Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3132.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 15x - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.404409\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −0.404409 | −0.121934 | −0.0609670 | − | 0.998140i | \(-0.519418\pi\) | ||||
−0.0609670 | + | 0.998140i | \(0.519418\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 4.12043 | 1.14280 | 0.571401 | − | 0.820671i | \(-0.306400\pi\) | ||||
0.571401 | + | 0.820671i | \(0.306400\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.31161 | 1.28826 | 0.644128 | − | 0.764918i | \(-0.277221\pi\) | ||||
0.644128 | + | 0.764918i | \(0.277221\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.71602 | −0.623098 | −0.311549 | − | 0.950230i | \(-0.600848\pi\) | ||||
−0.311549 | + | 0.950230i | \(0.600848\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.404409 | 0.0862204 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | −4.12043 | −0.808083 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.12043 | 1.69362 | 0.846811 | − | 0.531894i | \(-0.178520\pi\) | ||||
0.846811 | + | 0.531894i | \(0.178520\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −9.83645 | −1.76668 | −0.883340 | − | 0.468734i | \(-0.844710\pi\) | ||||
−0.883340 | + | 0.468734i | \(0.844710\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.404409 | 0.0703986 | ||||||||
\(34\) | −5.31161 | −0.910934 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.90720 | −1.29994 | −0.649968 | − | 0.759961i | \(-0.725218\pi\) | ||||
−0.649968 | + | 0.759961i | \(0.725218\pi\) | |||||||
\(38\) | 2.71602 | 0.440597 | ||||||||
\(39\) | −4.12043 | −0.659797 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −10.7160 | −1.67356 | −0.836781 | − | 0.547538i | \(-0.815565\pi\) | ||||
−0.836781 | + | 0.547538i | \(0.815565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.808819 | 0.123344 | 0.0616718 | − | 0.998096i | \(-0.480357\pi\) | ||||
0.0616718 | + | 0.998096i | \(0.480357\pi\) | |||||||
\(44\) | −0.404409 | −0.0609670 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −10.8365 | −1.58066 | −0.790330 | − | 0.612682i | \(-0.790091\pi\) | ||||
−0.790330 | + | 0.612682i | \(0.790091\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.00000 | 0.565685 | ||||||||
\(51\) | −5.31161 | −0.743775 | ||||||||
\(52\) | 4.12043 | 0.571401 | ||||||||
\(53\) | −0.191181 | −0.0262608 | −0.0131304 | − | 0.999914i | \(-0.504180\pi\) | ||||
−0.0131304 | + | 0.999914i | \(0.504180\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.404409 | −0.0545305 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.71602 | 0.359746 | ||||||||
\(58\) | −9.12043 | −1.19757 | ||||||||
\(59\) | −8.31161 | −1.08208 | −0.541040 | − | 0.840997i | \(-0.681969\pi\) | ||||
−0.541040 | + | 0.840997i | \(0.681969\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 9.83645 | 1.24923 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.12043 | 0.511077 | ||||||||
\(66\) | −0.404409 | −0.0497793 | ||||||||
\(67\) | 2.83645 | 0.346528 | 0.173264 | − | 0.984875i | \(-0.444569\pi\) | ||||
0.173264 | + | 0.984875i | \(0.444569\pi\) | |||||||
\(68\) | 5.31161 | 0.644128 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.92925 | −0.822351 | −0.411175 | − | 0.911556i | \(-0.634882\pi\) | ||||
−0.411175 | + | 0.911556i | \(0.634882\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 4.59559 | 0.537873 | 0.268937 | − | 0.963158i | \(-0.413328\pi\) | ||||
0.268937 | + | 0.963158i | \(0.413328\pi\) | |||||||
\(74\) | 7.90720 | 0.919194 | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | −2.71602 | −0.311549 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.12043 | 0.466547 | ||||||||
\(79\) | −9.92925 | −1.11713 | −0.558564 | − | 0.829461i | \(-0.688647\pi\) | ||||
−0.558564 | + | 0.829461i | \(0.688647\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.7160 | 1.18339 | ||||||||
\(83\) | −4.40441 | −0.483447 | −0.241723 | − | 0.970345i | \(-0.577713\pi\) | ||||
−0.241723 | + | 0.970345i | \(0.577713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.31161 | 0.576125 | ||||||||
\(86\) | −0.808819 | −0.0872172 | ||||||||
\(87\) | −9.12043 | −0.977813 | ||||||||
\(88\) | 0.404409 | 0.0431102 | ||||||||
\(89\) | 7.90720 | 0.838162 | 0.419081 | − | 0.907949i | \(-0.362352\pi\) | ||||
0.419081 | + | 0.907949i | \(0.362352\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 9.83645 | 1.01999 | ||||||||
\(94\) | 10.8365 | 1.11769 | ||||||||
\(95\) | −2.71602 | −0.278658 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 15.3613 | 1.55970 | 0.779852 | − | 0.625965i | \(-0.215295\pi\) | ||||
0.779852 | + | 0.625965i | \(0.215295\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.404409 | −0.0406447 | ||||||||
\(100\) | −4.00000 | −0.400000 | ||||||||
\(101\) | −5.19118 | −0.516542 | −0.258271 | − | 0.966073i | \(-0.583153\pi\) | ||||
−0.258271 | + | 0.966073i | \(0.583153\pi\) | |||||||
\(102\) | 5.31161 | 0.525928 | ||||||||
\(103\) | 16.8365 | 1.65895 | 0.829473 | − | 0.558548i | \(-0.188641\pi\) | ||||
0.829473 | + | 0.558548i | \(0.188641\pi\) | |||||||
\(104\) | −4.12043 | −0.404042 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.191181 | 0.0185692 | ||||||||
\(107\) | −9.59559 | −0.927641 | −0.463820 | − | 0.885929i | \(-0.653522\pi\) | ||||
−0.463820 | + | 0.885929i | \(0.653522\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −3.19118 | −0.305660 | −0.152830 | − | 0.988253i | \(-0.548839\pi\) | ||||
−0.152830 | + | 0.988253i | \(0.548839\pi\) | |||||||
\(110\) | 0.404409 | 0.0385589 | ||||||||
\(111\) | 7.90720 | 0.750519 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.7437 | −1.76325 | −0.881627 | − | 0.471946i | \(-0.843552\pi\) | ||||
−0.881627 | + | 0.471946i | \(0.843552\pi\) | |||||||
\(114\) | −2.71602 | −0.254379 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 9.12043 | 0.846811 | ||||||||
\(117\) | 4.12043 | 0.380934 | ||||||||
\(118\) | 8.31161 | 0.765146 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −10.8365 | −0.985132 | ||||||||
\(122\) | −10.0000 | −0.905357 | ||||||||
\(123\) | 10.7160 | 0.966231 | ||||||||
\(124\) | −9.83645 | −0.883340 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5956 | −1.02894 | −0.514471 | − | 0.857508i | \(-0.672012\pi\) | ||||
−0.514471 | + | 0.857508i | \(0.672012\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.808819 | −0.0712125 | ||||||||
\(130\) | −4.12043 | −0.361386 | ||||||||
\(131\) | 16.7657 | 1.46483 | 0.732413 | − | 0.680860i | \(-0.238394\pi\) | ||||
0.732413 | + | 0.680860i | \(0.238394\pi\) | |||||||
