Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(1,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, 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("637.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4507648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.758419\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.18322 | 1.54377 | 0.771885 | − | 0.635762i | \(-0.219314\pi\) | ||||
0.771885 | + | 0.635762i | \(0.219314\pi\) | |||||||
\(3\) | 1.75842 | 1.01522 | 0.507612 | − | 0.861586i | \(-0.330528\pi\) | ||||
0.507612 | + | 0.861586i | \(0.330528\pi\) | |||||||
\(4\) | 2.76645 | 1.38322 | ||||||||
\(5\) | 2.11065 | 0.943913 | 0.471957 | − | 0.881622i | \(-0.343548\pi\) | ||||
0.471957 | + | 0.881622i | \(0.343548\pi\) | |||||||
\(6\) | 3.83901 | 1.56727 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.67333 | 0.591610 | ||||||||
\(9\) | 0.0920365 | 0.0306788 | ||||||||
\(10\) | 4.60802 | 1.45718 | ||||||||
\(11\) | −5.76889 | −1.73939 | −0.869694 | − | 0.493592i | \(-0.835684\pi\) | ||||
−0.869694 | + | 0.493592i | \(0.835684\pi\) | |||||||
\(12\) | 4.86457 | 1.40428 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.71141 | 0.958283 | ||||||||
\(16\) | −1.87966 | −0.469915 | ||||||||
\(17\) | 1.64082 | 0.397958 | 0.198979 | − | 0.980004i | \(-0.436237\pi\) | ||||
0.198979 | + | 0.980004i | \(0.436237\pi\) | |||||||
\(18\) | 0.200936 | 0.0473611 | ||||||||
\(19\) | −2.67077 | −0.612716 | −0.306358 | − | 0.951916i | \(-0.599110\pi\) | ||||
−0.306358 | + | 0.951916i | \(0.599110\pi\) | |||||||
\(20\) | 5.83901 | 1.30564 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12.5948 | −2.68521 | ||||||||
\(23\) | 6.42469 | 1.33964 | 0.669820 | − | 0.742523i | \(-0.266371\pi\) | ||||
0.669820 | + | 0.742523i | \(0.266371\pi\) | |||||||
\(24\) | 2.94241 | 0.600616 | ||||||||
\(25\) | −0.545141 | −0.109028 | ||||||||
\(26\) | 2.18322 | 0.428165 | ||||||||
\(27\) | −5.11342 | −0.984078 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.04973 | −1.12341 | −0.561704 | − | 0.827338i | \(-0.689854\pi\) | ||||
−0.561704 | + | 0.827338i | \(0.689854\pi\) | |||||||
\(30\) | 8.10283 | 1.47937 | ||||||||
\(31\) | 5.12202 | 0.919942 | 0.459971 | − | 0.887934i | \(-0.347860\pi\) | ||||
0.459971 | + | 0.887934i | \(0.347860\pi\) | |||||||
\(32\) | −7.45036 | −1.31705 | ||||||||
\(33\) | −10.1441 | −1.76587 | ||||||||
\(34\) | 3.58227 | 0.614355 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.254614 | 0.0424357 | ||||||||
\(37\) | 5.74772 | 0.944919 | 0.472460 | − | 0.881352i | \(-0.343366\pi\) | ||||
0.472460 | + | 0.881352i | \(0.343366\pi\) | |||||||
\(38\) | −5.83087 | −0.945892 | ||||||||
\(39\) | 1.75842 | 0.281572 | ||||||||
\(40\) | 3.53181 | 0.558428 | ||||||||
\(41\) | −7.14100 | −1.11524 | −0.557619 | − | 0.830097i | \(-0.688285\pi\) | ||||
−0.557619 | + | 0.830097i | \(0.688285\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.47061 | −0.681761 | −0.340881 | − | 0.940107i | \(-0.610725\pi\) | ||||
−0.340881 | + | 0.940107i | \(0.610725\pi\) | |||||||
\(44\) | −15.9593 | −2.40596 | ||||||||
\(45\) | 0.194257 | 0.0289582 | ||||||||
\(46\) | 14.0265 | 2.06810 | ||||||||
\(47\) | 11.7910 | 1.71989 | 0.859947 | − | 0.510384i | \(-0.170497\pi\) | ||||
0.859947 | + | 0.510384i | \(0.170497\pi\) | |||||||
\(48\) | −3.30523 | −0.477069 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.19016 | −0.168314 | ||||||||
\(51\) | 2.88525 | 0.404016 | ||||||||
\(52\) | 2.76645 | 0.383637 | ||||||||
\(53\) | 3.44959 | 0.473838 | 0.236919 | − | 0.971529i | \(-0.423862\pi\) | ||||
0.236919 | + | 0.971529i | \(0.423862\pi\) | |||||||
\(54\) | −11.1637 | −1.51919 | ||||||||
\(55\) | −12.1761 | −1.64183 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.69633 | −0.622044 | ||||||||
\(58\) | −13.2079 | −1.73428 | ||||||||
\(59\) | 13.1805 | 1.71596 | 0.857981 | − | 0.513682i | \(-0.171719\pi\) | ||||
0.857981 | + | 0.513682i | \(0.171719\pi\) | |||||||
\(60\) | 10.2674 | 1.32552 | ||||||||
\(61\) | 6.24666 | 0.799803 | 0.399901 | − | 0.916558i | \(-0.369044\pi\) | ||||
0.399901 | + | 0.916558i | \(0.369044\pi\) | |||||||
\(62\) | 11.1825 | 1.42018 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.5065 | −1.56331 | ||||||||
\(65\) | 2.11065 | 0.261794 | ||||||||
\(66\) | −22.1469 | −2.72609 | ||||||||
\(67\) | 7.74216 | 0.945856 | 0.472928 | − | 0.881101i | \(-0.343197\pi\) | ||||
0.472928 | + | 0.881101i | \(0.343197\pi\) | |||||||
\(68\) | 4.53925 | 0.550465 | ||||||||
\(69\) | 11.2973 | 1.36003 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6372 | 1.61844 | 0.809221 | − | 0.587504i | \(-0.199889\pi\) | ||||
0.809221 | + | 0.587504i | \(0.199889\pi\) | |||||||
\(72\) | 0.154007 | 0.0181499 | ||||||||
\(73\) | −15.5041 | −1.81462 | −0.907308 | − | 0.420467i | \(-0.861866\pi\) | ||||
−0.907308 | + | 0.420467i | \(0.861866\pi\) | |||||||
\(74\) | 12.5485 | 1.45874 | ||||||||
\(75\) | −0.958586 | −0.110688 | ||||||||
\(76\) | −7.38854 | −0.847524 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.83901 | 0.434683 | ||||||||
\(79\) | 1.12214 | 0.126251 | 0.0631254 | − | 0.998006i | \(-0.479893\pi\) | ||||
0.0631254 | + | 0.998006i | \(0.479893\pi\) | |||||||
\(80\) | −3.96731 | −0.443559 | ||||||||
\(81\) | −9.26764 | −1.02974 | ||||||||
\(82\) | −15.5904 | −1.72167 | ||||||||
\(83\) | 4.96925 | 0.545446 | 0.272723 | − | 0.962093i | \(-0.412076\pi\) | ||||
0.272723 | + | 0.962093i | \(0.412076\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46321 | 0.375638 | ||||||||
\(86\) | −9.76032 | −1.05248 | ||||||||
\(87\) | −10.6380 | −1.14051 | ||||||||
\(88\) | −9.65324 | −1.02904 | ||||||||
\(89\) | 1.14630 | 0.121507 | 0.0607535 | − | 0.998153i | \(-0.480650\pi\) | ||||
0.0607535 | + | 0.998153i | \(0.480650\pi\) | |||||||
\(90\) | 0.424106 | 0.0447047 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 17.7736 | 1.85302 | ||||||||
\(93\) | 9.00665 | 0.933946 | ||||||||
\(94\) | 25.7423 | 2.65512 | ||||||||
\(95\) | −5.63707 | −0.578351 | ||||||||
\(96\) | −13.1009 | −1.33710 | ||||||||
\(97\) | −6.97223 | −0.707923 | −0.353961 | − | 0.935260i | \(-0.615166\pi\) | ||||
−0.353961 | + | 0.935260i | \(0.615166\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.530949 | −0.0533624 | ||||||||
\(100\) | −1.50810 | −0.150810 | ||||||||
\(101\) | −6.49919 | −0.646694 | −0.323347 | − | 0.946280i | \(-0.604808\pi\) | ||||
−0.323347 | + | 0.946280i | \(0.604808\pi\) | |||||||
\(102\) | 6.29914 | 0.623708 | ||||||||
\(103\) | −0.578048 | −0.0569568 | −0.0284784 | − | 0.999594i | \(-0.509066\pi\) | ||||
−0.0284784 | + | 0.999594i | \(0.509066\pi\) | |||||||
\(104\) | 1.67333 | 0.164083 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.53122 | 0.731497 | ||||||||
\(107\) | −16.2573 | −1.57165 | −0.785824 | − | 0.618450i | \(-0.787761\pi\) | ||||
−0.785824 | + | 0.618450i | \(0.787761\pi\) | |||||||
\(108\) | −14.1460 | −1.36120 | ||||||||
\(109\) | 1.78191 | 0.170676 | 0.0853378 | − | 0.996352i | \(-0.472803\pi\) | ||||
0.0853378 | + | 0.996352i | \(0.472803\pi\) | |||||||
