Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9801,2,Mod(1,9801)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9801, 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("9801.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9801 = 3^{4} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9801.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: | \(78.2613790211\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9801.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.381966 | 0.270091 | 0.135045 | − | 0.990839i | \(-0.456882\pi\) | ||||
0.135045 | + | 0.990839i | \(0.456882\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | −1.23607 | −0.552786 | −0.276393 | − | 0.961045i | \(-0.589139\pi\) | ||||
−0.276393 | + | 0.961045i | \(0.589139\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −1.47214 | −0.520479 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.472136 | −0.149302 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.47214 | 1.79505 | 0.897524 | − | 0.440966i | \(-0.145364\pi\) | ||||
0.897524 | + | 0.440966i | \(0.145364\pi\) | |||||||
\(14\) | 0.381966 | 0.102085 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | −4.85410 | −1.17729 | −0.588646 | − | 0.808391i | \(-0.700339\pi\) | ||||
−0.588646 | + | 0.808391i | \(0.700339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 2.29180 | 0.512461 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.61803 | 0.962927 | 0.481463 | − | 0.876466i | \(-0.340105\pi\) | ||||
0.481463 | + | 0.876466i | \(0.340105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 2.47214 | 0.484826 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.85410 | −0.350392 | ||||||||
\(29\) | 4.85410 | 0.901384 | 0.450692 | − | 0.892679i | \(-0.351177\pi\) | ||||
0.450692 | + | 0.892679i | \(0.351177\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.618034 | 0.111002 | 0.0555011 | − | 0.998459i | \(-0.482324\pi\) | ||||
0.0555011 | + | 0.998459i | \(0.482324\pi\) | |||||||
\(32\) | 4.14590 | 0.732898 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.85410 | −0.317976 | ||||||||
\(35\) | −1.23607 | −0.208934 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.09017 | −0.836819 | −0.418409 | − | 0.908259i | \(-0.637412\pi\) | ||||
−0.418409 | + | 0.908259i | \(0.637412\pi\) | |||||||
\(38\) | −0.381966 | −0.0619631 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.81966 | 0.287714 | ||||||||
\(41\) | 2.52786 | 0.394786 | 0.197393 | − | 0.980324i | \(-0.436752\pi\) | ||||
0.197393 | + | 0.980324i | \(0.436752\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.85410 | −0.282748 | −0.141374 | − | 0.989956i | \(-0.545152\pi\) | ||||
−0.141374 | + | 0.989956i | \(0.545152\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.76393 | 0.260078 | ||||||||
\(47\) | 11.9443 | 1.74225 | 0.871126 | − | 0.491060i | \(-0.163391\pi\) | ||||
0.871126 | + | 0.491060i | \(0.163391\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −1.32624 | −0.187558 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −12.0000 | −1.66410 | ||||||||
\(53\) | 4.09017 | 0.561828 | 0.280914 | − | 0.959733i | \(-0.409362\pi\) | ||||
0.280914 | + | 0.959733i | \(0.409362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.47214 | −0.196722 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.85410 | 0.243456 | ||||||||
\(59\) | 1.61803 | 0.210650 | 0.105325 | − | 0.994438i | \(-0.466412\pi\) | ||||
0.105325 | + | 0.994438i | \(0.466412\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8541 | −1.38973 | −0.694863 | − | 0.719142i | \(-0.744535\pi\) | ||||
−0.694863 | + | 0.719142i | \(0.744535\pi\) | |||||||
\(62\) | 0.236068 | 0.0299807 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | −8.00000 | −0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | 0.733017 | 0.366508 | − | 0.930415i | \(-0.380553\pi\) | ||||
0.366508 | + | 0.930415i | \(0.380553\pi\) | |||||||
\(68\) | 9.00000 | 1.09141 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.472136 | −0.0564310 | ||||||||
\(71\) | −2.90983 | −0.345333 | −0.172667 | − | 0.984980i | \(-0.555238\pi\) | ||||
−0.172667 | + | 0.984980i | \(0.555238\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.145898 | 0.0170761 | 0.00853804 | − | 0.999964i | \(-0.497282\pi\) | ||||
0.00853804 | + | 0.999964i | \(0.497282\pi\) | |||||||
\(74\) | −1.94427 | −0.226017 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.85410 | 0.212680 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5623 | −1.18835 | −0.594176 | − | 0.804335i | \(-0.702522\pi\) | ||||
−0.594176 | + | 0.804335i | \(0.702522\pi\) | |||||||
\(80\) | −3.88854 | −0.434752 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.965558 | 0.106628 | ||||||||
\(83\) | 9.76393 | 1.07173 | 0.535865 | − | 0.844303i | \(-0.319985\pi\) | ||||
0.535865 | + | 0.844303i | \(0.319985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | −0.708204 | −0.0763676 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.76393 | −0.716975 | −0.358488 | − | 0.933534i | \(-0.616707\pi\) | ||||
−0.358488 | + | 0.933534i | \(0.616707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.47214 | 0.678464 | ||||||||
\(92\) | −8.56231 | −0.892682 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.56231 | 0.470566 | ||||||||
\(95\) | 1.23607 | 0.126818 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | −2.29180 | −0.231506 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.43769 | 0.643769 | ||||||||
\(101\) | 8.47214 | 0.843009 | 0.421505 | − | 0.906826i | \(-0.361502\pi\) | ||||
0.421505 | + | 0.906826i | \(0.361502\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2361 | −1.00859 | −0.504295 | − | 0.863532i | \(-0.668248\pi\) | ||||
−0.504295 | + | 0.863532i | \(0.668248\pi\) | |||||||
\(104\) | −9.52786 | −0.934284 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.56231 | 0.151745 | ||||||||
\(107\) | −14.0344 | −1.35676 | −0.678380 | − | 0.734711i | \(-0.737318\pi\) | ||||
−0.678380 | + | 0.734711i | \(0.737318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.14590 | −0.684453 | −0.342226 | − | 0.939618i | \(-0.611181\pi\) | ||||
−0.342226 | + | 0.939618i | \(0.611181\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.14590 | 0.297259 | ||||||||
\(113\) | 17.2361 | 1.62143 | 0.810716 | − | 0.585439i | \(-0.199078\pi\) | ||||
0.810716 | + | 0.585439i | \(0.199078\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.70820 | −0.532293 | ||||||||
