Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4527,2,Mod(1,4527)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4527, 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("4527.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4527 = 3^{2} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4527.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: | \(36.1482769950\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-0.858231\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4527.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.58686 | 1.82919 | 0.914593 | − | 0.404375i | \(-0.132511\pi\) | ||||
0.914593 | + | 0.404375i | \(0.132511\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.69185 | 2.34592 | ||||||||
\(5\) | −1.44291 | −0.645289 | −0.322644 | − | 0.946520i | \(-0.604572\pi\) | ||||
−0.322644 | + | 0.946520i | \(0.604572\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.96509 | −0.742734 | −0.371367 | − | 0.928486i | \(-0.621111\pi\) | ||||
−0.371367 | + | 0.928486i | \(0.621111\pi\) | |||||||
\(8\) | 6.96343 | 2.46194 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.73261 | −1.18035 | ||||||||
\(11\) | −2.85614 | −0.861160 | −0.430580 | − | 0.902552i | \(-0.641691\pi\) | ||||
−0.430580 | + | 0.902552i | \(0.641691\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.84427 | −1.06621 | −0.533104 | − | 0.846050i | \(-0.678974\pi\) | ||||
−0.533104 | + | 0.846050i | \(0.678974\pi\) | |||||||
\(14\) | −5.08341 | −1.35860 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.62972 | 2.15743 | ||||||||
\(17\) | −1.30329 | −0.316095 | −0.158047 | − | 0.987432i | \(-0.550520\pi\) | ||||
−0.158047 | + | 0.987432i | \(0.550520\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.53196 | 0.810287 | 0.405143 | − | 0.914253i | \(-0.367222\pi\) | ||||
0.405143 | + | 0.914253i | \(0.367222\pi\) | |||||||
\(20\) | −6.76991 | −1.51380 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.38845 | −1.57522 | ||||||||
\(23\) | −4.20650 | −0.877115 | −0.438558 | − | 0.898703i | \(-0.644510\pi\) | ||||
−0.438558 | + | 0.898703i | \(0.644510\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.91801 | −0.583602 | ||||||||
\(26\) | −9.94458 | −1.95029 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.21989 | −1.74240 | ||||||||
\(29\) | 1.10402 | 0.205011 | 0.102506 | − | 0.994732i | \(-0.467314\pi\) | ||||
0.102506 | + | 0.994732i | \(0.467314\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.53201 | −0.634368 | −0.317184 | − | 0.948364i | \(-0.602737\pi\) | ||||
−0.317184 | + | 0.948364i | \(0.602737\pi\) | |||||||
\(32\) | 8.39703 | 1.48440 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.37144 | −0.578196 | ||||||||
\(35\) | 2.83545 | 0.479278 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.61903 | −1.08816 | −0.544081 | − | 0.839033i | \(-0.683121\pi\) | ||||
−0.544081 | + | 0.839033i | \(0.683121\pi\) | |||||||
\(38\) | 9.13668 | 1.48217 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.0476 | −1.58866 | ||||||||
\(41\) | −0.671095 | −0.104807 | −0.0524037 | − | 0.998626i | \(-0.516688\pi\) | ||||
−0.0524037 | + | 0.998626i | \(0.516688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.32289 | −0.659235 | −0.329617 | − | 0.944115i | \(-0.606920\pi\) | ||||
−0.329617 | + | 0.944115i | \(0.606920\pi\) | |||||||
\(44\) | −13.4006 | −2.02021 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.8816 | −1.60441 | ||||||||
\(47\) | 0.378524 | 0.0552134 | 0.0276067 | − | 0.999619i | \(-0.491211\pi\) | ||||
0.0276067 | + | 0.999619i | \(0.491211\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.13843 | −0.448347 | ||||||||
\(50\) | −7.54849 | −1.06752 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −18.0367 | −2.50124 | ||||||||
\(53\) | 7.13700 | 0.980342 | 0.490171 | − | 0.871626i | \(-0.336934\pi\) | ||||
0.490171 | + | 0.871626i | \(0.336934\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.12116 | 0.555697 | ||||||||
\(56\) | −13.6838 | −1.82857 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.85594 | 0.375004 | ||||||||
\(59\) | 13.8806 | 1.80709 | 0.903547 | − | 0.428489i | \(-0.140954\pi\) | ||||
0.903547 | + | 0.428489i | \(0.140954\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.51374 | −0.833999 | −0.417000 | − | 0.908907i | \(-0.636918\pi\) | ||||
−0.417000 | + | 0.908907i | \(0.636918\pi\) | |||||||
\(62\) | −9.13682 | −1.16038 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.46249 | 0.557812 | ||||||||
\(65\) | 5.54693 | 0.688012 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.55189 | −0.922610 | −0.461305 | − | 0.887242i | \(-0.652619\pi\) | ||||
−0.461305 | + | 0.887242i | \(0.652619\pi\) | |||||||
\(68\) | −6.11485 | −0.741534 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.33490 | 0.876688 | ||||||||
\(71\) | −0.0744967 | −0.00884113 | −0.00442057 | − | 0.999990i | \(-0.501407\pi\) | ||||
−0.00442057 | + | 0.999990i | \(0.501407\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.29052 | 0.385126 | 0.192563 | − | 0.981285i | \(-0.438320\pi\) | ||||
0.192563 | + | 0.981285i | \(0.438320\pi\) | |||||||
\(74\) | −17.1225 | −1.99045 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.5714 | 1.90087 | ||||||||
\(77\) | 5.61258 | 0.639612 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.57578 | 0.964850 | 0.482425 | − | 0.875937i | \(-0.339756\pi\) | ||||
0.482425 | + | 0.875937i | \(0.339756\pi\) | |||||||
\(80\) | −12.4519 | −1.39217 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.73603 | −0.191712 | ||||||||
\(83\) | −14.8165 | −1.62632 | −0.813158 | − | 0.582042i | \(-0.802254\pi\) | ||||
−0.813158 | + | 0.582042i | \(0.802254\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.88053 | 0.203973 | ||||||||
\(86\) | −11.1827 | −1.20586 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −19.8886 | −2.12013 | ||||||||
\(89\) | 17.5415 | 1.85940 | 0.929700 | − | 0.368318i | \(-0.120066\pi\) | ||||
0.929700 | + | 0.368318i | \(0.120066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.55432 | 0.791908 | ||||||||
\(92\) | −19.7362 | −2.05764 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.979188 | 0.100996 | ||||||||
\(95\) | −5.09630 | −0.522869 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.01702 | −0.814005 | −0.407003 | − | 0.913427i | \(-0.633426\pi\) | ||||
−0.407003 | + | 0.913427i | \(0.633426\pi\) | |||||||
\(98\) | −8.11867 | −0.820110 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.6909 | −1.36909 | ||||||||
\(101\) | −9.11148 | −0.906626 | −0.453313 | − | 0.891351i | \(-0.649758\pi\) | ||||
−0.453313 | + | 0.891351i | \(0.649758\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.2943 | −1.50699 | −0.753494 | − | 0.657455i | \(-0.771633\pi\) | ||||
