Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(829,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 690) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 829.4 | ||
Root | \(1.45161 + 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.829 |
Dual form | 2070.2.d.e.829.1 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.21432 | − | 0.311108i | −0.990274 | − | 0.139132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.622216i | − | 0.235175i | −0.993063 | − | 0.117588i | \(-0.962484\pi\) | ||
0.993063 | − | 0.117588i | \(-0.0375161\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.311108 | − | 2.21432i | 0.0983809 | − | 0.700229i | ||||
\(11\) | −4.42864 | −1.33529 | −0.667643 | − | 0.744482i | \(-0.732697\pi\) | ||||
−0.667643 | + | 0.744482i | \(0.732697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.37778i | 0.382129i | 0.981578 | + | 0.191064i | \(0.0611939\pi\) | ||||
−0.981578 | + | 0.191064i | \(0.938806\pi\) | |||||||
\(14\) | 0.622216 | 0.166294 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.42864i | 1.55917i | 0.626294 | + | 0.779587i | \(0.284571\pi\) | ||||
−0.626294 | + | 0.779587i | \(0.715429\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.37778 | 0.316085 | 0.158043 | − | 0.987432i | \(-0.449482\pi\) | ||||
0.158043 | + | 0.987432i | \(0.449482\pi\) | |||||||
\(20\) | 2.21432 | + | 0.311108i | 0.495137 | + | 0.0695658i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.42864i | − | 0.944189i | ||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.80642 | + | 1.37778i | 0.961285 | + | 0.275557i | ||||
\(26\) | −1.37778 | −0.270206 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.622216i | 0.117588i | ||||||||
\(29\) | −4.23506 | −0.786432 | −0.393216 | − | 0.919446i | \(-0.628637\pi\) | ||||
−0.393216 | + | 0.919446i | \(0.628637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.42864 | −1.10250 | ||||||||
\(35\) | −0.193576 | + | 1.37778i | −0.0327203 | + | 0.232888i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.8064i | − | 1.94096i | −0.241173 | − | 0.970482i | \(-0.577532\pi\) | ||
0.241173 | − | 0.970482i | \(-0.422468\pi\) | |||||||
\(38\) | 1.37778i | 0.223506i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.311108 | + | 2.21432i | −0.0491905 | + | 0.350115i | ||||
\(41\) | 10.8573 | 1.69562 | 0.847811 | − | 0.530298i | \(-0.177920\pi\) | ||||
0.847811 | + | 0.530298i | \(0.177920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.05086i | − | 0.160254i | −0.996785 | − | 0.0801270i | \(-0.974467\pi\) | ||
0.996785 | − | 0.0801270i | \(-0.0255326\pi\) | |||||||
\(44\) | 4.42864 | 0.667643 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | − | 11.6128i | − | 1.69391i | −0.531666 | − | 0.846954i | \(-0.678434\pi\) | ||
0.531666 | − | 0.846954i | \(-0.321566\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.61285 | 0.944693 | ||||||||
\(50\) | −1.37778 | + | 4.80642i | −0.194848 | + | 0.679731i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1.37778i | − | 0.191064i | ||||||
\(53\) | − | 3.37778i | − | 0.463974i | −0.972719 | − | 0.231987i | \(-0.925477\pi\) | ||
0.972719 | − | 0.231987i | \(-0.0745227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.80642 | + | 1.37778i | 1.32230 | + | 0.185780i | ||||
\(56\) | −0.622216 | −0.0831471 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 4.23506i | − | 0.556091i | ||||||
\(59\) | 9.61285 | 1.25149 | 0.625743 | − | 0.780029i | \(-0.284796\pi\) | ||||
0.625743 | + | 0.780029i | \(0.284796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.66370 | 1.10927 | 0.554637 | − | 0.832093i | \(-0.312857\pi\) | ||||
0.554637 | + | 0.832093i | \(0.312857\pi\) | |||||||
\(62\) | − | 4.00000i | − | 0.508001i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.428639 | − | 3.05086i | 0.0531662 | − | 0.378412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 11.8064i | − | 1.44238i | −0.692735 | − | 0.721192i | \(-0.743594\pi\) | ||
0.692735 | − | 0.721192i | \(-0.256406\pi\) | |||||||
\(68\) | − | 6.42864i | − | 0.779587i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.37778 | − | 0.193576i | −0.164677 | − | 0.0231368i | ||||
\(71\) | 6.99063 | 0.829635 | 0.414818 | − | 0.909905i | \(-0.363845\pi\) | ||||
0.414818 | + | 0.909905i | \(0.363845\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.75557i | 0.322515i | 0.986912 | + | 0.161257i | \(0.0515550\pi\) | ||||
−0.986912 | + | 0.161257i | \(0.948445\pi\) | |||||||
\(74\) | 11.8064 | 1.37247 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.37778 | −0.158043 | ||||||||
\(77\) | 2.75557i | 0.314026i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0415 | −1.35477 | −0.677387 | − | 0.735627i | \(-0.736888\pi\) | ||||
−0.677387 | + | 0.735627i | \(0.736888\pi\) | |||||||
\(80\) | −2.21432 | − | 0.311108i | −0.247568 | − | 0.0347829i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.8573i | 1.19899i | ||||||||
\(83\) | − | 2.19358i | − | 0.240776i | −0.992727 | − | 0.120388i | \(-0.961586\pi\) | ||
0.992727 | − | 0.120388i | \(-0.0384139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | − | 14.2351i | 0.216930 | − | 1.54401i | ||||
\(86\) | 1.05086 | 0.113317 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.42864i | 0.472095i | ||||||||
\(89\) | 2.75557 | 0.292090 | 0.146045 | − | 0.989278i | \(-0.453346\pi\) | ||||
0.146045 | + | 0.989278i | \(0.453346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.857279 | 0.0898673 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.6128 | 1.19777 | ||||||||
\(95\) | −3.05086 | − | 0.428639i | −0.313011 | − | 0.0439775i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.13335i | 0.216609i | 0.994118 | + | 0.108305i | \(0.0345422\pi\) | ||||
−0.994118 | + | 0.108305i | \(0.965458\pi\) | |||||||
\(98\) | 6.61285i | 0.667998i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.80642 | − | 1.37778i | −0.480642 | − | 0.137778i | ||||
\(101\) | −16.2351 | −1.61545 | −0.807725 | − | 0.589560i | \(-0.799301\pi\) | ||||
−0.807725 | + | 0.589560i | \(0.799301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2351i | 1.20556i | 0.797909 | + | 0.602778i | \(0.205940\pi\) | ||||
−0.797909 | + | 0.602778i | \(0.794060\pi\) | |||||||
\(104\) | 1.37778 | 0.135103 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.37778 | 0.328079 | ||||||||
\(107\) | − | 10.6637i | − | 1.03090i | −0.856920 | − | 0.515450i | \(-0.827625\pi\) | ||
0.856920 | − | 0.515450i | \(-0.172375\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.1526 | 1.45135 | 0.725676 | − | 0.688036i | \(-0.241527\pi\) | ||||
0.725676 | + | 0.688036i | \(0.241527\pi\) | |||||||
\(110\) | −1.37778 | + | 9.80642i | −0.131367 | + | 0.935006i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 0.622216i | − | 0.0587939i | ||||||
\(113\) | − | 14.4286i | − | 1.35733i | −0.734447 | − | 0.678666i | \(-0.762558\pi\) | ||
0.734447 | − | 0.678666i | \(-0.237442\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.311108 | + | 2.21432i | −0.0290110 | + | 0.206486i | ||||
\(116\) | 4.23506 | 0.393216 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.61285i | 0.884934i | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.61285 | 0.782986 | ||||||||
