Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.13856\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13856 | −0.805087 | −0.402543 | − | 0.915401i | \(-0.631874\pi\) | ||||
−0.402543 | + | 0.915401i | \(0.631874\pi\) | |||||||
\(3\) | −1.70367 | −0.983615 | −0.491808 | − | 0.870704i | \(-0.663664\pi\) | ||||
−0.491808 | + | 0.870704i | \(0.663664\pi\) | |||||||
\(4\) | −0.703671 | −0.351836 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.93974 | 0.791895 | ||||||||
\(7\) | −4.75660 | −1.79783 | −0.898913 | − | 0.438128i | \(-0.855642\pi\) | ||||
−0.898913 | + | 0.438128i | \(0.855642\pi\) | |||||||
\(8\) | 3.07830 | 1.08834 | ||||||||
\(9\) | −0.0975037 | −0.0325012 | ||||||||
\(10\) | −1.13856 | −0.360046 | ||||||||
\(11\) | 3.46027 | 1.04331 | 0.521655 | − | 0.853156i | \(-0.325315\pi\) | ||||
0.521655 | + | 0.853156i | \(0.325315\pi\) | |||||||
\(12\) | 1.19882 | 0.346071 | ||||||||
\(13\) | 1.17127 | 0.324853 | 0.162427 | − | 0.986721i | \(-0.448068\pi\) | ||||
0.162427 | + | 0.986721i | \(0.448068\pi\) | |||||||
\(14\) | 5.41569 | 1.44740 | ||||||||
\(15\) | −1.70367 | −0.439886 | ||||||||
\(16\) | −2.09750 | −0.524376 | ||||||||
\(17\) | −6.20500 | −1.50493 | −0.752467 | − | 0.658630i | \(-0.771136\pi\) | ||||
−0.752467 | + | 0.658630i | \(0.771136\pi\) | |||||||
\(18\) | 0.111014 | 0.0261663 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.703671 | −0.157346 | ||||||||
\(21\) | 8.10368 | 1.76837 | ||||||||
\(22\) | −3.93974 | −0.839955 | ||||||||
\(23\) | 5.05910 | 1.05490 | 0.527448 | − | 0.849587i | \(-0.323149\pi\) | ||||
0.527448 | + | 0.849587i | \(0.323149\pi\) | |||||||
\(24\) | −5.24442 | −1.07051 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.33357 | −0.261535 | ||||||||
\(27\) | 5.27713 | 1.01558 | ||||||||
\(28\) | 3.34708 | 0.632539 | ||||||||
\(29\) | −1.61070 | −0.299100 | −0.149550 | − | 0.988754i | \(-0.547782\pi\) | ||||
−0.149550 | + | 0.988754i | \(0.547782\pi\) | |||||||
\(30\) | 1.93974 | 0.354146 | ||||||||
\(31\) | 7.49400 | 1.34596 | 0.672981 | − | 0.739660i | \(-0.265014\pi\) | ||||
0.672981 | + | 0.739660i | \(0.265014\pi\) | |||||||
\(32\) | −3.76846 | −0.666177 | ||||||||
\(33\) | −5.89516 | −1.02622 | ||||||||
\(34\) | 7.06479 | 1.21160 | ||||||||
\(35\) | −4.75660 | −0.804012 | ||||||||
\(36\) | 0.0686106 | 0.0114351 | ||||||||
\(37\) | 5.98080 | 0.983237 | 0.491619 | − | 0.870811i | \(-0.336405\pi\) | ||||
0.491619 | + | 0.870811i | \(0.336405\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.99547 | −0.319531 | ||||||||
\(40\) | 3.07830 | 0.486723 | ||||||||
\(41\) | 5.43374 | 0.848607 | 0.424303 | − | 0.905520i | \(-0.360519\pi\) | ||||
0.424303 | + | 0.905520i | \(0.360519\pi\) | |||||||
\(42\) | −9.22656 | −1.42369 | ||||||||
\(43\) | −10.0664 | −1.53512 | −0.767559 | − | 0.640979i | \(-0.778529\pi\) | ||||
−0.767559 | + | 0.640979i | \(0.778529\pi\) | |||||||
\(44\) | −2.43489 | −0.367074 | ||||||||
\(45\) | −0.0975037 | −0.0145350 | ||||||||
\(46\) | −5.76011 | −0.849283 | ||||||||
\(47\) | −8.06479 | −1.17637 | −0.588185 | − | 0.808726i | \(-0.700158\pi\) | ||||
−0.588185 | + | 0.808726i | \(0.700158\pi\) | |||||||
\(48\) | 3.57346 | 0.515784 | ||||||||
\(49\) | 15.6252 | 2.23218 | ||||||||
\(50\) | −1.13856 | −0.161017 | ||||||||
\(51\) | 10.5713 | 1.48028 | ||||||||
\(52\) | −0.824193 | −0.114295 | ||||||||
\(53\) | 6.68283 | 0.917957 | 0.458978 | − | 0.888447i | \(-0.348216\pi\) | ||||
0.458978 | + | 0.888447i | \(0.348216\pi\) | |||||||
\(54\) | −6.00835 | −0.817633 | ||||||||
\(55\) | 3.46027 | 0.466583 | ||||||||
\(56\) | −14.6423 | −1.95665 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.83389 | 0.240801 | ||||||||
\(59\) | −2.17229 | −0.282808 | −0.141404 | − | 0.989952i | \(-0.545162\pi\) | ||||
−0.141404 | + | 0.989952i | \(0.545162\pi\) | |||||||
\(60\) | 1.19882 | 0.154768 | ||||||||
\(61\) | 6.20852 | 0.794919 | 0.397460 | − | 0.917620i | \(-0.369892\pi\) | ||||
0.397460 | + | 0.917620i | \(0.369892\pi\) | |||||||
\(62\) | −8.53240 | −1.08362 | ||||||||
\(63\) | 0.463786 | 0.0584315 | ||||||||
\(64\) | 8.48565 | 1.06071 | ||||||||
\(65\) | 1.17127 | 0.145279 | ||||||||
\(66\) | 6.71202 | 0.826193 | ||||||||
\(67\) | 5.62257 | 0.686906 | 0.343453 | − | 0.939170i | \(-0.388403\pi\) | ||||
0.343453 | + | 0.939170i | \(0.388403\pi\) | |||||||
\(68\) | 4.36628 | 0.529490 | ||||||||
\(69\) | −8.61905 | −1.03761 | ||||||||
\(70\) | 5.41569 | 0.647299 | ||||||||
\(71\) | −2.72287 | −0.323145 | −0.161573 | − | 0.986861i | \(-0.551657\pi\) | ||||
−0.161573 | + | 0.986861i | \(0.551657\pi\) | |||||||
\(72\) | −0.300146 | −0.0353725 | ||||||||
\(73\) | 3.15661 | 0.369453 | 0.184726 | − | 0.982790i | \(-0.440860\pi\) | ||||
0.184726 | + | 0.982790i | \(0.440860\pi\) | |||||||
\(74\) | −6.80953 | −0.791591 | ||||||||
\(75\) | −1.70367 | −0.196723 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.4591 | −1.87569 | ||||||||
\(78\) | 2.27197 | 0.257250 | ||||||||
\(79\) | −12.0783 | −1.35892 | −0.679458 | − | 0.733715i | \(-0.737785\pi\) | ||||
−0.679458 | + | 0.733715i | \(0.737785\pi\) | |||||||
\(80\) | −2.09750 | −0.234508 | ||||||||
\(81\) | −8.69798 | −0.966442 | ||||||||
\(82\) | −6.18666 | −0.683202 | ||||||||
\(83\) | −8.24958 | −0.905509 | −0.452754 | − | 0.891635i | \(-0.649559\pi\) | ||||
−0.452754 | + | 0.891635i | \(0.649559\pi\) | |||||||
\(84\) | −5.70233 | −0.622175 | ||||||||
\(85\) | −6.20500 | −0.673027 | ||||||||
\(86\) | 11.4613 | 1.23590 | ||||||||
\(87\) | 2.74410 | 0.294199 | ||||||||
\(88\) | 10.6518 | 1.13548 | ||||||||
\(89\) | −8.83490 | −0.936498 | −0.468249 | − | 0.883597i | \(-0.655115\pi\) | ||||
−0.468249 | + | 0.883597i | \(0.655115\pi\) | |||||||
\(90\) | 0.111014 | 0.0117019 | ||||||||
\(91\) | −5.57128 | −0.584029 | ||||||||
\(92\) | −3.55995 | −0.371150 | ||||||||
\(93\) | −12.7673 | −1.32391 | ||||||||
\(94\) | 9.18229 | 0.947080 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.42023 | 0.655262 | ||||||||
\(97\) | −0.707489 | −0.0718346 | −0.0359173 | − | 0.999355i | \(-0.511435\pi\) | ||||
−0.0359173 | + | 0.999355i | \(0.511435\pi\) | |||||||
\(98\) | −17.7903 | −1.79709 | ||||||||
\(99\) | −0.337389 | −0.0339089 | ||||||||
\(100\) | −0.703671 | −0.0703671 | ||||||||
\(101\) | −0.112658 | −0.0112099 | −0.00560497 | − | 0.999984i | \(-0.501784\pi\) | ||||
−0.00560497 | + | 0.999984i | \(0.501784\pi\) | |||||||
\(102\) | −12.0361 | −1.19175 | ||||||||
\(103\) | −11.3233 | −1.11572 | −0.557861 | − | 0.829934i | \(-0.688378\pi\) | ||||
−0.557861 | + | 0.829934i | \(0.688378\pi\) | |||||||
\(104\) | 3.60554 | 0.353552 | ||||||||
\(105\) | 8.10368 | 0.790838 | ||||||||
\(106\) | −7.60883 | −0.739035 | ||||||||
\(107\) | 2.17861 | 0.210614 | 0.105307 | − | 0.994440i | \(-0.466417\pi\) | ||||
0.105307 | + | 0.994440i | \(0.466417\pi\) | |||||||
\(108\) | −3.71336 | −0.357319 | ||||||||
\(109\) | 13.3663 | 1.28026 | 0.640129 | − | 0.768268i | \(-0.278881\pi\) | ||||
0.640129 | + | 0.768268i | \(0.278881\pi\) | |||||||
\(110\) | −3.93974 | −0.375639 | ||||||||
\(111\) | −10.1893 | −0.967127 | ||||||||
\(112\) | 9.97698 | 0.942736 | ||||||||
