Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57711 | −1.82229 | −0.911147 | − | 0.412081i | \(-0.864802\pi\) | ||||
−0.911147 | + | 0.412081i | \(0.864802\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.64151 | 2.32076 | ||||||||
\(5\) | 2.80201 | 1.25310 | 0.626548 | − | 0.779383i | \(-0.284467\pi\) | ||||
0.626548 | + | 0.779383i | \(0.284467\pi\) | |||||||
\(6\) | 2.57711 | 1.05210 | ||||||||
\(7\) | −2.75409 | −1.04095 | −0.520474 | − | 0.853878i | \(-0.674245\pi\) | ||||
−0.520474 | + | 0.853878i | \(0.674245\pi\) | |||||||
\(8\) | −6.80748 | −2.40681 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −7.22109 | −2.28351 | ||||||||
\(11\) | 5.08930 | 1.53448 | 0.767241 | − | 0.641359i | \(-0.221629\pi\) | ||||
0.767241 | + | 0.641359i | \(0.221629\pi\) | |||||||
\(12\) | −4.64151 | −1.33989 | ||||||||
\(13\) | 1.22692 | 0.340286 | 0.170143 | − | 0.985419i | \(-0.445577\pi\) | ||||
0.170143 | + | 0.985419i | \(0.445577\pi\) | |||||||
\(14\) | 7.09760 | 1.89691 | ||||||||
\(15\) | −2.80201 | −0.723475 | ||||||||
\(16\) | 8.26062 | 2.06516 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.57711 | −0.607431 | ||||||||
\(19\) | 4.27531 | 0.980823 | 0.490411 | − | 0.871491i | \(-0.336847\pi\) | ||||
0.490411 | + | 0.871491i | \(0.336847\pi\) | |||||||
\(20\) | 13.0056 | 2.90813 | ||||||||
\(21\) | 2.75409 | 0.600991 | ||||||||
\(22\) | −13.1157 | −2.79628 | ||||||||
\(23\) | 3.53882 | 0.737896 | 0.368948 | − | 0.929450i | \(-0.379718\pi\) | ||||
0.368948 | + | 0.929450i | \(0.379718\pi\) | |||||||
\(24\) | 6.80748 | 1.38957 | ||||||||
\(25\) | 2.85124 | 0.570248 | ||||||||
\(26\) | −3.16191 | −0.620101 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −12.7831 | −2.41579 | ||||||||
\(29\) | 5.81249 | 1.07935 | 0.539676 | − | 0.841873i | \(-0.318547\pi\) | ||||
0.539676 | + | 0.841873i | \(0.318547\pi\) | |||||||
\(30\) | 7.22109 | 1.31838 | ||||||||
\(31\) | 6.37475 | 1.14494 | 0.572469 | − | 0.819926i | \(-0.305986\pi\) | ||||
0.572469 | + | 0.819926i | \(0.305986\pi\) | |||||||
\(32\) | −7.67360 | −1.35651 | ||||||||
\(33\) | −5.08930 | −0.885933 | ||||||||
\(34\) | 2.57711 | 0.441971 | ||||||||
\(35\) | −7.71697 | −1.30441 | ||||||||
\(36\) | 4.64151 | 0.773586 | ||||||||
\(37\) | 5.23507 | 0.860641 | 0.430320 | − | 0.902676i | \(-0.358401\pi\) | ||||
0.430320 | + | 0.902676i | \(0.358401\pi\) | |||||||
\(38\) | −11.0179 | −1.78735 | ||||||||
\(39\) | −1.22692 | −0.196464 | ||||||||
\(40\) | −19.0746 | −3.01596 | ||||||||
\(41\) | −0.440553 | −0.0688028 | −0.0344014 | − | 0.999408i | \(-0.510952\pi\) | ||||
−0.0344014 | + | 0.999408i | \(0.510952\pi\) | |||||||
\(42\) | −7.09760 | −1.09518 | ||||||||
\(43\) | −1.81039 | −0.276081 | −0.138041 | − | 0.990427i | \(-0.544080\pi\) | ||||
−0.138041 | + | 0.990427i | \(0.544080\pi\) | |||||||
\(44\) | 23.6220 | 3.56116 | ||||||||
\(45\) | 2.80201 | 0.417698 | ||||||||
\(46\) | −9.11995 | −1.34466 | ||||||||
\(47\) | −6.02387 | −0.878672 | −0.439336 | − | 0.898323i | \(-0.644786\pi\) | ||||
−0.439336 | + | 0.898323i | \(0.644786\pi\) | |||||||
\(48\) | −8.26062 | −1.19232 | ||||||||
\(49\) | 0.585005 | 0.0835722 | ||||||||
\(50\) | −7.34797 | −1.03916 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 5.69475 | 0.789720 | ||||||||
\(53\) | −11.2066 | −1.53934 | −0.769672 | − | 0.638440i | \(-0.779580\pi\) | ||||
−0.769672 | + | 0.638440i | \(0.779580\pi\) | |||||||
\(54\) | 2.57711 | 0.350701 | ||||||||
\(55\) | 14.2602 | 1.92285 | ||||||||
\(56\) | 18.7484 | 2.50536 | ||||||||
\(57\) | −4.27531 | −0.566278 | ||||||||
\(58\) | −14.9794 | −1.96690 | ||||||||
\(59\) | −4.07358 | −0.530335 | −0.265168 | − | 0.964202i | \(-0.585427\pi\) | ||||
−0.265168 | + | 0.964202i | \(0.585427\pi\) | |||||||
\(60\) | −13.0056 | −1.67901 | ||||||||
\(61\) | 7.50948 | 0.961490 | 0.480745 | − | 0.876860i | \(-0.340366\pi\) | ||||
0.480745 | + | 0.876860i | \(0.340366\pi\) | |||||||
\(62\) | −16.4284 | −2.08641 | ||||||||
\(63\) | −2.75409 | −0.346983 | ||||||||
\(64\) | 3.25449 | 0.406811 | ||||||||
\(65\) | 3.43783 | 0.426410 | ||||||||
\(66\) | 13.1157 | 1.61443 | ||||||||
\(67\) | 12.4723 | 1.52373 | 0.761866 | − | 0.647735i | \(-0.224283\pi\) | ||||
0.761866 | + | 0.647735i | \(0.224283\pi\) | |||||||
\(68\) | −4.64151 | −0.562866 | ||||||||
\(69\) | −3.53882 | −0.426024 | ||||||||
\(70\) | 19.8875 | 2.37701 | ||||||||
\(71\) | 5.18453 | 0.615290 | 0.307645 | − | 0.951501i | \(-0.400459\pi\) | ||||
0.307645 | + | 0.951501i | \(0.400459\pi\) | |||||||
\(72\) | −6.80748 | −0.802269 | ||||||||
\(73\) | 7.17842 | 0.840170 | 0.420085 | − | 0.907485i | \(-0.362000\pi\) | ||||
0.420085 | + | 0.907485i | \(0.362000\pi\) | |||||||
\(74\) | −13.4914 | −1.56834 | ||||||||
\(75\) | −2.85124 | −0.329233 | ||||||||
\(76\) | 19.8439 | 2.27625 | ||||||||
\(77\) | −14.0164 | −1.59731 | ||||||||
\(78\) | 3.16191 | 0.358015 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 23.1463 | 2.58784 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.13535 | 0.125379 | ||||||||
\(83\) | 7.95637 | 0.873325 | 0.436662 | − | 0.899625i | \(-0.356160\pi\) | ||||
0.436662 | + | 0.899625i | \(0.356160\pi\) | |||||||
\(84\) | 12.7831 | 1.39475 | ||||||||
\(85\) | −2.80201 | −0.303920 | ||||||||
\(86\) | 4.66557 | 0.503101 | ||||||||
\(87\) | −5.81249 | −0.623164 | ||||||||
\(88\) | −34.6453 | −3.69320 | ||||||||
\(89\) | −9.67764 | −1.02583 | −0.512914 | − | 0.858440i | \(-0.671434\pi\) | ||||
−0.512914 | + | 0.858440i | \(0.671434\pi\) | |||||||
\(90\) | −7.22109 | −0.761170 | ||||||||
\(91\) | −3.37904 | −0.354220 | ||||||||
\(92\) | 16.4255 | 1.71248 | ||||||||
\(93\) | −6.37475 | −0.661030 | ||||||||
\(94\) | 15.5242 | 1.60120 | ||||||||
\(95\) | 11.9794 | 1.22906 | ||||||||
\(96\) | 7.67360 | 0.783183 | ||||||||
\(97\) | 6.88466 | 0.699031 | 0.349515 | − | 0.936931i | \(-0.386346\pi\) | ||||
0.349515 | + | 0.936931i | \(0.386346\pi\) | |||||||
\(98\) | −1.50763 | −0.152293 | ||||||||
\(99\) | 5.08930 | 0.511494 | ||||||||
\(100\) | 13.2341 | 1.32341 | ||||||||
\(101\) | 5.54339 | 0.551588 | 0.275794 | − | 0.961217i | \(-0.411059\pi\) | ||||
0.275794 | + | 0.961217i | \(0.411059\pi\) | |||||||
\(102\) | −2.57711 | −0.255172 | ||||||||
\(103\) | −8.01343 | −0.789587 | −0.394793 | − | 0.918770i | \(-0.629184\pi\) | ||||
−0.394793 | + | 0.918770i | \(0.629184\pi\) | |||||||
\(104\) | −8.35222 | −0.819002 | ||||||||
\(105\) | 7.71697 | 0.753100 | ||||||||
\(106\) | 28.8806 | 2.80514 | ||||||||
\(107\) | 16.4057 | 1.58600 | 0.793001 | − | 0.609220i | \(-0.208517\pi\) | ||||
0.793001 | + | 0.609220i | \(0.208517\pi\) | |||||||
\(108\) | −4.64151 | −0.446630 | ||||||||
\(109\) | 13.8530 | 1.32687 | 0.663437 | − | 0.748232i | \(-0.269097\pi\) | ||||
0.663437 | + | 0.748232i | \(0.269097\pi\) | |||||||
\(110\) | −36.7503 | −3.50400 | ||||||||
\(111\) | −5.23507 | −0.496891 | ||||||||
\(112\) | −22.7505 | −2.14972 | ||||||||
\(113\) | −14.5297 | −1.36684 | −0.683418 | − | 0.730028i | \(-0.739507\pi\) | ||||
−0.683418 | + | 0.730028i | \(0.739507\pi\) | |||||||
\(114\) | 11.0179 | 1.03193 | ||||||||
