Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, 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("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 47x^{6} - 165x^{5} - 45x^{4} + 207x^{3} + 12x^{2} - 76x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.06506\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.06506 | −1.46022 | −0.730108 | − | 0.683331i | \(-0.760530\pi\) | ||||
−0.730108 | + | 0.683331i | \(0.760530\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.26446 | 1.13223 | ||||||||
\(5\) | −0.608853 | −0.272287 | −0.136144 | − | 0.990689i | \(-0.543471\pi\) | ||||
−0.136144 | + | 0.990689i | \(0.543471\pi\) | |||||||
\(6\) | 2.06506 | 0.843056 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.546135 | −0.193088 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.25732 | 0.397599 | ||||||||
\(11\) | −1.10243 | −0.332396 | −0.166198 | − | 0.986092i | \(-0.553149\pi\) | ||||
−0.166198 | + | 0.986092i | \(0.553149\pi\) | |||||||
\(12\) | −2.26446 | −0.653695 | ||||||||
\(13\) | 1.84712 | 0.512299 | 0.256149 | − | 0.966637i | \(-0.417546\pi\) | ||||
0.256149 | + | 0.966637i | \(0.417546\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.608853 | 0.157205 | ||||||||
\(16\) | −3.40113 | −0.850282 | ||||||||
\(17\) | 5.88576 | 1.42751 | 0.713753 | − | 0.700397i | \(-0.246994\pi\) | ||||
0.713753 | + | 0.700397i | \(0.246994\pi\) | |||||||
\(18\) | −2.06506 | −0.486739 | ||||||||
\(19\) | 1.08814 | 0.249637 | 0.124818 | − | 0.992180i | \(-0.460165\pi\) | ||||
0.124818 | + | 0.992180i | \(0.460165\pi\) | |||||||
\(20\) | −1.37873 | −0.308293 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.27659 | 0.485370 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0.546135 | 0.111479 | ||||||||
\(25\) | −4.62930 | −0.925860 | ||||||||
\(26\) | −3.81441 | −0.748067 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.804169 | −0.149330 | −0.0746652 | − | 0.997209i | \(-0.523789\pi\) | ||||
−0.0746652 | + | 0.997209i | \(0.523789\pi\) | |||||||
\(30\) | −1.25732 | −0.229554 | ||||||||
\(31\) | 8.77360 | 1.57579 | 0.787893 | − | 0.615813i | \(-0.211172\pi\) | ||||
0.787893 | + | 0.615813i | \(0.211172\pi\) | |||||||
\(32\) | 8.11580 | 1.43468 | ||||||||
\(33\) | 1.10243 | 0.191909 | ||||||||
\(34\) | −12.1544 | −2.08447 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.26446 | 0.377411 | ||||||||
\(37\) | 9.11528 | 1.49854 | 0.749271 | − | 0.662263i | \(-0.230404\pi\) | ||||
0.749271 | + | 0.662263i | \(0.230404\pi\) | |||||||
\(38\) | −2.24707 | −0.364524 | ||||||||
\(39\) | −1.84712 | −0.295776 | ||||||||
\(40\) | 0.332516 | 0.0525754 | ||||||||
\(41\) | −9.79559 | −1.52981 | −0.764907 | − | 0.644140i | \(-0.777215\pi\) | ||||
−0.764907 | + | 0.644140i | \(0.777215\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.23469 | 0.798283 | 0.399142 | − | 0.916889i | \(-0.369308\pi\) | ||||
0.399142 | + | 0.916889i | \(0.369308\pi\) | |||||||
\(44\) | −2.49642 | −0.376350 | ||||||||
\(45\) | −0.608853 | −0.0907625 | ||||||||
\(46\) | −2.06506 | −0.304476 | ||||||||
\(47\) | −5.90878 | −0.861885 | −0.430942 | − | 0.902379i | \(-0.641819\pi\) | ||||
−0.430942 | + | 0.902379i | \(0.641819\pi\) | |||||||
\(48\) | 3.40113 | 0.490911 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.55977 | 1.35196 | ||||||||
\(51\) | −5.88576 | −0.824171 | ||||||||
\(52\) | 4.18274 | 0.580041 | ||||||||
\(53\) | 4.51013 | 0.619515 | 0.309757 | − | 0.950816i | \(-0.399752\pi\) | ||||
0.309757 | + | 0.950816i | \(0.399752\pi\) | |||||||
\(54\) | 2.06506 | 0.281019 | ||||||||
\(55\) | 0.671220 | 0.0905072 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.08814 | −0.144128 | ||||||||
\(58\) | 1.66066 | 0.218055 | ||||||||
\(59\) | −7.40064 | −0.963481 | −0.481741 | − | 0.876314i | \(-0.659995\pi\) | ||||
−0.481741 | + | 0.876314i | \(0.659995\pi\) | |||||||
\(60\) | 1.37873 | 0.177993 | ||||||||
\(61\) | 5.02768 | 0.643729 | 0.321864 | − | 0.946786i | \(-0.395690\pi\) | ||||
0.321864 | + | 0.946786i | \(0.395690\pi\) | |||||||
\(62\) | −18.1180 | −2.30099 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.95734 | −1.24467 | ||||||||
\(65\) | −1.12462 | −0.139492 | ||||||||
\(66\) | −2.27659 | −0.280229 | ||||||||
\(67\) | 2.06305 | 0.252042 | 0.126021 | − | 0.992028i | \(-0.459779\pi\) | ||||
0.126021 | + | 0.992028i | \(0.459779\pi\) | |||||||
\(68\) | 13.3281 | 1.61627 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.30092 | 0.510425 | 0.255213 | − | 0.966885i | \(-0.417855\pi\) | ||||
0.255213 | + | 0.966885i | \(0.417855\pi\) | |||||||
\(72\) | −0.546135 | −0.0643627 | ||||||||
\(73\) | −1.15613 | −0.135315 | −0.0676577 | − | 0.997709i | \(-0.521553\pi\) | ||||
−0.0676577 | + | 0.997709i | \(0.521553\pi\) | |||||||
\(74\) | −18.8236 | −2.18820 | ||||||||
\(75\) | 4.62930 | 0.534545 | ||||||||
\(76\) | 2.46406 | 0.282647 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.81441 | 0.431897 | ||||||||
\(79\) | 15.1716 | 1.70694 | 0.853469 | − | 0.521144i | \(-0.174495\pi\) | ||||
0.853469 | + | 0.521144i | \(0.174495\pi\) | |||||||
\(80\) | 2.07079 | 0.231521 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.2285 | 2.23386 | ||||||||
\(83\) | −10.7196 | −1.17663 | −0.588315 | − | 0.808632i | \(-0.700209\pi\) | ||||
−0.588315 | + | 0.808632i | \(0.700209\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.58356 | −0.388692 | ||||||||
\(86\) | −10.8099 | −1.16567 | ||||||||
\(87\) | 0.804169 | 0.0862160 | ||||||||
\(88\) | 0.602078 | 0.0641817 | ||||||||
\(89\) | −7.92167 | −0.839695 | −0.419847 | − | 0.907595i | \(-0.637916\pi\) | ||||
−0.419847 | + | 0.907595i | \(0.637916\pi\) | |||||||
\(90\) | 1.25732 | 0.132533 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.26446 | 0.236087 | ||||||||
\(93\) | −8.77360 | −0.909780 | ||||||||
\(94\) | 12.2020 | 1.25854 | ||||||||
\(95\) | −0.662518 | −0.0679729 | ||||||||
\(96\) | −8.11580 | −0.828315 | ||||||||
\(97\) | −17.0648 | −1.73267 | −0.866336 | − | 0.499461i | \(-0.833531\pi\) | ||||
−0.866336 | + | 0.499461i | \(0.833531\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.10243 | −0.110799 | ||||||||
\(100\) | −10.4829 | −1.04829 | ||||||||
\(101\) | −8.56557 | −0.852306 | −0.426153 | − | 0.904651i | \(-0.640131\pi\) | ||||
−0.426153 | + | 0.904651i | \(0.640131\pi\) | |||||||
\(102\) | 12.1544 | 1.20347 | ||||||||
\(103\) | 10.4373 | 1.02842 | 0.514208 | − | 0.857666i | \(-0.328086\pi\) | ||||
0.514208 | + | 0.857666i | \(0.328086\pi\) | |||||||
\(104\) | −1.00878 | −0.0989187 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.31369 | −0.904625 | ||||||||
\(107\) | −8.07268 | −0.780415 | −0.390208 | − | 0.920727i | \(-0.627597\pi\) | ||||
−0.390208 | + | 0.920727i | \(0.627597\pi\) | |||||||
\(108\) | −2.26446 | −0.217898 | ||||||||
\(109\) | 3.81163 | 0.365088 | 0.182544 | − | 0.983198i | \(-0.441567\pi\) | ||||
0.182544 | + | 0.983198i | \(0.441567\pi\) | |||||||
\(110\) | −1.38611 | −0.132160 | ||||||||
