Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.16186\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 | ||||||||
\(3\) | −3.16186 | −1.82550 | −0.912749 | − | 0.408520i | \(-0.866045\pi\) | ||||
−0.912749 | + | 0.408520i | \(0.866045\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.61035 | −0.720171 | −0.360085 | − | 0.932919i | \(-0.617252\pi\) | ||||
−0.360085 | + | 0.932919i | \(0.617252\pi\) | |||||||
\(6\) | 3.16186 | 1.29082 | ||||||||
\(7\) | 0.0905305 | 0.0342173 | 0.0171087 | − | 0.999854i | \(-0.494554\pi\) | ||||
0.0171087 | + | 0.999854i | \(0.494554\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.99733 | 2.33244 | ||||||||
\(10\) | 1.61035 | 0.509238 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −3.16186 | −0.912749 | ||||||||
\(13\) | 0.481640 | 0.133583 | 0.0667915 | − | 0.997767i | \(-0.478724\pi\) | ||||
0.0667915 | + | 0.997767i | \(0.478724\pi\) | |||||||
\(14\) | −0.0905305 | −0.0241953 | ||||||||
\(15\) | 5.09170 | 1.31467 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.419983 | 0.101861 | 0.0509305 | − | 0.998702i | \(-0.483781\pi\) | ||||
0.0509305 | + | 0.998702i | \(0.483781\pi\) | |||||||
\(18\) | −6.99733 | −1.64929 | ||||||||
\(19\) | −1.64931 | −0.378379 | −0.189189 | − | 0.981941i | \(-0.560586\pi\) | ||||
−0.189189 | + | 0.981941i | \(0.560586\pi\) | |||||||
\(20\) | −1.61035 | −0.360085 | ||||||||
\(21\) | −0.286244 | −0.0624637 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 0.827258 | 0.172495 | 0.0862476 | − | 0.996274i | \(-0.472512\pi\) | ||||
0.0862476 | + | 0.996274i | \(0.472512\pi\) | |||||||
\(24\) | 3.16186 | 0.645411 | ||||||||
\(25\) | −2.40677 | −0.481354 | ||||||||
\(26\) | −0.481640 | −0.0944574 | ||||||||
\(27\) | −12.6390 | −2.43238 | ||||||||
\(28\) | 0.0905305 | 0.0171087 | ||||||||
\(29\) | −0.561896 | −0.104341 | −0.0521707 | − | 0.998638i | \(-0.516614\pi\) | ||||
−0.0521707 | + | 0.998638i | \(0.516614\pi\) | |||||||
\(30\) | −5.09170 | −0.929612 | ||||||||
\(31\) | −8.42633 | −1.51341 | −0.756707 | − | 0.653754i | \(-0.773193\pi\) | ||||
−0.756707 | + | 0.653754i | \(0.773193\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.16186 | −0.550408 | ||||||||
\(34\) | −0.419983 | −0.0720265 | ||||||||
\(35\) | −0.145786 | −0.0246423 | ||||||||
\(36\) | 6.99733 | 1.16622 | ||||||||
\(37\) | 1.21121 | 0.199121 | 0.0995605 | − | 0.995032i | \(-0.468256\pi\) | ||||
0.0995605 | + | 0.995032i | \(0.468256\pi\) | |||||||
\(38\) | 1.64931 | 0.267554 | ||||||||
\(39\) | −1.52288 | −0.243855 | ||||||||
\(40\) | 1.61035 | 0.254619 | ||||||||
\(41\) | −7.62488 | −1.19081 | −0.595403 | − | 0.803427i | \(-0.703008\pi\) | ||||
−0.595403 | + | 0.803427i | \(0.703008\pi\) | |||||||
\(42\) | 0.286244 | 0.0441685 | ||||||||
\(43\) | 7.99759 | 1.21962 | 0.609811 | − | 0.792547i | \(-0.291245\pi\) | ||||
0.609811 | + | 0.792547i | \(0.291245\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −11.2682 | −1.67976 | ||||||||
\(46\) | −0.827258 | −0.121972 | ||||||||
\(47\) | 12.0094 | 1.75175 | 0.875873 | − | 0.482542i | \(-0.160286\pi\) | ||||
0.875873 | + | 0.482542i | \(0.160286\pi\) | |||||||
\(48\) | −3.16186 | −0.456375 | ||||||||
\(49\) | −6.99180 | −0.998829 | ||||||||
\(50\) | 2.40677 | 0.340369 | ||||||||
\(51\) | −1.32793 | −0.185947 | ||||||||
\(52\) | 0.481640 | 0.0667915 | ||||||||
\(53\) | 1.16240 | 0.159667 | 0.0798337 | − | 0.996808i | \(-0.474561\pi\) | ||||
0.0798337 | + | 0.996808i | \(0.474561\pi\) | |||||||
\(54\) | 12.6390 | 1.71995 | ||||||||
\(55\) | −1.61035 | −0.217140 | ||||||||
\(56\) | −0.0905305 | −0.0120976 | ||||||||
\(57\) | 5.21489 | 0.690730 | ||||||||
\(58\) | 0.561896 | 0.0737805 | ||||||||
\(59\) | 6.82384 | 0.888389 | 0.444194 | − | 0.895930i | \(-0.353490\pi\) | ||||
0.444194 | + | 0.895930i | \(0.353490\pi\) | |||||||
\(60\) | 5.09170 | 0.657335 | ||||||||
\(61\) | −2.12051 | −0.271503 | −0.135752 | − | 0.990743i | \(-0.543345\pi\) | ||||
−0.135752 | + | 0.990743i | \(0.543345\pi\) | |||||||
\(62\) | 8.42633 | 1.07015 | ||||||||
\(63\) | 0.633472 | 0.0798100 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.775610 | −0.0962025 | ||||||||
\(66\) | 3.16186 | 0.389198 | ||||||||
\(67\) | 8.17063 | 0.998201 | 0.499101 | − | 0.866544i | \(-0.333664\pi\) | ||||
0.499101 | + | 0.866544i | \(0.333664\pi\) | |||||||
\(68\) | 0.419983 | 0.0509305 | ||||||||
\(69\) | −2.61567 | −0.314890 | ||||||||
\(70\) | 0.145786 | 0.0174247 | ||||||||
\(71\) | 3.26805 | 0.387846 | 0.193923 | − | 0.981017i | \(-0.437879\pi\) | ||||
0.193923 | + | 0.981017i | \(0.437879\pi\) | |||||||
\(72\) | −6.99733 | −0.824644 | ||||||||
\(73\) | −0.788272 | −0.0922602 | −0.0461301 | − | 0.998935i | \(-0.514689\pi\) | ||||
−0.0461301 | + | 0.998935i | \(0.514689\pi\) | |||||||
\(74\) | −1.21121 | −0.140800 | ||||||||
\(75\) | 7.60986 | 0.878711 | ||||||||
\(76\) | −1.64931 | −0.189189 | ||||||||
\(77\) | 0.0905305 | 0.0103169 | ||||||||
\(78\) | 1.52288 | 0.172432 | ||||||||
\(79\) | 11.1043 | 1.24933 | 0.624665 | − | 0.780893i | \(-0.285236\pi\) | ||||
0.624665 | + | 0.780893i | \(0.285236\pi\) | |||||||
\(80\) | −1.61035 | −0.180043 | ||||||||
\(81\) | 18.9707 | 2.10785 | ||||||||
\(82\) | 7.62488 | 0.842027 | ||||||||
\(83\) | −7.46511 | −0.819403 | −0.409701 | − | 0.912220i | \(-0.634367\pi\) | ||||
−0.409701 | + | 0.912220i | \(0.634367\pi\) | |||||||
\(84\) | −0.286244 | −0.0312318 | ||||||||
\(85\) | −0.676320 | −0.0733572 | ||||||||
\(86\) | −7.99759 | −0.862403 | ||||||||
\(87\) | 1.77663 | 0.190475 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −8.38001 | −0.888280 | −0.444140 | − | 0.895958i | \(-0.646491\pi\) | ||||
−0.444140 | + | 0.895958i | \(0.646491\pi\) | |||||||
\(90\) | 11.2682 | 1.18777 | ||||||||
\(91\) | 0.0436031 | 0.00457085 | ||||||||
\(92\) | 0.827258 | 0.0862476 | ||||||||
\(93\) | 26.6428 | 2.76273 | ||||||||
\(94\) | −12.0094 | −1.23867 | ||||||||
\(95\) | 2.65597 | 0.272497 | ||||||||
\(96\) | 3.16186 | 0.322706 | ||||||||
\(97\) | 14.5344 | 1.47574 | 0.737872 | − | 0.674940i | \(-0.235831\pi\) | ||||
0.737872 | + | 0.674940i | \(0.235831\pi\) | |||||||
\(98\) | 6.99180 | 0.706279 | ||||||||
\(99\) | 6.99733 | 0.703259 | ||||||||
\(100\) | −2.40677 | −0.240677 | ||||||||
\(101\) | −2.15350 | −0.214282 | −0.107141 | − | 0.994244i | \(-0.534170\pi\) | ||||
−0.107141 | + | 0.994244i | \(0.534170\pi\) | |||||||
\(102\) | 1.32793 | 0.131484 | ||||||||
\(103\) | −14.1960 | −1.39877 | −0.699387 | − | 0.714743i | \(-0.746544\pi\) | ||||
−0.699387 | + | 0.714743i | \(0.746544\pi\) | |||||||
\(104\) | −0.481640 | −0.0472287 | ||||||||
\(105\) | 0.460954 | 0.0449845 | ||||||||
\(106\) | −1.16240 | −0.112902 | ||||||||
\(107\) | 14.9970 | 1.44982 | 0.724909 | − | 0.688845i | \(-0.241882\pi\) | ||||
0.724909 | + | 0.688845i | \(0.241882\pi\) | |||||||
\(108\) | −12.6390 | −1.21619 | ||||||||
\(109\) | 12.6556 | 1.21219 | 0.606095 | − | 0.795392i | \(-0.292735\pi\) | ||||
0.606095 | + | 0.795392i | \(0.292735\pi\) | |||||||
\(110\) | 1.61035 | 0.153541 | ||||||||
\(111\) | −3.82966 | −0.363495 | ||||||||
\(112\) | 0.0905305 | 0.00855433 | ||||||||
\(113\) | −3.43974 | −0.323583 | −0.161792 | − | 0.986825i | \(-0.551727\pi\) | ||||
