Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(107,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.be (of order \(6\), degree \(2\), 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: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.7 | ||
Character | \(\chi\) | \(=\) | 252.107 |
Dual form | 252.2.be.a.179.7 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.627710 | + | 1.26727i | −0.443858 | + | 0.896097i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.21196 | − | 1.59096i | −0.605981 | − | 0.795479i | ||||
\(5\) | −2.15525 | − | 1.24433i | −0.963856 | − | 0.556482i | −0.0664982 | − | 0.997787i | \(-0.521183\pi\) |
−0.897358 | + | 0.441304i | \(0.854516\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64453 | − | 0.0803545i | 0.999539 | − | 0.0303711i | ||||
\(8\) | 2.77694 | − | 0.537226i | 0.981796 | − | 0.189938i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.92978 | − | 1.95021i | 0.926477 | − | 0.616710i | ||||
\(11\) | 2.30393 | + | 3.99053i | 0.694662 | + | 1.20319i | 0.970294 | + | 0.241927i | \(0.0777796\pi\) |
−0.275632 | + | 0.961263i | \(0.588887\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.22221 | 1.44838 | 0.724190 | − | 0.689600i | \(-0.242214\pi\) | ||||
0.724190 | + | 0.689600i | \(0.242214\pi\) | |||||||
\(14\) | −1.55817 | + | 3.40178i | −0.416437 | + | 0.909164i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.06230 | + | 3.85636i | −0.265575 | + | 0.964090i | ||||
\(17\) | 4.85928 | − | 2.80550i | 1.17855 | − | 0.680435i | 0.222870 | − | 0.974848i | \(-0.428458\pi\) |
0.955678 | + | 0.294413i | \(0.0951243\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.76570 | − | 1.59678i | −0.634495 | − | 0.366326i | 0.147996 | − | 0.988988i | \(-0.452718\pi\) |
−0.782491 | + | 0.622662i | \(0.786051\pi\) | |||||||
\(20\) | 0.632394 | + | 4.93699i | 0.141408 | + | 1.10394i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.50329 | + | 0.414819i | −1.38651 | + | 0.0884397i | ||||
\(23\) | 0.359366 | − | 0.622440i | 0.0749329 | − | 0.129788i | −0.826124 | − | 0.563488i | \(-0.809459\pi\) |
0.901057 | + | 0.433700i | \(0.142792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.596726 | + | 1.03356i | 0.119345 | + | 0.206712i | ||||
\(26\) | −3.27803 | + | 6.61796i | −0.642875 | + | 1.29789i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.33291 | − | 4.10995i | −0.629861 | − | 0.776708i | ||||
\(29\) | − | 4.53656i | − | 0.842418i | −0.906964 | − | 0.421209i | \(-0.861606\pi\) | ||
0.906964 | − | 0.421209i | \(-0.138394\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.01944 | − | 0.588574i | 0.183097 | − | 0.105711i | −0.405650 | − | 0.914028i | \(-0.632955\pi\) |
0.588747 | + | 0.808317i | \(0.299621\pi\) | |||||||
\(32\) | −4.22025 | − | 3.76690i | −0.746041 | − | 0.665900i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.505125 | + | 7.91907i | 0.0866283 | + | 1.35811i | ||||
\(35\) | −5.79960 | − | 3.11749i | −0.980312 | − | 0.526952i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.35648 | + | 2.34949i | −0.223004 | + | 0.386254i | −0.955719 | − | 0.294282i | \(-0.904920\pi\) |
0.732715 | + | 0.680536i | \(0.238253\pi\) | |||||||
\(38\) | 3.75961 | − | 2.50258i | 0.609889 | − | 0.405972i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.65348 | − | 2.29758i | −1.05201 | − | 0.363279i | ||||
\(41\) | 3.83670i | 0.599192i | 0.954066 | + | 0.299596i | \(0.0968519\pi\) | ||||
−0.954066 | + | 0.299596i | \(0.903148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.1773i | 1.70453i | 0.523113 | + | 0.852263i | \(0.324771\pi\) | ||||
−0.523113 | + | 0.852263i | \(0.675229\pi\) | |||||||
\(44\) | 3.55649 | − | 8.50184i | 0.536161 | − | 1.28170i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.563224 | + | 0.846126i | 0.0830428 | + | 0.124754i | ||||
\(47\) | 2.70905 | − | 4.69222i | 0.395156 | − | 0.684430i | −0.597965 | − | 0.801522i | \(-0.704024\pi\) |
0.993121 | + | 0.117092i | \(0.0373572\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98709 | − | 0.425000i | 0.998155 | − | 0.0607142i | ||||
\(50\) | −1.68437 | + | 0.107439i | −0.238206 | + | 0.0151942i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.32912 | − | 8.30832i | −0.877690 | − | 1.15216i | ||||
\(53\) | −1.79114 | + | 1.03411i | −0.246032 | + | 0.142046i | −0.617946 | − | 0.786221i | \(-0.712035\pi\) |
0.371914 | + | 0.928267i | \(0.378702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 11.4674i | − | 1.54627i | ||||||
\(56\) | 7.30053 | − | 1.64385i | 0.975575 | − | 0.219669i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.74906 | + | 2.84764i | 0.754888 | + | 0.373914i | ||||
\(59\) | −2.05821 | − | 3.56492i | −0.267956 | − | 0.464113i | 0.700378 | − | 0.713772i | \(-0.253015\pi\) |
−0.968334 | + | 0.249659i | \(0.919681\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.505125 | − | 0.874903i | 0.0646747 | − | 0.112020i | −0.831875 | − | 0.554963i | \(-0.812732\pi\) |
0.896550 | + | 0.442943i | \(0.146066\pi\) | |||||||
\(62\) | 0.105972 | + | 1.66136i | 0.0134584 | + | 0.210993i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.42278 | − | 2.98369i | 0.927847 | − | 0.372961i | ||||
\(65\) | −11.2552 | − | 6.49816i | −1.39603 | − | 0.805998i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9505 | + | 6.32230i | −1.33782 | + | 0.772391i | −0.986484 | − | 0.163858i | \(-0.947606\pi\) |
−0.351337 | + | 0.936249i | \(0.614273\pi\) | |||||||
\(68\) | −10.3527 | − | 4.33075i | −1.25545 | − | 0.525180i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.59118 | − | 5.39280i | 0.907320 | − | 0.644563i | ||||
\(71\) | 7.31012 | 0.867552 | 0.433776 | − | 0.901021i | \(-0.357181\pi\) | ||||
0.433776 | + | 0.901021i | \(0.357181\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.81894 | − | 8.34664i | −0.564014 | − | 0.976900i | −0.997141 | − | 0.0755675i | \(-0.975923\pi\) |
0.433127 | − | 0.901333i | \(-0.357410\pi\) | |||||||
\(74\) | −2.12597 | − | 3.19383i | −0.247139 | − | 0.371275i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.811513 | + | 6.33534i | 0.0930870 | + | 0.726714i | ||||
\(77\) | 6.41348 | + | 10.3680i | 0.730884 | + | 1.18154i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.65524 | − | 4.41975i | −0.861281 | − | 0.497261i | 0.00315980 | − | 0.999995i | \(-0.498994\pi\) |
−0.864441 | + | 0.502734i | \(0.832328\pi\) | |||||||
\(80\) | 7.08811 | − | 6.98956i | 0.792475 | − | 0.781456i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.86215 | − | 2.40833i | −0.536934 | − | 0.265956i | ||||
\(83\) | −13.7657 | −1.51099 | −0.755493 | − | 0.655157i | \(-0.772603\pi\) | ||||
−0.755493 | + | 0.655157i | \(0.772603\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.9639 | −1.51460 | ||||||||
\(86\) | −14.1647 | − | 7.01612i | −1.52742 | − | 0.756567i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.54170 | + | 9.84373i | 0.910548 | + | 1.04935i | ||||
\(89\) | 7.38369 | + | 4.26297i | 0.782669 | + | 0.451874i | 0.837375 | − | 0.546628i | \(-0.184089\pi\) |
−0.0547061 | + | 0.998503i | \(0.517422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.8103 | − | 0.419628i | 1.44771 | − | 0.0439889i | ||||
\(92\) | −1.42581 | + | 0.182637i | −0.148651 | + | 0.0190412i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.24582 | + | 6.37846i | 0.437923 | + | 0.657888i | ||||
\(95\) | 3.97384 | + | 6.88289i | 0.407707 | + | 0.706170i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.7232 | −1.08878 | −0.544388 | − | 0.838833i | \(-0.683238\pi\) | ||||
−0.544388 | + | 0.838833i | \(0.683238\pi\) | |||||||
\(98\) | −3.84727 | + | 9.12132i | −0.388633 | + | 0.921393i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.921143 | − | 2.20200i | 0.0921143 | − | 0.220200i | ||||
\(101\) | 3.32268 | − | 1.91835i | 0.330619 | − | 0.190883i | −0.325497 | − | 0.945543i | \(-0.605532\pi\) |
0.656116 | + | 0.754660i | \(0.272198\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.4431 | + | 8.33870i | 1.42312 | + | 0.821636i | 0.996564 | − | 0.0828265i | \(-0.0263947\pi\) |
0.426552 | + | 0.904463i | \(0.359728\pi\) | |||||||
\(104\) | 14.5018 | − | 2.80550i | 1.42201 | − | 0.275102i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.186190 | − | 2.91898i | −0.0180844 | − | 0.283517i | ||||
\(107\) | −2.86844 | + | 4.96829i | −0.277303 | + | 0.480303i | −0.970714 | − | 0.240240i | \(-0.922774\pi\) |
0.693411 | + | 0.720543i | \(0.256107\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.41352 | + | 2.44830i | 0.135391 | + | 0.234504i | 0.925747 | − | 0.378144i | \(-0.123438\pi\) |
−0.790356 | + | 0.612648i | \(0.790104\pi\) | |||||||
\(110\) | 14.5324 | + | 7.19822i | 1.38561 | + | 0.686324i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.49941 | + | 10.2836i | −0.236172 | + | 0.971711i | ||||
\(113\) | 5.59651i | 0.526476i | 0.964731 | + | 0.263238i | \(0.0847904\pi\) | ||||
