Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.361.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.22188\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.28514 | 1.61584 | 0.807920 | − | 0.589292i | \(-0.200593\pi\) | ||||
0.807920 | + | 0.589292i | \(0.200593\pi\) | |||||||
\(3\) | 1.22188 | 0.705451 | 0.352725 | − | 0.935727i | \(-0.385255\pi\) | ||||
0.352725 | + | 0.935727i | \(0.385255\pi\) | |||||||
\(4\) | 3.22188 | 1.61094 | ||||||||
\(5\) | −2.50702 | −1.12117 | −0.560586 | − | 0.828096i | \(-0.689424\pi\) | ||||
−0.560586 | + | 0.828096i | \(0.689424\pi\) | |||||||
\(6\) | 2.79216 | 1.13990 | ||||||||
\(7\) | −4.50702 | −1.70349 | −0.851746 | − | 0.523954i | \(-0.824456\pi\) | ||||
−0.851746 | + | 0.523954i | \(0.824456\pi\) | |||||||
\(8\) | 2.79216 | 0.987178 | ||||||||
\(9\) | −1.50702 | −0.502340 | ||||||||
\(10\) | −5.72889 | −1.81164 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 3.93673 | 1.13644 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −10.2992 | −2.75257 | ||||||||
\(15\) | −3.06327 | −0.790932 | ||||||||
\(16\) | −0.0632663 | −0.0158166 | ||||||||
\(17\) | −3.22188 | −0.781420 | −0.390710 | − | 0.920514i | \(-0.627770\pi\) | ||||
−0.390710 | + | 0.920514i | \(0.627770\pi\) | |||||||
\(18\) | −3.44375 | −0.811700 | ||||||||
\(19\) | 2.34841 | 0.538762 | 0.269381 | − | 0.963034i | \(-0.413181\pi\) | ||||
0.269381 | + | 0.963034i | \(0.413181\pi\) | |||||||
\(20\) | −8.07730 | −1.80614 | ||||||||
\(21\) | −5.50702 | −1.20173 | ||||||||
\(22\) | −2.28514 | −0.487194 | ||||||||
\(23\) | 5.79216 | 1.20775 | 0.603875 | − | 0.797079i | \(-0.293623\pi\) | ||||
0.603875 | + | 0.797079i | \(0.293623\pi\) | |||||||
\(24\) | 3.41168 | 0.696405 | ||||||||
\(25\) | 1.28514 | 0.257028 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.50702 | −1.05983 | ||||||||
\(28\) | −14.5211 | −2.74422 | ||||||||
\(29\) | −0.619514 | −0.115041 | −0.0575204 | − | 0.998344i | \(-0.518319\pi\) | ||||
−0.0575204 | + | 0.998344i | \(0.518319\pi\) | |||||||
\(30\) | −7.00000 | −1.27802 | ||||||||
\(31\) | −6.01404 | −1.08015 | −0.540076 | − | 0.841616i | \(-0.681605\pi\) | ||||
−0.540076 | + | 0.841616i | \(0.681605\pi\) | |||||||
\(32\) | −5.72889 | −1.01274 | ||||||||
\(33\) | −1.22188 | −0.212701 | ||||||||
\(34\) | −7.36245 | −1.26265 | ||||||||
\(35\) | 11.2992 | 1.90991 | ||||||||
\(36\) | −4.85543 | −0.809238 | ||||||||
\(37\) | −5.06327 | −0.832396 | −0.416198 | − | 0.909274i | \(-0.636638\pi\) | ||||
−0.416198 | + | 0.909274i | \(0.636638\pi\) | |||||||
\(38\) | 5.36645 | 0.870553 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.00000 | −1.10680 | ||||||||
\(41\) | 8.36245 | 1.30599 | 0.652997 | − | 0.757360i | \(-0.273511\pi\) | ||||
0.652997 | + | 0.757360i | \(0.273511\pi\) | |||||||
\(42\) | −12.5843 | −1.94180 | ||||||||
\(43\) | 11.0913 | 1.69141 | 0.845707 | − | 0.533648i | \(-0.179179\pi\) | ||||
0.845707 | + | 0.533648i | \(0.179179\pi\) | |||||||
\(44\) | −3.22188 | −0.485716 | ||||||||
\(45\) | 3.77812 | 0.563209 | ||||||||
\(46\) | 13.2359 | 1.95153 | ||||||||
\(47\) | −6.74293 | −0.983558 | −0.491779 | − | 0.870720i | \(-0.663653\pi\) | ||||
−0.491779 | + | 0.870720i | \(0.663653\pi\) | |||||||
\(48\) | −0.0773036 | −0.0111578 | ||||||||
\(49\) | 13.3132 | 1.90189 | ||||||||
\(50\) | 2.93673 | 0.415317 | ||||||||
\(51\) | −3.93673 | −0.551253 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.06327 | −0.558133 | −0.279066 | − | 0.960272i | \(-0.590025\pi\) | ||||
−0.279066 | + | 0.960272i | \(0.590025\pi\) | |||||||
\(54\) | −12.5843 | −1.71251 | ||||||||
\(55\) | 2.50702 | 0.338046 | ||||||||
\(56\) | −12.5843 | −1.68165 | ||||||||
\(57\) | 2.86946 | 0.380070 | ||||||||
\(58\) | −1.41568 | −0.185888 | ||||||||
\(59\) | −11.0633 | −1.44031 | −0.720157 | − | 0.693811i | \(-0.755930\pi\) | ||||
−0.720157 | + | 0.693811i | \(0.755930\pi\) | |||||||
\(60\) | −9.86946 | −1.27414 | ||||||||
\(61\) | −0.144573 | −0.0185106 | −0.00925531 | − | 0.999957i | \(-0.502946\pi\) | ||||
−0.00925531 | + | 0.999957i | \(0.502946\pi\) | |||||||
\(62\) | −13.7429 | −1.74535 | ||||||||
\(63\) | 6.79216 | 0.855732 | ||||||||
\(64\) | −12.9648 | −1.62060 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.79216 | −0.343691 | ||||||||
\(67\) | −8.72889 | −1.06640 | −0.533202 | − | 0.845988i | \(-0.679011\pi\) | ||||
−0.533202 | + | 0.845988i | \(0.679011\pi\) | |||||||
\(68\) | −10.3805 | −1.25882 | ||||||||
\(69\) | 7.07730 | 0.852007 | ||||||||
\(70\) | 25.8202 | 3.08611 | ||||||||
\(71\) | 1.71486 | 0.203516 | 0.101758 | − | 0.994809i | \(-0.467553\pi\) | ||||
0.101758 | + | 0.994809i | \(0.467553\pi\) | |||||||
\(72\) | −4.20784 | −0.495899 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | −11.5703 | −1.34502 | ||||||||
\(75\) | 1.57028 | 0.181321 | ||||||||
\(76\) | 7.56628 | 0.867912 | ||||||||
\(77\) | 4.50702 | 0.513622 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.87347 | 0.210782 | 0.105391 | − | 0.994431i | \(-0.466391\pi\) | ||||
0.105391 | + | 0.994431i | \(0.466391\pi\) | |||||||
\(80\) | 0.158610 | 0.0177331 | ||||||||
\(81\) | −2.20784 | −0.245315 | ||||||||
\(82\) | 19.1094 | 2.11028 | ||||||||
\(83\) | 5.38049 | 0.590585 | 0.295293 | − | 0.955407i | \(-0.404583\pi\) | ||||
0.295293 | + | 0.955407i | \(0.404583\pi\) | |||||||
\(84\) | −17.7429 | −1.93591 | ||||||||
\(85\) | 8.07730 | 0.876107 | ||||||||
\(86\) | 25.3453 | 2.73305 | ||||||||
\(87\) | −0.756969 | −0.0811556 | ||||||||
\(88\) | −2.79216 | −0.297645 | ||||||||
\(89\) | 8.50702 | 0.901742 | 0.450871 | − | 0.892589i | \(-0.351113\pi\) | ||||
0.450871 | + | 0.892589i | \(0.351113\pi\) | |||||||
\(90\) | 8.63355 | 0.910056 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 18.6616 | 1.94561 | ||||||||
\(93\) | −7.34841 | −0.761994 | ||||||||
\(94\) | −15.4086 | −1.58927 | ||||||||
\(95\) | −5.88750 | −0.604045 | ||||||||
\(96\) | −7.00000 | −0.714435 | ||||||||
\(97\) | −0.112495 | −0.0114222 | −0.00571109 | − | 0.999984i | \(-0.501818\pi\) | ||||
−0.00571109 | + | 0.999984i | \(0.501818\pi\) | |||||||
\(98\) | 30.4226 | 3.07315 | ||||||||
\(99\) | 1.50702 | 0.151461 | ||||||||
\(100\) | 4.14057 | 0.414057 | ||||||||
\(101\) | −12.7570 | −1.26937 | −0.634683 | − | 0.772773i | \(-0.718869\pi\) | ||||
−0.634683 | + | 0.772773i | \(0.718869\pi\) | |||||||
\(102\) | −8.99600 | −0.890736 | ||||||||
\(103\) | 15.6304 | 1.54011 | 0.770056 | − | 0.637976i | \(-0.220228\pi\) | ||||
0.770056 | + | 0.637976i | \(0.220228\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.8062 | 1.34735 | ||||||||
\(106\) | −9.28514 | −0.901853 | ||||||||
\(107\) | −5.61951 | −0.543259 | −0.271629 | − | 0.962402i | \(-0.587563\pi\) | ||||
−0.271629 | + | 0.962402i | \(0.587563\pi\) | |||||||
\(108\) | −17.7429 | −1.70731 | ||||||||
\(109\) | −9.90466 | −0.948694 | −0.474347 | − | 0.880338i | \(-0.657316\pi\) | ||||
−0.474347 | + | 0.880338i | \(0.657316\pi\) | |||||||
\(110\) | 5.72889 | 0.546229 | ||||||||
\(111\) | −6.18668 | −0.587214 | ||||||||
\(112\) | 0.285142 | 0.0269434 | ||||||||
