Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(1,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 552.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.35026 | 1.49828 | 0.749141 | − | 0.662410i | \(-0.230466\pi\) | ||||
0.749141 | + | 0.662410i | \(0.230466\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.96239 | −1.11968 | −0.559839 | − | 0.828602i | \(-0.689137\pi\) | ||||
−0.559839 | + | 0.828602i | \(0.689137\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.61213 | 0.486075 | 0.243037 | − | 0.970017i | \(-0.421856\pi\) | ||||
0.243037 | + | 0.970017i | \(0.421856\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.35026 | 0.865034 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.96239 | 1.20356 | 0.601778 | − | 0.798663i | \(-0.294459\pi\) | ||||
0.601778 | + | 0.798663i | \(0.294459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.35026 | −0.309771 | −0.154886 | − | 0.987932i | \(-0.549501\pi\) | ||||
−0.154886 | + | 0.987932i | \(0.549501\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.96239 | −0.646446 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.22425 | 1.24485 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.92478 | −1.47159 | −0.735797 | − | 0.677202i | \(-0.763192\pi\) | ||||
−0.735797 | + | 0.677202i | \(0.763192\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.92478 | 1.06412 | 0.532061 | − | 0.846706i | \(-0.321418\pi\) | ||||
0.532061 | + | 0.846706i | \(0.321418\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.61213 | 0.280635 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.92478 | −1.67759 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.31265 | −0.380197 | −0.190099 | − | 0.981765i | \(-0.560881\pi\) | ||||
−0.190099 | + | 0.981765i | \(0.560881\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.22425 | −0.191196 | −0.0955982 | − | 0.995420i | \(-0.530476\pi\) | ||||
−0.0955982 | + | 0.995420i | \(0.530476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.57452 | −0.697607 | −0.348804 | − | 0.937196i | \(-0.613412\pi\) | ||||
−0.348804 | + | 0.937196i | \(0.613412\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.35026 | 0.499428 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.92478 | 0.280758 | 0.140379 | − | 0.990098i | \(-0.455168\pi\) | ||||
0.140379 | + | 0.990098i | \(0.455168\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.77575 | 0.253678 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.96239 | 0.694873 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.12601 | −0.566751 | −0.283375 | − | 0.959009i | \(-0.591454\pi\) | ||||
−0.283375 | + | 0.959009i | \(0.591454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.40105 | 0.728277 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.35026 | −0.178847 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.70052 | 0.351578 | 0.175789 | − | 0.984428i | \(-0.443752\pi\) | ||||
0.175789 | + | 0.984428i | \(0.443752\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.3127 | 1.83255 | 0.916274 | − | 0.400553i | \(-0.131182\pi\) | ||||
0.916274 | + | 0.400553i | \(0.131182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.96239 | −0.373226 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.70052 | 0.831098 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.57452 | 0.558866 | 0.279433 | − | 0.960165i | \(-0.409854\pi\) | ||||
0.279433 | + | 0.960165i | \(0.409854\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.6253 | −1.97306 | −0.986530 | − | 0.163580i | \(-0.947696\pi\) | ||||
−0.986530 | + | 0.163580i | \(0.947696\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.22425 | 0.718715 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.77575 | −0.544247 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.03761 | −0.566776 | −0.283388 | − | 0.959005i | \(-0.591458\pi\) | ||||
−0.283388 | + | 0.959005i | \(0.591458\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.0132 | −1.64791 | −0.823955 | − | 0.566655i | \(-0.808237\pi\) | ||||
−0.823955 | + | 0.566655i | \(0.808237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.6253 | 1.80327 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.92478 | −0.849625 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.73813 | −0.608241 | −0.304121 | − | 0.952634i | \(-0.598363\pi\) | ||||
−0.304121 | + | 0.952634i | \(0.598363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.92478 | −0.621085 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.92478 | 0.614371 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.52373 | −0.464125 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.7005 | 1.28954 | 0.644771 | − | 0.764375i | \(-0.276953\pi\) | ||||
0.644771 | + | 0.764375i | \(0.276953\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.61213 | 0.162025 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.4010 | −1.53246 | −0.766231 | − | 0.642566i | \(-0.777870\pi\) | ||||
−0.766231 | + | 0.642566i | \(0.777870\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6629 | −1.34625 | −0.673123 | − | 0.739530i | \(-0.735048\pi\) | ||||
−0.673123 | + | 0.739530i | \(0.735048\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.92478 | −0.968559 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.2374 | 1.76308 | 0.881539 | − | 0.472111i | \(-0.156508\pi\) | ||||
0.881539 | + | 0.472111i | \(0.156508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.4617 | −1.86409 | −0.932045 | − | 0.362341i | \(-0.881977\pi\) | ||||
−0.932045 | + | 0.362341i | \(0.881977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.31265 | −0.219507 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.66291 | 0.720866 | 0.360433 | − | 0.932785i | \(-0.382629\pi\) | ||||
0.360433 | + | 0.932785i | \(0.382629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.35026 | −0.312414 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.7005 | −1.34759 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.40105 | −0.763732 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.22425 | −0.110387 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.10157 | 0.366856 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4763 | −1.37330 | −0.686648 | − | 0.726990i | \(-0.740919\pi\) | ||||
