Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, 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("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.78390 | −1.96852 | −0.984259 | − | 0.176733i | \(-0.943447\pi\) | ||||
−0.984259 | + | 0.176733i | \(0.943447\pi\) | |||||||
\(3\) | 2.40470 | 1.38835 | 0.694177 | − | 0.719805i | \(-0.255769\pi\) | ||||
0.694177 | + | 0.719805i | \(0.255769\pi\) | |||||||
\(4\) | 5.75012 | 2.87506 | ||||||||
\(5\) | −2.23828 | −1.00099 | −0.500495 | − | 0.865739i | \(-0.666849\pi\) | ||||
−0.500495 | + | 0.865739i | \(0.666849\pi\) | |||||||
\(6\) | −6.69445 | −2.73300 | ||||||||
\(7\) | −0.0567746 | −0.0214588 | −0.0107294 | − | 0.999942i | \(-0.503415\pi\) | ||||
−0.0107294 | + | 0.999942i | \(0.503415\pi\) | |||||||
\(8\) | −10.4400 | −3.69109 | ||||||||
\(9\) | 2.78257 | 0.927524 | ||||||||
\(10\) | 6.23116 | 1.97047 | ||||||||
\(11\) | 4.46877 | 1.34739 | 0.673693 | − | 0.739012i | \(-0.264707\pi\) | ||||
0.673693 | + | 0.739012i | \(0.264707\pi\) | |||||||
\(12\) | 13.8273 | 3.99160 | ||||||||
\(13\) | −1.01079 | −0.280342 | −0.140171 | − | 0.990127i | \(-0.544765\pi\) | ||||
−0.140171 | + | 0.990127i | \(0.544765\pi\) | |||||||
\(14\) | 0.158055 | 0.0422420 | ||||||||
\(15\) | −5.38239 | −1.38973 | ||||||||
\(16\) | 17.5637 | 4.39092 | ||||||||
\(17\) | −2.51174 | −0.609186 | −0.304593 | − | 0.952483i | \(-0.598520\pi\) | ||||
−0.304593 | + | 0.952483i | \(0.598520\pi\) | |||||||
\(18\) | −7.74642 | −1.82585 | ||||||||
\(19\) | 5.87700 | 1.34828 | 0.674139 | − | 0.738605i | \(-0.264515\pi\) | ||||
0.674139 | + | 0.738605i | \(0.264515\pi\) | |||||||
\(20\) | −12.8704 | −2.87791 | ||||||||
\(21\) | −0.136526 | −0.0297924 | ||||||||
\(22\) | −12.4406 | −2.65235 | ||||||||
\(23\) | −3.02456 | −0.630663 | −0.315332 | − | 0.948982i | \(-0.602116\pi\) | ||||
−0.315332 | + | 0.948982i | \(0.602116\pi\) | |||||||
\(24\) | −25.1050 | −5.12454 | ||||||||
\(25\) | 0.00990820 | 0.00198164 | ||||||||
\(26\) | 2.81394 | 0.551859 | ||||||||
\(27\) | −0.522847 | −0.100622 | ||||||||
\(28\) | −0.326461 | −0.0616953 | ||||||||
\(29\) | 3.67472 | 0.682378 | 0.341189 | − | 0.939995i | \(-0.389170\pi\) | ||||
0.341189 | + | 0.939995i | \(0.389170\pi\) | |||||||
\(30\) | 14.9841 | 2.73570 | ||||||||
\(31\) | 1.96933 | 0.353702 | 0.176851 | − | 0.984238i | \(-0.443409\pi\) | ||||
0.176851 | + | 0.984238i | \(0.443409\pi\) | |||||||
\(32\) | −28.0156 | −4.95251 | ||||||||
\(33\) | 10.7460 | 1.87065 | ||||||||
\(34\) | 6.99244 | 1.19919 | ||||||||
\(35\) | 0.127078 | 0.0214800 | ||||||||
\(36\) | 16.0001 | 2.66669 | ||||||||
\(37\) | 8.75339 | 1.43905 | 0.719524 | − | 0.694468i | \(-0.244360\pi\) | ||||
0.719524 | + | 0.694468i | \(0.244360\pi\) | |||||||
\(38\) | −16.3610 | −2.65411 | ||||||||
\(39\) | −2.43064 | −0.389214 | ||||||||
\(40\) | 23.3676 | 3.69475 | ||||||||
\(41\) | 1.89435 | 0.295848 | 0.147924 | − | 0.988999i | \(-0.452741\pi\) | ||||
0.147924 | + | 0.988999i | \(0.452741\pi\) | |||||||
\(42\) | 0.380075 | 0.0586468 | ||||||||
\(43\) | 5.14850 | 0.785138 | 0.392569 | − | 0.919722i | \(-0.371586\pi\) | ||||
0.392569 | + | 0.919722i | \(0.371586\pi\) | |||||||
\(44\) | 25.6960 | 3.87382 | ||||||||
\(45\) | −6.22818 | −0.928443 | ||||||||
\(46\) | 8.42007 | 1.24147 | ||||||||
\(47\) | −3.40230 | −0.496276 | −0.248138 | − | 0.968725i | \(-0.579819\pi\) | ||||
−0.248138 | + | 0.968725i | \(0.579819\pi\) | |||||||
\(48\) | 42.2353 | 6.09614 | ||||||||
\(49\) | −6.99678 | −0.999540 | ||||||||
\(50\) | −0.0275835 | −0.00390089 | ||||||||
\(51\) | −6.03997 | −0.845765 | ||||||||
\(52\) | −5.81216 | −0.806002 | ||||||||
\(53\) | 3.90647 | 0.536594 | 0.268297 | − | 0.963336i | \(-0.413539\pi\) | ||||
0.268297 | + | 0.963336i | \(0.413539\pi\) | |||||||
\(54\) | 1.45555 | 0.198076 | ||||||||
\(55\) | −10.0024 | −1.34872 | ||||||||
\(56\) | 0.592726 | 0.0792063 | ||||||||
\(57\) | 14.1324 | 1.87189 | ||||||||
\(58\) | −10.2301 | −1.34327 | ||||||||
\(59\) | 2.25947 | 0.294158 | 0.147079 | − | 0.989125i | \(-0.453013\pi\) | ||||
0.147079 | + | 0.989125i | \(0.453013\pi\) | |||||||
\(60\) | −30.9494 | −3.99555 | ||||||||
\(61\) | 6.85031 | 0.877092 | 0.438546 | − | 0.898709i | \(-0.355494\pi\) | ||||
0.438546 | + | 0.898709i | \(0.355494\pi\) | |||||||
\(62\) | −5.48243 | −0.696269 | ||||||||
\(63\) | −0.157979 | −0.0199035 | ||||||||
\(64\) | 42.8654 | 5.35818 | ||||||||
\(65\) | 2.26243 | 0.280620 | ||||||||
\(66\) | −29.9160 | −3.68240 | ||||||||
\(67\) | −10.1207 | −1.23643 | −0.618217 | − | 0.786007i | \(-0.712145\pi\) | ||||
−0.618217 | + | 0.786007i | \(0.712145\pi\) | |||||||
\(68\) | −14.4428 | −1.75145 | ||||||||
\(69\) | −7.27314 | −0.875583 | ||||||||
\(70\) | −0.353772 | −0.0422838 | ||||||||
\(71\) | 0.569963 | 0.0676422 | 0.0338211 | − | 0.999428i | \(-0.489232\pi\) | ||||
0.0338211 | + | 0.999428i | \(0.489232\pi\) | |||||||
\(72\) | −29.0500 | −3.42358 | ||||||||
\(73\) | −8.05235 | −0.942456 | −0.471228 | − | 0.882011i | \(-0.656189\pi\) | ||||
−0.471228 | + | 0.882011i | \(0.656189\pi\) | |||||||
\(74\) | −24.3686 | −2.83279 | ||||||||
\(75\) | 0.0238262 | 0.00275121 | ||||||||
\(76\) | 33.7935 | 3.87638 | ||||||||
\(77\) | −0.253713 | −0.0289132 | ||||||||
\(78\) | 6.76668 | 0.766175 | ||||||||
\(79\) | 5.86218 | 0.659547 | 0.329774 | − | 0.944060i | \(-0.393028\pi\) | ||||
0.329774 | + | 0.944060i | \(0.393028\pi\) | |||||||
\(80\) | −39.3125 | −4.39527 | ||||||||
\(81\) | −9.60501 | −1.06722 | ||||||||
\(82\) | −5.27369 | −0.582382 | ||||||||
\(83\) | −7.74329 | −0.849937 | −0.424968 | − | 0.905208i | \(-0.639715\pi\) | ||||
−0.424968 | + | 0.905208i | \(0.639715\pi\) | |||||||
\(84\) | −0.785040 | −0.0856549 | ||||||||
\(85\) | 5.62198 | 0.609789 | ||||||||
\(86\) | −14.3329 | −1.54556 | ||||||||
\(87\) | 8.83659 | 0.947382 | ||||||||
\(88\) | −46.6539 | −4.97332 | ||||||||
\(89\) | 5.19256 | 0.550411 | 0.275205 | − | 0.961385i | \(-0.411254\pi\) | ||||
0.275205 | + | 0.961385i | \(0.411254\pi\) | |||||||
\(90\) | 17.3387 | 1.82766 | ||||||||
\(91\) | 0.0573871 | 0.00601581 | ||||||||
\(92\) | −17.3916 | −1.81320 | ||||||||
\(93\) | 4.73565 | 0.491064 | ||||||||
\(94\) | 9.47167 | 0.976928 | ||||||||
\(95\) | −13.1544 | −1.34961 | ||||||||
\(96\) | −67.3691 | −6.87583 | ||||||||
\(97\) | 14.6535 | 1.48784 | 0.743918 | − | 0.668270i | \(-0.232965\pi\) | ||||
0.743918 | + | 0.668270i | \(0.232965\pi\) | |||||||
\(98\) | 19.4784 | 1.96761 | ||||||||
\(99\) | 12.4347 | 1.24973 | ||||||||
\(100\) | 0.0569733 | 0.00569733 | ||||||||
\(101\) | 6.20740 | 0.617659 | 0.308830 | − | 0.951117i | \(-0.400063\pi\) | ||||
0.308830 | + | 0.951117i | \(0.400063\pi\) | |||||||
\(102\) | 16.8147 | 1.66490 | ||||||||
\(103\) | −1.03737 | −0.102215 | −0.0511073 | − | 0.998693i | \(-0.516275\pi\) | ||||
−0.0511073 | + | 0.998693i | \(0.516275\pi\) | |||||||
\(104\) | 10.5526 | 1.03477 | ||||||||
\(105\) | 0.305583 | 0.0298219 | ||||||||
\(106\) | −10.8752 | −1.05630 | ||||||||
\(107\) | −5.23587 | −0.506170 | −0.253085 | − | 0.967444i | \(-0.581445\pi\) | ||||
−0.253085 | + | 0.967444i | \(0.581445\pi\) | |||||||
\(108\) | −3.00643 | −0.289294 | ||||||||
