Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1932,2,Mod(1609,1932)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1932.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1932.k (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: | \(15.4270976705\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.28 | ||
Character | \(\chi\) | \(=\) | 1932.1609 |
Dual form | 1932.2.k.a.1609.26 |
$q$-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 \(\left(\mathbb{Z}/1932\mathbb{Z}\right)^\times\).
\(n\) | \(829\) | \(925\) | \(967\) | \(1289\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.18466 | 1.87143 | 0.935717 | − | 0.352750i | \(-0.114754\pi\) | ||||
0.935717 | + | 0.352750i | \(0.114754\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46306 | − | 0.966093i | 0.930949 | − | 0.365149i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.82537i | 0.550369i | 0.961391 | + | 0.275185i | \(0.0887390\pi\) | ||||
−0.961391 | + | 0.275185i | \(0.911261\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.63628i | − | 1.56322i | −0.623765 | − | 0.781612i | \(-0.714398\pi\) | ||
0.623765 | − | 0.781612i | \(-0.285602\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.18466i | 1.08047i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.34961 | −0.327328 | −0.163664 | − | 0.986516i | \(-0.552331\pi\) | ||||
−0.163664 | + | 0.986516i | \(0.552331\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.27595 | 0.980970 | 0.490485 | − | 0.871450i | \(-0.336820\pi\) | ||||
0.490485 | + | 0.871450i | \(0.336820\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.966093 | + | 2.46306i | 0.210819 | + | 0.537484i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.26310 | − | 4.62651i | 0.263374 | − | 0.964694i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.5113 | 2.50227 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.54797 | −1.03023 | −0.515116 | − | 0.857120i | \(-0.672251\pi\) | ||||
−0.515116 | + | 0.857120i | \(0.672251\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.52845i | 0.454123i | 0.973880 | + | 0.227061i | \(0.0729118\pi\) | ||||
−0.973880 | + | 0.227061i | \(0.927088\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.82537 | −0.317756 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.3071 | − | 4.04276i | 1.74221 | − | 0.683352i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.592620i | 0.0974261i | 0.998813 | + | 0.0487131i | \(0.0155120\pi\) | ||||
−0.998813 | + | 0.0487131i | \(0.984488\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.63628 | 0.902527 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.941186i | 0.146989i | 0.997296 | + | 0.0734943i | \(0.0234151\pi\) | ||||
−0.997296 | + | 0.0734943i | \(0.976585\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.90862i | 0.443560i | 0.975097 | + | 0.221780i | \(0.0711867\pi\) | ||||
−0.975097 | + | 0.221780i | \(0.928813\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.18466 | −0.623812 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.40543i | − | 0.350867i | −0.984491 | − | 0.175434i | \(-0.943867\pi\) | ||
0.984491 | − | 0.175434i | \(-0.0561328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.13333 | − | 4.75909i | 0.733333 | − | 0.679870i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1.34961i | − | 0.188983i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.80446i | − | 1.07202i | −0.844210 | − | 0.536012i | \(-0.819930\pi\) | ||
0.844210 | − | 0.536012i | \(-0.180070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.63854i | 1.02998i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.27595i | 0.566363i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.6435i | 1.51585i | 0.652341 | + | 0.757926i | \(0.273787\pi\) | ||||
−0.652341 | + | 0.757926i | \(0.726213\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.5488 | −1.47867 | −0.739335 | − | 0.673338i | \(-0.764860\pi\) | ||||
−0.739335 | + | 0.673338i | \(0.764860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.46306 | + | 0.966093i | −0.310316 | + | 0.121716i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 23.5859i | − | 2.92547i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.55560i | − | 1.16740i | −0.811968 | − | 0.583701i | \(-0.801604\pi\) | ||
0.811968 | − | 0.583701i | \(-0.198396\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.62651 | + | 1.26310i | 0.556966 | + | 0.152059i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.05917 | −0.600414 | −0.300207 | − | 0.953874i | \(-0.597056\pi\) | ||||
−0.300207 | + | 0.953874i | \(0.597056\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.229691i | 0.0268833i | 0.999910 | + | 0.0134417i | \(0.00427874\pi\) | ||||
−0.999910 | + | 0.0134417i | \(0.995721\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.5113i | 1.44469i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.76347 | + | 4.49599i | 0.200967 | + | 0.512366i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.67783i | 1.08884i | 0.838812 | + | 0.544420i | \(0.183250\pi\) | ||||
−0.838812 | + | 0.544420i | \(0.816750\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.18486 | 0.678876 | 0.339438 | − | 0.940628i | \(-0.389763\pi\) | ||||
0.339438 | + | 0.940628i | \(0.389763\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.64765 | −0.612573 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 5.54797i | − | 0.594805i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.7078 | −1.98302 | −0.991510 | − | 0.130028i | \(-0.958493\pi\) | ||||
−0.991510 | + | 0.130028i | \(0.958493\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.44517 | − | 13.8825i | −0.570809 | − | 1.45528i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.52845 | −0.262188 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.8934 | 1.83582 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1577 | −1.33596 | −0.667980 | − | 0.744179i | \(-0.732841\pi\) | ||||
−0.667980 | + | 0.744179i | \(0.732841\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.82537i | − | 0.183456i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.2453i | 1.41746i | 0.705479 | + | 0.708731i | \(0.250732\pi\) | ||||
−0.705479 | + | 0.708731i | \(0.749268\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.67757 | 0.165296 | 0.0826481 | − | 0.996579i | \(-0.473662\pi\) | ||||
0.0826481 | + | 0.996579i | \(0.473662\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.04276 | + | 10.3071i | 0.394533 | + | 1.00587i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.36527i | 0.228659i | 0.993443 | + | 0.114329i | \(0.0364719\pi\) | ||||
−0.993443 | + | 0.114329i | \(0.963528\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.9734i | 1.33841i | 0.743080 | + | 0.669203i | \(0.233364\pi\) | ||||
−0.743080 | + | 0.669203i | \(0.766636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.592620 | −0.0562490 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.50110i | − | 0.235284i | −0.993056 | − | 0.117642i | \(-0.962466\pi\) | ||