−0.686648 | + | 0.726990i | \(0.740919\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.57452 | −0.402764 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.775746 | 0.0677773 | 0.0338886 | − | 0.999426i | \(-0.489211\pi\) | ||||
0.0338886 | + | 0.999426i | \(0.489211\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.35026 | 0.288345 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.96239 | −0.765709 | −0.382854 | − | 0.923809i | \(-0.625059\pi\) | ||||
−0.382854 | + | 0.923809i | \(0.625059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.92478 | 0.162095 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.22425 | 0.269626 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.5501 | −2.20486 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.77575 | 0.146461 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.0508 | −0.823392 | −0.411696 | − | 0.911321i | \(-0.635064\pi\) | ||||
−0.411696 | + | 0.911321i | \(0.635064\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8496 | 0.964303 | 0.482152 | − | 0.876088i | \(-0.339855\pi\) | ||||
0.482152 | + | 0.876088i | \(0.339855\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.96239 | 0.401185 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.8496 | 1.59435 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.9380 | 1.83065 | 0.915324 | − | 0.402718i | \(-0.131935\pi\) | ||||
0.915324 | + | 0.402718i | \(0.131935\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.12601 | −0.327214 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.96239 | 0.233469 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.70052 | 0.524826 | 0.262413 | − | 0.964956i | \(-0.415482\pi\) | ||||
0.262413 | + | 0.964956i | \(0.415482\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.40105 | 0.420471 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.6253 | 1.90556 | 0.952781 | − | 0.303657i | \(-0.0982076\pi\) | ||||
0.952781 | + | 0.303657i | \(0.0982076\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.35026 | −0.103257 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.9248 | −1.81897 | −0.909484 | − | 0.415740i | \(-0.863523\pi\) | ||||
−0.909484 | + | 0.415740i | \(0.863523\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.4387 | −1.39383 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.70052 | 0.202984 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.3258 | 1.44448 | 0.722240 | − | 0.691643i | \(-0.243113\pi\) | ||||
0.722240 | + | 0.691643i | \(0.243113\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.2374 | 1.50424 | 0.752118 | − | 0.659028i | \(-0.229032\pi\) | ||||
0.752118 | + | 0.659028i | \(0.229032\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.3127 | 1.05802 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.74798 | −0.569643 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | 0.585018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.96239 | −0.215482 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.14903 | −0.662001 | −0.331000 | − | 0.943631i | \(-0.607386\pi\) | ||||
−0.331000 | + | 0.943631i | \(0.607386\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.77575 | −0.487729 | −0.243864 | − | 0.969809i | \(-0.578415\pi\) | ||||
−0.243864 | + | 0.969809i | \(0.578415\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.70052 | 0.479834 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.5501 | −1.74912 | −0.874560 | − | 0.484917i | \(-0.838850\pi\) | ||||
−0.874560 | + | 0.484917i | \(0.838850\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.3357 | −1.08712 | −0.543559 | − | 0.839371i | \(-0.682923\pi\) | ||||
−0.543559 | + | 0.839371i | \(0.682923\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.57452 | 0.322661 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.4763 | 1.64771 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.10157 | −0.286466 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.17679 | −0.150572 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.14903 | −0.354474 | −0.177237 | − | 0.984168i | \(-0.556716\pi\) | ||||
−0.177237 | + | 0.984168i | \(0.556716\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.6253 | −1.13915 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.3258 | −1.04521 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.5515 | −1.19147 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.92478 | 0.667613 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.55149 | 0.639615 | 0.319808 | − | 0.947482i | \(-0.396382\pi\) | ||||
0.319808 | + | 0.947482i | \(0.396382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.22425 | 0.414950 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.68735 | 0.244738 | 0.122369 | − | 0.992485i | \(-0.460951\pi\) | ||||
0.122369 | + | 0.992485i | \(0.460951\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.2374 | 0.808672 | 0.404336 | − | 0.914611i | \(-0.367503\pi\) | ||||
0.404336 | + | 0.914611i | \(0.367503\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.77575 | −0.314221 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.40105 | −0.222810 | −0.111405 | − | 0.993775i | \(-0.535535\pi\) | ||||
−0.111405 | + | 0.993775i | \(0.535535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.44851 | 0.420654 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.03761 | −0.327228 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.55149 | −0.100358 | −0.0501789 | − | 0.998740i | \(-0.515979\pi\) | ||||
−0.0501789 | + | 0.998740i | \(0.515979\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.7005 | 1.33344 | 0.666719 | − | 0.745309i | \(-0.267698\pi\) | ||||
0.666719 | + | 0.745309i | \(0.267698\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.94921 | 0.380081 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.70052 | −0.171830 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.0132 | −0.951421 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.46310 | 0.534186 | 0.267093 | − | 0.963671i | \(-0.413937\pi\) | ||||