−0.161792 | + | 0.986825i | \(0.551727\pi\) | |||||||
\(114\) | −5.21489 | −0.488420 | ||||||||
\(115\) | −1.33218 | −0.124226 | ||||||||
\(116\) | −0.561896 | −0.0521707 | ||||||||
\(117\) | 3.37020 | 0.311575 | ||||||||
\(118\) | −6.82384 | −0.628186 | ||||||||
\(119\) | 0.0380213 | 0.00348541 | ||||||||
\(120\) | −5.09170 | −0.464806 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.12051 | 0.191982 | ||||||||
\(123\) | 24.1088 | 2.17381 | ||||||||
\(124\) | −8.42633 | −0.756707 | ||||||||
\(125\) | 11.9275 | 1.06683 | ||||||||
\(126\) | −0.633472 | −0.0564342 | ||||||||
\(127\) | −10.0677 | −0.893364 | −0.446682 | − | 0.894693i | \(-0.647394\pi\) | ||||
−0.446682 | + | 0.894693i | \(0.647394\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −25.2872 | −2.22642 | ||||||||
\(130\) | 0.775610 | 0.0680255 | ||||||||
\(131\) | 3.84049 | 0.335545 | 0.167773 | − | 0.985826i | \(-0.446343\pi\) | ||||
0.167773 | + | 0.985826i | \(0.446343\pi\) | |||||||
\(132\) | −3.16186 | −0.275204 | ||||||||
\(133\) | −0.149313 | −0.0129471 | ||||||||
\(134\) | −8.17063 | −0.705835 | ||||||||
\(135\) | 20.3532 | 1.75173 | ||||||||
\(136\) | −0.419983 | −0.0360133 | ||||||||
\(137\) | −2.88628 | −0.246591 | −0.123296 | − | 0.992370i | \(-0.539346\pi\) | ||||
−0.123296 | + | 0.992370i | \(0.539346\pi\) | |||||||
\(138\) | 2.61567 | 0.222661 | ||||||||
\(139\) | −10.3432 | −0.877296 | −0.438648 | − | 0.898659i | \(-0.644543\pi\) | ||||
−0.438648 | + | 0.898659i | \(0.644543\pi\) | |||||||
\(140\) | −0.145786 | −0.0123212 | ||||||||
\(141\) | −37.9719 | −3.19781 | ||||||||
\(142\) | −3.26805 | −0.274248 | ||||||||
\(143\) | 0.481640 | 0.0402768 | ||||||||
\(144\) | 6.99733 | 0.583111 | ||||||||
\(145\) | 0.904849 | 0.0751436 | ||||||||
\(146\) | 0.788272 | 0.0652378 | ||||||||
\(147\) | 22.1071 | 1.82336 | ||||||||
\(148\) | 1.21121 | 0.0995605 | ||||||||
\(149\) | −10.9026 | −0.893175 | −0.446587 | − | 0.894740i | \(-0.647361\pi\) | ||||
−0.446587 | + | 0.894740i | \(0.647361\pi\) | |||||||
\(150\) | −7.60986 | −0.621343 | ||||||||
\(151\) | 1.16138 | 0.0945119 | 0.0472560 | − | 0.998883i | \(-0.484952\pi\) | ||||
0.0472560 | + | 0.998883i | \(0.484952\pi\) | |||||||
\(152\) | 1.64931 | 0.133777 | ||||||||
\(153\) | 2.93876 | 0.237585 | ||||||||
\(154\) | −0.0905305 | −0.00729516 | ||||||||
\(155\) | 13.5693 | 1.08992 | ||||||||
\(156\) | −1.52288 | −0.121928 | ||||||||
\(157\) | 12.4185 | 0.991105 | 0.495553 | − | 0.868578i | \(-0.334966\pi\) | ||||
0.495553 | + | 0.868578i | \(0.334966\pi\) | |||||||
\(158\) | −11.1043 | −0.883409 | ||||||||
\(159\) | −3.67533 | −0.291473 | ||||||||
\(160\) | 1.61035 | 0.127309 | ||||||||
\(161\) | 0.0748921 | 0.00590232 | ||||||||
\(162\) | −18.9707 | −1.49048 | ||||||||
\(163\) | −1.80088 | −0.141056 | −0.0705278 | − | 0.997510i | \(-0.522468\pi\) | ||||
−0.0705278 | + | 0.997510i | \(0.522468\pi\) | |||||||
\(164\) | −7.62488 | −0.595403 | ||||||||
\(165\) | 5.09170 | 0.396388 | ||||||||
\(166\) | 7.46511 | 0.579405 | ||||||||
\(167\) | 14.4726 | 1.11992 | 0.559962 | − | 0.828518i | \(-0.310816\pi\) | ||||
0.559962 | + | 0.828518i | \(0.310816\pi\) | |||||||
\(168\) | 0.286244 | 0.0220842 | ||||||||
\(169\) | −12.7680 | −0.982156 | ||||||||
\(170\) | 0.676320 | 0.0518714 | ||||||||
\(171\) | −11.5408 | −0.882547 | ||||||||
\(172\) | 7.99759 | 0.609811 | ||||||||
\(173\) | 16.6108 | 1.26289 | 0.631447 | − | 0.775419i | \(-0.282461\pi\) | ||||
0.631447 | + | 0.775419i | \(0.282461\pi\) | |||||||
\(174\) | −1.77663 | −0.134686 | ||||||||
\(175\) | −0.217886 | −0.0164706 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −21.5760 | −1.62175 | ||||||||
\(178\) | 8.38001 | 0.628108 | ||||||||
\(179\) | 14.6241 | 1.09306 | 0.546529 | − | 0.837440i | \(-0.315949\pi\) | ||||
0.546529 | + | 0.837440i | \(0.315949\pi\) | |||||||
\(180\) | −11.2682 | −0.839879 | ||||||||
\(181\) | −22.8349 | −1.69731 | −0.848653 | − | 0.528950i | \(-0.822586\pi\) | ||||
−0.848653 | + | 0.528950i | \(0.822586\pi\) | |||||||
\(182\) | −0.0436031 | −0.00323208 | ||||||||
\(183\) | 6.70475 | 0.495629 | ||||||||
\(184\) | −0.827258 | −0.0609862 | ||||||||
\(185\) | −1.95047 | −0.143401 | ||||||||
\(186\) | −26.6428 | −1.95355 | ||||||||
\(187\) | 0.419983 | 0.0307122 | ||||||||
\(188\) | 12.0094 | 0.875873 | ||||||||
\(189\) | −1.14421 | −0.0832294 | ||||||||
\(190\) | −2.65597 | −0.192685 | ||||||||
\(191\) | 20.0238 | 1.44887 | 0.724435 | − | 0.689343i | \(-0.242101\pi\) | ||||
0.724435 | + | 0.689343i | \(0.242101\pi\) | |||||||
\(192\) | −3.16186 | −0.228187 | ||||||||
\(193\) | −12.5215 | −0.901316 | −0.450658 | − | 0.892697i | \(-0.648811\pi\) | ||||
−0.450658 | + | 0.892697i | \(0.648811\pi\) | |||||||
\(194\) | −14.5344 | −1.04351 | ||||||||
\(195\) | 2.45237 | 0.175618 | ||||||||
\(196\) | −6.99180 | −0.499415 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | −6.99733 | −0.497279 | ||||||||
\(199\) | −6.27326 | −0.444699 | −0.222350 | − | 0.974967i | \(-0.571373\pi\) | ||||
−0.222350 | + | 0.974967i | \(0.571373\pi\) | |||||||
\(200\) | 2.40677 | 0.170184 | ||||||||
\(201\) | −25.8344 | −1.82222 | ||||||||
\(202\) | 2.15350 | 0.151520 | ||||||||
\(203\) | −0.0508687 | −0.00357028 | ||||||||
\(204\) | −1.32793 | −0.0929735 | ||||||||
\(205\) | 12.2787 | 0.857583 | ||||||||
\(206\) | 14.1960 | 0.989083 | ||||||||
\(207\) | 5.78860 | 0.402335 | ||||||||
\(208\) | 0.481640 | 0.0333957 | ||||||||
\(209\) | −1.64931 | −0.114085 | ||||||||
\(210\) | −0.460954 | −0.0318088 | ||||||||
\(211\) | 5.76182 | 0.396660 | 0.198330 | − | 0.980135i | \(-0.436448\pi\) | ||||
0.198330 | + | 0.980135i | \(0.436448\pi\) | |||||||
\(212\) | 1.16240 | 0.0798337 | ||||||||
\(213\) | −10.3331 | −0.708012 | ||||||||
\(214\) | −14.9970 | −1.02518 | ||||||||
\(215\) | −12.8789 | −0.878336 | ||||||||
\(216\) | 12.6390 | 0.859975 | ||||||||
\(217\) | −0.762840 | −0.0517850 | ||||||||
\(218\) | −12.6556 | −0.857148 | ||||||||
\(219\) | 2.49240 | 0.168421 | ||||||||
\(220\) | −1.61035 | −0.108570 | ||||||||
\(221\) | 0.202281 | 0.0136069 | ||||||||
\(222\) | 3.82966 | 0.257030 | ||||||||
\(223\) | −6.56179 | −0.439410 | −0.219705 | − | 0.975566i | \(-0.570509\pi\) | ||||
−0.219705 | + | 0.975566i | \(0.570509\pi\) | |||||||
\(224\) | −0.0905305 | −0.00604882 | ||||||||
\(225\) | −16.8410 | −1.12273 | ||||||||
\(226\) | 3.43974 | 0.228808 | ||||||||
\(227\) | 23.2625 | 1.54399 | 0.771995 | − | 0.635629i | \(-0.219259\pi\) | ||||
0.771995 | + | 0.635629i | \(0.219259\pi\) | |||||||
\(228\) | 5.21489 | 0.345365 | ||||||||
\(229\) | −26.6070 | −1.75824 | −0.879120 | − | 0.476600i | \(-0.841869\pi\) | ||||
−0.879120 | + | 0.476600i | \(0.841869\pi\) | |||||||
\(230\) | 1.33218 | 0.0878410 | ||||||||
\(231\) | −0.286244 | −0.0188335 | ||||||||
\(232\) | 0.561896 | 0.0368903 | ||||||||
\(233\) | −3.84104 | −0.251635 | −0.125817 | − | 0.992053i | \(-0.540155\pi\) | ||||
−0.125817 | + | 0.992053i | \(0.540155\pi\) | |||||||
\(234\) | −3.37020 | −0.220317 | ||||||||
\(235\) | −19.3393 | −1.26156 | ||||||||
\(236\) | 6.82384 | 0.444194 | ||||||||
\(237\) | −35.1101 | −2.28065 | ||||||||
\(238\) | −0.0380213 | −0.00246456 | ||||||||
