Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2576,2,Mod(1,2576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2576.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2576 = 2^{4} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2576.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: | \(20.5694635607\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.8580816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 12x^{3} + 10x^{2} + 20x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 644) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-3.18838\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2576.1 |
$q$-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 | 0 | ||||||||
\(3\) | 3.18838 | 1.84081 | 0.920405 | − | 0.390967i | \(-0.127859\pi\) | ||||
0.920405 | + | 0.390967i | \(0.127859\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.43522 | 1.53628 | 0.768138 | − | 0.640284i | \(-0.221183\pi\) | ||||
0.768138 | + | 0.640284i | \(0.221183\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.16574 | 2.38858 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.57602 | 0.776699 | 0.388349 | − | 0.921512i | \(-0.373045\pi\) | ||||
0.388349 | + | 0.921512i | \(0.373045\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.58972 | −0.440909 | −0.220455 | − | 0.975397i | \(-0.570754\pi\) | ||||
−0.220455 | + | 0.975397i | \(0.570754\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.9528 | 2.82799 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.77810 | −1.15886 | −0.579429 | − | 0.815022i | \(-0.696725\pi\) | ||||
−0.579429 | + | 0.815022i | \(0.696725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.65835 | −1.98636 | −0.993181 | − | 0.116583i | \(-0.962806\pi\) | ||||
−0.993181 | + | 0.116583i | \(0.962806\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.18838 | −0.695761 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.80073 | 1.36015 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.2819 | 2.55611 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.67205 | 1.42466 | 0.712332 | − | 0.701842i | \(-0.247639\pi\) | ||||
0.712332 | + | 0.701842i | \(0.247639\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.02494 | 0.902506 | 0.451253 | − | 0.892396i | \(-0.350977\pi\) | ||||
0.451253 | + | 0.892396i | \(0.350977\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.21332 | 1.42975 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.43522 | −0.580658 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.71840 | 0.611301 | 0.305651 | − | 0.952144i | \(-0.401126\pi\) | ||||
0.305651 | + | 0.952144i | \(0.401126\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.06863 | −0.811630 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.9665 | 1.86885 | 0.934425 | − | 0.356161i | \(-0.115915\pi\) | ||||
0.934425 | + | 0.356161i | \(0.115915\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.46104 | −1.13780 | −0.568899 | − | 0.822407i | \(-0.692631\pi\) | ||||
−0.568899 | + | 0.822407i | \(0.692631\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 24.6159 | 3.66952 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.43610 | 0.647072 | 0.323536 | − | 0.946216i | \(-0.395128\pi\) | ||||
0.323536 | + | 0.946216i | \(0.395128\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.2344 | −2.13324 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.06775 | 1.10819 | 0.554095 | − | 0.832453i | \(-0.313064\pi\) | ||||
0.554095 | + | 0.832453i | \(0.313064\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.84919 | 1.19322 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −27.6061 | −3.65651 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.88025 | 0.244788 | 0.122394 | − | 0.992482i | \(-0.460943\pi\) | ||||
0.122394 | + | 0.992482i | \(0.460943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.71682 | −0.731964 | −0.365982 | − | 0.930622i | \(-0.619267\pi\) | ||||
−0.365982 | + | 0.930622i | \(0.619267\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.16574 | −0.902798 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.46104 | −0.677359 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.2618 | −1.62018 | −0.810092 | − | 0.586303i | \(-0.800583\pi\) | ||||
−0.810092 | + | 0.586303i | \(0.800583\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.18838 | −0.383835 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.96647 | −0.708090 | −0.354045 | − | 0.935228i | \(-0.615194\pi\) | ||||
−0.354045 | + | 0.935228i | \(0.615194\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.8369 | −1.26836 | −0.634182 | − | 0.773184i | \(-0.718663\pi\) | ||||
−0.634182 | + | 0.773184i | \(0.718663\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 21.6833 | 2.50377 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.57602 | −0.293565 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.01282 | −0.226460 | −0.113230 | − | 0.993569i | \(-0.536120\pi\) | ||||
−0.113230 | + | 0.993569i | \(0.536120\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 20.8506 | 2.31673 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.43364 | −0.376891 | −0.188445 | − | 0.982084i | \(-0.560345\pi\) | ||||
−0.188445 | + | 0.982084i | \(0.560345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.4138 | −1.78033 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.4614 | 2.62254 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.82337 | −0.723276 | −0.361638 | − | 0.932319i | \(-0.617782\pi\) | ||||
−0.361638 | + | 0.932319i | \(0.617782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.58972 | 0.166648 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.0214 | 1.66134 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −29.7433 | −3.05160 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0258 | 1.01797 | 0.508984 | − | 0.860776i | \(-0.330021\pi\) | ||||
0.508984 | + | 0.860776i | \(0.330021\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.4591 | 1.85521 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.95473 | 0.393510 | 0.196755 | − | 0.980453i | \(-0.436960\pi\) | ||||
0.196755 | + | 0.980453i | \(0.436960\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.31424 | 0.129496 | 0.0647482 | − | 0.997902i | \(-0.479376\pi\) | ||||
0.0647482 | + | 0.997902i | \(0.479376\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.9528 | −1.06888 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.45928 | 0.914463 | 0.457231 | − | 0.889348i | \(-0.348841\pi\) | ||||
