Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.37 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.77382 | 1.02411 | 0.512057 | − | 0.858951i | \(-0.328884\pi\) | ||||
0.512057 | + | 0.858951i | \(0.328884\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.34355 | −1.49528 | −0.747641 | − | 0.664103i | \(-0.768813\pi\) | ||||
−0.747641 | + | 0.664103i | \(0.768813\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.838649 | 0.316980 | 0.158490 | − | 0.987361i | \(-0.449338\pi\) | ||||
0.158490 | + | 0.987361i | \(0.449338\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.146429 | 0.0488097 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.297273 | −0.0896313 | −0.0448157 | − | 0.998995i | \(-0.514270\pi\) | ||||
−0.0448157 | + | 0.998995i | \(0.514270\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.29535 | −0.359267 | −0.179633 | − | 0.983734i | \(-0.557491\pi\) | ||||
−0.179633 | + | 0.983734i | \(0.557491\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.93085 | −1.53134 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.69073 | 0.652597 | 0.326299 | − | 0.945267i | \(-0.394199\pi\) | ||||
0.326299 | + | 0.945267i | \(0.394199\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.59218 | −0.594688 | −0.297344 | − | 0.954770i | \(-0.596101\pi\) | ||||
−0.297344 | + | 0.954770i | \(0.596101\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.48761 | 0.324623 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.00797 | 1.04423 | 0.522117 | − | 0.852874i | \(-0.325142\pi\) | ||||
0.522117 | + | 0.852874i | \(0.325142\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.17933 | 1.23587 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.06171 | −0.974127 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.26847 | 0.792635 | 0.396317 | − | 0.918114i | \(-0.370288\pi\) | ||||
0.396317 | + | 0.918114i | \(0.370288\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.16112 | −0.208544 | −0.104272 | − | 0.994549i | \(-0.533251\pi\) | ||||
−0.104272 | + | 0.994549i | \(0.533251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.527309 | −0.0917927 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.80407 | −0.473974 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.31269 | 1.03780 | 0.518900 | − | 0.854835i | \(-0.326342\pi\) | ||||
0.518900 | + | 0.854835i | \(0.326342\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.29772 | −0.367930 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0977895 | 0.0152722 | 0.00763608 | − | 0.999971i | \(-0.497569\pi\) | ||||
0.00763608 | + | 0.999971i | \(0.497569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.74167 | 1.18059 | 0.590297 | − | 0.807186i | \(-0.299011\pi\) | ||||
0.590297 | + | 0.807186i | \(0.299011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.489594 | −0.0729843 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.23944 | −0.618385 | −0.309193 | − | 0.950999i | \(-0.600059\pi\) | ||||
−0.309193 | + | 0.950999i | \(0.600059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.29667 | −0.899524 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.77286 | 0.668334 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.41633 | −0.469269 | −0.234634 | − | 0.972084i | \(-0.575389\pi\) | ||||
−0.234634 | + | 0.972084i | \(0.575389\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.993949 | 0.134024 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.59806 | −0.609028 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.04471 | 0.656765 | 0.328382 | − | 0.944545i | \(-0.393497\pi\) | ||||
0.328382 | + | 0.944545i | \(0.393497\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.7533 | −1.50485 | −0.752426 | − | 0.658677i | \(-0.771117\pi\) | ||||
−0.752426 | + | 0.658677i | \(0.771117\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.122803 | 0.0154717 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.33108 | 0.537205 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.02906 | −0.492228 | −0.246114 | − | 0.969241i | \(-0.579154\pi\) | ||||
−0.246114 | + | 0.969241i | \(0.579154\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.88323 | 1.06942 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.77177 | −0.328949 | −0.164475 | − | 0.986381i | \(-0.552593\pi\) | ||||
−0.164475 | + | 0.986381i | \(0.552593\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.8527 | −1.50429 | −0.752146 | − | 0.658997i | \(-0.770981\pi\) | ||||
−0.752146 | + | 0.658997i | \(0.770981\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.9610 | 1.26567 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.249308 | −0.0284113 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.39050 | 1.05651 | 0.528257 | − | 0.849085i | \(-0.322846\pi\) | ||||
0.528257 | + | 0.849085i | \(0.322846\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.41785 | −1.04643 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.8476 | −1.73950 | −0.869750 | − | 0.493493i | \(-0.835720\pi\) | ||||
−0.869750 | + | 0.493493i | \(0.835720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.99658 | −0.975816 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.57148 | 0.811748 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7826 | −1.24895 | −0.624477 | − | 0.781043i | \(-0.714688\pi\) | ||||
−0.624477 | + | 0.781043i | \(0.714688\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.08635 | −0.113880 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.05962 | −0.213573 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.66710 | 0.889225 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.20439 | −0.833029 | −0.416515 | − | 0.909129i | \(-0.636749\pi\) | ||||
−0.416515 | + | 0.909129i | \(0.636749\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0435295 | −0.00437488 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.74409 | −0.472054 | −0.236027 | − | 0.971746i | \(-0.575845\pi\) | ||||
−0.236027 | + | 0.971746i | \(0.575845\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.44010 | −0.141898 | −0.0709488 | − | 0.997480i | \(-0.522603\pi\) | ||||
−0.0709488 | + | 0.997480i | \(0.522603\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.97390 | −0.485403 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.75172 | −0.556039 | −0.278020 | − | 0.960575i | \(-0.589678\pi\) | ||||
