Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(1,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, 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("750.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.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: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
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 | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.1 |
$q$-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 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.38197 | 0.900299 | 0.450149 | − | 0.892953i | \(-0.351371\pi\) | ||||
0.450149 | + | 0.892953i | \(0.351371\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.85410 | −1.76508 | −0.882539 | − | 0.470239i | \(-0.844168\pi\) | ||||
−0.882539 | + | 0.470239i | \(0.844168\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.38197 | 0.937989 | 0.468994 | − | 0.883201i | \(-0.344616\pi\) | ||||
0.468994 | + | 0.883201i | \(0.344616\pi\) | |||||||
\(14\) | −2.38197 | −0.636607 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.70820 | 1.86951 | 0.934757 | − | 0.355288i | \(-0.115617\pi\) | ||||
0.934757 | + | 0.355288i | \(0.115617\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.09017 | 0.938349 | 0.469175 | − | 0.883105i | \(-0.344551\pi\) | ||||
0.469175 | + | 0.883105i | \(0.344551\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.38197 | 0.519788 | ||||||||
\(22\) | 5.85410 | 1.24810 | ||||||||
\(23\) | −3.09017 | −0.644345 | −0.322172 | − | 0.946681i | \(-0.604413\pi\) | ||||
−0.322172 | + | 0.946681i | \(0.604413\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.38197 | −0.663258 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.38197 | 0.450149 | ||||||||
\(29\) | 5.70820 | 1.05999 | 0.529993 | − | 0.848002i | \(-0.322194\pi\) | ||||
0.529993 | + | 0.848002i | \(0.322194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.47214 | −1.16243 | −0.581215 | − | 0.813750i | \(-0.697422\pi\) | ||||
−0.581215 | + | 0.813750i | \(0.697422\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.85410 | −1.01907 | ||||||||
\(34\) | −7.70820 | −1.32195 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.61803 | −0.266003 | −0.133002 | − | 0.991116i | \(-0.542462\pi\) | ||||
−0.133002 | + | 0.991116i | \(0.542462\pi\) | |||||||
\(38\) | −4.09017 | −0.663513 | ||||||||
\(39\) | 3.38197 | 0.541548 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.381966 | 0.0596531 | 0.0298265 | − | 0.999555i | \(-0.490505\pi\) | ||||
0.0298265 | + | 0.999555i | \(0.490505\pi\) | |||||||
\(42\) | −2.38197 | −0.367545 | ||||||||
\(43\) | 7.70820 | 1.17549 | 0.587745 | − | 0.809046i | \(-0.300016\pi\) | ||||
0.587745 | + | 0.809046i | \(0.300016\pi\) | |||||||
\(44\) | −5.85410 | −0.882539 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.09017 | 0.455621 | ||||||||
\(47\) | 8.61803 | 1.25707 | 0.628535 | − | 0.777782i | \(-0.283655\pi\) | ||||
0.628535 | + | 0.777782i | \(0.283655\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.32624 | −0.189463 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.70820 | 1.07936 | ||||||||
\(52\) | 3.38197 | 0.468994 | ||||||||
\(53\) | 0.381966 | 0.0524671 | 0.0262335 | − | 0.999656i | \(-0.491649\pi\) | ||||
0.0262335 | + | 0.999656i | \(0.491649\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.38197 | −0.318304 | ||||||||
\(57\) | 4.09017 | 0.541756 | ||||||||
\(58\) | −5.70820 | −0.749524 | ||||||||
\(59\) | −10.8541 | −1.41308 | −0.706542 | − | 0.707671i | \(-0.749746\pi\) | ||||
−0.706542 | + | 0.707671i | \(0.749746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7082 | 1.49908 | 0.749541 | − | 0.661958i | \(-0.230274\pi\) | ||||
0.749541 | + | 0.661958i | \(0.230274\pi\) | |||||||
\(62\) | 6.47214 | 0.821962 | ||||||||
\(63\) | 2.38197 | 0.300100 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.85410 | 0.720590 | ||||||||
\(67\) | 3.23607 | 0.395349 | 0.197674 | − | 0.980268i | \(-0.436661\pi\) | ||||
0.197674 | + | 0.980268i | \(0.436661\pi\) | |||||||
\(68\) | 7.70820 | 0.934757 | ||||||||
\(69\) | −3.09017 | −0.372013 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.47214 | −0.530745 | −0.265372 | − | 0.964146i | \(-0.585495\pi\) | ||||
−0.265372 | + | 0.964146i | \(0.585495\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −8.00000 | −0.936329 | −0.468165 | − | 0.883641i | \(-0.655085\pi\) | ||||
−0.468165 | + | 0.883641i | \(0.655085\pi\) | |||||||
\(74\) | 1.61803 | 0.188093 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.09017 | 0.469175 | ||||||||
\(77\) | −13.9443 | −1.58910 | ||||||||
\(78\) | −3.38197 | −0.382932 | ||||||||
\(79\) | 12.4721 | 1.40322 | 0.701612 | − | 0.712559i | \(-0.252464\pi\) | ||||
0.701612 | + | 0.712559i | \(0.252464\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.381966 | −0.0421811 | ||||||||
\(83\) | 2.00000 | 0.219529 | 0.109764 | − | 0.993958i | \(-0.464990\pi\) | ||||
0.109764 | + | 0.993958i | \(0.464990\pi\) | |||||||
\(84\) | 2.38197 | 0.259894 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.70820 | −0.831197 | ||||||||
\(87\) | 5.70820 | 0.611984 | ||||||||
\(88\) | 5.85410 | 0.624049 | ||||||||
\(89\) | 15.5623 | 1.64960 | 0.824801 | − | 0.565424i | \(-0.191287\pi\) | ||||
0.824801 | + | 0.565424i | \(0.191287\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.05573 | 0.844470 | ||||||||
\(92\) | −3.09017 | −0.322172 | ||||||||
\(93\) | −6.47214 | −0.671129 | ||||||||
\(94\) | −8.61803 | −0.888882 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −14.1803 | −1.43980 | −0.719898 | − | 0.694080i | \(-0.755811\pi\) | ||||
−0.719898 | + | 0.694080i | \(0.755811\pi\) | |||||||
\(98\) | 1.32624 | 0.133970 | ||||||||
\(99\) | −5.85410 | −0.588359 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.7082 | −1.36402 | −0.682009 | − | 0.731344i | \(-0.738893\pi\) | ||||
−0.682009 | + | 0.731344i | \(0.738893\pi\) | |||||||
\(102\) | −7.70820 | −0.763226 | ||||||||
\(103\) | 2.90983 | 0.286714 | 0.143357 | − | 0.989671i | \(-0.454210\pi\) | ||||
0.143357 | + | 0.989671i | \(0.454210\pi\) | |||||||
\(104\) | −3.38197 | −0.331629 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.381966 | −0.0370998 | ||||||||
\(107\) | −2.00000 | −0.193347 | −0.0966736 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966736 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −1.70820 | −0.163616 | −0.0818081 | − | 0.996648i | \(-0.526069\pi\) | ||||
−0.0818081 | + | 0.996648i | \(0.526069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.61803 | −0.153577 | ||||||||
\(112\) | 2.38197 | 0.225075 | ||||||||
\(113\) | 3.70820 | 0.348838 | 0.174419 | − | 0.984671i | \(-0.444195\pi\) | ||||
0.174419 | + | 0.984671i | \(0.444195\pi\) | |||||||
\(114\) | −4.09017 | −0.383080 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.70820 | 0.529993 | ||||||||
