Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(1151,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1440.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.h (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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.4 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.1151 |
Dual form | 1440.2.h.a.1151.1 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.41421i | 1.29045i | 0.763992 | + | 0.645226i | \(0.223237\pi\) | ||||
−0.763992 | + | 0.645226i | \(0.776763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.58579 | −0.779644 | −0.389822 | − | 0.920890i | \(-0.627463\pi\) | ||||
−0.389822 | + | 0.920890i | \(0.627463\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.41421 | −0.946932 | −0.473466 | − | 0.880812i | \(-0.656997\pi\) | ||||
−0.473466 | + | 0.880812i | \(0.656997\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1.17157i | − 0.284148i | −0.989856 | − | 0.142074i | \(-0.954623\pi\) | ||||
0.989856 | − | 0.142074i | \(-0.0453771\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.82843 | −1.00680 | −0.503398 | − | 0.864054i | \(-0.667917\pi\) | ||||
−0.503398 | + | 0.864054i | \(0.667917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 6.00000i | − 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.48528i | 1.16479i | 0.812906 | + | 0.582395i | \(0.197884\pi\) | ||||
−0.812906 | + | 0.582395i | \(0.802116\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.41421 | −0.577107 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.07107 | −1.49127 | −0.745637 | − | 0.666352i | \(-0.767855\pi\) | ||||
−0.745637 | + | 0.666352i | \(0.767855\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 11.0711i | − 1.72901i | −0.502624 | − | 0.864505i | \(-0.667632\pi\) | ||||
0.502624 | − | 0.864505i | \(-0.332368\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 6.82843i | − 1.04133i | −0.853762 | − | 0.520663i | \(-0.825685\pi\) | ||||
0.853762 | − | 0.520663i | \(-0.174315\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.65685 | 0.825137 | 0.412568 | − | 0.910927i | \(-0.364632\pi\) | ||||
0.412568 | + | 0.910927i | \(0.364632\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.65685 | −0.665265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.17157i | − 0.160928i | −0.996758 | − | 0.0804640i | \(-0.974360\pi\) | ||||
0.996758 | − | 0.0804640i | \(-0.0256402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.58579i | − 0.348667i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.58579 | −0.857396 | −0.428698 | − | 0.903448i | \(-0.641028\pi\) | ||||
−0.428698 | + | 0.903448i | \(0.641028\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.8284 | 1.64251 | 0.821256 | − | 0.570560i | \(-0.193274\pi\) | ||||
0.821256 | + | 0.570560i | \(0.193274\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 3.41421i | − 0.423481i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000i | 0.977356i | 0.872464 | + | 0.488678i | \(0.162521\pi\) | ||||
−0.872464 | + | 0.488678i | \(0.837479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4853 | −1.22721 | −0.613605 | − | 0.789613i | \(-0.710281\pi\) | ||||
−0.613605 | + | 0.789613i | \(0.710281\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 8.82843i | − 1.00609i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.4853i | 1.62972i | 0.579657 | + | 0.814861i | \(0.303187\pi\) | ||||
−0.579657 | + | 0.814861i | \(0.696813\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.17157 | −1.00671 | −0.503355 | − | 0.864079i | \(-0.667901\pi\) | ||||
−0.503355 | + | 0.864079i | \(0.667901\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.17157 | 0.127075 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.24264i | 0.449719i | 0.974391 | + | 0.224860i | \(0.0721923\pi\) | ||||
−0.974391 | + | 0.224860i | \(0.927808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 11.6569i | − 1.22197i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.48528 | 0.252342 | 0.126171 | − | 0.992009i | \(-0.459731\pi\) | ||||
0.126171 | + | 0.992009i | \(0.459731\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 4.82843i | − 0.480446i | −0.970718 | − | 0.240223i | \(-0.922779\pi\) | ||||
0.970718 | − | 0.240223i | \(-0.0772206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.5563i | 1.72988i | 0.501877 | + | 0.864939i | \(0.332643\pi\) | ||||
−0.501877 | + | 0.864939i | \(0.667357\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.8284 | −1.43352 | −0.716759 | − | 0.697321i | \(-0.754375\pi\) | ||||
−0.716759 | + | 0.697321i | \(0.754375\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.17157 | −0.686912 | −0.343456 | − | 0.939169i | \(-0.611598\pi\) | ||||
−0.343456 | + | 0.939169i | \(0.611598\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.65685i | 0.155864i | 0.996959 | + | 0.0779319i | \(0.0248317\pi\) | ||||