\(116\) | −9.00000 | −0.835629 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.618034 | 0.0568946 | ||||||||
\(119\) | −4.85410 | −0.444975 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.14590 | −0.375352 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.14590 | −0.102905 | ||||||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5623 | 0.937253 | 0.468627 | − | 0.883396i | \(-0.344749\pi\) | ||||
0.468627 | + | 0.883396i | \(0.344749\pi\) | |||||||
\(128\) | −10.0902 | −0.891853 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.05573 | −0.268005 | ||||||||
\(131\) | −21.2361 | −1.85540 | −0.927702 | − | 0.373322i | \(-0.878219\pi\) | ||||
−0.927702 | + | 0.373322i | \(0.878219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 2.29180 | 0.197981 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.14590 | 0.612756 | ||||||||
\(137\) | −8.61803 | −0.736288 | −0.368144 | − | 0.929769i | \(-0.620007\pi\) | ||||
−0.368144 | + | 0.929769i | \(0.620007\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.70820 | −0.823439 | −0.411720 | − | 0.911311i | \(-0.635072\pi\) | ||||
−0.411720 | + | 0.911311i | \(0.635072\pi\) | |||||||
\(140\) | 2.29180 | 0.193692 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.11146 | −0.0932713 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 0.0557281 | 0.00461209 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.43769 | 0.775774 | ||||||||
\(149\) | 15.1803 | 1.24362 | 0.621811 | − | 0.783167i | \(-0.286397\pi\) | ||||
0.621811 | + | 0.783167i | \(0.286397\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.32624 | −0.352064 | −0.176032 | − | 0.984384i | \(-0.556326\pi\) | ||||
−0.176032 | + | 0.984384i | \(0.556326\pi\) | |||||||
\(152\) | 1.47214 | 0.119406 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.763932 | −0.0613605 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.14590 | 0.570305 | 0.285152 | − | 0.958482i | \(-0.407956\pi\) | ||||
0.285152 | + | 0.958482i | \(0.407956\pi\) | |||||||
\(158\) | −4.03444 | −0.320963 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.12461 | −0.405136 | ||||||||
\(161\) | 4.61803 | 0.363952 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.7082 | 1.62199 | 0.810996 | − | 0.585052i | \(-0.198926\pi\) | ||||
0.810996 | + | 0.585052i | \(0.198926\pi\) | |||||||
\(164\) | −4.68692 | −0.365987 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.72949 | 0.289465 | ||||||||
\(167\) | 5.76393 | 0.446026 | 0.223013 | − | 0.974815i | \(-0.428411\pi\) | ||||
0.223013 | + | 0.974815i | \(0.428411\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.8885 | 2.22220 | ||||||||
\(170\) | 2.29180 | 0.175773 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.43769 | 0.262122 | ||||||||
\(173\) | 23.0902 | 1.75551 | 0.877757 | − | 0.479107i | \(-0.159039\pi\) | ||||
0.877757 | + | 0.479107i | \(0.159039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.47214 | −0.262469 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.58359 | −0.193648 | ||||||||
\(179\) | −5.05573 | −0.377883 | −0.188941 | − | 0.981988i | \(-0.560506\pi\) | ||||
−0.188941 | + | 0.981988i | \(0.560506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.90983 | −0.736592 | −0.368296 | − | 0.929709i | \(-0.620059\pi\) | ||||
−0.368296 | + | 0.929709i | \(0.620059\pi\) | |||||||
\(182\) | 2.47214 | 0.183247 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.79837 | −0.501183 | ||||||||
\(185\) | 6.29180 | 0.462582 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −22.1459 | −1.61516 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.472136 | 0.0342523 | ||||||||
\(191\) | 5.94427 | 0.430112 | 0.215056 | − | 0.976602i | \(-0.431007\pi\) | ||||
0.215056 | + | 0.976602i | \(0.431007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.0000 | 0.791797 | 0.395899 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395899 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(194\) | 2.29180 | 0.164541 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.1246 | 0.794615 | ||||||||
\(197\) | −8.23607 | −0.586796 | −0.293398 | − | 0.955990i | \(-0.594786\pi\) | ||||
−0.293398 | + | 0.955990i | \(0.594786\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.14590 | −0.506559 | −0.253280 | − | 0.967393i | \(-0.581509\pi\) | ||||
−0.253280 | + | 0.967393i | \(0.581509\pi\) | |||||||
\(200\) | 5.11146 | 0.361435 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.23607 | 0.227689 | ||||||||
\(203\) | 4.85410 | 0.340691 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.12461 | −0.218232 | ||||||||
\(206\) | −3.90983 | −0.272411 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.3607 | 1.41176 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.4721 | −1.40936 | −0.704680 | − | 0.709525i | \(-0.748909\pi\) | ||||
−0.704680 | + | 0.709525i | \(0.748909\pi\) | |||||||
\(212\) | −7.58359 | −0.520843 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.36068 | −0.366449 | ||||||||
\(215\) | 2.29180 | 0.156299 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.618034 | 0.0419549 | ||||||||
\(218\) | −2.72949 | −0.184864 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.4164 | −2.11330 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.5066 | −1.03840 | −0.519199 | − | 0.854654i | \(-0.673770\pi\) | ||||
−0.519199 | + | 0.854654i | \(0.673770\pi\) | |||||||
\(224\) | 4.14590 | 0.277009 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.58359 | 0.437934 | ||||||||
\(227\) | 16.6180 | 1.10298 | 0.551489 | − | 0.834182i | \(-0.314060\pi\) | ||||
0.551489 | + | 0.834182i | \(0.314060\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1803 | 0.672736 | 0.336368 | − | 0.941731i | \(-0.390801\pi\) | ||||
0.336368 | + | 0.941731i | \(0.390801\pi\) | |||||||
\(230\) | −2.18034 | −0.143767 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.14590 | −0.469151 | ||||||||
\(233\) | 11.1246 | 0.728798 | 0.364399 | − | 0.931243i | \(-0.381275\pi\) | ||||
0.364399 | + | 0.931243i | \(0.381275\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.7639 | −0.963093 | ||||||||
\(236\) | −3.00000 | −0.195283 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.85410 | −0.120184 | ||||||||
\(239\) | −10.4721 | −0.677386 | −0.338693 | − | 0.940897i | \(-0.609985\pi\) | ||||
−0.338693 | + | 0.940897i | \(0.609985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.8328 | 1.72845 | 0.864227 | − | 0.503102i | \(-0.167808\pi\) | ||||
