Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8009,2,Mod(1,8009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8009, 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("8009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8009 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8009.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: | \(63.9521869788\) |
Analytic rank: | \(0\) |
Dimension: | \(361\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71747 | −1.92154 | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(3\) | −2.51708 | −1.45324 | −0.726620 | − | 0.687040i | \(-0.758910\pi\) | ||||
−0.726620 | + | 0.687040i | \(0.758910\pi\) | |||||||
\(4\) | 5.38462 | 2.69231 | ||||||||
\(5\) | −3.75245 | −1.67815 | −0.839074 | − | 0.544017i | \(-0.816903\pi\) | ||||
−0.839074 | + | 0.544017i | \(0.816903\pi\) | |||||||
\(6\) | 6.84009 | 2.79245 | ||||||||
\(7\) | −1.33469 | −0.504466 | −0.252233 | − | 0.967667i | \(-0.581165\pi\) | ||||
−0.252233 | + | 0.967667i | \(0.581165\pi\) | |||||||
\(8\) | −9.19758 | −3.25183 | ||||||||
\(9\) | 3.33572 | 1.11191 | ||||||||
\(10\) | 10.1972 | 3.22463 | ||||||||
\(11\) | −1.04481 | −0.315021 | −0.157511 | − | 0.987517i | \(-0.550347\pi\) | ||||
−0.157511 | + | 0.987517i | \(0.550347\pi\) | |||||||
\(12\) | −13.5535 | −3.91257 | ||||||||
\(13\) | −5.94502 | −1.64885 | −0.824427 | − | 0.565969i | \(-0.808502\pi\) | ||||
−0.824427 | + | 0.565969i | \(0.808502\pi\) | |||||||
\(14\) | 3.62698 | 0.969350 | ||||||||
\(15\) | 9.44524 | 2.43875 | ||||||||
\(16\) | 14.2249 | 3.55621 | ||||||||
\(17\) | −2.54378 | −0.616958 | −0.308479 | − | 0.951231i | \(-0.599820\pi\) | ||||
−0.308479 | + | 0.951231i | \(0.599820\pi\) | |||||||
\(18\) | −9.06469 | −2.13657 | ||||||||
\(19\) | −1.83561 | −0.421118 | −0.210559 | − | 0.977581i | \(-0.567528\pi\) | ||||
−0.210559 | + | 0.977581i | \(0.567528\pi\) | |||||||
\(20\) | −20.2055 | −4.51809 | ||||||||
\(21\) | 3.35953 | 0.733110 | ||||||||
\(22\) | 2.83923 | 0.605325 | ||||||||
\(23\) | 3.09202 | 0.644730 | 0.322365 | − | 0.946615i | \(-0.395522\pi\) | ||||
0.322365 | + | 0.946615i | \(0.395522\pi\) | |||||||
\(24\) | 23.1511 | 4.72569 | ||||||||
\(25\) | 9.08091 | 1.81618 | ||||||||
\(26\) | 16.1554 | 3.16833 | ||||||||
\(27\) | −0.845024 | −0.162625 | ||||||||
\(28\) | −7.18680 | −1.35818 | ||||||||
\(29\) | 0.322861 | 0.0599538 | 0.0299769 | − | 0.999551i | \(-0.490457\pi\) | ||||
0.0299769 | + | 0.999551i | \(0.490457\pi\) | |||||||
\(30\) | −25.6671 | −4.68615 | ||||||||
\(31\) | 9.30447 | 1.67113 | 0.835566 | − | 0.549390i | \(-0.185140\pi\) | ||||
0.835566 | + | 0.549390i | \(0.185140\pi\) | |||||||
\(32\) | −20.2604 | −3.58157 | ||||||||
\(33\) | 2.62987 | 0.457801 | ||||||||
\(34\) | 6.91264 | 1.18551 | ||||||||
\(35\) | 5.00837 | 0.846569 | ||||||||
\(36\) | 17.9615 | 2.99359 | ||||||||
\(37\) | −2.56474 | −0.421641 | −0.210820 | − | 0.977525i | \(-0.567613\pi\) | ||||
−0.210820 | + | 0.977525i | \(0.567613\pi\) | |||||||
\(38\) | 4.98821 | 0.809194 | ||||||||
\(39\) | 14.9641 | 2.39618 | ||||||||
\(40\) | 34.5135 | 5.45706 | ||||||||
\(41\) | 5.41955 | 0.846392 | 0.423196 | − | 0.906038i | \(-0.360908\pi\) | ||||
0.423196 | + | 0.906038i | \(0.360908\pi\) | |||||||
\(42\) | −9.12941 | −1.40870 | ||||||||
\(43\) | 1.76199 | 0.268700 | 0.134350 | − | 0.990934i | \(-0.457105\pi\) | ||||
0.134350 | + | 0.990934i | \(0.457105\pi\) | |||||||
\(44\) | −5.62589 | −0.848134 | ||||||||
\(45\) | −12.5171 | −1.86594 | ||||||||
\(46\) | −8.40245 | −1.23887 | ||||||||
\(47\) | −4.79012 | −0.698711 | −0.349355 | − | 0.936990i | \(-0.613599\pi\) | ||||
−0.349355 | + | 0.936990i | \(0.613599\pi\) | |||||||
\(48\) | −35.8052 | −5.16803 | ||||||||
\(49\) | −5.21860 | −0.745514 | ||||||||
\(50\) | −24.6771 | −3.48986 | ||||||||
\(51\) | 6.40292 | 0.896588 | ||||||||
\(52\) | −32.0117 | −4.43922 | ||||||||
\(53\) | −9.23591 | −1.26865 | −0.634325 | − | 0.773066i | \(-0.718722\pi\) | ||||
−0.634325 | + | 0.773066i | \(0.718722\pi\) | |||||||
\(54\) | 2.29632 | 0.312490 | ||||||||
\(55\) | 3.92059 | 0.528652 | ||||||||
\(56\) | 12.2759 | 1.64044 | ||||||||
\(57\) | 4.62039 | 0.611985 | ||||||||
\(58\) | −0.877363 | −0.115203 | ||||||||
\(59\) | −11.5247 | −1.50039 | −0.750196 | − | 0.661215i | \(-0.770041\pi\) | ||||
−0.750196 | + | 0.661215i | \(0.770041\pi\) | |||||||
\(60\) | 50.8590 | 6.56587 | ||||||||
\(61\) | 4.80873 | 0.615695 | 0.307847 | − | 0.951436i | \(-0.400391\pi\) | ||||
0.307847 | + | 0.951436i | \(0.400391\pi\) | |||||||
\(62\) | −25.2846 | −3.21114 | ||||||||
\(63\) | −4.45215 | −0.560918 | ||||||||
\(64\) | 26.6072 | 3.32590 | ||||||||
\(65\) | 22.3084 | 2.76702 | ||||||||
\(66\) | −7.14658 | −0.879683 | ||||||||
\(67\) | −9.76767 | −1.19331 | −0.596655 | − | 0.802498i | \(-0.703504\pi\) | ||||
−0.596655 | + | 0.802498i | \(0.703504\pi\) | |||||||
\(68\) | −13.6973 | −1.66104 | ||||||||
\(69\) | −7.78287 | −0.936947 | ||||||||
\(70\) | −13.6101 | −1.62671 | ||||||||
\(71\) | −4.53332 | −0.538006 | −0.269003 | − | 0.963139i | \(-0.586694\pi\) | ||||
−0.269003 | + | 0.963139i | \(0.586694\pi\) | |||||||
\(72\) | −30.6805 | −3.61573 | ||||||||
\(73\) | 12.5354 | 1.46716 | 0.733578 | − | 0.679606i | \(-0.237849\pi\) | ||||
0.733578 | + | 0.679606i | \(0.237849\pi\) | |||||||
\(74\) | 6.96959 | 0.810198 | ||||||||
\(75\) | −22.8574 | −2.63935 | ||||||||
\(76\) | −9.88406 | −1.13378 | ||||||||
\(77\) | 1.39450 | 0.158917 | ||||||||
\(78\) | −40.6645 | −4.60435 | ||||||||
\(79\) | 5.29492 | 0.595725 | 0.297863 | − | 0.954609i | \(-0.403726\pi\) | ||||
0.297863 | + | 0.954609i | \(0.403726\pi\) | |||||||
\(80\) | −53.3781 | −5.96786 | ||||||||
\(81\) | −7.88015 | −0.875572 | ||||||||
\(82\) | −14.7274 | −1.62637 | ||||||||
\(83\) | 4.14711 | 0.455205 | 0.227602 | − | 0.973754i | \(-0.426911\pi\) | ||||
0.227602 | + | 0.973754i | \(0.426911\pi\) | |||||||
\(84\) | 18.0898 | 1.97376 | ||||||||
\(85\) | 9.54543 | 1.03535 | ||||||||
\(86\) | −4.78813 | −0.516318 | ||||||||
\(87\) | −0.812668 | −0.0871272 | ||||||||
\(88\) | 9.60970 | 1.02440 | ||||||||
\(89\) | −0.157865 | −0.0167336 | −0.00836682 | − | 0.999965i | \(-0.502663\pi\) | ||||
−0.00836682 | + | 0.999965i | \(0.502663\pi\) | |||||||
\(90\) | 34.0148 | 3.58548 | ||||||||
\(91\) | 7.93477 | 0.831790 | ||||||||
\(92\) | 16.6493 | 1.73581 | ||||||||
\(93\) | −23.4201 | −2.42856 | ||||||||
\(94\) | 13.0170 | 1.34260 | ||||||||
\(95\) | 6.88805 | 0.706699 | ||||||||
\(96\) | 50.9972 | 5.20488 | ||||||||
\(97\) | 2.80427 | 0.284731 | 0.142365 | − | 0.989814i | \(-0.454529\pi\) | ||||
0.142365 | + | 0.989814i | \(0.454529\pi\) | |||||||
\(98\) | 14.1814 | 1.43253 | ||||||||
\(99\) | −3.48518 | −0.350274 | ||||||||
\(100\) | 48.8972 | 4.88972 | ||||||||
\(101\) | 2.05790 | 0.204769 | 0.102385 | − | 0.994745i | \(-0.467353\pi\) | ||||
0.102385 | + | 0.994745i | \(0.467353\pi\) | |||||||
\(102\) | −17.3997 | −1.72283 | ||||||||
\(103\) | −0.579080 | −0.0570585 | −0.0285292 | − | 0.999593i | \(-0.509082\pi\) | ||||
−0.0285292 | + | 0.999593i | \(0.509082\pi\) | |||||||
\(104\) | 54.6798 | 5.36180 | ||||||||
\(105\) | −12.6065 | −1.23027 | ||||||||
