2.34919 | ||||||||
\(215\) | −9.68383 | −0.660432 | ||||||||
\(216\) | 0.625344 | 0.0425493 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.68225 | −0.520308 | ||||||||
\(219\) | 8.31932 | 0.562168 | ||||||||
\(220\) | 23.5970 | 1.59091 | ||||||||
\(221\) | 7.13105 | 0.479686 | ||||||||
\(222\) | −10.9954 | −0.737960 | ||||||||
\(223\) | 28.4092 | 1.90242 | 0.951211 | − | 0.308542i | \(-0.0998411\pi\) | ||||
0.951211 | + | 0.308542i | \(0.0998411\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.46199 | 0.0974658 | ||||||||
\(226\) | 3.77170 | 0.250890 | ||||||||
\(227\) | −3.31311 | −0.219899 | −0.109949 | − | 0.993937i | \(-0.535069\pi\) | ||||
−0.109949 | + | 0.993937i | \(0.535069\pi\) | |||||||
\(228\) | 1.67374 | 0.110846 | ||||||||
\(229\) | −1.88776 | −0.124746 | −0.0623732 | − | 0.998053i | \(-0.519867\pi\) | ||||
−0.0623732 | + | 0.998053i | \(0.519867\pi\) | |||||||
\(230\) | −27.0223 | −1.78180 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.05786 | −0.332064 | ||||||||
\(233\) | 23.7227 | 1.55413 | 0.777064 | − | 0.629422i | \(-0.216708\pi\) | ||||
0.777064 | + | 0.629422i | \(0.216708\pi\) | |||||||
\(234\) | 3.51408 | 0.229722 | ||||||||
\(235\) | −7.61588 | −0.496805 | ||||||||
\(236\) | 18.5654 | 1.20850 | ||||||||
\(237\) | 4.79676 | 0.311583 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.9159 | 1.41762 | 0.708811 | − | 0.705399i | \(-0.249232\pi\) | ||||
0.708811 | + | 0.705399i | \(0.249232\pi\) | |||||||
\(240\) | −11.5563 | −0.745957 | ||||||||
\(241\) | 17.2445 | 1.11081 | 0.555406 | − | 0.831579i | \(-0.312563\pi\) | ||||
0.555406 | + | 0.831579i | \(0.312563\pi\) | |||||||
\(242\) | 37.8720 | 2.43450 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −14.1122 | −0.903444 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.76477 | −0.303790 | ||||||||
\(247\) | −1.83340 | −0.116656 | ||||||||
\(248\) | −2.21752 | −0.140812 | ||||||||
\(249\) | −15.3234 | −0.971078 | ||||||||
\(250\) | 17.2384 | 1.09025 | ||||||||
\(251\) | 3.72636 | 0.235206 | 0.117603 | − | 0.993061i | \(-0.462479\pi\) | ||||
0.117603 | + | 0.993061i | \(0.462479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.7590 | −1.93380 | ||||||||
\(254\) | 14.2780 | 0.895884 | ||||||||
\(255\) | 9.88734 | 0.619169 | ||||||||
\(256\) | 19.8847 | 1.24279 | ||||||||
\(257\) | −4.42999 | −0.276335 | −0.138168 | − | 0.990409i | \(-0.544121\pi\) | ||||
−0.138168 | + | 0.990409i | \(0.544121\pi\) | |||||||
\(258\) | −7.30160 | −0.454578 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.80060 | −0.483773 | ||||||||
\(261\) | 8.08812 | 0.500642 | ||||||||
\(262\) | 29.5854 | 1.82779 | ||||||||
\(263\) | 2.23297 | 0.137691 | 0.0688454 | − | 0.997627i | \(-0.478068\pi\) | ||||
0.0688454 | + | 0.997627i | \(0.478068\pi\) | |||||||
\(264\) | −3.46820 | −0.213453 | ||||||||
\(265\) | 8.42761 | 0.517704 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.6541 | −0.774418 | ||||||||
\(268\) | −10.2839 | −0.628187 | ||||||||
\(269\) | −4.87505 | −0.297237 | −0.148619 | − | 0.988895i | \(-0.547483\pi\) | ||||
−0.148619 | + | 0.988895i | \(0.547483\pi\) | |||||||
\(270\) | 4.87234 | 0.296521 | ||||||||
\(271\) | 16.5519 | 1.00545 | 0.502727 | − | 0.864445i | \(-0.332330\pi\) | ||||
0.502727 | + | 0.864445i | \(0.332330\pi\) | |||||||
\(272\) | −17.6821 | −1.07213 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −29.6205 | −1.78944 | ||||||||
\(275\) | −8.10829 | −0.488948 | ||||||||
\(276\) | −9.28268 | −0.558752 | ||||||||
\(277\) | 28.0841 | 1.68741 | 0.843704 | − | 0.536808i | \(-0.180370\pi\) | ||||
0.843704 | + | 0.536808i | \(0.180370\pi\) | |||||||
\(278\) | 19.7790 | 1.18627 | ||||||||
\(279\) | 3.54608 | 0.212298 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.2674 | 0.672158 | 0.336079 | − | 0.941834i | \(-0.390899\pi\) | ||||
0.336079 | + | 0.941834i | \(0.390899\pi\) | |||||||
\(282\) | −5.74237 | −0.341953 | ||||||||
\(283\) | −15.7952 | −0.938925 | −0.469463 | − | 0.882952i | \(-0.655552\pi\) | ||||
−0.469463 | + | 0.882952i | \(0.655552\pi\) | |||||||
\(284\) | 13.6994 | 0.812910 | ||||||||
\(285\) | −2.54204 | −0.150578 | ||||||||
\(286\) | −19.4893 | −1.15243 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.46278 | −0.439748 | ||||||||
\(289\) | −1.87161 | −0.110095 | ||||||||
\(290\) | −39.4080 | −2.31412 | ||||||||
\(291\) | 15.1241 | 0.886593 | ||||||||
\(292\) | −13.9244 | −0.814862 | ||||||||
\(293\) | −26.4573 | −1.54565 | −0.772827 | − | 0.634617i | \(-0.781158\pi\) | ||||
−0.772827 | + | 0.634617i | \(0.781158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.1967 | −1.64168 | ||||||||
\(296\) | −3.58735 | −0.208511 | ||||||||
\(297\) | 5.54608 | 0.321816 | ||||||||
\(298\) | 23.0159 | 1.33327 | ||||||||
\(299\) | 10.1682 | 0.588041 | ||||||||
\(300\) | −2.44699 | −0.141277 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 36.5060 | 2.10068 | ||||||||
\(303\) | 14.9817 | 0.860675 | ||||||||
\(304\) | 4.54608 | 0.260735 | ||||||||
\(305\) | 21.4334 | 1.22727 | ||||||||
\(306\) | 7.45505 | 0.426177 | ||||||||
\(307\) | −11.7875 | −0.672750 | −0.336375 | − | 0.941728i | \(-0.609201\pi\) | ||||
−0.336375 | + | 0.941728i | \(0.609201\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.36176 | 0.361908 | ||||||||
\(310\) | −17.2777 | −0.981306 | ||||||||
\(311\) | −2.39938 | −0.136056 | −0.0680281 | − | 0.997683i | \(-0.521671\pi\) | ||||