0.267093 | + | 0.963671i | \(0.413937\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.61213 | −0.101354 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.6253 | 1.04112 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.6253 | 1.16181 | 0.580907 | − | 0.813970i | \(-0.302698\pi\) | ||||
0.580907 | + | 0.813970i | \(0.302698\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.85097 | 0.425699 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.92478 | −0.490531 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.523730 | −0.0322946 | −0.0161473 | − | 0.999870i | \(-0.505140\pi\) | ||||
−0.0161473 | + | 0.999870i | \(0.505140\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.8232 | −0.849153 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.73813 | −0.351168 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.700523 | 0.0427117 | 0.0213558 | − | 0.999772i | \(-0.493202\pi\) | ||||
0.0213558 | + | 0.999772i | \(0.493202\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0752 | −0.612026 | −0.306013 | − | 0.952027i | \(-0.598995\pi\) | ||||
−0.306013 | + | 0.952027i | \(0.598995\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.92478 | −0.358584 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0343 | 0.605090 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.4749 | −1.35038 | −0.675192 | − | 0.737642i | \(-0.735939\pi\) | ||||
−0.675192 | + | 0.737642i | \(0.735939\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.92478 | 0.354707 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.8134 | 0.704726 | 0.352363 | − | 0.935863i | \(-0.385378\pi\) | ||||
0.352363 | + | 0.935863i | \(0.385378\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.1998 | 1.73575 | 0.867874 | − | 0.496784i | \(-0.165486\pi\) | ||||
0.867874 | + | 0.496784i | \(0.165486\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.52373 | −0.267963 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.62672 | 0.214078 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.62530 | 0.448547 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.7005 | 0.744518 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.27504 | 0.541854 | 0.270927 | − | 0.962600i | \(-0.412670\pi\) | ||||
0.270927 | + | 0.962600i | \(0.412670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.04746 | 0.526764 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.61213 | 0.0935451 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.5515 | 0.781095 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.4010 | −0.884767 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 47.9511 | 2.74567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.9511 | 1.82355 | 0.911774 | − | 0.410693i | \(-0.134713\pi\) | ||||
0.911774 | + | 0.410693i | \(0.134713\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6629 | −0.777256 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1490 | 0.745613 | 0.372807 | − | 0.927909i | \(-0.378395\pi\) | ||||
0.372807 | + | 0.927909i | \(0.378395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0263 | 1.35805 | 0.679025 | − | 0.734115i | \(-0.262403\pi\) | ||||
0.679025 | + | 0.734115i | \(0.262403\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.92478 | −0.559198 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.9248 | 1.56841 | 0.784206 | − | 0.620501i | \(-0.213071\pi\) | ||||
0.784206 | + | 0.620501i | \(0.213071\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.7757 | −0.715304 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.2374 | 1.01791 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.70052 | −0.372827 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.4485 | 0.690519 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.4617 | −1.07623 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.70194 | −0.314358 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.70052 | 0.368294 | 0.184147 | − | 0.982899i | \(-0.441048\pi\) | ||||
0.184147 | + | 0.982899i | \(0.441048\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.31265 | −0.126732 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.3258 | 0.837339 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.3733 | −0.565069 | −0.282534 | − | 0.959257i | \(-0.591175\pi\) | ||||
−0.282534 | + | 0.959257i | \(0.591175\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.66291 | 0.416192 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.55149 | 0.517242 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4763 | 0.835640 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.35026 | −0.180372 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.7743 | −0.954176 | −0.477088 | − | 0.878855i | \(-0.658308\pi\) | ||||
−0.477088 | + | 0.878855i | \(0.658308\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.6253 | 0.996989 | 0.498495 | − | 0.866893i | \(-0.333886\pi\) | ||||
0.498495 | + | 0.866893i | \(0.333886\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.7743 | −0.839583 | −0.419791 | − | 0.907621i | \(-0.637897\pi\) | ||||
−0.419791 | + | 0.907621i | \(0.637897\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −55.6991 | −2.95620 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.7005 | −0.778034 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.29948 | −0.279696 | −0.139848 | − | 0.990173i | \(-0.544661\pi\) | ||||
−0.139848 | + | 0.990173i | \(0.544661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1768 | −0.904042 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.40105 | −0.440941 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.70052 | 0.350721 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.51388 | 0.235623 | 0.117811 | − | 0.993036i | \(-0.462412\pi\) | ||||
0.117811 | + | 0.993036i | \(0.462412\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.22425 | −0.0637321 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2228 | 0.634578 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.6873 | 0.708704 | 0.354352 | − | 0.935112i | \(-0.384701\pi\) | ||||