\(113\) | 8.24995 | 0.776090 | 0.388045 | − | 0.921640i | \(-0.373150\pi\) | ||||
0.388045 | + | 0.921640i | \(0.373150\pi\) | |||||||
\(114\) | 6.55714 | 0.614132 | ||||||||
\(115\) | −14.5211 | −1.35410 | ||||||||
\(116\) | −1.99600 | −0.185324 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −25.2811 | −2.32732 | ||||||||
\(119\) | 14.5211 | 1.33114 | ||||||||
\(120\) | −8.55313 | −0.780791 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.330369 | −0.0299102 | ||||||||
\(123\) | 10.2179 | 0.921315 | ||||||||
\(124\) | −19.3765 | −1.74006 | ||||||||
\(125\) | 9.31322 | 0.832999 | ||||||||
\(126\) | 15.5211 | 1.38273 | ||||||||
\(127\) | −6.07730 | −0.539273 | −0.269637 | − | 0.962962i | \(-0.586904\pi\) | ||||
−0.269637 | + | 0.962962i | \(0.586904\pi\) | |||||||
\(128\) | −18.1686 | −1.60590 | ||||||||
\(129\) | 13.5522 | 1.19321 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.9508 | −1.04414 | −0.522072 | − | 0.852902i | \(-0.674841\pi\) | ||||
−0.522072 | + | 0.852902i | \(0.674841\pi\) | |||||||
\(132\) | −3.93673 | −0.342649 | ||||||||
\(133\) | −10.5843 | −0.917777 | ||||||||
\(134\) | −19.9468 | −1.72314 | ||||||||
\(135\) | 13.8062 | 1.18825 | ||||||||
\(136\) | −8.99600 | −0.771400 | ||||||||
\(137\) | 2.27111 | 0.194034 | 0.0970168 | − | 0.995283i | \(-0.469070\pi\) | ||||
0.0970168 | + | 0.995283i | \(0.469070\pi\) | |||||||
\(138\) | 16.1726 | 1.37671 | ||||||||
\(139\) | −10.1546 | −0.861303 | −0.430651 | − | 0.902518i | \(-0.641716\pi\) | ||||
−0.430651 | + | 0.902518i | \(0.641716\pi\) | |||||||
\(140\) | 36.4046 | 3.07675 | ||||||||
\(141\) | −8.23903 | −0.693851 | ||||||||
\(142\) | 3.91869 | 0.328849 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.0953435 | 0.00794529 | ||||||||
\(145\) | 1.55313 | 0.128981 | ||||||||
\(146\) | 4.57028 | 0.378239 | ||||||||
\(147\) | 16.2671 | 1.34169 | ||||||||
\(148\) | −16.3132 | −1.34094 | ||||||||
\(149\) | 10.9648 | 0.898272 | 0.449136 | − | 0.893463i | \(-0.351732\pi\) | ||||
0.449136 | + | 0.893463i | \(0.351732\pi\) | |||||||
\(150\) | 3.58832 | 0.292985 | ||||||||
\(151\) | 10.8835 | 0.885687 | 0.442843 | − | 0.896599i | \(-0.353970\pi\) | ||||
0.442843 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(152\) | 6.55714 | 0.531854 | ||||||||
\(153\) | 4.85543 | 0.392538 | ||||||||
\(154\) | 10.2992 | 0.829932 | ||||||||
\(155\) | 15.0773 | 1.21104 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.9820 | 1.11588 | 0.557941 | − | 0.829881i | \(-0.311592\pi\) | ||||
0.557941 | + | 0.829881i | \(0.311592\pi\) | |||||||
\(158\) | 4.28114 | 0.340589 | ||||||||
\(159\) | −4.96481 | −0.393735 | ||||||||
\(160\) | 14.3624 | 1.13545 | ||||||||
\(161\) | −26.1054 | −2.05739 | ||||||||
\(162\) | −5.04523 | −0.396390 | ||||||||
\(163\) | −1.39452 | −0.109227 | −0.0546137 | − | 0.998508i | \(-0.517393\pi\) | ||||
−0.0546137 | + | 0.998508i | \(0.517393\pi\) | |||||||
\(164\) | 26.9428 | 2.10388 | ||||||||
\(165\) | 3.06327 | 0.238475 | ||||||||
\(166\) | 12.2952 | 0.954291 | ||||||||
\(167\) | −23.8343 | −1.84435 | −0.922176 | − | 0.386771i | \(-0.873590\pi\) | ||||
−0.922176 | + | 0.386771i | \(0.873590\pi\) | |||||||
\(168\) | −15.3765 | −1.18632 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 18.4578 | 1.41565 | ||||||||
\(171\) | −3.53910 | −0.270641 | ||||||||
\(172\) | 35.7349 | 2.72476 | ||||||||
\(173\) | −7.39764 | −0.562432 | −0.281216 | − | 0.959644i | \(-0.590738\pi\) | ||||
−0.281216 | + | 0.959644i | \(0.590738\pi\) | |||||||
\(174\) | −1.72978 | −0.131135 | ||||||||
\(175\) | −5.79216 | −0.437846 | ||||||||
\(176\) | 0.0632663 | 0.00476888 | ||||||||
\(177\) | −13.5179 | −1.01607 | ||||||||
\(178\) | 19.4397 | 1.45707 | ||||||||
\(179\) | 18.5211 | 1.38433 | 0.692164 | − | 0.721740i | \(-0.256657\pi\) | ||||
0.692164 | + | 0.721740i | \(0.256657\pi\) | |||||||
\(180\) | 12.1726 | 0.907296 | ||||||||
\(181\) | −18.0561 | −1.34210 | −0.671051 | − | 0.741411i | \(-0.734157\pi\) | ||||
−0.671051 | + | 0.741411i | \(0.734157\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.176650 | −0.0130583 | ||||||||
\(184\) | 16.1726 | 1.19226 | ||||||||
\(185\) | 12.6937 | 0.933260 | ||||||||
\(186\) | −16.7922 | −1.23126 | ||||||||
\(187\) | 3.22188 | 0.235607 | ||||||||
\(188\) | −21.7249 | −1.58445 | ||||||||
\(189\) | 24.8202 | 1.80541 | ||||||||
\(190\) | −13.4538 | −0.976040 | ||||||||
\(191\) | −3.36245 | −0.243298 | −0.121649 | − | 0.992573i | \(-0.538818\pi\) | ||||
−0.121649 | + | 0.992573i | \(0.538818\pi\) | |||||||
\(192\) | −15.8414 | −1.14325 | ||||||||
\(193\) | −15.5984 | −1.12279 | −0.561397 | − | 0.827546i | \(-0.689736\pi\) | ||||
−0.561397 | + | 0.827546i | \(0.689736\pi\) | |||||||
\(194\) | −0.257068 | −0.0184564 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 42.8935 | 3.06382 | ||||||||
\(197\) | 21.0281 | 1.49819 | 0.749094 | − | 0.662464i | \(-0.230489\pi\) | ||||
0.749094 | + | 0.662464i | \(0.230489\pi\) | |||||||
\(198\) | 3.44375 | 0.244737 | ||||||||
\(199\) | −22.6124 | −1.60295 | −0.801475 | − | 0.598028i | \(-0.795951\pi\) | ||||
−0.801475 | + | 0.598028i | \(0.795951\pi\) | |||||||
\(200\) | 3.58832 | 0.253733 | ||||||||
\(201\) | −10.6656 | −0.752295 | ||||||||
\(202\) | −29.1515 | −2.05109 | ||||||||
\(203\) | 2.79216 | 0.195971 | ||||||||
\(204\) | −12.6837 | −0.888034 | ||||||||
\(205\) | −20.9648 | −1.46425 | ||||||||
\(206\) | 35.7178 | 2.48858 | ||||||||
\(207\) | −8.72889 | −0.606700 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.34841 | −0.162443 | ||||||||
\(210\) | 31.5491 | 2.17710 | ||||||||
\(211\) | 20.3765 | 1.40277 | 0.701387 | − | 0.712780i | \(-0.252564\pi\) | ||||
0.701387 | + | 0.712780i | \(0.252564\pi\) | |||||||
\(212\) | −13.0913 | −0.899117 | ||||||||
\(213\) | 2.09534 | 0.143571 | ||||||||
\(214\) | −12.8414 | −0.877819 | ||||||||
\(215\) | −27.8062 | −1.89637 | ||||||||
\(216\) | −15.3765 | −1.04624 | ||||||||
\(217\) | 27.1054 | 1.84003 | ||||||||
\(218\) | −22.6336 | −1.53294 | ||||||||
\(219\) | 2.44375 | 0.165133 | ||||||||
\(220\) | 8.07730 | 0.544572 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −14.1375 | −0.948844 | ||||||||
\(223\) | 17.7741 | 1.19024 | 0.595122 | − | 0.803636i | \(-0.297104\pi\) | ||||
0.595122 | + | 0.803636i | \(0.297104\pi\) | |||||||
\(224\) | 25.8202 | 1.72519 | ||||||||
\(225\) | −1.93673 | −0.129116 | ||||||||
\(226\) | 18.8523 | 1.25404 | ||||||||
\(227\) | −5.82024 | −0.386303 | −0.193151 | − | 0.981169i | \(-0.561871\pi\) | ||||
−0.193151 | + | 0.981169i | \(0.561871\pi\) | |||||||
\(228\) | 9.24506 | 0.612269 | ||||||||
\(229\) | −23.6656 | −1.56387 | −0.781934 | − | 0.623361i | \(-0.785767\pi\) | ||||
−0.781934 | + | 0.623361i | \(0.785767\pi\) | |||||||
\(230\) | −33.1827 | −2.18800 | ||||||||
\(231\) | 5.50702 | 0.362335 | ||||||||
\(232\) | −1.72978 | −0.113566 | ||||||||
\(233\) | −22.8875 | −1.49941 | −0.749705 | − | 0.661772i | \(-0.769805\pi\) | ||||
−0.749705 | + | 0.661772i | \(0.769805\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9047 | 1.10274 | ||||||||
\(236\) | −35.6445 | −2.32026 | ||||||||
