Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36333 | −0.964019 | −0.482009 | − | 0.876166i | \(-0.660093\pi\) | ||||
−0.482009 | + | 0.876166i | \(0.660093\pi\) | |||||||
\(3\) | 0.363328 | 0.209768 | 0.104884 | − | 0.994484i | \(-0.466553\pi\) | ||||
0.104884 | + | 0.994484i | \(0.466553\pi\) | |||||||
\(4\) | −0.141336 | −0.0706681 | ||||||||
\(5\) | 3.14134 | 1.40485 | 0.702424 | − | 0.711759i | \(-0.252101\pi\) | ||||
0.702424 | + | 0.711759i | \(0.252101\pi\) | |||||||
\(6\) | −0.495336 | −0.202220 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.91934 | 1.03214 | ||||||||
\(9\) | −2.86799 | −0.955998 | ||||||||
\(10\) | −4.28267 | −1.35430 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.0513514 | −0.0148239 | ||||||||
\(13\) | −4.77801 | −1.32518 | −0.662590 | − | 0.748982i | \(-0.730543\pi\) | ||||
−0.662590 | + | 0.748982i | \(0.730543\pi\) | |||||||
\(14\) | 1.36333 | 0.364365 | ||||||||
\(15\) | 1.14134 | 0.294692 | ||||||||
\(16\) | −3.69735 | −0.924338 | ||||||||
\(17\) | −4.77801 | −1.15884 | −0.579419 | − | 0.815030i | \(-0.696720\pi\) | ||||
−0.579419 | + | 0.815030i | \(0.696720\pi\) | |||||||
\(18\) | 3.91002 | 0.921599 | ||||||||
\(19\) | −7.00933 | −1.60805 | −0.804025 | − | 0.594595i | \(-0.797312\pi\) | ||||
−0.804025 | + | 0.594595i | \(0.797312\pi\) | |||||||
\(20\) | −0.443984 | −0.0992779 | ||||||||
\(21\) | −0.363328 | −0.0792847 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.14134 | 1.07204 | 0.536021 | − | 0.844204i | \(-0.319927\pi\) | ||||
0.536021 | + | 0.844204i | \(0.319927\pi\) | |||||||
\(24\) | 1.06068 | 0.216510 | ||||||||
\(25\) | 4.86799 | 0.973599 | ||||||||
\(26\) | 6.51399 | 1.27750 | ||||||||
\(27\) | −2.13201 | −0.410305 | ||||||||
\(28\) | 0.141336 | 0.0267100 | ||||||||
\(29\) | 7.00933 | 1.30160 | 0.650800 | − | 0.759249i | \(-0.274434\pi\) | ||||
0.650800 | + | 0.759249i | \(0.274434\pi\) | |||||||
\(30\) | −1.55602 | −0.284088 | ||||||||
\(31\) | −3.63667 | −0.653166 | −0.326583 | − | 0.945169i | \(-0.605897\pi\) | ||||
−0.326583 | + | 0.945169i | \(0.605897\pi\) | |||||||
\(32\) | −0.797984 | −0.141065 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.51399 | 1.11714 | ||||||||
\(35\) | −3.14134 | −0.530983 | ||||||||
\(36\) | 0.405351 | 0.0675585 | ||||||||
\(37\) | −9.86799 | −1.62229 | −0.811144 | − | 0.584846i | \(-0.801155\pi\) | ||||
−0.811144 | + | 0.584846i | \(0.801155\pi\) | |||||||
\(38\) | 9.55602 | 1.55019 | ||||||||
\(39\) | −1.73599 | −0.277980 | ||||||||
\(40\) | 9.17064 | 1.45001 | ||||||||
\(41\) | −3.22199 | −0.503191 | −0.251595 | − | 0.967833i | \(-0.580955\pi\) | ||||
−0.251595 | + | 0.967833i | \(0.580955\pi\) | |||||||
\(42\) | 0.495336 | 0.0764319 | ||||||||
\(43\) | 4.28267 | 0.653101 | 0.326551 | − | 0.945180i | \(-0.394114\pi\) | ||||
0.326551 | + | 0.945180i | \(0.394114\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.00933 | −1.34303 | ||||||||
\(46\) | −7.00933 | −1.03347 | ||||||||
\(47\) | −0.778008 | −0.113484 | −0.0567421 | − | 0.998389i | \(-0.518071\pi\) | ||||
−0.0567421 | + | 0.998389i | \(0.518071\pi\) | |||||||
\(48\) | −1.34335 | −0.193896 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.63667 | −0.938567 | ||||||||
\(51\) | −1.73599 | −0.243087 | ||||||||
\(52\) | 0.675305 | 0.0936480 | ||||||||
\(53\) | 2.28267 | 0.313549 | 0.156775 | − | 0.987634i | \(-0.449890\pi\) | ||||
0.156775 | + | 0.987634i | \(0.449890\pi\) | |||||||
\(54\) | 2.90663 | 0.395542 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.91934 | −0.390114 | ||||||||
\(57\) | −2.54669 | −0.337317 | ||||||||
\(58\) | −9.55602 | −1.25477 | ||||||||
\(59\) | −0.363328 | −0.0473013 | −0.0236507 | − | 0.999720i | \(-0.507529\pi\) | ||||
−0.0236507 | + | 0.999720i | \(0.507529\pi\) | |||||||
\(60\) | −0.161312 | −0.0208253 | ||||||||
\(61\) | 3.22199 | 0.412534 | 0.206267 | − | 0.978496i | \(-0.433868\pi\) | ||||
0.206267 | + | 0.978496i | \(0.433868\pi\) | |||||||
\(62\) | 4.95798 | 0.629664 | ||||||||
\(63\) | 2.86799 | 0.361333 | ||||||||
\(64\) | 8.48262 | 1.06033 | ||||||||
\(65\) | −15.0093 | −1.86168 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.59465 | −0.805665 | −0.402832 | − | 0.915274i | \(-0.631974\pi\) | ||||
−0.402832 | + | 0.915274i | \(0.631974\pi\) | |||||||
\(68\) | 0.675305 | 0.0818928 | ||||||||
\(69\) | 1.86799 | 0.224880 | ||||||||
\(70\) | 4.28267 | 0.511877 | ||||||||
\(71\) | −15.1600 | −1.79916 | −0.899580 | − | 0.436756i | \(-0.856127\pi\) | ||||
−0.899580 | + | 0.436756i | \(0.856127\pi\) | |||||||
\(72\) | −8.37266 | −0.986727 | ||||||||
\(73\) | −3.22199 | −0.377106 | −0.188553 | − | 0.982063i | \(-0.560380\pi\) | ||||
−0.188553 | + | 0.982063i | \(0.560380\pi\) | |||||||
\(74\) | 13.4533 | 1.56392 | ||||||||
\(75\) | 1.76868 | 0.204229 | ||||||||
\(76\) | 0.990671 | 0.113638 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.36672 | 0.267978 | ||||||||
\(79\) | −3.71733 | −0.418232 | −0.209116 | − | 0.977891i | \(-0.567059\pi\) | ||||
−0.209116 | + | 0.977891i | \(0.567059\pi\) | |||||||
\(80\) | −11.6146 | −1.29855 | ||||||||
\(81\) | 7.82936 | 0.869929 | ||||||||
\(82\) | 4.39263 | 0.485085 | ||||||||
\(83\) | 1.55602 | 0.170795 | 0.0853975 | − | 0.996347i | \(-0.472784\pi\) | ||||
0.0853975 | + | 0.996347i | \(0.472784\pi\) | |||||||
\(84\) | 0.0513514 | 0.00560290 | ||||||||
\(85\) | −15.0093 | −1.62799 | ||||||||
\(86\) | −5.83869 | −0.629602 | ||||||||
\(87\) | 2.54669 | 0.273034 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.58532 | −0.592043 | −0.296021 | − | 0.955181i | \(-0.595660\pi\) | ||||
−0.296021 | + | 0.955181i | \(0.595660\pi\) | |||||||
\(90\) | 12.2827 | 1.29471 | ||||||||
\(91\) | 4.77801 | 0.500871 | ||||||||
\(92\) | −0.726656 | −0.0757592 | ||||||||
\(93\) | −1.32131 | −0.137013 | ||||||||
\(94\) | 1.06068 | 0.109401 | ||||||||
\(95\) | −22.0187 | −2.25907 | ||||||||
\(96\) | −0.289930 | −0.0295909 | ||||||||
\(97\) | 6.15066 | 0.624505 | 0.312253 | − | 0.949999i | \(-0.398916\pi\) | ||||
0.312253 | + | 0.949999i | \(0.398916\pi\) | |||||||
\(98\) | −1.36333 | −0.137717 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.688023 | −0.0688023 | ||||||||
\(101\) | −10.7967 | −1.07431 | −0.537154 | − | 0.843484i | \(-0.680501\pi\) | ||||
−0.537154 | + | 0.843484i | \(0.680501\pi\) | |||||||
\(102\) | 2.36672 | 0.234340 | ||||||||
\(103\) | −13.2406 | −1.30464 | −0.652320 | − | 0.757944i | \(-0.726204\pi\) | ||||
−0.652320 | + | 0.757944i | \(0.726204\pi\) | |||||||
\(104\) | −13.9486 | −1.36778 | ||||||||
\(105\) | −1.14134 | −0.111383 | ||||||||
\(106\) | −3.11203 | −0.302267 | ||||||||
\(107\) | 14.0187 | 1.35523 | 0.677617 | − | 0.735415i | \(-0.263013\pi\) | ||||
0.677617 | + | 0.735415i | \(0.263013\pi\) | |||||||
\(108\) | 0.301330 | 0.0289955 | ||||||||
\(109\) | −15.5747 | −1.49178 | −0.745892 | − | 0.666067i | \(-0.767976\pi\) | ||||
−0.745892 | + | 0.666067i | \(0.767976\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.58532 | −0.340304 | ||||||||
\(112\) | 3.69735 | 0.349367 | ||||||||
\(113\) | 4.13201 | 0.388707 | 0.194353 | − | 0.980932i | \(-0.437739\pi\) | ||||
0.194353 | + | 0.980932i | \(0.437739\pi\) | |||||||
