Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(17,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.bj (of order \(4\), degree \(2\), 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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.12 | ||
Character | \(\chi\) | \(=\) | 1440.593 |
Dual form | 1440.2.bj.a.17.12 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | −0.215413 | − | 2.22567i | −0.0963358 | − | 0.995349i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.32063 | − | 2.32063i | 0.877115 | − | 0.877115i | −0.116120 | − | 0.993235i | \(-0.537046\pi\) |
0.993235 | + | 0.116120i | \(0.0370456\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.57646 | 1.68137 | 0.840683 | − | 0.541528i | \(-0.182154\pi\) | ||||
0.840683 | + | 0.541528i | \(0.182154\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.79226 | − | 1.79226i | 0.497083 | − | 0.497083i | −0.413446 | − | 0.910529i | \(-0.635675\pi\) |
0.910529 | + | 0.413446i | \(0.135675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.56203 | − | 5.56203i | −1.34899 | − | 1.34899i | −0.886758 | − | 0.462233i | \(-0.847048\pi\) |
−0.462233 | − | 0.886758i | \(-0.652952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.61960 | 0.600978 | 0.300489 | − | 0.953785i | \(-0.402850\pi\) | ||||
0.300489 | + | 0.953785i | \(0.402850\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.44948 | + | 4.44948i | −0.927781 | + | 0.927781i | −0.997562 | − | 0.0697816i | \(-0.977770\pi\) |
0.0697816 | + | 0.997562i | \(0.477770\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.90719 | + | 0.958877i | −0.981439 | + | 0.191775i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.12491i | 0.394587i | 0.980345 | + | 0.197293i | \(0.0632151\pi\) | ||||
−0.980345 | + | 0.197293i | \(0.936785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.52171 | 0.812123 | 0.406061 | − | 0.913846i | \(-0.366902\pi\) | ||||
0.406061 | + | 0.913846i | \(0.366902\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.66484 | − | 4.66506i | −0.957534 | − | 0.788538i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.02845 | + | 5.02845i | 0.826673 | + | 0.826673i | 0.987055 | − | 0.160382i | \(-0.0512727\pi\) |
−0.160382 | + | 0.987055i | \(0.551273\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.73215i | 0.270516i | 0.990810 | + | 0.135258i | \(0.0431863\pi\) | ||||
−0.990810 | + | 0.135258i | \(0.956814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.19790 | + | 1.19790i | −0.182678 | + | 0.182678i | −0.792522 | − | 0.609844i | \(-0.791232\pi\) |
0.609844 | + | 0.792522i | \(0.291232\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.849681 | − | 0.849681i | −0.123939 | − | 0.123939i | 0.642417 | − | 0.766355i | \(-0.277932\pi\) |
−0.766355 | + | 0.642417i | \(0.777932\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.77064i | − | 0.538663i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.22906 | − | 4.22906i | −0.580906 | − | 0.580906i | 0.354246 | − | 0.935152i | \(-0.384737\pi\) |
−0.935152 | + | 0.354246i | \(0.884737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.20124 | − | 12.4113i | −0.161976 | − | 1.67355i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.08999i | − | 1.05323i | −0.850105 | − | 0.526614i | \(-0.823461\pi\) | ||
0.850105 | − | 0.526614i | \(-0.176539\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.13786i | − | 0.401762i | −0.979616 | − | 0.200881i | \(-0.935620\pi\) | ||
0.979616 | − | 0.200881i | \(-0.0643805\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.37505 | − | 3.60290i | −0.542658 | − | 0.446884i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.86836 | + | 1.86836i | 0.228256 | + | 0.228256i | 0.811964 | − | 0.583708i | \(-0.198399\pi\) |
−0.583708 | + | 0.811964i | \(0.698399\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.95452i | − | 0.825350i | −0.910878 | − | 0.412675i | \(-0.864595\pi\) | ||
0.910878 | − | 0.412675i | \(-0.135405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.86607 | − | 5.86607i | −0.686572 | − | 0.686572i | 0.274901 | − | 0.961473i | \(-0.411355\pi\) |
−0.961473 | + | 0.274901i | \(0.911355\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.9409 | − | 12.9409i | 1.47475 | − | 1.47475i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.52204i | 0.283752i | 0.989884 | + | 0.141876i | \(0.0453134\pi\) | ||||
−0.989884 | + | 0.141876i | \(0.954687\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.694298 | + | 0.694298i | 0.0762091 | + | 0.0762091i | 0.744184 | − | 0.667975i | \(-0.232839\pi\) |
−0.667975 | + | 0.744184i | \(0.732839\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.1811 | + | 13.5774i | −1.21276 | + | 1.47267i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.1475 | −1.28763 | −0.643816 | − | 0.765180i | \(-0.722650\pi\) | ||||
−0.643816 | + | 0.765180i | \(0.722650\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 8.31834i | − | 0.871999i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.564297 | − | 5.83036i | −0.0578957 | − | 0.598183i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.09526 | − | 4.09526i | 0.415811 | − | 0.415811i | −0.467946 | − | 0.883757i | \(-0.655006\pi\) |
0.883757 | + | 0.467946i | \(0.155006\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.617937 | −0.0614871 | −0.0307435 | − | 0.999527i | \(-0.509788\pi\) | ||||
−0.0307435 | + | 0.999527i | \(0.509788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.59696 | + | 2.59696i | 0.255886 | + | 0.255886i | 0.823379 | − | 0.567493i | \(-0.192086\pi\) |
−0.567493 | + | 0.823379i | \(0.692086\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.74306 | + | 1.74306i | −0.168508 | + | 0.168508i | −0.786323 | − | 0.617815i | \(-0.788018\pi\) |
0.617815 | + | 0.786323i | \(0.288018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.1487 | 1.45098 | 0.725491 | − | 0.688231i | \(-0.241613\pi\) | ||||