0.864227 | + | 0.503102i | \(0.167808\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.1246 | 1.28835 | ||||||||
\(245\) | 7.41641 | 0.473817 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.47214 | −0.411812 | ||||||||
\(248\) | −0.909830 | −0.0577743 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.00000 | 0.252982 | ||||||||
\(251\) | 20.5623 | 1.29788 | 0.648941 | − | 0.760839i | \(-0.275212\pi\) | ||||
0.648941 | + | 0.760839i | \(0.275212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.03444 | 0.253143 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | −14.9098 | −0.930050 | −0.465025 | − | 0.885298i | \(-0.653955\pi\) | ||||
−0.465025 | + | 0.885298i | \(0.653955\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.09017 | −0.316288 | ||||||||
\(260\) | 14.8328 | 0.919892 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8.11146 | −0.501127 | ||||||||
\(263\) | 12.7082 | 0.783621 | 0.391811 | − | 0.920046i | \(-0.371849\pi\) | ||||
0.391811 | + | 0.920046i | \(0.371849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.05573 | −0.310571 | ||||||||
\(266\) | −0.381966 | −0.0234198 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.1246 | −0.679544 | ||||||||
\(269\) | −21.2705 | −1.29689 | −0.648443 | − | 0.761263i | \(-0.724579\pi\) | ||||
−0.648443 | + | 0.761263i | \(0.724579\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7639 | −0.653862 | −0.326931 | − | 0.945048i | \(-0.606015\pi\) | ||||
−0.326931 | + | 0.945048i | \(0.606015\pi\) | |||||||
\(272\) | −15.2705 | −0.925911 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.29180 | −0.198865 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.2361 | 1.15578 | 0.577892 | − | 0.816113i | \(-0.303876\pi\) | ||||
0.577892 | + | 0.816113i | \(0.303876\pi\) | |||||||
\(278\) | −3.70820 | −0.222403 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.81966 | 0.108745 | ||||||||
\(281\) | 9.32624 | 0.556357 | 0.278178 | − | 0.960529i | \(-0.410269\pi\) | ||||
0.278178 | + | 0.960529i | \(0.410269\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0000 | 1.01055 | 0.505273 | − | 0.862960i | \(-0.331392\pi\) | ||||
0.505273 | + | 0.862960i | \(0.331392\pi\) | |||||||
\(284\) | 5.39512 | 0.320142 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.52786 | 0.149215 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.56231 | 0.386018 | ||||||||
\(290\) | −2.29180 | −0.134579 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.270510 | −0.0158304 | ||||||||
\(293\) | 29.1803 | 1.70473 | 0.852367 | − | 0.522944i | \(-0.175166\pi\) | ||||
0.852367 | + | 0.522944i | \(0.175166\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | −0.116445 | ||||||||
\(296\) | 7.49342 | 0.435546 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.79837 | 0.335891 | ||||||||
\(299\) | 29.8885 | 1.72850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.85410 | −0.106869 | ||||||||
\(302\) | −1.65248 | −0.0950893 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.14590 | −0.180430 | ||||||||
\(305\) | 13.4164 | 0.768221 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.85410 | −0.448257 | −0.224129 | − | 0.974560i | \(-0.571954\pi\) | ||||
−0.224129 | + | 0.974560i | \(0.571954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.291796 | −0.0165729 | ||||||||
\(311\) | 15.1803 | 0.860798 | 0.430399 | − | 0.902639i | \(-0.358373\pi\) | ||||
0.430399 | + | 0.902639i | \(0.358373\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.47214 | 0.196257 | 0.0981284 | − | 0.995174i | \(-0.468714\pi\) | ||||
0.0981284 | + | 0.995174i | \(0.468714\pi\) | |||||||
\(314\) | 2.72949 | 0.154034 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.5836 | 1.10166 | ||||||||
\(317\) | 20.9443 | 1.17635 | 0.588174 | − | 0.808735i | \(-0.299847\pi\) | ||||
0.588174 | + | 0.808735i | \(0.299847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 5.81966 | 0.325329 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.76393 | 0.0983001 | ||||||||
\(323\) | 4.85410 | 0.270089 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.4721 | −1.24653 | ||||||||
\(326\) | 7.90983 | 0.438085 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.72136 | −0.205478 | ||||||||
\(329\) | 11.9443 | 0.658509 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4164 | 0.792397 | 0.396199 | − | 0.918165i | \(-0.370329\pi\) | ||||
0.396199 | + | 0.918165i | \(0.370329\pi\) | |||||||
\(332\) | −18.1033 | −0.993549 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.20163 | 0.120468 | ||||||||
\(335\) | −7.41641 | −0.405202 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.4721 | 0.624927 | 0.312464 | − | 0.949930i | \(-0.398846\pi\) | ||||
0.312464 | + | 0.949930i | \(0.398846\pi\) | |||||||
\(338\) | 11.0344 | 0.600195 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.1246 | −0.603317 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 2.72949 | 0.147164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.81966 | 0.474148 | ||||||||
\(347\) | 8.88854 | 0.477162 | 0.238581 | − | 0.971123i | \(-0.423318\pi\) | ||||
0.238581 | + | 0.971123i | \(0.423318\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.14590 | 0.221925 | 0.110962 | − | 0.993825i | \(-0.464607\pi\) | ||||
0.110962 | + | 0.993825i | \(0.464607\pi\) | |||||||
\(350\) | −1.32624 | −0.0708904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.4164 | −0.873757 | −0.436879 | − | 0.899520i | \(-0.643916\pi\) | ||||
−0.436879 | + | 0.899520i | \(0.643916\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.59675 | 0.190896 | ||||||||
\(356\) | 12.5410 | 0.664673 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.93112 | −0.102063 | ||||||||
\(359\) | 22.8541 | 1.20619 | 0.603097 | − | 0.797668i | \(-0.293933\pi\) | ||||
0.603097 | + | 0.797668i | \(0.293933\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | −3.78522 | −0.198947 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.0000 | −0.628971 | ||||||||
\(365\) | −0.180340 | −0.00943942 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7082 | −0.663363 | −0.331681 | − | 0.943391i | \(-0.607616\pi\) | ||||
−0.331681 | + | 0.943391i | \(0.607616\pi\) | |||||||
\(368\) | 14.5279 | 0.757317 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.40325 | 0.124939 | ||||||||
\(371\) | 4.09017 | 0.212351 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.65248 | 0.292674 | 0.146337 | − | 0.989235i | \(-0.453252\pi\) | ||||
