Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0539719364\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.737640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.880394 | −0.393724 | −0.196862 | − | 0.980431i | \(-0.563075\pi\) | ||||
−0.196862 | + | 0.980431i | \(0.563075\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.31313 | −0.496318 | −0.248159 | − | 0.968719i | \(-0.579826\pi\) | ||||
−0.248159 | + | 0.968719i | \(0.579826\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.880394 | −0.278405 | ||||||||
\(11\) | −0.806473 | −0.243161 | −0.121580 | − | 0.992582i | \(-0.538796\pi\) | ||||
−0.121580 | + | 0.992582i | \(0.538796\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0.854102 | 0.236885 | 0.118443 | − | 0.992961i | \(-0.462210\pi\) | ||||
0.118443 | + | 0.992961i | \(0.462210\pi\) | |||||||
\(14\) | −1.31313 | −0.350950 | ||||||||
\(15\) | −0.880394 | −0.227317 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.32429 | −0.762645 | −0.381323 | − | 0.924442i | \(-0.624531\pi\) | ||||
−0.381323 | + | 0.924442i | \(0.624531\pi\) | |||||||
\(20\) | −0.880394 | −0.196862 | ||||||||
\(21\) | −1.31313 | −0.286549 | ||||||||
\(22\) | −0.806473 | −0.171941 | ||||||||
\(23\) | −8.04763 | −1.67805 | −0.839023 | − | 0.544095i | \(-0.816873\pi\) | ||||
−0.839023 | + | 0.544095i | \(0.816873\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.22491 | −0.844981 | ||||||||
\(26\) | 0.854102 | 0.167503 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.31313 | −0.248159 | ||||||||
\(29\) | 4.13668 | 0.768162 | 0.384081 | − | 0.923299i | \(-0.374518\pi\) | ||||
0.384081 | + | 0.923299i | \(0.374518\pi\) | |||||||
\(30\) | −0.880394 | −0.160737 | ||||||||
\(31\) | −3.08082 | −0.553331 | −0.276666 | − | 0.960966i | \(-0.589229\pi\) | ||||
−0.276666 | + | 0.960966i | \(0.589229\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.806473 | −0.140389 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 1.15607 | 0.195412 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.6356 | −1.74848 | −0.874242 | − | 0.485490i | \(-0.838641\pi\) | ||||
−0.874242 | + | 0.485490i | \(0.838641\pi\) | |||||||
\(38\) | −3.32429 | −0.539272 | ||||||||
\(39\) | 0.854102 | 0.136766 | ||||||||
\(40\) | −0.880394 | −0.139202 | ||||||||
\(41\) | 2.28684 | 0.357145 | 0.178572 | − | 0.983927i | \(-0.442852\pi\) | ||||
0.178572 | + | 0.983927i | \(0.442852\pi\) | |||||||
\(42\) | −1.31313 | −0.202621 | ||||||||
\(43\) | 1.19862 | 0.182787 | 0.0913936 | − | 0.995815i | \(-0.470868\pi\) | ||||
0.0913936 | + | 0.995815i | \(0.470868\pi\) | |||||||
\(44\) | −0.806473 | −0.121580 | ||||||||
\(45\) | −0.880394 | −0.131241 | ||||||||
\(46\) | −8.04763 | −1.18656 | ||||||||
\(47\) | 1.81156 | 0.264243 | 0.132122 | − | 0.991234i | \(-0.457821\pi\) | ||||
0.132122 | + | 0.991234i | \(0.457821\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −5.27568 | −0.753669 | ||||||||
\(50\) | −4.22491 | −0.597492 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 0.854102 | 0.118443 | ||||||||
\(53\) | 5.11780 | 0.702983 | 0.351492 | − | 0.936191i | \(-0.385675\pi\) | ||||
0.351492 | + | 0.936191i | \(0.385675\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.710014 | 0.0957382 | ||||||||
\(56\) | −1.31313 | −0.175475 | ||||||||
\(57\) | −3.32429 | −0.440314 | ||||||||
\(58\) | 4.13668 | 0.543173 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | −0.880394 | −0.113658 | ||||||||
\(61\) | −4.72333 | −0.604761 | −0.302381 | − | 0.953187i | \(-0.597781\pi\) | ||||
−0.302381 | + | 0.953187i | \(0.597781\pi\) | |||||||
\(62\) | −3.08082 | −0.391264 | ||||||||
\(63\) | −1.31313 | −0.165439 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.751946 | −0.0932674 | ||||||||
\(66\) | −0.806473 | −0.0992700 | ||||||||
\(67\) | −5.94315 | −0.726072 | −0.363036 | − | 0.931775i | \(-0.618260\pi\) | ||||
−0.363036 | + | 0.931775i | \(0.618260\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −8.04763 | −0.968821 | ||||||||
\(70\) | 1.15607 | 0.138177 | ||||||||
\(71\) | −2.49235 | −0.295788 | −0.147894 | − | 0.989003i | \(-0.547249\pi\) | ||||
−0.147894 | + | 0.989003i | \(0.547249\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −3.28175 | −0.384100 | −0.192050 | − | 0.981385i | \(-0.561514\pi\) | ||||
−0.192050 | + | 0.981385i | \(0.561514\pi\) | |||||||
\(74\) | −10.6356 | −1.23637 | ||||||||
\(75\) | −4.22491 | −0.487850 | ||||||||
\(76\) | −3.32429 | −0.381323 | ||||||||
\(77\) | 1.05901 | 0.120685 | ||||||||
\(78\) | 0.854102 | 0.0967080 | ||||||||
\(79\) | 10.9474 | 1.23168 | 0.615840 | − | 0.787871i | \(-0.288817\pi\) | ||||
0.615840 | + | 0.787871i | \(0.288817\pi\) | |||||||
\(80\) | −0.880394 | −0.0984310 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.28684 | 0.252539 | ||||||||
\(83\) | −17.5576 | −1.92719 | −0.963597 | − | 0.267360i | \(-0.913849\pi\) | ||||
−0.963597 | + | 0.267360i | \(0.913849\pi\) | |||||||
\(84\) | −1.31313 | −0.143275 | ||||||||
\(85\) | −0.880394 | −0.0954921 | ||||||||
\(86\) | 1.19862 | 0.129250 | ||||||||
\(87\) | 4.13668 | 0.443499 | ||||||||
\(88\) | −0.806473 | −0.0859703 | ||||||||
\(89\) | −13.3627 | −1.41644 | −0.708222 | − | 0.705990i | \(-0.750502\pi\) | ||||
−0.708222 | + | 0.705990i | \(0.750502\pi\) | |||||||
\(90\) | −0.880394 | −0.0928016 | ||||||||
\(91\) | −1.12155 | −0.117570 | ||||||||
\(92\) | −8.04763 | −0.839023 | ||||||||
\(93\) | −3.08082 | −0.319466 | ||||||||
\(94\) | 1.81156 | 0.186848 | ||||||||
\(95\) | 2.92669 | 0.300272 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 14.6113 | 1.48355 | 0.741775 | − | 0.670649i | \(-0.233984\pi\) | ||||
0.741775 | + | 0.670649i | \(0.233984\pi\) | |||||||
\(98\) | −5.27568 | −0.532924 | ||||||||
\(99\) | −0.806473 | −0.0810536 | ||||||||
\(100\) | −4.22491 | −0.422491 | ||||||||
\(101\) | −16.4578 | −1.63762 | −0.818808 | − | 0.574068i | \(-0.805365\pi\) | ||||
−0.818808 | + | 0.574068i | \(0.805365\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 11.3727 | 1.12059 | 0.560295 | − | 0.828293i | \(-0.310688\pi\) | ||||
0.560295 | + | 0.828293i | \(0.310688\pi\) | |||||||
\(104\) | 0.854102 | 0.0837516 | ||||||||
\(105\) | 1.15607 | 0.112821 | ||||||||
\(106\) | 5.11780 | 0.497084 | ||||||||
\(107\) | 10.0131 | 0.968003 | 0.484002 | − | 0.875067i | \(-0.339183\pi\) | ||||
0.484002 | + | 0.875067i | \(0.339183\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 6.08703 | 0.583031 | 0.291516 | − | 0.956566i | \(-0.405840\pi\) | ||||
0.291516 | + | 0.956566i | \(0.405840\pi\) | |||||||
\(110\) | 0.710014 | 0.0676971 | ||||||||
\(111\) | −10.6356 | −1.00949 | ||||||||
\(112\) | −1.31313 | −0.124079 | ||||||||
\(113\) | −1.28948 | −0.121304 | −0.0606519 | − | 0.998159i | \(-0.519318\pi\) | ||||
−0.0606519 | + | 0.998159i | \(0.519318\pi\) | |||||||
\(114\) | −3.32429 | −0.311349 | ||||||||
\(115\) | 7.08508 | 0.660687 | ||||||||
\(116\) | 4.13668 | 0.384081 | ||||||||
\(117\) | 0.854102 | 0.0789618 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | −1.31313 | −0.120375 | ||||||||
\(120\) | −0.880394 | −0.0803686 | ||||||||
