Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,2,Mod(1,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, 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("880.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.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: | \(7.02683537787\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 880.1 |
$q$-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 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.56155 | −0.590211 | −0.295106 | − | 0.955465i | \(-0.595355\pi\) | ||||
−0.295106 | + | 0.955465i | \(0.595355\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.56155 | 0.863803 | 0.431902 | − | 0.901921i | \(-0.357843\pi\) | ||||
0.431902 | + | 0.901921i | \(0.357843\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.56155 | 0.358245 | 0.179122 | − | 0.983827i | \(-0.442674\pi\) | ||||
0.179122 | + | 0.983827i | \(0.442674\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.43845 | 0.532113 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.12311 | 0.651213 | 0.325606 | − | 0.945505i | \(-0.394432\pi\) | ||||
0.325606 | + | 0.945505i | \(0.394432\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.68466 | −0.498529 | −0.249264 | − | 0.968436i | \(-0.580189\pi\) | ||||
−0.249264 | + | 0.968436i | \(0.580189\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.43845 | −0.437958 | −0.218979 | − | 0.975730i | \(-0.570273\pi\) | ||||
−0.218979 | + | 0.975730i | \(0.570273\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.56155 | 0.271831 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.56155 | −0.263951 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.68466 | 1.09895 | 0.549476 | − | 0.835510i | \(-0.314828\pi\) | ||||
0.549476 | + | 0.835510i | \(0.314828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.12311 | −0.500097 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.24621 | 0.952538 | 0.476269 | − | 0.879300i | \(-0.341989\pi\) | ||||
0.476269 | + | 0.879300i | \(0.341989\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.561553 | −0.0837114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.87689 | 0.711368 | 0.355684 | − | 0.934606i | \(-0.384248\pi\) | ||||
0.355684 | + | 0.934606i | \(0.384248\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.56155 | −0.651650 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.56155 | −0.778773 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.438447 | 0.0602254 | 0.0301127 | − | 0.999547i | \(-0.490413\pi\) | ||||
0.0301127 | + | 0.999547i | \(0.490413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.43845 | −0.322980 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.12311 | 0.927349 | 0.463675 | − | 0.886006i | \(-0.346531\pi\) | ||||
0.463675 | + | 0.886006i | \(0.346531\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6847 | 1.88018 | 0.940089 | − | 0.340929i | \(-0.110742\pi\) | ||||
0.940089 | + | 0.340929i | \(0.110742\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.876894 | 0.110478 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.2462 | 1.25177 | 0.625887 | − | 0.779914i | \(-0.284737\pi\) | ||||
0.625887 | + | 0.779914i | \(0.284737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.87689 | −0.587109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.68466 | 1.03068 | 0.515340 | − | 0.856986i | \(-0.327666\pi\) | ||||
0.515340 | + | 0.856986i | \(0.327666\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.56155 | −0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.56155 | 0.177955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.36932 | −1.05413 | −0.527065 | − | 0.849825i | \(-0.676708\pi\) | ||||
−0.527065 | + | 0.849825i | \(0.676708\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.12311 | 0.342805 | 0.171403 | − | 0.985201i | \(-0.445170\pi\) | ||||
0.171403 | + | 0.985201i | \(0.445170\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.56155 | 0.386305 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.19224 | 0.449455 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.43845 | −0.894474 | −0.447237 | − | 0.894416i | \(-0.647592\pi\) | ||||
−0.447237 | + | 0.894416i | \(0.647592\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.12311 | −0.327390 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.80776 | 0.394847 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.56155 | 0.160212 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.12311 | −0.114034 | −0.0570170 | − | 0.998373i | \(-0.518159\pi\) | ||||
−0.0570170 | + | 0.998373i | \(0.518159\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.561553 | 0.0564382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.2462 | 1.21854 | 0.609272 | − | 0.792961i | \(-0.291462\pi\) | ||||
0.609272 | + | 0.792961i | \(0.291462\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.24621 | 0.615457 | 0.307729 | − | 0.951474i | \(-0.400431\pi\) | ||||
0.307729 | + | 0.951474i | \(0.400431\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.43845 | 0.237968 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0000 | 1.54678 | 0.773389 | − | 0.633932i | \(-0.218560\pi\) | ||||
0.773389 | + | 0.633932i | \(0.218560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.4924 | −1.38812 | −0.694061 | − | 0.719916i | \(-0.744180\pi\) | ||||
−0.694061 | + | 0.719916i | \(0.744180\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.4384 | −0.990774 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.8769 | −1.02321 | −0.511606 | − | 0.859220i | \(-0.670949\pi\) | ||||
−0.511606 | + | 0.859220i | \(0.670949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.12311 | 0.291231 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.12311 | −0.103831 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.56155 | −0.509827 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.12311 | −0.281601 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.24621 | 0.199319 | 0.0996595 | − | 0.995022i | \(-0.468225\pi\) | ||||
