Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(3905,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.3905");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3905.6 | ||
Root | \(-0.382683 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.3905 |
Dual form | 4032.2.k.f.3905.5 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 1.53073 | 0.684565 | 0.342282 | − | 0.939597i | \(-0.388800\pi\) | ||||
0.342282 | + | 0.939597i | \(0.388800\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.414214 | + | 2.61313i | −0.156558 | + | 0.987669i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.585786i | 0.176621i | 0.996093 | + | 0.0883106i | \(0.0281468\pi\) | ||||
−0.996093 | + | 0.0883106i | \(0.971853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.16478i | − | 0.600403i | −0.953876 | − | 0.300202i | \(-0.902946\pi\) | ||
0.953876 | − | 0.300202i | \(-0.0970540\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.86030 | −1.42133 | −0.710666 | − | 0.703529i | \(-0.751606\pi\) | ||||
−0.710666 | + | 0.703529i | \(0.751606\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.22625i | − | 1.19898i | −0.800381 | − | 0.599492i | \(-0.795369\pi\) | ||
0.800381 | − | 0.599492i | \(-0.204631\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.24264i | 0.467623i | 0.972282 | + | 0.233811i | \(0.0751198\pi\) | ||||
−0.972282 | + | 0.233811i | \(0.924880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.65685 | −0.531371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.41421i | − | 1.00539i | −0.864463 | − | 0.502697i | \(-0.832341\pi\) | ||
0.864463 | − | 0.502697i | \(-0.167659\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.32957i | 0.777614i | 0.921319 | + | 0.388807i | \(0.127113\pi\) | ||||
−0.921319 | + | 0.388807i | \(0.872887\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.634051 | + | 4.00000i | −0.107174 | + | 0.676123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.92177 | −1.39335 | −0.696673 | − | 0.717389i | \(-0.745337\pi\) | ||||
−0.696673 | + | 0.717389i | \(0.745337\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4853 | −1.59899 | −0.799495 | − | 0.600672i | \(-0.794900\pi\) | ||||
−0.799495 | + | 0.600672i | \(0.794900\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.39104 | 1.07809 | 0.539047 | − | 0.842276i | \(-0.318785\pi\) | ||||
0.539047 | + | 0.842276i | \(0.318785\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.65685 | − | 2.16478i | −0.950979 | − | 0.309255i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.41421i | 0.743699i | 0.928293 | + | 0.371850i | \(0.121276\pi\) | ||||
−0.928293 | + | 0.371850i | \(0.878724\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.896683i | 0.120909i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3.31371i | − | 0.411015i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.65685 | 1.17977 | 0.589886 | − | 0.807486i | \(-0.299173\pi\) | ||||
0.589886 | + | 0.807486i | \(0.299173\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.58579i | 0.544233i | 0.962264 | + | 0.272116i | \(0.0877236\pi\) | ||||
−0.962264 | + | 0.272116i | \(0.912276\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.6173i | − | 1.47674i | −0.674395 | − | 0.738371i | \(-0.735595\pi\) | ||
0.674395 | − | 0.738371i | \(-0.264405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.53073 | − | 0.242641i | −0.174443 | − | 0.0276515i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.34315 | −0.263624 | −0.131812 | − | 0.991275i | \(-0.542080\pi\) | ||||
−0.131812 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.5140 | −1.48335 | −0.741676 | − | 0.670759i | \(-0.765969\pi\) | ||||
−0.741676 | + | 0.670759i | \(0.765969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.97056 | −0.972994 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.86030 | −0.621191 | −0.310595 | − | 0.950542i | \(-0.600528\pi\) | ||||
−0.310595 | + | 0.950542i | \(0.600528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65685 | + | 0.896683i | 0.592999 | + | 0.0939979i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 8.00000i | − | 0.820783i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.28772i | − | 0.841490i | −0.907179 | − | 0.420745i | \(-0.861769\pi\) | ||
0.907179 | − | 0.420745i | \(-0.138231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.3128 | −1.62318 | −0.811592 | − | 0.584224i | \(-0.801399\pi\) | ||||
−0.811592 | + | 0.584224i | \(0.801399\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.7821i | − | 1.45652i | −0.685300 | − | 0.728260i | \(-0.740329\pi\) | ||
0.685300 | − | 0.728260i | \(-0.259671\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.0711i | − | 1.26363i | −0.775120 | − | 0.631814i | \(-0.782311\pi\) | ||
0.775120 | − | 0.631814i | \(-0.217689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.65685 | 0.924959 | 0.462479 | − | 0.886630i | \(-0.346960\pi\) | ||||
0.462479 | + | 0.886630i | \(0.346960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.2426i | 1.90427i | 0.305682 | + | 0.952134i | \(0.401116\pi\) | ||||