\(109\) | 8.82149 | 0.844946 | 0.422473 | − | 0.906376i | \(-0.361162\pi\) | ||||
0.422473 | + | 0.906376i | \(0.361162\pi\) | |||||||
\(110\) | 27.8457 | 2.65498 | ||||||||
\(111\) | 21.0493 | 1.99791 | ||||||||
\(112\) | −0.997170 | −0.0942237 | ||||||||
\(113\) | −5.71607 | −0.537723 | −0.268861 | − | 0.963179i | \(-0.586647\pi\) | ||||
−0.268861 | + | 0.963179i | \(0.586647\pi\) | |||||||
\(114\) | −39.3433 | −3.68484 | ||||||||
\(115\) | 6.76981 | 0.631288 | ||||||||
\(116\) | 21.1301 | 1.96188 | ||||||||
\(117\) | −2.81259 | −0.260024 | ||||||||
\(118\) | −6.29015 | −0.579055 | ||||||||
\(119\) | 0.142603 | 0.0130724 | ||||||||
\(120\) | 56.1921 | 5.12961 | ||||||||
\(121\) | 8.96992 | 0.815448 | ||||||||
\(122\) | −19.0706 | −1.72657 | ||||||||
\(123\) | 4.55534 | 0.410742 | ||||||||
\(124\) | 11.3239 | 1.01692 | ||||||||
\(125\) | 11.1692 | 0.999007 | ||||||||
\(126\) | 0.439800 | 0.0391805 | ||||||||
\(127\) | 17.5406 | 1.55648 | 0.778240 | − | 0.627967i | \(-0.216113\pi\) | ||||
0.778240 | + | 0.627967i | \(0.216113\pi\) | |||||||
\(128\) | −63.3020 | −5.59516 | ||||||||
\(129\) | 12.3806 | 1.09005 | ||||||||
\(130\) | −6.29839 | −0.552406 | ||||||||
\(131\) | 2.07094 | 0.180939 | 0.0904696 | − | 0.995899i | \(-0.471163\pi\) | ||||
0.0904696 | + | 0.995899i | \(0.471163\pi\) | |||||||
\(132\) | 61.7911 | 5.37822 | ||||||||
\(133\) | −0.333665 | −0.0289324 | ||||||||
\(134\) | 28.1749 | 2.43394 | ||||||||
\(135\) | 1.17028 | 0.100722 | ||||||||
\(136\) | 26.2225 | 2.24856 | ||||||||
\(137\) | −8.40350 | −0.717959 | −0.358980 | − | 0.933345i | \(-0.616875\pi\) | ||||
−0.358980 | + | 0.933345i | \(0.616875\pi\) | |||||||
\(138\) | 20.2477 | 1.72360 | ||||||||
\(139\) | −17.2908 | −1.46659 | −0.733294 | − | 0.679912i | \(-0.762018\pi\) | ||||
−0.733294 | + | 0.679912i | \(0.762018\pi\) | |||||||
\(140\) | 0.730712 | 0.0617564 | ||||||||
\(141\) | −8.18149 | −0.689006 | ||||||||
\(142\) | −1.58672 | −0.133155 | ||||||||
\(143\) | −4.51699 | −0.377729 | ||||||||
\(144\) | 48.8722 | 4.07268 | ||||||||
\(145\) | −8.22506 | −0.683054 | ||||||||
\(146\) | 22.4170 | 1.85524 | ||||||||
\(147\) | −16.8251 | −1.38771 | ||||||||
\(148\) | 50.3331 | 4.13735 | ||||||||
\(149\) | 7.76103 | 0.635809 | 0.317904 | − | 0.948123i | \(-0.397021\pi\) | ||||
0.317904 | + | 0.948123i | \(0.397021\pi\) | |||||||
\(150\) | −0.0663299 | −0.00541581 | ||||||||
\(151\) | 18.0287 | 1.46715 | 0.733577 | − | 0.679606i | \(-0.237849\pi\) | ||||
0.733577 | + | 0.679606i | \(0.237849\pi\) | |||||||
\(152\) | −61.3558 | −4.97662 | ||||||||
\(153\) | −6.98909 | −0.565035 | ||||||||
\(154\) | 0.706312 | 0.0569162 | ||||||||
\(155\) | −4.40792 | −0.354053 | ||||||||
\(156\) | −13.9765 | −1.11902 | ||||||||
\(157\) | 22.0998 | 1.76376 | 0.881878 | − | 0.471477i | \(-0.156279\pi\) | ||||
0.881878 | + | 0.471477i | \(0.156279\pi\) | |||||||
\(158\) | −16.3198 | −1.29833 | ||||||||
\(159\) | 9.39387 | 0.744983 | ||||||||
\(160\) | 62.7068 | 4.95741 | ||||||||
\(161\) | 0.171718 | 0.0135333 | ||||||||
\(162\) | 26.7394 | 2.10085 | ||||||||
\(163\) | 10.7572 | 0.842571 | 0.421285 | − | 0.906928i | \(-0.361579\pi\) | ||||
0.421285 | + | 0.906928i | \(0.361579\pi\) | |||||||
\(164\) | 10.8928 | 0.850581 | ||||||||
\(165\) | −24.0527 | −1.87250 | ||||||||
\(166\) | 21.5566 | 1.67312 | ||||||||
\(167\) | 17.4264 | 1.34850 | 0.674249 | − | 0.738504i | \(-0.264468\pi\) | ||||
0.674249 | + | 0.738504i | \(0.264468\pi\) | |||||||
\(168\) | 1.42533 | 0.109966 | ||||||||
\(169\) | −11.9783 | −0.921408 | ||||||||
\(170\) | −15.6511 | −1.20038 | ||||||||
\(171\) | 16.3532 | 1.25056 | ||||||||
\(172\) | 29.6045 | 2.25732 | ||||||||
\(173\) | −17.0785 | −1.29846 | −0.649228 | − | 0.760594i | \(-0.724908\pi\) | ||||
−0.649228 | + | 0.760594i | \(0.724908\pi\) | |||||||
\(174\) | −24.6002 | −1.86494 | ||||||||
\(175\) | −0.000562534 0 | −4.25236e−5 0 | ||||||||
\(176\) | 78.4880 | 5.91626 | ||||||||
\(177\) | 5.43334 | 0.408395 | ||||||||
\(178\) | −14.4556 | −1.08349 | ||||||||
\(179\) | 18.0292 | 1.34757 | 0.673785 | − | 0.738928i | \(-0.264668\pi\) | ||||
0.673785 | + | 0.738928i | \(0.264668\pi\) | |||||||
\(180\) | −35.8128 | −2.66933 | ||||||||
\(181\) | −12.3621 | −0.918868 | −0.459434 | − | 0.888212i | \(-0.651948\pi\) | ||||
−0.459434 | + | 0.888212i | \(0.651948\pi\) | |||||||
\(182\) | −0.159760 | −0.0118422 | ||||||||
\(183\) | 16.4729 | 1.21771 | ||||||||
\(184\) | 31.5763 | 2.32784 | ||||||||
\(185\) | −19.5926 | −1.44047 | ||||||||
\(186\) | −13.1836 | −0.966668 | ||||||||
\(187\) | −11.2244 | −0.820808 | ||||||||
\(188\) | −19.5636 | −1.42682 | ||||||||
\(189\) | 0.0296844 | 0.00215922 | ||||||||
\(190\) | 36.6206 | 2.65674 | ||||||||
\(191\) | −11.1927 | −0.809872 | −0.404936 | − | 0.914345i | \(-0.632706\pi\) | ||||
−0.404936 | + | 0.914345i | \(0.632706\pi\) | |||||||
\(192\) | 103.078 | 7.43904 | ||||||||
\(193\) | 0.729995 | 0.0525462 | 0.0262731 | − | 0.999655i | \(-0.491636\pi\) | ||||
0.0262731 | + | 0.999655i | \(0.491636\pi\) | |||||||
\(194\) | −40.7939 | −2.92883 | ||||||||
\(195\) | 5.44046 | 0.389600 | ||||||||
\(196\) | −40.2323 | −2.87374 | ||||||||
\(197\) | 10.1791 | 0.725233 | 0.362616 | − | 0.931938i | \(-0.381884\pi\) | ||||
0.362616 | + | 0.931938i | \(0.381884\pi\) | |||||||
\(198\) | −34.6170 | −2.46012 | ||||||||
\(199\) | 26.1440 | 1.85330 | 0.926649 | − | 0.375927i | \(-0.122676\pi\) | ||||
0.926649 | + | 0.375927i | \(0.122676\pi\) | |||||||
\(200\) | −0.103441 | −0.00731441 | ||||||||
\(201\) | −24.3371 | −1.71661 | ||||||||
\(202\) | −17.2808 | −1.21587 | ||||||||
\(203\) | −0.208631 | −0.0146430 | ||||||||
\(204\) | −34.7306 | −2.43163 | ||||||||
\(205\) | −4.24009 | −0.296141 | ||||||||
\(206\) | 2.88793 | 0.201211 | ||||||||
\(207\) | −8.41605 | −0.584956 | ||||||||
\(208\) | −17.7532 | −1.23096 | ||||||||
\(209\) | 26.2630 | 1.81665 | ||||||||
\(210\) | −0.850714 | −0.0587049 | ||||||||
\(211\) | −8.53671 | −0.587691 | −0.293846 | − | 0.955853i | \(-0.594935\pi\) | ||||
−0.293846 | + | 0.955853i | \(0.594935\pi\) | |||||||
\(212\) | 22.4627 | 1.54274 | ||||||||
\(213\) | 1.37059 | 0.0939112 | ||||||||
\(214\) | 14.5762 | 0.996405 | ||||||||
\(215\) | −11.5238 | −0.785916 | ||||||||
\(216\) | 5.45851 | 0.371405 | ||||||||
\(217\) | −0.111808 | −0.00759002 | ||||||||
\(218\) | −24.5582 | −1.66329 | ||||||||
\(219\) | −19.3635 | −1.30846 | ||||||||
\(220\) | −57.5149 | −3.87765 | ||||||||
\(221\) | 2.53884 | 0.170781 | ||||||||
\(222\) | −58.5991 | −3.93291 | ||||||||
\(223\) | −1.05085 | −0.0703702 | −0.0351851 | − | 0.999381i | \(-0.511202\pi\) | ||||
−0.0351851 | + | 0.999381i | \(0.511202\pi\) | |||||||
\(224\) | 1.59057 | 0.106275 | ||||||||
\(225\) | 0.0275703 | 0.00183802 | ||||||||
\(226\) | 15.9130 | 1.05852 | ||||||||
\(227\) | 6.64009 | 0.440718 | 0.220359 | − | 0.975419i | \(-0.429277\pi\) | ||||
0.220359 | + | 0.975419i | \(0.429277\pi\) | |||||||
\(228\) | 81.2632 | 5.38178 | ||||||||
\(229\) | −13.1696 | −0.870274 | −0.435137 | − | 0.900364i | \(-0.643300\pi\) | ||||
−0.435137 | + | 0.900364i | \(0.643300\pi\) | |||||||
\(230\) | −18.8465 | −1.24270 | ||||||||
\(231\) | −0.610102 | −0.0401418 | ||||||||
\(232\) | −38.3640 | −2.51872 | ||||||||