\(106\) | 25.0983 | 2.43776 | ||||||||
\(107\) | −9.05264 | −0.875152 | −0.437576 | − | 0.899182i | \(-0.644163\pi\) | ||||
−0.437576 | + | 0.899182i | \(0.644163\pi\) | |||||||
\(108\) | −4.55013 | −0.437836 | ||||||||
\(109\) | 11.4149 | 1.09335 | 0.546675 | − | 0.837345i | \(-0.315893\pi\) | ||||
0.546675 | + | 0.837345i | \(0.315893\pi\) | |||||||
\(110\) | −10.6541 | −1.01583 | ||||||||
\(111\) | 6.45567 | 0.612745 | ||||||||
\(112\) | −18.9858 | −1.79399 | ||||||||
\(113\) | −4.52023 | −0.425227 | −0.212614 | − | 0.977136i | \(-0.568198\pi\) | ||||
−0.212614 | + | 0.977136i | \(0.568198\pi\) | |||||||
\(114\) | −12.5557 | −1.17595 | ||||||||
\(115\) | −11.6026 | −1.08195 | ||||||||
\(116\) | 1.73848 | 0.161414 | ||||||||
\(117\) | −19.8309 | −1.83337 | ||||||||
\(118\) | 31.3181 | 2.88306 | ||||||||
\(119\) | 3.39517 | 0.311234 | ||||||||
\(120\) | −86.8734 | −7.93042 | ||||||||
\(121\) | −9.90838 | −0.900762 | ||||||||
\(122\) | −13.0676 | −1.18308 | ||||||||
\(123\) | −13.6415 | −1.23001 | ||||||||
\(124\) | 50.1010 | 4.49920 | ||||||||
\(125\) | −15.3134 | −1.36967 | ||||||||
\(126\) | 12.0986 | 1.07783 | ||||||||
\(127\) | −2.16752 | −0.192336 | −0.0961680 | − | 0.995365i | \(-0.530659\pi\) | ||||
−0.0961680 | + | 0.995365i | \(0.530659\pi\) | |||||||
\(128\) | −31.7834 | −2.80928 | ||||||||
\(129\) | −4.43507 | −0.390486 | ||||||||
\(130\) | −60.6224 | −5.31693 | ||||||||
\(131\) | −18.0575 | −1.57769 | −0.788845 | − | 0.614592i | \(-0.789321\pi\) | ||||
−0.788845 | + | 0.614592i | \(0.789321\pi\) | |||||||
\(132\) | 14.1608 | 1.23254 | ||||||||
\(133\) | 2.44997 | 0.212440 | ||||||||
\(134\) | 26.5433 | 2.29299 | ||||||||
\(135\) | 3.17091 | 0.272909 | ||||||||
\(136\) | 23.3966 | 2.00625 | ||||||||
\(137\) | 1.45768 | 0.124538 | 0.0622688 | − | 0.998059i | \(-0.480166\pi\) | ||||
0.0622688 | + | 0.998059i | \(0.480166\pi\) | |||||||
\(138\) | 21.1497 | 1.80038 | ||||||||
\(139\) | −2.89568 | −0.245608 | −0.122804 | − | 0.992431i | \(-0.539189\pi\) | ||||
−0.122804 | + | 0.992431i | \(0.539189\pi\) | |||||||
\(140\) | 26.9681 | 2.27922 | ||||||||
\(141\) | 12.0571 | 1.01539 | ||||||||
\(142\) | 12.3191 | 1.03380 | ||||||||
\(143\) | 6.21141 | 0.519424 | ||||||||
\(144\) | 47.4501 | 3.95417 | ||||||||
\(145\) | −1.21152 | −0.100611 | ||||||||
\(146\) | −34.0645 | −2.81920 | ||||||||
\(147\) | 13.1357 | 1.08341 | ||||||||
\(148\) | −13.8101 | −1.13519 | ||||||||
\(149\) | −6.53258 | −0.535170 | −0.267585 | − | 0.963534i | \(-0.586226\pi\) | ||||
−0.267585 | + | 0.963534i | \(0.586226\pi\) | |||||||
\(150\) | 62.1142 | 5.07161 | ||||||||
\(151\) | −24.1860 | −1.96823 | −0.984116 | − | 0.177527i | \(-0.943190\pi\) | ||||
−0.984116 | + | 0.177527i | \(0.943190\pi\) | |||||||
\(152\) | 16.8832 | 1.36941 | ||||||||
\(153\) | −8.48534 | −0.685999 | ||||||||
\(154\) | −3.78949 | −0.305366 | ||||||||
\(155\) | −34.9146 | −2.80441 | ||||||||
\(156\) | 80.5761 | 6.45125 | ||||||||
\(157\) | 24.3221 | 1.94112 | 0.970559 | − | 0.240862i | \(-0.0774300\pi\) | ||||
0.970559 | + | 0.240862i | \(0.0774300\pi\) | |||||||
\(158\) | −14.3888 | −1.14471 | ||||||||
\(159\) | 23.2476 | 1.84365 | ||||||||
\(160\) | 76.0262 | 6.01040 | ||||||||
\(161\) | −4.12689 | −0.325244 | ||||||||
\(162\) | 21.4140 | 1.68245 | ||||||||
\(163\) | −15.6945 | −1.22929 | −0.614646 | − | 0.788803i | \(-0.710701\pi\) | ||||
−0.614646 | + | 0.788803i | \(0.710701\pi\) | |||||||
\(164\) | 29.1822 | 2.27875 | ||||||||
\(165\) | −9.86846 | −0.768259 | ||||||||
\(166\) | −11.2696 | −0.874693 | ||||||||
\(167\) | −4.78679 | −0.370413 | −0.185206 | − | 0.982700i | \(-0.559295\pi\) | ||||
−0.185206 | + | 0.982700i | \(0.559295\pi\) | |||||||
\(168\) | −30.8995 | −2.38395 | ||||||||
\(169\) | 22.3433 | 1.71872 | ||||||||
\(170\) | −25.9394 | −1.98946 | ||||||||
\(171\) | −6.12308 | −0.468243 | ||||||||
\(172\) | 9.48762 | 0.723424 | ||||||||
\(173\) | −0.113620 | −0.00863837 | −0.00431918 | − | 0.999991i | \(-0.501375\pi\) | ||||
−0.00431918 | + | 0.999991i | \(0.501375\pi\) | |||||||
\(174\) | 2.20840 | 0.167418 | ||||||||
\(175\) | −12.1202 | −0.916202 | ||||||||
\(176\) | −14.8622 | −1.12028 | ||||||||
\(177\) | 29.0087 | 2.18043 | ||||||||
\(178\) | 0.428992 | 0.0321543 | ||||||||
\(179\) | −12.5008 | −0.934352 | −0.467176 | − | 0.884164i | \(-0.654729\pi\) | ||||
−0.467176 | + | 0.884164i | \(0.654729\pi\) | |||||||
\(180\) | −67.3999 | −5.02369 | ||||||||
\(181\) | −1.54703 | −0.114990 | −0.0574948 | − | 0.998346i | \(-0.518311\pi\) | ||||
−0.0574948 | + | 0.998346i | \(0.518311\pi\) | |||||||
\(182\) | −21.5625 | −1.59832 | ||||||||
\(183\) | −12.1040 | −0.894752 | ||||||||
\(184\) | −28.4391 | −2.09655 | ||||||||
\(185\) | 9.62407 | 0.707575 | ||||||||
\(186\) | 63.6434 | 4.66656 | ||||||||
\(187\) | 2.65776 | 0.194355 | ||||||||
\(188\) | −25.7930 | −1.88114 | ||||||||
\(189\) | 1.12785 | 0.0820387 | ||||||||
\(190\) | −18.7180 | −1.35795 | ||||||||
\(191\) | −21.1353 | −1.52929 | −0.764647 | − | 0.644450i | \(-0.777087\pi\) | ||||
−0.764647 | + | 0.644450i | \(0.777087\pi\) | |||||||
\(192\) | −66.9726 | −4.83333 | ||||||||
\(193\) | −14.1217 | −1.01650 | −0.508252 | − | 0.861208i | \(-0.669708\pi\) | ||||
−0.508252 | + | 0.861208i | \(0.669708\pi\) | |||||||
\(194\) | −7.62052 | −0.547121 | ||||||||
\(195\) | −56.1522 | −4.02114 | ||||||||
\(196\) | −28.1002 | −2.00715 | ||||||||
\(197\) | −22.5828 | −1.60896 | −0.804478 | − | 0.593983i | \(-0.797555\pi\) | ||||
−0.804478 | + | 0.593983i | \(0.797555\pi\) | |||||||
\(198\) | 9.47086 | 0.673064 | ||||||||
\(199\) | 16.7991 | 1.19086 | 0.595429 | − | 0.803408i | \(-0.296982\pi\) | ||||
0.595429 | + | 0.803408i | \(0.296982\pi\) | |||||||
\(200\) | −83.5224 | −5.90592 | ||||||||
\(201\) | 24.5861 | 1.73417 | ||||||||
\(202\) | −5.59228 | −0.393472 | ||||||||
\(203\) | −0.430920 | −0.0302446 | ||||||||
\(204\) | 34.4773 | 2.41389 | ||||||||
\(205\) | −20.3366 | −1.42037 | ||||||||
\(206\) | 1.57363 | 0.109640 | ||||||||
\(207\) | 10.3141 | 0.716878 | ||||||||
\(208\) | −84.5671 | −5.86368 | ||||||||
\(209\) | 1.91786 | 0.132661 | ||||||||
\(210\) | 34.2577 | 2.36400 | ||||||||
\(211\) | 7.05299 | 0.485548 | 0.242774 | − | 0.970083i | \(-0.421943\pi\) | ||||
0.242774 | + | 0.970083i | \(0.421943\pi\) | |||||||
\(212\) | −49.7319 | −3.41560 | ||||||||
\(213\) | 11.4108 | 0.781852 | ||||||||
\(214\) | 24.6002 | 1.68164 | ||||||||
\(215\) | −6.61177 | −0.450919 | ||||||||
\(216\) | 7.77217 | 0.528829 | ||||||||
\(217\) | −12.4186 | −0.843029 | ||||||||
\(218\) | −31.0196 | −2.10091 | ||||||||
\(219\) | −31.5526 | −2.13213 | ||||||||
\(220\) | 21.1109 | 1.42330 | ||||||||
\(221\) | 15.1229 | 1.01727 | ||||||||
\(222\) | −17.5430 | −1.17741 | ||||||||
\(223\) | −20.8463 | −1.39597 | −0.697986 | − | 0.716111i | \(-0.745920\pi\) | ||||
−0.697986 | + | 0.716111i | \(0.745920\pi\) | |||||||
\(224\) | 27.0414 | 1.80678 | ||||||||
\(225\) | 30.2913 | 2.01942 | ||||||||
\(226\) | 12.2836 | 0.817090 | ||||||||
\(227\) | 21.7550 | 1.44393 | 0.721966 | − | 0.691929i | \(-0.243239\pi\) | ||||
0.721966 | + | 0.691929i | \(0.243239\pi\) | |||||||
\(228\) | 24.8790 | 1.64765 | ||||||||
