Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 | ||||||||
\(3\) | 1.34513 | 0.776613 | 0.388307 | − | 0.921530i | \(-0.373060\pi\) | ||||
0.388307 | + | 0.921530i | \(0.373060\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.31517 | −1.03537 | −0.517687 | − | 0.855570i | \(-0.673207\pi\) | ||||
−0.517687 | + | 0.855570i | \(0.673207\pi\) | |||||||
\(6\) | 1.34513 | 0.549149 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.19062 | −0.396872 | ||||||||
\(10\) | −2.31517 | −0.732121 | ||||||||
\(11\) | 1.82099 | 0.549050 | 0.274525 | − | 0.961580i | \(-0.411479\pi\) | ||||
0.274525 | + | 0.961580i | \(0.411479\pi\) | |||||||
\(12\) | 1.34513 | 0.388307 | ||||||||
\(13\) | 1.02705 | 0.284853 | 0.142426 | − | 0.989805i | \(-0.454510\pi\) | ||||
0.142426 | + | 0.989805i | \(0.454510\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −3.11421 | −0.804086 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.30346 | −1.52881 | −0.764407 | − | 0.644734i | \(-0.776968\pi\) | ||||
−0.764407 | + | 0.644734i | \(0.776968\pi\) | |||||||
\(18\) | −1.19062 | −0.280631 | ||||||||
\(19\) | 3.88262 | 0.890735 | 0.445367 | − | 0.895348i | \(-0.353073\pi\) | ||||
0.445367 | + | 0.895348i | \(0.353073\pi\) | |||||||
\(20\) | −2.31517 | −0.517687 | ||||||||
\(21\) | 1.34513 | 0.293532 | ||||||||
\(22\) | 1.82099 | 0.388237 | ||||||||
\(23\) | −7.18335 | −1.49783 | −0.748916 | − | 0.662666i | \(-0.769425\pi\) | ||||
−0.748916 | + | 0.662666i | \(0.769425\pi\) | |||||||
\(24\) | 1.34513 | 0.274574 | ||||||||
\(25\) | 0.360007 | 0.0720014 | ||||||||
\(26\) | 1.02705 | 0.201421 | ||||||||
\(27\) | −5.63694 | −1.08483 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −4.35921 | −0.809485 | −0.404742 | − | 0.914431i | \(-0.632639\pi\) | ||||
−0.404742 | + | 0.914431i | \(0.632639\pi\) | |||||||
\(30\) | −3.11421 | −0.568575 | ||||||||
\(31\) | 0.296499 | 0.0532528 | 0.0266264 | − | 0.999645i | \(-0.491524\pi\) | ||||
0.0266264 | + | 0.999645i | \(0.491524\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.44948 | 0.426399 | ||||||||
\(34\) | −6.30346 | −1.08103 | ||||||||
\(35\) | −2.31517 | −0.391335 | ||||||||
\(36\) | −1.19062 | −0.198436 | ||||||||
\(37\) | −4.26392 | −0.700985 | −0.350492 | − | 0.936566i | \(-0.613986\pi\) | ||||
−0.350492 | + | 0.936566i | \(0.613986\pi\) | |||||||
\(38\) | 3.88262 | 0.629844 | ||||||||
\(39\) | 1.38152 | 0.221220 | ||||||||
\(40\) | −2.31517 | −0.366060 | ||||||||
\(41\) | −5.48050 | −0.855910 | −0.427955 | − | 0.903800i | \(-0.640766\pi\) | ||||
−0.427955 | + | 0.903800i | \(0.640766\pi\) | |||||||
\(42\) | 1.34513 | 0.207559 | ||||||||
\(43\) | 11.1174 | 1.69538 | 0.847692 | − | 0.530489i | \(-0.177992\pi\) | ||||
0.847692 | + | 0.530489i | \(0.177992\pi\) | |||||||
\(44\) | 1.82099 | 0.274525 | ||||||||
\(45\) | 2.75648 | 0.410911 | ||||||||
\(46\) | −7.18335 | −1.05913 | ||||||||
\(47\) | −0.609939 | −0.0889687 | −0.0444844 | − | 0.999010i | \(-0.514164\pi\) | ||||
−0.0444844 | + | 0.999010i | \(0.514164\pi\) | |||||||
\(48\) | 1.34513 | 0.194153 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.360007 | 0.0509127 | ||||||||
\(51\) | −8.47900 | −1.18730 | ||||||||
\(52\) | 1.02705 | 0.142426 | ||||||||
\(53\) | −9.07701 | −1.24682 | −0.623412 | − | 0.781894i | \(-0.714254\pi\) | ||||
−0.623412 | + | 0.781894i | \(0.714254\pi\) | |||||||
\(54\) | −5.63694 | −0.767090 | ||||||||
\(55\) | −4.21590 | −0.568472 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 5.22265 | 0.691756 | ||||||||
\(58\) | −4.35921 | −0.572392 | ||||||||
\(59\) | −9.71171 | −1.26436 | −0.632178 | − | 0.774823i | \(-0.717839\pi\) | ||||
−0.632178 | + | 0.774823i | \(0.717839\pi\) | |||||||
\(60\) | −3.11421 | −0.402043 | ||||||||
\(61\) | 13.3714 | 1.71203 | 0.856013 | − | 0.516954i | \(-0.172934\pi\) | ||||
0.856013 | + | 0.516954i | \(0.172934\pi\) | |||||||
\(62\) | 0.296499 | 0.0376554 | ||||||||
\(63\) | −1.19062 | −0.150003 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.37780 | −0.294929 | ||||||||
\(66\) | 2.44948 | 0.301510 | ||||||||
\(67\) | −5.27796 | −0.644805 | −0.322402 | − | 0.946603i | \(-0.604490\pi\) | ||||
−0.322402 | + | 0.946603i | \(0.604490\pi\) | |||||||
\(68\) | −6.30346 | −0.764407 | ||||||||
\(69\) | −9.66256 | −1.16324 | ||||||||
\(70\) | −2.31517 | −0.276716 | ||||||||
\(71\) | −2.69207 | −0.319490 | −0.159745 | − | 0.987158i | \(-0.551067\pi\) | ||||
−0.159745 | + | 0.987158i | \(0.551067\pi\) | |||||||
\(72\) | −1.19062 | −0.140315 | ||||||||
\(73\) | 1.73088 | 0.202584 | 0.101292 | − | 0.994857i | \(-0.467702\pi\) | ||||
0.101292 | + | 0.994857i | \(0.467702\pi\) | |||||||
\(74\) | −4.26392 | −0.495671 | ||||||||
\(75\) | 0.484257 | 0.0559172 | ||||||||
\(76\) | 3.88262 | 0.445367 | ||||||||
\(77\) | 1.82099 | 0.207521 | ||||||||
\(78\) | 1.38152 | 0.156426 | ||||||||
\(79\) | −2.85527 | −0.321243 | −0.160621 | − | 0.987016i | \(-0.551350\pi\) | ||||
−0.160621 | + | 0.987016i | \(0.551350\pi\) | |||||||
\(80\) | −2.31517 | −0.258844 | ||||||||
\(81\) | −4.01059 | −0.445621 | ||||||||
\(82\) | −5.48050 | −0.605220 | ||||||||
\(83\) | −0.509380 | −0.0559117 | −0.0279559 | − | 0.999609i | \(-0.508900\pi\) | ||||
−0.0279559 | + | 0.999609i | \(0.508900\pi\) | |||||||
\(84\) | 1.34513 | 0.146766 | ||||||||
\(85\) | 14.5936 | 1.58290 | ||||||||
\(86\) | 11.1174 | 1.19882 | ||||||||
\(87\) | −5.86372 | −0.628657 | ||||||||
\(88\) | 1.82099 | 0.194118 | ||||||||
\(89\) | −5.16029 | −0.546989 | −0.273495 | − | 0.961874i | \(-0.588180\pi\) | ||||
−0.273495 | + | 0.961874i | \(0.588180\pi\) | |||||||
\(90\) | 2.75648 | 0.290558 | ||||||||
\(91\) | 1.02705 | 0.107664 | ||||||||
\(92\) | −7.18335 | −0.748916 | ||||||||
\(93\) | 0.398831 | 0.0413568 | ||||||||
\(94\) | −0.609939 | −0.0629104 | ||||||||
\(95\) | −8.98893 | −0.922244 | ||||||||
\(96\) | 1.34513 | 0.137287 | ||||||||
\(97\) | −13.9570 | −1.41711 | −0.708557 | − | 0.705653i | \(-0.750654\pi\) | ||||
−0.708557 | + | 0.705653i | \(0.750654\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −2.16810 | −0.217902 | ||||||||
\(100\) | 0.360007 | 0.0360007 | ||||||||
\(101\) | −2.82966 | −0.281562 | −0.140781 | − | 0.990041i | \(-0.544961\pi\) | ||||
−0.140781 | + | 0.990041i | \(0.544961\pi\) | |||||||
\(102\) | −8.47900 | −0.839546 | ||||||||
\(103\) | 7.19060 | 0.708511 | 0.354255 | − | 0.935149i | \(-0.384734\pi\) | ||||
0.354255 | + | 0.935149i | \(0.384734\pi\) | |||||||
\(104\) | 1.02705 | 0.100711 | ||||||||
\(105\) | −3.11421 | −0.303916 | ||||||||
\(106\) | −9.07701 | −0.881637 | ||||||||
\(107\) | 7.35379 | 0.710918 | 0.355459 | − | 0.934692i | \(-0.384325\pi\) | ||||
0.355459 | + | 0.934692i | \(0.384325\pi\) | |||||||
\(108\) | −5.63694 | −0.542415 | ||||||||
\(109\) | 15.1216 | 1.44839 | 0.724193 | − | 0.689597i | \(-0.242212\pi\) | ||||
0.724193 | + | 0.689597i | \(0.242212\pi\) | |||||||
\(110\) | −4.21590 | −0.401971 | ||||||||
\(111\) | −5.73555 | −0.544394 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −11.0889 | −1.04316 | −0.521579 | − | 0.853203i | \(-0.674657\pi\) | ||||
−0.521579 | + | 0.853203i | \(0.674657\pi\) | |||||||