0.725491 | + | 0.688231i | \(0.241613\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.41591 | − | 2.41591i | 0.227270 | − | 0.227270i | −0.584281 | − | 0.811551i | \(-0.698624\pi\) |
0.811551 | + | 0.584281i | \(0.198624\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.8615 | + | 8.94459i | 1.01284 | + | 0.834087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25.8148 | −2.36644 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.0969 | 1.82699 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.19122 | + | 10.7152i | 0.285431 | + | 0.958399i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.40304 | − | 1.40304i | 0.124500 | − | 0.124500i | −0.642112 | − | 0.766611i | \(-0.721941\pi\) |
0.766611 | + | 0.642112i | \(0.221941\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.14182 | 0.623984 | 0.311992 | − | 0.950085i | \(-0.399004\pi\) | ||||
0.311992 | + | 0.950085i | \(0.399004\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.07912 | − | 6.07912i | 0.527127 | − | 0.527127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.58546 | + | 6.58546i | 0.562634 | + | 0.562634i | 0.930055 | − | 0.367421i | \(-0.119759\pi\) |
−0.367421 | + | 0.930055i | \(0.619759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.1568 | 1.28558 | 0.642791 | − | 0.766042i | \(-0.277776\pi\) | ||||
0.642791 | + | 0.766042i | \(0.277776\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.99446 | − | 9.99446i | 0.835779 | − | 0.835779i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.72935 | − | 0.457735i | 0.392751 | − | 0.0380128i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.51376i | 0.451705i | 0.974162 | + | 0.225852i | \(0.0725167\pi\) | ||||
−0.974162 | + | 0.225852i | \(0.927483\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.7042 | −1.19661 | −0.598307 | − | 0.801267i | \(-0.704160\pi\) | ||||
−0.598307 | + | 0.801267i | \(0.704160\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.974036 | − | 10.0638i | −0.0782365 | − | 0.808345i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3534 | − | 11.3534i | −0.906103 | − | 0.906103i | 0.0898521 | − | 0.995955i | \(-0.471361\pi\) |
−0.995955 | + | 0.0898521i | \(0.971361\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.6512i | 1.62754i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7245 | + | 11.7245i | −0.918331 | + | 0.918331i | −0.996908 | − | 0.0785768i | \(-0.974962\pi\) |
0.0785768 | + | 0.996908i | \(0.474962\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.91997 | + | 7.91997i | 0.612865 | + | 0.612865i | 0.943692 | − | 0.330826i | \(-0.107327\pi\) |
−0.330826 | + | 0.943692i | \(0.607327\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.57562i | 0.505817i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.22597 | − | 7.22597i | −0.549380 | − | 0.549380i | 0.376881 | − | 0.926262i | \(-0.376996\pi\) |
−0.926262 | + | 0.376881i | \(0.876996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.16258 | + | 13.6130i | −0.692626 | + | 1.02904i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7942i | 1.03103i | 0.856880 | + | 0.515515i | \(0.172399\pi\) | ||||
−0.856880 | + | 0.515515i | \(0.827601\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.3310i | − | 1.36254i | −0.732034 | − | 0.681268i | \(-0.761429\pi\) | ||
0.732034 | − | 0.681268i | \(-0.238571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.1085 | − | 12.2749i | 0.743190 | − | 0.902466i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −31.0165 | − | 31.0165i | −2.26815 | − | 2.26815i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.2206i | 0.884251i | 0.896953 | + | 0.442125i | \(0.145775\pi\) | ||||
−0.896953 | + | 0.442125i | \(0.854225\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.67882 | − | 1.67882i | −0.120844 | − | 0.120844i | 0.644099 | − | 0.764943i | \(-0.277233\pi\) |
−0.764943 | + | 0.644099i | \(0.777233\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.43727 | − | 4.43727i | 0.316143 | − | 0.316143i | −0.531141 | − | 0.847283i | \(-0.678237\pi\) |
0.847283 | + | 0.531141i | \(0.178237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2067i | 1.14886i | 0.818553 | + | 0.574432i | \(0.194777\pi\) | ||||
−0.818553 | + | 0.574432i | \(0.805223\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.93114 | + | 4.93114i | 0.346098 | + | 0.346098i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.85518 | − | 0.373128i | 0.269258 | − | 0.0260604i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.6081 | 1.01046 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.6302i | 1.55793i | 0.627068 | + | 0.778964i | \(0.284255\pi\) | ||||
−0.627068 | + | 0.778964i | \(0.715745\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.92417 | + | 2.40808i | 0.199427 | + | 0.164230i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4932 | − | 10.4932i | 0.712325 | − | 0.712325i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.9372 | −1.34112 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.8423 | − | 10.8423i | −0.726057 | − | 0.726057i | 0.243775 | − | 0.969832i | \(-0.421614\pi\) |
−0.969832 | + | 0.243775i | \(0.921614\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.6177 | + | 12.6177i | −0.837465 | + | 0.837465i | −0.988525 | − | 0.151059i | \(-0.951732\pi\) |
0.151059 | + | 0.988525i | \(0.451732\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.594060 | −0.0392566 | −0.0196283 | − | 0.999807i | \(-0.506248\pi\) | ||||
−0.0196283 | + | 0.999807i | \(0.506248\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.12779 | + | 5.12779i | −0.335933 | + | 0.335933i | −0.854834 | − | 0.518901i | \(-0.826341\pi\) |
