Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.361.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.22188\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22188 | −0.863997 | −0.431998 | − | 0.901874i | \(-0.642191\pi\) | ||||
−0.431998 | + | 0.901874i | \(0.642191\pi\) | |||||||
\(3\) | −2.50702 | −1.44743 | −0.723714 | − | 0.690100i | \(-0.757566\pi\) | ||||
−0.723714 | + | 0.690100i | \(0.757566\pi\) | |||||||
\(4\) | −0.507019 | −0.253509 | ||||||||
\(5\) | −2.28514 | −1.02195 | −0.510973 | − | 0.859597i | \(-0.670715\pi\) | ||||
−0.510973 | + | 0.859597i | \(0.670715\pi\) | |||||||
\(6\) | 3.06327 | 1.25057 | ||||||||
\(7\) | −0.285142 | −0.107774 | −0.0538869 | − | 0.998547i | \(-0.517161\pi\) | ||||
−0.0538869 | + | 0.998547i | \(0.517161\pi\) | |||||||
\(8\) | 3.06327 | 1.08303 | ||||||||
\(9\) | 3.28514 | 1.09505 | ||||||||
\(10\) | 2.79216 | 0.882959 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.27111 | 0.366936 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.348409 | 0.0931162 | ||||||||
\(15\) | 5.72889 | 1.47919 | ||||||||
\(16\) | −2.72889 | −0.682224 | ||||||||
\(17\) | 0.507019 | 0.122970 | 0.0614850 | − | 0.998108i | \(-0.480416\pi\) | ||||
0.0614850 | + | 0.998108i | \(0.480416\pi\) | |||||||
\(18\) | −4.01404 | −0.946118 | ||||||||
\(19\) | −3.95077 | −0.906369 | −0.453185 | − | 0.891417i | \(-0.649712\pi\) | ||||
−0.453185 | + | 0.891417i | \(0.649712\pi\) | |||||||
\(20\) | 1.15861 | 0.259073 | ||||||||
\(21\) | 0.714858 | 0.155995 | ||||||||
\(22\) | −1.22188 | −0.260505 | ||||||||
\(23\) | −0.0632663 | −0.0131919 | −0.00659597 | − | 0.999978i | \(-0.502100\pi\) | ||||
−0.00659597 | + | 0.999978i | \(0.502100\pi\) | |||||||
\(24\) | −7.67967 | −1.56761 | ||||||||
\(25\) | 0.221876 | 0.0443752 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.714858 | −0.137574 | ||||||||
\(28\) | 0.144573 | 0.0273216 | ||||||||
\(29\) | −10.7429 | −1.99491 | −0.997456 | − | 0.0712820i | \(-0.977291\pi\) | ||||
−0.997456 | + | 0.0712820i | \(0.977291\pi\) | |||||||
\(30\) | −7.00000 | −1.27802 | ||||||||
\(31\) | −3.57028 | −0.641242 | −0.320621 | − | 0.947208i | \(-0.603892\pi\) | ||||
−0.320621 | + | 0.947208i | \(0.603892\pi\) | |||||||
\(32\) | −2.79216 | −0.493589 | ||||||||
\(33\) | −2.50702 | −0.436416 | ||||||||
\(34\) | −0.619514 | −0.106246 | ||||||||
\(35\) | 0.651591 | 0.110139 | ||||||||
\(36\) | −1.66563 | −0.277605 | ||||||||
\(37\) | 7.72889 | 1.27062 | 0.635311 | − | 0.772256i | \(-0.280872\pi\) | ||||
0.635311 | + | 0.772256i | \(0.280872\pi\) | |||||||
\(38\) | 4.82735 | 0.783100 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.00000 | −1.10680 | ||||||||
\(41\) | −0.380486 | −0.0594219 | −0.0297110 | − | 0.999559i | \(-0.509459\pi\) | ||||
−0.0297110 | + | 0.999559i | \(0.509459\pi\) | |||||||
\(42\) | −0.873467 | −0.134779 | ||||||||
\(43\) | −5.41168 | −0.825273 | −0.412636 | − | 0.910896i | \(-0.635392\pi\) | ||||
−0.412636 | + | 0.910896i | \(0.635392\pi\) | |||||||
\(44\) | −0.507019 | −0.0764359 | ||||||||
\(45\) | −7.50702 | −1.11908 | ||||||||
\(46\) | 0.0773036 | 0.0113978 | ||||||||
\(47\) | −11.3624 | −1.65738 | −0.828692 | − | 0.559706i | \(-0.810914\pi\) | ||||
−0.828692 | + | 0.559706i | \(0.810914\pi\) | |||||||
\(48\) | 6.84139 | 0.987470 | ||||||||
\(49\) | −6.91869 | −0.988385 | ||||||||
\(50\) | −0.271105 | −0.0383401 | ||||||||
\(51\) | −1.27111 | −0.177990 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.72889 | −0.924285 | −0.462142 | − | 0.886806i | \(-0.652919\pi\) | ||||
−0.462142 | + | 0.886806i | \(0.652919\pi\) | |||||||
\(54\) | 0.873467 | 0.118864 | ||||||||
\(55\) | −2.28514 | −0.308129 | ||||||||
\(56\) | −0.873467 | −0.116722 | ||||||||
\(57\) | 9.90466 | 1.31190 | ||||||||
\(58\) | 13.1265 | 1.72360 | ||||||||
\(59\) | 13.7289 | 1.78735 | 0.893675 | − | 0.448715i | \(-0.148118\pi\) | ||||
0.893675 | + | 0.448715i | \(0.148118\pi\) | |||||||
\(60\) | −2.90466 | −0.374990 | ||||||||
\(61\) | −3.33437 | −0.426923 | −0.213461 | − | 0.976952i | \(-0.568474\pi\) | ||||
−0.213461 | + | 0.976952i | \(0.568474\pi\) | |||||||
\(62\) | 4.36245 | 0.554031 | ||||||||
\(63\) | −0.936734 | −0.118017 | ||||||||
\(64\) | 8.86946 | 1.10868 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.06327 | 0.377062 | ||||||||
\(67\) | 0.207839 | 0.0253916 | 0.0126958 | − | 0.999919i | \(-0.495959\pi\) | ||||
0.0126958 | + | 0.999919i | \(0.495959\pi\) | |||||||
\(68\) | −0.257068 | −0.0311741 | ||||||||
\(69\) | 0.158610 | 0.0190944 | ||||||||
\(70\) | −0.796164 | −0.0951598 | ||||||||
\(71\) | −2.77812 | −0.329703 | −0.164851 | − | 0.986318i | \(-0.552714\pi\) | ||||
−0.164851 | + | 0.986318i | \(0.552714\pi\) | |||||||
\(72\) | 10.0633 | 1.18597 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | −9.44375 | −1.09781 | ||||||||
\(75\) | −0.556248 | −0.0642299 | ||||||||
\(76\) | 2.00311 | 0.229773 | ||||||||
\(77\) | −0.285142 | −0.0324950 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.45779 | −0.389032 | −0.194516 | − | 0.980899i | \(-0.562314\pi\) | ||||
−0.194516 | + | 0.980899i | \(0.562314\pi\) | |||||||
\(80\) | 6.23591 | 0.697196 | ||||||||
\(81\) | −8.06327 | −0.895918 | ||||||||
\(82\) | 0.464907 | 0.0513404 | ||||||||
\(83\) | 4.74293 | 0.520604 | 0.260302 | − | 0.965527i | \(-0.416178\pi\) | ||||
0.260302 | + | 0.965527i | \(0.416178\pi\) | |||||||
\(84\) | −0.362446 | −0.0395461 | ||||||||
\(85\) | −1.15861 | −0.125669 | ||||||||
\(86\) | 6.61240 | 0.713033 | ||||||||
\(87\) | 26.9327 | 2.88749 | ||||||||
\(88\) | 3.06327 | 0.326545 | ||||||||
\(89\) | −3.71486 | −0.393774 | −0.196887 | − | 0.980426i | \(-0.563083\pi\) | ||||
−0.196887 | + | 0.980426i | \(0.563083\pi\) | |||||||
\(90\) | 9.17265 | 0.966882 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.0320772 | 0.00334428 | ||||||||
\(93\) | 8.95077 | 0.928152 | ||||||||
\(94\) | 13.8835 | 1.43197 | ||||||||
\(95\) | 9.02807 | 0.926261 | ||||||||
\(96\) | 7.00000 | 0.714435 | ||||||||
\(97\) | 15.0281 | 1.52587 | 0.762935 | − | 0.646475i | \(-0.223758\pi\) | ||||
0.762935 | + | 0.646475i | \(0.223758\pi\) | |||||||
\(98\) | 8.45379 | 0.853961 | ||||||||
\(99\) | 3.28514 | 0.330169 | ||||||||
\(100\) | −0.112495 | −0.0112495 | ||||||||
\(101\) | 14.9327 | 1.48586 | 0.742931 | − | 0.669368i | \(-0.233435\pi\) | ||||
0.742931 | + | 0.669368i | \(0.233435\pi\) | |||||||
\(102\) | 1.55313 | 0.153783 | ||||||||
\(103\) | −17.3905 | −1.71354 | −0.856769 | − | 0.515700i | \(-0.827532\pi\) | ||||
−0.856769 | + | 0.515700i | \(0.827532\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.63355 | −0.159418 | ||||||||
\(106\) | 8.22188 | 0.798579 | ||||||||
\(107\) | −15.7429 | −1.52193 | −0.760963 | − | 0.648795i | \(-0.775273\pi\) | ||||
−0.760963 | + | 0.648795i | \(0.775273\pi\) | |||||||
\(108\) | 0.362446 | 0.0348764 | ||||||||
\(109\) | 18.9648 | 1.81650 | 0.908250 | − | 0.418429i | \(-0.137419\pi\) | ||||
0.908250 | + | 0.418429i | \(0.137419\pi\) | |||||||
\(110\) | 2.79216 | 0.266222 | ||||||||
\(111\) | −19.3765 | −1.83913 | ||||||||
\(112\) | 0.778124 | 0.0735258 | ||||||||