\(121\) | −10.3496 | −0.940873 | ||||||||
\(122\) | −4.72333 | −0.427631 | ||||||||
\(123\) | 2.28684 | 0.206198 | ||||||||
\(124\) | −3.08082 | −0.276666 | ||||||||
\(125\) | 8.12155 | 0.726413 | ||||||||
\(126\) | −1.31313 | −0.116983 | ||||||||
\(127\) | 9.44374 | 0.837997 | 0.418998 | − | 0.907987i | \(-0.362381\pi\) | ||||
0.418998 | + | 0.907987i | \(0.362381\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.19862 | 0.105532 | ||||||||
\(130\) | −0.751946 | −0.0659500 | ||||||||
\(131\) | 0.750136 | 0.0655397 | 0.0327699 | − | 0.999463i | \(-0.489567\pi\) | ||||
0.0327699 | + | 0.999463i | \(0.489567\pi\) | |||||||
\(132\) | −0.806473 | −0.0701945 | ||||||||
\(133\) | 4.36524 | 0.378514 | ||||||||
\(134\) | −5.94315 | −0.513410 | ||||||||
\(135\) | −0.880394 | −0.0757722 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −9.06995 | −0.774898 | −0.387449 | − | 0.921891i | \(-0.626644\pi\) | ||||
−0.387449 | + | 0.921891i | \(0.626644\pi\) | |||||||
\(138\) | −8.04763 | −0.685060 | ||||||||
\(139\) | −0.267958 | −0.0227279 | −0.0113639 | − | 0.999935i | \(-0.503617\pi\) | ||||
−0.0113639 | + | 0.999935i | \(0.503617\pi\) | |||||||
\(140\) | 1.15607 | 0.0977061 | ||||||||
\(141\) | 1.81156 | 0.152561 | ||||||||
\(142\) | −2.49235 | −0.209154 | ||||||||
\(143\) | −0.688810 | −0.0576012 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.64191 | −0.302444 | ||||||||
\(146\) | −3.28175 | −0.271600 | ||||||||
\(147\) | −5.27568 | −0.435131 | ||||||||
\(148\) | −10.6356 | −0.874242 | ||||||||
\(149\) | −9.92488 | −0.813078 | −0.406539 | − | 0.913633i | \(-0.633264\pi\) | ||||
−0.406539 | + | 0.913633i | \(0.633264\pi\) | |||||||
\(150\) | −4.22491 | −0.344962 | ||||||||
\(151\) | 1.64036 | 0.133490 | 0.0667451 | − | 0.997770i | \(-0.478739\pi\) | ||||
0.0667451 | + | 0.997770i | \(0.478739\pi\) | |||||||
\(152\) | −3.32429 | −0.269636 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 1.05901 | 0.0853372 | ||||||||
\(155\) | 2.71233 | 0.217860 | ||||||||
\(156\) | 0.854102 | 0.0683829 | ||||||||
\(157\) | −18.9964 | −1.51608 | −0.758038 | − | 0.652210i | \(-0.773842\pi\) | ||||
−0.758038 | + | 0.652210i | \(0.773842\pi\) | |||||||
\(158\) | 10.9474 | 0.870930 | ||||||||
\(159\) | 5.11780 | 0.405868 | ||||||||
\(160\) | −0.880394 | −0.0696012 | ||||||||
\(161\) | 10.5676 | 0.832844 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 8.85048 | 0.693223 | 0.346612 | − | 0.938009i | \(-0.387332\pi\) | ||||
0.346612 | + | 0.938009i | \(0.387332\pi\) | |||||||
\(164\) | 2.28684 | 0.178572 | ||||||||
\(165\) | 0.710014 | 0.0552745 | ||||||||
\(166\) | −17.5576 | −1.36273 | ||||||||
\(167\) | 8.96268 | 0.693553 | 0.346777 | − | 0.937948i | \(-0.387276\pi\) | ||||
0.346777 | + | 0.937948i | \(0.387276\pi\) | |||||||
\(168\) | −1.31313 | −0.101310 | ||||||||
\(169\) | −12.2705 | −0.943885 | ||||||||
\(170\) | −0.880394 | −0.0675231 | ||||||||
\(171\) | −3.32429 | −0.254215 | ||||||||
\(172\) | 1.19862 | 0.0913936 | ||||||||
\(173\) | −2.15900 | −0.164146 | −0.0820730 | − | 0.996626i | \(-0.526154\pi\) | ||||
−0.0820730 | + | 0.996626i | \(0.526154\pi\) | |||||||
\(174\) | 4.13668 | 0.313601 | ||||||||
\(175\) | 5.54787 | 0.419379 | ||||||||
\(176\) | −0.806473 | −0.0607902 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | −13.3627 | −1.00158 | ||||||||
\(179\) | −12.8127 | −0.957665 | −0.478832 | − | 0.877906i | \(-0.658940\pi\) | ||||
−0.478832 | + | 0.877906i | \(0.658940\pi\) | |||||||
\(180\) | −0.880394 | −0.0656207 | ||||||||
\(181\) | −1.96862 | −0.146326 | −0.0731632 | − | 0.997320i | \(-0.523309\pi\) | ||||
−0.0731632 | + | 0.997320i | \(0.523309\pi\) | |||||||
\(182\) | −1.12155 | −0.0831348 | ||||||||
\(183\) | −4.72333 | −0.349159 | ||||||||
\(184\) | −8.04763 | −0.593279 | ||||||||
\(185\) | 9.36353 | 0.688420 | ||||||||
\(186\) | −3.08082 | −0.225897 | ||||||||
\(187\) | −0.806473 | −0.0589751 | ||||||||
\(188\) | 1.81156 | 0.132122 | ||||||||
\(189\) | −1.31313 | −0.0955164 | ||||||||
\(190\) | 2.92669 | 0.212324 | ||||||||
\(191\) | −4.28500 | −0.310051 | −0.155026 | − | 0.987910i | \(-0.549546\pi\) | ||||
−0.155026 | + | 0.987910i | \(0.549546\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 6.00607 | 0.432327 | 0.216163 | − | 0.976357i | \(-0.430646\pi\) | ||||
0.216163 | + | 0.976357i | \(0.430646\pi\) | |||||||
\(194\) | 14.6113 | 1.04903 | ||||||||
\(195\) | −0.751946 | −0.0538480 | ||||||||
\(196\) | −5.27568 | −0.376834 | ||||||||
\(197\) | −9.64678 | −0.687305 | −0.343652 | − | 0.939097i | \(-0.611664\pi\) | ||||
−0.343652 | + | 0.939097i | \(0.611664\pi\) | |||||||
\(198\) | −0.806473 | −0.0573135 | ||||||||
\(199\) | 9.95056 | 0.705377 | 0.352688 | − | 0.935741i | \(-0.385268\pi\) | ||||
0.352688 | + | 0.935741i | \(0.385268\pi\) | |||||||
\(200\) | −4.22491 | −0.298746 | ||||||||
\(201\) | −5.94315 | −0.419198 | ||||||||
\(202\) | −16.4578 | −1.15797 | ||||||||
\(203\) | −5.43201 | −0.381253 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −2.01332 | −0.140616 | ||||||||
\(206\) | 11.3727 | 0.792377 | ||||||||
\(207\) | −8.04763 | −0.559349 | ||||||||
\(208\) | 0.854102 | 0.0592213 | ||||||||
\(209\) | 2.68095 | 0.185445 | ||||||||
\(210\) | 1.15607 | 0.0797767 | ||||||||
\(211\) | 3.34766 | 0.230462 | 0.115231 | − | 0.993339i | \(-0.463239\pi\) | ||||
0.115231 | + | 0.993339i | \(0.463239\pi\) | |||||||
\(212\) | 5.11780 | 0.351492 | ||||||||
\(213\) | −2.49235 | −0.170773 | ||||||||
\(214\) | 10.0131 | 0.684482 | ||||||||
\(215\) | −1.05525 | −0.0719677 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 4.04553 | 0.274628 | ||||||||
\(218\) | 6.08703 | 0.412265 | ||||||||
\(219\) | −3.28175 | −0.221760 | ||||||||
\(220\) | 0.710014 | 0.0478691 | ||||||||
\(221\) | 0.854102 | 0.0574531 | ||||||||
\(222\) | −10.6356 | −0.713816 | ||||||||
\(223\) | −21.7814 | −1.45859 | −0.729294 | − | 0.684201i | \(-0.760151\pi\) | ||||
−0.729294 | + | 0.684201i | \(0.760151\pi\) | |||||||
\(224\) | −1.31313 | −0.0877374 | ||||||||
\(225\) | −4.22491 | −0.281660 | ||||||||
\(226\) | −1.28948 | −0.0857747 | ||||||||
\(227\) | 9.58881 | 0.636432 | 0.318216 | − | 0.948018i | \(-0.396916\pi\) | ||||
0.318216 | + | 0.948018i | \(0.396916\pi\) | |||||||
\(228\) | −3.32429 | −0.220157 | ||||||||
\(229\) | 18.5177 | 1.22368 | 0.611841 | − | 0.790981i | \(-0.290429\pi\) | ||||
0.611841 | + | 0.790981i | \(0.290429\pi\) | |||||||
\(230\) | 7.08508 | 0.467176 | ||||||||
\(231\) | 1.05901 | 0.0696775 | ||||||||
\(232\) | 4.13668 | 0.271586 | ||||||||
\(233\) | −9.25957 | −0.606614 | −0.303307 | − | 0.952893i | \(-0.598091\pi\) | ||||
−0.303307 | + | 0.952893i | \(0.598091\pi\) | |||||||
\(234\) | 0.854102 | 0.0558344 | ||||||||
\(235\) | −1.59489 | −0.104039 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | 10.9474 | 0.711111 | ||||||||
\(238\) | −1.31313 | −0.0851178 | ||||||||
\(239\) | −7.92592 | −0.512685 | −0.256343 | − | 0.966586i | \(-0.582518\pi\) | ||||
−0.256343 | + | 0.966586i | \(0.582518\pi\) | |||||||
\(240\) | −0.880394 | −0.0568292 | ||||||||
\(241\) | 1.38295 | 0.0890837 | 0.0445418 | − | 0.999008i | \(-0.485817\pi\) | ||||