0.354352 | + | 0.935112i | \(0.384701\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.10157 | 0.211804 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.8496 | −0.816294 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.3488 | 1.55892 | 0.779458 | − | 0.626455i | \(-0.215495\pi\) | ||||
0.779458 | + | 0.626455i | \(0.215495\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.4763 | −0.792873 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.3733 | 1.44981 | 0.724904 | − | 0.688850i | \(-0.241884\pi\) | ||||
0.724904 | + | 0.688850i | \(0.241884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0000 | −0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.57452 | −0.232536 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.4518 | 0.986247 | 0.493124 | − | 0.869959i | \(-0.335855\pi\) | ||||
0.493124 | + | 0.869959i | \(0.335855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.96239 | −0.250959 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.775746 | 0.0391312 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.8773 | −0.849190 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.8021 | −1.44554 | −0.722768 | − | 0.691091i | \(-0.757130\pi\) | ||||
−0.722768 | + | 0.691091i | \(0.757130\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.00000 | 0.200250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.1378 | −1.20538 | −0.602691 | − | 0.797974i | \(-0.705905\pi\) | ||||
−0.602691 | + | 0.797974i | \(0.705905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8496 | 0.590268 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.35026 | 0.166476 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.72829 | −0.184804 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.1768 | −1.39325 | −0.696626 | − | 0.717434i | \(-0.745316\pi\) | ||||
−0.696626 | + | 0.717434i | \(0.745316\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.96239 | −0.442082 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −50.2981 | −2.46903 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.4617 | −1.04847 | −0.524236 | − | 0.851573i | \(-0.675649\pi\) | ||||
−0.524236 | + | 0.851573i | \(0.675649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1636 | 0.641556 | 0.320778 | − | 0.947154i | \(-0.396056\pi\) | ||||
0.320778 | + | 0.947154i | \(0.396056\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.92478 | 0.0935859 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 30.8872 | 1.49825 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42.3996 | −2.05186 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.22425 | 0.155668 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.5223 | −1.03669 | −0.518347 | − | 0.855171i | \(-0.673452\pi\) | ||||
−0.518347 | + | 0.855171i | \(0.673452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.77575 | −0.133394 | −0.0666969 | − | 0.997773i | \(-0.521246\pi\) | ||||
−0.0666969 | + | 0.997773i | \(0.521246\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −26.5501 | −1.27298 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.35026 | 0.0645918 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.84955 | 0.183729 | 0.0918646 | − | 0.995772i | \(-0.470717\pi\) | ||||
0.0918646 | + | 0.995772i | \(0.470717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.77575 | 0.0845593 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.9525 | 1.28055 | 0.640277 | − | 0.768144i | \(-0.278820\pi\) | ||||
0.640277 | + | 0.768144i | \(0.278820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.2243 | −0.911317 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.0508 | −0.475386 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.07381 | 0.0506761 | 0.0253381 | − | 0.999679i | \(-0.491934\pi\) | ||||
0.0253381 | + | 0.999679i | \(0.491934\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.97365 | −0.0929357 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.8496 | 0.556741 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19.8496 | −0.930561 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.29948 | 0.341455 | 0.170728 | − | 0.985318i | \(-0.445388\pi\) | ||||
0.170728 | + | 0.985318i | \(0.445388\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.96239 | 0.231624 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.59754 | 0.260703 | 0.130352 | − | 0.991468i | \(-0.458389\pi\) | ||||
0.130352 | + | 0.991468i | \(0.458389\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.84955 | −0.178904 | −0.0894520 | − | 0.995991i | \(-0.528512\pi\) | ||||
−0.0894520 | + | 0.995991i | \(0.528512\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.8496 | 0.920501 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.68735 | −0.170630 | −0.0853151 | − | 0.996354i | \(-0.527190\pi\) | ||||
−0.0853151 | + | 0.996354i | \(0.527190\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.5515 | −0.625750 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.9380 | 1.05692 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.37470 | −0.339089 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.40437 | −0.385619 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.12601 | −0.188917 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.59895 | −0.118749 | −0.0593746 | − | 0.998236i | \(-0.518911\pi\) | ||||
−0.0593746 | + | 0.998236i | \(0.518911\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.62530 | −0.210896 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.96239 | 0.134793 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 42.5501 | 1.93210 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.2506 | 1.50673 | 0.753364 | − | 0.657603i | \(-0.228430\pi\) | ||||
0.753364 | + | 0.657603i | \(0.228430\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.70052 | 0.303008 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.9248 | −0.628416 | −0.314208 | − | 0.949354i | \(-0.601739\pi\) | ||||
−0.314208 | + | 0.949354i | \(0.601739\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −39.3258 | −1.77115 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.40105 | 0.242759 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 49.2506 | 2.20919 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.5975 | 0.877306 | 0.438653 | − | 0.898656i | \(-0.355456\pi\) | ||||