\(115\) | 9.91581 | 0.924654 | ||||||||
\(116\) | 26.9787 | 2.50491 | ||||||||
\(117\) | 1.22692 | 0.113429 | ||||||||
\(118\) | 10.4981 | 0.966427 | ||||||||
\(119\) | 2.75409 | 0.252467 | ||||||||
\(120\) | 19.0746 | 1.74127 | ||||||||
\(121\) | 14.9010 | 1.35463 | ||||||||
\(122\) | −19.3528 | −1.75212 | ||||||||
\(123\) | 0.440553 | 0.0397233 | ||||||||
\(124\) | 29.5885 | 2.65712 | ||||||||
\(125\) | −6.02084 | −0.538520 | ||||||||
\(126\) | 7.09760 | 0.632304 | ||||||||
\(127\) | −4.98610 | −0.442445 | −0.221222 | − | 0.975223i | \(-0.571005\pi\) | ||||
−0.221222 | + | 0.975223i | \(0.571005\pi\) | |||||||
\(128\) | 6.96001 | 0.615184 | ||||||||
\(129\) | 1.81039 | 0.159396 | ||||||||
\(130\) | −8.85968 | −0.777045 | ||||||||
\(131\) | −18.6708 | −1.63128 | −0.815639 | − | 0.578561i | \(-0.803615\pi\) | ||||
−0.815639 | + | 0.578561i | \(0.803615\pi\) | |||||||
\(132\) | −23.6220 | −2.05604 | ||||||||
\(133\) | −11.7746 | −1.02099 | ||||||||
\(134\) | −32.1425 | −2.77669 | ||||||||
\(135\) | −2.80201 | −0.241158 | ||||||||
\(136\) | 6.80748 | 0.583737 | ||||||||
\(137\) | −10.2748 | −0.877833 | −0.438916 | − | 0.898528i | \(-0.644638\pi\) | ||||
−0.438916 | + | 0.898528i | \(0.644638\pi\) | |||||||
\(138\) | 9.11995 | 0.776342 | ||||||||
\(139\) | 7.55783 | 0.641047 | 0.320524 | − | 0.947241i | \(-0.396141\pi\) | ||||
0.320524 | + | 0.947241i | \(0.396141\pi\) | |||||||
\(140\) | −35.8184 | −3.02721 | ||||||||
\(141\) | 6.02387 | 0.507302 | ||||||||
\(142\) | −13.3611 | −1.12124 | ||||||||
\(143\) | 6.24415 | 0.522162 | ||||||||
\(144\) | 8.26062 | 0.688385 | ||||||||
\(145\) | 16.2866 | 1.35253 | ||||||||
\(146\) | −18.4996 | −1.53104 | ||||||||
\(147\) | −0.585005 | −0.0482504 | ||||||||
\(148\) | 24.2987 | 1.99734 | ||||||||
\(149\) | −5.74625 | −0.470751 | −0.235376 | − | 0.971905i | \(-0.575632\pi\) | ||||
−0.235376 | + | 0.971905i | \(0.575632\pi\) | |||||||
\(150\) | 7.34797 | 0.599959 | ||||||||
\(151\) | −4.21207 | −0.342774 | −0.171387 | − | 0.985204i | \(-0.554825\pi\) | ||||
−0.171387 | + | 0.985204i | \(0.554825\pi\) | |||||||
\(152\) | −29.1041 | −2.36065 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 36.1218 | 2.91078 | ||||||||
\(155\) | 17.8621 | 1.43472 | ||||||||
\(156\) | −5.69475 | −0.455945 | ||||||||
\(157\) | −14.4654 | −1.15446 | −0.577232 | − | 0.816580i | \(-0.695867\pi\) | ||||
−0.577232 | + | 0.816580i | \(0.695867\pi\) | |||||||
\(158\) | −2.57711 | −0.205024 | ||||||||
\(159\) | 11.2066 | 0.888740 | ||||||||
\(160\) | −21.5015 | −1.69984 | ||||||||
\(161\) | −9.74624 | −0.768111 | ||||||||
\(162\) | −2.57711 | −0.202477 | ||||||||
\(163\) | 3.54647 | 0.277781 | 0.138891 | − | 0.990308i | \(-0.455646\pi\) | ||||
0.138891 | + | 0.990308i | \(0.455646\pi\) | |||||||
\(164\) | −2.04483 | −0.159675 | ||||||||
\(165\) | −14.2602 | −1.11016 | ||||||||
\(166\) | −20.5045 | −1.59146 | ||||||||
\(167\) | −6.13316 | −0.474598 | −0.237299 | − | 0.971437i | \(-0.576262\pi\) | ||||
−0.237299 | + | 0.971437i | \(0.576262\pi\) | |||||||
\(168\) | −18.7484 | −1.44647 | ||||||||
\(169\) | −11.4947 | −0.884206 | ||||||||
\(170\) | 7.22109 | 0.553832 | ||||||||
\(171\) | 4.27531 | 0.326941 | ||||||||
\(172\) | −8.40293 | −0.640717 | ||||||||
\(173\) | 13.9274 | 1.05888 | 0.529439 | − | 0.848348i | \(-0.322402\pi\) | ||||
0.529439 | + | 0.848348i | \(0.322402\pi\) | |||||||
\(174\) | 14.9794 | 1.13559 | ||||||||
\(175\) | −7.85257 | −0.593598 | ||||||||
\(176\) | 42.0408 | 3.16894 | ||||||||
\(177\) | 4.07358 | 0.306189 | ||||||||
\(178\) | 24.9404 | 1.86936 | ||||||||
\(179\) | −3.49755 | −0.261419 | −0.130710 | − | 0.991421i | \(-0.541726\pi\) | ||||
−0.130710 | + | 0.991421i | \(0.541726\pi\) | |||||||
\(180\) | 13.0056 | 0.969377 | ||||||||
\(181\) | −17.4680 | −1.29838 | −0.649191 | − | 0.760625i | \(-0.724893\pi\) | ||||
−0.649191 | + | 0.760625i | \(0.724893\pi\) | |||||||
\(182\) | 8.70817 | 0.645492 | ||||||||
\(183\) | −7.50948 | −0.555117 | ||||||||
\(184\) | −24.0905 | −1.77597 | ||||||||
\(185\) | 14.6687 | 1.07846 | ||||||||
\(186\) | 16.4284 | 1.20459 | ||||||||
\(187\) | −5.08930 | −0.372166 | ||||||||
\(188\) | −27.9599 | −2.03918 | ||||||||
\(189\) | 2.75409 | 0.200330 | ||||||||
\(190\) | −30.8724 | −2.23972 | ||||||||
\(191\) | −14.7246 | −1.06543 | −0.532716 | − | 0.846294i | \(-0.678828\pi\) | ||||
−0.532716 | + | 0.846294i | \(0.678828\pi\) | |||||||
\(192\) | −3.25449 | −0.234872 | ||||||||
\(193\) | 7.14114 | 0.514030 | 0.257015 | − | 0.966407i | \(-0.417261\pi\) | ||||
0.257015 | + | 0.966407i | \(0.417261\pi\) | |||||||
\(194\) | −17.7425 | −1.27384 | ||||||||
\(195\) | −3.43783 | −0.246188 | ||||||||
\(196\) | 2.71531 | 0.193951 | ||||||||
\(197\) | −12.5727 | −0.895770 | −0.447885 | − | 0.894091i | \(-0.647823\pi\) | ||||
−0.447885 | + | 0.894091i | \(0.647823\pi\) | |||||||
\(198\) | −13.1157 | −0.932092 | ||||||||
\(199\) | 25.6563 | 1.81873 | 0.909364 | − | 0.416001i | \(-0.136569\pi\) | ||||
0.909364 | + | 0.416001i | \(0.136569\pi\) | |||||||
\(200\) | −19.4098 | −1.37248 | ||||||||
\(201\) | −12.4723 | −0.879727 | ||||||||
\(202\) | −14.2859 | −1.00516 | ||||||||
\(203\) | −16.0081 | −1.12355 | ||||||||
\(204\) | 4.64151 | 0.324971 | ||||||||
\(205\) | −1.23443 | −0.0862165 | ||||||||
\(206\) | 20.6515 | 1.43886 | ||||||||
\(207\) | 3.53882 | 0.245965 | ||||||||
\(208\) | 10.1351 | 0.702743 | ||||||||
\(209\) | 21.7583 | 1.50505 | ||||||||
\(210\) | −19.8875 | −1.37237 | ||||||||
\(211\) | −8.62202 | −0.593565 | −0.296782 | − | 0.954945i | \(-0.595914\pi\) | ||||
−0.296782 | + | 0.954945i | \(0.595914\pi\) | |||||||
\(212\) | −52.0155 | −3.57244 | ||||||||
\(213\) | −5.18453 | −0.355238 | ||||||||
\(214\) | −42.2795 | −2.89016 | ||||||||
\(215\) | −5.07271 | −0.345956 | ||||||||
\(216\) | 6.80748 | 0.463190 | ||||||||
\(217\) | −17.5566 | −1.19182 | ||||||||
\(218\) | −35.7007 | −2.41795 | ||||||||
\(219\) | −7.17842 | −0.485073 | ||||||||
\(220\) | 66.1891 | 4.46247 | ||||||||
\(221\) | −1.22692 | −0.0825314 | ||||||||
\(222\) | 13.4914 | 0.905482 | ||||||||
\(223\) | 22.8458 | 1.52987 | 0.764934 | − | 0.644109i | \(-0.222772\pi\) | ||||
0.764934 | + | 0.644109i | \(0.222772\pi\) | |||||||
\(224\) | 21.1338 | 1.41206 | ||||||||
\(225\) | 2.85124 | 0.190083 | ||||||||
\(226\) | 37.4446 | 2.49078 | ||||||||
\(227\) | 29.4109 | 1.95207 | 0.976034 | − | 0.217618i | \(-0.0698287\pi\) | ||||
0.976034 | + | 0.217618i | \(0.0698287\pi\) | |||||||
\(228\) | −19.8439 | −1.31419 | ||||||||
\(229\) | −21.7889 | −1.43985 | −0.719926 | − | 0.694051i | \(-0.755824\pi\) | ||||
−0.719926 | + | 0.694051i | \(0.755824\pi\) | |||||||
\(230\) | −25.5542 | −1.68499 | ||||||||
\(231\) | 14.0164 | 0.922210 | ||||||||
\(232\) | −39.5684 | −2.59779 | ||||||||
\(233\) | 9.90516 | 0.648909 | 0.324454 | − | 0.945901i | \(-0.394819\pi\) | ||||
0.324454 | + | 0.945901i | \(0.394819\pi\) | |||||||
\(234\) | −3.16191 | −0.206700 | ||||||||
\(235\) | −16.8789 | −1.10106 | ||||||||
\(236\) | −18.9076 | −1.23078 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −7.09760 | −0.460069 | ||||||||
