Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.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: | \(32.1158316930\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.424610 | −0.245149 | −0.122574 | − | 0.992459i | \(-0.539115\pi\) | ||||
−0.122574 | + | 0.992459i | \(0.539115\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.05502 | −0.919033 | −0.459517 | − | 0.888169i | \(-0.651977\pi\) | ||||
−0.459517 | + | 0.888169i | \(0.651977\pi\) | |||||||
\(6\) | −0.424610 | −0.173346 | ||||||||
\(7\) | 3.71032 | 1.40237 | 0.701184 | − | 0.712980i | \(-0.252655\pi\) | ||||
0.701184 | + | 0.712980i | \(0.252655\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.81971 | −0.939902 | ||||||||
\(10\) | −2.05502 | −0.649855 | ||||||||
\(11\) | 0.844185 | 0.254531 | 0.127266 | − | 0.991869i | \(-0.459380\pi\) | ||||
0.127266 | + | 0.991869i | \(0.459380\pi\) | |||||||
\(12\) | −0.424610 | −0.122574 | ||||||||
\(13\) | 6.36186 | 1.76446 | 0.882232 | − | 0.470815i | \(-0.156040\pi\) | ||||
0.882232 | + | 0.470815i | \(0.156040\pi\) | |||||||
\(14\) | 3.71032 | 0.991624 | ||||||||
\(15\) | 0.872583 | 0.225300 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.24571 | −0.302130 | −0.151065 | − | 0.988524i | \(-0.548270\pi\) | ||||
−0.151065 | + | 0.988524i | \(0.548270\pi\) | |||||||
\(18\) | −2.81971 | −0.664611 | ||||||||
\(19\) | 4.46042 | 1.02329 | 0.511645 | − | 0.859197i | \(-0.329036\pi\) | ||||
0.511645 | + | 0.859197i | \(0.329036\pi\) | |||||||
\(20\) | −2.05502 | −0.459517 | ||||||||
\(21\) | −1.57544 | −0.343789 | ||||||||
\(22\) | 0.844185 | 0.179981 | ||||||||
\(23\) | −1.59263 | −0.332086 | −0.166043 | − | 0.986118i | \(-0.553099\pi\) | ||||
−0.166043 | + | 0.986118i | \(0.553099\pi\) | |||||||
\(24\) | −0.424610 | −0.0866732 | ||||||||
\(25\) | −0.776890 | −0.155378 | ||||||||
\(26\) | 6.36186 | 1.24766 | ||||||||
\(27\) | 2.47111 | 0.475565 | ||||||||
\(28\) | 3.71032 | 0.701184 | ||||||||
\(29\) | 1.82436 | 0.338776 | 0.169388 | − | 0.985549i | \(-0.445821\pi\) | ||||
0.169388 | + | 0.985549i | \(0.445821\pi\) | |||||||
\(30\) | 0.872583 | 0.159311 | ||||||||
\(31\) | 6.01560 | 1.08043 | 0.540217 | − | 0.841526i | \(-0.318342\pi\) | ||||
0.540217 | + | 0.841526i | \(0.318342\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.358450 | −0.0623981 | ||||||||
\(34\) | −1.24571 | −0.213638 | ||||||||
\(35\) | −7.62478 | −1.28882 | ||||||||
\(36\) | −2.81971 | −0.469951 | ||||||||
\(37\) | −2.03037 | −0.333791 | −0.166896 | − | 0.985975i | \(-0.553374\pi\) | ||||
−0.166896 | + | 0.985975i | \(0.553374\pi\) | |||||||
\(38\) | 4.46042 | 0.723575 | ||||||||
\(39\) | −2.70131 | −0.432556 | ||||||||
\(40\) | −2.05502 | −0.324927 | ||||||||
\(41\) | −9.59480 | −1.49846 | −0.749228 | − | 0.662312i | \(-0.769575\pi\) | ||||
−0.749228 | + | 0.662312i | \(0.769575\pi\) | |||||||
\(42\) | −1.57544 | −0.243095 | ||||||||
\(43\) | −3.91594 | −0.597175 | −0.298587 | − | 0.954382i | \(-0.596515\pi\) | ||||
−0.298587 | + | 0.954382i | \(0.596515\pi\) | |||||||
\(44\) | 0.844185 | 0.127266 | ||||||||
\(45\) | 5.79455 | 0.863801 | ||||||||
\(46\) | −1.59263 | −0.234820 | ||||||||
\(47\) | −10.4573 | −1.52536 | −0.762678 | − | 0.646778i | \(-0.776116\pi\) | ||||
−0.762678 | + | 0.646778i | \(0.776116\pi\) | |||||||
\(48\) | −0.424610 | −0.0612872 | ||||||||
\(49\) | 6.76645 | 0.966636 | ||||||||
\(50\) | −0.776890 | −0.109869 | ||||||||
\(51\) | 0.528942 | 0.0740667 | ||||||||
\(52\) | 6.36186 | 0.882232 | ||||||||
\(53\) | 11.0584 | 1.51899 | 0.759493 | − | 0.650516i | \(-0.225447\pi\) | ||||
0.759493 | + | 0.650516i | \(0.225447\pi\) | |||||||
\(54\) | 2.47111 | 0.336275 | ||||||||
\(55\) | −1.73482 | −0.233923 | ||||||||
\(56\) | 3.71032 | 0.495812 | ||||||||
\(57\) | −1.89394 | −0.250858 | ||||||||
\(58\) | 1.82436 | 0.239551 | ||||||||
\(59\) | −9.42185 | −1.22662 | −0.613310 | − | 0.789842i | \(-0.710163\pi\) | ||||
−0.613310 | + | 0.789842i | \(0.710163\pi\) | |||||||
\(60\) | 0.872583 | 0.112650 | ||||||||
\(61\) | 4.44405 | 0.569003 | 0.284501 | − | 0.958676i | \(-0.408172\pi\) | ||||
0.284501 | + | 0.958676i | \(0.408172\pi\) | |||||||
\(62\) | 6.01560 | 0.763982 | ||||||||
\(63\) | −10.4620 | −1.31809 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −13.0738 | −1.62160 | ||||||||
\(66\) | −0.358450 | −0.0441221 | ||||||||
\(67\) | 5.39038 | 0.658540 | 0.329270 | − | 0.944236i | \(-0.393197\pi\) | ||||
0.329270 | + | 0.944236i | \(0.393197\pi\) | |||||||
\(68\) | −1.24571 | −0.151065 | ||||||||
\(69\) | 0.676247 | 0.0814106 | ||||||||
\(70\) | −7.62478 | −0.911335 | ||||||||
\(71\) | 11.7903 | 1.39925 | 0.699623 | − | 0.714512i | \(-0.253351\pi\) | ||||
0.699623 | + | 0.714512i | \(0.253351\pi\) | |||||||
\(72\) | −2.81971 | −0.332306 | ||||||||
\(73\) | 15.1801 | 1.77669 | 0.888346 | − | 0.459175i | \(-0.151855\pi\) | ||||
0.888346 | + | 0.459175i | \(0.151855\pi\) | |||||||
\(74\) | −2.03037 | −0.236026 | ||||||||
\(75\) | 0.329876 | 0.0380908 | ||||||||
\(76\) | 4.46042 | 0.511645 | ||||||||
\(77\) | 3.13219 | 0.356947 | ||||||||
\(78\) | −2.70131 | −0.305863 | ||||||||
\(79\) | 8.93597 | 1.00538 | 0.502688 | − | 0.864468i | \(-0.332345\pi\) | ||||
0.502688 | + | 0.864468i | \(0.332345\pi\) | |||||||
\(80\) | −2.05502 | −0.229758 | ||||||||
\(81\) | 7.40986 | 0.823318 | ||||||||
\(82\) | −9.59480 | −1.05957 | ||||||||
\(83\) | 6.99898 | 0.768237 | 0.384119 | − | 0.923284i | \(-0.374505\pi\) | ||||
0.384119 | + | 0.923284i | \(0.374505\pi\) | |||||||
\(84\) | −1.57544 | −0.171894 | ||||||||
\(85\) | 2.55997 | 0.277667 | ||||||||
\(86\) | −3.91594 | −0.422266 | ||||||||
\(87\) | −0.774644 | −0.0830505 | ||||||||
\(88\) | 0.844185 | 0.0899904 | ||||||||
\(89\) | −6.60152 | −0.699760 | −0.349880 | − | 0.936794i | \(-0.613778\pi\) | ||||
−0.349880 | + | 0.936794i | \(0.613778\pi\) | |||||||
\(90\) | 5.79455 | 0.610800 | ||||||||
\(91\) | 23.6045 | 2.47443 | ||||||||
\(92\) | −1.59263 | −0.166043 | ||||||||
\(93\) | −2.55428 | −0.264867 | ||||||||
\(94\) | −10.4573 | −1.07859 | ||||||||
\(95\) | −9.16625 | −0.940437 | ||||||||
\(96\) | −0.424610 | −0.0433366 | ||||||||
\(97\) | 12.0468 | 1.22317 | 0.611584 | − | 0.791180i | \(-0.290533\pi\) | ||||
0.611584 | + | 0.791180i | \(0.290533\pi\) | |||||||
\(98\) | 6.76645 | 0.683515 | ||||||||
\(99\) | −2.38035 | −0.239234 | ||||||||
\(100\) | −0.776890 | −0.0776890 | ||||||||
\(101\) | 9.59434 | 0.954672 | 0.477336 | − | 0.878721i | \(-0.341602\pi\) | ||||
0.477336 | + | 0.878721i | \(0.341602\pi\) | |||||||
\(102\) | 0.528942 | 0.0523731 | ||||||||
\(103\) | −10.7695 | −1.06115 | −0.530576 | − | 0.847637i | \(-0.678024\pi\) | ||||
−0.530576 | + | 0.847637i | \(0.678024\pi\) | |||||||
\(104\) | 6.36186 | 0.623832 | ||||||||
\(105\) | 3.23756 | 0.315953 | ||||||||
\(106\) | 11.0584 | 1.07409 | ||||||||
\(107\) | 10.6939 | 1.03382 | 0.516910 | − | 0.856040i | \(-0.327082\pi\) | ||||
0.516910 | + | 0.856040i | \(0.327082\pi\) | |||||||
\(108\) | 2.47111 | 0.237782 | ||||||||
\(109\) | 0.791338 | 0.0757965 | 0.0378982 | − | 0.999282i | \(-0.487934\pi\) | ||||
0.0378982 | + | 0.999282i | \(0.487934\pi\) | |||||||
\(110\) | −1.73482 | −0.165408 | ||||||||
