Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(67,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("187.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(1.49320251780\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 21x^{14} + 172x^{12} + 700x^{10} + 1492x^{8} + 1620x^{6} + 840x^{4} + 196x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 67.10 | ||
Root | \(-0.420099i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 187.67 |
Dual form | 187.2.d.a.67.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(122\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.420099 | 0.297055 | 0.148528 | − | 0.988908i | \(-0.452547\pi\) | ||||
0.148528 | + | 0.988908i | \(0.452547\pi\) | |||||||
\(3\) | 0.0890922i | 0.0514374i | 0.999669 | + | 0.0257187i | \(0.00818742\pi\) | ||||
−0.999669 | + | 0.0257187i | \(0.991813\pi\) | |||||||
\(4\) | −1.82352 | −0.911758 | ||||||||
\(5\) | − | 3.34068i | − | 1.49400i | −0.664825 | − | 0.746999i | \(-0.731494\pi\) | ||
0.664825 | − | 0.746999i | \(-0.268506\pi\) | |||||||
\(6\) | 0.0374276i | 0.0152797i | ||||||||
\(7\) | − | 2.13044i | − | 0.805232i | −0.915369 | − | 0.402616i | \(-0.868101\pi\) | ||
0.915369 | − | 0.402616i | \(-0.131899\pi\) | |||||||
\(8\) | −1.60626 | −0.567897 | ||||||||
\(9\) | 2.99206 | 0.997354 | ||||||||
\(10\) | − | 1.40342i | − | 0.443800i | ||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | − | 0.162461i | − | 0.0468985i | ||||||
\(13\) | −2.81007 | −0.779373 | −0.389686 | − | 0.920948i | \(-0.627417\pi\) | ||||
−0.389686 | + | 0.920948i | \(0.627417\pi\) | |||||||
\(14\) | − | 0.894998i | − | 0.239198i | ||||||
\(15\) | 0.297629 | 0.0768474 | ||||||||
\(16\) | 2.97225 | 0.743062 | ||||||||
\(17\) | 4.03951 | − | 0.826028i | 0.979726 | − | 0.200341i | ||||
\(18\) | 1.25696 | 0.296269 | ||||||||
\(19\) | −1.49888 | −0.343866 | −0.171933 | − | 0.985109i | \(-0.555001\pi\) | ||||
−0.171933 | + | 0.985109i | \(0.555001\pi\) | |||||||
\(20\) | 6.09179i | 1.36217i | ||||||||
\(21\) | 0.189806 | 0.0414190 | ||||||||
\(22\) | − | 0.420099i | − | 0.0895655i | ||||||
\(23\) | 7.53789i | 1.57176i | 0.618380 | + | 0.785879i | \(0.287789\pi\) | ||||
−0.618380 | + | 0.785879i | \(0.712211\pi\) | |||||||
\(24\) | − | 0.143105i | − | 0.0292112i | ||||||
\(25\) | −6.16015 | −1.23203 | ||||||||
\(26\) | −1.18051 | −0.231517 | ||||||||
\(27\) | 0.533846i | 0.102739i | ||||||||
\(28\) | 3.88490i | 0.734177i | ||||||||
\(29\) | − | 5.21426i | − | 0.968263i | −0.874995 | − | 0.484132i | \(-0.839136\pi\) | ||
0.874995 | − | 0.484132i | \(-0.160864\pi\) | |||||||
\(30\) | 0.125034 | 0.0228279 | ||||||||
\(31\) | − | 1.28588i | − | 0.230951i | −0.993310 | − | 0.115476i | \(-0.963161\pi\) | ||
0.993310 | − | 0.115476i | \(-0.0368392\pi\) | |||||||
\(32\) | 4.46115 | 0.788628 | ||||||||
\(33\) | 0.0890922 | 0.0155090 | ||||||||
\(34\) | 1.69700 | − | 0.347014i | 0.291033 | − | 0.0595124i | ||||
\(35\) | −7.11713 | −1.20301 | ||||||||
\(36\) | −5.45608 | −0.909346 | ||||||||
\(37\) | 2.92929i | 0.481572i | 0.970578 | + | 0.240786i | \(0.0774053\pi\) | ||||
−0.970578 | + | 0.240786i | \(0.922595\pi\) | |||||||
\(38\) | −0.629677 | −0.102147 | ||||||||
\(39\) | − | 0.250355i | − | 0.0400889i | ||||||
\(40\) | 5.36599i | 0.848437i | ||||||||
\(41\) | 5.86187i | 0.915470i | 0.889089 | + | 0.457735i | \(0.151339\pi\) | ||||
−0.889089 | + | 0.457735i | \(0.848661\pi\) | |||||||
\(42\) | 0.0797373 | 0.0123037 | ||||||||
\(43\) | 5.20419 | 0.793631 | 0.396816 | − | 0.917898i | \(-0.370115\pi\) | ||||
0.396816 | + | 0.917898i | \(0.370115\pi\) | |||||||
\(44\) | 1.82352i | 0.274905i | ||||||||
\(45\) | − | 9.99553i | − | 1.49005i | ||||||
\(46\) | 3.16666i | 0.466899i | ||||||||
\(47\) | −5.15589 | −0.752064 | −0.376032 | − | 0.926607i | \(-0.622712\pi\) | ||||
−0.376032 | + | 0.926607i | \(0.622712\pi\) | |||||||
\(48\) | 0.264804i | 0.0382212i | ||||||||
\(49\) | 2.46121 | 0.351602 | ||||||||
\(50\) | −2.58787 | −0.365981 | ||||||||
\(51\) | 0.0735927 | + | 0.359889i | 0.0103050 | + | 0.0503946i | ||||
\(52\) | 5.12421 | 0.710600 | ||||||||
\(53\) | 11.7626 | 1.61572 | 0.807861 | − | 0.589373i | \(-0.200625\pi\) | ||||
0.807861 | + | 0.589373i | \(0.200625\pi\) | |||||||
\(54\) | 0.224268i | 0.0305190i | ||||||||
\(55\) | −3.34068 | −0.450457 | ||||||||
\(56\) | 3.42204i | 0.457289i | ||||||||
\(57\) | − | 0.133538i | − | 0.0176876i | ||||||
\(58\) | − | 2.19051i | − | 0.287627i | ||||||
\(59\) | 2.45417 | 0.319505 | 0.159753 | − | 0.987157i | \(-0.448930\pi\) | ||||
0.159753 | + | 0.987157i | \(0.448930\pi\) | |||||||
\(60\) | −0.542731 | −0.0700662 | ||||||||
\(61\) | − | 8.34393i | − | 1.06833i | −0.845380 | − | 0.534166i | \(-0.820626\pi\) | ||
0.845380 | − | 0.534166i | \(-0.179374\pi\) | |||||||
\(62\) | − | 0.540198i | − | 0.0686052i | ||||||
\(63\) | − | 6.37442i | − | 0.803101i | ||||||
\(64\) | −4.07037 | −0.508796 | ||||||||
\(65\) | 9.38754i | 1.16438i | ||||||||
\(66\) | 0.0374276 | 0.00460701 | ||||||||
\(67\) | 5.93567 | 0.725158 | 0.362579 | − | 0.931953i | \(-0.381896\pi\) | ||||
0.362579 | + | 0.931953i | \(0.381896\pi\) | |||||||
\(68\) | −7.36612 | + | 1.50628i | −0.893273 | + | 0.182663i | ||||
\(69\) | −0.671567 | −0.0808471 | ||||||||
\(70\) | −2.98990 | −0.357362 | ||||||||
\(71\) | 14.4899i | 1.71964i | 0.510599 | + | 0.859819i | \(0.329424\pi\) | ||||
−0.510599 | + | 0.859819i | \(0.670576\pi\) | |||||||
\(72\) | −4.80602 | −0.566395 | ||||||||
\(73\) | 5.99444i | 0.701596i | 0.936451 | + | 0.350798i | \(0.114090\pi\) | ||||
−0.936451 | + | 0.350798i | \(0.885910\pi\) | |||||||
\(74\) | 1.23059i | 0.143053i | ||||||||
\(75\) | − | 0.548821i | − | 0.0633724i | ||||||
\(76\) | 2.73323 | 0.313523 | ||||||||
\(77\) | −2.13044 | −0.242787 | ||||||||
\(78\) | − | 0.105174i | − | 0.0119086i | ||||||
\(79\) | − | 10.4774i | − | 1.17880i | −0.807842 | − | 0.589399i | \(-0.799365\pi\) | ||
0.807842 | − | 0.589399i | \(-0.200635\pi\) | |||||||
\(80\) | − | 9.92933i | − | 1.11013i | ||||||
\(81\) | 8.92863 | 0.992070 | ||||||||
\(82\) | 2.46257i | 0.271945i | ||||||||
\(83\) | −10.2104 | −1.12073 | −0.560367 | − | 0.828245i | \(-0.689340\pi\) | ||||
−0.560367 | + | 0.828245i | \(0.689340\pi\) | |||||||
\(84\) | −0.346114 | −0.0377642 | ||||||||
\(85\) | −2.75950 | − | 13.4947i | −0.299309 | − | 1.46371i | ||||
\(86\) | 2.18628 | 0.235752 | ||||||||
\(87\) | 0.464550 | 0.0498049 | ||||||||
\(88\) | 1.60626i | 0.171228i | ||||||||
\(89\) | 7.08143 | 0.750630 | 0.375315 | − | 0.926897i | \(-0.377535\pi\) | ||||
0.375315 | + | 0.926897i | \(0.377535\pi\) | |||||||
\(90\) | − | 4.19911i | − | 0.442625i | ||||||
\(91\) | 5.98669i | 0.627576i | ||||||||
\(92\) | − | 13.7455i | − | 1.43306i | ||||||
\(93\) | 0.114562 | 0.0118795 | ||||||||
\(94\) | −2.16598 | −0.223404 | ||||||||
\(95\) | 5.00727i | 0.513735i | ||||||||
\(96\) | 0.397454i | 0.0405650i | ||||||||
\(97\) | − | 14.3588i | − | 1.45791i | −0.684560 | − | 0.728956i | \(-0.740006\pi\) | ||
0.684560 | − | 0.728956i | \(-0.259994\pi\) | |||||||
\(98\) | 1.03395 | 0.104445 | ||||||||
\(99\) | − | 2.99206i | − | 0.300714i | ||||||
\(100\) | 11.2331 | 1.12331 | ||||||||
\(101\) | −13.0155 | −1.29510 | −0.647548 | − | 0.762025i | \(-0.724205\pi\) | ||||
−0.647548 | + | 0.762025i | \(0.724205\pi\) | |||||||
\(102\) | 0.0309162 | + | 0.151189i | 0.00306116 | + | 0.0149700i | ||||
\(103\) | −2.21395 | −0.218147 | −0.109073 | − | 0.994034i | \(-0.534788\pi\) | ||||
−0.109073 | + | 0.994034i | \(0.534788\pi\) | |||||||
\(104\) | 4.51369 | 0.442604 | ||||||||
\(105\) | − | 0.634081i | − | 0.0618800i | ||||||
\(106\) | 4.94147 | 0.479958 | ||||||||
\(107\) | 8.54382i | 0.825962i | 0.910740 | + | 0.412981i | \(0.135512\pi\) | ||||
−0.910740 | + | 0.412981i | \(0.864488\pi\) | |||||||
\(108\) | − | 0.973477i | − | 0.0936729i | ||||||