\(239\) | 5.28546 | 0.341888 | 0.170944 | − | 0.985281i | \(-0.445318\pi\) | ||||
0.170944 | + | 0.985281i | \(0.445318\pi\) | |||||||
\(240\) | −23.1463 | −1.49409 | ||||||||
\(241\) | −13.7238 | −0.884029 | −0.442014 | − | 0.897008i | \(-0.645736\pi\) | ||||
−0.442014 | + | 0.897008i | \(0.645736\pi\) | |||||||
\(242\) | −38.4015 | −2.46854 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 34.8554 | 2.23139 | ||||||||
\(245\) | 1.63919 | 0.104724 | ||||||||
\(246\) | −1.13535 | −0.0723876 | ||||||||
\(247\) | 5.24545 | 0.333760 | ||||||||
\(248\) | −43.3960 | −2.75565 | ||||||||
\(249\) | −7.95637 | −0.504214 | ||||||||
\(250\) | 15.5164 | 0.981342 | ||||||||
\(251\) | 8.56079 | 0.540352 | 0.270176 | − | 0.962811i | \(-0.412918\pi\) | ||||
0.270176 | + | 0.962811i | \(0.412918\pi\) | |||||||
\(252\) | −12.7831 | −0.805262 | ||||||||
\(253\) | 18.0101 | 1.13229 | ||||||||
\(254\) | 12.8497 | 0.806264 | ||||||||
\(255\) | 2.80201 | 0.175468 | ||||||||
\(256\) | −24.4457 | −1.52786 | ||||||||
\(257\) | −6.86639 | −0.428313 | −0.214157 | − | 0.976799i | \(-0.568700\pi\) | ||||
−0.214157 | + | 0.976799i | \(0.568700\pi\) | |||||||
\(258\) | −4.66557 | −0.290466 | ||||||||
\(259\) | −14.4179 | −0.895882 | ||||||||
\(260\) | 15.9567 | 0.989595 | ||||||||
\(261\) | 5.81249 | 0.359784 | ||||||||
\(262\) | 48.1169 | 2.97267 | ||||||||
\(263\) | −12.7383 | −0.785477 | −0.392739 | − | 0.919650i | \(-0.628472\pi\) | ||||
−0.392739 | + | 0.919650i | \(0.628472\pi\) | |||||||
\(264\) | 34.6453 | 2.13227 | ||||||||
\(265\) | −31.4009 | −1.92894 | ||||||||
\(266\) | 30.3444 | 1.86054 | ||||||||
\(267\) | 9.67764 | 0.592262 | ||||||||
\(268\) | 57.8903 | 3.53621 | ||||||||
\(269\) | −2.65708 | −0.162005 | −0.0810026 | − | 0.996714i | \(-0.525812\pi\) | ||||
−0.0810026 | + | 0.996714i | \(0.525812\pi\) | |||||||
\(270\) | 7.22109 | 0.439461 | ||||||||
\(271\) | 12.7171 | 0.772508 | 0.386254 | − | 0.922392i | \(-0.373769\pi\) | ||||
0.386254 | + | 0.922392i | \(0.373769\pi\) | |||||||
\(272\) | −8.26062 | −0.500874 | ||||||||
\(273\) | 3.37904 | 0.204509 | ||||||||
\(274\) | 26.4792 | 1.59967 | ||||||||
\(275\) | 14.5108 | 0.875035 | ||||||||
\(276\) | −16.4255 | −0.988699 | ||||||||
\(277\) | 3.12729 | 0.187900 | 0.0939502 | − | 0.995577i | \(-0.470051\pi\) | ||||
0.0939502 | + | 0.995577i | \(0.470051\pi\) | |||||||
\(278\) | −19.4774 | −1.16818 | ||||||||
\(279\) | 6.37475 | 0.381646 | ||||||||
\(280\) | 52.5332 | 3.13946 | ||||||||
\(281\) | −29.2396 | −1.74429 | −0.872145 | − | 0.489248i | \(-0.837271\pi\) | ||||
−0.872145 | + | 0.489248i | \(0.837271\pi\) | |||||||
\(282\) | −15.5242 | −0.924453 | ||||||||
\(283\) | −24.5281 | −1.45805 | −0.729024 | − | 0.684489i | \(-0.760026\pi\) | ||||
−0.729024 | + | 0.684489i | \(0.760026\pi\) | |||||||
\(284\) | 24.0641 | 1.42794 | ||||||||
\(285\) | −11.9794 | −0.709601 | ||||||||
\(286\) | −16.0919 | −0.951533 | ||||||||
\(287\) | 1.21332 | 0.0716201 | ||||||||
\(288\) | −7.67360 | −0.452171 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −41.9725 | −2.46471 | ||||||||
\(291\) | −6.88466 | −0.403586 | ||||||||
\(292\) | 33.3187 | 1.94983 | ||||||||
\(293\) | −27.0550 | −1.58057 | −0.790285 | − | 0.612739i | \(-0.790068\pi\) | ||||
−0.790285 | + | 0.612739i | \(0.790068\pi\) | |||||||
\(294\) | 1.50763 | 0.0879265 | ||||||||
\(295\) | −11.4142 | −0.664560 | ||||||||
\(296\) | −35.6376 | −2.07140 | ||||||||
\(297\) | −5.08930 | −0.295311 | ||||||||
\(298\) | 14.8087 | 0.857847 | ||||||||
\(299\) | 4.34185 | 0.251095 | ||||||||
\(300\) | −13.2341 | −0.764069 | ||||||||
\(301\) | 4.98596 | 0.287386 | ||||||||
\(302\) | 10.8550 | 0.624634 | ||||||||
\(303\) | −5.54339 | −0.318459 | ||||||||
\(304\) | 35.3167 | 2.02555 | ||||||||
\(305\) | 21.0416 | 1.20484 | ||||||||
\(306\) | 2.57711 | 0.147324 | ||||||||
\(307\) | 8.14904 | 0.465090 | 0.232545 | − | 0.972586i | \(-0.425295\pi\) | ||||
0.232545 | + | 0.972586i | \(0.425295\pi\) | |||||||
\(308\) | −65.0572 | −3.70698 | ||||||||
\(309\) | 8.01343 | 0.455868 | ||||||||
\(310\) | −46.0326 | −2.61448 | ||||||||
\(311\) | 13.4755 | 0.764127 | 0.382063 | − | 0.924136i | \(-0.375214\pi\) | ||||
0.382063 | + | 0.924136i | \(0.375214\pi\) | |||||||
\(312\) | 8.35222 | 0.472851 | ||||||||
\(313\) | 14.1793 | 0.801460 | 0.400730 | − | 0.916196i | \(-0.368757\pi\) | ||||
0.400730 | + | 0.916196i | \(0.368757\pi\) | |||||||
\(314\) | 37.2789 | 2.10377 | ||||||||
\(315\) | −7.71697 | −0.434802 | ||||||||
\(316\) | 4.64151 | 0.261106 | ||||||||
\(317\) | 1.59717 | 0.0897061 | 0.0448530 | − | 0.998994i | \(-0.485718\pi\) | ||||
0.0448530 | + | 0.998994i | \(0.485718\pi\) | |||||||
\(318\) | −28.8806 | −1.61955 | ||||||||
\(319\) | 29.5815 | 1.65624 | ||||||||
\(320\) | 9.11909 | 0.509773 | ||||||||
\(321\) | −16.4057 | −0.915679 | ||||||||
\(322\) | 25.1172 | 1.39972 | ||||||||
\(323\) | −4.27531 | −0.237884 | ||||||||
\(324\) | 4.64151 | 0.257862 | ||||||||
\(325\) | 3.49824 | 0.194047 | ||||||||
\(326\) | −9.13966 | −0.506199 | ||||||||
\(327\) | −13.8530 | −0.766071 | ||||||||
\(328\) | 2.99905 | 0.165595 | ||||||||
\(329\) | 16.5903 | 0.914652 | ||||||||
\(330\) | 36.7503 | 2.02304 | ||||||||
\(331\) | −18.4099 | −1.01190 | −0.505949 | − | 0.862564i | \(-0.668857\pi\) | ||||
−0.505949 | + | 0.862564i | \(0.668857\pi\) | |||||||
\(332\) | 36.9296 | 2.02677 | ||||||||
\(333\) | 5.23507 | 0.286880 | ||||||||
\(334\) | 15.8059 | 0.864858 | ||||||||
\(335\) | 34.9474 | 1.90938 | ||||||||
\(336\) | 22.7505 | 1.24114 | ||||||||
\(337\) | 18.4240 | 1.00362 | 0.501809 | − | 0.864978i | \(-0.332668\pi\) | ||||
0.501809 | + | 0.864978i | \(0.332668\pi\) | |||||||
\(338\) | 29.6231 | 1.61128 | ||||||||
\(339\) | 14.5297 | 0.789143 | ||||||||
\(340\) | −13.0056 | −0.705325 | ||||||||
\(341\) | 32.4430 | 1.75689 | ||||||||
\(342\) | −11.0179 | −0.595782 | ||||||||
\(343\) | 17.6675 | 0.953953 | ||||||||
\(344\) | 12.3242 | 0.664474 | ||||||||
\(345\) | −9.91581 | −0.533849 | ||||||||
\(346\) | −35.8924 | −1.92959 | ||||||||
\(347\) | −10.7338 | −0.576218 | −0.288109 | − | 0.957598i | \(-0.593027\pi\) | ||||
−0.288109 | + | 0.957598i | \(0.593027\pi\) | |||||||
\(348\) | −26.9787 | −1.44621 | ||||||||
\(349\) | −2.86848 | −0.153546 | −0.0767730 | − | 0.997049i | \(-0.524462\pi\) | ||||
−0.0767730 | + | 0.997049i | \(0.524462\pi\) | |||||||
\(350\) | 20.2370 | 1.08171 | ||||||||
\(351\) | −1.22692 | −0.0654880 | ||||||||
\(352\) | −39.0532 | −2.08154 | ||||||||
\(353\) | 24.4997 | 1.30399 | 0.651995 | − | 0.758223i | \(-0.273932\pi\) | ||||
0.651995 | + | 0.758223i | \(0.273932\pi\) | |||||||
\(354\) | −10.4981 | −0.557967 | ||||||||
\(355\) | 14.5271 | 0.771018 | ||||||||
\(356\) | −44.9189 | −2.38070 | ||||||||
\(357\) | −2.75409 | −0.145762 | ||||||||
\(358\) | 9.01358 | 0.476382 | ||||||||
\(359\) | 12.1833 | 0.643011 | 0.321505 | − | 0.946908i | \(-0.395811\pi\) | ||||
0.321505 | + | 0.946908i | \(0.395811\pi\) | |||||||
\(360\) | −19.0746 | −1.00532 | ||||||||
\(361\) | −0.721754 | −0.0379870 | ||||||||
\(362\) | 45.0169 | 2.36604 | ||||||||