\(132\) | 0.404409 | 0.0351993 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.83645 | −0.245032 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −5.31161 | −0.455467 | ||||||||
\(137\) | −9.64527 | −0.824051 | −0.412026 | − | 0.911172i | \(-0.635179\pi\) | ||||
−0.412026 | + | 0.911172i | \(0.635179\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −16.8641 | −1.43039 | −0.715197 | − | 0.698923i | \(-0.753663\pi\) | ||||
−0.715197 | + | 0.698923i | \(0.753663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.8365 | 0.912594 | ||||||||
\(142\) | 6.92925 | 0.581490 | ||||||||
\(143\) | −1.66634 | −0.139346 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 9.12043 | 0.757411 | ||||||||
\(146\) | −4.59559 | −0.380334 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.90720 | −0.649968 | ||||||||
\(149\) | −10.2132 | −0.836700 | −0.418350 | − | 0.908286i | \(-0.637391\pi\) | ||||
−0.418350 | + | 0.908286i | \(0.637391\pi\) | |||||||
\(150\) | −4.00000 | −0.326599 | ||||||||
\(151\) | 5.59559 | 0.455363 | 0.227681 | − | 0.973736i | \(-0.426886\pi\) | ||||
0.227681 | + | 0.973736i | \(0.426886\pi\) | |||||||
\(152\) | 2.71602 | 0.220298 | ||||||||
\(153\) | 5.31161 | 0.429418 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.83645 | −0.790083 | ||||||||
\(156\) | −4.12043 | −0.329899 | ||||||||
\(157\) | 22.7713 | 1.81735 | 0.908673 | − | 0.417508i | \(-0.137096\pi\) | ||||
0.908673 | + | 0.417508i | \(0.137096\pi\) | |||||||
\(158\) | 9.92925 | 0.789929 | ||||||||
\(159\) | 0.191181 | 0.0151617 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 24.7713 | 1.94024 | 0.970119 | − | 0.242631i | \(-0.0780105\pi\) | ||||
0.970119 | + | 0.242631i | \(0.0780105\pi\) | |||||||
\(164\) | −10.7160 | −0.836781 | ||||||||
\(165\) | 0.404409 | 0.0314832 | ||||||||
\(166\) | 4.40441 | 0.341848 | ||||||||
\(167\) | −19.0773 | −1.47625 | −0.738123 | − | 0.674666i | \(-0.764288\pi\) | ||||
−0.738123 | + | 0.674666i | \(0.764288\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.97795 | 0.305996 | ||||||||
\(170\) | −5.31161 | −0.407382 | ||||||||
\(171\) | −2.71602 | −0.207699 | ||||||||
\(172\) | 0.808819 | 0.0616718 | ||||||||
\(173\) | 6.24086 | 0.474484 | 0.237242 | − | 0.971451i | \(-0.423757\pi\) | ||||
0.237242 | + | 0.971451i | \(0.423757\pi\) | |||||||
\(174\) | 9.12043 | 0.691418 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.404409 | −0.0304835 | ||||||||
\(177\) | 8.31161 | 0.624739 | ||||||||
\(178\) | −7.90720 | −0.592670 | ||||||||
\(179\) | −11.2188 | −0.838534 | −0.419267 | − | 0.907863i | \(-0.637713\pi\) | ||||
−0.419267 | + | 0.907863i | \(0.637713\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 8.24086 | 0.612538 | 0.306269 | − | 0.951945i | \(-0.400919\pi\) | ||||
0.306269 | + | 0.951945i | \(0.400919\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.0000 | −0.739221 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −7.90720 | −0.581349 | ||||||||
\(186\) | −9.83645 | −0.721244 | ||||||||
\(187\) | −2.14807 | −0.157082 | ||||||||
\(188\) | −10.8365 | −0.790330 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.71602 | 0.197041 | ||||||||
\(191\) | 24.7713 | 1.79239 | 0.896194 | − | 0.443663i | \(-0.146321\pi\) | ||||
0.896194 | + | 0.443663i | \(0.146321\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −14.8585 | −1.06954 | −0.534769 | − | 0.844998i | \(-0.679601\pi\) | ||||
−0.534769 | + | 0.844998i | \(0.679601\pi\) | |||||||
\(194\) | −15.3613 | −1.10288 | ||||||||
\(195\) | −4.12043 | −0.295070 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.4320 | −0.814499 | −0.407250 | − | 0.913317i | \(-0.633512\pi\) | ||||
−0.407250 | + | 0.913317i | \(0.633512\pi\) | |||||||
\(198\) | 0.404409 | 0.0287401 | ||||||||
\(199\) | −8.62323 | −0.611284 | −0.305642 | − | 0.952146i | \(-0.598871\pi\) | ||||
−0.305642 | + | 0.952146i | \(0.598871\pi\) | |||||||
\(200\) | 4.00000 | 0.282843 | ||||||||
\(201\) | −2.83645 | −0.200068 | ||||||||
\(202\) | 5.19118 | 0.365250 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.31161 | −0.371887 | ||||||||
\(205\) | −10.7160 | −0.748439 | ||||||||
\(206\) | −16.8365 | −1.17305 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 4.12043 | 0.285701 | ||||||||
\(209\) | 1.09838 | 0.0759769 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.43204 | 0.511643 | 0.255821 | − | 0.966724i | \(-0.417654\pi\) | ||||
0.255821 | + | 0.966724i | \(0.417654\pi\) | |||||||
\(212\) | −0.191181 | −0.0131304 | ||||||||
\(213\) | 6.92925 | 0.474784 | ||||||||
\(214\) | 9.59559 | 0.655941 | ||||||||
\(215\) | 0.808819 | 0.0551610 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.19118 | 0.216134 | ||||||||
\(219\) | −4.59559 | −0.310541 | ||||||||
\(220\) | −0.404409 | −0.0272653 | ||||||||
\(221\) | 21.8861 | 1.47222 | ||||||||
\(222\) | −7.90720 | −0.530697 | ||||||||
\(223\) | 10.2188 | 0.684303 | 0.342151 | − | 0.939645i | \(-0.388844\pi\) | ||||
0.342151 | + | 0.939645i | \(0.388844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 18.7437 | 1.24681 | ||||||||
\(227\) | 12.2188 | 0.810991 | 0.405496 | − | 0.914097i | \(-0.367099\pi\) | ||||
0.405496 | + | 0.914097i | \(0.367099\pi\) | |||||||
\(228\) | 2.71602 | 0.179873 | ||||||||
\(229\) | 3.85193 | 0.254543 | 0.127271 | − | 0.991868i | \(-0.459378\pi\) | ||||
0.127271 | + | 0.991868i | \(0.459378\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.12043 | −0.598786 | ||||||||
\(233\) | −26.5304 | −1.73807 | −0.869033 | − | 0.494754i | \(-0.835258\pi\) | ||||
−0.869033 | + | 0.494754i | \(0.835258\pi\) | |||||||
\(234\) | −4.12043 | −0.269361 | ||||||||
\(235\) | −10.8365 | −0.706892 | ||||||||
\(236\) | −8.31161 | −0.541040 | ||||||||
\(237\) | 9.92925 | 0.644974 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −14.7933 | −0.952923 | −0.476461 | − | 0.879195i | \(-0.658081\pi\) | ||||
−0.476461 | + | 0.879195i | \(0.658081\pi\) | |||||||
\(242\) | 10.8365 | 0.696594 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.7160 | −0.683229 | ||||||||
\(247\) | −11.1912 | −0.712078 | ||||||||
\(248\) | 9.83645 | 0.624615 | ||||||||
\(249\) | 4.40441 | 0.279118 | ||||||||
\(250\) | 9.00000 | 0.569210 | ||||||||
\(251\) | 14.0220 | 0.885064 | 0.442532 | − | 0.896753i | \(-0.354080\pi\) | ||||
0.442532 | + | 0.896753i | \(0.354080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.404409 | 0.0254250 | ||||||||
\(254\) | 11.5956 | 0.727572 | ||||||||
\(255\) | −5.31161 | −0.332626 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.09838 | 0.442785 | 0.221393 | − | 0.975185i | \(-0.428940\pi\) | ||||
0.221393 | + | 0.975185i | \(0.428940\pi\) | |||||||
