Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1889,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.k (of order \(2\), degree \(1\), not 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} - 45 x^{12} + 306 x^{11} - 378 x^{10} + 1704 x^{9} + 917 x^{8} - 12522 x^{7} + 27090 x^{6} - 35292 x^{5} + 30948 x^{4} - 18000 x^{3} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.10 | ||
Root | \(3.41914 - 0.916156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1889 |
Dual form | 3024.2.k.l.1889.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.933004 | 0.417252 | 0.208626 | − | 0.977995i | \(-0.433101\pi\) | ||||
0.208626 | + | 0.977995i | \(0.433101\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.45692 | + | 0.981597i | −0.928629 | + | 0.371009i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.75675i | 0.529679i | 0.964293 | + | 0.264839i | \(0.0853189\pi\) | ||||
−0.964293 | + | 0.264839i | \(0.914681\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.20692i | − | 1.16679i | −0.812189 | − | 0.583395i | \(-0.801724\pi\) | ||
0.812189 | − | 0.583395i | \(-0.198276\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.231144 | −0.0560606 | −0.0280303 | − | 0.999607i | \(-0.508923\pi\) | ||||
−0.0280303 | + | 0.999607i | \(0.508923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.00597i | 1.14845i | 0.818698 | + | 0.574224i | \(0.194696\pi\) | ||||
−0.818698 | + | 0.574224i | \(0.805304\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.61601i | − | 0.545476i | −0.962088 | − | 0.272738i | \(-0.912071\pi\) | ||
0.962088 | − | 0.272738i | \(-0.0879292\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.12950 | −0.825901 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.77311i | − | 0.700649i | −0.936628 | − | 0.350324i | \(-0.886071\pi\) | ||
0.936628 | − | 0.350324i | \(-0.113929\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.840005i | 0.150869i | 0.997151 | + | 0.0754347i | \(0.0240344\pi\) | ||||
−0.997151 | + | 0.0754347i | \(0.975966\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.29232 | + | 0.915835i | −0.387473 | + | 0.154804i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.01636 | 0.495887 | 0.247944 | − | 0.968774i | \(-0.420245\pi\) | ||||
0.247944 | + | 0.968774i | \(0.420245\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.98174 | −1.40271 | −0.701356 | − | 0.712811i | \(-0.747422\pi\) | ||||
−0.701356 | + | 0.712811i | \(0.747422\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.40035 | −0.366050 | −0.183025 | − | 0.983108i | \(-0.558589\pi\) | ||||
−0.183025 | + | 0.983108i | \(0.558589\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.03019 | −0.150269 | −0.0751343 | − | 0.997173i | \(-0.523939\pi\) | ||||
−0.0751343 | + | 0.997173i | \(0.523939\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.07293 | − | 4.82342i | 0.724705 | − | 0.689060i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.04335i | 1.24220i | 0.783732 | + | 0.621100i | \(0.213314\pi\) | ||||
−0.783732 | + | 0.621100i | \(0.786686\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.63905i | 0.221010i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.77898 | −0.882548 | −0.441274 | − | 0.897372i | \(-0.645473\pi\) | ||||
−0.441274 | + | 0.897372i | \(0.645473\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.93236i | − | 1.14367i | −0.820368 | − | 0.571836i | \(-0.806232\pi\) | ||
0.820368 | − | 0.571836i | \(-0.193768\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.92508i | − | 0.486846i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.10252 | −0.134694 | −0.0673471 | − | 0.997730i | \(-0.521453\pi\) | ||||
−0.0673471 | + | 0.997730i | \(0.521453\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.21168i | − | 0.855869i | −0.903810 | − | 0.427934i | \(-0.859241\pi\) | ||
0.903810 | − | 0.427934i | \(-0.140759\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.44883i | − | 0.403655i | −0.979421 | − | 0.201828i | \(-0.935312\pi\) | ||
0.979421 | − | 0.201828i | \(-0.0646881\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.72442 | − | 4.31619i | −0.196516 | − | 0.491875i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.29783 | −0.596053 | −0.298026 | − | 0.954558i | \(-0.596328\pi\) | ||||
−0.298026 | + | 0.954558i | \(0.596328\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.8713 | −1.63234 | −0.816170 | − | 0.577812i | \(-0.803907\pi\) | ||||
−0.816170 | + | 0.577812i | \(0.803907\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.215658 | −0.0233914 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.0053 | −1.59056 | −0.795279 | − | 0.606244i | \(-0.792675\pi\) | ||||
−0.795279 | + | 0.606244i | \(0.792675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.12950 | + | 10.3361i | 0.432890 | + | 1.08352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.67059i | 0.479192i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.63905i | − | 0.166420i | −0.996532 | − | 0.0832102i | \(-0.973483\pi\) | ||
0.996532 | − | 0.0832102i | \(-0.0265173\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.58464 | −0.456189 | −0.228094 | − | 0.973639i | \(-0.573249\pi\) | ||||
−0.228094 | + | 0.973639i | \(0.573249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.1411i | 1.59043i | 0.606328 | + | 0.795215i | \(0.292642\pi\) | ||||
