Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.81149 | −1.04586 | −0.522931 | − | 0.852375i | \(-0.675161\pi\) | ||||
−0.522931 | + | 0.852375i | \(0.675161\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.26479 | −0.565633 | −0.282816 | − | 0.959174i | \(-0.591269\pi\) | ||||
−0.282816 | + | 0.959174i | \(0.591269\pi\) | |||||||
\(6\) | 1.81149 | 0.739536 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.281479 | 0.0938262 | ||||||||
\(10\) | 1.26479 | 0.399963 | ||||||||
\(11\) | −3.69998 | −1.11559 | −0.557793 | − | 0.829980i | \(-0.688352\pi\) | ||||
−0.557793 | + | 0.829980i | \(0.688352\pi\) | |||||||
\(12\) | −1.81149 | −0.522931 | ||||||||
\(13\) | −1.60916 | −0.446300 | −0.223150 | − | 0.974784i | \(-0.571634\pi\) | ||||
−0.223150 | + | 0.974784i | \(0.571634\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.29115 | 0.591574 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.22557 | 0.297244 | 0.148622 | − | 0.988894i | \(-0.452516\pi\) | ||||
0.148622 | + | 0.988894i | \(0.452516\pi\) | |||||||
\(18\) | −0.281479 | −0.0663452 | ||||||||
\(19\) | −8.48264 | −1.94605 | −0.973026 | − | 0.230696i | \(-0.925900\pi\) | ||||
−0.973026 | + | 0.230696i | \(0.925900\pi\) | |||||||
\(20\) | −1.26479 | −0.282816 | ||||||||
\(21\) | −1.81149 | −0.395298 | ||||||||
\(22\) | 3.69998 | 0.788838 | ||||||||
\(23\) | 2.94922 | 0.614954 | 0.307477 | − | 0.951555i | \(-0.400515\pi\) | ||||
0.307477 | + | 0.951555i | \(0.400515\pi\) | |||||||
\(24\) | 1.81149 | 0.369768 | ||||||||
\(25\) | −3.40030 | −0.680060 | ||||||||
\(26\) | 1.60916 | 0.315582 | ||||||||
\(27\) | 4.92456 | 0.947732 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −5.38169 | −0.999355 | −0.499677 | − | 0.866212i | \(-0.666548\pi\) | ||||
−0.499677 | + | 0.866212i | \(0.666548\pi\) | |||||||
\(30\) | −2.29115 | −0.418306 | ||||||||
\(31\) | 1.88362 | 0.338309 | 0.169154 | − | 0.985590i | \(-0.445896\pi\) | ||||
0.169154 | + | 0.985590i | \(0.445896\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.70245 | 1.16675 | ||||||||
\(34\) | −1.22557 | −0.210184 | ||||||||
\(35\) | −1.26479 | −0.213789 | ||||||||
\(36\) | 0.281479 | 0.0469131 | ||||||||
\(37\) | −5.44694 | −0.895471 | −0.447735 | − | 0.894166i | \(-0.647769\pi\) | ||||
−0.447735 | + | 0.894166i | \(0.647769\pi\) | |||||||
\(38\) | 8.48264 | 1.37607 | ||||||||
\(39\) | 2.91497 | 0.466768 | ||||||||
\(40\) | 1.26479 | 0.199981 | ||||||||
\(41\) | −3.98088 | −0.621709 | −0.310854 | − | 0.950458i | \(-0.600615\pi\) | ||||
−0.310854 | + | 0.950458i | \(0.600615\pi\) | |||||||
\(42\) | 1.81149 | 0.279518 | ||||||||
\(43\) | −12.2128 | −1.86244 | −0.931220 | − | 0.364457i | \(-0.881255\pi\) | ||||
−0.931220 | + | 0.364457i | \(0.881255\pi\) | |||||||
\(44\) | −3.69998 | −0.557793 | ||||||||
\(45\) | −0.356012 | −0.0530712 | ||||||||
\(46\) | −2.94922 | −0.434838 | ||||||||
\(47\) | 0.841801 | 0.122789 | 0.0613946 | − | 0.998114i | \(-0.480445\pi\) | ||||
0.0613946 | + | 0.998114i | \(0.480445\pi\) | |||||||
\(48\) | −1.81149 | −0.261465 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.40030 | 0.480875 | ||||||||
\(51\) | −2.22010 | −0.310876 | ||||||||
\(52\) | −1.60916 | −0.223150 | ||||||||
\(53\) | 1.85550 | 0.254873 | 0.127436 | − | 0.991847i | \(-0.459325\pi\) | ||||
0.127436 | + | 0.991847i | \(0.459325\pi\) | |||||||
\(54\) | −4.92456 | −0.670148 | ||||||||
\(55\) | 4.67971 | 0.631012 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 15.3662 | 2.03530 | ||||||||
\(58\) | 5.38169 | 0.706651 | ||||||||
\(59\) | −9.72023 | −1.26547 | −0.632733 | − | 0.774370i | \(-0.718067\pi\) | ||||
−0.632733 | + | 0.774370i | \(0.718067\pi\) | |||||||
\(60\) | 2.29115 | 0.295787 | ||||||||
\(61\) | −5.36202 | −0.686536 | −0.343268 | − | 0.939237i | \(-0.611534\pi\) | ||||
−0.343268 | + | 0.939237i | \(0.611534\pi\) | |||||||
\(62\) | −1.88362 | −0.239220 | ||||||||
\(63\) | 0.281479 | 0.0354630 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.03525 | 0.252442 | ||||||||
\(66\) | −6.70245 | −0.825015 | ||||||||
\(67\) | −1.54318 | −0.188529 | −0.0942646 | − | 0.995547i | \(-0.530050\pi\) | ||||
−0.0942646 | + | 0.995547i | \(0.530050\pi\) | |||||||
\(68\) | 1.22557 | 0.148622 | ||||||||
\(69\) | −5.34246 | −0.643157 | ||||||||
\(70\) | 1.26479 | 0.151172 | ||||||||
\(71\) | 0.705663 | 0.0837468 | 0.0418734 | − | 0.999123i | \(-0.486667\pi\) | ||||
0.0418734 | + | 0.999123i | \(0.486667\pi\) | |||||||
\(72\) | −0.281479 | −0.0331726 | ||||||||
\(73\) | 15.3830 | 1.80044 | 0.900220 | − | 0.435435i | \(-0.143405\pi\) | ||||
0.900220 | + | 0.435435i | \(0.143405\pi\) | |||||||
\(74\) | 5.44694 | 0.633193 | ||||||||
\(75\) | 6.15959 | 0.711248 | ||||||||
\(76\) | −8.48264 | −0.973026 | ||||||||
\(77\) | −3.69998 | −0.421652 | ||||||||
\(78\) | −2.91497 | −0.330055 | ||||||||
\(79\) | 3.15953 | 0.355475 | 0.177738 | − | 0.984078i | \(-0.443122\pi\) | ||||
0.177738 | + | 0.984078i | \(0.443122\pi\) | |||||||
\(80\) | −1.26479 | −0.141408 | ||||||||
\(81\) | −9.76521 | −1.08502 | ||||||||
\(82\) | 3.98088 | 0.439615 | ||||||||
\(83\) | −1.30049 | −0.142747 | −0.0713735 | − | 0.997450i | \(-0.522738\pi\) | ||||
−0.0713735 | + | 0.997450i | \(0.522738\pi\) | |||||||
\(84\) | −1.81149 | −0.197649 | ||||||||
\(85\) | −1.55009 | −0.168131 | ||||||||
\(86\) | 12.2128 | 1.31694 | ||||||||
\(87\) | 9.74885 | 1.04519 | ||||||||
\(88\) | 3.69998 | 0.394419 | ||||||||
\(89\) | −9.94355 | −1.05401 | −0.527007 | − | 0.849861i | \(-0.676686\pi\) | ||||
−0.527007 | + | 0.849861i | \(0.676686\pi\) | |||||||
\(90\) | 0.356012 | 0.0375270 | ||||||||
\(91\) | −1.60916 | −0.168686 | ||||||||
\(92\) | 2.94922 | 0.307477 | ||||||||
\(93\) | −3.41215 | −0.353824 | ||||||||
\(94\) | −0.841801 | −0.0868251 | ||||||||
\(95\) | 10.7288 | 1.10075 | ||||||||
\(96\) | 1.81149 | 0.184884 | ||||||||
\(97\) | −3.24220 | −0.329196 | −0.164598 | − | 0.986361i | \(-0.552633\pi\) | ||||
−0.164598 | + | 0.986361i | \(0.552633\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −1.04146 | −0.104671 | ||||||||
\(100\) | −3.40030 | −0.340030 | ||||||||
\(101\) | 1.22958 | 0.122348 | 0.0611740 | − | 0.998127i | \(-0.480516\pi\) | ||||
0.0611740 | + | 0.998127i | \(0.480516\pi\) | |||||||
\(102\) | 2.22010 | 0.219823 | ||||||||
\(103\) | −11.5690 | −1.13993 | −0.569963 | − | 0.821671i | \(-0.693042\pi\) | ||||
−0.569963 | + | 0.821671i | \(0.693042\pi\) | |||||||
\(104\) | 1.60916 | 0.157791 | ||||||||
\(105\) | 2.29115 | 0.223594 | ||||||||
\(106\) | −1.85550 | −0.180222 | ||||||||
\(107\) | 0.619641 | 0.0599029 | 0.0299515 | − | 0.999551i | \(-0.490465\pi\) | ||||
0.0299515 | + | 0.999551i | \(0.490465\pi\) | |||||||
\(108\) | 4.92456 | 0.473866 | ||||||||
\(109\) | −9.85275 | −0.943722 | −0.471861 | − | 0.881673i | \(-0.656418\pi\) | ||||
−0.471861 | + | 0.881673i | \(0.656418\pi\) | |||||||
\(110\) | −4.67971 | −0.446193 | ||||||||
\(111\) | 9.86704 | 0.936538 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −3.40332 | −0.320158 | −0.160079 | − | 0.987104i | \(-0.551175\pi\) | ||||
−0.160079 | + | 0.987104i | \(0.551175\pi\) | |||||||
\(114\) | −15.3662 | −1.43917 | ||||||||