0.518901 | + | 0.854834i | \(0.326341\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.70807 | + | 2.07414i | −0.111423 | + | 0.135302i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.1582 | 0.721763 | 0.360881 | − | 0.932612i | \(-0.382476\pi\) | ||||
0.360881 | + | 0.932612i | \(0.382476\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.9706 | −1.28642 | −0.643209 | − | 0.765691i | \(-0.722397\pi\) | ||||
−0.643209 | + | 0.765691i | \(0.722397\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.39219 | + | 0.812247i | −0.536158 | + | 0.0518925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.69500 | − | 4.69500i | 0.298736 | − | 0.298736i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.4134 | 1.28848 | 0.644240 | − | 0.764823i | \(-0.277174\pi\) | ||||
0.644240 | + | 0.764823i | \(0.277174\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.8123 | + | 24.8123i | −1.55994 | + | 1.55994i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.9742 | + | 13.9742i | 0.871688 | + | 0.871688i | 0.992656 | − | 0.120968i | \(-0.0385999\pi\) |
−0.120968 | + | 0.992656i | \(0.538600\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.3384 | 1.45017 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.4243 | − | 10.4243i | 0.642788 | − | 0.642788i | −0.308452 | − | 0.951240i | \(-0.599811\pi\) |
0.951240 | + | 0.308452i | \(0.0998109\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.50148 | + | 10.3235i | −0.522242 | + | 0.634166i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.5007i | 1.79869i | 0.437241 | + | 0.899345i | \(0.355956\pi\) | ||||
−0.437241 | + | 0.899345i | \(0.644044\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.3447 | 1.17511 | 0.587554 | − | 0.809185i | \(-0.300091\pi\) | ||||
0.587554 | + | 0.809185i | \(0.300091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −27.3648 | + | 5.34714i | −1.65016 | + | 0.322445i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.44346 | + | 1.44346i | 0.0867293 | + | 0.0867293i | 0.749140 | − | 0.662411i | \(-0.230467\pi\) |
−0.662411 | + | 0.749140i | \(0.730467\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 23.9276i | − | 1.42740i | −0.700450 | − | 0.713702i | \(-0.747017\pi\) | ||
0.700450 | − | 0.713702i | \(-0.252983\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.90740 | + | 7.90740i | −0.470046 | + | 0.470046i | −0.901930 | − | 0.431883i | \(-0.857849\pi\) |
0.431883 | + | 0.901930i | \(0.357849\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.01967 | + | 4.01967i | 0.237274 | + | 0.237274i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.8725i | 2.63956i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.38544 | + | 5.38544i | 0.314621 | + | 0.314621i | 0.846697 | − | 0.532076i | \(-0.178588\pi\) |
−0.532076 | + | 0.846697i | \(0.678588\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.0056 | + | 1.74269i | −1.04833 | + | 0.101463i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.9492i | 0.922368i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.55977i | 0.320460i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.98384 | + | 0.675938i | −0.399893 | + | 0.0387041i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.116076 | − | 0.116076i | −0.00662479 | − | 0.00662479i | 0.703787 | − | 0.710411i | \(-0.251491\pi\) |
−0.710411 | + | 0.703787i | \(0.751491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.42835i | − | 0.0809944i | −0.999180 | − | 0.0404972i | \(-0.987106\pi\) | ||
0.999180 | − | 0.0404972i | \(-0.0128942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.59396 | − | 6.59396i | −0.372712 | − | 0.372712i | 0.495752 | − | 0.868464i | \(-0.334893\pi\) |
−0.868464 | + | 0.495752i | \(0.834893\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.2572 | − | 11.2572i | 0.632269 | − | 0.632269i | −0.316367 | − | 0.948637i | \(-0.602463\pi\) |
0.948637 | + | 0.316367i | \(0.102463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.8495i | 0.663444i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.5703 | − | 14.5703i | −0.810714 | − | 0.810714i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.07640 | + | 10.5135i | −0.392528 | + | 0.583185i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.94359 | −0.217417 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 35.0445i | − | 1.92622i | −0.269113 | − | 0.963109i | \(-0.586730\pi\) | ||
0.269113 | − | 0.963109i | \(-0.413270\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.75587 | − | 4.56081i | 0.205205 | − | 0.249184i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.94865 | − | 1.94865i | 0.106150 | − | 0.106150i | −0.652037 | − | 0.758187i | \(-0.726085\pi\) |
0.758187 | + | 0.652037i | \(0.226085\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.2151 | 1.36548 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.49415 | + | 7.49415i | 0.404646 | + | 0.404646i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.0347 | − | 18.0347i | 0.968151 | − | 0.968151i | −0.0313569 | − | 0.999508i | \(-0.509983\pi\) |
0.999508 | + | 0.0313569i | \(0.00998286\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.54696 | 0.0828069 | 0.0414035 | − | 0.999143i | \(-0.486817\pi\) | ||||
0.0414035 | + | 0.999143i | \(0.486817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.4669 | − | 13.4669i | 0.716770 | − | 0.716770i | −0.251172 | − | 0.967942i | \(-0.580816\pi\) |
0.967942 | + | 0.251172i | \(0.0808161\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.4785 | + | 1.49810i | −0.821511 | + | 0.0795107i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.2230 | 1.70067 | 0.850334 | − | 0.526244i | \(-0.176400\pi\) | ||||
0.850334 | + | 0.526244i | \(0.176400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1377 | −0.638826 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.7923 | + | 14.3196i | −0.617237 | + | 0.749520i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.07186 | − | 7.07186i | 0.369148 | − | 0.369148i | −0.498018 | − | 0.867167i | \(-0.665939\pi\) |