−0.606328 | + | 0.795215i | \(0.707358\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 18.4601i | − | 1.78460i | −0.451441 | − | 0.892301i | \(-0.649090\pi\) | ||
0.451441 | − | 0.892301i | \(-0.350910\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.81132 | 0.843972 | 0.421986 | − | 0.906602i | \(-0.361333\pi\) | ||||
0.421986 | + | 0.906602i | \(0.361333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.9026i | − | 1.30785i | −0.756560 | − | 0.653924i | \(-0.773122\pi\) | ||
0.756560 | − | 0.653924i | \(-0.226878\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.44075i | − | 0.227601i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.567902 | − | 0.226890i | 0.0520595 | − | 0.0207990i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.91384 | 0.719440 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.51787 | −0.761861 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.61601 | −0.143398 | −0.0716989 | − | 0.997426i | \(-0.522842\pi\) | ||||
−0.0716989 | + | 0.997426i | \(0.522842\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.7239 | −1.54855 | −0.774273 | − | 0.632852i | \(-0.781884\pi\) | ||||
−0.774273 | + | 0.632852i | \(0.781884\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.91384 | − | 12.2993i | −0.426084 | − | 1.06648i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 14.9848i | − | 1.28024i | −0.768276 | − | 0.640118i | \(-0.778885\pi\) | ||
0.768276 | − | 0.640118i | \(-0.221115\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.05435i | 0.0894285i | 0.999000 | + | 0.0447143i | \(0.0142377\pi\) | ||||
−0.999000 | + | 0.0447143i | \(0.985762\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.39049 | 0.618024 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.52033i | − | 0.292347i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.45493i | − | 0.119193i | −0.998223 | − | 0.0595963i | \(-0.981019\pi\) | ||
0.998223 | − | 0.0595963i | \(-0.0189813\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.6757 | −1.03154 | −0.515768 | − | 0.856728i | \(-0.672493\pi\) | ||||
−0.515768 | + | 0.856728i | \(0.672493\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.783729i | 0.0629506i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.7953i | 1.73946i | 0.493530 | + | 0.869729i | \(0.335706\pi\) | ||||
−0.493530 | + | 0.869729i | \(0.664294\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.56787 | + | 6.42734i | 0.202376 | + | 0.506545i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.65936 | 0.678253 | 0.339127 | − | 0.940741i | \(-0.389868\pi\) | ||||
0.339127 | + | 0.940741i | \(0.389868\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.49611 | −0.580066 | −0.290033 | − | 0.957017i | \(-0.593666\pi\) | ||||
−0.290033 | + | 0.957017i | \(0.593666\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.69819 | −0.361399 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.71863 | −0.206694 | −0.103347 | − | 0.994645i | \(-0.532955\pi\) | ||||
−0.103347 | + | 0.994645i | \(0.532955\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.1459 | − | 4.05351i | 0.766955 | − | 0.306416i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18.3851i | − | 1.37417i | −0.726577 | − | 0.687085i | \(-0.758890\pi\) | ||
0.726577 | − | 0.687085i | \(-0.241110\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.45745i | 0.628638i | 0.949317 | + | 0.314319i | \(0.101776\pi\) | ||||
−0.949317 | + | 0.314319i | \(0.898224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.81428 | 0.206910 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.406061i | − | 0.0296941i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.3412i | 1.83362i | 0.399320 | + | 0.916812i | \(0.369246\pi\) | ||||
−0.399320 | + | 0.916812i | \(0.630754\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.404334 | −0.0291046 | −0.0145523 | − | 0.999894i | \(-0.504632\pi\) | ||||
−0.0145523 | + | 0.999894i | \(0.504632\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.58443i | 0.540369i | 0.962809 | + | 0.270184i | \(0.0870846\pi\) | ||||
−0.962809 | + | 0.270184i | \(0.912915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 25.7879i | − | 1.82806i | −0.405649 | − | 0.914029i | \(-0.632955\pi\) | ||
0.405649 | − | 0.914029i | \(-0.367045\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.70367 | + | 9.27024i | 0.259947 | + | 0.650643i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.38001 | −0.585285 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.79421 | −0.608308 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.69819 | 0.254594 | 0.127297 | − | 0.991865i | \(-0.459370\pi\) | ||||
0.127297 | + | 0.991865i | \(0.459370\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.23954 | −0.152735 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.824547 | − | 2.06383i | −0.0559739 | − | 0.140102i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.972404i | 0.0654110i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.17692i | − | 0.547567i | −0.961791 | − | 0.273784i | \(-0.911725\pi\) | ||
0.961791 | − | 0.273784i | \(-0.0882752\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.80735 | −0.319075 | −0.159538 | − | 0.987192i | \(-0.551000\pi\) | ||||