\(115\) | −3.73015 | −0.347838 | ||||||||
\(116\) | −5.38169 | −0.499677 | ||||||||
\(117\) | −0.452944 | −0.0418747 | ||||||||
\(118\) | 9.72023 | 0.894820 | ||||||||
\(119\) | 1.22557 | 0.112348 | ||||||||
\(120\) | −2.29115 | −0.209153 | ||||||||
\(121\) | 2.68984 | 0.244530 | ||||||||
\(122\) | 5.36202 | 0.485454 | ||||||||
\(123\) | 7.21131 | 0.650221 | ||||||||
\(124\) | 1.88362 | 0.169154 | ||||||||
\(125\) | 10.6246 | 0.950297 | ||||||||
\(126\) | −0.281479 | −0.0250761 | ||||||||
\(127\) | 17.4409 | 1.54763 | 0.773817 | − | 0.633410i | \(-0.218345\pi\) | ||||
0.773817 | + | 0.633410i | \(0.218345\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 22.1234 | 1.94785 | ||||||||
\(130\) | −2.03525 | −0.178503 | ||||||||
\(131\) | 3.14802 | 0.275044 | 0.137522 | − | 0.990499i | \(-0.456086\pi\) | ||||
0.137522 | + | 0.990499i | \(0.456086\pi\) | |||||||
\(132\) | 6.70245 | 0.583374 | ||||||||
\(133\) | −8.48264 | −0.735538 | ||||||||
\(134\) | 1.54318 | 0.133310 | ||||||||
\(135\) | −6.22855 | −0.536068 | ||||||||
\(136\) | −1.22557 | −0.105092 | ||||||||
\(137\) | −2.98165 | −0.254740 | −0.127370 | − | 0.991855i | \(-0.540654\pi\) | ||||
−0.127370 | + | 0.991855i | \(0.540654\pi\) | |||||||
\(138\) | 5.34246 | 0.454781 | ||||||||
\(139\) | −6.82476 | −0.578868 | −0.289434 | − | 0.957198i | \(-0.593467\pi\) | ||||
−0.289434 | + | 0.957198i | \(0.593467\pi\) | |||||||
\(140\) | −1.26479 | −0.106895 | ||||||||
\(141\) | −1.52491 | −0.128421 | ||||||||
\(142\) | −0.705663 | −0.0592179 | ||||||||
\(143\) | 5.95385 | 0.497886 | ||||||||
\(144\) | 0.281479 | 0.0234566 | ||||||||
\(145\) | 6.80673 | 0.565268 | ||||||||
\(146\) | −15.3830 | −1.27310 | ||||||||
\(147\) | −1.81149 | −0.149409 | ||||||||
\(148\) | −5.44694 | −0.447735 | ||||||||
\(149\) | 1.70491 | 0.139672 | 0.0698358 | − | 0.997558i | \(-0.477752\pi\) | ||||
0.0698358 | + | 0.997558i | \(0.477752\pi\) | |||||||
\(150\) | −6.15959 | −0.502928 | ||||||||
\(151\) | 19.2929 | 1.57004 | 0.785019 | − | 0.619472i | \(-0.212653\pi\) | ||||
0.785019 | + | 0.619472i | \(0.212653\pi\) | |||||||
\(152\) | 8.48264 | 0.688033 | ||||||||
\(153\) | 0.344972 | 0.0278893 | ||||||||
\(154\) | 3.69998 | 0.298153 | ||||||||
\(155\) | −2.38239 | −0.191358 | ||||||||
\(156\) | 2.91497 | 0.233384 | ||||||||
\(157\) | −10.4163 | −0.831309 | −0.415655 | − | 0.909523i | \(-0.636447\pi\) | ||||
−0.415655 | + | 0.909523i | \(0.636447\pi\) | |||||||
\(158\) | −3.15953 | −0.251359 | ||||||||
\(159\) | −3.36122 | −0.266562 | ||||||||
\(160\) | 1.26479 | 0.0999907 | ||||||||
\(161\) | 2.94922 | 0.232431 | ||||||||
\(162\) | 9.76521 | 0.767227 | ||||||||
\(163\) | −6.39508 | −0.500901 | −0.250451 | − | 0.968129i | \(-0.580579\pi\) | ||||
−0.250451 | + | 0.968129i | \(0.580579\pi\) | |||||||
\(164\) | −3.98088 | −0.310854 | ||||||||
\(165\) | −8.47722 | −0.659951 | ||||||||
\(166\) | 1.30049 | 0.100937 | ||||||||
\(167\) | −20.1081 | −1.55601 | −0.778005 | − | 0.628258i | \(-0.783768\pi\) | ||||
−0.778005 | + | 0.628258i | \(0.783768\pi\) | |||||||
\(168\) | 1.81149 | 0.139759 | ||||||||
\(169\) | −10.4106 | −0.800816 | ||||||||
\(170\) | 1.55009 | 0.118887 | ||||||||
\(171\) | −2.38768 | −0.182591 | ||||||||
\(172\) | −12.2128 | −0.931220 | ||||||||
\(173\) | −15.9922 | −1.21586 | −0.607931 | − | 0.793990i | \(-0.708000\pi\) | ||||
−0.607931 | + | 0.793990i | \(0.708000\pi\) | |||||||
\(174\) | −9.74885 | −0.739059 | ||||||||
\(175\) | −3.40030 | −0.257038 | ||||||||
\(176\) | −3.69998 | −0.278896 | ||||||||
\(177\) | 17.6080 | 1.32350 | ||||||||
\(178\) | 9.94355 | 0.745301 | ||||||||
\(179\) | 15.7842 | 1.17977 | 0.589885 | − | 0.807487i | \(-0.299173\pi\) | ||||
0.589885 | + | 0.807487i | \(0.299173\pi\) | |||||||
\(180\) | −0.356012 | −0.0265356 | ||||||||
\(181\) | −17.5280 | −1.30285 | −0.651424 | − | 0.758714i | \(-0.725828\pi\) | ||||
−0.651424 | + | 0.758714i | \(0.725828\pi\) | |||||||
\(182\) | 1.60916 | 0.119279 | ||||||||
\(183\) | 9.71322 | 0.718022 | ||||||||
\(184\) | −2.94922 | −0.217419 | ||||||||
\(185\) | 6.88925 | 0.506508 | ||||||||
\(186\) | 3.41215 | 0.250191 | ||||||||
\(187\) | −4.53458 | −0.331601 | ||||||||
\(188\) | 0.841801 | 0.0613946 | ||||||||
\(189\) | 4.92456 | 0.358209 | ||||||||
\(190\) | −10.7288 | −0.778348 | ||||||||
\(191\) | −25.0315 | −1.81122 | −0.905608 | − | 0.424116i | \(-0.860585\pi\) | ||||
−0.905608 | + | 0.424116i | \(0.860585\pi\) | |||||||
\(192\) | −1.81149 | −0.130733 | ||||||||
\(193\) | 1.36102 | 0.0979682 | 0.0489841 | − | 0.998800i | \(-0.484402\pi\) | ||||
0.0489841 | + | 0.998800i | \(0.484402\pi\) | |||||||
\(194\) | 3.24220 | 0.232777 | ||||||||
\(195\) | −3.68683 | −0.264019 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −7.39068 | −0.526564 | −0.263282 | − | 0.964719i | \(-0.584805\pi\) | ||||
−0.263282 | + | 0.964719i | \(0.584805\pi\) | |||||||
\(198\) | 1.04146 | 0.0740137 | ||||||||
\(199\) | −15.7798 | −1.11860 | −0.559300 | − | 0.828965i | \(-0.688930\pi\) | ||||
−0.559300 | + | 0.828965i | \(0.688930\pi\) | |||||||
\(200\) | 3.40030 | 0.240437 | ||||||||
\(201\) | 2.79545 | 0.197176 | ||||||||
\(202\) | −1.22958 | −0.0865131 | ||||||||
\(203\) | −5.38169 | −0.377721 | ||||||||
\(204\) | −2.22010 | −0.155438 | ||||||||
\(205\) | 5.03499 | 0.351659 | ||||||||
\(206\) | 11.5690 | 0.806049 | ||||||||
\(207\) | 0.830142 | 0.0576988 | ||||||||
\(208\) | −1.60916 | −0.111575 | ||||||||
\(209\) | 31.3856 | 2.17099 | ||||||||
\(210\) | −2.29115 | −0.158105 | ||||||||
\(211\) | 3.39957 | 0.234036 | 0.117018 | − | 0.993130i | \(-0.462666\pi\) | ||||
0.117018 | + | 0.993130i | \(0.462666\pi\) | |||||||
\(212\) | 1.85550 | 0.127436 | ||||||||
\(213\) | −1.27830 | −0.0875875 | ||||||||
\(214\) | −0.619641 | −0.0423578 | ||||||||
\(215\) | 15.4467 | 1.05346 | ||||||||
\(216\) | −4.92456 | −0.335074 | ||||||||
\(217\) | 1.88362 | 0.127869 | ||||||||
\(218\) | 9.85275 | 0.667312 | ||||||||
\(219\) | −27.8660 | −1.88301 | ||||||||
\(220\) | 4.67971 | 0.315506 | ||||||||
\(221\) | −1.97214 | −0.132660 | ||||||||
\(222\) | −9.86704 | −0.662233 | ||||||||
\(223\) | −19.6925 | −1.31870 | −0.659352 | − | 0.751834i | \(-0.729169\pi\) | ||||
−0.659352 | + | 0.751834i | \(0.729169\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −0.957111 | −0.0638074 | ||||||||
\(226\) | 3.40332 | 0.226386 | ||||||||
\(227\) | 21.0869 | 1.39959 | 0.699794 | − | 0.714345i | \(-0.253275\pi\) | ||||
0.699794 | + | 0.714345i | \(0.253275\pi\) | |||||||
\(228\) | 15.3662 | 1.01765 | ||||||||
\(229\) | −15.9648 | −1.05498 | −0.527492 | − | 0.849560i | \(-0.676867\pi\) | ||||
−0.527492 | + | 0.849560i | \(0.676867\pi\) | |||||||
\(230\) | 3.73015 | 0.245959 | ||||||||
\(231\) | 6.70245 | 0.440989 | ||||||||
\(232\) | 5.38169 | 0.353325 | ||||||||
\(233\) | 16.9445 | 1.11007 | 0.555036 | − | 0.831826i | \(-0.312704\pi\) | ||||
0.555036 | + | 0.831826i | \(0.312704\pi\) | |||||||
\(234\) | 0.452944 | 0.0296099 | ||||||||
\(235\) | −1.06470 | −0.0694536 | ||||||||
\(236\) | −9.72023 | −0.632733 | ||||||||
\(237\) | −5.72345 | −0.371778 | ||||||||
\(238\) | −1.22557 | −0.0794419 | ||||||||