\(237\) | 2.28915 | 0.148696 | ||||||||
\(238\) | 33.1827 | 2.15091 | ||||||||
\(239\) | −16.2007 | −1.04794 | −0.523969 | − | 0.851737i | \(-0.675549\pi\) | ||||
−0.523969 | + | 0.851737i | \(0.675549\pi\) | |||||||
\(240\) | 0.193802 | 0.0125098 | ||||||||
\(241\) | −0.193802 | −0.0124839 | −0.00624193 | − | 0.999981i | \(-0.501987\pi\) | ||||
−0.00624193 | + | 0.999981i | \(0.501987\pi\) | |||||||
\(242\) | 2.28514 | 0.146895 | ||||||||
\(243\) | 13.8234 | 0.886768 | ||||||||
\(244\) | −0.465795 | −0.0298195 | ||||||||
\(245\) | −33.3765 | −2.13235 | ||||||||
\(246\) | 23.3493 | 1.48870 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −16.7922 | −1.06630 | ||||||||
\(249\) | 6.57429 | 0.416629 | ||||||||
\(250\) | 21.2820 | 1.34599 | ||||||||
\(251\) | 8.14057 | 0.513828 | 0.256914 | − | 0.966434i | \(-0.417294\pi\) | ||||
0.256914 | + | 0.966434i | \(0.417294\pi\) | |||||||
\(252\) | 21.8835 | 1.37853 | ||||||||
\(253\) | −5.79216 | −0.364150 | ||||||||
\(254\) | −13.8875 | −0.871380 | ||||||||
\(255\) | 9.86946 | 0.618050 | ||||||||
\(256\) | −15.5883 | −0.974270 | ||||||||
\(257\) | −17.8975 | −1.11642 | −0.558209 | − | 0.829700i | \(-0.688511\pi\) | ||||
−0.558209 | + | 0.829700i | \(0.688511\pi\) | |||||||
\(258\) | 30.9688 | 1.92803 | ||||||||
\(259\) | 22.8202 | 1.41798 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.933619 | 0.0577896 | ||||||||
\(262\) | −27.3092 | −1.68717 | ||||||||
\(263\) | −15.5672 | −0.959913 | −0.479956 | − | 0.877292i | \(-0.659348\pi\) | ||||
−0.479956 | + | 0.877292i | \(0.659348\pi\) | |||||||
\(264\) | −3.41168 | −0.209974 | ||||||||
\(265\) | 10.1867 | 0.625763 | ||||||||
\(266\) | −24.1867 | −1.48298 | ||||||||
\(267\) | 10.3945 | 0.636134 | ||||||||
\(268\) | −28.1234 | −1.71791 | ||||||||
\(269\) | −1.49298 | −0.0910287 | −0.0455143 | − | 0.998964i | \(-0.514493\pi\) | ||||
−0.0455143 | + | 0.998964i | \(0.514493\pi\) | |||||||
\(270\) | 31.5491 | 1.92002 | ||||||||
\(271\) | −23.2711 | −1.41362 | −0.706809 | − | 0.707404i | \(-0.749866\pi\) | ||||
−0.706809 | + | 0.707404i | \(0.749866\pi\) | |||||||
\(272\) | 0.203836 | 0.0123594 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.18980 | 0.313527 | ||||||||
\(275\) | −1.28514 | −0.0774970 | ||||||||
\(276\) | 22.8022 | 1.37253 | ||||||||
\(277\) | −14.0602 | −0.844793 | −0.422396 | − | 0.906411i | \(-0.638811\pi\) | ||||
−0.422396 | + | 0.906411i | \(0.638811\pi\) | |||||||
\(278\) | −23.2047 | −1.39173 | ||||||||
\(279\) | 9.06327 | 0.542604 | ||||||||
\(280\) | 31.5491 | 1.88542 | ||||||||
\(281\) | −11.6797 | −0.696750 | −0.348375 | − | 0.937355i | \(-0.613266\pi\) | ||||
−0.348375 | + | 0.937355i | \(0.613266\pi\) | |||||||
\(282\) | −18.8274 | −1.12115 | ||||||||
\(283\) | −3.47183 | −0.206379 | −0.103189 | − | 0.994662i | \(-0.532905\pi\) | ||||
−0.103189 | + | 0.994662i | \(0.532905\pi\) | |||||||
\(284\) | 5.52506 | 0.327852 | ||||||||
\(285\) | −7.19380 | −0.426124 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −37.6897 | −2.22475 | ||||||||
\(288\) | 8.63355 | 0.508737 | ||||||||
\(289\) | −6.61951 | −0.389383 | ||||||||
\(290\) | 3.54913 | 0.208412 | ||||||||
\(291\) | −0.137455 | −0.00805778 | ||||||||
\(292\) | 6.44375 | 0.377092 | ||||||||
\(293\) | −6.37960 | −0.372700 | −0.186350 | − | 0.982483i | \(-0.559666\pi\) | ||||
−0.186350 | + | 0.982483i | \(0.559666\pi\) | |||||||
\(294\) | 37.1726 | 2.16795 | ||||||||
\(295\) | 27.7358 | 1.61484 | ||||||||
\(296\) | −14.1375 | −0.821723 | ||||||||
\(297\) | 5.50702 | 0.319550 | ||||||||
\(298\) | 25.0561 | 1.45146 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.05926 | 0.292097 | ||||||||
\(301\) | −49.9889 | −2.88131 | ||||||||
\(302\) | 24.8704 | 1.43113 | ||||||||
\(303\) | −15.5874 | −0.895475 | ||||||||
\(304\) | −0.148575 | −0.00852137 | ||||||||
\(305\) | 0.362446 | 0.0207536 | ||||||||
\(306\) | 11.0953 | 0.634279 | ||||||||
\(307\) | −5.06327 | −0.288976 | −0.144488 | − | 0.989507i | \(-0.546153\pi\) | ||||
−0.144488 | + | 0.989507i | \(0.546153\pi\) | |||||||
\(308\) | 14.5211 | 0.827414 | ||||||||
\(309\) | 19.0985 | 1.08647 | ||||||||
\(310\) | 34.4538 | 1.95684 | ||||||||
\(311\) | 2.91958 | 0.165554 | 0.0827771 | − | 0.996568i | \(-0.473621\pi\) | ||||
0.0827771 | + | 0.996568i | \(0.473621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.7882 | 0.892399 | 0.446200 | − | 0.894933i | \(-0.352777\pi\) | ||||
0.446200 | + | 0.894933i | \(0.352777\pi\) | |||||||
\(314\) | 31.9508 | 1.80309 | ||||||||
\(315\) | −17.0281 | −0.959423 | ||||||||
\(316\) | 6.03608 | 0.339556 | ||||||||
\(317\) | 20.4397 | 1.14801 | 0.574005 | − | 0.818852i | \(-0.305389\pi\) | ||||
0.574005 | + | 0.818852i | \(0.305389\pi\) | |||||||
\(318\) | −11.3453 | −0.636213 | ||||||||
\(319\) | 0.619514 | 0.0346861 | ||||||||
\(320\) | 32.5030 | 1.81697 | ||||||||
\(321\) | −6.86635 | −0.383242 | ||||||||
\(322\) | −59.6545 | −3.32442 | ||||||||
\(323\) | −7.56628 | −0.420999 | ||||||||
\(324\) | −7.11338 | −0.395188 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.18668 | −0.176494 | ||||||||
\(327\) | −12.1023 | −0.669257 | ||||||||
\(328\) | 23.3493 | 1.28925 | ||||||||
\(329\) | 30.3905 | 1.67548 | ||||||||
\(330\) | 7.00000 | 0.385337 | ||||||||
\(331\) | 28.2811 | 1.55447 | 0.777236 | − | 0.629209i | \(-0.216621\pi\) | ||||
0.777236 | + | 0.629209i | \(0.216621\pi\) | |||||||
\(332\) | 17.3353 | 0.951396 | ||||||||
\(333\) | 7.63044 | 0.418145 | ||||||||
\(334\) | −54.4647 | −2.98018 | ||||||||
\(335\) | 21.8835 | 1.19562 | ||||||||
\(336\) | 0.348409 | 0.0190073 | ||||||||
\(337\) | −31.9256 | −1.73910 | −0.869550 | − | 0.493846i | \(-0.835591\pi\) | ||||
−0.869550 | + | 0.493846i | \(0.835591\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.0804 | 0.547493 | ||||||||
\(340\) | 26.0241 | 1.41135 | ||||||||
\(341\) | 6.01404 | 0.325678 | ||||||||
\(342\) | −8.08734 | −0.437313 | ||||||||
\(343\) | −28.4538 | −1.53636 | ||||||||
\(344\) | 30.9688 | 1.66973 | ||||||||
\(345\) | −17.7429 | −0.955247 | ||||||||
\(346\) | −16.9047 | −0.908800 | ||||||||
\(347\) | −1.91869 | −0.103001 | −0.0515004 | − | 0.998673i | \(-0.516400\pi\) | ||||
−0.0515004 | + | 0.998673i | \(0.516400\pi\) | |||||||
\(348\) | −2.43886 | −0.130737 | ||||||||
\(349\) | 0.189799 | 0.0101597 | 0.00507985 | − | 0.999987i | \(-0.498383\pi\) | ||||
0.00507985 | + | 0.999987i | \(0.498383\pi\) | |||||||
\(350\) | −13.2359 | −0.707489 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.72889 | 0.305351 | ||||||||
\(353\) | 10.9499 | 0.582803 | 0.291402 | − | 0.956601i | \(-0.405878\pi\) | ||||
0.291402 | + | 0.956601i | \(0.405878\pi\) | |||||||
\(354\) | −30.8904 | −1.64181 | ||||||||
\(355\) | −4.29918 | −0.228177 | ||||||||
\(356\) | 27.4086 | 1.45265 | ||||||||
\(357\) | 17.7429 | 0.939056 | ||||||||
\(358\) | 42.3233 | 2.23685 | ||||||||
\(359\) | −3.79216 | −0.200143 | −0.100071 | − | 0.994980i | \(-0.531907\pi\) | ||||
−0.100071 | + | 0.994980i | \(0.531907\pi\) | |||||||
\(360\) | 10.5491 | 0.555988 | ||||||||
\(361\) | −13.4850 | −0.709736 | ||||||||