\(111\) | 0.862118 | 0.0818286 | ||||||||
\(112\) | 3.71032 | 0.350592 | ||||||||
\(113\) | −1.79381 | −0.168748 | −0.0843738 | − | 0.996434i | \(-0.526889\pi\) | ||||
−0.0843738 | + | 0.996434i | \(0.526889\pi\) | |||||||
\(114\) | −1.89394 | −0.177384 | ||||||||
\(115\) | 3.27289 | 0.305198 | ||||||||
\(116\) | 1.82436 | 0.169388 | ||||||||
\(117\) | −17.9386 | −1.65842 | ||||||||
\(118\) | −9.42185 | −0.867352 | ||||||||
\(119\) | −4.62199 | −0.423697 | ||||||||
\(120\) | 0.872583 | 0.0796556 | ||||||||
\(121\) | −10.2874 | −0.935214 | ||||||||
\(122\) | 4.44405 | 0.402346 | ||||||||
\(123\) | 4.07405 | 0.367345 | ||||||||
\(124\) | 6.01560 | 0.540217 | ||||||||
\(125\) | 11.8716 | 1.06183 | ||||||||
\(126\) | −10.4620 | −0.932029 | ||||||||
\(127\) | 20.0409 | 1.77834 | 0.889171 | − | 0.457575i | \(-0.151282\pi\) | ||||
0.889171 | + | 0.457575i | \(0.151282\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.66275 | 0.146397 | ||||||||
\(130\) | −13.0738 | −1.14664 | ||||||||
\(131\) | 0.607831 | 0.0531064 | 0.0265532 | − | 0.999647i | \(-0.491547\pi\) | ||||
0.0265532 | + | 0.999647i | \(0.491547\pi\) | |||||||
\(132\) | −0.358450 | −0.0311990 | ||||||||
\(133\) | 16.5496 | 1.43503 | ||||||||
\(134\) | 5.39038 | 0.465658 | ||||||||
\(135\) | −5.07818 | −0.437060 | ||||||||
\(136\) | −1.24571 | −0.106819 | ||||||||
\(137\) | 10.6998 | 0.914147 | 0.457073 | − | 0.889429i | \(-0.348898\pi\) | ||||
0.457073 | + | 0.889429i | \(0.348898\pi\) | |||||||
\(138\) | 0.676247 | 0.0575660 | ||||||||
\(139\) | −15.1789 | −1.28746 | −0.643728 | − | 0.765254i | \(-0.722613\pi\) | ||||
−0.643728 | + | 0.765254i | \(0.722613\pi\) | |||||||
\(140\) | −7.62478 | −0.644411 | ||||||||
\(141\) | 4.44029 | 0.373939 | ||||||||
\(142\) | 11.7903 | 0.989417 | ||||||||
\(143\) | 5.37059 | 0.449111 | ||||||||
\(144\) | −2.81971 | −0.234976 | ||||||||
\(145\) | −3.74911 | −0.311346 | ||||||||
\(146\) | 15.1801 | 1.25631 | ||||||||
\(147\) | −2.87311 | −0.236970 | ||||||||
\(148\) | −2.03037 | −0.166896 | ||||||||
\(149\) | 10.7807 | 0.883186 | 0.441593 | − | 0.897216i | \(-0.354414\pi\) | ||||
0.441593 | + | 0.897216i | \(0.354414\pi\) | |||||||
\(150\) | 0.329876 | 0.0269342 | ||||||||
\(151\) | −20.7420 | −1.68796 | −0.843981 | − | 0.536374i | \(-0.819794\pi\) | ||||
−0.843981 | + | 0.536374i | \(0.819794\pi\) | |||||||
\(152\) | 4.46042 | 0.361787 | ||||||||
\(153\) | 3.51254 | 0.283972 | ||||||||
\(154\) | 3.13219 | 0.252399 | ||||||||
\(155\) | −12.3622 | −0.992954 | ||||||||
\(156\) | −2.70131 | −0.216278 | ||||||||
\(157\) | −0.0174066 | −0.00138920 | −0.000694599 | − | 1.00000i | \(-0.500221\pi\) | ||||
−0.000694599 | 1.00000i | \(0.500221\pi\) | ||||||||
\(158\) | 8.93597 | 0.710908 | ||||||||
\(159\) | −4.69550 | −0.372378 | ||||||||
\(160\) | −2.05502 | −0.162464 | ||||||||
\(161\) | −5.90916 | −0.465707 | ||||||||
\(162\) | 7.40986 | 0.582174 | ||||||||
\(163\) | −1.34937 | −0.105691 | −0.0528455 | − | 0.998603i | \(-0.516829\pi\) | ||||
−0.0528455 | + | 0.998603i | \(0.516829\pi\) | |||||||
\(164\) | −9.59480 | −0.749228 | ||||||||
\(165\) | 0.736621 | 0.0573459 | ||||||||
\(166\) | 6.99898 | 0.543226 | ||||||||
\(167\) | −6.95361 | −0.538086 | −0.269043 | − | 0.963128i | \(-0.586707\pi\) | ||||
−0.269043 | + | 0.963128i | \(0.586707\pi\) | |||||||
\(168\) | −1.57544 | −0.121548 | ||||||||
\(169\) | 27.4733 | 2.11333 | ||||||||
\(170\) | 2.55997 | 0.196340 | ||||||||
\(171\) | −12.5771 | −0.961792 | ||||||||
\(172\) | −3.91594 | −0.298587 | ||||||||
\(173\) | −2.24992 | −0.171058 | −0.0855291 | − | 0.996336i | \(-0.527258\pi\) | ||||
−0.0855291 | + | 0.996336i | \(0.527258\pi\) | |||||||
\(174\) | −0.774644 | −0.0587256 | ||||||||
\(175\) | −2.88251 | −0.217897 | ||||||||
\(176\) | 0.844185 | 0.0636328 | ||||||||
\(177\) | 4.00062 | 0.300705 | ||||||||
\(178\) | −6.60152 | −0.494805 | ||||||||
\(179\) | −0.0932950 | −0.00697319 | −0.00348660 | − | 0.999994i | \(-0.501110\pi\) | ||||
−0.00348660 | + | 0.999994i | \(0.501110\pi\) | |||||||
\(180\) | 5.79455 | 0.431901 | ||||||||
\(181\) | 21.7581 | 1.61727 | 0.808635 | − | 0.588311i | \(-0.200207\pi\) | ||||
0.808635 | + | 0.588311i | \(0.200207\pi\) | |||||||
\(182\) | 23.6045 | 1.74968 | ||||||||
\(183\) | −1.88699 | −0.139490 | ||||||||
\(184\) | −1.59263 | −0.117410 | ||||||||
\(185\) | 4.17246 | 0.306765 | ||||||||
\(186\) | −2.55428 | −0.187289 | ||||||||
\(187\) | −1.05161 | −0.0769015 | ||||||||
\(188\) | −10.4573 | −0.762678 | ||||||||
\(189\) | 9.16859 | 0.666917 | ||||||||
\(190\) | −9.16625 | −0.664989 | ||||||||
\(191\) | −6.28030 | −0.454426 | −0.227213 | − | 0.973845i | \(-0.572961\pi\) | ||||
−0.227213 | + | 0.973845i | \(0.572961\pi\) | |||||||
\(192\) | −0.424610 | −0.0306436 | ||||||||
\(193\) | −14.0894 | −1.01418 | −0.507088 | − | 0.861895i | \(-0.669278\pi\) | ||||
−0.507088 | + | 0.861895i | \(0.669278\pi\) | |||||||
\(194\) | 12.0468 | 0.864910 | ||||||||
\(195\) | 5.55125 | 0.397534 | ||||||||
\(196\) | 6.76645 | 0.483318 | ||||||||
\(197\) | −4.04257 | −0.288021 | −0.144011 | − | 0.989576i | \(-0.546000\pi\) | ||||
−0.144011 | + | 0.989576i | \(0.546000\pi\) | |||||||
\(198\) | −2.38035 | −0.169164 | ||||||||
\(199\) | −2.51251 | −0.178107 | −0.0890536 | − | 0.996027i | \(-0.528384\pi\) | ||||
−0.0890536 | + | 0.996027i | \(0.528384\pi\) | |||||||
\(200\) | −0.776890 | −0.0549344 | ||||||||
\(201\) | −2.28881 | −0.161440 | ||||||||
\(202\) | 9.59434 | 0.675055 | ||||||||
\(203\) | 6.76897 | 0.475089 | ||||||||
\(204\) | 0.528942 | 0.0370334 | ||||||||
\(205\) | 19.7175 | 1.37713 | ||||||||
\(206\) | −10.7695 | −0.750348 | ||||||||
\(207\) | 4.49075 | 0.312128 | ||||||||
\(208\) | 6.36186 | 0.441116 | ||||||||
\(209\) | 3.76542 | 0.260459 | ||||||||
\(210\) | 3.23756 | 0.223413 | ||||||||
\(211\) | 5.25931 | 0.362066 | 0.181033 | − | 0.983477i | \(-0.442056\pi\) | ||||
0.181033 | + | 0.983477i | \(0.442056\pi\) | |||||||
\(212\) | 11.0584 | 0.759493 | ||||||||
\(213\) | −5.00627 | −0.343024 | ||||||||
\(214\) | 10.6939 | 0.731021 | ||||||||
\(215\) | 8.04733 | 0.548824 | ||||||||
\(216\) | 2.47111 | 0.168138 | ||||||||
\(217\) | 22.3198 | 1.51517 | ||||||||
\(218\) | 0.791338 | 0.0535962 | ||||||||
\(219\) | −6.44561 | −0.435554 | ||||||||
\(220\) | −1.73482 | −0.116961 | ||||||||
\(221\) | −7.92505 | −0.533097 | ||||||||
\(222\) | 0.862118 | 0.0578615 | ||||||||
\(223\) | 19.9512 | 1.33603 | 0.668016 | − | 0.744147i | \(-0.267144\pi\) | ||||
0.668016 | + | 0.744147i | \(0.267144\pi\) | |||||||
\(224\) | 3.71032 | 0.247906 | ||||||||
\(225\) | 2.19060 | 0.146040 | ||||||||
\(226\) | −1.79381 | −0.119323 | ||||||||
\(227\) | −28.2375 | −1.87419 | −0.937094 | − | 0.349078i | \(-0.886495\pi\) | ||||
−0.937094 | + | 0.349078i | \(0.886495\pi\) | |||||||
\(228\) | −1.89394 | −0.125429 | ||||||||
\(229\) | 23.7303 | 1.56814 | 0.784070 | − | 0.620672i | \(-0.213140\pi\) | ||||
0.784070 | + | 0.620672i | \(0.213140\pi\) | |||||||
\(230\) | 3.27289 | 0.215808 | ||||||||
\(231\) | −1.32996 | −0.0875051 | ||||||||
\(232\) | 1.82436 | 0.119775 | ||||||||
\(233\) | −1.53854 | −0.100793 | −0.0503966 | − | 0.998729i | \(-0.516049\pi\) | ||||
−0.0503966 | + | 0.998729i | \(0.516049\pi\) | |||||||