\(363\) | −14.9010 | −0.782098 | ||||||||
\(364\) | −15.6839 | −0.822058 | ||||||||
\(365\) | 20.1140 | 1.05281 | ||||||||
\(366\) | 19.3528 | 1.01159 | ||||||||
\(367\) | −22.5406 | −1.17661 | −0.588305 | − | 0.808639i | \(-0.700205\pi\) | ||||
−0.588305 | + | 0.808639i | \(0.700205\pi\) | |||||||
\(368\) | 29.2329 | 1.52387 | ||||||||
\(369\) | −0.440553 | −0.0229343 | ||||||||
\(370\) | −37.8029 | −1.96528 | ||||||||
\(371\) | 30.8639 | 1.60238 | ||||||||
\(372\) | −29.5885 | −1.53409 | ||||||||
\(373\) | 4.22920 | 0.218979 | 0.109490 | − | 0.993988i | \(-0.465078\pi\) | ||||
0.109490 | + | 0.993988i | \(0.465078\pi\) | |||||||
\(374\) | 13.1157 | 0.678197 | ||||||||
\(375\) | 6.02084 | 0.310915 | ||||||||
\(376\) | 41.0074 | 2.11480 | ||||||||
\(377\) | 7.13144 | 0.367288 | ||||||||
\(378\) | −7.09760 | −0.365061 | ||||||||
\(379\) | 26.6704 | 1.36996 | 0.684982 | − | 0.728560i | \(-0.259810\pi\) | ||||
0.684982 | + | 0.728560i | \(0.259810\pi\) | |||||||
\(380\) | 55.6027 | 2.85236 | ||||||||
\(381\) | 4.98610 | 0.255445 | ||||||||
\(382\) | 37.9468 | 1.94153 | ||||||||
\(383\) | 17.5451 | 0.896514 | 0.448257 | − | 0.893905i | \(-0.352045\pi\) | ||||
0.448257 | + | 0.893905i | \(0.352045\pi\) | |||||||
\(384\) | −6.96001 | −0.355177 | ||||||||
\(385\) | −39.2740 | −2.00159 | ||||||||
\(386\) | −18.4035 | −0.936715 | ||||||||
\(387\) | −1.81039 | −0.0920271 | ||||||||
\(388\) | 31.9552 | 1.62228 | ||||||||
\(389\) | 25.4334 | 1.28952 | 0.644761 | − | 0.764384i | \(-0.276957\pi\) | ||||
0.644761 | + | 0.764384i | \(0.276957\pi\) | |||||||
\(390\) | 8.85968 | 0.448627 | ||||||||
\(391\) | −3.53882 | −0.178966 | ||||||||
\(392\) | −3.98241 | −0.201142 | ||||||||
\(393\) | 18.6708 | 0.941819 | ||||||||
\(394\) | 32.4013 | 1.63236 | ||||||||
\(395\) | 2.80201 | 0.140984 | ||||||||
\(396\) | 23.6220 | 1.18705 | ||||||||
\(397\) | 15.1674 | 0.761229 | 0.380615 | − | 0.924734i | \(-0.375712\pi\) | ||||
0.380615 | + | 0.924734i | \(0.375712\pi\) | |||||||
\(398\) | −66.1192 | −3.31426 | ||||||||
\(399\) | 11.7746 | 0.589466 | ||||||||
\(400\) | 23.5530 | 1.17765 | ||||||||
\(401\) | −6.03797 | −0.301522 | −0.150761 | − | 0.988570i | \(-0.548172\pi\) | ||||
−0.150761 | + | 0.988570i | \(0.548172\pi\) | |||||||
\(402\) | 32.1425 | 1.60312 | ||||||||
\(403\) | 7.82129 | 0.389606 | ||||||||
\(404\) | 25.7297 | 1.28010 | ||||||||
\(405\) | 2.80201 | 0.139233 | ||||||||
\(406\) | 41.2547 | 2.04744 | ||||||||
\(407\) | 26.6428 | 1.32064 | ||||||||
\(408\) | −6.80748 | −0.337020 | ||||||||
\(409\) | 38.1362 | 1.88571 | 0.942856 | − | 0.333201i | \(-0.108129\pi\) | ||||
0.942856 | + | 0.333201i | \(0.108129\pi\) | |||||||
\(410\) | 3.18127 | 0.157112 | ||||||||
\(411\) | 10.2748 | 0.506817 | ||||||||
\(412\) | −37.1944 | −1.83244 | ||||||||
\(413\) | 11.2190 | 0.552051 | ||||||||
\(414\) | −9.11995 | −0.448221 | ||||||||
\(415\) | 22.2938 | 1.09436 | ||||||||
\(416\) | −9.41487 | −0.461602 | ||||||||
\(417\) | −7.55783 | −0.370109 | ||||||||
\(418\) | −56.0736 | −2.74265 | ||||||||
\(419\) | −36.4253 | −1.77949 | −0.889746 | − | 0.456456i | \(-0.849119\pi\) | ||||
−0.889746 | + | 0.456456i | \(0.849119\pi\) | |||||||
\(420\) | 35.8184 | 1.74776 | ||||||||
\(421\) | 29.2984 | 1.42792 | 0.713958 | − | 0.700188i | \(-0.246901\pi\) | ||||
0.713958 | + | 0.700188i | \(0.246901\pi\) | |||||||
\(422\) | 22.2199 | 1.08165 | ||||||||
\(423\) | −6.02387 | −0.292891 | ||||||||
\(424\) | 76.2886 | 3.70490 | ||||||||
\(425\) | −2.85124 | −0.138305 | ||||||||
\(426\) | 13.3611 | 0.647348 | ||||||||
\(427\) | −20.6818 | −1.00086 | ||||||||
\(428\) | 76.1475 | 3.68073 | ||||||||
\(429\) | −6.24415 | −0.301470 | ||||||||
\(430\) | 13.0730 | 0.630434 | ||||||||
\(431\) | −13.2517 | −0.638311 | −0.319156 | − | 0.947702i | \(-0.603399\pi\) | ||||
−0.319156 | + | 0.947702i | \(0.603399\pi\) | |||||||
\(432\) | −8.26062 | −0.397439 | ||||||||
\(433\) | 12.0821 | 0.580629 | 0.290315 | − | 0.956931i | \(-0.406240\pi\) | ||||
0.290315 | + | 0.956931i | \(0.406240\pi\) | |||||||
\(434\) | 45.2454 | 2.17185 | ||||||||
\(435\) | −16.2866 | −0.780884 | ||||||||
\(436\) | 64.2987 | 3.07935 | ||||||||
\(437\) | 15.1296 | 0.723745 | ||||||||
\(438\) | 18.4996 | 0.883945 | ||||||||
\(439\) | 19.4448 | 0.928048 | 0.464024 | − | 0.885823i | \(-0.346405\pi\) | ||||
0.464024 | + | 0.885823i | \(0.346405\pi\) | |||||||
\(440\) | −97.0764 | −4.62793 | ||||||||
\(441\) | 0.585005 | 0.0278574 | ||||||||
\(442\) | 3.16191 | 0.150397 | ||||||||
\(443\) | −12.8617 | −0.611078 | −0.305539 | − | 0.952180i | \(-0.598837\pi\) | ||||
−0.305539 | + | 0.952180i | \(0.598837\pi\) | |||||||
\(444\) | −24.2987 | −1.15316 | ||||||||
\(445\) | −27.1168 | −1.28546 | ||||||||
\(446\) | −58.8762 | −2.78787 | ||||||||
\(447\) | 5.74625 | 0.271788 | ||||||||
\(448\) | −8.96315 | −0.423469 | ||||||||
\(449\) | 0.817399 | 0.0385755 | 0.0192877 | − | 0.999814i | \(-0.493860\pi\) | ||||
0.0192877 | + | 0.999814i | \(0.493860\pi\) | |||||||
\(450\) | −7.34797 | −0.346387 | ||||||||
\(451\) | −2.24210 | −0.105577 | ||||||||
\(452\) | −67.4396 | −3.17209 | ||||||||
\(453\) | 4.21207 | 0.197900 | ||||||||
\(454\) | −75.7952 | −3.55724 | ||||||||
\(455\) | −9.46809 | −0.443871 | ||||||||
\(456\) | 29.1041 | 1.36292 | ||||||||
\(457\) | −0.511214 | −0.0239136 | −0.0119568 | − | 0.999929i | \(-0.503806\pi\) | ||||
−0.0119568 | + | 0.999929i | \(0.503806\pi\) | |||||||
\(458\) | 56.1525 | 2.62383 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 46.0244 | 2.14590 | ||||||||
\(461\) | 30.7659 | 1.43291 | 0.716456 | − | 0.697632i | \(-0.245763\pi\) | ||||
0.716456 | + | 0.697632i | \(0.245763\pi\) | |||||||
\(462\) | −36.1218 | −1.68054 | ||||||||
\(463\) | 8.17038 | 0.379710 | 0.189855 | − | 0.981812i | \(-0.439198\pi\) | ||||
0.189855 | + | 0.981812i | \(0.439198\pi\) | |||||||
\(464\) | 48.0147 | 2.22903 | ||||||||
\(465\) | −17.8621 | −0.828334 | ||||||||
\(466\) | −25.5267 | −1.18250 | ||||||||
\(467\) | −0.987753 | −0.0457078 | −0.0228539 | − | 0.999739i | \(-0.507275\pi\) | ||||
−0.0228539 | + | 0.999739i | \(0.507275\pi\) | |||||||
\(468\) | 5.69475 | 0.263240 | ||||||||
\(469\) | −34.3498 | −1.58613 | ||||||||
\(470\) | 43.4989 | 2.00646 | ||||||||
\(471\) | 14.4654 | 0.666530 | ||||||||
\(472\) | 27.7308 | 1.27641 | ||||||||
\(473\) | −9.21359 | −0.423641 | ||||||||
\(474\) | 2.57711 | 0.118371 | ||||||||
\(475\) | 12.1899 | 0.559312 | ||||||||
\(476\) | 12.7831 | 0.585914 | ||||||||
\(477\) | −11.2066 | −0.513114 | ||||||||
\(478\) | −13.6212 | −0.623021 | ||||||||
\(479\) | 13.2194 | 0.604012 | 0.302006 | − | 0.953306i | \(-0.402344\pi\) | ||||
0.302006 | + | 0.953306i | \(0.402344\pi\) | |||||||
\(480\) | 21.5015 | 0.981403 | ||||||||
\(481\) | 6.42300 | 0.292864 | ||||||||
\(482\) | 35.3678 | 1.61096 | ||||||||
\(483\) | 9.74624 | 0.443469 | ||||||||
\(484\) | 69.1630 | 3.14377 | ||||||||
\(485\) | 19.2909 | 0.875952 | ||||||||
\(486\) | 2.57711 | 0.116900 | ||||||||
\(487\) | 28.3574 | 1.28500 | 0.642498 | − | 0.766288i | \(-0.277898\pi\) | ||||
0.642498 | + | 0.766288i | \(0.277898\pi\) | |||||||