−0.159538 | + | 0.987192i | \(0.551000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.65010i | − | 0.241205i | −0.992701 | − | 0.120603i | \(-0.961517\pi\) | ||
0.992701 | − | 0.120603i | \(-0.0384827\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.0118i | 1.44204i | 0.692915 | + | 0.721020i | \(0.256326\pi\) | ||||
−0.692915 | + | 0.721020i | \(0.743674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.961172 | −0.0627000 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.64361i | 0.365055i | 0.983201 | + | 0.182527i | \(0.0584278\pi\) | ||||
−0.983201 | + | 0.182527i | \(0.941572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9479i | 1.60704i | 0.595280 | + | 0.803518i | \(0.297041\pi\) | ||||
−0.595280 | + | 0.803518i | \(0.702959\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.73307 | − | 4.50027i | 0.302385 | − | 0.287512i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.0597 | 1.34000 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.8598 | −1.06418 | −0.532089 | − | 0.846688i | \(-0.678593\pi\) | ||||
−0.532089 | + | 0.846688i | \(0.678593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.59567 | 0.288927 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.13580 | −0.0708496 | −0.0354248 | − | 0.999372i | \(-0.511278\pi\) | ||||
−0.0354248 | + | 0.999372i | \(0.511278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.41097 | + | 2.96085i | −0.460495 | + | 0.183979i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 0.485895i | − | 0.0299616i | −0.999888 | − | 0.0149808i | \(-0.995231\pi\) | ||
0.999888 | − | 0.0149808i | \(-0.00476871\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.43748i | 0.518310i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.3100 | −0.689585 | −0.344793 | − | 0.938679i | \(-0.612051\pi\) | ||||
−0.344793 | + | 0.938679i | \(0.612051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.00862i | 0.304252i | 0.988361 | + | 0.152126i | \(0.0486119\pi\) | ||||
−0.988361 | + | 0.152126i | \(0.951388\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 7.25449i | − | 0.437462i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.6717 | −1.24204 | −0.621022 | − | 0.783793i | \(-0.713282\pi\) | ||||
−0.621022 | + | 0.783793i | \(0.713282\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.9448i | 0.831878i | 0.909393 | + | 0.415939i | \(0.136547\pi\) | ||||
−0.909393 | + | 0.415939i | \(0.863453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 22.5944i | − | 1.34310i | −0.740961 | − | 0.671549i | \(-0.765629\pi\) | ||
0.740961 | − | 0.671549i | \(-0.234371\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.0674 | − | 8.81646i | 1.30260 | − | 0.520419i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9466 | −0.996857 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.27838 | −0.366787 | −0.183394 | − | 0.983040i | \(-0.558708\pi\) | ||||
−0.183394 | + | 0.983040i | \(0.558708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.32482 | −0.368245 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.0054 | −0.636456 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.89748 | − | 2.35618i | 0.339925 | − | 0.135808i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.33393i | − | 0.477199i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.1578i | − | 1.26461i | −0.774719 | − | 0.632306i | \(-0.782109\pi\) | ||
0.774719 | − | 0.632306i | \(-0.217891\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.1295 | 1.14144 | 0.570719 | − | 0.821145i | \(-0.306664\pi\) | ||||
0.570719 | + | 0.821145i | \(0.306664\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17.2233i | − | 0.973520i | −0.873536 | − | 0.486760i | \(-0.838179\pi\) | ||
0.873536 | − | 0.486760i | \(-0.161821\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 29.3779i | − | 1.65003i | −0.565113 | − | 0.825013i | \(-0.691168\pi\) | ||
0.565113 | − | 0.825013i | \(-0.308832\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.62839 | 0.371119 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.15710i | − | 0.0643827i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.3725i | 0.963652i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.53110 | − | 1.01123i | 0.139544 | − | 0.0557510i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2550 | −0.728562 | −0.364281 | − | 0.931289i | \(-0.618685\pi\) | ||||
−0.364281 | + | 0.931289i | \(0.618685\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.02866 | −0.0562015 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.1728 | 0.663097 | 0.331549 | − | 0.943438i | \(-0.392429\pi\) | ||||
0.331549 | + | 0.943438i | \(0.392429\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.47568 | −0.0799123 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.72915 | + | 16.8303i | −0.417335 | + | 0.908753i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 8.55745i | − | 0.459388i | −0.973263 | − | 0.229694i | \(-0.926227\pi\) | ||
0.973263 | − | 0.229694i | \(-0.0737725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.3840i | 1.14466i | 0.820024 | + | 0.572329i | \(0.193960\pi\) | ||||
−0.820024 | + | 0.572329i | \(0.806040\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.9774 | 1.91489 | 0.957443 | − | 0.288623i | \(-0.0931976\pi\) | ||||