\(109\) | − | 13.4901i | − | 1.29212i | −0.763288 | − | 0.646058i | \(-0.776416\pi\) | ||
0.763288 | − | 0.646058i | \(-0.223584\pi\) | |||||||
\(110\) | −1.40342 | −0.133811 | ||||||||
\(111\) | −0.260977 | −0.0247708 | ||||||||
\(112\) | − | 6.33220i | − | 0.598337i | ||||||
\(113\) | 1.47191i | 0.138466i | 0.997601 | + | 0.0692330i | \(0.0220552\pi\) | ||||
−0.997601 | + | 0.0692330i | \(0.977945\pi\) | |||||||
\(114\) | − | 0.0560993i | − | 0.00525419i | ||||||
\(115\) | 25.1817 | 2.34820 | ||||||||
\(116\) | 9.50829i | 0.882822i | ||||||||
\(117\) | −8.40790 | −0.777311 | ||||||||
\(118\) | 1.03099 | 0.0949107 | ||||||||
\(119\) | −1.75981 | − | 8.60596i | −0.161321 | − | 0.788907i | ||||
\(120\) | −0.478068 | −0.0436414 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | − | 3.50528i | − | 0.317353i | ||||||
\(123\) | −0.522246 | −0.0470894 | ||||||||
\(124\) | 2.34483i | 0.210572i | ||||||||
\(125\) | 3.87569i | 0.346652i | ||||||||
\(126\) | − | 2.67789i | − | 0.238565i | ||||||
\(127\) | 7.21406 | 0.640144 | 0.320072 | − | 0.947393i | \(-0.396293\pi\) | ||||
0.320072 | + | 0.947393i | \(0.396293\pi\) | |||||||
\(128\) | −10.6323 | −0.939768 | ||||||||
\(129\) | 0.463653i | 0.0408223i | ||||||||
\(130\) | 3.94370i | 0.345885i | ||||||||
\(131\) | 15.4247i | 1.34766i | 0.738884 | + | 0.673832i | \(0.235353\pi\) | ||||
−0.738884 | + | 0.673832i | \(0.764647\pi\) | |||||||
\(132\) | −0.162461 | −0.0141404 | ||||||||
\(133\) | 3.19327i | 0.276892i | ||||||||
\(134\) | 2.49357 | 0.215412 | ||||||||
\(135\) | 1.78341 | 0.153491 | ||||||||
\(136\) | −6.48850 | + | 1.32681i | −0.556384 | + | 0.113773i | ||||
\(137\) | −5.57577 | −0.476370 | −0.238185 | − | 0.971220i | \(-0.576553\pi\) | ||||
−0.238185 | + | 0.971220i | \(0.576553\pi\) | |||||||
\(138\) | −0.282125 | −0.0240160 | ||||||||
\(139\) | − | 1.40296i | − | 0.118997i | −0.998228 | − | 0.0594986i | \(-0.981050\pi\) | ||
0.998228 | − | 0.0594986i | \(-0.0189502\pi\) | |||||||
\(140\) | 12.9782 | 1.09686 | ||||||||
\(141\) | − | 0.459349i | − | 0.0386842i | ||||||
\(142\) | 6.08721i | 0.510827i | ||||||||
\(143\) | 2.81007i | 0.234990i | ||||||||
\(144\) | 8.89315 | 0.741096 | ||||||||
\(145\) | −17.4192 | −1.44658 | ||||||||
\(146\) | 2.51826i | 0.208413i | ||||||||
\(147\) | 0.219275i | 0.0180855i | ||||||||
\(148\) | − | 5.34161i | − | 0.439078i | ||||||
\(149\) | −13.5489 | −1.10997 | −0.554984 | − | 0.831861i | \(-0.687276\pi\) | ||||
−0.554984 | + | 0.831861i | \(0.687276\pi\) | |||||||
\(150\) | − | 0.230559i | − | 0.0188251i | ||||||
\(151\) | −21.9814 | −1.78882 | −0.894410 | − | 0.447248i | \(-0.852404\pi\) | ||||
−0.894410 | + | 0.447248i | \(0.852404\pi\) | |||||||
\(152\) | 2.40758 | 0.195281 | ||||||||
\(153\) | 12.0865 | − | 2.47153i | 0.977134 | − | 0.199811i | ||||
\(154\) | −0.894998 | −0.0721210 | ||||||||
\(155\) | −4.29572 | −0.345041 | ||||||||
\(156\) | 0.456527i | 0.0365514i | ||||||||
\(157\) | −5.98704 | −0.477818 | −0.238909 | − | 0.971042i | \(-0.576790\pi\) | ||||
−0.238909 | + | 0.971042i | \(0.576790\pi\) | |||||||
\(158\) | − | 4.40154i | − | 0.350168i | ||||||
\(159\) | 1.04796i | 0.0831085i | ||||||||
\(160\) | − | 14.9033i | − | 1.17821i | ||||||
\(161\) | 16.0590 | 1.26563 | ||||||||
\(162\) | 3.75091 | 0.294699 | ||||||||
\(163\) | 24.8721i | 1.94813i | 0.226266 | + | 0.974066i | \(0.427348\pi\) | ||||
−0.226266 | + | 0.974066i | \(0.572652\pi\) | |||||||
\(164\) | − | 10.6892i | − | 0.834687i | ||||||
\(165\) | − | 0.297629i | − | 0.0231704i | ||||||
\(166\) | −4.28937 | −0.332920 | ||||||||
\(167\) | 12.4223i | 0.961266i | 0.876922 | + | 0.480633i | \(0.159593\pi\) | ||||
−0.876922 | + | 0.480633i | \(0.840407\pi\) | |||||||
\(168\) | −0.304877 | −0.0235218 | ||||||||
\(169\) | −5.10351 | −0.392578 | ||||||||
\(170\) | −1.15926 | − | 5.66912i | −0.0889114 | − | 0.434802i | ||||
\(171\) | −4.48474 | −0.342956 | ||||||||
\(172\) | −9.48992 | −0.723600 | ||||||||
\(173\) | 24.6065i | 1.87079i | 0.353599 | + | 0.935397i | \(0.384958\pi\) | ||||
−0.353599 | + | 0.935397i | \(0.615042\pi\) | |||||||
\(174\) | 0.195157 | 0.0147948 | ||||||||
\(175\) | 13.1238i | 0.992070i | ||||||||
\(176\) | − | 2.97225i | − | 0.224041i | ||||||
\(177\) | 0.218647i | 0.0164345i | ||||||||
\(178\) | 2.97490 | 0.222978 | ||||||||
\(179\) | 12.3470 | 0.922859 | 0.461430 | − | 0.887177i | \(-0.347337\pi\) | ||||
0.461430 | + | 0.887177i | \(0.347337\pi\) | |||||||
\(180\) | 18.2270i | 1.35856i | ||||||||
\(181\) | − | 9.06052i | − | 0.673463i | −0.941601 | − | 0.336732i | \(-0.890678\pi\) | ||
0.941601 | − | 0.336732i | \(-0.109322\pi\) | |||||||
\(182\) | 2.51500i | 0.186425i | ||||||||
\(183\) | 0.743379 | 0.0549522 | ||||||||
\(184\) | − | 12.1078i | − | 0.892597i | ||||||
\(185\) | 9.78583 | 0.719468 | ||||||||
\(186\) | 0.0481274 | 0.00352887 | ||||||||
\(187\) | −0.826028 | − | 4.03951i | −0.0604052 | − | 0.295399i | ||||
\(188\) | 9.40185 | 0.685700 | ||||||||
\(189\) | 1.13733 | 0.0827285 | ||||||||
\(190\) | 2.10355i | 0.152608i | ||||||||
\(191\) | 17.0736 | 1.23540 | 0.617702 | − | 0.786412i | \(-0.288064\pi\) | ||||
0.617702 | + | 0.786412i | \(0.288064\pi\) | |||||||
\(192\) | − | 0.362638i | − | 0.0261711i | ||||||
\(193\) | 20.7292i | 1.49212i | 0.665877 | + | 0.746061i | \(0.268057\pi\) | ||||
−0.665877 | + | 0.746061i | \(0.731943\pi\) | |||||||
\(194\) | − | 6.03211i | − | 0.433080i | ||||||
\(195\) | −0.836357 | −0.0598928 | ||||||||
\(196\) | −4.48806 | −0.320576 | ||||||||
\(197\) | − | 15.1339i | − | 1.07824i | −0.842228 | − | 0.539122i | \(-0.818756\pi\) | ||
0.842228 | − | 0.539122i | \(-0.181244\pi\) | |||||||
\(198\) | − | 1.25696i | − | 0.0893285i | ||||||
\(199\) | 20.5506i | 1.45679i | 0.685155 | + | 0.728397i | \(0.259735\pi\) | ||||
−0.685155 | + | 0.728397i | \(0.740265\pi\) | |||||||
\(200\) | 9.89478 | 0.699666 | ||||||||
\(201\) | 0.528822i | 0.0373002i | ||||||||
\(202\) | −5.46782 | −0.384715 | ||||||||
\(203\) | −11.1087 | −0.779677 | ||||||||
\(204\) | −0.134197 | − | 0.656264i | −0.00939570 | − | 0.0459477i | ||||
\(205\) | 19.5826 | 1.36771 | ||||||||
\(206\) | −0.930077 | −0.0648015 | ||||||||
\(207\) | 22.5538i | 1.56760i | ||||||||
\(208\) | −8.35222 | −0.579122 | ||||||||
\(209\) | 1.49888i | 0.103680i | ||||||||
\(210\) | − | 0.266377i | − | 0.0183818i | ||||||
\(211\) | − | 15.7349i | − | 1.08324i | −0.840625 | − | 0.541618i | \(-0.817812\pi\) | ||
0.840625 | − | 0.541618i | \(-0.182188\pi\) | |||||||
\(212\) | −21.4494 | −1.47315 | ||||||||
\(213\) | −1.29094 | −0.0884537 | ||||||||
\(214\) | 3.58925i | 0.245356i | ||||||||
\(215\) | − | 17.3855i | − | 1.18568i | ||||||
\(216\) | − | 0.857494i | − | 0.0583450i | ||||||
\(217\) | −2.73950 | −0.185969 | ||||||||
\(218\) | − | 5.66717i | − | 0.383829i | ||||||
\(219\) | −0.534058 | −0.0360883 | ||||||||
\(220\) | 6.09179 | 0.410708 | ||||||||
\(221\) | −11.3513 | + | 2.32120i | −0.763572 | + | 0.156141i | ||||
\(222\) | −0.109636 | −0.00735830 | ||||||||
\(223\) | −7.41477 | −0.496530 | −0.248265 | − | 0.968692i | \(-0.579860\pi\) | ||||
−0.248265 | + | 0.968692i | \(0.579860\pi\) | |||||||
\(224\) | − | 9.50423i | − | 0.635028i | ||||||
\(225\) | −18.4315 | −1.22877 | ||||||||
\(226\) | 0.618350i | 0.0411320i | ||||||||
\(227\) | − | 6.82759i | − | 0.453163i | −0.973992 | − | 0.226582i | \(-0.927245\pi\) | ||
0.973992 | − | 0.226582i | \(-0.0727550\pi\) | |||||||
\(228\) | 0.243509i | 0.0161268i | ||||||||
\(229\) | −2.29082 | −0.151382 | −0.0756909 | − | 0.997131i | \(-0.524116\pi\) | ||||
−0.0756909 | + | 0.997131i | \(0.524116\pi\) | |||||||
\(230\) | 10.5788 | 0.697545 | ||||||||
\(231\) | − | 0.189806i | − | 0.0124883i | ||||||
\(232\) | 8.37543i | 0.549874i | ||||||||
\(233\) | 9.82817i | 0.643865i | 0.946763 | + | 0.321932i | \(0.104332\pi\) | ||||