\(258\) | 0.808819 | 0.0503548 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.12043 | 0.255538 | ||||||||
\(261\) | 9.12043 | 0.564541 | ||||||||
\(262\) | −16.7657 | −1.03579 | ||||||||
\(263\) | −8.80882 | −0.543175 | −0.271588 | − | 0.962414i | \(-0.587549\pi\) | ||||
−0.271588 | + | 0.962414i | \(0.587549\pi\) | |||||||
\(264\) | −0.404409 | −0.0248897 | ||||||||
\(265\) | −0.191181 | −0.0117442 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.90720 | −0.483913 | ||||||||
\(268\) | 2.83645 | 0.173264 | ||||||||
\(269\) | −4.49721 | −0.274199 | −0.137100 | − | 0.990557i | \(-0.543778\pi\) | ||||
−0.137100 | + | 0.990557i | \(0.543778\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 15.2685 | 0.927495 | 0.463748 | − | 0.885967i | \(-0.346504\pi\) | ||||
0.463748 | + | 0.885967i | \(0.346504\pi\) | |||||||
\(272\) | 5.31161 | 0.322064 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.64527 | 0.582692 | ||||||||
\(275\) | 1.61764 | 0.0975472 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −2.21323 | −0.132980 | −0.0664900 | − | 0.997787i | \(-0.521180\pi\) | ||||
−0.0664900 | + | 0.997787i | \(0.521180\pi\) | |||||||
\(278\) | 16.8641 | 1.01144 | ||||||||
\(279\) | −9.83645 | −0.588893 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.4110 | 1.75451 | 0.877256 | − | 0.480023i | \(-0.159372\pi\) | ||||
0.877256 | + | 0.480023i | \(0.159372\pi\) | |||||||
\(282\) | −10.8365 | −0.645301 | ||||||||
\(283\) | 27.0773 | 1.60958 | 0.804790 | − | 0.593560i | \(-0.202278\pi\) | ||||
0.804790 | + | 0.593560i | \(0.202278\pi\) | |||||||
\(284\) | −6.92925 | −0.411175 | ||||||||
\(285\) | 2.71602 | 0.160883 | ||||||||
\(286\) | 1.66634 | 0.0985328 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 11.2132 | 0.659602 | ||||||||
\(290\) | −9.12043 | −0.535570 | ||||||||
\(291\) | −15.3613 | −0.900495 | ||||||||
\(292\) | 4.59559 | 0.268937 | ||||||||
\(293\) | −19.8641 | −1.16047 | −0.580236 | − | 0.814448i | \(-0.697040\pi\) | ||||
−0.580236 | + | 0.814448i | \(0.697040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.31161 | −0.483921 | ||||||||
\(296\) | 7.90720 | 0.459597 | ||||||||
\(297\) | 0.404409 | 0.0234662 | ||||||||
\(298\) | 10.2132 | 0.591636 | ||||||||
\(299\) | −4.12043 | −0.238291 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.59559 | −0.321990 | ||||||||
\(303\) | 5.19118 | 0.298226 | ||||||||
\(304\) | −2.71602 | −0.155775 | ||||||||
\(305\) | 10.0000 | 0.572598 | ||||||||
\(306\) | −5.31161 | −0.303645 | ||||||||
\(307\) | −30.5745 | −1.74498 | −0.872490 | − | 0.488632i | \(-0.837496\pi\) | ||||
−0.872490 | + | 0.488632i | \(0.837496\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.8365 | −0.957792 | ||||||||
\(310\) | 9.83645 | 0.558673 | ||||||||
\(311\) | −7.07075 | −0.400945 | −0.200473 | − | 0.979699i | \(-0.564248\pi\) | ||||
−0.200473 | + | 0.979699i | \(0.564248\pi\) | |||||||
\(312\) | 4.12043 | 0.233273 | ||||||||
\(313\) | 7.68839 | 0.434573 | 0.217287 | − | 0.976108i | \(-0.430279\pi\) | ||||
0.217287 | + | 0.976108i | \(0.430279\pi\) | |||||||
\(314\) | −22.7713 | −1.28506 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.92925 | −0.558564 | ||||||||
\(317\) | −22.7933 | −1.28020 | −0.640101 | − | 0.768291i | \(-0.721107\pi\) | ||||
−0.640101 | + | 0.768291i | \(0.721107\pi\) | |||||||
\(318\) | −0.191181 | −0.0107209 | ||||||||
\(319\) | −3.68839 | −0.206510 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 9.59559 | 0.535574 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.4265 | −0.802709 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −16.4817 | −0.914242 | ||||||||
\(326\) | −24.7713 | −1.37195 | ||||||||
\(327\) | 3.19118 | 0.176473 | ||||||||
\(328\) | 10.7160 | 0.591693 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.404409 | −0.0222620 | ||||||||
\(331\) | −20.5304 | −1.12845 | −0.564227 | − | 0.825620i | \(-0.690826\pi\) | ||||
−0.564227 | + | 0.825620i | \(0.690826\pi\) | |||||||
\(332\) | −4.40441 | −0.241723 | ||||||||
\(333\) | −7.90720 | −0.433312 | ||||||||
\(334\) | 19.0773 | 1.04386 | ||||||||
\(335\) | 2.83645 | 0.154972 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7933 | 0.914791 | 0.457396 | − | 0.889263i | \(-0.348782\pi\) | ||||
0.457396 | + | 0.889263i | \(0.348782\pi\) | |||||||
\(338\) | −3.97795 | −0.216372 | ||||||||
\(339\) | 18.7437 | 1.01802 | ||||||||
\(340\) | 5.31161 | 0.288063 | ||||||||
\(341\) | 3.97795 | 0.215418 | ||||||||
\(342\) | 2.71602 | 0.146866 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.808819 | −0.0436086 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | −6.24086 | −0.335511 | ||||||||
\(347\) | 0.354728 | 0.0190428 | 0.00952141 | − | 0.999955i | \(-0.496969\pi\) | ||||
0.00952141 | + | 0.999955i | \(0.496969\pi\) | |||||||
\(348\) | −9.12043 | −0.488906 | ||||||||
\(349\) | 20.9292 | 1.12032 | 0.560159 | − | 0.828385i | \(-0.310740\pi\) | ||||
0.560159 | + | 0.828385i | \(0.310740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.12043 | −0.219932 | ||||||||
\(352\) | 0.404409 | 0.0215551 | ||||||||
\(353\) | −26.5304 | −1.41207 | −0.706036 | − | 0.708176i | \(-0.749518\pi\) | ||||
−0.706036 | + | 0.708176i | \(0.749518\pi\) | |||||||
\(354\) | −8.31161 | −0.441757 | ||||||||
\(355\) | −6.92925 | −0.367766 | ||||||||
\(356\) | 7.90720 | 0.419081 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.2188 | 0.592933 | ||||||||
\(359\) | 4.86409 | 0.256717 | 0.128358 | − | 0.991728i | \(-0.459029\pi\) | ||||
0.128358 | + | 0.991728i | \(0.459029\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −11.6232 | −0.611749 | ||||||||
\(362\) | −8.24086 | −0.433130 | ||||||||
\(363\) | 10.8365 | 0.568766 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.59559 | 0.240544 | ||||||||
\(366\) | 10.0000 | 0.522708 | ||||||||
\(367\) | −25.9569 | −1.35494 | −0.677469 | − | 0.735551i | \(-0.736923\pi\) | ||||
−0.677469 | + | 0.735551i | \(0.736923\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −10.7160 | −0.557854 | ||||||||
\(370\) | 7.90720 | 0.411076 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.83645 | 0.509996 | ||||||||
\(373\) | −13.6729 | −0.707956 | −0.353978 | − | 0.935254i | \(-0.615171\pi\) | ||||
−0.353978 | + | 0.935254i | \(0.615171\pi\) | |||||||
\(374\) | 2.14807 | 0.111074 | ||||||||
\(375\) | 9.00000 | 0.464758 | ||||||||
\(376\) | 10.8365 | 0.558847 | ||||||||
\(377\) | 37.5801 | 1.93547 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.4541 | −1.15339 | −0.576695 | − | 0.816960i | \(-0.695658\pi\) | ||||
−0.576695 | + | 0.816960i | \(0.695658\pi\) | |||||||
\(380\) | −2.71602 | −0.139329 | ||||||||
\(381\) | 11.5956 | 0.594060 | ||||||||