0.457231 | + | 0.889348i | \(0.348841\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.376752 | −0.0360863 | −0.0180431 | − | 0.999837i | \(-0.505744\pi\) | ||||
−0.0180431 | + | 0.999837i | \(0.505744\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.8557 | 1.12529 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.5741 | −1.46508 | −0.732542 | − | 0.680722i | \(-0.761666\pi\) | ||||
−0.732542 | + | 0.680722i | \(0.761666\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.43522 | −0.320336 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.3915 | −1.05315 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.77810 | 0.438007 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.36413 | −0.396739 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 38.1536 | 3.44020 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.18591 | 0.553285 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.8095 | −1.66907 | −0.834537 | − | 0.550952i | \(-0.814265\pi\) | ||||
−0.834537 | + | 0.550952i | \(0.814265\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −23.7886 | −2.09447 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.42348 | 0.124370 | 0.0621848 | − | 0.998065i | \(-0.480193\pi\) | ||||
0.0621848 | + | 0.998065i | \(0.480193\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.65835 | 0.750774 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 45.6264 | 3.92690 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.2145 | −1.38530 | −0.692651 | − | 0.721273i | \(-0.743557\pi\) | ||||
−0.692651 | + | 0.721273i | \(0.743557\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.59253 | −0.643990 | −0.321995 | − | 0.946741i | \(-0.604353\pi\) | ||||
−0.321995 | + | 0.946741i | \(0.604353\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.1440 | 1.19114 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.09515 | −0.342454 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 26.3552 | 2.18868 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.18838 | 0.262973 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.68576 | 0.711565 | 0.355782 | − | 0.934569i | \(-0.384214\pi\) | ||||
0.355782 | + | 0.934569i | \(0.384214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.3158 | −1.16500 | −0.582502 | − | 0.812829i | \(-0.697926\pi\) | ||||
−0.582502 | + | 0.812829i | \(0.697926\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −34.2386 | −2.76803 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.2618 | 1.38650 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.962781 | −0.0768383 | −0.0384191 | − | 0.999262i | \(-0.512232\pi\) | ||||
−0.0384191 | + | 0.999262i | \(0.512232\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 25.7230 | 2.03997 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.37763 | 0.107905 | 0.0539523 | − | 0.998544i | \(-0.482818\pi\) | ||||
0.0539523 | + | 0.998544i | \(0.482818\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 28.2145 | 2.19650 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00158 | 0.464416 | 0.232208 | − | 0.972666i | \(-0.425405\pi\) | ||||
0.232208 | + | 0.972666i | \(0.425405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4728 | −0.805599 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −62.0435 | −4.74458 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.08429 | −0.690666 | −0.345333 | − | 0.938480i | \(-0.612234\pi\) | ||||
−0.345333 | + | 0.938480i | \(0.612234\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.80073 | −0.514087 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.99495 | 0.450608 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.56232 | 0.116773 | 0.0583865 | − | 0.998294i | \(-0.481404\pi\) | ||||
0.0583865 | + | 0.998294i | \(0.481404\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.446616 | 0.0331967 | 0.0165984 | − | 0.999862i | \(-0.494716\pi\) | ||||
0.0165984 | + | 0.999862i | \(0.494716\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.2274 | −1.34741 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.7735 | 0.939128 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.3085 | −0.900084 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.2819 | −0.966119 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.0225 | 1.30406 | 0.652030 | − | 0.758193i | \(-0.273917\pi\) | ||||
0.652030 | + | 0.758193i | \(0.273917\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6701 | −0.912013 | −0.456007 | − | 0.889976i | \(-0.650721\pi\) | ||||
−0.456007 | + | 0.889976i | \(0.650721\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.4119 | −1.24689 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.46016 | 0.317773 | 0.158887 | − | 0.987297i | \(-0.449210\pi\) | ||||
0.158887 | + | 0.987297i | \(0.449210\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.4835 | −0.955821 | −0.477911 | − | 0.878408i | \(-0.658606\pi\) | ||||
−0.477911 | + | 0.878408i | \(0.658606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −42.2835 | −2.98245 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.67205 | −0.538473 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 41.1075 | 2.87107 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.16574 | −0.498053 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.3041 | −1.54281 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.3493 | −1.40091 | −0.700453 | − | 0.713698i | \(-0.747019\pi\) | ||||
−0.700453 | + | 0.713698i | \(0.747019\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.0234 | −1.30346 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.6303 | −1.74797 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.02494 | −0.341115 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −34.5521 | −2.33482 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.59584 | 0.510952 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0253 | −1.07313 | −0.536566 | − | 0.843858i | \(-0.680279\pi\) | ||||
−0.536566 | + | 0.843858i | \(0.680279\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 48.7323 | 3.24882 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.4266 | 1.09027 | 0.545137 | − | 0.838347i | \(-0.316478\pi\) | ||||
0.545137 | + | 0.838347i | \(0.316478\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.5316 | −0.894193 | −0.447097 | − | 0.894486i | \(-0.647542\pi\) | ||||
