Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.110609 | 0.0782121 | 0.0391060 | − | 0.999235i | \(-0.487549\pi\) | ||||
0.0391060 | + | 0.999235i | \(0.487549\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.98777 | −0.993883 | ||||||||
\(5\) | −0.0761036 | −0.0340345 | −0.0170173 | − | 0.999855i | \(-0.505417\pi\) | ||||
−0.0170173 | + | 0.999855i | \(0.505417\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.79648 | 1.43493 | 0.717467 | − | 0.696592i | \(-0.245301\pi\) | ||||
0.717467 | + | 0.696592i | \(0.245301\pi\) | |||||||
\(8\) | −0.441081 | −0.155946 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.00841771 | −0.00266191 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.86557 | 0.794765 | 0.397382 | − | 0.917653i | \(-0.369919\pi\) | ||||
0.397382 | + | 0.917653i | \(0.369919\pi\) | |||||||
\(14\) | 0.419923 | 0.112229 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.92674 | 0.981686 | ||||||||
\(17\) | 4.34025 | 1.05267 | 0.526333 | − | 0.850279i | \(-0.323567\pi\) | ||||
0.526333 | + | 0.850279i | \(0.323567\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.98182 | 1.83116 | 0.915578 | − | 0.402141i | \(-0.131734\pi\) | ||||
0.915578 | + | 0.402141i | \(0.131734\pi\) | |||||||
\(20\) | 0.151276 | 0.0338264 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.110609 | 0.0235818 | ||||||||
\(23\) | 8.82636 | 1.84042 | 0.920212 | − | 0.391421i | \(-0.128016\pi\) | ||||
0.920212 | + | 0.391421i | \(0.128016\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99421 | −0.998842 | ||||||||
\(26\) | 0.316956 | 0.0621602 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.54651 | −1.42616 | ||||||||
\(29\) | 8.77010 | 1.62857 | 0.814283 | − | 0.580468i | \(-0.197130\pi\) | ||||
0.814283 | + | 0.580468i | \(0.197130\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.15132 | 0.386389 | 0.193194 | − | 0.981160i | \(-0.438115\pi\) | ||||
0.193194 | + | 0.981160i | \(0.438115\pi\) | |||||||
\(32\) | 1.31649 | 0.232725 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.480069 | 0.0823312 | ||||||||
\(35\) | −0.288926 | −0.0488373 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.28709 | −1.52679 | −0.763394 | − | 0.645933i | \(-0.776468\pi\) | ||||
−0.763394 | + | 0.645933i | \(0.776468\pi\) | |||||||
\(38\) | 0.882858 | 0.143219 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0335679 | 0.00530754 | ||||||||
\(41\) | −3.66441 | −0.572284 | −0.286142 | − | 0.958187i | \(-0.592373\pi\) | ||||
−0.286142 | + | 0.958187i | \(0.592373\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.58502 | −0.546710 | −0.273355 | − | 0.961913i | \(-0.588133\pi\) | ||||
−0.273355 | + | 0.961913i | \(0.588133\pi\) | |||||||
\(44\) | −1.98777 | −0.299667 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.976271 | 0.143943 | ||||||||
\(47\) | 6.97477 | 1.01737 | 0.508687 | − | 0.860951i | \(-0.330131\pi\) | ||||
0.508687 | + | 0.860951i | \(0.330131\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.41325 | 1.05904 | ||||||||
\(50\) | −0.552402 | −0.0781215 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.69607 | −0.789903 | ||||||||
\(53\) | −9.56561 | −1.31394 | −0.656969 | − | 0.753918i | \(-0.728162\pi\) | ||||
−0.656969 | + | 0.753918i | \(0.728162\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0761036 | −0.0102618 | ||||||||
\(56\) | −1.67456 | −0.223772 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.970048 | 0.127374 | ||||||||
\(59\) | −4.57264 | −0.595307 | −0.297653 | − | 0.954674i | \(-0.596204\pi\) | ||||
−0.297653 | + | 0.954674i | \(0.596204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 0.237955 | 0.0302203 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.70787 | −0.963484 | ||||||||
\(65\) | −0.218080 | −0.0270495 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.56001 | −0.801433 | −0.400716 | − | 0.916202i | \(-0.631239\pi\) | ||||
−0.400716 | + | 0.916202i | \(0.631239\pi\) | |||||||
\(68\) | −8.62740 | −1.04623 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0319577 | −0.00381967 | ||||||||
\(71\) | 7.11249 | 0.844097 | 0.422049 | − | 0.906573i | \(-0.361311\pi\) | ||||
0.422049 | + | 0.906573i | \(0.361311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.09557 | −0.596392 | −0.298196 | − | 0.954505i | \(-0.596385\pi\) | ||||
−0.298196 | + | 0.954505i | \(0.596385\pi\) | |||||||
\(74\) | −1.02723 | −0.119413 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −15.8660 | −1.81995 | ||||||||
\(77\) | 3.79648 | 0.432649 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.57044 | 0.626724 | 0.313362 | − | 0.949634i | \(-0.398545\pi\) | ||||
0.313362 | + | 0.949634i | \(0.398545\pi\) | |||||||
\(80\) | −0.298839 | −0.0334112 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.405315 | −0.0447595 | ||||||||
\(83\) | 4.90970 | 0.538909 | 0.269455 | − | 0.963013i | \(-0.413157\pi\) | ||||
0.269455 | + | 0.963013i | \(0.413157\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.330309 | −0.0358270 | ||||||||
\(86\) | −0.396534 | −0.0427593 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.441081 | −0.0470194 | ||||||||
\(89\) | 6.47445 | 0.686290 | 0.343145 | − | 0.939282i | \(-0.388508\pi\) | ||||
0.343145 | + | 0.939282i | \(0.388508\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.8791 | 1.14044 | ||||||||
\(92\) | −17.5447 | −1.82917 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.771469 | 0.0795710 | ||||||||
\(95\) | −0.607445 | −0.0623226 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.14406 | 0.725370 | 0.362685 | − | 0.931912i | \(-0.381860\pi\) | ||||
0.362685 | + | 0.931912i | \(0.381860\pi\) | |||||||
\(98\) | 0.819969 | 0.0828294 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.92732 | 0.992732 | ||||||||
\(101\) | −9.53683 | −0.948951 | −0.474475 | − | 0.880269i | \(-0.657362\pi\) | ||||
−0.474475 | + | 0.880269i | \(0.657362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.6635 | 1.05070 | 0.525351 | − | 0.850886i | \(-0.323934\pi\) | ||||
0.525351 | + | 0.850886i | \(0.323934\pi\) | |||||||
\(104\) | −1.26395 | −0.123940 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.05804 | −0.102766 | ||||||||
\(107\) | −5.71072 | −0.552076 | −0.276038 | − | 0.961147i | \(-0.589022\pi\) | ||||
−0.276038 | + | 0.961147i | \(0.589022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.11069 | −0.776864 | −0.388432 | − | 0.921477i | \(-0.626983\pi\) | ||||
−0.388432 | + | 0.921477i | \(0.626983\pi\) | |||||||
\(110\) | −0.00841771 | −0.000802597 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 14.9078 | 1.40865 | ||||||||
\(113\) | −7.42753 | −0.698723 | −0.349362 | − | 0.936988i | \(-0.613602\pi\) | ||||