\(229\) | −0.668015 | −0.0441437 | −0.0220718 | − | 0.999756i | \(-0.507026\pi\) | ||||
−0.0220718 | + | 0.999756i | \(0.507026\pi\) | |||||||
\(230\) | 31.5298 | 2.07901 | ||||||||
\(231\) | −3.51006 | −0.230945 | ||||||||
\(232\) | −2.96954 | −0.194960 | ||||||||
\(233\) | 22.6038 | 1.48083 | 0.740413 | − | 0.672153i | \(-0.234630\pi\) | ||||
0.740413 | + | 0.672153i | \(0.234630\pi\) | |||||||
\(234\) | 53.8898 | 3.52289 | ||||||||
\(235\) | 17.9747 | 1.17254 | ||||||||
\(236\) | −62.0563 | −4.03952 | ||||||||
\(237\) | −13.3278 | −0.865731 | ||||||||
\(238\) | −9.22625 | −0.598049 | ||||||||
\(239\) | −15.3190 | −0.990905 | −0.495453 | − | 0.868635i | \(-0.664998\pi\) | ||||
−0.495453 | + | 0.868635i | \(0.664998\pi\) | |||||||
\(240\) | 134.357 | 8.67272 | ||||||||
\(241\) | 11.8272 | 0.761857 | 0.380928 | − | 0.924605i | \(-0.375604\pi\) | ||||
0.380928 | + | 0.924605i | \(0.375604\pi\) | |||||||
\(242\) | 26.9257 | 1.73085 | ||||||||
\(243\) | 22.3701 | 1.43504 | ||||||||
\(244\) | 25.8932 | 1.65764 | ||||||||
\(245\) | 19.5826 | 1.25108 | ||||||||
\(246\) | 37.0702 | 2.36351 | ||||||||
\(247\) | 10.9128 | 0.694362 | ||||||||
\(248\) | −85.5786 | −5.43425 | ||||||||
\(249\) | −10.4386 | −0.661522 | ||||||||
\(250\) | 41.6137 | 2.63188 | ||||||||
\(251\) | −3.00126 | −0.189438 | −0.0947190 | − | 0.995504i | \(-0.530195\pi\) | ||||
−0.0947190 | + | 0.995504i | \(0.530195\pi\) | |||||||
\(252\) | −23.9731 | −1.51016 | ||||||||
\(253\) | −3.23056 | −0.203104 | ||||||||
\(254\) | 5.89015 | 0.369581 | ||||||||
\(255\) | −24.0267 | −1.50461 | ||||||||
\(256\) | 33.1558 | 2.07224 | ||||||||
\(257\) | 2.91116 | 0.181593 | 0.0907965 | − | 0.995869i | \(-0.471059\pi\) | ||||
0.0907965 | + | 0.995869i | \(0.471059\pi\) | |||||||
\(258\) | 12.0521 | 0.750334 | ||||||||
\(259\) | 3.42314 | 0.212703 | ||||||||
\(260\) | 120.122 | 7.44967 | ||||||||
\(261\) | 1.07697 | 0.0666629 | ||||||||
\(262\) | 49.0706 | 3.03159 | ||||||||
\(263\) | 2.45269 | 0.151239 | 0.0756197 | − | 0.997137i | \(-0.475907\pi\) | ||||
0.0756197 | + | 0.997137i | \(0.475907\pi\) | |||||||
\(264\) | −24.1884 | −1.48869 | ||||||||
\(265\) | 34.6573 | 2.12898 | ||||||||
\(266\) | −6.65772 | −0.408211 | ||||||||
\(267\) | 0.397359 | 0.0243180 | ||||||||
\(268\) | −52.5951 | −3.21276 | ||||||||
\(269\) | 26.1297 | 1.59316 | 0.796579 | − | 0.604535i | \(-0.206641\pi\) | ||||
0.796579 | + | 0.604535i | \(0.206641\pi\) | |||||||
\(270\) | −8.61684 | −0.524404 | ||||||||
\(271\) | −18.1483 | −1.10243 | −0.551216 | − | 0.834362i | \(-0.685836\pi\) | ||||
−0.551216 | + | 0.834362i | \(0.685836\pi\) | |||||||
\(272\) | −36.1850 | −2.19404 | ||||||||
\(273\) | −19.9725 | −1.20879 | ||||||||
\(274\) | −3.96118 | −0.239304 | ||||||||
\(275\) | −9.48780 | −0.572136 | ||||||||
\(276\) | −41.9077 | −2.52255 | ||||||||
\(277\) | −14.5571 | −0.874649 | −0.437324 | − | 0.899304i | \(-0.644074\pi\) | ||||
−0.437324 | + | 0.899304i | \(0.644074\pi\) | |||||||
\(278\) | 7.86890 | 0.471945 | ||||||||
\(279\) | 31.0371 | 1.85814 | ||||||||
\(280\) | −46.0648 | −2.75290 | ||||||||
\(281\) | −33.3366 | −1.98869 | −0.994347 | − | 0.106177i | \(-0.966139\pi\) | ||||
−0.994347 | + | 0.106177i | \(0.966139\pi\) | |||||||
\(282\) | −32.7648 | −1.95112 | ||||||||
\(283\) | −10.0408 | −0.596862 | −0.298431 | − | 0.954431i | \(-0.596463\pi\) | ||||
−0.298431 | + | 0.954431i | \(0.596463\pi\) | |||||||
\(284\) | −24.4102 | −1.44848 | ||||||||
\(285\) | −17.3378 | −1.02700 | ||||||||
\(286\) | −16.8793 | −0.998093 | ||||||||
\(287\) | −7.23343 | −0.426976 | ||||||||
\(288\) | −67.5829 | −3.98236 | ||||||||
\(289\) | −10.5292 | −0.619362 | ||||||||
\(290\) | 3.29227 | 0.193328 | ||||||||
\(291\) | −7.05859 | −0.413782 | ||||||||
\(292\) | 67.4982 | 3.95003 | ||||||||
\(293\) | −26.3045 | −1.53673 | −0.768363 | − | 0.640014i | \(-0.778929\pi\) | ||||
−0.768363 | + | 0.640014i | \(0.778929\pi\) | |||||||
\(294\) | −35.6957 | −2.08181 | ||||||||
\(295\) | 43.2460 | 2.51788 | ||||||||
\(296\) | 23.5894 | 1.37111 | ||||||||
\(297\) | 0.882887 | 0.0512303 | ||||||||
\(298\) | 17.7521 | 1.02835 | ||||||||
\(299\) | −18.3821 | −1.06306 | ||||||||
\(300\) | −123.078 | −7.10594 | ||||||||
\(301\) | −2.35171 | −0.135550 | ||||||||
\(302\) | 65.7247 | 3.78203 | ||||||||
\(303\) | −5.17992 | −0.297579 | ||||||||
\(304\) | −26.1113 | −1.49759 | ||||||||
\(305\) | −18.0445 | −1.03323 | ||||||||
\(306\) | 23.0586 | 1.31817 | ||||||||
\(307\) | −17.9933 | −1.02693 | −0.513465 | − | 0.858110i | \(-0.671638\pi\) | ||||
−0.513465 | + | 0.858110i | \(0.671638\pi\) | |||||||
\(308\) | 7.50882 | 0.427855 | ||||||||
\(309\) | 1.45759 | 0.0829196 | ||||||||
\(310\) | 94.8792 | 5.38878 | ||||||||
\(311\) | 2.59728 | 0.147278 | 0.0736391 | − | 0.997285i | \(-0.476539\pi\) | ||||
0.0736391 | + | 0.997285i | \(0.476539\pi\) | |||||||
\(312\) | −137.634 | −7.79198 | ||||||||
\(313\) | −16.7931 | −0.949201 | −0.474601 | − | 0.880201i | \(-0.657407\pi\) | ||||
−0.474601 | + | 0.880201i | \(0.657407\pi\) | |||||||
\(314\) | −66.0946 | −3.72993 | ||||||||
\(315\) | 16.7065 | 0.941304 | ||||||||
\(316\) | 28.5111 | 1.60388 | ||||||||
\(317\) | −31.7081 | −1.78090 | −0.890451 | − | 0.455078i | \(-0.849611\pi\) | ||||
−0.890451 | + | 0.455078i | \(0.849611\pi\) | |||||||
\(318\) | −63.1745 | −3.54265 | ||||||||
\(319\) | −0.337328 | −0.0188867 | ||||||||
\(320\) | −99.8424 | −5.58136 | ||||||||
\(321\) | 22.7863 | 1.27180 | ||||||||
\(322\) | 11.2147 | 0.624969 | ||||||||
\(323\) | 4.66940 | 0.259812 | ||||||||
\(324\) | −42.4316 | −2.35731 | ||||||||
\(325\) | −53.9862 | −2.99462 | ||||||||
\(326\) | 42.6494 | 2.36213 | ||||||||
\(327\) | −28.7323 | −1.58890 | ||||||||
\(328\) | −49.8468 | −2.75233 | ||||||||
\(329\) | 6.39333 | 0.352476 | ||||||||
\(330\) | 26.8172 | 1.47624 | ||||||||
\(331\) | 8.76766 | 0.481914 | 0.240957 | − | 0.970536i | \(-0.422539\pi\) | ||||
0.240957 | + | 0.970536i | \(0.422539\pi\) | |||||||
\(332\) | 22.3306 | 1.22555 | ||||||||
\(333\) | −8.55524 | −0.468824 | ||||||||
\(334\) | 13.0079 | 0.711762 | ||||||||
\(335\) | 36.6527 | 2.00255 | ||||||||
\(336\) | 47.7889 | 2.60710 | ||||||||
\(337\) | 31.7261 | 1.72823 | 0.864115 | − | 0.503295i | \(-0.167879\pi\) | ||||
0.864115 | + | 0.503295i | \(0.167879\pi\) | |||||||
\(338\) | −60.7172 | −3.30258 | ||||||||
\(339\) | 11.3778 | 0.617957 | ||||||||
\(340\) | 51.3985 | 2.78747 | ||||||||
\(341\) | −9.72138 | −0.526442 | ||||||||
\(342\) | 16.6392 | 0.899747 | ||||||||
\(343\) | 16.3081 | 0.880552 | ||||||||
\(344\) | −16.2060 | −0.873769 | ||||||||
\(345\) | 29.2048 | 1.57234 | ||||||||
\(346\) | 0.308758 | 0.0165990 | ||||||||
\(347\) | −17.3318 | −0.930420 | −0.465210 | − | 0.885200i | \(-0.654021\pi\) | ||||
−0.465210 | + | 0.885200i | \(0.654021\pi\) | |||||||
\(348\) | −4.37591 | −0.234573 | ||||||||
\(349\) | −13.8614 | −0.741985 | −0.370993 | − | 0.928636i | \(-0.620983\pi\) | ||||
−0.370993 | + | 0.928636i | \(0.620983\pi\) | |||||||
\(350\) | 32.9362 | 1.76052 | ||||||||
\(351\) | 5.02369 | 0.268145 | ||||||||
\(352\) | 21.1682 | 1.12827 | ||||||||
\(353\) | −8.40589 | −0.447400 | −0.223700 | − | 0.974658i | \(-0.571814\pi\) | ||||
−0.223700 | + | 0.974658i | \(0.571814\pi\) | |||||||