\(362\) | −41.2609 | −2.16862 | ||||||||
\(363\) | 1.22188 | 0.0641319 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.01404 | −0.262447 | ||||||||
\(366\) | −0.403670 | −0.0211002 | ||||||||
\(367\) | −25.0069 | −1.30535 | −0.652675 | − | 0.757638i | \(-0.726353\pi\) | ||||
−0.652675 | + | 0.757638i | \(0.726353\pi\) | |||||||
\(368\) | −0.366449 | −0.0191025 | ||||||||
\(369\) | −12.6024 | −0.656053 | ||||||||
\(370\) | 29.0069 | 1.50800 | ||||||||
\(371\) | 18.3132 | 0.950775 | ||||||||
\(372\) | −23.6757 | −1.22753 | ||||||||
\(373\) | −8.67967 | −0.449416 | −0.224708 | − | 0.974426i | \(-0.572143\pi\) | ||||
−0.224708 | + | 0.974426i | \(0.572143\pi\) | |||||||
\(374\) | 7.36245 | 0.380703 | ||||||||
\(375\) | 11.3796 | 0.587640 | ||||||||
\(376\) | −18.8274 | −0.970947 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 56.7178 | 2.91725 | ||||||||
\(379\) | −14.7149 | −0.755851 | −0.377926 | − | 0.925836i | \(-0.623363\pi\) | ||||
−0.377926 | + | 0.925836i | \(0.623363\pi\) | |||||||
\(380\) | −18.9688 | −0.973079 | ||||||||
\(381\) | −7.42571 | −0.380431 | ||||||||
\(382\) | −7.68367 | −0.393131 | ||||||||
\(383\) | 5.39052 | 0.275443 | 0.137721 | − | 0.990471i | \(-0.456022\pi\) | ||||
0.137721 | + | 0.990471i | \(0.456022\pi\) | |||||||
\(384\) | −22.1998 | −1.13288 | ||||||||
\(385\) | −11.2992 | −0.575860 | ||||||||
\(386\) | −35.6445 | −1.81426 | ||||||||
\(387\) | −16.7149 | −0.849664 | ||||||||
\(388\) | −0.362446 | −0.0184004 | ||||||||
\(389\) | −21.5531 | −1.09279 | −0.546394 | − | 0.837529i | \(-0.684000\pi\) | ||||
−0.546394 | + | 0.837529i | \(0.684000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.6616 | −0.943759 | ||||||||
\(392\) | 37.1726 | 1.87750 | ||||||||
\(393\) | −14.6024 | −0.736592 | ||||||||
\(394\) | 48.0521 | 2.42083 | ||||||||
\(395\) | −4.69682 | −0.236323 | ||||||||
\(396\) | 4.85543 | 0.243994 | ||||||||
\(397\) | 17.5311 | 0.879860 | 0.439930 | − | 0.898032i | \(-0.355003\pi\) | ||||
0.439930 | + | 0.898032i | \(0.355003\pi\) | |||||||
\(398\) | −51.6725 | −2.59011 | ||||||||
\(399\) | −12.9327 | −0.647446 | ||||||||
\(400\) | −0.0813062 | −0.00406531 | ||||||||
\(401\) | 36.4366 | 1.81956 | 0.909779 | − | 0.415092i | \(-0.136251\pi\) | ||||
0.909779 | + | 0.415092i | \(0.136251\pi\) | |||||||
\(402\) | −24.3725 | −1.21559 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −41.1014 | −2.04487 | ||||||||
\(405\) | 5.53509 | 0.275041 | ||||||||
\(406\) | 6.38049 | 0.316658 | ||||||||
\(407\) | 5.06327 | 0.250977 | ||||||||
\(408\) | −10.9920 | −0.544185 | ||||||||
\(409\) | −28.8664 | −1.42735 | −0.713675 | − | 0.700477i | \(-0.752970\pi\) | ||||
−0.713675 | + | 0.700477i | \(0.752970\pi\) | |||||||
\(410\) | −47.9076 | −2.36599 | ||||||||
\(411\) | 2.77501 | 0.136881 | ||||||||
\(412\) | 50.3593 | 2.48103 | ||||||||
\(413\) | 49.8623 | 2.45357 | ||||||||
\(414\) | −19.9468 | −0.980330 | ||||||||
\(415\) | −13.4890 | −0.662148 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.4077 | −0.607606 | ||||||||
\(418\) | −5.36645 | −0.262482 | ||||||||
\(419\) | −4.20472 | −0.205414 | −0.102707 | − | 0.994712i | \(-0.532750\pi\) | ||||
−0.102707 | + | 0.994712i | \(0.532750\pi\) | |||||||
\(420\) | 44.4819 | 2.17049 | ||||||||
\(421\) | −13.5843 | −0.662059 | −0.331030 | − | 0.943620i | \(-0.607396\pi\) | ||||
−0.331030 | + | 0.943620i | \(0.607396\pi\) | |||||||
\(422\) | 46.5632 | 2.26666 | ||||||||
\(423\) | 10.1617 | 0.494080 | ||||||||
\(424\) | −11.3453 | −0.550976 | ||||||||
\(425\) | −4.14057 | −0.200847 | ||||||||
\(426\) | 4.78816 | 0.231987 | ||||||||
\(427\) | 0.651591 | 0.0315327 | ||||||||
\(428\) | −18.1054 | −0.875156 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −63.5411 | −3.06423 | ||||||||
\(431\) | 30.0381 | 1.44688 | 0.723442 | − | 0.690385i | \(-0.242559\pi\) | ||||
0.723442 | + | 0.690385i | \(0.242559\pi\) | |||||||
\(432\) | 0.348409 | 0.0167628 | ||||||||
\(433\) | 4.25707 | 0.204582 | 0.102291 | − | 0.994755i | \(-0.467383\pi\) | ||||
0.102291 | + | 0.994755i | \(0.467383\pi\) | |||||||
\(434\) | 61.9397 | 2.97320 | ||||||||
\(435\) | 1.89774 | 0.0909895 | ||||||||
\(436\) | −31.9116 | −1.52829 | ||||||||
\(437\) | 13.6024 | 0.650689 | ||||||||
\(438\) | 5.58432 | 0.266829 | ||||||||
\(439\) | −5.00311 | −0.238786 | −0.119393 | − | 0.992847i | \(-0.538095\pi\) | ||||
−0.119393 | + | 0.992847i | \(0.538095\pi\) | |||||||
\(440\) | 7.00000 | 0.333712 | ||||||||
\(441\) | −20.0633 | −0.955394 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.3101 | 1.34505 | 0.672527 | − | 0.740073i | \(-0.265209\pi\) | ||||
0.672527 | + | 0.740073i | \(0.265209\pi\) | |||||||
\(444\) | −19.9327 | −0.945966 | ||||||||
\(445\) | −21.3273 | −1.01101 | ||||||||
\(446\) | 40.6164 | 1.92324 | ||||||||
\(447\) | 13.3976 | 0.633687 | ||||||||
\(448\) | 58.4326 | 2.76068 | ||||||||
\(449\) | 5.72578 | 0.270216 | 0.135108 | − | 0.990831i | \(-0.456862\pi\) | ||||
0.135108 | + | 0.990831i | \(0.456862\pi\) | |||||||
\(450\) | −4.42571 | −0.208630 | ||||||||
\(451\) | −8.36245 | −0.393772 | ||||||||
\(452\) | 26.5803 | 1.25023 | ||||||||
\(453\) | 13.2983 | 0.624808 | ||||||||
\(454\) | −13.3001 | −0.624203 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.01201 | 0.375197 | ||||||||
\(457\) | 12.4899 | 0.584251 | 0.292126 | − | 0.956380i | \(-0.405637\pi\) | ||||
0.292126 | + | 0.956380i | \(0.405637\pi\) | |||||||
\(458\) | −54.0793 | −2.52696 | ||||||||
\(459\) | 17.7429 | 0.828169 | ||||||||
\(460\) | −46.7850 | −2.18136 | ||||||||
\(461\) | 13.1726 | 0.613511 | 0.306756 | − | 0.951788i | \(-0.400757\pi\) | ||||
0.306756 | + | 0.951788i | \(0.400757\pi\) | |||||||
\(462\) | 12.5843 | 0.585476 | ||||||||
\(463\) | 10.4086 | 0.483727 | 0.241863 | − | 0.970310i | \(-0.422241\pi\) | ||||
0.241863 | + | 0.970310i | \(0.422241\pi\) | |||||||
\(464\) | 0.0391944 | 0.00181955 | ||||||||
\(465\) | 18.4226 | 0.854328 | ||||||||
\(466\) | −52.3012 | −2.42281 | ||||||||
\(467\) | 23.3553 | 1.08076 | 0.540378 | − | 0.841422i | \(-0.318281\pi\) | ||||
0.540378 | + | 0.841422i | \(0.318281\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.3413 | 1.81661 | ||||||||
\(470\) | 38.6295 | 1.78185 | ||||||||
\(471\) | 17.0842 | 0.787199 | ||||||||
\(472\) | −30.8904 | −1.42185 | ||||||||
\(473\) | −11.0913 | −0.509980 | ||||||||
\(474\) | 5.23102 | 0.240269 | ||||||||
\(475\) | 3.01804 | 0.138477 | ||||||||
\(476\) | 46.7850 | 2.14439 | ||||||||
\(477\) | 6.12342 | 0.280372 | ||||||||
\(478\) | −37.0210 | −1.69330 | ||||||||
\(479\) | −8.22188 | −0.375667 | −0.187834 | − | 0.982201i | \(-0.560147\pi\) | ||||
−0.187834 | + | 0.982201i | \(0.560147\pi\) | |||||||
\(480\) | 17.5491 | 0.801005 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.442864 | −0.0201719 | ||||||||
\(483\) | −31.8975 | −1.45139 | ||||||||
\(484\) | 3.22188 | 0.146449 | ||||||||
\(485\) | 0.282028 | 0.0128062 | ||||||||
\(486\) | 31.5883 | 1.43288 | ||||||||
\(487\) | −3.73893 | −0.169427 | −0.0847135 | − | 0.996405i | \(-0.526998\pi\) | ||||
−0.0847135 | + | 0.996405i | \(0.526998\pi\) | |||||||