\(382\) | −24.7713 | −1.26741 | ||||||||
\(383\) | 12.3889 | 0.633045 | 0.316522 | − | 0.948585i | \(-0.397485\pi\) | ||||
0.316522 | + | 0.948585i | \(0.397485\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.8585 | 0.756278 | ||||||||
\(387\) | 0.808819 | 0.0411146 | ||||||||
\(388\) | 15.3613 | 0.779852 | ||||||||
\(389\) | 28.5370 | 1.44688 | 0.723442 | − | 0.690386i | \(-0.242559\pi\) | ||||
0.723442 | + | 0.690386i | \(0.242559\pi\) | |||||||
\(390\) | 4.12043 | 0.208646 | ||||||||
\(391\) | −5.31161 | −0.268620 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.7657 | −0.845718 | ||||||||
\(394\) | 11.4320 | 0.575938 | ||||||||
\(395\) | −9.92925 | −0.499595 | ||||||||
\(396\) | −0.404409 | −0.0203223 | ||||||||
\(397\) | 5.31161 | 0.266582 | 0.133291 | − | 0.991077i | \(-0.457445\pi\) | ||||
0.133291 | + | 0.991077i | \(0.457445\pi\) | |||||||
\(398\) | 8.62323 | 0.432243 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −6.21323 | −0.310274 | −0.155137 | − | 0.987893i | \(-0.549582\pi\) | ||||
−0.155137 | + | 0.987893i | \(0.549582\pi\) | |||||||
\(402\) | 2.83645 | 0.141469 | ||||||||
\(403\) | −40.5304 | −2.01896 | ||||||||
\(404\) | −5.19118 | −0.258271 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.19775 | 0.158506 | ||||||||
\(408\) | 5.31161 | 0.262964 | ||||||||
\(409\) | 28.1049 | 1.38970 | 0.694850 | − | 0.719155i | \(-0.255471\pi\) | ||||
0.694850 | + | 0.719155i | \(0.255471\pi\) | |||||||
\(410\) | 10.7160 | 0.529227 | ||||||||
\(411\) | 9.64527 | 0.475766 | ||||||||
\(412\) | 16.8365 | 0.829473 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −4.40441 | −0.216204 | ||||||||
\(416\) | −4.12043 | −0.202021 | ||||||||
\(417\) | 16.8641 | 0.825838 | ||||||||
\(418\) | −1.09838 | −0.0537237 | ||||||||
\(419\) | −11.0056 | −0.537658 | −0.268829 | − | 0.963188i | \(-0.586637\pi\) | ||||
−0.268829 | + | 0.963188i | \(0.586637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.4873 | −1.14470 | −0.572351 | − | 0.820009i | \(-0.693968\pi\) | ||||
−0.572351 | + | 0.820009i | \(0.693968\pi\) | |||||||
\(422\) | −7.43204 | −0.361786 | ||||||||
\(423\) | −10.8365 | −0.526886 | ||||||||
\(424\) | 0.191181 | 0.00928459 | ||||||||
\(425\) | −21.2465 | −1.03060 | ||||||||
\(426\) | −6.92925 | −0.335723 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.59559 | −0.463820 | ||||||||
\(429\) | 1.66634 | 0.0804517 | ||||||||
\(430\) | −0.808819 | −0.0390047 | ||||||||
\(431\) | 24.4817 | 1.17924 | 0.589622 | − | 0.807680i | \(-0.299277\pi\) | ||||
0.589622 | + | 0.807680i | \(0.299277\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 1.23527 | 0.0593635 | 0.0296818 | − | 0.999559i | \(-0.490551\pi\) | ||||
0.0296818 | + | 0.999559i | \(0.490551\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.12043 | −0.437291 | ||||||||
\(436\) | −3.19118 | −0.152830 | ||||||||
\(437\) | 2.71602 | 0.129925 | ||||||||
\(438\) | 4.59559 | 0.219586 | ||||||||
\(439\) | −22.6453 | −1.08080 | −0.540400 | − | 0.841408i | \(-0.681727\pi\) | ||||
−0.540400 | + | 0.841408i | \(0.681727\pi\) | |||||||
\(440\) | 0.404409 | 0.0192795 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.8861 | −1.04102 | ||||||||
\(443\) | −7.90162 | −0.375417 | −0.187709 | − | 0.982225i | \(-0.560106\pi\) | ||||
−0.187709 | + | 0.982225i | \(0.560106\pi\) | |||||||
\(444\) | 7.90720 | 0.375259 | ||||||||
\(445\) | 7.90720 | 0.374837 | ||||||||
\(446\) | −10.2188 | −0.483875 | ||||||||
\(447\) | 10.2132 | 0.483069 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.3889 | 0.773441 | 0.386721 | − | 0.922197i | \(-0.373608\pi\) | ||||
0.386721 | + | 0.922197i | \(0.373608\pi\) | |||||||
\(450\) | 4.00000 | 0.188562 | ||||||||
\(451\) | 4.33366 | 0.204064 | ||||||||
\(452\) | −18.7437 | −0.881627 | ||||||||
\(453\) | −5.59559 | −0.262904 | ||||||||
\(454\) | −12.2188 | −0.573457 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.71602 | −0.127189 | ||||||||
\(457\) | −31.0342 | −1.45172 | −0.725859 | − | 0.687843i | \(-0.758558\pi\) | ||||
−0.725859 | + | 0.687843i | \(0.758558\pi\) | |||||||
\(458\) | −3.85193 | −0.179989 | ||||||||
\(459\) | −5.31161 | −0.247925 | ||||||||
\(460\) | −1.00000 | −0.0466252 | ||||||||
\(461\) | 7.61764 | 0.354789 | 0.177394 | − | 0.984140i | \(-0.443233\pi\) | ||||
0.177394 | + | 0.984140i | \(0.443233\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.80882 | 0.409381 | 0.204690 | − | 0.978827i | \(-0.434381\pi\) | ||||
0.204690 | + | 0.978827i | \(0.434381\pi\) | |||||||
\(464\) | 9.12043 | 0.423405 | ||||||||
\(465\) | 9.83645 | 0.456155 | ||||||||
\(466\) | 26.5304 | 1.22900 | ||||||||
\(467\) | 0.808819 | 0.0374277 | 0.0187138 | − | 0.999825i | \(-0.494043\pi\) | ||||
0.0187138 | + | 0.999825i | \(0.494043\pi\) | |||||||
\(468\) | 4.12043 | 0.190467 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.8365 | 0.499848 | ||||||||
\(471\) | −22.7713 | −1.04925 | ||||||||
\(472\) | 8.31161 | 0.382573 | ||||||||
\(473\) | −0.327094 | −0.0150398 | ||||||||
\(474\) | −9.92925 | −0.456066 | ||||||||
\(475\) | 10.8641 | 0.498479 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.191181 | −0.00875359 | ||||||||
\(478\) | 16.0000 | 0.731823 | ||||||||
\(479\) | −28.3337 | −1.29460 | −0.647299 | − | 0.762236i | \(-0.724101\pi\) | ||||
−0.647299 | + | 0.762236i | \(0.724101\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −32.5811 | −1.48557 | ||||||||
\(482\) | 14.7933 | 0.673818 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8365 | −0.492566 | ||||||||
\(485\) | 15.3613 | 0.697520 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 18.7005 | 0.847402 | 0.423701 | − | 0.905802i | \(-0.360731\pi\) | ||||
0.423701 | + | 0.905802i | \(0.360731\pi\) | |||||||
\(488\) | −10.0000 | −0.452679 | ||||||||
\(489\) | −24.7713 | −1.12020 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.09280 | 0.229835 | 0.114917 | − | 0.993375i | \(-0.463340\pi\) | ||||
0.114917 | + | 0.993375i | \(0.463340\pi\) | |||||||
\(492\) | 10.7160 | 0.483116 | ||||||||
\(493\) | 48.4442 | 2.18182 | ||||||||
\(494\) | 11.1912 | 0.503515 | ||||||||
\(495\) | −0.404409 | −0.0181768 | ||||||||
\(496\) | −9.83645 | −0.441670 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.40441 | −0.197366 | ||||||||
\(499\) | 19.4873 | 0.872372 | 0.436186 | − | 0.899857i | \(-0.356329\pi\) | ||||
0.436186 | + | 0.899857i | \(0.356329\pi\) | |||||||
\(500\) | −9.00000 | −0.402492 | ||||||||
\(501\) | 19.0773 | 0.852312 | ||||||||
\(502\) | −14.0220 | −0.625835 | ||||||||
\(503\) | −2.99441 | −0.133514 | −0.0667571 | − | 0.997769i | \(-0.521265\pi\) | ||||