0.146337 | + | 0.989235i | \(0.453252\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.5836 | −0.906805 | ||||||||
\(377\) | 31.4164 | 1.61803 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7984 | 0.811508 | 0.405754 | − | 0.913982i | \(-0.367009\pi\) | ||||
0.405754 | + | 0.913982i | \(0.367009\pi\) | |||||||
\(380\) | −2.29180 | −0.117567 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.27051 | 0.116169 | ||||||||
\(383\) | 19.8541 | 1.01450 | 0.507249 | − | 0.861800i | \(-0.330663\pi\) | ||||
0.507249 | + | 0.861800i | \(0.330663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.20163 | 0.213857 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.1246 | −0.564767 | ||||||||
\(389\) | −22.6525 | −1.14853 | −0.574263 | − | 0.818671i | \(-0.694711\pi\) | ||||
−0.574263 | + | 0.818671i | \(0.694711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.4164 | −1.13365 | ||||||||
\(392\) | 8.83282 | 0.446125 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.14590 | −0.158488 | ||||||||
\(395\) | 13.0557 | 0.656905 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.12461 | −0.106631 | −0.0533156 | − | 0.998578i | \(-0.516979\pi\) | ||||
−0.0533156 | + | 0.998578i | \(0.516979\pi\) | |||||||
\(398\) | −2.72949 | −0.136817 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.9230 | −0.546149 | ||||||||
\(401\) | 14.5623 | 0.727207 | 0.363603 | − | 0.931554i | \(-0.381546\pi\) | ||||
0.363603 | + | 0.931554i | \(0.381546\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | 0.199254 | ||||||||
\(404\) | −15.7082 | −0.781512 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.85410 | 0.0920175 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.7426 | 1.66847 | 0.834233 | − | 0.551412i | \(-0.185911\pi\) | ||||
0.834233 | + | 0.551412i | \(0.185911\pi\) | |||||||
\(410\) | −1.19350 | −0.0589425 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18.9787 | 0.935014 | ||||||||
\(413\) | 1.61803 | 0.0796182 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0689 | −0.592438 | ||||||||
\(416\) | 26.8328 | 1.31559 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.09017 | 0.395231 | 0.197615 | − | 0.980280i | \(-0.436680\pi\) | ||||
0.197615 | + | 0.980280i | \(0.436680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.2361 | 0.498875 | 0.249438 | − | 0.968391i | \(-0.419754\pi\) | ||||
0.249438 | + | 0.968391i | \(0.419754\pi\) | |||||||
\(422\) | −7.81966 | −0.380655 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.02129 | −0.292420 | ||||||||
\(425\) | 16.8541 | 0.817544 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.8541 | −0.525267 | ||||||||
\(428\) | 26.0213 | 1.25779 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.875388 | 0.0422150 | ||||||||
\(431\) | 34.0689 | 1.64104 | 0.820520 | − | 0.571618i | \(-0.193684\pi\) | ||||
0.820520 | + | 0.571618i | \(0.193684\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.7426 | 0.708486 | 0.354243 | − | 0.935153i | \(-0.384739\pi\) | ||||
0.354243 | + | 0.935153i | \(0.384739\pi\) | |||||||
\(434\) | 0.236068 | 0.0113316 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.2492 | 0.634523 | ||||||||
\(437\) | −4.61803 | −0.220911 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.708204 | 0.0338007 | 0.0169004 | − | 0.999857i | \(-0.494620\pi\) | ||||
0.0169004 | + | 0.999857i | \(0.494620\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | −1.23607 | −0.0587274 | −0.0293637 | − | 0.999569i | \(-0.509348\pi\) | ||||
−0.0293637 | + | 0.999569i | \(0.509348\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.36068 | 0.396334 | ||||||||
\(446\) | −5.92299 | −0.280462 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.70820 | −0.222442 | ||||||||
\(449\) | 7.47214 | 0.352632 | 0.176316 | − | 0.984334i | \(-0.443582\pi\) | ||||
0.176316 | + | 0.984334i | \(0.443582\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −31.9574 | −1.50315 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.34752 | 0.297904 | ||||||||
\(455\) | −8.00000 | −0.375046 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00000 | 0.0467780 | 0.0233890 | − | 0.999726i | \(-0.492554\pi\) | ||||
0.0233890 | + | 0.999726i | \(0.492554\pi\) | |||||||
\(458\) | 3.88854 | 0.181700 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.5836 | 0.493463 | ||||||||
\(461\) | 16.1459 | 0.751989 | 0.375995 | − | 0.926622i | \(-0.377301\pi\) | ||||
0.375995 | + | 0.926622i | \(0.377301\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000 | 0.790057 | 0.395029 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395029 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(464\) | 15.2705 | 0.708916 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.24922 | 0.196841 | ||||||||
\(467\) | −0.763932 | −0.0353506 | −0.0176753 | − | 0.999844i | \(-0.505627\pi\) | ||||
−0.0176753 | + | 0.999844i | \(0.505627\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.00000 | 0.277054 | ||||||||
\(470\) | −5.63932 | −0.260122 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.38197 | −0.109639 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.47214 | 0.159313 | ||||||||
\(476\) | 9.00000 | 0.412514 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.00000 | −0.182956 | ||||||||
\(479\) | 11.7639 | 0.537508 | 0.268754 | − | 0.963209i | \(-0.413388\pi\) | ||||
0.268754 | + | 0.963209i | \(0.413388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.9443 | −1.50213 | ||||||||
\(482\) | 10.2492 | 0.466839 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.41641 | −0.336762 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.9787 | −0.588122 | −0.294061 | − | 0.955787i | \(-0.595007\pi\) | ||||
−0.294061 | + | 0.955787i | \(0.595007\pi\) | |||||||
\(488\) | 15.9787 | 0.723322 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.83282 | 0.127974 | ||||||||
\(491\) | −7.32624 | −0.330628 | −0.165314 | − | 0.986241i | \(-0.552864\pi\) | ||||
−0.165314 | + | 0.986241i | \(0.552864\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.5623 | −1.06119 | ||||||||
\(494\) | −2.47214 | −0.111227 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.94427 | 0.0873004 | ||||||||
\(497\) | −2.90983 | −0.130524 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.4164 | 1.71975 | 0.859877 | − | 0.510501i | \(-0.170540\pi\) | ||||
0.859877 | + | 0.510501i | \(0.170540\pi\) | |||||||
\(500\) | −19.4164 | −0.868328 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.85410 | 0.350546 | ||||||||