0.867167 | + | 0.498018i | \(0.165939\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.6282 | −1.01904 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.32291 | − | 5.32291i | 0.275610 | − | 0.275610i | −0.555744 | − | 0.831354i | \(-0.687566\pi\) |
0.831354 | + | 0.555744i | \(0.187566\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.80839 | + | 3.80839i | 0.196142 | + | 0.196142i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.7611 | −1.01506 | −0.507529 | − | 0.861635i | \(-0.669441\pi\) | ||||
−0.507529 | + | 0.861635i | \(0.669441\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.2191 | + | 13.2191i | −0.675466 | + | 0.675466i | −0.958971 | − | 0.283505i | \(-0.908503\pi\) |
0.283505 | + | 0.958971i | \(0.408503\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.5898 | − | 26.0145i | −1.60996 | − | 1.32582i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.1107i | 1.37457i | 0.726389 | + | 0.687284i | \(0.241197\pi\) | ||||
−0.726389 | + | 0.687284i | \(0.758803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 49.4963 | 2.50314 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.61322 | − | 0.543281i | 0.282432 | − | 0.0273354i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.68567 | − | 8.68567i | −0.435921 | − | 0.435921i | 0.454715 | − | 0.890637i | \(-0.349741\pi\) |
−0.890637 | + | 0.454715i | \(0.849741\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.09967i | 0.154790i | 0.997000 | + | 0.0773951i | \(0.0246603\pi\) | ||||
−0.997000 | + | 0.0773951i | \(0.975340\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.10407 | − | 8.10407i | 0.403692 | − | 0.403692i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.0410 | + | 28.0410i | 1.38994 | + | 1.38994i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.1083i | 0.697610i | 0.937195 | + | 0.348805i | \(0.113412\pi\) | ||||
−0.937195 | + | 0.348805i | \(0.886588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.7739 | − | 18.7739i | −0.923802 | − | 0.923802i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.39571 | − | 1.69484i | 0.0685129 | − | 0.0831963i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.4747i | 1.48878i | 0.667743 | + | 0.744392i | \(0.267261\pi\) | ||||
−0.667743 | + | 0.744392i | \(0.732739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 38.0605i | − | 1.85496i | −0.373878 | − | 0.927478i | \(-0.621972\pi\) | ||
0.373878 | − | 0.927478i | \(-0.378028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.6273 | + | 21.9607i | 1.58266 | + | 1.06525i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.28181 | − | 7.28181i | −0.352392 | − | 0.352392i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0050i | 1.44529i | 0.691220 | + | 0.722644i | \(0.257073\pi\) | ||||
−0.691220 | + | 0.722644i | \(0.742927\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.6496 | + | 20.6496i | 0.992355 | + | 0.992355i | 0.999971 | − | 0.00761624i | \(-0.00242435\pi\) |
−0.00761624 | + | 0.999971i | \(0.502424\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.6559 | + | 11.6559i | −0.557576 | + | 0.557576i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.227040i | 0.0108360i | 0.999985 | + | 0.00541802i | \(0.00172462\pi\) | ||||
−0.999985 | + | 0.00541802i | \(0.998275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3406 | + | 16.3406i | 0.776364 | + | 0.776364i | 0.979211 | − | 0.202846i | \(-0.0650192\pi\) |
−0.202846 | + | 0.979211i | \(0.565019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.61673 | + | 27.0363i | 0.124045 | + | 1.28164i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.4698 | −1.01322 | −0.506611 | − | 0.862175i | \(-0.669102\pi\) | ||||
−0.506611 | + | 0.862175i | \(0.669102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.65925i | 0.454836i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.5139 | + | 1.79188i | −0.867943 | + | 0.0840047i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.4509 | + | 19.4509i | −0.909876 | + | 0.909876i | −0.996262 | − | 0.0863855i | \(-0.972468\pi\) |
0.0863855 | + | 0.996262i | \(0.472468\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.2557 | 0.896828 | 0.448414 | − | 0.893826i | \(-0.351989\pi\) | ||||
0.448414 | + | 0.893826i | \(0.351989\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.6135 | − | 10.6135i | −0.493250 | − | 0.493250i | 0.416079 | − | 0.909329i | \(-0.363404\pi\) |
−0.909329 | + | 0.416079i | \(0.863404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.94796 | + | 1.94796i | −0.0901407 | + | 0.0901407i | −0.750739 | − | 0.660599i | \(-0.770303\pi\) |
0.660599 | + | 0.750739i | \(0.270303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.67152 | 0.400414 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.68004 | + | 6.68004i | −0.307149 | + | 0.307149i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.8549 | + | 2.51188i | −0.589823 | + | 0.115253i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.9363 | −0.910911 | −0.455456 | − | 0.890258i | \(-0.650524\pi\) | ||||
−0.455456 | + | 0.890258i | \(0.650524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0246 | 0.821850 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.99687 | − | 8.23252i | −0.453935 | − | 0.373820i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5407 | + | 18.5407i | −0.840161 | + | 0.840161i | −0.988880 | − | 0.148719i | \(-0.952485\pi\) |
0.148719 | + | 0.988880i | \(0.452485\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.08218 | −0.0488379 | −0.0244189 | − | 0.999702i | \(-0.507774\pi\) | ||||
−0.0244189 | + | 0.999702i | \(0.507774\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.8188 | − | 11.8188i | 0.532294 | − | 0.532294i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.1389 | − | 16.1389i | −0.723927 | − | 0.723927i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.6371 | 0.744779 | 0.372390 | − | 0.928076i | \(-0.378539\pi\) | ||||