0.993056 | − | 0.117642i | \(-0.0375336\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.28563 | − | 19.3603i | 0.492887 | − | 1.80536i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.63628i | 0.521074i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.32417 | + | 1.30385i | −0.304726 | + | 0.119523i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.66803 | 0.697094 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.941186 | −0.0848639 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31.4324 | 2.81140 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.82083 | 0.427779 | 0.213890 | − | 0.976858i | \(-0.431387\pi\) | ||||
0.213890 | + | 0.976858i | \(0.431387\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.90862 | −0.256090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3351i | 1.16510i | 0.812796 | + | 0.582548i | \(0.197944\pi\) | ||||
−0.812796 | + | 0.582548i | \(0.802056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.5319 | − | 4.13096i | 0.913233 | − | 0.358200i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 4.18466i | − | 0.360158i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.3538i | 1.05545i | 0.849414 | + | 0.527727i | \(0.176956\pi\) | ||||
−0.849414 | + | 0.527727i | \(0.823044\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.5018i | − | 1.14521i | −0.819833 | − | 0.572603i | \(-0.805934\pi\) | ||
0.819833 | − | 0.572603i | \(-0.194066\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.40543 | 0.202573 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.2883 | 0.860350 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.2163 | −1.92801 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.75909 | + | 5.13333i | 0.392523 | + | 0.423390i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7461i | 1.04420i | 0.852884 | + | 0.522101i | \(0.174851\pi\) | ||||
−0.852884 | + | 0.522101i | \(0.825149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.9527 | 1.37959 | 0.689794 | − | 0.724005i | \(-0.257701\pi\) | ||||
0.689794 | + | 0.724005i | \(0.257701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.34961 | 0.109109 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.5807i | 0.849862i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6179 | 0.927206 | 0.463603 | − | 0.886043i | \(-0.346556\pi\) | ||||
0.463603 | + | 0.886043i | \(0.346556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.80446 | 0.618934 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.35855 | − | 12.6156i | −0.107069 | − | 0.994252i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.74976 | 0.450356 | 0.225178 | − | 0.974318i | \(-0.427704\pi\) | ||||
0.225178 | + | 0.974318i | \(0.427704\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.63854 | −0.594659 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5553i | 1.51323i | 0.653858 | + | 0.756617i | \(0.273149\pi\) | ||||
−0.653858 | + | 0.756617i | \(0.726851\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.7677 | −1.44367 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.27595 | −0.326990 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 22.7092i | − | 1.72655i | −0.504734 | − | 0.863275i | \(-0.668410\pi\) | ||
0.504734 | − | 0.863275i | \(-0.331590\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30.8162 | − | 12.0871i | 2.32948 | − | 0.913700i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.6435 | −0.875177 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0764 | 0.902636 | 0.451318 | − | 0.892363i | \(-0.350954\pi\) | ||||
0.451318 | + | 0.892363i | \(0.350954\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.54990 | 0.263862 | 0.131931 | − | 0.991259i | \(-0.457882\pi\) | ||||
0.131931 | + | 0.991259i | \(0.457882\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.5488i | − | 0.853710i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.47991i | 0.182327i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.46353i | − | 0.180151i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.966093 | − | 2.46306i | −0.0702729 | − | 0.179161i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.51786i | 0.688688i | 0.938843 | + | 0.344344i | \(0.111899\pi\) | ||||
−0.938843 | + | 0.344344i | \(0.888101\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.10667 | −0.151641 | −0.0758206 | − | 0.997121i | \(-0.524158\pi\) | ||||
−0.0758206 | + | 0.997121i | \(0.524158\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.5859 | 1.68902 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.7016 | −1.26119 | −0.630593 | − | 0.776114i | \(-0.717188\pi\) | ||||
−0.630593 | + | 0.776114i | \(0.717188\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0241 | −0.710590 | −0.355295 | − | 0.934754i | \(-0.615620\pi\) | ||||
−0.355295 | + | 0.934754i | \(0.615620\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.55560 | 0.674000 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.6650 | + | 5.35985i | −0.959094 | + | 0.376188i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.93854i | 0.275080i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.26310 | + | 4.62651i | −0.0877914 | + | 0.321565i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.80518i | 0.539896i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8426 | 1.09065 | 0.545323 | − | 0.838226i | \(-0.316407\pi\) | ||||
0.545323 | + | 0.838226i | \(0.316407\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 5.05917i | − | 0.346649i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.1716i | 0.830094i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.44272 | + | 6.22772i | 0.165822 | + | 0.422765i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.229691 | −0.0155211 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.60677i | 0.511687i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.1995i | 1.62052i | 0.586071 | + | 0.810259i | \(0.300674\pi\) | ||||
−0.586071 | + | 0.810259i | \(0.699326\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.5113 | −0.834089 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.7083 | −1.17534 | −0.587671 | − | 0.809100i | \(-0.699955\pi\) | ||||
−0.587671 | + | 0.809100i | \(0.699955\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.9498 | 0.723584 | 0.361792 | − | 0.932259i | \(-0.382165\pi\) | ||||
0.361792 | + | 0.932259i | \(0.382165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.49599 | + | 1.76347i | −0.295814 | + | 0.116028i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7878 | 0.968784 | 0.484392 | − | 0.874851i | \(-0.339041\pi\) | ||||
0.484392 | + | 0.874851i | \(0.339041\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 10.0659i | − | 0.656625i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.67783 | −0.628643 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.80996 | −0.246446 | −0.123223 | − | 0.992379i | \(-0.539323\pi\) | ||||
