Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.18122 | −1.54235 | −0.771177 | − | 0.636621i | \(-0.780332\pi\) | ||||
−0.771177 | + | 0.636621i | \(0.780332\pi\) | |||||||
\(3\) | 1.64876 | 0.951910 | 0.475955 | − | 0.879470i | \(-0.342103\pi\) | ||||
0.475955 | + | 0.879470i | \(0.342103\pi\) | |||||||
\(4\) | 2.75771 | 1.37886 | ||||||||
\(5\) | −2.64324 | −1.18209 | −0.591047 | − | 0.806637i | \(-0.701285\pi\) | ||||
−0.591047 | + | 0.806637i | \(0.701285\pi\) | |||||||
\(6\) | −3.59630 | −1.46818 | ||||||||
\(7\) | −4.67385 | −1.76655 | −0.883275 | − | 0.468856i | \(-0.844666\pi\) | ||||
−0.883275 | + | 0.468856i | \(0.844666\pi\) | |||||||
\(8\) | −1.65274 | −0.584332 | ||||||||
\(9\) | −0.281605 | −0.0938682 | ||||||||
\(10\) | 5.76549 | 1.82321 | ||||||||
\(11\) | 5.50049 | 1.65846 | 0.829231 | − | 0.558907i | \(-0.188779\pi\) | ||||
0.829231 | + | 0.558907i | \(0.188779\pi\) | |||||||
\(12\) | 4.54680 | 1.31255 | ||||||||
\(13\) | −1.10509 | −0.306497 | −0.153248 | − | 0.988188i | \(-0.548973\pi\) | ||||
−0.153248 | + | 0.988188i | \(0.548973\pi\) | |||||||
\(14\) | 10.1947 | 2.72465 | ||||||||
\(15\) | −4.35806 | −1.12525 | ||||||||
\(16\) | −1.91044 | −0.477610 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0.614241 | 0.144778 | ||||||||
\(19\) | −7.14625 | −1.63946 | −0.819731 | − | 0.572748i | \(-0.805877\pi\) | ||||
−0.819731 | + | 0.572748i | \(0.805877\pi\) | |||||||
\(20\) | −7.28931 | −1.62994 | ||||||||
\(21\) | −7.70604 | −1.68160 | ||||||||
\(22\) | −11.9978 | −2.55793 | ||||||||
\(23\) | 4.56494 | 0.951856 | 0.475928 | − | 0.879484i | \(-0.342112\pi\) | ||||
0.475928 | + | 0.879484i | \(0.342112\pi\) | |||||||
\(24\) | −2.72496 | −0.556231 | ||||||||
\(25\) | 1.98674 | 0.397348 | ||||||||
\(26\) | 2.41044 | 0.472727 | ||||||||
\(27\) | −5.41056 | −1.04126 | ||||||||
\(28\) | −12.8891 | −2.43582 | ||||||||
\(29\) | 5.65182 | 1.04952 | 0.524758 | − | 0.851252i | \(-0.324156\pi\) | ||||
0.524758 | + | 0.851252i | \(0.324156\pi\) | |||||||
\(30\) | 9.50589 | 1.73553 | ||||||||
\(31\) | 7.52303 | 1.35118 | 0.675588 | − | 0.737280i | \(-0.263890\pi\) | ||||
0.675588 | + | 0.737280i | \(0.263890\pi\) | |||||||
\(32\) | 7.47257 | 1.32098 | ||||||||
\(33\) | 9.06897 | 1.57870 | ||||||||
\(34\) | −2.18122 | −0.374076 | ||||||||
\(35\) | 12.3541 | 2.08823 | ||||||||
\(36\) | −0.776585 | −0.129431 | ||||||||
\(37\) | −9.88532 | −1.62514 | −0.812568 | − | 0.582866i | \(-0.801931\pi\) | ||||
−0.812568 | + | 0.582866i | \(0.801931\pi\) | |||||||
\(38\) | 15.5875 | 2.52863 | ||||||||
\(39\) | −1.82202 | −0.291757 | ||||||||
\(40\) | 4.36859 | 0.690735 | ||||||||
\(41\) | 9.71363 | 1.51701 | 0.758507 | − | 0.651665i | \(-0.225929\pi\) | ||||
0.758507 | + | 0.651665i | \(0.225929\pi\) | |||||||
\(42\) | 16.8086 | 2.59362 | ||||||||
\(43\) | 6.36697 | 0.970954 | 0.485477 | − | 0.874250i | \(-0.338646\pi\) | ||||
0.485477 | + | 0.874250i | \(0.338646\pi\) | |||||||
\(44\) | 15.1688 | 2.28678 | ||||||||
\(45\) | 0.744350 | 0.110961 | ||||||||
\(46\) | −9.95713 | −1.46810 | ||||||||
\(47\) | −10.8208 | −1.57838 | −0.789189 | − | 0.614151i | \(-0.789499\pi\) | ||||
−0.789189 | + | 0.614151i | \(0.789499\pi\) | |||||||
\(48\) | −3.14985 | −0.454642 | ||||||||
\(49\) | 14.8449 | 2.12070 | ||||||||
\(50\) | −4.33351 | −0.612851 | ||||||||
\(51\) | 1.64876 | 0.230872 | ||||||||
\(52\) | −3.04752 | −0.422615 | ||||||||
\(53\) | 8.76412 | 1.20385 | 0.601923 | − | 0.798554i | \(-0.294402\pi\) | ||||
0.601923 | + | 0.798554i | \(0.294402\pi\) | |||||||
\(54\) | 11.8016 | 1.60600 | ||||||||
\(55\) | −14.5391 | −1.96046 | ||||||||
\(56\) | 7.72466 | 1.03225 | ||||||||
\(57\) | −11.7824 | −1.56062 | ||||||||
\(58\) | −12.3278 | −1.61873 | ||||||||
\(59\) | −9.82363 | −1.27893 | −0.639464 | − | 0.768821i | \(-0.720844\pi\) | ||||
−0.639464 | + | 0.768821i | \(0.720844\pi\) | |||||||
\(60\) | −12.0183 | −1.55155 | ||||||||
\(61\) | 1.13872 | 0.145799 | 0.0728993 | − | 0.997339i | \(-0.476775\pi\) | ||||
0.0728993 | + | 0.997339i | \(0.476775\pi\) | |||||||
\(62\) | −16.4094 | −2.08399 | ||||||||
\(63\) | 1.31618 | 0.165823 | ||||||||
\(64\) | −12.4784 | −1.55980 | ||||||||
\(65\) | 2.92102 | 0.362308 | ||||||||
\(66\) | −19.7814 | −2.43492 | ||||||||
\(67\) | 12.9490 | 1.58197 | 0.790983 | − | 0.611838i | \(-0.209569\pi\) | ||||
0.790983 | + | 0.611838i | \(0.209569\pi\) | |||||||
\(68\) | 2.75771 | 0.334422 | ||||||||
\(69\) | 7.52647 | 0.906080 | ||||||||
\(70\) | −26.9471 | −3.22079 | ||||||||
\(71\) | 3.21895 | 0.382019 | 0.191010 | − | 0.981588i | \(-0.438824\pi\) | ||||
0.191010 | + | 0.981588i | \(0.438824\pi\) | |||||||
\(72\) | 0.465419 | 0.0548502 | ||||||||
\(73\) | 9.53275 | 1.11572 | 0.557862 | − | 0.829934i | \(-0.311622\pi\) | ||||
0.557862 | + | 0.829934i | \(0.311622\pi\) | |||||||
\(74\) | 21.5620 | 2.50654 | ||||||||
\(75\) | 3.27565 | 0.378239 | ||||||||
\(76\) | −19.7073 | −2.26058 | ||||||||
\(77\) | −25.7085 | −2.92975 | ||||||||
\(78\) | 3.97423 | 0.449993 | ||||||||
\(79\) | −7.90519 | −0.889404 | −0.444702 | − | 0.895679i | \(-0.646690\pi\) | ||||
−0.444702 | + | 0.895679i | \(0.646690\pi\) | |||||||
\(80\) | 5.04976 | 0.564581 | ||||||||
\(81\) | −8.07588 | −0.897321 | ||||||||
\(82\) | −21.1875 | −2.33977 | ||||||||
\(83\) | −4.89734 | −0.537552 | −0.268776 | − | 0.963203i | \(-0.586619\pi\) | ||||
−0.268776 | + | 0.963203i | \(0.586619\pi\) | |||||||
\(84\) | −21.2510 | −2.31868 | ||||||||
\(85\) | −2.64324 | −0.286700 | ||||||||
\(86\) | −13.8877 | −1.49755 | ||||||||
\(87\) | 9.31846 | 0.999044 | ||||||||
\(88\) | −9.09088 | −0.969091 | ||||||||
\(89\) | −13.7981 | −1.46259 | −0.731295 | − | 0.682061i | \(-0.761084\pi\) | ||||
−0.731295 | + | 0.682061i | \(0.761084\pi\) | |||||||
\(90\) | −1.62359 | −0.171141 | ||||||||
\(91\) | 5.16503 | 0.541442 | ||||||||
\(92\) | 12.5888 | 1.31247 | ||||||||
\(93\) | 12.4036 | 1.28620 | ||||||||
\(94\) | 23.6026 | 2.43442 | ||||||||
\(95\) | 18.8893 | 1.93800 | ||||||||
\(96\) | 12.3204 | 1.25745 | ||||||||
\(97\) | 11.6986 | 1.18782 | 0.593909 | − | 0.804532i | \(-0.297584\pi\) | ||||
0.593909 | + | 0.804532i | \(0.297584\pi\) | |||||||
\(98\) | −32.3799 | −3.27087 | ||||||||
\(99\) | −1.54896 | −0.155677 | ||||||||
\(100\) | 5.47886 | 0.547886 | ||||||||
\(101\) | −11.4408 | −1.13841 | −0.569203 | − | 0.822197i | \(-0.692748\pi\) | ||||
−0.569203 | + | 0.822197i | \(0.692748\pi\) | |||||||
\(102\) | −3.59630 | −0.356086 | ||||||||
\(103\) | −0.169037 | −0.0166557 | −0.00832787 | − | 0.999965i | \(-0.502651\pi\) | ||||
−0.00832787 | + | 0.999965i | \(0.502651\pi\) | |||||||
\(104\) | 1.82643 | 0.179096 | ||||||||
\(105\) | 20.3689 | 1.98781 | ||||||||
\(106\) | −19.1165 | −1.85676 | ||||||||
\(107\) | 8.09262 | 0.782343 | 0.391171 | − | 0.920318i | \(-0.372070\pi\) | ||||
0.391171 | + | 0.920318i | \(0.372070\pi\) | |||||||
\(108\) | −14.9208 | −1.43575 | ||||||||
\(109\) | −13.0366 | −1.24868 | −0.624342 | − | 0.781151i | \(-0.714633\pi\) | ||||
−0.624342 | + | 0.781151i | \(0.714633\pi\) | |||||||
\(110\) | 31.7131 | 3.02372 | ||||||||
\(111\) | −16.2985 | −1.54698 | ||||||||