\(113\) | −14.6476 | −1.37793 | −0.688965 | − | 0.724795i | \(-0.741934\pi\) | ||||
−0.688965 | + | 0.724795i | \(0.741934\pi\) | |||||||
\(114\) | −12.1023 | −1.13348 | ||||||||
\(115\) | 0.144573 | 0.0134815 | ||||||||
\(116\) | 5.44687 | 0.505729 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.7750 | −1.54426 | ||||||||
\(119\) | −0.144573 | −0.0132529 | ||||||||
\(120\) | 17.5491 | 1.60201 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 4.07419 | 0.368860 | ||||||||
\(123\) | 0.953886 | 0.0860090 | ||||||||
\(124\) | 1.81020 | 0.162561 | ||||||||
\(125\) | 10.9187 | 0.976598 | ||||||||
\(126\) | 1.14457 | 0.101967 | ||||||||
\(127\) | 0.841390 | 0.0746613 | 0.0373307 | − | 0.999303i | \(-0.488115\pi\) | ||||
0.0373307 | + | 0.999303i | \(0.488115\pi\) | |||||||
\(128\) | −5.25307 | −0.464310 | ||||||||
\(129\) | 13.5672 | 1.19452 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.299180 | 0.0261395 | 0.0130697 | − | 0.999915i | \(-0.495840\pi\) | ||||
0.0130697 | + | 0.999915i | \(0.495840\pi\) | |||||||
\(132\) | 1.27111 | 0.110636 | ||||||||
\(133\) | 1.12653 | 0.0976828 | ||||||||
\(134\) | −0.253953 | −0.0219382 | ||||||||
\(135\) | 1.63355 | 0.140594 | ||||||||
\(136\) | 1.55313 | 0.133180 | ||||||||
\(137\) | −10.7922 | −0.922037 | −0.461018 | − | 0.887391i | \(-0.652516\pi\) | ||||
−0.461018 | + | 0.887391i | \(0.652516\pi\) | |||||||
\(138\) | −0.193802 | −0.0164975 | ||||||||
\(139\) | 3.68278 | 0.312369 | 0.156185 | − | 0.987728i | \(-0.450081\pi\) | ||||
0.156185 | + | 0.987728i | \(0.450081\pi\) | |||||||
\(140\) | −0.330369 | −0.0279213 | ||||||||
\(141\) | 28.4859 | 2.39894 | ||||||||
\(142\) | 3.39452 | 0.284862 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −8.96481 | −0.747067 | ||||||||
\(145\) | 24.5491 | 2.03869 | ||||||||
\(146\) | 2.44375 | 0.202246 | ||||||||
\(147\) | 17.3453 | 1.43062 | ||||||||
\(148\) | −3.91869 | −0.322115 | ||||||||
\(149\) | 10.8695 | 0.890461 | 0.445231 | − | 0.895416i | \(-0.353122\pi\) | ||||
0.445231 | + | 0.895416i | \(0.353122\pi\) | |||||||
\(150\) | 0.679666 | 0.0554945 | ||||||||
\(151\) | 11.4749 | 0.933817 | 0.466909 | − | 0.884306i | \(-0.345368\pi\) | ||||
0.466909 | + | 0.884306i | \(0.345368\pi\) | |||||||
\(152\) | −12.1023 | −0.981623 | ||||||||
\(153\) | 1.66563 | 0.134658 | ||||||||
\(154\) | 0.348409 | 0.0280756 | ||||||||
\(155\) | 8.15861 | 0.655315 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1234 | 1.28679 | 0.643394 | − | 0.765535i | \(-0.277526\pi\) | ||||
0.643394 | + | 0.765535i | \(0.277526\pi\) | |||||||
\(158\) | 4.22499 | 0.336122 | ||||||||
\(159\) | 16.8695 | 1.33784 | ||||||||
\(160\) | 6.38049 | 0.504422 | ||||||||
\(161\) | 0.0180399 | 0.00142174 | ||||||||
\(162\) | 9.85231 | 0.774071 | ||||||||
\(163\) | −18.3132 | −1.43440 | −0.717201 | − | 0.696866i | \(-0.754577\pi\) | ||||
−0.717201 | + | 0.696866i | \(0.754577\pi\) | |||||||
\(164\) | 0.192913 | 0.0150640 | ||||||||
\(165\) | 5.72889 | 0.445994 | ||||||||
\(166\) | −5.79528 | −0.449801 | ||||||||
\(167\) | −10.7741 | −0.833727 | −0.416863 | − | 0.908969i | \(-0.636871\pi\) | ||||
−0.416863 | + | 0.908969i | \(0.636871\pi\) | |||||||
\(168\) | 2.18980 | 0.168947 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.41568 | 0.108578 | ||||||||
\(171\) | −12.9788 | −0.992517 | ||||||||
\(172\) | 2.74382 | 0.209214 | ||||||||
\(173\) | −21.2500 | −1.61560 | −0.807802 | − | 0.589454i | \(-0.799343\pi\) | ||||
−0.807802 | + | 0.589454i | \(0.799343\pi\) | |||||||
\(174\) | −32.9085 | −2.49478 | ||||||||
\(175\) | −0.0632663 | −0.00478248 | ||||||||
\(176\) | −2.72889 | −0.205698 | ||||||||
\(177\) | −34.4186 | −2.58706 | ||||||||
\(178\) | 4.53910 | 0.340220 | ||||||||
\(179\) | 4.14457 | 0.309780 | 0.154890 | − | 0.987932i | \(-0.450498\pi\) | ||||
0.154890 | + | 0.987932i | \(0.450498\pi\) | |||||||
\(180\) | 3.80620 | 0.283697 | ||||||||
\(181\) | 20.2811 | 1.50749 | 0.753743 | − | 0.657170i | \(-0.228247\pi\) | ||||
0.753743 | + | 0.657170i | \(0.228247\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.35933 | 0.617940 | ||||||||
\(184\) | −0.193802 | −0.0142872 | ||||||||
\(185\) | −17.6616 | −1.29851 | ||||||||
\(186\) | −10.9367 | −0.801920 | ||||||||
\(187\) | 0.507019 | 0.0370769 | ||||||||
\(188\) | 5.76097 | 0.420162 | ||||||||
\(189\) | 0.203836 | 0.0148269 | ||||||||
\(190\) | −11.0312 | −0.800287 | ||||||||
\(191\) | 4.61951 | 0.334256 | 0.167128 | − | 0.985935i | \(-0.446551\pi\) | ||||
0.167128 | + | 0.985935i | \(0.446551\pi\) | |||||||
\(192\) | −22.2359 | −1.60474 | ||||||||
\(193\) | −5.69682 | −0.410066 | −0.205033 | − | 0.978755i | \(-0.565730\pi\) | ||||
−0.205033 | + | 0.978755i | \(0.565730\pi\) | |||||||
\(194\) | −18.3624 | −1.31835 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.50791 | 0.250565 | ||||||||
\(197\) | −1.85943 | −0.132479 | −0.0662395 | − | 0.997804i | \(-0.521100\pi\) | ||||
−0.0662395 | + | 0.997804i | \(0.521100\pi\) | |||||||
\(198\) | −4.01404 | −0.285265 | ||||||||
\(199\) | 8.26710 | 0.586039 | 0.293020 | − | 0.956106i | \(-0.405340\pi\) | ||||
0.293020 | + | 0.956106i | \(0.405340\pi\) | |||||||
\(200\) | 0.679666 | 0.0480596 | ||||||||
\(201\) | −0.521056 | −0.0367525 | ||||||||
\(202\) | −18.2459 | −1.28378 | ||||||||
\(203\) | 3.06327 | 0.214999 | ||||||||
\(204\) | 0.644474 | 0.0451222 | ||||||||
\(205\) | 0.869465 | 0.0607261 | ||||||||
\(206\) | 21.2491 | 1.48049 | ||||||||
\(207\) | −0.207839 | −0.0144458 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.95077 | −0.273281 | ||||||||
\(210\) | 1.99600 | 0.137737 | ||||||||
\(211\) | 2.81020 | 0.193462 | 0.0967311 | − | 0.995311i | \(-0.469161\pi\) | ||||
0.0967311 | + | 0.995311i | \(0.469161\pi\) | |||||||
\(212\) | 3.41168 | 0.234315 | ||||||||
\(213\) | 6.96481 | 0.477221 | ||||||||
\(214\) | 19.2359 | 1.31494 | ||||||||
\(215\) | 12.3664 | 0.843385 | ||||||||
\(216\) | −2.18980 | −0.148997 | ||||||||
\(217\) | 1.01804 | 0.0691091 | ||||||||
\(218\) | −23.1726 | −1.56945 | ||||||||
\(219\) | 5.01404 | 0.338817 | ||||||||
\(220\) | 1.15861 | 0.0781135 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 23.6757 | 1.58901 | ||||||||
\(223\) | −14.0602 | −0.941537 | −0.470769 | − | 0.882257i | \(-0.656023\pi\) | ||||
−0.470769 | + | 0.882257i | \(0.656023\pi\) | |||||||
\(224\) | 0.796164 | 0.0531959 | ||||||||
\(225\) | 0.728895 | 0.0485930 | ||||||||
\(226\) | 17.8975 | 1.19053 | ||||||||
\(227\) | −19.2038 | −1.27460 | −0.637302 | − | 0.770614i | \(-0.719949\pi\) | ||||
−0.637302 | + | 0.770614i | \(0.719949\pi\) | |||||||
\(228\) | −5.02185 | −0.332580 | ||||||||
\(229\) | 12.4789 | 0.824632 | 0.412316 | − | 0.911041i | \(-0.364720\pi\) | ||||
0.412316 | + | 0.911041i | \(0.364720\pi\) | |||||||
\(230\) | −0.176650 | −0.0116479 | ||||||||
\(231\) | 0.714858 | 0.0470342 | ||||||||
\(232\) | −32.9085 | −2.16055 | ||||||||
\(233\) | −7.97193 | −0.522258 | −0.261129 | − | 0.965304i | \(-0.584095\pi\) | ||||
−0.261129 | + | 0.965304i | \(0.584095\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.9648 | 1.69376 | ||||||||
\(236\) | −6.96081 | −0.453110 | ||||||||
\(237\) | 8.66874 | 0.563095 | ||||||||