−0.123223 | + | 0.992379i | \(0.539323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.90190 | −0.122512 | −0.0612562 | − | 0.998122i | \(-0.519511\pi\) | ||||
−0.0612562 | + | 0.998122i | \(0.519511\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.4812 | − | 19.9151i | 1.37238 | − | 1.27233i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 24.1005i | − | 1.53348i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.18486i | 0.391950i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.54304 | −0.349874 | −0.174937 | − | 0.984580i | \(-0.555972\pi\) | ||||
−0.174937 | + | 0.984580i | \(0.555972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.44508 | + | 2.30562i | 0.530938 | + | 0.144953i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 5.64765i | − | 0.353669i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 18.4310i | − | 1.14969i | −0.818261 | − | 0.574846i | \(-0.805062\pi\) | ||
0.818261 | − | 0.574846i | \(-0.194938\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.572526 | + | 1.45966i | 0.0355750 | + | 0.0906988i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.54797 | 0.343411 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.2412i | 1.12480i | 0.826865 | + | 0.562400i | \(0.190122\pi\) | ||||
−0.826865 | + | 0.562400i | \(0.809878\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 32.6590i | − | 2.00622i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 18.7078i | − | 1.14490i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.7654i | 0.717350i | 0.933463 | + | 0.358675i | \(0.116771\pi\) | ||||
−0.933463 | + | 0.358675i | \(0.883229\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 10.6020i | − | 0.644024i | −0.946736 | − | 0.322012i | \(-0.895641\pi\) | ||
0.946736 | − | 0.322012i | \(-0.104359\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.8825 | − | 5.44517i | 0.840207 | − | 0.329557i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.8378i | 1.37717i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.65673 | 0.0995434 | 0.0497717 | − | 0.998761i | \(-0.484151\pi\) | ||||
0.0497717 | + | 0.998761i | \(0.484151\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.52845i | − | 0.151374i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.69240i | − | 0.279925i | −0.990157 | − | 0.139963i | \(-0.955302\pi\) | ||
0.990157 | − | 0.139963i | \(-0.0446982\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.5213 | −1.04153 | −0.520766 | − | 0.853699i | \(-0.674354\pi\) | ||||
−0.520766 | + | 0.853699i | \(0.674354\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.8934i | 1.05991i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.909273 | + | 2.31820i | 0.0536727 | + | 0.136839i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1786 | −0.892856 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 13.1577i | − | 0.771317i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.1995 | −1.00481 | −0.502404 | − | 0.864633i | \(-0.667551\pi\) | ||||
−0.502404 | + | 0.864633i | \(0.667551\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 48.7239i | 2.83682i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.82537 | 0.105919 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −26.0763 | − | 7.11917i | −1.50803 | − | 0.411712i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.80999 | + | 7.16410i | 0.161965 | + | 0.412932i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.2453 | −0.818372 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −48.3277 | −2.76723 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.2741i | − | 1.04296i | −0.853265 | − | 0.521478i | \(-0.825381\pi\) | ||
0.853265 | − | 0.521478i | \(-0.174619\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.67757i | 0.0954338i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.5738i | 1.22334i | 0.791115 | + | 0.611668i | \(0.209501\pi\) | ||||
−0.791115 | + | 0.611668i | \(0.790499\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.2454 | −1.20086 | −0.600429 | − | 0.799678i | \(-0.705004\pi\) | ||||
−0.600429 | + | 0.799678i | \(0.705004\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.3071 | + | 4.04276i | −0.580737 | + | 0.227784i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.9417 | −0.839211 | −0.419606 | − | 0.907706i | \(-0.637832\pi\) | ||||
−0.419606 | + | 0.907706i | \(0.637832\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.1271i | − | 0.567008i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.36527 | −0.132016 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.77086 | −0.321099 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 70.5174i | − | 3.91160i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.9734 | −0.772729 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.32386 | − | 5.92471i | −0.128119 | − | 0.326640i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.6313 | −1.51875 | −0.759376 | − | 0.650652i | \(-0.774496\pi\) | ||||
−0.759376 | + | 0.650652i | \(0.774496\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 0.592620i | − | 0.0324754i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 39.9869i | − | 2.18472i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 34.9895i | − | 1.90600i | −0.302972 | − | 0.952999i | \(-0.597979\pi\) | ||
0.302972 | − | 0.952999i | \(-0.402021\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.50110 | 0.135841 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.61535 | −0.249935 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.04598 | − | 16.6812i | 0.434442 | − | 0.900700i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.3603 | + | 5.28563i | 1.04233 | + | 0.284569i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.9364 | 1.28497 | 0.642487 | − | 0.766296i | \(-0.277903\pi\) | ||||
0.642487 | + | 0.766296i | \(0.277903\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 35.3685i | − | 1.89323i | −0.322359 | − | 0.946617i | \(-0.604476\pi\) | ||
0.322359 | − | 0.946617i | \(-0.395524\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.63628 | −0.300842 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.4548i | 1.62095i | 0.585775 | + | 0.810473i | \(0.300790\pi\) | ||||
−0.585775 | + | 0.810473i | \(0.699210\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.1709 | −1.12363 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.30385 | − | 3.32417i | −0.0690069 | − | 0.175934i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.39530i | 0.179197i | 0.995978 | + | 0.0895986i | \(0.0285584\pi\) | ||||
−0.995978 | + | 0.0895986i | \(0.971442\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.716256 | −0.0376977 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.66803i | 0.402467i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.961179i | 0.0503104i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.1391 | −1.41665 | −0.708324 | − | 0.705887i | \(-0.750548\pi\) | ||||