−0.349362 | + | 0.936988i | \(0.613602\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.671717 | −0.0626380 | ||||||||
\(116\) | −17.4329 | −1.61860 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.505773 | −0.0465602 | ||||||||
\(119\) | 16.4777 | 1.51051 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.110609 | −0.0100140 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.27633 | −0.384025 | ||||||||
\(125\) | 0.760595 | 0.0680297 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.5087 | −1.10997 | −0.554983 | − | 0.831862i | \(-0.687275\pi\) | ||||
−0.554983 | + | 0.831862i | \(0.687275\pi\) | |||||||
\(128\) | −3.48555 | −0.308082 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0241215 | −0.00211559 | ||||||||
\(131\) | 17.7841 | 1.55380 | 0.776900 | − | 0.629624i | \(-0.216791\pi\) | ||||
0.776900 | + | 0.629624i | \(0.216791\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.3028 | 2.62759 | ||||||||
\(134\) | −0.725594 | −0.0626818 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.91440 | −0.164159 | ||||||||
\(137\) | −21.6229 | −1.84737 | −0.923685 | − | 0.383153i | \(-0.874838\pi\) | ||||
−0.923685 | + | 0.383153i | \(0.874838\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.746613 | 0.0633269 | 0.0316635 | − | 0.999499i | \(-0.489920\pi\) | ||||
0.0316635 | + | 0.999499i | \(0.489920\pi\) | |||||||
\(140\) | 0.574316 | 0.0485386 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.786702 | 0.0660186 | ||||||||
\(143\) | 2.86557 | 0.239631 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.667436 | −0.0554275 | ||||||||
\(146\) | −0.563614 | −0.0466450 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.4606 | 1.51745 | ||||||||
\(149\) | 5.42693 | 0.444591 | 0.222296 | − | 0.974979i | \(-0.428645\pi\) | ||||
0.222296 | + | 0.974979i | \(0.428645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.58101 | −0.210040 | −0.105020 | − | 0.994470i | \(-0.533491\pi\) | ||||
−0.105020 | + | 0.994470i | \(0.533491\pi\) | |||||||
\(152\) | −3.52063 | −0.285561 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.419923 | 0.0338384 | ||||||||
\(155\) | −0.163723 | −0.0131506 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.9785 | −1.51465 | −0.757325 | − | 0.653038i | \(-0.773494\pi\) | ||||
−0.757325 | + | 0.653038i | \(0.773494\pi\) | |||||||
\(158\) | 0.616139 | 0.0490174 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.100190 | −0.00792071 | ||||||||
\(161\) | 33.5091 | 2.64089 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.3676 | −0.890379 | −0.445189 | − | 0.895436i | \(-0.646864\pi\) | ||||
−0.445189 | + | 0.895436i | \(0.646864\pi\) | |||||||
\(164\) | 7.28398 | 0.568783 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.543055 | 0.0421492 | ||||||||
\(167\) | 11.8499 | 0.916969 | 0.458485 | − | 0.888702i | \(-0.348392\pi\) | ||||
0.458485 | + | 0.888702i | \(0.348392\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.78854 | −0.368349 | ||||||||
\(170\) | −0.0365350 | −0.00280210 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.12617 | 0.543366 | ||||||||
\(173\) | 9.34584 | 0.710551 | 0.355276 | − | 0.934762i | \(-0.384387\pi\) | ||||
0.355276 | + | 0.934762i | \(0.384387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.9604 | −1.43327 | ||||||||
\(176\) | 3.92674 | 0.295989 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.716130 | 0.0536762 | ||||||||
\(179\) | 17.0201 | 1.27215 | 0.636073 | − | 0.771629i | \(-0.280558\pi\) | ||||
0.636073 | + | 0.771629i | \(0.280558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6884 | 1.68641 | 0.843206 | − | 0.537590i | \(-0.180665\pi\) | ||||
0.843206 | + | 0.537590i | \(0.180665\pi\) | |||||||
\(182\) | 1.20332 | 0.0891958 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.89314 | −0.287006 | ||||||||
\(185\) | 0.706780 | 0.0519635 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.34025 | 0.317391 | ||||||||
\(188\) | −13.8642 | −1.01115 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0671887 | −0.00487438 | ||||||||
\(191\) | 19.8345 | 1.43517 | 0.717586 | − | 0.696470i | \(-0.245247\pi\) | ||||
0.717586 | + | 0.696470i | \(0.245247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.95311 | −0.500496 | −0.250248 | − | 0.968182i | \(-0.580512\pi\) | ||||
−0.250248 | + | 0.968182i | \(0.580512\pi\) | |||||||
\(194\) | 0.790195 | 0.0567327 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.7358 | −1.05256 | ||||||||
\(197\) | −3.09263 | −0.220341 | −0.110170 | − | 0.993913i | \(-0.535140\pi\) | ||||
−0.110170 | + | 0.993913i | \(0.535140\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.62476 | 0.398729 | 0.199364 | − | 0.979925i | \(-0.436112\pi\) | ||||
0.199364 | + | 0.979925i | \(0.436112\pi\) | |||||||
\(200\) | 2.20285 | 0.155765 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.05486 | −0.0742194 | ||||||||
\(203\) | 33.2955 | 2.33689 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.278874 | 0.0194774 | ||||||||
\(206\) | 1.17947 | 0.0821775 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.2523 | 0.780210 | ||||||||
\(209\) | 7.98182 | 0.552114 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.98551 | −0.549745 | −0.274873 | − | 0.961481i | \(-0.588636\pi\) | ||||
−0.274873 | + | 0.961481i | \(0.588636\pi\) | |||||||
\(212\) | 19.0142 | 1.30590 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.631654 | −0.0431790 | ||||||||
\(215\) | 0.272833 | 0.0186070 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.16745 | 0.554443 | ||||||||
\(218\) | −0.897113 | −0.0607601 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.151276 | 0.0101990 | ||||||||
\(221\) | 12.4373 | 0.836622 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7057 | 1.45352 | 0.726759 | − | 0.686892i | \(-0.241025\pi\) | ||||
0.726759 | + | 0.686892i | \(0.241025\pi\) | |||||||
\(224\) | 4.99804 | 0.333946 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.821549 | −0.0546486 | ||||||||
\(227\) | −23.0947 | −1.53285 | −0.766423 | − | 0.642336i | \(-0.777965\pi\) | ||||
−0.766423 | + | 0.642336i | \(0.777965\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.0725 | −1.39251 | −0.696257 | − | 0.717793i | \(-0.745152\pi\) | ||||
−0.696257 | + | 0.717793i | \(0.745152\pi\) | |||||||
\(230\) | −0.0742977 | −0.00489905 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.86833 | −0.253968 | ||||||||
\(233\) | −19.5223 | −1.27895 | −0.639475 | − | 0.768812i | \(-0.720848\pi\) | ||||
−0.639475 | + | 0.768812i | \(0.720848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.530805 | −0.0346259 | ||||||||
\(236\) | 9.08934 | 0.591665 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.82257 | 0.118140 | ||||||||
