Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.33452.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 7x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.180986\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.180986 | 0.104492 | 0.0522462 | − | 0.998634i | \(-0.483362\pi\) | ||||
0.0522462 | + | 0.998634i | \(0.483362\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.08332 | 1.82612 | 0.913058 | − | 0.407829i | \(-0.133714\pi\) | ||||
0.913058 | + | 0.407829i | \(0.133714\pi\) | |||||||
\(6\) | −0.180986 | −0.0738873 | ||||||||
\(7\) | −3.52528 | −1.33243 | −0.666216 | − | 0.745759i | \(-0.732087\pi\) | ||||
−0.666216 | + | 0.745759i | \(0.732087\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.96724 | −0.989081 | ||||||||
\(10\) | −4.08332 | −1.29126 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.180986 | 0.0522462 | ||||||||
\(13\) | −1.08332 | −0.300459 | −0.150230 | − | 0.988651i | \(-0.548001\pi\) | ||||
−0.150230 | + | 0.988651i | \(0.548001\pi\) | |||||||
\(14\) | 3.52528 | 0.942171 | ||||||||
\(15\) | 0.739025 | 0.190815 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.90234 | 0.946455 | 0.473228 | − | 0.880940i | \(-0.343089\pi\) | ||||
0.473228 | + | 0.880940i | \(0.343089\pi\) | |||||||
\(18\) | 2.96724 | 0.699386 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 4.08332 | 0.913058 | ||||||||
\(21\) | −0.638028 | −0.139229 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.34430 | −0.905848 | −0.452924 | − | 0.891549i | \(-0.649619\pi\) | ||||
−0.452924 | + | 0.891549i | \(0.649619\pi\) | |||||||
\(24\) | −0.180986 | −0.0369437 | ||||||||
\(25\) | 11.6735 | 2.33470 | ||||||||
\(26\) | 1.08332 | 0.212457 | ||||||||
\(27\) | −1.07999 | −0.207844 | ||||||||
\(28\) | −3.52528 | −0.666216 | ||||||||
\(29\) | 6.06565 | 1.12636 | 0.563181 | − | 0.826334i | \(-0.309577\pi\) | ||||
0.563181 | + | 0.826334i | \(0.309577\pi\) | |||||||
\(30\) | −0.739025 | −0.134927 | ||||||||
\(31\) | 7.26098 | 1.30411 | 0.652055 | − | 0.758172i | \(-0.273907\pi\) | ||||
0.652055 | + | 0.758172i | \(0.273907\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.90234 | −0.669245 | ||||||||
\(35\) | −14.3949 | −2.43318 | ||||||||
\(36\) | −2.96724 | −0.494541 | ||||||||
\(37\) | 0.754105 | 0.123974 | 0.0619870 | − | 0.998077i | \(-0.480256\pi\) | ||||
0.0619870 | + | 0.998077i | \(0.480256\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −0.196066 | −0.0313957 | ||||||||
\(40\) | −4.08332 | −0.645630 | ||||||||
\(41\) | −6.67351 | −1.04223 | −0.521114 | − | 0.853487i | \(-0.674483\pi\) | ||||
−0.521114 | + | 0.853487i | \(0.674483\pi\) | |||||||
\(42\) | 0.638028 | 0.0984498 | ||||||||
\(43\) | −4.60527 | −0.702297 | −0.351149 | − | 0.936320i | \(-0.614209\pi\) | ||||
−0.351149 | + | 0.936320i | \(0.614209\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.1162 | −1.80618 | ||||||||
\(46\) | 4.34430 | 0.640532 | ||||||||
\(47\) | 12.1666 | 1.77469 | 0.887344 | − | 0.461109i | \(-0.152548\pi\) | ||||
0.887344 | + | 0.461109i | \(0.152548\pi\) | |||||||
\(48\) | 0.180986 | 0.0261231 | ||||||||
\(49\) | 5.42762 | 0.775374 | ||||||||
\(50\) | −11.6735 | −1.65088 | ||||||||
\(51\) | 0.706269 | 0.0988974 | ||||||||
\(52\) | −1.08332 | −0.150230 | ||||||||
\(53\) | 4.42429 | 0.607722 | 0.303861 | − | 0.952716i | \(-0.401724\pi\) | ||||
0.303861 | + | 0.952716i | \(0.401724\pi\) | |||||||
\(54\) | 1.07999 | 0.146968 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.52528 | 0.471086 | ||||||||
\(57\) | 0.180986 | 0.0239722 | ||||||||
\(58\) | −6.06565 | −0.796458 | ||||||||
\(59\) | −3.54036 | −0.460916 | −0.230458 | − | 0.973082i | \(-0.574022\pi\) | ||||
−0.230458 | + | 0.973082i | \(0.574022\pi\) | |||||||
\(60\) | 0.739025 | 0.0954077 | ||||||||
\(61\) | −9.05057 | −1.15881 | −0.579403 | − | 0.815041i | \(-0.696714\pi\) | ||||
−0.579403 | + | 0.815041i | \(0.696714\pi\) | |||||||
\(62\) | −7.26098 | −0.922145 | ||||||||
\(63\) | 10.4604 | 1.31788 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.42355 | −0.548674 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.35864 | 0.165984 | 0.0829921 | − | 0.996550i | \(-0.473552\pi\) | ||||
0.0829921 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(68\) | 3.90234 | 0.473228 | ||||||||
\(69\) | −0.786258 | −0.0946543 | ||||||||
\(70\) | 14.3949 | 1.72052 | ||||||||
\(71\) | −8.96724 | −1.06422 | −0.532108 | − | 0.846676i | \(-0.678600\pi\) | ||||
−0.532108 | + | 0.846676i | \(0.678600\pi\) | |||||||
\(72\) | 2.96724 | 0.349693 | ||||||||
\(73\) | −8.26431 | −0.967264 | −0.483632 | − | 0.875271i | \(-0.660683\pi\) | ||||
−0.483632 | + | 0.875271i | \(0.660683\pi\) | |||||||
\(74\) | −0.754105 | −0.0876629 | ||||||||
\(75\) | 2.11274 | 0.243959 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.196066 | 0.0222001 | ||||||||
\(79\) | −11.5725 | −1.30201 | −0.651005 | − | 0.759074i | \(-0.725652\pi\) | ||||
−0.651005 | + | 0.759074i | \(0.725652\pi\) | |||||||
\(80\) | 4.08332 | 0.456529 | ||||||||
\(81\) | 8.70627 | 0.967363 | ||||||||
\(82\) | 6.67351 | 0.736966 | ||||||||
\(83\) | 17.6558 | 1.93798 | 0.968990 | − | 0.247100i | \(-0.0794777\pi\) | ||||
0.968990 | + | 0.247100i | \(0.0794777\pi\) | |||||||
\(84\) | −0.638028 | −0.0696145 | ||||||||
\(85\) | 15.9345 | 1.72834 | ||||||||
\(86\) | 4.60527 | 0.496599 | ||||||||
\(87\) | 1.09780 | 0.117696 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.2965 | 1.30342 | 0.651711 | − | 0.758467i | \(-0.274051\pi\) | ||||
0.651711 | + | 0.758467i | \(0.274051\pi\) | |||||||
\(90\) | 12.1162 | 1.27716 | ||||||||
\(91\) | 3.81901 | 0.400341 | ||||||||
\(92\) | −4.34430 | −0.452924 | ||||||||
\(93\) | 1.31414 | 0.136270 | ||||||||
\(94\) | −12.1666 | −1.25489 | ||||||||
\(95\) | 4.08332 | 0.418940 | ||||||||
\(96\) | −0.180986 | −0.0184718 | ||||||||
\(97\) | 16.4933 | 1.67464 | 0.837319 | − | 0.546715i | \(-0.184122\pi\) | ||||
0.837319 | + | 0.546715i | \(0.184122\pi\) | |||||||
\(98\) | −5.42762 | −0.548272 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.6735 | 1.16735 | ||||||||
\(101\) | 9.73916 | 0.969082 | 0.484541 | − | 0.874768i | \(-0.338987\pi\) | ||||
0.484541 | + | 0.874768i | \(0.338987\pi\) | |||||||
\(102\) | −0.706269 | −0.0699310 | ||||||||
\(103\) | −7.88799 | −0.777227 | −0.388613 | − | 0.921401i | \(-0.627046\pi\) | ||||
−0.388613 | + | 0.921401i | \(0.627046\pi\) | |||||||
\(104\) | 1.08332 | 0.106228 | ||||||||
\(105\) | −2.60527 | −0.254248 | ||||||||
\(106\) | −4.42429 | −0.429725 | ||||||||
\(107\) | 12.3510 | 1.19401 | 0.597006 | − | 0.802237i | \(-0.296357\pi\) | ||||
0.597006 | + | 0.802237i | \(0.296357\pi\) | |||||||
\(108\) | −1.07999 | −0.103922 | ||||||||
\(109\) | 15.9890 | 1.53147 | 0.765734 | − | 0.643158i | \(-0.222376\pi\) | ||||
0.765734 | + | 0.643158i | \(0.222376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.136483 | 0.0129544 | ||||||||
\(112\) | −3.52528 | −0.333108 | ||||||||
\(113\) | −0.326620 | −0.0307259 | −0.0153629 | − | 0.999882i | \(-0.504890\pi\) | ||||