\(234\) | −17.9386 | −1.17268 | ||||||||
\(235\) | 21.4900 | 1.40185 | ||||||||
\(236\) | −9.42185 | −0.613310 | ||||||||
\(237\) | −3.79431 | −0.246467 | ||||||||
\(238\) | −4.62199 | −0.299599 | ||||||||
\(239\) | 27.6458 | 1.78826 | 0.894129 | − | 0.447810i | \(-0.147796\pi\) | ||||
0.894129 | + | 0.447810i | \(0.147796\pi\) | |||||||
\(240\) | 0.872583 | 0.0563250 | ||||||||
\(241\) | −22.7447 | −1.46512 | −0.732558 | − | 0.680705i | \(-0.761674\pi\) | ||||
−0.732558 | + | 0.680705i | \(0.761674\pi\) | |||||||
\(242\) | −10.2874 | −0.661296 | ||||||||
\(243\) | −10.5596 | −0.677400 | ||||||||
\(244\) | 4.44405 | 0.284501 | ||||||||
\(245\) | −13.9052 | −0.888371 | ||||||||
\(246\) | 4.07405 | 0.259752 | ||||||||
\(247\) | 28.3766 | 1.80556 | ||||||||
\(248\) | 6.01560 | 0.381991 | ||||||||
\(249\) | −2.97184 | −0.188333 | ||||||||
\(250\) | 11.8716 | 0.750828 | ||||||||
\(251\) | −15.3512 | −0.968960 | −0.484480 | − | 0.874802i | \(-0.660991\pi\) | ||||
−0.484480 | + | 0.874802i | \(0.660991\pi\) | |||||||
\(252\) | −10.4620 | −0.659044 | ||||||||
\(253\) | −1.34447 | −0.0845263 | ||||||||
\(254\) | 20.0409 | 1.25748 | ||||||||
\(255\) | −1.08699 | −0.0680698 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.0406 | −0.751070 | −0.375535 | − | 0.926808i | \(-0.622541\pi\) | ||||
−0.375535 | + | 0.926808i | \(0.622541\pi\) | |||||||
\(258\) | 1.66275 | 0.103518 | ||||||||
\(259\) | −7.53333 | −0.468098 | ||||||||
\(260\) | −13.0738 | −0.810800 | ||||||||
\(261\) | −5.14417 | −0.318416 | ||||||||
\(262\) | 0.607831 | 0.0375519 | ||||||||
\(263\) | 20.5239 | 1.26556 | 0.632780 | − | 0.774332i | \(-0.281914\pi\) | ||||
0.632780 | + | 0.774332i | \(0.281914\pi\) | |||||||
\(264\) | −0.358450 | −0.0220610 | ||||||||
\(265\) | −22.7252 | −1.39600 | ||||||||
\(266\) | 16.5496 | 1.01472 | ||||||||
\(267\) | 2.80308 | 0.171545 | ||||||||
\(268\) | 5.39038 | 0.329270 | ||||||||
\(269\) | 8.83023 | 0.538389 | 0.269194 | − | 0.963086i | \(-0.413243\pi\) | ||||
0.269194 | + | 0.963086i | \(0.413243\pi\) | |||||||
\(270\) | −5.07818 | −0.309048 | ||||||||
\(271\) | 19.0015 | 1.15426 | 0.577129 | − | 0.816653i | \(-0.304173\pi\) | ||||
0.577129 | + | 0.816653i | \(0.304173\pi\) | |||||||
\(272\) | −1.24571 | −0.0755324 | ||||||||
\(273\) | −10.0227 | −0.606603 | ||||||||
\(274\) | 10.6998 | 0.646399 | ||||||||
\(275\) | −0.655839 | −0.0395486 | ||||||||
\(276\) | 0.676247 | 0.0407053 | ||||||||
\(277\) | −28.2096 | −1.69495 | −0.847475 | − | 0.530835i | \(-0.821878\pi\) | ||||
−0.847475 | + | 0.530835i | \(0.821878\pi\) | |||||||
\(278\) | −15.1789 | −0.910369 | ||||||||
\(279\) | −16.9622 | −1.01550 | ||||||||
\(280\) | −7.62478 | −0.455668 | ||||||||
\(281\) | −16.1237 | −0.961860 | −0.480930 | − | 0.876759i | \(-0.659701\pi\) | ||||
−0.480930 | + | 0.876759i | \(0.659701\pi\) | |||||||
\(282\) | 4.44029 | 0.264415 | ||||||||
\(283\) | −26.7967 | −1.59290 | −0.796450 | − | 0.604705i | \(-0.793291\pi\) | ||||
−0.796450 | + | 0.604705i | \(0.793291\pi\) | |||||||
\(284\) | 11.7903 | 0.699623 | ||||||||
\(285\) | 3.89208 | 0.230547 | ||||||||
\(286\) | 5.37059 | 0.317570 | ||||||||
\(287\) | −35.5997 | −2.10139 | ||||||||
\(288\) | −2.81971 | −0.166153 | ||||||||
\(289\) | −15.4482 | −0.908718 | ||||||||
\(290\) | −3.74911 | −0.220155 | ||||||||
\(291\) | −5.11519 | −0.299858 | ||||||||
\(292\) | 15.1801 | 0.888346 | ||||||||
\(293\) | 7.13880 | 0.417053 | 0.208527 | − | 0.978017i | \(-0.433133\pi\) | ||||
0.208527 | + | 0.978017i | \(0.433133\pi\) | |||||||
\(294\) | −2.87311 | −0.167563 | ||||||||
\(295\) | 19.3621 | 1.12731 | ||||||||
\(296\) | −2.03037 | −0.118013 | ||||||||
\(297\) | 2.08607 | 0.121046 | ||||||||
\(298\) | 10.7807 | 0.624507 | ||||||||
\(299\) | −10.1321 | −0.585954 | ||||||||
\(300\) | 0.329876 | 0.0190454 | ||||||||
\(301\) | −14.5294 | −0.837459 | ||||||||
\(302\) | −20.7420 | −1.19357 | ||||||||
\(303\) | −4.07386 | −0.234037 | ||||||||
\(304\) | 4.46042 | 0.255822 | ||||||||
\(305\) | −9.13262 | −0.522932 | ||||||||
\(306\) | 3.51254 | 0.200799 | ||||||||
\(307\) | 5.40001 | 0.308195 | 0.154097 | − | 0.988056i | \(-0.450753\pi\) | ||||
0.154097 | + | 0.988056i | \(0.450753\pi\) | |||||||
\(308\) | 3.13219 | 0.178473 | ||||||||
\(309\) | 4.57285 | 0.260140 | ||||||||
\(310\) | −12.3622 | −0.702125 | ||||||||
\(311\) | 10.8282 | 0.614013 | 0.307006 | − | 0.951707i | \(-0.400673\pi\) | ||||
0.307006 | + | 0.951707i | \(0.400673\pi\) | |||||||
\(312\) | −2.70131 | −0.152932 | ||||||||
\(313\) | −7.97695 | −0.450884 | −0.225442 | − | 0.974257i | \(-0.572383\pi\) | ||||
−0.225442 | + | 0.974257i | \(0.572383\pi\) | |||||||
\(314\) | −0.0174066 | −0.000982311 0 | ||||||||
\(315\) | 21.4996 | 1.21137 | ||||||||
\(316\) | 8.93597 | 0.502688 | ||||||||
\(317\) | −13.2265 | −0.742874 | −0.371437 | − | 0.928458i | \(-0.621135\pi\) | ||||
−0.371437 | + | 0.928458i | \(0.621135\pi\) | |||||||
\(318\) | −4.69550 | −0.263311 | ||||||||
\(319\) | 1.54010 | 0.0862291 | ||||||||
\(320\) | −2.05502 | −0.114879 | ||||||||
\(321\) | −4.54075 | −0.253440 | ||||||||
\(322\) | −5.90916 | −0.329305 | ||||||||
\(323\) | −5.55640 | −0.309166 | ||||||||
\(324\) | 7.40986 | 0.411659 | ||||||||
\(325\) | −4.94247 | −0.274159 | ||||||||
\(326\) | −1.34937 | −0.0747348 | ||||||||
\(327\) | −0.336010 | −0.0185814 | ||||||||
\(328\) | −9.59480 | −0.529784 | ||||||||
\(329\) | −38.8000 | −2.13911 | ||||||||
\(330\) | 0.736621 | 0.0405497 | ||||||||
\(331\) | −15.2737 | −0.839518 | −0.419759 | − | 0.907636i | \(-0.637885\pi\) | ||||
−0.419759 | + | 0.907636i | \(0.637885\pi\) | |||||||
\(332\) | 6.99898 | 0.384119 | ||||||||
\(333\) | 5.72506 | 0.313731 | ||||||||
\(334\) | −6.95361 | −0.380484 | ||||||||
\(335\) | −11.0773 | −0.605220 | ||||||||
\(336\) | −1.57544 | −0.0859472 | ||||||||
\(337\) | −25.7109 | −1.40056 | −0.700281 | − | 0.713867i | \(-0.746942\pi\) | ||||
−0.700281 | + | 0.713867i | \(0.746942\pi\) | |||||||
\(338\) | 27.4733 | 1.49435 | ||||||||
\(339\) | 0.761671 | 0.0413683 | ||||||||
\(340\) | 2.55997 | 0.138834 | ||||||||
\(341\) | 5.07828 | 0.275004 | ||||||||
\(342\) | −12.5771 | −0.680090 | ||||||||
\(343\) | −0.866531 | −0.0467883 | ||||||||
\(344\) | −3.91594 | −0.211133 | ||||||||
\(345\) | −1.38970 | −0.0748190 | ||||||||
\(346\) | −2.24992 | −0.120956 | ||||||||
\(347\) | −11.3063 | −0.606952 | −0.303476 | − | 0.952839i | \(-0.598147\pi\) | ||||
−0.303476 | + | 0.952839i | \(0.598147\pi\) | |||||||
\(348\) | −0.774644 | −0.0415253 | ||||||||
\(349\) | 16.2197 | 0.868219 | 0.434110 | − | 0.900860i | \(-0.357063\pi\) | ||||
0.434110 | + | 0.900860i | \(0.357063\pi\) | |||||||
\(350\) | −2.88251 | −0.154077 | ||||||||
\(351\) | 15.7208 | 0.839117 | ||||||||
\(352\) | 0.844185 | 0.0449952 | ||||||||
\(353\) | 29.6415 | 1.57766 | 0.788828 | − | 0.614614i | \(-0.210688\pi\) | ||||
0.788828 | + | 0.614614i | \(0.210688\pi\) | |||||||
\(354\) | 4.00062 | 0.212630 | ||||||||
\(355\) | −24.2292 | −1.28595 | ||||||||
\(356\) | −6.60152 | −0.349880 | ||||||||
\(357\) | 1.96254 | 0.103869 | ||||||||
\(358\) | −0.0932950 | −0.00493079 | ||||||||
\(359\) | 20.3512 | 1.07409 | 0.537046 | − | 0.843553i | \(-0.319540\pi\) | ||||