\(117\) | 3.38197 | 0.312663 | ||||||||
\(118\) | 10.8541 | 0.999201 | ||||||||
\(119\) | 18.3607 | 1.68312 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.2705 | 2.11550 | ||||||||
\(122\) | −11.7082 | −1.06001 | ||||||||
\(123\) | 0.381966 | 0.0344407 | ||||||||
\(124\) | −6.47214 | −0.581215 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.38197 | −0.212202 | ||||||||
\(127\) | −5.52786 | −0.490519 | −0.245259 | − | 0.969458i | \(-0.578873\pi\) | ||||
−0.245259 | + | 0.969458i | \(0.578873\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.70820 | 0.678670 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.3262 | −1.77591 | −0.887956 | − | 0.459929i | \(-0.847875\pi\) | ||||
−0.887956 | + | 0.459929i | \(0.847875\pi\) | |||||||
\(132\) | −5.85410 | −0.509534 | ||||||||
\(133\) | 9.74265 | 0.844795 | ||||||||
\(134\) | −3.23607 | −0.279554 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.70820 | −0.660973 | ||||||||
\(137\) | 4.94427 | 0.422418 | 0.211209 | − | 0.977441i | \(-0.432260\pi\) | ||||
0.211209 | + | 0.977441i | \(0.432260\pi\) | |||||||
\(138\) | 3.09017 | 0.263053 | ||||||||
\(139\) | −2.61803 | −0.222059 | −0.111029 | − | 0.993817i | \(-0.535415\pi\) | ||||
−0.111029 | + | 0.993817i | \(0.535415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.61803 | 0.725769 | ||||||||
\(142\) | 4.47214 | 0.375293 | ||||||||
\(143\) | −19.7984 | −1.65562 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.00000 | 0.662085 | ||||||||
\(147\) | −1.32624 | −0.109386 | ||||||||
\(148\) | −1.61803 | −0.133002 | ||||||||
\(149\) | −9.41641 | −0.771422 | −0.385711 | − | 0.922620i | \(-0.626044\pi\) | ||||
−0.385711 | + | 0.922620i | \(0.626044\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.291796 | −0.0237460 | −0.0118730 | − | 0.999930i | \(-0.503779\pi\) | ||||
−0.0118730 | + | 0.999930i | \(0.503779\pi\) | |||||||
\(152\) | −4.09017 | −0.331757 | ||||||||
\(153\) | 7.70820 | 0.623171 | ||||||||
\(154\) | 13.9443 | 1.12366 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.38197 | 0.270774 | ||||||||
\(157\) | −6.94427 | −0.554213 | −0.277107 | − | 0.960839i | \(-0.589376\pi\) | ||||
−0.277107 | + | 0.960839i | \(0.589376\pi\) | |||||||
\(158\) | −12.4721 | −0.992230 | ||||||||
\(159\) | 0.381966 | 0.0302919 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.36068 | −0.580103 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −24.0000 | −1.87983 | −0.939913 | − | 0.341415i | \(-0.889094\pi\) | ||||
−0.939913 | + | 0.341415i | \(0.889094\pi\) | |||||||
\(164\) | 0.381966 | 0.0298265 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | −1.90983 | −0.147787 | −0.0738935 | − | 0.997266i | \(-0.523543\pi\) | ||||
−0.0738935 | + | 0.997266i | \(0.523543\pi\) | |||||||
\(168\) | −2.38197 | −0.183773 | ||||||||
\(169\) | −1.56231 | −0.120177 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.09017 | 0.312783 | ||||||||
\(172\) | 7.70820 | 0.587745 | ||||||||
\(173\) | 4.38197 | 0.333155 | 0.166577 | − | 0.986028i | \(-0.446728\pi\) | ||||
0.166577 | + | 0.986028i | \(0.446728\pi\) | |||||||
\(174\) | −5.70820 | −0.432738 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.85410 | −0.441270 | ||||||||
\(177\) | −10.8541 | −0.815844 | ||||||||
\(178\) | −15.5623 | −1.16644 | ||||||||
\(179\) | 3.79837 | 0.283904 | 0.141952 | − | 0.989874i | \(-0.454662\pi\) | ||||
0.141952 | + | 0.989874i | \(0.454662\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4721 | −1.52168 | −0.760841 | − | 0.648938i | \(-0.775213\pi\) | ||||
−0.760841 | + | 0.648938i | \(0.775213\pi\) | |||||||
\(182\) | −8.05573 | −0.597130 | ||||||||
\(183\) | 11.7082 | 0.865495 | ||||||||
\(184\) | 3.09017 | 0.227810 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.47214 | 0.474560 | ||||||||
\(187\) | −45.1246 | −3.29984 | ||||||||
\(188\) | 8.61803 | 0.628535 | ||||||||
\(189\) | 2.38197 | 0.173263 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | −0.289430 | −0.144715 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144715 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 9.70820 | 0.698812 | 0.349406 | − | 0.936971i | \(-0.386383\pi\) | ||||
0.349406 | + | 0.936971i | \(0.386383\pi\) | |||||||
\(194\) | 14.1803 | 1.01809 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.32624 | −0.0947313 | ||||||||
\(197\) | −14.9443 | −1.06474 | −0.532368 | − | 0.846513i | \(-0.678698\pi\) | ||||
−0.532368 | + | 0.846513i | \(0.678698\pi\) | |||||||
\(198\) | 5.85410 | 0.416033 | ||||||||
\(199\) | −4.76393 | −0.337706 | −0.168853 | − | 0.985641i | \(-0.554006\pi\) | ||||
−0.168853 | + | 0.985641i | \(0.554006\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.23607 | 0.228255 | ||||||||
\(202\) | 13.7082 | 0.964506 | ||||||||
\(203\) | 13.5967 | 0.954305 | ||||||||
\(204\) | 7.70820 | 0.539682 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.90983 | −0.202737 | ||||||||
\(207\) | −3.09017 | −0.214782 | ||||||||
\(208\) | 3.38197 | 0.234497 | ||||||||
\(209\) | −23.9443 | −1.65626 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.5623 | −1.55325 | −0.776627 | − | 0.629961i | \(-0.783071\pi\) | ||||
−0.776627 | + | 0.629961i | \(0.783071\pi\) | |||||||
\(212\) | 0.381966 | 0.0262335 | ||||||||
\(213\) | −4.47214 | −0.306426 | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −15.4164 | −1.04653 | ||||||||
\(218\) | 1.70820 | 0.115694 | ||||||||
\(219\) | −8.00000 | −0.540590 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.0689 | 1.75358 | ||||||||
\(222\) | 1.61803 | 0.108595 | ||||||||
\(223\) | −28.9443 | −1.93825 | −0.969126 | − | 0.246566i | \(-0.920698\pi\) | ||||
−0.969126 | + | 0.246566i | \(0.920698\pi\) | |||||||
\(224\) | −2.38197 | −0.159152 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.70820 | −0.246666 | ||||||||
\(227\) | 10.7639 | 0.714427 | 0.357214 | − | 0.934023i | \(-0.383727\pi\) | ||||
0.357214 | + | 0.934023i | \(0.383727\pi\) | |||||||
\(228\) | 4.09017 | 0.270878 | ||||||||
\(229\) | −22.7639 | −1.50428 | −0.752141 | − | 0.659002i | \(-0.770979\pi\) | ||||
−0.752141 | + | 0.659002i | \(0.770979\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.9443 | −0.917466 | ||||||||
\(232\) | −5.70820 | −0.374762 | ||||||||
\(233\) | −2.47214 | −0.161955 | −0.0809775 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809775 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(234\) | −3.38197 | −0.221086 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.8541 | −0.706542 | ||||||||
\(237\) | 12.4721 | 0.810152 | ||||||||
\(238\) | −18.3607 | −1.19015 | ||||||||
\(239\) | −7.05573 | −0.456397 | −0.228199 | − | 0.973615i | \(-0.573284\pi\) | ||||
−0.228199 | + | 0.973615i | \(0.573284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0902 | 0.972043 | 0.486022 | − | 0.873947i | \(-0.338448\pi\) | ||||
0.486022 | + | 0.873947i | \(0.338448\pi\) | |||||||
