Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, 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("3240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.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: | \(25.8715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.29268.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 5x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 360) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.43292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3240.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.03717 | 1.14794 | 0.573972 | − | 0.818875i | \(-0.305402\pi\) | ||||
0.573972 | + | 0.818875i | \(0.305402\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.27114 | 1.58931 | 0.794655 | − | 0.607062i | \(-0.207652\pi\) | ||||
0.794655 | + | 0.607062i | \(0.207652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.513812 | −0.142506 | −0.0712528 | − | 0.997458i | \(-0.522700\pi\) | ||||
−0.0712528 | + | 0.997458i | \(0.522700\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.80320 | 0.679876 | 0.339938 | − | 0.940448i | \(-0.389594\pi\) | ||||
0.339938 | + | 0.940448i | \(0.389594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.29877 | 1.90387 | 0.951934 | − | 0.306304i | \(-0.0990923\pi\) | ||||
0.951934 | + | 0.306304i | \(0.0990923\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.03717 | 1.05032 | 0.525162 | − | 0.851003i | \(-0.324005\pi\) | ||||
0.525162 | + | 0.851003i | \(0.324005\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.78496 | −0.888544 | −0.444272 | − | 0.895892i | \(-0.646538\pi\) | ||||
−0.444272 | + | 0.895892i | \(0.646538\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.58816 | −1.54248 | −0.771239 | − | 0.636545i | \(-0.780363\pi\) | ||||
−0.771239 | + | 0.636545i | \(0.780363\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.03717 | 0.513376 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.58816 | −1.08309 | −0.541543 | − | 0.840673i | \(-0.682160\pi\) | ||||
−0.541543 | + | 0.840673i | \(0.682160\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.98175 | 1.24654 | 0.623270 | − | 0.782007i | \(-0.285804\pi\) | ||||
0.623270 | + | 0.782007i | \(0.285804\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.19680 | −0.182510 | −0.0912549 | − | 0.995828i | \(-0.529088\pi\) | ||||
−0.0912549 | + | 0.995828i | \(0.529088\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.62533 | −1.40400 | −0.701999 | − | 0.712178i | \(-0.747709\pi\) | ||||
−0.701999 | + | 0.712178i | \(0.747709\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.22442 | 0.317774 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.467941 | −0.0642766 | −0.0321383 | − | 0.999483i | \(-0.510232\pi\) | ||||
−0.0321383 | + | 0.999483i | \(0.510232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.27114 | 0.710761 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.757332 | −0.0985962 | −0.0492981 | − | 0.998784i | \(-0.515698\pi\) | ||||
−0.0492981 | + | 0.998784i | \(0.515698\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.271144 | −0.0347164 | −0.0173582 | − | 0.999849i | \(-0.505526\pi\) | ||||
−0.0173582 | + | 0.999849i | \(0.505526\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.513812 | −0.0637305 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.26159 | −0.887145 | −0.443572 | − | 0.896239i | \(-0.646289\pi\) | ||||
−0.443572 | + | 0.896239i | \(0.646289\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.48619 | 0.176378 | 0.0881891 | − | 0.996104i | \(-0.471892\pi\) | ||||
0.0881891 | + | 0.996104i | \(0.471892\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.31701 | 0.622309 | 0.311155 | − | 0.950359i | \(-0.399284\pi\) | ||||
0.311155 | + | 0.950359i | \(0.399284\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.0094 | 1.82444 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9635 | −1.79603 | −0.898017 | − | 0.439960i | \(-0.854993\pi\) | ||||
−0.898017 | + | 0.439960i | \(0.854993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0648 | 1.32428 | 0.662142 | − | 0.749379i | \(-0.269648\pi\) | ||||
0.662142 | + | 0.749379i | \(0.269648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.80320 | 0.304050 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.2529 | 1.61680 | 0.808402 | − | 0.588631i | \(-0.200333\pi\) | ||||
0.808402 | + | 0.588631i | \(0.200333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.56053 | −0.163588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.29877 | 0.851436 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.36374 | −0.646140 | −0.323070 | − | 0.946375i | \(-0.604715\pi\) | ||||
−0.323070 | + | 0.946375i | \(0.604715\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.07435 | −0.206405 | −0.103203 | − | 0.994660i | \(-0.532909\pi\) | ||||
−0.103203 | + | 0.994660i | \(0.532909\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.05610 | 0.498192 | 0.249096 | − | 0.968479i | \(-0.419866\pi\) | ||||
