Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8011,2,Mod(1,8011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8011.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: | \(63.9681570592\) |
Analytic rank: | \(0\) |
Dimension: | \(358\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61876 | −1.85174 | −0.925870 | − | 0.377842i | \(-0.876666\pi\) | ||||
−0.925870 | + | 0.377842i | \(0.876666\pi\) | |||||||
\(3\) | −0.901244 | −0.520333 | −0.260167 | − | 0.965564i | \(-0.583778\pi\) | ||||
−0.260167 | + | 0.965564i | \(0.583778\pi\) | |||||||
\(4\) | 4.85788 | 2.42894 | ||||||||
\(5\) | −1.31265 | −0.587034 | −0.293517 | − | 0.955954i | \(-0.594826\pi\) | ||||
−0.293517 | + | 0.955954i | \(0.594826\pi\) | |||||||
\(6\) | 2.36014 | 0.963522 | ||||||||
\(7\) | −2.24388 | −0.848106 | −0.424053 | − | 0.905637i | \(-0.639393\pi\) | ||||
−0.424053 | + | 0.905637i | \(0.639393\pi\) | |||||||
\(8\) | −7.48409 | −2.64603 | ||||||||
\(9\) | −2.18776 | −0.729253 | ||||||||
\(10\) | 3.43751 | 1.08703 | ||||||||
\(11\) | 5.25836 | 1.58546 | 0.792728 | − | 0.609576i | \(-0.208660\pi\) | ||||
0.792728 | + | 0.609576i | \(0.208660\pi\) | |||||||
\(12\) | −4.37814 | −1.26386 | ||||||||
\(13\) | −1.46998 | −0.407700 | −0.203850 | − | 0.979002i | \(-0.565345\pi\) | ||||
−0.203850 | + | 0.979002i | \(0.565345\pi\) | |||||||
\(14\) | 5.87617 | 1.57047 | ||||||||
\(15\) | 1.18302 | 0.305454 | ||||||||
\(16\) | 9.88325 | 2.47081 | ||||||||
\(17\) | −0.0584840 | −0.0141844 | −0.00709222 | − | 0.999975i | \(-0.502258\pi\) | ||||
−0.00709222 | + | 0.999975i | \(0.502258\pi\) | |||||||
\(18\) | 5.72921 | 1.35039 | ||||||||
\(19\) | 1.09397 | 0.250974 | 0.125487 | − | 0.992095i | \(-0.459951\pi\) | ||||
0.125487 | + | 0.992095i | \(0.459951\pi\) | |||||||
\(20\) | −6.37669 | −1.42587 | ||||||||
\(21\) | 2.02228 | 0.441298 | ||||||||
\(22\) | −13.7704 | −2.93585 | ||||||||
\(23\) | −6.84838 | −1.42799 | −0.713993 | − | 0.700152i | \(-0.753115\pi\) | ||||
−0.713993 | + | 0.700152i | \(0.753115\pi\) | |||||||
\(24\) | 6.74499 | 1.37682 | ||||||||
\(25\) | −3.27695 | −0.655391 | ||||||||
\(26\) | 3.84952 | 0.754954 | ||||||||
\(27\) | 4.67544 | 0.899788 | ||||||||
\(28\) | −10.9005 | −2.06000 | ||||||||
\(29\) | −4.73669 | −0.879582 | −0.439791 | − | 0.898100i | \(-0.644947\pi\) | ||||
−0.439791 | + | 0.898100i | \(0.644947\pi\) | |||||||
\(30\) | −3.09803 | −0.565620 | ||||||||
\(31\) | 7.80265 | 1.40140 | 0.700699 | − | 0.713457i | \(-0.252872\pi\) | ||||
0.700699 | + | 0.713457i | \(0.252872\pi\) | |||||||
\(32\) | −10.9136 | −1.92928 | ||||||||
\(33\) | −4.73907 | −0.824966 | ||||||||
\(34\) | 0.153155 | 0.0262659 | ||||||||
\(35\) | 2.94542 | 0.497867 | ||||||||
\(36\) | −10.6279 | −1.77131 | ||||||||
\(37\) | −8.81218 | −1.44871 | −0.724356 | − | 0.689426i | \(-0.757863\pi\) | ||||
−0.724356 | + | 0.689426i | \(0.757863\pi\) | |||||||
\(38\) | −2.86484 | −0.464739 | ||||||||
\(39\) | 1.32481 | 0.212140 | ||||||||
\(40\) | 9.82398 | 1.55331 | ||||||||
\(41\) | −5.59712 | −0.874123 | −0.437062 | − | 0.899432i | \(-0.643981\pi\) | ||||
−0.437062 | + | 0.899432i | \(0.643981\pi\) | |||||||
\(42\) | −5.29586 | −0.817169 | ||||||||
\(43\) | −3.28836 | −0.501470 | −0.250735 | − | 0.968056i | \(-0.580672\pi\) | ||||
−0.250735 | + | 0.968056i | \(0.580672\pi\) | |||||||
\(44\) | 25.5445 | 3.85098 | ||||||||
\(45\) | 2.87176 | 0.428096 | ||||||||
\(46\) | 17.9342 | 2.64426 | ||||||||
\(47\) | 2.16311 | 0.315521 | 0.157761 | − | 0.987477i | \(-0.449573\pi\) | ||||
0.157761 | + | 0.987477i | \(0.449573\pi\) | |||||||
\(48\) | −8.90722 | −1.28565 | ||||||||
\(49\) | −1.96501 | −0.280715 | ||||||||
\(50\) | 8.58154 | 1.21361 | ||||||||
\(51\) | 0.0527083 | 0.00738064 | ||||||||
\(52\) | −7.14100 | −0.990278 | ||||||||
\(53\) | 7.06719 | 0.970753 | 0.485377 | − | 0.874305i | \(-0.338682\pi\) | ||||
0.485377 | + | 0.874305i | \(0.338682\pi\) | |||||||
\(54\) | −12.2438 | −1.66617 | ||||||||
\(55\) | −6.90238 | −0.930717 | ||||||||
\(56\) | 16.7934 | 2.24411 | ||||||||
\(57\) | −0.985934 | −0.130590 | ||||||||
\(58\) | 12.4042 | 1.62876 | ||||||||
\(59\) | 2.06153 | 0.268389 | 0.134194 | − | 0.990955i | \(-0.457155\pi\) | ||||
0.134194 | + | 0.990955i | \(0.457155\pi\) | |||||||
\(60\) | 5.74695 | 0.741928 | ||||||||
\(61\) | 4.33875 | 0.555521 | 0.277760 | − | 0.960650i | \(-0.410408\pi\) | ||||
0.277760 | + | 0.960650i | \(0.410408\pi\) | |||||||
\(62\) | −20.4332 | −2.59502 | ||||||||
\(63\) | 4.90907 | 0.618484 | ||||||||
\(64\) | 8.81363 | 1.10170 | ||||||||
\(65\) | 1.92957 | 0.239334 | ||||||||
\(66\) | 12.4105 | 1.52762 | ||||||||
\(67\) | −0.888835 | −0.108589 | −0.0542943 | − | 0.998525i | \(-0.517291\pi\) | ||||
−0.0542943 | + | 0.998525i | \(0.517291\pi\) | |||||||
\(68\) | −0.284108 | −0.0344532 | ||||||||
\(69\) | 6.17206 | 0.743029 | ||||||||
\(70\) | −7.71334 | −0.921921 | ||||||||
\(71\) | 2.46324 | 0.292332 | 0.146166 | − | 0.989260i | \(-0.453307\pi\) | ||||
0.146166 | + | 0.989260i | \(0.453307\pi\) | |||||||
\(72\) | 16.3734 | 1.92962 | ||||||||
\(73\) | −3.08122 | −0.360629 | −0.180315 | − | 0.983609i | \(-0.557712\pi\) | ||||
−0.180315 | + | 0.983609i | \(0.557712\pi\) | |||||||
\(74\) | 23.0769 | 2.68264 | ||||||||
\(75\) | 2.95334 | 0.341022 | ||||||||
\(76\) | 5.31438 | 0.609601 | ||||||||
\(77\) | −11.7991 | −1.34464 | ||||||||
\(78\) | −3.46936 | −0.392828 | ||||||||
\(79\) | 0.809398 | 0.0910644 | 0.0455322 | − | 0.998963i | \(-0.485502\pi\) | ||||
0.0455322 | + | 0.998963i | \(0.485502\pi\) | |||||||
\(80\) | −12.9732 | −1.45045 | ||||||||
\(81\) | 2.34957 | 0.261063 | ||||||||
\(82\) | 14.6575 | 1.61865 | ||||||||
\(83\) | 0.294813 | 0.0323599 | 0.0161800 | − | 0.999869i | \(-0.494850\pi\) | ||||
0.0161800 | + | 0.999869i | \(0.494850\pi\) | |||||||
\(84\) | 9.82401 | 1.07189 | ||||||||
\(85\) | 0.0767689 | 0.00832675 | ||||||||
\(86\) | 8.61140 | 0.928592 | ||||||||
\(87\) | 4.26892 | 0.457676 | ||||||||
\(88\) | −39.3541 | −4.19516 | ||||||||
\(89\) | 4.84930 | 0.514025 | 0.257013 | − | 0.966408i | \(-0.417262\pi\) | ||||
0.257013 | + | 0.966408i | \(0.417262\pi\) | |||||||
\(90\) | −7.52043 | −0.792723 | ||||||||
\(91\) | 3.29846 | 0.345773 | ||||||||
\(92\) | −33.2686 | −3.46850 | ||||||||
\(93\) | −7.03209 | −0.729194 | ||||||||
\(94\) | −5.66465 | −0.584264 | ||||||||
\(95\) | −1.43600 | −0.147330 | ||||||||
\(96\) | 9.83584 | 1.00387 | ||||||||
\(97\) | −8.32931 | −0.845714 | −0.422857 | − | 0.906197i | \(-0.638973\pi\) | ||||
−0.422857 | + | 0.906197i | \(0.638973\pi\) | |||||||
\(98\) | 5.14588 | 0.519812 | ||||||||
\(99\) | −11.5040 | −1.15620 | ||||||||
\(100\) | −15.9191 | −1.59191 | ||||||||
\(101\) | −2.58697 | −0.257413 | −0.128706 | − | 0.991683i | \(-0.541082\pi\) | ||||
−0.128706 | + | 0.991683i | \(0.541082\pi\) | |||||||
\(102\) | −0.138030 | −0.0136670 | ||||||||
\(103\) | −0.273875 | −0.0269857 | −0.0134929 | − | 0.999909i | \(-0.504295\pi\) | ||||
−0.0134929 | + | 0.999909i | \(0.504295\pi\) | |||||||
\(104\) | 11.0015 | 1.07878 | ||||||||
\(105\) | −2.65455 | −0.259057 | ||||||||
\(106\) | −18.5072 | −1.79758 | ||||||||
\(107\) | 1.33036 | 0.128611 | 0.0643056 | − | 0.997930i | \(-0.479517\pi\) | ||||