\(242\) | −23.2705 | −1.49589 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 11.7082 | 0.749541 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.381966 | −0.0243533 | ||||||||
\(247\) | 13.8328 | 0.880161 | ||||||||
\(248\) | 6.47214 | 0.410981 | ||||||||
\(249\) | 2.00000 | 0.126745 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 2.38197 | 0.150050 | ||||||||
\(253\) | 18.0902 | 1.13732 | ||||||||
\(254\) | 5.52786 | 0.346849 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.5279 | 1.09336 | 0.546679 | − | 0.837342i | \(-0.315892\pi\) | ||||
0.546679 | + | 0.837342i | \(0.315892\pi\) | |||||||
\(258\) | −7.70820 | −0.479892 | ||||||||
\(259\) | −3.85410 | −0.239482 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.70820 | 0.353329 | ||||||||
\(262\) | 20.3262 | 1.25576 | ||||||||
\(263\) | 25.3262 | 1.56168 | 0.780841 | − | 0.624729i | \(-0.214791\pi\) | ||||
0.780841 | + | 0.624729i | \(0.214791\pi\) | |||||||
\(264\) | 5.85410 | 0.360295 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.74265 | −0.597360 | ||||||||
\(267\) | 15.5623 | 0.952398 | ||||||||
\(268\) | 3.23607 | 0.197674 | ||||||||
\(269\) | −9.41641 | −0.574129 | −0.287064 | − | 0.957911i | \(-0.592679\pi\) | ||||
−0.287064 | + | 0.957911i | \(0.592679\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.41641 | −0.572006 | −0.286003 | − | 0.958229i | \(-0.592327\pi\) | ||||
−0.286003 | + | 0.958229i | \(0.592327\pi\) | |||||||
\(272\) | 7.70820 | 0.467379 | ||||||||
\(273\) | 8.05573 | 0.487555 | ||||||||
\(274\) | −4.94427 | −0.298694 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.09017 | −0.186006 | ||||||||
\(277\) | 27.4508 | 1.64936 | 0.824681 | − | 0.565598i | \(-0.191355\pi\) | ||||
0.824681 | + | 0.565598i | \(0.191355\pi\) | |||||||
\(278\) | 2.61803 | 0.157019 | ||||||||
\(279\) | −6.47214 | −0.387477 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.5066 | 1.46194 | 0.730970 | − | 0.682410i | \(-0.239068\pi\) | ||||
0.730970 | + | 0.682410i | \(0.239068\pi\) | |||||||
\(282\) | −8.61803 | −0.513196 | ||||||||
\(283\) | 8.18034 | 0.486271 | 0.243135 | − | 0.969992i | \(-0.421824\pi\) | ||||
0.243135 | + | 0.969992i | \(0.421824\pi\) | |||||||
\(284\) | −4.47214 | −0.265372 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 19.7984 | 1.17070 | ||||||||
\(287\) | 0.909830 | 0.0537056 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 42.4164 | 2.49508 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.1803 | −0.831266 | ||||||||
\(292\) | −8.00000 | −0.468165 | ||||||||
\(293\) | −20.7984 | −1.21505 | −0.607527 | − | 0.794299i | \(-0.707838\pi\) | ||||
−0.607527 | + | 0.794299i | \(0.707838\pi\) | |||||||
\(294\) | 1.32624 | 0.0773478 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.61803 | 0.0940463 | ||||||||
\(297\) | −5.85410 | −0.339689 | ||||||||
\(298\) | 9.41641 | 0.545478 | ||||||||
\(299\) | −10.4508 | −0.604388 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.3607 | 1.05829 | ||||||||
\(302\) | 0.291796 | 0.0167910 | ||||||||
\(303\) | −13.7082 | −0.787516 | ||||||||
\(304\) | 4.09017 | 0.234587 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.70820 | −0.440649 | ||||||||
\(307\) | −6.18034 | −0.352731 | −0.176365 | − | 0.984325i | \(-0.556434\pi\) | ||||
−0.176365 | + | 0.984325i | \(0.556434\pi\) | |||||||
\(308\) | −13.9443 | −0.794549 | ||||||||
\(309\) | 2.90983 | 0.165534 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.94427 | 0.507183 | 0.253592 | − | 0.967311i | \(-0.418388\pi\) | ||||
0.253592 | + | 0.967311i | \(0.418388\pi\) | |||||||
\(312\) | −3.38197 | −0.191466 | ||||||||
\(313\) | 0.291796 | 0.0164933 | 0.00824664 | − | 0.999966i | \(-0.497375\pi\) | ||||
0.00824664 | + | 0.999966i | \(0.497375\pi\) | |||||||
\(314\) | 6.94427 | 0.391888 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.4721 | 0.701612 | ||||||||
\(317\) | 23.8541 | 1.33978 | 0.669890 | − | 0.742460i | \(-0.266341\pi\) | ||||
0.669890 | + | 0.742460i | \(0.266341\pi\) | |||||||
\(318\) | −0.381966 | −0.0214196 | ||||||||
\(319\) | −33.4164 | −1.87096 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00000 | −0.111629 | ||||||||
\(322\) | 7.36068 | 0.410195 | ||||||||
\(323\) | 31.5279 | 1.75426 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.0000 | 1.32924 | ||||||||
\(327\) | −1.70820 | −0.0944639 | ||||||||
\(328\) | −0.381966 | −0.0210905 | ||||||||
\(329\) | 20.5279 | 1.13174 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.47214 | 0.355741 | 0.177870 | − | 0.984054i | \(-0.443079\pi\) | ||||
0.177870 | + | 0.984054i | \(0.443079\pi\) | |||||||
\(332\) | 2.00000 | 0.109764 | ||||||||
\(333\) | −1.61803 | −0.0886677 | ||||||||
\(334\) | 1.90983 | 0.104501 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.38197 | 0.129947 | ||||||||
\(337\) | −20.8328 | −1.13484 | −0.567418 | − | 0.823430i | \(-0.692058\pi\) | ||||
−0.567418 | + | 0.823430i | \(0.692058\pi\) | |||||||
\(338\) | 1.56231 | 0.0849782 | ||||||||
\(339\) | 3.70820 | 0.201402 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.8885 | 2.05178 | ||||||||
\(342\) | −4.09017 | −0.221171 | ||||||||
\(343\) | −19.8328 | −1.07087 | ||||||||
\(344\) | −7.70820 | −0.415599 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.38197 | −0.235576 | ||||||||
\(347\) | −14.1803 | −0.761241 | −0.380620 | − | 0.924731i | \(-0.624289\pi\) | ||||
−0.380620 | + | 0.924731i | \(0.624289\pi\) | |||||||
\(348\) | 5.70820 | 0.305992 | ||||||||
\(349\) | −20.0000 | −1.07058 | −0.535288 | − | 0.844670i | \(-0.679797\pi\) | ||||
−0.535288 | + | 0.844670i | \(0.679797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.38197 | 0.180516 | ||||||||
\(352\) | 5.85410 | 0.312025 | ||||||||
\(353\) | −9.12461 | −0.485654 | −0.242827 | − | 0.970070i | \(-0.578075\pi\) | ||||
−0.242827 | + | 0.970070i | \(0.578075\pi\) | |||||||
\(354\) | 10.8541 | 0.576889 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.5623 | 0.824801 | ||||||||
\(357\) | 18.3607 | 0.971750 | ||||||||
\(358\) | −3.79837 | −0.200750 | ||||||||
\(359\) | −17.4164 | −0.919203 | −0.459601 | − | 0.888125i | \(-0.652008\pi\) | ||||
−0.459601 | + | 0.888125i | \(0.652008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.27051 | −0.119501 | ||||||||
\(362\) | 20.4721 | 1.07599 | ||||||||
\(363\) | 23.2705 | 1.22139 | ||||||||
\(364\) | 8.05573 | 0.422235 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −11.7082 | −0.611998 | ||||||||
\(367\) | 15.4164 | 0.804730 | 0.402365 | − | 0.915479i | \(-0.368188\pi\) | ||||
0.402365 | + | 0.915479i | \(0.368188\pi\) | |||||||
\(368\) | −3.09017 | −0.161086 | ||||||||
\(369\) | 0.381966 | 0.0198844 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.909830 | 0.0472360 | ||||||||
\(372\) | −6.47214 | −0.335565 | ||||||||
\(373\) | −19.3262 | −1.00067 | −0.500337 | − | 0.865831i | \(-0.666791\pi\) | ||||
