Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | 0.353553 | − | 0.935414i | \(-0.384973\pi\) | ||||
0.353553 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −3.56155 | −1.59277 | −0.796387 | − | 0.604787i | \(-0.793258\pi\) | ||||
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.56155 | −1.12626 | ||||||||
\(11\) | −3.56155 | −1.07385 | −0.536924 | − | 0.843630i | \(-0.680414\pi\) | ||||
−0.536924 | + | 0.843630i | \(0.680414\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.56155 | −0.987797 | −0.493899 | − | 0.869520i | \(-0.664429\pi\) | ||||
−0.493899 | + | 0.869520i | \(0.664429\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.56155 | 0.919589 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −5.12311 | −1.17532 | −0.587661 | − | 0.809108i | \(-0.699951\pi\) | ||||
−0.587661 | + | 0.809108i | \(0.699951\pi\) | |||||||
\(20\) | 3.56155 | 0.796387 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.56155 | −0.759326 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | 7.68466 | 1.53693 | ||||||||
\(26\) | −3.56155 | −0.698478 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 3.56155 | 0.650248 | ||||||||
\(31\) | −2.43845 | −0.437958 | −0.218979 | − | 0.975730i | \(-0.570273\pi\) | ||||
−0.218979 | + | 0.975730i | \(0.570273\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 3.56155 | 0.619987 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.43845 | 0.400878 | 0.200439 | − | 0.979706i | \(-0.435763\pi\) | ||||
0.200439 | + | 0.979706i | \(0.435763\pi\) | |||||||
\(38\) | −5.12311 | −0.831077 | ||||||||
\(39\) | 3.56155 | 0.570305 | ||||||||
\(40\) | 10.6847 | 1.68939 | ||||||||
\(41\) | 7.56155 | 1.18092 | 0.590458 | − | 0.807068i | \(-0.298947\pi\) | ||||
0.590458 | + | 0.807068i | \(0.298947\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.24621 | −0.647541 | −0.323771 | − | 0.946136i | \(-0.604951\pi\) | ||||
−0.323771 | + | 0.946136i | \(0.604951\pi\) | |||||||
\(44\) | 3.56155 | 0.536924 | ||||||||
\(45\) | −3.56155 | −0.530925 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 7.12311 | 1.03901 | 0.519506 | − | 0.854467i | \(-0.326116\pi\) | ||||
0.519506 | + | 0.854467i | \(0.326116\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 7.68466 | 1.08677 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.56155 | 0.493899 | ||||||||
\(53\) | −4.24621 | −0.583262 | −0.291631 | − | 0.956531i | \(-0.594198\pi\) | ||||
−0.291631 | + | 0.956531i | \(0.594198\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 12.6847 | 1.71040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.12311 | 0.678572 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | 9.56155 | 1.24481 | 0.622404 | − | 0.782696i | \(-0.286156\pi\) | ||||
0.622404 | + | 0.782696i | \(0.286156\pi\) | |||||||
\(60\) | −3.56155 | −0.459794 | ||||||||
\(61\) | −11.8078 | −1.51183 | −0.755915 | − | 0.654670i | \(-0.772808\pi\) | ||||
−0.755915 | + | 0.654670i | \(0.772808\pi\) | |||||||
\(62\) | −2.43845 | −0.309683 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 12.6847 | 1.57334 | ||||||||
\(66\) | 3.56155 | 0.438397 | ||||||||
\(67\) | 6.43845 | 0.786582 | 0.393291 | − | 0.919414i | \(-0.371337\pi\) | ||||
0.393291 | + | 0.919414i | \(0.371337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4384 | 1.23882 | 0.619408 | − | 0.785069i | \(-0.287373\pi\) | ||||
0.619408 | + | 0.785069i | \(0.287373\pi\) | |||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | −5.12311 | −0.599614 | −0.299807 | − | 0.954000i | \(-0.596922\pi\) | ||||
−0.299807 | + | 0.954000i | \(0.596922\pi\) | |||||||
\(74\) | 2.43845 | 0.283464 | ||||||||
\(75\) | −7.68466 | −0.887348 | ||||||||
\(76\) | 5.12311 | 0.587661 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.56155 | 0.403266 | ||||||||
\(79\) | −2.00000 | −0.225018 | −0.112509 | − | 0.993651i | \(-0.535889\pi\) | ||||
−0.112509 | + | 0.993651i | \(0.535889\pi\) | |||||||
\(80\) | 3.56155 | 0.398194 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.56155 | 0.835034 | ||||||||
\(83\) | −7.12311 | −0.781862 | −0.390931 | − | 0.920420i | \(-0.627847\pi\) | ||||
−0.390931 | + | 0.920420i | \(0.627847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.24621 | −0.457881 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 10.6847 | 1.13899 | ||||||||
\(89\) | 17.3693 | 1.84114 | 0.920572 | − | 0.390573i | \(-0.127723\pi\) | ||||
0.920572 | + | 0.390573i | \(0.127723\pi\) | |||||||
\(90\) | −3.56155 | −0.375421 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 2.43845 | 0.252855 | ||||||||
\(94\) | 7.12311 | 0.734692 | ||||||||
\(95\) | 18.2462 | 1.87202 | ||||||||
\(96\) | −5.00000 | −0.510310 | ||||||||
\(97\) | −13.3693 | −1.35745 | −0.678724 | − | 0.734393i | \(-0.737467\pi\) | ||||
−0.678724 | + | 0.734393i | \(0.737467\pi\) | |||||||
\(98\) | −7.00000 | −0.707107 | ||||||||
\(99\) | −3.56155 | −0.357950 | ||||||||
\(100\) | −7.68466 | −0.768466 | ||||||||
\(101\) | −7.56155 | −0.752403 | −0.376201 | − | 0.926538i | \(-0.622770\pi\) | ||||
−0.376201 | + | 0.926538i | \(0.622770\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.56155 | 0.153864 | 0.0769322 | − | 0.997036i | \(-0.475488\pi\) | ||||
0.0769322 | + | 0.997036i | \(0.475488\pi\) | |||||||
\(104\) | 10.6847 | 1.04772 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.24621 | −0.412428 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 12.6847 | 1.20943 | ||||||||
\(111\) | −2.43845 | −0.231447 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3693 | 1.25768 | 0.628840 | − | 0.777535i | \(-0.283530\pi\) | ||||
0.628840 | + | 0.777535i | \(0.283530\pi\) | |||||||
\(114\) | 5.12311 | 0.479823 | ||||||||
\(115\) | −3.56155 | −0.332117 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | −3.56155 | −0.329266 | ||||||||
\(118\) | 9.56155 | 0.880212 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −10.6847 | −0.975371 | ||||||||
\(121\) | 1.68466 | 0.153151 | ||||||||
\(122\) | −11.8078 | −1.06902 | ||||||||
\(123\) | −7.56155 | −0.681802 | ||||||||
\(124\) | 2.43845 | 0.218979 | ||||||||
\(125\) | −9.56155 | −0.855211 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8078 | 1.04777 | 0.523885 | − | 0.851789i | \(-0.324482\pi\) | ||||
0.523885 | + | 0.851789i | \(0.324482\pi\) | |||||||
\(128\) | −3.00000 | −0.265165 | ||||||||
\(129\) | 4.24621 | 0.373858 | ||||||||
\(130\) | 12.6847 | 1.11252 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | −3.56155 | −0.309993 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.43845 | 0.556197 | ||||||||