−0.996959 | + | 0.0779319i | \(0.975168\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.82843i | − 0.450253i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.31371 | −0.392155 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.7279i | 0.951949i | 0.879459 | + | 0.475975i | \(0.157905\pi\) | ||||
−0.879459 | + | 0.475975i | \(0.842095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7279 | −1.11204 | −0.556022 | − | 0.831168i | \(-0.687673\pi\) | ||||
−0.556022 | + | 0.831168i | \(0.687673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.3137i | 1.65008i | 0.565073 | + | 0.825041i | \(0.308848\pi\) | ||||
−0.565073 | + | 0.825041i | \(0.691152\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 3.65685i | − 0.310170i | −0.987901 | − | 0.155085i | \(-0.950435\pi\) | ||||
0.987901 | − | 0.155085i | \(-0.0495652\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.82843 | 0.738270 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.82843i | 0.723253i | 0.932323 | + | 0.361626i | \(0.117778\pi\) | ||||
−0.932323 | + | 0.361626i | \(0.882222\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 15.6569i | − 1.27414i | −0.770807 | − | 0.637068i | \(-0.780147\pi\) | ||||
0.770807 | − | 0.637068i | \(-0.219853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.48528 | −0.520910 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.75736 | −0.778722 | −0.389361 | − | 0.921085i | \(-0.627304\pi\) | ||||
−0.389361 | + | 0.921085i | \(0.627304\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 16.4853i | − 1.29922i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 0.485281i | − 0.0380102i | −0.999819 | − | 0.0190051i | \(-0.993950\pi\) | ||||
0.999819 | − | 0.0190051i | \(-0.00604987\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.7990 | 1.68686 | 0.843428 | − | 0.537242i | \(-0.180534\pi\) | ||||
0.843428 | + | 0.537242i | \(0.180534\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.34315 | −0.103319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 8.48528i | − 0.645124i | −0.946548 | − | 0.322562i | \(-0.895456\pi\) | ||||
0.946548 | − | 0.322562i | \(-0.104544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.41421i | − 0.258090i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.0416 | 1.79696 | 0.898478 | − | 0.439019i | \(-0.144674\pi\) | ||||
0.898478 | + | 0.439019i | \(0.144674\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.51472 | 0.112588 | 0.0562941 | − | 0.998414i | \(-0.482072\pi\) | ||||
0.0562941 | + | 0.998414i | \(0.482072\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 9.07107i | − 0.666918i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.02944i | 0.221534i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.51472 | 0.254316 | 0.127158 | − | 0.991882i | \(-0.459414\pi\) | ||||
0.127158 | + | 0.991882i | \(0.459414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.9706 | 1.36553 | 0.682765 | − | 0.730638i | \(-0.260777\pi\) | ||||
0.682765 | + | 0.730638i | \(0.260777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3137i | 1.51854i | 0.650776 | + | 0.759269i | \(0.274444\pi\) | ||||
−0.650776 | + | 0.759269i | \(0.725556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.6569i | 1.10988i | 0.831889 | + | 0.554942i | \(0.187260\pi\) | ||||
−0.831889 | + | 0.554942i | \(0.812740\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.4853 | 1.43778 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0711 | 0.773237 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 26.0000i | − 1.78991i | −0.446153 | − | 0.894957i | \(-0.647206\pi\) | ||||
0.446153 | − | 0.894957i | \(-0.352794\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.82843 | 0.465695 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.1421 | −1.50311 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000i | 0.269069i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2.72792i | − 0.182675i | −0.995820 | − | 0.0913376i | \(-0.970886\pi\) | ||||
0.995820 | − | 0.0913376i | \(-0.0291142\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.65685 | −0.375459 | −0.187729 | − | 0.982221i | \(-0.560113\pi\) | ||||
−0.187729 | + | 0.982221i | \(0.560113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.9706 | −0.989283 | −0.494641 | − | 0.869097i | \(-0.664701\pi\) | ||||
−0.494641 | + | 0.869097i | \(0.664701\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 2.14214i | − 0.140336i | −0.997535 | − | 0.0701680i | \(-0.977646\pi\) | ||||
0.997535 | − | 0.0701680i | \(-0.0223535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.65685i | 0.369012i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.4558 | −1.64660 | −0.823301 | − | 0.567605i | \(-0.807870\pi\) | ||||
−0.823301 | + | 0.567605i | \(0.807870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.9706 | 1.86616 | 0.933079 | − | 0.359671i | \(-0.117111\pi\) | ||||