\(110\) | −26.5832 | −2.53461 | ||||||||
\(111\) | 10.1069 | 0.959304 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.52215 | −0.707624 | −0.353812 | − | 0.935316i | \(-0.615115\pi\) | ||||
−0.353812 | + | 0.935316i | \(0.615115\pi\) | |||||||
\(114\) | −10.2531 | −0.960292 | ||||||||
\(115\) | 13.5603 | 1.26450 | ||||||||
\(116\) | −16.7363 | −1.55392 | ||||||||
\(117\) | 0.0920365 | 0.00850878 | ||||||||
\(118\) | 28.7760 | 2.64905 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.21040 | 0.566930 | ||||||||
\(121\) | 22.2801 | 2.02547 | ||||||||
\(122\) | 13.6378 | 1.23471 | ||||||||
\(123\) | −12.5569 | −1.13222 | ||||||||
\(124\) | 14.1698 | 1.27249 | ||||||||
\(125\) | −11.7039 | −1.04683 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.3056 | −1.71310 | −0.856549 | − | 0.516067i | \(-0.827396\pi\) | ||||
−0.856549 | + | 0.516067i | \(0.827396\pi\) | |||||||
\(128\) | −12.4036 | −1.09634 | ||||||||
\(129\) | −7.86120 | −0.692140 | ||||||||
\(130\) | 4.60802 | 0.404150 | ||||||||
\(131\) | 9.69703 | 0.847234 | 0.423617 | − | 0.905842i | \(-0.360760\pi\) | ||||
0.423617 | + | 0.905842i | \(0.360760\pi\) | |||||||
\(132\) | −28.0632 | −2.44259 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 16.9028 | 1.46018 | ||||||||
\(135\) | −10.7927 | −0.928884 | ||||||||
\(136\) | 2.74563 | 0.235436 | ||||||||
\(137\) | −15.4493 | −1.31993 | −0.659963 | − | 0.751298i | \(-0.729428\pi\) | ||||
−0.659963 | + | 0.751298i | \(0.729428\pi\) | |||||||
\(138\) | 24.6645 | 2.09958 | ||||||||
\(139\) | 3.84912 | 0.326478 | 0.163239 | − | 0.986587i | \(-0.447806\pi\) | ||||
0.163239 | + | 0.986587i | \(0.447806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.7335 | 1.74608 | ||||||||
\(142\) | 29.7731 | 2.49850 | ||||||||
\(143\) | −5.76889 | −0.482419 | ||||||||
\(144\) | −0.172997 | −0.0144164 | ||||||||
\(145\) | −12.7689 | −1.06040 | ||||||||
\(146\) | −33.8488 | −2.80135 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.9008 | 1.30704 | ||||||||
\(149\) | −1.04028 | −0.0852231 | −0.0426115 | − | 0.999092i | \(-0.513568\pi\) | ||||
−0.0426115 | + | 0.999092i | \(0.513568\pi\) | |||||||
\(150\) | −2.09280 | −0.170877 | ||||||||
\(151\) | −4.34336 | −0.353458 | −0.176729 | − | 0.984260i | \(-0.556552\pi\) | ||||
−0.176729 | + | 0.984260i | \(0.556552\pi\) | |||||||
\(152\) | −4.46906 | −0.362489 | ||||||||
\(153\) | 0.151016 | 0.0122089 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.8108 | 0.868345 | ||||||||
\(156\) | 4.86457 | 0.389478 | ||||||||
\(157\) | 0.336000 | 0.0268157 | 0.0134079 | − | 0.999910i | \(-0.495732\pi\) | ||||
0.0134079 | + | 0.999910i | \(0.495732\pi\) | |||||||
\(158\) | 2.44988 | 0.194902 | ||||||||
\(159\) | 6.06583 | 0.481052 | ||||||||
\(160\) | −15.7251 | −1.24318 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −20.2333 | −1.58968 | ||||||||
\(163\) | 6.79919 | 0.532553 | 0.266277 | − | 0.963897i | \(-0.414207\pi\) | ||||
0.266277 | + | 0.963897i | \(0.414207\pi\) | |||||||
\(164\) | −19.7552 | −1.54262 | ||||||||
\(165\) | −21.4107 | −1.66682 | ||||||||
\(166\) | 10.8490 | 0.842043 | ||||||||
\(167\) | 0.668649 | 0.0517416 | 0.0258708 | − | 0.999665i | \(-0.491764\pi\) | ||||
0.0258708 | + | 0.999665i | \(0.491764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 7.56094 | 0.579898 | ||||||||
\(171\) | −0.245808 | −0.0187974 | ||||||||
\(172\) | −12.3677 | −0.943029 | ||||||||
\(173\) | 25.1178 | 1.90967 | 0.954837 | − | 0.297131i | \(-0.0960298\pi\) | ||||
0.954837 | + | 0.297131i | \(0.0960298\pi\) | |||||||
\(174\) | −23.2250 | −1.76068 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.8436 | 0.817364 | ||||||||
\(177\) | 23.1769 | 1.74208 | ||||||||
\(178\) | 2.50262 | 0.187579 | ||||||||
\(179\) | −1.89527 | −0.141659 | −0.0708294 | − | 0.997488i | \(-0.522565\pi\) | ||||
−0.0708294 | + | 0.997488i | \(0.522565\pi\) | |||||||
\(180\) | 0.537403 | 0.0400556 | ||||||||
\(181\) | 11.3595 | 0.844347 | 0.422174 | − | 0.906515i | \(-0.361267\pi\) | ||||
0.422174 | + | 0.906515i | \(0.361267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.9842 | 0.811978 | ||||||||
\(184\) | 10.7506 | 0.792544 | ||||||||
\(185\) | 12.1314 | 0.891922 | ||||||||
\(186\) | 19.6635 | 1.44180 | ||||||||
\(187\) | −9.46573 | −0.692203 | ||||||||
\(188\) | 32.6192 | 2.37900 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.3070 | −0.892840 | ||||||||
\(191\) | −23.4407 | −1.69611 | −0.848055 | − | 0.529909i | \(-0.822226\pi\) | ||||
−0.848055 | + | 0.529909i | \(0.822226\pi\) | |||||||
\(192\) | −21.9916 | −1.58711 | ||||||||
\(193\) | −1.85210 | −0.133317 | −0.0666584 | − | 0.997776i | \(-0.521234\pi\) | ||||
−0.0666584 | + | 0.997776i | \(0.521234\pi\) | |||||||
\(194\) | −15.2219 | −1.09287 | ||||||||
\(195\) | 3.71141 | 0.265780 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.87082 | −0.703267 | −0.351634 | − | 0.936138i | \(-0.614374\pi\) | ||||
−0.351634 | + | 0.936138i | \(0.614374\pi\) | |||||||
\(198\) | −1.15918 | −0.0823792 | ||||||||
\(199\) | 12.2492 | 0.868324 | 0.434162 | − | 0.900835i | \(-0.357044\pi\) | ||||
0.434162 | + | 0.900835i | \(0.357044\pi\) | |||||||
\(200\) | −0.912199 | −0.0645022 | ||||||||
\(201\) | 13.6140 | 0.960255 | ||||||||
\(202\) | −14.1892 | −0.998347 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.98190 | 0.558845 | ||||||||
\(205\) | −15.0722 | −1.05269 | ||||||||
\(206\) | −1.26201 | −0.0879281 | ||||||||
\(207\) | 0.591306 | 0.0410986 | ||||||||
\(208\) | −1.87966 | −0.130331 | ||||||||
\(209\) | 15.4074 | 1.06575 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.739899 | −0.0509368 | −0.0254684 | − | 0.999676i | \(-0.508108\pi\) | ||||
−0.0254684 | + | 0.999676i | \(0.508108\pi\) | |||||||
\(212\) | 9.54312 | 0.655424 | ||||||||
\(213\) | 23.9800 | 1.64308 | ||||||||
\(214\) | −35.4932 | −2.42626 | ||||||||
\(215\) | −9.43591 | −0.643523 | ||||||||
\(216\) | −8.55641 | −0.582190 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.89029 | 0.263484 | ||||||||
\(219\) | −27.2627 | −1.84224 | ||||||||
\(220\) | −33.6847 | −2.27102 | ||||||||
\(221\) | 1.64082 | 0.110374 | ||||||||
\(222\) | 22.0656 | 1.48094 | ||||||||
\(223\) | 8.30577 | 0.556196 | 0.278098 | − | 0.960553i | \(-0.410296\pi\) | ||||
0.278098 | + | 0.960553i | \(0.410296\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0501729 | −0.00334486 | ||||||||
\(226\) | −16.4225 | −1.09241 | ||||||||
\(227\) | 13.2917 | 0.882198 | 0.441099 | − | 0.897458i | \(-0.354589\pi\) | ||||
0.441099 | + | 0.897458i | \(0.354589\pi\) | |||||||
\(228\) | −12.9921 | −0.860426 | ||||||||
\(229\) | 17.9207 | 1.18423 | 0.592115 | − | 0.805853i | \(-0.298293\pi\) | ||||
0.592115 | + | 0.805853i | \(0.298293\pi\) | |||||||
\(230\) | 29.6051 | 1.95210 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.1232 | −0.664619 | ||||||||
\(233\) | 6.29968 | 0.412705 | 0.206353 | − | 0.978478i | \(-0.433841\pi\) | ||||
0.206353 | + | 0.978478i | \(0.433841\pi\) | |||||||
\(234\) | 0.200936 | 0.0131356 | ||||||||
\(235\) | 24.8867 | 1.62343 | ||||||||