\(135\) | 3.56155 | 0.306530 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.75379 | 0.149836 | 0.0749181 | − | 0.997190i | \(-0.476130\pi\) | ||||
0.0749181 | + | 0.997190i | \(0.476130\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −19.6155 | −1.66377 | −0.831884 | − | 0.554950i | \(-0.812737\pi\) | ||||
−0.831884 | + | 0.554950i | \(0.812737\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.12311 | −0.599874 | ||||||||
\(142\) | 10.4384 | 0.875975 | ||||||||
\(143\) | 12.6847 | 1.06074 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 3.56155 | 0.295771 | ||||||||
\(146\) | −5.12311 | −0.423991 | ||||||||
\(147\) | 7.00000 | 0.577350 | ||||||||
\(148\) | −2.43845 | −0.200439 | ||||||||
\(149\) | −16.9309 | −1.38703 | −0.693515 | − | 0.720442i | \(-0.743939\pi\) | ||||
−0.693515 | + | 0.720442i | \(0.743939\pi\) | |||||||
\(150\) | −7.68466 | −0.627450 | ||||||||
\(151\) | 6.24621 | 0.508309 | 0.254155 | − | 0.967164i | \(-0.418203\pi\) | ||||
0.254155 | + | 0.967164i | \(0.418203\pi\) | |||||||
\(152\) | 15.3693 | 1.24662 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.68466 | 0.697569 | ||||||||
\(156\) | −3.56155 | −0.285152 | ||||||||
\(157\) | 19.1231 | 1.52619 | 0.763095 | − | 0.646286i | \(-0.223679\pi\) | ||||
0.763095 | + | 0.646286i | \(0.223679\pi\) | |||||||
\(158\) | −2.00000 | −0.159111 | ||||||||
\(159\) | 4.24621 | 0.336746 | ||||||||
\(160\) | −17.8078 | −1.40783 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 5.56155 | 0.435614 | 0.217807 | − | 0.975992i | \(-0.430110\pi\) | ||||
0.217807 | + | 0.975992i | \(0.430110\pi\) | |||||||
\(164\) | −7.56155 | −0.590458 | ||||||||
\(165\) | −12.6847 | −0.987499 | ||||||||
\(166\) | −7.12311 | −0.552860 | ||||||||
\(167\) | −6.93087 | −0.536327 | −0.268163 | − | 0.963373i | \(-0.586417\pi\) | ||||
−0.268163 | + | 0.963373i | \(0.586417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.315342 | −0.0242570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.12311 | −0.391774 | ||||||||
\(172\) | 4.24621 | 0.323771 | ||||||||
\(173\) | 10.4924 | 0.797724 | 0.398862 | − | 0.917011i | \(-0.369405\pi\) | ||||
0.398862 | + | 0.917011i | \(0.369405\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.56155 | 0.268462 | ||||||||
\(177\) | −9.56155 | −0.718690 | ||||||||
\(178\) | 17.3693 | 1.30189 | ||||||||
\(179\) | −16.4924 | −1.23270 | −0.616351 | − | 0.787472i | \(-0.711390\pi\) | ||||
−0.616351 | + | 0.787472i | \(0.711390\pi\) | |||||||
\(180\) | 3.56155 | 0.265462 | ||||||||
\(181\) | 18.4924 | 1.37453 | 0.687265 | − | 0.726406i | \(-0.258811\pi\) | ||||
0.687265 | + | 0.726406i | \(0.258811\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.8078 | 0.872855 | ||||||||
\(184\) | −3.00000 | −0.221163 | ||||||||
\(185\) | −8.68466 | −0.638509 | ||||||||
\(186\) | 2.43845 | 0.178796 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.12311 | −0.519506 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.2462 | 1.32372 | ||||||||
\(191\) | −19.5616 | −1.41542 | −0.707712 | − | 0.706501i | \(-0.750273\pi\) | ||||
−0.707712 | + | 0.706501i | \(0.750273\pi\) | |||||||
\(192\) | −7.00000 | −0.505181 | ||||||||
\(193\) | −6.87689 | −0.495010 | −0.247505 | − | 0.968887i | \(-0.579611\pi\) | ||||
−0.247505 | + | 0.968887i | \(0.579611\pi\) | |||||||
\(194\) | −13.3693 | −0.959861 | ||||||||
\(195\) | −12.6847 | −0.908367 | ||||||||
\(196\) | 7.00000 | 0.500000 | ||||||||
\(197\) | 12.2462 | 0.872506 | 0.436253 | − | 0.899824i | \(-0.356305\pi\) | ||||
0.436253 | + | 0.899824i | \(0.356305\pi\) | |||||||
\(198\) | −3.56155 | −0.253109 | ||||||||
\(199\) | 3.31534 | 0.235018 | 0.117509 | − | 0.993072i | \(-0.462509\pi\) | ||||
0.117509 | + | 0.993072i | \(0.462509\pi\) | |||||||
\(200\) | −23.0540 | −1.63016 | ||||||||
\(201\) | −6.43845 | −0.454133 | ||||||||
\(202\) | −7.56155 | −0.532029 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.9309 | −1.88093 | ||||||||
\(206\) | 1.56155 | 0.108799 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 3.56155 | 0.246949 | ||||||||
\(209\) | 18.2462 | 1.26212 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.1771 | 1.45789 | 0.728945 | − | 0.684572i | \(-0.240011\pi\) | ||||
0.728945 | + | 0.684572i | \(0.240011\pi\) | |||||||
\(212\) | 4.24621 | 0.291631 | ||||||||
\(213\) | −10.4384 | −0.715231 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.1231 | 1.03139 | ||||||||
\(216\) | 3.00000 | 0.204124 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.00000 | 0.135457 | ||||||||
\(219\) | 5.12311 | 0.346187 | ||||||||
\(220\) | −12.6847 | −0.855199 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2.43845 | −0.163658 | ||||||||
\(223\) | −28.4924 | −1.90799 | −0.953997 | − | 0.299817i | \(-0.903075\pi\) | ||||
−0.953997 | + | 0.299817i | \(0.903075\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.68466 | 0.512311 | ||||||||
\(226\) | 13.3693 | 0.889314 | ||||||||
\(227\) | −29.3693 | −1.94931 | −0.974655 | − | 0.223713i | \(-0.928182\pi\) | ||||
−0.974655 | + | 0.223713i | \(0.928182\pi\) | |||||||
\(228\) | −5.12311 | −0.339286 | ||||||||
\(229\) | 0.192236 | 0.0127033 | 0.00635165 | − | 0.999980i | \(-0.497978\pi\) | ||||
0.00635165 | + | 0.999980i | \(0.497978\pi\) | |||||||
\(230\) | −3.56155 | −0.234842 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | 9.12311 | 0.597675 | 0.298837 | − | 0.954304i | \(-0.403401\pi\) | ||||
0.298837 | + | 0.954304i | \(0.403401\pi\) | |||||||
\(234\) | −3.56155 | −0.232826 | ||||||||
\(235\) | −25.3693 | −1.65491 | ||||||||
\(236\) | −9.56155 | −0.622404 | ||||||||
\(237\) | 2.00000 | 0.129914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.4384 | 0.675207 | 0.337604 | − | 0.941288i | \(-0.390384\pi\) | ||||
0.337604 | + | 0.941288i | \(0.390384\pi\) | |||||||
\(240\) | −3.56155 | −0.229897 | ||||||||
\(241\) | −17.6155 | −1.13472 | −0.567358 | − | 0.823471i | \(-0.692034\pi\) | ||||
−0.567358 | + | 0.823471i | \(0.692034\pi\) | |||||||
\(242\) | 1.68466 | 0.108294 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.8078 | 0.755915 | ||||||||
\(245\) | 24.9309 | 1.59277 | ||||||||
\(246\) | −7.56155 | −0.482107 | ||||||||
\(247\) | 18.2462 | 1.16098 | ||||||||
\(248\) | 7.31534 | 0.464525 | ||||||||
\(249\) | 7.12311 | 0.451408 | ||||||||
\(250\) | −9.56155 | −0.604726 | ||||||||
\(251\) | 10.6847 | 0.674410 | 0.337205 | − | 0.941431i | \(-0.390519\pi\) | ||||
0.337205 | + | 0.941431i | \(0.390519\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.56155 | −0.223913 | ||||||||