\(488\) | −51.1206 | −2.31412 | ||||||||
\(489\) | −3.54647 | −0.160377 | ||||||||
\(490\) | −4.22438 | −0.190838 | ||||||||
\(491\) | 18.3357 | 0.827478 | 0.413739 | − | 0.910396i | \(-0.364223\pi\) | ||||
0.413739 | + | 0.910396i | \(0.364223\pi\) | |||||||
\(492\) | 2.04483 | 0.0921881 | ||||||||
\(493\) | −5.81249 | −0.261781 | ||||||||
\(494\) | −13.5181 | −0.608209 | ||||||||
\(495\) | 14.2602 | 0.640950 | ||||||||
\(496\) | 52.6594 | 2.36448 | ||||||||
\(497\) | −14.2787 | −0.640485 | ||||||||
\(498\) | 20.5045 | 0.918827 | ||||||||
\(499\) | −2.15154 | −0.0963163 | −0.0481581 | − | 0.998840i | \(-0.515335\pi\) | ||||
−0.0481581 | + | 0.998840i | \(0.515335\pi\) | |||||||
\(500\) | −27.9458 | −1.24977 | ||||||||
\(501\) | 6.13316 | 0.274010 | ||||||||
\(502\) | −22.0621 | −0.984681 | ||||||||
\(503\) | 15.2893 | 0.681718 | 0.340859 | − | 0.940114i | \(-0.389282\pi\) | ||||
0.340859 | + | 0.940114i | \(0.389282\pi\) | |||||||
\(504\) | 18.7484 | 0.835120 | ||||||||
\(505\) | 15.5326 | 0.691192 | ||||||||
\(506\) | −46.4142 | −2.06336 | ||||||||
\(507\) | 11.4947 | 0.510496 | ||||||||
\(508\) | −23.1430 | −1.02681 | ||||||||
\(509\) | −13.6807 | −0.606385 | −0.303192 | − | 0.952929i | \(-0.598052\pi\) | ||||
−0.303192 | + | 0.952929i | \(0.598052\pi\) | |||||||
\(510\) | −7.22109 | −0.319755 | ||||||||
\(511\) | −19.7700 | −0.874574 | ||||||||
\(512\) | 49.0793 | 2.16902 | ||||||||
\(513\) | −4.27531 | −0.188759 | ||||||||
\(514\) | 17.6955 | 0.780513 | ||||||||
\(515\) | −22.4537 | −0.989427 | ||||||||
\(516\) | 8.40293 | 0.369918 | ||||||||
\(517\) | −30.6573 | −1.34831 | ||||||||
\(518\) | 37.1564 | 1.63256 | ||||||||
\(519\) | −13.9274 | −0.611344 | ||||||||
\(520\) | −23.4030 | −1.02629 | ||||||||
\(521\) | −30.2671 | −1.32603 | −0.663013 | − | 0.748608i | \(-0.730723\pi\) | ||||
−0.663013 | + | 0.748608i | \(0.730723\pi\) | |||||||
\(522\) | −14.9794 | −0.655632 | ||||||||
\(523\) | 26.0430 | 1.13878 | 0.569391 | − | 0.822067i | \(-0.307179\pi\) | ||||
0.569391 | + | 0.822067i | \(0.307179\pi\) | |||||||
\(524\) | −86.6609 | −3.78580 | ||||||||
\(525\) | 7.85257 | 0.342714 | ||||||||
\(526\) | 32.8280 | 1.43137 | ||||||||
\(527\) | −6.37475 | −0.277688 | ||||||||
\(528\) | −42.0408 | −1.82959 | ||||||||
\(529\) | −10.4767 | −0.455510 | ||||||||
\(530\) | 80.9238 | 3.51510 | ||||||||
\(531\) | −4.07358 | −0.176778 | ||||||||
\(532\) | −54.6518 | −2.36946 | ||||||||
\(533\) | −0.540522 | −0.0234126 | ||||||||
\(534\) | −24.9404 | −1.07928 | ||||||||
\(535\) | 45.9690 | 1.98741 | ||||||||
\(536\) | −84.9048 | −3.66733 | ||||||||
\(537\) | 3.49755 | 0.150930 | ||||||||
\(538\) | 6.84761 | 0.295221 | ||||||||
\(539\) | 2.97727 | 0.128240 | ||||||||
\(540\) | −13.0056 | −0.559670 | ||||||||
\(541\) | 2.78093 | 0.119561 | 0.0597807 | − | 0.998212i | \(-0.480960\pi\) | ||||
0.0597807 | + | 0.998212i | \(0.480960\pi\) | |||||||
\(542\) | −32.7734 | −1.40774 | ||||||||
\(543\) | 17.4680 | 0.749621 | ||||||||
\(544\) | 7.67360 | 0.329003 | ||||||||
\(545\) | 38.8161 | 1.66270 | ||||||||
\(546\) | −8.70817 | −0.372675 | ||||||||
\(547\) | 16.6007 | 0.709795 | 0.354898 | − | 0.934905i | \(-0.384516\pi\) | ||||
0.354898 | + | 0.934905i | \(0.384516\pi\) | |||||||
\(548\) | −47.6905 | −2.03724 | ||||||||
\(549\) | 7.50948 | 0.320497 | ||||||||
\(550\) | −37.3960 | −1.59457 | ||||||||
\(551\) | 24.8502 | 1.05865 | ||||||||
\(552\) | 24.0905 | 1.02536 | ||||||||
\(553\) | −2.75409 | −0.117116 | ||||||||
\(554\) | −8.05937 | −0.342410 | ||||||||
\(555\) | −14.6687 | −0.622652 | ||||||||
\(556\) | 35.0798 | 1.48771 | ||||||||
\(557\) | −24.6908 | −1.04618 | −0.523092 | − | 0.852276i | \(-0.675222\pi\) | ||||
−0.523092 | + | 0.852276i | \(0.675222\pi\) | |||||||
\(558\) | −16.4284 | −0.695471 | ||||||||
\(559\) | −2.22119 | −0.0939465 | ||||||||
\(560\) | −63.7470 | −2.69380 | ||||||||
\(561\) | 5.08930 | 0.214870 | ||||||||
\(562\) | 75.3538 | 3.17861 | ||||||||
\(563\) | 1.92738 | 0.0812293 | 0.0406146 | − | 0.999175i | \(-0.487068\pi\) | ||||
0.0406146 | + | 0.999175i | \(0.487068\pi\) | |||||||
\(564\) | 27.9599 | 1.17732 | ||||||||
\(565\) | −40.7122 | −1.71278 | ||||||||
\(566\) | 63.2118 | 2.65699 | ||||||||
\(567\) | −2.75409 | −0.115661 | ||||||||
\(568\) | −35.2936 | −1.48089 | ||||||||
\(569\) | 33.3052 | 1.39623 | 0.698114 | − | 0.715987i | \(-0.254023\pi\) | ||||
0.698114 | + | 0.715987i | \(0.254023\pi\) | |||||||
\(570\) | 30.8724 | 1.29310 | ||||||||
\(571\) | 31.6065 | 1.32269 | 0.661346 | − | 0.750081i | \(-0.269986\pi\) | ||||
0.661346 | + | 0.750081i | \(0.269986\pi\) | |||||||
\(572\) | 28.9823 | 1.21181 | ||||||||
\(573\) | 14.7246 | 0.615127 | ||||||||
\(574\) | −3.12687 | −0.130513 | ||||||||
\(575\) | 10.0900 | 0.420784 | ||||||||
\(576\) | 3.25449 | 0.135604 | ||||||||
\(577\) | −25.2984 | −1.05319 | −0.526594 | − | 0.850117i | \(-0.676531\pi\) | ||||
−0.526594 | + | 0.850117i | \(0.676531\pi\) | |||||||
\(578\) | −2.57711 | −0.107194 | ||||||||
\(579\) | −7.14114 | −0.296776 | ||||||||
\(580\) | 75.5946 | 3.13889 | ||||||||
\(581\) | −21.9125 | −0.909086 | ||||||||
\(582\) | 17.7425 | 0.735452 | ||||||||
\(583\) | −57.0337 | −2.36209 | ||||||||
\(584\) | −48.8669 | −2.02213 | ||||||||
\(585\) | 3.43783 | 0.142137 | ||||||||
\(586\) | 69.7238 | 2.88026 | ||||||||
\(587\) | −29.5672 | −1.22037 | −0.610184 | − | 0.792260i | \(-0.708905\pi\) | ||||
−0.610184 | + | 0.792260i | \(0.708905\pi\) | |||||||
\(588\) | −2.71531 | −0.111978 | ||||||||
\(589\) | 27.2540 | 1.12298 | ||||||||
\(590\) | 29.4157 | 1.21102 | ||||||||
\(591\) | 12.5727 | 0.517173 | ||||||||
\(592\) | 43.2449 | 1.77736 | ||||||||
\(593\) | 34.0643 | 1.39885 | 0.699427 | − | 0.714704i | \(-0.253438\pi\) | ||||
0.699427 | + | 0.714704i | \(0.253438\pi\) | |||||||
\(594\) | 13.1157 | 0.538144 | ||||||||
\(595\) | 7.71697 | 0.316365 | ||||||||
\(596\) | −26.6713 | −1.09250 | ||||||||
\(597\) | −25.6563 | −1.05004 | ||||||||
\(598\) | −11.1894 | −0.457570 | ||||||||
\(599\) | 10.4664 | 0.427646 | 0.213823 | − | 0.976872i | \(-0.431408\pi\) | ||||
0.213823 | + | 0.976872i | \(0.431408\pi\) | |||||||
\(600\) | 19.4098 | 0.792400 | ||||||||
\(601\) | 2.79728 | 0.114103 | 0.0570516 | − | 0.998371i | \(-0.481830\pi\) | ||||
0.0570516 | + | 0.998371i | \(0.481830\pi\) | |||||||
\(602\) | −12.8494 | −0.523702 | ||||||||
\(603\) | 12.4723 | 0.507911 | ||||||||
\(604\) | −19.5504 | −0.795494 | ||||||||
\(605\) | 41.7526 | 1.69748 | ||||||||
\(606\) | 14.2859 | 0.580327 | ||||||||
\(607\) | −40.7507 | −1.65402 | −0.827011 | − | 0.562186i | \(-0.809960\pi\) | ||||
−0.827011 | + | 0.562186i | \(0.809960\pi\) | |||||||
\(608\) | −32.8070 | −1.33050 | ||||||||
\(609\) | 16.0081 | 0.648681 | ||||||||
\(610\) | −54.2266 | −2.19557 | ||||||||
\(611\) | −7.39080 | −0.299000 | ||||||||
\(612\) | −4.64151 | −0.187622 | ||||||||
\(613\) | −2.33241 | −0.0942052 | −0.0471026 | − | 0.998890i | \(-0.514999\pi\) | ||||
−0.0471026 | + | 0.998890i | \(0.514999\pi\) | |||||||
\(614\) | −21.0010 | −0.847532 | ||||||||
\(615\) | 1.23443 | 0.0497771 | ||||||||