−0.946763 | + | 0.321932i | \(0.895668\pi\) | |||||||
\(234\) | −3.53215 | −0.230904 | ||||||||
\(235\) | 17.2242i | 1.12358i | ||||||||
\(236\) | −4.47522 | −0.291312 | ||||||||
\(237\) | 0.933453 | 0.0606343 | ||||||||
\(238\) | −0.739293 | − | 3.61536i | −0.0479213 | − | 0.234349i | ||||
\(239\) | 1.89256 | 0.122419 | 0.0612096 | − | 0.998125i | \(-0.480504\pi\) | ||||
0.0612096 | + | 0.998125i | \(0.480504\pi\) | |||||||
\(240\) | 0.884625 | 0.0571023 | ||||||||
\(241\) | − | 25.2013i | − | 1.62336i | −0.584104 | − | 0.811679i | \(-0.698554\pi\) | ||
0.584104 | − | 0.811679i | \(-0.301446\pi\) | |||||||
\(242\) | −0.420099 | −0.0270050 | ||||||||
\(243\) | 2.39701i | 0.153768i | ||||||||
\(244\) | 15.2153i | 0.974060i | ||||||||
\(245\) | − | 8.22212i | − | 0.525292i | ||||||
\(246\) | −0.219395 | −0.0139881 | ||||||||
\(247\) | 4.21195 | 0.268000 | ||||||||
\(248\) | 2.06546i | 0.131157i | ||||||||
\(249\) | − | 0.909664i | − | 0.0576476i | ||||||
\(250\) | 1.62817i | 0.102975i | ||||||||
\(251\) | −7.89903 | −0.498582 | −0.249291 | − | 0.968429i | \(-0.580198\pi\) | ||||
−0.249291 | + | 0.968429i | \(0.580198\pi\) | |||||||
\(252\) | 11.6239i | 0.732234i | ||||||||
\(253\) | 7.53789 | 0.473903 | ||||||||
\(254\) | 3.03062 | 0.190158 | ||||||||
\(255\) | 1.20227 | − | 0.245850i | 0.0752894 | − | 0.0153957i | ||||
\(256\) | 3.67413 | 0.229633 | ||||||||
\(257\) | 12.7284 | 0.793974 | 0.396987 | − | 0.917824i | \(-0.370056\pi\) | ||||
0.396987 | + | 0.917824i | \(0.370056\pi\) | |||||||
\(258\) | 0.194780i | 0.0121265i | ||||||||
\(259\) | 6.24069 | 0.387777 | ||||||||
\(260\) | − | 17.1183i | − | 1.06163i | ||||||
\(261\) | − | 15.6014i | − | 0.965702i | ||||||
\(262\) | 6.47991i | 0.400330i | ||||||||
\(263\) | −20.8282 | −1.28432 | −0.642161 | − | 0.766570i | \(-0.721962\pi\) | ||||
−0.642161 | + | 0.766570i | \(0.721962\pi\) | |||||||
\(264\) | −0.143105 | −0.00880750 | ||||||||
\(265\) | − | 39.2952i | − | 2.41388i | ||||||
\(266\) | 1.34149i | 0.0822522i | ||||||||
\(267\) | 0.630900i | 0.0386105i | ||||||||
\(268\) | −10.8238 | −0.661169 | ||||||||
\(269\) | − | 17.2133i | − | 1.04951i | −0.851253 | − | 0.524756i | \(-0.824157\pi\) | ||
0.851253 | − | 0.524756i | \(-0.175843\pi\) | |||||||
\(270\) | 0.749209 | 0.0455954 | ||||||||
\(271\) | 25.2009 | 1.53085 | 0.765423 | − | 0.643528i | \(-0.222530\pi\) | ||||
0.765423 | + | 0.643528i | \(0.222530\pi\) | |||||||
\(272\) | 12.0064 | − | 2.45516i | 0.727997 | − | 0.148866i | ||||
\(273\) | −0.533368 | −0.0322809 | ||||||||
\(274\) | −2.34238 | −0.141508 | ||||||||
\(275\) | 6.16015i | 0.371471i | ||||||||
\(276\) | 1.22461 | 0.0737130 | ||||||||
\(277\) | 26.4237i | 1.58765i | 0.608149 | + | 0.793823i | \(0.291912\pi\) | ||||
−0.608149 | + | 0.793823i | \(0.708088\pi\) | |||||||
\(278\) | − | 0.589381i | − | 0.0353487i | ||||||
\(279\) | − | 3.84744i | − | 0.230340i | ||||||
\(280\) | 11.4319 | 0.683189 | ||||||||
\(281\) | 24.1420 | 1.44019 | 0.720096 | − | 0.693874i | \(-0.244098\pi\) | ||||
0.720096 | + | 0.693874i | \(0.244098\pi\) | |||||||
\(282\) | − | 0.192972i | − | 0.0114913i | ||||||
\(283\) | − | 20.4973i | − | 1.21844i | −0.793002 | − | 0.609219i | \(-0.791483\pi\) | ||
0.793002 | − | 0.609219i | \(-0.208517\pi\) | |||||||
\(284\) | − | 26.4226i | − | 1.56789i | ||||||
\(285\) | −0.446109 | −0.0264252 | ||||||||
\(286\) | 1.18051i | 0.0698049i | ||||||||
\(287\) | 12.4884 | 0.737165 | ||||||||
\(288\) | 13.3480 | 0.786541 | ||||||||
\(289\) | 15.6354 | − | 6.67351i | 0.919727 | − | 0.392559i | ||||
\(290\) | −7.31778 | −0.429715 | ||||||||
\(291\) | 1.27925 | 0.0749912 | ||||||||
\(292\) | − | 10.9310i | − | 0.639686i | ||||||
\(293\) | 8.54045 | 0.498938 | 0.249469 | − | 0.968383i | \(-0.419744\pi\) | ||||
0.249469 | + | 0.968383i | \(0.419744\pi\) | |||||||
\(294\) | 0.0921171i | 0.00537238i | ||||||||
\(295\) | − | 8.19859i | − | 0.477340i | ||||||
\(296\) | − | 4.70519i | − | 0.273484i | ||||||
\(297\) | 0.533846 | 0.0309769 | ||||||||
\(298\) | −5.69187 | −0.329721 | ||||||||
\(299\) | − | 21.1820i | − | 1.22499i | ||||||
\(300\) | 1.00078i | 0.0577803i | ||||||||
\(301\) | − | 11.0872i | − | 0.639057i | ||||||
\(302\) | −9.23437 | −0.531378 | ||||||||
\(303\) | − | 1.15958i | − | 0.0666163i | ||||||
\(304\) | −4.45503 | −0.255514 | ||||||||
\(305\) | −27.8744 | −1.59608 | ||||||||
\(306\) | 5.07752 | − | 1.03829i | 0.290263 | − | 0.0593549i | ||||
\(307\) | −19.3840 | −1.10631 | −0.553153 | − | 0.833080i | \(-0.686576\pi\) | ||||
−0.553153 | + | 0.833080i | \(0.686576\pi\) | |||||||
\(308\) | 3.88490 | 0.221363 | ||||||||
\(309\) | − | 0.197245i | − | 0.0112209i | ||||||
\(310\) | −1.80463 | −0.102496 | ||||||||
\(311\) | − | 16.7515i | − | 0.949888i | −0.880016 | − | 0.474944i | \(-0.842468\pi\) | ||
0.880016 | − | 0.474944i | \(-0.157532\pi\) | |||||||
\(312\) | 0.402135i | 0.0227664i | ||||||||
\(313\) | 20.2547i | 1.14486i | 0.819953 | + | 0.572431i | \(0.194000\pi\) | ||||
−0.819953 | + | 0.572431i | \(0.806000\pi\) | |||||||
\(314\) | −2.51515 | −0.141938 | ||||||||
\(315\) | −21.2949 | −1.19983 | ||||||||
\(316\) | 19.1057i | 1.07478i | ||||||||
\(317\) | 8.62805i | 0.484599i | 0.970201 | + | 0.242300i | \(0.0779017\pi\) | ||||
−0.970201 | + | 0.242300i | \(0.922098\pi\) | |||||||
\(318\) | 0.440247i | 0.0246878i | ||||||||
\(319\) | −5.21426 | −0.291942 | ||||||||
\(320\) | 13.5978i | 0.760140i | ||||||||
\(321\) | −0.761187 | −0.0424853 | ||||||||
\(322\) | 6.74639 | 0.375962 | ||||||||
\(323\) | −6.05474 | + | 1.23812i | −0.336895 | + | 0.0688906i | ||||
\(324\) | −16.2815 | −0.904528 | ||||||||
\(325\) | 17.3104 | 0.960210 | ||||||||
\(326\) | 10.4487i | 0.578702i | ||||||||
\(327\) | 1.20186 | 0.0664631 | ||||||||
\(328\) | − | 9.41566i | − | 0.519893i | ||||||
\(329\) | 10.9843i | 0.605586i | ||||||||
\(330\) | − | 0.125034i | − | 0.00688287i | ||||||
\(331\) | −31.2792 | −1.71926 | −0.859630 | − | 0.510916i | \(-0.829306\pi\) | ||||
−0.859630 | + | 0.510916i | \(0.829306\pi\) | |||||||
\(332\) | 18.6188 | 1.02184 | ||||||||
\(333\) | 8.76462i | 0.480298i | ||||||||
\(334\) | 5.21860i | 0.285549i | ||||||||
\(335\) | − | 19.8292i | − | 1.08338i | ||||||
\(336\) | 0.564150 | 0.0307769 | ||||||||
\(337\) | 26.7786i | 1.45872i | 0.684128 | + | 0.729362i | \(0.260183\pi\) | ||||
−0.684128 | + | 0.729362i | \(0.739817\pi\) | |||||||
\(338\) | −2.14398 | −0.116617 | ||||||||
\(339\) | −0.131136 | −0.00712233 | ||||||||
\(340\) | 5.03199 | + | 24.6079i | 0.272898 | + | 1.33455i | ||||
\(341\) | −1.28588 | −0.0696344 | ||||||||
\(342\) | −1.88403 | −0.101877 | ||||||||
\(343\) | − | 20.1566i | − | 1.08835i | ||||||
\(344\) | −8.35926 | −0.450701 | ||||||||
\(345\) | 2.24349i | 0.120785i | ||||||||
\(346\) | 10.3372i | 0.555729i | ||||||||
\(347\) | 4.23949i | 0.227588i | 0.993504 | + | 0.113794i | \(0.0363004\pi\) | ||||
−0.993504 | + | 0.113794i | \(0.963700\pi\) | |||||||
\(348\) | −0.847114 | −0.0454101 | ||||||||
\(349\) | 3.71727 | 0.198981 | 0.0994904 | − | 0.995039i | \(-0.468279\pi\) | ||||
0.0994904 | + | 0.995039i | \(0.468279\pi\) | |||||||
\(350\) | 5.51332i | 0.294699i | ||||||||
\(351\) | − | 1.50014i | − | 0.0800718i | ||||||
\(352\) | − | 4.46115i | − | 0.237780i | ||||||
\(353\) | −21.8301 | −1.16190 | −0.580950 | − | 0.813939i | \(-0.697319\pi\) | ||||
−0.580950 | + | 0.813939i | \(0.697319\pi\) | |||||||
\(354\) | 0.0918535i | 0.00488196i | ||||||||
\(355\) | 48.4062 | 2.56914 | ||||||||
\(356\) | −12.9131 | −0.684393 | ||||||||
\(357\) | 0.766724 | − | 0.156785i | 0.0405793 | − | 0.00829794i | ||||
\(358\) | 5.18697 | 0.274140 | ||||||||
\(359\) | −27.1882 | −1.43494 | −0.717470 | − | 0.696589i | \(-0.754700\pi\) | ||||
−0.717470 | + | 0.696589i | \(0.754700\pi\) | |||||||
\(360\) | 16.0554i | 0.846193i | ||||||||