0.372390 | + | 0.928076i | \(0.378539\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.0316 | − | 23.0316i | 1.02693 | − | 1.02693i | 0.0273024 | − | 0.999627i | \(-0.491308\pi\) |
0.999627 | − | 0.0273024i | \(-0.00869169\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.133112 | + | 1.37532i | 0.00592341 | + | 0.0612011i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 25.0494i | − | 1.11030i | −0.831751 | − | 0.555148i | \(-0.812662\pi\) | ||
0.831751 | − | 0.555148i | \(-0.187338\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.2260 | −1.20441 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.22055 | − | 6.33939i | 0.230045 | − | 0.279347i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.73821 | − | 4.73821i | −0.208386 | − | 0.208386i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.1278i | 0.531327i | 0.964066 | + | 0.265663i | \(0.0855909\pi\) | ||||
−0.964066 | + | 0.265663i | \(0.914409\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.8272 | − | 15.8272i | 0.692077 | − | 0.692077i | −0.270611 | − | 0.962689i | \(-0.587226\pi\) |
0.962689 | + | 0.270611i | \(0.0872259\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.1499 | − | 25.1499i | −1.09555 | − | 1.09555i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 16.5957i | − | 0.721554i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.10446 | + | 3.10446i | 0.134469 | + | 0.134469i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.25496 | + | 3.50400i | 0.183958 | + | 0.151491i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 21.0268i | − | 0.905690i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.09722i | 0.391120i | 0.980692 | + | 0.195560i | \(0.0626524\pi\) | ||||
−0.980692 | + | 0.195560i | \(0.937348\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.26323 | − | 33.7160i | −0.139782 | − | 1.44423i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.5935 | + | 28.5935i | 1.22257 | + | 1.22257i | 0.966715 | + | 0.255856i | \(0.0823573\pi\) |
0.255856 | + | 0.966715i | \(0.417643\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.56643i | 0.237138i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.85272 | + | 5.85272i | 0.248883 | + | 0.248883i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.5733 | + | 27.5733i | −1.16832 | + | 1.16832i | −0.185716 | + | 0.982604i | \(0.559460\pi\) |
−0.982604 | + | 0.185716i | \(0.940540\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.29389i | 0.181612i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.6071 | + | 10.6071i | 0.447036 | + | 0.447036i | 0.894368 | − | 0.447332i | \(-0.147626\pi\) |
−0.447332 | + | 0.894368i | \(0.647626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.89743 | − | 4.85659i | −0.248107 | − | 0.204318i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.8127 | −0.579060 | −0.289530 | − | 0.957169i | \(-0.593499\pi\) | ||||
−0.289530 | + | 0.957169i | \(0.593499\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 27.2118i | − | 1.13878i | −0.822068 | − | 0.569390i | \(-0.807179\pi\) | ||
0.822068 | − | 0.569390i | \(-0.192821\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.5680 | − | 26.1010i | 0.732634 | − | 1.08849i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.7851 | − | 23.7851i | 0.990188 | − | 0.990188i | −0.00976420 | − | 0.999952i | \(-0.503108\pi\) |
0.999952 | + | 0.00976420i | \(0.00310809\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.22241 | 0.133688 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.5832 | − | 23.5832i | −0.976715 | − | 0.976715i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.8981 | − | 20.8981i | 0.862557 | − | 0.862557i | −0.129077 | − | 0.991635i | \(-0.541202\pi\) |
0.991635 | + | 0.129077i | \(0.0412016\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.8451 | 0.488068 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.5965 | − | 15.5965i | 0.640471 | − | 0.640471i | −0.310200 | − | 0.950671i | \(-0.600396\pi\) |
0.950671 | + | 0.310200i | \(0.100396\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.56086 | + | 57.4553i | 0.227973 | + | 2.35544i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.7577 | −0.725558 | −0.362779 | − | 0.931875i | \(-0.618172\pi\) | ||||
−0.362779 | + | 0.931875i | \(0.618172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.1083 | 0.412325 | 0.206163 | − | 0.978518i | \(-0.433902\pi\) | ||||
0.206163 | + | 0.978518i | \(0.433902\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.32914 | − | 44.7290i | −0.176005 | − | 1.81849i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.9642 | − | 15.9642i | 0.647966 | − | 0.647966i | −0.304535 | − | 0.952501i | \(-0.598501\pi\) |
0.952501 | + | 0.304535i | \(0.0985011\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.04570 | −0.123216 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.9357 | + | 16.9357i | −0.684026 | + | 0.684026i | −0.960905 | − | 0.276878i | \(-0.910700\pi\) |
0.276878 | + | 0.960905i | \(0.410700\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.84335 | + | 8.84335i | 0.356020 | + | 0.356020i | 0.862344 | − | 0.506324i | \(-0.168996\pi\) |
−0.506324 | + | 0.862344i | \(0.668996\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.27180 | 0.292278 | 0.146139 | − | 0.989264i | \(-0.453315\pi\) | ||||
0.146139 | + | 0.989264i | \(0.453315\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.1898 | + | 28.1898i | −1.12940 | + | 1.12940i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1611 | − | 9.41079i | 0.926444 | − | 0.376432i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 55.9369i | − | 2.23035i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.2389 | 0.527031 | 0.263515 | − | 0.964655i | \(-0.415118\pi\) | ||||
