Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1003,2,Mod(1,1003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1003, 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("1003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.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: | \(8.00899532273\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.75660\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75660 | −1.94921 | −0.974605 | − | 0.223932i | \(-0.928110\pi\) | ||||
−0.974605 | + | 0.223932i | \(0.928110\pi\) | |||||||
\(3\) | 1.84224 | 1.06362 | 0.531808 | − | 0.846865i | \(-0.321513\pi\) | ||||
0.531808 | + | 0.846865i | \(0.321513\pi\) | |||||||
\(4\) | 5.59883 | 2.79942 | ||||||||
\(5\) | −0.0856374 | −0.0382982 | −0.0191491 | − | 0.999817i | \(-0.506096\pi\) | ||||
−0.0191491 | + | 0.999817i | \(0.506096\pi\) | |||||||
\(6\) | −5.07830 | −2.07321 | ||||||||
\(7\) | −0.236068 | −0.0892253 | −0.0446127 | − | 0.999004i | \(-0.514205\pi\) | ||||
−0.0446127 | + | 0.999004i | \(0.514205\pi\) | |||||||
\(8\) | −9.92054 | −3.50744 | ||||||||
\(9\) | 0.393832 | 0.131277 | ||||||||
\(10\) | 0.236068 | 0.0746512 | ||||||||
\(11\) | −2.52053 | −0.759968 | −0.379984 | − | 0.924993i | \(-0.624071\pi\) | ||||
−0.379984 | + | 0.924993i | \(0.624071\pi\) | |||||||
\(12\) | 10.3144 | 2.97750 | ||||||||
\(13\) | −0.243402 | −0.0675075 | −0.0337537 | − | 0.999430i | \(-0.510746\pi\) | ||||
−0.0337537 | + | 0.999430i | \(0.510746\pi\) | |||||||
\(14\) | 0.650745 | 0.173919 | ||||||||
\(15\) | −0.157764 | −0.0407346 | ||||||||
\(16\) | 16.1493 | 4.03732 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.08564 | −0.255887 | ||||||||
\(19\) | 0.722871 | 0.165838 | 0.0829190 | − | 0.996556i | \(-0.473576\pi\) | ||||
0.0829190 | + | 0.996556i | \(0.473576\pi\) | |||||||
\(20\) | −0.479470 | −0.107213 | ||||||||
\(21\) | −0.434893 | −0.0949014 | ||||||||
\(22\) | 6.94809 | 1.48134 | ||||||||
\(23\) | −7.44107 | −1.55157 | −0.775785 | − | 0.630997i | \(-0.782646\pi\) | ||||
−0.775785 | + | 0.630997i | \(0.782646\pi\) | |||||||
\(24\) | −18.2760 | −3.73057 | ||||||||
\(25\) | −4.99267 | −0.998533 | ||||||||
\(26\) | 0.670961 | 0.131586 | ||||||||
\(27\) | −4.80118 | −0.923987 | ||||||||
\(28\) | −1.32171 | −0.249779 | ||||||||
\(29\) | 1.99267 | 0.370029 | 0.185014 | − | 0.982736i | \(-0.440767\pi\) | ||||
0.185014 | + | 0.982736i | \(0.440767\pi\) | |||||||
\(30\) | 0.434893 | 0.0794002 | ||||||||
\(31\) | 0.670961 | 0.120508 | 0.0602541 | − | 0.998183i | \(-0.480809\pi\) | ||||
0.0602541 | + | 0.998183i | \(0.480809\pi\) | |||||||
\(32\) | −24.6760 | −4.36214 | ||||||||
\(33\) | −4.64341 | −0.808314 | ||||||||
\(34\) | 2.75660 | 0.472753 | ||||||||
\(35\) | 0.0202163 | 0.00341717 | ||||||||
\(36\) | 2.20500 | 0.367500 | ||||||||
\(37\) | −8.56511 | −1.40809 | −0.704047 | − | 0.710153i | \(-0.748626\pi\) | ||||
−0.704047 | + | 0.710153i | \(0.748626\pi\) | |||||||
\(38\) | −1.99267 | −0.323253 | ||||||||
\(39\) | −0.448403 | −0.0718020 | ||||||||
\(40\) | 0.849569 | 0.134329 | ||||||||
\(41\) | −2.34192 | −0.365747 | −0.182873 | − | 0.983136i | \(-0.558540\pi\) | ||||
−0.182873 | + | 0.983136i | \(0.558540\pi\) | |||||||
\(42\) | 1.19882 | 0.184983 | ||||||||
\(43\) | 5.36277 | 0.817814 | 0.408907 | − | 0.912576i | \(-0.365910\pi\) | ||||
0.408907 | + | 0.912576i | \(0.365910\pi\) | |||||||
\(44\) | −14.1120 | −2.12747 | ||||||||
\(45\) | −0.0337268 | −0.00502769 | ||||||||
\(46\) | 20.5120 | 3.02434 | ||||||||
\(47\) | −5.67829 | −0.828264 | −0.414132 | − | 0.910217i | \(-0.635915\pi\) | ||||
−0.414132 | + | 0.910217i | \(0.635915\pi\) | |||||||
\(48\) | 29.7508 | 4.29415 | ||||||||
\(49\) | −6.94427 | −0.992039 | ||||||||
\(50\) | 13.7628 | 1.94635 | ||||||||
\(51\) | −1.84224 | −0.257965 | ||||||||
\(52\) | −1.36277 | −0.188982 | ||||||||
\(53\) | 6.85575 | 0.941709 | 0.470855 | − | 0.882211i | \(-0.343946\pi\) | ||||
0.470855 | + | 0.882211i | \(0.343946\pi\) | |||||||
\(54\) | 13.2349 | 1.80104 | ||||||||
\(55\) | 0.215852 | 0.0291054 | ||||||||
\(56\) | 2.34192 | 0.312952 | ||||||||
\(57\) | 1.33170 | 0.176388 | ||||||||
\(58\) | −5.49298 | −0.721264 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | −0.883296 | −0.114033 | ||||||||
\(61\) | 2.52671 | 0.323512 | 0.161756 | − | 0.986831i | \(-0.448284\pi\) | ||||
0.161756 | + | 0.986831i | \(0.448284\pi\) | |||||||
\(62\) | −1.84957 | −0.234896 | ||||||||
\(63\) | −0.0929712 | −0.0117133 | ||||||||
\(64\) | 35.7232 | 4.46540 | ||||||||
\(65\) | 0.0208443 | 0.00258542 | ||||||||
\(66\) | 12.8000 | 1.57557 | ||||||||
\(67\) | 1.90703 | 0.232981 | 0.116490 | − | 0.993192i | \(-0.462836\pi\) | ||||
0.116490 | + | 0.993192i | \(0.462836\pi\) | |||||||
\(68\) | −5.59883 | −0.678958 | ||||||||
\(69\) | −13.7082 | −1.65027 | ||||||||
\(70\) | −0.0557281 | −0.00666078 | ||||||||
\(71\) | −2.04458 | −0.242647 | −0.121323 | − | 0.992613i | \(-0.538714\pi\) | ||||
−0.121323 | + | 0.992613i | \(0.538714\pi\) | |||||||
\(72\) | −3.90703 | −0.460448 | ||||||||
\(73\) | 9.29064 | 1.08739 | 0.543694 | − | 0.839284i | \(-0.317025\pi\) | ||||
0.543694 | + | 0.839284i | \(0.317025\pi\) | |||||||
\(74\) | 23.6106 | 2.74467 | ||||||||
\(75\) | −9.19767 | −1.06206 | ||||||||
\(76\) | 4.04724 | 0.464250 | ||||||||
\(77\) | 0.595016 | 0.0678084 | ||||||||
\(78\) | 1.23607 | 0.139957 | ||||||||
\(79\) | 14.9241 | 1.67909 | 0.839544 | − | 0.543292i | \(-0.182822\pi\) | ||||
0.839544 | + | 0.543292i | \(0.182822\pi\) | |||||||
\(80\) | −1.38298 | −0.154622 | ||||||||
\(81\) | −10.0264 | −1.11404 | ||||||||
\(82\) | 6.45574 | 0.712917 | ||||||||
\(83\) | −6.73638 | −0.739414 | −0.369707 | − | 0.929148i | \(-0.620542\pi\) | ||||
−0.369707 | + | 0.929148i | \(0.620542\pi\) | |||||||
\(84\) | −2.43489 | −0.265669 | ||||||||
\(85\) | 0.0856374 | 0.00928868 | ||||||||
\(86\) | −14.7830 | −1.59409 | ||||||||
\(87\) | 3.67096 | 0.393568 | ||||||||
\(88\) | 25.0050 | 2.66554 | ||||||||
\(89\) | −12.3892 | −1.31325 | −0.656624 | − | 0.754218i | \(-0.728016\pi\) | ||||
−0.656624 | + | 0.754218i | \(0.728016\pi\) | |||||||
\(90\) | 0.0929712 | 0.00980002 | ||||||||
\(91\) | 0.0574594 | 0.00602338 | ||||||||
\(92\) | −41.6613 | −4.34349 | ||||||||
\(93\) | 1.23607 | 0.128174 | ||||||||
\(94\) | 15.6528 | 1.61446 | ||||||||
\(95\) | −0.0619049 | −0.00635130 | ||||||||
\(96\) | −45.4590 | −4.63964 | ||||||||
\(97\) | −13.6636 | −1.38733 | −0.693666 | − | 0.720297i | \(-0.744005\pi\) | ||||
−0.693666 | + | 0.720297i | \(0.744005\pi\) | |||||||
\(98\) | 19.1426 | 1.93369 | ||||||||
\(99\) | −0.992666 | −0.0997667 | ||||||||
\(100\) | −27.9531 | −2.79531 | ||||||||
\(101\) | 11.2490 | 1.11931 | 0.559656 | − | 0.828725i | \(-0.310933\pi\) | ||||
0.559656 | + | 0.828725i | \(0.310933\pi\) | |||||||
\(102\) | 5.07830 | 0.502827 | ||||||||
\(103\) | −7.22140 | −0.711546 | −0.355773 | − | 0.934572i | \(-0.615782\pi\) | ||||
−0.355773 | + | 0.934572i | \(0.615782\pi\) | |||||||
\(104\) | 2.41468 | 0.236779 | ||||||||
\(105\) | 0.0372431 | 0.00363455 | ||||||||
\(106\) | −18.8985 | −1.83559 | ||||||||
\(107\) | 5.00618 | 0.483965 | 0.241983 | − | 0.970281i | \(-0.422202\pi\) | ||||
0.241983 | + | 0.970281i | \(0.422202\pi\) | |||||||
\(108\) | −26.8810 | −2.58662 | ||||||||