\(239\) | −8.05007 | −0.520716 | −0.260358 | − | 0.965512i | \(-0.583841\pi\) | ||||
−0.260358 | + | 0.965512i | \(0.583841\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.0330 | −1.03278 | −0.516388 | − | 0.856355i | \(-0.672724\pi\) | ||||
−0.516388 | + | 0.856355i | \(0.672724\pi\) | |||||||
\(242\) | 0.110609 | 0.00711019 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.98777 | 0.127254 | ||||||||
\(245\) | −0.564175 | −0.0360438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.8724 | 1.45534 | ||||||||
\(248\) | −0.948908 | −0.0602557 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.0841283 | 0.00532074 | ||||||||
\(251\) | 18.4562 | 1.16494 | 0.582471 | − | 0.812851i | \(-0.302086\pi\) | ||||
0.582471 | + | 0.812851i | \(0.302086\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.82636 | 0.554908 | ||||||||
\(254\) | −1.38357 | −0.0868128 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.0302 | 0.939388 | ||||||||
\(257\) | 4.27534 | 0.266689 | 0.133344 | − | 0.991070i | \(-0.457428\pi\) | ||||
0.133344 | + | 0.991070i | \(0.457428\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −35.2582 | −2.19084 | ||||||||
\(260\) | 0.433491 | 0.0268840 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.96707 | 0.121526 | ||||||||
\(263\) | −26.3258 | −1.62332 | −0.811659 | − | 0.584132i | \(-0.801435\pi\) | ||||
−0.811659 | + | 0.584132i | \(0.801435\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.727977 | 0.0447193 | ||||||||
\(266\) | 3.35175 | 0.205509 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.0398 | 0.796530 | ||||||||
\(269\) | −23.7635 | −1.44889 | −0.724444 | − | 0.689333i | \(-0.757903\pi\) | ||||
−0.724444 | + | 0.689333i | \(0.757903\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.94283 | −0.361001 | −0.180501 | − | 0.983575i | \(-0.557772\pi\) | ||||
−0.180501 | + | 0.983575i | \(0.557772\pi\) | |||||||
\(272\) | 17.0431 | 1.03339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.39168 | −0.144487 | ||||||||
\(275\) | −4.99421 | −0.301162 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.28627 | −0.137369 | −0.0686844 | − | 0.997638i | \(-0.521880\pi\) | ||||
−0.0686844 | + | 0.997638i | \(0.521880\pi\) | |||||||
\(278\) | 0.0825818 | 0.00495293 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.127440 | 0.00761597 | ||||||||
\(281\) | 11.7431 | 0.700536 | 0.350268 | − | 0.936650i | \(-0.386091\pi\) | ||||
0.350268 | + | 0.936650i | \(0.386091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.9783 | −1.42536 | −0.712682 | − | 0.701487i | \(-0.752520\pi\) | ||||
−0.712682 | + | 0.701487i | \(0.752520\pi\) | |||||||
\(284\) | −14.1380 | −0.838934 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.316956 | 0.0187420 | ||||||||
\(287\) | −13.9118 | −0.821190 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.83778 | 0.108105 | ||||||||
\(290\) | −0.0738241 | −0.00433510 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.1288 | 0.592743 | ||||||||
\(293\) | 29.2544 | 1.70906 | 0.854531 | − | 0.519401i | \(-0.173845\pi\) | ||||
0.854531 | + | 0.519401i | \(0.173845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.347994 | 0.0202610 | ||||||||
\(296\) | 4.09636 | 0.238096 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.600265 | 0.0347724 | ||||||||
\(299\) | 25.2925 | 1.46270 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.6104 | −0.784493 | ||||||||
\(302\) | −0.285482 | −0.0164277 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 31.3426 | 1.79762 | ||||||||
\(305\) | 0.0761036 | 0.00435768 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5984 | −0.661954 | −0.330977 | − | 0.943639i | \(-0.607378\pi\) | ||||
−0.330977 | + | 0.943639i | \(0.607378\pi\) | |||||||
\(308\) | −7.54651 | −0.430002 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.0181092 | −0.00102853 | ||||||||
\(311\) | 25.0665 | 1.42139 | 0.710695 | − | 0.703501i | \(-0.248381\pi\) | ||||
0.710695 | + | 0.703501i | \(0.248381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.6390 | −1.27963 | −0.639816 | − | 0.768528i | \(-0.720989\pi\) | ||||
−0.639816 | + | 0.768528i | \(0.720989\pi\) | |||||||
\(314\) | −2.09919 | −0.118464 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.0727 | −0.622890 | ||||||||
\(317\) | −20.0501 | −1.12613 | −0.563063 | − | 0.826414i | \(-0.690377\pi\) | ||||
−0.563063 | + | 0.826414i | \(0.690377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.77010 | 0.491031 | ||||||||
\(320\) | 0.586597 | 0.0327917 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.70639 | 0.206549 | ||||||||
\(323\) | 34.6431 | 1.92759 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.3112 | −0.793844 | ||||||||
\(326\) | −1.25735 | −0.0696384 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.61630 | 0.0892453 | ||||||||
\(329\) | 26.4796 | 1.45987 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3521 | −0.788865 | −0.394433 | − | 0.918925i | \(-0.629059\pi\) | ||||
−0.394433 | + | 0.918925i | \(0.629059\pi\) | |||||||
\(332\) | −9.75933 | −0.535613 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.31070 | 0.0717181 | ||||||||
\(335\) | 0.499240 | 0.0272764 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.9937 | 1.14360 | 0.571800 | − | 0.820393i | \(-0.306245\pi\) | ||||
0.571800 | + | 0.820393i | \(0.306245\pi\) | |||||||
\(338\) | −0.529653 | −0.0288093 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.656576 | 0.0356078 | ||||||||
\(341\) | 2.15132 | 0.116501 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.56890 | 0.0847127 | ||||||||
\(344\) | 1.58128 | 0.0852571 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.03373 | 0.0555737 | ||||||||
\(347\) | 28.1758 | 1.51256 | 0.756278 | − | 0.654250i | \(-0.227016\pi\) | ||||
0.756278 | + | 0.654250i | \(0.227016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.23859 | 0.441002 | 0.220501 | − | 0.975387i | \(-0.429231\pi\) | ||||
0.220501 | + | 0.975387i | \(0.429231\pi\) | |||||||
\(350\) | −2.09718 | −0.112099 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.31649 | 0.0701694 | ||||||||
\(353\) | −11.3361 | −0.603359 | −0.301680 | − | 0.953409i | \(-0.597547\pi\) | ||||
−0.301680 | + | 0.953409i | \(0.597547\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.541286 | −0.0287285 | ||||||||
\(356\) | −12.8697 | −0.682092 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.88257 | 0.0994972 | ||||||||
\(359\) | −18.9216 | −0.998643 | −0.499322 | − | 0.866417i | \(-0.666417\pi\) | ||||
−0.499322 | + | 0.866417i | \(0.666417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 44.7095 | 2.35313 | ||||||||