−0.753494 | + | 0.657455i | \(0.771633\pi\) | |||||||
\(104\) | −26.7693 | −2.62494 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.4624 | 1.79323 | ||||||||
\(107\) | −3.50420 | −0.338764 | −0.169382 | − | 0.985550i | \(-0.554177\pi\) | ||||
−0.169382 | + | 0.985550i | \(0.554177\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.49301 | 0.238787 | 0.119393 | − | 0.992847i | \(-0.461905\pi\) | ||||
0.119393 | + | 0.992847i | \(0.461905\pi\) | |||||||
\(110\) | 10.6609 | 1.01647 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −16.9582 | −1.60240 | ||||||||
\(113\) | 14.5343 | 1.36727 | 0.683634 | − | 0.729825i | \(-0.260399\pi\) | ||||
0.683634 | + | 0.729825i | \(0.260399\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.06959 | 0.565993 | ||||||||
\(116\) | 5.17989 | 0.480941 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 35.9070 | 3.30551 | ||||||||
\(119\) | 2.56109 | 0.234774 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.84244 | −0.258404 | ||||||||
\(122\) | −16.8501 | −1.52554 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16.5716 | −1.48818 | ||||||||
\(125\) | 11.4250 | 1.02188 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.52702 | 0.490443 | 0.245222 | − | 0.969467i | \(-0.421139\pi\) | ||||
0.245222 | + | 0.969467i | \(0.421139\pi\) | |||||||
\(128\) | −5.25021 | −0.464057 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 14.3491 | 1.25850 | ||||||||
\(131\) | 21.2174 | 1.85377 | 0.926885 | − | 0.375346i | \(-0.122476\pi\) | ||||
0.926885 | + | 0.375346i | \(0.122476\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.94061 | −0.601827 | ||||||||
\(134\) | −19.5357 | −1.68763 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.07538 | −0.778208 | ||||||||
\(137\) | −11.6794 | −0.997835 | −0.498917 | − | 0.866650i | \(-0.666269\pi\) | ||||
−0.498917 | + | 0.866650i | \(0.666269\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8676 | −0.921778 | −0.460889 | − | 0.887458i | \(-0.652469\pi\) | ||||
−0.460889 | + | 0.887458i | \(0.652469\pi\) | |||||||
\(140\) | 13.3035 | 1.12435 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.192713 | −0.0161721 | ||||||||
\(143\) | 10.9798 | 0.918175 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.59300 | −0.132292 | ||||||||
\(146\) | 8.51212 | 0.704468 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −31.0555 | −2.55274 | ||||||||
\(149\) | 7.40209 | 0.606403 | 0.303202 | − | 0.952926i | \(-0.401944\pi\) | ||||
0.303202 | + | 0.952926i | \(0.401944\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.09188 | 0.495750 | 0.247875 | − | 0.968792i | \(-0.420268\pi\) | ||||
0.247875 | + | 0.968792i | \(0.420268\pi\) | |||||||
\(152\) | 24.5945 | 1.99488 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.5189 | 1.16997 | ||||||||
\(155\) | 5.09637 | 0.409350 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.22790 | 0.177806 | 0.0889028 | − | 0.996040i | \(-0.471664\pi\) | ||||
0.0889028 | + | 0.996040i | \(0.471664\pi\) | |||||||
\(158\) | 22.1843 | 1.76489 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.1162 | −0.957866 | ||||||||
\(161\) | 8.26614 | 0.651463 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.7370 | −1.46759 | −0.733797 | − | 0.679368i | \(-0.762254\pi\) | ||||
−0.733797 | + | 0.679368i | \(0.762254\pi\) | |||||||
\(164\) | −3.14867 | −0.245870 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −38.3281 | −2.97484 | ||||||||
\(167\) | −22.7237 | −1.75841 | −0.879205 | − | 0.476443i | \(-0.841926\pi\) | ||||
−0.879205 | + | 0.476443i | \(0.841926\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.77838 | 0.136798 | ||||||||
\(170\) | 4.86468 | 0.373104 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −20.2823 | −1.54651 | ||||||||
\(173\) | 2.25141 | 0.171172 | 0.0855859 | − | 0.996331i | \(-0.472724\pi\) | ||||
0.0855859 | + | 0.996331i | \(0.472724\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.73415 | 0.433461 | ||||||||
\(176\) | −24.6477 | −1.85789 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 45.3775 | 3.40119 | ||||||||
\(179\) | −15.8986 | −1.18832 | −0.594159 | − | 0.804348i | \(-0.702515\pi\) | ||||
−0.594159 | + | 0.804348i | \(0.702515\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5942 | 1.23344 | 0.616718 | − | 0.787184i | \(-0.288462\pi\) | ||||
0.616718 | + | 0.787184i | \(0.288462\pi\) | |||||||
\(182\) | 19.5420 | 1.44855 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −29.2916 | −2.15941 | ||||||||
\(185\) | 9.55066 | 0.702179 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.72239 | 0.272208 | ||||||||
\(188\) | 1.77598 | 0.129526 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.1834 | −0.956425 | ||||||||
\(191\) | 2.03640 | 0.147348 | 0.0736742 | − | 0.997282i | \(-0.476527\pi\) | ||||
0.0736742 | + | 0.997282i | \(0.476527\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.1384 | −1.08968 | −0.544841 | − | 0.838539i | \(-0.683410\pi\) | ||||
−0.544841 | + | 0.838539i | \(0.683410\pi\) | |||||||
\(194\) | −20.7389 | −1.48897 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.7250 | −1.05179 | ||||||||
\(197\) | 6.01285 | 0.428398 | 0.214199 | − | 0.976790i | \(-0.431286\pi\) | ||||
0.214199 | + | 0.976790i | \(0.431286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.5513 | 1.66951 | 0.834753 | − | 0.550624i | \(-0.185610\pi\) | ||||
0.834753 | + | 0.550624i | \(0.185610\pi\) | |||||||
\(200\) | −20.3194 | −1.43680 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23.5701 | −1.65839 | ||||||||
\(203\) | −2.16950 | −0.152269 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.968329 | 0.0676311 | ||||||||
\(206\) | −39.5641 | −2.75656 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −33.1749 | −2.30027 | ||||||||
\(209\) | −10.0878 | −0.697786 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.35555 | 0.162163 | 0.0810814 | − | 0.996707i | \(-0.474163\pi\) | ||||
0.0810814 | + | 0.996707i | \(0.474163\pi\) | |||||||
\(212\) | 33.4857 | 2.29981 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.06488 | −0.619662 | ||||||||
\(215\) | 6.23754 | 0.425397 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.94071 | 0.471166 | ||||||||
\(218\) | 6.44906 | 0.436785 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 19.3358 | 1.30362 | ||||||||
\(221\) | 5.01020 | 0.337023 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6268 | 0.912519 | 0.456260 | − | 0.889847i | \(-0.349189\pi\) | ||||
0.456260 | + | 0.889847i | \(0.349189\pi\) | |||||||
\(224\) | −16.5009 | −1.10251 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 37.5981 | 2.50099 | ||||||||
\(227\) | −11.9812 | −0.795218 | −0.397609 | − | 0.917555i | \(-0.630160\pi\) | ||||