\(113\) | −11.8586 | −1.11557 | −0.557783 | − | 0.829987i | \(-0.688348\pi\) | ||||
−0.557783 | + | 0.829987i | \(0.688348\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.05910 | 0.471764 | ||||||||
\(116\) | 1.13340 | 0.105234 | ||||||||
\(117\) | −0.114204 | −0.0105581 | ||||||||
\(118\) | 2.47329 | 0.227685 | ||||||||
\(119\) | 29.5147 | 2.70561 | ||||||||
\(120\) | −5.24442 | −0.478748 | ||||||||
\(121\) | 0.973466 | 0.0884969 | ||||||||
\(122\) | −7.06880 | −0.639979 | ||||||||
\(123\) | −9.25730 | −0.834703 | ||||||||
\(124\) | −5.27331 | −0.473557 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.528050 | −0.0470424 | ||||||||
\(127\) | −20.0596 | −1.78000 | −0.890000 | − | 0.455960i | \(-0.849296\pi\) | ||||
−0.890000 | + | 0.455960i | \(0.849296\pi\) | |||||||
\(128\) | −2.12452 | −0.187783 | ||||||||
\(129\) | 17.1499 | 1.50996 | ||||||||
\(130\) | −1.33357 | −0.116962 | ||||||||
\(131\) | 9.21953 | 0.805514 | 0.402757 | − | 0.915307i | \(-0.368052\pi\) | ||||
0.402757 | + | 0.915307i | \(0.368052\pi\) | |||||||
\(132\) | 4.14826 | 0.361059 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.40165 | −0.553019 | ||||||||
\(135\) | 5.27713 | 0.454183 | ||||||||
\(136\) | −19.1009 | −1.63789 | ||||||||
\(137\) | −3.46596 | −0.296117 | −0.148058 | − | 0.988979i | \(-0.547302\pi\) | ||||
−0.148058 | + | 0.988979i | \(0.547302\pi\) | |||||||
\(138\) | 9.81334 | 0.835367 | ||||||||
\(139\) | −1.92271 | −0.163082 | −0.0815412 | − | 0.996670i | \(-0.525984\pi\) | ||||
−0.0815412 | + | 0.996670i | \(0.525984\pi\) | |||||||
\(140\) | 3.34708 | 0.282880 | ||||||||
\(141\) | 13.7398 | 1.15710 | ||||||||
\(142\) | 3.10016 | 0.260160 | ||||||||
\(143\) | 4.05293 | 0.338923 | ||||||||
\(144\) | 0.204514 | 0.0170429 | ||||||||
\(145\) | −1.61070 | −0.133761 | ||||||||
\(146\) | −3.59400 | −0.297442 | ||||||||
\(147\) | −26.6203 | −2.19560 | ||||||||
\(148\) | −4.20852 | −0.345938 | ||||||||
\(149\) | 3.37579 | 0.276555 | 0.138278 | − | 0.990393i | \(-0.455843\pi\) | ||||
0.138278 | + | 0.990393i | \(0.455843\pi\) | |||||||
\(150\) | 1.93974 | 0.158379 | ||||||||
\(151\) | −19.6888 | −1.60225 | −0.801125 | − | 0.598497i | \(-0.795765\pi\) | ||||
−0.801125 | + | 0.598497i | \(0.795765\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.605011 | 0.0489122 | ||||||||
\(154\) | 18.7398 | 1.51009 | ||||||||
\(155\) | 7.49400 | 0.601932 | ||||||||
\(156\) | 1.40415 | 0.112422 | ||||||||
\(157\) | 10.8049 | 0.862321 | 0.431161 | − | 0.902275i | \(-0.358104\pi\) | ||||
0.431161 | + | 0.902275i | \(0.358104\pi\) | |||||||
\(158\) | 13.7519 | 1.09404 | ||||||||
\(159\) | −11.3853 | −0.902916 | ||||||||
\(160\) | −3.76846 | −0.297923 | ||||||||
\(161\) | −24.0641 | −1.89652 | ||||||||
\(162\) | 9.90321 | 0.778070 | ||||||||
\(163\) | −2.40117 | −0.188074 | −0.0940369 | − | 0.995569i | \(-0.529977\pi\) | ||||
−0.0940369 | + | 0.995569i | \(0.529977\pi\) | |||||||
\(164\) | −3.82356 | −0.298570 | ||||||||
\(165\) | −5.89516 | −0.458938 | ||||||||
\(166\) | 9.39268 | 0.729013 | ||||||||
\(167\) | −18.8862 | −1.46146 | −0.730728 | − | 0.682668i | \(-0.760819\pi\) | ||||
−0.730728 | + | 0.682668i | \(0.760819\pi\) | |||||||
\(168\) | 24.9456 | 1.92459 | ||||||||
\(169\) | −11.6281 | −0.894470 | ||||||||
\(170\) | 7.06479 | 0.541845 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.08346 | 0.540109 | ||||||||
\(173\) | −7.01969 | −0.533697 | −0.266848 | − | 0.963738i | \(-0.585982\pi\) | ||||
−0.266848 | + | 0.963738i | \(0.585982\pi\) | |||||||
\(174\) | −3.12434 | −0.236856 | ||||||||
\(175\) | −4.75660 | −0.359565 | ||||||||
\(176\) | −7.25793 | −0.547087 | ||||||||
\(177\) | 3.70087 | 0.278174 | ||||||||
\(178\) | 10.0591 | 0.753962 | ||||||||
\(179\) | 9.61639 | 0.718763 | 0.359381 | − | 0.933191i | \(-0.382988\pi\) | ||||
0.359381 | + | 0.933191i | \(0.382988\pi\) | |||||||
\(180\) | 0.0686106 | 0.00511393 | ||||||||
\(181\) | −18.4974 | −1.37490 | −0.687449 | − | 0.726232i | \(-0.741270\pi\) | ||||
−0.687449 | + | 0.726232i | \(0.741270\pi\) | |||||||
\(182\) | 6.34326 | 0.470194 | ||||||||
\(183\) | −10.5773 | −0.781895 | ||||||||
\(184\) | 15.5735 | 1.14809 | ||||||||
\(185\) | 5.98080 | 0.439717 | ||||||||
\(186\) | 14.5364 | 1.06586 | ||||||||
\(187\) | −21.4710 | −1.57011 | ||||||||
\(188\) | 5.67496 | 0.413889 | ||||||||
\(189\) | −25.1012 | −1.82584 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8586 | −0.785703 | −0.392852 | − | 0.919602i | \(-0.628511\pi\) | ||||
−0.392852 | + | 0.919602i | \(0.628511\pi\) | |||||||
\(192\) | −14.4568 | −1.04333 | ||||||||
\(193\) | 12.5059 | 0.900192 | 0.450096 | − | 0.892980i | \(-0.351390\pi\) | ||||
0.450096 | + | 0.892980i | \(0.351390\pi\) | |||||||
\(194\) | 0.805522 | 0.0578331 | ||||||||
\(195\) | −1.99547 | −0.142898 | ||||||||
\(196\) | −10.9950 | −0.785359 | ||||||||
\(197\) | −10.0643 | −0.717049 | −0.358525 | − | 0.933520i | \(-0.616720\pi\) | ||||
−0.358525 | + | 0.933520i | \(0.616720\pi\) | |||||||
\(198\) | 0.384139 | 0.0272996 | ||||||||
\(199\) | 4.81054 | 0.341010 | 0.170505 | − | 0.985357i | \(-0.445460\pi\) | ||||
0.170505 | + | 0.985357i | \(0.445460\pi\) | |||||||
\(200\) | 3.07830 | 0.217669 | ||||||||
\(201\) | −9.57901 | −0.675651 | ||||||||
\(202\) | 0.128269 | 0.00902497 | ||||||||
\(203\) | 7.66145 | 0.537729 | ||||||||
\(204\) | −7.43871 | −0.520814 | ||||||||
\(205\) | 5.43374 | 0.379509 | ||||||||
\(206\) | 12.8924 | 0.898253 | ||||||||
\(207\) | −0.493281 | −0.0342854 | ||||||||
\(208\) | −2.45675 | −0.170345 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −9.22656 | −0.636693 | ||||||||
\(211\) | 1.42250 | 0.0979288 | 0.0489644 | − | 0.998801i | \(-0.484408\pi\) | ||||
0.0489644 | + | 0.998801i | \(0.484408\pi\) | |||||||
\(212\) | −4.70251 | −0.322970 | ||||||||
\(213\) | 4.63888 | 0.317851 | ||||||||
\(214\) | −2.48049 | −0.169563 | ||||||||
\(215\) | −10.0664 | −0.686525 | ||||||||
\(216\) | 16.2446 | 1.10531 | ||||||||
\(217\) | −35.6459 | −2.41980 | ||||||||
\(218\) | −15.2184 | −1.03072 | ||||||||
\(219\) | −5.37782 | −0.363400 | ||||||||
\(220\) | −2.43489 | −0.164160 | ||||||||
\(221\) | −7.26776 | −0.488883 | ||||||||
\(222\) | 11.6012 | 0.778621 | ||||||||
\(223\) | 0.280645 | 0.0187934 | 0.00939668 | − | 0.999956i | \(-0.497009\pi\) | ||||
0.00939668 | + | 0.999956i | \(0.497009\pi\) | |||||||
\(224\) | 17.9251 | 1.19767 | ||||||||
\(225\) | −0.0975037 | −0.00650025 | ||||||||
\(226\) | 13.5018 | 0.898128 | ||||||||
\(227\) | 19.0252 | 1.26275 | 0.631375 | − | 0.775478i | \(-0.282491\pi\) | ||||
0.631375 | + | 0.775478i | \(0.282491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.6753 | 0.771523 | 0.385762 | − | 0.922598i | \(-0.373939\pi\) | ||||
0.385762 | + | 0.922598i | \(0.373939\pi\) | |||||||
\(230\) | −5.76011 | −0.379811 | ||||||||
\(231\) | 28.0409 | 1.84496 | ||||||||
\(232\) | −4.95822 | −0.325523 | ||||||||
\(233\) | −18.1431 | −1.18859 | −0.594297 | − | 0.804246i | \(-0.702570\pi\) | ||||
−0.594297 | + | 0.804246i | \(0.702570\pi\) | |||||||
\(234\) | 0.130028 | 0.00850021 | ||||||||
\(235\) | −8.06479 | −0.526089 | ||||||||