\(361\) | −16.7534 | −0.881756 | ||||||||
\(362\) | − | 3.80632i | − | 0.200056i | ||||||
\(363\) | − | 0.0890922i | − | 0.00467613i | ||||||
\(364\) | − | 10.9168i | − | 0.572198i | ||||||
\(365\) | 20.0255 | 1.04818 | ||||||||
\(366\) | 0.312293 | 0.0163238 | ||||||||
\(367\) | − | 28.3700i | − | 1.48090i | −0.672110 | − | 0.740451i | \(-0.734612\pi\) | ||
0.672110 | − | 0.740451i | \(-0.265388\pi\) | |||||||
\(368\) | 22.4045i | 1.16791i | ||||||||
\(369\) | 17.5391i | 0.913047i | ||||||||
\(370\) | 4.11102 | 0.213722 | ||||||||
\(371\) | − | 25.0596i | − | 1.30103i | ||||||
\(372\) | −0.208906 | −0.0108313 | ||||||||
\(373\) | 9.60655 | 0.497408 | 0.248704 | − | 0.968579i | \(-0.419995\pi\) | ||||
0.248704 | + | 0.968579i | \(0.419995\pi\) | |||||||
\(374\) | −0.347014 | − | 1.69700i | −0.0179437 | − | 0.0877496i | ||||
\(375\) | −0.345293 | −0.0178309 | ||||||||
\(376\) | 8.28168 | 0.427095 | ||||||||
\(377\) | 14.6524i | 0.754638i | ||||||||
\(378\) | 0.477791 | 0.0245749 | ||||||||
\(379\) | 14.9152i | 0.766141i | 0.923719 | + | 0.383071i | \(0.125133\pi\) | ||||
−0.923719 | + | 0.383071i | \(0.874867\pi\) | |||||||
\(380\) | − | 9.13085i | − | 0.468403i | ||||||
\(381\) | 0.642716i | 0.0329273i | ||||||||
\(382\) | 7.17262 | 0.366983 | ||||||||
\(383\) | 23.0508 | 1.17784 | 0.588919 | − | 0.808192i | \(-0.299554\pi\) | ||||
0.588919 | + | 0.808192i | \(0.299554\pi\) | |||||||
\(384\) | − | 0.947251i | − | 0.0483392i | ||||||
\(385\) | 7.11713i | 0.362723i | ||||||||
\(386\) | 8.70833i | 0.443243i | ||||||||
\(387\) | 15.5713 | 0.791531 | ||||||||
\(388\) | 26.1835i | 1.32926i | ||||||||
\(389\) | 18.2973 | 0.927710 | 0.463855 | − | 0.885911i | \(-0.346466\pi\) | ||||
0.463855 | + | 0.885911i | \(0.346466\pi\) | |||||||
\(390\) | −0.351353 | −0.0177914 | ||||||||
\(391\) | 6.22651 | + | 30.4494i | 0.314888 | + | 1.53989i | ||||
\(392\) | −3.95334 | −0.199674 | ||||||||
\(393\) | −1.37422 | −0.0693204 | ||||||||
\(394\) | − | 6.35773i | − | 0.320298i | ||||||
\(395\) | −35.0016 | −1.76112 | ||||||||
\(396\) | 5.45608i | 0.274178i | ||||||||
\(397\) | − | 0.409232i | − | 0.0205388i | −0.999947 | − | 0.0102694i | \(-0.996731\pi\) | ||
0.999947 | − | 0.0102694i | \(-0.00326891\pi\) | |||||||
\(398\) | 8.63330i | 0.432748i | ||||||||
\(399\) | −0.284496 | −0.0142426 | ||||||||
\(400\) | −18.3095 | −0.915474 | ||||||||
\(401\) | 7.92981i | 0.395996i | 0.980202 | + | 0.197998i | \(0.0634439\pi\) | ||||
−0.980202 | + | 0.197998i | \(0.936556\pi\) | |||||||
\(402\) | 0.222158i | 0.0110802i | ||||||||
\(403\) | 3.61342i | 0.179997i | ||||||||
\(404\) | 23.7341 | 1.18081 | ||||||||
\(405\) | − | 29.8277i | − | 1.48215i | ||||||
\(406\) | −4.66675 | −0.231607 | ||||||||
\(407\) | 2.92929 | 0.145200 | ||||||||
\(408\) | −0.118209 | − | 0.578074i | −0.00585220 | − | 0.0286189i | ||||
\(409\) | 8.02278 | 0.396701 | 0.198351 | − | 0.980131i | \(-0.436442\pi\) | ||||
0.198351 | + | 0.980131i | \(0.436442\pi\) | |||||||
\(410\) | 8.22664 | 0.406285 | ||||||||
\(411\) | − | 0.496758i | − | 0.0245033i | ||||||
\(412\) | 4.03717 | 0.198897 | ||||||||
\(413\) | − | 5.22846i | − | 0.257276i | ||||||
\(414\) | 9.47484i | 0.465663i | ||||||||
\(415\) | 34.1096i | 1.67437i | ||||||||
\(416\) | −12.5361 | −0.614635 | ||||||||
\(417\) | 0.124993 | 0.00612091 | ||||||||
\(418\) | 0.629677i | 0.0307985i | ||||||||
\(419\) | − | 19.3962i | − | 0.947565i | −0.880642 | − | 0.473782i | \(-0.842888\pi\) | ||
0.880642 | − | 0.473782i | \(-0.157112\pi\) | |||||||
\(420\) | 1.15626i | 0.0564196i | ||||||||
\(421\) | −7.41456 | −0.361364 | −0.180682 | − | 0.983542i | \(-0.557830\pi\) | ||||
−0.180682 | + | 0.983542i | \(0.557830\pi\) | |||||||
\(422\) | − | 6.61022i | − | 0.321781i | ||||||
\(423\) | −15.4267 | −0.750074 | ||||||||
\(424\) | −18.8938 | −0.917564 | ||||||||
\(425\) | −24.8840 | + | 5.08846i | −1.20705 | + | 0.246826i | ||||
\(426\) | −0.542323 | −0.0262756 | ||||||||
\(427\) | −17.7763 | −0.860254 | ||||||||
\(428\) | − | 15.5798i | − | 0.753078i | ||||||
\(429\) | −0.250355 | −0.0120873 | ||||||||
\(430\) | − | 7.30365i | − | 0.352213i | ||||||
\(431\) | 7.11737i | 0.342831i | 0.985199 | + | 0.171416i | \(0.0548341\pi\) | ||||
−0.985199 | + | 0.171416i | \(0.945166\pi\) | |||||||
\(432\) | 1.58672i | 0.0763412i | ||||||||
\(433\) | 4.49645 | 0.216086 | 0.108043 | − | 0.994146i | \(-0.465542\pi\) | ||||
0.108043 | + | 0.994146i | \(0.465542\pi\) | |||||||
\(434\) | −1.15086 | −0.0552431 | ||||||||
\(435\) | − | 1.55191i | − | 0.0744085i | ||||||
\(436\) | 24.5994i | 1.17810i | ||||||||
\(437\) | − | 11.2984i | − | 0.540474i | ||||||
\(438\) | −0.224357 | −0.0107202 | ||||||||
\(439\) | − | 7.38699i | − | 0.352562i | −0.984340 | − | 0.176281i | \(-0.943593\pi\) | ||
0.984340 | − | 0.176281i | \(-0.0564067\pi\) | |||||||
\(440\) | 5.36599 | 0.255814 | ||||||||
\(441\) | 7.36410 | 0.350671 | ||||||||
\(442\) | −4.76868 | + | 0.975133i | −0.226823 | + | 0.0463823i | ||||
\(443\) | 25.0046 | 1.18801 | 0.594003 | − | 0.804463i | \(-0.297547\pi\) | ||||
0.594003 | + | 0.804463i | \(0.297547\pi\) | |||||||
\(444\) | 0.475896 | 0.0225850 | ||||||||
\(445\) | − | 23.6568i | − | 1.12144i | ||||||
\(446\) | −3.11494 | −0.147497 | ||||||||
\(447\) | − | 1.20710i | − | 0.0570938i | ||||||
\(448\) | 8.67169i | 0.409699i | ||||||||
\(449\) | 20.6423i | 0.974168i | 0.873355 | + | 0.487084i | \(0.161939\pi\) | ||||
−0.873355 | + | 0.487084i | \(0.838061\pi\) | |||||||
\(450\) | −7.74308 | −0.365012 | ||||||||
\(451\) | 5.86187 | 0.276024 | ||||||||
\(452\) | − | 2.68406i | − | 0.126247i | ||||||
\(453\) | − | 1.95837i | − | 0.0920123i | ||||||
\(454\) | − | 2.86827i | − | 0.134614i | ||||||
\(455\) | 19.9996 | 0.937597 | ||||||||
\(456\) | 0.214497i | 0.0100447i | ||||||||
\(457\) | −30.2346 | −1.41431 | −0.707157 | − | 0.707056i | \(-0.750023\pi\) | ||||
−0.707157 | + | 0.707056i | \(0.750023\pi\) | |||||||
\(458\) | −0.962373 | −0.0449687 | ||||||||
\(459\) | 0.440972 | + | 2.15648i | 0.0205828 | + | 0.100656i | ||||
\(460\) | −45.9192 | −2.14099 | ||||||||
\(461\) | 29.1681 | 1.35849 | 0.679247 | − | 0.733909i | \(-0.262306\pi\) | ||||
0.679247 | + | 0.733909i | \(0.262306\pi\) | |||||||
\(462\) | − | 0.0797373i | − | 0.00370971i | ||||||
\(463\) | −9.72292 | −0.451862 | −0.225931 | − | 0.974143i | \(-0.572542\pi\) | ||||
−0.225931 | + | 0.974143i | \(0.572542\pi\) | |||||||
\(464\) | − | 15.4981i | − | 0.719479i | ||||||
\(465\) | − | 0.382715i | − | 0.0177480i | ||||||
\(466\) | 4.12880i | 0.191263i | ||||||||
\(467\) | −12.1689 | −0.563110 | −0.281555 | − | 0.959545i | \(-0.590850\pi\) | ||||
−0.281555 | + | 0.959545i | \(0.590850\pi\) | |||||||
\(468\) | 15.3319 | 0.708720 | ||||||||
\(469\) | − | 12.6456i | − | 0.583920i | ||||||
\(470\) | 7.23586i | 0.333766i | ||||||||
\(471\) | − | 0.533399i | − | 0.0245777i | ||||||
\(472\) | −3.94202 | −0.181446 | ||||||||
\(473\) | − | 5.20419i | − | 0.239289i | ||||||
\(474\) | 0.392143 | 0.0180117 | ||||||||
\(475\) | 9.23331 | 0.423653 | ||||||||
\(476\) | 3.20904 | + | 15.6931i | 0.147086 | + | 0.719292i | ||||
\(477\) | 35.1945 | 1.61145 | ||||||||
\(478\) | 0.795061 | 0.0363653 | ||||||||
\(479\) | − | 9.41235i | − | 0.430061i | −0.976607 | − | 0.215031i | \(-0.931015\pi\) | ||
0.976607 | − | 0.215031i | \(-0.0689851\pi\) | |||||||
\(480\) | 1.32777 | 0.0606040 | ||||||||
\(481\) | − | 8.23151i | − | 0.375324i | ||||||
\(482\) | − | 10.5870i | − | 0.482227i | ||||||
\(483\) | 1.43073i | 0.0651007i | ||||||||
\(484\) | 1.82352 | 0.0828871 | ||||||||
\(485\) | −47.9681 | −2.17812 | ||||||||
\(486\) | 1.00698i | 0.0456776i | ||||||||
\(487\) | 3.03498i | 0.137528i | 0.997633 | + | 0.0687640i | \(0.0219056\pi\) | ||||
−0.997633 | + | 0.0687640i | \(0.978094\pi\) | |||||||
