Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 825) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.618034 | 0.252311 | ||||||||
\(7\) | 0.763932 | 0.288739 | 0.144370 | − | 0.989524i | \(-0.453885\pi\) | ||||
0.144370 | + | 0.989524i | \(0.453885\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | −0.472136 | −0.126184 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | −0.618034 | −0.145672 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.763932 | −0.166704 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.38197 | 0.496674 | 0.248337 | − | 0.968674i | \(-0.420116\pi\) | ||||
0.248337 | + | 0.968674i | \(0.420116\pi\) | |||||||
\(24\) | −2.23607 | −0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.763932 | −0.149819 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.23607 | −0.233595 | ||||||||
\(29\) | 5.85410 | 1.08708 | 0.543540 | − | 0.839383i | \(-0.317084\pi\) | ||||
0.543540 | + | 0.839383i | \(0.317084\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00000 | 1.25724 | 0.628619 | − | 0.777714i | \(-0.283621\pi\) | ||||
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.23607 | 0.211984 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.61803 | −0.269672 | ||||||||
\(37\) | −7.47214 | −1.22841 | −0.614206 | − | 0.789146i | \(-0.710524\pi\) | ||||
−0.614206 | + | 0.789146i | \(0.710524\pi\) | |||||||
\(38\) | 3.09017 | 0.501292 | ||||||||
\(39\) | −1.23607 | −0.197929 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.52786 | −0.394786 | −0.197393 | − | 0.980324i | \(-0.563248\pi\) | ||||
−0.197393 | + | 0.980324i | \(0.563248\pi\) | |||||||
\(42\) | 0.472136 | 0.0728522 | ||||||||
\(43\) | 2.09017 | 0.318748 | 0.159374 | − | 0.987218i | \(-0.449052\pi\) | ||||
0.159374 | + | 0.987218i | \(0.449052\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.47214 | −0.217055 | ||||||||
\(47\) | 5.09017 | 0.742478 | 0.371239 | − | 0.928537i | \(-0.378933\pi\) | ||||
0.371239 | + | 0.928537i | \(0.378933\pi\) | |||||||
\(48\) | −1.85410 | −0.267617 | ||||||||
\(49\) | −6.41641 | −0.916630 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | −7.61803 | −1.04642 | −0.523209 | − | 0.852205i | \(-0.675265\pi\) | ||||
−0.523209 | + | 0.852205i | \(0.675265\pi\) | |||||||
\(54\) | 0.618034 | 0.0841038 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.70820 | 0.228268 | ||||||||
\(57\) | 5.00000 | 0.662266 | ||||||||
\(58\) | −3.61803 | −0.475071 | ||||||||
\(59\) | −6.70820 | −0.873334 | −0.436667 | − | 0.899623i | \(-0.643841\pi\) | ||||
−0.436667 | + | 0.899623i | \(0.643841\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.00000 | −0.896258 | −0.448129 | − | 0.893969i | \(-0.647910\pi\) | ||||
−0.448129 | + | 0.893969i | \(0.647910\pi\) | |||||||
\(62\) | −4.32624 | −0.549433 | ||||||||
\(63\) | 0.763932 | 0.0962464 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.38197 | −1.14619 | −0.573095 | − | 0.819489i | \(-0.694257\pi\) | ||||
−0.573095 | + | 0.819489i | \(0.694257\pi\) | |||||||
\(68\) | 3.23607 | 0.392431 | ||||||||
\(69\) | −2.38197 | −0.286755 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | 13.4721 | 1.57679 | 0.788397 | − | 0.615167i | \(-0.210911\pi\) | ||||
0.788397 | + | 0.615167i | \(0.210911\pi\) | |||||||
\(74\) | 4.61803 | 0.536836 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.09017 | 0.928006 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.763932 | 0.0864983 | ||||||||
\(79\) | 8.09017 | 0.910215 | 0.455108 | − | 0.890436i | \(-0.349601\pi\) | ||||
0.455108 | + | 0.890436i | \(0.349601\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.56231 | 0.172528 | ||||||||
\(83\) | 5.70820 | 0.626557 | 0.313278 | − | 0.949661i | \(-0.398573\pi\) | ||||
0.313278 | + | 0.949661i | \(0.398573\pi\) | |||||||
\(84\) | 1.23607 | 0.134866 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.29180 | −0.139298 | ||||||||
\(87\) | −5.85410 | −0.627626 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8541 | 1.15053 | 0.575266 | − | 0.817966i | \(-0.304898\pi\) | ||||
0.575266 | + | 0.817966i | \(0.304898\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.944272 | 0.0989866 | ||||||||
\(92\) | −3.85410 | −0.401818 | ||||||||
\(93\) | −7.00000 | −0.725866 | ||||||||
\(94\) | −3.14590 | −0.324475 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.61803 | 0.573388 | ||||||||
\(97\) | 11.4721 | 1.16482 | 0.582409 | − | 0.812896i | \(-0.302110\pi\) | ||||
0.582409 | + | 0.812896i | \(0.302110\pi\) | |||||||
\(98\) | 3.96556 | 0.400582 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.562306 | 0.0559515 | 0.0279758 | − | 0.999609i | \(-0.491094\pi\) | ||||
0.0279758 | + | 0.999609i | \(0.491094\pi\) | |||||||
\(102\) | −1.23607 | −0.122389 | ||||||||
\(103\) | 2.38197 | 0.234702 | 0.117351 | − | 0.993090i | \(-0.462560\pi\) | ||||
0.117351 | + | 0.993090i | \(0.462560\pi\) | |||||||
\(104\) | 2.76393 | 0.271026 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.70820 | 0.457301 | ||||||||
\(107\) | −2.85410 | −0.275916 | −0.137958 | − | 0.990438i | \(-0.544054\pi\) | ||||
−0.137958 | + | 0.990438i | \(0.544054\pi\) | |||||||
\(108\) | 1.61803 | 0.155695 | ||||||||
\(109\) | −4.14590 | −0.397105 | −0.198553 | − | 0.980090i | \(-0.563624\pi\) | ||||
−0.198553 | + | 0.980090i | \(0.563624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.47214 | 0.709224 | ||||||||
\(112\) | 1.41641 | 0.133838 | ||||||||
\(113\) | 5.47214 | 0.514775 | 0.257388 | − | 0.966308i | \(-0.417138\pi\) | ||||
0.257388 | + | 0.966308i | \(0.417138\pi\) | |||||||
\(114\) | −3.09017 | −0.289421 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.47214 | −0.879466 | ||||||||
\(117\) | 1.23607 | 0.114275 | ||||||||
\(118\) | 4.14590 | 0.381661 | ||||||||
\(119\) | −1.52786 | −0.140059 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 4.32624 | 0.391679 | ||||||||
\(123\) | 2.52786 | 0.227930 | ||||||||
\(124\) | −11.3262 | −1.01713 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.472136 | −0.0420612 | ||||||||
\(127\) | −15.9443 | −1.41483 | −0.707413 | − | 0.706801i | \(-0.750138\pi\) | ||||
−0.707413 | + | 0.706801i | \(0.750138\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | −2.09017 | −0.184029 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.1803 | −1.15157 | −0.575786 | − | 0.817601i | \(-0.695304\pi\) | ||||
−0.575786 | + | 0.817601i | \(0.695304\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.81966 | −0.331207 | ||||||||
