Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.12375 | −1.50172 | −0.750859 | − | 0.660463i | \(-0.770360\pi\) | ||||
−0.750859 | + | 0.660463i | \(0.770360\pi\) | |||||||
\(3\) | 2.77384 | 1.60148 | 0.800738 | − | 0.599015i | \(-0.204441\pi\) | ||||
0.800738 | + | 0.599015i | \(0.204441\pi\) | |||||||
\(4\) | 2.51031 | 1.25515 | ||||||||
\(5\) | −3.45627 | −1.54569 | −0.772845 | − | 0.634595i | \(-0.781167\pi\) | ||||
−0.772845 | + | 0.634595i | \(0.781167\pi\) | |||||||
\(6\) | −5.89093 | −2.40496 | ||||||||
\(7\) | 3.25214 | 1.22919 | 0.614596 | − | 0.788842i | \(-0.289319\pi\) | ||||
0.614596 | + | 0.788842i | \(0.289319\pi\) | |||||||
\(8\) | −1.08377 | −0.383171 | ||||||||
\(9\) | 4.69417 | 1.56472 | ||||||||
\(10\) | 7.34024 | 2.32119 | ||||||||
\(11\) | −5.33496 | −1.60855 | −0.804276 | − | 0.594256i | \(-0.797447\pi\) | ||||
−0.804276 | + | 0.594256i | \(0.797447\pi\) | |||||||
\(12\) | 6.96319 | 2.01010 | ||||||||
\(13\) | 2.17050 | 0.601988 | 0.300994 | − | 0.953626i | \(-0.402682\pi\) | ||||
0.300994 | + | 0.953626i | \(0.402682\pi\) | |||||||
\(14\) | −6.90672 | −1.84590 | ||||||||
\(15\) | −9.58712 | −2.47538 | ||||||||
\(16\) | −2.71896 | −0.679741 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −9.96923 | −2.34977 | ||||||||
\(19\) | 2.09406 | 0.480409 | 0.240205 | − | 0.970722i | \(-0.422785\pi\) | ||||
0.240205 | + | 0.970722i | \(0.422785\pi\) | |||||||
\(20\) | −8.67630 | −1.94008 | ||||||||
\(21\) | 9.02090 | 1.96852 | ||||||||
\(22\) | 11.3301 | 2.41559 | ||||||||
\(23\) | −5.48026 | −1.14271 | −0.571356 | − | 0.820702i | \(-0.693582\pi\) | ||||
−0.571356 | + | 0.820702i | \(0.693582\pi\) | |||||||
\(24\) | −3.00620 | −0.613638 | ||||||||
\(25\) | 6.94578 | 1.38916 | ||||||||
\(26\) | −4.60959 | −0.904016 | ||||||||
\(27\) | 4.69934 | 0.904389 | ||||||||
\(28\) | 8.16387 | 1.54283 | ||||||||
\(29\) | −2.09170 | −0.388419 | −0.194209 | − | 0.980960i | \(-0.562214\pi\) | ||||
−0.194209 | + | 0.980960i | \(0.562214\pi\) | |||||||
\(30\) | 20.3606 | 3.71733 | ||||||||
\(31\) | −0.138192 | −0.0248200 | −0.0124100 | − | 0.999923i | \(-0.503950\pi\) | ||||
−0.0124100 | + | 0.999923i | \(0.503950\pi\) | |||||||
\(32\) | 7.94194 | 1.40395 | ||||||||
\(33\) | −14.7983 | −2.57606 | ||||||||
\(34\) | −2.12375 | −0.364220 | ||||||||
\(35\) | −11.2403 | −1.89995 | ||||||||
\(36\) | 11.7838 | 1.96397 | ||||||||
\(37\) | −5.49802 | −0.903869 | −0.451934 | − | 0.892051i | \(-0.649266\pi\) | ||||
−0.451934 | + | 0.892051i | \(0.649266\pi\) | |||||||
\(38\) | −4.44725 | −0.721439 | ||||||||
\(39\) | 6.02061 | 0.964069 | ||||||||
\(40\) | 3.74580 | 0.592263 | ||||||||
\(41\) | −0.386277 | −0.0603264 | −0.0301632 | − | 0.999545i | \(-0.509603\pi\) | ||||
−0.0301632 | + | 0.999545i | \(0.509603\pi\) | |||||||
\(42\) | −19.1581 | −2.95616 | ||||||||
\(43\) | 4.98086 | 0.759574 | 0.379787 | − | 0.925074i | \(-0.375997\pi\) | ||||
0.379787 | + | 0.925074i | \(0.375997\pi\) | |||||||
\(44\) | −13.3924 | −2.01898 | ||||||||
\(45\) | −16.2243 | −2.41857 | ||||||||
\(46\) | 11.6387 | 1.71603 | ||||||||
\(47\) | 8.26855 | 1.20609 | 0.603046 | − | 0.797706i | \(-0.293954\pi\) | ||||
0.603046 | + | 0.797706i | \(0.293954\pi\) | |||||||
\(48\) | −7.54196 | −1.08859 | ||||||||
\(49\) | 3.57640 | 0.510914 | ||||||||
\(50\) | −14.7511 | −2.08612 | ||||||||
\(51\) | 2.77384 | 0.388415 | ||||||||
\(52\) | 5.44862 | 0.755588 | ||||||||
\(53\) | −3.34813 | −0.459901 | −0.229950 | − | 0.973202i | \(-0.573856\pi\) | ||||
−0.229950 | + | 0.973202i | \(0.573856\pi\) | |||||||
\(54\) | −9.98022 | −1.35814 | ||||||||
\(55\) | 18.4391 | 2.48632 | ||||||||
\(56\) | −3.52457 | −0.470990 | ||||||||
\(57\) | 5.80857 | 0.769364 | ||||||||
\(58\) | 4.44225 | 0.583295 | ||||||||
\(59\) | 0.787488 | 0.102522 | 0.0512611 | − | 0.998685i | \(-0.483676\pi\) | ||||
0.0512611 | + | 0.998685i | \(0.483676\pi\) | |||||||
\(60\) | −24.0666 | −3.10699 | ||||||||
\(61\) | −3.36097 | −0.430329 | −0.215164 | − | 0.976578i | \(-0.569029\pi\) | ||||
−0.215164 | + | 0.976578i | \(0.569029\pi\) | |||||||
\(62\) | 0.293485 | 0.0372727 | ||||||||
\(63\) | 15.2661 | 1.92334 | ||||||||
\(64\) | −11.4288 | −1.42859 | ||||||||
\(65\) | −7.50182 | −0.930487 | ||||||||
\(66\) | 31.4279 | 3.86851 | ||||||||
\(67\) | 13.5469 | 1.65502 | 0.827508 | − | 0.561454i | \(-0.189758\pi\) | ||||
0.827508 | + | 0.561454i | \(0.189758\pi\) | |||||||
\(68\) | 2.51031 | 0.304420 | ||||||||
\(69\) | −15.2013 | −1.83003 | ||||||||
\(70\) | 23.8715 | 2.85319 | ||||||||
\(71\) | −10.4534 | −1.24059 | −0.620294 | − | 0.784370i | \(-0.712987\pi\) | ||||
−0.620294 | + | 0.784370i | \(0.712987\pi\) | |||||||
\(72\) | −5.08740 | −0.599555 | ||||||||
\(73\) | −11.8049 | −1.38166 | −0.690828 | − | 0.723019i | \(-0.742754\pi\) | ||||
−0.690828 | + | 0.723019i | \(0.742754\pi\) | |||||||
\(74\) | 11.6764 | 1.35736 | ||||||||
\(75\) | 19.2664 | 2.22470 | ||||||||
\(76\) | 5.25673 | 0.602988 | ||||||||
\(77\) | −17.3500 | −1.97722 | ||||||||
\(78\) | −12.7863 | −1.44776 | ||||||||
\(79\) | 1.66029 | 0.186797 | 0.0933987 | − | 0.995629i | \(-0.470227\pi\) | ||||
0.0933987 | + | 0.995629i | \(0.470227\pi\) | |||||||
\(80\) | 9.39746 | 1.05067 | ||||||||
\(81\) | −1.04730 | −0.116367 | ||||||||
\(82\) | 0.820356 | 0.0905932 | ||||||||
\(83\) | −7.83301 | −0.859785 | −0.429892 | − | 0.902880i | \(-0.641449\pi\) | ||||
−0.429892 | + | 0.902880i | \(0.641449\pi\) | |||||||
\(84\) | 22.6452 | 2.47080 | ||||||||
\(85\) | −3.45627 | −0.374885 | ||||||||
\(86\) | −10.5781 | −1.14067 | ||||||||
\(87\) | −5.80203 | −0.622043 | ||||||||
\(88\) | 5.78187 | 0.616350 | ||||||||
\(89\) | −2.30221 | −0.244034 | −0.122017 | − | 0.992528i | \(-0.538936\pi\) | ||||
−0.122017 | + | 0.992528i | \(0.538936\pi\) | |||||||
\(90\) | 34.4563 | 3.63201 | ||||||||
\(91\) | 7.05876 | 0.739959 | ||||||||
\(92\) | −13.7571 | −1.43428 | ||||||||
\(93\) | −0.383322 | −0.0397486 | ||||||||
\(94\) | −17.5603 | −1.81121 | ||||||||
\(95\) | −7.23762 | −0.742564 | ||||||||
\(96\) | 22.0296 | 2.24839 | ||||||||
\(97\) | −10.9355 | −1.11034 | −0.555168 | − | 0.831738i | \(-0.687346\pi\) | ||||
−0.555168 | + | 0.831738i | \(0.687346\pi\) | |||||||
\(98\) | −7.59537 | −0.767249 | ||||||||
\(99\) | −25.0432 | −2.51694 | ||||||||
\(100\) | 17.4360 | 1.74360 | ||||||||
\(101\) | −6.17367 | −0.614303 | −0.307152 | − | 0.951661i | \(-0.599376\pi\) | ||||
−0.307152 | + | 0.951661i | \(0.599376\pi\) | |||||||
\(102\) | −5.89093 | −0.583289 | ||||||||
\(103\) | −8.54660 | −0.842122 | −0.421061 | − | 0.907032i | \(-0.638342\pi\) | ||||
−0.421061 | + | 0.907032i | \(0.638342\pi\) | |||||||
\(104\) | −2.35232 | −0.230664 | ||||||||
\(105\) | −31.1786 | −3.04272 | ||||||||
\(106\) | 7.11059 | 0.690641 | ||||||||
\(107\) | 13.6454 | 1.31915 | 0.659575 | − | 0.751639i | \(-0.270736\pi\) | ||||
0.659575 | + | 0.751639i | \(0.270736\pi\) | |||||||
\(108\) | 11.7968 | 1.13515 | ||||||||
\(109\) | −18.5972 | −1.78129 | −0.890646 | − | 0.454698i | \(-0.849747\pi\) | ||||
−0.890646 | + | 0.454698i | \(0.849747\pi\) | |||||||
\(110\) | −39.1599 | −3.73375 | ||||||||
\(111\) | −15.2506 | −1.44752 | ||||||||