\(112\) | 8.92912 | 0.843723 | ||||||||
\(113\) | 9.19528 | 0.865020 | 0.432510 | − | 0.901629i | \(-0.357628\pi\) | ||||
0.432510 | + | 0.901629i | \(0.357628\pi\) | |||||||
\(114\) | 25.7000 | 2.40703 | ||||||||
\(115\) | −12.0662 | −1.12518 | ||||||||
\(116\) | 15.5861 | 1.44713 | ||||||||
\(117\) | 0.311199 | 0.0287703 | ||||||||
\(118\) | 21.4275 | 1.97256 | ||||||||
\(119\) | −4.67385 | −0.428451 | ||||||||
\(120\) | 7.20274 | 0.657518 | ||||||||
\(121\) | 19.2554 | 1.75049 | ||||||||
\(122\) | −2.48381 | −0.224873 | ||||||||
\(123\) | 16.0154 | 1.44406 | ||||||||
\(124\) | 20.7464 | 1.86308 | ||||||||
\(125\) | 7.96478 | 0.712392 | ||||||||
\(126\) | −2.87087 | −0.255758 | ||||||||
\(127\) | 0.175459 | 0.0155695 | 0.00778474 | − | 0.999970i | \(-0.497522\pi\) | ||||
0.00778474 | + | 0.999970i | \(0.497522\pi\) | |||||||
\(128\) | 12.2730 | 1.08479 | ||||||||
\(129\) | 10.4976 | 0.924260 | ||||||||
\(130\) | −6.37139 | −0.558808 | ||||||||
\(131\) | 9.63318 | 0.841655 | 0.420827 | − | 0.907141i | \(-0.361740\pi\) | ||||
0.420827 | + | 0.907141i | \(0.361740\pi\) | |||||||
\(132\) | 25.0096 | 2.17681 | ||||||||
\(133\) | 33.4005 | 2.89619 | ||||||||
\(134\) | −28.2445 | −2.43995 | ||||||||
\(135\) | 14.3014 | 1.23087 | ||||||||
\(136\) | −1.65274 | −0.141721 | ||||||||
\(137\) | 15.7231 | 1.34332 | 0.671658 | − | 0.740861i | \(-0.265582\pi\) | ||||
0.671658 | + | 0.740861i | \(0.265582\pi\) | |||||||
\(138\) | −16.4169 | −1.39750 | ||||||||
\(139\) | −11.9971 | −1.01758 | −0.508789 | − | 0.860891i | \(-0.669907\pi\) | ||||
−0.508789 | + | 0.860891i | \(0.669907\pi\) | |||||||
\(140\) | 34.0692 | 2.87937 | ||||||||
\(141\) | −17.8409 | −1.50247 | ||||||||
\(142\) | −7.02124 | −0.589209 | ||||||||
\(143\) | −6.07854 | −0.508313 | ||||||||
\(144\) | 0.537989 | 0.0448324 | ||||||||
\(145\) | −14.9391 | −1.24063 | ||||||||
\(146\) | −20.7930 | −1.72084 | ||||||||
\(147\) | 24.4756 | 2.01871 | ||||||||
\(148\) | −27.2609 | −2.24083 | ||||||||
\(149\) | −2.56632 | −0.210241 | −0.105120 | − | 0.994459i | \(-0.533523\pi\) | ||||
−0.105120 | + | 0.994459i | \(0.533523\pi\) | |||||||
\(150\) | −7.14490 | −0.583379 | ||||||||
\(151\) | −18.9500 | −1.54213 | −0.771065 | − | 0.636756i | \(-0.780276\pi\) | ||||
−0.771065 | + | 0.636756i | \(0.780276\pi\) | |||||||
\(152\) | 11.8109 | 0.957990 | ||||||||
\(153\) | −0.281605 | −0.0227664 | ||||||||
\(154\) | 56.0758 | 4.51872 | ||||||||
\(155\) | −19.8852 | −1.59722 | ||||||||
\(156\) | −5.02462 | −0.402292 | ||||||||
\(157\) | 6.29363 | 0.502287 | 0.251143 | − | 0.967950i | \(-0.419193\pi\) | ||||
0.251143 | + | 0.967950i | \(0.419193\pi\) | |||||||
\(158\) | 17.2430 | 1.37178 | ||||||||
\(159\) | 14.4499 | 1.14595 | ||||||||
\(160\) | −19.7518 | −1.56152 | ||||||||
\(161\) | −21.3358 | −1.68150 | ||||||||
\(162\) | 17.6153 | 1.38399 | ||||||||
\(163\) | −11.1721 | −0.875066 | −0.437533 | − | 0.899202i | \(-0.644148\pi\) | ||||
−0.437533 | + | 0.899202i | \(0.644148\pi\) | |||||||
\(164\) | 26.7874 | 2.09174 | ||||||||
\(165\) | −23.9715 | −1.86618 | ||||||||
\(166\) | 10.6822 | 0.829096 | ||||||||
\(167\) | 14.1528 | 1.09518 | 0.547589 | − | 0.836748i | \(-0.315546\pi\) | ||||
0.547589 | + | 0.836748i | \(0.315546\pi\) | |||||||
\(168\) | 12.7361 | 0.982610 | ||||||||
\(169\) | −11.7788 | −0.906060 | ||||||||
\(170\) | 5.76549 | 0.442193 | ||||||||
\(171\) | 2.01242 | 0.153894 | ||||||||
\(172\) | 17.5583 | 1.33881 | ||||||||
\(173\) | 18.4078 | 1.39952 | 0.699761 | − | 0.714377i | \(-0.253290\pi\) | ||||
0.699761 | + | 0.714377i | \(0.253290\pi\) | |||||||
\(174\) | −20.3256 | −1.54088 | ||||||||
\(175\) | −9.28572 | −0.701935 | ||||||||
\(176\) | −10.5084 | −0.792098 | ||||||||
\(177\) | −16.1968 | −1.21742 | ||||||||
\(178\) | 30.0966 | 2.25583 | ||||||||
\(179\) | −18.7020 | −1.39785 | −0.698927 | − | 0.715193i | \(-0.746339\pi\) | ||||
−0.698927 | + | 0.715193i | \(0.746339\pi\) | |||||||
\(180\) | 2.05270 | 0.153000 | ||||||||
\(181\) | −11.6832 | −0.868403 | −0.434201 | − | 0.900816i | \(-0.642969\pi\) | ||||
−0.434201 | + | 0.900816i | \(0.642969\pi\) | |||||||
\(182\) | −11.2661 | −0.835096 | ||||||||
\(183\) | 1.87748 | 0.138787 | ||||||||
\(184\) | −7.54466 | −0.556199 | ||||||||
\(185\) | 26.1293 | 1.92107 | ||||||||
\(186\) | −27.0550 | −1.98377 | ||||||||
\(187\) | 5.50049 | 0.402236 | ||||||||
\(188\) | −29.8407 | −2.17636 | ||||||||
\(189\) | 25.2882 | 1.83944 | ||||||||
\(190\) | −41.2017 | −2.98908 | ||||||||
\(191\) | −7.32065 | −0.529704 | −0.264852 | − | 0.964289i | \(-0.585323\pi\) | ||||
−0.264852 | + | 0.964289i | \(0.585323\pi\) | |||||||
\(192\) | −20.5739 | −1.48479 | ||||||||
\(193\) | −0.631958 | −0.0454894 | −0.0227447 | − | 0.999741i | \(-0.507240\pi\) | ||||
−0.0227447 | + | 0.999741i | \(0.507240\pi\) | |||||||
\(194\) | −25.5173 | −1.83204 | ||||||||
\(195\) | 4.81605 | 0.344885 | ||||||||
\(196\) | 40.9379 | 2.92414 | ||||||||
\(197\) | 10.9726 | 0.781762 | 0.390881 | − | 0.920441i | \(-0.372170\pi\) | ||||
0.390881 | + | 0.920441i | \(0.372170\pi\) | |||||||
\(198\) | 3.37863 | 0.240109 | ||||||||
\(199\) | 14.9202 | 1.05766 | 0.528832 | − | 0.848727i | \(-0.322630\pi\) | ||||
0.528832 | + | 0.848727i | \(0.322630\pi\) | |||||||
\(200\) | −3.28356 | −0.232183 | ||||||||
\(201\) | 21.3497 | 1.50589 | ||||||||
\(202\) | 24.9549 | 1.75582 | ||||||||
\(203\) | −26.4157 | −1.85402 | ||||||||
\(204\) | 4.54680 | 0.318339 | ||||||||
\(205\) | −25.6755 | −1.79325 | ||||||||
\(206\) | 0.368707 | 0.0256891 | ||||||||
\(207\) | −1.28551 | −0.0893490 | ||||||||
\(208\) | 2.11121 | 0.146386 | ||||||||
\(209\) | −39.3079 | −2.71899 | ||||||||
\(210\) | −44.4291 | −3.06590 | ||||||||
\(211\) | −11.8753 | −0.817532 | −0.408766 | − | 0.912639i | \(-0.634041\pi\) | ||||
−0.408766 | + | 0.912639i | \(0.634041\pi\) | |||||||
\(212\) | 24.1689 | 1.65993 | ||||||||
\(213\) | 5.30726 | 0.363648 | ||||||||
\(214\) | −17.6518 | −1.20665 | ||||||||
\(215\) | −16.8295 | −1.14776 | ||||||||
\(216\) | 8.94225 | 0.608443 | ||||||||
\(217\) | −35.1615 | −2.38692 | ||||||||
\(218\) | 28.4358 | 1.92591 | ||||||||
\(219\) | 15.7172 | 1.06207 | ||||||||
\(220\) | −40.0948 | −2.70319 | ||||||||
\(221\) | −1.10509 | −0.0743364 | ||||||||
\(222\) | 35.5505 | 2.38600 | ||||||||
\(223\) | −2.17541 | −0.145676 | −0.0728382 | − | 0.997344i | \(-0.523206\pi\) | ||||
−0.0728382 | + | 0.997344i | \(0.523206\pi\) | |||||||
\(224\) | −34.9257 | −2.33357 | ||||||||
\(225\) | −0.559475 | −0.0372983 | ||||||||
\(226\) | −20.0569 | −1.33417 | ||||||||
\(227\) | −15.6433 | −1.03828 | −0.519141 | − | 0.854689i | \(-0.673748\pi\) | ||||
−0.519141 | + | 0.854689i | \(0.673748\pi\) | |||||||
\(228\) | −32.4926 | −2.15187 | ||||||||
\(229\) | −14.9613 | −0.988671 | −0.494336 | − | 0.869271i | \(-0.664589\pi\) | ||||
−0.494336 | + | 0.869271i | \(0.664589\pi\) | |||||||
\(230\) | 26.3191 | 1.73543 | ||||||||
\(231\) | −42.3870 | −2.78886 | ||||||||
\(232\) | −9.34098 | −0.613265 | ||||||||
\(233\) | −21.2252 | −1.39051 | −0.695254 | − | 0.718764i | \(-0.744708\pi\) | ||||
−0.695254 | + | 0.718764i | \(0.744708\pi\) | |||||||
