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: | \(1\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
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 | ||||||||
\(3\) | −1.40012 | −0.808357 | −0.404179 | − | 0.914680i | \(-0.632443\pi\) | ||||
−0.404179 | + | 0.914680i | \(0.632443\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.65031 | −0.738040 | −0.369020 | − | 0.929421i | \(-0.620307\pi\) | ||||
−0.369020 | + | 0.929421i | \(0.620307\pi\) | |||||||
\(6\) | 1.40012 | 0.571595 | ||||||||
\(7\) | 2.90659 | 1.09859 | 0.549294 | − | 0.835629i | \(-0.314897\pi\) | ||||
0.549294 | + | 0.835629i | \(0.314897\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.03967 | −0.346558 | ||||||||
\(10\) | 1.65031 | 0.521873 | ||||||||
\(11\) | −1.47758 | −0.445506 | −0.222753 | − | 0.974875i | \(-0.571504\pi\) | ||||
−0.222753 | + | 0.974875i | \(0.571504\pi\) | |||||||
\(12\) | −1.40012 | −0.404179 | ||||||||
\(13\) | 1.93520 | 0.536729 | 0.268364 | − | 0.963317i | \(-0.413517\pi\) | ||||
0.268364 | + | 0.963317i | \(0.413517\pi\) | |||||||
\(14\) | −2.90659 | −0.776818 | ||||||||
\(15\) | 2.31062 | 0.596600 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.62573 | 0.394298 | 0.197149 | − | 0.980374i | \(-0.436832\pi\) | ||||
0.197149 | + | 0.980374i | \(0.436832\pi\) | |||||||
\(18\) | 1.03967 | 0.245054 | ||||||||
\(19\) | −4.58896 | −1.05278 | −0.526389 | − | 0.850244i | \(-0.676455\pi\) | ||||
−0.526389 | + | 0.850244i | \(0.676455\pi\) | |||||||
\(20\) | −1.65031 | −0.369020 | ||||||||
\(21\) | −4.06956 | −0.888051 | ||||||||
\(22\) | 1.47758 | 0.315020 | ||||||||
\(23\) | 7.27839 | 1.51765 | 0.758825 | − | 0.651295i | \(-0.225774\pi\) | ||||
0.758825 | + | 0.651295i | \(0.225774\pi\) | |||||||
\(24\) | 1.40012 | 0.285798 | ||||||||
\(25\) | −2.27649 | −0.455297 | ||||||||
\(26\) | −1.93520 | −0.379524 | ||||||||
\(27\) | 5.65601 | 1.08850 | ||||||||
\(28\) | 2.90659 | 0.549294 | ||||||||
\(29\) | −2.46680 | −0.458073 | −0.229036 | − | 0.973418i | \(-0.573557\pi\) | ||||
−0.229036 | + | 0.973418i | \(0.573557\pi\) | |||||||
\(30\) | −2.31062 | −0.421860 | ||||||||
\(31\) | −6.97572 | −1.25288 | −0.626438 | − | 0.779471i | \(-0.715488\pi\) | ||||
−0.626438 | + | 0.779471i | \(0.715488\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.06878 | 0.360128 | ||||||||
\(34\) | −1.62573 | −0.278810 | ||||||||
\(35\) | −4.79676 | −0.810801 | ||||||||
\(36\) | −1.03967 | −0.173279 | ||||||||
\(37\) | −0.384716 | −0.0632468 | −0.0316234 | − | 0.999500i | \(-0.510068\pi\) | ||||
−0.0316234 | + | 0.999500i | \(0.510068\pi\) | |||||||
\(38\) | 4.58896 | 0.744427 | ||||||||
\(39\) | −2.70951 | −0.433869 | ||||||||
\(40\) | 1.65031 | 0.260937 | ||||||||
\(41\) | 4.62974 | 0.723045 | 0.361522 | − | 0.932363i | \(-0.382257\pi\) | ||||
0.361522 | + | 0.932363i | \(0.382257\pi\) | |||||||
\(42\) | 4.06956 | 0.627947 | ||||||||
\(43\) | −7.14262 | −1.08924 | −0.544620 | − | 0.838683i | \(-0.683326\pi\) | ||||
−0.544620 | + | 0.838683i | \(0.683326\pi\) | |||||||
\(44\) | −1.47758 | −0.222753 | ||||||||
\(45\) | 1.71578 | 0.255774 | ||||||||
\(46\) | −7.27839 | −1.07314 | ||||||||
\(47\) | 11.8044 | 1.72185 | 0.860925 | − | 0.508732i | \(-0.169886\pi\) | ||||
0.860925 | + | 0.508732i | \(0.169886\pi\) | |||||||
\(48\) | −1.40012 | −0.202089 | ||||||||
\(49\) | 1.44825 | 0.206894 | ||||||||
\(50\) | 2.27649 | 0.321944 | ||||||||
\(51\) | −2.27621 | −0.318733 | ||||||||
\(52\) | 1.93520 | 0.268364 | ||||||||
\(53\) | 8.66181 | 1.18979 | 0.594895 | − | 0.803803i | \(-0.297194\pi\) | ||||
0.594895 | + | 0.803803i | \(0.297194\pi\) | |||||||
\(54\) | −5.65601 | −0.769686 | ||||||||
\(55\) | 2.43846 | 0.328801 | ||||||||
\(56\) | −2.90659 | −0.388409 | ||||||||
\(57\) | 6.42507 | 0.851021 | ||||||||
\(58\) | 2.46680 | 0.323906 | ||||||||
\(59\) | −9.12278 | −1.18769 | −0.593843 | − | 0.804581i | \(-0.702390\pi\) | ||||
−0.593843 | + | 0.804581i | \(0.702390\pi\) | |||||||
\(60\) | 2.31062 | 0.298300 | ||||||||
\(61\) | −11.6084 | −1.48630 | −0.743151 | − | 0.669123i | \(-0.766670\pi\) | ||||
−0.743151 | + | 0.669123i | \(0.766670\pi\) | |||||||
\(62\) | 6.97572 | 0.885917 | ||||||||
\(63\) | −3.02191 | −0.380724 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.19368 | −0.396127 | ||||||||
\(66\) | −2.06878 | −0.254649 | ||||||||
\(67\) | 10.4861 | 1.28108 | 0.640541 | − | 0.767924i | \(-0.278710\pi\) | ||||
0.640541 | + | 0.767924i | \(0.278710\pi\) | |||||||
\(68\) | 1.62573 | 0.197149 | ||||||||
\(69\) | −10.1906 | −1.22680 | ||||||||
\(70\) | 4.79676 | 0.573323 | ||||||||
\(71\) | −1.89812 | −0.225265 | −0.112632 | − | 0.993637i | \(-0.535928\pi\) | ||||
−0.112632 | + | 0.993637i | \(0.535928\pi\) | |||||||
\(72\) | 1.03967 | 0.122527 | ||||||||
\(73\) | 10.6912 | 1.25131 | 0.625654 | − | 0.780101i | \(-0.284832\pi\) | ||||
0.625654 | + | 0.780101i | \(0.284832\pi\) | |||||||
\(74\) | 0.384716 | 0.0447223 | ||||||||
\(75\) | 3.18734 | 0.368043 | ||||||||
\(76\) | −4.58896 | −0.526389 | ||||||||
\(77\) | −4.29471 | −0.489427 | ||||||||
\(78\) | 2.70951 | 0.306791 | ||||||||
\(79\) | 0.0708345 | 0.00796951 | 0.00398475 | − | 0.999992i | \(-0.498732\pi\) | ||||
0.00398475 | + | 0.999992i | \(0.498732\pi\) | |||||||
\(80\) | −1.65031 | −0.184510 | ||||||||
\(81\) | −4.80005 | −0.533339 | ||||||||
\(82\) | −4.62974 | −0.511270 | ||||||||
\(83\) | −7.35376 | −0.807180 | −0.403590 | − | 0.914940i | \(-0.632238\pi\) | ||||
−0.403590 | + | 0.914940i | \(0.632238\pi\) | |||||||
\(84\) | −4.06956 | −0.444026 | ||||||||
\(85\) | −2.68296 | −0.291007 | ||||||||
\(86\) | 7.14262 | 0.770209 | ||||||||
\(87\) | 3.45380 | 0.370286 | ||||||||
\(88\) | 1.47758 | 0.157510 | ||||||||
\(89\) | 12.1510 | 1.28801 | 0.644003 | − | 0.765023i | \(-0.277273\pi\) | ||||
0.644003 | + | 0.765023i | \(0.277273\pi\) | |||||||
\(90\) | −1.71578 | −0.180859 | ||||||||
\(91\) | 5.62484 | 0.589643 | ||||||||
\(92\) | 7.27839 | 0.758825 | ||||||||
\(93\) | 9.76682 | 1.01277 | ||||||||
\(94\) | −11.8044 | −1.21753 | ||||||||
\(95\) | 7.57319 | 0.776993 | ||||||||
\(96\) | 1.40012 | 0.142899 | ||||||||
\(97\) | 2.36355 | 0.239982 | 0.119991 | − | 0.992775i | \(-0.461713\pi\) | ||||
0.119991 | + | 0.992775i | \(0.461713\pi\) | |||||||
\(98\) | −1.44825 | −0.146296 | ||||||||
\(99\) | 1.53620 | 0.154394 | ||||||||
\(100\) | −2.27649 | −0.227649 | ||||||||
\(101\) | −8.01069 | −0.797094 | −0.398547 | − | 0.917148i | \(-0.630485\pi\) | ||||
−0.398547 | + | 0.917148i | \(0.630485\pi\) | |||||||
\(102\) | 2.27621 | 0.225379 | ||||||||
\(103\) | −8.12874 | −0.800949 | −0.400475 | − | 0.916308i | \(-0.631155\pi\) | ||||
−0.400475 | + | 0.916308i | \(0.631155\pi\) | |||||||
\(104\) | −1.93520 | −0.189762 | ||||||||
\(105\) | 6.71603 | 0.655417 | ||||||||
\(106\) | −8.66181 | −0.841309 | ||||||||
\(107\) | −10.0663 | −0.973147 | −0.486573 | − | 0.873640i | \(-0.661753\pi\) | ||||
−0.486573 | + | 0.873640i | \(0.661753\pi\) | |||||||
\(108\) | 5.65601 | 0.544250 | ||||||||
\(109\) | −0.143903 | −0.0137834 | −0.00689171 | − | 0.999976i | \(-0.502194\pi\) | ||||
−0.00689171 | + | 0.999976i | \(0.502194\pi\) | |||||||
\(110\) | −2.43846 | −0.232498 | ||||||||