\(112\) | −8.84245 | −0.835533 | ||||||||
\(113\) | −0.859000 | −0.0808079 | −0.0404039 | − | 0.999183i | \(-0.512864\pi\) | ||||
−0.0404039 | + | 0.999183i | \(0.512864\pi\) | |||||||
\(114\) | −12.3359 | −1.15537 | ||||||||
\(115\) | 18.9412 | 1.76628 | ||||||||
\(116\) | −5.25081 | −0.487526 | ||||||||
\(117\) | 10.1887 | 0.941944 | ||||||||
\(118\) | −1.67243 | −0.153959 | ||||||||
\(119\) | 3.25214 | 0.298123 | ||||||||
\(120\) | 10.3902 | 0.948494 | ||||||||
\(121\) | 17.4618 | 1.58744 | ||||||||
\(122\) | 7.13787 | 0.646232 | ||||||||
\(123\) | −1.07147 | −0.0966112 | ||||||||
\(124\) | −0.346905 | −0.0311530 | ||||||||
\(125\) | −6.72512 | −0.601513 | ||||||||
\(126\) | −32.4213 | −2.88832 | ||||||||
\(127\) | 4.76165 | 0.422528 | 0.211264 | − | 0.977429i | \(-0.432242\pi\) | ||||
0.211264 | + | 0.977429i | \(0.432242\pi\) | |||||||
\(128\) | 8.38793 | 0.741395 | ||||||||
\(129\) | 13.8161 | 1.21644 | ||||||||
\(130\) | 15.9320 | 1.39733 | ||||||||
\(131\) | −7.60287 | −0.664266 | −0.332133 | − | 0.943233i | \(-0.607768\pi\) | ||||
−0.332133 | + | 0.943233i | \(0.607768\pi\) | |||||||
\(132\) | −37.1484 | −3.23335 | ||||||||
\(133\) | 6.81016 | 0.590516 | ||||||||
\(134\) | −28.7702 | −2.48537 | ||||||||
\(135\) | −16.2422 | −1.39790 | ||||||||
\(136\) | −1.08377 | −0.0929325 | ||||||||
\(137\) | 2.73494 | 0.233662 | 0.116831 | − | 0.993152i | \(-0.462726\pi\) | ||||
0.116831 | + | 0.993152i | \(0.462726\pi\) | |||||||
\(138\) | 32.2838 | 2.74818 | ||||||||
\(139\) | 0.258845 | 0.0219549 | 0.0109775 | − | 0.999940i | \(-0.496506\pi\) | ||||
0.0109775 | + | 0.999940i | \(0.496506\pi\) | |||||||
\(140\) | −28.2165 | −2.38473 | ||||||||
\(141\) | 22.9356 | 1.93153 | ||||||||
\(142\) | 22.2003 | 1.86301 | ||||||||
\(143\) | −11.5795 | −0.968329 | ||||||||
\(144\) | −12.7633 | −1.06361 | ||||||||
\(145\) | 7.22947 | 0.600375 | ||||||||
\(146\) | 25.0706 | 2.07486 | ||||||||
\(147\) | 9.92034 | 0.818216 | ||||||||
\(148\) | −13.8017 | −1.13450 | ||||||||
\(149\) | 1.20004 | 0.0983114 | 0.0491557 | − | 0.998791i | \(-0.484347\pi\) | ||||
0.0491557 | + | 0.998791i | \(0.484347\pi\) | |||||||
\(150\) | −40.9171 | −3.34087 | ||||||||
\(151\) | 3.05105 | 0.248291 | 0.124146 | − | 0.992264i | \(-0.460381\pi\) | ||||
0.124146 | + | 0.992264i | \(0.460381\pi\) | |||||||
\(152\) | −2.26948 | −0.184079 | ||||||||
\(153\) | 4.69417 | 0.379501 | ||||||||
\(154\) | 36.8471 | 2.96923 | ||||||||
\(155\) | 0.477628 | 0.0383640 | ||||||||
\(156\) | 15.1136 | 1.21006 | ||||||||
\(157\) | 5.87738 | 0.469066 | 0.234533 | − | 0.972108i | \(-0.424644\pi\) | ||||
0.234533 | + | 0.972108i | \(0.424644\pi\) | |||||||
\(158\) | −3.52604 | −0.280517 | ||||||||
\(159\) | −9.28716 | −0.736520 | ||||||||
\(160\) | −27.4495 | −2.17007 | ||||||||
\(161\) | −17.8225 | −1.40461 | ||||||||
\(162\) | 2.22420 | 0.174750 | ||||||||
\(163\) | −1.60461 | −0.125683 | −0.0628413 | − | 0.998024i | \(-0.520016\pi\) | ||||
−0.0628413 | + | 0.998024i | \(0.520016\pi\) | |||||||
\(164\) | −0.969676 | −0.0757190 | ||||||||
\(165\) | 51.1469 | 3.98178 | ||||||||
\(166\) | 16.6354 | 1.29115 | ||||||||
\(167\) | 12.1562 | 0.940671 | 0.470336 | − | 0.882488i | \(-0.344133\pi\) | ||||
0.470336 | + | 0.882488i | \(0.344133\pi\) | |||||||
\(168\) | −9.77658 | −0.754279 | ||||||||
\(169\) | −8.28893 | −0.637610 | ||||||||
\(170\) | 7.34024 | 0.562971 | ||||||||
\(171\) | 9.82985 | 0.751707 | ||||||||
\(172\) | 12.5035 | 0.953383 | ||||||||
\(173\) | −11.2445 | −0.854901 | −0.427450 | − | 0.904039i | \(-0.640588\pi\) | ||||
−0.427450 | + | 0.904039i | \(0.640588\pi\) | |||||||
\(174\) | 12.3221 | 0.934133 | ||||||||
\(175\) | 22.5886 | 1.70754 | ||||||||
\(176\) | 14.5056 | 1.09340 | ||||||||
\(177\) | 2.18436 | 0.164187 | ||||||||
\(178\) | 4.88932 | 0.366470 | ||||||||
\(179\) | 25.7743 | 1.92646 | 0.963232 | − | 0.268671i | \(-0.0865846\pi\) | ||||
0.963232 | + | 0.268671i | \(0.0865846\pi\) | |||||||
\(180\) | −40.7280 | −3.03569 | ||||||||
\(181\) | −9.62684 | −0.715557 | −0.357779 | − | 0.933806i | \(-0.616466\pi\) | ||||
−0.357779 | + | 0.933806i | \(0.616466\pi\) | |||||||
\(182\) | −14.9910 | −1.11121 | ||||||||
\(183\) | −9.32279 | −0.689161 | ||||||||
\(184\) | 5.93934 | 0.437854 | ||||||||
\(185\) | 19.0026 | 1.39710 | ||||||||
\(186\) | 0.814080 | 0.0596912 | ||||||||
\(187\) | −5.33496 | −0.390131 | ||||||||
\(188\) | 20.7566 | 1.51383 | ||||||||
\(189\) | 15.2829 | 1.11167 | ||||||||
\(190\) | 15.3709 | 1.11512 | ||||||||
\(191\) | 11.9297 | 0.863205 | 0.431603 | − | 0.902064i | \(-0.357948\pi\) | ||||
0.431603 | + | 0.902064i | \(0.357948\pi\) | |||||||
\(192\) | −31.7015 | −2.28786 | ||||||||
\(193\) | −8.62887 | −0.621119 | −0.310560 | − | 0.950554i | \(-0.600516\pi\) | ||||
−0.310560 | + | 0.950554i | \(0.600516\pi\) | |||||||
\(194\) | 23.2243 | 1.66741 | ||||||||
\(195\) | −20.8088 | −1.49015 | ||||||||
\(196\) | 8.97787 | 0.641276 | ||||||||
\(197\) | −11.3723 | −0.810241 | −0.405120 | − | 0.914263i | \(-0.632770\pi\) | ||||
−0.405120 | + | 0.914263i | \(0.632770\pi\) | |||||||
\(198\) | 53.1855 | 3.77973 | ||||||||
\(199\) | −6.68690 | −0.474022 | −0.237011 | − | 0.971507i | \(-0.576168\pi\) | ||||
−0.237011 | + | 0.971507i | \(0.576168\pi\) | |||||||
\(200\) | −7.52762 | −0.532283 | ||||||||
\(201\) | 37.5769 | 2.65047 | ||||||||
\(202\) | 13.1113 | 0.922510 | ||||||||
\(203\) | −6.80250 | −0.477442 | ||||||||
\(204\) | 6.96319 | 0.487521 | ||||||||
\(205\) | 1.33508 | 0.0932459 | ||||||||
\(206\) | 18.1508 | 1.26463 | ||||||||
\(207\) | −25.7252 | −1.78803 | ||||||||
\(208\) | −5.90151 | −0.409196 | ||||||||
\(209\) | −11.1717 | −0.772764 | ||||||||
\(210\) | 66.2156 | 4.56931 | ||||||||
\(211\) | −26.7490 | −1.84148 | −0.920738 | − | 0.390182i | \(-0.872412\pi\) | ||||
−0.920738 | + | 0.390182i | \(0.872412\pi\) | |||||||
\(212\) | −8.40484 | −0.577247 | ||||||||
\(213\) | −28.9960 | −1.98677 | ||||||||
\(214\) | −28.9794 | −1.98099 | ||||||||
\(215\) | −17.2152 | −1.17407 | ||||||||
\(216\) | −5.09300 | −0.346535 | ||||||||
\(217\) | −0.449419 | −0.0305086 | ||||||||
\(218\) | 39.4958 | 2.67500 | ||||||||
\(219\) | −32.7448 | −2.21269 | ||||||||
\(220\) | 46.2877 | 3.12072 | ||||||||
\(221\) | 2.17050 | 0.146004 | ||||||||
\(222\) | 32.3885 | 2.17377 | ||||||||
\(223\) | −14.6372 | −0.980177 | −0.490089 | − | 0.871673i | \(-0.663036\pi\) | ||||
−0.490089 | + | 0.871673i | \(0.663036\pi\) | |||||||
\(224\) | 25.8283 | 1.72572 | ||||||||
\(225\) | 32.6046 | 2.17364 | ||||||||
\(226\) | 1.82430 | 0.121351 | ||||||||
\(227\) | −9.01583 | −0.598402 | −0.299201 | − | 0.954190i | \(-0.596720\pi\) | ||||
−0.299201 | + | 0.954190i | \(0.596720\pi\) | |||||||
\(228\) | 14.5813 | 0.965671 | ||||||||
\(229\) | 9.90426 | 0.654492 | 0.327246 | − | 0.944939i | \(-0.393879\pi\) | ||||
0.327246 | + | 0.944939i | \(0.393879\pi\) | |||||||
\(230\) | −40.2264 | −2.65245 | ||||||||
\(231\) | −48.1262 | −3.16647 | ||||||||
\(232\) | 2.26692 | 0.148831 | ||||||||
\(233\) | −20.1515 | −1.32017 | −0.660085 | − | 0.751191i | \(-0.729480\pi\) | ||||
−0.660085 | + | 0.751191i | \(0.729480\pi\) | |||||||