\(362\) | 2.50953 | 0.131898 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.6250 | −1.13346 | ||||||||
\(365\) | 0.387791 | 0.0202979 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.65543 | 0.399610 | 0.199805 | − | 0.979836i | \(-0.435969\pi\) | ||||
0.199805 | + | 0.979836i | \(0.435969\pi\) | |||||||
\(368\) | 34.6589 | 1.80672 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.0781760 | 0.00406418 | ||||||||
\(371\) | −36.3156 | −1.88541 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.0460594 | −0.00238487 | −0.00119243 | − | 0.999999i | \(-0.500380\pi\) | ||||
−0.00119243 | + | 0.999999i | \(0.500380\pi\) | |||||||
\(374\) | 0.480069 | 0.0248238 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.07644 | −0.158655 | ||||||||
\(377\) | 25.1313 | 1.29433 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.07669 | 0.312139 | 0.156069 | − | 0.987746i | \(-0.450118\pi\) | ||||
0.156069 | + | 0.987746i | \(0.450118\pi\) | |||||||
\(380\) | 1.20746 | 0.0619413 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.19386 | 0.112248 | ||||||||
\(383\) | 19.1399 | 0.978002 | 0.489001 | − | 0.872283i | \(-0.337361\pi\) | ||||
0.489001 | + | 0.872283i | \(0.337361\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.288926 | −0.0147250 | ||||||||
\(386\) | −0.769074 | −0.0391449 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.2007 | −0.720932 | ||||||||
\(389\) | −30.0214 | −1.52215 | −0.761073 | − | 0.648666i | \(-0.775327\pi\) | ||||
−0.761073 | + | 0.648666i | \(0.775327\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.3086 | 1.93735 | ||||||||
\(392\) | −3.26985 | −0.165152 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.342071 | −0.0172333 | ||||||||
\(395\) | −0.423930 | −0.0213303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.6843 | 1.18868 | 0.594342 | − | 0.804213i | \(-0.297413\pi\) | ||||
0.594342 | + | 0.804213i | \(0.297413\pi\) | |||||||
\(398\) | 0.622147 | 0.0311854 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.6110 | −0.980549 | ||||||||
\(401\) | 17.4907 | 0.873443 | 0.436722 | − | 0.899597i | \(-0.356140\pi\) | ||||
0.436722 | + | 0.899597i | \(0.356140\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.16476 | 0.307088 | ||||||||
\(404\) | 18.9570 | 0.943146 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.68277 | 0.182773 | ||||||||
\(407\) | −9.28709 | −0.460344 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.0343 | −0.595058 | −0.297529 | − | 0.954713i | \(-0.596162\pi\) | ||||
−0.297529 | + | 0.954713i | \(0.596162\pi\) | |||||||
\(410\) | 0.0308459 | 0.00152337 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21.1964 | −1.04427 | ||||||||
\(413\) | −17.3599 | −0.854226 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.373645 | −0.0183415 | ||||||||
\(416\) | 3.77250 | 0.184962 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.882858 | 0.0431820 | ||||||||
\(419\) | 4.71859 | 0.230518 | 0.115259 | − | 0.993335i | \(-0.463230\pi\) | ||||
0.115259 | + | 0.993335i | \(0.463230\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.31420 | −0.161524 | −0.0807622 | − | 0.996733i | \(-0.525735\pi\) | ||||
−0.0807622 | + | 0.996733i | \(0.525735\pi\) | |||||||
\(422\) | −0.883266 | −0.0429967 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.21921 | 0.204903 | ||||||||
\(425\) | −21.6761 | −1.05145 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.79648 | −0.183724 | ||||||||
\(428\) | 11.3516 | 0.548699 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0301776 | 0.00145529 | ||||||||
\(431\) | 27.1154 | 1.30610 | 0.653051 | − | 0.757314i | \(-0.273489\pi\) | ||||
0.653051 | + | 0.757314i | \(0.273489\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.4342 | −1.07812 | −0.539059 | − | 0.842268i | \(-0.681220\pi\) | ||||
−0.539059 | + | 0.842268i | \(0.681220\pi\) | |||||||
\(434\) | 0.903390 | 0.0433641 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.1222 | 0.772111 | ||||||||
\(437\) | 70.4504 | 3.37010 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.76170 | 0.465900 | 0.232950 | − | 0.972489i | \(-0.425162\pi\) | ||||
0.232950 | + | 0.972489i | \(0.425162\pi\) | |||||||
\(440\) | 0.0335679 | 0.00160028 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.37567 | 0.0654339 | ||||||||
\(443\) | −22.8703 | −1.08660 | −0.543300 | − | 0.839539i | \(-0.682825\pi\) | ||||
−0.543300 | + | 0.839539i | \(0.682825\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.492729 | −0.0233576 | ||||||||
\(446\) | 2.40083 | 0.113683 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −29.2628 | −1.38254 | ||||||||
\(449\) | 11.6616 | 0.550344 | 0.275172 | − | 0.961395i | \(-0.411265\pi\) | ||||
0.275172 | + | 0.961395i | \(0.411265\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.66441 | −0.172550 | ||||||||
\(452\) | 14.7642 | 0.694449 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.55447 | −0.119887 | ||||||||
\(455\) | −0.827935 | −0.0388142 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.9533 | −1.21405 | −0.607023 | − | 0.794684i | \(-0.707636\pi\) | ||||
−0.607023 | + | 0.794684i | \(0.707636\pi\) | |||||||
\(458\) | −2.33081 | −0.108911 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.33522 | 0.0622548 | ||||||||
\(461\) | 19.5400 | 0.910066 | 0.455033 | − | 0.890474i | \(-0.349627\pi\) | ||||
0.455033 | + | 0.890474i | \(0.349627\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.5942 | 0.724724 | 0.362362 | − | 0.932037i | \(-0.381970\pi\) | ||||
0.362362 | + | 0.932037i | \(0.381970\pi\) | |||||||
\(464\) | 34.4379 | 1.59874 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.15934 | −0.100029 | ||||||||
\(467\) | 2.26539 | 0.104830 | 0.0524149 | − | 0.998625i | \(-0.483308\pi\) | ||||
0.0524149 | + | 0.998625i | \(0.483308\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.9049 | −1.15000 | ||||||||
\(470\) | −0.0587116 | −0.00270816 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.01691 | 0.0928356 | ||||||||
\(473\) | −3.58502 | −0.164839 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −39.8629 | −1.82903 | ||||||||
\(476\) | −32.7538 | −1.50127 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.890407 | −0.0407263 | ||||||||
\(479\) | 42.1326 | 1.92509 | 0.962545 | − | 0.271123i | \(-0.0873949\pi\) | ||||
0.962545 | + | 0.271123i | \(0.0873949\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.6128 | −1.21344 | ||||||||
\(482\) | −1.77339 | −0.0807756 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.98777 | −0.0903530 | ||||||||
\(485\) | −0.543689 | −0.0246876 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.6975 | 0.756638 | 0.378319 | − | 0.925675i | \(-0.376502\pi\) | ||||