0.438653 | + | 0.898656i | \(0.355456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.6253 | 1.10018 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.4749 | 1.26963 | 0.634816 | − | 0.772664i | \(-0.281076\pi\) | ||||
0.634816 | + | 0.772664i | \(0.281076\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −51.5975 | −2.29606 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −39.6239 | −1.75630 | −0.878149 | − | 0.478387i | \(-0.841222\pi\) | ||||
−0.878149 | + | 0.478387i | \(0.841222\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.92478 | −0.262097 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.35026 | −0.0596155 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45.7743 | −2.01706 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.10299 | 0.136469 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.9248 | −1.05018 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.2130 | −0.797926 | −0.398963 | − | 0.916967i | \(-0.630630\pi\) | ||||
−0.398963 | + | 0.916967i | \(0.630630\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.8265 | −1.08559 | −0.542794 | − | 0.839866i | \(-0.682634\pi\) | ||||
−0.542794 | + | 0.839866i | \(0.682634\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.4387 | −0.804729 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.4010 | 1.28073 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.70052 | 0.117193 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.44851 | −0.106057 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 61.1002 | 2.64159 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.3258 | 0.833971 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.86273 | 0.123306 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.47486 | 0.278376 | 0.139188 | − | 0.990266i | \(-0.455551\pi\) | ||||
0.139188 | + | 0.990266i | \(0.455551\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.2374 | 0.868471 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −65.2017 | −2.79294 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.55008 | 0.109033 | 0.0545167 | − | 0.998513i | \(-0.482638\pi\) | ||||
0.0545167 | + | 0.998513i | \(0.482638\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.3127 | 0.610849 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.7005 | 0.455858 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.9234 | 0.634606 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.74798 | −0.328884 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.75131 | −0.201319 | −0.100660 | − | 0.994921i | \(-0.532095\pi\) | ||||
−0.100660 | + | 0.994921i | \(0.532095\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.14903 | −0.386963 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.6873 | 0.829723 | 0.414861 | − | 0.909885i | \(-0.363830\pi\) | ||||
0.414861 | + | 0.909885i | \(0.363830\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.6728 | 1.08006 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.96239 | −0.124409 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.48612 | −0.0623013 | −0.0311507 | − | 0.999515i | \(-0.509917\pi\) | ||||
−0.0311507 | + | 0.999515i | \(0.509917\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.1246 | −0.465550 | −0.232775 | − | 0.972531i | \(-0.574781\pi\) | ||||
−0.232775 | + | 0.972531i | \(0.574781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.14903 | −0.382206 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.22425 | −0.259569 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.176793 | 0.00736000 | 0.00368000 | − | 0.999993i | \(-0.498829\pi\) | ||||
0.00368000 | + | 0.999993i | \(0.498829\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.77575 | −0.281590 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.4749 | 1.84513 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.65165 | −0.275483 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.70052 | 0.277033 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.6728 | −0.564335 | −0.282168 | − | 0.959365i | \(-0.591053\pi\) | ||||
−0.282168 | + | 0.959365i | \(0.591053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.5501 | −1.00986 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.2243 | 0.871576 | 0.435788 | − | 0.900049i | \(-0.356470\pi\) | ||||
0.435788 | + | 0.900049i | \(0.356470\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −49.2506 | −2.01908 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.3357 | −0.627647 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.0000 | −1.30748 | −0.653742 | − | 0.756717i | \(-0.726802\pi\) | ||||
−0.653742 | + | 0.756717i | \(0.726802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.1768 | 1.63885 | 0.819423 | − | 0.573190i | \(-0.194294\pi\) | ||||
0.819423 | + | 0.573190i | \(0.194294\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.57452 | 0.186289 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.1457 | −1.14429 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0000 | −0.974130 | −0.487065 | − | 0.873366i | \(-0.661933\pi\) | ||||
−0.487065 | + | 0.873366i | \(0.661933\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 23.4763 | 0.951306 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.84955 | 0.155736 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.3127 | 0.578083 | 0.289041 | − | 0.957317i | \(-0.406664\pi\) | ||||
0.289041 | + | 0.957317i | \(0.406664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.10157 | −0.165391 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.6907 | −0.832975 | −0.416488 | − | 0.909141i | \(-0.636739\pi\) | ||||
−0.416488 | + | 0.909141i | \(0.636739\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.3028 | 1.29836 | 0.649180 | − | 0.760635i | \(-0.275112\pi\) | ||||