−0.0667571 | + | 0.997769i | \(0.521265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.19118 | −0.231005 | ||||||||
\(506\) | −0.404409 | −0.0179782 | ||||||||
\(507\) | −3.97795 | −0.176667 | ||||||||
\(508\) | −11.5956 | −0.514471 | ||||||||
\(509\) | −11.7437 | −0.520528 | −0.260264 | − | 0.965537i | \(-0.583810\pi\) | ||||
−0.260264 | + | 0.965537i | \(0.583810\pi\) | |||||||
\(510\) | 5.31161 | 0.235202 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.71602 | 0.119915 | ||||||||
\(514\) | −7.09838 | −0.313096 | ||||||||
\(515\) | 16.8365 | 0.741903 | ||||||||
\(516\) | −0.808819 | −0.0356063 | ||||||||
\(517\) | 4.38236 | 0.192736 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.24086 | −0.273943 | ||||||||
\(520\) | −4.12043 | −0.180693 | ||||||||
\(521\) | 5.21882 | 0.228640 | 0.114320 | − | 0.993444i | \(-0.463531\pi\) | ||||
0.114320 | + | 0.993444i | \(0.463531\pi\) | |||||||
\(522\) | −9.12043 | −0.399190 | ||||||||
\(523\) | −26.4541 | −1.15676 | −0.578378 | − | 0.815769i | \(-0.696314\pi\) | ||||
−0.578378 | + | 0.815769i | \(0.696314\pi\) | |||||||
\(524\) | 16.7657 | 0.732413 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.80882 | 0.384083 | ||||||||
\(527\) | −52.2474 | −2.27593 | ||||||||
\(528\) | 0.404409 | 0.0175997 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0.191181 | 0.00830439 | ||||||||
\(531\) | −8.31161 | −0.360693 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −44.1546 | −1.91255 | ||||||||
\(534\) | 7.90720 | 0.342178 | ||||||||
\(535\) | −9.59559 | −0.414854 | ||||||||
\(536\) | −2.83645 | −0.122516 | ||||||||
\(537\) | 11.2188 | 0.484128 | ||||||||
\(538\) | 4.49721 | 0.193888 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −3.31161 | −0.142377 | −0.0711887 | − | 0.997463i | \(-0.522679\pi\) | ||||
−0.0711887 | + | 0.997463i | \(0.522679\pi\) | |||||||
\(542\) | −15.2685 | −0.655838 | ||||||||
\(543\) | −8.24086 | −0.353649 | ||||||||
\(544\) | −5.31161 | −0.227734 | ||||||||
\(545\) | −3.19118 | −0.136695 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.95130 | 0.168945 | 0.0844726 | − | 0.996426i | \(-0.473079\pi\) | ||||
0.0844726 | + | 0.996426i | \(0.473079\pi\) | |||||||
\(548\) | −9.64527 | −0.412026 | ||||||||
\(549\) | 10.0000 | 0.426790 | ||||||||
\(550\) | −1.61764 | −0.0689763 | ||||||||
\(551\) | −24.7713 | −1.05529 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.21323 | 0.0940310 | ||||||||
\(555\) | 7.90720 | 0.335642 | ||||||||
\(556\) | −16.8641 | −0.715197 | ||||||||
\(557\) | 2.60118 | 0.110215 | 0.0551077 | − | 0.998480i | \(-0.482450\pi\) | ||||
0.0551077 | + | 0.998480i | \(0.482450\pi\) | |||||||
\(558\) | 9.83645 | 0.416410 | ||||||||
\(559\) | 3.33268 | 0.140957 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.14807 | 0.0906914 | ||||||||
\(562\) | −29.4110 | −1.24063 | ||||||||
\(563\) | −25.4100 | −1.07090 | −0.535452 | − | 0.844566i | \(-0.679859\pi\) | ||||
−0.535452 | + | 0.844566i | \(0.679859\pi\) | |||||||
\(564\) | 10.8365 | 0.456297 | ||||||||
\(565\) | −18.7437 | −0.788552 | ||||||||
\(566\) | −27.0773 | −1.13814 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.92925 | 0.290745 | ||||||||
\(569\) | −16.5956 | −0.695723 | −0.347862 | − | 0.937546i | \(-0.613092\pi\) | ||||
−0.347862 | + | 0.937546i | \(0.613092\pi\) | |||||||
\(570\) | −2.71602 | −0.113762 | ||||||||
\(571\) | 32.6574 | 1.36667 | 0.683335 | − | 0.730105i | \(-0.260529\pi\) | ||||
0.683335 | + | 0.730105i | \(0.260529\pi\) | |||||||
\(572\) | −1.66634 | −0.0696732 | ||||||||
\(573\) | −24.7713 | −1.03484 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 0.545910 | 0.0227265 | 0.0113633 | − | 0.999935i | \(-0.496383\pi\) | ||||
0.0113633 | + | 0.999935i | \(0.496383\pi\) | |||||||
\(578\) | −11.2132 | −0.466409 | ||||||||
\(579\) | 14.8585 | 0.617498 | ||||||||
\(580\) | 9.12043 | 0.378705 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 15.3613 | 0.636746 | ||||||||
\(583\) | 0.0773155 | 0.00320208 | ||||||||
\(584\) | −4.59559 | −0.190167 | ||||||||
\(585\) | 4.12043 | 0.170359 | ||||||||
\(586\) | 19.8641 | 0.820578 | ||||||||
\(587\) | 8.82097 | 0.364080 | 0.182040 | − | 0.983291i | \(-0.441730\pi\) | ||||
0.182040 | + | 0.983291i | \(0.441730\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.7160 | 1.10081 | ||||||||
\(590\) | 8.31161 | 0.342184 | ||||||||
\(591\) | 11.4320 | 0.470251 | ||||||||
\(592\) | −7.90720 | −0.324984 | ||||||||
\(593\) | −40.0553 | −1.64487 | −0.822436 | − | 0.568857i | \(-0.807386\pi\) | ||||
−0.822436 | + | 0.568857i | \(0.807386\pi\) | |||||||
\(594\) | −0.404409 | −0.0165931 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.2132 | −0.418350 | ||||||||
\(597\) | 8.62323 | 0.352925 | ||||||||
\(598\) | 4.12043 | 0.168497 | ||||||||
\(599\) | −24.4166 | −0.997634 | −0.498817 | − | 0.866707i | \(-0.666232\pi\) | ||||
−0.498817 | + | 0.866707i | \(0.666232\pi\) | |||||||
\(600\) | −4.00000 | −0.163299 | ||||||||
\(601\) | −9.21323 | −0.375815 | −0.187908 | − | 0.982187i | \(-0.560171\pi\) | ||||
−0.187908 | + | 0.982187i | \(0.560171\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.83645 | 0.115509 | ||||||||
\(604\) | 5.59559 | 0.227681 | ||||||||
\(605\) | −10.8365 | −0.440564 | ||||||||
\(606\) | −5.19118 | −0.210877 | ||||||||
\(607\) | 33.6950 | 1.36764 | 0.683818 | − | 0.729653i | \(-0.260318\pi\) | ||||
0.683818 | + | 0.729653i | \(0.260318\pi\) | |||||||
\(608\) | 2.71602 | 0.110149 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.0000 | −0.404888 | ||||||||
\(611\) | −44.6509 | −1.80638 | ||||||||
\(612\) | 5.31161 | 0.214709 | ||||||||
\(613\) | −24.4265 | −0.986575 | −0.493288 | − | 0.869866i | \(-0.664205\pi\) | ||||
−0.493288 | + | 0.869866i | \(0.664205\pi\) | |||||||
\(614\) | 30.5745 | 1.23389 | ||||||||
\(615\) | 10.7160 | 0.432112 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.41000 | −0.0970228 | −0.0485114 | − | 0.998823i | \(-0.515448\pi\) | ||||
−0.0485114 | + | 0.998823i | \(0.515448\pi\) | |||||||
\(618\) | 16.8365 | 0.677261 | ||||||||
\(619\) | 45.8486 | 1.84281 | 0.921406 | − | 0.388602i | \(-0.127042\pi\) | ||||
0.921406 | + | 0.388602i | \(0.127042\pi\) | |||||||
\(620\) | −9.83645 | −0.395041 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 7.07075 | 0.283511 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.12043 | −0.164949 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −7.68839 | −0.307290 | ||||||||
\(627\) | −1.09838 | −0.0438653 | ||||||||
\(628\) | 22.7713 | 0.908673 | ||||||||
\(629\) | −42.0000 | −1.67465 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.5745 | −1.33658 | −0.668290 | − | 0.743901i | \(-0.732974\pi\) | ||||