\(236\) | 1.52858 | 0.0995020 | ||||||||
\(237\) | 20.5775 | 1.33665 | ||||||||
\(238\) | −33.6044 | −2.17825 | ||||||||
\(239\) | −27.2177 | −1.76057 | −0.880285 | − | 0.474446i | \(-0.842648\pi\) | ||||
−0.880285 | + | 0.474446i | \(0.842648\pi\) | |||||||
\(240\) | 3.57346 | 0.230666 | ||||||||
\(241\) | −9.53341 | −0.614101 | −0.307051 | − | 0.951693i | \(-0.599342\pi\) | ||||
−0.307051 | + | 0.951693i | \(0.599342\pi\) | |||||||
\(242\) | −1.10835 | −0.0712477 | ||||||||
\(243\) | −1.01288 | −0.0649764 | ||||||||
\(244\) | −4.36876 | −0.279681 | ||||||||
\(245\) | 15.6252 | 0.998259 | ||||||||
\(246\) | 10.5400 | 0.672008 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 23.0688 | 1.46487 | ||||||||
\(249\) | 14.0546 | 0.890672 | ||||||||
\(250\) | −1.13856 | −0.0720091 | ||||||||
\(251\) | −10.1985 | −0.643725 | −0.321863 | − | 0.946786i | \(-0.604309\pi\) | ||||
−0.321863 | + | 0.946786i | \(0.604309\pi\) | |||||||
\(252\) | −0.326353 | −0.0205583 | ||||||||
\(253\) | 17.5059 | 1.10058 | ||||||||
\(254\) | 22.8391 | 1.43305 | ||||||||
\(255\) | 10.5713 | 0.661999 | ||||||||
\(256\) | −14.5524 | −0.909524 | ||||||||
\(257\) | 20.9818 | 1.30881 | 0.654405 | − | 0.756144i | \(-0.272919\pi\) | ||||
0.654405 | + | 0.756144i | \(0.272919\pi\) | |||||||
\(258\) | −19.5263 | −1.21565 | ||||||||
\(259\) | −28.4483 | −1.76769 | ||||||||
\(260\) | −0.824193 | −0.0511143 | ||||||||
\(261\) | 0.157049 | 0.00972110 | ||||||||
\(262\) | −10.4970 | −0.648508 | ||||||||
\(263\) | −24.4437 | −1.50726 | −0.753632 | − | 0.657296i | \(-0.771700\pi\) | ||||
−0.753632 | + | 0.657296i | \(0.771700\pi\) | |||||||
\(264\) | −18.1471 | −1.11688 | ||||||||
\(265\) | 6.68283 | 0.410523 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.0518 | 0.921153 | ||||||||
\(268\) | −3.95644 | −0.241678 | ||||||||
\(269\) | 28.7189 | 1.75102 | 0.875512 | − | 0.483197i | \(-0.160525\pi\) | ||||
0.875512 | + | 0.483197i | \(0.160525\pi\) | |||||||
\(270\) | −6.00835 | −0.365657 | ||||||||
\(271\) | −20.9374 | −1.27186 | −0.635929 | − | 0.771748i | \(-0.719383\pi\) | ||||
−0.635929 | + | 0.771748i | \(0.719383\pi\) | |||||||
\(272\) | 13.0150 | 0.789151 | ||||||||
\(273\) | 9.49164 | 0.574460 | ||||||||
\(274\) | 3.94622 | 0.238400 | ||||||||
\(275\) | 3.46027 | 0.208662 | ||||||||
\(276\) | 6.06498 | 0.365069 | ||||||||
\(277\) | −18.7217 | −1.12488 | −0.562439 | − | 0.826839i | \(-0.690137\pi\) | ||||
−0.562439 | + | 0.826839i | \(0.690137\pi\) | |||||||
\(278\) | 2.18913 | 0.131295 | ||||||||
\(279\) | −0.730692 | −0.0437454 | ||||||||
\(280\) | −14.6423 | −0.875042 | ||||||||
\(281\) | 19.1468 | 1.14220 | 0.571100 | − | 0.820880i | \(-0.306517\pi\) | ||||
0.571100 | + | 0.820880i | \(0.306517\pi\) | |||||||
\(282\) | −15.6436 | −0.931563 | ||||||||
\(283\) | −17.9013 | −1.06412 | −0.532062 | − | 0.846705i | \(-0.678583\pi\) | ||||
−0.532062 | + | 0.846705i | \(0.678583\pi\) | |||||||
\(284\) | 1.91601 | 0.113694 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.61452 | −0.272862 | ||||||||
\(287\) | −25.8461 | −1.52565 | ||||||||
\(288\) | 0.367439 | 0.0216516 | ||||||||
\(289\) | 21.5020 | 1.26483 | ||||||||
\(290\) | 1.83389 | 0.107689 | ||||||||
\(291\) | 1.20533 | 0.0706576 | ||||||||
\(292\) | −2.22121 | −0.129987 | ||||||||
\(293\) | 6.42187 | 0.375170 | 0.187585 | − | 0.982248i | \(-0.439934\pi\) | ||||
0.187585 | + | 0.982248i | \(0.439934\pi\) | |||||||
\(294\) | 30.3089 | 1.76765 | ||||||||
\(295\) | −2.17229 | −0.126476 | ||||||||
\(296\) | 18.4107 | 1.07010 | ||||||||
\(297\) | 18.2603 | 1.05957 | ||||||||
\(298\) | −3.84355 | −0.222651 | ||||||||
\(299\) | 5.92560 | 0.342686 | ||||||||
\(300\) | 1.19882 | 0.0692142 | ||||||||
\(301\) | 47.8820 | 2.75987 | ||||||||
\(302\) | 22.4169 | 1.28995 | ||||||||
\(303\) | 0.191933 | 0.0110263 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.20852 | 0.355499 | ||||||||
\(306\) | −0.688844 | −0.0393786 | ||||||||
\(307\) | 6.15675 | 0.351384 | 0.175692 | − | 0.984445i | \(-0.443784\pi\) | ||||
0.175692 | + | 0.984445i | \(0.443784\pi\) | |||||||
\(308\) | 11.5818 | 0.659935 | ||||||||
\(309\) | 19.2913 | 1.09744 | ||||||||
\(310\) | −8.53240 | −0.484608 | ||||||||
\(311\) | 3.34988 | 0.189954 | 0.0949772 | − | 0.995479i | \(-0.469722\pi\) | ||||
0.0949772 | + | 0.995479i | \(0.469722\pi\) | |||||||
\(312\) | −6.14265 | −0.347759 | ||||||||
\(313\) | 24.2386 | 1.37005 | 0.685023 | − | 0.728521i | \(-0.259792\pi\) | ||||
0.685023 | + | 0.728521i | \(0.259792\pi\) | |||||||
\(314\) | −12.3020 | −0.694243 | ||||||||
\(315\) | 0.463786 | 0.0261314 | ||||||||
\(316\) | 8.49916 | 0.478115 | ||||||||
\(317\) | 10.9842 | 0.616933 | 0.308466 | − | 0.951235i | \(-0.400184\pi\) | ||||
0.308466 | + | 0.951235i | \(0.400184\pi\) | |||||||
\(318\) | 12.9629 | 0.726926 | ||||||||
\(319\) | −5.57346 | −0.312054 | ||||||||
\(320\) | 8.48565 | 0.474362 | ||||||||
\(321\) | −3.71163 | −0.207163 | ||||||||
\(322\) | 27.3986 | 1.52686 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 6.12052 | 0.340029 | ||||||||
\(325\) | 1.17127 | 0.0649706 | ||||||||
\(326\) | 2.73388 | 0.151416 | ||||||||
\(327\) | −22.7718 | −1.25928 | ||||||||
\(328\) | 16.7267 | 0.923577 | ||||||||
\(329\) | 38.3610 | 2.11491 | ||||||||
\(330\) | 6.71202 | 0.369485 | ||||||||
\(331\) | 25.2522 | 1.38799 | 0.693994 | − | 0.719981i | \(-0.255849\pi\) | ||||
0.693994 | + | 0.719981i | \(0.255849\pi\) | |||||||
\(332\) | 5.80499 | 0.318590 | ||||||||
\(333\) | −0.583150 | −0.0319564 | ||||||||
\(334\) | 21.5031 | 1.17660 | ||||||||
\(335\) | 5.62257 | 0.307194 | ||||||||
\(336\) | −16.9975 | −0.927290 | ||||||||
\(337\) | 8.26425 | 0.450182 | 0.225091 | − | 0.974338i | \(-0.427732\pi\) | ||||
0.225091 | + | 0.974338i | \(0.427732\pi\) | |||||||
\(338\) | 13.2394 | 0.720126 | ||||||||
\(339\) | 20.2032 | 1.09729 | ||||||||
\(340\) | 4.36628 | 0.236795 | ||||||||
\(341\) | 25.9312 | 1.40426 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −41.0267 | −2.21524 | ||||||||
\(344\) | −30.9876 | −1.67074 | ||||||||
\(345\) | −8.61905 | −0.464034 | ||||||||
\(346\) | 7.99237 | 0.429672 | ||||||||
\(347\) | 21.3088 | 1.14391 | 0.571957 | − | 0.820283i | \(-0.306184\pi\) | ||||
0.571957 | + | 0.820283i | \(0.306184\pi\) | |||||||
\(348\) | −1.93095 | −0.103510 | ||||||||
\(349\) | −23.2574 | −1.24494 | −0.622470 | − | 0.782644i | \(-0.713871\pi\) | ||||
−0.622470 | + | 0.782644i | \(0.713871\pi\) | |||||||
\(350\) | 5.41569 | 0.289481 | ||||||||
\(351\) | 6.18097 | 0.329916 | ||||||||
\(352\) | −13.0399 | −0.695029 | ||||||||
\(353\) | 24.7741 | 1.31859 | 0.659296 | − | 0.751883i | \(-0.270854\pi\) | ||||
0.659296 | + | 0.751883i | \(0.270854\pi\) | |||||||
\(354\) | −4.21368 | −0.223954 | ||||||||
\(355\) | −2.72287 | −0.144515 | ||||||||
\(356\) | 6.21687 | 0.329493 | ||||||||
\(357\) | −50.2834 | −2.66128 | ||||||||
\(358\) | −10.9489 | −0.578666 | ||||||||
\(359\) | −3.85028 | −0.203210 | −0.101605 | − | 0.994825i | \(-0.532398\pi\) | ||||
−0.101605 | + | 0.994825i | \(0.532398\pi\) | |||||||
\(360\) | −0.300146 | −0.0158191 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 21.0604 | 1.10691 | ||||||||