−0.0680281 | + | 0.997683i | \(0.521671\pi\) | |||||||
\(312\) | 1.14651 | 0.0649081 | ||||||||
\(313\) | −6.66058 | −0.376478 | −0.188239 | − | 0.982123i | \(-0.560278\pi\) | ||||
−0.188239 | + | 0.982123i | \(0.560278\pi\) | |||||||
\(314\) | −11.3664 | −0.641443 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.02853 | −0.451640 | ||||||||
\(317\) | −18.3376 | −1.02994 | −0.514972 | − | 0.857207i | \(-0.672198\pi\) | ||||
−0.514972 | + | 0.857207i | \(0.672198\pi\) | |||||||
\(318\) | 6.35442 | 0.356338 | ||||||||
\(319\) | −44.8573 | −2.51153 | ||||||||
\(320\) | 13.2485 | 0.740614 | ||||||||
\(321\) | −17.9296 | −1.00073 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.88952 | −0.216419 | ||||||||
\(324\) | 1.67374 | 0.0929855 | ||||||||
\(325\) | 2.68041 | 0.148682 | ||||||||
\(326\) | −4.42919 | −0.245310 | ||||||||
\(327\) | 4.00806 | 0.221646 | ||||||||
\(328\) | −1.55456 | −0.0858360 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −27.0223 | −1.48753 | ||||||||
\(331\) | −3.09099 | −0.169896 | −0.0849482 | − | 0.996385i | \(-0.527072\pi\) | ||||
−0.0849482 | + | 0.996385i | \(0.527072\pi\) | |||||||
\(332\) | 25.6473 | 1.40758 | ||||||||
\(333\) | 5.73661 | 0.314364 | ||||||||
\(334\) | 18.0501 | 0.987658 | ||||||||
\(335\) | 15.6189 | 0.853353 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8233 | 0.916425 | 0.458213 | − | 0.888843i | \(-0.348490\pi\) | ||||
0.458213 | + | 0.888843i | \(0.348490\pi\) | |||||||
\(338\) | −18.4744 | −1.00487 | ||||||||
\(339\) | −1.96781 | −0.106877 | ||||||||
\(340\) | −16.5488 | −0.897486 | ||||||||
\(341\) | −19.6668 | −1.06502 | ||||||||
\(342\) | −1.91670 | −0.103643 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.38223 | −0.128441 | ||||||||
\(345\) | 14.0984 | 0.759031 | ||||||||
\(346\) | 26.0251 | 1.39912 | ||||||||
\(347\) | −26.8877 | −1.44341 | −0.721705 | − | 0.692201i | \(-0.756641\pi\) | ||||
−0.721705 | + | 0.692201i | \(0.756641\pi\) | |||||||
\(348\) | −13.5374 | −0.725681 | ||||||||
\(349\) | 4.80367 | 0.257134 | 0.128567 | − | 0.991701i | \(-0.458962\pi\) | ||||
0.128567 | + | 0.991701i | \(0.458962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.83340 | −0.0978597 | ||||||||
\(352\) | 41.3891 | 2.20605 | ||||||||
\(353\) | 12.5775 | 0.669432 | 0.334716 | − | 0.942319i | \(-0.391360\pi\) | ||||
0.334716 | + | 0.942319i | \(0.391360\pi\) | |||||||
\(354\) | −21.2603 | −1.12997 | ||||||||
\(355\) | −20.8064 | −1.10429 | ||||||||
\(356\) | 21.1797 | 1.12252 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.98960 | 0.158005 | ||||||||
\(359\) | −31.3332 | −1.65370 | −0.826851 | − | 0.562421i | \(-0.809870\pi\) | ||||
−0.826851 | + | 0.562421i | \(0.809870\pi\) | |||||||
\(360\) | 1.58965 | 0.0837820 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −35.5229 | −1.86704 | ||||||||
\(363\) | −19.7590 | −1.03708 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.1481 | 1.10694 | ||||||||
\(366\) | 16.1608 | 0.844738 | ||||||||
\(367\) | 21.0841 | 1.10058 | 0.550290 | − | 0.834973i | \(-0.314517\pi\) | ||||
0.550290 | + | 0.834973i | \(0.314517\pi\) | |||||||
\(368\) | −25.2129 | −1.31431 | ||||||||
\(369\) | 2.48592 | 0.129412 | ||||||||
\(370\) | −27.9507 | −1.45309 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.93521 | −0.307726 | ||||||||
\(373\) | −23.6097 | −1.22246 | −0.611231 | − | 0.791452i | \(-0.709325\pi\) | ||||
−0.611231 | + | 0.791452i | \(0.709325\pi\) | |||||||
\(374\) | −41.3463 | −2.13796 | ||||||||
\(375\) | −8.99378 | −0.464437 | ||||||||
\(376\) | −1.87351 | −0.0966189 | ||||||||
\(377\) | 14.8288 | 0.763720 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.13803 | 0.366656 | 0.183328 | − | 0.983052i | \(-0.441313\pi\) | ||||
0.183328 | + | 0.983052i | \(0.441313\pi\) | |||||||
\(380\) | 4.25472 | 0.218262 | ||||||||
\(381\) | −7.44928 | −0.381638 | ||||||||
\(382\) | −44.8145 | −2.29291 | ||||||||
\(383\) | 9.41729 | 0.481201 | 0.240600 | − | 0.970624i | \(-0.422656\pi\) | ||||
0.240600 | + | 0.970624i | \(0.422656\pi\) | |||||||
\(384\) | −4.93619 | −0.251899 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.2557 | 1.64177 | ||||||||
\(387\) | 3.80947 | 0.193646 | ||||||||
\(388\) | −25.3139 | −1.28512 | ||||||||
\(389\) | −28.0721 | −1.42331 | −0.711655 | − | 0.702529i | \(-0.752054\pi\) | ||||
−0.711655 | + | 0.702529i | \(0.752054\pi\) | |||||||
\(390\) | 8.93294 | 0.452337 | ||||||||
\(391\) | 21.5716 | 1.09092 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.4356 | −0.778623 | ||||||||
\(394\) | −44.3155 | −2.23258 | ||||||||
\(395\) | 12.1936 | 0.613526 | ||||||||
\(396\) | −9.28268 | −0.466472 | ||||||||
\(397\) | 6.59078 | 0.330782 | 0.165391 | − | 0.986228i | \(-0.447111\pi\) | ||||
0.165391 | + | 0.986228i | \(0.447111\pi\) | |||||||
\(398\) | −23.3382 | −1.16984 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.64630 | −0.332315 | ||||||||
\(401\) | 34.1865 | 1.70719 | 0.853596 | − | 0.520936i | \(-0.174417\pi\) | ||||
0.853596 | + | 0.520936i | \(0.174417\pi\) | |||||||
\(402\) | 11.7767 | 0.587367 | ||||||||
\(403\) | 6.50138 | 0.323857 | ||||||||
\(404\) | −25.0754 | −1.24755 | ||||||||
\(405\) | −2.54204 | −0.126315 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.8157 | −1.57704 | ||||||||
\(408\) | 2.43229 | 0.120416 | ||||||||
\(409\) | 33.4555 | 1.65427 | 0.827134 | − | 0.562005i | \(-0.189970\pi\) | ||||