\(234\) | −21.6382 | −1.41453 | ||||||||
\(235\) | −28.5783 | −1.86424 | ||||||||
\(236\) | 1.97684 | 0.128681 | ||||||||
\(237\) | 4.60538 | 0.299151 | ||||||||
\(238\) | −6.90672 | −0.447696 | ||||||||
\(239\) | −20.8975 | −1.35175 | −0.675873 | − | 0.737018i | \(-0.736233\pi\) | ||||
−0.675873 | + | 0.737018i | \(0.736233\pi\) | |||||||
\(240\) | 26.0670 | 1.68262 | ||||||||
\(241\) | 21.2359 | 1.36793 | 0.683963 | − | 0.729517i | \(-0.260255\pi\) | ||||
0.683963 | + | 0.729517i | \(0.260255\pi\) | |||||||
\(242\) | −37.0845 | −2.38389 | ||||||||
\(243\) | −17.0031 | −1.09075 | ||||||||
\(244\) | −8.43709 | −0.540129 | ||||||||
\(245\) | −12.3610 | −0.789714 | ||||||||
\(246\) | 2.27553 | 0.145083 | ||||||||
\(247\) | 4.54515 | 0.289201 | ||||||||
\(248\) | 0.149768 | 0.00951030 | ||||||||
\(249\) | −21.7275 | −1.37692 | ||||||||
\(250\) | 14.2825 | 0.903303 | ||||||||
\(251\) | 10.8205 | 0.682987 | 0.341493 | − | 0.939884i | \(-0.389067\pi\) | ||||
0.341493 | + | 0.939884i | \(0.389067\pi\) | |||||||
\(252\) | 38.3226 | 2.41410 | ||||||||
\(253\) | 29.2370 | 1.83811 | ||||||||
\(254\) | −10.1125 | −0.634518 | ||||||||
\(255\) | −9.58712 | −0.600368 | ||||||||
\(256\) | 5.04365 | 0.315228 | ||||||||
\(257\) | −24.3139 | −1.51666 | −0.758329 | − | 0.651872i | \(-0.773984\pi\) | ||||
−0.758329 | + | 0.651872i | \(0.773984\pi\) | |||||||
\(258\) | −29.3419 | −1.82675 | ||||||||
\(259\) | −17.8803 | −1.11103 | ||||||||
\(260\) | −18.8319 | −1.16790 | ||||||||
\(261\) | −9.81879 | −0.607768 | ||||||||
\(262\) | 16.1466 | 0.997540 | ||||||||
\(263\) | 11.0228 | 0.679693 | 0.339847 | − | 0.940481i | \(-0.389625\pi\) | ||||
0.339847 | + | 0.940481i | \(0.389625\pi\) | |||||||
\(264\) | 16.0380 | 0.987069 | ||||||||
\(265\) | 11.5720 | 0.710864 | ||||||||
\(266\) | −14.4631 | −0.886788 | ||||||||
\(267\) | −6.38596 | −0.390815 | ||||||||
\(268\) | 34.0069 | 2.07730 | ||||||||
\(269\) | 31.6610 | 1.93040 | 0.965202 | − | 0.261505i | \(-0.0842189\pi\) | ||||
0.965202 | + | 0.261505i | \(0.0842189\pi\) | |||||||
\(270\) | 34.4943 | 2.09926 | ||||||||
\(271\) | 16.2337 | 0.986125 | 0.493063 | − | 0.869994i | \(-0.335877\pi\) | ||||
0.493063 | + | 0.869994i | \(0.335877\pi\) | |||||||
\(272\) | −2.71896 | −0.164861 | ||||||||
\(273\) | 19.5798 | 1.18503 | ||||||||
\(274\) | −5.80833 | −0.350894 | ||||||||
\(275\) | −37.0555 | −2.23453 | ||||||||
\(276\) | −38.1600 | −2.29697 | ||||||||
\(277\) | 9.75341 | 0.586026 | 0.293013 | − | 0.956108i | \(-0.405342\pi\) | ||||
0.293013 | + | 0.956108i | \(0.405342\pi\) | |||||||
\(278\) | −0.549721 | −0.0329701 | ||||||||
\(279\) | −0.648696 | −0.0388364 | ||||||||
\(280\) | 12.1818 | 0.728005 | ||||||||
\(281\) | −30.9772 | −1.84794 | −0.923971 | − | 0.382462i | \(-0.875076\pi\) | ||||
−0.923971 | + | 0.382462i | \(0.875076\pi\) | |||||||
\(282\) | −48.7095 | −2.90061 | ||||||||
\(283\) | −22.1500 | −1.31668 | −0.658339 | − | 0.752721i | \(-0.728741\pi\) | ||||
−0.658339 | + | 0.752721i | \(0.728741\pi\) | |||||||
\(284\) | −26.2412 | −1.55713 | ||||||||
\(285\) | −20.0760 | −1.18920 | ||||||||
\(286\) | 24.5920 | 1.45416 | ||||||||
\(287\) | −1.25623 | −0.0741528 | ||||||||
\(288\) | 37.2808 | 2.19679 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −15.3536 | −0.901593 | ||||||||
\(291\) | −30.3334 | −1.77818 | ||||||||
\(292\) | −29.6339 | −1.73419 | ||||||||
\(293\) | −11.4551 | −0.669215 | −0.334608 | − | 0.942358i | \(-0.608604\pi\) | ||||
−0.334608 | + | 0.942358i | \(0.608604\pi\) | |||||||
\(294\) | −21.0683 | −1.22873 | ||||||||
\(295\) | −2.72177 | −0.158467 | ||||||||
\(296\) | 5.95859 | 0.346336 | ||||||||
\(297\) | −25.0708 | −1.45476 | ||||||||
\(298\) | −2.54859 | −0.147636 | ||||||||
\(299\) | −11.8949 | −0.687899 | ||||||||
\(300\) | 48.3647 | 2.79234 | ||||||||
\(301\) | 16.1984 | 0.933663 | ||||||||
\(302\) | −6.47967 | −0.372863 | ||||||||
\(303\) | −17.1247 | −0.983791 | ||||||||
\(304\) | −5.69366 | −0.326554 | ||||||||
\(305\) | 11.6164 | 0.665154 | ||||||||
\(306\) | −9.96923 | −0.569903 | ||||||||
\(307\) | 0.681164 | 0.0388761 | 0.0194381 | − | 0.999811i | \(-0.493812\pi\) | ||||
0.0194381 | + | 0.999811i | \(0.493812\pi\) | |||||||
\(308\) | −43.5540 | −2.48172 | ||||||||
\(309\) | −23.7069 | −1.34864 | ||||||||
\(310\) | −1.01436 | −0.0576119 | ||||||||
\(311\) | 10.1569 | 0.575946 | 0.287973 | − | 0.957639i | \(-0.407019\pi\) | ||||
0.287973 | + | 0.957639i | \(0.407019\pi\) | |||||||
\(312\) | −6.52495 | −0.369403 | ||||||||
\(313\) | 18.9282 | 1.06988 | 0.534942 | − | 0.844889i | \(-0.320334\pi\) | ||||
0.534942 | + | 0.844889i | \(0.320334\pi\) | |||||||
\(314\) | −12.4821 | −0.704405 | ||||||||
\(315\) | −52.7636 | −2.97289 | ||||||||
\(316\) | 4.16785 | 0.234460 | ||||||||
\(317\) | −23.7066 | −1.33149 | −0.665747 | − | 0.746178i | \(-0.731887\pi\) | ||||
−0.665747 | + | 0.746178i | \(0.731887\pi\) | |||||||
\(318\) | 19.7236 | 1.10604 | ||||||||
\(319\) | 11.1591 | 0.624792 | ||||||||
\(320\) | 39.5008 | 2.20816 | ||||||||
\(321\) | 37.8501 | 2.11259 | ||||||||
\(322\) | 37.8506 | 2.10933 | ||||||||
\(323\) | 2.09406 | 0.116516 | ||||||||
\(324\) | −2.62904 | −0.146058 | ||||||||
\(325\) | 15.0758 | 0.836255 | ||||||||
\(326\) | 3.40778 | 0.188740 | ||||||||
\(327\) | −51.5857 | −2.85269 | ||||||||
\(328\) | 0.418636 | 0.0231153 | ||||||||
\(329\) | 26.8905 | 1.48252 | ||||||||
\(330\) | −108.623 | −5.97951 | ||||||||
\(331\) | 15.5842 | 0.856587 | 0.428294 | − | 0.903640i | \(-0.359115\pi\) | ||||
0.428294 | + | 0.903640i | \(0.359115\pi\) | |||||||
\(332\) | −19.6633 | −1.07916 | ||||||||
\(333\) | −25.8086 | −1.41430 | ||||||||
\(334\) | −25.8166 | −1.41262 | ||||||||
\(335\) | −46.8217 | −2.55814 | ||||||||
\(336\) | −24.5275 | −1.33808 | ||||||||
\(337\) | −16.8724 | −0.919099 | −0.459549 | − | 0.888152i | \(-0.651989\pi\) | ||||
−0.459549 | + | 0.888152i | \(0.651989\pi\) | |||||||
\(338\) | 17.6036 | 0.957510 | ||||||||
\(339\) | −2.38272 | −0.129412 | ||||||||
\(340\) | −8.67630 | −0.470538 | ||||||||
\(341\) | 0.737249 | 0.0399243 | ||||||||
\(342\) | −20.8761 | −1.12885 | ||||||||
\(343\) | −11.1340 | −0.601181 | ||||||||
\(344\) | −5.39811 | −0.291046 | ||||||||
\(345\) | 52.5398 | 2.82865 | ||||||||
\(346\) | 23.8804 | 1.28382 | ||||||||
\(347\) | 33.8328 | 1.81624 | 0.908119 | − | 0.418712i | \(-0.137518\pi\) | ||||
0.908119 | + | 0.418712i | \(0.137518\pi\) | |||||||
\(348\) | −14.5649 | −0.780761 | ||||||||
\(349\) | −15.0963 | −0.808088 | −0.404044 | − | 0.914739i | \(-0.632396\pi\) | ||||
−0.404044 | + | 0.914739i | \(0.632396\pi\) | |||||||
\(350\) | −47.9726 | −2.56424 | ||||||||
\(351\) | 10.1999 | 0.544431 | ||||||||
\(352\) | −42.3699 | −2.25833 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | −4.63904 | −0.246562 | ||||||||
\(355\) | 36.1297 | 1.91756 | ||||||||
\(356\) | −5.77927 | −0.306301 | ||||||||
\(357\) | 9.02090 | 0.477436 | ||||||||
\(358\) | −54.7382 | −2.89300 | ||||||||
\(359\) | −32.1092 | −1.69466 | −0.847328 | − | 0.531069i | \(-0.821790\pi\) | ||||
−0.847328 | + | 0.531069i | \(0.821790\pi\) | |||||||
\(360\) | 17.5834 | 0.926726 | ||||||||