\(503\) | 9.52786 | 0.424826 | 0.212413 | − | 0.977180i | \(-0.431868\pi\) | ||||
0.212413 | + | 0.977180i | \(0.431868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.4721 | −0.466004 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.5836 | −0.868881 | ||||||||
\(509\) | −27.1803 | −1.20475 | −0.602374 | − | 0.798214i | \(-0.705778\pi\) | ||||
−0.602374 | + | 0.798214i | \(0.705778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.145898 | 0.00645415 | ||||||||
\(512\) | 22.3050 | 0.985749 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.69505 | −0.251198 | ||||||||
\(515\) | 12.6525 | 0.557535 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.94427 | −0.0854264 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 11.7771 | 0.516459 | ||||||||
\(521\) | −40.3607 | −1.76823 | −0.884117 | − | 0.467266i | \(-0.845239\pi\) | ||||
−0.884117 | + | 0.467266i | \(0.845239\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | 39.3738 | 1.72005 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.85410 | 0.211649 | ||||||||
\(527\) | −3.00000 | −0.130682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.67376 | −0.0727723 | ||||||||
\(530\) | −1.93112 | −0.0838823 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.85410 | 0.0803855 | ||||||||
\(533\) | 16.3607 | 0.708660 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.3475 | 0.749999 | ||||||||
\(536\) | −8.83282 | −0.381520 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.12461 | −0.350277 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.9098 | 0.512044 | 0.256022 | − | 0.966671i | \(-0.417588\pi\) | ||||
0.256022 | + | 0.966671i | \(0.417588\pi\) | |||||||
\(542\) | −4.11146 | −0.176602 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −20.1246 | −0.862836 | ||||||||
\(545\) | 8.83282 | 0.378356 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.3262 | 1.38217 | 0.691085 | − | 0.722773i | \(-0.257133\pi\) | ||||
0.691085 | + | 0.722773i | \(0.257133\pi\) | |||||||
\(548\) | 15.9787 | 0.682577 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.85410 | −0.206792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.5623 | −0.449155 | ||||||||
\(554\) | 7.34752 | 0.312166 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.0000 | 0.763370 | ||||||||
\(557\) | 0.652476 | 0.0276463 | 0.0138231 | − | 0.999904i | \(-0.495600\pi\) | ||||
0.0138231 | + | 0.999904i | \(0.495600\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | −3.88854 | −0.164321 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.56231 | 0.150267 | ||||||||
\(563\) | 20.3050 | 0.855752 | 0.427876 | − | 0.903838i | \(-0.359262\pi\) | ||||
0.427876 | + | 0.903838i | \(0.359262\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.3050 | −0.896306 | ||||||||
\(566\) | 6.49342 | 0.272939 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.28367 | 0.179739 | ||||||||
\(569\) | −38.7984 | −1.62651 | −0.813256 | − | 0.581906i | \(-0.802307\pi\) | ||||
−0.813256 | + | 0.581906i | \(0.802307\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.5279 | 0.775367 | 0.387683 | − | 0.921793i | \(-0.373275\pi\) | ||||
0.387683 | + | 0.921793i | \(0.373275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.965558 | 0.0403016 | ||||||||
\(575\) | −16.0344 | −0.668682 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.4164 | 1.47440 | 0.737202 | − | 0.675672i | \(-0.236147\pi\) | ||||
0.737202 | + | 0.675672i | \(0.236147\pi\) | |||||||
\(578\) | 2.50658 | 0.104260 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.1246 | 0.461924 | ||||||||
\(581\) | 9.76393 | 0.405076 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.214782 | −0.00888773 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.1459 | 0.460433 | ||||||||
\(587\) | 13.4164 | 0.553754 | 0.276877 | − | 0.960905i | \(-0.410700\pi\) | ||||
0.276877 | + | 0.960905i | \(0.410700\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.618034 | −0.0254656 | ||||||||
\(590\) | −0.763932 | −0.0314506 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.0132 | −0.658137 | ||||||||
\(593\) | 10.9443 | 0.449427 | 0.224714 | − | 0.974425i | \(-0.427855\pi\) | ||||
0.224714 | + | 0.974425i | \(0.427855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | 0.245976 | ||||||||
\(596\) | −28.1459 | −1.15290 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.4164 | 0.466852 | ||||||||
\(599\) | −13.3607 | −0.545903 | −0.272951 | − | 0.962028i | \(-0.588000\pi\) | ||||
−0.272951 | + | 0.962028i | \(0.588000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.4721 | 0.712703 | 0.356352 | − | 0.934352i | \(-0.384021\pi\) | ||||
0.356352 | + | 0.934352i | \(0.384021\pi\) | |||||||
\(602\) | −0.708204 | −0.0288642 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.02129 | 0.326382 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.58359 | 0.145454 | 0.0727268 | − | 0.997352i | \(-0.476830\pi\) | ||||
0.0727268 | + | 0.997352i | \(0.476830\pi\) | |||||||
\(608\) | −4.14590 | −0.168138 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.12461 | 0.207489 | ||||||||
\(611\) | 77.3050 | 3.12742 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.8541 | −0.801900 | −0.400950 | − | 0.916100i | \(-0.631320\pi\) | ||||
−0.400950 | + | 0.916100i | \(0.631320\pi\) | |||||||
\(614\) | −3.00000 | −0.121070 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.1591 | −1.09338 | −0.546691 | − | 0.837334i | \(-0.684113\pi\) | ||||
−0.546691 | + | 0.837334i | \(0.684113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.5623 | 1.10782 | 0.553911 | − | 0.832576i | \(-0.313135\pi\) | ||||
0.553911 | + | 0.832576i | \(0.313135\pi\) | |||||||
\(620\) | 1.41641 | 0.0568843 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.79837 | 0.232494 | ||||||||
\(623\) | −6.76393 | −0.270991 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 1.32624 | 0.0530071 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.2492 | −0.528702 | ||||||||
\(629\) | 24.7082 | 0.985181 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.8885 | −0.433466 | −0.216733 | − | 0.976231i | \(-0.569540\pi\) | ||||
−0.216733 | + | 0.976231i | \(0.569540\pi\) | |||||||
\(632\) | 15.5492 | 0.618512 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.00000 | 0.317721 | ||||||||
\(635\) | −13.0557 | −0.518101 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −38.8328 | −1.53861 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.4721 | 0.493004 | ||||||||