−0.447097 | + | 0.894486i | \(0.647542\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.21332 | −0.540397 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.50524 | 0.229636 | 0.114818 | − | 0.993387i | \(-0.463372\pi\) | ||||
0.114818 | + | 0.993387i | \(0.463372\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.2390 | 0.994081 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.41763 | −0.416870 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.7418 | 1.34167 | 0.670836 | − | 0.741605i | \(-0.265935\pi\) | ||||
0.670836 | + | 0.741605i | \(0.265935\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.95754 | −0.254928 | −0.127464 | − | 0.991843i | \(-0.540684\pi\) | ||||
−0.127464 | + | 0.991843i | \(0.540684\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 26.6338 | 1.70856 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.43522 | 0.219468 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.7644 | 0.875806 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.9477 | −0.693784 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.8150 | 1.88191 | 0.940953 | − | 0.338537i | \(-0.109932\pi\) | ||||
0.940953 | + | 0.338537i | \(0.109932\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.57602 | −0.161953 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −52.3334 | −3.27724 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.44930 | 0.215161 | 0.107581 | − | 0.994196i | \(-0.465690\pi\) | ||||
0.107581 | + | 0.994196i | \(0.465690\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.71840 | −0.231050 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 54.9759 | 3.40293 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.05493 | 0.496688 | 0.248344 | − | 0.968672i | \(-0.420114\pi\) | ||||
0.248344 | + | 0.968672i | \(0.420114\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.7145 | 1.70249 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.7555 | −1.33141 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.43452 | 0.270377 | 0.135189 | − | 0.990820i | \(-0.456836\pi\) | ||||
0.135189 | + | 0.990820i | \(0.456836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0253 | 1.45943 | 0.729716 | − | 0.683750i | \(-0.239652\pi\) | ||||
0.729716 | + | 0.683750i | \(0.239652\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.06863 | 0.306767 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.5188 | 1.05642 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.330404 | −0.0198520 | −0.00992602 | − | 0.999951i | \(-0.503160\pi\) | ||||
−0.00992602 | + | 0.999951i | \(0.503160\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 36.0074 | 2.15571 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.7483 | 1.53601 | 0.768006 | − | 0.640442i | \(-0.221249\pi\) | ||||
0.768006 | + | 0.640442i | \(0.221249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.8104 | 1.29649 | 0.648247 | − | 0.761431i | \(-0.275503\pi\) | ||||
0.648247 | + | 0.761431i | \(0.275503\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −94.8329 | −5.61742 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.9665 | −0.706359 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.83021 | 0.342954 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 31.9661 | 1.87389 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.1487 | −0.884996 | −0.442498 | − | 0.896769i | \(-0.645908\pi\) | ||||
−0.442498 | + | 0.896769i | \(0.645908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.45908 | 0.376062 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 34.2145 | 1.98533 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.58972 | 0.0919360 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.46104 | 0.430047 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.6092 | 0.724377 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.6385 | −1.12450 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.3183 | 0.645969 | 0.322984 | − | 0.946404i | \(-0.395314\pi\) | ||||
0.322984 | + | 0.946404i | \(0.395314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.19031 | 0.238378 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.13357 | 0.177688 | 0.0888441 | − | 0.996046i | \(-0.471683\pi\) | ||||
0.0888441 | + | 0.996046i | \(0.471683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.12744 | −0.515914 | −0.257957 | − | 0.966156i | \(-0.583049\pi\) | ||||
−0.257957 | + | 0.966156i | \(0.583049\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.6159 | −1.38695 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −33.8032 | −1.89858 | −0.949288 | − | 0.314407i | \(-0.898194\pi\) | ||||
−0.949288 | + | 0.314407i | \(0.898194\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.7634 | 1.10654 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.1597 | 1.68335 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.3704 | 2.30191 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.8113 | −0.599701 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.20123 | −0.0664279 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.43610 | −0.244570 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.6448 | −0.585094 | −0.292547 | − | 0.956251i | \(-0.594503\pi\) | ||||
−0.292547 | + | 0.956251i | \(0.594503\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.6451 | 1.46014 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −45.5571 | −2.48905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.8838 | −1.84577 | −0.922883 | − | 0.385081i | \(-0.874174\pi\) | ||||
−0.922883 | + | 0.385081i | \(0.874174\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −49.6560 | −2.69694 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.9443 | 0.700975 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.9528 | −0.589677 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.91254 | −0.478450 | −0.239225 | − | 0.970964i | \(-0.576893\pi\) | ||||
−0.239225 | + | 0.970964i | \(0.576893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.03353 | 0.430025 | 0.215012 | − | 0.976611i | \(-0.431021\pi\) | ||||
0.215012 | + | 0.976611i | \(0.431021\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.1146 | −1.12701 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.8221 | 1.05503 | 0.527513 | − | 0.849547i | \(-0.323125\pi\) | ||||
0.527513 | + | 0.849547i | \(0.323125\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.4961 | −1.08782 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.2344 | 0.806288 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.1547 | 0.641500 | 0.320750 | − | 0.947164i | \(-0.396065\pi\) | ||||