\(361\) | −14.6149 | −0.769207 | ||||||||
\(362\) | 20.4450 | 1.07456 | ||||||||
\(363\) | 48.4363 | 2.54224 | ||||||||
\(364\) | 17.7197 | 0.928763 | ||||||||
\(365\) | 40.8008 | 2.13561 | ||||||||
\(366\) | 19.7993 | 1.03492 | ||||||||
\(367\) | −16.7185 | −0.872701 | −0.436350 | − | 0.899777i | \(-0.643729\pi\) | ||||
−0.436350 | + | 0.899777i | \(0.643729\pi\) | |||||||
\(368\) | 14.9006 | 0.776749 | ||||||||
\(369\) | −1.81325 | −0.0943941 | ||||||||
\(370\) | −40.3568 | −2.09805 | ||||||||
\(371\) | −10.8886 | −0.565307 | ||||||||
\(372\) | −0.962257 | −0.0498907 | ||||||||
\(373\) | −8.86264 | −0.458890 | −0.229445 | − | 0.973322i | \(-0.573691\pi\) | ||||
−0.229445 | + | 0.973322i | \(0.573691\pi\) | |||||||
\(374\) | 11.3301 | 0.585867 | ||||||||
\(375\) | −18.6544 | −0.963308 | ||||||||
\(376\) | −8.96121 | −0.462139 | ||||||||
\(377\) | −4.54003 | −0.233824 | ||||||||
\(378\) | −32.4571 | −1.66941 | ||||||||
\(379\) | 17.5325 | 0.900586 | 0.450293 | − | 0.892881i | \(-0.351320\pi\) | ||||
0.450293 | + | 0.892881i | \(0.351320\pi\) | |||||||
\(380\) | −18.1687 | −0.932032 | ||||||||
\(381\) | 13.2080 | 0.676668 | ||||||||
\(382\) | −25.3358 | −1.29629 | ||||||||
\(383\) | −16.5227 | −0.844268 | −0.422134 | − | 0.906533i | \(-0.638719\pi\) | ||||
−0.422134 | + | 0.906533i | \(0.638719\pi\) | |||||||
\(384\) | 23.2667 | 1.18733 | ||||||||
\(385\) | 59.9663 | 3.05617 | ||||||||
\(386\) | 18.3255 | 0.932746 | ||||||||
\(387\) | 23.3810 | 1.18852 | ||||||||
\(388\) | −27.4516 | −1.39364 | ||||||||
\(389\) | 25.5025 | 1.29303 | 0.646514 | − | 0.762902i | \(-0.276226\pi\) | ||||
0.646514 | + | 0.762902i | \(0.276226\pi\) | |||||||
\(390\) | 44.1927 | 2.23779 | ||||||||
\(391\) | −5.48026 | −0.277148 | ||||||||
\(392\) | −3.87599 | −0.195767 | ||||||||
\(393\) | −21.0891 | −1.06381 | ||||||||
\(394\) | 24.1518 | 1.21675 | ||||||||
\(395\) | −5.73841 | −0.288731 | ||||||||
\(396\) | −62.8662 | −3.15915 | ||||||||
\(397\) | −27.7984 | −1.39516 | −0.697581 | − | 0.716506i | \(-0.745740\pi\) | ||||
−0.697581 | + | 0.716506i | \(0.745740\pi\) | |||||||
\(398\) | 14.2013 | 0.711847 | ||||||||
\(399\) | 18.8903 | 0.945696 | ||||||||
\(400\) | −18.8853 | −0.944266 | ||||||||
\(401\) | −36.1883 | −1.80716 | −0.903578 | − | 0.428423i | \(-0.859069\pi\) | ||||
−0.903578 | + | 0.428423i | \(0.859069\pi\) | |||||||
\(402\) | −79.8038 | −3.98025 | ||||||||
\(403\) | −0.299946 | −0.0149414 | ||||||||
\(404\) | −15.4978 | −0.771045 | ||||||||
\(405\) | 3.61974 | 0.179866 | ||||||||
\(406\) | 14.4468 | 0.716982 | ||||||||
\(407\) | 29.3317 | 1.45392 | ||||||||
\(408\) | −3.00620 | −0.148829 | ||||||||
\(409\) | −9.40959 | −0.465274 | −0.232637 | − | 0.972564i | \(-0.574735\pi\) | ||||
−0.232637 | + | 0.972564i | \(0.574735\pi\) | |||||||
\(410\) | −2.83537 | −0.140029 | ||||||||
\(411\) | 7.58628 | 0.374203 | ||||||||
\(412\) | −21.4546 | −1.05699 | ||||||||
\(413\) | 2.56102 | 0.126019 | ||||||||
\(414\) | 54.6339 | 2.68511 | ||||||||
\(415\) | 27.0730 | 1.32896 | ||||||||
\(416\) | 17.2380 | 0.845161 | ||||||||
\(417\) | 0.717993 | 0.0351603 | ||||||||
\(418\) | 23.7259 | 1.16047 | ||||||||
\(419\) | 33.4725 | 1.63524 | 0.817619 | − | 0.575759i | \(-0.195293\pi\) | ||||
0.817619 | + | 0.575759i | \(0.195293\pi\) | |||||||
\(420\) | −78.2680 | −3.81909 | ||||||||
\(421\) | −8.50570 | −0.414542 | −0.207271 | − | 0.978284i | \(-0.566458\pi\) | ||||
−0.207271 | + | 0.978284i | \(0.566458\pi\) | |||||||
\(422\) | 56.8081 | 2.76538 | ||||||||
\(423\) | 38.8140 | 1.88720 | ||||||||
\(424\) | 3.62860 | 0.176220 | ||||||||
\(425\) | 6.94578 | 0.336920 | ||||||||
\(426\) | 61.5801 | 2.98357 | ||||||||
\(427\) | −10.9304 | −0.528957 | ||||||||
\(428\) | 34.2542 | 1.65574 | ||||||||
\(429\) | −32.1197 | −1.55075 | ||||||||
\(430\) | 36.5607 | 1.76311 | ||||||||
\(431\) | 8.98731 | 0.432903 | 0.216452 | − | 0.976293i | \(-0.430552\pi\) | ||||
0.216452 | + | 0.976293i | \(0.430552\pi\) | |||||||
\(432\) | −12.7773 | −0.614750 | ||||||||
\(433\) | 25.3643 | 1.21893 | 0.609464 | − | 0.792813i | \(-0.291385\pi\) | ||||
0.609464 | + | 0.792813i | \(0.291385\pi\) | |||||||
\(434\) | 0.954454 | 0.0458153 | ||||||||
\(435\) | 20.0534 | 0.961485 | ||||||||
\(436\) | −46.6848 | −2.23580 | ||||||||
\(437\) | −11.4760 | −0.548970 | ||||||||
\(438\) | 69.5417 | 3.32283 | ||||||||
\(439\) | −6.48964 | −0.309734 | −0.154867 | − | 0.987935i | \(-0.549495\pi\) | ||||
−0.154867 | + | 0.987935i | \(0.549495\pi\) | |||||||
\(440\) | −19.9837 | −0.952685 | ||||||||
\(441\) | 16.7882 | 0.799439 | ||||||||
\(442\) | −4.60959 | −0.219256 | ||||||||
\(443\) | 6.52882 | 0.310193 | 0.155097 | − | 0.987899i | \(-0.450431\pi\) | ||||
0.155097 | + | 0.987899i | \(0.450431\pi\) | |||||||
\(444\) | −38.2837 | −1.81687 | ||||||||
\(445\) | 7.95706 | 0.377201 | ||||||||
\(446\) | 31.0857 | 1.47195 | ||||||||
\(447\) | 3.32873 | 0.157443 | ||||||||
\(448\) | −37.1679 | −1.75602 | ||||||||
\(449\) | 15.5154 | 0.732216 | 0.366108 | − | 0.930572i | \(-0.380690\pi\) | ||||
0.366108 | + | 0.930572i | \(0.380690\pi\) | |||||||
\(450\) | −69.2441 | −3.26420 | ||||||||
\(451\) | 2.06078 | 0.0970382 | ||||||||
\(452\) | −2.15636 | −0.101426 | ||||||||
\(453\) | 8.46313 | 0.397632 | ||||||||
\(454\) | 19.1474 | 0.898631 | ||||||||
\(455\) | −24.3970 | −1.14375 | ||||||||
\(456\) | −6.29515 | −0.294797 | ||||||||
\(457\) | −7.17015 | −0.335405 | −0.167703 | − | 0.985838i | \(-0.553635\pi\) | ||||
−0.167703 | + | 0.985838i | \(0.553635\pi\) | |||||||
\(458\) | −21.0342 | −0.982862 | ||||||||
\(459\) | 4.69934 | 0.219346 | ||||||||
\(460\) | 47.5483 | 2.21695 | ||||||||
\(461\) | 11.8457 | 0.551710 | 0.275855 | − | 0.961199i | \(-0.411039\pi\) | ||||
0.275855 | + | 0.961199i | \(0.411039\pi\) | |||||||
\(462\) | 102.208 | 4.75514 | ||||||||
\(463\) | 0.272759 | 0.0126762 | 0.00633809 | − | 0.999980i | \(-0.497983\pi\) | ||||
0.00633809 | + | 0.999980i | \(0.497983\pi\) | |||||||
\(464\) | 5.68726 | 0.264024 | ||||||||
\(465\) | 1.32486 | 0.0614390 | ||||||||
\(466\) | 42.7968 | 1.98252 | ||||||||
\(467\) | −15.0793 | −0.697786 | −0.348893 | − | 0.937163i | \(-0.613442\pi\) | ||||
−0.348893 | + | 0.937163i | \(0.613442\pi\) | |||||||
\(468\) | 25.5768 | 1.18229 | ||||||||
\(469\) | 44.0564 | 2.03433 | ||||||||
\(470\) | 60.6932 | 2.79957 | ||||||||
\(471\) | 16.3029 | 0.751198 | ||||||||
\(472\) | −0.853455 | −0.0392835 | ||||||||
\(473\) | −26.5727 | −1.22181 | ||||||||
\(474\) | −9.78066 | −0.449241 | ||||||||
\(475\) | 14.5448 | 0.667363 | ||||||||
\(476\) | 8.16387 | 0.374190 | ||||||||
\(477\) | −15.7167 | −0.719617 | ||||||||
\(478\) | 44.3810 | 2.02994 | ||||||||
\(479\) | −22.2481 | −1.01654 | −0.508270 | − | 0.861198i | \(-0.669715\pi\) | ||||
−0.508270 | + | 0.861198i | \(0.669715\pi\) | |||||||
\(480\) | −76.1403 | −3.47531 | ||||||||
\(481\) | −11.9334 | −0.544118 | ||||||||
\(482\) | −45.0998 | −2.05424 | ||||||||
\(483\) | −49.4368 | −2.24945 | ||||||||
\(484\) | 43.8346 | 1.99248 | ||||||||
\(485\) | 37.7961 | 1.71623 | ||||||||
\(486\) | 36.1102 | 1.63799 | ||||||||