\(109\) | −11.1977 | −1.07254 | −0.536271 | − | 0.844046i | \(-0.680168\pi\) | ||||
−0.536271 | + | 0.844046i | \(0.680168\pi\) | |||||||
\(110\) | −0.595016 | −0.0567326 | ||||||||
\(111\) | −15.7789 | −1.49767 | ||||||||
\(112\) | −3.81233 | −0.360231 | ||||||||
\(113\) | 7.45863 | 0.701648 | 0.350824 | − | 0.936441i | \(-0.385901\pi\) | ||||
0.350824 | + | 0.936441i | \(0.385901\pi\) | |||||||
\(114\) | −3.67096 | −0.343817 | ||||||||
\(115\) | 0.637234 | 0.0594224 | ||||||||
\(116\) | 11.1566 | 1.03586 | ||||||||
\(117\) | −0.0958595 | −0.00886221 | ||||||||
\(118\) | 2.75660 | 0.253765 | ||||||||
\(119\) | 0.236068 | 0.0216403 | ||||||||
\(120\) | 1.56511 | 0.142874 | ||||||||
\(121\) | −4.64693 | −0.422448 | ||||||||
\(122\) | −6.96512 | −0.630592 | ||||||||
\(123\) | −4.31437 | −0.389014 | ||||||||
\(124\) | 3.75660 | 0.337352 | ||||||||
\(125\) | 0.855746 | 0.0765403 | ||||||||
\(126\) | 0.256284 | 0.0228316 | ||||||||
\(127\) | −9.83842 | −0.873018 | −0.436509 | − | 0.899700i | \(-0.643785\pi\) | ||||
−0.436509 | + | 0.899700i | \(0.643785\pi\) | |||||||
\(128\) | −49.1226 | −4.34187 | ||||||||
\(129\) | 9.87948 | 0.869840 | ||||||||
\(130\) | −0.0574594 | −0.00503952 | ||||||||
\(131\) | −8.72553 | −0.762353 | −0.381177 | − | 0.924502i | \(-0.624481\pi\) | ||||
−0.381177 | + | 0.924502i | \(0.624481\pi\) | |||||||
\(132\) | −25.9977 | −2.26281 | ||||||||
\(133\) | −0.170647 | −0.0147970 | ||||||||
\(134\) | −5.25691 | −0.454128 | ||||||||
\(135\) | 0.411160 | 0.0353870 | ||||||||
\(136\) | 9.92054 | 0.850679 | ||||||||
\(137\) | 12.2451 | 1.04617 | 0.523086 | − | 0.852280i | \(-0.324781\pi\) | ||||
0.523086 | + | 0.852280i | \(0.324781\pi\) | |||||||
\(138\) | 37.7880 | 3.21673 | ||||||||
\(139\) | 16.3317 | 1.38524 | 0.692618 | − | 0.721304i | \(-0.256457\pi\) | ||||
0.692618 | + | 0.721304i | \(0.256457\pi\) | |||||||
\(140\) | 0.113187 | 0.00956609 | ||||||||
\(141\) | −10.4608 | −0.880955 | ||||||||
\(142\) | 5.63608 | 0.472969 | ||||||||
\(143\) | 0.613501 | 0.0513036 | ||||||||
\(144\) | 6.36011 | 0.530009 | ||||||||
\(145\) | −0.170647 | −0.0141714 | ||||||||
\(146\) | −25.6106 | −2.11954 | ||||||||
\(147\) | −12.7930 | −1.05515 | ||||||||
\(148\) | −47.9546 | −3.94184 | ||||||||
\(149\) | 5.82820 | 0.477464 | 0.238732 | − | 0.971085i | \(-0.423268\pi\) | ||||
0.238732 | + | 0.971085i | \(0.423268\pi\) | |||||||
\(150\) | 25.3543 | 2.07017 | ||||||||
\(151\) | −15.9408 | −1.29724 | −0.648620 | − | 0.761112i | \(-0.724654\pi\) | ||||
−0.648620 | + | 0.761112i | \(0.724654\pi\) | |||||||
\(152\) | −7.17127 | −0.581667 | ||||||||
\(153\) | −0.393832 | −0.0318395 | ||||||||
\(154\) | −1.64022 | −0.132173 | ||||||||
\(155\) | −0.0574594 | −0.00461525 | ||||||||
\(156\) | −2.51054 | −0.201004 | ||||||||
\(157\) | −2.38766 | −0.190556 | −0.0952778 | − | 0.995451i | \(-0.530374\pi\) | ||||
−0.0952778 | + | 0.995451i | \(0.530374\pi\) | |||||||
\(158\) | −41.1396 | −3.27289 | ||||||||
\(159\) | 12.6299 | 1.00162 | ||||||||
\(160\) | 2.11319 | 0.167062 | ||||||||
\(161\) | 1.75660 | 0.138439 | ||||||||
\(162\) | 27.6387 | 2.17150 | ||||||||
\(163\) | 4.21585 | 0.330211 | 0.165105 | − | 0.986276i | \(-0.447204\pi\) | ||||
0.165105 | + | 0.986276i | \(0.447204\pi\) | |||||||
\(164\) | −13.1120 | −1.02388 | ||||||||
\(165\) | 0.397650 | 0.0309570 | ||||||||
\(166\) | 18.5695 | 1.44127 | ||||||||
\(167\) | −12.4519 | −0.963558 | −0.481779 | − | 0.876293i | \(-0.660009\pi\) | ||||
−0.481779 | + | 0.876293i | \(0.660009\pi\) | |||||||
\(168\) | 4.31437 | 0.332861 | ||||||||
\(169\) | −12.9408 | −0.995443 | ||||||||
\(170\) | −0.236068 | −0.0181056 | ||||||||
\(171\) | 0.284690 | 0.0217708 | ||||||||
\(172\) | 30.0252 | 2.28940 | ||||||||
\(173\) | −2.93902 | −0.223450 | −0.111725 | − | 0.993739i | \(-0.535638\pi\) | ||||
−0.111725 | + | 0.993739i | \(0.535638\pi\) | |||||||
\(174\) | −10.1194 | −0.767147 | ||||||||
\(175\) | 1.17861 | 0.0890944 | ||||||||
\(176\) | −40.7047 | −3.06823 | ||||||||
\(177\) | −1.84224 | −0.138471 | ||||||||
\(178\) | 34.1519 | 2.55980 | ||||||||
\(179\) | 20.6862 | 1.54616 | 0.773080 | − | 0.634309i | \(-0.218715\pi\) | ||||
0.773080 | + | 0.634309i | \(0.218715\pi\) | |||||||
\(180\) | −0.188831 | −0.0140746 | ||||||||
\(181\) | −5.55044 | −0.412561 | −0.206280 | − | 0.978493i | \(-0.566136\pi\) | ||||
−0.206280 | + | 0.978493i | \(0.566136\pi\) | |||||||
\(182\) | −0.158392 | −0.0117408 | ||||||||
\(183\) | 4.65479 | 0.344092 | ||||||||
\(184\) | 73.8194 | 5.44204 | ||||||||
\(185\) | 0.733494 | 0.0539275 | ||||||||
\(186\) | −3.40734 | −0.249838 | ||||||||
\(187\) | 2.52053 | 0.184319 | ||||||||
\(188\) | −31.7918 | −2.31866 | ||||||||
\(189\) | 1.13340 | 0.0824430 | ||||||||
\(190\) | 0.170647 | 0.0123800 | ||||||||
\(191\) | −11.3252 | −0.819464 | −0.409732 | − | 0.912206i | \(-0.634378\pi\) | ||||
−0.409732 | + | 0.912206i | \(0.634378\pi\) | |||||||
\(192\) | 65.8106 | 4.74947 | ||||||||
\(193\) | 4.21937 | 0.303717 | 0.151858 | − | 0.988402i | \(-0.451474\pi\) | ||||
0.151858 | + | 0.988402i | \(0.451474\pi\) | |||||||
\(194\) | 37.6651 | 2.70420 | ||||||||
\(195\) | 0.0384001 | 0.00274989 | ||||||||
\(196\) | −38.8798 | −2.77713 | ||||||||
\(197\) | −15.8478 | −1.12911 | −0.564554 | − | 0.825396i | \(-0.690952\pi\) | ||||
−0.564554 | + | 0.825396i | \(0.690952\pi\) | |||||||
\(198\) | 2.73638 | 0.194466 | ||||||||
\(199\) | 11.1988 | 0.793864 | 0.396932 | − | 0.917848i | \(-0.370075\pi\) | ||||
0.396932 | + | 0.917848i | \(0.370075\pi\) | |||||||
\(200\) | 49.5299 | 3.50230 | ||||||||
\(201\) | 3.51320 | 0.247802 | ||||||||
\(202\) | −31.0088 | −2.18177 | ||||||||
\(203\) | −0.470405 | −0.0330159 | ||||||||
\(204\) | −10.3144 | −0.722150 | ||||||||
\(205\) | 0.200556 | 0.0140074 | ||||||||
\(206\) | 19.9065 | 1.38695 | ||||||||
\(207\) | −2.93053 | −0.203686 | ||||||||
\(208\) | −3.93076 | −0.272549 | ||||||||
\(209\) | −1.82202 | −0.126032 | ||||||||
\(210\) | −0.102664 | −0.00708451 | ||||||||
\(211\) | 13.1701 | 0.906668 | 0.453334 | − | 0.891341i | \(-0.350234\pi\) | ||||
0.453334 | + | 0.891341i | \(0.350234\pi\) | |||||||
\(212\) | 38.3842 | 2.63624 | ||||||||
\(213\) | −3.76659 | −0.258083 | ||||||||
\(214\) | −13.8000 | −0.943350 | ||||||||
\(215\) | −0.459253 | −0.0313208 | ||||||||
\(216\) | 47.6302 | 3.24083 | ||||||||
\(217\) | −0.158392 | −0.0107524 | ||||||||
\(218\) | 30.8675 | 2.09061 | ||||||||
\(219\) | 17.1155 | 1.15656 | ||||||||
\(220\) | 1.20852 | 0.0814783 | ||||||||
\(221\) | 0.243402 | 0.0163730 | ||||||||
\(222\) | 43.4962 | 2.91927 | ||||||||
\(223\) | −15.9948 | −1.07109 | −0.535545 | − | 0.844506i | \(-0.679894\pi\) | ||||
−0.535545 | + | 0.844506i | \(0.679894\pi\) | |||||||
\(224\) | 5.82521 | 0.389213 | ||||||||
\(225\) | −1.96627 | −0.131085 | ||||||||
\(226\) | −20.5604 | −1.36766 | ||||||||
\(227\) | −20.3454 | −1.35037 | −0.675187 | − | 0.737647i | \(-0.735937\pi\) | ||||
−0.675187 | + | 0.737647i | \(0.735937\pi\) | |||||||
\(228\) | 7.45596 | 0.493783 | ||||||||
\(229\) | 15.7818 | 1.04289 | 0.521446 | − | 0.853284i | \(-0.325393\pi\) | ||||
0.521446 | + | 0.853284i | \(0.325393\pi\) | |||||||
\(230\) | −1.75660 | −0.115827 | ||||||||
\(231\) | 1.09616 | 0.0721221 | ||||||||