\(488\) | −0.403670 | −0.0182733 | ||||||||
\(489\) | −1.70393 | −0.0770546 | ||||||||
\(490\) | −76.2700 | −3.44553 | ||||||||
\(491\) | −8.17665 | −0.369007 | −0.184504 | − | 0.982832i | \(-0.559068\pi\) | ||||
−0.184504 | + | 0.982832i | \(0.559068\pi\) | |||||||
\(492\) | 32.9207 | 1.48418 | ||||||||
\(493\) | 1.99600 | 0.0898952 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.77812 | −0.169814 | ||||||||
\(496\) | 0.380486 | 0.0170843 | ||||||||
\(497\) | −7.72889 | −0.346688 | ||||||||
\(498\) | 15.0232 | 0.673205 | ||||||||
\(499\) | 0.918694 | 0.0411264 | 0.0205632 | − | 0.999789i | \(-0.493454\pi\) | ||||
0.0205632 | + | 0.999789i | \(0.493454\pi\) | |||||||
\(500\) | 30.0060 | 1.34191 | ||||||||
\(501\) | −29.1225 | −1.30110 | ||||||||
\(502\) | 18.6024 | 0.830264 | ||||||||
\(503\) | −18.1085 | −0.807418 | −0.403709 | − | 0.914887i | \(-0.632279\pi\) | ||||
−0.403709 | + | 0.914887i | \(0.632279\pi\) | |||||||
\(504\) | 18.9648 | 0.844760 | ||||||||
\(505\) | 31.9820 | 1.42318 | ||||||||
\(506\) | −13.2359 | −0.588408 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.5803 | −0.868736 | ||||||||
\(509\) | −20.4086 | −0.904594 | −0.452297 | − | 0.891867i | \(-0.649395\pi\) | ||||
−0.452297 | + | 0.891867i | \(0.649395\pi\) | |||||||
\(510\) | 22.5531 | 0.998670 | ||||||||
\(511\) | −9.01404 | −0.398758 | ||||||||
\(512\) | 0.715746 | 0.0316318 | ||||||||
\(513\) | −12.9327 | −0.570994 | ||||||||
\(514\) | −40.8984 | −1.80395 | ||||||||
\(515\) | −39.1858 | −1.72673 | ||||||||
\(516\) | 43.6637 | 1.92219 | ||||||||
\(517\) | 6.74293 | 0.296554 | ||||||||
\(518\) | 52.1475 | 2.29123 | ||||||||
\(519\) | −9.03900 | −0.396768 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0069 | −0.526033 | −0.263016 | − | 0.964791i | \(-0.584717\pi\) | ||||
−0.263016 | + | 0.964791i | \(0.584717\pi\) | |||||||
\(522\) | 2.13345 | 0.0933787 | ||||||||
\(523\) | 17.8414 | 0.780150 | 0.390075 | − | 0.920783i | \(-0.372449\pi\) | ||||
0.390075 | + | 0.920783i | \(0.372449\pi\) | |||||||
\(524\) | −38.5039 | −1.68205 | ||||||||
\(525\) | −7.07730 | −0.308879 | ||||||||
\(526\) | −35.5732 | −1.55107 | ||||||||
\(527\) | 19.3765 | 0.844053 | ||||||||
\(528\) | 0.0773036 | 0.00336421 | ||||||||
\(529\) | 10.5491 | 0.458658 | ||||||||
\(530\) | 23.2780 | 1.01113 | ||||||||
\(531\) | 16.6725 | 0.723527 | ||||||||
\(532\) | −34.1014 | −1.47848 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 23.7530 | 1.02789 | ||||||||
\(535\) | 14.0882 | 0.609087 | ||||||||
\(536\) | −24.3725 | −1.05273 | ||||||||
\(537\) | 22.6304 | 0.976575 | ||||||||
\(538\) | −3.41168 | −0.147088 | ||||||||
\(539\) | −13.3132 | −0.573441 | ||||||||
\(540\) | 44.4819 | 1.91419 | ||||||||
\(541\) | 19.1234 | 0.822180 | 0.411090 | − | 0.911595i | \(-0.365148\pi\) | ||||
0.411090 | + | 0.911595i | \(0.365148\pi\) | |||||||
\(542\) | −53.1778 | −2.28418 | ||||||||
\(543\) | −22.0624 | −0.946787 | ||||||||
\(544\) | 18.4578 | 0.791371 | ||||||||
\(545\) | 24.8312 | 1.06365 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.1225 | −1.88654 | −0.943272 | − | 0.332022i | \(-0.892269\pi\) | ||||
−0.943272 | + | 0.332022i | \(0.892269\pi\) | |||||||
\(548\) | 7.31722 | 0.312576 | ||||||||
\(549\) | 0.217874 | 0.00929862 | ||||||||
\(550\) | −2.93673 | −0.125223 | ||||||||
\(551\) | −1.45487 | −0.0619796 | ||||||||
\(552\) | 19.7610 | 0.841083 | ||||||||
\(553\) | −8.44375 | −0.359065 | ||||||||
\(554\) | −32.1295 | −1.36505 | ||||||||
\(555\) | 15.5101 | 0.658368 | ||||||||
\(556\) | −32.7169 | −1.38751 | ||||||||
\(557\) | 21.3453 | 0.904429 | 0.452215 | − | 0.891909i | \(-0.350634\pi\) | ||||
0.452215 | + | 0.891909i | \(0.350634\pi\) | |||||||
\(558\) | 20.7109 | 0.876760 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.714858 | −0.0302082 | ||||||||
\(561\) | 3.93673 | 0.166209 | ||||||||
\(562\) | −26.6897 | −1.12584 | ||||||||
\(563\) | −19.9187 | −0.839473 | −0.419736 | − | 0.907646i | \(-0.637877\pi\) | ||||
−0.419736 | + | 0.907646i | \(0.637877\pi\) | |||||||
\(564\) | −26.5451 | −1.11775 | ||||||||
\(565\) | −20.6828 | −0.870131 | ||||||||
\(566\) | −7.93362 | −0.333475 | ||||||||
\(567\) | 9.95077 | 0.417893 | ||||||||
\(568\) | 4.78816 | 0.200907 | ||||||||
\(569\) | 46.4217 | 1.94610 | 0.973050 | − | 0.230596i | \(-0.0740675\pi\) | ||||
0.973050 | + | 0.230596i | \(0.0740675\pi\) | |||||||
\(570\) | −16.4389 | −0.688548 | ||||||||
\(571\) | −5.67878 | −0.237649 | −0.118825 | − | 0.992915i | \(-0.537913\pi\) | ||||
−0.118825 | + | 0.992915i | \(0.537913\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.10849 | −0.171635 | ||||||||
\(574\) | −86.1263 | −3.59484 | ||||||||
\(575\) | 7.44375 | 0.310426 | ||||||||
\(576\) | 19.5382 | 0.814092 | ||||||||
\(577\) | 6.37648 | 0.265456 | 0.132728 | − | 0.991152i | \(-0.457626\pi\) | ||||
0.132728 | + | 0.991152i | \(0.457626\pi\) | |||||||
\(578\) | −15.1265 | −0.629181 | ||||||||
\(579\) | −19.0593 | −0.792076 | ||||||||
\(580\) | 5.00400 | 0.207780 | ||||||||
\(581\) | −24.2500 | −1.00606 | ||||||||
\(582\) | −0.314105 | −0.0130201 | ||||||||
\(583\) | 4.06327 | 0.168283 | ||||||||
\(584\) | 5.58432 | 0.231081 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.5783 | −0.602224 | ||||||||
\(587\) | 0.873467 | 0.0360519 | 0.0180259 | − | 0.999838i | \(-0.494262\pi\) | ||||
0.0180259 | + | 0.999838i | \(0.494262\pi\) | |||||||
\(588\) | 52.4106 | 2.16138 | ||||||||
\(589\) | −14.1234 | −0.581945 | ||||||||
\(590\) | 63.3803 | 2.60933 | ||||||||
\(591\) | 25.6937 | 1.05690 | ||||||||
\(592\) | 0.320334 | 0.0131657 | ||||||||
\(593\) | −18.7850 | −0.771409 | −0.385705 | − | 0.922622i | \(-0.626042\pi\) | ||||
−0.385705 | + | 0.922622i | \(0.626042\pi\) | |||||||
\(594\) | 12.5843 | 0.516341 | ||||||||
\(595\) | −36.4046 | −1.49244 | ||||||||
\(596\) | 35.3273 | 1.44706 | ||||||||
\(597\) | −27.6295 | −1.13080 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.7601 | 0.480504 | 0.240252 | − | 0.970711i | \(-0.422770\pi\) | ||||
0.240252 | + | 0.970711i | \(0.422770\pi\) | |||||||
\(600\) | 4.38449 | 0.178996 | ||||||||
\(601\) | 28.5171 | 1.16323 | 0.581617 | − | 0.813462i | \(-0.302420\pi\) | ||||
0.581617 | + | 0.813462i | \(0.302420\pi\) | |||||||
\(602\) | −114.232 | −4.65574 | ||||||||
\(603\) | 13.1546 | 0.535697 | ||||||||
\(604\) | 35.0653 | 1.42679 | ||||||||
\(605\) | −2.50702 | −0.101925 | ||||||||
\(606\) | −35.6195 | −1.44694 | ||||||||
\(607\) | 15.4718 | 0.627982 | 0.313991 | − | 0.949426i | \(-0.398334\pi\) | ||||
0.313991 | + | 0.949426i | \(0.398334\pi\) | |||||||
\(608\) | −13.4538 | −0.545623 | ||||||||
\(609\) | 3.41168 | 0.138248 | ||||||||
\(610\) | 0.828241 | 0.0335345 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 15.6436 | 0.632354 | ||||||||
\(613\) | 19.5883 | 0.791165 | 0.395582 | − | 0.918430i | \(-0.370543\pi\) | ||||
0.395582 | + | 0.918430i | \(0.370543\pi\) | |||||||
\(614\) | −11.5703 | −0.466939 | ||||||||
\(615\) | −25.6164 | −1.03295 | ||||||||
\(616\) | 12.5843 | 0.507037 | ||||||||
\(617\) | 29.3101 | 1.17998 | 0.589990 | − | 0.807410i | \(-0.299132\pi\) | ||||