0.933079 | + | 0.359671i | \(0.117111\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 4.65685i | − 0.297516i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.8995 | −0.877328 | −0.438664 | − | 0.898651i | \(-0.644548\pi\) | ||||
−0.438664 | + | 0.898651i | \(0.644548\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.4853 | 0.784943 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 30.9706i | − 1.92442i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.51472 | 0.586703 | 0.293351 | − | 0.956005i | \(-0.405229\pi\) | ||||
0.293351 | + | 0.956005i | \(0.405229\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.17157 | 0.0719691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.65685i | 0.466847i | 0.972375 | + | 0.233423i | \(0.0749928\pi\) | ||||
−0.972375 | + | 0.233423i | \(0.925007\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 22.0000i | − 1.33640i | −0.743980 | − | 0.668202i | \(-0.767064\pi\) | ||||
0.743980 | − | 0.668202i | \(-0.232936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.58579 | 0.155929 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.27208 | −0.316768 | −0.158384 | − | 0.987378i | \(-0.550628\pi\) | ||||
−0.158384 | + | 0.987378i | \(0.550628\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5858i | 1.34736i | 0.739025 | + | 0.673678i | \(0.235286\pi\) | ||||
−0.739025 | + | 0.673678i | \(0.764714\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.31371i | 0.434755i | 0.976088 | + | 0.217377i | \(0.0697502\pi\) | ||||
−0.976088 | + | 0.217377i | \(0.930250\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 37.7990 | 2.23120 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.6274 | 0.919260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.3137i | 1.71253i | 0.516541 | + | 0.856263i | \(0.327219\pi\) | ||||
−0.516541 | + | 0.856263i | \(0.672781\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 6.58579i | − 0.383439i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.4853 | 0.953368 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.3137 | 1.34378 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.8284i | 0.734554i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.0000i | 1.36975i | 0.728659 | + | 0.684876i | \(0.240144\pi\) | ||||
−0.728659 | + | 0.684876i | \(0.759856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.1421 | −1.48238 | −0.741192 | − | 0.671293i | \(-0.765739\pi\) | ||||
−0.741192 | + | 0.671293i | \(0.765739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.65685 | 0.432791 | 0.216395 | − | 0.976306i | \(-0.430570\pi\) | ||||
0.216395 | + | 0.976306i | \(0.430570\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.6274i | 0.933889i | 0.884287 | + | 0.466944i | \(0.154645\pi\) | ||||
−0.884287 | + | 0.466944i | \(0.845355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.5147i | 0.868657i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.41421 | 0.189386 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.3137i | 1.06480i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 28.9706i | − 1.59237i | −0.605056 | − | 0.796183i | \(-0.706849\pi\) | ||||
0.605056 | − | 0.796183i | \(-0.293151\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.4853 | −1.44275 | −0.721373 | − | 0.692547i | \(-0.756488\pi\) | ||||
−0.721373 | + | 0.692547i | \(0.756488\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 16.7696i | − 0.908122i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.3431 | 1.19944 | 0.599721 | − | 0.800209i | \(-0.295278\pi\) | ||||
0.599721 | + | 0.800209i | \(0.295278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.4558 | 1.68379 | 0.841896 | − | 0.539639i | \(-0.181439\pi\) | ||||
0.841896 | + | 0.539639i | \(0.181439\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.85786i | − 0.0988841i | −0.998777 | − | 0.0494421i | \(-0.984256\pi\) | ||||
0.998777 | − | 0.0494421i | \(-0.0157443\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 5.65685i | − 0.300235i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.8284 | 0.993726 | 0.496863 | − | 0.867829i | \(-0.334485\pi\) | ||||
0.496863 | + | 0.867829i | \(0.334485\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 10.4853i | − 0.548825i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 24.8701i | − 1.29821i | −0.760700 | − | 0.649103i | \(-0.775144\pi\) | ||||
0.760700 | − | 0.649103i | \(-0.224856\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.7279 | −0.555471 | −0.277735 | − | 0.960658i | \(-0.589584\pi\) | ||||
−0.277735 | + | 0.960658i | \(0.589584\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.4853i | 1.05505i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.31371i | 0.478413i | 0.970969 | + | 0.239207i | \(0.0768873\pi\) | ||||