−0.0153629 | + | 0.999882i | \(0.504890\pi\) | |||||||
\(114\) | −0.180986 | −0.0169509 | ||||||||
\(115\) | −17.7392 | −1.65419 | ||||||||
\(116\) | 6.06565 | 0.563181 | ||||||||
\(117\) | 3.21448 | 0.297179 | ||||||||
\(118\) | 3.54036 | 0.325917 | ||||||||
\(119\) | −13.7568 | −1.26109 | ||||||||
\(120\) | −0.739025 | −0.0674634 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.05057 | 0.819400 | ||||||||
\(123\) | −1.20781 | −0.108905 | ||||||||
\(124\) | 7.26098 | 0.652055 | ||||||||
\(125\) | 27.2501 | 2.43732 | ||||||||
\(126\) | −10.4604 | −0.931884 | ||||||||
\(127\) | 2.52862 | 0.224378 | 0.112189 | − | 0.993687i | \(-0.464214\pi\) | ||||
0.112189 | + | 0.993687i | \(0.464214\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.833491 | −0.0733848 | ||||||||
\(130\) | 4.42355 | 0.387971 | ||||||||
\(131\) | 12.6080 | 1.10157 | 0.550783 | − | 0.834648i | \(-0.314329\pi\) | ||||
0.550783 | + | 0.834648i | \(0.314329\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.52528 | −0.305681 | ||||||||
\(134\) | −1.35864 | −0.117369 | ||||||||
\(135\) | −4.40994 | −0.379547 | ||||||||
\(136\) | −3.90234 | −0.334622 | ||||||||
\(137\) | 0.489194 | 0.0417947 | 0.0208973 | − | 0.999782i | \(-0.493348\pi\) | ||||
0.0208973 | + | 0.999782i | \(0.493348\pi\) | |||||||
\(138\) | 0.786258 | 0.0669307 | ||||||||
\(139\) | −14.0245 | −1.18954 | −0.594770 | − | 0.803896i | \(-0.702757\pi\) | ||||
−0.594770 | + | 0.803896i | \(0.702757\pi\) | |||||||
\(140\) | −14.3949 | −1.21659 | ||||||||
\(141\) | 2.20199 | 0.185441 | ||||||||
\(142\) | 8.96724 | 0.752514 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.96724 | −0.247270 | ||||||||
\(145\) | 24.7680 | 2.05687 | ||||||||
\(146\) | 8.26431 | 0.683959 | ||||||||
\(147\) | 0.982324 | 0.0810207 | ||||||||
\(148\) | 0.754105 | 0.0619870 | ||||||||
\(149\) | 19.0204 | 1.55821 | 0.779106 | − | 0.626892i | \(-0.215673\pi\) | ||||
0.779106 | + | 0.626892i | \(0.215673\pi\) | |||||||
\(150\) | −2.11274 | −0.172505 | ||||||||
\(151\) | 13.9043 | 1.13152 | 0.565759 | − | 0.824571i | \(-0.308583\pi\) | ||||
0.565759 | + | 0.824571i | \(0.308583\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −11.5792 | −0.936121 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 29.6489 | 2.38146 | ||||||||
\(156\) | −0.196066 | −0.0156979 | ||||||||
\(157\) | 3.19273 | 0.254808 | 0.127404 | − | 0.991851i | \(-0.459336\pi\) | ||||
0.127404 | + | 0.991851i | \(0.459336\pi\) | |||||||
\(158\) | 11.5725 | 0.920660 | ||||||||
\(159\) | 0.800735 | 0.0635024 | ||||||||
\(160\) | −4.08332 | −0.322815 | ||||||||
\(161\) | 15.3149 | 1.20698 | ||||||||
\(162\) | −8.70627 | −0.684029 | ||||||||
\(163\) | 6.15998 | 0.482487 | 0.241243 | − | 0.970465i | \(-0.422445\pi\) | ||||
0.241243 | + | 0.970465i | \(0.422445\pi\) | |||||||
\(164\) | −6.67351 | −0.521114 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.6558 | −1.37036 | ||||||||
\(167\) | −6.92075 | −0.535544 | −0.267772 | − | 0.963482i | \(-0.586287\pi\) | ||||
−0.267772 | + | 0.963482i | \(0.586287\pi\) | |||||||
\(168\) | 0.638028 | 0.0492249 | ||||||||
\(169\) | −11.8264 | −0.909724 | ||||||||
\(170\) | −15.9345 | −1.22212 | ||||||||
\(171\) | −2.96724 | −0.226911 | ||||||||
\(172\) | −4.60527 | −0.351149 | ||||||||
\(173\) | 22.3444 | 1.69882 | 0.849408 | − | 0.527737i | \(-0.176959\pi\) | ||||
0.849408 | + | 0.527737i | \(0.176959\pi\) | |||||||
\(174\) | −1.09780 | −0.0832239 | ||||||||
\(175\) | −41.1524 | −3.11083 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.640757 | −0.0481622 | ||||||||
\(178\) | −12.2965 | −0.921659 | ||||||||
\(179\) | 2.37705 | 0.177669 | 0.0888346 | − | 0.996046i | \(-0.471686\pi\) | ||||
0.0888346 | + | 0.996046i | \(0.471686\pi\) | |||||||
\(180\) | −12.1162 | −0.903089 | ||||||||
\(181\) | −25.5137 | −1.89642 | −0.948208 | − | 0.317650i | \(-0.897106\pi\) | ||||
−0.948208 | + | 0.317650i | \(0.897106\pi\) | |||||||
\(182\) | −3.81901 | −0.283084 | ||||||||
\(183\) | −1.63803 | −0.121086 | ||||||||
\(184\) | 4.34430 | 0.320266 | ||||||||
\(185\) | 3.07925 | 0.226391 | ||||||||
\(186\) | −1.31414 | −0.0963572 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.1666 | 0.887344 | ||||||||
\(189\) | 3.80727 | 0.276938 | ||||||||
\(190\) | −4.08332 | −0.296235 | ||||||||
\(191\) | −19.8580 | −1.43687 | −0.718436 | − | 0.695593i | \(-0.755142\pi\) | ||||
−0.718436 | + | 0.695593i | \(0.755142\pi\) | |||||||
\(192\) | 0.180986 | 0.0130616 | ||||||||
\(193\) | 22.5464 | 1.62293 | 0.811464 | − | 0.584403i | \(-0.198671\pi\) | ||||
0.811464 | + | 0.584403i | \(0.198671\pi\) | |||||||
\(194\) | −16.4933 | −1.18415 | ||||||||
\(195\) | −0.800601 | −0.0573323 | ||||||||
\(196\) | 5.42762 | 0.387687 | ||||||||
\(197\) | 12.3333 | 0.878710 | 0.439355 | − | 0.898313i | \(-0.355207\pi\) | ||||
0.439355 | + | 0.898313i | \(0.355207\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.86625 | 0.486735 | 0.243368 | − | 0.969934i | \(-0.421748\pi\) | ||||
0.243368 | + | 0.969934i | \(0.421748\pi\) | |||||||
\(200\) | −11.6735 | −0.825442 | ||||||||
\(201\) | 0.245895 | 0.0173441 | ||||||||
\(202\) | −9.73916 | −0.685245 | ||||||||
\(203\) | −21.3831 | −1.50080 | ||||||||
\(204\) | 0.706269 | 0.0494487 | ||||||||
\(205\) | −27.2501 | −1.90323 | ||||||||
\(206\) | 7.88799 | 0.549582 | ||||||||
\(207\) | 12.8906 | 0.895958 | ||||||||
\(208\) | −1.08332 | −0.0751148 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.60527 | 0.179781 | ||||||||
\(211\) | −8.80740 | −0.606326 | −0.303163 | − | 0.952939i | \(-0.598043\pi\) | ||||
−0.303163 | + | 0.952939i | \(0.598043\pi\) | |||||||
\(212\) | 4.42429 | 0.303861 | ||||||||
\(213\) | −1.62295 | −0.111203 | ||||||||
\(214\) | −12.3510 | −0.844294 | ||||||||
\(215\) | −18.8048 | −1.28248 | ||||||||
\(216\) | 1.07999 | 0.0734839 | ||||||||
\(217\) | −25.5970 | −1.73764 | ||||||||
\(218\) | −15.9890 | −1.08291 | ||||||||
\(219\) | −1.49573 | −0.101072 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.22748 | −0.284371 | ||||||||
\(222\) | −0.136483 | −0.00916011 | ||||||||
\(223\) | 3.80467 | 0.254780 | 0.127390 | − | 0.991853i | \(-0.459340\pi\) | ||||
0.127390 | + | 0.991853i | \(0.459340\pi\) | |||||||
\(224\) | 3.52528 | 0.235543 | ||||||||
\(225\) | −34.6382 | −2.30921 | ||||||||
\(226\) | 0.326620 | 0.0217265 | ||||||||
\(227\) | 5.58353 | 0.370592 | 0.185296 | − | 0.982683i | \(-0.440676\pi\) | ||||
0.185296 | + | 0.982683i | \(0.440676\pi\) | |||||||
\(228\) | 0.180986 | 0.0119861 | ||||||||
\(229\) | 13.4343 | 0.887762 | 0.443881 | − | 0.896086i | \(-0.353601\pi\) | ||||
0.443881 | + | 0.896086i | \(0.353601\pi\) | |||||||
\(230\) | 17.7392 | 1.16969 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.06565 | −0.398229 | ||||||||
\(233\) | 6.10113 | 0.399698 | 0.199849 | − | 0.979827i | \(-0.435955\pi\) | ||||
0.199849 | + | 0.979827i | \(0.435955\pi\) | |||||||
\(234\) | −3.21448 | −0.210137 | ||||||||
\(235\) | 49.6803 | 3.24079 | ||||||||
\(236\) | −3.54036 | −0.230458 | ||||||||
\(237\) | −2.09447 | −0.136050 | ||||||||