0.0996595 | + | 0.995022i | \(0.468225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.75379 | −0.858773 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.68466 | −0.409301 | −0.204650 | − | 0.978835i | \(-0.565606\pi\) | ||||
−0.204650 | + | 0.978835i | \(0.565606\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.43845 | −0.211440 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.56155 | 0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.6155 | −1.84674 | −0.923370 | − | 0.383912i | \(-0.874577\pi\) | ||||
−0.923370 | + | 0.383912i | \(0.874577\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.61553 | −0.641343 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.00000 | −0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.68466 | −0.222949 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.12311 | 0.587504 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.6847 | 1.20301 | 0.601507 | − | 0.798867i | \(-0.294567\pi\) | ||||
0.601507 | + | 0.798867i | \(0.294567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.87689 | −0.396876 | −0.198438 | − | 0.980113i | \(-0.563587\pi\) | ||||
−0.198438 | + | 0.980113i | \(0.563587\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.43845 | −0.195861 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.80776 | −0.463510 | −0.231755 | − | 0.972774i | \(-0.574447\pi\) | ||||
−0.231755 | + | 0.972774i | \(0.574447\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.684658 | −0.0542969 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.87689 | −0.384353 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.8078 | −1.86477 | −0.932384 | − | 0.361469i | \(-0.882275\pi\) | ||||
−0.932384 | + | 0.361469i | \(0.882275\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.56155 | 0.121567 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.43845 | 0.498222 | 0.249111 | − | 0.968475i | \(-0.419862\pi\) | ||||
0.249111 | + | 0.968475i | \(0.419862\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.876894 | −0.0670578 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.2462 | −0.931062 | −0.465531 | − | 0.885032i | \(-0.654137\pi\) | ||||
−0.465531 | + | 0.885032i | \(0.654137\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.56155 | −0.118042 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.1231 | −0.836064 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.2462 | −0.765838 | −0.382919 | − | 0.923782i | \(-0.625081\pi\) | ||||
−0.382919 | + | 0.923782i | \(0.625081\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2462 | 0.910254 | 0.455127 | − | 0.890427i | \(-0.349594\pi\) | ||||
0.455127 | + | 0.890427i | \(0.349594\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.9309 | −1.69510 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.68466 | 0.491466 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.56155 | −0.260447 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.68466 | −0.631716 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.24621 | 0.451960 | 0.225980 | − | 0.974132i | \(-0.427442\pi\) | ||||
0.225980 | + | 0.974132i | \(0.427442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.8078 | 1.85768 | 0.928842 | − | 0.370477i | \(-0.120806\pi\) | ||||
0.928842 | + | 0.370477i | \(0.120806\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.12311 | −0.223650 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.3693 | 1.38001 | 0.690003 | − | 0.723806i | \(-0.257609\pi\) | ||||
0.690003 | + | 0.723806i | \(0.257609\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.8078 | −1.40414 | −0.702068 | − | 0.712110i | \(-0.747740\pi\) | ||||
−0.702068 | + | 0.712110i | \(0.747740\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.0000 | −1.12855 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.19224 | 0.294237 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.75379 | −0.121897 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.56155 | −0.108015 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.6847 | −1.42399 | −0.711995 | − | 0.702184i | \(-0.752208\pi\) | ||||
−0.711995 | + | 0.702184i | \(0.752208\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.5616 | −0.929222 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.24621 | 0.425988 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.80776 | 0.258488 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.12311 | 0.211040 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.12311 | 0.479152 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.87689 | −0.326581 | −0.163291 | − | 0.986578i | \(-0.552211\pi\) | ||||
−0.163291 | + | 0.986578i | \(0.552211\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.1231 | −0.738266 | −0.369133 | − | 0.929376i | \(-0.620345\pi\) | ||||
−0.369133 | + | 0.929376i | \(0.620345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.7386 | 1.63477 | 0.817387 | − | 0.576088i | \(-0.195422\pi\) | ||||
0.817387 | + | 0.576088i | \(0.195422\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.43845 | −0.160438 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.93087 | −0.585081 | −0.292540 | − | 0.956253i | \(-0.594501\pi\) | ||||
−0.292540 | + | 0.956253i | \(0.594501\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.87689 | 0.318134 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.6307 | 0.950365 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.6155 | 1.01008 | 0.505042 | − | 0.863095i | \(-0.331477\pi\) | ||||
0.505042 | + | 0.863095i | \(0.331477\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.246211 | 0.0158599 | 0.00792993 | − | 0.999969i | \(-0.497476\pi\) | ||||
0.00792993 | + | 0.999969i | \(0.497476\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.56155 | −0.291427 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.12311 | 0.198718 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.87689 | −0.309061 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.6155 | −0.733166 | −0.366583 | − | 0.930385i | \(-0.619472\pi\) | ||||
−0.366583 | + | 0.930385i | \(0.619472\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.12311 | −0.196348 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.56155 | −0.348278 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.7386 | 1.29364 | 0.646820 | − | 0.762643i | \(-0.276098\pi\) | ||||