\(114\) | 5.22265 | 0.489146 | ||||||||
\(115\) | 16.6307 | 1.55082 | ||||||||
\(116\) | −4.35921 | −0.404742 | ||||||||
\(117\) | −1.22282 | −0.113050 | ||||||||
\(118\) | −9.71171 | −0.894035 | ||||||||
\(119\) | −6.30346 | −0.577837 | ||||||||
\(120\) | −3.11421 | −0.284287 | ||||||||
\(121\) | −7.68399 | −0.698544 | ||||||||
\(122\) | 13.3714 | 1.21059 | ||||||||
\(123\) | −7.37200 | −0.664711 | ||||||||
\(124\) | 0.296499 | 0.0266264 | ||||||||
\(125\) | 10.7424 | 0.960827 | ||||||||
\(126\) | −1.19062 | −0.106068 | ||||||||
\(127\) | −11.4104 | −1.01251 | −0.506254 | − | 0.862384i | \(-0.668970\pi\) | ||||
−0.506254 | + | 0.862384i | \(0.668970\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 14.9544 | 1.31666 | ||||||||
\(130\) | −2.37780 | −0.208547 | ||||||||
\(131\) | −7.65248 | −0.668600 | −0.334300 | − | 0.942467i | \(-0.608500\pi\) | ||||
−0.334300 | + | 0.942467i | \(0.608500\pi\) | |||||||
\(132\) | 2.44948 | 0.213200 | ||||||||
\(133\) | 3.88262 | 0.336666 | ||||||||
\(134\) | −5.27796 | −0.455946 | ||||||||
\(135\) | 13.0505 | 1.12321 | ||||||||
\(136\) | −6.30346 | −0.540517 | ||||||||
\(137\) | −1.38279 | −0.118139 | −0.0590697 | − | 0.998254i | \(-0.518813\pi\) | ||||
−0.0590697 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(138\) | −9.66256 | −0.822532 | ||||||||
\(139\) | 6.48252 | 0.549840 | 0.274920 | − | 0.961467i | \(-0.411349\pi\) | ||||
0.274920 | + | 0.961467i | \(0.411349\pi\) | |||||||
\(140\) | −2.31517 | −0.195667 | ||||||||
\(141\) | −0.820450 | −0.0690943 | ||||||||
\(142\) | −2.69207 | −0.225914 | ||||||||
\(143\) | 1.87025 | 0.156398 | ||||||||
\(144\) | −1.19062 | −0.0992179 | ||||||||
\(145\) | 10.0923 | 0.838120 | ||||||||
\(146\) | 1.73088 | 0.143248 | ||||||||
\(147\) | 1.34513 | 0.110945 | ||||||||
\(148\) | −4.26392 | −0.350492 | ||||||||
\(149\) | 1.57774 | 0.129253 | 0.0646267 | − | 0.997910i | \(-0.479414\pi\) | ||||
0.0646267 | + | 0.997910i | \(0.479414\pi\) | |||||||
\(150\) | 0.484257 | 0.0395394 | ||||||||
\(151\) | −11.1141 | −0.904455 | −0.452228 | − | 0.891903i | \(-0.649371\pi\) | ||||
−0.452228 | + | 0.891903i | \(0.649371\pi\) | |||||||
\(152\) | 3.88262 | 0.314922 | ||||||||
\(153\) | 7.50500 | 0.606743 | ||||||||
\(154\) | 1.82099 | 0.146740 | ||||||||
\(155\) | −0.686445 | −0.0551366 | ||||||||
\(156\) | 1.38152 | 0.110610 | ||||||||
\(157\) | 4.42246 | 0.352951 | 0.176475 | − | 0.984305i | \(-0.443530\pi\) | ||||
0.176475 | + | 0.984305i | \(0.443530\pi\) | |||||||
\(158\) | −2.85527 | −0.227153 | ||||||||
\(159\) | −12.2098 | −0.968299 | ||||||||
\(160\) | −2.31517 | −0.183030 | ||||||||
\(161\) | −7.18335 | −0.566127 | ||||||||
\(162\) | −4.01059 | −0.315102 | ||||||||
\(163\) | 4.51935 | 0.353983 | 0.176991 | − | 0.984212i | \(-0.443364\pi\) | ||||
0.176991 | + | 0.984212i | \(0.443364\pi\) | |||||||
\(164\) | −5.48050 | −0.427955 | ||||||||
\(165\) | −5.67095 | −0.441483 | ||||||||
\(166\) | −0.509380 | −0.0395356 | ||||||||
\(167\) | −8.47745 | −0.656004 | −0.328002 | − | 0.944677i | \(-0.606375\pi\) | ||||
−0.328002 | + | 0.944677i | \(0.606375\pi\) | |||||||
\(168\) | 1.34513 | 0.103779 | ||||||||
\(169\) | −11.9452 | −0.918859 | ||||||||
\(170\) | 14.5936 | 1.11928 | ||||||||
\(171\) | −4.62271 | −0.353507 | ||||||||
\(172\) | 11.1174 | 0.847692 | ||||||||
\(173\) | 2.07783 | 0.157974 | 0.0789872 | − | 0.996876i | \(-0.474831\pi\) | ||||
0.0789872 | + | 0.996876i | \(0.474831\pi\) | |||||||
\(174\) | −5.86372 | −0.444527 | ||||||||
\(175\) | 0.360007 | 0.0272140 | ||||||||
\(176\) | 1.82099 | 0.137262 | ||||||||
\(177\) | −13.0635 | −0.981916 | ||||||||
\(178\) | −5.16029 | −0.386780 | ||||||||
\(179\) | 7.41172 | 0.553978 | 0.276989 | − | 0.960873i | \(-0.410663\pi\) | ||||
0.276989 | + | 0.960873i | \(0.410663\pi\) | |||||||
\(180\) | 2.75648 | 0.205456 | ||||||||
\(181\) | 19.8167 | 1.47297 | 0.736483 | − | 0.676456i | \(-0.236485\pi\) | ||||
0.736483 | + | 0.676456i | \(0.236485\pi\) | |||||||
\(182\) | 1.02705 | 0.0761301 | ||||||||
\(183\) | 17.9863 | 1.32958 | ||||||||
\(184\) | −7.18335 | −0.529563 | ||||||||
\(185\) | 9.87171 | 0.725782 | ||||||||
\(186\) | 0.398831 | 0.0292437 | ||||||||
\(187\) | −11.4786 | −0.839395 | ||||||||
\(188\) | −0.609939 | −0.0444844 | ||||||||
\(189\) | −5.63694 | −0.410027 | ||||||||
\(190\) | −8.98893 | −0.652125 | ||||||||
\(191\) | −5.71144 | −0.413265 | −0.206633 | − | 0.978419i | \(-0.566251\pi\) | ||||
−0.206633 | + | 0.978419i | \(0.566251\pi\) | |||||||
\(192\) | 1.34513 | 0.0970767 | ||||||||
\(193\) | −0.155001 | −0.0111572 | −0.00557859 | − | 0.999984i | \(-0.501776\pi\) | ||||
−0.00557859 | + | 0.999984i | \(0.501776\pi\) | |||||||
\(194\) | −13.9570 | −1.00205 | ||||||||
\(195\) | −3.19846 | −0.229046 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −1.30758 | −0.0931609 | −0.0465805 | − | 0.998915i | \(-0.514832\pi\) | ||||
−0.0465805 | + | 0.998915i | \(0.514832\pi\) | |||||||
\(198\) | −2.16810 | −0.154080 | ||||||||
\(199\) | −20.2631 | −1.43642 | −0.718208 | − | 0.695829i | \(-0.755037\pi\) | ||||
−0.718208 | + | 0.695829i | \(0.755037\pi\) | |||||||
\(200\) | 0.360007 | 0.0254563 | ||||||||
\(201\) | −7.09956 | −0.500764 | ||||||||
\(202\) | −2.82966 | −0.199094 | ||||||||
\(203\) | −4.35921 | −0.305956 | ||||||||
\(204\) | −8.47900 | −0.593649 | ||||||||
\(205\) | 12.6883 | 0.886188 | ||||||||
\(206\) | 7.19060 | 0.500993 | ||||||||
\(207\) | 8.55260 | 0.594447 | ||||||||
\(208\) | 1.02705 | 0.0712132 | ||||||||
\(209\) | 7.07022 | 0.489058 | ||||||||
\(210\) | −3.11421 | −0.214901 | ||||||||
\(211\) | −10.2278 | −0.704113 | −0.352057 | − | 0.935979i | \(-0.614518\pi\) | ||||
−0.352057 | + | 0.935979i | \(0.614518\pi\) | |||||||
\(212\) | −9.07701 | −0.623412 | ||||||||
\(213\) | −3.62120 | −0.248120 | ||||||||
\(214\) | 7.35379 | 0.502695 | ||||||||
\(215\) | −25.7386 | −1.75536 | ||||||||
\(216\) | −5.63694 | −0.383545 | ||||||||
\(217\) | 0.296499 | 0.0201277 | ||||||||
\(218\) | 15.1216 | 1.02416 | ||||||||
\(219\) | 2.32826 | 0.157329 | ||||||||
\(220\) | −4.21590 | −0.284236 | ||||||||
\(221\) | −6.47398 | −0.435487 | ||||||||
\(222\) | −5.73555 | −0.384945 | ||||||||
\(223\) | −0.988408 | −0.0661887 | −0.0330943 | − | 0.999452i | \(-0.510536\pi\) | ||||
−0.0330943 | + | 0.999452i | \(0.510536\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −0.428630 | −0.0285753 | ||||||||
\(226\) | −11.0889 | −0.737624 | ||||||||
\(227\) | −8.40225 | −0.557677 | −0.278838 | − | 0.960338i | \(-0.589949\pi\) | ||||
−0.278838 | + | 0.960338i | \(0.589949\pi\) | |||||||
\(228\) | 5.22265 | 0.345878 | ||||||||
\(229\) | −4.93262 | −0.325957 | −0.162978 | − | 0.986630i | \(-0.552110\pi\) | ||||
−0.162978 | + | 0.986630i | \(0.552110\pi\) | |||||||
\(230\) | 16.6307 | 1.09659 | ||||||||
\(231\) | 2.44948 | 0.161164 | ||||||||
\(232\) | −4.35921 | −0.286196 | ||||||||
\(233\) | 9.11465 | 0.597120 | 0.298560 | − | 0.954391i | \(-0.403494\pi\) | ||||
0.298560 | + | 0.954391i | \(0.403494\pi\) | |||||||
\(234\) | −1.22282 | −0.0799384 | ||||||||
\(235\) | 1.41211 | 0.0921160 | ||||||||
\(236\) | −9.71171 | −0.632178 | ||||||||
\(237\) | −3.84072 | −0.249481 | ||||||||