−0.278020 | + | 0.960575i | \(0.589678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.93535 | 0.664287 | 0.332143 | − | 0.943229i | \(-0.392228\pi\) | ||||
0.332143 | + | 0.943229i | \(0.392228\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.1976 | 1.06283 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.6893 | −1.75814 | −0.879071 | − | 0.476691i | \(-0.841836\pi\) | ||||
−0.879071 | + | 0.476691i | \(0.841836\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.7444 | −1.56142 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.189678 | −0.0175357 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.25658 | 0.206860 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9116 | −0.991966 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.173461 | 0.0156404 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.94316 | −0.352687 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9674 | −0.973196 | −0.486598 | − | 0.873626i | \(-0.661762\pi\) | ||||
−0.486598 | + | 0.873626i | \(0.661762\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.7323 | 1.20906 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.3875 | 1.60653 | 0.803263 | − | 0.595625i | \(-0.203096\pi\) | ||||
0.803263 | + | 0.595625i | \(0.203096\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.17393 | −0.188504 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.9241 | 1.45659 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.2031 | −1.12801 | −0.564007 | − | 0.825770i | \(-0.690741\pi\) | ||||
−0.564007 | + | 0.825770i | \(0.690741\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.2135 | −1.46003 | −0.730014 | − | 0.683432i | \(-0.760487\pi\) | ||||
−0.730014 | + | 0.683432i | \(0.760487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.51999 | −0.633297 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.385075 | 0.0322016 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.2718 | −1.18521 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.1691 | −0.921215 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.64240 | −0.134551 | −0.0672753 | − | 0.997734i | \(-0.521431\pi\) | ||||
−0.0672753 | + | 0.997734i | \(0.521431\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.4309 | −1.33713 | −0.668564 | − | 0.743655i | \(-0.733091\pi\) | ||||
−0.668564 | + | 0.743655i | \(0.733091\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.394001 | 0.0318531 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.88228 | 0.311832 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.2844 | 1.45925 | 0.729627 | − | 0.683845i | \(-0.239694\pi\) | ||||
0.729627 | + | 0.683845i | \(0.239694\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.05994 | −0.480585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.19993 | 0.331001 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1749 | 0.796960 | 0.398480 | − | 0.917177i | \(-0.369538\pi\) | ||||
0.398480 | + | 0.917177i | \(0.369538\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.76308 | 0.137256 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.99023 | −0.308773 | −0.154387 | − | 0.988010i | \(-0.549340\pi\) | ||||
−0.154387 | + | 0.988010i | \(0.549340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3221 | −0.870927 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.379571 | −0.0290266 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.6567 | −0.886241 | −0.443121 | − | 0.896462i | \(-0.646129\pi\) | ||||
−0.443121 | + | 0.896462i | \(0.646129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.18229 | 0.391744 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.94839 | 0.672602 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1000 | 0.904399 | 0.452199 | − | 0.891917i | \(-0.350640\pi\) | ||||
0.452199 | + | 0.891917i | \(0.350640\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.13687 | −0.381820 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.8482 | −1.54114 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.1068 | −1.55180 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.799881 | −0.0584931 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.24500 | −0.308779 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.2013 | 0.955213 | 0.477607 | − | 0.878574i | \(-0.341504\pi\) | ||||
0.477607 | + | 0.878574i | \(0.341504\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0529 | 1.08353 | 0.541765 | − | 0.840530i | \(-0.317756\pi\) | ||||
0.541765 | + | 0.840530i | \(0.317756\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.68256 | 0.550159 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.6452 | 1.96964 | 0.984821 | − | 0.173572i | \(-0.0555310\pi\) | ||||
0.984821 | + | 0.173572i | \(0.0555310\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.08758 | −0.289761 | −0.144880 | − | 0.989449i | \(-0.546280\pi\) | ||||
−0.144880 | + | 0.989449i | \(0.546280\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.14681 | −0.504097 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.57975 | 0.251249 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.326964 | −0.0228362 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.733314 | 0.0509688 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.770587 | 0.0533026 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.92644 | 0.614522 | 0.307261 | − | 0.951625i | \(-0.400588\pi\) | ||||
0.307261 | + | 0.951625i | \(0.400588\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.91662 | −0.336881 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.8847 | −1.76532 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.973777 | −0.0661043 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22.7983 | −1.54057 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.48545 | −0.234456 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.07168 | 0.540519 | 0.270260 | − | 0.962787i | \(-0.412890\pi\) | ||||
0.270260 | + | 0.962787i | \(0.412890\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.904835 | 0.0603223 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.8324 | −0.718970 | −0.359485 | − | 0.933151i | \(-0.617048\pi\) | ||||
−0.359485 | + | 0.933151i | \(0.617048\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.06858 | −0.268860 | −0.134430 | − | 0.990923i | \(-0.542920\pi\) | ||||
−0.134430 | + | 0.990923i | \(0.542920\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.442227 | −0.0290964 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.37960 | 0.286917 | 0.143459 | − | 0.989656i | \(-0.454178\pi\) | ||||