\(122\) | 8.66370i | 0.784375i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.00000 | 0.359211 | ||||||||
\(125\) | −10.2143 | − | 4.54617i | −0.913597 | − | 0.406622i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.99063i | 0.442847i | 0.975178 | + | 0.221423i | \(0.0710703\pi\) | ||||
−0.975178 | + | 0.221423i | \(0.928930\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.05086 | + | 0.428639i | 0.267578 | + | 0.0375942i | ||||
\(131\) | −0.755569 | −0.0660143 | −0.0330072 | − | 0.999455i | \(-0.510508\pi\) | ||||
−0.0330072 | + | 0.999455i | \(0.510508\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.857279i | − | 0.0743355i | ||||||
\(134\) | 11.8064 | 1.01992 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.42864 | 0.551251 | ||||||||
\(137\) | 12.9175i | 1.10362i | 0.833971 | + | 0.551808i | \(0.186062\pi\) | ||||
−0.833971 | + | 0.551808i | \(0.813938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1017 | 1.19609 | 0.598046 | − | 0.801462i | \(-0.295944\pi\) | ||||
0.598046 | + | 0.801462i | \(0.295944\pi\) | |||||||
\(140\) | 0.193576 | − | 1.37778i | 0.0163602 | − | 0.116444i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.99063i | 0.586641i | ||||||||
\(143\) | − | 6.10171i | − | 0.510251i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.37778 | + | 1.31756i | 0.778783 | + | 0.109418i | ||||
\(146\) | −2.75557 | −0.228052 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.8064i | 0.970482i | ||||||||
\(149\) | 12.4286 | 1.01819 | 0.509097 | − | 0.860709i | \(-0.329979\pi\) | ||||
0.509097 | + | 0.860709i | \(0.329979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.85728 | −0.395280 | −0.197640 | − | 0.980275i | \(-0.563328\pi\) | ||||
−0.197640 | + | 0.980275i | \(0.563328\pi\) | |||||||
\(152\) | − | 1.37778i | − | 0.111753i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.75557 | −0.222050 | ||||||||
\(155\) | 8.85728 | + | 1.24443i | 0.711434 | + | 0.0999551i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.90813i | 0.790755i | 0.918519 | + | 0.395378i | \(0.129386\pi\) | ||||
−0.918519 | + | 0.395378i | \(0.870614\pi\) | |||||||
\(158\) | − | 12.0415i | − | 0.957969i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.311108 | − | 2.21432i | 0.0245952 | − | 0.175057i | ||||
\(161\) | −0.622216 | −0.0490375 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1017i | 0.791227i | 0.918417 | + | 0.395614i | \(0.129468\pi\) | ||||
−0.918417 | + | 0.395614i | \(0.870532\pi\) | |||||||
\(164\) | −10.8573 | −0.847811 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.19358 | 0.170255 | ||||||||
\(167\) | 1.89829i | 0.146894i | 0.997299 | + | 0.0734470i | \(0.0234000\pi\) | ||||
−0.997299 | + | 0.0734470i | \(0.976600\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1017 | 0.853978 | ||||||||
\(170\) | 14.2351 | + | 2.00000i | 1.09178 | + | 0.153393i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.05086i | 0.0801270i | ||||||||
\(173\) | − | 21.2257i | − | 1.61376i | −0.590716 | − | 0.806880i | \(-0.701154\pi\) | ||
0.590716 | − | 0.806880i | \(-0.298846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.857279 | − | 2.99063i | 0.0648042 | − | 0.226071i | ||||
\(176\) | −4.42864 | −0.333821 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.75557i | 0.206539i | ||||||||
\(179\) | 0.488863 | 0.0365393 | 0.0182697 | − | 0.999833i | \(-0.494184\pi\) | ||||
0.0182697 | + | 0.999833i | \(0.494184\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.9304 | −1.55575 | −0.777873 | − | 0.628422i | \(-0.783701\pi\) | ||||
−0.777873 | + | 0.628422i | \(0.783701\pi\) | |||||||
\(182\) | 0.857279i | 0.0635457i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −3.67307 | + | 26.1432i | −0.270050 | + | 1.92209i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 28.4701i | − | 2.08194i | ||||||
\(188\) | 11.6128i | 0.846954i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.428639 | − | 3.05086i | 0.0310968 | − | 0.221332i | ||||
\(191\) | −18.9590 | −1.37182 | −0.685912 | − | 0.727684i | \(-0.740597\pi\) | ||||
−0.685912 | + | 0.727684i | \(0.740597\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.24443i | − | 0.0895761i | −0.998997 | − | 0.0447881i | \(-0.985739\pi\) | ||
0.998997 | − | 0.0447881i | \(-0.0142613\pi\) | |||||||
\(194\) | −2.13335 | −0.153166 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.61285 | −0.472346 | ||||||||
\(197\) | − | 15.2444i | − | 1.08612i | −0.839694 | − | 0.543060i | \(-0.817265\pi\) | ||
0.839694 | − | 0.543060i | \(-0.182735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.5303 | 1.03003 | 0.515015 | − | 0.857181i | \(-0.327786\pi\) | ||||
0.515015 | + | 0.857181i | \(0.327786\pi\) | |||||||
\(200\) | 1.37778 | − | 4.80642i | 0.0974241 | − | 0.339865i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 16.2351i | − | 1.14230i | ||||||
\(203\) | 2.63512i | 0.184949i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.0415 | − | 3.37778i | −1.67913 | − | 0.235915i | ||||
\(206\) | −12.2351 | −0.852457 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.37778i | 0.0955322i | ||||||||
\(209\) | −6.10171 | −0.422064 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.266706 | 0.0183608 | 0.00918041 | − | 0.999958i | \(-0.497078\pi\) | ||||
0.00918041 | + | 0.999958i | \(0.497078\pi\) | |||||||
\(212\) | 3.37778i | 0.231987i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.6637 | 0.728956 | ||||||||
\(215\) | −0.326929 | + | 2.32693i | −0.0222964 | + | 0.158695i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.48886i | 0.168955i | ||||||||
\(218\) | 15.1526i | 1.02626i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.80642 | − | 1.37778i | −0.661149 | − | 0.0928902i | ||||
\(221\) | −8.85728 | −0.595805 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.990632i | − | 0.0663376i | −0.999450 | − | 0.0331688i | \(-0.989440\pi\) | ||
0.999450 | − | 0.0331688i | \(-0.0105599\pi\) | |||||||
\(224\) | 0.622216 | 0.0415735 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.4286 | 0.959779 | ||||||||
\(227\) | − | 17.1526i | − | 1.13846i | −0.822180 | − | 0.569228i | \(-0.807242\pi\) | ||
0.822180 | − | 0.569228i | \(-0.192758\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.15257 | −0.472655 | −0.236327 | − | 0.971673i | \(-0.575944\pi\) | ||||
−0.236327 | + | 0.971673i | \(0.575944\pi\) | |||||||
\(230\) | −2.21432 | − | 0.311108i | −0.146008 | − | 0.0205138i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.23506i | 0.278046i | ||||||||
\(233\) | 3.71456i | 0.243349i | 0.992570 | + | 0.121674i | \(0.0388264\pi\) | ||||
−0.992570 | + | 0.121674i | \(0.961174\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.61285 | + | 25.7146i | −0.235676 | + | 1.67743i | ||||
\(236\) | −9.61285 | −0.625743 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.00000i | 0.259281i | ||||||||
\(239\) | 27.8479 | 1.80133 | 0.900666 | − | 0.434512i | \(-0.143079\pi\) | ||||
0.900666 | + | 0.434512i | \(0.143079\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.12399 | −0.458896 | −0.229448 | − | 0.973321i | \(-0.573692\pi\) | ||||
−0.229448 | + | 0.973321i | \(0.573692\pi\) | |||||||
\(242\) | 8.61285i | 0.553655i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.66370 | −0.554637 | ||||||||