0.957443 | + | 0.288623i | \(0.0931976\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 6.72853i | − | 0.357113i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 0.864752i | − | 0.0456399i | −0.999740 | − | 0.0228199i | \(-0.992736\pi\) | ||
0.999740 | − | 0.0228199i | \(-0.00726444\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.05971 | −0.318932 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.21778i | − | 0.168426i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 28.2287i | − | 1.47352i | −0.676152 | − | 0.736762i | \(-0.736354\pi\) | ||
0.676152 | − | 0.736762i | \(-0.263646\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.87693 | − | 22.2188i | −0.460867 | − | 1.15354i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.5074 | 1.16539 | 0.582694 | − | 0.812691i | \(-0.301999\pi\) | ||||
0.582694 | + | 0.812691i | \(0.301999\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.8732 | −0.817510 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.3306 | 0.787478 | 0.393739 | − | 0.919222i | \(-0.371181\pi\) | ||||
0.393739 | + | 0.919222i | \(0.371181\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.2215 | 1.59534 | 0.797671 | − | 0.603093i | \(-0.206065\pi\) | ||||
0.797671 | + | 0.603093i | \(0.206065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.60889 | − | 4.02702i | −0.0819966 | − | 0.205236i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 10.4695i | − | 0.530826i | −0.964135 | − | 0.265413i | \(-0.914492\pi\) | ||
0.964135 | − | 0.265413i | \(-0.0855084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.604675i | 0.0305797i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.94290 | −0.248704 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.27161i | − | 0.114009i | −0.998374 | − | 0.0570044i | \(-0.981845\pi\) | ||
0.998374 | − | 0.0570044i | \(-0.0181549\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.0822i | 0.853043i | 0.904477 | + | 0.426522i | \(0.140261\pi\) | ||||
−0.904477 | + | 0.426522i | \(0.859739\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.53384 | 0.176033 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.29898i | 0.262661i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.4145i | 1.70169i | 0.525418 | + | 0.850844i | \(0.323909\pi\) | ||||
−0.525418 | + | 0.850844i | \(0.676091\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.6554 | − | 6.65423i | 0.819560 | − | 0.327433i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8750 | −0.681098 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.4899 | −1.73380 | −0.866898 | − | 0.498486i | \(-0.833890\pi\) | ||||
−0.866898 | + | 0.498486i | \(0.833890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.1464 | −1.61546 | −0.807728 | − | 0.589555i | \(-0.799303\pi\) | ||||
−0.807728 | + | 0.589555i | \(0.799303\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.954509 | 0.0463005 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.76798 | + | 21.9461i | 0.424312 | + | 1.06205i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.80071i | 0.327578i | 0.986495 | + | 0.163789i | \(0.0523717\pi\) | ||||
−0.986495 | + | 0.163789i | \(0.947628\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.1067i | 0.725982i | 0.931793 | + | 0.362991i | \(0.118245\pi\) | ||||
−0.931793 | + | 0.362991i | \(0.881755\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.0957 | 0.626451 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.25619i | − | 0.394046i | −0.980399 | − | 0.197023i | \(-0.936873\pi\) | ||
0.980399 | − | 0.197023i | \(-0.0631274\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.0749i | 0.953788i | 0.878961 | + | 0.476894i | \(0.158238\pi\) | ||||
−0.878961 | + | 0.476894i | \(0.841762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0000 | −0.663664 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.18983i | 0.244923i | 0.992473 | + | 0.122462i | \(0.0390788\pi\) | ||||
−0.992473 | + | 0.122462i | \(0.960921\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 15.7786i | − | 0.742987i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.85284 | + | 9.64361i | 0.180624 | + | 0.452099i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.5074 | −0.912517 | −0.456259 | − | 0.889847i | \(-0.650811\pi\) | ||||
−0.456259 | + | 0.889847i | \(0.650811\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.1566 | −1.59083 | −0.795416 | − | 0.606064i | \(-0.792748\pi\) | ||||
−0.795416 | + | 0.606064i | \(0.792748\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.23866 | 0.429357 | 0.214678 | − | 0.976685i | \(-0.431130\pi\) | ||||
0.214678 | + | 0.976685i | \(0.431130\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.4374 | −0.760630 | −0.380315 | − | 0.924857i | \(-0.624184\pi\) | ||||
−0.380315 | + | 0.924857i | \(0.624184\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.70881 | − | 1.08223i | 0.125081 | − | 0.0499728i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4.21681i | − | 0.193889i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 20.6722i | − | 0.948504i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.1011 | 1.51243 | 0.756215 | − | 0.654323i | \(-0.227046\pi\) | ||||