−0.500337 | + | 0.865831i | \(0.666791\pi\) | |||||||
\(374\) | 45.1246 | 2.33334 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.61803 | −0.444441 | ||||||||
\(377\) | 19.3050 | 0.994256 | ||||||||
\(378\) | −2.38197 | −0.122515 | ||||||||
\(379\) | 35.9230 | 1.84524 | 0.922620 | − | 0.385710i | \(-0.126044\pi\) | ||||
0.922620 | + | 0.385710i | \(0.126044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.52786 | −0.283201 | ||||||||
\(382\) | 4.00000 | 0.204658 | ||||||||
\(383\) | 27.0344 | 1.38140 | 0.690698 | − | 0.723144i | \(-0.257304\pi\) | ||||
0.690698 | + | 0.723144i | \(0.257304\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.70820 | −0.494135 | ||||||||
\(387\) | 7.70820 | 0.391830 | ||||||||
\(388\) | −14.1803 | −0.719898 | ||||||||
\(389\) | −34.5410 | −1.75130 | −0.875650 | − | 0.482947i | \(-0.839566\pi\) | ||||
−0.875650 | + | 0.482947i | \(0.839566\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.8197 | −1.20461 | ||||||||
\(392\) | 1.32624 | 0.0669851 | ||||||||
\(393\) | −20.3262 | −1.02532 | ||||||||
\(394\) | 14.9443 | 0.752882 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.85410 | −0.294180 | ||||||||
\(397\) | 23.3262 | 1.17071 | 0.585355 | − | 0.810777i | \(-0.300955\pi\) | ||||
0.585355 | + | 0.810777i | \(0.300955\pi\) | |||||||
\(398\) | 4.76393 | 0.238794 | ||||||||
\(399\) | 9.74265 | 0.487742 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.32624 | −0.0662292 | −0.0331146 | − | 0.999452i | \(-0.510543\pi\) | ||||
−0.0331146 | + | 0.999452i | \(0.510543\pi\) | |||||||
\(402\) | −3.23607 | −0.161400 | ||||||||
\(403\) | −21.8885 | −1.09035 | ||||||||
\(404\) | −13.7082 | −0.682009 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.5967 | −0.674795 | ||||||||
\(407\) | 9.47214 | 0.469516 | ||||||||
\(408\) | −7.70820 | −0.381613 | ||||||||
\(409\) | −4.85410 | −0.240020 | −0.120010 | − | 0.992773i | \(-0.538293\pi\) | ||||
−0.120010 | + | 0.992773i | \(0.538293\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.94427 | 0.243883 | ||||||||
\(412\) | 2.90983 | 0.143357 | ||||||||
\(413\) | −25.8541 | −1.27220 | ||||||||
\(414\) | 3.09017 | 0.151874 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.38197 | −0.165815 | ||||||||
\(417\) | −2.61803 | −0.128206 | ||||||||
\(418\) | 23.9443 | 1.17115 | ||||||||
\(419\) | 17.8885 | 0.873913 | 0.436956 | − | 0.899483i | \(-0.356056\pi\) | ||||
0.436956 | + | 0.899483i | \(0.356056\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.1246 | −1.22450 | −0.612249 | − | 0.790665i | \(-0.709735\pi\) | ||||
−0.612249 | + | 0.790665i | \(0.709735\pi\) | |||||||
\(422\) | 22.5623 | 1.09832 | ||||||||
\(423\) | 8.61803 | 0.419023 | ||||||||
\(424\) | −0.381966 | −0.0185499 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.47214 | 0.216676 | ||||||||
\(427\) | 27.8885 | 1.34962 | ||||||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | −19.7984 | −0.955874 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.2361 | 0.830232 | 0.415116 | − | 0.909768i | \(-0.363741\pi\) | ||||
0.415116 | + | 0.909768i | \(0.363741\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 38.3607 | 1.84350 | 0.921748 | − | 0.387789i | \(-0.126761\pi\) | ||||
0.921748 | + | 0.387789i | \(0.126761\pi\) | |||||||
\(434\) | 15.4164 | 0.740011 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.70820 | −0.0818081 | ||||||||
\(437\) | −12.6393 | −0.604621 | ||||||||
\(438\) | 8.00000 | 0.382255 | ||||||||
\(439\) | −32.6525 | −1.55842 | −0.779209 | − | 0.626764i | \(-0.784379\pi\) | ||||
−0.779209 | + | 0.626764i | \(0.784379\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.32624 | −0.0631542 | ||||||||
\(442\) | −26.0689 | −1.23997 | ||||||||
\(443\) | −13.1246 | −0.623569 | −0.311785 | − | 0.950153i | \(-0.600927\pi\) | ||||
−0.311785 | + | 0.950153i | \(0.600927\pi\) | |||||||
\(444\) | −1.61803 | −0.0767885 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 28.9443 | 1.37055 | ||||||||
\(447\) | −9.41641 | −0.445381 | ||||||||
\(448\) | 2.38197 | 0.112537 | ||||||||
\(449\) | 16.5623 | 0.781624 | 0.390812 | − | 0.920471i | \(-0.372194\pi\) | ||||
0.390812 | + | 0.920471i | \(0.372194\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.23607 | −0.105292 | ||||||||
\(452\) | 3.70820 | 0.174419 | ||||||||
\(453\) | −0.291796 | −0.0137098 | ||||||||
\(454\) | −10.7639 | −0.505176 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.09017 | −0.191540 | ||||||||
\(457\) | 33.8885 | 1.58524 | 0.792620 | − | 0.609716i | \(-0.208717\pi\) | ||||
0.792620 | + | 0.609716i | \(0.208717\pi\) | |||||||
\(458\) | 22.7639 | 1.06369 | ||||||||
\(459\) | 7.70820 | 0.359788 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.5967 | 0.912712 | 0.456356 | − | 0.889797i | \(-0.349154\pi\) | ||||
0.456356 | + | 0.889797i | \(0.349154\pi\) | |||||||
\(462\) | 13.9443 | 0.648746 | ||||||||
\(463\) | −15.0557 | −0.699699 | −0.349850 | − | 0.936806i | \(-0.613767\pi\) | ||||
−0.349850 | + | 0.936806i | \(0.613767\pi\) | |||||||
\(464\) | 5.70820 | 0.264997 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.47214 | 0.114519 | ||||||||
\(467\) | 21.2361 | 0.982688 | 0.491344 | − | 0.870966i | \(-0.336506\pi\) | ||||
0.491344 | + | 0.870966i | \(0.336506\pi\) | |||||||
\(468\) | 3.38197 | 0.156331 | ||||||||
\(469\) | 7.70820 | 0.355932 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.94427 | −0.319975 | ||||||||
\(472\) | 10.8541 | 0.499601 | ||||||||
\(473\) | −45.1246 | −2.07483 | ||||||||
\(474\) | −12.4721 | −0.572864 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 18.3607 | 0.841560 | ||||||||
\(477\) | 0.381966 | 0.0174890 | ||||||||
\(478\) | 7.05573 | 0.322721 | ||||||||
\(479\) | −9.12461 | −0.416914 | −0.208457 | − | 0.978032i | \(-0.566844\pi\) | ||||
−0.208457 | + | 0.978032i | \(0.566844\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.47214 | −0.249508 | ||||||||
\(482\) | −15.0902 | −0.687338 | ||||||||
\(483\) | −7.36068 | −0.334923 | ||||||||
\(484\) | 23.2705 | 1.05775 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −12.7984 | −0.579950 | −0.289975 | − | 0.957034i | \(-0.593647\pi\) | ||||
−0.289975 | + | 0.957034i | \(0.593647\pi\) | |||||||
\(488\) | −11.7082 | −0.530005 | ||||||||
\(489\) | −24.0000 | −1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.0344 | 0.497977 | 0.248989 | − | 0.968506i | \(-0.419902\pi\) | ||||
0.248989 | + | 0.968506i | \(0.419902\pi\) | |||||||
\(492\) | 0.381966 | 0.0172204 | ||||||||
\(493\) | 44.0000 | 1.98166 | ||||||||
\(494\) | −13.8328 | −0.622368 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.47214 | −0.290607 | ||||||||
\(497\) | −10.6525 | −0.477829 | ||||||||
\(498\) | −2.00000 | −0.0896221 | ||||||||
\(499\) | −5.38197 | −0.240930 | −0.120465 | − | 0.992718i | \(-0.538439\pi\) | ||||