\(239\) | −22.6659 | −1.46613 | −0.733067 | − | 0.680156i | \(-0.761912\pi\) | ||||
−0.733067 | + | 0.680156i | \(0.761912\pi\) | |||||||
\(240\) | 5.09170 | 0.328668 | ||||||||
\(241\) | 8.64726 | 0.557019 | 0.278510 | − | 0.960433i | \(-0.410160\pi\) | ||||
0.278510 | + | 0.960433i | \(0.410160\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −22.0656 | −1.41551 | ||||||||
\(244\) | −2.12051 | −0.135752 | ||||||||
\(245\) | 11.2593 | 0.719328 | ||||||||
\(246\) | −24.1088 | −1.53712 | ||||||||
\(247\) | −0.794376 | −0.0505449 | ||||||||
\(248\) | 8.42633 | 0.535073 | ||||||||
\(249\) | 23.6036 | 1.49582 | ||||||||
\(250\) | −11.9275 | −0.754361 | ||||||||
\(251\) | 9.71156 | 0.612988 | 0.306494 | − | 0.951873i | \(-0.400844\pi\) | ||||
0.306494 | + | 0.951873i | \(0.400844\pi\) | |||||||
\(252\) | 0.633472 | 0.0399050 | ||||||||
\(253\) | 0.827258 | 0.0520092 | ||||||||
\(254\) | 10.0677 | 0.631703 | ||||||||
\(255\) | 2.13843 | 0.133914 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.38542 | 0.460690 | 0.230345 | − | 0.973109i | \(-0.426015\pi\) | ||||
0.230345 | + | 0.973109i | \(0.426015\pi\) | |||||||
\(258\) | 25.2872 | 1.57431 | ||||||||
\(259\) | 0.109651 | 0.00681339 | ||||||||
\(260\) | −0.775610 | −0.0481013 | ||||||||
\(261\) | −3.93177 | −0.243371 | ||||||||
\(262\) | −3.84049 | −0.237266 | ||||||||
\(263\) | −7.42250 | −0.457691 | −0.228845 | − | 0.973463i | \(-0.573495\pi\) | ||||
−0.228845 | + | 0.973463i | \(0.573495\pi\) | |||||||
\(264\) | 3.16186 | 0.194599 | ||||||||
\(265\) | −1.87187 | −0.114988 | ||||||||
\(266\) | 0.149313 | 0.00915498 | ||||||||
\(267\) | 26.4964 | 1.62155 | ||||||||
\(268\) | 8.17063 | 0.499101 | ||||||||
\(269\) | −20.6674 | −1.26011 | −0.630056 | − | 0.776550i | \(-0.716968\pi\) | ||||
−0.630056 | + | 0.776550i | \(0.716968\pi\) | |||||||
\(270\) | −20.3532 | −1.23866 | ||||||||
\(271\) | −20.5331 | −1.24730 | −0.623649 | − | 0.781704i | \(-0.714351\pi\) | ||||
−0.623649 | + | 0.781704i | \(0.714351\pi\) | |||||||
\(272\) | 0.419983 | 0.0254652 | ||||||||
\(273\) | −0.137867 | −0.00834408 | ||||||||
\(274\) | 2.88628 | 0.174366 | ||||||||
\(275\) | −2.40677 | −0.145134 | ||||||||
\(276\) | −2.61567 | −0.157445 | ||||||||
\(277\) | 13.5361 | 0.813307 | 0.406653 | − | 0.913583i | \(-0.366696\pi\) | ||||
0.406653 | + | 0.913583i | \(0.366696\pi\) | |||||||
\(278\) | 10.3432 | 0.620342 | ||||||||
\(279\) | −58.9619 | −3.52995 | ||||||||
\(280\) | 0.145786 | 0.00871237 | ||||||||
\(281\) | −9.89976 | −0.590570 | −0.295285 | − | 0.955409i | \(-0.595415\pi\) | ||||
−0.295285 | + | 0.955409i | \(0.595415\pi\) | |||||||
\(282\) | 37.9719 | 2.26119 | ||||||||
\(283\) | 1.91549 | 0.113864 | 0.0569320 | − | 0.998378i | \(-0.481868\pi\) | ||||
0.0569320 | + | 0.998378i | \(0.481868\pi\) | |||||||
\(284\) | 3.26805 | 0.193923 | ||||||||
\(285\) | −8.39781 | −0.497443 | ||||||||
\(286\) | −0.481640 | −0.0284800 | ||||||||
\(287\) | −0.690284 | −0.0407462 | ||||||||
\(288\) | −6.99733 | −0.412322 | ||||||||
\(289\) | −16.8236 | −0.989624 | ||||||||
\(290\) | −0.904849 | −0.0531346 | ||||||||
\(291\) | −45.9557 | −2.69397 | ||||||||
\(292\) | −0.788272 | −0.0461301 | ||||||||
\(293\) | 8.73898 | 0.510537 | 0.255268 | − | 0.966870i | \(-0.417836\pi\) | ||||
0.255268 | + | 0.966870i | \(0.417836\pi\) | |||||||
\(294\) | −22.1071 | −1.28931 | ||||||||
\(295\) | −10.9888 | −0.639791 | ||||||||
\(296\) | −1.21121 | −0.0703999 | ||||||||
\(297\) | −12.6390 | −0.733389 | ||||||||
\(298\) | 10.9026 | 0.631570 | ||||||||
\(299\) | 0.398441 | 0.0230424 | ||||||||
\(300\) | 7.60986 | 0.439356 | ||||||||
\(301\) | 0.724026 | 0.0417322 | ||||||||
\(302\) | −1.16138 | −0.0668300 | ||||||||
\(303\) | 6.80907 | 0.391171 | ||||||||
\(304\) | −1.64931 | −0.0945947 | ||||||||
\(305\) | 3.41476 | 0.195529 | ||||||||
\(306\) | −2.93876 | −0.167998 | ||||||||
\(307\) | −29.4724 | −1.68208 | −0.841040 | − | 0.540972i | \(-0.818056\pi\) | ||||
−0.841040 | + | 0.540972i | \(0.818056\pi\) | |||||||
\(308\) | 0.0905305 | 0.00515846 | ||||||||
\(309\) | 44.8857 | 2.55346 | ||||||||
\(310\) | −13.5693 | −0.770687 | ||||||||
\(311\) | 15.7060 | 0.890607 | 0.445303 | − | 0.895380i | \(-0.353096\pi\) | ||||
0.445303 | + | 0.895380i | \(0.353096\pi\) | |||||||
\(312\) | 1.52288 | 0.0862159 | ||||||||
\(313\) | −9.38008 | −0.530194 | −0.265097 | − | 0.964222i | \(-0.585404\pi\) | ||||
−0.265097 | + | 0.964222i | \(0.585404\pi\) | |||||||
\(314\) | −12.4185 | −0.700817 | ||||||||
\(315\) | −1.02011 | −0.0574768 | ||||||||
\(316\) | 11.1043 | 0.624665 | ||||||||
\(317\) | 0.406226 | 0.0228159 | 0.0114080 | − | 0.999935i | \(-0.496369\pi\) | ||||
0.0114080 | + | 0.999935i | \(0.496369\pi\) | |||||||
\(318\) | 3.67533 | 0.206102 | ||||||||
\(319\) | −0.561896 | −0.0314601 | ||||||||
\(320\) | −1.61035 | −0.0900213 | ||||||||
\(321\) | −47.4185 | −2.64664 | ||||||||
\(322\) | −0.0748921 | −0.00417357 | ||||||||
\(323\) | −0.692684 | −0.0385420 | ||||||||
\(324\) | 18.9707 | 1.05393 | ||||||||
\(325\) | −1.15920 | −0.0643007 | ||||||||
\(326\) | 1.80088 | 0.0997414 | ||||||||
\(327\) | −40.0153 | −2.21285 | ||||||||
\(328\) | 7.62488 | 0.421013 | ||||||||
\(329\) | 1.08721 | 0.0599400 | ||||||||
\(330\) | −5.09170 | −0.280289 | ||||||||
\(331\) | 32.8525 | 1.80573 | 0.902867 | − | 0.429919i | \(-0.141458\pi\) | ||||
0.902867 | + | 0.429919i | \(0.141458\pi\) | |||||||
\(332\) | −7.46511 | −0.409701 | ||||||||
\(333\) | 8.47521 | 0.464439 | ||||||||
\(334\) | −14.4726 | −0.791906 | ||||||||
\(335\) | −13.1576 | −0.718875 | ||||||||
\(336\) | −0.286244 | −0.0156159 | ||||||||
\(337\) | −1.57192 | −0.0856279 | −0.0428139 | − | 0.999083i | \(-0.513632\pi\) | ||||
−0.0428139 | + | 0.999083i | \(0.513632\pi\) | |||||||
\(338\) | 12.7680 | 0.694489 | ||||||||
\(339\) | 10.8760 | 0.590701 | ||||||||
\(340\) | −0.676320 | −0.0366786 | ||||||||
\(341\) | −8.42633 | −0.456311 | ||||||||
\(342\) | 11.5408 | 0.624055 | ||||||||
\(343\) | −1.26669 | −0.0683946 | ||||||||
\(344\) | −7.99759 | −0.431201 | ||||||||
\(345\) | 4.21215 | 0.226774 | ||||||||
\(346\) | −16.6108 | −0.893001 | ||||||||
\(347\) | −33.0672 | −1.77514 | −0.887571 | − | 0.460671i | \(-0.847609\pi\) | ||||
−0.887571 | + | 0.460671i | \(0.847609\pi\) | |||||||
\(348\) | 1.77663 | 0.0952376 | ||||||||
\(349\) | −17.8947 | −0.957879 | −0.478939 | − | 0.877848i | \(-0.658979\pi\) | ||||
−0.478939 | + | 0.877848i | \(0.658979\pi\) | |||||||
\(350\) | 0.217886 | 0.0116465 | ||||||||
\(351\) | −6.08745 | −0.324924 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 0.965407 | 0.0513834 | 0.0256917 | − | 0.999670i | \(-0.491821\pi\) | ||||
0.0256917 | + | 0.999670i | \(0.491821\pi\) | |||||||
\(354\) | 21.5760 | 1.14675 | ||||||||
\(355\) | −5.26270 | −0.279315 | ||||||||
\(356\) | −8.38001 | −0.444140 | ||||||||
\(357\) | −0.120218 | −0.00636261 | ||||||||
\(358\) | −14.6241 | −0.772909 | ||||||||
\(359\) | 4.14233 | 0.218624 | 0.109312 | − | 0.994008i | \(-0.465135\pi\) | ||||
0.109312 | + | 0.994008i | \(0.465135\pi\) | |||||||
\(360\) | 11.2682 | 0.593884 | ||||||||
\(361\) | −16.2798 | −0.856830 | ||||||||
\(362\) | 22.8349 | 1.20018 | ||||||||