\(239\) | 10.9737 | 0.709828 | 0.354914 | − | 0.934899i | \(-0.384510\pi\) | ||||
0.354914 | + | 0.934899i | \(0.384510\pi\) | |||||||
\(240\) | 2.29115 | 0.147893 | ||||||||
\(241\) | 14.2772 | 0.919677 | 0.459839 | − | 0.888003i | \(-0.347907\pi\) | ||||
0.459839 | + | 0.888003i | \(0.347907\pi\) | |||||||
\(242\) | −2.68984 | −0.172909 | ||||||||
\(243\) | 2.91584 | 0.187051 | ||||||||
\(244\) | −5.36202 | −0.343268 | ||||||||
\(245\) | −1.26479 | −0.0808047 | ||||||||
\(246\) | −7.21131 | −0.459776 | ||||||||
\(247\) | 13.6499 | 0.868523 | ||||||||
\(248\) | −1.88362 | −0.119610 | ||||||||
\(249\) | 2.35581 | 0.149294 | ||||||||
\(250\) | −10.6246 | −0.671961 | ||||||||
\(251\) | −2.05705 | −0.129840 | −0.0649198 | − | 0.997890i | \(-0.520679\pi\) | ||||
−0.0649198 | + | 0.997890i | \(0.520679\pi\) | |||||||
\(252\) | 0.281479 | 0.0177315 | ||||||||
\(253\) | −10.9120 | −0.686034 | ||||||||
\(254\) | −17.4409 | −1.09434 | ||||||||
\(255\) | 2.80797 | 0.175842 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.6689 | −1.35167 | −0.675835 | − | 0.737053i | \(-0.736217\pi\) | ||||
−0.675835 | + | 0.737053i | \(0.736217\pi\) | |||||||
\(258\) | −22.1234 | −1.37734 | ||||||||
\(259\) | −5.44694 | −0.338456 | ||||||||
\(260\) | 2.03525 | 0.126221 | ||||||||
\(261\) | −1.51483 | −0.0937657 | ||||||||
\(262\) | −3.14802 | −0.194485 | ||||||||
\(263\) | 11.9621 | 0.737612 | 0.368806 | − | 0.929506i | \(-0.379767\pi\) | ||||
0.368806 | + | 0.929506i | \(0.379767\pi\) | |||||||
\(264\) | −6.70245 | −0.412508 | ||||||||
\(265\) | −2.34683 | −0.144164 | ||||||||
\(266\) | 8.48264 | 0.520104 | ||||||||
\(267\) | 18.0126 | 1.10235 | ||||||||
\(268\) | −1.54318 | −0.0942646 | ||||||||
\(269\) | 8.82775 | 0.538238 | 0.269119 | − | 0.963107i | \(-0.413268\pi\) | ||||
0.269119 | + | 0.963107i | \(0.413268\pi\) | |||||||
\(270\) | 6.22855 | 0.379058 | ||||||||
\(271\) | 5.09600 | 0.309560 | 0.154780 | − | 0.987949i | \(-0.450533\pi\) | ||||
0.154780 | + | 0.987949i | \(0.450533\pi\) | |||||||
\(272\) | 1.22557 | 0.0743111 | ||||||||
\(273\) | 2.91497 | 0.176422 | ||||||||
\(274\) | 2.98165 | 0.180128 | ||||||||
\(275\) | 12.5810 | 0.758664 | ||||||||
\(276\) | −5.34246 | −0.321578 | ||||||||
\(277\) | 13.3444 | 0.801786 | 0.400893 | − | 0.916125i | \(-0.368700\pi\) | ||||
0.400893 | + | 0.916125i | \(0.368700\pi\) | |||||||
\(278\) | 6.82476 | 0.409322 | ||||||||
\(279\) | 0.530200 | 0.0317422 | ||||||||
\(280\) | 1.26479 | 0.0755859 | ||||||||
\(281\) | 24.0353 | 1.43382 | 0.716912 | − | 0.697163i | \(-0.245555\pi\) | ||||
0.716912 | + | 0.697163i | \(0.245555\pi\) | |||||||
\(282\) | 1.52491 | 0.0908070 | ||||||||
\(283\) | −6.07700 | −0.361240 | −0.180620 | − | 0.983553i | \(-0.557810\pi\) | ||||
−0.180620 | + | 0.983553i | \(0.557810\pi\) | |||||||
\(284\) | 0.705663 | 0.0418734 | ||||||||
\(285\) | −19.4350 | −1.15123 | ||||||||
\(286\) | −5.95385 | −0.352058 | ||||||||
\(287\) | −3.98088 | −0.234984 | ||||||||
\(288\) | −0.281479 | −0.0165863 | ||||||||
\(289\) | −15.4980 | −0.911646 | ||||||||
\(290\) | −6.80673 | −0.399705 | ||||||||
\(291\) | 5.87320 | 0.344293 | ||||||||
\(292\) | 15.3830 | 0.900220 | ||||||||
\(293\) | 28.1074 | 1.64205 | 0.821025 | − | 0.570892i | \(-0.193403\pi\) | ||||
0.821025 | + | 0.570892i | \(0.193403\pi\) | |||||||
\(294\) | 1.81149 | 0.105648 | ||||||||
\(295\) | 12.2941 | 0.715789 | ||||||||
\(296\) | 5.44694 | 0.316597 | ||||||||
\(297\) | −18.2208 | −1.05728 | ||||||||
\(298\) | −1.70491 | −0.0987628 | ||||||||
\(299\) | −4.74576 | −0.274454 | ||||||||
\(300\) | 6.15959 | 0.355624 | ||||||||
\(301\) | −12.2128 | −0.703936 | ||||||||
\(302\) | −19.2929 | −1.11018 | ||||||||
\(303\) | −2.22737 | −0.127959 | ||||||||
\(304\) | −8.48264 | −0.486513 | ||||||||
\(305\) | 6.78185 | 0.388327 | ||||||||
\(306\) | −0.344972 | −0.0197207 | ||||||||
\(307\) | −19.3194 | −1.10261 | −0.551307 | − | 0.834302i | \(-0.685871\pi\) | ||||
−0.551307 | + | 0.834302i | \(0.685871\pi\) | |||||||
\(308\) | −3.69998 | −0.210826 | ||||||||
\(309\) | 20.9570 | 1.19220 | ||||||||
\(310\) | 2.38239 | 0.135311 | ||||||||
\(311\) | −2.74556 | −0.155686 | −0.0778432 | − | 0.996966i | \(-0.524803\pi\) | ||||
−0.0778432 | + | 0.996966i | \(0.524803\pi\) | |||||||
\(312\) | −2.91497 | −0.165027 | ||||||||
\(313\) | 10.0581 | 0.568515 | 0.284257 | − | 0.958748i | \(-0.408253\pi\) | ||||
0.284257 | + | 0.958748i | \(0.408253\pi\) | |||||||
\(314\) | 10.4163 | 0.587824 | ||||||||
\(315\) | −0.356012 | −0.0200590 | ||||||||
\(316\) | 3.15953 | 0.177738 | ||||||||
\(317\) | 35.4943 | 1.99356 | 0.996780 | − | 0.0801895i | \(-0.0255525\pi\) | ||||
0.996780 | + | 0.0801895i | \(0.0255525\pi\) | |||||||
\(318\) | 3.36122 | 0.188488 | ||||||||
\(319\) | 19.9121 | 1.11487 | ||||||||
\(320\) | −1.26479 | −0.0707041 | ||||||||
\(321\) | −1.12247 | −0.0626502 | ||||||||
\(322\) | −2.94922 | −0.164353 | ||||||||
\(323\) | −10.3961 | −0.578453 | ||||||||
\(324\) | −9.76521 | −0.542511 | ||||||||
\(325\) | 5.47162 | 0.303511 | ||||||||
\(326\) | 6.39508 | 0.354191 | ||||||||
\(327\) | 17.8481 | 0.987002 | ||||||||
\(328\) | 3.98088 | 0.219807 | ||||||||
\(329\) | 0.841801 | 0.0464100 | ||||||||
\(330\) | 8.47722 | 0.466656 | ||||||||
\(331\) | 11.8033 | 0.648768 | 0.324384 | − | 0.945925i | \(-0.394843\pi\) | ||||
0.324384 | + | 0.945925i | \(0.394843\pi\) | |||||||
\(332\) | −1.30049 | −0.0713735 | ||||||||
\(333\) | −1.53320 | −0.0840186 | ||||||||
\(334\) | 20.1081 | 1.10027 | ||||||||
\(335\) | 1.95180 | 0.106638 | ||||||||
\(336\) | −1.81149 | −0.0988246 | ||||||||
\(337\) | −20.4124 | −1.11193 | −0.555967 | − | 0.831205i | \(-0.687652\pi\) | ||||
−0.555967 | + | 0.831205i | \(0.687652\pi\) | |||||||
\(338\) | 10.4106 | 0.566263 | ||||||||
\(339\) | 6.16507 | 0.334841 | ||||||||
\(340\) | −1.55009 | −0.0840656 | ||||||||
\(341\) | −6.96936 | −0.377412 | ||||||||
\(342\) | 2.38768 | 0.129111 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 12.2128 | 0.658472 | ||||||||
\(345\) | 6.75711 | 0.363791 | ||||||||
\(346\) | 15.9922 | 0.859744 | ||||||||
\(347\) | 22.9837 | 1.23383 | 0.616914 | − | 0.787030i | \(-0.288383\pi\) | ||||
0.616914 | + | 0.787030i | \(0.288383\pi\) | |||||||
\(348\) | 9.74885 | 0.522593 | ||||||||
\(349\) | −18.7096 | −1.00150 | −0.500752 | − | 0.865591i | \(-0.666943\pi\) | ||||
−0.500752 | + | 0.865591i | \(0.666943\pi\) | |||||||
\(350\) | 3.40030 | 0.181754 | ||||||||
\(351\) | −7.92440 | −0.422973 | ||||||||
\(352\) | 3.69998 | 0.197209 | ||||||||
\(353\) | −27.0394 | −1.43916 | −0.719582 | − | 0.694408i | \(-0.755666\pi\) | ||||
−0.719582 | + | 0.694408i | \(0.755666\pi\) | |||||||
\(354\) | −17.6080 | −0.935857 | ||||||||
\(355\) | −0.892518 | −0.0473699 | ||||||||
\(356\) | −9.94355 | −0.527007 | ||||||||
\(357\) | −2.22010 | −0.117500 | ||||||||
\(358\) | −15.7842 | −0.834223 | ||||||||
\(359\) | 29.9526 | 1.58084 | 0.790418 | − | 0.612568i | \(-0.209863\pi\) | ||||
0.790418 | + | 0.612568i | \(0.209863\pi\) | |||||||
\(360\) | 0.356012 | 0.0187635 | ||||||||
\(361\) | 52.9552 | 2.78712 | ||||||||
\(362\) | 17.5280 | 0.921252 | ||||||||