\(111\) | −9.11528 | −0.865184 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.89428 | 0.836703 | 0.418352 | − | 0.908285i | \(-0.362608\pi\) | ||||
0.418352 | + | 0.908285i | \(0.362608\pi\) | |||||||
\(114\) | 2.24707 | 0.210458 | ||||||||
\(115\) | −0.608853 | −0.0567758 | ||||||||
\(116\) | −1.82101 | −0.169077 | ||||||||
\(117\) | 1.84712 | 0.170766 | ||||||||
\(118\) | 15.2827 | 1.40689 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.332516 | −0.0303544 | ||||||||
\(121\) | −9.78464 | −0.889513 | ||||||||
\(122\) | −10.3825 | −0.939984 | ||||||||
\(123\) | 9.79559 | 0.883239 | ||||||||
\(124\) | 19.8675 | 1.78416 | ||||||||
\(125\) | 5.86283 | 0.524387 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.91043 | 0.701937 | 0.350969 | − | 0.936387i | \(-0.385852\pi\) | ||||
0.350969 | + | 0.936387i | \(0.385852\pi\) | |||||||
\(128\) | 4.33089 | 0.382800 | ||||||||
\(129\) | −5.23469 | −0.460889 | ||||||||
\(130\) | 2.32241 | 0.203689 | ||||||||
\(131\) | 0.475706 | 0.0415627 | 0.0207813 | − | 0.999784i | \(-0.493385\pi\) | ||||
0.0207813 | + | 0.999784i | \(0.493385\pi\) | |||||||
\(132\) | 2.49642 | 0.217286 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.26033 | −0.368036 | ||||||||
\(135\) | 0.608853 | 0.0524017 | ||||||||
\(136\) | −3.21442 | −0.275634 | ||||||||
\(137\) | −8.27302 | −0.706812 | −0.353406 | − | 0.935470i | \(-0.614977\pi\) | ||||
−0.353406 | + | 0.935470i | \(0.614977\pi\) | |||||||
\(138\) | 2.06506 | 0.175789 | ||||||||
\(139\) | −2.48191 | −0.210513 | −0.105257 | − | 0.994445i | \(-0.533566\pi\) | ||||
−0.105257 | + | 0.994445i | \(0.533566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.90878 | 0.497609 | ||||||||
\(142\) | −8.88165 | −0.745331 | ||||||||
\(143\) | −2.03633 | −0.170286 | ||||||||
\(144\) | −3.40113 | −0.283427 | ||||||||
\(145\) | 0.489621 | 0.0406608 | ||||||||
\(146\) | 2.38749 | 0.197590 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.6412 | 1.69670 | ||||||||
\(149\) | 20.5957 | 1.68726 | 0.843631 | − | 0.536924i | \(-0.180414\pi\) | ||||
0.843631 | + | 0.536924i | \(0.180414\pi\) | |||||||
\(150\) | −9.55977 | −0.780552 | ||||||||
\(151\) | 12.7948 | 1.04123 | 0.520613 | − | 0.853793i | \(-0.325703\pi\) | ||||
0.520613 | + | 0.853793i | \(0.325703\pi\) | |||||||
\(152\) | −0.594272 | −0.0482018 | ||||||||
\(153\) | 5.88576 | 0.475835 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.34183 | −0.429066 | ||||||||
\(156\) | −4.18274 | −0.334887 | ||||||||
\(157\) | −4.57005 | −0.364730 | −0.182365 | − | 0.983231i | \(-0.558375\pi\) | ||||
−0.182365 | + | 0.983231i | \(0.558375\pi\) | |||||||
\(158\) | −31.3302 | −2.49250 | ||||||||
\(159\) | −4.51013 | −0.357677 | ||||||||
\(160\) | −4.94133 | −0.390646 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.06506 | −0.162246 | ||||||||
\(163\) | −21.7544 | −1.70393 | −0.851967 | − | 0.523596i | \(-0.824590\pi\) | ||||
−0.851967 | + | 0.523596i | \(0.824590\pi\) | |||||||
\(164\) | −22.1818 | −1.73211 | ||||||||
\(165\) | −0.671220 | −0.0522544 | ||||||||
\(166\) | 22.1366 | 1.71814 | ||||||||
\(167\) | −3.92341 | −0.303602 | −0.151801 | − | 0.988411i | \(-0.548507\pi\) | ||||
−0.151801 | + | 0.988411i | \(0.548507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.58815 | −0.737550 | ||||||||
\(170\) | 7.40026 | 0.567574 | ||||||||
\(171\) | 1.08814 | 0.0832122 | ||||||||
\(172\) | 11.8538 | 0.903842 | ||||||||
\(173\) | −24.0171 | −1.82599 | −0.912993 | − | 0.407976i | \(-0.866235\pi\) | ||||
−0.912993 | + | 0.407976i | \(0.866235\pi\) | |||||||
\(174\) | −1.66066 | −0.125894 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.74952 | 0.282630 | ||||||||
\(177\) | 7.40064 | 0.556266 | ||||||||
\(178\) | 16.3587 | 1.22614 | ||||||||
\(179\) | 20.1690 | 1.50750 | 0.753752 | − | 0.657159i | \(-0.228242\pi\) | ||||
0.753752 | + | 0.657159i | \(0.228242\pi\) | |||||||
\(180\) | −1.37873 | −0.102764 | ||||||||
\(181\) | 16.7087 | 1.24195 | 0.620973 | − | 0.783832i | \(-0.286738\pi\) | ||||
0.620973 | + | 0.783832i | \(0.286738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.02768 | −0.371657 | ||||||||
\(184\) | −0.546135 | −0.0402616 | ||||||||
\(185\) | −5.54986 | −0.408034 | ||||||||
\(186\) | 18.1180 | 1.32848 | ||||||||
\(187\) | −6.48865 | −0.474497 | ||||||||
\(188\) | −13.3802 | −0.975854 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.36814 | 0.0992551 | ||||||||
\(191\) | 3.50958 | 0.253944 | 0.126972 | − | 0.991906i | \(-0.459474\pi\) | ||||
0.126972 | + | 0.991906i | \(0.459474\pi\) | |||||||
\(192\) | 9.95734 | 0.718609 | ||||||||
\(193\) | −13.6422 | −0.981987 | −0.490993 | − | 0.871163i | \(-0.663366\pi\) | ||||
−0.490993 | + | 0.871163i | \(0.663366\pi\) | |||||||
\(194\) | 35.2399 | 2.53008 | ||||||||
\(195\) | 1.12462 | 0.0805360 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.4651 | −0.959349 | −0.479675 | − | 0.877447i | \(-0.659245\pi\) | ||||
−0.479675 | + | 0.877447i | \(0.659245\pi\) | |||||||
\(198\) | 2.27659 | 0.161790 | ||||||||
\(199\) | 14.2974 | 1.01352 | 0.506760 | − | 0.862087i | \(-0.330843\pi\) | ||||
0.506760 | + | 0.862087i | \(0.330843\pi\) | |||||||
\(200\) | 2.52822 | 0.178772 | ||||||||
\(201\) | −2.06305 | −0.145517 | ||||||||
\(202\) | 17.6884 | 1.24455 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −13.3281 | −0.933153 | ||||||||
\(205\) | 5.96408 | 0.416549 | ||||||||
\(206\) | −21.5536 | −1.50171 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −6.28229 | −0.435598 | ||||||||
\(209\) | −1.19960 | −0.0829782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.83108 | 0.194900 | 0.0974499 | − | 0.995240i | \(-0.468931\pi\) | ||||
0.0974499 | + | 0.995240i | \(0.468931\pi\) | |||||||
\(212\) | 10.2130 | 0.701435 | ||||||||
\(213\) | −4.30092 | −0.294694 | ||||||||
\(214\) | 16.6706 | 1.13958 | ||||||||
\(215\) | −3.18716 | −0.217362 | ||||||||
\(216\) | 0.546135 | 0.0371598 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.87123 | −0.533107 | ||||||||
\(219\) | 1.15613 | 0.0781243 | ||||||||
\(220\) | 1.51995 | 0.102475 | ||||||||
\(221\) | 10.8717 | 0.731310 | ||||||||
\(222\) | 18.8236 | 1.26336 | ||||||||
\(223\) | 4.78780 | 0.320615 | 0.160307 | − | 0.987067i | \(-0.448751\pi\) | ||||
0.160307 | + | 0.987067i | \(0.448751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.62930 | −0.308620 | ||||||||
\(226\) | −18.3672 | −1.22177 | ||||||||
\(227\) | 19.2951 | 1.28066 | 0.640331 | − | 0.768099i | \(-0.278797\pi\) | ||||
0.640331 | + | 0.768099i | \(0.278797\pi\) | |||||||
\(228\) | −2.46406 | −0.163186 | ||||||||
\(229\) | 8.12954 | 0.537215 | 0.268607 | − | 0.963250i | \(-0.413437\pi\) | ||||
0.268607 | + | 0.963250i | \(0.413437\pi\) | |||||||
\(230\) | 1.25732 | 0.0829050 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.439185 | 0.0288339 | ||||||||
\(233\) | 7.94940 | 0.520783 | 0.260391 | − | 0.965503i | \(-0.416148\pi\) | ||||
0.260391 | + | 0.965503i | \(0.416148\pi\) | |||||||
\(234\) | −3.81441 | −0.249356 | ||||||||