−0.397609 | + | 0.917555i | \(0.630160\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.2066 | 1.79786 | 0.898932 | − | 0.438087i | \(-0.144344\pi\) | ||||
0.898932 | + | 0.438087i | \(0.144344\pi\) | |||||||
\(230\) | 15.7012 | 1.03531 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.68776 | 0.504726 | ||||||||
\(233\) | −14.4504 | −0.946679 | −0.473339 | − | 0.880880i | \(-0.656952\pi\) | ||||
−0.473339 | + | 0.880880i | \(0.656952\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.546176 | −0.0356286 | ||||||||
\(236\) | 65.1254 | 4.23930 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.62517 | 0.429446 | ||||||||
\(239\) | 23.9361 | 1.54830 | 0.774148 | − | 0.633005i | \(-0.218179\pi\) | ||||
0.774148 | + | 0.633005i | \(0.218179\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.7734 | −0.887224 | −0.443612 | − | 0.896219i | \(-0.646303\pi\) | ||||
−0.443612 | + | 0.896219i | \(0.646303\pi\) | |||||||
\(242\) | −7.35300 | −0.472668 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −30.5615 | −1.95650 | ||||||||
\(245\) | 4.52847 | 0.289313 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.5778 | −0.863934 | ||||||||
\(248\) | −24.5949 | −1.56178 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 29.5548 | 1.86921 | ||||||||
\(251\) | 8.26975 | 0.521982 | 0.260991 | − | 0.965341i | \(-0.415951\pi\) | ||||
0.260991 | + | 0.965341i | \(0.415951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0144 | 0.755336 | ||||||||
\(254\) | 14.2976 | 0.897112 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −22.5065 | −1.40666 | ||||||||
\(257\) | 20.1486 | 1.25684 | 0.628418 | − | 0.777876i | \(-0.283703\pi\) | ||||
0.628418 | + | 0.777876i | \(0.283703\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.0070 | 0.808214 | ||||||||
\(260\) | 26.0253 | 1.61402 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 54.8863 | 3.39089 | ||||||||
\(263\) | 27.9229 | 1.72180 | 0.860900 | − | 0.508774i | \(-0.169901\pi\) | ||||
0.860900 | + | 0.508774i | \(0.169901\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.2980 | −0.632604 | ||||||||
\(266\) | −17.9544 | −1.10085 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −35.4323 | −2.16437 | ||||||||
\(269\) | −11.6165 | −0.708269 | −0.354135 | − | 0.935194i | \(-0.615225\pi\) | ||||
−0.354135 | + | 0.935194i | \(0.615225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.27787 | −0.199117 | −0.0995583 | − | 0.995032i | \(-0.531743\pi\) | ||||
−0.0995583 | + | 0.995032i | \(0.531743\pi\) | |||||||
\(272\) | −11.2471 | −0.681953 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30.2129 | −1.82523 | ||||||||
\(275\) | 8.33426 | 0.502575 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1157 | 0.607795 | 0.303897 | − | 0.952705i | \(-0.401712\pi\) | ||||
0.303897 | + | 0.952705i | \(0.401712\pi\) | |||||||
\(278\) | −28.1130 | −1.68610 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.7444 | 1.17995 | ||||||||
\(281\) | −16.7656 | −1.00015 | −0.500077 | − | 0.865981i | \(-0.666695\pi\) | ||||
−0.500077 | + | 0.865981i | \(0.666695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4382 | 0.917705 | 0.458852 | − | 0.888513i | \(-0.348261\pi\) | ||||
0.458852 | + | 0.888513i | \(0.348261\pi\) | |||||||
\(284\) | −0.349527 | −0.0207406 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 28.4031 | 1.67951 | ||||||||
\(287\) | 1.31876 | 0.0778440 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3014 | −0.900084 | ||||||||
\(290\) | −4.12087 | −0.241986 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.4386 | 0.903477 | ||||||||
\(293\) | 7.52887 | 0.439841 | 0.219921 | − | 0.975518i | \(-0.429420\pi\) | ||||
0.219921 | + | 0.975518i | \(0.429420\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.0284 | −1.16610 | ||||||||
\(296\) | −46.0911 | −2.67899 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.1482 | 1.10922 | ||||||||
\(299\) | 16.1709 | 0.935187 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.49487 | 0.489636 | ||||||||
\(302\) | 15.7588 | 0.906819 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 30.4798 | 1.74814 | ||||||||
\(305\) | 9.39874 | 0.538170 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1932 | 0.981265 | 0.490632 | − | 0.871367i | \(-0.336766\pi\) | ||||
0.490632 | + | 0.871367i | \(0.336766\pi\) | |||||||
\(308\) | 26.3333 | 1.50048 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.1836 | 0.748778 | ||||||||
\(311\) | −10.1595 | −0.576094 | −0.288047 | − | 0.957616i | \(-0.593006\pi\) | ||||
−0.288047 | + | 0.957616i | \(0.593006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.6909 | 1.50866 | 0.754329 | − | 0.656496i | \(-0.227962\pi\) | ||||
0.754329 | + | 0.656496i | \(0.227962\pi\) | |||||||
\(314\) | 5.76326 | 0.325240 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 40.2362 | 2.26346 | ||||||||
\(317\) | −19.3855 | −1.08880 | −0.544398 | − | 0.838827i | \(-0.683242\pi\) | ||||
−0.544398 | + | 0.838827i | \(0.683242\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.15324 | −0.176548 | ||||||||
\(320\) | −6.43898 | −0.359950 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 21.3833 | 1.19165 | ||||||||
\(323\) | −4.60317 | −0.256127 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.2176 | 0.622241 | ||||||||
\(326\) | −48.4700 | −2.68450 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.67312 | −0.258030 | ||||||||
\(329\) | −0.743833 | −0.0410088 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.0579 | −1.43227 | −0.716135 | − | 0.697962i | \(-0.754090\pi\) | ||||
−0.716135 | + | 0.697962i | \(0.754090\pi\) | |||||||
\(332\) | −69.5165 | −3.81521 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −58.7830 | −3.21646 | ||||||||
\(335\) | 10.8967 | 0.595350 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6240 | −0.633199 | −0.316600 | − | 0.948559i | \(-0.602541\pi\) | ||||
−0.316600 | + | 0.948559i | \(0.602541\pi\) | |||||||
\(338\) | 4.60042 | 0.250230 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.82317 | 0.478504 | ||||||||
\(341\) | 10.0879 | 0.546292 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9229 | 1.07574 | ||||||||
\(344\) | −30.1021 | −1.62300 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.82409 | 0.313105 | ||||||||
\(347\) | −24.5102 | −1.31578 | −0.657888 | − | 0.753115i | \(-0.728550\pi\) | ||||
−0.657888 | + | 0.753115i | \(0.728550\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.6510 | 0.570133 | 0.285066 | − | 0.958508i | \(-0.407984\pi\) | ||||
0.285066 | + | 0.958508i | \(0.407984\pi\) | |||||||
\(350\) | 14.8334 | 0.792881 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −23.9831 | −1.27830 | ||||||||