\(238\) | 13.7568 | 0.891723 | ||||||||
\(239\) | 3.36137 | 0.217429 | 0.108714 | − | 0.994073i | \(-0.465327\pi\) | ||||
0.108714 | + | 0.994073i | \(0.465327\pi\) | |||||||
\(240\) | 0.739025 | 0.0477039 | ||||||||
\(241\) | 7.88799 | 0.508110 | 0.254055 | − | 0.967190i | \(-0.418236\pi\) | ||||
0.254055 | + | 0.967190i | \(0.418236\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.81568 | 0.308926 | ||||||||
\(244\) | −9.05057 | −0.579403 | ||||||||
\(245\) | 22.1627 | 1.41592 | ||||||||
\(246\) | 1.20781 | 0.0770074 | ||||||||
\(247\) | −1.08332 | −0.0689301 | ||||||||
\(248\) | −7.26098 | −0.461072 | ||||||||
\(249\) | 3.19546 | 0.202504 | ||||||||
\(250\) | −27.2501 | −1.72345 | ||||||||
\(251\) | −12.7254 | −0.803221 | −0.401611 | − | 0.915811i | \(-0.631549\pi\) | ||||
−0.401611 | + | 0.915811i | \(0.631549\pi\) | |||||||
\(252\) | 10.4604 | 0.658942 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.52862 | −0.158659 | ||||||||
\(255\) | 2.88392 | 0.180598 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.2979 | −0.767124 | −0.383562 | − | 0.923515i | \(-0.625303\pi\) | ||||
−0.383562 | + | 0.923515i | \(0.625303\pi\) | |||||||
\(258\) | 0.833491 | 0.0518909 | ||||||||
\(259\) | −2.65843 | −0.165187 | ||||||||
\(260\) | −4.42355 | −0.274337 | ||||||||
\(261\) | −17.9982 | −1.11406 | ||||||||
\(262\) | −12.6080 | −0.778925 | ||||||||
\(263\) | −7.82369 | −0.482429 | −0.241215 | − | 0.970472i | \(-0.577546\pi\) | ||||
−0.241215 | + | 0.970472i | \(0.577546\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0658 | 1.10977 | ||||||||
\(266\) | 3.52528 | 0.216149 | ||||||||
\(267\) | 2.22549 | 0.136198 | ||||||||
\(268\) | 1.35864 | 0.0829921 | ||||||||
\(269\) | 2.10113 | 0.128108 | 0.0640541 | − | 0.997946i | \(-0.479597\pi\) | ||||
0.0640541 | + | 0.997946i | \(0.479597\pi\) | |||||||
\(270\) | 4.40994 | 0.268381 | ||||||||
\(271\) | −16.0841 | −0.977037 | −0.488518 | − | 0.872554i | \(-0.662463\pi\) | ||||
−0.488518 | + | 0.872554i | \(0.662463\pi\) | |||||||
\(272\) | 3.90234 | 0.236614 | ||||||||
\(273\) | 0.691189 | 0.0418327 | ||||||||
\(274\) | −0.489194 | −0.0295533 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.786258 | −0.0473272 | ||||||||
\(277\) | −2.06431 | −0.124032 | −0.0620161 | − | 0.998075i | \(-0.519753\pi\) | ||||
−0.0620161 | + | 0.998075i | \(0.519753\pi\) | |||||||
\(278\) | 14.0245 | 0.841132 | ||||||||
\(279\) | −21.5451 | −1.28987 | ||||||||
\(280\) | 14.3949 | 0.860258 | ||||||||
\(281\) | 10.5108 | 0.627022 | 0.313511 | − | 0.949585i | \(-0.398495\pi\) | ||||
0.313511 | + | 0.949585i | \(0.398495\pi\) | |||||||
\(282\) | −2.20199 | −0.131127 | ||||||||
\(283\) | 16.4480 | 0.977733 | 0.488867 | − | 0.872358i | \(-0.337410\pi\) | ||||
0.488867 | + | 0.872358i | \(0.337410\pi\) | |||||||
\(284\) | −8.96724 | −0.532108 | ||||||||
\(285\) | 0.739025 | 0.0437761 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.5260 | 1.38870 | ||||||||
\(288\) | 2.96724 | 0.174847 | ||||||||
\(289\) | −1.77178 | −0.104222 | ||||||||
\(290\) | −24.7680 | −1.45443 | ||||||||
\(291\) | 2.98505 | 0.174987 | ||||||||
\(292\) | −8.26431 | −0.483632 | ||||||||
\(293\) | 25.4166 | 1.48485 | 0.742427 | − | 0.669927i | \(-0.233675\pi\) | ||||
0.742427 | + | 0.669927i | \(0.233675\pi\) | |||||||
\(294\) | −0.982324 | −0.0572903 | ||||||||
\(295\) | −14.4564 | −0.841686 | ||||||||
\(296\) | −0.754105 | −0.0438315 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.0204 | −1.10182 | ||||||||
\(299\) | 4.70627 | 0.272171 | ||||||||
\(300\) | 2.11274 | 0.121979 | ||||||||
\(301\) | 16.2349 | 0.935763 | ||||||||
\(302\) | −13.9043 | −0.800104 | ||||||||
\(303\) | 1.76265 | 0.101262 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −36.9564 | −2.11612 | ||||||||
\(306\) | 11.5792 | 0.661938 | ||||||||
\(307\) | −3.07925 | −0.175742 | −0.0878711 | − | 0.996132i | \(-0.528006\pi\) | ||||
−0.0878711 | + | 0.996132i | \(0.528006\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.42762 | −0.0812143 | ||||||||
\(310\) | −29.6489 | −1.68394 | ||||||||
\(311\) | 22.8309 | 1.29462 | 0.647311 | − | 0.762226i | \(-0.275894\pi\) | ||||
0.647311 | + | 0.762226i | \(0.275894\pi\) | |||||||
\(312\) | 0.196066 | 0.0111001 | ||||||||
\(313\) | 0.646443 | 0.0365391 | 0.0182696 | − | 0.999833i | \(-0.494184\pi\) | ||||
0.0182696 | + | 0.999833i | \(0.494184\pi\) | |||||||
\(314\) | −3.19273 | −0.180176 | ||||||||
\(315\) | 42.7131 | 2.40661 | ||||||||
\(316\) | −11.5725 | −0.651005 | ||||||||
\(317\) | −16.4376 | −0.923228 | −0.461614 | − | 0.887081i | \(-0.652730\pi\) | ||||
−0.461614 | + | 0.887081i | \(0.652730\pi\) | |||||||
\(318\) | −0.800735 | −0.0449030 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.08332 | 0.228265 | ||||||||
\(321\) | 2.23535 | 0.124765 | ||||||||
\(322\) | −15.3149 | −0.853464 | ||||||||
\(323\) | 3.90234 | 0.217132 | ||||||||
\(324\) | 8.70627 | 0.483682 | ||||||||
\(325\) | −12.6462 | −0.701483 | ||||||||
\(326\) | −6.15998 | −0.341170 | ||||||||
\(327\) | 2.89379 | 0.160027 | ||||||||
\(328\) | 6.67351 | 0.368483 | ||||||||
\(329\) | −42.8909 | −2.36465 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.9201 | −1.42470 | −0.712350 | − | 0.701824i | \(-0.752369\pi\) | ||||
−0.712350 | + | 0.701824i | \(0.752369\pi\) | |||||||
\(332\) | 17.6558 | 0.968990 | ||||||||
\(333\) | −2.23761 | −0.122620 | ||||||||
\(334\) | 6.92075 | 0.378686 | ||||||||
\(335\) | 5.54776 | 0.303107 | ||||||||
\(336\) | −0.638028 | −0.0348073 | ||||||||
\(337\) | 30.1177 | 1.64061 | 0.820307 | − | 0.571923i | \(-0.193802\pi\) | ||||
0.820307 | + | 0.571923i | \(0.193802\pi\) | |||||||
\(338\) | 11.8264 | 0.643272 | ||||||||
\(339\) | −0.0591138 | −0.00321062 | ||||||||
\(340\) | 15.9345 | 0.864169 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.96724 | 0.160450 | ||||||||
\(343\) | 5.54309 | 0.299299 | ||||||||
\(344\) | 4.60527 | 0.248300 | ||||||||
\(345\) | −3.21054 | −0.172850 | ||||||||
\(346\) | −22.3444 | −1.20124 | ||||||||
\(347\) | −14.8604 | −0.797750 | −0.398875 | − | 0.917005i | \(-0.630599\pi\) | ||||
−0.398875 | + | 0.917005i | \(0.630599\pi\) | |||||||
\(348\) | 1.09780 | 0.0588482 | ||||||||
\(349\) | −21.7760 | −1.16564 | −0.582821 | − | 0.812601i | \(-0.698051\pi\) | ||||
−0.582821 | + | 0.812601i | \(0.698051\pi\) | |||||||
\(350\) | 41.1524 | 2.19969 | ||||||||
\(351\) | 1.16997 | 0.0624486 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.4658 | −1.35541 | −0.677705 | − | 0.735334i | \(-0.737025\pi\) | ||||
−0.677705 | + | 0.735334i | \(0.737025\pi\) | |||||||
\(354\) | 0.640757 | 0.0340558 | ||||||||
\(355\) | −36.6161 | −1.94338 | ||||||||
\(356\) | 12.2965 | 0.651711 | ||||||||
\(357\) | −2.48980 | −0.131774 | ||||||||
\(358\) | −2.37705 | −0.125631 | ||||||||
\(359\) | 1.72728 | 0.0911622 | 0.0455811 | − | 0.998961i | \(-0.485486\pi\) | ||||
0.0455811 | + | 0.998961i | \(0.485486\pi\) | |||||||
\(360\) | 12.1162 | 0.638580 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 25.5137 | 1.34097 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.81901 | 0.200171 | ||||||||