0.537046 | + | 0.843553i | \(0.319540\pi\) | |||||||
\(360\) | 5.79455 | 0.305400 | ||||||||
\(361\) | 0.895308 | 0.0471215 | ||||||||
\(362\) | 21.7581 | 1.14358 | ||||||||
\(363\) | 4.36812 | 0.229267 | ||||||||
\(364\) | 23.6045 | 1.23721 | ||||||||
\(365\) | −31.1953 | −1.63284 | ||||||||
\(366\) | −1.88699 | −0.0986346 | ||||||||
\(367\) | 21.3358 | 1.11372 | 0.556860 | − | 0.830606i | \(-0.312006\pi\) | ||||
0.556860 | + | 0.830606i | \(0.312006\pi\) | |||||||
\(368\) | −1.59263 | −0.0830215 | ||||||||
\(369\) | 27.0545 | 1.40840 | ||||||||
\(370\) | 4.17246 | 0.216916 | ||||||||
\(371\) | 41.0301 | 2.13018 | ||||||||
\(372\) | −2.55428 | −0.132434 | ||||||||
\(373\) | −31.0301 | −1.60668 | −0.803339 | − | 0.595523i | \(-0.796945\pi\) | ||||
−0.803339 | + | 0.595523i | \(0.796945\pi\) | |||||||
\(374\) | −1.05161 | −0.0543775 | ||||||||
\(375\) | −5.04082 | −0.260307 | ||||||||
\(376\) | −10.4573 | −0.539295 | ||||||||
\(377\) | 11.6064 | 0.597758 | ||||||||
\(378\) | 9.16859 | 0.471581 | ||||||||
\(379\) | −4.29950 | −0.220850 | −0.110425 | − | 0.993884i | \(-0.535221\pi\) | ||||
−0.110425 | + | 0.993884i | \(0.535221\pi\) | |||||||
\(380\) | −9.16625 | −0.470219 | ||||||||
\(381\) | −8.50957 | −0.435958 | ||||||||
\(382\) | −6.28030 | −0.321328 | ||||||||
\(383\) | −1.37802 | −0.0704134 | −0.0352067 | − | 0.999380i | \(-0.511209\pi\) | ||||
−0.0352067 | + | 0.999380i | \(0.511209\pi\) | |||||||
\(384\) | −0.424610 | −0.0216683 | ||||||||
\(385\) | −6.43672 | −0.328046 | ||||||||
\(386\) | −14.0894 | −0.717130 | ||||||||
\(387\) | 11.0418 | 0.561286 | ||||||||
\(388\) | 12.0468 | 0.611584 | ||||||||
\(389\) | 30.2447 | 1.53347 | 0.766734 | − | 0.641964i | \(-0.221880\pi\) | ||||
0.766734 | + | 0.641964i | \(0.221880\pi\) | |||||||
\(390\) | 5.55125 | 0.281099 | ||||||||
\(391\) | 1.98396 | 0.100333 | ||||||||
\(392\) | 6.76645 | 0.341758 | ||||||||
\(393\) | −0.258091 | −0.0130190 | ||||||||
\(394\) | −4.04257 | −0.203662 | ||||||||
\(395\) | −18.3636 | −0.923974 | ||||||||
\(396\) | −2.38035 | −0.119617 | ||||||||
\(397\) | 36.3903 | 1.82638 | 0.913188 | − | 0.407538i | \(-0.133612\pi\) | ||||
0.913188 | + | 0.407538i | \(0.133612\pi\) | |||||||
\(398\) | −2.51251 | −0.125941 | ||||||||
\(399\) | −7.02711 | −0.351796 | ||||||||
\(400\) | −0.776890 | −0.0388445 | ||||||||
\(401\) | 34.3590 | 1.71581 | 0.857904 | − | 0.513810i | \(-0.171766\pi\) | ||||
0.857904 | + | 0.513810i | \(0.171766\pi\) | |||||||
\(402\) | −2.28881 | −0.114156 | ||||||||
\(403\) | 38.2704 | 1.90639 | ||||||||
\(404\) | 9.59434 | 0.477336 | ||||||||
\(405\) | −15.2274 | −0.756656 | ||||||||
\(406\) | 6.76897 | 0.335938 | ||||||||
\(407\) | −1.71401 | −0.0849604 | ||||||||
\(408\) | 0.528942 | 0.0261866 | ||||||||
\(409\) | 18.4837 | 0.913961 | 0.456981 | − | 0.889477i | \(-0.348931\pi\) | ||||
0.456981 | + | 0.889477i | \(0.348931\pi\) | |||||||
\(410\) | 19.7175 | 0.973778 | ||||||||
\(411\) | −4.54325 | −0.224102 | ||||||||
\(412\) | −10.7695 | −0.530576 | ||||||||
\(413\) | −34.9581 | −1.72017 | ||||||||
\(414\) | 4.49075 | 0.220708 | ||||||||
\(415\) | −14.3830 | −0.706036 | ||||||||
\(416\) | 6.36186 | 0.311916 | ||||||||
\(417\) | 6.44511 | 0.315619 | ||||||||
\(418\) | 3.76542 | 0.184172 | ||||||||
\(419\) | 25.5378 | 1.24760 | 0.623801 | − | 0.781583i | \(-0.285588\pi\) | ||||
0.623801 | + | 0.781583i | \(0.285588\pi\) | |||||||
\(420\) | 3.23756 | 0.157977 | ||||||||
\(421\) | 30.4856 | 1.48578 | 0.742888 | − | 0.669416i | \(-0.233455\pi\) | ||||
0.742888 | + | 0.669416i | \(0.233455\pi\) | |||||||
\(422\) | 5.25931 | 0.256019 | ||||||||
\(423\) | 29.4866 | 1.43369 | ||||||||
\(424\) | 11.0584 | 0.537043 | ||||||||
\(425\) | 0.967782 | 0.0469443 | ||||||||
\(426\) | −5.00627 | −0.242554 | ||||||||
\(427\) | 16.4888 | 0.797951 | ||||||||
\(428\) | 10.6939 | 0.516910 | ||||||||
\(429\) | −2.28041 | −0.110099 | ||||||||
\(430\) | 8.04733 | 0.388077 | ||||||||
\(431\) | 3.38191 | 0.162901 | 0.0814505 | − | 0.996677i | \(-0.474045\pi\) | ||||
0.0814505 | + | 0.996677i | \(0.474045\pi\) | |||||||
\(432\) | 2.47111 | 0.118891 | ||||||||
\(433\) | 19.2457 | 0.924891 | 0.462445 | − | 0.886648i | \(-0.346972\pi\) | ||||
0.462445 | + | 0.886648i | \(0.346972\pi\) | |||||||
\(434\) | 22.3198 | 1.07138 | ||||||||
\(435\) | 1.59191 | 0.0763262 | ||||||||
\(436\) | 0.791338 | 0.0378982 | ||||||||
\(437\) | −7.10379 | −0.339820 | ||||||||
\(438\) | −6.44561 | −0.307983 | ||||||||
\(439\) | −38.1157 | −1.81916 | −0.909582 | − | 0.415525i | \(-0.863598\pi\) | ||||
−0.909582 | + | 0.415525i | \(0.863598\pi\) | |||||||
\(440\) | −1.73482 | −0.0827042 | ||||||||
\(441\) | −19.0794 | −0.908543 | ||||||||
\(442\) | −7.92505 | −0.376956 | ||||||||
\(443\) | −39.9123 | −1.89629 | −0.948145 | − | 0.317838i | \(-0.897043\pi\) | ||||
−0.948145 | + | 0.317838i | \(0.897043\pi\) | |||||||
\(444\) | 0.862118 | 0.0409143 | ||||||||
\(445\) | 13.5663 | 0.643103 | ||||||||
\(446\) | 19.9512 | 0.944717 | ||||||||
\(447\) | −4.57758 | −0.216512 | ||||||||
\(448\) | 3.71032 | 0.175296 | ||||||||
\(449\) | −20.8390 | −0.983455 | −0.491728 | − | 0.870749i | \(-0.663634\pi\) | ||||
−0.491728 | + | 0.870749i | \(0.663634\pi\) | |||||||
\(450\) | 2.19060 | 0.103266 | ||||||||
\(451\) | −8.09978 | −0.381404 | ||||||||
\(452\) | −1.79381 | −0.0843738 | ||||||||
\(453\) | 8.80727 | 0.413802 | ||||||||
\(454\) | −28.2375 | −1.32525 | ||||||||
\(455\) | −48.5078 | −2.27408 | ||||||||
\(456\) | −1.89394 | −0.0886918 | ||||||||
\(457\) | −28.9031 | −1.35203 | −0.676014 | − | 0.736889i | \(-0.736294\pi\) | ||||
−0.676014 | + | 0.736889i | \(0.736294\pi\) | |||||||
\(458\) | 23.7303 | 1.10884 | ||||||||
\(459\) | −3.07829 | −0.143682 | ||||||||
\(460\) | 3.27289 | 0.152599 | ||||||||
\(461\) | −27.8908 | −1.29900 | −0.649501 | − | 0.760360i | \(-0.725022\pi\) | ||||
−0.649501 | + | 0.760360i | \(0.725022\pi\) | |||||||
\(462\) | −1.32996 | −0.0618754 | ||||||||
\(463\) | −14.6630 | −0.681448 | −0.340724 | − | 0.940163i | \(-0.610672\pi\) | ||||
−0.340724 | + | 0.940163i | \(0.610672\pi\) | |||||||
\(464\) | 1.82436 | 0.0846940 | ||||||||
\(465\) | 5.24911 | 0.243422 | ||||||||
\(466\) | −1.53854 | −0.0712715 | ||||||||
\(467\) | −15.9437 | −0.737785 | −0.368892 | − | 0.929472i | \(-0.620263\pi\) | ||||
−0.368892 | + | 0.929472i | \(0.620263\pi\) | |||||||
\(468\) | −17.9386 | −0.829211 | ||||||||
\(469\) | 20.0000 | 0.923516 | ||||||||
\(470\) | 21.4900 | 0.991260 | ||||||||
\(471\) | 0.00739102 | 0.000340560 0 | ||||||||
\(472\) | −9.42185 | −0.433676 | ||||||||
\(473\) | −3.30578 | −0.152000 | ||||||||
\(474\) | −3.79431 | −0.174278 | ||||||||
\(475\) | −3.46525 | −0.158997 | ||||||||
\(476\) | −4.62199 | −0.211849 | ||||||||
\(477\) | −31.1814 | −1.42770 | ||||||||
\(478\) | 27.6458 | 1.26449 | ||||||||
\(479\) | −26.9483 | −1.23130 | −0.615650 | − | 0.788020i | \(-0.711107\pi\) | ||||
−0.615650 | + | 0.788020i | \(0.711107\pi\) | |||||||
\(480\) | 0.872583 | 0.0398278 | ||||||||
\(481\) | −12.9170 | −0.588963 | ||||||||
\(482\) | −22.7447 | −1.03599 | ||||||||
\(483\) | 2.50909 | 0.114168 | ||||||||
\(484\) | −10.2874 | −0.467607 | ||||||||
\(485\) | −24.7564 | −1.12413 | ||||||||