0.249096 | + | 0.968479i | \(0.419866\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.2901 | −1.28480 | −0.642400 | − | 0.766370i | \(-0.722061\pi\) | ||||
−0.642400 | + | 0.766370i | \(0.722061\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.34549 | 0.799353 | 0.399676 | − | 0.916656i | \(-0.369122\pi\) | ||||
0.399676 | + | 0.916656i | \(0.369122\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.10197 | −0.479953 | −0.239976 | − | 0.970779i | \(-0.577140\pi\) | ||||
−0.239976 | + | 0.970779i | \(0.577140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.03717 | 0.469719 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.51381 | 0.780460 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.7850 | 1.52591 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0830 | −0.983461 | −0.491731 | − | 0.870747i | \(-0.663635\pi\) | ||||
−0.491731 | + | 0.870747i | \(0.663635\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.55116 | 0.135525 | 0.0677627 | − | 0.997701i | \(-0.478414\pi\) | ||||
0.0677627 | + | 0.997701i | \(0.478414\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.2048 | 2.18553 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.81258 | −0.411166 | −0.205583 | − | 0.978640i | \(-0.565909\pi\) | ||||
−0.205583 | + | 0.978640i | \(0.565909\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.4657 | −1.82070 | −0.910349 | − | 0.413842i | \(-0.864187\pi\) | ||||
−0.910349 | + | 0.413842i | \(0.864187\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.70837 | −0.226486 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.78496 | −0.397369 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.7943 | −1.21200 | −0.605999 | − | 0.795465i | \(-0.707227\pi\) | ||||
−0.605999 | + | 0.795465i | \(0.707227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.981753 | 0.0798939 | 0.0399469 | − | 0.999202i | \(-0.487281\pi\) | ||||
0.0399469 | + | 0.999202i | \(0.487281\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.58816 | −0.689817 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.86154 | −0.547610 | −0.273805 | − | 0.961785i | \(-0.588282\pi\) | ||||
−0.273805 | + | 0.961785i | \(0.588282\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.2988 | 1.20571 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.90741 | −0.384378 | −0.192189 | − | 0.981358i | \(-0.561559\pi\) | ||||
−0.192189 | + | 0.981358i | \(0.561559\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.47664 | 0.269030 | 0.134515 | − | 0.990912i | \(-0.457052\pi\) | ||||
0.134515 | + | 0.990912i | \(0.457052\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7360 | −0.979692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5423 | 0.801515 | 0.400758 | − | 0.916184i | \(-0.368747\pi\) | ||||
0.400758 | + | 0.916184i | \(0.368747\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.03717 | 0.229589 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.90741 | 0.366797 | 0.183398 | − | 0.983039i | \(-0.441290\pi\) | ||||
0.183398 | + | 0.983039i | \(0.441290\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.21504 | 0.387631 | 0.193816 | − | 0.981038i | \(-0.437914\pi\) | ||||
0.193816 | + | 0.981038i | \(0.437914\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.58816 | −0.484371 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.7761 | 1.08053 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.6901 | 1.85887 | 0.929436 | − | 0.368983i | \(-0.120294\pi\) | ||||
0.929436 | + | 0.368983i | \(0.120294\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.19680 | 0.230111 | 0.115055 | − | 0.993359i | \(-0.463295\pi\) | ||||
0.115055 | + | 0.993359i | \(0.463295\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.6808 | 0.974713 | 0.487357 | − | 0.873203i | \(-0.337961\pi\) | ||||
0.487357 | + | 0.873203i | \(0.337961\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.95413 | −0.422077 | −0.211039 | − | 0.977478i | \(-0.567685\pi\) | ||||
−0.211039 | + | 0.977478i | \(0.567685\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.5327 | −1.02000 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.98175 | 0.557470 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 43.7440 | 3.02584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5882 | 1.00429 | 0.502145 | − | 0.864783i | \(-0.332544\pi\) | ||||
0.502145 | + | 0.864783i | \(0.332544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.19680 | −0.0816209 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.0837 | −1.77068 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.44032 | −0.0968863 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.7740 | −1.85989 | −0.929943 | − | 0.367703i | \(-0.880144\pi\) | ||||
−0.929943 | + | 0.367703i | \(0.880144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.8411 | 0.852291 | 0.426145 | − | 0.904655i | \(-0.359871\pi\) | ||||
0.426145 | + | 0.904655i | \(0.359871\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.9060 | 1.71192 | 0.855959 | − | 0.517043i | \(-0.172967\pi\) | ||||