\(365\) | −33.7458 | −1.76634 | ||||||||
\(366\) | 1.63803 | 0.0856211 | ||||||||
\(367\) | 12.6231 | 0.658919 | 0.329460 | − | 0.944170i | \(-0.393133\pi\) | ||||
0.329460 | + | 0.944170i | \(0.393133\pi\) | |||||||
\(368\) | −4.34430 | −0.226462 | ||||||||
\(369\) | 19.8019 | 1.03085 | ||||||||
\(370\) | −3.07925 | −0.160083 | ||||||||
\(371\) | −15.5969 | −0.809748 | ||||||||
\(372\) | 1.31414 | 0.0681348 | ||||||||
\(373\) | −1.96997 | −0.102001 | −0.0510007 | − | 0.998699i | \(-0.516241\pi\) | ||||
−0.0510007 | + | 0.998699i | \(0.516241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.93189 | 0.254682 | ||||||||
\(376\) | −12.1666 | −0.627447 | ||||||||
\(377\) | −6.57104 | −0.338426 | ||||||||
\(378\) | −3.80727 | −0.195825 | ||||||||
\(379\) | −12.1837 | −0.625835 | −0.312918 | − | 0.949780i | \(-0.601306\pi\) | ||||
−0.312918 | + | 0.949780i | \(0.601306\pi\) | |||||||
\(380\) | 4.08332 | 0.209470 | ||||||||
\(381\) | 0.457644 | 0.0234458 | ||||||||
\(382\) | 19.8580 | 1.01602 | ||||||||
\(383\) | 36.3472 | 1.85725 | 0.928627 | − | 0.371016i | \(-0.120990\pi\) | ||||
0.928627 | + | 0.371016i | \(0.120990\pi\) | |||||||
\(384\) | −0.180986 | −0.00923591 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.5464 | −1.14758 | ||||||||
\(387\) | 13.6650 | 0.694629 | ||||||||
\(388\) | 16.4933 | 0.837319 | ||||||||
\(389\) | 14.3444 | 0.727291 | 0.363646 | − | 0.931537i | \(-0.381532\pi\) | ||||
0.363646 | + | 0.931537i | \(0.381532\pi\) | |||||||
\(390\) | 0.800601 | 0.0405400 | ||||||||
\(391\) | −16.9529 | −0.857345 | ||||||||
\(392\) | −5.42762 | −0.274136 | ||||||||
\(393\) | 2.28187 | 0.115105 | ||||||||
\(394\) | −12.3333 | −0.621342 | ||||||||
\(395\) | −47.2543 | −2.37762 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.8468 | −1.74891 | −0.874456 | − | 0.485105i | \(-0.838781\pi\) | ||||
−0.874456 | + | 0.485105i | \(0.838781\pi\) | |||||||
\(398\) | −6.86625 | −0.344174 | ||||||||
\(399\) | −0.638028 | −0.0319413 | ||||||||
\(400\) | 11.6735 | 0.583676 | ||||||||
\(401\) | 34.6599 | 1.73083 | 0.865417 | − | 0.501053i | \(-0.167054\pi\) | ||||
0.865417 | + | 0.501053i | \(0.167054\pi\) | |||||||
\(402\) | −0.245895 | −0.0122641 | ||||||||
\(403\) | −7.86597 | −0.391832 | ||||||||
\(404\) | 9.73916 | 0.484541 | ||||||||
\(405\) | 35.5505 | 1.76652 | ||||||||
\(406\) | 21.3831 | 1.06123 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.706269 | −0.0349655 | ||||||||
\(409\) | 36.3459 | 1.79719 | 0.898595 | − | 0.438780i | \(-0.144589\pi\) | ||||
0.898595 | + | 0.438780i | \(0.144589\pi\) | |||||||
\(410\) | 27.2501 | 1.34579 | ||||||||
\(411\) | 0.0885374 | 0.00436723 | ||||||||
\(412\) | −7.88799 | −0.388613 | ||||||||
\(413\) | 12.4808 | 0.614139 | ||||||||
\(414\) | −12.8906 | −0.633538 | ||||||||
\(415\) | 72.0945 | 3.53898 | ||||||||
\(416\) | 1.08332 | 0.0531142 | ||||||||
\(417\) | −2.53824 | −0.124298 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.2663 | 0.501542 | 0.250771 | − | 0.968046i | \(-0.419316\pi\) | ||||
0.250771 | + | 0.968046i | \(0.419316\pi\) | |||||||
\(420\) | −2.60527 | −0.127124 | ||||||||
\(421\) | −3.27805 | −0.159762 | −0.0798811 | − | 0.996804i | \(-0.525454\pi\) | ||||
−0.0798811 | + | 0.996804i | \(0.525454\pi\) | |||||||
\(422\) | 8.80740 | 0.428737 | ||||||||
\(423\) | −36.1014 | −1.75531 | ||||||||
\(424\) | −4.42429 | −0.214862 | ||||||||
\(425\) | 45.5540 | 2.20969 | ||||||||
\(426\) | 1.62295 | 0.0786321 | ||||||||
\(427\) | 31.9058 | 1.54403 | ||||||||
\(428\) | 12.3510 | 0.597006 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.8048 | 0.906848 | ||||||||
\(431\) | 15.2775 | 0.735893 | 0.367946 | − | 0.929847i | \(-0.380061\pi\) | ||||
0.367946 | + | 0.929847i | \(0.380061\pi\) | |||||||
\(432\) | −1.07999 | −0.0519610 | ||||||||
\(433\) | 33.8113 | 1.62487 | 0.812435 | − | 0.583052i | \(-0.198142\pi\) | ||||
0.812435 | + | 0.583052i | \(0.198142\pi\) | |||||||
\(434\) | 25.5970 | 1.22869 | ||||||||
\(435\) | 4.48266 | 0.214927 | ||||||||
\(436\) | 15.9890 | 0.765734 | ||||||||
\(437\) | −4.34430 | −0.207816 | ||||||||
\(438\) | 1.49573 | 0.0714685 | ||||||||
\(439\) | −5.15290 | −0.245935 | −0.122967 | − | 0.992411i | \(-0.539241\pi\) | ||||
−0.122967 | + | 0.992411i | \(0.539241\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.1051 | −0.766908 | ||||||||
\(442\) | 4.22748 | 0.201081 | ||||||||
\(443\) | 0.986260 | 0.0468586 | 0.0234293 | − | 0.999725i | \(-0.492542\pi\) | ||||
0.0234293 | + | 0.999725i | \(0.492542\pi\) | |||||||
\(444\) | 0.136483 | 0.00647718 | ||||||||
\(445\) | 50.2104 | 2.38020 | ||||||||
\(446\) | −3.80467 | −0.180156 | ||||||||
\(447\) | 3.44243 | 0.162821 | ||||||||
\(448\) | −3.52528 | −0.166554 | ||||||||
\(449\) | −28.3689 | −1.33881 | −0.669406 | − | 0.742897i | \(-0.733451\pi\) | ||||
−0.669406 | + | 0.742897i | \(0.733451\pi\) | |||||||
\(450\) | 34.6382 | 1.63286 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.326620 | −0.0153629 | ||||||||
\(453\) | 2.51649 | 0.118235 | ||||||||
\(454\) | −5.58353 | −0.262048 | ||||||||
\(455\) | 15.5943 | 0.731070 | ||||||||
\(456\) | −0.180986 | −0.00847546 | ||||||||
\(457\) | −4.74943 | −0.222169 | −0.111085 | − | 0.993811i | \(-0.535432\pi\) | ||||
−0.111085 | + | 0.993811i | \(0.535432\pi\) | |||||||
\(458\) | −13.4343 | −0.627743 | ||||||||
\(459\) | −4.21448 | −0.196715 | ||||||||
\(460\) | −17.7392 | −0.827093 | ||||||||
\(461\) | 0.587462 | 0.0273608 | 0.0136804 | − | 0.999906i | \(-0.495645\pi\) | ||||
0.0136804 | + | 0.999906i | \(0.495645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.2324 | −1.12618 | −0.563088 | − | 0.826397i | \(-0.690387\pi\) | ||||
−0.563088 | + | 0.826397i | \(0.690387\pi\) | |||||||
\(464\) | 6.06565 | 0.281591 | ||||||||
\(465\) | 5.36604 | 0.248844 | ||||||||
\(466\) | −6.10113 | −0.282629 | ||||||||
\(467\) | 36.0423 | 1.66784 | 0.833919 | − | 0.551887i | \(-0.186092\pi\) | ||||
0.833919 | + | 0.551887i | \(0.186092\pi\) | |||||||
\(468\) | 3.21448 | 0.148589 | ||||||||
\(469\) | −4.78959 | −0.221163 | ||||||||
\(470\) | −49.6803 | −2.29158 | ||||||||
\(471\) | 0.577841 | 0.0266255 | ||||||||
\(472\) | 3.54036 | 0.162958 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.09447 | 0.0962020 | ||||||||
\(475\) | 11.6735 | 0.535618 | ||||||||
\(476\) | −13.7568 | −0.630543 | ||||||||
\(477\) | −13.1279 | −0.601087 | ||||||||
\(478\) | −3.36137 | −0.153745 | ||||||||
\(479\) | −10.3904 | −0.474749 | −0.237374 | − | 0.971418i | \(-0.576287\pi\) | ||||
−0.237374 | + | 0.971418i | \(0.576287\pi\) | |||||||
\(480\) | −0.739025 | −0.0337317 | ||||||||
\(481\) | −0.816938 | −0.0372492 | ||||||||
\(482\) | −7.88799 | −0.359288 | ||||||||
\(483\) | 2.77178 | 0.126120 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 67.3473 | 3.05808 | ||||||||
\(486\) | −4.81568 | −0.218444 | ||||||||
\(487\) | 27.5903 | 1.25024 | 0.625118 | − | 0.780530i | \(-0.285051\pi\) | ||||
0.625118 | + | 0.780530i | \(0.285051\pi\) | |||||||