\(354\) | −78.8302 | −4.18978 | ||||||||
\(355\) | 17.0111 | 0.902854 | ||||||||
\(356\) | −0.850042 | −0.0450521 | ||||||||
\(357\) | −8.54592 | −0.452298 | ||||||||
\(358\) | 33.9704 | 1.79539 | ||||||||
\(359\) | 17.8469 | 0.941921 | 0.470960 | − | 0.882154i | \(-0.343907\pi\) | ||||
0.470960 | + | 0.882154i | \(0.343907\pi\) | |||||||
\(360\) | 115.127 | 6.06773 | ||||||||
\(361\) | −15.6305 | −0.822660 | ||||||||
\(362\) | 4.20399 | 0.220957 | ||||||||
\(363\) | 24.9402 | 1.30902 | ||||||||
\(364\) | 42.7257 | 2.23944 | ||||||||
\(365\) | −47.0384 | −2.46210 | ||||||||
\(366\) | 32.8921 | 1.71930 | ||||||||
\(367\) | −0.474684 | −0.0247783 | −0.0123892 | − | 0.999923i | \(-0.503944\pi\) | ||||
−0.0123892 | + | 0.999923i | \(0.503944\pi\) | |||||||
\(368\) | 43.9835 | 2.29280 | ||||||||
\(369\) | 18.0781 | 0.941108 | ||||||||
\(370\) | −26.1531 | −1.35963 | ||||||||
\(371\) | 12.3271 | 0.639991 | ||||||||
\(372\) | −126.108 | −6.53842 | ||||||||
\(373\) | −15.3175 | −0.793112 | −0.396556 | − | 0.918011i | \(-0.629795\pi\) | ||||
−0.396556 | + | 0.918011i | \(0.629795\pi\) | |||||||
\(374\) | −7.22238 | −0.373461 | ||||||||
\(375\) | 38.5452 | 1.99046 | ||||||||
\(376\) | 44.0575 | 2.27209 | ||||||||
\(377\) | −1.91942 | −0.0988550 | ||||||||
\(378\) | −3.06488 | −0.157640 | ||||||||
\(379\) | 7.47492 | 0.383961 | 0.191980 | − | 0.981399i | \(-0.438509\pi\) | ||||
0.191980 | + | 0.981399i | \(0.438509\pi\) | |||||||
\(380\) | 37.0895 | 1.90265 | ||||||||
\(381\) | 5.45582 | 0.279510 | ||||||||
\(382\) | 57.4343 | 2.93860 | ||||||||
\(383\) | −3.76601 | −0.192434 | −0.0962170 | − | 0.995360i | \(-0.530674\pi\) | ||||
−0.0962170 | + | 0.995360i | \(0.530674\pi\) | |||||||
\(384\) | 80.0015 | 4.08256 | ||||||||
\(385\) | −5.23278 | −0.266687 | ||||||||
\(386\) | 38.3753 | 1.95325 | ||||||||
\(387\) | 5.87748 | 0.298769 | ||||||||
\(388\) | 15.0999 | 0.766583 | ||||||||
\(389\) | −10.3920 | −0.526895 | −0.263448 | − | 0.964674i | \(-0.584860\pi\) | ||||
−0.263448 | + | 0.964674i | \(0.584860\pi\) | |||||||
\(390\) | 152.592 | 7.72678 | ||||||||
\(391\) | −7.86542 | −0.397771 | ||||||||
\(392\) | 47.9985 | 2.42429 | ||||||||
\(393\) | 45.4522 | 2.29276 | ||||||||
\(394\) | 61.3679 | 3.09167 | ||||||||
\(395\) | −19.8689 | −0.999715 | ||||||||
\(396\) | −18.7664 | −0.943045 | ||||||||
\(397\) | −27.8298 | −1.39674 | −0.698369 | − | 0.715738i | \(-0.746091\pi\) | ||||
−0.698369 | + | 0.715738i | \(0.746091\pi\) | |||||||
\(398\) | −45.6510 | −2.28828 | ||||||||
\(399\) | −6.16679 | −0.308726 | ||||||||
\(400\) | 129.175 | 6.45873 | ||||||||
\(401\) | −30.2231 | −1.50927 | −0.754635 | − | 0.656144i | \(-0.772186\pi\) | ||||
−0.754635 | + | 0.656144i | \(0.772186\pi\) | |||||||
\(402\) | −66.8117 | −3.33227 | ||||||||
\(403\) | −55.3153 | −2.75545 | ||||||||
\(404\) | 11.0810 | 0.551302 | ||||||||
\(405\) | 29.5699 | 1.46934 | ||||||||
\(406\) | 1.17101 | 0.0581162 | ||||||||
\(407\) | 2.67966 | 0.132826 | ||||||||
\(408\) | −58.8913 | −2.91556 | ||||||||
\(409\) | −12.3463 | −0.610486 | −0.305243 | − | 0.952274i | \(-0.598738\pi\) | ||||
−0.305243 | + | 0.952274i | \(0.598738\pi\) | |||||||
\(410\) | 55.2641 | 2.72930 | ||||||||
\(411\) | −3.66909 | −0.180983 | ||||||||
\(412\) | −3.11812 | −0.153619 | ||||||||
\(413\) | 15.3820 | 0.756897 | ||||||||
\(414\) | −28.0282 | −1.37751 | ||||||||
\(415\) | −15.5618 | −0.763901 | ||||||||
\(416\) | 120.449 | 5.90548 | ||||||||
\(417\) | 7.28866 | 0.356927 | ||||||||
\(418\) | −5.21172 | −0.254913 | ||||||||
\(419\) | −11.1549 | −0.544952 | −0.272476 | − | 0.962163i | \(-0.587843\pi\) | ||||
−0.272476 | + | 0.962163i | \(0.587843\pi\) | |||||||
\(420\) | −67.8811 | −3.31226 | ||||||||
\(421\) | −26.2734 | −1.28049 | −0.640245 | − | 0.768171i | \(-0.721167\pi\) | ||||
−0.640245 | + | 0.768171i | \(0.721167\pi\) | |||||||
\(422\) | −19.1663 | −0.932999 | ||||||||
\(423\) | −15.9785 | −0.776900 | ||||||||
\(424\) | 84.9480 | 4.12544 | ||||||||
\(425\) | −23.0999 | −1.12051 | ||||||||
\(426\) | −31.0083 | −1.50236 | ||||||||
\(427\) | −6.41817 | −0.310597 | ||||||||
\(428\) | −48.7450 | −2.35618 | ||||||||
\(429\) | −15.6346 | −0.754847 | ||||||||
\(430\) | 17.9673 | 0.866458 | ||||||||
\(431\) | −3.90288 | −0.187995 | −0.0939977 | − | 0.995572i | \(-0.529965\pi\) | ||||
−0.0939977 | + | 0.995572i | \(0.529965\pi\) | |||||||
\(432\) | −12.0203 | −0.578329 | ||||||||
\(433\) | −18.4307 | −0.885724 | −0.442862 | − | 0.896590i | \(-0.646037\pi\) | ||||
−0.442862 | + | 0.896590i | \(0.646037\pi\) | |||||||
\(434\) | 33.7471 | 1.61991 | ||||||||
\(435\) | 3.04950 | 0.146212 | ||||||||
\(436\) | 61.4649 | 2.94364 | ||||||||
\(437\) | −5.67574 | −0.271507 | ||||||||
\(438\) | 85.7431 | 4.09697 | ||||||||
\(439\) | −27.8073 | −1.32717 | −0.663585 | − | 0.748101i | \(-0.730966\pi\) | ||||
−0.663585 | + | 0.748101i | \(0.730966\pi\) | |||||||
\(440\) | −36.0599 | −1.71909 | ||||||||
\(441\) | −17.4078 | −0.828941 | ||||||||
\(442\) | −41.0958 | −1.95473 | ||||||||
\(443\) | 16.6767 | 0.792334 | 0.396167 | − | 0.918178i | \(-0.370340\pi\) | ||||
0.396167 | + | 0.918178i | \(0.370340\pi\) | |||||||
\(444\) | 34.7613 | 1.64970 | ||||||||
\(445\) | 0.592381 | 0.0280815 | ||||||||
\(446\) | 56.6491 | 2.68241 | ||||||||
\(447\) | 16.4431 | 0.777730 | ||||||||
\(448\) | −35.5124 | −1.67780 | ||||||||
\(449\) | 8.59046 | 0.405409 | 0.202704 | − | 0.979240i | \(-0.435027\pi\) | ||||
0.202704 | + | 0.979240i | \(0.435027\pi\) | |||||||
\(450\) | −82.3156 | −3.88040 | ||||||||
\(451\) | −5.66239 | −0.266631 | ||||||||
\(452\) | −24.3397 | −1.14484 | ||||||||
\(453\) | 60.8783 | 2.86031 | ||||||||
\(454\) | −59.1185 | −2.77457 | ||||||||
\(455\) | −29.7749 | −1.39587 | ||||||||
\(456\) | −42.4964 | −1.99008 | ||||||||
\(457\) | −11.9797 | −0.560386 | −0.280193 | − | 0.959944i | \(-0.590398\pi\) | ||||
−0.280193 | + | 0.959944i | \(0.590398\pi\) | |||||||
\(458\) | 1.81531 | 0.0848238 | ||||||||
\(459\) | 2.14956 | 0.100333 | ||||||||
\(460\) | −62.4758 | −2.91295 | ||||||||
\(461\) | −12.3030 | −0.573009 | −0.286505 | − | 0.958079i | \(-0.592493\pi\) | ||||
−0.286505 | + | 0.958079i | \(0.592493\pi\) | |||||||
\(462\) | 9.53847 | 0.443770 | ||||||||
\(463\) | 11.4955 | 0.534240 | 0.267120 | − | 0.963663i | \(-0.413928\pi\) | ||||
0.267120 | + | 0.963663i | \(0.413928\pi\) | |||||||
\(464\) | 4.59265 | 0.213209 | ||||||||
\(465\) | 87.8830 | 4.07548 | ||||||||
\(466\) | −61.4251 | −2.84546 | ||||||||
\(467\) | 14.3311 | 0.663165 | 0.331582 | − | 0.943426i | \(-0.392417\pi\) | ||||
0.331582 | + | 0.943426i | \(0.392417\pi\) | |||||||
\(468\) | −106.782 | −4.93599 | ||||||||
\(469\) | 13.0368 | 0.601985 | ||||||||
\(470\) | −48.8456 | −2.25308 | ||||||||
\(471\) | −61.2209 | −2.82091 | ||||||||
\(472\) | 106.000 | 4.87903 | ||||||||
\(473\) | −1.84094 | −0.0846463 | ||||||||
\(474\) | 36.2177 | 1.66354 | ||||||||
\(475\) | −16.6690 | −0.764827 | ||||||||
\(476\) | 18.2817 | 0.837939 | ||||||||
\(477\) | −30.8084 | −1.41062 | ||||||||
\(478\) | 41.6289 | 1.90406 | ||||||||
\(479\) | 24.9027 | 1.13783 | 0.568916 | − | 0.822396i | \(-0.307363\pi\) | ||||
0.568916 | + | 0.822396i | \(0.307363\pi\) | |||||||