−0.708324 | + | 0.705887i | \(0.750548\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.941186i | − | 0.0489962i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.53983 | − | 19.2228i | −0.391448 | − | 0.998001i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 20.1619i | − | 1.04394i | −0.852963 | − | 0.521972i | \(-0.825196\pi\) | ||
0.852963 | − | 0.521972i | \(-0.174804\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 31.4324i | 1.62316i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.2699i | 1.61048i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.8262i | − | 0.658840i | −0.944184 | − | 0.329420i | \(-0.893147\pi\) | ||
0.944184 | − | 0.329420i | \(-0.106853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.82083i | 0.246978i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.15646 | −0.365678 | −0.182839 | − | 0.983143i | \(-0.558529\pi\) | ||||
−0.182839 | + | 0.983143i | \(0.558529\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.37953 | + | 18.8142i | 0.376096 | + | 0.958859i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2.90862i | − | 0.147853i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.9304i | 1.31472i | 0.753575 | + | 0.657362i | \(0.228328\pi\) | ||||
−0.753575 | + | 0.657362i | \(0.771672\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.70469 | + | 6.24397i | −0.0862097 | + | 0.315771i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.3351 | −0.672668 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 40.4984i | 2.03769i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.3619i | 1.27288i | 0.771327 | + | 0.636439i | \(0.219593\pi\) | ||||
−0.771327 | + | 0.636439i | \(0.780407\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.13096 | + | 10.5319i | 0.206807 | + | 0.527256i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 11.5114i | − | 0.574852i | −0.957803 | − | 0.287426i | \(-0.907200\pi\) | ||
0.957803 | − | 0.287426i | \(-0.0927996\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.2511 | 0.709896 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.18466 | 0.207937 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.08175 | −0.0536203 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 32.9472i | − | 1.62913i | −0.580070 | − | 0.814566i | \(-0.696975\pi\) | ||
0.580070 | − | 0.814566i | \(-0.303025\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.3538 | −0.609367 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.2487 | + | 28.6786i | 0.553511 | + | 1.41118i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.8815 | 1.27047 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.5018 | 0.661185 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.1690 | 0.936469 | 0.468234 | − | 0.883604i | \(-0.344890\pi\) | ||||
0.468234 | + | 0.883604i | \(0.344890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.8573i | 1.30894i | 0.756087 | + | 0.654471i | \(0.227109\pi\) | ||||
−0.756087 | + | 0.654471i | \(0.772891\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.40543i | 0.116956i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.8854 | −0.819063 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.4453 | + | 11.1572i | −1.37657 | + | 0.539934i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.2883i | 0.496723i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 31.8793i | − | 1.53557i | −0.640705 | − | 0.767787i | \(-0.721358\pi\) | ||
0.640705 | − | 0.767787i | \(-0.278642\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.21633 | 0.442909 | 0.221454 | − | 0.975171i | \(-0.428920\pi\) | ||||
0.221454 | + | 0.975171i | \(0.428920\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 23.2163i | − | 1.11314i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.40094 | − | 19.7827i | 0.258362 | − | 0.946336i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.8254i | 1.51894i | 0.650539 | + | 0.759472i | \(0.274543\pi\) | ||||
−0.650539 | + | 0.759472i | \(0.725457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.13333 | + | 4.75909i | −0.244444 | + | 0.226623i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.72364 | 0.414473 | 0.207236 | − | 0.978291i | \(-0.433553\pi\) | ||||
0.207236 | + | 0.978291i | \(0.433553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −78.2856 | −3.71109 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.7461 | −0.602870 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.14168 | 0.431422 | 0.215711 | − | 0.976457i | \(-0.430793\pi\) | ||||
0.215711 | + | 0.976457i | \(0.430793\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.71801 | −0.0808980 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.9527i | 0.796506i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.7862 | − | 58.0935i | −1.06823 | − | 2.72346i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.78417i | − | 0.410906i | −0.978667 | − | 0.205453i | \(-0.934133\pi\) | ||
0.978667 | − | 0.205453i | \(-0.0658668\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.34961i | 0.0629943i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12.7282i | − | 0.592810i | −0.955062 | − | 0.296405i | \(-0.904212\pi\) | ||
0.955062 | − | 0.296405i | \(-0.0957878\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.736780 | 0.0342411 | 0.0171205 | − | 0.999853i | \(-0.494550\pi\) | ||||
0.0171205 | + | 0.999853i | \(0.494550\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.5807 | −0.490668 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.5289 | −0.811140 | −0.405570 | − | 0.914064i | \(-0.632927\pi\) | ||||
−0.405570 | + | 0.914064i | \(0.632927\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.23160 | − | 23.5360i | −0.426275 | − | 1.08679i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.6179i | 0.535323i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.30930 | −0.244122 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 53.4979 | 2.45465 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.80446i | 0.357342i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.2212 | 0.695475 | 0.347737 | − | 0.937592i | \(-0.386950\pi\) | ||||
0.347737 | + | 0.937592i | \(0.386950\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.34017 | 0.152299 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.6156 | − | 1.35855i | 0.574031 | − | 0.0618162i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −55.0604 | −2.50016 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.00583 | −0.0908928 | −0.0454464 | − | 0.998967i | \(-0.514471\pi\) | ||||
−0.0454464 | + | 0.998967i | \(0.514471\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.74976i | 0.260013i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.9197 | 1.03435 | 0.517175 | − | 0.855880i | \(-0.326984\pi\) | ||||