\(238\) | 0.176650 | 0.0114505 | ||||||||
\(239\) | −18.9468 | −1.22556 | −0.612782 | − | 0.790252i | \(-0.709950\pi\) | ||||
−0.612782 | + | 0.790252i | \(0.709950\pi\) | |||||||
\(240\) | −15.6336 | −1.00914 | ||||||||
\(241\) | 15.6336 | 1.00705 | 0.503523 | − | 0.863982i | \(-0.332037\pi\) | ||||
0.503523 | + | 0.863982i | \(0.332037\pi\) | |||||||
\(242\) | −1.22188 | −0.0785452 | ||||||||
\(243\) | 22.3593 | 1.43435 | ||||||||
\(244\) | 1.69059 | 0.108229 | ||||||||
\(245\) | 15.8102 | 1.01008 | ||||||||
\(246\) | −1.16553 | −0.0743115 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.9367 | −0.694483 | ||||||||
\(249\) | −11.8906 | −0.753537 | ||||||||
\(250\) | −13.3413 | −0.843777 | ||||||||
\(251\) | 3.88750 | 0.245377 | 0.122689 | − | 0.992445i | \(-0.460848\pi\) | ||||
0.122689 | + | 0.992445i | \(0.460848\pi\) | |||||||
\(252\) | 0.474941 | 0.0299185 | ||||||||
\(253\) | −0.0632663 | −0.00397752 | ||||||||
\(254\) | −1.02807 | −0.0645071 | ||||||||
\(255\) | 2.90466 | 0.181897 | ||||||||
\(256\) | −11.3203 | −0.707521 | ||||||||
\(257\) | 14.0452 | 0.876117 | 0.438059 | − | 0.898946i | \(-0.355666\pi\) | ||||
0.438059 | + | 0.898946i | \(0.355666\pi\) | |||||||
\(258\) | −16.5774 | −1.03206 | ||||||||
\(259\) | −2.20384 | −0.136940 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −35.2921 | −2.18452 | ||||||||
\(262\) | −0.365561 | −0.0225844 | ||||||||
\(263\) | 20.1194 | 1.24062 | 0.620308 | − | 0.784358i | \(-0.287008\pi\) | ||||
0.620308 | + | 0.784358i | \(0.287008\pi\) | |||||||
\(264\) | −7.67967 | −0.472651 | ||||||||
\(265\) | 15.3765 | 0.944570 | ||||||||
\(266\) | −1.37648 | −0.0843976 | ||||||||
\(267\) | 9.31322 | 0.569960 | ||||||||
\(268\) | −0.105378 | −0.00643700 | ||||||||
\(269\) | −6.28514 | −0.383212 | −0.191606 | − | 0.981472i | \(-0.561370\pi\) | ||||
−0.191606 | + | 0.981472i | \(0.561370\pi\) | |||||||
\(270\) | −1.99600 | −0.121473 | ||||||||
\(271\) | 31.7922 | 1.93124 | 0.965618 | − | 0.259965i | \(-0.0837109\pi\) | ||||
0.965618 | + | 0.259965i | \(0.0837109\pi\) | |||||||
\(272\) | −1.38360 | −0.0838931 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.1867 | 0.796637 | ||||||||
\(275\) | 0.221876 | 0.0133796 | ||||||||
\(276\) | −0.0804181 | −0.00484060 | ||||||||
\(277\) | 16.8343 | 1.01147 | 0.505737 | − | 0.862688i | \(-0.331221\pi\) | ||||
0.505737 | + | 0.862688i | \(0.331221\pi\) | |||||||
\(278\) | −4.49990 | −0.269886 | ||||||||
\(279\) | −11.7289 | −0.702191 | ||||||||
\(280\) | 1.99600 | 0.119284 | ||||||||
\(281\) | −9.09134 | −0.542344 | −0.271172 | − | 0.962531i | \(-0.587411\pi\) | ||||
−0.271172 | + | 0.962531i | \(0.587411\pi\) | |||||||
\(282\) | −34.8062 | −2.07268 | ||||||||
\(283\) | 23.1546 | 1.37640 | 0.688199 | − | 0.725522i | \(-0.258401\pi\) | ||||
0.688199 | + | 0.725522i | \(0.258401\pi\) | |||||||
\(284\) | 1.40856 | 0.0835827 | ||||||||
\(285\) | −22.6336 | −1.34070 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.108493 | 0.00640412 | ||||||||
\(288\) | −9.17265 | −0.540503 | ||||||||
\(289\) | −16.7429 | −0.984878 | ||||||||
\(290\) | −29.9960 | −1.76143 | ||||||||
\(291\) | −37.6757 | −2.20859 | ||||||||
\(292\) | 1.01404 | 0.0593420 | ||||||||
\(293\) | 22.3734 | 1.30707 | 0.653533 | − | 0.756898i | \(-0.273286\pi\) | ||||
0.653533 | + | 0.756898i | \(0.273286\pi\) | |||||||
\(294\) | −21.1938 | −1.23605 | ||||||||
\(295\) | −31.3725 | −1.82658 | ||||||||
\(296\) | 23.6757 | 1.37612 | ||||||||
\(297\) | −0.714858 | −0.0414802 | ||||||||
\(298\) | −13.2811 | −0.769356 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.282028 | 0.0162829 | ||||||||
\(301\) | 1.54310 | 0.0889427 | ||||||||
\(302\) | −14.0210 | −0.806815 | ||||||||
\(303\) | −37.4366 | −2.15068 | ||||||||
\(304\) | 10.7812 | 0.618346 | ||||||||
\(305\) | 7.61951 | 0.436292 | ||||||||
\(306\) | −2.03519 | −0.116344 | ||||||||
\(307\) | 7.72889 | 0.441111 | 0.220556 | − | 0.975374i | \(-0.429213\pi\) | ||||
0.220556 | + | 0.975374i | \(0.429213\pi\) | |||||||
\(308\) | 0.144573 | 0.00823779 | ||||||||
\(309\) | 43.5984 | 2.48022 | ||||||||
\(310\) | −9.96881 | −0.566190 | ||||||||
\(311\) | −23.7218 | −1.34514 | −0.672569 | − | 0.740034i | \(-0.734809\pi\) | ||||
−0.672569 | + | 0.740034i | \(0.734809\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.48987 | 0.140736 | 0.0703678 | − | 0.997521i | \(-0.477583\pi\) | ||||
0.0703678 | + | 0.997521i | \(0.477583\pi\) | |||||||
\(314\) | −19.7008 | −1.11178 | ||||||||
\(315\) | 2.14057 | 0.120607 | ||||||||
\(316\) | 1.75316 | 0.0986232 | ||||||||
\(317\) | −5.53910 | −0.311107 | −0.155553 | − | 0.987827i | \(-0.549716\pi\) | ||||
−0.155553 | + | 0.987827i | \(0.549716\pi\) | |||||||
\(318\) | −20.6124 | −1.15589 | ||||||||
\(319\) | −10.7429 | −0.601489 | ||||||||
\(320\) | −20.2680 | −1.13302 | ||||||||
\(321\) | 39.4678 | 2.20288 | ||||||||
\(322\) | −0.0220425 | −0.00122838 | ||||||||
\(323\) | −2.00311 | −0.111456 | ||||||||
\(324\) | 4.08823 | 0.227124 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.3765 | 1.23932 | ||||||||
\(327\) | −47.5451 | −2.62925 | ||||||||
\(328\) | −1.16553 | −0.0643556 | ||||||||
\(329\) | 3.23992 | 0.178622 | ||||||||
\(330\) | −7.00000 | −0.385337 | ||||||||
\(331\) | −19.7750 | −1.08693 | −0.543466 | − | 0.839431i | \(-0.682888\pi\) | ||||
−0.543466 | + | 0.839431i | \(0.682888\pi\) | |||||||
\(332\) | −2.40475 | −0.131978 | ||||||||
\(333\) | 25.3905 | 1.39139 | ||||||||
\(334\) | 13.1646 | 0.720337 | ||||||||
\(335\) | −0.474941 | −0.0259488 | ||||||||
\(336\) | −1.95077 | −0.106423 | ||||||||
\(337\) | 19.1858 | 1.04512 | 0.522558 | − | 0.852603i | \(-0.324978\pi\) | ||||
0.522558 | + | 0.852603i | \(0.324978\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.7218 | 1.99445 | ||||||||
\(340\) | 0.587437 | 0.0318582 | ||||||||
\(341\) | −3.57028 | −0.193342 | ||||||||
\(342\) | 15.8585 | 0.857532 | ||||||||
\(343\) | 3.96881 | 0.214296 | ||||||||
\(344\) | −16.5774 | −0.893794 | ||||||||
\(345\) | −0.362446 | −0.0195134 | ||||||||
\(346\) | 25.9648 | 1.39588 | ||||||||
\(347\) | −1.39452 | −0.0748619 | −0.0374310 | − | 0.999299i | \(-0.511917\pi\) | ||||
−0.0374310 | + | 0.999299i | \(0.511917\pi\) | |||||||
\(348\) | −13.6554 | −0.732006 | ||||||||
\(349\) | −8.18668 | −0.438223 | −0.219112 | − | 0.975700i | \(-0.570316\pi\) | ||||
−0.219112 | + | 0.975700i | \(0.570316\pi\) | |||||||
\(350\) | 0.0773036 | 0.00413205 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.79216 | −0.148823 | ||||||||
\(353\) | −24.8171 | −1.32088 | −0.660441 | − | 0.750878i | \(-0.729631\pi\) | ||||
−0.660441 | + | 0.750878i | \(0.729631\pi\) | |||||||
\(354\) | 42.0553 | 2.23521 | ||||||||
\(355\) | 6.34841 | 0.336939 | ||||||||
\(356\) | 1.88350 | 0.0998254 | ||||||||
\(357\) | 0.362446 | 0.0191827 | ||||||||
\(358\) | −5.06415 | −0.267649 | ||||||||
\(359\) | −2.06327 | −0.108895 | −0.0544475 | − | 0.998517i | \(-0.517340\pi\) | ||||
−0.0544475 | + | 0.998517i | \(0.517340\pi\) | |||||||
\(360\) | −22.9960 | −1.21200 | ||||||||
\(361\) | −3.39141 | −0.178495 | ||||||||
\(362\) | −24.7810 | −1.30246 | ||||||||