0.827134 | + | 0.562005i | \(0.189970\pi\) | |||||||
\(410\) | −12.1122 | −0.598181 | ||||||||
\(411\) | 15.4539 | 0.762285 | ||||||||
\(412\) | −10.6479 | −0.524586 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10.6302 | 0.522444 | ||||||||
\(415\) | −38.9526 | −1.91211 | ||||||||
\(416\) | −13.6823 | −0.670828 | ||||||||
\(417\) | −10.3193 | −0.505339 | ||||||||
\(418\) | 10.6302 | 0.519938 | ||||||||
\(419\) | 30.4418 | 1.48718 | 0.743590 | − | 0.668636i | \(-0.233121\pi\) | ||||
0.743590 | + | 0.668636i | \(0.233121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.4678 | −0.851328 | −0.425664 | − | 0.904881i | \(-0.639959\pi\) | ||||
−0.425664 | + | 0.904881i | \(0.639959\pi\) | |||||||
\(422\) | −13.3325 | −0.649017 | ||||||||
\(423\) | 2.99597 | 0.145669 | ||||||||
\(424\) | 2.07320 | 0.100683 | ||||||||
\(425\) | 5.68643 | 0.275833 | ||||||||
\(426\) | −15.6880 | −0.760087 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 30.0094 | 1.45056 | ||||||||
\(429\) | 10.1682 | 0.490924 | ||||||||
\(430\) | −18.5610 | −0.895091 | ||||||||
\(431\) | 24.8969 | 1.19924 | 0.599621 | − | 0.800284i | \(-0.295318\pi\) | ||||
0.599621 | + | 0.800284i | \(0.295318\pi\) | |||||||
\(432\) | 4.54608 | 0.218723 | ||||||||
\(433\) | 11.3177 | 0.543895 | 0.271948 | − | 0.962312i | \(-0.412332\pi\) | ||||
0.271948 | + | 0.962312i | \(0.412332\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.5604 | 0.985794 | ||||||||
\(436\) | −6.70845 | −0.321277 | ||||||||
\(437\) | −5.54608 | −0.265305 | ||||||||
\(438\) | 15.9456 | 0.761912 | ||||||||
\(439\) | −12.7424 | −0.608162 | −0.304081 | − | 0.952646i | \(-0.598349\pi\) | ||||
−0.304081 | + | 0.952646i | \(0.598349\pi\) | |||||||
\(440\) | −8.81633 | −0.420302 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.6681 | 0.650125 | ||||||||
\(443\) | −22.6140 | −1.07443 | −0.537213 | − | 0.843447i | \(-0.680523\pi\) | ||||
−0.537213 | + | 0.843447i | \(0.680523\pi\) | |||||||
\(444\) | −9.60159 | −0.455671 | ||||||||
\(445\) | −32.1673 | −1.52487 | ||||||||
\(446\) | 54.4519 | 2.57837 | ||||||||
\(447\) | −12.0081 | −0.567962 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.06578 | 0.239069 | 0.119534 | − | 0.992830i | \(-0.461860\pi\) | ||||
0.119534 | + | 0.992830i | \(0.461860\pi\) | |||||||
\(450\) | 2.80219 | 0.132097 | ||||||||
\(451\) | −13.7871 | −0.649210 | ||||||||
\(452\) | 3.29360 | 0.154918 | ||||||||
\(453\) | −19.0463 | −0.894872 | ||||||||
\(454\) | −6.35023 | −0.298031 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.625344 | −0.0292844 | ||||||||
\(457\) | −7.79559 | −0.364662 | −0.182331 | − | 0.983237i | \(-0.558364\pi\) | ||||
−0.182331 | + | 0.983237i | \(0.558364\pi\) | |||||||
\(458\) | −3.61826 | −0.169070 | ||||||||
\(459\) | −3.88952 | −0.181547 | ||||||||
\(460\) | −23.5970 | −1.10022 | ||||||||
\(461\) | −6.89680 | −0.321216 | −0.160608 | − | 0.987018i | \(-0.551345\pi\) | ||||
−0.160608 | + | 0.987018i | \(0.551345\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6950 | 0.497037 | 0.248518 | − | 0.968627i | \(-0.420056\pi\) | ||||
0.248518 | + | 0.968627i | \(0.420056\pi\) | |||||||
\(464\) | −36.7692 | −1.70697 | ||||||||
\(465\) | 9.01428 | 0.418027 | ||||||||
\(466\) | 45.4694 | 2.10633 | ||||||||
\(467\) | −11.2146 | −0.518952 | −0.259476 | − | 0.965750i | \(-0.583550\pi\) | ||||
−0.259476 | + | 0.965750i | \(0.583550\pi\) | |||||||
\(468\) | 3.06863 | 0.141848 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −14.5974 | −0.673326 | ||||||||
\(471\) | 5.93019 | 0.273249 | ||||||||
\(472\) | −6.93641 | −0.319274 | ||||||||
\(473\) | −21.1276 | −0.971447 | ||||||||
\(474\) | 9.19396 | 0.422292 | ||||||||
\(475\) | −1.46199 | −0.0670806 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.31529 | −0.151797 | ||||||||
\(478\) | 42.0062 | 1.92132 | ||||||||
\(479\) | 35.4607 | 1.62024 | 0.810120 | − | 0.586264i | \(-0.199402\pi\) | ||||
0.810120 | + | 0.586264i | \(0.199402\pi\) | |||||||
\(480\) | −18.9707 | −0.865890 | ||||||||
\(481\) | 10.5175 | 0.479557 | ||||||||
\(482\) | 33.0524 | 1.50550 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 33.0713 | 1.50324 | ||||||||
\(485\) | 38.4462 | 1.74575 | ||||||||
\(486\) | −1.91670 | −0.0869433 | ||||||||
\(487\) | 8.58734 | 0.389129 | 0.194565 | − | 0.980890i | \(-0.437671\pi\) | ||||
0.194565 | + | 0.980890i | \(0.437671\pi\) | |||||||
\(488\) | 5.27263 | 0.238681 | ||||||||
\(489\) | 2.31084 | 0.104500 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.7384 | −1.52259 | −0.761297 | − | 0.648403i | \(-0.775437\pi\) | ||||
−0.761297 | + | 0.648403i | \(0.775437\pi\) | |||||||
\(492\) | −4.16078 | −0.187583 | ||||||||
\(493\) | 31.4589 | 1.41684 | ||||||||
\(494\) | −3.51408 | −0.158106 | ||||||||
\(495\) | 14.0984 | 0.633674 | ||||||||
\(496\) | −16.1207 | −0.723842 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −29.3703 | −1.31611 | ||||||||
\(499\) | −10.9364 | −0.489581 | −0.244790 | − | 0.969576i | \(-0.578719\pi\) | ||||
−0.244790 | + | 0.969576i | \(0.578719\pi\) | |||||||
\(500\) | 15.0532 | 0.673202 | ||||||||
\(501\) | −9.41729 | −0.420733 | ||||||||
\(502\) | 7.14232 | 0.318777 | ||||||||
\(503\) | −22.9454 | −1.02309 | −0.511543 | − | 0.859258i | \(-0.670926\pi\) | ||||
−0.511543 | + | 0.859258i | \(0.670926\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.0841 | 1.69472 | ||||||||
\(506\) | −58.9557 | −2.62090 | ||||||||