\(238\) | −6.30346 | −0.408593 | ||||||||
\(239\) | −10.0198 | −0.648128 | −0.324064 | − | 0.946035i | \(-0.605049\pi\) | ||||
−0.324064 | + | 0.946035i | \(0.605049\pi\) | |||||||
\(240\) | −3.11421 | −0.201021 | ||||||||
\(241\) | −13.9163 | −0.896425 | −0.448213 | − | 0.893927i | \(-0.647939\pi\) | ||||
−0.448213 | + | 0.893927i | \(0.647939\pi\) | |||||||
\(242\) | −7.68399 | −0.493946 | ||||||||
\(243\) | 11.5160 | 0.738754 | ||||||||
\(244\) | 13.3714 | 0.856013 | ||||||||
\(245\) | −2.31517 | −0.147911 | ||||||||
\(246\) | −7.37200 | −0.470022 | ||||||||
\(247\) | 3.98765 | 0.253728 | ||||||||
\(248\) | 0.296499 | 0.0188277 | ||||||||
\(249\) | −0.685184 | −0.0434218 | ||||||||
\(250\) | 10.7424 | 0.679407 | ||||||||
\(251\) | −13.4977 | −0.851966 | −0.425983 | − | 0.904731i | \(-0.640072\pi\) | ||||
−0.425983 | + | 0.904731i | \(0.640072\pi\) | |||||||
\(252\) | −1.19062 | −0.0750017 | ||||||||
\(253\) | −13.0808 | −0.822384 | ||||||||
\(254\) | −11.4104 | −0.715952 | ||||||||
\(255\) | 19.6303 | 1.22930 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.65029 | 0.352456 | 0.176228 | − | 0.984349i | \(-0.443610\pi\) | ||||
0.176228 | + | 0.984349i | \(0.443610\pi\) | |||||||
\(258\) | 14.9544 | 0.931017 | ||||||||
\(259\) | −4.26392 | −0.264947 | ||||||||
\(260\) | −2.37780 | −0.147465 | ||||||||
\(261\) | 5.19014 | 0.321262 | ||||||||
\(262\) | −7.65248 | −0.472772 | ||||||||
\(263\) | −24.9351 | −1.53756 | −0.768781 | − | 0.639512i | \(-0.779136\pi\) | ||||
−0.768781 | + | 0.639512i | \(0.779136\pi\) | |||||||
\(264\) | 2.44948 | 0.150755 | ||||||||
\(265\) | 21.0148 | 1.29093 | ||||||||
\(266\) | 3.88262 | 0.238059 | ||||||||
\(267\) | −6.94128 | −0.424799 | ||||||||
\(268\) | −5.27796 | −0.322402 | ||||||||
\(269\) | −1.32265 | −0.0806431 | −0.0403216 | − | 0.999187i | \(-0.512838\pi\) | ||||
−0.0403216 | + | 0.999187i | \(0.512838\pi\) | |||||||
\(270\) | 13.0505 | 0.794226 | ||||||||
\(271\) | 32.6461 | 1.98311 | 0.991554 | − | 0.129695i | \(-0.0413997\pi\) | ||||
0.991554 | + | 0.129695i | \(0.0413997\pi\) | |||||||
\(272\) | −6.30346 | −0.382203 | ||||||||
\(273\) | 1.38152 | 0.0836135 | ||||||||
\(274\) | −1.38279 | −0.0835371 | ||||||||
\(275\) | 0.655570 | 0.0395323 | ||||||||
\(276\) | −9.66256 | −0.581618 | ||||||||
\(277\) | −33.1231 | −1.99017 | −0.995087 | − | 0.0990054i | \(-0.968434\pi\) | ||||
−0.995087 | + | 0.0990054i | \(0.968434\pi\) | |||||||
\(278\) | 6.48252 | 0.388796 | ||||||||
\(279\) | −0.353016 | −0.0211345 | ||||||||
\(280\) | −2.31517 | −0.138358 | ||||||||
\(281\) | 14.1641 | 0.844961 | 0.422480 | − | 0.906372i | \(-0.361160\pi\) | ||||
0.422480 | + | 0.906372i | \(0.361160\pi\) | |||||||
\(282\) | −0.820450 | −0.0488571 | ||||||||
\(283\) | 5.71975 | 0.340004 | 0.170002 | − | 0.985444i | \(-0.445623\pi\) | ||||
0.170002 | + | 0.985444i | \(0.445623\pi\) | |||||||
\(284\) | −2.69207 | −0.159745 | ||||||||
\(285\) | −12.0913 | −0.716227 | ||||||||
\(286\) | 1.87025 | 0.110590 | ||||||||
\(287\) | −5.48050 | −0.323504 | ||||||||
\(288\) | −1.19062 | −0.0701577 | ||||||||
\(289\) | 22.7336 | 1.33727 | ||||||||
\(290\) | 10.0923 | 0.592641 | ||||||||
\(291\) | −18.7740 | −1.10055 | ||||||||
\(292\) | 1.73088 | 0.101292 | ||||||||
\(293\) | 17.3120 | 1.01138 | 0.505688 | − | 0.862717i | \(-0.331239\pi\) | ||||
0.505688 | + | 0.862717i | \(0.331239\pi\) | |||||||
\(294\) | 1.34513 | 0.0784498 | ||||||||
\(295\) | 22.4842 | 1.30908 | ||||||||
\(296\) | −4.26392 | −0.247836 | ||||||||
\(297\) | −10.2648 | −0.595625 | ||||||||
\(298\) | 1.57774 | 0.0913960 | ||||||||
\(299\) | −7.37766 | −0.426661 | ||||||||
\(300\) | 0.484257 | 0.0279586 | ||||||||
\(301\) | 11.1174 | 0.640795 | ||||||||
\(302\) | −11.1141 | −0.639547 | ||||||||
\(303\) | −3.80627 | −0.218665 | ||||||||
\(304\) | 3.88262 | 0.222684 | ||||||||
\(305\) | −30.9569 | −1.77259 | ||||||||
\(306\) | 7.50500 | 0.429032 | ||||||||
\(307\) | 28.9215 | 1.65064 | 0.825319 | − | 0.564667i | \(-0.190995\pi\) | ||||
0.825319 | + | 0.564667i | \(0.190995\pi\) | |||||||
\(308\) | 1.82099 | 0.103761 | ||||||||
\(309\) | 9.67232 | 0.550239 | ||||||||
\(310\) | −0.686445 | −0.0389875 | ||||||||
\(311\) | 5.72167 | 0.324446 | 0.162223 | − | 0.986754i | \(-0.448134\pi\) | ||||
0.162223 | + | 0.986754i | \(0.448134\pi\) | |||||||
\(312\) | 1.38152 | 0.0782132 | ||||||||
\(313\) | 7.28299 | 0.411659 | 0.205829 | − | 0.978588i | \(-0.434011\pi\) | ||||
0.205829 | + | 0.978588i | \(0.434011\pi\) | |||||||
\(314\) | 4.42246 | 0.249574 | ||||||||
\(315\) | 2.75648 | 0.155310 | ||||||||
\(316\) | −2.85527 | −0.160621 | ||||||||
\(317\) | 23.5361 | 1.32192 | 0.660960 | − | 0.750421i | \(-0.270149\pi\) | ||||
0.660960 | + | 0.750421i | \(0.270149\pi\) | |||||||
\(318\) | −12.2098 | −0.684691 | ||||||||
\(319\) | −7.93808 | −0.444447 | ||||||||
\(320\) | −2.31517 | −0.129422 | ||||||||
\(321\) | 9.89183 | 0.552108 | ||||||||
\(322\) | −7.18335 | −0.400312 | ||||||||
\(323\) | −24.4740 | −1.36177 | ||||||||
\(324\) | −4.01059 | −0.222811 | ||||||||
\(325\) | 0.369746 | 0.0205098 | ||||||||
\(326\) | 4.51935 | 0.250304 | ||||||||
\(327\) | 20.3406 | 1.12484 | ||||||||
\(328\) | −5.48050 | −0.302610 | ||||||||
\(329\) | −0.609939 | −0.0336270 | ||||||||
\(330\) | −5.67095 | −0.312176 | ||||||||
\(331\) | −25.2029 | −1.38528 | −0.692639 | − | 0.721284i | \(-0.743552\pi\) | ||||
−0.692639 | + | 0.721284i | \(0.743552\pi\) | |||||||
\(332\) | −0.509380 | −0.0279559 | ||||||||
\(333\) | 5.07669 | 0.278201 | ||||||||
\(334\) | −8.47745 | −0.463865 | ||||||||
\(335\) | 12.2194 | 0.667615 | ||||||||
\(336\) | 1.34513 | 0.0733831 | ||||||||
\(337\) | −5.43691 | −0.296167 | −0.148084 | − | 0.988975i | \(-0.547310\pi\) | ||||
−0.148084 | + | 0.988975i | \(0.547310\pi\) | |||||||
\(338\) | −11.9452 | −0.649731 | ||||||||
\(339\) | −14.9161 | −0.810130 | ||||||||
\(340\) | 14.5936 | 0.791448 | ||||||||
\(341\) | 0.539922 | 0.0292384 | ||||||||
\(342\) | −4.62271 | −0.249968 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 11.1174 | 0.599409 | ||||||||
\(345\) | 22.3705 | 1.20438 | ||||||||
\(346\) | 2.07783 | 0.111705 | ||||||||
\(347\) | −20.6599 | −1.10908 | −0.554540 | − | 0.832157i | \(-0.687106\pi\) | ||||
−0.554540 | + | 0.832157i | \(0.687106\pi\) | |||||||
\(348\) | −5.86372 | −0.314328 | ||||||||
\(349\) | −26.4503 | −1.41585 | −0.707927 | − | 0.706286i | \(-0.750369\pi\) | ||||
−0.707927 | + | 0.706286i | \(0.750369\pi\) | |||||||
\(350\) | 0.360007 | 0.0192432 | ||||||||
\(351\) | −5.78942 | −0.309017 | ||||||||
\(352\) | 1.82099 | 0.0970592 | ||||||||
\(353\) | 18.9614 | 1.00921 | 0.504606 | − | 0.863349i | \(-0.331638\pi\) | ||||
0.504606 | + | 0.863349i | \(0.331638\pi\) | |||||||
\(354\) | −13.0635 | −0.694320 | ||||||||
\(355\) | 6.23260 | 0.330792 | ||||||||
\(356\) | −5.16029 | −0.273495 | ||||||||
\(357\) | −8.47900 | −0.448756 | ||||||||
\(358\) | 7.41172 | 0.391722 | ||||||||
\(359\) | −0.980074 | −0.0517263 | −0.0258632 | − | 0.999665i | \(-0.508233\pi\) | ||||
−0.0258632 | + | 0.999665i | \(0.508233\pi\) | |||||||
\(360\) | 2.75648 | 0.145279 | ||||||||
\(361\) | −3.92524 | −0.206592 | ||||||||