\(245\) | −14.6430 | − | 2.05731i | −0.935504 | − | 0.131437i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.89829i | 0.120785i | ||||||||
\(248\) | 4.00000i | 0.254000i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.54617 | − | 10.2143i | 0.287525 | − | 0.646010i | ||||
\(251\) | 22.4099 | 1.41450 | 0.707250 | − | 0.706963i | \(-0.249935\pi\) | ||||
0.707250 | + | 0.706963i | \(0.249935\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.42864i | 0.278426i | ||||||||
\(254\) | −4.99063 | −0.313140 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.7146i | 0.730734i | 0.930864 | + | 0.365367i | \(0.119057\pi\) | ||||
−0.930864 | + | 0.365367i | \(0.880943\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.34614 | −0.456467 | ||||||||
\(260\) | −0.428639 | + | 3.05086i | −0.0265831 | + | 0.189206i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 0.755569i | − | 0.0466792i | ||||||
\(263\) | − | 8.47013i | − | 0.522290i | −0.965300 | − | 0.261145i | \(-0.915900\pi\) | ||
0.965300 | − | 0.261145i | \(-0.0841001\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.05086 | + | 7.47949i | −0.0645535 | + | 0.459462i | ||||
\(266\) | 0.857279 | 0.0525631 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.8064i | 0.721192i | ||||||||
\(269\) | 28.8256 | 1.75753 | 0.878765 | − | 0.477255i | \(-0.158368\pi\) | ||||
0.878765 | + | 0.477255i | \(0.158368\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8350 | −0.840417 | −0.420208 | − | 0.907428i | \(-0.638043\pi\) | ||||
−0.420208 | + | 0.907428i | \(0.638043\pi\) | |||||||
\(272\) | 6.42864i | 0.389794i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.9175 | −0.780375 | ||||||||
\(275\) | −21.2859 | − | 6.10171i | −1.28359 | − | 0.367947i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.88892i | 0.173578i | 0.996227 | + | 0.0867892i | \(0.0276607\pi\) | ||||
−0.996227 | + | 0.0867892i | \(0.972339\pi\) | |||||||
\(278\) | 14.1017i | 0.845764i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.37778 | + | 0.193576i | 0.0823384 | + | 0.0115684i | ||||
\(281\) | −5.51114 | −0.328767 | −0.164383 | − | 0.986397i | \(-0.552563\pi\) | ||||
−0.164383 | + | 0.986397i | \(0.552563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8.19358i | − | 0.487058i | −0.969894 | − | 0.243529i | \(-0.921695\pi\) | ||
0.969894 | − | 0.243529i | \(-0.0783050\pi\) | |||||||
\(284\) | −6.99063 | −0.414818 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.10171 | 0.360802 | ||||||||
\(287\) | − | 6.75557i | − | 0.398769i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −24.3274 | −1.43102 | ||||||||
\(290\) | −1.31756 | + | 9.37778i | −0.0773699 | + | 0.550682i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 2.75557i | − | 0.161257i | ||||||
\(293\) | 12.6222i | 0.737398i | 0.929549 | + | 0.368699i | \(0.120197\pi\) | ||||
−0.929549 | + | 0.368699i | \(0.879803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.2859 | − | 2.99063i | −1.23931 | − | 0.174121i | ||||
\(296\) | −11.8064 | −0.686234 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.4286i | 0.719972i | ||||||||
\(299\) | 1.37778 | 0.0796793 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.653858 | −0.0376878 | ||||||||
\(302\) | − | 4.85728i | − | 0.279505i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.37778 | 0.0790214 | ||||||||
\(305\) | −19.1842 | − | 2.69535i | −1.09848 | − | 0.154335i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.653858i | − | 0.0373177i | −0.999826 | − | 0.0186588i | \(-0.994060\pi\) | ||
0.999826 | − | 0.0186588i | \(-0.00593964\pi\) | |||||||
\(308\) | − | 2.75557i | − | 0.157013i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.24443 | + | 8.85728i | −0.0706789 | + | 0.503060i | ||||
\(311\) | 13.0923 | 0.742399 | 0.371199 | − | 0.928553i | \(-0.378947\pi\) | ||||
0.371199 | + | 0.928553i | \(0.378947\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 11.2573i | − | 0.636302i | −0.948040 | − | 0.318151i | \(-0.896938\pi\) | ||
0.948040 | − | 0.318151i | \(-0.103062\pi\) | |||||||
\(314\) | −9.90813 | −0.559148 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.0415 | 0.677387 | ||||||||
\(317\) | 22.4701i | 1.26205i | 0.775763 | + | 0.631024i | \(0.217365\pi\) | ||||
−0.775763 | + | 0.631024i | \(0.782635\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.7556 | 1.05011 | ||||||||
\(320\) | 2.21432 | + | 0.311108i | 0.123784 | + | 0.0173915i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 0.622216i | − | 0.0346747i | ||||||
\(323\) | 8.85728i | 0.492832i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.89829 | + | 6.62222i | −0.105298 | + | 0.367334i | ||||
\(326\) | −10.1017 | −0.559482 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 10.8573i | − | 0.599493i | ||||||
\(329\) | −7.22570 | −0.398365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.4479 | −1.61860 | −0.809300 | − | 0.587395i | \(-0.800153\pi\) | ||||
−0.809300 | + | 0.587395i | \(0.800153\pi\) | |||||||
\(332\) | 2.19358i | 0.120388i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.89829 | −0.103870 | ||||||||
\(335\) | −3.67307 | + | 26.1432i | −0.200681 | + | 1.42836i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 24.6222i | − | 1.34126i | −0.741793 | − | 0.670629i | \(-0.766024\pi\) | ||
0.741793 | − | 0.670629i | \(-0.233976\pi\) | |||||||
\(338\) | 11.1017i | 0.603853i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.00000 | + | 14.2351i | −0.108465 | + | 0.772005i | ||||
\(341\) | 17.7146 | 0.959297 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.47013i | − | 0.457344i | ||||||
\(344\) | −1.05086 | −0.0566583 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.2257 | 1.14110 | ||||||||
\(347\) | − | 26.1017i | − | 1.40121i | −0.713548 | − | 0.700607i | \(-0.752913\pi\) | ||
0.713548 | − | 0.700607i | \(-0.247087\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.2257 | 1.13619 | 0.568093 | − | 0.822965i | \(-0.307681\pi\) | ||||
0.568093 | + | 0.822965i | \(0.307681\pi\) | |||||||
\(350\) | 2.99063 | + | 0.857279i | 0.159856 | + | 0.0458235i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.42864i | − | 0.236047i | ||||||
\(353\) | − | 4.28544i | − | 0.228091i | −0.993476 | − | 0.114046i | \(-0.963619\pi\) | ||
0.993476 | − | 0.114046i | \(-0.0363810\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.4795 | − | 2.17484i | −0.821566 | − | 0.115429i | ||||
\(356\) | −2.75557 | −0.146045 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.488863i | 0.0258372i | ||||||||
\(359\) | −4.65386 | −0.245621 | −0.122811 | − | 0.992430i | \(-0.539191\pi\) | ||||
−0.122811 | + | 0.992430i | \(0.539191\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1017 | −0.900090 | ||||||||
\(362\) | − | 20.9304i | − | 1.10008i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.857279 | −0.0449336 | ||||||||
\(365\) | 0.857279 | − | 6.10171i | 0.0448720 | − | 0.319378i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.88892i | 0.255200i | 0.991826 | + | 0.127600i | \(0.0407273\pi\) | ||||
−0.991826 | + | 0.127600i | \(0.959273\pi\) | |||||||
\(368\) | − | 1.00000i | − | 0.0521286i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −26.1432 | − | 3.67307i | −1.35912 | − | 0.190954i | ||||