\(234\) | −0.678792 | −0.0443740 | ||||||||
\(235\) | 28.6020 | 1.86579 | ||||||||
\(236\) | −27.0908 | −1.76346 | ||||||||
\(237\) | −13.0337 | −0.846632 | ||||||||
\(238\) | 10.1947 | 0.660824 | ||||||||
\(239\) | 3.36650 | 0.217761 | 0.108880 | − | 0.994055i | \(-0.465273\pi\) | ||||
0.108880 | + | 0.994055i | \(0.465273\pi\) | |||||||
\(240\) | 8.32583 | 0.537430 | ||||||||
\(241\) | −11.0635 | −0.712661 | −0.356331 | − | 0.934360i | \(-0.615972\pi\) | ||||
−0.356331 | + | 0.934360i | \(0.615972\pi\) | |||||||
\(242\) | −42.0003 | −2.69988 | ||||||||
\(243\) | 2.91653 | 0.187096 | ||||||||
\(244\) | 3.14028 | 0.201036 | ||||||||
\(245\) | −39.2387 | −2.50687 | ||||||||
\(246\) | −34.9331 | −2.22725 | ||||||||
\(247\) | 7.89726 | 0.502490 | ||||||||
\(248\) | −12.4336 | −0.789535 | ||||||||
\(249\) | −8.07451 | −0.511701 | ||||||||
\(250\) | −17.3729 | −1.09876 | ||||||||
\(251\) | 17.3055 | 1.09231 | 0.546157 | − | 0.837683i | \(-0.316090\pi\) | ||||
0.546157 | + | 0.837683i | \(0.316090\pi\) | |||||||
\(252\) | 3.62964 | 0.228646 | ||||||||
\(253\) | 25.1094 | 1.57862 | ||||||||
\(254\) | −0.382715 | −0.0240137 | ||||||||
\(255\) | −4.35806 | −0.272913 | ||||||||
\(256\) | −1.81331 | −0.113332 | ||||||||
\(257\) | −9.41460 | −0.587266 | −0.293633 | − | 0.955918i | \(-0.594864\pi\) | ||||
−0.293633 | + | 0.955918i | \(0.594864\pi\) | |||||||
\(258\) | −22.8975 | −1.42554 | ||||||||
\(259\) | 46.2025 | 2.87088 | ||||||||
\(260\) | 8.05535 | 0.499572 | ||||||||
\(261\) | −1.59158 | −0.0985162 | ||||||||
\(262\) | −21.0121 | −1.29813 | ||||||||
\(263\) | −11.3323 | −0.698781 | −0.349391 | − | 0.936977i | \(-0.613611\pi\) | ||||
−0.349391 | + | 0.936977i | \(0.613611\pi\) | |||||||
\(264\) | −14.9886 | −0.922487 | ||||||||
\(265\) | −23.1657 | −1.42306 | ||||||||
\(266\) | −72.8538 | −4.46696 | ||||||||
\(267\) | −22.7496 | −1.39225 | ||||||||
\(268\) | 35.7095 | 2.18131 | ||||||||
\(269\) | 2.26739 | 0.138245 | 0.0691225 | − | 0.997608i | \(-0.477980\pi\) | ||||
0.0691225 | + | 0.997608i | \(0.477980\pi\) | |||||||
\(270\) | −31.1946 | −1.89844 | ||||||||
\(271\) | −23.7134 | −1.44049 | −0.720243 | − | 0.693721i | \(-0.755970\pi\) | ||||
−0.720243 | + | 0.693721i | \(0.755970\pi\) | |||||||
\(272\) | −1.91044 | −0.115838 | ||||||||
\(273\) | 8.51587 | 0.515404 | ||||||||
\(274\) | −34.2956 | −2.07187 | ||||||||
\(275\) | 10.9280 | 0.658986 | ||||||||
\(276\) | 20.7558 | 1.24936 | ||||||||
\(277\) | 28.0322 | 1.68429 | 0.842147 | − | 0.539249i | \(-0.181292\pi\) | ||||
0.842147 | + | 0.539249i | \(0.181292\pi\) | |||||||
\(278\) | 26.1682 | 1.56947 | ||||||||
\(279\) | −2.11852 | −0.126832 | ||||||||
\(280\) | −20.4182 | −1.22022 | ||||||||
\(281\) | −19.0212 | −1.13471 | −0.567354 | − | 0.823474i | \(-0.692033\pi\) | ||||
−0.567354 | + | 0.823474i | \(0.692033\pi\) | |||||||
\(282\) | 38.9148 | 2.31735 | ||||||||
\(283\) | −3.08146 | −0.183174 | −0.0915869 | − | 0.995797i | \(-0.529194\pi\) | ||||
−0.0915869 | + | 0.995797i | \(0.529194\pi\) | |||||||
\(284\) | 8.87695 | 0.526750 | ||||||||
\(285\) | 31.1438 | 1.84480 | ||||||||
\(286\) | 13.2586 | 0.783999 | ||||||||
\(287\) | −45.4000 | −2.67988 | ||||||||
\(288\) | −2.10431 | −0.123998 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 32.5855 | 1.91349 | ||||||||
\(291\) | 19.2882 | 1.13069 | ||||||||
\(292\) | 26.2886 | 1.53842 | ||||||||
\(293\) | −29.5383 | −1.72565 | −0.862824 | − | 0.505504i | \(-0.831307\pi\) | ||||
−0.862824 | + | 0.505504i | \(0.831307\pi\) | |||||||
\(294\) | −53.3866 | −3.11357 | ||||||||
\(295\) | 25.9662 | 1.51181 | ||||||||
\(296\) | 16.3379 | 0.949619 | ||||||||
\(297\) | −29.7608 | −1.72690 | ||||||||
\(298\) | 5.59770 | 0.324266 | ||||||||
\(299\) | −5.04467 | −0.291741 | ||||||||
\(300\) | 9.03330 | 0.521538 | ||||||||
\(301\) | −29.7583 | −1.71524 | ||||||||
\(302\) | 41.3341 | 2.37851 | ||||||||
\(303\) | −18.8631 | −1.08366 | ||||||||
\(304\) | 13.6525 | 0.783025 | ||||||||
\(305\) | −3.00993 | −0.172348 | ||||||||
\(306\) | 0.614241 | 0.0351138 | ||||||||
\(307\) | 18.4904 | 1.05530 | 0.527651 | − | 0.849461i | \(-0.323073\pi\) | ||||
0.527651 | + | 0.849461i | \(0.323073\pi\) | |||||||
\(308\) | −70.8966 | −4.03971 | ||||||||
\(309\) | −0.278701 | −0.0158548 | ||||||||
\(310\) | 43.3739 | 2.46347 | ||||||||
\(311\) | −24.0884 | −1.36593 | −0.682963 | − | 0.730453i | \(-0.739309\pi\) | ||||
−0.682963 | + | 0.730453i | \(0.739309\pi\) | |||||||
\(312\) | 3.01133 | 0.170483 | ||||||||
\(313\) | 11.7331 | 0.663195 | 0.331597 | − | 0.943421i | \(-0.392412\pi\) | ||||
0.331597 | + | 0.943421i | \(0.392412\pi\) | |||||||
\(314\) | −13.7278 | −0.774704 | ||||||||
\(315\) | −3.47898 | −0.196018 | ||||||||
\(316\) | −21.8003 | −1.22636 | ||||||||
\(317\) | −30.4121 | −1.70811 | −0.854056 | − | 0.520180i | \(-0.825865\pi\) | ||||
−0.854056 | + | 0.520180i | \(0.825865\pi\) | |||||||
\(318\) | −31.5184 | −1.76746 | ||||||||
\(319\) | 31.0878 | 1.74058 | ||||||||
\(320\) | 32.9835 | 1.84383 | ||||||||
\(321\) | 13.3428 | 0.744720 | ||||||||
\(322\) | 46.5381 | 2.59347 | ||||||||
\(323\) | −7.14625 | −0.397628 | ||||||||
\(324\) | −22.2710 | −1.23728 | ||||||||
\(325\) | −2.19553 | −0.121786 | ||||||||
\(326\) | 24.3688 | 1.34966 | ||||||||
\(327\) | −21.4942 | −1.18863 | ||||||||
\(328\) | −16.0541 | −0.886439 | ||||||||
\(329\) | 50.5749 | 2.78828 | ||||||||
\(330\) | 52.2871 | 2.87831 | ||||||||
\(331\) | 24.1752 | 1.32879 | 0.664395 | − | 0.747381i | \(-0.268689\pi\) | ||||
0.664395 | + | 0.747381i | \(0.268689\pi\) | |||||||
\(332\) | −13.5055 | −0.741208 | ||||||||
\(333\) | 2.78375 | 0.152549 | ||||||||
\(334\) | −30.8704 | −1.68915 | ||||||||
\(335\) | −34.2272 | −1.87003 | ||||||||
\(336\) | 14.7219 | 0.803148 | ||||||||
\(337\) | 23.3202 | 1.27033 | 0.635166 | − | 0.772376i | \(-0.280932\pi\) | ||||
0.635166 | + | 0.772376i | \(0.280932\pi\) | |||||||
\(338\) | 25.6921 | 1.39746 | ||||||||
\(339\) | 15.1608 | 0.823420 | ||||||||
\(340\) | −7.28931 | −0.395318 | ||||||||
\(341\) | 41.3803 | 2.24087 | ||||||||
\(342\) | −4.38952 | −0.237358 | ||||||||
\(343\) | −36.6658 | −1.97977 | ||||||||
\(344\) | −10.5229 | −0.567359 | ||||||||
\(345\) | −19.8943 | −1.07107 | ||||||||
\(346\) | −40.1515 | −2.15856 | ||||||||
\(347\) | −1.03700 | −0.0556693 | −0.0278346 | − | 0.999613i | \(-0.508861\pi\) | ||||
−0.0278346 | + | 0.999613i | \(0.508861\pi\) | |||||||
\(348\) | 25.6977 | 1.37754 | ||||||||
\(349\) | 6.92713 | 0.370801 | 0.185400 | − | 0.982663i | \(-0.440642\pi\) | ||||
0.185400 | + | 0.982663i | \(0.440642\pi\) | |||||||
\(350\) | 20.2542 | 1.08263 | ||||||||
\(351\) | 5.97916 | 0.319144 | ||||||||
\(352\) | 41.1028 | 2.19079 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | 35.3287 | 1.87770 | ||||||||
\(355\) | −8.50847 | −0.451583 | ||||||||
\(356\) | −38.0511 | −2.01670 | ||||||||
\(357\) | −7.70604 | −0.407847 | ||||||||
\(358\) | 40.7932 | 2.15599 | ||||||||
\(359\) | −11.1618 | −0.589095 | −0.294547 | − | 0.955637i | \(-0.595169\pi\) | ||||
−0.294547 | + | 0.955637i | \(0.595169\pi\) | |||||||
\(360\) | −1.23022 | −0.0648381 | ||||||||