\(114\) | 3.47197 | 0.325180 | ||||||||
\(115\) | 16.1507 | 1.50606 | ||||||||
\(116\) | −0.990671 | −0.0919815 | ||||||||
\(117\) | 13.7033 | 1.26687 | ||||||||
\(118\) | 0.495336 | 0.0455993 | ||||||||
\(119\) | 4.77801 | 0.437999 | ||||||||
\(120\) | 3.33195 | 0.304164 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.39263 | −0.397690 | ||||||||
\(123\) | −1.17064 | −0.105553 | ||||||||
\(124\) | 0.513993 | 0.0461579 | ||||||||
\(125\) | −0.414680 | −0.0370901 | ||||||||
\(126\) | −3.91002 | −0.348332 | ||||||||
\(127\) | 22.0187 | 1.95384 | 0.976920 | − | 0.213606i | \(-0.0685208\pi\) | ||||
0.976920 | + | 0.213606i | \(0.0685208\pi\) | |||||||
\(128\) | −9.96862 | −0.881110 | ||||||||
\(129\) | 1.55602 | 0.137000 | ||||||||
\(130\) | 20.4626 | 1.79469 | ||||||||
\(131\) | 15.0093 | 1.31137 | 0.655686 | − | 0.755034i | \(-0.272380\pi\) | ||||
0.655686 | + | 0.755034i | \(0.272380\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.00933 | 0.607786 | ||||||||
\(134\) | 8.99067 | 0.776676 | ||||||||
\(135\) | −6.69735 | −0.576416 | ||||||||
\(136\) | −13.9486 | −1.19609 | ||||||||
\(137\) | −10.6974 | −0.913936 | −0.456968 | − | 0.889483i | \(-0.651065\pi\) | ||||
−0.456968 | + | 0.889483i | \(0.651065\pi\) | |||||||
\(138\) | −2.54669 | −0.216788 | ||||||||
\(139\) | 4.10270 | 0.347987 | 0.173993 | − | 0.984747i | \(-0.444333\pi\) | ||||
0.173993 | + | 0.984747i | \(0.444333\pi\) | |||||||
\(140\) | 0.443984 | 0.0375235 | ||||||||
\(141\) | −0.282672 | −0.0238053 | ||||||||
\(142\) | 20.6680 | 1.73442 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.6040 | 0.883665 | ||||||||
\(145\) | 22.0187 | 1.82855 | ||||||||
\(146\) | 4.39263 | 0.363537 | ||||||||
\(147\) | 0.363328 | 0.0299668 | ||||||||
\(148\) | 1.39470 | 0.114644 | ||||||||
\(149\) | 14.0187 | 1.14845 | 0.574227 | − | 0.818696i | \(-0.305303\pi\) | ||||
0.574227 | + | 0.818696i | \(0.305303\pi\) | |||||||
\(150\) | −2.41129 | −0.196881 | ||||||||
\(151\) | −6.82936 | −0.555765 | −0.277883 | − | 0.960615i | \(-0.589633\pi\) | ||||
−0.277883 | + | 0.960615i | \(0.589633\pi\) | |||||||
\(152\) | −20.4626 | −1.65974 | ||||||||
\(153\) | 13.7033 | 1.10785 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.4240 | −0.917598 | ||||||||
\(156\) | 0.245357 | 0.0196443 | ||||||||
\(157\) | −23.4427 | −1.87093 | −0.935464 | − | 0.353421i | \(-0.885018\pi\) | ||||
−0.935464 | + | 0.353421i | \(0.885018\pi\) | |||||||
\(158\) | 5.06794 | 0.403183 | ||||||||
\(159\) | 0.829359 | 0.0657725 | ||||||||
\(160\) | −2.50674 | −0.198175 | ||||||||
\(161\) | −5.14134 | −0.405194 | ||||||||
\(162\) | −10.6740 | −0.838628 | ||||||||
\(163\) | −0.990671 | −0.0775954 | −0.0387977 | − | 0.999247i | \(-0.512353\pi\) | ||||
−0.0387977 | + | 0.999247i | \(0.512353\pi\) | |||||||
\(164\) | 0.455384 | 0.0355595 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.12136 | −0.164649 | ||||||||
\(167\) | 0.565344 | 0.0437477 | 0.0218738 | − | 0.999761i | \(-0.493037\pi\) | ||||
0.0218738 | + | 0.999761i | \(0.493037\pi\) | |||||||
\(168\) | −1.06068 | −0.0818332 | ||||||||
\(169\) | 9.82936 | 0.756105 | ||||||||
\(170\) | 20.4626 | 1.56941 | ||||||||
\(171\) | 20.1027 | 1.53729 | ||||||||
\(172\) | −0.605296 | −0.0461534 | ||||||||
\(173\) | −17.2406 | −1.31078 | −0.655391 | − | 0.755290i | \(-0.727496\pi\) | ||||
−0.655391 | + | 0.755290i | \(0.727496\pi\) | |||||||
\(174\) | −3.47197 | −0.263209 | ||||||||
\(175\) | −4.86799 | −0.367986 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.132007 | −0.00992228 | ||||||||
\(178\) | 7.61462 | 0.570740 | ||||||||
\(179\) | 11.3213 | 0.846194 | 0.423097 | − | 0.906084i | \(-0.360943\pi\) | ||||
0.423097 | + | 0.906084i | \(0.360943\pi\) | |||||||
\(180\) | 1.27334 | 0.0949094 | ||||||||
\(181\) | 14.8773 | 1.10582 | 0.552911 | − | 0.833240i | \(-0.313517\pi\) | ||||
0.552911 | + | 0.833240i | \(0.313517\pi\) | |||||||
\(182\) | −6.51399 | −0.482849 | ||||||||
\(183\) | 1.17064 | 0.0865363 | ||||||||
\(184\) | 15.0093 | 1.10650 | ||||||||
\(185\) | −30.9987 | −2.27907 | ||||||||
\(186\) | 1.80137 | 0.132083 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.109961 | 0.00801970 | ||||||||
\(189\) | 2.13201 | 0.155081 | ||||||||
\(190\) | 30.0187 | 2.17778 | ||||||||
\(191\) | 3.84934 | 0.278528 | 0.139264 | − | 0.990255i | \(-0.455526\pi\) | ||||
0.139264 | + | 0.990255i | \(0.455526\pi\) | |||||||
\(192\) | 3.08197 | 0.222422 | ||||||||
\(193\) | −2.54669 | −0.183315 | −0.0916573 | − | 0.995791i | \(-0.529216\pi\) | ||||
−0.0916573 | + | 0.995791i | \(0.529216\pi\) | |||||||
\(194\) | −8.38538 | −0.602035 | ||||||||
\(195\) | −5.45331 | −0.390520 | ||||||||
\(196\) | −0.141336 | −0.0100954 | ||||||||
\(197\) | −10.5467 | −0.751420 | −0.375710 | − | 0.926737i | \(-0.622601\pi\) | ||||
−0.375710 | + | 0.926737i | \(0.622601\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6846 | 0.828302 | 0.414151 | − | 0.910208i | \(-0.364079\pi\) | ||||
0.414151 | + | 0.910208i | \(0.364079\pi\) | |||||||
\(200\) | 14.2113 | 1.00489 | ||||||||
\(201\) | −2.39602 | −0.169002 | ||||||||
\(202\) | 14.7194 | 1.03565 | ||||||||
\(203\) | −7.00933 | −0.491958 | ||||||||
\(204\) | 0.245357 | 0.0171785 | ||||||||
\(205\) | −10.1214 | −0.706906 | ||||||||
\(206\) | 18.0514 | 1.25770 | ||||||||
\(207\) | −14.7453 | −1.02487 | ||||||||
\(208\) | 17.6660 | 1.22492 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.55602 | 0.107375 | ||||||||
\(211\) | 11.1120 | 0.764984 | 0.382492 | − | 0.923959i | \(-0.375066\pi\) | ||||
0.382492 | + | 0.923959i | \(0.375066\pi\) | |||||||
\(212\) | −0.322624 | −0.0221579 | ||||||||
\(213\) | −5.50805 | −0.377406 | ||||||||
\(214\) | −19.1120 | −1.30647 | ||||||||
\(215\) | 13.4533 | 0.917508 | ||||||||
\(216\) | −6.22406 | −0.423494 | ||||||||
\(217\) | 3.63667 | 0.246873 | ||||||||
\(218\) | 21.2334 | 1.43811 | ||||||||
\(219\) | −1.17064 | −0.0791046 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.8294 | 1.53567 | ||||||||
\(222\) | 4.88797 | 0.328059 | ||||||||
\(223\) | 28.0407 | 1.87774 | 0.938872 | − | 0.344266i | \(-0.111872\pi\) | ||||
0.938872 | + | 0.344266i | \(0.111872\pi\) | |||||||
\(224\) | 0.797984 | 0.0533175 | ||||||||
\(225\) | −13.9614 | −0.930758 | ||||||||
\(226\) | −5.63328 | −0.374720 | ||||||||
\(227\) | −23.0093 | −1.52718 | −0.763591 | − | 0.645700i | \(-0.776566\pi\) | ||||
−0.763591 | + | 0.645700i | \(0.776566\pi\) | |||||||
\(228\) | 0.359939 | 0.0238375 | ||||||||
\(229\) | 13.4240 | 0.887083 | 0.443542 | − | 0.896254i | \(-0.353722\pi\) | ||||
0.443542 | + | 0.896254i | \(0.353722\pi\) | |||||||
\(230\) | −22.0187 | −1.45187 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.4626 | 1.34344 | ||||||||
\(233\) | −3.53736 | −0.231740 | −0.115870 | − | 0.993264i | \(-0.536966\pi\) | ||||
−0.115870 | + | 0.993264i | \(0.536966\pi\) | |||||||
\(234\) | −18.6821 | −1.22129 | ||||||||
\(235\) | −2.44398 | −0.159428 | ||||||||
\(236\) | 0.0513514 | 0.00334269 | ||||||||
\(237\) | −1.35061 | −0.0877316 | ||||||||
\(238\) | −6.51399 | −0.422239 | ||||||||
\(239\) | 22.0187 | 1.42427 | 0.712134 | − | 0.702043i | \(-0.247729\pi\) | ||||