\(487\) | −43.2599 | −1.96029 | −0.980147 | − | 0.198270i | \(-0.936468\pi\) | ||||
−0.980147 | + | 0.198270i | \(0.936468\pi\) | |||||||
\(488\) | 3.64252 | 0.164889 | ||||||||
\(489\) | −4.45092 | −0.201277 | ||||||||
\(490\) | 26.2516 | 1.18593 | ||||||||
\(491\) | 14.2569 | 0.643404 | 0.321702 | − | 0.946841i | \(-0.395745\pi\) | ||||
0.321702 | + | 0.946841i | \(0.395745\pi\) | |||||||
\(492\) | −2.68972 | −0.121262 | ||||||||
\(493\) | −2.09170 | −0.0942054 | ||||||||
\(494\) | −9.65275 | −0.434298 | ||||||||
\(495\) | 86.5560 | 3.89040 | ||||||||
\(496\) | 0.375739 | 0.0168712 | ||||||||
\(497\) | −33.9958 | −1.52492 | ||||||||
\(498\) | 46.1437 | 2.06775 | ||||||||
\(499\) | −33.3879 | −1.49465 | −0.747323 | − | 0.664461i | \(-0.768661\pi\) | ||||
−0.747323 | + | 0.664461i | \(0.768661\pi\) | |||||||
\(500\) | −16.8821 | −0.754992 | ||||||||
\(501\) | 33.7192 | 1.50646 | ||||||||
\(502\) | −22.9801 | −1.02565 | ||||||||
\(503\) | −7.96211 | −0.355013 | −0.177506 | − | 0.984120i | \(-0.556803\pi\) | ||||
−0.177506 | + | 0.984120i | \(0.556803\pi\) | |||||||
\(504\) | −16.5449 | −0.736969 | ||||||||
\(505\) | 21.3378 | 0.949522 | ||||||||
\(506\) | −62.0920 | −2.76032 | ||||||||
\(507\) | −22.9921 | −1.02112 | ||||||||
\(508\) | 11.9532 | 0.530338 | ||||||||
\(509\) | −0.0505329 | −0.00223983 | −0.00111992 | − | 0.999999i | \(-0.500356\pi\) | ||||
−0.00111992 | + | 0.999999i | \(0.500356\pi\) | |||||||
\(510\) | 20.3606 | 0.901584 | ||||||||
\(511\) | −38.3911 | −1.69832 | ||||||||
\(512\) | −27.4873 | −1.21478 | ||||||||
\(513\) | 9.84068 | 0.434477 | ||||||||
\(514\) | 51.6366 | 2.27759 | ||||||||
\(515\) | 29.5393 | 1.30166 | ||||||||
\(516\) | 34.6827 | 1.52682 | ||||||||
\(517\) | −44.1124 | −1.94006 | ||||||||
\(518\) | 37.9733 | 1.66845 | ||||||||
\(519\) | −31.1903 | −1.36910 | ||||||||
\(520\) | 8.13025 | 0.356535 | ||||||||
\(521\) | −28.7497 | −1.25955 | −0.629773 | − | 0.776779i | \(-0.716852\pi\) | ||||
−0.629773 | + | 0.776779i | \(0.716852\pi\) | |||||||
\(522\) | 20.8526 | 0.912695 | ||||||||
\(523\) | 17.0733 | 0.746565 | 0.373283 | − | 0.927718i | \(-0.378232\pi\) | ||||
0.373283 | + | 0.927718i | \(0.378232\pi\) | |||||||
\(524\) | −19.0856 | −0.833757 | ||||||||
\(525\) | 62.6571 | 2.73458 | ||||||||
\(526\) | −23.4096 | −1.02071 | ||||||||
\(527\) | −0.138192 | −0.00601974 | ||||||||
\(528\) | 40.2361 | 1.75105 | ||||||||
\(529\) | 7.03320 | 0.305791 | ||||||||
\(530\) | −24.5761 | −1.06752 | ||||||||
\(531\) | 3.69660 | 0.160419 | ||||||||
\(532\) | 17.0956 | 0.741189 | ||||||||
\(533\) | −0.838415 | −0.0363158 | ||||||||
\(534\) | 13.5622 | 0.586893 | ||||||||
\(535\) | −47.1621 | −2.03900 | ||||||||
\(536\) | −14.6817 | −0.634153 | ||||||||
\(537\) | 71.4938 | 3.08518 | ||||||||
\(538\) | −67.2400 | −2.89892 | ||||||||
\(539\) | −19.0800 | −0.821832 | ||||||||
\(540\) | −40.7729 | −1.75459 | ||||||||
\(541\) | 29.5546 | 1.27065 | 0.635325 | − | 0.772245i | \(-0.280866\pi\) | ||||
0.635325 | + | 0.772245i | \(0.280866\pi\) | |||||||
\(542\) | −34.4762 | −1.48088 | ||||||||
\(543\) | −26.7033 | −1.14595 | ||||||||
\(544\) | 7.94194 | 0.340508 | ||||||||
\(545\) | 64.2770 | 2.75332 | ||||||||
\(546\) | −41.5827 | −1.77957 | ||||||||
\(547\) | −27.0705 | −1.15745 | −0.578727 | − | 0.815522i | \(-0.696450\pi\) | ||||
−0.578727 | + | 0.815522i | \(0.696450\pi\) | |||||||
\(548\) | 6.86555 | 0.293282 | ||||||||
\(549\) | −15.7770 | −0.673345 | ||||||||
\(550\) | 78.6965 | 3.35563 | ||||||||
\(551\) | −4.38014 | −0.186600 | ||||||||
\(552\) | 16.4747 | 0.701212 | ||||||||
\(553\) | 5.39950 | 0.229610 | ||||||||
\(554\) | −20.7138 | −0.880045 | ||||||||
\(555\) | 52.7101 | 2.23742 | ||||||||
\(556\) | 0.649780 | 0.0275568 | ||||||||
\(557\) | 1.65013 | 0.0699183 | 0.0349592 | − | 0.999389i | \(-0.488870\pi\) | ||||
0.0349592 | + | 0.999389i | \(0.488870\pi\) | |||||||
\(558\) | 1.37767 | 0.0583213 | ||||||||
\(559\) | 10.8110 | 0.457255 | ||||||||
\(560\) | 30.5618 | 1.29147 | ||||||||
\(561\) | −14.7983 | −0.624785 | ||||||||
\(562\) | 65.7877 | 2.77509 | ||||||||
\(563\) | 17.7696 | 0.748898 | 0.374449 | − | 0.927247i | \(-0.377832\pi\) | ||||
0.374449 | + | 0.927247i | \(0.377832\pi\) | |||||||
\(564\) | 57.5755 | 2.42436 | ||||||||
\(565\) | 2.96893 | 0.124904 | ||||||||
\(566\) | 47.0410 | 1.97728 | ||||||||
\(567\) | −3.40596 | −0.143037 | ||||||||
\(568\) | 11.3291 | 0.475357 | ||||||||
\(569\) | −8.77672 | −0.367939 | −0.183970 | − | 0.982932i | \(-0.558895\pi\) | ||||
−0.183970 | + | 0.982932i | \(0.558895\pi\) | |||||||
\(570\) | 42.6363 | 1.78584 | ||||||||
\(571\) | 19.0828 | 0.798591 | 0.399296 | − | 0.916822i | \(-0.369255\pi\) | ||||
0.399296 | + | 0.916822i | \(0.369255\pi\) | |||||||
\(572\) | −29.0682 | −1.21540 | ||||||||
\(573\) | 33.0911 | 1.38240 | ||||||||
\(574\) | 2.66791 | 0.111356 | ||||||||
\(575\) | −38.0646 | −1.58740 | ||||||||
\(576\) | −53.6485 | −2.23535 | ||||||||
\(577\) | 21.3664 | 0.889497 | 0.444748 | − | 0.895656i | \(-0.353293\pi\) | ||||
0.444748 | + | 0.895656i | \(0.353293\pi\) | |||||||
\(578\) | −2.12375 | −0.0883363 | ||||||||
\(579\) | −23.9351 | −0.994707 | ||||||||
\(580\) | 18.1482 | 0.753564 | ||||||||
\(581\) | −25.4740 | −1.05684 | ||||||||
\(582\) | 64.4205 | 2.67032 | ||||||||
\(583\) | 17.8621 | 0.739774 | ||||||||
\(584\) | 12.7938 | 0.529410 | ||||||||
\(585\) | −35.2148 | −1.45595 | ||||||||
\(586\) | 24.3278 | 1.00497 | ||||||||
\(587\) | −2.40200 | −0.0991411 | −0.0495705 | − | 0.998771i | \(-0.515785\pi\) | ||||
−0.0495705 | + | 0.998771i | \(0.515785\pi\) | |||||||
\(588\) | 24.9031 | 1.02699 | ||||||||
\(589\) | −0.289382 | −0.0119238 | ||||||||
\(590\) | 5.78035 | 0.237973 | ||||||||
\(591\) | −31.5448 | −1.29758 | ||||||||
\(592\) | 14.9489 | 0.614397 | ||||||||
\(593\) | 8.23432 | 0.338143 | 0.169072 | − | 0.985604i | \(-0.445923\pi\) | ||||
0.169072 | + | 0.985604i | \(0.445923\pi\) | |||||||
\(594\) | 53.2441 | 2.18463 | ||||||||
\(595\) | −11.2403 | −0.460805 | ||||||||
\(596\) | 3.01248 | 0.123396 | ||||||||
\(597\) | −18.5484 | −0.759134 | ||||||||
\(598\) | 25.2618 | 1.03303 | ||||||||
\(599\) | 3.74730 | 0.153110 | 0.0765552 | − | 0.997065i | \(-0.475608\pi\) | ||||
0.0765552 | + | 0.997065i | \(0.475608\pi\) | |||||||
\(600\) | −20.8804 | −0.852438 | ||||||||
\(601\) | 38.8161 | 1.58334 | 0.791671 | − | 0.610947i | \(-0.209211\pi\) | ||||
0.791671 | + | 0.610947i | \(0.209211\pi\) | |||||||
\(602\) | −34.4014 | −1.40210 | ||||||||
\(603\) | 63.5914 | 2.58964 | ||||||||
\(604\) | 7.65909 | 0.311644 | ||||||||
\(605\) | −60.3527 | −2.45369 | ||||||||
\(606\) | 36.3687 | 1.47738 | ||||||||
\(607\) | 6.46851 | 0.262549 | 0.131274 | − | 0.991346i | \(-0.458093\pi\) | ||||
0.131274 | + | 0.991346i | \(0.458093\pi\) | |||||||
\(608\) | 16.6309 | 0.674471 | ||||||||
\(609\) | −18.8690 | −0.764611 | ||||||||
\(610\) | −24.6704 | −0.998874 | ||||||||
\(611\) | 17.9469 | 0.726053 | ||||||||
\(612\) | 11.7838 | 0.476332 | ||||||||
\(613\) | −8.22936 | −0.332381 | −0.166190 | − | 0.986094i | \(-0.553147\pi\) | ||||
−0.166190 | + | 0.986094i | \(0.553147\pi\) | |||||||
\(614\) | −1.44662 | −0.0583809 | ||||||||