\(363\) | −1.65847 | −0.0870469 | ||||||||
\(364\) | 3.92035 | 0.205482 | ||||||||
\(365\) | 3.15661 | 0.165224 | ||||||||
\(366\) | 12.0429 | 0.629493 | ||||||||
\(367\) | −28.6314 | −1.49455 | −0.747274 | − | 0.664517i | \(-0.768638\pi\) | ||||
−0.747274 | + | 0.664517i | \(0.768638\pi\) | |||||||
\(368\) | −10.6115 | −0.553162 | ||||||||
\(369\) | −0.529809 | −0.0275808 | ||||||||
\(370\) | −6.80953 | −0.354010 | ||||||||
\(371\) | −31.7875 | −1.65033 | ||||||||
\(372\) | 8.98399 | 0.465798 | ||||||||
\(373\) | −22.9648 | −1.18907 | −0.594537 | − | 0.804069i | \(-0.702664\pi\) | ||||
−0.594537 | + | 0.804069i | \(0.702664\pi\) | |||||||
\(374\) | 24.4461 | 1.26408 | ||||||||
\(375\) | −1.70367 | −0.0879772 | ||||||||
\(376\) | −24.8259 | −1.28030 | ||||||||
\(377\) | −1.88657 | −0.0971634 | ||||||||
\(378\) | 28.5793 | 1.46996 | ||||||||
\(379\) | 19.3472 | 0.993801 | 0.496901 | − | 0.867807i | \(-0.334471\pi\) | ||||
0.496901 | + | 0.867807i | \(0.334471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.1750 | 1.75084 | ||||||||
\(382\) | 12.3633 | 0.632559 | ||||||||
\(383\) | −6.13972 | −0.313725 | −0.156863 | − | 0.987620i | \(-0.550138\pi\) | ||||
−0.156863 | + | 0.987620i | \(0.550138\pi\) | |||||||
\(384\) | 3.61949 | 0.184706 | ||||||||
\(385\) | −16.4591 | −0.838834 | ||||||||
\(386\) | −14.2387 | −0.724732 | ||||||||
\(387\) | 0.981515 | 0.0498932 | ||||||||
\(388\) | 0.497840 | 0.0252740 | ||||||||
\(389\) | 3.66728 | 0.185939 | 0.0929693 | − | 0.995669i | \(-0.470364\pi\) | ||||
0.0929693 | + | 0.995669i | \(0.470364\pi\) | |||||||
\(390\) | 2.27197 | 0.115046 | ||||||||
\(391\) | −31.3917 | −1.58755 | ||||||||
\(392\) | 48.0992 | 2.42938 | ||||||||
\(393\) | −15.7070 | −0.792316 | ||||||||
\(394\) | 11.4588 | 0.577287 | ||||||||
\(395\) | −12.0783 | −0.607725 | ||||||||
\(396\) | 0.237411 | 0.0119304 | ||||||||
\(397\) | 24.5839 | 1.23383 | 0.616914 | − | 0.787030i | \(-0.288382\pi\) | ||||
0.616914 | + | 0.787030i | \(0.288382\pi\) | |||||||
\(398\) | −5.47711 | −0.274543 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.09750 | −0.104875 | ||||||||
\(401\) | −6.84605 | −0.341876 | −0.170938 | − | 0.985282i | \(-0.554680\pi\) | ||||
−0.170938 | + | 0.985282i | \(0.554680\pi\) | |||||||
\(402\) | 10.9063 | 0.543957 | ||||||||
\(403\) | 8.77753 | 0.437240 | ||||||||
\(404\) | 0.0792746 | 0.00394406 | ||||||||
\(405\) | −8.69798 | −0.432206 | ||||||||
\(406\) | −8.72306 | −0.432918 | ||||||||
\(407\) | 20.6952 | 1.02582 | ||||||||
\(408\) | 32.5416 | 1.61105 | ||||||||
\(409\) | −7.92406 | −0.391819 | −0.195910 | − | 0.980622i | \(-0.562766\pi\) | ||||
−0.195910 | + | 0.980622i | \(0.562766\pi\) | |||||||
\(410\) | −6.18666 | −0.305537 | ||||||||
\(411\) | 5.90486 | 0.291265 | ||||||||
\(412\) | 7.96792 | 0.392551 | ||||||||
\(413\) | 10.3327 | 0.508440 | ||||||||
\(414\) | 0.561633 | 0.0276027 | ||||||||
\(415\) | −8.24958 | −0.404956 | ||||||||
\(416\) | −4.41391 | −0.216410 | ||||||||
\(417\) | 3.27567 | 0.160410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.66830 | 0.0815018 | 0.0407509 | − | 0.999169i | \(-0.487025\pi\) | ||||
0.0407509 | + | 0.999169i | \(0.487025\pi\) | |||||||
\(420\) | −5.70233 | −0.278245 | ||||||||
\(421\) | 19.0982 | 0.930790 | 0.465395 | − | 0.885103i | \(-0.345912\pi\) | ||||
0.465395 | + | 0.885103i | \(0.345912\pi\) | |||||||
\(422\) | −1.61960 | −0.0788411 | ||||||||
\(423\) | 0.786347 | 0.0382335 | ||||||||
\(424\) | 20.5718 | 0.999054 | ||||||||
\(425\) | −6.20500 | −0.300987 | ||||||||
\(426\) | −5.28166 | −0.255897 | ||||||||
\(427\) | −29.5314 | −1.42913 | ||||||||
\(428\) | −1.53302 | −0.0741015 | ||||||||
\(429\) | −6.90486 | −0.333370 | ||||||||
\(430\) | 11.4613 | 0.552712 | ||||||||
\(431\) | 18.5276 | 0.892442 | 0.446221 | − | 0.894923i | \(-0.352769\pi\) | ||||
0.446221 | + | 0.894923i | \(0.352769\pi\) | |||||||
\(432\) | −11.0688 | −0.532548 | ||||||||
\(433\) | −21.8081 | −1.04803 | −0.524016 | − | 0.851708i | \(-0.675567\pi\) | ||||
−0.524016 | + | 0.851708i | \(0.675567\pi\) | |||||||
\(434\) | 40.5852 | 1.94815 | ||||||||
\(435\) | 2.74410 | 0.131570 | ||||||||
\(436\) | −9.40547 | −0.450440 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 6.12300 | 0.292568 | ||||||||
\(439\) | 19.6692 | 0.938759 | 0.469379 | − | 0.882997i | \(-0.344478\pi\) | ||||
0.469379 | + | 0.882997i | \(0.344478\pi\) | |||||||
\(440\) | 10.6518 | 0.507803 | ||||||||
\(441\) | −1.52352 | −0.0725485 | ||||||||
\(442\) | 8.27481 | 0.393593 | ||||||||
\(443\) | 3.48680 | 0.165663 | 0.0828315 | − | 0.996564i | \(-0.473604\pi\) | ||||
0.0828315 | + | 0.996564i | \(0.473604\pi\) | |||||||
\(444\) | 7.16993 | 0.340270 | ||||||||
\(445\) | −8.83490 | −0.418815 | ||||||||
\(446\) | −0.319532 | −0.0151303 | ||||||||
\(447\) | −5.75124 | −0.272024 | ||||||||
\(448\) | −40.3628 | −1.90696 | ||||||||
\(449\) | −8.06276 | −0.380505 | −0.190253 | − | 0.981735i | \(-0.560931\pi\) | ||||
−0.190253 | + | 0.981735i | \(0.560931\pi\) | |||||||
\(450\) | 0.111014 | 0.00523326 | ||||||||
\(451\) | 18.8022 | 0.885361 | ||||||||
\(452\) | 8.34458 | 0.392496 | ||||||||
\(453\) | 33.5432 | 1.57600 | ||||||||
\(454\) | −21.6615 | −1.01662 | ||||||||
\(455\) | −5.57128 | −0.261186 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.7296 | −1.20358 | −0.601790 | − | 0.798654i | \(-0.705546\pi\) | ||||
−0.601790 | + | 0.798654i | \(0.705546\pi\) | |||||||
\(458\) | −13.2930 | −0.621143 | ||||||||
\(459\) | −32.7446 | −1.52839 | ||||||||
\(460\) | −3.55995 | −0.165983 | ||||||||
\(461\) | 7.48361 | 0.348547 | 0.174273 | − | 0.984697i | \(-0.444242\pi\) | ||||
0.174273 | + | 0.984697i | \(0.444242\pi\) | |||||||
\(462\) | −31.9264 | −1.48535 | ||||||||
\(463\) | 24.4776 | 1.13757 | 0.568786 | − | 0.822485i | \(-0.307413\pi\) | ||||
0.568786 | + | 0.822485i | \(0.307413\pi\) | |||||||
\(464\) | 3.37845 | 0.156841 | ||||||||
\(465\) | −12.7673 | −0.592070 | ||||||||
\(466\) | 20.6571 | 0.956921 | ||||||||
\(467\) | 6.03350 | 0.279197 | 0.139599 | − | 0.990208i | \(-0.455419\pi\) | ||||
0.139599 | + | 0.990208i | \(0.455419\pi\) | |||||||
\(468\) | 0.0803618 | 0.00371473 | ||||||||
\(469\) | −26.7443 | −1.23494 | ||||||||
\(470\) | 9.18229 | 0.423547 | ||||||||
\(471\) | −18.4079 | −0.848192 | ||||||||
\(472\) | −6.68697 | −0.307793 | ||||||||
\(473\) | −34.8326 | −1.60160 | ||||||||
\(474\) | −23.4288 | −1.07612 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −20.7687 | −0.951930 | ||||||||
\(477\) | −0.651600 | −0.0298347 | ||||||||
\(478\) | 30.9891 | 1.41741 | ||||||||
\(479\) | 22.2776 | 1.01789 | 0.508945 | − | 0.860799i | \(-0.330036\pi\) | ||||
0.508945 | + | 0.860799i | \(0.330036\pi\) | |||||||
\(480\) | 6.42023 | 0.293042 | ||||||||
\(481\) | 7.00516 | 0.319408 | ||||||||
\(482\) | 10.8544 | 0.494405 | ||||||||
\(483\) | 40.9974 | 1.86544 | ||||||||
\(484\) | −0.685000 | −0.0311364 | ||||||||
\(485\) | −0.707489 | −0.0321254 | ||||||||
\(486\) | 1.15323 | 0.0523117 | ||||||||
\(487\) | −21.2868 | −0.964598 | −0.482299 | − | 0.876007i | \(-0.660198\pi\) | ||||
−0.482299 | + | 0.876007i | \(0.660198\pi\) | |||||||