\(486\) | −10.5596 | −0.478994 | ||||||||
\(487\) | −19.0499 | −0.863235 | −0.431617 | − | 0.902057i | \(-0.642057\pi\) | ||||
−0.431617 | + | 0.902057i | \(0.642057\pi\) | |||||||
\(488\) | 4.44405 | 0.201173 | ||||||||
\(489\) | 0.572957 | 0.0259100 | ||||||||
\(490\) | −13.9052 | −0.628173 | ||||||||
\(491\) | −7.88816 | −0.355988 | −0.177994 | − | 0.984032i | \(-0.556961\pi\) | ||||
−0.177994 | + | 0.984032i | \(0.556961\pi\) | |||||||
\(492\) | 4.07405 | 0.183672 | ||||||||
\(493\) | −2.27263 | −0.102354 | ||||||||
\(494\) | 28.3766 | 1.27672 | ||||||||
\(495\) | 4.89167 | 0.219864 | ||||||||
\(496\) | 6.01560 | 0.270108 | ||||||||
\(497\) | 43.7456 | 1.96226 | ||||||||
\(498\) | −2.97184 | −0.133171 | ||||||||
\(499\) | −18.1973 | −0.814621 | −0.407310 | − | 0.913290i | \(-0.633533\pi\) | ||||
−0.407310 | + | 0.913290i | \(0.633533\pi\) | |||||||
\(500\) | 11.8716 | 0.530915 | ||||||||
\(501\) | 2.95257 | 0.131911 | ||||||||
\(502\) | −15.3512 | −0.685158 | ||||||||
\(503\) | −5.19012 | −0.231416 | −0.115708 | − | 0.993283i | \(-0.536914\pi\) | ||||
−0.115708 | + | 0.993283i | \(0.536914\pi\) | |||||||
\(504\) | −10.4620 | −0.466015 | ||||||||
\(505\) | −19.7166 | −0.877376 | ||||||||
\(506\) | −1.34447 | −0.0597691 | ||||||||
\(507\) | −11.6655 | −0.518081 | ||||||||
\(508\) | 20.0409 | 0.889171 | ||||||||
\(509\) | −2.49385 | −0.110538 | −0.0552689 | − | 0.998472i | \(-0.517602\pi\) | ||||
−0.0552689 | + | 0.998472i | \(0.517602\pi\) | |||||||
\(510\) | −1.08699 | −0.0481326 | ||||||||
\(511\) | 56.3228 | 2.49158 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 11.0222 | 0.486640 | ||||||||
\(514\) | −12.0406 | −0.531086 | ||||||||
\(515\) | 22.1316 | 0.975234 | ||||||||
\(516\) | 1.66275 | 0.0731984 | ||||||||
\(517\) | −8.82791 | −0.388251 | ||||||||
\(518\) | −7.53333 | −0.330996 | ||||||||
\(519\) | 0.955339 | 0.0419347 | ||||||||
\(520\) | −13.0738 | −0.573322 | ||||||||
\(521\) | 16.8407 | 0.737802 | 0.368901 | − | 0.929469i | \(-0.379734\pi\) | ||||
0.368901 | + | 0.929469i | \(0.379734\pi\) | |||||||
\(522\) | −5.14417 | −0.225154 | ||||||||
\(523\) | 1.12989 | 0.0494065 | 0.0247033 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247033 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(524\) | 0.607831 | 0.0265532 | ||||||||
\(525\) | 1.22394 | 0.0534173 | ||||||||
\(526\) | 20.5239 | 0.894886 | ||||||||
\(527\) | −7.49371 | −0.326431 | ||||||||
\(528\) | −0.358450 | −0.0155995 | ||||||||
\(529\) | −20.4635 | −0.889719 | ||||||||
\(530\) | −22.7252 | −0.987120 | ||||||||
\(531\) | 26.5669 | 1.15290 | ||||||||
\(532\) | 16.5496 | 0.717514 | ||||||||
\(533\) | −61.0408 | −2.64397 | ||||||||
\(534\) | 2.80308 | 0.121301 | ||||||||
\(535\) | −21.9762 | −0.950115 | ||||||||
\(536\) | 5.39038 | 0.232829 | ||||||||
\(537\) | 0.0396140 | 0.00170947 | ||||||||
\(538\) | 8.83023 | 0.380698 | ||||||||
\(539\) | 5.71214 | 0.246039 | ||||||||
\(540\) | −5.07818 | −0.218530 | ||||||||
\(541\) | −8.88136 | −0.381839 | −0.190920 | − | 0.981606i | \(-0.561147\pi\) | ||||
−0.190920 | + | 0.981606i | \(0.561147\pi\) | |||||||
\(542\) | 19.0015 | 0.816183 | ||||||||
\(543\) | −9.23873 | −0.396472 | ||||||||
\(544\) | −1.24571 | −0.0534095 | ||||||||
\(545\) | −1.62622 | −0.0696595 | ||||||||
\(546\) | −10.0227 | −0.428933 | ||||||||
\(547\) | −16.4258 | −0.702315 | −0.351157 | − | 0.936316i | \(-0.614212\pi\) | ||||
−0.351157 | + | 0.936316i | \(0.614212\pi\) | |||||||
\(548\) | 10.6998 | 0.457073 | ||||||||
\(549\) | −12.5309 | −0.534807 | ||||||||
\(550\) | −0.655839 | −0.0279651 | ||||||||
\(551\) | 8.13742 | 0.346666 | ||||||||
\(552\) | 0.676247 | 0.0287830 | ||||||||
\(553\) | 33.1553 | 1.40991 | ||||||||
\(554\) | −28.2096 | −1.19851 | ||||||||
\(555\) | −1.77167 | −0.0752032 | ||||||||
\(556\) | −15.1789 | −0.643728 | ||||||||
\(557\) | −33.2856 | −1.41036 | −0.705178 | − | 0.709030i | \(-0.749133\pi\) | ||||
−0.705178 | + | 0.709030i | \(0.749133\pi\) | |||||||
\(558\) | −16.9622 | −0.718068 | ||||||||
\(559\) | −24.9127 | −1.05369 | ||||||||
\(560\) | −7.62478 | −0.322206 | ||||||||
\(561\) | 0.446525 | 0.0188523 | ||||||||
\(562\) | −16.1237 | −0.680138 | ||||||||
\(563\) | 11.8854 | 0.500910 | 0.250455 | − | 0.968128i | \(-0.419420\pi\) | ||||
0.250455 | + | 0.968128i | \(0.419420\pi\) | |||||||
\(564\) | 4.44029 | 0.186970 | ||||||||
\(565\) | 3.68632 | 0.155085 | ||||||||
\(566\) | −26.7967 | −1.12635 | ||||||||
\(567\) | 27.4929 | 1.15459 | ||||||||
\(568\) | 11.7903 | 0.494708 | ||||||||
\(569\) | −45.9701 | −1.92717 | −0.963584 | − | 0.267405i | \(-0.913834\pi\) | ||||
−0.963584 | + | 0.267405i | \(0.913834\pi\) | |||||||
\(570\) | 3.89208 | 0.163021 | ||||||||
\(571\) | 40.9461 | 1.71354 | 0.856770 | − | 0.515699i | \(-0.172468\pi\) | ||||
0.856770 | + | 0.515699i | \(0.172468\pi\) | |||||||
\(572\) | 5.37059 | 0.224556 | ||||||||
\(573\) | 2.66668 | 0.111402 | ||||||||
\(574\) | −35.5997 | −1.48590 | ||||||||
\(575\) | 1.23730 | 0.0515989 | ||||||||
\(576\) | −2.81971 | −0.117488 | ||||||||
\(577\) | −37.8734 | −1.57669 | −0.788345 | − | 0.615233i | \(-0.789062\pi\) | ||||
−0.788345 | + | 0.615233i | \(0.789062\pi\) | |||||||
\(578\) | −15.4482 | −0.642560 | ||||||||
\(579\) | 5.98249 | 0.248624 | ||||||||
\(580\) | −3.74911 | −0.155673 | ||||||||
\(581\) | 25.9684 | 1.07735 | ||||||||
\(582\) | −5.11519 | −0.212032 | ||||||||
\(583\) | 9.33532 | 0.386629 | ||||||||
\(584\) | 15.1801 | 0.628155 | ||||||||
\(585\) | 36.8642 | 1.52415 | ||||||||
\(586\) | 7.13880 | 0.294901 | ||||||||
\(587\) | −23.4310 | −0.967099 | −0.483550 | − | 0.875317i | \(-0.660653\pi\) | ||||
−0.483550 | + | 0.875317i | \(0.660653\pi\) | |||||||
\(588\) | −2.87311 | −0.118485 | ||||||||
\(589\) | 26.8321 | 1.10560 | ||||||||
\(590\) | 19.3621 | 0.797125 | ||||||||
\(591\) | 1.71652 | 0.0706081 | ||||||||
\(592\) | −2.03037 | −0.0834478 | ||||||||
\(593\) | 7.64818 | 0.314073 | 0.157036 | − | 0.987593i | \(-0.449806\pi\) | ||||
0.157036 | + | 0.987593i | \(0.449806\pi\) | |||||||
\(594\) | 2.08607 | 0.0855925 | ||||||||
\(595\) | 9.49828 | 0.389392 | ||||||||
\(596\) | 10.7807 | 0.441593 | ||||||||
\(597\) | 1.06684 | 0.0436628 | ||||||||
\(598\) | −10.1321 | −0.414332 | ||||||||
\(599\) | −23.7044 | −0.968535 | −0.484268 | − | 0.874920i | \(-0.660914\pi\) | ||||
−0.484268 | + | 0.874920i | \(0.660914\pi\) | |||||||
\(600\) | 0.329876 | 0.0134671 | ||||||||
\(601\) | −29.9557 | −1.22192 | −0.610959 | − | 0.791662i | \(-0.709216\pi\) | ||||
−0.610959 | + | 0.791662i | \(0.709216\pi\) | |||||||
\(602\) | −14.5294 | −0.592173 | ||||||||
\(603\) | −15.1993 | −0.618963 | ||||||||
\(604\) | −20.7420 | −0.843981 | ||||||||
\(605\) | 21.1407 | 0.859492 | ||||||||
\(606\) | −4.07386 | −0.165489 | ||||||||
\(607\) | 25.9893 | 1.05487 | 0.527437 | − | 0.849594i | \(-0.323153\pi\) | ||||
0.527437 | + | 0.849594i | \(0.323153\pi\) | |||||||
\(608\) | 4.46042 | 0.180894 | ||||||||
\(609\) | −2.87417 | −0.116467 | ||||||||
\(610\) | −9.13262 | −0.369769 | ||||||||
\(611\) | −66.5280 | −2.69144 | ||||||||
\(612\) | 3.51254 | 0.141986 | ||||||||
\(613\) | −12.3380 | −0.498326 | −0.249163 | − | 0.968462i | \(-0.580155\pi\) | ||||