\(371\) | −2.10171 | −0.109115 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 23.4193i | − | 1.21260i | −0.795235 | − | 0.606302i | \(-0.792652\pi\) | ||
0.795235 | − | 0.606302i | \(-0.207348\pi\) | |||||||
\(374\) | 28.4701 | 1.47216 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.6128 | −0.598887 | ||||||||
\(377\) | − | 5.83500i | − | 0.300518i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.90766 | 0.252089 | 0.126045 | − | 0.992025i | \(-0.459772\pi\) | ||||
0.126045 | + | 0.992025i | \(0.459772\pi\) | |||||||
\(380\) | 3.05086 | + | 0.428639i | 0.156506 | + | 0.0219887i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 18.9590i | − | 0.970026i | ||||||
\(383\) | − | 19.8796i | − | 1.01580i | −0.861417 | − | 0.507899i | \(-0.830422\pi\) | ||
0.861417 | − | 0.507899i | \(-0.169578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.857279 | − | 6.10171i | 0.0436910 | − | 0.310972i | ||||
\(386\) | 1.24443 | 0.0633399 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 2.13335i | − | 0.108305i | ||||||
\(389\) | −0.161933 | −0.00821034 | −0.00410517 | − | 0.999992i | \(-0.501307\pi\) | ||||
−0.00410517 | + | 0.999992i | \(0.501307\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.42864 | 0.325110 | ||||||||
\(392\) | − | 6.61285i | − | 0.333999i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.2444 | 0.768003 | ||||||||
\(395\) | 26.6637 | + | 3.74620i | 1.34160 | + | 0.188492i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.76494i | 0.0885796i | 0.999019 | + | 0.0442898i | \(0.0141025\pi\) | ||||
−0.999019 | + | 0.0442898i | \(0.985898\pi\) | |||||||
\(398\) | 14.5303i | 0.728341i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.80642 | + | 1.37778i | 0.240321 | + | 0.0688892i | ||||
\(401\) | 31.3461 | 1.56535 | 0.782676 | − | 0.622430i | \(-0.213854\pi\) | ||||
0.782676 | + | 0.622430i | \(0.213854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.51114i | − | 0.274529i | ||||||
\(404\) | 16.2351 | 0.807725 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.63512 | −0.130779 | ||||||||
\(407\) | 52.2864i | 2.59174i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.51114 | 0.173615 | 0.0868073 | − | 0.996225i | \(-0.472334\pi\) | ||||
0.0868073 | + | 0.996225i | \(0.472334\pi\) | |||||||
\(410\) | 3.37778 | − | 24.0415i | 0.166817 | − | 1.18732i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 12.2351i | − | 0.602778i | ||||||
\(413\) | − | 5.98126i | − | 0.294319i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.682439 | + | 4.85728i | −0.0334996 | + | 0.238434i | ||||
\(416\) | −1.37778 | −0.0675514 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 6.10171i | − | 0.298444i | ||||||
\(419\) | −19.7748 | −0.966061 | −0.483031 | − | 0.875603i | \(-0.660464\pi\) | ||||
−0.483031 | + | 0.875603i | \(0.660464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.8064 | 0.575410 | 0.287705 | − | 0.957719i | \(-0.407108\pi\) | ||||
0.287705 | + | 0.957719i | \(0.407108\pi\) | |||||||
\(422\) | 0.266706i | 0.0129831i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.37778 | −0.164040 | ||||||||
\(425\) | −8.85728 | + | 30.8988i | −0.429641 | + | 1.49881i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.39069i | − | 0.260874i | ||||||
\(428\) | 10.6637i | 0.515450i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.32693 | − | 0.326929i | −0.112214 | − | 0.0157659i | ||||
\(431\) | −24.9403 | −1.20133 | −0.600665 | − | 0.799501i | \(-0.705097\pi\) | ||||
−0.600665 | + | 0.799501i | \(0.705097\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.0513i | 1.54029i | 0.637870 | + | 0.770144i | \(0.279816\pi\) | ||||
−0.637870 | + | 0.770144i | \(0.720184\pi\) | |||||||
\(434\) | −2.48886 | −0.119469 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.1526 | −0.725676 | ||||||||
\(437\) | − | 1.37778i | − | 0.0659084i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.470127 | −0.0224379 | −0.0112190 | − | 0.999937i | \(-0.503571\pi\) | ||||
−0.0112190 | + | 0.999937i | \(0.503571\pi\) | |||||||
\(440\) | 1.37778 | − | 9.80642i | 0.0656833 | − | 0.467503i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 8.85728i | − | 0.421298i | ||||||
\(443\) | − | 0.653858i | − | 0.0310658i | −0.999879 | − | 0.0155329i | \(-0.995056\pi\) | ||
0.999879 | − | 0.0155329i | \(-0.00494447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.10171 | − | 0.857279i | −0.289249 | − | 0.0406389i | ||||
\(446\) | 0.990632 | 0.0469078 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.622216i | 0.0293969i | ||||||||
\(449\) | 17.1427 | 0.809015 | 0.404508 | − | 0.914535i | \(-0.367443\pi\) | ||||
0.404508 | + | 0.914535i | \(0.367443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.0830 | −2.26414 | ||||||||
\(452\) | 14.4286i | 0.678666i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.1526 | 0.805010 | ||||||||
\(455\) | −1.89829 | − | 0.266706i | −0.0889932 | − | 0.0125034i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.00937i | 0.0472162i | 0.999721 | + | 0.0236081i | \(0.00751540\pi\) | ||||
−0.999721 | + | 0.0236081i | \(0.992485\pi\) | |||||||
\(458\) | − | 7.15257i | − | 0.334217i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.311108 | − | 2.21432i | 0.0145055 | − | 0.103243i | ||||
\(461\) | −20.3180 | −0.946305 | −0.473153 | − | 0.880980i | \(-0.656884\pi\) | ||||
−0.473153 | + | 0.880980i | \(0.656884\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.4572i | − | 0.578936i | −0.957188 | − | 0.289468i | \(-0.906522\pi\) | ||
0.957188 | − | 0.289468i | \(-0.0934784\pi\) | |||||||
\(464\) | −4.23506 | −0.196608 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.71456 | −0.172074 | ||||||||
\(467\) | 15.7877i | 0.730567i | 0.930896 | + | 0.365284i | \(0.119028\pi\) | ||||
−0.930896 | + | 0.365284i | \(0.880972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.34614 | −0.339213 | ||||||||
\(470\) | −25.7146 | − | 3.61285i | −1.18612 | − | 0.166648i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 9.61285i | − | 0.442467i | ||||||
\(473\) | 4.65386i | 0.213985i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.62222 | + | 1.89829i | 0.303848 | + | 0.0870995i | ||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.8479i | 1.27373i | ||||||||
\(479\) | 5.12399 | 0.234121 | 0.117060 | − | 0.993125i | \(-0.462653\pi\) | ||||
0.117060 | + | 0.993125i | \(0.462653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.2667 | 0.741698 | ||||||||
\(482\) | − | 7.12399i | − | 0.324489i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.61285 | −0.391493 | ||||||||
\(485\) | 0.663703 | − | 4.72393i | 0.0301372 | − | 0.214502i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.2128i | − | 1.05187i | −0.850524 | − | 0.525936i | \(-0.823715\pi\) | ||
0.850524 | − | 0.525936i | \(-0.176285\pi\) | |||||||
\(488\) | − | 8.66370i | − | 0.392187i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.05731 | − | 14.6430i | 0.0929397 | − | 0.661501i | ||||
\(491\) | 40.1847 | 1.81351 | 0.906755 | − | 0.421658i | \(-0.138552\pi\) | ||||
0.906755 | + | 0.421658i | \(0.138552\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 27.2257i | − | 1.22618i | ||||||