−0.120465 | + | 0.992718i | \(0.538439\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.90983 | −0.0853249 | ||||||||
\(502\) | 24.0000 | 1.07117 | ||||||||
\(503\) | −30.1459 | −1.34414 | −0.672070 | − | 0.740488i | \(-0.734594\pi\) | ||||
−0.672070 | + | 0.740488i | \(0.734594\pi\) | |||||||
\(504\) | −2.38197 | −0.106101 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −18.0902 | −0.804206 | ||||||||
\(507\) | −1.56231 | −0.0693844 | ||||||||
\(508\) | −5.52786 | −0.245259 | ||||||||
\(509\) | 12.2918 | 0.544824 | 0.272412 | − | 0.962181i | \(-0.412179\pi\) | ||||
0.272412 | + | 0.962181i | \(0.412179\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.0557 | −0.842976 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.09017 | 0.180585 | ||||||||
\(514\) | −17.5279 | −0.773121 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.70820 | 0.339335 | ||||||||
\(517\) | −50.4508 | −2.21883 | ||||||||
\(518\) | 3.85410 | 0.169340 | ||||||||
\(519\) | 4.38197 | 0.192347 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.09017 | 0.0477612 | 0.0238806 | − | 0.999715i | \(-0.492398\pi\) | ||||
0.0238806 | + | 0.999715i | \(0.492398\pi\) | |||||||
\(522\) | −5.70820 | −0.249841 | ||||||||
\(523\) | 32.3607 | 1.41503 | 0.707517 | − | 0.706696i | \(-0.249815\pi\) | ||||
0.707517 | + | 0.706696i | \(0.249815\pi\) | |||||||
\(524\) | −20.3262 | −0.887956 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25.3262 | −1.10428 | ||||||||
\(527\) | −49.8885 | −2.17318 | ||||||||
\(528\) | −5.85410 | −0.254767 | ||||||||
\(529\) | −13.4508 | −0.584820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.8541 | −0.471028 | ||||||||
\(532\) | 9.74265 | 0.422397 | ||||||||
\(533\) | 1.29180 | 0.0559539 | ||||||||
\(534\) | −15.5623 | −0.673447 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.23607 | −0.139777 | ||||||||
\(537\) | 3.79837 | 0.163912 | ||||||||
\(538\) | 9.41641 | 0.405970 | ||||||||
\(539\) | 7.76393 | 0.334416 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.4164 | −0.576816 | −0.288408 | − | 0.957508i | \(-0.593126\pi\) | ||||
−0.288408 | + | 0.957508i | \(0.593126\pi\) | |||||||
\(542\) | 9.41641 | 0.404469 | ||||||||
\(543\) | −20.4721 | −0.878543 | ||||||||
\(544\) | −7.70820 | −0.330487 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.05573 | −0.344753 | ||||||||
\(547\) | −0.763932 | −0.0326634 | −0.0163317 | − | 0.999867i | \(-0.505199\pi\) | ||||
−0.0163317 | + | 0.999867i | \(0.505199\pi\) | |||||||
\(548\) | 4.94427 | 0.211209 | ||||||||
\(549\) | 11.7082 | 0.499694 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.3475 | 0.994638 | ||||||||
\(552\) | 3.09017 | 0.131526 | ||||||||
\(553\) | 29.7082 | 1.26332 | ||||||||
\(554\) | −27.4508 | −1.16627 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.61803 | −0.111029 | ||||||||
\(557\) | 13.4508 | 0.569931 | 0.284965 | − | 0.958538i | \(-0.408018\pi\) | ||||
0.284965 | + | 0.958538i | \(0.408018\pi\) | |||||||
\(558\) | 6.47214 | 0.273987 | ||||||||
\(559\) | 26.0689 | 1.10260 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −45.1246 | −1.90516 | ||||||||
\(562\) | −24.5066 | −1.03375 | ||||||||
\(563\) | 6.94427 | 0.292666 | 0.146333 | − | 0.989235i | \(-0.453253\pi\) | ||||
0.146333 | + | 0.989235i | \(0.453253\pi\) | |||||||
\(564\) | 8.61803 | 0.362885 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.18034 | −0.343845 | ||||||||
\(567\) | 2.38197 | 0.100033 | ||||||||
\(568\) | 4.47214 | 0.187647 | ||||||||
\(569\) | 27.9230 | 1.17059 | 0.585296 | − | 0.810820i | \(-0.300978\pi\) | ||||
0.585296 | + | 0.810820i | \(0.300978\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.27051 | 0.178715 | 0.0893576 | − | 0.996000i | \(-0.471519\pi\) | ||||
0.0893576 | + | 0.996000i | \(0.471519\pi\) | |||||||
\(572\) | −19.7984 | −0.827812 | ||||||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | −0.909830 | −0.0379756 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 9.23607 | 0.384503 | 0.192251 | − | 0.981346i | \(-0.438421\pi\) | ||||
0.192251 | + | 0.981346i | \(0.438421\pi\) | |||||||
\(578\) | −42.4164 | −1.76429 | ||||||||
\(579\) | 9.70820 | 0.403459 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.76393 | 0.197641 | ||||||||
\(582\) | 14.1803 | 0.587794 | ||||||||
\(583\) | −2.23607 | −0.0926085 | ||||||||
\(584\) | 8.00000 | 0.331042 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.7984 | 0.859173 | ||||||||
\(587\) | 25.2361 | 1.04160 | 0.520802 | − | 0.853678i | \(-0.325633\pi\) | ||||
0.520802 | + | 0.853678i | \(0.325633\pi\) | |||||||
\(588\) | −1.32624 | −0.0546931 | ||||||||
\(589\) | −26.4721 | −1.09077 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.9443 | −0.614725 | ||||||||
\(592\) | −1.61803 | −0.0665008 | ||||||||
\(593\) | 31.3050 | 1.28554 | 0.642770 | − | 0.766059i | \(-0.277785\pi\) | ||||
0.642770 | + | 0.766059i | \(0.277785\pi\) | |||||||
\(594\) | 5.85410 | 0.240197 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.41641 | −0.385711 | ||||||||
\(597\) | −4.76393 | −0.194975 | ||||||||
\(598\) | 10.4508 | 0.427367 | ||||||||
\(599\) | −6.76393 | −0.276367 | −0.138183 | − | 0.990407i | \(-0.544126\pi\) | ||||
−0.138183 | + | 0.990407i | \(0.544126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.4377 | 0.425762 | 0.212881 | − | 0.977078i | \(-0.431715\pi\) | ||||
0.212881 | + | 0.977078i | \(0.431715\pi\) | |||||||
\(602\) | −18.3607 | −0.748325 | ||||||||
\(603\) | 3.23607 | 0.131783 | ||||||||
\(604\) | −0.291796 | −0.0118730 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.7082 | 0.556858 | ||||||||
\(607\) | −9.97871 | −0.405023 | −0.202512 | − | 0.979280i | \(-0.564910\pi\) | ||||
−0.202512 | + | 0.979280i | \(0.564910\pi\) | |||||||
\(608\) | −4.09017 | −0.165878 | ||||||||
\(609\) | 13.5967 | 0.550968 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.1459 | 1.17912 | ||||||||
\(612\) | 7.70820 | 0.311586 | ||||||||
\(613\) | −31.7426 | −1.28207 | −0.641037 | − | 0.767510i | \(-0.721495\pi\) | ||||
−0.641037 | + | 0.767510i | \(0.721495\pi\) | |||||||
\(614\) | 6.18034 | 0.249418 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.9443 | 0.561831 | ||||||||
\(617\) | 5.52786 | 0.222543 | 0.111272 | − | 0.993790i | \(-0.464508\pi\) | ||||
0.111272 | + | 0.993790i | \(0.464508\pi\) | |||||||
\(618\) | −2.90983 | −0.117051 | ||||||||
\(619\) | −11.8541 | −0.476457 | −0.238228 | − | 0.971209i | \(-0.576567\pi\) | ||||
−0.238228 | + | 0.971209i | \(0.576567\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.09017 | −0.124004 | ||||||||
\(622\) | −8.94427 | −0.358633 | ||||||||
\(623\) | 37.0689 | 1.48513 | ||||||||
\(624\) | 3.38197 | 0.135387 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.291796 | −0.0116625 | ||||||||
\(627\) | −23.9443 | −0.956242 | ||||||||
\(628\) | −6.94427 | −0.277107 | ||||||||