\(232\) | −19.7683 | −1.29785 | ||||||||
\(233\) | 11.2247 | 0.735354 | 0.367677 | − | 0.929954i | \(-0.380153\pi\) | ||||
0.367677 | + | 0.929954i | \(0.380153\pi\) | |||||||
\(234\) | 0.264246 | 0.0172743 | ||||||||
\(235\) | 0.486275 | 0.0317211 | ||||||||
\(236\) | −5.59883 | −0.364453 | ||||||||
\(237\) | 27.4936 | 1.78590 | ||||||||
\(238\) | −0.650745 | −0.0421815 | ||||||||
\(239\) | 4.13639 | 0.267561 | 0.133780 | − | 0.991011i | \(-0.457288\pi\) | ||||
0.133780 | + | 0.991011i | \(0.457288\pi\) | |||||||
\(240\) | −2.54778 | −0.164458 | ||||||||
\(241\) | 25.2416 | 1.62596 | 0.812978 | − | 0.582295i | \(-0.197845\pi\) | ||||
0.812978 | + | 0.582295i | \(0.197845\pi\) | |||||||
\(242\) | 12.8097 | 0.823439 | ||||||||
\(243\) | −4.06745 | −0.260927 | ||||||||
\(244\) | 14.1466 | 0.905644 | ||||||||
\(245\) | 0.594690 | 0.0379933 | ||||||||
\(246\) | 11.8930 | 0.758269 | ||||||||
\(247\) | −0.175948 | −0.0111953 | ||||||||
\(248\) | −6.65629 | −0.422675 | ||||||||
\(249\) | −12.4100 | −0.786452 | ||||||||
\(250\) | −2.35895 | −0.149193 | ||||||||
\(251\) | 3.30704 | 0.208738 | 0.104369 | − | 0.994539i | \(-0.466718\pi\) | ||||
0.104369 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(252\) | −0.520530 | −0.0327903 | ||||||||
\(253\) | 18.7554 | 1.17914 | ||||||||
\(254\) | 27.1206 | 1.70170 | ||||||||
\(255\) | 0.157764 | 0.00987958 | ||||||||
\(256\) | 63.9648 | 3.99780 | ||||||||
\(257\) | 4.12318 | 0.257197 | 0.128599 | − | 0.991697i | \(-0.458952\pi\) | ||||
0.128599 | + | 0.991697i | \(0.458952\pi\) | |||||||
\(258\) | −27.2338 | −1.69550 | ||||||||
\(259\) | 2.02195 | 0.125638 | ||||||||
\(260\) | 0.116704 | 0.00723766 | ||||||||
\(261\) | 0.784776 | 0.0485764 | ||||||||
\(262\) | 24.0528 | 1.48599 | ||||||||
\(263\) | −30.7273 | −1.89472 | −0.947362 | − | 0.320164i | \(-0.896262\pi\) | ||||
−0.947362 | + | 0.320164i | \(0.896262\pi\) | |||||||
\(264\) | 46.0651 | 2.83511 | ||||||||
\(265\) | −0.587108 | −0.0360658 | ||||||||
\(266\) | 0.470405 | 0.0288424 | ||||||||
\(267\) | −22.8238 | −1.39679 | ||||||||
\(268\) | 10.6771 | 0.652210 | ||||||||
\(269\) | 6.53670 | 0.398550 | 0.199275 | − | 0.979944i | \(-0.436141\pi\) | ||||
0.199275 | + | 0.979944i | \(0.436141\pi\) | |||||||
\(270\) | −1.13340 | −0.0689768 | ||||||||
\(271\) | 11.7276 | 0.712399 | 0.356199 | − | 0.934410i | \(-0.384072\pi\) | ||||
0.356199 | + | 0.934410i | \(0.384072\pi\) | |||||||
\(272\) | −16.1493 | −0.979194 | ||||||||
\(273\) | 0.105854 | 0.00640656 | ||||||||
\(274\) | −33.7549 | −2.03921 | ||||||||
\(275\) | 12.5842 | 0.758854 | ||||||||
\(276\) | −76.7500 | −4.61980 | ||||||||
\(277\) | −23.5035 | −1.41219 | −0.706096 | − | 0.708116i | \(-0.749545\pi\) | ||||
−0.706096 | + | 0.708116i | \(0.749545\pi\) | |||||||
\(278\) | −45.0199 | −2.70012 | ||||||||
\(279\) | 0.264246 | 0.0158200 | ||||||||
\(280\) | −0.200556 | −0.0119855 | ||||||||
\(281\) | 23.0865 | 1.37723 | 0.688613 | − | 0.725129i | \(-0.258220\pi\) | ||||
0.688613 | + | 0.725129i | \(0.258220\pi\) | |||||||
\(282\) | 28.8361 | 1.71717 | ||||||||
\(283\) | −9.04724 | −0.537802 | −0.268901 | − | 0.963168i | \(-0.586661\pi\) | ||||
−0.268901 | + | 0.963168i | \(0.586661\pi\) | |||||||
\(284\) | −11.4472 | −0.679269 | ||||||||
\(285\) | −0.114043 | −0.00675534 | ||||||||
\(286\) | −1.69118 | −0.100001 | ||||||||
\(287\) | 0.552853 | 0.0326339 | ||||||||
\(288\) | −9.71820 | −0.572650 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.470405 | 0.0276231 | ||||||||
\(291\) | −25.1716 | −1.47559 | ||||||||
\(292\) | 52.0167 | 3.04405 | ||||||||
\(293\) | −29.5020 | −1.72353 | −0.861764 | − | 0.507309i | \(-0.830640\pi\) | ||||
−0.861764 | + | 0.507309i | \(0.830640\pi\) | |||||||
\(294\) | 35.2651 | 2.05670 | ||||||||
\(295\) | 0.0856374 | 0.00498600 | ||||||||
\(296\) | 84.9705 | 4.93881 | ||||||||
\(297\) | 12.1015 | 0.702201 | ||||||||
\(298\) | −16.0660 | −0.930678 | ||||||||
\(299\) | 1.81117 | 0.104743 | ||||||||
\(300\) | −51.4962 | −2.97314 | ||||||||
\(301\) | −1.26598 | −0.0729697 | ||||||||
\(302\) | 43.9423 | 2.52859 | ||||||||
\(303\) | 20.7232 | 1.19052 | ||||||||
\(304\) | 11.6738 | 0.669541 | ||||||||
\(305\) | −0.216381 | −0.0123899 | ||||||||
\(306\) | 1.08564 | 0.0620618 | ||||||||
\(307\) | 10.0443 | 0.573261 | 0.286631 | − | 0.958041i | \(-0.407465\pi\) | ||||
0.286631 | + | 0.958041i | \(0.407465\pi\) | |||||||
\(308\) | 3.33140 | 0.189824 | ||||||||
\(309\) | −13.3035 | −0.756811 | ||||||||
\(310\) | 0.158392 | 0.00899608 | ||||||||
\(311\) | 22.6044 | 1.28178 | 0.640888 | − | 0.767634i | \(-0.278566\pi\) | ||||
0.640888 | + | 0.767634i | \(0.278566\pi\) | |||||||
\(312\) | 4.44840 | 0.251841 | ||||||||
\(313\) | −15.3936 | −0.870098 | −0.435049 | − | 0.900407i | \(-0.643269\pi\) | ||||
−0.435049 | + | 0.900407i | \(0.643269\pi\) | |||||||
\(314\) | 6.58181 | 0.371433 | ||||||||
\(315\) | 0.00796181 | 0.000448597 0 | ||||||||
\(316\) | 83.5573 | 4.70047 | ||||||||
\(317\) | −0.376276 | −0.0211338 | −0.0105669 | − | 0.999944i | \(-0.503364\pi\) | ||||
−0.0105669 | + | 0.999944i | \(0.503364\pi\) | |||||||
\(318\) | −34.8156 | −1.95236 | ||||||||
\(319\) | −5.02258 | −0.281210 | ||||||||
\(320\) | −3.05924 | −0.171017 | ||||||||
\(321\) | 9.22256 | 0.514753 | ||||||||
\(322\) | −4.84224 | −0.269847 | ||||||||
\(323\) | −0.722871 | −0.0402216 | ||||||||
\(324\) | −56.1361 | −3.11867 | ||||||||
\(325\) | 1.21522 | 0.0674085 | ||||||||
\(326\) | −11.6214 | −0.643650 | ||||||||
\(327\) | −20.6287 | −1.14077 | ||||||||
\(328\) | 23.2331 | 1.28283 | ||||||||
\(329\) | 1.34046 | 0.0739021 | ||||||||
\(330\) | −1.09616 | −0.0603417 | ||||||||
\(331\) | −11.1262 | −0.611550 | −0.305775 | − | 0.952104i | \(-0.598915\pi\) | ||||
−0.305775 | + | 0.952104i | \(0.598915\pi\) | |||||||
\(332\) | −37.7159 | −2.06993 | ||||||||
\(333\) | −3.37322 | −0.184851 | ||||||||
\(334\) | 34.3249 | 1.87818 | ||||||||
\(335\) | −0.163313 | −0.00892274 | ||||||||
\(336\) | −7.02320 | −0.383147 | ||||||||
\(337\) | −22.3740 | −1.21879 | −0.609394 | − | 0.792868i | \(-0.708587\pi\) | ||||
−0.609394 | + | 0.792868i | \(0.708587\pi\) | |||||||
\(338\) | 35.6725 | 1.94033 | ||||||||
\(339\) | 13.7405 | 0.746284 | ||||||||
\(340\) | 0.479470 | 0.0260029 | ||||||||
\(341\) | −1.69118 | −0.0915824 | ||||||||
\(342\) | −0.784776 | −0.0424358 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | −53.2015 | −2.86843 | ||||||||
\(345\) | 1.17394 | 0.0632026 | ||||||||
\(346\) | 8.10171 | 0.435551 | ||||||||
\(347\) | 36.6939 | 1.96983 | 0.984915 | − | 0.173036i | \(-0.0553578\pi\) | ||||
0.984915 | + | 0.173036i | \(0.0553578\pi\) | |||||||
\(348\) | 20.5531 | 1.10176 | ||||||||
\(349\) | −13.9924 | −0.748994 | −0.374497 | − | 0.927228i | \(-0.622185\pi\) | ||||
−0.374497 | + | 0.927228i | \(0.622185\pi\) | |||||||
\(350\) | −3.24895 | −0.173664 | ||||||||
\(351\) | 1.16861 | 0.0623760 | ||||||||
\(352\) | 62.1966 | 3.31509 | ||||||||
\(353\) | −12.1757 | −0.648045 | −0.324023 | − | 0.946049i | \(-0.605035\pi\) | ||||
−0.324023 | + | 0.946049i | \(0.605035\pi\) | |||||||
\(354\) | 5.07830 | 0.269909 | ||||||||
\(355\) | 0.175092 | 0.00929293 | ||||||||
\(356\) | −69.3648 | −3.67633 | ||||||||
\(357\) | 0.434893 | 0.0230170 | ||||||||