\(353\) | −1.04651 | −0.0557003 | −0.0278501 | − | 0.999612i | \(-0.508866\pi\) | ||||
−0.0278501 | + | 0.999612i | \(0.508866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.107492 | 0.00570508 | ||||||||
\(356\) | 82.3022 | 4.36201 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −41.1275 | −2.17365 | ||||||||
\(359\) | 24.0194 | 1.26769 | 0.633847 | − | 0.773459i | \(-0.281475\pi\) | ||||
0.633847 | + | 0.773459i | \(0.281475\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.52528 | −0.343436 | ||||||||
\(362\) | 42.9268 | 2.25618 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 35.4437 | 1.85776 | ||||||||
\(365\) | −4.74793 | −0.248518 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.6963 | −0.975937 | −0.487969 | − | 0.872861i | \(-0.662262\pi\) | ||||
−0.487969 | + | 0.872861i | \(0.662262\pi\) | |||||||
\(368\) | −36.3009 | −1.89231 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 24.7062 | 1.28442 | ||||||||
\(371\) | −14.0248 | −0.728133 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.3008 | −1.20647 | −0.603235 | − | 0.797564i | \(-0.706122\pi\) | ||||
−0.603235 | + | 0.797564i | \(0.706122\pi\) | |||||||
\(374\) | 9.62931 | 0.497920 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.63582 | 0.135932 | ||||||||
\(377\) | −4.24415 | −0.218585 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.79951 | −0.503367 | −0.251683 | − | 0.967810i | \(-0.580984\pi\) | ||||
−0.251683 | + | 0.967810i | \(0.580984\pi\) | |||||||
\(380\) | −23.9110 | −1.22661 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.26787 | 0.269528 | ||||||||
\(383\) | 1.97295 | 0.100813 | 0.0504066 | − | 0.998729i | \(-0.483948\pi\) | ||||
0.0504066 | + | 0.998729i | \(0.483948\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.09844 | −0.412735 | ||||||||
\(386\) | −39.1608 | −1.99323 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −37.6146 | −1.90959 | ||||||||
\(389\) | 6.61202 | 0.335243 | 0.167621 | − | 0.985851i | \(-0.446391\pi\) | ||||
0.167621 | + | 0.985851i | \(0.446391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.48230 | 0.277252 | ||||||||
\(392\) | −21.8542 | −1.10380 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.5544 | 0.783619 | ||||||||
\(395\) | −12.3741 | −0.622607 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.61750 | −0.382311 | −0.191156 | − | 0.981560i | \(-0.561224\pi\) | ||||
−0.191156 | + | 0.981560i | \(0.561224\pi\) | |||||||
\(398\) | 60.9239 | 3.05384 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −25.1816 | −1.25908 | ||||||||
\(401\) | −25.8162 | −1.28920 | −0.644601 | − | 0.764519i | \(-0.722976\pi\) | ||||
−0.644601 | + | 0.764519i | \(0.722976\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.5780 | 0.676368 | ||||||||
\(404\) | −42.7497 | −2.12687 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.61218 | −0.278528 | ||||||||
\(407\) | 18.9049 | 0.937081 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6924 | −0.677044 | −0.338522 | − | 0.940958i | \(-0.609927\pi\) | ||||
−0.338522 | + | 0.940958i | \(0.609927\pi\) | |||||||
\(410\) | 2.50493 | 0.123710 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −71.7583 | −3.53528 | ||||||||
\(413\) | −27.2765 | −1.34219 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.3788 | 1.04944 | ||||||||
\(416\) | −32.2804 | −1.58268 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −26.0957 | −1.27638 | ||||||||
\(419\) | −24.0027 | −1.17261 | −0.586305 | − | 0.810091i | \(-0.699418\pi\) | ||||
−0.586305 | + | 0.810091i | \(0.699418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.1293 | 1.51715 | 0.758573 | − | 0.651588i | \(-0.225897\pi\) | ||||
0.758573 | + | 0.651588i | \(0.225897\pi\) | |||||||
\(422\) | 6.09348 | 0.296626 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 49.6979 | 2.41355 | ||||||||
\(425\) | 3.80302 | 0.184474 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.8001 | 0.619439 | ||||||||
\(428\) | −16.4412 | −0.794714 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.1357 | 0.778130 | ||||||||
\(431\) | −28.0585 | −1.35153 | −0.675766 | − | 0.737116i | \(-0.736187\pi\) | ||||
−0.675766 | + | 0.737116i | \(0.736187\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.6011 | −0.990026 | −0.495013 | − | 0.868886i | \(-0.664837\pi\) | ||||
−0.495013 | + | 0.868886i | \(0.664837\pi\) | |||||||
\(434\) | 17.9547 | 0.861851 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.6968 | 0.560175 | ||||||||
\(437\) | −14.8572 | −0.710715 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.4050 | −1.73752 | −0.868758 | − | 0.495238i | \(-0.835081\pi\) | ||||
−0.868758 | + | 0.495238i | \(0.835081\pi\) | |||||||
\(440\) | 28.6974 | 1.36809 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.9607 | 0.616477 | ||||||||
\(443\) | 28.1192 | 1.33598 | 0.667992 | − | 0.744169i | \(-0.267154\pi\) | ||||
0.667992 | + | 0.744169i | \(0.267154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.3109 | −1.19985 | ||||||||
\(446\) | 35.2507 | 1.66917 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.76920 | −0.414306 | ||||||||
\(449\) | 12.9493 | 0.611116 | 0.305558 | − | 0.952173i | \(-0.401157\pi\) | ||||
0.305558 | + | 0.952173i | \(0.401157\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.91674 | 0.0902559 | ||||||||
\(452\) | 68.1925 | 3.20750 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.9936 | −1.45460 | ||||||||
\(455\) | −10.9002 | −0.511010 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.149626 | 0.00699919 | 0.00349960 | − | 0.999994i | \(-0.498886\pi\) | ||||
0.00349960 | + | 0.999994i | \(0.498886\pi\) | |||||||
\(458\) | 70.3797 | 3.28863 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 28.4776 | 1.32777 | ||||||||
\(461\) | −38.9917 | −1.81603 | −0.908013 | − | 0.418942i | \(-0.862401\pi\) | ||||
−0.908013 | + | 0.418942i | \(0.862401\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.1386 | −0.935918 | −0.467959 | − | 0.883750i | \(-0.655011\pi\) | ||||
−0.467959 | + | 0.883750i | \(0.655011\pi\) | |||||||
\(464\) | 9.52738 | 0.442298 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −37.3812 | −1.73165 | ||||||||
\(467\) | −14.8664 | −0.687936 | −0.343968 | − | 0.938981i | \(-0.611771\pi\) | ||||
−0.343968 | + | 0.938981i | \(0.611771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.8401 | 0.685254 | ||||||||
\(470\) | −1.41288 | −0.0651713 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 96.6562 | 4.44896 | ||||||||
\(473\) | 12.3468 | 0.567707 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.3063 | −0.472885 | ||||||||
\(476\) | 12.0162 | 0.550762 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 61.9193 | 2.83212 | ||||||||