\(507\) | 9.63864 | 0.428067 | ||||||||
\(508\) | 12.4682 | 0.553185 | ||||||||
\(509\) | −7.57001 | −0.335535 | −0.167767 | − | 0.985827i | \(-0.553656\pi\) | ||||
−0.167767 | + | 0.985827i | \(0.553656\pi\) | |||||||
\(510\) | 18.9511 | 0.839167 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 28.2406 | 1.24807 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −8.49096 | −0.374520 | ||||||||
\(515\) | 16.1719 | 0.712618 | ||||||||
\(516\) | −6.37605 | −0.280690 | ||||||||
\(517\) | −16.6159 | −0.730765 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.5781 | −0.596011 | ||||||||
\(520\) | 2.91447 | 0.127808 | ||||||||
\(521\) | 0.827184 | 0.0362396 | 0.0181198 | − | 0.999836i | \(-0.494232\pi\) | ||||
0.0181198 | + | 0.999836i | \(0.494232\pi\) | |||||||
\(522\) | 15.5025 | 0.678526 | ||||||||
\(523\) | 17.2414 | 0.753915 | 0.376958 | − | 0.926230i | \(-0.376970\pi\) | ||||
0.376958 | + | 0.926230i | \(0.376970\pi\) | |||||||
\(524\) | 25.8352 | 1.12861 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.27993 | 0.186614 | ||||||||
\(527\) | 13.7925 | 0.600812 | ||||||||
\(528\) | −25.2129 | −1.09725 | ||||||||
\(529\) | 7.75895 | 0.337346 | ||||||||
\(530\) | 16.1532 | 0.701651 | ||||||||
\(531\) | 11.0922 | 0.481358 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.55769 | 0.197415 | ||||||||
\(534\) | −24.2541 | −1.04958 | ||||||||
\(535\) | −45.5778 | −1.97050 | ||||||||
\(536\) | 3.84226 | 0.165961 | ||||||||
\(537\) | −1.55976 | −0.0673087 | ||||||||
\(538\) | −9.34401 | −0.402849 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.25472 | 0.183094 | ||||||||
\(541\) | 34.1280 | 1.46728 | 0.733638 | − | 0.679540i | \(-0.237821\pi\) | ||||
0.733638 | + | 0.679540i | \(0.237821\pi\) | |||||||
\(542\) | 31.7250 | 1.36270 | ||||||||
\(543\) | 18.5334 | 0.795343 | ||||||||
\(544\) | −29.0266 | −1.24451 | ||||||||
\(545\) | 10.1887 | 0.436435 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.0101 | 1.28314 | 0.641569 | − | 0.767066i | \(-0.278284\pi\) | ||||
0.641569 | + | 0.767066i | \(0.278284\pi\) | |||||||
\(548\) | −25.8658 | −1.10493 | ||||||||
\(549\) | −8.43157 | −0.359850 | ||||||||
\(550\) | −15.5412 | −0.662677 | ||||||||
\(551\) | −8.08812 | −0.344565 | ||||||||
\(552\) | 3.46820 | 0.147617 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 53.8287 | 2.28696 | ||||||||
\(555\) | 14.5827 | 0.619002 | ||||||||
\(556\) | 17.2719 | 0.732490 | ||||||||
\(557\) | −34.9066 | −1.47904 | −0.739521 | − | 0.673134i | \(-0.764948\pi\) | ||||
−0.739521 | + | 0.673134i | \(0.764948\pi\) | |||||||
\(558\) | 6.79676 | 0.287730 | ||||||||
\(559\) | 6.98428 | 0.295403 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.5716 | 0.910753 | ||||||||
\(562\) | 21.5963 | 0.910984 | ||||||||
\(563\) | −20.8358 | −0.878123 | −0.439061 | − | 0.898457i | \(-0.644689\pi\) | ||||
−0.439061 | + | 0.898457i | \(0.644689\pi\) | |||||||
\(564\) | −5.01447 | −0.211147 | ||||||||
\(565\) | −5.00226 | −0.210447 | ||||||||
\(566\) | −30.2746 | −1.27254 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.11838 | −0.214763 | ||||||||
\(569\) | 32.3180 | 1.35484 | 0.677421 | − | 0.735595i | \(-0.263097\pi\) | ||||
0.677421 | + | 0.735595i | \(0.263097\pi\) | |||||||
\(570\) | −4.87234 | −0.204080 | ||||||||
\(571\) | 20.4451 | 0.855599 | 0.427800 | − | 0.903874i | \(-0.359289\pi\) | ||||
0.427800 | + | 0.903874i | \(0.359289\pi\) | |||||||
\(572\) | −17.0189 | −0.711595 | ||||||||
\(573\) | 23.3811 | 0.976757 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.10829 | 0.338139 | ||||||||
\(576\) | −5.21175 | −0.217156 | ||||||||
\(577\) | −20.1462 | −0.838699 | −0.419349 | − | 0.907825i | \(-0.637742\pi\) | ||||
−0.419349 | + | 0.907825i | \(0.637742\pi\) | |||||||
\(578\) | −3.58732 | −0.149213 | ||||||||
\(579\) | −16.8288 | −0.699379 | ||||||||
\(580\) | −34.4127 | −1.42891 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 28.9885 | 1.20161 | ||||||||
\(583\) | 18.3869 | 0.761506 | ||||||||
\(584\) | 5.20244 | 0.215278 | ||||||||
\(585\) | −4.66058 | −0.192691 | ||||||||
\(586\) | −50.7108 | −2.09484 | ||||||||
\(587\) | 9.60605 | 0.396484 | 0.198242 | − | 0.980153i | \(-0.436477\pi\) | ||||
0.198242 | + | 0.980153i | \(0.436477\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.54608 | −0.146113 | ||||||||
\(590\) | −54.0447 | −2.22498 | ||||||||
\(591\) | 23.1207 | 0.951059 | ||||||||
\(592\) | −26.0791 | −1.07184 | ||||||||
\(593\) | −36.4249 | −1.49579 | −0.747895 | − | 0.663817i | \(-0.768936\pi\) | ||||
−0.747895 | + | 0.663817i | \(0.768936\pi\) | |||||||
\(594\) | 10.6302 | 0.436161 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.0984 | 0.823261 | ||||||||
\(597\) | 12.1762 | 0.498340 | ||||||||
\(598\) | 19.4893 | 0.796979 | ||||||||
\(599\) | 12.6358 | 0.516284 | 0.258142 | − | 0.966107i | \(-0.416890\pi\) | ||||
0.258142 | + | 0.966107i | \(0.416890\pi\) | |||||||
\(600\) | 0.914245 | 0.0373239 | ||||||||
\(601\) | 2.95144 | 0.120392 | 0.0601960 | − | 0.998187i | \(-0.480827\pi\) | ||||
0.0601960 | + | 0.998187i | \(0.480827\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.14424 | −0.250213 | ||||||||
\(604\) | 31.8785 | 1.29712 | ||||||||
\(605\) | −50.2281 | −2.04206 | ||||||||
\(606\) | 28.7154 | 1.16648 | ||||||||
\(607\) | 3.09215 | 0.125507 | 0.0627533 | − | 0.998029i | \(-0.480012\pi\) | ||||
0.0627533 | + | 0.998029i | \(0.480012\pi\) | |||||||