\(358\) | −57.0236 | −3.01379 | ||||||||
\(359\) | −14.6095 | −0.771058 | −0.385529 | − | 0.922696i | \(-0.625981\pi\) | ||||
−0.385529 | + | 0.922696i | \(0.625981\pi\) | |||||||
\(360\) | 0.334588 | 0.0176343 | ||||||||
\(361\) | −18.4775 | −0.972498 | ||||||||
\(362\) | 15.3003 | 0.804168 | ||||||||
\(363\) | −8.56073 | −0.449322 | ||||||||
\(364\) | 0.321705 | 0.0168619 | ||||||||
\(365\) | −0.795626 | −0.0416450 | ||||||||
\(366\) | −12.8314 | −0.670707 | ||||||||
\(367\) | 9.93694 | 0.518704 | 0.259352 | − | 0.965783i | \(-0.416491\pi\) | ||||
0.259352 | + | 0.965783i | \(0.416491\pi\) | |||||||
\(368\) | −120.168 | −6.26418 | ||||||||
\(369\) | −0.922324 | −0.0480143 | ||||||||
\(370\) | −2.02195 | −0.105116 | ||||||||
\(371\) | −1.61842 | −0.0840243 | ||||||||
\(372\) | 6.92054 | 0.358813 | ||||||||
\(373\) | 3.90703 | 0.202298 | 0.101149 | − | 0.994871i | \(-0.467748\pi\) | ||||
0.101149 | + | 0.994871i | \(0.467748\pi\) | |||||||
\(374\) | −6.94809 | −0.359277 | ||||||||
\(375\) | 1.57649 | 0.0814094 | ||||||||
\(376\) | 56.3317 | 2.90509 | ||||||||
\(377\) | −0.485018 | −0.0249797 | ||||||||
\(378\) | −3.12434 | −0.160699 | ||||||||
\(379\) | −28.6285 | −1.47055 | −0.735274 | − | 0.677770i | \(-0.762947\pi\) | ||||
−0.735274 | + | 0.677770i | \(0.762947\pi\) | |||||||
\(380\) | −0.346595 | −0.0177799 | ||||||||
\(381\) | −18.1247 | −0.928556 | ||||||||
\(382\) | 31.2191 | 1.59731 | ||||||||
\(383\) | 18.4504 | 0.942773 | 0.471387 | − | 0.881927i | \(-0.343754\pi\) | ||||
0.471387 | + | 0.881927i | \(0.343754\pi\) | |||||||
\(384\) | −90.4954 | −4.61807 | ||||||||
\(385\) | −0.0509557 | −0.00259694 | ||||||||
\(386\) | −11.6311 | −0.592008 | ||||||||
\(387\) | 2.11203 | 0.107361 | ||||||||
\(388\) | −76.5004 | −3.88372 | ||||||||
\(389\) | 8.95894 | 0.454236 | 0.227118 | − | 0.973867i | \(-0.427070\pi\) | ||||
0.227118 | + | 0.973867i | \(0.427070\pi\) | |||||||
\(390\) | −0.105854 | −0.00536011 | ||||||||
\(391\) | 7.44107 | 0.376311 | ||||||||
\(392\) | 68.8909 | 3.47952 | ||||||||
\(393\) | −16.0745 | −0.810851 | ||||||||
\(394\) | 43.6860 | 2.20087 | ||||||||
\(395\) | −1.27806 | −0.0643061 | ||||||||
\(396\) | −5.55777 | −0.279289 | ||||||||
\(397\) | 30.8281 | 1.54722 | 0.773610 | − | 0.633662i | \(-0.218449\pi\) | ||||
0.773610 | + | 0.633662i | \(0.218449\pi\) | |||||||
\(398\) | −30.8707 | −1.54741 | ||||||||
\(399\) | −0.314372 | −0.0157383 | ||||||||
\(400\) | −80.6279 | −4.03140 | ||||||||
\(401\) | 3.17243 | 0.158424 | 0.0792118 | − | 0.996858i | \(-0.474760\pi\) | ||||
0.0792118 | + | 0.996858i | \(0.474760\pi\) | |||||||
\(402\) | −9.68447 | −0.483018 | ||||||||
\(403\) | −0.163313 | −0.00813520 | ||||||||
\(404\) | 62.9810 | 3.13342 | ||||||||
\(405\) | 0.858634 | 0.0426659 | ||||||||
\(406\) | 1.29672 | 0.0643550 | ||||||||
\(407\) | 21.5886 | 1.07011 | ||||||||
\(408\) | 18.2760 | 0.904795 | ||||||||
\(409\) | 28.5540 | 1.41190 | 0.705952 | − | 0.708260i | \(-0.250520\pi\) | ||||
0.705952 | + | 0.708260i | \(0.250520\pi\) | |||||||
\(410\) | −0.552853 | −0.0273034 | ||||||||
\(411\) | 22.5584 | 1.11272 | ||||||||
\(412\) | −40.4314 | −1.99191 | ||||||||
\(413\) | 0.236068 | 0.0116161 | ||||||||
\(414\) | 8.07830 | 0.397027 | ||||||||
\(415\) | 0.576886 | 0.0283182 | ||||||||
\(416\) | 6.00618 | 0.294477 | ||||||||
\(417\) | 30.0868 | 1.47336 | ||||||||
\(418\) | 5.02258 | 0.245662 | ||||||||
\(419\) | 24.2074 | 1.18261 | 0.591303 | − | 0.806449i | \(-0.298614\pi\) | ||||
0.591303 | + | 0.806449i | \(0.298614\pi\) | |||||||
\(420\) | 0.208518 | 0.0101746 | ||||||||
\(421\) | −15.0173 | −0.731900 | −0.365950 | − | 0.930635i | \(-0.619256\pi\) | ||||
−0.365950 | + | 0.930635i | \(0.619256\pi\) | |||||||
\(422\) | −36.3047 | −1.76729 | ||||||||
\(423\) | −2.23630 | −0.108732 | ||||||||
\(424\) | −68.0127 | −3.30299 | ||||||||
\(425\) | 4.99267 | 0.242180 | ||||||||
\(426\) | 10.3830 | 0.503057 | ||||||||
\(427\) | −0.596475 | −0.0288654 | ||||||||
\(428\) | 28.0288 | 1.35482 | ||||||||
\(429\) | 1.13021 | 0.0545673 | ||||||||
\(430\) | 1.26598 | 0.0610508 | ||||||||
\(431\) | 16.3024 | 0.785257 | 0.392629 | − | 0.919697i | \(-0.371566\pi\) | ||||
0.392629 | + | 0.919697i | \(0.371566\pi\) | |||||||
\(432\) | −77.5355 | −3.73043 | ||||||||
\(433\) | −25.2725 | −1.21452 | −0.607258 | − | 0.794504i | \(-0.707731\pi\) | ||||
−0.607258 | + | 0.794504i | \(0.707731\pi\) | |||||||
\(434\) | 0.436624 | 0.0209586 | ||||||||
\(435\) | −0.314372 | −0.0150730 | ||||||||
\(436\) | −62.6939 | −3.00249 | ||||||||
\(437\) | −5.37894 | −0.257309 | ||||||||
\(438\) | −47.1807 | −2.25438 | ||||||||
\(439\) | 1.02778 | 0.0490532 | 0.0245266 | − | 0.999699i | \(-0.492192\pi\) | ||||
0.0245266 | + | 0.999699i | \(0.492192\pi\) | |||||||
\(440\) | −2.14137 | −0.102086 | ||||||||
\(441\) | −2.73488 | −0.130232 | ||||||||
\(442\) | −0.670961 | −0.0319144 | ||||||||
\(443\) | −30.5595 | −1.45193 | −0.725963 | − | 0.687734i | \(-0.758606\pi\) | ||||
−0.725963 | + | 0.687734i | \(0.758606\pi\) | |||||||
\(444\) | −88.3437 | −4.19261 | ||||||||
\(445\) | 1.06098 | 0.0502951 | ||||||||
\(446\) | 44.0912 | 2.08778 | ||||||||
\(447\) | 10.7369 | 0.507838 | ||||||||
\(448\) | −8.43311 | −0.398427 | ||||||||
\(449\) | 35.1296 | 1.65787 | 0.828934 | − | 0.559347i | \(-0.188948\pi\) | ||||
0.828934 | + | 0.559347i | \(0.188948\pi\) | |||||||
\(450\) | 5.42023 | 0.255512 | ||||||||
\(451\) | 5.90288 | 0.277956 | ||||||||
\(452\) | 41.7596 | 1.96421 | ||||||||
\(453\) | −29.3666 | −1.37976 | ||||||||
\(454\) | 56.0842 | 2.63216 | ||||||||
\(455\) | −0.00492067 | −0.000230685 0 | ||||||||
\(456\) | −13.2112 | −0.618670 | ||||||||
\(457\) | −35.7939 | −1.67437 | −0.837183 | − | 0.546923i | \(-0.815799\pi\) | ||||
−0.837183 | + | 0.546923i | \(0.815799\pi\) | |||||||
\(458\) | −43.5042 | −2.03282 | ||||||||
\(459\) | 4.80118 | 0.224100 | ||||||||
\(460\) | 3.56777 | 0.166348 | ||||||||
\(461\) | 13.3921 | 0.623734 | 0.311867 | − | 0.950126i | \(-0.399046\pi\) | ||||
0.311867 | + | 0.950126i | \(0.399046\pi\) | |||||||
\(462\) | −3.02167 | −0.140581 | ||||||||
\(463\) | 35.0042 | 1.62678 | 0.813391 | − | 0.581718i | \(-0.197619\pi\) | ||||
0.813391 | + | 0.581718i | \(0.197619\pi\) | |||||||
\(464\) | 32.1801 | 1.49392 | ||||||||
\(465\) | −0.105854 | −0.00490885 | ||||||||
\(466\) | −30.9420 | −1.43336 | ||||||||
\(467\) | 31.7710 | 1.47019 | 0.735093 | − | 0.677966i | \(-0.237139\pi\) | ||||
0.735093 | + | 0.677966i | \(0.237139\pi\) | |||||||
\(468\) | −0.536701 | −0.0248090 | ||||||||
\(469\) | −0.450188 | −0.0207878 | ||||||||
\(470\) | −1.34046 | −0.0618310 | ||||||||
\(471\) | −4.39862 | −0.202678 | ||||||||
\(472\) | 9.92054 | 0.456630 | ||||||||
\(473\) | −13.5170 | −0.621513 | ||||||||
\(474\) | −75.7889 | −3.48110 | ||||||||
\(475\) | −3.60906 | −0.165595 | ||||||||
\(476\) | 1.32171 | 0.0605803 | ||||||||
\(477\) | 2.70001 | 0.123625 | ||||||||
\(478\) | −11.4024 | −0.521532 | ||||||||
\(479\) | −5.85956 | −0.267730 | −0.133865 | − | 0.991000i | \(-0.542739\pi\) | ||||
−0.133865 | + | 0.991000i | \(0.542739\pi\) | |||||||
\(480\) | 3.89299 | 0.177690 | ||||||||
\(481\) | 2.08476 | 0.0950570 | ||||||||
\(482\) | −69.5810 | −3.16933 | ||||||||
\(483\) | 3.23607 | 0.147246 | ||||||||