0.517175 | + | 0.855880i | \(0.326984\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.48759 | 0.337224 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 7.63854i | − | 0.343327i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.4611 | + | 4.88763i | −0.558955 | + | 0.219240i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.1508 | −1.52880 | −0.764400 | − | 0.644743i | \(-0.776964\pi\) | ||||
−0.764400 | + | 0.644743i | \(0.776964\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.5553 | −0.873666 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.3500 | 1.44241 | 0.721207 | − | 0.692720i | \(-0.243588\pi\) | ||||
0.721207 | + | 0.692720i | \(0.243588\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 59.6118i | 2.65269i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 18.7677i | − | 0.833501i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 15.3113i | − | 0.678660i | −0.940667 | − | 0.339330i | \(-0.889800\pi\) | ||
0.940667 | − | 0.339330i | \(-0.110200\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.221903 | + | 0.565743i | 0.00981641 | + | 0.0250270i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 4.27595i | − | 0.188788i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.02007 | 0.309341 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.39079 | 0.193107 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.7092 | 0.996824 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.5112 | 1.59958 | 0.799792 | − | 0.600278i | \(-0.204943\pi\) | ||||
0.799792 | + | 0.600278i | \(0.204943\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.0196 | −1.09403 | −0.547015 | − | 0.837123i | \(-0.684236\pi\) | ||||
−0.547015 | + | 0.837123i | \(0.684236\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.0871 | + | 30.8162i | 0.527525 | + | 1.34493i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 3.41242i | − | 0.148647i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.8092 | − | 11.6875i | −0.861268 | − | 0.508151i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 11.6435i | − | 0.505284i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.30479 | 0.229776 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.89782i | 0.427920i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0764i | 0.521137i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.68709 | + | 9.37022i | 0.374179 | + | 0.403604i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5238 | 0.624426 | 0.312213 | − | 0.950012i | \(-0.398930\pi\) | ||||
0.312213 | + | 0.950012i | \(0.398930\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.54990i | 0.152341i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 58.4737i | 2.50474i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.0343 | 1.62623 | 0.813116 | − | 0.582102i | \(-0.197770\pi\) | ||||
0.813116 | + | 0.582102i | \(0.197770\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.5488 | 0.492890 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.7228 | −1.01063 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.34968 | + | 23.8371i | 0.397589 | + | 1.01366i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.47991 | −0.105266 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15.1605i | − | 0.642372i | −0.947016 | − | 0.321186i | \(-0.895918\pi\) | ||
0.947016 | − | 0.321186i | \(-0.104082\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.3938 | 0.693383 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.46353 | 0.104010 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0126 | −0.506270 | −0.253135 | − | 0.967431i | \(-0.581462\pi\) | ||||
−0.253135 | + | 0.967431i | \(0.581462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 10.4663i | − | 0.440319i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.46306 | − | 0.966093i | 0.103439 | − | 0.0405721i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 14.2498i | − | 0.597385i | −0.954349 | − | 0.298692i | \(-0.903450\pi\) | ||
0.954349 | − | 0.298692i | \(-0.0965504\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 43.8426i | − | 1.83476i | −0.398017 | − | 0.917378i | \(-0.630302\pi\) | ||
0.398017 | − | 0.917378i | \(-0.369698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.51786 | −0.397614 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.8030 | − | 57.8838i | 0.659033 | − | 2.41392i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.3434i | 1.09669i | 0.836252 | + | 0.548345i | \(0.184742\pi\) | ||||
−0.836252 | + | 0.548345i | \(0.815258\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 2.10667i | − | 0.0875501i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.2337 | − | 5.97515i | 0.632000 | − | 0.247891i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.2460 | 0.590009 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23.5859i | 0.975157i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 41.1320i | − | 1.69770i | −0.528635 | − | 0.848849i | \(-0.677296\pi\) | ||
0.528635 | − | 0.848849i | \(-0.322704\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.8115i | 0.445481i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 17.7016i | − | 0.728146i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.1990i | 0.788409i | 0.919023 | + | 0.394205i | \(0.128980\pi\) | ||||
−0.919023 | + | 0.394205i | \(0.871020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.9105 | + | 5.45615i | −0.570274 | + | 0.223680i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 10.0241i | − | 0.410259i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.2099 | −1.39778 | −0.698889 | − | 0.715230i | \(-0.746322\pi\) | ||||
−0.698889 | + | 0.715230i | \(0.746322\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 44.4374i | − | 1.81264i | −0.422594 | − | 0.906319i | \(-0.638880\pi\) | ||
0.422594 | − | 0.906319i | \(-0.361120\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.55560i | 0.389134i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.0881 | 1.30457 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.08184i | − | 0.246854i | −0.992354 | − | 0.123427i | \(-0.960611\pi\) | ||
0.992354 | − | 0.123427i | \(-0.0393885\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.35985 | − | 13.6650i | −0.217192 | − | 0.553733i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.5577 | −0.548484 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.98116i | 0.403135i | 0.979475 | + | 0.201568i | \(0.0646036\pi\) | ||||
−0.979475 | + | 0.201568i | \(0.935396\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.93854 | −0.158817 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 13.6405i | − | 0.549147i | −0.961566 | − | 0.274574i | \(-0.911463\pi\) | ||
0.961566 | − | 0.274574i | \(-0.0885367\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.3459 | −0.456030 | −0.228015 | − | 0.973658i | \(-0.573224\pi\) | ||||