0.712134 | + | 0.702043i | \(0.247729\pi\) | |||||||
\(240\) | −4.21992 | −0.272395 | ||||||||
\(241\) | −0.315366 | −0.0203145 | −0.0101573 | − | 0.999948i | \(-0.503233\pi\) | ||||
−0.0101573 | + | 0.999948i | \(0.503233\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.24065 | 0.592788 | ||||||||
\(244\) | −0.455384 | −0.0291530 | ||||||||
\(245\) | 3.14134 | 0.200693 | ||||||||
\(246\) | 1.59597 | 0.101755 | ||||||||
\(247\) | 33.4906 | 2.13096 | ||||||||
\(248\) | −10.6167 | −0.674161 | ||||||||
\(249\) | 0.565344 | 0.0358272 | ||||||||
\(250\) | 0.565344 | 0.0357555 | ||||||||
\(251\) | 18.6460 | 1.17693 | 0.588463 | − | 0.808524i | \(-0.299733\pi\) | ||||
0.588463 | + | 0.808524i | \(0.299733\pi\) | |||||||
\(252\) | −0.405351 | −0.0255347 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −30.0187 | −1.88354 | ||||||||
\(255\) | −5.45331 | −0.341500 | ||||||||
\(256\) | −3.37473 | −0.210920 | ||||||||
\(257\) | −8.54669 | −0.533128 | −0.266564 | − | 0.963817i | \(-0.585888\pi\) | ||||
−0.266564 | + | 0.963817i | \(0.585888\pi\) | |||||||
\(258\) | −2.12136 | −0.132070 | ||||||||
\(259\) | 9.86799 | 0.613167 | ||||||||
\(260\) | 2.12136 | 0.131561 | ||||||||
\(261\) | −20.1027 | −1.24433 | ||||||||
\(262\) | −20.4626 | −1.26419 | ||||||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.17064 | 0.440489 | ||||||||
\(266\) | −9.55602 | −0.585917 | ||||||||
\(267\) | −2.02930 | −0.124191 | ||||||||
\(268\) | 0.932062 | 0.0569348 | ||||||||
\(269\) | 7.55602 | 0.460698 | 0.230349 | − | 0.973108i | \(-0.426013\pi\) | ||||
0.230349 | + | 0.973108i | \(0.426013\pi\) | |||||||
\(270\) | 9.13069 | 0.555676 | ||||||||
\(271\) | 14.0187 | 0.851573 | 0.425786 | − | 0.904824i | \(-0.359998\pi\) | ||||
0.425786 | + | 0.904824i | \(0.359998\pi\) | |||||||
\(272\) | 17.6660 | 1.07116 | ||||||||
\(273\) | 1.73599 | 0.105067 | ||||||||
\(274\) | 14.5840 | 0.881052 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.264015 | −0.0158918 | ||||||||
\(277\) | −6.01866 | −0.361626 | −0.180813 | − | 0.983517i | \(-0.557873\pi\) | ||||
−0.180813 | + | 0.983517i | \(0.557873\pi\) | |||||||
\(278\) | −5.59333 | −0.335466 | ||||||||
\(279\) | 10.4299 | 0.624425 | ||||||||
\(280\) | −9.17064 | −0.548051 | ||||||||
\(281\) | −20.6680 | −1.23295 | −0.616476 | − | 0.787374i | \(-0.711440\pi\) | ||||
−0.616476 | + | 0.787374i | \(0.711440\pi\) | |||||||
\(282\) | 0.385375 | 0.0229487 | ||||||||
\(283\) | 9.91595 | 0.589442 | 0.294721 | − | 0.955583i | \(-0.404773\pi\) | ||||
0.294721 | + | 0.955583i | \(0.404773\pi\) | |||||||
\(284\) | 2.14265 | 0.127143 | ||||||||
\(285\) | −8.00000 | −0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.22199 | 0.190188 | ||||||||
\(288\) | 2.28861 | 0.134858 | ||||||||
\(289\) | 5.82936 | 0.342903 | ||||||||
\(290\) | −30.0187 | −1.76276 | ||||||||
\(291\) | 2.23471 | 0.131001 | ||||||||
\(292\) | 0.455384 | 0.0266493 | ||||||||
\(293\) | −26.7967 | −1.56548 | −0.782739 | − | 0.622350i | \(-0.786178\pi\) | ||||
−0.782739 | + | 0.622350i | \(0.786178\pi\) | |||||||
\(294\) | −0.495336 | −0.0288886 | ||||||||
\(295\) | −1.14134 | −0.0664512 | ||||||||
\(296\) | −28.8081 | −1.67443 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.1120 | −1.10713 | ||||||||
\(299\) | −24.5653 | −1.42065 | ||||||||
\(300\) | −0.249978 | −0.0144325 | ||||||||
\(301\) | −4.28267 | −0.246849 | ||||||||
\(302\) | 9.31066 | 0.535768 | ||||||||
\(303\) | −3.92273 | −0.225355 | ||||||||
\(304\) | 25.9160 | 1.48638 | ||||||||
\(305\) | 10.1214 | 0.579547 | ||||||||
\(306\) | −18.6821 | −1.06798 | ||||||||
\(307\) | 11.8973 | 0.679015 | 0.339507 | − | 0.940603i | \(-0.389740\pi\) | ||||
0.339507 | + | 0.940603i | \(0.389740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.81070 | −0.273671 | ||||||||
\(310\) | 15.5747 | 0.884582 | ||||||||
\(311\) | −21.2406 | −1.20445 | −0.602223 | − | 0.798328i | \(-0.705718\pi\) | ||||
−0.602223 | + | 0.798328i | \(0.705718\pi\) | |||||||
\(312\) | −5.06794 | −0.286915 | ||||||||
\(313\) | −12.6974 | −0.717697 | −0.358848 | − | 0.933396i | \(-0.616830\pi\) | ||||
−0.358848 | + | 0.933396i | \(0.616830\pi\) | |||||||
\(314\) | 31.9600 | 1.80361 | ||||||||
\(315\) | 9.00933 | 0.507618 | ||||||||
\(316\) | 0.525393 | 0.0295556 | ||||||||
\(317\) | −11.8680 | −0.666573 | −0.333286 | − | 0.942826i | \(-0.608158\pi\) | ||||
−0.333286 | + | 0.942826i | \(0.608158\pi\) | |||||||
\(318\) | −1.13069 | −0.0634059 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 26.6468 | 1.48960 | ||||||||
\(321\) | 5.09337 | 0.284284 | ||||||||
\(322\) | 7.00933 | 0.390615 | ||||||||
\(323\) | 33.4906 | 1.86347 | ||||||||
\(324\) | −1.10657 | −0.0614762 | ||||||||
\(325\) | −23.2593 | −1.29019 | ||||||||
\(326\) | 1.35061 | 0.0748034 | ||||||||
\(327\) | −5.65872 | −0.312928 | ||||||||
\(328\) | −9.40610 | −0.519365 | ||||||||
\(329\) | 0.778008 | 0.0428930 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.8867 | −0.653349 | −0.326675 | − | 0.945137i | \(-0.605928\pi\) | ||||
−0.326675 | + | 0.945137i | \(0.605928\pi\) | |||||||
\(332\) | −0.219921 | −0.0120697 | ||||||||
\(333\) | 28.3013 | 1.55090 | ||||||||
\(334\) | −0.770750 | −0.0421736 | ||||||||
\(335\) | −20.7160 | −1.13184 | ||||||||
\(336\) | 1.34335 | 0.0732859 | ||||||||
\(337\) | 0.990671 | 0.0539653 | 0.0269827 | − | 0.999636i | \(-0.491410\pi\) | ||||
0.0269827 | + | 0.999636i | \(0.491410\pi\) | |||||||
\(338\) | −13.4006 | −0.728899 | ||||||||
\(339\) | 1.50127 | 0.0815381 | ||||||||
\(340\) | 2.12136 | 0.115047 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −27.4066 | −1.48198 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 12.5026 | 0.674095 | ||||||||
\(345\) | 5.86799 | 0.315922 | ||||||||
\(346\) | 23.5047 | 1.26362 | ||||||||
\(347\) | −15.1893 | −0.815404 | −0.407702 | − | 0.913115i | \(-0.633670\pi\) | ||||
−0.407702 | + | 0.913115i | \(0.633670\pi\) | |||||||
\(348\) | −0.359939 | −0.0192947 | ||||||||
\(349\) | −29.7033 | −1.58998 | −0.794990 | − | 0.606622i | \(-0.792524\pi\) | ||||
−0.794990 | + | 0.606622i | \(0.792524\pi\) | |||||||
\(350\) | 6.63667 | 0.354745 | ||||||||
\(351\) | 10.1867 | 0.543728 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.71601 | −0.357457 | −0.178729 | − | 0.983898i | \(-0.557198\pi\) | ||||
−0.178729 | + | 0.983898i | \(0.557198\pi\) | |||||||
\(354\) | 0.179969 | 0.00956527 | ||||||||
\(355\) | −47.6226 | −2.52755 | ||||||||
\(356\) | 0.789407 | 0.0418385 | ||||||||
\(357\) | 1.73599 | 0.0918781 | ||||||||
\(358\) | −15.4347 | −0.815747 | ||||||||
\(359\) | 17.7360 | 0.936069 | 0.468035 | − | 0.883710i | \(-0.344962\pi\) | ||||
0.468035 | + | 0.883710i | \(0.344962\pi\) | |||||||
\(360\) | −26.3013 | −1.38620 | ||||||||
\(361\) | 30.1307 | 1.58583 | ||||||||
\(362\) | −20.2827 | −1.06603 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.675305 | −0.0353956 | ||||||||
\(365\) | −10.1214 | −0.529776 | ||||||||
\(366\) | −1.59597 | −0.0834226 | ||||||||
\(367\) | −8.09931 | −0.422781 | −0.211390 | − | 0.977402i | \(-0.567799\pi\) | ||||
−0.211390 | + | 0.977402i | \(0.567799\pi\) | |||||||
\(368\) | −19.0093 | −0.990930 | ||||||||
\(369\) | 9.24065 | 0.481049 | ||||||||