−0.964731 | + | 0.263238i | \(0.915210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.54904 | + | 0.894341i | −0.144449 | + | 0.0833977i | ||||
\(116\) | −7.21748 | + | 5.49813i | −0.670126 | + | 0.510489i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.80968 | − | 0.370576i | 0.534825 | − | 0.0341143i | ||||
\(119\) | 12.6251 | − | 7.80971i | 1.15734 | − | 0.715915i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.11623 | + | 8.86157i | −0.465112 | + | 0.805597i | ||||
\(122\) | 0.791669 | + | 1.18932i | 0.0716743 | + | 0.107676i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.17192 | − | 0.908559i | −0.195044 | − | 0.0815910i | ||||
\(125\) | 9.47322i | 0.847311i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.2266i | − | 1.35114i | −0.737294 | − | 0.675572i | \(-0.763897\pi\) | ||
0.737294 | − | 0.675572i | \(-0.236103\pi\) | |||||||
\(128\) | −0.878205 | + | 11.2796i | −0.0776231 | + | 0.996983i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.2999 | − | 10.1844i | 1.34189 | − | 0.893230i | ||||
\(131\) | −2.07666 | + | 3.59688i | −0.181438 | + | 0.314261i | −0.942371 | − | 0.334571i | \(-0.891409\pi\) |
0.760932 | + | 0.648831i | \(0.224742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.44228 | − | 4.00049i | −0.645328 | − | 0.346886i | ||||
\(134\) | −1.13832 | − | 17.8459i | −0.0983356 | − | 1.54165i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.9867 | − | 10.4012i | 1.02785 | − | 0.891899i | ||||
\(137\) | −14.1437 | + | 8.16585i | −1.20838 | + | 0.697656i | −0.962404 | − | 0.271621i | \(-0.912440\pi\) |
−0.245971 | + | 0.969277i | \(0.579107\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.2903i | − | 0.872811i | −0.899750 | − | 0.436406i | \(-0.856251\pi\) | ||
0.899750 | − | 0.436406i | \(-0.143749\pi\) | |||||||
\(140\) | 2.06910 | + | 13.0052i | 0.174871 | + | 1.09914i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.58863 | + | 9.26392i | −0.385070 | + | 0.777411i | ||||
\(143\) | 12.0316 | + | 20.8394i | 1.00614 | + | 1.74268i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.64499 | + | 9.77740i | −0.468791 | + | 0.811969i | ||||
\(146\) | 13.6024 | − | 0.867640i | 1.12574 | − | 0.0718064i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.38194 | − | 0.689389i | 0.442393 | − | 0.0566674i | ||||
\(149\) | 4.89898 | + | 2.82843i | 0.401340 | + | 0.231714i | 0.687062 | − | 0.726599i | \(-0.258900\pi\) |
−0.285722 | + | 0.958313i | \(0.592233\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5330 | + | 6.08123i | −0.857164 | + | 0.494884i | −0.863061 | − | 0.505099i | \(-0.831456\pi\) |
0.00589781 | + | 0.999983i | \(0.498123\pi\) | |||||||
\(152\) | −8.53800 | − | 2.94835i | −0.692523 | − | 0.239142i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −17.1648 | + | 1.61957i | −1.38318 | + | 0.130509i | ||||
\(155\) | −2.92953 | −0.235305 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.51950 | − | 6.09596i | −0.280887 | − | 0.486510i | 0.690716 | − | 0.723126i | \(-0.257295\pi\) |
−0.971603 | + | 0.236615i | \(0.923962\pi\) | |||||||
\(158\) | 10.4063 | − | 6.92695i | 0.827881 | − | 0.551079i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.40840 | + | 13.3700i | 0.348515 | + | 1.05699i | ||||
\(161\) | 0.900338 | − | 1.67494i | 0.0709566 | − | 0.132004i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.54904 | − | 0.894341i | −0.121330 | − | 0.0700502i | 0.438107 | − | 0.898923i | \(-0.355649\pi\) |
−0.559437 | + | 0.828873i | \(0.688983\pi\) | |||||||
\(164\) | 6.10403 | − | 4.64993i | 0.476645 | − | 0.363099i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.64089 | − | 17.4449i | 0.670663 | − | 1.35399i | ||||
\(167\) | −8.26973 | −0.639931 | −0.319965 | − | 0.947429i | \(-0.603671\pi\) | ||||
−0.319965 | + | 0.947429i | \(0.603671\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.2715 | 1.09781 | ||||||||
\(170\) | 8.76529 | − | 17.6961i | 0.672267 | − | 1.35723i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.7827 | − | 13.5465i | 1.35592 | − | 1.03291i | ||||
\(173\) | −16.7552 | − | 9.67360i | −1.27387 | − | 0.735470i | −0.298158 | − | 0.954517i | \(-0.596372\pi\) |
−0.975714 | + | 0.219046i | \(0.929705\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.66111 | + | 2.68533i | 0.125568 | + | 0.202992i | ||||
\(176\) | −17.8364 | + | 4.64566i | −1.34447 | + | 0.350180i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.0372 | + | 6.68124i | −0.752317 | + | 0.500780i | ||||
\(179\) | −6.02688 | − | 10.4389i | −0.450470 | − | 0.780237i | 0.547945 | − | 0.836514i | \(-0.315410\pi\) |
−0.998415 | + | 0.0562770i | \(0.982077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7992 | 1.54599 | 0.772997 | − | 0.634410i | \(-0.218757\pi\) | ||||
0.772997 | + | 0.634410i | \(0.218757\pi\) | |||||||
\(182\) | −8.13707 | + | 17.7648i | −0.603160 | + | 1.31682i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.663546 | − | 1.92154i | 0.0489173 | − | 0.141658i | ||||
\(185\) | 5.84709 | − | 3.37582i | 0.429887 | − | 0.248195i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.3909 | + | 12.9274i | 1.63739 | + | 0.945345i | ||||
\(188\) | −10.7484 | + | 1.37679i | −0.783907 | + | 0.100413i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.2169 | + | 0.715482i | −0.813761 | + | 0.0519065i | ||||
\(191\) | −5.30815 | + | 9.19399i | −0.384084 | + | 0.665253i | −0.991642 | − | 0.129022i | \(-0.958816\pi\) |
0.607557 | + | 0.794276i | \(0.292149\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.49634 | − | 11.2520i | −0.467617 | − | 0.809936i | 0.531699 | − | 0.846934i | \(-0.321554\pi\) |
−0.999315 | + | 0.0369977i | \(0.988221\pi\) | |||||||
\(194\) | 6.73106 | − | 13.5892i | 0.483262 | − | 0.975650i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.14424 | − | 10.6011i | −0.653160 | − | 0.757220i | ||||
\(197\) | − | 3.18852i | − | 0.227173i | −0.993528 | − | 0.113586i | \(-0.963766\pi\) | ||
0.993528 | − | 0.113586i | \(-0.0362339\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.1672 | + | 7.02473i | −0.862509 | + | 0.497970i | −0.864852 | − | 0.502027i | \(-0.832588\pi\) |
0.00234247 | + | 0.999997i | \(0.499254\pi\) | |||||||
\(200\) | 2.21233 | + | 2.54956i | 0.156435 | + | 0.180281i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.345395 | + | 5.41491i | 0.0243019 | + | 0.380992i | ||||
\(203\) | −0.364533 | − | 11.9971i | −0.0255852 | − | 0.842029i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.77413 | − | 8.26904i | 0.333440 | − | 0.577534i | ||||
\(206\) | −19.6335 | + | 13.0690i | −1.36793 | + | 0.910561i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.54755 | + | 20.1387i | −0.384653 | + | 1.39637i | ||||
\(209\) | − | 14.7155i | − | 1.01789i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.12962i | 0.628509i | 0.949339 | + | 0.314255i | \(0.101755\pi\) | ||||
−0.949339 | + | 0.314255i | \(0.898245\pi\) | |||||||
\(212\) | 3.81602 | + | 1.59632i | 0.262085 | + | 0.109636i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.49563 | − | 6.75374i | −0.307315 | − | 0.461676i | ||||
\(215\) | 13.9083 | − | 24.0899i | 0.948539 | − | 1.64292i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.64865 | − | 1.63842i | 0.179802 | − | 0.111223i | ||||
\(218\) | −3.98994 | + | 0.254502i | −0.270233 | + | 0.0172371i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −18.2442 | + | 13.8981i | −1.23003 | + | 0.937009i | ||||
\(221\) | 25.3762 | − | 14.6509i | 1.70699 | − | 0.985528i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 23.8384i | − | 1.59634i | −0.602434 | − | 0.798168i | \(-0.705802\pi\) | ||
0.602434 | − | 0.798168i | \(-0.294198\pi\) | |||||||
\(224\) | −11.4633 | − | 9.62256i | −0.765921 | − | 0.642935i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.09231 | − | 3.51298i | −0.471773 | − | 0.233680i | ||||
\(227\) | −5.00619 | − | 8.67097i | −0.332272 | − | 0.575512i | 0.650685 | − | 0.759348i | \(-0.274482\pi\) |
−0.982957 | + | 0.183836i | \(0.941149\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.66815 | − | 4.62137i | 0.176316 | − | 0.305389i | −0.764300 | − | 0.644861i | \(-0.776915\pi\) |
0.940616 | + | 0.339472i | \(0.110248\pi\) | |||||||
\(230\) | −0.161024 | − | 2.52445i | −0.0106176 | − | 0.166457i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.43716 | − | 12.5977i | −0.160007 | − | 0.827082i | ||||
\(233\) | 7.59347 | + | 4.38409i | 0.497465 | + | 0.287211i | 0.727666 | − | 0.685932i | \(-0.240605\pi\) |
−0.230201 | + | 0.973143i | \(0.573938\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.6774 | + | 6.74192i | −0.761747 | + | 0.439795i | ||||
\(236\) | −3.17717 | + | 7.59507i | −0.206816 | + | 0.494397i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.97215 | + | 20.9016i | 0.127836 | + | 1.35485i | ||||
\(239\) | 13.1385 | 0.849860 | 0.424930 | − | 0.905226i | \(-0.360299\pi\) | ||||