−0.305682 | + | 0.952134i | \(0.598884\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.43289i | 0.320118i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.42742 | − | 15.3137i | 0.222521 | − | 1.40381i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6569 | 0.968805 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7206 | −1.04832 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9706 | 1.50589 | 0.752947 | − | 0.658081i | \(-0.228632\pi\) | ||||
0.752947 | + | 0.658081i | \(0.228632\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.39104 | 0.645758 | 0.322879 | − | 0.946440i | \(-0.395349\pi\) | ||||
0.322879 | + | 0.946440i | \(0.395349\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.6569 | + | 2.16478i | 1.18420 | + | 0.187711i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 9.89949i | − | 0.845771i | −0.906183 | − | 0.422885i | \(-0.861017\pi\) | ||
0.906183 | − | 0.422885i | \(-0.138983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.4525i | 0.886570i | 0.896381 | + | 0.443285i | \(0.146187\pi\) | ||||
−0.896381 | + | 0.443285i | \(0.853813\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.26810 | 0.106044 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.28772i | − | 0.688258i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.2426i | 1.33065i | 0.746554 | + | 0.665324i | \(0.231707\pi\) | ||||
−0.746554 | + | 0.665324i | \(0.768293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.1421 | −0.988113 | −0.494056 | − | 0.869430i | \(-0.664486\pi\) | ||||
−0.494056 | + | 0.869430i | \(0.664486\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.62742i | 0.532327i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 16.5754i | − | 1.32286i | −0.750005 | − | 0.661432i | \(-0.769949\pi\) | ||
0.750005 | − | 0.661432i | \(-0.230051\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.86030 | − | 0.928932i | −0.461857 | − | 0.0732101i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.34315 | 0.496834 | 0.248417 | − | 0.968653i | \(-0.420090\pi\) | ||||
0.248417 | + | 0.968653i | \(0.420090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.5140 | −1.04574 | −0.522871 | − | 0.852412i | \(-0.675139\pi\) | ||||
−0.522871 | + | 0.852412i | \(0.675139\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.31371 | 0.639516 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.4357 | −1.70576 | −0.852879 | − | 0.522109i | \(-0.825145\pi\) | ||||
−0.852879 | + | 0.522109i | \(0.825145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.10051 | − | 6.94269i | 0.0831904 | − | 0.524818i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 3.89949i | − | 0.291462i | −0.989324 | − | 0.145731i | \(-0.953447\pi\) | ||
0.989324 | − | 0.145731i | \(-0.0465534\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.4107i | − | 1.07114i | −0.844492 | − | 0.535568i | \(-0.820098\pi\) | ||
0.844492 | − | 0.535568i | \(-0.179902\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.12293 | −0.450167 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.43289i | − | 0.251037i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.7279i | 1.64453i | 0.569101 | + | 0.822267i | \(0.307291\pi\) | ||||
−0.569101 | + | 0.822267i | \(0.692709\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.65685 | −0.407189 | −0.203595 | − | 0.979055i | \(-0.565262\pi\) | ||||
−0.203595 | + | 0.979055i | \(0.565262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.3848i | − | 1.02487i | −0.858725 | − | 0.512436i | \(-0.828743\pi\) | ||
0.858725 | − | 0.512436i | \(-0.171257\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.43289i | 0.243351i | 0.992570 | + | 0.121675i | \(0.0388267\pi\) | ||||
−0.992570 | + | 0.121675i | \(0.961173\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.1480 | + | 2.24264i | 0.992996 | + | 0.157403i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.6569 | −0.953836 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.06147 | 0.211766 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.8284 | −1.70926 | −0.854630 | − | 0.519238i | \(-0.826216\pi\) | ||||
−0.854630 | + | 0.519238i | \(0.826216\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.0502 | −1.09461 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.3137 | − | 1.79337i | −0.768025 | − | 0.121742i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.6863i | 0.853372i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.43289i | 0.229883i | 0.993372 | + | 0.114942i | \(0.0366681\pi\) | ||||
−0.993372 | + | 0.114942i | \(0.963332\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.12293 | −0.406393 | −0.203197 | − | 0.979138i | \(-0.565133\pi\) | ||||
−0.203197 | + | 0.979138i | \(0.565133\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 23.0698i | − | 1.52449i | −0.647286 | − | 0.762247i | \(-0.724096\pi\) | ||
0.647286 | − | 0.762247i | \(-0.275904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.72792i | − | 0.309736i | −0.987935 | − | 0.154868i | \(-0.950505\pi\) | ||
0.987935 | − | 0.154868i | \(-0.0494953\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3137 | 0.738025 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.0711i | 1.10424i | 0.833766 | + | 0.552118i | \(0.186180\pi\) | ||||
−0.833766 | + | 0.552118i | \(0.813820\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.9469i | 1.09164i | 0.837901 | + | 0.545822i | \(0.183782\pi\) | ||||