\(111\) | 0.538646 | 0.0511261 | ||||||||
\(112\) | 2.90659 | 0.274647 | ||||||||
\(113\) | −1.58797 | −0.149384 | −0.0746919 | − | 0.997207i | \(-0.523797\pi\) | ||||
−0.0746919 | + | 0.997207i | \(0.523797\pi\) | |||||||
\(114\) | −6.42507 | −0.601763 | ||||||||
\(115\) | −12.0116 | −1.12009 | ||||||||
\(116\) | −2.46680 | −0.229036 | ||||||||
\(117\) | −2.01198 | −0.186008 | ||||||||
\(118\) | 9.12278 | 0.839820 | ||||||||
\(119\) | 4.72533 | 0.433170 | ||||||||
\(120\) | −2.31062 | −0.210930 | ||||||||
\(121\) | −8.81677 | −0.801524 | ||||||||
\(122\) | 11.6084 | 1.05097 | ||||||||
\(123\) | −6.48218 | −0.584478 | ||||||||
\(124\) | −6.97572 | −0.626438 | ||||||||
\(125\) | 12.0084 | 1.07407 | ||||||||
\(126\) | 3.02191 | 0.269213 | ||||||||
\(127\) | 7.21707 | 0.640411 | 0.320206 | − | 0.947348i | \(-0.396248\pi\) | ||||
0.320206 | + | 0.947348i | \(0.396248\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.0005 | 0.880495 | ||||||||
\(130\) | 3.19368 | 0.280104 | ||||||||
\(131\) | 19.5680 | 1.70967 | 0.854833 | − | 0.518903i | \(-0.173659\pi\) | ||||
0.854833 | + | 0.518903i | \(0.173659\pi\) | |||||||
\(132\) | 2.06878 | 0.180064 | ||||||||
\(133\) | −13.3382 | −1.15657 | ||||||||
\(134\) | −10.4861 | −0.905862 | ||||||||
\(135\) | −9.33416 | −0.803357 | ||||||||
\(136\) | −1.62573 | −0.139405 | ||||||||
\(137\) | −7.74120 | −0.661376 | −0.330688 | − | 0.943740i | \(-0.607281\pi\) | ||||
−0.330688 | + | 0.943740i | \(0.607281\pi\) | |||||||
\(138\) | 10.1906 | 0.867481 | ||||||||
\(139\) | −19.6411 | −1.66594 | −0.832969 | − | 0.553319i | \(-0.813361\pi\) | ||||
−0.832969 | + | 0.553319i | \(0.813361\pi\) | |||||||
\(140\) | −4.79676 | −0.405401 | ||||||||
\(141\) | −16.5275 | −1.39187 | ||||||||
\(142\) | 1.89812 | 0.159286 | ||||||||
\(143\) | −2.85941 | −0.239116 | ||||||||
\(144\) | −1.03967 | −0.0866396 | ||||||||
\(145\) | 4.07097 | 0.338076 | ||||||||
\(146\) | −10.6912 | −0.884809 | ||||||||
\(147\) | −2.02772 | −0.167244 | ||||||||
\(148\) | −0.384716 | −0.0316234 | ||||||||
\(149\) | 17.7835 | 1.45688 | 0.728440 | − | 0.685109i | \(-0.240246\pi\) | ||||
0.728440 | + | 0.685109i | \(0.240246\pi\) | |||||||
\(150\) | −3.18734 | −0.260246 | ||||||||
\(151\) | 10.8627 | 0.883992 | 0.441996 | − | 0.897017i | \(-0.354271\pi\) | ||||
0.441996 | + | 0.897017i | \(0.354271\pi\) | |||||||
\(152\) | 4.58896 | 0.372213 | ||||||||
\(153\) | −1.69023 | −0.136647 | ||||||||
\(154\) | 4.29471 | 0.346077 | ||||||||
\(155\) | 11.5121 | 0.924673 | ||||||||
\(156\) | −2.70951 | −0.216934 | ||||||||
\(157\) | −6.32757 | −0.504995 | −0.252498 | − | 0.967597i | \(-0.581252\pi\) | ||||
−0.252498 | + | 0.967597i | \(0.581252\pi\) | |||||||
\(158\) | −0.0708345 | −0.00563529 | ||||||||
\(159\) | −12.1275 | −0.961776 | ||||||||
\(160\) | 1.65031 | 0.130468 | ||||||||
\(161\) | 21.1553 | 1.66727 | ||||||||
\(162\) | 4.80005 | 0.377128 | ||||||||
\(163\) | 4.72853 | 0.370367 | 0.185184 | − | 0.982704i | \(-0.440712\pi\) | ||||
0.185184 | + | 0.982704i | \(0.440712\pi\) | |||||||
\(164\) | 4.62974 | 0.361522 | ||||||||
\(165\) | −3.41412 | −0.265789 | ||||||||
\(166\) | 7.35376 | 0.570762 | ||||||||
\(167\) | 1.95392 | 0.151199 | 0.0755993 | − | 0.997138i | \(-0.475913\pi\) | ||||
0.0755993 | + | 0.997138i | \(0.475913\pi\) | |||||||
\(168\) | 4.06956 | 0.313973 | ||||||||
\(169\) | −9.25499 | −0.711922 | ||||||||
\(170\) | 2.68296 | 0.205773 | ||||||||
\(171\) | 4.77102 | 0.364849 | ||||||||
\(172\) | −7.14262 | −0.544620 | ||||||||
\(173\) | 7.13429 | 0.542410 | 0.271205 | − | 0.962522i | \(-0.412578\pi\) | ||||
0.271205 | + | 0.962522i | \(0.412578\pi\) | |||||||
\(174\) | −3.45380 | −0.261832 | ||||||||
\(175\) | −6.61680 | −0.500183 | ||||||||
\(176\) | −1.47758 | −0.111377 | ||||||||
\(177\) | 12.7730 | 0.960074 | ||||||||
\(178\) | −12.1510 | −0.910757 | ||||||||
\(179\) | −14.6705 | −1.09652 | −0.548262 | − | 0.836307i | \(-0.684710\pi\) | ||||
−0.548262 | + | 0.836307i | \(0.684710\pi\) | |||||||
\(180\) | 1.71578 | 0.127887 | ||||||||
\(181\) | −15.1348 | −1.12496 | −0.562482 | − | 0.826810i | \(-0.690153\pi\) | ||||
−0.562482 | + | 0.826810i | \(0.690153\pi\) | |||||||
\(182\) | −5.62484 | −0.416941 | ||||||||
\(183\) | 16.2531 | 1.20146 | ||||||||
\(184\) | −7.27839 | −0.536570 | ||||||||
\(185\) | 0.634899 | 0.0466787 | ||||||||
\(186\) | −9.76682 | −0.716138 | ||||||||
\(187\) | −2.40214 | −0.175662 | ||||||||
\(188\) | 11.8044 | 0.860925 | ||||||||
\(189\) | 16.4397 | 1.19581 | ||||||||
\(190\) | −7.57319 | −0.549417 | ||||||||
\(191\) | 9.90307 | 0.716561 | 0.358281 | − | 0.933614i | \(-0.383363\pi\) | ||||
0.358281 | + | 0.933614i | \(0.383363\pi\) | |||||||
\(192\) | −1.40012 | −0.101045 | ||||||||
\(193\) | 8.52394 | 0.613567 | 0.306783 | − | 0.951779i | \(-0.400747\pi\) | ||||
0.306783 | + | 0.951779i | \(0.400747\pi\) | |||||||
\(194\) | −2.36355 | −0.169693 | ||||||||
\(195\) | 4.47152 | 0.320212 | ||||||||
\(196\) | 1.44825 | 0.103447 | ||||||||
\(197\) | −5.02868 | −0.358278 | −0.179139 | − | 0.983824i | \(-0.557331\pi\) | ||||
−0.179139 | + | 0.983824i | \(0.557331\pi\) | |||||||
\(198\) | −1.53620 | −0.109173 | ||||||||
\(199\) | −4.44613 | −0.315178 | −0.157589 | − | 0.987505i | \(-0.550372\pi\) | ||||
−0.157589 | + | 0.987505i | \(0.550372\pi\) | |||||||
\(200\) | 2.27649 | 0.160972 | ||||||||
\(201\) | −14.6818 | −1.03557 | ||||||||
\(202\) | 8.01069 | 0.563630 | ||||||||
\(203\) | −7.16996 | −0.503233 | ||||||||
\(204\) | −2.27621 | −0.159367 | ||||||||
\(205\) | −7.64050 | −0.533636 | ||||||||
\(206\) | 8.12874 | 0.566357 | ||||||||
\(207\) | −7.56716 | −0.525954 | ||||||||
\(208\) | 1.93520 | 0.134182 | ||||||||
\(209\) | 6.78053 | 0.469019 | ||||||||
\(210\) | −6.71603 | −0.463450 | ||||||||
\(211\) | −26.5811 | −1.82992 | −0.914959 | − | 0.403548i | \(-0.867777\pi\) | ||||
−0.914959 | + | 0.403548i | \(0.867777\pi\) | |||||||
\(212\) | 8.66181 | 0.594895 | ||||||||
\(213\) | 2.65758 | 0.182095 | ||||||||
\(214\) | 10.0663 | 0.688119 | ||||||||
\(215\) | 11.7875 | 0.803902 | ||||||||
\(216\) | −5.65601 | −0.384843 | ||||||||
\(217\) | −20.2755 | −1.37639 | ||||||||
\(218\) | 0.143903 | 0.00974635 | ||||||||
\(219\) | −14.9689 | −1.01150 | ||||||||
\(220\) | 2.43846 | 0.164401 | ||||||||
\(221\) | 3.14612 | 0.211631 | ||||||||
\(222\) | −0.538646 | −0.0361516 | ||||||||
\(223\) | −10.0803 | −0.675028 | −0.337514 | − | 0.941321i | \(-0.609586\pi\) | ||||
−0.337514 | + | 0.941321i | \(0.609586\pi\) | |||||||
\(224\) | −2.90659 | −0.194205 | ||||||||
\(225\) | 2.36680 | 0.157787 | ||||||||
\(226\) | 1.58797 | 0.105630 | ||||||||
\(227\) | 8.71957 | 0.578738 | 0.289369 | − | 0.957218i | \(-0.406555\pi\) | ||||
0.289369 | + | 0.957218i | \(0.406555\pi\) | |||||||
\(228\) | 6.42507 | 0.425511 | ||||||||
\(229\) | −0.865941 | −0.0572230 | −0.0286115 | − | 0.999591i | \(-0.509109\pi\) | ||||
−0.0286115 | + | 0.999591i | \(0.509109\pi\) | |||||||
\(230\) | 12.0116 | 0.792020 | ||||||||
\(231\) | 6.01309 | 0.395632 | ||||||||
\(232\) | 2.46680 | 0.161953 | ||||||||
\(233\) | −15.3585 | −1.00617 | −0.503084 | − | 0.864238i | \(-0.667801\pi\) | ||||