\(362\) | 19.8167 | 1.04154 | ||||||||
\(363\) | −10.3360 | −0.542499 | ||||||||
\(364\) | 1.02705 | 0.0538321 | ||||||||
\(365\) | −4.00727 | −0.209750 | ||||||||
\(366\) | 17.9863 | 0.940157 | ||||||||
\(367\) | −18.7161 | −0.976974 | −0.488487 | − | 0.872571i | \(-0.662451\pi\) | ||||
−0.488487 | + | 0.872571i | \(0.662451\pi\) | |||||||
\(368\) | −7.18335 | −0.374458 | ||||||||
\(369\) | 6.52517 | 0.339687 | ||||||||
\(370\) | 9.87171 | 0.513206 | ||||||||
\(371\) | −9.07701 | −0.471255 | ||||||||
\(372\) | 0.398831 | 0.0206784 | ||||||||
\(373\) | −11.2753 | −0.583814 | −0.291907 | − | 0.956447i | \(-0.594290\pi\) | ||||
−0.291907 | + | 0.956447i | \(0.594290\pi\) | |||||||
\(374\) | −11.4786 | −0.593542 | ||||||||
\(375\) | 14.4499 | 0.746191 | ||||||||
\(376\) | −0.609939 | −0.0314552 | ||||||||
\(377\) | −4.47713 | −0.230584 | ||||||||
\(378\) | −5.63694 | −0.289933 | ||||||||
\(379\) | −8.30266 | −0.426479 | −0.213239 | − | 0.977000i | \(-0.568401\pi\) | ||||
−0.213239 | + | 0.977000i | \(0.568401\pi\) | |||||||
\(380\) | −8.98893 | −0.461122 | ||||||||
\(381\) | −15.3485 | −0.786328 | ||||||||
\(382\) | −5.71144 | −0.292223 | ||||||||
\(383\) | 25.5669 | 1.30641 | 0.653205 | − | 0.757181i | \(-0.273424\pi\) | ||||
0.653205 | + | 0.757181i | \(0.273424\pi\) | |||||||
\(384\) | 1.34513 | 0.0686436 | ||||||||
\(385\) | −4.21590 | −0.214862 | ||||||||
\(386\) | −0.155001 | −0.00788932 | ||||||||
\(387\) | −13.2365 | −0.672850 | ||||||||
\(388\) | −13.9570 | −0.708557 | ||||||||
\(389\) | 29.9086 | 1.51643 | 0.758213 | − | 0.652007i | \(-0.226073\pi\) | ||||
0.758213 | + | 0.652007i | \(0.226073\pi\) | |||||||
\(390\) | −3.19846 | −0.161960 | ||||||||
\(391\) | 45.2799 | 2.28990 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −10.2936 | −0.519244 | ||||||||
\(394\) | −1.30758 | −0.0658747 | ||||||||
\(395\) | 6.61043 | 0.332607 | ||||||||
\(396\) | −2.16810 | −0.108951 | ||||||||
\(397\) | 31.8776 | 1.59989 | 0.799945 | − | 0.600074i | \(-0.204862\pi\) | ||||
0.799945 | + | 0.600074i | \(0.204862\pi\) | |||||||
\(398\) | −20.2631 | −1.01570 | ||||||||
\(399\) | 5.22265 | 0.261459 | ||||||||
\(400\) | 0.360007 | 0.0180003 | ||||||||
\(401\) | −11.4030 | −0.569438 | −0.284719 | − | 0.958611i | \(-0.591900\pi\) | ||||
−0.284719 | + | 0.958611i | \(0.591900\pi\) | |||||||
\(402\) | −7.09956 | −0.354094 | ||||||||
\(403\) | 0.304520 | 0.0151692 | ||||||||
\(404\) | −2.82966 | −0.140781 | ||||||||
\(405\) | 9.28519 | 0.461385 | ||||||||
\(406\) | −4.35921 | −0.216344 | ||||||||
\(407\) | −7.76457 | −0.384876 | ||||||||
\(408\) | −8.47900 | −0.419773 | ||||||||
\(409\) | −34.8689 | −1.72415 | −0.862077 | − | 0.506777i | \(-0.830837\pi\) | ||||
−0.862077 | + | 0.506777i | \(0.830837\pi\) | |||||||
\(410\) | 12.6883 | 0.626630 | ||||||||
\(411\) | −1.86003 | −0.0917486 | ||||||||
\(412\) | 7.19060 | 0.354255 | ||||||||
\(413\) | −9.71171 | −0.477882 | ||||||||
\(414\) | 8.55260 | 0.420337 | ||||||||
\(415\) | 1.17930 | 0.0578896 | ||||||||
\(416\) | 1.02705 | 0.0503553 | ||||||||
\(417\) | 8.71986 | 0.427013 | ||||||||
\(418\) | 7.07022 | 0.345816 | ||||||||
\(419\) | 19.6912 | 0.961980 | 0.480990 | − | 0.876726i | \(-0.340277\pi\) | ||||
0.480990 | + | 0.876726i | \(0.340277\pi\) | |||||||
\(420\) | −3.11421 | −0.151958 | ||||||||
\(421\) | 23.1688 | 1.12918 | 0.564589 | − | 0.825372i | \(-0.309035\pi\) | ||||
0.564589 | + | 0.825372i | \(0.309035\pi\) | |||||||
\(422\) | −10.2278 | −0.497883 | ||||||||
\(423\) | 0.726203 | 0.0353092 | ||||||||
\(424\) | −9.07701 | −0.440819 | ||||||||
\(425\) | −2.26929 | −0.110077 | ||||||||
\(426\) | −3.62120 | −0.175448 | ||||||||
\(427\) | 13.3714 | 0.647085 | ||||||||
\(428\) | 7.35379 | 0.355459 | ||||||||
\(429\) | 2.51574 | 0.121461 | ||||||||
\(430\) | −25.7386 | −1.24123 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | −5.63694 | −0.271207 | ||||||||
\(433\) | −1.13204 | −0.0544025 | −0.0272012 | − | 0.999630i | \(-0.508659\pi\) | ||||
−0.0272012 | + | 0.999630i | \(0.508659\pi\) | |||||||
\(434\) | 0.296499 | 0.0142324 | ||||||||
\(435\) | 13.5755 | 0.650895 | ||||||||
\(436\) | 15.1216 | 0.724193 | ||||||||
\(437\) | −27.8902 | −1.33417 | ||||||||
\(438\) | 2.32826 | 0.111249 | ||||||||
\(439\) | −25.1495 | −1.20032 | −0.600161 | − | 0.799879i | \(-0.704897\pi\) | ||||
−0.600161 | + | 0.799879i | \(0.704897\pi\) | |||||||
\(440\) | −4.21590 | −0.200985 | ||||||||
\(441\) | −1.19062 | −0.0566960 | ||||||||
\(442\) | −6.47398 | −0.307936 | ||||||||
\(443\) | 39.4788 | 1.87570 | 0.937848 | − | 0.347046i | \(-0.112815\pi\) | ||||
0.937848 | + | 0.347046i | \(0.112815\pi\) | |||||||
\(444\) | −5.73555 | −0.272197 | ||||||||
\(445\) | 11.9469 | 0.566339 | ||||||||
\(446\) | −0.988408 | −0.0468025 | ||||||||
\(447\) | 2.12227 | 0.100380 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −10.1433 | −0.478692 | −0.239346 | − | 0.970934i | \(-0.576933\pi\) | ||||
−0.239346 | + | 0.970934i | \(0.576933\pi\) | |||||||
\(450\) | −0.428630 | −0.0202058 | ||||||||
\(451\) | −9.97994 | −0.469937 | ||||||||
\(452\) | −11.0889 | −0.521579 | ||||||||
\(453\) | −14.9500 | −0.702412 | ||||||||
\(454\) | −8.40225 | −0.394337 | ||||||||
\(455\) | −2.37780 | −0.111473 | ||||||||
\(456\) | 5.22265 | 0.244573 | ||||||||
\(457\) | 12.6043 | 0.589604 | 0.294802 | − | 0.955558i | \(-0.404746\pi\) | ||||
0.294802 | + | 0.955558i | \(0.404746\pi\) | |||||||
\(458\) | −4.93262 | −0.230486 | ||||||||
\(459\) | 35.5322 | 1.65850 | ||||||||
\(460\) | 16.6307 | 0.775408 | ||||||||
\(461\) | −18.0661 | −0.841424 | −0.420712 | − | 0.907194i | \(-0.638220\pi\) | ||||
−0.420712 | + | 0.907194i | \(0.638220\pi\) | |||||||
\(462\) | 2.44948 | 0.113960 | ||||||||
\(463\) | −22.1284 | −1.02839 | −0.514196 | − | 0.857673i | \(-0.671910\pi\) | ||||
−0.514196 | + | 0.857673i | \(0.671910\pi\) | |||||||
\(464\) | −4.35921 | −0.202371 | ||||||||
\(465\) | −0.923360 | −0.0428198 | ||||||||
\(466\) | 9.11465 | 0.422228 | ||||||||
\(467\) | 27.8531 | 1.28889 | 0.644445 | − | 0.764651i | \(-0.277089\pi\) | ||||
0.644445 | + | 0.764651i | \(0.277089\pi\) | |||||||
\(468\) | −1.22282 | −0.0565250 | ||||||||
\(469\) | −5.27796 | −0.243713 | ||||||||
\(470\) | 1.41211 | 0.0651359 | ||||||||
\(471\) | 5.94880 | 0.274106 | ||||||||
\(472\) | −9.71171 | −0.447018 | ||||||||
\(473\) | 20.2446 | 0.930850 | ||||||||
\(474\) | −3.84072 | −0.176410 | ||||||||
\(475\) | 1.39777 | 0.0641341 | ||||||||
\(476\) | −6.30346 | −0.288919 | ||||||||
\(477\) | 10.8072 | 0.494829 | ||||||||
\(478\) | −10.0198 | −0.458296 | ||||||||
\(479\) | 7.54256 | 0.344628 | 0.172314 | − | 0.985042i | \(-0.444876\pi\) | ||||
0.172314 | + | 0.985042i | \(0.444876\pi\) | |||||||
\(480\) | −3.11421 | −0.142144 | ||||||||
\(481\) | −4.37927 | −0.199678 | ||||||||
\(482\) | −13.9163 | −0.633868 | ||||||||
\(483\) | −9.66256 | −0.439662 | ||||||||
\(484\) | −7.68399 | −0.349272 | ||||||||
\(485\) | 32.3127 | 1.46724 | ||||||||
\(486\) | 11.5160 | 0.522378 | ||||||||
\(487\) | 8.94353 | 0.405270 | 0.202635 | − | 0.979254i | \(-0.435049\pi\) | ||||
0.202635 | + | 0.979254i | \(0.435049\pi\) | |||||||