\(488\) | 13.4025i | 0.606703i | ||||||||
\(489\) | −2.21591 | −0.100207 | ||||||||
\(490\) | − | 3.45411i | − | 0.156041i | ||||||
\(491\) | 8.61942 | 0.388989 | 0.194494 | − | 0.980904i | \(-0.437693\pi\) | ||||
0.194494 | + | 0.980904i | \(0.437693\pi\) | |||||||
\(492\) | 0.952325 | 0.0429341 | ||||||||
\(493\) | −4.30712 | − | 21.0631i | −0.193983 | − | 0.948633i | ||||
\(494\) | 1.76944 | 0.0796107 | ||||||||
\(495\) | −9.99553 | −0.449265 | ||||||||
\(496\) | − | 3.82196i | − | 0.171611i | ||||||
\(497\) | 30.8700 | 1.38471 | ||||||||
\(498\) | − | 0.382149i | − | 0.0171245i | ||||||
\(499\) | 0.575704i | 0.0257721i | 0.999917 | + | 0.0128860i | \(0.00410186\pi\) | ||||
−0.999917 | + | 0.0128860i | \(0.995898\pi\) | |||||||
\(500\) | − | 7.06738i | − | 0.316063i | ||||||
\(501\) | −1.10673 | −0.0494450 | ||||||||
\(502\) | −3.31838 | −0.148106 | ||||||||
\(503\) | 8.31424i | 0.370714i | 0.982671 | + | 0.185357i | \(0.0593441\pi\) | ||||
−0.982671 | + | 0.185357i | \(0.940656\pi\) | |||||||
\(504\) | 10.2390i | 0.456079i | ||||||||
\(505\) | 43.4808i | 1.93487i | ||||||||
\(506\) | 3.16666 | 0.140775 | ||||||||
\(507\) | − | 0.454683i | − | 0.0201932i | ||||||
\(508\) | −13.1550 | −0.583657 | ||||||||
\(509\) | 31.2778 | 1.38636 | 0.693182 | − | 0.720762i | \(-0.256208\pi\) | ||||
0.693182 | + | 0.720762i | \(0.256208\pi\) | |||||||
\(510\) | 0.505075 | − | 0.103281i | 0.0223651 | − | 0.00457337i | ||||
\(511\) | 12.7708 | 0.564947 | ||||||||
\(512\) | 22.8080 | 1.00798 | ||||||||
\(513\) | − | 0.800170i | − | 0.0353284i | ||||||
\(514\) | 5.34718 | 0.235854 | ||||||||
\(515\) | 7.39609i | 0.325911i | ||||||||
\(516\) | − | 0.845478i | − | 0.0372201i | ||||||
\(517\) | 5.15589i | 0.226756i | ||||||||
\(518\) | 2.62171 | 0.115191 | ||||||||
\(519\) | −2.19224 | −0.0962288 | ||||||||
\(520\) | − | 15.0788i | − | 0.661249i | ||||||
\(521\) | 11.0557i | 0.484357i | 0.970232 | + | 0.242179i | \(0.0778620\pi\) | ||||
−0.970232 | + | 0.242179i | \(0.922138\pi\) | |||||||
\(522\) | − | 6.55413i | − | 0.286866i | ||||||
\(523\) | 33.5485 | 1.46697 | 0.733486 | − | 0.679704i | \(-0.237892\pi\) | ||||
0.733486 | + | 0.679704i | \(0.237892\pi\) | |||||||
\(524\) | − | 28.1272i | − | 1.22874i | ||||||
\(525\) | −1.16923 | −0.0510295 | ||||||||
\(526\) | −8.74991 | −0.381514 | ||||||||
\(527\) | −1.06217 | − | 5.19434i | −0.0462691 | − | 0.226269i | ||||
\(528\) | 0.264804 | 0.0115241 | ||||||||
\(529\) | −33.8197 | −1.47042 | ||||||||
\(530\) | − | 16.5079i | − | 0.717057i | ||||||
\(531\) | 7.34302 | 0.318660 | ||||||||
\(532\) | − | 5.82299i | − | 0.252459i | ||||||
\(533\) | − | 16.4722i | − | 0.713492i | ||||||
\(534\) | 0.265041i | 0.0114694i | ||||||||
\(535\) | 28.5422 | 1.23399 | ||||||||
\(536\) | −9.53421 | −0.411815 | ||||||||
\(537\) | 1.10002i | 0.0474695i | ||||||||
\(538\) | − | 7.23128i | − | 0.311763i | ||||||
\(539\) | − | 2.46121i | − | 0.106012i | ||||||
\(540\) | −3.25208 | −0.139947 | ||||||||
\(541\) | − | 0.0518839i | − | 0.00223066i | −0.999999 | − | 0.00111533i | \(-0.999645\pi\) | ||
0.999999 | − | 0.00111533i | \(-0.000355021\pi\) | |||||||
\(542\) | 10.5869 | 0.454745 | ||||||||
\(543\) | 0.807222 | 0.0346412 | ||||||||
\(544\) | 18.0209 | − | 3.68504i | 0.772639 | − | 0.157995i | ||||
\(545\) | −45.0661 | −1.93042 | ||||||||
\(546\) | −0.224067 | −0.00958919 | ||||||||
\(547\) | − | 11.2925i | − | 0.482831i | −0.970422 | − | 0.241415i | \(-0.922388\pi\) | ||
0.970422 | − | 0.241415i | \(-0.0776116\pi\) | |||||||
\(548\) | 10.1675 | 0.434335 | ||||||||
\(549\) | − | 24.9656i | − | 1.06550i | ||||||
\(550\) | 2.58787i | 0.110347i | ||||||||
\(551\) | 7.81554i | 0.332953i | ||||||||
\(552\) | 1.07871 | 0.0459129 | ||||||||
\(553\) | −22.3215 | −0.949205 | ||||||||
\(554\) | 11.1006i | 0.471618i | ||||||||
\(555\) | 0.871841i | 0.0370076i | ||||||||
\(556\) | 2.55832i | 0.108497i | ||||||||
\(557\) | −16.1450 | −0.684084 | −0.342042 | − | 0.939685i | \(-0.611118\pi\) | ||||
−0.342042 | + | 0.939685i | \(0.611118\pi\) | |||||||
\(558\) | − | 1.61631i | − | 0.0684237i | ||||||
\(559\) | −14.6241 | −0.618535 | ||||||||
\(560\) | −21.1539 | −0.893914 | ||||||||
\(561\) | 0.359889 | − | 0.0735927i | 0.0151945 | − | 0.00310709i | ||||
\(562\) | 10.1420 | 0.427816 | ||||||||
\(563\) | 4.97294 | 0.209585 | 0.104792 | − | 0.994494i | \(-0.466582\pi\) | ||||
0.104792 | + | 0.994494i | \(0.466582\pi\) | |||||||
\(564\) | 0.837631i | 0.0352706i | ||||||||
\(565\) | 4.91719 | 0.206868 | ||||||||
\(566\) | − | 8.61089i | − | 0.361943i | ||||||
\(567\) | − | 19.0219i | − | 0.798846i | ||||||
\(568\) | − | 23.2745i | − | 0.976578i | ||||||
\(569\) | 35.0006 | 1.46730 | 0.733650 | − | 0.679528i | \(-0.237815\pi\) | ||||
0.733650 | + | 0.679528i | \(0.237815\pi\) | |||||||
\(570\) | −0.187410 | −0.00784974 | ||||||||
\(571\) | − | 22.3287i | − | 0.934425i | −0.884145 | − | 0.467213i | \(-0.845258\pi\) | ||
0.884145 | − | 0.467213i | \(-0.154742\pi\) | |||||||
\(572\) | − | 5.12421i | − | 0.214254i | ||||||
\(573\) | 1.52113i | 0.0635460i | ||||||||
\(574\) | 5.24636 | 0.218979 | ||||||||
\(575\) | − | 46.4345i | − | 1.93645i | ||||||
\(576\) | −12.1788 | −0.507450 | ||||||||
\(577\) | −28.3996 | −1.18229 | −0.591145 | − | 0.806566i | \(-0.701324\pi\) | ||||
−0.591145 | + | 0.806566i | \(0.701324\pi\) | |||||||
\(578\) | 6.56840 | − | 2.80354i | 0.273209 | − | 0.116612i | ||||
\(579\) | −1.84681 | −0.0767509 | ||||||||
\(580\) | 31.7641 | 1.31893 | ||||||||
\(581\) | 21.7526i | 0.902451i | ||||||||
\(582\) | 0.537414 | 0.0222765 | ||||||||
\(583\) | − | 11.7626i | − | 0.487158i | ||||||
\(584\) | − | 9.62861i | − | 0.398435i | ||||||
\(585\) | 28.0881i | 1.16130i | ||||||||
\(586\) | 3.58783 | 0.148212 | ||||||||
\(587\) | −22.5993 | −0.932774 | −0.466387 | − | 0.884581i | \(-0.654445\pi\) | ||||
−0.466387 | + | 0.884581i | \(0.654445\pi\) | |||||||
\(588\) | − | 0.399851i | − | 0.0164896i | ||||||
\(589\) | 1.92738i | 0.0794163i | ||||||||
\(590\) | − | 3.44422i | − | 0.141796i | ||||||
\(591\) | 1.34831 | 0.0554620 | ||||||||
\(592\) | 8.70657i | 0.357838i | ||||||||
\(593\) | −17.1377 | −0.703762 | −0.351881 | − | 0.936045i | \(-0.614458\pi\) | ||||
−0.351881 | + | 0.936045i | \(0.614458\pi\) | |||||||
\(594\) | 0.224268 | 0.00920184 | ||||||||
\(595\) | −28.7498 | + | 5.87895i | −1.17863 | + | 0.241014i | ||||
\(596\) | 24.7066 | 1.01202 | ||||||||
\(597\) | −1.83090 | −0.0749337 | ||||||||
\(598\) | − | 8.89853i | − | 0.363888i | ||||||
\(599\) | 18.9060 | 0.772477 | 0.386238 | − | 0.922399i | \(-0.373774\pi\) | ||||
0.386238 | + | 0.922399i | \(0.373774\pi\) | |||||||
\(600\) | 0.881547i | 0.0359890i | ||||||||
\(601\) | − | 33.0976i | − | 1.35008i | −0.737782 | − | 0.675039i | \(-0.764127\pi\) | ||
0.737782 | − | 0.675039i | \(-0.235873\pi\) | |||||||
\(602\) | − | 4.65774i | − | 0.189835i | ||||||
\(603\) | 17.7599 | 0.723239 | ||||||||
\(604\) | 40.0834 | 1.63097 | ||||||||
\(605\) | 3.34068i | 0.135818i | ||||||||
\(606\) | − | 0.487140i | − | 0.0197887i | ||||||
\(607\) | 22.1714i | 0.899908i | 0.893052 | + | 0.449954i | \(0.148560\pi\) | ||||
−0.893052 | + | 0.449954i | \(0.851440\pi\) | |||||||
\(608\) | −6.68672 | −0.271182 | ||||||||
\(609\) | − | 0.989697i | − | 0.0401045i | ||||||
\(610\) | −11.7100 | −0.474125 | ||||||||
\(611\) | 14.4884 | 0.586138 | ||||||||
\(612\) | −22.0399 | + | 4.50687i | −0.890910 | + | 0.182180i | ||||
\(613\) | −10.2847 | −0.415396 | −0.207698 | − | 0.978193i | \(-0.566597\pi\) | ||||
−0.207698 | + | 0.978193i | \(0.566597\pi\) | |||||||
\(614\) | −8.14322 | −0.328634 | ||||||||
\(615\) | 1.74466i | 0.0703514i | ||||||||
\(616\) | 3.42204 | 0.137878 | ||||||||
\(617\) | 6.36379i | 0.256197i | 0.991761 | + | 0.128098i | \(0.0408873\pi\) | ||||
−0.991761 | + | 0.128098i | \(0.959113\pi\) | |||||||