0.646820 | + | 0.762643i | \(0.276098\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.4384 | −0.648614 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.50758 | 0.0933167 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.8078 | 0.974748 | 0.487374 | − | 0.873193i | \(-0.337955\pi\) | ||||
0.487374 | + | 0.873193i | \(0.337955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.438447 | 0.0269336 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.1771 | 0.806424 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.6155 | 1.31792 | 0.658961 | − | 0.752177i | \(-0.270996\pi\) | ||||
0.658961 | + | 0.752177i | \(0.270996\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.49242 | 0.272895 | 0.136448 | − | 0.990647i | \(-0.456431\pi\) | ||||
0.136448 | + | 0.990647i | \(0.456431\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.87689 | 0.295163 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.12311 | −0.0674809 | −0.0337404 | − | 0.999431i | \(-0.510742\pi\) | ||||
−0.0337404 | + | 0.999431i | \(0.510742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.36932 | 0.0819789 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.24621 | 0.491928 | 0.245964 | − | 0.969279i | \(-0.420896\pi\) | ||||
0.245964 | + | 0.969279i | \(0.420896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.36932 | −0.0813974 | −0.0406987 | − | 0.999171i | \(-0.512958\pi\) | ||||
−0.0406987 | + | 0.999171i | \(0.512958\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.43845 | −0.144441 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.12311 | −0.184351 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.31534 | −0.253844 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.75379 | 0.102809 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.4924 | −1.08034 | −0.540169 | − | 0.841556i | \(-0.681640\pi\) | ||||
−0.540169 | + | 0.841556i | \(0.681640\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.12311 | 0.414723 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.56155 | −0.322714 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.24621 | 0.361228 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.75379 | −0.562199 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.1231 | −1.09859 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.6847 | 0.840841 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.6155 | −0.891225 | −0.445613 | − | 0.895226i | \(-0.647014\pi\) | ||||
−0.445613 | + | 0.895226i | \(0.647014\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.75379 | −0.554874 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.5616 | 1.67628 | 0.838141 | − | 0.545454i | \(-0.183643\pi\) | ||||
0.838141 | + | 0.545454i | \(0.183643\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.49242 | −0.140880 | −0.0704400 | − | 0.997516i | \(-0.522440\pi\) | ||||
−0.0704400 | + | 0.997516i | \(0.522440\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.876894 | 0.0494074 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.8078 | 1.89883 | 0.949417 | − | 0.314019i | \(-0.101676\pi\) | ||||
0.949417 | + | 0.314019i | \(0.101676\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.68466 | 0.150312 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.9848 | −1.39452 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.56155 | 0.309453 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.6307 | 1.25148 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.61553 | −0.419858 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.4924 | −1.34623 | −0.673113 | − | 0.739540i | \(-0.735043\pi\) | ||||
−0.673113 | + | 0.739540i | \(0.735043\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.75379 | −0.205706 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.2462 | 0.559810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.6847 | 0.799924 | 0.399962 | − | 0.916532i | \(-0.369023\pi\) | ||||
0.399962 | + | 0.916532i | \(0.369023\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.9848 | 0.922490 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.43845 | 0.132049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0540 | 0.974823 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.87689 | −0.262563 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.1231 | 1.45604 | 0.728022 | − | 0.685553i | \(-0.240440\pi\) | ||||
0.728022 | + | 0.685553i | \(0.240440\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.4924 | −1.20399 | −0.601996 | − | 0.798499i | \(-0.705628\pi\) | ||||
−0.601996 | + | 0.798499i | \(0.705628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.1231 | 0.593707 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50758 | −0.0802403 | −0.0401201 | − | 0.999195i | \(-0.512774\pi\) | ||||
−0.0401201 | + | 0.999195i | \(0.512774\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.68466 | 0.460934 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.68466 | 0.459641 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.75379 | −0.514785 | −0.257393 | − | 0.966307i | \(-0.582863\pi\) | ||||
−0.257393 | + | 0.966307i | \(0.582863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5616 | −0.871661 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.56155 | −0.0819603 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.7386 | −1.81334 | −0.906671 | − | 0.421839i | \(-0.861385\pi\) | ||||
−0.906671 | + | 0.421839i | \(0.861385\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.12311 | −0.0584665 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.684658 | −0.0355457 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | 0.103556 | 0.0517780 | − | 0.998659i | \(-0.483511\pi\) | ||||
0.0517780 | + | 0.998659i | \(0.483511\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.56155 | −0.0806382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.36932 | −0.276534 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.8769 | 0.866908 | 0.433454 | − | 0.901176i | \(-0.357295\pi\) | ||||