\(608\) | 7.46278 | 0.302656 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 41.0814 | 1.66334 | ||||||||
\(611\) | 5.49281 | 0.222215 | ||||||||
\(612\) | 6.51005 | 0.263153 | ||||||||
\(613\) | −22.9195 | −0.925709 | −0.462855 | − | 0.886434i | \(-0.653175\pi\) | ||||
−0.462855 | + | 0.886434i | \(0.653175\pi\) | |||||||
\(614\) | −22.5932 | −0.911785 | ||||||||
\(615\) | 6.31932 | 0.254820 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.8913 | −0.559242 | −0.279621 | − | 0.960110i | \(-0.590209\pi\) | ||||
−0.279621 | + | 0.960110i | \(0.590209\pi\) | |||||||
\(618\) | 12.1936 | 0.490498 | ||||||||
\(619\) | 42.8963 | 1.72415 | 0.862074 | − | 0.506783i | \(-0.169165\pi\) | ||||
0.862074 | + | 0.506783i | \(0.169165\pi\) | |||||||
\(620\) | −15.0876 | −0.605931 | ||||||||
\(621\) | −5.54608 | −0.222556 | ||||||||
\(622\) | −4.59889 | −0.184399 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.33478 | 0.333658 | ||||||||
\(625\) | −30.1725 | −1.20690 | ||||||||
\(626\) | −12.7663 | −0.510246 | ||||||||
\(627\) | −5.54608 | −0.221489 | ||||||||
\(628\) | −9.92559 | −0.396074 | ||||||||
\(629\) | 22.3127 | 0.889664 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.0613 | 1.55501 | 0.777504 | − | 0.628878i | \(-0.216486\pi\) | ||||
0.777504 | + | 0.628878i | \(0.216486\pi\) | |||||||
\(632\) | 2.99963 | 0.119319 | ||||||||
\(633\) | 6.95597 | 0.276475 | ||||||||
\(634\) | −35.1477 | −1.39590 | ||||||||
\(635\) | −18.9364 | −0.751468 | ||||||||
\(636\) | 5.54893 | 0.220029 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −85.9780 | −3.40390 | ||||||||
\(639\) | 8.18491 | 0.323790 | ||||||||
\(640\) | −12.5480 | −0.496003 | ||||||||
\(641\) | 49.8109 | 1.96741 | 0.983705 | − | 0.179789i | \(-0.0575416\pi\) | ||||
0.983705 | + | 0.179789i | \(0.0575416\pi\) | |||||||
\(642\) | −34.3656 | −1.35630 | ||||||||
\(643\) | −19.9187 | −0.785515 | −0.392758 | − | 0.919642i | \(-0.628479\pi\) | ||||
−0.392758 | + | 0.919642i | \(0.628479\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.68383 | 0.381300 | ||||||||
\(646\) | −7.45505 | −0.293315 | ||||||||
\(647\) | 38.5332 | 1.51490 | 0.757448 | − | 0.652896i | \(-0.226446\pi\) | ||||
0.757448 | + | 0.652896i | \(0.226446\pi\) | |||||||
\(648\) | −0.625344 | −0.0245658 | ||||||||
\(649\) | −61.5179 | −2.41479 | ||||||||
\(650\) | 5.13754 | 0.201511 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.86775 | −0.151473 | ||||||||
\(653\) | −1.47322 | −0.0576515 | −0.0288257 | − | 0.999584i | \(-0.509177\pi\) | ||||
−0.0288257 | + | 0.999584i | \(0.509177\pi\) | |||||||
\(654\) | 7.68225 | 0.300400 | ||||||||
\(655\) | −39.2380 | −1.53315 | ||||||||
\(656\) | −11.3012 | −0.441237 | ||||||||
\(657\) | −8.31932 | −0.324568 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.4063 | 1.37923 | 0.689616 | − | 0.724175i | \(-0.257779\pi\) | ||||
0.689616 | + | 0.724175i | \(0.257779\pi\) | |||||||
\(660\) | −23.5970 | −0.918512 | ||||||||
\(661\) | −12.2390 | −0.476043 | −0.238022 | − | 0.971260i | \(-0.576499\pi\) | ||||
−0.238022 | + | 0.971260i | \(0.576499\pi\) | |||||||
\(662\) | −5.92451 | −0.230262 | ||||||||
\(663\) | −7.13105 | −0.276947 | ||||||||
\(664\) | −9.58236 | −0.371868 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.9954 | 0.426062 | ||||||||
\(667\) | 44.8573 | 1.73688 | ||||||||
\(668\) | 15.7621 | 0.609853 | ||||||||
\(669\) | −28.4092 | −1.09836 | ||||||||
\(670\) | 29.9368 | 1.15656 | ||||||||
\(671\) | 46.7621 | 1.80523 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.6565 | −1.52864 | −0.764322 | − | 0.644835i | \(-0.776926\pi\) | ||||
−0.764322 | + | 0.644835i | \(0.776926\pi\) | |||||||
\(674\) | 32.2453 | 1.24204 | ||||||||
\(675\) | −1.46199 | −0.0562719 | ||||||||
\(676\) | −16.1326 | −0.620484 | ||||||||
\(677\) | 12.7354 | 0.489463 | 0.244731 | − | 0.969591i | \(-0.421300\pi\) | ||||
0.244731 | + | 0.969591i | \(0.421300\pi\) | |||||||
\(678\) | −3.77170 | −0.144851 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.18299 | 0.237107 | ||||||||
\(681\) | 3.31311 | 0.126958 | ||||||||
\(682\) | −37.6954 | −1.44343 | ||||||||
\(683\) | −10.2019 | −0.390366 | −0.195183 | − | 0.980767i | \(-0.562530\pi\) | ||||
−0.195183 | + | 0.980767i | \(0.562530\pi\) | |||||||
\(684\) | −1.67374 | −0.0639970 | ||||||||
\(685\) | 39.2845 | 1.50098 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.88776 | 0.0720224 | ||||||||
\(688\) | −17.3181 | −0.660247 | ||||||||
\(689\) | −6.07825 | −0.231563 | ||||||||
\(690\) | 27.0223 | 1.02872 | ||||||||
\(691\) | 16.3435 | 0.621736 | 0.310868 | − | 0.950453i | \(-0.399380\pi\) | ||||
0.310868 | + | 0.950453i | \(0.399380\pi\) | |||||||
\(692\) | 22.7262 | 0.863919 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −51.5357 | −1.95627 | ||||||||
\(695\) | −26.2322 | −0.995043 | ||||||||
\(696\) | 5.05786 | 0.191718 | ||||||||
\(697\) | 9.66905 | 0.366241 | ||||||||
\(698\) | 9.20719 | 0.348497 | ||||||||
\(699\) | −23.7227 | −0.897276 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.9807 | 0.754660 | 0.377330 | − | 0.926079i | \(-0.376842\pi\) | ||||
0.377330 | + | 0.926079i | \(0.376842\pi\) | |||||||
\(702\) | −3.51408 | −0.132630 | ||||||||
\(703\) | −5.73661 | −0.216360 | ||||||||
\(704\) | 28.9048 | 1.08939 | ||||||||
\(705\) | 7.61588 | 0.286831 | ||||||||
\(706\) | 24.1073 | 0.907289 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −18.5654 | −0.697729 | ||||||||