\(494\) | −1.89829 | −0.0854081 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | − | 4.34968i | − | 0.195110i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.5718 | −1.36858 | −0.684292 | − | 0.729208i | \(-0.739888\pi\) | ||||
−0.684292 | + | 0.729208i | \(0.739888\pi\) | |||||||
\(500\) | 10.2143 | + | 4.54617i | 0.456798 | + | 0.203311i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.4099i | 1.00020i | ||||||||
\(503\) | − | 23.4291i | − | 1.04465i | −0.852746 | − | 0.522326i | \(-0.825064\pi\) | ||
0.852746 | − | 0.522326i | \(-0.174936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 35.9496 | + | 5.05086i | 1.59974 | + | 0.224760i | ||||
\(506\) | −4.42864 | −0.196877 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 4.99063i | − | 0.221423i | ||||||
\(509\) | −17.2128 | −0.762943 | −0.381472 | − | 0.924381i | \(-0.624583\pi\) | ||||
−0.381472 | + | 0.924381i | \(0.624583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.71456 | 0.0758476 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.7146 | −0.516707 | ||||||||
\(515\) | 3.80642 | − | 27.0923i | 0.167731 | − | 1.19383i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51.4291i | 2.26185i | ||||||||
\(518\) | − | 7.34614i | − | 0.322771i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.05086 | − | 0.428639i | −0.133789 | − | 0.0187971i | ||||
\(521\) | −22.3684 | −0.979978 | −0.489989 | − | 0.871729i | \(-0.662999\pi\) | ||||
−0.489989 | + | 0.871729i | \(0.662999\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 30.2953i | − | 1.32472i | −0.749186 | − | 0.662360i | \(-0.769555\pi\) | ||
0.749186 | − | 0.662360i | \(-0.230445\pi\) | |||||||
\(524\) | 0.755569 | 0.0330072 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.47013 | 0.369315 | ||||||||
\(527\) | − | 25.7146i | − | 1.12014i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | −7.47949 | − | 1.05086i | −0.324888 | − | 0.0456462i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.857279i | 0.0371678i | ||||||||
\(533\) | 14.9590i | 0.647946i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.31756 | + | 23.6128i | −0.143431 | + | 1.02087i | ||||
\(536\) | −11.8064 | −0.509960 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 28.8256i | 1.24276i | ||||||||
\(539\) | −29.2859 | −1.26143 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.4479 | 1.35205 | 0.676024 | − | 0.736879i | \(-0.263701\pi\) | ||||
0.676024 | + | 0.736879i | \(0.263701\pi\) | |||||||
\(542\) | − | 13.8350i | − | 0.594264i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.42864 | −0.275626 | ||||||||
\(545\) | −33.5526 | − | 4.71408i | −1.43724 | − | 0.201929i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.8573i | 0.891793i | 0.895085 | + | 0.445896i | \(0.147115\pi\) | ||||
−0.895085 | + | 0.445896i | \(0.852885\pi\) | |||||||
\(548\) | − | 12.9175i | − | 0.551808i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.10171 | − | 21.2859i | 0.260178 | − | 0.907635i | ||||
\(551\) | −5.83500 | −0.248580 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.49240i | 0.318609i | ||||||||
\(554\) | −2.88892 | −0.122739 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.1017 | −0.598046 | ||||||||
\(557\) | − | 36.3180i | − | 1.53884i | −0.638740 | − | 0.769422i | \(-0.720544\pi\) | ||
0.638740 | − | 0.769422i | \(-0.279456\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.44785 | 0.0612376 | ||||||||
\(560\) | −0.193576 | + | 1.37778i | −0.00818009 | + | 0.0582220i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 5.51114i | − | 0.232473i | ||||||
\(563\) | 2.58073i | 0.108765i | 0.998520 | + | 0.0543824i | \(0.0173190\pi\) | ||||
−0.998520 | + | 0.0543824i | \(0.982681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.48886 | + | 31.9496i | −0.188848 | + | 1.34413i | ||||
\(566\) | 8.19358 | 0.344402 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.99063i | − | 0.293320i | ||||||
\(569\) | −36.3497 | −1.52386 | −0.761929 | − | 0.647661i | \(-0.775747\pi\) | ||||
−0.761929 | + | 0.647661i | \(0.775747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.9309 | −1.92215 | −0.961074 | − | 0.276292i | \(-0.910894\pi\) | ||||
−0.961074 | + | 0.276292i | \(0.910894\pi\) | |||||||
\(572\) | 6.10171i | 0.255125i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.75557 | 0.281972 | ||||||||
\(575\) | 1.37778 | − | 4.80642i | 0.0574576 | − | 0.200442i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.00000i | 0.166522i | 0.996528 | + | 0.0832611i | \(0.0265335\pi\) | ||||
−0.996528 | + | 0.0832611i | \(0.973466\pi\) | |||||||
\(578\) | − | 24.3274i | − | 1.01189i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.37778 | − | 1.31756i | −0.389391 | − | 0.0547088i | ||||
\(581\) | −1.36488 | −0.0566247 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.9590i | 0.619538i | ||||||||
\(584\) | 2.75557 | 0.114026 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.6222 | −0.521419 | ||||||||
\(587\) | − | 42.1847i | − | 1.74115i | −0.492037 | − | 0.870574i | \(-0.663748\pi\) | ||
0.492037 | − | 0.870574i | \(-0.336252\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.51114 | −0.227082 | ||||||||
\(590\) | 2.99063 | − | 21.2859i | 0.123122 | − | 0.876327i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 11.8064i | − | 0.485241i | ||||||
\(593\) | 18.7368i | 0.769430i | 0.923036 | + | 0.384715i | \(0.125700\pi\) | ||||
−0.923036 | + | 0.384715i | \(0.874300\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.85728 | − | 1.24443i | −0.363113 | − | 0.0510167i | ||||
\(596\) | −12.4286 | −0.509097 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.37778i | 0.0563418i | ||||||||
\(599\) | −41.5625 | −1.69820 | −0.849098 | − | 0.528235i | \(-0.822854\pi\) | ||||
−0.849098 | + | 0.528235i | \(0.822854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.7146 | 0.967337 | 0.483668 | − | 0.875251i | \(-0.339304\pi\) | ||||
0.483668 | + | 0.875251i | \(0.339304\pi\) | |||||||
\(602\) | − | 0.653858i | − | 0.0266493i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.85728 | 0.197640 | ||||||||
\(605\) | −19.0716 | − | 2.67952i | −0.775371 | − | 0.108938i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.74266i | 0.111321i | 0.998450 | + | 0.0556606i | \(0.0177265\pi\) | ||||
−0.998450 | + | 0.0556606i | \(0.982274\pi\) | |||||||
\(608\) | 1.37778i | 0.0558765i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.69535 | − | 19.1842i | 0.109131 | − | 0.776746i | ||||
\(611\) | 16.0000 | 0.647291 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.0731i | 0.972305i | 0.873874 | + | 0.486152i | \(0.161600\pi\) | ||||
−0.873874 | + | 0.486152i | \(0.838400\pi\) | |||||||
\(614\) | 0.653858 | 0.0263876 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.75557 | 0.111025 | ||||||||
\(617\) | 39.4893i | 1.58978i | 0.606753 | + | 0.794890i | \(0.292472\pi\) | ||||
−0.606753 | + | 0.794890i | \(0.707528\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.6222 | 0.909264 | 0.454632 | − | 0.890679i | \(-0.349771\pi\) | ||||
0.454632 | + | 0.890679i | \(0.349771\pi\) | |||||||
\(620\) | −8.85728 | − | 1.24443i | −0.355717 | − | 0.0499776i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.0923i | 0.524955i | ||||||||