\(488\) | 9.05057 | 0.409700 | ||||||||
\(489\) | 1.11487 | 0.0504162 | ||||||||
\(490\) | −22.1627 | −1.00121 | ||||||||
\(491\) | −27.0436 | −1.22046 | −0.610231 | − | 0.792224i | \(-0.708923\pi\) | ||||
−0.610231 | + | 0.792224i | \(0.708923\pi\) | |||||||
\(492\) | −1.20781 | −0.0544525 | ||||||||
\(493\) | 23.6702 | 1.06605 | ||||||||
\(494\) | 1.08332 | 0.0487409 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.26098 | 0.326027 | ||||||||
\(497\) | 31.6121 | 1.41800 | ||||||||
\(498\) | −3.19546 | −0.143192 | ||||||||
\(499\) | 20.2663 | 0.907244 | 0.453622 | − | 0.891194i | \(-0.350132\pi\) | ||||
0.453622 | + | 0.891194i | \(0.350132\pi\) | |||||||
\(500\) | 27.2501 | 1.21866 | ||||||||
\(501\) | −1.25256 | −0.0559602 | ||||||||
\(502\) | 12.7254 | 0.567963 | ||||||||
\(503\) | −43.4573 | −1.93767 | −0.968833 | − | 0.247716i | \(-0.920320\pi\) | ||||
−0.968833 | + | 0.247716i | \(0.920320\pi\) | |||||||
\(504\) | −10.4604 | −0.465942 | ||||||||
\(505\) | 39.7681 | 1.76966 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.14042 | −0.0950593 | ||||||||
\(508\) | 2.52862 | 0.112189 | ||||||||
\(509\) | 19.3824 | 0.859109 | 0.429554 | − | 0.903041i | \(-0.358671\pi\) | ||||
0.429554 | + | 0.903041i | \(0.358671\pi\) | |||||||
\(510\) | −2.88392 | −0.127702 | ||||||||
\(511\) | 29.1340 | 1.28881 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.07999 | −0.0476827 | ||||||||
\(514\) | 12.2979 | 0.542439 | ||||||||
\(515\) | −32.2092 | −1.41931 | ||||||||
\(516\) | −0.833491 | −0.0366924 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.65843 | 0.116805 | ||||||||
\(519\) | 4.04403 | 0.177513 | ||||||||
\(520\) | 4.42355 | 0.193985 | ||||||||
\(521\) | −16.0302 | −0.702294 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(522\) | 17.9982 | 0.787762 | ||||||||
\(523\) | 34.7772 | 1.52070 | 0.760351 | − | 0.649512i | \(-0.225027\pi\) | ||||
0.760351 | + | 0.649512i | \(0.225027\pi\) | |||||||
\(524\) | 12.6080 | 0.550783 | ||||||||
\(525\) | −7.44802 | −0.325058 | ||||||||
\(526\) | 7.82369 | 0.341129 | ||||||||
\(527\) | 28.3348 | 1.23428 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.12709 | −0.179439 | ||||||||
\(530\) | −18.0658 | −0.784727 | ||||||||
\(531\) | 10.5051 | 0.455883 | ||||||||
\(532\) | −3.52528 | −0.152840 | ||||||||
\(533\) | 7.22956 | 0.313147 | ||||||||
\(534\) | −2.22549 | −0.0963064 | ||||||||
\(535\) | 50.4329 | 2.18041 | ||||||||
\(536\) | −1.35864 | −0.0586843 | ||||||||
\(537\) | 0.430214 | 0.0185651 | ||||||||
\(538\) | −2.10113 | −0.0905862 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.40994 | −0.189774 | ||||||||
\(541\) | 18.9863 | 0.816283 | 0.408142 | − | 0.912919i | \(-0.366177\pi\) | ||||
0.408142 | + | 0.912919i | \(0.366177\pi\) | |||||||
\(542\) | 16.0841 | 0.690869 | ||||||||
\(543\) | −4.61762 | −0.198161 | ||||||||
\(544\) | −3.90234 | −0.167311 | ||||||||
\(545\) | 65.2882 | 2.79664 | ||||||||
\(546\) | −0.691189 | −0.0295802 | ||||||||
\(547\) | −10.9784 | −0.469402 | −0.234701 | − | 0.972068i | \(-0.575411\pi\) | ||||
−0.234701 | + | 0.972068i | \(0.575411\pi\) | |||||||
\(548\) | 0.489194 | 0.0208973 | ||||||||
\(549\) | 26.8552 | 1.14615 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.06565 | 0.258405 | ||||||||
\(552\) | 0.786258 | 0.0334654 | ||||||||
\(553\) | 40.7964 | 1.73484 | ||||||||
\(554\) | 2.06431 | 0.0877039 | ||||||||
\(555\) | 0.557302 | 0.0236562 | ||||||||
\(556\) | −14.0245 | −0.594770 | ||||||||
\(557\) | −27.3905 | −1.16057 | −0.580287 | − | 0.814412i | \(-0.697059\pi\) | ||||
−0.580287 | + | 0.814412i | \(0.697059\pi\) | |||||||
\(558\) | 21.5451 | 0.912076 | ||||||||
\(559\) | 4.98899 | 0.211012 | ||||||||
\(560\) | −14.3949 | −0.608294 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.5108 | −0.443372 | ||||||||
\(563\) | −23.4427 | −0.987992 | −0.493996 | − | 0.869464i | \(-0.664464\pi\) | ||||
−0.493996 | + | 0.869464i | \(0.664464\pi\) | |||||||
\(564\) | 2.20199 | 0.0927207 | ||||||||
\(565\) | −1.33370 | −0.0561090 | ||||||||
\(566\) | −16.4480 | −0.691362 | ||||||||
\(567\) | −30.6921 | −1.28895 | ||||||||
\(568\) | 8.96724 | 0.376257 | ||||||||
\(569\) | −16.5370 | −0.693268 | −0.346634 | − | 0.938000i | \(-0.612675\pi\) | ||||
−0.346634 | + | 0.938000i | \(0.612675\pi\) | |||||||
\(570\) | −0.739025 | −0.0309543 | ||||||||
\(571\) | −26.9700 | −1.12866 | −0.564329 | − | 0.825550i | \(-0.690865\pi\) | ||||
−0.564329 | + | 0.825550i | \(0.690865\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.59402 | −0.150142 | ||||||||
\(574\) | −23.5260 | −0.981957 | ||||||||
\(575\) | −50.7132 | −2.11489 | ||||||||
\(576\) | −2.96724 | −0.123635 | ||||||||
\(577\) | 1.66931 | 0.0694943 | 0.0347472 | − | 0.999396i | \(-0.488937\pi\) | ||||
0.0347472 | + | 0.999396i | \(0.488937\pi\) | |||||||
\(578\) | 1.77178 | 0.0736964 | ||||||||
\(579\) | 4.08059 | 0.169584 | ||||||||
\(580\) | 24.7680 | 1.02843 | ||||||||
\(581\) | −62.2418 | −2.58223 | ||||||||
\(582\) | −2.98505 | −0.123734 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 8.26431 | 0.341979 | ||||||||
\(585\) | 13.1257 | 0.542683 | ||||||||
\(586\) | −25.4166 | −1.04995 | ||||||||
\(587\) | −19.7023 | −0.813202 | −0.406601 | − | 0.913606i | \(-0.633286\pi\) | ||||
−0.406601 | + | 0.913606i | \(0.633286\pi\) | |||||||
\(588\) | 0.982324 | 0.0405104 | ||||||||
\(589\) | 7.26098 | 0.299183 | ||||||||
\(590\) | 14.4564 | 0.595162 | ||||||||
\(591\) | 2.23215 | 0.0918186 | ||||||||
\(592\) | 0.754105 | 0.0309935 | ||||||||
\(593\) | −25.3604 | −1.04142 | −0.520712 | − | 0.853732i | \(-0.674334\pi\) | ||||
−0.520712 | + | 0.853732i | \(0.674334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −56.1736 | −2.30289 | ||||||||
\(596\) | 19.0204 | 0.779106 | ||||||||
\(597\) | 1.24270 | 0.0508602 | ||||||||
\(598\) | −4.70627 | −0.192454 | ||||||||
\(599\) | −8.05463 | −0.329103 | −0.164552 | − | 0.986368i | \(-0.552618\pi\) | ||||
−0.164552 | + | 0.986368i | \(0.552618\pi\) | |||||||
\(600\) | −2.11274 | −0.0862525 | ||||||||
\(601\) | −31.5522 | −1.28704 | −0.643521 | − | 0.765428i | \(-0.722527\pi\) | ||||
−0.643521 | + | 0.765428i | \(0.722527\pi\) | |||||||
\(602\) | −16.2349 | −0.661684 | ||||||||
\(603\) | −4.03142 | −0.164172 | ||||||||
\(604\) | 13.9043 | 0.565759 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.76265 | −0.0716029 | ||||||||
\(607\) | −35.8403 | −1.45471 | −0.727356 | − | 0.686260i | \(-0.759251\pi\) | ||||
−0.727356 | + | 0.686260i | \(0.759251\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −3.87005 | −0.156822 | ||||||||
\(610\) | 36.9564 | 1.49632 | ||||||||
\(611\) | −13.1804 | −0.533221 | ||||||||
\(612\) | −11.5792 | −0.468061 | ||||||||
\(613\) | 19.3522 | 0.781629 | 0.390814 | − | 0.920470i | \(-0.372193\pi\) | ||||
0.390814 | + | 0.920470i | \(0.372193\pi\) | |||||||
\(614\) | 3.07925 | 0.124269 | ||||||||
\(615\) | −4.93189 | −0.198873 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.2966 | −0.776852 | −0.388426 | − | 0.921480i | \(-0.626981\pi\) | ||||