\(480\) | −191.364 | −8.73455 | ||||||||
\(481\) | 15.2474 | 0.695223 | ||||||||
\(482\) | −32.1400 | −1.46394 | ||||||||
\(483\) | 10.3877 | 0.472658 | ||||||||
\(484\) | −53.3528 | −2.42513 | ||||||||
\(485\) | −10.5229 | −0.477821 | ||||||||
\(486\) | −60.7899 | −2.75749 | ||||||||
\(487\) | 20.1953 | 0.915139 | 0.457569 | − | 0.889174i | \(-0.348720\pi\) | ||||
0.457569 | + | 0.889174i | \(0.348720\pi\) | |||||||
\(488\) | −44.2286 | −2.00214 | ||||||||
\(489\) | 39.5045 | 1.78646 | ||||||||
\(490\) | −53.2149 | −2.40400 | ||||||||
\(491\) | 32.1955 | 1.45296 | 0.726482 | − | 0.687185i | \(-0.241154\pi\) | ||||
0.726482 | + | 0.687185i | \(0.241154\pi\) | |||||||
\(492\) | −73.4541 | −3.31157 | ||||||||
\(493\) | −0.821289 | −0.0369890 | ||||||||
\(494\) | −29.6550 | −1.33424 | ||||||||
\(495\) | 13.0780 | 0.587811 | ||||||||
\(496\) | 132.355 | 5.94291 | ||||||||
\(497\) | 6.05058 | 0.271406 | ||||||||
\(498\) | 28.3666 | 1.27114 | ||||||||
\(499\) | 7.65470 | 0.342671 | 0.171336 | − | 0.985213i | \(-0.445192\pi\) | ||||
0.171336 | + | 0.985213i | \(0.445192\pi\) | |||||||
\(500\) | −82.4569 | −3.68758 | ||||||||
\(501\) | 12.0487 | 0.538298 | ||||||||
\(502\) | 8.15583 | 0.364012 | ||||||||
\(503\) | −30.1901 | −1.34611 | −0.673055 | − | 0.739593i | \(-0.735018\pi\) | ||||
−0.673055 | + | 0.739593i | \(0.735018\pi\) | |||||||
\(504\) | 40.9490 | 1.82401 | ||||||||
\(505\) | −7.72219 | −0.343633 | ||||||||
\(506\) | 8.77894 | 0.390271 | ||||||||
\(507\) | −56.2400 | −2.49771 | ||||||||
\(508\) | −11.6712 | −0.517828 | ||||||||
\(509\) | −34.1259 | −1.51261 | −0.756303 | − | 0.654222i | \(-0.772996\pi\) | ||||
−0.756303 | + | 0.654222i | \(0.772996\pi\) | |||||||
\(510\) | 65.2916 | 2.89116 | ||||||||
\(511\) | −16.7309 | −0.740130 | ||||||||
\(512\) | −26.5330 | −1.17260 | ||||||||
\(513\) | 1.55113 | 0.0684843 | ||||||||
\(514\) | −7.91097 | −0.348938 | ||||||||
\(515\) | 2.17297 | 0.0957526 | ||||||||
\(516\) | −23.8811 | −1.05131 | ||||||||
\(517\) | 5.00475 | 0.220109 | ||||||||
\(518\) | −9.30225 | −0.408717 | ||||||||
\(519\) | 0.285991 | 0.0125536 | ||||||||
\(520\) | −205.183 | −8.99789 | ||||||||
\(521\) | −25.1286 | −1.10091 | −0.550453 | − | 0.834866i | \(-0.685545\pi\) | ||||
−0.550453 | + | 0.834866i | \(0.685545\pi\) | |||||||
\(522\) | −2.92663 | −0.128095 | ||||||||
\(523\) | 21.5163 | 0.940841 | 0.470421 | − | 0.882442i | \(-0.344102\pi\) | ||||
0.470421 | + | 0.882442i | \(0.344102\pi\) | |||||||
\(524\) | −97.2327 | −4.24763 | ||||||||
\(525\) | 30.5076 | 1.33146 | ||||||||
\(526\) | −6.66510 | −0.290612 | ||||||||
\(527\) | −23.6686 | −1.03102 | ||||||||
\(528\) | 37.4095 | 1.62804 | ||||||||
\(529\) | −13.4394 | −0.584323 | ||||||||
\(530\) | −94.1801 | −4.09092 | ||||||||
\(531\) | −38.4432 | −1.66829 | ||||||||
\(532\) | 13.1922 | 0.571953 | ||||||||
\(533\) | −32.2194 | −1.39558 | ||||||||
\(534\) | −1.07981 | −0.0467280 | ||||||||
\(535\) | 33.9696 | 1.46863 | ||||||||
\(536\) | 89.8389 | 3.88045 | ||||||||
\(537\) | 31.4655 | 1.35784 | ||||||||
\(538\) | −71.0066 | −3.06131 | ||||||||
\(539\) | 5.45243 | 0.234853 | ||||||||
\(540\) | 17.0741 | 0.734754 | ||||||||
\(541\) | −1.86994 | −0.0803951 | −0.0401975 | − | 0.999192i | \(-0.512799\pi\) | ||||
−0.0401975 | + | 0.999192i | \(0.512799\pi\) | |||||||
\(542\) | 49.3175 | 2.11837 | ||||||||
\(543\) | 3.89400 | 0.167108 | ||||||||
\(544\) | 51.5381 | 2.20968 | ||||||||
\(545\) | −42.8339 | −1.83480 | ||||||||
\(546\) | 54.2746 | 2.32274 | ||||||||
\(547\) | 0.960869 | 0.0410838 | 0.0205419 | − | 0.999789i | \(-0.493461\pi\) | ||||
0.0205419 | + | 0.999789i | \(0.493461\pi\) | |||||||
\(548\) | 7.84902 | 0.335294 | ||||||||
\(549\) | 16.0405 | 0.684594 | ||||||||
\(550\) | 25.7828 | 1.09938 | ||||||||
\(551\) | −0.592647 | −0.0252476 | ||||||||
\(552\) | 71.5835 | 3.04680 | ||||||||
\(553\) | −7.06708 | −0.300523 | ||||||||
\(554\) | 39.5583 | 1.68067 | ||||||||
\(555\) | −24.2246 | −1.02828 | ||||||||
\(556\) | −15.5921 | −0.661252 | ||||||||
\(557\) | 15.1091 | 0.640192 | 0.320096 | − | 0.947385i | \(-0.396285\pi\) | ||||
0.320096 | + | 0.947385i | \(0.396285\pi\) | |||||||
\(558\) | −84.3421 | −3.57049 | ||||||||
\(559\) | −10.4750 | −0.443047 | ||||||||
\(560\) | 71.2433 | 3.01058 | ||||||||
\(561\) | −6.68982 | −0.282444 | ||||||||
\(562\) | 90.5910 | 3.82135 | ||||||||
\(563\) | −35.0821 | −1.47853 | −0.739266 | − | 0.673413i | \(-0.764828\pi\) | ||||
−0.739266 | + | 0.673413i | \(0.764828\pi\) | |||||||
\(564\) | 64.9230 | 2.73375 | ||||||||
\(565\) | 16.9619 | 0.713594 | ||||||||
\(566\) | 27.2855 | 1.14689 | ||||||||
\(567\) | 10.5176 | 0.441696 | ||||||||
\(568\) | 41.6956 | 1.74951 | ||||||||
\(569\) | 20.7571 | 0.870181 | 0.435090 | − | 0.900387i | \(-0.356716\pi\) | ||||
0.435090 | + | 0.900387i | \(0.356716\pi\) | |||||||
\(570\) | 47.1148 | 1.97342 | ||||||||
\(571\) | −18.3475 | −0.767818 | −0.383909 | − | 0.923371i | \(-0.625422\pi\) | ||||
−0.383909 | + | 0.923371i | \(0.625422\pi\) | |||||||
\(572\) | 33.4460 | 1.39845 | ||||||||
\(573\) | 53.1992 | 2.22243 | ||||||||
\(574\) | 19.6566 | 0.820450 | ||||||||
\(575\) | 28.0783 | 1.17095 | ||||||||
\(576\) | 88.7541 | 3.69809 | ||||||||
\(577\) | −6.29193 | −0.261937 | −0.130968 | − | 0.991387i | \(-0.541809\pi\) | ||||
−0.130968 | + | 0.991387i | \(0.541809\pi\) | |||||||
\(578\) | 28.6126 | 1.19013 | ||||||||
\(579\) | 35.5456 | 1.47722 | ||||||||
\(580\) | −6.52357 | −0.270877 | ||||||||
\(581\) | −5.53512 | −0.229635 | ||||||||
\(582\) | 19.1815 | 0.795098 | ||||||||
\(583\) | 9.64975 | 0.399652 | ||||||||
\(584\) | −115.295 | −4.77095 | ||||||||
\(585\) | 74.4146 | 3.07666 | ||||||||
\(586\) | 71.4816 | 2.95288 | ||||||||
\(587\) | −5.39298 | −0.222592 | −0.111296 | − | 0.993787i | \(-0.535500\pi\) | ||||
−0.111296 | + | 0.993787i | \(0.535500\pi\) | |||||||
\(588\) | 70.7305 | 2.91688 | ||||||||
\(589\) | −17.0794 | −0.703744 | ||||||||
\(590\) | −117.520 | −4.83820 | ||||||||
\(591\) | 56.8427 | 2.33820 | ||||||||
\(592\) | −36.4831 | −1.49944 | ||||||||
\(593\) | 36.9276 | 1.51643 | 0.758217 | − | 0.652002i | \(-0.226071\pi\) | ||||
0.758217 | + | 0.652002i | \(0.226071\pi\) | |||||||
\(594\) | −2.39921 | −0.0984410 | ||||||||
\(595\) | −12.7402 | −0.522297 | ||||||||
\(596\) | −35.1754 | −1.44084 | ||||||||
\(597\) | −42.2848 | −1.73060 | ||||||||
\(598\) | 49.9527 | 2.04272 | ||||||||
\(599\) | 47.7380 | 1.95052 | 0.975262 | − | 0.221053i | \(-0.0709493\pi\) | ||||
0.975262 | + | 0.221053i | \(0.0709493\pi\) | |||||||
\(600\) | 210.233 | 8.58272 | ||||||||
\(601\) | 28.5087 | 1.16290 | 0.581448 | − | 0.813584i | \(-0.302486\pi\) | ||||
0.581448 | + | 0.813584i | \(0.302486\pi\) | |||||||
\(602\) | 6.39068 | 0.260465 | ||||||||
\(603\) | −32.5822 | −1.32685 | ||||||||
\(604\) | −130.233 | −5.29909 | ||||||||
\(605\) | 37.1807 | 1.51161 | ||||||||
\(606\) | 14.0763 | 0.571809 | ||||||||
\(607\) | −28.1427 | −1.14228 | −0.571139 | − | 0.820853i | \(-0.693498\pi\) | ||||
−0.571139 | + | 0.820853i | \(0.693498\pi\) | |||||||
\(608\) | 37.1902 | 1.50826 | ||||||||
\(609\) | 1.08466 | 0.0439527 | ||||||||
\(610\) | 49.0354 | 1.98538 | ||||||||