\(134\) | 5.79837 | 0.500903 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.47214 | −0.383482 | ||||||||
\(137\) | 18.7082 | 1.59835 | 0.799175 | − | 0.601099i | \(-0.205270\pi\) | ||||
0.799175 | + | 0.601099i | \(0.205270\pi\) | |||||||
\(138\) | 1.47214 | 0.125317 | ||||||||
\(139\) | −21.1803 | −1.79649 | −0.898246 | − | 0.439492i | \(-0.855158\pi\) | ||||
−0.898246 | + | 0.439492i | \(0.855158\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.09017 | −0.428670 | ||||||||
\(142\) | 4.94427 | 0.414914 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.85410 | 0.154508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.32624 | −0.689084 | ||||||||
\(147\) | 6.41641 | 0.529216 | ||||||||
\(148\) | 12.0902 | 0.993806 | ||||||||
\(149\) | −20.1246 | −1.64867 | −0.824336 | − | 0.566101i | \(-0.808451\pi\) | ||||
−0.824336 | + | 0.566101i | \(0.808451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7639 | 0.875956 | 0.437978 | − | 0.898986i | \(-0.355695\pi\) | ||||
0.437978 | + | 0.898986i | \(0.355695\pi\) | |||||||
\(152\) | −11.1803 | −0.906845 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | −3.32624 | −0.265463 | −0.132731 | − | 0.991152i | \(-0.542375\pi\) | ||||
−0.132731 | + | 0.991152i | \(0.542375\pi\) | |||||||
\(158\) | −5.00000 | −0.397779 | ||||||||
\(159\) | 7.61803 | 0.604149 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.81966 | 0.143409 | ||||||||
\(162\) | −0.618034 | −0.0485573 | ||||||||
\(163\) | 13.5623 | 1.06228 | 0.531141 | − | 0.847284i | \(-0.321763\pi\) | ||||
0.531141 | + | 0.847284i | \(0.321763\pi\) | |||||||
\(164\) | 4.09017 | 0.319389 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.52786 | −0.273815 | ||||||||
\(167\) | 20.0344 | 1.55031 | 0.775156 | − | 0.631770i | \(-0.217671\pi\) | ||||
0.775156 | + | 0.631770i | \(0.217671\pi\) | |||||||
\(168\) | −1.70820 | −0.131791 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.00000 | −0.382360 | ||||||||
\(172\) | −3.38197 | −0.257872 | ||||||||
\(173\) | −3.56231 | −0.270837 | −0.135419 | − | 0.990788i | \(-0.543238\pi\) | ||||
−0.135419 | + | 0.990788i | \(0.543238\pi\) | |||||||
\(174\) | 3.61803 | 0.274282 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.70820 | 0.504219 | ||||||||
\(178\) | −6.70820 | −0.502801 | ||||||||
\(179\) | −19.4721 | −1.45542 | −0.727708 | − | 0.685887i | \(-0.759414\pi\) | ||||
−0.727708 | + | 0.685887i | \(0.759414\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.23607 | −0.389194 | −0.194597 | − | 0.980883i | \(-0.562340\pi\) | ||||
−0.194597 | + | 0.980883i | \(0.562340\pi\) | |||||||
\(182\) | −0.583592 | −0.0432587 | ||||||||
\(183\) | 7.00000 | 0.517455 | ||||||||
\(184\) | 5.32624 | 0.392655 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.32624 | 0.317215 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.23607 | −0.600677 | ||||||||
\(189\) | −0.763932 | −0.0555679 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4164 | 0.753705 | 0.376852 | − | 0.926273i | \(-0.377006\pi\) | ||||
0.376852 | + | 0.926273i | \(0.377006\pi\) | |||||||
\(192\) | 0.236068 | 0.0170367 | ||||||||
\(193\) | 21.0344 | 1.51409 | 0.757046 | − | 0.653361i | \(-0.226642\pi\) | ||||
0.757046 | + | 0.653361i | \(0.226642\pi\) | |||||||
\(194\) | −7.09017 | −0.509045 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.3820 | 0.741569 | ||||||||
\(197\) | −14.2361 | −1.01428 | −0.507139 | − | 0.861864i | \(-0.669297\pi\) | ||||
−0.507139 | + | 0.861864i | \(0.669297\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.7984 | 1.40347 | 0.701735 | − | 0.712438i | \(-0.252409\pi\) | ||||
0.701735 | + | 0.712438i | \(0.252409\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.38197 | 0.661753 | ||||||||
\(202\) | −0.347524 | −0.0244517 | ||||||||
\(203\) | 4.47214 | 0.313882 | ||||||||
\(204\) | −3.23607 | −0.226570 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.47214 | −0.102569 | ||||||||
\(207\) | 2.38197 | 0.165558 | ||||||||
\(208\) | 2.29180 | 0.158907 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.85410 | 0.265327 | 0.132664 | − | 0.991161i | \(-0.457647\pi\) | ||||
0.132664 | + | 0.991161i | \(0.457647\pi\) | |||||||
\(212\) | 12.3262 | 0.846569 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 1.76393 | 0.120580 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | 5.34752 | 0.363014 | ||||||||
\(218\) | 2.56231 | 0.173541 | ||||||||
\(219\) | −13.4721 | −0.910363 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.47214 | −0.166294 | ||||||||
\(222\) | −4.61803 | −0.309942 | ||||||||
\(223\) | 8.03444 | 0.538026 | 0.269013 | − | 0.963137i | \(-0.413303\pi\) | ||||
0.269013 | + | 0.963137i | \(0.413303\pi\) | |||||||
\(224\) | −4.29180 | −0.286758 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.38197 | −0.224965 | ||||||||
\(227\) | −25.9443 | −1.72198 | −0.860991 | − | 0.508620i | \(-0.830156\pi\) | ||||
−0.860991 | + | 0.508620i | \(0.830156\pi\) | |||||||
\(228\) | −8.09017 | −0.535785 | ||||||||
\(229\) | 18.0902 | 1.19543 | 0.597716 | − | 0.801708i | \(-0.296075\pi\) | ||||
0.597716 | + | 0.801708i | \(0.296075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.0902 | 0.859412 | ||||||||
\(233\) | 23.2705 | 1.52450 | 0.762251 | − | 0.647282i | \(-0.224094\pi\) | ||||
0.762251 | + | 0.647282i | \(0.224094\pi\) | |||||||
\(234\) | −0.763932 | −0.0499398 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.8541 | 0.706542 | ||||||||
\(237\) | −8.09017 | −0.525513 | ||||||||
\(238\) | 0.944272 | 0.0612081 | ||||||||
\(239\) | 7.03444 | 0.455020 | 0.227510 | − | 0.973776i | \(-0.426942\pi\) | ||||
0.227510 | + | 0.973776i | \(0.426942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.61803 | 0.104227 | 0.0521134 | − | 0.998641i | \(-0.483404\pi\) | ||||
0.0521134 | + | 0.998641i | \(0.483404\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.3262 | 0.725088 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.56231 | −0.0996090 | ||||||||
\(247\) | −6.18034 | −0.393246 | ||||||||
\(248\) | 15.6525 | 0.993933 | ||||||||
\(249\) | −5.70820 | −0.361743 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.52786 | 0.475155 | 0.237577 | − | 0.971369i | \(-0.423647\pi\) | ||||
0.237577 | + | 0.971369i | \(0.423647\pi\) | |||||||
\(252\) | −1.23607 | −0.0778650 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 9.85410 | 0.618301 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | −10.5623 | −0.658859 | −0.329429 | − | 0.944180i | \(-0.606856\pi\) | ||||
−0.329429 | + | 0.944180i | \(0.606856\pi\) | |||||||