−0.503084 | + | 0.864238i | \(0.667801\pi\) | |||||||
\(234\) | 2.01198 | 0.131527 | ||||||||
\(235\) | −19.4809 | −1.27079 | ||||||||
\(236\) | −9.12278 | −0.593843 | ||||||||
\(237\) | −0.0991766 | −0.00644221 | ||||||||
\(238\) | −4.72533 | −0.306298 | ||||||||
\(239\) | 5.03414 | 0.325631 | 0.162816 | − | 0.986657i | \(-0.447942\pi\) | ||||
0.162816 | + | 0.986657i | \(0.447942\pi\) | |||||||
\(240\) | 2.31062 | 0.149150 | ||||||||
\(241\) | −22.3399 | −1.43904 | −0.719520 | − | 0.694472i | \(-0.755638\pi\) | ||||
−0.719520 | + | 0.694472i | \(0.755638\pi\) | |||||||
\(242\) | 8.81677 | 0.566763 | ||||||||
\(243\) | −10.2474 | −0.657372 | ||||||||
\(244\) | −11.6084 | −0.743151 | ||||||||
\(245\) | −2.39007 | −0.152696 | ||||||||
\(246\) | 6.48218 | 0.413289 | ||||||||
\(247\) | −8.88056 | −0.565056 | ||||||||
\(248\) | 6.97572 | 0.442959 | ||||||||
\(249\) | 10.2961 | 0.652490 | ||||||||
\(250\) | −12.0084 | −0.759480 | ||||||||
\(251\) | −2.27835 | −0.143808 | −0.0719040 | − | 0.997412i | \(-0.522908\pi\) | ||||
−0.0719040 | + | 0.997412i | \(0.522908\pi\) | |||||||
\(252\) | −3.02191 | −0.190362 | ||||||||
\(253\) | −10.7544 | −0.676122 | ||||||||
\(254\) | −7.21707 | −0.452839 | ||||||||
\(255\) | 3.75645 | 0.235238 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.5894 | −1.47146 | −0.735732 | − | 0.677272i | \(-0.763162\pi\) | ||||
−0.735732 | + | 0.677272i | \(0.763162\pi\) | |||||||
\(258\) | −10.0005 | −0.622604 | ||||||||
\(259\) | −1.11821 | −0.0694822 | ||||||||
\(260\) | −3.19368 | −0.198064 | ||||||||
\(261\) | 2.56467 | 0.158749 | ||||||||
\(262\) | −19.5680 | −1.20892 | ||||||||
\(263\) | −13.5376 | −0.834762 | −0.417381 | − | 0.908731i | \(-0.637052\pi\) | ||||
−0.417381 | + | 0.908731i | \(0.637052\pi\) | |||||||
\(264\) | −2.06878 | −0.127325 | ||||||||
\(265\) | −14.2946 | −0.878113 | ||||||||
\(266\) | 13.3382 | 0.817818 | ||||||||
\(267\) | −17.0128 | −1.04117 | ||||||||
\(268\) | 10.4861 | 0.640541 | ||||||||
\(269\) | −1.51496 | −0.0923689 | −0.0461844 | − | 0.998933i | \(-0.514706\pi\) | ||||
−0.0461844 | + | 0.998933i | \(0.514706\pi\) | |||||||
\(270\) | 9.33416 | 0.568059 | ||||||||
\(271\) | 8.60064 | 0.522451 | 0.261226 | − | 0.965278i | \(-0.415873\pi\) | ||||
0.261226 | + | 0.965278i | \(0.415873\pi\) | |||||||
\(272\) | 1.62573 | 0.0985744 | ||||||||
\(273\) | −7.87543 | −0.476642 | ||||||||
\(274\) | 7.74120 | 0.467663 | ||||||||
\(275\) | 3.36368 | 0.202838 | ||||||||
\(276\) | −10.1906 | −0.613402 | ||||||||
\(277\) | 24.2507 | 1.45708 | 0.728542 | − | 0.685001i | \(-0.240198\pi\) | ||||
0.728542 | + | 0.685001i | \(0.240198\pi\) | |||||||
\(278\) | 19.6411 | 1.17800 | ||||||||
\(279\) | 7.25248 | 0.434195 | ||||||||
\(280\) | 4.79676 | 0.286661 | ||||||||
\(281\) | −15.1651 | −0.904674 | −0.452337 | − | 0.891847i | \(-0.649410\pi\) | ||||
−0.452337 | + | 0.891847i | \(0.649410\pi\) | |||||||
\(282\) | 16.5275 | 0.984201 | ||||||||
\(283\) | −14.8211 | −0.881025 | −0.440513 | − | 0.897746i | \(-0.645203\pi\) | ||||
−0.440513 | + | 0.897746i | \(0.645203\pi\) | |||||||
\(284\) | −1.89812 | −0.112632 | ||||||||
\(285\) | −10.6033 | −0.628088 | ||||||||
\(286\) | 2.85941 | 0.169080 | ||||||||
\(287\) | 13.4568 | 0.794327 | ||||||||
\(288\) | 1.03967 | 0.0612634 | ||||||||
\(289\) | −14.3570 | −0.844529 | ||||||||
\(290\) | −4.07097 | −0.239056 | ||||||||
\(291\) | −3.30925 | −0.193991 | ||||||||
\(292\) | 10.6912 | 0.625654 | ||||||||
\(293\) | −8.95875 | −0.523376 | −0.261688 | − | 0.965153i | \(-0.584279\pi\) | ||||
−0.261688 | + | 0.965153i | \(0.584279\pi\) | |||||||
\(294\) | 2.02772 | 0.118259 | ||||||||
\(295\) | 15.0554 | 0.876559 | ||||||||
\(296\) | 0.384716 | 0.0223611 | ||||||||
\(297\) | −8.35719 | −0.484934 | ||||||||
\(298\) | −17.7835 | −1.03017 | ||||||||
\(299\) | 14.0852 | 0.814566 | ||||||||
\(300\) | 3.18734 | 0.184021 | ||||||||
\(301\) | −20.7607 | −1.19662 | ||||||||
\(302\) | −10.8627 | −0.625077 | ||||||||
\(303\) | 11.2159 | 0.644337 | ||||||||
\(304\) | −4.58896 | −0.263195 | ||||||||
\(305\) | 19.1574 | 1.09695 | ||||||||
\(306\) | 1.69023 | 0.0966241 | ||||||||
\(307\) | −12.2361 | −0.698350 | −0.349175 | − | 0.937058i | \(-0.613538\pi\) | ||||
−0.349175 | + | 0.937058i | \(0.613538\pi\) | |||||||
\(308\) | −4.29471 | −0.244714 | ||||||||
\(309\) | 11.3812 | 0.647453 | ||||||||
\(310\) | −11.5121 | −0.653842 | ||||||||
\(311\) | −22.2251 | −1.26027 | −0.630134 | − | 0.776487i | \(-0.717000\pi\) | ||||
−0.630134 | + | 0.776487i | \(0.717000\pi\) | |||||||
\(312\) | 2.70951 | 0.153396 | ||||||||
\(313\) | −11.3648 | −0.642376 | −0.321188 | − | 0.947015i | \(-0.604082\pi\) | ||||
−0.321188 | + | 0.947015i | \(0.604082\pi\) | |||||||
\(314\) | 6.32757 | 0.357086 | ||||||||
\(315\) | 4.98707 | 0.280990 | ||||||||
\(316\) | 0.0708345 | 0.00398475 | ||||||||
\(317\) | −19.2327 | −1.08022 | −0.540108 | − | 0.841595i | \(-0.681617\pi\) | ||||
−0.540108 | + | 0.841595i | \(0.681617\pi\) | |||||||
\(318\) | 12.1275 | 0.680078 | ||||||||
\(319\) | 3.64488 | 0.204074 | ||||||||
\(320\) | −1.65031 | −0.0922550 | ||||||||
\(321\) | 14.0940 | 0.786651 | ||||||||
\(322\) | −21.1553 | −1.17894 | ||||||||
\(323\) | −7.46040 | −0.415108 | ||||||||
\(324\) | −4.80005 | −0.266670 | ||||||||
\(325\) | −4.40546 | −0.244371 | ||||||||
\(326\) | −4.72853 | −0.261889 | ||||||||
\(327\) | 0.201481 | 0.0111419 | ||||||||
\(328\) | −4.62974 | −0.255635 | ||||||||
\(329\) | 34.3105 | 1.89160 | ||||||||
\(330\) | 3.41412 | 0.187941 | ||||||||
\(331\) | −14.7493 | −0.810697 | −0.405348 | − | 0.914162i | \(-0.632850\pi\) | ||||
−0.405348 | + | 0.914162i | \(0.632850\pi\) | |||||||
\(332\) | −7.35376 | −0.403590 | ||||||||
\(333\) | 0.399979 | 0.0219187 | ||||||||
\(334\) | −1.95392 | −0.106914 | ||||||||
\(335\) | −17.3053 | −0.945490 | ||||||||
\(336\) | −4.06956 | −0.222013 | ||||||||
\(337\) | −20.3698 | −1.10961 | −0.554806 | − | 0.831980i | \(-0.687207\pi\) | ||||
−0.554806 | + | 0.831980i | \(0.687207\pi\) | |||||||
\(338\) | 9.25499 | 0.503405 | ||||||||
\(339\) | 2.22334 | 0.120756 | ||||||||
\(340\) | −2.68296 | −0.145504 | ||||||||
\(341\) | 10.3072 | 0.558164 | ||||||||
\(342\) | −4.77102 | −0.257987 | ||||||||
\(343\) | −16.1366 | −0.871297 | ||||||||
\(344\) | 7.14262 | 0.385104 | ||||||||
\(345\) | 16.8176 | 0.905430 | ||||||||
\(346\) | −7.13429 | −0.383542 | ||||||||
\(347\) | −5.92891 | −0.318281 | −0.159140 | − | 0.987256i | \(-0.550872\pi\) | ||||
−0.159140 | + | 0.987256i | \(0.550872\pi\) | |||||||
\(348\) | 3.45380 | 0.185143 | ||||||||
\(349\) | −5.89385 | −0.315490 | −0.157745 | − | 0.987480i | \(-0.550422\pi\) | ||||
−0.157745 | + | 0.987480i | \(0.550422\pi\) | |||||||
\(350\) | 6.61680 | 0.353683 | ||||||||
\(351\) | 10.9455 | 0.584229 | ||||||||
\(352\) | 1.47758 | 0.0787551 | ||||||||
\(353\) | −31.6290 | −1.68344 | −0.841721 | − | 0.539913i | \(-0.818457\pi\) | ||||
−0.841721 | + | 0.539913i | \(0.818457\pi\) | |||||||
\(354\) | −12.7730 | −0.678875 | ||||||||
\(355\) | 3.13248 | 0.166255 | ||||||||
\(356\) | 12.1510 | 0.644003 | ||||||||
\(357\) | −6.61601 | −0.350156 | ||||||||
\(358\) | 14.6705 | 0.775360 | ||||||||
