Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, 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("1950.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214 | 1.34840 | 0.674200 | − | 0.738549i | \(-0.264489\pi\) | ||||
0.674200 | + | 0.738549i | \(0.264489\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −3.23607 | −0.864876 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.23607 | 1.75500 | 0.877502 | − | 0.479573i | \(-0.159208\pi\) | ||||
0.877502 | + | 0.479573i | \(0.159208\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.76393 | −0.634089 | −0.317045 | − | 0.948411i | \(-0.602691\pi\) | ||||
−0.317045 | + | 0.948411i | \(0.602691\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.23607 | 0.706168 | ||||||||
\(22\) | −4.47214 | −0.953463 | ||||||||
\(23\) | 2.76393 | 0.576320 | 0.288160 | − | 0.957582i | \(-0.406957\pi\) | ||||
0.288160 | + | 0.957582i | \(0.406957\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.23607 | 0.611559 | ||||||||
\(29\) | −3.70820 | −0.688596 | −0.344298 | − | 0.938860i | \(-0.611883\pi\) | ||||
−0.344298 | + | 0.938860i | \(0.611883\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.47214 | 0.778499 | ||||||||
\(34\) | −7.23607 | −1.24098 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.9443 | −1.79923 | −0.899614 | − | 0.436687i | \(-0.856152\pi\) | ||||
−0.899614 | + | 0.436687i | \(0.856152\pi\) | |||||||
\(38\) | 2.76393 | 0.448369 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.52786 | 0.550960 | 0.275480 | − | 0.961307i | \(-0.411163\pi\) | ||||
0.275480 | + | 0.961307i | \(0.411163\pi\) | |||||||
\(42\) | −3.23607 | −0.499336 | ||||||||
\(43\) | −2.47214 | −0.376997 | −0.188499 | − | 0.982073i | \(-0.560362\pi\) | ||||
−0.188499 | + | 0.982073i | \(0.560362\pi\) | |||||||
\(44\) | 4.47214 | 0.674200 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.76393 | −0.407520 | ||||||||
\(47\) | 12.9443 | 1.88812 | 0.944058 | − | 0.329779i | \(-0.106974\pi\) | ||||
0.944058 | + | 0.329779i | \(0.106974\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.23607 | 1.01325 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.23607 | −0.432438 | ||||||||
\(57\) | −2.76393 | −0.366092 | ||||||||
\(58\) | 3.70820 | 0.486911 | ||||||||
\(59\) | −8.47214 | −1.10298 | −0.551489 | − | 0.834182i | \(-0.685940\pi\) | ||||
−0.551489 | + | 0.834182i | \(0.685940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.9443 | −1.40127 | −0.700635 | − | 0.713520i | \(-0.747100\pi\) | ||||
−0.700635 | + | 0.713520i | \(0.747100\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 3.23607 | 0.407706 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.47214 | −0.550482 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 7.23607 | 0.877502 | ||||||||
\(69\) | 2.76393 | 0.332738 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.47214 | −0.293389 | −0.146694 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146694 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 13.2361 | 1.54916 | 0.774582 | − | 0.632473i | \(-0.217960\pi\) | ||||
0.774582 | + | 0.632473i | \(0.217960\pi\) | |||||||
\(74\) | 10.9443 | 1.27225 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.76393 | −0.317045 | ||||||||
\(77\) | 14.4721 | 1.64925 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.52786 | −0.389587 | ||||||||
\(83\) | −4.94427 | −0.542704 | −0.271352 | − | 0.962480i | \(-0.587471\pi\) | ||||
−0.271352 | + | 0.962480i | \(0.587471\pi\) | |||||||
\(84\) | 3.23607 | 0.353084 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.47214 | 0.266577 | ||||||||
\(87\) | −3.70820 | −0.397561 | ||||||||
\(88\) | −4.47214 | −0.476731 | ||||||||
\(89\) | 0.472136 | 0.0500463 | 0.0250232 | − | 0.999687i | \(-0.492034\pi\) | ||||
0.0250232 | + | 0.999687i | \(0.492034\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.23607 | 0.339232 | ||||||||
\(92\) | 2.76393 | 0.288160 | ||||||||
\(93\) | −4.00000 | −0.414781 | ||||||||
\(94\) | −12.9443 | −1.33510 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −3.70820 | −0.376511 | −0.188256 | − | 0.982120i | \(-0.560283\pi\) | ||||
−0.188256 | + | 0.982120i | \(0.560283\pi\) | |||||||
\(98\) | −3.47214 | −0.350739 | ||||||||
\(99\) | 4.47214 | 0.449467 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.23607 | −0.919023 | −0.459512 | − | 0.888172i | \(-0.651976\pi\) | ||||
−0.459512 | + | 0.888172i | \(0.651976\pi\) | |||||||
\(102\) | −7.23607 | −0.716477 | ||||||||
\(103\) | 8.47214 | 0.834784 | 0.417392 | − | 0.908726i | \(-0.362944\pi\) | ||||
0.417392 | + | 0.908726i | \(0.362944\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.472136 | 0.0458579 | ||||||||
\(107\) | −1.52786 | −0.147704 | −0.0738521 | − | 0.997269i | \(-0.523529\pi\) | ||||
−0.0738521 | + | 0.997269i | \(0.523529\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −2.29180 | −0.219514 | −0.109757 | − | 0.993958i | \(-0.535007\pi\) | ||||
−0.109757 | + | 0.993958i | \(0.535007\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.9443 | −1.03878 | ||||||||
\(112\) | 3.23607 | 0.305780 | ||||||||
\(113\) | 18.6525 | 1.75468 | 0.877339 | − | 0.479872i | \(-0.159317\pi\) | ||||
0.877339 | + | 0.479872i | \(0.159317\pi\) | |||||||
\(114\) | 2.76393 | 0.258866 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.70820 | −0.344298 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 8.47214 | 0.779923 | ||||||||
\(119\) | 23.4164 | 2.14658 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 10.9443 | 0.990848 | ||||||||
\(123\) | 3.52786 | 0.318097 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.23607 | −0.288292 | ||||||||
\(127\) | 21.4164 | 1.90040 | 0.950199 | − | 0.311642i | \(-0.100879\pi\) | ||||
0.950199 | + | 0.311642i | \(0.100879\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.47214 | −0.217659 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.70820 | 0.848210 | 0.424105 | − | 0.905613i | \(-0.360589\pi\) | ||||
0.424105 | + | 0.905613i | \(0.360589\pi\) | |||||||
\(132\) | 4.47214 | 0.389249 | ||||||||
\(133\) | −8.94427 | −0.775567 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.23607 | −0.620488 | ||||||||
\(137\) | −19.8885 | −1.69919 | −0.849596 | − | 0.527433i | \(-0.823154\pi\) | ||||
−0.849596 | + | 0.527433i | \(0.823154\pi\) | |||||||
\(138\) | −2.76393 | −0.235282 | ||||||||
\(139\) | −6.47214 | −0.548959 | −0.274480 | − | 0.961593i | \(-0.588506\pi\) | ||||