0.263515 | + | 0.964655i | \(0.415118\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.42494 | − | 2.82047i | −0.135914 | − | 0.111927i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.75796 | − | 6.75796i | −0.267760 | − | 0.267760i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.7648i | 0.662171i | 0.943601 | + | 0.331086i | \(0.107415\pi\) | ||||
−0.943601 | + | 0.331086i | \(0.892585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.3834 | + | 35.3834i | −1.39538 | + | 1.39538i | −0.582690 | + | 0.812695i | \(0.698000\pi\) |
−0.812695 | + | 0.582690i | \(0.802000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.0431 | − | 23.0431i | −0.905919 | − | 0.905919i | 0.0900206 | − | 0.995940i | \(-0.471307\pi\) |
−0.995940 | + | 0.0900206i | \(0.971307\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 45.1135i | − | 1.77086i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.6390 | + | 31.6390i | 1.23813 | + | 1.23813i | 0.960765 | + | 0.277365i | \(0.0894612\pi\) |
0.277365 | + | 0.960765i | \(0.410539\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.53844 | − | 15.8953i | −0.0601120 | − | 0.621082i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 20.2093i | − | 0.787242i | −0.919273 | − | 0.393621i | \(-0.871222\pi\) | ||
0.919273 | − | 0.393621i | \(-0.128778\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.1882i | 1.71872i | 0.511369 | + | 0.859361i | \(0.329139\pi\) | ||||
−0.511369 | + | 0.859361i | \(0.670861\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.8396 | − | 12.2206i | −0.575456 | − | 0.473894i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.45476 | − | 9.45476i | −0.366090 | − | 0.366090i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 17.4982i | − | 0.675509i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.8238 | − | 23.8238i | −0.918340 | − | 0.918340i | 0.0785687 | − | 0.996909i | \(-0.474965\pi\) |
−0.996909 | + | 0.0785687i | \(0.974965\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.72866 | − | 5.72866i | 0.220170 | − | 0.220170i | −0.588400 | − | 0.808570i | \(-0.700242\pi\) |
0.808570 | + | 0.588400i | \(0.200242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 19.0072i | − | 0.729429i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.0998 | − | 33.0998i | −1.26653 | − | 1.26653i | −0.947869 | − | 0.318659i | \(-0.896768\pi\) |
−0.318659 | − | 0.947869i | \(-0.603232\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.2384 | − | 16.0756i | 0.505815 | − | 0.614219i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.1591 | −0.577517 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 0.570988i | − | 0.0217214i | −0.999941 | − | 0.0108607i | \(-0.996543\pi\) | ||
0.999941 | − | 0.0108607i | \(-0.00345714\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.26498 | − | 33.7340i | −0.123848 | − | 1.27960i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.63426 | − | 9.63426i | 0.364924 | − | 0.364924i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.9738 | 0.981018 | 0.490509 | − | 0.871436i | \(-0.336811\pi\) | ||||
0.490509 | + | 0.871436i | \(0.336811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.1725 | + | 13.1725i | 0.496812 | + | 0.496812i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.43400 | + | 1.43400i | −0.0539313 | + | 0.0539313i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.8807 | 1.34753 | 0.673764 | − | 0.738947i | \(-0.264677\pi\) | ||||
0.673764 | + | 0.738947i | \(0.264677\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.1192 | + | 20.1192i | −0.753472 | + | 0.753472i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.3973 | − | 20.0914i | −0.912407 | − | 0.751376i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.2588 | −0.904699 | −0.452350 | − | 0.891841i | \(-0.649414\pi\) | ||||
−0.452350 | + | 0.891841i | \(0.649414\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0532 | 0.448883 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.03753 | − | 10.4274i | −0.0756720 | − | 0.387263i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.7764 | + | 23.7764i | −0.881819 | + | 0.881819i | −0.993719 | − | 0.111900i | \(-0.964306\pi\) |
0.111900 | + | 0.993719i | \(0.464306\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.3255 | 0.492862 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.58667 | − | 1.58667i | 0.0586051 | − | 0.0586051i | −0.677197 | − | 0.735802i | \(-0.736805\pi\) |
0.735802 | + | 0.677197i | \(0.236805\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.4188 | + | 10.4188i | 0.383782 | + | 0.383782i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.6836 | 0.944786 | 0.472393 | − | 0.881388i | \(-0.343390\pi\) | ||||
0.472393 | + | 0.881388i | \(0.343390\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.375129 | + | 0.375129i | −0.0137622 | + | 0.0137622i | −0.713954 | − | 0.700192i | \(-0.753098\pi\) |
0.700192 | + | 0.713954i | \(0.253098\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2718 | − | 1.18774i | 0.449604 | − | 0.0435153i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.09000i | 0.295602i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.4813 | −1.84209 | −0.921045 | − | 0.389457i | \(-0.872663\pi\) | ||||
−0.921045 | + | 0.389457i | \(0.872663\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.16749 | + | 32.7268i | 0.115277 | + | 1.19105i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.30248 | − | 7.30248i | −0.265413 | − | 0.265413i | 0.561836 | − | 0.827249i | \(-0.310095\pi\) |
−0.827249 | + | 0.561836i | \(0.810095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13.1137i | − | 0.475371i | −0.971342 | − | 0.237685i | \(-0.923611\pi\) | ||