\(359\) | 12.1567 | 0.641605 | 0.320803 | − | 0.947146i | \(-0.396047\pi\) | ||||
0.320803 | + | 0.947146i | \(0.396047\pi\) | |||||||
\(360\) | −1.71578 | −0.0904297 | ||||||||
\(361\) | 2.05851 | 0.108343 | ||||||||
\(362\) | 15.1348 | 0.795469 | ||||||||
\(363\) | 12.3445 | 0.647918 | ||||||||
\(364\) | 5.62484 | 0.294822 | ||||||||
\(365\) | −17.6437 | −0.923516 | ||||||||
\(366\) | −16.2531 | −0.849563 | ||||||||
\(367\) | 4.28416 | 0.223631 | 0.111816 | − | 0.993729i | \(-0.464333\pi\) | ||||
0.111816 | + | 0.993729i | \(0.464333\pi\) | |||||||
\(368\) | 7.27839 | 0.379412 | ||||||||
\(369\) | −4.81343 | −0.250577 | ||||||||
\(370\) | −0.634899 | −0.0330068 | ||||||||
\(371\) | 25.1763 | 1.30709 | ||||||||
\(372\) | 9.76682 | 0.506386 | ||||||||
\(373\) | 18.3368 | 0.949444 | 0.474722 | − | 0.880136i | \(-0.342549\pi\) | ||||
0.474722 | + | 0.880136i | \(0.342549\pi\) | |||||||
\(374\) | 2.40214 | 0.124212 | ||||||||
\(375\) | −16.8132 | −0.868230 | ||||||||
\(376\) | −11.8044 | −0.608766 | ||||||||
\(377\) | −4.77375 | −0.245861 | ||||||||
\(378\) | −16.4397 | −0.845567 | ||||||||
\(379\) | −4.42412 | −0.227252 | −0.113626 | − | 0.993524i | \(-0.536247\pi\) | ||||
−0.113626 | + | 0.993524i | \(0.536247\pi\) | |||||||
\(380\) | 7.57319 | 0.388496 | ||||||||
\(381\) | −10.1047 | −0.517681 | ||||||||
\(382\) | −9.90307 | −0.506685 | ||||||||
\(383\) | 17.4977 | 0.894090 | 0.447045 | − | 0.894511i | \(-0.352476\pi\) | ||||
0.447045 | + | 0.894511i | \(0.352476\pi\) | |||||||
\(384\) | 1.40012 | 0.0714494 | ||||||||
\(385\) | 7.08759 | 0.361217 | ||||||||
\(386\) | −8.52394 | −0.433857 | ||||||||
\(387\) | 7.42600 | 0.377485 | ||||||||
\(388\) | 2.36355 | 0.119991 | ||||||||
\(389\) | −21.4150 | −1.08578 | −0.542892 | − | 0.839802i | \(-0.682671\pi\) | ||||
−0.542892 | + | 0.839802i | \(0.682671\pi\) | |||||||
\(390\) | −4.47152 | −0.226424 | ||||||||
\(391\) | 11.8327 | 0.598405 | ||||||||
\(392\) | −1.44825 | −0.0731479 | ||||||||
\(393\) | −27.3975 | −1.38202 | ||||||||
\(394\) | 5.02868 | 0.253341 | ||||||||
\(395\) | −0.116899 | −0.00588182 | ||||||||
\(396\) | 1.53620 | 0.0771969 | ||||||||
\(397\) | 29.7543 | 1.49332 | 0.746662 | − | 0.665204i | \(-0.231655\pi\) | ||||
0.746662 | + | 0.665204i | \(0.231655\pi\) | |||||||
\(398\) | 4.44613 | 0.222864 | ||||||||
\(399\) | 18.6750 | 0.934921 | ||||||||
\(400\) | −2.27649 | −0.113824 | ||||||||
\(401\) | −21.7075 | −1.08402 | −0.542010 | − | 0.840372i | \(-0.682337\pi\) | ||||
−0.542010 | + | 0.840372i | \(0.682337\pi\) | |||||||
\(402\) | 14.6818 | 0.732260 | ||||||||
\(403\) | −13.4994 | −0.672455 | ||||||||
\(404\) | −8.01069 | −0.398547 | ||||||||
\(405\) | 7.92156 | 0.393626 | ||||||||
\(406\) | 7.16996 | 0.355839 | ||||||||
\(407\) | 0.568447 | 0.0281769 | ||||||||
\(408\) | 2.27621 | 0.112689 | ||||||||
\(409\) | 7.31365 | 0.361637 | 0.180818 | − | 0.983517i | \(-0.442125\pi\) | ||||
0.180818 | + | 0.983517i | \(0.442125\pi\) | |||||||
\(410\) | 7.64050 | 0.377337 | ||||||||
\(411\) | 10.8386 | 0.534628 | ||||||||
\(412\) | −8.12874 | −0.400475 | ||||||||
\(413\) | −26.5162 | −1.30478 | ||||||||
\(414\) | 7.56716 | 0.371906 | ||||||||
\(415\) | 12.1360 | 0.595731 | ||||||||
\(416\) | −1.93520 | −0.0948811 | ||||||||
\(417\) | 27.4999 | 1.34667 | ||||||||
\(418\) | −6.78053 | −0.331647 | ||||||||
\(419\) | −13.1699 | −0.643394 | −0.321697 | − | 0.946843i | \(-0.604253\pi\) | ||||
−0.321697 | + | 0.946843i | \(0.604253\pi\) | |||||||
\(420\) | 6.71603 | 0.327709 | ||||||||
\(421\) | −8.80366 | −0.429064 | −0.214532 | − | 0.976717i | \(-0.568823\pi\) | ||||
−0.214532 | + | 0.976717i | \(0.568823\pi\) | |||||||
\(422\) | 26.5811 | 1.29395 | ||||||||
\(423\) | −12.2727 | −0.596721 | ||||||||
\(424\) | −8.66181 | −0.420654 | ||||||||
\(425\) | −3.70095 | −0.179523 | ||||||||
\(426\) | −2.65758 | −0.128760 | ||||||||
\(427\) | −33.7408 | −1.63283 | ||||||||
\(428\) | −10.0663 | −0.486573 | ||||||||
\(429\) | 4.00351 | 0.193291 | ||||||||
\(430\) | −11.7875 | −0.568445 | ||||||||
\(431\) | 10.3251 | 0.497342 | 0.248671 | − | 0.968588i | \(-0.420006\pi\) | ||||
0.248671 | + | 0.968588i | \(0.420006\pi\) | |||||||
\(432\) | 5.65601 | 0.272125 | ||||||||
\(433\) | −2.40470 | −0.115563 | −0.0577813 | − | 0.998329i | \(-0.518403\pi\) | ||||
−0.0577813 | + | 0.998329i | \(0.518403\pi\) | |||||||
\(434\) | 20.2755 | 0.973257 | ||||||||
\(435\) | −5.69984 | −0.273286 | ||||||||
\(436\) | −0.143903 | −0.00689171 | ||||||||
\(437\) | −33.4002 | −1.59775 | ||||||||
\(438\) | 14.9689 | 0.715242 | ||||||||
\(439\) | −4.75041 | −0.226725 | −0.113362 | − | 0.993554i | \(-0.536162\pi\) | ||||
−0.113362 | + | 0.993554i | \(0.536162\pi\) | |||||||
\(440\) | −2.43846 | −0.116249 | ||||||||
\(441\) | −1.50571 | −0.0717007 | ||||||||
\(442\) | −3.14612 | −0.149646 | ||||||||
\(443\) | −8.62907 | −0.409979 | −0.204990 | − | 0.978764i | \(-0.565716\pi\) | ||||
−0.204990 | + | 0.978764i | \(0.565716\pi\) | |||||||
\(444\) | 0.538646 | 0.0255630 | ||||||||
\(445\) | −20.0529 | −0.950599 | ||||||||
\(446\) | 10.0803 | 0.477317 | ||||||||
\(447\) | −24.8990 | −1.17768 | ||||||||
\(448\) | 2.90659 | 0.137323 | ||||||||
\(449\) | −37.8750 | −1.78743 | −0.893715 | − | 0.448636i | \(-0.851910\pi\) | ||||
−0.893715 | + | 0.448636i | \(0.851910\pi\) | |||||||
\(450\) | −2.36680 | −0.111572 | ||||||||
\(451\) | −6.84080 | −0.322121 | ||||||||
\(452\) | −1.58797 | −0.0746919 | ||||||||
\(453\) | −15.2090 | −0.714581 | ||||||||
\(454\) | −8.71957 | −0.409230 | ||||||||
\(455\) | −9.28271 | −0.435180 | ||||||||
\(456\) | −6.42507 | −0.300882 | ||||||||
\(457\) | −18.4506 | −0.863084 | −0.431542 | − | 0.902093i | \(-0.642030\pi\) | ||||
−0.431542 | + | 0.902093i | \(0.642030\pi\) | |||||||
\(458\) | 0.865941 | 0.0404628 | ||||||||
\(459\) | 9.19515 | 0.429193 | ||||||||
\(460\) | −12.0116 | −0.560043 | ||||||||
\(461\) | −22.9386 | −1.06836 | −0.534179 | − | 0.845372i | \(-0.679379\pi\) | ||||
−0.534179 | + | 0.845372i | \(0.679379\pi\) | |||||||
\(462\) | −6.01309 | −0.279754 | ||||||||
\(463\) | 11.8503 | 0.550730 | 0.275365 | − | 0.961340i | \(-0.411201\pi\) | ||||
0.275365 | + | 0.961340i | \(0.411201\pi\) | |||||||
\(464\) | −2.46680 | −0.114518 | ||||||||
\(465\) | −16.1183 | −0.747466 | ||||||||
\(466\) | 15.3585 | 0.711468 | ||||||||
\(467\) | −13.6621 | −0.632207 | −0.316103 | − | 0.948725i | \(-0.602375\pi\) | ||||
−0.316103 | + | 0.948725i | \(0.602375\pi\) | |||||||
\(468\) | −2.01198 | −0.0930039 | ||||||||
\(469\) | 30.4788 | 1.40738 | ||||||||
\(470\) | 19.4809 | 0.898587 | ||||||||
\(471\) | 8.85934 | 0.408217 | ||||||||
\(472\) | 9.12278 | 0.419910 | ||||||||
\(473\) | 10.5538 | 0.485263 | ||||||||
\(474\) | 0.0991766 | 0.00455533 | ||||||||
\(475\) | 10.4467 | 0.479327 | ||||||||
\(476\) | 4.72533 | 0.216585 | ||||||||
\(477\) | −9.00546 | −0.412332 | ||||||||
\(478\) | −5.03414 | −0.230256 | ||||||||
\(479\) | 18.8825 | 0.862765 | 0.431382 | − | 0.902169i | \(-0.358026\pi\) | ||||
0.431382 | + | 0.902169i | \(0.358026\pi\) | |||||||
\(480\) | −2.31062 | −0.105465 | ||||||||
\(481\) | −0.744503 | −0.0339464 | ||||||||
\(482\) | 22.3399 | 1.01756 | ||||||||
\(483\) | −29.6199 | −1.34775 | ||||||||