0.0445418 | + | 0.999008i | \(0.485817\pi\) | |||||||
\(242\) | −10.3496 | −0.665298 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.72333 | −0.302381 | ||||||||
\(245\) | 4.64468 | 0.296737 | ||||||||
\(246\) | 2.28684 | 0.145804 | ||||||||
\(247\) | −2.83929 | −0.180659 | ||||||||
\(248\) | −3.08082 | −0.195632 | ||||||||
\(249\) | −17.5576 | −1.11267 | ||||||||
\(250\) | 8.12155 | 0.513652 | ||||||||
\(251\) | −2.68604 | −0.169541 | −0.0847707 | − | 0.996400i | \(-0.527016\pi\) | ||||
−0.0847707 | + | 0.996400i | \(0.527016\pi\) | |||||||
\(252\) | −1.31313 | −0.0827196 | ||||||||
\(253\) | 6.49019 | 0.408035 | ||||||||
\(254\) | 9.44374 | 0.592553 | ||||||||
\(255\) | −0.880394 | −0.0551324 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.7337 | −0.856686 | −0.428343 | − | 0.903616i | \(-0.640903\pi\) | ||||
−0.428343 | + | 0.903616i | \(0.640903\pi\) | |||||||
\(258\) | 1.19862 | 0.0746225 | ||||||||
\(259\) | 13.9660 | 0.867804 | ||||||||
\(260\) | −0.751946 | −0.0466337 | ||||||||
\(261\) | 4.13668 | 0.256054 | ||||||||
\(262\) | 0.750136 | 0.0463436 | ||||||||
\(263\) | −18.0752 | −1.11456 | −0.557281 | − | 0.830324i | \(-0.688156\pi\) | ||||
−0.557281 | + | 0.830324i | \(0.688156\pi\) | |||||||
\(264\) | −0.806473 | −0.0496350 | ||||||||
\(265\) | −4.50568 | −0.276781 | ||||||||
\(266\) | 4.36524 | 0.267650 | ||||||||
\(267\) | −13.3627 | −0.817784 | ||||||||
\(268\) | −5.94315 | −0.363036 | ||||||||
\(269\) | −23.2846 | −1.41968 | −0.709842 | − | 0.704361i | \(-0.751234\pi\) | ||||
−0.709842 | + | 0.704361i | \(0.751234\pi\) | |||||||
\(270\) | −0.880394 | −0.0535791 | ||||||||
\(271\) | −6.71428 | −0.407863 | −0.203932 | − | 0.978985i | \(-0.565372\pi\) | ||||
−0.203932 | + | 0.978985i | \(0.565372\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −1.12155 | −0.0678793 | ||||||||
\(274\) | −9.06995 | −0.547936 | ||||||||
\(275\) | 3.40727 | 0.205466 | ||||||||
\(276\) | −8.04763 | −0.484410 | ||||||||
\(277\) | −24.3896 | −1.46543 | −0.732716 | − | 0.680535i | \(-0.761748\pi\) | ||||
−0.732716 | + | 0.680535i | \(0.761748\pi\) | |||||||
\(278\) | −0.267958 | −0.0160710 | ||||||||
\(279\) | −3.08082 | −0.184444 | ||||||||
\(280\) | 1.15607 | 0.0690887 | ||||||||
\(281\) | 11.7140 | 0.698800 | 0.349400 | − | 0.936974i | \(-0.386385\pi\) | ||||
0.349400 | + | 0.936974i | \(0.386385\pi\) | |||||||
\(282\) | 1.81156 | 0.107877 | ||||||||
\(283\) | 14.7340 | 0.875847 | 0.437923 | − | 0.899012i | \(-0.355714\pi\) | ||||
0.437923 | + | 0.899012i | \(0.355714\pi\) | |||||||
\(284\) | −2.49235 | −0.147894 | ||||||||
\(285\) | 2.92669 | 0.173362 | ||||||||
\(286\) | −0.688810 | −0.0407302 | ||||||||
\(287\) | −3.00293 | −0.177257 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −3.64191 | −0.213860 | ||||||||
\(291\) | 14.6113 | 0.856528 | ||||||||
\(292\) | −3.28175 | −0.192050 | ||||||||
\(293\) | 12.4874 | 0.729522 | 0.364761 | − | 0.931101i | \(-0.381151\pi\) | ||||
0.364761 | + | 0.931101i | \(0.381151\pi\) | |||||||
\(294\) | −5.27568 | −0.307684 | ||||||||
\(295\) | −0.880394 | −0.0512585 | ||||||||
\(296\) | −10.6356 | −0.618183 | ||||||||
\(297\) | −0.806473 | −0.0467963 | ||||||||
\(298\) | −9.92488 | −0.574933 | ||||||||
\(299\) | −6.87350 | −0.397505 | ||||||||
\(300\) | −4.22491 | −0.243925 | ||||||||
\(301\) | −1.57394 | −0.0907205 | ||||||||
\(302\) | 1.64036 | 0.0943919 | ||||||||
\(303\) | −16.4578 | −0.945478 | ||||||||
\(304\) | −3.32429 | −0.190661 | ||||||||
\(305\) | 4.15839 | 0.238109 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 20.1040 | 1.14739 | 0.573697 | − | 0.819068i | \(-0.305509\pi\) | ||||
0.573697 | + | 0.819068i | \(0.305509\pi\) | |||||||
\(308\) | 1.05901 | 0.0603425 | ||||||||
\(309\) | 11.3727 | 0.646973 | ||||||||
\(310\) | 2.71233 | 0.154050 | ||||||||
\(311\) | 34.3174 | 1.94596 | 0.972980 | − | 0.230890i | \(-0.0741639\pi\) | ||||
0.972980 | + | 0.230890i | \(0.0741639\pi\) | |||||||
\(312\) | 0.854102 | 0.0483540 | ||||||||
\(313\) | −29.1995 | −1.65045 | −0.825226 | − | 0.564803i | \(-0.808952\pi\) | ||||
−0.825226 | + | 0.564803i | \(0.808952\pi\) | |||||||
\(314\) | −18.9964 | −1.07203 | ||||||||
\(315\) | 1.15607 | 0.0651374 | ||||||||
\(316\) | 10.9474 | 0.615840 | ||||||||
\(317\) | −12.5378 | −0.704194 | −0.352097 | − | 0.935963i | \(-0.614531\pi\) | ||||
−0.352097 | + | 0.935963i | \(0.614531\pi\) | |||||||
\(318\) | 5.11780 | 0.286992 | ||||||||
\(319\) | −3.33612 | −0.186787 | ||||||||
\(320\) | −0.880394 | −0.0492155 | ||||||||
\(321\) | 10.0131 | 0.558877 | ||||||||
\(322\) | 10.5676 | 0.588910 | ||||||||
\(323\) | −3.32429 | −0.184969 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.60850 | −0.200164 | ||||||||
\(326\) | 8.85048 | 0.490183 | ||||||||
\(327\) | 6.08703 | 0.336613 | ||||||||
\(328\) | 2.28684 | 0.126270 | ||||||||
\(329\) | −2.37882 | −0.131149 | ||||||||
\(330\) | 0.710014 | 0.0390850 | ||||||||
\(331\) | 3.30684 | 0.181761 | 0.0908803 | − | 0.995862i | \(-0.471032\pi\) | ||||
0.0908803 | + | 0.995862i | \(0.471032\pi\) | |||||||
\(332\) | −17.5576 | −0.963597 | ||||||||
\(333\) | −10.6356 | −0.582828 | ||||||||
\(334\) | 8.96268 | 0.490416 | ||||||||
\(335\) | 5.23231 | 0.285872 | ||||||||
\(336\) | −1.31313 | −0.0716373 | ||||||||
\(337\) | −1.00120 | −0.0545389 | −0.0272695 | − | 0.999628i | \(-0.508681\pi\) | ||||
−0.0272695 | + | 0.999628i | \(0.508681\pi\) | |||||||
\(338\) | −12.2705 | −0.667428 | ||||||||
\(339\) | −1.28948 | −0.0700347 | ||||||||
\(340\) | −0.880394 | −0.0477461 | ||||||||
\(341\) | 2.48460 | 0.134548 | ||||||||
\(342\) | −3.32429 | −0.179757 | ||||||||
\(343\) | 16.1196 | 0.870377 | ||||||||
\(344\) | 1.19862 | 0.0646250 | ||||||||
\(345\) | 7.08508 | 0.381448 | ||||||||
\(346\) | −2.15900 | −0.116069 | ||||||||
\(347\) | −1.79449 | −0.0963331 | −0.0481666 | − | 0.998839i | \(-0.515338\pi\) | ||||
−0.0481666 | + | 0.998839i | \(0.515338\pi\) | |||||||
\(348\) | 4.13668 | 0.221749 | ||||||||
\(349\) | 16.4028 | 0.878023 | 0.439012 | − | 0.898481i | \(-0.355329\pi\) | ||||
0.439012 | + | 0.898481i | \(0.355329\pi\) | |||||||
\(350\) | 5.54787 | 0.296546 | ||||||||
\(351\) | 0.854102 | 0.0455886 | ||||||||
\(352\) | −0.806473 | −0.0429852 | ||||||||
\(353\) | −31.3537 | −1.66879 | −0.834394 | − | 0.551168i | \(-0.814182\pi\) | ||||
−0.834394 | + | 0.551168i | \(0.814182\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | 2.19425 | 0.116459 | ||||||||
\(356\) | −13.3627 | −0.708222 | ||||||||
\(357\) | −1.31313 | −0.0694984 | ||||||||
\(358\) | −12.8127 | −0.677171 | ||||||||
\(359\) | 24.0213 | 1.26780 | 0.633899 | − | 0.773416i | \(-0.281454\pi\) | ||||
0.633899 | + | 0.773416i | \(0.281454\pi\) | |||||||
\(360\) | −0.880394 | −0.0464008 | ||||||||
\(361\) | −7.94907 | −0.418372 | ||||||||
\(362\) | −1.96862 | −0.103468 | ||||||||
\(363\) | −10.3496 | −0.543213 | ||||||||
\(364\) | −1.12155 | −0.0587852 | ||||||||
\(365\) | 2.88924 | 0.151229 | ||||||||
\(366\) | −4.72333 | −0.246893 | ||||||||
\(367\) | −17.0572 | −0.890378 | −0.445189 | − | 0.895437i | \(-0.646864\pi\) | ||||