\(709\) | −2.38955 | −0.0897414 | −0.0448707 | − | 0.998993i | \(-0.514288\pi\) | ||||
−0.0448707 | + | 0.998993i | \(0.514288\pi\) | |||||||
\(710\) | −39.8796 | −1.49666 | ||||||||
\(711\) | −4.79676 | −0.179893 | ||||||||
\(712\) | −7.91316 | −0.296558 | ||||||||
\(713\) | 19.6668 | 0.736527 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.8479 | 0.966659 | ||||||||
\(716\) | 2.61063 | 0.0975640 | ||||||||
\(717\) | −21.9159 | −0.818464 | ||||||||
\(718\) | −60.0563 | −2.24128 | ||||||||
\(719\) | −48.8139 | −1.82045 | −0.910225 | − | 0.414113i | \(-0.864092\pi\) | ||||
−0.910225 | + | 0.414113i | \(0.864092\pi\) | |||||||
\(720\) | 11.5563 | 0.430679 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.91670 | 0.0713322 | ||||||||
\(723\) | −17.2445 | −0.641328 | ||||||||
\(724\) | −31.0200 | −1.15285 | ||||||||
\(725\) | 11.8247 | 0.439159 | ||||||||
\(726\) | −37.8720 | −1.40556 | ||||||||
\(727\) | 27.4034 | 1.01634 | 0.508168 | − | 0.861258i | \(-0.330323\pi\) | ||||
0.508168 | + | 0.861258i | \(0.330323\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 40.5345 | 1.50025 | ||||||||
\(731\) | 14.8170 | 0.548027 | ||||||||
\(732\) | 14.1122 | 0.521604 | ||||||||
\(733\) | −16.5229 | −0.610288 | −0.305144 | − | 0.952306i | \(-0.598705\pi\) | ||||
−0.305144 | + | 0.952306i | \(0.598705\pi\) | |||||||
\(734\) | 40.4119 | 1.49163 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41.3891 | −1.52562 | ||||||||
\(737\) | 34.0764 | 1.25522 | ||||||||
\(738\) | 4.76477 | 0.175393 | ||||||||
\(739\) | −22.6771 | −0.834192 | −0.417096 | − | 0.908863i | \(-0.636952\pi\) | ||||
−0.417096 | + | 0.908863i | \(0.636952\pi\) | |||||||
\(740\) | −24.4077 | −0.897243 | ||||||||
\(741\) | 1.83340 | 0.0673516 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.2185 | 0.558313 | 0.279156 | − | 0.960246i | \(-0.409945\pi\) | ||||
0.279156 | + | 0.960246i | \(0.409945\pi\) | |||||||
\(744\) | 2.21752 | 0.0812981 | ||||||||
\(745\) | −30.5250 | −1.11835 | ||||||||
\(746\) | −45.2526 | −1.65682 | ||||||||
\(747\) | 15.3234 | 0.560652 | ||||||||
\(748\) | −36.1052 | −1.32014 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −17.2384 | −0.629457 | ||||||||
\(751\) | −12.3674 | −0.451294 | −0.225647 | − | 0.974209i | \(-0.572450\pi\) | ||||
−0.225647 | + | 0.974209i | \(0.572450\pi\) | |||||||
\(752\) | −13.6199 | −0.496667 | ||||||||
\(753\) | −3.72636 | −0.135796 | ||||||||
\(754\) | 28.4223 | 1.03508 | ||||||||
\(755\) | −48.4165 | −1.76206 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.9271 | −0.542536 | −0.271268 | − | 0.962504i | \(-0.587443\pi\) | ||||
−0.271268 | + | 0.962504i | \(0.587443\pi\) | |||||||
\(758\) | 13.6815 | 0.496933 | ||||||||
\(759\) | 30.7590 | 1.11648 | ||||||||
\(760\) | −1.58965 | −0.0576627 | ||||||||
\(761\) | −15.2563 | −0.553041 | −0.276520 | − | 0.961008i | \(-0.589181\pi\) | ||||
−0.276520 | + | 0.961008i | \(0.589181\pi\) | |||||||
\(762\) | −14.2780 | −0.517239 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −39.1338 | −1.41581 | ||||||||
\(765\) | −9.88734 | −0.357477 | ||||||||
\(766\) | 18.0501 | 0.652177 | ||||||||
\(767\) | 20.3364 | 0.734303 | ||||||||
\(768\) | −19.8847 | −0.717527 | ||||||||
\(769\) | 10.7563 | 0.387883 | 0.193941 | − | 0.981013i | \(-0.437873\pi\) | ||||
0.193941 | + | 0.981013i | \(0.437873\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.42999 | 0.159542 | ||||||||
\(772\) | 28.1670 | 1.01375 | ||||||||
\(773\) | 13.8026 | 0.496444 | 0.248222 | − | 0.968703i | \(-0.420154\pi\) | ||||
0.248222 | + | 0.968703i | \(0.420154\pi\) | |||||||
\(774\) | 7.30160 | 0.262451 | ||||||||
\(775\) | 5.18432 | 0.186226 | ||||||||
\(776\) | 9.45779 | 0.339515 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −53.8057 | −1.92903 | ||||||||
\(779\) | −2.48592 | −0.0890674 | ||||||||
\(780\) | 7.80060 | 0.279306 | ||||||||
\(781\) | −45.3941 | −1.62433 | ||||||||
\(782\) | 41.3463 | 1.47854 | ||||||||
\(783\) | −8.08812 | −0.289046 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.0748 | 0.538043 | ||||||||
\(786\) | −29.5854 | −1.05528 | ||||||||
\(787\) | 19.6101 | 0.699023 | 0.349512 | − | 0.936932i | \(-0.386347\pi\) | ||||
0.349512 | + | 0.936932i | \(0.386347\pi\) | |||||||
\(788\) | −38.6980 | −1.37856 | ||||||||
\(789\) | −2.23297 | −0.0794958 | ||||||||
\(790\) | 23.3714 | 0.831519 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.46820 | 0.123237 | ||||||||
\(793\) | −15.4584 | −0.548945 | ||||||||
\(794\) | 12.6325 | 0.448312 | ||||||||
\(795\) | −8.42761 | −0.298897 | ||||||||
\(796\) | −20.3798 | −0.722345 | ||||||||
\(797\) | 25.2766 | 0.895344 | 0.447672 | − | 0.894198i | \(-0.352253\pi\) | ||||
0.447672 | + | 0.894198i | \(0.352253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.6529 | 0.412250 | ||||||||
\(800\) | −10.9105 | −0.385744 | ||||||||
\(801\) | 12.6541 | 0.447111 | ||||||||
\(802\) | 65.5252 | 2.31378 | ||||||||
\(803\) | 46.1396 | 1.62823 | ||||||||
\(804\) | 10.2839 | 0.362684 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.4612 | 0.438927 | ||||||||
\(807\) | 4.87505 | 0.171610 | ||||||||
\(808\) | 9.36870 | 0.329590 | ||||||||
\(809\) | 36.3718 | 1.27876 | 0.639382 | − | 0.768889i | \(-0.279190\pi\) | ||||
0.639382 | + | 0.768889i | \(0.279190\pi\) | |||||||
\(810\) | −4.87234 | −0.171196 | ||||||||