\(236\) | 36.4633 | 2.37356 | ||||||||
\(237\) | 1.97320 | 0.128173 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.41783 | 0.609189 | 0.304594 | − | 0.952482i | \(-0.401479\pi\) | ||||
0.304594 | + | 0.952482i | \(0.401479\pi\) | |||||||
\(240\) | −6.97619 | −0.450311 | ||||||||
\(241\) | −19.9493 | −1.28505 | −0.642524 | − | 0.766266i | \(-0.722113\pi\) | ||||
−0.642524 | + | 0.766266i | \(0.722113\pi\) | |||||||
\(242\) | 48.6424 | 3.12685 | ||||||||
\(243\) | −0.956137 | −0.0613362 | ||||||||
\(244\) | 17.2811 | 1.10631 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −27.4144 | −1.74788 | ||||||||
\(247\) | −2.67077 | −0.169937 | ||||||||
\(248\) | 8.57080 | 0.544246 | ||||||||
\(249\) | 8.73802 | 0.553750 | ||||||||
\(250\) | −25.5521 | −1.61606 | ||||||||
\(251\) | 1.22202 | 0.0771330 | 0.0385665 | − | 0.999256i | \(-0.487721\pi\) | ||||
0.0385665 | + | 0.999256i | \(0.487721\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −37.0633 | −2.33015 | ||||||||
\(254\) | −42.1484 | −2.64463 | ||||||||
\(255\) | 6.08977 | 0.381356 | ||||||||
\(256\) | −2.06691 | −0.129182 | ||||||||
\(257\) | −22.4240 | −1.39877 | −0.699386 | − | 0.714745i | \(-0.746543\pi\) | ||||
−0.699386 | + | 0.714745i | \(0.746543\pi\) | |||||||
\(258\) | −17.1627 | −1.06850 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.83901 | 0.362120 | ||||||||
\(261\) | −0.556797 | −0.0344648 | ||||||||
\(262\) | 21.1707 | 1.30793 | ||||||||
\(263\) | 8.99048 | 0.554377 | 0.277188 | − | 0.960816i | \(-0.410597\pi\) | ||||
0.277188 | + | 0.960816i | \(0.410597\pi\) | |||||||
\(264\) | −16.9744 | −1.04470 | ||||||||
\(265\) | 7.28090 | 0.447262 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.01567 | 0.123357 | ||||||||
\(268\) | 21.4183 | 1.30833 | ||||||||
\(269\) | −22.2054 | −1.35389 | −0.676945 | − | 0.736034i | \(-0.736697\pi\) | ||||
−0.676945 | + | 0.736034i | \(0.736697\pi\) | |||||||
\(270\) | −23.5627 | −1.43398 | ||||||||
\(271\) | −10.8423 | −0.658624 | −0.329312 | − | 0.944221i | \(-0.606817\pi\) | ||||
−0.329312 | + | 0.944221i | \(0.606817\pi\) | |||||||
\(272\) | −3.08419 | −0.187006 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −33.7293 | −2.03766 | ||||||||
\(275\) | 3.14486 | 0.189642 | ||||||||
\(276\) | 31.2534 | 1.88123 | ||||||||
\(277\) | 5.88828 | 0.353792 | 0.176896 | − | 0.984230i | \(-0.443394\pi\) | ||||
0.176896 | + | 0.984230i | \(0.443394\pi\) | |||||||
\(278\) | 8.40347 | 0.504006 | ||||||||
\(279\) | 0.471413 | 0.0282227 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.9071 | 1.60514 | 0.802572 | − | 0.596556i | \(-0.203465\pi\) | ||||
0.802572 | + | 0.596556i | \(0.203465\pi\) | |||||||
\(282\) | 45.2658 | 2.69554 | ||||||||
\(283\) | −3.49717 | −0.207885 | −0.103943 | − | 0.994583i | \(-0.533146\pi\) | ||||
−0.103943 | + | 0.994583i | \(0.533146\pi\) | |||||||
\(284\) | 37.7267 | 2.23867 | ||||||||
\(285\) | −9.91232 | −0.587155 | ||||||||
\(286\) | −12.5948 | −0.744744 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.685705 | −0.0404056 | ||||||||
\(289\) | −14.3077 | −0.841630 | ||||||||
\(290\) | −27.8773 | −1.63701 | ||||||||
\(291\) | −12.2601 | −0.718700 | ||||||||
\(292\) | −42.8913 | −2.51002 | ||||||||
\(293\) | 1.00509 | 0.0587179 | 0.0293589 | − | 0.999569i | \(-0.490653\pi\) | ||||
0.0293589 | + | 0.999569i | \(0.490653\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.8196 | 1.61972 | ||||||||
\(296\) | 9.61780 | 0.559024 | ||||||||
\(297\) | 29.4988 | 1.71169 | ||||||||
\(298\) | −2.27116 | −0.131565 | ||||||||
\(299\) | 6.42469 | 0.371549 | ||||||||
\(300\) | −2.65188 | −0.153106 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.48252 | −0.545657 | ||||||||
\(303\) | −11.4283 | −0.656539 | ||||||||
\(304\) | 5.02013 | 0.287924 | ||||||||
\(305\) | 13.1845 | 0.754944 | ||||||||
\(306\) | 0.329700 | 0.0188477 | ||||||||
\(307\) | 4.25772 | 0.243001 | 0.121501 | − | 0.992591i | \(-0.461229\pi\) | ||||
0.121501 | + | 0.992591i | \(0.461229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.01645 | −0.0578238 | ||||||||
\(310\) | 23.6024 | 1.34052 | ||||||||
\(311\) | −6.94043 | −0.393556 | −0.196778 | − | 0.980448i | \(-0.563048\pi\) | ||||
−0.196778 | + | 0.980448i | \(0.563048\pi\) | |||||||
\(312\) | 2.94241 | 0.166581 | ||||||||
\(313\) | −9.96299 | −0.563142 | −0.281571 | − | 0.959540i | \(-0.590855\pi\) | ||||
−0.281571 | + | 0.959540i | \(0.590855\pi\) | |||||||
\(314\) | 0.733563 | 0.0413973 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.10435 | 0.174633 | ||||||||
\(317\) | 3.75345 | 0.210815 | 0.105407 | − | 0.994429i | \(-0.466385\pi\) | ||||
0.105407 | + | 0.994429i | \(0.466385\pi\) | |||||||
\(318\) | 13.2430 | 0.742633 | ||||||||
\(319\) | 34.9003 | 1.95404 | ||||||||
\(320\) | −26.3968 | −1.47563 | ||||||||
\(321\) | −28.5871 | −1.59557 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.38225 | −0.243835 | ||||||||
\(324\) | −25.6384 | −1.42436 | ||||||||
\(325\) | −0.545141 | −0.0302390 | ||||||||
\(326\) | 14.8441 | 0.822140 | ||||||||
\(327\) | 3.13334 | 0.173274 | ||||||||
\(328\) | −11.9492 | −0.659785 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −46.7444 | −2.57319 | ||||||||
\(331\) | −19.9812 | −1.09827 | −0.549134 | − | 0.835734i | \(-0.685042\pi\) | ||||
−0.549134 | + | 0.835734i | \(0.685042\pi\) | |||||||
\(332\) | 13.7472 | 0.754474 | ||||||||
\(333\) | 0.529000 | 0.0289890 | ||||||||
\(334\) | 1.45981 | 0.0798771 | ||||||||
\(335\) | 16.3410 | 0.892805 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.4887 | 1.00714 | 0.503571 | − | 0.863954i | \(-0.332019\pi\) | ||||
0.503571 | + | 0.863954i | \(0.332019\pi\) | |||||||
\(338\) | 2.18322 | 0.118751 | ||||||||
\(339\) | −13.2271 | −0.718397 | ||||||||
\(340\) | 9.58078 | 0.519591 | ||||||||
\(341\) | −29.5484 | −1.60013 | ||||||||
\(342\) | −0.536653 | −0.0290189 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.48078 | −0.403337 | ||||||||
\(345\) | 23.8447 | 1.28375 | ||||||||
\(346\) | 54.8377 | 2.94810 | ||||||||
\(347\) | −0.796100 | −0.0427369 | −0.0213684 | − | 0.999772i | \(-0.506802\pi\) | ||||
−0.0213684 | + | 0.999772i | \(0.506802\pi\) | |||||||
\(348\) | −29.4294 | −1.57758 | ||||||||
\(349\) | −11.3725 | −0.608754 | −0.304377 | − | 0.952552i | \(-0.598448\pi\) | ||||
−0.304377 | + | 0.952552i | \(0.598448\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.11342 | −0.272934 | ||||||||
\(352\) | 42.9803 | 2.29086 | ||||||||
\(353\) | 24.1068 | 1.28307 | 0.641537 | − | 0.767092i | \(-0.278297\pi\) | ||||
0.641537 | + | 0.767092i | \(0.278297\pi\) | |||||||
\(354\) | 50.6003 | 2.68938 | ||||||||
\(355\) | 28.7835 | 1.52767 | ||||||||
\(356\) | 3.17117 | 0.168072 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.13778 | −0.218689 | ||||||||
\(359\) | 9.07182 | 0.478792 | 0.239396 | − | 0.970922i | \(-0.423051\pi\) | ||||
0.239396 | + | 0.970922i | \(0.423051\pi\) | |||||||
\(360\) | 0.325056 | 0.0171319 | ||||||||
\(361\) | −11.8670 | −0.624579 | ||||||||
\(362\) | 24.8003 | 1.30348 | ||||||||