\(623\) | − | 1.71456i | − | 0.0686923i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | + | 13.2444i | 0.848137 | + | 0.529777i | ||||
\(626\) | 11.2573 | 0.449934 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 9.90813i | − | 0.395378i | ||||||
\(629\) | 75.8992 | 3.02630 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.93978 | 0.236459 | 0.118229 | − | 0.992986i | \(-0.462278\pi\) | ||||
0.118229 | + | 0.992986i | \(0.462278\pi\) | |||||||
\(632\) | 12.0415i | 0.478985i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.4701 | −0.892403 | ||||||||
\(635\) | 1.55262 | − | 11.0509i | 0.0616140 | − | 0.438540i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.11108i | 0.360994i | ||||||||
\(638\) | 18.7556i | 0.742540i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.311108 | + | 2.21432i | −0.0122976 | + | 0.0875287i | ||||
\(641\) | −19.8163 | −0.782696 | −0.391348 | − | 0.920243i | \(-0.627991\pi\) | ||||
−0.391348 | + | 0.920243i | \(0.627991\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 44.7467i | − | 1.76464i | −0.470653 | − | 0.882318i | \(-0.655982\pi\) | ||
0.470653 | − | 0.882318i | \(-0.344018\pi\) | |||||||
\(644\) | 0.622216 | 0.0245187 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.85728 | −0.348485 | ||||||||
\(647\) | − | 32.9403i | − | 1.29501i | −0.762059 | − | 0.647507i | \(-0.775811\pi\) | ||
0.762059 | − | 0.647507i | \(-0.224189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −42.5718 | −1.67109 | ||||||||
\(650\) | −6.62222 | − | 1.89829i | −0.259745 | − | 0.0744571i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 10.1017i | − | 0.395614i | ||||||
\(653\) | 37.2257i | 1.45675i | 0.685177 | + | 0.728377i | \(0.259725\pi\) | ||||
−0.685177 | + | 0.728377i | \(0.740275\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.67307 | + | 0.235063i | 0.0653723 | + | 0.00918468i | ||||
\(656\) | 10.8573 | 0.423906 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 7.22570i | − | 0.281687i | ||||||
\(659\) | 24.6953 | 0.961994 | 0.480997 | − | 0.876722i | \(-0.340275\pi\) | ||||
0.480997 | + | 0.876722i | \(0.340275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.8287 | −0.576770 | −0.288385 | − | 0.957515i | \(-0.593118\pi\) | ||||
−0.288385 | + | 0.957515i | \(0.593118\pi\) | |||||||
\(662\) | − | 29.4479i | − | 1.14452i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.19358 | −0.0851273 | ||||||||
\(665\) | −0.266706 | + | 1.89829i | −0.0103424 | + | 0.0736125i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.23506i | 0.163982i | ||||||||
\(668\) | − | 1.89829i | − | 0.0734470i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −26.1432 | − | 3.67307i | −1.01000 | − | 0.141903i | ||||
\(671\) | −38.3684 | −1.48120 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.77430i | − | 0.338225i | −0.985597 | − | 0.169112i | \(-0.945910\pi\) | ||
0.985597 | − | 0.169112i | \(-0.0540901\pi\) | |||||||
\(674\) | 24.6222 | 0.948412 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.1017 | −0.426989 | ||||||||
\(677\) | 12.8256i | 0.492929i | 0.969152 | + | 0.246465i | \(0.0792689\pi\) | ||||
−0.969152 | + | 0.246465i | \(0.920731\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.32741 | 0.0509412 | ||||||||
\(680\) | −14.2351 | − | 2.00000i | −0.545890 | − | 0.0766965i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.7146i | 0.678325i | ||||||||
\(683\) | 8.47013i | 0.324100i | 0.986783 | + | 0.162050i | \(0.0518106\pi\) | ||||
−0.986783 | + | 0.162050i | \(0.948189\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.01874 | − | 28.6035i | 0.153548 | − | 1.09288i | ||||
\(686\) | 8.47013 | 0.323391 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 1.05086i | − | 0.0400635i | ||||||
\(689\) | 4.65386 | 0.177298 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.7975 | 0.981384 | 0.490692 | − | 0.871333i | \(-0.336744\pi\) | ||||
0.490692 | + | 0.871333i | \(0.336744\pi\) | |||||||
\(692\) | 21.2257i | 0.806880i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.1017 | 0.990807 | ||||||||
\(695\) | −31.2257 | − | 4.38715i | −1.18446 | − | 0.166414i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 69.7975i | 2.64377i | ||||||||
\(698\) | 21.2257i | 0.803404i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.857279 | + | 2.99063i | −0.0324021 | + | 0.113035i | ||||
\(701\) | −7.45091 | −0.281417 | −0.140709 | − | 0.990051i | \(-0.544938\pi\) | ||||
−0.140709 | + | 0.990051i | \(0.544938\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.2667i | − | 0.613510i | ||||||
\(704\) | 4.42864 | 0.166911 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.28544 | 0.161285 | ||||||||
\(707\) | 10.1017i | 0.379914i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.2543 | −0.497775 | −0.248887 | − | 0.968532i | \(-0.580065\pi\) | ||||
−0.248887 | + | 0.968532i | \(0.580065\pi\) | |||||||
\(710\) | 2.17484 | − | 15.4795i | 0.0816203 | − | 0.580935i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 2.75557i | − | 0.103269i | ||||||
\(713\) | 4.00000i | 0.149801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.89829 | + | 13.5111i | −0.0709920 | + | 0.505288i | ||||
\(716\) | −0.488863 | −0.0182697 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 4.65386i | − | 0.173680i | ||||||
\(719\) | −2.33677 | −0.0871469 | −0.0435735 | − | 0.999050i | \(-0.513874\pi\) | ||||
−0.0435735 | + | 0.999050i | \(0.513874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.61285 | 0.283517 | ||||||||
\(722\) | − | 17.1017i | − | 0.636460i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.9304 | 0.777873 | ||||||||
\(725\) | −20.3555 | − | 5.83500i | −0.755985 | − | 0.216707i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.37778i | − | 0.125275i | −0.998036 | − | 0.0626375i | \(-0.980049\pi\) | ||
0.998036 | − | 0.0626375i | \(-0.0199512\pi\) | |||||||
\(728\) | − | 0.857279i | − | 0.0317729i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.10171 | + | 0.857279i | 0.225834 | + | 0.0317293i | ||||
\(731\) | 6.75557 | 0.249864 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.0509i | − | 0.777531i | −0.921337 | − | 0.388766i | \(-0.872902\pi\) | ||
0.921337 | − | 0.388766i | \(-0.127098\pi\) | |||||||
\(734\) | −4.88892 | −0.180453 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 52.2864i | 1.92599i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.6351 | 0.832646 | 0.416323 | − | 0.909217i | \(-0.363318\pi\) | ||||
0.416323 | + | 0.909217i | \(0.363318\pi\) | |||||||
\(740\) | 3.67307 | − | 26.1432i | 0.135025 | − | 0.961043i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 2.10171i | − | 0.0771562i | ||||||
\(743\) | − | 3.87955i | − | 0.142327i | −0.997465 | − | 0.0711635i | \(-0.977329\pi\) | ||
0.997465 | − | 0.0711635i | \(-0.0226712\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.5210 | − | 3.86665i | −1.00829 | − | 0.141663i | ||||
\(746\) | 23.4193 | 0.857440 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 28.4701i | 1.04097i | ||||||||
\(749\) | −6.63512 | −0.242442 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.7748 | 0.721592 | 0.360796 | − | 0.932645i | \(-0.382505\pi\) | ||||