\(479\) | 35.2515 | 1.61068 | 0.805342 | − | 0.592810i | \(-0.201982\pi\) | ||||
0.805342 | + | 0.592810i | \(0.201982\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.4453 | 1.16021 | ||||||||
\(482\) | −35.6299 | −1.62290 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.3363 | −0.606195 | ||||||||
\(485\) | 11.5678 | 0.525268 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.4362 | 1.24325 | 0.621626 | − | 0.783314i | \(-0.286472\pi\) | ||||
0.621626 | + | 0.783314i | \(0.286472\pi\) | |||||||
\(488\) | −45.3580 | −2.05326 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.7145 | 0.529208 | ||||||||
\(491\) | 4.83937 | 0.218398 | 0.109199 | − | 0.994020i | \(-0.465171\pi\) | ||||
0.109199 | + | 0.994020i | \(0.465171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.43886 | −0.0648030 | ||||||||
\(494\) | −35.1238 | −1.58030 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.4803 | −1.36860 | ||||||||
\(497\) | 0.146393 | 0.00656661 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.7739 | 0.750904 | 0.375452 | − | 0.926842i | \(-0.377488\pi\) | ||||
0.375452 | + | 0.926842i | \(0.377488\pi\) | |||||||
\(500\) | 53.6042 | 2.39725 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.3927 | 0.954803 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.1470 | 0.585036 | ||||||||
\(506\) | 31.0795 | 1.38165 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 25.9319 | 1.15054 | ||||||||
\(509\) | 27.5401 | 1.22069 | 0.610347 | − | 0.792134i | \(-0.291030\pi\) | ||||
0.610347 | + | 0.792134i | \(0.291030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.46617 | −0.286046 | ||||||||
\(512\) | −47.7209 | −2.10898 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 52.1216 | 2.29899 | ||||||||
\(515\) | 22.0682 | 0.972443 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.08112 | −0.0475475 | ||||||||
\(518\) | 33.6472 | 1.47837 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 38.6256 | 1.69385 | ||||||||
\(521\) | −25.7250 | −1.12703 | −0.563515 | − | 0.826106i | \(-0.690551\pi\) | ||||
−0.563515 | + | 0.826106i | \(0.690551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.5746 | −1.29321 | −0.646605 | − | 0.762825i | \(-0.723812\pi\) | ||||
−0.646605 | + | 0.762825i | \(0.723812\pi\) | |||||||
\(524\) | 99.5486 | 4.34880 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 72.2327 | 3.14949 | ||||||||
\(527\) | 4.60324 | 0.200520 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.30539 | −0.230669 | ||||||||
\(530\) | −26.6396 | −1.15715 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −32.5643 | −1.41184 | ||||||||
\(533\) | 2.57987 | 0.111746 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.05624 | 0.218601 | ||||||||
\(536\) | −52.5870 | −2.27141 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30.0502 | −1.29556 | ||||||||
\(539\) | 8.96380 | 0.386098 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1889 | −0.567035 | −0.283517 | − | 0.958967i | \(-0.591501\pi\) | ||||
−0.283517 | + | 0.958967i | \(0.591501\pi\) | |||||||
\(542\) | −8.47940 | −0.364222 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.9438 | −0.469211 | ||||||||
\(545\) | −3.59718 | −0.154086 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.9543 | −0.767673 | −0.383836 | − | 0.923401i | \(-0.625397\pi\) | ||||
−0.383836 | + | 0.923401i | \(0.625397\pi\) | |||||||
\(548\) | −54.7977 | −2.34084 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.5596 | 0.919303 | ||||||||
\(551\) | 3.89935 | 0.166118 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.8522 | −0.716627 | ||||||||
\(554\) | 26.1680 | 1.11177 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −50.9891 | −2.16242 | ||||||||
\(557\) | −9.47412 | −0.401431 | −0.200716 | − | 0.979650i | \(-0.564327\pi\) | ||||
−0.200716 | + | 0.979650i | \(0.564327\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.6183 | 0.702881 | ||||||||
\(560\) | 24.4691 | 1.03401 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −43.3703 | −1.82947 | ||||||||
\(563\) | 33.2995 | 1.40341 | 0.701704 | − | 0.712469i | \(-0.252423\pi\) | ||||
0.701704 | + | 0.712469i | \(0.252423\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.9716 | −0.882283 | ||||||||
\(566\) | 39.9364 | 1.67865 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.518752 | −0.0217664 | ||||||||
\(569\) | 28.8525 | 1.20956 | 0.604780 | − | 0.796393i | \(-0.293261\pi\) | ||||
0.604780 | + | 0.796393i | \(0.293261\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.7379 | 0.951550 | 0.475775 | − | 0.879567i | \(-0.342168\pi\) | ||||
0.475775 | + | 0.879567i | \(0.342168\pi\) | |||||||
\(572\) | 51.5154 | 2.15397 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.41145 | 0.142391 | ||||||||
\(575\) | 12.2746 | 0.511886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.60031 | −0.191513 | −0.0957567 | − | 0.995405i | \(-0.530527\pi\) | ||||
−0.0957567 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(578\) | −39.5827 | −1.64642 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.47411 | −0.310346 | ||||||||
\(581\) | 29.1156 | 1.20792 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.3843 | −0.844231 | ||||||||
\(584\) | 22.9133 | 0.948159 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.4761 | 0.804552 | ||||||||
\(587\) | −32.6537 | −1.34776 | −0.673881 | − | 0.738839i | \(-0.735374\pi\) | ||||
−0.673881 | + | 0.738839i | \(0.735374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.4749 | −0.514020 | ||||||||
\(590\) | −51.8106 | −2.13301 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −57.1204 | −2.34763 | ||||||||
\(593\) | 36.4077 | 1.49509 | 0.747543 | − | 0.664214i | \(-0.231233\pi\) | ||||
0.747543 | + | 0.664214i | \(0.231233\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.69542 | −0.151497 | ||||||||
\(596\) | 34.7295 | 1.42257 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 41.8318 | 1.71063 | ||||||||
\(599\) | 40.2375 | 1.64406 | 0.822031 | − | 0.569443i | \(-0.192841\pi\) | ||||
0.822031 | + | 0.569443i | \(0.192841\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.80257 | 0.359065 | 0.179532 | − | 0.983752i | \(-0.442542\pi\) | ||||
0.179532 | + | 0.983752i | \(0.442542\pi\) | |||||||
\(602\) | 21.9750 | 0.895635 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 28.5822 | 1.16299 | ||||||||
\(605\) | 4.10139 | 0.166745 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.3824 | 0.543176 | 0.271588 | − | 0.962414i | \(-0.412451\pi\) | ||||
0.271588 | + | 0.962414i | \(0.412451\pi\) | |||||||
\(608\) | 29.6579 | 1.20279 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.3132 | 0.984414 | ||||||||