\(811\) | −38.3409 | −1.34633 | −0.673165 | − | 0.739492i | \(-0.735066\pi\) | ||||
−0.673165 | + | 0.739492i | \(0.735066\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.5519 | −0.580500 | ||||||||
\(814\) | −60.9811 | −2.13739 | ||||||||
\(815\) | 5.87426 | 0.205766 | ||||||||
\(816\) | 17.6821 | 0.618996 | ||||||||
\(817\) | −3.80947 | −0.133276 | ||||||||
\(818\) | 64.1241 | 2.24205 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.5769 | −0.369361 | ||||||||
\(821\) | 7.02009 | 0.245003 | 0.122501 | − | 0.992468i | \(-0.460908\pi\) | ||||
0.122501 | + | 0.992468i | \(0.460908\pi\) | |||||||
\(822\) | 29.6205 | 1.03313 | ||||||||
\(823\) | −18.4767 | −0.644056 | −0.322028 | − | 0.946730i | \(-0.604365\pi\) | ||||
−0.322028 | + | 0.946730i | \(0.604365\pi\) | |||||||
\(824\) | 3.97829 | 0.138590 | ||||||||
\(825\) | 8.10829 | 0.282294 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.2879 | −1.05321 | −0.526606 | − | 0.850109i | \(-0.676536\pi\) | ||||
−0.526606 | + | 0.850109i | \(0.676536\pi\) | |||||||
\(828\) | 9.28268 | 0.322596 | ||||||||
\(829\) | −5.07259 | −0.176178 | −0.0880891 | − | 0.996113i | \(-0.528076\pi\) | ||||
−0.0880891 | + | 0.996113i | \(0.528076\pi\) | |||||||
\(830\) | −74.6605 | −2.59150 | ||||||||
\(831\) | −28.0841 | −0.974226 | ||||||||
\(832\) | −9.55523 | −0.331268 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −19.7790 | −0.684892 | ||||||||
\(835\) | −23.9392 | −0.828449 | ||||||||
\(836\) | 9.28268 | 0.321048 | ||||||||
\(837\) | −3.54608 | −0.122570 | ||||||||
\(838\) | 58.3478 | 2.01559 | ||||||||
\(839\) | −5.10458 | −0.176230 | −0.0881149 | − | 0.996110i | \(-0.528084\pi\) | ||||
−0.0881149 | + | 0.996110i | \(0.528084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.4177 | 1.25578 | ||||||||
\(842\) | −33.4805 | −1.15381 | ||||||||
\(843\) | −11.2674 | −0.388071 | ||||||||
\(844\) | −11.6425 | −0.400751 | ||||||||
\(845\) | 24.5019 | 0.842889 | ||||||||
\(846\) | 5.74237 | 0.197427 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.0716 | 0.517559 | ||||||||
\(849\) | 15.7952 | 0.542089 | ||||||||
\(850\) | 10.8992 | 0.373839 | ||||||||
\(851\) | 31.8157 | 1.09063 | ||||||||
\(852\) | −13.6994 | −0.469334 | ||||||||
\(853\) | 38.4821 | 1.31760 | 0.658800 | − | 0.752318i | \(-0.271064\pi\) | ||||
0.658800 | + | 0.752318i | \(0.271064\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.54204 | 0.0869361 | ||||||||
\(856\) | −11.2122 | −0.383224 | ||||||||
\(857\) | 47.8034 | 1.63293 | 0.816466 | − | 0.577394i | \(-0.195930\pi\) | ||||
0.816466 | + | 0.577394i | \(0.195930\pi\) | |||||||
\(858\) | 19.4893 | 0.665355 | ||||||||
\(859\) | 10.5654 | 0.360486 | 0.180243 | − | 0.983622i | \(-0.442312\pi\) | ||||
0.180243 | + | 0.983622i | \(0.442312\pi\) | |||||||
\(860\) | −16.2082 | −0.552695 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 47.7199 | 1.62535 | ||||||||
\(863\) | 1.30828 | 0.0445344 | 0.0222672 | − | 0.999752i | \(-0.492912\pi\) | ||||
0.0222672 | + | 0.999752i | \(0.492912\pi\) | |||||||
\(864\) | 7.46278 | 0.253889 | ||||||||
\(865\) | −34.5161 | −1.17358 | ||||||||
\(866\) | 21.6927 | 0.737148 | ||||||||
\(867\) | 1.87161 | 0.0635633 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.6032 | 0.902452 | ||||||||
\(870\) | 39.4080 | 1.33606 | ||||||||
\(871\) | −11.2649 | −0.381695 | ||||||||
\(872\) | 2.50642 | 0.0848780 | ||||||||
\(873\) | −15.1241 | −0.511875 | ||||||||
\(874\) | −10.6302 | −0.359571 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.9244 | 0.470461 | ||||||||
\(877\) | 47.8543 | 1.61592 | 0.807962 | − | 0.589235i | \(-0.200571\pi\) | ||||
0.807962 | + | 0.589235i | \(0.200571\pi\) | |||||||
\(878\) | −24.4234 | −0.824249 | ||||||||
\(879\) | 26.4573 | 0.892384 | ||||||||
\(880\) | −64.0922 | −2.16055 | ||||||||
\(881\) | −45.8583 | −1.54501 | −0.772503 | − | 0.635011i | \(-0.780995\pi\) | ||||
−0.772503 | + | 0.635011i | \(0.780995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.6217 | 0.963196 | 0.481598 | − | 0.876392i | \(-0.340056\pi\) | ||||
0.481598 | + | 0.876392i | \(0.340056\pi\) | |||||||
\(884\) | 11.9355 | 0.401435 | ||||||||
\(885\) | 28.1967 | 0.947823 | ||||||||
\(886\) | −43.3443 | −1.45618 | ||||||||
\(887\) | 58.2209 | 1.95487 | 0.977434 | − | 0.211243i | \(-0.0677511\pi\) | ||||
0.977434 | + | 0.211243i | \(0.0677511\pi\) | |||||||
\(888\) | 3.58735 | 0.120384 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −61.6550 | −2.06668 | ||||||||
\(891\) | −5.54608 | −0.185801 | ||||||||
\(892\) | 47.5496 | 1.59208 | ||||||||
\(893\) | −2.99597 | −0.100256 | ||||||||
\(894\) | −23.0159 | −0.769765 | ||||||||
\(895\) | −3.96498 | −0.132535 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.1682 | −0.339506 | ||||||||
\(898\) | 9.70958 | 0.324013 | ||||||||
\(899\) | 28.6811 | 0.956568 | ||||||||
\(900\) | 2.44699 | 0.0815662 | ||||||||
\(901\) | −12.8949 | −0.429591 | ||||||||
\(902\) | −26.4258 | −0.879881 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.23056 | −0.0409278 | ||||||||
\(905\) | 47.1126 | 1.56608 | ||||||||
\(906\) | −36.5060 | −1.21283 | ||||||||
\(907\) | −34.9591 | −1.16080 | −0.580399 | − | 0.814332i | \(-0.697104\pi\) | ||||
−0.580399 | + | 0.814332i | \(0.697104\pi\) | |||||||
\(908\) | −5.54527 | −0.184026 | ||||||||
\(909\) | −14.9817 | −0.496911 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.7994 | 0.490325 | 0.245162 | − | 0.969482i | \(-0.421159\pi\) | ||||