\(233\) | 19.2115 | 1.25858 | 0.629292 | − | 0.777169i | \(-0.283345\pi\) | ||||
0.629292 | + | 0.777169i | \(0.283345\pi\) | |||||||
\(234\) | 7.82999 | 0.511863 | ||||||||
\(235\) | 7.61530 | 0.496767 | ||||||||
\(236\) | 12.9922 | 0.845722 | ||||||||
\(237\) | 14.0968 | 0.915685 | ||||||||
\(238\) | −0.396993 | −0.0257332 | ||||||||
\(239\) | 14.2038 | 0.918768 | 0.459384 | − | 0.888238i | \(-0.348070\pi\) | ||||
0.459384 | + | 0.888238i | \(0.348070\pi\) | |||||||
\(240\) | −94.5346 | −6.10218 | ||||||||
\(241\) | 14.7231 | 0.948401 | 0.474200 | − | 0.880417i | \(-0.342737\pi\) | ||||
0.474200 | + | 0.880417i | \(0.342737\pi\) | |||||||
\(242\) | −24.9714 | −1.60522 | ||||||||
\(243\) | −21.5286 | −1.38106 | ||||||||
\(244\) | 39.3901 | 2.52169 | ||||||||
\(245\) | 15.6608 | 1.00053 | ||||||||
\(246\) | −12.6816 | −0.808552 | ||||||||
\(247\) | −5.94041 | −0.377979 | ||||||||
\(248\) | −20.5598 | −1.30555 | ||||||||
\(249\) | −18.6203 | −1.18001 | ||||||||
\(250\) | −31.0941 | −1.96656 | ||||||||
\(251\) | 18.4452 | 1.16425 | 0.582124 | − | 0.813100i | \(-0.302222\pi\) | ||||
0.582124 | + | 0.813100i | \(0.302222\pi\) | |||||||
\(252\) | −0.908401 | −0.0572239 | ||||||||
\(253\) | −13.5160 | −0.849747 | ||||||||
\(254\) | −48.8315 | −3.06396 | ||||||||
\(255\) | 13.5192 | 0.846603 | ||||||||
\(256\) | 90.4960 | 5.65600 | ||||||||
\(257\) | 1.10325 | 0.0688190 | 0.0344095 | − | 0.999408i | \(-0.489045\pi\) | ||||
0.0344095 | + | 0.999408i | \(0.489045\pi\) | |||||||
\(258\) | −34.4664 | −2.14578 | ||||||||
\(259\) | −0.496970 | −0.0308802 | ||||||||
\(260\) | 13.0093 | 0.806800 | ||||||||
\(261\) | 10.2252 | 0.632923 | ||||||||
\(262\) | −5.76531 | −0.356182 | ||||||||
\(263\) | 3.75153 | 0.231329 | 0.115665 | − | 0.993288i | \(-0.463100\pi\) | ||||
0.115665 | + | 0.993288i | \(0.463100\pi\) | |||||||
\(264\) | −112.189 | −6.90473 | ||||||||
\(265\) | −8.74378 | −0.537126 | ||||||||
\(266\) | 0.928890 | 0.0569539 | ||||||||
\(267\) | 12.4866 | 0.764164 | ||||||||
\(268\) | −58.1950 | −3.55482 | ||||||||
\(269\) | −17.3095 | −1.05538 | −0.527690 | − | 0.849437i | \(-0.676942\pi\) | ||||
−0.527690 | + | 0.849437i | \(0.676942\pi\) | |||||||
\(270\) | −3.25794 | −0.198272 | ||||||||
\(271\) | 10.5614 | 0.641560 | 0.320780 | − | 0.947154i | \(-0.396055\pi\) | ||||
0.320780 | + | 0.947154i | \(0.396055\pi\) | |||||||
\(272\) | −44.1153 | −2.67489 | ||||||||
\(273\) | 0.137999 | 0.00835206 | ||||||||
\(274\) | 23.3945 | 1.41332 | ||||||||
\(275\) | 0.0442775 | 0.00267003 | ||||||||
\(276\) | −41.8215 | −2.51736 | ||||||||
\(277\) | −27.4220 | −1.64763 | −0.823815 | − | 0.566859i | \(-0.808158\pi\) | ||||
−0.823815 | + | 0.566859i | \(0.808158\pi\) | |||||||
\(278\) | 48.1360 | 2.88700 | ||||||||
\(279\) | 5.47981 | 0.328068 | ||||||||
\(280\) | −1.32669 | −0.0792848 | ||||||||
\(281\) | 4.46092 | 0.266116 | 0.133058 | − | 0.991108i | \(-0.457520\pi\) | ||||
0.133058 | + | 0.991108i | \(0.457520\pi\) | |||||||
\(282\) | 22.7765 | 1.35632 | ||||||||
\(283\) | −8.18035 | −0.486272 | −0.243136 | − | 0.969992i | \(-0.578176\pi\) | ||||
−0.243136 | + | 0.969992i | \(0.578176\pi\) | |||||||
\(284\) | 3.27736 | 0.194475 | ||||||||
\(285\) | −31.6324 | −1.87374 | ||||||||
\(286\) | 12.5749 | 0.743567 | ||||||||
\(287\) | −0.107551 | −0.00634854 | ||||||||
\(288\) | −77.9555 | −4.59357 | ||||||||
\(289\) | −10.6912 | −0.628893 | ||||||||
\(290\) | 22.8978 | 1.34460 | ||||||||
\(291\) | 35.2372 | 2.06564 | ||||||||
\(292\) | −46.3020 | −2.70962 | ||||||||
\(293\) | 20.1651 | 1.17806 | 0.589030 | − | 0.808111i | \(-0.299510\pi\) | ||||
0.589030 | + | 0.808111i | \(0.299510\pi\) | |||||||
\(294\) | 46.8396 | 2.73174 | ||||||||
\(295\) | −5.05733 | −0.294449 | ||||||||
\(296\) | −91.3852 | −5.31166 | ||||||||
\(297\) | −2.33648 | −0.135576 | ||||||||
\(298\) | −21.6060 | −1.25160 | ||||||||
\(299\) | 3.05719 | 0.176802 | ||||||||
\(300\) | 0.137004 | 0.00790991 | ||||||||
\(301\) | −0.292304 | −0.0168481 | ||||||||
\(302\) | −50.1902 | −2.88812 | ||||||||
\(303\) | 14.9269 | 0.857529 | ||||||||
\(304\) | 103.222 | 5.92017 | ||||||||
\(305\) | −15.3329 | −0.877961 | ||||||||
\(306\) | 19.4570 | 1.11228 | ||||||||
\(307\) | 19.2709 | 1.09985 | 0.549924 | − | 0.835215i | \(-0.314657\pi\) | ||||
0.549924 | + | 0.835215i | \(0.314657\pi\) | |||||||
\(308\) | −1.45888 | −0.0831274 | ||||||||
\(309\) | −2.49455 | −0.141910 | ||||||||
\(310\) | 12.2712 | 0.696959 | ||||||||
\(311\) | −14.8811 | −0.843829 | −0.421914 | − | 0.906636i | \(-0.638642\pi\) | ||||
−0.421914 | + | 0.906636i | \(0.638642\pi\) | |||||||
\(312\) | 25.3759 | 1.43663 | ||||||||
\(313\) | 7.69713 | 0.435068 | 0.217534 | − | 0.976053i | \(-0.430199\pi\) | ||||
0.217534 | + | 0.976053i | \(0.430199\pi\) | |||||||
\(314\) | −61.5237 | −3.47199 | ||||||||
\(315\) | 0.353603 | 0.0199232 | ||||||||
\(316\) | 33.7083 | 1.89624 | ||||||||
\(317\) | 8.39183 | 0.471332 | 0.235666 | − | 0.971834i | \(-0.424273\pi\) | ||||
0.235666 | + | 0.971834i | \(0.424273\pi\) | |||||||
\(318\) | −26.1516 | −1.46651 | ||||||||
\(319\) | 16.4215 | 0.919427 | ||||||||
\(320\) | −95.9449 | −5.36349 | ||||||||
\(321\) | −12.5907 | −0.702743 | ||||||||
\(322\) | −0.478046 | −0.0266405 | ||||||||
\(323\) | −14.7615 | −0.821352 | ||||||||
\(324\) | −55.2300 | −3.06833 | ||||||||
\(325\) | −0.0100151 | −0.000555538 0 | ||||||||
\(326\) | −29.9471 | −1.65862 | ||||||||
\(327\) | 21.2130 | 1.17308 | ||||||||
\(328\) | −19.7770 | −1.09200 | ||||||||
\(329\) | 0.193164 | 0.0106495 | ||||||||
\(330\) | 66.9604 | 3.68605 | ||||||||
\(331\) | −31.0620 | −1.70732 | −0.853662 | − | 0.520827i | \(-0.825624\pi\) | ||||
−0.853662 | + | 0.520827i | \(0.825624\pi\) | |||||||
\(332\) | −44.5249 | −2.44362 | ||||||||
\(333\) | 24.3569 | 1.33475 | ||||||||
\(334\) | −48.5135 | −2.65454 | ||||||||
\(335\) | 22.6529 | 1.23766 | ||||||||
\(336\) | −2.39789 | −0.130816 | ||||||||
\(337\) | 6.34005 | 0.345364 | 0.172682 | − | 0.984978i | \(-0.444757\pi\) | ||||
0.172682 | + | 0.984978i | \(0.444757\pi\) | |||||||
\(338\) | 33.3465 | 1.81381 | ||||||||
\(339\) | −13.7454 | −0.746549 | ||||||||
\(340\) | 32.3271 | 1.75318 | ||||||||
\(341\) | 8.80049 | 0.476573 | ||||||||
\(342\) | −45.5257 | −2.46175 | ||||||||
\(343\) | 0.794661 | 0.0429077 | ||||||||
\(344\) | −53.7502 | −2.89802 | ||||||||
\(345\) | 16.2793 | 0.876451 | ||||||||
\(346\) | 47.5449 | 2.55603 | ||||||||
\(347\) | −24.9725 | −1.34060 | −0.670298 | − | 0.742092i | \(-0.733834\pi\) | ||||
−0.670298 | + | 0.742092i | \(0.733834\pi\) | |||||||
\(348\) | 50.8115 | 2.72378 | ||||||||
\(349\) | −1.90366 | −0.101900 | −0.0509502 | − | 0.998701i | \(-0.516225\pi\) | ||||
−0.0509502 | + | 0.998701i | \(0.516225\pi\) | |||||||
\(350\) | 0.00156604 | 8.37084e−5 0 | ||||||||
\(351\) | 0.528488 | 0.0282086 | ||||||||
\(352\) | −125.195 | −6.67294 | ||||||||
\(353\) | 4.32797 | 0.230354 | 0.115177 | − | 0.993345i | \(-0.463256\pi\) | ||||
0.115177 | + | 0.993345i | \(0.463256\pi\) | |||||||
\(354\) | −15.1259 | −0.803933 | ||||||||
\(355\) | −1.27574 | −0.0677092 | ||||||||
\(356\) | 29.8579 | 1.58246 | ||||||||
\(357\) | 0.342917 | 0.0181491 | ||||||||
\(358\) | −50.1917 | −2.65271 | ||||||||