0.0643056 | + | 0.997930i | \(0.479517\pi\) | |||||||
\(108\) | 22.7127 | 2.18553 | ||||||||
\(109\) | −15.4832 | −1.48302 | −0.741512 | − | 0.670940i | \(-0.765891\pi\) | ||||
−0.741512 | + | 0.670940i | \(0.765891\pi\) | |||||||
\(110\) | 18.0756 | 1.72345 | ||||||||
\(111\) | 7.94192 | 0.753814 | ||||||||
\(112\) | −22.1768 | −2.09551 | ||||||||
\(113\) | −14.9630 | −1.40760 | −0.703802 | − | 0.710396i | \(-0.748516\pi\) | ||||
−0.703802 | + | 0.710396i | \(0.748516\pi\) | |||||||
\(114\) | 2.58192 | 0.241819 | ||||||||
\(115\) | 8.98952 | 0.838277 | ||||||||
\(116\) | −23.0103 | −2.13645 | ||||||||
\(117\) | 3.21597 | 0.297316 | ||||||||
\(118\) | −5.39865 | −0.496986 | ||||||||
\(119\) | 0.131231 | 0.0120299 | ||||||||
\(120\) | −8.85380 | −0.808238 | ||||||||
\(121\) | 16.6504 | 1.51367 | ||||||||
\(122\) | −11.3621 | −1.02868 | ||||||||
\(123\) | 5.04437 | 0.454836 | ||||||||
\(124\) | 37.9044 | 3.40391 | ||||||||
\(125\) | 10.8647 | 0.971771 | ||||||||
\(126\) | −12.8556 | −1.14527 | ||||||||
\(127\) | −0.830429 | −0.0736887 | −0.0368443 | − | 0.999321i | \(-0.511731\pi\) | ||||
−0.0368443 | + | 0.999321i | \(0.511731\pi\) | |||||||
\(128\) | −1.25348 | −0.110793 | ||||||||
\(129\) | 2.96361 | 0.260932 | ||||||||
\(130\) | −5.05307 | −0.443184 | ||||||||
\(131\) | 9.17248 | 0.801404 | 0.400702 | − | 0.916209i | \(-0.368766\pi\) | ||||
0.400702 | + | 0.916209i | \(0.368766\pi\) | |||||||
\(132\) | −23.0218 | −2.00379 | ||||||||
\(133\) | −2.45474 | −0.212853 | ||||||||
\(134\) | 2.32764 | 0.201078 | ||||||||
\(135\) | −6.13720 | −0.528206 | ||||||||
\(136\) | 0.437699 | 0.0375324 | ||||||||
\(137\) | −12.5284 | −1.07037 | −0.535186 | − | 0.844734i | \(-0.679758\pi\) | ||||
−0.535186 | + | 0.844734i | \(0.679758\pi\) | |||||||
\(138\) | −16.1631 | −1.37590 | ||||||||
\(139\) | −17.6971 | −1.50105 | −0.750524 | − | 0.660843i | \(-0.770199\pi\) | ||||
−0.750524 | + | 0.660843i | \(0.770199\pi\) | |||||||
\(140\) | 14.3085 | 1.20929 | ||||||||
\(141\) | −1.94949 | −0.164176 | ||||||||
\(142\) | −6.45061 | −0.541323 | ||||||||
\(143\) | −7.72970 | −0.646390 | ||||||||
\(144\) | −21.6222 | −1.80185 | ||||||||
\(145\) | 6.21761 | 0.516345 | ||||||||
\(146\) | 8.06895 | 0.667791 | ||||||||
\(147\) | 1.77095 | 0.146066 | ||||||||
\(148\) | −42.8085 | −3.51884 | ||||||||
\(149\) | −16.0671 | −1.31627 | −0.658133 | − | 0.752902i | \(-0.728653\pi\) | ||||
−0.658133 | + | 0.752902i | \(0.728653\pi\) | |||||||
\(150\) | −7.73406 | −0.631484 | ||||||||
\(151\) | 8.18383 | 0.665991 | 0.332995 | − | 0.942928i | \(-0.391941\pi\) | ||||
0.332995 | + | 0.942928i | \(0.391941\pi\) | |||||||
\(152\) | −8.18738 | −0.664084 | ||||||||
\(153\) | 0.127949 | 0.0103440 | ||||||||
\(154\) | 30.8990 | 2.48991 | ||||||||
\(155\) | −10.2421 | −0.822668 | ||||||||
\(156\) | 6.43578 | 0.515275 | ||||||||
\(157\) | 1.48627 | 0.118617 | 0.0593085 | − | 0.998240i | \(-0.481110\pi\) | ||||
0.0593085 | + | 0.998240i | \(0.481110\pi\) | |||||||
\(158\) | −2.11962 | −0.168628 | ||||||||
\(159\) | −6.36926 | −0.505115 | ||||||||
\(160\) | 14.3258 | 1.13255 | ||||||||
\(161\) | 15.3669 | 1.21108 | ||||||||
\(162\) | −6.15295 | −0.483421 | ||||||||
\(163\) | −7.00634 | −0.548779 | −0.274390 | − | 0.961619i | \(-0.588476\pi\) | ||||
−0.274390 | + | 0.961619i | \(0.588476\pi\) | |||||||
\(164\) | −27.1901 | −2.12319 | ||||||||
\(165\) | 6.22073 | 0.484283 | ||||||||
\(166\) | −0.772043 | −0.0599221 | ||||||||
\(167\) | −5.34483 | −0.413595 | −0.206798 | − | 0.978384i | \(-0.566304\pi\) | ||||
−0.206798 | + | 0.978384i | \(0.566304\pi\) | |||||||
\(168\) | −15.1349 | −1.16769 | ||||||||
\(169\) | −10.8392 | −0.833781 | ||||||||
\(170\) | −0.201039 | −0.0154190 | ||||||||
\(171\) | −2.39334 | −0.183024 | ||||||||
\(172\) | −15.9744 | −1.21804 | ||||||||
\(173\) | 12.3255 | 0.937087 | 0.468543 | − | 0.883440i | \(-0.344779\pi\) | ||||
0.468543 | + | 0.883440i | \(0.344779\pi\) | |||||||
\(174\) | −11.1793 | −0.847497 | ||||||||
\(175\) | 7.35309 | 0.555841 | ||||||||
\(176\) | 51.9697 | 3.91736 | ||||||||
\(177\) | −1.85794 | −0.139652 | ||||||||
\(178\) | −12.6991 | −0.951841 | ||||||||
\(179\) | 18.8803 | 1.41118 | 0.705589 | − | 0.708621i | \(-0.250683\pi\) | ||||
0.705589 | + | 0.708621i | \(0.250683\pi\) | |||||||
\(180\) | 13.9507 | 1.03982 | ||||||||
\(181\) | −8.94589 | −0.664943 | −0.332472 | − | 0.943113i | \(-0.607883\pi\) | ||||
−0.332472 | + | 0.943113i | \(0.607883\pi\) | |||||||
\(182\) | −8.63787 | −0.640281 | ||||||||
\(183\) | −3.91028 | −0.289056 | ||||||||
\(184\) | 51.2539 | 3.77849 | ||||||||
\(185\) | 11.5673 | 0.850444 | ||||||||
\(186\) | 18.4153 | 1.35028 | ||||||||
\(187\) | −0.307530 | −0.0224888 | ||||||||
\(188\) | 10.5081 | 0.766383 | ||||||||
\(189\) | −10.4911 | −0.763116 | ||||||||
\(190\) | 3.76053 | 0.272817 | ||||||||
\(191\) | −2.48542 | −0.179839 | −0.0899195 | − | 0.995949i | \(-0.528661\pi\) | ||||
−0.0899195 | + | 0.995949i | \(0.528661\pi\) | |||||||
\(192\) | −7.94323 | −0.573253 | ||||||||
\(193\) | −5.86390 | −0.422093 | −0.211046 | − | 0.977476i | \(-0.567687\pi\) | ||||
−0.211046 | + | 0.977476i | \(0.567687\pi\) | |||||||
\(194\) | 21.8124 | 1.56604 | ||||||||
\(195\) | −1.73901 | −0.124533 | ||||||||
\(196\) | −9.54578 | −0.681841 | ||||||||
\(197\) | −10.2518 | −0.730409 | −0.365204 | − | 0.930927i | \(-0.619001\pi\) | ||||
−0.365204 | + | 0.930927i | \(0.619001\pi\) | |||||||
\(198\) | 30.1262 | 2.14098 | ||||||||
\(199\) | −22.2605 | −1.57800 | −0.789001 | − | 0.614392i | \(-0.789401\pi\) | ||||
−0.789001 | + | 0.614392i | \(0.789401\pi\) | |||||||
\(200\) | 24.5250 | 1.73418 | ||||||||
\(201\) | 0.801058 | 0.0565022 | ||||||||
\(202\) | 6.77463 | 0.476661 | ||||||||
\(203\) | 10.6286 | 0.745979 | ||||||||
\(204\) | 0.256051 | 0.0179271 | ||||||||
\(205\) | 7.34705 | 0.513140 | ||||||||
\(206\) | 0.717212 | 0.0499706 | ||||||||
\(207\) | 14.9826 | 1.04136 | ||||||||
\(208\) | −14.5282 | −1.00735 | ||||||||
\(209\) | 5.75249 | 0.397908 | ||||||||
\(210\) | 6.95161 | 0.479706 | ||||||||
\(211\) | 0.289562 | 0.0199343 | 0.00996714 | − | 0.999950i | \(-0.496827\pi\) | ||||
0.00996714 | + | 0.999950i | \(0.496827\pi\) | |||||||
\(212\) | 34.3316 | 2.35790 | ||||||||
\(213\) | −2.21998 | −0.152110 | ||||||||
\(214\) | −3.48390 | −0.238154 | ||||||||
\(215\) | 4.31646 | 0.294380 | ||||||||
\(216\) | −34.9914 | −2.38086 | ||||||||
\(217\) | −17.5082 | −1.18853 | ||||||||
\(218\) | 40.5468 | 2.74617 | ||||||||
\(219\) | 2.77693 | 0.187647 | ||||||||
\(220\) | −33.5309 | −2.26066 | ||||||||
\(221\) | 0.0859704 | 0.00578299 | ||||||||
\(222\) | −20.7979 | −1.39587 | ||||||||
\(223\) | 22.8791 | 1.53210 | 0.766049 | − | 0.642783i | \(-0.222220\pi\) | ||||
0.766049 | + | 0.642783i | \(0.222220\pi\) | |||||||
\(224\) | 24.4889 | 1.63623 | ||||||||
\(225\) | 7.16919 | 0.477946 | ||||||||
\(226\) | 39.1846 | 2.60652 | ||||||||
\(227\) | 25.1983 | 1.67247 | 0.836234 | − | 0.548373i | \(-0.184753\pi\) | ||||
0.836234 | + | 0.548373i | \(0.184753\pi\) | |||||||
\(228\) | −4.78955 | −0.317196 | ||||||||
\(229\) | 7.13969 | 0.471804 | 0.235902 | − | 0.971777i | \(-0.424196\pi\) | ||||
0.235902 | + | 0.971777i | \(0.424196\pi\) | |||||||