\(235\) | 3.59758 | 0.234680 | ||||||||
\(236\) | −16.7585 | −1.09088 | ||||||||
\(237\) | −15.1716 | −0.985501 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.7789 | 1.02065 | 0.510326 | − | 0.859981i | \(-0.329525\pi\) | ||||
0.510326 | + | 0.859981i | \(0.329525\pi\) | |||||||
\(240\) | −2.07079 | −0.133669 | ||||||||
\(241\) | −11.2656 | −0.725680 | −0.362840 | − | 0.931851i | \(-0.618193\pi\) | ||||
−0.362840 | + | 0.931851i | \(0.618193\pi\) | |||||||
\(242\) | 20.2059 | 1.29888 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.3850 | 0.728851 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.2285 | −1.28972 | ||||||||
\(247\) | 2.00993 | 0.127889 | ||||||||
\(248\) | −4.79157 | −0.304265 | ||||||||
\(249\) | 10.7196 | 0.679328 | ||||||||
\(250\) | −12.1071 | −0.765719 | ||||||||
\(251\) | −2.27255 | −0.143442 | −0.0717209 | − | 0.997425i | \(-0.522849\pi\) | ||||
−0.0717209 | + | 0.997425i | \(0.522849\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.10243 | −0.0693094 | ||||||||
\(254\) | −16.3355 | −1.02498 | ||||||||
\(255\) | 3.58356 | 0.224411 | ||||||||
\(256\) | 10.9711 | 0.685697 | ||||||||
\(257\) | −0.871285 | −0.0543492 | −0.0271746 | − | 0.999631i | \(-0.508651\pi\) | ||||
−0.0271746 | + | 0.999631i | \(0.508651\pi\) | |||||||
\(258\) | 10.8099 | 0.672998 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.54667 | −0.157938 | ||||||||
\(261\) | −0.804169 | −0.0497768 | ||||||||
\(262\) | −0.982361 | −0.0606905 | ||||||||
\(263\) | −5.33476 | −0.328956 | −0.164478 | − | 0.986381i | \(-0.552594\pi\) | ||||
−0.164478 | + | 0.986381i | \(0.552594\pi\) | |||||||
\(264\) | −0.602078 | −0.0370553 | ||||||||
\(265\) | −2.74601 | −0.168686 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.92167 | 0.484798 | ||||||||
\(268\) | 4.67171 | 0.285370 | ||||||||
\(269\) | 22.7388 | 1.38641 | 0.693203 | − | 0.720742i | \(-0.256199\pi\) | ||||
0.693203 | + | 0.720742i | \(0.256199\pi\) | |||||||
\(270\) | −1.25732 | −0.0765179 | ||||||||
\(271\) | −6.42151 | −0.390079 | −0.195039 | − | 0.980795i | \(-0.562483\pi\) | ||||
−0.195039 | + | 0.980795i | \(0.562483\pi\) | |||||||
\(272\) | −20.0182 | −1.21378 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.0843 | 1.03210 | ||||||||
\(275\) | 5.10349 | 0.307752 | ||||||||
\(276\) | −2.26446 | −0.136305 | ||||||||
\(277\) | 14.0353 | 0.843298 | 0.421649 | − | 0.906759i | \(-0.361452\pi\) | ||||
0.421649 | + | 0.906759i | \(0.361452\pi\) | |||||||
\(278\) | 5.12530 | 0.307395 | ||||||||
\(279\) | 8.77360 | 0.525262 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.5278 | 1.46321 | 0.731603 | − | 0.681731i | \(-0.238773\pi\) | ||||
0.731603 | + | 0.681731i | \(0.238773\pi\) | |||||||
\(282\) | −12.2020 | −0.726617 | ||||||||
\(283\) | −4.39941 | −0.261518 | −0.130759 | − | 0.991414i | \(-0.541741\pi\) | ||||
−0.130759 | + | 0.991414i | \(0.541741\pi\) | |||||||
\(284\) | 9.73928 | 0.577920 | ||||||||
\(285\) | 0.662518 | 0.0392442 | ||||||||
\(286\) | 4.20513 | 0.248655 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.11580 | 0.478228 | ||||||||
\(289\) | 17.6422 | 1.03777 | ||||||||
\(290\) | −1.01110 | −0.0593736 | ||||||||
\(291\) | 17.0648 | 1.00036 | ||||||||
\(292\) | −2.61803 | −0.153208 | ||||||||
\(293\) | 13.3413 | 0.779407 | 0.389704 | − | 0.920940i | \(-0.372577\pi\) | ||||
0.389704 | + | 0.920940i | \(0.372577\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.50590 | 0.262344 | ||||||||
\(296\) | −4.97818 | −0.289351 | ||||||||
\(297\) | 1.10243 | 0.0639696 | ||||||||
\(298\) | −42.5312 | −2.46377 | ||||||||
\(299\) | 1.84712 | 0.106822 | ||||||||
\(300\) | 10.4829 | 0.605230 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −26.4220 | −1.52042 | ||||||||
\(303\) | 8.56557 | 0.492079 | ||||||||
\(304\) | −3.70091 | −0.212262 | ||||||||
\(305\) | −3.06112 | −0.175279 | ||||||||
\(306\) | −12.1544 | −0.694823 | ||||||||
\(307\) | 24.5499 | 1.40114 | 0.700569 | − | 0.713585i | \(-0.252930\pi\) | ||||
0.700569 | + | 0.713585i | \(0.252930\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.4373 | −0.593756 | ||||||||
\(310\) | 11.0312 | 0.626530 | ||||||||
\(311\) | 26.0773 | 1.47871 | 0.739355 | − | 0.673315i | \(-0.235130\pi\) | ||||
0.739355 | + | 0.673315i | \(0.235130\pi\) | |||||||
\(312\) | 1.00878 | 0.0571108 | ||||||||
\(313\) | 24.1973 | 1.36771 | 0.683857 | − | 0.729616i | \(-0.260301\pi\) | ||||
0.683857 | + | 0.729616i | \(0.260301\pi\) | |||||||
\(314\) | 9.43741 | 0.532584 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 34.3555 | 1.93265 | ||||||||
\(317\) | 3.60976 | 0.202744 | 0.101372 | − | 0.994849i | \(-0.467677\pi\) | ||||
0.101372 | + | 0.994849i | \(0.467677\pi\) | |||||||
\(318\) | 9.31369 | 0.522286 | ||||||||
\(319\) | 0.886542 | 0.0496368 | ||||||||
\(320\) | 6.06256 | 0.338907 | ||||||||
\(321\) | 8.07268 | 0.450573 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.40453 | 0.356358 | ||||||||
\(324\) | 2.26446 | 0.125804 | ||||||||
\(325\) | −8.55087 | −0.474317 | ||||||||
\(326\) | 44.9240 | 2.48811 | ||||||||
\(327\) | −3.81163 | −0.210784 | ||||||||
\(328\) | 5.34972 | 0.295389 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.38611 | 0.0763027 | ||||||||
\(331\) | 8.23405 | 0.452584 | 0.226292 | − | 0.974059i | \(-0.427340\pi\) | ||||
0.226292 | + | 0.974059i | \(0.427340\pi\) | |||||||
\(332\) | −24.2742 | −1.33222 | ||||||||
\(333\) | 9.11528 | 0.499514 | ||||||||
\(334\) | 8.10206 | 0.443325 | ||||||||
\(335\) | −1.25610 | −0.0686279 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.1865 | 1.42647 | 0.713235 | − | 0.700925i | \(-0.247229\pi\) | ||||
0.713235 | + | 0.700925i | \(0.247229\pi\) | |||||||
\(338\) | 19.8001 | 1.07698 | ||||||||
\(339\) | −8.89428 | −0.483071 | ||||||||
\(340\) | −8.11485 | −0.440090 | ||||||||
\(341\) | −9.67231 | −0.523785 | ||||||||
\(342\) | −2.24707 | −0.121508 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.85885 | −0.154139 | ||||||||
\(345\) | 0.608853 | 0.0327795 | ||||||||
\(346\) | 49.5967 | 2.66633 | ||||||||
\(347\) | −5.92735 | −0.318197 | −0.159098 | − | 0.987263i | \(-0.550859\pi\) | ||||
−0.159098 | + | 0.987263i | \(0.550859\pi\) | |||||||
\(348\) | 1.82101 | 0.0976165 | ||||||||
\(349\) | 29.6319 | 1.58616 | 0.793080 | − | 0.609118i | \(-0.208476\pi\) | ||||
0.793080 | + | 0.609118i | \(0.208476\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.84712 | −0.0985919 | ||||||||
\(352\) | −8.94712 | −0.476883 | ||||||||
\(353\) | −14.2388 | −0.757853 | −0.378926 | − | 0.925427i | \(-0.623707\pi\) | ||||
−0.378926 | + | 0.925427i | \(0.623707\pi\) | |||||||
\(354\) | −15.2827 | −0.812269 | ||||||||
\(355\) | −2.61863 | −0.138982 | ||||||||
\(356\) | −17.9383 | −0.950730 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −41.6502 | −2.20128 | ||||||||
\(359\) | 2.78230 | 0.146844 | 0.0734220 | − | 0.997301i | \(-0.476608\pi\) | ||||
0.0734220 | + | 0.997301i | \(0.476608\pi\) | |||||||
\(360\) | 0.332516 | 0.0175251 | ||||||||