\(363\) | −2.50702 | −0.131584 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.57028 | 0.239220 | ||||||||
\(366\) | −10.2141 | −0.533898 | ||||||||
\(367\) | 25.5803 | 1.33528 | 0.667641 | − | 0.744483i | \(-0.267304\pi\) | ||||
0.667641 | + | 0.744483i | \(0.267304\pi\) | |||||||
\(368\) | 0.172647 | 0.00899985 | ||||||||
\(369\) | −1.24995 | −0.0650698 | ||||||||
\(370\) | 21.5803 | 1.12191 | ||||||||
\(371\) | 1.91869 | 0.0996136 | ||||||||
\(372\) | −4.53821 | −0.235295 | ||||||||
\(373\) | 12.0913 | 0.626066 | 0.313033 | − | 0.949742i | \(-0.398655\pi\) | ||||
0.313033 | + | 0.949742i | \(0.398655\pi\) | |||||||
\(374\) | −0.619514 | −0.0320343 | ||||||||
\(375\) | −27.3734 | −1.41355 | ||||||||
\(376\) | −34.8062 | −1.79499 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.249063 | −0.0128104 | ||||||||
\(379\) | 15.7781 | 0.810468 | 0.405234 | − | 0.914213i | \(-0.367190\pi\) | ||||
0.405234 | + | 0.914213i | \(0.367190\pi\) | |||||||
\(380\) | −4.57740 | −0.234816 | ||||||||
\(381\) | −2.10938 | −0.108067 | ||||||||
\(382\) | −5.64447 | −0.288796 | ||||||||
\(383\) | 21.7601 | 1.11189 | 0.555944 | − | 0.831220i | \(-0.312357\pi\) | ||||
0.555944 | + | 0.831220i | \(0.312357\pi\) | |||||||
\(384\) | 13.1695 | 0.672055 | ||||||||
\(385\) | 0.651591 | 0.0332082 | ||||||||
\(386\) | 6.96081 | 0.354296 | ||||||||
\(387\) | −17.7781 | −0.903713 | ||||||||
\(388\) | −7.61951 | −0.386822 | ||||||||
\(389\) | 4.54913 | 0.230650 | 0.115325 | − | 0.993328i | \(-0.463209\pi\) | ||||
0.115325 | + | 0.993328i | \(0.463209\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.0320772 | −0.00162221 | ||||||||
\(392\) | −21.1938 | −1.07045 | ||||||||
\(393\) | −0.750049 | −0.0378350 | ||||||||
\(394\) | 2.27199 | 0.114461 | ||||||||
\(395\) | 7.90154 | 0.397570 | ||||||||
\(396\) | −1.66563 | −0.0837010 | ||||||||
\(397\) | 13.8726 | 0.696245 | 0.348122 | − | 0.937449i | \(-0.386819\pi\) | ||||
0.348122 | + | 0.937449i | \(0.386819\pi\) | |||||||
\(398\) | −10.1014 | −0.506336 | ||||||||
\(399\) | −2.82424 | −0.141389 | ||||||||
\(400\) | −0.605477 | −0.0302738 | ||||||||
\(401\) | 12.0241 | 0.600453 | 0.300227 | − | 0.953868i | \(-0.402938\pi\) | ||||
0.300227 | + | 0.953868i | \(0.402938\pi\) | |||||||
\(402\) | 0.636666 | 0.0317540 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.57117 | −0.376680 | ||||||||
\(405\) | 18.4257 | 0.915581 | ||||||||
\(406\) | −3.74293 | −0.185759 | ||||||||
\(407\) | 7.72889 | 0.383107 | ||||||||
\(408\) | −3.89373 | −0.192769 | ||||||||
\(409\) | −17.4678 | −0.863728 | −0.431864 | − | 0.901939i | \(-0.642144\pi\) | ||||
−0.431864 | + | 0.901939i | \(0.642144\pi\) | |||||||
\(410\) | −1.06238 | −0.0524671 | ||||||||
\(411\) | 27.0561 | 1.33458 | ||||||||
\(412\) | 8.81732 | 0.434398 | ||||||||
\(413\) | −3.91469 | −0.192629 | ||||||||
\(414\) | 0.253953 | 0.0124811 | ||||||||
\(415\) | −10.8383 | −0.532030 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.23280 | −0.452132 | ||||||||
\(418\) | 4.82735 | 0.236114 | ||||||||
\(419\) | 23.4999 | 1.14805 | 0.574023 | − | 0.818839i | \(-0.305382\pi\) | ||||
0.574023 | + | 0.818839i | \(0.305382\pi\) | |||||||
\(420\) | 0.828241 | 0.0404140 | ||||||||
\(421\) | 1.87347 | 0.0913072 | 0.0456536 | − | 0.998957i | \(-0.485463\pi\) | ||||
0.0456536 | + | 0.998957i | \(0.485463\pi\) | |||||||
\(422\) | −3.43372 | −0.167151 | ||||||||
\(423\) | −37.3273 | −1.81491 | ||||||||
\(424\) | −20.6124 | −1.00103 | ||||||||
\(425\) | 0.112495 | 0.00545683 | ||||||||
\(426\) | −8.51013 | −0.412317 | ||||||||
\(427\) | 0.950771 | 0.0460110 | ||||||||
\(428\) | 7.98196 | 0.385823 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.1103 | −0.728682 | ||||||||
\(431\) | 6.15772 | 0.296607 | 0.148304 | − | 0.988942i | \(-0.452619\pi\) | ||||
0.148304 | + | 0.988942i | \(0.452619\pi\) | |||||||
\(432\) | 1.95077 | 0.0938565 | ||||||||
\(433\) | 22.3624 | 1.07467 | 0.537335 | − | 0.843369i | \(-0.319431\pi\) | ||||
0.537335 | + | 0.843369i | \(0.319431\pi\) | |||||||
\(434\) | −1.24392 | −0.0597100 | ||||||||
\(435\) | −61.5451 | −2.95086 | ||||||||
\(436\) | −9.61551 | −0.460499 | ||||||||
\(437\) | 0.249951 | 0.0119568 | ||||||||
\(438\) | −6.12653 | −0.292737 | ||||||||
\(439\) | −38.5632 | −1.84052 | −0.920260 | − | 0.391308i | \(-0.872023\pi\) | ||||
−0.920260 | + | 0.391308i | \(0.872023\pi\) | |||||||
\(440\) | −7.00000 | −0.333712 | ||||||||
\(441\) | −22.7289 | −1.08233 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.4819 | −1.21068 | −0.605340 | − | 0.795967i | \(-0.706963\pi\) | ||||
−0.605340 | + | 0.795967i | \(0.706963\pi\) | |||||||
\(444\) | 9.82424 | 0.466238 | ||||||||
\(445\) | 8.48898 | 0.402416 | ||||||||
\(446\) | 17.1798 | 0.813485 | ||||||||
\(447\) | −27.2500 | −1.28888 | ||||||||
\(448\) | −2.52906 | −0.119487 | ||||||||
\(449\) | 36.3553 | 1.71571 | 0.857857 | − | 0.513888i | \(-0.171795\pi\) | ||||
0.857857 | + | 0.513888i | \(0.171795\pi\) | |||||||
\(450\) | −0.890619 | −0.0419842 | ||||||||
\(451\) | −0.380486 | −0.0179164 | ||||||||
\(452\) | 7.42660 | 0.349318 | ||||||||
\(453\) | −28.7679 | −1.35163 | ||||||||
\(454\) | 23.4647 | 1.10125 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 30.3406 | 1.42083 | ||||||||
\(457\) | 16.2780 | 0.761454 | 0.380727 | − | 0.924688i | \(-0.375674\pi\) | ||||
0.380727 | + | 0.924688i | \(0.375674\pi\) | |||||||
\(458\) | −15.2477 | −0.712479 | ||||||||
\(459\) | −0.362446 | −0.0169175 | ||||||||
\(460\) | −0.0733010 | −0.00341768 | ||||||||
\(461\) | 2.80620 | 0.130698 | 0.0653488 | − | 0.997862i | \(-0.479184\pi\) | ||||
0.0653488 | + | 0.997862i | \(0.479184\pi\) | |||||||
\(462\) | −0.873467 | −0.0406374 | ||||||||
\(463\) | 18.8835 | 0.877591 | 0.438795 | − | 0.898587i | \(-0.355405\pi\) | ||||
0.438795 | + | 0.898587i | \(0.355405\pi\) | |||||||
\(464\) | 29.3163 | 1.36098 | ||||||||
\(465\) | −20.4538 | −0.948522 | ||||||||
\(466\) | 9.74071 | 0.451229 | ||||||||
\(467\) | −25.6295 | −1.18599 | −0.592997 | − | 0.805205i | \(-0.702055\pi\) | ||||
−0.592997 | + | 0.805205i | \(0.702055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.0592637 | −0.00273654 | ||||||||
\(470\) | −31.7258 | −1.46340 | ||||||||
\(471\) | −40.4217 | −1.86253 | ||||||||
\(472\) | 42.0553 | 1.93575 | ||||||||
\(473\) | −5.41168 | −0.248829 | ||||||||
\(474\) | −10.5921 | −0.486513 | ||||||||
\(475\) | −0.876582 | −0.0402203 | ||||||||
\(476\) | 0.0733010 | 0.00335974 | ||||||||
\(477\) | −22.1054 | −1.01214 | ||||||||
\(478\) | 23.1506 | 1.05888 | ||||||||
\(479\) | 4.49298 | 0.205290 | 0.102645 | − | 0.994718i | \(-0.467270\pi\) | ||||
0.102645 | + | 0.994718i | \(0.467270\pi\) | |||||||
\(480\) | −15.9960 | −0.730114 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −19.1023 | −0.870084 | ||||||||
\(483\) | −0.0452264 | −0.00205787 | ||||||||
\(484\) | −0.507019 | −0.0230463 | ||||||||
\(485\) | −34.3413 | −1.55936 | ||||||||
\(486\) | −27.3203 | −1.23928 | ||||||||
\(487\) | −21.8093 | −0.988274 | −0.494137 | − | 0.869384i | \(-0.664516\pi\) | ||||
−0.494137 | + | 0.869384i | \(0.664516\pi\) | |||||||