\(258\) | 1.29180 | 0.0804237 | ||||||||
\(259\) | −5.70820 | −0.354691 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.85410 | 0.362360 | ||||||||
\(262\) | 8.14590 | 0.503255 | ||||||||
\(263\) | 27.2148 | 1.67814 | 0.839068 | − | 0.544027i | \(-0.183101\pi\) | ||||
0.839068 | + | 0.544027i | \(0.183101\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.36068 | 0.144743 | ||||||||
\(267\) | −10.8541 | −0.664260 | ||||||||
\(268\) | 15.1803 | 0.927287 | ||||||||
\(269\) | −5.85410 | −0.356931 | −0.178465 | − | 0.983946i | \(-0.557113\pi\) | ||||
−0.178465 | + | 0.983946i | \(0.557113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.6180 | −1.25246 | −0.626228 | − | 0.779640i | \(-0.715402\pi\) | ||||
−0.626228 | + | 0.779640i | \(0.715402\pi\) | |||||||
\(272\) | −3.70820 | −0.224843 | ||||||||
\(273\) | −0.944272 | −0.0571499 | ||||||||
\(274\) | −11.5623 | −0.698504 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.85410 | 0.231990 | ||||||||
\(277\) | 8.65248 | 0.519877 | 0.259938 | − | 0.965625i | \(-0.416298\pi\) | ||||
0.259938 | + | 0.965625i | \(0.416298\pi\) | |||||||
\(278\) | 13.0902 | 0.785096 | ||||||||
\(279\) | 7.00000 | 0.419079 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0902 | −0.601929 | −0.300965 | − | 0.953635i | \(-0.597309\pi\) | ||||
−0.300965 | + | 0.953635i | \(0.597309\pi\) | |||||||
\(282\) | 3.14590 | 0.187336 | ||||||||
\(283\) | −13.0344 | −0.774817 | −0.387409 | − | 0.921908i | \(-0.626630\pi\) | ||||
−0.387409 | + | 0.921908i | \(0.626630\pi\) | |||||||
\(284\) | 12.9443 | 0.768101 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.93112 | −0.113990 | ||||||||
\(288\) | −5.61803 | −0.331046 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.4721 | −0.672509 | ||||||||
\(292\) | −21.7984 | −1.27565 | ||||||||
\(293\) | −16.5279 | −0.965568 | −0.482784 | − | 0.875739i | \(-0.660374\pi\) | ||||
−0.482784 | + | 0.875739i | \(0.660374\pi\) | |||||||
\(294\) | −3.96556 | −0.231276 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −16.7082 | −0.971145 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.4377 | 0.720496 | ||||||||
\(299\) | 2.94427 | 0.170272 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.59675 | 0.0920350 | ||||||||
\(302\) | −6.65248 | −0.382807 | ||||||||
\(303\) | −0.562306 | −0.0323036 | ||||||||
\(304\) | −9.27051 | −0.531700 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.23607 | 0.0706613 | ||||||||
\(307\) | −12.1246 | −0.691988 | −0.345994 | − | 0.938237i | \(-0.612458\pi\) | ||||
−0.345994 | + | 0.938237i | \(0.612458\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.38197 | −0.135505 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.4721 | 1.21757 | 0.608787 | − | 0.793334i | \(-0.291657\pi\) | ||||
0.608787 | + | 0.793334i | \(0.291657\pi\) | |||||||
\(312\) | −2.76393 | −0.156477 | ||||||||
\(313\) | 0.472136 | 0.0266867 | 0.0133434 | − | 0.999911i | \(-0.495753\pi\) | ||||
0.0133434 | + | 0.999911i | \(0.495753\pi\) | |||||||
\(314\) | 2.05573 | 0.116011 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.0902 | −0.736380 | ||||||||
\(317\) | 30.4164 | 1.70836 | 0.854178 | − | 0.519981i | \(-0.174061\pi\) | ||||
0.854178 | + | 0.519981i | \(0.174061\pi\) | |||||||
\(318\) | −4.70820 | −0.264023 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.85410 | 0.159300 | ||||||||
\(322\) | −1.12461 | −0.0626722 | ||||||||
\(323\) | 10.0000 | 0.556415 | ||||||||
\(324\) | −1.61803 | −0.0898908 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.38197 | −0.464234 | ||||||||
\(327\) | 4.14590 | 0.229269 | ||||||||
\(328\) | −5.65248 | −0.312106 | ||||||||
\(329\) | 3.88854 | 0.214382 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5967 | 1.18706 | 0.593532 | − | 0.804810i | \(-0.297733\pi\) | ||||
0.593532 | + | 0.804810i | \(0.297733\pi\) | |||||||
\(332\) | −9.23607 | −0.506895 | ||||||||
\(333\) | −7.47214 | −0.409471 | ||||||||
\(334\) | −12.3820 | −0.677511 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.41641 | −0.0772714 | ||||||||
\(337\) | 22.1459 | 1.20636 | 0.603182 | − | 0.797604i | \(-0.293899\pi\) | ||||
0.603182 | + | 0.797604i | \(0.293899\pi\) | |||||||
\(338\) | 7.09017 | 0.385654 | ||||||||
\(339\) | −5.47214 | −0.297206 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.09017 | 0.167097 | ||||||||
\(343\) | −10.2492 | −0.553406 | ||||||||
\(344\) | 4.67376 | 0.251992 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.20163 | 0.118360 | ||||||||
\(347\) | −5.81966 | −0.312416 | −0.156208 | − | 0.987724i | \(-0.549927\pi\) | ||||
−0.156208 | + | 0.987724i | \(0.549927\pi\) | |||||||
\(348\) | 9.47214 | 0.507760 | ||||||||
\(349\) | −27.7639 | −1.48617 | −0.743085 | − | 0.669197i | \(-0.766638\pi\) | ||||
−0.743085 | + | 0.669197i | \(0.766638\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.23607 | −0.0659764 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.8328 | −1.90719 | −0.953594 | − | 0.301095i | \(-0.902648\pi\) | ||||
−0.953594 | + | 0.301095i | \(0.902648\pi\) | |||||||
\(354\) | −4.14590 | −0.220352 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −17.5623 | −0.930800 | ||||||||
\(357\) | 1.52786 | 0.0808631 | ||||||||
\(358\) | 12.0344 | 0.636040 | ||||||||
\(359\) | −16.7082 | −0.881825 | −0.440913 | − | 0.897550i | \(-0.645345\pi\) | ||||
−0.440913 | + | 0.897550i | \(0.645345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 3.23607 | 0.170084 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.52786 | −0.0800818 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.32624 | −0.226136 | ||||||||
\(367\) | −18.1246 | −0.946097 | −0.473049 | − | 0.881036i | \(-0.656846\pi\) | ||||
−0.473049 | + | 0.881036i | \(0.656846\pi\) | |||||||
\(368\) | 4.41641 | 0.230221 | ||||||||
\(369\) | −2.52786 | −0.131595 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.81966 | −0.302142 | ||||||||
\(372\) | 11.3262 | 0.587238 | ||||||||
\(373\) | −9.74265 | −0.504455 | −0.252228 | − | 0.967668i | \(-0.581163\pi\) | ||||
−0.252228 | + | 0.967668i | \(0.581163\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.3820 | 0.586980 | ||||||||
\(377\) | 7.23607 | 0.372676 | ||||||||
\(378\) | 0.472136 | 0.0242841 | ||||||||
\(379\) | −5.00000 | −0.256833 | −0.128416 | − | 0.991720i | \(-0.540989\pi\) | ||||
−0.128416 | + | 0.991720i | \(0.540989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.9443 | 0.816850 | ||||||||
\(382\) | −6.43769 | −0.329381 | ||||||||
\(383\) | −31.3607 | −1.60246 | −0.801228 | − | 0.598359i | \(-0.795820\pi\) | ||||