\(641\) | −20.4508 | −0.807760 | −0.403880 | − | 0.914812i | \(-0.632339\pi\) | ||||
−0.403880 | + | 0.914812i | \(0.632339\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.85410 | −0.270299 | −0.135150 | − | 0.990825i | \(-0.543152\pi\) | ||||
−0.135150 | + | 0.990825i | \(0.543152\pi\) | |||||||
\(644\) | −8.56231 | −0.337402 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.85410 | 0.0729487 | ||||||||
\(647\) | −4.18034 | −0.164346 | −0.0821731 | − | 0.996618i | \(-0.526186\pi\) | ||||
−0.0821731 | + | 0.996618i | \(0.526186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −8.58359 | −0.336676 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −38.3951 | −1.50367 | ||||||||
\(653\) | −1.36068 | −0.0532475 | −0.0266238 | − | 0.999646i | \(-0.508476\pi\) | ||||
−0.0266238 | + | 0.999646i | \(0.508476\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.2492 | 1.02564 | ||||||||
\(656\) | 7.95240 | 0.310489 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.56231 | 0.177857 | ||||||||
\(659\) | −9.97871 | −0.388715 | −0.194358 | − | 0.980931i | \(-0.562262\pi\) | ||||
−0.194358 | + | 0.980931i | \(0.562262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.29180 | −0.166932 | −0.0834658 | − | 0.996511i | \(-0.526599\pi\) | ||||
−0.0834658 | + | 0.996511i | \(0.526599\pi\) | |||||||
\(662\) | 5.50658 | 0.214019 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.3738 | −0.557813 | ||||||||
\(665\) | 1.23607 | 0.0479327 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.4164 | 0.867967 | ||||||||
\(668\) | −10.6869 | −0.413489 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.83282 | −0.109441 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.5623 | 1.13954 | 0.569772 | − | 0.821803i | \(-0.307032\pi\) | ||||
0.569772 | + | 0.821803i | \(0.307032\pi\) | |||||||
\(674\) | 4.38197 | 0.168787 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −53.5623 | −2.06009 | ||||||||
\(677\) | −6.05573 | −0.232741 | −0.116370 | − | 0.993206i | \(-0.537126\pi\) | ||||
−0.116370 | + | 0.993206i | \(0.537126\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.00000 | 0.230259 | ||||||||
\(680\) | −8.83282 | −0.338723 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.52786 | −0.211518 | −0.105759 | − | 0.994392i | \(-0.533727\pi\) | ||||
−0.105759 | + | 0.994392i | \(0.533727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.6525 | 0.407010 | ||||||||
\(686\) | −4.96556 | −0.189586 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.83282 | −0.222374 | ||||||||
\(689\) | 26.4721 | 1.00851 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.5967 | 0.555286 | 0.277643 | − | 0.960684i | \(-0.410447\pi\) | ||||
0.277643 | + | 0.960684i | \(0.410447\pi\) | |||||||
\(692\) | −42.8115 | −1.62745 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.39512 | 0.128877 | ||||||||
\(695\) | 12.0000 | 0.455186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.2705 | −0.464779 | ||||||||
\(698\) | 1.58359 | 0.0599398 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.43769 | 0.243322 | ||||||||
\(701\) | 47.7214 | 1.80241 | 0.901205 | − | 0.433392i | \(-0.142683\pi\) | ||||
0.901205 | + | 0.433392i | \(0.142683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.09017 | 0.191979 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.27051 | −0.235994 | ||||||||
\(707\) | 8.47214 | 0.318627 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.7639 | −0.967585 | −0.483792 | − | 0.875183i | \(-0.660741\pi\) | ||||
−0.483792 | + | 0.875183i | \(0.660741\pi\) | |||||||
\(710\) | 1.37384 | 0.0515591 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.95743 | 0.373170 | ||||||||
\(713\) | 2.85410 | 0.106887 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.37384 | 0.350317 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.72949 | 0.325782 | ||||||||
\(719\) | −19.5967 | −0.730835 | −0.365418 | − | 0.930844i | \(-0.619074\pi\) | ||||
−0.365418 | + | 0.930844i | \(0.619074\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2361 | −0.381211 | ||||||||
\(722\) | −6.87539 | −0.255875 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.3738 | 0.682858 | ||||||||
\(725\) | −16.8541 | −0.625946 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.8328 | 0.698470 | 0.349235 | − | 0.937035i | \(-0.386441\pi\) | ||||
0.349235 | + | 0.937035i | \(0.386441\pi\) | |||||||
\(728\) | −9.52786 | −0.353126 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.0688837 | −0.00254950 | ||||||||
\(731\) | 9.00000 | 0.332877 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.4721 | −1.79036 | −0.895180 | − | 0.445706i | \(-0.852953\pi\) | ||||
−0.895180 | + | 0.445706i | \(0.852953\pi\) | |||||||
\(734\) | −4.85410 | −0.179168 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.1459 | 0.705727 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.5410 | −1.56490 | −0.782448 | − | 0.622715i | \(-0.786029\pi\) | ||||
−0.782448 | + | 0.622715i | \(0.786029\pi\) | |||||||
\(740\) | −11.6656 | −0.428837 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.56231 | 0.0573541 | ||||||||
\(743\) | 42.3607 | 1.55406 | 0.777031 | − | 0.629462i | \(-0.216725\pi\) | ||||
0.777031 | + | 0.629462i | \(0.216725\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.7639 | −0.687457 | ||||||||
\(746\) | 2.15905 | 0.0790486 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.0344 | −0.512807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.2492 | −1.14030 | −0.570150 | − | 0.821540i | \(-0.693115\pi\) | ||||
−0.570150 | + | 0.821540i | \(0.693115\pi\) | |||||||
\(752\) | 37.5755 | 1.37024 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0000 | 0.437014 | ||||||||
\(755\) | 5.34752 | 0.194616 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.0000 | 0.399802 | 0.199901 | − | 0.979816i | \(-0.435938\pi\) | ||||
0.199901 | + | 0.979816i | \(0.435938\pi\) | |||||||
\(758\) | 6.03444 | 0.219181 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.81966 | −0.0660060 | ||||||||
\(761\) | −6.97871 | −0.252978 | −0.126489 | − | 0.991968i | \(-0.540371\pi\) | ||||
−0.126489 | + | 0.991968i | \(0.540371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.14590 | −0.258699 | ||||||||
\(764\) | −11.0213 | −0.398736 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.58359 | 0.274006 | ||||||||
\(767\) | 10.4721 | 0.378127 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.7984 | 0.569704 | 0.284852 | − | 0.958572i | \(-0.408056\pi\) | ||||