\(359\) | 16.4668 | 0.869084 | 0.434542 | − | 0.900651i | \(-0.356910\pi\) | ||||
0.434542 | + | 0.900651i | \(0.356910\pi\) | |||||||
\(360\) | 65.0221 | 3.42697 | ||||||||
\(361\) | 15.5392 | 0.817852 | ||||||||
\(362\) | 34.4149 | 1.80881 | ||||||||
\(363\) | 21.5700 | 1.13213 | ||||||||
\(364\) | 0.329983 | 0.0172958 | ||||||||
\(365\) | 18.0234 | 0.943389 | ||||||||
\(366\) | −45.8590 | −2.39709 | ||||||||
\(367\) | −13.1276 | −0.685255 | −0.342627 | − | 0.939471i | \(-0.611317\pi\) | ||||
−0.342627 | + | 0.939471i | \(0.611317\pi\) | |||||||
\(368\) | −53.1223 | −2.76919 | ||||||||
\(369\) | 5.27117 | 0.274406 | ||||||||
\(370\) | 54.5438 | 2.83560 | ||||||||
\(371\) | −0.221788 | −0.0115147 | ||||||||
\(372\) | 27.2306 | 1.41184 | ||||||||
\(373\) | 15.6166 | 0.808594 | 0.404297 | − | 0.914628i | \(-0.367516\pi\) | ||||
0.404297 | + | 0.914628i | \(0.367516\pi\) | |||||||
\(374\) | 31.2476 | 1.61578 | ||||||||
\(375\) | 26.8586 | 1.38697 | ||||||||
\(376\) | 35.5199 | 1.83180 | ||||||||
\(377\) | −3.71437 | −0.191300 | ||||||||
\(378\) | −0.0826385 | −0.00425047 | ||||||||
\(379\) | 17.2449 | 0.885811 | 0.442905 | − | 0.896568i | \(-0.353948\pi\) | ||||
0.442905 | + | 0.896568i | \(0.353948\pi\) | |||||||
\(380\) | −75.6394 | −3.88022 | ||||||||
\(381\) | 42.1799 | 2.16094 | ||||||||
\(382\) | 31.1593 | 1.59425 | ||||||||
\(383\) | 7.85704 | 0.401476 | 0.200738 | − | 0.979645i | \(-0.435666\pi\) | ||||
0.200738 | + | 0.979645i | \(0.435666\pi\) | |||||||
\(384\) | −152.222 | −7.76806 | ||||||||
\(385\) | 0.567881 | 0.0289419 | ||||||||
\(386\) | −2.03224 | −0.103438 | ||||||||
\(387\) | 14.3261 | 0.728235 | ||||||||
\(388\) | 84.2594 | 4.27762 | ||||||||
\(389\) | −35.5138 | −1.80062 | −0.900310 | − | 0.435250i | \(-0.856660\pi\) | ||||
−0.900310 | + | 0.435250i | \(0.856660\pi\) | |||||||
\(390\) | −15.1457 | −0.766934 | ||||||||
\(391\) | 7.59689 | 0.384191 | ||||||||
\(392\) | 73.0462 | 3.68939 | ||||||||
\(393\) | 4.97999 | 0.251207 | ||||||||
\(394\) | −28.3377 | −1.42763 | ||||||||
\(395\) | −13.1212 | −0.660200 | ||||||||
\(396\) | 71.5010 | 3.59306 | ||||||||
\(397\) | 7.95230 | 0.399115 | 0.199557 | − | 0.979886i | \(-0.436050\pi\) | ||||
0.199557 | + | 0.979886i | \(0.436050\pi\) | |||||||
\(398\) | −72.7824 | −3.64825 | ||||||||
\(399\) | −0.802363 | −0.0401684 | ||||||||
\(400\) | 0.174024 | 0.00870121 | ||||||||
\(401\) | 1.36633 | 0.0682310 | 0.0341155 | − | 0.999418i | \(-0.489139\pi\) | ||||
0.0341155 | + | 0.999418i | \(0.489139\pi\) | |||||||
\(402\) | 67.7522 | 3.37917 | ||||||||
\(403\) | −1.99058 | −0.0991578 | ||||||||
\(404\) | 35.6933 | 1.77581 | ||||||||
\(405\) | 21.4987 | 1.06828 | ||||||||
\(406\) | 0.580808 | 0.0288250 | ||||||||
\(407\) | 39.1169 | 1.93895 | ||||||||
\(408\) | 63.0572 | 3.12180 | ||||||||
\(409\) | 15.7814 | 0.780340 | 0.390170 | − | 0.920743i | \(-0.372416\pi\) | ||||
0.390170 | + | 0.920743i | \(0.372416\pi\) | |||||||
\(410\) | 11.8040 | 0.582959 | ||||||||
\(411\) | −20.2079 | −0.996781 | ||||||||
\(412\) | −5.96498 | −0.293874 | ||||||||
\(413\) | −0.128280 | −0.00631227 | ||||||||
\(414\) | 23.4295 | 1.15150 | ||||||||
\(415\) | 17.3317 | 0.850779 | ||||||||
\(416\) | 28.3179 | 1.38840 | ||||||||
\(417\) | −41.5792 | −2.03614 | ||||||||
\(418\) | −73.1137 | −3.57611 | ||||||||
\(419\) | 17.3206 | 0.846166 | 0.423083 | − | 0.906091i | \(-0.360948\pi\) | ||||
0.423083 | + | 0.906091i | \(0.360948\pi\) | |||||||
\(420\) | 1.75714 | 0.0857397 | ||||||||
\(421\) | 23.6432 | 1.15230 | 0.576150 | − | 0.817344i | \(-0.304554\pi\) | ||||
0.576150 | + | 0.817344i | \(0.304554\pi\) | |||||||
\(422\) | 23.7654 | 1.15688 | ||||||||
\(423\) | −9.46714 | −0.460308 | ||||||||
\(424\) | −40.7835 | −1.98062 | ||||||||
\(425\) | −0.0248868 | −0.00120719 | ||||||||
\(426\) | −3.81559 | −0.184866 | ||||||||
\(427\) | −0.388923 | −0.0188213 | ||||||||
\(428\) | −30.1069 | −1.45527 | ||||||||
\(429\) | −10.8620 | −0.524422 | ||||||||
\(430\) | 32.0811 | 1.54709 | ||||||||
\(431\) | 26.2928 | 1.26648 | 0.633240 | − | 0.773955i | \(-0.281724\pi\) | ||||
0.633240 | + | 0.773955i | \(0.281724\pi\) | |||||||
\(432\) | −9.18310 | −0.441822 | ||||||||
\(433\) | 13.8904 | 0.667529 | 0.333765 | − | 0.942656i | \(-0.391681\pi\) | ||||
0.333765 | + | 0.942656i | \(0.391681\pi\) | |||||||
\(434\) | 0.311263 | 0.0149411 | ||||||||
\(435\) | −19.7788 | −0.948320 | ||||||||
\(436\) | 50.7247 | 2.42927 | ||||||||
\(437\) | −17.7753 | −0.850309 | ||||||||
\(438\) | 53.9060 | 2.57573 | ||||||||
\(439\) | −8.88645 | −0.424127 | −0.212063 | − | 0.977256i | \(-0.568018\pi\) | ||||
−0.212063 | + | 0.977256i | \(0.568018\pi\) | |||||||
\(440\) | 104.425 | 4.97825 | ||||||||
\(441\) | −19.4690 | −0.927097 | ||||||||
\(442\) | −7.06788 | −0.336185 | ||||||||
\(443\) | 37.5090 | 1.78211 | 0.891054 | − | 0.453897i | \(-0.149967\pi\) | ||||
0.891054 | + | 0.453897i | \(0.149967\pi\) | |||||||
\(444\) | 121.036 | 5.74410 | ||||||||
\(445\) | −11.6224 | −0.550956 | ||||||||
\(446\) | 2.92547 | 0.138525 | ||||||||
\(447\) | 18.6629 | 0.882727 | ||||||||
\(448\) | −2.43367 | −0.114980 | ||||||||
\(449\) | −24.6199 | −1.16188 | −0.580942 | − | 0.813945i | \(-0.697316\pi\) | ||||
−0.580942 | + | 0.813945i | \(0.697316\pi\) | |||||||
\(450\) | −0.0767530 | −0.00361817 | ||||||||
\(451\) | 8.46543 | 0.398621 | ||||||||
\(452\) | −32.8681 | −1.54599 | ||||||||
\(453\) | 43.3536 | 2.03693 | ||||||||
\(454\) | −18.4854 | −0.867562 | ||||||||
\(455\) | −0.128449 | −0.00602176 | ||||||||
\(456\) | −147.542 | −6.90930 | ||||||||
\(457\) | 5.64598 | 0.264108 | 0.132054 | − | 0.991243i | \(-0.457843\pi\) | ||||
0.132054 | + | 0.991243i | \(0.457843\pi\) | |||||||
\(458\) | 36.6630 | 1.71315 | ||||||||
\(459\) | 1.31325 | 0.0612974 | ||||||||
\(460\) | 38.9272 | 1.81499 | ||||||||
\(461\) | 34.3504 | 1.59986 | 0.799929 | − | 0.600094i | \(-0.204870\pi\) | ||||
0.799929 | + | 0.600094i | \(0.204870\pi\) | |||||||
\(462\) | 1.69847 | 0.0790198 | ||||||||
\(463\) | 10.2102 | 0.474507 | 0.237253 | − | 0.971448i | \(-0.423753\pi\) | ||||
0.237253 | + | 0.971448i | \(0.423753\pi\) | |||||||
\(464\) | 64.5416 | 2.99627 | ||||||||
\(465\) | −10.5997 | −0.491550 | ||||||||
\(466\) | −53.4829 | −2.47755 | ||||||||
\(467\) | −29.2100 | −1.35168 | −0.675839 | − | 0.737049i | \(-0.736219\pi\) | ||||
−0.675839 | + | 0.737049i | \(0.736219\pi\) | |||||||
\(468\) | −16.1728 | −0.747586 | ||||||||
\(469\) | 0.574596 | 0.0265324 | ||||||||
\(470\) | −21.2003 | −0.977895 | ||||||||
\(471\) | 53.1434 | 2.44872 | ||||||||
\(472\) | −23.5888 | −1.08576 | ||||||||
\(473\) | 23.0075 | 1.05788 | ||||||||
\(474\) | −39.2441 | −1.80254 | ||||||||
\(475\) | 0.0582305 | 0.00267180 | ||||||||
\(476\) | 0.819984 | 0.0375839 | ||||||||
\(477\) | 10.8700 | 0.497704 | ||||||||
\(478\) | −39.5420 | −1.80861 | ||||||||
\(479\) | 31.7894 | 1.45250 | 0.726248 | − | 0.687433i | \(-0.241263\pi\) | ||||
0.726248 | + | 0.687433i | \(0.241263\pi\) | |||||||
\(480\) | 150.791 | 6.88264 | ||||||||
\(481\) | −8.84783 | −0.403426 | ||||||||
\(482\) | −40.9878 | −1.86694 | ||||||||
\(483\) | 0.412930 | 0.0187890 | ||||||||
\(484\) | 51.5782 | 2.34446 | ||||||||