\(230\) | −23.5414 | −1.55227 | ||||||||
\(231\) | 10.6339 | 0.699659 | ||||||||
\(232\) | 35.4499 | 2.32740 | ||||||||
\(233\) | −15.3423 | −1.00510 | −0.502552 | − | 0.864547i | \(-0.667606\pi\) | ||||
−0.502552 | + | 0.864547i | \(0.667606\pi\) | |||||||
\(234\) | −8.42183 | −0.550552 | ||||||||
\(235\) | −2.83940 | −0.185222 | ||||||||
\(236\) | 10.0147 | 0.651901 | ||||||||
\(237\) | −0.729465 | −0.0473838 | ||||||||
\(238\) | −0.343662 | −0.0222763 | ||||||||
\(239\) | 26.6429 | 1.72339 | 0.861693 | − | 0.507430i | \(-0.169404\pi\) | ||||
0.861693 | + | 0.507430i | \(0.169404\pi\) | |||||||
\(240\) | 11.6920 | 0.754718 | ||||||||
\(241\) | −3.32320 | −0.214066 | −0.107033 | − | 0.994255i | \(-0.534135\pi\) | ||||
−0.107033 | + | 0.994255i | \(0.534135\pi\) | |||||||
\(242\) | −43.6032 | −2.80292 | ||||||||
\(243\) | −16.1438 | −1.03563 | ||||||||
\(244\) | 21.0772 | 1.34933 | ||||||||
\(245\) | 2.57936 | 0.164790 | ||||||||
\(246\) | −13.2100 | −0.842237 | ||||||||
\(247\) | −1.60812 | −0.102322 | ||||||||
\(248\) | −58.3958 | −3.70814 | ||||||||
\(249\) | −0.265698 | −0.0168379 | ||||||||
\(250\) | −28.4521 | −1.79947 | ||||||||
\(251\) | 0.495028 | 0.0312459 | 0.0156229 | − | 0.999878i | \(-0.495027\pi\) | ||||
0.0156229 | + | 0.999878i | \(0.495027\pi\) | |||||||
\(252\) | 23.8477 | 1.50226 | ||||||||
\(253\) | −36.0113 | −2.26401 | ||||||||
\(254\) | 2.17469 | 0.136452 | ||||||||
\(255\) | −0.0691875 | −0.00433269 | ||||||||
\(256\) | −14.3447 | −0.896543 | ||||||||
\(257\) | −0.936392 | −0.0584105 | −0.0292053 | − | 0.999573i | \(-0.509298\pi\) | ||||
−0.0292053 | + | 0.999573i | \(0.509298\pi\) | |||||||
\(258\) | −7.76098 | −0.483177 | ||||||||
\(259\) | 19.7735 | 1.22866 | ||||||||
\(260\) | 9.37362 | 0.581327 | ||||||||
\(261\) | 10.3627 | 0.641438 | ||||||||
\(262\) | −24.0205 | −1.48399 | ||||||||
\(263\) | −7.05732 | −0.435173 | −0.217586 | − | 0.976041i | \(-0.569818\pi\) | ||||
−0.217586 | + | 0.976041i | \(0.569818\pi\) | |||||||
\(264\) | 35.4676 | 2.18288 | ||||||||
\(265\) | −9.27674 | −0.569865 | ||||||||
\(266\) | 6.42836 | 0.394148 | ||||||||
\(267\) | −4.37041 | −0.267465 | ||||||||
\(268\) | −4.31786 | −0.263755 | ||||||||
\(269\) | −22.9255 | −1.39780 | −0.698898 | − | 0.715222i | \(-0.746326\pi\) | ||||
−0.698898 | + | 0.715222i | \(0.746326\pi\) | |||||||
\(270\) | 16.0718 | 0.978101 | ||||||||
\(271\) | 20.1635 | 1.22484 | 0.612422 | − | 0.790531i | \(-0.290195\pi\) | ||||
0.612422 | + | 0.790531i | \(0.290195\pi\) | |||||||
\(272\) | −0.578011 | −0.0350471 | ||||||||
\(273\) | −2.97272 | −0.179917 | ||||||||
\(274\) | 32.8088 | 1.98205 | ||||||||
\(275\) | −17.2314 | −1.03909 | ||||||||
\(276\) | 29.9832 | 1.80477 | ||||||||
\(277\) | −6.68451 | −0.401634 | −0.200817 | − | 0.979629i | \(-0.564360\pi\) | ||||
−0.200817 | + | 0.979629i | \(0.564360\pi\) | |||||||
\(278\) | 46.3444 | 2.77955 | ||||||||
\(279\) | −17.0703 | −1.02197 | ||||||||
\(280\) | −22.0438 | −1.31737 | ||||||||
\(281\) | 4.30473 | 0.256798 | 0.128399 | − | 0.991723i | \(-0.459016\pi\) | ||||
0.128399 | + | 0.991723i | \(0.459016\pi\) | |||||||
\(282\) | 5.10523 | 0.304012 | ||||||||
\(283\) | −13.8808 | −0.825126 | −0.412563 | − | 0.910929i | \(-0.635366\pi\) | ||||
−0.412563 | + | 0.910929i | \(0.635366\pi\) | |||||||
\(284\) | 11.9661 | 0.710058 | ||||||||
\(285\) | 1.29419 | 0.0766609 | ||||||||
\(286\) | 20.2422 | 1.19695 | ||||||||
\(287\) | 12.5593 | 0.741350 | ||||||||
\(288\) | 23.8764 | 1.40693 | ||||||||
\(289\) | −16.9966 | −0.999799 | ||||||||
\(290\) | −16.2824 | −0.956136 | ||||||||
\(291\) | 7.50674 | 0.440053 | ||||||||
\(292\) | −14.9682 | −0.875947 | ||||||||
\(293\) | 18.1249 | 1.05887 | 0.529434 | − | 0.848351i | \(-0.322404\pi\) | ||||
0.529434 | + | 0.848351i | \(0.322404\pi\) | |||||||
\(294\) | −4.63769 | −0.270476 | ||||||||
\(295\) | −2.70607 | −0.157553 | ||||||||
\(296\) | 65.9511 | 3.83333 | ||||||||
\(297\) | 24.5851 | 1.42657 | ||||||||
\(298\) | 42.0757 | 2.43738 | ||||||||
\(299\) | 10.0670 | 0.582190 | ||||||||
\(300\) | 14.3470 | 0.828322 | ||||||||
\(301\) | 7.37867 | 0.425300 | ||||||||
\(302\) | −21.4315 | −1.23324 | ||||||||
\(303\) | 2.33149 | 0.133940 | ||||||||
\(304\) | 10.8120 | 0.620110 | ||||||||
\(305\) | −5.69526 | −0.326110 | ||||||||
\(306\) | −0.335067 | −0.0191545 | ||||||||
\(307\) | −13.9760 | −0.797654 | −0.398827 | − | 0.917026i | \(-0.630583\pi\) | ||||
−0.398827 | + | 0.917026i | \(0.630583\pi\) | |||||||
\(308\) | −57.3188 | −3.26604 | ||||||||
\(309\) | 0.246828 | 0.0140416 | ||||||||
\(310\) | 26.8217 | 1.52337 | ||||||||
\(311\) | 1.31078 | 0.0743274 | 0.0371637 | − | 0.999309i | \(-0.488168\pi\) | ||||
0.0371637 | + | 0.999309i | \(0.488168\pi\) | |||||||
\(312\) | −9.91502 | −0.561328 | ||||||||
\(313\) | −20.4467 | −1.15572 | −0.577858 | − | 0.816137i | \(-0.696111\pi\) | ||||
−0.577858 | + | 0.816137i | \(0.696111\pi\) | |||||||
\(314\) | −3.89217 | −0.219648 | ||||||||
\(315\) | −6.44388 | −0.363071 | ||||||||
\(316\) | 3.93196 | 0.221190 | ||||||||
\(317\) | −24.4394 | −1.37266 | −0.686328 | − | 0.727292i | \(-0.740778\pi\) | ||||
−0.686328 | + | 0.727292i | \(0.740778\pi\) | |||||||
\(318\) | 16.6795 | 0.935342 | ||||||||
\(319\) | −24.9072 | −1.39454 | ||||||||
\(320\) | −11.5692 | −0.646738 | ||||||||
\(321\) | −1.19898 | −0.0669207 | ||||||||
\(322\) | −40.2423 | −2.24261 | ||||||||
\(323\) | −0.0639797 | −0.00355993 | ||||||||
\(324\) | 11.4139 | 0.634107 | ||||||||
\(325\) | 4.81706 | 0.267203 | ||||||||
\(326\) | 18.3479 | 1.01620 | ||||||||
\(327\) | 13.9542 | 0.771667 | ||||||||
\(328\) | 41.8894 | 2.31295 | ||||||||
\(329\) | −4.85375 | −0.267596 | ||||||||
\(330\) | −16.2906 | −0.896766 | ||||||||
\(331\) | −2.15567 | −0.118486 | −0.0592431 | − | 0.998244i | \(-0.518869\pi\) | ||||
−0.0592431 | + | 0.998244i | \(0.518869\pi\) | |||||||
\(332\) | 1.43217 | 0.0786003 | ||||||||
\(333\) | 19.2789 | 1.05648 | ||||||||
\(334\) | 13.9968 | 0.765871 | ||||||||
\(335\) | 1.16673 | 0.0637452 | ||||||||
\(336\) | 19.9867 | 1.09036 | ||||||||
\(337\) | −5.23249 | −0.285032 | −0.142516 | − | 0.989792i | \(-0.545519\pi\) | ||||
−0.142516 | + | 0.989792i | \(0.545519\pi\) | |||||||
\(338\) | 28.3851 | 1.54395 | ||||||||
\(339\) | 13.4854 | 0.732424 | ||||||||
\(340\) | 0.372934 | 0.0202252 | ||||||||
\(341\) | 41.0292 | 2.22185 | ||||||||
\(342\) | 6.26758 | 0.338912 | ||||||||
\(343\) | 20.1164 | 1.08618 | ||||||||
\(344\) | 24.6104 | 1.32690 | ||||||||
\(345\) | −8.10175 | −0.436184 | ||||||||
\(346\) | −32.2773 | −1.73524 | ||||||||
\(347\) | −1.45563 | −0.0781424 | −0.0390712 | − | 0.999236i | \(-0.512440\pi\) | ||||
−0.0390712 | + | 0.999236i | \(0.512440\pi\) | |||||||
\(348\) | 20.7379 | 1.11167 | ||||||||
\(349\) | −0.812222 | −0.0434773 | −0.0217386 | − | 0.999764i | \(-0.506920\pi\) | ||||
−0.0217386 | + | 0.999764i | \(0.506920\pi\) | |||||||
\(350\) | −19.2559 | −1.02927 | ||||||||
\(351\) | −6.87281 | −0.366843 | ||||||||
\(352\) | −57.3878 | −3.05878 | ||||||||
\(353\) | 10.6193 | 0.565209 | 0.282605 | − | 0.959236i | \(-0.408802\pi\) | ||||
0.282605 | + | 0.959236i | \(0.408802\pi\) | |||||||
\(354\) | 4.86550 | 0.258599 | ||||||||
\(355\) | −3.23336 | −0.171609 | ||||||||