−0.970969 | + | 0.239207i | \(0.923113\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.3431 | −0.528510 | −0.264255 | − | 0.964453i | \(-0.585126\pi\) | ||||
−0.264255 | + | 0.964453i | \(0.585126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.82843 | 0.449938 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.3431i | 0.625822i | 0.949782 | + | 0.312911i | \(0.101304\pi\) | ||||
−0.949782 | + | 0.312911i | \(0.898696\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.65685i | 0.286079i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.4853 | −0.728834 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.7279 | 0.739173 | 0.369587 | − | 0.929196i | \(-0.379499\pi\) | ||||
0.369587 | + | 0.929196i | \(0.379499\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 0.727922i | − 0.0363507i | −0.999835 | − | 0.0181753i | \(-0.994214\pi\) | ||||
0.999835 | − | 0.0181753i | \(-0.00578571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 22.1421i | − 1.10298i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.4558 | 1.16266 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.2843 | −1.89304 | −0.946518 | − | 0.322652i | \(-0.895426\pi\) | ||||
−0.946518 | + | 0.322652i | \(0.895426\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 22.4853i | − 1.10643i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 9.17157i | − 0.450215i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.3848 | 1.87522 | 0.937610 | − | 0.347690i | \(-0.113034\pi\) | ||||
0.937610 | + | 0.347690i | \(0.113034\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.17157i | 0.0568296i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.7990i | 2.11958i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.14214 | −0.103183 | −0.0515915 | − | 0.998668i | \(-0.516429\pi\) | ||||
−0.0515915 | + | 0.998668i | \(0.516429\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.4853 | −0.696118 | −0.348059 | − | 0.937473i | \(-0.613159\pi\) | ||||
−0.348059 | + | 0.937473i | \(0.613159\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 18.2843i | − 0.872661i | −0.899787 | − | 0.436330i | \(-0.856278\pi\) | ||||
0.899787 | − | 0.436330i | \(-0.143722\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.6274 | 1.26511 | 0.632553 | − | 0.774517i | \(-0.282007\pi\) | ||||
0.632553 | + | 0.774517i | \(0.282007\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.24264 | −0.201120 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 18.5858i | − 0.877117i | −0.898703 | − | 0.438559i | \(-0.855489\pi\) | ||||
0.898703 | − | 0.438559i | \(-0.144511\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.6274i | 1.34801i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.6569 | 0.546482 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.48528 | 0.116257 | 0.0581283 | − | 0.998309i | \(-0.481487\pi\) | ||||
0.0581283 | + | 0.998309i | \(0.481487\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 24.8284i | − 1.15638i | −0.815904 | − | 0.578188i | \(-0.803760\pi\) | ||||
0.815904 | − | 0.578188i | \(-0.196240\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 17.0711i | − 0.793360i | −0.917957 | − | 0.396680i | \(-0.870162\pi\) | ||||
0.917957 | − | 0.396680i | \(-0.129838\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.1127 | −1.43972 | −0.719862 | − | 0.694117i | \(-0.755795\pi\) | ||||
−0.719862 | + | 0.694117i | \(0.755795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.3137 | −1.26123 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.6569i | 0.811863i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.3137 | −1.24800 | −0.623998 | − | 0.781426i | \(-0.714493\pi\) | ||||
−0.623998 | + | 0.781426i | \(0.714493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.9706 | 1.41214 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.48528i | 0.112851i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 10.7279i | − 0.486129i | −0.970010 | − | 0.243064i | \(-0.921847\pi\) | ||||
0.970010 | − | 0.243064i | \(-0.0781526\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.0711 | 1.40222 | 0.701109 | − | 0.713054i | \(-0.252689\pi\) | ||||
0.701109 | + | 0.713054i | \(0.252689\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.02944 | −0.316590 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 19.3137i | − 0.866338i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.6274i | 0.833878i | 0.908935 | + | 0.416939i | \(0.136897\pi\) | ||||
−0.908935 | + | 0.416939i | \(0.863103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.2843 | −1.61784 | −0.808918 | − | 0.587922i | \(-0.799946\pi\) | ||||
−0.808918 | + | 0.587922i | \(0.799946\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.82843 | 0.214862 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.14214i | 0.360894i | 0.983585 | + | 0.180447i | \(0.0577544\pi\) | ||||