\(254\) | 11.8078 | 0.740885 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −4.24621 | −0.264871 | −0.132436 | − | 0.991192i | \(-0.542280\pi\) | ||||
−0.132436 | + | 0.991192i | \(0.542280\pi\) | |||||||
\(258\) | 4.24621 | 0.264358 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −12.6847 | −0.786669 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −4.00000 | −0.247121 | ||||||||
\(263\) | −23.3693 | −1.44101 | −0.720507 | − | 0.693448i | \(-0.756091\pi\) | ||||
−0.720507 | + | 0.693448i | \(0.756091\pi\) | |||||||
\(264\) | −10.6847 | −0.657595 | ||||||||
\(265\) | 15.1231 | 0.929005 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.3693 | −1.06298 | ||||||||
\(268\) | −6.43845 | −0.393291 | ||||||||
\(269\) | −4.93087 | −0.300640 | −0.150320 | − | 0.988637i | \(-0.548030\pi\) | ||||
−0.150320 | + | 0.988637i | \(0.548030\pi\) | |||||||
\(270\) | 3.56155 | 0.216749 | ||||||||
\(271\) | −13.5616 | −0.823806 | −0.411903 | − | 0.911228i | \(-0.635136\pi\) | ||||
−0.411903 | + | 0.911228i | \(0.635136\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.75379 | 0.105950 | ||||||||
\(275\) | −27.3693 | −1.65043 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 12.9309 | 0.776941 | 0.388470 | − | 0.921461i | \(-0.373004\pi\) | ||||
0.388470 | + | 0.921461i | \(0.373004\pi\) | |||||||
\(278\) | −19.6155 | −1.17646 | ||||||||
\(279\) | −2.43845 | −0.145986 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.24621 | −0.253308 | −0.126654 | − | 0.991947i | \(-0.540424\pi\) | ||||
−0.126654 | + | 0.991947i | \(0.540424\pi\) | |||||||
\(282\) | −7.12311 | −0.424175 | ||||||||
\(283\) | 0.684658 | 0.0406987 | 0.0203494 | − | 0.999793i | \(-0.493522\pi\) | ||||
0.0203494 | + | 0.999793i | \(0.493522\pi\) | |||||||
\(284\) | −10.4384 | −0.619408 | ||||||||
\(285\) | −18.2462 | −1.08081 | ||||||||
\(286\) | 12.6847 | 0.750060 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.00000 | 0.294628 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 3.56155 | 0.209142 | ||||||||
\(291\) | 13.3693 | 0.783723 | ||||||||
\(292\) | 5.12311 | 0.299807 | ||||||||
\(293\) | −16.0000 | −0.934730 | −0.467365 | − | 0.884064i | \(-0.654797\pi\) | ||||
−0.467365 | + | 0.884064i | \(0.654797\pi\) | |||||||
\(294\) | 7.00000 | 0.408248 | ||||||||
\(295\) | −34.0540 | −1.98270 | ||||||||
\(296\) | −7.31534 | −0.425196 | ||||||||
\(297\) | 3.56155 | 0.206662 | ||||||||
\(298\) | −16.9309 | −0.980779 | ||||||||
\(299\) | −3.56155 | −0.205970 | ||||||||
\(300\) | 7.68466 | 0.443674 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.24621 | 0.359429 | ||||||||
\(303\) | 7.56155 | 0.434400 | ||||||||
\(304\) | 5.12311 | 0.293830 | ||||||||
\(305\) | 42.0540 | 2.40800 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.31534 | −0.417509 | −0.208754 | − | 0.977968i | \(-0.566941\pi\) | ||||
−0.208754 | + | 0.977968i | \(0.566941\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.56155 | −0.0888336 | ||||||||
\(310\) | 8.68466 | 0.493255 | ||||||||
\(311\) | 16.8769 | 0.957001 | 0.478500 | − | 0.878087i | \(-0.341181\pi\) | ||||
0.478500 | + | 0.878087i | \(0.341181\pi\) | |||||||
\(312\) | −10.6847 | −0.604900 | ||||||||
\(313\) | −3.75379 | −0.212177 | −0.106088 | − | 0.994357i | \(-0.533833\pi\) | ||||
−0.106088 | + | 0.994357i | \(0.533833\pi\) | |||||||
\(314\) | 19.1231 | 1.07918 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | 8.93087 | 0.501608 | 0.250804 | − | 0.968038i | \(-0.419305\pi\) | ||||
0.250804 | + | 0.968038i | \(0.419305\pi\) | |||||||
\(318\) | 4.24621 | 0.238116 | ||||||||
\(319\) | 3.56155 | 0.199409 | ||||||||
\(320\) | −24.9309 | −1.39368 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −27.3693 | −1.51818 | ||||||||
\(326\) | 5.56155 | 0.308026 | ||||||||
\(327\) | −2.00000 | −0.110600 | ||||||||
\(328\) | −22.6847 | −1.25255 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −12.6847 | −0.698267 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | 7.12311 | 0.390931 | ||||||||
\(333\) | 2.43845 | 0.133626 | ||||||||
\(334\) | −6.93087 | −0.379240 | ||||||||
\(335\) | −22.9309 | −1.25285 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.8078 | −1.29689 | −0.648446 | − | 0.761261i | \(-0.724581\pi\) | ||||
−0.648446 | + | 0.761261i | \(0.724581\pi\) | |||||||
\(338\) | −0.315342 | −0.0171523 | ||||||||
\(339\) | −13.3693 | −0.726122 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.68466 | 0.470301 | ||||||||
\(342\) | −5.12311 | −0.277026 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.7386 | 0.686821 | ||||||||
\(345\) | 3.56155 | 0.191748 | ||||||||
\(346\) | 10.4924 | 0.564076 | ||||||||
\(347\) | 24.4924 | 1.31482 | 0.657411 | − | 0.753532i | \(-0.271652\pi\) | ||||
0.657411 | + | 0.753532i | \(0.271652\pi\) | |||||||
\(348\) | −1.00000 | −0.0536056 | ||||||||
\(349\) | 22.3002 | 1.19370 | 0.596851 | − | 0.802352i | \(-0.296418\pi\) | ||||
0.596851 | + | 0.802352i | \(0.296418\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.56155 | 0.190102 | ||||||||
\(352\) | −17.8078 | −0.949157 | ||||||||
\(353\) | 10.4924 | 0.558455 | 0.279228 | − | 0.960225i | \(-0.409922\pi\) | ||||
0.279228 | + | 0.960225i | \(0.409922\pi\) | |||||||
\(354\) | −9.56155 | −0.508191 | ||||||||
\(355\) | −37.1771 | −1.97315 | ||||||||
\(356\) | −17.3693 | −0.920572 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.4924 | −0.871652 | ||||||||
\(359\) | −5.12311 | −0.270387 | −0.135194 | − | 0.990819i | \(-0.543166\pi\) | ||||
−0.135194 | + | 0.990819i | \(0.543166\pi\) | |||||||
\(360\) | 10.6847 | 0.563131 | ||||||||
\(361\) | 7.24621 | 0.381380 | ||||||||
\(362\) | 18.4924 | 0.971940 | ||||||||
\(363\) | −1.68466 | −0.0884216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.2462 | 0.955050 | ||||||||
\(366\) | 11.8078 | 0.617202 | ||||||||
\(367\) | 24.7386 | 1.29135 | 0.645673 | − | 0.763614i | \(-0.276577\pi\) | ||||
0.645673 | + | 0.763614i | \(0.276577\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 7.56155 | 0.393639 | ||||||||
\(370\) | −8.68466 | −0.451494 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.43845 | −0.126428 | ||||||||
\(373\) | 2.49242 | 0.129053 | 0.0645264 | − | 0.997916i | \(-0.479446\pi\) | ||||
0.0645264 | + | 0.997916i | \(0.479446\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.56155 | 0.493756 | ||||||||
\(376\) | −21.3693 | −1.10204 | ||||||||
\(377\) | 3.56155 | 0.183429 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.0000 | 1.54100 | 0.770498 | − | 0.637442i | \(-0.220007\pi\) | ||||
0.770498 | + | 0.637442i | \(0.220007\pi\) | |||||||