\(616\) | 95.4162 | 3.84443 | ||||||||
\(617\) | 0.890091 | 0.0358337 | 0.0179168 | − | 0.999839i | \(-0.494297\pi\) | ||||
0.0179168 | + | 0.999839i | \(0.494297\pi\) | |||||||
\(618\) | −20.6515 | −0.830726 | ||||||||
\(619\) | 25.6620 | 1.03144 | 0.515722 | − | 0.856756i | \(-0.327524\pi\) | ||||
0.515722 | + | 0.856756i | \(0.327524\pi\) | |||||||
\(620\) | 82.9071 | 3.32963 | ||||||||
\(621\) | −3.53882 | −0.142008 | ||||||||
\(622\) | −34.7279 | −1.39246 | ||||||||
\(623\) | 26.6531 | 1.06783 | ||||||||
\(624\) | −10.1351 | −0.405729 | ||||||||
\(625\) | −31.1266 | −1.24507 | ||||||||
\(626\) | −36.5416 | −1.46050 | ||||||||
\(627\) | −21.7583 | −0.868943 | ||||||||
\(628\) | −67.1413 | −2.67923 | ||||||||
\(629\) | −5.23507 | −0.208736 | ||||||||
\(630\) | 19.8875 | 0.792338 | ||||||||
\(631\) | −28.9704 | −1.15329 | −0.576647 | − | 0.816994i | \(-0.695639\pi\) | ||||
−0.576647 | + | 0.816994i | \(0.695639\pi\) | |||||||
\(632\) | −6.80748 | −0.270787 | ||||||||
\(633\) | 8.62202 | 0.342695 | ||||||||
\(634\) | −4.11609 | −0.163471 | ||||||||
\(635\) | −13.9711 | −0.554425 | ||||||||
\(636\) | 52.0155 | 2.06255 | ||||||||
\(637\) | 0.717753 | 0.0284384 | ||||||||
\(638\) | −76.2348 | −3.01817 | ||||||||
\(639\) | 5.18453 | 0.205097 | ||||||||
\(640\) | 19.5020 | 0.770884 | ||||||||
\(641\) | −40.2458 | −1.58961 | −0.794807 | − | 0.606863i | \(-0.792428\pi\) | ||||
−0.794807 | + | 0.606863i | \(0.792428\pi\) | |||||||
\(642\) | 42.2795 | 1.66864 | ||||||||
\(643\) | −43.7309 | −1.72458 | −0.862289 | − | 0.506416i | \(-0.830970\pi\) | ||||
−0.862289 | + | 0.506416i | \(0.830970\pi\) | |||||||
\(644\) | −45.2373 | −1.78260 | ||||||||
\(645\) | 5.07271 | 0.199738 | ||||||||
\(646\) | 11.0179 | 0.433495 | ||||||||
\(647\) | −18.0131 | −0.708168 | −0.354084 | − | 0.935214i | \(-0.615207\pi\) | ||||
−0.354084 | + | 0.935214i | \(0.615207\pi\) | |||||||
\(648\) | −6.80748 | −0.267423 | ||||||||
\(649\) | −20.7317 | −0.813789 | ||||||||
\(650\) | −9.01535 | −0.353611 | ||||||||
\(651\) | 17.5566 | 0.688098 | ||||||||
\(652\) | 16.4610 | 0.644663 | ||||||||
\(653\) | 21.4209 | 0.838265 | 0.419132 | − | 0.907925i | \(-0.362334\pi\) | ||||
0.419132 | + | 0.907925i | \(0.362334\pi\) | |||||||
\(654\) | 35.7007 | 1.39601 | ||||||||
\(655\) | −52.3158 | −2.04415 | ||||||||
\(656\) | −3.63924 | −0.142088 | ||||||||
\(657\) | 7.17842 | 0.280057 | ||||||||
\(658\) | −42.7550 | −1.66676 | ||||||||
\(659\) | 16.6786 | 0.649705 | 0.324852 | − | 0.945765i | \(-0.394685\pi\) | ||||
0.324852 | + | 0.945765i | \(0.394685\pi\) | |||||||
\(660\) | −66.1891 | −2.57641 | ||||||||
\(661\) | 21.3001 | 0.828479 | 0.414239 | − | 0.910168i | \(-0.364048\pi\) | ||||
0.414239 | + | 0.910168i | \(0.364048\pi\) | |||||||
\(662\) | 47.4443 | 1.84397 | ||||||||
\(663\) | 1.22692 | 0.0476495 | ||||||||
\(664\) | −54.1628 | −2.10192 | ||||||||
\(665\) | −32.9924 | −1.27939 | ||||||||
\(666\) | −13.4914 | −0.522780 | ||||||||
\(667\) | 20.5694 | 0.796449 | ||||||||
\(668\) | −28.4672 | −1.10143 | ||||||||
\(669\) | −22.8458 | −0.883270 | ||||||||
\(670\) | −90.0635 | −3.47946 | ||||||||
\(671\) | 38.2180 | 1.47539 | ||||||||
\(672\) | −21.1338 | −0.815253 | ||||||||
\(673\) | −24.5742 | −0.947267 | −0.473633 | − | 0.880722i | \(-0.657058\pi\) | ||||
−0.473633 | + | 0.880722i | \(0.657058\pi\) | |||||||
\(674\) | −47.4807 | −1.82889 | ||||||||
\(675\) | −2.85124 | −0.109744 | ||||||||
\(676\) | −53.3527 | −2.05203 | ||||||||
\(677\) | −0.965852 | −0.0371207 | −0.0185603 | − | 0.999828i | \(-0.505908\pi\) | ||||
−0.0185603 | + | 0.999828i | \(0.505908\pi\) | |||||||
\(678\) | −37.4446 | −1.43805 | ||||||||
\(679\) | −18.9610 | −0.727655 | ||||||||
\(680\) | 19.0746 | 0.731478 | ||||||||
\(681\) | −29.4109 | −1.12703 | ||||||||
\(682\) | −83.6093 | −3.20156 | ||||||||
\(683\) | 31.2478 | 1.19566 | 0.597831 | − | 0.801622i | \(-0.296029\pi\) | ||||
0.597831 | + | 0.801622i | \(0.296029\pi\) | |||||||
\(684\) | 19.8439 | 0.758750 | ||||||||
\(685\) | −28.7900 | −1.10001 | ||||||||
\(686\) | −45.5311 | −1.73838 | ||||||||
\(687\) | 21.7889 | 0.831298 | ||||||||
\(688\) | −14.9549 | −0.570150 | ||||||||
\(689\) | −13.7496 | −0.523817 | ||||||||
\(690\) | 25.5542 | 0.972830 | ||||||||
\(691\) | 21.5915 | 0.821379 | 0.410690 | − | 0.911775i | \(-0.365288\pi\) | ||||
0.410690 | + | 0.911775i | \(0.365288\pi\) | |||||||
\(692\) | 64.6441 | 2.45740 | ||||||||
\(693\) | −14.0164 | −0.532438 | ||||||||
\(694\) | 27.6621 | 1.05004 | ||||||||
\(695\) | 21.1771 | 0.803293 | ||||||||
\(696\) | 39.5684 | 1.49984 | ||||||||
\(697\) | 0.440553 | 0.0166871 | ||||||||
\(698\) | 7.39239 | 0.279806 | ||||||||
\(699\) | −9.90516 | −0.374648 | ||||||||
\(700\) | −36.4478 | −1.37760 | ||||||||
\(701\) | −42.9615 | −1.62263 | −0.811316 | − | 0.584608i | \(-0.801248\pi\) | ||||
−0.811316 | + | 0.584608i | \(0.801248\pi\) | |||||||
\(702\) | 3.16191 | 0.119338 | ||||||||
\(703\) | 22.3815 | 0.844136 | ||||||||
\(704\) | 16.5631 | 0.624244 | ||||||||
\(705\) | 16.8789 | 0.635697 | ||||||||
\(706\) | −63.1386 | −2.37625 | ||||||||
\(707\) | −15.2670 | −0.574174 | ||||||||
\(708\) | 18.9076 | 0.710590 | ||||||||
\(709\) | 12.7478 | 0.478755 | 0.239377 | − | 0.970927i | \(-0.423057\pi\) | ||||
0.239377 | + | 0.970927i | \(0.423057\pi\) | |||||||
\(710\) | −37.4379 | −1.40502 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 65.8803 | 2.46897 | ||||||||
\(713\) | 22.5591 | 0.844845 | ||||||||
\(714\) | 7.09760 | 0.265621 | ||||||||
\(715\) | 17.4962 | 0.654319 | ||||||||
\(716\) | −16.2339 | −0.606690 | ||||||||
\(717\) | −5.28546 | −0.197389 | ||||||||
\(718\) | −31.3978 | −1.17175 | ||||||||
\(719\) | 47.6229 | 1.77603 | 0.888017 | − | 0.459810i | \(-0.152083\pi\) | ||||
0.888017 | + | 0.459810i | \(0.152083\pi\) | |||||||
\(720\) | 23.1463 | 0.862612 | ||||||||
\(721\) | 22.0697 | 0.821918 | ||||||||
\(722\) | 1.86004 | 0.0692236 | ||||||||
\(723\) | 13.7238 | 0.510394 | ||||||||
\(724\) | −81.0777 | −3.01323 | ||||||||
\(725\) | 16.5728 | 0.615498 | ||||||||
\(726\) | 38.4015 | 1.42521 | ||||||||
\(727\) | 19.5951 | 0.726743 | 0.363371 | − | 0.931644i | \(-0.381626\pi\) | ||||
0.363371 | + | 0.931644i | \(0.381626\pi\) | |||||||
\(728\) | 23.0027 | 0.852539 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −51.8360 | −1.91854 | ||||||||
\(731\) | 1.81039 | 0.0669595 | ||||||||
\(732\) | −34.8554 | −1.28829 | ||||||||
\(733\) | 5.04366 | 0.186292 | 0.0931459 | − | 0.995652i | \(-0.470308\pi\) | ||||
0.0931459 | + | 0.995652i | \(0.470308\pi\) | |||||||
\(734\) | 58.0897 | 2.14413 | ||||||||
\(735\) | −1.63919 | −0.0604624 | ||||||||
\(736\) | −27.1555 | −1.00097 | ||||||||
\(737\) | 63.4752 | 2.33814 | ||||||||
\(738\) | 1.13535 | 0.0417930 | ||||||||
\(739\) | −17.1244 | −0.629931 | −0.314965 | − | 0.949103i | \(-0.601993\pi\) | ||||
−0.314965 | + | 0.949103i | \(0.601993\pi\) | |||||||
\(740\) | 68.0850 | 2.50285 | ||||||||
\(741\) | −5.24545 | −0.192696 | ||||||||
\(742\) | −79.5399 | −2.92000 | ||||||||
\(743\) | 19.2144 | 0.704909 | 0.352455 | − | 0.935829i | \(-0.385347\pi\) | ||||