0.360796 | + | 0.932645i | \(0.382505\pi\) | |||||||
\(752\) | − | 11.6128i | − | 0.423477i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.83500 | 0.212498 | ||||||||
\(755\) | 10.7556 | + | 1.51114i | 0.391435 | + | 0.0549959i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.19358i | 0.297801i | 0.988852 | + | 0.148900i | \(0.0475733\pi\) | ||||
−0.988852 | + | 0.148900i | \(0.952427\pi\) | |||||||
\(758\) | 4.90766i | 0.178254i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.428639 | + | 3.05086i | −0.0155484 | + | 0.110666i | ||||
\(761\) | 45.1624 | 1.63714 | 0.818568 | − | 0.574410i | \(-0.194768\pi\) | ||||
0.818568 | + | 0.574410i | \(0.194768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 9.42816i | − | 0.341322i | ||||||
\(764\) | 18.9590 | 0.685912 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.8796 | 0.718277 | ||||||||
\(767\) | 13.2444i | 0.478229i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.4924 | −1.06352 | −0.531762 | − | 0.846894i | \(-0.678470\pi\) | ||||
−0.531762 | + | 0.846894i | \(0.678470\pi\) | |||||||
\(770\) | 6.10171 | + | 0.857279i | 0.219890 | + | 0.0308942i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.24443i | 0.0447881i | ||||||||
\(773\) | − | 41.0923i | − | 1.47799i | −0.673712 | − | 0.738994i | \(-0.735301\pi\) | ||
0.673712 | − | 0.738994i | \(-0.264699\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.2257 | − | 5.51114i | −0.690607 | − | 0.197966i | ||||
\(776\) | 2.13335 | 0.0765829 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 0.161933i | − | 0.00580559i | ||||||
\(779\) | 14.9590 | 0.535961 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.9590 | −1.10780 | ||||||||
\(782\) | 6.42864i | 0.229888i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.61285 | 0.236173 | ||||||||
\(785\) | 3.08250 | − | 21.9398i | 0.110019 | − | 0.783064i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.0919i | 0.359736i | 0.983691 | + | 0.179868i | \(0.0575671\pi\) | ||||
−0.983691 | + | 0.179868i | \(0.942433\pi\) | |||||||
\(788\) | 15.2444i | 0.543060i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.74620 | + | 26.6637i | −0.133284 | + | 0.948652i | ||||
\(791\) | −8.97773 | −0.319211 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.9367i | 0.423885i | ||||||||
\(794\) | −1.76494 | −0.0626353 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.5303 | −0.515015 | ||||||||
\(797\) | 25.2958i | 0.896022i | 0.894028 | + | 0.448011i | \(0.147867\pi\) | ||||
−0.894028 | + | 0.448011i | \(0.852133\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 74.6548 | 2.64110 | ||||||||
\(800\) | −1.37778 | + | 4.80642i | −0.0487120 | + | 0.169933i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 31.3461i | 1.10687i | ||||||||
\(803\) | − | 12.2034i | − | 0.430649i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.37778 | + | 0.193576i | 0.0485605 | + | 0.00682266i | ||||
\(806\) | 5.51114 | 0.194122 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.2351i | 0.571148i | ||||||||
\(809\) | 43.4479 | 1.52755 | 0.763773 | − | 0.645485i | \(-0.223345\pi\) | ||||
0.763773 | + | 0.645485i | \(0.223345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.65386 | −0.303878 | −0.151939 | − | 0.988390i | \(-0.548552\pi\) | ||||
−0.151939 | + | 0.988390i | \(0.548552\pi\) | |||||||
\(812\) | − | 2.63512i | − | 0.0924747i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −52.2864 | −1.83264 | ||||||||
\(815\) | 3.14272 | − | 22.3684i | 0.110085 | − | 0.783531i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.44785i | − | 0.0506539i | ||||||
\(818\) | 3.51114i | 0.122764i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.0415 | + | 3.37778i | 0.839565 | + | 0.117957i | ||||
\(821\) | −2.78721 | −0.0972744 | −0.0486372 | − | 0.998817i | \(-0.515488\pi\) | ||||
−0.0486372 | + | 0.998817i | \(0.515488\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 29.9684i | − | 1.04463i | −0.852752 | − | 0.522316i | \(-0.825068\pi\) | ||
0.852752 | − | 0.522316i | \(-0.174932\pi\) | |||||||
\(824\) | 12.2351 | 0.426229 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.98126 | 0.208115 | ||||||||
\(827\) | − | 47.2543i | − | 1.64319i | −0.570070 | − | 0.821596i | \(-0.693084\pi\) | ||
0.570070 | − | 0.821596i | \(-0.306916\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.1624 | 1.84641 | 0.923203 | − | 0.384312i | \(-0.125561\pi\) | ||||
0.923203 | + | 0.384312i | \(0.125561\pi\) | |||||||
\(830\) | −4.85728 | − | 0.682439i | −0.168599 | − | 0.0236878i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1.37778i | − | 0.0477661i | ||||||
\(833\) | 42.5116i | 1.47294i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.590573 | − | 4.20342i | 0.0204376 | − | 0.145465i | ||||
\(836\) | 6.10171 | 0.211032 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 19.7748i | − | 0.683108i | ||||||
\(839\) | −17.3274 | −0.598208 | −0.299104 | − | 0.954220i | \(-0.596688\pi\) | ||||
−0.299104 | + | 0.954220i | \(0.596688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0642 | −0.381525 | ||||||||
\(842\) | 11.8064i | 0.406876i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.266706 | −0.00918041 | ||||||||
\(845\) | −24.5827 | − | 3.45383i | −0.845672 | − | 0.118815i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.35905i | − | 0.184139i | ||||||
\(848\) | − | 3.37778i | − | 0.115994i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −30.8988 | − | 8.85728i | −1.05982 | − | 0.303802i | ||||
\(851\) | −11.8064 | −0.404719 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17.7649i | − | 0.608260i | −0.952631 | − | 0.304130i | \(-0.901634\pi\) | ||
0.952631 | − | 0.304130i | \(-0.0983657\pi\) | |||||||
\(854\) | 5.39069 | 0.184466 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.6637 | −0.364478 | ||||||||
\(857\) | − | 10.0830i | − | 0.344428i | −0.985060 | − | 0.172214i | \(-0.944908\pi\) | ||
0.985060 | − | 0.172214i | \(-0.0550920\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.12399 | −0.174828 | −0.0874141 | − | 0.996172i | \(-0.527860\pi\) | ||||
−0.0874141 | + | 0.996172i | \(0.527860\pi\) | |||||||
\(860\) | 0.326929 | − | 2.32693i | 0.0111482 | − | 0.0793476i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 24.9403i | − | 0.849468i | ||||||
\(863\) | 49.2070i | 1.67502i | 0.546419 | + | 0.837512i | \(0.315991\pi\) | ||||
−0.546419 | + | 0.837512i | \(0.684009\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.60348 | + | 47.0005i | −0.224525 | + | 1.59806i | ||||
\(866\) | −32.0513 | −1.08915 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 2.48886i | − | 0.0844775i | ||||||
\(869\) | 53.3274 | 1.80901 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2667 | 0.551176 | ||||||||
\(872\) | − | 15.1526i | − | 0.513131i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.37778 | 0.0466043 | ||||||||
\(875\) | −2.82870 | + | 6.35551i | −0.0956275 | + | 0.214855i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 9.11108i | − | 0.307659i | −0.988097 | − | 0.153830i | \(-0.950839\pi\) | ||
0.988097 | − | 0.153830i | \(-0.0491607\pi\) | |||||||
\(878\) | − | 0.470127i | − | 0.0158660i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.80642 | + | 1.37778i | 0.330574 | + | 0.0464451i | ||||