0.284852 | + | 0.958572i | \(0.408056\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.3951 | −0.734036 | ||||||||
\(773\) | 23.6525 | 0.850720 | 0.425360 | − | 0.905024i | \(-0.360147\pi\) | ||||
0.425360 | + | 0.905024i | \(0.360147\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.14590 | −0.0770829 | ||||||||
\(776\) | −8.83282 | −0.317080 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.65248 | −0.310206 | ||||||||
\(779\) | −2.52786 | −0.0905701 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −8.56231 | −0.306187 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.8754 | −0.674121 | ||||||||
\(785\) | −8.83282 | −0.315257 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.0000 | −1.28326 | −0.641631 | − | 0.767014i | \(-0.721742\pi\) | ||||
−0.641631 | + | 0.767014i | \(0.721742\pi\) | |||||||
\(788\) | 15.2705 | 0.543989 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.98684 | 0.177424 | ||||||||
\(791\) | 17.2361 | 0.612844 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −70.2492 | −2.49462 | ||||||||
\(794\) | −0.811529 | −0.0288001 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.2492 | 0.469606 | ||||||||
\(797\) | 24.2705 | 0.859706 | 0.429853 | − | 0.902899i | \(-0.358565\pi\) | ||||
0.429853 | + | 0.902899i | \(0.358565\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −57.9787 | −2.05114 | ||||||||
\(800\) | −14.3951 | −0.508944 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.56231 | 0.196412 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.70820 | −0.201188 | ||||||||
\(806\) | 1.52786 | 0.0538167 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.4721 | −0.438768 | ||||||||
\(809\) | 18.0902 | 0.636017 | 0.318008 | − | 0.948088i | \(-0.396986\pi\) | ||||
0.318008 | + | 0.948088i | \(0.396986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.68692 | −0.305039 | −0.152519 | − | 0.988300i | \(-0.548739\pi\) | ||||
−0.152519 | + | 0.988300i | \(0.548739\pi\) | |||||||
\(812\) | −9.00000 | −0.315838 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.5967 | −0.896615 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.85410 | 0.0648668 | ||||||||
\(818\) | 12.8885 | 0.450637 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.79335 | 0.202313 | ||||||||
\(821\) | −38.2148 | −1.33371 | −0.666853 | − | 0.745190i | \(-0.732359\pi\) | ||||
−0.666853 | + | 0.745190i | \(0.732359\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.2918 | −1.47420 | −0.737100 | − | 0.675784i | \(-0.763805\pi\) | ||||
−0.737100 | + | 0.675784i | \(0.763805\pi\) | |||||||
\(824\) | 15.0689 | 0.524949 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.618034 | 0.0215042 | ||||||||
\(827\) | 57.0344 | 1.98328 | 0.991641 | − | 0.129028i | \(-0.0411858\pi\) | ||||
0.991641 | + | 0.129028i | \(0.0411858\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.5410 | 1.51224 | 0.756121 | − | 0.654432i | \(-0.227092\pi\) | ||||
0.756121 | + | 0.654432i | \(0.227092\pi\) | |||||||
\(830\) | −4.60990 | −0.160012 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −30.4721 | −1.05643 | ||||||||
\(833\) | 29.1246 | 1.00911 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.12461 | −0.246557 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.09017 | 0.106748 | ||||||||
\(839\) | −17.2918 | −0.596979 | −0.298490 | − | 0.954413i | \(-0.596483\pi\) | ||||
−0.298490 | + | 0.954413i | \(0.596483\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.43769 | −0.187507 | ||||||||
\(842\) | 3.90983 | 0.134742 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 37.9574 | 1.30655 | ||||||||
\(845\) | −35.7082 | −1.22840 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.8673 | 0.441863 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.43769 | 0.220811 | ||||||||
\(851\) | −23.5066 | −0.805795 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.4377 | 1.21336 | 0.606682 | − | 0.794945i | \(-0.292500\pi\) | ||||
0.606682 | + | 0.794945i | \(0.292500\pi\) | |||||||
\(854\) | −4.14590 | −0.141870 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.6606 | 0.706165 | ||||||||
\(857\) | −25.3607 | −0.866304 | −0.433152 | − | 0.901321i | \(-0.642599\pi\) | ||||
−0.433152 | + | 0.901321i | \(0.642599\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.5623 | −1.11101 | −0.555506 | − | 0.831513i | \(-0.687475\pi\) | ||||
−0.555506 | + | 0.831513i | \(0.687475\pi\) | |||||||
\(860\) | −4.24922 | −0.144897 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.0132 | 0.443230 | ||||||||
\(863\) | 14.4508 | 0.491913 | 0.245956 | − | 0.969281i | \(-0.420898\pi\) | ||||
0.245956 | + | 0.969281i | \(0.420898\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.5410 | −0.970424 | ||||||||
\(866\) | 5.63119 | 0.191356 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.14590 | −0.0388943 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.8328 | 1.31580 | ||||||||
\(872\) | 10.5197 | 0.356243 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.76393 | −0.0596659 | ||||||||
\(875\) | 10.4721 | 0.354023 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.5967 | −0.391594 | −0.195797 | − | 0.980644i | \(-0.562729\pi\) | ||||
−0.195797 | + | 0.980644i | \(0.562729\pi\) | |||||||
\(878\) | 0.270510 | 0.00912926 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.81966 | 0.0613059 | 0.0306530 | − | 0.999530i | \(-0.490241\pi\) | ||||
0.0306530 | + | 0.999530i | \(0.490241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.6525 | −1.19980 | −0.599901 | − | 0.800074i | \(-0.704793\pi\) | ||||
−0.599901 | + | 0.800074i | \(0.704793\pi\) | |||||||
\(884\) | 58.2492 | 1.95913 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.472136 | −0.0158617 | ||||||||
\(887\) | 4.03444 | 0.135463 | 0.0677316 | − | 0.997704i | \(-0.478424\pi\) | ||||
0.0677316 | + | 0.997704i | \(0.478424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.5623 | 0.354248 | ||||||||
\(890\) | 3.19350 | 0.107046 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.7508 | 0.962647 | ||||||||
\(893\) | −11.9443 | −0.399700 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.24922 | 0.208889 | ||||||||
\(896\) | −10.0902 | −0.337089 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.85410 | 0.0952426 | ||||||||
\(899\) | 3.00000 | 0.100056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.8541 | −0.661436 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −25.3738 | −0.843921 | ||||||||