0.424930 | + | 0.905226i | \(0.360299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0319 | + | 19.1078i | 0.710627 | + | 1.23084i | 0.964622 | + | 0.263636i | \(0.0849218\pi\) |
−0.253996 | + | 0.967205i | \(0.581745\pi\) | |||||||
\(242\) | −8.01852 | − | 12.0462i | −0.515450 | − | 0.774356i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.00413 | + | 0.256715i | −0.128301 | + | 0.0164345i | ||||
\(245\) | −15.5877 | − | 7.77828i | −0.995864 | − | 0.496936i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.4431 | − | 8.33870i | −0.918989 | − | 0.530579i | ||||
\(248\) | 2.51473 | − | 2.18210i | 0.159685 | − | 0.138564i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.0052 | − | 5.94643i | −0.759273 | − | 0.376085i | ||||
\(251\) | −26.5149 | −1.67361 | −0.836804 | − | 0.547503i | \(-0.815579\pi\) | ||||
−0.836804 | + | 0.547503i | \(0.815579\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.31182 | 0.208212 | ||||||||
\(254\) | 19.2963 | + | 9.55789i | 1.21076 | + | 0.599715i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.7430 | − | 8.19322i | −0.858940 | − | 0.512076i | ||||
\(257\) | 14.6698 | + | 8.46961i | 0.915076 | + | 0.528320i | 0.882061 | − | 0.471135i | \(-0.156156\pi\) |
0.0330154 | + | 0.999455i | \(0.489489\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.39846 | + | 6.32230i | −0.211170 | + | 0.392848i | ||||
\(260\) | 3.30250 | + | 25.7820i | 0.204812 | + | 1.59893i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.25469 | − | 4.88949i | −0.201075 | − | 0.302073i | ||||
\(263\) | 6.97969 | + | 12.0892i | 0.430386 | + | 0.745451i | 0.996906 | − | 0.0785971i | \(-0.0250441\pi\) |
−0.566520 | + | 0.824048i | \(0.691711\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.14712 | 0.316185 | ||||||||
\(266\) | 9.74130 | − | 6.92026i | 0.597277 | − | 0.424308i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 23.3301 | + | 9.75948i | 1.42512 | + | 0.596155i | ||||
\(269\) | −13.4582 | + | 7.77008i | −0.820559 | + | 0.473750i | −0.850609 | − | 0.525798i | \(-0.823767\pi\) |
0.0300501 | + | 0.999548i | \(0.490433\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.197214 | − | 0.113861i | −0.0119799 | − | 0.00691658i | 0.493998 | − | 0.869463i | \(-0.335535\pi\) |
−0.505978 | + | 0.862546i | \(0.668868\pi\) | |||||||
\(272\) | 5.65703 | + | 21.7194i | 0.343008 | + | 1.31693i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.47025 | − | 23.0497i | −0.0888208 | − | 1.39248i | ||||
\(275\) | −2.74964 | + | 4.76251i | −0.165809 | + | 0.287190i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.05140 | + | 15.6775i | 0.543846 | + | 0.941968i | 0.998679 | + | 0.0513915i | \(0.0163656\pi\) |
−0.454833 | + | 0.890577i | \(0.650301\pi\) | |||||||
\(278\) | 13.0406 | + | 6.45932i | 0.782124 | + | 0.387404i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −17.7799 | − | 5.54139i | −1.06255 | − | 0.331161i | ||||
\(281\) | − | 16.5594i | − | 0.987854i | −0.869503 | − | 0.493927i | \(-0.835561\pi\) | ||
0.869503 | − | 0.493927i | \(-0.164439\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.76570 | + | 1.59678i | −0.164404 | + | 0.0949185i | −0.579944 | − | 0.814656i | \(-0.696926\pi\) |
0.415541 | + | 0.909575i | \(0.363592\pi\) | |||||||
\(284\) | −8.85958 | − | 11.6301i | −0.525720 | − | 0.690120i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −33.9616 | + | 2.16627i | −2.00819 | + | 0.128094i | ||||
\(287\) | 0.308296 | + | 10.1463i | 0.0181981 | + | 0.598915i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.24171 | − | 12.5430i | 0.425983 | − | 0.737824i | ||||
\(290\) | −8.84723 | − | 13.2911i | −0.519527 | − | 0.780481i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.43880 | + | 17.7825i | −0.435323 | + | 1.04064i | ||||
\(293\) | − | 3.17751i | − | 0.185632i | −0.995683 | − | 0.0928160i | \(-0.970413\pi\) | ||
0.995683 | − | 0.0928160i | \(-0.0295868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2444i | 0.596451i | ||||||||
\(296\) | −2.50465 | + | 7.25312i | −0.145580 | + | 0.421579i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.65953 | + | 4.43291i | −0.385776 | + | 0.256792i | ||||
\(299\) | 1.87668 | − | 3.25051i | 0.108531 | − | 0.187982i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.898148 | + | 29.5588i | 0.0517684 | + | 1.70374i | ||||
\(302\) | −1.09491 | − | 17.1654i | −0.0630052 | − | 0.987760i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.09575 | − | 8.96927i | 0.521677 | − | 0.514423i | ||||
\(305\) | −2.17734 | + | 1.25709i | −0.124674 | + | 0.0719807i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8559i | 0.619579i | 0.950805 | + | 0.309790i | \(0.100259\pi\) | ||||
−0.950805 | + | 0.309790i | \(0.899741\pi\) | |||||||
\(308\) | 8.72209 | − | 22.7691i | 0.496987 | − | 1.29739i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.83889 | − | 3.71251i | 0.104442 | − | 0.210856i | ||||
\(311\) | −9.34103 | − | 16.1791i | −0.529681 | − | 0.917434i | −0.999401 | − | 0.0346188i | \(-0.988978\pi\) |
0.469720 | − | 0.882816i | \(-0.344355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.91566 | − | 13.7103i | 0.447420 | − | 0.774954i | −0.550798 | − | 0.834639i | \(-0.685676\pi\) |
0.998217 | + | 0.0596853i | \(0.0190097\pi\) | |||||||
\(314\) | 9.93447 | − | 0.633680i | 0.560635 | − | 0.0357606i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.24621 | + | 17.5357i | 0.126359 | + | 0.986462i | ||||
\(317\) | −5.31592 | − | 3.06915i | −0.298572 | − | 0.172380i | 0.343229 | − | 0.939252i | \(-0.388479\pi\) |
−0.641801 | + | 0.766871i | \(0.721813\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.1033 | − | 10.4519i | 1.01359 | − | 0.585196i | ||||
\(320\) | −19.7106 | − | 2.80582i | −1.10186 | − | 0.156850i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.55745 | + | 2.19235i | 0.0867934 | + | 0.122175i | ||||
\(323\) | −17.9191 | −0.997043 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.11623 | + | 5.39747i | 0.172857 | + | 0.299398i | ||||
\(326\) | 2.10572 | − | 1.40167i | 0.116625 | − | 0.0776316i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.06117 | + | 10.6543i | 0.113809 | + | 0.588284i | ||||
\(329\) | 6.78713 | − | 12.6264i | 0.374187 | − | 0.696116i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.336392 | − | 0.194216i | −0.0184898 | − | 0.0106751i | 0.490727 | − | 0.871314i | \(-0.336731\pi\) |
−0.509216 | + | 0.860639i | \(0.670065\pi\) | |||||||
\(332\) | 16.6835 | + | 21.9007i | 0.915628 | + | 1.20196i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.19099 | − | 10.4800i | 0.284038 | − | 0.573440i | ||||
\(335\) | 31.4681 | 1.71929 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.10384 | 0.332497 | 0.166249 | − | 0.986084i | \(-0.446835\pi\) | ||||
0.166249 | + | 0.986084i | \(0.446835\pi\) | |||||||
\(338\) | −8.95834 | + | 18.0858i | −0.487269 | + | 0.983740i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.9237 | + | 22.2160i | 0.917818 | + | 1.20483i | ||||
\(341\) | 4.69745 | + | 2.71207i | 0.254381 | + | 0.146867i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4434 | − | 1.68537i | 0.995851 | − | 0.0910013i | ||||
\(344\) | 6.00475 | + | 31.0388i | 0.323754 | + | 1.67350i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.7765 | − | 15.1612i | 1.22447 | − | 0.815069i | ||||
\(347\) | 14.5134 | + | 25.1380i | 0.779120 | + | 1.34948i | 0.932449 | + | 0.361301i | \(0.117667\pi\) |
−0.153329 | + | 0.988175i | \(0.548999\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.2889 | −1.46074 | −0.730371 | − | 0.683050i | \(-0.760653\pi\) | ||||
−0.730371 | + | 0.683050i | \(0.760653\pi\) | |||||||
\(350\) | −4.44575 | + | 0.419474i | −0.237635 | + | 0.0224218i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.30876 | − | 25.5197i | 0.282958 | − | 1.36021i | ||||
\(353\) | −26.2242 | + | 15.1406i | −1.39578 | + | 0.805851i | −0.993947 | − | 0.109864i | \(-0.964959\pi\) |
−0.401829 | + | 0.915715i | \(0.631625\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.7551 | − | 9.09622i | −0.836195 | − | 0.482777i | ||||
\(356\) | −2.16653 | − | 16.9137i | −0.114826 | − | 0.896424i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.0120 | − | 1.08513i | 0.899113 | − | 0.0573508i | ||||
\(359\) | 10.3890 | − | 17.9943i | 0.548312 | − | 0.949704i | −0.450079 | − | 0.892989i | \(-0.648604\pi\) |
0.998390 | − | 0.0567148i | \(-0.0180626\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.40061 | − | 7.62208i | −0.231611 | − | 0.401162i | ||||
\(362\) | −13.0559 | + | 26.3583i | −0.686201 | + | 1.38536i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.4052 | − | 21.4630i | −0.912278 | − | 1.12497i | ||||
\(365\) | 23.9854i | 1.25545i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.7384 | − | 10.2412i | 0.925934 | − | 0.534589i | 0.0404110 | − | 0.999183i | \(-0.487133\pi\) |
0.885523 | + | 0.464595i | \(0.153800\pi\) | |||||||
\(368\) | 2.01860 | + | 2.04706i | 0.105227 | + | 0.106710i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.607810 | + | 9.52889i | 0.0315985 | + | 0.495384i | ||||