−0.983585 | + | 0.180447i | \(0.942246\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 35.7990i | − 1.58365i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.5563 | −0.773625 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.6274 | −0.643313 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.727922i | 0.0318908i | 0.999873 | + | 0.0159454i | \(0.00507580\pi\) | ||||
−0.999873 | + | 0.0159454i | \(0.994924\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.51472i | − 0.328596i | −0.986411 | − | 0.164298i | \(-0.947464\pi\) | ||||
0.986411 | − | 0.164298i | \(-0.0525358\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.59798 | 0.330973 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.7990i | 1.63726i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 14.8284i | − 0.641089i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0416 | 0.518670 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.8284 | 1.23943 | 0.619715 | − | 0.784827i | \(-0.287248\pi\) | ||||
0.619715 | + | 0.784827i | \(0.287248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 7.17157i | − 0.307196i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4853i | 0.704860i | 0.935838 | + | 0.352430i | \(0.114644\pi\) | ||||
−0.935838 | + | 0.352430i | \(0.885356\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −49.4558 | −2.10308 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.4853i | 0.867989i | 0.900915 | + | 0.433995i | \(0.142896\pi\) | ||||
−0.900915 | + | 0.433995i | \(0.857104\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.3137i | 0.986065i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.34315 | 0.267332 | 0.133666 | − | 0.991026i | \(-0.457325\pi\) | ||||
0.133666 | + | 0.991026i | \(0.457325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.65685 | −0.0697044 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 9.21320i | − 0.386238i | −0.981175 | − | 0.193119i | \(-0.938140\pi\) | ||||
0.981175 | − | 0.193119i | \(-0.0618603\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.97056i | 0.208012i | 0.994577 | + | 0.104006i | \(0.0331660\pi\) | ||||
−0.994577 | + | 0.104006i | \(0.966834\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.82843 | 0.201359 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.4558 | 0.643435 | 0.321718 | − | 0.946836i | \(-0.395740\pi\) | ||||
0.321718 | + | 0.946836i | \(0.395740\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 31.3137i | − 1.29911i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.02944i | 0.125466i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.1421 | −1.07900 | −0.539501 | − | 0.841985i | \(-0.681387\pi\) | ||||
−0.539501 | + | 0.841985i | \(0.681387\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.3431i | 0.424742i | 0.977189 | + | 0.212371i | \(0.0681185\pi\) | ||||
−0.977189 | + | 0.212371i | \(0.931881\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000i | 0.163984i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.1421 | −1.72188 | −0.860940 | − | 0.508706i | \(-0.830124\pi\) | ||||
−0.860940 | + | 0.508706i | \(0.830124\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6863 | 0.680648 | 0.340324 | − | 0.940308i | \(-0.389463\pi\) | ||||
0.340324 | + | 0.940308i | \(0.389463\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 4.31371i | − 0.175377i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.21320i | 0.130420i | 0.997872 | + | 0.0652100i | \(0.0207717\pi\) | ||||
−0.997872 | + | 0.0652100i | \(0.979228\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.3137 | −0.781349 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.21320 | −0.129780 | −0.0648900 | − | 0.997892i | \(-0.520670\pi\) | ||||
−0.0648900 | + | 0.997892i | \(0.520670\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 26.8284i | − 1.08007i | −0.841642 | − | 0.540036i | \(-0.818411\pi\) | ||||
0.841642 | − | 0.540036i | \(-0.181589\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9706i | 0.923265i | 0.887071 | + | 0.461632i | \(0.152736\pi\) | ||||
−0.887071 | + | 0.461632i | \(0.847264\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.4853 | −0.580341 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.6274i | 0.423743i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.17157i | 0.285496i | 0.989759 | + | 0.142748i | \(0.0455938\pi\) | ||||
−0.989759 | + | 0.142748i | \(0.954406\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.7279 | −0.425725 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.8995 | 0.629961 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 43.5563i | − 1.72037i | −0.509980 | − | 0.860186i | \(-0.670347\pi\) | ||||
0.509980 | − | 0.860186i | \(-0.329653\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.1127i | 1.38471i | 0.721557 | + | 0.692355i | \(0.243427\pi\) | ||||