−0.837901 | + | 0.545822i | \(0.816218\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.1899 | − | 3.31371i | −0.651007 | − | 0.211705i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.3137 | −0.719874 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.2960 | 1.78603 | 0.893015 | − | 0.450026i | \(-0.148585\pi\) | ||||
0.893015 | + | 0.450026i | \(0.148585\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.31371 | −0.0825921 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.1062 | −1.12943 | −0.564716 | − | 0.825285i | \(-0.691014\pi\) | ||||
−0.564716 | + | 0.825285i | \(0.691014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.65685 | − | 10.4525i | 0.102952 | − | 0.649487i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 6.72792i | − | 0.414861i | −0.978250 | − | 0.207431i | \(-0.933490\pi\) | ||
0.978250 | − | 0.207431i | \(-0.0665102\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.28772i | 0.509111i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.59220 | 0.279991 | 0.139996 | − | 0.990152i | \(-0.455291\pi\) | ||||
0.139996 | + | 0.990152i | \(0.455291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.5754i | 1.00689i | 0.864028 | + | 0.503443i | \(0.167934\pi\) | ||||
−0.864028 | + | 0.503443i | \(0.832066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.55635i | − | 0.0938514i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.34315 | −0.501291 | −0.250646 | − | 0.968079i | \(-0.580643\pi\) | ||||
−0.250646 | + | 0.968079i | \(0.580643\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.89949i | 0.590554i | 0.955412 | + | 0.295277i | \(0.0954120\pi\) | ||||
−0.955412 | + | 0.295277i | \(0.904588\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.3379i | 1.44674i | 0.690462 | + | 0.723369i | \(0.257407\pi\) | ||||
−0.690462 | + | 0.723369i | \(0.742593\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.69552 | − | 23.3137i | 0.218140 | − | 1.37616i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.3431 | 1.02019 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.7151 | −0.625985 | −0.312992 | − | 0.949756i | \(-0.601331\pi\) | ||||
−0.312992 | + | 0.949756i | \(0.601331\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.85483 | 0.280762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.34315 | − | 27.3994i | 0.250335 | − | 1.57927i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.1313i | − | 1.49139i | −0.666288 | − | 0.745695i | \(-0.732118\pi\) | ||
0.666288 | − | 0.745695i | \(-0.267882\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.5641 | −1.67643 | −0.838214 | − | 0.545341i | \(-0.816400\pi\) | ||||
−0.838214 | + | 0.545341i | \(0.816400\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.65914i | − | 0.489443i | −0.969593 | − | 0.244722i | \(-0.921303\pi\) | ||
0.969593 | − | 0.244722i | \(-0.0786966\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.3848i | 0.807930i | 0.914775 | + | 0.403965i | \(0.132368\pi\) | ||||
−0.914775 | + | 0.403965i | \(0.867632\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.17157 | 0.177574 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.6274i | 1.70416i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.75152i | 0.319037i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.06147 | + | 19.3137i | −0.168784 | + | 1.06480i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.828427 | 0.0455345 | 0.0227672 | − | 0.999741i | \(-0.492752\pi\) | ||||
0.0227672 | + | 0.999741i | \(0.492752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.7821 | 0.807631 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | −0.435788 | −0.217894 | − | 0.975972i | \(-0.569919\pi\) | ||||
−0.217894 | + | 0.975972i | \(0.569919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.53620 | −0.137343 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.41421 | − | 16.4985i | 0.454325 | − | 0.890836i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 17.5563i | − | 0.942474i | −0.882007 | − | 0.471237i | \(-0.843808\pi\) | ||
0.882007 | − | 0.471237i | \(-0.156192\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5754i | 0.887263i | 0.896209 | + | 0.443631i | \(0.146310\pi\) | ||||
−0.896209 | + | 0.443631i | \(0.853690\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.262632 | 0.0139785 | 0.00698926 | − | 0.999976i | \(-0.497775\pi\) | ||||
0.00698926 | + | 0.999976i | \(0.497775\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.01962i | 0.372563i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.3848i | 1.49809i | 0.662518 | + | 0.749046i | \(0.269488\pi\) | ||||
−0.662518 | + | 0.749046i | \(0.730512\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.31371 | −0.437564 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 19.3137i | − | 1.01093i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.6788i | 0.818424i | 0.912439 | + | 0.409212i | \(0.134196\pi\) | ||||
−0.912439 | + | 0.409212i | \(0.865804\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.1480 | − | 2.24264i | −0.734529 | − | 0.116432i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.31371 | −0.275133 | −0.137567 | − | 0.990493i | \(-0.543928\pi\) | ||||
−0.137567 | + | 0.990493i | \(0.543928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.7206 | −0.603642 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.8284 | −0.864418 | −0.432209 | − | 0.901773i | \(-0.642266\pi\) | ||||