\(371\) | −4.65362 | + | 2.87867i | −0.241604 | + | 0.149453i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.9800 | − | 20.7499i | 0.620299 | − | 1.07439i | −0.369130 | − | 0.929378i | \(-0.620344\pi\) |
0.989430 | − | 0.145012i | \(-0.0463222\pi\) | |||||||
\(374\) | −30.4375 | + | 20.2607i | −1.57389 | + | 1.04766i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.00209 | − | 14.4854i | 0.257963 | − | 0.747026i | ||||
\(377\) | − | 23.6909i | − | 1.22014i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.00154i | − | 0.154179i | −0.997024 | − | 0.0770894i | \(-0.975437\pi\) | ||
0.997024 | − | 0.0770894i | \(-0.0245627\pi\) | |||||||
\(380\) | 6.13426 | − | 14.6640i | 0.314681 | − | 0.752248i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.31931 | − | 12.4980i | −0.425653 | − | 0.639455i | ||||
\(383\) | −14.3407 | + | 24.8389i | −0.732777 | + | 1.26921i | 0.222915 | + | 0.974838i | \(0.428443\pi\) |
−0.955692 | + | 0.294369i | \(0.904890\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.921460 | − | 30.3260i | −0.0469620 | − | 1.54556i | ||||
\(386\) | 18.3372 | − | 1.16965i | 0.933337 | − | 0.0595338i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.9961 | + | 17.0602i | 0.659778 | + | 0.866099i | ||||
\(389\) | 10.4739 | − | 6.04712i | 0.531049 | − | 0.306601i | −0.210395 | − | 0.977617i | \(-0.567475\pi\) |
0.741443 | + | 0.671015i | \(0.234142\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.03281i | − | 0.203948i | ||||||
\(392\) | 19.1744 | − | 4.93384i | 0.968453 | − | 0.249197i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.04073 | + | 2.00147i | 0.203569 | + | 0.100832i | ||||
\(395\) | 10.9993 | + | 19.0513i | 0.553434 | + | 0.958576i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.62914 | + | 4.55381i | −0.131953 | + | 0.228549i | −0.924429 | − | 0.381353i | \(-0.875458\pi\) |
0.792476 | + | 0.609903i | \(0.208791\pi\) | |||||||
\(398\) | −1.26479 | − | 19.8286i | −0.0633981 | − | 0.993920i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.61968 | + | 1.20324i | −0.230984 | + | 0.0601621i | ||||
\(401\) | 16.0622 | + | 9.27350i | 0.802106 | + | 0.463096i | 0.844207 | − | 0.536017i | \(-0.180072\pi\) |
−0.0421007 | + | 0.999113i | \(0.513405\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.32373 | − | 3.07366i | 0.265194 | − | 0.153110i | ||||
\(404\) | −7.07897 | − | 2.96128i | −0.352192 | − | 0.147329i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.4324 | + | 7.06871i | 0.765896 | + | 0.350814i | ||||
\(407\) | −12.5009 | −0.619649 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.76122 | + | 15.1749i | 0.433214 | + | 0.750349i | 0.997148 | − | 0.0754709i | \(-0.0240460\pi\) |
−0.563934 | + | 0.825820i | \(0.690713\pi\) | |||||||
\(410\) | 7.48236 | + | 11.2407i | 0.369527 | + | 0.555138i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.23789 | − | 33.0845i | −0.208786 | − | 1.62996i | ||||
\(413\) | −5.72945 | − | 9.26215i | −0.281928 | − | 0.455761i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.6686 | + | 17.1292i | 1.45637 | + | 0.840837i | ||||
\(416\) | −22.0390 | − | 19.6715i | −1.08055 | − | 0.964476i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.6485 | + | 9.23704i | 0.912129 | + | 0.451799i | ||||
\(419\) | 26.9149 | 1.31488 | 0.657439 | − | 0.753508i | \(-0.271640\pi\) | ||||
0.657439 | + | 0.753508i | \(0.271640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.71296 | −0.229695 | −0.114848 | − | 0.993383i | \(-0.536638\pi\) | ||||
−0.114848 | + | 0.993383i | \(0.536638\pi\) | |||||||
\(422\) | −11.5697 | − | 5.73075i | −0.563205 | − | 0.278969i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.41833 | + | 3.83391i | −0.214573 | + | 0.186191i | ||||
\(425\) | 5.79932 | + | 3.34824i | 0.281308 | + | 0.162413i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.26552 | − | 2.35430i | 0.0612427 | − | 0.113932i | ||||
\(428\) | 11.3808 | − | 1.45780i | 0.550111 | − | 0.0704654i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.7981 | + | 32.7471i | 1.05120 | + | 1.57920i | ||||
\(431\) | 1.91047 | + | 3.30903i | 0.0920239 | + | 0.159390i | 0.908363 | − | 0.418183i | \(-0.137333\pi\) |
−0.816339 | + | 0.577573i | \(0.804000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.7992 | −1.67234 | −0.836172 | − | 0.548467i | \(-0.815212\pi\) | ||||
−0.836172 | + | 0.548467i | \(0.815212\pi\) | |||||||
\(434\) | 0.413743 | + | 4.38501i | 0.0198603 | + | 0.210487i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.18200 | − | 5.21610i | 0.104499 | − | 0.249806i | ||||
\(437\) | −1.98779 | + | 1.14765i | −0.0950891 | + | 0.0548997i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.7278 | − | 17.7407i | −1.46656 | − | 0.846717i | −0.467256 | − | 0.884122i | \(-0.654757\pi\) |
−0.999300 | + | 0.0374052i | \(0.988091\pi\) | |||||||
\(440\) | −6.16060 | − | 31.8444i | −0.293695 | − | 1.51812i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.63787 | + | 41.3550i | 0.125471 | + | 1.96706i | ||||
\(443\) | −5.47919 | + | 9.49024i | −0.260324 | + | 0.450895i | −0.966328 | − | 0.257313i | \(-0.917163\pi\) |
0.706004 | + | 0.708208i | \(0.250496\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.6091 | − | 18.3755i | −0.502920 | − | 0.871083i | ||||
\(446\) | 30.2098 | + | 14.9636i | 1.43047 | + | 0.708546i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19.3900 | − | 8.48690i | 0.916092 | − | 0.400968i | ||||
\(449\) | 27.1675i | 1.28211i | 0.767494 | + | 0.641056i | \(0.221503\pi\) | ||||
−0.767494 | + | 0.641056i | \(0.778497\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.3105 | + | 8.83951i | −0.720942 | + | 0.416236i | ||||
\(452\) | 8.90382 | − | 6.78276i | 0.418800 | − | 0.319034i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.1309 | − | 0.901354i | 0.663197 | − | 0.0423026i | ||||
\(455\) | −30.2867 | − | 16.2802i | −1.41986 | − | 0.763227i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.2807 | + | 33.3952i | −0.901914 | + | 1.56216i | −0.0769071 | + | 0.997038i | \(0.524505\pi\) |
−0.825007 | + | 0.565123i | \(0.808829\pi\) | |||||||
\(458\) | 4.18172 | + | 6.28216i | 0.195399 | + | 0.293546i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.30024 | + | 1.38056i | 0.153874 | + | 0.0643689i | ||||
\(461\) | 13.5543i | 0.631287i | 0.948878 | + | 0.315643i | \(0.102220\pi\) | ||||
−0.948878 | + | 0.315643i | \(0.897780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7564i | 0.825212i | 0.910910 | + | 0.412606i | \(0.135381\pi\) | ||||
−0.910910 | + | 0.412606i | \(0.864619\pi\) | |||||||
\(464\) | 17.4946 | + | 4.81918i | 0.812167 | + | 0.223725i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.3223 | + | 6.87106i | −0.478173 | + | 0.318296i | ||||
\(467\) | 5.39965 | − | 9.35248i | 0.249866 | − | 0.432781i | −0.713622 | − | 0.700531i | \(-0.752947\pi\) |
0.963488 | + | 0.267750i | \(0.0862800\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.4510 | + | 17.5994i | −1.31375 | + | 0.812666i | ||||
\(470\) | −1.21387 | − | 19.0304i | −0.0559916 | − | 0.877805i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.63068 | − | 8.79384i | −0.351231 | − | 0.404769i | ||||
\(473\) | −44.6035 | + | 25.7518i | −2.05087 | + | 1.18407i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.81135i | − | 0.174877i | ||||||
\(476\) | −27.7260 | − | 10.6209i | −1.27082 | − | 0.486808i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.24717 | + | 16.6501i | −0.377217 | + | 0.761557i | ||||
\(479\) | −9.48360 | − | 16.4261i | −0.433317 | − | 0.750527i | 0.563840 | − | 0.825884i | \(-0.309324\pi\) |
−0.997157 | + | 0.0753575i | \(0.975990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.08381 | + | 12.2695i | −0.322994 | + | 0.559442i | ||||
\(482\) | −31.1396 | + | 1.98627i | −1.41837 | + | 0.0904721i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.2991 | − | 2.60017i | 0.922685 | − | 0.118190i | ||||
\(485\) | 23.1112 | + | 13.3432i | 1.04942 | + | 0.605885i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.5847 | + | 7.26579i | −0.570268 | + | 0.329245i | −0.757257 | − | 0.653118i | \(-0.773461\pi\) |
0.186988 | + | 0.982362i | \(0.440127\pi\) | |||||||
\(488\) | 0.932682 | − | 2.70092i | 0.0422205 | − | 0.122265i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 19.6418 | − | 14.8714i | 0.887325 | − | 0.671822i | ||||
\(491\) | 26.0025 | 1.17348 | 0.586738 | − | 0.809777i | \(-0.300412\pi\) | ||||
0.586738 | + | 0.809777i | \(0.300412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7273 | − | 22.0444i | −0.573210 | − | 0.992829i | ||||
\(494\) | 19.6335 | − | 13.0690i | 0.883351 | − | 0.588002i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.18680 | + | 4.55657i | 0.0532891 | + | 0.204596i | ||||
\(497\) | 19.3318 | − | 0.587401i | 0.867152 | − | 0.0263485i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.37527 | + | 1.37136i | 0.106332 | + | 0.0613907i | 0.552223 | − | 0.833697i | \(-0.313780\pi\) |