0.433454 | + | 0.901176i | \(0.357295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.50758 | −0.179699 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.63068 | 0.338812 | 0.169406 | − | 0.985546i | \(-0.445815\pi\) | ||||
0.169406 | + | 0.985546i | \(0.445815\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.56155 | 0.0795841 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.50758 | −0.178300 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.7538 | 0.798749 | 0.399374 | − | 0.916788i | \(-0.369227\pi\) | ||||
0.399374 | + | 0.916788i | \(0.369227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.1231 | 0.562520 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.31534 | 0.369010 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.36932 | −0.471421 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0000 | −0.903394 | −0.451697 | − | 0.892171i | \(-0.649181\pi\) | ||||
−0.451697 | + | 0.892171i | \(0.649181\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.80776 | 0.190627 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.5616 | −0.577356 | −0.288678 | − | 0.957426i | \(-0.593216\pi\) | ||||
−0.288678 | + | 0.957426i | \(0.593216\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.87689 | −0.242935 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.68466 | −0.331346 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.12311 | −0.0555340 | −0.0277670 | − | 0.999614i | \(-0.508840\pi\) | ||||
−0.0277670 | + | 0.999614i | \(0.508840\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 33.7538 | 1.66495 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.1231 | −0.547332 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.12311 | 0.153307 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.7386 | 0.917635 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.7386 | −1.11085 | −0.555427 | − | 0.831565i | \(-0.687445\pi\) | ||||
−0.555427 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.6155 | −1.63832 | −0.819160 | − | 0.573565i | \(-0.805560\pi\) | ||||
−0.819160 | + | 0.573565i | \(0.805560\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.73863 | −0.133157 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.56155 | 0.172761 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.9309 | −1.10970 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.12311 | 0.150785 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.63068 | 0.414764 | 0.207382 | − | 0.978260i | \(-0.433506\pi\) | ||||
0.207382 | + | 0.978260i | \(0.433506\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.19224 | 0.201002 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.87689 | 0.233293 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7538 | 0.847342 | 0.423671 | − | 0.905816i | \(-0.360741\pi\) | ||||
0.423671 | + | 0.905816i | \(0.360741\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.56155 | 0.121979 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.00000 | 0.190046 | 0.0950229 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950229 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.43845 | −0.400021 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.9309 | −1.08459 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.00000 | −0.0941763 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.61553 | 0.357809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.12311 | −0.146413 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.4384 | 1.14318 | 0.571591 | − | 0.820539i | \(-0.306326\pi\) | ||||
0.571591 | + | 0.820539i | \(0.306326\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.8078 | 0.924547 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.4384 | 0.765615 | 0.382807 | − | 0.923828i | \(-0.374957\pi\) | ||||
0.382807 | + | 0.923828i | \(0.374957\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3693 | −0.807221 | −0.403610 | − | 0.914931i | \(-0.632245\pi\) | ||||
−0.403610 | + | 0.914931i | \(0.632245\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.80776 | 0.176581 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.9309 | 0.876016 | 0.438008 | − | 0.898971i | \(-0.355684\pi\) | ||||
0.438008 | + | 0.898971i | \(0.355684\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.06913 | 0.417883 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.24621 | −0.287201 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.56155 | 0.0716490 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.246211 | −0.0112732 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.9848 | −1.50712 | −0.753558 | − | 0.657381i | \(-0.771664\pi\) | ||||
−0.753558 | + | 0.657381i | \(0.771664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3693 | 0.609588 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.61553 | 0.346519 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.12311 | −0.0509976 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.2462 | −0.645557 | −0.322779 | − | 0.946474i | \(-0.604617\pi\) | ||||
−0.322779 | + | 0.946474i | \(0.604617\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 37.1771 | 1.68121 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0540 | 1.35632 | 0.678158 | − | 0.734916i | \(-0.262778\pi\) | ||||
0.678158 | + | 0.734916i | \(0.262778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.56155 | −0.430631 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.561553 | 0.0252399 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.5616 | −0.608319 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.4924 | 0.738302 | 0.369151 | − | 0.929369i | \(-0.379648\pi\) | ||||
0.369151 | + | 0.929369i | \(0.379648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.0540 | −0.449178 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.24621 | −0.100154 | −0.0500768 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500768 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.2462 | 0.544949 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.0540 | 0.624159 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.36932 | −0.149342 | −0.0746712 | − | 0.997208i | \(-0.523791\pi\) | ||||