\(488\) | −10.2141 | −0.462369 | ||||||||
\(489\) | 45.9116 | 2.07619 | ||||||||
\(490\) | −19.3181 | −0.872703 | ||||||||
\(491\) | 0.359332 | 0.0162164 | 0.00810820 | − | 0.999967i | \(-0.497419\pi\) | ||||
0.00810820 | + | 0.999967i | \(0.497419\pi\) | |||||||
\(492\) | −0.483638 | −0.0218041 | ||||||||
\(493\) | −5.44687 | −0.245315 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.50702 | −0.337415 | ||||||||
\(496\) | 9.74293 | 0.437471 | ||||||||
\(497\) | 0.792161 | 0.0355333 | ||||||||
\(498\) | 14.5289 | 0.651054 | ||||||||
\(499\) | −0.394523 | −0.0176613 | −0.00883064 | − | 0.999961i | \(-0.502811\pi\) | ||||
−0.00883064 | + | 0.999961i | \(0.502811\pi\) | |||||||
\(500\) | −5.53598 | −0.247577 | ||||||||
\(501\) | 27.0109 | 1.20676 | ||||||||
\(502\) | −4.75005 | −0.212005 | ||||||||
\(503\) | −25.5812 | −1.14061 | −0.570305 | − | 0.821433i | \(-0.693175\pi\) | ||||
−0.570305 | + | 0.821433i | \(0.693175\pi\) | |||||||
\(504\) | −2.86946 | −0.127816 | ||||||||
\(505\) | −34.1234 | −1.51847 | ||||||||
\(506\) | 0.0773036 | 0.00343656 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.426600 | −0.0189273 | ||||||||
\(509\) | −8.88350 | −0.393754 | −0.196877 | − | 0.980428i | \(-0.563080\pi\) | ||||
−0.196877 | + | 0.980428i | \(0.563080\pi\) | |||||||
\(510\) | −3.54913 | −0.157158 | ||||||||
\(511\) | 0.570285 | 0.0252279 | ||||||||
\(512\) | 24.3382 | 1.07561 | ||||||||
\(513\) | 2.82424 | 0.124693 | ||||||||
\(514\) | −17.1615 | −0.756963 | ||||||||
\(515\) | 39.7398 | 1.75115 | ||||||||
\(516\) | −6.87881 | −0.302823 | ||||||||
\(517\) | −11.3624 | −0.499720 | ||||||||
\(518\) | 2.69281 | 0.118315 | ||||||||
\(519\) | 53.2740 | 2.33847 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.5803 | 1.69023 | 0.845117 | − | 0.534581i | \(-0.179531\pi\) | ||||
0.845117 | + | 0.534581i | \(0.179531\pi\) | |||||||
\(522\) | 43.1225 | 1.88742 | ||||||||
\(523\) | 24.2359 | 1.05976 | 0.529881 | − | 0.848072i | \(-0.322236\pi\) | ||||
0.529881 | + | 0.848072i | \(0.322236\pi\) | |||||||
\(524\) | −0.151690 | −0.00662660 | ||||||||
\(525\) | 0.158610 | 0.00692230 | ||||||||
\(526\) | −24.5834 | −1.07189 | ||||||||
\(527\) | −1.81020 | −0.0788536 | ||||||||
\(528\) | 6.84139 | 0.297733 | ||||||||
\(529\) | −22.9960 | −0.999826 | ||||||||
\(530\) | −18.7882 | −0.816105 | ||||||||
\(531\) | 45.1014 | 1.95723 | ||||||||
\(532\) | −0.571173 | −0.0247635 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −11.3796 | −0.492443 | ||||||||
\(535\) | 35.9748 | 1.55533 | ||||||||
\(536\) | 0.636666 | 0.0274998 | ||||||||
\(537\) | −10.3905 | −0.448384 | ||||||||
\(538\) | 7.67967 | 0.331094 | ||||||||
\(539\) | −6.91869 | −0.298009 | ||||||||
\(540\) | −0.828241 | −0.0356418 | ||||||||
\(541\) | 9.10538 | 0.391471 | 0.195735 | − | 0.980657i | \(-0.437291\pi\) | ||||
0.195735 | + | 0.980657i | \(0.437291\pi\) | |||||||
\(542\) | −38.8461 | −1.66858 | ||||||||
\(543\) | −50.8452 | −2.18198 | ||||||||
\(544\) | −1.41568 | −0.0606967 | ||||||||
\(545\) | −43.3373 | −1.85637 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.0109 | −1.79626 | −0.898129 | − | 0.439733i | \(-0.855073\pi\) | ||||
−0.898129 | + | 0.439733i | \(0.855073\pi\) | |||||||
\(548\) | 5.47183 | 0.233745 | ||||||||
\(549\) | −10.9539 | −0.467500 | ||||||||
\(550\) | −0.271105 | −0.0115600 | ||||||||
\(551\) | 42.4429 | 1.80813 | ||||||||
\(552\) | 0.485864 | 0.0206798 | ||||||||
\(553\) | 0.985963 | 0.0419274 | ||||||||
\(554\) | −20.5694 | −0.873910 | ||||||||
\(555\) | 44.2780 | 1.87950 | ||||||||
\(556\) | −1.86724 | −0.0791885 | ||||||||
\(557\) | 10.6124 | 0.449662 | 0.224831 | − | 0.974398i | \(-0.427817\pi\) | ||||
0.224831 | + | 0.974398i | \(0.427817\pi\) | |||||||
\(558\) | 14.3313 | 0.606690 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.77812 | −0.0751394 | ||||||||
\(561\) | −1.27111 | −0.0536661 | ||||||||
\(562\) | 11.1085 | 0.468583 | ||||||||
\(563\) | −19.3945 | −0.817382 | −0.408691 | − | 0.912673i | \(-0.634015\pi\) | ||||
−0.408691 | + | 0.912673i | \(0.634015\pi\) | |||||||
\(564\) | −14.4429 | −0.608154 | ||||||||
\(565\) | 33.4718 | 1.40817 | ||||||||
\(566\) | −28.2921 | −1.18920 | ||||||||
\(567\) | 2.29918 | 0.0965565 | ||||||||
\(568\) | −8.51013 | −0.357077 | ||||||||
\(569\) | 33.6625 | 1.41121 | 0.705603 | − | 0.708607i | \(-0.250676\pi\) | ||||
0.705603 | + | 0.708607i | \(0.250676\pi\) | |||||||
\(570\) | 27.6554 | 1.15836 | ||||||||
\(571\) | −11.0250 | −0.461380 | −0.230690 | − | 0.973027i | \(-0.574098\pi\) | ||||
−0.230690 | + | 0.973027i | \(0.574098\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.5812 | −0.483812 | ||||||||
\(574\) | −0.132565 | −0.00553314 | ||||||||
\(575\) | −0.0140373 | −0.000585395 0 | ||||||||
\(576\) | 29.1375 | 1.21406 | ||||||||
\(577\) | 11.1898 | 0.465837 | 0.232919 | − | 0.972496i | \(-0.425172\pi\) | ||||
0.232919 | + | 0.972496i | \(0.425172\pi\) | |||||||
\(578\) | 20.4578 | 0.850932 | ||||||||
\(579\) | 14.2820 | 0.593541 | ||||||||
\(580\) | −12.4469 | −0.516828 | ||||||||
\(581\) | −1.35241 | −0.0561075 | ||||||||
\(582\) | 46.0350 | 1.90821 | ||||||||
\(583\) | −6.72889 | −0.278682 | ||||||||
\(584\) | −6.12653 | −0.253518 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.3375 | −1.12930 | ||||||||
\(587\) | 4.45779 | 0.183993 | 0.0919963 | − | 0.995759i | \(-0.470675\pi\) | ||||
0.0919963 | + | 0.995759i | \(0.470675\pi\) | |||||||
\(588\) | −8.79439 | −0.362674 | ||||||||
\(589\) | 14.1054 | 0.581202 | ||||||||
\(590\) | 38.3333 | 1.57816 | ||||||||
\(591\) | 4.66163 | 0.191754 | ||||||||
\(592\) | −21.0913 | −0.866849 | ||||||||
\(593\) | −28.0733 | −1.15283 | −0.576416 | − | 0.817156i | \(-0.695549\pi\) | ||||
−0.576416 | + | 0.817156i | \(0.695549\pi\) | |||||||
\(594\) | 0.873467 | 0.0358388 | ||||||||
\(595\) | 0.330369 | 0.0135438 | ||||||||
\(596\) | −5.51102 | −0.225740 | ||||||||
\(597\) | −20.7258 | −0.848250 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.6304 | 0.720360 | 0.360180 | − | 0.932883i | \(-0.382715\pi\) | ||||
0.360180 | + | 0.932883i | \(0.382715\pi\) | |||||||
\(600\) | −1.70393 | −0.0695628 | ||||||||
\(601\) | 6.69771 | 0.273205 | 0.136603 | − | 0.990626i | \(-0.456382\pi\) | ||||
0.136603 | + | 0.990626i | \(0.456382\pi\) | |||||||
\(602\) | −1.88548 | −0.0768462 | ||||||||
\(603\) | 0.682780 | 0.0278050 | ||||||||
\(604\) | −5.81801 | −0.236731 | ||||||||
\(605\) | −2.28514 | −0.0929043 | ||||||||
\(606\) | 45.7429 | 1.85818 | ||||||||
\(607\) | −11.1546 | −0.452752 | −0.226376 | − | 0.974040i | \(-0.572688\pi\) | ||||
−0.226376 | + | 0.974040i | \(0.572688\pi\) | |||||||
\(608\) | 11.0312 | 0.447374 | ||||||||
\(609\) | −7.67967 | −0.311196 | ||||||||
\(610\) | −9.31010 | −0.376955 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.844505 | −0.0341371 | ||||||||
\(613\) | −15.3203 | −0.618782 | −0.309391 | − | 0.950935i | \(-0.600125\pi\) | ||||
−0.309391 | + | 0.950935i | \(0.600125\pi\) | |||||||
\(614\) | −9.44375 | −0.381119 | ||||||||
\(615\) | −2.17976 | −0.0878966 | ||||||||
\(616\) | −0.873467 | −0.0351930 | ||||||||
\(617\) | 24.4819 | 0.985603 | 0.492801 | − | 0.870142i | \(-0.335973\pi\) | ||||