\(356\) | 23.5573 | 1.24854 | ||||||||
\(357\) | −0.118271 | −0.00625957 | ||||||||
\(358\) | −49.4428 | −2.61313 | ||||||||
\(359\) | 22.5915 | 1.19233 | 0.596166 | − | 0.802861i | \(-0.296690\pi\) | ||||
0.596166 | + | 0.802861i | \(0.296690\pi\) | |||||||
\(360\) | −21.4925 | −1.13275 | ||||||||
\(361\) | −17.8032 | −0.937012 | ||||||||
\(362\) | 23.4271 | 1.23130 | ||||||||
\(363\) | −15.0060 | −0.787613 | ||||||||
\(364\) | 16.0235 | 0.839861 | ||||||||
\(365\) | 4.04455 | 0.211702 | ||||||||
\(366\) | 10.2401 | 0.535256 | ||||||||
\(367\) | 18.7786 | 0.980237 | 0.490118 | − | 0.871656i | \(-0.336954\pi\) | ||||
0.490118 | + | 0.871656i | \(0.336954\pi\) | |||||||
\(368\) | −67.6843 | −3.52829 | ||||||||
\(369\) | 12.2452 | 0.637457 | ||||||||
\(370\) | −30.2919 | −1.57480 | ||||||||
\(371\) | −15.8579 | −0.823302 | ||||||||
\(372\) | −34.1611 | −1.77117 | ||||||||
\(373\) | −19.7564 | −1.02295 | −0.511473 | − | 0.859300i | \(-0.670900\pi\) | ||||
−0.511473 | + | 0.859300i | \(0.670900\pi\) | |||||||
\(374\) | 0.805345 | 0.0416434 | ||||||||
\(375\) | −9.79177 | −0.505645 | ||||||||
\(376\) | −16.1889 | −0.834878 | ||||||||
\(377\) | 6.96286 | 0.358605 | ||||||||
\(378\) | 27.4737 | 1.41309 | ||||||||
\(379\) | −6.31261 | −0.324257 | −0.162128 | − | 0.986770i | \(-0.551836\pi\) | ||||
−0.162128 | + | 0.986770i | \(0.551836\pi\) | |||||||
\(380\) | −6.97591 | −0.357857 | ||||||||
\(381\) | 0.748419 | 0.0383427 | ||||||||
\(382\) | 6.50872 | 0.333015 | ||||||||
\(383\) | 12.9466 | 0.661538 | 0.330769 | − | 0.943712i | \(-0.392692\pi\) | ||||
0.330769 | + | 0.943712i | \(0.392692\pi\) | |||||||
\(384\) | 1.12970 | 0.0576495 | ||||||||
\(385\) | 15.4881 | 0.789347 | ||||||||
\(386\) | 15.3561 | 0.781606 | ||||||||
\(387\) | 7.19413 | 0.365698 | ||||||||
\(388\) | −40.4628 | −2.05419 | ||||||||
\(389\) | −7.44001 | −0.377224 | −0.188612 | − | 0.982052i | \(-0.560399\pi\) | ||||
−0.188612 | + | 0.982052i | \(0.560399\pi\) | |||||||
\(390\) | 4.55405 | 0.230603 | ||||||||
\(391\) | 0.400521 | 0.0202552 | ||||||||
\(392\) | 14.7063 | 0.742781 | ||||||||
\(393\) | −8.26664 | −0.416997 | ||||||||
\(394\) | 26.8469 | 1.35253 | ||||||||
\(395\) | −1.06245 | −0.0534579 | ||||||||
\(396\) | −55.8852 | −2.80834 | ||||||||
\(397\) | −23.5160 | −1.18023 | −0.590117 | − | 0.807318i | \(-0.700918\pi\) | ||||
−0.590117 | + | 0.807318i | \(0.700918\pi\) | |||||||
\(398\) | 58.2947 | 2.92205 | ||||||||
\(399\) | 2.21232 | 0.110754 | ||||||||
\(400\) | −32.3870 | −1.61935 | ||||||||
\(401\) | −14.4370 | −0.720950 | −0.360475 | − | 0.932769i | \(-0.617385\pi\) | ||||
−0.360475 | + | 0.932769i | \(0.617385\pi\) | |||||||
\(402\) | −2.09777 | −0.104627 | ||||||||
\(403\) | −11.4698 | −0.571349 | ||||||||
\(404\) | −12.5672 | −0.625240 | ||||||||
\(405\) | −3.08416 | −0.153253 | ||||||||
\(406\) | −27.8336 | −1.38136 | ||||||||
\(407\) | −46.3376 | −2.29687 | ||||||||
\(408\) | −0.394474 | −0.0195294 | ||||||||
\(409\) | −5.62839 | −0.278306 | −0.139153 | − | 0.990271i | \(-0.544438\pi\) | ||||
−0.139153 | + | 0.990271i | \(0.544438\pi\) | |||||||
\(410\) | −19.2401 | −0.950202 | ||||||||
\(411\) | 11.2911 | 0.556950 | ||||||||
\(412\) | −1.33045 | −0.0655467 | ||||||||
\(413\) | −4.62583 | −0.227622 | ||||||||
\(414\) | −39.2358 | −1.92833 | ||||||||
\(415\) | −0.386985 | −0.0189964 | ||||||||
\(416\) | 16.0428 | 0.786565 | ||||||||
\(417\) | 15.9494 | 0.781046 | ||||||||
\(418\) | −15.0644 | −0.736823 | ||||||||
\(419\) | −21.2788 | −1.03954 | −0.519769 | − | 0.854307i | \(-0.673982\pi\) | ||||
−0.519769 | + | 0.854307i | \(0.673982\pi\) | |||||||
\(420\) | −12.8955 | −0.629234 | ||||||||
\(421\) | −0.291480 | −0.0142059 | −0.00710294 | − | 0.999975i | \(-0.502261\pi\) | ||||
−0.00710294 | + | 0.999975i | \(0.502261\pi\) | |||||||
\(422\) | −0.758292 | −0.0369131 | ||||||||
\(423\) | −4.73236 | −0.230095 | ||||||||
\(424\) | −52.8915 | −2.56864 | ||||||||
\(425\) | 0.191649 | 0.00929635 | ||||||||
\(426\) | 5.81357 | 0.281669 | ||||||||
\(427\) | −9.73564 | −0.471141 | ||||||||
\(428\) | 6.46275 | 0.312389 | ||||||||
\(429\) | 6.96634 | 0.336338 | ||||||||
\(430\) | −11.3037 | −0.545115 | ||||||||
\(431\) | 10.8396 | 0.522123 | 0.261062 | − | 0.965322i | \(-0.415927\pi\) | ||||
0.261062 | + | 0.965322i | \(0.415927\pi\) | |||||||
\(432\) | 46.2085 | 2.22321 | ||||||||
\(433\) | 19.2482 | 0.925010 | 0.462505 | − | 0.886617i | \(-0.346951\pi\) | ||||
0.462505 | + | 0.886617i | \(0.346951\pi\) | |||||||
\(434\) | 45.8497 | 2.20086 | ||||||||
\(435\) | −5.60359 | −0.268671 | ||||||||
\(436\) | −75.2157 | −3.60218 | ||||||||
\(437\) | −7.49193 | −0.358388 | ||||||||
\(438\) | −7.27210 | −0.347474 | ||||||||
\(439\) | 24.1607 | 1.15313 | 0.576563 | − | 0.817053i | \(-0.304394\pi\) | ||||
0.576563 | + | 0.817053i | \(0.304394\pi\) | |||||||
\(440\) | 51.6581 | 2.46270 | ||||||||
\(441\) | 4.29896 | 0.204713 | ||||||||
\(442\) | −0.225135 | −0.0107086 | ||||||||
\(443\) | 2.85937 | 0.135853 | 0.0679264 | − | 0.997690i | \(-0.478362\pi\) | ||||
0.0679264 | + | 0.997690i | \(0.478362\pi\) | |||||||
\(444\) | 38.5809 | 1.83097 | ||||||||
\(445\) | −6.36543 | −0.301750 | ||||||||
\(446\) | −59.9147 | −2.83705 | ||||||||
\(447\) | 14.4803 | 0.684897 | ||||||||
\(448\) | −19.7767 | −0.934362 | ||||||||
\(449\) | −13.4059 | −0.632662 | −0.316331 | − | 0.948649i | \(-0.602451\pi\) | ||||
−0.316331 | + | 0.948649i | \(0.602451\pi\) | |||||||
\(450\) | −18.7744 | −0.885031 | ||||||||
\(451\) | −29.4317 | −1.38588 | ||||||||
\(452\) | −72.6887 | −3.41899 | ||||||||
\(453\) | −7.37563 | −0.346537 | ||||||||
\(454\) | −65.9881 | −3.09698 | ||||||||
\(455\) | −4.32972 | −0.202980 | ||||||||
\(456\) | 7.37882 | 0.345545 | ||||||||
\(457\) | 18.8094 | 0.879865 | 0.439933 | − | 0.898031i | \(-0.355002\pi\) | ||||
0.439933 | + | 0.898031i | \(0.355002\pi\) | |||||||
\(458\) | −18.6971 | −0.873659 | ||||||||
\(459\) | −0.273438 | −0.0127630 | ||||||||
\(460\) | 43.6700 | 2.03613 | ||||||||
\(461\) | 11.1609 | 0.519817 | 0.259908 | − | 0.965633i | \(-0.416308\pi\) | ||||
0.259908 | + | 0.965633i | \(0.416308\pi\) | |||||||
\(462\) | −27.8476 | −1.29559 | ||||||||
\(463\) | −11.9519 | −0.555454 | −0.277727 | − | 0.960660i | \(-0.589581\pi\) | ||||
−0.277727 | + | 0.960660i | \(0.589581\pi\) | |||||||
\(464\) | −46.8139 | −2.17328 | ||||||||
\(465\) | 9.23067 | 0.428062 | ||||||||
\(466\) | 40.1776 | 1.86119 | ||||||||
\(467\) | 23.8755 | 1.10483 | 0.552414 | − | 0.833570i | \(-0.313707\pi\) | ||||
0.552414 | + | 0.833570i | \(0.313707\pi\) | |||||||
\(468\) | 15.6228 | 0.722164 | ||||||||
\(469\) | 1.99444 | 0.0920946 | ||||||||
\(470\) | 7.43569 | 0.342983 | ||||||||
\(471\) | −1.33949 | −0.0617204 | ||||||||
\(472\) | −15.4287 | −0.710164 | ||||||||
\(473\) | −17.2914 | −0.795058 | ||||||||
\(474\) | 1.91029 | 0.0877426 | ||||||||
\(475\) | −3.58489 | −0.164486 | ||||||||
\(476\) | 0.637504 | 0.0292200 | ||||||||
\(477\) | −15.4613 | −0.707925 | ||||||||
\(478\) | −69.7712 | −3.19126 | ||||||||
\(479\) | −10.3133 | −0.471228 | −0.235614 | − | 0.971847i | \(-0.575710\pi\) | ||||
−0.235614 | + | 0.971847i | \(0.575710\pi\) | |||||||
\(480\) | −12.9110 | −0.589304 | ||||||||