\(361\) | −17.8159 | −0.937682 | ||||||||
\(362\) | −34.5044 | −1.81351 | ||||||||
\(363\) | 9.78464 | 0.513561 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.703916 | 0.0368447 | ||||||||
\(366\) | 10.3825 | 0.542700 | ||||||||
\(367\) | −6.66447 | −0.347883 | −0.173941 | − | 0.984756i | \(-0.555650\pi\) | ||||
−0.173941 | + | 0.984756i | \(0.555650\pi\) | |||||||
\(368\) | −3.40113 | −0.177296 | ||||||||
\(369\) | −9.79559 | −0.509938 | ||||||||
\(370\) | 11.4608 | 0.595818 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −19.8675 | −1.03008 | ||||||||
\(373\) | −19.0824 | −0.988048 | −0.494024 | − | 0.869448i | \(-0.664475\pi\) | ||||
−0.494024 | + | 0.869448i | \(0.664475\pi\) | |||||||
\(374\) | 13.3994 | 0.692869 | ||||||||
\(375\) | −5.86283 | −0.302755 | ||||||||
\(376\) | 3.22700 | 0.166420 | ||||||||
\(377\) | −1.48540 | −0.0765018 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.2631 | 0.681282 | 0.340641 | − | 0.940193i | \(-0.389356\pi\) | ||||
0.340641 | + | 0.940193i | \(0.389356\pi\) | |||||||
\(380\) | −1.50025 | −0.0769611 | ||||||||
\(381\) | −7.91043 | −0.405264 | ||||||||
\(382\) | −7.24748 | −0.370813 | ||||||||
\(383\) | −3.11602 | −0.159221 | −0.0796105 | − | 0.996826i | \(-0.525368\pi\) | ||||
−0.0796105 | + | 0.996826i | \(0.525368\pi\) | |||||||
\(384\) | −4.33089 | −0.221010 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 28.1719 | 1.43391 | ||||||||
\(387\) | 5.23469 | 0.266094 | ||||||||
\(388\) | −38.6427 | −1.96179 | ||||||||
\(389\) | −9.98409 | −0.506214 | −0.253107 | − | 0.967438i | \(-0.581452\pi\) | ||||
−0.253107 | + | 0.967438i | \(0.581452\pi\) | |||||||
\(390\) | −2.32241 | −0.117600 | ||||||||
\(391\) | 5.88576 | 0.297656 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.475706 | −0.0239962 | ||||||||
\(394\) | 27.8062 | 1.40086 | ||||||||
\(395\) | −9.23727 | −0.464777 | ||||||||
\(396\) | −2.49642 | −0.125450 | ||||||||
\(397\) | 5.64444 | 0.283286 | 0.141643 | − | 0.989918i | \(-0.454761\pi\) | ||||
0.141643 | + | 0.989918i | \(0.454761\pi\) | |||||||
\(398\) | −29.5251 | −1.47996 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.7448 | 0.787242 | ||||||||
\(401\) | 38.5622 | 1.92571 | 0.962853 | − | 0.270028i | \(-0.0870328\pi\) | ||||
0.962853 | + | 0.270028i | \(0.0870328\pi\) | |||||||
\(402\) | 4.26033 | 0.212486 | ||||||||
\(403\) | 16.2059 | 0.807273 | ||||||||
\(404\) | −19.3964 | −0.965008 | ||||||||
\(405\) | −0.608853 | −0.0302542 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0490 | −0.498110 | ||||||||
\(408\) | 3.21442 | 0.159138 | ||||||||
\(409\) | −36.8071 | −1.81999 | −0.909997 | − | 0.414614i | \(-0.863917\pi\) | ||||
−0.909997 | + | 0.414614i | \(0.863917\pi\) | |||||||
\(410\) | −12.3162 | −0.608252 | ||||||||
\(411\) | 8.27302 | 0.408078 | ||||||||
\(412\) | 23.6349 | 1.16441 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.06506 | −0.101492 | ||||||||
\(415\) | 6.52667 | 0.320382 | ||||||||
\(416\) | 14.9908 | 0.734987 | ||||||||
\(417\) | 2.48191 | 0.121540 | ||||||||
\(418\) | 2.47725 | 0.121166 | ||||||||
\(419\) | −6.45390 | −0.315293 | −0.157647 | − | 0.987496i | \(-0.550391\pi\) | ||||
−0.157647 | + | 0.987496i | \(0.550391\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.9287 | 1.45863 | 0.729317 | − | 0.684176i | \(-0.239838\pi\) | ||||
0.729317 | + | 0.684176i | \(0.239838\pi\) | |||||||
\(422\) | −5.84635 | −0.284596 | ||||||||
\(423\) | −5.90878 | −0.287295 | ||||||||
\(424\) | −2.46314 | −0.119621 | ||||||||
\(425\) | −27.2469 | −1.32167 | ||||||||
\(426\) | 8.88165 | 0.430317 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −18.2803 | −0.883612 | ||||||||
\(429\) | 2.03633 | 0.0983147 | ||||||||
\(430\) | 6.58167 | 0.317396 | ||||||||
\(431\) | 7.74839 | 0.373227 | 0.186613 | − | 0.982433i | \(-0.440249\pi\) | ||||
0.186613 | + | 0.982433i | \(0.440249\pi\) | |||||||
\(432\) | 3.40113 | 0.163637 | ||||||||
\(433\) | 5.17696 | 0.248789 | 0.124394 | − | 0.992233i | \(-0.460301\pi\) | ||||
0.124394 | + | 0.992233i | \(0.460301\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.489621 | −0.0234755 | ||||||||
\(436\) | 8.63130 | 0.413364 | ||||||||
\(437\) | 1.08814 | 0.0520528 | ||||||||
\(438\) | −2.38749 | −0.114078 | ||||||||
\(439\) | −30.2921 | −1.44576 | −0.722881 | − | 0.690973i | \(-0.757182\pi\) | ||||
−0.722881 | + | 0.690973i | \(0.757182\pi\) | |||||||
\(440\) | −0.366577 | −0.0174759 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.4507 | −1.06787 | ||||||||
\(443\) | 38.2021 | 1.81504 | 0.907519 | − | 0.420012i | \(-0.137974\pi\) | ||||
0.907519 | + | 0.420012i | \(0.137974\pi\) | |||||||
\(444\) | −20.6412 | −0.979589 | ||||||||
\(445\) | 4.82313 | 0.228638 | ||||||||
\(446\) | −9.88708 | −0.468167 | ||||||||
\(447\) | −20.5957 | −0.974141 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.95568 | 0.139487 | 0.0697435 | − | 0.997565i | \(-0.477782\pi\) | ||||
0.0697435 | + | 0.997565i | \(0.477782\pi\) | |||||||
\(450\) | 9.55977 | 0.450652 | ||||||||
\(451\) | 10.7990 | 0.508504 | ||||||||
\(452\) | 20.1408 | 0.947343 | ||||||||
\(453\) | −12.7948 | −0.601152 | ||||||||
\(454\) | −39.8455 | −1.87004 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.594272 | 0.0278293 | ||||||||
\(457\) | 17.6954 | 0.827758 | 0.413879 | − | 0.910332i | \(-0.364174\pi\) | ||||
0.413879 | + | 0.910332i | \(0.364174\pi\) | |||||||
\(458\) | −16.7880 | −0.784450 | ||||||||
\(459\) | −5.88576 | −0.274724 | ||||||||
\(460\) | −1.37873 | −0.0642834 | ||||||||
\(461\) | −11.7447 | −0.547005 | −0.273503 | − | 0.961871i | \(-0.588182\pi\) | ||||
−0.273503 | + | 0.961871i | \(0.588182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.0872 | 1.25885 | 0.629424 | − | 0.777062i | \(-0.283291\pi\) | ||||
0.629424 | + | 0.777062i | \(0.283291\pi\) | |||||||
\(464\) | 2.73508 | 0.126973 | ||||||||
\(465\) | 5.34183 | 0.247722 | ||||||||
\(466\) | −16.4160 | −0.760455 | ||||||||
\(467\) | 23.1520 | 1.07135 | 0.535673 | − | 0.844426i | \(-0.320058\pi\) | ||||
0.535673 | + | 0.844426i | \(0.320058\pi\) | |||||||
\(468\) | 4.18274 | 0.193347 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.42921 | −0.342684 | ||||||||
\(471\) | 4.57005 | 0.210577 | ||||||||
\(472\) | 4.04175 | 0.186037 | ||||||||
\(473\) | −5.77090 | −0.265346 | ||||||||
\(474\) | 31.3302 | 1.43904 | ||||||||
\(475\) | −5.03733 | −0.231128 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.51013 | 0.206505 | ||||||||
\(478\) | −32.5843 | −1.49037 | ||||||||
\(479\) | 22.3675 | 1.02200 | 0.510999 | − | 0.859581i | \(-0.329275\pi\) | ||||
0.510999 | + | 0.859581i | \(0.329275\pi\) | |||||||
\(480\) | 4.94133 | 0.225540 | ||||||||
\(481\) | 16.8370 | 0.767701 | ||||||||
\(482\) | 23.2641 | 1.05965 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22.1570 | −1.00714 | ||||||||
\(485\) | 10.3900 | 0.471785 | ||||||||
\(486\) | 2.06506 | 0.0936729 | ||||||||
\(487\) | 41.8522 | 1.89650 | 0.948252 | − | 0.317518i | \(-0.102849\pi\) | ||||