−0.445891 | + | 0.895087i | \(0.647113\pi\) | |||||||
\(500\) | 15.0715 | − | 11.4812i | 0.674018 | − | 0.513454i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.6437 | − | 33.6017i | 0.742844 | − | 1.49972i | ||||
\(503\) | −21.5337 | −0.960139 | −0.480070 | − | 0.877230i | \(-0.659389\pi\) | ||||
−0.480070 | + | 0.877230i | \(0.659389\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.54826 | −0.424892 | ||||||||
\(506\) | −2.07886 | + | 4.19698i | −0.0924167 | + | 0.186579i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −24.2249 | + | 18.4541i | −1.07481 | + | 0.818767i | ||||
\(509\) | −11.3748 | − | 6.56726i | −0.504180 | − | 0.291089i | 0.226258 | − | 0.974067i | \(-0.427351\pi\) |
−0.730438 | + | 0.682979i | \(0.760684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.4145 | − | 21.6857i | −0.593423 | − | 0.959320i | ||||
\(512\) | 19.0097 | − | 12.2732i | 0.840117 | − | 0.542405i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.9417 | + | 13.2742i | −0.879589 | + | 0.585499i | ||||
\(515\) | −20.7522 | − | 35.9439i | −0.914452 | − | 1.58388i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.9659 | 1.09800 | ||||||||
\(518\) | −5.87883 | − | 8.27534i | −0.258301 | − | 0.363597i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −34.7458 | − | 11.9984i | −1.52371 | − | 0.526167i | ||||
\(521\) | −6.30391 | + | 3.63957i | −0.276179 | + | 0.159452i | −0.631693 | − | 0.775219i | \(-0.717639\pi\) |
0.355513 | + | 0.934671i | \(0.384306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.41646 | − | 1.39515i | −0.105665 | − | 0.0610055i | 0.446236 | − | 0.894915i | \(-0.352764\pi\) |
−0.551901 | + | 0.833910i | \(0.686097\pi\) | |||||||
\(524\) | 8.23931 | − | 1.05540i | 0.359936 | − | 0.0461053i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.7015 | + | 1.25668i | −0.859027 | + | 0.0547938i | ||||
\(527\) | 3.30250 | − | 5.72009i | 0.143859 | − | 0.249171i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2417 | + | 19.4712i | 0.488770 | + | 0.846575i | ||||
\(530\) | −3.23090 | + | 6.52281i | −0.140341 | + | 0.283333i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.65514 | + | 16.6888i | 0.115115 | + | 0.723551i | ||||
\(533\) | 20.0360i | 0.867858i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.3644 | − | 7.13859i | 0.534560 | − | 0.308628i | ||||
\(536\) | −27.0125 | + | 23.4395i | −1.16676 | + | 1.01243i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.39899 | − | 21.9325i | −0.0603146 | − | 0.945578i | ||||
\(539\) | 17.7938 | + | 26.9030i | 0.766432 | + | 1.15880i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.303559 | + | 0.525780i | −0.0130510 | + | 0.0226050i | −0.872477 | − | 0.488655i | \(-0.837488\pi\) |
0.859426 | + | 0.511260i | \(0.170821\pi\) | |||||||
\(542\) | 0.268086 | − | 0.178452i | 0.0115153 | − | 0.00766515i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −31.0754 | − | 6.46448i | −1.33235 | − | 0.277162i | ||||
\(545\) | − | 7.03558i | − | 0.301371i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 11.1295i | − | 0.475865i | −0.971282 | − | 0.237933i | \(-0.923530\pi\) | ||
0.971282 | − | 0.237933i | \(-0.0764697\pi\) | |||||||
\(548\) | 30.1331 | + | 12.6053i | 1.28722 | + | 0.538472i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.30943 | − | 6.47402i | −0.183755 | − | 0.276053i | ||||
\(551\) | −7.24387 | + | 12.5467i | −0.308599 | + | 0.534509i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.5997 | − | 11.0730i | −0.875986 | − | 0.470874i | ||||
\(554\) | −25.5493 | + | 1.62969i | −1.08549 | + | 0.0692387i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.3714 | + | 12.4714i | −0.694303 | + | 0.528907i | ||||
\(557\) | 25.6805 | − | 14.8266i | 1.08812 | − | 0.628225i | 0.155043 | − | 0.987908i | \(-0.450448\pi\) |
0.933075 | + | 0.359682i | \(0.117115\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 58.3703i | 2.46880i | ||||||||
\(560\) | 18.1831 | − | 19.0537i | 0.768376 | − | 0.805164i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.9853 | + | 10.3945i | 0.885213 | + | 0.438466i | ||||
\(563\) | −16.4174 | − | 28.4358i | −0.691910 | − | 1.19842i | −0.971211 | − | 0.238220i | \(-0.923436\pi\) |
0.279301 | − | 0.960204i | \(-0.409897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.96392 | − | 12.0619i | 0.292974 | − | 0.507447i | ||||
\(566\) | −0.287496 | − | 4.50721i | −0.0120844 | − | 0.189452i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.2998 | − | 3.92718i | 0.851759 | − | 0.164781i | ||||
\(569\) | 7.94054 | + | 4.58447i | 0.332885 | + | 0.192191i | 0.657121 | − | 0.753785i | \(-0.271774\pi\) |
−0.324236 | + | 0.945976i | \(0.605107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.1743 | − | 12.2250i | 0.886115 | − | 0.511599i | 0.0134453 | − | 0.999910i | \(-0.495720\pi\) |
0.872670 | + | 0.488311i | \(0.162387\pi\) | |||||||
\(572\) | 18.5727 | − | 44.3984i | 0.776565 | − | 1.85639i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.0516 | − | 5.97822i | −0.544764 | − | 0.249526i | ||||
\(575\) | 0.857772 | 0.0357716 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.00925 | + | 10.4083i | 0.250168 | + | 0.433304i | 0.963572 | − | 0.267449i | \(-0.0861807\pi\) |
−0.713404 | + | 0.700753i | \(0.752847\pi\) | |||||||
\(578\) | 11.3497 | + | 17.0506i | 0.472087 | + | 0.709211i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 22.3969 | − | 2.86889i | 0.929983 | − | 0.119124i | ||||
\(581\) | −36.4039 | + | 1.10614i | −1.51029 | + | 0.0458904i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.25333 | − | 4.76506i | −0.341818 | − | 0.197349i | ||||
\(584\) | −17.8659 | − | 20.5893i | −0.739297 | − | 0.851989i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.02677 | + | 1.99455i | 0.166344 | + | 0.0823942i | ||||
\(587\) | 18.8618 | 0.778510 | 0.389255 | − | 0.921130i | \(-0.372733\pi\) | ||||
0.389255 | + | 0.921130i | \(0.372733\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.75929 | −0.154899 | ||||||||
\(590\) | −12.9824 | − | 6.43049i | −0.534478 | − | 0.264739i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.61949 | − | 7.72693i | −0.313159 | − | 0.317575i | ||||
\(593\) | −7.65096 | − | 4.41729i | −0.314187 | − | 0.181396i | 0.334611 | − | 0.942356i | \(-0.391395\pi\) |
−0.648799 | + | 0.760960i | \(0.724728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.9280 | + | 1.12206i | −1.51390 | + | 0.0460001i | ||||
\(596\) | −1.43746 | − | 11.2220i | −0.0588808 | − | 0.459672i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.94127 | + | 4.41865i | 0.120278 | + | 0.180692i | ||||
\(599\) | −13.9015 | − | 24.0781i | −0.568000 | − | 0.983805i | −0.996764 | − | 0.0803885i | \(-0.974384\pi\) |
0.428763 | − | 0.903417i | \(-0.358949\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1977 | −0.497556 | −0.248778 | − | 0.968561i | \(-0.580029\pi\) | ||||
−0.248778 | + | 0.968561i | \(0.580029\pi\) | |||||||
\(602\) | −38.0228 | − | 17.4161i | −1.54969 | − | 0.709829i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22.4406 | + | 9.38736i | 0.913094 | + | 0.381966i | ||||
\(605\) | 22.0535 | − | 12.7326i | 0.896601 | − | 0.517653i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.10887 | − | 5.25901i | −0.369718 | − | 0.213457i | 0.303617 | − | 0.952794i | \(-0.401806\pi\) |
−0.673335 | + | 0.739337i | \(0.735139\pi\) | |||||||
\(608\) | 5.65703 | + | 17.1569i | 0.229423 | + | 0.695804i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.226336 | − | 3.54837i | −0.00916408 | − | 0.143669i | ||||
\(611\) | 14.1472 | − | 24.5037i | 0.572336 | − | 0.991315i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.7052 | − | 34.1304i | −0.795884 | − | 1.37851i | −0.922276 | − | 0.386532i | \(-0.873673\pi\) |
0.126392 | − | 0.991980i | \(-0.459660\pi\) | |||||||
\(614\) | −13.7574 | − | 6.81436i | −0.555203 | − | 0.275005i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 23.3798 | + | 25.3457i | 0.941998 | + | 1.02121i | ||||
\(617\) | − | 35.9618i | − | 1.44777i | −0.689922 | − | 0.723884i | \(-0.742355\pi\) | ||
0.689922 | − | 0.723884i | \(-0.257645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.1743 | − | 12.2250i | 0.851065 | − | 0.491363i | −0.00994487 | − | 0.999951i | \(-0.503166\pi\) |
0.861010 | + | 0.508588i | \(0.169832\pi\) | |||||||
\(620\) | 3.55047 | + | 4.66076i | 0.142590 | + | 0.187181i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.3668 | − | 1.68183i | 1.05721 | − | 0.0674354i | ||||
\(623\) | 19.8689 | + | 10.6803i | 0.796032 | + | 0.427895i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.7715 | − | 25.5849i | 0.590859 | − | 1.02340i | ||||
\(626\) | 12.4060 | + | 18.6374i | 0.495843 | + | 0.744901i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.43292 | + | 12.9875i | −0.216797 | + | 0.518256i | ||||