−0.432209 | + | 0.901773i | \(0.642266\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.2960 | 1.44586 | 0.722930 | − | 0.690921i | \(-0.242795\pi\) | ||||
0.722930 | + | 0.690921i | \(0.242795\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.34315 | − | 0.371418i | −0.119418 | − | 0.0189292i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.727922i | 0.0369071i | 0.999830 | + | 0.0184536i | \(0.00587428\pi\) | ||||
−0.999830 | + | 0.0184536i | \(0.994126\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 13.1426i | − | 0.664647i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.58673 | −0.180468 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.65914i | 0.434590i | 0.976106 | + | 0.217295i | \(0.0697233\pi\) | ||||
−0.976106 | + | 0.217295i | \(0.930277\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 31.5563i | − | 1.57585i | −0.615772 | − | 0.787924i | \(-0.711156\pi\) | ||
0.615772 | − | 0.787924i | \(-0.288844\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.37258 | 0.466882 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.34315i | − | 0.116145i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.6173i | − | 0.623885i | −0.950101 | − | 0.311942i | \(-0.899020\pi\) | ||
0.950101 | − | 0.311942i | \(-0.100980\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.6863 | −1.01545 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.65914 | −0.423027 | −0.211513 | − | 0.977375i | \(-0.567839\pi\) | ||||
−0.211513 | + | 0.977375i | \(0.567839\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.9706 | 0.729621 | 0.364810 | − | 0.931082i | \(-0.381134\pi\) | ||||
0.364810 | + | 0.931082i | \(0.381134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.5700 | 0.755254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.2426i | − | 0.493371i | −0.969096 | − | 0.246685i | \(-0.920659\pi\) | ||
0.969096 | − | 0.246685i | \(-0.0793414\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 33.8937i | − | 1.62883i | −0.580284 | − | 0.814414i | \(-0.697059\pi\) | ||
0.580284 | − | 0.814414i | \(-0.302941\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.7206 | 0.560673 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.43289i | − | 0.163843i | −0.996639 | − | 0.0819213i | \(-0.973894\pi\) | ||
0.996639 | − | 0.0819213i | \(-0.0261056\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 8.58579i | − | 0.407923i | −0.978979 | − | 0.203962i | \(-0.934618\pi\) | ||
0.978979 | − | 0.203962i | \(-0.0653817\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.97056 | −0.425245 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9.41421i | − | 0.444284i | −0.975014 | − | 0.222142i | \(-0.928695\pi\) | ||
0.975014 | − | 0.222142i | \(-0.0713049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.22625i | − | 0.246095i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.65914 | + | 1.37258i | 0.405947 | + | 0.0643477i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.3137 | −0.529233 | −0.264616 | − | 0.964354i | \(-0.585245\pi\) | ||||
−0.264616 | + | 0.964354i | \(0.585245\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7151 | 0.499054 | 0.249527 | − | 0.968368i | \(-0.419725\pi\) | ||||
0.249527 | + | 0.968368i | \(0.419725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.6569 | −1.37827 | −0.689135 | − | 0.724633i | \(-0.742010\pi\) | ||||
−0.689135 | + | 0.724633i | \(0.742010\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.8322 | −1.42675 | −0.713373 | − | 0.700784i | \(-0.752833\pi\) | ||||
−0.713373 | + | 0.700784i | \(0.752833\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | + | 25.2346i | −0.184703 | + | 1.16522i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.14214i | − | 0.282416i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.8854i | 0.637105i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.4412 | 1.07106 | 0.535528 | − | 0.844517i | \(-0.320113\pi\) | ||||
0.535528 | + | 0.844517i | \(0.320113\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.65914i | 0.394823i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 12.6863i | − | 0.576055i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.4558 | 1.78791 | 0.893957 | − | 0.448152i | \(-0.147918\pi\) | ||||
0.893957 | + | 0.448152i | \(0.147918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.5269i | 1.19714i | 0.801069 | + | 0.598571i | \(0.204265\pi\) | ||||
−0.801069 | + | 0.598571i | \(0.795735\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.7289i | 1.42900i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.9832 | − | 1.89949i | −0.537522 | − | 0.0852040i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.17157 | 0.321044 | 0.160522 | − | 0.987032i | \(-0.448682\pi\) | ||||
0.160522 | + | 0.987032i | \(0.448682\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.6369 | 0.875566 | 0.437783 | − | 0.899081i | \(-0.355764\pi\) | ||||
0.437783 | + | 0.899081i | \(0.355764\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.9706 | −1.11118 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.1899 | 0.451658 | 0.225829 | − | 0.974167i | \(-0.427491\pi\) | ||||