−0.801228 | + | 0.598359i | \(0.795820\pi\) | |||||||
\(384\) | −11.3820 | −0.580834 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0000 | −0.661683 | ||||||||
\(387\) | 2.09017 | 0.106249 | ||||||||
\(388\) | −18.5623 | −0.942358 | ||||||||
\(389\) | −38.9443 | −1.97455 | −0.987276 | − | 0.159013i | \(-0.949169\pi\) | ||||
−0.987276 | + | 0.159013i | \(0.949169\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.76393 | −0.240922 | ||||||||
\(392\) | −14.3475 | −0.724659 | ||||||||
\(393\) | 13.1803 | 0.664860 | ||||||||
\(394\) | 8.79837 | 0.443256 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.2705 | 1.82036 | 0.910182 | − | 0.414208i | \(-0.135941\pi\) | ||||
0.910182 | + | 0.414208i | \(0.135941\pi\) | |||||||
\(398\) | −12.2361 | −0.613339 | ||||||||
\(399\) | 3.81966 | 0.191222 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.88854 | 0.244122 | 0.122061 | − | 0.992523i | \(-0.461050\pi\) | ||||
0.122061 | + | 0.992523i | \(0.461050\pi\) | |||||||
\(402\) | −5.79837 | −0.289197 | ||||||||
\(403\) | 8.65248 | 0.431011 | ||||||||
\(404\) | −0.909830 | −0.0452657 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.76393 | −0.137172 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.47214 | 0.221404 | ||||||||
\(409\) | −36.3050 | −1.79516 | −0.897582 | − | 0.440847i | \(-0.854678\pi\) | ||||
−0.897582 | + | 0.440847i | \(0.854678\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.7082 | −0.922808 | ||||||||
\(412\) | −3.85410 | −0.189878 | ||||||||
\(413\) | −5.12461 | −0.252166 | ||||||||
\(414\) | −1.47214 | −0.0723515 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.94427 | −0.340471 | ||||||||
\(417\) | 21.1803 | 1.03721 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.5967 | 1.20163 | 0.600815 | − | 0.799388i | \(-0.294843\pi\) | ||||
0.600815 | + | 0.799388i | \(0.294843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.85410 | 0.139100 | 0.0695502 | − | 0.997578i | \(-0.477844\pi\) | ||||
0.0695502 | + | 0.997578i | \(0.477844\pi\) | |||||||
\(422\) | −2.38197 | −0.115952 | ||||||||
\(423\) | 5.09017 | 0.247493 | ||||||||
\(424\) | −17.0344 | −0.827266 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.94427 | −0.239551 | ||||||||
\(427\) | −5.34752 | −0.258785 | ||||||||
\(428\) | 4.61803 | 0.223221 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.8885 | −0.957997 | −0.478999 | − | 0.877816i | \(-0.659000\pi\) | ||||
−0.478999 | + | 0.877816i | \(0.659000\pi\) | |||||||
\(432\) | −1.85410 | −0.0892055 | ||||||||
\(433\) | 28.0344 | 1.34725 | 0.673625 | − | 0.739074i | \(-0.264736\pi\) | ||||
0.673625 | + | 0.739074i | \(0.264736\pi\) | |||||||
\(434\) | −3.30495 | −0.158643 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.70820 | 0.321265 | ||||||||
\(437\) | −11.9098 | −0.569724 | ||||||||
\(438\) | 8.32624 | 0.397843 | ||||||||
\(439\) | −9.67376 | −0.461703 | −0.230852 | − | 0.972989i | \(-0.574151\pi\) | ||||
−0.230852 | + | 0.972989i | \(0.574151\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.41641 | −0.305543 | ||||||||
\(442\) | 1.52786 | 0.0726731 | ||||||||
\(443\) | 25.2705 | 1.20064 | 0.600319 | − | 0.799761i | \(-0.295040\pi\) | ||||
0.600319 | + | 0.799761i | \(0.295040\pi\) | |||||||
\(444\) | −12.0902 | −0.573774 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.96556 | −0.235126 | ||||||||
\(447\) | 20.1246 | 0.951861 | ||||||||
\(448\) | −0.180340 | −0.00852026 | ||||||||
\(449\) | −0.729490 | −0.0344268 | −0.0172134 | − | 0.999852i | \(-0.505479\pi\) | ||||
−0.0172134 | + | 0.999852i | \(0.505479\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −8.85410 | −0.416462 | ||||||||
\(453\) | −10.7639 | −0.505734 | ||||||||
\(454\) | 16.0344 | 0.752534 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.1803 | 0.523567 | ||||||||
\(457\) | −1.47214 | −0.0688636 | −0.0344318 | − | 0.999407i | \(-0.510962\pi\) | ||||
−0.0344318 | + | 0.999407i | \(0.510962\pi\) | |||||||
\(458\) | −11.1803 | −0.522423 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.9443 | −1.20835 | −0.604173 | − | 0.796853i | \(-0.706496\pi\) | ||||
−0.604173 | + | 0.796853i | \(0.706496\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.2705 | −1.54621 | −0.773106 | − | 0.634277i | \(-0.781298\pi\) | ||||
−0.773106 | + | 0.634277i | \(0.781298\pi\) | |||||||
\(464\) | 10.8541 | 0.503889 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.3820 | −0.666232 | ||||||||
\(467\) | 4.88854 | 0.226215 | 0.113107 | − | 0.993583i | \(-0.463920\pi\) | ||||
0.113107 | + | 0.993583i | \(0.463920\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | −7.16718 | −0.330950 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.32624 | 0.153265 | ||||||||
\(472\) | −15.0000 | −0.690431 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 5.00000 | 0.229658 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.47214 | 0.113310 | ||||||||
\(477\) | −7.61803 | −0.348806 | ||||||||
\(478\) | −4.34752 | −0.198851 | ||||||||
\(479\) | −33.4164 | −1.52683 | −0.763417 | − | 0.645906i | \(-0.776480\pi\) | ||||
−0.763417 | + | 0.645906i | \(0.776480\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.23607 | −0.421128 | ||||||||
\(482\) | −1.00000 | −0.0455488 | ||||||||
\(483\) | −1.81966 | −0.0827974 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.618034 | 0.0280346 | ||||||||
\(487\) | −14.1803 | −0.642573 | −0.321286 | − | 0.946982i | \(-0.604115\pi\) | ||||
−0.321286 | + | 0.946982i | \(0.604115\pi\) | |||||||
\(488\) | −15.6525 | −0.708554 | ||||||||
\(489\) | −13.5623 | −0.613309 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.7984 | −1.43504 | −0.717520 | − | 0.696538i | \(-0.754723\pi\) | ||||
−0.717520 | + | 0.696538i | \(0.754723\pi\) | |||||||
\(492\) | −4.09017 | −0.184399 | ||||||||
\(493\) | −11.7082 | −0.527311 | ||||||||
\(494\) | 3.81966 | 0.171855 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.9787 | 0.582761 | ||||||||
\(497\) | −6.11146 | −0.274136 | ||||||||
\(498\) | 3.52786 | 0.158087 | ||||||||
\(499\) | −11.1803 | −0.500501 | −0.250250 | − | 0.968181i | \(-0.580513\pi\) | ||||
−0.250250 | + | 0.968181i | \(0.580513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.0344 | −0.895073 | ||||||||
\(502\) | −4.65248 | −0.207650 | ||||||||
\(503\) | 21.8885 | 0.975962 | 0.487981 | − | 0.872854i | \(-0.337734\pi\) | ||||
0.487981 | + | 0.872854i | \(0.337734\pi\) | |||||||
\(504\) | 1.70820 | 0.0760895 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.4721 | 0.509495 | ||||||||