\(618\) | − | 0.0828626i | − | 0.00333322i | ||||||
\(619\) | 22.7974i | 0.916304i | 0.888874 | + | 0.458152i | \(0.151488\pi\) | ||||
−0.888874 | + | 0.458152i | \(0.848512\pi\) | |||||||
\(620\) | 7.83332 | 0.314594 | ||||||||
\(621\) | −4.02407 | −0.161480 | ||||||||
\(622\) | − | 7.03727i | − | 0.282169i | ||||||
\(623\) | − | 15.0866i | − | 0.604431i | ||||||
\(624\) | − | 0.744117i | − | 0.0297885i | ||||||
\(625\) | −17.8533 | −0.714133 | ||||||||
\(626\) | 8.50898i | 0.340087i | ||||||||
\(627\) | −0.133538 | −0.00533301 | ||||||||
\(628\) | 10.9175 | 0.435655 | ||||||||
\(629\) | 2.41968 | + | 11.8329i | 0.0964788 | + | 0.471809i | ||||
\(630\) | −8.94597 | −0.356416 | ||||||||
\(631\) | −39.6141 | −1.57701 | −0.788506 | − | 0.615027i | \(-0.789145\pi\) | ||||
−0.788506 | + | 0.615027i | \(0.789145\pi\) | |||||||
\(632\) | 16.8294i | 0.669436i | ||||||||
\(633\) | 1.40186 | 0.0557188 | ||||||||
\(634\) | 3.62464i | 0.143953i | ||||||||
\(635\) | − | 24.0999i | − | 0.956374i | ||||||
\(636\) | − | 1.91097i | − | 0.0757749i | ||||||
\(637\) | −6.91617 | −0.274029 | ||||||||
\(638\) | −2.19051 | −0.0867229 | ||||||||
\(639\) | 43.3548i | 1.71509i | ||||||||
\(640\) | 35.5190i | 1.40401i | ||||||||
\(641\) | 33.3856i | 1.31865i | 0.751856 | + | 0.659327i | \(0.229159\pi\) | ||||
−0.751856 | + | 0.659327i | \(0.770841\pi\) | |||||||
\(642\) | −0.319774 | −0.0126205 | ||||||||
\(643\) | − | 4.37156i | − | 0.172397i | −0.996278 | − | 0.0861987i | \(-0.972528\pi\) | ||
0.996278 | − | 0.0861987i | \(-0.0274720\pi\) | |||||||
\(644\) | −29.2839 | −1.15395 | ||||||||
\(645\) | 1.54892 | 0.0609885 | ||||||||
\(646\) | −2.54359 | + | 0.520131i | −0.100076 | + | 0.0204643i | ||||
\(647\) | 20.5578 | 0.808212 | 0.404106 | − | 0.914712i | \(-0.367583\pi\) | ||||
0.404106 | + | 0.914712i | \(0.367583\pi\) | |||||||
\(648\) | −14.3417 | −0.563394 | ||||||||
\(649\) | − | 2.45417i | − | 0.0963345i | ||||||
\(650\) | 7.27210 | 0.285235 | ||||||||
\(651\) | − | 0.244068i | − | 0.00956577i | ||||||
\(652\) | − | 45.3546i | − | 1.77622i | ||||||
\(653\) | 19.1123i | 0.747921i | 0.927445 | + | 0.373961i | \(0.122000\pi\) | ||||
−0.927445 | + | 0.373961i | \(0.878000\pi\) | |||||||
\(654\) | 0.504901 | 0.0197432 | ||||||||
\(655\) | 51.5291 | 2.01341 | ||||||||
\(656\) | 17.4229i | 0.680250i | ||||||||
\(657\) | 17.9357i | 0.699740i | ||||||||
\(658\) | 4.61451i | 0.179892i | ||||||||
\(659\) | −6.04282 | −0.235395 | −0.117697 | − | 0.993050i | \(-0.537551\pi\) | ||||
−0.117697 | + | 0.993050i | \(0.537551\pi\) | |||||||
\(660\) | 0.542731i | 0.0211258i | ||||||||
\(661\) | 21.6939 | 0.843795 | 0.421898 | − | 0.906643i | \(-0.361364\pi\) | ||||
0.421898 | + | 0.906643i | \(0.361364\pi\) | |||||||
\(662\) | −13.1404 | −0.510715 | ||||||||
\(663\) | −0.206800 | − | 1.01131i | −0.00803146 | − | 0.0392762i | ||||
\(664\) | 16.4005 | 0.636462 | ||||||||
\(665\) | 10.6677 | 0.413676 | ||||||||
\(666\) | 3.68201i | 0.142675i | ||||||||
\(667\) | 39.3045 | 1.52188 | ||||||||
\(668\) | − | 22.6523i | − | 0.876443i | ||||||
\(669\) | − | 0.660598i | − | 0.0255402i | ||||||
\(670\) | − | 8.33023i | − | 0.321825i | ||||||
\(671\) | −8.34393 | −0.322114 | ||||||||
\(672\) | 0.846753 | 0.0326642 | ||||||||
\(673\) | 7.33990i | 0.282932i | 0.989943 | + | 0.141466i | \(0.0451816\pi\) | ||||
−0.989943 | + | 0.141466i | \(0.954818\pi\) | |||||||
\(674\) | 11.2497i | 0.433321i | ||||||||
\(675\) | − | 3.28857i | − | 0.126577i | ||||||
\(676\) | 9.30634 | 0.357936 | ||||||||
\(677\) | 24.5267i | 0.942638i | 0.881963 | + | 0.471319i | \(0.156222\pi\) | ||||
−0.881963 | + | 0.471319i | \(0.843778\pi\) | |||||||
\(678\) | −0.0550901 | −0.00211572 | ||||||||
\(679\) | −30.5905 | −1.17396 | ||||||||
\(680\) | 4.43246 | + | 21.6760i | 0.169977 | + | 0.831236i | ||||
\(681\) | 0.608285 | 0.0233095 | ||||||||
\(682\) | −0.540198 | −0.0206852 | ||||||||
\(683\) | − | 43.4617i | − | 1.66301i | −0.555514 | − | 0.831507i | \(-0.687478\pi\) | ||
0.555514 | − | 0.831507i | \(-0.312522\pi\) | |||||||
\(684\) | 8.17799 | 0.312693 | ||||||||
\(685\) | 18.6269i | 0.711696i | ||||||||
\(686\) | − | 8.46776i | − | 0.323301i | ||||||
\(687\) | − | 0.204094i | − | 0.00778669i | ||||||
\(688\) | 15.4681 | 0.589717 | ||||||||
\(689\) | −33.0538 | −1.25925 | ||||||||
\(690\) | 0.942488i | 0.0358799i | ||||||||
\(691\) | − | 5.25512i | − | 0.199914i | −0.994992 | − | 0.0999571i | \(-0.968129\pi\) | ||
0.994992 | − | 0.0999571i | \(-0.0318706\pi\) | |||||||
\(692\) | − | 44.8703i | − | 1.70571i | ||||||
\(693\) | −6.37442 | −0.242144 | ||||||||
\(694\) | 1.78101i | 0.0676061i | ||||||||
\(695\) | −4.68683 | −0.177782 | ||||||||
\(696\) | −0.746186 | −0.0282841 | ||||||||
\(697\) | 4.84207 | + | 23.6791i | 0.183406 | + | 0.896909i | ||||
\(698\) | 1.56162 | 0.0591083 | ||||||||
\(699\) | −0.875613 | −0.0331187 | ||||||||
\(700\) | − | 23.9316i | − | 0.904528i | ||||||
\(701\) | −25.4768 | −0.962247 | −0.481124 | − | 0.876653i | \(-0.659771\pi\) | ||||
−0.481124 | + | 0.876653i | \(0.659771\pi\) | |||||||
\(702\) | − | 0.630209i | − | 0.0237857i | ||||||
\(703\) | − | 4.39065i | − | 0.165596i | ||||||
\(704\) | 4.07037i | 0.153408i | ||||||||
\(705\) | −1.53454 | −0.0577941 | ||||||||
\(706\) | −9.17081 | −0.345148 | ||||||||
\(707\) | 27.7289i | 1.04285i | ||||||||
\(708\) | − | 0.398707i | − | 0.0149843i | ||||||
\(709\) | 33.0135i | 1.23985i | 0.784661 | + | 0.619925i | \(0.212837\pi\) | ||||
−0.784661 | + | 0.619925i | \(0.787163\pi\) | |||||||
\(710\) | 20.3354 | 0.763175 | ||||||||
\(711\) | − | 31.3490i | − | 1.17568i | ||||||
\(712\) | −11.3746 | −0.426281 | ||||||||
\(713\) | 9.69283 | 0.362999 | ||||||||
\(714\) | 0.322100 | − | 0.0658653i | 0.0120543 | − | 0.00246495i | ||||
\(715\) | 9.38754 | 0.351074 | ||||||||
\(716\) | −22.5150 | −0.841425 | ||||||||
\(717\) | 0.168612i | 0.00629693i | ||||||||
\(718\) | −11.4218 | −0.426256 | ||||||||
\(719\) | 11.5472i | 0.430636i | 0.976544 | + | 0.215318i | \(0.0690788\pi\) | ||||
−0.976544 | + | 0.215318i | \(0.930921\pi\) | |||||||
\(720\) | − | 29.7092i | − | 1.10720i | ||||||
\(721\) | 4.71669i | 0.175659i | ||||||||
\(722\) | −7.03808 | −0.261930 | ||||||||
\(723\) | 2.24524 | 0.0835013 | ||||||||
\(724\) | 16.5220i | 0.614036i | ||||||||
\(725\) | 32.1206i | 1.19293i | ||||||||
\(726\) | − | 0.0374276i | − | 0.00138907i | ||||||
\(727\) | 3.50071 | 0.129834 | 0.0649171 | − | 0.997891i | \(-0.479322\pi\) | ||||
0.0649171 | + | 0.997891i | \(0.479322\pi\) | |||||||
\(728\) | − | 9.61616i | − | 0.356399i | ||||||
\(729\) | 26.5723 | 0.984160 | ||||||||
\(730\) | 8.41270 | 0.311368 | ||||||||
\(731\) | 21.0224 | − | 4.29881i | 0.777541 | − | 0.158997i | ||||
\(732\) | −1.35556 | −0.0501031 | ||||||||
\(733\) | 23.8165 | 0.879682 | 0.439841 | − | 0.898076i | \(-0.355035\pi\) | ||||
0.439841 | + | 0.898076i | \(0.355035\pi\) | |||||||
\(734\) | − | 11.9182i | − | 0.439910i | ||||||
\(735\) | 0.732527 | 0.0270197 | ||||||||
\(736\) | 33.6276i | 1.23953i | ||||||||
\(737\) | − | 5.93567i | − | 0.218643i | ||||||
\(738\) | 7.36815i | 0.271225i | ||||||||
\(739\) | −13.0431 | −0.479799 | −0.239899 | − | 0.970798i | \(-0.577114\pi\) | ||||
−0.239899 | + | 0.970798i | \(0.577114\pi\) | |||||||
\(740\) | −17.8446 | −0.655981 | ||||||||
\(741\) | 0.375252i | 0.0137852i | ||||||||
\(742\) | − | 10.5275i | − | 0.386478i | ||||||
\(743\) | 0.202655i | 0.00743470i | 0.999993 | + | 0.00371735i | \(0.00118327\pi\) | ||||
−0.999993 | + | 0.00371735i | \(0.998817\pi\) | |||||||
\(744\) | −0.184016 | −0.00674635 | ||||||||
\(745\) | 45.2625i | 1.65829i | ||||||||
\(746\) | 4.03571 | 0.147758 | ||||||||
\(747\) | −30.5501 | −1.11777 | ||||||||
\(748\) | 1.50628 | + | 7.36612i | 0.0550749 | + | 0.269332i | ||||
\(749\) | 18.2021 | 0.665091 | ||||||||