−0.0746712 | + | 0.997208i | \(0.523791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.12311 | 0.138158 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.68466 | 0.383437 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.24621 | 0.275241 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.87689 | −0.214486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.1231 | 0.839411 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.7386 | −1.78479 | −0.892396 | − | 0.451253i | \(-0.850977\pi\) | ||||
−0.892396 | + | 0.451253i | \(0.850977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.4924 | 1.59570 | 0.797851 | − | 0.602855i | \(-0.205970\pi\) | ||||
0.797851 | + | 0.602855i | \(0.205970\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.43845 | 0.106423 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.68466 | −0.378310 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.2462 | −0.575922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.00000 | 0.173259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.0000 | 0.691740 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.0000 | 0.690451 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.56155 | 0.196480 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.5464 | 1.57125 | 0.785626 | − | 0.618701i | \(-0.212341\pi\) | ||||
0.785626 | + | 0.618701i | \(0.212341\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.1231 | −0.820651 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.4924 | −0.620787 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0000 | 0.684111 | 0.342055 | − | 0.939680i | \(-0.388877\pi\) | ||||
0.342055 | + | 0.939680i | \(0.388877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.24621 | −0.351940 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.19224 | −0.178595 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.6307 | 0.622160 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.4384 | −0.443087 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.5076 | 0.572334 | 0.286167 | − | 0.958180i | \(-0.407619\pi\) | ||||
0.286167 | + | 0.958180i | \(0.407619\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.4924 | 0.528373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.56155 | 0.234809 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.1231 | 0.468783 | 0.234392 | − | 0.972142i | \(-0.424690\pi\) | ||||
0.234392 | + | 0.972142i | \(0.424690\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.8769 | −0.457594 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.9309 | 0.459053 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.1080 | 1.93295 | 0.966473 | − | 0.256769i | \(-0.0826578\pi\) | ||||
0.966473 | + | 0.256769i | \(0.0826578\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.4233 | 1.31502 | 0.657512 | − | 0.753444i | \(-0.271609\pi\) | ||||
0.657512 | + | 0.753444i | \(0.271609\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.75379 | −0.407470 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.12311 | 0.130243 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.7386 | −1.02988 | −0.514941 | − | 0.857225i | \(-0.672186\pi\) | ||||
−0.514941 | + | 0.857225i | \(0.672186\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.3002 | −1.67482 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.87689 | −0.202328 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.438447 | −0.0181586 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.12311 | −0.0464347 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.6847 | −1.84433 | −0.922167 | − | 0.386793i | \(-0.873583\pi\) | ||||
−0.922167 | + | 0.386793i | \(0.873583\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.80776 | −0.156896 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.2462 | −1.24416 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.4924 | 1.41643 | 0.708217 | − | 0.705995i | \(-0.249500\pi\) | ||||
0.708217 | + | 0.705995i | \(0.249500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.56155 | −0.228001 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.9309 | 1.26592 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.5616 | 0.880981 | 0.440491 | − | 0.897757i | \(-0.354805\pi\) | ||||
0.440491 | + | 0.897757i | \(0.354805\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.0000 | −1.22373 | −0.611863 | − | 0.790964i | \(-0.709580\pi\) | ||||
−0.611863 | + | 0.790964i | \(0.709580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.75379 | −0.234312 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.192236 | −0.00780262 | −0.00390131 | − | 0.999992i | \(-0.501242\pi\) | ||||
−0.00390131 | + | 0.999992i | \(0.501242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.54640 | −0.265273 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.75379 | 0.394596 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.7386 | −1.32230 | −0.661150 | − | 0.750253i | \(-0.729932\pi\) | ||||
−0.661150 | + | 0.750253i | \(0.729932\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.12311 | −0.125936 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.3693 | −1.26288 | −0.631441 | − | 0.775424i | \(-0.717536\pi\) | ||||
−0.631441 | + | 0.775424i | \(0.717536\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.4924 | −0.984434 | −0.492217 | − | 0.870473i | \(-0.663813\pi\) | ||||
−0.492217 | + | 0.870473i | \(0.663813\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.3693 | 0.697007 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.1771 | 0.527929 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.43845 | 0.0973822 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.8078 | 0.949278 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.80776 | −0.151585 | −0.0757923 | − | 0.997124i | \(-0.524149\pi\) | ||||
−0.0757923 | + | 0.997124i | \(0.524149\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.3002 | 1.28382 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.24621 | 0.0891382 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.12311 | −0.361471 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.87689 | −0.192927 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.17708 | 0.283478 | 0.141739 | − | 0.989904i | \(-0.454731\pi\) | ||||