−0.388426 | + | 0.921480i | \(0.626981\pi\) | |||||||
\(618\) | 1.42762 | 0.0574272 | ||||||||
\(619\) | −8.91408 | −0.358287 | −0.179144 | − | 0.983823i | \(-0.557333\pi\) | ||||
−0.179144 | + | 0.983823i | \(0.557333\pi\) | |||||||
\(620\) | 29.6489 | 1.19073 | ||||||||
\(621\) | 4.69179 | 0.188275 | ||||||||
\(622\) | −22.8309 | −0.915435 | ||||||||
\(623\) | −43.3485 | −1.73672 | ||||||||
\(624\) | −0.196066 | −0.00784893 | ||||||||
\(625\) | 52.9033 | 2.11613 | ||||||||
\(626\) | −0.646443 | −0.0258371 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.19273 | 0.127404 | ||||||||
\(629\) | 2.94277 | 0.117336 | ||||||||
\(630\) | −42.7131 | −1.70173 | ||||||||
\(631\) | −9.54383 | −0.379934 | −0.189967 | − | 0.981790i | \(-0.560838\pi\) | ||||
−0.189967 | + | 0.981790i | \(0.560838\pi\) | |||||||
\(632\) | 11.5725 | 0.460330 | ||||||||
\(633\) | −1.59402 | −0.0633565 | ||||||||
\(634\) | 16.4376 | 0.652821 | ||||||||
\(635\) | 10.3251 | 0.409741 | ||||||||
\(636\) | 0.800735 | 0.0317512 | ||||||||
\(637\) | −5.87985 | −0.232968 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.6080 | 1.05260 | ||||||||
\(640\) | −4.08332 | −0.161407 | ||||||||
\(641\) | 15.7458 | 0.621923 | 0.310961 | − | 0.950423i | \(-0.399349\pi\) | ||||
0.310961 | + | 0.950423i | \(0.399349\pi\) | |||||||
\(642\) | −2.23535 | −0.0882224 | ||||||||
\(643\) | −18.0423 | −0.711518 | −0.355759 | − | 0.934578i | \(-0.615778\pi\) | ||||
−0.355759 | + | 0.934578i | \(0.615778\pi\) | |||||||
\(644\) | 15.3149 | 0.603491 | ||||||||
\(645\) | −3.40341 | −0.134009 | ||||||||
\(646\) | −3.90234 | −0.153535 | ||||||||
\(647\) | 13.5850 | 0.534081 | 0.267041 | − | 0.963685i | \(-0.413954\pi\) | ||||
0.267041 | + | 0.963685i | \(0.413954\pi\) | |||||||
\(648\) | −8.70627 | −0.342015 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 12.6462 | 0.496023 | ||||||||
\(651\) | −4.63270 | −0.181570 | ||||||||
\(652\) | 6.15998 | 0.241243 | ||||||||
\(653\) | −11.9429 | −0.467362 | −0.233681 | − | 0.972313i | \(-0.575077\pi\) | ||||
−0.233681 | + | 0.972313i | \(0.575077\pi\) | |||||||
\(654\) | −2.89379 | −0.113156 | ||||||||
\(655\) | 51.4825 | 2.01159 | ||||||||
\(656\) | −6.67351 | −0.260557 | ||||||||
\(657\) | 24.5222 | 0.956703 | ||||||||
\(658\) | 42.8909 | 1.67206 | ||||||||
\(659\) | 12.2721 | 0.478054 | 0.239027 | − | 0.971013i | \(-0.423172\pi\) | ||||
0.239027 | + | 0.971013i | \(0.423172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.9831 | 0.660564 | 0.330282 | − | 0.943882i | \(-0.392856\pi\) | ||||
0.330282 | + | 0.943882i | \(0.392856\pi\) | |||||||
\(662\) | 25.9201 | 1.00742 | ||||||||
\(663\) | −0.765116 | −0.0297146 | ||||||||
\(664\) | −17.6558 | −0.685179 | ||||||||
\(665\) | −14.3949 | −0.558209 | ||||||||
\(666\) | 2.23761 | 0.0867057 | ||||||||
\(667\) | −26.3510 | −1.02031 | ||||||||
\(668\) | −6.92075 | −0.267772 | ||||||||
\(669\) | 0.688593 | 0.0266225 | ||||||||
\(670\) | −5.54776 | −0.214329 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.638028 | 0.0246124 | ||||||||
\(673\) | 45.7965 | 1.76533 | 0.882663 | − | 0.470006i | \(-0.155748\pi\) | ||||
0.882663 | + | 0.470006i | \(0.155748\pi\) | |||||||
\(674\) | −30.1177 | −1.16009 | ||||||||
\(675\) | −12.6073 | −0.485254 | ||||||||
\(676\) | −11.8264 | −0.454862 | ||||||||
\(677\) | −7.64483 | −0.293815 | −0.146907 | − | 0.989150i | \(-0.546932\pi\) | ||||
−0.146907 | + | 0.989150i | \(0.546932\pi\) | |||||||
\(678\) | 0.0591138 | 0.00227025 | ||||||||
\(679\) | −58.1434 | −2.23134 | ||||||||
\(680\) | −15.9345 | −0.611060 | ||||||||
\(681\) | 1.01054 | 0.0387240 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.5426 | −1.51306 | −0.756528 | − | 0.653961i | \(-0.773106\pi\) | ||||
−0.756528 | + | 0.653961i | \(0.773106\pi\) | |||||||
\(684\) | −2.96724 | −0.113455 | ||||||||
\(685\) | 1.99754 | 0.0763220 | ||||||||
\(686\) | −5.54309 | −0.211636 | ||||||||
\(687\) | 2.43142 | 0.0927645 | ||||||||
\(688\) | −4.60527 | −0.175574 | ||||||||
\(689\) | −4.79292 | −0.182596 | ||||||||
\(690\) | 3.21054 | 0.122223 | ||||||||
\(691\) | −14.9274 | −0.567866 | −0.283933 | − | 0.958844i | \(-0.591639\pi\) | ||||
−0.283933 | + | 0.958844i | \(0.591639\pi\) | |||||||
\(692\) | 22.3444 | 0.849408 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.8604 | 0.564094 | ||||||||
\(695\) | −57.2664 | −2.17224 | ||||||||
\(696\) | −1.09780 | −0.0416119 | ||||||||
\(697\) | −26.0423 | −0.986422 | ||||||||
\(698\) | 21.7760 | 0.824233 | ||||||||
\(699\) | 1.10422 | 0.0417655 | ||||||||
\(700\) | −41.1524 | −1.55542 | ||||||||
\(701\) | −35.9728 | −1.35867 | −0.679337 | − | 0.733827i | \(-0.737732\pi\) | ||||
−0.679337 | + | 0.733827i | \(0.737732\pi\) | |||||||
\(702\) | −1.16997 | −0.0441579 | ||||||||
\(703\) | 0.754105 | 0.0284416 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.99145 | 0.338638 | ||||||||
\(706\) | 25.4658 | 0.958419 | ||||||||
\(707\) | −34.3333 | −1.29124 | ||||||||
\(708\) | −0.640757 | −0.0240811 | ||||||||
\(709\) | −0.311540 | −0.0117001 | −0.00585007 | − | 0.999983i | \(-0.501862\pi\) | ||||
−0.00585007 | + | 0.999983i | \(0.501862\pi\) | |||||||
\(710\) | 36.6161 | 1.37418 | ||||||||
\(711\) | 34.3385 | 1.28779 | ||||||||
\(712\) | −12.2965 | −0.460829 | ||||||||
\(713\) | −31.5438 | −1.18133 | ||||||||
\(714\) | 2.48980 | 0.0931783 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.37705 | 0.0888346 | ||||||||
\(717\) | 0.608362 | 0.0227197 | ||||||||
\(718\) | −1.72728 | −0.0644614 | ||||||||
\(719\) | −35.7163 | −1.33199 | −0.665996 | − | 0.745955i | \(-0.731993\pi\) | ||||
−0.665996 | + | 0.745955i | \(0.731993\pi\) | |||||||
\(720\) | −12.1162 | −0.451545 | ||||||||
\(721\) | 27.8074 | 1.03560 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 1.42762 | 0.0530937 | ||||||||
\(724\) | −25.5137 | −0.948208 | ||||||||
\(725\) | 70.8074 | 2.62972 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.6337 | 0.653997 | 0.326999 | − | 0.945025i | \(-0.393963\pi\) | ||||
0.326999 | + | 0.945025i | \(0.393963\pi\) | |||||||
\(728\) | −3.81901 | −0.141542 | ||||||||
\(729\) | −25.2472 | −0.935083 | ||||||||
\(730\) | 33.7458 | 1.24899 | ||||||||
\(731\) | −17.9713 | −0.664693 | ||||||||
\(732\) | −1.63803 | −0.0605432 | ||||||||
\(733\) | 6.19680 | 0.228884 | 0.114442 | − | 0.993430i | \(-0.463492\pi\) | ||||
0.114442 | + | 0.993430i | \(0.463492\pi\) | |||||||
\(734\) | −12.6231 | −0.465926 | ||||||||
\(735\) | 4.01114 | 0.147953 | ||||||||
\(736\) | 4.34430 | 0.160133 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −19.8019 | −0.728920 | ||||||||
\(739\) | 5.18257 | 0.190644 | 0.0953219 | − | 0.995446i | \(-0.469612\pi\) | ||||
0.0953219 | + | 0.995446i | \(0.469612\pi\) | |||||||
\(740\) | 3.07925 | 0.113196 | ||||||||
\(741\) | −0.196066 | −0.00720267 | ||||||||
\(742\) | 15.5969 | 0.572579 | ||||||||
\(743\) | 51.1819 | 1.87768 | 0.938840 | − | 0.344353i | \(-0.111902\pi\) | ||||
0.938840 | + | 0.344353i | \(0.111902\pi\) | |||||||
\(744\) | −1.31414 | −0.0481786 | ||||||||