\(611\) | −1.45515 | −0.0588689 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.6160 | −0.630725 | −0.315363 | − | 0.948971i | \(-0.602126\pi\) | ||||
−0.315363 | + | 0.948971i | \(0.602126\pi\) | |||||||
\(614\) | 44.4763 | 1.79492 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 39.0828 | 1.57469 | ||||||||
\(617\) | −4.29634 | −0.172964 | −0.0864820 | − | 0.996253i | \(-0.527563\pi\) | ||||
−0.0864820 | + | 0.996253i | \(0.527563\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.8380 | −0.435614 | −0.217807 | − | 0.975992i | \(-0.569890\pi\) | ||||
−0.217807 | + | 0.975992i | \(0.569890\pi\) | |||||||
\(620\) | 23.9114 | 0.960305 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.2813 | −1.05378 | ||||||||
\(623\) | −34.4707 | −1.38104 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.89515 | −0.0758062 | ||||||||
\(626\) | 69.0456 | 2.75962 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.4529 | 0.417118 | ||||||||
\(629\) | 8.62653 | 0.343962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.5073 | 1.17467 | 0.587334 | − | 0.809345i | \(-0.300178\pi\) | ||||
0.587334 | + | 0.809345i | \(0.300178\pi\) | |||||||
\(632\) | 59.7168 | 2.37541 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −50.1475 | −1.99161 | ||||||||
\(635\) | −7.97499 | −0.316478 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0649 | 0.478031 | ||||||||
\(638\) | −8.15699 | −0.322938 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.57558 | 0.299451 | ||||||||
\(641\) | −7.72732 | −0.305211 | −0.152605 | − | 0.988287i | \(-0.548766\pi\) | ||||
−0.152605 | + | 0.988287i | \(0.548766\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.0167 | 0.395021 | 0.197511 | − | 0.980301i | \(-0.436714\pi\) | ||||
0.197511 | + | 0.980301i | \(0.436714\pi\) | |||||||
\(644\) | 38.7834 | 1.52828 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.9078 | −0.468505 | ||||||||
\(647\) | 13.6884 | 0.538147 | 0.269074 | − | 0.963120i | \(-0.413282\pi\) | ||||
0.269074 | + | 0.963120i | \(0.413282\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.6449 | −1.55620 | ||||||||
\(650\) | 29.0184 | 1.13819 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −87.9111 | −3.44286 | ||||||||
\(653\) | −38.1399 | −1.49253 | −0.746264 | − | 0.665650i | \(-0.768155\pi\) | ||||
−0.746264 | + | 0.665650i | \(0.768155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.6147 | −1.19622 | ||||||||
\(656\) | −5.79136 | −0.226115 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.92419 | −0.0750128 | ||||||||
\(659\) | −31.5253 | −1.22805 | −0.614026 | − | 0.789286i | \(-0.710451\pi\) | ||||
−0.614026 | + | 0.789286i | \(0.710451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.1122 | −1.17123 | −0.585614 | − | 0.810590i | \(-0.699146\pi\) | ||||
−0.585614 | + | 0.810590i | \(0.699146\pi\) | |||||||
\(662\) | −67.4080 | −2.61989 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −103.173 | −4.00390 | ||||||||
\(665\) | 10.0147 | 0.388352 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.64405 | −0.179818 | ||||||||
\(668\) | −106.616 | −4.12510 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 28.1882 | 1.08901 | ||||||||
\(671\) | 18.6042 | 0.718207 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.7982 | −1.57265 | −0.786327 | − | 0.617810i | \(-0.788020\pi\) | ||||
−0.786327 | + | 0.617810i | \(0.788020\pi\) | |||||||
\(674\) | −30.0697 | −1.15824 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.34388 | 0.320918 | ||||||||
\(677\) | −3.18994 | −0.122599 | −0.0612997 | − | 0.998119i | \(-0.519525\pi\) | ||||
−0.0612997 | + | 0.998119i | \(0.519525\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.7542 | 0.604589 | ||||||||
\(680\) | 13.0950 | 0.502169 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26.0961 | 0.999270 | ||||||||
\(683\) | −25.0239 | −0.957512 | −0.478756 | − | 0.877948i | \(-0.658912\pi\) | ||||
−0.478756 | + | 0.877948i | \(0.658912\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.8523 | 0.643892 | ||||||||
\(686\) | 51.5378 | 1.96772 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −37.3054 | −1.42225 | ||||||||
\(689\) | −27.4365 | −1.04525 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.5349 | 1.38985 | 0.694927 | − | 0.719081i | \(-0.255437\pi\) | ||||
0.694927 | + | 0.719081i | \(0.255437\pi\) | |||||||
\(692\) | 10.5633 | 0.401556 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −63.4045 | −2.40680 | ||||||||
\(695\) | 15.6810 | 0.594813 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.874633 | 0.0331291 | ||||||||
\(698\) | 27.5525 | 1.04288 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 26.9037 | 1.01687 | ||||||||
\(701\) | −40.6252 | −1.53439 | −0.767196 | − | 0.641413i | \(-0.778348\pi\) | ||||
−0.767196 | + | 0.641413i | \(0.778348\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.3781 | −0.881723 | ||||||||
\(704\) | −12.7455 | −0.480365 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.70718 | −0.101886 | ||||||||
\(707\) | 17.9049 | 0.673382 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.3401 | −1.10189 | −0.550945 | − | 0.834542i | \(-0.685733\pi\) | ||||
−0.550945 | + | 0.834542i | \(0.685733\pi\) | |||||||
\(710\) | 0.278067 | 0.0104357 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 122.149 | 4.57774 | ||||||||
\(713\) | 14.8574 | 0.556414 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.8428 | −0.592488 | ||||||||
\(716\) | −74.5938 | −2.78770 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 62.1347 | 2.31885 | ||||||||
\(719\) | 5.69273 | 0.212303 | 0.106152 | − | 0.994350i | \(-0.466147\pi\) | ||||
0.106152 | + | 0.994350i | \(0.466147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.0546 | 1.11929 | ||||||||
\(722\) | −16.8800 | −0.628208 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 77.8574 | 2.89355 | ||||||||
\(725\) | −3.22154 | −0.119645 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.4072 | 1.16483 | 0.582414 | − | 0.812892i | \(-0.302108\pi\) | ||||
0.582414 | + | 0.812892i | \(0.302108\pi\) | |||||||
\(728\) | 52.6040 | 1.94963 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.2822 | −0.454585 | ||||||||
\(731\) | 5.63399 | 0.208381 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.6365 | 1.75949 | 0.879747 | − | 0.475441i | \(-0.157712\pi\) | ||||
0.879747 | + | 0.475441i | \(0.157712\pi\) | |||||||
\(734\) | −48.3646 | −1.78517 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35.3221 | −1.30199 | ||||||||
\(737\) | 21.5693 | 0.794515 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.88794 | 0.363734 | 0.181867 | − | 0.983323i | \(-0.441786\pi\) | ||||
0.181867 | + | 0.983323i | \(0.441786\pi\) | |||||||
\(740\) | 44.8102 | 1.64726 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −36.2803 | −1.33189 | ||||||||