0.756215 | + | 0.654323i | \(0.227046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 12.6896i | − | 0.578596i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.52924i | − | 0.0694393i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.1137 | 1.59115 | 0.795576 | − | 0.605853i | \(-0.207168\pi\) | ||||
0.795576 | + | 0.605853i | \(0.207168\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9560i | 0.494439i | 0.968959 | + | 0.247220i | \(0.0795169\pi\) | ||||
−0.968959 | + | 0.247220i | \(0.920483\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.872131i | 0.0392788i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.07896 | + | 17.7185i | 0.317535 | + | 0.794785i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0985 | 0.541605 | 0.270802 | − | 0.962635i | \(-0.412711\pi\) | ||||
0.270802 | + | 0.962635i | \(0.412711\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.5594 | 0.782936 | 0.391468 | − | 0.920192i | \(-0.371967\pi\) | ||||
0.391468 | + | 0.920192i | \(0.371967\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.27749 | −0.190346 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.06881 | 0.0916984 | 0.0458492 | − | 0.998948i | \(-0.485401\pi\) | ||||
0.0458492 | + | 0.998948i | \(0.485401\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.38537 | + | 8.47352i | 0.149760 | + | 0.374846i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.0597i | 0.663610i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.80978i | − | 0.0795941i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.9440 | 1.22425 | 0.612123 | − | 0.790762i | \(-0.290316\pi\) | ||||
0.612123 | + | 0.790762i | \(0.290316\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.2026i | 1.36439i | 0.731168 | + | 0.682197i | \(0.238976\pi\) | ||||
−0.731168 | + | 0.682197i | \(0.761024\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 0.194162i | − | 0.00845783i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.1565 | 0.702456 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.7855i | 1.63667i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 17.2233i | − | 0.744629i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.47352 | + | 8.91185i | 0.364980 | + | 0.383861i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.9905 | 1.63334 | 0.816669 | − | 0.577107i | \(-0.195818\pi\) | ||||
0.816669 | + | 0.577107i | \(0.195818\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.22101 | 0.352149 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.4173 | −1.34330 | −0.671652 | − | 0.740866i | \(-0.734415\pi\) | ||||
−0.671652 | + | 0.740866i | \(0.734415\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.8881 | 0.804659 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.0164 | − | 5.20034i | 0.553512 | − | 0.221141i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.8158i | 1.39045i | 0.718791 | + | 0.695226i | \(0.244696\pi\) | ||||
−0.718791 | + | 0.695226i | \(0.755304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0981i | 0.427104i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.4092 | 0.986579 | 0.493289 | − | 0.869865i | \(-0.335794\pi\) | ||||
0.493289 | + | 0.869865i | \(0.335794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 12.9712i | − | 0.545702i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 33.2320i | − | 1.39316i | −0.717480 | − | 0.696579i | \(-0.754704\pi\) | ||
0.717480 | − | 0.696579i | \(-0.245296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5996 | −0.820220 | −0.410110 | − | 0.912036i | \(-0.634510\pi\) | ||||
−0.410110 | + | 0.912036i | \(0.634510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8028i | 0.450509i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.3337i | 0.471830i | 0.971774 | + | 0.235915i | \(0.0758086\pi\) | ||||
−0.971774 | + | 0.235915i | \(0.924191\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.5377 | − | 14.5977i | 1.51584 | − | 0.605613i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.8869 | −0.657967 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.6923 | −0.523866 | −0.261933 | − | 0.965086i | \(-0.584360\pi\) | ||||
−0.261933 | + | 0.965086i | \(0.584360\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.20504 | −0.173266 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.2663 | 0.544783 | 0.272392 | − | 0.962186i | \(-0.412185\pi\) | ||||
0.272392 | + | 0.962186i | \(0.412185\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.529856 | − | 0.211690i | 0.0217220 | − | 0.00867843i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.74613i | 0.193921i | 0.995288 | + | 0.0969607i | \(0.0309121\pi\) | ||||
−0.995288 | + | 0.0969607i | \(0.969088\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.0666i | − | 0.940908i | −0.882425 | − | 0.470454i | \(-0.844090\pi\) | ||
0.882425 | − | 0.470454i | \(-0.155910\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.38365 | 0.300188 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.6212i | 1.44582i | 0.690942 | + | 0.722910i | \(0.257196\pi\) | ||||
−0.690942 | + | 0.722910i | \(0.742804\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.33393i | 0.175332i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.8931 | 1.36893 | 0.684466 | − | 0.729045i | \(-0.260036\pi\) | ||||
0.684466 | + | 0.729045i | \(0.260036\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.09014i | − | 0.0438872i | −0.999759 | − | 0.0219436i | \(-0.993015\pi\) | ||