\(363\) | −4.87260 | −0.255745 | ||||||||
\(364\) | −1.60916 | −0.0843428 | ||||||||
\(365\) | −19.4563 | −1.01839 | ||||||||
\(366\) | −9.71322 | −0.507718 | ||||||||
\(367\) | 13.0823 | 0.682893 | 0.341446 | − | 0.939901i | \(-0.389083\pi\) | ||||
0.341446 | + | 0.939901i | \(0.389083\pi\) | |||||||
\(368\) | 2.94922 | 0.153739 | ||||||||
\(369\) | −1.12053 | −0.0583326 | ||||||||
\(370\) | −6.88925 | −0.358155 | ||||||||
\(371\) | 1.85550 | 0.0963329 | ||||||||
\(372\) | −3.41215 | −0.176912 | ||||||||
\(373\) | −15.2780 | −0.791065 | −0.395533 | − | 0.918452i | \(-0.629440\pi\) | ||||
−0.395533 | + | 0.918452i | \(0.629440\pi\) | |||||||
\(374\) | 4.53458 | 0.234478 | ||||||||
\(375\) | −19.2464 | −0.993879 | ||||||||
\(376\) | −0.841801 | −0.0434126 | ||||||||
\(377\) | 8.65999 | 0.446012 | ||||||||
\(378\) | −4.92456 | −0.253292 | ||||||||
\(379\) | 24.4251 | 1.25463 | 0.627315 | − | 0.778765i | \(-0.284154\pi\) | ||||
0.627315 | + | 0.778765i | \(0.284154\pi\) | |||||||
\(380\) | 10.7288 | 0.550375 | ||||||||
\(381\) | −31.5940 | −1.61861 | ||||||||
\(382\) | 25.0315 | 1.28072 | ||||||||
\(383\) | 2.42731 | 0.124030 | 0.0620149 | − | 0.998075i | \(-0.480247\pi\) | ||||
0.0620149 | + | 0.998075i | \(0.480247\pi\) | |||||||
\(384\) | 1.81149 | 0.0924420 | ||||||||
\(385\) | 4.67971 | 0.238500 | ||||||||
\(386\) | −1.36102 | −0.0692740 | ||||||||
\(387\) | −3.43765 | −0.174746 | ||||||||
\(388\) | −3.24220 | −0.164598 | ||||||||
\(389\) | 11.3762 | 0.576794 | 0.288397 | − | 0.957511i | \(-0.406878\pi\) | ||||
0.288397 | + | 0.957511i | \(0.406878\pi\) | |||||||
\(390\) | 3.68683 | 0.186690 | ||||||||
\(391\) | 3.61447 | 0.182792 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −5.70259 | −0.287657 | ||||||||
\(394\) | 7.39068 | 0.372337 | ||||||||
\(395\) | −3.99616 | −0.201069 | ||||||||
\(396\) | −1.04146 | −0.0523356 | ||||||||
\(397\) | −14.7057 | −0.738056 | −0.369028 | − | 0.929418i | \(-0.620309\pi\) | ||||
−0.369028 | + | 0.929418i | \(0.620309\pi\) | |||||||
\(398\) | 15.7798 | 0.790970 | ||||||||
\(399\) | 15.3662 | 0.769271 | ||||||||
\(400\) | −3.40030 | −0.170015 | ||||||||
\(401\) | 16.3247 | 0.815219 | 0.407609 | − | 0.913156i | \(-0.366363\pi\) | ||||
0.407609 | + | 0.913156i | \(0.366363\pi\) | |||||||
\(402\) | −2.79545 | −0.139424 | ||||||||
\(403\) | −3.03105 | −0.150987 | ||||||||
\(404\) | 1.22958 | 0.0611740 | ||||||||
\(405\) | 12.3510 | 0.613725 | ||||||||
\(406\) | 5.38169 | 0.267089 | ||||||||
\(407\) | 20.1535 | 0.998974 | ||||||||
\(408\) | 2.22010 | 0.109911 | ||||||||
\(409\) | −31.4450 | −1.55486 | −0.777429 | − | 0.628971i | \(-0.783476\pi\) | ||||
−0.777429 | + | 0.628971i | \(0.783476\pi\) | |||||||
\(410\) | −5.03499 | −0.248660 | ||||||||
\(411\) | 5.40122 | 0.266422 | ||||||||
\(412\) | −11.5690 | −0.569963 | ||||||||
\(413\) | −9.72023 | −0.478301 | ||||||||
\(414\) | −0.830142 | −0.0407992 | ||||||||
\(415\) | 1.64485 | 0.0807424 | ||||||||
\(416\) | 1.60916 | 0.0788955 | ||||||||
\(417\) | 12.3629 | 0.605416 | ||||||||
\(418\) | −31.3856 | −1.53512 | ||||||||
\(419\) | 25.4766 | 1.24461 | 0.622307 | − | 0.782773i | \(-0.286195\pi\) | ||||
0.622307 | + | 0.782773i | \(0.286195\pi\) | |||||||
\(420\) | 2.29115 | 0.111797 | ||||||||
\(421\) | −31.6146 | −1.54080 | −0.770400 | − | 0.637561i | \(-0.779943\pi\) | ||||
−0.770400 | + | 0.637561i | \(0.779943\pi\) | |||||||
\(422\) | −3.39957 | −0.165488 | ||||||||
\(423\) | 0.236949 | 0.0115209 | ||||||||
\(424\) | −1.85550 | −0.0901112 | ||||||||
\(425\) | −4.16730 | −0.202144 | ||||||||
\(426\) | 1.27830 | 0.0619337 | ||||||||
\(427\) | −5.36202 | −0.259486 | ||||||||
\(428\) | 0.619641 | 0.0299515 | ||||||||
\(429\) | −10.7853 | −0.520720 | ||||||||
\(430\) | −15.4467 | −0.744907 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | 4.92456 | 0.236933 | ||||||||
\(433\) | 34.8395 | 1.67428 | 0.837139 | − | 0.546990i | \(-0.184226\pi\) | ||||
0.837139 | + | 0.546990i | \(0.184226\pi\) | |||||||
\(434\) | −1.88362 | −0.0904168 | ||||||||
\(435\) | −12.3303 | −0.591192 | ||||||||
\(436\) | −9.85275 | −0.471861 | ||||||||
\(437\) | −25.0172 | −1.19673 | ||||||||
\(438\) | 27.8660 | 1.33149 | ||||||||
\(439\) | 11.0042 | 0.525201 | 0.262601 | − | 0.964905i | \(-0.415420\pi\) | ||||
0.262601 | + | 0.964905i | \(0.415420\pi\) | |||||||
\(440\) | −4.67971 | −0.223096 | ||||||||
\(441\) | 0.281479 | 0.0134037 | ||||||||
\(442\) | 1.97214 | 0.0938049 | ||||||||
\(443\) | 4.80323 | 0.228208 | 0.114104 | − | 0.993469i | \(-0.463600\pi\) | ||||
0.114104 | + | 0.993469i | \(0.463600\pi\) | |||||||
\(444\) | 9.86704 | 0.468269 | ||||||||
\(445\) | 12.5765 | 0.596185 | ||||||||
\(446\) | 19.6925 | 0.932465 | ||||||||
\(447\) | −3.08842 | −0.146077 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 0.0286033 | 0.00134987 | 0.000674936 | − | 1.00000i | \(-0.499785\pi\) | ||||
0.000674936 | 1.00000i | \(0.499785\pi\) | ||||||||
\(450\) | 0.957111 | 0.0451187 | ||||||||
\(451\) | 14.7292 | 0.693569 | ||||||||
\(452\) | −3.40332 | −0.160079 | ||||||||
\(453\) | −34.9489 | −1.64204 | ||||||||
\(454\) | −21.0869 | −0.989658 | ||||||||
\(455\) | 2.03525 | 0.0954141 | ||||||||
\(456\) | −15.3662 | −0.719587 | ||||||||
\(457\) | −9.61452 | −0.449748 | −0.224874 | − | 0.974388i | \(-0.572197\pi\) | ||||
−0.224874 | + | 0.974388i | \(0.572197\pi\) | |||||||
\(458\) | 15.9648 | 0.745986 | ||||||||
\(459\) | 6.03539 | 0.281708 | ||||||||
\(460\) | −3.73015 | −0.173919 | ||||||||
\(461\) | 34.0608 | 1.58637 | 0.793186 | − | 0.608980i | \(-0.208421\pi\) | ||||
0.793186 | + | 0.608980i | \(0.208421\pi\) | |||||||
\(462\) | −6.70245 | −0.311826 | ||||||||
\(463\) | −22.6241 | −1.05143 | −0.525715 | − | 0.850661i | \(-0.676202\pi\) | ||||
−0.525715 | + | 0.850661i | \(0.676202\pi\) | |||||||
\(464\) | −5.38169 | −0.249839 | ||||||||
\(465\) | 4.31567 | 0.200134 | ||||||||
\(466\) | −16.9445 | −0.784940 | ||||||||
\(467\) | 26.5106 | 1.22676 | 0.613381 | − | 0.789787i | \(-0.289809\pi\) | ||||
0.613381 | + | 0.789787i | \(0.289809\pi\) | |||||||
\(468\) | −0.452944 | −0.0209373 | ||||||||
\(469\) | −1.54318 | −0.0712574 | ||||||||
\(470\) | 1.06470 | 0.0491111 | ||||||||
\(471\) | 18.8689 | 0.869434 | ||||||||
\(472\) | 9.72023 | 0.447410 | ||||||||
\(473\) | 45.1872 | 2.07771 | ||||||||
\(474\) | 5.72345 | 0.262887 | ||||||||
\(475\) | 28.8435 | 1.32343 | ||||||||
\(476\) | 1.22557 | 0.0561739 | ||||||||
\(477\) | 0.522284 | 0.0239138 | ||||||||
\(478\) | −10.9737 | −0.501924 | ||||||||
\(479\) | 20.3244 | 0.928644 | 0.464322 | − | 0.885667i | \(-0.346298\pi\) | ||||
0.464322 | + | 0.885667i | \(0.346298\pi\) | |||||||
\(480\) | −2.29115 | −0.104576 | ||||||||
\(481\) | 8.76498 | 0.399649 | ||||||||
\(482\) | −14.2772 | −0.650310 | ||||||||
\(483\) | −5.34246 | −0.243090 | ||||||||
\(484\) | 2.68984 | 0.122265 | ||||||||
\(485\) | 4.10072 | 0.186204 | ||||||||
\(486\) | −2.91584 | −0.132265 | ||||||||
\(487\) | 24.8261 | 1.12498 | 0.562489 | − | 0.826805i | \(-0.309844\pi\) | ||||
0.562489 | + | 0.826805i | \(0.309844\pi\) | |||||||
\(488\) | 5.36202 | 0.242727 | ||||||||
\(489\) | 11.5846 | 0.523873 | ||||||||