\(881\) | 9.71456 | 0.327292 | 0.163646 | − | 0.986519i | \(-0.447675\pi\) | ||||
0.163646 | + | 0.986519i | \(0.447675\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 33.3274i | − | 1.12156i | −0.827966 | − | 0.560778i | \(-0.810502\pi\) | ||
0.827966 | − | 0.560778i | \(-0.189498\pi\) | |||||||
\(884\) | 8.85728 | 0.297903 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.653858 | 0.0219668 | ||||||||
\(887\) | − | 53.5941i | − | 1.79951i | −0.436391 | − | 0.899757i | \(-0.643744\pi\) | ||
0.436391 | − | 0.899757i | \(-0.356256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.10525 | 0.104147 | ||||||||
\(890\) | 0.857279 | − | 6.10171i | 0.0287361 | − | 0.204530i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.990632i | 0.0331688i | ||||||||
\(893\) | − | 16.0000i | − | 0.535420i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.08250 | − | 0.152089i | −0.0361839 | − | 0.00508377i | ||||
\(896\) | −0.622216 | −0.0207868 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.1427i | 0.572060i | ||||||||
\(899\) | 16.9403 | 0.564989 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.7146 | 0.723417 | ||||||||
\(902\) | − | 48.0830i | − | 1.60099i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.4286 | −0.479889 | ||||||||
\(905\) | 46.3466 | + | 6.51161i | 1.54061 | + | 0.216453i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.56199i | − | 0.0850696i | −0.999095 | − | 0.0425348i | \(-0.986457\pi\) | ||
0.999095 | − | 0.0425348i | \(-0.0135433\pi\) | |||||||
\(908\) | 17.1526i | 0.569228i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.266706 | − | 1.89829i | 0.00884122 | − | 0.0629277i | ||||
\(911\) | −8.47013 | −0.280628 | −0.140314 | − | 0.990107i | \(-0.544811\pi\) | ||||
−0.140314 | + | 0.990107i | \(0.544811\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.71456i | 0.321505i | ||||||||
\(914\) | −1.00937 | −0.0333869 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.15257 | 0.236327 | ||||||||
\(917\) | 0.470127i | 0.0155250i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.8988 | 1.21718 | 0.608589 | − | 0.793486i | \(-0.291736\pi\) | ||||
0.608589 | + | 0.793486i | \(0.291736\pi\) | |||||||
\(920\) | 2.21432 | + | 0.311108i | 0.0730040 | + | 0.0102569i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 20.3180i | − | 0.669139i | ||||||
\(923\) | 9.63158i | 0.317027i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.2667 | − | 56.7467i | 0.534846 | − | 1.86582i | ||||
\(926\) | 12.4572 | 0.409370 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 4.23506i | − | 0.139023i | ||||||
\(929\) | −0.164996 | −0.00541334 | −0.00270667 | − | 0.999996i | \(-0.500862\pi\) | ||||
−0.00270667 | + | 0.999996i | \(0.500862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.11108 | 0.298604 | ||||||||
\(932\) | − | 3.71456i | − | 0.121674i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.7877 | −0.516589 | ||||||||
\(935\) | −8.85728 | + | 63.0420i | −0.289664 | + | 2.06169i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.3180i | 1.31713i | 0.752523 | + | 0.658566i | \(0.228837\pi\) | ||||
−0.752523 | + | 0.658566i | \(0.771163\pi\) | |||||||
\(938\) | − | 7.34614i | − | 0.239860i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.61285 | − | 25.7146i | 0.117838 | − | 0.838716i | ||||
\(941\) | −53.3689 | −1.73978 | −0.869888 | − | 0.493249i | \(-0.835809\pi\) | ||||
−0.869888 | + | 0.493249i | \(0.835809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 10.8573i | − | 0.353562i | ||||||
\(944\) | 9.61285 | 0.312872 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.65386 | −0.151310 | ||||||||
\(947\) | 44.6735i | 1.45170i | 0.687856 | + | 0.725848i | \(0.258552\pi\) | ||||
−0.687856 | + | 0.725848i | \(0.741448\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.79658 | −0.123242 | ||||||||
\(950\) | −1.89829 | + | 6.62222i | −0.0615887 | + | 0.214853i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 4.00000i | − | 0.129641i | ||||||
\(953\) | 21.2672i | 0.688912i | 0.938803 | + | 0.344456i | \(0.111937\pi\) | ||||
−0.938803 | + | 0.344456i | \(0.888063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.9813 | + | 5.89829i | 1.35848 | + | 0.190864i | ||||
\(956\) | −27.8479 | −0.900666 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.12399i | 0.165548i | ||||||||
\(959\) | 8.03747 | 0.259543 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 16.2667i | 0.524460i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.12399 | 0.229448 | ||||||||
\(965\) | −0.387152 | + | 2.75557i | −0.0124629 | + | 0.0887049i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 10.9461i | − | 0.352002i | −0.984390 | − | 0.176001i | \(-0.943684\pi\) | ||
0.984390 | − | 0.176001i | \(-0.0563162\pi\) | |||||||
\(968\) | − | 8.61285i | − | 0.276827i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.72393 | + | 0.663703i | 0.151676 | + | 0.0213102i | ||||
\(971\) | 16.8988 | 0.542307 | 0.271154 | − | 0.962536i | \(-0.412595\pi\) | ||||
0.271154 | + | 0.962536i | \(0.412595\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.77430i | − | 0.281291i | ||||||
\(974\) | 23.2128 | 0.743786 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.66370 | 0.277318 | ||||||||
\(977\) | 59.2484i | 1.89553i | 0.318976 | + | 0.947763i | \(0.396661\pi\) | ||||
−0.318976 | + | 0.947763i | \(0.603339\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.2034 | −0.390023 | ||||||||
\(980\) | 14.6430 | + | 2.05731i | 0.467752 | + | 0.0657183i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 40.1847i | 1.28234i | ||||||||
\(983\) | 23.8163i | 0.759621i | 0.925064 | + | 0.379810i | \(0.124011\pi\) | ||||
−0.925064 | + | 0.379810i | \(0.875989\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.74266 | + | 33.7560i | −0.151114 | + | 1.07556i | ||||
\(986\) | 27.2257 | 0.867043 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 1.89829i | − | 0.0603926i | ||||||
\(989\) | −1.05086 | −0.0334152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.7146 | 0.943914 | 0.471957 | − | 0.881622i | \(-0.343548\pi\) | ||||
0.471957 | + | 0.881622i | \(0.343548\pi\) | |||||||
\(992\) | − | 4.00000i | − | 0.127000i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.34968 | 0.137963 | ||||||||
\(995\) | −32.1748 | − | 4.52051i | −1.02001 | − | 0.143310i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 22.7052i | − | 0.719081i | −0.933130 | − | 0.359540i | \(-0.882934\pi\) | ||
0.933130 | − | 0.359540i | \(-0.117066\pi\) | |||||||
\(998\) | − | 30.5718i | − | 0.967735i | ||||||
\(999\) | 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 | 2070.2.d.e.829.4 | 6 | ||
3.2 | odd | 2 | 690.2.d.c.139.3 | ✓ | 6 | ||
5.4 | even | 2 | inner | 2070.2.d.e.829.1 | 6 | ||
15.2 | even | 4 | 3450.2.a.bt.1.2 | 3 | |||
15.8 | even | 4 | 3450.2.a.bo.1.2 | 3 | |||
15.14 | odd | 2 | 690.2.d.c.139.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.c.139.3 | ✓ | 6 | 3.2 | odd | 2 | ||
690.2.d.c.139.6 | yes | 6 | 15.14 | odd | 2 | ||
2070.2.d.e.829.1 | 6 | 5.4 | even | 2 | inner | ||
2070.2.d.e.829.4 | 6 | 1.1 | even | 1 | trivial | ||
3450.2.a.bo.1.2 | 3 | 15.8 | even | 4 | |||
3450.2.a.bt.1.2 | 3 | 15.2 | even | 4 |