\(484\) | −8.81677 | −0.400762 | ||||||||
\(485\) | −3.90059 | −0.177117 | ||||||||
\(486\) | 10.2474 | 0.464832 | ||||||||
\(487\) | −8.95896 | −0.405969 | −0.202985 | − | 0.979182i | \(-0.565064\pi\) | ||||
−0.202985 | + | 0.979182i | \(0.565064\pi\) | |||||||
\(488\) | 11.6084 | 0.525487 | ||||||||
\(489\) | −6.62049 | −0.299389 | ||||||||
\(490\) | 2.39007 | 0.107972 | ||||||||
\(491\) | 4.69705 | 0.211975 | 0.105988 | − | 0.994367i | \(-0.466200\pi\) | ||||
0.105988 | + | 0.994367i | \(0.466200\pi\) | |||||||
\(492\) | −6.48218 | −0.292239 | ||||||||
\(493\) | −4.01035 | −0.180617 | ||||||||
\(494\) | 8.88056 | 0.399555 | ||||||||
\(495\) | −2.53520 | −0.113949 | ||||||||
\(496\) | −6.97572 | −0.313219 | ||||||||
\(497\) | −5.51704 | −0.247473 | ||||||||
\(498\) | −10.2961 | −0.461380 | ||||||||
\(499\) | 25.0161 | 1.11987 | 0.559937 | − | 0.828535i | \(-0.310825\pi\) | ||||
0.559937 | + | 0.828535i | \(0.310825\pi\) | |||||||
\(500\) | 12.0084 | 0.537034 | ||||||||
\(501\) | −2.73571 | −0.122222 | ||||||||
\(502\) | 2.27835 | 0.101688 | ||||||||
\(503\) | −4.80007 | −0.214025 | −0.107012 | − | 0.994258i | \(-0.534128\pi\) | ||||
−0.107012 | + | 0.994258i | \(0.534128\pi\) | |||||||
\(504\) | 3.02191 | 0.134606 | ||||||||
\(505\) | 13.2201 | 0.588287 | ||||||||
\(506\) | 10.7544 | 0.478090 | ||||||||
\(507\) | 12.9581 | 0.575488 | ||||||||
\(508\) | 7.21707 | 0.320206 | ||||||||
\(509\) | 37.1712 | 1.64759 | 0.823793 | − | 0.566891i | \(-0.191854\pi\) | ||||
0.823793 | + | 0.566891i | \(0.191854\pi\) | |||||||
\(510\) | −3.75645 | −0.166338 | ||||||||
\(511\) | 31.0749 | 1.37467 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −25.9552 | −1.14595 | ||||||||
\(514\) | 23.5894 | 1.04048 | ||||||||
\(515\) | 13.4149 | 0.591132 | ||||||||
\(516\) | 10.0005 | 0.440247 | ||||||||
\(517\) | −17.4419 | −0.767094 | ||||||||
\(518\) | 1.11821 | 0.0491313 | ||||||||
\(519\) | −9.98883 | −0.438461 | ||||||||
\(520\) | 3.19368 | 0.140052 | ||||||||
\(521\) | 6.35043 | 0.278217 | 0.139109 | − | 0.990277i | \(-0.455576\pi\) | ||||
0.139109 | + | 0.990277i | \(0.455576\pi\) | |||||||
\(522\) | −2.56467 | −0.112252 | ||||||||
\(523\) | 9.09306 | 0.397612 | 0.198806 | − | 0.980039i | \(-0.436294\pi\) | ||||
0.198806 | + | 0.980039i | \(0.436294\pi\) | |||||||
\(524\) | 19.5680 | 0.854833 | ||||||||
\(525\) | 9.26430 | 0.404327 | ||||||||
\(526\) | 13.5376 | 0.590266 | ||||||||
\(527\) | −11.3406 | −0.494006 | ||||||||
\(528\) | 2.06878 | 0.0900320 | ||||||||
\(529\) | 29.9750 | 1.30326 | ||||||||
\(530\) | 14.2946 | 0.620920 | ||||||||
\(531\) | 9.48473 | 0.411602 | ||||||||
\(532\) | −13.3382 | −0.578284 | ||||||||
\(533\) | 8.95949 | 0.388079 | ||||||||
\(534\) | 17.0128 | 0.736217 | ||||||||
\(535\) | 16.6125 | 0.718221 | ||||||||
\(536\) | −10.4861 | −0.452931 | ||||||||
\(537\) | 20.5404 | 0.886383 | ||||||||
\(538\) | 1.51496 | 0.0653147 | ||||||||
\(539\) | −2.13991 | −0.0921723 | ||||||||
\(540\) | −9.33416 | −0.401678 | ||||||||
\(541\) | −25.7443 | −1.10683 | −0.553417 | − | 0.832905i | \(-0.686676\pi\) | ||||
−0.553417 | + | 0.832905i | \(0.686676\pi\) | |||||||
\(542\) | −8.60064 | −0.369429 | ||||||||
\(543\) | 21.1905 | 0.909372 | ||||||||
\(544\) | −1.62573 | −0.0697026 | ||||||||
\(545\) | 0.237484 | 0.0101727 | ||||||||
\(546\) | 7.87543 | 0.337037 | ||||||||
\(547\) | 28.5635 | 1.22129 | 0.610643 | − | 0.791906i | \(-0.290911\pi\) | ||||
0.610643 | + | 0.791906i | \(0.290911\pi\) | |||||||
\(548\) | −7.74120 | −0.330688 | ||||||||
\(549\) | 12.0690 | 0.515090 | ||||||||
\(550\) | −3.36368 | −0.143428 | ||||||||
\(551\) | 11.3200 | 0.482249 | ||||||||
\(552\) | 10.1906 | 0.433740 | ||||||||
\(553\) | 0.205887 | 0.00875520 | ||||||||
\(554\) | −24.2507 | −1.03031 | ||||||||
\(555\) | −0.888932 | −0.0377331 | ||||||||
\(556\) | −19.6411 | −0.832969 | ||||||||
\(557\) | −37.9765 | −1.60911 | −0.804557 | − | 0.593875i | \(-0.797597\pi\) | ||||
−0.804557 | + | 0.593875i | \(0.797597\pi\) | |||||||
\(558\) | −7.25248 | −0.307022 | ||||||||
\(559\) | −13.8224 | −0.584626 | ||||||||
\(560\) | −4.79676 | −0.202700 | ||||||||
\(561\) | 3.36328 | 0.141998 | ||||||||
\(562\) | 15.1651 | 0.639701 | ||||||||
\(563\) | −30.9187 | −1.30307 | −0.651535 | − | 0.758619i | \(-0.725875\pi\) | ||||
−0.651535 | + | 0.758619i | \(0.725875\pi\) | |||||||
\(564\) | −16.5275 | −0.695935 | ||||||||
\(565\) | 2.62064 | 0.110251 | ||||||||
\(566\) | 14.8211 | 0.622979 | ||||||||
\(567\) | −13.9518 | −0.585920 | ||||||||
\(568\) | 1.89812 | 0.0796432 | ||||||||
\(569\) | −7.10343 | −0.297791 | −0.148896 | − | 0.988853i | \(-0.547572\pi\) | ||||
−0.148896 | + | 0.988853i | \(0.547572\pi\) | |||||||
\(570\) | 10.6033 | 0.444125 | ||||||||
\(571\) | 15.0307 | 0.629014 | 0.314507 | − | 0.949255i | \(-0.398161\pi\) | ||||
0.314507 | + | 0.949255i | \(0.398161\pi\) | |||||||
\(572\) | −2.85941 | −0.119558 | ||||||||
\(573\) | −13.8655 | −0.579238 | ||||||||
\(574\) | −13.4568 | −0.561674 | ||||||||
\(575\) | −16.5691 | −0.690981 | ||||||||
\(576\) | −1.03967 | −0.0433198 | ||||||||
\(577\) | −1.45580 | −0.0606058 | −0.0303029 | − | 0.999541i | \(-0.509647\pi\) | ||||
−0.0303029 | + | 0.999541i | \(0.509647\pi\) | |||||||
\(578\) | 14.3570 | 0.597172 | ||||||||
\(579\) | −11.9345 | −0.495981 | ||||||||
\(580\) | 4.07097 | 0.169038 | ||||||||
\(581\) | −21.3744 | −0.886758 | ||||||||
\(582\) | 3.30925 | 0.137173 | ||||||||
\(583\) | −12.7985 | −0.530059 | ||||||||
\(584\) | −10.6912 | −0.442404 | ||||||||
\(585\) | 3.32039 | 0.137281 | ||||||||
\(586\) | 8.95875 | 0.370082 | ||||||||
\(587\) | 9.29236 | 0.383537 | 0.191768 | − | 0.981440i | \(-0.438578\pi\) | ||||
0.191768 | + | 0.981440i | \(0.438578\pi\) | |||||||
\(588\) | −2.02772 | −0.0836220 | ||||||||
\(589\) | 32.0113 | 1.31900 | ||||||||
\(590\) | −15.0554 | −0.619821 | ||||||||
\(591\) | 7.04073 | 0.289617 | ||||||||
\(592\) | −0.384716 | −0.0158117 | ||||||||
\(593\) | 6.01596 | 0.247046 | 0.123523 | − | 0.992342i | \(-0.460581\pi\) | ||||
0.123523 | + | 0.992342i | \(0.460581\pi\) | |||||||
\(594\) | 8.35719 | 0.342900 | ||||||||
\(595\) | −7.79825 | −0.319697 | ||||||||
\(596\) | 17.7835 | 0.728440 | ||||||||
\(597\) | 6.22510 | 0.254776 | ||||||||
\(598\) | −14.0852 | −0.575985 | ||||||||
\(599\) | −29.2689 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(600\) | −3.18734 | −0.130123 | ||||||||
\(601\) | 12.9928 | 0.529986 | 0.264993 | − | 0.964250i | \(-0.414630\pi\) | ||||
0.264993 | + | 0.964250i | \(0.414630\pi\) | |||||||
\(602\) | 20.7607 | 0.846141 | ||||||||
\(603\) | −10.9021 | −0.443970 | ||||||||
\(604\) | 10.8627 | 0.441996 | ||||||||
\(605\) | 14.5504 | 0.591557 | ||||||||
\(606\) | −11.2159 | −0.455615 | ||||||||
\(607\) | 20.1275 | 0.816949 | 0.408474 | − | 0.912770i | \(-0.366061\pi\) | ||||
0.408474 | + | 0.912770i | \(0.366061\pi\) | |||||||
\(608\) | 4.58896 | 0.186107 | ||||||||
\(609\) | 10.0388 | 0.406792 | ||||||||
\(610\) | −19.1574 | −0.775661 | ||||||||
\(611\) | 22.8439 | 0.924166 | ||||||||
\(612\) | −1.69023 | −0.0683235 | ||||||||
\(613\) | 27.8629 | 1.12537 | 0.562687 | − | 0.826670i | \(-0.309768\pi\) | ||||
0.562687 | + | 0.826670i | \(0.309768\pi\) | |||||||