0.999759 | − | 0.0219436i | \(-0.00698543\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 21.1907i | − | 0.851725i | −0.904788 | − | 0.425862i | \(-0.859971\pi\) | ||
0.904788 | − | 0.425862i | \(-0.140029\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.8668 | − | 14.7291i | 1.47704 | − | 0.590111i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.7003 | 0.508012 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.697214 | −0.0277997 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.9020 | 0.593239 | 0.296620 | − | 0.954996i | \(-0.404141\pi\) | ||||
0.296620 | + | 0.954996i | \(0.404141\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.50775 | −0.0598331 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.2917 | − | 21.3414i | −0.803988 | − | 0.845578i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.3260i | 0.960818i | 0.877045 | + | 0.480409i | \(0.159512\pi\) | ||||
−0.877045 | + | 0.480409i | \(0.840488\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.4341i | 0.884714i | 0.896839 | + | 0.442357i | \(0.145858\pi\) | ||||
−0.896839 | + | 0.442357i | \(0.854142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.5251 | 1.47526 | 0.737631 | − | 0.675204i | \(-0.235944\pi\) | ||||
0.737631 | + | 0.675204i | \(0.235944\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.9089i | − | 0.467467i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.4549i | 1.15266i | 0.817217 | + | 0.576330i | \(0.195516\pi\) | ||||
−0.817217 | + | 0.576330i | \(0.804484\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.5365 | −0.646134 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 43.8012i | − | 1.70625i | −0.521703 | − | 0.853127i | \(-0.674703\pi\) | ||
0.521703 | − | 0.853127i | \(-0.325297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 8.90182i | − | 0.346241i | −0.984901 | − | 0.173120i | \(-0.944615\pi\) | ||
0.984901 | − | 0.173120i | \(-0.0553850\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.58464 | − | 11.4753i | −0.177785 | − | 0.444992i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.87050 | −0.382187 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.6919 | 0.605778 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.0761 | 0.812423 | 0.406211 | − | 0.913779i | \(-0.366850\pi\) | ||||
0.406211 | + | 0.913779i | \(0.366850\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.1464 | 1.19705 | 0.598526 | − | 0.801103i | \(-0.295753\pi\) | ||||
0.598526 | + | 0.801103i | \(0.295753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.60889 | + | 4.02702i | 0.0617435 | + | 0.154543i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.5805i | 0.749225i | 0.927181 | + | 0.374613i | \(0.122224\pi\) | ||||
−0.927181 | + | 0.374613i | \(0.877776\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 13.9809i | − | 0.534182i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.0446 | 1.44939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.1739i | 1.30004i | 0.759919 | + | 0.650018i | \(0.225239\pi\) | ||||
−0.759919 | + | 0.650018i | \(0.774761\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.983710i | 0.0373143i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.07608 | 0.0786370 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 42.1904i | − | 1.59351i | −0.604304 | − | 0.796754i | \(-0.706549\pi\) | ||
0.604304 | − | 0.796754i | \(-0.293451\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.0998i | 0.569501i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.2641 | − | 4.50027i | 0.423630 | − | 0.169250i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.4937 | −1.40810 | −0.704052 | − | 0.710148i | \(-0.748628\pi\) | ||||
−0.704052 | + | 0.710148i | \(0.748628\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.19746 | 0.0822956 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.89536 | 0.257872 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.26820 | −0.121883 | −0.0609416 | − | 0.998141i | \(-0.519410\pi\) | ||||
−0.0609416 | + | 0.998141i | \(0.519410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.8441 | − | 39.6574i | −0.590063 | − | 1.47692i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.5811i | 0.578666i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.3997i | 0.793671i | 0.917890 | + | 0.396836i | \(0.129892\pi\) | ||||
−0.917890 | + | 0.396836i | \(0.870108\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.554827 | 0.0205210 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.3611i | − | 1.45384i | −0.686724 | − | 0.726919i | \(-0.740952\pi\) | ||
0.686724 | − | 0.726919i | \(-0.259048\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.93685i | − | 0.0713447i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.40433 | 0.345944 | 0.172972 | − | 0.984927i | \(-0.444663\pi\) | ||||
0.172972 | + | 0.984927i | \(0.444663\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.8880i | 1.20654i | 0.797535 | + | 0.603272i | \(0.206137\pi\) | ||||
−0.797535 | + | 0.603272i | \(0.793863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.35746i | − | 0.0497334i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.1203 | + | 45.3549i | 0.662103 | + | 1.65723i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.9081 | 0.872419 | 0.436209 | − | 0.899845i | \(-0.356321\pi\) | ||||