\(508\) | 25.7984 | 1.14462 | ||||||||
\(509\) | 0.527864 | 0.0233972 | 0.0116986 | − | 0.999932i | \(-0.496276\pi\) | ||||
0.0116986 | + | 0.999932i | \(0.496276\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2918 | 0.455282 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 5.00000 | 0.220755 | ||||||||
\(514\) | 6.52786 | 0.287932 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.38197 | 0.148883 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.52786 | 0.155005 | ||||||||
\(519\) | 3.56231 | 0.156368 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3607 | −0.672964 | −0.336482 | − | 0.941690i | \(-0.609237\pi\) | ||||
−0.336482 | + | 0.941690i | \(0.609237\pi\) | |||||||
\(522\) | −3.61803 | −0.158357 | ||||||||
\(523\) | −8.23607 | −0.360138 | −0.180069 | − | 0.983654i | \(-0.557632\pi\) | ||||
−0.180069 | + | 0.983654i | \(0.557632\pi\) | |||||||
\(524\) | 21.3262 | 0.931641 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.8197 | −0.733372 | ||||||||
\(527\) | −14.0000 | −0.609850 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3262 | −0.753315 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.70820 | −0.291111 | ||||||||
\(532\) | 6.18034 | 0.267952 | ||||||||
\(533\) | −3.12461 | −0.135342 | ||||||||
\(534\) | 6.70820 | 0.290292 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −20.9787 | −0.906142 | ||||||||
\(537\) | 19.4721 | 0.840285 | ||||||||
\(538\) | 3.61803 | 0.155985 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.618034 | −0.0265714 | −0.0132857 | − | 0.999912i | \(-0.504229\pi\) | ||||
−0.0132857 | + | 0.999912i | \(0.504229\pi\) | |||||||
\(542\) | 12.7426 | 0.547344 | ||||||||
\(543\) | 5.23607 | 0.224701 | ||||||||
\(544\) | 11.2361 | 0.481742 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.583592 | 0.0249754 | ||||||||
\(547\) | 25.3607 | 1.08434 | 0.542172 | − | 0.840267i | \(-0.317602\pi\) | ||||
0.542172 | + | 0.840267i | \(0.317602\pi\) | |||||||
\(548\) | −30.2705 | −1.29309 | ||||||||
\(549\) | −7.00000 | −0.298753 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.2705 | −1.24697 | ||||||||
\(552\) | −5.32624 | −0.226700 | ||||||||
\(553\) | 6.18034 | 0.262815 | ||||||||
\(554\) | −5.34752 | −0.227195 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 34.2705 | 1.45339 | ||||||||
\(557\) | −31.3951 | −1.33025 | −0.665127 | − | 0.746730i | \(-0.731623\pi\) | ||||
−0.665127 | + | 0.746730i | \(0.731623\pi\) | |||||||
\(558\) | −4.32624 | −0.183144 | ||||||||
\(559\) | 2.58359 | 0.109274 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.23607 | 0.263053 | ||||||||
\(563\) | −36.3262 | −1.53097 | −0.765484 | − | 0.643455i | \(-0.777500\pi\) | ||||
−0.765484 | + | 0.643455i | \(0.777500\pi\) | |||||||
\(564\) | 8.23607 | 0.346801 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.05573 | 0.338608 | ||||||||
\(567\) | 0.763932 | 0.0320821 | ||||||||
\(568\) | −17.8885 | −0.750587 | ||||||||
\(569\) | 2.43769 | 0.102193 | 0.0510967 | − | 0.998694i | \(-0.483728\pi\) | ||||
0.0510967 | + | 0.998694i | \(0.483728\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0901699 | −0.00377349 | −0.00188675 | − | 0.999998i | \(-0.500601\pi\) | ||||
−0.00188675 | + | 0.999998i | \(0.500601\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.4164 | −0.435152 | ||||||||
\(574\) | 1.19350 | 0.0498155 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.236068 | −0.00983617 | ||||||||
\(577\) | −46.0132 | −1.91555 | −0.957776 | − | 0.287514i | \(-0.907171\pi\) | ||||
−0.957776 | + | 0.287514i | \(0.907171\pi\) | |||||||
\(578\) | 8.03444 | 0.334189 | ||||||||
\(579\) | −21.0344 | −0.874162 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.36068 | 0.180911 | ||||||||
\(582\) | 7.09017 | 0.293897 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 30.1246 | 1.24657 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.2148 | 0.421969 | ||||||||
\(587\) | −19.3820 | −0.799979 | −0.399990 | − | 0.916520i | \(-0.630986\pi\) | ||||
−0.399990 | + | 0.916520i | \(0.630986\pi\) | |||||||
\(588\) | −10.3820 | −0.428145 | ||||||||
\(589\) | −35.0000 | −1.44215 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.2361 | 0.585594 | ||||||||
\(592\) | −13.8541 | −0.569400 | ||||||||
\(593\) | −38.8885 | −1.59696 | −0.798481 | − | 0.602021i | \(-0.794362\pi\) | ||||
−0.798481 | + | 0.602021i | \(0.794362\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 32.5623 | 1.33380 | ||||||||
\(597\) | −19.7984 | −0.810294 | ||||||||
\(598\) | −1.81966 | −0.0744114 | ||||||||
\(599\) | −22.2361 | −0.908541 | −0.454271 | − | 0.890864i | \(-0.650100\pi\) | ||||
−0.454271 | + | 0.890864i | \(0.650100\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.3607 | −1.40160 | −0.700801 | − | 0.713357i | \(-0.747174\pi\) | ||||
−0.700801 | + | 0.713357i | \(0.747174\pi\) | |||||||
\(602\) | −0.986844 | −0.0402208 | ||||||||
\(603\) | −9.38197 | −0.382063 | ||||||||
\(604\) | −17.4164 | −0.708664 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.347524 | 0.0141172 | ||||||||
\(607\) | 33.0000 | 1.33943 | 0.669714 | − | 0.742619i | \(-0.266417\pi\) | ||||
0.669714 | + | 0.742619i | \(0.266417\pi\) | |||||||
\(608\) | 28.0902 | 1.13921 | ||||||||
\(609\) | −4.47214 | −0.181220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.29180 | 0.254539 | ||||||||
\(612\) | 3.23607 | 0.130810 | ||||||||
\(613\) | −8.23607 | −0.332652 | −0.166326 | − | 0.986071i | \(-0.553190\pi\) | ||||
−0.166326 | + | 0.986071i | \(0.553190\pi\) | |||||||
\(614\) | 7.49342 | 0.302410 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.2492 | −1.53986 | −0.769928 | − | 0.638131i | \(-0.779708\pi\) | ||||
−0.769928 | + | 0.638131i | \(0.779708\pi\) | |||||||
\(618\) | 1.47214 | 0.0592180 | ||||||||
\(619\) | 7.11146 | 0.285834 | 0.142917 | − | 0.989735i | \(-0.454352\pi\) | ||||
0.142917 | + | 0.989735i | \(0.454352\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.38197 | −0.0955850 | ||||||||
\(622\) | −13.2705 | −0.532099 | ||||||||
\(623\) | 8.29180 | 0.332204 | ||||||||
\(624\) | −2.29180 | −0.0917453 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.291796 | −0.0116625 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.38197 | 0.214764 | ||||||||
\(629\) | 14.9443 | 0.595867 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.6312 | 1.53788 | 0.768942 | − | 0.639319i | \(-0.220784\pi\) | ||||
0.768942 | + | 0.639319i | \(0.220784\pi\) | |||||||
\(632\) | 18.0902 | 0.719588 | ||||||||