\(380\) | −18.2462 | −0.936011 | ||||||||
\(381\) | −11.8078 | −0.604930 | ||||||||
\(382\) | −19.5616 | −1.00086 | ||||||||
\(383\) | 8.87689 | 0.453588 | 0.226794 | − | 0.973943i | \(-0.427176\pi\) | ||||
0.226794 | + | 0.973943i | \(0.427176\pi\) | |||||||
\(384\) | 3.00000 | 0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.87689 | −0.350025 | ||||||||
\(387\) | −4.24621 | −0.215847 | ||||||||
\(388\) | 13.3693 | 0.678724 | ||||||||
\(389\) | 38.2462 | 1.93916 | 0.969580 | − | 0.244775i | \(-0.0787141\pi\) | ||||
0.969580 | + | 0.244775i | \(0.0787141\pi\) | |||||||
\(390\) | −12.6847 | −0.642313 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 21.0000 | 1.06066 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 12.2462 | 0.616955 | ||||||||
\(395\) | 7.12311 | 0.358402 | ||||||||
\(396\) | 3.56155 | 0.178975 | ||||||||
\(397\) | −15.7538 | −0.790660 | −0.395330 | − | 0.918539i | \(-0.629370\pi\) | ||||
−0.395330 | + | 0.918539i | \(0.629370\pi\) | |||||||
\(398\) | 3.31534 | 0.166183 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.68466 | −0.384233 | ||||||||
\(401\) | −2.19224 | −0.109475 | −0.0547375 | − | 0.998501i | \(-0.517432\pi\) | ||||
−0.0547375 | + | 0.998501i | \(0.517432\pi\) | |||||||
\(402\) | −6.43845 | −0.321121 | ||||||||
\(403\) | 8.68466 | 0.432614 | ||||||||
\(404\) | 7.56155 | 0.376201 | ||||||||
\(405\) | −3.56155 | −0.176975 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.68466 | −0.430483 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.2462 | 1.00111 | 0.500555 | − | 0.865705i | \(-0.333129\pi\) | ||||
0.500555 | + | 0.865705i | \(0.333129\pi\) | |||||||
\(410\) | −26.9309 | −1.33002 | ||||||||
\(411\) | −1.75379 | −0.0865080 | ||||||||
\(412\) | −1.56155 | −0.0769322 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 25.3693 | 1.24533 | ||||||||
\(416\) | −17.8078 | −0.873097 | ||||||||
\(417\) | 19.6155 | 0.960577 | ||||||||
\(418\) | 18.2462 | 0.892451 | ||||||||
\(419\) | 23.1231 | 1.12964 | 0.564819 | − | 0.825215i | \(-0.308946\pi\) | ||||
0.564819 | + | 0.825215i | \(0.308946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.8078 | 0.965371 | 0.482686 | − | 0.875794i | \(-0.339661\pi\) | ||||
0.482686 | + | 0.875794i | \(0.339661\pi\) | |||||||
\(422\) | 21.1771 | 1.03088 | ||||||||
\(423\) | 7.12311 | 0.346337 | ||||||||
\(424\) | 12.7386 | 0.618643 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.4384 | −0.505744 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.6847 | −0.612421 | ||||||||
\(430\) | 15.1231 | 0.729301 | ||||||||
\(431\) | 20.8769 | 1.00560 | 0.502802 | − | 0.864401i | \(-0.332302\pi\) | ||||
0.502802 | + | 0.864401i | \(0.332302\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −20.8769 | −1.00328 | −0.501640 | − | 0.865077i | \(-0.667270\pi\) | ||||
−0.501640 | + | 0.865077i | \(0.667270\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.56155 | −0.170763 | ||||||||
\(436\) | −2.00000 | −0.0957826 | ||||||||
\(437\) | −5.12311 | −0.245071 | ||||||||
\(438\) | 5.12311 | 0.244791 | ||||||||
\(439\) | 29.8617 | 1.42522 | 0.712612 | − | 0.701559i | \(-0.247512\pi\) | ||||
0.712612 | + | 0.701559i | \(0.247512\pi\) | |||||||
\(440\) | −38.0540 | −1.81415 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.87689 | 0.231708 | 0.115854 | − | 0.993266i | \(-0.463039\pi\) | ||||
0.115854 | + | 0.993266i | \(0.463039\pi\) | |||||||
\(444\) | 2.43845 | 0.115724 | ||||||||
\(445\) | −61.8617 | −2.93253 | ||||||||
\(446\) | −28.4924 | −1.34916 | ||||||||
\(447\) | 16.9309 | 0.800803 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.3153 | 0.817161 | 0.408581 | − | 0.912722i | \(-0.366024\pi\) | ||||
0.408581 | + | 0.912722i | \(0.366024\pi\) | |||||||
\(450\) | 7.68466 | 0.362258 | ||||||||
\(451\) | −26.9309 | −1.26813 | ||||||||
\(452\) | −13.3693 | −0.628840 | ||||||||
\(453\) | −6.24621 | −0.293473 | ||||||||
\(454\) | −29.3693 | −1.37837 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.3693 | −0.719734 | ||||||||
\(457\) | −1.12311 | −0.0525367 | −0.0262683 | − | 0.999655i | \(-0.508362\pi\) | ||||
−0.0262683 | + | 0.999655i | \(0.508362\pi\) | |||||||
\(458\) | 0.192236 | 0.00898260 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.56155 | 0.166058 | ||||||||
\(461\) | −38.3002 | −1.78382 | −0.891909 | − | 0.452215i | \(-0.850634\pi\) | ||||
−0.891909 | + | 0.452215i | \(0.850634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4924 | 0.952364 | 0.476182 | − | 0.879347i | \(-0.342020\pi\) | ||||
0.476182 | + | 0.879347i | \(0.342020\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | −8.68466 | −0.402741 | ||||||||
\(466\) | 9.12311 | 0.422620 | ||||||||
\(467\) | 25.4233 | 1.17645 | 0.588225 | − | 0.808697i | \(-0.299827\pi\) | ||||
0.588225 | + | 0.808697i | \(0.299827\pi\) | |||||||
\(468\) | 3.56155 | 0.164633 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −25.3693 | −1.17020 | ||||||||
\(471\) | −19.1231 | −0.881146 | ||||||||
\(472\) | −28.6847 | −1.32032 | ||||||||
\(473\) | 15.1231 | 0.695361 | ||||||||
\(474\) | 2.00000 | 0.0918630 | ||||||||
\(475\) | −39.3693 | −1.80639 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.24621 | −0.194421 | ||||||||
\(478\) | 10.4384 | 0.477443 | ||||||||
\(479\) | 21.3153 | 0.973923 | 0.486961 | − | 0.873423i | \(-0.338105\pi\) | ||||
0.486961 | + | 0.873423i | \(0.338105\pi\) | |||||||
\(480\) | 17.8078 | 0.812810 | ||||||||
\(481\) | −8.68466 | −0.395986 | ||||||||
\(482\) | −17.6155 | −0.802365 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.68466 | −0.0765754 | ||||||||
\(485\) | 47.6155 | 2.16211 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −10.7386 | −0.486614 | −0.243307 | − | 0.969949i | \(-0.578232\pi\) | ||||
−0.243307 | + | 0.969949i | \(0.578232\pi\) | |||||||
\(488\) | 35.4233 | 1.60354 | ||||||||
\(489\) | −5.56155 | −0.251502 | ||||||||
\(490\) | 24.9309 | 1.12626 | ||||||||
\(491\) | −2.63068 | −0.118721 | −0.0593605 | − | 0.998237i | \(-0.518906\pi\) | ||||
−0.0593605 | + | 0.998237i | \(0.518906\pi\) | |||||||
\(492\) | 7.56155 | 0.340901 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 18.2462 | 0.820936 | ||||||||
\(495\) | 12.6847 | 0.570133 | ||||||||
\(496\) | 2.43845 | 0.109490 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.12311 | 0.319194 | ||||||||
\(499\) | 5.36932 | 0.240364 | 0.120182 | − | 0.992752i | \(-0.461652\pi\) | ||||
0.120182 | + | 0.992752i | \(0.461652\pi\) | |||||||
\(500\) | 9.56155 | 0.427606 | ||||||||
\(501\) | 6.93087 | 0.309648 | ||||||||