\(484\) | −26.0174 | −1.18261 | ||||||||
\(485\) | 1.17012 | 0.0531323 | ||||||||
\(486\) | 11.2123 | 0.508602 | ||||||||
\(487\) | 5.13519 | 0.232698 | 0.116349 | − | 0.993208i | \(-0.462881\pi\) | ||||
0.116349 | + | 0.993208i | \(0.462881\pi\) | |||||||
\(488\) | −25.0663 | −1.13470 | ||||||||
\(489\) | 7.76659 | 0.351217 | ||||||||
\(490\) | −1.63932 | −0.0740569 | ||||||||
\(491\) | −29.6469 | −1.33795 | −0.668974 | − | 0.743286i | \(-0.733266\pi\) | ||||
−0.668974 | + | 0.743286i | \(0.733266\pi\) | |||||||
\(492\) | −24.1555 | −1.08901 | ||||||||
\(493\) | −1.99267 | −0.0897452 | ||||||||
\(494\) | 0.485018 | 0.0218220 | ||||||||
\(495\) | 0.0850094 | 0.00382089 | ||||||||
\(496\) | 10.8355 | 0.486530 | ||||||||
\(497\) | 0.482659 | 0.0216502 | ||||||||
\(498\) | 34.2094 | 1.53296 | ||||||||
\(499\) | −9.62164 | −0.430724 | −0.215362 | − | 0.976534i | \(-0.569093\pi\) | ||||
−0.215362 | + | 0.976534i | \(0.569093\pi\) | |||||||
\(500\) | 4.79118 | 0.214268 | ||||||||
\(501\) | −22.9394 | −1.02486 | ||||||||
\(502\) | −9.11617 | −0.406875 | ||||||||
\(503\) | 1.16776 | 0.0520678 | 0.0260339 | − | 0.999661i | \(-0.491712\pi\) | ||||
0.0260339 | + | 0.999661i | \(0.491712\pi\) | |||||||
\(504\) | 0.922324 | 0.0410836 | ||||||||
\(505\) | −0.963331 | −0.0428677 | ||||||||
\(506\) | −51.7012 | −2.29840 | ||||||||
\(507\) | −23.8399 | −1.05877 | ||||||||
\(508\) | −55.0837 | −2.44394 | ||||||||
\(509\) | 32.0068 | 1.41867 | 0.709337 | − | 0.704869i | \(-0.248994\pi\) | ||||
0.709337 | + | 0.704869i | \(0.248994\pi\) | |||||||
\(510\) | −0.434893 | −0.0192574 | ||||||||
\(511\) | −2.19322 | −0.0970224 | ||||||||
\(512\) | −78.0802 | −3.45069 | ||||||||
\(513\) | −3.47063 | −0.153232 | ||||||||
\(514\) | −11.3660 | −0.501331 | ||||||||
\(515\) | 0.618422 | 0.0272509 | ||||||||
\(516\) | 55.3136 | 2.43504 | ||||||||
\(517\) | 14.3123 | 0.629455 | ||||||||
\(518\) | −5.57370 | −0.244894 | ||||||||
\(519\) | −5.41438 | −0.237665 | ||||||||
\(520\) | −0.206787 | −0.00906820 | ||||||||
\(521\) | 25.8464 | 1.13235 | 0.566176 | − | 0.824285i | \(-0.308422\pi\) | ||||
0.566176 | + | 0.824285i | \(0.308422\pi\) | |||||||
\(522\) | −2.16331 | −0.0946856 | ||||||||
\(523\) | 39.6079 | 1.73193 | 0.865966 | − | 0.500102i | \(-0.166704\pi\) | ||||
0.865966 | + | 0.500102i | \(0.166704\pi\) | |||||||
\(524\) | −48.8528 | −2.13414 | ||||||||
\(525\) | 2.17127 | 0.0947622 | ||||||||
\(526\) | 84.7027 | 3.69321 | ||||||||
\(527\) | −0.670961 | −0.0292275 | ||||||||
\(528\) | −74.9877 | −3.26342 | ||||||||
\(529\) | 32.3695 | 1.40737 | ||||||||
\(530\) | 1.61842 | 0.0702998 | ||||||||
\(531\) | −0.393832 | −0.0170909 | ||||||||
\(532\) | −0.955423 | −0.0414228 | ||||||||
\(533\) | 0.570028 | 0.0246906 | ||||||||
\(534\) | 62.9159 | 2.72264 | ||||||||
\(535\) | −0.428716 | −0.0185350 | ||||||||
\(536\) | −18.9188 | −0.817166 | ||||||||
\(537\) | 38.1089 | 1.64452 | ||||||||
\(538\) | −18.0191 | −0.776857 | ||||||||
\(539\) | 17.5032 | 0.753918 | ||||||||
\(540\) | 2.30202 | 0.0990631 | ||||||||
\(541\) | 5.02147 | 0.215890 | 0.107945 | − | 0.994157i | \(-0.465573\pi\) | ||||
0.107945 | + | 0.994157i | \(0.465573\pi\) | |||||||
\(542\) | −32.3282 | −1.38861 | ||||||||
\(543\) | −10.2252 | −0.438806 | ||||||||
\(544\) | 24.6760 | 1.05797 | ||||||||
\(545\) | 0.958939 | 0.0410765 | ||||||||
\(546\) | −0.291796 | −0.0124877 | ||||||||
\(547\) | 33.7551 | 1.44327 | 0.721633 | − | 0.692276i | \(-0.243392\pi\) | ||||
0.721633 | + | 0.692276i | \(0.243392\pi\) | |||||||
\(548\) | 68.5585 | 2.92867 | ||||||||
\(549\) | 0.995099 | 0.0424698 | ||||||||
\(550\) | −34.6895 | −1.47916 | ||||||||
\(551\) | 1.44044 | 0.0613649 | ||||||||
\(552\) | 135.993 | 5.78824 | ||||||||
\(553\) | −3.52309 | −0.149817 | ||||||||
\(554\) | 64.7898 | 2.75266 | ||||||||
\(555\) | 1.35127 | 0.0573581 | ||||||||
\(556\) | 91.4385 | 3.87786 | ||||||||
\(557\) | −4.49735 | −0.190559 | −0.0952795 | − | 0.995451i | \(-0.530374\pi\) | ||||
−0.0952795 | + | 0.995451i | \(0.530374\pi\) | |||||||
\(558\) | −0.728420 | −0.0308365 | ||||||||
\(559\) | −1.30531 | −0.0552086 | ||||||||
\(560\) | 0.326478 | 0.0137962 | ||||||||
\(561\) | 4.64341 | 0.196045 | ||||||||
\(562\) | −63.6402 | −2.68450 | ||||||||
\(563\) | 17.4255 | 0.734399 | 0.367200 | − | 0.930142i | \(-0.380317\pi\) | ||||
0.367200 | + | 0.930142i | \(0.380317\pi\) | |||||||
\(564\) | −58.5680 | −2.46616 | ||||||||
\(565\) | −0.638737 | −0.0268719 | ||||||||
\(566\) | 24.9396 | 1.04829 | ||||||||
\(567\) | 2.36691 | 0.0994009 | ||||||||
\(568\) | 20.2833 | 0.851069 | ||||||||
\(569\) | −8.28770 | −0.347438 | −0.173719 | − | 0.984795i | \(-0.555579\pi\) | ||||
−0.173719 | + | 0.984795i | \(0.555579\pi\) | |||||||
\(570\) | 0.314372 | 0.0131676 | ||||||||
\(571\) | 28.2431 | 1.18194 | 0.590969 | − | 0.806694i | \(-0.298746\pi\) | ||||
0.590969 | + | 0.806694i | \(0.298746\pi\) | |||||||
\(572\) | 3.43489 | 0.143620 | ||||||||
\(573\) | −20.8637 | −0.871595 | ||||||||
\(574\) | −1.52399 | −0.0636102 | ||||||||
\(575\) | 37.1508 | 1.54929 | ||||||||
\(576\) | 14.0690 | 0.586207 | ||||||||
\(577\) | −20.2009 | −0.840974 | −0.420487 | − | 0.907299i | \(-0.638141\pi\) | ||||
−0.420487 | + | 0.907299i | \(0.638141\pi\) | |||||||
\(578\) | −2.75660 | −0.114659 | ||||||||
\(579\) | 7.77307 | 0.323038 | ||||||||
\(580\) | −0.955423 | −0.0396718 | ||||||||
\(581\) | 1.59024 | 0.0659744 | ||||||||
\(582\) | 69.3880 | 2.87623 | ||||||||
\(583\) | −17.2801 | −0.715669 | ||||||||
\(584\) | −92.1682 | −3.81395 | ||||||||
\(585\) | 0.00820916 | 0.000339407 0 | ||||||||
\(586\) | 81.3253 | 3.35952 | ||||||||
\(587\) | 41.6693 | 1.71988 | 0.859938 | − | 0.510399i | \(-0.170502\pi\) | ||||
0.859938 | + | 0.510399i | \(0.170502\pi\) | |||||||
\(588\) | −71.6258 | −2.95380 | ||||||||
\(589\) | 0.485018 | 0.0199848 | ||||||||
\(590\) | −0.236068 | −0.00971876 | ||||||||
\(591\) | −29.1954 | −1.20094 | ||||||||
\(592\) | −138.320 | −5.68493 | ||||||||
\(593\) | 44.1769 | 1.81413 | 0.907063 | − | 0.420994i | \(-0.138319\pi\) | ||||
0.907063 | + | 0.420994i | \(0.138319\pi\) | |||||||
\(594\) | −33.3590 | −1.36874 | ||||||||
\(595\) | −0.0202163 | −0.000828786 0 | ||||||||
\(596\) | 32.6311 | 1.33662 | ||||||||
\(597\) | 20.6309 | 0.844365 | ||||||||
\(598\) | −4.99267 | −0.204165 | ||||||||
\(599\) | 32.5816 | 1.33125 | 0.665625 | − | 0.746287i | \(-0.268165\pi\) | ||||
0.665625 | + | 0.746287i | \(0.268165\pi\) | |||||||
\(600\) | 91.2458 | 3.72510 | ||||||||
\(601\) | 8.11906 | 0.331183 | 0.165592 | − | 0.986194i | \(-0.447047\pi\) | ||||
0.165592 | + | 0.986194i | \(0.447047\pi\) | |||||||
\(602\) | 3.48979 | 0.142233 | ||||||||
\(603\) | 0.751050 | 0.0305851 | ||||||||
\(604\) | −89.2496 | −3.63152 | ||||||||
\(605\) | 0.397951 | 0.0161790 | ||||||||
\(606\) | −57.1256 | −2.32057 | ||||||||
\(607\) | −23.3707 | −0.948586 | −0.474293 | − | 0.880367i | \(-0.657296\pi\) | ||||
−0.474293 | + | 0.880367i | \(0.657296\pi\) | |||||||
\(608\) | −17.8376 | −0.723409 | ||||||||
\(609\) | −0.866596 | −0.0351163 | ||||||||
\(610\) | 0.596475 | 0.0241506 | ||||||||
\(611\) | 1.38211 | 0.0559141 | ||||||||
\(612\) | −2.20500 | −0.0891319 | ||||||||
\(613\) | 0.363394 | 0.0146773 | 0.00733867 | − | 0.999973i | \(-0.497664\pi\) | ||||