\(370\) | 42.2614 | 2.19706 | ||||||||
\(371\) | −2.28267 | −0.118510 | ||||||||
\(372\) | 0.186748 | 0.00968244 | ||||||||
\(373\) | 0.565344 | 0.0292724 | 0.0146362 | − | 0.999893i | \(-0.495341\pi\) | ||||
0.0146362 | + | 0.999893i | \(0.495341\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.150665 | −0.00778030 | ||||||||
\(376\) | −2.27127 | −0.117132 | ||||||||
\(377\) | −33.4906 | −1.72486 | ||||||||
\(378\) | −2.90663 | −0.149501 | ||||||||
\(379\) | −22.5360 | −1.15760 | −0.578799 | − | 0.815470i | \(-0.696479\pi\) | ||||
−0.578799 | + | 0.815470i | \(0.696479\pi\) | |||||||
\(380\) | 3.11203 | 0.159644 | ||||||||
\(381\) | 8.00000 | 0.409852 | ||||||||
\(382\) | −5.24791 | −0.268506 | ||||||||
\(383\) | 21.3913 | 1.09305 | 0.546523 | − | 0.837444i | \(-0.315951\pi\) | ||||
0.546523 | + | 0.837444i | \(0.315951\pi\) | |||||||
\(384\) | −3.62188 | −0.184828 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.47197 | 0.176719 | ||||||||
\(387\) | −12.2827 | −0.624363 | ||||||||
\(388\) | −0.869311 | −0.0441326 | ||||||||
\(389\) | 10.6787 | 0.541431 | 0.270716 | − | 0.962659i | \(-0.412740\pi\) | ||||
0.270716 | + | 0.962659i | \(0.412740\pi\) | |||||||
\(390\) | 7.43466 | 0.376468 | ||||||||
\(391\) | −24.5653 | −1.24232 | ||||||||
\(392\) | 2.91934 | 0.147449 | ||||||||
\(393\) | 5.45331 | 0.275083 | ||||||||
\(394\) | 14.3786 | 0.724383 | ||||||||
\(395\) | −11.6774 | −0.587553 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.9160 | −1.20031 | −0.600154 | − | 0.799885i | \(-0.704894\pi\) | ||||
−0.600154 | + | 0.799885i | \(0.704894\pi\) | |||||||
\(398\) | −15.9300 | −0.798498 | ||||||||
\(399\) | 2.54669 | 0.127494 | ||||||||
\(400\) | −17.9987 | −0.899934 | ||||||||
\(401\) | 11.6587 | 0.582209 | 0.291104 | − | 0.956691i | \(-0.405977\pi\) | ||||
0.291104 | + | 0.956691i | \(0.405977\pi\) | |||||||
\(402\) | 3.26656 | 0.162921 | ||||||||
\(403\) | 17.3760 | 0.865563 | ||||||||
\(404\) | 1.52596 | 0.0759193 | ||||||||
\(405\) | 24.5946 | 1.22212 | ||||||||
\(406\) | 9.55602 | 0.474257 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.06794 | −0.250900 | ||||||||
\(409\) | 32.8153 | 1.62261 | 0.811307 | − | 0.584621i | \(-0.198757\pi\) | ||||
0.811307 | + | 0.584621i | \(0.198757\pi\) | |||||||
\(410\) | 13.7987 | 0.681471 | ||||||||
\(411\) | −3.88665 | −0.191714 | ||||||||
\(412\) | 1.87138 | 0.0921964 | ||||||||
\(413\) | 0.363328 | 0.0178782 | ||||||||
\(414\) | 20.1027 | 0.987994 | ||||||||
\(415\) | 4.88797 | 0.239941 | ||||||||
\(416\) | 3.81277 | 0.186937 | ||||||||
\(417\) | 1.49063 | 0.0729964 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.7967 | 0.527452 | 0.263726 | − | 0.964598i | \(-0.415049\pi\) | ||||
0.263726 | + | 0.964598i | \(0.415049\pi\) | |||||||
\(420\) | 0.161312 | 0.00787122 | ||||||||
\(421\) | −1.15198 | −0.0561442 | −0.0280721 | − | 0.999606i | \(-0.508937\pi\) | ||||
−0.0280721 | + | 0.999606i | \(0.508937\pi\) | |||||||
\(422\) | −15.1493 | −0.737459 | ||||||||
\(423\) | 2.23132 | 0.108491 | ||||||||
\(424\) | 6.66391 | 0.323628 | ||||||||
\(425\) | −23.2593 | −1.12824 | ||||||||
\(426\) | 7.50929 | 0.363826 | ||||||||
\(427\) | −3.22199 | −0.155923 | ||||||||
\(428\) | −1.98134 | −0.0957718 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.3413 | −0.884495 | ||||||||
\(431\) | −31.9600 | −1.53946 | −0.769731 | − | 0.638369i | \(-0.779609\pi\) | ||||
−0.769731 | + | 0.638369i | \(0.779609\pi\) | |||||||
\(432\) | 7.88278 | 0.379261 | ||||||||
\(433\) | −4.43334 | −0.213053 | −0.106526 | − | 0.994310i | \(-0.533973\pi\) | ||||
−0.106526 | + | 0.994310i | \(0.533973\pi\) | |||||||
\(434\) | −4.95798 | −0.237991 | ||||||||
\(435\) | 8.00000 | 0.383571 | ||||||||
\(436\) | 2.20126 | 0.105421 | ||||||||
\(437\) | −36.0373 | −1.72390 | ||||||||
\(438\) | 1.59597 | 0.0762583 | ||||||||
\(439\) | −27.4720 | −1.31117 | −0.655583 | − | 0.755123i | \(-0.727577\pi\) | ||||
−0.655583 | + | 0.755123i | \(0.727577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.86799 | −0.136571 | ||||||||
\(442\) | −31.1239 | −1.48041 | ||||||||
\(443\) | −7.79073 | −0.370149 | −0.185074 | − | 0.982725i | \(-0.559253\pi\) | ||||
−0.185074 | + | 0.982725i | \(0.559253\pi\) | |||||||
\(444\) | 0.506735 | 0.0240486 | ||||||||
\(445\) | −17.5454 | −0.831730 | ||||||||
\(446\) | −38.2287 | −1.81018 | ||||||||
\(447\) | 5.09337 | 0.240908 | ||||||||
\(448\) | −8.48262 | −0.400766 | ||||||||
\(449\) | 20.5106 | 0.967955 | 0.483978 | − | 0.875080i | \(-0.339192\pi\) | ||||
0.483978 | + | 0.875080i | \(0.339192\pi\) | |||||||
\(450\) | 19.0339 | 0.897268 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.584002 | −0.0274691 | ||||||||
\(453\) | −2.48130 | −0.116582 | ||||||||
\(454\) | 31.3693 | 1.47223 | ||||||||
\(455\) | 15.0093 | 0.703648 | ||||||||
\(456\) | −7.43466 | −0.348160 | ||||||||
\(457\) | −8.56534 | −0.400670 | −0.200335 | − | 0.979727i | \(-0.564203\pi\) | ||||
−0.200335 | + | 0.979727i | \(0.564203\pi\) | |||||||
\(458\) | −18.3013 | −0.855165 | ||||||||
\(459\) | 10.1867 | 0.475477 | ||||||||
\(460\) | −2.28267 | −0.106430 | ||||||||
\(461\) | 9.66598 | 0.450189 | 0.225095 | − | 0.974337i | \(-0.427731\pi\) | ||||
0.225095 | + | 0.974337i | \(0.427731\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4240 | 0.530919 | 0.265459 | − | 0.964122i | \(-0.414476\pi\) | ||||
0.265459 | + | 0.964122i | \(0.414476\pi\) | |||||||
\(464\) | −25.9160 | −1.20312 | ||||||||
\(465\) | −4.15066 | −0.192482 | ||||||||
\(466\) | 4.82258 | 0.223402 | ||||||||
\(467\) | 18.2207 | 0.843152 | 0.421576 | − | 0.906793i | \(-0.361477\pi\) | ||||
0.421576 | + | 0.906793i | \(0.361477\pi\) | |||||||
\(468\) | −1.93677 | −0.0895272 | ||||||||
\(469\) | 6.59465 | 0.304513 | ||||||||
\(470\) | 3.33195 | 0.153692 | ||||||||
\(471\) | −8.51738 | −0.392460 | ||||||||
\(472\) | −1.06068 | −0.0488218 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.84132 | 0.0845749 | ||||||||
\(475\) | −34.1214 | −1.56560 | ||||||||
\(476\) | −0.675305 | −0.0309526 | ||||||||
\(477\) | −6.54669 | −0.299752 | ||||||||
\(478\) | −30.0187 | −1.37302 | ||||||||
\(479\) | 3.47197 | 0.158638 | 0.0793192 | − | 0.996849i | \(-0.474725\pi\) | ||||
0.0793192 | + | 0.996849i | \(0.474725\pi\) | |||||||
\(480\) | −0.910768 | −0.0415707 | ||||||||
\(481\) | 47.1493 | 2.14983 | ||||||||
\(482\) | 0.429948 | 0.0195836 | ||||||||
\(483\) | −1.86799 | −0.0849966 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.3213 | 0.877335 | ||||||||
\(486\) | −12.5980 | −0.571459 | ||||||||
\(487\) | −27.4613 | −1.24439 | −0.622196 | − | 0.782862i | \(-0.713759\pi\) | ||||
−0.622196 | + | 0.782862i | \(0.713759\pi\) | |||||||
\(488\) | 9.40610 | 0.425794 | ||||||||
\(489\) | −0.359939 | −0.0162770 | ||||||||
\(490\) | −4.28267 | −0.193471 | ||||||||
\(491\) | −6.26401 | −0.282691 | −0.141346 | − | 0.989960i | \(-0.545143\pi\) | ||||
−0.141346 | + | 0.989960i | \(0.545143\pi\) | |||||||
\(492\) | 0.165454 | 0.00745923 | ||||||||
\(493\) | −33.4906 | −1.50834 | ||||||||
\(494\) | −45.6587 | −2.05428 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.4461 | 0.603746 | ||||||||
\(497\) | 15.1600 | 0.680019 | ||||||||