\(611\) | 28.4774 | 1.15207 | ||||||||
\(612\) | −45.6903 | −1.84692 | ||||||||
\(613\) | 12.7874 | 0.516477 | 0.258238 | − | 0.966081i | \(-0.416858\pi\) | ||||
0.258238 | + | 0.966081i | \(0.416858\pi\) | |||||||
\(614\) | 48.8961 | 1.97329 | ||||||||
\(615\) | 51.1890 | 2.06414 | ||||||||
\(616\) | −12.8260 | −0.516773 | ||||||||
\(617\) | −21.5598 | −0.867966 | −0.433983 | − | 0.900921i | \(-0.642892\pi\) | ||||
−0.433983 | + | 0.900921i | \(0.642892\pi\) | |||||||
\(618\) | −3.96096 | −0.159333 | ||||||||
\(619\) | −32.7241 | −1.31529 | −0.657647 | − | 0.753326i | \(-0.728448\pi\) | ||||
−0.657647 | + | 0.753326i | \(0.728448\pi\) | |||||||
\(620\) | −188.002 | −7.55033 | ||||||||
\(621\) | −2.61283 | −0.104849 | ||||||||
\(622\) | −7.05801 | −0.283000 | ||||||||
\(623\) | 0.210701 | 0.00844155 | ||||||||
\(624\) | 212.863 | 8.52133 | ||||||||
\(625\) | 12.0584 | 0.482334 | ||||||||
\(626\) | 45.6346 | 1.82393 | ||||||||
\(627\) | −4.82742 | −0.192788 | ||||||||
\(628\) | 130.965 | 5.22609 | ||||||||
\(629\) | 6.52414 | 0.260135 | ||||||||
\(630\) | −45.3993 | −1.80875 | ||||||||
\(631\) | 5.23767 | 0.208508 | 0.104254 | − | 0.994551i | \(-0.466754\pi\) | ||||
0.104254 | + | 0.994551i | \(0.466754\pi\) | |||||||
\(632\) | −48.7004 | −1.93720 | ||||||||
\(633\) | −17.7530 | −0.705618 | ||||||||
\(634\) | 86.1656 | 3.42207 | ||||||||
\(635\) | 8.13351 | 0.322768 | ||||||||
\(636\) | 125.179 | 4.96368 | ||||||||
\(637\) | 31.0247 | 1.22924 | ||||||||
\(638\) | 0.916676 | 0.0362915 | ||||||||
\(639\) | −15.1219 | −0.598212 | ||||||||
\(640\) | 119.266 | 4.71439 | ||||||||
\(641\) | 12.2482 | 0.483774 | 0.241887 | − | 0.970304i | \(-0.422234\pi\) | ||||
0.241887 | + | 0.970304i | \(0.422234\pi\) | |||||||
\(642\) | −61.9209 | −2.44382 | ||||||||
\(643\) | 20.3344 | 0.801910 | 0.400955 | − | 0.916098i | \(-0.368678\pi\) | ||||
0.400955 | + | 0.916098i | \(0.368678\pi\) | |||||||
\(644\) | −22.2217 | −0.875658 | ||||||||
\(645\) | 16.6424 | 0.655293 | ||||||||
\(646\) | −12.6889 | −0.499239 | ||||||||
\(647\) | 29.8406 | 1.17316 | 0.586578 | − | 0.809893i | \(-0.300475\pi\) | ||||
0.586578 | + | 0.809893i | \(0.300475\pi\) | |||||||
\(648\) | 72.4783 | 2.84722 | ||||||||
\(649\) | 12.0411 | 0.472655 | ||||||||
\(650\) | 146.706 | 5.75427 | ||||||||
\(651\) | 31.2587 | 1.22512 | ||||||||
\(652\) | −84.5091 | −3.30963 | ||||||||
\(653\) | 31.1075 | 1.21733 | 0.608665 | − | 0.793427i | \(-0.291705\pi\) | ||||
0.608665 | + | 0.793427i | \(0.291705\pi\) | |||||||
\(654\) | 78.0790 | 3.05313 | ||||||||
\(655\) | 67.7599 | 2.64760 | ||||||||
\(656\) | 77.0924 | 3.00995 | ||||||||
\(657\) | 41.8145 | 1.63134 | ||||||||
\(658\) | −17.3736 | −0.677295 | ||||||||
\(659\) | −43.7653 | −1.70486 | −0.852428 | − | 0.522845i | \(-0.824871\pi\) | ||||
−0.852428 | + | 0.522845i | \(0.824871\pi\) | |||||||
\(660\) | −53.1379 | −2.06839 | ||||||||
\(661\) | 1.46110 | 0.0568300 | 0.0284150 | − | 0.999596i | \(-0.490954\pi\) | ||||
0.0284150 | + | 0.999596i | \(0.490954\pi\) | |||||||
\(662\) | −23.8258 | −0.926016 | ||||||||
\(663\) | −38.0655 | −1.47834 | ||||||||
\(664\) | −38.1434 | −1.48025 | ||||||||
\(665\) | −9.19341 | −0.356505 | ||||||||
\(666\) | 23.2486 | 0.900864 | ||||||||
\(667\) | 0.998291 | 0.0386540 | ||||||||
\(668\) | −25.7750 | −0.997265 | ||||||||
\(669\) | 52.4719 | 2.02868 | ||||||||
\(670\) | −99.6025 | −3.84798 | ||||||||
\(671\) | −5.02420 | −0.193957 | ||||||||
\(672\) | −68.0655 | −2.62568 | ||||||||
\(673\) | −28.5847 | −1.10186 | −0.550930 | − | 0.834551i | \(-0.685727\pi\) | ||||
−0.550930 | + | 0.834551i | \(0.685727\pi\) | |||||||
\(674\) | −86.2145 | −3.32086 | ||||||||
\(675\) | −7.67358 | −0.295356 | ||||||||
\(676\) | 120.310 | 4.62732 | ||||||||
\(677\) | 47.4088 | 1.82207 | 0.911035 | − | 0.412329i | \(-0.135285\pi\) | ||||
0.911035 | + | 0.412329i | \(0.135285\pi\) | |||||||
\(678\) | −30.9188 | −1.18743 | ||||||||
\(679\) | −3.74284 | −0.143637 | ||||||||
\(680\) | −87.7948 | −3.36678 | ||||||||
\(681\) | −54.7592 | −2.09838 | ||||||||
\(682\) | 26.4175 | 1.01158 | ||||||||
\(683\) | 13.2348 | 0.506415 | 0.253208 | − | 0.967412i | \(-0.418514\pi\) | ||||
0.253208 | + | 0.967412i | \(0.418514\pi\) | |||||||
\(684\) | −32.9704 | −1.26066 | ||||||||
\(685\) | −5.46986 | −0.208993 | ||||||||
\(686\) | −44.3166 | −1.69201 | ||||||||
\(687\) | 1.68145 | 0.0641514 | ||||||||
\(688\) | 25.0640 | 0.955556 | ||||||||
\(689\) | 54.9077 | 2.09182 | ||||||||
\(690\) | −79.3631 | −3.02130 | ||||||||
\(691\) | 47.5370 | 1.80839 | 0.904196 | − | 0.427118i | \(-0.140471\pi\) | ||||
0.904196 | + | 0.427118i | \(0.140471\pi\) | |||||||
\(692\) | −0.611800 | −0.0232572 | ||||||||
\(693\) | 4.65164 | 0.176701 | ||||||||
\(694\) | 47.0986 | 1.78784 | ||||||||
\(695\) | 10.8659 | 0.412167 | ||||||||
\(696\) | 7.47458 | 0.283323 | ||||||||
\(697\) | −13.7862 | −0.522189 | ||||||||
\(698\) | 37.6680 | 1.42575 | ||||||||
\(699\) | −56.8957 | −2.15199 | ||||||||
\(700\) | −65.2627 | −2.46670 | ||||||||
\(701\) | −44.8623 | −1.69443 | −0.847213 | − | 0.531254i | \(-0.821721\pi\) | ||||
−0.847213 | + | 0.531254i | \(0.821721\pi\) | |||||||
\(702\) | −13.6517 | −0.515250 | ||||||||
\(703\) | 4.70786 | 0.177560 | ||||||||
\(704\) | −27.7994 | −1.04773 | ||||||||
\(705\) | −45.2438 | −1.70398 | ||||||||
\(706\) | 22.8427 | 0.859696 | ||||||||
\(707\) | −2.74667 | −0.103299 | ||||||||
\(708\) | 156.201 | 5.87039 | ||||||||
\(709\) | 8.09550 | 0.304033 | 0.152016 | − | 0.988378i | \(-0.451423\pi\) | ||||
0.152016 | + | 0.988378i | \(0.451423\pi\) | |||||||
\(710\) | −46.2270 | −1.73487 | ||||||||
\(711\) | 17.6623 | 0.662390 | ||||||||
\(712\) | 1.45197 | 0.0544150 | ||||||||
\(713\) | 28.7696 | 1.07743 | ||||||||
\(714\) | 23.2232 | 0.869108 | ||||||||
\(715\) | −23.3080 | −0.871670 | ||||||||
\(716\) | −67.3119 | −2.51556 | ||||||||
\(717\) | 38.5593 | 1.44002 | ||||||||
\(718\) | −48.4982 | −1.80994 | ||||||||
\(719\) | 31.1676 | 1.16236 | 0.581178 | − | 0.813776i | \(-0.302592\pi\) | ||||
0.581178 | + | 0.813776i | \(0.302592\pi\) | |||||||
\(720\) | −178.054 | −6.63569 | ||||||||
\(721\) | 0.772893 | 0.0287840 | ||||||||
\(722\) | 42.4754 | 1.58077 | ||||||||
\(723\) | −29.7701 | −1.10716 | ||||||||
\(724\) | −8.33015 | −0.309588 | ||||||||
\(725\) | 2.93187 | 0.108887 | ||||||||
\(726\) | −67.7742 | −2.51534 | ||||||||
\(727\) | 41.0518 | 1.52253 | 0.761264 | − | 0.648442i | \(-0.224579\pi\) | ||||
0.761264 | + | 0.648442i | \(0.224579\pi\) | |||||||
\(728\) | −72.9807 | −2.70484 | ||||||||
\(729\) | −32.6669 | −1.20989 | ||||||||
\(730\) | 127.825 | 4.73103 | ||||||||
\(731\) | −4.48211 | −0.165777 | ||||||||
\(732\) | −65.1753 | −2.40895 | ||||||||
\(733\) | 20.3056 | 0.750004 | 0.375002 | − | 0.927024i | \(-0.377642\pi\) | ||||
0.375002 | + | 0.927024i | \(0.377642\pi\) | |||||||
\(734\) | 1.28994 | 0.0476125 | ||||||||
\(735\) | −49.2909 | −1.81812 | ||||||||
\(736\) | −62.6455 | −2.30914 | ||||||||
\(737\) | 10.2053 | 0.375918 | ||||||||
\(738\) | −49.1266 | −1.80837 | ||||||||
\(739\) | −1.64940 | −0.0606743 | −0.0303372 | − | 0.999540i | \(-0.509658\pi\) | ||||
−0.0303372 | + | 0.999540i | \(0.509658\pi\) | |||||||