0.855959 | + | 0.517043i | \(0.172967\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.71998 | 0.374729 | 0.187364 | − | 0.982290i | \(-0.440006\pi\) | ||||
0.187364 | + | 0.982290i | \(0.440006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.62533 | −0.627887 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0467 | 0.714553 | 0.357277 | − | 0.933999i | \(-0.383705\pi\) | ||||
0.357277 | + | 0.933999i | \(0.383705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4862 | 0.804306 | 0.402153 | − | 0.915572i | \(-0.368262\pi\) | ||||
0.402153 | + | 0.915572i | \(0.368262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.22442 | 0.142113 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.26400 | −0.271312 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.22442 | 0.519121 | 0.259560 | − | 0.965727i | \(-0.416422\pi\) | ||||
0.259560 | + | 0.965727i | \(0.416422\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.5517 | 1.66929 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.8317 | 1.04993 | 0.524966 | − | 0.851123i | \(-0.324078\pi\) | ||||
0.524966 | + | 0.851123i | \(0.324078\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.0094 | −1.24332 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.1202 | 0.747365 | 0.373682 | − | 0.927557i | \(-0.378095\pi\) | ||||
0.373682 | + | 0.927557i | \(0.378095\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.467941 | −0.0287454 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.5859 | −1.37709 | −0.688544 | − | 0.725195i | \(-0.741750\pi\) | ||||
−0.688544 | + | 0.725195i | \(0.741750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.9818 | −0.667094 | −0.333547 | − | 0.942733i | \(-0.608246\pi\) | ||||
−0.333547 | + | 0.942733i | \(0.608246\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.27114 | 0.317862 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.7178 | 1.72548 | 0.862741 | − | 0.505646i | \(-0.168746\pi\) | ||||
0.862741 | + | 0.505646i | \(0.168746\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.3090 | −1.45015 | −0.725077 | − | 0.688668i | \(-0.758196\pi\) | ||||
−0.725077 | + | 0.688668i | \(0.758196\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6245 | 0.869335 | 0.434668 | − | 0.900591i | \(-0.356866\pi\) | ||||
0.434668 | + | 0.900591i | \(0.356866\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.2420 | 1.43096 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.14206 | −0.537768 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.6901 | 0.916627 | 0.458314 | − | 0.888791i | \(-0.348454\pi\) | ||||
0.458314 | + | 0.888791i | \(0.348454\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.757332 | −0.0440936 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.58816 | −0.149677 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.63488 | −0.209511 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.271144 | −0.0155256 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.3920 | −1.50627 | −0.753137 | − | 0.657864i | \(-0.771460\pi\) | ||||
−0.753137 | + | 0.657864i | \(0.771460\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.0285 | −0.795482 | −0.397741 | − | 0.917498i | \(-0.630206\pi\) | ||||
−0.397741 | + | 0.917498i | \(0.630206\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.4110 | −1.94502 | −0.972511 | − | 0.232855i | \(-0.925193\pi\) | ||||
−0.972511 | + | 0.232855i | \(0.925193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.19456 | −0.123259 | −0.0616295 | − | 0.998099i | \(-0.519630\pi\) | ||||
−0.0616295 | + | 0.998099i | \(0.519630\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.2222 | −1.41217 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.2631 | 1.29439 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.513812 | −0.0285011 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −29.2338 | −1.61171 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8980 | 0.708940 | 0.354470 | − | 0.935067i | \(-0.384661\pi\) | ||||
0.354470 | + | 0.935067i | \(0.384661\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.26159 | −0.396743 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.8126 | 0.697946 | 0.348973 | − | 0.937133i | \(-0.386531\pi\) | ||||
0.348973 | + | 0.937133i | \(0.386531\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −45.2694 | −2.45148 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.5043 | −0.783157 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.18793 | 0.439551 | 0.219775 | − | 0.975550i | \(-0.429468\pi\) | ||||
0.219775 | + | 0.975550i | \(0.429468\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.34464 | 0.286092 | 0.143046 | − | 0.989716i | \(-0.454310\pi\) | ||||
0.143046 | + | 0.989716i | \(0.454310\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.8317 | −0.789411 | −0.394705 | − | 0.918808i | \(-0.629153\pi\) | ||||
−0.394705 | + | 0.918808i | \(0.629153\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.48619 | 0.0788787 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.55031 | 0.345712 | 0.172856 | − | 0.984947i | \(-0.444700\pi\) | ||||