\(745\) | 77.6664 | 2.84548 | ||||||||
\(746\) | 1.96997 | 0.0721258 | ||||||||
\(747\) | −52.3892 | −1.91682 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43.5406 | −1.59094 | ||||||||
\(750\) | −4.93189 | −0.180087 | ||||||||
\(751\) | −32.0673 | −1.17015 | −0.585075 | − | 0.810979i | \(-0.698935\pi\) | ||||
−0.585075 | + | 0.810979i | \(0.698935\pi\) | |||||||
\(752\) | 12.1666 | 0.443672 | ||||||||
\(753\) | −2.30313 | −0.0839305 | ||||||||
\(754\) | 6.57104 | 0.239303 | ||||||||
\(755\) | 56.7758 | 2.06628 | ||||||||
\(756\) | 3.80727 | 0.138469 | ||||||||
\(757\) | −21.1762 | −0.769661 | −0.384830 | − | 0.922987i | \(-0.625740\pi\) | ||||
−0.384830 | + | 0.922987i | \(0.625740\pi\) | |||||||
\(758\) | 12.1837 | 0.442532 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.08332 | −0.148118 | ||||||||
\(761\) | −25.5169 | −0.924986 | −0.462493 | − | 0.886623i | \(-0.653045\pi\) | ||||
−0.462493 | + | 0.886623i | \(0.653045\pi\) | |||||||
\(762\) | −0.457644 | −0.0165787 | ||||||||
\(763\) | −56.3657 | −2.04058 | ||||||||
\(764\) | −19.8580 | −0.718436 | ||||||||
\(765\) | −47.2815 | −1.70947 | ||||||||
\(766\) | −36.3472 | −1.31328 | ||||||||
\(767\) | 3.83535 | 0.138486 | ||||||||
\(768\) | 0.180986 | 0.00653078 | ||||||||
\(769\) | 2.92274 | 0.105397 | 0.0526984 | − | 0.998610i | \(-0.483218\pi\) | ||||
0.0526984 | + | 0.998610i | \(0.483218\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.22576 | −0.0801587 | ||||||||
\(772\) | 22.5464 | 0.811464 | ||||||||
\(773\) | −34.7509 | −1.24990 | −0.624952 | − | 0.780663i | \(-0.714881\pi\) | ||||
−0.624952 | + | 0.780663i | \(0.714881\pi\) | |||||||
\(774\) | −13.6650 | −0.491177 | ||||||||
\(775\) | 84.7611 | 3.04471 | ||||||||
\(776\) | −16.4933 | −0.592074 | ||||||||
\(777\) | −0.481140 | −0.0172608 | ||||||||
\(778\) | −14.3444 | −0.514273 | ||||||||
\(779\) | −6.67351 | −0.239103 | ||||||||
\(780\) | −0.800601 | −0.0286661 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 16.9529 | 0.606234 | ||||||||
\(783\) | −6.55083 | −0.234108 | ||||||||
\(784\) | 5.42762 | 0.193843 | ||||||||
\(785\) | 13.0370 | 0.465309 | ||||||||
\(786\) | −2.28187 | −0.0813918 | ||||||||
\(787\) | 17.8238 | 0.635351 | 0.317675 | − | 0.948200i | \(-0.397098\pi\) | ||||
0.317675 | + | 0.948200i | \(0.397098\pi\) | |||||||
\(788\) | 12.3333 | 0.439355 | ||||||||
\(789\) | −1.41598 | −0.0504102 | ||||||||
\(790\) | 47.2543 | 1.68123 | ||||||||
\(791\) | 1.15143 | 0.0409401 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.80467 | 0.348174 | ||||||||
\(794\) | 34.8468 | 1.23667 | ||||||||
\(795\) | 3.26966 | 0.115963 | ||||||||
\(796\) | 6.86625 | 0.243368 | ||||||||
\(797\) | −46.0418 | −1.63088 | −0.815441 | − | 0.578840i | \(-0.803506\pi\) | ||||
−0.815441 | + | 0.578840i | \(0.803506\pi\) | |||||||
\(798\) | 0.638028 | 0.0225859 | ||||||||
\(799\) | 47.4783 | 1.67966 | ||||||||
\(800\) | −11.6735 | −0.412721 | ||||||||
\(801\) | −36.4866 | −1.28919 | ||||||||
\(802\) | −34.6599 | −1.22388 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.245895 | 0.00867205 | ||||||||
\(805\) | 62.5355 | 2.20409 | ||||||||
\(806\) | 7.86597 | 0.277067 | ||||||||
\(807\) | 0.380276 | 0.0133863 | ||||||||
\(808\) | −9.73916 | −0.342622 | ||||||||
\(809\) | 53.4229 | 1.87825 | 0.939125 | − | 0.343575i | \(-0.111638\pi\) | ||||
0.939125 | + | 0.343575i | \(0.111638\pi\) | |||||||
\(810\) | −35.5505 | −1.24912 | ||||||||
\(811\) | −42.7552 | −1.50134 | −0.750669 | − | 0.660678i | \(-0.770269\pi\) | ||||
−0.750669 | + | 0.660678i | \(0.770269\pi\) | |||||||
\(812\) | −21.3831 | −0.750400 | ||||||||
\(813\) | −2.91099 | −0.102093 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.1532 | 0.881077 | ||||||||
\(816\) | 0.706269 | 0.0247244 | ||||||||
\(817\) | −4.60527 | −0.161118 | ||||||||
\(818\) | −36.3459 | −1.27080 | ||||||||
\(819\) | −11.3319 | −0.395970 | ||||||||
\(820\) | −27.2501 | −0.951615 | ||||||||
\(821\) | −27.5151 | −0.960285 | −0.480143 | − | 0.877190i | \(-0.659415\pi\) | ||||
−0.480143 | + | 0.877190i | \(0.659415\pi\) | |||||||
\(822\) | −0.0885374 | −0.00308810 | ||||||||
\(823\) | 10.3745 | 0.361631 | 0.180815 | − | 0.983517i | \(-0.442126\pi\) | ||||
0.180815 | + | 0.983517i | \(0.442126\pi\) | |||||||
\(824\) | 7.88799 | 0.274791 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.4808 | −0.434262 | ||||||||
\(827\) | −53.1407 | −1.84788 | −0.923941 | − | 0.382534i | \(-0.875051\pi\) | ||||
−0.923941 | + | 0.382534i | \(0.875051\pi\) | |||||||
\(828\) | 12.8906 | 0.447979 | ||||||||
\(829\) | −22.8587 | −0.793916 | −0.396958 | − | 0.917837i | \(-0.629934\pi\) | ||||
−0.396958 | + | 0.917837i | \(0.629934\pi\) | |||||||
\(830\) | −72.0945 | −2.50244 | ||||||||
\(831\) | −0.373611 | −0.0129604 | ||||||||
\(832\) | −1.08332 | −0.0375574 | ||||||||
\(833\) | 21.1804 | 0.733857 | ||||||||
\(834\) | 2.53824 | 0.0878919 | ||||||||
\(835\) | −28.2596 | −0.977965 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.84177 | −0.271051 | ||||||||
\(838\) | −10.2663 | −0.354643 | ||||||||
\(839\) | 52.4169 | 1.80963 | 0.904816 | − | 0.425803i | \(-0.140008\pi\) | ||||
0.904816 | + | 0.425803i | \(0.140008\pi\) | |||||||
\(840\) | 2.60527 | 0.0898904 | ||||||||
\(841\) | 7.79205 | 0.268691 | ||||||||
\(842\) | 3.27805 | 0.112969 | ||||||||
\(843\) | 1.90231 | 0.0655191 | ||||||||
\(844\) | −8.80740 | −0.303163 | ||||||||
\(845\) | −48.2911 | −1.66126 | ||||||||
\(846\) | 36.1014 | 1.24119 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.42429 | 0.151931 | ||||||||
\(849\) | 2.97687 | 0.102166 | ||||||||
\(850\) | −45.5540 | −1.56249 | ||||||||
\(851\) | −3.27606 | −0.112302 | ||||||||
\(852\) | −1.62295 | −0.0556013 | ||||||||
\(853\) | −0.889115 | −0.0304427 | −0.0152214 | − | 0.999884i | \(-0.504845\pi\) | ||||
−0.0152214 | + | 0.999884i | \(0.504845\pi\) | |||||||
\(854\) | −31.9058 | −1.09179 | ||||||||
\(855\) | −12.1162 | −0.414366 | ||||||||
\(856\) | −12.3510 | −0.422147 | ||||||||
\(857\) | −35.7742 | −1.22202 | −0.611012 | − | 0.791621i | \(-0.709237\pi\) | ||||
−0.611012 | + | 0.791621i | \(0.709237\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.5139 | 1.14348 | 0.571740 | − | 0.820435i | \(-0.306268\pi\) | ||||
0.571740 | + | 0.820435i | \(0.306268\pi\) | |||||||
\(860\) | −18.8048 | −0.641238 | ||||||||
\(861\) | 4.25789 | 0.145108 | ||||||||
\(862\) | −15.2775 | −0.520355 | ||||||||
\(863\) | 28.9111 | 0.984146 | 0.492073 | − | 0.870554i | \(-0.336239\pi\) | ||||
0.492073 | + | 0.870554i | \(0.336239\pi\) | |||||||
\(864\) | 1.07999 | 0.0367420 | ||||||||
\(865\) | 91.2395 | 3.10224 | ||||||||
\(866\) | −33.8113 | −1.14896 | ||||||||
\(867\) | −0.320668 | −0.0108905 | ||||||||
\(868\) | −25.5970 | −0.868818 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −4.48266 | −0.151977 | ||||||||
\(871\) | −1.47184 | −0.0498715 | ||||||||
\(872\) | −15.9890 | −0.541455 | ||||||||
\(873\) | −48.9395 | −1.65635 | ||||||||
\(874\) | 4.34430 | 0.146948 | ||||||||
\(875\) | −96.0643 | −3.24757 | ||||||||