0.492801 | + | 0.870142i | \(0.335973\pi\) | |||||||
\(618\) | −53.2718 | −2.14291 | ||||||||
\(619\) | 14.3624 | 0.577275 | 0.288638 | − | 0.957438i | \(-0.406798\pi\) | ||||
0.288638 | + | 0.957438i | \(0.406798\pi\) | |||||||
\(620\) | −4.13657 | −0.166129 | ||||||||
\(621\) | 0.0452264 | 0.00181487 | ||||||||
\(622\) | 28.9851 | 1.16220 | ||||||||
\(623\) | 1.05926 | 0.0424385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.0602 | −1.04241 | ||||||||
\(626\) | −3.04231 | −0.121595 | ||||||||
\(627\) | 9.90466 | 0.395554 | ||||||||
\(628\) | −8.17487 | −0.326213 | ||||||||
\(629\) | 3.91869 | 0.156249 | ||||||||
\(630\) | −2.61551 | −0.104204 | ||||||||
\(631\) | 25.4186 | 1.01190 | 0.505949 | − | 0.862563i | \(-0.331142\pi\) | ||||
0.505949 | + | 0.862563i | \(0.331142\pi\) | |||||||
\(632\) | −10.5921 | −0.421332 | ||||||||
\(633\) | −7.04523 | −0.280023 | ||||||||
\(634\) | 6.76809 | 0.268795 | ||||||||
\(635\) | −1.92270 | −0.0762999 | ||||||||
\(636\) | −8.55313 | −0.339154 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.1265 | 0.519684 | ||||||||
\(639\) | −9.12653 | −0.361040 | ||||||||
\(640\) | 12.0040 | 0.474500 | ||||||||
\(641\) | −18.6897 | −0.738199 | −0.369099 | − | 0.929390i | \(-0.620334\pi\) | ||||
−0.369099 | + | 0.929390i | \(0.620334\pi\) | |||||||
\(642\) | −48.2248 | −1.90328 | ||||||||
\(643\) | 0.221876 | 0.00874994 | 0.00437497 | − | 0.999990i | \(-0.498607\pi\) | ||||
0.00437497 | + | 0.999990i | \(0.498607\pi\) | |||||||
\(644\) | −0.00914657 | −0.000360425 0 | ||||||||
\(645\) | −31.0029 | −1.22074 | ||||||||
\(646\) | 2.44756 | 0.0962979 | ||||||||
\(647\) | −10.0602 | −0.395505 | −0.197753 | − | 0.980252i | \(-0.563364\pi\) | ||||
−0.197753 | + | 0.980252i | \(0.563364\pi\) | |||||||
\(648\) | −24.6999 | −0.970305 | ||||||||
\(649\) | 13.7289 | 0.538906 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.55225 | −0.100030 | ||||||||
\(652\) | 9.28514 | 0.363634 | ||||||||
\(653\) | 25.1375 | 0.983705 | 0.491852 | − | 0.870679i | \(-0.336320\pi\) | ||||
0.491852 | + | 0.870679i | \(0.336320\pi\) | |||||||
\(654\) | 58.0943 | 2.27167 | ||||||||
\(655\) | −0.683668 | −0.0267131 | ||||||||
\(656\) | 1.03831 | 0.0405390 | ||||||||
\(657\) | −6.57028 | −0.256331 | ||||||||
\(658\) | −3.95878 | −0.154329 | ||||||||
\(659\) | −30.7530 | −1.19797 | −0.598983 | − | 0.800762i | \(-0.704428\pi\) | ||||
−0.598983 | + | 0.800762i | \(0.704428\pi\) | |||||||
\(660\) | −2.90466 | −0.113064 | ||||||||
\(661\) | 44.1335 | 1.71659 | 0.858296 | − | 0.513155i | \(-0.171523\pi\) | ||||
0.858296 | + | 0.513155i | \(0.171523\pi\) | |||||||
\(662\) | 24.1626 | 0.939107 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.5289 | 0.563829 | ||||||||
\(665\) | −2.57429 | −0.0998266 | ||||||||
\(666\) | −31.0241 | −1.20216 | ||||||||
\(667\) | 0.679666 | 0.0263168 | ||||||||
\(668\) | 5.46268 | 0.211357 | ||||||||
\(669\) | 35.2491 | 1.36281 | ||||||||
\(670\) | 0.580320 | 0.0224197 | ||||||||
\(671\) | −3.33437 | −0.128722 | ||||||||
\(672\) | −1.99600 | −0.0769973 | ||||||||
\(673\) | 19.6516 | 0.757513 | 0.378757 | − | 0.925496i | \(-0.376352\pi\) | ||||
0.378757 | + | 0.925496i | \(0.376352\pi\) | |||||||
\(674\) | −23.4427 | −0.902978 | ||||||||
\(675\) | −0.158610 | −0.00610490 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.0250 | 1.00022 | 0.500110 | − | 0.865962i | \(-0.333293\pi\) | ||||
0.500110 | + | 0.865962i | \(0.333293\pi\) | |||||||
\(678\) | −44.8695 | −1.72320 | ||||||||
\(679\) | −4.28514 | −0.164449 | ||||||||
\(680\) | −3.54913 | −0.136103 | ||||||||
\(681\) | 48.1444 | 1.84490 | ||||||||
\(682\) | 4.36245 | 0.167047 | ||||||||
\(683\) | 14.4609 | 0.553331 | 0.276666 | − | 0.960966i | \(-0.410771\pi\) | ||||
0.276666 | + | 0.960966i | \(0.410771\pi\) | |||||||
\(684\) | 6.58052 | 0.251612 | ||||||||
\(685\) | 24.6616 | 0.942272 | ||||||||
\(686\) | −4.84940 | −0.185151 | ||||||||
\(687\) | −31.2849 | −1.19360 | ||||||||
\(688\) | 14.7679 | 0.563021 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.442864 | 0.0168596 | ||||||||
\(691\) | −8.71085 | −0.331377 | −0.165688 | − | 0.986178i | \(-0.552985\pi\) | ||||
−0.165688 | + | 0.986178i | \(0.552985\pi\) | |||||||
\(692\) | 10.7741 | 0.409571 | ||||||||
\(693\) | −0.936734 | −0.0355836 | ||||||||
\(694\) | 1.70393 | 0.0646805 | ||||||||
\(695\) | −8.41568 | −0.319225 | ||||||||
\(696\) | 82.5021 | 3.12724 | ||||||||
\(697\) | −0.192913 | −0.00730712 | ||||||||
\(698\) | 10.0031 | 0.378623 | ||||||||
\(699\) | 19.9858 | 0.755931 | ||||||||
\(700\) | 0.0320772 | 0.00121240 | ||||||||
\(701\) | 37.5732 | 1.41912 | 0.709560 | − | 0.704645i | \(-0.248894\pi\) | ||||
0.709560 | + | 0.704645i | \(0.248894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.5351 | −1.15165 | ||||||||
\(704\) | 8.86946 | 0.334281 | ||||||||
\(705\) | −65.0943 | −2.45159 | ||||||||
\(706\) | 30.3234 | 1.14124 | ||||||||
\(707\) | −4.25796 | −0.160137 | ||||||||
\(708\) | 17.4509 | 0.655844 | ||||||||
\(709\) | 10.9196 | 0.410094 | 0.205047 | − | 0.978752i | \(-0.434265\pi\) | ||||
0.205047 | + | 0.978752i | \(0.434265\pi\) | |||||||
\(710\) | −7.75697 | −0.291114 | ||||||||
\(711\) | −11.3593 | −0.426008 | ||||||||
\(712\) | −11.3796 | −0.426468 | ||||||||
\(713\) | 0.225879 | 0.00845923 | ||||||||
\(714\) | −0.442864 | −0.0165738 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.10138 | −0.0785321 | ||||||||
\(717\) | 47.4999 | 1.77392 | ||||||||
\(718\) | 2.52106 | 0.0940850 | ||||||||
\(719\) | 34.6093 | 1.29071 | 0.645354 | − | 0.763883i | \(-0.276710\pi\) | ||||
0.645354 | + | 0.763883i | \(0.276710\pi\) | |||||||
\(720\) | 20.4859 | 0.763463 | ||||||||
\(721\) | 4.95878 | 0.184674 | ||||||||
\(722\) | 4.14388 | 0.154219 | ||||||||
\(723\) | −39.1936 | −1.45763 | ||||||||
\(724\) | −10.2829 | −0.382162 | ||||||||
\(725\) | −2.38360 | −0.0885247 | ||||||||
\(726\) | 3.06327 | 0.113688 | ||||||||
\(727\) | 19.3281 | 0.716841 | 0.358421 | − | 0.933560i | \(-0.383315\pi\) | ||||
0.358421 | + | 0.933560i | \(0.383315\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31.8655 | −1.18020 | ||||||||
\(730\) | −5.58432 | −0.206685 | ||||||||
\(731\) | −2.74382 | −0.101484 | ||||||||
\(732\) | −4.23834 | −0.156653 | ||||||||
\(733\) | 8.03519 | 0.296787 | 0.148393 | − | 0.988928i | \(-0.452590\pi\) | ||||
0.148393 | + | 0.988928i | \(0.452590\pi\) | |||||||
\(734\) | −31.2560 | −1.15368 | ||||||||
\(735\) | −39.6365 | −1.46201 | ||||||||
\(736\) | 0.176650 | 0.00651140 | ||||||||
\(737\) | 0.207839 | 0.00765584 | ||||||||
\(738\) | 1.52729 | 0.0562201 | ||||||||
\(739\) | −15.0290 | −0.552849 | −0.276425 | − | 0.961036i | \(-0.589150\pi\) | ||||
−0.276425 | + | 0.961036i | \(0.589150\pi\) | |||||||
\(740\) | 8.95477 | 0.329184 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.34441 | −0.0860659 | ||||||||
\(743\) | −41.7006 | −1.52985 | −0.764924 | − | 0.644121i | \(-0.777223\pi\) | ||||
−0.764924 | + | 0.644121i | \(0.777223\pi\) | |||||||
\(744\) | 27.4186 | 1.00521 | ||||||||
\(745\) | −24.8383 | −0.910004 | ||||||||