−0.445189 | + | 0.895437i | \(0.646864\pi\) | |||||||
\(368\) | −8.04763 | −0.419512 | ||||||||
\(369\) | 2.28684 | 0.119048 | ||||||||
\(370\) | 9.36353 | 0.486787 | ||||||||
\(371\) | −6.72035 | −0.348903 | ||||||||
\(372\) | −3.08082 | −0.159733 | ||||||||
\(373\) | 14.1389 | 0.732085 | 0.366043 | − | 0.930598i | \(-0.380712\pi\) | ||||
0.366043 | + | 0.930598i | \(0.380712\pi\) | |||||||
\(374\) | −0.806473 | −0.0417017 | ||||||||
\(375\) | 8.12155 | 0.419395 | ||||||||
\(376\) | 1.81156 | 0.0934241 | ||||||||
\(377\) | 3.53315 | 0.181966 | ||||||||
\(378\) | −1.31313 | −0.0675403 | ||||||||
\(379\) | 10.6967 | 0.549455 | 0.274728 | − | 0.961522i | \(-0.411412\pi\) | ||||
0.274728 | + | 0.961522i | \(0.411412\pi\) | |||||||
\(380\) | 2.92669 | 0.150136 | ||||||||
\(381\) | 9.44374 | 0.483818 | ||||||||
\(382\) | −4.28500 | −0.219240 | ||||||||
\(383\) | 21.9782 | 1.12303 | 0.561516 | − | 0.827466i | \(-0.310218\pi\) | ||||
0.561516 | + | 0.827466i | \(0.310218\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.932343 | −0.0475166 | ||||||||
\(386\) | 6.00607 | 0.305701 | ||||||||
\(387\) | 1.19862 | 0.0609290 | ||||||||
\(388\) | 14.6113 | 0.741775 | ||||||||
\(389\) | 33.1693 | 1.68175 | 0.840875 | − | 0.541229i | \(-0.182041\pi\) | ||||
0.840875 | + | 0.541229i | \(0.182041\pi\) | |||||||
\(390\) | −0.751946 | −0.0380763 | ||||||||
\(391\) | −8.04763 | −0.406986 | ||||||||
\(392\) | −5.27568 | −0.266462 | ||||||||
\(393\) | 0.750136 | 0.0378394 | ||||||||
\(394\) | −9.64678 | −0.485998 | ||||||||
\(395\) | −9.63804 | −0.484942 | ||||||||
\(396\) | −0.806473 | −0.0405268 | ||||||||
\(397\) | 31.3458 | 1.57320 | 0.786602 | − | 0.617461i | \(-0.211839\pi\) | ||||
0.786602 | + | 0.617461i | \(0.211839\pi\) | |||||||
\(398\) | 9.95056 | 0.498777 | ||||||||
\(399\) | 4.36524 | 0.218535 | ||||||||
\(400\) | −4.22491 | −0.211245 | ||||||||
\(401\) | −1.06479 | −0.0531729 | −0.0265864 | − | 0.999647i | \(-0.508464\pi\) | ||||
−0.0265864 | + | 0.999647i | \(0.508464\pi\) | |||||||
\(402\) | −5.94315 | −0.296418 | ||||||||
\(403\) | −2.63133 | −0.131076 | ||||||||
\(404\) | −16.4578 | −0.818808 | ||||||||
\(405\) | −0.880394 | −0.0437471 | ||||||||
\(406\) | −5.43201 | −0.269586 | ||||||||
\(407\) | 8.57734 | 0.425163 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −17.8012 | −0.880213 | −0.440106 | − | 0.897946i | \(-0.645059\pi\) | ||||
−0.440106 | + | 0.897946i | \(0.645059\pi\) | |||||||
\(410\) | −2.01332 | −0.0994308 | ||||||||
\(411\) | −9.06995 | −0.447388 | ||||||||
\(412\) | 11.3727 | 0.560295 | ||||||||
\(413\) | −1.31313 | −0.0646151 | ||||||||
\(414\) | −8.04763 | −0.395519 | ||||||||
\(415\) | 15.4576 | 0.758782 | ||||||||
\(416\) | 0.854102 | 0.0418758 | ||||||||
\(417\) | −0.267958 | −0.0131219 | ||||||||
\(418\) | 2.68095 | 0.131130 | ||||||||
\(419\) | −27.8247 | −1.35933 | −0.679663 | − | 0.733525i | \(-0.737874\pi\) | ||||
−0.679663 | + | 0.733525i | \(0.737874\pi\) | |||||||
\(420\) | 1.15607 | 0.0564107 | ||||||||
\(421\) | 27.2478 | 1.32798 | 0.663989 | − | 0.747742i | \(-0.268862\pi\) | ||||
0.663989 | + | 0.747742i | \(0.268862\pi\) | |||||||
\(422\) | 3.34766 | 0.162961 | ||||||||
\(423\) | 1.81156 | 0.0880811 | ||||||||
\(424\) | 5.11780 | 0.248542 | ||||||||
\(425\) | −4.22491 | −0.204938 | ||||||||
\(426\) | −2.49235 | −0.120755 | ||||||||
\(427\) | 6.20237 | 0.300154 | ||||||||
\(428\) | 10.0131 | 0.484002 | ||||||||
\(429\) | −0.688810 | −0.0332561 | ||||||||
\(430\) | −1.05525 | −0.0508888 | ||||||||
\(431\) | 3.75967 | 0.181097 | 0.0905484 | − | 0.995892i | \(-0.471138\pi\) | ||||
0.0905484 | + | 0.995892i | \(0.471138\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 27.9332 | 1.34239 | 0.671193 | − | 0.741283i | \(-0.265782\pi\) | ||||
0.671193 | + | 0.741283i | \(0.265782\pi\) | |||||||
\(434\) | 4.04553 | 0.194191 | ||||||||
\(435\) | −3.64191 | −0.174616 | ||||||||
\(436\) | 6.08703 | 0.291516 | ||||||||
\(437\) | 26.7527 | 1.27975 | ||||||||
\(438\) | −3.28175 | −0.156808 | ||||||||
\(439\) | −2.91484 | −0.139118 | −0.0695588 | − | 0.997578i | \(-0.522159\pi\) | ||||
−0.0695588 | + | 0.997578i | \(0.522159\pi\) | |||||||
\(440\) | 0.710014 | 0.0338486 | ||||||||
\(441\) | −5.27568 | −0.251223 | ||||||||
\(442\) | 0.854102 | 0.0406255 | ||||||||
\(443\) | 7.62100 | 0.362085 | 0.181042 | − | 0.983475i | \(-0.442053\pi\) | ||||
0.181042 | + | 0.983475i | \(0.442053\pi\) | |||||||
\(444\) | −10.6356 | −0.504744 | ||||||||
\(445\) | 11.7644 | 0.557688 | ||||||||
\(446\) | −21.7814 | −1.03138 | ||||||||
\(447\) | −9.92488 | −0.469431 | ||||||||
\(448\) | −1.31313 | −0.0620397 | ||||||||
\(449\) | 23.7416 | 1.12043 | 0.560217 | − | 0.828346i | \(-0.310718\pi\) | ||||
0.560217 | + | 0.828346i | \(0.310718\pi\) | |||||||
\(450\) | −4.22491 | −0.199164 | ||||||||
\(451\) | −1.84428 | −0.0868436 | ||||||||
\(452\) | −1.28948 | −0.0606519 | ||||||||
\(453\) | 1.64036 | 0.0770706 | ||||||||
\(454\) | 9.58881 | 0.450025 | ||||||||
\(455\) | 0.987405 | 0.0462903 | ||||||||
\(456\) | −3.32429 | −0.155674 | ||||||||
\(457\) | −16.1234 | −0.754219 | −0.377109 | − | 0.926169i | \(-0.623082\pi\) | ||||
−0.377109 | + | 0.926169i | \(0.623082\pi\) | |||||||
\(458\) | 18.5177 | 0.865274 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 7.08508 | 0.330344 | ||||||||
\(461\) | 24.0954 | 1.12223 | 0.561117 | − | 0.827736i | \(-0.310372\pi\) | ||||
0.561117 | + | 0.827736i | \(0.310372\pi\) | |||||||
\(462\) | 1.05901 | 0.0492694 | ||||||||
\(463\) | −8.23296 | −0.382618 | −0.191309 | − | 0.981530i | \(-0.561273\pi\) | ||||
−0.191309 | + | 0.981530i | \(0.561273\pi\) | |||||||
\(464\) | 4.13668 | 0.192041 | ||||||||
\(465\) | 2.71233 | 0.125781 | ||||||||
\(466\) | −9.25957 | −0.428941 | ||||||||
\(467\) | −17.6501 | −0.816748 | −0.408374 | − | 0.912815i | \(-0.633904\pi\) | ||||
−0.408374 | + | 0.912815i | \(0.633904\pi\) | |||||||
\(468\) | 0.854102 | 0.0394809 | ||||||||
\(469\) | 7.80415 | 0.360362 | ||||||||
\(470\) | −1.59489 | −0.0735666 | ||||||||
\(471\) | −18.9964 | −0.875307 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | −0.966651 | −0.0444466 | ||||||||
\(474\) | 10.9474 | 0.502831 | ||||||||
\(475\) | 14.0448 | 0.644421 | ||||||||
\(476\) | −1.31313 | −0.0601874 | ||||||||
\(477\) | 5.11780 | 0.234328 | ||||||||
\(478\) | −7.92592 | −0.362523 | ||||||||
\(479\) | 28.9556 | 1.32302 | 0.661508 | − | 0.749938i | \(-0.269917\pi\) | ||||
0.661508 | + | 0.749938i | \(0.269917\pi\) | |||||||
\(480\) | −0.880394 | −0.0401843 | ||||||||
\(481\) | −9.08390 | −0.414190 | ||||||||
\(482\) | 1.38295 | 0.0629917 | ||||||||
\(483\) | 10.5676 | 0.480843 | ||||||||
\(484\) | −10.3496 | −0.470436 | ||||||||
\(485\) | −12.8637 | −0.584109 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 12.0378 | 0.545483 | 0.272742 | − | 0.962087i | \(-0.412070\pi\) | ||||
0.272742 | + | 0.962087i | \(0.412070\pi\) | |||||||
\(488\) | −4.72333 | −0.213815 | ||||||||
\(489\) | 8.85048 | 0.400233 | ||||||||
\(490\) | 4.64468 | 0.209825 | ||||||||
\(491\) | −1.57084 | −0.0708909 | −0.0354455 | − | 0.999372i | \(-0.511285\pi\) | ||||