0.352455 | + | 0.935829i | \(0.385347\pi\) | |||||||
\(744\) | 43.3960 | 1.59097 | ||||||||
\(745\) | −16.1010 | −0.589896 | ||||||||
\(746\) | −10.8991 | −0.399045 | ||||||||
\(747\) | 7.95637 | 0.291108 | ||||||||
\(748\) | −23.6220 | −0.863708 | ||||||||
\(749\) | −45.1829 | −1.65095 | ||||||||
\(750\) | −15.5164 | −0.566578 | ||||||||
\(751\) | −18.2066 | −0.664368 | −0.332184 | − | 0.943215i | \(-0.607785\pi\) | ||||
−0.332184 | + | 0.943215i | \(0.607785\pi\) | |||||||
\(752\) | −49.7609 | −1.81459 | ||||||||
\(753\) | −8.56079 | −0.311972 | ||||||||
\(754\) | −18.3785 | −0.669307 | ||||||||
\(755\) | −11.8023 | −0.429528 | ||||||||
\(756\) | 12.7831 | 0.464918 | ||||||||
\(757\) | −0.914931 | −0.0332537 | −0.0166269 | − | 0.999862i | \(-0.505293\pi\) | ||||
−0.0166269 | + | 0.999862i | \(0.505293\pi\) | |||||||
\(758\) | −68.7325 | −2.49648 | ||||||||
\(759\) | −18.0101 | −0.653726 | ||||||||
\(760\) | −81.5498 | −2.95812 | ||||||||
\(761\) | 48.7468 | 1.76707 | 0.883534 | − | 0.468367i | \(-0.155157\pi\) | ||||
0.883534 | + | 0.468367i | \(0.155157\pi\) | |||||||
\(762\) | −12.8497 | −0.465497 | ||||||||
\(763\) | −38.1523 | −1.38121 | ||||||||
\(764\) | −68.3442 | −2.47261 | ||||||||
\(765\) | −2.80201 | −0.101307 | ||||||||
\(766\) | −45.2158 | −1.63371 | ||||||||
\(767\) | −4.99795 | −0.180465 | ||||||||
\(768\) | 24.4457 | 0.882109 | ||||||||
\(769\) | 18.9249 | 0.682451 | 0.341225 | − | 0.939982i | \(-0.389158\pi\) | ||||
0.341225 | + | 0.939982i | \(0.389158\pi\) | |||||||
\(770\) | 101.214 | 3.64748 | ||||||||
\(771\) | 6.86639 | 0.247287 | ||||||||
\(772\) | 33.1457 | 1.19294 | ||||||||
\(773\) | −4.36566 | −0.157022 | −0.0785109 | − | 0.996913i | \(-0.525017\pi\) | ||||
−0.0785109 | + | 0.996913i | \(0.525017\pi\) | |||||||
\(774\) | 4.66557 | 0.167700 | ||||||||
\(775\) | 18.1759 | 0.652899 | ||||||||
\(776\) | −46.8672 | −1.68243 | ||||||||
\(777\) | 14.4179 | 0.517238 | ||||||||
\(778\) | −65.5446 | −2.34989 | ||||||||
\(779\) | −1.88350 | −0.0674833 | ||||||||
\(780\) | −15.9567 | −0.571343 | ||||||||
\(781\) | 26.3856 | 0.944152 | ||||||||
\(782\) | 9.11995 | 0.326129 | ||||||||
\(783\) | −5.81249 | −0.207721 | ||||||||
\(784\) | 4.83251 | 0.172590 | ||||||||
\(785\) | −40.5321 | −1.44665 | ||||||||
\(786\) | −48.1169 | −1.71627 | ||||||||
\(787\) | 24.4857 | 0.872820 | 0.436410 | − | 0.899748i | \(-0.356250\pi\) | ||||
0.436410 | + | 0.899748i | \(0.356250\pi\) | |||||||
\(788\) | −58.3565 | −2.07886 | ||||||||
\(789\) | 12.7383 | 0.453496 | ||||||||
\(790\) | −7.22109 | −0.256915 | ||||||||
\(791\) | 40.0160 | 1.42280 | ||||||||
\(792\) | −34.6453 | −1.23107 | ||||||||
\(793\) | 9.21351 | 0.327181 | ||||||||
\(794\) | −39.0881 | −1.38718 | ||||||||
\(795\) | 31.4009 | 1.11368 | ||||||||
\(796\) | 119.084 | 4.22083 | ||||||||
\(797\) | 11.1652 | 0.395493 | 0.197747 | − | 0.980253i | \(-0.436638\pi\) | ||||
0.197747 | + | 0.980253i | \(0.436638\pi\) | |||||||
\(798\) | −30.3444 | −1.07418 | ||||||||
\(799\) | 6.02387 | 0.213109 | ||||||||
\(800\) | −21.8793 | −0.773549 | ||||||||
\(801\) | −9.67764 | −0.341943 | ||||||||
\(802\) | 15.5605 | 0.549461 | ||||||||
\(803\) | 36.5331 | 1.28923 | ||||||||
\(804\) | −57.8903 | −2.04163 | ||||||||
\(805\) | −27.3090 | −0.962516 | ||||||||
\(806\) | −20.1563 | −0.709977 | ||||||||
\(807\) | 2.65708 | 0.0935338 | ||||||||
\(808\) | −37.7365 | −1.32757 | ||||||||
\(809\) | −37.5180 | −1.31906 | −0.659531 | − | 0.751678i | \(-0.729245\pi\) | ||||
−0.659531 | + | 0.751678i | \(0.729245\pi\) | |||||||
\(810\) | −7.22109 | −0.253723 | ||||||||
\(811\) | −25.2277 | −0.885866 | −0.442933 | − | 0.896555i | \(-0.646062\pi\) | ||||
−0.442933 | + | 0.896555i | \(0.646062\pi\) | |||||||
\(812\) | −74.3018 | −2.60748 | ||||||||
\(813\) | −12.7171 | −0.446008 | ||||||||
\(814\) | −68.6616 | −2.40659 | ||||||||
\(815\) | 9.93724 | 0.348086 | ||||||||
\(816\) | 8.26062 | 0.289180 | ||||||||
\(817\) | −7.73995 | −0.270787 | ||||||||
\(818\) | −98.2812 | −3.43632 | ||||||||
\(819\) | −3.37904 | −0.118073 | ||||||||
\(820\) | −5.72963 | −0.200087 | ||||||||
\(821\) | −39.6582 | −1.38408 | −0.692041 | − | 0.721859i | \(-0.743288\pi\) | ||||
−0.692041 | + | 0.721859i | \(0.743288\pi\) | |||||||
\(822\) | −26.4792 | −0.923570 | ||||||||
\(823\) | −7.60901 | −0.265234 | −0.132617 | − | 0.991167i | \(-0.542338\pi\) | ||||
−0.132617 | + | 0.991167i | \(0.542338\pi\) | |||||||
\(824\) | 54.5513 | 1.90038 | ||||||||
\(825\) | −14.5108 | −0.505202 | ||||||||
\(826\) | −28.9126 | −1.00600 | ||||||||
\(827\) | 19.4383 | 0.675936 | 0.337968 | − | 0.941158i | \(-0.390260\pi\) | ||||
0.337968 | + | 0.941158i | \(0.390260\pi\) | |||||||
\(828\) | 16.4255 | 0.570826 | ||||||||
\(829\) | −38.1869 | −1.32629 | −0.663143 | − | 0.748492i | \(-0.730778\pi\) | ||||
−0.663143 | + | 0.748492i | \(0.730778\pi\) | |||||||
\(830\) | −57.4536 | −1.99424 | ||||||||
\(831\) | −3.12729 | −0.108484 | ||||||||
\(832\) | 3.99299 | 0.138432 | ||||||||
\(833\) | −0.585005 | −0.0202692 | ||||||||
\(834\) | 19.4774 | 0.674447 | ||||||||
\(835\) | −17.1852 | −0.594717 | ||||||||
\(836\) | 100.992 | 3.49286 | ||||||||
\(837\) | −6.37475 | −0.220343 | ||||||||
\(838\) | 93.8721 | 3.24276 | ||||||||
\(839\) | 29.0385 | 1.00252 | 0.501260 | − | 0.865297i | \(-0.332870\pi\) | ||||
0.501260 | + | 0.865297i | \(0.332870\pi\) | |||||||
\(840\) | −52.5332 | −1.81257 | ||||||||
\(841\) | 4.78499 | 0.165000 | ||||||||
\(842\) | −75.5053 | −2.60208 | ||||||||
\(843\) | 29.2396 | 1.00707 | ||||||||
\(844\) | −40.0192 | −1.37752 | ||||||||
\(845\) | −32.2081 | −1.10799 | ||||||||
\(846\) | 15.5242 | 0.533733 | ||||||||
\(847\) | −41.0386 | −1.41010 | ||||||||
\(848\) | −92.5734 | −3.17898 | ||||||||
\(849\) | 24.5281 | 0.841804 | ||||||||
\(850\) | 7.34797 | 0.252033 | ||||||||
\(851\) | 18.5260 | 0.635063 | ||||||||
\(852\) | −24.0641 | −0.824421 | ||||||||
\(853\) | −39.3760 | −1.34821 | −0.674105 | − | 0.738636i | \(-0.735470\pi\) | ||||
−0.674105 | + | 0.738636i | \(0.735470\pi\) | |||||||
\(854\) | 53.2993 | 1.82386 | ||||||||
\(855\) | 11.9794 | 0.409688 | ||||||||
\(856\) | −111.682 | −3.81720 | ||||||||
\(857\) | −22.4273 | −0.766103 | −0.383052 | − | 0.923727i | \(-0.625127\pi\) | ||||
−0.383052 | + | 0.923727i | \(0.625127\pi\) | |||||||
\(858\) | 16.0919 | 0.549368 | ||||||||
\(859\) | −26.9153 | −0.918339 | −0.459170 | − | 0.888349i | \(-0.651853\pi\) | ||||
−0.459170 | + | 0.888349i | \(0.651853\pi\) | |||||||
\(860\) | −23.5451 | −0.802880 | ||||||||
\(861\) | −1.21332 | −0.0413499 | ||||||||
\(862\) | 34.1511 | 1.16319 | ||||||||
\(863\) | 19.3259 | 0.657861 | 0.328930 | − | 0.944354i | \(-0.393312\pi\) | ||||
0.328930 | + | 0.944354i | \(0.393312\pi\) | |||||||
\(864\) | 7.67360 | 0.261061 | ||||||||
\(865\) | 39.0246 | 1.32688 | ||||||||
\(866\) | −31.1370 | −1.05808 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −81.4893 | −2.76593 | ||||||||
\(869\) | 5.08930 | 0.172643 | ||||||||
\(870\) | 41.9725 | 1.42300 | ||||||||
\(871\) | 15.3025 | 0.518504 | ||||||||
\(872\) | −94.3038 | −3.19353 | ||||||||