\(746\) | −14.7741 | −0.540919 | ||||||||
\(747\) | 15.5812 | 0.570087 | ||||||||
\(748\) | −0.257068 | −0.00939933 | ||||||||
\(749\) | 4.48898 | 0.164024 | ||||||||
\(750\) | 33.4469 | 1.22131 | ||||||||
\(751\) | −26.1827 | −0.955420 | −0.477710 | − | 0.878518i | \(-0.658533\pi\) | ||||
−0.477710 | + | 0.878518i | \(0.658533\pi\) | |||||||
\(752\) | 31.0069 | 1.13071 | ||||||||
\(753\) | −9.74605 | −0.355166 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.2219 | −0.954312 | ||||||||
\(756\) | −0.103349 | −0.00375876 | ||||||||
\(757\) | 50.3734 | 1.83085 | 0.915426 | − | 0.402487i | \(-0.131854\pi\) | ||||
0.915426 | + | 0.402487i | \(0.131854\pi\) | |||||||
\(758\) | −19.2789 | −0.700242 | ||||||||
\(759\) | 0.158610 | 0.00575717 | ||||||||
\(760\) | 27.6554 | 1.00317 | ||||||||
\(761\) | −15.0882 | −0.546948 | −0.273474 | − | 0.961879i | \(-0.588173\pi\) | ||||
−0.273474 | + | 0.961879i | \(0.588173\pi\) | |||||||
\(762\) | 2.57740 | 0.0933694 | ||||||||
\(763\) | −5.40767 | −0.195771 | ||||||||
\(764\) | −2.34218 | −0.0847371 | ||||||||
\(765\) | −3.80620 | −0.137613 | ||||||||
\(766\) | −26.5881 | −0.960668 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 28.3803 | 1.02409 | ||||||||
\(769\) | 34.1094 | 1.23002 | 0.615008 | − | 0.788521i | \(-0.289153\pi\) | ||||
0.615008 | + | 0.788521i | \(0.289153\pi\) | |||||||
\(770\) | −0.796164 | −0.0286918 | ||||||||
\(771\) | −35.2116 | −1.26812 | ||||||||
\(772\) | 2.88839 | 0.103956 | ||||||||
\(773\) | 16.5772 | 0.596241 | 0.298120 | − | 0.954528i | \(-0.403640\pi\) | ||||
0.298120 | + | 0.954528i | \(0.403640\pi\) | |||||||
\(774\) | 21.7227 | 0.780805 | ||||||||
\(775\) | −0.792161 | −0.0284553 | ||||||||
\(776\) | 46.0350 | 1.65256 | ||||||||
\(777\) | 5.52506 | 0.198210 | ||||||||
\(778\) | −5.55847 | −0.199281 | ||||||||
\(779\) | 1.50321 | 0.0538582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.77812 | −0.0994091 | ||||||||
\(782\) | 0.0391944 | 0.00140159 | ||||||||
\(783\) | 7.67967 | 0.274449 | ||||||||
\(784\) | 18.8804 | 0.674300 | ||||||||
\(785\) | −36.8443 | −1.31503 | ||||||||
\(786\) | 0.916467 | 0.0326893 | ||||||||
\(787\) | 21.7670 | 0.775910 | 0.387955 | − | 0.921678i | \(-0.373182\pi\) | ||||
0.387955 | + | 0.921678i | \(0.373182\pi\) | |||||||
\(788\) | 0.942766 | 0.0335846 | ||||||||
\(789\) | −50.4397 | −1.79570 | ||||||||
\(790\) | −9.65471 | −0.343499 | ||||||||
\(791\) | 4.17665 | 0.148505 | ||||||||
\(792\) | 10.0633 | 0.357583 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −16.9506 | −0.601553 | ||||||||
\(795\) | −38.5491 | −1.36720 | ||||||||
\(796\) | −4.19158 | −0.148566 | ||||||||
\(797\) | −28.9717 | −1.02623 | −0.513116 | − | 0.858319i | \(-0.671509\pi\) | ||||
−0.513116 | + | 0.858319i | \(0.671509\pi\) | |||||||
\(798\) | 3.45087 | 0.122159 | ||||||||
\(799\) | −5.76097 | −0.203809 | ||||||||
\(800\) | −0.619514 | −0.0219031 | ||||||||
\(801\) | −12.2038 | −0.431201 | ||||||||
\(802\) | −14.6919 | −0.518790 | ||||||||
\(803\) | −2.00000 | −0.0705785 | ||||||||
\(804\) | 0.264185 | 0.00931709 | ||||||||
\(805\) | −0.0412238 | −0.00145295 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.7570 | 0.554672 | ||||||||
\(808\) | 45.7429 | 1.60923 | ||||||||
\(809\) | −48.4257 | −1.70256 | −0.851279 | − | 0.524714i | \(-0.824172\pi\) | ||||
−0.851279 | + | 0.524714i | \(0.824172\pi\) | |||||||
\(810\) | −22.5139 | −0.791059 | ||||||||
\(811\) | 50.7499 | 1.78207 | 0.891034 | − | 0.453936i | \(-0.149981\pi\) | ||||
0.891034 | + | 0.453936i | \(0.149981\pi\) | |||||||
\(812\) | −1.55313 | −0.0545043 | ||||||||
\(813\) | −79.7035 | −2.79533 | ||||||||
\(814\) | −9.44375 | −0.331003 | ||||||||
\(815\) | 41.8483 | 1.46588 | ||||||||
\(816\) | 3.46871 | 0.121429 | ||||||||
\(817\) | 21.3803 | 0.748002 | ||||||||
\(818\) | 21.3435 | 0.746259 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.440835 | −0.0153946 | ||||||||
\(821\) | −24.2600 | −0.846679 | −0.423340 | − | 0.905971i | \(-0.639142\pi\) | ||||
−0.423340 | + | 0.905971i | \(0.639142\pi\) | |||||||
\(822\) | −33.0593 | −1.15307 | ||||||||
\(823\) | 25.5171 | 0.889469 | 0.444734 | − | 0.895663i | \(-0.353298\pi\) | ||||
0.444734 | + | 0.895663i | \(0.353298\pi\) | |||||||
\(824\) | −53.2718 | −1.85581 | ||||||||
\(825\) | −0.556248 | −0.0193661 | ||||||||
\(826\) | 4.78327 | 0.166431 | ||||||||
\(827\) | 8.82112 | 0.306741 | 0.153370 | − | 0.988169i | \(-0.450987\pi\) | ||||
0.153370 | + | 0.988169i | \(0.450987\pi\) | |||||||
\(828\) | 0.105378 | 0.00366215 | ||||||||
\(829\) | −19.4718 | −0.676285 | −0.338142 | − | 0.941095i | \(-0.609799\pi\) | ||||
−0.338142 | + | 0.941095i | \(0.609799\pi\) | |||||||
\(830\) | 13.2430 | 0.459672 | ||||||||
\(831\) | −42.2038 | −1.46403 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.50791 | −0.121542 | ||||||||
\(834\) | 11.2813 | 0.390641 | ||||||||
\(835\) | 24.6204 | 0.852024 | ||||||||
\(836\) | 2.00311 | 0.0692792 | ||||||||
\(837\) | 2.55225 | 0.0882185 | ||||||||
\(838\) | −28.7140 | −0.991908 | ||||||||
\(839\) | −24.3905 | −0.842054 | −0.421027 | − | 0.907048i | \(-0.638330\pi\) | ||||
−0.421027 | + | 0.907048i | \(0.638330\pi\) | |||||||
\(840\) | −5.00400 | −0.172654 | ||||||||
\(841\) | 86.4106 | 2.97968 | ||||||||
\(842\) | −2.28915 | −0.0788892 | ||||||||
\(843\) | 22.7922 | 0.785004 | ||||||||
\(844\) | −1.42482 | −0.0490445 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 45.6093 | 1.56808 | ||||||||
\(847\) | −0.285142 | −0.00979761 | ||||||||
\(848\) | 18.3624 | 0.630569 | ||||||||
\(849\) | −58.0490 | −1.99224 | ||||||||
\(850\) | −0.137455 | −0.00471468 | ||||||||
\(851\) | −0.488979 | −0.0167620 | ||||||||
\(852\) | −3.53129 | −0.120980 | ||||||||
\(853\) | −11.8984 | −0.407394 | −0.203697 | − | 0.979034i | \(-0.565296\pi\) | ||||
−0.203697 | + | 0.979034i | \(0.565296\pi\) | |||||||
\(854\) | −1.16172 | −0.0397534 | ||||||||
\(855\) | 29.6585 | 1.01430 | ||||||||
\(856\) | −48.2248 | −1.64829 | ||||||||
\(857\) | 38.5030 | 1.31524 | 0.657619 | − | 0.753351i | \(-0.271564\pi\) | ||||
0.657619 | + | 0.753351i | \(0.271564\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.8804 | 0.814788 | 0.407394 | − | 0.913252i | \(-0.366438\pi\) | ||||
0.407394 | + | 0.913252i | \(0.366438\pi\) | |||||||
\(860\) | −6.27002 | −0.213806 | ||||||||
\(861\) | −0.271993 | −0.00926951 | ||||||||
\(862\) | −7.52397 | −0.256268 | ||||||||
\(863\) | −32.7289 | −1.11410 | −0.557052 | − | 0.830477i | \(-0.688068\pi\) | ||||
−0.557052 | + | 0.830477i | \(0.688068\pi\) | |||||||
\(864\) | 1.99600 | 0.0679052 | ||||||||
\(865\) | 48.5592 | 1.65106 | ||||||||
\(866\) | −27.3241 | −0.928512 | ||||||||
\(867\) | 41.9748 | 1.42554 | ||||||||
\(868\) | −0.516165 | −0.0175198 | ||||||||
\(869\) | −3.45779 | −0.117297 | ||||||||
\(870\) | 75.2005 | 2.54954 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 58.0943 | 1.96732 | ||||||||
\(873\) | 49.3694 | 1.67090 | ||||||||
\(874\) | −0.305409 | −0.0103306 | ||||||||
\(875\) | −3.11338 | −0.105252 | ||||||||
\(876\) | −2.54221 | −0.0858933 | ||||||||
\(877\) | 26.6344 | 0.899381 | 0.449691 | − | 0.893184i | \(-0.351534\pi\) | ||||