\(488\) | 13.3714 | 0.605293 | ||||||||
\(489\) | 6.07913 | 0.274908 | ||||||||
\(490\) | −2.31517 | −0.104589 | ||||||||
\(491\) | −35.8923 | −1.61980 | −0.809898 | − | 0.586570i | \(-0.800478\pi\) | ||||
−0.809898 | + | 0.586570i | \(0.800478\pi\) | |||||||
\(492\) | −7.37200 | −0.332356 | ||||||||
\(493\) | 27.4781 | 1.23755 | ||||||||
\(494\) | 3.98765 | 0.179413 | ||||||||
\(495\) | 5.01952 | 0.225611 | ||||||||
\(496\) | 0.296499 | 0.0133132 | ||||||||
\(497\) | −2.69207 | −0.120756 | ||||||||
\(498\) | −0.685184 | −0.0307038 | ||||||||
\(499\) | −27.1444 | −1.21515 | −0.607574 | − | 0.794263i | \(-0.707857\pi\) | ||||
−0.607574 | + | 0.794263i | \(0.707857\pi\) | |||||||
\(500\) | 10.7424 | 0.480413 | ||||||||
\(501\) | −11.4033 | −0.509462 | ||||||||
\(502\) | −13.4977 | −0.602431 | ||||||||
\(503\) | 32.7114 | 1.45853 | 0.729264 | − | 0.684232i | \(-0.239863\pi\) | ||||
0.729264 | + | 0.684232i | \(0.239863\pi\) | |||||||
\(504\) | −1.19062 | −0.0530342 | ||||||||
\(505\) | 6.55115 | 0.291522 | ||||||||
\(506\) | −13.0808 | −0.581513 | ||||||||
\(507\) | −16.0678 | −0.713598 | ||||||||
\(508\) | −11.4104 | −0.506254 | ||||||||
\(509\) | 40.7537 | 1.80638 | 0.903189 | − | 0.429243i | \(-0.141220\pi\) | ||||
0.903189 | + | 0.429243i | \(0.141220\pi\) | |||||||
\(510\) | 19.6303 | 0.869245 | ||||||||
\(511\) | 1.73088 | 0.0765695 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −21.8861 | −0.966295 | ||||||||
\(514\) | 5.65029 | 0.249224 | ||||||||
\(515\) | −16.6475 | −0.733574 | ||||||||
\(516\) | 14.9544 | 0.658329 | ||||||||
\(517\) | −1.11069 | −0.0488483 | ||||||||
\(518\) | −4.26392 | −0.187346 | ||||||||
\(519\) | 2.79496 | 0.122685 | ||||||||
\(520\) | −2.37780 | −0.104273 | ||||||||
\(521\) | 6.12635 | 0.268400 | 0.134200 | − | 0.990954i | \(-0.457154\pi\) | ||||
0.134200 | + | 0.990954i | \(0.457154\pi\) | |||||||
\(522\) | 5.19014 | 0.227166 | ||||||||
\(523\) | 5.51300 | 0.241067 | 0.120533 | − | 0.992709i | \(-0.461540\pi\) | ||||
0.120533 | + | 0.992709i | \(0.461540\pi\) | |||||||
\(524\) | −7.65248 | −0.334300 | ||||||||
\(525\) | 0.484257 | 0.0211347 | ||||||||
\(526\) | −24.9351 | −1.08722 | ||||||||
\(527\) | −1.86897 | −0.0814136 | ||||||||
\(528\) | 2.44948 | 0.106600 | ||||||||
\(529\) | 28.6004 | 1.24350 | ||||||||
\(530\) | 21.0148 | 0.912825 | ||||||||
\(531\) | 11.5629 | 0.501787 | ||||||||
\(532\) | 3.88262 | 0.168333 | ||||||||
\(533\) | −5.62875 | −0.243808 | ||||||||
\(534\) | −6.94128 | −0.300378 | ||||||||
\(535\) | −17.0253 | −0.736066 | ||||||||
\(536\) | −5.27796 | −0.227973 | ||||||||
\(537\) | 9.96976 | 0.430227 | ||||||||
\(538\) | −1.32265 | −0.0570233 | ||||||||
\(539\) | 1.82099 | 0.0784357 | ||||||||
\(540\) | 13.0505 | 0.561603 | ||||||||
\(541\) | 37.8923 | 1.62912 | 0.814560 | − | 0.580080i | \(-0.196979\pi\) | ||||
0.814560 | + | 0.580080i | \(0.196979\pi\) | |||||||
\(542\) | 32.6461 | 1.40227 | ||||||||
\(543\) | 26.6562 | 1.14393 | ||||||||
\(544\) | −6.30346 | −0.270259 | ||||||||
\(545\) | −35.0091 | −1.49962 | ||||||||
\(546\) | 1.38152 | 0.0591237 | ||||||||
\(547\) | 27.3533 | 1.16954 | 0.584771 | − | 0.811199i | \(-0.301185\pi\) | ||||
0.584771 | + | 0.811199i | \(0.301185\pi\) | |||||||
\(548\) | −1.38279 | −0.0590697 | ||||||||
\(549\) | −15.9201 | −0.679455 | ||||||||
\(550\) | 0.655570 | 0.0279536 | ||||||||
\(551\) | −16.9252 | −0.721036 | ||||||||
\(552\) | −9.66256 | −0.411266 | ||||||||
\(553\) | −2.85527 | −0.121418 | ||||||||
\(554\) | −33.1231 | −1.40727 | ||||||||
\(555\) | 13.2788 | 0.563652 | ||||||||
\(556\) | 6.48252 | 0.274920 | ||||||||
\(557\) | 35.1948 | 1.49125 | 0.745626 | − | 0.666365i | \(-0.232151\pi\) | ||||
0.745626 | + | 0.666365i | \(0.232151\pi\) | |||||||
\(558\) | −0.353016 | −0.0149444 | ||||||||
\(559\) | 11.4181 | 0.482935 | ||||||||
\(560\) | −2.31517 | −0.0978337 | ||||||||
\(561\) | −15.4402 | −0.651885 | ||||||||
\(562\) | 14.1641 | 0.597478 | ||||||||
\(563\) | −35.9112 | −1.51347 | −0.756737 | − | 0.653719i | \(-0.773208\pi\) | ||||
−0.756737 | + | 0.653719i | \(0.773208\pi\) | |||||||
\(564\) | −0.820450 | −0.0345472 | ||||||||
\(565\) | 25.6727 | 1.08006 | ||||||||
\(566\) | 5.71975 | 0.240419 | ||||||||
\(567\) | −4.01059 | −0.168429 | ||||||||
\(568\) | −2.69207 | −0.112957 | ||||||||
\(569\) | 31.6055 | 1.32497 | 0.662486 | − | 0.749074i | \(-0.269501\pi\) | ||||
0.662486 | + | 0.749074i | \(0.269501\pi\) | |||||||
\(570\) | −12.0913 | −0.506449 | ||||||||
\(571\) | −0.521750 | −0.0218345 | −0.0109173 | − | 0.999940i | \(-0.503475\pi\) | ||||
−0.0109173 | + | 0.999940i | \(0.503475\pi\) | |||||||
\(572\) | 1.87025 | 0.0781992 | ||||||||
\(573\) | −7.68265 | −0.320947 | ||||||||
\(574\) | −5.48050 | −0.228752 | ||||||||
\(575\) | −2.58605 | −0.107846 | ||||||||
\(576\) | −1.19062 | −0.0496090 | ||||||||
\(577\) | 34.6602 | 1.44292 | 0.721462 | − | 0.692454i | \(-0.243471\pi\) | ||||
0.721462 | + | 0.692454i | \(0.243471\pi\) | |||||||
\(578\) | 22.7336 | 0.945594 | ||||||||
\(579\) | −0.208496 | −0.00866482 | ||||||||
\(580\) | 10.0923 | 0.419060 | ||||||||
\(581\) | −0.509380 | −0.0211326 | ||||||||
\(582\) | −18.7740 | −0.778206 | ||||||||
\(583\) | −16.5292 | −0.684568 | ||||||||
\(584\) | 1.73088 | 0.0716242 | ||||||||
\(585\) | 2.83104 | 0.117049 | ||||||||
\(586\) | 17.3120 | 0.715150 | ||||||||
\(587\) | −28.5654 | −1.17902 | −0.589510 | − | 0.807761i | \(-0.700679\pi\) | ||||
−0.589510 | + | 0.807761i | \(0.700679\pi\) | |||||||
\(588\) | 1.34513 | 0.0554724 | ||||||||
\(589\) | 1.15119 | 0.0474341 | ||||||||
\(590\) | 22.4842 | 0.925662 | ||||||||
\(591\) | −1.75886 | −0.0723500 | ||||||||
\(592\) | −4.26392 | −0.175246 | ||||||||
\(593\) | 14.1410 | 0.580701 | 0.290351 | − | 0.956920i | \(-0.406228\pi\) | ||||
0.290351 | + | 0.956920i | \(0.406228\pi\) | |||||||
\(594\) | −10.2648 | −0.421171 | ||||||||
\(595\) | 14.5936 | 0.598278 | ||||||||
\(596\) | 1.57774 | 0.0646267 | ||||||||
\(597\) | −27.2566 | −1.11554 | ||||||||
\(598\) | −7.37766 | −0.301695 | ||||||||
\(599\) | −24.2444 | −0.990600 | −0.495300 | − | 0.868722i | \(-0.664942\pi\) | ||||
−0.495300 | + | 0.868722i | \(0.664942\pi\) | |||||||
\(600\) | 0.484257 | 0.0197697 | ||||||||
\(601\) | −36.7763 | −1.50013 | −0.750067 | − | 0.661361i | \(-0.769979\pi\) | ||||
−0.750067 | + | 0.661361i | \(0.769979\pi\) | |||||||
\(602\) | 11.1174 | 0.453110 | ||||||||
\(603\) | 6.28402 | 0.255905 | ||||||||
\(604\) | −11.1141 | −0.452228 | ||||||||
\(605\) | 17.7897 | 0.723255 | ||||||||
\(606\) | −3.80627 | −0.154619 | ||||||||
\(607\) | −4.36633 | −0.177224 | −0.0886119 | − | 0.996066i | \(-0.528243\pi\) | ||||
−0.0886119 | + | 0.996066i | \(0.528243\pi\) | |||||||
\(608\) | 3.88262 | 0.157461 | ||||||||
\(609\) | −5.86372 | −0.237610 | ||||||||
\(610\) | −30.9569 | −1.25341 | ||||||||
\(611\) | −0.626439 | −0.0253430 | ||||||||
\(612\) | 7.50500 | 0.303372 | ||||||||
\(613\) | 26.4880 | 1.06984 | 0.534920 | − | 0.844903i | \(-0.320342\pi\) | ||||
0.534920 | + | 0.844903i | \(0.320342\pi\) | |||||||
\(614\) | 28.9215 | 1.16718 | ||||||||
\(615\) | 17.0674 | 0.688225 | ||||||||