0.436209 | + | 0.899845i | \(0.356321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.8265 | −0.430411 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.2944 | 1.75529 | 0.877645 | − | 0.479312i | \(-0.159114\pi\) | ||||
0.877645 | + | 0.479312i | \(0.159114\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.5737 | −1.25330 | −0.626648 | − | 0.779302i | \(-0.715574\pi\) | ||||
−0.626648 | + | 0.779302i | \(0.715574\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.6487 | + | 8.64917i | −0.783737 | + | 0.313121i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.5186i | 1.02975i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.1831i | 1.19661i | 0.801267 | + | 0.598307i | \(0.204160\pi\) | ||||
−0.801267 | + | 0.598307i | \(0.795840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.5014 | 1.34883 | 0.674415 | − | 0.738352i | \(-0.264396\pi\) | ||||
0.674415 | + | 0.738352i | \(0.264396\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.46880i | − | 0.124603i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 44.9623i | − | 1.61094i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.6691 | 0.453335 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.3352i | 0.725793i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.33842i | 0.332879i | 0.986052 | + | 0.166439i | \(0.0532270\pi\) | ||||
−0.986052 | + | 0.166439i | \(0.946773\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.6468 | + | 34.1576i | 0.485223 | + | 1.21451i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.5777 | −1.33442 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.6239 | −1.12018 | −0.560089 | − | 0.828433i | \(-0.689233\pi\) | ||||
−0.560089 | + | 0.828433i | \(0.689233\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.238122 | 0.00842416 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.05872 | 0.213808 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.39583 | + | 5.99673i | 0.0844420 | + | 0.211357i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 27.7318i | − | 0.974998i | −0.873123 | − | 0.487499i | \(-0.837909\pi\) | ||
0.873123 | − | 0.487499i | \(-0.162091\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.45321i | 0.296832i | 0.988925 | + | 0.148416i | \(0.0474175\pi\) | ||||
−0.988925 | + | 0.148416i | \(0.952582\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.07922 | 0.283003 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 12.0161i | − | 0.420390i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 0.496589i | − | 0.0173311i | −0.999962 | − | 0.00866554i | \(-0.997242\pi\) | ||
0.999962 | − | 0.00866554i | \(-0.00275836\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.0721 | −1.67569 | −0.837844 | − | 0.545910i | \(-0.816184\pi\) | ||||
−0.837844 | + | 0.545910i | \(0.816184\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.6211i | 0.404107i | 0.979375 | + | 0.202053i | \(0.0647614\pi\) | ||||
−0.979375 | + | 0.202053i | \(0.935239\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.4221i | 1.36919i | 0.728926 | + | 0.684593i | \(0.240020\pi\) | ||||
−0.728926 | + | 0.684593i | \(0.759980\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.17258 | + | 1.11490i | −0.0406274 | + | 0.0386291i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.99390 | −0.242034 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.9656 | −0.827384 | −0.413692 | − | 0.910417i | \(-0.635761\pi\) | ||||
−0.413692 | + | 0.910417i | \(0.635761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.7636 | 0.509091 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.38343 | −0.150795 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.4437 | + | 7.76821i | −0.668093 | + | 0.266919i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 7.89084i | − | 0.270495i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17.9030i | − | 0.612988i | −0.951873 | − | 0.306494i | \(-0.900844\pi\) | ||
0.951873 | − | 0.306494i | \(-0.0991559\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.1623 | −0.517934 | −0.258967 | − | 0.965886i | \(-0.583382\pi\) | ||||
−0.258967 | + | 0.965886i | \(0.583382\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 19.8862i | − | 0.678508i | −0.940695 | − | 0.339254i | \(-0.889825\pi\) | ||
0.940695 | − | 0.339254i | \(-0.110175\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.1813i | 0.721018i | 0.932756 | + | 0.360509i | \(0.117397\pi\) | ||||
−0.932756 | + | 0.360509i | \(0.882603\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.53649 | −0.0862434 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.30695i | − | 0.315717i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.63821i | 0.157160i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.9277 | − | 8.36112i | 0.707487 | − | 0.282657i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.89802 | −0.165394 | −0.0826972 | − | 0.996575i | \(-0.526353\pi\) | ||||
−0.0826972 | + | 0.996575i | \(0.526353\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0502 | 0.473362 | 0.236681 | − | 0.971587i | \(-0.423940\pi\) | ||||
0.236681 | + | 0.971587i | \(0.423940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.4928 | −0.588679 | −0.294340 | − | 0.955701i | \(-0.595100\pi\) | ||||