0.971342 | − | 0.237685i | \(-0.0763887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.1545 | − | 35.1545i | 1.27268 | − | 1.27268i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.4994 | − | 14.4994i | −0.523541 | − | 0.523541i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.1276i | 0.581577i | 0.956787 | + | 0.290788i | \(0.0939175\pi\) | ||||
−0.956787 | + | 0.290788i | \(0.906082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.60986 | + | 7.60986i | 0.273708 | + | 0.273708i | 0.830591 | − | 0.556883i | \(-0.188003\pi\) |
−0.556883 | + | 0.830591i | \(0.688003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.1889 | + | 4.33576i | −0.797049 | + | 0.155745i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.53753i | 0.162574i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 38.7816i | − | 1.38771i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.8233 | + | 27.7147i | −0.814598 | + | 0.989179i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.1198 | + | 24.1198i | 0.859779 | + | 0.859779i | 0.991312 | − | 0.131533i | \(-0.0419899\pi\) |
−0.131533 | + | 0.991312i | \(0.541990\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.2129i | − | 0.398683i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.62386 | − | 5.62386i | −0.199709 | − | 0.199709i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.34128 | − | 9.34128i | 0.330885 | − | 0.330885i | −0.522037 | − | 0.852923i | \(-0.674828\pi\) |
0.852923 | + | 0.522037i | \(0.174828\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.45191i | 0.334385i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.7119 | − | 32.7119i | −1.15438 | − | 1.15438i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 45.9627 | − | 4.44854i | 1.61997 | − | 0.156791i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.47429 | 0.297940 | 0.148970 | − | 0.988842i | \(-0.452404\pi\) | ||||
0.148970 | + | 0.988842i | \(0.452404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.25683i | 0.0792481i | 0.999215 | + | 0.0396240i | \(0.0126160\pi\) | ||||
−0.999215 | + | 0.0396240i | \(0.987384\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.6204 | + | 23.5692i | 1.00253 | + | 0.825592i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.13802 | + | 3.13802i | −0.109785 | + | 0.109785i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.8885 | −0.903515 | −0.451757 | − | 0.892141i | \(-0.649203\pi\) | ||||
−0.451757 | + | 0.892141i | \(0.649203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.4100 | + | 32.4100i | 1.12974 | + | 1.12974i | 0.990219 | + | 0.139522i | \(0.0445567\pi\) |
0.139522 | + | 0.990219i | \(0.455443\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.2295 | − | 18.2295i | 0.633901 | − | 0.633901i | −0.315143 | − | 0.949044i | \(-0.602053\pi\) |
0.949044 | + | 0.315143i | \(0.102053\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.3355 | −0.497894 | −0.248947 | − | 0.968517i | \(-0.580085\pi\) | ||||
−0.248947 | + | 0.968517i | \(0.580085\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.9724 | + | 20.9724i | −0.726652 | + | 0.726652i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.9211 | − | 19.3333i | 0.550974 | − | 0.669056i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.2314 | −1.00918 | −0.504590 | − | 0.863359i | \(-0.668356\pi\) | ||||
−0.504590 | + | 0.863359i | \(0.668356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.4847 | 0.844301 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.6351 | − | 1.41648i | 0.503464 | − | 0.0487283i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.6375 | − | 46.6375i | 1.60248 | − | 1.60248i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −44.7480 | −1.53394 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.2054 | + | 28.2054i | −0.965735 | + | 0.965735i | −0.999432 | − | 0.0336967i | \(-0.989272\pi\) |
0.0336967 | + | 0.999432i | \(0.489272\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.8982 | − | 12.8982i | −0.440593 | − | 0.440593i | 0.451619 | − | 0.892211i | \(-0.350847\pi\) |
−0.892211 | + | 0.451619i | \(0.850847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.2270 | −0.485421 | −0.242710 | − | 0.970099i | \(-0.578036\pi\) | ||||
−0.242710 | + | 0.970099i | \(0.578036\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.78453 | + | 3.78453i | −0.128827 | + | 0.128827i | −0.768580 | − | 0.639753i | \(-0.779036\pi\) |
0.639753 | + | 0.768580i | \(0.279036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.5260 | + | 17.6392i | −0.493900 | + | 0.599750i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.0641i | 0.477090i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.69716 | 0.226924 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.2717 | + | 17.4604i | 1.09098 | + | 0.590271i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.4253 | + | 18.4253i | 0.622177 | + | 0.622177i | 0.946088 | − | 0.323910i | \(-0.104998\pi\) |
−0.323910 | + | 0.946088i | \(0.604998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.06935i | − | 0.0697181i | −0.999392 | − | 0.0348591i | \(-0.988902\pi\) | ||
0.999392 | − | 0.0348591i | \(-0.0110982\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.3458 | − | 37.3458i | 1.25679 | − | 1.25679i | 0.304170 | − | 0.952618i | \(-0.401621\pi\) |
0.952618 | − | 0.304170i | \(-0.0983790\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.7113 | + | 20.7113i | 0.695418 | + | 0.695418i | 0.963419 | − | 0.268001i | \(-0.0863629\pi\) |
−0.268001 | + | 0.963419i | \(0.586363\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.51188i | − | 0.218401i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.22583 | − | 2.22583i | −0.0744844 | − | 0.0744844i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.7014 | − | 2.97147i | 1.02623 | − | 0.0993251i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.60824i | 0.320453i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.0443i | 1.56727i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.7988 | + | 3.94875i | −1.35620 | + | 0.131261i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5449 | + | 10.5449i | 0.350139 | + | 0.350139i | 0.860161 | − | 0.510022i | \(-0.170363\pi\) |