0.948252 | + | 0.317518i | \(0.102849\pi\) | |||||||
\(488\) | −2.74580 | −0.124296 | ||||||||
\(489\) | 21.7544 | 0.983766 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.2658 | 0.734063 | 0.367032 | − | 0.930209i | \(-0.380374\pi\) | ||||
0.367032 | + | 0.930209i | \(0.380374\pi\) | |||||||
\(492\) | 22.1818 | 1.00003 | ||||||||
\(493\) | −4.73315 | −0.213170 | ||||||||
\(494\) | −4.15061 | −0.186745 | ||||||||
\(495\) | 0.671220 | 0.0301691 | ||||||||
\(496\) | −29.8401 | −1.33986 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −22.1366 | −0.991966 | ||||||||
\(499\) | −19.8250 | −0.887489 | −0.443744 | − | 0.896153i | \(-0.646350\pi\) | ||||
−0.443744 | + | 0.896153i | \(0.646350\pi\) | |||||||
\(500\) | 13.2762 | 0.593728 | ||||||||
\(501\) | 3.92341 | 0.175285 | ||||||||
\(502\) | 4.69294 | 0.209456 | ||||||||
\(503\) | 9.18201 | 0.409406 | 0.204703 | − | 0.978824i | \(-0.434377\pi\) | ||||
0.204703 | + | 0.978824i | \(0.434377\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.21517 | 0.232072 | ||||||||
\(506\) | 2.27659 | 0.101207 | ||||||||
\(507\) | 9.58815 | 0.425825 | ||||||||
\(508\) | 17.9129 | 0.794756 | ||||||||
\(509\) | −32.8014 | −1.45390 | −0.726948 | − | 0.686692i | \(-0.759062\pi\) | ||||
−0.726948 | + | 0.686692i | \(0.759062\pi\) | |||||||
\(510\) | −7.40026 | −0.327689 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −31.3178 | −1.38407 | ||||||||
\(513\) | −1.08814 | −0.0480426 | ||||||||
\(514\) | 1.79925 | 0.0793617 | ||||||||
\(515\) | −6.35477 | −0.280025 | ||||||||
\(516\) | −11.8538 | −0.521834 | ||||||||
\(517\) | 6.51404 | 0.286487 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.0171 | 1.05423 | ||||||||
\(520\) | 0.614197 | 0.0269343 | ||||||||
\(521\) | 6.86356 | 0.300698 | 0.150349 | − | 0.988633i | \(-0.451960\pi\) | ||||
0.150349 | + | 0.988633i | \(0.451960\pi\) | |||||||
\(522\) | 1.66066 | 0.0726849 | ||||||||
\(523\) | 9.76622 | 0.427047 | 0.213524 | − | 0.976938i | \(-0.431506\pi\) | ||||
0.213524 | + | 0.976938i | \(0.431506\pi\) | |||||||
\(524\) | 1.07722 | 0.0470586 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.0166 | 0.480347 | ||||||||
\(527\) | 51.6393 | 2.24944 | ||||||||
\(528\) | −3.74952 | −0.163177 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 5.67067 | 0.246318 | ||||||||
\(531\) | −7.40064 | −0.321160 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.0936 | −0.783722 | ||||||||
\(534\) | −16.3587 | −0.707910 | ||||||||
\(535\) | 4.91508 | 0.212497 | ||||||||
\(536\) | −1.12671 | −0.0486663 | ||||||||
\(537\) | −20.1690 | −0.870357 | ||||||||
\(538\) | −46.9568 | −2.02445 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.37873 | 0.0593309 | ||||||||
\(541\) | −4.64207 | −0.199578 | −0.0997891 | − | 0.995009i | \(-0.531817\pi\) | ||||
−0.0997891 | + | 0.995009i | \(0.531817\pi\) | |||||||
\(542\) | 13.2608 | 0.569600 | ||||||||
\(543\) | −16.7087 | −0.717038 | ||||||||
\(544\) | 47.7676 | 2.04802 | ||||||||
\(545\) | −2.32072 | −0.0994088 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.6976 | 0.927722 | 0.463861 | − | 0.885908i | \(-0.346464\pi\) | ||||
0.463861 | + | 0.885908i | \(0.346464\pi\) | |||||||
\(548\) | −18.7340 | −0.800275 | ||||||||
\(549\) | 5.02768 | 0.214576 | ||||||||
\(550\) | −10.5390 | −0.449385 | ||||||||
\(551\) | −0.875049 | −0.0372783 | ||||||||
\(552\) | 0.546135 | 0.0232451 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −28.9836 | −1.23140 | ||||||||
\(555\) | 5.54986 | 0.235579 | ||||||||
\(556\) | −5.62021 | −0.238350 | ||||||||
\(557\) | −32.1596 | −1.36265 | −0.681323 | − | 0.731983i | \(-0.738595\pi\) | ||||
−0.681323 | + | 0.731983i | \(0.738595\pi\) | |||||||
\(558\) | −18.1180 | −0.766996 | ||||||||
\(559\) | 9.66910 | 0.408960 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.48865 | 0.273951 | ||||||||
\(562\) | −50.6513 | −2.13660 | ||||||||
\(563\) | −12.3159 | −0.519055 | −0.259528 | − | 0.965736i | \(-0.583567\pi\) | ||||
−0.259528 | + | 0.965736i | \(0.583567\pi\) | |||||||
\(564\) | 13.3802 | 0.563409 | ||||||||
\(565\) | −5.41531 | −0.227824 | ||||||||
\(566\) | 9.08503 | 0.381872 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.34888 | −0.0985570 | ||||||||
\(569\) | −26.2350 | −1.09983 | −0.549914 | − | 0.835221i | \(-0.685340\pi\) | ||||
−0.549914 | + | 0.835221i | \(0.685340\pi\) | |||||||
\(570\) | −1.36814 | −0.0573050 | ||||||||
\(571\) | −5.59829 | −0.234281 | −0.117141 | − | 0.993115i | \(-0.537373\pi\) | ||||
−0.117141 | + | 0.993115i | \(0.537373\pi\) | |||||||
\(572\) | −4.61119 | −0.192803 | ||||||||
\(573\) | −3.50958 | −0.146615 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.62930 | −0.193055 | ||||||||
\(576\) | −9.95734 | −0.414889 | ||||||||
\(577\) | −10.1348 | −0.421915 | −0.210958 | − | 0.977495i | \(-0.567658\pi\) | ||||
−0.210958 | + | 0.977495i | \(0.567658\pi\) | |||||||
\(578\) | −36.4321 | −1.51538 | ||||||||
\(579\) | 13.6422 | 0.566950 | ||||||||
\(580\) | 1.10873 | 0.0460375 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −35.2399 | −1.46074 | ||||||||
\(583\) | −4.97212 | −0.205924 | ||||||||
\(584\) | 0.631406 | 0.0261278 | ||||||||
\(585\) | −1.12462 | −0.0464975 | ||||||||
\(586\) | −27.5506 | −1.13810 | ||||||||
\(587\) | 27.2323 | 1.12400 | 0.561999 | − | 0.827138i | \(-0.310032\pi\) | ||||
0.561999 | + | 0.827138i | \(0.310032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.54691 | 0.393374 | ||||||||
\(590\) | −9.30495 | −0.383079 | ||||||||
\(591\) | 13.4651 | 0.553880 | ||||||||
\(592\) | −31.0022 | −1.27418 | ||||||||
\(593\) | 38.3547 | 1.57504 | 0.787519 | − | 0.616290i | \(-0.211365\pi\) | ||||
0.787519 | + | 0.616290i | \(0.211365\pi\) | |||||||
\(594\) | −2.27659 | −0.0934095 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 46.6381 | 1.91037 | ||||||||
\(597\) | −14.2974 | −0.585155 | ||||||||
\(598\) | −3.81441 | −0.155983 | ||||||||
\(599\) | −6.88378 | −0.281264 | −0.140632 | − | 0.990062i | \(-0.544913\pi\) | ||||
−0.140632 | + | 0.990062i | \(0.544913\pi\) | |||||||
\(600\) | −2.52822 | −0.103214 | ||||||||
\(601\) | 1.80012 | 0.0734283 | 0.0367141 | − | 0.999326i | \(-0.488311\pi\) | ||||
0.0367141 | + | 0.999326i | \(0.488311\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.06305 | 0.0840141 | ||||||||
\(604\) | 28.9734 | 1.17891 | ||||||||
\(605\) | 5.95741 | 0.242203 | ||||||||
\(606\) | −17.6884 | −0.718542 | ||||||||
\(607\) | 2.93517 | 0.119135 | 0.0595674 | − | 0.998224i | \(-0.481028\pi\) | ||||
0.0595674 | + | 0.998224i | \(0.481028\pi\) | |||||||
\(608\) | 8.83113 | 0.358150 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.32139 | 0.255946 | ||||||||
\(611\) | −10.9142 | −0.441542 | ||||||||
\(612\) | 13.3281 | 0.538756 | ||||||||
\(613\) | 31.7390 | 1.28192 | 0.640962 | − | 0.767572i | \(-0.278535\pi\) | ||||
0.640962 | + | 0.767572i | \(0.278535\pi\) | |||||||
\(614\) | −50.6970 | −2.04596 | ||||||||