\(743\) | −17.7935 | −0.652782 | −0.326391 | − | 0.945235i | \(-0.605833\pi\) | ||||
−0.326391 | + | 0.945235i | \(0.605833\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.6806 | −0.391305 | ||||||||
\(746\) | −60.2759 | −2.20686 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.4649 | 0.638579 | ||||||||
\(749\) | 6.88606 | 0.251611 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.7934 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(752\) | 3.26656 | 0.119119 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.9790 | −0.399832 | ||||||||
\(755\) | −8.79003 | −0.319902 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.950190 | 0.0345353 | 0.0172676 | − | 0.999851i | \(-0.494503\pi\) | ||||
0.0172676 | + | 0.999851i | \(0.494503\pi\) | |||||||
\(758\) | −25.3499 | −0.920752 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −35.4877 | −1.28727 | ||||||||
\(761\) | 5.00434 | 0.181407 | 0.0907035 | − | 0.995878i | \(-0.471088\pi\) | ||||
0.0907035 | + | 0.995878i | \(0.471088\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.89898 | −0.177355 | ||||||||
\(764\) | 9.55445 | 0.345668 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.10375 | 0.184406 | ||||||||
\(767\) | −53.3605 | −1.92674 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.5794 | 0.597870 | 0.298935 | − | 0.954274i | \(-0.403369\pi\) | ||||
0.298935 | + | 0.954274i | \(0.403369\pi\) | |||||||
\(770\) | −20.9495 | −0.754969 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −71.0268 | −2.55631 | ||||||||
\(773\) | 30.4696 | 1.09592 | 0.547958 | − | 0.836506i | \(-0.315405\pi\) | ||||
0.547958 | + | 0.836506i | \(0.315405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3064 | 0.370218 | ||||||||
\(776\) | −55.8259 | −2.00403 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.1044 | 0.613221 | ||||||||
\(779\) | −2.37028 | −0.0849240 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.212773 | 0.00761363 | ||||||||
\(782\) | 14.1819 | 0.507145 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −27.0837 | −0.967277 | ||||||||
\(785\) | −3.21465 | −0.114736 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.7903 | 1.06191 | 0.530954 | − | 0.847400i | \(-0.321834\pi\) | ||||
0.530954 | + | 0.847400i | \(0.321834\pi\) | |||||||
\(788\) | 28.2114 | 1.00499 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.0100 | −1.13886 | ||||||||
\(791\) | −28.5611 | −1.01552 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.0406 | 0.889216 | ||||||||
\(794\) | −19.7054 | −0.699318 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 110.499 | 3.91653 | ||||||||
\(797\) | −0.503125 | −0.0178216 | −0.00891081 | − | 0.999960i | \(-0.502836\pi\) | ||||
−0.00891081 | + | 0.999960i | \(0.502836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.493327 | −0.0174527 | ||||||||
\(800\) | −24.5026 | −0.866299 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −66.7830 | −2.35819 | ||||||||
\(803\) | −9.39820 | −0.331655 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.9273 | −0.420382 | ||||||||
\(806\) | 35.1244 | 1.23720 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −63.4471 | −2.23206 | ||||||||
\(809\) | 21.1371 | 0.743142 | 0.371571 | − | 0.928405i | \(-0.378819\pi\) | ||||
0.371571 | + | 0.928405i | \(0.378819\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.7238 | 0.552139 | 0.276069 | − | 0.961138i | \(-0.410968\pi\) | ||||
0.276069 | + | 0.961138i | \(0.410968\pi\) | |||||||
\(812\) | −10.1789 | −0.357211 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 48.9043 | 1.71410 | ||||||||
\(815\) | 27.0358 | 0.947023 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.2683 | −0.534169 | ||||||||
\(818\) | −35.4202 | −1.23844 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.54325 | 0.158657 | ||||||||
\(821\) | 42.7588 | 1.49229 | 0.746147 | − | 0.665781i | \(-0.231902\pi\) | ||||
0.746147 | + | 0.665781i | \(0.231902\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.2920 | −1.16049 | −0.580243 | − | 0.814444i | \(-0.697042\pi\) | ||||
−0.580243 | + | 0.814444i | \(0.697042\pi\) | |||||||
\(824\) | −106.500 | −3.71012 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −70.5605 | −2.45511 | ||||||||
\(827\) | −14.2343 | −0.494975 | −0.247487 | − | 0.968891i | \(-0.579605\pi\) | ||||
−0.247487 | + | 0.968891i | \(0.579605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.3766 | −0.429855 | −0.214928 | − | 0.976630i | \(-0.568952\pi\) | ||||
−0.214928 | + | 0.976630i | \(0.568952\pi\) | |||||||
\(830\) | 55.3040 | 1.91963 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.1550 | −0.594743 | ||||||||
\(833\) | 4.09029 | 0.141720 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.7882 | 1.13468 | ||||||||
\(836\) | −47.3303 | −1.63695 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −62.0917 | −2.14492 | ||||||||
\(839\) | −31.6864 | −1.09394 | −0.546969 | − | 0.837153i | \(-0.684218\pi\) | ||||
−0.546969 | + | 0.837153i | \(0.684218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7811 | −0.957970 | ||||||||
\(842\) | 80.5270 | 2.77514 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.0519 | 0.380421 | ||||||||
\(845\) | −2.56604 | −0.0882745 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.58565 | 0.191925 | ||||||||
\(848\) | 61.5903 | 2.11502 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.83789 | 0.337437 | ||||||||
\(851\) | 27.8429 | 0.954443 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2234 | 1.03483 | 0.517416 | − | 0.855734i | \(-0.326894\pi\) | ||||
0.517416 | + | 0.855734i | \(0.326894\pi\) | |||||||
\(854\) | 33.1120 | 1.13307 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24.4012 | −0.834017 | ||||||||
\(857\) | 31.4206 | 1.07331 | 0.536653 | − | 0.843803i | \(-0.319688\pi\) | ||||
0.536653 | + | 0.843803i | \(0.319688\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.5866 | 0.941244 | 0.470622 | − | 0.882335i | \(-0.344030\pi\) | ||||
0.470622 | + | 0.882335i | \(0.344030\pi\) | |||||||
\(860\) | 29.2656 | 0.997948 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −72.5835 | −2.47220 | ||||||||
\(863\) | −40.3690 | −1.37418 | −0.687088 | − | 0.726574i | \(-0.741111\pi\) | ||||
−0.687088 | + | 0.726574i | \(0.741111\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.24859 | −0.110455 | ||||||||
\(866\) | −53.2922 | −1.81094 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.5648 | 1.10532 | ||||||||
\(869\) | −24.4937 | −0.830890 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.0315 | 0.983694 | ||||||||
\(872\) | 17.3599 | 0.587879 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −38.4334 | −1.30003 | ||||||||