\(485\) | −32.7987 | −1.48931 | ||||||||
\(486\) | 59.9336 | 2.71864 | ||||||||
\(487\) | 3.65311 | 0.165538 | 0.0827692 | − | 0.996569i | \(-0.473624\pi\) | ||||
0.0827692 | + | 0.996569i | \(0.473624\pi\) | |||||||
\(488\) | −71.5171 | −3.23743 | ||||||||
\(489\) | 25.8679 | 1.16979 | ||||||||
\(490\) | −43.5981 | −1.96956 | ||||||||
\(491\) | −38.0504 | −1.71719 | −0.858595 | − | 0.512655i | \(-0.828662\pi\) | ||||
−0.858595 | + | 0.512655i | \(0.828662\pi\) | |||||||
\(492\) | 26.1938 | 1.18091 | ||||||||
\(493\) | −9.22993 | −0.415695 | ||||||||
\(494\) | 16.5375 | 0.744059 | ||||||||
\(495\) | −27.8323 | −1.25097 | ||||||||
\(496\) | 34.5887 | 1.55308 | ||||||||
\(497\) | −0.0323594 | −0.00145152 | ||||||||
\(498\) | 51.8371 | 2.32288 | ||||||||
\(499\) | 8.21311 | 0.367669 | 0.183835 | − | 0.982957i | \(-0.441149\pi\) | ||||
0.183835 | + | 0.982957i | \(0.441149\pi\) | |||||||
\(500\) | 64.2245 | 2.87221 | ||||||||
\(501\) | 41.9053 | 1.87219 | ||||||||
\(502\) | −51.3496 | −2.29184 | ||||||||
\(503\) | 41.8858 | 1.86760 | 0.933799 | − | 0.357799i | \(-0.116473\pi\) | ||||
0.933799 | + | 0.357799i | \(0.116473\pi\) | |||||||
\(504\) | 1.64930 | 0.0734658 | ||||||||
\(505\) | −13.8939 | −0.618271 | ||||||||
\(506\) | 37.6274 | 1.67274 | ||||||||
\(507\) | −28.8042 | −1.27924 | ||||||||
\(508\) | 100.861 | 4.47498 | ||||||||
\(509\) | −36.1271 | −1.60131 | −0.800653 | − | 0.599129i | \(-0.795514\pi\) | ||||
−0.800653 | + | 0.599129i | \(0.795514\pi\) | |||||||
\(510\) | −37.6361 | −1.66655 | ||||||||
\(511\) | 0.457169 | 0.0202240 | ||||||||
\(512\) | −125.328 | −5.53877 | ||||||||
\(513\) | −3.07277 | −0.135666 | ||||||||
\(514\) | −3.07135 | −0.135471 | ||||||||
\(515\) | 2.32192 | 0.102316 | ||||||||
\(516\) | 71.1899 | 3.13396 | ||||||||
\(517\) | −15.2041 | −0.668675 | ||||||||
\(518\) | 1.38352 | 0.0607882 | ||||||||
\(519\) | −41.0687 | −1.80271 | ||||||||
\(520\) | −23.6197 | −1.03579 | ||||||||
\(521\) | −13.3411 | −0.584482 | −0.292241 | − | 0.956345i | \(-0.594401\pi\) | ||||
−0.292241 | + | 0.956345i | \(0.594401\pi\) | |||||||
\(522\) | −28.4659 | −1.24592 | ||||||||
\(523\) | 22.7016 | 0.992670 | 0.496335 | − | 0.868131i | \(-0.334679\pi\) | ||||
0.496335 | + | 0.868131i | \(0.334679\pi\) | |||||||
\(524\) | 11.9082 | 0.520211 | ||||||||
\(525\) | −0.00135272 | −5.90377e−5 0 | ||||||||
\(526\) | −10.4439 | −0.455376 | ||||||||
\(527\) | −4.94644 | −0.215471 | ||||||||
\(528\) | 188.740 | 8.21386 | ||||||||
\(529\) | −13.8521 | −0.602264 | ||||||||
\(530\) | 24.3418 | 1.05734 | ||||||||
\(531\) | 6.28714 | 0.272839 | ||||||||
\(532\) | −1.91861 | −0.0831824 | ||||||||
\(533\) | −1.91479 | −0.0829388 | ||||||||
\(534\) | −34.7614 | −1.50427 | ||||||||
\(535\) | 11.7193 | 0.506672 | ||||||||
\(536\) | 105.659 | 4.56379 | ||||||||
\(537\) | 43.3549 | 1.87090 | ||||||||
\(538\) | 48.1880 | 2.07753 | ||||||||
\(539\) | −31.2670 | −1.34677 | ||||||||
\(540\) | 6.72924 | 0.289581 | ||||||||
\(541\) | −37.2425 | −1.60118 | −0.800591 | − | 0.599212i | \(-0.795481\pi\) | ||||
−0.800591 | + | 0.599212i | \(0.795481\pi\) | |||||||
\(542\) | −29.4020 | −1.26292 | ||||||||
\(543\) | −29.7271 | −1.27571 | ||||||||
\(544\) | 70.3679 | 3.01700 | ||||||||
\(545\) | −19.7450 | −0.845783 | ||||||||
\(546\) | −0.384175 | −0.0164412 | ||||||||
\(547\) | −24.5951 | −1.05161 | −0.525804 | − | 0.850605i | \(-0.676236\pi\) | ||||
−0.525804 | + | 0.850605i | \(0.676236\pi\) | |||||||
\(548\) | −48.3212 | −2.06418 | ||||||||
\(549\) | 19.0615 | 0.813524 | ||||||||
\(550\) | −0.123264 | −0.00525600 | ||||||||
\(551\) | 21.5964 | 0.920035 | ||||||||
\(552\) | 75.9315 | 3.23186 | ||||||||
\(553\) | −0.332823 | −0.0141531 | ||||||||
\(554\) | 76.3403 | 3.24339 | ||||||||
\(555\) | −47.1142 | −1.99989 | ||||||||
\(556\) | −99.4243 | −4.21653 | ||||||||
\(557\) | −23.7094 | −1.00460 | −0.502300 | − | 0.864694i | \(-0.667513\pi\) | ||||
−0.502300 | + | 0.864694i | \(0.667513\pi\) | |||||||
\(558\) | −15.2553 | −0.645807 | ||||||||
\(559\) | −5.20404 | −0.220108 | ||||||||
\(560\) | 2.23195 | 0.0943170 | ||||||||
\(561\) | −26.9913 | −1.13957 | ||||||||
\(562\) | −12.4188 | −0.523855 | ||||||||
\(563\) | −26.8891 | −1.13324 | −0.566620 | − | 0.823979i | \(-0.691749\pi\) | ||||
−0.566620 | + | 0.823979i | \(0.691749\pi\) | |||||||
\(564\) | −47.0446 | −1.98094 | ||||||||
\(565\) | 12.7942 | 0.538255 | ||||||||
\(566\) | 22.7733 | 0.957234 | ||||||||
\(567\) | 0.545320 | 0.0229013 | ||||||||
\(568\) | −5.95041 | −0.249673 | ||||||||
\(569\) | −3.35316 | −0.140572 | −0.0702859 | − | 0.997527i | \(-0.522391\pi\) | ||||
−0.0702859 | + | 0.997527i | \(0.522391\pi\) | |||||||
\(570\) | 88.0614 | 3.68849 | ||||||||
\(571\) | 16.6016 | 0.694757 | 0.347378 | − | 0.937725i | \(-0.387072\pi\) | ||||
0.347378 | + | 0.937725i | \(0.387072\pi\) | |||||||
\(572\) | −25.9732 | −1.08600 | ||||||||
\(573\) | −26.9150 | −1.12439 | ||||||||
\(574\) | 0.299412 | 0.0124972 | ||||||||
\(575\) | −0.0299679 | −0.00124975 | ||||||||
\(576\) | 119.276 | 4.96984 | ||||||||
\(577\) | −41.9998 | −1.74847 | −0.874237 | − | 0.485500i | \(-0.838638\pi\) | ||||
−0.874237 | + | 0.485500i | \(0.838638\pi\) | |||||||
\(578\) | 29.7632 | 1.23799 | ||||||||
\(579\) | 1.75542 | 0.0729526 | ||||||||
\(580\) | −47.2951 | −1.96382 | ||||||||
\(581\) | 0.439622 | 0.0182386 | ||||||||
\(582\) | −98.0971 | −4.06625 | ||||||||
\(583\) | 17.4571 | 0.723000 | ||||||||
\(584\) | 84.0664 | 3.47869 | ||||||||
\(585\) | 6.29538 | 0.260282 | ||||||||
\(586\) | −56.1378 | −2.31903 | ||||||||
\(587\) | −19.1794 | −0.791617 | −0.395808 | − | 0.918333i | \(-0.629536\pi\) | ||||
−0.395808 | + | 0.918333i | \(0.629536\pi\) | |||||||
\(588\) | −96.7466 | −3.98976 | ||||||||
\(589\) | 11.5738 | 0.476889 | ||||||||
\(590\) | 14.0791 | 0.579628 | ||||||||
\(591\) | 24.4777 | 1.00688 | ||||||||
\(592\) | 153.742 | 6.31874 | ||||||||
\(593\) | 46.0608 | 1.89149 | 0.945745 | − | 0.324909i | \(-0.105334\pi\) | ||||
0.945745 | + | 0.324909i | \(0.105334\pi\) | |||||||
\(594\) | 6.50454 | 0.266885 | ||||||||
\(595\) | −0.319186 | −0.0130853 | ||||||||
\(596\) | 44.6269 | 1.82799 | ||||||||
\(597\) | 62.8684 | 2.57303 | ||||||||
\(598\) | −8.51092 | −0.348037 | ||||||||
\(599\) | −3.92338 | −0.160305 | −0.0801524 | − | 0.996783i | \(-0.525541\pi\) | ||||
−0.0801524 | + | 0.996783i | \(0.525541\pi\) | |||||||
\(600\) | −0.248745 | −0.0101550 | ||||||||
\(601\) | −44.3363 | −1.80851 | −0.904257 | − | 0.426989i | \(-0.859574\pi\) | ||||
−0.904257 | + | 0.426989i | \(0.859574\pi\) | |||||||
\(602\) | 0.813746 | 0.0331658 | ||||||||
\(603\) | −28.1614 | −1.14682 | ||||||||
\(604\) | 103.667 | 4.21816 | ||||||||
\(605\) | −20.0772 | −0.816255 | ||||||||
\(606\) | −41.5551 | −1.68806 | ||||||||
\(607\) | 33.5928 | 1.36349 | 0.681745 | − | 0.731590i | \(-0.261221\pi\) | ||||
0.681745 | + | 0.731590i | \(0.261221\pi\) | |||||||
\(608\) | −164.648 | −6.67735 | ||||||||
\(609\) | −0.501694 | −0.0203297 | ||||||||
\(610\) | 42.6854 | 1.72828 | ||||||||
\(611\) | 3.43900 | 0.139127 | ||||||||
\(612\) | −40.1881 | −1.62451 | ||||||||
\(613\) | 38.2029 | 1.54300 | 0.771500 | − | 0.636229i | \(-0.219507\pi\) | ||||