0.378319 | + | 0.925675i | \(0.376502\pi\) | |||||||
\(488\) | 0.441081 | 0.0199668 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.0624026 | −0.00281906 | ||||||||
\(491\) | 12.2889 | 0.554590 | 0.277295 | − | 0.960785i | \(-0.410562\pi\) | ||||
0.277295 | + | 0.960785i | \(0.410562\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.0644 | 1.71434 | ||||||||
\(494\) | 2.52989 | 0.113825 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.44769 | 0.379313 | ||||||||
\(497\) | 27.0024 | 1.21122 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.4398 | 0.691181 | 0.345591 | − | 0.938385i | \(-0.387679\pi\) | ||||
0.345591 | + | 0.938385i | \(0.387679\pi\) | |||||||
\(500\) | −1.51188 | −0.0676135 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.04141 | 0.0911126 | ||||||||
\(503\) | −6.34296 | −0.282818 | −0.141409 | − | 0.989951i | \(-0.545163\pi\) | ||||
−0.141409 | + | 0.989951i | \(0.545163\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.725787 | 0.0322971 | ||||||||
\(506\) | 0.976271 | 0.0434006 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 24.8643 | 1.10318 | ||||||||
\(509\) | 10.7065 | 0.474559 | 0.237279 | − | 0.971441i | \(-0.423744\pi\) | ||||
0.237279 | + | 0.971441i | \(0.423744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.3452 | −0.855783 | ||||||||
\(512\) | 8.63356 | 0.381553 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.472890 | 0.0208583 | ||||||||
\(515\) | −0.811527 | −0.0357601 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.97477 | 0.306750 | ||||||||
\(518\) | −3.89986 | −0.171350 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.0961909 | 0.00421825 | ||||||||
\(521\) | −23.3915 | −1.02480 | −0.512401 | − | 0.858746i | \(-0.671244\pi\) | ||||
−0.512401 | + | 0.858746i | \(0.671244\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.600364 | 0.0262521 | 0.0131260 | − | 0.999914i | \(-0.495822\pi\) | ||||
0.0131260 | + | 0.999914i | \(0.495822\pi\) | |||||||
\(524\) | −35.3505 | −1.54430 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.91186 | −0.126963 | ||||||||
\(527\) | 9.33728 | 0.406738 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.9046 | 2.38716 | ||||||||
\(530\) | 0.0805205 | 0.00349759 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −60.2349 | −2.61151 | ||||||||
\(533\) | −10.5006 | −0.454831 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.434606 | 0.0187896 | ||||||||
\(536\) | 2.89350 | 0.124980 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.62845 | −0.113321 | ||||||||
\(539\) | 7.41325 | 0.319311 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.4295 | −0.491393 | −0.245697 | − | 0.969347i | \(-0.579017\pi\) | ||||
−0.245697 | + | 0.969347i | \(0.579017\pi\) | |||||||
\(542\) | −0.657328 | −0.0282347 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.71392 | 0.244982 | ||||||||
\(545\) | 0.617253 | 0.0264402 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.3464 | 0.527894 | 0.263947 | − | 0.964537i | \(-0.414976\pi\) | ||||
0.263947 | + | 0.964537i | \(0.414976\pi\) | |||||||
\(548\) | 42.9813 | 1.83607 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.552402 | −0.0235545 | ||||||||
\(551\) | 70.0014 | 2.98216 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.1481 | 0.899307 | ||||||||
\(554\) | −0.252882 | −0.0107439 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.48409 | −0.0629395 | ||||||||
\(557\) | 0.0358158 | 0.00151757 | 0.000758783 | − | 1.00000i | \(-0.499758\pi\) | ||||
0.000758783 | 1.00000i | \(0.499758\pi\) | ||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.2731 | −0.434506 | ||||||||
\(560\) | −1.13454 | −0.0479429 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.29889 | 0.0547904 | ||||||||
\(563\) | −34.8146 | −1.46726 | −0.733631 | − | 0.679548i | \(-0.762176\pi\) | ||||
−0.733631 | + | 0.679548i | \(0.762176\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.565261 | 0.0237807 | ||||||||
\(566\) | −2.65221 | −0.111481 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.13719 | −0.131633 | ||||||||
\(569\) | −1.86930 | −0.0783650 | −0.0391825 | − | 0.999232i | \(-0.512475\pi\) | ||||
−0.0391825 | + | 0.999232i | \(0.512475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.4826 | −0.899019 | −0.449510 | − | 0.893275i | \(-0.648401\pi\) | ||||
−0.449510 | + | 0.893275i | \(0.648401\pi\) | |||||||
\(572\) | −5.69607 | −0.238165 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.53877 | −0.0642270 | ||||||||
\(575\) | −44.0807 | −1.83829 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.99358 | −0.416038 | −0.208019 | − | 0.978125i | \(-0.566702\pi\) | ||||
−0.208019 | + | 0.978125i | \(0.566702\pi\) | |||||||
\(578\) | 0.203274 | 0.00845509 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.32671 | 0.0550885 | ||||||||
\(581\) | 18.6396 | 0.773299 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.56561 | −0.396167 | ||||||||
\(584\) | 2.24756 | 0.0930047 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.23579 | 0.133669 | ||||||||
\(587\) | 38.0086 | 1.56878 | 0.784391 | − | 0.620267i | \(-0.212976\pi\) | ||||
0.784391 | + | 0.620267i | \(0.212976\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1715 | 0.707538 | ||||||||
\(590\) | 0.0384911 | 0.00158466 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −36.4680 | −1.49883 | ||||||||
\(593\) | 2.69125 | 0.110516 | 0.0552582 | − | 0.998472i | \(-0.482402\pi\) | ||||
0.0552582 | + | 0.998472i | \(0.482402\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.25401 | −0.0514094 | ||||||||
\(596\) | −10.7875 | −0.441872 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.79757 | 0.114401 | ||||||||
\(599\) | −38.5122 | −1.57357 | −0.786784 | − | 0.617229i | \(-0.788255\pi\) | ||||
−0.786784 | + | 0.617229i | \(0.788255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.39375 | −0.260806 | −0.130403 | − | 0.991461i | \(-0.541627\pi\) | ||||
−0.130403 | + | 0.991461i | \(0.541627\pi\) | |||||||
\(602\) | −1.50543 | −0.0613568 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.13045 | 0.208755 | ||||||||
\(605\) | −0.0761036 | −0.00309405 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.9533 | −0.891056 | −0.445528 | − | 0.895268i | \(-0.646984\pi\) | ||||
−0.445528 | + | 0.895268i | \(0.646984\pi\) | |||||||
\(608\) | 10.5080 | 0.426157 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.00841771 | 0.000340823 0 | ||||||||
\(611\) | 19.9867 | 0.808573 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0981 | −0.529028 | −0.264514 | − | 0.964382i | \(-0.585212\pi\) | ||||
−0.264514 | + | 0.964382i | \(0.585212\pi\) | |||||||