−0.294340 | + | 0.955701i | \(0.595100\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.286309 | −0.00961331 | −0.00480665 | − | 0.999988i | \(-0.501530\pi\) | ||||
−0.00480665 | + | 0.999988i | \(0.501530\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.97041 | − | 1.58627i | 0.133163 | − | 0.0532019i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.15710i | − | 0.172576i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 17.1534i | − | 0.573376i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.16943 | 0.105706 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.09031i | − | 0.0696385i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.89084i | 0.262300i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.5299 | 0.548865 | 0.274432 | − | 0.961606i | \(-0.411510\pi\) | ||||
0.274432 | + | 0.961606i | \(0.411510\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 48.8889i | − | 1.61976i | −0.586594 | − | 0.809881i | \(-0.699532\pi\) | ||
0.586594 | − | 0.809881i | \(-0.300468\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 26.1251i | − | 0.864616i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 43.5463 | − | 17.3977i | 1.43803 | − | 0.574524i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.24441 | 0.271958 | 0.135979 | − | 0.990712i | \(-0.456582\pi\) | ||||
0.135979 | + | 0.990712i | \(0.456582\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.3390 | −0.998619 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.4561 | −0.409553 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.4613 | −0.638504 | −0.319252 | − | 0.947670i | \(-0.603432\pi\) | ||||
−0.319252 | + | 0.947670i | \(0.603432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.1459 | + | 25.3949i | 0.791349 | + | 0.832286i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 0.378857i | − | 0.0123899i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.2022i | − | 0.627310i | −0.949537 | − | 0.313655i | \(-0.898446\pi\) | ||
0.949537 | − | 0.313655i | \(-0.101554\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.3809 | −1.05559 | −0.527794 | − | 0.849373i | \(-0.676981\pi\) | ||||
−0.527794 | + | 0.849373i | \(0.676981\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.4963i | 0.765146i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.5365i | 1.77220i | 0.463496 | + | 0.886099i | \(0.346595\pi\) | ||||
−0.463496 | + | 0.886099i | \(0.653405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.5090 | −0.470981 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 41.5158i | − | 1.34483i | −0.740175 | − | 0.672414i | \(-0.765257\pi\) | ||
0.740175 | − | 0.672414i | \(-0.234743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.6434i | 0.765084i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.7090 | + | 36.8165i | 0.474979 | + | 1.18887i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.2944 | 0.977238 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.377245 | −0.0121439 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.7358 | −1.08487 | −0.542435 | − | 0.840098i | \(-0.682497\pi\) | ||||
−0.542435 | + | 0.840098i | \(0.682497\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.5369 | −1.17253 | −0.586263 | − | 0.810121i | \(-0.699401\pi\) | ||||
−0.586263 | + | 0.810121i | \(0.699401\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.03494 | − | 2.59045i | −0.0331788 | − | 0.0830460i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.7254i | 1.43089i | 0.698669 | + | 0.715445i | \(0.253776\pi\) | ||||
−0.698669 | + | 0.715445i | \(0.746224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 26.3605i | − | 0.842484i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.7614 | 1.39577 | 0.697885 | − | 0.716209i | \(-0.254124\pi\) | ||||
0.697885 | + | 0.716209i | \(0.254124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.07631i | 0.225470i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.27935i | 0.199672i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.4844 | 0.555410 | 0.277705 | − | 0.960666i | \(-0.410426\pi\) | ||||
0.277705 | + | 0.960666i | \(0.410426\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 24.0602i | − | 0.762761i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 23.3062i | − | 0.738115i | −0.929407 | − | 0.369058i | \(-0.879680\pi\) | ||
0.929407 | − | 0.369058i | \(-0.120320\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3024.2.k.l.1889.10 | 16 | ||
3.2 | odd | 2 | inner | 3024.2.k.l.1889.8 | 16 | ||
4.3 | odd | 2 | 1512.2.k.b.377.9 | yes | 16 | ||
7.6 | odd | 2 | inner | 3024.2.k.l.1889.7 | 16 | ||
12.11 | even | 2 | 1512.2.k.b.377.7 | ✓ | 16 | ||
21.20 | even | 2 | inner | 3024.2.k.l.1889.9 | 16 | ||
28.27 | even | 2 | 1512.2.k.b.377.8 | yes | 16 | ||
84.83 | odd | 2 | 1512.2.k.b.377.10 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.k.b.377.7 | ✓ | 16 | 12.11 | even | 2 | ||
1512.2.k.b.377.8 | yes | 16 | 28.27 | even | 2 | ||
1512.2.k.b.377.9 | yes | 16 | 4.3 | odd | 2 | ||
1512.2.k.b.377.10 | yes | 16 | 84.83 | odd | 2 | ||
3024.2.k.l.1889.7 | 16 | 7.6 | odd | 2 | inner | ||
3024.2.k.l.1889.8 | 16 | 3.2 | odd | 2 | inner | ||
3024.2.k.l.1889.9 | 16 | 21.20 | even | 2 | inner | ||
3024.2.k.l.1889.10 | 16 | 1.1 | even | 1 | trivial |