\(498\) | −0.770750 | −0.0345381 | ||||||||
\(499\) | −20.6680 | −0.925229 | −0.462614 | − | 0.886560i | \(-0.653089\pi\) | ||||
−0.462614 | + | 0.886560i | \(0.653089\pi\) | |||||||
\(500\) | 0.0586092 | 0.00262108 | ||||||||
\(501\) | 0.205406 | 0.00917685 | ||||||||
\(502\) | −25.4206 | −1.13458 | ||||||||
\(503\) | 22.0187 | 0.981763 | 0.490882 | − | 0.871226i | \(-0.336675\pi\) | ||||
0.490882 | + | 0.871226i | \(0.336675\pi\) | |||||||
\(504\) | 8.37266 | 0.372948 | ||||||||
\(505\) | −33.9160 | −1.50924 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.57128 | 0.158606 | ||||||||
\(508\) | −3.11203 | −0.138074 | ||||||||
\(509\) | 21.4240 | 0.949602 | 0.474801 | − | 0.880093i | \(-0.342520\pi\) | ||||
0.474801 | + | 0.880093i | \(0.342520\pi\) | |||||||
\(510\) | 7.43466 | 0.329212 | ||||||||
\(511\) | 3.22199 | 0.142533 | ||||||||
\(512\) | 24.5381 | 1.08444 | ||||||||
\(513\) | 14.9439 | 0.659791 | ||||||||
\(514\) | 11.6519 | 0.513945 | ||||||||
\(515\) | −41.5933 | −1.83282 | ||||||||
\(516\) | −0.219921 | −0.00968149 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.4533 | −0.591105 | ||||||||
\(519\) | −6.26401 | −0.274960 | ||||||||
\(520\) | −43.8174 | −1.92152 | ||||||||
\(521\) | 13.9453 | 0.610953 | 0.305476 | − | 0.952200i | \(-0.401184\pi\) | ||||
0.305476 | + | 0.952200i | \(0.401184\pi\) | |||||||
\(522\) | 27.4066 | 1.19955 | ||||||||
\(523\) | −18.4813 | −0.808131 | −0.404065 | − | 0.914730i | \(-0.632403\pi\) | ||||
−0.404065 | + | 0.914730i | \(0.632403\pi\) | |||||||
\(524\) | −2.12136 | −0.0926721 | ||||||||
\(525\) | −1.76868 | −0.0771915 | ||||||||
\(526\) | −21.8133 | −0.951103 | ||||||||
\(527\) | 17.3760 | 0.756912 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.43334 | 0.149276 | ||||||||
\(530\) | −9.77594 | −0.424640 | ||||||||
\(531\) | 1.04202 | 0.0452199 | ||||||||
\(532\) | −0.990671 | −0.0429510 | ||||||||
\(533\) | 15.3947 | 0.666819 | ||||||||
\(534\) | 2.76661 | 0.119723 | ||||||||
\(535\) | 44.0373 | 1.90390 | ||||||||
\(536\) | −19.2520 | −0.831562 | ||||||||
\(537\) | 4.11335 | 0.177504 | ||||||||
\(538\) | −10.3013 | −0.444122 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.946578 | 0.0407342 | ||||||||
\(541\) | 37.4533 | 1.61024 | 0.805122 | − | 0.593109i | \(-0.202100\pi\) | ||||
0.805122 | + | 0.593109i | \(0.202100\pi\) | |||||||
\(542\) | −19.1120 | −0.820932 | ||||||||
\(543\) | 5.40535 | 0.231966 | ||||||||
\(544\) | 3.81277 | 0.163471 | ||||||||
\(545\) | −48.9253 | −2.09573 | ||||||||
\(546\) | −2.36672 | −0.101286 | ||||||||
\(547\) | −17.1307 | −0.732455 | −0.366228 | − | 0.930525i | \(-0.619351\pi\) | ||||
−0.366228 | + | 0.930525i | \(0.619351\pi\) | |||||||
\(548\) | 1.51192 | 0.0645861 | ||||||||
\(549\) | −9.24065 | −0.394381 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −49.1307 | −2.09304 | ||||||||
\(552\) | 5.45331 | 0.232108 | ||||||||
\(553\) | 3.71733 | 0.158077 | ||||||||
\(554\) | 8.20541 | 0.348614 | ||||||||
\(555\) | −11.2627 | −0.478075 | ||||||||
\(556\) | −0.579860 | −0.0245915 | ||||||||
\(557\) | 24.5653 | 1.04087 | 0.520434 | − | 0.853902i | \(-0.325770\pi\) | ||||
0.520434 | + | 0.853902i | \(0.325770\pi\) | |||||||
\(558\) | −14.2194 | −0.601957 | ||||||||
\(559\) | −20.4626 | −0.865478 | ||||||||
\(560\) | 11.6146 | 0.490807 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.1773 | 1.18859 | ||||||||
\(563\) | −15.0093 | −0.632568 | −0.316284 | − | 0.948665i | \(-0.602435\pi\) | ||||
−0.316284 | + | 0.948665i | \(0.602435\pi\) | |||||||
\(564\) | 0.0399518 | 0.00168227 | ||||||||
\(565\) | 12.9800 | 0.546074 | ||||||||
\(566\) | −13.5187 | −0.568233 | ||||||||
\(567\) | −7.82936 | −0.328802 | ||||||||
\(568\) | −44.2572 | −1.85699 | ||||||||
\(569\) | 12.1027 | 0.507372 | 0.253686 | − | 0.967287i | \(-0.418357\pi\) | ||||
0.253686 | + | 0.967287i | \(0.418357\pi\) | |||||||
\(570\) | 10.9066 | 0.456828 | ||||||||
\(571\) | 38.9439 | 1.62975 | 0.814877 | − | 0.579634i | \(-0.196805\pi\) | ||||
0.814877 | + | 0.579634i | \(0.196805\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.39857 | 0.0584262 | ||||||||
\(574\) | −4.39263 | −0.183345 | ||||||||
\(575\) | 25.0280 | 1.04374 | ||||||||
\(576\) | −24.3281 | −1.01367 | ||||||||
\(577\) | 38.1507 | 1.58823 | 0.794116 | − | 0.607766i | \(-0.207934\pi\) | ||||
0.794116 | + | 0.607766i | \(0.207934\pi\) | |||||||
\(578\) | −7.94733 | −0.330565 | ||||||||
\(579\) | −0.925283 | −0.0384535 | ||||||||
\(580\) | −3.11203 | −0.129220 | ||||||||
\(581\) | −1.55602 | −0.0645544 | ||||||||
\(582\) | −3.04664 | −0.126287 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.40610 | −0.389227 | ||||||||
\(585\) | 43.0466 | 1.77976 | ||||||||
\(586\) | 36.5327 | 1.50915 | ||||||||
\(587\) | −34.7967 | −1.43621 | −0.718106 | − | 0.695934i | \(-0.754991\pi\) | ||||
−0.718106 | + | 0.695934i | \(0.754991\pi\) | |||||||
\(588\) | −0.0513514 | −0.00211770 | ||||||||
\(589\) | 25.4906 | 1.05032 | ||||||||
\(590\) | 1.55602 | 0.0640602 | ||||||||
\(591\) | −3.83191 | −0.157624 | ||||||||
\(592\) | 36.4854 | 1.49954 | ||||||||
\(593\) | −18.5913 | −0.763452 | −0.381726 | − | 0.924276i | \(-0.624670\pi\) | ||||
−0.381726 | + | 0.924276i | \(0.624670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0093 | 0.615322 | ||||||||
\(596\) | −1.98134 | −0.0811590 | ||||||||
\(597\) | 4.24536 | 0.173751 | ||||||||
\(598\) | 33.4906 | 1.36953 | ||||||||
\(599\) | 24.6680 | 1.00791 | 0.503955 | − | 0.863730i | \(-0.331878\pi\) | ||||
0.503955 | + | 0.863730i | \(0.331878\pi\) | |||||||
\(600\) | 5.16338 | 0.210794 | ||||||||
\(601\) | −30.1286 | −1.22897 | −0.614486 | − | 0.788928i | \(-0.710637\pi\) | ||||
−0.614486 | + | 0.788928i | \(0.710637\pi\) | |||||||
\(602\) | 5.83869 | 0.237967 | ||||||||
\(603\) | 18.9134 | 0.770213 | ||||||||
\(604\) | 0.965235 | 0.0392749 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.34797 | 0.217247 | ||||||||
\(607\) | −13.6587 | −0.554390 | −0.277195 | − | 0.960814i | \(-0.589405\pi\) | ||||
−0.277195 | + | 0.960814i | \(0.589405\pi\) | |||||||
\(608\) | 5.59333 | 0.226840 | ||||||||
\(609\) | −2.54669 | −0.103197 | ||||||||
\(610\) | −13.7987 | −0.558694 | ||||||||
\(611\) | 3.71733 | 0.150387 | ||||||||
\(612\) | −1.93677 | −0.0782893 | ||||||||
\(613\) | −45.0280 | −1.81866 | −0.909332 | − | 0.416072i | \(-0.863406\pi\) | ||||
−0.909332 | + | 0.416072i | \(0.863406\pi\) | |||||||
\(614\) | −16.2199 | −0.654583 | ||||||||
\(615\) | −3.67738 | −0.148286 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.26401 | −0.332697 | −0.166348 | − | 0.986067i | \(-0.553198\pi\) | ||||
−0.166348 | + | 0.986067i | \(0.553198\pi\) | |||||||
\(618\) | 6.55857 | 0.263824 | ||||||||
\(619\) | 43.0500 | 1.73033 | 0.865163 | − | 0.501490i | \(-0.167215\pi\) | ||||
0.865163 | + | 0.501490i | \(0.167215\pi\) | |||||||
\(620\) | 1.61462 | 0.0648449 | ||||||||
\(621\) | −10.9614 | −0.439864 | ||||||||
\(622\) | 28.9580 | 1.16111 | ||||||||
\(623\) | 5.58532 | 0.223771 | ||||||||
\(624\) | 6.41855 | 0.256948 | ||||||||
\(625\) | −25.6426 | −1.02570 | ||||||||
\(626\) | 17.3107 | 0.691873 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.31330 | 0.132215 | ||||||||