−0.721557 | + | 0.692355i | \(0.756573\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.6863 | −0.498750 | −0.249375 | − | 0.968407i | \(-0.580225\pi\) | ||||
−0.249375 | + | 0.968407i | \(0.580225\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.0294 | 0.668464 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 19.6569i | − 0.769232i | −0.923077 | − | 0.384616i | \(-0.874334\pi\) | ||||
0.923077 | − | 0.384616i | \(-0.125666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 12.7279i | − 0.497321i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.58579 | −0.256546 | −0.128273 | − | 0.991739i | \(-0.540943\pi\) | ||||
−0.128273 | + | 0.991739i | \(0.540943\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.4264 | −1.57240 | −0.786202 | − | 0.617969i | \(-0.787956\pi\) | ||||
−0.786202 | + | 0.617969i | \(0.787956\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.9706i | 1.12174i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.1716 | −1.28057 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 51.4558 | 1.98348 | 0.991739 | − | 0.128276i | \(-0.0409443\pi\) | ||||
0.991739 | + | 0.128276i | \(0.0409443\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.68629i | 0.256975i | 0.991711 | + | 0.128488i | \(0.0410122\pi\) | ||||
−0.991711 | + | 0.128488i | \(0.958988\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.48528i | 0.325635i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.8284 | −0.414338 | −0.207169 | − | 0.978305i | \(-0.566425\pi\) | ||||
−0.207169 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.3137 | −0.737939 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.00000i | 0.152388i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000i | 0.304334i | 0.988355 | + | 0.152167i | \(0.0486252\pi\) | ||||
−0.988355 | + | 0.152167i | \(0.951375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.65685 | 0.138712 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.9706 | −0.491295 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 9.51472i | − 0.359366i | −0.983725 | − | 0.179683i | \(-0.942493\pi\) | ||||
0.983725 | − | 0.179683i | \(-0.0575072\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.4853 | 0.619993 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.97056 | 0.261785 | 0.130892 | − | 0.991397i | \(-0.458216\pi\) | ||||
0.130892 | + | 0.991397i | \(0.458216\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 31.3137i | − 1.17271i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.82843i | 0.330164i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.8284 | 0.403832 | 0.201916 | − | 0.979403i | \(-0.435283\pi\) | ||||
0.201916 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.9411 | −2.23232 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.00000i | 0.222834i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 26.9289i | − 0.998739i | −0.866389 | − | 0.499369i | \(-0.833565\pi\) | ||||
0.866389 | − | 0.499369i | \(-0.166435\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.1005 | −0.446942 | −0.223471 | − | 0.974711i | \(-0.571739\pi\) | ||||
−0.223471 | + | 0.974711i | \(0.571739\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 20.6863i | − 0.761989i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 22.3431i | − 0.821906i | −0.911657 | − | 0.410953i | \(-0.865196\pi\) | ||||
0.911657 | − | 0.410953i | \(-0.134804\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.0000 | −1.76095 | −0.880475 | − | 0.474093i | \(-0.842776\pi\) | ||||
−0.880475 | + | 0.474093i | \(0.842776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.82843 | −0.323449 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 50.6274i | − 1.84989i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.8284i | 1.05196i | 0.850496 | + | 0.525982i | \(0.176302\pi\) | ||||
−0.850496 | + | 0.525982i | \(0.823698\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.6569 | 0.569811 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −52.8701 | −1.92159 | −0.960797 | − | 0.277251i | \(-0.910577\pi\) | ||||
−0.960797 | + | 0.277251i | \(0.910577\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.8701i | 1.11904i | 0.828817 | + | 0.559519i | \(0.189014\pi\) | ||||
−0.828817 | + | 0.559519i | \(0.810986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 24.4853i | − 0.886427i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.4853 | 0.811896 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.34315 | −0.0844960 | −0.0422480 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422480 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 41.3137i | − 1.48595i | −0.669319 | − | 0.742975i | \(-0.733414\pi\) | ||||
0.669319 | − | 0.742975i | \(-0.266586\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 6.48528i | − 0.232958i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.6274 | 0.523410 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 9.75736i | − 0.348255i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.1421i | 1.50220i | 0.660186 | + | 0.751102i | \(0.270478\pi\) | ||||