−0.228015 | + | 0.973658i | \(0.573224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.62651 | − | 1.26310i | −0.185655 | − | 0.0506864i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −46.0784 | + | 18.0734i | −1.84609 | + | 0.724097i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 68.9770 | 2.75908 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.80518 | −0.311709 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 0.799805i | − | 0.0318903i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0968i | 0.481565i | 0.970579 | + | 0.240782i | \(0.0774040\pi\) | ||||
−0.970579 | + | 0.240782i | \(0.922596\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.8426i | 0.629685i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.1735 | 0.800561 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.8236 | − | 28.9329i | −1.06279 | − | 1.14636i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.05917 | 0.200138 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.9652i | 0.867571i | 0.901016 | + | 0.433786i | \(0.142823\pi\) | ||||
−0.901016 | + | 0.433786i | \(0.857177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.5336 | 1.36187 | 0.680936 | − | 0.732343i | \(-0.261573\pi\) | ||||
0.680936 | + | 0.732343i | \(0.261573\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.1716 | −0.479255 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.4249i | 0.960240i | 0.877203 | + | 0.480120i | \(0.159407\pi\) | ||||
−0.877203 | + | 0.480120i | \(0.840593\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.2536 | −0.834278 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.22772 | + | 2.44272i | −0.244084 | + | 0.0957376i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.28377 | −0.285036 | −0.142518 | − | 0.989792i | \(-0.545520\pi\) | ||||
−0.142518 | + | 0.989792i | \(0.545520\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 55.8029i | 2.18040i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.229691i | − | 0.00896111i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.05252i | − | 0.196818i | −0.995146 | − | 0.0984092i | \(-0.968625\pi\) | ||
0.995146 | − | 0.0984092i | \(-0.0313754\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.8335 | −0.654747 | −0.327374 | − | 0.944895i | \(-0.606164\pi\) | ||||
−0.327374 | + | 0.944895i | \(0.606164\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.60677 | −0.295422 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 44.0725 | − | 17.2867i | 1.70906 | − | 0.670348i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.00763 | + | 25.6677i | −0.271336 | + | 0.993859i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.1995 | −0.935607 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 21.0808i | − | 0.813814i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.9364 | 1.42379 | 0.711896 | − | 0.702284i | \(-0.247837\pi\) | ||||
0.711896 | + | 0.702284i | \(0.247837\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 12.5113i | − | 0.481562i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.40366 | −0.284546 | −0.142273 | − | 0.989827i | \(-0.545441\pi\) | ||||
−0.142273 | + | 0.989827i | \(0.545441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.4082 | + | 12.7115i | −1.24371 | + | 0.487824i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 17.7083i | − | 0.678583i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.3099 | −0.509288 | −0.254644 | − | 0.967035i | \(-0.581958\pi\) | ||||
−0.254644 | + | 0.967035i | \(0.581958\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 51.6963i | 1.97521i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.9498i | 0.417762i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −43.9881 | −1.67581 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.1229i | − | 0.765511i | −0.923850 | − | 0.382755i | \(-0.874975\pi\) | ||
0.923850 | − | 0.382755i | \(-0.125025\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.76347 | − | 4.49599i | −0.0669888 | − | 0.170789i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 56.5003i | − | 2.14318i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.27023i | − | 0.0481135i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.7878i | 0.559328i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.6451i | 0.477598i | 0.971069 | + | 0.238799i | \(0.0767536\pi\) | ||||
−0.971069 | + | 0.238799i | \(0.923246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.53401i | 0.0955721i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.0659 | 0.379103 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.7623 | + | 35.0871i | 0.517584 | + | 1.31959i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 23.4317i | − | 0.879996i | −0.897999 | − | 0.439998i | \(-0.854979\pi\) | ||
0.897999 | − | 0.439998i | \(-0.145021\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 9.67783i | − | 0.362947i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.6979 | + | 3.19368i | 0.438090 | + | 0.119604i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43.0529 | 1.61009 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 3.80996i | − | 0.142286i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5922i | 0.432317i | 0.976358 | + | 0.216159i | \(0.0693528\pi\) | ||||
−0.976358 | + | 0.216159i | \(0.930647\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.13196 | − | 1.62069i | 0.153882 | − | 0.0603577i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.90190i | − | 0.0707326i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −69.4125 | −2.57792 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.2282 | −1.78869 | −0.894343 | − | 0.447382i | \(-0.852356\pi\) | ||||
−0.894343 | + | 0.447382i | \(0.852356\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.92549i | − | 0.145190i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.4926 | 0.793849 | 0.396924 | − | 0.917851i | \(-0.370077\pi\) | ||||
0.396924 | + | 0.917851i | \(0.370077\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19.9151 | + | 21.4812i | 0.734581 | + | 0.792347i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.4425 | 0.642502 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.5260 | −0.902203 | −0.451101 | − | 0.892473i | \(-0.648969\pi\) | ||||
−0.451101 | + | 0.892473i | \(0.648969\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.1005 | 0.885352 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 34.1958i | − | 1.25452i | −0.778809 | − | 0.627262i | \(-0.784176\pi\) | ||
0.778809 | − | 0.627262i | \(-0.215824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.3380i | 1.95415i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.18486 | −0.226292 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.28507 | + | 5.82579i | 0.0834945 | + | 0.212870i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.5018i | 0.894082i | 0.894513 | + | 0.447041i | \(0.147522\pi\) | ||||