\(481\) | 12.9537 | 0.590640 | ||||||||
\(482\) | 8.70264 | 0.396394 | ||||||||
\(483\) | −13.8494 | −0.630168 | ||||||||
\(484\) | 80.8855 | 3.67661 | ||||||||
\(485\) | 10.9335 | 0.496463 | ||||||||
\(486\) | 42.2768 | 1.91771 | ||||||||
\(487\) | −22.7203 | −1.02955 | −0.514777 | − | 0.857324i | \(-0.672125\pi\) | ||||
−0.514777 | + | 0.857324i | \(0.672125\pi\) | |||||||
\(488\) | −32.4716 | −1.46992 | ||||||||
\(489\) | 6.31443 | 0.285548 | ||||||||
\(490\) | −6.75473 | −0.305147 | ||||||||
\(491\) | −3.37996 | −0.152536 | −0.0762678 | − | 0.997087i | \(-0.524300\pi\) | ||||
−0.0762678 | + | 0.997087i | \(0.524300\pi\) | |||||||
\(492\) | 24.5050 | 1.10477 | ||||||||
\(493\) | 0.277021 | 0.0124764 | ||||||||
\(494\) | 4.21127 | 0.189474 | ||||||||
\(495\) | 15.1007 | 0.678728 | ||||||||
\(496\) | 77.1156 | 3.46259 | ||||||||
\(497\) | −5.52720 | −0.247929 | ||||||||
\(498\) | 0.695799 | 0.0311795 | ||||||||
\(499\) | 2.66008 | 0.119082 | 0.0595408 | − | 0.998226i | \(-0.481036\pi\) | ||||
0.0595408 | + | 0.998226i | \(0.481036\pi\) | |||||||
\(500\) | 52.7796 | 2.36037 | ||||||||
\(501\) | 4.81699 | 0.215207 | ||||||||
\(502\) | −1.29636 | −0.0578593 | ||||||||
\(503\) | −19.1406 | −0.853438 | −0.426719 | − | 0.904384i | \(-0.640331\pi\) | ||||
−0.426719 | + | 0.904384i | \(0.640331\pi\) | |||||||
\(504\) | −36.7399 | −1.63653 | ||||||||
\(505\) | 3.39578 | 0.151110 | ||||||||
\(506\) | 94.3047 | 4.19236 | ||||||||
\(507\) | 9.76872 | 0.433844 | ||||||||
\(508\) | −4.03413 | −0.178985 | ||||||||
\(509\) | 22.0754 | 0.978474 | 0.489237 | − | 0.872151i | \(-0.337275\pi\) | ||||
0.489237 | + | 0.872151i | \(0.337275\pi\) | |||||||
\(510\) | 0.181185 | 0.00802301 | ||||||||
\(511\) | 6.91388 | 0.305852 | ||||||||
\(512\) | 40.0722 | 1.77096 | ||||||||
\(513\) | 5.11479 | 0.225823 | ||||||||
\(514\) | 2.45218 | 0.108161 | ||||||||
\(515\) | 0.359502 | 0.0158415 | ||||||||
\(516\) | 14.3969 | 0.633787 | ||||||||
\(517\) | 11.3744 | 0.500245 | ||||||||
\(518\) | −51.7818 | −2.27516 | ||||||||
\(519\) | −11.1082 | −0.487598 | ||||||||
\(520\) | −14.4411 | −0.633283 | ||||||||
\(521\) | −27.1076 | −1.18761 | −0.593803 | − | 0.804611i | \(-0.702374\pi\) | ||||
−0.593803 | + | 0.804611i | \(0.702374\pi\) | |||||||
\(522\) | −27.1375 | −1.18778 | ||||||||
\(523\) | −21.3228 | −0.932382 | −0.466191 | − | 0.884684i | \(-0.654374\pi\) | ||||
−0.466191 | + | 0.884684i | \(0.654374\pi\) | |||||||
\(524\) | 44.5588 | 1.94656 | ||||||||
\(525\) | −6.62693 | −0.289223 | ||||||||
\(526\) | 18.4814 | 0.805827 | ||||||||
\(527\) | −0.456330 | −0.0198780 | ||||||||
\(528\) | −46.8374 | −2.03834 | ||||||||
\(529\) | 23.9004 | 1.03915 | ||||||||
\(530\) | 24.2935 | 1.05524 | ||||||||
\(531\) | −4.51014 | −0.195723 | ||||||||
\(532\) | −11.9248 | −0.517007 | ||||||||
\(533\) | 8.22767 | 0.356380 | ||||||||
\(534\) | 11.4450 | 0.495275 | ||||||||
\(535\) | −1.74630 | −0.0754991 | ||||||||
\(536\) | 6.65213 | 0.287328 | ||||||||
\(537\) | −17.0157 | −0.734283 | ||||||||
\(538\) | 60.0364 | 2.58835 | ||||||||
\(539\) | −10.3327 | −0.445062 | ||||||||
\(540\) | −29.8138 | −1.28298 | ||||||||
\(541\) | −11.3051 | −0.486044 | −0.243022 | − | 0.970021i | \(-0.578139\pi\) | ||||
−0.243022 | + | 0.970021i | \(0.578139\pi\) | |||||||
\(542\) | −52.8032 | −2.26809 | ||||||||
\(543\) | 8.06243 | 0.345992 | ||||||||
\(544\) | 0.638272 | 0.0273657 | ||||||||
\(545\) | 20.3240 | 0.870586 | ||||||||
\(546\) | 7.78482 | 0.333160 | ||||||||
\(547\) | 34.3608 | 1.46916 | 0.734580 | − | 0.678522i | \(-0.237379\pi\) | ||||
0.734580 | + | 0.678522i | \(0.237379\pi\) | |||||||
\(548\) | −60.8614 | −2.59987 | ||||||||
\(549\) | −9.49215 | −0.405115 | ||||||||
\(550\) | 45.1249 | 1.92413 | ||||||||
\(551\) | −5.18180 | −0.220752 | ||||||||
\(552\) | −46.1923 | −1.96608 | ||||||||
\(553\) | −1.81619 | −0.0772323 | ||||||||
\(554\) | 17.5051 | 0.743721 | ||||||||
\(555\) | −10.4249 | −0.442514 | ||||||||
\(556\) | −85.9704 | −3.64596 | ||||||||
\(557\) | −32.7272 | −1.38670 | −0.693349 | − | 0.720602i | \(-0.743865\pi\) | ||||
−0.693349 | + | 0.720602i | \(0.743865\pi\) | |||||||
\(558\) | 44.7030 | 1.89243 | ||||||||
\(559\) | 4.83383 | 0.204449 | ||||||||
\(560\) | 29.1104 | 1.23014 | ||||||||
\(561\) | 0.277159 | 0.0117017 | ||||||||
\(562\) | −11.2730 | −0.475524 | ||||||||
\(563\) | −12.0272 | −0.506887 | −0.253444 | − | 0.967350i | \(-0.581563\pi\) | ||||
−0.253444 | + | 0.967350i | \(0.581563\pi\) | |||||||
\(564\) | −9.47037 | −0.398775 | ||||||||
\(565\) | 19.6412 | 0.826312 | ||||||||
\(566\) | 36.3503 | 1.52792 | ||||||||
\(567\) | −5.27215 | −0.221409 | ||||||||
\(568\) | −18.4351 | −0.773519 | ||||||||
\(569\) | −24.0773 | −1.00937 | −0.504686 | − | 0.863303i | \(-0.668392\pi\) | ||||
−0.504686 | + | 0.863303i | \(0.668392\pi\) | |||||||
\(570\) | −3.38915 | −0.141956 | ||||||||
\(571\) | 17.2168 | 0.720500 | 0.360250 | − | 0.932856i | \(-0.382691\pi\) | ||||
0.360250 | + | 0.932856i | \(0.382691\pi\) | |||||||
\(572\) | −37.5500 | −1.57004 | ||||||||
\(573\) | 2.23997 | 0.0935762 | ||||||||
\(574\) | −32.8896 | −1.37279 | ||||||||
\(575\) | 22.4418 | 0.935890 | ||||||||
\(576\) | −19.2821 | −0.803421 | ||||||||
\(577\) | 17.9542 | 0.747444 | 0.373722 | − | 0.927541i | \(-0.378081\pi\) | ||||
0.373722 | + | 0.927541i | \(0.378081\pi\) | |||||||
\(578\) | 44.5099 | 1.85137 | ||||||||
\(579\) | 5.28481 | 0.219629 | ||||||||
\(580\) | 30.2044 | 1.25417 | ||||||||
\(581\) | −0.661524 | −0.0274446 | ||||||||
\(582\) | −19.6583 | −0.814864 | ||||||||
\(583\) | 37.1618 | 1.53909 | ||||||||
\(584\) | 23.0601 | 0.954234 | ||||||||
\(585\) | −4.22143 | −0.174535 | ||||||||
\(586\) | −47.4647 | −1.96075 | ||||||||
\(587\) | 17.0435 | 0.703460 | 0.351730 | − | 0.936102i | \(-0.385594\pi\) | ||||
0.351730 | + | 0.936102i | \(0.385594\pi\) | |||||||
\(588\) | 8.60307 | 0.354785 | ||||||||
\(589\) | 8.53587 | 0.351714 | ||||||||
\(590\) | 7.08653 | 0.291748 | ||||||||
\(591\) | 9.23935 | 0.380056 | ||||||||
\(592\) | −87.0929 | −3.57950 | ||||||||
\(593\) | 39.0129 | 1.60207 | 0.801034 | − | 0.598619i | \(-0.204283\pi\) | ||||
0.801034 | + | 0.598619i | \(0.204283\pi\) | |||||||
\(594\) | −64.3825 | −2.64164 | ||||||||
\(595\) | −0.172260 | −0.00706197 | ||||||||
\(596\) | −78.0519 | −3.19713 | ||||||||
\(597\) | 20.0621 | 0.821087 | ||||||||
\(598\) | −26.3630 | −1.07806 | ||||||||
\(599\) | 34.2148 | 1.39798 | 0.698990 | − | 0.715132i | \(-0.253633\pi\) | ||||
0.698990 | + | 0.715132i | \(0.253633\pi\) | |||||||
\(600\) | −22.1030 | −0.902353 | ||||||||
\(601\) | 8.26767 | 0.337245 | 0.168623 | − | 0.985681i | \(-0.446068\pi\) | ||||
0.168623 | + | 0.985681i | \(0.446068\pi\) | |||||||
\(602\) | −19.3229 | −0.787545 | ||||||||
\(603\) | 1.94456 | 0.0791885 | ||||||||
\(604\) | 39.7561 | 1.61765 | ||||||||
\(605\) | −21.8561 | −0.888576 | ||||||||
\(606\) | −6.10560 | −0.248023 | ||||||||
\(607\) | −44.9054 | −1.82265 | −0.911326 | − | 0.411685i | \(-0.864940\pi\) | ||||
−0.911326 | + | 0.411685i | \(0.864940\pi\) | |||||||
\(608\) | −11.9392 | −0.484198 | ||||||||
\(609\) | −9.57893 | −0.388158 | ||||||||
\(610\) | 14.9145 | 0.603870 | ||||||||