\(614\) | 12.2361 | 0.493808 | ||||||||
\(615\) | 10.6976 | 0.431368 | ||||||||
\(616\) | 4.29471 | 0.173039 | ||||||||
\(617\) | 5.49399 | 0.221180 | 0.110590 | − | 0.993866i | \(-0.464726\pi\) | ||||
0.110590 | + | 0.993866i | \(0.464726\pi\) | |||||||
\(618\) | −11.3812 | −0.457819 | ||||||||
\(619\) | −1.84044 | −0.0739735 | −0.0369868 | − | 0.999316i | \(-0.511776\pi\) | ||||
−0.0369868 | + | 0.999316i | \(0.511776\pi\) | |||||||
\(620\) | 11.5121 | 0.462336 | ||||||||
\(621\) | 41.1667 | 1.65196 | ||||||||
\(622\) | 22.2251 | 0.891143 | ||||||||
\(623\) | 35.3180 | 1.41499 | ||||||||
\(624\) | −2.70951 | −0.108467 | ||||||||
\(625\) | −8.43519 | −0.337408 | ||||||||
\(626\) | 11.3648 | 0.454229 | ||||||||
\(627\) | −9.49353 | −0.379135 | ||||||||
\(628\) | −6.32757 | −0.252498 | ||||||||
\(629\) | −0.625444 | −0.0249381 | ||||||||
\(630\) | −4.98707 | −0.198690 | ||||||||
\(631\) | 0.733207 | 0.0291885 | 0.0145943 | − | 0.999893i | \(-0.495354\pi\) | ||||
0.0145943 | + | 0.999893i | \(0.495354\pi\) | |||||||
\(632\) | −0.0708345 | −0.00281765 | ||||||||
\(633\) | 37.2166 | 1.47923 | ||||||||
\(634\) | 19.2327 | 0.763829 | ||||||||
\(635\) | −11.9104 | −0.472649 | ||||||||
\(636\) | −12.1275 | −0.480888 | ||||||||
\(637\) | 2.80267 | 0.111046 | ||||||||
\(638\) | −3.64488 | −0.144302 | ||||||||
\(639\) | 1.97342 | 0.0780674 | ||||||||
\(640\) | 1.65031 | 0.0652341 | ||||||||
\(641\) | 43.0323 | 1.69967 | 0.849836 | − | 0.527047i | \(-0.176701\pi\) | ||||
0.849836 | + | 0.527047i | \(0.176701\pi\) | |||||||
\(642\) | −14.0940 | −0.556246 | ||||||||
\(643\) | −10.3797 | −0.409335 | −0.204668 | − | 0.978832i | \(-0.565611\pi\) | ||||
−0.204668 | + | 0.978832i | \(0.565611\pi\) | |||||||
\(644\) | 21.1553 | 0.833635 | ||||||||
\(645\) | −16.5039 | −0.649840 | ||||||||
\(646\) | 7.46040 | 0.293526 | ||||||||
\(647\) | 39.7372 | 1.56223 | 0.781115 | − | 0.624387i | \(-0.214651\pi\) | ||||
0.781115 | + | 0.624387i | \(0.214651\pi\) | |||||||
\(648\) | 4.80005 | 0.188564 | ||||||||
\(649\) | 13.4796 | 0.529121 | ||||||||
\(650\) | 4.40546 | 0.172796 | ||||||||
\(651\) | 28.3881 | 1.11262 | ||||||||
\(652\) | 4.72853 | 0.185184 | ||||||||
\(653\) | −3.15386 | −0.123420 | −0.0617100 | − | 0.998094i | \(-0.519655\pi\) | ||||
−0.0617100 | + | 0.998094i | \(0.519655\pi\) | |||||||
\(654\) | −0.201481 | −0.00787854 | ||||||||
\(655\) | −32.2933 | −1.26180 | ||||||||
\(656\) | 4.62974 | 0.180761 | ||||||||
\(657\) | −11.1154 | −0.433651 | ||||||||
\(658\) | −34.3105 | −1.33756 | ||||||||
\(659\) | −8.11269 | −0.316025 | −0.158013 | − | 0.987437i | \(-0.550509\pi\) | ||||
−0.158013 | + | 0.987437i | \(0.550509\pi\) | |||||||
\(660\) | −3.41412 | −0.132894 | ||||||||
\(661\) | −24.0240 | −0.934424 | −0.467212 | − | 0.884145i | \(-0.654741\pi\) | ||||
−0.467212 | + | 0.884145i | \(0.654741\pi\) | |||||||
\(662\) | 14.7493 | 0.573249 | ||||||||
\(663\) | −4.40493 | −0.171073 | ||||||||
\(664\) | 7.35376 | 0.285381 | ||||||||
\(665\) | 22.0121 | 0.853594 | ||||||||
\(666\) | −0.399979 | −0.0154989 | ||||||||
\(667\) | −17.9543 | −0.695194 | ||||||||
\(668\) | 1.95392 | 0.0755993 | ||||||||
\(669\) | 14.1136 | 0.545664 | ||||||||
\(670\) | 17.3053 | 0.668562 | ||||||||
\(671\) | 17.1523 | 0.662157 | ||||||||
\(672\) | 4.06956 | 0.156987 | ||||||||
\(673\) | −3.92915 | −0.151458 | −0.0757288 | − | 0.997128i | \(-0.524128\pi\) | ||||
−0.0757288 | + | 0.997128i | \(0.524128\pi\) | |||||||
\(674\) | 20.3698 | 0.784614 | ||||||||
\(675\) | −12.8758 | −0.495591 | ||||||||
\(676\) | −9.25499 | −0.355961 | ||||||||
\(677\) | 17.1535 | 0.659262 | 0.329631 | − | 0.944110i | \(-0.393076\pi\) | ||||
0.329631 | + | 0.944110i | \(0.393076\pi\) | |||||||
\(678\) | −2.22334 | −0.0853870 | ||||||||
\(679\) | 6.86987 | 0.263641 | ||||||||
\(680\) | 2.68296 | 0.102887 | ||||||||
\(681\) | −12.2084 | −0.467827 | ||||||||
\(682\) | −10.3072 | −0.394682 | ||||||||
\(683\) | 39.1194 | 1.49686 | 0.748432 | − | 0.663212i | \(-0.230807\pi\) | ||||
0.748432 | + | 0.663212i | \(0.230807\pi\) | |||||||
\(684\) | 4.77102 | 0.182425 | ||||||||
\(685\) | 12.7754 | 0.488122 | ||||||||
\(686\) | 16.1366 | 0.616100 | ||||||||
\(687\) | 1.21242 | 0.0462566 | ||||||||
\(688\) | −7.14262 | −0.272310 | ||||||||
\(689\) | 16.7623 | 0.638595 | ||||||||
\(690\) | −16.8176 | −0.640236 | ||||||||
\(691\) | −35.6947 | −1.35789 | −0.678946 | − | 0.734188i | \(-0.737563\pi\) | ||||
−0.678946 | + | 0.734188i | \(0.737563\pi\) | |||||||
\(692\) | 7.13429 | 0.271205 | ||||||||
\(693\) | 4.46510 | 0.169615 | ||||||||
\(694\) | 5.92891 | 0.225058 | ||||||||
\(695\) | 32.4139 | 1.22953 | ||||||||
\(696\) | −3.45380 | −0.130916 | ||||||||
\(697\) | 7.52672 | 0.285095 | ||||||||
\(698\) | 5.89385 | 0.223085 | ||||||||
\(699\) | 21.5037 | 0.813343 | ||||||||
\(700\) | −6.61680 | −0.250092 | ||||||||
\(701\) | −9.98116 | −0.376983 | −0.188492 | − | 0.982075i | \(-0.560360\pi\) | ||||
−0.188492 | + | 0.982075i | \(0.560360\pi\) | |||||||
\(702\) | −10.9455 | −0.413113 | ||||||||
\(703\) | 1.76544 | 0.0665849 | ||||||||
\(704\) | −1.47758 | −0.0556883 | ||||||||
\(705\) | 27.2755 | 1.02726 | ||||||||
\(706\) | 31.6290 | 1.19037 | ||||||||
\(707\) | −23.2838 | −0.875677 | ||||||||
\(708\) | 12.7730 | 0.480037 | ||||||||
\(709\) | −27.9187 | −1.04851 | −0.524255 | − | 0.851561i | \(-0.675656\pi\) | ||||
−0.524255 | + | 0.851561i | \(0.675656\pi\) | |||||||
\(710\) | −3.13248 | −0.117560 | ||||||||
\(711\) | −0.0736449 | −0.00276190 | ||||||||
\(712\) | −12.1510 | −0.455379 | ||||||||
\(713\) | −50.7720 | −1.90143 | ||||||||
\(714\) | 6.61601 | 0.247598 | ||||||||
\(715\) | 4.71891 | 0.176477 | ||||||||
\(716\) | −14.6705 | −0.548262 | ||||||||
\(717\) | −7.04838 | −0.263226 | ||||||||
\(718\) | −12.1567 | −0.453683 | ||||||||
\(719\) | 10.2850 | 0.383566 | 0.191783 | − | 0.981437i | \(-0.438573\pi\) | ||||
0.191783 | + | 0.981437i | \(0.438573\pi\) | |||||||
\(720\) | 1.71578 | 0.0639435 | ||||||||
\(721\) | −23.6269 | −0.879912 | ||||||||
\(722\) | −2.05851 | −0.0766099 | ||||||||
\(723\) | 31.2785 | 1.16326 | ||||||||
\(724\) | −15.1348 | −0.562482 | ||||||||
\(725\) | 5.61563 | 0.208559 | ||||||||
\(726\) | −12.3445 | −0.458147 | ||||||||
\(727\) | 24.1344 | 0.895096 | 0.447548 | − | 0.894260i | \(-0.352297\pi\) | ||||
0.447548 | + | 0.894260i | \(0.352297\pi\) | |||||||
\(728\) | −5.62484 | −0.208470 | ||||||||
\(729\) | 28.7477 | 1.06473 | ||||||||
\(730\) | 17.6437 | 0.653024 | ||||||||
\(731\) | −11.6120 | −0.429484 | ||||||||
\(732\) | 16.2531 | 0.600732 | ||||||||
\(733\) | 22.3073 | 0.823939 | 0.411970 | − | 0.911198i | \(-0.364841\pi\) | ||||
0.411970 | + | 0.911198i | \(0.364841\pi\) | |||||||
\(734\) | −4.28416 | −0.158131 | ||||||||
\(735\) | 3.34637 | 0.123433 | ||||||||
\(736\) | −7.27839 | −0.268285 | ||||||||
\(737\) | −15.4940 | −0.570730 | ||||||||
\(738\) | 4.81343 | 0.177185 | ||||||||
\(739\) | −20.0881 | −0.738954 | −0.369477 | − | 0.929240i | \(-0.620463\pi\) | ||||
−0.369477 | + | 0.929240i | \(0.620463\pi\) | |||||||
\(740\) | 0.634899 | 0.0233394 | ||||||||
\(741\) | 12.4338 | 0.456768 | ||||||||
\(742\) | −25.1763 | −0.924251 | ||||||||