−0.668290 | + | 0.743901i | \(0.732974\pi\) | |||||||
\(632\) | 9.92925 | 0.394964 | ||||||||
\(633\) | −7.43204 | −0.295397 | ||||||||
\(634\) | 22.7933 | 0.905239 | ||||||||
\(635\) | −11.5956 | −0.460157 | ||||||||
\(636\) | 0.191181 | 0.00758083 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.68839 | 0.146025 | ||||||||
\(639\) | −6.92925 | −0.274117 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −33.4110 | −1.31965 | −0.659827 | − | 0.751417i | \(-0.729370\pi\) | ||||
−0.659827 | + | 0.751417i | \(0.729370\pi\) | |||||||
\(642\) | −9.59559 | −0.378708 | ||||||||
\(643\) | 11.5248 | 0.454495 | 0.227248 | − | 0.973837i | \(-0.427027\pi\) | ||||
0.227248 | + | 0.973837i | \(0.427027\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.808819 | −0.0318472 | ||||||||
\(646\) | 14.4265 | 0.567601 | ||||||||
\(647\) | −48.3402 | −1.90045 | −0.950225 | − | 0.311564i | \(-0.899147\pi\) | ||||
−0.950225 | + | 0.311564i | \(0.899147\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 3.36129 | 0.131942 | ||||||||
\(650\) | 16.4817 | 0.646466 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.7713 | 0.970119 | ||||||||
\(653\) | 25.7989 | 1.00959 | 0.504795 | − | 0.863239i | \(-0.331568\pi\) | ||||
0.504795 | + | 0.863239i | \(0.331568\pi\) | |||||||
\(654\) | −3.19118 | −0.124785 | ||||||||
\(655\) | 16.7657 | 0.655090 | ||||||||
\(656\) | −10.7160 | −0.418390 | ||||||||
\(657\) | 4.59559 | 0.179291 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.1856 | −0.552592 | −0.276296 | − | 0.961073i | \(-0.589107\pi\) | ||||
−0.276296 | + | 0.961073i | \(0.589107\pi\) | |||||||
\(660\) | 0.404409 | 0.0157416 | ||||||||
\(661\) | −47.3017 | −1.83982 | −0.919912 | − | 0.392125i | \(-0.871740\pi\) | ||||
−0.919912 | + | 0.392125i | \(0.871740\pi\) | |||||||
\(662\) | 20.5304 | 0.797938 | ||||||||
\(663\) | −21.8861 | −0.849987 | ||||||||
\(664\) | 4.40441 | 0.170924 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.90720 | 0.306398 | ||||||||
\(667\) | −9.12043 | −0.353145 | ||||||||
\(668\) | −19.0773 | −0.738123 | ||||||||
\(669\) | −10.2188 | −0.395082 | ||||||||
\(670\) | −2.83645 | −0.109582 | ||||||||
\(671\) | −4.04409 | −0.156120 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.448503 | 0.0172885 | 0.00864425 | − | 0.999963i | \(-0.497248\pi\) | ||||
0.00864425 | + | 0.999963i | \(0.497248\pi\) | |||||||
\(674\) | −16.7933 | −0.646855 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 3.97795 | 0.152998 | ||||||||
\(677\) | −16.6176 | −0.638668 | −0.319334 | − | 0.947642i | \(-0.603459\pi\) | ||||
−0.319334 | + | 0.947642i | \(0.603459\pi\) | |||||||
\(678\) | −18.7437 | −0.719846 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.31161 | −0.203691 | ||||||||
\(681\) | −12.2188 | −0.468226 | ||||||||
\(682\) | −3.97795 | −0.152324 | ||||||||
\(683\) | −27.2033 | −1.04091 | −0.520453 | − | 0.853890i | \(-0.674237\pi\) | ||||
−0.520453 | + | 0.853890i | \(0.674237\pi\) | |||||||
\(684\) | −2.71602 | −0.103850 | ||||||||
\(685\) | −9.64527 | −0.368527 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.85193 | −0.146960 | ||||||||
\(688\) | 0.808819 | 0.0308359 | ||||||||
\(689\) | −0.787750 | −0.0300109 | ||||||||
\(690\) | −1.00000 | −0.0380693 | ||||||||
\(691\) | 45.0122 | 1.71234 | 0.856172 | − | 0.516692i | \(-0.172837\pi\) | ||||
0.856172 | + | 0.516692i | \(0.172837\pi\) | |||||||
\(692\) | 6.24086 | 0.237242 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.354728 | −0.0134653 | ||||||||
\(695\) | −16.8641 | −0.639691 | ||||||||
\(696\) | 9.12043 | 0.345709 | ||||||||
\(697\) | −56.9194 | −2.15597 | ||||||||
\(698\) | −20.9292 | −0.792184 | ||||||||
\(699\) | 26.5304 | 1.00347 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.6232 | −1.34547 | −0.672735 | − | 0.739883i | \(-0.734881\pi\) | ||||
−0.672735 | + | 0.739883i | \(0.734881\pi\) | |||||||
\(702\) | 4.12043 | 0.155516 | ||||||||
\(703\) | 21.4761 | 0.809988 | ||||||||
\(704\) | −0.404409 | −0.0152417 | ||||||||
\(705\) | 10.8365 | 0.408124 | ||||||||
\(706\) | 26.5304 | 0.998486 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.31161 | 0.312370 | ||||||||
\(709\) | −20.1922 | −0.758332 | −0.379166 | − | 0.925329i | \(-0.623789\pi\) | ||||
−0.379166 | + | 0.925329i | \(0.623789\pi\) | |||||||
\(710\) | 6.92925 | 0.260050 | ||||||||
\(711\) | −9.92925 | −0.372376 | ||||||||
\(712\) | −7.90720 | −0.296335 | ||||||||
\(713\) | 9.83645 | 0.368378 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.66634 | −0.0623176 | ||||||||
\(716\) | −11.2188 | −0.419267 | ||||||||
\(717\) | 16.0000 | 0.597531 | ||||||||
\(718\) | −4.86409 | −0.181526 | ||||||||
\(719\) | 0.977953 | 0.0364715 | 0.0182358 | − | 0.999834i | \(-0.494195\pi\) | ||||
0.0182358 | + | 0.999834i | \(0.494195\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11.6232 | 0.432572 | ||||||||
\(723\) | 14.7933 | 0.550170 | ||||||||
\(724\) | 8.24086 | 0.306269 | ||||||||
\(725\) | −36.4817 | −1.35490 | ||||||||
\(726\) | −10.8365 | −0.402178 | ||||||||
\(727\) | −36.9348 | −1.36984 | −0.684919 | − | 0.728620i | \(-0.740162\pi\) | ||||
−0.684919 | + | 0.728620i | \(0.740162\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.59559 | −0.170090 | ||||||||
\(731\) | 4.29613 | 0.158898 | ||||||||
\(732\) | −10.0000 | −0.369611 | ||||||||
\(733\) | −35.6354 | −1.31622 | −0.658111 | − | 0.752921i | \(-0.728644\pi\) | ||||
−0.658111 | + | 0.752921i | \(0.728644\pi\) | |||||||
\(734\) | 25.9569 | 0.958086 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −1.14709 | −0.0422535 | ||||||||
\(738\) | 10.7160 | 0.394462 | ||||||||
\(739\) | −33.8697 | −1.24592 | −0.622958 | − | 0.782255i | \(-0.714069\pi\) | ||||
−0.622958 | + | 0.782255i | \(0.714069\pi\) | |||||||
\(740\) | −7.90720 | −0.290675 | ||||||||
\(741\) | 11.1912 | 0.411118 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.1537 | 0.776052 | 0.388026 | − | 0.921648i | \(-0.373157\pi\) | ||||
0.388026 | + | 0.921648i | \(0.373157\pi\) | |||||||
\(744\) | −9.83645 | −0.360622 | ||||||||
\(745\) | −10.2132 | −0.374184 | ||||||||
\(746\) | 13.6729 | 0.500601 | ||||||||
\(747\) | −4.40441 | −0.161149 | ||||||||
\(748\) | −2.14807 | −0.0785411 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.00000 | −0.328634 | ||||||||
\(751\) | 20.9789 | 0.765532 | 0.382766 | − | 0.923845i | \(-0.374972\pi\) | ||||
0.382766 | + | 0.923845i | \(0.374972\pi\) | |||||||
\(752\) | −10.8365 | −0.395165 | ||||||||
\(753\) | −14.0220 | −0.510992 | ||||||||
\(754\) | −37.5801 | −1.36859 | ||||||||
\(755\) | 5.59559 | 0.203644 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.95688 | −0.180161 | −0.0900805 | − | 0.995934i | \(-0.528712\pi\) | ||||