\(611\) | −3.17973 | −0.128638 | ||||||||
\(612\) | 0.621560 | 0.0251251 | ||||||||
\(613\) | −8.11165 | −0.327626 | −0.163813 | − | 0.986491i | \(-0.552379\pi\) | ||||
−0.163813 | + | 0.986491i | \(0.552379\pi\) | |||||||
\(614\) | 36.5998 | 1.47705 | ||||||||
\(615\) | −6.62149 | −0.267004 | ||||||||
\(616\) | 88.3058 | 3.55794 | ||||||||
\(617\) | 22.2908 | 0.897393 | 0.448696 | − | 0.893684i | \(-0.351888\pi\) | ||||
0.448696 | + | 0.893684i | \(0.351888\pi\) | |||||||
\(618\) | −0.646383 | −0.0260014 | ||||||||
\(619\) | 2.00944 | 0.0807661 | 0.0403831 | − | 0.999184i | \(-0.487142\pi\) | ||||
0.0403831 | + | 0.999184i | \(0.487142\pi\) | |||||||
\(620\) | −49.7551 | −1.99821 | ||||||||
\(621\) | −32.0192 | −1.28489 | ||||||||
\(622\) | −3.43261 | −0.137635 | ||||||||
\(623\) | −10.8813 | −0.435948 | ||||||||
\(624\) | 13.0935 | 0.524158 | ||||||||
\(625\) | 2.12320 | 0.0849281 | ||||||||
\(626\) | 53.5449 | 2.14009 | ||||||||
\(627\) | −5.18440 | −0.207045 | ||||||||
\(628\) | 7.22011 | 0.288114 | ||||||||
\(629\) | 0.515371 | 0.0205492 | ||||||||
\(630\) | 16.8749 | 0.672314 | ||||||||
\(631\) | −7.57409 | −0.301520 | −0.150760 | − | 0.988570i | \(-0.548172\pi\) | ||||
−0.150760 | + | 0.988570i | \(0.548172\pi\) | |||||||
\(632\) | −6.05761 | −0.240959 | ||||||||
\(633\) | −0.260966 | −0.0103725 | ||||||||
\(634\) | 64.0009 | 2.54180 | ||||||||
\(635\) | 1.09006 | 0.0432578 | ||||||||
\(636\) | −30.9411 | −1.22690 | ||||||||
\(637\) | 2.88853 | 0.114448 | ||||||||
\(638\) | 65.2260 | 2.58232 | ||||||||
\(639\) | −5.38897 | −0.213184 | ||||||||
\(640\) | 1.64538 | 0.0650395 | ||||||||
\(641\) | 45.6521 | 1.80315 | 0.901575 | − | 0.432624i | \(-0.142412\pi\) | ||||
0.901575 | + | 0.432624i | \(0.142412\pi\) | |||||||
\(642\) | 3.13984 | 0.123920 | ||||||||
\(643\) | 2.39068 | 0.0942793 | 0.0471397 | − | 0.998888i | \(-0.484989\pi\) | ||||
0.0471397 | + | 0.998888i | \(0.484989\pi\) | |||||||
\(644\) | 74.6508 | 2.94165 | ||||||||
\(645\) | −3.89018 | −0.153176 | ||||||||
\(646\) | 0.167547 | 0.00659206 | ||||||||
\(647\) | 12.3138 | 0.484107 | 0.242053 | − | 0.970263i | \(-0.422179\pi\) | ||||
0.242053 | + | 0.970263i | \(0.422179\pi\) | |||||||
\(648\) | −17.5844 | −0.690780 | ||||||||
\(649\) | 10.8403 | 0.425519 | ||||||||
\(650\) | −12.6147 | −0.494790 | ||||||||
\(651\) | 15.7792 | 0.618434 | ||||||||
\(652\) | −34.0360 | −1.33295 | ||||||||
\(653\) | 45.4456 | 1.77842 | 0.889212 | − | 0.457495i | \(-0.151253\pi\) | ||||
0.889212 | + | 0.457495i | \(0.151253\pi\) | |||||||
\(654\) | −36.5425 | −1.42893 | ||||||||
\(655\) | −12.0402 | −0.470451 | ||||||||
\(656\) | −55.3177 | −2.15979 | ||||||||
\(657\) | 6.74096 | 0.262990 | ||||||||
\(658\) | 12.7108 | 0.495518 | ||||||||
\(659\) | 7.72380 | 0.300876 | 0.150438 | − | 0.988619i | \(-0.451932\pi\) | ||||
0.150438 | + | 0.988619i | \(0.451932\pi\) | |||||||
\(660\) | 30.2196 | 1.17629 | ||||||||
\(661\) | 29.9995 | 1.16685 | 0.583423 | − | 0.812169i | \(-0.301713\pi\) | ||||
0.583423 | + | 0.812169i | \(0.301713\pi\) | |||||||
\(662\) | 5.64517 | 0.219406 | ||||||||
\(663\) | −0.0774803 | −0.00300908 | ||||||||
\(664\) | −2.20641 | −0.0856252 | ||||||||
\(665\) | 3.22221 | 0.124952 | ||||||||
\(666\) | −50.4868 | −1.95632 | ||||||||
\(667\) | 32.4387 | 1.25603 | ||||||||
\(668\) | −25.9645 | −1.00460 | ||||||||
\(669\) | −20.6196 | −0.797201 | ||||||||
\(670\) | −3.05538 | −0.118039 | ||||||||
\(671\) | 22.8147 | 0.880753 | ||||||||
\(672\) | −22.0704 | −0.851386 | ||||||||
\(673\) | −14.6450 | −0.564524 | −0.282262 | − | 0.959337i | \(-0.591085\pi\) | ||||
−0.282262 | + | 0.959337i | \(0.591085\pi\) | |||||||
\(674\) | 13.7026 | 0.527805 | ||||||||
\(675\) | −15.3212 | −0.589713 | ||||||||
\(676\) | −52.6553 | −2.02520 | ||||||||
\(677\) | 35.0577 | 1.34738 | 0.673688 | − | 0.739016i | \(-0.264709\pi\) | ||||
0.673688 | + | 0.739016i | \(0.264709\pi\) | |||||||
\(678\) | −35.3148 | −1.35626 | ||||||||
\(679\) | 18.6900 | 0.717255 | ||||||||
\(680\) | −0.574545 | −0.0220328 | ||||||||
\(681\) | −22.7098 | −0.870241 | ||||||||
\(682\) | −107.445 | −4.11430 | ||||||||
\(683\) | 36.1070 | 1.38160 | 0.690798 | − | 0.723047i | \(-0.257259\pi\) | ||||
0.690798 | + | 0.723047i | \(0.257259\pi\) | |||||||
\(684\) | −11.6266 | −0.444553 | ||||||||
\(685\) | 16.4454 | 0.628345 | ||||||||
\(686\) | −52.6799 | −2.01133 | ||||||||
\(687\) | −6.43461 | −0.245496 | ||||||||
\(688\) | −32.4997 | −1.23904 | ||||||||
\(689\) | −10.3886 | −0.395776 | ||||||||
\(690\) | 21.2165 | 0.807699 | ||||||||
\(691\) | −30.8427 | −1.17331 | −0.586657 | − | 0.809836i | \(-0.699556\pi\) | ||||
−0.586657 | + | 0.809836i | \(0.699556\pi\) | |||||||
\(692\) | 59.8756 | 2.27613 | ||||||||
\(693\) | 25.8136 | 0.980579 | ||||||||
\(694\) | 3.81194 | 0.144699 | ||||||||
\(695\) | 23.2301 | 0.881167 | ||||||||
\(696\) | −31.9490 | −1.21102 | ||||||||
\(697\) | 0.327342 | 0.0123990 | ||||||||
\(698\) | 2.12701 | 0.0805086 | ||||||||
\(699\) | 13.8271 | 0.522989 | ||||||||
\(700\) | 35.7204 | 1.35011 | ||||||||
\(701\) | −14.1942 | −0.536106 | −0.268053 | − | 0.963404i | \(-0.586380\pi\) | ||||
−0.268053 | + | 0.963404i | \(0.586380\pi\) | |||||||
\(702\) | 17.9982 | 0.679299 | ||||||||
\(703\) | −9.64026 | −0.363589 | ||||||||
\(704\) | 46.3453 | 1.74670 | ||||||||
\(705\) | 2.55899 | 0.0963771 | ||||||||
\(706\) | −27.8094 | −1.04662 | ||||||||
\(707\) | 5.80484 | 0.218313 | ||||||||
\(708\) | −9.02568 | −0.339206 | ||||||||
\(709\) | −25.7519 | −0.967135 | −0.483567 | − | 0.875307i | \(-0.660659\pi\) | ||||
−0.483567 | + | 0.875307i | \(0.660659\pi\) | |||||||
\(710\) | 8.46738 | 0.317775 | ||||||||
\(711\) | −1.77077 | −0.0664090 | ||||||||
\(712\) | −36.2927 | −1.36012 | ||||||||
\(713\) | −53.4356 | −2.00118 | ||||||||
\(714\) | 0.309723 | 0.0115911 | ||||||||
\(715\) | 10.1464 | 0.379453 | ||||||||
\(716\) | 91.7181 | 3.42767 | ||||||||
\(717\) | −24.0118 | −0.896735 | ||||||||
\(718\) | −59.1616 | −2.20789 | ||||||||
\(719\) | −9.25780 | −0.345258 | −0.172629 | − | 0.984987i | \(-0.555226\pi\) | ||||
−0.172629 | + | 0.984987i | \(0.555226\pi\) | |||||||
\(720\) | 28.3823 | 1.05775 | ||||||||
\(721\) | 0.614543 | 0.0228868 | ||||||||
\(722\) | 46.6223 | 1.73510 | ||||||||
\(723\) | 2.99501 | 0.111386 | ||||||||
\(724\) | −43.4581 | −1.61511 | ||||||||
\(725\) | 15.5219 | 0.576470 | ||||||||
\(726\) | 39.2972 | 1.45845 | ||||||||
\(727\) | 2.91949 | 0.108278 | 0.0541389 | − | 0.998533i | \(-0.482759\pi\) | ||||
0.0541389 | + | 0.998533i | \(0.482759\pi\) | |||||||
\(728\) | −24.6860 | −0.914924 | ||||||||
\(729\) | 7.50084 | 0.277809 | ||||||||
\(730\) | −10.5917 | −0.392016 | ||||||||
\(731\) | 0.192316 | 0.00711307 | ||||||||
\(732\) | −18.9957 | −0.702100 | ||||||||
\(733\) | 25.0044 | 0.923558 | 0.461779 | − | 0.886995i | \(-0.347211\pi\) | ||||
0.461779 | + | 0.886995i | \(0.347211\pi\) | |||||||
\(734\) | −49.1766 | −1.81514 | ||||||||
\(735\) | −2.32464 | −0.0857455 | ||||||||
\(736\) | 74.7407 | 2.75498 | ||||||||
\(737\) | −4.67382 | −0.172162 | ||||||||
\(738\) | −32.0671 | −1.18040 | ||||||||
\(739\) | 24.1406 | 0.888028 | 0.444014 | − | 0.896020i | \(-0.353554\pi\) | ||||
0.444014 | + | 0.896020i | \(0.353554\pi\) | |||||||