0.771500 | + | 0.636229i | \(0.219507\pi\) | |||||||
\(614\) | −53.6483 | −2.16507 | ||||||||
\(615\) | −10.1961 | −0.411148 | ||||||||
\(616\) | 2.64876 | 0.106721 | ||||||||
\(617\) | −17.0650 | −0.687012 | −0.343506 | − | 0.939151i | \(-0.611615\pi\) | ||||
−0.343506 | + | 0.939151i | \(0.611615\pi\) | |||||||
\(618\) | 6.94459 | 0.279353 | ||||||||
\(619\) | 38.0997 | 1.53136 | 0.765678 | − | 0.643224i | \(-0.222403\pi\) | ||||
0.765678 | + | 0.643224i | \(0.222403\pi\) | |||||||
\(620\) | −25.3461 | −1.01792 | ||||||||
\(621\) | 1.58138 | 0.0634585 | ||||||||
\(622\) | 41.4275 | 1.66109 | ||||||||
\(623\) | −0.294806 | −0.0118111 | ||||||||
\(624\) | −42.6910 | −1.70901 | ||||||||
\(625\) | −25.0494 | −1.00198 | ||||||||
\(626\) | −21.4281 | −0.856438 | ||||||||
\(627\) | 63.1546 | 2.52215 | ||||||||
\(628\) | 127.077 | 5.07091 | ||||||||
\(629\) | −21.9862 | −0.876648 | ||||||||
\(630\) | −0.984396 | −0.0392193 | ||||||||
\(631\) | −25.3340 | −1.00853 | −0.504265 | − | 0.863549i | \(-0.668237\pi\) | ||||
−0.504265 | + | 0.863549i | \(0.668237\pi\) | |||||||
\(632\) | −61.2011 | −2.43445 | ||||||||
\(633\) | −20.5282 | −0.815923 | ||||||||
\(634\) | −23.3621 | −0.927826 | ||||||||
\(635\) | −39.2609 | −1.55802 | ||||||||
\(636\) | 54.0159 | 2.14187 | ||||||||
\(637\) | 7.07227 | 0.280213 | ||||||||
\(638\) | −45.7159 | −1.80991 | ||||||||
\(639\) | 1.58596 | 0.0627398 | ||||||||
\(640\) | 141.688 | 5.60070 | ||||||||
\(641\) | −9.05500 | −0.357651 | −0.178825 | − | 0.983881i | \(-0.557230\pi\) | ||||
−0.178825 | + | 0.983881i | \(0.557230\pi\) | |||||||
\(642\) | 35.0512 | 1.38336 | ||||||||
\(643\) | 7.79552 | 0.307425 | 0.153713 | − | 0.988116i | \(-0.450877\pi\) | ||||
0.153713 | + | 0.988116i | \(0.450877\pi\) | |||||||
\(644\) | 0.987399 | 0.0389090 | ||||||||
\(645\) | −27.7112 | −1.09113 | ||||||||
\(646\) | 41.0946 | 1.61685 | ||||||||
\(647\) | 36.4734 | 1.43392 | 0.716959 | − | 0.697116i | \(-0.245534\pi\) | ||||
0.716959 | + | 0.697116i | \(0.245534\pi\) | |||||||
\(648\) | 100.276 | 3.93922 | ||||||||
\(649\) | 10.0971 | 0.396344 | ||||||||
\(650\) | 0.0278811 | 0.00109359 | ||||||||
\(651\) | −0.268864 | −0.0105376 | ||||||||
\(652\) | 61.8554 | 2.42244 | ||||||||
\(653\) | 47.4205 | 1.85571 | 0.927855 | − | 0.372942i | \(-0.121651\pi\) | ||||
0.927855 | + | 0.372942i | \(0.121651\pi\) | |||||||
\(654\) | −59.0550 | −2.30923 | ||||||||
\(655\) | −4.63536 | −0.181118 | ||||||||
\(656\) | 33.2718 | 1.29904 | ||||||||
\(657\) | −22.4062 | −0.874151 | ||||||||
\(658\) | −0.537750 | −0.0209637 | ||||||||
\(659\) | 1.74351 | 0.0679177 | 0.0339588 | − | 0.999423i | \(-0.489188\pi\) | ||||
0.0339588 | + | 0.999423i | \(0.489188\pi\) | |||||||
\(660\) | −138.306 | −5.38355 | ||||||||
\(661\) | 25.1401 | 0.977836 | 0.488918 | − | 0.872330i | \(-0.337392\pi\) | ||||
0.488918 | + | 0.872330i | \(0.337392\pi\) | |||||||
\(662\) | 86.4738 | 3.36090 | ||||||||
\(663\) | 6.10514 | 0.237104 | ||||||||
\(664\) | 80.8399 | 3.13720 | ||||||||
\(665\) | 0.746836 | 0.0289610 | ||||||||
\(666\) | −67.8074 | −2.62748 | ||||||||
\(667\) | −11.1144 | −0.430351 | ||||||||
\(668\) | 100.204 | 3.87701 | ||||||||
\(669\) | −2.52698 | −0.0976986 | ||||||||
\(670\) | −63.0634 | −2.43635 | ||||||||
\(671\) | 30.6125 | 1.18178 | ||||||||
\(672\) | 3.82485 | 0.147547 | ||||||||
\(673\) | 46.2881 | 1.78428 | 0.892138 | − | 0.451763i | \(-0.149205\pi\) | ||||
0.892138 | + | 0.451763i | \(0.149205\pi\) | |||||||
\(674\) | −17.6501 | −0.679856 | ||||||||
\(675\) | −0.00518047 | −0.000199396 0 | ||||||||
\(676\) | −68.8767 | −2.64911 | ||||||||
\(677\) | −33.3594 | −1.28211 | −0.641053 | − | 0.767497i | \(-0.721502\pi\) | ||||
−0.641053 | + | 0.767497i | \(0.721502\pi\) | |||||||
\(678\) | 38.2660 | 1.46960 | ||||||||
\(679\) | −0.831946 | −0.0319272 | ||||||||
\(680\) | −58.6934 | −2.25079 | ||||||||
\(681\) | 15.9674 | 0.611873 | ||||||||
\(682\) | −24.4997 | −0.938143 | ||||||||
\(683\) | 11.8600 | 0.453812 | 0.226906 | − | 0.973917i | \(-0.427139\pi\) | ||||
0.226906 | + | 0.973917i | \(0.427139\pi\) | |||||||
\(684\) | 94.0329 | 3.59544 | ||||||||
\(685\) | 18.8094 | 0.718670 | ||||||||
\(686\) | −2.21226 | −0.0844645 | ||||||||
\(687\) | −31.6690 | −1.20825 | ||||||||
\(688\) | 90.4265 | 3.44748 | ||||||||
\(689\) | −3.94861 | −0.150430 | ||||||||
\(690\) | −45.3201 | −1.72531 | ||||||||
\(691\) | −18.6628 | −0.709966 | −0.354983 | − | 0.934873i | \(-0.615513\pi\) | ||||
−0.354983 | + | 0.934873i | \(0.615513\pi\) | |||||||
\(692\) | −98.2036 | −3.73314 | ||||||||
\(693\) | −0.705974 | −0.0268177 | ||||||||
\(694\) | 69.5211 | 2.63899 | ||||||||
\(695\) | 38.7017 | 1.46804 | ||||||||
\(696\) | −92.2539 | −3.49687 | ||||||||
\(697\) | −4.75812 | −0.180226 | ||||||||
\(698\) | 5.29959 | 0.200593 | ||||||||
\(699\) | 46.1978 | 1.74736 | ||||||||
\(700\) | −0.00323464 | −0.000122258 0 | ||||||||
\(701\) | 6.71903 | 0.253774 | 0.126887 | − | 0.991917i | \(-0.459501\pi\) | ||||
0.126887 | + | 0.991917i | \(0.459501\pi\) | |||||||
\(702\) | −1.47126 | −0.0555291 | ||||||||
\(703\) | 51.4437 | 1.94024 | ||||||||
\(704\) | 191.556 | 7.21953 | ||||||||
\(705\) | 18.3125 | 0.689689 | ||||||||
\(706\) | −12.0486 | −0.453457 | ||||||||
\(707\) | −0.352423 | −0.0132542 | ||||||||
\(708\) | 31.2424 | 1.17416 | ||||||||
\(709\) | −45.6265 | −1.71354 | −0.856769 | − | 0.515701i | \(-0.827532\pi\) | ||||
−0.856769 | + | 0.515701i | \(0.827532\pi\) | |||||||
\(710\) | 3.55153 | 0.133287 | ||||||||
\(711\) | 16.3120 | 0.611746 | ||||||||
\(712\) | −54.2103 | −2.03162 | ||||||||
\(713\) | −5.95635 | −0.223067 | ||||||||
\(714\) | −0.954648 | −0.0357268 | ||||||||
\(715\) | 10.1103 | 0.378103 | ||||||||
\(716\) | 103.670 | 3.87434 | ||||||||
\(717\) | 34.1559 | 1.27557 | ||||||||
\(718\) | −45.8420 | −1.71081 | ||||||||
\(719\) | 13.2163 | 0.492883 | 0.246442 | − | 0.969158i | \(-0.420739\pi\) | ||||
0.246442 | + | 0.969158i | \(0.420739\pi\) | |||||||
\(720\) | −109.390 | −4.07672 | ||||||||
\(721\) | 0.0588960 | 0.00219340 | ||||||||
\(722\) | −43.2596 | −1.60996 | ||||||||
\(723\) | 35.4047 | 1.31672 | ||||||||
\(724\) | −71.0836 | −2.64180 | ||||||||
\(725\) | 0.0364099 | 0.00135223 | ||||||||
\(726\) | −60.0487 | −2.22862 | ||||||||
\(727\) | −40.0931 | −1.48697 | −0.743486 | − | 0.668752i | \(-0.766829\pi\) | ||||
−0.743486 | + | 0.668752i | \(0.766829\pi\) | |||||||
\(728\) | −0.599121 | −0.0222049 | ||||||||
\(729\) | −22.9548 | −0.850177 | ||||||||
\(730\) | −50.1755 | −1.85708 | ||||||||
\(731\) | −12.9317 | −0.478295 | ||||||||
\(732\) | 94.7213 | 3.50100 | ||||||||
\(733\) | −14.6344 | −0.540535 | −0.270267 | − | 0.962785i | \(-0.587112\pi\) | ||||
−0.270267 | + | 0.962785i | \(0.587112\pi\) | |||||||
\(734\) | 36.5460 | 1.34894 | ||||||||
\(735\) | 37.6594 | 1.38909 | ||||||||
\(736\) | 84.7348 | 3.12336 | ||||||||
\(737\) | −45.2269 | −1.66595 | ||||||||
\(738\) | −14.6744 | −0.540174 | ||||||||
\(739\) | −48.2744 | −1.77580 | −0.887900 | − | 0.460036i | \(-0.847837\pi\) | ||||
−0.887900 | + | 0.460036i | \(0.847837\pi\) | |||||||
\(740\) | −112.660 | −4.14145 | ||||||||
\(741\) | −14.2849 | −0.524769 | ||||||||
\(742\) | 0.617437 | 0.0226668 | ||||||||