\(750\) | −0.145057 | −0.00529675 | ||||||||
\(751\) | − | 44.7298i | − | 1.63221i | −0.577901 | − | 0.816107i | \(-0.696128\pi\) | ||
0.577901 | − | 0.816107i | \(-0.303872\pi\) | |||||||
\(752\) | −15.3246 | −0.558830 | ||||||||
\(753\) | − | 0.703742i | − | 0.0256458i | ||||||
\(754\) | 6.15547i | 0.224169i | ||||||||
\(755\) | 73.4328i | 2.67249i | ||||||||
\(756\) | −2.07394 | −0.0754284 | ||||||||
\(757\) | 16.9831 | 0.617260 | 0.308630 | − | 0.951182i | \(-0.400130\pi\) | ||||
0.308630 | + | 0.951182i | \(0.400130\pi\) | |||||||
\(758\) | 6.26586i | 0.227586i | ||||||||
\(759\) | 0.671567i | 0.0243763i | ||||||||
\(760\) | − | 8.04296i | − | 0.291749i | ||||||
\(761\) | −43.0108 | −1.55914 | −0.779571 | − | 0.626314i | \(-0.784563\pi\) | ||||
−0.779571 | + | 0.626314i | \(0.784563\pi\) | |||||||
\(762\) | 0.270005i | 0.00978123i | ||||||||
\(763\) | −28.7399 | −1.04045 | ||||||||
\(764\) | −31.1340 | −1.12639 | ||||||||
\(765\) | −8.25659 | − | 40.3771i | −0.298518 | − | 1.45984i | ||||
\(766\) | 9.68360 | 0.349883 | ||||||||
\(767\) | −6.89638 | −0.249014 | ||||||||
\(768\) | 0.327336i | 0.0118117i | ||||||||
\(769\) | 20.1757 | 0.727555 | 0.363777 | − | 0.931486i | \(-0.381487\pi\) | ||||
0.363777 | + | 0.931486i | \(0.381487\pi\) | |||||||
\(770\) | 2.98990i | 0.107749i | ||||||||
\(771\) | 1.13400i | 0.0408400i | ||||||||
\(772\) | − | 37.8001i | − | 1.36046i | ||||||
\(773\) | −30.3126 | −1.09027 | −0.545134 | − | 0.838349i | \(-0.683521\pi\) | ||||
−0.545134 | + | 0.838349i | \(0.683521\pi\) | |||||||
\(774\) | 6.54147 | 0.235128 | ||||||||
\(775\) | 7.92122i | 0.284539i | ||||||||
\(776\) | 23.0639i | 0.827945i | ||||||||
\(777\) | 0.555997i | 0.0199463i | ||||||||
\(778\) | 7.68669 | 0.275581 | ||||||||
\(779\) | − | 8.78622i | − | 0.314799i | ||||||
\(780\) | 1.52511 | 0.0546077 | ||||||||
\(781\) | 14.4899 | 0.518490 | ||||||||
\(782\) | 2.61575 | + | 12.7918i | 0.0935391 | + | 0.457433i | ||||
\(783\) | 2.78361 | 0.0994781 | ||||||||
\(784\) | 7.31532 | 0.261262 | ||||||||
\(785\) | 20.0008i | 0.713859i | ||||||||
\(786\) | −0.577310 | −0.0205920 | ||||||||
\(787\) | 10.1837i | 0.363010i | 0.983390 | + | 0.181505i | \(0.0580969\pi\) | ||||
−0.983390 | + | 0.181505i | \(0.941903\pi\) | |||||||
\(788\) | 27.5969i | 0.983097i | ||||||||
\(789\) | − | 1.85563i | − | 0.0660621i | ||||||
\(790\) | −14.7041 | −0.523150 | ||||||||
\(791\) | 3.13583 | 0.111497 | ||||||||
\(792\) | 4.80602i | 0.170774i | ||||||||
\(793\) | 23.4470i | 0.832628i | ||||||||
\(794\) | − | 0.171918i | − | 0.00610115i | ||||||
\(795\) | 3.50089 | 0.124164 | ||||||||
\(796\) | − | 37.4744i | − | 1.32824i | ||||||
\(797\) | −31.8636 | −1.12867 | −0.564333 | − | 0.825547i | \(-0.690867\pi\) | ||||
−0.564333 | + | 0.825547i | \(0.690867\pi\) | |||||||
\(798\) | −0.119516 | −0.00423084 | ||||||||
\(799\) | −20.8273 | + | 4.25891i | −0.736816 | + | 0.150669i | ||||
\(800\) | −27.4814 | −0.971613 | ||||||||
\(801\) | 21.1881 | 0.748644 | ||||||||
\(802\) | 3.33131i | 0.117632i | ||||||||
\(803\) | 5.99444 | 0.211539 | ||||||||
\(804\) | − | 0.964316i | − | 0.0340088i | ||||||
\(805\) | − | 53.6481i | − | 1.89085i | ||||||
\(806\) | 1.51799i | 0.0534690i | ||||||||
\(807\) | 1.53357 | 0.0539842 | ||||||||
\(808\) | 20.9063 | 0.735481 | ||||||||
\(809\) | 0.299585i | 0.0105328i | 0.999986 | + | 0.00526642i | \(0.00167636\pi\) | ||||
−0.999986 | + | 0.00526642i | \(0.998324\pi\) | |||||||
\(810\) | − | 12.5306i | − | 0.440280i | ||||||
\(811\) | − | 13.4057i | − | 0.470736i | −0.971906 | − | 0.235368i | \(-0.924370\pi\) | ||
0.971906 | − | 0.235368i | \(-0.0756296\pi\) | |||||||
\(812\) | 20.2569 | 0.710877 | ||||||||
\(813\) | 2.24520i | 0.0787427i | ||||||||
\(814\) | 1.23059 | 0.0431323 | ||||||||
\(815\) | 83.0897 | 2.91050 | ||||||||
\(816\) | 0.218736 | + | 1.06968i | 0.00765728 | + | 0.0374463i | ||||
\(817\) | −7.80044 | −0.272903 | ||||||||
\(818\) | 3.37036 | 0.117842 | ||||||||
\(819\) | 17.9126i | 0.625915i | ||||||||
\(820\) | −35.7092 | −1.24702 | ||||||||
\(821\) | 38.0715i | 1.32870i | 0.747420 | + | 0.664352i | \(0.231292\pi\) | ||||
−0.747420 | + | 0.664352i | \(0.768708\pi\) | |||||||
\(822\) | − | 0.208688i | − | 0.00727882i | ||||||
\(823\) | − | 10.4077i | − | 0.362790i | −0.983410 | − | 0.181395i | \(-0.941939\pi\) | ||
0.983410 | − | 0.181395i | \(-0.0580612\pi\) | |||||||
\(824\) | 3.55617 | 0.123885 | ||||||||
\(825\) | −0.548821 | −0.0191075 | ||||||||
\(826\) | − | 2.19647i | − | 0.0764251i | ||||||
\(827\) | − | 22.0710i | − | 0.767483i | −0.923441 | − | 0.383742i | \(-0.874635\pi\) | ||
0.923441 | − | 0.383742i | \(-0.125365\pi\) | |||||||
\(828\) | − | 41.1273i | − | 1.42927i | ||||||
\(829\) | −4.28264 | −0.148742 | −0.0743710 | − | 0.997231i | \(-0.523695\pi\) | ||||
−0.0743710 | + | 0.997231i | \(0.523695\pi\) | |||||||
\(830\) | 14.3294i | 0.497381i | ||||||||
\(831\) | −2.35414 | −0.0816643 | ||||||||
\(832\) | 11.4380 | 0.396542 | ||||||||
\(833\) | 9.94210 | − | 2.03303i | 0.344473 | − | 0.0704403i | ||||
\(834\) | 0.0525093 | 0.00181825 | ||||||||
\(835\) | 41.4989 | 1.43613 | ||||||||
\(836\) | − | 2.73323i | − | 0.0945307i | ||||||
\(837\) | 0.686463 | 0.0237276 | ||||||||
\(838\) | − | 8.14832i | − | 0.281479i | ||||||
\(839\) | 34.0693i | 1.17620i | 0.808787 | + | 0.588102i | \(0.200125\pi\) | ||||
−0.808787 | + | 0.588102i | \(0.799875\pi\) | |||||||
\(840\) | 1.01850i | 0.0351415i | ||||||||
\(841\) | 1.81152 | 0.0624661 | ||||||||
\(842\) | −3.11485 | −0.107345 | ||||||||
\(843\) | 2.15087i | 0.0740797i | ||||||||
\(844\) | 28.6929i | 0.987649i | ||||||||
\(845\) | 17.0492i | 0.586511i | ||||||||
\(846\) | −6.48076 | −0.222813 | ||||||||
\(847\) | 2.13044i | 0.0732029i | ||||||||
\(848\) | 34.9614 | 1.20058 | ||||||||
\(849\) | 1.82615 | 0.0626732 | ||||||||
\(850\) | −10.4538 | + | 2.13766i | −0.358561 | + | 0.0733210i | ||||
\(851\) | −22.0807 | −0.756915 | ||||||||
\(852\) | 2.35405 | 0.0806484 | ||||||||
\(853\) | − | 14.6084i | − | 0.500182i | −0.968222 | − | 0.250091i | \(-0.919540\pi\) | ||
0.968222 | − | 0.250091i | \(-0.0804605\pi\) | |||||||
\(854\) | −7.46780 | −0.255543 | ||||||||
\(855\) | 14.9821i | 0.512376i | ||||||||
\(856\) | − | 13.7236i | − | 0.469062i | ||||||
\(857\) | 34.1152i | 1.16535i | 0.812704 | + | 0.582677i | \(0.197995\pi\) | ||||
−0.812704 | + | 0.582677i | \(0.802005\pi\) | |||||||
\(858\) | −0.105174 | −0.00359058 | ||||||||
\(859\) | −42.1275 | −1.43737 | −0.718686 | − | 0.695335i | \(-0.755256\pi\) | ||||
−0.718686 | + | 0.695335i | \(0.755256\pi\) | |||||||
\(860\) | 31.7028i | 1.08106i | ||||||||
\(861\) | 1.11262i | 0.0379179i | ||||||||
\(862\) | 2.99000i | 0.101840i | ||||||||
\(863\) | −21.9531 | −0.747291 | −0.373645 | − | 0.927572i | \(-0.621892\pi\) | ||||
−0.373645 | + | 0.927572i | \(0.621892\pi\) | |||||||
\(864\) | 2.38157i | 0.0810226i | ||||||||
\(865\) | 82.2023 | 2.79496 | ||||||||
\(866\) | 1.88896 | 0.0641893 | ||||||||
\(867\) | 0.594557 | + | 1.39299i | 0.0201922 | + | 0.0473084i | ||||
\(868\) | 4.99552 | 0.169559 | ||||||||
\(869\) | −10.4774 | −0.355421 | ||||||||
\(870\) | − | 0.651957i | − | 0.0221034i | ||||||
\(871\) | −16.6797 | −0.565168 | ||||||||
\(872\) | 21.6685i | 0.733789i | ||||||||
\(873\) | − | 42.9623i | − | 1.45405i | ||||||
\(874\) | − | 4.74644i | − | 0.160551i | ||||||
\(875\) | 8.25693 | 0.279135 | ||||||||
\(876\) | 0.973863 | 0.0329038 | ||||||||
\(877\) | − | 25.7006i | − | 0.867849i | −0.900949 | − | 0.433925i | \(-0.857128\pi\) | ||
0.900949 | − | 0.433925i | \(-0.142872\pi\) | |||||||
\(878\) | − | 3.10327i | − | 0.104730i | ||||||
\(879\) | 0.760887i | 0.0256641i | ||||||||
\(880\) | −9.92933 | −0.334718 | ||||||||
\(881\) | − | 34.8945i | − | 1.17563i | −0.808997 | − | 0.587813i | \(-0.799989\pi\) | ||