\(740\) | 56.1925 | 2.06568 | ||||||||
\(741\) | 1.44931 | 0.0532416 | ||||||||
\(742\) | 41.5280 | 1.52454 | ||||||||
\(743\) | 41.7345 | 1.53109 | 0.765544 | − | 0.643383i | \(-0.222470\pi\) | ||||
0.765544 | + | 0.643383i | \(0.222470\pi\) | |||||||
\(744\) | 52.6288 | 1.92947 | ||||||||
\(745\) | 21.0904 | 0.772693 | ||||||||
\(746\) | 51.7371 | 1.89423 | ||||||||
\(747\) | −0.644979 | −0.0235986 | ||||||||
\(748\) | −1.49394 | −0.0546240 | ||||||||
\(749\) | −2.98518 | −0.109076 | ||||||||
\(750\) | 25.6423 | 0.936323 | ||||||||
\(751\) | 38.2762 | 1.39672 | 0.698359 | − | 0.715748i | \(-0.253914\pi\) | ||||
0.698359 | + | 0.715748i | \(0.253914\pi\) | |||||||
\(752\) | 21.3785 | 0.779594 | ||||||||
\(753\) | −0.446141 | −0.0162583 | ||||||||
\(754\) | −18.2340 | −0.664044 | ||||||||
\(755\) | −10.7425 | −0.390959 | ||||||||
\(756\) | −50.9646 | −1.85356 | ||||||||
\(757\) | 44.6475 | 1.62274 | 0.811371 | − | 0.584532i | \(-0.198722\pi\) | ||||
0.811371 | + | 0.584532i | \(0.198722\pi\) | |||||||
\(758\) | 16.5312 | 0.600439 | ||||||||
\(759\) | 32.4549 | 1.17804 | ||||||||
\(760\) | 10.7471 | 0.389840 | ||||||||
\(761\) | 54.9865 | 1.99326 | 0.996629 | − | 0.0820385i | \(-0.0261431\pi\) | ||||
0.996629 | + | 0.0820385i | \(0.0261431\pi\) | |||||||
\(762\) | −1.95993 | −0.0710007 | ||||||||
\(763\) | 34.7425 | 1.25776 | ||||||||
\(764\) | −12.0739 | −0.436818 | ||||||||
\(765\) | −0.167952 | −0.00607231 | ||||||||
\(766\) | −33.9039 | −1.22500 | ||||||||
\(767\) | −3.03042 | −0.109422 | ||||||||
\(768\) | 12.9281 | 0.466501 | ||||||||
\(769\) | 43.8665 | 1.58187 | 0.790933 | − | 0.611902i | \(-0.209596\pi\) | ||||
0.790933 | + | 0.611902i | \(0.209596\pi\) | |||||||
\(770\) | −40.5596 | −1.46166 | ||||||||
\(771\) | 0.843917 | 0.0303929 | ||||||||
\(772\) | −28.4861 | −1.02524 | ||||||||
\(773\) | 41.9860 | 1.51013 | 0.755066 | − | 0.655649i | \(-0.227605\pi\) | ||||
0.755066 | + | 0.655649i | \(0.227605\pi\) | |||||||
\(774\) | −18.8397 | −0.677178 | ||||||||
\(775\) | −25.5689 | −0.918463 | ||||||||
\(776\) | 62.3374 | 2.23778 | ||||||||
\(777\) | −17.8207 | −0.639314 | ||||||||
\(778\) | 19.4836 | 0.698520 | ||||||||
\(779\) | −6.12308 | −0.219382 | ||||||||
\(780\) | −8.44792 | −0.302484 | ||||||||
\(781\) | 12.9526 | 0.463480 | ||||||||
\(782\) | −1.04887 | −0.0375074 | ||||||||
\(783\) | −22.1461 | −0.791438 | ||||||||
\(784\) | −19.4207 | −0.693595 | ||||||||
\(785\) | −1.95095 | −0.0696323 | ||||||||
\(786\) | 21.6483 | 0.772170 | ||||||||
\(787\) | 17.4984 | 0.623749 | 0.311875 | − | 0.950123i | \(-0.399043\pi\) | ||||
0.311875 | + | 0.950123i | \(0.399043\pi\) | |||||||
\(788\) | −49.8019 | −1.77412 | ||||||||
\(789\) | 6.36037 | 0.226435 | ||||||||
\(790\) | 2.78231 | 0.0989901 | ||||||||
\(791\) | 33.5753 | 1.19380 | ||||||||
\(792\) | 86.0972 | 3.05933 | ||||||||
\(793\) | −6.37789 | −0.226486 | ||||||||
\(794\) | 61.5826 | 2.18549 | ||||||||
\(795\) | 8.36060 | 0.296520 | ||||||||
\(796\) | −108.139 | −3.83287 | ||||||||
\(797\) | −26.2150 | −0.928584 | −0.464292 | − | 0.885682i | \(-0.653691\pi\) | ||||
−0.464292 | + | 0.885682i | \(0.653691\pi\) | |||||||
\(798\) | −5.79352 | −0.205088 | ||||||||
\(799\) | −0.126507 | −0.00447550 | ||||||||
\(800\) | 35.7635 | 1.26443 | ||||||||
\(801\) | −10.6091 | −0.374855 | ||||||||
\(802\) | 37.8070 | 1.33501 | ||||||||
\(803\) | −16.2022 | −0.571762 | ||||||||
\(804\) | 3.89144 | 0.137241 | ||||||||
\(805\) | −20.1714 | −0.710948 | ||||||||
\(806\) | 30.0365 | 1.05799 | ||||||||
\(807\) | 20.6615 | 0.727320 | ||||||||
\(808\) | 19.3611 | 0.681121 | ||||||||
\(809\) | 45.1262 | 1.58655 | 0.793276 | − | 0.608862i | \(-0.208374\pi\) | ||||
0.793276 | + | 0.608862i | \(0.208374\pi\) | |||||||
\(810\) | 8.07665 | 0.283785 | ||||||||
\(811\) | −40.2914 | −1.41482 | −0.707411 | − | 0.706803i | \(-0.750137\pi\) | ||||
−0.707411 | + | 0.706803i | \(0.750137\pi\) | |||||||
\(812\) | 51.6323 | 1.81194 | ||||||||
\(813\) | −18.1722 | −0.637327 | ||||||||
\(814\) | 121.347 | 4.25321 | ||||||||
\(815\) | 9.19687 | 0.322152 | ||||||||
\(816\) | 0.520929 | 0.0182362 | ||||||||
\(817\) | −3.59737 | −0.125856 | ||||||||
\(818\) | 14.7394 | 0.515350 | ||||||||
\(819\) | −7.21624 | −0.252156 | ||||||||
\(820\) | 35.6911 | 1.24639 | ||||||||
\(821\) | −18.0485 | −0.629896 | −0.314948 | − | 0.949109i | \(-0.601987\pi\) | ||||
−0.314948 | + | 0.949109i | \(0.601987\pi\) | |||||||
\(822\) | −29.5687 | −1.03133 | ||||||||
\(823\) | 43.8574 | 1.52877 | 0.764387 | − | 0.644758i | \(-0.223042\pi\) | ||||
0.764387 | + | 0.644758i | \(0.223042\pi\) | |||||||
\(824\) | 2.04971 | 0.0714050 | ||||||||
\(825\) | 15.5297 | 0.540675 | ||||||||
\(826\) | 12.1139 | 0.421497 | ||||||||
\(827\) | −3.22810 | −0.112252 | −0.0561261 | − | 0.998424i | \(-0.517875\pi\) | ||||
−0.0561261 | + | 0.998424i | \(0.517875\pi\) | |||||||
\(828\) | 72.7838 | 2.52941 | ||||||||
\(829\) | −33.7011 | −1.17049 | −0.585243 | − | 0.810858i | \(-0.699001\pi\) | ||||
−0.585243 | + | 0.810858i | \(0.699001\pi\) | |||||||
\(830\) | 1.01342 | 0.0351763 | ||||||||
\(831\) | 6.02438 | 0.208983 | ||||||||
\(832\) | −12.9559 | −0.449164 | ||||||||
\(833\) | 0.114921 | 0.00398179 | ||||||||
\(834\) | −41.7676 | −1.44629 | ||||||||
\(835\) | 7.01588 | 0.242794 | ||||||||
\(836\) | 27.9449 | 0.966496 | ||||||||
\(837\) | 36.4808 | 1.26096 | ||||||||
\(838\) | 55.7240 | 1.92495 | ||||||||
\(839\) | −53.8946 | −1.86065 | −0.930324 | − | 0.366738i | \(-0.880475\pi\) | ||||
−0.930324 | + | 0.366738i | \(0.880475\pi\) | |||||||
\(840\) | 19.8669 | 0.685472 | ||||||||
\(841\) | −6.56373 | −0.226336 | ||||||||
\(842\) | 0.763316 | 0.0263056 | ||||||||
\(843\) | −3.87961 | −0.133621 | ||||||||
\(844\) | 1.40666 | 0.0484192 | ||||||||
\(845\) | 14.2280 | 0.489458 | ||||||||
\(846\) | 12.3929 | 0.426076 | ||||||||
\(847\) | −37.3614 | −1.28375 | ||||||||
\(848\) | 69.8468 | 2.39855 | ||||||||
\(849\) | 12.5100 | 0.429341 | ||||||||
\(850\) | −0.501883 | −0.0172144 | ||||||||
\(851\) | 60.3492 | 2.06874 | ||||||||
\(852\) | −10.7844 | −0.369467 | ||||||||
\(853\) | −9.47927 | −0.324564 | −0.162282 | − | 0.986744i | \(-0.551885\pi\) | ||||
−0.162282 | + | 0.986744i | \(0.551885\pi\) | |||||||
\(854\) | 25.4953 | 0.872430 | ||||||||
\(855\) | 3.14162 | 0.107441 | ||||||||
\(856\) | −9.95657 | −0.340309 | ||||||||
\(857\) | 7.70389 | 0.263160 | 0.131580 | − | 0.991306i | \(-0.457995\pi\) | ||||
0.131580 | + | 0.991306i | \(0.457995\pi\) | |||||||
\(858\) | −18.2432 | −0.622811 | ||||||||
\(859\) | 33.6201 | 1.14710 | 0.573552 | − | 0.819169i | \(-0.305565\pi\) | ||||
0.573552 | + | 0.819169i | \(0.305565\pi\) | |||||||
\(860\) | 20.9688 | 0.715031 | ||||||||
\(861\) | −11.3190 | −0.385749 | ||||||||
\(862\) | −28.3862 | −0.966837 | ||||||||
\(863\) | 24.1626 | 0.822505 | 0.411253 | − | 0.911521i | \(-0.365091\pi\) | ||||
0.411253 | + | 0.911521i | \(0.365091\pi\) | |||||||
\(864\) | −51.0260 | −1.73594 | ||||||||
\(865\) | −16.1790 | −0.550102 | ||||||||
\(866\) | −50.4064 | −1.71288 | ||||||||
\(867\) | 15.3181 | 0.520229 | ||||||||
\(868\) | −85.0528 | −2.88688 | ||||||||
\(869\) | 4.25611 | 0.144379 | ||||||||
\(870\) | 14.6744 | 0.497510 | ||||||||