0.320750 | + | 0.947164i | \(0.396065\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 55.9670 | 2.94563 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.9145 | −0.730320 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −37.2272 | −1.94856 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.57274 | 0.134296 | 0.0671479 | − | 0.997743i | \(-0.478610\pi\) | ||||
0.0671479 | + | 0.997743i | \(0.478610\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 85.7486 | 4.46390 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.06775 | −0.418857 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.59521 | −0.445043 | −0.222522 | − | 0.974928i | \(-0.571429\pi\) | ||||
−0.222522 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.7230 | 1.01849 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.1964 | −0.628148 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.8780 | −1.22653 | −0.613266 | − | 0.789877i | \(-0.710145\pi\) | ||||
−0.613266 | + | 0.789877i | \(0.710145\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −59.9718 | −3.07245 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.0902 | −0.719977 | −0.359988 | − | 0.932957i | \(-0.617219\pi\) | ||||
−0.359988 | + | 0.932957i | \(0.617219\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.84919 | −0.450997 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −53.4639 | −2.71772 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.1429 | −1.42690 | −0.713450 | − | 0.700706i | \(-0.752869\pi\) | ||||
−0.713450 | + | 0.700706i | \(0.752869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.77810 | 0.241639 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.53858 | 0.228941 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.91448 | −0.347905 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.7590 | 1.29281 | 0.646403 | − | 0.762996i | \(-0.276272\pi\) | ||||
0.646403 | + | 0.762996i | \(0.276272\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 27.6061 | 1.38203 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.1745 | −1.15728 | −0.578640 | − | 0.815583i | \(-0.696416\pi\) | ||||
−0.578640 | + | 0.815583i | \(0.696416\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.98826 | −0.397923 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 71.6264 | 3.55915 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.57867 | 0.474797 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.9443 | −0.541161 | −0.270581 | − | 0.962697i | \(-0.587216\pi\) | ||||
−0.270581 | + | 0.962697i | \(0.587216\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −51.6981 | −2.55008 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.88025 | −0.0925212 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.7953 | −0.579008 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.2078 | −1.18546 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.0867 | 0.932449 | 0.466224 | − | 0.884667i | \(-0.345614\pi\) | ||||
0.466224 | + | 0.884667i | \(0.345614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.7325 | 1.49781 | 0.748905 | − | 0.662678i | \(-0.230580\pi\) | ||||
0.748905 | + | 0.662678i | \(0.230580\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 31.7879 | 1.54558 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −32.4946 | −1.57622 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.71682 | 0.276656 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.0569 | −0.630392 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.5758 | 0.557588 | 0.278794 | − | 0.960351i | \(-0.410065\pi\) | ||||
0.278794 | + | 0.960351i | \(0.410065\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.8000 | 1.76850 | 0.884249 | − | 0.467017i | \(-0.154671\pi\) | ||||
0.884249 | + | 0.467017i | \(0.154671\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 84.0302 | 4.02894 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.65835 | 0.414185 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.6519 | 1.55839 | 0.779194 | − | 0.626782i | \(-0.215628\pi\) | ||||
0.779194 | + | 0.626782i | \(0.215628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.16574 | 0.341226 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.881489 | 0.0418808 | 0.0209404 | − | 0.999781i | \(-0.493334\pi\) | ||||
0.0209404 | + | 0.999781i | \(0.493334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.4398 | −1.11115 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.6935 | 1.30986 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.2990 | −0.486041 | −0.243021 | − | 0.970021i | \(-0.578138\pi\) | ||||
−0.243021 | + | 0.970021i | \(0.578138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.8259 | 1.45153 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −45.6442 | −2.14455 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.46104 | 0.256018 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.57798 | −0.260927 | −0.130463 | − | 0.991453i | \(-0.541647\pi\) | ||||
−0.130463 | + | 0.991453i | \(0.541647\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −63.4624 | −2.96217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.9542 | 1.90742 | 0.953712 | − | 0.300720i | \(-0.0972270\pi\) | ||||
0.953712 | + | 0.300720i | \(0.0972270\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.44626 | −0.113687 | −0.0568437 | − | 0.998383i | \(-0.518104\pi\) | ||||
−0.0568437 | + | 0.998383i | \(0.518104\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 55.0370 | 2.55228 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.1401 | −1.85746 | −0.928731 | − | 0.370754i | \(-0.879099\pi\) | ||||
−0.928731 | + | 0.370754i | \(0.879099\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.2618 | 0.612372 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.06971 | −0.141445 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.2198 | −0.883727 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −58.8831 | −2.70174 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 57.8114 | 2.64700 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.4010 | −1.29767 | −0.648837 | − | 0.760927i | \(-0.724744\pi\) | ||||
−0.648837 | + | 0.760927i | \(0.724744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.91122 | −0.269529 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.18838 | 0.145076 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.4409 | 1.56388 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2832 | 1.05506 | 0.527531 | − | 0.849536i | \(-0.323118\pi\) | ||||