\(615\) | 3.70329 | 0.149331 | ||||||||
\(616\) | 18.8034 | 0.757612 | ||||||||
\(617\) | −34.4999 | −1.38891 | −0.694457 | − | 0.719534i | \(-0.744355\pi\) | ||||
−0.694457 | + | 0.719534i | \(0.744355\pi\) | |||||||
\(618\) | 50.3474 | 2.02527 | ||||||||
\(619\) | −10.3352 | −0.415407 | −0.207704 | − | 0.978192i | \(-0.566599\pi\) | ||||
−0.207704 | + | 0.978192i | \(0.566599\pi\) | |||||||
\(620\) | 1.19900 | 0.0481528 | ||||||||
\(621\) | −25.7536 | −1.03346 | ||||||||
\(622\) | −21.5707 | −0.864908 | ||||||||
\(623\) | −7.48711 | −0.299965 | ||||||||
\(624\) | −16.3698 | −0.655317 | ||||||||
\(625\) | −11.4851 | −0.459403 | ||||||||
\(626\) | −40.1987 | −1.60666 | ||||||||
\(627\) | −30.9885 | −1.23756 | ||||||||
\(628\) | 14.7540 | 0.588751 | ||||||||
\(629\) | −5.49802 | −0.219220 | ||||||||
\(630\) | 112.057 | 4.46445 | ||||||||
\(631\) | −14.6205 | −0.582033 | −0.291016 | − | 0.956718i | \(-0.593993\pi\) | ||||
−0.291016 | + | 0.956718i | \(0.593993\pi\) | |||||||
\(632\) | −1.79937 | −0.0715752 | ||||||||
\(633\) | −74.1973 | −2.94908 | ||||||||
\(634\) | 50.3468 | 1.99953 | ||||||||
\(635\) | −16.4575 | −0.653097 | ||||||||
\(636\) | −23.3137 | −0.924446 | ||||||||
\(637\) | 7.76257 | 0.307564 | ||||||||
\(638\) | −23.6992 | −0.938261 | ||||||||
\(639\) | −49.0699 | −1.94118 | ||||||||
\(640\) | −28.9909 | −1.14597 | ||||||||
\(641\) | 32.2579 | 1.27411 | 0.637055 | − | 0.770819i | \(-0.280153\pi\) | ||||
0.637055 | + | 0.770819i | \(0.280153\pi\) | |||||||
\(642\) | −80.3841 | −3.17251 | ||||||||
\(643\) | −2.10214 | −0.0829004 | −0.0414502 | − | 0.999141i | \(-0.513198\pi\) | ||||
−0.0414502 | + | 0.999141i | \(0.513198\pi\) | |||||||
\(644\) | −44.7401 | −1.76301 | ||||||||
\(645\) | −47.7521 | −1.88024 | ||||||||
\(646\) | −4.44725 | −0.174975 | ||||||||
\(647\) | −1.97648 | −0.0777036 | −0.0388518 | − | 0.999245i | \(-0.512370\pi\) | ||||
−0.0388518 | + | 0.999245i | \(0.512370\pi\) | |||||||
\(648\) | 1.13503 | 0.0445882 | ||||||||
\(649\) | −4.20122 | −0.164912 | ||||||||
\(650\) | −32.0172 | −1.25582 | ||||||||
\(651\) | −1.24662 | −0.0488587 | ||||||||
\(652\) | −4.02806 | −0.157751 | ||||||||
\(653\) | −32.0659 | −1.25483 | −0.627417 | − | 0.778683i | \(-0.715888\pi\) | ||||
−0.627417 | + | 0.778683i | \(0.715888\pi\) | |||||||
\(654\) | 109.555 | 4.28394 | ||||||||
\(655\) | 26.2776 | 1.02675 | ||||||||
\(656\) | 1.05027 | 0.0410063 | ||||||||
\(657\) | −55.4141 | −2.16191 | ||||||||
\(658\) | −57.1086 | −2.22632 | ||||||||
\(659\) | 30.5102 | 1.18851 | 0.594254 | − | 0.804277i | \(-0.297447\pi\) | ||||
0.594254 | + | 0.804277i | \(0.297447\pi\) | |||||||
\(660\) | 128.395 | 4.99775 | ||||||||
\(661\) | −29.5973 | −1.15120 | −0.575600 | − | 0.817731i | \(-0.695232\pi\) | ||||
−0.575600 | + | 0.817731i | \(0.695232\pi\) | |||||||
\(662\) | −33.0970 | −1.28635 | ||||||||
\(663\) | 6.02061 | 0.233821 | ||||||||
\(664\) | 8.48918 | 0.329444 | ||||||||
\(665\) | −23.5377 | −0.912754 | ||||||||
\(666\) | 54.8110 | 2.12388 | ||||||||
\(667\) | 11.4630 | 0.443851 | ||||||||
\(668\) | 30.5157 | 1.18069 | ||||||||
\(669\) | −40.6011 | −1.56973 | ||||||||
\(670\) | 99.4375 | 3.84160 | ||||||||
\(671\) | 17.9307 | 0.692206 | ||||||||
\(672\) | 71.6434 | 2.76370 | ||||||||
\(673\) | −36.7815 | −1.41782 | −0.708912 | − | 0.705297i | \(-0.750814\pi\) | ||||
−0.708912 | + | 0.705297i | \(0.750814\pi\) | |||||||
\(674\) | 35.8328 | 1.38023 | ||||||||
\(675\) | 32.6406 | 1.25634 | ||||||||
\(676\) | −20.8078 | −0.800300 | ||||||||
\(677\) | 4.43458 | 0.170435 | 0.0852173 | − | 0.996362i | \(-0.472842\pi\) | ||||
0.0852173 | + | 0.996362i | \(0.472842\pi\) | |||||||
\(678\) | 5.06031 | 0.194340 | ||||||||
\(679\) | −35.5639 | −1.36482 | ||||||||
\(680\) | 3.74580 | 0.143645 | ||||||||
\(681\) | −25.0084 | −0.958326 | ||||||||
\(682\) | −1.56573 | −0.0599550 | ||||||||
\(683\) | 29.1217 | 1.11431 | 0.557155 | − | 0.830409i | \(-0.311893\pi\) | ||||
0.557155 | + | 0.830409i | \(0.311893\pi\) | |||||||
\(684\) | 24.6760 | 0.943509 | ||||||||
\(685\) | −9.45268 | −0.361168 | ||||||||
\(686\) | 23.6459 | 0.902803 | ||||||||
\(687\) | 27.4728 | 1.04815 | ||||||||
\(688\) | −13.5428 | −0.516314 | ||||||||
\(689\) | −7.26711 | −0.276855 | ||||||||
\(690\) | −111.581 | −4.24783 | ||||||||
\(691\) | −10.0907 | −0.383867 | −0.191933 | − | 0.981408i | \(-0.561476\pi\) | ||||
−0.191933 | + | 0.981408i | \(0.561476\pi\) | |||||||
\(692\) | −28.2271 | −1.07303 | ||||||||
\(693\) | −81.4440 | −3.09380 | ||||||||
\(694\) | −71.8523 | −2.72748 | ||||||||
\(695\) | −0.894636 | −0.0339355 | ||||||||
\(696\) | 6.28807 | 0.238349 | ||||||||
\(697\) | −0.386277 | −0.0146313 | ||||||||
\(698\) | 32.0608 | 1.21352 | ||||||||
\(699\) | −55.8970 | −2.11422 | ||||||||
\(700\) | 56.7044 | 2.14323 | ||||||||
\(701\) | 13.5832 | 0.513031 | 0.256516 | − | 0.966540i | \(-0.417426\pi\) | ||||
0.256516 | + | 0.966540i | \(0.417426\pi\) | |||||||
\(702\) | −21.6621 | −0.817582 | ||||||||
\(703\) | −11.5132 | −0.434227 | ||||||||
\(704\) | 60.9720 | 2.29797 | ||||||||
\(705\) | −79.2716 | −2.98554 | ||||||||
\(706\) | −2.12375 | −0.0799283 | ||||||||
\(707\) | −20.0776 | −0.755097 | ||||||||
\(708\) | 5.48342 | 0.206080 | ||||||||
\(709\) | 31.6082 | 1.18707 | 0.593535 | − | 0.804808i | \(-0.297732\pi\) | ||||
0.593535 | + | 0.804808i | \(0.297732\pi\) | |||||||
\(710\) | −76.7303 | −2.87964 | ||||||||
\(711\) | 7.79368 | 0.292286 | ||||||||
\(712\) | 2.49507 | 0.0935067 | ||||||||
\(713\) | 0.757328 | 0.0283621 | ||||||||
\(714\) | −19.1581 | −0.716975 | ||||||||
\(715\) | 40.0219 | 1.49674 | ||||||||
\(716\) | 64.7015 | 2.41801 | ||||||||
\(717\) | −57.9662 | −2.16479 | ||||||||
\(718\) | 68.1918 | 2.54490 | ||||||||
\(719\) | 43.4527 | 1.62051 | 0.810257 | − | 0.586075i | \(-0.199328\pi\) | ||||
0.810257 | + | 0.586075i | \(0.199328\pi\) | |||||||
\(720\) | 44.1133 | 1.64400 | ||||||||
\(721\) | −27.7947 | −1.03513 | ||||||||
\(722\) | 31.0384 | 1.15513 | ||||||||
\(723\) | 58.9050 | 2.19070 | ||||||||
\(724\) | −24.1663 | −0.898135 | ||||||||
\(725\) | −14.5285 | −0.539574 | ||||||||
\(726\) | −102.866 | −3.81773 | ||||||||
\(727\) | 7.15838 | 0.265490 | 0.132745 | − | 0.991150i | \(-0.457621\pi\) | ||||
0.132745 | + | 0.991150i | \(0.457621\pi\) | |||||||
\(728\) | −7.65007 | −0.283531 | ||||||||
\(729\) | −44.0218 | −1.63044 | ||||||||
\(730\) | −86.6507 | −3.20709 | ||||||||
\(731\) | 4.98086 | 0.184224 | ||||||||
\(732\) | −23.4031 | −0.865003 | ||||||||
\(733\) | −22.2259 | −0.820931 | −0.410465 | − | 0.911876i | \(-0.634634\pi\) | ||||
−0.410465 | + | 0.911876i | \(0.634634\pi\) | |||||||
\(734\) | 35.5060 | 1.31055 | ||||||||
\(735\) | −34.2873 | −1.26471 | ||||||||
\(736\) | −43.5238 | −1.60431 | ||||||||
\(737\) | −72.2722 | −2.66218 | ||||||||
\(738\) | 3.85089 | 0.141753 | ||||||||
\(739\) | 9.10012 | 0.334753 | 0.167377 | − | 0.985893i | \(-0.446470\pi\) | ||||
0.167377 | + | 0.985893i | \(0.446470\pi\) | |||||||
\(740\) | 47.7025 | 1.75358 | ||||||||
\(741\) | 12.6075 | 0.463148 | ||||||||
\(742\) | 23.1246 | 0.848931 | ||||||||