\(615\) | −5.96408 | −0.240495 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.7807 | −1.68203 | −0.841013 | − | 0.541015i | \(-0.818040\pi\) | ||||
−0.841013 | + | 0.541015i | \(0.818040\pi\) | |||||||
\(618\) | 21.5536 | 0.867012 | ||||||||
\(619\) | 27.2170 | 1.09394 | 0.546972 | − | 0.837151i | \(-0.315780\pi\) | ||||
0.546972 | + | 0.837151i | \(0.315780\pi\) | |||||||
\(620\) | −12.0964 | −0.485803 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −53.8512 | −2.15924 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.28229 | 0.251493 | ||||||||
\(625\) | 19.5769 | 0.783076 | ||||||||
\(626\) | −49.9689 | −1.99716 | ||||||||
\(627\) | 1.19960 | 0.0479075 | ||||||||
\(628\) | −10.3487 | −0.412959 | ||||||||
\(629\) | 53.6503 | 2.13918 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.8728 | 1.02998 | 0.514990 | − | 0.857196i | \(-0.327795\pi\) | ||||
0.514990 | + | 0.857196i | \(0.327795\pi\) | |||||||
\(632\) | −8.28574 | −0.329589 | ||||||||
\(633\) | −2.83108 | −0.112525 | ||||||||
\(634\) | −7.45437 | −0.296051 | ||||||||
\(635\) | −4.81629 | −0.191129 | ||||||||
\(636\) | −10.2130 | −0.404973 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.83076 | −0.0724805 | ||||||||
\(639\) | 4.30092 | 0.170142 | ||||||||
\(640\) | −2.63687 | −0.104232 | ||||||||
\(641\) | −13.3591 | −0.527651 | −0.263826 | − | 0.964570i | \(-0.584984\pi\) | ||||
−0.263826 | + | 0.964570i | \(0.584984\pi\) | |||||||
\(642\) | −16.6706 | −0.657934 | ||||||||
\(643\) | 43.4719 | 1.71436 | 0.857182 | − | 0.515014i | \(-0.172213\pi\) | ||||
0.857182 | + | 0.515014i | \(0.172213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.18716 | 0.125494 | ||||||||
\(646\) | −13.2257 | −0.520360 | ||||||||
\(647\) | −46.1515 | −1.81440 | −0.907201 | − | 0.420698i | \(-0.861785\pi\) | ||||
−0.907201 | + | 0.420698i | \(0.861785\pi\) | |||||||
\(648\) | −0.546135 | −0.0214542 | ||||||||
\(649\) | 8.15871 | 0.320257 | ||||||||
\(650\) | 17.6580 | 0.692605 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −49.2620 | −1.92925 | ||||||||
\(653\) | −33.5965 | −1.31473 | −0.657367 | − | 0.753570i | \(-0.728330\pi\) | ||||
−0.657367 | + | 0.753570i | \(0.728330\pi\) | |||||||
\(654\) | 7.87123 | 0.307790 | ||||||||
\(655\) | −0.289635 | −0.0113170 | ||||||||
\(656\) | 33.3161 | 1.30077 | ||||||||
\(657\) | −1.15613 | −0.0451051 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.2122 | 0.397809 | 0.198905 | − | 0.980019i | \(-0.436262\pi\) | ||||
0.198905 | + | 0.980019i | \(0.436262\pi\) | |||||||
\(660\) | −1.51995 | −0.0591641 | ||||||||
\(661\) | 18.0200 | 0.700895 | 0.350448 | − | 0.936582i | \(-0.386029\pi\) | ||||
0.350448 | + | 0.936582i | \(0.386029\pi\) | |||||||
\(662\) | −17.0038 | −0.660871 | ||||||||
\(663\) | −10.8717 | −0.422222 | ||||||||
\(664\) | 5.85436 | 0.227193 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.8236 | −0.729399 | ||||||||
\(667\) | −0.804169 | −0.0311375 | ||||||||
\(668\) | −8.88442 | −0.343748 | ||||||||
\(669\) | −4.78780 | −0.185107 | ||||||||
\(670\) | 2.59391 | 0.100212 | ||||||||
\(671\) | −5.54268 | −0.213973 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.5777 | −1.56415 | −0.782077 | − | 0.623181i | \(-0.785840\pi\) | ||||
−0.782077 | + | 0.623181i | \(0.785840\pi\) | |||||||
\(674\) | −54.0767 | −2.08296 | ||||||||
\(675\) | 4.62930 | 0.178182 | ||||||||
\(676\) | −21.7120 | −0.835078 | ||||||||
\(677\) | 25.9423 | 0.997044 | 0.498522 | − | 0.866877i | \(-0.333876\pi\) | ||||
0.498522 | + | 0.866877i | \(0.333876\pi\) | |||||||
\(678\) | 18.3672 | 0.705388 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.95711 | 0.0750518 | ||||||||
\(681\) | −19.2951 | −0.739390 | ||||||||
\(682\) | 19.9739 | 0.764839 | ||||||||
\(683\) | −25.8167 | −0.987848 | −0.493924 | − | 0.869505i | \(-0.664438\pi\) | ||||
−0.493924 | + | 0.869505i | \(0.664438\pi\) | |||||||
\(684\) | 2.46406 | 0.0942156 | ||||||||
\(685\) | 5.03705 | 0.192456 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.12954 | −0.310161 | ||||||||
\(688\) | −17.8039 | −0.678766 | ||||||||
\(689\) | 8.33076 | 0.317377 | ||||||||
\(690\) | −1.25732 | −0.0478652 | ||||||||
\(691\) | −15.6020 | −0.593528 | −0.296764 | − | 0.954951i | \(-0.595907\pi\) | ||||
−0.296764 | + | 0.954951i | \(0.595907\pi\) | |||||||
\(692\) | −54.3859 | −2.06744 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.2403 | 0.464636 | ||||||||
\(695\) | 1.51112 | 0.0573201 | ||||||||
\(696\) | −0.439185 | −0.0166473 | ||||||||
\(697\) | −57.6545 | −2.18382 | ||||||||
\(698\) | −61.1916 | −2.31614 | ||||||||
\(699\) | −7.94940 | −0.300674 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.6350 | 1.45922 | 0.729612 | − | 0.683861i | \(-0.239701\pi\) | ||||
0.729612 | + | 0.683861i | \(0.239701\pi\) | |||||||
\(702\) | 3.81441 | 0.143966 | ||||||||
\(703\) | 9.91871 | 0.374091 | ||||||||
\(704\) | 10.9773 | 0.413722 | ||||||||
\(705\) | −3.59758 | −0.135493 | ||||||||
\(706\) | 29.4039 | 1.10663 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 16.7585 | 0.629823 | ||||||||
\(709\) | −43.3432 | −1.62779 | −0.813894 | − | 0.581013i | \(-0.802656\pi\) | ||||
−0.813894 | + | 0.581013i | \(0.802656\pi\) | |||||||
\(710\) | 5.40762 | 0.202944 | ||||||||
\(711\) | 15.1716 | 0.568979 | ||||||||
\(712\) | 4.32630 | 0.162135 | ||||||||
\(713\) | 8.77360 | 0.328574 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.23982 | 0.0463667 | ||||||||
\(716\) | 45.6720 | 1.70684 | ||||||||
\(717\) | −15.7789 | −0.589274 | ||||||||
\(718\) | −5.74560 | −0.214424 | ||||||||
\(719\) | −29.4485 | −1.09824 | −0.549122 | − | 0.835742i | \(-0.685038\pi\) | ||||
−0.549122 | + | 0.835742i | \(0.685038\pi\) | |||||||
\(720\) | 2.07079 | 0.0771737 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 36.7910 | 1.36922 | ||||||||
\(723\) | 11.2656 | 0.418971 | ||||||||
\(724\) | 37.8362 | 1.40617 | ||||||||
\(725\) | 3.72274 | 0.138259 | ||||||||
\(726\) | −20.2059 | −0.749910 | ||||||||
\(727\) | −50.1254 | −1.85905 | −0.929524 | − | 0.368763i | \(-0.879782\pi\) | ||||
−0.929524 | + | 0.368763i | \(0.879782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.45363 | −0.0538012 | ||||||||
\(731\) | 30.8101 | 1.13955 | ||||||||
\(732\) | −11.3850 | −0.420802 | ||||||||
\(733\) | −20.9760 | −0.774766 | −0.387383 | − | 0.921919i | \(-0.626621\pi\) | ||||
−0.387383 | + | 0.921919i | \(0.626621\pi\) | |||||||
\(734\) | 13.7625 | 0.507984 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.11580 | 0.299152 | ||||||||
\(737\) | −2.27438 | −0.0837778 | ||||||||
\(738\) | 20.2285 | 0.744620 | ||||||||
\(739\) | 11.5852 | 0.426168 | 0.213084 | − | 0.977034i | \(-0.431649\pi\) | ||||
0.213084 | + | 0.977034i | \(0.431649\pi\) | |||||||
\(740\) | −12.5675 | −0.461990 | ||||||||
\(741\) | −2.00993 | −0.0738365 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.7847 | −1.64299 | −0.821495 | − | 0.570216i | \(-0.806860\pi\) | ||||
−0.821495 | + | 0.570216i | \(0.806860\pi\) | |||||||
\(744\) | 4.79157 | 0.175668 | ||||||||
\(745\) | −12.5397 | −0.459420 | ||||||||