\(614\) | −1.28288 | −0.0517728 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.67456 | −0.0674698 | ||||||||
\(617\) | 5.20052 | 0.209365 | 0.104683 | − | 0.994506i | \(-0.466617\pi\) | ||||
0.104683 | + | 0.994506i | \(0.466617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.8564 | 1.68235 | 0.841175 | − | 0.540762i | \(-0.181864\pi\) | ||||
0.841175 | + | 0.540762i | \(0.181864\pi\) | |||||||
\(620\) | 0.325444 | 0.0130701 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.77257 | 0.111170 | ||||||||
\(623\) | 24.5801 | 0.984781 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9132 | 0.996526 | ||||||||
\(626\) | −2.50407 | −0.100083 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 37.7249 | 1.50539 | ||||||||
\(629\) | −40.3083 | −1.60720 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.4353 | −1.21161 | −0.605805 | − | 0.795613i | \(-0.707149\pi\) | ||||
−0.605805 | + | 0.795613i | \(0.707149\pi\) | |||||||
\(632\) | −2.45702 | −0.0977349 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.21771 | −0.0880767 | ||||||||
\(635\) | 0.951955 | 0.0377772 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.2432 | 0.841685 | ||||||||
\(638\) | 0.970048 | 0.0384046 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.265262 | 0.0104854 | ||||||||
\(641\) | 5.45615 | 0.215505 | 0.107752 | − | 0.994178i | \(-0.465635\pi\) | ||||
0.107752 | + | 0.994178i | \(0.465635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.9108 | 0.548587 | 0.274294 | − | 0.961646i | \(-0.411556\pi\) | ||||
0.274294 | + | 0.961646i | \(0.411556\pi\) | |||||||
\(644\) | −66.6082 | −2.62473 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.83183 | 0.150761 | ||||||||
\(647\) | 34.4350 | 1.35378 | 0.676891 | − | 0.736084i | \(-0.263327\pi\) | ||||
0.676891 | + | 0.736084i | \(0.263327\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.57264 | −0.179492 | ||||||||
\(650\) | −1.58295 | −0.0620882 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.5961 | 0.884932 | ||||||||
\(653\) | 18.1858 | 0.711665 | 0.355833 | − | 0.934550i | \(-0.384197\pi\) | ||||
0.355833 | + | 0.934550i | \(0.384197\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.35343 | −0.0528829 | ||||||||
\(656\) | −14.3892 | −0.561803 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.92887 | 0.114179 | ||||||||
\(659\) | −40.3831 | −1.57310 | −0.786551 | − | 0.617525i | \(-0.788135\pi\) | ||||
−0.786551 | + | 0.617525i | \(0.788135\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0696 | −0.858408 | −0.429204 | − | 0.903208i | \(-0.641206\pi\) | ||||
−0.429204 | + | 0.903208i | \(0.641206\pi\) | |||||||
\(662\) | −1.58747 | −0.0616988 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.16558 | −0.0840406 | ||||||||
\(665\) | −2.30615 | −0.0894288 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 77.4080 | 2.99725 | ||||||||
\(668\) | −23.5547 | −0.911360 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.0552203 | 0.00213334 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.2391 | −0.972897 | −0.486448 | − | 0.873709i | \(-0.661708\pi\) | ||||
−0.486448 | + | 0.873709i | \(0.661708\pi\) | |||||||
\(674\) | 2.32209 | 0.0894434 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.51849 | 0.366096 | ||||||||
\(677\) | −29.9067 | −1.14941 | −0.574704 | − | 0.818362i | \(-0.694883\pi\) | ||||
−0.574704 | + | 0.818362i | \(0.694883\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.1223 | 1.04086 | ||||||||
\(680\) | 0.145693 | 0.00558707 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.237955 | 0.00911176 | ||||||||
\(683\) | −36.2768 | −1.38809 | −0.694046 | − | 0.719931i | \(-0.744174\pi\) | ||||
−0.694046 | + | 0.719931i | \(0.744174\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.64558 | 0.0628744 | ||||||||
\(686\) | 0.173534 | 0.00662556 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.0774 | −0.536697 | ||||||||
\(689\) | −27.4109 | −1.04427 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.1636 | −1.41377 | −0.706885 | − | 0.707328i | \(-0.749900\pi\) | ||||
−0.706885 | + | 0.707328i | \(0.749900\pi\) | |||||||
\(692\) | −18.5773 | −0.706205 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.11649 | 0.118300 | ||||||||
\(695\) | −0.0568199 | −0.00215530 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.9044 | −0.602424 | ||||||||
\(698\) | 0.911259 | 0.0344917 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 37.6888 | 1.42450 | ||||||||
\(701\) | −22.1251 | −0.835654 | −0.417827 | − | 0.908527i | \(-0.637208\pi\) | ||||
−0.417827 | + | 0.908527i | \(0.637208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −74.1279 | −2.79579 | ||||||||
\(704\) | −7.70787 | −0.290501 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.25387 | −0.0471900 | ||||||||
\(707\) | −36.2064 | −1.36168 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.10803 | −0.116724 | −0.0583622 | − | 0.998295i | \(-0.518588\pi\) | ||||
−0.0583622 | + | 0.998295i | \(0.518588\pi\) | |||||||
\(710\) | −0.0598709 | −0.00224691 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.85576 | −0.107024 | ||||||||
\(713\) | 18.9883 | 0.711119 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.218080 | −0.00815572 | ||||||||
\(716\) | −33.8321 | −1.26436 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.09289 | −0.0781060 | ||||||||
\(719\) | 31.2247 | 1.16448 | 0.582242 | − | 0.813016i | \(-0.302176\pi\) | ||||
0.582242 | + | 0.813016i | \(0.302176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.4836 | 1.50769 | ||||||||
\(722\) | 4.94526 | 0.184043 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −45.0992 | −1.67610 | ||||||||
\(725\) | −43.7997 | −1.62668 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.9601 | 1.44495 | 0.722475 | − | 0.691397i | \(-0.243005\pi\) | ||||
0.722475 | + | 0.691397i | \(0.243005\pi\) | |||||||
\(728\) | −4.79855 | −0.177846 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.0428930 | 0.00158754 | ||||||||
\(731\) | −15.5599 | −0.575503 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.872224 | 0.0322163 | 0.0161082 | − | 0.999870i | \(-0.494872\pi\) | ||||
0.0161082 | + | 0.999870i | \(0.494872\pi\) | |||||||
\(734\) | 0.846757 | 0.0312544 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.6199 | 0.428313 | ||||||||
\(737\) | −6.56001 | −0.241641 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.8816 | −1.65100 | −0.825499 | − | 0.564404i | \(-0.809106\pi\) | ||||
−0.825499 | + | 0.564404i | \(0.809106\pi\) | |||||||
\(740\) | −1.40491 | −0.0516457 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.01682 | −0.147462 | ||||||||
\(743\) | −17.1705 | −0.629924 | −0.314962 | − | 0.949104i | \(-0.601992\pi\) | ||||