0.589990 | + | 0.807410i | \(0.299132\pi\) | |||||||
\(618\) | 43.6427 | 1.75557 | ||||||||
\(619\) | 3.74293 | 0.150441 | 0.0752206 | − | 0.997167i | \(-0.476034\pi\) | ||||
0.0752206 | + | 0.997167i | \(0.476034\pi\) | |||||||
\(620\) | 48.5772 | 1.95091 | ||||||||
\(621\) | −31.8975 | −1.28000 | ||||||||
\(622\) | 6.67166 | 0.267509 | ||||||||
\(623\) | −38.3413 | −1.53611 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.7741 | −1.19096 | ||||||||
\(626\) | 36.0782 | 1.44197 | ||||||||
\(627\) | −2.86946 | −0.114595 | ||||||||
\(628\) | 45.0481 | 1.79762 | ||||||||
\(629\) | 16.3132 | 0.650451 | ||||||||
\(630\) | −38.9116 | −1.55027 | ||||||||
\(631\) | 22.5179 | 0.896425 | 0.448213 | − | 0.893927i | \(-0.352061\pi\) | ||||
0.448213 | + | 0.893927i | \(0.352061\pi\) | |||||||
\(632\) | 5.23102 | 0.208079 | ||||||||
\(633\) | 24.8975 | 0.989588 | ||||||||
\(634\) | 46.7077 | 1.85500 | ||||||||
\(635\) | 15.2359 | 0.604619 | ||||||||
\(636\) | −15.9960 | −0.634283 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.41568 | 0.0560472 | ||||||||
\(639\) | −2.58432 | −0.102234 | ||||||||
\(640\) | 45.5491 | 1.80049 | ||||||||
\(641\) | 26.5812 | 1.04989 | 0.524947 | − | 0.851135i | \(-0.324085\pi\) | ||||
0.524947 | + | 0.851135i | \(0.324085\pi\) | |||||||
\(642\) | −15.6906 | −0.619258 | ||||||||
\(643\) | −1.28514 | −0.0506811 | −0.0253405 | − | 0.999679i | \(-0.508067\pi\) | ||||
−0.0253405 | + | 0.999679i | \(0.508067\pi\) | |||||||
\(644\) | −84.1083 | −3.31433 | ||||||||
\(645\) | −33.9757 | −1.33779 | ||||||||
\(646\) | −17.2900 | −0.680267 | ||||||||
\(647\) | −13.7741 | −0.541517 | −0.270758 | − | 0.962647i | \(-0.587274\pi\) | ||||
−0.270758 | + | 0.962647i | \(0.587274\pi\) | |||||||
\(648\) | −6.16464 | −0.242170 | ||||||||
\(649\) | 11.0633 | 0.434271 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.1194 | 1.29805 | ||||||||
\(652\) | −4.49298 | −0.175959 | ||||||||
\(653\) | 15.5382 | 0.608057 | 0.304029 | − | 0.952663i | \(-0.401668\pi\) | ||||
0.304029 | + | 0.952663i | \(0.401668\pi\) | |||||||
\(654\) | −27.6554 | −1.08141 | ||||||||
\(655\) | 29.9608 | 1.17067 | ||||||||
\(656\) | −0.529061 | −0.0206564 | ||||||||
\(657\) | −3.01404 | −0.117589 | ||||||||
\(658\) | 69.4467 | 2.70731 | ||||||||
\(659\) | 20.3734 | 0.793634 | 0.396817 | − | 0.917898i | \(-0.370115\pi\) | ||||
0.396817 | + | 0.917898i | \(0.370115\pi\) | |||||||
\(660\) | 9.86946 | 0.384168 | ||||||||
\(661\) | −0.989077 | −0.0384706 | −0.0192353 | − | 0.999815i | \(-0.506123\pi\) | ||||
−0.0192353 | + | 0.999815i | \(0.506123\pi\) | |||||||
\(662\) | 64.6264 | 2.51178 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.0232 | 0.583013 | ||||||||
\(665\) | 26.5351 | 1.02899 | ||||||||
\(666\) | 17.4366 | 0.675656 | ||||||||
\(667\) | −3.58832 | −0.138940 | ||||||||
\(668\) | −76.7911 | −2.97114 | ||||||||
\(669\) | 21.7178 | 0.839658 | ||||||||
\(670\) | 50.0069 | 1.93194 | ||||||||
\(671\) | 0.144573 | 0.00558116 | ||||||||
\(672\) | 31.5491 | 1.21703 | ||||||||
\(673\) | 30.2992 | 1.16795 | 0.583974 | − | 0.811773i | \(-0.301497\pi\) | ||||
0.583974 | + | 0.811773i | \(0.301497\pi\) | |||||||
\(674\) | −72.9546 | −2.81011 | ||||||||
\(675\) | −7.07730 | −0.272406 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.6788 | 0.794750 | 0.397375 | − | 0.917656i | \(-0.369921\pi\) | ||||
0.397375 | + | 0.917656i | \(0.369921\pi\) | |||||||
\(678\) | 23.0352 | 0.884661 | ||||||||
\(679\) | 0.507019 | 0.0194576 | ||||||||
\(680\) | 22.5531 | 0.864873 | ||||||||
\(681\) | −7.11161 | −0.272517 | ||||||||
\(682\) | 13.7429 | 0.526244 | ||||||||
\(683\) | 0.439750 | 0.0168266 | 0.00841328 | − | 0.999965i | \(-0.497322\pi\) | ||||
0.00841328 | + | 0.999965i | \(0.497322\pi\) | |||||||
\(684\) | −11.4025 | −0.435987 | ||||||||
\(685\) | −5.69370 | −0.217545 | ||||||||
\(686\) | −65.0210 | −2.48251 | ||||||||
\(687\) | −28.9165 | −1.10323 | ||||||||
\(688\) | −0.701708 | −0.0267524 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −40.5451 | −1.54353 | ||||||||
\(691\) | −20.0421 | −0.762438 | −0.381219 | − | 0.924485i | \(-0.624496\pi\) | ||||
−0.381219 | + | 0.924485i | \(0.624496\pi\) | |||||||
\(692\) | −23.8343 | −0.906043 | ||||||||
\(693\) | −6.79216 | −0.258013 | ||||||||
\(694\) | −4.38449 | −0.166433 | ||||||||
\(695\) | 25.4578 | 0.965669 | ||||||||
\(696\) | −2.11358 | −0.0801151 | ||||||||
\(697\) | −26.9428 | −1.02053 | ||||||||
\(698\) | 0.433718 | 0.0164165 | ||||||||
\(699\) | −27.9657 | −1.05776 | ||||||||
\(700\) | −18.6616 | −0.705343 | ||||||||
\(701\) | −36.9898 | −1.39708 | −0.698542 | − | 0.715569i | \(-0.746168\pi\) | ||||
−0.698542 | + | 0.715569i | \(0.746168\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.8906 | −0.448463 | ||||||||
\(704\) | 12.9648 | 0.488630 | ||||||||
\(705\) | 20.6554 | 0.777927 | ||||||||
\(706\) | 25.0220 | 0.941717 | ||||||||
\(707\) | 57.4959 | 2.16236 | ||||||||
\(708\) | −43.5531 | −1.63683 | ||||||||
\(709\) | −33.8022 | −1.26947 | −0.634734 | − | 0.772731i | \(-0.718890\pi\) | ||||
−0.634734 | + | 0.772731i | \(0.718890\pi\) | |||||||
\(710\) | −9.82424 | −0.368697 | ||||||||
\(711\) | −2.82335 | −0.105884 | ||||||||
\(712\) | 23.7530 | 0.890180 | ||||||||
\(713\) | −34.8343 | −1.30455 | ||||||||
\(714\) | 40.5451 | 1.51736 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 59.6725 | 2.23007 | ||||||||
\(717\) | −19.7953 | −0.739268 | ||||||||
\(718\) | −8.66563 | −0.323398 | ||||||||
\(719\) | 12.2210 | 0.455766 | 0.227883 | − | 0.973689i | \(-0.426820\pi\) | ||||
0.227883 | + | 0.973689i | \(0.426820\pi\) | |||||||
\(720\) | −0.239028 | −0.00890805 | ||||||||
\(721\) | −70.4467 | −2.62357 | ||||||||
\(722\) | −30.8151 | −1.14682 | ||||||||
\(723\) | −0.236802 | −0.00880674 | ||||||||
\(724\) | −58.1747 | −2.16204 | ||||||||
\(725\) | −0.796164 | −0.0295688 | ||||||||
\(726\) | 2.79216 | 0.103627 | ||||||||
\(727\) | 35.2771 | 1.30836 | 0.654178 | − | 0.756340i | \(-0.273015\pi\) | ||||
0.654178 | + | 0.756340i | \(0.273015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.5139 | 0.870887 | ||||||||
\(730\) | −11.4578 | −0.424072 | ||||||||
\(731\) | −35.7349 | −1.32170 | ||||||||
\(732\) | −0.569144 | −0.0210362 | ||||||||
\(733\) | −17.0953 | −0.631431 | −0.315715 | − | 0.948854i | \(-0.602245\pi\) | ||||
−0.315715 | + | 0.948854i | \(0.602245\pi\) | |||||||
\(734\) | −57.1444 | −2.10924 | ||||||||
\(735\) | −40.7819 | −1.50426 | ||||||||
\(736\) | −33.1827 | −1.22313 | ||||||||
\(737\) | 8.72889 | 0.321533 | ||||||||
\(738\) | −28.7982 | −1.06008 | ||||||||
\(739\) | 43.2279 | 1.59016 | 0.795082 | − | 0.606502i | \(-0.207428\pi\) | ||||
0.795082 | + | 0.606502i | \(0.207428\pi\) | |||||||
\(740\) | 40.8975 | 1.50342 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 41.8483 | 1.53630 | ||||||||
\(743\) | −1.45868 | −0.0535137 | −0.0267568 | − | 0.999642i | \(-0.508518\pi\) | ||||
−0.0267568 | + | 0.999642i | \(0.508518\pi\) | |||||||
\(744\) | −20.5179 | −0.752224 | ||||||||
\(745\) | −27.4890 | −1.00712 | ||||||||