0.172856 | + | 0.984947i | \(0.444700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 49.8695 | 2.62471 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.31701 | 0.278305 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.1202 | −1.46786 | −0.733932 | − | 0.679223i | \(-0.762317\pi\) | ||||
−0.733932 | + | 0.679223i | \(0.762317\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.42122 | −0.0737860 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.7360 | −0.918335 | −0.459168 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459168 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.45857 | 0.126623 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.8228 | 0.812763 | 0.406381 | − | 0.913703i | \(-0.366790\pi\) | ||||
0.406381 | + | 0.913703i | \(0.366790\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.11135 | −0.363373 | −0.181686 | − | 0.983357i | \(-0.558156\pi\) | ||||
−0.181686 | + | 0.983357i | \(0.558156\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.0094 | 0.815913 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.74761 | 0.291415 | 0.145708 | − | 0.989328i | \(-0.453454\pi\) | ||||
0.145708 | + | 0.989328i | \(0.453454\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.1202 | 0.714090 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.9635 | −0.803211 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.35710 | 0.319054 | 0.159527 | − | 0.987194i | \(-0.449003\pi\) | ||||
0.159527 | + | 0.987194i | \(0.449003\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.1100 | −1.75331 | −0.876654 | − | 0.481121i | \(-0.840230\pi\) | ||||
−0.876654 | + | 0.481121i | \(0.840230\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.41269 | 0.219812 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −34.7271 | −1.72136 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.8504 | 1.22877 | 0.614387 | − | 0.789005i | \(-0.289403\pi\) | ||||
0.614387 | + | 0.789005i | \(0.289403\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.30015 | −0.113183 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0648 | 0.592238 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.37535 | 0.164897 | 0.0824483 | − | 0.996595i | \(-0.473726\pi\) | ||||
0.0824483 | + | 0.996595i | \(0.473726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.96351 | −0.193169 | −0.0965847 | − | 0.995325i | \(-0.530792\pi\) | ||||
−0.0965847 | + | 0.995325i | \(0.530792\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.80320 | 0.135975 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.823510 | −0.0398524 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.62516 | 0.367291 | 0.183645 | − | 0.982993i | \(-0.441210\pi\) | ||||
0.183645 | + | 0.982993i | \(0.441210\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.29024 | −0.350347 | −0.175173 | − | 0.984538i | \(-0.556049\pi\) | ||||
−0.175173 | + | 0.984538i | \(0.556049\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 41.8023 | 1.99968 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.3905 | 1.73682 | 0.868411 | − | 0.495844i | \(-0.165141\pi\) | ||||
0.868411 | + | 0.495844i | \(0.165141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.3738 | −1.68066 | −0.840330 | − | 0.542076i | \(-0.817639\pi\) | ||||
−0.840330 | + | 0.542076i | \(0.817639\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.2529 | 0.723057 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.9425 | −0.705181 | −0.352591 | − | 0.935778i | \(-0.614699\pi\) | ||||
−0.352591 | + | 0.935778i | \(0.614699\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.0730 | 1.98114 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.56053 | −0.0731590 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.7841 | −0.598015 | −0.299008 | − | 0.954251i | \(-0.596656\pi\) | ||||
−0.299008 | + | 0.954251i | \(0.596656\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.11443 | 0.377927 | 0.188963 | − | 0.981984i | \(-0.439487\pi\) | ||||
0.188963 | + | 0.981984i | \(0.439487\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.5605 | −1.00200 | −0.501002 | − | 0.865446i | \(-0.667035\pi\) | ||||
−0.501002 | + | 0.865446i | \(0.667035\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.8602 | −1.42804 | −0.714019 | − | 0.700127i | \(-0.753127\pi\) | ||||
−0.714019 | + | 0.700127i | \(0.753127\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.0547 | −1.01839 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.30849 | −0.290065 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.29877 | 0.380774 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.06412 | −0.0486208 | −0.0243104 | − | 0.999704i | \(-0.507739\pi\) | ||||
−0.0243104 | + | 0.999704i | \(0.507739\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.38507 | 0.154346 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.36374 | −0.288962 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.0182 | −1.22431 | −0.612157 | − | 0.790736i | \(-0.709698\pi\) | ||||