0.649180 | + | 0.760635i | \(0.275112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.9986 | 0.681034 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.3799 | −0.695197 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.17679 | −0.0869327 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.4763 | −0.457589 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.58769 | 0.142824 | 0.0714118 | − | 0.997447i | \(-0.477250\pi\) | ||||
0.0714118 | + | 0.997447i | \(0.477250\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.14903 | −0.204656 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −51.8496 | −2.05759 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.55149 | 0.140715 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.6253 | −0.657687 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.71179 | 0.146607 | 0.0733034 | − | 0.997310i | \(-0.476646\pi\) | ||||
0.0733034 | + | 0.997310i | \(0.476646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.1246 | 1.70067 | 0.850334 | − | 0.526243i | \(-0.176400\pi\) | ||||
0.850334 | + | 0.526243i | \(0.176400\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.3258 | −0.603454 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.1016 | −1.10479 | −0.552393 | − | 0.833584i | \(-0.686285\pi\) | ||||
−0.552393 | + | 0.833584i | \(0.686285\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.35359 | 0.170893 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.5515 | −0.687897 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.0000 | −0.391330 | −0.195665 | − | 0.980671i | \(-0.562687\pi\) | ||||
−0.195665 | + | 0.980671i | \(0.562687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.59895 | 0.101549 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.8350 | −1.31802 | −0.659012 | − | 0.752133i | \(-0.729025\pi\) | ||||
−0.659012 | + | 0.752133i | \(0.729025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.6107 | 0.646082 | 0.323041 | − | 0.946385i | \(-0.395295\pi\) | ||||
0.323041 | + | 0.946385i | \(0.395295\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.92478 | 0.385446 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.4010 | 0.519670 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.92478 | 0.306849 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.55149 | 0.369282 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.0738 | 0.890754 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.17679 | 0.315192 | 0.157596 | − | 0.987504i | \(-0.449626\pi\) | ||||
0.157596 | + | 0.987504i | \(0.449626\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.22425 | 0.239572 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.8989 | 1.80247 | 0.901236 | − | 0.433328i | \(-0.142661\pi\) | ||||
0.901236 | + | 0.433328i | \(0.142661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.6239 | −1.44387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.68735 | 0.141300 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.92619 | −0.188495 | −0.0942477 | − | 0.995549i | \(-0.530045\pi\) | ||||
−0.0942477 | + | 0.995549i | \(0.530045\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.0263 | −1.14725 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.2374 | 0.466887 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.25202 | −0.314377 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.1016 | −1.37337 | −0.686684 | − | 0.726956i | \(-0.740934\pi\) | ||||
−0.686684 | + | 0.726956i | \(0.740934\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.77575 | −0.181416 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.4010 | −0.508331 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.07522 | −0.230115 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.40105 | −0.128639 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.2736 | 1.74773 | 0.873865 | − | 0.486168i | \(-0.161606\pi\) | ||||
0.873865 | + | 0.486168i | \(0.161606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.12268 | 0.117774 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.44851 | 0.242865 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.6239 | 1.71586 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.5647 | 0.997657 | 0.498828 | − | 0.866701i | \(-0.333764\pi\) | ||||
0.498828 | + | 0.866701i | \(0.333764\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.03761 | −0.188925 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.92478 | −0.221885 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.8021 | 0.403975 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.55149 | −0.0579416 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.5501 | −0.990151 | −0.495075 | − | 0.868850i | \(-0.664860\pi\) | ||||
−0.495075 | + | 0.868850i | \(0.664860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.4749 | 1.50736 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.7005 | 0.769861 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −49.3258 | −1.83192 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.4387 | 0.683852 | 0.341926 | − | 0.939727i | \(-0.388921\pi\) | ||||
0.341926 | + | 0.939727i | \(0.388921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.7005 | −0.839609 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.1162 | 0.743007 | 0.371504 | − | 0.928431i | \(-0.378842\pi\) | ||||
0.371504 | + | 0.928431i | \(0.378842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.94921 | 0.219440 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.37470 | 0.271651 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.6516 | −1.27468 | −0.637341 | − | 0.770582i | \(-0.719966\pi\) | ||||
−0.637341 | + | 0.770582i | \(0.719966\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.70052 | −0.0992062 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.32582 | −0.122013 | −0.0610063 | − | 0.998137i | \(-0.519431\pi\) | ||||
−0.0610063 | + | 0.998137i | \(0.519431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.6728 | −1.23367 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.0132 | −0.549303 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −54.0263 | −1.97408 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.1114 | 1.02580 | 0.512900 | − | 0.858448i | \(-0.328571\pi\) | ||||