0.245162 | + | 0.969482i | \(0.421159\pi\) | |||||||
\(912\) | −4.54608 | −0.150536 | ||||||||
\(913\) | −84.9845 | −2.81258 | ||||||||
\(914\) | −14.9418 | −0.494231 | ||||||||
\(915\) | −21.4334 | −0.708567 | ||||||||
\(916\) | −3.15961 | −0.104396 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.45505 | −0.246053 | ||||||||
\(919\) | 0.762136 | 0.0251405 | 0.0125703 | − | 0.999921i | \(-0.495999\pi\) | ||||
0.0125703 | + | 0.999921i | \(0.495999\pi\) | |||||||
\(920\) | 8.81633 | 0.290666 | ||||||||
\(921\) | 11.7875 | 0.388412 | ||||||||
\(922\) | −13.2191 | −0.435348 | ||||||||
\(923\) | 15.0062 | 0.493936 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.38685 | 0.275758 | ||||||||
\(926\) | 20.4990 | 0.673640 | ||||||||
\(927\) | −6.36176 | −0.208948 | ||||||||
\(928\) | −60.3598 | −1.98141 | ||||||||
\(929\) | −26.5680 | −0.871667 | −0.435833 | − | 0.900027i | \(-0.643546\pi\) | ||||
−0.435833 | + | 0.900027i | \(0.643546\pi\) | |||||||
\(930\) | 17.2777 | 0.566557 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 39.7057 | 1.30060 | ||||||||
\(933\) | 2.39938 | 0.0785521 | ||||||||
\(934\) | −21.4951 | −0.703341 | ||||||||
\(935\) | 54.8359 | 1.79333 | ||||||||
\(936\) | −1.14651 | −0.0374747 | ||||||||
\(937\) | 28.7590 | 0.939514 | 0.469757 | − | 0.882796i | \(-0.344342\pi\) | ||||
0.469757 | + | 0.882796i | \(0.344342\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.66058 | 0.217360 | ||||||||
\(940\) | −12.7470 | −0.415761 | ||||||||
\(941\) | 34.1732 | 1.11402 | 0.557008 | − | 0.830507i | \(-0.311949\pi\) | ||||
0.557008 | + | 0.830507i | \(0.311949\pi\) | |||||||
\(942\) | 11.3664 | 0.370337 | ||||||||
\(943\) | 13.7871 | 0.448970 | ||||||||
\(944\) | −50.4258 | −1.64122 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −40.4952 | −1.31661 | ||||||||
\(947\) | −40.5626 | −1.31811 | −0.659054 | − | 0.752096i | \(-0.729043\pi\) | ||||
−0.659054 | + | 0.752096i | \(0.729043\pi\) | |||||||
\(948\) | 8.02853 | 0.260755 | ||||||||
\(949\) | −15.2526 | −0.495122 | ||||||||
\(950\) | −2.80219 | −0.0909151 | ||||||||
\(951\) | 18.3376 | 0.594638 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.6589 | −1.25229 | −0.626143 | − | 0.779709i | \(-0.715367\pi\) | ||||
−0.626143 | + | 0.779709i | \(0.715367\pi\) | |||||||
\(954\) | −6.35442 | −0.205732 | ||||||||
\(955\) | 59.4357 | 1.92329 | ||||||||
\(956\) | 36.6815 | 1.18636 | ||||||||
\(957\) | 44.8573 | 1.45003 | ||||||||
\(958\) | 67.9675 | 2.19593 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −13.2485 | −0.427594 | ||||||||
\(961\) | −18.4254 | −0.594366 | ||||||||
\(962\) | 20.1589 | 0.649949 | ||||||||
\(963\) | 17.9296 | 0.577773 | ||||||||
\(964\) | 28.8627 | 0.929606 | ||||||||
\(965\) | −42.7794 | −1.37712 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.83153 | 0.219687 | 0.109844 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109844 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(968\) | −12.3561 | −0.397141 | ||||||||
\(969\) | 3.88952 | 0.124949 | ||||||||
\(970\) | 73.6899 | 2.36604 | ||||||||
\(971\) | −57.7215 | −1.85237 | −0.926186 | − | 0.377068i | \(-0.876932\pi\) | ||||
−0.926186 | + | 0.377068i | \(0.876932\pi\) | |||||||
\(972\) | −1.67374 | −0.0536852 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.4593 | 0.527392 | ||||||||
\(975\) | −2.68041 | −0.0858418 | ||||||||
\(976\) | 38.3305 | 1.22693 | ||||||||
\(977\) | 38.7294 | 1.23906 | 0.619532 | − | 0.784972i | \(-0.287323\pi\) | ||||
0.619532 | + | 0.784972i | \(0.287323\pi\) | |||||||
\(978\) | 4.42919 | 0.141630 | ||||||||
\(979\) | −70.1806 | −2.24298 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00806 | −0.127968 | ||||||||
\(982\) | −64.6665 | −2.06359 | ||||||||
\(983\) | −44.7814 | −1.42831 | −0.714153 | − | 0.699990i | \(-0.753188\pi\) | ||||
−0.714153 | + | 0.699990i | \(0.753188\pi\) | |||||||
\(984\) | 1.55456 | 0.0495574 | ||||||||
\(985\) | 58.7739 | 1.87269 | ||||||||
\(986\) | 60.2973 | 1.92026 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.06863 | −0.0976263 | ||||||||
\(989\) | 21.1276 | 0.671818 | ||||||||
\(990\) | 27.0223 | 0.858826 | ||||||||
\(991\) | 22.1647 | 0.704086 | 0.352043 | − | 0.935984i | \(-0.385487\pi\) | ||||
0.352043 | + | 0.935984i | \(0.385487\pi\) | |||||||
\(992\) | −26.4636 | −0.840219 | ||||||||
\(993\) | 3.09099 | 0.0980897 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.9525 | 0.981261 | ||||||||
\(996\) | −25.6473 | −0.812666 | ||||||||
\(997\) | −5.54303 | −0.175549 | −0.0877747 | − | 0.996140i | \(-0.527976\pi\) | ||||
−0.0877747 | + | 0.996140i | \(0.527976\pi\) | |||||||
\(998\) | −20.9618 | −0.663535 | ||||||||
\(999\) | −5.73661 | −0.181498 |
(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 | 2793.2.a.be.1.4 | 5 | ||
3.2 | odd | 2 | 8379.2.a.ce.1.2 | 5 | |||
7.6 | odd | 2 | 399.2.a.f.1.4 | ✓ | 5 | ||
21.20 | even | 2 | 1197.2.a.p.1.2 | 5 | |||
28.27 | even | 2 | 6384.2.a.cc.1.5 | 5 | |||
35.34 | odd | 2 | 9975.2.a.bq.1.2 | 5 | |||
133.132 | even | 2 | 7581.2.a.x.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
399.2.a.f.1.4 | ✓ | 5 | 7.6 | odd | 2 | ||
1197.2.a.p.1.2 | 5 | 21.20 | even | 2 | |||
2793.2.a.be.1.4 | 5 | 1.1 | even | 1 | trivial | ||
6384.2.a.cc.1.5 | 5 | 28.27 | even | 2 | |||
7581.2.a.x.1.2 | 5 | 133.132 | even | 2 | |||
8379.2.a.ce.1.2 | 5 | 3.2 | odd | 2 | |||
9975.2.a.bq.1.2 | 5 | 35.34 | odd | 2 |