\(629\) | −12.4721 | −0.497297 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.7082 | 1.34190 | 0.670951 | − | 0.741502i | \(-0.265886\pi\) | ||||
0.670951 | + | 0.741502i | \(0.265886\pi\) | |||||||
\(632\) | −12.4721 | −0.496115 | ||||||||
\(633\) | −22.5623 | −0.896771 | ||||||||
\(634\) | −23.8541 | −0.947367 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.381966 | 0.0151459 | ||||||||
\(637\) | −4.48529 | −0.177714 | ||||||||
\(638\) | 33.4164 | 1.32297 | ||||||||
\(639\) | −4.47214 | −0.176915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.1459 | −1.15119 | −0.575597 | − | 0.817734i | \(-0.695230\pi\) | ||||
−0.575597 | + | 0.817734i | \(0.695230\pi\) | |||||||
\(642\) | 2.00000 | 0.0789337 | ||||||||
\(643\) | −15.0557 | −0.593740 | −0.296870 | − | 0.954918i | \(-0.595943\pi\) | ||||
−0.296870 | + | 0.954918i | \(0.595943\pi\) | |||||||
\(644\) | −7.36068 | −0.290051 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.5279 | −1.24045 | ||||||||
\(647\) | 14.8541 | 0.583975 | 0.291988 | − | 0.956422i | \(-0.405683\pi\) | ||||
0.291988 | + | 0.956422i | \(0.405683\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 63.5410 | 2.49420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.4164 | −0.604217 | ||||||||
\(652\) | −24.0000 | −0.939913 | ||||||||
\(653\) | 12.1459 | 0.475306 | 0.237653 | − | 0.971350i | \(-0.423622\pi\) | ||||
0.237653 | + | 0.971350i | \(0.423622\pi\) | |||||||
\(654\) | 1.70820 | 0.0667961 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.381966 | 0.0149133 | ||||||||
\(657\) | −8.00000 | −0.312110 | ||||||||
\(658\) | −20.5279 | −0.800259 | ||||||||
\(659\) | 14.5066 | 0.565096 | 0.282548 | − | 0.959253i | \(-0.408820\pi\) | ||||
0.282548 | + | 0.959253i | \(0.408820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.875388 | −0.0340487 | −0.0170243 | − | 0.999855i | \(-0.505419\pi\) | ||||
−0.0170243 | + | 0.999855i | \(0.505419\pi\) | |||||||
\(662\) | −6.47214 | −0.251547 | ||||||||
\(663\) | 26.0689 | 1.01243 | ||||||||
\(664\) | −2.00000 | −0.0776151 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.61803 | 0.0626975 | ||||||||
\(667\) | −17.6393 | −0.682997 | ||||||||
\(668\) | −1.90983 | −0.0738935 | ||||||||
\(669\) | −28.9443 | −1.11905 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −68.5410 | −2.64600 | ||||||||
\(672\) | −2.38197 | −0.0918863 | ||||||||
\(673\) | −9.52786 | −0.367272 | −0.183636 | − | 0.982994i | \(-0.558787\pi\) | ||||
−0.183636 | + | 0.982994i | \(0.558787\pi\) | |||||||
\(674\) | 20.8328 | 0.802450 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.56231 | −0.0600887 | ||||||||
\(677\) | −24.7426 | −0.950937 | −0.475469 | − | 0.879733i | \(-0.657721\pi\) | ||||
−0.475469 | + | 0.879733i | \(0.657721\pi\) | |||||||
\(678\) | −3.70820 | −0.142413 | ||||||||
\(679\) | −33.7771 | −1.29625 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.7639 | 0.412475 | ||||||||
\(682\) | −37.8885 | −1.45083 | ||||||||
\(683\) | −29.8885 | −1.14365 | −0.571827 | − | 0.820374i | \(-0.693765\pi\) | ||||
−0.571827 | + | 0.820374i | \(0.693765\pi\) | |||||||
\(684\) | 4.09017 | 0.156392 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.8328 | 0.757220 | ||||||||
\(687\) | −22.7639 | −0.868498 | ||||||||
\(688\) | 7.70820 | 0.293873 | ||||||||
\(689\) | 1.29180 | 0.0492135 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.8885 | −1.28918 | −0.644590 | − | 0.764528i | \(-0.722972\pi\) | ||||
−0.644590 | + | 0.764528i | \(0.722972\pi\) | |||||||
\(692\) | 4.38197 | 0.166577 | ||||||||
\(693\) | −13.9443 | −0.529699 | ||||||||
\(694\) | 14.1803 | 0.538278 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.70820 | −0.216369 | ||||||||
\(697\) | 2.94427 | 0.111522 | ||||||||
\(698\) | 20.0000 | 0.757011 | ||||||||
\(699\) | −2.47214 | −0.0935048 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.7082 | −0.668830 | −0.334415 | − | 0.942426i | \(-0.608539\pi\) | ||||
−0.334415 | + | 0.942426i | \(0.608539\pi\) | |||||||
\(702\) | −3.38197 | −0.127644 | ||||||||
\(703\) | −6.61803 | −0.249604 | ||||||||
\(704\) | −5.85410 | −0.220635 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.12461 | 0.343409 | ||||||||
\(707\) | −32.6525 | −1.22802 | ||||||||
\(708\) | −10.8541 | −0.407922 | ||||||||
\(709\) | 18.6525 | 0.700508 | 0.350254 | − | 0.936655i | \(-0.386095\pi\) | ||||
0.350254 | + | 0.936655i | \(0.386095\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.4721 | 0.467742 | ||||||||
\(712\) | −15.5623 | −0.583222 | ||||||||
\(713\) | 20.0000 | 0.749006 | ||||||||
\(714\) | −18.3607 | −0.687131 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.79837 | 0.141952 | ||||||||
\(717\) | −7.05573 | −0.263501 | ||||||||
\(718\) | 17.4164 | 0.649975 | ||||||||
\(719\) | 12.1115 | 0.451681 | 0.225841 | − | 0.974164i | \(-0.427487\pi\) | ||||
0.225841 | + | 0.974164i | \(0.427487\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.93112 | 0.258128 | ||||||||
\(722\) | 2.27051 | 0.0844996 | ||||||||
\(723\) | 15.0902 | 0.561209 | ||||||||
\(724\) | −20.4721 | −0.760841 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −23.2705 | −0.863650 | ||||||||
\(727\) | −12.6738 | −0.470044 | −0.235022 | − | 0.971990i | \(-0.575516\pi\) | ||||
−0.235022 | + | 0.971990i | \(0.575516\pi\) | |||||||
\(728\) | −8.05573 | −0.298565 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 59.4164 | 2.19760 | ||||||||
\(732\) | 11.7082 | 0.432748 | ||||||||
\(733\) | 17.9230 | 0.662001 | 0.331000 | − | 0.943631i | \(-0.392614\pi\) | ||||
0.331000 | + | 0.943631i | \(0.392614\pi\) | |||||||
\(734\) | −15.4164 | −0.569030 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.09017 | 0.113905 | ||||||||
\(737\) | −18.9443 | −0.697821 | ||||||||
\(738\) | −0.381966 | −0.0140604 | ||||||||
\(739\) | 23.3262 | 0.858070 | 0.429035 | − | 0.903288i | \(-0.358854\pi\) | ||||
0.429035 | + | 0.903288i | \(0.358854\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.8328 | 0.508161 | ||||||||
\(742\) | −0.909830 | −0.0334009 | ||||||||
\(743\) | −38.1459 | −1.39944 | −0.699719 | − | 0.714419i | \(-0.746691\pi\) | ||||
−0.699719 | + | 0.714419i | \(0.746691\pi\) | |||||||
\(744\) | 6.47214 | 0.237280 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19.3262 | 0.707584 | ||||||||
\(747\) | 2.00000 | 0.0731762 | ||||||||
\(748\) | −45.1246 | −1.64992 | ||||||||
\(749\) | −4.76393 | −0.174070 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.06888 | −0.148476 | −0.0742378 | − | 0.997241i | \(-0.523652\pi\) | ||||
−0.0742378 | + | 0.997241i | \(0.523652\pi\) | |||||||
\(752\) | 8.61803 | 0.314267 | ||||||||
\(753\) | −24.0000 | −0.874609 | ||||||||
\(754\) | −19.3050 | −0.703045 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.38197 | 0.0866313 | ||||||||
\(757\) | 11.6738 | 0.424290 | 0.212145 | − | 0.977238i | \(-0.431955\pi\) | ||||
0.212145 | + | 0.977238i | \(0.431955\pi\) | |||||||
\(758\) | −35.9230 | −1.30478 | ||||||||