0.00733867 | + | 0.999973i | \(0.497664\pi\) | |||||||
\(614\) | −27.6882 | −1.11741 | ||||||||
\(615\) | 0.369472 | 0.0148985 | ||||||||
\(616\) | −5.90288 | −0.237834 | ||||||||
\(617\) | 13.7417 | 0.553220 | 0.276610 | − | 0.960982i | \(-0.410789\pi\) | ||||
0.276610 | + | 0.960982i | \(0.410789\pi\) | |||||||
\(618\) | 36.6725 | 1.47518 | ||||||||
\(619\) | −36.5267 | −1.46813 | −0.734065 | − | 0.679079i | \(-0.762379\pi\) | ||||
−0.734065 | + | 0.679079i | \(0.762379\pi\) | |||||||
\(620\) | −0.321705 | −0.0129200 | ||||||||
\(621\) | 35.7259 | 1.43363 | ||||||||
\(622\) | −62.3112 | −2.49845 | ||||||||
\(623\) | 2.92468 | 0.117175 | ||||||||
\(624\) | −7.24139 | −0.289888 | ||||||||
\(625\) | 24.8900 | 0.995602 | ||||||||
\(626\) | 42.4340 | 1.69600 | ||||||||
\(627\) | −3.35659 | −0.134049 | ||||||||
\(628\) | −13.3681 | −0.533445 | ||||||||
\(629\) | 8.56511 | 0.341513 | ||||||||
\(630\) | −0.0219475 | −0.000874410 0 | ||||||||
\(631\) | −40.9431 | −1.62992 | −0.814960 | − | 0.579517i | \(-0.803241\pi\) | ||||
−0.814960 | + | 0.579517i | \(0.803241\pi\) | |||||||
\(632\) | −148.055 | −5.88930 | ||||||||
\(633\) | 24.2625 | 0.964346 | ||||||||
\(634\) | 1.03724 | 0.0411942 | ||||||||
\(635\) | 0.842537 | 0.0334351 | ||||||||
\(636\) | 70.7127 | 2.80394 | ||||||||
\(637\) | 1.69025 | 0.0669701 | ||||||||
\(638\) | 13.8452 | 0.548138 | ||||||||
\(639\) | −0.805220 | −0.0318540 | ||||||||
\(640\) | 4.20673 | 0.166286 | ||||||||
\(641\) | −13.9640 | −0.551543 | −0.275772 | − | 0.961223i | \(-0.588933\pi\) | ||||
−0.275772 | + | 0.961223i | \(0.588933\pi\) | |||||||
\(642\) | −25.4229 | −1.00336 | ||||||||
\(643\) | −48.3429 | −1.90646 | −0.953229 | − | 0.302249i | \(-0.902262\pi\) | ||||
−0.953229 | + | 0.302249i | \(0.902262\pi\) | |||||||
\(644\) | 9.83490 | 0.387549 | ||||||||
\(645\) | −0.846053 | −0.0333133 | ||||||||
\(646\) | 1.99267 | 0.0784004 | ||||||||
\(647\) | 27.9262 | 1.09789 | 0.548946 | − | 0.835858i | \(-0.315029\pi\) | ||||
0.548946 | + | 0.835858i | \(0.315029\pi\) | |||||||
\(648\) | 99.4672 | 3.90744 | ||||||||
\(649\) | 2.52053 | 0.0989395 | ||||||||
\(650\) | −3.34988 | −0.131393 | ||||||||
\(651\) | −0.291796 | −0.0114364 | ||||||||
\(652\) | 23.6039 | 0.924398 | ||||||||
\(653\) | −48.6822 | −1.90508 | −0.952540 | − | 0.304413i | \(-0.901540\pi\) | ||||
−0.952540 | + | 0.304413i | \(0.901540\pi\) | |||||||
\(654\) | 56.8652 | 2.22360 | ||||||||
\(655\) | 0.747232 | 0.0291968 | ||||||||
\(656\) | −37.8203 | −1.47664 | ||||||||
\(657\) | 3.65895 | 0.142749 | ||||||||
\(658\) | −3.69512 | −0.144051 | ||||||||
\(659\) | −8.01235 | −0.312117 | −0.156058 | − | 0.987748i | \(-0.549879\pi\) | ||||
−0.156058 | + | 0.987748i | \(0.549879\pi\) | |||||||
\(660\) | 2.22637 | 0.0866615 | ||||||||
\(661\) | −43.0909 | −1.67604 | −0.838021 | − | 0.545638i | \(-0.816287\pi\) | ||||
−0.838021 | + | 0.545638i | \(0.816287\pi\) | |||||||
\(662\) | 30.6704 | 1.19204 | ||||||||
\(663\) | 0.448403 | 0.0174145 | ||||||||
\(664\) | 66.8285 | 2.59345 | ||||||||
\(665\) | 0.0146138 | 0.000566697 0 | ||||||||
\(666\) | 9.29860 | 0.360313 | ||||||||
\(667\) | −14.8276 | −0.574126 | ||||||||
\(668\) | −69.7162 | −2.69740 | ||||||||
\(669\) | −29.4662 | −1.13923 | ||||||||
\(670\) | 0.450188 | 0.0173923 | ||||||||
\(671\) | −6.36864 | −0.245859 | ||||||||
\(672\) | 10.7314 | 0.413973 | ||||||||
\(673\) | −3.34903 | −0.129096 | −0.0645478 | − | 0.997915i | \(-0.520560\pi\) | ||||
−0.0645478 | + | 0.997915i | \(0.520560\pi\) | |||||||
\(674\) | 61.6760 | 2.37567 | ||||||||
\(675\) | 23.9707 | 0.922631 | ||||||||
\(676\) | −72.4531 | −2.78666 | ||||||||
\(677\) | −49.1335 | −1.88836 | −0.944178 | − | 0.329436i | \(-0.893141\pi\) | ||||
−0.944178 | + | 0.329436i | \(0.893141\pi\) | |||||||
\(678\) | −37.8772 | −1.45466 | ||||||||
\(679\) | 3.22554 | 0.123785 | ||||||||
\(680\) | −0.849569 | −0.0325795 | ||||||||
\(681\) | −37.4811 | −1.43628 | ||||||||
\(682\) | 4.66190 | 0.178513 | ||||||||
\(683\) | −22.2710 | −0.852176 | −0.426088 | − | 0.904682i | \(-0.640109\pi\) | ||||
−0.426088 | + | 0.904682i | \(0.640109\pi\) | |||||||
\(684\) | 1.59393 | 0.0609455 | ||||||||
\(685\) | −1.04864 | −0.0400665 | ||||||||
\(686\) | −9.07416 | −0.346453 | ||||||||
\(687\) | 29.0739 | 1.10924 | ||||||||
\(688\) | 86.6048 | 3.30178 | ||||||||
\(689\) | −1.66870 | −0.0635724 | ||||||||
\(690\) | −3.23607 | −0.123195 | ||||||||
\(691\) | 41.6463 | 1.58430 | 0.792150 | − | 0.610326i | \(-0.208962\pi\) | ||||
0.792150 | + | 0.610326i | \(0.208962\pi\) | |||||||
\(692\) | −16.4551 | −0.625529 | ||||||||
\(693\) | 0.234337 | 0.00890172 | ||||||||
\(694\) | −101.150 | −3.83961 | ||||||||
\(695\) | −1.39860 | −0.0530521 | ||||||||
\(696\) | −36.4179 | −1.38042 | ||||||||
\(697\) | 2.34192 | 0.0887066 | ||||||||
\(698\) | 38.5713 | 1.45995 | ||||||||
\(699\) | 20.6785 | 0.782134 | ||||||||
\(700\) | 6.59883 | 0.249412 | ||||||||
\(701\) | −35.6854 | −1.34782 | −0.673910 | − | 0.738813i | \(-0.735387\pi\) | ||||
−0.673910 | + | 0.738813i | \(0.735387\pi\) | |||||||
\(702\) | −3.22140 | −0.121584 | ||||||||
\(703\) | −6.19147 | −0.233516 | ||||||||
\(704\) | −90.0415 | −3.39356 | ||||||||
\(705\) | 0.895832 | 0.0337390 | ||||||||
\(706\) | 33.5634 | 1.26318 | ||||||||
\(707\) | −2.65552 | −0.0998710 | ||||||||
\(708\) | −10.3144 | −0.387638 | ||||||||
\(709\) | 0.673948 | 0.0253107 | 0.0126553 | − | 0.999920i | \(-0.495972\pi\) | ||||
0.0126553 | + | 0.999920i | \(0.495972\pi\) | |||||||
\(710\) | −0.482659 | −0.0181139 | ||||||||
\(711\) | 5.87758 | 0.220426 | ||||||||
\(712\) | 122.907 | 4.60614 | ||||||||
\(713\) | −4.99267 | −0.186977 | ||||||||
\(714\) | −1.19882 | −0.0448649 | ||||||||
\(715\) | −0.0525387 | −0.00196484 | ||||||||
\(716\) | 115.819 | 4.32834 | ||||||||
\(717\) | 7.62021 | 0.284582 | ||||||||
\(718\) | 40.2724 | 1.50295 | ||||||||
\(719\) | −37.5874 | −1.40177 | −0.700887 | − | 0.713273i | \(-0.747212\pi\) | ||||
−0.700887 | + | 0.713273i | \(0.747212\pi\) | |||||||
\(720\) | −0.544663 | −0.0202984 | ||||||||
\(721\) | 1.70474 | 0.0634879 | ||||||||
\(722\) | 50.9349 | 1.89560 | ||||||||
\(723\) | 46.5010 | 1.72939 | ||||||||
\(724\) | −31.0760 | −1.15493 | ||||||||
\(725\) | −9.94872 | −0.369486 | ||||||||
\(726\) | 23.5985 | 0.875823 | ||||||||
\(727\) | 11.4772 | 0.425664 | 0.212832 | − | 0.977089i | \(-0.431731\pi\) | ||||
0.212832 | + | 0.977089i | \(0.431731\pi\) | |||||||
\(728\) | −0.570028 | −0.0211266 | ||||||||
\(729\) | 22.5860 | 0.836517 | ||||||||
\(730\) | 2.19322 | 0.0811748 | ||||||||
\(731\) | −5.36277 | −0.198349 | ||||||||
\(732\) | 26.0614 | 0.963257 | ||||||||
\(733\) | −15.0467 | −0.555763 | −0.277881 | − | 0.960615i | \(-0.589632\pi\) | ||||
−0.277881 | + | 0.960615i | \(0.589632\pi\) | |||||||
\(734\) | −27.3921 | −1.01106 | ||||||||
\(735\) | 1.09556 | 0.0404103 | ||||||||
\(736\) | 183.616 | 6.76816 | ||||||||
\(737\) | −4.80672 | −0.177058 | ||||||||
\(738\) | 2.54248 | 0.0935899 | ||||||||
\(739\) | −22.3369 | −0.821678 | −0.410839 | − | 0.911708i | \(-0.634764\pi\) | ||||
−0.410839 | + | 0.911708i | \(0.634764\pi\) | |||||||
\(740\) | 4.10671 | 0.150966 | ||||||||
\(741\) | −0.324138 | −0.0119075 | ||||||||
\(742\) | 4.46134 | 0.163781 | ||||||||