0.143459 | + | 0.989656i | \(0.454178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.1748 | 0.924660 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.6570 | 1.08199 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.4530 | −1.45236 | −0.726182 | − | 0.687502i | \(-0.758707\pi\) | ||||
−0.726182 | + | 0.687502i | \(0.758707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.50796 | −0.0971362 | −0.0485681 | − | 0.998820i | \(-0.515466\pi\) | ||||
−0.0485681 | + | 0.998820i | \(0.515466\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.52040 | −0.0975337 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.0532 | 1.34504 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.35780 | 0.213652 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −28.1108 | −1.78145 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5663 | −0.666939 | −0.333469 | − | 0.942761i | \(-0.608219\pi\) | ||||
−0.333469 | + | 0.942761i | \(0.608219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.48874 | −0.0935961 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.9583 | −0.999347 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.34538 | −0.395814 | −0.197907 | − | 0.980221i | \(-0.563414\pi\) | ||||
−0.197907 | + | 0.980221i | \(0.563414\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.29413 | 0.328961 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.625029 | 0.0386883 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.1599 | 1.55142 | 0.775711 | − | 0.631088i | \(-0.217391\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.4227 | 0.701689 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.9002 | −1.27907 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.8199 | 1.02553 | 0.512765 | − | 0.858529i | \(-0.328621\pi\) | ||||
0.512765 | + | 0.858529i | \(0.328621\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.7714 | −0.897298 | −0.448649 | − | 0.893708i | \(-0.648095\pi\) | ||||
−0.448649 | + | 0.893708i | \(0.648095\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.92698 | −0.116626 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.83695 | −0.110772 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3951 | −0.985086 | −0.492543 | − | 0.870288i | \(-0.663933\pi\) | ||||
−0.492543 | + | 0.870288i | \(0.663933\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.170023 | −0.0101790 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.11245 | 0.126018 | 0.0630092 | − | 0.998013i | \(-0.479930\pi\) | ||||
0.0630092 | + | 0.998013i | \(0.479930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.9049 | 1.36156 | 0.680778 | − | 0.732490i | \(-0.261642\pi\) | ||||
0.680778 | + | 0.732490i | \(0.261642\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.3738 | 0.910668 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0820111 | 0.00484096 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.75999 | −0.574117 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.5531 | −0.853117 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.4136 | −1.71836 | −0.859181 | − | 0.511672i | \(-0.829026\pi\) | ||||
−0.859181 | + | 0.511672i | \(0.829026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.8672 | −0.982048 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.50471 | 0.0873123 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.48710 | −0.375159 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.49255 | 0.374224 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.41514 | −0.483437 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 39.2977 | 2.25018 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.96347 | 0.511572 | 0.255786 | − | 0.966733i | \(-0.417666\pi\) | ||||
0.255786 | + | 0.966733i | \(0.417666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.55448 | −0.145319 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.27774 | −0.242568 | −0.121284 | − | 0.992618i | \(-0.538701\pi\) | ||||
−0.121284 | + | 0.992618i | \(0.538701\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.98402 | 0.112143 | 0.0560716 | − | 0.998427i | \(-0.482142\pi\) | ||||
0.0560716 | + | 0.998427i | \(0.482142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.410597 | −0.0231345 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.1918 | 1.19025 | 0.595126 | − | 0.803632i | \(-0.297102\pi\) | ||||
0.595126 | + | 0.803632i | \(0.297102\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.26890 | −0.0710449 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.2025 | −0.569448 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.97486 | −0.388091 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.00443 | −0.444006 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.3021 | 0.680305 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.55540 | −0.196015 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.2369 | −1.27721 | −0.638607 | − | 0.769533i | \(-0.720489\pi\) | ||||
−0.638607 | + | 0.769533i | \(0.720489\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.924363 | 0.0506548 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.4714 | 0.736019 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.4801 | −1.17010 | −0.585049 | − | 0.810998i | \(-0.698925\pi\) | ||||
−0.585049 | + | 0.810998i | \(0.698925\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −33.1514 | −1.80054 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.345172 | 0.0186921 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.1512 | −0.602110 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −29.7015 | −1.59908 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.3974 | 1.73919 | 0.869593 | − | 0.493770i | \(-0.164381\pi\) | ||||
0.869593 | + | 0.493770i | \(0.164381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.97027 | −0.480167 | −0.240084 | − | 0.970752i | \(-0.577175\pi\) | ||||
−0.240084 | + | 0.970752i | \(0.577175\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.55672 | 0.349972 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.98482 | 0.318540 | 0.159270 | − | 0.987235i | \(-0.449086\pi\) | ||||
0.159270 | + | 0.987235i | \(0.449086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.26757 | 0.491872 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.00275 | 0.211848 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.69118 | 0.0892571 | 0.0446285 | − | 0.999004i | \(-0.485790\pi\) | ||||