\(746\) | 39.4062 | 1.44276 | ||||||||
\(747\) | −10.7196 | −0.392210 | ||||||||
\(748\) | −14.6933 | −0.537241 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.1071 | 0.442088 | ||||||||
\(751\) | −22.2887 | −0.813325 | −0.406662 | − | 0.913579i | \(-0.633307\pi\) | ||||
−0.406662 | + | 0.913579i | \(0.633307\pi\) | |||||||
\(752\) | 20.0965 | 0.732845 | ||||||||
\(753\) | 2.27255 | 0.0828162 | ||||||||
\(754\) | 3.06743 | 0.111709 | ||||||||
\(755\) | −7.79015 | −0.283513 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.3724 | −1.24929 | −0.624643 | − | 0.780910i | \(-0.714756\pi\) | ||||
−0.624643 | + | 0.780910i | \(0.714756\pi\) | |||||||
\(758\) | −27.3892 | −0.994820 | ||||||||
\(759\) | 1.10243 | 0.0400158 | ||||||||
\(760\) | 0.361824 | 0.0131248 | ||||||||
\(761\) | 43.7206 | 1.58487 | 0.792435 | − | 0.609956i | \(-0.208813\pi\) | ||||
0.792435 | + | 0.609956i | \(0.208813\pi\) | |||||||
\(762\) | 16.3355 | 0.591773 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.94731 | 0.287524 | ||||||||
\(765\) | −3.58356 | −0.129564 | ||||||||
\(766\) | 6.43476 | 0.232497 | ||||||||
\(767\) | −13.6699 | −0.493590 | ||||||||
\(768\) | −10.9711 | −0.395887 | ||||||||
\(769\) | −2.96450 | −0.106903 | −0.0534513 | − | 0.998570i | \(-0.517022\pi\) | ||||
−0.0534513 | + | 0.998570i | \(0.517022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.871285 | 0.0313785 | ||||||||
\(772\) | −30.8923 | −1.11184 | ||||||||
\(773\) | 22.2038 | 0.798615 | 0.399307 | − | 0.916817i | \(-0.369251\pi\) | ||||
0.399307 | + | 0.916817i | \(0.369251\pi\) | |||||||
\(774\) | −10.8099 | −0.388556 | ||||||||
\(775\) | −40.6156 | −1.45896 | ||||||||
\(776\) | 9.31971 | 0.334558 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.6177 | 0.739181 | ||||||||
\(779\) | −10.6590 | −0.381898 | ||||||||
\(780\) | 2.54667 | 0.0911855 | ||||||||
\(781\) | −4.74147 | −0.169663 | ||||||||
\(782\) | −12.1544 | −0.434642 | ||||||||
\(783\) | 0.804169 | 0.0287387 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.78249 | 0.0993112 | ||||||||
\(786\) | 0.982361 | 0.0350397 | ||||||||
\(787\) | −34.6515 | −1.23519 | −0.617596 | − | 0.786495i | \(-0.711893\pi\) | ||||
−0.617596 | + | 0.786495i | \(0.711893\pi\) | |||||||
\(788\) | −30.4913 | −1.08621 | ||||||||
\(789\) | 5.33476 | 0.189923 | ||||||||
\(790\) | 19.0755 | 0.678676 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.602078 | 0.0213939 | ||||||||
\(793\) | 9.28673 | 0.329781 | ||||||||
\(794\) | −11.6561 | −0.413660 | ||||||||
\(795\) | 2.74601 | 0.0973909 | ||||||||
\(796\) | 32.3761 | 1.14754 | ||||||||
\(797\) | −22.4200 | −0.794158 | −0.397079 | − | 0.917784i | \(-0.629976\pi\) | ||||
−0.397079 | + | 0.917784i | \(0.629976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.7777 | −1.23035 | ||||||||
\(800\) | −37.5705 | −1.32832 | ||||||||
\(801\) | −7.92167 | −0.279898 | ||||||||
\(802\) | −79.6332 | −2.81195 | ||||||||
\(803\) | 1.27456 | 0.0449783 | ||||||||
\(804\) | −4.67171 | −0.164759 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −33.4661 | −1.17879 | ||||||||
\(807\) | −22.7388 | −0.800442 | ||||||||
\(808\) | 4.67796 | 0.164570 | ||||||||
\(809\) | 26.0244 | 0.914970 | 0.457485 | − | 0.889217i | \(-0.348750\pi\) | ||||
0.457485 | + | 0.889217i | \(0.348750\pi\) | |||||||
\(810\) | 1.25732 | 0.0441776 | ||||||||
\(811\) | −45.2644 | −1.58945 | −0.794724 | − | 0.606970i | \(-0.792385\pi\) | ||||
−0.794724 | + | 0.606970i | \(0.792385\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.42151 | 0.225212 | ||||||||
\(814\) | 20.7517 | 0.727348 | ||||||||
\(815\) | 13.2452 | 0.463959 | ||||||||
\(816\) | 20.0182 | 0.700778 | ||||||||
\(817\) | 5.69608 | 0.199281 | ||||||||
\(818\) | 76.0088 | 2.65759 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.5054 | 0.471630 | ||||||||
\(821\) | 7.28729 | 0.254328 | 0.127164 | − | 0.991882i | \(-0.459413\pi\) | ||||
0.127164 | + | 0.991882i | \(0.459413\pi\) | |||||||
\(822\) | −17.0843 | −0.595882 | ||||||||
\(823\) | 3.29869 | 0.114985 | 0.0574925 | − | 0.998346i | \(-0.481689\pi\) | ||||
0.0574925 | + | 0.998346i | \(0.481689\pi\) | |||||||
\(824\) | −5.70017 | −0.198575 | ||||||||
\(825\) | −5.10349 | −0.177681 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.8022 | −1.69702 | −0.848510 | − | 0.529179i | \(-0.822500\pi\) | ||||
−0.848510 | + | 0.529179i | \(0.822500\pi\) | |||||||
\(828\) | 2.26446 | 0.0786956 | ||||||||
\(829\) | 24.7978 | 0.861263 | 0.430631 | − | 0.902528i | \(-0.358291\pi\) | ||||
0.430631 | + | 0.902528i | \(0.358291\pi\) | |||||||
\(830\) | −13.4780 | −0.467827 | ||||||||
\(831\) | −14.0353 | −0.486878 | ||||||||
\(832\) | −18.3924 | −0.637642 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.12530 | −0.177475 | ||||||||
\(835\) | 2.38878 | 0.0826671 | ||||||||
\(836\) | −2.71646 | −0.0939506 | ||||||||
\(837\) | −8.77360 | −0.303260 | ||||||||
\(838\) | 13.3277 | 0.460397 | ||||||||
\(839\) | −6.27230 | −0.216544 | −0.108272 | − | 0.994121i | \(-0.534532\pi\) | ||||
−0.108272 | + | 0.994121i | \(0.534532\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3533 | −0.977700 | ||||||||
\(842\) | −61.8044 | −2.12992 | ||||||||
\(843\) | −24.5278 | −0.844782 | ||||||||
\(844\) | 6.41089 | 0.220672 | ||||||||
\(845\) | 5.83777 | 0.200826 | ||||||||
\(846\) | 12.2020 | 0.419513 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15.3395 | −0.526762 | ||||||||
\(849\) | 4.39941 | 0.150987 | ||||||||
\(850\) | 56.2665 | 1.92993 | ||||||||
\(851\) | 9.11528 | 0.312468 | ||||||||
\(852\) | −9.73928 | −0.333662 | ||||||||
\(853\) | −1.75188 | −0.0599834 | −0.0299917 | − | 0.999550i | \(-0.509548\pi\) | ||||
−0.0299917 | + | 0.999550i | \(0.509548\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.662518 | −0.0226576 | ||||||||
\(856\) | 4.40878 | 0.150689 | ||||||||
\(857\) | −15.0955 | −0.515653 | −0.257826 | − | 0.966191i | \(-0.583006\pi\) | ||||
−0.257826 | + | 0.966191i | \(0.583006\pi\) | |||||||
\(858\) | −4.20513 | −0.143561 | ||||||||
\(859\) | 9.58801 | 0.327139 | 0.163569 | − | 0.986532i | \(-0.447699\pi\) | ||||
0.163569 | + | 0.986532i | \(0.447699\pi\) | |||||||
\(860\) | −7.21721 | −0.246105 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.0009 | −0.544992 | ||||||||
\(863\) | 34.3335 | 1.16872 | 0.584362 | − | 0.811493i | \(-0.301345\pi\) | ||||
0.584362 | + | 0.811493i | \(0.301345\pi\) | |||||||
\(864\) | −8.11580 | −0.276105 | ||||||||
\(865\) | 14.6229 | 0.497193 | ||||||||
\(866\) | −10.6907 | −0.363285 | ||||||||
\(867\) | −17.6422 | −0.599159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.7257 | −0.567379 | ||||||||
\(870\) | 1.01110 | 0.0342793 | ||||||||
\(871\) | 3.81071 | 0.129121 | ||||||||
\(872\) | −2.08166 | −0.0704941 | ||||||||
\(873\) | −17.0648 | −0.577557 | ||||||||
\(874\) | −2.24707 | −0.0760084 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.61803 | 0.0884549 | ||||||||
\(877\) | 17.6058 | 0.594505 | 0.297252 | − | 0.954799i | \(-0.403930\pi\) | ||||