−0.249163 | + | 0.968462i | \(0.580155\pi\) | |||||||
\(614\) | 5.40001 | 0.217927 | ||||||||
\(615\) | −8.37226 | −0.337602 | ||||||||
\(616\) | 3.13219 | 0.126200 | ||||||||
\(617\) | −1.04812 | −0.0421958 | −0.0210979 | − | 0.999777i | \(-0.506716\pi\) | ||||
−0.0210979 | + | 0.999777i | \(0.506716\pi\) | |||||||
\(618\) | 4.57285 | 0.183947 | ||||||||
\(619\) | −38.7536 | −1.55764 | −0.778819 | − | 0.627249i | \(-0.784181\pi\) | ||||
−0.778819 | + | 0.627249i | \(0.784181\pi\) | |||||||
\(620\) | −12.3622 | −0.496477 | ||||||||
\(621\) | −3.93556 | −0.157929 | ||||||||
\(622\) | 10.8282 | 0.434173 | ||||||||
\(623\) | −24.4937 | −0.981321 | ||||||||
\(624\) | −2.70131 | −0.108139 | ||||||||
\(625\) | −20.5120 | −0.820480 | ||||||||
\(626\) | −7.97695 | −0.318823 | ||||||||
\(627\) | −1.59883 | −0.0638513 | ||||||||
\(628\) | −0.0174066 | −0.000694599 0 | ||||||||
\(629\) | 2.52926 | 0.100848 | ||||||||
\(630\) | 21.4996 | 0.856566 | ||||||||
\(631\) | −14.2614 | −0.567738 | −0.283869 | − | 0.958863i | \(-0.591618\pi\) | ||||
−0.283869 | + | 0.958863i | \(0.591618\pi\) | |||||||
\(632\) | 8.93597 | 0.355454 | ||||||||
\(633\) | −2.23316 | −0.0887599 | ||||||||
\(634\) | −13.2265 | −0.525291 | ||||||||
\(635\) | −41.1844 | −1.63435 | ||||||||
\(636\) | −4.69550 | −0.186189 | ||||||||
\(637\) | 43.0473 | 1.70559 | ||||||||
\(638\) | 1.54010 | 0.0609732 | ||||||||
\(639\) | −33.2451 | −1.31515 | ||||||||
\(640\) | −2.05502 | −0.0812318 | ||||||||
\(641\) | 21.9342 | 0.866350 | 0.433175 | − | 0.901310i | \(-0.357393\pi\) | ||||
0.433175 | + | 0.901310i | \(0.357393\pi\) | |||||||
\(642\) | −4.54075 | −0.179209 | ||||||||
\(643\) | 26.5916 | 1.04867 | 0.524336 | − | 0.851511i | \(-0.324314\pi\) | ||||
0.524336 | + | 0.851511i | \(0.324314\pi\) | |||||||
\(644\) | −5.90916 | −0.232854 | ||||||||
\(645\) | −3.41698 | −0.134543 | ||||||||
\(646\) | −5.55640 | −0.218613 | ||||||||
\(647\) | 25.1098 | 0.987169 | 0.493584 | − | 0.869698i | \(-0.335686\pi\) | ||||
0.493584 | + | 0.869698i | \(0.335686\pi\) | |||||||
\(648\) | 7.40986 | 0.291087 | ||||||||
\(649\) | −7.95379 | −0.312213 | ||||||||
\(650\) | −4.94247 | −0.193860 | ||||||||
\(651\) | −9.47721 | −0.371441 | ||||||||
\(652\) | −1.34937 | −0.0528455 | ||||||||
\(653\) | 21.4459 | 0.839244 | 0.419622 | − | 0.907699i | \(-0.362163\pi\) | ||||
0.419622 | + | 0.907699i | \(0.362163\pi\) | |||||||
\(654\) | −0.336010 | −0.0131390 | ||||||||
\(655\) | −1.24911 | −0.0488066 | ||||||||
\(656\) | −9.59480 | −0.374614 | ||||||||
\(657\) | −42.8033 | −1.66992 | ||||||||
\(658\) | −38.8000 | −1.51258 | ||||||||
\(659\) | 27.7830 | 1.08227 | 0.541136 | − | 0.840935i | \(-0.317994\pi\) | ||||
0.541136 | + | 0.840935i | \(0.317994\pi\) | |||||||
\(660\) | 0.736621 | 0.0286729 | ||||||||
\(661\) | 16.5641 | 0.644270 | 0.322135 | − | 0.946694i | \(-0.395599\pi\) | ||||
0.322135 | + | 0.946694i | \(0.395599\pi\) | |||||||
\(662\) | −15.2737 | −0.593629 | ||||||||
\(663\) | 3.36506 | 0.130688 | ||||||||
\(664\) | 6.99898 | 0.271613 | ||||||||
\(665\) | −34.0097 | −1.31884 | ||||||||
\(666\) | 5.72506 | 0.221841 | ||||||||
\(667\) | −2.90554 | −0.112503 | ||||||||
\(668\) | −6.95361 | −0.269043 | ||||||||
\(669\) | −8.47149 | −0.327527 | ||||||||
\(670\) | −11.0773 | −0.427955 | ||||||||
\(671\) | 3.75160 | 0.144829 | ||||||||
\(672\) | −1.57544 | −0.0607739 | ||||||||
\(673\) | 4.93101 | 0.190076 | 0.0950382 | − | 0.995474i | \(-0.469703\pi\) | ||||
0.0950382 | + | 0.995474i | \(0.469703\pi\) | |||||||
\(674\) | −25.7109 | −0.990347 | ||||||||
\(675\) | −1.91978 | −0.0738923 | ||||||||
\(676\) | 27.4733 | 1.05667 | ||||||||
\(677\) | −21.5899 | −0.829766 | −0.414883 | − | 0.909875i | \(-0.636177\pi\) | ||||
−0.414883 | + | 0.909875i | \(0.636177\pi\) | |||||||
\(678\) | 0.761671 | 0.0292518 | ||||||||
\(679\) | 44.6974 | 1.71533 | ||||||||
\(680\) | 2.55997 | 0.0981702 | ||||||||
\(681\) | 11.9899 | 0.459455 | ||||||||
\(682\) | 5.07828 | 0.194457 | ||||||||
\(683\) | −18.7222 | −0.716385 | −0.358192 | − | 0.933648i | \(-0.616607\pi\) | ||||
−0.358192 | + | 0.933648i | \(0.616607\pi\) | |||||||
\(684\) | −12.5771 | −0.480896 | ||||||||
\(685\) | −21.9883 | −0.840131 | ||||||||
\(686\) | −0.866531 | −0.0330843 | ||||||||
\(687\) | −10.0761 | −0.384428 | ||||||||
\(688\) | −3.91594 | −0.149294 | ||||||||
\(689\) | 70.3519 | 2.68020 | ||||||||
\(690\) | −1.38970 | −0.0529050 | ||||||||
\(691\) | −20.8934 | −0.794822 | −0.397411 | − | 0.917641i | \(-0.630091\pi\) | ||||
−0.397411 | + | 0.917641i | \(0.630091\pi\) | |||||||
\(692\) | −2.24992 | −0.0855291 | ||||||||
\(693\) | −8.83187 | −0.335495 | ||||||||
\(694\) | −11.3063 | −0.429180 | ||||||||
\(695\) | 31.1929 | 1.18322 | ||||||||
\(696\) | −0.774644 | −0.0293628 | ||||||||
\(697\) | 11.9524 | 0.452728 | ||||||||
\(698\) | 16.2197 | 0.613924 | ||||||||
\(699\) | 0.653280 | 0.0247093 | ||||||||
\(700\) | −2.88251 | −0.108949 | ||||||||
\(701\) | −36.4697 | −1.37744 | −0.688721 | − | 0.725026i | \(-0.741828\pi\) | ||||
−0.688721 | + | 0.725026i | \(0.741828\pi\) | |||||||
\(702\) | 15.7208 | 0.593345 | ||||||||
\(703\) | −9.05631 | −0.341565 | ||||||||
\(704\) | 0.844185 | 0.0318164 | ||||||||
\(705\) | −9.12488 | −0.343663 | ||||||||
\(706\) | 29.6415 | 1.11557 | ||||||||
\(707\) | 35.5980 | 1.33880 | ||||||||
\(708\) | 4.00062 | 0.150352 | ||||||||
\(709\) | 24.8416 | 0.932944 | 0.466472 | − | 0.884536i | \(-0.345525\pi\) | ||||
0.466472 | + | 0.884536i | \(0.345525\pi\) | |||||||
\(710\) | −24.2292 | −0.909307 | ||||||||
\(711\) | −25.1968 | −0.944955 | ||||||||
\(712\) | −6.60152 | −0.247403 | ||||||||
\(713\) | −9.58062 | −0.358797 | ||||||||
\(714\) | 1.96254 | 0.0734464 | ||||||||
\(715\) | −11.0367 | −0.412748 | ||||||||
\(716\) | −0.0932950 | −0.00348660 | ||||||||
\(717\) | −11.7387 | −0.438389 | ||||||||
\(718\) | 20.3512 | 0.759498 | ||||||||
\(719\) | 4.48805 | 0.167376 | 0.0836879 | − | 0.996492i | \(-0.473330\pi\) | ||||
0.0836879 | + | 0.996492i | \(0.473330\pi\) | |||||||
\(720\) | 5.79455 | 0.215950 | ||||||||
\(721\) | −39.9583 | −1.48813 | ||||||||
\(722\) | 0.895308 | 0.0333199 | ||||||||
\(723\) | 9.65764 | 0.359171 | ||||||||
\(724\) | 21.7581 | 0.808635 | ||||||||
\(725\) | −1.41733 | −0.0526383 | ||||||||
\(726\) | 4.36812 | 0.162116 | ||||||||
\(727\) | 6.63570 | 0.246105 | 0.123052 | − | 0.992400i | \(-0.460732\pi\) | ||||
0.123052 | + | 0.992400i | \(0.460732\pi\) | |||||||
\(728\) | 23.6045 | 0.874842 | ||||||||
\(729\) | −17.7459 | −0.657254 | ||||||||
\(730\) | −31.1953 | −1.15459 | ||||||||
\(731\) | 4.87813 | 0.180424 | ||||||||
\(732\) | −1.88699 | −0.0697452 | ||||||||
\(733\) | −48.1406 | −1.77811 | −0.889056 | − | 0.457799i | \(-0.848638\pi\) | ||||
−0.889056 | + | 0.457799i | \(0.848638\pi\) | |||||||
\(734\) | 21.3358 | 0.787519 | ||||||||
\(735\) | 5.90429 | 0.217783 | ||||||||
\(736\) | −1.59263 | −0.0587051 | ||||||||
\(737\) | 4.55048 | 0.167619 | ||||||||
\(738\) | 27.0545 | 0.995890 | ||||||||
\(739\) | 51.5187 | 1.89515 | 0.947574 | − | 0.319537i | \(-0.103527\pi\) | ||||
0.947574 | + | 0.319537i | \(0.103527\pi\) | |||||||
\(740\) | 4.17246 | 0.153383 | ||||||||
\(741\) | −12.0490 | −0.442630 | ||||||||