0.225829 | + | 0.974167i | \(0.427491\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.9706 | + | 5.22625i | 1.45853 | + | 0.231196i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 22.6274i | − | 0.997083i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.32957i | 0.190414i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.86030 | 0.256745 | 0.128372 | − | 0.991726i | \(-0.459025\pi\) | ||||
0.128372 | + | 0.991726i | \(0.459025\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.65914i | 0.378638i | 0.981916 | + | 0.189319i | \(0.0606280\pi\) | ||||
−0.981916 | + | 0.189319i | \(0.939372\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 25.3726i | − | 1.10525i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.9706 | 0.781329 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.3137i | 0.836570i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 20.0083i | − | 0.865035i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.26810 | − | 3.89949i | 0.0546210 | − | 0.167963i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.3431 | −0.702647 | −0.351323 | − | 0.936254i | \(-0.614268\pi\) | ||||
−0.351323 | + | 0.936254i | \(0.614268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.7821 | 0.633194 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.34315 | −0.271213 | −0.135607 | − | 0.990763i | \(-0.543298\pi\) | ||||
−0.135607 | + | 0.990763i | \(0.543298\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.2960 | −1.20545 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.970563 | − | 6.12293i | 0.0412725 | − | 0.260374i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 26.1005i | − | 1.10591i | −0.833210 | − | 0.552957i | \(-0.813499\pi\) | ||
0.833210 | − | 0.552957i | \(-0.186501\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.6984i | 0.960039i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −45.6143 | −1.92241 | −0.961207 | − | 0.275827i | \(-0.911048\pi\) | ||||
−0.961207 | + | 0.275827i | \(0.911048\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.9861i | 1.30359i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.24264i | 0.177861i | 0.996038 | + | 0.0889304i | \(0.0283449\pi\) | ||||
−0.996038 | + | 0.0889304i | \(0.971655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.9706 | 0.877591 | 0.438795 | − | 0.898587i | \(-0.355405\pi\) | ||||
0.438795 | + | 0.898587i | \(0.355405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.95837i | − | 0.248481i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 4.32957i | − | 0.180242i | −0.995931 | − | 0.0901212i | \(-0.971275\pi\) | ||
0.995931 | − | 0.0901212i | \(-0.0287254\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.59767 | − | 35.3137i | 0.232230 | − | 1.46506i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.17157 | −0.131353 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.85483 | −0.200380 | −0.100190 | − | 0.994968i | \(-0.531945\pi\) | ||||
−0.100190 | + | 0.994968i | \(0.531945\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.6274 | 0.932346 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.32410 | −0.136504 | −0.0682522 | − | 0.997668i | \(-0.521742\pi\) | ||||
−0.0682522 | + | 0.997668i | \(0.521742\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.71573 | − | 23.4412i | 0.152330 | − | 0.960996i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 11.2132i | − | 0.458159i | −0.973408 | − | 0.229080i | \(-0.926428\pi\) | ||
0.973408 | − | 0.229080i | \(-0.0735716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.8937i | 1.38255i | 0.722590 | + | 0.691277i | \(0.242951\pi\) | ||||
−0.722590 | + | 0.691277i | \(0.757049\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.3128 | 0.663210 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.22625i | 0.212127i | 0.994359 | + | 0.106064i | \(0.0338247\pi\) | ||||
−0.994359 | + | 0.106064i | \(0.966175\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 16.0000i | − | 0.647291i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.31371 | −0.0530602 | −0.0265301 | − | 0.999648i | \(-0.508446\pi\) | ||||
−0.0265301 | + | 0.999648i | \(0.508446\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.2426i | 0.492870i | 0.969159 | + | 0.246435i | \(0.0792592\pi\) | ||||
−0.969159 | + | 0.246435i | \(0.920741\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 19.1116i | − | 0.768162i | −0.923299 | − | 0.384081i | \(-0.874518\pi\) | ||
0.923299 | − | 0.384081i | \(-0.125482\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.42742 | − | 15.3137i | 0.0972524 | − | 0.613531i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.65685 | −0.186274 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.4412 | 0.934662 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.5980 | −1.57637 | −0.788185 | − | 0.615438i | \(-0.788979\pi\) | ||||
−0.788185 | + | 0.615438i | \(0.788979\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.9774 | 1.03088 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.68629 | + | 14.4107i | −0.185678 | + | 0.570971i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.8701i | 0.745322i | 0.927967 | + | 0.372661i | \(0.121555\pi\) | ||||
−0.927967 | + | 0.372661i | \(0.878445\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.8854i | 0.547586i | 0.961789 | + | 0.273793i | \(0.0882784\pi\) | ||||