\(616\) | 1.82099 | 0.0733698 | ||||||||
\(617\) | 33.4978 | 1.34857 | 0.674285 | − | 0.738471i | \(-0.264452\pi\) | ||||
0.674285 | + | 0.738471i | \(0.264452\pi\) | |||||||
\(618\) | 9.67232 | 0.389078 | ||||||||
\(619\) | 27.8173 | 1.11807 | 0.559036 | − | 0.829143i | \(-0.311171\pi\) | ||||
0.559036 | + | 0.829143i | \(0.311171\pi\) | |||||||
\(620\) | −0.686445 | −0.0275683 | ||||||||
\(621\) | 40.4921 | 1.62489 | ||||||||
\(622\) | 5.72167 | 0.229418 | ||||||||
\(623\) | −5.16029 | −0.206743 | ||||||||
\(624\) | 1.38152 | 0.0553051 | ||||||||
\(625\) | −26.6704 | −1.06682 | ||||||||
\(626\) | 7.28299 | 0.291087 | ||||||||
\(627\) | 9.51040 | 0.379809 | ||||||||
\(628\) | 4.42246 | 0.176475 | ||||||||
\(629\) | 26.8775 | 1.07168 | ||||||||
\(630\) | 2.75648 | 0.109821 | ||||||||
\(631\) | −28.6059 | −1.13878 | −0.569390 | − | 0.822067i | \(-0.692821\pi\) | ||||
−0.569390 | + | 0.822067i | \(0.692821\pi\) | |||||||
\(632\) | −2.85527 | −0.113576 | ||||||||
\(633\) | −13.7578 | −0.546824 | ||||||||
\(634\) | 23.5361 | 0.934739 | ||||||||
\(635\) | 26.4170 | 1.04833 | ||||||||
\(636\) | −12.2098 | −0.484150 | ||||||||
\(637\) | 1.02705 | 0.0406933 | ||||||||
\(638\) | −7.93808 | −0.314272 | ||||||||
\(639\) | 3.20522 | 0.126797 | ||||||||
\(640\) | −2.31517 | −0.0915151 | ||||||||
\(641\) | −47.7228 | −1.88494 | −0.942468 | − | 0.334296i | \(-0.891501\pi\) | ||||
−0.942468 | + | 0.334296i | \(0.891501\pi\) | |||||||
\(642\) | 9.89183 | 0.390399 | ||||||||
\(643\) | 18.9928 | 0.749002 | 0.374501 | − | 0.927227i | \(-0.377814\pi\) | ||||
0.374501 | + | 0.927227i | \(0.377814\pi\) | |||||||
\(644\) | −7.18335 | −0.283063 | ||||||||
\(645\) | −34.6218 | −1.36323 | ||||||||
\(646\) | −24.4740 | −0.962915 | ||||||||
\(647\) | 8.92520 | 0.350886 | 0.175443 | − | 0.984490i | \(-0.443864\pi\) | ||||
0.175443 | + | 0.984490i | \(0.443864\pi\) | |||||||
\(648\) | −4.01059 | −0.157551 | ||||||||
\(649\) | −17.6849 | −0.694195 | ||||||||
\(650\) | 0.369746 | 0.0145026 | ||||||||
\(651\) | 0.398831 | 0.0156314 | ||||||||
\(652\) | 4.51935 | 0.176991 | ||||||||
\(653\) | 33.0459 | 1.29319 | 0.646593 | − | 0.762835i | \(-0.276193\pi\) | ||||
0.646593 | + | 0.762835i | \(0.276193\pi\) | |||||||
\(654\) | 20.3406 | 0.795379 | ||||||||
\(655\) | 17.7168 | 0.692252 | ||||||||
\(656\) | −5.48050 | −0.213978 | ||||||||
\(657\) | −2.06081 | −0.0803998 | ||||||||
\(658\) | −0.609939 | −0.0237779 | ||||||||
\(659\) | −29.9660 | −1.16731 | −0.583654 | − | 0.812002i | \(-0.698378\pi\) | ||||
−0.583654 | + | 0.812002i | \(0.698378\pi\) | |||||||
\(660\) | −5.67095 | −0.220742 | ||||||||
\(661\) | 11.5059 | 0.447530 | 0.223765 | − | 0.974643i | \(-0.428165\pi\) | ||||
0.223765 | + | 0.974643i | \(0.428165\pi\) | |||||||
\(662\) | −25.2029 | −0.979540 | ||||||||
\(663\) | −8.70837 | −0.338205 | ||||||||
\(664\) | −0.509380 | −0.0197678 | ||||||||
\(665\) | −8.98893 | −0.348576 | ||||||||
\(666\) | 5.07669 | 0.196718 | ||||||||
\(667\) | 31.3137 | 1.21247 | ||||||||
\(668\) | −8.47745 | −0.328002 | ||||||||
\(669\) | −1.32954 | −0.0514030 | ||||||||
\(670\) | 12.2194 | 0.472075 | ||||||||
\(671\) | 24.3491 | 0.939987 | ||||||||
\(672\) | 1.34513 | 0.0518897 | ||||||||
\(673\) | −9.05346 | −0.348985 | −0.174493 | − | 0.984658i | \(-0.555828\pi\) | ||||
−0.174493 | + | 0.984658i | \(0.555828\pi\) | |||||||
\(674\) | −5.43691 | −0.209422 | ||||||||
\(675\) | −2.02934 | −0.0781092 | ||||||||
\(676\) | −11.9452 | −0.459429 | ||||||||
\(677\) | 41.6816 | 1.60196 | 0.800978 | − | 0.598694i | \(-0.204314\pi\) | ||||
0.800978 | + | 0.598694i | \(0.204314\pi\) | |||||||
\(678\) | −14.9161 | −0.572848 | ||||||||
\(679\) | −13.9570 | −0.535619 | ||||||||
\(680\) | 14.5936 | 0.559638 | ||||||||
\(681\) | −11.3022 | −0.433099 | ||||||||
\(682\) | 0.539922 | 0.0206747 | ||||||||
\(683\) | 26.0177 | 0.995540 | 0.497770 | − | 0.867309i | \(-0.334152\pi\) | ||||
0.497770 | + | 0.867309i | \(0.334152\pi\) | |||||||
\(684\) | −4.62271 | −0.176754 | ||||||||
\(685\) | 3.20138 | 0.122318 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −6.63504 | −0.253143 | ||||||||
\(688\) | 11.1174 | 0.423846 | ||||||||
\(689\) | −9.32255 | −0.355161 | ||||||||
\(690\) | 22.3705 | 0.851629 | ||||||||
\(691\) | 15.4502 | 0.587755 | 0.293877 | − | 0.955843i | \(-0.405054\pi\) | ||||
0.293877 | + | 0.955843i | \(0.405054\pi\) | |||||||
\(692\) | 2.07783 | 0.0789872 | ||||||||
\(693\) | −2.16810 | −0.0823593 | ||||||||
\(694\) | −20.6599 | −0.784238 | ||||||||
\(695\) | −15.0081 | −0.569291 | ||||||||
\(696\) | −5.86372 | −0.222264 | ||||||||
\(697\) | 34.5461 | 1.30853 | ||||||||
\(698\) | −26.4503 | −1.00116 | ||||||||
\(699\) | 12.2604 | 0.463732 | ||||||||
\(700\) | 0.360007 | 0.0136070 | ||||||||
\(701\) | 11.9344 | 0.450757 | 0.225378 | − | 0.974271i | \(-0.427638\pi\) | ||||
0.225378 | + | 0.974271i | \(0.427638\pi\) | |||||||
\(702\) | −5.78942 | −0.218508 | ||||||||
\(703\) | −16.5552 | −0.624392 | ||||||||
\(704\) | 1.82099 | 0.0686312 | ||||||||
\(705\) | 1.89948 | 0.0715385 | ||||||||
\(706\) | 18.9614 | 0.713621 | ||||||||
\(707\) | −2.82966 | −0.106420 | ||||||||
\(708\) | −13.0635 | −0.490958 | ||||||||
\(709\) | −37.0282 | −1.39062 | −0.695312 | − | 0.718708i | \(-0.744734\pi\) | ||||
−0.695312 | + | 0.718708i | \(0.744734\pi\) | |||||||
\(710\) | 6.23260 | 0.233905 | ||||||||
\(711\) | 3.39953 | 0.127492 | ||||||||
\(712\) | −5.16029 | −0.193390 | ||||||||
\(713\) | −2.12985 | −0.0797637 | ||||||||
\(714\) | −8.47900 | −0.317319 | ||||||||
\(715\) | −4.32995 | −0.161931 | ||||||||
\(716\) | 7.41172 | 0.276989 | ||||||||
\(717\) | −13.4780 | −0.503345 | ||||||||
\(718\) | −0.980074 | −0.0365760 | ||||||||
\(719\) | 18.2126 | 0.679214 | 0.339607 | − | 0.940567i | \(-0.389706\pi\) | ||||
0.339607 | + | 0.940567i | \(0.389706\pi\) | |||||||
\(720\) | 2.75648 | 0.102728 | ||||||||
\(721\) | 7.19060 | 0.267792 | ||||||||
\(722\) | −3.92524 | −0.146082 | ||||||||
\(723\) | −18.7192 | −0.696176 | ||||||||
\(724\) | 19.8167 | 0.736483 | ||||||||
\(725\) | −1.56935 | −0.0582840 | ||||||||
\(726\) | −10.3360 | −0.383605 | ||||||||
\(727\) | −18.4884 | −0.685698 | −0.342849 | − | 0.939391i | \(-0.611392\pi\) | ||||
−0.342849 | + | 0.939391i | \(0.611392\pi\) | |||||||
\(728\) | 1.02705 | 0.0380651 | ||||||||
\(729\) | 27.5224 | 1.01935 | ||||||||
\(730\) | −4.00727 | −0.148316 | ||||||||
\(731\) | −70.0779 | −2.59193 | ||||||||
\(732\) | 17.9863 | 0.664791 | ||||||||
\(733\) | −5.28196 | −0.195094 | −0.0975469 | − | 0.995231i | \(-0.531100\pi\) | ||||
−0.0975469 | + | 0.995231i | \(0.531100\pi\) | |||||||
\(734\) | −18.7161 | −0.690825 | ||||||||
\(735\) | −3.11421 | −0.114869 | ||||||||
\(736\) | −7.18335 | −0.264782 | ||||||||
\(737\) | −9.61111 | −0.354030 | ||||||||
\(738\) | 6.52517 | 0.240195 | ||||||||
\(739\) | −47.4158 | −1.74422 | −0.872110 | − | 0.489310i | \(-0.837249\pi\) | ||||
−0.872110 | + | 0.489310i | \(0.837249\pi\) | |||||||
\(740\) | 9.87171 | 0.362891 | ||||||||
\(741\) | 5.36393 | 0.197049 | ||||||||
\(742\) | −9.07701 | −0.333227 | ||||||||
\(743\) | 32.9494 | 1.20880 | 0.604399 | − | 0.796682i | \(-0.293413\pi\) | ||||