0.297252 | + | 0.954799i | \(0.403930\pi\) | |||||||
\(878\) | 62.5549 | 2.11112 | ||||||||
\(879\) | −13.3413 | −0.449991 | ||||||||
\(880\) | −2.28290 | −0.0769567 | ||||||||
\(881\) | 39.5494 | 1.33245 | 0.666227 | − | 0.745749i | \(-0.267908\pi\) | ||||
0.666227 | + | 0.745749i | \(0.267908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.340528 | 0.0114597 | 0.00572983 | − | 0.999984i | \(-0.498176\pi\) | ||||
0.00572983 | + | 0.999984i | \(0.498176\pi\) | |||||||
\(884\) | 24.6186 | 0.828013 | ||||||||
\(885\) | −4.50590 | −0.151464 | ||||||||
\(886\) | −78.8896 | −2.65035 | ||||||||
\(887\) | 30.0962 | 1.01053 | 0.505266 | − | 0.862964i | \(-0.331394\pi\) | ||||
0.505266 | + | 0.862964i | \(0.331394\pi\) | |||||||
\(888\) | 4.97818 | 0.167057 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.96004 | −0.333861 | ||||||||
\(891\) | −1.10243 | −0.0369329 | ||||||||
\(892\) | 10.8418 | 0.363010 | ||||||||
\(893\) | −6.42959 | −0.215158 | ||||||||
\(894\) | 42.5312 | 1.42246 | ||||||||
\(895\) | −12.2800 | −0.410474 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.84712 | −0.0616735 | ||||||||
\(898\) | −6.10364 | −0.203681 | ||||||||
\(899\) | −7.05546 | −0.235313 | ||||||||
\(900\) | −10.4829 | −0.349429 | ||||||||
\(901\) | 26.5456 | 0.884361 | ||||||||
\(902\) | −22.3005 | −0.742526 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.85748 | −0.161557 | ||||||||
\(905\) | −10.1731 | −0.338166 | ||||||||
\(906\) | 26.4220 | 0.877812 | ||||||||
\(907\) | 31.8853 | 1.05873 | 0.529366 | − | 0.848393i | \(-0.322430\pi\) | ||||
0.529366 | + | 0.848393i | \(0.322430\pi\) | |||||||
\(908\) | 43.6931 | 1.45001 | ||||||||
\(909\) | −8.56557 | −0.284102 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.7297 | 1.21691 | 0.608454 | − | 0.793589i | \(-0.291790\pi\) | ||||
0.608454 | + | 0.793589i | \(0.291790\pi\) | |||||||
\(912\) | 3.70091 | 0.122549 | ||||||||
\(913\) | 11.8177 | 0.391107 | ||||||||
\(914\) | −36.5421 | −1.20871 | ||||||||
\(915\) | 3.06112 | 0.101198 | ||||||||
\(916\) | 18.4090 | 0.608252 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12.1544 | 0.401156 | ||||||||
\(919\) | −29.3315 | −0.967556 | −0.483778 | − | 0.875191i | \(-0.660736\pi\) | ||||
−0.483778 | + | 0.875191i | \(0.660736\pi\) | |||||||
\(920\) | 0.332516 | 0.0109627 | ||||||||
\(921\) | −24.5499 | −0.808947 | ||||||||
\(922\) | 24.2535 | 0.798746 | ||||||||
\(923\) | 7.94431 | 0.261490 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.1973 | −1.38744 | ||||||||
\(926\) | −55.9366 | −1.83819 | ||||||||
\(927\) | 10.4373 | 0.342805 | ||||||||
\(928\) | −6.52647 | −0.214242 | ||||||||
\(929\) | −1.30704 | −0.0428826 | −0.0214413 | − | 0.999770i | \(-0.506826\pi\) | ||||
−0.0214413 | + | 0.999770i | \(0.506826\pi\) | |||||||
\(930\) | −11.0312 | −0.361727 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18.0011 | 0.589647 | ||||||||
\(933\) | −26.0773 | −0.853734 | ||||||||
\(934\) | −47.8102 | −1.56440 | ||||||||
\(935\) | 3.95064 | 0.129200 | ||||||||
\(936\) | −1.00878 | −0.0329729 | ||||||||
\(937\) | −4.77786 | −0.156086 | −0.0780430 | − | 0.996950i | \(-0.524867\pi\) | ||||
−0.0780430 | + | 0.996950i | \(0.524867\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.1973 | −0.789650 | ||||||||
\(940\) | 8.14660 | 0.265713 | ||||||||
\(941\) | −33.4004 | −1.08882 | −0.544411 | − | 0.838819i | \(-0.683247\pi\) | ||||
−0.544411 | + | 0.838819i | \(0.683247\pi\) | |||||||
\(942\) | −9.43741 | −0.307488 | ||||||||
\(943\) | −9.79559 | −0.318988 | ||||||||
\(944\) | 25.1705 | 0.819231 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.9172 | 0.387463 | ||||||||
\(947\) | 35.8911 | 1.16630 | 0.583152 | − | 0.812363i | \(-0.301819\pi\) | ||||
0.583152 | + | 0.812363i | \(0.301819\pi\) | |||||||
\(948\) | −34.3555 | −1.11582 | ||||||||
\(949\) | −2.13552 | −0.0693219 | ||||||||
\(950\) | 10.4024 | 0.337498 | ||||||||
\(951\) | −3.60976 | −0.117055 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.4876 | −1.37631 | −0.688154 | − | 0.725564i | \(-0.741579\pi\) | ||||
−0.688154 | + | 0.725564i | \(0.741579\pi\) | |||||||
\(954\) | −9.31369 | −0.301542 | ||||||||
\(955\) | −2.13682 | −0.0691457 | ||||||||
\(956\) | 35.7308 | 1.15562 | ||||||||
\(957\) | −0.886542 | −0.0286578 | ||||||||
\(958\) | −46.1903 | −1.49234 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.06256 | −0.195668 | ||||||||
\(961\) | 45.9761 | 1.48310 | ||||||||
\(962\) | −34.7694 | −1.12101 | ||||||||
\(963\) | −8.07268 | −0.260138 | ||||||||
\(964\) | −25.5105 | −0.821638 | ||||||||
\(965\) | 8.30609 | 0.267383 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.9129 | −1.63725 | −0.818624 | − | 0.574330i | \(-0.805263\pi\) | ||||
−0.818624 | + | 0.574330i | \(0.805263\pi\) | |||||||
\(968\) | 5.34374 | 0.171754 | ||||||||
\(969\) | −6.40453 | −0.205743 | ||||||||
\(970\) | −21.4559 | −0.688908 | ||||||||
\(971\) | −16.7372 | −0.537123 | −0.268561 | − | 0.963263i | \(-0.586548\pi\) | ||||
−0.268561 | + | 0.963263i | \(0.586548\pi\) | |||||||
\(972\) | −2.26446 | −0.0726327 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −86.4272 | −2.76931 | ||||||||
\(975\) | 8.55087 | 0.273847 | ||||||||
\(976\) | −17.0998 | −0.547351 | ||||||||
\(977\) | 47.3729 | 1.51559 | 0.757797 | − | 0.652491i | \(-0.226276\pi\) | ||||
0.757797 | + | 0.652491i | \(0.226276\pi\) | |||||||
\(978\) | −44.9240 | −1.43651 | ||||||||
\(979\) | 8.73310 | 0.279111 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.81163 | 0.121696 | ||||||||
\(982\) | −33.5897 | −1.07189 | ||||||||
\(983\) | 35.2609 | 1.12465 | 0.562323 | − | 0.826918i | \(-0.309908\pi\) | ||||
0.562323 | + | 0.826918i | \(0.309908\pi\) | |||||||
\(984\) | −5.34972 | −0.170543 | ||||||||
\(985\) | 8.19827 | 0.261219 | ||||||||
\(986\) | 9.77422 | 0.311275 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.55141 | 0.144800 | ||||||||
\(989\) | 5.23469 | 0.166454 | ||||||||
\(990\) | −1.38611 | −0.0440534 | ||||||||
\(991\) | 16.9164 | 0.537369 | 0.268684 | − | 0.963228i | \(-0.413411\pi\) | ||||
0.268684 | + | 0.963228i | \(0.413411\pi\) | |||||||
\(992\) | 71.2048 | 2.26075 | ||||||||
\(993\) | −8.23405 | −0.261300 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.70504 | −0.275968 | ||||||||
\(996\) | 24.2742 | 0.769157 | ||||||||
\(997\) | −52.3647 | −1.65841 | −0.829203 | − | 0.558947i | \(-0.811205\pi\) | ||||
−0.829203 | + | 0.558947i | \(0.811205\pi\) | |||||||
\(998\) | 40.9398 | 1.29593 | ||||||||
\(999\) | −9.11528 | −0.288395 |
(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 | 3381.2.a.bi.1.2 | 10 | ||
7.2 | even | 3 | 483.2.i.h.277.9 | ✓ | 20 | ||
7.4 | even | 3 | 483.2.i.h.415.9 | yes | 20 | ||
7.6 | odd | 2 | 3381.2.a.bj.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.9 | ✓ | 20 | 7.2 | even | 3 | ||
483.2.i.h.415.9 | yes | 20 | 7.4 | even | 3 | ||
3381.2.a.bi.1.2 | 10 | 1.1 | even | 1 | trivial | ||
3381.2.a.bj.1.2 | 10 | 7.6 | odd | 2 |