\(742\) | 41.0301 | 1.50626 | ||||||||
\(743\) | 53.1507 | 1.94991 | 0.974956 | − | 0.222398i | \(-0.0713885\pi\) | ||||
0.974956 | + | 0.222398i | \(0.0713885\pi\) | |||||||
\(744\) | −2.55428 | −0.0936446 | ||||||||
\(745\) | −22.1545 | −0.811677 | ||||||||
\(746\) | −31.0301 | −1.13609 | ||||||||
\(747\) | −19.7351 | −0.722068 | ||||||||
\(748\) | −1.05161 | −0.0384507 | ||||||||
\(749\) | 39.6778 | 1.44980 | ||||||||
\(750\) | −5.04082 | −0.184065 | ||||||||
\(751\) | −13.0622 | −0.476647 | −0.238324 | − | 0.971186i | \(-0.576598\pi\) | ||||
−0.238324 | + | 0.971186i | \(0.576598\pi\) | |||||||
\(752\) | −10.4573 | −0.381339 | ||||||||
\(753\) | 6.51828 | 0.237539 | ||||||||
\(754\) | 11.6064 | 0.422679 | ||||||||
\(755\) | 42.6253 | 1.55129 | ||||||||
\(756\) | 9.16859 | 0.333458 | ||||||||
\(757\) | −22.6331 | −0.822615 | −0.411308 | − | 0.911497i | \(-0.634928\pi\) | ||||
−0.411308 | + | 0.911497i | \(0.634928\pi\) | |||||||
\(758\) | −4.29950 | −0.156165 | ||||||||
\(759\) | 0.570877 | 0.0207215 | ||||||||
\(760\) | −9.16625 | −0.332495 | ||||||||
\(761\) | 44.9768 | 1.63041 | 0.815203 | − | 0.579175i | \(-0.196625\pi\) | ||||
0.815203 | + | 0.579175i | \(0.196625\pi\) | |||||||
\(762\) | −8.50957 | −0.308269 | ||||||||
\(763\) | 2.93612 | 0.106295 | ||||||||
\(764\) | −6.28030 | −0.227213 | ||||||||
\(765\) | −7.21835 | −0.260980 | ||||||||
\(766\) | −1.37802 | −0.0497898 | ||||||||
\(767\) | −59.9405 | −2.16433 | ||||||||
\(768\) | −0.424610 | −0.0153218 | ||||||||
\(769\) | 23.3725 | 0.842833 | 0.421416 | − | 0.906867i | \(-0.361533\pi\) | ||||
0.421416 | + | 0.906867i | \(0.361533\pi\) | |||||||
\(770\) | −6.43672 | −0.231963 | ||||||||
\(771\) | 5.11255 | 0.184124 | ||||||||
\(772\) | −14.0894 | −0.507088 | ||||||||
\(773\) | −31.9137 | −1.14786 | −0.573929 | − | 0.818905i | \(-0.694581\pi\) | ||||
−0.573929 | + | 0.818905i | \(0.694581\pi\) | |||||||
\(774\) | 11.0418 | 0.396889 | ||||||||
\(775\) | −4.67346 | −0.167876 | ||||||||
\(776\) | 12.0468 | 0.432455 | ||||||||
\(777\) | 3.19873 | 0.114754 | ||||||||
\(778\) | 30.2447 | 1.08433 | ||||||||
\(779\) | −42.7968 | −1.53335 | ||||||||
\(780\) | 5.55125 | 0.198767 | ||||||||
\(781\) | 9.95316 | 0.356152 | ||||||||
\(782\) | 1.98396 | 0.0709462 | ||||||||
\(783\) | 4.50820 | 0.161110 | ||||||||
\(784\) | 6.76645 | 0.241659 | ||||||||
\(785\) | 0.0357709 | 0.00127672 | ||||||||
\(786\) | −0.258091 | −0.00920581 | ||||||||
\(787\) | 0.755053 | 0.0269147 | 0.0134574 | − | 0.999909i | \(-0.495716\pi\) | ||||
0.0134574 | + | 0.999909i | \(0.495716\pi\) | |||||||
\(788\) | −4.04257 | −0.144011 | ||||||||
\(789\) | −8.71467 | −0.310250 | ||||||||
\(790\) | −18.3636 | −0.653348 | ||||||||
\(791\) | −6.65561 | −0.236646 | ||||||||
\(792\) | −2.38035 | −0.0845822 | ||||||||
\(793\) | 28.2725 | 1.00398 | ||||||||
\(794\) | 36.3903 | 1.29144 | ||||||||
\(795\) | 9.64936 | 0.342227 | ||||||||
\(796\) | −2.51251 | −0.0890536 | ||||||||
\(797\) | −8.51913 | −0.301763 | −0.150881 | − | 0.988552i | \(-0.548211\pi\) | ||||
−0.150881 | + | 0.988552i | \(0.548211\pi\) | |||||||
\(798\) | −7.02711 | −0.248757 | ||||||||
\(799\) | 13.0268 | 0.460856 | ||||||||
\(800\) | −0.776890 | −0.0274672 | ||||||||
\(801\) | 18.6144 | 0.657706 | ||||||||
\(802\) | 34.3590 | 1.21326 | ||||||||
\(803\) | 12.8148 | 0.452224 | ||||||||
\(804\) | −2.28881 | −0.0807202 | ||||||||
\(805\) | 12.1434 | 0.428000 | ||||||||
\(806\) | 38.2704 | 1.34802 | ||||||||
\(807\) | −3.74941 | −0.131985 | ||||||||
\(808\) | 9.59434 | 0.337528 | ||||||||
\(809\) | 5.18639 | 0.182344 | 0.0911718 | − | 0.995835i | \(-0.470939\pi\) | ||||
0.0911718 | + | 0.995835i | \(0.470939\pi\) | |||||||
\(810\) | −15.2274 | −0.535037 | ||||||||
\(811\) | 13.4138 | 0.471022 | 0.235511 | − | 0.971872i | \(-0.424324\pi\) | ||||
0.235511 | + | 0.971872i | \(0.424324\pi\) | |||||||
\(812\) | 6.76897 | 0.237544 | ||||||||
\(813\) | −8.06822 | −0.282965 | ||||||||
\(814\) | −1.71401 | −0.0600760 | ||||||||
\(815\) | 2.77299 | 0.0971334 | ||||||||
\(816\) | 0.528942 | 0.0185167 | ||||||||
\(817\) | −17.4667 | −0.611083 | ||||||||
\(818\) | 18.4837 | 0.646268 | ||||||||
\(819\) | −66.5578 | −2.32572 | ||||||||
\(820\) | 19.7175 | 0.688565 | ||||||||
\(821\) | −22.8863 | −0.798736 | −0.399368 | − | 0.916791i | \(-0.630770\pi\) | ||||
−0.399368 | + | 0.916791i | \(0.630770\pi\) | |||||||
\(822\) | −4.54325 | −0.158464 | ||||||||
\(823\) | 19.7213 | 0.687443 | 0.343721 | − | 0.939072i | \(-0.388312\pi\) | ||||
0.343721 | + | 0.939072i | \(0.388312\pi\) | |||||||
\(824\) | −10.7695 | −0.375174 | ||||||||
\(825\) | 0.278476 | 0.00969529 | ||||||||
\(826\) | −34.9581 | −1.21635 | ||||||||
\(827\) | −6.65999 | −0.231590 | −0.115795 | − | 0.993273i | \(-0.536942\pi\) | ||||
−0.115795 | + | 0.993273i | \(0.536942\pi\) | |||||||
\(828\) | 4.49075 | 0.156064 | ||||||||
\(829\) | 6.07068 | 0.210843 | 0.105422 | − | 0.994428i | \(-0.466381\pi\) | ||||
0.105422 | + | 0.994428i | \(0.466381\pi\) | |||||||
\(830\) | −14.3830 | −0.499243 | ||||||||
\(831\) | 11.9781 | 0.415515 | ||||||||
\(832\) | 6.36186 | 0.220558 | ||||||||
\(833\) | −8.42906 | −0.292050 | ||||||||
\(834\) | 6.44511 | 0.223176 | ||||||||
\(835\) | 14.2898 | 0.494519 | ||||||||
\(836\) | 3.76542 | 0.130230 | ||||||||
\(837\) | 14.8652 | 0.513816 | ||||||||
\(838\) | 25.5378 | 0.882187 | ||||||||
\(839\) | −34.3310 | −1.18524 | −0.592620 | − | 0.805483i | \(-0.701906\pi\) | ||||
−0.592620 | + | 0.805483i | \(0.701906\pi\) | |||||||
\(840\) | 3.23756 | 0.111706 | ||||||||
\(841\) | −25.6717 | −0.885231 | ||||||||
\(842\) | 30.4856 | 1.05060 | ||||||||
\(843\) | 6.84630 | 0.235799 | ||||||||
\(844\) | 5.25931 | 0.181033 | ||||||||
\(845\) | −56.4582 | −1.94222 | ||||||||
\(846\) | 29.4866 | 1.01377 | ||||||||
\(847\) | −38.1693 | −1.31151 | ||||||||
\(848\) | 11.0584 | 0.379746 | ||||||||
\(849\) | 11.3782 | 0.390497 | ||||||||
\(850\) | 0.967782 | 0.0331947 | ||||||||
\(851\) | 3.23363 | 0.110848 | ||||||||
\(852\) | −5.00627 | −0.171512 | ||||||||
\(853\) | −8.79085 | −0.300993 | −0.150496 | − | 0.988611i | \(-0.548087\pi\) | ||||
−0.150496 | + | 0.988611i | \(0.548087\pi\) | |||||||
\(854\) | 16.4888 | 0.564237 | ||||||||
\(855\) | 25.8461 | 0.883919 | ||||||||
\(856\) | 10.6939 | 0.365511 | ||||||||
\(857\) | −33.7434 | −1.15265 | −0.576327 | − | 0.817219i | \(-0.695514\pi\) | ||||
−0.576327 | + | 0.817219i | \(0.695514\pi\) | |||||||
\(858\) | −2.28041 | −0.0778518 | ||||||||
\(859\) | −1.90843 | −0.0651147 | −0.0325574 | − | 0.999470i | \(-0.510365\pi\) | ||||
−0.0325574 | + | 0.999470i | \(0.510365\pi\) | |||||||
\(860\) | 8.04733 | 0.274412 | ||||||||
\(861\) | 15.1160 | 0.515153 | ||||||||
\(862\) | 3.38191 | 0.115188 | ||||||||
\(863\) | 48.0888 | 1.63696 | 0.818481 | − | 0.574533i | \(-0.194816\pi\) | ||||
0.818481 | + | 0.574533i | \(0.194816\pi\) | |||||||
\(864\) | 2.47111 | 0.0840688 | ||||||||
\(865\) | 4.62363 | 0.157208 | ||||||||
\(866\) | 19.2457 | 0.653997 | ||||||||
\(867\) | 6.55946 | 0.222771 | ||||||||
\(868\) | 22.3198 | 0.757583 | ||||||||
\(869\) | 7.54361 | 0.255900 | ||||||||
\(870\) | 1.59191 | 0.0539708 | ||||||||
\(871\) | 34.2929 | 1.16197 | ||||||||