\(363\) | −3.16186 | −0.165954 | ||||||||
\(364\) | 0.0436031 | 0.00228543 | ||||||||
\(365\) | 1.26939 | 0.0664431 | ||||||||
\(366\) | −6.70475 | −0.350463 | ||||||||
\(367\) | −34.2662 | −1.78868 | −0.894340 | − | 0.447388i | \(-0.852354\pi\) | ||||
−0.894340 | + | 0.447388i | \(0.852354\pi\) | |||||||
\(368\) | 0.827258 | 0.0431238 | ||||||||
\(369\) | −53.3538 | −2.77749 | ||||||||
\(370\) | 1.95047 | 0.101400 | ||||||||
\(371\) | 0.105232 | 0.00546339 | ||||||||
\(372\) | 26.6428 | 1.38137 | ||||||||
\(373\) | −22.9046 | −1.18596 | −0.592979 | − | 0.805218i | \(-0.702048\pi\) | ||||
−0.592979 | + | 0.805218i | \(0.702048\pi\) | |||||||
\(374\) | −0.419983 | −0.0217168 | ||||||||
\(375\) | −37.7130 | −1.94749 | ||||||||
\(376\) | −12.0094 | −0.619336 | ||||||||
\(377\) | −0.270632 | −0.0139382 | ||||||||
\(378\) | 1.14421 | 0.0588521 | ||||||||
\(379\) | 0.208774 | 0.0107240 | 0.00536200 | − | 0.999986i | \(-0.498293\pi\) | ||||
0.00536200 | + | 0.999986i | \(0.498293\pi\) | |||||||
\(380\) | 2.65597 | 0.136249 | ||||||||
\(381\) | 31.8326 | 1.63083 | ||||||||
\(382\) | −20.0238 | −1.02451 | ||||||||
\(383\) | −24.4168 | −1.24764 | −0.623819 | − | 0.781569i | \(-0.714420\pi\) | ||||
−0.623819 | + | 0.781569i | \(0.714420\pi\) | |||||||
\(384\) | 3.16186 | 0.161353 | ||||||||
\(385\) | −0.145786 | −0.00742994 | ||||||||
\(386\) | 12.5215 | 0.637327 | ||||||||
\(387\) | 55.9618 | 2.84470 | ||||||||
\(388\) | 14.5344 | 0.737872 | ||||||||
\(389\) | 2.00470 | 0.101642 | 0.0508211 | − | 0.998708i | \(-0.483816\pi\) | ||||
0.0508211 | + | 0.998708i | \(0.483816\pi\) | |||||||
\(390\) | −2.45237 | −0.124180 | ||||||||
\(391\) | 0.347434 | 0.0175705 | ||||||||
\(392\) | 6.99180 | 0.353139 | ||||||||
\(393\) | −12.1431 | −0.612537 | ||||||||
\(394\) | −1.00000 | −0.0503793 | ||||||||
\(395\) | −17.8818 | −0.899730 | ||||||||
\(396\) | 6.99733 | 0.351629 | ||||||||
\(397\) | 4.97318 | 0.249597 | 0.124798 | − | 0.992182i | \(-0.460172\pi\) | ||||
0.124798 | + | 0.992182i | \(0.460172\pi\) | |||||||
\(398\) | 6.27326 | 0.314450 | ||||||||
\(399\) | 0.472107 | 0.0236349 | ||||||||
\(400\) | −2.40677 | −0.120339 | ||||||||
\(401\) | −5.06123 | −0.252746 | −0.126373 | − | 0.991983i | \(-0.540334\pi\) | ||||
−0.126373 | + | 0.991983i | \(0.540334\pi\) | |||||||
\(402\) | 25.8344 | 1.28850 | ||||||||
\(403\) | −4.05846 | −0.202166 | ||||||||
\(404\) | −2.15350 | −0.107141 | ||||||||
\(405\) | −30.5494 | −1.51801 | ||||||||
\(406\) | 0.0508687 | 0.00252457 | ||||||||
\(407\) | 1.21121 | 0.0600372 | ||||||||
\(408\) | 1.32793 | 0.0657422 | ||||||||
\(409\) | 13.7553 | 0.680158 | 0.340079 | − | 0.940397i | \(-0.389546\pi\) | ||||
0.340079 | + | 0.940397i | \(0.389546\pi\) | |||||||
\(410\) | −12.2787 | −0.606403 | ||||||||
\(411\) | 9.12599 | 0.450152 | ||||||||
\(412\) | −14.1960 | −0.699387 | ||||||||
\(413\) | 0.617766 | 0.0303983 | ||||||||
\(414\) | −5.78860 | −0.284494 | ||||||||
\(415\) | 12.0215 | 0.590110 | ||||||||
\(416\) | −0.481640 | −0.0236144 | ||||||||
\(417\) | 32.7036 | 1.60150 | ||||||||
\(418\) | 1.64931 | 0.0806706 | ||||||||
\(419\) | −1.85667 | −0.0907042 | −0.0453521 | − | 0.998971i | \(-0.514441\pi\) | ||||
−0.0453521 | + | 0.998971i | \(0.514441\pi\) | |||||||
\(420\) | 0.460954 | 0.0224923 | ||||||||
\(421\) | 6.84016 | 0.333369 | 0.166684 | − | 0.986010i | \(-0.446694\pi\) | ||||
0.166684 | + | 0.986010i | \(0.446694\pi\) | |||||||
\(422\) | −5.76182 | −0.280481 | ||||||||
\(423\) | 84.0335 | 4.08585 | ||||||||
\(424\) | −1.16240 | −0.0564509 | ||||||||
\(425\) | −1.01080 | −0.0490312 | ||||||||
\(426\) | 10.3331 | 0.500640 | ||||||||
\(427\) | −0.191971 | −0.00929012 | ||||||||
\(428\) | 14.9970 | 0.724909 | ||||||||
\(429\) | −1.52288 | −0.0735252 | ||||||||
\(430\) | 12.8789 | 0.621077 | ||||||||
\(431\) | −5.73620 | −0.276303 | −0.138152 | − | 0.990411i | \(-0.544116\pi\) | ||||
−0.138152 | + | 0.990411i | \(0.544116\pi\) | |||||||
\(432\) | −12.6390 | −0.608094 | ||||||||
\(433\) | 16.0484 | 0.771236 | 0.385618 | − | 0.922659i | \(-0.373988\pi\) | ||||
0.385618 | + | 0.922659i | \(0.373988\pi\) | |||||||
\(434\) | 0.762840 | 0.0366175 | ||||||||
\(435\) | −2.86100 | −0.137175 | ||||||||
\(436\) | 12.6556 | 0.606095 | ||||||||
\(437\) | −1.36441 | −0.0652685 | ||||||||
\(438\) | −2.49240 | −0.119092 | ||||||||
\(439\) | −14.8135 | −0.707012 | −0.353506 | − | 0.935432i | \(-0.615011\pi\) | ||||
−0.353506 | + | 0.935432i | \(0.615011\pi\) | |||||||
\(440\) | 1.61035 | 0.0767705 | ||||||||
\(441\) | −48.9240 | −2.32971 | ||||||||
\(442\) | −0.202281 | −0.00962152 | ||||||||
\(443\) | −15.7001 | −0.745933 | −0.372966 | − | 0.927845i | \(-0.621659\pi\) | ||||
−0.372966 | + | 0.927845i | \(0.621659\pi\) | |||||||
\(444\) | −3.82966 | −0.181748 | ||||||||
\(445\) | 13.4948 | 0.639713 | ||||||||
\(446\) | 6.56179 | 0.310710 | ||||||||
\(447\) | 34.4724 | 1.63049 | ||||||||
\(448\) | 0.0905305 | 0.00427717 | ||||||||
\(449\) | 12.0150 | 0.567021 | 0.283511 | − | 0.958969i | \(-0.408501\pi\) | ||||
0.283511 | + | 0.958969i | \(0.408501\pi\) | |||||||
\(450\) | 16.8410 | 0.793891 | ||||||||
\(451\) | −7.62488 | −0.359041 | ||||||||
\(452\) | −3.43974 | −0.161792 | ||||||||
\(453\) | −3.67212 | −0.172531 | ||||||||
\(454\) | −23.2625 | −1.09177 | ||||||||
\(455\) | −0.0702163 | −0.00329179 | ||||||||
\(456\) | −5.21489 | −0.244210 | ||||||||
\(457\) | 1.13638 | 0.0531574 | 0.0265787 | − | 0.999647i | \(-0.491539\pi\) | ||||
0.0265787 | + | 0.999647i | \(0.491539\pi\) | |||||||
\(458\) | 26.6070 | 1.24326 | ||||||||
\(459\) | −5.30817 | −0.247764 | ||||||||
\(460\) | −1.33218 | −0.0621130 | ||||||||
\(461\) | 16.5049 | 0.768710 | 0.384355 | − | 0.923185i | \(-0.374424\pi\) | ||||
0.384355 | + | 0.923185i | \(0.374424\pi\) | |||||||
\(462\) | 0.286244 | 0.0133173 | ||||||||
\(463\) | −37.7903 | −1.75626 | −0.878131 | − | 0.478420i | \(-0.841210\pi\) | ||||
−0.878131 | + | 0.478420i | \(0.841210\pi\) | |||||||
\(464\) | −0.561896 | −0.0260854 | ||||||||
\(465\) | −42.9043 | −1.98964 | ||||||||
\(466\) | 3.84104 | 0.177933 | ||||||||
\(467\) | 1.47313 | 0.0681685 | 0.0340843 | − | 0.999419i | \(-0.489149\pi\) | ||||
0.0340843 | + | 0.999419i | \(0.489149\pi\) | |||||||
\(468\) | 3.37020 | 0.155787 | ||||||||
\(469\) | 0.739691 | 0.0341558 | ||||||||
\(470\) | 19.3393 | 0.892055 | ||||||||
\(471\) | −39.2656 | −1.80926 | ||||||||
\(472\) | −6.82384 | −0.314093 | ||||||||
\(473\) | 7.99759 | 0.367730 | ||||||||
\(474\) | 35.1101 | 1.61266 | ||||||||
\(475\) | 3.96952 | 0.182134 | ||||||||
\(476\) | 0.0380213 | 0.00174270 | ||||||||
\(477\) | 8.13367 | 0.372415 | ||||||||
\(478\) | 22.6659 | 1.03671 | ||||||||
\(479\) | 8.78124 | 0.401225 | 0.200612 | − | 0.979671i | \(-0.435707\pi\) | ||||
0.200612 | + | 0.979671i | \(0.435707\pi\) | |||||||
\(480\) | −5.09170 | −0.232403 | ||||||||
\(481\) | 0.583365 | 0.0265992 | ||||||||
\(482\) | −8.64726 | −0.393872 | ||||||||
\(483\) | −0.236798 | −0.0107747 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −23.4055 | −1.06279 | ||||||||
\(486\) | 22.0656 | 1.00091 | ||||||||
\(487\) | 38.7747 | 1.75705 | 0.878525 | − | 0.477697i | \(-0.158528\pi\) | ||||