\(490\) | 1.26479 | 0.0571375 | ||||||||
\(491\) | 10.4468 | 0.471459 | 0.235729 | − | 0.971819i | \(-0.424252\pi\) | ||||
0.235729 | + | 0.971819i | \(0.424252\pi\) | |||||||
\(492\) | 7.21131 | 0.325111 | ||||||||
\(493\) | −6.59564 | −0.297053 | ||||||||
\(494\) | −13.6499 | −0.614139 | ||||||||
\(495\) | 1.31724 | 0.0592054 | ||||||||
\(496\) | 1.88362 | 0.0845771 | ||||||||
\(497\) | 0.705663 | 0.0316533 | ||||||||
\(498\) | −2.35581 | −0.105566 | ||||||||
\(499\) | −35.0560 | −1.56932 | −0.784660 | − | 0.619926i | \(-0.787163\pi\) | ||||
−0.784660 | + | 0.619926i | \(0.787163\pi\) | |||||||
\(500\) | 10.6246 | 0.475148 | ||||||||
\(501\) | 36.4255 | 1.62737 | ||||||||
\(502\) | 2.05705 | 0.0918104 | ||||||||
\(503\) | −25.9380 | −1.15652 | −0.578260 | − | 0.815852i | \(-0.696268\pi\) | ||||
−0.578260 | + | 0.815852i | \(0.696268\pi\) | |||||||
\(504\) | −0.281479 | −0.0125381 | ||||||||
\(505\) | −1.55517 | −0.0692040 | ||||||||
\(506\) | 10.9120 | 0.485099 | ||||||||
\(507\) | 18.8587 | 0.837543 | ||||||||
\(508\) | 17.4409 | 0.773817 | ||||||||
\(509\) | 16.2577 | 0.720610 | 0.360305 | − | 0.932835i | \(-0.382673\pi\) | ||||
0.360305 | + | 0.932835i | \(0.382673\pi\) | |||||||
\(510\) | −2.80797 | −0.124339 | ||||||||
\(511\) | 15.3830 | 0.680502 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −41.7733 | −1.84434 | ||||||||
\(514\) | 21.6689 | 0.955776 | ||||||||
\(515\) | 14.6324 | 0.644779 | ||||||||
\(516\) | 22.1234 | 0.973927 | ||||||||
\(517\) | −3.11464 | −0.136982 | ||||||||
\(518\) | 5.44694 | 0.239325 | ||||||||
\(519\) | 28.9696 | 1.27162 | ||||||||
\(520\) | −2.03525 | −0.0892517 | ||||||||
\(521\) | 26.5759 | 1.16431 | 0.582155 | − | 0.813078i | \(-0.302210\pi\) | ||||
0.582155 | + | 0.813078i | \(0.302210\pi\) | |||||||
\(522\) | 1.51483 | 0.0663024 | ||||||||
\(523\) | −4.51580 | −0.197462 | −0.0987312 | − | 0.995114i | \(-0.531478\pi\) | ||||
−0.0987312 | + | 0.995114i | \(0.531478\pi\) | |||||||
\(524\) | 3.14802 | 0.137522 | ||||||||
\(525\) | 6.15959 | 0.268826 | ||||||||
\(526\) | −11.9621 | −0.521570 | ||||||||
\(527\) | 2.30851 | 0.100560 | ||||||||
\(528\) | 6.70245 | 0.291687 | ||||||||
\(529\) | −14.3021 | −0.621831 | ||||||||
\(530\) | 2.34683 | 0.101940 | ||||||||
\(531\) | −2.73604 | −0.118734 | ||||||||
\(532\) | −8.48264 | −0.367769 | ||||||||
\(533\) | 6.40587 | 0.277469 | ||||||||
\(534\) | −18.0126 | −0.779481 | ||||||||
\(535\) | −0.783717 | −0.0338831 | ||||||||
\(536\) | 1.54318 | 0.0666552 | ||||||||
\(537\) | −28.5929 | −1.23388 | ||||||||
\(538\) | −8.82775 | −0.380592 | ||||||||
\(539\) | −3.69998 | −0.159369 | ||||||||
\(540\) | −6.22855 | −0.268034 | ||||||||
\(541\) | 10.9554 | 0.471011 | 0.235505 | − | 0.971873i | \(-0.424325\pi\) | ||||
0.235505 | + | 0.971873i | \(0.424325\pi\) | |||||||
\(542\) | −5.09600 | −0.218892 | ||||||||
\(543\) | 31.7517 | 1.36260 | ||||||||
\(544\) | −1.22557 | −0.0525459 | ||||||||
\(545\) | 12.4617 | 0.533800 | ||||||||
\(546\) | −2.91497 | −0.124749 | ||||||||
\(547\) | −3.64746 | −0.155954 | −0.0779770 | − | 0.996955i | \(-0.524846\pi\) | ||||
−0.0779770 | + | 0.996955i | \(0.524846\pi\) | |||||||
\(548\) | −2.98165 | −0.127370 | ||||||||
\(549\) | −1.50929 | −0.0644151 | ||||||||
\(550\) | −12.5810 | −0.536457 | ||||||||
\(551\) | 45.6510 | 1.94480 | ||||||||
\(552\) | 5.34246 | 0.227390 | ||||||||
\(553\) | 3.15953 | 0.134357 | ||||||||
\(554\) | −13.3444 | −0.566948 | ||||||||
\(555\) | −12.4798 | −0.529737 | ||||||||
\(556\) | −6.82476 | −0.289434 | ||||||||
\(557\) | −30.2262 | −1.28072 | −0.640362 | − | 0.768073i | \(-0.721216\pi\) | ||||
−0.640362 | + | 0.768073i | \(0.721216\pi\) | |||||||
\(558\) | −0.530200 | −0.0224451 | ||||||||
\(559\) | 19.6524 | 0.831208 | ||||||||
\(560\) | −1.26479 | −0.0534473 | ||||||||
\(561\) | 8.21433 | 0.346809 | ||||||||
\(562\) | −24.0353 | −1.01387 | ||||||||
\(563\) | −2.76600 | −0.116573 | −0.0582864 | − | 0.998300i | \(-0.518564\pi\) | ||||
−0.0582864 | + | 0.998300i | \(0.518564\pi\) | |||||||
\(564\) | −1.52491 | −0.0642103 | ||||||||
\(565\) | 4.30450 | 0.181092 | ||||||||
\(566\) | 6.07700 | 0.255435 | ||||||||
\(567\) | −9.76521 | −0.410100 | ||||||||
\(568\) | −0.705663 | −0.0296090 | ||||||||
\(569\) | −28.5638 | −1.19746 | −0.598728 | − | 0.800952i | \(-0.704327\pi\) | ||||
−0.598728 | + | 0.800952i | \(0.704327\pi\) | |||||||
\(570\) | 19.4350 | 0.814045 | ||||||||
\(571\) | 15.5867 | 0.652283 | 0.326142 | − | 0.945321i | \(-0.394251\pi\) | ||||
0.326142 | + | 0.945321i | \(0.394251\pi\) | |||||||
\(572\) | 5.95385 | 0.248943 | ||||||||
\(573\) | 45.3442 | 1.89428 | ||||||||
\(574\) | 3.98088 | 0.166159 | ||||||||
\(575\) | −10.0282 | −0.418205 | ||||||||
\(576\) | 0.281479 | 0.0117283 | ||||||||
\(577\) | −36.1615 | −1.50542 | −0.752712 | − | 0.658350i | \(-0.771255\pi\) | ||||
−0.752712 | + | 0.658350i | \(0.771255\pi\) | |||||||
\(578\) | 15.4980 | 0.644631 | ||||||||
\(579\) | −2.46546 | −0.102461 | ||||||||
\(580\) | 6.80673 | 0.282634 | ||||||||
\(581\) | −1.30049 | −0.0539533 | ||||||||
\(582\) | −5.87320 | −0.243452 | ||||||||
\(583\) | −6.86532 | −0.284332 | ||||||||
\(584\) | −15.3830 | −0.636552 | ||||||||
\(585\) | 0.572880 | 0.0236857 | ||||||||
\(586\) | −28.1074 | −1.16110 | ||||||||
\(587\) | 40.4034 | 1.66763 | 0.833813 | − | 0.552048i | \(-0.186153\pi\) | ||||
0.833813 | + | 0.552048i | \(0.186153\pi\) | |||||||
\(588\) | −1.81149 | −0.0747044 | ||||||||
\(589\) | −15.9781 | −0.658366 | ||||||||
\(590\) | −12.2941 | −0.506139 | ||||||||
\(591\) | 13.3881 | 0.550713 | ||||||||
\(592\) | −5.44694 | −0.223868 | ||||||||
\(593\) | 9.29155 | 0.381558 | 0.190779 | − | 0.981633i | \(-0.438899\pi\) | ||||
0.190779 | + | 0.981633i | \(0.438899\pi\) | |||||||
\(594\) | 18.2208 | 0.747607 | ||||||||
\(595\) | −1.55009 | −0.0635476 | ||||||||
\(596\) | 1.70491 | 0.0698358 | ||||||||
\(597\) | 28.5849 | 1.16990 | ||||||||
\(598\) | 4.74576 | 0.194068 | ||||||||
\(599\) | 21.6832 | 0.885950 | 0.442975 | − | 0.896534i | \(-0.353923\pi\) | ||||
0.442975 | + | 0.896534i | \(0.353923\pi\) | |||||||
\(600\) | −6.15959 | −0.251464 | ||||||||
\(601\) | 7.90326 | 0.322381 | 0.161190 | − | 0.986923i | \(-0.448467\pi\) | ||||
0.161190 | + | 0.986923i | \(0.448467\pi\) | |||||||
\(602\) | 12.2128 | 0.497758 | ||||||||
\(603\) | −0.434372 | −0.0176890 | ||||||||
\(604\) | 19.2929 | 0.785019 | ||||||||
\(605\) | −3.40209 | −0.138314 | ||||||||
\(606\) | 2.22737 | 0.0904807 | ||||||||
\(607\) | −1.56999 | −0.0637241 | −0.0318620 | − | 0.999492i | \(-0.510144\pi\) | ||||
−0.0318620 | + | 0.999492i | \(0.510144\pi\) | |||||||
\(608\) | 8.48264 | 0.344017 | ||||||||
\(609\) | 9.74885 | 0.395044 | ||||||||
\(610\) | −6.78185 | −0.274589 | ||||||||
\(611\) | −1.35459 | −0.0548009 | ||||||||
\(612\) | 0.344972 | 0.0139447 | ||||||||
\(613\) | 1.33177 | 0.0537898 | 0.0268949 | − | 0.999638i | \(-0.491438\pi\) | ||||
0.0268949 | + | 0.999638i | \(0.491438\pi\) | |||||||
\(614\) | 19.3194 | 0.779667 | ||||||||
\(615\) | −9.12081 | −0.367787 | ||||||||
\(616\) | 3.69998 | 0.149076 | ||||||||