\(629\) | 47.1493 | 1.87997 | ||||||||
\(630\) | −12.2827 | −0.489353 | ||||||||
\(631\) | 1.03863 | 0.0413473 | 0.0206737 | − | 0.999786i | \(-0.493419\pi\) | ||||
0.0206737 | + | 0.999786i | \(0.493419\pi\) | |||||||
\(632\) | −10.8522 | −0.431676 | ||||||||
\(633\) | 4.03731 | 0.160469 | ||||||||
\(634\) | 16.1800 | 0.642589 | ||||||||
\(635\) | 69.1680 | 2.74485 | ||||||||
\(636\) | −0.117218 | −0.00464801 | ||||||||
\(637\) | −4.77801 | −0.189312 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 43.4787 | 1.71999 | ||||||||
\(640\) | −31.3148 | −1.23783 | ||||||||
\(641\) | 33.6413 | 1.32875 | 0.664376 | − | 0.747399i | \(-0.268698\pi\) | ||||
0.664376 | + | 0.747399i | \(0.268698\pi\) | |||||||
\(642\) | −6.94394 | −0.274055 | ||||||||
\(643\) | −21.0314 | −0.829396 | −0.414698 | − | 0.909959i | \(-0.636113\pi\) | ||||
−0.414698 | + | 0.909959i | \(0.636113\pi\) | |||||||
\(644\) | 0.726656 | 0.0286343 | ||||||||
\(645\) | 4.88797 | 0.192464 | ||||||||
\(646\) | −45.6587 | −1.79642 | ||||||||
\(647\) | 25.2300 | 0.991894 | 0.495947 | − | 0.868353i | \(-0.334821\pi\) | ||||
0.495947 | + | 0.868353i | \(0.334821\pi\) | |||||||
\(648\) | 22.8566 | 0.897892 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 31.7101 | 1.24377 | ||||||||
\(651\) | 1.32131 | 0.0517860 | ||||||||
\(652\) | 0.140018 | 0.00548351 | ||||||||
\(653\) | 20.6387 | 0.807656 | 0.403828 | − | 0.914835i | \(-0.367679\pi\) | ||||
0.403828 | + | 0.914835i | \(0.367679\pi\) | |||||||
\(654\) | 7.71469 | 0.301668 | ||||||||
\(655\) | 47.1493 | 1.84228 | ||||||||
\(656\) | 11.9128 | 0.465118 | ||||||||
\(657\) | 9.24065 | 0.360512 | ||||||||
\(658\) | −1.06068 | −0.0413496 | ||||||||
\(659\) | −18.5067 | −0.720920 | −0.360460 | − | 0.932775i | \(-0.617380\pi\) | ||||
−0.360460 | + | 0.932775i | \(0.617380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.8001 | 0.653446 | 0.326723 | − | 0.945120i | \(-0.394056\pi\) | ||||
0.326723 | + | 0.945120i | \(0.394056\pi\) | |||||||
\(662\) | 16.2054 | 0.629841 | ||||||||
\(663\) | 8.29455 | 0.322134 | ||||||||
\(664\) | 4.54255 | 0.176285 | ||||||||
\(665\) | 22.0187 | 0.853847 | ||||||||
\(666\) | −38.5840 | −1.49510 | ||||||||
\(667\) | 36.0373 | 1.39537 | ||||||||
\(668\) | −0.0799036 | −0.00309156 | ||||||||
\(669\) | 10.1880 | 0.393890 | ||||||||
\(670\) | 28.2427 | 1.09111 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.289930 | 0.0111843 | ||||||||
\(673\) | 17.5560 | 0.676735 | 0.338367 | − | 0.941014i | \(-0.390125\pi\) | ||||
0.338367 | + | 0.941014i | \(0.390125\pi\) | |||||||
\(674\) | −1.35061 | −0.0520236 | ||||||||
\(675\) | −10.3786 | −0.399472 | ||||||||
\(676\) | −1.38924 | −0.0534324 | ||||||||
\(677\) | −3.64732 | −0.140178 | −0.0700889 | − | 0.997541i | \(-0.522328\pi\) | ||||
−0.0700889 | + | 0.997541i | \(0.522328\pi\) | |||||||
\(678\) | −2.04673 | −0.0786042 | ||||||||
\(679\) | −6.15066 | −0.236041 | ||||||||
\(680\) | −43.8174 | −1.68032 | ||||||||
\(681\) | −8.35994 | −0.320354 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.4720 | 1.05119 | 0.525593 | − | 0.850736i | \(-0.323844\pi\) | ||||
0.525593 | + | 0.850736i | \(0.323844\pi\) | |||||||
\(684\) | −2.84124 | −0.108637 | ||||||||
\(685\) | −33.6040 | −1.28394 | ||||||||
\(686\) | 1.36333 | 0.0520521 | ||||||||
\(687\) | 4.87732 | 0.186081 | ||||||||
\(688\) | −15.8345 | −0.603686 | ||||||||
\(689\) | −10.9066 | −0.415509 | ||||||||
\(690\) | −8.00000 | −0.304555 | ||||||||
\(691\) | −5.95666 | −0.226602 | −0.113301 | − | 0.993561i | \(-0.536142\pi\) | ||||
−0.113301 | + | 0.993561i | \(0.536142\pi\) | |||||||
\(692\) | 2.43673 | 0.0926304 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.7080 | 0.786065 | ||||||||
\(695\) | 12.8880 | 0.488869 | ||||||||
\(696\) | 7.43466 | 0.281810 | ||||||||
\(697\) | 15.3947 | 0.583116 | ||||||||
\(698\) | 40.4953 | 1.53277 | ||||||||
\(699\) | −1.28522 | −0.0486116 | ||||||||
\(700\) | 0.688023 | 0.0260048 | ||||||||
\(701\) | 7.36927 | 0.278333 | 0.139167 | − | 0.990269i | \(-0.455558\pi\) | ||||
0.139167 | + | 0.990269i | \(0.455558\pi\) | |||||||
\(702\) | −13.8879 | −0.524164 | ||||||||
\(703\) | 69.1680 | 2.60872 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.887968 | −0.0334428 | ||||||||
\(706\) | 9.15613 | 0.344595 | ||||||||
\(707\) | 10.7967 | 0.406050 | ||||||||
\(708\) | 0.0186574 | 0.000701189 0 | ||||||||
\(709\) | −34.7160 | −1.30379 | −0.651894 | − | 0.758310i | \(-0.726025\pi\) | ||||
−0.651894 | + | 0.758310i | \(0.726025\pi\) | |||||||
\(710\) | 64.9253 | 2.43660 | ||||||||
\(711\) | 10.6613 | 0.399829 | ||||||||
\(712\) | −16.3055 | −0.611073 | ||||||||
\(713\) | −18.6974 | −0.700221 | ||||||||
\(714\) | −2.36672 | −0.0885722 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.60011 | −0.0597989 | ||||||||
\(717\) | 8.00000 | 0.298765 | ||||||||
\(718\) | −24.1800 | −0.902388 | ||||||||
\(719\) | −4.06200 | −0.151487 | −0.0757435 | − | 0.997127i | \(-0.524133\pi\) | ||||
−0.0757435 | + | 0.997127i | \(0.524133\pi\) | |||||||
\(720\) | 33.3107 | 1.24141 | ||||||||
\(721\) | 13.2406 | 0.493108 | ||||||||
\(722\) | −41.0780 | −1.52877 | ||||||||
\(723\) | −0.114581 | −0.00426133 | ||||||||
\(724\) | −2.10270 | −0.0781463 | ||||||||
\(725\) | 34.1214 | 1.26724 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.5433 | −1.13279 | −0.566394 | − | 0.824135i | \(-0.691662\pi\) | ||||
−0.566394 | + | 0.824135i | \(0.691662\pi\) | |||||||
\(728\) | 13.9486 | 0.516971 | ||||||||
\(729\) | −20.1307 | −0.745581 | ||||||||
\(730\) | 13.7987 | 0.510714 | ||||||||
\(731\) | −20.4626 | −0.756838 | ||||||||
\(732\) | −0.165454 | −0.00611535 | ||||||||
\(733\) | −30.8340 | −1.13888 | −0.569440 | − | 0.822033i | \(-0.692840\pi\) | ||||
−0.569440 | + | 0.822033i | \(0.692840\pi\) | |||||||
\(734\) | 11.0420 | 0.407568 | ||||||||
\(735\) | 1.14134 | 0.0420988 | ||||||||
\(736\) | −4.10270 | −0.151228 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.5980 | −0.463740 | ||||||||
\(739\) | 22.2241 | 0.817525 | 0.408763 | − | 0.912641i | \(-0.365960\pi\) | ||||
0.408763 | + | 0.912641i | \(0.365960\pi\) | |||||||
\(740\) | 4.38123 | 0.161057 | ||||||||
\(741\) | 12.1681 | 0.447006 | ||||||||
\(742\) | 3.11203 | 0.114246 | ||||||||
\(743\) | −31.1493 | −1.14276 | −0.571379 | − | 0.820686i | \(-0.693591\pi\) | ||||
−0.571379 | + | 0.820686i | \(0.693591\pi\) | |||||||
\(744\) | −3.85735 | −0.141417 | ||||||||
\(745\) | 44.0373 | 1.61340 | ||||||||
\(746\) | −0.770750 | −0.0282192 | ||||||||
\(747\) | −4.46264 | −0.163280 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.0187 | −0.512231 | ||||||||
\(750\) | 0.205406 | 0.00750035 | ||||||||
\(751\) | 11.9894 | 0.437498 | 0.218749 | − | 0.975781i | \(-0.429802\pi\) | ||||
0.218749 | + | 0.975781i | \(0.429802\pi\) | |||||||
\(752\) | 2.87657 | 0.104898 | ||||||||
\(753\) | 6.77462 | 0.246881 | ||||||||
\(754\) | 45.6587 | 1.66279 | ||||||||
\(755\) | −21.4533 | −0.780766 | ||||||||
\(756\) | −0.301330 | −0.0109593 | ||||||||
\(757\) | −11.4533 | −0.416278 | −0.208139 | − | 0.978099i | \(-0.566741\pi\) | ||||
−0.208139 | + | 0.978099i | \(0.566741\pi\) | |||||||