\(502\) | 10.6847 | 0.476880 | ||||||||
\(503\) | 16.6307 | 0.741526 | 0.370763 | − | 0.928728i | \(-0.379096\pi\) | ||||
0.370763 | + | 0.928728i | \(0.379096\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.9309 | 1.19841 | ||||||||
\(506\) | −3.56155 | −0.158330 | ||||||||
\(507\) | 0.315342 | 0.0140048 | ||||||||
\(508\) | −11.8078 | −0.523885 | ||||||||
\(509\) | −10.0000 | −0.443242 | −0.221621 | − | 0.975133i | \(-0.571135\pi\) | ||||
−0.221621 | + | 0.975133i | \(0.571135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 5.12311 | 0.226191 | ||||||||
\(514\) | −4.24621 | −0.187292 | ||||||||
\(515\) | −5.56155 | −0.245071 | ||||||||
\(516\) | −4.24621 | −0.186929 | ||||||||
\(517\) | −25.3693 | −1.11574 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.4924 | −0.460566 | ||||||||
\(520\) | −38.0540 | −1.66878 | ||||||||
\(521\) | −28.2462 | −1.23749 | −0.618744 | − | 0.785592i | \(-0.712358\pi\) | ||||
−0.618744 | + | 0.785592i | \(0.712358\pi\) | |||||||
\(522\) | −1.00000 | −0.0437688 | ||||||||
\(523\) | −7.80776 | −0.341410 | −0.170705 | − | 0.985322i | \(-0.554604\pi\) | ||||
−0.170705 | + | 0.985322i | \(0.554604\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.3693 | −1.01895 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −3.56155 | −0.154997 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 15.1231 | 0.656906 | ||||||||
\(531\) | 9.56155 | 0.414936 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.9309 | −1.16651 | ||||||||
\(534\) | −17.3693 | −0.751644 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −19.3153 | −0.834296 | ||||||||
\(537\) | 16.4924 | 0.711701 | ||||||||
\(538\) | −4.93087 | −0.212585 | ||||||||
\(539\) | 24.9309 | 1.07385 | ||||||||
\(540\) | −3.56155 | −0.153265 | ||||||||
\(541\) | −4.24621 | −0.182559 | −0.0912794 | − | 0.995825i | \(-0.529096\pi\) | ||||
−0.0912794 | + | 0.995825i | \(0.529096\pi\) | |||||||
\(542\) | −13.5616 | −0.582519 | ||||||||
\(543\) | −18.4924 | −0.793586 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.12311 | −0.305120 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.2462 | 1.80632 | 0.903159 | − | 0.429307i | \(-0.141242\pi\) | ||||
0.903159 | + | 0.429307i | \(0.141242\pi\) | |||||||
\(548\) | −1.75379 | −0.0749181 | ||||||||
\(549\) | −11.8078 | −0.503943 | ||||||||
\(550\) | −27.3693 | −1.16703 | ||||||||
\(551\) | 5.12311 | 0.218252 | ||||||||
\(552\) | 3.00000 | 0.127688 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.9309 | 0.549380 | ||||||||
\(555\) | 8.68466 | 0.368643 | ||||||||
\(556\) | 19.6155 | 0.831884 | ||||||||
\(557\) | −3.17708 | −0.134617 | −0.0673086 | − | 0.997732i | \(-0.521441\pi\) | ||||
−0.0673086 | + | 0.997732i | \(0.521441\pi\) | |||||||
\(558\) | −2.43845 | −0.103228 | ||||||||
\(559\) | 15.1231 | 0.639639 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.24621 | −0.179116 | ||||||||
\(563\) | 15.0691 | 0.635088 | 0.317544 | − | 0.948244i | \(-0.397142\pi\) | ||||
0.317544 | + | 0.948244i | \(0.397142\pi\) | |||||||
\(564\) | 7.12311 | 0.299937 | ||||||||
\(565\) | −47.6155 | −2.00320 | ||||||||
\(566\) | 0.684658 | 0.0287783 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31.3153 | −1.31396 | ||||||||
\(569\) | −30.7386 | −1.28863 | −0.644315 | − | 0.764760i | \(-0.722858\pi\) | ||||
−0.644315 | + | 0.764760i | \(0.722858\pi\) | |||||||
\(570\) | −18.2462 | −0.764250 | ||||||||
\(571\) | −13.1771 | −0.551444 | −0.275722 | − | 0.961237i | \(-0.588917\pi\) | ||||
−0.275722 | + | 0.961237i | \(0.588917\pi\) | |||||||
\(572\) | −12.6847 | −0.530372 | ||||||||
\(573\) | 19.5616 | 0.817196 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.68466 | 0.320472 | ||||||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | −5.12311 | −0.213278 | −0.106639 | − | 0.994298i | \(-0.534009\pi\) | ||||
−0.106639 | + | 0.994298i | \(0.534009\pi\) | |||||||
\(578\) | −17.0000 | −0.707107 | ||||||||
\(579\) | 6.87689 | 0.285794 | ||||||||
\(580\) | −3.56155 | −0.147885 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 13.3693 | 0.554176 | ||||||||
\(583\) | 15.1231 | 0.626335 | ||||||||
\(584\) | 15.3693 | 0.635987 | ||||||||
\(585\) | 12.6847 | 0.524446 | ||||||||
\(586\) | −16.0000 | −0.660954 | ||||||||
\(587\) | 35.2311 | 1.45414 | 0.727071 | − | 0.686563i | \(-0.240881\pi\) | ||||
0.727071 | + | 0.686563i | \(0.240881\pi\) | |||||||
\(588\) | −7.00000 | −0.288675 | ||||||||
\(589\) | 12.4924 | 0.514741 | ||||||||
\(590\) | −34.0540 | −1.40198 | ||||||||
\(591\) | −12.2462 | −0.503742 | ||||||||
\(592\) | −2.43845 | −0.100220 | ||||||||
\(593\) | 4.63068 | 0.190159 | 0.0950797 | − | 0.995470i | \(-0.469689\pi\) | ||||
0.0950797 | + | 0.995470i | \(0.469689\pi\) | |||||||
\(594\) | 3.56155 | 0.146132 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.9309 | 0.693515 | ||||||||
\(597\) | −3.31534 | −0.135688 | ||||||||
\(598\) | −3.56155 | −0.145643 | ||||||||
\(599\) | 20.9848 | 0.857418 | 0.428709 | − | 0.903443i | \(-0.358969\pi\) | ||||
0.428709 | + | 0.903443i | \(0.358969\pi\) | |||||||
\(600\) | 23.0540 | 0.941175 | ||||||||
\(601\) | 12.2462 | 0.499533 | 0.249767 | − | 0.968306i | \(-0.419646\pi\) | ||||
0.249767 | + | 0.968306i | \(0.419646\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.43845 | 0.262194 | ||||||||
\(604\) | −6.24621 | −0.254155 | ||||||||
\(605\) | −6.00000 | −0.243935 | ||||||||
\(606\) | 7.56155 | 0.307167 | ||||||||
\(607\) | −35.2311 | −1.42998 | −0.714992 | − | 0.699132i | \(-0.753570\pi\) | ||||
−0.714992 | + | 0.699132i | \(0.753570\pi\) | |||||||
\(608\) | −25.6155 | −1.03885 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 42.0540 | 1.70272 | ||||||||
\(611\) | −25.3693 | −1.02633 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.4924 | −0.423785 | −0.211892 | − | 0.977293i | \(-0.567963\pi\) | ||||
−0.211892 | + | 0.977293i | \(0.567963\pi\) | |||||||
\(614\) | −7.31534 | −0.295223 | ||||||||
\(615\) | 26.9309 | 1.08596 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.6155 | 1.75590 | 0.877948 | − | 0.478757i | \(-0.158912\pi\) | ||||
0.877948 | + | 0.478757i | \(0.158912\pi\) | |||||||
\(618\) | −1.56155 | −0.0628149 | ||||||||
\(619\) | −8.24621 | −0.331443 | −0.165722 | − | 0.986173i | \(-0.552995\pi\) | ||||
−0.165722 | + | 0.986173i | \(0.552995\pi\) | |||||||
\(620\) | −8.68466 | −0.348784 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 16.8769 | 0.676702 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.56155 | −0.142576 | ||||||||
\(625\) | −4.36932 | −0.174773 | ||||||||