\(629\) | 15.2224i | 0.606958i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.08034i | 0.202245i | 0.994874 | + | 0.101123i | \(0.0322434\pi\) | ||||
−0.994874 | + | 0.101123i | \(0.967757\pi\) | |||||||
\(632\) | −23.6325 | − | 8.16079i | −0.940051 | − | 0.324619i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.22630 | − | 4.81019i | 0.286993 | − | 0.191037i | ||||
\(635\) | −18.9470 | + | 32.8171i | −0.751887 | + | 1.30231i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.4880 | − | 2.21944i | 1.44571 | − | 0.0879373i | ||||
\(638\) | 1.88185 | + | 29.5026i | 0.0745031 | + | 1.16802i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.9283 | − | 23.2175i | 0.629621 | − | 0.917752i | ||||
\(641\) | 23.1295 | − | 13.3538i | 0.913561 | − | 0.527445i | 0.0319859 | − | 0.999488i | \(-0.489817\pi\) |
0.881575 | + | 0.472044i | \(0.156483\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.3919i | 0.961924i | 0.876741 | + | 0.480962i | \(0.159713\pi\) | ||||
−0.876741 | + | 0.480962i | \(0.840287\pi\) | |||||||
\(644\) | −3.75593 | + | 0.597559i | −0.148004 | + | 0.0235471i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.2480 | − | 22.7083i | 0.442545 | − | 0.893447i | ||||
\(647\) | 2.41921 | + | 4.19019i | 0.0951088 | + | 0.164733i | 0.909654 | − | 0.415367i | \(-0.136347\pi\) |
−0.814545 | + | 0.580100i | \(0.803013\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.48395 | − | 16.4267i | 0.372278 | − | 0.644804i | ||||
\(650\) | −8.79615 | + | 0.561071i | −0.345014 | + | 0.0220070i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.454522 | + | 3.54837i | 0.0178004 | + | 0.138965i | ||||
\(653\) | −19.5592 | − | 11.2925i | −0.765412 | − | 0.441911i | 0.0658236 | − | 0.997831i | \(-0.479033\pi\) |
−0.831235 | + | 0.555921i | \(0.812366\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.95142 | − | 5.16811i | 0.349761 | − | 0.201935i | ||||
\(656\) | −14.7957 | − | 4.07572i | −0.577675 | − | 0.159130i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.7407 | + | 16.5269i | 0.457702 | + | 0.644284i | ||||
\(659\) | −13.4237 | −0.522911 | −0.261456 | − | 0.965215i | \(-0.584203\pi\) | ||||
−0.261456 | + | 0.965215i | \(0.584203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.10185 | + | 12.3008i | 0.276230 | + | 0.478444i | 0.970445 | − | 0.241324i | \(-0.0775815\pi\) |
−0.694215 | + | 0.719768i | \(0.744248\pi\) | |||||||
\(662\) | 0.457281 | − | 0.304389i | 0.0177727 | − | 0.0118304i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −38.2266 | + | 7.39531i | −1.48348 | + | 0.286994i | ||||
\(665\) | 11.0620 | + | 17.8827i | 0.428967 | + | 0.693462i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.82373 | − | 1.63028i | −0.109335 | − | 0.0631248i | ||||
\(668\) | 10.0226 | + | 13.1568i | 0.387786 | + | 0.509052i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −19.7529 | + | 39.8787i | −0.763120 | + | 1.54065i | ||||
\(671\) | 4.65510 | 0.179708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.3016 | 0.435643 | 0.217822 | − | 0.975989i | \(-0.430105\pi\) | ||||
0.217822 | + | 0.975989i | \(0.430105\pi\) | |||||||
\(674\) | −3.83144 | + | 7.73523i | −0.147582 | + | 0.297950i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.2965 | − | 22.7053i | −0.665249 | − | 0.873281i | ||||
\(677\) | 2.75180 | + | 1.58875i | 0.105760 | + | 0.0610608i | 0.551947 | − | 0.833879i | \(-0.313885\pi\) |
−0.446187 | + | 0.894940i | \(0.647218\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.3579 | + | 0.861658i | −1.08827 | + | 0.0330674i | ||||
\(680\) | −38.7770 | + | 7.50178i | −1.48703 | + | 0.287680i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.38557 | + | 4.25056i | −0.244516 | + | 0.162762i | ||||
\(683\) | −3.13262 | − | 5.42586i | −0.119866 | − | 0.207615i | 0.799848 | − | 0.600202i | \(-0.204913\pi\) |
−0.919715 | + | 0.392588i | \(0.871580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.6441 | 1.55293 | ||||||||
\(686\) | −9.44129 | + | 24.4308i | −0.360470 | + | 0.932771i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −43.1038 | − | 11.8737i | −1.64332 | − | 0.452679i | ||||
\(689\) | −9.35369 | + | 5.40036i | −0.356347 | + | 0.205737i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.9691 | + | 8.06506i | 0.531409 | + | 0.306809i | 0.741590 | − | 0.670853i | \(-0.234072\pi\) |
−0.210181 | + | 0.977663i | \(0.567405\pi\) | |||||||
\(692\) | 4.91632 | + | 38.3808i | 0.186890 | + | 1.45902i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −40.9669 | + | 2.61311i | −1.55508 | + | 0.0991923i | ||||
\(695\) | −12.8045 | + | 22.1781i | −0.485704 | + | 0.841264i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.7639 | + | 18.6436i | 0.407711 | + | 0.706176i | ||||
\(698\) | 17.1295 | − | 34.5825i | 0.648362 | − | 1.30897i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.25905 | − | 5.89728i | 0.0853841 | − | 0.222896i | ||||
\(701\) | − | 50.8903i | − | 1.92210i | −0.276373 | − | 0.961050i | \(-0.589133\pi\) | ||
0.276373 | − | 0.961050i | \(-0.410867\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.50322 | − | 4.33198i | 0.282989 | − | 0.163384i | ||||
\(704\) | 29.0081 | + | 22.7466i | 1.09328 | + | 0.857295i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.72603 | − | 42.7371i | −0.102595 | − | 1.60843i | ||||
\(707\) | 8.63278 | − | 5.34013i | 0.324669 | − | 0.200836i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.6871 | + | 18.5107i | −0.401364 | + | 0.695182i | −0.993891 | − | 0.110368i | \(-0.964797\pi\) |
0.592527 | + | 0.805550i | \(0.298130\pi\) | |||||||
\(710\) | 21.4170 | − | 14.2562i | 0.803767 | − | 0.535027i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22.7942 | + | 7.87131i | 0.854250 | + | 0.294990i | ||||
\(713\) | − | 0.846054i | − | 0.0316850i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 59.8854i | − | 2.23959i | ||||||
\(716\) | −9.30346 | + | 22.2400i | −0.347686 | + | 0.831149i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.2824 | + | 24.4609i | 0.607655 | + | 0.912874i | ||||
\(719\) | −12.1927 | + | 21.1183i | −0.454709 | + | 0.787579i | −0.998671 | − | 0.0515302i | \(-0.983590\pi\) |
0.543962 | + | 0.839110i | \(0.316923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.8651 | + | 20.8914i | 1.44741 | + | 0.778036i | ||||
\(722\) | 12.4216 | − | 0.792321i | 0.462283 | − | 0.0294871i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −25.2079 | − | 33.0907i | −0.936843 | − | 1.22981i | ||||
\(725\) | 4.68881 | − | 2.70708i | 0.174138 | − | 0.100539i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.0825i | 1.37531i | 0.726037 | + | 0.687656i | \(0.241360\pi\) | ||||
−0.726037 | + | 0.687656i | \(0.758640\pi\) | |||||||
\(728\) | 38.1249 | − | 8.58452i | 1.41300 | − | 0.318164i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −30.3961 | − | 15.0559i | −1.12501 | − | 0.557243i | ||||
\(731\) | 31.3580 | + | 54.3137i | 1.15982 | + | 2.00887i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.5631 | + | 39.0805i | −0.833388 | + | 1.44347i | 0.0619491 | + | 0.998079i | \(0.480268\pi\) |
−0.895337 | + | 0.445390i | \(0.853065\pi\) | |||||||
\(734\) | 1.84392 | + | 28.9079i | 0.0680602 | + | 1.06701i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.86128 | + | 1.27315i | −0.142329 | + | 0.0469291i | ||||
\(737\) | −50.4586 | − | 29.1323i | −1.85867 | − | 1.07310i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.2786 | − | 21.5228i | 1.37132 | − | 0.791729i | 0.380222 | − | 0.924895i | \(-0.375848\pi\) |
0.991094 | + | 0.133166i | \(0.0425143\pi\) | |||||||
\(740\) | −12.4572 | − | 5.21112i | −0.457937 | − | 0.191565i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.726939 | − | 7.70438i | −0.0266868 | − | 0.282837i | ||||
\(743\) | 7.52770 | 0.276165 | 0.138082 | − | 0.990421i | \(-0.455906\pi\) | ||||
0.138082 | + | 0.990421i | \(0.455906\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.03901 | − | 12.1919i | −0.257889 | − | 0.446677i | ||||
\(746\) | 18.7759 | + | 28.2068i | 0.687433 | + | 1.03272i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.56996 | − | 51.2905i | −0.240222 | − | 1.87537i | ||||
\(749\) | −7.18646 | + | 13.3693i | −0.262588 | + | 0.488503i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.1316 | + | 22.0153i | 1.39144 | + | 0.803349i | 0.993475 | − | 0.114051i | \(-0.0363828\pi\) |
0.397966 | + | 0.917400i | \(0.369716\pi\) | |||||||
\(752\) | 15.2171 | + | 15.4316i | 0.554909 | + | 0.562733i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 30.0228 | + | 14.8710i | 1.09337 | + | 0.541569i | ||||
\(755\) | 30.2683 | 1.10158 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.64185 | 0.277748 | 0.138874 | − | 0.990310i | \(-0.455652\pi\) | ||||
0.138874 | + | 0.990310i | \(0.455652\pi\) | |||||||
\(758\) | 3.80377 | + | 1.88410i | 0.138159 | + | 0.0684335i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 14.7328 | + | 16.9785i | 0.534414 | + | 0.615876i | ||||