\(363\) | 39.1778 | 2.05630 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.7238 | −1.71284 | ||||||||
\(366\) | 23.9810 | 1.25351 | ||||||||
\(367\) | −31.5507 | −1.64693 | −0.823467 | − | 0.567364i | \(-0.807963\pi\) | ||||
−0.823467 | + | 0.567364i | \(0.807963\pi\) | |||||||
\(368\) | −12.0762 | −0.629517 | ||||||||
\(369\) | −0.657233 | −0.0342142 | ||||||||
\(370\) | 26.4856 | 1.37692 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 24.9164 | 1.29186 | ||||||||
\(373\) | −16.0581 | −0.831457 | −0.415728 | − | 0.909489i | \(-0.636473\pi\) | ||||
−0.415728 | + | 0.909489i | \(0.636473\pi\) | |||||||
\(374\) | −20.6658 | −1.06860 | ||||||||
\(375\) | −20.5803 | −1.06276 | ||||||||
\(376\) | 19.7302 | 1.01751 | ||||||||
\(377\) | −6.04973 | −0.311577 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.36895 | −0.275785 | −0.137892 | − | 0.990447i | \(-0.544033\pi\) | ||||
−0.137892 | + | 0.990447i | \(0.544033\pi\) | |||||||
\(380\) | −15.5947 | −0.799989 | ||||||||
\(381\) | −33.9474 | −1.73918 | ||||||||
\(382\) | −51.1762 | −2.61840 | ||||||||
\(383\) | 34.5075 | 1.76325 | 0.881625 | − | 0.471951i | \(-0.156450\pi\) | ||||
0.881625 | + | 0.471951i | \(0.156450\pi\) | |||||||
\(384\) | −21.8108 | −1.11303 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.04353 | −0.205810 | ||||||||
\(387\) | −0.411459 | −0.0209156 | ||||||||
\(388\) | −19.2883 | −0.979216 | ||||||||
\(389\) | 22.9210 | 1.16214 | 0.581070 | − | 0.813854i | \(-0.302634\pi\) | ||||
0.581070 | + | 0.813854i | \(0.302634\pi\) | |||||||
\(390\) | 8.10283 | 0.410303 | ||||||||
\(391\) | 10.5418 | 0.533120 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.0514 | 0.860131 | ||||||||
\(394\) | −21.5502 | −1.08568 | ||||||||
\(395\) | 2.36845 | 0.119170 | ||||||||
\(396\) | −1.46884 | −0.0738121 | ||||||||
\(397\) | 10.8294 | 0.543510 | 0.271755 | − | 0.962366i | \(-0.412396\pi\) | ||||
0.271755 | + | 0.962366i | \(0.412396\pi\) | |||||||
\(398\) | 26.7427 | 1.34049 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.02468 | 0.0512340 | ||||||||
\(401\) | 37.5415 | 1.87473 | 0.937367 | − | 0.348342i | \(-0.113255\pi\) | ||||
0.937367 | + | 0.348342i | \(0.113255\pi\) | |||||||
\(402\) | 29.7223 | 1.48241 | ||||||||
\(403\) | 5.12202 | 0.255146 | ||||||||
\(404\) | −17.9797 | −0.894523 | ||||||||
\(405\) | −19.5608 | −0.971983 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −33.1580 | −1.64358 | ||||||||
\(408\) | 4.82797 | 0.239020 | ||||||||
\(409\) | −20.4727 | −1.01231 | −0.506155 | − | 0.862443i | \(-0.668934\pi\) | ||||
−0.506155 | + | 0.862443i | \(0.668934\pi\) | |||||||
\(410\) | −32.9059 | −1.62511 | ||||||||
\(411\) | −27.1664 | −1.34002 | ||||||||
\(412\) | −1.59914 | −0.0787840 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.29095 | 0.0634468 | ||||||||
\(415\) | 10.4884 | 0.514854 | ||||||||
\(416\) | −7.45036 | −0.365284 | ||||||||
\(417\) | 6.76836 | 0.331448 | ||||||||
\(418\) | 33.6377 | 1.64527 | ||||||||
\(419\) | −15.4980 | −0.757127 | −0.378564 | − | 0.925575i | \(-0.623582\pi\) | ||||
−0.378564 | + | 0.925575i | \(0.623582\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.9390 | 0.874293 | 0.437147 | − | 0.899390i | \(-0.355989\pi\) | ||||
0.437147 | + | 0.899390i | \(0.355989\pi\) | |||||||
\(422\) | −1.61536 | −0.0786346 | ||||||||
\(423\) | 1.08520 | 0.0527643 | ||||||||
\(424\) | 5.77229 | 0.280327 | ||||||||
\(425\) | −0.894480 | −0.0433886 | ||||||||
\(426\) | 52.3535 | 2.53654 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −44.9749 | −2.17394 | ||||||||
\(429\) | −10.1441 | −0.489763 | ||||||||
\(430\) | −20.6007 | −0.993452 | ||||||||
\(431\) | 21.4438 | 1.03291 | 0.516456 | − | 0.856313i | \(-0.327251\pi\) | ||||
0.516456 | + | 0.856313i | \(0.327251\pi\) | |||||||
\(432\) | 9.61149 | 0.462433 | ||||||||
\(433\) | −14.9365 | −0.717800 | −0.358900 | − | 0.933376i | \(-0.616848\pi\) | ||||
−0.358900 | + | 0.933376i | \(0.616848\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.4531 | −1.07654 | ||||||||
\(436\) | 4.92955 | 0.236083 | ||||||||
\(437\) | −17.1589 | −0.820819 | ||||||||
\(438\) | −59.5204 | −2.84400 | ||||||||
\(439\) | −3.59323 | −0.171495 | −0.0857476 | − | 0.996317i | \(-0.527328\pi\) | ||||
−0.0857476 | + | 0.996317i | \(0.527328\pi\) | |||||||
\(440\) | −20.3746 | −0.971323 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.58227 | 0.170391 | ||||||||
\(443\) | −13.6534 | −0.648694 | −0.324347 | − | 0.945938i | \(-0.605145\pi\) | ||||
−0.324347 | + | 0.945938i | \(0.605145\pi\) | |||||||
\(444\) | 27.9602 | 1.32693 | ||||||||
\(445\) | 2.41943 | 0.114692 | ||||||||
\(446\) | 18.1333 | 0.858638 | ||||||||
\(447\) | −1.82925 | −0.0865205 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.72412 | −0.411717 | −0.205858 | − | 0.978582i | \(-0.565999\pi\) | ||||
−0.205858 | + | 0.978582i | \(0.565999\pi\) | |||||||
\(450\) | −0.109538 | −0.00516369 | ||||||||
\(451\) | 41.1957 | 1.93983 | ||||||||
\(452\) | −20.8096 | −0.978803 | ||||||||
\(453\) | −7.63745 | −0.358839 | ||||||||
\(454\) | 29.0186 | 1.36191 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.85848 | −0.368007 | ||||||||
\(457\) | −30.4659 | −1.42514 | −0.712568 | − | 0.701603i | \(-0.752468\pi\) | ||||
−0.712568 | + | 0.701603i | \(0.752468\pi\) | |||||||
\(458\) | 39.1247 | 1.82818 | ||||||||
\(459\) | −8.39021 | −0.391621 | ||||||||
\(460\) | 37.5139 | 1.74909 | ||||||||
\(461\) | 5.22253 | 0.243237 | 0.121619 | − | 0.992577i | \(-0.461191\pi\) | ||||
0.121619 | + | 0.992577i | \(0.461191\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.6220 | 0.958386 | 0.479193 | − | 0.877709i | \(-0.340929\pi\) | ||||
0.479193 | + | 0.877709i | \(0.340929\pi\) | |||||||
\(464\) | 11.3714 | 0.527906 | ||||||||
\(465\) | 19.0099 | 0.881564 | ||||||||
\(466\) | 13.7536 | 0.637122 | ||||||||
\(467\) | 1.67149 | 0.0773474 | 0.0386737 | − | 0.999252i | \(-0.487687\pi\) | ||||
0.0386737 | + | 0.999252i | \(0.487687\pi\) | |||||||
\(468\) | 0.254614 | 0.0117696 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 54.3332 | 2.50620 | ||||||||
\(471\) | 0.590829 | 0.0272240 | ||||||||
\(472\) | 22.0553 | 1.01518 | ||||||||
\(473\) | 25.7905 | 1.18585 | ||||||||
\(474\) | 4.30792 | 0.197869 | ||||||||
\(475\) | 1.45595 | 0.0668034 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.317489 | 0.0145368 | ||||||||
\(478\) | 20.5612 | 0.940447 | ||||||||
\(479\) | 10.6439 | 0.486333 | 0.243166 | − | 0.969985i | \(-0.421814\pi\) | ||||
0.243166 | + | 0.969985i | \(0.421814\pi\) | |||||||
\(480\) | −27.6514 | −1.26211 | ||||||||
\(481\) | 5.74772 | 0.262073 | ||||||||
\(482\) | −43.5537 | −1.98382 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 61.6369 | 2.80168 | ||||||||
\(485\) | −14.7160 | −0.668217 | ||||||||
\(486\) | −2.08746 | −0.0946890 | ||||||||
\(487\) | −31.8312 | −1.44241 | −0.721206 | − | 0.692721i | \(-0.756412\pi\) | ||||
−0.721206 | + | 0.692721i | \(0.756412\pi\) | |||||||
\(488\) | 10.4527 | 0.473171 | ||||||||
\(489\) | 11.9558 | 0.540661 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.87077 | 0.310074 | 0.155037 | − | 0.987909i | \(-0.450450\pi\) | ||||