\(488\) | 19.1117 | 0.865146 | ||||||||
\(489\) | 4.09080 | 0.184992 | ||||||||
\(490\) | −17.7903 | −0.803685 | ||||||||
\(491\) | −33.6313 | −1.51776 | −0.758879 | − | 0.651232i | \(-0.774253\pi\) | ||||
−0.758879 | + | 0.651232i | \(0.774253\pi\) | |||||||
\(492\) | 6.51410 | 0.293678 | ||||||||
\(493\) | 9.99440 | 0.450125 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.337389 | −0.0151645 | ||||||||
\(496\) | −15.7187 | −0.705790 | ||||||||
\(497\) | 12.9516 | 0.580959 | ||||||||
\(498\) | −16.0020 | −0.717068 | ||||||||
\(499\) | −35.2646 | −1.57866 | −0.789330 | − | 0.613969i | \(-0.789572\pi\) | ||||
−0.789330 | + | 0.613969i | \(0.789572\pi\) | |||||||
\(500\) | −0.703671 | −0.0314691 | ||||||||
\(501\) | 32.1759 | 1.43751 | ||||||||
\(502\) | 11.6117 | 0.518254 | ||||||||
\(503\) | 1.00821 | 0.0449538 | 0.0224769 | − | 0.999747i | \(-0.492845\pi\) | ||||
0.0224769 | + | 0.999747i | \(0.492845\pi\) | |||||||
\(504\) | 1.42767 | 0.0635937 | ||||||||
\(505\) | −0.112658 | −0.00501324 | ||||||||
\(506\) | −19.9315 | −0.886065 | ||||||||
\(507\) | 19.8105 | 0.879815 | ||||||||
\(508\) | 14.1154 | 0.626268 | ||||||||
\(509\) | −22.0570 | −0.977660 | −0.488830 | − | 0.872379i | \(-0.662576\pi\) | ||||
−0.488830 | + | 0.872379i | \(0.662576\pi\) | |||||||
\(510\) | −12.0361 | −0.532967 | ||||||||
\(511\) | −15.0147 | −0.664212 | ||||||||
\(512\) | 20.8179 | 0.920029 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23.8891 | −1.05371 | ||||||||
\(515\) | −11.3233 | −0.498966 | ||||||||
\(516\) | −12.0679 | −0.531259 | ||||||||
\(517\) | −27.9064 | −1.22732 | ||||||||
\(518\) | 32.3902 | 1.42314 | ||||||||
\(519\) | 11.9592 | 0.524952 | ||||||||
\(520\) | 3.60554 | 0.158113 | ||||||||
\(521\) | 16.4008 | 0.718532 | 0.359266 | − | 0.933235i | \(-0.383027\pi\) | ||||
0.359266 | + | 0.933235i | \(0.383027\pi\) | |||||||
\(522\) | −0.178811 | −0.00782633 | ||||||||
\(523\) | 17.8476 | 0.780419 | 0.390210 | − | 0.920726i | \(-0.372403\pi\) | ||||
0.390210 | + | 0.920726i | \(0.372403\pi\) | |||||||
\(524\) | −6.48752 | −0.283409 | ||||||||
\(525\) | 8.10368 | 0.353674 | ||||||||
\(526\) | 27.8308 | 1.21348 | ||||||||
\(527\) | −46.5003 | −2.02558 | ||||||||
\(528\) | 12.3651 | 0.538123 | ||||||||
\(529\) | 2.59453 | 0.112806 | ||||||||
\(530\) | −7.60883 | −0.330506 | ||||||||
\(531\) | 0.211806 | 0.00919162 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.36440 | 0.275673 | ||||||||
\(534\) | −17.1374 | −0.741608 | ||||||||
\(535\) | 2.17861 | 0.0941895 | ||||||||
\(536\) | 17.3080 | 0.747590 | ||||||||
\(537\) | −16.3832 | −0.706986 | ||||||||
\(538\) | −32.6983 | −1.40973 | ||||||||
\(539\) | 54.0675 | 2.32885 | ||||||||
\(540\) | −3.71336 | −0.159798 | ||||||||
\(541\) | 22.1825 | 0.953699 | 0.476849 | − | 0.878985i | \(-0.341779\pi\) | ||||
0.476849 | + | 0.878985i | \(0.341779\pi\) | |||||||
\(542\) | 23.8386 | 1.02396 | ||||||||
\(543\) | 31.5134 | 1.35237 | ||||||||
\(544\) | 23.3833 | 1.00255 | ||||||||
\(545\) | 13.3663 | 0.572549 | ||||||||
\(546\) | −10.8068 | −0.462490 | ||||||||
\(547\) | −24.9289 | −1.06588 | −0.532941 | − | 0.846152i | \(-0.678913\pi\) | ||||
−0.532941 | + | 0.846152i | \(0.678913\pi\) | |||||||
\(548\) | 2.43890 | 0.104184 | ||||||||
\(549\) | −0.605354 | −0.0258359 | ||||||||
\(550\) | −3.93974 | −0.167991 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −26.5321 | −1.12928 | ||||||||
\(553\) | 57.4516 | 2.44309 | ||||||||
\(554\) | 21.3159 | 0.905625 | ||||||||
\(555\) | −10.1893 | −0.432512 | ||||||||
\(556\) | 1.35296 | 0.0573782 | ||||||||
\(557\) | −7.31171 | −0.309807 | −0.154904 | − | 0.987930i | \(-0.549507\pi\) | ||||
−0.154904 | + | 0.987930i | \(0.549507\pi\) | |||||||
\(558\) | 0.831940 | 0.0352188 | ||||||||
\(559\) | −11.7906 | −0.498688 | ||||||||
\(560\) | 9.97698 | 0.421604 | ||||||||
\(561\) | 36.5795 | 1.54439 | ||||||||
\(562\) | −21.7998 | −0.919570 | ||||||||
\(563\) | 16.5614 | 0.697978 | 0.348989 | − | 0.937127i | \(-0.386525\pi\) | ||||
0.348989 | + | 0.937127i | \(0.386525\pi\) | |||||||
\(564\) | −9.66827 | −0.407108 | ||||||||
\(565\) | −11.8586 | −0.498897 | ||||||||
\(566\) | 20.3818 | 0.856712 | ||||||||
\(567\) | 41.3728 | 1.73749 | ||||||||
\(568\) | −8.38183 | −0.351694 | ||||||||
\(569\) | −31.2306 | −1.30926 | −0.654628 | − | 0.755951i | \(-0.727175\pi\) | ||||
−0.654628 | + | 0.755951i | \(0.727175\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.27375 | −0.0533049 | −0.0266525 | − | 0.999645i | \(-0.508485\pi\) | ||||
−0.0266525 | + | 0.999645i | \(0.508485\pi\) | |||||||
\(572\) | −2.85193 | −0.119245 | ||||||||
\(573\) | 18.4995 | 0.772830 | ||||||||
\(574\) | 29.4274 | 1.22828 | ||||||||
\(575\) | 5.05910 | 0.210979 | ||||||||
\(576\) | −0.827382 | −0.0344743 | ||||||||
\(577\) | −1.77096 | −0.0737262 | −0.0368631 | − | 0.999320i | \(-0.511737\pi\) | ||||
−0.0368631 | + | 0.999320i | \(0.511737\pi\) | |||||||
\(578\) | −24.4815 | −1.01829 | ||||||||
\(579\) | −21.3059 | −0.885442 | ||||||||
\(580\) | 1.13340 | 0.0470620 | ||||||||
\(581\) | 39.2399 | 1.62795 | ||||||||
\(582\) | −1.37234 | −0.0568855 | ||||||||
\(583\) | 23.1244 | 0.957714 | ||||||||
\(584\) | 9.71700 | 0.402092 | ||||||||
\(585\) | −0.114204 | −0.00472174 | ||||||||
\(586\) | −7.31171 | −0.302044 | ||||||||
\(587\) | 8.25987 | 0.340921 | 0.170461 | − | 0.985364i | \(-0.445474\pi\) | ||||
0.170461 | + | 0.985364i | \(0.445474\pi\) | |||||||
\(588\) | 18.7319 | 0.772491 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 2.47329 | 0.101824 | ||||||||
\(591\) | 17.1462 | 0.705300 | ||||||||
\(592\) | −12.5448 | −0.515586 | ||||||||
\(593\) | −20.8241 | −0.855141 | −0.427571 | − | 0.903982i | \(-0.640630\pi\) | ||||
−0.427571 | + | 0.903982i | \(0.640630\pi\) | |||||||
\(594\) | −20.7905 | −0.853045 | ||||||||
\(595\) | 29.5147 | 1.20998 | ||||||||
\(596\) | −2.37545 | −0.0973021 | ||||||||
\(597\) | −8.19558 | −0.335423 | ||||||||
\(598\) | −6.74668 | −0.275892 | ||||||||
\(599\) | −40.0833 | −1.63776 | −0.818880 | − | 0.573965i | \(-0.805405\pi\) | ||||
−0.818880 | + | 0.573965i | \(0.805405\pi\) | |||||||
\(600\) | −5.24442 | −0.214102 | ||||||||
\(601\) | −48.3109 | −1.97064 | −0.985321 | − | 0.170710i | \(-0.945394\pi\) | ||||
−0.985321 | + | 0.170710i | \(0.945394\pi\) | |||||||
\(602\) | −54.5167 | −2.22194 | ||||||||
\(603\) | −0.548221 | −0.0223253 | ||||||||
\(604\) | 13.8544 | 0.563729 | ||||||||
\(605\) | 0.973466 | 0.0395770 | ||||||||
\(606\) | −0.218528 | −0.00887710 | ||||||||
\(607\) | 23.7640 | 0.964552 | 0.482276 | − | 0.876019i | \(-0.339810\pi\) | ||||
0.482276 | + | 0.876019i | \(0.339810\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.0526 | −0.528918 | ||||||||
\(610\) | −7.06880 | −0.286207 | ||||||||
\(611\) | −9.44609 | −0.382148 | ||||||||
\(612\) | −0.425729 | −0.0172091 | ||||||||
\(613\) | 4.70479 | 0.190025 | 0.0950123 | − | 0.995476i | \(-0.469711\pi\) | ||||
0.0950123 | + | 0.995476i | \(0.469711\pi\) | |||||||
\(614\) | −7.00985 | −0.282895 | ||||||||
\(615\) | −9.25730 | −0.373290 | ||||||||
\(616\) | −50.6661 | −2.04140 | ||||||||