\(633\) | −3.85410 | −0.153187 | ||||||||
\(634\) | −18.7984 | −0.746579 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.3262 | −0.488767 | ||||||||
\(637\) | −7.93112 | −0.314242 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | −0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.236068 | −0.00932412 | −0.00466206 | − | 0.999989i | \(-0.501484\pi\) | ||||
−0.00466206 | + | 0.999989i | \(0.501484\pi\) | |||||||
\(642\) | −1.76393 | −0.0696168 | ||||||||
\(643\) | −29.3262 | −1.15651 | −0.578257 | − | 0.815855i | \(-0.696267\pi\) | ||||
−0.578257 | + | 0.815855i | \(0.696267\pi\) | |||||||
\(644\) | −2.94427 | −0.116021 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.18034 | −0.243162 | ||||||||
\(647\) | −17.5967 | −0.691800 | −0.345900 | − | 0.938271i | \(-0.612426\pi\) | ||||
−0.345900 | + | 0.938271i | \(0.612426\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.34752 | −0.209586 | ||||||||
\(652\) | −21.9443 | −0.859404 | ||||||||
\(653\) | 23.4377 | 0.917188 | 0.458594 | − | 0.888646i | \(-0.348353\pi\) | ||||
0.458594 | + | 0.888646i | \(0.348353\pi\) | |||||||
\(654\) | −2.56231 | −0.100194 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.68692 | −0.182993 | ||||||||
\(657\) | 13.4721 | 0.525598 | ||||||||
\(658\) | −2.40325 | −0.0936885 | ||||||||
\(659\) | −12.9656 | −0.505066 | −0.252533 | − | 0.967588i | \(-0.581264\pi\) | ||||
−0.252533 | + | 0.967588i | \(0.581264\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.90983 | 0.152075 | 0.0760374 | − | 0.997105i | \(-0.475773\pi\) | ||||
0.0760374 | + | 0.997105i | \(0.475773\pi\) | |||||||
\(662\) | −13.3475 | −0.518766 | ||||||||
\(663\) | 2.47214 | 0.0960098 | ||||||||
\(664\) | 12.7639 | 0.495337 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.61803 | 0.178945 | ||||||||
\(667\) | 13.9443 | 0.539924 | ||||||||
\(668\) | −32.4164 | −1.25423 | ||||||||
\(669\) | −8.03444 | −0.310629 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.29180 | 0.165560 | ||||||||
\(673\) | −27.3050 | −1.05253 | −0.526264 | − | 0.850321i | \(-0.676408\pi\) | ||||
−0.526264 | + | 0.850321i | \(0.676408\pi\) | |||||||
\(674\) | −13.6869 | −0.527200 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.5623 | 0.713935 | ||||||||
\(677\) | 11.9443 | 0.459056 | 0.229528 | − | 0.973302i | \(-0.426282\pi\) | ||||
0.229528 | + | 0.973302i | \(0.426282\pi\) | |||||||
\(678\) | 3.38197 | 0.129884 | ||||||||
\(679\) | 8.76393 | 0.336329 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.9443 | 0.994187 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.29180 | −0.0876931 | −0.0438466 | − | 0.999038i | \(-0.513961\pi\) | ||||
−0.0438466 | + | 0.999038i | \(0.513961\pi\) | |||||||
\(684\) | 8.09017 | 0.309335 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.33437 | 0.241847 | ||||||||
\(687\) | −18.0902 | −0.690183 | ||||||||
\(688\) | 3.87539 | 0.147748 | ||||||||
\(689\) | −9.41641 | −0.358737 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.3050 | 1.26698 | 0.633490 | − | 0.773751i | \(-0.281622\pi\) | ||||
0.633490 | + | 0.773751i | \(0.281622\pi\) | |||||||
\(692\) | 5.76393 | 0.219112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.59675 | 0.136531 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.0902 | −0.496182 | ||||||||
\(697\) | 5.05573 | 0.191499 | ||||||||
\(698\) | 17.1591 | 0.649480 | ||||||||
\(699\) | −23.2705 | −0.880172 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.5836 | −0.513045 | −0.256523 | − | 0.966538i | \(-0.582577\pi\) | ||||
−0.256523 | + | 0.966538i | \(0.582577\pi\) | |||||||
\(702\) | 0.763932 | 0.0288328 | ||||||||
\(703\) | 37.3607 | 1.40908 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.1459 | 0.833472 | ||||||||
\(707\) | 0.429563 | 0.0161554 | ||||||||
\(708\) | −10.8541 | −0.407922 | ||||||||
\(709\) | 41.1803 | 1.54656 | 0.773280 | − | 0.634065i | \(-0.218615\pi\) | ||||
0.773280 | + | 0.634065i | \(0.218615\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.09017 | 0.303405 | ||||||||
\(712\) | 24.2705 | 0.909576 | ||||||||
\(713\) | 16.6738 | 0.624437 | ||||||||
\(714\) | −0.944272 | −0.0353385 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 31.5066 | 1.17746 | ||||||||
\(717\) | −7.03444 | −0.262706 | ||||||||
\(718\) | 10.3262 | 0.385372 | ||||||||
\(719\) | 38.0902 | 1.42052 | 0.710262 | − | 0.703938i | \(-0.248577\pi\) | ||||
0.710262 | + | 0.703938i | \(0.248577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.81966 | 0.0677677 | ||||||||
\(722\) | −3.70820 | −0.138005 | ||||||||
\(723\) | −1.61803 | −0.0601753 | ||||||||
\(724\) | 8.47214 | 0.314864 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.3262 | 1.38435 | 0.692177 | − | 0.721728i | \(-0.256652\pi\) | ||||
0.692177 | + | 0.721728i | \(0.256652\pi\) | |||||||
\(728\) | 2.11146 | 0.0782558 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.18034 | −0.154615 | ||||||||
\(732\) | −11.3262 | −0.418630 | ||||||||
\(733\) | −1.85410 | −0.0684828 | −0.0342414 | − | 0.999414i | \(-0.510902\pi\) | ||||
−0.0342414 | + | 0.999414i | \(0.510902\pi\) | |||||||
\(734\) | 11.2016 | 0.413460 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.3820 | −0.493266 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.56231 | 0.0575093 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.18034 | 0.227040 | ||||||||
\(742\) | 3.59675 | 0.132041 | ||||||||
\(743\) | −0.347524 | −0.0127494 | −0.00637471 | − | 0.999980i | \(-0.502029\pi\) | ||||
−0.00637471 | + | 0.999980i | \(0.502029\pi\) | |||||||
\(744\) | −15.6525 | −0.573848 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.02129 | 0.220455 | ||||||||
\(747\) | 5.70820 | 0.208852 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.18034 | −0.0796679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.8885 | −1.67450 | −0.837248 | − | 0.546823i | \(-0.815837\pi\) | ||||
−0.837248 | + | 0.546823i | \(0.815837\pi\) | |||||||
\(752\) | 9.43769 | 0.344157 | ||||||||
\(753\) | −7.52786 | −0.274331 | ||||||||
\(754\) | −4.47214 | −0.162866 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.23607 | 0.0449554 | ||||||||
\(757\) | −24.1803 | −0.878849 | −0.439425 | − | 0.898279i | \(-0.644818\pi\) | ||||
−0.439425 | + | 0.898279i | \(0.644818\pi\) | |||||||
\(758\) | 3.09017 | 0.112240 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.0344 | −1.41500 | −0.707499 | − | 0.706715i | \(-0.750176\pi\) | ||||
−0.707499 | + | 0.706715i | \(0.750176\pi\) | |||||||
\(762\) | −9.85410 | −0.356976 | ||||||||