\(361\) | 32.0689 | 1.68784 | ||||||||
\(362\) | 25.4835 | 1.33938 | ||||||||
\(363\) | 31.7475 | 1.66631 | ||||||||
\(364\) | 14.2437 | 0.746571 | ||||||||
\(365\) | −25.1974 | −1.31889 | ||||||||
\(366\) | −4.09519 | −0.214059 | ||||||||
\(367\) | −24.9662 | −1.30323 | −0.651613 | − | 0.758552i | \(-0.725907\pi\) | ||||
−0.651613 | + | 0.758552i | \(0.725907\pi\) | |||||||
\(368\) | −8.72105 | −0.454616 | ||||||||
\(369\) | −2.73540 | −0.142399 | ||||||||
\(370\) | −56.9937 | −2.96296 | ||||||||
\(371\) | −40.9622 | −2.12665 | ||||||||
\(372\) | 34.2057 | 1.77348 | ||||||||
\(373\) | 3.45430 | 0.178857 | 0.0894285 | − | 0.995993i | \(-0.471496\pi\) | ||||
0.0894285 | + | 0.995993i | \(0.471496\pi\) | |||||||
\(374\) | −11.9978 | −0.620390 | ||||||||
\(375\) | 13.1320 | 0.678133 | ||||||||
\(376\) | 17.8840 | 0.922296 | ||||||||
\(377\) | −6.24577 | −0.321673 | ||||||||
\(378\) | −55.1590 | −2.83707 | ||||||||
\(379\) | 21.7587 | 1.11767 | 0.558833 | − | 0.829280i | \(-0.311249\pi\) | ||||
0.558833 | + | 0.829280i | \(0.311249\pi\) | |||||||
\(380\) | 52.0913 | 2.67223 | ||||||||
\(381\) | 0.289289 | 0.0148207 | ||||||||
\(382\) | 15.9679 | 0.816991 | ||||||||
\(383\) | −19.4263 | −0.992639 | −0.496320 | − | 0.868140i | \(-0.665316\pi\) | ||||
−0.496320 | + | 0.868140i | \(0.665316\pi\) | |||||||
\(384\) | 20.2352 | 1.03262 | ||||||||
\(385\) | 67.9538 | 3.46325 | ||||||||
\(386\) | 1.37844 | 0.0701607 | ||||||||
\(387\) | −1.79297 | −0.0911417 | ||||||||
\(388\) | 32.2615 | 1.63783 | ||||||||
\(389\) | −23.4435 | −1.18863 | −0.594316 | − | 0.804231i | \(-0.702577\pi\) | ||||
−0.594316 | + | 0.804231i | \(0.702577\pi\) | |||||||
\(390\) | −10.5049 | −0.531935 | ||||||||
\(391\) | 4.56494 | 0.230859 | ||||||||
\(392\) | −24.5347 | −1.23919 | ||||||||
\(393\) | 15.8828 | 0.801179 | ||||||||
\(394\) | −23.9335 | −1.20575 | ||||||||
\(395\) | 20.8954 | 1.05136 | ||||||||
\(396\) | −4.27160 | −0.214656 | ||||||||
\(397\) | −20.9917 | −1.05355 | −0.526773 | − | 0.850006i | \(-0.676598\pi\) | ||||
−0.526773 | + | 0.850006i | \(0.676598\pi\) | |||||||
\(398\) | −32.5442 | −1.63129 | ||||||||
\(399\) | 55.0693 | 2.75691 | ||||||||
\(400\) | −3.79555 | −0.189777 | ||||||||
\(401\) | 18.1974 | 0.908736 | 0.454368 | − | 0.890814i | \(-0.349865\pi\) | ||||
0.454368 | + | 0.890814i | \(0.349865\pi\) | |||||||
\(402\) | −46.5683 | −2.32261 | ||||||||
\(403\) | −8.31362 | −0.414131 | ||||||||
\(404\) | −31.5505 | −1.56970 | ||||||||
\(405\) | 21.3465 | 1.06072 | ||||||||
\(406\) | 57.6185 | 2.85956 | ||||||||
\(407\) | −54.3741 | −2.69523 | ||||||||
\(408\) | −2.72496 | −0.134906 | ||||||||
\(409\) | −11.3284 | −0.560151 | −0.280076 | − | 0.959978i | \(-0.590360\pi\) | ||||
−0.280076 | + | 0.959978i | \(0.590360\pi\) | |||||||
\(410\) | 56.0038 | 2.76583 | ||||||||
\(411\) | 25.9236 | 1.27872 | ||||||||
\(412\) | −0.466157 | −0.0229659 | ||||||||
\(413\) | 45.9142 | 2.25929 | ||||||||
\(414\) | 2.80397 | 0.137808 | ||||||||
\(415\) | 12.9449 | 0.635438 | ||||||||
\(416\) | −8.25787 | −0.404875 | ||||||||
\(417\) | −19.7803 | −0.968643 | ||||||||
\(418\) | 85.7392 | 4.19364 | ||||||||
\(419\) | 12.1615 | 0.594128 | 0.297064 | − | 0.954858i | \(-0.403993\pi\) | ||||
0.297064 | + | 0.954858i | \(0.403993\pi\) | |||||||
\(420\) | 56.1717 | 2.74090 | ||||||||
\(421\) | 1.35865 | 0.0662168 | 0.0331084 | − | 0.999452i | \(-0.489459\pi\) | ||||
0.0331084 | + | 0.999452i | \(0.489459\pi\) | |||||||
\(422\) | 25.9027 | 1.26092 | ||||||||
\(423\) | 3.04719 | 0.148160 | ||||||||
\(424\) | −14.4848 | −0.703445 | ||||||||
\(425\) | 1.98674 | 0.0963710 | ||||||||
\(426\) | −11.5763 | −0.560874 | ||||||||
\(427\) | −5.32223 | −0.257561 | ||||||||
\(428\) | 22.3171 | 1.07874 | ||||||||
\(429\) | −10.0220 | −0.483868 | ||||||||
\(430\) | 36.7087 | 1.77025 | ||||||||
\(431\) | −2.82202 | −0.135932 | −0.0679660 | − | 0.997688i | \(-0.521651\pi\) | ||||
−0.0679660 | + | 0.997688i | \(0.521651\pi\) | |||||||
\(432\) | 10.3366 | 0.497318 | ||||||||
\(433\) | −34.6263 | −1.66403 | −0.832017 | − | 0.554750i | \(-0.812814\pi\) | ||||
−0.832017 | + | 0.554750i | \(0.812814\pi\) | |||||||
\(434\) | 76.6949 | 3.68147 | ||||||||
\(435\) | −24.6310 | −1.18096 | ||||||||
\(436\) | −35.9513 | −1.72176 | ||||||||
\(437\) | −32.6222 | −1.56053 | ||||||||
\(438\) | −34.2826 | −1.63809 | ||||||||
\(439\) | 4.69435 | 0.224049 | 0.112025 | − | 0.993705i | \(-0.464266\pi\) | ||||
0.112025 | + | 0.993705i | \(0.464266\pi\) | |||||||
\(440\) | 24.0294 | 1.14556 | ||||||||
\(441\) | −4.18039 | −0.199066 | ||||||||
\(442\) | 2.41044 | 0.114653 | ||||||||
\(443\) | 11.4305 | 0.543080 | 0.271540 | − | 0.962427i | \(-0.412467\pi\) | ||||
0.271540 | + | 0.962427i | \(0.412467\pi\) | |||||||
\(444\) | −44.9465 | −2.13307 | ||||||||
\(445\) | 36.4716 | 1.72892 | ||||||||
\(446\) | 4.74505 | 0.224685 | ||||||||
\(447\) | −4.23123 | −0.200130 | ||||||||
\(448\) | 58.3223 | 2.75547 | ||||||||
\(449\) | −16.7634 | −0.791114 | −0.395557 | − | 0.918441i | \(-0.629448\pi\) | ||||
−0.395557 | + | 0.918441i | \(0.629448\pi\) | |||||||
\(450\) | 1.22034 | 0.0575273 | ||||||||
\(451\) | 53.4297 | 2.51591 | ||||||||
\(452\) | 25.3580 | 1.19274 | ||||||||
\(453\) | −31.2440 | −1.46797 | ||||||||
\(454\) | 34.1215 | 1.60140 | ||||||||
\(455\) | −13.6524 | −0.640036 | ||||||||
\(456\) | 19.4733 | 0.911920 | ||||||||
\(457\) | −30.3576 | −1.42007 | −0.710035 | − | 0.704166i | \(-0.751321\pi\) | ||||
−0.710035 | + | 0.704166i | \(0.751321\pi\) | |||||||
\(458\) | 32.6339 | 1.52488 | ||||||||
\(459\) | −5.41056 | −0.252544 | ||||||||
\(460\) | −33.2753 | −1.55147 | ||||||||
\(461\) | 7.70326 | 0.358777 | 0.179388 | − | 0.983778i | \(-0.442588\pi\) | ||||
0.179388 | + | 0.983778i | \(0.442588\pi\) | |||||||
\(462\) | 92.4553 | 4.30141 | ||||||||
\(463\) | −2.81145 | −0.130659 | −0.0653296 | − | 0.997864i | \(-0.520810\pi\) | ||||
−0.0653296 | + | 0.997864i | \(0.520810\pi\) | |||||||
\(464\) | −10.7975 | −0.501260 | ||||||||
\(465\) | −32.7858 | −1.52041 | ||||||||
\(466\) | 46.2968 | 2.14466 | ||||||||
\(467\) | 16.1892 | 0.749149 | 0.374574 | − | 0.927197i | \(-0.377789\pi\) | ||||
0.374574 | + | 0.927197i | \(0.377789\pi\) | |||||||
\(468\) | 0.858197 | 0.0396702 | ||||||||
\(469\) | −60.5215 | −2.79462 | ||||||||
\(470\) | −62.3873 | −2.87771 | ||||||||
\(471\) | 10.3767 | 0.478131 | ||||||||
\(472\) | 16.2359 | 0.747318 | ||||||||
\(473\) | 35.0215 | 1.61029 | ||||||||
\(474\) | 28.4294 | 1.30581 | ||||||||
\(475\) | −14.1977 | −0.651437 | ||||||||
\(476\) | −12.8891 | −0.590773 | ||||||||
\(477\) | −2.46802 | −0.113003 | ||||||||
\(478\) | −7.34307 | −0.335864 | ||||||||
\(479\) | −0.523321 | −0.0239111 | −0.0119556 | − | 0.999929i | \(-0.503806\pi\) | ||||
−0.0119556 | + | 0.999929i | \(0.503806\pi\) | |||||||
\(480\) | −32.5659 | −1.48642 | ||||||||
\(481\) | 10.9242 | 0.498099 | ||||||||
\(482\) | 24.1319 | 1.09918 | ||||||||
\(483\) | −35.1776 | −1.60064 | ||||||||
\(484\) | 53.1009 | 2.41368 | ||||||||
\(485\) | −30.9224 | −1.40411 | ||||||||
\(486\) | −6.36159 | −0.288568 | ||||||||
\(487\) | 21.5007 | 0.974288 | 0.487144 | − | 0.873322i | \(-0.338039\pi\) | ||||