\(617\) | 2.11358 | 0.0850893 | 0.0425447 | − | 0.999095i | \(-0.486454\pi\) | ||||
0.0425447 | + | 0.999095i | \(0.486454\pi\) | |||||||
\(618\) | −21.9643 | −0.883536 | ||||||||
\(619\) | −34.0091 | −1.36694 | −0.683470 | − | 0.729978i | \(-0.739530\pi\) | ||||
−0.683470 | + | 0.729978i | \(0.739530\pi\) | |||||||
\(620\) | −5.27331 | −0.211781 | ||||||||
\(621\) | 26.6975 | 1.07134 | ||||||||
\(622\) | −3.81406 | −0.152930 | ||||||||
\(623\) | 42.0241 | 1.68366 | ||||||||
\(624\) | 4.18550 | 0.167554 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −27.5972 | −1.10301 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.60307 | −0.303395 | ||||||||
\(629\) | −37.1109 | −1.47971 | ||||||||
\(630\) | −0.528050 | −0.0210380 | ||||||||
\(631\) | 9.57620 | 0.381223 | 0.190611 | − | 0.981666i | \(-0.438953\pi\) | ||||
0.190611 | + | 0.981666i | \(0.438953\pi\) | |||||||
\(632\) | −37.1807 | −1.47897 | ||||||||
\(633\) | −2.42347 | −0.0963242 | ||||||||
\(634\) | −12.5062 | −0.496684 | ||||||||
\(635\) | −20.0596 | −0.796041 | ||||||||
\(636\) | 8.01154 | 0.317678 | ||||||||
\(637\) | 18.3014 | 0.725129 | ||||||||
\(638\) | 6.34574 | 0.251230 | ||||||||
\(639\) | 0.265490 | 0.0105026 | ||||||||
\(640\) | −2.12452 | −0.0839792 | ||||||||
\(641\) | −23.8257 | −0.941058 | −0.470529 | − | 0.882384i | \(-0.655937\pi\) | ||||
−0.470529 | + | 0.882384i | \(0.655937\pi\) | |||||||
\(642\) | 4.22593 | 0.166784 | ||||||||
\(643\) | 27.3687 | 1.07931 | 0.539657 | − | 0.841885i | \(-0.318554\pi\) | ||||
0.539657 | + | 0.841885i | \(0.318554\pi\) | |||||||
\(644\) | 16.9332 | 0.667263 | ||||||||
\(645\) | 17.1499 | 0.675277 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.5660 | −1.51619 | −0.758093 | − | 0.652147i | \(-0.773869\pi\) | ||||
−0.758093 | + | 0.652147i | \(0.773869\pi\) | |||||||
\(648\) | −26.7750 | −1.05182 | ||||||||
\(649\) | −7.51671 | −0.295057 | ||||||||
\(650\) | −1.33357 | −0.0523070 | ||||||||
\(651\) | 60.7290 | 2.38016 | ||||||||
\(652\) | 1.68963 | 0.0661711 | ||||||||
\(653\) | −14.6990 | −0.575216 | −0.287608 | − | 0.957748i | \(-0.592860\pi\) | ||||
−0.287608 | + | 0.957748i | \(0.592860\pi\) | |||||||
\(654\) | 25.9271 | 1.01383 | ||||||||
\(655\) | 9.21953 | 0.360237 | ||||||||
\(656\) | −11.3973 | −0.444989 | ||||||||
\(657\) | −0.307781 | −0.0120077 | ||||||||
\(658\) | −43.6764 | −1.70268 | ||||||||
\(659\) | −7.91649 | −0.308383 | −0.154191 | − | 0.988041i | \(-0.549277\pi\) | ||||
−0.154191 | + | 0.988041i | \(0.549277\pi\) | |||||||
\(660\) | 4.14826 | 0.161471 | ||||||||
\(661\) | −33.2446 | −1.29307 | −0.646533 | − | 0.762886i | \(-0.723782\pi\) | ||||
−0.646533 | + | 0.762886i | \(0.723782\pi\) | |||||||
\(662\) | −28.7513 | −1.11745 | ||||||||
\(663\) | 12.3819 | 0.480872 | ||||||||
\(664\) | −25.3947 | −0.985506 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.663954 | 0.0257277 | ||||||||
\(667\) | −8.14870 | −0.315519 | ||||||||
\(668\) | 13.2897 | 0.514193 | ||||||||
\(669\) | −0.478127 | −0.0184854 | ||||||||
\(670\) | −6.40165 | −0.247317 | ||||||||
\(671\) | 21.4831 | 0.829348 | ||||||||
\(672\) | −30.5384 | −1.17805 | ||||||||
\(673\) | −34.7182 | −1.33829 | −0.669144 | − | 0.743133i | \(-0.733339\pi\) | ||||
−0.669144 | + | 0.743133i | \(0.733339\pi\) | |||||||
\(674\) | −9.40938 | −0.362436 | ||||||||
\(675\) | 5.27713 | 0.203117 | ||||||||
\(676\) | 8.18237 | 0.314707 | ||||||||
\(677\) | −13.6369 | −0.524107 | −0.262054 | − | 0.965053i | \(-0.584400\pi\) | ||||
−0.262054 | + | 0.965053i | \(0.584400\pi\) | |||||||
\(678\) | −23.0027 | −0.883412 | ||||||||
\(679\) | 3.36524 | 0.129146 | ||||||||
\(680\) | −19.1009 | −0.732485 | ||||||||
\(681\) | −32.4128 | −1.24206 | ||||||||
\(682\) | −29.5244 | −1.13055 | ||||||||
\(683\) | −32.0188 | −1.22516 | −0.612582 | − | 0.790407i | \(-0.709869\pi\) | ||||
−0.612582 | + | 0.790407i | \(0.709869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.46596 | −0.132427 | ||||||||
\(686\) | 46.7116 | 1.78346 | ||||||||
\(687\) | −19.8908 | −0.758882 | ||||||||
\(688\) | 21.1144 | 0.804979 | ||||||||
\(689\) | 7.82743 | 0.298201 | ||||||||
\(690\) | 9.81334 | 0.373588 | ||||||||
\(691\) | −42.5000 | −1.61678 | −0.808389 | − | 0.588649i | \(-0.799660\pi\) | ||||
−0.808389 | + | 0.588649i | \(0.799660\pi\) | |||||||
\(692\) | 4.93955 | 0.187774 | ||||||||
\(693\) | 1.60482 | 0.0609622 | ||||||||
\(694\) | −24.2614 | −0.920950 | ||||||||
\(695\) | −1.92271 | −0.0729326 | ||||||||
\(696\) | 8.44719 | 0.320190 | ||||||||
\(697\) | −33.7163 | −1.27710 | ||||||||
\(698\) | 26.4800 | 1.00228 | ||||||||
\(699\) | 30.9099 | 1.16912 | ||||||||
\(700\) | 3.34708 | 0.126508 | ||||||||
\(701\) | 17.0007 | 0.642108 | 0.321054 | − | 0.947061i | \(-0.395963\pi\) | ||||
0.321054 | + | 0.947061i | \(0.395963\pi\) | |||||||
\(702\) | −7.03743 | −0.265611 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 29.3626 | 1.10665 | ||||||||
\(705\) | 13.7398 | 0.517469 | ||||||||
\(706\) | −28.2069 | −1.06158 | ||||||||
\(707\) | 0.535871 | 0.0201535 | ||||||||
\(708\) | −2.60420 | −0.0978717 | ||||||||
\(709\) | −2.22434 | −0.0835369 | −0.0417685 | − | 0.999127i | \(-0.513299\pi\) | ||||
−0.0417685 | + | 0.999127i | \(0.513299\pi\) | |||||||
\(710\) | 3.10016 | 0.116347 | ||||||||
\(711\) | 1.17768 | 0.0441664 | ||||||||
\(712\) | −27.1965 | −1.01923 | ||||||||
\(713\) | 37.9129 | 1.41985 | ||||||||
\(714\) | 57.2508 | 2.14256 | ||||||||
\(715\) | 4.05293 | 0.151571 | ||||||||
\(716\) | −6.76678 | −0.252886 | ||||||||
\(717\) | 46.3701 | 1.73172 | ||||||||
\(718\) | 4.38380 | 0.163602 | ||||||||
\(719\) | 29.4500 | 1.09830 | 0.549150 | − | 0.835724i | \(-0.314952\pi\) | ||||
0.549150 | + | 0.835724i | \(0.314952\pi\) | |||||||
\(720\) | 0.204514 | 0.00762180 | ||||||||
\(721\) | 53.8606 | 2.00587 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.2418 | 0.604039 | ||||||||
\(724\) | 13.0161 | 0.483739 | ||||||||
\(725\) | −1.61070 | −0.0598199 | ||||||||
\(726\) | 1.88827 | 0.0700803 | ||||||||
\(727\) | −5.16809 | −0.191674 | −0.0958368 | − | 0.995397i | \(-0.530553\pi\) | ||||
−0.0958368 | + | 0.995397i | \(0.530553\pi\) | |||||||
\(728\) | −17.1501 | −0.635625 | ||||||||
\(729\) | 27.8196 | 1.03035 | ||||||||
\(730\) | −3.59400 | −0.133020 | ||||||||
\(731\) | 62.4623 | 2.31025 | ||||||||
\(732\) | 7.44293 | 0.275098 | ||||||||
\(733\) | 6.04955 | 0.223445 | 0.111723 | − | 0.993739i | \(-0.464363\pi\) | ||||
0.111723 | + | 0.993739i | \(0.464363\pi\) | |||||||
\(734\) | 32.5987 | 1.20324 | ||||||||
\(735\) | −26.6203 | −0.981903 | ||||||||
\(736\) | −19.0651 | −0.702747 | ||||||||
\(737\) | 19.4556 | 0.716656 | ||||||||
\(738\) | 0.603222 | 0.0222049 | ||||||||
\(739\) | −27.1443 | −0.998518 | −0.499259 | − | 0.866453i | \(-0.666394\pi\) | ||||
−0.499259 | + | 0.866453i | \(0.666394\pi\) | |||||||
\(740\) | −4.20852 | −0.154708 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 36.1921 | 1.32866 | ||||||||
\(743\) | 36.3675 | 1.33419 | 0.667097 | − | 0.744971i | \(-0.267537\pi\) | ||||
0.667097 | + | 0.744971i | \(0.267537\pi\) | |||||||
\(744\) | −39.3016 | −1.44087 | ||||||||
\(745\) | 3.37579 | 0.123679 | ||||||||