\(626\) | −3.75379 | −0.150032 | ||||||||
\(627\) | −18.2462 | −0.728683 | ||||||||
\(628\) | −19.1231 | −0.763095 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.4384 | 1.21174 | 0.605868 | − | 0.795565i | \(-0.292826\pi\) | ||||
0.605868 | + | 0.795565i | \(0.292826\pi\) | |||||||
\(632\) | 6.00000 | 0.238667 | ||||||||
\(633\) | −21.1771 | −0.841713 | ||||||||
\(634\) | 8.93087 | 0.354690 | ||||||||
\(635\) | −42.0540 | −1.66886 | ||||||||
\(636\) | −4.24621 | −0.168373 | ||||||||
\(637\) | 24.9309 | 0.987797 | ||||||||
\(638\) | 3.56155 | 0.141003 | ||||||||
\(639\) | 10.4384 | 0.412939 | ||||||||
\(640\) | 10.6847 | 0.422348 | ||||||||
\(641\) | −38.7386 | −1.53008 | −0.765042 | − | 0.643980i | \(-0.777282\pi\) | ||||
−0.765042 | + | 0.643980i | \(0.777282\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.4924 | 0.650398 | 0.325199 | − | 0.945646i | \(-0.394569\pi\) | ||||
0.325199 | + | 0.945646i | \(0.394569\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.1231 | −0.595472 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.6847 | 0.970454 | 0.485227 | − | 0.874388i | \(-0.338737\pi\) | ||||
0.485227 | + | 0.874388i | \(0.338737\pi\) | |||||||
\(648\) | −3.00000 | −0.117851 | ||||||||
\(649\) | −34.0540 | −1.33674 | ||||||||
\(650\) | −27.3693 | −1.07351 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.56155 | −0.217807 | ||||||||
\(653\) | 43.5616 | 1.70470 | 0.852348 | − | 0.522976i | \(-0.175178\pi\) | ||||
0.852348 | + | 0.522976i | \(0.175178\pi\) | |||||||
\(654\) | −2.00000 | −0.0782062 | ||||||||
\(655\) | 14.2462 | 0.556646 | ||||||||
\(656\) | −7.56155 | −0.295229 | ||||||||
\(657\) | −5.12311 | −0.199871 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.1231 | 1.29029 | 0.645147 | − | 0.764059i | \(-0.276796\pi\) | ||||
0.645147 | + | 0.764059i | \(0.276796\pi\) | |||||||
\(660\) | 12.6847 | 0.493750 | ||||||||
\(661\) | 17.6155 | 0.685165 | 0.342582 | − | 0.939488i | \(-0.388698\pi\) | ||||
0.342582 | + | 0.939488i | \(0.388698\pi\) | |||||||
\(662\) | 20.0000 | 0.777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.3693 | 0.829290 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.43845 | 0.0944879 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 6.93087 | 0.268163 | ||||||||
\(669\) | 28.4924 | 1.10158 | ||||||||
\(670\) | −22.9309 | −0.885897 | ||||||||
\(671\) | 42.0540 | 1.62348 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.0000 | −1.15642 | −0.578208 | − | 0.815890i | \(-0.696248\pi\) | ||||
−0.578208 | + | 0.815890i | \(0.696248\pi\) | |||||||
\(674\) | −23.8078 | −0.917041 | ||||||||
\(675\) | −7.68466 | −0.295783 | ||||||||
\(676\) | 0.315342 | 0.0121285 | ||||||||
\(677\) | −46.2462 | −1.77739 | −0.888693 | − | 0.458502i | \(-0.848386\pi\) | ||||
−0.888693 | + | 0.458502i | \(0.848386\pi\) | |||||||
\(678\) | −13.3693 | −0.513446 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.3693 | 1.12543 | ||||||||
\(682\) | 8.68466 | 0.332553 | ||||||||
\(683\) | 9.56155 | 0.365863 | 0.182931 | − | 0.983126i | \(-0.441441\pi\) | ||||
0.182931 | + | 0.983126i | \(0.441441\pi\) | |||||||
\(684\) | 5.12311 | 0.195887 | ||||||||
\(685\) | −6.24621 | −0.238655 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.192236 | −0.00733426 | ||||||||
\(688\) | 4.24621 | 0.161885 | ||||||||
\(689\) | 15.1231 | 0.576144 | ||||||||
\(690\) | 3.56155 | 0.135586 | ||||||||
\(691\) | 24.1080 | 0.917110 | 0.458555 | − | 0.888666i | \(-0.348367\pi\) | ||||
0.458555 | + | 0.888666i | \(0.348367\pi\) | |||||||
\(692\) | −10.4924 | −0.398862 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.4924 | 0.929720 | ||||||||
\(695\) | 69.8617 | 2.65001 | ||||||||
\(696\) | −3.00000 | −0.113715 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 22.3002 | 0.844075 | ||||||||
\(699\) | −9.12311 | −0.345068 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0540 | 0.606350 | 0.303175 | − | 0.952935i | \(-0.401953\pi\) | ||||
0.303175 | + | 0.952935i | \(0.401953\pi\) | |||||||
\(702\) | 3.56155 | 0.134422 | ||||||||
\(703\) | −12.4924 | −0.471161 | ||||||||
\(704\) | −24.9309 | −0.939618 | ||||||||
\(705\) | 25.3693 | 0.955464 | ||||||||
\(706\) | 10.4924 | 0.394888 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.56155 | 0.359345 | ||||||||
\(709\) | 1.12311 | 0.0421791 | 0.0210896 | − | 0.999778i | \(-0.493286\pi\) | ||||
0.0210896 | + | 0.999778i | \(0.493286\pi\) | |||||||
\(710\) | −37.1771 | −1.39523 | ||||||||
\(711\) | −2.00000 | −0.0750059 | ||||||||
\(712\) | −52.1080 | −1.95283 | ||||||||
\(713\) | −2.43845 | −0.0913206 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −45.1771 | −1.68953 | ||||||||
\(716\) | 16.4924 | 0.616351 | ||||||||
\(717\) | −10.4384 | −0.389831 | ||||||||
\(718\) | −5.12311 | −0.191193 | ||||||||
\(719\) | 40.3002 | 1.50294 | 0.751472 | − | 0.659765i | \(-0.229344\pi\) | ||||
0.751472 | + | 0.659765i | \(0.229344\pi\) | |||||||
\(720\) | 3.56155 | 0.132731 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.24621 | 0.269676 | ||||||||
\(723\) | 17.6155 | 0.655129 | ||||||||
\(724\) | −18.4924 | −0.687265 | ||||||||
\(725\) | −7.68466 | −0.285401 | ||||||||
\(726\) | −1.68466 | −0.0625235 | ||||||||
\(727\) | −48.7386 | −1.80762 | −0.903808 | − | 0.427938i | \(-0.859240\pi\) | ||||
−0.903808 | + | 0.427938i | \(0.859240\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 18.2462 | 0.675323 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −11.8078 | −0.436428 | ||||||||
\(733\) | −33.5616 | −1.23962 | −0.619812 | − | 0.784750i | \(-0.712791\pi\) | ||||
−0.619812 | + | 0.784750i | \(0.712791\pi\) | |||||||
\(734\) | 24.7386 | 0.913120 | ||||||||
\(735\) | −24.9309 | −0.919589 | ||||||||
\(736\) | 5.00000 | 0.184302 | ||||||||
\(737\) | −22.9309 | −0.844669 | ||||||||
\(738\) | 7.56155 | 0.278345 | ||||||||
\(739\) | −30.5464 | −1.12367 | −0.561834 | − | 0.827250i | \(-0.689904\pi\) | ||||
−0.561834 | + | 0.827250i | \(0.689904\pi\) | |||||||
\(740\) | 8.68466 | 0.319254 | ||||||||
\(741\) | −18.2462 | −0.670291 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.3002 | −0.818114 | −0.409057 | − | 0.912509i | \(-0.634142\pi\) | ||||
−0.409057 | + | 0.912509i | \(0.634142\pi\) | |||||||
\(744\) | −7.31534 | −0.268193 | ||||||||
\(745\) | 60.3002 | 2.20923 | ||||||||
\(746\) | 2.49242 | 0.0912541 | ||||||||
\(747\) | −7.12311 | −0.260621 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.56155 | 0.349139 | ||||||||
\(751\) | 19.8617 | 0.724765 | 0.362383 | − | 0.932029i | \(-0.381963\pi\) | ||||