−0.314962 | + | 0.949104i | \(0.601992\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.413009 | −0.0151315 | ||||||||
\(746\) | −0.00509457 | −0.000186525 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.62740 | −0.315449 | ||||||||
\(749\) | −21.6806 | −0.792192 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.10694 | −0.295827 | −0.147913 | − | 0.989000i | \(-0.547256\pi\) | ||||
−0.147913 | + | 0.989000i | \(0.547256\pi\) | |||||||
\(752\) | 27.3881 | 0.998742 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.77974 | 0.101232 | ||||||||
\(755\) | 0.196424 | 0.00714861 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.1699 | −1.56904 | −0.784519 | − | 0.620105i | \(-0.787090\pi\) | ||||
−0.784519 | + | 0.620105i | \(0.787090\pi\) | |||||||
\(758\) | 0.672134 | 0.0244130 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.267933 | 0.00971894 | ||||||||
\(761\) | 5.86825 | 0.212724 | 0.106362 | − | 0.994327i | \(-0.466080\pi\) | ||||
0.106362 | + | 0.994327i | \(0.466080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.7921 | −1.11475 | ||||||||
\(764\) | −39.4263 | −1.42639 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.11704 | 0.0764916 | ||||||||
\(767\) | −13.1032 | −0.473129 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4647 | 0.413426 | 0.206713 | − | 0.978402i | \(-0.433723\pi\) | ||||
0.206713 | + | 0.978402i | \(0.433723\pi\) | |||||||
\(770\) | −0.0319577 | −0.00115167 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.8212 | 0.497434 | ||||||||
\(773\) | −9.19356 | −0.330669 | −0.165335 | − | 0.986238i | \(-0.552870\pi\) | ||||
−0.165335 | + | 0.986238i | \(0.552870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.7442 | −0.385941 | ||||||||
\(776\) | −3.15111 | −0.113118 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.32063 | −0.119050 | ||||||||
\(779\) | −29.2486 | −1.04794 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.11249 | 0.254505 | ||||||||
\(782\) | 4.23726 | 0.151524 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 29.1099 | 1.03964 | ||||||||
\(785\) | 1.44433 | 0.0515505 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.3426 | 1.50935 | 0.754675 | − | 0.656098i | \(-0.227794\pi\) | ||||
0.754675 | + | 0.656098i | \(0.227794\pi\) | |||||||
\(788\) | 6.14742 | 0.218993 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.0468904 | −0.00166828 | ||||||||
\(791\) | −28.1985 | −1.00262 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.86557 | −0.101759 | ||||||||
\(794\) | 2.61969 | 0.0929694 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.1807 | −0.396290 | ||||||||
\(797\) | 33.9733 | 1.20340 | 0.601698 | − | 0.798723i | \(-0.294491\pi\) | ||||
0.601698 | + | 0.798723i | \(0.294491\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.2722 | 1.07096 | ||||||||
\(800\) | −6.57485 | −0.232456 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.93462 | 0.0683138 | ||||||||
\(803\) | −5.09557 | −0.179819 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.55016 | −0.0898814 | ||||||||
\(806\) | 0.681875 | 0.0240180 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.20652 | 0.147985 | ||||||||
\(809\) | 30.1801 | 1.06108 | 0.530538 | − | 0.847661i | \(-0.321990\pi\) | ||||
0.530538 | + | 0.847661i | \(0.321990\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.6481 | −0.654823 | −0.327411 | − | 0.944882i | \(-0.606176\pi\) | ||||
−0.327411 | + | 0.944882i | \(0.606176\pi\) | |||||||
\(812\) | −66.1836 | −2.32259 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.02723 | −0.0360045 | ||||||||
\(815\) | 0.865114 | 0.0303036 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.6150 | −1.00111 | ||||||||
\(818\) | −1.33110 | −0.0465407 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.554337 | −0.0193583 | ||||||||
\(821\) | −9.96643 | −0.347831 | −0.173915 | − | 0.984761i | \(-0.555642\pi\) | ||||
−0.173915 | + | 0.984761i | \(0.555642\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.7617 | 1.17686 | 0.588430 | − | 0.808548i | \(-0.299746\pi\) | ||||
0.588430 | + | 0.808548i | \(0.299746\pi\) | |||||||
\(824\) | −4.70345 | −0.163852 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.92016 | −0.0668108 | ||||||||
\(827\) | 4.59052 | 0.159628 | 0.0798141 | − | 0.996810i | \(-0.474567\pi\) | ||||
0.0798141 | + | 0.996810i | \(0.474567\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.64187 | −0.0917560 | −0.0458780 | − | 0.998947i | \(-0.514609\pi\) | ||||
−0.0458780 | + | 0.998947i | \(0.514609\pi\) | |||||||
\(830\) | −0.0413284 | −0.00143453 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.0874 | −0.765743 | ||||||||
\(833\) | 32.1754 | 1.11481 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.901816 | −0.0312086 | ||||||||
\(836\) | −15.8660 | −0.548737 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.521917 | 0.0180293 | ||||||||
\(839\) | −36.6518 | −1.26536 | −0.632681 | − | 0.774413i | \(-0.718045\pi\) | ||||
−0.632681 | + | 0.774413i | \(0.718045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.9146 | 1.65223 | ||||||||
\(842\) | −0.366579 | −0.0126332 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.8733 | 0.546383 | ||||||||
\(845\) | 0.364425 | 0.0125366 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.79648 | 0.130449 | ||||||||
\(848\) | −37.5617 | −1.28987 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.39757 | −0.0822358 | ||||||||
\(851\) | −81.9712 | −2.80994 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0204 | 0.788204 | 0.394102 | − | 0.919067i | \(-0.371056\pi\) | ||||
0.394102 | + | 0.919067i | \(0.371056\pi\) | |||||||
\(854\) | −0.419923 | −0.0143695 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.51889 | 0.0860939 | ||||||||
\(857\) | −6.71504 | −0.229382 | −0.114691 | − | 0.993401i | \(-0.536588\pi\) | ||||
−0.114691 | + | 0.993401i | \(0.536588\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.6212 | −1.89777 | −0.948886 | − | 0.315620i | \(-0.897787\pi\) | ||||
−0.948886 | + | 0.315620i | \(0.897787\pi\) | |||||||
\(860\) | −0.542327 | −0.0184932 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.99920 | 0.102153 | ||||||||
\(863\) | −10.1564 | −0.345726 | −0.172863 | − | 0.984946i | \(-0.555302\pi\) | ||||
−0.172863 | + | 0.984946i | \(0.555302\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.711252 | −0.0241833 | ||||||||
\(866\) | −2.48141 | −0.0843219 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16.2350 | −0.551051 | ||||||||
\(869\) | 5.57044 | 0.188964 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.7981 | −0.636951 | ||||||||
\(872\) | 3.57748 | 0.121149 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.79243 | 0.263583 | ||||||||