\(743\) | 2.62523 | 0.0963105 | 0.0481552 | − | 0.998840i | \(-0.484666\pi\) | ||||
0.0481552 | + | 0.998840i | \(0.484666\pi\) | |||||||
\(744\) | 0.415433 | 0.0152305 | ||||||||
\(745\) | −4.14767 | −0.151959 | ||||||||
\(746\) | 18.8220 | 0.689124 | ||||||||
\(747\) | −36.7695 | −1.34532 | ||||||||
\(748\) | −13.3924 | −0.489675 | ||||||||
\(749\) | 44.3767 | 1.62149 | ||||||||
\(750\) | 39.6172 | 1.44662 | ||||||||
\(751\) | −20.3009 | −0.740790 | −0.370395 | − | 0.928874i | \(-0.620778\pi\) | ||||
−0.370395 | + | 0.928874i | \(0.620778\pi\) | |||||||
\(752\) | −22.4819 | −0.819830 | ||||||||
\(753\) | 30.0144 | 1.09379 | ||||||||
\(754\) | 9.64189 | 0.351137 | ||||||||
\(755\) | −10.5453 | −0.383781 | ||||||||
\(756\) | 38.3648 | 1.39532 | ||||||||
\(757\) | −16.3892 | −0.595677 | −0.297838 | − | 0.954616i | \(-0.596266\pi\) | ||||
−0.297838 | + | 0.954616i | \(0.596266\pi\) | |||||||
\(758\) | −37.2347 | −1.35243 | ||||||||
\(759\) | 81.0985 | 2.94369 | ||||||||
\(760\) | 7.84391 | 0.284529 | ||||||||
\(761\) | −43.8451 | −1.58938 | −0.794692 | − | 0.607013i | \(-0.792368\pi\) | ||||
−0.794692 | + | 0.607013i | \(0.792368\pi\) | |||||||
\(762\) | −28.0505 | −1.01616 | ||||||||
\(763\) | −60.4807 | −2.18955 | ||||||||
\(764\) | 29.9473 | 1.08346 | ||||||||
\(765\) | −16.2243 | −0.586590 | ||||||||
\(766\) | 35.0900 | 1.26785 | ||||||||
\(767\) | 1.70924 | 0.0617171 | ||||||||
\(768\) | 13.9903 | 0.504830 | ||||||||
\(769\) | 20.6350 | 0.744118 | 0.372059 | − | 0.928209i | \(-0.378652\pi\) | ||||
0.372059 | + | 0.928209i | \(0.378652\pi\) | |||||||
\(770\) | −127.353 | −4.58950 | ||||||||
\(771\) | −67.4427 | −2.42889 | ||||||||
\(772\) | −21.6611 | −0.779601 | ||||||||
\(773\) | −27.5680 | −0.991552 | −0.495776 | − | 0.868450i | \(-0.665116\pi\) | ||||
−0.495776 | + | 0.868450i | \(0.665116\pi\) | |||||||
\(774\) | −49.6554 | −1.78482 | ||||||||
\(775\) | −0.959851 | −0.0344789 | ||||||||
\(776\) | 11.8516 | 0.425448 | ||||||||
\(777\) | −49.5971 | −1.77928 | ||||||||
\(778\) | −54.1609 | −1.94176 | ||||||||
\(779\) | −0.808887 | −0.0289814 | ||||||||
\(780\) | −52.2366 | −1.87037 | ||||||||
\(781\) | 55.7684 | 1.99555 | ||||||||
\(782\) | 11.6387 | 0.416199 | ||||||||
\(783\) | −9.82961 | −0.351282 | ||||||||
\(784\) | −9.72410 | −0.347289 | ||||||||
\(785\) | −20.3138 | −0.725030 | ||||||||
\(786\) | 44.7880 | 1.59754 | ||||||||
\(787\) | 20.1260 | 0.717413 | 0.358707 | − | 0.933450i | \(-0.383218\pi\) | ||||
0.358707 | + | 0.933450i | \(0.383218\pi\) | |||||||
\(788\) | −28.5479 | −1.01698 | ||||||||
\(789\) | 30.5754 | 1.08851 | ||||||||
\(790\) | 12.1869 | 0.433592 | ||||||||
\(791\) | −2.79359 | −0.0993285 | ||||||||
\(792\) | 27.1411 | 0.964416 | ||||||||
\(793\) | −7.29499 | −0.259053 | ||||||||
\(794\) | 59.0368 | 2.09514 | ||||||||
\(795\) | 32.0989 | 1.13843 | ||||||||
\(796\) | −16.7862 | −0.594971 | ||||||||
\(797\) | −15.6676 | −0.554973 | −0.277487 | − | 0.960729i | \(-0.589501\pi\) | ||||
−0.277487 | + | 0.960729i | \(0.589501\pi\) | |||||||
\(798\) | −40.1182 | −1.42017 | ||||||||
\(799\) | 8.26855 | 0.292520 | ||||||||
\(800\) | 55.1629 | 1.95030 | ||||||||
\(801\) | −10.8070 | −0.381846 | ||||||||
\(802\) | 76.8548 | 2.71384 | ||||||||
\(803\) | 62.9786 | 2.22247 | ||||||||
\(804\) | 94.3295 | 3.32675 | ||||||||
\(805\) | 61.5995 | 2.17110 | ||||||||
\(806\) | 0.637009 | 0.0224377 | ||||||||
\(807\) | 87.8224 | 3.09149 | ||||||||
\(808\) | 6.69084 | 0.235383 | ||||||||
\(809\) | 25.4862 | 0.896047 | 0.448023 | − | 0.894022i | \(-0.352128\pi\) | ||||
0.448023 | + | 0.894022i | \(0.352128\pi\) | |||||||
\(810\) | −7.68743 | −0.270109 | ||||||||
\(811\) | −12.6195 | −0.443132 | −0.221566 | − | 0.975145i | \(-0.571117\pi\) | ||||
−0.221566 | + | 0.975145i | \(0.571117\pi\) | |||||||
\(812\) | −17.0764 | −0.599263 | ||||||||
\(813\) | 45.0295 | 1.57926 | ||||||||
\(814\) | −62.2932 | −2.18338 | ||||||||
\(815\) | 5.54595 | 0.194266 | ||||||||
\(816\) | −7.54196 | −0.264021 | ||||||||
\(817\) | 10.4302 | 0.364907 | ||||||||
\(818\) | 19.9836 | 0.698711 | ||||||||
\(819\) | 33.1350 | 1.15783 | ||||||||
\(820\) | 3.35146 | 0.117038 | ||||||||
\(821\) | 35.6448 | 1.24401 | 0.622006 | − | 0.783012i | \(-0.286318\pi\) | ||||
0.622006 | + | 0.783012i | \(0.286318\pi\) | |||||||
\(822\) | −16.1113 | −0.561948 | ||||||||
\(823\) | −10.0908 | −0.351745 | −0.175872 | − | 0.984413i | \(-0.556275\pi\) | ||||
−0.175872 | + | 0.984413i | \(0.556275\pi\) | |||||||
\(824\) | 9.26255 | 0.322676 | ||||||||
\(825\) | −102.786 | −3.57854 | ||||||||
\(826\) | −5.43896 | −0.189246 | ||||||||
\(827\) | −3.64299 | −0.126679 | −0.0633396 | − | 0.997992i | \(-0.520175\pi\) | ||||
−0.0633396 | + | 0.997992i | \(0.520175\pi\) | |||||||
\(828\) | −64.5783 | −2.24425 | ||||||||
\(829\) | −24.2726 | −0.843022 | −0.421511 | − | 0.906823i | \(-0.638500\pi\) | ||||
−0.421511 | + | 0.906823i | \(0.638500\pi\) | |||||||
\(830\) | −57.4962 | −1.99572 | ||||||||
\(831\) | 27.0544 | 0.938506 | ||||||||
\(832\) | −24.8061 | −0.859997 | ||||||||
\(833\) | 3.57640 | 0.123915 | ||||||||
\(834\) | −1.52484 | −0.0528008 | ||||||||
\(835\) | −42.0149 | −1.45399 | ||||||||
\(836\) | −28.0445 | −0.969938 | ||||||||
\(837\) | −0.649411 | −0.0224469 | ||||||||
\(838\) | −71.0872 | −2.45567 | ||||||||
\(839\) | 8.70905 | 0.300670 | 0.150335 | − | 0.988635i | \(-0.451965\pi\) | ||||
0.150335 | + | 0.988635i | \(0.451965\pi\) | |||||||
\(840\) | 33.7904 | 1.16588 | ||||||||
\(841\) | −24.6248 | −0.849131 | ||||||||
\(842\) | 18.0640 | 0.622525 | ||||||||
\(843\) | −85.9255 | −2.95943 | ||||||||
\(844\) | −67.1482 | −2.31134 | ||||||||
\(845\) | 28.6488 | 0.985547 | ||||||||
\(846\) | −82.4311 | −2.83404 | ||||||||
\(847\) | 56.7883 | 1.95127 | ||||||||
\(848\) | 9.10344 | 0.312614 | ||||||||
\(849\) | −61.4404 | −2.10863 | ||||||||
\(850\) | −14.7511 | −0.505958 | ||||||||
\(851\) | 30.1305 | 1.03286 | ||||||||
\(852\) | −72.7888 | −2.49370 | ||||||||
\(853\) | 1.95559 | 0.0669583 | 0.0334791 | − | 0.999439i | \(-0.489341\pi\) | ||||
0.0334791 | + | 0.999439i | \(0.489341\pi\) | |||||||
\(854\) | 23.2133 | 0.794343 | ||||||||
\(855\) | −33.9746 | −1.16191 | ||||||||
\(856\) | −14.7885 | −0.505459 | ||||||||
\(857\) | −19.5164 | −0.666669 | −0.333334 | − | 0.942809i | \(-0.608174\pi\) | ||||
−0.333334 | + | 0.942809i | \(0.608174\pi\) | |||||||
\(858\) | 68.2142 | 2.32880 | ||||||||
\(859\) | −24.8796 | −0.848883 | −0.424441 | − | 0.905455i | \(-0.639529\pi\) | ||||
−0.424441 | + | 0.905455i | \(0.639529\pi\) | |||||||
\(860\) | −43.2154 | −1.47363 | ||||||||
\(861\) | −3.48457 | −0.118754 | ||||||||
\(862\) | −19.0868 | −0.650098 | ||||||||
\(863\) | −34.7878 | −1.18419 | −0.592095 | − | 0.805868i | \(-0.701699\pi\) | ||||
−0.592095 | + | 0.805868i | \(0.701699\pi\) | |||||||
\(864\) | 37.3219 | 1.26972 | ||||||||
\(865\) | 38.8639 | 1.32141 | ||||||||
\(866\) | −53.8673 | −1.83049 | ||||||||
\(867\) | 2.77384 | 0.0942044 | ||||||||
\(868\) | −1.12818 | −0.0382930 | ||||||||
\(869\) | −8.85759 | −0.300473 | ||||||||
\(870\) | −42.5883 | −1.44388 | ||||||||
\(871\) | 29.4035 | 0.996300 | ||||||||