−0.660186 | + | 0.751102i | \(0.729522\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.65685 | −0.201135 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −43.7990 | −1.55535 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 18.8284i | − 0.666937i | −0.942761 | − | 0.333469i | \(-0.891781\pi\) | ||||
0.942761 | − | 0.333469i | \(-0.108219\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 6.62742i | − 0.234461i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.1127 | 0.956786 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.4853 | 0.581030 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.0416i | 1.26716i | 0.773679 | + | 0.633578i | \(0.218414\pi\) | ||||
−0.773679 | + | 0.633578i | \(0.781586\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 3.37258i | − 0.118427i | −0.998245 | − | 0.0592137i | \(-0.981141\pi\) | ||||
0.998245 | − | 0.0592137i | \(-0.0188593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.485281 | 0.0169987 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.3137i | 1.02306i | 0.859267 | + | 0.511528i | \(0.170920\pi\) | ||||
−0.859267 | + | 0.511528i | \(0.829080\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 6.24264i | − 0.217605i | −0.994063 | − | 0.108802i | \(-0.965298\pi\) | ||||
0.994063 | − | 0.108802i | \(-0.0347016\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.6274 | −1.48230 | −0.741150 | − | 0.671339i | \(-0.765719\pi\) | ||||
−0.741150 | + | 0.671339i | \(0.765719\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.4558 | −0.675729 | −0.337865 | − | 0.941195i | \(-0.609705\pi\) | ||||
−0.337865 | + | 0.941195i | \(0.609705\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.45584i | 0.189034i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.7990i | 0.754385i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.4264 | −1.46472 | −0.732361 | − | 0.680916i | \(-0.761582\pi\) | ||||
−0.732361 | + | 0.680916i | \(0.761582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.34315i | − 0.0462056i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 14.7279i | − 0.506057i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.7990 | 1.50141 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.7574 | 0.744958 | 0.372479 | − | 0.928041i | \(-0.378508\pi\) | ||||
0.372479 | + | 0.928041i | \(0.378508\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.7990i | 1.22287i | 0.791295 | + | 0.611435i | \(0.209407\pi\) | ||||
−0.791295 | + | 0.611435i | \(0.790593\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 26.0000i | − 0.887109i | −0.896248 | − | 0.443554i | \(-0.853717\pi\) | ||||
0.896248 | − | 0.443554i | \(-0.146283\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.20101 | 0.211085 | 0.105542 | − | 0.994415i | \(-0.466342\pi\) | ||||
0.105542 | + | 0.994415i | \(0.466342\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.48528 | 0.288508 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 37.4558i | − 1.27060i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 27.3137i | − 0.925490i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.41421 | 0.115421 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.55635 | −0.0525542 | −0.0262771 | − | 0.999655i | \(-0.508365\pi\) | ||||
−0.0262771 | + | 0.999655i | \(0.508365\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 35.3553i | − 1.19115i | −0.803299 | − | 0.595576i | \(-0.796924\pi\) | ||||
0.803299 | − | 0.595576i | \(-0.203076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.4264i | 1.42776i | 0.700267 | + | 0.713881i | \(0.253064\pi\) | ||||
−0.700267 | + | 0.713881i | \(0.746936\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.8284 | 0.430736 | 0.215368 | − | 0.976533i | \(-0.430905\pi\) | ||||
0.215368 | + | 0.976533i | \(0.430905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.6274 | −1.22844 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0416i | 0.803623i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.9117 | 1.29778 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.37258 | −0.0457274 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.51472i | 0.0503510i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.85786i | 0.0616894i | 0.999524 | + | 0.0308447i | \(0.00981973\pi\) | ||||
−0.999524 | + | 0.0308447i | \(0.990180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.3431 | −0.607736 | −0.303868 | − | 0.952714i | \(-0.598278\pi\) | ||||
−0.303868 | + | 0.952714i | \(0.598278\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.7157 | 0.784876 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 43.4558i | − 1.43504i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.8284i | 0.423171i | 0.977360 | + | 0.211585i | \(0.0678626\pi\) | ||||