\(875\) | 2.88758 | 0.0976181 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.2582 | −1.42696 | −0.713480 | − | 0.700676i | \(-0.752882\pi\) | ||||
−0.713480 | + | 0.700676i | \(0.752882\pi\) | |||||||
\(878\) | 1.07973 | 0.0364390 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.298839 | −0.0100739 | ||||||||
\(881\) | −12.3079 | −0.414664 | −0.207332 | − | 0.978271i | \(-0.566478\pi\) | ||||
−0.207332 | + | 0.978271i | \(0.566478\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.4863 | 0.958639 | 0.479320 | − | 0.877640i | \(-0.340883\pi\) | ||||
0.479320 | + | 0.877640i | \(0.340883\pi\) | |||||||
\(884\) | −24.7224 | −0.831504 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.52965 | −0.0849852 | ||||||||
\(887\) | 28.3316 | 0.951284 | 0.475642 | − | 0.879639i | \(-0.342216\pi\) | ||||
0.475642 | + | 0.879639i | \(0.342216\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47.4889 | −1.59273 | ||||||||
\(890\) | −0.0545000 | −0.00182685 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −43.1458 | −1.44463 | ||||||||
\(893\) | 55.6714 | 1.86297 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.29529 | −0.0432969 | ||||||||
\(896\) | −13.2328 | −0.442077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.28987 | 0.0430436 | ||||||||
\(899\) | 18.8673 | 0.629260 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.5172 | −1.38314 | ||||||||
\(902\) | −0.405315 | −0.0134955 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.27614 | 0.108963 | ||||||||
\(905\) | −1.72667 | −0.0573963 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.6810 | 0.587087 | 0.293544 | − | 0.955946i | \(-0.405165\pi\) | ||||
0.293544 | + | 0.955946i | \(0.405165\pi\) | |||||||
\(908\) | 45.9068 | 1.52347 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.0915767 | −0.00303574 | ||||||||
\(911\) | −58.8525 | −1.94987 | −0.974934 | − | 0.222493i | \(-0.928581\pi\) | ||||
−0.974934 | + | 0.222493i | \(0.928581\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.90970 | 0.162487 | ||||||||
\(914\) | −2.87066 | −0.0949531 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 41.8873 | 1.38400 | ||||||||
\(917\) | 67.5168 | 2.22960 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.4730 | 1.26911 | 0.634554 | − | 0.772878i | \(-0.281184\pi\) | ||||
0.634554 | + | 0.772878i | \(0.281184\pi\) | |||||||
\(920\) | 0.296282 | 0.00976813 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.16129 | 0.0711782 | ||||||||
\(923\) | 20.3813 | 0.670859 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.3816 | 1.52502 | ||||||||
\(926\) | 1.72485 | 0.0566822 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.5458 | 0.379009 | ||||||||
\(929\) | −34.7384 | −1.13973 | −0.569865 | − | 0.821738i | \(-0.693005\pi\) | ||||
−0.569865 | + | 0.821738i | \(0.693005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 59.1713 | 1.93926 | ||||||||
\(932\) | 38.8058 | 1.27113 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.250572 | 0.00819896 | ||||||||
\(935\) | −0.330309 | −0.0108022 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.40555 | 0.143923 | 0.0719616 | − | 0.997407i | \(-0.477074\pi\) | ||||
0.0719616 | + | 0.997407i | \(0.477074\pi\) | |||||||
\(938\) | −2.75470 | −0.0899442 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.05512 | 0.0344141 | ||||||||
\(941\) | 52.8759 | 1.72370 | 0.861852 | − | 0.507160i | \(-0.169305\pi\) | ||||
0.861852 | + | 0.507160i | \(0.169305\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.3434 | −1.05324 | ||||||||
\(944\) | −17.9556 | −0.584405 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.396534 | −0.0128924 | ||||||||
\(947\) | 19.7608 | 0.642138 | 0.321069 | − | 0.947056i | \(-0.395958\pi\) | ||||
0.321069 | + | 0.947056i | \(0.395958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.6017 | −0.473991 | ||||||||
\(950\) | −4.40918 | −0.143053 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.26799 | −0.235557 | ||||||||
\(953\) | −21.8127 | −0.706583 | −0.353291 | − | 0.935513i | \(-0.614938\pi\) | ||||
−0.353291 | + | 0.935513i | \(0.614938\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.50947 | −0.0488454 | ||||||||
\(956\) | 16.0017 | 0.517531 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.66023 | 0.150565 | ||||||||
\(959\) | −82.0909 | −2.65085 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.3718 | −0.850704 | ||||||||
\(962\) | −2.94360 | −0.0949055 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31.8698 | 1.02646 | ||||||||
\(965\) | 0.529157 | 0.0170342 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.5254 | 0.467107 | 0.233553 | − | 0.972344i | \(-0.424965\pi\) | ||||
0.233553 | + | 0.972344i | \(0.424965\pi\) | |||||||
\(968\) | −0.441081 | −0.0141769 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.0601366 | −0.00193087 | ||||||||
\(971\) | 21.6701 | 0.695426 | 0.347713 | − | 0.937601i | \(-0.386958\pi\) | ||||
0.347713 | + | 0.937601i | \(0.386958\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.83450 | 0.0908699 | ||||||||
\(974\) | 1.84689 | 0.0591783 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.92674 | −0.125692 | ||||||||
\(977\) | 41.3933 | 1.32429 | 0.662145 | − | 0.749376i | \(-0.269646\pi\) | ||||
0.662145 | + | 0.749376i | \(0.269646\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.47445 | 0.206924 | ||||||||
\(980\) | 1.12145 | 0.0358233 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.35926 | 0.0433757 | ||||||||
\(983\) | −42.7148 | −1.36239 | −0.681196 | − | 0.732101i | \(-0.738540\pi\) | ||||
−0.681196 | + | 0.732101i | \(0.738540\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.235360 | 0.00749919 | ||||||||
\(986\) | 4.21025 | 0.134082 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −45.4650 | −1.44644 | ||||||||
\(989\) | −31.6426 | −1.00618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.59075 | −0.0505317 | −0.0252659 | − | 0.999681i | \(-0.508043\pi\) | ||||
−0.0252659 | + | 0.999681i | \(0.508043\pi\) | |||||||
\(992\) | 2.83220 | 0.0899226 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.98670 | 0.0947323 | ||||||||
\(995\) | −0.428064 | −0.0135706 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.25667 | 0.103140 | 0.0515699 | − | 0.998669i | \(-0.483578\pi\) | ||||
0.0515699 | + | 0.998669i | \(0.483578\pi\) | |||||||
\(998\) | 1.70778 | 0.0540587 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.o.1.13 | yes | 25 | |
3.2 | odd | 2 | 6039.2.a.n.1.13 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.n.1.13 | ✓ | 25 | 3.2 | odd | 2 | ||
6039.2.a.o.1.13 | yes | 25 | 1.1 | even | 1 | trivial |