\(872\) | 20.1551 | 0.682538 | ||||||||
\(873\) | −51.3333 | −1.73737 | ||||||||
\(874\) | 24.3721 | 0.824397 | ||||||||
\(875\) | −21.8710 | −0.739375 | ||||||||
\(876\) | −82.1996 | −2.77727 | ||||||||
\(877\) | −13.9567 | −0.471285 | −0.235643 | − | 0.971840i | \(-0.575719\pi\) | ||||
−0.235643 | + | 0.971840i | \(0.575719\pi\) | |||||||
\(878\) | 13.7824 | 0.465133 | ||||||||
\(879\) | −31.7746 | −1.07173 | ||||||||
\(880\) | −50.1351 | −1.69005 | ||||||||
\(881\) | 22.0636 | 0.743341 | 0.371671 | − | 0.928365i | \(-0.378785\pi\) | ||||
0.371671 | + | 0.928365i | \(0.378785\pi\) | |||||||
\(882\) | −35.6539 | −1.20053 | ||||||||
\(883\) | 10.2822 | 0.346024 | 0.173012 | − | 0.984920i | \(-0.444650\pi\) | ||||
0.173012 | + | 0.984920i | \(0.444650\pi\) | |||||||
\(884\) | 5.44862 | 0.183257 | ||||||||
\(885\) | −7.54973 | −0.253782 | ||||||||
\(886\) | −13.8656 | −0.465823 | ||||||||
\(887\) | −25.0117 | −0.839809 | −0.419905 | − | 0.907568i | \(-0.637936\pi\) | ||||
−0.419905 | + | 0.907568i | \(0.637936\pi\) | |||||||
\(888\) | 16.5281 | 0.554648 | ||||||||
\(889\) | 15.4855 | 0.519368 | ||||||||
\(890\) | −16.8988 | −0.566449 | ||||||||
\(891\) | 5.58730 | 0.187182 | ||||||||
\(892\) | −36.7438 | −1.23027 | ||||||||
\(893\) | 17.3148 | 0.579418 | ||||||||
\(894\) | −7.06938 | −0.236435 | ||||||||
\(895\) | −89.0829 | −2.97771 | ||||||||
\(896\) | 27.2787 | 0.911317 | ||||||||
\(897\) | −32.9945 | −1.10165 | ||||||||
\(898\) | −32.9508 | −1.09958 | ||||||||
\(899\) | 0.289056 | 0.00964056 | ||||||||
\(900\) | 81.8477 | 2.72826 | ||||||||
\(901\) | −3.34813 | −0.111542 | ||||||||
\(902\) | −4.37657 | −0.145724 | ||||||||
\(903\) | 44.9318 | 1.49524 | ||||||||
\(904\) | 0.930958 | 0.0309632 | ||||||||
\(905\) | 33.2729 | 1.10603 | ||||||||
\(906\) | −17.9736 | −0.597131 | ||||||||
\(907\) | 43.5721 | 1.44679 | 0.723394 | − | 0.690435i | \(-0.242581\pi\) | ||||
0.723394 | + | 0.690435i | \(0.242581\pi\) | |||||||
\(908\) | −22.6325 | −0.751087 | ||||||||
\(909\) | −28.9802 | −0.961214 | ||||||||
\(910\) | 51.8130 | 1.71758 | ||||||||
\(911\) | 49.6188 | 1.64394 | 0.821972 | − | 0.569528i | \(-0.192874\pi\) | ||||
0.821972 | + | 0.569528i | \(0.192874\pi\) | |||||||
\(912\) | −15.7933 | −0.522968 | ||||||||
\(913\) | 41.7888 | 1.38301 | ||||||||
\(914\) | 15.2276 | 0.503684 | ||||||||
\(915\) | 32.2220 | 1.06523 | ||||||||
\(916\) | 24.8628 | 0.821489 | ||||||||
\(917\) | −24.7256 | −0.816511 | ||||||||
\(918\) | −9.98022 | −0.329396 | ||||||||
\(919\) | 23.4578 | 0.773802 | 0.386901 | − | 0.922121i | \(-0.373546\pi\) | ||||
0.386901 | + | 0.922121i | \(0.373546\pi\) | |||||||
\(920\) | −20.5279 | −0.676786 | ||||||||
\(921\) | 1.88944 | 0.0622591 | ||||||||
\(922\) | −25.1573 | −0.828513 | ||||||||
\(923\) | −22.6890 | −0.746819 | ||||||||
\(924\) | −120.812 | −3.97441 | ||||||||
\(925\) | −38.1880 | −1.25561 | ||||||||
\(926\) | −0.579272 | −0.0190361 | ||||||||
\(927\) | −40.1192 | −1.31769 | ||||||||
\(928\) | −16.6121 | −0.545321 | ||||||||
\(929\) | −13.1018 | −0.429857 | −0.214928 | − | 0.976630i | \(-0.568952\pi\) | ||||
−0.214928 | + | 0.976630i | \(0.568952\pi\) | |||||||
\(930\) | −2.81368 | −0.0922641 | ||||||||
\(931\) | 7.48918 | 0.245448 | ||||||||
\(932\) | −50.5866 | −1.65702 | ||||||||
\(933\) | 28.1736 | 0.922363 | ||||||||
\(934\) | 32.0246 | 1.04788 | ||||||||
\(935\) | 18.4391 | 0.603022 | ||||||||
\(936\) | −11.0422 | −0.360925 | ||||||||
\(937\) | −50.8397 | −1.66086 | −0.830430 | − | 0.557123i | \(-0.811905\pi\) | ||||
−0.830430 | + | 0.557123i | \(0.811905\pi\) | |||||||
\(938\) | −93.5646 | −3.05499 | ||||||||
\(939\) | 52.5037 | 1.71339 | ||||||||
\(940\) | −71.7404 | −2.33991 | ||||||||
\(941\) | −43.5663 | −1.42022 | −0.710111 | − | 0.704090i | \(-0.751355\pi\) | ||||
−0.710111 | + | 0.704090i | \(0.751355\pi\) | |||||||
\(942\) | −34.6232 | −1.12809 | ||||||||
\(943\) | 2.11690 | 0.0689357 | ||||||||
\(944\) | −2.14115 | −0.0696885 | ||||||||
\(945\) | −52.8218 | −1.71829 | ||||||||
\(946\) | 56.4338 | 1.83482 | ||||||||
\(947\) | −17.9416 | −0.583024 | −0.291512 | − | 0.956567i | \(-0.594158\pi\) | ||||
−0.291512 | + | 0.956567i | \(0.594158\pi\) | |||||||
\(948\) | 11.5609 | 0.375481 | ||||||||
\(949\) | −25.6225 | −0.831741 | ||||||||
\(950\) | −30.8896 | −1.00219 | ||||||||
\(951\) | −65.7582 | −2.13235 | ||||||||
\(952\) | −3.52457 | −0.114232 | ||||||||
\(953\) | −13.1344 | −0.425467 | −0.212733 | − | 0.977110i | \(-0.568237\pi\) | ||||
−0.212733 | + | 0.977110i | \(0.568237\pi\) | |||||||
\(954\) | 33.3783 | 1.08066 | ||||||||
\(955\) | −41.2323 | −1.33425 | ||||||||
\(956\) | −52.4592 | −1.69665 | ||||||||
\(957\) | 30.9536 | 1.00059 | ||||||||
\(958\) | 47.2493 | 1.52656 | ||||||||
\(959\) | 8.89440 | 0.287215 | ||||||||
\(960\) | 109.569 | 3.53632 | ||||||||
\(961\) | −30.9809 | −0.999384 | ||||||||
\(962\) | 25.3436 | 0.817112 | ||||||||
\(963\) | 64.0538 | 2.06410 | ||||||||
\(964\) | 53.3087 | 1.71696 | ||||||||
\(965\) | 29.8237 | 0.960058 | ||||||||
\(966\) | 104.991 | 3.37804 | ||||||||
\(967\) | 4.39456 | 0.141320 | 0.0706598 | − | 0.997500i | \(-0.477490\pi\) | ||||
0.0706598 | + | 0.997500i | \(0.477490\pi\) | |||||||
\(968\) | −18.9246 | −0.608260 | ||||||||
\(969\) | 5.80857 | 0.186598 | ||||||||
\(970\) | −80.2695 | −2.57730 | ||||||||
\(971\) | −40.0968 | −1.28677 | −0.643384 | − | 0.765543i | \(-0.722470\pi\) | ||||
−0.643384 | + | 0.765543i | \(0.722470\pi\) | |||||||
\(972\) | −42.6829 | −1.36906 | ||||||||
\(973\) | 0.841798 | 0.0269868 | ||||||||
\(974\) | 91.8733 | 2.94381 | ||||||||
\(975\) | 41.8178 | 1.33924 | ||||||||
\(976\) | 9.13837 | 0.292512 | ||||||||
\(977\) | 45.2401 | 1.44736 | 0.723679 | − | 0.690136i | \(-0.242449\pi\) | ||||
0.723679 | + | 0.690136i | \(0.242449\pi\) | |||||||
\(978\) | 9.45263 | 0.302262 | ||||||||
\(979\) | 12.2822 | 0.392542 | ||||||||
\(980\) | −31.0299 | −0.991214 | ||||||||
\(981\) | −87.2985 | −2.78723 | ||||||||
\(982\) | −30.2780 | −0.966211 | ||||||||
\(983\) | −60.4109 | −1.92681 | −0.963404 | − | 0.268052i | \(-0.913620\pi\) | ||||
−0.963404 | + | 0.268052i | \(0.913620\pi\) | |||||||
\(984\) | 1.16123 | 0.0370186 | ||||||||
\(985\) | 39.3056 | 1.25238 | ||||||||
\(986\) | 4.44225 | 0.141470 | ||||||||
\(987\) | 74.5897 | 2.37422 | ||||||||
\(988\) | 11.4097 | 0.362992 | ||||||||
\(989\) | −27.2964 | −0.867975 | ||||||||
\(990\) | −183.823 | −5.84228 | ||||||||
\(991\) | 58.5089 | 1.85860 | 0.929298 | − | 0.369330i | \(-0.120413\pi\) | ||||
0.929298 | + | 0.369330i | \(0.120413\pi\) | |||||||
\(992\) | −1.09751 | −0.0348461 | ||||||||
\(993\) | 43.2281 | 1.37180 | ||||||||
\(994\) | 72.1986 | 2.29000 | ||||||||
\(995\) | 23.1117 | 0.732691 | ||||||||
\(996\) | −54.5427 | −1.72825 | ||||||||
\(997\) | 5.56772 | 0.176332 | 0.0881658 | − | 0.996106i | \(-0.471899\pi\) | ||||
0.0881658 | + | 0.996106i | \(0.471899\pi\) | |||||||
\(998\) | 70.9074 | 2.24454 | ||||||||
\(999\) | −25.8371 | −0.817449 |
(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 | 6001.2.a.b.1.18 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.18 | ✓ | 114 | 1.1 | even | 1 | trivial |