−0.977360 | + | 0.211585i | \(0.932137\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.3137 | 0.635718 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.07107 | 0.298255 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 45.8995i | − 1.50591i | −0.658070 | − | 0.752957i | \(-0.728627\pi\) | ||||
0.658070 | − | 0.752957i | \(-0.271373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.02944 | −0.0990732 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.9706 | −0.489067 | −0.244533 | − | 0.969641i | \(-0.578635\pi\) | ||||
−0.244533 | + | 0.969641i | \(0.578635\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.2843i | 1.37843i | 0.724558 | + | 0.689214i | \(0.242044\pi\) | ||||
−0.724558 | + | 0.689214i | \(0.757956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 53.4558i | 1.74076i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −51.5980 | −1.67671 | −0.838355 | − | 0.545125i | \(-0.816482\pi\) | ||||
−0.838355 | + | 0.545125i | \(0.816482\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.7990 | 1.16208 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 45.2548i | − 1.46595i | −0.680257 | − | 0.732974i | \(-0.738132\pi\) | ||||
0.680257 | − | 0.732974i | \(-0.261868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.51472i | 0.113734i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −65.9411 | −2.12935 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0589 | −0.356738 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.9706i | 0.610684i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 26.7279i | − 0.859512i | −0.902945 | − | 0.429756i | \(-0.858600\pi\) | ||||
0.902945 | − | 0.429756i | \(-0.141400\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.0711 | −0.868752 | −0.434376 | − | 0.900732i | \(-0.643031\pi\) | ||||
−0.434376 | + | 0.900732i | \(0.643031\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.4853 | 0.400260 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.1716i | 1.18922i | 0.804013 | + | 0.594612i | \(0.202694\pi\) | ||||
−0.804013 | + | 0.594612i | \(0.797306\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 10.9706i | − 0.350621i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.5980 | 1.26298 | 0.631490 | − | 0.775384i | \(-0.282444\pi\) | ||||
0.631490 | + | 0.775384i | \(0.282444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.3137 | −0.679111 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.9706i | 1.04840i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.3431i | 0.519157i | 0.965722 | + | 0.259579i | \(0.0835837\pi\) | ||||
−0.965722 | + | 0.259579i | \(0.916416\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.6569 | −0.496356 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.27208 | 0.166968 | 0.0834842 | − | 0.996509i | \(-0.473395\pi\) | ||||
0.0834842 | + | 0.996509i | \(0.473395\pi\) | |||||||
\(998\) | 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 | 1440.2.h.a.1151.4 | yes | 4 | |
3.2 | odd | 2 | 1440.2.h.d.1151.2 | yes | 4 | ||
4.3 | odd | 2 | 1440.2.h.d.1151.3 | yes | 4 | ||
5.2 | odd | 4 | 7200.2.o.b.7199.2 | 4 | |||
5.3 | odd | 4 | 7200.2.o.j.7199.3 | 4 | |||
5.4 | even | 2 | 7200.2.h.c.1151.1 | 4 | |||
8.3 | odd | 2 | 2880.2.h.a.1151.1 | 4 | |||
8.5 | even | 2 | 2880.2.h.d.1151.2 | 4 | |||
12.11 | even | 2 | inner | 1440.2.h.a.1151.1 | ✓ | 4 | |
15.2 | even | 4 | 7200.2.o.e.7199.2 | 4 | |||
15.8 | even | 4 | 7200.2.o.m.7199.3 | 4 | |||
15.14 | odd | 2 | 7200.2.h.i.1151.1 | 4 | |||
20.3 | even | 4 | 7200.2.o.e.7199.1 | 4 | |||
20.7 | even | 4 | 7200.2.o.m.7199.4 | 4 | |||
20.19 | odd | 2 | 7200.2.h.i.1151.4 | 4 | |||
24.5 | odd | 2 | 2880.2.h.a.1151.4 | 4 | |||
24.11 | even | 2 | 2880.2.h.d.1151.3 | 4 | |||
60.23 | odd | 4 | 7200.2.o.b.7199.1 | 4 | |||
60.47 | odd | 4 | 7200.2.o.j.7199.4 | 4 | |||
60.59 | even | 2 | 7200.2.h.c.1151.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.h.a.1151.1 | ✓ | 4 | 12.11 | even | 2 | inner | |
1440.2.h.a.1151.4 | yes | 4 | 1.1 | even | 1 | trivial | |
1440.2.h.d.1151.2 | yes | 4 | 3.2 | odd | 2 | ||
1440.2.h.d.1151.3 | yes | 4 | 4.3 | odd | 2 | ||
2880.2.h.a.1151.1 | 4 | 8.3 | odd | 2 | |||
2880.2.h.a.1151.4 | 4 | 24.5 | odd | 2 | |||
2880.2.h.d.1151.2 | 4 | 8.5 | even | 2 | |||
2880.2.h.d.1151.3 | 4 | 24.11 | even | 2 | |||
7200.2.h.c.1151.1 | 4 | 5.4 | even | 2 | |||
7200.2.h.c.1151.4 | 4 | 60.59 | even | 2 | |||
7200.2.h.i.1151.1 | 4 | 15.14 | odd | 2 | |||
7200.2.h.i.1151.4 | 4 | 20.19 | odd | 2 | |||
7200.2.o.b.7199.1 | 4 | 60.23 | odd | 4 | |||
7200.2.o.b.7199.2 | 4 | 5.2 | odd | 4 | |||
7200.2.o.e.7199.1 | 4 | 20.3 | even | 4 | |||
7200.2.o.e.7199.2 | 4 | 15.2 | even | 4 | |||
7200.2.o.j.7199.3 | 4 | 5.3 | odd | 4 | |||
7200.2.o.j.7199.4 | 4 | 60.47 | odd | 4 | |||
7200.2.o.m.7199.3 | 4 | 15.8 | even | 4 | |||
7200.2.o.m.7199.4 | 4 | 20.7 | even | 4 |