0.155037 | + | 0.987909i | \(0.450450\pi\) | |||||||
\(492\) | −34.7379 | −1.56611 | ||||||||
\(493\) | −9.92654 | −0.447069 | ||||||||
\(494\) | −5.83087 | −0.262343 | ||||||||
\(495\) | −1.12065 | −0.0503694 | ||||||||
\(496\) | −9.62765 | −0.432294 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 19.0770 | 0.854862 | ||||||||
\(499\) | 0.344335 | 0.0154145 | 0.00770727 | − | 0.999970i | \(-0.497547\pi\) | ||||
0.00770727 | + | 0.999970i | \(0.497547\pi\) | |||||||
\(500\) | −32.3782 | −1.44800 | ||||||||
\(501\) | 1.17576 | 0.0525293 | ||||||||
\(502\) | 2.66793 | 0.119076 | ||||||||
\(503\) | 30.0808 | 1.34123 | 0.670617 | − | 0.741803i | \(-0.266029\pi\) | ||||
0.670617 | + | 0.741803i | \(0.266029\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.7175 | −0.610423 | ||||||||
\(506\) | −80.9174 | −3.59722 | ||||||||
\(507\) | 1.75842 | 0.0780941 | ||||||||
\(508\) | −53.4080 | −2.36960 | ||||||||
\(509\) | 33.3105 | 1.47646 | 0.738232 | − | 0.674547i | \(-0.235661\pi\) | ||||
0.738232 | + | 0.674547i | \(0.235661\pi\) | |||||||
\(510\) | 13.2953 | 0.588726 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.2947 | 0.896908 | ||||||||
\(513\) | 13.6568 | 0.602960 | ||||||||
\(514\) | −48.9565 | −2.15938 | ||||||||
\(515\) | −1.22006 | −0.0537622 | ||||||||
\(516\) | −21.7476 | −0.957385 | ||||||||
\(517\) | −68.0210 | −2.99156 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 44.1677 | 1.93875 | ||||||||
\(520\) | 3.53181 | 0.154880 | ||||||||
\(521\) | 32.7726 | 1.43579 | 0.717897 | − | 0.696149i | \(-0.245105\pi\) | ||||
0.717897 | + | 0.696149i | \(0.245105\pi\) | |||||||
\(522\) | −1.21561 | −0.0532058 | ||||||||
\(523\) | 25.2616 | 1.10461 | 0.552307 | − | 0.833641i | \(-0.313748\pi\) | ||||
0.552307 | + | 0.833641i | \(0.313748\pi\) | |||||||
\(524\) | 26.8263 | 1.17191 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.6282 | 0.855830 | ||||||||
\(527\) | 8.40432 | 0.366098 | ||||||||
\(528\) | 19.0675 | 0.829807 | ||||||||
\(529\) | 18.2766 | 0.794636 | ||||||||
\(530\) | 15.8958 | 0.690469 | ||||||||
\(531\) | 1.21309 | 0.0526437 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.14100 | −0.309311 | ||||||||
\(534\) | 4.40065 | 0.190435 | ||||||||
\(535\) | −34.3134 | −1.48350 | ||||||||
\(536\) | 12.9552 | 0.559578 | ||||||||
\(537\) | −3.33267 | −0.143815 | ||||||||
\(538\) | −48.4794 | −2.09009 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −29.8573 | −1.28485 | ||||||||
\(541\) | 13.1630 | 0.565920 | 0.282960 | − | 0.959132i | \(-0.408684\pi\) | ||||
0.282960 | + | 0.959132i | \(0.408684\pi\) | |||||||
\(542\) | −23.6712 | −1.01676 | ||||||||
\(543\) | 19.9748 | 0.857201 | ||||||||
\(544\) | −12.2247 | −0.524130 | ||||||||
\(545\) | 3.76099 | 0.161103 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.79349 | −0.119441 | −0.0597204 | − | 0.998215i | \(-0.519021\pi\) | ||||
−0.0597204 | + | 0.998215i | \(0.519021\pi\) | |||||||
\(548\) | −42.7398 | −1.82575 | ||||||||
\(549\) | 0.574921 | 0.0245370 | ||||||||
\(550\) | 6.86592 | 0.292764 | ||||||||
\(551\) | 16.1574 | 0.688330 | ||||||||
\(552\) | 18.9040 | 0.804610 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.8554 | 0.546174 | ||||||||
\(555\) | 21.3322 | 0.905500 | ||||||||
\(556\) | 10.6484 | 0.451592 | ||||||||
\(557\) | −4.61284 | −0.195452 | −0.0977262 | − | 0.995213i | \(-0.531157\pi\) | ||||
−0.0977262 | + | 0.995213i | \(0.531157\pi\) | |||||||
\(558\) | 1.02920 | 0.0435694 | ||||||||
\(559\) | −4.47061 | −0.189087 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.6447 | −0.702740 | ||||||||
\(562\) | 58.7441 | 2.47797 | ||||||||
\(563\) | 40.2805 | 1.69762 | 0.848811 | − | 0.528697i | \(-0.177319\pi\) | ||||
0.848811 | + | 0.528697i | \(0.177319\pi\) | |||||||
\(564\) | 57.3582 | 2.41522 | ||||||||
\(565\) | −15.8767 | −0.667936 | ||||||||
\(566\) | −7.63510 | −0.320927 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22.8195 | 0.957486 | ||||||||
\(569\) | 7.19869 | 0.301785 | 0.150892 | − | 0.988550i | \(-0.451785\pi\) | ||||
0.150892 | + | 0.988550i | \(0.451785\pi\) | |||||||
\(570\) | −21.6408 | −0.906432 | ||||||||
\(571\) | 11.3820 | 0.476323 | 0.238161 | − | 0.971226i | \(-0.423455\pi\) | ||||
0.238161 | + | 0.971226i | \(0.423455\pi\) | |||||||
\(572\) | −15.9593 | −0.667294 | ||||||||
\(573\) | −41.2186 | −1.72193 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.50236 | −0.146059 | ||||||||
\(576\) | −1.15105 | −0.0479604 | ||||||||
\(577\) | −35.6257 | −1.48312 | −0.741560 | − | 0.670887i | \(-0.765914\pi\) | ||||
−0.741560 | + | 0.670887i | \(0.765914\pi\) | |||||||
\(578\) | −31.2369 | −1.29928 | ||||||||
\(579\) | −3.25676 | −0.135346 | ||||||||
\(580\) | −35.3245 | −1.46677 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −26.7665 | −1.10951 | ||||||||
\(583\) | −19.9003 | −0.824188 | ||||||||
\(584\) | −25.9434 | −1.07354 | ||||||||
\(585\) | 0.194257 | 0.00803155 | ||||||||
\(586\) | 2.19433 | 0.0906469 | ||||||||
\(587\) | 4.14755 | 0.171188 | 0.0855938 | − | 0.996330i | \(-0.472721\pi\) | ||||
0.0855938 | + | 0.996330i | \(0.472721\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.6797 | −0.563663 | ||||||||
\(590\) | 60.7362 | 2.50047 | ||||||||
\(591\) | −17.3570 | −0.713973 | ||||||||
\(592\) | −10.8038 | −0.444032 | ||||||||
\(593\) | −24.1313 | −0.990953 | −0.495476 | − | 0.868621i | \(-0.665006\pi\) | ||||
−0.495476 | + | 0.868621i | \(0.665006\pi\) | |||||||
\(594\) | 64.4023 | 2.64246 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.87788 | −0.117883 | ||||||||
\(597\) | 21.5393 | 0.881543 | ||||||||
\(598\) | 14.0265 | 0.573587 | ||||||||
\(599\) | −48.5607 | −1.98414 | −0.992068 | − | 0.125703i | \(-0.959881\pi\) | ||||
−0.992068 | + | 0.125703i | \(0.959881\pi\) | |||||||
\(600\) | −1.60403 | −0.0654841 | ||||||||
\(601\) | −33.2069 | −1.35454 | −0.677270 | − | 0.735735i | \(-0.736837\pi\) | ||||
−0.677270 | + | 0.735735i | \(0.736837\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.712562 | 0.0290178 | ||||||||
\(604\) | −12.0157 | −0.488911 | ||||||||
\(605\) | 47.0257 | 1.91186 | ||||||||
\(606\) | −24.9505 | −1.01354 | ||||||||
\(607\) | −21.7946 | −0.884616 | −0.442308 | − | 0.896863i | \(-0.645840\pi\) | ||||
−0.442308 | + | 0.896863i | \(0.645840\pi\) | |||||||
\(608\) | 19.8982 | 0.806978 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 28.7847 | 1.16546 | ||||||||
\(611\) | 11.7910 | 0.477013 | ||||||||
\(612\) | 0.417777 | 0.0168876 | ||||||||
\(613\) | −22.7991 | −0.920847 | −0.460423 | − | 0.887700i | \(-0.652302\pi\) | ||||
−0.460423 | + | 0.887700i | \(0.652302\pi\) | |||||||
\(614\) | 9.29554 | 0.375138 | ||||||||
\(615\) | −26.5032 | −1.06871 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.5433 | −1.71273 | −0.856364 | − | 0.516373i | \(-0.827282\pi\) | ||||
−0.856364 | + | 0.516373i | \(0.827282\pi\) | |||||||
\(618\) | −2.21913 | −0.0892667 | ||||||||
\(619\) | −44.1285 | −1.77367 | −0.886836 | − | 0.462084i | \(-0.847102\pi\) | ||||
−0.886836 | + | 0.462084i | \(0.847102\pi\) | |||||||