−0.0354455 | + | 0.999372i | \(0.511285\pi\) | |||||||
\(492\) | 2.28684 | 0.103099 | ||||||||
\(493\) | 4.13668 | 0.186307 | ||||||||
\(494\) | −2.83929 | −0.127746 | ||||||||
\(495\) | 0.710014 | 0.0319127 | ||||||||
\(496\) | −3.08082 | −0.138333 | ||||||||
\(497\) | 3.27279 | 0.146805 | ||||||||
\(498\) | −17.5576 | −0.786773 | ||||||||
\(499\) | 10.5078 | 0.470393 | 0.235196 | − | 0.971948i | \(-0.424427\pi\) | ||||
0.235196 | + | 0.971948i | \(0.424427\pi\) | |||||||
\(500\) | 8.12155 | 0.363207 | ||||||||
\(501\) | 8.96268 | 0.400423 | ||||||||
\(502\) | −2.68604 | −0.119884 | ||||||||
\(503\) | −15.8471 | −0.706588 | −0.353294 | − | 0.935512i | \(-0.614939\pi\) | ||||
−0.353294 | + | 0.935512i | \(0.614939\pi\) | |||||||
\(504\) | −1.31313 | −0.0584916 | ||||||||
\(505\) | 14.4894 | 0.644768 | ||||||||
\(506\) | 6.49019 | 0.288524 | ||||||||
\(507\) | −12.2705 | −0.544952 | ||||||||
\(508\) | 9.44374 | 0.418998 | ||||||||
\(509\) | −36.0403 | −1.59746 | −0.798730 | − | 0.601690i | \(-0.794494\pi\) | ||||
−0.798730 | + | 0.601690i | \(0.794494\pi\) | |||||||
\(510\) | −0.880394 | −0.0389845 | ||||||||
\(511\) | 4.30938 | 0.190636 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.32429 | −0.146771 | ||||||||
\(514\) | −13.7337 | −0.605769 | ||||||||
\(515\) | −10.0125 | −0.441203 | ||||||||
\(516\) | 1.19862 | 0.0527661 | ||||||||
\(517\) | −1.46097 | −0.0642536 | ||||||||
\(518\) | 13.9660 | 0.613630 | ||||||||
\(519\) | −2.15900 | −0.0947697 | ||||||||
\(520\) | −0.751946 | −0.0329750 | ||||||||
\(521\) | −11.4615 | −0.502137 | −0.251068 | − | 0.967969i | \(-0.580782\pi\) | ||||
−0.251068 | + | 0.967969i | \(0.580782\pi\) | |||||||
\(522\) | 4.13668 | 0.181058 | ||||||||
\(523\) | −29.3343 | −1.28270 | −0.641350 | − | 0.767249i | \(-0.721625\pi\) | ||||
−0.641350 | + | 0.767249i | \(0.721625\pi\) | |||||||
\(524\) | 0.750136 | 0.0327699 | ||||||||
\(525\) | 5.54787 | 0.242129 | ||||||||
\(526\) | −18.0752 | −0.788115 | ||||||||
\(527\) | −3.08082 | −0.134203 | ||||||||
\(528\) | −0.806473 | −0.0350972 | ||||||||
\(529\) | 41.7643 | 1.81584 | ||||||||
\(530\) | −4.50568 | −0.195714 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 4.36524 | 0.189257 | ||||||||
\(533\) | 1.95320 | 0.0846023 | ||||||||
\(534\) | −13.3627 | −0.578261 | ||||||||
\(535\) | −8.81547 | −0.381126 | ||||||||
\(536\) | −5.94315 | −0.256705 | ||||||||
\(537\) | −12.8127 | −0.552908 | ||||||||
\(538\) | −23.2846 | −1.00387 | ||||||||
\(539\) | 4.25469 | 0.183263 | ||||||||
\(540\) | −0.880394 | −0.0378861 | ||||||||
\(541\) | 37.7165 | 1.62156 | 0.810780 | − | 0.585350i | \(-0.199043\pi\) | ||||
0.810780 | + | 0.585350i | \(0.199043\pi\) | |||||||
\(542\) | −6.71428 | −0.288403 | ||||||||
\(543\) | −1.96862 | −0.0844816 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | −5.35898 | −0.229553 | ||||||||
\(546\) | −1.12155 | −0.0479979 | ||||||||
\(547\) | 43.8934 | 1.87675 | 0.938373 | − | 0.345625i | \(-0.112333\pi\) | ||||
0.938373 | + | 0.345625i | \(0.112333\pi\) | |||||||
\(548\) | −9.06995 | −0.387449 | ||||||||
\(549\) | −4.72333 | −0.201587 | ||||||||
\(550\) | 3.40727 | 0.145287 | ||||||||
\(551\) | −13.7515 | −0.585835 | ||||||||
\(552\) | −8.04763 | −0.342530 | ||||||||
\(553\) | −14.3754 | −0.611305 | ||||||||
\(554\) | −24.3896 | −1.03622 | ||||||||
\(555\) | 9.36353 | 0.397460 | ||||||||
\(556\) | −0.267958 | −0.0113639 | ||||||||
\(557\) | −6.77350 | −0.287002 | −0.143501 | − | 0.989650i | \(-0.545836\pi\) | ||||
−0.143501 | + | 0.989650i | \(0.545836\pi\) | |||||||
\(558\) | −3.08082 | −0.130421 | ||||||||
\(559\) | 1.02374 | 0.0432996 | ||||||||
\(560\) | 1.15607 | 0.0488531 | ||||||||
\(561\) | −0.806473 | −0.0340493 | ||||||||
\(562\) | 11.7140 | 0.494126 | ||||||||
\(563\) | 21.6865 | 0.913978 | 0.456989 | − | 0.889472i | \(-0.348928\pi\) | ||||
0.456989 | + | 0.889472i | \(0.348928\pi\) | |||||||
\(564\) | 1.81156 | 0.0762805 | ||||||||
\(565\) | 1.13525 | 0.0477602 | ||||||||
\(566\) | 14.7340 | 0.619317 | ||||||||
\(567\) | −1.31313 | −0.0551464 | ||||||||
\(568\) | −2.49235 | −0.104577 | ||||||||
\(569\) | −16.8081 | −0.704633 | −0.352317 | − | 0.935881i | \(-0.614606\pi\) | ||||
−0.352317 | + | 0.935881i | \(0.614606\pi\) | |||||||
\(570\) | 2.92669 | 0.122585 | ||||||||
\(571\) | −31.5062 | −1.31849 | −0.659246 | − | 0.751927i | \(-0.729125\pi\) | ||||
−0.659246 | + | 0.751927i | \(0.729125\pi\) | |||||||
\(572\) | −0.688810 | −0.0288006 | ||||||||
\(573\) | −4.28500 | −0.179008 | ||||||||
\(574\) | −3.00293 | −0.125340 | ||||||||
\(575\) | 34.0005 | 1.41792 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −14.7803 | −0.615313 | −0.307656 | − | 0.951498i | \(-0.599545\pi\) | ||||
−0.307656 | + | 0.951498i | \(0.599545\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 6.00607 | 0.249604 | ||||||||
\(580\) | −3.64191 | −0.151222 | ||||||||
\(581\) | 23.0554 | 0.956500 | ||||||||
\(582\) | 14.6113 | 0.605657 | ||||||||
\(583\) | −4.12736 | −0.170938 | ||||||||
\(584\) | −3.28175 | −0.135800 | ||||||||
\(585\) | −0.751946 | −0.0310891 | ||||||||
\(586\) | 12.4874 | 0.515850 | ||||||||
\(587\) | −18.6535 | −0.769913 | −0.384957 | − | 0.922935i | \(-0.625784\pi\) | ||||
−0.384957 | + | 0.922935i | \(0.625784\pi\) | |||||||
\(588\) | −5.27568 | −0.217565 | ||||||||
\(589\) | 10.2415 | 0.421996 | ||||||||
\(590\) | −0.880394 | −0.0362452 | ||||||||
\(591\) | −9.64678 | −0.396815 | ||||||||
\(592\) | −10.6356 | −0.437121 | ||||||||
\(593\) | 0.602001 | 0.0247212 | 0.0123606 | − | 0.999924i | \(-0.496065\pi\) | ||||
0.0123606 | + | 0.999924i | \(0.496065\pi\) | |||||||
\(594\) | −0.806473 | −0.0330900 | ||||||||
\(595\) | 1.15607 | 0.0473944 | ||||||||
\(596\) | −9.92488 | −0.406539 | ||||||||
\(597\) | 9.95056 | 0.407249 | ||||||||
\(598\) | −6.87350 | −0.281078 | ||||||||
\(599\) | −40.4299 | −1.65192 | −0.825961 | − | 0.563727i | \(-0.809367\pi\) | ||||
−0.825961 | + | 0.563727i | \(0.809367\pi\) | |||||||
\(600\) | −4.22491 | −0.172481 | ||||||||
\(601\) | 11.4505 | 0.467076 | 0.233538 | − | 0.972348i | \(-0.424970\pi\) | ||||
0.233538 | + | 0.972348i | \(0.424970\pi\) | |||||||
\(602\) | −1.57394 | −0.0641491 | ||||||||
\(603\) | −5.94315 | −0.242024 | ||||||||
\(604\) | 1.64036 | 0.0667451 | ||||||||
\(605\) | 9.11172 | 0.370444 | ||||||||
\(606\) | −16.4578 | −0.668554 | ||||||||
\(607\) | 10.6778 | 0.433400 | 0.216700 | − | 0.976238i | \(-0.430471\pi\) | ||||
0.216700 | + | 0.976238i | \(0.430471\pi\) | |||||||
\(608\) | −3.32429 | −0.134818 | ||||||||
\(609\) | −5.43201 | −0.220116 | ||||||||
\(610\) | 4.15839 | 0.168368 | ||||||||
\(611\) | 1.54726 | 0.0625954 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 15.3644 | 0.620560 | 0.310280 | − | 0.950645i | \(-0.399577\pi\) | ||||
0.310280 | + | 0.950645i | \(0.399577\pi\) | |||||||
\(614\) | 20.1040 | 0.811330 | ||||||||
\(615\) | −2.01332 | −0.0811849 | ||||||||
\(616\) | 1.05901 | 0.0426686 | ||||||||
\(617\) | −25.7269 | −1.03573 | −0.517863 | − | 0.855464i | \(-0.673272\pi\) | ||||
−0.517863 | + | 0.855464i | \(0.673272\pi\) | |||||||