\(743\) | −12.9134 | −0.473748 | −0.236874 | − | 0.971540i | \(-0.576123\pi\) | ||||
−0.236874 | + | 0.971540i | \(0.576123\pi\) | |||||||
\(744\) | −12.2625 | −0.449564 | ||||||||
\(745\) | −0.499112 | −0.0182860 | ||||||||
\(746\) | −10.7701 | −0.394322 | ||||||||
\(747\) | −2.65300 | −0.0970684 | ||||||||
\(748\) | 14.1120 | 0.515987 | ||||||||
\(749\) | −1.18180 | −0.0431820 | ||||||||
\(750\) | −4.34574 | −0.158684 | ||||||||
\(751\) | −25.5796 | −0.933413 | −0.466706 | − | 0.884412i | \(-0.654559\pi\) | ||||
−0.466706 | + | 0.884412i | \(0.654559\pi\) | |||||||
\(752\) | −91.7003 | −3.34397 | ||||||||
\(753\) | 6.09234 | 0.222017 | ||||||||
\(754\) | 1.33700 | 0.0486907 | ||||||||
\(755\) | 1.36513 | 0.0496820 | ||||||||
\(756\) | 6.34574 | 0.230792 | ||||||||
\(757\) | 28.0754 | 1.02042 | 0.510208 | − | 0.860051i | \(-0.329568\pi\) | ||||
0.510208 | + | 0.860051i | \(0.329568\pi\) | |||||||
\(758\) | 78.9173 | 2.86641 | ||||||||
\(759\) | 34.5519 | 1.25416 | ||||||||
\(760\) | 0.614130 | 0.0222768 | ||||||||
\(761\) | −49.7060 | −1.80184 | −0.900920 | − | 0.433984i | \(-0.857107\pi\) | ||||
−0.900920 | + | 0.433984i | \(0.857107\pi\) | |||||||
\(762\) | 49.9625 | 1.80995 | ||||||||
\(763\) | 2.64341 | 0.0956979 | ||||||||
\(764\) | −63.4080 | −2.29402 | ||||||||
\(765\) | 0.0337268 | 0.00121939 | ||||||||
\(766\) | −50.8604 | −1.83766 | ||||||||
\(767\) | 0.243402 | 0.00878873 | ||||||||
\(768\) | 117.838 | 4.25212 | ||||||||
\(769\) | −14.5900 | −0.526129 | −0.263065 | − | 0.964778i | \(-0.584733\pi\) | ||||
−0.263065 | + | 0.964778i | \(0.584733\pi\) | |||||||
\(770\) | 0.140464 | 0.00506198 | ||||||||
\(771\) | 7.59587 | 0.273559 | ||||||||
\(772\) | 23.6235 | 0.850230 | ||||||||
\(773\) | 21.7414 | 0.781984 | 0.390992 | − | 0.920394i | \(-0.372132\pi\) | ||||
0.390992 | + | 0.920394i | \(0.372132\pi\) | |||||||
\(774\) | −5.82202 | −0.209268 | ||||||||
\(775\) | −3.34988 | −0.120331 | ||||||||
\(776\) | 135.551 | 4.86598 | ||||||||
\(777\) | 3.72490 | 0.133630 | ||||||||
\(778\) | −24.6962 | −0.885402 | ||||||||
\(779\) | −1.69291 | −0.0606547 | ||||||||
\(780\) | 0.214996 | 0.00769809 | ||||||||
\(781\) | 5.15342 | 0.184404 | ||||||||
\(782\) | −20.5120 | −0.733509 | ||||||||
\(783\) | −9.56714 | −0.341902 | ||||||||
\(784\) | −112.145 | −4.00518 | ||||||||
\(785\) | 0.204473 | 0.00729794 | ||||||||
\(786\) | 44.3109 | 1.58052 | ||||||||
\(787\) | 38.3701 | 1.36775 | 0.683874 | − | 0.729600i | \(-0.260294\pi\) | ||||
0.683874 | + | 0.729600i | \(0.260294\pi\) | |||||||
\(788\) | −88.7291 | −3.16084 | ||||||||
\(789\) | −56.6069 | −2.01526 | ||||||||
\(790\) | 3.52309 | 0.125346 | ||||||||
\(791\) | −1.76074 | −0.0626048 | ||||||||
\(792\) | 9.84778 | 0.349926 | ||||||||
\(793\) | −0.615005 | −0.0218395 | ||||||||
\(794\) | −84.9808 | −3.01586 | ||||||||
\(795\) | −1.08159 | −0.0383601 | ||||||||
\(796\) | 62.7004 | 2.22236 | ||||||||
\(797\) | 35.1878 | 1.24642 | 0.623208 | − | 0.782056i | \(-0.285829\pi\) | ||||
0.623208 | + | 0.782056i | \(0.285829\pi\) | |||||||
\(798\) | 0.866596 | 0.0306772 | ||||||||
\(799\) | 5.67829 | 0.200884 | ||||||||
\(800\) | 123.199 | 4.35574 | ||||||||
\(801\) | −4.87925 | −0.172400 | ||||||||
\(802\) | −8.74512 | −0.308801 | ||||||||
\(803\) | −23.4173 | −0.826380 | ||||||||
\(804\) | 19.6698 | 0.693700 | ||||||||
\(805\) | −0.150431 | −0.00530198 | ||||||||
\(806\) | 0.450188 | 0.0158572 | ||||||||
\(807\) | 12.0421 | 0.423904 | ||||||||
\(808\) | −111.596 | −3.92592 | ||||||||
\(809\) | −13.8123 | −0.485616 | −0.242808 | − | 0.970074i | \(-0.578069\pi\) | ||||
−0.242808 | + | 0.970074i | \(0.578069\pi\) | |||||||
\(810\) | −2.36691 | −0.0831648 | ||||||||
\(811\) | 12.2833 | 0.431325 | 0.215663 | − | 0.976468i | \(-0.430809\pi\) | ||||
0.215663 | + | 0.976468i | \(0.430809\pi\) | |||||||
\(812\) | −2.63372 | −0.0924254 | ||||||||
\(813\) | 21.6049 | 0.757718 | ||||||||
\(814\) | −59.5111 | −2.08586 | ||||||||
\(815\) | −0.361035 | −0.0126465 | ||||||||
\(816\) | −29.7508 | −1.04149 | ||||||||
\(817\) | 3.87659 | 0.135625 | ||||||||
\(818\) | −78.7118 | −2.75209 | ||||||||
\(819\) | 0.0226294 | 0.000790734 0 | ||||||||
\(820\) | 1.12288 | 0.0392127 | ||||||||
\(821\) | −16.6387 | −0.580693 | −0.290347 | − | 0.956922i | \(-0.593771\pi\) | ||||
−0.290347 | + | 0.956922i | \(0.593771\pi\) | |||||||
\(822\) | −62.1845 | −2.16893 | ||||||||
\(823\) | 7.19288 | 0.250728 | 0.125364 | − | 0.992111i | \(-0.459990\pi\) | ||||
0.125364 | + | 0.992111i | \(0.459990\pi\) | |||||||
\(824\) | 71.6402 | 2.49570 | ||||||||
\(825\) | 23.1830 | 0.807128 | ||||||||
\(826\) | −0.650745 | −0.0226423 | ||||||||
\(827\) | 12.5974 | 0.438056 | 0.219028 | − | 0.975719i | \(-0.429711\pi\) | ||||
0.219028 | + | 0.975719i | \(0.429711\pi\) | |||||||
\(828\) | −16.4076 | −0.570202 | ||||||||
\(829\) | −29.8496 | −1.03672 | −0.518360 | − | 0.855163i | \(-0.673457\pi\) | ||||
−0.518360 | + | 0.855163i | \(0.673457\pi\) | |||||||
\(830\) | −1.59024 | −0.0551982 | ||||||||
\(831\) | −43.2991 | −1.50203 | ||||||||
\(832\) | −8.69509 | −0.301448 | ||||||||
\(833\) | 6.94427 | 0.240605 | ||||||||
\(834\) | −82.9373 | −2.87188 | ||||||||
\(835\) | 1.06635 | 0.0369026 | ||||||||
\(836\) | −10.2012 | −0.352815 | ||||||||
\(837\) | −3.22140 | −0.111348 | ||||||||
\(838\) | −66.7300 | −2.30515 | ||||||||
\(839\) | −39.1941 | −1.35313 | −0.676565 | − | 0.736383i | \(-0.736532\pi\) | ||||
−0.676565 | + | 0.736383i | \(0.736532\pi\) | |||||||
\(840\) | −0.369472 | −0.0127480 | ||||||||
\(841\) | −25.0293 | −0.863079 | ||||||||
\(842\) | 41.3967 | 1.42663 | ||||||||
\(843\) | 42.5308 | 1.46484 | ||||||||
\(844\) | 73.7373 | 2.53814 | ||||||||
\(845\) | 1.10821 | 0.0381237 | ||||||||
\(846\) | 6.16457 | 0.211942 | ||||||||
\(847\) | 1.09699 | 0.0376930 | ||||||||
\(848\) | 110.715 | 3.80198 | ||||||||
\(849\) | −16.6671 | −0.572015 | ||||||||
\(850\) | −13.7628 | −0.472059 | ||||||||
\(851\) | 63.7336 | 2.18476 | ||||||||
\(852\) | −21.0885 | −0.722481 | ||||||||
\(853\) | −27.5883 | −0.944606 | −0.472303 | − | 0.881436i | \(-0.656577\pi\) | ||||
−0.472303 | + | 0.881436i | \(0.656577\pi\) | |||||||
\(854\) | 1.64424 | 0.0562648 | ||||||||
\(855\) | −0.0243801 | −0.000833783 0 | ||||||||
\(856\) | −49.6640 | −1.69748 | ||||||||
\(857\) | −31.1275 | −1.06330 | −0.531648 | − | 0.846966i | \(-0.678427\pi\) | ||||
−0.531648 | + | 0.846966i | \(0.678427\pi\) | |||||||
\(858\) | −3.11555 | −0.106363 | ||||||||
\(859\) | 18.8182 | 0.642069 | 0.321035 | − | 0.947067i | \(-0.395969\pi\) | ||||
0.321035 | + | 0.947067i | \(0.395969\pi\) | |||||||
\(860\) | −2.57128 | −0.0876801 | ||||||||
\(861\) | 1.01848 | 0.0347099 | ||||||||
\(862\) | −44.9391 | −1.53063 | ||||||||
\(863\) | 32.6988 | 1.11308 | 0.556541 | − | 0.830820i | \(-0.312128\pi\) | ||||
0.556541 | + | 0.830820i | \(0.312128\pi\) | |||||||
\(864\) | 118.474 | 4.03056 | ||||||||
\(865\) | 0.251690 | 0.00855773 | ||||||||
\(866\) | 69.6660 | 2.36735 | ||||||||
\(867\) | 1.84224 | 0.0625656 | ||||||||
\(868\) | −0.886813 | −0.0301004 | ||||||||
\(869\) | −37.6165 | −1.27605 | ||||||||
\(870\) | 0.866596 | 0.0293804 | ||||||||
\(871\) | −0.464174 | −0.0157279 | ||||||||
\(872\) | 111.087 | 3.76188 | ||||||||
\(873\) | −5.38118 | −0.182125 | ||||||||