\(746\) | 26.1469 | 0.957307 | ||||||||
\(747\) | 0.804365 | 0.0294302 | ||||||||
\(748\) | 15.1085 | 0.552422 | ||||||||
\(749\) | −10.3628 | −0.378647 | ||||||||
\(750\) | 1.93974 | 0.0708293 | ||||||||
\(751\) | −30.6467 | −1.11831 | −0.559157 | − | 0.829062i | \(-0.688875\pi\) | ||||
−0.559157 | + | 0.829062i | \(0.688875\pi\) | |||||||
\(752\) | 16.9159 | 0.616861 | ||||||||
\(753\) | 17.3749 | 0.633178 | ||||||||
\(754\) | 2.14798 | 0.0782250 | ||||||||
\(755\) | −19.6888 | −0.716548 | ||||||||
\(756\) | 17.6630 | 0.642396 | ||||||||
\(757\) | −8.24452 | −0.299652 | −0.149826 | − | 0.988712i | \(-0.547871\pi\) | ||||
−0.149826 | + | 0.988712i | \(0.547871\pi\) | |||||||
\(758\) | −22.0281 | −0.800096 | ||||||||
\(759\) | −29.8242 | −1.08255 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.2064 | 0.406231 | 0.203116 | − | 0.979155i | \(-0.434893\pi\) | ||||
0.203116 | + | 0.979155i | \(0.434893\pi\) | |||||||
\(762\) | −38.9104 | −1.40957 | ||||||||
\(763\) | −63.5780 | −2.30168 | ||||||||
\(764\) | 7.64091 | 0.276438 | ||||||||
\(765\) | 0.605011 | 0.0218742 | ||||||||
\(766\) | 6.99047 | 0.252576 | ||||||||
\(767\) | −2.54435 | −0.0918711 | ||||||||
\(768\) | 24.7925 | 0.894622 | ||||||||
\(769\) | −26.1536 | −0.943122 | −0.471561 | − | 0.881833i | \(-0.656309\pi\) | ||||
−0.471561 | + | 0.881833i | \(0.656309\pi\) | |||||||
\(770\) | 18.7398 | 0.675334 | ||||||||
\(771\) | −35.7461 | −1.28737 | ||||||||
\(772\) | −8.80002 | −0.316720 | ||||||||
\(773\) | −14.5134 | −0.522010 | −0.261005 | − | 0.965337i | \(-0.584054\pi\) | ||||
−0.261005 | + | 0.965337i | \(0.584054\pi\) | |||||||
\(774\) | −1.11752 | −0.0401684 | ||||||||
\(775\) | 7.49400 | 0.269192 | ||||||||
\(776\) | −2.17787 | −0.0781808 | ||||||||
\(777\) | 48.4665 | 1.73873 | ||||||||
\(778\) | −4.17544 | −0.149697 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.40415 | 0.0502768 | ||||||||
\(781\) | −9.42187 | −0.337141 | ||||||||
\(782\) | 35.7415 | 1.27811 | ||||||||
\(783\) | −8.49987 | −0.303761 | ||||||||
\(784\) | −32.7740 | −1.17050 | ||||||||
\(785\) | 10.8049 | 0.385642 | ||||||||
\(786\) | 17.8835 | 0.637883 | ||||||||
\(787\) | 48.3569 | 1.72374 | 0.861869 | − | 0.507130i | \(-0.169294\pi\) | ||||
0.861869 | + | 0.507130i | \(0.169294\pi\) | |||||||
\(788\) | 7.08193 | 0.252283 | ||||||||
\(789\) | 41.6441 | 1.48257 | ||||||||
\(790\) | 13.7519 | 0.489272 | ||||||||
\(791\) | 56.4068 | 2.00559 | ||||||||
\(792\) | −1.03859 | −0.0369046 | ||||||||
\(793\) | 7.27188 | 0.258232 | ||||||||
\(794\) | −27.9903 | −0.993339 | ||||||||
\(795\) | −11.3853 | −0.403796 | ||||||||
\(796\) | −3.38504 | −0.119980 | ||||||||
\(797\) | −28.0793 | −0.994619 | −0.497310 | − | 0.867573i | \(-0.665679\pi\) | ||||
−0.497310 | + | 0.867573i | \(0.665679\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.0421 | 1.77036 | ||||||||
\(800\) | −3.76846 | −0.133235 | ||||||||
\(801\) | 0.861436 | 0.0304373 | ||||||||
\(802\) | 7.79467 | 0.275239 | ||||||||
\(803\) | 10.9227 | 0.385454 | ||||||||
\(804\) | 6.74047 | 0.237718 | ||||||||
\(805\) | −24.0641 | −0.848149 | ||||||||
\(806\) | −9.99378 | −0.352016 | ||||||||
\(807\) | −48.9276 | −1.72233 | ||||||||
\(808\) | −0.346797 | −0.0122003 | ||||||||
\(809\) | −33.4598 | −1.17638 | −0.588191 | − | 0.808722i | \(-0.700160\pi\) | ||||
−0.588191 | + | 0.808722i | \(0.700160\pi\) | |||||||
\(810\) | 9.90321 | 0.347963 | ||||||||
\(811\) | −10.8723 | −0.381778 | −0.190889 | − | 0.981612i | \(-0.561137\pi\) | ||||
−0.190889 | + | 0.981612i | \(0.561137\pi\) | |||||||
\(812\) | −5.39115 | −0.189192 | ||||||||
\(813\) | 35.6705 | 1.25102 | ||||||||
\(814\) | −23.5628 | −0.825875 | ||||||||
\(815\) | −2.40117 | −0.0841092 | ||||||||
\(816\) | −22.1733 | −0.776221 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 9.02205 | 0.315448 | ||||||||
\(819\) | 0.543221 | 0.0189817 | ||||||||
\(820\) | −3.82356 | −0.133525 | ||||||||
\(821\) | −26.8644 | −0.937576 | −0.468788 | − | 0.883311i | \(-0.655309\pi\) | ||||
−0.468788 | + | 0.883311i | \(0.655309\pi\) | |||||||
\(822\) | −6.72306 | −0.234494 | ||||||||
\(823\) | −26.6654 | −0.929496 | −0.464748 | − | 0.885443i | \(-0.653855\pi\) | ||||
−0.464748 | + | 0.885443i | \(0.653855\pi\) | |||||||
\(824\) | −34.8567 | −1.21429 | ||||||||
\(825\) | −5.89516 | −0.205243 | ||||||||
\(826\) | −11.7645 | −0.409338 | ||||||||
\(827\) | 20.5863 | 0.715856 | 0.357928 | − | 0.933749i | \(-0.383483\pi\) | ||||
0.357928 | + | 0.933749i | \(0.383483\pi\) | |||||||
\(828\) | 0.347108 | 0.0120628 | ||||||||
\(829\) | 23.1471 | 0.803932 | 0.401966 | − | 0.915655i | \(-0.368327\pi\) | ||||
0.401966 | + | 0.915655i | \(0.368327\pi\) | |||||||
\(830\) | 9.39268 | 0.326025 | ||||||||
\(831\) | 31.8956 | 1.10645 | ||||||||
\(832\) | 9.93902 | 0.344574 | ||||||||
\(833\) | −96.9546 | −3.35928 | ||||||||
\(834\) | −3.72956 | −0.129144 | ||||||||
\(835\) | −18.8862 | −0.653583 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.5468 | 1.36694 | ||||||||
\(838\) | −1.89947 | −0.0656160 | ||||||||
\(839\) | −41.4744 | −1.43186 | −0.715928 | − | 0.698174i | \(-0.753996\pi\) | ||||
−0.715928 | + | 0.698174i | \(0.753996\pi\) | |||||||
\(840\) | 24.9456 | 0.860705 | ||||||||
\(841\) | −26.4056 | −0.910539 | ||||||||
\(842\) | −21.7445 | −0.749367 | ||||||||
\(843\) | −32.6198 | −1.12349 | ||||||||
\(844\) | −1.00097 | −0.0344548 | ||||||||
\(845\) | −11.6281 | −0.400019 | ||||||||
\(846\) | −0.895307 | −0.0307813 | ||||||||
\(847\) | −4.63039 | −0.159102 | ||||||||
\(848\) | −14.0173 | −0.481355 | ||||||||
\(849\) | 30.4980 | 1.04669 | ||||||||
\(850\) | 7.06479 | 0.242320 | ||||||||
\(851\) | 30.2575 | 1.03721 | ||||||||
\(852\) | −3.26425 | −0.111831 | ||||||||
\(853\) | 49.7956 | 1.70497 | 0.852484 | − | 0.522753i | \(-0.175095\pi\) | ||||
0.852484 | + | 0.522753i | \(0.175095\pi\) | |||||||
\(854\) | 33.6234 | 1.15057 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.70642 | 0.229221 | ||||||||
\(857\) | 37.3465 | 1.27573 | 0.637866 | − | 0.770148i | \(-0.279818\pi\) | ||||
0.637866 | + | 0.770148i | \(0.279818\pi\) | |||||||
\(858\) | 7.86162 | 0.268391 | ||||||||
\(859\) | −23.7810 | −0.811397 | −0.405698 | − | 0.914007i | \(-0.632972\pi\) | ||||
−0.405698 | + | 0.914007i | \(0.632972\pi\) | |||||||
\(860\) | 7.08346 | 0.241544 | ||||||||
\(861\) | 44.0333 | 1.50065 | ||||||||
\(862\) | −21.0948 | −0.718493 | ||||||||
\(863\) | 28.6969 | 0.976855 | 0.488427 | − | 0.872605i | \(-0.337571\pi\) | ||||
0.488427 | + | 0.872605i | \(0.337571\pi\) | |||||||
\(864\) | −19.8867 | −0.676558 | ||||||||
\(865\) | −7.01969 | −0.238677 | ||||||||
\(866\) | 24.8300 | 0.843757 | ||||||||
\(867\) | −36.6324 | −1.24410 | ||||||||
\(868\) | 25.0830 | 0.851373 | ||||||||
\(869\) | −41.7942 | −1.41777 | ||||||||
\(870\) | −3.12434 | −0.105925 | ||||||||
\(871\) | 6.58557 | 0.223144 | ||||||||
\(872\) | 41.1455 | 1.39336 | ||||||||
\(873\) | 0.0689828 | 0.00233471 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.75660 | −0.160802 | ||||||||
\(876\) | 3.78422 | 0.127857 | ||||||||
\(877\) | 33.4018 | 1.12790 | 0.563950 | − | 0.825809i | \(-0.309281\pi\) | ||||