0.362383 | + | 0.932029i | \(0.381963\pi\) | |||||||
\(752\) | −7.12311 | −0.259753 | ||||||||
\(753\) | −10.6847 | −0.389371 | ||||||||
\(754\) | 3.56155 | 0.129704 | ||||||||
\(755\) | −22.2462 | −0.809623 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.6847 | 0.751797 | 0.375898 | − | 0.926661i | \(-0.377334\pi\) | ||||
0.375898 | + | 0.926661i | \(0.377334\pi\) | |||||||
\(758\) | 30.0000 | 1.08965 | ||||||||
\(759\) | 3.56155 | 0.129276 | ||||||||
\(760\) | −54.7386 | −1.98558 | ||||||||
\(761\) | −18.9848 | −0.688200 | −0.344100 | − | 0.938933i | \(-0.611816\pi\) | ||||
−0.344100 | + | 0.938933i | \(0.611816\pi\) | |||||||
\(762\) | −11.8078 | −0.427750 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 19.5616 | 0.707712 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.87689 | 0.320735 | ||||||||
\(767\) | −34.0540 | −1.22962 | ||||||||
\(768\) | 17.0000 | 0.613435 | ||||||||
\(769\) | −5.56155 | −0.200555 | −0.100277 | − | 0.994960i | \(-0.531973\pi\) | ||||
−0.100277 | + | 0.994960i | \(0.531973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.24621 | 0.152924 | ||||||||
\(772\) | 6.87689 | 0.247505 | ||||||||
\(773\) | −44.0000 | −1.58257 | −0.791285 | − | 0.611448i | \(-0.790588\pi\) | ||||
−0.791285 | + | 0.611448i | \(0.790588\pi\) | |||||||
\(774\) | −4.24621 | −0.152627 | ||||||||
\(775\) | −18.7386 | −0.673112 | ||||||||
\(776\) | 40.1080 | 1.43979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38.2462 | 1.37119 | ||||||||
\(779\) | −38.7386 | −1.38796 | ||||||||
\(780\) | 12.6847 | 0.454184 | ||||||||
\(781\) | −37.1771 | −1.33030 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | −68.1080 | −2.43088 | ||||||||
\(786\) | 4.00000 | 0.142675 | ||||||||
\(787\) | −17.9460 | −0.639707 | −0.319853 | − | 0.947467i | \(-0.603634\pi\) | ||||
−0.319853 | + | 0.947467i | \(0.603634\pi\) | |||||||
\(788\) | −12.2462 | −0.436253 | ||||||||
\(789\) | 23.3693 | 0.831970 | ||||||||
\(790\) | 7.12311 | 0.253429 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 10.6847 | 0.379663 | ||||||||
\(793\) | 42.0540 | 1.49338 | ||||||||
\(794\) | −15.7538 | −0.559081 | ||||||||
\(795\) | −15.1231 | −0.536361 | ||||||||
\(796\) | −3.31534 | −0.117509 | ||||||||
\(797\) | 32.1080 | 1.13732 | 0.568661 | − | 0.822572i | \(-0.307462\pi\) | ||||
0.568661 | + | 0.822572i | \(0.307462\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 38.4233 | 1.35847 | ||||||||
\(801\) | 17.3693 | 0.613715 | ||||||||
\(802\) | −2.19224 | −0.0774105 | ||||||||
\(803\) | 18.2462 | 0.643895 | ||||||||
\(804\) | 6.43845 | 0.227067 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.68466 | 0.305904 | ||||||||
\(807\) | 4.93087 | 0.173575 | ||||||||
\(808\) | 22.6847 | 0.798043 | ||||||||
\(809\) | −2.30019 | −0.0808703 | −0.0404351 | − | 0.999182i | \(-0.512874\pi\) | ||||
−0.0404351 | + | 0.999182i | \(0.512874\pi\) | |||||||
\(810\) | −3.56155 | −0.125140 | ||||||||
\(811\) | −18.2462 | −0.640711 | −0.320356 | − | 0.947297i | \(-0.603802\pi\) | ||||
−0.320356 | + | 0.947297i | \(0.603802\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.5616 | 0.475624 | ||||||||
\(814\) | −8.68466 | −0.304397 | ||||||||
\(815\) | −19.8078 | −0.693836 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.7538 | 0.761069 | ||||||||
\(818\) | 20.2462 | 0.707892 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 26.9309 | 0.940467 | ||||||||
\(821\) | 3.36932 | 0.117590 | 0.0587950 | − | 0.998270i | \(-0.481274\pi\) | ||||
0.0587950 | + | 0.998270i | \(0.481274\pi\) | |||||||
\(822\) | −1.75379 | −0.0611704 | ||||||||
\(823\) | 28.3002 | 0.986482 | 0.493241 | − | 0.869893i | \(-0.335812\pi\) | ||||
0.493241 | + | 0.869893i | \(0.335812\pi\) | |||||||
\(824\) | −4.68466 | −0.163198 | ||||||||
\(825\) | 27.3693 | 0.952877 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.9309 | −0.866931 | −0.433466 | − | 0.901170i | \(-0.642709\pi\) | ||||
−0.433466 | + | 0.901170i | \(0.642709\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −40.3542 | −1.40156 | −0.700779 | − | 0.713378i | \(-0.747164\pi\) | ||||
−0.700779 | + | 0.713378i | \(0.747164\pi\) | |||||||
\(830\) | 25.3693 | 0.880582 | ||||||||
\(831\) | −12.9309 | −0.448567 | ||||||||
\(832\) | −24.9309 | −0.864322 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.6155 | 0.679230 | ||||||||
\(835\) | 24.6847 | 0.854248 | ||||||||
\(836\) | −18.2462 | −0.631058 | ||||||||
\(837\) | 2.43845 | 0.0842851 | ||||||||
\(838\) | 23.1231 | 0.798774 | ||||||||
\(839\) | 49.8078 | 1.71955 | 0.859777 | − | 0.510669i | \(-0.170602\pi\) | ||||
0.859777 | + | 0.510669i | \(0.170602\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 19.8078 | 0.682621 | ||||||||
\(843\) | 4.24621 | 0.146247 | ||||||||
\(844\) | −21.1771 | −0.728945 | ||||||||
\(845\) | 1.12311 | 0.0386360 | ||||||||
\(846\) | 7.12311 | 0.244897 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.24621 | 0.145815 | ||||||||
\(849\) | −0.684658 | −0.0234974 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.43845 | 0.0835889 | ||||||||
\(852\) | 10.4384 | 0.357615 | ||||||||
\(853\) | −19.3693 | −0.663193 | −0.331596 | − | 0.943421i | \(-0.607587\pi\) | ||||
−0.331596 | + | 0.943421i | \(0.607587\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.2462 | 0.624007 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.7538 | 0.538139 | 0.269070 | − | 0.963121i | \(-0.413284\pi\) | ||||
0.269070 | + | 0.963121i | \(0.413284\pi\) | |||||||
\(858\) | −12.6847 | −0.433047 | ||||||||
\(859\) | 12.9848 | 0.443037 | 0.221519 | − | 0.975156i | \(-0.428899\pi\) | ||||
0.221519 | + | 0.975156i | \(0.428899\pi\) | |||||||
\(860\) | −15.1231 | −0.515694 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.8769 | 0.711070 | ||||||||
\(863\) | −22.9309 | −0.780576 | −0.390288 | − | 0.920693i | \(-0.627625\pi\) | ||||
−0.390288 | + | 0.920693i | \(0.627625\pi\) | |||||||
\(864\) | −5.00000 | −0.170103 | ||||||||
\(865\) | −37.3693 | −1.27059 | ||||||||
\(866\) | −20.8769 | −0.709426 | ||||||||
\(867\) | 17.0000 | 0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.12311 | 0.241635 | ||||||||
\(870\) | −3.56155 | −0.120748 | ||||||||
\(871\) | −22.9309 | −0.776983 | ||||||||
\(872\) | −6.00000 | −0.203186 | ||||||||
\(873\) | −13.3693 | −0.452483 | ||||||||
\(874\) | −5.12311 | −0.173292 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.12311 | −0.173094 | ||||||||
\(877\) | 33.2311 | 1.12213 | 0.561067 | − | 0.827771i | \(-0.310391\pi\) | ||||
0.561067 | + | 0.827771i | \(0.310391\pi\) | |||||||
\(878\) | 29.8617 | 1.00778 | ||||||||