\(740\) | 51.8219 | 1.90501 | ||||||||
\(741\) | −27.4683 | −1.00907 | ||||||||
\(742\) | −33.4984 | −1.22977 | ||||||||
\(743\) | 11.5753 | 0.424658 | 0.212329 | − | 0.977198i | \(-0.431895\pi\) | ||||
0.212329 | + | 0.977198i | \(0.431895\pi\) | |||||||
\(744\) | 215.409 | 7.89726 | ||||||||
\(745\) | 24.5132 | 0.898094 | ||||||||
\(746\) | 41.6249 | 1.52399 | ||||||||
\(747\) | 13.8336 | 0.506145 | ||||||||
\(748\) | 14.3110 | 0.523264 | ||||||||
\(749\) | 12.0825 | 0.441484 | ||||||||
\(750\) | −104.745 | −3.82475 | ||||||||
\(751\) | −2.26450 | −0.0826327 | −0.0413164 | − | 0.999146i | \(-0.513155\pi\) | ||||
−0.0413164 | + | 0.999146i | \(0.513155\pi\) | |||||||
\(752\) | −68.1388 | −2.48477 | ||||||||
\(753\) | 7.55444 | 0.275299 | ||||||||
\(754\) | 5.21595 | 0.189954 | ||||||||
\(755\) | 90.7570 | 3.30299 | ||||||||
\(756\) | 6.07302 | 0.220873 | ||||||||
\(757\) | −43.3662 | −1.57617 | −0.788086 | − | 0.615565i | \(-0.788928\pi\) | ||||
−0.788086 | + | 0.615565i | \(0.788928\pi\) | |||||||
\(758\) | −20.3128 | −0.737796 | ||||||||
\(759\) | 8.13160 | 0.295158 | ||||||||
\(760\) | −63.3533 | −2.29807 | ||||||||
\(761\) | 11.8292 | 0.428808 | 0.214404 | − | 0.976745i | \(-0.431219\pi\) | ||||
0.214404 | + | 0.976745i | \(0.431219\pi\) | |||||||
\(762\) | −14.8260 | −0.537090 | ||||||||
\(763\) | −15.2354 | −0.551558 | ||||||||
\(764\) | −113.805 | −4.11733 | ||||||||
\(765\) | 31.8408 | 1.15121 | ||||||||
\(766\) | 10.2340 | 0.369769 | ||||||||
\(767\) | 68.5148 | 2.47393 | ||||||||
\(768\) | −83.4560 | −3.01146 | ||||||||
\(769\) | 6.22058 | 0.224320 | 0.112160 | − | 0.993690i | \(-0.464223\pi\) | ||||
0.112160 | + | 0.993690i | \(0.464223\pi\) | |||||||
\(770\) | 14.2199 | 0.512449 | ||||||||
\(771\) | −7.32763 | −0.263898 | ||||||||
\(772\) | −76.0401 | −2.73674 | ||||||||
\(773\) | −2.38462 | −0.0857690 | −0.0428845 | − | 0.999080i | \(-0.513655\pi\) | ||||
−0.0428845 | + | 0.999080i | \(0.513655\pi\) | |||||||
\(774\) | −15.9719 | −0.574096 | ||||||||
\(775\) | 84.4930 | 3.03508 | ||||||||
\(776\) | −25.7925 | −0.925898 | ||||||||
\(777\) | −8.61632 | −0.309109 | ||||||||
\(778\) | 28.2399 | 1.01245 | ||||||||
\(779\) | −9.94819 | −0.356431 | ||||||||
\(780\) | −302.358 | −10.8262 | ||||||||
\(781\) | 4.73645 | 0.169483 | ||||||||
\(782\) | 21.3740 | 0.764333 | ||||||||
\(783\) | −0.272825 | −0.00974998 | ||||||||
\(784\) | −74.2338 | −2.65121 | ||||||||
\(785\) | −91.2677 | −3.25749 | ||||||||
\(786\) | −123.515 | −4.40563 | ||||||||
\(787\) | −25.9313 | −0.924352 | −0.462176 | − | 0.886788i | \(-0.652931\pi\) | ||||
−0.462176 | + | 0.886788i | \(0.652931\pi\) | |||||||
\(788\) | −121.600 | −4.33180 | ||||||||
\(789\) | −6.17363 | −0.219787 | ||||||||
\(790\) | 53.9932 | 1.92099 | ||||||||
\(791\) | 6.03311 | 0.214513 | ||||||||
\(792\) | 32.0552 | 1.13903 | ||||||||
\(793\) | −28.5880 | −1.01519 | ||||||||
\(794\) | 75.6266 | 2.68389 | ||||||||
\(795\) | −87.2355 | −3.09392 | ||||||||
\(796\) | 90.4569 | 3.20616 | ||||||||
\(797\) | 10.2032 | 0.361416 | 0.180708 | − | 0.983537i | \(-0.442161\pi\) | ||||
0.180708 | + | 0.983537i | \(0.442161\pi\) | |||||||
\(798\) | 16.7580 | 0.593228 | ||||||||
\(799\) | 12.1850 | 0.431075 | ||||||||
\(800\) | −183.983 | −6.50478 | ||||||||
\(801\) | −0.526592 | −0.0186062 | ||||||||
\(802\) | 82.1303 | 2.90012 | ||||||||
\(803\) | −13.0971 | −0.462185 | ||||||||
\(804\) | 132.386 | 4.66891 | ||||||||
\(805\) | 15.4860 | 0.545808 | ||||||||
\(806\) | 150.317 | 5.29471 | ||||||||
\(807\) | −65.7707 | −2.31524 | ||||||||
\(808\) | −18.9277 | −0.665875 | ||||||||
\(809\) | −33.3895 | −1.17391 | −0.586955 | − | 0.809619i | \(-0.699674\pi\) | ||||
−0.586955 | + | 0.809619i | \(0.699674\pi\) | |||||||
\(810\) | −80.3552 | −2.82339 | ||||||||
\(811\) | −15.2417 | −0.535207 | −0.267603 | − | 0.963529i | \(-0.586232\pi\) | ||||
−0.267603 | + | 0.963529i | \(0.586232\pi\) | |||||||
\(812\) | −2.32034 | −0.0814279 | ||||||||
\(813\) | 45.6809 | 1.60210 | ||||||||
\(814\) | −7.28188 | −0.255230 | ||||||||
\(815\) | 58.8931 | 2.06293 | ||||||||
\(816\) | 91.0806 | 3.18846 | ||||||||
\(817\) | −3.23432 | −0.113155 | ||||||||
\(818\) | 33.5507 | 1.17307 | ||||||||
\(819\) | 26.4681 | 0.924872 | ||||||||
\(820\) | −109.505 | −3.82408 | ||||||||
\(821\) | −34.3763 | −1.19974 | −0.599871 | − | 0.800097i | \(-0.704781\pi\) | ||||
−0.599871 | + | 0.800097i | \(0.704781\pi\) | |||||||
\(822\) | 9.97063 | 0.347766 | ||||||||
\(823\) | −33.1032 | −1.15390 | −0.576952 | − | 0.816778i | \(-0.695758\pi\) | ||||
−0.576952 | + | 0.816778i | \(0.695758\pi\) | |||||||
\(824\) | 5.32613 | 0.185545 | ||||||||
\(825\) | 23.8816 | 0.831451 | ||||||||
\(826\) | −41.7999 | −1.45441 | ||||||||
\(827\) | −46.3840 | −1.61293 | −0.806465 | − | 0.591282i | \(-0.798622\pi\) | ||||
−0.806465 | + | 0.591282i | \(0.798622\pi\) | |||||||
\(828\) | 55.5374 | 1.93006 | ||||||||
\(829\) | −40.3324 | −1.40080 | −0.700401 | − | 0.713749i | \(-0.746996\pi\) | ||||
−0.700401 | + | 0.713749i | \(0.746996\pi\) | |||||||
\(830\) | 42.2888 | 1.46786 | ||||||||
\(831\) | 36.6413 | 1.27107 | ||||||||
\(832\) | −158.181 | −5.48393 | ||||||||
\(833\) | 13.2750 | 0.459951 | ||||||||
\(834\) | −19.8067 | −0.685849 | ||||||||
\(835\) | 17.9622 | 0.621607 | ||||||||
\(836\) | 10.3269 | 0.357165 | ||||||||
\(837\) | −7.86250 | −0.271768 | ||||||||
\(838\) | 30.3130 | 1.04715 | ||||||||
\(839\) | −27.1286 | −0.936582 | −0.468291 | − | 0.883574i | \(-0.655130\pi\) | ||||
−0.468291 | + | 0.883574i | \(0.655130\pi\) | |||||||
\(840\) | 115.949 | 4.00062 | ||||||||
\(841\) | −28.8958 | −0.996406 | ||||||||
\(842\) | 71.3972 | 2.46051 | ||||||||
\(843\) | 83.9110 | 2.89005 | ||||||||
\(844\) | 37.9777 | 1.30724 | ||||||||
\(845\) | −83.8423 | −2.88426 | ||||||||
\(846\) | 43.4209 | 1.49284 | ||||||||
\(847\) | 13.2246 | 0.454403 | ||||||||
\(848\) | −131.380 | −4.51159 | ||||||||
\(849\) | 25.2735 | 0.867384 | ||||||||
\(850\) | 62.7731 | 2.15310 | ||||||||
\(851\) | −7.93022 | −0.271844 | ||||||||
\(852\) | 61.4425 | 2.10499 | ||||||||
\(853\) | −23.8505 | −0.816626 | −0.408313 | − | 0.912842i | \(-0.633883\pi\) | ||||
−0.408313 | + | 0.912842i | \(0.633883\pi\) | |||||||
\(854\) | 17.4411 | 0.596824 | ||||||||
\(855\) | 22.9766 | 0.785782 | ||||||||
\(856\) | 83.2623 | 2.84585 | ||||||||
\(857\) | −12.3311 | −0.421223 | −0.210612 | − | 0.977570i | \(-0.567546\pi\) | ||||
−0.210612 | + | 0.977570i | \(0.567546\pi\) | |||||||
\(858\) | 42.4866 | 1.45047 | ||||||||
\(859\) | −0.0563227 | −0.00192171 | −0.000960854 | − | 1.00000i | \(-0.500306\pi\) | ||||
−0.000960854 | 1.00000i | \(0.500306\pi\) | ||||||||
\(860\) | −35.6018 | −1.21401 | ||||||||
\(861\) | 18.2072 | 0.620498 | ||||||||
\(862\) | 10.6060 | 0.361240 | ||||||||
\(863\) | 19.9725 | 0.679871 | 0.339935 | − | 0.940449i | \(-0.389595\pi\) | ||||
0.339935 | + | 0.940449i | \(0.389595\pi\) | |||||||
\(864\) | 17.1205 | 0.582452 | ||||||||
\(865\) | 0.426354 | 0.0144965 | ||||||||
\(866\) | 50.0848 | 1.70195 | ||||||||
\(867\) | 26.5028 | 0.900082 | ||||||||
\(868\) | −66.8694 | −2.26969 | ||||||||
\(869\) | −5.53217 | −0.187666 | ||||||||