0.141739 | + | 0.989904i | \(0.454731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.3153 | −0.446234 | −0.223117 | − | 0.974792i | \(-0.571623\pi\) | ||||
−0.223117 | + | 0.974792i | \(0.571623\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.75379 | −0.384055 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.87689 | 0.191731 | 0.0958653 | − | 0.995394i | \(-0.469438\pi\) | ||||
0.0958653 | + | 0.995394i | \(0.469438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.12311 | −0.279606 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.94602 | −0.233043 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.80776 | 0.383807 | 0.191904 | − | 0.981414i | \(-0.438534\pi\) | ||||
0.191904 | + | 0.981414i | \(0.438534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.68466 | −0.183045 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.12311 | 0.0438165 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.8078 | −1.55069 | −0.775345 | − | 0.631538i | \(-0.782424\pi\) | ||||
−0.775345 | + | 0.631538i | \(0.782424\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.246211 | −0.00957651 | −0.00478825 | − | 0.999989i | \(-0.501524\pi\) | ||||
−0.00478825 | + | 0.999989i | \(0.501524\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.1231 | −0.431986 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.43845 | −0.0945589 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.38447 | −0.324648 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.61553 | 0.294433 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.6847 | −0.566895 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.7926 | 1.95791 | 0.978956 | − | 0.204073i | \(-0.0654181\pi\) | ||||
0.978956 | + | 0.204073i | \(0.0654181\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.56155 | 0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.6155 | −0.523287 | −0.261644 | − | 0.965165i | \(-0.584265\pi\) | ||||
−0.261644 | + | 0.965165i | \(0.584265\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.75379 | 0.0673042 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.3693 | 0.665594 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.93087 | −0.112147 | −0.0560733 | − | 0.998427i | \(-0.517858\pi\) | ||||
−0.0560733 | + | 0.998427i | \(0.517858\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.6155 | −0.825887 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −38.6307 | −1.47385 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.876894 | 0.0334070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.3693 | 0.812927 | 0.406464 | − | 0.913667i | \(-0.366762\pi\) | ||||
0.406464 | + | 0.913667i | \(0.366762\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.876894 | −0.0333105 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.0000 | −0.455186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.12311 | 0.269807 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.9460 | 0.527487 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.6847 | 1.76326 | 0.881628 | − | 0.471946i | \(-0.156448\pi\) | ||||
0.881628 | + | 0.471946i | \(0.156448\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.4384 | 0.393693 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.61553 | −0.286817 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.1231 | −0.719198 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.4924 | 1.29539 | 0.647695 | − | 0.761900i | \(-0.275733\pi\) | ||||
0.647695 | + | 0.761900i | \(0.275733\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.26137 | 0.197317 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.61553 | −0.285204 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.00000 | −0.0747958 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.3845 | −0.910655 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −53.1771 | −1.98317 | −0.991585 | − | 0.129455i | \(-0.958677\pi\) | ||||
−0.991585 | + | 0.129455i | \(0.958677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.75379 | −0.363250 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.384472 | −0.0142987 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.68466 | −0.0997057 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.6155 | 0.875851 | 0.437926 | − | 0.899011i | \(-0.355713\pi\) | ||||
0.437926 | + | 0.899011i | \(0.355713\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.2462 | 0.822806 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.8769 | −0.401747 | −0.200874 | − | 0.979617i | \(-0.564378\pi\) | ||||
−0.200874 | + | 0.979617i | \(0.564378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.12311 | 0.262740 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.2462 | −0.377424 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.73863 | −0.247885 | −0.123942 | − | 0.992289i | \(-0.539554\pi\) | ||||
−0.123942 | + | 0.992289i | \(0.539554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.87689 | −0.179157 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.56155 | −0.0572878 | −0.0286439 | − | 0.999590i | \(-0.509119\pi\) | ||||
−0.0286439 | + | 0.999590i | \(0.509119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.6847 | 0.538004 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.75379 | −0.0641678 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.9848 | −0.912926 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.1771 | −1.06469 | −0.532343 | − | 0.846529i | \(-0.678688\pi\) | ||||
−0.532343 | + | 0.846529i | \(0.678688\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.1383 | 0.660995 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.87689 | −0.177488 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.87689 | 0.177020 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.7386 | 0.461775 | 0.230888 | − | 0.972980i | \(-0.425837\pi\) | ||||