\(743\) | −25.2529 | −0.926437 | −0.463219 | − | 0.886244i | \(-0.653306\pi\) | ||||
−0.463219 | + | 0.886244i | \(0.653306\pi\) | |||||||
\(744\) | −49.4401 | −1.81256 | ||||||||
\(745\) | −17.3714 | −0.636438 | ||||||||
\(746\) | −43.4750 | −1.59173 | ||||||||
\(747\) | −21.5463 | −0.788337 | ||||||||
\(748\) | −64.5416 | −2.35987 | ||||||||
\(749\) | 0.297264 | 0.0108618 | ||||||||
\(750\) | −74.7719 | −2.73028 | ||||||||
\(751\) | −15.0796 | −0.550261 | −0.275131 | − | 0.961407i | \(-0.588721\pi\) | ||||
−0.275131 | + | 0.961407i | \(0.588721\pi\) | |||||||
\(752\) | −59.7568 | −2.17911 | ||||||||
\(753\) | 44.3550 | 1.61639 | ||||||||
\(754\) | 10.3404 | 0.376577 | ||||||||
\(755\) | −40.3533 | −1.46861 | ||||||||
\(756\) | 0.170689 | 0.00620790 | ||||||||
\(757\) | 36.7887 | 1.33711 | 0.668553 | − | 0.743664i | \(-0.266914\pi\) | ||||
0.668553 | + | 0.743664i | \(0.266914\pi\) | |||||||
\(758\) | −48.0081 | −1.74373 | ||||||||
\(759\) | −32.5020 | −1.17975 | ||||||||
\(760\) | 137.332 | 4.98154 | ||||||||
\(761\) | 30.8702 | 1.11904 | 0.559521 | − | 0.828816i | \(-0.310985\pi\) | ||||
0.559521 | + | 0.828816i | \(0.310985\pi\) | |||||||
\(762\) | −117.425 | −4.25386 | ||||||||
\(763\) | −0.500837 | −0.0181315 | ||||||||
\(764\) | −64.3591 | −2.32843 | ||||||||
\(765\) | 15.6436 | 0.565594 | ||||||||
\(766\) | −21.8732 | −0.790313 | ||||||||
\(767\) | −2.28385 | −0.0824649 | ||||||||
\(768\) | 217.616 | 7.85252 | ||||||||
\(769\) | 29.9751 | 1.08093 | 0.540464 | − | 0.841367i | \(-0.318249\pi\) | ||||
0.540464 | + | 0.841367i | \(0.318249\pi\) | |||||||
\(770\) | −1.58093 | −0.0569726 | ||||||||
\(771\) | 2.65299 | 0.0955451 | ||||||||
\(772\) | 4.19756 | 0.151073 | ||||||||
\(773\) | −3.31481 | −0.119225 | −0.0596127 | − | 0.998222i | \(-0.518987\pi\) | ||||
−0.0596127 | + | 0.998222i | \(0.518987\pi\) | |||||||
\(774\) | −39.8824 | −1.43354 | ||||||||
\(775\) | 0.0195125 | 0.000700911 0 | ||||||||
\(776\) | −152.982 | −5.49174 | ||||||||
\(777\) | −1.19506 | −0.0428726 | ||||||||
\(778\) | 98.8669 | 3.54455 | ||||||||
\(779\) | 11.1331 | 0.398885 | ||||||||
\(780\) | 31.2833 | 1.12012 | ||||||||
\(781\) | 2.54704 | 0.0911401 | ||||||||
\(782\) | −21.1490 | −0.756287 | ||||||||
\(783\) | −1.92131 | −0.0686622 | ||||||||
\(784\) | −122.889 | −4.38890 | ||||||||
\(785\) | −49.4656 | −1.76550 | ||||||||
\(786\) | −13.8638 | −0.494506 | ||||||||
\(787\) | 51.0005 | 1.81797 | 0.908986 | − | 0.416826i | \(-0.136858\pi\) | ||||
0.908986 | + | 0.416826i | \(0.136858\pi\) | |||||||
\(788\) | 58.5312 | 2.08509 | ||||||||
\(789\) | 9.02130 | 0.321167 | ||||||||
\(790\) | 36.5282 | 1.29962 | ||||||||
\(791\) | 0.324528 | 0.0115389 | ||||||||
\(792\) | −129.818 | −4.61288 | ||||||||
\(793\) | −6.92422 | −0.245886 | ||||||||
\(794\) | −22.1384 | −0.785664 | ||||||||
\(795\) | −21.0261 | −0.745720 | ||||||||
\(796\) | 150.331 | 5.32835 | ||||||||
\(797\) | −3.27665 | −0.116065 | −0.0580325 | − | 0.998315i | \(-0.518483\pi\) | ||||
−0.0580325 | + | 0.998315i | \(0.518483\pi\) | |||||||
\(798\) | 2.23370 | 0.0790721 | ||||||||
\(799\) | 8.54568 | 0.302324 | ||||||||
\(800\) | −0.277584 | −0.00981408 | ||||||||
\(801\) | 14.4487 | 0.510519 | ||||||||
\(802\) | −3.80372 | −0.134314 | ||||||||
\(803\) | −35.9841 | −1.26985 | ||||||||
\(804\) | −139.941 | −4.93535 | ||||||||
\(805\) | −0.384353 | −0.0135467 | ||||||||
\(806\) | 5.54158 | 0.195194 | ||||||||
\(807\) | −41.6241 | −1.46524 | ||||||||
\(808\) | −64.8052 | −2.27984 | ||||||||
\(809\) | −32.8470 | −1.15484 | −0.577420 | − | 0.816447i | \(-0.695941\pi\) | ||||
−0.577420 | + | 0.816447i | \(0.695941\pi\) | |||||||
\(810\) | −59.8504 | −2.10293 | ||||||||
\(811\) | −14.6067 | −0.512910 | −0.256455 | − | 0.966556i | \(-0.582555\pi\) | ||||
−0.256455 | + | 0.966556i | \(0.582555\pi\) | |||||||
\(812\) | −1.19965 | −0.0420996 | ||||||||
\(813\) | 25.3970 | 0.890712 | ||||||||
\(814\) | −108.898 | −3.81686 | ||||||||
\(815\) | −24.0777 | −0.843405 | ||||||||
\(816\) | −106.084 | −3.71368 | ||||||||
\(817\) | 30.2577 | 1.05858 | ||||||||
\(818\) | −43.9339 | −1.53611 | ||||||||
\(819\) | 0.159684 | 0.00557981 | ||||||||
\(820\) | −24.3811 | −0.851424 | ||||||||
\(821\) | −31.2432 | −1.09039 | −0.545197 | − | 0.838308i | \(-0.683545\pi\) | ||||
−0.545197 | + | 0.838308i | \(0.683545\pi\) | |||||||
\(822\) | 56.2568 | 1.96218 | ||||||||
\(823\) | −20.0259 | −0.698058 | −0.349029 | − | 0.937112i | \(-0.613488\pi\) | ||||
−0.349029 | + | 0.937112i | \(0.613488\pi\) | |||||||
\(824\) | 10.8301 | 0.377284 | ||||||||
\(825\) | 0.106474 | 0.00370695 | ||||||||
\(826\) | 0.357121 | 0.0124258 | ||||||||
\(827\) | −4.55756 | −0.158482 | −0.0792409 | − | 0.996855i | \(-0.525250\pi\) | ||||
−0.0792409 | + | 0.996855i | \(0.525250\pi\) | |||||||
\(828\) | −48.3933 | −1.68178 | ||||||||
\(829\) | −45.9058 | −1.59437 | −0.797187 | − | 0.603733i | \(-0.793679\pi\) | ||||
−0.797187 | + | 0.603733i | \(0.793679\pi\) | |||||||
\(830\) | −48.2497 | −1.67477 | ||||||||
\(831\) | −65.9417 | −2.28749 | ||||||||
\(832\) | −43.3279 | −1.50213 | ||||||||
\(833\) | 17.5741 | 0.608905 | ||||||||
\(834\) | 115.752 | 4.00818 | ||||||||
\(835\) | −39.0053 | −1.34983 | ||||||||
\(836\) | 151.015 | 5.22298 | ||||||||
\(837\) | −1.02966 | −0.0355902 | ||||||||
\(838\) | −48.2188 | −1.66569 | ||||||||
\(839\) | 21.0535 | 0.726848 | 0.363424 | − | 0.931624i | \(-0.381608\pi\) | ||||
0.363424 | + | 0.931624i | \(0.381608\pi\) | |||||||
\(840\) | −3.19028 | −0.110075 | ||||||||
\(841\) | −15.4964 | −0.534360 | ||||||||
\(842\) | −65.8205 | −2.26832 | ||||||||
\(843\) | 10.7272 | 0.369463 | ||||||||
\(844\) | −49.0871 | −1.68965 | ||||||||
\(845\) | 26.8108 | 0.922321 | ||||||||
\(846\) | 26.3556 | 0.906124 | ||||||||
\(847\) | −0.509264 | −0.0174985 | ||||||||
\(848\) | 68.6119 | 2.35614 | ||||||||
\(849\) | −19.6713 | −0.675117 | ||||||||
\(850\) | 0.0692824 | 0.00237637 | ||||||||
\(851\) | −26.4751 | −0.907555 | ||||||||
\(852\) | 7.88106 | 0.270001 | ||||||||
\(853\) | 2.19428 | 0.0751307 | 0.0375653 | − | 0.999294i | \(-0.488040\pi\) | ||||
0.0375653 | + | 0.999294i | \(0.488040\pi\) | |||||||
\(854\) | 1.08273 | 0.0370501 | ||||||||
\(855\) | −36.6031 | −1.25180 | ||||||||
\(856\) | 54.6624 | 1.86832 | ||||||||
\(857\) | −22.9582 | −0.784237 | −0.392119 | − | 0.919915i | \(-0.628258\pi\) | ||||
−0.392119 | + | 0.919915i | \(0.628258\pi\) | |||||||
\(858\) | 30.2387 | 1.03233 | ||||||||
\(859\) | −28.8325 | −0.983752 | −0.491876 | − | 0.870665i | \(-0.663689\pi\) | ||||
−0.491876 | + | 0.870665i | \(0.663689\pi\) | |||||||
\(860\) | −66.2632 | −2.25956 | ||||||||
\(861\) | −0.258628 | −0.00881401 | ||||||||
\(862\) | −73.1967 | −2.49309 | ||||||||
\(863\) | 20.3072 | 0.691265 | 0.345633 | − | 0.938370i | \(-0.387664\pi\) | ||||
0.345633 | + | 0.938370i | \(0.387664\pi\) | |||||||
\(864\) | 14.6479 | 0.498330 | ||||||||
\(865\) | 38.2265 | 1.29974 | ||||||||
\(866\) | −38.6695 | −1.31404 | ||||||||
\(867\) | −25.7090 | −0.873125 | ||||||||
\(868\) | −0.642910 | −0.0218218 | ||||||||
\(869\) | 26.1968 | 0.888664 | ||||||||
\(870\) | 55.0623 | 1.86679 | ||||||||
\(871\) | 10.2298 | 0.346625 | ||||||||