−0.961789 | + | 0.273793i | \(0.911722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.58673 | −0.141009 | −0.0705045 | − | 0.997511i | \(-0.522461\pi\) | ||||
−0.0705045 | + | 0.997511i | \(0.522461\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 41.2132i | 1.61280i | 0.591372 | + | 0.806399i | \(0.298586\pi\) | ||||
−0.591372 | + | 0.806399i | \(0.701414\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.3137 | 0.442063 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.4142i | 1.84700i | 0.383604 | + | 0.923498i | \(0.374683\pi\) | ||||
−0.383604 | + | 0.923498i | \(0.625317\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 37.4804i | − | 1.45782i | −0.684609 | − | 0.728910i | \(-0.740027\pi\) | ||
0.684609 | − | 0.728910i | \(-0.259973\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.9050 | + | 3.31371i | 0.810661 | + | 0.128500i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.1421 | 0.470145 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.6569 | −0.526433 | −0.263217 | − | 0.964737i | \(-0.584783\pi\) | ||||
−0.263217 | + | 0.964737i | \(0.584783\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.8770 | 1.76319 | 0.881597 | − | 0.472002i | \(-0.156469\pi\) | ||||
0.881597 | + | 0.472002i | \(0.156469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.6569 | + | 3.43289i | 0.831114 | + | 0.131742i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 34.7279i | − | 1.32883i | −0.747365 | − | 0.664414i | \(-0.768681\pi\) | ||
0.747365 | − | 0.664414i | \(-0.231319\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 15.1535i | − | 0.578985i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.7206 | 0.446519 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 31.3575i | − | 1.19290i | −0.802652 | − | 0.596448i | \(-0.796578\pi\) | ||
0.802652 | − | 0.596448i | \(-0.203422\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.0000i | 0.606915i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.2843 | 1.98041 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.9289i | 1.09263i | 0.837580 | + | 0.546315i | \(0.183970\pi\) | ||||
−0.837580 | + | 0.546315i | \(0.816030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.9050i | 0.788447i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.75699 | − | 42.6274i | 0.254123 | − | 1.60317i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.2843 | 0.912015 | 0.456007 | − | 0.889976i | \(-0.349279\pi\) | ||||
0.456007 | + | 0.889976i | \(0.349279\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.70967 | −0.363630 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.94113 | 0.0725940 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.9050 | 0.779625 | 0.389813 | − | 0.920894i | \(-0.372540\pi\) | ||||
0.389813 | + | 0.920894i | \(0.372540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.6274 | + | 6.12293i | 1.43856 | + | 0.228030i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.3848i | 0.534237i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.12293i | 0.227087i | 0.993533 | + | 0.113544i | \(0.0362201\pi\) | ||||
−0.993533 | + | 0.113544i | \(0.963780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 61.4469 | 2.27270 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.49435i | 0.239874i | 0.992781 | + | 0.119937i | \(0.0382693\pi\) | ||||
−0.992781 | + | 0.119937i | \(0.961731\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.65685i | 0.208373i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.2843 | −1.48188 | −0.740940 | − | 0.671571i | \(-0.765620\pi\) | ||||
−0.740940 | + | 0.671571i | \(0.765620\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.6985i | 1.74989i | 0.484224 | + | 0.874944i | \(0.339102\pi\) | ||||
−0.484224 | + | 0.874944i | \(0.660898\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.8632i | 0.910916i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.1563 | + | 5.41421i | 1.24805 | + | 0.197831i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.5147 | 0.493159 | 0.246580 | − | 0.969123i | \(-0.420693\pi\) | ||||
0.246580 | + | 0.969123i | \(0.420693\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.5864 | −0.676428 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.5980 | 1.00307 | 0.501533 | − | 0.865139i | \(-0.332770\pi\) | ||||
0.501533 | + | 0.865139i | \(0.332770\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.3015 | 1.06218 | 0.531090 | − | 0.847316i | \(-0.321783\pi\) | ||||
0.531090 | + | 0.847316i | \(0.321783\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.00000 | + | 25.2346i | −0.144810 | + | 0.913553i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.8937i | 1.22224i | 0.791539 | + | 0.611119i | \(0.209280\pi\) | ||||
−0.791539 | + | 0.611119i | \(0.790720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.3128 | −0.586731 | −0.293365 | − | 0.956000i | \(-0.594775\pi\) | ||||
−0.293365 | + | 0.956000i | \(0.594775\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 11.5030i | − | 0.413201i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.6274i | 1.67060i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.68629 | −0.0961231 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 25.3726i | − | 0.905586i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38.2233i | − | 1.36251i | −0.732045 | − | 0.681256i | \(-0.761434\pi\) | ||