\(758\) | 30.7240 | 1.11595 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −64.2800 | −2.33168 | ||||||||
\(761\) | 7.89004 | 0.286014 | 0.143007 | − | 0.989722i | \(-0.454323\pi\) | ||||
0.143007 | + | 0.989722i | \(0.454323\pi\) | |||||||
\(762\) | −10.9066 | −0.395105 | ||||||||
\(763\) | 15.5747 | 0.563841 | ||||||||
\(764\) | −0.544050 | −0.0196830 | ||||||||
\(765\) | 43.0466 | 1.55635 | ||||||||
\(766\) | −29.1634 | −1.05372 | ||||||||
\(767\) | 1.73599 | 0.0626828 | ||||||||
\(768\) | −1.22613 | −0.0442443 | ||||||||
\(769\) | −48.8153 | −1.76033 | −0.880163 | − | 0.474672i | \(-0.842567\pi\) | ||||
−0.880163 | + | 0.474672i | \(0.842567\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.10525 | −0.111833 | ||||||||
\(772\) | 0.359939 | 0.0129545 | ||||||||
\(773\) | −3.19608 | −0.114955 | −0.0574774 | − | 0.998347i | \(-0.518306\pi\) | ||||
−0.0574774 | + | 0.998347i | \(0.518306\pi\) | |||||||
\(774\) | 16.7453 | 0.601898 | ||||||||
\(775\) | −17.7033 | −0.635921 | ||||||||
\(776\) | 17.9559 | 0.644579 | ||||||||
\(777\) | 3.58532 | 0.128623 | ||||||||
\(778\) | −14.5586 | −0.521950 | ||||||||
\(779\) | 22.5840 | 0.809156 | ||||||||
\(780\) | 0.770750 | 0.0275973 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 33.4906 | 1.19762 | ||||||||
\(783\) | −14.9439 | −0.534053 | ||||||||
\(784\) | −3.69735 | −0.132048 | ||||||||
\(785\) | −73.6413 | −2.62837 | ||||||||
\(786\) | −7.43466 | −0.265185 | ||||||||
\(787\) | −42.4813 | −1.51429 | −0.757147 | − | 0.653244i | \(-0.773408\pi\) | ||||
−0.757147 | + | 0.653244i | \(0.773408\pi\) | |||||||
\(788\) | 1.49063 | 0.0531014 | ||||||||
\(789\) | 5.81325 | 0.206957 | ||||||||
\(790\) | 15.9201 | 0.566412 | ||||||||
\(791\) | −4.13201 | −0.146917 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.3947 | −0.546682 | ||||||||
\(794\) | 32.6053 | 1.15712 | ||||||||
\(795\) | 2.60530 | 0.0924003 | ||||||||
\(796\) | −1.65146 | −0.0585345 | ||||||||
\(797\) | −28.8587 | −1.02223 | −0.511113 | − | 0.859513i | \(-0.670767\pi\) | ||||
−0.511113 | + | 0.859513i | \(0.670767\pi\) | |||||||
\(798\) | −3.47197 | −0.122906 | ||||||||
\(799\) | 3.71733 | 0.131510 | ||||||||
\(800\) | −3.88458 | −0.137341 | ||||||||
\(801\) | 16.0187 | 0.565991 | ||||||||
\(802\) | −15.8947 | −0.561260 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.338644 | 0.0119431 | ||||||||
\(805\) | −16.1507 | −0.569236 | ||||||||
\(806\) | −23.6893 | −0.834418 | ||||||||
\(807\) | 2.74531 | 0.0966396 | ||||||||
\(808\) | −31.5192 | −1.10884 | ||||||||
\(809\) | −29.4533 | −1.03552 | −0.517762 | − | 0.855525i | \(-0.673235\pi\) | ||||
−0.517762 | + | 0.855525i | \(0.673235\pi\) | |||||||
\(810\) | −33.5306 | −1.17814 | ||||||||
\(811\) | −2.48130 | −0.0871302 | −0.0435651 | − | 0.999051i | \(-0.513872\pi\) | ||||
−0.0435651 | + | 0.999051i | \(0.513872\pi\) | |||||||
\(812\) | 0.990671 | 0.0347657 | ||||||||
\(813\) | 5.09337 | 0.178632 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.11203 | −0.109010 | ||||||||
\(816\) | 6.41855 | 0.224694 | ||||||||
\(817\) | −30.0187 | −1.05022 | ||||||||
\(818\) | −44.7381 | −1.56423 | ||||||||
\(819\) | −13.7033 | −0.478832 | ||||||||
\(820\) | 1.43051 | 0.0499557 | ||||||||
\(821\) | −14.0187 | −0.489255 | −0.244627 | − | 0.969617i | \(-0.578666\pi\) | ||||
−0.244627 | + | 0.969617i | \(0.578666\pi\) | |||||||
\(822\) | 5.29878 | 0.184816 | ||||||||
\(823\) | −42.7933 | −1.49168 | −0.745840 | − | 0.666125i | \(-0.767952\pi\) | ||||
−0.745840 | + | 0.666125i | \(0.767952\pi\) | |||||||
\(824\) | −38.6540 | −1.34658 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.495336 | −0.0172349 | ||||||||
\(827\) | 9.17064 | 0.318894 | 0.159447 | − | 0.987206i | \(-0.449029\pi\) | ||||
0.159447 | + | 0.987206i | \(0.449029\pi\) | |||||||
\(828\) | 2.08405 | 0.0724256 | ||||||||
\(829\) | 29.1973 | 1.01406 | 0.507032 | − | 0.861927i | \(-0.330743\pi\) | ||||
0.507032 | + | 0.861927i | \(0.330743\pi\) | |||||||
\(830\) | −6.66391 | −0.231308 | ||||||||
\(831\) | −2.18675 | −0.0758575 | ||||||||
\(832\) | −40.5300 | −1.40513 | ||||||||
\(833\) | −4.77801 | −0.165548 | ||||||||
\(834\) | −2.03221 | −0.0703698 | ||||||||
\(835\) | 1.77594 | 0.0614588 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.75341 | 0.267997 | ||||||||
\(838\) | −14.7194 | −0.508473 | ||||||||
\(839\) | 19.7326 | 0.681245 | 0.340622 | − | 0.940200i | \(-0.389362\pi\) | ||||
0.340622 | + | 0.940200i | \(0.389362\pi\) | |||||||
\(840\) | −3.33195 | −0.114963 | ||||||||
\(841\) | 20.1307 | 0.694162 | ||||||||
\(842\) | 1.57053 | 0.0541241 | ||||||||
\(843\) | −7.50929 | −0.258634 | ||||||||
\(844\) | −1.57053 | −0.0540599 | ||||||||
\(845\) | 30.8773 | 1.06221 | ||||||||
\(846\) | −3.04202 | −0.104587 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.43984 | −0.289825 | ||||||||
\(849\) | 3.60275 | 0.123646 | ||||||||
\(850\) | 31.7101 | 1.08765 | ||||||||
\(851\) | −50.7347 | −1.73916 | ||||||||
\(852\) | 0.778487 | 0.0266705 | ||||||||
\(853\) | 28.3527 | 0.970777 | 0.485389 | − | 0.874298i | \(-0.338678\pi\) | ||||
0.485389 | + | 0.874298i | \(0.338678\pi\) | |||||||
\(854\) | 4.39263 | 0.150313 | ||||||||
\(855\) | 63.1493 | 2.15966 | ||||||||
\(856\) | 40.9253 | 1.39880 | ||||||||
\(857\) | −13.2033 | −0.451017 | −0.225509 | − | 0.974241i | \(-0.572404\pi\) | ||||
−0.225509 | + | 0.974241i | \(0.572404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.8260 | −0.710573 | −0.355286 | − | 0.934757i | \(-0.615617\pi\) | ||||
−0.355286 | + | 0.934757i | \(0.615617\pi\) | |||||||
\(860\) | −1.90144 | −0.0648385 | ||||||||
\(861\) | 1.17064 | 0.0398953 | ||||||||
\(862\) | 43.5720 | 1.48407 | ||||||||
\(863\) | 34.9439 | 1.18951 | 0.594753 | − | 0.803909i | \(-0.297250\pi\) | ||||
0.594753 | + | 0.803909i | \(0.297250\pi\) | |||||||
\(864\) | 1.70131 | 0.0578797 | ||||||||
\(865\) | −54.1587 | −1.84145 | ||||||||
\(866\) | 6.04409 | 0.205387 | ||||||||
\(867\) | 2.11797 | 0.0719301 | ||||||||
\(868\) | −0.513993 | −0.0174461 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −10.9066 | −0.369769 | ||||||||
\(871\) | 31.5093 | 1.06765 | ||||||||
\(872\) | −45.4678 | −1.53973 | ||||||||
\(873\) | −17.6401 | −0.597026 | ||||||||
\(874\) | 49.1307 | 1.66187 | ||||||||
\(875\) | 0.414680 | 0.0140187 | ||||||||
\(876\) | 0.165454 | 0.00559017 | ||||||||
\(877\) | 26.4813 | 0.894210 | 0.447105 | − | 0.894481i | \(-0.352455\pi\) | ||||
0.447105 | + | 0.894481i | \(0.352455\pi\) | |||||||
\(878\) | 37.4533 | 1.26399 | ||||||||
\(879\) | −9.73599 | −0.328387 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.2627 | 0.581595 | 0.290798 | − | 0.956785i | \(-0.406079\pi\) | ||||
0.290798 | + | 0.956785i | \(0.406079\pi\) | |||||||
\(882\) | 3.91002 | 0.131657 | ||||||||
\(883\) | −44.6027 | −1.50100 | −0.750499 | − | 0.660871i | \(-0.770187\pi\) | ||||
−0.750499 | + | 0.660871i | \(0.770187\pi\) | |||||||
\(884\) | −3.22661 | −0.108523 | ||||||||
\(885\) | −0.414680 | −0.0139393 | ||||||||
\(886\) | 10.6213 | 0.356830 | ||||||||
\(887\) | −30.7894 | −1.03381 | −0.516904 | − | 0.856044i | \(-0.672915\pi\) | ||||
−0.516904 | + | 0.856044i | \(0.672915\pi\) | |||||||