\(617\) | 38.8458 | 1.56387 | 0.781936 | − | 0.623358i | \(-0.214232\pi\) | ||||
0.781936 | + | 0.623358i | \(0.214232\pi\) | |||||||
\(618\) | −20.9570 | −0.843016 | ||||||||
\(619\) | 15.8900 | 0.638671 | 0.319336 | − | 0.947642i | \(-0.396540\pi\) | ||||
0.319336 | + | 0.947642i | \(0.396540\pi\) | |||||||
\(620\) | −2.38239 | −0.0956792 | ||||||||
\(621\) | 14.5236 | 0.582812 | ||||||||
\(622\) | 2.74556 | 0.110087 | ||||||||
\(623\) | −9.94355 | −0.398380 | ||||||||
\(624\) | 2.91497 | 0.116692 | ||||||||
\(625\) | 3.56351 | 0.142540 | ||||||||
\(626\) | −10.0581 | −0.402001 | ||||||||
\(627\) | −56.8545 | −2.27055 | ||||||||
\(628\) | −10.4163 | −0.415655 | ||||||||
\(629\) | −6.67560 | −0.266174 | ||||||||
\(630\) | 0.356012 | 0.0141839 | ||||||||
\(631\) | −7.42086 | −0.295420 | −0.147710 | − | 0.989031i | \(-0.547190\pi\) | ||||
−0.147710 | + | 0.989031i | \(0.547190\pi\) | |||||||
\(632\) | −3.15953 | −0.125680 | ||||||||
\(633\) | −6.15827 | −0.244769 | ||||||||
\(634\) | −35.4943 | −1.40966 | ||||||||
\(635\) | −22.0592 | −0.875392 | ||||||||
\(636\) | −3.36122 | −0.133281 | ||||||||
\(637\) | −1.60916 | −0.0637572 | ||||||||
\(638\) | −19.9121 | −0.788329 | ||||||||
\(639\) | 0.198629 | 0.00785764 | ||||||||
\(640\) | 1.26479 | 0.0499954 | ||||||||
\(641\) | 8.61857 | 0.340413 | 0.170206 | − | 0.985408i | \(-0.445557\pi\) | ||||
0.170206 | + | 0.985408i | \(0.445557\pi\) | |||||||
\(642\) | 1.12247 | 0.0443004 | ||||||||
\(643\) | 32.5802 | 1.28484 | 0.642420 | − | 0.766353i | \(-0.277931\pi\) | ||||
0.642420 | + | 0.766353i | \(0.277931\pi\) | |||||||
\(644\) | 2.94922 | 0.116215 | ||||||||
\(645\) | −27.9815 | −1.10177 | ||||||||
\(646\) | 10.3961 | 0.409028 | ||||||||
\(647\) | −27.6517 | −1.08710 | −0.543550 | − | 0.839377i | \(-0.682920\pi\) | ||||
−0.543550 | + | 0.839377i | \(0.682920\pi\) | |||||||
\(648\) | 9.76521 | 0.383614 | ||||||||
\(649\) | 35.9646 | 1.41174 | ||||||||
\(650\) | −5.47162 | −0.214614 | ||||||||
\(651\) | −3.41215 | −0.133733 | ||||||||
\(652\) | −6.39508 | −0.250451 | ||||||||
\(653\) | −10.4012 | −0.407030 | −0.203515 | − | 0.979072i | \(-0.565237\pi\) | ||||
−0.203515 | + | 0.979072i | \(0.565237\pi\) | |||||||
\(654\) | −17.8481 | −0.697916 | ||||||||
\(655\) | −3.98159 | −0.155574 | ||||||||
\(656\) | −3.98088 | −0.155427 | ||||||||
\(657\) | 4.32998 | 0.168929 | ||||||||
\(658\) | −0.841801 | −0.0328168 | ||||||||
\(659\) | −9.48292 | −0.369402 | −0.184701 | − | 0.982795i | \(-0.559132\pi\) | ||||
−0.184701 | + | 0.982795i | \(0.559132\pi\) | |||||||
\(660\) | −8.47722 | −0.329975 | ||||||||
\(661\) | 26.3470 | 1.02478 | 0.512389 | − | 0.858754i | \(-0.328761\pi\) | ||||
0.512389 | + | 0.858754i | \(0.328761\pi\) | |||||||
\(662\) | −11.8033 | −0.458748 | ||||||||
\(663\) | 3.57250 | 0.138744 | ||||||||
\(664\) | 1.30049 | 0.0504687 | ||||||||
\(665\) | 10.7288 | 0.416045 | ||||||||
\(666\) | 1.53320 | 0.0594101 | ||||||||
\(667\) | −15.8718 | −0.614558 | ||||||||
\(668\) | −20.1081 | −0.778005 | ||||||||
\(669\) | 35.6726 | 1.37918 | ||||||||
\(670\) | −1.95180 | −0.0754047 | ||||||||
\(671\) | 19.8394 | 0.765890 | ||||||||
\(672\) | 1.81149 | 0.0698796 | ||||||||
\(673\) | 9.72527 | 0.374882 | 0.187441 | − | 0.982276i | \(-0.439981\pi\) | ||||
0.187441 | + | 0.982276i | \(0.439981\pi\) | |||||||
\(674\) | 20.4124 | 0.786255 | ||||||||
\(675\) | −16.7450 | −0.644514 | ||||||||
\(676\) | −10.4106 | −0.400408 | ||||||||
\(677\) | 11.8866 | 0.456840 | 0.228420 | − | 0.973563i | \(-0.426644\pi\) | ||||
0.228420 | + | 0.973563i | \(0.426644\pi\) | |||||||
\(678\) | −6.16507 | −0.236768 | ||||||||
\(679\) | −3.24220 | −0.124424 | ||||||||
\(680\) | 1.55009 | 0.0594433 | ||||||||
\(681\) | −38.1986 | −1.46377 | ||||||||
\(682\) | 6.96936 | 0.266871 | ||||||||
\(683\) | 44.2105 | 1.69167 | 0.845835 | − | 0.533445i | \(-0.179103\pi\) | ||||
0.845835 | + | 0.533445i | \(0.179103\pi\) | |||||||
\(684\) | −2.38768 | −0.0912954 | ||||||||
\(685\) | 3.77117 | 0.144089 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 28.9200 | 1.10337 | ||||||||
\(688\) | −12.2128 | −0.465610 | ||||||||
\(689\) | −2.98580 | −0.113750 | ||||||||
\(690\) | −6.75711 | −0.257239 | ||||||||
\(691\) | 23.9389 | 0.910677 | 0.455339 | − | 0.890318i | \(-0.349518\pi\) | ||||
0.455339 | + | 0.890318i | \(0.349518\pi\) | |||||||
\(692\) | −15.9922 | −0.607931 | ||||||||
\(693\) | −1.04146 | −0.0395620 | ||||||||
\(694\) | −22.9837 | −0.872448 | ||||||||
\(695\) | 8.63191 | 0.327427 | ||||||||
\(696\) | −9.74885 | −0.369529 | ||||||||
\(697\) | −4.87885 | −0.184800 | ||||||||
\(698\) | 18.7096 | 0.708170 | ||||||||
\(699\) | −30.6947 | −1.16098 | ||||||||
\(700\) | −3.40030 | −0.128519 | ||||||||
\(701\) | 15.9629 | 0.602910 | 0.301455 | − | 0.953480i | \(-0.402528\pi\) | ||||
0.301455 | + | 0.953480i | \(0.402528\pi\) | |||||||
\(702\) | 7.92440 | 0.299087 | ||||||||
\(703\) | 46.2044 | 1.74263 | ||||||||
\(704\) | −3.69998 | −0.139448 | ||||||||
\(705\) | 1.92870 | 0.0726389 | ||||||||
\(706\) | 27.0394 | 1.01764 | ||||||||
\(707\) | 1.22958 | 0.0462432 | ||||||||
\(708\) | 17.6080 | 0.661751 | ||||||||
\(709\) | 1.43886 | 0.0540375 | 0.0270187 | − | 0.999635i | \(-0.491399\pi\) | ||||
0.0270187 | + | 0.999635i | \(0.491399\pi\) | |||||||
\(710\) | 0.892518 | 0.0334956 | ||||||||
\(711\) | 0.889342 | 0.0333529 | ||||||||
\(712\) | 9.94355 | 0.372650 | ||||||||
\(713\) | 5.55521 | 0.208044 | ||||||||
\(714\) | 2.22010 | 0.0830852 | ||||||||
\(715\) | −7.53039 | −0.281621 | ||||||||
\(716\) | 15.7842 | 0.589885 | ||||||||
\(717\) | −19.8787 | −0.742382 | ||||||||
\(718\) | −29.9526 | −1.11782 | ||||||||
\(719\) | 2.49023 | 0.0928699 | 0.0464349 | − | 0.998921i | \(-0.485214\pi\) | ||||
0.0464349 | + | 0.998921i | \(0.485214\pi\) | |||||||
\(720\) | −0.356012 | −0.0132678 | ||||||||
\(721\) | −11.5690 | −0.430851 | ||||||||
\(722\) | −52.9552 | −1.97079 | ||||||||
\(723\) | −25.8630 | −0.961855 | ||||||||
\(724\) | −17.5280 | −0.651424 | ||||||||
\(725\) | 18.2994 | 0.679621 | ||||||||
\(726\) | 4.87260 | 0.180839 | ||||||||
\(727\) | −21.6123 | −0.801558 | −0.400779 | − | 0.916175i | \(-0.631260\pi\) | ||||
−0.400779 | + | 0.916175i | \(0.631260\pi\) | |||||||
\(728\) | 1.60916 | 0.0596394 | ||||||||
\(729\) | 24.0136 | 0.889393 | ||||||||
\(730\) | 19.4563 | 0.720109 | ||||||||
\(731\) | −14.9677 | −0.553600 | ||||||||
\(732\) | 9.71322 | 0.359011 | ||||||||
\(733\) | −38.2633 | −1.41329 | −0.706644 | − | 0.707569i | \(-0.749792\pi\) | ||||
−0.706644 | + | 0.707569i | \(0.749792\pi\) | |||||||
\(734\) | −13.0823 | −0.482878 | ||||||||
\(735\) | 2.29115 | 0.0845105 | ||||||||
\(736\) | −2.94922 | −0.108710 | ||||||||
\(737\) | 5.70973 | 0.210321 | ||||||||
\(738\) | 1.12053 | 0.0412474 | ||||||||
\(739\) | 37.8254 | 1.39143 | 0.695715 | − | 0.718318i | \(-0.255088\pi\) | ||||
0.695715 | + | 0.718318i | \(0.255088\pi\) | |||||||
\(740\) | 6.88925 | 0.253254 | ||||||||
\(741\) | −24.7266 | −0.908355 | ||||||||
\(742\) | −1.85550 | −0.0681176 | ||||||||
\(743\) | −28.0878 | −1.03044 | −0.515222 | − | 0.857057i | \(-0.672290\pi\) | ||||
−0.515222 | + | 0.857057i | \(0.672290\pi\) | |||||||