0.512900 | + | 0.858448i | \(0.328571\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.46310 | 0.308412 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.6991 | 1.44480 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.6859 | 1.55145 | 0.775723 | − | 0.631073i | \(-0.217385\pi\) | ||||
0.775723 | + | 0.631073i | \(0.217385\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.61213 | −0.0585165 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.7743 | −0.861819 | −0.430909 | − | 0.902395i | \(-0.641807\pi\) | ||||
−0.430909 | + | 0.902395i | \(0.641807\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 57.6531 | 2.08718 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.6253 | 0.601089 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.40105 | 0.195021 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.2243 | −1.19810 | −0.599049 | − | 0.800713i | \(-0.704454\pi\) | ||||
−0.599049 | + | 0.800713i | \(0.704454\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.6253 | 0.670774 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.27645 | 0.153813 | 0.0769067 | − | 0.997038i | \(-0.475496\pi\) | ||||
0.0769067 | + | 0.997038i | \(0.475496\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.8773 | 1.32467 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.85097 | 0.245777 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.65306 | 0.0592271 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.8021 | −0.959054 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.92478 | −0.283208 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 76.8481 | 2.74283 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.0230 | −0.678098 | −0.339049 | − | 0.940769i | \(-0.610105\pi\) | ||||
−0.339049 | + | 0.940769i | \(0.610105\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.523730 | −0.0186453 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.7005 | −0.807138 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.6253 | 1.01651 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.8232 | −0.490259 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.35026 | −0.260360 | −0.130180 | − | 0.991490i | \(-0.541555\pi\) | ||||
−0.130180 | + | 0.991490i | \(0.541555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.55149 | 0.337908 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.73813 | −0.202747 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.22425 | 0.113781 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.92478 | 0.349802 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.700523 | 0.0246596 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.3733 | −0.927235 | −0.463618 | − | 0.886035i | \(-0.653449\pi\) | ||||
−0.463618 | + | 0.886035i | \(0.653449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.99859 | −0.315983 | −0.157992 | − | 0.987440i | \(-0.550502\pi\) | ||||
−0.157992 | + | 0.987440i | \(0.550502\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.0752 | −0.353353 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.4485 | 0.786337 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.17679 | 0.216099 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.92478 | −0.207028 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.10299 | 0.317696 | 0.158848 | − | 0.987303i | \(-0.449222\pi\) | ||||
0.158848 | + | 0.987303i | \(0.449222\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.7743 | −1.17730 | −0.588650 | − | 0.808388i | \(-0.700340\pi\) | ||||
−0.588650 | + | 0.808388i | \(0.700340\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.0343 | 0.349349 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.4156 | 0.814241 | 0.407121 | − | 0.913374i | \(-0.366533\pi\) | ||||
0.407121 | + | 0.913374i | \(0.366533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.7757 | −0.374257 | −0.187129 | − | 0.982335i | \(-0.559918\pi\) | ||||
−0.187129 | + | 0.982335i | \(0.559918\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.4749 | −0.779644 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.81194 | 0.305316 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 82.5012 | 2.85507 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.92478 | 0.204790 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.92478 | −0.204546 | −0.102273 | − | 0.994756i | \(-0.532612\pi\) | ||||
−0.102273 | + | 0.994756i | \(0.532612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.8021 | 1.16559 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.8134 | 0.406874 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.1524 | −1.03727 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.8872 | 0.855133 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.1998 | 1.00214 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.31265 | 0.0792766 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.0000 | 1.30110 | 0.650548 | − | 0.759465i | \(-0.274539\pi\) | ||||
0.650548 | + | 0.759465i | \(0.274539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.52373 | −0.154708 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.62672 | 0.123598 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.2995 | 0.861204 | 0.430602 | − | 0.902542i | \(-0.358301\pi\) | ||||
0.430602 | + | 0.902542i | \(0.358301\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −80.1543 | −2.72533 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.62530 | 0.258969 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.12127 | −0.275495 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.14903 | 0.310003 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.7005 | 0.429848 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.1504 | −0.410760 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.6253 | 1.03414 | 0.517071 | − | 0.855942i | \(-0.327022\pi\) | ||||
0.517071 | + | 0.855942i | \(0.327022\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.27504 | 0.312839 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.1866 | −1.48869 | −0.744343 | − | 0.667798i | \(-0.767237\pi\) | ||||
−0.744343 | + | 0.667798i | \(0.767237\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.70052 | −0.225491 | −0.112745 | − | 0.993624i | \(-0.535964\pi\) | ||||