\(888\) | −10.4668 | −0.351242 | ||||||||
\(889\) | −22.0187 | −0.738482 | ||||||||
\(890\) | 23.9201 | 0.801803 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.96316 | −0.132697 | ||||||||
\(893\) | 5.45331 | 0.182488 | ||||||||
\(894\) | −6.94394 | −0.232240 | ||||||||
\(895\) | 35.5640 | 1.18877 | ||||||||
\(896\) | 9.96862 | 0.333028 | ||||||||
\(897\) | −8.92528 | −0.298007 | ||||||||
\(898\) | −27.9627 | −0.933127 | ||||||||
\(899\) | −25.4906 | −0.850160 | ||||||||
\(900\) | 1.97325 | 0.0657748 | ||||||||
\(901\) | −10.9066 | −0.363352 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.55602 | −0.0517810 | ||||||||
\(904\) | 12.0628 | 0.401201 | ||||||||
\(905\) | 46.7347 | 1.55351 | ||||||||
\(906\) | 3.38283 | 0.112387 | ||||||||
\(907\) | 23.7801 | 0.789605 | 0.394802 | − | 0.918766i | \(-0.370813\pi\) | ||||
0.394802 | + | 0.918766i | \(0.370813\pi\) | |||||||
\(908\) | 3.25205 | 0.107923 | ||||||||
\(909\) | 30.9648 | 1.02704 | ||||||||
\(910\) | −20.4626 | −0.678330 | ||||||||
\(911\) | 49.0280 | 1.62437 | 0.812185 | − | 0.583400i | \(-0.198278\pi\) | ||||
0.812185 | + | 0.583400i | \(0.198278\pi\) | |||||||
\(912\) | 9.41600 | 0.311795 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 11.6774 | 0.386253 | ||||||||
\(915\) | 3.67738 | 0.121570 | ||||||||
\(916\) | −1.89730 | −0.0626885 | ||||||||
\(917\) | −15.0093 | −0.495652 | ||||||||
\(918\) | −13.8879 | −0.458368 | ||||||||
\(919\) | 40.0000 | 1.31948 | 0.659739 | − | 0.751495i | \(-0.270667\pi\) | ||||
0.659739 | + | 0.751495i | \(0.270667\pi\) | |||||||
\(920\) | 47.1493 | 1.55447 | ||||||||
\(921\) | 4.32262 | 0.142435 | ||||||||
\(922\) | −13.1779 | −0.433991 | ||||||||
\(923\) | 72.4346 | 2.38421 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48.0373 | −1.57946 | ||||||||
\(926\) | −15.5747 | −0.511816 | ||||||||
\(927\) | 37.9741 | 1.24723 | ||||||||
\(928\) | −5.59333 | −0.183610 | ||||||||
\(929\) | −56.5840 | −1.85646 | −0.928230 | − | 0.372006i | \(-0.878670\pi\) | ||||
−0.928230 | + | 0.372006i | \(0.878670\pi\) | |||||||
\(930\) | 5.65872 | 0.185557 | ||||||||
\(931\) | −7.00933 | −0.229721 | ||||||||
\(932\) | 0.499956 | 0.0163766 | ||||||||
\(933\) | −7.71733 | −0.252654 | ||||||||
\(934\) | −24.8408 | −0.812814 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 40.0046 | 1.30759 | ||||||||
\(937\) | −16.8153 | −0.549333 | −0.274666 | − | 0.961540i | \(-0.588567\pi\) | ||||
−0.274666 | + | 0.961540i | \(0.588567\pi\) | |||||||
\(938\) | −8.99067 | −0.293556 | ||||||||
\(939\) | −4.61331 | −0.150550 | ||||||||
\(940\) | 0.345423 | 0.0112665 | ||||||||
\(941\) | 7.25931 | 0.236647 | 0.118323 | − | 0.992975i | \(-0.462248\pi\) | ||||
0.118323 | + | 0.992975i | \(0.462248\pi\) | |||||||
\(942\) | 11.6120 | 0.378339 | ||||||||
\(943\) | −16.5653 | −0.539442 | ||||||||
\(944\) | 1.34335 | 0.0437224 | ||||||||
\(945\) | 6.69735 | 0.217865 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.6040 | −0.832017 | −0.416009 | − | 0.909361i | \(-0.636571\pi\) | ||||
−0.416009 | + | 0.909361i | \(0.636571\pi\) | |||||||
\(948\) | 0.190890 | 0.00619982 | ||||||||
\(949\) | 15.3947 | 0.499733 | ||||||||
\(950\) | 46.5186 | 1.50926 | ||||||||
\(951\) | −4.31198 | −0.139825 | ||||||||
\(952\) | 13.9486 | 0.452078 | ||||||||
\(953\) | 7.14935 | 0.231590 | 0.115795 | − | 0.993273i | \(-0.463058\pi\) | ||||
0.115795 | + | 0.993273i | \(0.463058\pi\) | |||||||
\(954\) | 8.92528 | 0.288967 | ||||||||
\(955\) | 12.0921 | 0.391290 | ||||||||
\(956\) | −3.11203 | −0.100650 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.73344 | −0.152930 | ||||||||
\(959\) | 10.6974 | 0.345436 | ||||||||
\(960\) | 9.68152 | 0.312470 | ||||||||
\(961\) | −17.7746 | −0.573375 | ||||||||
\(962\) | −64.2800 | −2.07247 | ||||||||
\(963\) | −40.2054 | −1.29560 | ||||||||
\(964\) | 0.0445726 | 0.00143559 | ||||||||
\(965\) | −8.00000 | −0.257529 | ||||||||
\(966\) | 2.54669 | 0.0819383 | ||||||||
\(967\) | 15.9600 | 0.513241 | 0.256620 | − | 0.966512i | \(-0.417391\pi\) | ||||
0.256620 | + | 0.966512i | \(0.417391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.1681 | 0.390895 | ||||||||
\(970\) | −26.3413 | −0.845768 | ||||||||
\(971\) | −30.4779 | −0.978083 | −0.489041 | − | 0.872261i | \(-0.662653\pi\) | ||||
−0.489041 | + | 0.872261i | \(0.662653\pi\) | |||||||
\(972\) | −1.30604 | −0.0418912 | ||||||||
\(973\) | −4.10270 | −0.131527 | ||||||||
\(974\) | 37.4388 | 1.19962 | ||||||||
\(975\) | −8.45076 | −0.270641 | ||||||||
\(976\) | −11.9128 | −0.381321 | ||||||||
\(977\) | 4.13201 | 0.132195 | 0.0660973 | − | 0.997813i | \(-0.478945\pi\) | ||||
0.0660973 | + | 0.997813i | \(0.478945\pi\) | |||||||
\(978\) | 0.490715 | 0.0156913 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.443984 | −0.0141826 | ||||||||
\(981\) | 44.6680 | 1.42614 | ||||||||
\(982\) | 8.53991 | 0.272519 | ||||||||
\(983\) | −25.0246 | −0.798161 | −0.399080 | − | 0.916916i | \(-0.630671\pi\) | ||||
−0.399080 | + | 0.916916i | \(0.630671\pi\) | |||||||
\(984\) | −3.41750 | −0.108946 | ||||||||
\(985\) | −33.1307 | −1.05563 | ||||||||
\(986\) | 45.6587 | 1.45407 | ||||||||
\(987\) | 0.282672 | 0.00899756 | ||||||||
\(988\) | −4.73344 | −0.150591 | ||||||||
\(989\) | 22.0187 | 0.700153 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.5747 | −0.875938 | −0.437969 | − | 0.898990i | \(-0.644302\pi\) | ||||
−0.437969 | + | 0.898990i | \(0.644302\pi\) | |||||||
\(992\) | 2.90201 | 0.0921388 | ||||||||
\(993\) | −4.31876 | −0.137052 | ||||||||
\(994\) | −20.6680 | −0.655551 | ||||||||
\(995\) | 36.7054 | 1.16364 | ||||||||
\(996\) | −0.0799036 | −0.00253184 | ||||||||
\(997\) | 23.6846 | 0.750100 | 0.375050 | − | 0.927005i | \(-0.377626\pi\) | ||||
0.375050 | + | 0.927005i | \(0.377626\pi\) | |||||||
\(998\) | 28.1773 | 0.891938 | ||||||||
\(999\) | 21.0386 | 0.665633 |
(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 | 847.2.a.i.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 7623.2.a.ce.1.2 | 3 | |||
7.6 | odd | 2 | 5929.2.a.t.1.2 | 3 | |||
11.2 | odd | 10 | 847.2.f.t.323.2 | 12 | |||
11.3 | even | 5 | 847.2.f.u.372.2 | 12 | |||
11.4 | even | 5 | 847.2.f.u.148.2 | 12 | |||
11.5 | even | 5 | 847.2.f.u.729.2 | 12 | |||
11.6 | odd | 10 | 847.2.f.t.729.2 | 12 | |||
11.7 | odd | 10 | 847.2.f.t.148.2 | 12 | |||
11.8 | odd | 10 | 847.2.f.t.372.2 | 12 | |||
11.9 | even | 5 | 847.2.f.u.323.2 | 12 | |||
11.10 | odd | 2 | 847.2.a.j.1.2 | yes | 3 | ||
33.32 | even | 2 | 7623.2.a.bz.1.2 | 3 | |||
77.76 | even | 2 | 5929.2.a.y.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
847.2.a.j.1.2 | yes | 3 | 11.10 | odd | 2 | ||
847.2.f.t.148.2 | 12 | 11.7 | odd | 10 | |||
847.2.f.t.323.2 | 12 | 11.2 | odd | 10 | |||
847.2.f.t.372.2 | 12 | 11.8 | odd | 10 | |||
847.2.f.t.729.2 | 12 | 11.6 | odd | 10 | |||
847.2.f.u.148.2 | 12 | 11.4 | even | 5 | |||
847.2.f.u.323.2 | 12 | 11.9 | even | 5 | |||
847.2.f.u.372.2 | 12 | 11.3 | even | 5 | |||
847.2.f.u.729.2 | 12 | 11.5 | even | 5 | |||
5929.2.a.t.1.2 | 3 | 7.6 | odd | 2 | |||
5929.2.a.y.1.2 | 3 | 77.76 | even | 2 | |||
7623.2.a.bz.1.2 | 3 | 33.32 | even | 2 | |||
7623.2.a.ce.1.2 | 3 | 3.2 | odd | 2 |