\(761\) | 15.1210 | + | 8.73011i | 0.548135 | + | 0.316466i | 0.748370 | − | 0.663282i | \(-0.230837\pi\) |
−0.200234 | + | 0.979748i | \(0.564170\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.93484 | + | 6.36101i | 0.142451 | + | 0.230284i | ||||
\(764\) | 21.0605 | − | 2.69771i | 0.761943 | − | 0.0975996i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.4758 | − | 33.7652i | −0.812084 | − | 1.21999i | ||||
\(767\) | −10.7484 | − | 18.6168i | −0.388102 | − | 0.672212i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.13489 | 0.113047 | 0.0565235 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565235 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(770\) | 39.0097 | + | 17.8682i | 1.40581 | + | 0.643925i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.0281 | + | 23.9724i | −0.360921 | + | 0.862785i | ||||
\(773\) | 16.4737 | − | 9.51107i | 0.592516 | − | 0.342090i | −0.173575 | − | 0.984821i | \(-0.555532\pi\) |
0.766092 | + | 0.642731i | \(0.222199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.21665 | + | 0.702436i | 0.0437035 | + | 0.0252322i | ||||
\(776\) | −29.7777 | + | 5.76078i | −1.06896 | + | 0.206800i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.08877 | + | 17.0692i | 0.0390344 | + | 0.611959i | ||||
\(779\) | 6.12635 | − | 10.6112i | 0.219499 | − | 0.380184i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.8420 | + | 29.1713i | 0.602656 | + | 1.04383i | ||||
\(782\) | 5.11067 | + | 2.53143i | 0.182757 | + | 0.0905238i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.78343 | + | 27.3962i | −0.206551 | + | 0.978436i | ||||
\(785\) | 17.5177i | 0.625235i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.98235 | + | 2.29921i | −0.141956 | + | 0.0819581i | −0.569296 | − | 0.822133i | \(-0.692784\pi\) |
0.427340 | + | 0.904091i | \(0.359451\pi\) | |||||||
\(788\) | −5.07281 | + | 3.86437i | −0.180711 | + | 0.137662i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −31.0476 | + | 1.98040i | −1.10462 | + | 0.0704594i | ||||
\(791\) | 0.449705 | + | 14.8001i | 0.0159897 | + | 0.526233i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.63787 | − | 4.56893i | 0.0936735 | − | 0.162247i | ||||
\(794\) | −4.12058 | − | 6.19031i | −0.146234 | − | 0.219686i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.9222 | + | 10.8438i | 0.918789 | + | 0.384348i | ||||
\(797\) | 40.4802i | 1.43388i | 0.697134 | + | 0.716941i | \(0.254458\pi\) | ||||
−0.697134 | + | 0.716941i | \(0.745542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 30.4010i | − | 1.07551i | ||||||
\(800\) | 1.37498 | − | 6.60969i | 0.0486131 | − | 0.233688i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.8344 | + | 14.5341i | −0.771001 | + | 0.513217i | ||||
\(803\) | 22.2050 | − | 38.4602i | 0.783598 | − | 1.35723i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.02463 | + | 2.48958i | −0.141850 | + | 0.0877463i | ||||
\(806\) | 0.553406 | + | 8.67599i | 0.0194929 | + | 0.305599i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.19629 | − | 7.11217i | 0.288344 | − | 0.250205i | ||||
\(809\) | −8.54248 | + | 4.93200i | −0.300338 | + | 0.173400i | −0.642595 | − | 0.766206i | \(-0.722142\pi\) |
0.342257 | + | 0.939606i | \(0.388809\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28.0467i | − | 0.984854i | −0.870354 | − | 0.492427i | \(-0.836110\pi\) | ||
0.870354 | − | 0.492427i | \(-0.163890\pi\) | |||||||
\(812\) | −18.6450 | + | 15.1199i | −0.654313 | + | 0.530606i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.84697 | − | 15.8421i | 0.275036 | − | 0.555266i | ||||
\(815\) | 2.22571 | + | 3.85505i | 0.0779634 | + | 0.135037i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.8477 | − | 30.9131i | 0.624412 | − | 1.08151i | ||||
\(818\) | −24.7302 | + | 1.57744i | −0.864671 | + | 0.0551539i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.9418 | + | 2.42631i | −0.661475 | + | 0.0847303i | ||||
\(821\) | 22.9634 | + | 13.2579i | 0.801427 | + | 0.462704i | 0.843970 | − | 0.536391i | \(-0.180213\pi\) |
−0.0425431 | + | 0.999095i | \(0.513546\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.6534 | + | 10.1922i | −0.615359 | + | 0.355277i | −0.775060 | − | 0.631888i | \(-0.782280\pi\) |
0.159701 | + | 0.987165i | \(0.448947\pi\) | |||||||
\(824\) | 44.5872 | + | 15.3969i | 1.55327 | + | 0.536376i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.3341 | − | 1.44683i | 0.533542 | − | 0.0503418i | ||||
\(827\) | −17.5032 | −0.608645 | −0.304322 | − | 0.952569i | \(-0.598430\pi\) | ||||
−0.304322 | + | 0.952569i | \(0.598430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.39915 | − | 9.35160i | −0.187520 | − | 0.324794i | 0.756903 | − | 0.653528i | \(-0.226712\pi\) |
−0.944423 | + | 0.328733i | \(0.893378\pi\) | |||||||
\(830\) | −40.3306 | + | 26.8460i | −1.39989 | + | 0.931839i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 38.7633 | − | 15.5814i | 1.34388 | − | 0.540189i | ||||
\(833\) | 32.7598 | − | 21.6675i | 1.13506 | − | 0.750734i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.8233 | + | 10.2903i | 0.616801 | + | 0.356110i | ||||
\(836\) | −23.4117 | + | 17.8346i | −0.809711 | + | 0.616822i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.8947 | + | 34.1085i | −0.583619 | + | 1.17826i | ||||
\(839\) | −8.78448 | −0.303274 | −0.151637 | − | 0.988436i | \(-0.548454\pi\) | ||||
−0.151637 | + | 0.988436i | \(0.548454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.41964 | 0.290332 | ||||||||
\(842\) | 2.95837 | − | 5.97260i | 0.101952 | − | 0.205829i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.5248 | − | 11.0647i | 0.499966 | − | 0.380864i | ||||
\(845\) | −30.7585 | − | 17.7584i | −1.05813 | − | 0.610909i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.8180 | + | 23.8458i | −0.440430 | + | 0.819352i | ||||
\(848\) | −2.08519 | − | 8.00581i | −0.0716057 | − | 0.274921i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.88342 | + | 5.24760i | −0.270399 | + | 0.179991i | ||||
\(851\) | 0.974943 | + | 1.68865i | 0.0334206 | + | 0.0578862i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.87338 | 0.132622 | 0.0663110 | − | 0.997799i | \(-0.478877\pi\) | ||||
0.0663110 | + | 0.997799i | \(0.478877\pi\) | |||||||
\(854\) | 2.18916 | + | 3.08157i | 0.0749115 | + | 0.105449i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.29640 | + | 15.3376i | −0.181027 | + | 0.524230i | ||||
\(857\) | 37.4794 | − | 21.6387i | 1.28027 | − | 0.739165i | 0.303374 | − | 0.952872i | \(-0.401887\pi\) |
0.976898 | + | 0.213707i | \(0.0685536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.7614 | − | 7.94516i | −0.469534 | − | 0.271086i | 0.246511 | − | 0.969140i | \(-0.420716\pi\) |
−0.716045 | + | 0.698055i | \(0.754049\pi\) | |||||||
\(860\) | −55.1824 | + | 7.06848i | −1.88170 | + | 0.241033i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.39266 | + | 0.343976i | −0.183675 | + | 0.0117159i | ||||
\(863\) | −5.27921 | + | 9.14387i | −0.179707 | + | 0.311261i | −0.941780 | − | 0.336230i | \(-0.890848\pi\) |
0.762073 | + | 0.647491i | \(0.224181\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0744 | + | 41.6980i | 0.818553 | + | 1.41777i | ||||
\(866\) | 21.8438 | − | 44.1001i | 0.742283 | − | 1.49858i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.81672 | − | 2.22819i | −0.197432 | − | 0.0756296i | ||||
\(869\) | − | 40.7313i | − | 1.38171i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.1860 | + | 33.0163i | −1.93767 | + | 1.11872i | ||||
\(872\) | 5.24056 | + | 6.03939i | 0.177468 | + | 0.204519i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.206633 | − | 3.23947i | −0.00698945 | − | 0.109577i | ||||
\(875\) | 0.761215 | + | 25.0522i | 0.0257338 | + | 0.846920i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.877972 | − | 1.52069i | 0.0296470 | − | 0.0513501i | −0.850821 | − | 0.525455i | \(-0.823895\pi\) |
0.880468 | + | 0.474105i | \(0.157228\pi\) | |||||||
\(878\) | 41.7704 | − | 27.8045i | 1.40968 | − | 0.938355i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 44.2226 | + | 12.1819i | 1.49074 | + | 0.410650i | ||||
\(881\) | − | 39.9987i | − | 1.34759i | −0.738917 | − | 0.673796i | \(-0.764663\pi\) | ||
0.738917 | − | 0.673796i | \(-0.235337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.9005i | − | 0.535096i | −0.963545 | − | 0.267548i | \(-0.913787\pi\) | ||
0.963545 | − | 0.267548i | \(-0.0862133\pi\) | |||||||
\(884\) | −54.0639 | − | 22.6161i | −1.81837 | − | 0.760660i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.58738 | − | 12.9007i | −0.288499 | − | 0.433409i | ||||
\(887\) | −16.6867 | + | 28.9023i | −0.560286 | + | 0.970443i | 0.437186 | + | 0.899371i | \(0.355975\pi\) |
−0.997471 | + | 0.0710719i | \(0.977358\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.22353 | − | 40.2672i | −0.0410357 | − | 1.35052i | ||||