−0.612157 | + | 0.790736i | \(0.709698\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.2338 | 0.732621 | 0.366310 | − | 0.930493i | \(-0.380621\pi\) | ||||
0.366310 | + | 0.930493i | \(0.380621\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.4132 | −0.604100 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.51381 | 0.202472 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.7208 | 0.927592 | 0.463796 | − | 0.885942i | \(-0.346487\pi\) | ||||
0.463796 | + | 0.885942i | \(0.346487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.47834 | −0.244267 | −0.122134 | − | 0.992514i | \(-0.538974\pi\) | ||||
−0.122134 | + | 0.992514i | \(0.538974\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.07435 | −0.0923072 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.71061 | −0.386091 | −0.193045 | − | 0.981190i | \(-0.561836\pi\) | ||||
−0.193045 | + | 0.981190i | \(0.561836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.1487 | 0.714376 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.05610 | 0.222798 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −50.7365 | −2.23139 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.87041 | −0.125755 | −0.0628774 | − | 0.998021i | \(-0.520028\pi\) | ||||
−0.0628774 | + | 0.998021i | \(0.520028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.65295 | −0.290913 | −0.145457 | − | 0.989365i | \(-0.546465\pi\) | ||||
−0.145457 | + | 0.989365i | \(0.546465\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.0743 | −1.04869 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.37311 | 0.103179 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.10112 | −0.177639 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.2901 | −0.574580 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.7252 | 0.505042 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.79348 | 0.335068 | 0.167534 | − | 0.985866i | \(-0.446420\pi\) | ||||
0.167534 | + | 0.985866i | \(0.446420\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.34549 | 0.357482 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.7580 | −0.502736 | −0.251368 | − | 0.967892i | \(-0.580880\pi\) | ||||
−0.251368 | + | 0.967892i | \(0.580880\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.7092 | −1.69167 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −48.4839 | −2.06175 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.7827 | 0.711107 | 0.355553 | − | 0.934656i | \(-0.384292\pi\) | ||||
0.355553 | + | 0.934656i | \(0.384292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.614928 | 0.0260087 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.7486 | −1.08518 | −0.542588 | − | 0.839999i | \(-0.682555\pi\) | ||||
−0.542588 | + | 0.839999i | \(0.682555\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.10197 | −0.214641 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.11308 | −0.214351 | −0.107176 | − | 0.994240i | \(-0.534181\pi\) | ||||
−0.107176 | + | 0.994240i | \(0.534181\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.4657 | 1.06571 | 0.532853 | − | 0.846208i | \(-0.321120\pi\) | ||||
0.532853 | + | 0.846208i | \(0.321120\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.03717 | 0.210065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.7164 | 1.86157 | 0.930783 | − | 0.365571i | \(-0.119126\pi\) | ||||
0.930783 | + | 0.365571i | \(0.119126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.6429 | 1.52020 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.46658 | −0.102155 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40.9156 | −1.68877 | −0.844383 | − | 0.535740i | \(-0.820033\pi\) | ||||
−0.844383 | + | 0.535740i | \(0.820033\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −71.2711 | −2.93668 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.9729 | −0.491667 | −0.245834 | − | 0.969312i | \(-0.579062\pi\) | ||||
−0.245834 | + | 0.969312i | \(0.579062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.51381 | 0.349032 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.3571 | 0.586615 | 0.293308 | − | 0.956018i | \(-0.405244\pi\) | ||||
0.293308 | + | 0.956018i | \(0.405244\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.6420 | 1.82099 | 0.910493 | − | 0.413524i | \(-0.135702\pi\) | ||||
0.910493 | + | 0.413524i | \(0.135702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.7850 | 0.682405 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.7740 | −1.20849 | −0.604245 | − | 0.796798i | \(-0.706525\pi\) | ||||
−0.604245 | + | 0.796798i | \(0.706525\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.94561 | 0.200078 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.4132 | 1.34955 | 0.674773 | − | 0.738025i | \(-0.264241\pi\) | ||||
0.674773 | + | 0.738025i | \(0.264241\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −44.5881 | −1.79505 | −0.897525 | − | 0.440963i | \(-0.854637\pi\) | ||||
−0.897525 | + | 0.440963i | \(0.854637\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.9533 | −1.48528 | −0.742638 | − | 0.669693i | \(-0.766426\pi\) | ||||