0.230888 | + | 0.972980i | \(0.425837\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.6307 | 0.819286 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | −0.0723102 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.2462 | 0.514401 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.7386 | −0.892098 | −0.446049 | − | 0.895009i | \(-0.647169\pi\) | ||||
−0.446049 | + | 0.895009i | \(0.647169\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.3845 | −1.16630 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.3153 | −0.910530 | −0.455265 | − | 0.890356i | \(-0.650455\pi\) | ||||
−0.455265 | + | 0.890356i | \(0.650455\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.43845 | −0.0875916 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.3002 | 0.584766 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.12311 | 0.111897 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.68466 | −0.310762 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.9309 | −0.533586 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.80776 | −0.207288 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.26137 | 0.187547 | 0.0937737 | − | 0.995594i | \(-0.470107\pi\) | ||||
0.0937737 | + | 0.995594i | \(0.470107\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.6847 | −0.878797 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.9848 | 0.603912 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.3693 | 1.04294 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.684658 | −0.0242823 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.2462 | −1.42559 | −0.712797 | − | 0.701370i | \(-0.752572\pi\) | ||||
−0.712797 | + | 0.701370i | \(0.752572\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.3693 | 0.614482 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.73863 | 0.167431 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.00000 | 0.0705785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.87689 | −0.171888 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33.7538 | −1.18819 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.4924 | −0.931424 | −0.465712 | − | 0.884936i | \(-0.654202\pi\) | ||||
−0.465712 | + | 0.884936i | \(0.654202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.8078 | −1.67876 | −0.839379 | − | 0.543547i | \(-0.817081\pi\) | ||||
−0.839379 | + | 0.543547i | \(0.817081\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.01515 | −0.246032 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.8078 | −0.833950 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.75379 | 0.341242 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.75379 | 0.0612823 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.00000 | −0.0698005 | −0.0349002 | − | 0.999391i | \(-0.511111\pi\) | ||||
−0.0349002 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.5076 | 0.679991 | 0.339996 | − | 0.940427i | \(-0.389574\pi\) | ||||
0.339996 | + | 0.940427i | \(0.389574\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.56155 | 0.0543663 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.4924 | −0.990779 | −0.495389 | − | 0.868671i | \(-0.664975\pi\) | ||||
−0.495389 | + | 0.868671i | \(0.664975\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.3693 | −0.672724 | −0.336362 | − | 0.941733i | \(-0.609197\pi\) | ||||
−0.336362 | + | 0.941733i | \(0.609197\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.75379 | 0.0608383 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.2462 | −0.562898 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.43845 | 0.222812 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.5616 | −0.468756 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.4924 | −1.53605 | −0.768025 | − | 0.640420i | \(-0.778760\pi\) | ||||
−0.768025 | + | 0.640420i | \(0.778760\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.7926 | −0.751469 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.8769 | −0.443504 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.56155 | −0.0536556 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.13826 | 0.0733849 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.8769 | 0.715651 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.2462 | −0.693217 | −0.346609 | − | 0.938010i | \(-0.612667\pi\) | ||||
−0.346609 | + | 0.938010i | \(0.612667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.876894 | −0.0299892 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.4233 | −1.00508 | −0.502540 | − | 0.864554i | \(-0.667601\pi\) | ||||
−0.502540 | + | 0.864554i | \(0.667601\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.1231 | 1.60782 | 0.803910 | − | 0.594751i | \(-0.202749\pi\) | ||||
0.803910 | + | 0.594751i | \(0.202749\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.87689 | 0.166204 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.6155 | 1.07621 | 0.538103 | − | 0.842879i | \(-0.319141\pi\) | ||||
0.538103 | + | 0.842879i | \(0.319141\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.2462 | −0.416384 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.73863 | 0.228856 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.36932 | 0.317832 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.4924 | 0.694359 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.630683 | 0.0213454 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.56155 | −0.0527901 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.7538 | −0.531968 | −0.265984 | − | 0.963977i | \(-0.585697\pi\) | ||||
−0.265984 | + | 0.963977i | \(0.585697\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.8769 | 0.973993 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.9309 | −1.17552 | −0.587759 | − | 0.809036i | \(-0.699990\pi\) | ||||
−0.587759 | + | 0.809036i | \(0.699990\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.1231 | −0.373899 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.7538 | 0.461807 | 0.230904 | − | 0.972977i | \(-0.425832\pi\) | ||||