\(744\) | 3.41215 | 0.125096 | ||||||||
\(745\) | −2.15636 | −0.0790029 | ||||||||
\(746\) | 15.2780 | 0.559368 | ||||||||
\(747\) | −0.366059 | −0.0133934 | ||||||||
\(748\) | −4.53458 | −0.165801 | ||||||||
\(749\) | 0.619641 | 0.0226412 | ||||||||
\(750\) | 19.2464 | 0.702778 | ||||||||
\(751\) | 26.0289 | 0.949810 | 0.474905 | − | 0.880037i | \(-0.342482\pi\) | ||||
0.474905 | + | 0.880037i | \(0.342482\pi\) | |||||||
\(752\) | 0.841801 | 0.0306973 | ||||||||
\(753\) | 3.72631 | 0.135794 | ||||||||
\(754\) | −8.65999 | −0.315378 | ||||||||
\(755\) | −24.4016 | −0.888065 | ||||||||
\(756\) | 4.92456 | 0.179105 | ||||||||
\(757\) | −33.3381 | −1.21170 | −0.605848 | − | 0.795581i | \(-0.707166\pi\) | ||||
−0.605848 | + | 0.795581i | \(0.707166\pi\) | |||||||
\(758\) | −24.4251 | −0.887158 | ||||||||
\(759\) | 19.7670 | 0.717496 | ||||||||
\(760\) | −10.7288 | −0.389174 | ||||||||
\(761\) | −27.6007 | −1.00052 | −0.500262 | − | 0.865874i | \(-0.666763\pi\) | ||||
−0.500262 | + | 0.865874i | \(0.666763\pi\) | |||||||
\(762\) | 31.5940 | 1.14453 | ||||||||
\(763\) | −9.85275 | −0.356693 | ||||||||
\(764\) | −25.0315 | −0.905608 | ||||||||
\(765\) | −0.436318 | −0.0157751 | ||||||||
\(766\) | −2.42731 | −0.0877023 | ||||||||
\(767\) | 15.6414 | 0.564778 | ||||||||
\(768\) | −1.81149 | −0.0653663 | ||||||||
\(769\) | 6.25353 | 0.225508 | 0.112754 | − | 0.993623i | \(-0.464033\pi\) | ||||
0.112754 | + | 0.993623i | \(0.464033\pi\) | |||||||
\(770\) | −4.67971 | −0.168645 | ||||||||
\(771\) | 39.2529 | 1.41366 | ||||||||
\(772\) | 1.36102 | 0.0489841 | ||||||||
\(773\) | −33.9778 | −1.22210 | −0.611049 | − | 0.791593i | \(-0.709252\pi\) | ||||
−0.611049 | + | 0.791593i | \(0.709252\pi\) | |||||||
\(774\) | 3.43765 | 0.123564 | ||||||||
\(775\) | −6.40488 | −0.230070 | ||||||||
\(776\) | 3.24220 | 0.116388 | ||||||||
\(777\) | 9.86704 | 0.353978 | ||||||||
\(778\) | −11.3762 | −0.407855 | ||||||||
\(779\) | 33.7684 | 1.20988 | ||||||||
\(780\) | −3.68683 | −0.132010 | ||||||||
\(781\) | −2.61094 | −0.0934267 | ||||||||
\(782\) | −3.61447 | −0.129253 | ||||||||
\(783\) | −26.5025 | −0.947121 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 13.1744 | 0.470216 | ||||||||
\(786\) | 5.70259 | 0.203404 | ||||||||
\(787\) | −55.8348 | −1.99030 | −0.995148 | − | 0.0983889i | \(-0.968631\pi\) | ||||
−0.995148 | + | 0.0983889i | \(0.968631\pi\) | |||||||
\(788\) | −7.39068 | −0.263282 | ||||||||
\(789\) | −21.6691 | −0.771440 | ||||||||
\(790\) | 3.99616 | 0.142177 | ||||||||
\(791\) | −3.40332 | −0.121008 | ||||||||
\(792\) | 1.04146 | 0.0370068 | ||||||||
\(793\) | 8.62834 | 0.306401 | ||||||||
\(794\) | 14.7057 | 0.521885 | ||||||||
\(795\) | 4.25124 | 0.150776 | ||||||||
\(796\) | −15.7798 | −0.559300 | ||||||||
\(797\) | −18.4166 | −0.652349 | −0.326175 | − | 0.945310i | \(-0.605760\pi\) | ||||
−0.326175 | + | 0.945310i | \(0.605760\pi\) | |||||||
\(798\) | −15.3662 | −0.543957 | ||||||||
\(799\) | 1.03169 | 0.0364984 | ||||||||
\(800\) | 3.40030 | 0.120219 | ||||||||
\(801\) | −2.79890 | −0.0988942 | ||||||||
\(802\) | −16.3247 | −0.576447 | ||||||||
\(803\) | −56.9166 | −2.00854 | ||||||||
\(804\) | 2.79545 | 0.0985878 | ||||||||
\(805\) | −3.73015 | −0.131471 | ||||||||
\(806\) | 3.03105 | 0.106764 | ||||||||
\(807\) | −15.9913 | −0.562922 | ||||||||
\(808\) | −1.22958 | −0.0432565 | ||||||||
\(809\) | −47.5677 | −1.67239 | −0.836196 | − | 0.548431i | \(-0.815225\pi\) | ||||
−0.836196 | + | 0.548431i | \(0.815225\pi\) | |||||||
\(810\) | −12.3510 | −0.433969 | ||||||||
\(811\) | −0.655007 | −0.0230004 | −0.0115002 | − | 0.999934i | \(-0.503661\pi\) | ||||
−0.0115002 | + | 0.999934i | \(0.503661\pi\) | |||||||
\(812\) | −5.38169 | −0.188860 | ||||||||
\(813\) | −9.23132 | −0.323757 | ||||||||
\(814\) | −20.1535 | −0.706381 | ||||||||
\(815\) | 8.08846 | 0.283326 | ||||||||
\(816\) | −2.22010 | −0.0777191 | ||||||||
\(817\) | 103.597 | 3.62441 | ||||||||
\(818\) | 31.4450 | 1.09945 | ||||||||
\(819\) | −0.452944 | −0.0158271 | ||||||||
\(820\) | 5.03499 | 0.175830 | ||||||||
\(821\) | 32.6022 | 1.13783 | 0.568913 | − | 0.822398i | \(-0.307364\pi\) | ||||
0.568913 | + | 0.822398i | \(0.307364\pi\) | |||||||
\(822\) | −5.40122 | −0.188389 | ||||||||
\(823\) | 50.4042 | 1.75698 | 0.878491 | − | 0.477759i | \(-0.158551\pi\) | ||||
0.878491 | + | 0.477759i | \(0.158551\pi\) | |||||||
\(824\) | 11.5690 | 0.403024 | ||||||||
\(825\) | −22.7903 | −0.793458 | ||||||||
\(826\) | 9.72023 | 0.338210 | ||||||||
\(827\) | 48.3992 | 1.68300 | 0.841502 | − | 0.540253i | \(-0.181672\pi\) | ||||
0.841502 | + | 0.540253i | \(0.181672\pi\) | |||||||
\(828\) | 0.830142 | 0.0288494 | ||||||||
\(829\) | −7.08727 | −0.246151 | −0.123076 | − | 0.992397i | \(-0.539276\pi\) | ||||
−0.123076 | + | 0.992397i | \(0.539276\pi\) | |||||||
\(830\) | −1.64485 | −0.0570935 | ||||||||
\(831\) | −24.1731 | −0.838557 | ||||||||
\(832\) | −1.60916 | −0.0557875 | ||||||||
\(833\) | 1.22557 | 0.0424635 | ||||||||
\(834\) | −12.3629 | −0.428094 | ||||||||
\(835\) | 25.4326 | 0.880130 | ||||||||
\(836\) | 31.3856 | 1.08549 | ||||||||
\(837\) | 9.27601 | 0.320626 | ||||||||
\(838\) | −25.4766 | −0.880075 | ||||||||
\(839\) | −1.15223 | −0.0397792 | −0.0198896 | − | 0.999802i | \(-0.506331\pi\) | ||||
−0.0198896 | + | 0.999802i | \(0.506331\pi\) | |||||||
\(840\) | −2.29115 | −0.0790523 | ||||||||
\(841\) | −0.0373990 | −0.00128962 | ||||||||
\(842\) | 31.6146 | 1.08951 | ||||||||
\(843\) | −43.5396 | −1.49958 | ||||||||
\(844\) | 3.39957 | 0.117018 | ||||||||
\(845\) | 13.1673 | 0.452968 | ||||||||
\(846\) | −0.236949 | −0.00814647 | ||||||||
\(847\) | 2.68984 | 0.0924238 | ||||||||
\(848\) | 1.85550 | 0.0637182 | ||||||||
\(849\) | 11.0084 | 0.377807 | ||||||||
\(850\) | 4.16730 | 0.142937 | ||||||||
\(851\) | −16.0642 | −0.550673 | ||||||||
\(852\) | −1.27830 | −0.0437938 | ||||||||
\(853\) | 31.3149 | 1.07220 | 0.536100 | − | 0.844154i | \(-0.319897\pi\) | ||||
0.536100 | + | 0.844154i | \(0.319897\pi\) | |||||||
\(854\) | 5.36202 | 0.183485 | ||||||||
\(855\) | 3.01993 | 0.103279 | ||||||||
\(856\) | −0.619641 | −0.0211789 | ||||||||
\(857\) | 5.45441 | 0.186319 | 0.0931595 | − | 0.995651i | \(-0.470303\pi\) | ||||
0.0931595 | + | 0.995651i | \(0.470303\pi\) | |||||||
\(858\) | 10.7853 | 0.368204 | ||||||||
\(859\) | −19.4755 | −0.664495 | −0.332248 | − | 0.943192i | \(-0.607807\pi\) | ||||
−0.332248 | + | 0.943192i | \(0.607807\pi\) | |||||||
\(860\) | 15.4467 | 0.526729 | ||||||||
\(861\) | 7.21131 | 0.245761 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | −20.7381 | −0.705933 | −0.352966 | − | 0.935636i | \(-0.614827\pi\) | ||||
−0.352966 | + | 0.935636i | \(0.614827\pi\) | |||||||
\(864\) | −4.92456 | −0.167537 | ||||||||
\(865\) | 20.2268 | 0.687731 | ||||||||
\(866\) | −34.8395 | −1.18389 | ||||||||
\(867\) | 28.0744 | 0.953455 | ||||||||
\(868\) | 1.88362 | 0.0639343 | ||||||||
\(869\) | −11.6902 | −0.396563 | ||||||||
\(870\) | 12.3303 | 0.418036 | ||||||||
\(871\) | 2.48322 | 0.0841407 | ||||||||
\(872\) | 9.85275 | 0.333656 | ||||||||
\(873\) | −0.912611 | −0.0308872 | ||||||||