0.449691 | + | 0.893184i | \(0.351534\pi\) | |||||||
\(878\) | 47.1194 | 1.59020 | ||||||||
\(879\) | −56.0905 | −1.89188 | ||||||||
\(880\) | 6.23591 | 0.210213 | ||||||||
\(881\) | 0.349297 | 0.0117681 | 0.00588406 | − | 0.999983i | \(-0.498127\pi\) | ||||
0.00588406 | + | 0.999983i | \(0.498127\pi\) | |||||||
\(882\) | 27.7719 | 0.935128 | ||||||||
\(883\) | −32.5039 | −1.09384 | −0.546922 | − | 0.837184i | \(-0.684200\pi\) | ||||
−0.546922 | + | 0.837184i | \(0.684200\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 78.6514 | 2.64384 | ||||||||
\(886\) | 31.1357 | 1.04602 | ||||||||
\(887\) | 29.1375 | 0.978340 | 0.489170 | − | 0.872188i | \(-0.337300\pi\) | ||||
0.489170 | + | 0.872188i | \(0.337300\pi\) | |||||||
\(888\) | −59.3553 | −1.99183 | ||||||||
\(889\) | −0.239916 | −0.00804653 | ||||||||
\(890\) | −10.3725 | −0.347686 | ||||||||
\(891\) | −8.06327 | −0.270130 | ||||||||
\(892\) | 7.12876 | 0.238689 | ||||||||
\(893\) | 44.8904 | 1.50220 | ||||||||
\(894\) | 33.2961 | 1.11359 | ||||||||
\(895\) | −9.47094 | −0.316579 | ||||||||
\(896\) | 1.49787 | 0.0500404 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −44.4217 | −1.48237 | ||||||||
\(899\) | 38.3553 | 1.27922 | ||||||||
\(900\) | −0.369563 | −0.0123188 | ||||||||
\(901\) | −3.41168 | −0.113659 | ||||||||
\(902\) | 0.464907 | 0.0154797 | ||||||||
\(903\) | −3.86858 | −0.128738 | ||||||||
\(904\) | −44.8695 | −1.49234 | ||||||||
\(905\) | −46.3453 | −1.54057 | ||||||||
\(906\) | 35.1508 | 1.16781 | ||||||||
\(907\) | −0.664740 | −0.0220723 | −0.0110362 | − | 0.999939i | \(-0.503513\pi\) | ||||
−0.0110362 | + | 0.999939i | \(0.503513\pi\) | |||||||
\(908\) | 9.73670 | 0.323124 | ||||||||
\(909\) | 49.0561 | 1.62709 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5522 | 0.813452 | 0.406726 | − | 0.913550i | \(-0.366670\pi\) | ||||
0.406726 | + | 0.913550i | \(0.366670\pi\) | |||||||
\(912\) | −27.0288 | −0.895012 | ||||||||
\(913\) | 4.74293 | 0.156968 | ||||||||
\(914\) | −19.8897 | −0.657894 | ||||||||
\(915\) | −19.1023 | −0.631501 | ||||||||
\(916\) | −6.32706 | −0.209052 | ||||||||
\(917\) | −0.0853089 | −0.00281715 | ||||||||
\(918\) | 0.442864 | 0.0146167 | ||||||||
\(919\) | −21.0561 | −0.694578 | −0.347289 | − | 0.937758i | \(-0.612898\pi\) | ||||
−0.347289 | + | 0.937758i | \(0.612898\pi\) | |||||||
\(920\) | 0.442864 | 0.0146008 | ||||||||
\(921\) | −19.3765 | −0.638477 | ||||||||
\(922\) | −3.42883 | −0.112922 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.362446 | −0.0119236 | ||||||||
\(925\) | 1.71486 | 0.0563842 | ||||||||
\(926\) | −23.0733 | −0.758236 | ||||||||
\(927\) | −57.1303 | −1.87641 | ||||||||
\(928\) | 29.9960 | 0.984667 | ||||||||
\(929\) | −2.97104 | −0.0974766 | −0.0487383 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487383 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(930\) | 24.9920 | 0.819520 | ||||||||
\(931\) | 27.3342 | 0.895841 | ||||||||
\(932\) | 4.04191 | 0.132397 | ||||||||
\(933\) | 59.4709 | 1.94699 | ||||||||
\(934\) | 31.3161 | 1.02470 | ||||||||
\(935\) | −1.15861 | −0.0378906 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.0350 | 1.69991 | 0.849955 | − | 0.526856i | \(-0.176629\pi\) | ||||
0.849955 | + | 0.526856i | \(0.176629\pi\) | |||||||
\(938\) | 0.0724129 | 0.00236436 | ||||||||
\(939\) | −6.24214 | −0.203705 | ||||||||
\(940\) | −13.1646 | −0.429383 | ||||||||
\(941\) | −44.2108 | −1.44123 | −0.720615 | − | 0.693336i | \(-0.756140\pi\) | ||||
−0.720615 | + | 0.693336i | \(0.756140\pi\) | |||||||
\(942\) | 49.3903 | 1.60922 | ||||||||
\(943\) | 0.0240719 | 0.000783891 0 | ||||||||
\(944\) | −37.4647 | −1.21937 | ||||||||
\(945\) | −0.465795 | −0.0151523 | ||||||||
\(946\) | 6.61240 | 0.214988 | ||||||||
\(947\) | −17.9969 | −0.584820 | −0.292410 | − | 0.956293i | \(-0.594457\pi\) | ||||
−0.292410 | + | 0.956293i | \(0.594457\pi\) | |||||||
\(948\) | −4.39521 | −0.142750 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.07107 | 0.0347502 | ||||||||
\(951\) | 13.8866 | 0.450304 | ||||||||
\(952\) | −0.442864 | −0.0143533 | ||||||||
\(953\) | 6.50390 | 0.210682 | 0.105341 | − | 0.994436i | \(-0.466407\pi\) | ||||
0.105341 | + | 0.994436i | \(0.466407\pi\) | |||||||
\(954\) | 27.0100 | 0.874482 | ||||||||
\(955\) | −10.5562 | −0.341592 | ||||||||
\(956\) | 9.60636 | 0.310692 | ||||||||
\(957\) | 26.9327 | 0.870612 | ||||||||
\(958\) | −5.48987 | −0.177370 | ||||||||
\(959\) | 3.07730 | 0.0993713 | ||||||||
\(960\) | 50.8122 | 1.63996 | ||||||||
\(961\) | −18.2531 | −0.588809 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −51.7178 | −1.66658 | ||||||||
\(964\) | −7.92650 | −0.255295 | ||||||||
\(965\) | 13.0180 | 0.419066 | ||||||||
\(966\) | 0.0552611 | 0.00177800 | ||||||||
\(967\) | −27.4429 | −0.882503 | −0.441252 | − | 0.897383i | \(-0.645465\pi\) | ||||
−0.441252 | + | 0.897383i | \(0.645465\pi\) | |||||||
\(968\) | 3.06327 | 0.0984571 | ||||||||
\(969\) | 5.02185 | 0.161325 | ||||||||
\(970\) | 41.9608 | 1.34728 | ||||||||
\(971\) | 27.2780 | 0.875393 | 0.437697 | − | 0.899123i | \(-0.355794\pi\) | ||||
0.437697 | + | 0.899123i | \(0.355794\pi\) | |||||||
\(972\) | −11.3366 | −0.363622 | ||||||||
\(973\) | −1.05012 | −0.0336652 | ||||||||
\(974\) | 26.6483 | 0.853866 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.09915 | 0.291257 | ||||||||
\(977\) | −7.17665 | −0.229601 | −0.114801 | − | 0.993389i | \(-0.536623\pi\) | ||||
−0.114801 | + | 0.993389i | \(0.536623\pi\) | |||||||
\(978\) | −56.0983 | −1.79382 | ||||||||
\(979\) | −3.71486 | −0.118727 | ||||||||
\(980\) | −8.01607 | −0.256064 | ||||||||
\(981\) | 62.3021 | 1.98915 | ||||||||
\(982\) | −0.439059 | −0.0140109 | ||||||||
\(983\) | −28.4326 | −0.906860 | −0.453430 | − | 0.891292i | \(-0.649800\pi\) | ||||
−0.453430 | + | 0.891292i | \(0.649800\pi\) | |||||||
\(984\) | 2.92201 | 0.0931501 | ||||||||
\(985\) | 4.24906 | 0.135386 | ||||||||
\(986\) | 6.65540 | 0.211951 | ||||||||
\(987\) | −8.12253 | −0.258543 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.342377 | 0.0108869 | ||||||||
\(990\) | 9.17265 | 0.291526 | ||||||||
\(991\) | 42.7490 | 1.35797 | 0.678983 | − | 0.734154i | \(-0.262421\pi\) | ||||
0.678983 | + | 0.734154i | \(0.262421\pi\) | |||||||
\(992\) | 9.96881 | 0.316510 | ||||||||
\(993\) | 49.5763 | 1.57326 | ||||||||
\(994\) | −0.967923 | −0.0307006 | ||||||||
\(995\) | −18.8915 | −0.598901 | ||||||||
\(996\) | 6.02877 | 0.191029 | ||||||||
\(997\) | −28.7859 | −0.911660 | −0.455830 | − | 0.890067i | \(-0.650657\pi\) | ||||
−0.455830 | + | 0.890067i | \(0.650657\pi\) | |||||||
\(998\) | 0.482059 | 0.0152593 | ||||||||
\(999\) | −5.52506 | −0.174805 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1859.2.a.f.1.2 | 3 | ||
13.3 | even | 3 | 143.2.e.b.100.2 | ✓ | 6 | ||
13.9 | even | 3 | 143.2.e.b.133.2 | yes | 6 | ||
13.12 | even | 2 | 1859.2.a.g.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.b.100.2 | ✓ | 6 | 13.3 | even | 3 | ||
143.2.e.b.133.2 | yes | 6 | 13.9 | even | 3 | ||
1859.2.a.f.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1859.2.a.g.1.2 | 3 | 13.12 | even | 2 |