\(620\) | 29.9075 | 1.20112 | ||||||||
\(621\) | −32.8521 | −1.31831 | ||||||||
\(622\) | −15.1525 | −0.607559 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.30523 | −0.132315 | ||||||||
\(625\) | −21.9771 | −0.879085 | ||||||||
\(626\) | −21.7514 | −0.869361 | ||||||||
\(627\) | 27.0926 | 1.08197 | ||||||||
\(628\) | 0.929528 | 0.0370922 | ||||||||
\(629\) | 9.43098 | 0.376038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.09226 | 0.361957 | 0.180979 | − | 0.983487i | \(-0.442074\pi\) | ||||
0.180979 | + | 0.983487i | \(0.442074\pi\) | |||||||
\(632\) | 1.87771 | 0.0746912 | ||||||||
\(633\) | −1.30105 | −0.0517122 | ||||||||
\(634\) | 8.19461 | 0.325449 | ||||||||
\(635\) | −40.7475 | −1.61701 | ||||||||
\(636\) | 16.7808 | 0.665402 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 76.1950 | 3.01659 | ||||||||
\(639\) | 1.25512 | 0.0496519 | ||||||||
\(640\) | −26.1797 | −1.03485 | ||||||||
\(641\) | −22.6642 | −0.895181 | −0.447591 | − | 0.894239i | \(-0.647718\pi\) | ||||
−0.447591 | + | 0.894239i | \(0.647718\pi\) | |||||||
\(642\) | −62.4119 | −2.46320 | ||||||||
\(643\) | 24.3792 | 0.961422 | 0.480711 | − | 0.876879i | \(-0.340379\pi\) | ||||
0.480711 | + | 0.876879i | \(0.340379\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.5923 | −0.653320 | ||||||||
\(646\) | −9.56742 | −0.376425 | ||||||||
\(647\) | −37.0364 | −1.45605 | −0.728026 | − | 0.685549i | \(-0.759562\pi\) | ||||
−0.728026 | + | 0.685549i | \(0.759562\pi\) | |||||||
\(648\) | −15.5078 | −0.609203 | ||||||||
\(649\) | −76.0372 | −2.98472 | ||||||||
\(650\) | −1.19016 | −0.0466820 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.8096 | 0.736641 | ||||||||
\(653\) | 18.7341 | 0.733122 | 0.366561 | − | 0.930394i | \(-0.380535\pi\) | ||||
0.366561 | + | 0.930394i | \(0.380535\pi\) | |||||||
\(654\) | 6.84077 | 0.267495 | ||||||||
\(655\) | 20.4671 | 0.799715 | ||||||||
\(656\) | 13.4227 | 0.524067 | ||||||||
\(657\) | −1.42694 | −0.0556703 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.5206 | −1.11100 | −0.555502 | − | 0.831515i | \(-0.687474\pi\) | ||||
−0.555502 | + | 0.831515i | \(0.687474\pi\) | |||||||
\(660\) | −59.2317 | −2.30559 | ||||||||
\(661\) | −19.9758 | −0.776968 | −0.388484 | − | 0.921455i | \(-0.627001\pi\) | ||||
−0.388484 | + | 0.921455i | \(0.627001\pi\) | |||||||
\(662\) | −43.6234 | −1.69547 | ||||||||
\(663\) | 2.88525 | 0.112054 | ||||||||
\(664\) | 8.31517 | 0.322691 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.15492 | 0.0447524 | ||||||||
\(667\) | −38.8677 | −1.50496 | ||||||||
\(668\) | 1.84978 | 0.0715702 | ||||||||
\(669\) | 14.6050 | 0.564663 | ||||||||
\(670\) | 35.6760 | 1.37829 | ||||||||
\(671\) | −36.0363 | −1.39117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.18849 | −0.161454 | −0.0807272 | − | 0.996736i | \(-0.525724\pi\) | ||||
−0.0807272 | + | 0.996736i | \(0.525724\pi\) | |||||||
\(674\) | 40.3649 | 1.55480 | ||||||||
\(675\) | 2.78753 | 0.107292 | ||||||||
\(676\) | 2.76645 | 0.106402 | ||||||||
\(677\) | −38.3396 | −1.47351 | −0.736755 | − | 0.676159i | \(-0.763643\pi\) | ||||
−0.736755 | + | 0.676159i | \(0.763643\pi\) | |||||||
\(678\) | −28.8776 | −1.10904 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.79507 | 0.222231 | ||||||||
\(681\) | 23.3723 | 0.895628 | ||||||||
\(682\) | −64.5106 | −2.47024 | ||||||||
\(683\) | −2.61207 | −0.0999482 | −0.0499741 | − | 0.998751i | \(-0.515914\pi\) | ||||
−0.0499741 | + | 0.998751i | \(0.515914\pi\) | |||||||
\(684\) | −0.680016 | −0.0260010 | ||||||||
\(685\) | −32.6082 | −1.24589 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.5120 | 1.20226 | ||||||||
\(688\) | 8.40322 | 0.320370 | ||||||||
\(689\) | 3.44959 | 0.131419 | ||||||||
\(690\) | 52.0582 | 1.98182 | ||||||||
\(691\) | −40.9185 | −1.55661 | −0.778307 | − | 0.627884i | \(-0.783921\pi\) | ||||
−0.778307 | + | 0.627884i | \(0.783921\pi\) | |||||||
\(692\) | 69.4872 | 2.64151 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.73806 | −0.0659759 | ||||||||
\(695\) | 8.12415 | 0.308167 | ||||||||
\(696\) | −17.8008 | −0.674737 | ||||||||
\(697\) | −11.7171 | −0.443817 | ||||||||
\(698\) | −24.8286 | −0.939776 | ||||||||
\(699\) | 11.0775 | 0.418988 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.762896 | −0.0288142 | −0.0144071 | − | 0.999896i | \(-0.504586\pi\) | ||||
−0.0144071 | + | 0.999896i | \(0.504586\pi\) | |||||||
\(702\) | −11.1637 | −0.421347 | ||||||||
\(703\) | −15.3508 | −0.578967 | ||||||||
\(704\) | 72.1484 | 2.71920 | ||||||||
\(705\) | 43.7613 | 1.64814 | ||||||||
\(706\) | 52.6304 | 1.98077 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 64.1178 | 2.40969 | ||||||||
\(709\) | 2.65281 | 0.0996284 | 0.0498142 | − | 0.998759i | \(-0.484137\pi\) | ||||
0.0498142 | + | 0.998759i | \(0.484137\pi\) | |||||||
\(710\) | 62.8407 | 2.35837 | ||||||||
\(711\) | 0.103278 | 0.00387323 | ||||||||
\(712\) | 1.91813 | 0.0718848 | ||||||||
\(713\) | 32.9074 | 1.23239 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.1761 | −0.455362 | ||||||||
\(716\) | −5.24315 | −0.195946 | ||||||||
\(717\) | 16.5605 | 0.618463 | ||||||||
\(718\) | 19.8058 | 0.739145 | ||||||||
\(719\) | 11.0443 | 0.411883 | 0.205942 | − | 0.978564i | \(-0.433974\pi\) | ||||
0.205942 | + | 0.978564i | \(0.433974\pi\) | |||||||
\(720\) | −0.365138 | −0.0136079 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −25.9083 | −0.964206 | ||||||||
\(723\) | −35.0792 | −1.30461 | ||||||||
\(724\) | 31.4255 | 1.16792 | ||||||||
\(725\) | 3.29796 | 0.122483 | ||||||||
\(726\) | 85.5338 | 3.17446 | ||||||||
\(727\) | 3.46566 | 0.128534 | 0.0642672 | − | 0.997933i | \(-0.479529\pi\) | ||||
0.0642672 | + | 0.997933i | \(0.479529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.1216 | 0.967468 | ||||||||
\(730\) | −71.4432 | −2.64423 | ||||||||
\(731\) | −7.33547 | −0.271312 | ||||||||
\(732\) | 30.3873 | 1.12315 | ||||||||
\(733\) | −29.0332 | −1.07236 | −0.536182 | − | 0.844102i | \(-0.680134\pi\) | ||||
−0.536182 | + | 0.844102i | \(0.680134\pi\) | |||||||
\(734\) | −68.8822 | −2.54249 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −47.8663 | −1.76437 | ||||||||
\(737\) | −44.6637 | −1.64521 | ||||||||
\(738\) | −1.43488 | −0.0528188 | ||||||||
\(739\) | 47.5522 | 1.74924 | 0.874618 | − | 0.484813i | \(-0.161112\pi\) | ||||
0.874618 | + | 0.484813i | \(0.161112\pi\) | |||||||
\(740\) | 33.5610 | 1.23373 | ||||||||
\(741\) | −4.69633 | −0.172524 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.6122 | 0.462697 | 0.231349 | − | 0.972871i | \(-0.425686\pi\) | ||||
0.231349 | + | 0.972871i | \(0.425686\pi\) | |||||||
\(744\) | 15.0711 | 0.552532 | ||||||||
\(745\) | −2.19567 | −0.0804432 | ||||||||
\(746\) | −35.0584 | −1.28358 | ||||||||
\(747\) | 0.457353 | 0.0167337 | ||||||||
\(748\) | −26.1864 | −0.957471 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −44.9313 | −1.64066 | ||||||||
\(751\) | −7.70781 | −0.281262 | −0.140631 | − | 0.990062i | \(-0.544913\pi\) | ||||
−0.140631 | + | 0.990062i | \(0.544913\pi\) | |||||||