\(746\) | −19.8343 | −0.726184 | ||||||||
\(747\) | −8.10849 | −0.296674 | ||||||||
\(748\) | 10.3805 | 0.379548 | ||||||||
\(749\) | 25.3273 | 0.925438 | ||||||||
\(750\) | 26.0040 | 0.949532 | ||||||||
\(751\) | 15.3593 | 0.560470 | 0.280235 | − | 0.959931i | \(-0.409588\pi\) | ||||
0.280235 | + | 0.959931i | \(0.409588\pi\) | |||||||
\(752\) | 0.426600 | 0.0155565 | ||||||||
\(753\) | 9.94677 | 0.362480 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.2851 | −0.993008 | ||||||||
\(756\) | 79.9677 | 2.90840 | ||||||||
\(757\) | 34.3796 | 1.24955 | 0.624774 | − | 0.780806i | \(-0.285191\pi\) | ||||
0.624774 | + | 0.780806i | \(0.285191\pi\) | |||||||
\(758\) | −33.6255 | −1.22133 | ||||||||
\(759\) | −7.07730 | −0.256890 | ||||||||
\(760\) | −16.4389 | −0.596300 | ||||||||
\(761\) | 3.88662 | 0.140890 | 0.0704449 | − | 0.997516i | \(-0.477558\pi\) | ||||
0.0704449 | + | 0.997516i | \(0.477558\pi\) | |||||||
\(762\) | −16.9688 | −0.614715 | ||||||||
\(763\) | 44.6405 | 1.61609 | ||||||||
\(764\) | −10.8334 | −0.391938 | ||||||||
\(765\) | −12.1726 | −0.440103 | ||||||||
\(766\) | 12.3181 | 0.445071 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −19.0470 | −0.687300 | ||||||||
\(769\) | −39.4257 | −1.42173 | −0.710864 | − | 0.703330i | \(-0.751696\pi\) | ||||
−0.710864 | + | 0.703330i | \(0.751696\pi\) | |||||||
\(770\) | −25.8202 | −0.930497 | ||||||||
\(771\) | −21.8686 | −0.787578 | ||||||||
\(772\) | −50.2560 | −1.80875 | ||||||||
\(773\) | 24.4406 | 0.879069 | 0.439534 | − | 0.898226i | \(-0.355143\pi\) | ||||
0.439534 | + | 0.898226i | \(0.355143\pi\) | |||||||
\(774\) | −38.1958 | −1.37292 | ||||||||
\(775\) | −7.72889 | −0.277630 | ||||||||
\(776\) | −0.314105 | −0.0112757 | ||||||||
\(777\) | 27.8835 | 1.00032 | ||||||||
\(778\) | −49.2520 | −1.76577 | ||||||||
\(779\) | 19.6384 | 0.703620 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.71486 | −0.0613624 | ||||||||
\(782\) | −42.6445 | −1.52496 | ||||||||
\(783\) | 3.41168 | 0.121923 | ||||||||
\(784\) | −0.842278 | −0.0300814 | ||||||||
\(785\) | −35.0530 | −1.25110 | ||||||||
\(786\) | −33.3685 | −1.19021 | ||||||||
\(787\) | 36.8171 | 1.31239 | 0.656194 | − | 0.754592i | \(-0.272165\pi\) | ||||
0.656194 | + | 0.754592i | \(0.272165\pi\) | |||||||
\(788\) | 67.7499 | 2.41349 | ||||||||
\(789\) | −19.0212 | −0.677171 | ||||||||
\(790\) | −10.7329 | −0.381859 | ||||||||
\(791\) | −37.1827 | −1.32206 | ||||||||
\(792\) | 4.20784 | 0.149519 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 40.0610 | 1.42171 | ||||||||
\(795\) | 12.4469 | 0.441445 | ||||||||
\(796\) | −72.8543 | −2.58225 | ||||||||
\(797\) | 11.5219 | 0.408128 | 0.204064 | − | 0.978958i | \(-0.434585\pi\) | ||||
0.204064 | + | 0.978958i | \(0.434585\pi\) | |||||||
\(798\) | −29.5531 | −1.04617 | ||||||||
\(799\) | 21.7249 | 0.768571 | ||||||||
\(800\) | −7.36245 | −0.260302 | ||||||||
\(801\) | −12.8202 | −0.452981 | ||||||||
\(802\) | 83.2629 | 2.94012 | ||||||||
\(803\) | −2.00000 | −0.0705785 | ||||||||
\(804\) | −34.3633 | −1.21190 | ||||||||
\(805\) | 65.4467 | 2.30669 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.82424 | −0.0642162 | ||||||||
\(808\) | −35.6195 | −1.25309 | ||||||||
\(809\) | −24.4649 | −0.860140 | −0.430070 | − | 0.902795i | \(-0.641511\pi\) | ||||
−0.430070 | + | 0.902795i | \(0.641511\pi\) | |||||||
\(810\) | 12.6485 | 0.444422 | ||||||||
\(811\) | −9.19291 | −0.322807 | −0.161403 | − | 0.986889i | \(-0.551602\pi\) | ||||
−0.161403 | + | 0.986889i | \(0.551602\pi\) | |||||||
\(812\) | 8.99600 | 0.315698 | ||||||||
\(813\) | −28.4344 | −0.997238 | ||||||||
\(814\) | 11.5703 | 0.405538 | ||||||||
\(815\) | 3.49610 | 0.122463 | ||||||||
\(816\) | 0.249063 | 0.00871894 | ||||||||
\(817\) | 26.0470 | 0.911269 | ||||||||
\(818\) | −65.9637 | −2.30637 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −67.5460 | −2.35881 | ||||||||
\(821\) | −30.5952 | −1.06778 | −0.533891 | − | 0.845553i | \(-0.679271\pi\) | ||||
−0.533891 | + | 0.845553i | \(0.679271\pi\) | |||||||
\(822\) | 6.34129 | 0.221178 | ||||||||
\(823\) | −19.2148 | −0.669784 | −0.334892 | − | 0.942256i | \(-0.608700\pi\) | ||||
−0.334892 | + | 0.942256i | \(0.608700\pi\) | |||||||
\(824\) | 43.6427 | 1.52037 | ||||||||
\(825\) | −1.57028 | −0.0546703 | ||||||||
\(826\) | 113.943 | 3.96457 | ||||||||
\(827\) | −28.4990 | −0.991008 | −0.495504 | − | 0.868606i | \(-0.665017\pi\) | ||||
−0.495504 | + | 0.868606i | \(0.665017\pi\) | |||||||
\(828\) | −28.1234 | −0.977356 | ||||||||
\(829\) | −6.68278 | −0.232103 | −0.116051 | − | 0.993243i | \(-0.537024\pi\) | ||||
−0.116051 | + | 0.993243i | \(0.537024\pi\) | |||||||
\(830\) | −30.8242 | −1.06992 | ||||||||
\(831\) | −17.1798 | −0.595959 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −42.8935 | −1.48617 | ||||||||
\(834\) | −28.3533 | −0.981794 | ||||||||
\(835\) | 59.7530 | 2.06784 | ||||||||
\(836\) | −7.56628 | −0.261685 | ||||||||
\(837\) | 33.1194 | 1.14477 | ||||||||
\(838\) | −9.60839 | −0.331916 | ||||||||
\(839\) | −8.63044 | −0.297956 | −0.148978 | − | 0.988841i | \(-0.547598\pi\) | ||||
−0.148978 | + | 0.988841i | \(0.547598\pi\) | |||||||
\(840\) | 38.5491 | 1.33007 | ||||||||
\(841\) | −28.6162 | −0.986766 | ||||||||
\(842\) | −31.0421 | −1.06978 | ||||||||
\(843\) | −14.2711 | −0.491523 | ||||||||
\(844\) | 65.6505 | 2.25978 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 23.2210 | 0.798354 | ||||||||
\(847\) | −4.50702 | −0.154863 | ||||||||
\(848\) | 0.257068 | 0.00882775 | ||||||||
\(849\) | −4.24214 | −0.145590 | ||||||||
\(850\) | −9.46179 | −0.324537 | ||||||||
\(851\) | −29.3273 | −1.00533 | ||||||||
\(852\) | 6.75094 | 0.231283 | ||||||||
\(853\) | 18.2631 | 0.625317 | 0.312658 | − | 0.949866i | \(-0.398781\pi\) | ||||
0.312658 | + | 0.949866i | \(0.398781\pi\) | |||||||
\(854\) | 1.48898 | 0.0509518 | ||||||||
\(855\) | 8.87258 | 0.303436 | ||||||||
\(856\) | −15.6906 | −0.536293 | ||||||||
\(857\) | 1.22899 | 0.0419816 | 0.0209908 | − | 0.999780i | \(-0.493318\pi\) | ||||
0.0209908 | + | 0.999780i | \(0.493318\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.15772 | 0.141860 | 0.0709298 | − | 0.997481i | \(-0.477403\pi\) | ||||
0.0709298 | + | 0.997481i | \(0.477403\pi\) | |||||||
\(860\) | −89.5881 | −3.05493 | ||||||||
\(861\) | −46.0521 | −1.56945 | ||||||||
\(862\) | 68.6414 | 2.33793 | ||||||||
\(863\) | 30.0633 | 1.02337 | 0.511683 | − | 0.859174i | \(-0.329022\pi\) | ||||
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(864\) | 31.5491 | 1.07332 | ||||||||
\(865\) | 18.5460 | 0.630583 | ||||||||
\(866\) | 9.72801 | 0.330571 | ||||||||
\(867\) | −8.08823 | −0.274691 | ||||||||
\(868\) | 87.3302 | 2.96418 | ||||||||
\(869\) | −1.87347 | −0.0635530 | ||||||||
\(870\) | 4.33660 | 0.147024 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −27.6554 | −0.936530 | ||||||||
\(873\) | 0.169533 | 0.00573781 | ||||||||
\(874\) | 31.0833 | 1.05141 | ||||||||
\(875\) | −41.9748 | −1.41901 | ||||||||
\(876\) | 7.87347 | 0.266020 | ||||||||