0.0446285 | + | 0.999004i | \(0.485790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2806 | −0.646347 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.3552 | −1.01589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 42.9736 | 2.24934 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1243 | 0.789481 | 0.394741 | − | 0.918793i | \(-0.370834\pi\) | ||||
0.394741 | + | 0.918793i | \(0.370834\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.0143192 | 0.000745430 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.86510 | −0.148749 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.18552 | 0.0613839 | 0.0306919 | − | 0.999529i | \(-0.490229\pi\) | ||||
0.0306919 | + | 0.999529i | \(0.490229\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.99445 | −0.361192 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.52918 | −0.284767 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.7848 | −1.47857 | −0.739287 | − | 0.673390i | \(-0.764837\pi\) | ||||
−0.739287 | + | 0.673390i | \(0.764837\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.4541 | −0.996664 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.3351 | −1.34566 | −0.672829 | − | 0.739798i | \(-0.734921\pi\) | ||||
−0.672829 | + | 0.739798i | \(0.734921\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.833574 | 0.0424829 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.13361 | 0.0576245 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.72684 | −0.0875544 | −0.0437772 | − | 0.999041i | \(-0.513939\pi\) | ||||
−0.0437772 | + | 0.999041i | \(0.513939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.4751 | 0.681465 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.6161 | 1.64527 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −31.3976 | −1.57978 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.7181 | −0.839057 | −0.419528 | − | 0.907742i | \(-0.637804\pi\) | ||||
−0.419528 | + | 0.907742i | \(0.637804\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.85616 | −0.193049 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.2971 | 1.11346 | 0.556731 | − | 0.830693i | \(-0.312055\pi\) | ||||
0.556731 | + | 0.830693i | \(0.312055\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.50407 | 0.0749230 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 31.4890 | 1.56470 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.87659 | −0.0930194 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.7115 | −1.86471 | −0.932356 | − | 0.361541i | \(-0.882251\pi\) | ||||
−0.932356 | + | 0.361541i | \(0.882251\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.4198 | −1.15521 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.23074 | 0.208181 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 52.9873 | 2.60104 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.5336 | −1.49524 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.6033 | −1.73934 | −0.869668 | − | 0.493638i | \(-0.835667\pi\) | ||||
−0.869668 | + | 0.493638i | \(0.835667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4505 | 0.899223 | 0.449611 | − | 0.893224i | \(-0.351562\pi\) | ||||
0.449611 | + | 0.893224i | \(0.351562\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.620777 | −0.0301832 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.6269 | 0.806523 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.85687 | −0.477008 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.683052 | 0.0329781 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.3236 | −0.738114 | −0.369057 | − | 0.929407i | \(-0.620319\pi\) | ||||
−0.369057 | + | 0.929407i | \(0.620319\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.2338 | −1.21266 | −0.606329 | − | 0.795214i | \(-0.707359\pi\) | ||||
−0.606329 | + | 0.795214i | \(0.707359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.3156 | −1.21379 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.9816 | −0.620994 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0447 | −0.479406 | −0.239703 | − | 0.970846i | \(-0.577050\pi\) | ||||
−0.239703 | + | 0.970846i | \(0.577050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.922016 | −0.0439055 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.8947 | 1.27780 | 0.638902 | − | 0.769288i | \(-0.279389\pi\) | ||||
0.638902 | + | 0.769288i | \(0.279389\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.3957 | 1.86754 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.91332 | −0.137795 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.2235 | 1.28476 | 0.642379 | − | 0.766387i | \(-0.277948\pi\) | ||||
0.642379 | + | 0.766387i | \(0.277948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0290702 | −0.00136886 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −29.1454 | −1.36937 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.63226 | 0.170283 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.9248 | −0.744929 | −0.372465 | − | 0.928046i | \(-0.621487\pi\) | ||||
−0.372465 | + | 0.928046i | \(0.621487\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.6197 | −0.635713 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.5077 | 1.42088 | 0.710442 | − | 0.703756i | \(-0.248495\pi\) | ||||
0.710442 | + | 0.703756i | \(0.248495\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.96729 | −0.323797 | −0.161899 | − | 0.986807i | \(-0.551762\pi\) | ||||
−0.161899 | + | 0.986807i | \(0.551762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.88646 | 0.319352 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.5795 | −0.674660 | −0.337330 | − | 0.941386i | \(-0.609524\pi\) | ||||
−0.337330 | + | 0.941386i | \(0.609524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.37897 | −0.156026 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.4332 | 1.49444 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.30139 | −0.105818 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0180 | −0.734955 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.500250 | −0.0229049 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.8995 | −0.543702 | −0.271851 | − | 0.962339i | \(-0.587636\pi\) | ||||