\(618\) | 11.3727 | 0.457479 | ||||||||
\(619\) | −2.94720 | −0.118458 | −0.0592290 | − | 0.998244i | \(-0.518864\pi\) | ||||
−0.0592290 | + | 0.998244i | \(0.518864\pi\) | |||||||
\(620\) | 2.71233 | 0.108930 | ||||||||
\(621\) | −8.04763 | −0.322940 | ||||||||
\(622\) | 34.3174 | 1.37600 | ||||||||
\(623\) | 17.5470 | 0.703006 | ||||||||
\(624\) | 0.854102 | 0.0341914 | ||||||||
\(625\) | 13.9744 | 0.558975 | ||||||||
\(626\) | −29.1995 | −1.16705 | ||||||||
\(627\) | 2.68095 | 0.107067 | ||||||||
\(628\) | −18.9964 | −0.758038 | ||||||||
\(629\) | −10.6356 | −0.424070 | ||||||||
\(630\) | 1.15607 | 0.0460591 | ||||||||
\(631\) | 24.5502 | 0.977330 | 0.488665 | − | 0.872472i | \(-0.337484\pi\) | ||||
0.488665 | + | 0.872472i | \(0.337484\pi\) | |||||||
\(632\) | 10.9474 | 0.435465 | ||||||||
\(633\) | 3.34766 | 0.133057 | ||||||||
\(634\) | −12.5378 | −0.497941 | ||||||||
\(635\) | −8.31421 | −0.329939 | ||||||||
\(636\) | 5.11780 | 0.202934 | ||||||||
\(637\) | −4.50597 | −0.178533 | ||||||||
\(638\) | −3.33612 | −0.132078 | ||||||||
\(639\) | −2.49235 | −0.0985960 | ||||||||
\(640\) | −0.880394 | −0.0348006 | ||||||||
\(641\) | −7.98353 | −0.315331 | −0.157665 | − | 0.987493i | \(-0.550397\pi\) | ||||
−0.157665 | + | 0.987493i | \(0.550397\pi\) | |||||||
\(642\) | 10.0131 | 0.395186 | ||||||||
\(643\) | 5.46145 | 0.215379 | 0.107689 | − | 0.994185i | \(-0.465655\pi\) | ||||
0.107689 | + | 0.994185i | \(0.465655\pi\) | |||||||
\(644\) | 10.5676 | 0.416422 | ||||||||
\(645\) | −1.05525 | −0.0415506 | ||||||||
\(646\) | −3.32429 | −0.130793 | ||||||||
\(647\) | −10.1019 | −0.397147 | −0.198573 | − | 0.980086i | \(-0.563631\pi\) | ||||
−0.198573 | + | 0.980086i | \(0.563631\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −0.806473 | −0.0316568 | ||||||||
\(650\) | −3.60850 | −0.141537 | ||||||||
\(651\) | 4.04553 | 0.158557 | ||||||||
\(652\) | 8.85048 | 0.346612 | ||||||||
\(653\) | 5.12597 | 0.200595 | 0.100297 | − | 0.994958i | \(-0.468021\pi\) | ||||
0.100297 | + | 0.994958i | \(0.468021\pi\) | |||||||
\(654\) | 6.08703 | 0.238022 | ||||||||
\(655\) | −0.660415 | −0.0258046 | ||||||||
\(656\) | 2.28684 | 0.0892862 | ||||||||
\(657\) | −3.28175 | −0.128033 | ||||||||
\(658\) | −2.37882 | −0.0927361 | ||||||||
\(659\) | 30.9922 | 1.20729 | 0.603643 | − | 0.797255i | \(-0.293715\pi\) | ||||
0.603643 | + | 0.797255i | \(0.293715\pi\) | |||||||
\(660\) | 0.710014 | 0.0276372 | ||||||||
\(661\) | 2.39792 | 0.0932683 | 0.0466342 | − | 0.998912i | \(-0.485150\pi\) | ||||
0.0466342 | + | 0.998912i | \(0.485150\pi\) | |||||||
\(662\) | 3.30684 | 0.128524 | ||||||||
\(663\) | 0.854102 | 0.0331706 | ||||||||
\(664\) | −17.5576 | −0.681366 | ||||||||
\(665\) | −3.84313 | −0.149030 | ||||||||
\(666\) | −10.6356 | −0.412122 | ||||||||
\(667\) | −33.2905 | −1.28901 | ||||||||
\(668\) | 8.96268 | 0.346777 | ||||||||
\(669\) | −21.7814 | −0.842116 | ||||||||
\(670\) | 5.23231 | 0.202142 | ||||||||
\(671\) | 3.80924 | 0.147054 | ||||||||
\(672\) | −1.31313 | −0.0506552 | ||||||||
\(673\) | 37.5403 | 1.44707 | 0.723535 | − | 0.690288i | \(-0.242516\pi\) | ||||
0.723535 | + | 0.690288i | \(0.242516\pi\) | |||||||
\(674\) | −1.00120 | −0.0385648 | ||||||||
\(675\) | −4.22491 | −0.162617 | ||||||||
\(676\) | −12.2705 | −0.471943 | ||||||||
\(677\) | −22.4298 | −0.862047 | −0.431024 | − | 0.902341i | \(-0.641847\pi\) | ||||
−0.431024 | + | 0.902341i | \(0.641847\pi\) | |||||||
\(678\) | −1.28948 | −0.0495220 | ||||||||
\(679\) | −19.1865 | −0.736312 | ||||||||
\(680\) | −0.880394 | −0.0337616 | ||||||||
\(681\) | 9.58881 | 0.367444 | ||||||||
\(682\) | 2.48460 | 0.0951401 | ||||||||
\(683\) | 6.80437 | 0.260362 | 0.130181 | − | 0.991490i | \(-0.458444\pi\) | ||||
0.130181 | + | 0.991490i | \(0.458444\pi\) | |||||||
\(684\) | −3.32429 | −0.127108 | ||||||||
\(685\) | 7.98513 | 0.305096 | ||||||||
\(686\) | 16.1196 | 0.615449 | ||||||||
\(687\) | 18.5177 | 0.706493 | ||||||||
\(688\) | 1.19862 | 0.0456968 | ||||||||
\(689\) | 4.37112 | 0.166526 | ||||||||
\(690\) | 7.08508 | 0.269724 | ||||||||
\(691\) | 9.95991 | 0.378893 | 0.189446 | − | 0.981891i | \(-0.439331\pi\) | ||||
0.189446 | + | 0.981891i | \(0.439331\pi\) | |||||||
\(692\) | −2.15900 | −0.0820730 | ||||||||
\(693\) | 1.05901 | 0.0402283 | ||||||||
\(694\) | −1.79449 | −0.0681178 | ||||||||
\(695\) | 0.235908 | 0.00894851 | ||||||||
\(696\) | 4.13668 | 0.156800 | ||||||||
\(697\) | 2.28684 | 0.0866203 | ||||||||
\(698\) | 16.4028 | 0.620856 | ||||||||
\(699\) | −9.25957 | −0.350229 | ||||||||
\(700\) | 5.54787 | 0.209690 | ||||||||
\(701\) | 19.1599 | 0.723659 | 0.361829 | − | 0.932244i | \(-0.382152\pi\) | ||||
0.361829 | + | 0.932244i | \(0.382152\pi\) | |||||||
\(702\) | 0.854102 | 0.0322360 | ||||||||
\(703\) | 35.3559 | 1.33347 | ||||||||
\(704\) | −0.806473 | −0.0303951 | ||||||||
\(705\) | −1.59489 | −0.0600669 | ||||||||
\(706\) | −31.3537 | −1.18001 | ||||||||
\(707\) | 21.6113 | 0.812778 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | 34.7234 | 1.30406 | 0.652032 | − | 0.758192i | \(-0.273917\pi\) | ||||
0.652032 | + | 0.758192i | \(0.273917\pi\) | |||||||
\(710\) | 2.19425 | 0.0823489 | ||||||||
\(711\) | 10.9474 | 0.410560 | ||||||||
\(712\) | −13.3627 | −0.500789 | ||||||||
\(713\) | 24.7933 | 0.928516 | ||||||||
\(714\) | −1.31313 | −0.0491428 | ||||||||
\(715\) | 0.606424 | 0.0226790 | ||||||||
\(716\) | −12.8127 | −0.478832 | ||||||||
\(717\) | −7.92592 | −0.295999 | ||||||||
\(718\) | 24.0213 | 0.896468 | ||||||||
\(719\) | −1.24564 | −0.0464544 | −0.0232272 | − | 0.999730i | \(-0.507394\pi\) | ||||
−0.0232272 | + | 0.999730i | \(0.507394\pi\) | |||||||
\(720\) | −0.880394 | −0.0328103 | ||||||||
\(721\) | −14.9339 | −0.556169 | ||||||||
\(722\) | −7.94907 | −0.295834 | ||||||||
\(723\) | 1.38295 | 0.0514325 | ||||||||
\(724\) | −1.96862 | −0.0731632 | ||||||||
\(725\) | −17.4771 | −0.649083 | ||||||||
\(726\) | −10.3496 | −0.384110 | ||||||||
\(727\) | 0.00913483 | 0.000338792 0 | 0.000169396 | − | 1.00000i | \(-0.499946\pi\) | ||||
0.000169396 | 1.00000i | \(0.499946\pi\) | ||||||||
\(728\) | −1.12155 | −0.0415674 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.88924 | 0.106935 | ||||||||
\(731\) | 1.19862 | 0.0443324 | ||||||||
\(732\) | −4.72333 | −0.174579 | ||||||||
\(733\) | 20.3541 | 0.751797 | 0.375899 | − | 0.926661i | \(-0.377334\pi\) | ||||
0.375899 | + | 0.926661i | \(0.377334\pi\) | |||||||
\(734\) | −17.0572 | −0.629593 | ||||||||
\(735\) | 4.64468 | 0.171321 | ||||||||
\(736\) | −8.04763 | −0.296640 | ||||||||
\(737\) | 4.79299 | 0.176552 | ||||||||
\(738\) | 2.28684 | 0.0841798 | ||||||||
\(739\) | −10.7639 | −0.395956 | −0.197978 | − | 0.980206i | \(-0.563438\pi\) | ||||
−0.197978 | + | 0.980206i | \(0.563438\pi\) | |||||||
\(740\) | 9.36353 | 0.344210 | ||||||||
\(741\) | −2.83929 | −0.104304 | ||||||||
\(742\) | −6.72035 | −0.246712 | ||||||||
\(743\) | 1.17610 | 0.0431470 | 0.0215735 | − | 0.999767i | \(-0.493132\pi\) | ||||
0.0215735 | + | 0.999767i | \(0.493132\pi\) | |||||||
\(744\) | −3.08082 | −0.112948 | ||||||||