−0.894513 | + | 0.447041i | \(0.852478\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 5.54304i | − | 0.202000i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 70.9411 | 2.58181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 30.9296i | − | 1.12416i | −0.827084 | − | 0.562078i | \(-0.810002\pi\) | ||
0.827084 | − | 0.562078i | \(-0.189998\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.30562 | + | 8.44508i | −0.0836886 | + | 0.306537i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 26.6994i | − | 0.967851i | −0.875109 | − | 0.483925i | \(-0.839211\pi\) | ||
0.875109 | − | 0.483925i | \(-0.160789\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.4996 | + | 34.4172i | 0.488717 | + | 1.24599i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.64765 | 0.204191 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 65.6259 | 2.36961 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.64634 | 0.131490 | 0.0657451 | − | 0.997836i | \(-0.479058\pi\) | ||||
0.0657451 | + | 0.997836i | \(0.479058\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.4310 | 0.663776 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −55.0457 | −1.97986 | −0.989928 | − | 0.141571i | \(-0.954785\pi\) | ||||
−0.989928 | + | 0.141571i | \(0.954785\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.6343i | 1.13634i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.45966 | + | 0.572526i | −0.0523650 | + | 0.0205392i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.02446i | 0.144191i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 9.23485i | − | 0.330449i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.54797i | 0.198268i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.6167 | 1.73521 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.4562 | −0.479661 | −0.239831 | − | 0.970815i | \(-0.577092\pi\) | ||||
−0.239831 | + | 0.970815i | \(0.577092\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.2412 | −0.649404 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.41630 | − | 6.16037i | −0.0859137 | − | 0.219038i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 65.0922i | 2.31149i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 32.6590 | 1.15829 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.1027 | −1.27882 | −0.639411 | − | 0.768865i | \(-0.720822\pi\) | ||||
−0.639411 | + | 0.768865i | \(0.720822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.24638i | 0.114849i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.7078 | 0.661007 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.419271 | −0.0147957 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.68506 | − | 52.7921i | −0.200372 | − | 1.86068i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.7654 | −0.414162 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.8480 | −0.451713 | −0.225857 | − | 0.974161i | \(-0.572518\pi\) | ||||
−0.225857 | + | 0.974161i | \(0.572518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.5522i | 1.21329i | 0.794973 | + | 0.606645i | \(0.207485\pi\) | ||||
−0.794973 | + | 0.606645i | \(0.792515\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.6020 | 0.371828 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.0608 | 0.842812 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.4371i | 0.435119i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.44517 | + | 13.8825i | 0.190270 | + | 0.485094i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.2393 | 1.82317 | 0.911583 | − | 0.411116i | \(-0.134861\pi\) | ||||
0.911583 | + | 0.411116i | \(0.134861\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.6554 | 1.55659 | 0.778295 | − | 0.627899i | \(-0.216085\pi\) | ||||
0.778295 | + | 0.627899i | \(0.216085\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.8378 | −0.795110 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.0087i | − | 0.939185i | −0.882883 | − | 0.469593i | \(-0.844401\pi\) | ||
0.882883 | − | 0.469593i | \(-0.155599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 32.9928i | − | 1.14589i | −0.819595 | − | 0.572943i | \(-0.805802\pi\) | ||
0.819595 | − | 0.572943i | \(-0.194198\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.65673i | 0.0574714i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.92798 | + | 6.42290i | −0.240040 | + | 0.222540i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 81.8322i | 2.83192i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.52845 | 0.0873960 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.8396 | −0.753987 | −0.376994 | − | 0.926216i | \(-0.623042\pi\) | ||||
−0.376994 | + | 0.926216i | \(0.623042\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.77997 | 0.0613783 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.69240 | 0.161615 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −78.5362 | −2.70173 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.8868 | − | 7.40803i | 0.648959 | − | 0.254543i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 17.5213i | − | 0.601329i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.74176 | + | 0.748537i | 0.0939864 | + | 0.0256595i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.9620i | 0.375332i | 0.982233 | + | 0.187666i | \(0.0600922\pi\) | ||||
−0.982233 | + | 0.187666i | \(0.939908\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.8934 | −0.611941 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 12.6558i | − | 0.432314i | −0.976359 | − | 0.216157i | \(-0.930648\pi\) | ||
0.976359 | − | 0.216157i | \(-0.0693523\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9.16755i | − | 0.312793i | −0.987694 | − | 0.156396i | \(-0.950012\pi\) | ||
0.987694 | − | 0.156396i | \(-0.0499877\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.31820 | + | 0.909273i | −0.0790040 | + | 0.0309879i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.3252 | 1.44077 | 0.720384 | − | 0.693576i | \(-0.243966\pi\) | ||||
0.720384 | + | 0.693576i | \(0.243966\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 95.0302i | − | 3.23112i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 15.1786i | − | 0.515491i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.6656 | −0.599264 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.8581 | −1.82491 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.1577 | 0.445320 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 77.4198 | − | 30.3666i | 2.61727 | − | 1.02658i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.7990 | −1.68159 | −0.840796 | − | 0.541351i | \(-0.817913\pi\) | ||||
−0.840796 | + | 0.541351i | \(0.817913\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 17.1995i | − | 0.580126i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.2859 | −0.750830 | −0.375415 | − | 0.926857i | \(-0.622500\pi\) | ||||
−0.375415 | + | 0.926857i | \(0.622500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.8981 | −1.54459 | −0.772297 | − | 0.635262i | \(-0.780892\pi\) | ||||