\(752\) | −22.1631 | −0.808204 | ||||||||
\(753\) | 2.14882 | 0.0783073 | ||||||||
\(754\) | −13.2079 | −0.481003 | ||||||||
\(755\) | −9.16734 | −0.333633 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.39454 | 0.0870311 | 0.0435156 | − | 0.999053i | \(-0.486144\pi\) | ||||
0.0435156 | + | 0.999053i | \(0.486144\pi\) | |||||||
\(758\) | −11.7216 | −0.425748 | ||||||||
\(759\) | −65.1729 | −2.36563 | ||||||||
\(760\) | −9.43265 | −0.342158 | ||||||||
\(761\) | −41.3296 | −1.49820 | −0.749098 | − | 0.662459i | \(-0.769513\pi\) | ||||
−0.749098 | + | 0.662459i | \(0.769513\pi\) | |||||||
\(762\) | −74.1146 | −2.68489 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −64.8475 | −2.34610 | ||||||||
\(765\) | 0.318742 | 0.0115241 | ||||||||
\(766\) | 75.3374 | 2.72205 | ||||||||
\(767\) | 13.1805 | 0.475922 | ||||||||
\(768\) | −3.63450 | −0.131149 | ||||||||
\(769\) | 36.7414 | 1.32493 | 0.662464 | − | 0.749094i | \(-0.269511\pi\) | ||||
0.662464 | + | 0.749094i | \(0.269511\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.4308 | −1.42007 | ||||||||
\(772\) | −5.12373 | −0.184407 | ||||||||
\(773\) | −23.9672 | −0.862040 | −0.431020 | − | 0.902342i | \(-0.641846\pi\) | ||||
−0.431020 | + | 0.902342i | \(0.641846\pi\) | |||||||
\(774\) | −0.898306 | −0.0322889 | ||||||||
\(775\) | −2.79222 | −0.100300 | ||||||||
\(776\) | −11.6668 | −0.418814 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 50.0415 | 1.79408 | ||||||||
\(779\) | 19.0720 | 0.683324 | ||||||||
\(780\) | 10.2674 | 0.367633 | ||||||||
\(781\) | −78.6718 | −2.81510 | ||||||||
\(782\) | 23.0150 | 0.823015 | ||||||||
\(783\) | 30.9348 | 1.10552 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.709180 | 0.0253117 | ||||||||
\(786\) | 37.2270 | 1.32784 | ||||||||
\(787\) | 36.0134 | 1.28374 | 0.641870 | − | 0.766814i | \(-0.278159\pi\) | ||||
0.641870 | + | 0.766814i | \(0.278159\pi\) | |||||||
\(788\) | −27.3071 | −0.972776 | ||||||||
\(789\) | 15.8090 | 0.562816 | ||||||||
\(790\) | 5.17085 | 0.183971 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.888450 | −0.0315697 | ||||||||
\(793\) | 6.24666 | 0.221825 | ||||||||
\(794\) | 23.6429 | 0.839054 | ||||||||
\(795\) | 12.8029 | 0.454071 | ||||||||
\(796\) | 33.8868 | 1.20109 | ||||||||
\(797\) | −18.8155 | −0.666478 | −0.333239 | − | 0.942842i | \(-0.608142\pi\) | ||||
−0.333239 | + | 0.942842i | \(0.608142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.3469 | 0.684445 | ||||||||
\(800\) | 4.06150 | 0.143596 | ||||||||
\(801\) | 0.105501 | 0.00372770 | ||||||||
\(802\) | 81.9614 | 2.89416 | ||||||||
\(803\) | 89.4414 | 3.15632 | ||||||||
\(804\) | 37.6623 | 1.32825 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.1825 | 0.393886 | ||||||||
\(807\) | −39.0465 | −1.37450 | ||||||||
\(808\) | −10.8753 | −0.382591 | ||||||||
\(809\) | −47.3322 | −1.66411 | −0.832056 | − | 0.554692i | \(-0.812836\pi\) | ||||
−0.832056 | + | 0.554692i | \(0.812836\pi\) | |||||||
\(810\) | −42.7055 | −1.50052 | ||||||||
\(811\) | 19.2555 | 0.676153 | 0.338077 | − | 0.941119i | \(-0.390224\pi\) | ||||
0.338077 | + | 0.941119i | \(0.390224\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.0653 | −0.668650 | ||||||||
\(814\) | −72.3912 | −2.53731 | ||||||||
\(815\) | 14.3507 | 0.502684 | ||||||||
\(816\) | −5.42329 | −0.189853 | ||||||||
\(817\) | 11.9400 | 0.417726 | ||||||||
\(818\) | −44.6964 | −1.56277 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −41.6964 | −1.45610 | ||||||||
\(821\) | 41.5165 | 1.44894 | 0.724468 | − | 0.689308i | \(-0.242085\pi\) | ||||
0.724468 | + | 0.689308i | \(0.242085\pi\) | |||||||
\(822\) | −59.3102 | −2.06868 | ||||||||
\(823\) | 24.5627 | 0.856201 | 0.428100 | − | 0.903731i | \(-0.359183\pi\) | ||||
0.428100 | + | 0.903731i | \(0.359183\pi\) | |||||||
\(824\) | −0.967262 | −0.0336962 | ||||||||
\(825\) | 5.52998 | 0.192529 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.580957 | −0.0202019 | −0.0101009 | − | 0.999949i | \(-0.503215\pi\) | ||||
−0.0101009 | + | 0.999949i | \(0.503215\pi\) | |||||||
\(828\) | 1.63582 | 0.0568486 | ||||||||
\(829\) | 14.6630 | 0.509268 | 0.254634 | − | 0.967038i | \(-0.418045\pi\) | ||||
0.254634 | + | 0.967038i | \(0.418045\pi\) | |||||||
\(830\) | 22.8984 | 0.794815 | ||||||||
\(831\) | 10.3541 | 0.359178 | ||||||||
\(832\) | −12.5065 | −0.433583 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.7768 | 0.511679 | ||||||||
\(835\) | 1.41129 | 0.0488396 | ||||||||
\(836\) | 42.6237 | 1.47417 | ||||||||
\(837\) | −26.1910 | −0.905294 | ||||||||
\(838\) | −33.8356 | −1.16883 | ||||||||
\(839\) | 25.6151 | 0.884332 | 0.442166 | − | 0.896933i | \(-0.354210\pi\) | ||||
0.442166 | + | 0.896933i | \(0.354210\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.59929 | 0.262044 | ||||||||
\(842\) | 39.1648 | 1.34971 | ||||||||
\(843\) | 47.3140 | 1.62958 | ||||||||
\(844\) | −2.04689 | −0.0704569 | ||||||||
\(845\) | 2.11065 | 0.0726087 | ||||||||
\(846\) | 2.36924 | 0.0814560 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.48406 | −0.222664 | ||||||||
\(849\) | −6.14949 | −0.211050 | ||||||||
\(850\) | −1.95285 | −0.0669820 | ||||||||
\(851\) | 36.9273 | 1.26585 | ||||||||
\(852\) | 66.3394 | 2.27275 | ||||||||
\(853\) | −0.587340 | −0.0201101 | −0.0100551 | − | 0.999949i | \(-0.503201\pi\) | ||||
−0.0100551 | + | 0.999949i | \(0.503201\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.518816 | −0.0177431 | ||||||||
\(856\) | −27.2037 | −0.929803 | ||||||||
\(857\) | 31.1680 | 1.06468 | 0.532340 | − | 0.846531i | \(-0.321313\pi\) | ||||
0.532340 | + | 0.846531i | \(0.321313\pi\) | |||||||
\(858\) | −22.1469 | −0.756082 | ||||||||
\(859\) | −22.7944 | −0.777735 | −0.388867 | − | 0.921294i | \(-0.627134\pi\) | ||||
−0.388867 | + | 0.921294i | \(0.627134\pi\) | |||||||
\(860\) | −26.1039 | −0.890137 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 46.8166 | 1.59458 | ||||||||
\(863\) | 50.6249 | 1.72329 | 0.861646 | − | 0.507510i | \(-0.169434\pi\) | ||||
0.861646 | + | 0.507510i | \(0.169434\pi\) | |||||||
\(864\) | 38.0968 | 1.29608 | ||||||||
\(865\) | 53.0150 | 1.80257 | ||||||||
\(866\) | −32.6096 | −1.10812 | ||||||||
\(867\) | −25.1589 | −0.854442 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.47352 | −0.219599 | ||||||||
\(870\) | −49.0200 | −1.66193 | ||||||||
\(871\) | 7.74216 | 0.262333 | ||||||||
\(872\) | 2.98171 | 0.100973 | ||||||||
\(873\) | −0.641700 | −0.0217182 | ||||||||
\(874\) | −37.4615 | −1.26716 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −75.4208 | −2.54823 | ||||||||
\(877\) | 11.9495 | 0.403505 | 0.201753 | − | 0.979436i | \(-0.435336\pi\) | ||||
0.201753 | + | 0.979436i | \(0.435336\pi\) | |||||||
\(878\) | −7.84480 | −0.264749 | ||||||||
\(879\) | 1.76737 | 0.0596118 | ||||||||
\(880\) | 22.8870 | 0.771520 | ||||||||
\(881\) | 54.6400 | 1.84087 | 0.920434 | − | 0.390898i | \(-0.127835\pi\) | ||||
0.920434 | + | 0.390898i | \(0.127835\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.7256 | −0.899388 | −0.449694 | − | 0.893183i | \(-0.648467\pi\) | ||||