0.487144 | + | 0.873322i | \(0.338039\pi\) | |||||||
\(488\) | −1.88201 | −0.0851948 | ||||||||
\(489\) | −18.4201 | −0.832984 | ||||||||
\(490\) | 85.5881 | 3.86647 | ||||||||
\(491\) | −30.3021 | −1.36752 | −0.683758 | − | 0.729709i | \(-0.739656\pi\) | ||||
−0.683758 | + | 0.729709i | \(0.739656\pi\) | |||||||
\(492\) | 44.1659 | 1.99115 | ||||||||
\(493\) | 5.65182 | 0.254545 | ||||||||
\(494\) | −17.2256 | −0.775018 | ||||||||
\(495\) | 4.09429 | 0.184025 | ||||||||
\(496\) | −14.3723 | −0.645335 | ||||||||
\(497\) | −15.0449 | −0.674856 | ||||||||
\(498\) | 17.6123 | 0.789225 | ||||||||
\(499\) | −16.3743 | −0.733016 | −0.366508 | − | 0.930415i | \(-0.619447\pi\) | ||||
−0.366508 | + | 0.930415i | \(0.619447\pi\) | |||||||
\(500\) | 21.9646 | 0.982287 | ||||||||
\(501\) | 23.3345 | 1.04251 | ||||||||
\(502\) | −37.7471 | −1.68474 | ||||||||
\(503\) | −9.66908 | −0.431123 | −0.215562 | − | 0.976490i | \(-0.569158\pi\) | ||||
−0.215562 | + | 0.976490i | \(0.569158\pi\) | |||||||
\(504\) | −2.17530 | −0.0968956 | ||||||||
\(505\) | 30.2409 | 1.34570 | ||||||||
\(506\) | −54.7691 | −2.43478 | ||||||||
\(507\) | −19.4203 | −0.862487 | ||||||||
\(508\) | 0.483866 | 0.0214681 | ||||||||
\(509\) | 8.29485 | 0.367663 | 0.183831 | − | 0.982958i | \(-0.441150\pi\) | ||||
0.183831 | + | 0.982958i | \(0.441150\pi\) | |||||||
\(510\) | 9.50589 | 0.420928 | ||||||||
\(511\) | −44.5547 | −1.97098 | ||||||||
\(512\) | −20.5908 | −0.909995 | ||||||||
\(513\) | 38.6653 | 1.70711 | ||||||||
\(514\) | 20.5353 | 0.905773 | ||||||||
\(515\) | 0.446807 | 0.0196887 | ||||||||
\(516\) | 28.9493 | 1.27442 | ||||||||
\(517\) | −59.5198 | −2.61768 | ||||||||
\(518\) | −100.778 | −4.42792 | ||||||||
\(519\) | 30.3500 | 1.33222 | ||||||||
\(520\) | −4.82769 | −0.211708 | ||||||||
\(521\) | 19.4041 | 0.850110 | 0.425055 | − | 0.905168i | \(-0.360255\pi\) | ||||
0.425055 | + | 0.905168i | \(0.360255\pi\) | |||||||
\(522\) | 3.47158 | 0.151947 | ||||||||
\(523\) | 5.33776 | 0.233404 | 0.116702 | − | 0.993167i | \(-0.462768\pi\) | ||||
0.116702 | + | 0.993167i | \(0.462768\pi\) | |||||||
\(524\) | 26.5655 | 1.16052 | ||||||||
\(525\) | −15.3099 | −0.668178 | ||||||||
\(526\) | 24.7183 | 1.07777 | ||||||||
\(527\) | 7.52303 | 0.327708 | ||||||||
\(528\) | −17.3257 | −0.754006 | ||||||||
\(529\) | −2.16133 | −0.0939710 | ||||||||
\(530\) | 50.5295 | 2.19486 | ||||||||
\(531\) | 2.76638 | 0.120051 | ||||||||
\(532\) | 92.1091 | 3.99344 | ||||||||
\(533\) | −10.7344 | −0.464960 | ||||||||
\(534\) | 49.6219 | 2.14735 | ||||||||
\(535\) | −21.3908 | −0.924803 | ||||||||
\(536\) | −21.4013 | −0.924393 | ||||||||
\(537\) | −30.8350 | −1.33063 | ||||||||
\(538\) | −4.94566 | −0.213223 | ||||||||
\(539\) | 81.6542 | 3.51709 | ||||||||
\(540\) | 39.4393 | 1.69720 | ||||||||
\(541\) | −6.81084 | −0.292821 | −0.146410 | − | 0.989224i | \(-0.546772\pi\) | ||||
−0.146410 | + | 0.989224i | \(0.546772\pi\) | |||||||
\(542\) | 51.7241 | 2.22174 | ||||||||
\(543\) | −19.2627 | −0.826641 | ||||||||
\(544\) | 7.47257 | 0.320384 | ||||||||
\(545\) | 34.4590 | 1.47606 | ||||||||
\(546\) | −18.5750 | −0.794935 | ||||||||
\(547\) | −21.9443 | −0.938269 | −0.469135 | − | 0.883127i | \(-0.655434\pi\) | ||||
−0.469135 | + | 0.883127i | \(0.655434\pi\) | |||||||
\(548\) | 43.3599 | 1.85224 | ||||||||
\(549\) | −0.320670 | −0.0136859 | ||||||||
\(550\) | −23.8365 | −1.01639 | ||||||||
\(551\) | −40.3893 | −1.72064 | ||||||||
\(552\) | −12.4393 | −0.529451 | ||||||||
\(553\) | 36.9477 | 1.57118 | ||||||||
\(554\) | −61.1444 | −2.59778 | ||||||||
\(555\) | 43.0808 | 1.82868 | ||||||||
\(556\) | −33.0845 | −1.40310 | ||||||||
\(557\) | 2.23207 | 0.0945757 | 0.0472879 | − | 0.998881i | \(-0.484942\pi\) | ||||
0.0472879 | + | 0.998881i | \(0.484942\pi\) | |||||||
\(558\) | 4.62095 | 0.195621 | ||||||||
\(559\) | −7.03608 | −0.297594 | ||||||||
\(560\) | −23.6018 | −0.997360 | ||||||||
\(561\) | 9.06897 | 0.382892 | ||||||||
\(562\) | 41.4894 | 1.75012 | ||||||||
\(563\) | 32.3468 | 1.36326 | 0.681628 | − | 0.731699i | \(-0.261272\pi\) | ||||
0.681628 | + | 0.731699i | \(0.261272\pi\) | |||||||
\(564\) | −49.2000 | −2.07169 | ||||||||
\(565\) | −24.3054 | −1.02254 | ||||||||
\(566\) | 6.72134 | 0.282519 | ||||||||
\(567\) | 37.7455 | 1.58516 | ||||||||
\(568\) | −5.32009 | −0.223226 | ||||||||
\(569\) | −16.7498 | −0.702189 | −0.351094 | − | 0.936340i | \(-0.614190\pi\) | ||||
−0.351094 | + | 0.936340i | \(0.614190\pi\) | |||||||
\(570\) | −67.9315 | −2.84534 | ||||||||
\(571\) | −16.9115 | −0.707725 | −0.353863 | − | 0.935297i | \(-0.615132\pi\) | ||||
−0.353863 | + | 0.935297i | \(0.615132\pi\) | |||||||
\(572\) | −16.7629 | −0.700891 | ||||||||
\(573\) | −12.0700 | −0.504230 | ||||||||
\(574\) | 99.0274 | 4.13332 | ||||||||
\(575\) | 9.06934 | 0.378218 | ||||||||
\(576\) | 3.51398 | 0.146416 | ||||||||
\(577\) | −42.4968 | −1.76916 | −0.884582 | − | 0.466386i | \(-0.845556\pi\) | ||||
−0.884582 | + | 0.466386i | \(0.845556\pi\) | |||||||
\(578\) | −2.18122 | −0.0907267 | ||||||||
\(579\) | −1.04195 | −0.0433018 | ||||||||
\(580\) | −41.1978 | −1.71065 | ||||||||
\(581\) | 22.8894 | 0.949613 | ||||||||
\(582\) | −42.0718 | −1.74393 | ||||||||
\(583\) | 48.2070 | 1.99653 | ||||||||
\(584\) | −15.7552 | −0.651953 | ||||||||
\(585\) | −0.822574 | −0.0340093 | ||||||||
\(586\) | 64.4296 | 2.66156 | ||||||||
\(587\) | −44.0400 | −1.81773 | −0.908863 | − | 0.417096i | \(-0.863048\pi\) | ||||
−0.908863 | + | 0.417096i | \(0.863048\pi\) | |||||||
\(588\) | 67.4967 | 2.78352 | ||||||||
\(589\) | −53.7614 | −2.21520 | ||||||||
\(590\) | −56.6381 | −2.33175 | ||||||||
\(591\) | 18.0911 | 0.744167 | ||||||||
\(592\) | 18.8853 | 0.776182 | ||||||||
\(593\) | 26.3240 | 1.08100 | 0.540499 | − | 0.841344i | \(-0.318235\pi\) | ||||
0.540499 | + | 0.841344i | \(0.318235\pi\) | |||||||
\(594\) | 64.9147 | 2.66348 | ||||||||
\(595\) | 12.3541 | 0.506470 | ||||||||
\(596\) | −7.07717 | −0.289892 | ||||||||
\(597\) | 24.5997 | 1.00680 | ||||||||
\(598\) | 11.0035 | 0.449968 | ||||||||
\(599\) | −41.3234 | −1.68843 | −0.844214 | − | 0.536006i | \(-0.819932\pi\) | ||||
−0.844214 | + | 0.536006i | \(0.819932\pi\) | |||||||
\(600\) | −5.41379 | −0.221017 | ||||||||
\(601\) | −14.2454 | −0.581080 | −0.290540 | − | 0.956863i | \(-0.593835\pi\) | ||||
−0.290540 | + | 0.956863i | \(0.593835\pi\) | |||||||
\(602\) | 64.9093 | 2.64550 | ||||||||
\(603\) | −3.64649 | −0.148496 | ||||||||
\(604\) | −52.2587 | −2.12638 | ||||||||
\(605\) | −50.8968 | −2.06925 | ||||||||
\(606\) | 41.1446 | 1.67139 | ||||||||
\(607\) | −25.9277 | −1.05237 | −0.526186 | − | 0.850369i | \(-0.676379\pi\) | ||||
−0.526186 | + | 0.850369i | \(0.676379\pi\) | |||||||
\(608\) | −53.4009 | −2.16569 | ||||||||
\(609\) | −43.5531 | −1.76486 | ||||||||
\(610\) | 6.56530 | 0.265821 | ||||||||
\(611\) | 11.9580 | 0.483768 | ||||||||
\(612\) | −0.776585 | −0.0313916 | ||||||||
\(613\) | 7.06578 | 0.285384 | 0.142692 | − | 0.989767i | \(-0.454424\pi\) | ||||
0.142692 | + | 0.989767i | \(0.454424\pi\) | |||||||
\(614\) | −40.3316 | −1.62765 | ||||||||