−0.0900805 | + | 0.995934i | \(0.528712\pi\) | |||||||
\(758\) | 22.4541 | 0.815569 | ||||||||
\(759\) | −0.404409 | −0.0146791 | ||||||||
\(760\) | 2.71602 | 0.0985205 | ||||||||
\(761\) | 19.5689 | 0.709373 | 0.354687 | − | 0.934985i | \(-0.384588\pi\) | ||||
0.354687 | + | 0.934985i | \(0.384588\pi\) | |||||||
\(762\) | −11.5956 | −0.420064 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 24.7713 | 0.896194 | ||||||||
\(765\) | 5.31161 | 0.192042 | ||||||||
\(766\) | −12.3889 | −0.447630 | ||||||||
\(767\) | −34.2474 | −1.23660 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 4.92366 | 0.177552 | 0.0887759 | − | 0.996052i | \(-0.471705\pi\) | ||||
0.0887759 | + | 0.996052i | \(0.471705\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.09838 | −0.255642 | ||||||||
\(772\) | −14.8585 | −0.534769 | ||||||||
\(773\) | −2.02763 | −0.0729289 | −0.0364645 | − | 0.999335i | \(-0.511610\pi\) | ||||
−0.0364645 | + | 0.999335i | \(0.511610\pi\) | |||||||
\(774\) | −0.808819 | −0.0290724 | ||||||||
\(775\) | 39.3458 | 1.41334 | ||||||||
\(776\) | −15.3613 | −0.551438 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.5370 | −1.02310 | ||||||||
\(779\) | 29.1049 | 1.04279 | ||||||||
\(780\) | −4.12043 | −0.147535 | ||||||||
\(781\) | 2.80225 | 0.100273 | ||||||||
\(782\) | 5.31161 | 0.189943 | ||||||||
\(783\) | −9.12043 | −0.325938 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.7713 | 0.812742 | ||||||||
\(786\) | 16.7657 | 0.598013 | ||||||||
\(787\) | −0.268497 | −0.00957088 | −0.00478544 | − | 0.999989i | \(-0.501523\pi\) | ||||
−0.00478544 | + | 0.999989i | \(0.501523\pi\) | |||||||
\(788\) | −11.4320 | −0.407250 | ||||||||
\(789\) | 8.80882 | 0.313602 | ||||||||
\(790\) | 9.92925 | 0.353267 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.404409 | 0.0143701 | ||||||||
\(793\) | 41.2043 | 1.46321 | ||||||||
\(794\) | −5.31161 | −0.188502 | ||||||||
\(795\) | 0.191181 | 0.00678050 | ||||||||
\(796\) | −8.62323 | −0.305642 | ||||||||
\(797\) | −16.0497 | −0.568509 | −0.284254 | − | 0.958749i | \(-0.591746\pi\) | ||||
−0.284254 | + | 0.958749i | \(0.591746\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −57.5590 | −2.03629 | ||||||||
\(800\) | 4.00000 | 0.141421 | ||||||||
\(801\) | 7.90720 | 0.279387 | ||||||||
\(802\) | 6.21323 | 0.219397 | ||||||||
\(803\) | −1.85850 | −0.0655850 | ||||||||
\(804\) | −2.83645 | −0.100034 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 40.5304 | 1.42762 | ||||||||
\(807\) | 4.49721 | 0.158309 | ||||||||
\(808\) | 5.19118 | 0.182625 | ||||||||
\(809\) | −7.72161 | −0.271477 | −0.135739 | − | 0.990745i | \(-0.543341\pi\) | ||||
−0.135739 | + | 0.990745i | \(0.543341\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −23.2465 | −0.816293 | −0.408147 | − | 0.912916i | \(-0.633825\pi\) | ||||
−0.408147 | + | 0.912916i | \(0.633825\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.2685 | −0.535490 | ||||||||
\(814\) | −3.19775 | −0.112081 | ||||||||
\(815\) | 24.7713 | 0.867700 | ||||||||
\(816\) | −5.31161 | −0.185944 | ||||||||
\(817\) | −2.19677 | −0.0768552 | ||||||||
\(818\) | −28.1049 | −0.982667 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.7160 | −0.374220 | ||||||||
\(821\) | −39.1204 | −1.36531 | −0.682656 | − | 0.730740i | \(-0.739175\pi\) | ||||
−0.682656 | + | 0.730740i | \(0.739175\pi\) | |||||||
\(822\) | −9.64527 | −0.336417 | ||||||||
\(823\) | 42.1546 | 1.46942 | 0.734709 | − | 0.678382i | \(-0.237319\pi\) | ||||
0.734709 | + | 0.678382i | \(0.237319\pi\) | |||||||
\(824\) | −16.8365 | −0.586526 | ||||||||
\(825\) | −1.61764 | −0.0563189 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.3294 | 1.88922 | 0.944608 | − | 0.328200i | \(-0.106442\pi\) | ||||
0.944608 | + | 0.328200i | \(0.106442\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | 18.6397 | 0.647383 | 0.323691 | − | 0.946163i | \(-0.395076\pi\) | ||||
0.323691 | + | 0.946163i | \(0.395076\pi\) | |||||||
\(830\) | 4.40441 | 0.152879 | ||||||||
\(831\) | 2.21323 | 0.0767760 | ||||||||
\(832\) | 4.12043 | 0.142850 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.8641 | −0.583956 | ||||||||
\(835\) | −19.0773 | −0.660198 | ||||||||
\(836\) | 1.09838 | 0.0379884 | ||||||||
\(837\) | 9.83645 | 0.339998 | ||||||||
\(838\) | 11.0056 | 0.380182 | ||||||||
\(839\) | 32.9569 | 1.13780 | 0.568899 | − | 0.822407i | \(-0.307370\pi\) | ||||
0.568899 | + | 0.822407i | \(0.307370\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 54.1823 | 1.86835 | ||||||||
\(842\) | 23.4873 | 0.809426 | ||||||||
\(843\) | −29.4110 | −1.01297 | ||||||||
\(844\) | 7.43204 | 0.255821 | ||||||||
\(845\) | 3.97795 | 0.136846 | ||||||||
\(846\) | 10.8365 | 0.372565 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.191181 | −0.00656519 | ||||||||
\(849\) | −27.0773 | −0.929291 | ||||||||
\(850\) | 21.2465 | 0.728747 | ||||||||
\(851\) | 7.90720 | 0.271055 | ||||||||
\(852\) | 6.92925 | 0.237392 | ||||||||
\(853\) | −25.0497 | −0.857685 | −0.428842 | − | 0.903379i | \(-0.641078\pi\) | ||||
−0.428842 | + | 0.903379i | \(0.641078\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.71602 | −0.0928860 | ||||||||
\(856\) | 9.59559 | 0.327971 | ||||||||
\(857\) | −4.04870 | −0.138301 | −0.0691505 | − | 0.997606i | \(-0.522029\pi\) | ||||
−0.0691505 | + | 0.997606i | \(0.522029\pi\) | |||||||
\(858\) | −1.66634 | −0.0568879 | ||||||||
\(859\) | 47.7769 | 1.63013 | 0.815063 | − | 0.579372i | \(-0.196702\pi\) | ||||
0.815063 | + | 0.579372i | \(0.196702\pi\) | |||||||
\(860\) | 0.808819 | 0.0275805 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.4817 | −0.833851 | ||||||||
\(863\) | −24.8852 | −0.847101 | −0.423550 | − | 0.905873i | \(-0.639216\pi\) | ||||
−0.423550 | + | 0.905873i | \(0.639216\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 6.24086 | 0.212196 | ||||||||
\(866\) | −1.23527 | −0.0419763 | ||||||||
\(867\) | −11.2132 | −0.380821 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.01548 | 0.136216 | ||||||||
\(870\) | 9.12043 | 0.309212 | ||||||||
\(871\) | 11.6874 | 0.396013 | ||||||||
\(872\) | 3.19118 | 0.108067 | ||||||||
\(873\) | 15.3613 | 0.519901 | ||||||||
\(874\) | −2.71602 | −0.0918708 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.59559 | −0.155271 | ||||||||
\(877\) | −4.06516 | −0.137271 | −0.0686354 | − | 0.997642i | \(-0.521865\pi\) | ||||
−0.0686354 | + | 0.997642i | \(0.521865\pi\) | |||||||
\(878\) | 22.6453 | 0.764241 | ||||||||
\(879\) | 19.8641 | 0.669999 | ||||||||
\(880\) | −0.404409 | −0.0136326 | ||||||||
\(881\) | −12.2132 | −0.411474 | −0.205737 | − | 0.978607i | \(-0.565959\pi\) | ||||