0.808997 | − | 0.587813i | \(-0.200011\pi\) | |||||||
\(882\) | 3.09365 | 0.104169 | ||||||||
\(883\) | −44.8367 | −1.50887 | −0.754437 | − | 0.656373i | \(-0.772090\pi\) | ||||
−0.754437 | + | 0.656373i | \(0.772090\pi\) | |||||||
\(884\) | 20.6993 | − | 4.23274i | 0.696193 | − | 0.142362i | ||||
\(885\) | 0.730430 | 0.0245531 | ||||||||
\(886\) | 10.5044 | 0.352903 | ||||||||
\(887\) | − | 12.5888i | − | 0.422689i | −0.977412 | − | 0.211345i | \(-0.932216\pi\) | ||
0.977412 | − | 0.211345i | \(-0.0677842\pi\) | |||||||
\(888\) | 0.419196 | 0.0140673 | ||||||||
\(889\) | − | 15.3691i | − | 0.515464i | ||||||
\(890\) | − | 9.93820i | − | 0.333129i | ||||||
\(891\) | − | 8.92863i | − | 0.299120i | ||||||
\(892\) | 13.5210 | 0.452715 | ||||||||
\(893\) | 7.72805 | 0.258609 | ||||||||
\(894\) | − | 0.507102i | − | 0.0169600i | ||||||
\(895\) | − | 41.2474i | − | 1.37875i | ||||||
\(896\) | 22.6514i | 0.756731i | ||||||||
\(897\) | 1.88715 | 0.0630101 | ||||||||
\(898\) | 8.67179i | 0.289382i | ||||||||
\(899\) | −6.70492 | −0.223622 | ||||||||
\(900\) | 33.6102 | 1.12034 | ||||||||
\(901\) | 47.5153 | − | 9.71627i | 1.58296 | − | 0.323696i | ||||
\(902\) | 2.46257 | 0.0819944 | ||||||||
\(903\) | 0.987785 | 0.0328714 | ||||||||
\(904\) | − | 2.36427i | − | 0.0786345i | ||||||
\(905\) | −30.2683 | −1.00615 | ||||||||
\(906\) | − | 0.822710i | − | 0.0273327i | ||||||
\(907\) | 3.23283i | 0.107344i | 0.998559 | + | 0.0536722i | \(0.0170926\pi\) | ||||
−0.998559 | + | 0.0536722i | \(0.982907\pi\) | |||||||
\(908\) | 12.4502i | 0.413175i | ||||||||
\(909\) | −38.9433 | −1.29167 | ||||||||
\(910\) | 8.40183 | 0.278518 | ||||||||
\(911\) | − | 38.6527i | − | 1.28062i | −0.768116 | − | 0.640310i | \(-0.778806\pi\) | ||
0.768116 | − | 0.640310i | \(-0.221194\pi\) | |||||||
\(912\) | − | 0.396909i | − | 0.0131430i | ||||||
\(913\) | 10.2104i | 0.337914i | ||||||||
\(914\) | −12.7015 | −0.420129 | ||||||||
\(915\) | − | 2.48339i | − | 0.0820984i | ||||||
\(916\) | 4.17735 | 0.138024 | ||||||||
\(917\) | 32.8615 | 1.08518 | ||||||||
\(918\) | 0.185252 | + | 0.905935i | 0.00611423 | + | 0.0299003i | ||||
\(919\) | −55.5566 | −1.83264 | −0.916321 | − | 0.400443i | \(-0.868856\pi\) | ||||
−0.916321 | + | 0.400443i | \(0.868856\pi\) | |||||||
\(920\) | −40.4482 | −1.33354 | ||||||||
\(921\) | − | 1.72697i | − | 0.0569055i | ||||||
\(922\) | 12.2535 | 0.403548 | ||||||||
\(923\) | − | 40.7177i | − | 1.34024i | ||||||
\(924\) | 0.346114i | 0.0113863i | ||||||||
\(925\) | − | 18.0449i | − | 0.593312i | ||||||
\(926\) | −4.08459 | −0.134228 | ||||||||
\(927\) | −6.62427 | −0.217569 | ||||||||
\(928\) | − | 23.2616i | − | 0.763599i | ||||||
\(929\) | 0.121044i | 0.00397132i | 0.999998 | + | 0.00198566i | \(0.000632056\pi\) | ||||
−0.999998 | + | 0.00198566i | \(0.999368\pi\) | |||||||
\(930\) | − | 0.160778i | − | 0.00527213i | ||||||
\(931\) | −3.68905 | −0.120904 | ||||||||
\(932\) | − | 17.9218i | − | 0.587049i | ||||||
\(933\) | 1.49242 | 0.0488597 | ||||||||
\(934\) | −5.11215 | −0.167275 | ||||||||
\(935\) | −13.4947 | + | 2.75950i | −0.441325 | + | 0.0902452i | ||||
\(936\) | 13.5052 | 0.441433 | ||||||||
\(937\) | −37.8307 | −1.23588 | −0.617938 | − | 0.786227i | \(-0.712032\pi\) | ||||
−0.617938 | + | 0.786227i | \(0.712032\pi\) | |||||||
\(938\) | − | 5.31241i | − | 0.173456i | ||||||
\(939\) | −1.80453 | −0.0588888 | ||||||||
\(940\) | − | 31.4086i | − | 1.02443i | ||||||
\(941\) | − | 38.3847i | − | 1.25131i | −0.780102 | − | 0.625653i | \(-0.784833\pi\) | ||
0.780102 | − | 0.625653i | \(-0.215167\pi\) | |||||||
\(942\) | − | 0.224080i | − | 0.00730093i | ||||||
\(943\) | −44.1861 | −1.43890 | ||||||||
\(944\) | 7.29439 | 0.237412 | ||||||||
\(945\) | − | 3.79945i | − | 0.123596i | ||||||
\(946\) | − | 2.18628i | − | 0.0710819i | ||||||
\(947\) | − | 25.7810i | − | 0.837768i | −0.908040 | − | 0.418884i | \(-0.862421\pi\) | ||
0.908040 | − | 0.418884i | \(-0.137579\pi\) | |||||||
\(948\) | −1.70217 | −0.0552838 | ||||||||
\(949\) | − | 16.8448i | − | 0.546805i | ||||||
\(950\) | 3.87891 | 0.125848 | ||||||||
\(951\) | −0.768692 | −0.0249265 | ||||||||
\(952\) | 2.82670 | + | 13.8234i | 0.0916139 | + | 0.448018i | ||||
\(953\) | 23.3685 | 0.756979 | 0.378490 | − | 0.925606i | \(-0.376444\pi\) | ||||
0.378490 | + | 0.925606i | \(0.376444\pi\) | |||||||
\(954\) | 14.7852 | 0.478688 | ||||||||
\(955\) | − | 57.0375i | − | 1.84569i | ||||||
\(956\) | −3.45111 | −0.111617 | ||||||||
\(957\) | − | 0.464550i | − | 0.0150168i | ||||||
\(958\) | − | 3.95412i | − | 0.127752i | ||||||
\(959\) | 11.8789i | 0.383589i | ||||||||
\(960\) | −1.21146 | −0.0390996 | ||||||||
\(961\) | 29.3465 | 0.946662 | ||||||||
\(962\) | − | 3.45805i | − | 0.111492i | ||||||
\(963\) | 25.5636i | 0.823777i | ||||||||
\(964\) | 45.9550i | 1.48011i | ||||||||
\(965\) | 69.2497 | 2.22923 | ||||||||
\(966\) | 0.601051i | 0.0193385i | ||||||||
\(967\) | 2.00843 | 0.0645867 | 0.0322933 | − | 0.999478i | \(-0.489719\pi\) | ||||
0.0322933 | + | 0.999478i | \(0.489719\pi\) | |||||||
\(968\) | 1.60626 | 0.0516270 | ||||||||
\(969\) | −0.110306 | − | 0.539430i | −0.00354355 | − | 0.0173290i | ||||
\(970\) | −20.1513 | −0.647021 | ||||||||
\(971\) | −28.1844 | −0.904479 | −0.452240 | − | 0.891896i | \(-0.649375\pi\) | ||||
−0.452240 | + | 0.891896i | \(0.649375\pi\) | |||||||
\(972\) | − | 4.37099i | − | 0.140199i | ||||||
\(973\) | −2.98892 | −0.0958204 | ||||||||
\(974\) | 1.27499i | 0.0408534i | ||||||||
\(975\) | 1.54223i | 0.0493907i | ||||||||
\(976\) | − | 24.8002i | − | 0.793836i | ||||||
\(977\) | 21.6336 | 0.692119 | 0.346060 | − | 0.938213i | \(-0.387519\pi\) | ||||
0.346060 | + | 0.938213i | \(0.387519\pi\) | |||||||
\(978\) | −0.930901 | −0.0297669 | ||||||||
\(979\) | − | 7.08143i | − | 0.226323i | ||||||
\(980\) | 14.9932i | 0.478939i | ||||||||
\(981\) | − | 40.3632i | − | 1.28870i | ||||||
\(982\) | 3.62101 | 0.115551 | ||||||||
\(983\) | 8.38196i | 0.267343i | 0.991026 | + | 0.133671i | \(0.0426767\pi\) | ||||
−0.991026 | + | 0.133671i | \(0.957323\pi\) | |||||||
\(984\) | 0.838862 | 0.0267419 | ||||||||
\(985\) | −50.5574 | −1.61089 | ||||||||
\(986\) | −1.80942 | − | 8.84858i | −0.0576237 | − | 0.281796i | ||||
\(987\) | −0.978618 | −0.0311498 | ||||||||
\(988\) | −7.68056 | −0.244351 | ||||||||
\(989\) | 39.2286i | 1.24740i | ||||||||
\(990\) | −4.19911 | −0.133457 | ||||||||
\(991\) | − | 3.74342i | − | 0.118914i | −0.998231 | − | 0.0594569i | \(-0.981063\pi\) | ||
0.998231 | − | 0.0594569i | \(-0.0189369\pi\) | |||||||
\(992\) | − | 5.73651i | − | 0.182134i | ||||||
\(993\) | − | 2.78673i | − | 0.0884343i | ||||||
\(994\) | 12.9684 | 0.411334 | ||||||||
\(995\) | 68.6531 | 2.17645 | ||||||||
\(996\) | 1.65879i | 0.0525607i | ||||||||
\(997\) | − | 6.81952i | − | 0.215976i | −0.994152 | − | 0.107988i | \(-0.965559\pi\) | ||
0.994152 | − | 0.107988i | \(-0.0344409\pi\) | |||||||
\(998\) | 0.241853i | 0.00765572i | ||||||||
\(999\) | −1.56379 | −0.0494761 |
(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 | 187.2.d.a.67.10 | yes | 16 | |
3.2 | odd | 2 | 1683.2.g.b.1189.8 | 16 | |||
4.3 | odd | 2 | 2992.2.b.g.1937.8 | 16 | |||
17.4 | even | 4 | 3179.2.a.bc.1.4 | 8 | |||
17.13 | even | 4 | 3179.2.a.bb.1.4 | 8 | |||
17.16 | even | 2 | inner | 187.2.d.a.67.9 | ✓ | 16 | |
51.50 | odd | 2 | 1683.2.g.b.1189.7 | 16 | |||
68.67 | odd | 2 | 2992.2.b.g.1937.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.d.a.67.9 | ✓ | 16 | 17.16 | even | 2 | inner | |
187.2.d.a.67.10 | yes | 16 | 1.1 | even | 1 | trivial | |
1683.2.g.b.1189.7 | 16 | 51.50 | odd | 2 | |||
1683.2.g.b.1189.8 | 16 | 3.2 | odd | 2 | |||
2992.2.b.g.1937.8 | 16 | 4.3 | odd | 2 | |||
2992.2.b.g.1937.9 | 16 | 68.67 | odd | 2 | |||
3179.2.a.bb.1.4 | 8 | 17.13 | even | 4 | |||
3179.2.a.bc.1.4 | 8 | 17.4 | even | 4 |