\(879\) | 16.0000 | 0.539667 | ||||||||
\(880\) | −12.6847 | −0.427600 | ||||||||
\(881\) | 36.1080 | 1.21651 | 0.608254 | − | 0.793743i | \(-0.291870\pi\) | ||||
0.608254 | + | 0.793743i | \(0.291870\pi\) | |||||||
\(882\) | −7.00000 | −0.235702 | ||||||||
\(883\) | 54.7386 | 1.84210 | 0.921051 | − | 0.389442i | \(-0.127332\pi\) | ||||
0.921051 | + | 0.389442i | \(0.127332\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 34.0540 | 1.14471 | ||||||||
\(886\) | 4.87689 | 0.163842 | ||||||||
\(887\) | 4.49242 | 0.150841 | 0.0754204 | − | 0.997152i | \(-0.475970\pi\) | ||||
0.0754204 | + | 0.997152i | \(0.475970\pi\) | |||||||
\(888\) | 7.31534 | 0.245487 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −61.8617 | −2.07361 | ||||||||
\(891\) | −3.56155 | −0.119317 | ||||||||
\(892\) | 28.4924 | 0.953997 | ||||||||
\(893\) | −36.4924 | −1.22117 | ||||||||
\(894\) | 16.9309 | 0.566253 | ||||||||
\(895\) | 58.7386 | 1.96342 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.56155 | 0.118917 | ||||||||
\(898\) | 17.3153 | 0.577820 | ||||||||
\(899\) | 2.43845 | 0.0813268 | ||||||||
\(900\) | −7.68466 | −0.256155 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −26.9309 | −0.896700 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −40.1080 | −1.33397 | ||||||||
\(905\) | −65.8617 | −2.18932 | ||||||||
\(906\) | −6.24621 | −0.207516 | ||||||||
\(907\) | 2.00000 | 0.0664089 | 0.0332045 | − | 0.999449i | \(-0.489429\pi\) | ||||
0.0332045 | + | 0.999449i | \(0.489429\pi\) | |||||||
\(908\) | 29.3693 | 0.974655 | ||||||||
\(909\) | −7.56155 | −0.250801 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.3153 | −0.971261 | −0.485630 | − | 0.874164i | \(-0.661410\pi\) | ||||
−0.485630 | + | 0.874164i | \(0.661410\pi\) | |||||||
\(912\) | −5.12311 | −0.169643 | ||||||||
\(913\) | 25.3693 | 0.839602 | ||||||||
\(914\) | −1.12311 | −0.0371490 | ||||||||
\(915\) | −42.0540 | −1.39026 | ||||||||
\(916\) | −0.192236 | −0.00635165 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.8078 | 0.389502 | 0.194751 | − | 0.980853i | \(-0.437610\pi\) | ||||
0.194751 | + | 0.980853i | \(0.437610\pi\) | |||||||
\(920\) | 10.6847 | 0.352263 | ||||||||
\(921\) | 7.31534 | 0.241049 | ||||||||
\(922\) | −38.3002 | −1.26135 | ||||||||
\(923\) | −37.1771 | −1.22370 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.7386 | 0.616122 | ||||||||
\(926\) | 20.4924 | 0.673423 | ||||||||
\(927\) | 1.56155 | 0.0512881 | ||||||||
\(928\) | −5.00000 | −0.164133 | ||||||||
\(929\) | 14.0000 | 0.459325 | 0.229663 | − | 0.973270i | \(-0.426238\pi\) | ||||
0.229663 | + | 0.973270i | \(0.426238\pi\) | |||||||
\(930\) | −8.68466 | −0.284781 | ||||||||
\(931\) | 35.8617 | 1.17532 | ||||||||
\(932\) | −9.12311 | −0.298837 | ||||||||
\(933\) | −16.8769 | −0.552525 | ||||||||
\(934\) | 25.4233 | 0.831876 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.6847 | 0.349239 | ||||||||
\(937\) | 18.9848 | 0.620208 | 0.310104 | − | 0.950703i | \(-0.399636\pi\) | ||||
0.310104 | + | 0.950703i | \(0.399636\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.75379 | 0.122500 | ||||||||
\(940\) | 25.3693 | 0.827456 | ||||||||
\(941\) | −44.5464 | −1.45217 | −0.726086 | − | 0.687604i | \(-0.758662\pi\) | ||||
−0.726086 | + | 0.687604i | \(0.758662\pi\) | |||||||
\(942\) | −19.1231 | −0.623064 | ||||||||
\(943\) | 7.56155 | 0.246238 | ||||||||
\(944\) | −9.56155 | −0.311202 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.1231 | 0.491695 | ||||||||
\(947\) | −49.4773 | −1.60780 | −0.803898 | − | 0.594768i | \(-0.797244\pi\) | ||||
−0.803898 | + | 0.594768i | \(0.797244\pi\) | |||||||
\(948\) | −2.00000 | −0.0649570 | ||||||||
\(949\) | 18.2462 | 0.592297 | ||||||||
\(950\) | −39.3693 | −1.27731 | ||||||||
\(951\) | −8.93087 | −0.289603 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.9848 | 0.874125 | 0.437062 | − | 0.899431i | \(-0.356019\pi\) | ||||
0.437062 | + | 0.899431i | \(0.356019\pi\) | |||||||
\(954\) | −4.24621 | −0.137476 | ||||||||
\(955\) | 69.6695 | 2.25445 | ||||||||
\(956\) | −10.4384 | −0.337604 | ||||||||
\(957\) | −3.56155 | −0.115129 | ||||||||
\(958\) | 21.3153 | 0.688667 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 24.9309 | 0.804640 | ||||||||
\(961\) | −25.0540 | −0.808193 | ||||||||
\(962\) | −8.68466 | −0.280005 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.6155 | 0.567358 | ||||||||
\(965\) | 24.4924 | 0.788439 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.7538 | 1.21408 | 0.607040 | − | 0.794671i | \(-0.292357\pi\) | ||||
0.607040 | + | 0.794671i | \(0.292357\pi\) | |||||||
\(968\) | −5.05398 | −0.162441 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 47.6155 | 1.52884 | ||||||||
\(971\) | 17.8078 | 0.571478 | 0.285739 | − | 0.958307i | \(-0.407761\pi\) | ||||
0.285739 | + | 0.958307i | \(0.407761\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.7386 | −0.344088 | ||||||||
\(975\) | 27.3693 | 0.876520 | ||||||||
\(976\) | 11.8078 | 0.377957 | ||||||||
\(977\) | −15.1771 | −0.485558 | −0.242779 | − | 0.970082i | \(-0.578059\pi\) | ||||
−0.242779 | + | 0.970082i | \(0.578059\pi\) | |||||||
\(978\) | −5.56155 | −0.177839 | ||||||||
\(979\) | −61.8617 | −1.97711 | ||||||||
\(980\) | −24.9309 | −0.796387 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | −2.63068 | −0.0839485 | ||||||||
\(983\) | −7.56155 | −0.241176 | −0.120588 | − | 0.992703i | \(-0.538478\pi\) | ||||
−0.120588 | + | 0.992703i | \(0.538478\pi\) | |||||||
\(984\) | 22.6847 | 0.723160 | ||||||||
\(985\) | −43.6155 | −1.38971 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.2462 | −0.580489 | ||||||||
\(989\) | −4.24621 | −0.135022 | ||||||||
\(990\) | 12.6847 | 0.403145 | ||||||||
\(991\) | −11.5076 | −0.365550 | −0.182775 | − | 0.983155i | \(-0.558508\pi\) | ||||
−0.182775 | + | 0.983155i | \(0.558508\pi\) | |||||||
\(992\) | −12.1922 | −0.387104 | ||||||||
\(993\) | −20.0000 | −0.634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.8078 | −0.374331 | ||||||||
\(996\) | −7.12311 | −0.225704 | ||||||||
\(997\) | −24.7386 | −0.783480 | −0.391740 | − | 0.920076i | \(-0.628127\pi\) | ||||
−0.391740 | + | 0.920076i | \(0.628127\pi\) | |||||||
\(998\) | 5.36932 | 0.169963 | ||||||||
\(999\) | −2.43845 | −0.0771491 |
(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 | 2001.2.a.f.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 6003.2.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.f.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
6003.2.a.d.1.2 | 2 | 3.2 | odd | 2 |