\(874\) | 14.8276 | 0.501550 | ||||||||
\(875\) | −0.202014 | −0.00682933 | ||||||||
\(876\) | 95.8271 | 3.23770 | ||||||||
\(877\) | 13.6701 | 0.461607 | 0.230803 | − | 0.973000i | \(-0.425865\pi\) | ||||
0.230803 | + | 0.973000i | \(0.425865\pi\) | |||||||
\(878\) | −2.83317 | −0.0956149 | ||||||||
\(879\) | −54.3497 | −1.83317 | ||||||||
\(880\) | 3.48585 | 0.117508 | ||||||||
\(881\) | −52.2246 | −1.75949 | −0.879746 | − | 0.475443i | \(-0.842288\pi\) | ||||
−0.879746 | + | 0.475443i | \(0.842288\pi\) | |||||||
\(882\) | 7.53896 | 0.253850 | ||||||||
\(883\) | 40.5188 | 1.36357 | 0.681783 | − | 0.731555i | \(-0.261205\pi\) | ||||
0.681783 | + | 0.731555i | \(0.261205\pi\) | |||||||
\(884\) | 1.36277 | 0.0458348 | ||||||||
\(885\) | 0.157764 | 0.00530319 | ||||||||
\(886\) | 84.2403 | 2.83011 | ||||||||
\(887\) | 38.3375 | 1.28725 | 0.643623 | − | 0.765342i | \(-0.277430\pi\) | ||||
0.643623 | + | 0.765342i | \(0.277430\pi\) | |||||||
\(888\) | 156.536 | 5.25299 | ||||||||
\(889\) | 2.32254 | 0.0778953 | ||||||||
\(890\) | −2.92468 | −0.0980356 | ||||||||
\(891\) | 25.2718 | 0.846638 | ||||||||
\(892\) | −89.5522 | −2.99843 | ||||||||
\(893\) | −4.10468 | −0.137358 | ||||||||
\(894\) | −29.5974 | −0.989883 | ||||||||
\(895\) | −1.77151 | −0.0592152 | ||||||||
\(896\) | 11.5963 | 0.387404 | ||||||||
\(897\) | 3.33660 | 0.111406 | ||||||||
\(898\) | −96.8382 | −3.23153 | ||||||||
\(899\) | 1.33700 | 0.0445915 | ||||||||
\(900\) | −11.0088 | −0.366961 | ||||||||
\(901\) | −6.85575 | −0.228398 | ||||||||
\(902\) | −16.2719 | −0.541794 | ||||||||
\(903\) | −2.33223 | −0.0776117 | ||||||||
\(904\) | −73.9936 | −2.46099 | ||||||||
\(905\) | 0.475325 | 0.0158003 | ||||||||
\(906\) | 80.9520 | 2.68945 | ||||||||
\(907\) | 11.0883 | 0.368181 | 0.184090 | − | 0.982909i | \(-0.441066\pi\) | ||||
0.184090 | + | 0.982909i | \(0.441066\pi\) | |||||||
\(908\) | −113.911 | −3.78026 | ||||||||
\(909\) | 4.43020 | 0.146940 | ||||||||
\(910\) | 0.0135643 | 0.000449653 0 | ||||||||
\(911\) | −18.1245 | −0.600491 | −0.300245 | − | 0.953862i | \(-0.597069\pi\) | ||||
−0.300245 | + | 0.953862i | \(0.597069\pi\) | |||||||
\(912\) | 21.5060 | 0.712134 | ||||||||
\(913\) | 16.9793 | 0.561931 | ||||||||
\(914\) | 98.6693 | 3.26369 | ||||||||
\(915\) | −0.398624 | −0.0131781 | ||||||||
\(916\) | 88.3599 | 2.91949 | ||||||||
\(917\) | 2.05982 | 0.0680212 | ||||||||
\(918\) | −13.2349 | −0.436817 | ||||||||
\(919\) | 20.3942 | 0.672741 | 0.336371 | − | 0.941730i | \(-0.390801\pi\) | ||||
0.336371 | + | 0.941730i | \(0.390801\pi\) | |||||||
\(920\) | −6.32171 | −0.208420 | ||||||||
\(921\) | 18.5041 | 0.609729 | ||||||||
\(922\) | −36.9168 | −1.21579 | ||||||||
\(923\) | 0.497654 | 0.0163805 | ||||||||
\(924\) | 6.13722 | 0.201900 | ||||||||
\(925\) | 42.7627 | 1.40603 | ||||||||
\(926\) | −96.4924 | −3.17094 | ||||||||
\(927\) | −2.84402 | −0.0934099 | ||||||||
\(928\) | −49.1710 | −1.61412 | ||||||||
\(929\) | 11.3149 | 0.371230 | 0.185615 | − | 0.982623i | \(-0.440572\pi\) | ||||
0.185615 | + | 0.982623i | \(0.440572\pi\) | |||||||
\(930\) | 0.291796 | 0.00956837 | ||||||||
\(931\) | −5.01982 | −0.164518 | ||||||||
\(932\) | 62.8452 | 2.05856 | ||||||||
\(933\) | 41.6426 | 1.36332 | ||||||||
\(934\) | −87.5798 | −2.86570 | ||||||||
\(935\) | −0.215852 | −0.00705911 | ||||||||
\(936\) | 0.950978 | 0.0310837 | ||||||||
\(937\) | −44.0194 | −1.43805 | −0.719025 | − | 0.694984i | \(-0.755411\pi\) | ||||
−0.719025 | + | 0.694984i | \(0.755411\pi\) | |||||||
\(938\) | 1.24099 | 0.0405197 | ||||||||
\(939\) | −28.3586 | −0.925449 | ||||||||
\(940\) | 2.72257 | 0.0888005 | ||||||||
\(941\) | −10.5419 | −0.343658 | −0.171829 | − | 0.985127i | \(-0.554968\pi\) | ||||
−0.171829 | + | 0.985127i | \(0.554968\pi\) | |||||||
\(942\) | 12.1252 | 0.395062 | ||||||||
\(943\) | 17.4264 | 0.567482 | ||||||||
\(944\) | −16.1493 | −0.525614 | ||||||||
\(945\) | −0.0970618 | −0.00315742 | ||||||||
\(946\) | 37.2610 | 1.21146 | ||||||||
\(947\) | −21.7442 | −0.706591 | −0.353296 | − | 0.935512i | \(-0.614939\pi\) | ||||
−0.353296 | + | 0.935512i | \(0.614939\pi\) | |||||||
\(948\) | 153.932 | 4.99949 | ||||||||
\(949\) | −2.26136 | −0.0734068 | ||||||||
\(950\) | 9.94872 | 0.322779 | ||||||||
\(951\) | −0.693190 | −0.0224782 | ||||||||
\(952\) | −2.34192 | −0.0759021 | ||||||||
\(953\) | −15.7927 | −0.511575 | −0.255788 | − | 0.966733i | \(-0.582335\pi\) | ||||
−0.255788 | + | 0.966733i | \(0.582335\pi\) | |||||||
\(954\) | −7.44285 | −0.240971 | ||||||||
\(955\) | 0.969863 | 0.0313840 | ||||||||
\(956\) | 23.1590 | 0.749015 | ||||||||
\(957\) | −9.25277 | −0.299100 | ||||||||
\(958\) | 16.1525 | 0.521862 | ||||||||
\(959\) | −2.89068 | −0.0933450 | ||||||||
\(960\) | −5.63585 | −0.181896 | ||||||||
\(961\) | −30.5498 | −0.985478 | ||||||||
\(962\) | −5.74685 | −0.185286 | ||||||||
\(963\) | 1.97159 | 0.0635337 | ||||||||
\(964\) | 141.324 | 4.55173 | ||||||||
\(965\) | −0.361336 | −0.0116318 | ||||||||
\(966\) | −8.92054 | −0.287014 | ||||||||
\(967\) | −33.9655 | −1.09226 | −0.546128 | − | 0.837702i | \(-0.683899\pi\) | ||||
−0.546128 | + | 0.837702i | \(0.683899\pi\) | |||||||
\(968\) | 46.1000 | 1.48171 | ||||||||
\(969\) | −1.33170 | −0.0427804 | ||||||||
\(970\) | −3.22554 | −0.103566 | ||||||||
\(971\) | 17.6534 | 0.566525 | 0.283262 | − | 0.959042i | \(-0.408583\pi\) | ||||
0.283262 | + | 0.959042i | \(0.408583\pi\) | |||||||
\(972\) | −22.7730 | −0.730444 | ||||||||
\(973\) | −3.85539 | −0.123598 | ||||||||
\(974\) | −14.1557 | −0.453576 | ||||||||
\(975\) | 2.23873 | 0.0716967 | ||||||||
\(976\) | 40.8045 | 1.30612 | ||||||||
\(977\) | −19.1541 | −0.612793 | −0.306396 | − | 0.951904i | \(-0.599123\pi\) | ||||
−0.306396 | + | 0.951904i | \(0.599123\pi\) | |||||||
\(978\) | −21.4094 | −0.684596 | ||||||||
\(979\) | 31.2273 | 0.998027 | ||||||||
\(980\) | 3.32957 | 0.106359 | ||||||||
\(981\) | −4.41000 | −0.140801 | ||||||||
\(982\) | 81.7247 | 2.60794 | ||||||||
\(983\) | 39.0710 | 1.24617 | 0.623085 | − | 0.782154i | \(-0.285879\pi\) | ||||
0.623085 | + | 0.782154i | \(0.285879\pi\) | |||||||
\(984\) | 42.8009 | 1.36444 | ||||||||
\(985\) | 1.35716 | 0.0432428 | ||||||||
\(986\) | 5.49298 | 0.174932 | ||||||||
\(987\) | 2.46945 | 0.0786035 | ||||||||
\(988\) | −0.985105 | −0.0313404 | ||||||||
\(989\) | −39.9047 | −1.26890 | ||||||||
\(990\) | −0.234337 | −0.00744771 | ||||||||
\(991\) | −38.2233 | −1.21420 | −0.607101 | − | 0.794625i | \(-0.707668\pi\) | ||||
−0.607101 | + | 0.794625i | \(0.707668\pi\) | |||||||
\(992\) | −16.5566 | −0.525673 | ||||||||
\(993\) | −20.4970 | −0.650453 | ||||||||
\(994\) | −1.33050 | −0.0422008 | ||||||||
\(995\) | −0.959039 | −0.0304036 | ||||||||
\(996\) | −69.4815 | −2.20161 | ||||||||
\(997\) | −46.2303 | −1.46413 | −0.732065 | − | 0.681235i | \(-0.761443\pi\) | ||||
−0.732065 | + | 0.681235i | \(0.761443\pi\) | |||||||
\(998\) | 26.5230 | 0.839571 | ||||||||
\(999\) | 41.1226 | 1.30106 |
(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 | 1003.2.a.f.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 9027.2.a.i.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1003.2.a.f.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9027.2.a.i.1.4 | 4 | 3.2 | odd | 2 |