−0.205737 | + | 0.978607i | \(0.565959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.14248 | −0.173058 | −0.0865291 | − | 0.996249i | \(-0.527578\pi\) | ||||
−0.0865291 | + | 0.996249i | \(0.527578\pi\) | |||||||
\(884\) | 21.8861 | 0.736110 | ||||||||
\(885\) | 8.31161 | 0.279392 | ||||||||
\(886\) | 7.90162 | 0.265460 | ||||||||
\(887\) | 30.3824 | 1.02014 | 0.510070 | − | 0.860133i | \(-0.329620\pi\) | ||||
0.510070 | + | 0.860133i | \(0.329620\pi\) | |||||||
\(888\) | −7.90720 | −0.265348 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −7.90720 | −0.265050 | ||||||||
\(891\) | −0.404409 | −0.0135482 | ||||||||
\(892\) | 10.2188 | 0.342151 | ||||||||
\(893\) | 29.4320 | 0.984906 | ||||||||
\(894\) | −10.2132 | −0.341581 | ||||||||
\(895\) | −11.2188 | −0.375004 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.12043 | 0.137577 | ||||||||
\(898\) | −16.3889 | −0.546906 | ||||||||
\(899\) | −89.7127 | −2.99209 | ||||||||
\(900\) | −4.00000 | −0.133333 | ||||||||
\(901\) | −1.01548 | −0.0338306 | ||||||||
\(902\) | −4.33366 | −0.144295 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.7437 | 0.623405 | ||||||||
\(905\) | 8.24086 | 0.273936 | ||||||||
\(906\) | 5.59559 | 0.185901 | ||||||||
\(907\) | −13.8796 | −0.460864 | −0.230432 | − | 0.973088i | \(-0.574014\pi\) | ||||
−0.230432 | + | 0.973088i | \(0.574014\pi\) | |||||||
\(908\) | 12.2188 | 0.405496 | ||||||||
\(909\) | −5.19118 | −0.172181 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.3017 | −0.904546 | −0.452273 | − | 0.891879i | \(-0.649387\pi\) | ||||
−0.452273 | + | 0.891879i | \(0.649387\pi\) | |||||||
\(912\) | 2.71602 | 0.0899365 | ||||||||
\(913\) | 1.78118 | 0.0589486 | ||||||||
\(914\) | 31.0342 | 1.02652 | ||||||||
\(915\) | −10.0000 | −0.330590 | ||||||||
\(916\) | 3.85193 | 0.127271 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.31161 | 0.175309 | ||||||||
\(919\) | 38.4541 | 1.26848 | 0.634242 | − | 0.773135i | \(-0.281312\pi\) | ||||
0.634242 | + | 0.773135i | \(0.281312\pi\) | |||||||
\(920\) | 1.00000 | 0.0329690 | ||||||||
\(921\) | 30.5745 | 1.00746 | ||||||||
\(922\) | −7.61764 | −0.250874 | ||||||||
\(923\) | −28.5515 | −0.939784 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.6288 | 1.03995 | ||||||||
\(926\) | −8.80882 | −0.289476 | ||||||||
\(927\) | 16.8365 | 0.552982 | ||||||||
\(928\) | −9.12043 | −0.299393 | ||||||||
\(929\) | 53.0674 | 1.74109 | 0.870543 | − | 0.492093i | \(-0.163768\pi\) | ||||
0.870543 | + | 0.492093i | \(0.163768\pi\) | |||||||
\(930\) | −9.83645 | −0.322550 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −26.5304 | −0.869033 | ||||||||
\(933\) | 7.07075 | 0.231486 | ||||||||
\(934\) | −0.808819 | −0.0264654 | ||||||||
\(935\) | −2.14807 | −0.0702493 | ||||||||
\(936\) | −4.12043 | −0.134681 | ||||||||
\(937\) | −29.1645 | −0.952763 | −0.476382 | − | 0.879239i | \(-0.658052\pi\) | ||||
−0.476382 | + | 0.879239i | \(0.658052\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.68839 | −0.250901 | ||||||||
\(940\) | −10.8365 | −0.353446 | ||||||||
\(941\) | 26.0220 | 0.848294 | 0.424147 | − | 0.905593i | \(-0.360574\pi\) | ||||
0.424147 | + | 0.905593i | \(0.360574\pi\) | |||||||
\(942\) | 22.7713 | 0.741929 | ||||||||
\(943\) | 10.7160 | 0.348962 | ||||||||
\(944\) | −8.31161 | −0.270520 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.327094 | 0.0106347 | ||||||||
\(947\) | −12.9227 | −0.419931 | −0.209965 | − | 0.977709i | \(-0.567335\pi\) | ||||
−0.209965 | + | 0.977709i | \(0.567335\pi\) | |||||||
\(948\) | 9.92925 | 0.322487 | ||||||||
\(949\) | 18.9358 | 0.614683 | ||||||||
\(950\) | −10.8641 | −0.352478 | ||||||||
\(951\) | 22.7933 | 0.739125 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.5680 | 0.407116 | 0.203558 | − | 0.979063i | \(-0.434749\pi\) | ||||
0.203558 | + | 0.979063i | \(0.434749\pi\) | |||||||
\(954\) | 0.191181 | 0.00618972 | ||||||||
\(955\) | 24.7713 | 0.801580 | ||||||||
\(956\) | −16.0000 | −0.517477 | ||||||||
\(957\) | 3.68839 | 0.119229 | ||||||||
\(958\) | 28.3337 | 0.915419 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 65.7558 | 2.12116 | ||||||||
\(962\) | 32.5811 | 1.05046 | ||||||||
\(963\) | −9.59559 | −0.309214 | ||||||||
\(964\) | −14.7933 | −0.476461 | ||||||||
\(965\) | −14.8585 | −0.478312 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8309 | 0.412613 | 0.206306 | − | 0.978487i | \(-0.433856\pi\) | ||||
0.206306 | + | 0.978487i | \(0.433856\pi\) | |||||||
\(968\) | 10.8365 | 0.348297 | ||||||||
\(969\) | 14.4265 | 0.463445 | ||||||||
\(970\) | −15.3613 | −0.493221 | ||||||||
\(971\) | −22.4044 | −0.718992 | −0.359496 | − | 0.933147i | \(-0.617051\pi\) | ||||
−0.359496 | + | 0.933147i | \(0.617051\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18.7005 | −0.599204 | ||||||||
\(975\) | 16.4817 | 0.527838 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | −20.5094 | −0.656153 | −0.328076 | − | 0.944651i | \(-0.606400\pi\) | ||||
−0.328076 | + | 0.944651i | \(0.606400\pi\) | |||||||
\(978\) | 24.7713 | 0.792099 | ||||||||
\(979\) | −3.19775 | −0.102200 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.19118 | −0.101887 | ||||||||
\(982\) | −5.09280 | −0.162518 | ||||||||
\(983\) | 4.53043 | 0.144498 | 0.0722491 | − | 0.997387i | \(-0.476982\pi\) | ||||
0.0722491 | + | 0.997387i | \(0.476982\pi\) | |||||||
\(984\) | −10.7160 | −0.341614 | ||||||||
\(985\) | −11.4320 | −0.364255 | ||||||||
\(986\) | −48.4442 | −1.54278 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.1912 | −0.356039 | ||||||||
\(989\) | −0.808819 | −0.0257189 | ||||||||
\(990\) | 0.404409 | 0.0128530 | ||||||||
\(991\) | −31.4100 | −0.997771 | −0.498886 | − | 0.866668i | \(-0.666257\pi\) | ||||
−0.498886 | + | 0.866668i | \(0.666257\pi\) | |||||||
\(992\) | 9.83645 | 0.312308 | ||||||||
\(993\) | 20.5304 | 0.651513 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.62323 | −0.273375 | ||||||||
\(996\) | 4.40441 | 0.139559 | ||||||||
\(997\) | 18.4752 | 0.585114 | 0.292557 | − | 0.956248i | \(-0.405494\pi\) | ||||
0.292557 | + | 0.956248i | \(0.405494\pi\) | |||||||
\(998\) | −19.4873 | −0.616860 | ||||||||
\(999\) | 7.90720 | 0.250173 |
(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 | 6762.2.a.ce.1.2 | 3 | ||
7.2 | even | 3 | 966.2.i.k.277.3 | ✓ | 6 | ||
7.4 | even | 3 | 966.2.i.k.415.3 | yes | 6 | ||
7.6 | odd | 2 | 6762.2.a.cf.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.k.277.3 | ✓ | 6 | 7.2 | even | 3 | ||
966.2.i.k.415.3 | yes | 6 | 7.4 | even | 3 | ||
6762.2.a.ce.1.2 | 3 | 1.1 | even | 1 | trivial | ||
6762.2.a.cf.1.2 | 3 | 7.6 | odd | 2 |