\(615\) | −42.3326 | −1.70702 | ||||||||
\(616\) | 42.4894 | 1.71195 | ||||||||
\(617\) | −5.05958 | −0.203691 | −0.101845 | − | 0.994800i | \(-0.532475\pi\) | ||||
−0.101845 | + | 0.994800i | \(0.532475\pi\) | |||||||
\(618\) | 0.607908 | 0.0244537 | ||||||||
\(619\) | −0.790826 | −0.0317860 | −0.0158930 | − | 0.999874i | \(-0.505059\pi\) | ||||
−0.0158930 | + | 0.999874i | \(0.505059\pi\) | |||||||
\(620\) | −54.8377 | −2.20233 | ||||||||
\(621\) | −24.6989 | −0.991133 | ||||||||
\(622\) | 52.5420 | 2.10674 | ||||||||
\(623\) | 64.4901 | 2.58374 | ||||||||
\(624\) | 3.48087 | 0.139346 | ||||||||
\(625\) | −30.9866 | −1.23946 | ||||||||
\(626\) | −25.5925 | −1.02288 | ||||||||
\(627\) | −64.8092 | −2.58823 | ||||||||
\(628\) | 17.3560 | 0.692582 | ||||||||
\(629\) | −9.88532 | −0.394153 | ||||||||
\(630\) | 7.58842 | 0.302330 | ||||||||
\(631\) | −13.1303 | −0.522708 | −0.261354 | − | 0.965243i | \(-0.584169\pi\) | ||||
−0.261354 | + | 0.965243i | \(0.584169\pi\) | |||||||
\(632\) | 13.0652 | 0.519707 | ||||||||
\(633\) | −19.5795 | −0.778216 | ||||||||
\(634\) | 66.3354 | 2.63452 | ||||||||
\(635\) | −0.463781 | −0.0184046 | ||||||||
\(636\) | 39.8487 | 1.58010 | ||||||||
\(637\) | −16.4049 | −0.649987 | ||||||||
\(638\) | −67.8092 | −2.68459 | ||||||||
\(639\) | −0.906472 | −0.0358595 | ||||||||
\(640\) | −32.4406 | −1.28233 | ||||||||
\(641\) | 20.1518 | 0.795949 | 0.397974 | − | 0.917397i | \(-0.369713\pi\) | ||||
0.397974 | + | 0.917397i | \(0.369713\pi\) | |||||||
\(642\) | −29.1035 | −1.14862 | ||||||||
\(643\) | 25.0807 | 0.989085 | 0.494543 | − | 0.869153i | \(-0.335336\pi\) | ||||
0.494543 | + | 0.869153i | \(0.335336\pi\) | |||||||
\(644\) | −58.8382 | −2.31855 | ||||||||
\(645\) | −27.7477 | −1.09256 | ||||||||
\(646\) | 15.5875 | 0.613284 | ||||||||
\(647\) | −20.6832 | −0.813142 | −0.406571 | − | 0.913619i | \(-0.633276\pi\) | ||||
−0.406571 | + | 0.913619i | \(0.633276\pi\) | |||||||
\(648\) | 13.3473 | 0.524333 | ||||||||
\(649\) | −54.0348 | −2.12105 | ||||||||
\(650\) | 4.78892 | 0.187837 | ||||||||
\(651\) | −57.9727 | −2.27213 | ||||||||
\(652\) | −30.8095 | −1.20659 | ||||||||
\(653\) | −23.5925 | −0.923246 | −0.461623 | − | 0.887076i | \(-0.652733\pi\) | ||||
−0.461623 | + | 0.887076i | \(0.652733\pi\) | |||||||
\(654\) | 46.8836 | 1.83330 | ||||||||
\(655\) | −25.4628 | −0.994915 | ||||||||
\(656\) | −18.5573 | −0.724542 | ||||||||
\(657\) | −2.68447 | −0.104731 | ||||||||
\(658\) | −110.315 | −4.30052 | ||||||||
\(659\) | 26.1511 | 1.01870 | 0.509352 | − | 0.860558i | \(-0.329885\pi\) | ||||
0.509352 | + | 0.860558i | \(0.329885\pi\) | |||||||
\(660\) | −66.1065 | −2.57319 | ||||||||
\(661\) | −25.4722 | −0.990752 | −0.495376 | − | 0.868679i | \(-0.664970\pi\) | ||||
−0.495376 | + | 0.868679i | \(0.664970\pi\) | |||||||
\(662\) | −52.7315 | −2.04947 | ||||||||
\(663\) | −1.82202 | −0.0707616 | ||||||||
\(664\) | 8.09402 | 0.314109 | ||||||||
\(665\) | −88.2857 | −3.42357 | ||||||||
\(666\) | −6.07197 | −0.235284 | ||||||||
\(667\) | 25.8002 | 0.998987 | ||||||||
\(668\) | 39.0294 | 1.51009 | ||||||||
\(669\) | −3.58672 | −0.138671 | ||||||||
\(670\) | 74.6571 | 2.88426 | ||||||||
\(671\) | 6.26354 | 0.241801 | ||||||||
\(672\) | −57.5839 | −2.22135 | ||||||||
\(673\) | 28.0645 | 1.08181 | 0.540903 | − | 0.841085i | \(-0.318083\pi\) | ||||
0.540903 | + | 0.841085i | \(0.318083\pi\) | |||||||
\(674\) | −50.8664 | −1.95930 | ||||||||
\(675\) | −10.7494 | −0.413744 | ||||||||
\(676\) | −32.4825 | −1.24933 | ||||||||
\(677\) | 28.2970 | 1.08754 | 0.543771 | − | 0.839234i | \(-0.316996\pi\) | ||||
0.543771 | + | 0.839234i | \(0.316996\pi\) | |||||||
\(678\) | −33.0690 | −1.27001 | ||||||||
\(679\) | −54.6777 | −2.09834 | ||||||||
\(680\) | 4.36859 | 0.167528 | ||||||||
\(681\) | −25.7920 | −0.988351 | ||||||||
\(682\) | −90.2596 | −3.45622 | ||||||||
\(683\) | −21.8896 | −0.837582 | −0.418791 | − | 0.908083i | \(-0.637546\pi\) | ||||
−0.418791 | + | 0.908083i | \(0.637546\pi\) | |||||||
\(684\) | 5.54968 | 0.212197 | ||||||||
\(685\) | −41.5600 | −1.58793 | ||||||||
\(686\) | 79.9762 | 3.05350 | ||||||||
\(687\) | −24.6675 | −0.941125 | ||||||||
\(688\) | −12.1637 | −0.463738 | ||||||||
\(689\) | −9.68515 | −0.368975 | ||||||||
\(690\) | 43.3938 | 1.65197 | ||||||||
\(691\) | 34.5680 | 1.31503 | 0.657514 | − | 0.753442i | \(-0.271608\pi\) | ||||
0.657514 | + | 0.753442i | \(0.271608\pi\) | |||||||
\(692\) | 50.7635 | 1.92974 | ||||||||
\(693\) | 7.23963 | 0.275011 | ||||||||
\(694\) | 2.26193 | 0.0858617 | ||||||||
\(695\) | 31.7112 | 1.20287 | ||||||||
\(696\) | −15.4010 | −0.583773 | ||||||||
\(697\) | 9.71363 | 0.367930 | ||||||||
\(698\) | −15.1096 | −0.571906 | ||||||||
\(699\) | −34.9951 | −1.32364 | ||||||||
\(700\) | −25.6074 | −0.967867 | ||||||||
\(701\) | 22.7657 | 0.859849 | 0.429925 | − | 0.902865i | \(-0.358540\pi\) | ||||
0.429925 | + | 0.902865i | \(0.358540\pi\) | |||||||
\(702\) | −13.0419 | −0.492233 | ||||||||
\(703\) | 70.6430 | 2.66435 | ||||||||
\(704\) | −68.6375 | −2.58687 | ||||||||
\(705\) | 47.1578 | 1.77606 | ||||||||
\(706\) | −2.18122 | −0.0820912 | ||||||||
\(707\) | 53.4727 | 2.01105 | ||||||||
\(708\) | −44.6660 | −1.67865 | ||||||||
\(709\) | 15.3999 | 0.578356 | 0.289178 | − | 0.957275i | \(-0.406618\pi\) | ||||
0.289178 | + | 0.957275i | \(0.406618\pi\) | |||||||
\(710\) | 18.5588 | 0.696501 | ||||||||
\(711\) | 2.22614 | 0.0834868 | ||||||||
\(712\) | 22.8046 | 0.854638 | ||||||||
\(713\) | 34.3422 | 1.28612 | ||||||||
\(714\) | 16.8086 | 0.629044 | ||||||||
\(715\) | 16.0671 | 0.600874 | ||||||||
\(716\) | −51.5748 | −1.92744 | ||||||||
\(717\) | 5.55053 | 0.207288 | ||||||||
\(718\) | 24.3462 | 0.908593 | ||||||||
\(719\) | −35.2080 | −1.31304 | −0.656519 | − | 0.754310i | \(-0.727972\pi\) | ||||
−0.656519 | + | 0.754310i | \(0.727972\pi\) | |||||||
\(720\) | −1.42204 | −0.0529962 | ||||||||
\(721\) | 0.790055 | 0.0294232 | ||||||||
\(722\) | −69.9494 | −2.60325 | ||||||||
\(723\) | −18.2410 | −0.678389 | ||||||||
\(724\) | −32.2188 | −1.19740 | ||||||||
\(725\) | 11.2287 | 0.417023 | ||||||||
\(726\) | −69.2482 | −2.57004 | ||||||||
\(727\) | 8.14471 | 0.302071 | 0.151035 | − | 0.988528i | \(-0.451739\pi\) | ||||
0.151035 | + | 0.988528i | \(0.451739\pi\) | |||||||
\(728\) | −8.53645 | −0.316382 | ||||||||
\(729\) | 29.0363 | 1.07542 | ||||||||
\(730\) | 54.9610 | 2.03420 | ||||||||
\(731\) | 6.36697 | 0.235491 | ||||||||
\(732\) | 5.17755 | 0.191368 | ||||||||
\(733\) | −35.9498 | −1.32783 | −0.663917 | − | 0.747806i | \(-0.731107\pi\) | ||||
−0.663917 | + | 0.747806i | \(0.731107\pi\) | |||||||
\(734\) | 54.4568 | 2.01004 | ||||||||
\(735\) | −64.6949 | −2.38631 | ||||||||
\(736\) | 34.1118 | 1.25738 | ||||||||
\(737\) | 71.2256 | 2.62363 | ||||||||
\(738\) | 5.96651 | 0.219630 | ||||||||
\(739\) | −0.647430 | −0.0238161 | −0.0119080 | − | 0.999929i | \(-0.503791\pi\) | ||||
−0.0119080 | + | 0.999929i | \(0.503791\pi\) | |||||||
\(740\) | 72.0572 | 2.64887 | ||||||||
\(741\) | 13.0206 | 0.478325 | ||||||||
\(742\) | 89.3475 | 3.28005 | ||||||||