\(743\) | −38.5492 | −1.41423 | −0.707116 | − | 0.707097i | \(-0.750004\pi\) | ||||
−0.707116 | + | 0.707097i | \(0.750004\pi\) | |||||||
\(744\) | −9.76682 | −0.358069 | ||||||||
\(745\) | −29.3482 | −1.07524 | ||||||||
\(746\) | −18.3368 | −0.671358 | ||||||||
\(747\) | 7.64552 | 0.279735 | ||||||||
\(748\) | −2.40214 | −0.0878310 | ||||||||
\(749\) | −29.2586 | −1.06909 | ||||||||
\(750\) | 16.8132 | 0.613932 | ||||||||
\(751\) | −2.61394 | −0.0953840 | −0.0476920 | − | 0.998862i | \(-0.515187\pi\) | ||||
−0.0476920 | + | 0.998862i | \(0.515187\pi\) | |||||||
\(752\) | 11.8044 | 0.430462 | ||||||||
\(753\) | 3.18995 | 0.116248 | ||||||||
\(754\) | 4.77375 | 0.173850 | ||||||||
\(755\) | −17.9268 | −0.652421 | ||||||||
\(756\) | 16.4397 | 0.597906 | ||||||||
\(757\) | 49.1286 | 1.78561 | 0.892805 | − | 0.450444i | \(-0.148734\pi\) | ||||
0.892805 | + | 0.450444i | \(0.148734\pi\) | |||||||
\(758\) | 4.42412 | 0.160691 | ||||||||
\(759\) | 15.0574 | 0.546548 | ||||||||
\(760\) | −7.57319 | −0.274708 | ||||||||
\(761\) | −25.5828 | −0.927375 | −0.463688 | − | 0.885999i | \(-0.653474\pi\) | ||||
−0.463688 | + | 0.885999i | \(0.653474\pi\) | |||||||
\(762\) | 10.1047 | 0.366056 | ||||||||
\(763\) | −0.418267 | −0.0151423 | ||||||||
\(764\) | 9.90307 | 0.358281 | ||||||||
\(765\) | 2.78940 | 0.100851 | ||||||||
\(766\) | −17.4977 | −0.632217 | ||||||||
\(767\) | −17.6544 | −0.637465 | ||||||||
\(768\) | −1.40012 | −0.0505223 | ||||||||
\(769\) | −37.0420 | −1.33577 | −0.667885 | − | 0.744264i | \(-0.732800\pi\) | ||||
−0.667885 | + | 0.744264i | \(0.732800\pi\) | |||||||
\(770\) | −7.08759 | −0.255419 | ||||||||
\(771\) | 33.0279 | 1.18947 | ||||||||
\(772\) | 8.52394 | 0.306783 | ||||||||
\(773\) | −46.6837 | −1.67910 | −0.839548 | − | 0.543286i | \(-0.817180\pi\) | ||||
−0.839548 | + | 0.543286i | \(0.817180\pi\) | |||||||
\(774\) | −7.42600 | −0.266922 | ||||||||
\(775\) | 15.8801 | 0.570431 | ||||||||
\(776\) | −2.36355 | −0.0848466 | ||||||||
\(777\) | 1.56562 | 0.0561664 | ||||||||
\(778\) | 21.4150 | 0.767766 | ||||||||
\(779\) | −21.2457 | −0.761206 | ||||||||
\(780\) | 4.47152 | 0.160106 | ||||||||
\(781\) | 2.80461 | 0.100357 | ||||||||
\(782\) | −11.8327 | −0.423137 | ||||||||
\(783\) | −13.9522 | −0.498612 | ||||||||
\(784\) | 1.44825 | 0.0517234 | ||||||||
\(785\) | 10.4424 | 0.372707 | ||||||||
\(786\) | 27.3975 | 0.977237 | ||||||||
\(787\) | −21.4946 | −0.766199 | −0.383100 | − | 0.923707i | \(-0.625143\pi\) | ||||
−0.383100 | + | 0.923707i | \(0.625143\pi\) | |||||||
\(788\) | −5.02868 | −0.179139 | ||||||||
\(789\) | 18.9542 | 0.674786 | ||||||||
\(790\) | 0.116899 | 0.00415907 | ||||||||
\(791\) | −4.61558 | −0.164111 | ||||||||
\(792\) | −1.53620 | −0.0545864 | ||||||||
\(793\) | −22.4646 | −0.797741 | ||||||||
\(794\) | −29.7543 | −1.05594 | ||||||||
\(795\) | 20.0142 | 0.709829 | ||||||||
\(796\) | −4.44613 | −0.157589 | ||||||||
\(797\) | 16.4977 | 0.584379 | 0.292190 | − | 0.956360i | \(-0.405616\pi\) | ||||
0.292190 | + | 0.956360i | \(0.405616\pi\) | |||||||
\(798\) | −18.6750 | −0.661089 | ||||||||
\(799\) | 19.1908 | 0.678921 | ||||||||
\(800\) | 2.27649 | 0.0804859 | ||||||||
\(801\) | −12.6331 | −0.446369 | ||||||||
\(802\) | 21.7075 | 0.766518 | ||||||||
\(803\) | −15.7970 | −0.557465 | ||||||||
\(804\) | −14.6818 | −0.517786 | ||||||||
\(805\) | −34.9127 | −1.23051 | ||||||||
\(806\) | 13.4994 | 0.475497 | ||||||||
\(807\) | 2.12112 | 0.0746671 | ||||||||
\(808\) | 8.01069 | 0.281815 | ||||||||
\(809\) | 9.89800 | 0.347995 | 0.173997 | − | 0.984746i | \(-0.444332\pi\) | ||||
0.173997 | + | 0.984746i | \(0.444332\pi\) | |||||||
\(810\) | −7.92156 | −0.278335 | ||||||||
\(811\) | −35.5614 | −1.24873 | −0.624365 | − | 0.781133i | \(-0.714642\pi\) | ||||
−0.624365 | + | 0.781133i | \(0.714642\pi\) | |||||||
\(812\) | −7.16996 | −0.251616 | ||||||||
\(813\) | −12.0419 | −0.422327 | ||||||||
\(814\) | −0.568447 | −0.0199240 | ||||||||
\(815\) | −7.80353 | −0.273346 | ||||||||
\(816\) | −2.27621 | −0.0796833 | ||||||||
\(817\) | 32.7772 | 1.14673 | ||||||||
\(818\) | −7.31365 | −0.255716 | ||||||||
\(819\) | −5.84800 | −0.204346 | ||||||||
\(820\) | −7.64050 | −0.266818 | ||||||||
\(821\) | 37.6772 | 1.31494 | 0.657472 | − | 0.753479i | \(-0.271626\pi\) | ||||
0.657472 | + | 0.753479i | \(0.271626\pi\) | |||||||
\(822\) | −10.8386 | −0.378039 | ||||||||
\(823\) | 4.86689 | 0.169649 | 0.0848245 | − | 0.996396i | \(-0.472967\pi\) | ||||
0.0848245 | + | 0.996396i | \(0.472967\pi\) | |||||||
\(824\) | 8.12874 | 0.283178 | ||||||||
\(825\) | −4.70954 | −0.163965 | ||||||||
\(826\) | 26.5162 | 0.922616 | ||||||||
\(827\) | 5.70654 | 0.198436 | 0.0992179 | − | 0.995066i | \(-0.468366\pi\) | ||||
0.0992179 | + | 0.995066i | \(0.468366\pi\) | |||||||
\(828\) | −7.56716 | −0.262977 | ||||||||
\(829\) | 4.51774 | 0.156908 | 0.0784539 | − | 0.996918i | \(-0.475002\pi\) | ||||
0.0784539 | + | 0.996918i | \(0.475002\pi\) | |||||||
\(830\) | −12.1360 | −0.421246 | ||||||||
\(831\) | −33.9538 | −1.17785 | ||||||||
\(832\) | 1.93520 | 0.0670911 | ||||||||
\(833\) | 2.35447 | 0.0815776 | ||||||||
\(834\) | −27.4999 | −0.952242 | ||||||||
\(835\) | −3.22456 | −0.111591 | ||||||||
\(836\) | 6.78053 | 0.234510 | ||||||||
\(837\) | −39.4548 | −1.36376 | ||||||||
\(838\) | 13.1699 | 0.454948 | ||||||||
\(839\) | 8.52761 | 0.294406 | 0.147203 | − | 0.989106i | \(-0.452973\pi\) | ||||
0.147203 | + | 0.989106i | \(0.452973\pi\) | |||||||
\(840\) | −6.71603 | −0.231725 | ||||||||
\(841\) | −22.9149 | −0.790169 | ||||||||
\(842\) | 8.80366 | 0.303394 | ||||||||
\(843\) | 21.2329 | 0.731300 | ||||||||
\(844\) | −26.5811 | −0.914959 | ||||||||
\(845\) | 15.2736 | 0.525427 | ||||||||
\(846\) | 12.2727 | 0.421946 | ||||||||
\(847\) | −25.6267 | −0.880544 | ||||||||
\(848\) | 8.66181 | 0.297448 | ||||||||
\(849\) | 20.7513 | 0.712183 | ||||||||
\(850\) | 3.70095 | 0.126942 | ||||||||
\(851\) | −2.80011 | −0.0959865 | ||||||||
\(852\) | 2.65758 | 0.0910473 | ||||||||
\(853\) | 4.36409 | 0.149424 | 0.0747119 | − | 0.997205i | \(-0.476196\pi\) | ||||
0.0747119 | + | 0.997205i | \(0.476196\pi\) | |||||||
\(854\) | 33.7408 | 1.15459 | ||||||||
\(855\) | −7.87365 | −0.269273 | ||||||||
\(856\) | 10.0663 | 0.344059 | ||||||||
\(857\) | 53.4010 | 1.82414 | 0.912071 | − | 0.410032i | \(-0.134482\pi\) | ||||
0.912071 | + | 0.410032i | \(0.134482\pi\) | |||||||
\(858\) | −4.00351 | −0.136677 | ||||||||
\(859\) | −4.85224 | −0.165556 | −0.0827782 | − | 0.996568i | \(-0.526379\pi\) | ||||
−0.0827782 | + | 0.996568i | \(0.526379\pi\) | |||||||
\(860\) | 11.7875 | 0.401951 | ||||||||
\(861\) | −18.8410 | −0.642100 | ||||||||
\(862\) | −10.3251 | −0.351674 | ||||||||
\(863\) | 40.8772 | 1.39147 | 0.695737 | − | 0.718296i | \(-0.255078\pi\) | ||||
0.695737 | + | 0.718296i | \(0.255078\pi\) | |||||||
\(864\) | −5.65601 | −0.192422 | ||||||||
\(865\) | −11.7738 | −0.400320 | ||||||||
\(866\) | 2.40470 | 0.0817150 | ||||||||
\(867\) | 20.1015 | 0.682682 | ||||||||
\(868\) | −20.2755 | −0.688197 | ||||||||
\(869\) | −0.104663 | −0.00355046 | ||||||||
\(870\) | 5.69984 | 0.193243 | ||||||||
\(871\) | 20.2927 | 0.687594 | ||||||||