−0.510022 | + | 0.860161i | \(0.670363\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 26.8997i | − | 0.891226i | −0.895226 | − | 0.445613i | \(-0.852986\pi\) | ||
0.895226 | − | 0.445613i | \(-0.147014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.87172 | + | 3.87172i | 0.128135 | + | 0.128135i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.5735 | − | 16.5735i | 0.547306 | − | 0.547306i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.3696i | − | 1.00180i | −0.865505 | − | 0.500900i | \(-0.833002\pi\) | ||
0.865505 | − | 0.500900i | \(-0.166998\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.4643 | − | 12.4643i | −0.410267 | − | 0.410267i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.4973 | − | 19.8539i | −0.969864 | − | 0.652793i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.6162 | 1.03729 | 0.518646 | − | 0.854989i | \(-0.326436\pi\) | ||||
0.518646 | + | 0.854989i | \(0.326436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 9.87758i | − | 0.323724i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −62.3510 | + | 75.7137i | −2.03910 | + | 2.47610i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.51188 | + | 3.51188i | −0.114728 | + | 0.114728i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.647412 | + | 0.762140i | \(0.275851\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.7342 | 0.806312 | 0.403156 | − | 0.915131i | \(-0.367913\pi\) | ||||
0.403156 | + | 0.915131i | \(0.367913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.70715 | − | 7.70715i | −0.250979 | − | 0.250979i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.0920 | − | 23.0920i | 0.750389 | − | 0.750389i | −0.224163 | − | 0.974552i | \(-0.571965\pi\) |
0.974552 | + | 0.224163i | \(0.0719648\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.0270 | −0.682566 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.1149 | − | 32.1149i | 1.04030 | − | 1.04030i | 0.0411513 | − | 0.999153i | \(-0.486897\pi\) |
0.999153 | − | 0.0411513i | \(-0.0131026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.1990 | − | 2.63248i | 0.880138 | − | 0.0851850i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.5648 | 0.986990 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.5542 | −0.340457 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.37485 | + | 4.09813i | −0.108640 | + | 0.131924i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.3972 | − | 29.3972i | 0.945349 | − | 0.945349i | −0.0532327 | − | 0.998582i | \(-0.516953\pi\) |
0.998582 | + | 0.0532327i | \(0.0169525\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.7956 | 1.30919 | 0.654596 | − | 0.755979i | \(-0.272839\pi\) | ||||
0.654596 | + | 0.755979i | \(0.272839\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.1733 | − | 35.1733i | 1.12760 | − | 1.12760i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.32380 | − | 8.32380i | −0.266302 | − | 0.266302i | 0.561306 | − | 0.827608i | \(-0.310299\pi\) |
−0.827608 | + | 0.561306i | \(0.810299\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −67.7400 | −2.16498 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0382 | − | 16.0382i | 0.511539 | − | 0.511539i | −0.403458 | − | 0.914998i | \(-0.632192\pi\) |
0.914998 | + | 0.403458i | \(0.132192\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.8317 | − | 8.92005i | −0.345128 | − | 0.284216i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 10.6601i | − | 0.338970i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.7160 | −0.753362 | −0.376681 | − | 0.926343i | \(-0.622935\pi\) | ||||
−0.376681 | + | 0.926343i | \(0.622935\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.0708 | − | 3.49114i | 1.14352 | − | 0.110677i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.4793 | − | 22.4793i | −0.711926 | − | 0.711926i | 0.255012 | − | 0.966938i | \(-0.417921\pi\) |
−0.966938 | + | 0.255012i | \(0.917921\pi\) | |||||||
\(998\) | 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.bj.a.593.12 | 48 | ||
3.2 | odd | 2 | inner | 1440.2.bj.a.593.14 | 48 | ||
4.3 | odd | 2 | 360.2.x.a.53.12 | yes | 48 | ||
5.2 | odd | 4 | inner | 1440.2.bj.a.17.11 | 48 | ||
8.3 | odd | 2 | 360.2.x.a.53.24 | yes | 48 | ||
8.5 | even | 2 | inner | 1440.2.bj.a.593.13 | 48 | ||
12.11 | even | 2 | 360.2.x.a.53.13 | yes | 48 | ||
15.2 | even | 4 | inner | 1440.2.bj.a.17.13 | 48 | ||
20.7 | even | 4 | 360.2.x.a.197.1 | yes | 48 | ||
24.5 | odd | 2 | inner | 1440.2.bj.a.593.11 | 48 | ||
24.11 | even | 2 | 360.2.x.a.53.1 | ✓ | 48 | ||
40.27 | even | 4 | 360.2.x.a.197.13 | yes | 48 | ||
40.37 | odd | 4 | inner | 1440.2.bj.a.17.14 | 48 | ||
60.47 | odd | 4 | 360.2.x.a.197.24 | yes | 48 | ||
120.77 | even | 4 | inner | 1440.2.bj.a.17.12 | 48 | ||
120.107 | odd | 4 | 360.2.x.a.197.12 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.x.a.53.1 | ✓ | 48 | 24.11 | even | 2 | ||
360.2.x.a.53.12 | yes | 48 | 4.3 | odd | 2 | ||
360.2.x.a.53.13 | yes | 48 | 12.11 | even | 2 | ||
360.2.x.a.53.24 | yes | 48 | 8.3 | odd | 2 | ||
360.2.x.a.197.1 | yes | 48 | 20.7 | even | 4 | ||
360.2.x.a.197.12 | yes | 48 | 120.107 | odd | 4 | ||
360.2.x.a.197.13 | yes | 48 | 40.27 | even | 4 | ||
360.2.x.a.197.24 | yes | 48 | 60.47 | odd | 4 | ||
1440.2.bj.a.17.11 | 48 | 5.2 | odd | 4 | inner | ||
1440.2.bj.a.17.12 | 48 | 120.77 | even | 4 | inner | ||
1440.2.bj.a.17.13 | 48 | 15.2 | even | 4 | inner | ||
1440.2.bj.a.17.14 | 48 | 40.37 | odd | 4 | inner | ||
1440.2.bj.a.593.11 | 48 | 24.5 | odd | 2 | inner | ||
1440.2.bj.a.593.12 | 48 | 1.1 | even | 1 | trivial | ||
1440.2.bj.a.593.13 | 48 | 8.5 | even | 2 | inner | ||
1440.2.bj.a.593.14 | 48 | 3.2 | odd | 2 | inner |