\(743\) | 2.03924 | 0.0748125 | 0.0374063 | − | 0.999300i | \(-0.488090\pi\) | ||||
0.0374063 | + | 0.999300i | \(0.488090\pi\) | |||||||
\(744\) | −20.5000 | −0.751565 | ||||||||
\(745\) | 6.78340 | 0.248525 | ||||||||
\(746\) | −7.53459 | −0.275861 | ||||||||
\(747\) | 1.37911 | 0.0504591 | ||||||||
\(748\) | 15.1688 | 0.554626 | ||||||||
\(749\) | −37.8237 | −1.38205 | ||||||||
\(750\) | −28.6437 | −1.04592 | ||||||||
\(751\) | 19.2799 | 0.703534 | 0.351767 | − | 0.936088i | \(-0.385581\pi\) | ||||
0.351767 | + | 0.936088i | \(0.385581\pi\) | |||||||
\(752\) | 20.6725 | 0.753850 | ||||||||
\(753\) | 28.5326 | 1.03978 | ||||||||
\(754\) | 13.6234 | 0.496134 | ||||||||
\(755\) | 50.0895 | 1.82294 | ||||||||
\(756\) | 69.7375 | 2.53633 | ||||||||
\(757\) | −48.7157 | −1.77060 | −0.885302 | − | 0.465017i | \(-0.846048\pi\) | ||||
−0.885302 | + | 0.465017i | \(0.846048\pi\) | |||||||
\(758\) | −47.4604 | −1.72384 | ||||||||
\(759\) | 41.3993 | 1.50270 | ||||||||
\(760\) | −31.2191 | −1.13244 | ||||||||
\(761\) | −8.89585 | −0.322474 | −0.161237 | − | 0.986916i | \(-0.551548\pi\) | ||||
−0.161237 | + | 0.986916i | \(0.551548\pi\) | |||||||
\(762\) | −0.631003 | −0.0228588 | ||||||||
\(763\) | 60.9313 | 2.20586 | ||||||||
\(764\) | −20.1883 | −0.730385 | ||||||||
\(765\) | 0.744350 | 0.0269120 | ||||||||
\(766\) | 42.3731 | 1.53100 | ||||||||
\(767\) | 10.8560 | 0.391987 | ||||||||
\(768\) | −2.98970 | −0.107882 | ||||||||
\(769\) | −0.859414 | −0.0309913 | −0.0154956 | − | 0.999880i | \(-0.504933\pi\) | ||||
−0.0154956 | + | 0.999880i | \(0.504933\pi\) | |||||||
\(770\) | −148.222 | −5.34155 | ||||||||
\(771\) | −15.5224 | −0.559024 | ||||||||
\(772\) | −1.74276 | −0.0627233 | ||||||||
\(773\) | −23.5183 | −0.845894 | −0.422947 | − | 0.906154i | \(-0.639004\pi\) | ||||
−0.422947 | + | 0.906154i | \(0.639004\pi\) | |||||||
\(774\) | 3.91086 | 0.140573 | ||||||||
\(775\) | 14.9463 | 0.536887 | ||||||||
\(776\) | −19.3348 | −0.694079 | ||||||||
\(777\) | 76.1766 | 2.73282 | ||||||||
\(778\) | 51.1354 | 1.83329 | ||||||||
\(779\) | −69.4160 | −2.48709 | ||||||||
\(780\) | 13.2813 | 0.475547 | ||||||||
\(781\) | 17.7058 | 0.633564 | ||||||||
\(782\) | −9.95713 | −0.356066 | ||||||||
\(783\) | −30.5795 | −1.09282 | ||||||||
\(784\) | −28.3603 | −1.01287 | ||||||||
\(785\) | −16.6356 | −0.593750 | ||||||||
\(786\) | −34.6438 | −1.23570 | ||||||||
\(787\) | 29.8587 | 1.06435 | 0.532174 | − | 0.846635i | \(-0.321375\pi\) | ||||
0.532174 | + | 0.846635i | \(0.321375\pi\) | |||||||
\(788\) | 30.2592 | 1.07794 | ||||||||
\(789\) | −18.6842 | −0.665177 | ||||||||
\(790\) | −45.5773 | −1.62157 | ||||||||
\(791\) | −42.9774 | −1.52810 | ||||||||
\(792\) | 2.56004 | 0.0909669 | ||||||||
\(793\) | −1.25839 | −0.0446868 | ||||||||
\(794\) | 45.7876 | 1.62494 | ||||||||
\(795\) | −38.1946 | −1.35462 | ||||||||
\(796\) | 41.1456 | 1.45837 | ||||||||
\(797\) | 2.50267 | 0.0886493 | 0.0443246 | − | 0.999017i | \(-0.485886\pi\) | ||||
0.0443246 | + | 0.999017i | \(0.485886\pi\) | |||||||
\(798\) | −120.118 | −4.25214 | ||||||||
\(799\) | −10.8208 | −0.382813 | ||||||||
\(800\) | 14.8460 | 0.524887 | ||||||||
\(801\) | 3.88560 | 0.137291 | ||||||||
\(802\) | −39.6926 | −1.40159 | ||||||||
\(803\) | 52.4348 | 1.85039 | ||||||||
\(804\) | 58.8763 | 2.07641 | ||||||||
\(805\) | 56.3958 | 1.98769 | ||||||||
\(806\) | 18.1338 | 0.638737 | ||||||||
\(807\) | 3.73836 | 0.131597 | ||||||||
\(808\) | 18.9087 | 0.665206 | ||||||||
\(809\) | 50.5059 | 1.77569 | 0.887847 | − | 0.460139i | \(-0.152200\pi\) | ||||
0.887847 | + | 0.460139i | \(0.152200\pi\) | |||||||
\(810\) | −46.5615 | −1.63600 | ||||||||
\(811\) | −49.3818 | −1.73403 | −0.867015 | − | 0.498281i | \(-0.833965\pi\) | ||||
−0.867015 | + | 0.498281i | \(0.833965\pi\) | |||||||
\(812\) | −72.8471 | −2.55643 | ||||||||
\(813\) | −39.0976 | −1.37121 | ||||||||
\(814\) | 118.602 | 4.15699 | ||||||||
\(815\) | 29.5306 | 1.03441 | ||||||||
\(816\) | −3.14985 | −0.110267 | ||||||||
\(817\) | −45.5000 | −1.59184 | ||||||||
\(818\) | 24.7096 | 0.863952 | ||||||||
\(819\) | −1.45450 | −0.0508242 | ||||||||
\(820\) | −70.8056 | −2.47264 | ||||||||
\(821\) | 19.4132 | 0.677524 | 0.338762 | − | 0.940872i | \(-0.389992\pi\) | ||||
0.338762 | + | 0.940872i | \(0.389992\pi\) | |||||||
\(822\) | −56.5450 | −1.97223 | ||||||||
\(823\) | 3.75774 | 0.130987 | 0.0654933 | − | 0.997853i | \(-0.479138\pi\) | ||||
0.0654933 | + | 0.997853i | \(0.479138\pi\) | |||||||
\(824\) | 0.279375 | 0.00973248 | ||||||||
\(825\) | 18.0177 | 0.627295 | ||||||||
\(826\) | −100.149 | −3.48462 | ||||||||
\(827\) | −27.8959 | −0.970036 | −0.485018 | − | 0.874504i | \(-0.661187\pi\) | ||||
−0.485018 | + | 0.874504i | \(0.661187\pi\) | |||||||
\(828\) | −3.54506 | −0.123200 | ||||||||
\(829\) | −4.67155 | −0.162250 | −0.0811248 | − | 0.996704i | \(-0.525851\pi\) | ||||
−0.0811248 | + | 0.996704i | \(0.525851\pi\) | |||||||
\(830\) | −28.2356 | −0.980070 | ||||||||
\(831\) | 46.2183 | 1.60329 | ||||||||
\(832\) | 13.7898 | 0.478075 | ||||||||
\(833\) | 14.8449 | 0.514345 | ||||||||
\(834\) | 43.1450 | 1.49399 | ||||||||
\(835\) | −37.4093 | −1.29460 | ||||||||
\(836\) | −108.400 | −3.74909 | ||||||||
\(837\) | −40.7038 | −1.40693 | ||||||||
\(838\) | −26.5269 | −0.916356 | ||||||||
\(839\) | −0.528468 | −0.0182448 | −0.00912238 | − | 0.999958i | \(-0.502904\pi\) | ||||
−0.00912238 | + | 0.999958i | \(0.502904\pi\) | |||||||
\(840\) | −33.6646 | −1.16154 | ||||||||
\(841\) | 2.94302 | 0.101483 | ||||||||
\(842\) | −2.96352 | −0.102130 | ||||||||
\(843\) | −31.3613 | −1.08014 | ||||||||
\(844\) | −32.7488 | −1.12726 | ||||||||
\(845\) | 31.1342 | 1.07105 | ||||||||
\(846\) | −6.64659 | −0.228514 | ||||||||
\(847\) | −89.9970 | −3.09233 | ||||||||
\(848\) | −16.7433 | −0.574969 | ||||||||
\(849\) | −5.08058 | −0.174365 | ||||||||
\(850\) | −4.33351 | −0.148638 | ||||||||
\(851\) | −45.1259 | −1.54690 | ||||||||
\(852\) | 14.6359 | 0.501418 | ||||||||
\(853\) | 45.5367 | 1.55915 | 0.779573 | − | 0.626311i | \(-0.215436\pi\) | ||||
0.779573 | + | 0.626311i | \(0.215436\pi\) | |||||||
\(854\) | 11.6089 | 0.397250 | ||||||||
\(855\) | −5.31931 | −0.181917 | ||||||||
\(856\) | −13.3750 | −0.457148 | ||||||||
\(857\) | −7.14436 | −0.244047 | −0.122023 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122023 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(858\) | 21.8602 | 0.746296 | ||||||||
\(859\) | 5.22864 | 0.178399 | 0.0891994 | − | 0.996014i | \(-0.471569\pi\) | ||||
0.0891994 | + | 0.996014i | \(0.471569\pi\) | |||||||
\(860\) | −46.4108 | −1.58260 | ||||||||
\(861\) | −74.8536 | −2.55100 | ||||||||
\(862\) | 6.15545 | 0.209655 | ||||||||
\(863\) | 17.1660 | 0.584337 | 0.292169 | − | 0.956367i | \(-0.405623\pi\) | ||||
0.292169 | + | 0.956367i | \(0.405623\pi\) | |||||||
\(864\) | −40.4308 | −1.37548 | ||||||||
\(865\) | −48.6564 | −1.65437 | ||||||||
\(866\) | 75.5275 | 2.56653 | ||||||||
\(867\) | 1.64876 | 0.0559947 | ||||||||
\(868\) | −96.9654 | −3.29122 | ||||||||
\(869\) | −43.4825 | −1.47504 | ||||||||
\(870\) | 53.7255 | 1.82147 | ||||||||
\(871\) | −14.3098 | −0.484868 | ||||||||