0.604399 | + | 0.796682i | \(0.293413\pi\) | |||||||
\(744\) | 0.398831 | 0.0146218 | ||||||||
\(745\) | −3.65273 | −0.133826 | ||||||||
\(746\) | −11.2753 | −0.412819 | ||||||||
\(747\) | 0.606476 | 0.0221898 | ||||||||
\(748\) | −11.4786 | −0.419697 | ||||||||
\(749\) | 7.35379 | 0.268702 | ||||||||
\(750\) | 14.4499 | 0.527636 | ||||||||
\(751\) | −14.3356 | −0.523114 | −0.261557 | − | 0.965188i | \(-0.584236\pi\) | ||||
−0.261557 | + | 0.965188i | \(0.584236\pi\) | |||||||
\(752\) | −0.609939 | −0.0222422 | ||||||||
\(753\) | −18.1562 | −0.661648 | ||||||||
\(754\) | −4.47713 | −0.163047 | ||||||||
\(755\) | 25.7311 | 0.936450 | ||||||||
\(756\) | −5.63694 | −0.205013 | ||||||||
\(757\) | −37.1488 | −1.35020 | −0.675098 | − | 0.737728i | \(-0.735899\pi\) | ||||
−0.675098 | + | 0.737728i | \(0.735899\pi\) | |||||||
\(758\) | −8.30266 | −0.301566 | ||||||||
\(759\) | −17.5954 | −0.638674 | ||||||||
\(760\) | −8.98893 | −0.326063 | ||||||||
\(761\) | −10.6962 | −0.387737 | −0.193868 | − | 0.981028i | \(-0.562103\pi\) | ||||
−0.193868 | + | 0.981028i | \(0.562103\pi\) | |||||||
\(762\) | −15.3485 | −0.556018 | ||||||||
\(763\) | 15.1216 | 0.547439 | ||||||||
\(764\) | −5.71144 | −0.206633 | ||||||||
\(765\) | −17.3753 | −0.628207 | ||||||||
\(766\) | 25.5669 | 0.923771 | ||||||||
\(767\) | −9.97442 | −0.360155 | ||||||||
\(768\) | 1.34513 | 0.0485383 | ||||||||
\(769\) | −12.6391 | −0.455778 | −0.227889 | − | 0.973687i | \(-0.573182\pi\) | ||||
−0.227889 | + | 0.973687i | \(0.573182\pi\) | |||||||
\(770\) | −4.21590 | −0.151931 | ||||||||
\(771\) | 7.60040 | 0.273722 | ||||||||
\(772\) | −0.155001 | −0.00557859 | ||||||||
\(773\) | 15.1688 | 0.545583 | 0.272791 | − | 0.962073i | \(-0.412053\pi\) | ||||
0.272791 | + | 0.962073i | \(0.412053\pi\) | |||||||
\(774\) | −13.2365 | −0.475777 | ||||||||
\(775\) | 0.106742 | 0.00383427 | ||||||||
\(776\) | −13.9570 | −0.501026 | ||||||||
\(777\) | −5.73555 | −0.205762 | ||||||||
\(778\) | 29.9086 | 1.07228 | ||||||||
\(779\) | −21.2787 | −0.762389 | ||||||||
\(780\) | −3.19846 | −0.114523 | ||||||||
\(781\) | −4.90224 | −0.175416 | ||||||||
\(782\) | 45.2799 | 1.61921 | ||||||||
\(783\) | 24.5726 | 0.878153 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −10.2387 | −0.365436 | ||||||||
\(786\) | −10.2936 | −0.367161 | ||||||||
\(787\) | 5.30568 | 0.189127 | 0.0945635 | − | 0.995519i | \(-0.469854\pi\) | ||||
0.0945635 | + | 0.995519i | \(0.469854\pi\) | |||||||
\(788\) | −1.30758 | −0.0465805 | ||||||||
\(789\) | −33.5410 | −1.19409 | ||||||||
\(790\) | 6.61043 | 0.235188 | ||||||||
\(791\) | −11.0889 | −0.394277 | ||||||||
\(792\) | −2.16810 | −0.0770401 | ||||||||
\(793\) | 13.7331 | 0.487675 | ||||||||
\(794\) | 31.8776 | 1.13129 | ||||||||
\(795\) | 28.2677 | 1.00255 | ||||||||
\(796\) | −20.2631 | −0.718208 | ||||||||
\(797\) | −1.89545 | −0.0671403 | −0.0335701 | − | 0.999436i | \(-0.510688\pi\) | ||||
−0.0335701 | + | 0.999436i | \(0.510688\pi\) | |||||||
\(798\) | 5.22265 | 0.184880 | ||||||||
\(799\) | 3.84473 | 0.136017 | ||||||||
\(800\) | 0.360007 | 0.0127282 | ||||||||
\(801\) | 6.14392 | 0.217085 | ||||||||
\(802\) | −11.4030 | −0.402653 | ||||||||
\(803\) | 3.15191 | 0.111229 | ||||||||
\(804\) | −7.09956 | −0.250382 | ||||||||
\(805\) | 16.6307 | 0.586154 | ||||||||
\(806\) | 0.304520 | 0.0107262 | ||||||||
\(807\) | −1.77914 | −0.0626285 | ||||||||
\(808\) | −2.82966 | −0.0995472 | ||||||||
\(809\) | 46.1206 | 1.62152 | 0.810758 | − | 0.585382i | \(-0.199055\pi\) | ||||
0.810758 | + | 0.585382i | \(0.199055\pi\) | |||||||
\(810\) | 9.28519 | 0.326248 | ||||||||
\(811\) | 20.5964 | 0.723238 | 0.361619 | − | 0.932326i | \(-0.382224\pi\) | ||||
0.361619 | + | 0.932326i | \(0.382224\pi\) | |||||||
\(812\) | −4.35921 | −0.152978 | ||||||||
\(813\) | 43.9133 | 1.54011 | ||||||||
\(814\) | −7.76457 | −0.272148 | ||||||||
\(815\) | −10.4631 | −0.366505 | ||||||||
\(816\) | −8.47900 | −0.296824 | ||||||||
\(817\) | 43.1646 | 1.51014 | ||||||||
\(818\) | −34.8689 | −1.21916 | ||||||||
\(819\) | −1.22282 | −0.0427289 | ||||||||
\(820\) | 12.6883 | 0.443094 | ||||||||
\(821\) | −28.8291 | −1.00614 | −0.503072 | − | 0.864245i | \(-0.667797\pi\) | ||||
−0.503072 | + | 0.864245i | \(0.667797\pi\) | |||||||
\(822\) | −1.86003 | −0.0648760 | ||||||||
\(823\) | −15.4151 | −0.537338 | −0.268669 | − | 0.963233i | \(-0.586584\pi\) | ||||
−0.268669 | + | 0.963233i | \(0.586584\pi\) | |||||||
\(824\) | 7.19060 | 0.250496 | ||||||||
\(825\) | 0.881829 | 0.0307013 | ||||||||
\(826\) | −9.71171 | −0.337914 | ||||||||
\(827\) | 23.0588 | 0.801832 | 0.400916 | − | 0.916115i | \(-0.368692\pi\) | ||||
0.400916 | + | 0.916115i | \(0.368692\pi\) | |||||||
\(828\) | 8.55260 | 0.297223 | ||||||||
\(829\) | 28.6997 | 0.996783 | 0.498391 | − | 0.866952i | \(-0.333924\pi\) | ||||
0.498391 | + | 0.866952i | \(0.333924\pi\) | |||||||
\(830\) | 1.17930 | 0.0409341 | ||||||||
\(831\) | −44.5550 | −1.54560 | ||||||||
\(832\) | 1.02705 | 0.0356066 | ||||||||
\(833\) | −6.30346 | −0.218402 | ||||||||
\(834\) | 8.71986 | 0.301944 | ||||||||
\(835\) | 19.6267 | 0.679211 | ||||||||
\(836\) | 7.07022 | 0.244529 | ||||||||
\(837\) | −1.67135 | −0.0577702 | ||||||||
\(838\) | 19.6912 | 0.680222 | ||||||||
\(839\) | 42.0912 | 1.45315 | 0.726575 | − | 0.687087i | \(-0.241111\pi\) | ||||
0.726575 | + | 0.687087i | \(0.241111\pi\) | |||||||
\(840\) | −3.11421 | −0.107451 | ||||||||
\(841\) | −9.99730 | −0.344734 | ||||||||
\(842\) | 23.1688 | 0.798450 | ||||||||
\(843\) | 19.0526 | 0.656208 | ||||||||
\(844\) | −10.2278 | −0.352057 | ||||||||
\(845\) | 27.6551 | 0.951364 | ||||||||
\(846\) | 0.726203 | 0.0249674 | ||||||||
\(847\) | −7.68399 | −0.264025 | ||||||||
\(848\) | −9.07701 | −0.311706 | ||||||||
\(849\) | 7.69383 | 0.264052 | ||||||||
\(850\) | −2.26929 | −0.0778360 | ||||||||
\(851\) | 30.6292 | 1.04996 | ||||||||
\(852\) | −3.62120 | −0.124060 | ||||||||
\(853\) | −9.34734 | −0.320047 | −0.160023 | − | 0.987113i | \(-0.551157\pi\) | ||||
−0.160023 | + | 0.987113i | \(0.551157\pi\) | |||||||
\(854\) | 13.3714 | 0.457558 | ||||||||
\(855\) | 10.7024 | 0.366013 | ||||||||
\(856\) | 7.35379 | 0.251347 | ||||||||
\(857\) | −9.37499 | −0.320244 | −0.160122 | − | 0.987097i | \(-0.551189\pi\) | ||||
−0.160122 | + | 0.987097i | \(0.551189\pi\) | |||||||
\(858\) | 2.51574 | 0.0858859 | ||||||||
\(859\) | −30.5504 | −1.04236 | −0.521182 | − | 0.853445i | \(-0.674509\pi\) | ||||
−0.521182 | + | 0.853445i | \(0.674509\pi\) | |||||||
\(860\) | −25.7386 | −0.877679 | ||||||||
\(861\) | −7.37200 | −0.251237 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 36.2743 | 1.23479 | 0.617396 | − | 0.786652i | \(-0.288187\pi\) | ||||
0.617396 | + | 0.786652i | \(0.288187\pi\) | |||||||
\(864\) | −5.63694 | −0.191773 | ||||||||
\(865\) | −4.81052 | −0.163563 | ||||||||
\(866\) | −1.13204 | −0.0384684 | ||||||||
\(867\) | 30.5798 | 1.03854 | ||||||||
\(868\) | 0.296499 | 0.0100638 | ||||||||
\(869\) | −5.19942 | −0.176378 | ||||||||
\(870\) | 13.5755 | 0.460252 | ||||||||
\(871\) | −5.42073 | −0.183674 | ||||||||
\(872\) | 15.1216 | 0.512082 | ||||||||
\(873\) | 16.6174 | 0.562413 | ||||||||