0.878525 | + | 0.477697i | \(0.158528\pi\) | |||||||
\(488\) | 2.12051 | 0.0959910 | ||||||||
\(489\) | 5.69412 | 0.257497 | ||||||||
\(490\) | −11.2593 | −0.508641 | ||||||||
\(491\) | −12.6103 | −0.569094 | −0.284547 | − | 0.958662i | \(-0.591843\pi\) | ||||
−0.284547 | + | 0.958662i | \(0.591843\pi\) | |||||||
\(492\) | 24.1088 | 1.08691 | ||||||||
\(493\) | −0.235987 | −0.0106283 | ||||||||
\(494\) | 0.794376 | 0.0357407 | ||||||||
\(495\) | −11.2682 | −0.506466 | ||||||||
\(496\) | −8.42633 | −0.378353 | ||||||||
\(497\) | 0.295858 | 0.0132710 | ||||||||
\(498\) | −23.6036 | −1.05770 | ||||||||
\(499\) | 40.8293 | 1.82777 | 0.913885 | − | 0.405974i | \(-0.133068\pi\) | ||||
0.913885 | + | 0.405974i | \(0.133068\pi\) | |||||||
\(500\) | 11.9275 | 0.533414 | ||||||||
\(501\) | −45.7603 | −2.04442 | ||||||||
\(502\) | −9.71156 | −0.433448 | ||||||||
\(503\) | 0.743243 | 0.0331396 | 0.0165698 | − | 0.999863i | \(-0.494725\pi\) | ||||
0.0165698 | + | 0.999863i | \(0.494725\pi\) | |||||||
\(504\) | −0.633472 | −0.0282171 | ||||||||
\(505\) | 3.46790 | 0.154319 | ||||||||
\(506\) | −0.827258 | −0.0367761 | ||||||||
\(507\) | 40.3707 | 1.79292 | ||||||||
\(508\) | −10.0677 | −0.446682 | ||||||||
\(509\) | 9.84334 | 0.436298 | 0.218149 | − | 0.975915i | \(-0.429998\pi\) | ||||
0.218149 | + | 0.975915i | \(0.429998\pi\) | |||||||
\(510\) | −2.13843 | −0.0946912 | ||||||||
\(511\) | −0.0713627 | −0.00315690 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 20.8457 | 0.920359 | ||||||||
\(514\) | −7.38542 | −0.325757 | ||||||||
\(515\) | 22.8606 | 1.00736 | ||||||||
\(516\) | −25.2872 | −1.11321 | ||||||||
\(517\) | 12.0094 | 0.528171 | ||||||||
\(518\) | −0.109651 | −0.00481779 | ||||||||
\(519\) | −52.5209 | −2.30541 | ||||||||
\(520\) | 0.775610 | 0.0340127 | ||||||||
\(521\) | 3.77380 | 0.165333 | 0.0826667 | − | 0.996577i | \(-0.473656\pi\) | ||||
0.0826667 | + | 0.996577i | \(0.473656\pi\) | |||||||
\(522\) | 3.93177 | 0.172089 | ||||||||
\(523\) | 8.14264 | 0.356053 | 0.178026 | − | 0.984026i | \(-0.443029\pi\) | ||||
0.178026 | + | 0.984026i | \(0.443029\pi\) | |||||||
\(524\) | 3.84049 | 0.167773 | ||||||||
\(525\) | 0.688925 | 0.0300671 | ||||||||
\(526\) | 7.42250 | 0.323636 | ||||||||
\(527\) | −3.53892 | −0.154158 | ||||||||
\(528\) | −3.16186 | −0.137602 | ||||||||
\(529\) | −22.3156 | −0.970245 | ||||||||
\(530\) | 1.87187 | 0.0813086 | ||||||||
\(531\) | 47.7487 | 2.07212 | ||||||||
\(532\) | −0.149313 | −0.00647355 | ||||||||
\(533\) | −3.67245 | −0.159071 | ||||||||
\(534\) | −26.4964 | −1.14661 | ||||||||
\(535\) | −24.1505 | −1.04412 | ||||||||
\(536\) | −8.17063 | −0.352917 | ||||||||
\(537\) | −46.2394 | −1.99538 | ||||||||
\(538\) | 20.6674 | 0.891033 | ||||||||
\(539\) | −6.99180 | −0.301158 | ||||||||
\(540\) | 20.3532 | 0.875863 | ||||||||
\(541\) | −31.8864 | −1.37090 | −0.685452 | − | 0.728118i | \(-0.740395\pi\) | ||||
−0.685452 | + | 0.728118i | \(0.740395\pi\) | |||||||
\(542\) | 20.5331 | 0.881973 | ||||||||
\(543\) | 72.2007 | 3.09843 | ||||||||
\(544\) | −0.419983 | −0.0180066 | ||||||||
\(545\) | −20.3800 | −0.872984 | ||||||||
\(546\) | 0.137867 | 0.00590016 | ||||||||
\(547\) | −29.2911 | −1.25240 | −0.626198 | − | 0.779664i | \(-0.715390\pi\) | ||||
−0.626198 | + | 0.779664i | \(0.715390\pi\) | |||||||
\(548\) | −2.88628 | −0.123296 | ||||||||
\(549\) | −14.8379 | −0.633267 | ||||||||
\(550\) | 2.40677 | 0.102625 | ||||||||
\(551\) | 0.926743 | 0.0394806 | ||||||||
\(552\) | 2.61567 | 0.111330 | ||||||||
\(553\) | 1.00528 | 0.0427487 | ||||||||
\(554\) | −13.5361 | −0.575095 | ||||||||
\(555\) | 6.16709 | 0.261779 | ||||||||
\(556\) | −10.3432 | −0.438648 | ||||||||
\(557\) | −18.4722 | −0.782691 | −0.391346 | − | 0.920244i | \(-0.627990\pi\) | ||||
−0.391346 | + | 0.920244i | \(0.627990\pi\) | |||||||
\(558\) | 58.9619 | 2.49605 | ||||||||
\(559\) | 3.85196 | 0.162921 | ||||||||
\(560\) | −0.145786 | −0.00616058 | ||||||||
\(561\) | −1.32793 | −0.0560651 | ||||||||
\(562\) | 9.89976 | 0.417596 | ||||||||
\(563\) | −15.1463 | −0.638338 | −0.319169 | − | 0.947698i | \(-0.603404\pi\) | ||||
−0.319169 | + | 0.947698i | \(0.603404\pi\) | |||||||
\(564\) | −37.9719 | −1.59890 | ||||||||
\(565\) | 5.53918 | 0.233035 | ||||||||
\(566\) | −1.91549 | −0.0805140 | ||||||||
\(567\) | 1.71743 | 0.0721251 | ||||||||
\(568\) | −3.26805 | −0.137124 | ||||||||
\(569\) | −39.5200 | −1.65677 | −0.828383 | − | 0.560162i | \(-0.810739\pi\) | ||||
−0.828383 | + | 0.560162i | \(0.810739\pi\) | |||||||
\(570\) | 8.39781 | 0.351745 | ||||||||
\(571\) | −2.41783 | −0.101183 | −0.0505916 | − | 0.998719i | \(-0.516111\pi\) | ||||
−0.0505916 | + | 0.998719i | \(0.516111\pi\) | |||||||
\(572\) | 0.481640 | 0.0201384 | ||||||||
\(573\) | −63.3123 | −2.64491 | ||||||||
\(574\) | 0.690284 | 0.0288119 | ||||||||
\(575\) | −1.99102 | −0.0830313 | ||||||||
\(576\) | 6.99733 | 0.291556 | ||||||||
\(577\) | −20.2179 | −0.841683 | −0.420841 | − | 0.907134i | \(-0.638265\pi\) | ||||
−0.420841 | + | 0.907134i | \(0.638265\pi\) | |||||||
\(578\) | 16.8236 | 0.699770 | ||||||||
\(579\) | 39.5911 | 1.64535 | ||||||||
\(580\) | 0.904849 | 0.0375718 | ||||||||
\(581\) | −0.675821 | −0.0280378 | ||||||||
\(582\) | 45.9557 | 1.90492 | ||||||||
\(583\) | 1.16240 | 0.0481415 | ||||||||
\(584\) | 0.788272 | 0.0326189 | ||||||||
\(585\) | −5.42720 | −0.224387 | ||||||||
\(586\) | −8.73898 | −0.361004 | ||||||||
\(587\) | −37.3524 | −1.54170 | −0.770848 | − | 0.637019i | \(-0.780167\pi\) | ||||
−0.770848 | + | 0.637019i | \(0.780167\pi\) | |||||||
\(588\) | 22.1071 | 0.911681 | ||||||||
\(589\) | 13.8977 | 0.572643 | ||||||||
\(590\) | 10.9888 | 0.452401 | ||||||||
\(591\) | −3.16186 | −0.130061 | ||||||||
\(592\) | 1.21121 | 0.0497803 | ||||||||
\(593\) | 22.3854 | 0.919260 | 0.459630 | − | 0.888110i | \(-0.347982\pi\) | ||||
0.459630 | + | 0.888110i | \(0.347982\pi\) | |||||||
\(594\) | 12.6390 | 0.518584 | ||||||||
\(595\) | −0.0612276 | −0.00251009 | ||||||||
\(596\) | −10.9026 | −0.446587 | ||||||||
\(597\) | 19.8351 | 0.811798 | ||||||||
\(598\) | −0.398441 | −0.0162934 | ||||||||
\(599\) | 25.0022 | 1.02156 | 0.510781 | − | 0.859711i | \(-0.329356\pi\) | ||||
0.510781 | + | 0.859711i | \(0.329356\pi\) | |||||||
\(600\) | −7.60986 | −0.310671 | ||||||||
\(601\) | −11.6416 | −0.474869 | −0.237435 | − | 0.971404i | \(-0.576307\pi\) | ||||
−0.237435 | + | 0.971404i | \(0.576307\pi\) | |||||||
\(602\) | −0.724026 | −0.0295091 | ||||||||
\(603\) | 57.1726 | 2.32825 | ||||||||
\(604\) | 1.16138 | 0.0472560 | ||||||||
\(605\) | −1.61035 | −0.0654701 | ||||||||
\(606\) | −6.80907 | −0.276599 | ||||||||
\(607\) | 16.5455 | 0.671561 | 0.335780 | − | 0.941940i | \(-0.391000\pi\) | ||||
0.335780 | + | 0.941940i | \(0.391000\pi\) | |||||||
\(608\) | 1.64931 | 0.0668885 | ||||||||
\(609\) | 0.160840 | 0.00651755 | ||||||||
\(610\) | −3.41476 | −0.138260 | ||||||||
\(611\) | 5.78419 | 0.234003 | ||||||||
\(612\) | 2.93876 | 0.118792 | ||||||||
\(613\) | −39.2445 | −1.58507 | −0.792536 | − | 0.609825i | \(-0.791240\pi\) | ||||
−0.792536 | + | 0.609825i | \(0.791240\pi\) | |||||||
\(614\) | 29.4724 | 1.18941 | ||||||||
\(615\) | −38.8236 | −1.56552 | ||||||||