\(877\) | −54.3092 | −1.83389 | −0.916946 | − | 0.399011i | \(-0.869353\pi\) | ||||
−0.916946 | + | 0.399011i | \(0.869353\pi\) | |||||||
\(878\) | −11.4328 | −0.385839 | ||||||||
\(879\) | −7.79508 | −0.262921 | ||||||||
\(880\) | −0.158610 | −0.00534674 | ||||||||
\(881\) | 32.8162 | 1.10561 | 0.552803 | − | 0.833312i | \(-0.313558\pi\) | ||||
0.552803 | + | 0.833312i | \(0.313558\pi\) | |||||||
\(882\) | −45.8474 | −1.54376 | ||||||||
\(883\) | −38.3444 | −1.29039 | −0.645196 | − | 0.764017i | \(-0.723224\pi\) | ||||
−0.645196 | + | 0.764017i | \(0.723224\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.8897 | 1.13919 | ||||||||
\(886\) | 64.6926 | 2.17339 | ||||||||
\(887\) | 19.5382 | 0.656029 | 0.328014 | − | 0.944673i | \(-0.393621\pi\) | ||||
0.328014 | + | 0.944673i | \(0.393621\pi\) | |||||||
\(888\) | −17.2742 | −0.579685 | ||||||||
\(889\) | 27.3905 | 0.918649 | ||||||||
\(890\) | −48.7358 | −1.63363 | ||||||||
\(891\) | 2.20784 | 0.0739654 | ||||||||
\(892\) | 57.2660 | 1.91741 | ||||||||
\(893\) | −15.8352 | −0.529903 | ||||||||
\(894\) | 30.6155 | 1.02394 | ||||||||
\(895\) | −46.4326 | −1.55207 | ||||||||
\(896\) | 81.8864 | 2.73563 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.0842 | 0.436626 | ||||||||
\(899\) | 3.72578 | 0.124262 | ||||||||
\(900\) | −6.23992 | −0.207997 | ||||||||
\(901\) | 13.0913 | 0.436136 | ||||||||
\(902\) | −19.1094 | −0.636273 | ||||||||
\(903\) | −61.0802 | −2.03262 | ||||||||
\(904\) | 23.0352 | 0.766139 | ||||||||
\(905\) | 45.2671 | 1.50473 | ||||||||
\(906\) | 30.3885 | 1.00959 | ||||||||
\(907\) | 39.2600 | 1.30361 | 0.651803 | − | 0.758388i | \(-0.274013\pi\) | ||||
0.651803 | + | 0.758388i | \(0.274013\pi\) | |||||||
\(908\) | −18.7521 | −0.622310 | ||||||||
\(909\) | 19.2250 | 0.637653 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.1194 | −0.368403 | −0.184201 | − | 0.982889i | \(-0.558970\pi\) | ||||
−0.184201 | + | 0.982889i | \(0.558970\pi\) | |||||||
\(912\) | −0.181540 | −0.00601141 | ||||||||
\(913\) | −5.38049 | −0.178068 | ||||||||
\(914\) | 28.5411 | 0.944057 | ||||||||
\(915\) | 0.442864 | 0.0146406 | ||||||||
\(916\) | −76.2477 | −2.51930 | ||||||||
\(917\) | 53.8623 | 1.77869 | ||||||||
\(918\) | 40.5451 | 1.33819 | ||||||||
\(919\) | 8.77501 | 0.289461 | 0.144730 | − | 0.989471i | \(-0.453769\pi\) | ||||
0.144730 | + | 0.989471i | \(0.453769\pi\) | |||||||
\(920\) | −40.5451 | −1.33673 | ||||||||
\(921\) | −6.18668 | −0.203858 | ||||||||
\(922\) | 30.1014 | 0.991336 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 17.7429 | 0.583700 | ||||||||
\(925\) | −6.50702 | −0.213949 | ||||||||
\(926\) | 23.7850 | 0.781625 | ||||||||
\(927\) | −23.5554 | −0.773660 | ||||||||
\(928\) | 3.54913 | 0.116506 | ||||||||
\(929\) | −25.2279 | −0.827701 | −0.413850 | − | 0.910345i | \(-0.635816\pi\) | ||||
−0.413850 | + | 0.910345i | \(0.635816\pi\) | |||||||
\(930\) | 42.0983 | 1.38046 | ||||||||
\(931\) | 31.2649 | 1.02466 | ||||||||
\(932\) | −73.7407 | −2.41546 | ||||||||
\(933\) | 3.56737 | 0.116790 | ||||||||
\(934\) | 53.3703 | 1.74633 | ||||||||
\(935\) | −8.07730 | −0.264156 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.68589 | 0.185750 | 0.0928750 | − | 0.995678i | \(-0.470394\pi\) | ||||
0.0928750 | + | 0.995678i | \(0.470394\pi\) | |||||||
\(938\) | 89.9005 | 2.93535 | ||||||||
\(939\) | 19.2912 | 0.629544 | ||||||||
\(940\) | 54.4647 | 1.77644 | ||||||||
\(941\) | −12.2468 | −0.399235 | −0.199618 | − | 0.979874i | \(-0.563970\pi\) | ||||
−0.199618 | + | 0.979874i | \(0.563970\pi\) | |||||||
\(942\) | 39.0399 | 1.27199 | ||||||||
\(943\) | 48.4366 | 1.57731 | ||||||||
\(944\) | 0.699932 | 0.0227809 | ||||||||
\(945\) | −62.2248 | −2.02417 | ||||||||
\(946\) | −25.3453 | −0.824047 | ||||||||
\(947\) | 27.5663 | 0.895784 | 0.447892 | − | 0.894088i | \(-0.352175\pi\) | ||||
0.447892 | + | 0.894088i | \(0.352175\pi\) | |||||||
\(948\) | 7.37534 | 0.239540 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6.89665 | 0.223757 | ||||||||
\(951\) | 24.9748 | 0.809865 | ||||||||
\(952\) | 40.5451 | 1.31408 | ||||||||
\(953\) | 12.3444 | 0.399875 | 0.199937 | − | 0.979809i | \(-0.435926\pi\) | ||||
0.199937 | + | 0.979809i | \(0.435926\pi\) | |||||||
\(954\) | 13.9929 | 0.453036 | ||||||||
\(955\) | 8.42972 | 0.272779 | ||||||||
\(956\) | −52.1967 | −1.68816 | ||||||||
\(957\) | 0.756969 | 0.0244693 | ||||||||
\(958\) | −18.7882 | −0.607018 | ||||||||
\(959\) | −10.2359 | −0.330535 | ||||||||
\(960\) | 39.7147 | 1.28179 | ||||||||
\(961\) | 5.16864 | 0.166730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.46871 | 0.272900 | ||||||||
\(964\) | −0.624405 | −0.0201107 | ||||||||
\(965\) | 39.1054 | 1.25885 | ||||||||
\(966\) | −72.8904 | −2.34521 | ||||||||
\(967\) | −13.5451 | −0.435582 | −0.217791 | − | 0.975995i | \(-0.569885\pi\) | ||||
−0.217791 | + | 0.975995i | \(0.569885\pi\) | |||||||
\(968\) | 2.79216 | 0.0897435 | ||||||||
\(969\) | −9.24506 | −0.296994 | ||||||||
\(970\) | 0.644474 | 0.0206928 | ||||||||
\(971\) | −1.48987 | −0.0478121 | −0.0239061 | − | 0.999714i | \(-0.507610\pi\) | ||||
−0.0239061 | + | 0.999714i | \(0.507610\pi\) | |||||||
\(972\) | 44.5371 | 1.42853 | ||||||||
\(973\) | 45.7670 | 1.46722 | ||||||||
\(974\) | −8.54399 | −0.273767 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.00914657 | 0.000292775 0 | ||||||||
\(977\) | 40.1827 | 1.28556 | 0.642779 | − | 0.766052i | \(-0.277781\pi\) | ||||
0.642779 | + | 0.766052i | \(0.277781\pi\) | |||||||
\(978\) | −3.89373 | −0.124508 | ||||||||
\(979\) | −8.50702 | −0.271885 | ||||||||
\(980\) | −107.535 | −3.43508 | ||||||||
\(981\) | 14.9265 | 0.476567 | ||||||||
\(982\) | −18.6848 | −0.596256 | ||||||||
\(983\) | −26.9617 | −0.859944 | −0.429972 | − | 0.902842i | \(-0.641477\pi\) | ||||
−0.429972 | + | 0.902842i | \(0.641477\pi\) | |||||||
\(984\) | 28.5299 | 0.909502 | ||||||||
\(985\) | −52.7178 | −1.67973 | ||||||||
\(986\) | 4.56114 | 0.145256 | ||||||||
\(987\) | 37.1335 | 1.18197 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64.2428 | 2.04280 | ||||||||
\(990\) | −8.63355 | −0.274392 | ||||||||
\(991\) | −41.9225 | −1.33171 | −0.665856 | − | 0.746080i | \(-0.731934\pi\) | ||||
−0.665856 | + | 0.746080i | \(0.731934\pi\) | |||||||
\(992\) | 34.4538 | 1.09391 | ||||||||
\(993\) | 34.5561 | 1.09660 | ||||||||
\(994\) | −17.6616 | −0.560193 | ||||||||
\(995\) | 56.6897 | 1.79718 | ||||||||
\(996\) | 21.1815 | 0.671163 | ||||||||
\(997\) | −39.4037 | −1.24793 | −0.623963 | − | 0.781454i | \(-0.714479\pi\) | ||||
−0.623963 | + | 0.781454i | \(0.714479\pi\) | |||||||
\(998\) | 2.09935 | 0.0664536 | ||||||||
\(999\) | 27.8835 | 0.882195 |
(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 | 1859.2.a.g.1.3 | 3 | ||
13.4 | even | 6 | 143.2.e.b.133.3 | yes | 6 | ||
13.10 | even | 6 | 143.2.e.b.100.3 | ✓ | 6 | ||
13.12 | even | 2 | 1859.2.a.f.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.b.100.3 | ✓ | 6 | 13.10 | even | 6 | ||
143.2.e.b.133.3 | yes | 6 | 13.4 | even | 6 | ||
1859.2.a.f.1.1 | 3 | 13.12 | even | 2 | |||
1859.2.a.g.1.3 | 3 | 1.1 | even | 1 | trivial |