\(870\) | −8.28691 | −0.280953 | ||||||||
\(871\) | 58.0690 | 1.96759 | ||||||||
\(872\) | −104.990 | −3.55539 | ||||||||
\(873\) | 9.35426 | 0.316594 | ||||||||
\(874\) | 15.4236 | 0.521712 | ||||||||
\(875\) | 20.4387 | 0.690954 | ||||||||
\(876\) | −169.899 | −5.74035 | ||||||||
\(877\) | −4.42541 | −0.149436 | −0.0747178 | − | 0.997205i | \(-0.523806\pi\) | ||||
−0.0747178 | + | 0.997205i | \(0.523806\pi\) | |||||||
\(878\) | 75.5654 | 2.55021 | ||||||||
\(879\) | 66.2107 | 2.23323 | ||||||||
\(880\) | 55.7699 | 1.88000 | ||||||||
\(881\) | 4.27070 | 0.143884 | 0.0719418 | − | 0.997409i | \(-0.477080\pi\) | ||||
0.0719418 | + | 0.997409i | \(0.477080\pi\) | |||||||
\(882\) | 47.3050 | 1.59284 | ||||||||
\(883\) | −24.1680 | −0.813319 | −0.406659 | − | 0.913580i | \(-0.633306\pi\) | ||||
−0.406659 | + | 0.913580i | \(0.633306\pi\) | |||||||
\(884\) | 81.4308 | 2.73881 | ||||||||
\(885\) | −108.854 | −3.65908 | ||||||||
\(886\) | −45.3184 | −1.52250 | ||||||||
\(887\) | 28.6411 | 0.961675 | 0.480838 | − | 0.876810i | \(-0.340333\pi\) | ||||
0.480838 | + | 0.876810i | \(0.340333\pi\) | |||||||
\(888\) | −59.3765 | −1.99254 | ||||||||
\(889\) | 2.89297 | 0.0970270 | ||||||||
\(890\) | −1.60977 | −0.0539597 | ||||||||
\(891\) | 8.23324 | 0.275824 | ||||||||
\(892\) | −112.249 | −3.75839 | ||||||||
\(893\) | 8.79279 | 0.294240 | ||||||||
\(894\) | −44.6834 | −1.49444 | ||||||||
\(895\) | 46.9086 | 1.56798 | ||||||||
\(896\) | 42.4210 | 1.41719 | ||||||||
\(897\) | 46.2693 | 1.54489 | ||||||||
\(898\) | −23.3443 | −0.779009 | ||||||||
\(899\) | 3.00405 | 0.100191 | ||||||||
\(900\) | 163.107 | 5.43691 | ||||||||
\(901\) | 23.4942 | 0.782704 | ||||||||
\(902\) | 15.3873 | 0.512343 | ||||||||
\(903\) | 5.91945 | 0.196987 | ||||||||
\(904\) | 41.5751 | 1.38277 | ||||||||
\(905\) | 5.80515 | 0.192970 | ||||||||
\(906\) | −165.435 | −5.49620 | ||||||||
\(907\) | 7.73813 | 0.256940 | 0.128470 | − | 0.991713i | \(-0.458993\pi\) | ||||
0.128470 | + | 0.991713i | \(0.458993\pi\) | |||||||
\(908\) | 117.142 | 3.88751 | ||||||||
\(909\) | 6.86458 | 0.227684 | ||||||||
\(910\) | 80.9122 | 2.68221 | ||||||||
\(911\) | 12.2845 | 0.407004 | 0.203502 | − | 0.979075i | \(-0.434768\pi\) | ||||
0.203502 | + | 0.979075i | \(0.434768\pi\) | |||||||
\(912\) | 65.7244 | 2.17635 | ||||||||
\(913\) | −4.33293 | −0.143399 | ||||||||
\(914\) | 32.5544 | 1.07680 | ||||||||
\(915\) | 45.4196 | 1.50153 | ||||||||
\(916\) | −3.59701 | −0.118848 | ||||||||
\(917\) | 24.1012 | 0.795891 | ||||||||
\(918\) | −5.84135 | −0.192793 | ||||||||
\(919\) | 21.8605 | 0.721112 | 0.360556 | − | 0.932738i | \(-0.382587\pi\) | ||||
0.360556 | + | 0.932738i | \(0.382587\pi\) | |||||||
\(920\) | 106.716 | 3.51833 | ||||||||
\(921\) | 45.2906 | 1.49238 | ||||||||
\(922\) | 33.4331 | 1.10106 | ||||||||
\(923\) | 26.9507 | 0.887093 | ||||||||
\(924\) | −18.9003 | −0.621776 | ||||||||
\(925\) | −23.2902 | −0.765776 | ||||||||
\(926\) | −31.2386 | −1.02656 | ||||||||
\(927\) | −1.93165 | −0.0634436 | ||||||||
\(928\) | −6.54129 | −0.214729 | ||||||||
\(929\) | 16.1279 | 0.529140 | 0.264570 | − | 0.964367i | \(-0.414770\pi\) | ||||
0.264570 | + | 0.964367i | \(0.414770\pi\) | |||||||
\(930\) | −238.819 | −7.83118 | ||||||||
\(931\) | 9.57932 | 0.313949 | ||||||||
\(932\) | 121.713 | 3.98684 | ||||||||
\(933\) | −6.53757 | −0.214030 | ||||||||
\(934\) | −38.9443 | −1.27430 | ||||||||
\(935\) | −9.97314 | −0.326157 | ||||||||
\(936\) | 182.396 | 5.96181 | ||||||||
\(937\) | −15.7586 | −0.514812 | −0.257406 | − | 0.966303i | \(-0.582868\pi\) | ||||
−0.257406 | + | 0.966303i | \(0.582868\pi\) | |||||||
\(938\) | −35.4271 | −1.15674 | ||||||||
\(939\) | 42.2696 | 1.37942 | ||||||||
\(940\) | 96.7869 | 3.15684 | ||||||||
\(941\) | 9.96310 | 0.324788 | 0.162394 | − | 0.986726i | \(-0.448078\pi\) | ||||
0.162394 | + | 0.986726i | \(0.448078\pi\) | |||||||
\(942\) | 166.366 | 5.42049 | ||||||||
\(943\) | 16.7573 | 0.545694 | ||||||||
\(944\) | −163.938 | −5.33572 | ||||||||
\(945\) | −4.23219 | −0.137673 | ||||||||
\(946\) | 5.00268 | 0.162651 | ||||||||
\(947\) | 32.5681 | 1.05832 | 0.529160 | − | 0.848522i | \(-0.322507\pi\) | ||||
0.529160 | + | 0.848522i | \(0.322507\pi\) | |||||||
\(948\) | −71.7649 | −2.33082 | ||||||||
\(949\) | −74.5232 | −2.41912 | ||||||||
\(950\) | 45.2975 | 1.46964 | ||||||||
\(951\) | 79.8119 | 2.58808 | ||||||||
\(952\) | −31.2273 | −1.01208 | ||||||||
\(953\) | −35.9811 | −1.16554 | −0.582772 | − | 0.812636i | \(-0.698032\pi\) | ||||
−0.582772 | + | 0.812636i | \(0.698032\pi\) | |||||||
\(954\) | 83.7207 | 2.71056 | ||||||||
\(955\) | 79.3091 | 2.56638 | ||||||||
\(956\) | −82.4871 | −2.66782 | ||||||||
\(957\) | 0.849082 | 0.0274469 | ||||||||
\(958\) | −67.6722 | −2.18639 | ||||||||
\(959\) | −1.94555 | −0.0628250 | ||||||||
\(960\) | 251.312 | 8.11105 | ||||||||
\(961\) | 55.5732 | 1.79268 | ||||||||
\(962\) | −41.4344 | −1.33590 | ||||||||
\(963\) | −30.1970 | −0.973085 | ||||||||
\(964\) | 63.6849 | 2.05115 | ||||||||
\(965\) | 52.9912 | 1.70585 | ||||||||
\(966\) | −28.2283 | −0.908230 | ||||||||
\(967\) | 32.3913 | 1.04163 | 0.520817 | − | 0.853668i | \(-0.325627\pi\) | ||||
0.520817 | + | 0.853668i | \(0.325627\pi\) | |||||||
\(968\) | 91.1331 | 2.92913 | ||||||||
\(969\) | −11.7533 | −0.377569 | ||||||||
\(970\) | 28.5956 | 0.918150 | ||||||||
\(971\) | 1.25162 | 0.0401665 | 0.0200833 | − | 0.999798i | \(-0.493607\pi\) | ||||
0.0200833 | + | 0.999798i | \(0.493607\pi\) | |||||||
\(972\) | 120.454 | 3.86357 | ||||||||
\(973\) | 3.86483 | 0.123901 | ||||||||
\(974\) | −54.8802 | −1.75847 | ||||||||
\(975\) | 135.888 | 4.35190 | ||||||||
\(976\) | 68.4035 | 2.18954 | ||||||||
\(977\) | 47.0942 | 1.50668 | 0.753339 | − | 0.657632i | \(-0.228442\pi\) | ||||
0.753339 | + | 0.657632i | \(0.228442\pi\) | |||||||
\(978\) | −107.352 | −3.43274 | ||||||||
\(979\) | 0.164938 | 0.00527146 | ||||||||
\(980\) | 105.445 | 3.36830 | ||||||||
\(981\) | 38.0769 | 1.21570 | ||||||||
\(982\) | −87.4903 | −2.79193 | ||||||||
\(983\) | −57.0428 | −1.81938 | −0.909691 | − | 0.415286i | \(-0.863681\pi\) | ||||
−0.909691 | + | 0.415286i | \(0.863681\pi\) | |||||||
\(984\) | 125.468 | 3.99979 | ||||||||
\(985\) | 84.7408 | 2.70007 | ||||||||
\(986\) | 2.23182 | 0.0710757 | ||||||||
\(987\) | −16.0926 | −0.512232 | ||||||||
\(988\) | 58.7610 | 1.86944 | ||||||||
\(989\) | 5.44809 | 0.173239 | ||||||||
\(990\) | −35.5389 | −1.12950 | ||||||||
\(991\) | −5.08157 | −0.161421 | −0.0807106 | − | 0.996738i | \(-0.525719\pi\) | ||||
−0.0807106 | + | 0.996738i | \(0.525719\pi\) | |||||||
\(992\) | −188.512 | −5.98527 | ||||||||
\(993\) | −22.0689 | −0.700337 | ||||||||
\(994\) | −16.4422 | −0.521516 | ||||||||
\(995\) | −63.0379 | −1.99844 | ||||||||
\(996\) | −56.2080 | −1.78102 | ||||||||
\(997\) | 27.9138 | 0.884038 | 0.442019 | − | 0.897006i | \(-0.354262\pi\) | ||||
0.442019 | + | 0.897006i | \(0.354262\pi\) | |||||||
\(998\) | −20.8014 | −0.658456 | ||||||||
\(999\) | 2.16727 | 0.0685693 |
(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 | 8009.2.a.b.1.9 | ✓ | 361 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8009.2.a.b.1.9 | ✓ | 361 | 1.1 | even | 1 | trivial |