−0.271851 | + | 0.962339i | \(0.587636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.17717 | −0.372847 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.44992 | 0.338983 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.4318 | 1.24561 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.1105 | 0.820663 | 0.410331 | − | 0.911936i | \(-0.365413\pi\) | ||||
0.410331 | + | 0.911936i | \(0.365413\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.0484 | 0.816178 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.41825 | 0.0640049 | 0.0320024 | − | 0.999488i | \(-0.489812\pi\) | ||||
0.0320024 | + | 0.999488i | \(0.489812\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.4853 | 0.517271 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.145543 | 0.00654168 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.32455 | −0.104270 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.0810 | −0.675118 | −0.337559 | − | 0.941304i | \(-0.609601\pi\) | ||||
−0.337559 | + | 0.941304i | \(0.609601\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.07795 | −0.316219 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.6085 | 1.27559 | 0.637794 | − | 0.770207i | \(-0.279847\pi\) | ||||
0.637794 | + | 0.770207i | \(0.279847\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.8621 | 0.705854 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.0833 | −0.891929 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.5883 | 0.956887 | 0.478443 | − | 0.878118i | \(-0.341201\pi\) | ||||
0.478443 | + | 0.878118i | \(0.341201\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.7789 | −0.476830 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.1209 | 0.579301 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.81506 | 0.212177 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.26027 | 0.0554267 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.6768 | −0.907612 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3717 | 1.28680 | 0.643398 | − | 0.765532i | \(-0.277524\pi\) | ||||
0.643398 | + | 0.765532i | \(0.277524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.73648 | 0.250839 | 0.125419 | − | 0.992104i | \(-0.459972\pi\) | ||||
0.125419 | + | 0.992104i | \(0.459972\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.19244 | 0.401191 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.12427 | −0.136095 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.07981 | 0.0904264 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.738693 | 0.0320565 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.126672 | −0.00548678 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.2312 | 0.831435 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.4633 | 0.926208 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.87183 | 0.0806255 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.9411 | 1.54523 | 0.772614 | − | 0.634876i | \(-0.218949\pi\) | ||||
0.772614 | + | 0.634876i | \(0.218949\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.11187 | −0.391028 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.1887 | −0.993295 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.0642 | 0.473073 | 0.236536 | − | 0.971623i | \(-0.423988\pi\) | ||||
0.236536 | + | 0.971623i | \(0.423988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.72102 | −0.0734515 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.0647 | −0.471370 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.87533 | 0.334893 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −37.4396 | −1.58922 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.5527 | 1.08270 | 0.541352 | − | 0.840796i | \(-0.317913\pi\) | ||||
0.541352 | + | 0.840796i | \(0.317913\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.0282 | −0.424148 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.41884 | −0.0599036 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.0701 | −1.39374 | −0.696869 | − | 0.717198i | \(-0.745424\pi\) | ||||
−0.696869 | + | 0.717198i | \(0.745424\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 62.4887 | 2.62892 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.89827 | −0.331696 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.7223 | 1.37179 | 0.685895 | − | 0.727701i | \(-0.259411\pi\) | ||||
0.685895 | + | 0.727701i | \(0.259411\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.8069 | 0.954437 | 0.477219 | − | 0.878785i | \(-0.341645\pi\) | ||||
0.477219 | + | 0.878785i | \(0.341645\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.4167 | 0.978247 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.9459 | 1.29053 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.2941 | 0.803226 | 0.401613 | − | 0.915810i | \(-0.368450\pi\) | ||||
0.401613 | + | 0.915810i | \(0.368450\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.7011 | 1.10966 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.2906 | −0.551386 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.01558 | 0.0420612 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.634198 | 0.0262208 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.86822 | 0.159658 | 0.0798292 | − | 0.996809i | \(-0.474563\pi\) | ||||
0.0798292 | + | 0.996809i | \(0.474563\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00985 | 0.124019 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 49.0376 | 2.01714 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.8742 | 0.734007 | 0.367004 | − | 0.930219i | \(-0.380384\pi\) | ||||
0.367004 | + | 0.930219i | \(0.380384\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.54498 | −0.309314 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.25062 | −0.296748 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.5041 | −0.429184 | −0.214592 | − | 0.976704i | \(-0.568842\pi\) | ||||
−0.214592 | + | 0.976704i | \(0.568842\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9813 | −0.692682 | −0.346341 | − | 0.938109i | \(-0.612576\pi\) | ||||
−0.346341 | + | 0.938109i | \(0.612576\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.589972 | −0.0240255 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.4836 | 1.48327 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0223 | −0.569149 | −0.284574 | − | 0.958654i | \(-0.591852\pi\) | ||||
−0.284574 | + | 0.958654i | \(0.591852\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.34982 | 0.257308 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.49157 | 0.222165 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.9887 | −1.29201 | −0.646005 | − | 0.763333i | \(-0.723561\pi\) | ||||