\(759\) | 18.0902 | 0.656632 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 55.0344 | 1.99500 | 0.997498 | − | 0.0706879i | \(-0.0225194\pi\) | ||||
0.997498 | + | 0.0706879i | \(0.0225194\pi\) | |||||||
\(762\) | 5.52786 | 0.200253 | ||||||||
\(763\) | −4.06888 | −0.147303 | ||||||||
\(764\) | −4.00000 | −0.144715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.0344 | −0.976794 | ||||||||
\(767\) | −36.7082 | −1.32546 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 11.6738 | 0.420967 | 0.210483 | − | 0.977597i | \(-0.432496\pi\) | ||||
0.210483 | + | 0.977597i | \(0.432496\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.5279 | 0.631251 | ||||||||
\(772\) | 9.70820 | 0.349406 | ||||||||
\(773\) | −26.9443 | −0.969118 | −0.484559 | − | 0.874759i | \(-0.661020\pi\) | ||||
−0.484559 | + | 0.874759i | \(0.661020\pi\) | |||||||
\(774\) | −7.70820 | −0.277066 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.1803 | 0.509045 | ||||||||
\(777\) | −3.85410 | −0.138265 | ||||||||
\(778\) | 34.5410 | 1.23836 | ||||||||
\(779\) | 1.56231 | 0.0559754 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.1803 | 0.936806 | ||||||||
\(782\) | 23.8197 | 0.851789 | ||||||||
\(783\) | 5.70820 | 0.203995 | ||||||||
\(784\) | −1.32624 | −0.0473656 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 20.3262 | 0.725013 | ||||||||
\(787\) | −10.5836 | −0.377264 | −0.188632 | − | 0.982048i | \(-0.560405\pi\) | ||||
−0.188632 | + | 0.982048i | \(0.560405\pi\) | |||||||
\(788\) | −14.9443 | −0.532368 | ||||||||
\(789\) | 25.3262 | 0.901638 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.83282 | 0.314059 | ||||||||
\(792\) | 5.85410 | 0.208016 | ||||||||
\(793\) | 39.5967 | 1.40612 | ||||||||
\(794\) | −23.3262 | −0.827817 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.76393 | −0.168853 | ||||||||
\(797\) | −33.8673 | −1.19964 | −0.599820 | − | 0.800135i | \(-0.704761\pi\) | ||||
−0.599820 | + | 0.800135i | \(0.704761\pi\) | |||||||
\(798\) | −9.74265 | −0.344886 | ||||||||
\(799\) | 66.4296 | 2.35011 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.5623 | 0.549867 | ||||||||
\(802\) | 1.32624 | 0.0468311 | ||||||||
\(803\) | 46.8328 | 1.65269 | ||||||||
\(804\) | 3.23607 | 0.114127 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.8885 | 0.770991 | ||||||||
\(807\) | −9.41641 | −0.331473 | ||||||||
\(808\) | 13.7082 | 0.482253 | ||||||||
\(809\) | 46.3262 | 1.62874 | 0.814372 | − | 0.580343i | \(-0.197082\pi\) | ||||
0.814372 | + | 0.580343i | \(0.197082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.27051 | −0.114843 | −0.0574216 | − | 0.998350i | \(-0.518288\pi\) | ||||
−0.0574216 | + | 0.998350i | \(0.518288\pi\) | |||||||
\(812\) | 13.5967 | 0.477152 | ||||||||
\(813\) | −9.41641 | −0.330248 | ||||||||
\(814\) | −9.47214 | −0.331998 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.70820 | 0.269841 | ||||||||
\(817\) | 31.5279 | 1.10302 | ||||||||
\(818\) | 4.85410 | 0.169720 | ||||||||
\(819\) | 8.05573 | 0.281490 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.8885 | −1.04312 | −0.521559 | − | 0.853215i | \(-0.674649\pi\) | ||||
−0.521559 | + | 0.853215i | \(0.674649\pi\) | |||||||
\(822\) | −4.94427 | −0.172451 | ||||||||
\(823\) | −34.9230 | −1.21734 | −0.608669 | − | 0.793424i | \(-0.708296\pi\) | ||||
−0.608669 | + | 0.793424i | \(0.708296\pi\) | |||||||
\(824\) | −2.90983 | −0.101369 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25.8541 | 0.899579 | ||||||||
\(827\) | 5.81966 | 0.202369 | 0.101185 | − | 0.994868i | \(-0.467737\pi\) | ||||
0.101185 | + | 0.994868i | \(0.467737\pi\) | |||||||
\(828\) | −3.09017 | −0.107391 | ||||||||
\(829\) | 5.63932 | 0.195862 | 0.0979308 | − | 0.995193i | \(-0.468778\pi\) | ||||
0.0979308 | + | 0.995193i | \(0.468778\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.4508 | 0.952259 | ||||||||
\(832\) | 3.38197 | 0.117249 | ||||||||
\(833\) | −10.2229 | −0.354203 | ||||||||
\(834\) | 2.61803 | 0.0906551 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −23.9443 | −0.828130 | ||||||||
\(837\) | −6.47214 | −0.223710 | ||||||||
\(838\) | −17.8885 | −0.617949 | ||||||||
\(839\) | 23.3475 | 0.806046 | 0.403023 | − | 0.915190i | \(-0.367959\pi\) | ||||
0.403023 | + | 0.915190i | \(0.367959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.58359 | 0.123572 | ||||||||
\(842\) | 25.1246 | 0.865851 | ||||||||
\(843\) | 24.5066 | 0.844051 | ||||||||
\(844\) | −22.5623 | −0.776627 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.61803 | −0.296294 | ||||||||
\(847\) | 55.4296 | 1.90458 | ||||||||
\(848\) | 0.381966 | 0.0131168 | ||||||||
\(849\) | 8.18034 | 0.280749 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.00000 | 0.171398 | ||||||||
\(852\) | −4.47214 | −0.153213 | ||||||||
\(853\) | 48.2705 | 1.65275 | 0.826375 | − | 0.563120i | \(-0.190399\pi\) | ||||
0.826375 | + | 0.563120i | \(0.190399\pi\) | |||||||
\(854\) | −27.8885 | −0.954326 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.00000 | 0.0683586 | ||||||||
\(857\) | 3.70820 | 0.126670 | 0.0633349 | − | 0.997992i | \(-0.479826\pi\) | ||||
0.0633349 | + | 0.997992i | \(0.479826\pi\) | |||||||
\(858\) | 19.7984 | 0.675905 | ||||||||
\(859\) | −1.03444 | −0.0352947 | −0.0176474 | − | 0.999844i | \(-0.505618\pi\) | ||||
−0.0176474 | + | 0.999844i | \(0.505618\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.909830 | 0.0310069 | ||||||||
\(862\) | −17.2361 | −0.587063 | ||||||||
\(863\) | 11.0344 | 0.375617 | 0.187808 | − | 0.982206i | \(-0.439862\pi\) | ||||
0.187808 | + | 0.982206i | \(0.439862\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −38.3607 | −1.30355 | ||||||||
\(867\) | 42.4164 | 1.44054 | ||||||||
\(868\) | −15.4164 | −0.523267 | ||||||||
\(869\) | −73.0132 | −2.47680 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.9443 | 0.370833 | ||||||||
\(872\) | 1.70820 | 0.0578471 | ||||||||
\(873\) | −14.1803 | −0.479932 | ||||||||
\(874\) | 12.6393 | 0.427531 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.00000 | −0.270295 | ||||||||
\(877\) | −8.97871 | −0.303190 | −0.151595 | − | 0.988443i | \(-0.548441\pi\) | ||||
−0.151595 | + | 0.988443i | \(0.548441\pi\) | |||||||
\(878\) | 32.6525 | 1.10197 | ||||||||
\(879\) | −20.7984 | −0.701512 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.1591 | −0.544412 | −0.272206 | − | 0.962239i | \(-0.587753\pi\) | ||||
−0.272206 | + | 0.962239i | \(0.587753\pi\) | |||||||
\(882\) | 1.32624 | 0.0446568 | ||||||||
\(883\) | −7.41641 | −0.249582 | −0.124791 | − | 0.992183i | \(-0.539826\pi\) | ||||
−0.124791 | + | 0.992183i | \(0.539826\pi\) | |||||||
\(884\) | 26.0689 | 0.876791 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.1246 | 0.440930 | ||||||||
\(887\) | −27.0344 | −0.907728 | −0.453864 | − | 0.891071i | \(-0.649955\pi\) | ||||