0.732045 | − | 0.681256i | \(-0.238566\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −52.8966 | − | 8.38478i | −1.88079 | − | 0.298128i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.4357 | 0.794715 | 0.397357 | − | 0.917664i | \(-0.369927\pi\) | ||||
0.397357 | + | 0.917664i | \(0.369927\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.3137 | −1.53233 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.39104 | 0.260824 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.97056 | − | 1.42195i | −0.316171 | − | 0.0501171i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.07107i | 0.248606i | 0.992244 | + | 0.124303i | \(0.0396694\pi\) | ||||
−0.992244 | + | 0.124303i | \(0.960331\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.2459i | 0.430011i | 0.976613 | + | 0.215005i | \(0.0689769\pi\) | ||||
−0.976613 | + | 0.215005i | \(0.931023\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.70967 | 0.340115 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.7987i | 1.91716i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 39.3553i | − | 1.37351i | −0.726889 | − | 0.686755i | \(-0.759034\pi\) | ||
0.726889 | − | 0.686755i | \(-0.240966\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.6569 | 0.754910 | 0.377455 | − | 0.926028i | \(-0.376799\pi\) | ||||
0.377455 | + | 0.926028i | \(0.376799\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 55.0122i | 1.91296i | 0.291796 | + | 0.956481i | \(0.405747\pi\) | ||||
−0.291796 | + | 0.956481i | \(0.594253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.8239i | 0.375930i | 0.982176 | + | 0.187965i | \(0.0601892\pi\) | ||||
−0.982176 | + | 0.187965i | \(0.939811\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 39.0112 | + | 12.6863i | 1.35166 | + | 0.439554i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.6863 | −0.715879 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.7373 | −1.78617 | −0.893084 | − | 0.449890i | \(-0.851463\pi\) | ||||
−0.893084 | + | 0.449890i | \(0.851463\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.313708 | −0.0108175 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.7261 | 0.437790 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.41421 | + | 27.8477i | −0.151674 | + | 0.956858i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 8.97056i | − | 0.307507i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.5641i | 1.01226i | 0.862458 | + | 0.506129i | \(0.168924\pi\) | ||||
−0.862458 | + | 0.506129i | \(0.831076\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.86030 | 0.200184 | 0.100092 | − | 0.994978i | \(-0.468086\pi\) | ||||
0.100092 | + | 0.994978i | \(0.468086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.8854i | 0.473763i | 0.971539 | + | 0.236882i | \(0.0761254\pi\) | ||||
−0.971539 | + | 0.236882i | \(0.923875\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.5858i | 0.700748i | 0.936610 | + | 0.350374i | \(0.113946\pi\) | ||||
−0.936610 | + | 0.350374i | \(0.886054\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.3431 | −1.16770 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.37258i | − | 0.0465617i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 20.9050i | − | 0.708339i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.85483 | − | 30.6274i | 0.164123 | − | 1.03540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0000 | 0.472746 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.0112 | 1.31432 | 0.657160 | − | 0.753751i | \(-0.271758\pi\) | ||||
0.657160 | + | 0.753751i | \(0.271758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.14214 | 0.139394 | 0.0696970 | − | 0.997568i | \(-0.477797\pi\) | ||||
0.0696970 | + | 0.997568i | \(0.477797\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.0502 | 0.538912 | 0.269456 | − | 0.963013i | \(-0.413156\pi\) | ||||
0.269456 | + | 0.963013i | \(0.413156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.02944 | + | 44.3462i | −0.235760 | + | 1.48732i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 38.6274i | − | 1.29262i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.96909i | − | 0.199525i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.4412 | 0.781808 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 31.7289i | − | 1.05704i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 22.0589i | − | 0.733262i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.2010 | 0.338719 | 0.169359 | − | 0.985554i | \(-0.445830\pi\) | ||||
0.169359 | + | 0.985554i | \(0.445830\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.1838i | 0.668718i | 0.942446 | + | 0.334359i | \(0.108520\pi\) | ||||
−0.942446 | + | 0.334359i | \(0.891480\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 7.91630i | − | 0.261991i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.06147 | + | 19.3137i | −0.101099 | + | 0.637795i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.7990 | −1.24687 | −0.623437 | − | 0.781874i | \(-0.714264\pi\) | ||||
−0.623437 | + | 0.781874i | \(0.714264\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.92724 | 0.326759 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.6274 | 0.349427 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.1171 | 0.660021 | 0.330010 | − | 0.943977i | \(-0.392948\pi\) | ||||