\(890\) | 29.9462 | − | 1.91015i | 1.00380 | − | 0.0640284i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −37.9259 | + | 28.8912i | −1.26985 | + | 0.967349i | ||||
\(893\) | −14.9848 | + | 8.65150i | −0.501449 | + | 0.289511i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.9978i | 1.00272i | ||||||||
\(896\) | −1.41608 | + | 29.8997i | −0.0473078 | + | 0.998880i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34.4286 | − | 17.0533i | −1.14890 | − | 0.569075i | ||||
\(899\) | −2.67010 | − | 4.62475i | −0.0890529 | − | 0.154244i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.80242 | + | 10.0501i | −0.193307 | + | 0.334817i | ||||
\(902\) | −1.59154 | − | 24.9512i | −0.0529923 | − | 0.830784i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.00659 | + | 15.5412i | 0.0999977 | + | 0.516892i | ||||
\(905\) | −44.8275 | − | 25.8812i | −1.49012 | − | 0.860319i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.8593 | − | 18.3940i | 1.05787 | − | 0.610762i | 0.133028 | − | 0.991112i | \(-0.457530\pi\) |
0.924842 | + | 0.380351i | \(0.124197\pi\) | |||||||
\(908\) | −7.72785 | + | 18.4735i | −0.256458 | + | 0.613065i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 39.6427 | − | 28.1623i | 1.31414 | − | 0.933573i | ||||
\(911\) | −46.9066 | −1.55409 | −0.777043 | − | 0.629448i | \(-0.783281\pi\) | ||||
−0.777043 | + | 0.629448i | \(0.783281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.7154 | − | 54.9326i | −1.04963 | − | 1.81800i | ||||
\(914\) | −30.2181 | − | 45.3964i | −0.999527 | − | 1.50158i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.5861 | + | 1.35601i | −0.349775 | + | 0.0448037i | ||||
\(917\) | −5.20276 | + | 9.67892i | −0.171810 | + | 0.319626i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.6017 | − | 9.00763i | −0.514652 | − | 0.297134i | 0.220092 | − | 0.975479i | \(-0.429364\pi\) |
−0.734744 | + | 0.678345i | \(0.762698\pi\) | |||||||
\(920\) | −3.82114 | + | 3.31572i | −0.125979 | + | 0.109316i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.1770 | − | 8.50816i | −0.565694 | − | 0.280201i | ||||
\(923\) | 38.1750 | 1.25654 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.23779 | −0.106458 | ||||||||
\(926\) | −22.5023 | − | 11.1459i | −0.739470 | − | 0.366277i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.0888 | + | 19.1454i | −0.560966 | + | 0.628478i | ||||
\(929\) | 28.2618 | + | 16.3170i | 0.927241 | + | 0.535343i | 0.885938 | − | 0.463804i | \(-0.153516\pi\) |
0.0413031 | + | 0.999147i | \(0.486849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.0028 | − | 9.98139i | −0.655565 | − | 0.327127i | ||||
\(932\) | −2.22808 | − | 17.3942i | −0.0729833 | − | 0.569768i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.46272 | + | 12.7135i | 0.276909 | + | 0.415998i | ||||
\(935\) | −32.1720 | − | 55.7235i | −1.05214 | − | 1.82235i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.08001 | 0.133288 | 0.0666441 | − | 0.997777i | \(-0.478771\pi\) | ||||
0.0666441 | + | 0.997777i | \(0.478771\pi\) | |||||||
\(938\) | −4.44431 | − | 47.1025i | −0.145112 | − | 1.53795i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24.8786 | + | 10.4072i | 0.811451 | + | 0.339447i | ||||
\(941\) | 21.3871 | − | 12.3478i | 0.697198 | − | 0.402527i | −0.109105 | − | 0.994030i | \(-0.534798\pi\) |
0.806303 | + | 0.591503i | \(0.201465\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.38811 | + | 1.37878i | 0.0777677 | + | 0.0448992i | ||||
\(944\) | 15.9341 | − | 4.15018i | 0.518609 | − | 0.135077i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.63657 | − | 72.6895i | −0.150748 | − | 2.36334i | ||||
\(947\) | 18.4653 | − | 31.9828i | 0.600040 | − | 1.03930i | −0.392774 | − | 0.919635i | \(-0.628485\pi\) |
0.992814 | − | 0.119665i | \(-0.0381822\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.1655 | − | 43.5879i | −0.816906 | − | 1.41492i | ||||
\(950\) | 4.83003 | + | 2.39242i | 0.156707 | + | 0.0776205i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 30.8635 | − | 28.4696i | 1.00029 | − | 0.922705i | ||||
\(953\) | 61.5883i | 1.99504i | 0.0703720 | + | 0.997521i | \(0.477581\pi\) | ||||
−0.0703720 | + | 0.997521i | \(0.522419\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.8807 | − | 13.2102i | 0.740404 | − | 0.427472i | ||||
\(956\) | −15.9234 | − | 20.9028i | −0.514998 | − | 0.676046i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.7693 | − | 1.70750i | 0.864876 | − | 0.0551669i | ||||
\(959\) | −36.7472 | + | 22.7314i | −1.18663 | + | 0.734034i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.8072 | + | 25.6468i | −0.477650 | + | 0.827315i | ||||
\(962\) | −11.1023 | − | 16.6788i | −0.357951 | − | 0.537747i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.0295 | − | 40.7092i | 0.548483 | − | 1.31115i | ||||
\(965\) | 32.3344i | 1.04088i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.8368i | 0.734381i | 0.930146 | + | 0.367191i | \(0.119680\pi\) | ||||
−0.930146 | + | 0.367191i | \(0.880320\pi\) | |||||||
\(968\) | −9.44679 | + | 27.3566i | −0.303631 | + | 0.879275i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −31.4166 | + | 20.9125i | −1.00873 | + | 0.671459i | ||||
\(971\) | 24.0937 | − | 41.7315i | 0.773203 | − | 1.33923i | −0.162596 | − | 0.986693i | \(-0.551987\pi\) |
0.935799 | − | 0.352534i | \(-0.114680\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.826871 | − | 27.2130i | −0.0265083 | − | 0.872409i | ||||
\(974\) | −1.30819 | − | 20.5091i | −0.0419172 | − | 0.657154i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.83735 | + | 2.87736i | 0.0908213 | + | 0.0921019i | ||||
\(977\) | −27.2570 | + | 15.7368i | −0.872028 | + | 0.503466i | −0.868022 | − | 0.496526i | \(-0.834609\pi\) |
−0.00400663 | + | 0.999992i | \(0.501275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 39.2865i | 1.25560i | ||||||||
\(980\) | 6.51681 | + | 34.2264i | 0.208172 | + | 1.09332i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.3220 | + | 32.9523i | −0.520857 | + | 1.05155i | ||||
\(983\) | −20.0440 | − | 34.7172i | −0.639304 | − | 1.10731i | −0.985586 | − | 0.169176i | \(-0.945889\pi\) |
0.346282 | − | 0.938130i | \(-0.387444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.96758 | + | 6.87205i | −0.126418 | + | 0.218962i | ||||
\(986\) | 35.9253 | − | 2.29153i | 1.14410 | − | 0.0729772i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.23789 | + | 33.0845i | 0.134825 | + | 1.05256i | ||||
\(989\) | 6.95721 | + | 4.01675i | 0.221226 | + | 0.127725i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.6593 | − | 25.7841i | 1.41865 | − | 0.819058i | 0.422469 | − | 0.906377i | \(-0.361163\pi\) |
0.996180 | + | 0.0873196i | \(0.0278301\pi\) | |||||||
\(992\) | −6.51939 | − | 1.35620i | −0.206991 | − | 0.0430594i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.3904 | + | 24.8674i | −0.361281 | + | 0.788747i | ||||
\(995\) | 34.9644 | 1.10845 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.7581 | + | 18.6335i | 0.340712 | + | 0.590130i | 0.984565 | − | 0.175019i | \(-0.0559986\pi\) |
−0.643853 | + | 0.765149i | \(0.722665\pi\) | |||||||
\(998\) | −3.22887 | + | 2.14930i | −0.102208 | + | 0.0680349i | ||||
\(999\) | 0 | 0 |
(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 | 252.2.be.a.107.7 | yes | 32 | |
3.2 | odd | 2 | inner | 252.2.be.a.107.10 | yes | 32 | |
4.3 | odd | 2 | inner | 252.2.be.a.107.12 | yes | 32 | |
7.2 | even | 3 | 1764.2.e.i.1079.15 | 16 | |||
7.4 | even | 3 | inner | 252.2.be.a.179.5 | yes | 32 | |
7.5 | odd | 6 | 1764.2.e.h.1079.15 | 16 | |||
12.11 | even | 2 | inner | 252.2.be.a.107.5 | ✓ | 32 | |
21.2 | odd | 6 | 1764.2.e.i.1079.2 | 16 | |||
21.5 | even | 6 | 1764.2.e.h.1079.2 | 16 | |||
21.11 | odd | 6 | inner | 252.2.be.a.179.12 | yes | 32 | |
28.11 | odd | 6 | inner | 252.2.be.a.179.10 | yes | 32 | |
28.19 | even | 6 | 1764.2.e.h.1079.1 | 16 | |||
28.23 | odd | 6 | 1764.2.e.i.1079.1 | 16 | |||
84.11 | even | 6 | inner | 252.2.be.a.179.7 | yes | 32 | |
84.23 | even | 6 | 1764.2.e.i.1079.16 | 16 | |||
84.47 | odd | 6 | 1764.2.e.h.1079.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.be.a.107.5 | ✓ | 32 | 12.11 | even | 2 | inner | |
252.2.be.a.107.7 | yes | 32 | 1.1 | even | 1 | trivial | |
252.2.be.a.107.10 | yes | 32 | 3.2 | odd | 2 | inner | |
252.2.be.a.107.12 | yes | 32 | 4.3 | odd | 2 | inner | |
252.2.be.a.179.5 | yes | 32 | 7.4 | even | 3 | inner | |
252.2.be.a.179.7 | yes | 32 | 84.11 | even | 6 | inner | |
252.2.be.a.179.10 | yes | 32 | 28.11 | odd | 6 | inner | |
252.2.be.a.179.12 | yes | 32 | 21.11 | odd | 6 | inner | |
1764.2.e.h.1079.1 | 16 | 28.19 | even | 6 | |||
1764.2.e.h.1079.2 | 16 | 21.5 | even | 6 | |||
1764.2.e.h.1079.15 | 16 | 7.5 | odd | 6 | |||
1764.2.e.h.1079.16 | 16 | 84.47 | odd | 6 | |||
1764.2.e.i.1079.1 | 16 | 28.23 | odd | 6 | |||
1764.2.e.i.1079.2 | 16 | 21.2 | odd | 6 | |||
1764.2.e.i.1079.15 | 16 | 7.2 | even | 3 | |||
1764.2.e.i.1079.16 | 16 | 84.23 | even | 6 |