−0.646005 | + | 0.763333i | \(0.723561\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.579975 | −0.0233868 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.4234 | 0.902734 | 0.451367 | − | 0.892338i | \(-0.350937\pi\) | ||||
0.451367 | + | 0.892338i | \(0.350937\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.9749 | −1.04402 | −0.522009 | − | 0.852940i | \(-0.674817\pi\) | ||||
−0.522009 | + | 0.852940i | \(0.674817\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.3489 | −1.01722 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.88147 | −0.395893 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.7125 | −0.708500 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.36688 | 0.0545880 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9857 | 0.677265 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.28039 | 0.0509713 | 0.0254857 | − | 0.999675i | \(-0.491887\pi\) | ||||
0.0254857 | + | 0.999675i | \(0.491887\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.8339 | 0.629340 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.6699 | 1.45520 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.15642 | 0.323169 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.405869 | −0.0160559 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.02127 | 0.0403378 | 0.0201689 | − | 0.999797i | \(-0.493580\pi\) | ||||
0.0201689 | + | 0.999797i | \(0.493580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.3204 | 1.31403 | 0.657014 | − | 0.753878i | \(-0.271819\pi\) | ||||
0.657014 | + | 0.753878i | \(0.271819\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −45.9147 | −1.80789 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.19602 | 0.322219 | 0.161109 | − | 0.986937i | \(-0.448493\pi\) | ||||
0.161109 | + | 0.986937i | \(0.448493\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.49966 | −0.0588667 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.72730 | −0.0676983 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.4705 | −0.605408 | −0.302704 | − | 0.953085i | \(-0.597889\pi\) | ||||
−0.302704 | + | 0.953085i | \(0.597889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −61.4796 | −2.40221 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.88201 | −0.0734241 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.9045 | 1.00909 | 0.504547 | − | 0.863384i | \(-0.331659\pi\) | ||||
0.504547 | + | 0.863384i | \(0.331659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.8453 | −1.19974 | −0.599872 | − | 0.800096i | \(-0.704782\pi\) | ||||
−0.599872 | + | 0.800096i | \(0.704782\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.18255 | −0.240110 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.26865 | 0.281866 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.3764 | 0.827697 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.3177 | 0.553554 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.49394 | 0.134882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.75901 | −0.260541 | −0.130270 | − | 0.991479i | \(-0.541585\pi\) | ||||
−0.130270 | + | 0.991479i | \(0.541585\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −31.2780 | −1.20389 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.4418 | −0.747208 | −0.373604 | − | 0.927588i | \(-0.621878\pi\) | ||||
−0.373604 | + | 0.927588i | \(0.621878\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.88060 | −0.264053 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.2147 | −0.736307 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.82651 | 0.108153 | 0.0540767 | − | 0.998537i | \(-0.482778\pi\) | ||||
0.0540767 | + | 0.998537i | \(0.482778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.1451 | 1.68670 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.21693 | −0.275343 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.42536 | 0.168593 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.0757 | −0.497421 | −0.248711 | − | 0.968578i | \(-0.580007\pi\) | ||||
−0.248711 | + | 0.968578i | \(0.580007\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0365060 | −0.00138675 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 57.5542 | 2.18315 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.263125 | 0.00996656 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.76861 | 0.293836 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0613 | 0.984321 | 0.492160 | − | 0.870505i | \(-0.336207\pi\) | ||||
0.492160 | + | 0.870505i | \(0.336207\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.3637 | −0.617167 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.1435 | 0.946957 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.97862 | −0.149632 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.89091 | −0.0710144 | −0.0355072 | − | 0.999369i | \(-0.511305\pi\) | ||||
−0.0355072 | + | 0.999369i | \(0.511305\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.37504 | 0.0515681 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.81488 | −0.217769 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.28752 | −0.0481504 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.8276 | −1.48739 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.8096 | 1.22359 | 0.611796 | − | 0.791016i | \(-0.290448\pi\) | ||||
0.611796 | + | 0.791016i | \(0.290448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.20774 | −0.0449786 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.67485 | −0.0994786 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.3763 | 0.979591 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.1519 | −1.74877 | −0.874384 | − | 0.485235i | \(-0.838734\pi\) | ||||
−0.874384 | + | 0.485235i | \(0.838734\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.5566 | 0.946542 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.8307 | 0.770452 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.47504 | 0.349968 | 0.174984 | − | 0.984571i | \(-0.444013\pi\) | ||||
0.174984 | + | 0.984571i | \(0.444013\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 37.3446 | 1.37748 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.19773 | 0.0441190 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.5448 | −0.792540 | −0.396270 | − | 0.918134i | \(-0.629695\pi\) | ||||