−0.112745 | + | 0.993624i | \(0.535964\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.04746 | 0.304127 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.5764 | −1.09381 | −0.546905 | − | 0.837195i | \(-0.684194\pi\) | ||||
−0.546905 | + | 0.837195i | \(0.684194\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.8467 | 1.53765 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.61213 | 0.0540083 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.59895 | −0.0869706 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64.7466 | 2.16424 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.9525 | −1.56595 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.4749 | −0.682116 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.5515 | 0.450965 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 67.8007 | 2.25377 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.75272 | −0.0581982 | −0.0290991 | − | 0.999577i | \(-0.509264\pi\) | ||||
−0.0290991 | + | 0.999577i | \(0.509264\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.4010 | −0.510820 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.67276 | −0.320473 | −0.160236 | − | 0.987079i | \(-0.551226\pi\) | ||||
−0.160236 | + | 0.987079i | \(0.551226\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.2031 | −0.801007 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 47.9511 | 1.58522 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.29806 | −0.0758887 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.4109 | 0.838228 | 0.419114 | − | 0.907934i | \(-0.362341\pi\) | ||||
0.419114 | + | 0.907934i | \(0.362341\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.9511 | 1.05283 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.2506 | −1.09446 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.3945 | −0.473289 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.6629 | −0.448749 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.0263 | 0.788279 | 0.394139 | − | 0.919051i | \(-0.371043\pi\) | ||||
0.394139 | + | 0.919051i | \(0.371043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.39772 | −0.0785822 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.1490 | 0.430480 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.8021 | 0.876522 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.8496 | −1.62851 | −0.814257 | − | 0.580505i | \(-0.802855\pi\) | ||||
−0.814257 | + | 0.580505i | \(0.802855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0263 | 0.784070 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.2012 | −0.984532 | −0.492266 | − | 0.870445i | \(-0.663831\pi\) | ||||
−0.492266 | + | 0.870445i | \(0.663831\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.22425 | 0.0398672 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.92478 | −0.322853 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.8218 | −0.351661 | −0.175830 | − | 0.984420i | \(-0.556261\pi\) | ||||
−0.175830 | + | 0.984420i | \(0.556261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.9248 | 0.905523 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.6893 | −1.09130 | −0.545651 | − | 0.838012i | \(-0.683718\pi\) | ||||
−0.545651 | + | 0.838012i | \(0.683718\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.6516 | −0.991864 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.7757 | −0.412981 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.5501 | 0.857347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.10299 | 0.132354 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.2374 | 0.587693 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.7005 | −0.730756 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.0249 | 1.38359 | 0.691794 | − | 0.722095i | \(-0.256820\pi\) | ||||
0.691794 | + | 0.722095i | \(0.256820\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.70052 | −0.215252 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.0381 | 1.34907 | 0.674534 | − | 0.738244i | \(-0.264345\pi\) | ||||
0.674534 | + | 0.738244i | \(0.264345\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.8496 | 0.379879 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.4485 | 0.398671 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.1881 | 0.357938 | 0.178969 | − | 0.983855i | \(-0.442724\pi\) | ||||
0.178969 | + | 0.983855i | \(0.442724\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.25060 | −0.295651 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.4617 | −0.621364 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.9234 | −0.603562 | −0.301781 | − | 0.953377i | \(-0.597581\pi\) | ||||
−0.301781 | + | 0.953377i | \(0.597581\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −82.2492 | −2.62068 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.70194 | −0.181495 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.57452 | 0.145461 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62.1279 | −1.97356 | −0.986779 | − | 0.162071i | \(-0.948183\pi\) | ||||
−0.986779 | + | 0.162071i | \(0.948183\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.70052 | 0.212635 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.3785 | −1.62881 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.8759 | −1.76961 | −0.884804 | − | 0.465964i | \(-0.845708\pi\) | ||||
−0.884804 | + | 0.465964i | \(0.845708\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.31265 | −0.0731690 |
(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 | 552.2.a.g.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 1656.2.a.n.1.1 | 3 | |||
4.3 | odd | 2 | 1104.2.a.o.1.3 | 3 | |||
8.3 | odd | 2 | 4416.2.a.bs.1.1 | 3 | |||
8.5 | even | 2 | 4416.2.a.bp.1.1 | 3 | |||
12.11 | even | 2 | 3312.2.a.bf.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.a.g.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1104.2.a.o.1.3 | 3 | 4.3 | odd | 2 | |||
1656.2.a.n.1.1 | 3 | 3.2 | odd | 2 | |||
3312.2.a.bf.1.1 | 3 | 12.11 | even | 2 | |||
4416.2.a.bp.1.1 | 3 | 8.5 | even | 2 | |||
4416.2.a.bs.1.1 | 3 | 8.3 | odd | 2 |