−0.449694 | + | 0.893183i | \(0.648467\pi\) | |||||||
\(884\) | 4.53925 | 0.152671 | ||||||||
\(885\) | 48.9185 | 1.64438 | ||||||||
\(886\) | −29.8084 | −1.00143 | ||||||||
\(887\) | −5.82278 | −0.195510 | −0.0977549 | − | 0.995211i | \(-0.531166\pi\) | ||||
−0.0977549 | + | 0.995211i | \(0.531166\pi\) | |||||||
\(888\) | 16.9121 | 0.567534 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.28215 | 0.177058 | ||||||||
\(891\) | 53.4640 | 1.79111 | ||||||||
\(892\) | 22.9775 | 0.769343 | ||||||||
\(893\) | −31.4910 | −1.05381 | ||||||||
\(894\) | −3.99365 | −0.133568 | ||||||||
\(895\) | −4.00025 | −0.133714 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.2973 | 0.377206 | ||||||||
\(898\) | −19.0467 | −0.635595 | ||||||||
\(899\) | −30.9868 | −1.03347 | ||||||||
\(900\) | −0.138801 | −0.00462669 | ||||||||
\(901\) | 5.66017 | 0.188568 | ||||||||
\(902\) | 89.9392 | 2.99465 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.5870 | −0.418638 | ||||||||
\(905\) | 23.9760 | 0.796990 | ||||||||
\(906\) | −16.6742 | −0.553964 | ||||||||
\(907\) | −54.4672 | −1.80855 | −0.904276 | − | 0.426948i | \(-0.859589\pi\) | ||||
−0.904276 | + | 0.426948i | \(0.859589\pi\) | |||||||
\(908\) | 36.7707 | 1.22028 | ||||||||
\(909\) | −0.598163 | −0.0198398 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.94815 | 0.197071 | 0.0985355 | − | 0.995134i | \(-0.468584\pi\) | ||||
0.0985355 | + | 0.995134i | \(0.468584\pi\) | |||||||
\(912\) | 8.82750 | 0.292308 | ||||||||
\(913\) | −28.6671 | −0.948742 | ||||||||
\(914\) | −66.5138 | −2.20008 | ||||||||
\(915\) | 23.1839 | 0.766437 | ||||||||
\(916\) | 49.5766 | 1.63806 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −18.3177 | −0.604573 | ||||||||
\(919\) | 13.6480 | 0.450207 | 0.225103 | − | 0.974335i | \(-0.427728\pi\) | ||||
0.225103 | + | 0.974335i | \(0.427728\pi\) | |||||||
\(920\) | 22.6908 | 0.748093 | ||||||||
\(921\) | 7.48686 | 0.246700 | ||||||||
\(922\) | 11.4019 | 0.375503 | ||||||||
\(923\) | 13.6372 | 0.448875 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.13332 | −0.103023 | ||||||||
\(926\) | 45.0224 | 1.47953 | ||||||||
\(927\) | −0.0532015 | −0.00174737 | ||||||||
\(928\) | 45.0727 | 1.47958 | ||||||||
\(929\) | 36.3062 | 1.19117 | 0.595585 | − | 0.803293i | \(-0.296920\pi\) | ||||
0.595585 | + | 0.803293i | \(0.296920\pi\) | |||||||
\(930\) | 41.5028 | 1.36093 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17.4277 | 0.570864 | ||||||||
\(933\) | −12.2042 | −0.399547 | ||||||||
\(934\) | 3.64923 | 0.119406 | ||||||||
\(935\) | −19.9789 | −0.653379 | ||||||||
\(936\) | 0.154007 | 0.00503388 | ||||||||
\(937\) | 27.7384 | 0.906175 | 0.453087 | − | 0.891466i | \(-0.350323\pi\) | ||||
0.453087 | + | 0.891466i | \(0.350323\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.5191 | −0.571715 | ||||||||
\(940\) | 68.8478 | 2.24557 | ||||||||
\(941\) | −31.9163 | −1.04044 | −0.520222 | − | 0.854031i | \(-0.674151\pi\) | ||||
−0.520222 | + | 0.854031i | \(0.674151\pi\) | |||||||
\(942\) | 1.28991 | 0.0420275 | ||||||||
\(943\) | −45.8787 | −1.49402 | ||||||||
\(944\) | −24.7750 | −0.806356 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 56.3063 | 1.83067 | ||||||||
\(947\) | 23.1657 | 0.752785 | 0.376392 | − | 0.926460i | \(-0.377164\pi\) | ||||
0.376392 | + | 0.926460i | \(0.377164\pi\) | |||||||
\(948\) | 5.45874 | 0.177292 | ||||||||
\(949\) | −15.5041 | −0.503284 | ||||||||
\(950\) | 3.17865 | 0.103129 | ||||||||
\(951\) | 6.60014 | 0.214024 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.7340 | 0.833607 | 0.416803 | − | 0.908997i | \(-0.363150\pi\) | ||||
0.416803 | + | 0.908997i | \(0.363150\pi\) | |||||||
\(954\) | 0.693147 | 0.0224415 | ||||||||
\(955\) | −49.4752 | −1.60098 | ||||||||
\(956\) | 26.0539 | 0.842645 | ||||||||
\(957\) | 61.3693 | 1.98379 | ||||||||
\(958\) | 23.2380 | 0.750786 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −46.4166 | −1.49809 | ||||||||
\(961\) | −4.76494 | −0.153708 | ||||||||
\(962\) | 12.5485 | 0.404581 | ||||||||
\(963\) | −1.49626 | −0.0482164 | ||||||||
\(964\) | −55.1887 | −1.77751 | ||||||||
\(965\) | −3.90913 | −0.125839 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.2544 | 0.522706 | 0.261353 | − | 0.965243i | \(-0.415831\pi\) | ||||
0.261353 | + | 0.965243i | \(0.415831\pi\) | |||||||
\(968\) | 37.2819 | 1.19829 | ||||||||
\(969\) | −7.70584 | −0.247547 | ||||||||
\(970\) | −32.1282 | −1.03157 | ||||||||
\(971\) | 39.7465 | 1.27553 | 0.637763 | − | 0.770232i | \(-0.279860\pi\) | ||||
0.637763 | + | 0.770232i | \(0.279860\pi\) | |||||||
\(972\) | −2.64510 | −0.0848418 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −69.4946 | −2.22675 | ||||||||
\(975\) | −0.958586 | −0.0306993 | ||||||||
\(976\) | −11.7416 | −0.375839 | ||||||||
\(977\) | −26.1884 | −0.837842 | −0.418921 | − | 0.908023i | \(-0.637592\pi\) | ||||
−0.418921 | + | 0.908023i | \(0.637592\pi\) | |||||||
\(978\) | 26.1022 | 0.834655 | ||||||||
\(979\) | −6.61286 | −0.211348 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.164000 | 0.00523613 | ||||||||
\(982\) | 15.0004 | 0.478682 | ||||||||
\(983\) | 12.2915 | 0.392039 | 0.196020 | − | 0.980600i | \(-0.437198\pi\) | ||||
0.196020 | + | 0.980600i | \(0.437198\pi\) | |||||||
\(984\) | −21.0117 | −0.669830 | ||||||||
\(985\) | −20.8339 | −0.663823 | ||||||||
\(986\) | −21.6718 | −0.690171 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.38854 | −0.235061 | ||||||||
\(989\) | −28.7223 | −0.913315 | ||||||||
\(990\) | −2.44662 | −0.0777588 | ||||||||
\(991\) | 11.4681 | 0.364298 | 0.182149 | − | 0.983271i | \(-0.441695\pi\) | ||||
0.182149 | + | 0.983271i | \(0.441695\pi\) | |||||||
\(992\) | −38.1609 | −1.21161 | ||||||||
\(993\) | −35.1354 | −1.11499 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.8539 | 0.819623 | ||||||||
\(996\) | 24.1733 | 0.765960 | ||||||||
\(997\) | −5.30214 | −0.167920 | −0.0839602 | − | 0.996469i | \(-0.526757\pi\) | ||||
−0.0839602 | + | 0.996469i | \(0.526757\pi\) | |||||||
\(998\) | 0.751758 | 0.0237965 | ||||||||
\(999\) | −29.3905 | −0.929874 |
(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 | 637.2.a.n.1.6 | yes | 6 | |
3.2 | odd | 2 | 5733.2.a.br.1.1 | 6 | |||
7.2 | even | 3 | 637.2.e.n.508.1 | 12 | |||
7.3 | odd | 6 | 637.2.e.o.79.1 | 12 | |||
7.4 | even | 3 | 637.2.e.n.79.1 | 12 | |||
7.5 | odd | 6 | 637.2.e.o.508.1 | 12 | |||
7.6 | odd | 2 | 637.2.a.m.1.6 | ✓ | 6 | ||
13.12 | even | 2 | 8281.2.a.cd.1.1 | 6 | |||
21.20 | even | 2 | 5733.2.a.bu.1.1 | 6 | |||
91.90 | odd | 2 | 8281.2.a.cc.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.a.m.1.6 | ✓ | 6 | 7.6 | odd | 2 | ||
637.2.a.n.1.6 | yes | 6 | 1.1 | even | 1 | trivial | |
637.2.e.n.79.1 | 12 | 7.4 | even | 3 | |||
637.2.e.n.508.1 | 12 | 7.2 | even | 3 | |||
637.2.e.o.79.1 | 12 | 7.3 | odd | 6 | |||
637.2.e.o.508.1 | 12 | 7.5 | odd | 6 | |||
5733.2.a.br.1.1 | 6 | 3.2 | odd | 2 | |||
5733.2.a.bu.1.1 | 6 | 21.20 | even | 2 | |||
8281.2.a.cc.1.1 | 6 | 91.90 | odd | 2 | |||
8281.2.a.cd.1.1 | 6 | 13.12 | even | 2 |