0.330010 | + | 0.943977i | \(0.392948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.3137 | + | 34.7904i | −0.370792 | + | 1.14021i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5.25483i | − | 0.171851i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.58673i | − | 0.117173i | −0.998282 | − | 0.0585867i | \(-0.981341\pi\) | ||
0.998282 | − | 0.0585867i | \(-0.0186594\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.4357 | −0.731384 | −0.365692 | − | 0.930736i | \(-0.619168\pi\) | ||||
−0.365692 | + | 0.930736i | \(0.619168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 20.0083i | − | 0.651561i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.5858i | 0.798931i | 0.916748 | + | 0.399465i | \(0.130804\pi\) | ||||
−0.916748 | + | 0.399465i | \(0.869196\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.3137 | −0.886640 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 53.2132i | − | 1.72374i | −0.507125 | − | 0.861872i | \(-0.669292\pi\) | ||
0.507125 | − | 0.861872i | \(-0.330708\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.7904i | 1.12579i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.8686 | + | 4.10051i | 0.835342 | + | 0.132412i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.2548 | 0.395317 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.65914 | −0.278748 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.6569 | −0.953700 | −0.476850 | − | 0.878985i | \(-0.658222\pi\) | ||||
−0.476850 | + | 0.878985i | \(0.658222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.4412 | 0.752264 | 0.376132 | − | 0.926566i | \(-0.377254\pi\) | ||||
0.376132 | + | 0.926566i | \(0.377254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.3137 | − | 4.32957i | −0.875637 | − | 0.138800i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.8995i | 0.572656i | 0.958132 | + | 0.286328i | \(0.0924346\pi\) | ||||
−0.958132 | + | 0.286328i | \(0.907565\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.43289i | − | 0.109716i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.5864 | −0.592813 | −0.296407 | − | 0.955062i | \(-0.595788\pi\) | ||||
−0.296407 | + | 0.955062i | \(0.595788\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 22.0193i | − | 0.701592i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 23.5147i | − | 0.747725i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.8579 | 0.884934 | 0.442467 | − | 0.896785i | \(-0.354103\pi\) | ||||
0.442467 | + | 0.896785i | \(0.354103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.25483i | 0.166589i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.0559i | 1.71197i | 0.517003 | + | 0.855984i | \(0.327048\pi\) | ||||
−0.517003 | + | 0.855984i | \(0.672952\pi\) | |||||||
\(998\) | 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 | 4032.2.k.f.3905.6 | 8 | ||
3.2 | odd | 2 | inner | 4032.2.k.f.3905.4 | 8 | ||
4.3 | odd | 2 | 4032.2.k.e.3905.5 | 8 | |||
7.6 | odd | 2 | inner | 4032.2.k.f.3905.3 | 8 | ||
8.3 | odd | 2 | 1008.2.k.c.881.3 | 8 | |||
8.5 | even | 2 | 504.2.k.a.377.4 | yes | 8 | ||
12.11 | even | 2 | 4032.2.k.e.3905.3 | 8 | |||
21.20 | even | 2 | inner | 4032.2.k.f.3905.5 | 8 | ||
24.5 | odd | 2 | 504.2.k.a.377.6 | yes | 8 | ||
24.11 | even | 2 | 1008.2.k.c.881.5 | 8 | |||
28.27 | even | 2 | 4032.2.k.e.3905.4 | 8 | |||
56.5 | odd | 6 | 3528.2.bl.b.521.4 | 16 | |||
56.13 | odd | 2 | 504.2.k.a.377.5 | yes | 8 | ||
56.27 | even | 2 | 1008.2.k.c.881.6 | 8 | |||
56.37 | even | 6 | 3528.2.bl.b.521.6 | 16 | |||
56.45 | odd | 6 | 3528.2.bl.b.1097.3 | 16 | |||
56.53 | even | 6 | 3528.2.bl.b.1097.5 | 16 | |||
84.83 | odd | 2 | 4032.2.k.e.3905.6 | 8 | |||
168.5 | even | 6 | 3528.2.bl.b.521.5 | 16 | |||
168.53 | odd | 6 | 3528.2.bl.b.1097.4 | 16 | |||
168.83 | odd | 2 | 1008.2.k.c.881.4 | 8 | |||
168.101 | even | 6 | 3528.2.bl.b.1097.6 | 16 | |||
168.125 | even | 2 | 504.2.k.a.377.3 | ✓ | 8 | ||
168.149 | odd | 6 | 3528.2.bl.b.521.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.k.a.377.3 | ✓ | 8 | 168.125 | even | 2 | ||
504.2.k.a.377.4 | yes | 8 | 8.5 | even | 2 | ||
504.2.k.a.377.5 | yes | 8 | 56.13 | odd | 2 | ||
504.2.k.a.377.6 | yes | 8 | 24.5 | odd | 2 | ||
1008.2.k.c.881.3 | 8 | 8.3 | odd | 2 | |||
1008.2.k.c.881.4 | 8 | 168.83 | odd | 2 | |||
1008.2.k.c.881.5 | 8 | 24.11 | even | 2 | |||
1008.2.k.c.881.6 | 8 | 56.27 | even | 2 | |||
3528.2.bl.b.521.3 | 16 | 168.149 | odd | 6 | |||
3528.2.bl.b.521.4 | 16 | 56.5 | odd | 6 | |||
3528.2.bl.b.521.5 | 16 | 168.5 | even | 6 | |||
3528.2.bl.b.521.6 | 16 | 56.37 | even | 6 | |||
3528.2.bl.b.1097.3 | 16 | 56.45 | odd | 6 | |||
3528.2.bl.b.1097.4 | 16 | 168.53 | odd | 6 | |||
3528.2.bl.b.1097.5 | 16 | 56.53 | even | 6 | |||
3528.2.bl.b.1097.6 | 16 | 168.101 | even | 6 | |||
4032.2.k.e.3905.3 | 8 | 12.11 | even | 2 | |||
4032.2.k.e.3905.4 | 8 | 28.27 | even | 2 | |||
4032.2.k.e.3905.5 | 8 | 4.3 | odd | 2 | |||
4032.2.k.e.3905.6 | 8 | 84.83 | odd | 2 | |||
4032.2.k.f.3905.3 | 8 | 7.6 | odd | 2 | inner | ||
4032.2.k.f.3905.4 | 8 | 3.2 | odd | 2 | inner | ||
4032.2.k.f.3905.5 | 8 | 21.20 | even | 2 | inner | ||
4032.2.k.f.3905.6 | 8 | 1.1 | even | 1 | trivial |