\(872\) | 0.143903 | 0.00487318 | ||||||||
\(873\) | −2.45732 | −0.0831678 | ||||||||
\(874\) | 33.4002 | 1.12978 | ||||||||
\(875\) | 34.9036 | 1.17996 | ||||||||
\(876\) | −14.9689 | −0.505752 | ||||||||
\(877\) | −32.9586 | −1.11293 | −0.556467 | − | 0.830870i | \(-0.687843\pi\) | ||||
−0.556467 | + | 0.830870i | \(0.687843\pi\) | |||||||
\(878\) | 4.75041 | 0.160318 | ||||||||
\(879\) | 12.5433 | 0.423075 | ||||||||
\(880\) | 2.43846 | 0.0822003 | ||||||||
\(881\) | −15.1301 | −0.509746 | −0.254873 | − | 0.966975i | \(-0.582034\pi\) | ||||
−0.254873 | + | 0.966975i | \(0.582034\pi\) | |||||||
\(882\) | 1.50571 | 0.0507000 | ||||||||
\(883\) | −39.0156 | −1.31298 | −0.656490 | − | 0.754335i | \(-0.727960\pi\) | ||||
−0.656490 | + | 0.754335i | \(0.727960\pi\) | |||||||
\(884\) | 3.14612 | 0.105815 | ||||||||
\(885\) | −21.0793 | −0.708573 | ||||||||
\(886\) | 8.62907 | 0.289899 | ||||||||
\(887\) | −24.7990 | −0.832670 | −0.416335 | − | 0.909211i | \(-0.636686\pi\) | ||||
−0.416335 | + | 0.909211i | \(0.636686\pi\) | |||||||
\(888\) | −0.538646 | −0.0180758 | ||||||||
\(889\) | 20.9770 | 0.703548 | ||||||||
\(890\) | 20.0529 | 0.672175 | ||||||||
\(891\) | 7.09245 | 0.237606 | ||||||||
\(892\) | −10.0803 | −0.337514 | ||||||||
\(893\) | −54.1699 | −1.81273 | ||||||||
\(894\) | 24.8990 | 0.832746 | ||||||||
\(895\) | 24.2108 | 0.809279 | ||||||||
\(896\) | −2.90659 | −0.0971023 | ||||||||
\(897\) | −19.7209 | −0.658460 | ||||||||
\(898\) | 37.8750 | 1.26390 | ||||||||
\(899\) | 17.2077 | 0.573908 | ||||||||
\(900\) | 2.36680 | 0.0788935 | ||||||||
\(901\) | 14.0818 | 0.469131 | ||||||||
\(902\) | 6.84080 | 0.227774 | ||||||||
\(903\) | 29.0673 | 0.967300 | ||||||||
\(904\) | 1.58797 | 0.0528152 | ||||||||
\(905\) | 24.9771 | 0.830268 | ||||||||
\(906\) | 15.2090 | 0.505285 | ||||||||
\(907\) | 15.4638 | 0.513468 | 0.256734 | − | 0.966482i | \(-0.417354\pi\) | ||||
0.256734 | + | 0.966482i | \(0.417354\pi\) | |||||||
\(908\) | 8.71957 | 0.289369 | ||||||||
\(909\) | 8.32851 | 0.276239 | ||||||||
\(910\) | 9.28271 | 0.307719 | ||||||||
\(911\) | 19.0998 | 0.632806 | 0.316403 | − | 0.948625i | \(-0.397525\pi\) | ||||
0.316403 | + | 0.948625i | \(0.397525\pi\) | |||||||
\(912\) | 6.42507 | 0.212755 | ||||||||
\(913\) | 10.8657 | 0.359604 | ||||||||
\(914\) | 18.4506 | 0.610292 | ||||||||
\(915\) | −26.8226 | −0.886728 | ||||||||
\(916\) | −0.865941 | −0.0286115 | ||||||||
\(917\) | 56.8762 | 1.87822 | ||||||||
\(918\) | −9.19515 | −0.303485 | ||||||||
\(919\) | 35.3335 | 1.16554 | 0.582772 | − | 0.812636i | \(-0.301968\pi\) | ||||
0.582772 | + | 0.812636i | \(0.301968\pi\) | |||||||
\(920\) | 12.0116 | 0.396010 | ||||||||
\(921\) | 17.1319 | 0.564516 | ||||||||
\(922\) | 22.9386 | 0.755443 | ||||||||
\(923\) | −3.67324 | −0.120906 | ||||||||
\(924\) | 6.01309 | 0.197816 | ||||||||
\(925\) | 0.875799 | 0.0287961 | ||||||||
\(926\) | −11.8503 | −0.389425 | ||||||||
\(927\) | 8.45125 | 0.277575 | ||||||||
\(928\) | 2.46680 | 0.0809766 | ||||||||
\(929\) | −44.1815 | −1.44955 | −0.724774 | − | 0.688987i | \(-0.758056\pi\) | ||||
−0.724774 | + | 0.688987i | \(0.758056\pi\) | |||||||
\(930\) | 16.1183 | 0.528538 | ||||||||
\(931\) | −6.64598 | −0.217813 | ||||||||
\(932\) | −15.3585 | −0.503084 | ||||||||
\(933\) | 31.1177 | 1.01875 | ||||||||
\(934\) | 13.6621 | 0.447038 | ||||||||
\(935\) | 3.96427 | 0.129646 | ||||||||
\(936\) | 2.01198 | 0.0657637 | ||||||||
\(937\) | −1.89370 | −0.0618644 | −0.0309322 | − | 0.999521i | \(-0.509848\pi\) | ||||
−0.0309322 | + | 0.999521i | \(0.509848\pi\) | |||||||
\(938\) | −30.4788 | −0.995168 | ||||||||
\(939\) | 15.9120 | 0.519270 | ||||||||
\(940\) | −19.4809 | −0.635397 | ||||||||
\(941\) | −2.09446 | −0.0682776 | −0.0341388 | − | 0.999417i | \(-0.510869\pi\) | ||||
−0.0341388 | + | 0.999417i | \(0.510869\pi\) | |||||||
\(942\) | −8.85934 | −0.288653 | ||||||||
\(943\) | 33.6971 | 1.09733 | ||||||||
\(944\) | −9.12278 | −0.296921 | ||||||||
\(945\) | −27.1306 | −0.882557 | ||||||||
\(946\) | −10.5538 | −0.343133 | ||||||||
\(947\) | 60.9845 | 1.98173 | 0.990865 | − | 0.134854i | \(-0.0430566\pi\) | ||||
0.990865 | + | 0.134854i | \(0.0430566\pi\) | |||||||
\(948\) | −0.0991766 | −0.00322111 | ||||||||
\(949\) | 20.6896 | 0.671613 | ||||||||
\(950\) | −10.4467 | −0.338935 | ||||||||
\(951\) | 26.9280 | 0.873201 | ||||||||
\(952\) | −4.72533 | −0.153149 | ||||||||
\(953\) | −25.8728 | −0.838103 | −0.419051 | − | 0.907962i | \(-0.637637\pi\) | ||||
−0.419051 | + | 0.907962i | \(0.637637\pi\) | |||||||
\(954\) | 9.00546 | 0.291562 | ||||||||
\(955\) | −16.3431 | −0.528851 | ||||||||
\(956\) | 5.03414 | 0.162816 | ||||||||
\(957\) | −5.10326 | −0.164965 | ||||||||
\(958\) | −18.8825 | −0.610067 | ||||||||
\(959\) | −22.5005 | −0.726579 | ||||||||
\(960\) | 2.31062 | 0.0745750 | ||||||||
\(961\) | 17.6607 | 0.569699 | ||||||||
\(962\) | 0.744503 | 0.0240037 | ||||||||
\(963\) | 10.4657 | 0.337252 | ||||||||
\(964\) | −22.3399 | −0.719520 | ||||||||
\(965\) | −14.0671 | −0.452837 | ||||||||
\(966\) | 29.6199 | 0.953003 | ||||||||
\(967\) | 46.7466 | 1.50327 | 0.751635 | − | 0.659579i | \(-0.229265\pi\) | ||||
0.751635 | + | 0.659579i | \(0.229265\pi\) | |||||||
\(968\) | 8.81677 | 0.283382 | ||||||||
\(969\) | 10.4454 | 0.335556 | ||||||||
\(970\) | 3.90059 | 0.125240 | ||||||||
\(971\) | 16.1187 | 0.517275 | 0.258637 | − | 0.965974i | \(-0.416727\pi\) | ||||
0.258637 | + | 0.965974i | \(0.416727\pi\) | |||||||
\(972\) | −10.2474 | −0.328686 | ||||||||
\(973\) | −57.0887 | −1.83018 | ||||||||
\(974\) | 8.95896 | 0.287064 | ||||||||
\(975\) | 6.16816 | 0.197539 | ||||||||
\(976\) | −11.6084 | −0.371576 | ||||||||
\(977\) | −4.13779 | −0.132380 | −0.0661898 | − | 0.997807i | \(-0.521084\pi\) | ||||
−0.0661898 | + | 0.997807i | \(0.521084\pi\) | |||||||
\(978\) | 6.62049 | 0.211700 | ||||||||
\(979\) | −17.9541 | −0.573814 | ||||||||
\(980\) | −2.39007 | −0.0763478 | ||||||||
\(981\) | 0.149612 | 0.00477676 | ||||||||
\(982\) | −4.69705 | −0.149889 | ||||||||
\(983\) | 42.3130 | 1.34958 | 0.674788 | − | 0.738011i | \(-0.264235\pi\) | ||||
0.674788 | + | 0.738011i | \(0.264235\pi\) | |||||||
\(984\) | 6.48218 | 0.206644 | ||||||||
\(985\) | 8.29886 | 0.264424 | ||||||||
\(986\) | 4.01035 | 0.127715 | ||||||||
\(987\) | −48.0388 | −1.52909 | ||||||||
\(988\) | −8.88056 | −0.282528 | ||||||||
\(989\) | −51.9868 | −1.65308 | ||||||||
\(990\) | 2.53520 | 0.0805740 | ||||||||
\(991\) | 55.7726 | 1.77168 | 0.885838 | − | 0.463995i | \(-0.153585\pi\) | ||||
0.885838 | + | 0.463995i | \(0.153585\pi\) | |||||||
\(992\) | 6.97572 | 0.221479 | ||||||||
\(993\) | 20.6508 | 0.655333 | ||||||||
\(994\) | 5.51704 | 0.174990 | ||||||||
\(995\) | 7.33748 | 0.232614 | ||||||||
\(996\) | 10.2961 | 0.326245 | ||||||||
\(997\) | 55.2400 | 1.74947 | 0.874735 | − | 0.484602i | \(-0.161036\pi\) | ||||
0.874735 | + | 0.484602i | \(0.161036\pi\) | |||||||
\(998\) | −25.0161 | −0.791871 | ||||||||
\(999\) | −2.17596 | −0.0688442 |
(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.d.1.13 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.d.1.13 | ✓ | 37 | 1.1 | even | 1 | trivial |