−0.274480 | + | 0.961593i | \(0.588506\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9443 | 1.09010 | ||||||||
\(142\) | 2.47214 | 0.207457 | ||||||||
\(143\) | 4.47214 | 0.373979 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.2361 | −1.09542 | ||||||||
\(147\) | 3.47214 | 0.286377 | ||||||||
\(148\) | −10.9443 | −0.899614 | ||||||||
\(149\) | 13.5279 | 1.10825 | 0.554123 | − | 0.832435i | \(-0.313054\pi\) | ||||
0.554123 | + | 0.832435i | \(0.313054\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.4164 | −1.58008 | −0.790042 | − | 0.613052i | \(-0.789942\pi\) | ||||
−0.790042 | + | 0.613052i | \(0.789942\pi\) | |||||||
\(152\) | 2.76393 | 0.224184 | ||||||||
\(153\) | 7.23607 | 0.585001 | ||||||||
\(154\) | −14.4721 | −1.16620 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −18.9443 | −1.51192 | −0.755959 | − | 0.654619i | \(-0.772829\pi\) | ||||
−0.755959 | + | 0.654619i | \(0.772829\pi\) | |||||||
\(158\) | 4.00000 | 0.318223 | ||||||||
\(159\) | −0.472136 | −0.0374428 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.94427 | 0.704907 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 12.9443 | 1.01387 | 0.506937 | − | 0.861983i | \(-0.330778\pi\) | ||||
0.506937 | + | 0.861983i | \(0.330778\pi\) | |||||||
\(164\) | 3.52786 | 0.275480 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.94427 | 0.383750 | ||||||||
\(167\) | −19.4164 | −1.50249 | −0.751243 | − | 0.660025i | \(-0.770546\pi\) | ||||
−0.751243 | + | 0.660025i | \(0.770546\pi\) | |||||||
\(168\) | −3.23607 | −0.249668 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.76393 | −0.211363 | ||||||||
\(172\) | −2.47214 | −0.188499 | ||||||||
\(173\) | −22.9443 | −1.74442 | −0.872210 | − | 0.489131i | \(-0.837314\pi\) | ||||
−0.872210 | + | 0.489131i | \(0.837314\pi\) | |||||||
\(174\) | 3.70820 | 0.281118 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.47214 | 0.337100 | ||||||||
\(177\) | −8.47214 | −0.636805 | ||||||||
\(178\) | −0.472136 | −0.0353881 | ||||||||
\(179\) | 8.18034 | 0.611427 | 0.305714 | − | 0.952124i | \(-0.401105\pi\) | ||||
0.305714 | + | 0.952124i | \(0.401105\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4164 | 1.29455 | 0.647276 | − | 0.762256i | \(-0.275908\pi\) | ||||
0.647276 | + | 0.762256i | \(0.275908\pi\) | |||||||
\(182\) | −3.23607 | −0.239873 | ||||||||
\(183\) | −10.9443 | −0.809024 | ||||||||
\(184\) | −2.76393 | −0.203760 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | 32.3607 | 2.36645 | ||||||||
\(188\) | 12.9443 | 0.944058 | ||||||||
\(189\) | 3.23607 | 0.235389 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.4721 | 1.62603 | 0.813013 | − | 0.582245i | \(-0.197826\pi\) | ||||
0.813013 | + | 0.582245i | \(0.197826\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −8.29180 | −0.596857 | −0.298428 | − | 0.954432i | \(-0.596462\pi\) | ||||
−0.298428 | + | 0.954432i | \(0.596462\pi\) | |||||||
\(194\) | 3.70820 | 0.266234 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.47214 | 0.248010 | ||||||||
\(197\) | −14.9443 | −1.06474 | −0.532368 | − | 0.846513i | \(-0.678698\pi\) | ||||
−0.532368 | + | 0.846513i | \(0.678698\pi\) | |||||||
\(198\) | −4.47214 | −0.317821 | ||||||||
\(199\) | −0.944272 | −0.0669377 | −0.0334688 | − | 0.999440i | \(-0.510655\pi\) | ||||
−0.0334688 | + | 0.999440i | \(0.510655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.23607 | 0.649847 | ||||||||
\(203\) | −12.0000 | −0.842235 | ||||||||
\(204\) | 7.23607 | 0.506626 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.47214 | −0.590282 | ||||||||
\(207\) | 2.76393 | 0.192107 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −12.3607 | −0.855006 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8885 | 0.956127 | 0.478063 | − | 0.878325i | \(-0.341339\pi\) | ||||
0.478063 | + | 0.878325i | \(0.341339\pi\) | |||||||
\(212\) | −0.472136 | −0.0324264 | ||||||||
\(213\) | −2.47214 | −0.169388 | ||||||||
\(214\) | 1.52786 | 0.104443 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −12.9443 | −0.878714 | ||||||||
\(218\) | 2.29180 | 0.155220 | ||||||||
\(219\) | 13.2361 | 0.894411 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.23607 | 0.486751 | ||||||||
\(222\) | 10.9443 | 0.734531 | ||||||||
\(223\) | 16.7639 | 1.12260 | 0.561298 | − | 0.827614i | \(-0.310302\pi\) | ||||
0.561298 | + | 0.827614i | \(0.310302\pi\) | |||||||
\(224\) | −3.23607 | −0.216219 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.6525 | −1.24074 | ||||||||
\(227\) | 7.05573 | 0.468305 | 0.234153 | − | 0.972200i | \(-0.424768\pi\) | ||||
0.234153 | + | 0.972200i | \(0.424768\pi\) | |||||||
\(228\) | −2.76393 | −0.183046 | ||||||||
\(229\) | 9.70820 | 0.641536 | 0.320768 | − | 0.947158i | \(-0.396059\pi\) | ||||
0.320768 | + | 0.947158i | \(0.396059\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.4721 | 0.952197 | ||||||||
\(232\) | 3.70820 | 0.243456 | ||||||||
\(233\) | 20.1803 | 1.32206 | 0.661029 | − | 0.750360i | \(-0.270120\pi\) | ||||
0.661029 | + | 0.750360i | \(0.270120\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.47214 | −0.551489 | ||||||||
\(237\) | −4.00000 | −0.259828 | ||||||||
\(238\) | −23.4164 | −1.51786 | ||||||||
\(239\) | −21.8885 | −1.41585 | −0.707926 | − | 0.706287i | \(-0.750369\pi\) | ||||
−0.707926 | + | 0.706287i | \(0.750369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.52786 | 0.227250 | 0.113625 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113625 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(242\) | −9.00000 | −0.578542 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −10.9443 | −0.700635 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.52786 | −0.224928 | ||||||||
\(247\) | −2.76393 | −0.175865 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −4.94427 | −0.313331 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.29180 | 0.144657 | 0.0723284 | − | 0.997381i | \(-0.476957\pi\) | ||||
0.0723284 | + | 0.997381i | \(0.476957\pi\) | |||||||
\(252\) | 3.23607 | 0.203853 | ||||||||
\(253\) | 12.3607 | 0.777109 | ||||||||
\(254\) | −21.4164 | −1.34378 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.763932 | 0.0476528 | 0.0238264 | − | 0.999716i | \(-0.492415\pi\) | ||||
0.0238264 | + | 0.999716i | \(0.492415\pi\) | |||||||
\(258\) | 2.47214 | 0.153908 | ||||||||
\(259\) | −35.4164 | −2.20067 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.70820 | −0.229532 | ||||||||
\(262\) | −9.70820 | −0.599775 | ||||||||
\(263\) | 10.1803 | 0.627747 | 0.313873 | − | 0.949465i | \(-0.398373\pi\) | ||||