\(745\) | 8.73780 | 0.320128 | ||||||||
\(746\) | 14.1389 | 0.517663 | ||||||||
\(747\) | −17.5576 | −0.642398 | ||||||||
\(748\) | −0.806473 | −0.0294876 | ||||||||
\(749\) | −13.1485 | −0.480437 | ||||||||
\(750\) | 8.12155 | 0.296557 | ||||||||
\(751\) | −4.00320 | −0.146079 | −0.0730393 | − | 0.997329i | \(-0.523270\pi\) | ||||
−0.0730393 | + | 0.997329i | \(0.523270\pi\) | |||||||
\(752\) | 1.81156 | 0.0660608 | ||||||||
\(753\) | −2.68604 | −0.0978848 | ||||||||
\(754\) | 3.53315 | 0.128670 | ||||||||
\(755\) | −1.44416 | −0.0525583 | ||||||||
\(756\) | −1.31313 | −0.0477582 | ||||||||
\(757\) | 17.2749 | 0.627868 | 0.313934 | − | 0.949445i | \(-0.398353\pi\) | ||||
0.313934 | + | 0.949445i | \(0.398353\pi\) | |||||||
\(758\) | 10.6967 | 0.388523 | ||||||||
\(759\) | 6.49019 | 0.235579 | ||||||||
\(760\) | 2.92669 | 0.106162 | ||||||||
\(761\) | 45.7027 | 1.65672 | 0.828361 | − | 0.560195i | \(-0.189274\pi\) | ||||
0.828361 | + | 0.560195i | \(0.189274\pi\) | |||||||
\(762\) | 9.44374 | 0.342111 | ||||||||
\(763\) | −7.99308 | −0.289369 | ||||||||
\(764\) | −4.28500 | −0.155026 | ||||||||
\(765\) | −0.880394 | −0.0318307 | ||||||||
\(766\) | 21.9782 | 0.794104 | ||||||||
\(767\) | 0.854102 | 0.0308398 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 37.0407 | 1.33572 | 0.667861 | − | 0.744286i | \(-0.267210\pi\) | ||||
0.667861 | + | 0.744286i | \(0.267210\pi\) | |||||||
\(770\) | −0.932343 | −0.0335993 | ||||||||
\(771\) | −13.7337 | −0.494608 | ||||||||
\(772\) | 6.00607 | 0.216163 | ||||||||
\(773\) | −2.82968 | −0.101776 | −0.0508882 | − | 0.998704i | \(-0.516205\pi\) | ||||
−0.0508882 | + | 0.998704i | \(0.516205\pi\) | |||||||
\(774\) | 1.19862 | 0.0430833 | ||||||||
\(775\) | 13.0162 | 0.467555 | ||||||||
\(776\) | 14.6113 | 0.524514 | ||||||||
\(777\) | 13.9660 | 0.501027 | ||||||||
\(778\) | 33.1693 | 1.18918 | ||||||||
\(779\) | −7.60214 | −0.272375 | ||||||||
\(780\) | −0.751946 | −0.0269240 | ||||||||
\(781\) | 2.01002 | 0.0719241 | ||||||||
\(782\) | −8.04763 | −0.287783 | ||||||||
\(783\) | 4.13668 | 0.147833 | ||||||||
\(784\) | −5.27568 | −0.188417 | ||||||||
\(785\) | 16.7243 | 0.596916 | ||||||||
\(786\) | 0.750136 | 0.0267565 | ||||||||
\(787\) | −20.5531 | −0.732637 | −0.366319 | − | 0.930489i | \(-0.619382\pi\) | ||||
−0.366319 | + | 0.930489i | \(0.619382\pi\) | |||||||
\(788\) | −9.64678 | −0.343652 | ||||||||
\(789\) | −18.0752 | −0.643493 | ||||||||
\(790\) | −9.63804 | −0.342906 | ||||||||
\(791\) | 1.69325 | 0.0602052 | ||||||||
\(792\) | −0.806473 | −0.0286568 | ||||||||
\(793\) | −4.03421 | −0.143259 | ||||||||
\(794\) | 31.3458 | 1.11242 | ||||||||
\(795\) | −4.50568 | −0.159800 | ||||||||
\(796\) | 9.95056 | 0.352688 | ||||||||
\(797\) | −10.2033 | −0.361420 | −0.180710 | − | 0.983536i | \(-0.557840\pi\) | ||||
−0.180710 | + | 0.983536i | \(0.557840\pi\) | |||||||
\(798\) | 4.36524 | 0.154528 | ||||||||
\(799\) | 1.81156 | 0.0640884 | ||||||||
\(800\) | −4.22491 | −0.149373 | ||||||||
\(801\) | −13.3627 | −0.472148 | ||||||||
\(802\) | −1.06479 | −0.0375989 | ||||||||
\(803\) | 2.64665 | 0.0933981 | ||||||||
\(804\) | −5.94315 | −0.209599 | ||||||||
\(805\) | −9.30366 | −0.327911 | ||||||||
\(806\) | −2.63133 | −0.0926848 | ||||||||
\(807\) | −23.2846 | −0.819655 | ||||||||
\(808\) | −16.4578 | −0.578984 | ||||||||
\(809\) | −27.4509 | −0.965122 | −0.482561 | − | 0.875862i | \(-0.660293\pi\) | ||||
−0.482561 | + | 0.875862i | \(0.660293\pi\) | |||||||
\(810\) | −0.880394 | −0.0309339 | ||||||||
\(811\) | −22.0488 | −0.774237 | −0.387119 | − | 0.922030i | \(-0.626530\pi\) | ||||
−0.387119 | + | 0.922030i | \(0.626530\pi\) | |||||||
\(812\) | −5.43201 | −0.190626 | ||||||||
\(813\) | −6.71428 | −0.235480 | ||||||||
\(814\) | 8.57734 | 0.300636 | ||||||||
\(815\) | −7.79191 | −0.272939 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −3.98455 | −0.139402 | ||||||||
\(818\) | −17.8012 | −0.622404 | ||||||||
\(819\) | −1.12155 | −0.0391901 | ||||||||
\(820\) | −2.01332 | −0.0703082 | ||||||||
\(821\) | −15.1607 | −0.529110 | −0.264555 | − | 0.964371i | \(-0.585225\pi\) | ||||
−0.264555 | + | 0.964371i | \(0.585225\pi\) | |||||||
\(822\) | −9.06995 | −0.316351 | ||||||||
\(823\) | −39.2010 | −1.36646 | −0.683231 | − | 0.730203i | \(-0.739426\pi\) | ||||
−0.683231 | + | 0.730203i | \(0.739426\pi\) | |||||||
\(824\) | 11.3727 | 0.396188 | ||||||||
\(825\) | 3.40727 | 0.118626 | ||||||||
\(826\) | −1.31313 | −0.0456898 | ||||||||
\(827\) | 22.0141 | 0.765504 | 0.382752 | − | 0.923851i | \(-0.374976\pi\) | ||||
0.382752 | + | 0.923851i | \(0.374976\pi\) | |||||||
\(828\) | −8.04763 | −0.279674 | ||||||||
\(829\) | −34.8762 | −1.21130 | −0.605651 | − | 0.795731i | \(-0.707087\pi\) | ||||
−0.605651 | + | 0.795731i | \(0.707087\pi\) | |||||||
\(830\) | 15.4576 | 0.536540 | ||||||||
\(831\) | −24.3896 | −0.846067 | ||||||||
\(832\) | 0.854102 | 0.0296107 | ||||||||
\(833\) | −5.27568 | −0.182792 | ||||||||
\(834\) | −0.267958 | −0.00927862 | ||||||||
\(835\) | −7.89069 | −0.273069 | ||||||||
\(836\) | 2.68095 | 0.0927227 | ||||||||
\(837\) | −3.08082 | −0.106489 | ||||||||
\(838\) | −27.8247 | −0.961188 | ||||||||
\(839\) | 25.3696 | 0.875855 | 0.437928 | − | 0.899010i | \(-0.355713\pi\) | ||||
0.437928 | + | 0.899010i | \(0.355713\pi\) | |||||||
\(840\) | 1.15607 | 0.0398884 | ||||||||
\(841\) | −11.8879 | −0.409927 | ||||||||
\(842\) | 27.2478 | 0.939023 | ||||||||
\(843\) | 11.7140 | 0.403452 | ||||||||
\(844\) | 3.34766 | 0.115231 | ||||||||
\(845\) | 10.8029 | 0.371630 | ||||||||
\(846\) | 1.81156 | 0.0622828 | ||||||||
\(847\) | 13.5904 | 0.466972 | ||||||||
\(848\) | 5.11780 | 0.175746 | ||||||||
\(849\) | 14.7340 | 0.505670 | ||||||||
\(850\) | −4.22491 | −0.144913 | ||||||||
\(851\) | 85.5915 | 2.93404 | ||||||||
\(852\) | −2.49235 | −0.0853867 | ||||||||
\(853\) | 54.2940 | 1.85899 | 0.929496 | − | 0.368833i | \(-0.120243\pi\) | ||||
0.929496 | + | 0.368833i | \(0.120243\pi\) | |||||||
\(854\) | 6.20237 | 0.212241 | ||||||||
\(855\) | 2.92669 | 0.100091 | ||||||||
\(856\) | 10.0131 | 0.342241 | ||||||||
\(857\) | −48.2525 | −1.64827 | −0.824137 | − | 0.566391i | \(-0.808339\pi\) | ||||
−0.824137 | + | 0.566391i | \(0.808339\pi\) | |||||||
\(858\) | −0.688810 | −0.0235156 | ||||||||
\(859\) | 20.1892 | 0.688846 | 0.344423 | − | 0.938815i | \(-0.388075\pi\) | ||||
0.344423 | + | 0.938815i | \(0.388075\pi\) | |||||||
\(860\) | −1.05525 | −0.0359838 | ||||||||
\(861\) | −3.00293 | −0.102340 | ||||||||
\(862\) | 3.75967 | 0.128055 | ||||||||
\(863\) | 18.2720 | 0.621987 | 0.310994 | − | 0.950412i | \(-0.399338\pi\) | ||||
0.310994 | + | 0.950412i | \(0.399338\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 1.90077 | 0.0646282 | ||||||||
\(866\) | 27.9332 | 0.949210 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 4.04553 | 0.137314 | ||||||||
\(869\) | −8.82879 | −0.299496 | ||||||||
\(870\) | −3.64191 | −0.123472 | ||||||||
\(871\) | −5.07606 | −0.171996 | ||||||||
\(872\) | 6.08703 | 0.206133 | ||||||||
\(873\) | 14.6113 | 0.494517 | ||||||||
\(874\) | 26.7527 | 0.904923 | ||||||||