0.230904 | + | 0.972977i | \(0.425832\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.50758 | −0.117640 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.00000 | 0.234509 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.61553 | 0.254844 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.2462 | −0.342493 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.75379 | −0.325670 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.54640 | 0.218335 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.56155 | 0.0520229 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.2311 | 0.506858 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.2462 | 0.407078 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.0540 | −1.52920 | −0.764599 | − | 0.644507i | \(-0.777063\pi\) | ||||
−0.764599 | + | 0.644507i | \(0.777063\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.87689 | −0.228092 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.9309 | 1.02479 | 0.512393 | − | 0.858751i | \(-0.328759\pi\) | ||||
0.512393 | + | 0.858751i | \(0.328759\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.12311 | −0.103360 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22.9309 | −0.758071 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.31534 | 0.241574 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | −0.263896 | −0.131948 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131948 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.3845 | 0.803496 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.3693 | 0.571718 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.68466 | 0.219790 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.50758 | −0.115204 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.94602 | 0.260701 | 0.130350 | − | 0.991468i | \(-0.458390\pi\) | ||||
0.130350 | + | 0.991468i | \(0.458390\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.12311 | −0.233450 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −46.1619 | −1.51127 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.56155 | −0.116475 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.0000 | −1.37208 | −0.686040 | − | 0.727564i | \(-0.740653\pi\) | ||||
−0.686040 | + | 0.727564i | \(0.740653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.89205 | 0.127012 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.9309 | −1.07352 | −0.536758 | − | 0.843736i | \(-0.680351\pi\) | ||||
−0.536758 | + | 0.843736i | \(0.680351\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.24621 | 0.203405 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.68466 | −0.282512 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.3153 | 0.887629 | 0.443815 | − | 0.896119i | \(-0.353625\pi\) | ||||
0.443815 | + | 0.896119i | \(0.353625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −52.7926 | −1.71192 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.1771 | 0.362061 | 0.181031 | − | 0.983477i | \(-0.442057\pi\) | ||||
0.181031 | + | 0.983477i | \(0.442057\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.24621 | 0.202123 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.19224 | −0.135516 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.7538 | 1.08997 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0540 | −0.808193 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.98485 | −0.289533 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.8078 | 0.830781 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.5464 | 1.88273 | 0.941363 | − | 0.337397i | \(-0.109546\pi\) | ||||
0.941363 | + | 0.337397i | \(0.109546\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.68466 | −0.278991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.2462 | 0.328817 | 0.164408 | − | 0.986392i | \(-0.447429\pi\) | ||||
0.164408 | + | 0.986392i | \(0.447429\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.7386 | 0.600733 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.12311 | −0.100019 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.1231 | −1.05970 | −0.529851 | − | 0.848091i | \(-0.677752\pi\) | ||||
−0.529851 | + | 0.848091i | \(0.677752\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.43845 | 0.269694 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.13826 | 0.259835 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.1231 | −0.865093 | −0.432546 | − | 0.901612i | \(-0.642385\pi\) | ||||
−0.432546 | + | 0.901612i | \(0.642385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.3693 | 0.617158 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.8920 | 0.378528 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.5076 | 0.620305 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38.2462 | 1.21371 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.8078 | −0.627948 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.8617 | −1.38912 | −0.694558 | − | 0.719437i | \(-0.744400\pi\) | ||||
−0.694558 | + | 0.719437i | \(0.744400\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 37.1771 | 1.17623 |
(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 | 880.2.a.o.1.1 | 2 | ||
3.2 | odd | 2 | 7920.2.a.bu.1.1 | 2 | |||
4.3 | odd | 2 | 440.2.a.e.1.2 | ✓ | 2 | ||
5.2 | odd | 4 | 4400.2.b.t.4049.3 | 4 | |||
5.3 | odd | 4 | 4400.2.b.t.4049.2 | 4 | |||
5.4 | even | 2 | 4400.2.a.bj.1.2 | 2 | |||
8.3 | odd | 2 | 3520.2.a.bp.1.1 | 2 | |||
8.5 | even | 2 | 3520.2.a.bk.1.2 | 2 | |||
11.10 | odd | 2 | 9680.2.a.bs.1.1 | 2 | |||
12.11 | even | 2 | 3960.2.a.w.1.2 | 2 | |||
20.3 | even | 4 | 2200.2.b.i.1849.3 | 4 | |||
20.7 | even | 4 | 2200.2.b.i.1849.2 | 4 | |||
20.19 | odd | 2 | 2200.2.a.s.1.1 | 2 | |||
44.43 | even | 2 | 4840.2.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.a.e.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
880.2.a.o.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2200.2.a.s.1.1 | 2 | 20.19 | odd | 2 | |||
2200.2.b.i.1849.2 | 4 | 20.7 | even | 4 | |||
2200.2.b.i.1849.3 | 4 | 20.3 | even | 4 | |||
3520.2.a.bk.1.2 | 2 | 8.5 | even | 2 | |||
3520.2.a.bp.1.1 | 2 | 8.3 | odd | 2 | |||
3960.2.a.w.1.2 | 2 | 12.11 | even | 2 | |||
4400.2.a.bj.1.2 | 2 | 5.4 | even | 2 | |||
4400.2.b.t.4049.2 | 4 | 5.3 | odd | 4 | |||
4400.2.b.t.4049.3 | 4 | 5.2 | odd | 4 | |||
4840.2.a.j.1.2 | 2 | 44.43 | even | 2 | |||
7920.2.a.bu.1.1 | 2 | 3.2 | odd | 2 | |||
9680.2.a.bs.1.1 | 2 | 11.10 | odd | 2 |