0.313873 | + | 0.949465i | \(0.398373\pi\) | |||||||
\(264\) | −4.47214 | −0.275241 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.94427 | 0.548408 | ||||||||
\(267\) | 0.472136 | 0.0288943 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.76393 | 0.412404 | 0.206202 | − | 0.978509i | \(-0.433890\pi\) | ||||
0.206202 | + | 0.978509i | \(0.433890\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.4164 | −0.693497 | −0.346749 | − | 0.937958i | \(-0.612714\pi\) | ||||
−0.346749 | + | 0.937958i | \(0.612714\pi\) | |||||||
\(272\) | 7.23607 | 0.438751 | ||||||||
\(273\) | 3.23607 | 0.195856 | ||||||||
\(274\) | 19.8885 | 1.20151 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.76393 | 0.166369 | ||||||||
\(277\) | 20.8328 | 1.25172 | 0.625861 | − | 0.779934i | \(-0.284748\pi\) | ||||
0.625861 | + | 0.779934i | \(0.284748\pi\) | |||||||
\(278\) | 6.47214 | 0.388173 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.4721 | 1.45989 | 0.729943 | − | 0.683508i | \(-0.239547\pi\) | ||||
0.729943 | + | 0.683508i | \(0.239547\pi\) | |||||||
\(282\) | −12.9443 | −0.770820 | ||||||||
\(283\) | −11.4164 | −0.678635 | −0.339318 | − | 0.940672i | \(-0.610196\pi\) | ||||
−0.339318 | + | 0.940672i | \(0.610196\pi\) | |||||||
\(284\) | −2.47214 | −0.146694 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.47214 | −0.264443 | ||||||||
\(287\) | 11.4164 | 0.673889 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 35.3607 | 2.08004 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.70820 | −0.217379 | ||||||||
\(292\) | 13.2361 | 0.774582 | ||||||||
\(293\) | 2.94427 | 0.172006 | 0.0860031 | − | 0.996295i | \(-0.472591\pi\) | ||||
0.0860031 | + | 0.996295i | \(0.472591\pi\) | |||||||
\(294\) | −3.47214 | −0.202499 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.9443 | 0.636123 | ||||||||
\(297\) | 4.47214 | 0.259500 | ||||||||
\(298\) | −13.5279 | −0.783648 | ||||||||
\(299\) | 2.76393 | 0.159842 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 19.4164 | 1.11729 | ||||||||
\(303\) | −9.23607 | −0.530598 | ||||||||
\(304\) | −2.76393 | −0.158522 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.23607 | −0.413658 | ||||||||
\(307\) | −24.3607 | −1.39034 | −0.695169 | − | 0.718847i | \(-0.744670\pi\) | ||||
−0.695169 | + | 0.718847i | \(0.744670\pi\) | |||||||
\(308\) | 14.4721 | 0.824626 | ||||||||
\(309\) | 8.47214 | 0.481963 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.4721 | −1.27428 | −0.637139 | − | 0.770749i | \(-0.719882\pi\) | ||||
−0.637139 | + | 0.770749i | \(0.719882\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −19.4164 | −1.09748 | −0.548740 | − | 0.835993i | \(-0.684892\pi\) | ||||
−0.548740 | + | 0.835993i | \(0.684892\pi\) | |||||||
\(314\) | 18.9443 | 1.06909 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 13.4164 | 0.753541 | 0.376770 | − | 0.926307i | \(-0.377035\pi\) | ||||
0.376770 | + | 0.926307i | \(0.377035\pi\) | |||||||
\(318\) | 0.472136 | 0.0264761 | ||||||||
\(319\) | −16.5836 | −0.928503 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.52786 | −0.0852771 | ||||||||
\(322\) | −8.94427 | −0.498445 | ||||||||
\(323\) | −20.0000 | −1.11283 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.9443 | −0.716917 | ||||||||
\(327\) | −2.29180 | −0.126737 | ||||||||
\(328\) | −3.52786 | −0.194794 | ||||||||
\(329\) | 41.8885 | 2.30939 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.76393 | −0.151919 | −0.0759597 | − | 0.997111i | \(-0.524202\pi\) | ||||
−0.0759597 | + | 0.997111i | \(0.524202\pi\) | |||||||
\(332\) | −4.94427 | −0.271352 | ||||||||
\(333\) | −10.9443 | −0.599742 | ||||||||
\(334\) | 19.4164 | 1.06242 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.23607 | 0.176542 | ||||||||
\(337\) | −6.47214 | −0.352560 | −0.176280 | − | 0.984340i | \(-0.556406\pi\) | ||||
−0.176280 | + | 0.984340i | \(0.556406\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 18.6525 | 1.01306 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.8885 | −0.968719 | ||||||||
\(342\) | 2.76393 | 0.149456 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | 2.47214 | 0.133289 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.9443 | 1.23349 | ||||||||
\(347\) | 1.52786 | 0.0820200 | 0.0410100 | − | 0.999159i | \(-0.486942\pi\) | ||||
0.0410100 | + | 0.999159i | \(0.486942\pi\) | |||||||
\(348\) | −3.70820 | −0.198781 | ||||||||
\(349\) | −15.2361 | −0.815568 | −0.407784 | − | 0.913078i | \(-0.633698\pi\) | ||||
−0.407784 | + | 0.913078i | \(0.633698\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −4.47214 | −0.238366 | ||||||||
\(353\) | −26.9443 | −1.43410 | −0.717049 | − | 0.697022i | \(-0.754508\pi\) | ||||
−0.717049 | + | 0.697022i | \(0.754508\pi\) | |||||||
\(354\) | 8.47214 | 0.450289 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.472136 | 0.0250232 | ||||||||
\(357\) | 23.4164 | 1.23933 | ||||||||
\(358\) | −8.18034 | −0.432344 | ||||||||
\(359\) | 6.47214 | 0.341586 | 0.170793 | − | 0.985307i | \(-0.445367\pi\) | ||||
0.170793 | + | 0.985307i | \(0.445367\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3607 | −0.597931 | ||||||||
\(362\) | −17.4164 | −0.915386 | ||||||||
\(363\) | 9.00000 | 0.472377 | ||||||||
\(364\) | 3.23607 | 0.169616 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.9443 | 0.572066 | ||||||||
\(367\) | 0.472136 | 0.0246453 | 0.0123226 | − | 0.999924i | \(-0.496077\pi\) | ||||
0.0123226 | + | 0.999924i | \(0.496077\pi\) | |||||||
\(368\) | 2.76393 | 0.144080 | ||||||||
\(369\) | 3.52786 | 0.183653 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.52786 | −0.0793227 | ||||||||
\(372\) | −4.00000 | −0.207390 | ||||||||
\(373\) | 2.00000 | 0.103556 | 0.0517780 | − | 0.998659i | \(-0.483511\pi\) | ||||
0.0517780 | + | 0.998659i | \(0.483511\pi\) | |||||||
\(374\) | −32.3607 | −1.67333 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.9443 | −0.667550 | ||||||||
\(377\) | −3.70820 | −0.190982 | ||||||||
\(378\) | −3.23607 | −0.166445 | ||||||||
\(379\) | −35.1246 | −1.80423 | −0.902115 | − | 0.431496i | \(-0.857986\pi\) | ||||
−0.902115 | + | 0.431496i | \(0.857986\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.4164 | 1.09720 | ||||||||
\(382\) | −22.4721 | −1.14977 | ||||||||
\(383\) | 5.52786 | 0.282461 | 0.141230 | − | 0.989977i | \(-0.454894\pi\) | ||||
0.141230 | + | 0.989977i | \(0.454894\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.29180 | 0.422041 | ||||||||