\(873\) | 6.88466 | 0.233010 | ||||||||
\(874\) | −38.9906 | −1.31888 | ||||||||
\(875\) | 16.5819 | 0.560571 | ||||||||
\(876\) | −33.3187 | −1.12574 | ||||||||
\(877\) | −1.19412 | −0.0403224 | −0.0201612 | − | 0.999797i | \(-0.506418\pi\) | ||||
−0.0201612 | + | 0.999797i | \(0.506418\pi\) | |||||||
\(878\) | −50.1114 | −1.69118 | ||||||||
\(879\) | 27.0550 | 0.912543 | ||||||||
\(880\) | 117.799 | 3.97099 | ||||||||
\(881\) | 11.9002 | 0.400929 | 0.200465 | − | 0.979701i | \(-0.435755\pi\) | ||||
0.200465 | + | 0.979701i | \(0.435755\pi\) | |||||||
\(882\) | −1.50763 | −0.0507644 | ||||||||
\(883\) | 34.0166 | 1.14475 | 0.572375 | − | 0.819992i | \(-0.306022\pi\) | ||||
0.572375 | + | 0.819992i | \(0.306022\pi\) | |||||||
\(884\) | −5.69475 | −0.191535 | ||||||||
\(885\) | 11.4142 | 0.383684 | ||||||||
\(886\) | 33.1461 | 1.11356 | ||||||||
\(887\) | 41.8345 | 1.40466 | 0.702332 | − | 0.711850i | \(-0.252142\pi\) | ||||
0.702332 | + | 0.711850i | \(0.252142\pi\) | |||||||
\(888\) | 35.6376 | 1.19592 | ||||||||
\(889\) | 13.7322 | 0.460562 | ||||||||
\(890\) | 69.8831 | 2.34249 | ||||||||
\(891\) | 5.08930 | 0.170498 | ||||||||
\(892\) | 106.039 | 3.55045 | ||||||||
\(893\) | −25.7539 | −0.861822 | ||||||||
\(894\) | −14.8087 | −0.495278 | ||||||||
\(895\) | −9.80015 | −0.327583 | ||||||||
\(896\) | −19.1685 | −0.640374 | ||||||||
\(897\) | −4.34185 | −0.144970 | ||||||||
\(898\) | −2.10653 | −0.0702958 | ||||||||
\(899\) | 37.0531 | 1.23579 | ||||||||
\(900\) | 13.2341 | 0.441136 | ||||||||
\(901\) | 11.2066 | 0.373346 | ||||||||
\(902\) | 5.77816 | 0.192392 | ||||||||
\(903\) | −4.98596 | −0.165922 | ||||||||
\(904\) | 98.9104 | 3.28971 | ||||||||
\(905\) | −48.9453 | −1.62700 | ||||||||
\(906\) | −10.8550 | −0.360633 | ||||||||
\(907\) | 48.3897 | 1.60675 | 0.803377 | − | 0.595471i | \(-0.203034\pi\) | ||||
0.803377 | + | 0.595471i | \(0.203034\pi\) | |||||||
\(908\) | 136.511 | 4.53028 | ||||||||
\(909\) | 5.54339 | 0.183863 | ||||||||
\(910\) | 24.4003 | 0.808864 | ||||||||
\(911\) | 27.9654 | 0.926533 | 0.463267 | − | 0.886219i | \(-0.346677\pi\) | ||||
0.463267 | + | 0.886219i | \(0.346677\pi\) | |||||||
\(912\) | −35.3167 | −1.16945 | ||||||||
\(913\) | 40.4923 | 1.34010 | ||||||||
\(914\) | 1.31746 | 0.0435775 | ||||||||
\(915\) | −21.0416 | −0.695614 | ||||||||
\(916\) | −101.133 | −3.34154 | ||||||||
\(917\) | 51.4211 | 1.69808 | ||||||||
\(918\) | −2.57711 | −0.0850574 | ||||||||
\(919\) | −43.4493 | −1.43326 | −0.716631 | − | 0.697453i | \(-0.754317\pi\) | ||||
−0.716631 | + | 0.697453i | \(0.754317\pi\) | |||||||
\(920\) | −67.5017 | −2.22546 | ||||||||
\(921\) | −8.14904 | −0.268520 | ||||||||
\(922\) | −79.2873 | −2.61119 | ||||||||
\(923\) | 6.36099 | 0.209375 | ||||||||
\(924\) | 65.0572 | 2.14023 | ||||||||
\(925\) | 14.9264 | 0.490779 | ||||||||
\(926\) | −21.0560 | −0.691943 | ||||||||
\(927\) | −8.01343 | −0.263196 | ||||||||
\(928\) | −44.6027 | −1.46415 | ||||||||
\(929\) | −31.0643 | −1.01919 | −0.509594 | − | 0.860415i | \(-0.670204\pi\) | ||||
−0.509594 | + | 0.860415i | \(0.670204\pi\) | |||||||
\(930\) | 46.0326 | 1.50947 | ||||||||
\(931\) | 2.50108 | 0.0819695 | ||||||||
\(932\) | 45.9750 | 1.50596 | ||||||||
\(933\) | −13.4755 | −0.441169 | ||||||||
\(934\) | 2.54555 | 0.0832930 | ||||||||
\(935\) | −14.2602 | −0.466360 | ||||||||
\(936\) | −8.35222 | −0.273001 | ||||||||
\(937\) | 29.5595 | 0.965668 | 0.482834 | − | 0.875712i | \(-0.339608\pi\) | ||||
0.482834 | + | 0.875712i | \(0.339608\pi\) | |||||||
\(938\) | 88.5233 | 2.89039 | ||||||||
\(939\) | −14.1793 | −0.462723 | ||||||||
\(940\) | −78.3438 | −2.55529 | ||||||||
\(941\) | −58.8939 | −1.91989 | −0.959943 | − | 0.280197i | \(-0.909600\pi\) | ||||
−0.959943 | + | 0.280197i | \(0.909600\pi\) | |||||||
\(942\) | −37.2789 | −1.21461 | ||||||||
\(943\) | −1.55904 | −0.0507693 | ||||||||
\(944\) | −33.6503 | −1.09522 | ||||||||
\(945\) | 7.71697 | 0.251033 | ||||||||
\(946\) | 23.7445 | 0.771999 | ||||||||
\(947\) | −41.5581 | −1.35046 | −0.675228 | − | 0.737609i | \(-0.735955\pi\) | ||||
−0.675228 | + | 0.737609i | \(0.735955\pi\) | |||||||
\(948\) | −4.64151 | −0.150749 | ||||||||
\(949\) | 8.80733 | 0.285898 | ||||||||
\(950\) | −31.4148 | −1.01923 | ||||||||
\(951\) | −1.59717 | −0.0517918 | ||||||||
\(952\) | −18.7484 | −0.607639 | ||||||||
\(953\) | 2.91263 | 0.0943494 | 0.0471747 | − | 0.998887i | \(-0.484978\pi\) | ||||
0.0471747 | + | 0.998887i | \(0.484978\pi\) | |||||||
\(954\) | 28.8806 | 0.935046 | ||||||||
\(955\) | −41.2583 | −1.33509 | ||||||||
\(956\) | 24.5325 | 0.793439 | ||||||||
\(957\) | −29.5815 | −0.956233 | ||||||||
\(958\) | −34.0680 | −1.10069 | ||||||||
\(959\) | 28.2976 | 0.913778 | ||||||||
\(960\) | −9.11909 | −0.294317 | ||||||||
\(961\) | 9.63739 | 0.310883 | ||||||||
\(962\) | −16.5528 | −0.533684 | ||||||||
\(963\) | 16.4057 | 0.528668 | ||||||||
\(964\) | −63.6993 | −2.05162 | ||||||||
\(965\) | 20.0095 | 0.644129 | ||||||||
\(966\) | −25.1172 | −0.808131 | ||||||||
\(967\) | −2.35895 | −0.0758586 | −0.0379293 | − | 0.999280i | \(-0.512076\pi\) | ||||
−0.0379293 | + | 0.999280i | \(0.512076\pi\) | |||||||
\(968\) | −101.438 | −3.26034 | ||||||||
\(969\) | 4.27531 | 0.137343 | ||||||||
\(970\) | −49.7147 | −1.59624 | ||||||||
\(971\) | 35.3450 | 1.13427 | 0.567137 | − | 0.823623i | \(-0.308051\pi\) | ||||
0.567137 | + | 0.823623i | \(0.308051\pi\) | |||||||
\(972\) | −4.64151 | −0.148877 | ||||||||
\(973\) | −20.8149 | −0.667297 | ||||||||
\(974\) | −73.0802 | −2.34164 | ||||||||
\(975\) | −3.49824 | −0.112033 | ||||||||
\(976\) | 62.0330 | 1.98563 | ||||||||
\(977\) | −7.53500 | −0.241066 | −0.120533 | − | 0.992709i | \(-0.538460\pi\) | ||||
−0.120533 | + | 0.992709i | \(0.538460\pi\) | |||||||
\(978\) | 9.13966 | 0.292254 | ||||||||
\(979\) | −49.2524 | −1.57411 | ||||||||
\(980\) | 7.60832 | 0.243039 | ||||||||
\(981\) | 13.8530 | 0.442291 | ||||||||
\(982\) | −47.2531 | −1.50791 | ||||||||
\(983\) | 48.2940 | 1.54034 | 0.770169 | − | 0.637839i | \(-0.220172\pi\) | ||||
0.770169 | + | 0.637839i | \(0.220172\pi\) | |||||||
\(984\) | −2.99905 | −0.0956064 | ||||||||
\(985\) | −35.2289 | −1.12248 | ||||||||
\(986\) | 14.9794 | 0.477042 | ||||||||
\(987\) | −16.5903 | −0.528075 | ||||||||
\(988\) | 24.3468 | 0.774576 | ||||||||
\(989\) | −6.40664 | −0.203719 | ||||||||
\(990\) | −36.7503 | −1.16800 | ||||||||
\(991\) | 58.9217 | 1.87171 | 0.935854 | − | 0.352387i | \(-0.114630\pi\) | ||||
0.935854 | + | 0.352387i | \(0.114630\pi\) | |||||||
\(992\) | −48.9172 | −1.55312 | ||||||||
\(993\) | 18.4099 | 0.584219 | ||||||||
\(994\) | 36.7977 | 1.16715 | ||||||||
\(995\) | 71.8892 | 2.27904 | ||||||||
\(996\) | −36.9296 | −1.17016 | ||||||||
\(997\) | −32.2089 | −1.02007 | −0.510034 | − | 0.860154i | \(-0.670367\pi\) | ||||
−0.510034 | + | 0.860154i | \(0.670367\pi\) | |||||||
\(998\) | 5.54477 | 0.175517 | ||||||||
\(999\) | −5.23507 | −0.165630 |
(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 | 4029.2.a.l.1.3 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.3 | ✓ | 32 | 1.1 | even | 1 | trivial |