\(874\) | −27.8902 | −0.943401 | ||||||||
\(875\) | 10.7424 | 0.363158 | ||||||||
\(876\) | 2.32826 | 0.0786647 | ||||||||
\(877\) | 47.2987 | 1.59716 | 0.798582 | − | 0.601887i | \(-0.205584\pi\) | ||||
0.798582 | + | 0.601887i | \(0.205584\pi\) | |||||||
\(878\) | −25.1495 | −0.848756 | ||||||||
\(879\) | 23.2869 | 0.785447 | ||||||||
\(880\) | −4.21590 | −0.142118 | ||||||||
\(881\) | 23.0318 | 0.775961 | 0.387981 | − | 0.921668i | \(-0.373173\pi\) | ||||
0.387981 | + | 0.921668i | \(0.373173\pi\) | |||||||
\(882\) | −1.19062 | −0.0400901 | ||||||||
\(883\) | −13.6038 | −0.457804 | −0.228902 | − | 0.973450i | \(-0.573513\pi\) | ||||
−0.228902 | + | 0.973450i | \(0.573513\pi\) | |||||||
\(884\) | −6.47398 | −0.217743 | ||||||||
\(885\) | 30.2443 | 1.01665 | ||||||||
\(886\) | 39.4788 | 1.32632 | ||||||||
\(887\) | −26.5315 | −0.890839 | −0.445420 | − | 0.895322i | \(-0.646946\pi\) | ||||
−0.445420 | + | 0.895322i | \(0.646946\pi\) | |||||||
\(888\) | −5.73555 | −0.192472 | ||||||||
\(889\) | −11.4104 | −0.382692 | ||||||||
\(890\) | 11.9469 | 0.400462 | ||||||||
\(891\) | −7.30325 | −0.244668 | ||||||||
\(892\) | −0.988408 | −0.0330943 | ||||||||
\(893\) | −2.36816 | −0.0792475 | ||||||||
\(894\) | 2.12227 | 0.0709794 | ||||||||
\(895\) | −17.1594 | −0.573575 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −9.92394 | −0.331351 | ||||||||
\(898\) | −10.1433 | −0.338487 | ||||||||
\(899\) | −1.29250 | −0.0431073 | ||||||||
\(900\) | −0.428630 | −0.0142877 | ||||||||
\(901\) | 57.2166 | 1.90616 | ||||||||
\(902\) | −9.97994 | −0.332296 | ||||||||
\(903\) | 14.9544 | 0.497650 | ||||||||
\(904\) | −11.0889 | −0.368812 | ||||||||
\(905\) | −45.8791 | −1.52507 | ||||||||
\(906\) | −14.9500 | −0.496680 | ||||||||
\(907\) | −18.4609 | −0.612985 | −0.306493 | − | 0.951873i | \(-0.599155\pi\) | ||||
−0.306493 | + | 0.951873i | \(0.599155\pi\) | |||||||
\(908\) | −8.40225 | −0.278838 | ||||||||
\(909\) | 3.36904 | 0.111744 | ||||||||
\(910\) | −2.37780 | −0.0788232 | ||||||||
\(911\) | −25.1156 | −0.832117 | −0.416059 | − | 0.909338i | \(-0.636589\pi\) | ||||
−0.416059 | + | 0.909338i | \(0.636589\pi\) | |||||||
\(912\) | 5.22265 | 0.172939 | ||||||||
\(913\) | −0.927577 | −0.0306983 | ||||||||
\(914\) | 12.6043 | 0.416913 | ||||||||
\(915\) | −41.6412 | −1.37662 | ||||||||
\(916\) | −4.93262 | −0.162978 | ||||||||
\(917\) | −7.65248 | −0.252707 | ||||||||
\(918\) | 35.5322 | 1.17274 | ||||||||
\(919\) | −8.97466 | −0.296047 | −0.148023 | − | 0.988984i | \(-0.547291\pi\) | ||||
−0.148023 | + | 0.988984i | \(0.547291\pi\) | |||||||
\(920\) | 16.6307 | 0.548297 | ||||||||
\(921\) | 38.9033 | 1.28191 | ||||||||
\(922\) | −18.0661 | −0.594977 | ||||||||
\(923\) | −2.76490 | −0.0910077 | ||||||||
\(924\) | 2.44948 | 0.0805819 | ||||||||
\(925\) | −1.53504 | −0.0504719 | ||||||||
\(926\) | −22.1284 | −0.727183 | ||||||||
\(927\) | −8.56124 | −0.281188 | ||||||||
\(928\) | −4.35921 | −0.143098 | ||||||||
\(929\) | −21.8055 | −0.715415 | −0.357708 | − | 0.933834i | \(-0.616442\pi\) | ||||
−0.357708 | + | 0.933834i | \(0.616442\pi\) | |||||||
\(930\) | −0.923360 | −0.0302782 | ||||||||
\(931\) | 3.88262 | 0.127248 | ||||||||
\(932\) | 9.11465 | 0.298560 | ||||||||
\(933\) | 7.69641 | 0.251969 | ||||||||
\(934\) | 27.8531 | 0.911383 | ||||||||
\(935\) | 26.5748 | 0.869088 | ||||||||
\(936\) | −1.22282 | −0.0399692 | ||||||||
\(937\) | −23.1819 | −0.757319 | −0.378659 | − | 0.925536i | \(-0.623615\pi\) | ||||
−0.378659 | + | 0.925536i | \(0.623615\pi\) | |||||||
\(938\) | −5.27796 | −0.172331 | ||||||||
\(939\) | 9.79660 | 0.319700 | ||||||||
\(940\) | 1.41211 | 0.0460580 | ||||||||
\(941\) | −59.3173 | −1.93369 | −0.966844 | − | 0.255369i | \(-0.917803\pi\) | ||||
−0.966844 | + | 0.255369i | \(0.917803\pi\) | |||||||
\(942\) | 5.94880 | 0.193822 | ||||||||
\(943\) | 39.3683 | 1.28201 | ||||||||
\(944\) | −9.71171 | −0.316089 | ||||||||
\(945\) | 13.0505 | 0.424532 | ||||||||
\(946\) | 20.2446 | 0.658210 | ||||||||
\(947\) | 40.8224 | 1.32655 | 0.663274 | − | 0.748376i | \(-0.269166\pi\) | ||||
0.663274 | + | 0.748376i | \(0.269166\pi\) | |||||||
\(948\) | −3.84072 | −0.124741 | ||||||||
\(949\) | 1.77770 | 0.0577066 | ||||||||
\(950\) | 1.39777 | 0.0453497 | ||||||||
\(951\) | 31.6592 | 1.02662 | ||||||||
\(952\) | −6.30346 | −0.204296 | ||||||||
\(953\) | −42.5019 | −1.37677 | −0.688385 | − | 0.725346i | \(-0.741680\pi\) | ||||
−0.688385 | + | 0.725346i | \(0.741680\pi\) | |||||||
\(954\) | 10.8072 | 0.349897 | ||||||||
\(955\) | 13.2230 | 0.427885 | ||||||||
\(956\) | −10.0198 | −0.324064 | ||||||||
\(957\) | −10.6778 | −0.345164 | ||||||||
\(958\) | 7.54256 | 0.243689 | ||||||||
\(959\) | −1.38279 | −0.0446525 | ||||||||
\(960\) | −3.11421 | −0.100511 | ||||||||
\(961\) | −30.9121 | −0.997164 | ||||||||
\(962\) | −4.37927 | −0.141193 | ||||||||
\(963\) | −8.75553 | −0.282143 | ||||||||
\(964\) | −13.9163 | −0.448213 | ||||||||
\(965\) | 0.358853 | 0.0115519 | ||||||||
\(966\) | −9.66256 | −0.310888 | ||||||||
\(967\) | −24.4206 | −0.785313 | −0.392656 | − | 0.919685i | \(-0.628444\pi\) | ||||
−0.392656 | + | 0.919685i | \(0.628444\pi\) | |||||||
\(968\) | −7.68399 | −0.246973 | ||||||||
\(969\) | −32.9207 | −1.05757 | ||||||||
\(970\) | 32.3127 | 1.03750 | ||||||||
\(971\) | 47.1755 | 1.51394 | 0.756968 | − | 0.653452i | \(-0.226680\pi\) | ||||
0.756968 | + | 0.653452i | \(0.226680\pi\) | |||||||
\(972\) | 11.5160 | 0.369377 | ||||||||
\(973\) | 6.48252 | 0.207820 | ||||||||
\(974\) | 8.94353 | 0.286569 | ||||||||
\(975\) | 0.497357 | 0.0159282 | ||||||||
\(976\) | 13.3714 | 0.428007 | ||||||||
\(977\) | −8.43250 | −0.269780 | −0.134890 | − | 0.990861i | \(-0.543068\pi\) | ||||
−0.134890 | + | 0.990861i | \(0.543068\pi\) | |||||||
\(978\) | 6.07913 | 0.194389 | ||||||||
\(979\) | −9.39684 | −0.300324 | ||||||||
\(980\) | −2.31517 | −0.0739554 | ||||||||
\(981\) | −18.0040 | −0.574824 | ||||||||
\(982\) | −35.8923 | −1.14537 | ||||||||
\(983\) | −6.61558 | −0.211004 | −0.105502 | − | 0.994419i | \(-0.533645\pi\) | ||||
−0.105502 | + | 0.994419i | \(0.533645\pi\) | |||||||
\(984\) | −7.37200 | −0.235011 | ||||||||
\(985\) | 3.02726 | 0.0964565 | ||||||||
\(986\) | 27.4781 | 0.875081 | ||||||||
\(987\) | −0.820450 | −0.0261152 | ||||||||
\(988\) | 3.98765 | 0.126864 | ||||||||
\(989\) | −79.8599 | −2.53940 | ||||||||
\(990\) | 5.01952 | 0.159531 | ||||||||
\(991\) | 11.7155 | 0.372156 | 0.186078 | − | 0.982535i | \(-0.440422\pi\) | ||||
0.186078 | + | 0.982535i | \(0.440422\pi\) | |||||||
\(992\) | 0.296499 | 0.00941385 | ||||||||
\(993\) | −33.9013 | −1.07583 | ||||||||
\(994\) | −2.69207 | −0.0853874 | ||||||||
\(995\) | 46.9126 | 1.48723 | ||||||||
\(996\) | −0.685184 | −0.0217109 | ||||||||
\(997\) | −11.1932 | −0.354493 | −0.177246 | − | 0.984167i | \(-0.556719\pi\) | ||||
−0.177246 | + | 0.984167i | \(0.556719\pi\) | |||||||
\(998\) | −27.1444 | −0.859240 | ||||||||
\(999\) | 24.0355 | 0.760449 |
(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 | 6034.2.a.m.1.17 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.m.1.17 | ✓ | 21 | 1.1 | even | 1 | trivial |