\(387\) | −2.47214 | −0.125666 | ||||||||
\(388\) | −3.70820 | −0.188256 | ||||||||
\(389\) | 12.6525 | 0.641506 | 0.320753 | − | 0.947163i | \(-0.396064\pi\) | ||||
0.320753 | + | 0.947163i | \(0.396064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.0000 | 1.01144 | ||||||||
\(392\) | −3.47214 | −0.175369 | ||||||||
\(393\) | 9.70820 | 0.489714 | ||||||||
\(394\) | 14.9443 | 0.752882 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.47214 | 0.224733 | ||||||||
\(397\) | 17.4164 | 0.874104 | 0.437052 | − | 0.899436i | \(-0.356022\pi\) | ||||
0.437052 | + | 0.899436i | \(0.356022\pi\) | |||||||
\(398\) | 0.944272 | 0.0473321 | ||||||||
\(399\) | −8.94427 | −0.447774 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.4721 | −1.22208 | −0.611040 | − | 0.791600i | \(-0.709249\pi\) | ||||
−0.611040 | + | 0.791600i | \(0.709249\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | −9.23607 | −0.459512 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | −48.9443 | −2.42608 | ||||||||
\(408\) | −7.23607 | −0.358239 | ||||||||
\(409\) | 6.00000 | 0.296681 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.8885 | −0.981030 | ||||||||
\(412\) | 8.47214 | 0.417392 | ||||||||
\(413\) | −27.4164 | −1.34907 | ||||||||
\(414\) | −2.76393 | −0.135840 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −6.47214 | −0.316942 | ||||||||
\(418\) | 12.3607 | 0.604581 | ||||||||
\(419\) | 27.5967 | 1.34819 | 0.674095 | − | 0.738645i | \(-0.264534\pi\) | ||||
0.674095 | + | 0.738645i | \(0.264534\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7082 | −0.668097 | −0.334048 | − | 0.942556i | \(-0.608415\pi\) | ||||
−0.334048 | + | 0.942556i | \(0.608415\pi\) | |||||||
\(422\) | −13.8885 | −0.676084 | ||||||||
\(423\) | 12.9443 | 0.629372 | ||||||||
\(424\) | 0.472136 | 0.0229289 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.47214 | 0.119775 | ||||||||
\(427\) | −35.4164 | −1.71392 | ||||||||
\(428\) | −1.52786 | −0.0738521 | ||||||||
\(429\) | 4.47214 | 0.215917 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8328 | −0.714472 | −0.357236 | − | 0.934014i | \(-0.616281\pi\) | ||||
−0.357236 | + | 0.934014i | \(0.616281\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −9.52786 | −0.457880 | −0.228940 | − | 0.973441i | \(-0.573526\pi\) | ||||
−0.228940 | + | 0.973441i | \(0.573526\pi\) | |||||||
\(434\) | 12.9443 | 0.621345 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.29180 | −0.109757 | ||||||||
\(437\) | −7.63932 | −0.365438 | ||||||||
\(438\) | −13.2361 | −0.632444 | ||||||||
\(439\) | −4.94427 | −0.235977 | −0.117989 | − | 0.993015i | \(-0.537645\pi\) | ||||
−0.117989 | + | 0.993015i | \(0.537645\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.47214 | 0.165340 | ||||||||
\(442\) | −7.23607 | −0.344185 | ||||||||
\(443\) | −22.4721 | −1.06768 | −0.533842 | − | 0.845584i | \(-0.679252\pi\) | ||||
−0.533842 | + | 0.845584i | \(0.679252\pi\) | |||||||
\(444\) | −10.9443 | −0.519392 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.7639 | −0.793795 | ||||||||
\(447\) | 13.5279 | 0.639846 | ||||||||
\(448\) | 3.23607 | 0.152890 | ||||||||
\(449\) | 0.472136 | 0.0222815 | 0.0111407 | − | 0.999938i | \(-0.496454\pi\) | ||||
0.0111407 | + | 0.999938i | \(0.496454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.7771 | 0.742914 | ||||||||
\(452\) | 18.6525 | 0.877339 | ||||||||
\(453\) | −19.4164 | −0.912262 | ||||||||
\(454\) | −7.05573 | −0.331142 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.76393 | 0.129433 | ||||||||
\(457\) | −3.70820 | −0.173462 | −0.0867312 | − | 0.996232i | \(-0.527642\pi\) | ||||
−0.0867312 | + | 0.996232i | \(0.527642\pi\) | |||||||
\(458\) | −9.70820 | −0.453635 | ||||||||
\(459\) | 7.23607 | 0.337751 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.8885 | 1.95094 | 0.975472 | − | 0.220124i | \(-0.0706461\pi\) | ||||
0.975472 | + | 0.220124i | \(0.0706461\pi\) | |||||||
\(462\) | −14.4721 | −0.673305 | ||||||||
\(463\) | −22.2918 | −1.03599 | −0.517994 | − | 0.855384i | \(-0.673321\pi\) | ||||
−0.517994 | + | 0.855384i | \(0.673321\pi\) | |||||||
\(464\) | −3.70820 | −0.172149 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.1803 | −0.934836 | ||||||||
\(467\) | 6.47214 | 0.299495 | 0.149747 | − | 0.988724i | \(-0.452154\pi\) | ||||
0.149747 | + | 0.988724i | \(0.452154\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.9443 | −0.872906 | ||||||||
\(472\) | 8.47214 | 0.389962 | ||||||||
\(473\) | −11.0557 | −0.508343 | ||||||||
\(474\) | 4.00000 | 0.183726 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 23.4164 | 1.07329 | ||||||||
\(477\) | −0.472136 | −0.0216176 | ||||||||
\(478\) | 21.8885 | 1.00116 | ||||||||
\(479\) | −36.0000 | −1.64488 | −0.822441 | − | 0.568850i | \(-0.807388\pi\) | ||||
−0.822441 | + | 0.568850i | \(0.807388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.9443 | −0.499016 | ||||||||
\(482\) | −3.52786 | −0.160690 | ||||||||
\(483\) | 8.94427 | 0.406978 | ||||||||
\(484\) | 9.00000 | 0.409091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −23.5967 | −1.06927 | −0.534635 | − | 0.845083i | \(-0.679551\pi\) | ||||
−0.534635 | + | 0.845083i | \(0.679551\pi\) | |||||||
\(488\) | 10.9443 | 0.495424 | ||||||||
\(489\) | 12.9443 | 0.585360 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.1803 | −0.730209 | −0.365104 | − | 0.930967i | \(-0.618967\pi\) | ||||
−0.365104 | + | 0.930967i | \(0.618967\pi\) | |||||||
\(492\) | 3.52786 | 0.159048 | ||||||||
\(493\) | −26.8328 | −1.20849 | ||||||||
\(494\) | 2.76393 | 0.124355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 4.94427 | 0.221558 | ||||||||
\(499\) | −39.1246 | −1.75146 | −0.875729 | − | 0.482803i | \(-0.839619\pi\) | ||||
−0.875729 | + | 0.482803i | \(0.839619\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.4164 | −0.867461 | ||||||||
\(502\) | −2.29180 | −0.102288 | ||||||||
\(503\) | −30.7639 | −1.37170 | −0.685848 | − | 0.727745i | \(-0.740569\pi\) | ||||
−0.685848 | + | 0.727745i | \(0.740569\pi\) | |||||||
\(504\) | −3.23607 | −0.144146 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.3607 | −0.549499 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 21.4164 | 0.950199 | ||||||||
\(509\) | −15.0557 | −0.667333 | −0.333667 | − | 0.942691i | \(-0.608286\pi\) | ||||
−0.333667 | + | 0.942691i | \(0.608286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.8328 | 1.89481 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.76393 | −0.122031 | ||||||||
\(514\) | −0.763932 | −0.0336956 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.47214 | −0.108830 | ||||||||
\(517\) | 57.8885 | 2.54594 | ||||||||
\(518\) | 35.4164 | 1.55611 | ||||||||
\(519\) | −22.9443 | −1.00714 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.8328 | 0.912702 | 0.456351 | − | 0.889800i | \(-0.349156\pi\) | ||||
0.456351 | + | 0.889800i | \(0.349156\pi\) | |||||||
\(522\) | 3.70820 | 0.162304 | ||||||||
\(523\) | 8.00000 | 0.349816 | 0.174908 | − | 0.984585i | \(-0.444037\pi\) | ||||
0.174908 | + | 0.984585i | \(0.444037\pi\) | |||||||
\(524\) | 9.70820 | 0.424105 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.1803 | −0.443884 | ||||||||
\(527\) | −28.9443 | −1.26083 | ||||||||
\(528\) | 4.47214 | 0.194625 | ||||||||
\(529\) | −15.3607 | −0.667856 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.47214 | −0.367659 | ||||||||
\(532\) | −8.94427 | −0.387783 | ||||||||
\(533\) | 3.52786 | 0.152809 | ||||||||
\(534\) | −0.472136 | −0.0204313 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.18034 | 0.353008 | ||||||||
\(538\) | −6.76393 | −0.291614 | ||||||||
\(539\) | 15.5279 | 0.668832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.76393 | −0.204817 | −0.102409 | − | 0.994742i | \(-0.532655\pi\) | ||||
−0.102409 | + | 0.994742i | \(0.532655\pi\) | |||||||
\(542\) | 11.4164 | 0.490377 | ||||||||
\(543\) | 17.4164 | 0.747410 | ||||||||
\(544\) | −7.23607 | −0.310244 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.23607 | −0.138491 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | −19.8885 | −0.849596 | ||||||||
\(549\) | −10.9443 | −0.467090 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.2492 | 0.436632 | ||||||||
\(552\) | −2.76393 | −0.117641 | ||||||||
\(553\) | −12.9443 | −0.550446 | ||||||||
\(554\) | −20.8328 | −0.885102 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.47214 | −0.274480 | ||||||||
\(557\) | 19.3050 | 0.817977 | 0.408989 | − | 0.912540i | \(-0.365882\pi\) | ||||
0.408989 | + | 0.912540i | \(0.365882\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | −2.47214 | −0.104560 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.3607 | 1.36627 | ||||||||
\(562\) | −24.4721 | −1.03229 | ||||||||
\(563\) | −19.4164 | −0.818304 | −0.409152 | − | 0.912466i | \(-0.634175\pi\) | ||||
−0.409152 | + | 0.912466i | \(0.634175\pi\) | |||||||
\(564\) | 12.9443 | 0.545052 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.4164 | 0.479867 | ||||||||
\(567\) | 3.23607 | 0.135902 | ||||||||
\(568\) | 2.47214 | 0.103729 | ||||||||
\(569\) | 34.9443 | 1.46494 | 0.732470 | − | 0.680799i | \(-0.238367\pi\) | ||||
0.732470 | + | 0.680799i | \(0.238367\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.58359 | −0.359212 | −0.179606 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179606 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(572\) | 4.47214 | 0.186989 | ||||||||
\(573\) | 22.4721 | 0.938787 | ||||||||
\(574\) | −11.4164 | −0.476512 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −43.1246 | −1.79530 | −0.897651 | − | 0.440708i | \(-0.854727\pi\) | ||||
−0.897651 | + | 0.440708i | \(0.854727\pi\) | |||||||
\(578\) | −35.3607 | −1.47081 | ||||||||
\(579\) | −8.29180 | −0.344595 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.0000 | −0.663792 | ||||||||
\(582\) | 3.70820 | 0.153710 | ||||||||
\(583\) | −2.11146 | −0.0874476 | ||||||||
\(584\) | −13.2361 | −0.547712 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.94427 | −0.121627 | ||||||||
\(587\) | −2.11146 | −0.0871491 | −0.0435746 | − | 0.999050i | \(-0.513875\pi\) | ||||
−0.0435746 | + | 0.999050i | \(0.513875\pi\) | |||||||
\(588\) | 3.47214 | 0.143188 | ||||||||
\(589\) | 11.0557 | 0.455543 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.9443 | −0.614725 | ||||||||
\(592\) | −10.9443 | −0.449807 | ||||||||
\(593\) | 3.52786 | 0.144872 | 0.0724360 | − | 0.997373i | \(-0.476923\pi\) | ||||
0.0724360 | + | 0.997373i | \(0.476923\pi\) | |||||||
\(594\) | −4.47214 | −0.183494 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.5279 | 0.554123 | ||||||||
\(597\) | −0.944272 | −0.0386465 | ||||||||
\(598\) | −2.76393 | −0.113026 | ||||||||
\(599\) | −6.11146 | −0.249707 | −0.124854 | − | 0.992175i | \(-0.539846\pi\) | ||||
−0.124854 | + | 0.992175i | \(0.539846\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.4164 | 0.547267 | 0.273633 | − | 0.961834i | \(-0.411775\pi\) | ||||
0.273633 | + | 0.961834i | \(0.411775\pi\) | |||||||
\(602\) | 8.00000 | 0.326056 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.4164 | −0.790042 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.23607 | 0.375190 | ||||||||
\(607\) | 1.41641 | 0.0574902 | 0.0287451 | − | 0.999587i | \(-0.490849\pi\) | ||||
0.0287451 | + | 0.999587i | \(0.490849\pi\) | |||||||
\(608\) | 2.76393 | 0.112092 | ||||||||
\(609\) | −12.0000 | −0.486265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.9443 | 0.523669 | ||||||||
\(612\) | 7.23607 | 0.292501 | ||||||||
\(613\) | 18.0000 | 0.727013 | 0.363507 | − | 0.931592i | \(-0.381579\pi\) | ||||
0.363507 | + | 0.931592i | \(0.381579\pi\) | |||||||
\(614\) | 24.3607 | 0.983117 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.4721 | −0.583099 | ||||||||
\(617\) | 35.8885 | 1.44482 | 0.722409 | − | 0.691466i | \(-0.243035\pi\) | ||||
0.722409 | + | 0.691466i | \(0.243035\pi\) | |||||||
\(618\) | −8.47214 | −0.340799 | ||||||||
\(619\) | −25.2361 | −1.01432 | −0.507162 | − | 0.861851i | \(-0.669305\pi\) | ||||
−0.507162 | + | 0.861851i | \(0.669305\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.76393 | 0.110913 | ||||||||
\(622\) | 22.4721 | 0.901051 | ||||||||
\(623\) | 1.52786 | 0.0612126 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19.4164 | 0.776036 | ||||||||
\(627\) | −12.3607 | −0.493638 | ||||||||
\(628\) | −18.9443 | −0.755959 | ||||||||
\(629\) | −79.1935 | −3.15765 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5836 | −0.500945 | −0.250472 | − | 0.968124i | \(-0.580586\pi\) | ||||
−0.250472 | + | 0.968124i | \(0.580586\pi\) | |||||||
\(632\) | 4.00000 | 0.159111 | ||||||||
\(633\) | 13.8885 | 0.552020 | ||||||||
\(634\) | −13.4164 | −0.532834 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.472136 | −0.0187214 | ||||||||
\(637\) | 3.47214 | 0.137571 | ||||||||
\(638\) | 16.5836 | 0.656551 | ||||||||
\(639\) | −2.47214 | −0.0977962 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.3050 | −0.920490 | −0.460245 | − | 0.887792i | \(-0.652238\pi\) | ||||
−0.460245 | + | 0.887792i | \(0.652238\pi\) | |||||||
\(642\) | 1.52786 | 0.0603000 | ||||||||
\(643\) | 19.0557 | 0.751485 | 0.375742 | − | 0.926724i | \(-0.377388\pi\) | ||||
0.375742 | + | 0.926724i | \(0.377388\pi\) | |||||||
\(644\) | 8.94427 | 0.352454 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.0000 | 0.786889 | ||||||||
\(647\) | −3.70820 | −0.145785 | −0.0728923 | − | 0.997340i | \(-0.523223\pi\) | ||||
−0.0728923 | + | 0.997340i | \(0.523223\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −37.8885 | −1.48726 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.9443 | −0.507326 | ||||||||
\(652\) | 12.9443 | 0.506937 | ||||||||
\(653\) | −30.3607 | −1.18811 | −0.594053 | − | 0.804426i | \(-0.702473\pi\) | ||||
−0.594053 | + | 0.804426i | \(0.702473\pi\) | |||||||
\(654\) | 2.29180 | 0.0896163 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.52786 | 0.137740 | ||||||||
\(657\) | 13.2361 | 0.516388 | ||||||||
\(658\) | −41.8885 | −1.63299 | ||||||||
\(659\) | −10.0689 | −0.392228 | −0.196114 | − | 0.980581i | \(-0.562832\pi\) | ||||
−0.196114 | + | 0.980581i | \(0.562832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.7082 | −1.62226 | −0.811131 | − | 0.584865i | \(-0.801147\pi\) | ||||
−0.811131 | + | 0.584865i | \(0.801147\pi\) | |||||||
\(662\) | 2.76393 | 0.107423 | ||||||||
\(663\) | 7.23607 | 0.281026 | ||||||||
\(664\) | 4.94427 | 0.191875 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.9443 | 0.424082 | ||||||||
\(667\) | −10.2492 | −0.396852 | ||||||||
\(668\) | −19.4164 | −0.751243 | ||||||||
\(669\) | 16.7639 | 0.648131 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −48.9443 | −1.88947 | ||||||||
\(672\) | −3.23607 | −0.124834 | ||||||||
\(673\) | 44.0000 | 1.69608 | 0.848038 | − | 0.529936i | \(-0.177784\pi\) | ||||
0.848038 | + | 0.529936i | \(0.177784\pi\) | |||||||
\(674\) | 6.47214 | 0.249297 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 27.5279 | 1.05798 | 0.528991 | − | 0.848628i | \(-0.322571\pi\) | ||||
0.528991 | + | 0.848628i | \(0.322571\pi\) | |||||||
\(678\) | −18.6525 | −0.716344 | ||||||||
\(679\) | −12.0000 | −0.460518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.05573 | 0.270376 | ||||||||
\(682\) | 17.8885 | 0.684988 | ||||||||
\(683\) | −41.8885 | −1.60282 | −0.801410 | − | 0.598115i | \(-0.795917\pi\) | ||||
−0.801410 | + | 0.598115i | \(0.795917\pi\) | |||||||
\(684\) | −2.76393 | −0.105682 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11.4164 | 0.435880 | ||||||||
\(687\) | 9.70820 | 0.370391 | ||||||||
\(688\) | −2.47214 | −0.0942493 | ||||||||
\(689\) | −0.472136 | −0.0179869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.291796 | 0.0111004 | 0.00555022 | − | 0.999985i | \(-0.498233\pi\) | ||||
0.00555022 | + | 0.999985i | \(0.498233\pi\) | |||||||
\(692\) | −22.9443 | −0.872210 | ||||||||
\(693\) | 14.4721 | 0.549751 | ||||||||
\(694\) | −1.52786 | −0.0579969 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.70820 | 0.140559 | ||||||||
\(697\) | 25.5279 | 0.966937 | ||||||||
\(698\) | 15.2361 | 0.576694 | ||||||||
\(699\) | 20.1803 | 0.763291 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.0689 | −0.909069 | −0.454535 | − | 0.890729i | \(-0.650194\pi\) | ||||
−0.454535 | + | 0.890729i | \(0.650194\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 30.2492 | 1.14087 | ||||||||
\(704\) | 4.47214 | 0.168550 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.9443 | 1.01406 | ||||||||
\(707\) | −29.8885 | −1.12407 | ||||||||
\(708\) | −8.47214 | −0.318402 | ||||||||
\(709\) | 32.5410 | 1.22210 | 0.611052 | − | 0.791591i | \(-0.290747\pi\) | ||||
0.611052 | + | 0.791591i | \(0.290747\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | −0.150012 | ||||||||
\(712\) | −0.472136 | −0.0176940 | ||||||||
\(713\) | −11.0557 | −0.414040 | ||||||||
\(714\) | −23.4164 | −0.876337 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.18034 | 0.305714 | ||||||||
\(717\) | −21.8885 | −0.817443 | ||||||||
\(718\) | −6.47214 | −0.241538 | ||||||||
\(719\) | 20.9443 | 0.781090 | 0.390545 | − | 0.920584i | \(-0.372287\pi\) | ||||
0.390545 | + | 0.920584i | \(0.372287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.4164 | 1.02104 | ||||||||
\(722\) | 11.3607 | 0.422801 | ||||||||
\(723\) | 3.52786 | 0.131203 | ||||||||
\(724\) | 17.4164 | 0.647276 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.00000 | −0.334021 | ||||||||
\(727\) | 18.0000 | 0.667583 | 0.333792 | − | 0.942647i | \(-0.391672\pi\) | ||||
0.333792 | + | 0.942647i | \(0.391672\pi\) | |||||||
\(728\) | −3.23607 | −0.119937 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.8885 | −0.661632 | ||||||||
\(732\) | −10.9443 | −0.404512 | ||||||||
\(733\) | 33.4164 | 1.23426 | 0.617132 | − | 0.786860i | \(-0.288295\pi\) | ||||
0.617132 | + | 0.786860i | \(0.288295\pi\) | |||||||
\(734\) | −0.472136 | −0.0174269 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.76393 | −0.101880 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.52786 | −0.129862 | ||||||||
\(739\) | −0.291796 | −0.0107339 | −0.00536695 | − | 0.999986i | \(-0.501708\pi\) | ||||
−0.00536695 | + | 0.999986i | \(0.501708\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.76393 | −0.101536 | ||||||||
\(742\) | 1.52786 | 0.0560897 | ||||||||
\(743\) | 28.3607 | 1.04045 | 0.520226 | − | 0.854029i | \(-0.325848\pi\) | ||||
0.520226 | + | 0.854029i | \(0.325848\pi\) | |||||||
\(744\) | 4.00000 | 0.146647 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.00000 | −0.0732252 | ||||||||
\(747\) | −4.94427 | −0.180901 | ||||||||
\(748\) | 32.3607 | 1.18322 | ||||||||
\(749\) | −4.94427 | −0.180660 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.8328 | −1.70895 | −0.854477 | − | 0.519489i | \(-0.826122\pi\) | ||||
−0.854477 | + | 0.519489i | \(0.826122\pi\) | |||||||
\(752\) | 12.9443 | 0.472029 | ||||||||
\(753\) | 2.29180 | 0.0835177 | ||||||||
\(754\) | 3.70820 | 0.135045 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.23607 | 0.117695 | ||||||||
\(757\) | −38.0000 | −1.38113 | −0.690567 | − | 0.723269i | \(-0.742639\pi\) | ||||
−0.690567 | + | 0.723269i | \(0.742639\pi\) | |||||||
\(758\) | 35.1246 | 1.27578 | ||||||||
\(759\) | 12.3607 | 0.448664 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.52786 | 0.272885 | 0.136442 | − | 0.990648i | \(-0.456433\pi\) | ||||
0.136442 | + | 0.990648i | \(0.456433\pi\) | |||||||
\(762\) | −21.4164 | −0.775835 | ||||||||
\(763\) | −7.41641 | −0.268492 | ||||||||
\(764\) | 22.4721 | 0.813013 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.52786 | −0.199730 | ||||||||
\(767\) | −8.47214 | −0.305911 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −4.83282 | −0.174276 | −0.0871379 | − | 0.996196i | \(-0.527772\pi\) | ||||
−0.0871379 | + | 0.996196i | \(0.527772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.763932 | 0.0275123 | ||||||||
\(772\) | −8.29180 | −0.298428 | ||||||||
\(773\) | −2.94427 | −0.105898 | −0.0529491 | − | 0.998597i | \(-0.516862\pi\) | ||||
−0.0529491 | + | 0.998597i | \(0.516862\pi\) | |||||||
\(774\) | 2.47214 | 0.0888591 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.70820 | 0.133117 | ||||||||
\(777\) | −35.4164 | −1.27056 | ||||||||
\(778\) | −12.6525 | −0.453613 | ||||||||
\(779\) | −9.75078 | −0.349358 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.0557 | −0.395605 | ||||||||
\(782\) | −20.0000 | −0.715199 | ||||||||
\(783\) | −3.70820 | −0.132520 | ||||||||
\(784\) | 3.47214 | 0.124005 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.70820 | −0.346280 | ||||||||
\(787\) | 28.9443 | 1.03175 | 0.515876 | − | 0.856663i | \(-0.327467\pi\) | ||||
0.515876 | + | 0.856663i | \(0.327467\pi\) | |||||||
\(788\) | −14.9443 | −0.532368 | ||||||||
\(789\) | 10.1803 | 0.362430 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 60.3607 | 2.14618 | ||||||||
\(792\) | −4.47214 | −0.158910 | ||||||||
\(793\) | −10.9443 | −0.388642 | ||||||||
\(794\) | −17.4164 | −0.618085 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.944272 | −0.0334688 | ||||||||
\(797\) | 9.05573 | 0.320770 | 0.160385 | − | 0.987055i | \(-0.448726\pi\) | ||||
0.160385 | + | 0.987055i | \(0.448726\pi\) | |||||||
\(798\) | 8.94427 | 0.316624 | ||||||||
\(799\) | 93.6656 | 3.31365 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.472136 | 0.0166821 | ||||||||
\(802\) | 24.4721 | 0.864141 | ||||||||
\(803\) | 59.1935 | 2.08889 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | 6.76393 | 0.238102 | ||||||||
\(808\) | 9.23607 | 0.324924 | ||||||||
\(809\) | 31.5279 | 1.10846 | 0.554230 | − | 0.832363i | \(-0.313013\pi\) | ||||
0.554230 | + | 0.832363i | \(0.313013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.29180 | 0.150705 | 0.0753527 | − | 0.997157i | \(-0.475992\pi\) | ||||
0.0753527 | + | 0.997157i | \(0.475992\pi\) | |||||||
\(812\) | −12.0000 | −0.421117 | ||||||||
\(813\) | −11.4164 | −0.400391 | ||||||||
\(814\) | 48.9443 | 1.71550 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.23607 | 0.253313 | ||||||||
\(817\) | 6.83282 | 0.239050 | ||||||||
\(818\) | −6.00000 | −0.209785 | ||||||||
\(819\) | 3.23607 | 0.113077 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.4721 | −1.06348 | −0.531742 | − | 0.846906i | \(-0.678463\pi\) | ||||
−0.531742 | + | 0.846906i | \(0.678463\pi\) | |||||||
\(822\) | 19.8885 | 0.693693 | ||||||||
\(823\) | 48.2492 | 1.68186 | 0.840931 | − | 0.541142i | \(-0.182008\pi\) | ||||
0.840931 | + | 0.541142i | \(0.182008\pi\) | |||||||
\(824\) | −8.47214 | −0.295141 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27.4164 | 0.953939 | ||||||||
\(827\) | −41.8885 | −1.45661 | −0.728304 | − | 0.685254i | \(-0.759691\pi\) | ||||
−0.728304 | + | 0.685254i | \(0.759691\pi\) | |||||||
\(828\) | 2.76393 | 0.0960533 | ||||||||
\(829\) | 42.7214 | 1.48377 | 0.741887 | − | 0.670525i | \(-0.233931\pi\) | ||||
0.741887 | + | 0.670525i | \(0.233931\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.8328 | 0.722682 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 25.1246 | 0.870516 | ||||||||
\(834\) | 6.47214 | 0.224112 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.3607 | −0.427503 | ||||||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | −27.5967 | −0.953314 | ||||||||
\(839\) | −51.7771 | −1.78754 | −0.893772 | − | 0.448522i | \(-0.851951\pi\) | ||||
−0.893772 | + | 0.448522i | \(0.851951\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2492 | −0.525835 | ||||||||
\(842\) | 13.7082 | 0.472416 | ||||||||
\(843\) | 24.4721 | 0.842865 | ||||||||
\(844\) | 13.8885 | 0.478063 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.9443 | −0.445033 | ||||||||
\(847\) | 29.1246 | 1.00073 | ||||||||
\(848\) | −0.472136 | −0.0162132 | ||||||||
\(849\) | −11.4164 | −0.391810 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.2492 | −1.03693 | ||||||||
\(852\) | −2.47214 | −0.0846940 | ||||||||
\(853\) | 41.4164 | 1.41807 | 0.709035 | − | 0.705173i | \(-0.249131\pi\) | ||||
0.709035 | + | 0.705173i | \(0.249131\pi\) | |||||||
\(854\) | 35.4164 | 1.21192 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.52786 | 0.0522213 | ||||||||
\(857\) | −0.180340 | −0.00616029 | −0.00308015 | − | 0.999995i | \(-0.500980\pi\) | ||||
−0.00308015 | + | 0.999995i | \(0.500980\pi\) | |||||||
\(858\) | −4.47214 | −0.152676 | ||||||||
\(859\) | 36.0000 | 1.22830 | 0.614152 | − | 0.789188i | \(-0.289498\pi\) | ||||
0.614152 | + | 0.789188i | \(0.289498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.4164 | 0.389070 | ||||||||
\(862\) | 14.8328 | 0.505208 | ||||||||
\(863\) | 22.4721 | 0.764960 | 0.382480 | − | 0.923964i | \(-0.375070\pi\) | ||||
0.382480 | + | 0.923964i | \(0.375070\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.52786 | 0.323770 | ||||||||
\(867\) | 35.3607 | 1.20091 | ||||||||
\(868\) | −12.9443 | −0.439357 | ||||||||
\(869\) | −17.8885 | −0.606827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.29180 | 0.0776100 | ||||||||
\(873\) | −3.70820 | −0.125504 | ||||||||
\(874\) | 7.63932 | 0.258404 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.2361 | 0.447205 | ||||||||
\(877\) | 24.4721 | 0.826365 | 0.413183 | − | 0.910648i | \(-0.364417\pi\) | ||||
0.413183 | + | 0.910648i | \(0.364417\pi\) | |||||||
\(878\) | 4.94427 | 0.166861 | ||||||||
\(879\) | 2.94427 | 0.0993078 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3607 | 1.15764 | 0.578820 | − | 0.815455i | \(-0.303513\pi\) | ||||
0.578820 | + | 0.815455i | \(0.303513\pi\) | |||||||
\(882\) | −3.47214 | −0.116913 | ||||||||
\(883\) | 25.8885 | 0.871219 | 0.435609 | − | 0.900136i | \(-0.356533\pi\) | ||||
0.435609 | + | 0.900136i | \(0.356533\pi\) | |||||||
\(884\) | 7.23607 | 0.243375 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.4721 | 0.754966 | ||||||||
\(887\) | −10.1803 | −0.341822 | −0.170911 | − | 0.985286i | \(-0.554671\pi\) | ||||
−0.170911 | + | 0.985286i | \(0.554671\pi\) | |||||||
\(888\) | 10.9443 | 0.367266 | ||||||||
\(889\) | 69.3050 | 2.32441 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.47214 | 0.149822 | ||||||||
\(892\) | 16.7639 | 0.561298 | ||||||||
\(893\) | −35.7771 | −1.19723 | ||||||||
\(894\) | −13.5279 | −0.452439 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.23607 | −0.108109 | ||||||||
\(897\) | 2.76393 | 0.0922850 | ||||||||
\(898\) | −0.472136 | −0.0157554 | ||||||||
\(899\) | 14.8328 | 0.494702 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.41641 | −0.113817 | ||||||||
\(902\) | −15.7771 | −0.525320 | ||||||||
\(903\) | −8.00000 | −0.266223 | ||||||||
\(904\) | −18.6525 | −0.620372 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 19.4164 | 0.645067 | ||||||||
\(907\) | 45.5279 | 1.51173 | 0.755864 | − | 0.654729i | \(-0.227217\pi\) | ||||
0.755864 | + | 0.654729i | \(0.227217\pi\) | |||||||
\(908\) | 7.05573 | 0.234153 | ||||||||
\(909\) | −9.23607 | −0.306341 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.0557 | −0.366293 | −0.183146 | − | 0.983086i | \(-0.558628\pi\) | ||||
−0.183146 | + | 0.983086i | \(0.558628\pi\) | |||||||
\(912\) | −2.76393 | −0.0915229 | ||||||||
\(913\) | −22.1115 | −0.731782 | ||||||||
\(914\) | 3.70820 | 0.122656 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.70820 | 0.320768 | ||||||||
\(917\) | 31.4164 | 1.03746 | ||||||||
\(918\) | −7.23607 | −0.238826 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.3607 | −0.802712 | ||||||||
\(922\) | −41.8885 | −1.37953 | ||||||||
\(923\) | −2.47214 | −0.0813713 | ||||||||
\(924\) | 14.4721 | 0.476098 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.2918 | 0.732554 | ||||||||
\(927\) | 8.47214 | 0.278261 | ||||||||
\(928\) | 3.70820 | 0.121728 | ||||||||
\(929\) | 32.4721 | 1.06538 | 0.532688 | − | 0.846312i | \(-0.321182\pi\) | ||||
0.532688 | + | 0.846312i | \(0.321182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.59675 | −0.314521 | ||||||||
\(932\) | 20.1803 | 0.661029 | ||||||||
\(933\) | −22.4721 | −0.735705 | ||||||||
\(934\) | −6.47214 | −0.211775 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 19.7771 | 0.646089 | 0.323045 | − | 0.946384i | \(-0.395294\pi\) | ||||
0.323045 | + | 0.946384i | \(0.395294\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.4164 | −0.633631 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.5279 | −1.22337 | −0.611687 | − | 0.791100i | \(-0.709509\pi\) | ||||
−0.611687 | + | 0.791100i | \(0.709509\pi\) | |||||||
\(942\) | 18.9443 | 0.617238 | ||||||||
\(943\) | 9.75078 | 0.317529 | ||||||||
\(944\) | −8.47214 | −0.275745 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.0557 | 0.359453 | ||||||||
\(947\) | 4.94427 | 0.160667 | 0.0803336 | − | 0.996768i | \(-0.474401\pi\) | ||||
0.0803336 | + | 0.996768i | \(0.474401\pi\) | |||||||
\(948\) | −4.00000 | −0.129914 | ||||||||
\(949\) | 13.2361 | 0.429661 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.4164 | 0.435057 | ||||||||
\(952\) | −23.4164 | −0.758930 | ||||||||
\(953\) | 29.1246 | 0.943439 | 0.471719 | − | 0.881749i | \(-0.343634\pi\) | ||||
0.471719 | + | 0.881749i | \(0.343634\pi\) | |||||||
\(954\) | 0.472136 | 0.0152860 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21.8885 | −0.707926 | ||||||||
\(957\) | −16.5836 | −0.536071 | ||||||||
\(958\) | 36.0000 | 1.16311 | ||||||||
\(959\) | −64.3607 | −2.07831 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 10.9443 | 0.352857 | ||||||||
\(963\) | −1.52786 | −0.0492347 | ||||||||
\(964\) | 3.52786 | 0.113625 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.94427 | −0.287777 | ||||||||
\(967\) | −56.5410 | −1.81824 | −0.909118 | − | 0.416538i | \(-0.863243\pi\) | ||||
−0.909118 | + | 0.416538i | \(0.863243\pi\) | |||||||
\(968\) | −9.00000 | −0.289271 | ||||||||
\(969\) | −20.0000 | −0.642493 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.2361 | 0.745681 | 0.372840 | − | 0.927895i | \(-0.378384\pi\) | ||||
0.372840 | + | 0.927895i | \(0.378384\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −20.9443 | −0.671443 | ||||||||
\(974\) | 23.5967 | 0.756089 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.9443 | −0.350318 | ||||||||
\(977\) | −10.3607 | −0.331468 | −0.165734 | − | 0.986171i | \(-0.552999\pi\) | ||||
−0.165734 | + | 0.986171i | \(0.552999\pi\) | |||||||
\(978\) | −12.9443 | −0.413912 | ||||||||
\(979\) | 2.11146 | 0.0674824 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.29180 | −0.0731714 | ||||||||
\(982\) | 16.1803 | 0.516335 | ||||||||
\(983\) | −7.41641 | −0.236547 | −0.118273 | − | 0.992981i | \(-0.537736\pi\) | ||||
−0.118273 | + | 0.992981i | \(0.537736\pi\) | |||||||
\(984\) | −3.52786 | −0.112464 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 26.8328 | 0.854531 | ||||||||
\(987\) | 41.8885 | 1.33333 | ||||||||
\(988\) | −2.76393 | −0.0879324 | ||||||||
\(989\) | −6.83282 | −0.217271 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.9443 | 0.792381 | 0.396190 | − | 0.918168i | \(-0.370332\pi\) | ||||
0.396190 | + | 0.918168i | \(0.370332\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | −2.76393 | −0.0877107 | ||||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.94427 | −0.156665 | ||||||||
\(997\) | 43.8885 | 1.38996 | 0.694982 | − | 0.719027i | \(-0.255412\pi\) | ||||
0.694982 | + | 0.719027i | \(0.255412\pi\) | |||||||
\(998\) | 39.1246 | 1.23847 | ||||||||
\(999\) | −10.9443 | −0.346261 |
(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 | 1950.2.a.be.1.2 | 2 | ||
3.2 | odd | 2 | 5850.2.a.cm.1.2 | 2 | |||
5.2 | odd | 4 | 390.2.e.e.79.2 | ✓ | 4 | ||
5.3 | odd | 4 | 390.2.e.e.79.3 | yes | 4 | ||
5.4 | even | 2 | 1950.2.a.bf.1.1 | 2 | |||
15.2 | even | 4 | 1170.2.e.e.469.3 | 4 | |||
15.8 | even | 4 | 1170.2.e.e.469.2 | 4 | |||
15.14 | odd | 2 | 5850.2.a.cf.1.1 | 2 | |||
20.3 | even | 4 | 3120.2.l.k.1249.1 | 4 | |||
20.7 | even | 4 | 3120.2.l.k.1249.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.e.e.79.2 | ✓ | 4 | 5.2 | odd | 4 | ||
390.2.e.e.79.3 | yes | 4 | 5.3 | odd | 4 | ||
1170.2.e.e.469.2 | 4 | 15.8 | even | 4 | |||
1170.2.e.e.469.3 | 4 | 15.2 | even | 4 | |||
1950.2.a.be.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1950.2.a.bf.1.1 | 2 | 5.4 | even | 2 | |||
3120.2.l.k.1249.1 | 4 | 20.3 | even | 4 | |||
3120.2.l.k.1249.4 | 4 | 20.7 | even | 4 | |||
5850.2.a.cf.1.1 | 2 | 15.14 | odd | 2 | |||
5850.2.a.cm.1.2 | 2 | 3.2 | odd | 2 |