\(872\) | 21.5462 | 0.729646 | ||||||||
\(873\) | −3.29439 | −0.111498 | ||||||||
\(874\) | 71.1562 | 2.40689 | ||||||||
\(875\) | −37.2262 | −1.25848 | ||||||||
\(876\) | 43.3435 | 1.46444 | ||||||||
\(877\) | 29.6336 | 1.00065 | 0.500327 | − | 0.865836i | \(-0.333213\pi\) | ||||
0.500327 | + | 0.865836i | \(0.333213\pi\) | |||||||
\(878\) | −10.2394 | −0.345563 | ||||||||
\(879\) | −48.7015 | −1.64266 | ||||||||
\(880\) | 27.7762 | 0.936335 | ||||||||
\(881\) | −7.52513 | −0.253528 | −0.126764 | − | 0.991933i | \(-0.540459\pi\) | ||||
−0.126764 | + | 0.991933i | \(0.540459\pi\) | |||||||
\(882\) | 9.11834 | 0.307031 | ||||||||
\(883\) | 42.5541 | 1.43206 | 0.716030 | − | 0.698070i | \(-0.245957\pi\) | ||||
0.716030 | + | 0.698070i | \(0.245957\pi\) | |||||||
\(884\) | −3.04752 | −0.102499 | ||||||||
\(885\) | 42.8120 | 1.43911 | ||||||||
\(886\) | −24.9324 | −0.837622 | ||||||||
\(887\) | 32.0265 | 1.07534 | 0.537672 | − | 0.843154i | \(-0.319304\pi\) | ||||
0.537672 | + | 0.843154i | \(0.319304\pi\) | |||||||
\(888\) | 26.9371 | 0.903951 | ||||||||
\(889\) | −0.820070 | −0.0275043 | ||||||||
\(890\) | −79.5526 | −2.66661 | ||||||||
\(891\) | −44.4213 | −1.48817 | ||||||||
\(892\) | −5.99917 | −0.200867 | ||||||||
\(893\) | 77.3283 | 2.58769 | ||||||||
\(894\) | 9.22924 | 0.308672 | ||||||||
\(895\) | 49.4340 | 1.65240 | ||||||||
\(896\) | −57.3623 | −1.91634 | ||||||||
\(897\) | −8.31743 | −0.277711 | ||||||||
\(898\) | 36.5646 | 1.22018 | ||||||||
\(899\) | 42.5188 | 1.41808 | ||||||||
\(900\) | −1.54287 | −0.0514291 | ||||||||
\(901\) | 8.76412 | 0.291975 | ||||||||
\(902\) | −116.542 | −3.88042 | ||||||||
\(903\) | −49.0641 | −1.63275 | ||||||||
\(904\) | −15.1974 | −0.505458 | ||||||||
\(905\) | 30.8814 | 1.02653 | ||||||||
\(906\) | 68.1499 | 2.26413 | ||||||||
\(907\) | −30.2403 | −1.00411 | −0.502056 | − | 0.864835i | \(-0.667423\pi\) | ||||
−0.502056 | + | 0.864835i | \(0.667423\pi\) | |||||||
\(908\) | −43.1397 | −1.43164 | ||||||||
\(909\) | 3.22179 | 0.106860 | ||||||||
\(910\) | 29.7789 | 0.987162 | ||||||||
\(911\) | −19.7051 | −0.652859 | −0.326429 | − | 0.945222i | \(-0.605846\pi\) | ||||
−0.326429 | + | 0.945222i | \(0.605846\pi\) | |||||||
\(912\) | 22.5096 | 0.745369 | ||||||||
\(913\) | −26.9378 | −0.891510 | ||||||||
\(914\) | 66.2166 | 2.19025 | ||||||||
\(915\) | −4.96263 | −0.164060 | ||||||||
\(916\) | −41.2590 | −1.36324 | ||||||||
\(917\) | −45.0240 | −1.48682 | ||||||||
\(918\) | 11.8016 | 0.389512 | ||||||||
\(919\) | 26.3134 | 0.868000 | 0.434000 | − | 0.900913i | \(-0.357102\pi\) | ||||
0.434000 | + | 0.900913i | \(0.357102\pi\) | |||||||
\(920\) | 19.9424 | 0.657480 | ||||||||
\(921\) | 30.4861 | 1.00455 | ||||||||
\(922\) | −16.8025 | −0.553361 | ||||||||
\(923\) | −3.55723 | −0.117088 | ||||||||
\(924\) | −116.891 | −3.84544 | ||||||||
\(925\) | −19.6395 | −0.645744 | ||||||||
\(926\) | 6.13239 | 0.201523 | ||||||||
\(927\) | 0.0476017 | 0.00156345 | ||||||||
\(928\) | 42.2336 | 1.38639 | ||||||||
\(929\) | 22.5947 | 0.741308 | 0.370654 | − | 0.928771i | \(-0.379134\pi\) | ||||
0.370654 | + | 0.928771i | \(0.379134\pi\) | |||||||
\(930\) | 71.5130 | 2.34501 | ||||||||
\(931\) | −106.085 | −3.47681 | ||||||||
\(932\) | −58.5330 | −1.91731 | ||||||||
\(933\) | −39.7158 | −1.30024 | ||||||||
\(934\) | −35.3123 | −1.15545 | ||||||||
\(935\) | −14.5391 | −0.475481 | ||||||||
\(936\) | −0.514330 | −0.0168114 | ||||||||
\(937\) | −5.19506 | −0.169715 | −0.0848576 | − | 0.996393i | \(-0.527044\pi\) | ||||
−0.0848576 | + | 0.996393i | \(0.527044\pi\) | |||||||
\(938\) | 132.011 | 4.31030 | ||||||||
\(939\) | 19.3450 | 0.631301 | ||||||||
\(940\) | 78.8763 | 2.57266 | ||||||||
\(941\) | 12.6686 | 0.412984 | 0.206492 | − | 0.978448i | \(-0.433795\pi\) | ||||
0.206492 | + | 0.978448i | \(0.433795\pi\) | |||||||
\(942\) | −22.6338 | −0.737448 | ||||||||
\(943\) | 44.3421 | 1.44398 | ||||||||
\(944\) | 18.7675 | 0.610829 | ||||||||
\(945\) | −66.8428 | −2.17440 | ||||||||
\(946\) | −76.3895 | −2.48364 | ||||||||
\(947\) | −21.7199 | −0.705802 | −0.352901 | − | 0.935661i | \(-0.614805\pi\) | ||||
−0.352901 | + | 0.935661i | \(0.614805\pi\) | |||||||
\(948\) | −35.9433 | −1.16738 | ||||||||
\(949\) | −10.5346 | −0.341966 | ||||||||
\(950\) | 30.9684 | 1.00475 | ||||||||
\(951\) | −50.1421 | −1.62597 | ||||||||
\(952\) | 7.72466 | 0.250358 | ||||||||
\(953\) | −12.5369 | −0.406110 | −0.203055 | − | 0.979167i | \(-0.565087\pi\) | ||||
−0.203055 | + | 0.979167i | \(0.565087\pi\) | |||||||
\(954\) | 5.38329 | 0.174290 | ||||||||
\(955\) | 19.3503 | 0.626160 | ||||||||
\(956\) | 9.28384 | 0.300261 | ||||||||
\(957\) | 51.2561 | 1.65688 | ||||||||
\(958\) | 1.14148 | 0.0368794 | ||||||||
\(959\) | −73.4875 | −2.37304 | ||||||||
\(960\) | 54.3818 | 1.75516 | ||||||||
\(961\) | 25.5959 | 0.825675 | ||||||||
\(962\) | −23.8280 | −0.768246 | ||||||||
\(963\) | −2.27892 | −0.0734372 | ||||||||
\(964\) | −30.5099 | −0.982658 | ||||||||
\(965\) | 1.67042 | 0.0537727 | ||||||||
\(966\) | 76.7300 | 2.46875 | ||||||||
\(967\) | 32.3634 | 1.04074 | 0.520369 | − | 0.853942i | \(-0.325795\pi\) | ||||
0.520369 | + | 0.853942i | \(0.325795\pi\) | |||||||
\(968\) | −31.8242 | −1.02287 | ||||||||
\(969\) | −11.7824 | −0.378506 | ||||||||
\(970\) | 67.4484 | 2.16564 | ||||||||
\(971\) | −42.8684 | −1.37571 | −0.687856 | − | 0.725847i | \(-0.741448\pi\) | ||||
−0.687856 | + | 0.725847i | \(0.741448\pi\) | |||||||
\(972\) | 8.04296 | 0.257978 | ||||||||
\(973\) | 56.0726 | 1.79760 | ||||||||
\(974\) | −46.8976 | −1.50270 | ||||||||
\(975\) | −3.61989 | −0.115929 | ||||||||
\(976\) | −2.17547 | −0.0696350 | ||||||||
\(977\) | 25.3736 | 0.811772 | 0.405886 | − | 0.913924i | \(-0.366963\pi\) | ||||
0.405886 | + | 0.913924i | \(0.366963\pi\) | |||||||
\(978\) | 40.1782 | 1.28476 | ||||||||
\(979\) | −75.8961 | −2.42565 | ||||||||
\(980\) | −108.209 | −3.45661 | ||||||||
\(981\) | 3.67118 | 0.117212 | ||||||||
\(982\) | 66.0956 | 2.10919 | ||||||||
\(983\) | −17.1070 | −0.545627 | −0.272814 | − | 0.962067i | \(-0.587954\pi\) | ||||
−0.272814 | + | 0.962067i | \(0.587954\pi\) | |||||||
\(984\) | −26.4693 | −0.843810 | ||||||||
\(985\) | −29.0032 | −0.924117 | ||||||||
\(986\) | −12.3278 | −0.392599 | ||||||||
\(987\) | 83.3856 | 2.65419 | ||||||||
\(988\) | 21.7784 | 0.692862 | ||||||||
\(989\) | 29.0648 | 0.924208 | ||||||||
\(990\) | −8.93055 | −0.283831 | ||||||||
\(991\) | 21.2800 | 0.675981 | 0.337991 | − | 0.941149i | \(-0.390253\pi\) | ||||
0.337991 | + | 0.941149i | \(0.390253\pi\) | |||||||
\(992\) | 56.2163 | 1.78487 | ||||||||
\(993\) | 39.8590 | 1.26489 | ||||||||
\(994\) | 32.8162 | 1.04087 | ||||||||
\(995\) | −39.4377 | −1.25026 | ||||||||
\(996\) | −22.2672 | −0.705563 | ||||||||
\(997\) | 53.0334 | 1.67958 | 0.839792 | − | 0.542908i | \(-0.182677\pi\) | ||||
0.839792 | + | 0.542908i | \(0.182677\pi\) | |||||||
\(998\) | 35.7160 | 1.13057 | ||||||||
\(999\) | 53.4852 | 1.69220 |
(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 | 6001.2.a.b.1.17 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.17 | ✓ | 114 | 1.1 | even | 1 | trivial |