−0.742638 | + | 0.669693i | \(0.766426\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 46.3257 | 1.85600 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.4679 | −0.736365 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.10197 | −0.0438687 | −0.0219344 | − | 0.999759i | \(-0.506982\pi\) | ||||
−0.0219344 | + | 0.999759i | \(0.506982\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.0830 | −0.439817 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.14293 | −0.0452847 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5691 | −0.535946 | −0.267973 | − | 0.963426i | \(-0.586354\pi\) | ||||
−0.267973 | + | 0.963426i | \(0.586354\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.72953 | 0.383695 | 0.191848 | − | 0.981425i | \(-0.438552\pi\) | ||||
0.191848 | + | 0.981425i | \(0.438552\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.5786 | −1.51668 | −0.758341 | − | 0.651858i | \(-0.773990\pi\) | ||||
−0.758341 | + | 0.651858i | \(0.773990\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.99201 | −0.156700 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.1304 | 0.670366 | 0.335183 | − | 0.942153i | \(-0.391202\pi\) | ||||
0.335183 | + | 0.942153i | \(0.391202\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.55116 | 0.0606088 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.6630 | −0.921780 | −0.460890 | − | 0.887457i | \(-0.652470\pi\) | ||||
−0.460890 | + | 0.887457i | \(0.652470\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.4301 | 0.716847 | 0.358424 | − | 0.933559i | \(-0.383314\pi\) | ||||
0.358424 | + | 0.933559i | \(0.383314\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.2048 | 0.977400 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.1026 | −0.933258 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.42924 | −0.0551751 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.4964 | −0.635890 | −0.317945 | − | 0.948109i | \(-0.602993\pi\) | ||||
−0.317945 | + | 0.948109i | \(0.602993\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.1028 | 0.388283 | 0.194141 | − | 0.980974i | \(-0.437808\pi\) | ||||
0.194141 | + | 0.980974i | \(0.437808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.3278 | −0.741732 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.16917 | −0.312585 | −0.156292 | − | 0.987711i | \(-0.549954\pi\) | ||||
−0.156292 | + | 0.987711i | \(0.549954\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.81258 | −0.183879 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.240434 | 0.00915979 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.51466 | −0.133704 | −0.0668521 | − | 0.997763i | \(-0.521296\pi\) | ||||
−0.0668521 | + | 0.997763i | \(0.521296\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.4657 | −0.814241 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.3745 | 0.847493 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.9897 | 1.28378 | 0.641888 | − | 0.766799i | \(-0.278152\pi\) | ||||
0.641888 | + | 0.766799i | \(0.278152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.6736 | −2.06205 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.30015 | −0.236941 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.99777 | −0.150139 | −0.0750696 | − | 0.997178i | \(-0.523918\pi\) | ||||
−0.0750696 | + | 0.997178i | \(0.523918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.2600 | −1.62010 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.70837 | −0.101287 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.2142 | −1.23868 | −0.619340 | − | 0.785123i | \(-0.712600\pi\) | ||||
−0.619340 | + | 0.785123i | \(0.712600\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3562 | 0.571897 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.78496 | −0.177709 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.5888 | −1.02321 | −0.511607 | − | 0.859220i | \(-0.670949\pi\) | ||||
−0.511607 | + | 0.859220i | \(0.670949\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.35487 | −0.124084 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.71860 | 0.358965 | 0.179482 | − | 0.983761i | \(-0.442558\pi\) | ||||
0.179482 | + | 0.983761i | \(0.442558\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.2769 | −1.40995 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.2355 | 1.33294 | 0.666472 | − | 0.745530i | \(-0.267803\pi\) | ||||
0.666472 | + | 0.745530i | \(0.267803\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.6814 | 0.758728 | 0.379364 | − | 0.925247i | \(-0.376143\pi\) | ||||
0.379364 | + | 0.925247i | \(0.376143\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.7943 | −0.542022 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.3642 | −1.47488 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.0749 | 1.06096 | 0.530478 | − | 0.847699i | \(-0.322012\pi\) | ||||
0.530478 | + | 0.847699i | \(0.322012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.981753 | 0.0357296 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.1202 | −0.803973 | −0.401986 | − | 0.915646i | \(-0.631680\pi\) | ||||