\(871\) | 1.30657 | 0.0442715 | ||||||||
\(872\) | 115.878 | 3.92412 | ||||||||
\(873\) | 18.2225 | 0.616739 | ||||||||
\(874\) | 19.6195 | 0.663641 | ||||||||
\(875\) | −24.3791 | −0.824165 | ||||||||
\(876\) | 13.4900 | 0.455784 | ||||||||
\(877\) | −43.9049 | −1.48256 | −0.741282 | − | 0.671194i | \(-0.765782\pi\) | ||||
−0.741282 | + | 0.671194i | \(0.765782\pi\) | |||||||
\(878\) | −63.2709 | −2.13529 | ||||||||
\(879\) | −16.3350 | −0.550965 | ||||||||
\(880\) | −68.2179 | −2.29963 | ||||||||
\(881\) | 48.8546 | 1.64595 | 0.822976 | − | 0.568076i | \(-0.192312\pi\) | ||||
0.822976 | + | 0.568076i | \(0.192312\pi\) | |||||||
\(882\) | −11.2579 | −0.379074 | ||||||||
\(883\) | −28.7852 | −0.968700 | −0.484350 | − | 0.874874i | \(-0.660944\pi\) | ||||
−0.484350 | + | 0.874874i | \(0.660944\pi\) | |||||||
\(884\) | 0.417634 | 0.0140465 | ||||||||
\(885\) | 2.43883 | 0.0819803 | ||||||||
\(886\) | −7.48799 | −0.251564 | ||||||||
\(887\) | −1.30317 | −0.0437562 | −0.0218781 | − | 0.999761i | \(-0.506965\pi\) | ||||
−0.0218781 | + | 0.999761i | \(0.506965\pi\) | |||||||
\(888\) | −59.4381 | −1.99461 | ||||||||
\(889\) | 1.86338 | 0.0624958 | ||||||||
\(890\) | 16.6695 | 0.558763 | ||||||||
\(891\) | 12.3549 | 0.413904 | ||||||||
\(892\) | 111.144 | 3.72137 | ||||||||
\(893\) | 2.36637 | 0.0791877 | ||||||||
\(894\) | −37.9205 | −1.26825 | ||||||||
\(895\) | −24.7832 | −0.828410 | ||||||||
\(896\) | 2.81267 | 0.0939646 | ||||||||
\(897\) | −9.07283 | −0.302933 | ||||||||
\(898\) | 35.1067 | 1.17153 | ||||||||
\(899\) | −36.9588 | −1.23264 | ||||||||
\(900\) | 34.8271 | 1.16090 | ||||||||
\(901\) | −0.413317 | −0.0137696 | ||||||||
\(902\) | 77.0744 | 2.56630 | ||||||||
\(903\) | −6.64999 | −0.221298 | ||||||||
\(904\) | 111.985 | 3.72456 | ||||||||
\(905\) | 11.7428 | 0.390344 | ||||||||
\(906\) | 19.3150 | 0.641697 | ||||||||
\(907\) | 24.6075 | 0.817077 | 0.408539 | − | 0.912741i | \(-0.366039\pi\) | ||||
0.408539 | + | 0.912741i | \(0.366039\pi\) | |||||||
\(908\) | 122.410 | 4.06233 | ||||||||
\(909\) | 5.65966 | 0.187719 | ||||||||
\(910\) | 11.3385 | 0.375867 | ||||||||
\(911\) | 10.0081 | 0.331585 | 0.165792 | − | 0.986161i | \(-0.446982\pi\) | ||||
0.165792 | + | 0.986161i | \(0.446982\pi\) | |||||||
\(912\) | −9.74424 | −0.322664 | ||||||||
\(913\) | 1.55023 | 0.0513052 | ||||||||
\(914\) | −49.2572 | −1.62928 | ||||||||
\(915\) | 5.13282 | 0.169686 | ||||||||
\(916\) | 34.6838 | 1.14598 | ||||||||
\(917\) | −20.5819 | −0.679676 | ||||||||
\(918\) | 0.716067 | 0.0236337 | ||||||||
\(919\) | 53.6454 | 1.76960 | 0.884800 | − | 0.465972i | \(-0.154295\pi\) | ||||
0.884800 | + | 0.465972i | \(0.154295\pi\) | |||||||
\(920\) | −67.2784 | −2.21810 | ||||||||
\(921\) | 12.5958 | 0.415046 | ||||||||
\(922\) | −29.2278 | −0.962566 | ||||||||
\(923\) | −3.62091 | −0.119184 | ||||||||
\(924\) | 51.6582 | 1.69943 | ||||||||
\(925\) | 28.8771 | 0.949473 | ||||||||
\(926\) | 31.2992 | 1.02856 | ||||||||
\(927\) | 0.599173 | 0.0196794 | ||||||||
\(928\) | 51.6945 | 1.69696 | ||||||||
\(929\) | 11.9246 | 0.391234 | 0.195617 | − | 0.980680i | \(-0.437329\pi\) | ||||
0.195617 | + | 0.980680i | \(0.437329\pi\) | |||||||
\(930\) | −24.1729 | −0.792659 | ||||||||
\(931\) | −2.14966 | −0.0704523 | ||||||||
\(932\) | −74.5308 | −2.44134 | ||||||||
\(933\) | −1.18133 | −0.0386750 | ||||||||
\(934\) | −62.5242 | −2.04585 | ||||||||
\(935\) | 0.403678 | 0.0132017 | ||||||||
\(936\) | −24.0686 | −0.786707 | ||||||||
\(937\) | 57.5435 | 1.87986 | 0.939932 | − | 0.341362i | \(-0.110888\pi\) | ||||
0.939932 | + | 0.341362i | \(0.110888\pi\) | |||||||
\(938\) | −5.22295 | −0.170535 | ||||||||
\(939\) | 18.4275 | 0.601358 | ||||||||
\(940\) | −13.7935 | −0.449893 | ||||||||
\(941\) | 35.6327 | 1.16159 | 0.580796 | − | 0.814049i | \(-0.302741\pi\) | ||||
0.580796 | + | 0.814049i | \(0.302741\pi\) | |||||||
\(942\) | 3.50780 | 0.114290 | ||||||||
\(943\) | 38.3312 | 1.24824 | ||||||||
\(944\) | 20.3747 | 0.663138 | ||||||||
\(945\) | 13.7711 | 0.447975 | ||||||||
\(946\) | 45.2819 | 1.47224 | ||||||||
\(947\) | −13.4996 | −0.438678 | −0.219339 | − | 0.975649i | \(-0.570390\pi\) | ||||
−0.219339 | + | 0.975649i | \(0.570390\pi\) | |||||||
\(948\) | −3.54365 | −0.115093 | ||||||||
\(949\) | 4.52933 | 0.147028 | ||||||||
\(950\) | 9.38796 | 0.304585 | ||||||||
\(951\) | 22.0259 | 0.714239 | ||||||||
\(952\) | −0.982144 | −0.0318315 | ||||||||
\(953\) | 9.77739 | 0.316721 | 0.158360 | − | 0.987381i | \(-0.449379\pi\) | ||||
0.158360 | + | 0.987381i | \(0.449379\pi\) | |||||||
\(954\) | 40.4894 | 1.31089 | ||||||||
\(955\) | 3.26249 | 0.105572 | ||||||||
\(956\) | 129.428 | 4.18600 | ||||||||
\(957\) | 22.4475 | 0.725625 | ||||||||
\(958\) | 27.0081 | 0.872591 | ||||||||
\(959\) | 28.1122 | 0.907789 | ||||||||
\(960\) | 10.4267 | 0.336519 | ||||||||
\(961\) | 29.8814 | 0.963915 | ||||||||
\(962\) | −33.9227 | −1.09371 | ||||||||
\(963\) | −2.91052 | −0.0937901 | ||||||||
\(964\) | −16.1437 | −0.519953 | ||||||||
\(965\) | 7.69724 | 0.247783 | ||||||||
\(966\) | 36.2681 | 1.16691 | ||||||||
\(967\) | 6.63701 | 0.213432 | 0.106716 | − | 0.994290i | \(-0.465966\pi\) | ||||
0.106716 | + | 0.994290i | \(0.465966\pi\) | |||||||
\(968\) | −124.613 | −4.00521 | ||||||||
\(969\) | 0.0576613 | 0.00185235 | ||||||||
\(970\) | −28.6321 | −0.919320 | ||||||||
\(971\) | −34.7681 | −1.11576 | −0.557881 | − | 0.829921i | \(-0.688385\pi\) | ||||
−0.557881 | + | 0.829921i | \(0.688385\pi\) | |||||||
\(972\) | −78.4249 | −2.51548 | ||||||||
\(973\) | 39.7102 | 1.27305 | ||||||||
\(974\) | 59.4989 | 1.90647 | ||||||||
\(975\) | −4.34135 | −0.139034 | ||||||||
\(976\) | 42.8810 | 1.37259 | ||||||||
\(977\) | −55.2328 | −1.76705 | −0.883527 | − | 0.468380i | \(-0.844838\pi\) | ||||
−0.883527 | + | 0.468380i | \(0.844838\pi\) | |||||||
\(978\) | −16.5359 | −0.528761 | ||||||||
\(979\) | 25.4994 | 0.814964 | ||||||||
\(980\) | 12.5302 | 0.400264 | ||||||||
\(981\) | 33.8736 | 1.08150 | ||||||||
\(982\) | 8.85129 | 0.282456 | ||||||||
\(983\) | 34.8213 | 1.11063 | 0.555313 | − | 0.831641i | \(-0.312598\pi\) | ||||
0.555313 | + | 0.831641i | \(0.312598\pi\) | |||||||
\(984\) | −37.7525 | −1.20351 | ||||||||
\(985\) | 13.4570 | 0.428775 | ||||||||
\(986\) | −0.725449 | −0.0231030 | ||||||||
\(987\) | 4.37441 | 0.139239 | ||||||||
\(988\) | −7.81204 | −0.248534 | ||||||||
\(989\) | 22.5199 | 0.716092 | ||||||||
\(990\) | −39.5452 | −1.25683 | ||||||||
\(991\) | 9.66400 | 0.306987 | 0.153493 | − | 0.988150i | \(-0.450948\pi\) | ||||
0.153493 | + | 0.988150i | \(0.450948\pi\) | |||||||
\(992\) | −85.1553 | −2.70368 | ||||||||
\(993\) | 1.94278 | 0.0616524 | ||||||||
\(994\) | 14.4744 | 0.459100 | ||||||||
\(995\) | 29.2201 | 0.926341 | ||||||||
\(996\) | −1.29073 | −0.0408984 | ||||||||
\(997\) | −35.9193 | −1.13758 | −0.568788 | − | 0.822484i | \(-0.692588\pi\) | ||||
−0.568788 | + | 0.822484i | \(0.692588\pi\) | |||||||
\(998\) | −6.96611 | −0.220508 | ||||||||
\(999\) | −41.2008 | −1.30353 |
(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 | 8011.2.a.b.1.13 | ✓ | 358 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8011.2.a.b.1.13 | ✓ | 358 | 1.1 | even | 1 | trivial |