0.527531 | + | 0.849536i | \(0.323118\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.39241 | 0.198632 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.8105 | 0.668389 | 0.334195 | − | 0.942504i | \(-0.391536\pi\) | ||||
0.334195 | + | 0.942504i | \(0.391536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.6578 | −1.65099 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 63.4110 | 2.85011 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.96647 | 0.267633 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.2189 | −0.905122 | −0.452561 | − | 0.891733i | \(-0.649490\pi\) | ||||
−0.452561 | + | 0.891733i | \(0.649490\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.1353 | 0.854902 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.9852 | 0.578982 | 0.289491 | − | 0.957181i | \(-0.406514\pi\) | ||||
0.289491 | + | 0.957181i | \(0.406514\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5854 | 0.604541 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.3912 | −1.48295 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.0213 | −0.710131 | −0.355065 | − | 0.934841i | \(-0.615541\pi\) | ||||
−0.355065 | + | 0.934841i | \(0.615541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8369 | 0.479397 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −115.000 | −5.07736 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.51472 | 0.198942 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.4275 | 0.502580 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.9641 | −1.27138 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.5855 | 0.814245 | 0.407123 | − | 0.913374i | \(-0.366532\pi\) | ||||
0.407123 | + | 0.913374i | \(0.366532\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.32718 | −0.145488 | −0.0727438 | − | 0.997351i | \(-0.523176\pi\) | ||||
−0.0727438 | + | 0.997351i | \(0.523176\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.6833 | −0.946336 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.0097 | −1.04588 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.4734 | 0.584696 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.0234 | −0.823993 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.4947 | 1.40487 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.98125 | 0.214957 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.57602 | 0.110957 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.1858 | 1.42677 | 0.713385 | − | 0.700772i | \(-0.247161\pi\) | ||||
0.713385 | + | 0.700772i | \(0.247161\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.42398 | 0.0611089 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.29422 | −0.0554385 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3057 | 0.996478 | 0.498239 | − | 0.867040i | \(-0.333980\pi\) | ||||
0.498239 | + | 0.867040i | \(0.333980\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40.9652 | −1.74835 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −66.4273 | −2.82990 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.01282 | 0.0855938 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 40.7268 | 1.72876 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.60608 | −0.237537 | −0.118769 | − | 0.992922i | \(-0.537895\pi\) | ||||
−0.118769 | + | 0.992922i | \(0.537895\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.8610 | 0.501666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −39.2440 | −1.65688 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.3041 | −0.434265 | −0.217133 | − | 0.976142i | \(-0.569670\pi\) | ||||
−0.217133 | + | 0.976142i | \(0.569670\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −53.5003 | −2.25078 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.8506 | −0.875643 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.54318 | 0.274304 | 0.137152 | − | 0.990550i | \(-0.456205\pi\) | ||||
0.137152 | + | 0.990550i | \(0.456205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.80730 | 0.117482 | 0.0587410 | − | 0.998273i | \(-0.481291\pi\) | ||||
0.0587410 | + | 0.998273i | \(0.481291\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 57.4624 | 2.40053 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.80073 | −0.283610 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.48194 | −0.269847 | −0.134923 | − | 0.990856i | \(-0.543079\pi\) | ||||
−0.134923 | + | 0.990856i | \(0.543079\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.3970 | −1.67884 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.43364 | 0.142451 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.7827 | 0.860730 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −39.1324 | −1.61793 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.0813 | 1.07649 | 0.538245 | − | 0.842788i | \(-0.319087\pi\) | ||||
0.538245 | + | 0.842788i | \(0.319087\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −43.5077 | −1.79270 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.2207 | 0.584960 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.51092 | 0.0620462 | 0.0310231 | − | 0.999519i | \(-0.490123\pi\) | ||||
0.0310231 | + | 0.999519i | \(0.490123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.4138 | 0.672901 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −42.9905 | −1.75949 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.3940 | 1.69131 | 0.845656 | − | 0.533728i | \(-0.179209\pi\) | ||||
0.845656 | + | 0.533728i | \(0.179209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.4401 | 1.16010 | 0.580049 | − | 0.814582i | \(-0.303033\pi\) | ||||
0.580049 | + | 0.814582i | \(0.303033\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −95.0304 | −3.86994 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.9917 | −0.609501 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.95069 | 0.160354 | 0.0801768 | − | 0.996781i | \(-0.474452\pi\) | ||||
0.0801768 | + | 0.996781i | \(0.474452\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.4614 | −0.991225 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.05216 | −0.285300 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.9389 | 1.49195 | 0.745974 | − | 0.665975i | \(-0.231984\pi\) | ||||
0.745974 | + | 0.665975i | \(0.231984\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 131.066 | 5.28509 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.69561 | 0.229297 | 0.114648 | − | 0.993406i | \(-0.463426\pi\) | ||||