−0.772297 | + | 0.635262i | \(0.780892\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −48.7239 | −1.63784 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.69739i | 0.0905696i | 0.998974 | + | 0.0452848i | \(0.0144195\pi\) | ||||
−0.998974 | + | 0.0452848i | \(0.985580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.8740 | − | 4.65737i | 0.398241 | − | 0.156203i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.82537i | 0.0611521i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 10.2855i | − | 0.344190i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.5357 | 1.68922 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.11917 | − | 26.0763i | 0.237702 | − | 0.870662i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 14.0278i | − | 0.467852i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.5330i | 0.350904i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.16410 | + | 2.80999i | −0.238406 | + | 0.0935108i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.8551 | 0.493800 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 17.3172i | − | 0.575009i | −0.957779 | − | 0.287504i | \(-0.907174\pi\) | ||
0.957779 | − | 0.287504i | \(-0.0928255\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 14.2453i | − | 0.472487i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.1520i | 0.369483i | 0.982787 | + | 0.184742i | \(0.0591448\pi\) | ||||
−0.982787 | + | 0.184742i | \(0.940855\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.2896i | 0.373633i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 48.3277i | − | 1.59766i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.8830 | + | 32.8452i | 0.425433 | + | 1.08465i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.90313i | − | 0.0957655i | −0.998853 | − | 0.0478828i | \(-0.984753\pi\) | ||
0.998853 | − | 0.0478828i | \(-0.0152474\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.2741 | 0.602151 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.5149i | 0.938580i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.41447i | 0.243786i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.67757 | −0.0550987 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 42.4157i | − | 1.39161i | −0.718229 | − | 0.695807i | \(-0.755047\pi\) | ||
0.718229 | − | 0.695807i | \(-0.244953\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.9499 | − | 20.3496i | 0.719378 | − | 0.666932i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.5738 | −0.706293 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 10.3090i | − | 0.337141i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.6954 | 0.708757 | 0.354378 | − | 0.935102i | \(-0.384692\pi\) | ||||
0.354378 | + | 0.935102i | \(0.384692\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 21.2454i | − | 0.693316i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.2006 | 1.01711 | 0.508556 | − | 0.861029i | \(-0.330180\pi\) | ||||
0.508556 | + | 0.861029i | \(0.330180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.35441 | + | 1.18881i | 0.141799 | + | 0.0387130i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.04276 | − | 10.3071i | −0.131511 | − | 0.335289i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.3015 | −0.757197 | −0.378598 | − | 0.925561i | \(-0.623594\pi\) | ||||
−0.378598 | + | 0.925561i | \(0.623594\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.29460 | 0.0420246 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 14.9417i | − | 0.484519i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.59921i | 0.213769i | 0.994271 | + | 0.106885i | \(0.0340875\pi\) | ||||
−0.994271 | + | 0.106885i | \(0.965912\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.8290i | 1.28884i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.1271 | 0.327362 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.9349 | + | 30.4281i | 0.385398 | + | 0.982574i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.6069 | 0.793772 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2.36527i | − | 0.0762196i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.81567 | −0.283787 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.6781 | −0.568489 | −0.284245 | − | 0.958752i | \(-0.591743\pi\) | ||||
−0.284245 | + | 0.958752i | \(0.591743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5.77086i | − | 0.185387i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.4369 | −1.29768 | −0.648841 | − | 0.760924i | \(-0.724746\pi\) | ||||
−0.648841 | + | 0.760924i | \(0.724746\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.0440 | − | 33.2557i | −0.418170 | − | 1.06613i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 70.5174 | 2.25837 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.5277i | 0.752719i | 0.926474 | + | 0.376360i | \(0.122824\pi\) | ||||
−0.926474 | + | 0.376360i | \(0.877176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 34.1486i | − | 1.09139i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 13.9734i | − | 0.446135i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.6661 | −0.659147 | −0.329573 | − | 0.944130i | \(-0.606905\pi\) | ||||
−0.329573 | + | 0.944130i | \(0.606905\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −74.0750 | −2.36023 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.92471 | − | 2.32386i | 0.188585 | − | 0.0739694i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.4567 | + | 3.67387i | 0.427900 | + | 0.116822i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.8115 | 0.438737 | 0.219368 | − | 0.975642i | \(-0.429600\pi\) | ||||
0.219368 | + | 0.975642i | \(0.429600\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 27.6313i | − | 0.876852i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.9474 | −1.32982 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.36830i | 0.170016i | 0.996380 | + | 0.0850079i | \(0.0270915\pi\) | ||||
−0.996380 | + | 0.0850079i | \(0.972908\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.592620 | 0.0187497 |
(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 | 1932.2.k.a.1609.28 | yes | 32 | |
3.2 | odd | 2 | 5796.2.k.d.5473.1 | 32 | |||
7.6 | odd | 2 | inner | 1932.2.k.a.1609.25 | ✓ | 32 | |
21.20 | even | 2 | 5796.2.k.d.5473.31 | 32 | |||
23.22 | odd | 2 | inner | 1932.2.k.a.1609.27 | yes | 32 | |
69.68 | even | 2 | 5796.2.k.d.5473.32 | 32 | |||
161.160 | even | 2 | inner | 1932.2.k.a.1609.26 | yes | 32 | |
483.482 | odd | 2 | 5796.2.k.d.5473.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.k.a.1609.25 | ✓ | 32 | 7.6 | odd | 2 | inner | |
1932.2.k.a.1609.26 | yes | 32 | 161.160 | even | 2 | inner | |
1932.2.k.a.1609.27 | yes | 32 | 23.22 | odd | 2 | inner | |
1932.2.k.a.1609.28 | yes | 32 | 1.1 | even | 1 | trivial | |
5796.2.k.d.5473.1 | 32 | 3.2 | odd | 2 | |||
5796.2.k.d.5473.2 | 32 | 483.482 | odd | 2 | |||
5796.2.k.d.5473.31 | 32 | 21.20 | even | 2 | |||
5796.2.k.d.5473.32 | 32 | 69.68 | even | 2 |