\(616\) | −0.0905305 | −0.00364758 | ||||||||
\(617\) | 4.59232 | 0.184880 | 0.0924400 | − | 0.995718i | \(-0.470533\pi\) | ||||
0.0924400 | + | 0.995718i | \(0.470533\pi\) | |||||||
\(618\) | −44.8857 | −1.80557 | ||||||||
\(619\) | −16.0564 | −0.645363 | −0.322681 | − | 0.946508i | \(-0.604584\pi\) | ||||
−0.322681 | + | 0.946508i | \(0.604584\pi\) | |||||||
\(620\) | 13.5693 | 0.544958 | ||||||||
\(621\) | −10.4557 | −0.419573 | ||||||||
\(622\) | −15.7060 | −0.629754 | ||||||||
\(623\) | −0.758647 | −0.0303945 | ||||||||
\(624\) | −1.52288 | −0.0609639 | ||||||||
\(625\) | −7.17360 | −0.286944 | ||||||||
\(626\) | 9.38008 | 0.374903 | ||||||||
\(627\) | 5.21489 | 0.208263 | ||||||||
\(628\) | 12.4185 | 0.495553 | ||||||||
\(629\) | 0.508686 | 0.0202826 | ||||||||
\(630\) | 1.02011 | 0.0406423 | ||||||||
\(631\) | −5.86225 | −0.233372 | −0.116686 | − | 0.993169i | \(-0.537227\pi\) | ||||
−0.116686 | + | 0.993169i | \(0.537227\pi\) | |||||||
\(632\) | −11.1043 | −0.441705 | ||||||||
\(633\) | −18.2180 | −0.724102 | ||||||||
\(634\) | −0.406226 | −0.0161333 | ||||||||
\(635\) | 16.2125 | 0.643374 | ||||||||
\(636\) | −3.67533 | −0.145736 | ||||||||
\(637\) | −3.36753 | −0.133427 | ||||||||
\(638\) | 0.561896 | 0.0222457 | ||||||||
\(639\) | 22.8676 | 0.904629 | ||||||||
\(640\) | 1.61035 | 0.0636547 | ||||||||
\(641\) | 19.5228 | 0.771103 | 0.385551 | − | 0.922686i | \(-0.374011\pi\) | ||||
0.385551 | + | 0.922686i | \(0.374011\pi\) | |||||||
\(642\) | 47.4185 | 1.87146 | ||||||||
\(643\) | 0.210958 | 0.00831936 | 0.00415968 | − | 0.999991i | \(-0.498676\pi\) | ||||
0.00415968 | + | 0.999991i | \(0.498676\pi\) | |||||||
\(644\) | 0.0748921 | 0.00295116 | ||||||||
\(645\) | 40.7213 | 1.60340 | ||||||||
\(646\) | 0.692684 | 0.0272533 | ||||||||
\(647\) | 2.15038 | 0.0845402 | 0.0422701 | − | 0.999106i | \(-0.486541\pi\) | ||||
0.0422701 | + | 0.999106i | \(0.486541\pi\) | |||||||
\(648\) | −18.9707 | −0.745239 | ||||||||
\(649\) | 6.82384 | 0.267859 | ||||||||
\(650\) | 1.15920 | 0.0454675 | ||||||||
\(651\) | 2.41199 | 0.0945334 | ||||||||
\(652\) | −1.80088 | −0.0705278 | ||||||||
\(653\) | 13.3050 | 0.520664 | 0.260332 | − | 0.965519i | \(-0.416168\pi\) | ||||
0.260332 | + | 0.965519i | \(0.416168\pi\) | |||||||
\(654\) | 40.0153 | 1.56472 | ||||||||
\(655\) | −6.18453 | −0.241650 | ||||||||
\(656\) | −7.62488 | −0.297701 | ||||||||
\(657\) | −5.51580 | −0.215192 | ||||||||
\(658\) | −1.08721 | −0.0423840 | ||||||||
\(659\) | 6.26635 | 0.244102 | 0.122051 | − | 0.992524i | \(-0.461053\pi\) | ||||
0.122051 | + | 0.992524i | \(0.461053\pi\) | |||||||
\(660\) | 5.09170 | 0.198194 | ||||||||
\(661\) | −26.6034 | −1.03475 | −0.517376 | − | 0.855758i | \(-0.673091\pi\) | ||||
−0.517376 | + | 0.855758i | \(0.673091\pi\) | |||||||
\(662\) | −32.8525 | −1.27685 | ||||||||
\(663\) | −0.639583 | −0.0248393 | ||||||||
\(664\) | 7.46511 | 0.289703 | ||||||||
\(665\) | 0.240447 | 0.00932412 | ||||||||
\(666\) | −8.47521 | −0.328408 | ||||||||
\(667\) | −0.464833 | −0.0179984 | ||||||||
\(668\) | 14.4726 | 0.559962 | ||||||||
\(669\) | 20.7474 | 0.802142 | ||||||||
\(670\) | 13.1576 | 0.508322 | ||||||||
\(671\) | −2.12051 | −0.0818614 | ||||||||
\(672\) | 0.286244 | 0.0110421 | ||||||||
\(673\) | 16.9958 | 0.655139 | 0.327570 | − | 0.944827i | \(-0.393770\pi\) | ||||
0.327570 | + | 0.944827i | \(0.393770\pi\) | |||||||
\(674\) | 1.57192 | 0.0605481 | ||||||||
\(675\) | 30.4192 | 1.17083 | ||||||||
\(676\) | −12.7680 | −0.491078 | ||||||||
\(677\) | 8.01111 | 0.307892 | 0.153946 | − | 0.988079i | \(-0.450802\pi\) | ||||
0.153946 | + | 0.988079i | \(0.450802\pi\) | |||||||
\(678\) | −10.8760 | −0.417689 | ||||||||
\(679\) | 1.31581 | 0.0504960 | ||||||||
\(680\) | 0.676320 | 0.0259357 | ||||||||
\(681\) | −73.5528 | −2.81855 | ||||||||
\(682\) | 8.42633 | 0.322661 | ||||||||
\(683\) | 39.8758 | 1.52581 | 0.762903 | − | 0.646513i | \(-0.223773\pi\) | ||||
0.762903 | + | 0.646513i | \(0.223773\pi\) | |||||||
\(684\) | −11.5408 | −0.441274 | ||||||||
\(685\) | 4.64792 | 0.177588 | ||||||||
\(686\) | 1.26669 | 0.0483623 | ||||||||
\(687\) | 84.1275 | 3.20967 | ||||||||
\(688\) | 7.99759 | 0.304905 | ||||||||
\(689\) | 0.559857 | 0.0213288 | ||||||||
\(690\) | −4.21215 | −0.160354 | ||||||||
\(691\) | −27.8331 | −1.05882 | −0.529411 | − | 0.848366i | \(-0.677587\pi\) | ||||
−0.529411 | + | 0.848366i | \(0.677587\pi\) | |||||||
\(692\) | 16.6108 | 0.631447 | ||||||||
\(693\) | 0.633472 | 0.0240636 | ||||||||
\(694\) | 33.0672 | 1.25521 | ||||||||
\(695\) | 16.6561 | 0.631803 | ||||||||
\(696\) | −1.77663 | −0.0673431 | ||||||||
\(697\) | −3.20232 | −0.121297 | ||||||||
\(698\) | 17.8947 | 0.677323 | ||||||||
\(699\) | 12.1448 | 0.459359 | ||||||||
\(700\) | −0.217886 | −0.00823532 | ||||||||
\(701\) | −5.61712 | −0.212156 | −0.106078 | − | 0.994358i | \(-0.533829\pi\) | ||||
−0.106078 | + | 0.994358i | \(0.533829\pi\) | |||||||
\(702\) | 6.08745 | 0.229756 | ||||||||
\(703\) | −1.99766 | −0.0753431 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 61.1480 | 2.30297 | ||||||||
\(706\) | −0.965407 | −0.0363336 | ||||||||
\(707\) | −0.194958 | −0.00733214 | ||||||||
\(708\) | −21.5760 | −0.810876 | ||||||||
\(709\) | −16.9164 | −0.635308 | −0.317654 | − | 0.948207i | \(-0.602895\pi\) | ||||
−0.317654 | + | 0.948207i | \(0.602895\pi\) | |||||||
\(710\) | 5.26270 | 0.197506 | ||||||||
\(711\) | 77.7004 | 2.91399 | ||||||||
\(712\) | 8.38001 | 0.314054 | ||||||||
\(713\) | −6.97075 | −0.261057 | ||||||||
\(714\) | 0.120218 | 0.00449904 | ||||||||
\(715\) | −0.775610 | −0.0290062 | ||||||||
\(716\) | 14.6241 | 0.546529 | ||||||||
\(717\) | 71.6663 | 2.67643 | ||||||||
\(718\) | −4.14233 | −0.154590 | ||||||||
\(719\) | 0.492657 | 0.0183730 | 0.00918650 | − | 0.999958i | \(-0.497076\pi\) | ||||
0.00918650 | + | 0.999958i | \(0.497076\pi\) | |||||||
\(720\) | −11.2682 | −0.419940 | ||||||||
\(721\) | −1.28517 | −0.0478623 | ||||||||
\(722\) | 16.2798 | 0.605870 | ||||||||
\(723\) | −27.3414 | −1.01684 | ||||||||
\(724\) | −22.8349 | −0.848653 | ||||||||
\(725\) | 1.35235 | 0.0502252 | ||||||||
\(726\) | 3.16186 | 0.117347 | ||||||||
\(727\) | −21.0884 | −0.782125 | −0.391062 | − | 0.920364i | \(-0.627892\pi\) | ||||
−0.391062 | + | 0.920364i | \(0.627892\pi\) | |||||||
\(728\) | −0.0436031 | −0.00161604 | ||||||||
\(729\) | 12.8561 | 0.476153 | ||||||||
\(730\) | −1.26939 | −0.0469824 | ||||||||
\(731\) | 3.35886 | 0.124232 | ||||||||
\(732\) | 6.70475 | 0.247815 | ||||||||
\(733\) | 24.5006 | 0.904951 | 0.452476 | − | 0.891777i | \(-0.350541\pi\) | ||||
0.452476 | + | 0.891777i | \(0.350541\pi\) | |||||||
\(734\) | 34.2662 | 1.26479 | ||||||||
\(735\) | −35.6001 | −1.31313 | ||||||||
\(736\) | −0.827258 | −0.0304931 | ||||||||
\(737\) | 8.17063 | 0.300969 | ||||||||
\(738\) | 53.3538 | 1.96398 | ||||||||
\(739\) | 3.13925 | 0.115479 | 0.0577397 | − | 0.998332i | \(-0.481611\pi\) | ||||
0.0577397 | + | 0.998332i | \(0.481611\pi\) | |||||||
\(740\) | −1.95047 | −0.0717006 | ||||||||
\(741\) | 2.51170 | 0.0922697 | ||||||||
\(742\) | −0.105232 | −0.00386320 | ||||||||
\(743\) | 24.7621 | 0.908434 | 0.454217 | − | 0.890891i | \(-0.349919\pi\) | ||||