0.114648 | + | 0.993406i | \(0.463426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.0162 | −0.764327 | −0.382163 | − | 0.924095i | \(-0.624821\pi\) | ||||
−0.382163 | + | 0.924095i | \(0.624821\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.2819 | −0.532986 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.82337 | 0.273372 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.7537 | −0.510148 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −71.1138 | −2.84001 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.7669 | −0.708412 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.5641 | 1.17693 | 0.588464 | − | 0.808524i | \(-0.299733\pi\) | ||||
0.588464 | + | 0.808524i | \(0.299733\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −64.8814 | −2.57880 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −64.6148 | −2.56416 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.58972 | −0.0629871 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −42.7542 | −1.69133 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.70647 | 0.264890 | 0.132445 | − | 0.991190i | \(-0.457717\pi\) | ||||
0.132445 | + | 0.991190i | \(0.457717\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0912 | 0.871193 | 0.435597 | − | 0.900142i | \(-0.356537\pi\) | ||||
0.435597 | + | 0.900142i | \(0.356537\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −81.7191 | −3.21769 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.4343 | −0.567472 | −0.283736 | − | 0.958902i | \(-0.591574\pi\) | ||||
−0.283736 | + | 0.958902i | \(0.591574\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.84357 | 0.190127 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.0214 | −0.627928 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.94368 | 0.389126 | 0.194563 | − | 0.980890i | \(-0.437671\pi\) | ||||
0.194563 | + | 0.980890i | \(0.437671\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.88995 | 0.191066 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −77.6545 | −3.02959 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.8406 | 1.16243 | 0.581213 | − | 0.813751i | \(-0.302578\pi\) | ||||
0.581213 | + | 0.813751i | \(0.302578\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.4960 | 1.49732 | 0.748660 | − | 0.662954i | \(-0.230698\pi\) | ||||
0.748660 | + | 0.662954i | \(0.230698\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.2184 | 0.940565 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 29.7433 | 1.15340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.67205 | −0.297063 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −51.0946 | −1.97543 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.7266 | −0.568515 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.9336 | −0.999668 | −0.499834 | − | 0.866121i | \(-0.666606\pi\) | ||||
−0.499834 | + | 0.866121i | \(0.666606\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 90.3270 | 3.47669 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.75584 | 0.105915 | 0.0529577 | − | 0.998597i | \(-0.483135\pi\) | ||||
0.0529577 | + | 0.998597i | \(0.483135\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0258 | −0.384756 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 52.3743 | 2.00699 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.4205 | −1.39359 | −0.696796 | − | 0.717269i | \(-0.745392\pi\) | ||||
−0.696796 | + | 0.717269i | \(0.745392\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55.7005 | −2.12821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.1438 | −1.64604 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.8255 | −0.488612 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.47424 | 0.0941245 | 0.0470622 | − | 0.998892i | \(-0.485014\pi\) | ||||
0.0470622 | + | 0.998892i | \(0.485014\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.4591 | −0.701203 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.0820 | −0.989347 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −57.1770 | −2.16573 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.1760 | 0.422715 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.6538 | −1.34663 | −0.673313 | − | 0.739358i | \(-0.735129\pi\) | ||||
−0.673313 | + | 0.739358i | \(0.735129\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.1952 | −1.21427 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 48.5876 | 1.82991 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.95473 | −0.148733 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.9263 | 1.27413 | 0.637064 | − | 0.770811i | \(-0.280149\pi\) | ||||
0.637064 | + | 0.770811i | \(0.280149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.4234 | −0.540918 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.02494 | −0.188186 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.0677 | −0.526104 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 66.1325 | 2.46976 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.1883 | 0.752898 | 0.376449 | − | 0.926437i | \(-0.377145\pi\) | ||||
0.376449 | + | 0.926437i | \(0.377145\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.31424 | −0.0489450 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.6181 | −0.469273 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 52.1756 | 1.93775 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.7092 | −0.545536 | −0.272768 | − | 0.962080i | \(-0.587939\pi\) | ||||
−0.272768 | + | 0.962080i | \(0.587939\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.3666 | 0.828392 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.6496 | 1.31855 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.3029 | 0.934583 | 0.467292 | − | 0.884103i | \(-0.345230\pi\) | ||||
0.467292 | + | 0.884103i | \(0.345230\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.9528 | 0.403999 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −34.1626 | −1.25839 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.12066 | −0.114796 | −0.0573978 | − | 0.998351i | \(-0.518280\pi\) | ||||
−0.0573978 | + | 0.998351i | \(0.518280\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 43.8860 | 1.61219 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.89456 | −0.179564 | −0.0897820 | − | 0.995961i | \(-0.528617\pi\) | ||||