−0.401986 | + | 0.915646i | \(0.631680\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.2907 | 0.554289 | 0.277145 | − | 0.960828i | \(-0.410612\pi\) | ||||
0.277145 | + | 0.960828i | \(0.410612\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.3467 | 0.917612 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.389126 | 0.0140505 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.9978 | 1.00963 | 0.504813 | − | 0.863229i | \(-0.331562\pi\) | ||||
0.504813 | + | 0.863229i | \(0.331562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.4853 | −0.664871 | −0.332436 | − | 0.943126i | \(-0.607870\pi\) | ||||
−0.332436 | + | 0.943126i | \(0.607870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.58816 | −0.308496 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 66.2387 | 2.37325 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.83391 | 0.280319 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.86154 | −0.244899 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.92616 | 0.318183 | 0.159092 | − | 0.987264i | \(-0.449143\pi\) | ||||
0.159092 | + | 0.987264i | \(0.449143\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.4956 | −0.550959 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.139317 | 0.00494728 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.4555 | −1.14963 | −0.574816 | − | 0.818283i | \(-0.694926\pi\) | ||||
−0.574816 | + | 0.818283i | \(0.694926\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.9818 | −0.954546 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.0267 | 0.989042 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.2988 | 0.539211 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.4759 | 0.438631 | 0.219315 | − | 0.975654i | \(-0.429618\pi\) | ||||
0.219315 | + | 0.975654i | \(0.429618\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0632 | −0.564057 | −0.282028 | − | 0.959406i | \(-0.591007\pi\) | ||||
−0.282028 | + | 0.959406i | \(0.591007\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.90741 | −0.171899 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.93194 | −0.347475 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.6149 | 1.66177 | 0.830886 | − | 0.556443i | \(-0.187834\pi\) | ||||
0.830886 | + | 0.556443i | \(0.187834\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.7553 | 0.618910 | 0.309455 | − | 0.950914i | \(-0.399853\pi\) | ||||
0.309455 | + | 0.950914i | \(0.399853\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.2420 | 0.842976 | 0.421488 | − | 0.906834i | \(-0.361508\pi\) | ||||
0.421488 | + | 0.906834i | \(0.361508\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.3816 | −1.05520 | −0.527599 | − | 0.849494i | \(-0.676908\pi\) | ||||
−0.527599 | + | 0.849494i | \(0.676908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.23550 | 0.216047 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.47664 | 0.120314 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.6434 | −0.367451 | −0.183726 | − | 0.982978i | \(-0.558816\pi\) | ||||
−0.183726 | + | 0.982978i | \(0.558816\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.10420 | −0.210490 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.7360 | −0.438132 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 50.9788 | 1.75165 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.1857 | −1.13759 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.1492 | 0.929571 | 0.464785 | − | 0.885423i | \(-0.346131\pi\) | ||||
0.464785 | + | 0.885423i | \(0.346131\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.1666 | 1.47454 | 0.737271 | − | 0.675597i | \(-0.236114\pi\) | ||||
0.737271 | + | 0.675597i | \(0.236114\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.61972 | −0.225862 | −0.112931 | − | 0.993603i | \(-0.536024\pi\) | ||||
−0.112931 | + | 0.993603i | \(0.536024\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.31055 | 0.180773 | 0.0903866 | − | 0.995907i | \(-0.471190\pi\) | ||||
0.0903866 | + | 0.995907i | \(0.471190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.5423 | 0.358449 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −84.1459 | −2.85446 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.73109 | 0.126423 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.03717 | 0.102675 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.12022 | −0.0715946 | −0.0357973 | − | 0.999359i | \(-0.511397\pi\) | ||||
−0.0357973 | + | 0.999359i | \(0.511397\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.5668 | 0.760296 | 0.380148 | − | 0.924926i | \(-0.375873\pi\) | ||||
0.380148 | + | 0.924926i | \(0.375873\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.5399 | 1.39793 | 0.698964 | − | 0.715157i | \(-0.253645\pi\) | ||||
0.698964 | + | 0.715157i | \(0.253645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.4497 | −1.45890 | −0.729449 | − | 0.684035i | \(-0.760223\pi\) | ||||