\(876\) | −1.49573 | −0.0505359 | ||||||||
\(877\) | 24.6284 | 0.831642 | 0.415821 | − | 0.909446i | \(-0.363494\pi\) | ||||
0.415821 | + | 0.909446i | \(0.363494\pi\) | |||||||
\(878\) | 5.15290 | 0.173902 | ||||||||
\(879\) | 4.60006 | 0.155156 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.5997 | 1.60368 | 0.801838 | − | 0.597542i | \(-0.203856\pi\) | ||||
0.801838 | + | 0.597542i | \(0.203856\pi\) | |||||||
\(882\) | 16.1051 | 0.542286 | ||||||||
\(883\) | 37.4768 | 1.26120 | 0.630598 | − | 0.776110i | \(-0.282810\pi\) | ||||
0.630598 | + | 0.776110i | \(0.282810\pi\) | |||||||
\(884\) | −4.22748 | −0.142186 | ||||||||
\(885\) | −2.61642 | −0.0879499 | ||||||||
\(886\) | −0.986260 | −0.0331340 | ||||||||
\(887\) | −25.5777 | −0.858815 | −0.429408 | − | 0.903111i | \(-0.641278\pi\) | ||||
−0.429408 | + | 0.903111i | \(0.641278\pi\) | |||||||
\(888\) | −0.136483 | −0.00458006 | ||||||||
\(889\) | −8.91408 | −0.298969 | ||||||||
\(890\) | −50.2104 | −1.68306 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.80467 | 0.127390 | ||||||||
\(893\) | 12.1666 | 0.407141 | ||||||||
\(894\) | −3.44243 | −0.115132 | ||||||||
\(895\) | 9.70627 | 0.324445 | ||||||||
\(896\) | 3.52528 | 0.117771 | ||||||||
\(897\) | 0.851770 | 0.0284398 | ||||||||
\(898\) | 28.3689 | 0.946683 | ||||||||
\(899\) | 44.0425 | 1.46890 | ||||||||
\(900\) | −34.6382 | −1.15461 | ||||||||
\(901\) | 17.2650 | 0.575182 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.93829 | 0.0977802 | ||||||||
\(904\) | 0.326620 | 0.0108632 | ||||||||
\(905\) | −104.181 | −3.46308 | ||||||||
\(906\) | −2.51649 | −0.0836048 | ||||||||
\(907\) | −33.4531 | −1.11079 | −0.555396 | − | 0.831586i | \(-0.687433\pi\) | ||||
−0.555396 | + | 0.831586i | \(0.687433\pi\) | |||||||
\(908\) | 5.58353 | 0.185296 | ||||||||
\(909\) | −28.8985 | −0.958501 | ||||||||
\(910\) | −15.5943 | −0.516945 | ||||||||
\(911\) | −33.3522 | −1.10501 | −0.552504 | − | 0.833510i | \(-0.686328\pi\) | ||||
−0.552504 | + | 0.833510i | \(0.686328\pi\) | |||||||
\(912\) | 0.180986 | 0.00599305 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 4.74943 | 0.157097 | ||||||||
\(915\) | −6.68859 | −0.221118 | ||||||||
\(916\) | 13.4343 | 0.443881 | ||||||||
\(917\) | −44.4468 | −1.46776 | ||||||||
\(918\) | 4.21448 | 0.139099 | ||||||||
\(919\) | −54.4174 | −1.79506 | −0.897532 | − | 0.440949i | \(-0.854642\pi\) | ||||
−0.897532 | + | 0.440949i | \(0.854642\pi\) | |||||||
\(920\) | 17.7392 | 0.584843 | ||||||||
\(921\) | −0.557302 | −0.0183637 | ||||||||
\(922\) | −0.587462 | −0.0193470 | ||||||||
\(923\) | 9.71441 | 0.319754 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.80305 | 0.289443 | ||||||||
\(926\) | 24.2324 | 0.796327 | ||||||||
\(927\) | 23.4056 | 0.768741 | ||||||||
\(928\) | −6.06565 | −0.199115 | ||||||||
\(929\) | −20.4289 | −0.670250 | −0.335125 | − | 0.942174i | \(-0.608778\pi\) | ||||
−0.335125 | + | 0.942174i | \(0.608778\pi\) | |||||||
\(930\) | −5.36604 | −0.175959 | ||||||||
\(931\) | 5.42762 | 0.177883 | ||||||||
\(932\) | 6.10113 | 0.199849 | ||||||||
\(933\) | 4.13208 | 0.135278 | ||||||||
\(934\) | −36.0423 | −1.17934 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.21448 | −0.105069 | ||||||||
\(937\) | −10.7981 | −0.352759 | −0.176380 | − | 0.984322i | \(-0.556439\pi\) | ||||
−0.176380 | + | 0.984322i | \(0.556439\pi\) | |||||||
\(938\) | 4.78959 | 0.156386 | ||||||||
\(939\) | 0.116997 | 0.00381806 | ||||||||
\(940\) | 49.6803 | 1.62039 | ||||||||
\(941\) | −45.1998 | −1.47347 | −0.736736 | − | 0.676181i | \(-0.763634\pi\) | ||||
−0.736736 | + | 0.676181i | \(0.763634\pi\) | |||||||
\(942\) | −0.577841 | −0.0188271 | ||||||||
\(943\) | 28.9917 | 0.944100 | ||||||||
\(944\) | −3.54036 | −0.115229 | ||||||||
\(945\) | 15.5463 | 0.505721 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.6435 | −0.833301 | −0.416651 | − | 0.909067i | \(-0.636796\pi\) | ||||
−0.416651 | + | 0.909067i | \(0.636796\pi\) | |||||||
\(948\) | −2.09447 | −0.0680251 | ||||||||
\(949\) | 8.95290 | 0.290623 | ||||||||
\(950\) | −11.6735 | −0.378739 | ||||||||
\(951\) | −2.97498 | −0.0964704 | ||||||||
\(952\) | 13.7568 | 0.445862 | ||||||||
\(953\) | 30.6312 | 0.992242 | 0.496121 | − | 0.868253i | \(-0.334757\pi\) | ||||
0.496121 | + | 0.868253i | \(0.334757\pi\) | |||||||
\(954\) | 13.1279 | 0.425033 | ||||||||
\(955\) | −81.0865 | −2.62390 | ||||||||
\(956\) | 3.36137 | 0.108714 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.3904 | 0.335698 | ||||||||
\(959\) | −1.72455 | −0.0556886 | ||||||||
\(960\) | 0.739025 | 0.0238519 | ||||||||
\(961\) | 21.7218 | 0.700702 | ||||||||
\(962\) | 0.816938 | 0.0263391 | ||||||||
\(963\) | −36.6483 | −1.18098 | ||||||||
\(964\) | 7.88799 | 0.254055 | ||||||||
\(965\) | 92.0643 | 2.96365 | ||||||||
\(966\) | −2.77178 | −0.0891806 | ||||||||
\(967\) | −7.40068 | −0.237990 | −0.118995 | − | 0.992895i | \(-0.537967\pi\) | ||||
−0.118995 | + | 0.992895i | \(0.537967\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.706269 | 0.0226886 | ||||||||
\(970\) | −67.3473 | −2.16239 | ||||||||
\(971\) | 16.1436 | 0.518074 | 0.259037 | − | 0.965867i | \(-0.416595\pi\) | ||||
0.259037 | + | 0.965867i | \(0.416595\pi\) | |||||||
\(972\) | 4.81568 | 0.154463 | ||||||||
\(973\) | 49.4402 | 1.58498 | ||||||||
\(974\) | −27.5903 | −0.884051 | ||||||||
\(975\) | −2.28878 | −0.0732997 | ||||||||
\(976\) | −9.05057 | −0.289702 | ||||||||
\(977\) | 13.0674 | 0.418063 | 0.209032 | − | 0.977909i | \(-0.432969\pi\) | ||||
0.209032 | + | 0.977909i | \(0.432969\pi\) | |||||||
\(978\) | −1.11487 | −0.0356496 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 22.1627 | 0.707962 | ||||||||
\(981\) | −47.4432 | −1.51475 | ||||||||
\(982\) | 27.0436 | 0.862997 | ||||||||
\(983\) | 33.2009 | 1.05894 | 0.529472 | − | 0.848327i | \(-0.322390\pi\) | ||||
0.529472 | + | 0.848327i | \(0.322390\pi\) | |||||||
\(984\) | 1.20781 | 0.0385037 | ||||||||
\(985\) | 50.3608 | 1.60463 | ||||||||
\(986\) | −23.6702 | −0.753812 | ||||||||
\(987\) | −7.76265 | −0.247088 | ||||||||
\(988\) | −1.08332 | −0.0344650 | ||||||||
\(989\) | 20.0067 | 0.636175 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.31422 | −0.137046 | −0.0685228 | − | 0.997650i | \(-0.521829\pi\) | ||||
−0.0685228 | + | 0.997650i | \(0.521829\pi\) | |||||||
\(992\) | −7.26098 | −0.230536 | ||||||||
\(993\) | −4.69119 | −0.148870 | ||||||||
\(994\) | −31.6121 | −1.00267 | ||||||||
\(995\) | 28.0371 | 0.888836 | ||||||||
\(996\) | 3.19546 | 0.101252 | ||||||||
\(997\) | −49.2187 | −1.55877 | −0.779386 | − | 0.626545i | \(-0.784469\pi\) | ||||
−0.779386 | + | 0.626545i | \(0.784469\pi\) | |||||||
\(998\) | −20.2663 | −0.641519 | ||||||||
\(999\) | −0.814425 | −0.0257673 |
(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 | 4598.2.a.br.1.2 | ✓ | 4 | |
11.10 | odd | 2 | 4598.2.a.bu.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.br.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4598.2.a.bu.1.2 | yes | 4 | 11.10 | odd | 2 |