−0.0897820 | + | 0.995961i | \(0.528617\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.8375 | 1.09316 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.6046 | −0.900233 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.45928 | −0.345635 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.9050 | 0.543893 | 0.271946 | − | 0.962312i | \(-0.412333\pi\) | ||||
0.271946 | + | 0.962312i | \(0.412333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 95.0614 | 3.46423 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −49.1780 | −1.78977 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.57059 | 0.129775 | 0.0648877 | − | 0.997893i | \(-0.479331\pi\) | ||||
0.0648877 | + | 0.997893i | \(0.479331\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.21332 | −0.298125 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.13853 | −0.0412717 | −0.0206359 | − | 0.999787i | \(-0.506569\pi\) | ||||
−0.0206359 | + | 0.999787i | \(0.506569\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.376752 | 0.0136393 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −117.617 | −4.25246 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.98908 | −0.107929 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.3160 | −0.985040 | −0.492520 | − | 0.870301i | \(-0.663924\pi\) | ||||
−0.492520 | + | 0.870301i | \(0.663924\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.9977 | 0.396071 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.23845 | 0.296316 | 0.148158 | − | 0.988964i | \(-0.452666\pi\) | ||||
0.148158 | + | 0.988964i | \(0.452666\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.1733 | 1.22754 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.8557 | −0.425319 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −103.610 | −3.71221 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.3697 | −0.549973 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 101.900 | 3.64160 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.30736 | −0.118045 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.3493 | 1.01055 | 0.505273 | − | 0.862960i | \(-0.331392\pi\) | ||||
0.505273 | + | 0.862960i | \(0.331392\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.6821 | 0.914308 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.5741 | 0.553750 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.08815 | 0.322730 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 88.3642 | 3.13395 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.7795 | −1.01942 | −0.509712 | − | 0.860345i | \(-0.670248\pi\) | ||||
−0.509712 | + | 0.860345i | \(0.670248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.1961 | −0.749865 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.8945 | −1.72760 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.9161 | −0.985137 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.43522 | 0.121076 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.1389 | 0.497713 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.5797 | 0.899334 | 0.449667 | − | 0.893196i | \(-0.351543\pi\) | ||||
0.449667 | + | 0.893196i | \(0.351543\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.4158 | 1.20850 | 0.604250 | − | 0.796794i | \(-0.293473\pi\) | ||||
0.604250 | + | 0.796794i | \(0.293473\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 76.6016 | 2.68654 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.73247 | 0.165771 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 64.6003 | 2.26008 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.3915 | 0.398052 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.2951 | −1.26671 | −0.633354 | − | 0.773862i | \(-0.718322\pi\) | ||||
−0.633354 | + | 0.773862i | \(0.718322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.63499 | 0.335855 | 0.167927 | − | 0.985799i | \(-0.446293\pi\) | ||||
0.167927 | + | 0.985799i | \(0.446293\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 55.8566 | 1.94468 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0345 | 0.627120 | 0.313560 | − | 0.949568i | \(-0.398478\pi\) | ||||
0.313560 | + | 0.949568i | \(0.398478\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5070 | −1.09428 | −0.547142 | − | 0.837040i | \(-0.684284\pi\) | ||||
−0.547142 | + | 0.837040i | \(0.684284\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.05345 | −0.0365438 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.77810 | −0.165551 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.6168 | 0.713472 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 66.7410 | 2.30691 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.88698 | 0.272289 | 0.136144 | − | 0.990689i | \(-0.456529\pi\) | ||||
0.136144 | + | 0.990689i | \(0.456529\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.8604 | 1.02967 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 82.0951 | 2.82751 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35.9763 | −1.23762 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.36413 | 0.149953 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 69.5397 | 2.38660 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.71840 | −0.127465 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.4196 | −0.938830 | −0.469415 | − | 0.882978i | \(-0.655535\pi\) | ||||
−0.469415 | + | 0.882978i | \(0.655535\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −213.133 | −7.28900 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.6512 | 1.73021 | 0.865105 | − | 0.501590i | \(-0.167251\pi\) | ||||
0.865105 | + | 0.501590i | \(0.167251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.0138 | −1.77469 | −0.887345 | − | 0.461107i | \(-0.847453\pi\) | ||||
−0.887345 | + | 0.461107i | \(0.847453\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −38.1536 | −1.30027 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.8208 | 0.504506 | 0.252253 | − | 0.967661i | \(-0.418828\pi\) | ||||
0.252253 | + | 0.967661i | \(0.418828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.2065 | −1.06105 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.5889 | 0.631313 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.18506 | −0.175891 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.0825 | 0.714354 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 71.8424 | 2.43150 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.18591 | −0.209122 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.9784 | −0.910996 | −0.455498 | − | 0.890237i | \(-0.650539\pi\) | ||||