\(872\) | −92.0962 | −3.11877 | ||||||||
\(873\) | 40.7744 | 1.38000 | ||||||||
\(874\) | 49.4848 | 1.67385 | ||||||||
\(875\) | −0.634129 | −0.0214375 | ||||||||
\(876\) | −111.342 | −3.76191 | ||||||||
\(877\) | −4.45487 | −0.150430 | −0.0752152 | − | 0.997167i | \(-0.523964\pi\) | ||||
−0.0752152 | + | 0.997167i | \(0.523964\pi\) | |||||||
\(878\) | 24.7390 | 0.834901 | ||||||||
\(879\) | 48.4910 | 1.63556 | ||||||||
\(880\) | −175.678 | −5.92212 | ||||||||
\(881\) | 39.7804 | 1.34024 | 0.670118 | − | 0.742255i | \(-0.266244\pi\) | ||||
0.670118 | + | 0.742255i | \(0.266244\pi\) | |||||||
\(882\) | 54.1999 | 1.82501 | ||||||||
\(883\) | −10.3635 | −0.348758 | −0.174379 | − | 0.984679i | \(-0.555792\pi\) | ||||
−0.174379 | + | 0.984679i | \(0.555792\pi\) | |||||||
\(884\) | 14.5986 | 0.491005 | ||||||||
\(885\) | −12.1614 | −0.408799 | ||||||||
\(886\) | −104.422 | −3.50811 | ||||||||
\(887\) | 20.4859 | 0.687849 | 0.343924 | − | 0.938997i | \(-0.388244\pi\) | ||||
0.343924 | + | 0.938997i | \(0.388244\pi\) | |||||||
\(888\) | −219.754 | −7.37446 | ||||||||
\(889\) | −0.995863 | −0.0334002 | ||||||||
\(890\) | 32.3557 | 1.08457 | ||||||||
\(891\) | −42.9226 | −1.43796 | ||||||||
\(892\) | −6.04252 | −0.202319 | ||||||||
\(893\) | −19.9953 | −0.669118 | ||||||||
\(894\) | −51.9559 | −1.73766 | ||||||||
\(895\) | −40.3545 | −1.34890 | ||||||||
\(896\) | 3.59395 | 0.120065 | ||||||||
\(897\) | 7.35161 | 0.245463 | ||||||||
\(898\) | 68.5394 | 2.28719 | ||||||||
\(899\) | 7.23674 | 0.241359 | ||||||||
\(900\) | 0.158532 | 0.00528442 | ||||||||
\(901\) | −9.81202 | −0.326886 | ||||||||
\(902\) | −23.5669 | −0.784693 | ||||||||
\(903\) | −0.702902 | −0.0233911 | ||||||||
\(904\) | 59.6757 | 1.98478 | ||||||||
\(905\) | 27.6699 | 0.919778 | ||||||||
\(906\) | −120.692 | −4.00973 | ||||||||
\(907\) | 39.2596 | 1.30359 | 0.651796 | − | 0.758394i | \(-0.274016\pi\) | ||||
0.651796 | + | 0.758394i | \(0.274016\pi\) | |||||||
\(908\) | 38.1814 | 1.26709 | ||||||||
\(909\) | 17.2725 | 0.572894 | ||||||||
\(910\) | 0.357589 | 0.0118539 | ||||||||
\(911\) | 25.0309 | 0.829310 | 0.414655 | − | 0.909979i | \(-0.363902\pi\) | ||||
0.414655 | + | 0.909979i | \(0.363902\pi\) | |||||||
\(912\) | 248.217 | 8.21929 | ||||||||
\(913\) | −34.6030 | −1.14519 | ||||||||
\(914\) | −15.7179 | −0.519901 | ||||||||
\(915\) | −36.8710 | −1.21892 | ||||||||
\(916\) | −75.7270 | −2.50209 | ||||||||
\(917\) | −0.117577 | −0.00388273 | ||||||||
\(918\) | −3.65597 | −0.120665 | ||||||||
\(919\) | −29.4287 | −0.970763 | −0.485381 | − | 0.874303i | \(-0.661319\pi\) | ||||
−0.485381 | + | 0.874303i | \(0.661319\pi\) | |||||||
\(920\) | −70.6767 | −2.33014 | ||||||||
\(921\) | 46.3407 | 1.52698 | ||||||||
\(922\) | −95.6283 | −3.14935 | ||||||||
\(923\) | −0.576112 | −0.0189630 | ||||||||
\(924\) | −3.50816 | −0.115410 | ||||||||
\(925\) | 0.0867303 | 0.00285167 | ||||||||
\(926\) | −28.4241 | −0.934075 | ||||||||
\(927\) | −2.88655 | −0.0948066 | ||||||||
\(928\) | −102.950 | −3.37948 | ||||||||
\(929\) | 27.2482 | 0.893984 | 0.446992 | − | 0.894538i | \(-0.352495\pi\) | ||||
0.446992 | + | 0.894538i | \(0.352495\pi\) | |||||||
\(930\) | 29.5086 | 0.967625 | ||||||||
\(931\) | −41.1201 | −1.34766 | ||||||||
\(932\) | 110.468 | 3.61851 | ||||||||
\(933\) | −35.7845 | −1.17153 | ||||||||
\(934\) | 81.3179 | 2.66080 | ||||||||
\(935\) | 25.1233 | 0.821621 | ||||||||
\(936\) | 29.3634 | 0.959774 | ||||||||
\(937\) | −26.6447 | −0.870445 | −0.435222 | − | 0.900323i | \(-0.643330\pi\) | ||||
−0.435222 | + | 0.900323i | \(0.643330\pi\) | |||||||
\(938\) | −1.59962 | −0.0522294 | ||||||||
\(939\) | 18.5093 | 0.604027 | ||||||||
\(940\) | 43.7889 | 1.42824 | ||||||||
\(941\) | 41.2145 | 1.34355 | 0.671777 | − | 0.740753i | \(-0.265531\pi\) | ||||
0.671777 | + | 0.740753i | \(0.265531\pi\) | |||||||
\(942\) | −147.946 | −4.82034 | ||||||||
\(943\) | −5.72957 | −0.186581 | ||||||||
\(944\) | 39.6846 | 1.29162 | ||||||||
\(945\) | −0.0664421 | −0.00216136 | ||||||||
\(946\) | −64.0506 | −2.08246 | ||||||||
\(947\) | 22.1283 | 0.719072 | 0.359536 | − | 0.933131i | \(-0.382935\pi\) | ||||
0.359536 | + | 0.933131i | \(0.382935\pi\) | |||||||
\(948\) | 81.0582 | 2.63265 | ||||||||
\(949\) | 8.13923 | 0.264210 | ||||||||
\(950\) | −0.162108 | −0.00525948 | ||||||||
\(951\) | 20.1798 | 0.654376 | ||||||||
\(952\) | −1.48877 | −0.0482514 | ||||||||
\(953\) | 44.0188 | 1.42591 | 0.712954 | − | 0.701211i | \(-0.247357\pi\) | ||||
0.712954 | + | 0.701211i | \(0.247357\pi\) | |||||||
\(954\) | −30.2611 | −0.979740 | ||||||||
\(955\) | 25.0523 | 0.810674 | ||||||||
\(956\) | 81.6736 | 2.64151 | ||||||||
\(957\) | 39.4887 | 1.27649 | ||||||||
\(958\) | −88.4987 | −2.85926 | ||||||||
\(959\) | 0.477105 | 0.0154065 | ||||||||
\(960\) | −230.719 | −7.44641 | ||||||||
\(961\) | −27.1217 | −0.874895 | ||||||||
\(962\) | 24.6315 | 0.794152 | ||||||||
\(963\) | −14.5692 | −0.469485 | ||||||||
\(964\) | 84.6599 | 2.72671 | ||||||||
\(965\) | −1.63393 | −0.0525982 | ||||||||
\(966\) | −1.14956 | −0.0369864 | ||||||||
\(967\) | −57.7420 | −1.85686 | −0.928429 | − | 0.371510i | \(-0.878840\pi\) | ||||
−0.928429 | + | 0.371510i | \(0.878840\pi\) | |||||||
\(968\) | −93.6459 | −3.00989 | ||||||||
\(969\) | −35.4969 | −1.14033 | ||||||||
\(970\) | 91.3083 | 2.93173 | ||||||||
\(971\) | 6.71945 | 0.215638 | 0.107819 | − | 0.994171i | \(-0.465613\pi\) | ||||
0.107819 | + | 0.994171i | \(0.465613\pi\) | |||||||
\(972\) | −123.792 | −3.97063 | ||||||||
\(973\) | 0.981679 | 0.0314712 | ||||||||
\(974\) | −10.1699 | −0.325865 | ||||||||
\(975\) | −0.0240833 | −0.000771282 0 | ||||||||
\(976\) | 120.317 | 3.85124 | ||||||||
\(977\) | −58.3875 | −1.86798 | −0.933991 | − | 0.357297i | \(-0.883698\pi\) | ||||
−0.933991 | + | 0.357297i | \(0.883698\pi\) | |||||||
\(978\) | −72.0137 | −2.30274 | ||||||||
\(979\) | 23.2044 | 0.741615 | ||||||||
\(980\) | 90.0513 | 2.87658 | ||||||||
\(981\) | 24.5464 | 0.783708 | ||||||||
\(982\) | 105.929 | 3.38032 | ||||||||
\(983\) | −25.2729 | −0.806081 | −0.403041 | − | 0.915182i | \(-0.632047\pi\) | ||||
−0.403041 | + | 0.915182i | \(0.632047\pi\) | |||||||
\(984\) | −47.5577 | −1.51608 | ||||||||
\(985\) | −22.7838 | −0.725951 | ||||||||
\(986\) | 25.6953 | 0.818304 | ||||||||
\(987\) | 0.464501 | 0.0147852 | ||||||||
\(988\) | −34.1581 | −1.08671 | ||||||||
\(989\) | −15.5719 | −0.495158 | ||||||||
\(990\) | 77.4826 | 2.46256 | ||||||||
\(991\) | −21.3350 | −0.677727 | −0.338864 | − | 0.940835i | \(-0.610043\pi\) | ||||
−0.338864 | + | 0.940835i | \(0.610043\pi\) | |||||||
\(992\) | −55.1720 | −1.75171 | ||||||||
\(993\) | −74.6948 | −2.37037 | ||||||||
\(994\) | 0.0900855 | 0.00285734 | ||||||||
\(995\) | −58.5176 | −1.85513 | ||||||||
\(996\) | −107.069 | −3.39261 | ||||||||
\(997\) | −23.5253 | −0.745054 | −0.372527 | − | 0.928021i | \(-0.621509\pi\) | ||||
−0.372527 | + | 0.928021i | \(0.621509\pi\) | |||||||
\(998\) | −22.8645 | −0.723763 | ||||||||
\(999\) | −4.57668 | −0.144800 |
(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 | 4019.2.a.b.1.3 | ✓ | 186 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.b.1.3 | ✓ | 186 | 1.1 | even | 1 | trivial |