−0.729449 | + | 0.684035i | \(0.760223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.6611 | −1.12896 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −79.8784 | −2.67303 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.90741 | 0.164037 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41.0940 | 1.37056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.31173 | −0.0437002 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.21504 | 0.173354 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.38266 | 0.145524 | 0.0727620 | − | 0.997349i | \(-0.476819\pi\) | ||||
0.0727620 | + | 0.997349i | \(0.476819\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.6719 | 0.486101 | 0.243051 | − | 0.970014i | \(-0.421852\pi\) | ||||
0.243051 | + | 0.970014i | \(0.421852\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 63.5953 | 2.10470 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.71114 | 0.155575 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.3233 | −1.23118 | −0.615591 | − | 0.788066i | \(-0.711083\pi\) | ||||
−0.615591 | + | 0.788066i | \(0.711083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.763621 | −0.0251349 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.58816 | −0.216617 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.3250 | −0.634033 | −0.317016 | − | 0.948420i | \(-0.602681\pi\) | ||||
−0.317016 | + | 0.948420i | \(0.602681\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.4599 | 0.605000 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.7761 | 0.483230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.8339 | −0.517271 | −0.258636 | − | 0.965975i | \(-0.583273\pi\) | ||||
−0.258636 | + | 0.965975i | \(0.583273\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.35933 | −0.142110 | −0.0710551 | − | 0.997472i | \(-0.522637\pi\) | ||||
−0.0710551 | + | 0.997472i | \(0.522637\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.2055 | 1.30927 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.6316 | 1.28785 | 0.643927 | − | 0.765087i | \(-0.277304\pi\) | ||||
0.643927 | + | 0.765087i | \(0.277304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.73194 | −0.0886826 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.3922 | −1.24365 | −0.621823 | − | 0.783158i | \(-0.713608\pi\) | ||||
−0.621823 | + | 0.783158i | \(0.713608\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.6901 | 0.831313 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.6166 | −0.471996 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 42.7565 | 1.37924 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.19680 | 0.102909 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.3257 | −1.68268 | −0.841340 | − | 0.540506i | \(-0.818233\pi\) | ||||
−0.841340 | + | 0.540506i | \(0.818233\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.4831 | −1.45962 | −0.729811 | − | 0.683649i | \(-0.760392\pi\) | ||||
−0.729811 | + | 0.683649i | \(0.760392\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −65.1951 | −2.09006 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.03511 | 0.0651090 | 0.0325545 | − | 0.999470i | \(-0.489636\pi\) | ||||
0.0325545 | + | 0.999470i | \(0.489636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 80.4002 | 2.56960 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.4130 | 0.810550 | 0.405275 | − | 0.914195i | \(-0.367176\pi\) | ||||
0.405275 | + | 0.914195i | \(0.367176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.6808 | 0.435905 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.02848 | −0.191694 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.259533 | −0.00824435 | −0.00412218 | − | 0.999992i | \(-0.501312\pi\) | ||||
−0.00412218 | + | 0.999992i | \(0.501312\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.95413 | −0.188759 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.9140 | −1.54912 | −0.774561 | − | 0.632499i | \(-0.782029\pi\) | ||||
−0.774561 | + | 0.632499i | \(0.782029\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3240.2.a.u.1.4 | 4 | ||
3.2 | odd | 2 | 3240.2.a.s.1.4 | 4 | |||
4.3 | odd | 2 | 6480.2.a.cb.1.1 | 4 | |||
9.2 | odd | 6 | 1080.2.q.e.361.1 | 8 | |||
9.4 | even | 3 | 360.2.q.e.241.3 | yes | 8 | ||
9.5 | odd | 6 | 1080.2.q.e.721.1 | 8 | |||
9.7 | even | 3 | 360.2.q.e.121.3 | ✓ | 8 | ||
12.11 | even | 2 | 6480.2.a.bz.1.1 | 4 | |||
36.7 | odd | 6 | 720.2.q.l.481.2 | 8 | |||
36.11 | even | 6 | 2160.2.q.l.1441.4 | 8 | |||
36.23 | even | 6 | 2160.2.q.l.721.4 | 8 | |||
36.31 | odd | 6 | 720.2.q.l.241.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.q.e.121.3 | ✓ | 8 | 9.7 | even | 3 | ||
360.2.q.e.241.3 | yes | 8 | 9.4 | even | 3 | ||
720.2.q.l.241.2 | 8 | 36.31 | odd | 6 | |||
720.2.q.l.481.2 | 8 | 36.7 | odd | 6 | |||
1080.2.q.e.361.1 | 8 | 9.2 | odd | 6 | |||
1080.2.q.e.721.1 | 8 | 9.5 | odd | 6 | |||
2160.2.q.l.721.4 | 8 | 36.23 | even | 6 | |||
2160.2.q.l.1441.4 | 8 | 36.11 | even | 6 | |||
3240.2.a.s.1.4 | 4 | 3.2 | odd | 2 | |||
3240.2.a.u.1.4 | 4 | 1.1 | even | 1 | trivial | ||
6480.2.a.bz.1.1 | 4 | 12.11 | even | 2 | |||
6480.2.a.cb.1.1 | 4 | 4.3 | odd | 2 |