\(763\) | −3.16718 | −0.114660 | ||||||||
\(764\) | −16.8541 | −0.609760 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.3820 | 0.700299 | ||||||||
\(767\) | −8.29180 | −0.299399 | ||||||||
\(768\) | 6.56231 | 0.236797 | ||||||||
\(769\) | −12.7639 | −0.460279 | −0.230140 | − | 0.973158i | \(-0.573918\pi\) | ||||
−0.230140 | + | 0.973158i | \(0.573918\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5623 | 0.380392 | ||||||||
\(772\) | −34.0344 | −1.22493 | ||||||||
\(773\) | −10.5066 | −0.377895 | −0.188948 | − | 0.981987i | \(-0.560508\pi\) | ||||
−0.188948 | + | 0.981987i | \(0.560508\pi\) | |||||||
\(774\) | −1.29180 | −0.0464327 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 25.6525 | 0.920870 | ||||||||
\(777\) | 5.70820 | 0.204781 | ||||||||
\(778\) | 24.0689 | 0.862911 | ||||||||
\(779\) | 12.6393 | 0.452851 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 2.94427 | 0.105287 | ||||||||
\(783\) | −5.85410 | −0.209209 | ||||||||
\(784\) | −11.8967 | −0.424881 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.14590 | −0.290555 | ||||||||
\(787\) | 8.20163 | 0.292356 | 0.146178 | − | 0.989258i | \(-0.453303\pi\) | ||||
0.146178 | + | 0.989258i | \(0.453303\pi\) | |||||||
\(788\) | 23.0344 | 0.820568 | ||||||||
\(789\) | −27.2148 | −0.968872 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.18034 | 0.148636 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.65248 | −0.307258 | ||||||||
\(794\) | −22.4164 | −0.795529 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −32.0344 | −1.13543 | ||||||||
\(797\) | 28.7082 | 1.01690 | 0.508448 | − | 0.861092i | \(-0.330219\pi\) | ||||
0.508448 | + | 0.861092i | \(0.330219\pi\) | |||||||
\(798\) | −2.36068 | −0.0835672 | ||||||||
\(799\) | −10.1803 | −0.360155 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.8541 | 0.383511 | ||||||||
\(802\) | −3.02129 | −0.106685 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −15.1803 | −0.535369 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.34752 | −0.188359 | ||||||||
\(807\) | 5.85410 | 0.206074 | ||||||||
\(808\) | 1.25735 | 0.0442336 | ||||||||
\(809\) | −45.3262 | −1.59359 | −0.796793 | − | 0.604253i | \(-0.793472\pi\) | ||||
−0.796793 | + | 0.604253i | \(0.793472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6312 | 1.21607 | 0.608033 | − | 0.793912i | \(-0.291959\pi\) | ||||
0.608033 | + | 0.793912i | \(0.291959\pi\) | |||||||
\(812\) | −7.23607 | −0.253936 | ||||||||
\(813\) | 20.6180 | 0.723106 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.70820 | 0.129813 | ||||||||
\(817\) | −10.4508 | −0.365629 | ||||||||
\(818\) | 22.4377 | 0.784516 | ||||||||
\(819\) | 0.944272 | 0.0329955 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.1803 | −1.50700 | −0.753502 | − | 0.657445i | \(-0.771637\pi\) | ||||
−0.753502 | + | 0.657445i | \(0.771637\pi\) | |||||||
\(822\) | 11.5623 | 0.403282 | ||||||||
\(823\) | 25.4721 | 0.887903 | 0.443951 | − | 0.896051i | \(-0.353576\pi\) | ||||
0.443951 | + | 0.896051i | \(0.353576\pi\) | |||||||
\(824\) | 5.32624 | 0.185548 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.16718 | 0.110200 | ||||||||
\(827\) | 24.5836 | 0.854855 | 0.427428 | − | 0.904050i | \(-0.359420\pi\) | ||||
0.427428 | + | 0.904050i | \(0.359420\pi\) | |||||||
\(828\) | −3.85410 | −0.133939 | ||||||||
\(829\) | 2.88854 | 0.100323 | 0.0501616 | − | 0.998741i | \(-0.484026\pi\) | ||||
0.0501616 | + | 0.998741i | \(0.484026\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.65248 | −0.300151 | ||||||||
\(832\) | −0.291796 | −0.0101162 | ||||||||
\(833\) | 12.8328 | 0.444631 | ||||||||
\(834\) | −13.0902 | −0.453276 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.00000 | −0.241955 | ||||||||
\(838\) | −15.2016 | −0.525131 | ||||||||
\(839\) | −26.3050 | −0.908148 | −0.454074 | − | 0.890964i | \(-0.650030\pi\) | ||||
−0.454074 | + | 0.890964i | \(0.650030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.27051 | 0.181742 | ||||||||
\(842\) | −1.76393 | −0.0607891 | ||||||||
\(843\) | 10.0902 | 0.347524 | ||||||||
\(844\) | −6.23607 | −0.214654 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.14590 | −0.108158 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.1246 | −0.485041 | ||||||||
\(849\) | 13.0344 | 0.447341 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.7984 | −0.610120 | ||||||||
\(852\) | −12.9443 | −0.443463 | ||||||||
\(853\) | 21.3607 | 0.731376 | 0.365688 | − | 0.930738i | \(-0.380834\pi\) | ||||
0.365688 | + | 0.930738i | \(0.380834\pi\) | |||||||
\(854\) | 3.30495 | 0.113093 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.38197 | −0.218131 | ||||||||
\(857\) | −35.0132 | −1.19603 | −0.598013 | − | 0.801486i | \(-0.704043\pi\) | ||||
−0.598013 | + | 0.801486i | \(0.704043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.72949 | −0.195488 | −0.0977438 | − | 0.995212i | \(-0.531163\pi\) | ||||
−0.0977438 | + | 0.995212i | \(0.531163\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.93112 | 0.0658123 | ||||||||
\(862\) | 12.2918 | 0.418660 | ||||||||
\(863\) | −6.03444 | −0.205415 | −0.102707 | − | 0.994712i | \(-0.532751\pi\) | ||||
−0.102707 | + | 0.994712i | \(0.532751\pi\) | |||||||
\(864\) | 5.61803 | 0.191129 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.3262 | −0.588770 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | −8.65248 | −0.293684 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.5967 | −0.392941 | ||||||||
\(872\) | −9.27051 | −0.313939 | ||||||||
\(873\) | 11.4721 | 0.388273 | ||||||||
\(874\) | 7.36068 | 0.248979 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21.7984 | 0.736499 | ||||||||
\(877\) | −16.4721 | −0.556225 | −0.278112 | − | 0.960549i | \(-0.589709\pi\) | ||||
−0.278112 | + | 0.960549i | \(0.589709\pi\) | |||||||
\(878\) | 5.97871 | 0.201772 | ||||||||
\(879\) | 16.5279 | 0.557471 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.8541 | −0.803665 | −0.401833 | − | 0.915713i | \(-0.631627\pi\) | ||||
−0.401833 | + | 0.915713i | \(0.631627\pi\) | |||||||
\(882\) | 3.96556 | 0.133527 | ||||||||
\(883\) | 18.7639 | 0.631457 | 0.315728 | − | 0.948850i | \(-0.397751\pi\) | ||||
0.315728 | + | 0.948850i | \(0.397751\pi\) | |||||||
\(884\) | 4.00000 | 0.134535 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.6180 | −0.524698 | ||||||||
\(887\) | −53.8328 | −1.80753 | −0.903765 | − | 0.428030i | \(-0.859208\pi\) | ||||
−0.903765 | + | 0.428030i | \(0.859208\pi\) | |||||||