\(872\) | 0.791338 | 0.0267981 | ||||||||
\(873\) | −33.9684 | −1.14966 | ||||||||
\(874\) | −7.10379 | −0.240289 | ||||||||
\(875\) | 44.0475 | 1.48908 | ||||||||
\(876\) | −6.44561 | −0.217777 | ||||||||
\(877\) | 8.36376 | 0.282424 | 0.141212 | − | 0.989979i | \(-0.454900\pi\) | ||||
0.141212 | + | 0.989979i | \(0.454900\pi\) | |||||||
\(878\) | −38.1157 | −1.28634 | ||||||||
\(879\) | −3.03121 | −0.102240 | ||||||||
\(880\) | −1.73482 | −0.0584807 | ||||||||
\(881\) | 27.3248 | 0.920596 | 0.460298 | − | 0.887764i | \(-0.347743\pi\) | ||||
0.460298 | + | 0.887764i | \(0.347743\pi\) | |||||||
\(882\) | −19.0794 | −0.642437 | ||||||||
\(883\) | −8.46958 | −0.285024 | −0.142512 | − | 0.989793i | \(-0.545518\pi\) | ||||
−0.142512 | + | 0.989793i | \(0.545518\pi\) | |||||||
\(884\) | −7.92505 | −0.266548 | ||||||||
\(885\) | −8.22135 | −0.276358 | ||||||||
\(886\) | −39.9123 | −1.34088 | ||||||||
\(887\) | 25.2990 | 0.849459 | 0.424729 | − | 0.905320i | \(-0.360369\pi\) | ||||
0.424729 | + | 0.905320i | \(0.360369\pi\) | |||||||
\(888\) | 0.862118 | 0.0289308 | ||||||||
\(889\) | 74.3581 | 2.49389 | ||||||||
\(890\) | 13.5663 | 0.454742 | ||||||||
\(891\) | 6.25529 | 0.209560 | ||||||||
\(892\) | 19.9512 | 0.668016 | ||||||||
\(893\) | −46.6440 | −1.56088 | ||||||||
\(894\) | −4.57758 | −0.153097 | ||||||||
\(895\) | 0.191723 | 0.00640860 | ||||||||
\(896\) | 3.71032 | 0.123953 | ||||||||
\(897\) | 4.30219 | 0.143646 | ||||||||
\(898\) | −20.8390 | −0.695408 | ||||||||
\(899\) | 10.9746 | 0.366025 | ||||||||
\(900\) | 2.19060 | 0.0730201 | ||||||||
\(901\) | −13.7756 | −0.458931 | ||||||||
\(902\) | −8.09978 | −0.269693 | ||||||||
\(903\) | 6.16932 | 0.205302 | ||||||||
\(904\) | −1.79381 | −0.0596613 | ||||||||
\(905\) | −44.7134 | −1.48632 | ||||||||
\(906\) | 8.80727 | 0.292602 | ||||||||
\(907\) | −30.4682 | −1.01168 | −0.505841 | − | 0.862627i | \(-0.668818\pi\) | ||||
−0.505841 | + | 0.862627i | \(0.668818\pi\) | |||||||
\(908\) | −28.2375 | −0.937094 | ||||||||
\(909\) | −27.0532 | −0.897299 | ||||||||
\(910\) | −48.5078 | −1.60802 | ||||||||
\(911\) | 37.6830 | 1.24849 | 0.624247 | − | 0.781227i | \(-0.285406\pi\) | ||||
0.624247 | + | 0.781227i | \(0.285406\pi\) | |||||||
\(912\) | −1.89394 | −0.0627146 | ||||||||
\(913\) | 5.90843 | 0.195540 | ||||||||
\(914\) | −28.9031 | −0.956029 | ||||||||
\(915\) | 3.87781 | 0.128196 | ||||||||
\(916\) | 23.7303 | 0.784070 | ||||||||
\(917\) | 2.25525 | 0.0744748 | ||||||||
\(918\) | −3.07829 | −0.101599 | ||||||||
\(919\) | −14.6225 | −0.482351 | −0.241176 | − | 0.970481i | \(-0.577533\pi\) | ||||
−0.241176 | + | 0.970481i | \(0.577533\pi\) | |||||||
\(920\) | 3.27289 | 0.107904 | ||||||||
\(921\) | −2.29290 | −0.0755537 | ||||||||
\(922\) | −27.8908 | −0.918534 | ||||||||
\(923\) | 75.0080 | 2.46892 | ||||||||
\(924\) | −1.32996 | −0.0437525 | ||||||||
\(925\) | 1.57738 | 0.0518639 | ||||||||
\(926\) | −14.6630 | −0.481857 | ||||||||
\(927\) | 30.3669 | 0.997379 | ||||||||
\(928\) | 1.82436 | 0.0598877 | ||||||||
\(929\) | −46.7438 | −1.53361 | −0.766807 | − | 0.641878i | \(-0.778156\pi\) | ||||
−0.766807 | + | 0.641878i | \(0.778156\pi\) | |||||||
\(930\) | 5.24911 | 0.172125 | ||||||||
\(931\) | 30.1812 | 0.989149 | ||||||||
\(932\) | −1.53854 | −0.0503966 | ||||||||
\(933\) | −4.59778 | −0.150525 | ||||||||
\(934\) | −15.9437 | −0.521693 | ||||||||
\(935\) | 2.16108 | 0.0706750 | ||||||||
\(936\) | −17.9386 | −0.586341 | ||||||||
\(937\) | −14.9122 | −0.487160 | −0.243580 | − | 0.969881i | \(-0.578322\pi\) | ||||
−0.243580 | + | 0.969881i | \(0.578322\pi\) | |||||||
\(938\) | 20.0000 | 0.653024 | ||||||||
\(939\) | 3.38709 | 0.110534 | ||||||||
\(940\) | 21.4900 | 0.700927 | ||||||||
\(941\) | −44.5540 | −1.45242 | −0.726210 | − | 0.687473i | \(-0.758720\pi\) | ||||
−0.726210 | + | 0.687473i | \(0.758720\pi\) | |||||||
\(942\) | 0.00739102 | 0.000240812 0 | ||||||||
\(943\) | 15.2810 | 0.497617 | ||||||||
\(944\) | −9.42185 | −0.306655 | ||||||||
\(945\) | −18.8416 | −0.612919 | ||||||||
\(946\) | −3.30578 | −0.107480 | ||||||||
\(947\) | 14.5801 | 0.473788 | 0.236894 | − | 0.971535i | \(-0.423871\pi\) | ||||
0.236894 | + | 0.971535i | \(0.423871\pi\) | |||||||
\(948\) | −3.79431 | −0.123233 | ||||||||
\(949\) | 96.5735 | 3.13491 | ||||||||
\(950\) | −3.46525 | −0.112428 | ||||||||
\(951\) | 5.61611 | 0.182115 | ||||||||
\(952\) | −4.62199 | −0.149800 | ||||||||
\(953\) | −13.6884 | −0.443412 | −0.221706 | − | 0.975114i | \(-0.571163\pi\) | ||||
−0.221706 | + | 0.975114i | \(0.571163\pi\) | |||||||
\(954\) | −31.1814 | −1.00953 | ||||||||
\(955\) | 12.9061 | 0.417633 | ||||||||
\(956\) | 27.6458 | 0.894129 | ||||||||
\(957\) | −0.653943 | −0.0211390 | ||||||||
\(958\) | −26.9483 | −0.870661 | ||||||||
\(959\) | 39.6997 | 1.28197 | ||||||||
\(960\) | 0.872583 | 0.0281625 | ||||||||
\(961\) | 5.18742 | 0.167336 | ||||||||
\(962\) | −12.9170 | −0.416460 | ||||||||
\(963\) | −30.1537 | −0.971690 | ||||||||
\(964\) | −22.7447 | −0.732558 | ||||||||
\(965\) | 28.9539 | 0.932061 | ||||||||
\(966\) | 2.50909 | 0.0807287 | ||||||||
\(967\) | −24.6304 | −0.792062 | −0.396031 | − | 0.918237i | \(-0.629613\pi\) | ||||
−0.396031 | + | 0.918237i | \(0.629613\pi\) | |||||||
\(968\) | −10.2874 | −0.330648 | ||||||||
\(969\) | 2.35930 | 0.0757917 | ||||||||
\(970\) | −24.7564 | −0.794881 | ||||||||
\(971\) | 19.4244 | 0.623358 | 0.311679 | − | 0.950187i | \(-0.399109\pi\) | ||||
0.311679 | + | 0.950187i | \(0.399109\pi\) | |||||||
\(972\) | −10.5596 | −0.338700 | ||||||||
\(973\) | −56.3185 | −1.80549 | ||||||||
\(974\) | −19.0499 | −0.610399 | ||||||||
\(975\) | 2.09862 | 0.0672098 | ||||||||
\(976\) | 4.44405 | 0.142251 | ||||||||
\(977\) | 21.7544 | 0.695985 | 0.347992 | − | 0.937497i | \(-0.386863\pi\) | ||||
0.347992 | + | 0.937497i | \(0.386863\pi\) | |||||||
\(978\) | 0.572957 | 0.0183211 | ||||||||
\(979\) | −5.57291 | −0.178111 | ||||||||
\(980\) | −13.9052 | −0.444185 | ||||||||
\(981\) | −2.23134 | −0.0712412 | ||||||||
\(982\) | −7.88816 | −0.251721 | ||||||||
\(983\) | 2.43517 | 0.0776697 | 0.0388349 | − | 0.999246i | \(-0.487635\pi\) | ||||
0.0388349 | + | 0.999246i | \(0.487635\pi\) | |||||||
\(984\) | 4.07405 | 0.129876 | ||||||||
\(985\) | 8.30757 | 0.264701 | ||||||||
\(986\) | −2.27263 | −0.0723754 | ||||||||
\(987\) | 16.4749 | 0.524401 | ||||||||
\(988\) | 28.3766 | 0.902779 | ||||||||
\(989\) | 6.23664 | 0.198314 | ||||||||
\(990\) | 4.89167 | 0.155468 | ||||||||
\(991\) | 56.7974 | 1.80423 | 0.902115 | − | 0.431496i | \(-0.142014\pi\) | ||||
0.902115 | + | 0.431496i | \(0.142014\pi\) | |||||||
\(992\) | 6.01560 | 0.190995 | ||||||||
\(993\) | 6.48536 | 0.205807 | ||||||||
\(994\) | 43.7456 | 1.38753 | ||||||||
\(995\) | 5.16327 | 0.163687 | ||||||||
\(996\) | −2.97184 | −0.0941663 | ||||||||
\(997\) | −7.35595 | −0.232965 | −0.116483 | − | 0.993193i | \(-0.537162\pi\) | ||||
−0.116483 | + | 0.993193i | \(0.537162\pi\) | |||||||
\(998\) | −18.1973 | −0.576024 | ||||||||
\(999\) | −5.01727 | −0.158739 |
(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 | 4022.2.a.f.1.19 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.f.1.19 | ✓ | 50 | 1.1 | even | 1 | trivial |