−0.455498 | + | 0.890237i | \(0.650539\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −48.2997 | −1.62911 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.39919 | 0.215594 | 0.107797 | − | 0.994173i | \(-0.465620\pi\) | ||||
0.107797 | + | 0.994173i | \(0.465620\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.5755 | −0.995295 | −0.497648 | − | 0.867379i | \(-0.665803\pi\) | ||||
−0.497648 | + | 0.867379i | \(0.665803\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.5940 | 0.692259 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.8147 | −0.598159 | −0.299080 | − | 0.954228i | \(-0.596680\pi\) | ||||
−0.299080 | + | 0.954228i | \(0.596680\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.8095 | 0.630851 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 53.7116 | 1.79941 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.4093 | −1.28532 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.36690 | 0.179396 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.06863 | 0.169237 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.5516 | 1.28577 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.5485 | −1.28424 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.7886 | 0.791635 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.53423 | 0.0509994 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.3725 | −1.53977 | −0.769887 | − | 0.638180i | \(-0.779688\pi\) | ||||
−0.769887 | + | 0.638180i | \(0.779688\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28.3386 | 0.939931 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.1122 | 0.533821 | 0.266910 | − | 0.963721i | \(-0.413997\pi\) | ||||
0.266910 | + | 0.963721i | \(0.413997\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.84511 | −0.292731 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −62.6150 | −2.06999 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.42348 | −0.0470073 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.6441 | −1.04384 | −0.521922 | − | 0.852993i | \(-0.674785\pi\) | ||||
−0.521922 | + | 0.852993i | \(0.674785\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.0869 | 1.18911 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.48503 | 0.312204 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.2879 | 0.831459 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.41753 | 0.309312 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.2983 | −0.600349 | −0.300175 | − | 0.953884i | \(-0.597045\pi\) | ||||
−0.300175 | + | 0.953884i | \(0.597045\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.65835 | −0.283766 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.99099 | 0.327090 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −42.2823 | −1.38278 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.6984 | 0.708856 | 0.354428 | − | 0.935083i | \(-0.384676\pi\) | ||||
0.354428 | + | 0.935083i | \(0.384676\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.1017 | −0.949699 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.9481 | −1.66086 | −0.830430 | − | 0.557123i | \(-0.811905\pi\) | ||||
−0.830430 | + | 0.557123i | \(0.811905\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.9665 | −0.389682 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −45.6264 | −1.48423 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.6818 | 1.58195 | 0.790973 | − | 0.611852i | \(-0.209575\pi\) | ||||
0.790973 | + | 0.611852i | \(0.209575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.2277 | 0.559234 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −107.777 | −3.49492 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.3462 | 0.594291 | 0.297146 | − | 0.954832i | \(-0.403965\pi\) | ||||
0.297146 | + | 0.954832i | \(0.403965\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 61.9112 | 2.00340 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 63.0130 | 2.03692 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.2145 | 0.523595 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.74997 | −0.185483 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 67.7827 | 2.18427 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −43.5246 | −1.40111 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7034 | 0.826567 | 0.413283 | − | 0.910602i | \(-0.364382\pi\) | ||||
0.413283 | + | 0.910602i | \(0.364382\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 131.905 | 4.23738 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.27074 | −0.297512 | −0.148756 | − | 0.988874i | \(-0.547527\pi\) | ||||
−0.148756 | + | 0.988874i | \(0.547527\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.59253 | 0.243405 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −34.4704 | −1.10394 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.7630 | 0.824230 | 0.412115 | − | 0.911132i | \(-0.364790\pi\) | ||||
0.412115 | + | 0.911132i | \(0.364790\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.5771 | −0.561767 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.69970 | −0.0861949 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.11509 | −0.0355660 | −0.0177830 | − | 0.999842i | \(-0.505661\pi\) | ||||
−0.0177830 | + | 0.999842i | \(0.505661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.3216 | 0.488188 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.1440 | −0.450207 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.46104 | 0.237247 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.9530 | −1.80917 | −0.904586 | − | 0.426291i | \(-0.859820\pi\) | ||||
−0.904586 | + | 0.426291i | \(0.859820\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.9398 | −1.07705 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −46.3188 | −1.46841 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.6313 | −0.843423 | −0.421711 | − | 0.906730i | \(-0.638570\pi\) | ||||
−0.421711 | + | 0.906730i | \(0.638570\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 49.3876 | 1.56255 |
(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 | 2576.2.a.bc.1.5 | 5 | ||
4.3 | odd | 2 | 644.2.a.c.1.1 | ✓ | 5 | ||
12.11 | even | 2 | 5796.2.a.s.1.1 | 5 | |||
28.27 | even | 2 | 4508.2.a.g.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
644.2.a.c.1.1 | ✓ | 5 | 4.3 | odd | 2 | ||
2576.2.a.bc.1.5 | 5 | 1.1 | even | 1 | trivial | ||
4508.2.a.g.1.5 | 5 | 28.27 | even | 2 | |||
5796.2.a.s.1.1 | 5 | 12.11 | even | 2 |