\(888\) | 16.7082 | 0.560691 | ||||||||
\(889\) | −12.1803 | −0.408515 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.0000 | −0.435272 | ||||||||
\(893\) | −25.4508 | −0.851680 | ||||||||
\(894\) | −12.4377 | −0.415979 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 8.69505 | 0.290481 | ||||||||
\(897\) | −2.94427 | −0.0983064 | ||||||||
\(898\) | 0.450850 | 0.0150450 | ||||||||
\(899\) | 40.9787 | 1.36672 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.2361 | 0.507587 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.59675 | −0.0531364 | ||||||||
\(904\) | 12.2361 | 0.406966 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.65248 | 0.221014 | ||||||||
\(907\) | 9.11146 | 0.302541 | 0.151270 | − | 0.988492i | \(-0.451664\pi\) | ||||
0.151270 | + | 0.988492i | \(0.451664\pi\) | |||||||
\(908\) | 41.9787 | 1.39311 | ||||||||
\(909\) | 0.562306 | 0.0186505 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −58.9017 | −1.95150 | −0.975750 | − | 0.218887i | \(-0.929757\pi\) | ||||
−0.975750 | + | 0.218887i | \(0.929757\pi\) | |||||||
\(912\) | 9.27051 | 0.306977 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.909830 | 0.0300945 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29.2705 | −0.967125 | ||||||||
\(917\) | −10.0689 | −0.332504 | ||||||||
\(918\) | −1.23607 | −0.0407963 | ||||||||
\(919\) | 17.7639 | 0.585978 | 0.292989 | − | 0.956116i | \(-0.405350\pi\) | ||||
0.292989 | + | 0.956116i | \(0.405350\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.1246 | 0.399520 | ||||||||
\(922\) | 16.0344 | 0.528066 | ||||||||
\(923\) | −9.88854 | −0.325485 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20.5623 | 0.675719 | ||||||||
\(927\) | 2.38197 | 0.0782340 | ||||||||
\(928\) | −32.8885 | −1.07962 | ||||||||
\(929\) | −4.14590 | −0.136023 | −0.0680113 | − | 0.997685i | \(-0.521665\pi\) | ||||
−0.0680113 | + | 0.997685i | \(0.521665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.0820 | 1.05145 | ||||||||
\(932\) | −37.6525 | −1.23335 | ||||||||
\(933\) | −21.4721 | −0.702966 | ||||||||
\(934\) | −3.02129 | −0.0988595 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.76393 | 0.0903419 | ||||||||
\(937\) | −41.7984 | −1.36549 | −0.682747 | − | 0.730655i | \(-0.739215\pi\) | ||||
−0.682747 | + | 0.730655i | \(0.739215\pi\) | |||||||
\(938\) | 4.42956 | 0.144630 | ||||||||
\(939\) | −0.472136 | −0.0154076 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.70820 | −0.120884 | −0.0604420 | − | 0.998172i | \(-0.519251\pi\) | ||||
−0.0604420 | + | 0.998172i | \(0.519251\pi\) | |||||||
\(942\) | −2.05573 | −0.0669792 | ||||||||
\(943\) | −6.02129 | −0.196080 | ||||||||
\(944\) | −12.4377 | −0.404812 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.5623 | −0.505707 | −0.252853 | − | 0.967505i | \(-0.581369\pi\) | ||||
−0.252853 | + | 0.967505i | \(0.581369\pi\) | |||||||
\(948\) | 13.0902 | 0.425149 | ||||||||
\(949\) | 16.6525 | 0.540562 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.4164 | −0.986320 | ||||||||
\(952\) | −3.41641 | −0.110726 | ||||||||
\(953\) | −37.9098 | −1.22802 | −0.614010 | − | 0.789298i | \(-0.710445\pi\) | ||||
−0.614010 | + | 0.789298i | \(0.710445\pi\) | |||||||
\(954\) | 4.70820 | 0.152434 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.3820 | −0.368119 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.6525 | 0.667251 | ||||||||
\(959\) | 14.2918 | 0.461506 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 5.70820 | 0.184040 | ||||||||
\(963\) | −2.85410 | −0.0919722 | ||||||||
\(964\) | −2.61803 | −0.0843212 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.12461 | 0.0361838 | ||||||||
\(967\) | 48.3262 | 1.55407 | 0.777034 | − | 0.629459i | \(-0.216724\pi\) | ||||
0.777034 | + | 0.629459i | \(0.216724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.0000 | −0.321246 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.5410 | 1.14057 | 0.570283 | − | 0.821448i | \(-0.306834\pi\) | ||||
0.570283 | + | 0.821448i | \(0.306834\pi\) | |||||||
\(972\) | 1.61803 | 0.0518985 | ||||||||
\(973\) | −16.1803 | −0.518718 | ||||||||
\(974\) | 8.76393 | 0.280814 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.9787 | −0.415439 | ||||||||
\(977\) | −34.9098 | −1.11686 | −0.558432 | − | 0.829550i | \(-0.688597\pi\) | ||||
−0.558432 | + | 0.829550i | \(0.688597\pi\) | |||||||
\(978\) | 8.38197 | 0.268026 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.14590 | −0.132368 | ||||||||
\(982\) | 19.6525 | 0.627136 | ||||||||
\(983\) | −19.0000 | −0.606006 | −0.303003 | − | 0.952990i | \(-0.597989\pi\) | ||||
−0.303003 | + | 0.952990i | \(0.597989\pi\) | |||||||
\(984\) | 5.65248 | 0.180194 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.23607 | 0.230443 | ||||||||
\(987\) | −3.88854 | −0.123774 | ||||||||
\(988\) | 10.0000 | 0.318142 | ||||||||
\(989\) | 4.97871 | 0.158314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | −39.3262 | −1.24861 | ||||||||
\(993\) | −21.5967 | −0.685352 | ||||||||
\(994\) | 3.77709 | 0.119802 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.23607 | 0.292656 | ||||||||
\(997\) | 24.7082 | 0.782517 | 0.391258 | − | 0.920281i | \(-0.372040\pi\) | ||||
0.391258 | + | 0.920281i | \(0.372040\pi\) | |||||||
\(998\) | 6.90983 | 0.218727 | ||||||||
\(999\) | 7.47214 | 0.236408 |
(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 | 9075.2.a.bt.1.1 | 2 | ||
5.4 | even | 2 | 9075.2.a.bc.1.2 | 2 | |||
11.2 | odd | 10 | 825.2.n.b.301.1 | ✓ | 4 | ||
11.6 | odd | 10 | 825.2.n.b.751.1 | yes | 4 | ||
11.10 | odd | 2 | 9075.2.a.z.1.2 | 2 | |||
55.2 | even | 20 | 825.2.bx.c.499.2 | 8 | |||
55.13 | even | 20 | 825.2.bx.c.499.1 | 8 | |||
55.17 | even | 20 | 825.2.bx.c.124.1 | 8 | |||
55.24 | odd | 10 | 825.2.n.d.301.1 | yes | 4 | ||
55.28 | even | 20 | 825.2.bx.c.124.2 | 8 | |||
55.39 | odd | 10 | 825.2.n.d.751.1 | yes | 4 | ||
55.54 | odd | 2 | 9075.2.a.by.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.n.b.301.1 | ✓ | 4 | 11.2 | odd | 10 | ||
825.2.n.b.751.1 | yes | 4 | 11.6 | odd | 10 | ||
825.2.n.d.301.1 | yes | 4 | 55.24 | odd | 10 | ||
825.2.n.d.751.1 | yes | 4 | 55.39 | odd | 10 | ||
825.2.bx.c.124.1 | 8 | 55.17 | even | 20 | |||
825.2.bx.c.124.2 | 8 | 55.28 | even | 20 | |||
825.2.bx.c.499.1 | 8 | 55.13 | even | 20 | |||
825.2.bx.c.499.2 | 8 | 55.2 | even | 20 | |||
9075.2.a.z.1.2 | 2 | 11.10 | odd | 2 | |||
9075.2.a.bc.1.2 | 2 | 5.4 | even | 2 | |||
9075.2.a.bt.1.1 | 2 | 1.1 | even | 1 | trivial | ||
9075.2.a.by.1.1 | 2 | 55.54 | odd | 2 |