\(875\) | −22.4511 | −0.758985 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.330616 | −0.0111641 | −0.00558205 | − | 0.999984i | \(-0.501777\pi\) | ||||
−0.00558205 | + | 0.999984i | \(0.501777\pi\) | |||||||
\(878\) | −94.1746 | −3.17824 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 35.5644 | 1.19888 | ||||||||
\(881\) | 4.51734 | 0.152193 | 0.0760965 | − | 0.997100i | \(-0.475754\pi\) | ||||
0.0760965 | + | 0.997100i | \(0.475754\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.7445 | −1.57308 | −0.786539 | − | 0.617540i | \(-0.788129\pi\) | ||||
−0.786539 | + | 0.617540i | \(0.788129\pi\) | |||||||
\(884\) | 23.5071 | 0.790629 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 72.7404 | 2.44376 | ||||||||
\(887\) | 9.29057 | 0.311947 | 0.155973 | − | 0.987761i | \(-0.450149\pi\) | ||||
0.155973 | + | 0.987761i | \(0.450149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.8611 | −0.364269 | ||||||||
\(890\) | −65.4757 | −2.19475 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 63.9349 | 2.14070 | ||||||||
\(893\) | 1.33693 | 0.0447387 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.9403 | 0.766808 | ||||||||
\(896\) | 10.3171 | 0.344671 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33.4981 | 1.11785 | ||||||||
\(899\) | −3.89941 | −0.130053 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.30159 | −0.309881 | ||||||||
\(902\) | 4.95835 | 0.165095 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 101.208 | 3.36614 | ||||||||
\(905\) | −23.9439 | −0.795923 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.0423 | −0.798313 | −0.399156 | − | 0.916883i | \(-0.630697\pi\) | ||||
−0.399156 | + | 0.916883i | \(0.630697\pi\) | |||||||
\(908\) | −56.2138 | −1.86552 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −28.1973 | −0.934732 | ||||||||
\(911\) | −6.04735 | −0.200358 | −0.100179 | − | 0.994969i | \(-0.531941\pi\) | ||||
−0.100179 | + | 0.994969i | \(0.531941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.3179 | 1.40052 | ||||||||
\(914\) | 0.387061 | 0.0128028 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 127.649 | 4.21765 | ||||||||
\(917\) | −41.6940 | −1.37686 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.8990 | −1.15121 | −0.575606 | − | 0.817727i | \(-0.695234\pi\) | ||||
−0.575606 | + | 0.817727i | \(0.695234\pi\) | |||||||
\(920\) | 42.2652 | 1.39344 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −100.866 | −3.32185 | ||||||||
\(923\) | 0.286385 | 0.00942648 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.3144 | 0.635054 | ||||||||
\(926\) | −52.0956 | −1.71197 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.27048 | 0.304319 | ||||||||
\(929\) | −39.8343 | −1.30692 | −0.653460 | − | 0.756961i | \(-0.726683\pi\) | ||||
−0.653460 | + | 0.756961i | \(0.726683\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.0848 | −0.363289 | ||||||||
\(932\) | −67.7992 | −2.22084 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38.4573 | −1.25836 | ||||||||
\(935\) | −5.37108 | −0.175653 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.6822 | 0.348971 | 0.174485 | − | 0.984660i | \(-0.444174\pi\) | ||||
0.174485 | + | 0.984660i | \(0.444174\pi\) | |||||||
\(938\) | 38.3894 | 1.25346 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.56257 | −0.0835819 | ||||||||
\(941\) | 1.40329 | 0.0457459 | 0.0228729 | − | 0.999738i | \(-0.492719\pi\) | ||||
0.0228729 | + | 0.999738i | \(0.492719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.82296 | 0.0919281 | ||||||||
\(944\) | 119.785 | 3.89868 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.9395 | 1.03844 | ||||||||
\(947\) | −9.93625 | −0.322885 | −0.161442 | − | 0.986882i | \(-0.551615\pi\) | ||||
−0.161442 | + | 0.986882i | \(0.551615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.6496 | −0.410625 | ||||||||
\(950\) | −26.6609 | −0.864995 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17.8339 | 0.578001 | ||||||||
\(953\) | −11.4560 | −0.371097 | −0.185548 | − | 0.982635i | \(-0.559406\pi\) | ||||
−0.185548 | + | 0.982635i | \(0.559406\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.93834 | −0.0950823 | ||||||||
\(956\) | 112.304 | 3.63218 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 91.1908 | 2.94624 | ||||||||
\(959\) | 22.9510 | 0.741126 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.5249 | −0.597578 | ||||||||
\(962\) | 65.8234 | 2.12223 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −64.6227 | −2.08136 | ||||||||
\(965\) | 21.8433 | 0.703160 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0337 | −1.03014 | −0.515068 | − | 0.857150i | \(-0.672233\pi\) | ||||
−0.515068 | + | 0.857150i | \(0.672233\pi\) | |||||||
\(968\) | −19.7931 | −0.636175 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 29.9244 | 0.960814 | ||||||||
\(971\) | 21.7771 | 0.698859 | 0.349429 | − | 0.936963i | \(-0.386375\pi\) | ||||
0.349429 | + | 0.936963i | \(0.386375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.3558 | 0.684636 | ||||||||
\(974\) | 70.9736 | 2.27414 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −56.2118 | −1.79930 | ||||||||
\(977\) | −48.8640 | −1.56330 | −0.781649 | − | 0.623719i | \(-0.785621\pi\) | ||||
−0.781649 | + | 0.623719i | \(0.785621\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −50.1012 | −1.60124 | ||||||||
\(980\) | 21.2469 | 0.678706 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.5188 | 0.399490 | ||||||||
\(983\) | −43.9288 | −1.40111 | −0.700555 | − | 0.713598i | \(-0.747064\pi\) | ||||
−0.700555 | + | 0.713598i | \(0.747064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.67600 | −0.276440 | ||||||||
\(986\) | −3.72213 | −0.118537 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −63.7049 | −2.02672 | ||||||||
\(989\) | 18.1842 | 0.578225 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0715 | 0.574060 | 0.287030 | − | 0.957922i | \(-0.407332\pi\) | ||||
0.287030 | + | 0.957922i | \(0.407332\pi\) | |||||||
\(992\) | −29.6584 | −0.941655 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.378697 | 0.0120115 | ||||||||
\(995\) | −33.9824 | −1.07731 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.5966 | −1.15903 | −0.579514 | − | 0.814963i | \(-0.696757\pi\) | ||||
−0.579514 | + | 0.814963i | \(0.696757\pi\) | |||||||
\(998\) | 43.3918 | 1.37354 | ||||||||
\(999\) | 0 | 0 |
(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 | 4527.2.a.k.1.10 | 10 | ||
3.2 | odd | 2 | 503.2.a.e.1.1 | ✓ | 10 | ||
12.11 | even | 2 | 8048.2.a.p.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.1 | ✓ | 10 | 3.2 | odd | 2 | ||
4527.2.a.k.1.10 | 10 | 1.1 | even | 1 | trivial | ||
8048.2.a.p.1.8 | 10 | 12.11 | even | 2 |