−0.453864 | + | 0.891071i | \(0.649955\pi\) | |||||||
\(888\) | 1.61803 | 0.0542977 | ||||||||
\(889\) | −13.1672 | −0.441613 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.85410 | −0.196120 | ||||||||
\(892\) | −28.9443 | −0.969126 | ||||||||
\(893\) | 35.2492 | 1.17957 | ||||||||
\(894\) | 9.41641 | 0.314932 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.38197 | −0.0795759 | ||||||||
\(897\) | −10.4508 | −0.348944 | ||||||||
\(898\) | −16.5623 | −0.552691 | ||||||||
\(899\) | −36.9443 | −1.23216 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.94427 | 0.0980879 | ||||||||
\(902\) | 2.23607 | 0.0744529 | ||||||||
\(903\) | 18.3607 | 0.611005 | ||||||||
\(904\) | −3.70820 | −0.123333 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.291796 | 0.00969428 | ||||||||
\(907\) | −16.6525 | −0.552936 | −0.276468 | − | 0.961023i | \(-0.589164\pi\) | ||||
−0.276468 | + | 0.961023i | \(0.589164\pi\) | |||||||
\(908\) | 10.7639 | 0.357214 | ||||||||
\(909\) | −13.7082 | −0.454672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.0557 | −0.962659 | −0.481330 | − | 0.876540i | \(-0.659846\pi\) | ||||
−0.481330 | + | 0.876540i | \(0.659846\pi\) | |||||||
\(912\) | 4.09017 | 0.135439 | ||||||||
\(913\) | −11.7082 | −0.387485 | ||||||||
\(914\) | −33.8885 | −1.12093 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.7639 | −0.752141 | ||||||||
\(917\) | −48.4164 | −1.59885 | ||||||||
\(918\) | −7.70820 | −0.254409 | ||||||||
\(919\) | 36.7639 | 1.21273 | 0.606365 | − | 0.795186i | \(-0.292627\pi\) | ||||
0.606365 | + | 0.795186i | \(0.292627\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.18034 | −0.203649 | ||||||||
\(922\) | −19.5967 | −0.645385 | ||||||||
\(923\) | −15.1246 | −0.497833 | ||||||||
\(924\) | −13.9443 | −0.458733 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.0557 | 0.494762 | ||||||||
\(927\) | 2.90983 | 0.0955714 | ||||||||
\(928\) | −5.70820 | −0.187381 | ||||||||
\(929\) | 41.8115 | 1.37179 | 0.685896 | − | 0.727700i | \(-0.259411\pi\) | ||||
0.685896 | + | 0.727700i | \(0.259411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.42454 | −0.177782 | ||||||||
\(932\) | −2.47214 | −0.0809775 | ||||||||
\(933\) | 8.94427 | 0.292822 | ||||||||
\(934\) | −21.2361 | −0.694865 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.38197 | −0.110543 | ||||||||
\(937\) | 6.65248 | 0.217327 | 0.108663 | − | 0.994079i | \(-0.465343\pi\) | ||||
0.108663 | + | 0.994079i | \(0.465343\pi\) | |||||||
\(938\) | −7.70820 | −0.251682 | ||||||||
\(939\) | 0.291796 | 0.00952240 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.1803 | −0.592662 | −0.296331 | − | 0.955085i | \(-0.595763\pi\) | ||||
−0.296331 | + | 0.955085i | \(0.595763\pi\) | |||||||
\(942\) | 6.94427 | 0.226257 | ||||||||
\(943\) | −1.18034 | −0.0384372 | ||||||||
\(944\) | −10.8541 | −0.353271 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 45.1246 | 1.46713 | ||||||||
\(947\) | 13.8885 | 0.451317 | 0.225659 | − | 0.974206i | \(-0.427547\pi\) | ||||
0.225659 | + | 0.974206i | \(0.427547\pi\) | |||||||
\(948\) | 12.4721 | 0.405076 | ||||||||
\(949\) | −27.0557 | −0.878266 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.8541 | 0.773522 | ||||||||
\(952\) | −18.3607 | −0.595073 | ||||||||
\(953\) | −22.5410 | −0.730175 | −0.365088 | − | 0.930973i | \(-0.618961\pi\) | ||||
−0.365088 | + | 0.930973i | \(0.618961\pi\) | |||||||
\(954\) | −0.381966 | −0.0123666 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.05573 | −0.228199 | ||||||||
\(957\) | −33.4164 | −1.08020 | ||||||||
\(958\) | 9.12461 | 0.294803 | ||||||||
\(959\) | 11.7771 | 0.380302 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 5.47214 | 0.176429 | ||||||||
\(963\) | −2.00000 | −0.0644491 | ||||||||
\(964\) | 15.0902 | 0.486022 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 7.36068 | 0.236826 | ||||||||
\(967\) | 58.6869 | 1.88724 | 0.943622 | − | 0.331025i | \(-0.107394\pi\) | ||||
0.943622 | + | 0.331025i | \(0.107394\pi\) | |||||||
\(968\) | −23.2705 | −0.747943 | ||||||||
\(969\) | 31.5279 | 1.01282 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.72949 | −0.215960 | −0.107980 | − | 0.994153i | \(-0.534438\pi\) | ||||
−0.107980 | + | 0.994153i | \(0.534438\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −6.23607 | −0.199919 | ||||||||
\(974\) | 12.7984 | 0.410086 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.7082 | 0.374770 | ||||||||
\(977\) | 9.30495 | 0.297692 | 0.148846 | − | 0.988860i | \(-0.452444\pi\) | ||||
0.148846 | + | 0.988860i | \(0.452444\pi\) | |||||||
\(978\) | 24.0000 | 0.767435 | ||||||||
\(979\) | −91.1033 | −2.91167 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.70820 | −0.0545388 | ||||||||
\(982\) | −11.0344 | −0.352123 | ||||||||
\(983\) | −22.2148 | −0.708541 | −0.354271 | − | 0.935143i | \(-0.615271\pi\) | ||||
−0.354271 | + | 0.935143i | \(0.615271\pi\) | |||||||
\(984\) | −0.381966 | −0.0121766 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −44.0000 | −1.40125 | ||||||||
\(987\) | 20.5279 | 0.653409 | ||||||||
\(988\) | 13.8328 | 0.440080 | ||||||||
\(989\) | −23.8197 | −0.757421 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.1115 | 0.511797 | 0.255899 | − | 0.966704i | \(-0.417629\pi\) | ||||
0.255899 | + | 0.966704i | \(0.417629\pi\) | |||||||
\(992\) | 6.47214 | 0.205491 | ||||||||
\(993\) | 6.47214 | 0.205387 | ||||||||
\(994\) | 10.6525 | 0.337876 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.00000 | 0.0633724 | ||||||||
\(997\) | 4.09017 | 0.129537 | 0.0647685 | − | 0.997900i | \(-0.479369\pi\) | ||||
0.0647685 | + | 0.997900i | \(0.479369\pi\) | |||||||
\(998\) | 5.38197 | 0.170363 | ||||||||
\(999\) | −1.61803 | −0.0511923 |
(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 | 750.2.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 2250.2.a.p.1.1 | 2 | |||
4.3 | odd | 2 | 6000.2.a.a.1.2 | 2 | |||
5.2 | odd | 4 | 750.2.c.a.499.1 | 4 | |||
5.3 | odd | 4 | 750.2.c.a.499.4 | 4 | |||
5.4 | even | 2 | 750.2.a.e.1.2 | yes | 2 | ||
15.2 | even | 4 | 2250.2.c.g.1999.3 | 4 | |||
15.8 | even | 4 | 2250.2.c.g.1999.2 | 4 | |||
15.14 | odd | 2 | 2250.2.a.a.1.2 | 2 | |||
20.3 | even | 4 | 6000.2.f.k.1249.1 | 4 | |||
20.7 | even | 4 | 6000.2.f.k.1249.4 | 4 | |||
20.19 | odd | 2 | 6000.2.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
750.2.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
750.2.a.e.1.2 | yes | 2 | 5.4 | even | 2 | ||
750.2.c.a.499.1 | 4 | 5.2 | odd | 4 | |||
750.2.c.a.499.4 | 4 | 5.3 | odd | 4 | |||
2250.2.a.a.1.2 | 2 | 15.14 | odd | 2 | |||
2250.2.a.p.1.1 | 2 | 3.2 | odd | 2 | |||
2250.2.c.g.1999.2 | 4 | 15.8 | even | 4 | |||
2250.2.c.g.1999.3 | 4 | 15.2 | even | 4 | |||
6000.2.a.a.1.2 | 2 | 4.3 | odd | 2 | |||
6000.2.a.bb.1.1 | 2 | 20.19 | odd | 2 | |||
6000.2.f.k.1249.1 | 4 | 20.3 | even | 4 | |||
6000.2.f.k.1249.4 | 4 | 20.7 | even | 4 |