0.454217 | + | 0.890891i | \(0.349919\pi\) | |||||||
\(744\) | −26.6428 | −0.976774 | ||||||||
\(745\) | 17.5570 | 0.643238 | ||||||||
\(746\) | 22.9046 | 0.838599 | ||||||||
\(747\) | −52.2359 | −1.91121 | ||||||||
\(748\) | 0.419983 | 0.0153561 | ||||||||
\(749\) | 1.35769 | 0.0496089 | ||||||||
\(750\) | 37.7130 | 1.37709 | ||||||||
\(751\) | −42.8569 | −1.56387 | −0.781935 | − | 0.623360i | \(-0.785767\pi\) | ||||
−0.781935 | + | 0.623360i | \(0.785767\pi\) | |||||||
\(752\) | 12.0094 | 0.437936 | ||||||||
\(753\) | −30.7066 | −1.11901 | ||||||||
\(754\) | 0.270632 | 0.00985582 | ||||||||
\(755\) | −1.87023 | −0.0680647 | ||||||||
\(756\) | −1.14421 | −0.0416147 | ||||||||
\(757\) | −12.8451 | −0.466863 | −0.233431 | − | 0.972373i | \(-0.574995\pi\) | ||||
−0.233431 | + | 0.972373i | \(0.574995\pi\) | |||||||
\(758\) | −0.208774 | −0.00758301 | ||||||||
\(759\) | −2.61567 | −0.0949428 | ||||||||
\(760\) | −2.65597 | −0.0963423 | ||||||||
\(761\) | −41.1022 | −1.48995 | −0.744977 | − | 0.667090i | \(-0.767540\pi\) | ||||
−0.744977 | + | 0.667090i | \(0.767540\pi\) | |||||||
\(762\) | −31.8326 | −1.15317 | ||||||||
\(763\) | 1.14572 | 0.0414779 | ||||||||
\(764\) | 20.0238 | 0.724435 | ||||||||
\(765\) | −4.73244 | −0.171102 | ||||||||
\(766\) | 24.4168 | 0.882214 | ||||||||
\(767\) | 3.28664 | 0.118674 | ||||||||
\(768\) | −3.16186 | −0.114094 | ||||||||
\(769\) | −14.1741 | −0.511132 | −0.255566 | − | 0.966792i | \(-0.582262\pi\) | ||||
−0.255566 | + | 0.966792i | \(0.582262\pi\) | |||||||
\(770\) | 0.145786 | 0.00525376 | ||||||||
\(771\) | −23.3516 | −0.840989 | ||||||||
\(772\) | −12.5215 | −0.450658 | ||||||||
\(773\) | 16.3094 | 0.586607 | 0.293304 | − | 0.956019i | \(-0.405245\pi\) | ||||
0.293304 | + | 0.956019i | \(0.405245\pi\) | |||||||
\(774\) | −55.9618 | −2.01151 | ||||||||
\(775\) | 20.2802 | 0.728488 | ||||||||
\(776\) | −14.5344 | −0.521755 | ||||||||
\(777\) | −0.346701 | −0.0124378 | ||||||||
\(778\) | −2.00470 | −0.0718719 | ||||||||
\(779\) | 12.5758 | 0.450575 | ||||||||
\(780\) | 2.45237 | 0.0878088 | ||||||||
\(781\) | 3.26805 | 0.116940 | ||||||||
\(782\) | −0.347434 | −0.0124242 | ||||||||
\(783\) | 7.10180 | 0.253798 | ||||||||
\(784\) | −6.99180 | −0.249707 | ||||||||
\(785\) | −19.9982 | −0.713765 | ||||||||
\(786\) | 12.1431 | 0.433129 | ||||||||
\(787\) | −5.25108 | −0.187181 | −0.0935904 | − | 0.995611i | \(-0.529834\pi\) | ||||
−0.0935904 | + | 0.995611i | \(0.529834\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | 23.4689 | 0.835514 | ||||||||
\(790\) | 17.8818 | 0.636205 | ||||||||
\(791\) | −0.311401 | −0.0110722 | ||||||||
\(792\) | −6.99733 | −0.248639 | ||||||||
\(793\) | −1.02132 | −0.0362682 | ||||||||
\(794\) | −4.97318 | −0.176492 | ||||||||
\(795\) | 5.91857 | 0.209910 | ||||||||
\(796\) | −6.27326 | −0.222350 | ||||||||
\(797\) | 41.2924 | 1.46265 | 0.731325 | − | 0.682029i | \(-0.238902\pi\) | ||||
0.731325 | + | 0.682029i | \(0.238902\pi\) | |||||||
\(798\) | −0.472107 | −0.0167124 | ||||||||
\(799\) | 5.04373 | 0.178434 | ||||||||
\(800\) | 2.40677 | 0.0850922 | ||||||||
\(801\) | −58.6377 | −2.07186 | ||||||||
\(802\) | 5.06123 | 0.178718 | ||||||||
\(803\) | −0.788272 | −0.0278175 | ||||||||
\(804\) | −25.8344 | −0.911108 | ||||||||
\(805\) | −0.120602 | −0.00425068 | ||||||||
\(806\) | 4.05846 | 0.142953 | ||||||||
\(807\) | 65.3472 | 2.30033 | ||||||||
\(808\) | 2.15350 | 0.0757600 | ||||||||
\(809\) | −15.5840 | −0.547903 | −0.273952 | − | 0.961743i | \(-0.588331\pi\) | ||||
−0.273952 | + | 0.961743i | \(0.588331\pi\) | |||||||
\(810\) | 30.5494 | 1.07340 | ||||||||
\(811\) | 5.66060 | 0.198771 | 0.0993853 | − | 0.995049i | \(-0.468312\pi\) | ||||
0.0993853 | + | 0.995049i | \(0.468312\pi\) | |||||||
\(812\) | −0.0508687 | −0.00178514 | ||||||||
\(813\) | 64.9228 | 2.27694 | ||||||||
\(814\) | −1.21121 | −0.0424527 | ||||||||
\(815\) | 2.90004 | 0.101584 | ||||||||
\(816\) | −1.32793 | −0.0464867 | ||||||||
\(817\) | −13.1905 | −0.461479 | ||||||||
\(818\) | −13.7553 | −0.480944 | ||||||||
\(819\) | 0.305106 | 0.0106613 | ||||||||
\(820\) | 12.2787 | 0.428792 | ||||||||
\(821\) | −39.8262 | −1.38994 | −0.694972 | − | 0.719037i | \(-0.744583\pi\) | ||||
−0.694972 | + | 0.719037i | \(0.744583\pi\) | |||||||
\(822\) | −9.12599 | −0.318305 | ||||||||
\(823\) | −3.71062 | −0.129344 | −0.0646720 | − | 0.997907i | \(-0.520600\pi\) | ||||
−0.0646720 | + | 0.997907i | \(0.520600\pi\) | |||||||
\(824\) | 14.1960 | 0.494541 | ||||||||
\(825\) | 7.60986 | 0.264941 | ||||||||
\(826\) | −0.617766 | −0.0214948 | ||||||||
\(827\) | 3.26348 | 0.113482 | 0.0567411 | − | 0.998389i | \(-0.481929\pi\) | ||||
0.0567411 | + | 0.998389i | \(0.481929\pi\) | |||||||
\(828\) | 5.78860 | 0.201168 | ||||||||
\(829\) | 6.39376 | 0.222064 | 0.111032 | − | 0.993817i | \(-0.464584\pi\) | ||||
0.111032 | + | 0.993817i | \(0.464584\pi\) | |||||||
\(830\) | −12.0215 | −0.417271 | ||||||||
\(831\) | −42.7993 | −1.48469 | ||||||||
\(832\) | 0.481640 | 0.0166979 | ||||||||
\(833\) | −2.93644 | −0.101742 | ||||||||
\(834\) | −32.7036 | −1.13243 | ||||||||
\(835\) | −23.3060 | −0.806537 | ||||||||
\(836\) | −1.64931 | −0.0570427 | ||||||||
\(837\) | 106.500 | 3.68119 | ||||||||
\(838\) | 1.85667 | 0.0641375 | ||||||||
\(839\) | 11.5824 | 0.399869 | 0.199934 | − | 0.979809i | \(-0.435927\pi\) | ||||
0.199934 | + | 0.979809i | \(0.435927\pi\) | |||||||
\(840\) | −0.460954 | −0.0159044 | ||||||||
\(841\) | −28.6843 | −0.989113 | ||||||||
\(842\) | −6.84016 | −0.235727 | ||||||||
\(843\) | 31.3016 | 1.07808 | ||||||||
\(844\) | 5.76182 | 0.198330 | ||||||||
\(845\) | 20.5610 | 0.707320 | ||||||||
\(846\) | −84.0335 | −2.88913 | ||||||||
\(847\) | 0.0905305 | 0.00311067 | ||||||||
\(848\) | 1.16240 | 0.0399168 | ||||||||
\(849\) | −6.05650 | −0.207859 | ||||||||
\(850\) | 1.01080 | 0.0346703 | ||||||||
\(851\) | 1.00198 | 0.0343474 | ||||||||
\(852\) | −10.3331 | −0.354006 | ||||||||
\(853\) | −11.7851 | −0.403513 | −0.201757 | − | 0.979436i | \(-0.564665\pi\) | ||||
−0.201757 | + | 0.979436i | \(0.564665\pi\) | |||||||
\(854\) | 0.191971 | 0.00656911 | ||||||||
\(855\) | 18.5847 | 0.635585 | ||||||||
\(856\) | −14.9970 | −0.512588 | ||||||||
\(857\) | −20.3899 | −0.696507 | −0.348253 | − | 0.937400i | \(-0.613225\pi\) | ||||
−0.348253 | + | 0.937400i | \(0.613225\pi\) | |||||||
\(858\) | 1.52288 | 0.0519902 | ||||||||
\(859\) | 26.7342 | 0.912159 | 0.456079 | − | 0.889939i | \(-0.349253\pi\) | ||||
0.456079 | + | 0.889939i | \(0.349253\pi\) | |||||||
\(860\) | −12.8789 | −0.439168 | ||||||||
\(861\) | 2.18258 | 0.0743821 | ||||||||
\(862\) | 5.73620 | 0.195376 | ||||||||
\(863\) | −50.8908 | −1.73234 | −0.866171 | − | 0.499748i | \(-0.833426\pi\) | ||||
−0.866171 | + | 0.499748i | \(0.833426\pi\) | |||||||
\(864\) | 12.6390 | 0.429987 | ||||||||
\(865\) | −26.7492 | −0.909500 | ||||||||
\(866\) | −16.0484 | −0.545346 | ||||||||
\(867\) | 53.1938 | 1.80656 | ||||||||
\(868\) | −0.762840 | −0.0258925 | ||||||||
\(869\) | 11.1043 | 0.376687 | ||||||||
\(870\) | 2.86100 | 0.0969971 | ||||||||
\(871\) | 3.93530 | 0.133343 | ||||||||
\(872\) | −12.6556 | −0.428574 | ||||||||