\(874\) | 25.0172 | 0.846218 | ||||||||
\(875\) | 10.6246 | 0.359178 | ||||||||
\(876\) | −27.8660 | −0.941506 | ||||||||
\(877\) | 6.27229 | 0.211800 | 0.105900 | − | 0.994377i | \(-0.466228\pi\) | ||||
0.105900 | + | 0.994377i | \(0.466228\pi\) | |||||||
\(878\) | −11.0042 | −0.371373 | ||||||||
\(879\) | −50.9161 | −1.71736 | ||||||||
\(880\) | 4.67971 | 0.157753 | ||||||||
\(881\) | −13.3039 | −0.448219 | −0.224109 | − | 0.974564i | \(-0.571947\pi\) | ||||
−0.224109 | + | 0.974564i | \(0.571947\pi\) | |||||||
\(882\) | −0.281479 | −0.00947788 | ||||||||
\(883\) | −27.1088 | −0.912282 | −0.456141 | − | 0.889907i | \(-0.650769\pi\) | ||||
−0.456141 | + | 0.889907i | \(0.650769\pi\) | |||||||
\(884\) | −1.97214 | −0.0663301 | ||||||||
\(885\) | −22.2705 | −0.748616 | ||||||||
\(886\) | −4.80323 | −0.161368 | ||||||||
\(887\) | −45.6506 | −1.53280 | −0.766399 | − | 0.642365i | \(-0.777953\pi\) | ||||
−0.766399 | + | 0.642365i | \(0.777953\pi\) | |||||||
\(888\) | −9.86704 | −0.331116 | ||||||||
\(889\) | 17.4409 | 0.584950 | ||||||||
\(890\) | −12.5765 | −0.421566 | ||||||||
\(891\) | 36.1310 | 1.21044 | ||||||||
\(892\) | −19.6925 | −0.659352 | ||||||||
\(893\) | −7.14070 | −0.238954 | ||||||||
\(894\) | 3.08842 | 0.103292 | ||||||||
\(895\) | −19.9638 | −0.667316 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 8.59687 | 0.287041 | ||||||||
\(898\) | −0.0286033 | −0.000954503 0 | ||||||||
\(899\) | −10.1371 | −0.338090 | ||||||||
\(900\) | −0.957111 | −0.0319037 | ||||||||
\(901\) | 2.27405 | 0.0757595 | ||||||||
\(902\) | −14.7292 | −0.490428 | ||||||||
\(903\) | 22.1234 | 0.736220 | ||||||||
\(904\) | 3.40332 | 0.113193 | ||||||||
\(905\) | 22.1693 | 0.736933 | ||||||||
\(906\) | 34.9489 | 1.16110 | ||||||||
\(907\) | −27.2585 | −0.905103 | −0.452552 | − | 0.891738i | \(-0.649486\pi\) | ||||
−0.452552 | + | 0.891738i | \(0.649486\pi\) | |||||||
\(908\) | 21.0869 | 0.699794 | ||||||||
\(909\) | 0.346101 | 0.0114794 | ||||||||
\(910\) | −2.03525 | −0.0674680 | ||||||||
\(911\) | −50.4963 | −1.67302 | −0.836509 | − | 0.547954i | \(-0.815407\pi\) | ||||
−0.836509 | + | 0.547954i | \(0.815407\pi\) | |||||||
\(912\) | 15.3662 | 0.508825 | ||||||||
\(913\) | 4.81177 | 0.159246 | ||||||||
\(914\) | 9.61452 | 0.318020 | ||||||||
\(915\) | −12.2852 | −0.406137 | ||||||||
\(916\) | −15.9648 | −0.527492 | ||||||||
\(917\) | 3.14802 | 0.103957 | ||||||||
\(918\) | −6.03539 | −0.199198 | ||||||||
\(919\) | −58.4139 | −1.92690 | −0.963449 | − | 0.267892i | \(-0.913673\pi\) | ||||
−0.963449 | + | 0.267892i | \(0.913673\pi\) | |||||||
\(920\) | 3.73015 | 0.122979 | ||||||||
\(921\) | 34.9968 | 1.15318 | ||||||||
\(922\) | −34.0608 | −1.12173 | ||||||||
\(923\) | −1.13552 | −0.0373762 | ||||||||
\(924\) | 6.70245 | 0.220495 | ||||||||
\(925\) | 18.5212 | 0.608973 | ||||||||
\(926\) | 22.6241 | 0.743473 | ||||||||
\(927\) | −3.25642 | −0.106955 | ||||||||
\(928\) | 5.38169 | 0.176663 | ||||||||
\(929\) | −27.4308 | −0.899974 | −0.449987 | − | 0.893035i | \(-0.648571\pi\) | ||||
−0.449987 | + | 0.893035i | \(0.648571\pi\) | |||||||
\(930\) | −4.31567 | −0.141516 | ||||||||
\(931\) | −8.48264 | −0.278007 | ||||||||
\(932\) | 16.9445 | 0.555036 | ||||||||
\(933\) | 4.97354 | 0.162826 | ||||||||
\(934\) | −26.5106 | −0.867452 | ||||||||
\(935\) | 5.73531 | 0.187565 | ||||||||
\(936\) | 0.452944 | 0.0148049 | ||||||||
\(937\) | −29.2519 | −0.955619 | −0.477809 | − | 0.878464i | \(-0.658569\pi\) | ||||
−0.477809 | + | 0.878464i | \(0.658569\pi\) | |||||||
\(938\) | 1.54318 | 0.0503866 | ||||||||
\(939\) | −18.2200 | −0.594588 | ||||||||
\(940\) | −1.06470 | −0.0347268 | ||||||||
\(941\) | 15.4059 | 0.502217 | 0.251108 | − | 0.967959i | \(-0.419205\pi\) | ||||
0.251108 | + | 0.967959i | \(0.419205\pi\) | |||||||
\(942\) | −18.8689 | −0.614783 | ||||||||
\(943\) | −11.7405 | −0.382323 | ||||||||
\(944\) | −9.72023 | −0.316366 | ||||||||
\(945\) | −6.22855 | −0.202615 | ||||||||
\(946\) | −45.1872 | −1.46916 | ||||||||
\(947\) | −27.6419 | −0.898242 | −0.449121 | − | 0.893471i | \(-0.648263\pi\) | ||||
−0.449121 | + | 0.893471i | \(0.648263\pi\) | |||||||
\(948\) | −5.72345 | −0.185889 | ||||||||
\(949\) | −24.7536 | −0.803537 | ||||||||
\(950\) | −28.8435 | −0.935807 | ||||||||
\(951\) | −64.2974 | −2.08499 | ||||||||
\(952\) | −1.22557 | −0.0397210 | ||||||||
\(953\) | 4.41701 | 0.143081 | 0.0715405 | − | 0.997438i | \(-0.477208\pi\) | ||||
0.0715405 | + | 0.997438i | \(0.477208\pi\) | |||||||
\(954\) | −0.522284 | −0.0169096 | ||||||||
\(955\) | 31.6597 | 1.02448 | ||||||||
\(956\) | 10.9737 | 0.354914 | ||||||||
\(957\) | −36.0705 | −1.16600 | ||||||||
\(958\) | −20.3244 | −0.656650 | ||||||||
\(959\) | −2.98165 | −0.0962826 | ||||||||
\(960\) | 2.29115 | 0.0739467 | ||||||||
\(961\) | −27.4520 | −0.885547 | ||||||||
\(962\) | −8.76498 | −0.282594 | ||||||||
\(963\) | 0.174416 | 0.00562047 | ||||||||
\(964\) | 14.2772 | 0.459839 | ||||||||
\(965\) | −1.72141 | −0.0554140 | ||||||||
\(966\) | 5.34246 | 0.171891 | ||||||||
\(967\) | −9.02948 | −0.290368 | −0.145184 | − | 0.989405i | \(-0.546377\pi\) | ||||
−0.145184 | + | 0.989405i | \(0.546377\pi\) | |||||||
\(968\) | −2.68984 | −0.0864546 | ||||||||
\(969\) | 18.8323 | 0.604982 | ||||||||
\(970\) | −4.10072 | −0.131666 | ||||||||
\(971\) | 52.2268 | 1.67604 | 0.838018 | − | 0.545642i | \(-0.183714\pi\) | ||||
0.838018 | + | 0.545642i | \(0.183714\pi\) | |||||||
\(972\) | 2.91584 | 0.0935257 | ||||||||
\(973\) | −6.82476 | −0.218792 | ||||||||
\(974\) | −24.8261 | −0.795479 | ||||||||
\(975\) | −9.91175 | −0.317430 | ||||||||
\(976\) | −5.36202 | −0.171634 | ||||||||
\(977\) | −9.07541 | −0.290348 | −0.145174 | − | 0.989406i | \(-0.546374\pi\) | ||||
−0.145174 | + | 0.989406i | \(0.546374\pi\) | |||||||
\(978\) | −11.5846 | −0.370434 | ||||||||
\(979\) | 36.7909 | 1.17584 | ||||||||
\(980\) | −1.26479 | −0.0404023 | ||||||||
\(981\) | −2.77334 | −0.0885459 | ||||||||
\(982\) | −10.4468 | −0.333372 | ||||||||
\(983\) | −55.4641 | −1.76903 | −0.884516 | − | 0.466510i | \(-0.845511\pi\) | ||||
−0.884516 | + | 0.466510i | \(0.845511\pi\) | |||||||
\(984\) | −7.21131 | −0.229888 | ||||||||
\(985\) | 9.34768 | 0.297842 | ||||||||
\(986\) | 6.59564 | 0.210048 | ||||||||
\(987\) | −1.52491 | −0.0485384 | ||||||||
\(988\) | 13.6499 | 0.434262 | ||||||||
\(989\) | −36.0183 | −1.14532 | ||||||||
\(990\) | −1.31724 | −0.0418646 | ||||||||
\(991\) | 10.5969 | 0.336623 | 0.168311 | − | 0.985734i | \(-0.446169\pi\) | ||||
0.168311 | + | 0.985734i | \(0.446169\pi\) | |||||||
\(992\) | −1.88362 | −0.0598051 | ||||||||
\(993\) | −21.3815 | −0.678522 | ||||||||
\(994\) | −0.705663 | −0.0223823 | ||||||||
\(995\) | 19.9582 | 0.632717 | ||||||||
\(996\) | 2.35581 | 0.0746468 | ||||||||
\(997\) | 25.9340 | 0.821339 | 0.410669 | − | 0.911784i | \(-0.365295\pi\) | ||||
0.410669 | + | 0.911784i | \(0.365295\pi\) | |||||||
\(998\) | 35.0560 | 1.10968 | ||||||||
\(999\) | −26.8238 | −0.848666 |
(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 | 6034.2.a.p.1.7 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.p.1.7 | ✓ | 27 | 1.1 | even | 1 | trivial |