−0.396270 | + | 0.918134i | \(0.629695\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.95612 | 0.218804 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.8284 | 0.947550 | 0.473775 | − | 0.880646i | \(-0.342891\pi\) | ||||
0.473775 | + | 0.880646i | \(0.342891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.49144 | 0.201191 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.32055 | −0.0849046 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.82367 | −0.176253 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.7427 | −0.683021 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 54.9375 | 1.99938 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.222073 | 0.00807139 | 0.00403570 | − | 0.999992i | \(-0.498715\pi\) | ||||
0.00403570 | + | 0.999992i | \(0.498715\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.64075 | −0.0958531 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.5022 | −1.64945 | −0.824726 | − | 0.565532i | \(-0.808671\pi\) | ||||
−0.824726 | + | 0.565532i | \(0.808671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.81633 | 0.210565 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.31736 | −0.0476293 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.53469 | −0.235954 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.1900 | 0.980496 | 0.490248 | − | 0.871583i | \(-0.336906\pi\) | ||||
0.490248 | + | 0.871583i | \(0.336906\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.2555 | −0.405359 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.8941 | 1.29102 | 0.645511 | − | 0.763751i | \(-0.276645\pi\) | ||||
0.645511 | + | 0.763751i | \(0.276645\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.17498 | −0.257733 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.39083 | 0.336894 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.253488 | −0.00908216 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.823975 | 0.0294841 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.6058 | −0.772127 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −61.1348 | −2.18200 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.3722 | −1.47476 | −0.737380 | − | 0.675478i | \(-0.763937\pi\) | ||||
−0.737380 | + | 0.675478i | \(0.763937\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 44.6290 | 1.58883 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.6738 | −0.557295 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.2247 | 0.540644 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.2617 | 0.718610 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.9129 | 1.13041 | 0.565207 | − | 0.824949i | \(-0.308796\pi\) | ||||
0.565207 | + | 0.824949i | \(0.308796\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.4072 | −0.403556 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.72532 | −0.0609611 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.82076 | 0.134832 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.0427 | −0.494940 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.8355 | 1.05026 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.8494 | −0.381445 | −0.190723 | − | 0.981644i | \(-0.561083\pi\) | ||||
−0.190723 | + | 0.981644i | \(0.561083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.3176 | −0.678331 | −0.339166 | − | 0.940727i | \(-0.610145\pi\) | ||||
−0.339166 | + | 0.940727i | \(0.610145\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.2017 | −0.918935 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34.0203 | −1.19168 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.0678 | −0.702085 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.159073 | −0.00555847 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.499718 | 0.0174403 | 0.00872013 | − | 0.999962i | \(-0.497224\pi\) | ||||
0.00872013 | + | 0.999962i | \(0.497224\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.3239 | −0.464440 | −0.232220 | − | 0.972663i | \(-0.574599\pi\) | ||||
−0.232220 | + | 0.972663i | \(0.574599\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.25842 | −0.113444 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.7089 | −1.76332 | −0.881661 | − | 0.471883i | \(-0.843574\pi\) | ||||
−0.881661 | + | 0.471883i | \(0.843574\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.2587 | −1.74556 | −0.872778 | − | 0.488117i | \(-0.837684\pi\) | ||||
−0.872778 | + | 0.488117i | \(0.837684\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.0819 | −1.00884 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.9426 | −0.587027 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.3415 | 0.461703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.87728 | 0.203149 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.50592 | −0.293657 | −0.146828 | − | 0.989162i | \(-0.546907\pi\) | ||||
−0.146828 | + | 0.989162i | \(0.546907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7802 | −0.371730 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.74711 | 0.129057 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.8559 | 1.30228 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.15103 | −0.314433 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.6291 | 1.39439 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.6138 | 1.08371 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.0777 | −0.379295 | −0.189647 | − | 0.981852i | \(-0.560734\pi\) | ||||
−0.189647 | + | 0.981852i | \(0.560734\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.26912 | 0.0434029 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.07021 | 0.309832 | 0.154916 | − | 0.987928i | \(-0.450489\pi\) | ||||
0.154916 | + | 0.987928i | \(0.450489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.8995 | −1.39547 | −0.697737 | − | 0.716354i | \(-0.745810\pi\) | ||||
−0.697737 | + | 0.716354i | \(0.745810\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.145473 | 0.00495770 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.0328 | −0.477682 | −0.238841 | − | 0.971059i | \(-0.576767\pi\) | ||||
−0.238841 | + | 0.971059i | \(0.576767\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.9747 | 1.32518 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.3124 | −0.587961 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.79154 | −0.0946967 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.21906 | 0.176841 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.20136 | −0.0406600 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.30693 | −0.111795 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.8320 | −0.838518 | −0.419259 | − | 0.907867i | \(-0.637710\pi\) | ||||
−0.419259 | + | 0.907867i | \(0.637710\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −52.1744 | −1.75980 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.31728 | 0.111762 | 0.0558811 | − | 0.998437i | \(-0.482203\pi\) | ||||
0.0558811 | + | 0.998437i | \(0.482203\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.25743 | −0.176927 | −0.0884633 | − | 0.996079i | \(-0.528196\pi\) | ||||
−0.0884633 | + | 0.996079i | \(0.528196\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29.9194 | −1.00573 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.16812 | −0.240682 | −0.120341 | − | 0.992733i | \(-0.538399\pi\) | ||||
−0.120341 | + | 0.992733i | \(0.538399\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.19777 | −0.308483 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.79968 | 0.0937926 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.9894 | 0.367746 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.4571 | −1.35233 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.5069 | −0.384206 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.95623 | −0.165299 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.19241 | −0.306243 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.5166 | 0.383248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.1754 | 0.570929 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.8851 | 1.39077 | 0.695386 | − | 0.718636i | \(-0.255233\pi\) | ||||
0.695386 | + | 0.718636i | \(0.255233\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.694673 | −0.0230408 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.7780 | 1.58296 | 0.791478 | − | 0.611197i | \(-0.209312\pi\) | ||||
0.791478 | + | 0.611197i | \(0.209312\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.71107 | 0.155914 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 69.7069 | 2.30444 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.4207 | 0.509236 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.4339 | 1.56470 | 0.782350 | − | 0.622840i | \(-0.214021\pi\) | ||||
0.782350 | + | 0.622840i | \(0.214021\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.8996 | 0.523909 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.59043 | 0.118181 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.0082 | 1.28258 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.210873 | −0.00692598 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.0929 | 0.527991 | 0.263996 | − | 0.964524i | \(-0.414960\pi\) | ||||
0.263996 | + | 0.964524i | \(0.414960\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3221 | 0.534936 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.58793 | −0.248418 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.67444 | 0.0874637 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.8755 | 1.66203 | 0.831015 | − | 0.556251i | \(-0.187761\pi\) | ||||
0.831015 | + | 0.556251i | \(0.187761\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.51929 | 0.114848 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.6160 | 1.32404 | 0.662021 | − | 0.749485i | \(-0.269699\pi\) | ||||
0.662021 | + | 0.749485i | \(0.269699\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.489727 | 0.0159477 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.1934 | 0.461711 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.3798 | 1.76711 | 0.883553 | − | 0.468332i | \(-0.155145\pi\) | ||||
0.883553 | + | 0.468332i | \(0.155145\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.6488 | 0.540442 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37.5905 | 1.21895 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.3359 | −1.30661 | −0.653304 | − | 0.757096i | \(-0.726618\pi\) | ||||
−0.653304 | + | 0.757096i | \(0.726618\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44.1392 | −1.42831 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.25080 | −0.0727581 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.0727 | −0.357557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6518 | −0.956509 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.842219 | −0.0271401 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −50.3301 | −1.62018 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.8958 | −1.28296 | −0.641481 | − | 0.767139i | \(-0.721680\pi\) | ||||
−0.641481 | + | 0.767139i | \(0.721680\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.3721 | −0.397450 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.8777 | −1.15137 | −0.575684 | − | 0.817672i | \(-0.695264\pi\) | ||||
−0.575684 | + | 0.817672i | \(0.695264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.4361 | −0.462799 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.1984 | −0.454713 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.6239 | −0.339890 | −0.169945 | − | 0.985454i | \(-0.554359\pi\) | ||||
−0.169945 | + | 0.985454i | \(0.554359\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.50265 | 0.111945 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.01554 | 0.0324237 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.7017 | 1.33008 | 0.665039 | − | 0.746809i | \(-0.268415\pi\) | ||||
0.665039 | + | 0.746809i | \(0.268415\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −92.4333 | −2.94517 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.30663 | −0.200742 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.7701 | 1.23282 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.2323 | −1.37332 | −0.686660 | − | 0.726979i | \(-0.740924\pi\) | ||||
−0.686660 | + | 0.726979i | \(0.740924\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −41.2180 | −1.30801 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.6670 | 0.433274 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.4982 | 0.744195 | 0.372098 | − | 0.928194i | \(-0.378639\pi\) | ||||
0.372098 | + | 0.928194i | \(0.378639\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.9530 | −1.01095 |
(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 | 6008.2.a.b.1.37 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.37 | ✓ | 44 | 1.1 | even | 1 | trivial |