0.563950 | + | 0.825809i | \(0.309281\pi\) | |||||||
\(878\) | −22.3946 | −0.755782 | ||||||||
\(879\) | −10.9408 | −0.369023 | ||||||||
\(880\) | −7.25793 | −0.244665 | ||||||||
\(881\) | −33.0377 | −1.11307 | −0.556535 | − | 0.830824i | \(-0.687869\pi\) | ||||
−0.556535 | + | 0.830824i | \(0.687869\pi\) | |||||||
\(882\) | 1.73462 | 0.0584078 | ||||||||
\(883\) | −32.1095 | −1.08057 | −0.540286 | − | 0.841482i | \(-0.681684\pi\) | ||||
−0.540286 | + | 0.841482i | \(0.681684\pi\) | |||||||
\(884\) | 5.11412 | 0.172006 | ||||||||
\(885\) | 3.70087 | 0.124403 | ||||||||
\(886\) | −3.96995 | −0.133373 | ||||||||
\(887\) | 13.6924 | 0.459747 | 0.229873 | − | 0.973221i | \(-0.426169\pi\) | ||||
0.229873 | + | 0.973221i | \(0.426169\pi\) | |||||||
\(888\) | −31.3658 | −1.05257 | ||||||||
\(889\) | 95.4154 | 3.20013 | ||||||||
\(890\) | 10.0591 | 0.337182 | ||||||||
\(891\) | −30.0974 | −1.00830 | ||||||||
\(892\) | −0.197482 | −0.00661218 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 6.54815 | 0.219003 | ||||||||
\(895\) | 9.61639 | 0.321440 | ||||||||
\(896\) | 10.1055 | 0.337601 | ||||||||
\(897\) | −10.0953 | −0.337071 | ||||||||
\(898\) | 9.17997 | 0.306340 | ||||||||
\(899\) | −12.0706 | −0.402576 | ||||||||
\(900\) | 0.0686106 | 0.00228702 | ||||||||
\(901\) | −41.4670 | −1.38146 | ||||||||
\(902\) | −21.4075 | −0.712792 | ||||||||
\(903\) | −81.5752 | −2.71465 | ||||||||
\(904\) | −36.5045 | −1.21412 | ||||||||
\(905\) | −18.4974 | −0.614873 | ||||||||
\(906\) | −38.1911 | −1.26881 | ||||||||
\(907\) | 32.4144 | 1.07630 | 0.538151 | − | 0.842848i | \(-0.319123\pi\) | ||||
0.538151 | + | 0.842848i | \(0.319123\pi\) | |||||||
\(908\) | −13.3875 | −0.444280 | ||||||||
\(909\) | 0.0109846 | 0.000364337 0 | ||||||||
\(910\) | 6.34326 | 0.210277 | ||||||||
\(911\) | 7.16536 | 0.237399 | 0.118699 | − | 0.992930i | \(-0.462128\pi\) | ||||
0.118699 | + | 0.992930i | \(0.462128\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.5458 | −0.944727 | ||||||||
\(914\) | 29.2948 | 0.968987 | ||||||||
\(915\) | −10.5773 | −0.349674 | ||||||||
\(916\) | −8.21555 | −0.271449 | ||||||||
\(917\) | −43.8536 | −1.44817 | ||||||||
\(918\) | 37.2818 | 1.23048 | ||||||||
\(919\) | −13.3921 | −0.441765 | −0.220883 | − | 0.975300i | \(-0.570894\pi\) | ||||
−0.220883 | + | 0.975300i | \(0.570894\pi\) | |||||||
\(920\) | 15.5735 | 0.513442 | ||||||||
\(921\) | −10.4891 | −0.345627 | ||||||||
\(922\) | −8.52058 | −0.280610 | ||||||||
\(923\) | −3.18923 | −0.104975 | ||||||||
\(924\) | −19.7316 | −0.649122 | ||||||||
\(925\) | 5.98080 | 0.196647 | ||||||||
\(926\) | −27.8694 | −0.915844 | ||||||||
\(927\) | 1.10407 | 0.0362624 | ||||||||
\(928\) | 6.06987 | 0.199253 | ||||||||
\(929\) | 8.49231 | 0.278624 | 0.139312 | − | 0.990249i | \(-0.455511\pi\) | ||||
0.139312 | + | 0.990249i | \(0.455511\pi\) | |||||||
\(930\) | 14.5364 | 0.476667 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.7668 | 0.418190 | ||||||||
\(933\) | −5.70710 | −0.186842 | ||||||||
\(934\) | −6.86953 | −0.224778 | ||||||||
\(935\) | −21.4710 | −0.702176 | ||||||||
\(936\) | −0.351554 | −0.0114909 | ||||||||
\(937\) | −50.7981 | −1.65950 | −0.829751 | − | 0.558134i | \(-0.811517\pi\) | ||||
−0.829751 | + | 0.558134i | \(0.811517\pi\) | |||||||
\(938\) | 30.4501 | 0.994231 | ||||||||
\(939\) | −41.2946 | −1.34760 | ||||||||
\(940\) | 5.67496 | 0.185097 | ||||||||
\(941\) | 3.94534 | 0.128614 | 0.0643072 | − | 0.997930i | \(-0.479516\pi\) | ||||
0.0643072 | + | 0.997930i | \(0.479516\pi\) | |||||||
\(942\) | 20.9586 | 0.682868 | ||||||||
\(943\) | 27.4898 | 0.895192 | ||||||||
\(944\) | 4.55639 | 0.148298 | ||||||||
\(945\) | −25.1012 | −0.816541 | ||||||||
\(946\) | 39.6591 | 1.28943 | ||||||||
\(947\) | 1.12607 | 0.0365924 | 0.0182962 | − | 0.999833i | \(-0.494176\pi\) | ||||
0.0182962 | + | 0.999833i | \(0.494176\pi\) | |||||||
\(948\) | −14.4798 | −0.470281 | ||||||||
\(949\) | 3.69725 | 0.120018 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.7134 | −0.606824 | ||||||||
\(952\) | 90.8552 | 2.94463 | ||||||||
\(953\) | −51.9998 | −1.68444 | −0.842220 | − | 0.539135i | \(-0.818751\pi\) | ||||
−0.842220 | + | 0.539135i | \(0.818751\pi\) | |||||||
\(954\) | 0.741889 | 0.0240195 | ||||||||
\(955\) | −10.8586 | −0.351377 | ||||||||
\(956\) | 19.1523 | 0.619431 | ||||||||
\(957\) | 9.49534 | 0.306941 | ||||||||
\(958\) | −25.3645 | −0.819490 | ||||||||
\(959\) | 16.4862 | 0.532366 | ||||||||
\(960\) | −14.4568 | −0.466590 | ||||||||
\(961\) | 25.1600 | 0.811612 | ||||||||
\(962\) | −7.97583 | −0.257151 | ||||||||
\(963\) | −0.212422 | −0.00684522 | ||||||||
\(964\) | 6.70839 | 0.216063 | ||||||||
\(965\) | 12.5059 | 0.402578 | ||||||||
\(966\) | −46.6781 | −1.50184 | ||||||||
\(967\) | −24.6191 | −0.791696 | −0.395848 | − | 0.918316i | \(-0.629549\pi\) | ||||
−0.395848 | + | 0.918316i | \(0.629549\pi\) | |||||||
\(968\) | 2.99662 | 0.0963152 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.805522 | 0.0258637 | ||||||||
\(971\) | −53.3884 | −1.71332 | −0.856658 | − | 0.515884i | \(-0.827463\pi\) | ||||
−0.856658 | + | 0.515884i | \(0.827463\pi\) | |||||||
\(972\) | 0.712736 | 0.0228610 | ||||||||
\(973\) | 9.14557 | 0.293194 | ||||||||
\(974\) | 24.2364 | 0.776585 | ||||||||
\(975\) | −1.99547 | −0.0639061 | ||||||||
\(976\) | −13.0224 | −0.416837 | ||||||||
\(977\) | −21.4513 | −0.686288 | −0.343144 | − | 0.939283i | \(-0.611492\pi\) | ||||
−0.343144 | + | 0.939283i | \(0.611492\pi\) | |||||||
\(978\) | −4.65764 | −0.148935 | ||||||||
\(979\) | −30.5711 | −0.977058 | ||||||||
\(980\) | −10.9950 | −0.351223 | ||||||||
\(981\) | −1.30326 | −0.0416100 | ||||||||
\(982\) | 38.2914 | 1.22193 | ||||||||
\(983\) | 14.5902 | 0.465355 | 0.232677 | − | 0.972554i | \(-0.425251\pi\) | ||||
0.232677 | + | 0.972554i | \(0.425251\pi\) | |||||||
\(984\) | −28.4968 | −0.908444 | ||||||||
\(985\) | −10.0643 | −0.320674 | ||||||||
\(986\) | −11.3793 | −0.362390 | ||||||||
\(987\) | −65.3545 | −2.08026 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50.9271 | −1.61939 | ||||||||
\(990\) | 0.384139 | 0.0122087 | ||||||||
\(991\) | −5.62007 | −0.178527 | −0.0892636 | − | 0.996008i | \(-0.528451\pi\) | ||||
−0.0892636 | + | 0.996008i | \(0.528451\pi\) | |||||||
\(992\) | −28.2409 | −0.896648 | ||||||||
\(993\) | −43.0215 | −1.36525 | ||||||||
\(994\) | −14.7462 | −0.467722 | ||||||||
\(995\) | 4.81054 | 0.152504 | ||||||||
\(996\) | −9.88980 | −0.313370 | ||||||||
\(997\) | 31.1721 | 0.987230 | 0.493615 | − | 0.869681i | \(-0.335675\pi\) | ||||
0.493615 | + | 0.869681i | \(0.335675\pi\) | |||||||
\(998\) | 40.1510 | 1.27096 | ||||||||
\(999\) | 31.5615 | 0.998560 |
(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 | 1805.2.a.j.1.2 | ✓ | 4 | |
5.4 | even | 2 | 9025.2.a.bo.1.3 | 4 | |||
19.18 | odd | 2 | 1805.2.a.n.1.3 | yes | 4 | ||
95.94 | odd | 2 | 9025.2.a.bh.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.j.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1805.2.a.n.1.3 | yes | 4 | 19.18 | odd | 2 | ||
9025.2.a.bh.1.2 | 4 | 95.94 | odd | 2 | |||
9025.2.a.bo.1.3 | 4 | 5.4 | even | 2 |