\(875\) | −10.6647 | −0.360532 | ||||||||
\(876\) | −3.28175 | −0.110880 | ||||||||
\(877\) | −46.7999 | −1.58032 | −0.790160 | − | 0.612900i | \(-0.790003\pi\) | ||||
−0.790160 | + | 0.612900i | \(0.790003\pi\) | |||||||
\(878\) | −2.91484 | −0.0983709 | ||||||||
\(879\) | 12.4874 | 0.421190 | ||||||||
\(880\) | 0.710014 | 0.0239346 | ||||||||
\(881\) | 31.0324 | 1.04551 | 0.522754 | − | 0.852484i | \(-0.324905\pi\) | ||||
0.522754 | + | 0.852484i | \(0.324905\pi\) | |||||||
\(882\) | −5.27568 | −0.177641 | ||||||||
\(883\) | −44.9979 | −1.51430 | −0.757150 | − | 0.653241i | \(-0.773409\pi\) | ||||
−0.757150 | + | 0.653241i | \(0.773409\pi\) | |||||||
\(884\) | 0.854102 | 0.0287266 | ||||||||
\(885\) | −0.880394 | −0.0295941 | ||||||||
\(886\) | 7.62100 | 0.256032 | ||||||||
\(887\) | 35.3204 | 1.18594 | 0.592971 | − | 0.805224i | \(-0.297955\pi\) | ||||
0.592971 | + | 0.805224i | \(0.297955\pi\) | |||||||
\(888\) | −10.6356 | −0.356908 | ||||||||
\(889\) | −12.4009 | −0.415913 | ||||||||
\(890\) | 11.7644 | 0.394345 | ||||||||
\(891\) | −0.806473 | −0.0270179 | ||||||||
\(892\) | −21.7814 | −0.729294 | ||||||||
\(893\) | −6.02216 | −0.201524 | ||||||||
\(894\) | −9.92488 | −0.331938 | ||||||||
\(895\) | 11.2802 | 0.377056 | ||||||||
\(896\) | −1.31313 | −0.0438687 | ||||||||
\(897\) | −6.87350 | −0.229499 | ||||||||
\(898\) | 23.7416 | 0.792266 | ||||||||
\(899\) | −12.7444 | −0.425048 | ||||||||
\(900\) | −4.22491 | −0.140830 | ||||||||
\(901\) | 5.11780 | 0.170499 | ||||||||
\(902\) | −1.84428 | −0.0614077 | ||||||||
\(903\) | −1.57394 | −0.0523775 | ||||||||
\(904\) | −1.28948 | −0.0428873 | ||||||||
\(905\) | 1.73316 | 0.0576122 | ||||||||
\(906\) | 1.64036 | 0.0544972 | ||||||||
\(907\) | 25.4875 | 0.846299 | 0.423149 | − | 0.906060i | \(-0.360925\pi\) | ||||
0.423149 | + | 0.906060i | \(0.360925\pi\) | |||||||
\(908\) | 9.58881 | 0.318216 | ||||||||
\(909\) | −16.4578 | −0.545872 | ||||||||
\(910\) | 0.987405 | 0.0327322 | ||||||||
\(911\) | −53.4244 | −1.77003 | −0.885015 | − | 0.465562i | \(-0.845852\pi\) | ||||
−0.885015 | + | 0.465562i | \(0.845852\pi\) | |||||||
\(912\) | −3.32429 | −0.110078 | ||||||||
\(913\) | 14.1597 | 0.468618 | ||||||||
\(914\) | −16.1234 | −0.533313 | ||||||||
\(915\) | 4.15839 | 0.137472 | ||||||||
\(916\) | 18.5177 | 0.611841 | ||||||||
\(917\) | −0.985029 | −0.0325285 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 41.4575 | 1.36756 | 0.683778 | − | 0.729690i | \(-0.260336\pi\) | ||||
0.683778 | + | 0.729690i | \(0.260336\pi\) | |||||||
\(920\) | 7.08508 | 0.233588 | ||||||||
\(921\) | 20.1040 | 0.662448 | ||||||||
\(922\) | 24.0954 | 0.793539 | ||||||||
\(923\) | −2.12873 | −0.0700678 | ||||||||
\(924\) | 1.05901 | 0.0348388 | ||||||||
\(925\) | 44.9345 | 1.47744 | ||||||||
\(926\) | −8.23296 | −0.270552 | ||||||||
\(927\) | 11.3727 | 0.373530 | ||||||||
\(928\) | 4.13668 | 0.135793 | ||||||||
\(929\) | −15.1093 | −0.495720 | −0.247860 | − | 0.968796i | \(-0.579727\pi\) | ||||
−0.247860 | + | 0.968796i | \(0.579727\pi\) | |||||||
\(930\) | 2.71233 | 0.0889409 | ||||||||
\(931\) | 17.5379 | 0.574782 | ||||||||
\(932\) | −9.25957 | −0.303307 | ||||||||
\(933\) | 34.3174 | 1.12350 | ||||||||
\(934\) | −17.6501 | −0.577528 | ||||||||
\(935\) | 0.710014 | 0.0232199 | ||||||||
\(936\) | 0.854102 | 0.0279172 | ||||||||
\(937\) | 12.2498 | 0.400183 | 0.200091 | − | 0.979777i | \(-0.435876\pi\) | ||||
0.200091 | + | 0.979777i | \(0.435876\pi\) | |||||||
\(938\) | 7.80415 | 0.254815 | ||||||||
\(939\) | −29.1995 | −0.952889 | ||||||||
\(940\) | −1.59489 | −0.0520195 | ||||||||
\(941\) | −13.0741 | −0.426205 | −0.213102 | − | 0.977030i | \(-0.568357\pi\) | ||||
−0.213102 | + | 0.977030i | \(0.568357\pi\) | |||||||
\(942\) | −18.9964 | −0.618936 | ||||||||
\(943\) | −18.4037 | −0.599305 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | 1.15607 | 0.0376071 | ||||||||
\(946\) | −0.966651 | −0.0314285 | ||||||||
\(947\) | 1.10440 | 0.0358881 | 0.0179441 | − | 0.999839i | \(-0.494288\pi\) | ||||
0.0179441 | + | 0.999839i | \(0.494288\pi\) | |||||||
\(948\) | 10.9474 | 0.355556 | ||||||||
\(949\) | −2.80295 | −0.0909877 | ||||||||
\(950\) | 14.0448 | 0.455675 | ||||||||
\(951\) | −12.5378 | −0.406567 | ||||||||
\(952\) | −1.31313 | −0.0425589 | ||||||||
\(953\) | −57.2641 | −1.85497 | −0.927484 | − | 0.373863i | \(-0.878033\pi\) | ||||
−0.927484 | + | 0.373863i | \(0.878033\pi\) | |||||||
\(954\) | 5.11780 | 0.165695 | ||||||||
\(955\) | 3.77248 | 0.122075 | ||||||||
\(956\) | −7.92592 | −0.256343 | ||||||||
\(957\) | −3.33612 | −0.107841 | ||||||||
\(958\) | 28.9556 | 0.935514 | ||||||||
\(959\) | 11.9101 | 0.384596 | ||||||||
\(960\) | −0.880394 | −0.0284146 | ||||||||
\(961\) | −21.5086 | −0.693824 | ||||||||
\(962\) | −9.08390 | −0.292877 | ||||||||
\(963\) | 10.0131 | 0.322668 | ||||||||
\(964\) | 1.38295 | 0.0445418 | ||||||||
\(965\) | −5.28771 | −0.170217 | ||||||||
\(966\) | 10.5676 | 0.340007 | ||||||||
\(967\) | 23.6296 | 0.759878 | 0.379939 | − | 0.925012i | \(-0.375945\pi\) | ||||
0.379939 | + | 0.925012i | \(0.375945\pi\) | |||||||
\(968\) | −10.3496 | −0.332649 | ||||||||
\(969\) | −3.32429 | −0.106792 | ||||||||
\(970\) | −12.8637 | −0.413028 | ||||||||
\(971\) | −17.7369 | −0.569203 | −0.284601 | − | 0.958646i | \(-0.591861\pi\) | ||||
−0.284601 | + | 0.958646i | \(0.591861\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0.351864 | 0.0112803 | ||||||||
\(974\) | 12.0378 | 0.385715 | ||||||||
\(975\) | −3.60850 | −0.115565 | ||||||||
\(976\) | −4.72333 | −0.151190 | ||||||||
\(977\) | −41.4950 | −1.32754 | −0.663772 | − | 0.747935i | \(-0.731045\pi\) | ||||
−0.663772 | + | 0.747935i | \(0.731045\pi\) | |||||||
\(978\) | 8.85048 | 0.283007 | ||||||||
\(979\) | 10.7767 | 0.344424 | ||||||||
\(980\) | 4.64468 | 0.148369 | ||||||||
\(981\) | 6.08703 | 0.194344 | ||||||||
\(982\) | −1.57084 | −0.0501274 | ||||||||
\(983\) | 16.4299 | 0.524031 | 0.262016 | − | 0.965064i | \(-0.415613\pi\) | ||||
0.262016 | + | 0.965064i | \(0.415613\pi\) | |||||||
\(984\) | 2.28684 | 0.0729019 | ||||||||
\(985\) | 8.49296 | 0.270608 | ||||||||
\(986\) | 4.13668 | 0.131739 | ||||||||
\(987\) | −2.37882 | −0.0757187 | ||||||||
\(988\) | −2.83929 | −0.0903297 | ||||||||
\(989\) | −9.64601 | −0.306725 | ||||||||
\(990\) | 0.710014 | 0.0225657 | ||||||||
\(991\) | −38.0071 | −1.20733 | −0.603667 | − | 0.797236i | \(-0.706294\pi\) | ||||
−0.603667 | + | 0.797236i | \(0.706294\pi\) | |||||||
\(992\) | −3.08082 | −0.0978161 | ||||||||
\(993\) | 3.30684 | 0.104940 | ||||||||
\(994\) | 3.27279 | 0.103807 | ||||||||
\(995\) | −8.76041 | −0.277724 | ||||||||
\(996\) | −17.5576 | −0.556333 | ||||||||
\(997\) | −0.443231 | −0.0140373 | −0.00701864 | − | 0.999975i | \(-0.502234\pi\) | ||||
−0.00701864 | + | 0.999975i | \(0.502234\pi\) | |||||||
\(998\) | 10.5078 | 0.332618 | ||||||||
\(999\) | −10.6356 | −0.336496 |
(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 | 6018.2.a.o.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.o.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial |