Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(1,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.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: | \(15.6506787962\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.41421 | 1.39385 | 0.696923 | − | 0.717146i | \(-0.254552\pi\) | ||||
0.696923 | + | 0.717146i | \(0.254552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.82843 | −1.45583 | −0.727913 | − | 0.685670i | \(-0.759509\pi\) | ||||
−0.727913 | + | 0.685670i | \(0.759509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.65685 | −0.886917 | −0.443459 | − | 0.896295i | \(-0.646249\pi\) | ||||
−0.443459 | + | 0.896295i | \(0.646249\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65685 | −1.29777 | −0.648886 | − | 0.760886i | \(-0.724765\pi\) | ||||
−0.648886 | + | 0.760886i | \(0.724765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.41421 | −1.75448 | −0.877242 | − | 0.480048i | \(-0.840619\pi\) | ||||
−0.877242 | + | 0.480048i | \(0.840619\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.17157 | −0.403251 | −0.201625 | − | 0.979463i | \(-0.564622\pi\) | ||||
−0.201625 | + | 0.979463i | \(0.564622\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.82843 | 0.867211 | 0.433606 | − | 0.901103i | \(-0.357241\pi\) | ||||
0.433606 | + | 0.901103i | \(0.357241\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.6569 | −2.02920 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.65685 | −0.929981 | −0.464991 | − | 0.885316i | \(-0.653942\pi\) | ||||
−0.464991 | + | 0.885316i | \(0.653942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.82843 | −0.773167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.171573 | −0.0267952 | −0.0133976 | − | 0.999910i | \(-0.504265\pi\) | ||||
−0.0133976 | + | 0.999910i | \(0.504265\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.8995 | 1.96715 | 0.983577 | − | 0.180488i | \(-0.0577676\pi\) | ||||
0.983577 | + | 0.180488i | \(0.0577676\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.82843 | −0.421637 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.343146 | −0.0500530 | −0.0250265 | − | 0.999687i | \(-0.507967\pi\) | ||||
−0.0250265 | + | 0.999687i | \(0.507967\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.82843 | −1.23623 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65685 | 0.777029 | 0.388514 | − | 0.921443i | \(-0.372988\pi\) | ||||
0.388514 | + | 0.921443i | \(0.372988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.82843 | 0.651065 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.6569 | −1.80889 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.65685 | 0.596249 | 0.298125 | − | 0.954527i | \(-0.403639\pi\) | ||||
0.298125 | + | 0.954527i | \(0.403639\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.89949 | 0.842907 | 0.421454 | − | 0.906850i | \(-0.361520\pi\) | ||||
0.421454 | + | 0.906850i | \(0.361520\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −20.3137 | −2.44548 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.65685 | 0.896167 | 0.448084 | − | 0.893992i | \(-0.352107\pi\) | ||||
0.448084 | + | 0.893992i | \(0.352107\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.41421 | 0.278769 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.2426 | 1.45357 | 0.726784 | − | 0.686866i | \(-0.241014\pi\) | ||||
0.726784 | + | 0.686866i | \(0.241014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65685 | 0.396642 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.24264 | −0.562070 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.6569 | 1.76562 | 0.882812 | − | 0.469727i | \(-0.155648\pi\) | ||||
0.882812 | + | 0.469727i | \(0.155648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.6569 | 1.20876 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.65685 | 0.580381 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.6569 | −1.37257 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.48528 | −0.545806 | −0.272903 | − | 0.962042i | \(-0.587984\pi\) | ||||
−0.272903 | + | 0.962042i | \(0.587984\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4142 | −1.02614 | −0.513071 | − | 0.858346i | \(-0.671492\pi\) | ||||
−0.513071 | + | 0.858346i | \(0.671492\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.41421 | −0.813433 | −0.406716 | − | 0.913554i | \(-0.633326\pi\) | ||||
−0.406716 | + | 0.913554i | \(0.633326\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.31371 | −0.413178 | −0.206589 | − | 0.978428i | \(-0.566236\pi\) | ||||
−0.206589 | + | 0.978428i | \(0.566236\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.6569 | −1.29625 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3137 | −1.06430 | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.41421 | 0.784629 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.65685 | −0.522976 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.414214 | −0.0373484 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.6569 | −1.38932 | −0.694661 | − | 0.719338i | \(-0.744445\pi\) | ||||
−0.694661 | + | 0.719338i | \(0.744445\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 31.1421 | 2.74191 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.34315 | −0.204722 | −0.102361 | − | 0.994747i | \(-0.532640\pi\) | ||||
−0.102361 | + | 0.994747i | \(0.532640\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.414214 | 0.0356498 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.00000 | −0.341743 | −0.170872 | − | 0.985293i | \(-0.554658\pi\) | ||||
−0.170872 | + | 0.985293i | \(0.554658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4853 | 1.22863 | 0.614313 | − | 0.789063i | \(-0.289433\pi\) | ||||
0.614313 | + | 0.789063i | \(0.289433\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.828427 | −0.0697661 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.65685 | 0.807547 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.17157 | 0.180339 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.65685 | −0.545351 | −0.272675 | − | 0.962106i | \(-0.587908\pi\) | ||||
−0.272675 | + | 0.962106i | \(0.587908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8284 | −1.36948 | −0.684739 | − | 0.728788i | \(-0.740084\pi\) | ||||
−0.684739 | + | 0.728788i | \(0.740084\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.3431 | −0.836194 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.82843 | −0.387829 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.3137 | 1.70102 | 0.850510 | − | 0.525960i | \(-0.176294\pi\) | ||||
0.850510 | + | 0.525960i | \(0.176294\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.6569 | 1.08306 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.34315 | −0.340181 | −0.170091 | − | 0.985428i | \(-0.554406\pi\) | ||||
−0.170091 | + | 0.985428i | \(0.554406\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.6569 | 0.907485 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0711 | 0.934087 | 0.467044 | − | 0.884234i | \(-0.345319\pi\) | ||||
0.467044 | + | 0.884234i | \(0.345319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.0000 | −1.22355 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.6569 | −1.64654 | −0.823270 | − | 0.567650i | \(-0.807853\pi\) | ||||
−0.823270 | + | 0.567650i | \(0.807853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.65685 | 0.725854 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.4853 | 0.783707 | 0.391853 | − | 0.920028i | \(-0.371834\pi\) | ||||
0.391853 | + | 0.920028i | \(0.371834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.82843 | 0.730541 | 0.365271 | − | 0.930901i | \(-0.380976\pi\) | ||||
0.365271 | + | 0.930901i | \(0.380976\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2426 | 0.831080 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.65685 | 0.415900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.6569 | 1.29120 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.4853 | −1.62698 | −0.813489 | − | 0.581580i | \(-0.802435\pi\) | ||||
−0.813489 | + | 0.581580i | \(0.802435\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.3137 | 1.24627 | 0.623134 | − | 0.782115i | \(-0.285859\pi\) | ||||
0.623134 | + | 0.782115i | \(0.285859\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.82843 | 0.345771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6569 | 0.830516 | 0.415258 | − | 0.909704i | \(-0.363691\pi\) | ||||
0.415258 | + | 0.909704i | \(0.363691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.686292 | 0.0486499 | 0.0243250 | − | 0.999704i | \(-0.492256\pi\) | ||||
0.0243250 | + | 0.999704i | \(0.492256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.6569 | 1.17488 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.171573 | 0.0119832 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −23.7990 | −1.65414 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.3137 | 1.88933 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.6274 | −1.28236 | −0.641182 | − | 0.767389i | \(-0.721556\pi\) | ||||
−0.641182 | + | 0.767389i | \(0.721556\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.9706 | −1.98503 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.8995 | −0.879738 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.4853 | 1.24912 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.31371 | 0.491973 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.9706 | −1.27036 | −0.635181 | − | 0.772363i | \(-0.719075\pi\) | ||||
−0.635181 | + | 0.772363i | \(0.719075\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0000 | −0.929213 | −0.464606 | − | 0.885517i | \(-0.653804\pi\) | ||||
−0.464606 | + | 0.885517i | \(0.653804\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000 | 0.925146 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.343146 | 0.0224802 | 0.0112401 | − | 0.999937i | \(-0.496422\pi\) | ||||
0.0112401 | + | 0.999937i | \(0.496422\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.343146 | 0.0223844 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.65685 | −0.627280 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.5147 | −0.874194 | −0.437097 | − | 0.899414i | \(-0.643993\pi\) | ||||
−0.437097 | + | 0.899414i | \(0.643993\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6569 | −1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3137 | 0.719874 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 31.9706 | 2.02605 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.4558 | −1.48052 | −0.740260 | − | 0.672321i | \(-0.765298\pi\) | ||||
−0.740260 | + | 0.672321i | \(0.765298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.6274 | 2.55422 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.82843 | 0.552858 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.31371 | 0.456217 | 0.228108 | − | 0.973636i | \(-0.426746\pi\) | ||||
0.228108 | + | 0.973636i | \(0.426746\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.14214 | −0.380189 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.72792 | 0.599849 | 0.299925 | − | 0.953963i | \(-0.403038\pi\) | ||||
0.299925 | + | 0.953963i | \(0.403038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.65685 | −0.347498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 40.2132 | 2.46101 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.65685 | −0.283933 | −0.141967 | − | 0.989871i | \(-0.545343\pi\) | ||||
−0.141967 | + | 0.989871i | \(0.545343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.3137 | −1.17322 | −0.586612 | − | 0.809868i | \(-0.699539\pi\) | ||||
−0.586612 | + | 0.809868i | \(0.699539\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.82843 | −0.291165 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.6274 | −0.999045 | −0.499522 | − | 0.866301i | \(-0.666491\pi\) | ||||
−0.499522 | + | 0.866301i | \(0.666491\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.6569 | 0.817614 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3137 | 1.51009 | 0.755045 | − | 0.655673i | \(-0.227615\pi\) | ||||
0.755045 | + | 0.655673i | \(0.227615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0000 | −1.06999 | −0.534994 | − | 0.844856i | \(-0.679686\pi\) | ||||
−0.534994 | + | 0.844856i | \(0.679686\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.6569 | 0.808962 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.4853 | −0.849142 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.9706 | 0.991431 | 0.495715 | − | 0.868485i | \(-0.334906\pi\) | ||||
0.495715 | + | 0.868485i | \(0.334906\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.8284 | 0.973213 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.2426 | −0.760770 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.65685 | −0.266651 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.2426 | −0.755797 | −0.377899 | − | 0.925847i | \(-0.623353\pi\) | ||||
−0.377899 | + | 0.925847i | \(0.623353\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.1421 | −1.43029 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3431 | −0.586506 | −0.293253 | − | 0.956035i | \(-0.594738\pi\) | ||||
−0.293253 | + | 0.956035i | \(0.594738\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9706 | 0.733140 | 0.366570 | − | 0.930391i | \(-0.380532\pi\) | ||||
0.366570 | + | 0.930391i | \(0.380532\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.0000 | −1.23564 | −0.617822 | − | 0.786318i | \(-0.711985\pi\) | ||||
−0.617822 | + | 0.786318i | \(0.711985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4853 | 0.587063 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.3137 | −1.13380 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.6863 | 1.15102 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.4142 | −0.575907 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.51472 | 0.522976 | 0.261488 | − | 0.965207i | \(-0.415787\pi\) | ||||
0.261488 | + | 0.965207i | \(0.415787\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.0000 | −0.876795 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.89949 | −0.376960 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.97056 | −0.488658 | −0.244329 | − | 0.969692i | \(-0.578568\pi\) | ||||
−0.244329 | + | 0.969692i | \(0.578568\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.3137 | −1.48348 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.3137 | −1.26251 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.3137 | 1.09365 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.3848 | −1.36273 | −0.681363 | − | 0.731946i | \(-0.738613\pi\) | ||||
−0.681363 | + | 0.731946i | \(0.738613\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.17157 | −0.223299 | −0.111650 | − | 0.993748i | \(-0.535613\pi\) | ||||
−0.111650 | + | 0.993748i | \(0.535613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.828427 | 0.0442182 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.3431 | −1.18921 | −0.594603 | − | 0.804020i | \(-0.702691\pi\) | ||||
−0.594603 | + | 0.804020i | \(0.702691\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.0000 | 0.636894 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.4853 | 0.553392 | 0.276696 | − | 0.960958i | \(-0.410761\pi\) | ||||
0.276696 | + | 0.960958i | \(0.410761\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.7279 | 1.56031 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.65685 | −0.400778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.4142 | −1.27441 | −0.637206 | − | 0.770694i | \(-0.719910\pi\) | ||||
−0.637206 | + | 0.770694i | \(0.719910\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.485281 | −0.0252627 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0000 | 0.621336 | 0.310668 | − | 0.950518i | \(-0.399447\pi\) | ||||
0.310668 | + | 0.950518i | \(0.399447\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.41421 | −0.124669 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.34315 | 0.223683 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.3137 | 1.40301 | 0.701505 | − | 0.712664i | \(-0.252512\pi\) | ||||
0.701505 | + | 0.712664i | \(0.252512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.7990 | −1.93650 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.8995 | −0.965719 | −0.482860 | − | 0.875698i | \(-0.660402\pi\) | ||||
−0.482860 | + | 0.875698i | \(0.660402\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 36.4853 | 1.85465 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.3137 | −0.877840 | −0.438920 | − | 0.898526i | \(-0.644639\pi\) | ||||
−0.438920 | + | 0.898526i | \(0.644639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.7696 | 1.55608 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.65685 | −0.285351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.6274 | −1.03526 | −0.517630 | − | 0.855604i | \(-0.673186\pi\) | ||||
−0.517630 | + | 0.855604i | \(0.673186\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.68629 | −0.483710 | −0.241855 | − | 0.970312i | \(-0.577756\pi\) | ||||
−0.241855 | + | 0.970312i | \(0.577756\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.65685 | −0.481042 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.48528 | 0.471327 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.3137 | 1.35389 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.14214 | −0.155369 | −0.0776843 | − | 0.996978i | \(-0.524753\pi\) | ||||
−0.0776843 | + | 0.996978i | \(0.524753\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.65685 | −0.476337 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.2426 | −0.650056 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 34.9706 | 1.71252 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.31371 | −0.357298 | −0.178649 | − | 0.983913i | \(-0.557173\pi\) | ||||
−0.178649 | + | 0.983913i | \(0.557173\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.6569 | 1.88402 | 0.942010 | − | 0.335585i | \(-0.108934\pi\) | ||||
0.942010 | + | 0.335585i | \(0.108934\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.970563 | −0.0471904 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.65685 | −0.177383 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.3137 | 1.12560 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.82843 | 0.232577 | 0.116289 | − | 0.993215i | \(-0.462900\pi\) | ||||
0.116289 | + | 0.993215i | \(0.462900\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.31371 | −0.159247 | −0.0796233 | − | 0.996825i | \(-0.525372\pi\) | ||||
−0.0796233 | + | 0.996825i | \(0.525372\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.24264 | 0.251365 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 47.5980 | 2.27692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.6569 | 1.41544 | 0.707722 | − | 0.706491i | \(-0.249723\pi\) | ||||
0.707722 | + | 0.706491i | \(0.249723\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.4142 | −0.874886 | −0.437443 | − | 0.899246i | \(-0.644116\pi\) | ||||
−0.437443 | + | 0.899246i | \(0.644116\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.6569 | −0.789611 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.0711 | −0.760135 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.48528 | 0.447638 | 0.223819 | − | 0.974631i | \(-0.428148\pi\) | ||||
0.223819 | + | 0.974631i | \(0.428148\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.828427 | 0.0390091 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −40.6274 | −1.90884 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.97056 | −0.232513 | −0.116257 | − | 0.993219i | \(-0.537089\pi\) | ||||
−0.116257 | + | 0.993219i | \(0.537089\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.51472 | 0.0707010 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.3137 | 0.992678 | 0.496339 | − | 0.868129i | \(-0.334677\pi\) | ||||
0.496339 | + | 0.868129i | \(0.334677\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.89949 | −0.227699 | −0.113849 | − | 0.993498i | \(-0.536318\pi\) | ||||
−0.113849 | + | 0.993498i | \(0.536318\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.6569 | −0.540574 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.8701 | −0.734379 | −0.367189 | − | 0.930146i | \(-0.619680\pi\) | ||||
−0.367189 | + | 0.930146i | \(0.619680\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 51.4558 | 2.37096 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −62.2843 | −2.86383 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.65685 | −0.259554 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.0000 | 0.732590 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.4853 | 0.844614 | 0.422307 | − | 0.906453i | \(-0.361220\pi\) | ||||
0.422307 | + | 0.906453i | \(0.361220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3137 | 0.515861 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000 | 0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.2843 | 0.828539 | 0.414270 | − | 0.910154i | \(-0.364037\pi\) | ||||
0.414270 | + | 0.910154i | \(0.364037\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.4853 | −0.474161 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.4853 | 0.834229 | 0.417115 | − | 0.908854i | \(-0.363041\pi\) | ||||
0.417115 | + | 0.908854i | \(0.363041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.94113 | 0.357650 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.6569 | 0.613830 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.8579 | 0.709896 | 0.354948 | − | 0.934886i | \(-0.384499\pi\) | ||||
0.354948 | + | 0.934886i | \(0.384499\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.1421 | 1.30197 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.0711 | 0.805749 | 0.402875 | − | 0.915255i | \(-0.368011\pi\) | ||||
0.402875 | + | 0.915255i | \(0.368011\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.48528 | 0.244092 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.7279 | −0.964971 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.5147 | 0.732002 | 0.366001 | − | 0.930614i | \(-0.380727\pi\) | ||||
0.366001 | + | 0.930614i | \(0.380727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.34315 | 0.103452 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.4142 | 0.458905 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.65685 | 0.0728684 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −52.2843 | −2.29502 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.62742 | 0.377974 | 0.188987 | − | 0.981980i | \(-0.439480\pi\) | ||||
0.188987 | + | 0.981980i | \(0.439480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.9411 | 1.74650 | 0.873252 | − | 0.487269i | \(-0.162007\pi\) | ||||
0.873252 | + | 0.487269i | \(0.162007\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.6569 | −0.769145 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 47.7990 | 2.07822 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3137 | 0.490973 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.343146 | 0.0148633 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.41421 | 0.363778 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.3137 | 1.09237 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.51472 | −0.280090 | −0.140045 | − | 0.990145i | \(-0.544725\pi\) | ||||
−0.140045 | + | 0.990145i | \(0.544725\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.7279 | 1.01826 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.31371 | 0.184779 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.7279 | −1.18556 | −0.592780 | − | 0.805364i | \(-0.701970\pi\) | ||||
−0.592780 | + | 0.805364i | \(0.701970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.1716 | 0.562149 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.2843 | 0.523328 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.6569 | 0.579701 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.31371 | 0.225149 | 0.112575 | − | 0.993643i | \(-0.464090\pi\) | ||||
0.112575 | + | 0.993643i | \(0.464090\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.7990 | −1.09118 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 42.6274 | 1.79973 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.0711 | −0.424445 | −0.212222 | − | 0.977221i | \(-0.568070\pi\) | ||||
−0.212222 | + | 0.977221i | \(0.568070\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.3137 | 0.475971 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.62742 | 0.361680 | 0.180840 | − | 0.983513i | \(-0.442118\pi\) | ||||
0.180840 | + | 0.983513i | \(0.442118\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9706 | 0.542801 | 0.271401 | − | 0.962466i | \(-0.412513\pi\) | ||||
0.271401 | + | 0.962466i | \(0.412513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −54.2843 | −2.26776 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.41421 | −0.350897 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.2843 | −1.42727 | −0.713636 | − | 0.700516i | \(-0.752953\pi\) | ||||
−0.713636 | + | 0.700516i | \(0.752953\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 41.7990 | 1.73711 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.3137 | −1.13122 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.65685 | 0.233882 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.3137 | 1.87030 | 0.935148 | − | 0.354256i | \(-0.115266\pi\) | ||||
0.935148 | + | 0.354256i | \(0.115266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.3137 | −1.12544 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.1421 | 1.15761 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.9411 | 1.55806 | 0.779028 | − | 0.626990i | \(-0.215713\pi\) | ||||
0.779028 | + | 0.626990i | \(0.215713\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.65685 | 0.0678105 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.62742 | −0.107353 | −0.0536767 | − | 0.998558i | \(-0.517094\pi\) | ||||
−0.0536767 | + | 0.998558i | \(0.517094\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.0000 | 1.38689 | 0.693444 | − | 0.720510i | \(-0.256092\pi\) | ||||
0.693444 | + | 0.720510i | \(0.256092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.5147 | 0.794701 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.3137 | −0.500623 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7574 | −0.761338 | −0.380669 | − | 0.924711i | \(-0.624306\pi\) | ||||
−0.380669 | + | 0.924711i | \(0.624306\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.686292 | 0.0277644 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.02944 | 0.203137 | 0.101569 | − | 0.994829i | \(-0.467614\pi\) | ||||
0.101569 | + | 0.994829i | \(0.467614\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.414214 | 0.0167027 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.3137 | −1.42168 | −0.710838 | − | 0.703356i | \(-0.751684\pi\) | ||||
−0.710838 | + | 0.703356i | \(0.751684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.4558 | 0.460449 | 0.230225 | − | 0.973138i | \(-0.426054\pi\) | ||||
0.230225 | + | 0.973138i | \(0.426054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.48528 | 0.139860 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 65.9411 | 2.63343 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.6863 | 0.824816 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4853 | −0.735887 | −0.367944 | − | 0.929848i | \(-0.619938\pi\) | ||||
−0.367944 | + | 0.929848i | \(0.619938\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −44.9706 | −1.78742 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.6569 | 0.621323 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33.9411 | −1.34269 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.1127 | −1.90034 | −0.950169 | − | 0.311736i | \(-0.899089\pi\) | ||||
−0.950169 | + | 0.311736i | \(0.899089\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.0000 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.1421 | −1.22622 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.2426 | 1.14965 | 0.574823 | − | 0.818277i | \(-0.305071\pi\) | ||||
0.574823 | + | 0.818277i | \(0.305071\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.3137 | −0.758129 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.34315 | −0.169960 | −0.0849802 | − | 0.996383i | \(-0.527083\pi\) | ||||
−0.0849802 | + | 0.996383i | \(0.527083\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.34315 | 0.0915543 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.6569 | 0.844914 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.3137 | 1.37563 | 0.687813 | − | 0.725888i | \(-0.258571\pi\) | ||||
0.687813 | + | 0.725888i | \(0.258571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.6863 | 1.07687 | 0.538436 | − | 0.842666i | \(-0.319015\pi\) | ||||
0.538436 | + | 0.842666i | \(0.319015\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.6569 | 0.685735 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.2721 | 0.707498 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −45.7990 | −1.77069 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.4853 | −0.868035 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.65685 | 0.218056 | 0.109028 | − | 0.994039i | \(-0.465226\pi\) | ||||
0.109028 | + | 0.994039i | \(0.465226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.414214 | −0.0159431 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.9706 | 0.421633 | 0.210816 | − | 0.977526i | \(-0.432388\pi\) | ||||
0.210816 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.7990 | −1.29518 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.0711 | −0.614942 | −0.307471 | − | 0.951557i | \(-0.599483\pi\) | ||||
−0.307471 | + | 0.951557i | \(0.599483\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00000 | 0.152832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33.7990 | 1.28951 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.3137 | −0.431018 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7696 | −1.17053 | −0.585264 | − | 0.810842i | \(-0.699009\pi\) | ||||
−0.585264 | + | 0.810842i | \(0.699009\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.4853 | −0.549458 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.627417 | 0.0237651 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.828427 | 0.0313340 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.0000 | −0.415464 | −0.207732 | − | 0.978186i | \(-0.566608\pi\) | ||||
−0.207732 | + | 0.978186i | \(0.566608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.0000 | 1.20690 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.828427 | 0.0312004 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.4264 | 1.85625 | 0.928124 | − | 0.372272i | \(-0.121421\pi\) | ||||
0.928124 | + | 0.372272i | \(0.121421\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.3137 | −0.424297 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40.6274 | −1.52151 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.65685 | −0.361146 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32.6274 | −1.21849 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.7990 | −0.514615 | −0.257308 | − | 0.966330i | \(-0.582835\pi\) | ||||
−0.257308 | + | 0.966330i | \(0.582835\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.1421 | 0.897856 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.17157 | −0.0806502 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.9289 | −0.887475 | −0.443737 | − | 0.896157i | \(-0.646348\pi\) | ||||
−0.443737 | + | 0.896157i | \(0.646348\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.1716 | −1.74470 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.65685 | 0.135069 | 0.0675345 | − | 0.997717i | \(-0.478487\pi\) | ||||
0.0675345 | + | 0.997717i | \(0.478487\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.3137 | −1.22713 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.1716 | 0.410953 | 0.205476 | − | 0.978662i | \(-0.434126\pi\) | ||||
0.205476 | + | 0.978662i | \(0.434126\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.3137 | 1.00339 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.2426 | −0.705944 | −0.352972 | − | 0.935634i | \(-0.614829\pi\) | ||||
−0.352972 | + | 0.935634i | \(0.614829\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.65685 | 0.243888 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 37.4558 | 1.37044 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0000 | −0.437886 | −0.218943 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218943 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −56.6274 | −2.06362 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.8284 | 0.612449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.00000 | 0.218074 | 0.109037 | − | 0.994038i | \(-0.465223\pi\) | ||||
0.109037 | + | 0.994038i | \(0.465223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 98.0833 | 3.56020 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.9411 | −0.867865 | −0.433933 | − | 0.900945i | \(-0.642874\pi\) | ||||
−0.433933 | + | 0.900945i | \(0.642874\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.3431 | 0.373957 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.00000 | −0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.2548 | 1.70405 | 0.852026 | − | 0.523499i | \(-0.175374\pi\) | ||||
0.852026 | + | 0.523499i | \(0.175374\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6569 | 0.635896 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.6569 | −1.28249 | −0.641244 | − | 0.767337i | \(-0.721581\pi\) | ||||
−0.641244 | + | 0.767337i | \(0.721581\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.82843 | 0.173442 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.970563 | 0.0347740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 57.9411 | 2.07330 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.899495 | 0.0321453 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.3137 | −0.760719 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.41421 | 0.157350 | 0.0786749 | − | 0.996900i | \(-0.474931\pi\) | ||||
0.0786749 | + | 0.996900i | \(0.474931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.4853 | 0.836098 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.31371 | −0.330739 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.6569 | −0.484359 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.6863 | 0.449372 | 0.224686 | − | 0.974431i | \(-0.427864\pi\) | ||||
0.224686 | + | 0.974431i | \(0.427864\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.25483 | 0.0443928 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 47.1127 | 1.66465 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.9706 | −1.30466 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.2426 | −0.395760 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.02944 | −0.0713512 | −0.0356756 | − | 0.999363i | \(-0.511358\pi\) | ||||
−0.0356756 | + | 0.999363i | \(0.511358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.8579 | −0.837763 | −0.418881 | − | 0.908041i | \(-0.637578\pi\) | ||||
−0.418881 | + | 0.908041i | \(0.637578\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −46.6274 | −1.63529 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.34315 | 0.152134 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −72.9706 | −2.55292 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.6274 | 0.440700 | 0.220350 | − | 0.975421i | \(-0.429280\pi\) | ||||
0.220350 | + | 0.975421i | \(0.429280\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −52.0122 | −1.81303 | −0.906516 | − | 0.422172i | \(-0.861268\pi\) | ||||
−0.906516 | + | 0.422172i | \(0.861268\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.6569 | −0.405840 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.5269 | −1.79177 | −0.895883 | − | 0.444290i | \(-0.853456\pi\) | ||||
−0.895883 | + | 0.444290i | \(0.853456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.3137 | 0.601330 | 0.300665 | − | 0.953730i | \(-0.402791\pi\) | ||||
0.300665 | + | 0.953730i | \(0.402791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.1421 | −1.39252 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0711 | −0.417737 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.14214 | 0.281098 | 0.140549 | − | 0.990074i | \(-0.455113\pi\) | ||||
0.140549 | + | 0.990074i | \(0.455113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2843 | −0.837389 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 61.1127 | 2.10483 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −43.4558 | −1.49140 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.5980 | 1.63164 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.3137 | −1.20912 | −0.604559 | − | 0.796560i | \(-0.706651\pi\) | ||||
−0.604559 | + | 0.796560i | \(0.706651\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.0000 | 0.547188 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.9706 | −0.511385 | −0.255692 | − | 0.966758i | \(-0.582303\pi\) | ||||
−0.255692 | + | 0.966758i | \(0.582303\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.6274 | −0.499081 | −0.249541 | − | 0.968364i | \(-0.580280\pi\) | ||||
−0.249541 | + | 0.968364i | \(0.580280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.0122 | 0.885465 | 0.442733 | − | 0.896654i | \(-0.354009\pi\) | ||||
0.442733 | + | 0.896654i | \(0.354009\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.6569 | 0.736355 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.75736 | −0.297416 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.3137 | 0.655173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.7990 | −0.467561 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.9706 | −0.574367 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.2843 | 0.955092 | 0.477546 | − | 0.878607i | \(-0.341526\pi\) | ||||
0.477546 | + | 0.878607i | \(0.341526\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 40.9706 | 1.38190 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.4558 | −0.823938 | −0.411969 | − | 0.911198i | \(-0.635159\pi\) | ||||
−0.411969 | + | 0.911198i | \(0.635159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.3137 | 0.986485 | 0.493242 | − | 0.869892i | \(-0.335812\pi\) | ||||
0.493242 | + | 0.869892i | \(0.335812\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.65685 | −0.324612 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.4142 | −0.685442 | −0.342721 | − | 0.939437i | \(-0.611349\pi\) | ||||
−0.342721 | + | 0.939437i | \(0.611349\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 45.7990 | 1.53432 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.94113 | 0.0649573 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.4853 | −0.350484 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40.6274 | 1.35651 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.4853 | −0.349704 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.6863 | −0.689160 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.82843 | −0.326708 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.78680 | 0.125739 | 0.0628693 | − | 0.998022i | \(-0.479975\pi\) | ||||
0.0628693 | + | 0.998022i | \(0.479975\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.5147 | −0.514591 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.51472 | −0.0501849 | −0.0250924 | − | 0.999685i | \(-0.507988\pi\) | ||||
−0.0250924 | + | 0.999685i | \(0.507988\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −63.9411 | −2.11614 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.2426 | −0.371670 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 57.2548 | 1.88866 | 0.944331 | − | 0.328996i | \(-0.106710\pi\) | ||||
0.944331 | + | 0.328996i | \(0.106710\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.9706 | −1.05347 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.65685 | −0.185996 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.4558 | −0.967457 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.7990 | −1.60104 | −0.800521 | − | 0.599304i | \(-0.795444\pi\) | ||||
−0.800521 | + | 0.599304i | \(0.795444\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.9706 | −0.817500 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.6569 | −0.577441 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.6274 | 0.869880 | 0.434940 | − | 0.900459i | \(-0.356770\pi\) | ||||
0.434940 | + | 0.900459i | \(0.356770\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.3137 | 1.02188 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.0000 | 0.325991 | 0.162995 | − | 0.986627i | \(-0.447884\pi\) | ||||
0.162995 | + | 0.986627i | \(0.447884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.44365 | 0.0470117 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.8995 | 1.00410 | 0.502049 | − | 0.864839i | \(-0.332580\pi\) | ||||
0.502049 | + | 0.864839i | \(0.332580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.3137 | −0.497104 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −53.1127 | −1.72230 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.37258 | −0.303608 | −0.151804 | − | 0.988411i | \(-0.548508\pi\) | ||||
−0.151804 | + | 0.988411i | \(0.548508\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.4853 | 0.727607 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.3137 | 0.818276 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.68629 | −0.247945 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.7990 | −0.766912 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.3137 | −0.557348 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.2426 | −1.06901 | −0.534506 | − | 0.845165i | \(-0.679502\pi\) | ||||
−0.534506 | + | 0.845165i | \(0.679502\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.9411 | 1.60434 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.00000 | −0.256732 | −0.128366 | − | 0.991727i | \(-0.540973\pi\) | ||||
−0.128366 | + | 0.991727i | \(0.540973\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.82843 | −0.154633 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.2843 | −0.840908 | −0.420454 | − | 0.907314i | \(-0.638129\pi\) | ||||
−0.420454 | + | 0.907314i | \(0.638129\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −80.4264 | −2.57044 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.2010 | −0.389548 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.61522 | 0.147203 | 0.0736014 | − | 0.997288i | \(-0.476551\pi\) | ||||
0.0736014 | + | 0.997288i | \(0.476551\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.6569 | −0.371418 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −108.539 | −3.45134 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.828427 | −0.0263159 | −0.0131579 | − | 0.999913i | \(-0.504188\pi\) | ||||
−0.0131579 | + | 0.999913i | \(0.504188\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.9706 | 0.728949 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.686292 | −0.0217569 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.6569 | 0.812561 | 0.406280 | − | 0.913748i | \(-0.366826\pi\) | ||||
0.406280 | + | 0.913748i | \(0.366826\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.34315 | 0.0741339 |
(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 | 1960.2.a.t.1.2 | 2 | ||
4.3 | odd | 2 | 3920.2.a.bp.1.1 | 2 | |||
5.4 | even | 2 | 9800.2.a.br.1.1 | 2 | |||
7.2 | even | 3 | 1960.2.q.q.361.1 | 4 | |||
7.3 | odd | 6 | 280.2.q.d.121.2 | yes | 4 | ||
7.4 | even | 3 | 1960.2.q.q.961.1 | 4 | |||
7.5 | odd | 6 | 280.2.q.d.81.2 | ✓ | 4 | ||
7.6 | odd | 2 | 1960.2.a.p.1.1 | 2 | |||
21.5 | even | 6 | 2520.2.bi.k.361.1 | 4 | |||
21.17 | even | 6 | 2520.2.bi.k.1801.1 | 4 | |||
28.3 | even | 6 | 560.2.q.j.401.1 | 4 | |||
28.19 | even | 6 | 560.2.q.j.81.1 | 4 | |||
28.27 | even | 2 | 3920.2.a.bz.1.2 | 2 | |||
35.3 | even | 12 | 1400.2.bh.g.849.1 | 8 | |||
35.12 | even | 12 | 1400.2.bh.g.249.1 | 8 | |||
35.17 | even | 12 | 1400.2.bh.g.849.4 | 8 | |||
35.19 | odd | 6 | 1400.2.q.h.1201.1 | 4 | |||
35.24 | odd | 6 | 1400.2.q.h.401.1 | 4 | |||
35.33 | even | 12 | 1400.2.bh.g.249.4 | 8 | |||
35.34 | odd | 2 | 9800.2.a.bz.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.d.81.2 | ✓ | 4 | 7.5 | odd | 6 | ||
280.2.q.d.121.2 | yes | 4 | 7.3 | odd | 6 | ||
560.2.q.j.81.1 | 4 | 28.19 | even | 6 | |||
560.2.q.j.401.1 | 4 | 28.3 | even | 6 | |||
1400.2.q.h.401.1 | 4 | 35.24 | odd | 6 | |||
1400.2.q.h.1201.1 | 4 | 35.19 | odd | 6 | |||
1400.2.bh.g.249.1 | 8 | 35.12 | even | 12 | |||
1400.2.bh.g.249.4 | 8 | 35.33 | even | 12 | |||
1400.2.bh.g.849.1 | 8 | 35.3 | even | 12 | |||
1400.2.bh.g.849.4 | 8 | 35.17 | even | 12 | |||
1960.2.a.p.1.1 | 2 | 7.6 | odd | 2 | |||
1960.2.a.t.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1960.2.q.q.361.1 | 4 | 7.2 | even | 3 | |||
1960.2.q.q.961.1 | 4 | 7.4 | even | 3 | |||
2520.2.bi.k.361.1 | 4 | 21.5 | even | 6 | |||
2520.2.bi.k.1801.1 | 4 | 21.17 | even | 6 | |||
3920.2.a.bp.1.1 | 2 | 4.3 | odd | 2 | |||
3920.2.a.bz.1.2 | 2 | 28.27 | even | 2 | |||
9800.2.a.br.1.1 | 2 | 5.4 | even | 2 | |||
9800.2.a.bz.1.2 | 2 | 35.34 | odd | 2 |