\(905\) | 12.2492 | 0.407178 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.5836 | −0.484240 | −0.242120 | − | 0.970246i | \(-0.577843\pi\) | ||||
−0.242120 | + | 0.970246i | \(0.577843\pi\) | |||||||
\(908\) | −30.8115 | −1.02252 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.05573 | −0.101296 | ||||||||
\(911\) | −19.1803 | −0.635473 | −0.317737 | − | 0.948179i | \(-0.602923\pi\) | ||||
−0.317737 | + | 0.948179i | \(0.602923\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.381966 | 0.0126343 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.8754 | −0.623660 | ||||||||
\(917\) | −21.2361 | −0.701277 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.8673 | 0.886269 | 0.443135 | − | 0.896455i | \(-0.353866\pi\) | ||||
0.443135 | + | 0.896455i | \(0.353866\pi\) | |||||||
\(920\) | 8.40325 | 0.277047 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.16718 | 0.203105 | ||||||||
\(923\) | −18.8328 | −0.619890 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.6738 | 0.581110 | ||||||||
\(926\) | 6.49342 | 0.213387 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.1246 | 0.660623 | ||||||||
\(929\) | −48.2705 | −1.58370 | −0.791852 | − | 0.610713i | \(-0.790883\pi\) | ||||
−0.791852 | + | 0.610713i | \(0.790883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | −20.6262 | −0.675632 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.291796 | −0.00954786 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.0344 | 0.752502 | 0.376251 | − | 0.926518i | \(-0.377213\pi\) | ||||
0.376251 | + | 0.926518i | \(0.377213\pi\) | |||||||
\(938\) | 2.29180 | 0.0748298 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 27.3738 | 0.892836 | ||||||||
\(941\) | −27.1591 | −0.885360 | −0.442680 | − | 0.896680i | \(-0.645972\pi\) | ||||
−0.442680 | + | 0.896680i | \(0.645972\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.6738 | 0.380150 | ||||||||
\(944\) | 5.09017 | 0.165671 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.7082 | 1.19286 | 0.596428 | − | 0.802666i | \(-0.296586\pi\) | ||||
0.596428 | + | 0.802666i | \(0.296586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.944272 | 0.0306524 | ||||||||
\(950\) | 1.32624 | 0.0430288 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.14590 | 0.231600 | ||||||||
\(953\) | 9.49342 | 0.307522 | 0.153761 | − | 0.988108i | \(-0.450861\pi\) | ||||
0.153761 | + | 0.988108i | \(0.450861\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.34752 | −0.237760 | ||||||||
\(956\) | 19.4164 | 0.627972 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.49342 | 0.145176 | ||||||||
\(959\) | −8.61803 | −0.278291 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6180 | −0.987679 | ||||||||
\(962\) | −12.5836 | −0.405711 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −49.7508 | −1.60236 | ||||||||
\(965\) | −13.5967 | −0.437695 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.4853 | −1.68781 | −0.843907 | − | 0.536490i | \(-0.819750\pi\) | ||||
−0.843907 | + | 0.536490i | \(0.819750\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.83282 | −0.0909562 | ||||||||
\(971\) | 9.27051 | 0.297505 | 0.148752 | − | 0.988874i | \(-0.452474\pi\) | ||||
0.148752 | + | 0.988874i | \(0.452474\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.70820 | −0.311231 | ||||||||
\(974\) | −4.95743 | −0.158846 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.1459 | −1.09298 | ||||||||
\(977\) | 15.7639 | 0.504333 | 0.252166 | − | 0.967684i | \(-0.418857\pi\) | ||||
0.252166 | + | 0.967684i | \(0.418857\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −13.7508 | −0.439252 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.79837 | −0.0892997 | ||||||||
\(983\) | 9.25735 | 0.295264 | 0.147632 | − | 0.989042i | \(-0.452835\pi\) | ||||
0.147632 | + | 0.989042i | \(0.452835\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.1803 | 0.324373 | ||||||||
\(986\) | −9.00000 | −0.286618 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.0000 | 0.381771 | ||||||||
\(989\) | −8.56231 | −0.272265 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5967 | 0.654277 | 0.327139 | − | 0.944976i | \(-0.393916\pi\) | ||||
0.327139 | + | 0.944976i | \(0.393916\pi\) | |||||||
\(992\) | 2.56231 | 0.0813533 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.11146 | −0.0352532 | ||||||||
\(995\) | 8.83282 | 0.280019 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.38197 | −0.233789 | −0.116895 | − | 0.993144i | \(-0.537294\pi\) | ||||
−0.116895 | + | 0.993144i | \(0.537294\pi\) | |||||||
\(998\) | 14.6738 | 0.464490 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9801.2.a.bc.1.1 | 2 | ||
3.2 | odd | 2 | 9801.2.a.m.1.2 | 2 | |||
9.4 | even | 3 | 1089.2.e.d.727.2 | 4 | |||
9.7 | even | 3 | 1089.2.e.d.364.2 | 4 | |||
11.7 | odd | 10 | 891.2.f.b.82.1 | 4 | |||
11.8 | odd | 10 | 891.2.f.b.163.1 | 4 | |||
11.10 | odd | 2 | 9801.2.a.n.1.2 | 2 | |||
33.8 | even | 10 | 891.2.f.a.163.1 | 4 | |||
33.29 | even | 10 | 891.2.f.a.82.1 | 4 | |||
33.32 | even | 2 | 9801.2.a.bb.1.1 | 2 | |||
99.7 | odd | 30 | 99.2.m.a.49.1 | yes | 8 | ||
99.29 | even | 30 | 297.2.n.a.280.1 | 8 | |||
99.40 | odd | 30 | 99.2.m.a.16.1 | ✓ | 8 | ||
99.41 | even | 30 | 297.2.n.a.262.1 | 8 | |||
99.43 | odd | 6 | 1089.2.e.g.364.1 | 4 | |||
99.52 | odd | 30 | 99.2.m.a.31.1 | yes | 8 | ||
99.74 | even | 30 | 297.2.n.a.64.1 | 8 | |||
99.76 | odd | 6 | 1089.2.e.g.727.1 | 4 | |||
99.85 | odd | 30 | 99.2.m.a.97.1 | yes | 8 | ||
99.95 | even | 30 | 297.2.n.a.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.a.16.1 | ✓ | 8 | 99.40 | odd | 30 | ||
99.2.m.a.31.1 | yes | 8 | 99.52 | odd | 30 | ||
99.2.m.a.49.1 | yes | 8 | 99.7 | odd | 30 | ||
99.2.m.a.97.1 | yes | 8 | 99.85 | odd | 30 | ||
297.2.n.a.64.1 | 8 | 99.74 | even | 30 | |||
297.2.n.a.181.1 | 8 | 99.95 | even | 30 | |||
297.2.n.a.262.1 | 8 | 99.41 | even | 30 | |||
297.2.n.a.280.1 | 8 | 99.29 | even | 30 | |||
891.2.f.a.82.1 | 4 | 33.29 | even | 10 | |||
891.2.f.a.163.1 | 4 | 33.8 | even | 10 | |||
891.2.f.b.82.1 | 4 | 11.7 | odd | 10 | |||
891.2.f.b.163.1 | 4 | 11.8 | odd | 10 | |||
1089.2.e.d.364.2 | 4 | 9.7 | even | 3 | |||
1089.2.e.d.727.2 | 4 | 9.4 | even | 3 | |||
1089.2.e.g.364.1 | 4 | 99.43 | odd | 6 | |||
1089.2.e.g.727.1 | 4 | 99.76 | odd | 6 | |||
9801.2.a.m.1.2 | 2 | 3.2 | odd | 2 | |||
9801.2.a.n.1.2 | 2 | 11.10 | odd | 2 | |||
9801.2.a.bb.1.1 | 2 | 33.32 | even | 2 | |||
9801.2.a.bc.1.1 | 2 | 1.1 | even | 1 | trivial |