\(873\) | 101.702 | 3.44209 | ||||||||
\(874\) | 1.36441 | 0.0461518 | ||||||||
\(875\) | 1.07980 | 0.0365040 | ||||||||
\(876\) | 2.49240 | 0.0842105 | ||||||||
\(877\) | 2.08367 | 0.0703604 | 0.0351802 | − | 0.999381i | \(-0.488799\pi\) | ||||
0.0351802 | + | 0.999381i | \(0.488799\pi\) | |||||||
\(878\) | 14.8135 | 0.499933 | ||||||||
\(879\) | −27.6314 | −0.931984 | ||||||||
\(880\) | −1.61035 | −0.0542849 | ||||||||
\(881\) | −18.6018 | −0.626712 | −0.313356 | − | 0.949636i | \(-0.601453\pi\) | ||||
−0.313356 | + | 0.949636i | \(0.601453\pi\) | |||||||
\(882\) | 48.9240 | 1.64736 | ||||||||
\(883\) | 12.2050 | 0.410732 | 0.205366 | − | 0.978685i | \(-0.434161\pi\) | ||||
0.205366 | + | 0.978685i | \(0.434161\pi\) | |||||||
\(884\) | 0.202281 | 0.00680344 | ||||||||
\(885\) | 34.7449 | 1.16794 | ||||||||
\(886\) | 15.7001 | 0.527454 | ||||||||
\(887\) | 6.67456 | 0.224110 | 0.112055 | − | 0.993702i | \(-0.464257\pi\) | ||||
0.112055 | + | 0.993702i | \(0.464257\pi\) | |||||||
\(888\) | 3.82966 | 0.128515 | ||||||||
\(889\) | −0.911434 | −0.0305685 | ||||||||
\(890\) | −13.4948 | −0.452345 | ||||||||
\(891\) | 18.9707 | 0.635542 | ||||||||
\(892\) | −6.56179 | −0.219705 | ||||||||
\(893\) | −19.8072 | −0.662823 | ||||||||
\(894\) | −34.4724 | −1.15293 | ||||||||
\(895\) | −23.5500 | −0.787188 | ||||||||
\(896\) | −0.0905305 | −0.00302441 | ||||||||
\(897\) | −1.25981 | −0.0420639 | ||||||||
\(898\) | −12.0150 | −0.400945 | ||||||||
\(899\) | 4.73472 | 0.157912 | ||||||||
\(900\) | −16.8410 | −0.561366 | ||||||||
\(901\) | 0.488187 | 0.0162639 | ||||||||
\(902\) | 7.62488 | 0.253881 | ||||||||
\(903\) | −2.28927 | −0.0761820 | ||||||||
\(904\) | 3.43974 | 0.114404 | ||||||||
\(905\) | 36.7722 | 1.22235 | ||||||||
\(906\) | 3.67212 | 0.121998 | ||||||||
\(907\) | 2.05244 | 0.0681501 | 0.0340750 | − | 0.999419i | \(-0.489151\pi\) | ||||
0.0340750 | + | 0.999419i | \(0.489151\pi\) | |||||||
\(908\) | 23.2625 | 0.771995 | ||||||||
\(909\) | −15.0688 | −0.499800 | ||||||||
\(910\) | 0.0702163 | 0.00232765 | ||||||||
\(911\) | 0.884430 | 0.0293025 | 0.0146512 | − | 0.999893i | \(-0.495336\pi\) | ||||
0.0146512 | + | 0.999893i | \(0.495336\pi\) | |||||||
\(912\) | 5.21489 | 0.172682 | ||||||||
\(913\) | −7.46511 | −0.247059 | ||||||||
\(914\) | −1.13638 | −0.0375880 | ||||||||
\(915\) | −10.7970 | −0.356938 | ||||||||
\(916\) | −26.6070 | −0.879120 | ||||||||
\(917\) | 0.347681 | 0.0114815 | ||||||||
\(918\) | 5.30817 | 0.175196 | ||||||||
\(919\) | 48.9391 | 1.61435 | 0.807176 | − | 0.590311i | \(-0.200995\pi\) | ||||
0.807176 | + | 0.590311i | \(0.200995\pi\) | |||||||
\(920\) | 1.33218 | 0.0439205 | ||||||||
\(921\) | 93.1876 | 3.07064 | ||||||||
\(922\) | −16.5049 | −0.543560 | ||||||||
\(923\) | 1.57402 | 0.0518096 | ||||||||
\(924\) | −0.286244 | −0.00941675 | ||||||||
\(925\) | −2.91509 | −0.0958477 | ||||||||
\(926\) | 37.7903 | 1.24186 | ||||||||
\(927\) | −99.3342 | −3.26256 | ||||||||
\(928\) | 0.561896 | 0.0184451 | ||||||||
\(929\) | −13.6229 | −0.446954 | −0.223477 | − | 0.974709i | \(-0.571741\pi\) | ||||
−0.223477 | + | 0.974709i | \(0.571741\pi\) | |||||||
\(930\) | 42.9043 | 1.40689 | ||||||||
\(931\) | 11.5317 | 0.377936 | ||||||||
\(932\) | −3.84104 | −0.125817 | ||||||||
\(933\) | −49.6602 | −1.62580 | ||||||||
\(934\) | −1.47313 | −0.0482024 | ||||||||
\(935\) | −0.676320 | −0.0221180 | ||||||||
\(936\) | −3.37020 | −0.110158 | ||||||||
\(937\) | −18.8355 | −0.615327 | −0.307664 | − | 0.951495i | \(-0.599547\pi\) | ||||
−0.307664 | + | 0.951495i | \(0.599547\pi\) | |||||||
\(938\) | −0.739691 | −0.0241518 | ||||||||
\(939\) | 29.6585 | 0.967868 | ||||||||
\(940\) | −19.3393 | −0.630778 | ||||||||
\(941\) | −56.7175 | −1.84894 | −0.924469 | − | 0.381257i | \(-0.875491\pi\) | ||||
−0.924469 | + | 0.381257i | \(0.875491\pi\) | |||||||
\(942\) | 39.2656 | 1.27934 | ||||||||
\(943\) | −6.30774 | −0.205408 | ||||||||
\(944\) | 6.82384 | 0.222097 | ||||||||
\(945\) | 1.84259 | 0.0599394 | ||||||||
\(946\) | −7.99759 | −0.260024 | ||||||||
\(947\) | 30.7764 | 1.00010 | 0.500049 | − | 0.865997i | \(-0.333315\pi\) | ||||
0.500049 | + | 0.865997i | \(0.333315\pi\) | |||||||
\(948\) | −35.1101 | −1.14032 | ||||||||
\(949\) | −0.379663 | −0.0123244 | ||||||||
\(950\) | −3.96952 | −0.128788 | ||||||||
\(951\) | −1.28443 | −0.0416505 | ||||||||
\(952\) | −0.0380213 | −0.00123228 | ||||||||
\(953\) | −32.8697 | −1.06475 | −0.532377 | − | 0.846507i | \(-0.678701\pi\) | ||||
−0.532377 | + | 0.846507i | \(0.678701\pi\) | |||||||
\(954\) | −8.13367 | −0.263337 | ||||||||
\(955\) | −32.2453 | −1.04343 | ||||||||
\(956\) | −22.6659 | −0.733067 | ||||||||
\(957\) | 1.77663 | 0.0574304 | ||||||||
\(958\) | −8.78124 | −0.283709 | ||||||||
\(959\) | −0.261296 | −0.00843769 | ||||||||
\(960\) | 5.09170 | 0.164334 | ||||||||
\(961\) | 40.0031 | 1.29042 | ||||||||
\(962\) | −0.583365 | −0.0188085 | ||||||||
\(963\) | 104.939 | 3.38162 | ||||||||
\(964\) | 8.64726 | 0.278510 | ||||||||
\(965\) | 20.1640 | 0.649102 | ||||||||
\(966\) | 0.236798 | 0.00761885 | ||||||||
\(967\) | 15.2791 | 0.491341 | 0.245671 | − | 0.969353i | \(-0.420992\pi\) | ||||
0.245671 | + | 0.969353i | \(0.420992\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 2.19017 | 0.0703583 | ||||||||
\(970\) | 23.4055 | 0.751505 | ||||||||
\(971\) | −35.4425 | −1.13741 | −0.568703 | − | 0.822543i | \(-0.692555\pi\) | ||||
−0.568703 | + | 0.822543i | \(0.692555\pi\) | |||||||
\(972\) | −22.0656 | −0.707754 | ||||||||
\(973\) | −0.936372 | −0.0300187 | ||||||||
\(974\) | −38.7747 | −1.24242 | ||||||||
\(975\) | 3.66522 | 0.117381 | ||||||||
\(976\) | −2.12051 | −0.0678759 | ||||||||
\(977\) | −54.1371 | −1.73200 | −0.866000 | − | 0.500043i | \(-0.833317\pi\) | ||||
−0.866000 | + | 0.500043i | \(0.833317\pi\) | |||||||
\(978\) | −5.69412 | −0.182078 | ||||||||
\(979\) | −8.38001 | −0.267826 | ||||||||
\(980\) | 11.2593 | 0.359664 | ||||||||
\(981\) | 88.5557 | 2.82737 | ||||||||
\(982\) | 12.6103 | 0.402410 | ||||||||
\(983\) | 5.14061 | 0.163960 | 0.0819800 | − | 0.996634i | \(-0.473876\pi\) | ||||
0.0819800 | + | 0.996634i | \(0.473876\pi\) | |||||||
\(984\) | −24.1088 | −0.768559 | ||||||||
\(985\) | −1.61035 | −0.0513100 | ||||||||
\(986\) | 0.235987 | 0.00751535 | ||||||||
\(987\) | −3.43761 | −0.109420 | ||||||||
\(988\) | −0.794376 | −0.0252725 | ||||||||
\(989\) | 6.61607 | 0.210379 | ||||||||
\(990\) | 11.2682 | 0.358126 | ||||||||
\(991\) | 49.4147 | 1.56971 | 0.784855 | − | 0.619679i | \(-0.212737\pi\) | ||||
0.784855 | + | 0.619679i | \(0.212737\pi\) | |||||||
\(992\) | 8.42633 | 0.267536 | ||||||||
\(993\) | −103.875 | −3.29637 | ||||||||
\(994\) | −0.295858 | −0.00938405 | ||||||||
\(995\) | 10.1021 | 0.320259 | ||||||||
\(996\) | 23.6036 | 0.747909 | ||||||||
\(997\) | 60.0884 | 1.90302 | 0.951509 | − | 0.307621i | \(-0.0995328\pi\) | ||||
0.951509 | + | 0.307621i | \(0.0995328\pi\) | |||||||
\(998\) | −40.8293 | −1.29243 | ||||||||
\(999\) | −15.3084 | −0.484337 |
(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 | 4334.2.a.a.1.1 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.a.1.1 | ✓ | 15 | 1.1 | even | 1 | trivial |