Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(841,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.q (of order \(3\), degree \(2\), 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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 841.2 | ||
Root | \(1.68614 - 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.841 |
Dual form | 4020.2.q.i.3781.2 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.18614 | − | 2.05446i | 0.448319 | − | 0.776511i | −0.549958 | − | 0.835192i | \(-0.685356\pi\) |
0.998277 | + | 0.0586811i | \(0.0186895\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.18614 | − | 3.78651i | 0.659146 | − | 1.14167i | −0.321691 | − | 0.946845i | \(-0.604251\pi\) |
0.980837 | − | 0.194830i | \(-0.0624155\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.813859 | − | 1.40965i | −0.197390 | − | 0.341889i | 0.750291 | − | 0.661107i | \(-0.229913\pi\) |
−0.947681 | + | 0.319218i | \(0.896580\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.18614 | − | 5.51856i | −0.730951 | − | 1.26604i | −0.956477 | − | 0.291807i | \(-0.905744\pi\) |
0.225526 | − | 0.974237i | \(-0.427590\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.18614 | − | 2.05446i | 0.258837 | − | 0.448319i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.813859 | − | 1.40965i | −0.169701 | − | 0.293931i | 0.768613 | − | 0.639713i | \(-0.220947\pi\) |
−0.938315 | + | 0.345782i | \(0.887614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.18614 | + | 3.78651i | −0.405956 | + | 0.703137i | −0.994432 | − | 0.105378i | \(-0.966395\pi\) |
0.588476 | + | 0.808515i | \(0.299728\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.87228 | + | 6.70699i | −0.695482 | + | 1.20461i | 0.274536 | + | 0.961577i | \(0.411476\pi\) |
−0.970018 | + | 0.243034i | \(0.921857\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.18614 | − | 3.78651i | 0.380558 | − | 0.659146i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.18614 | + | 2.05446i | −0.200494 | + | 0.347266i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.55842 | − | 7.89542i | −0.749400 | − | 1.29800i | −0.948111 | − | 0.317941i | \(-0.897009\pi\) |
0.198711 | − | 0.980058i | \(-0.436325\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.18614 | − | 8.98266i | 0.809939 | − | 1.40286i | −0.102966 | − | 0.994685i | \(-0.532833\pi\) |
0.912906 | − | 0.408171i | \(-0.133833\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.37228 | 0.514268 | 0.257134 | − | 0.966376i | \(-0.417222\pi\) | ||||
0.257134 | + | 0.966376i | \(0.417222\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.813859 | − | 1.40965i | 0.118714 | − | 0.205618i | −0.800545 | − | 0.599273i | \(-0.795456\pi\) |
0.919258 | + | 0.393655i | \(0.128790\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.686141 | + | 1.18843i | 0.0980201 | + | 0.169776i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.813859 | − | 1.40965i | −0.113963 | − | 0.197390i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.74456 | −1.20116 | −0.600579 | − | 0.799565i | \(-0.705063\pi\) | ||||
−0.600579 | + | 0.799565i | \(0.705063\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.18614 | + | 3.78651i | −0.294779 | + | 0.510572i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.18614 | − | 5.51856i | −0.422015 | − | 0.730951i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.74456 | −0.357312 | −0.178656 | − | 0.983912i | \(-0.557175\pi\) | ||||
−0.178656 | + | 0.983912i | \(0.557175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.50000 | − | 9.52628i | −0.704203 | − | 1.21972i | −0.966978 | − | 0.254858i | \(-0.917971\pi\) |
0.262776 | − | 0.964857i | \(-0.415362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.18614 | − | 2.05446i | 0.149440 | − | 0.258837i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.500000 | − | 0.866025i | −0.0620174 | − | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.05842 | + | 8.11663i | −0.129307 | + | 0.991605i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.813859 | − | 1.40965i | −0.0979772 | − | 0.169701i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.55842 | + | 11.3595i | −0.778341 | + | 1.34813i | 0.154556 | + | 0.987984i | \(0.450605\pi\) |
−0.932897 | + | 0.360143i | \(0.882728\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.50000 | + | 11.2583i | 0.760767 | + | 1.31769i | 0.942455 | + | 0.334332i | \(0.108511\pi\) |
−0.181688 | + | 0.983356i | \(0.558156\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.18614 | − | 8.98266i | −0.591016 | − | 1.02367i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.12772 | − | 3.68532i | 0.239387 | − | 0.414631i | −0.721152 | − | 0.692777i | \(-0.756387\pi\) |
0.960539 | + | 0.278147i | \(0.0897202\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.55842 | − | 6.16337i | −0.390588 | − | 0.676517i | 0.601940 | − | 0.798542i | \(-0.294395\pi\) |
−0.992527 | + | 0.122024i | \(0.961061\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.813859 | + | 1.40965i | 0.0882754 | + | 0.152898i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.18614 | + | 3.78651i | −0.234379 | + | 0.405956i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.4891 | −1.21784 | −0.608922 | − | 0.793230i | \(-0.708398\pi\) | ||||
−0.608922 | + | 0.793230i | \(0.708398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.37228 | 0.248683 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.87228 | + | 6.70699i | −0.401537 | + | 0.695482i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.18614 | + | 5.51856i | 0.326891 | + | 0.566192i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.500000 | + | 0.866025i | 0.0507673 | + | 0.0879316i | 0.890292 | − | 0.455389i | \(-0.150500\pi\) |
−0.839525 | + | 0.543321i | \(0.817167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.18614 | − | 3.78651i | 0.219715 | − | 0.380558i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.93070 | − | 13.7364i | 0.789134 | − | 1.36682i | −0.137363 | − | 0.990521i | \(-0.543863\pi\) |
0.926498 | − | 0.376300i | \(-0.122804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.55842 | + | 13.0916i | −0.744753 | + | 1.28995i | 0.205556 | + | 0.978645i | \(0.434100\pi\) |
−0.950310 | + | 0.311306i | \(0.899234\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.18614 | + | 2.05446i | −0.115755 | + | 0.200494i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1168 | 1.16058 | 0.580292 | − | 0.814409i | \(-0.302939\pi\) | ||||
0.580292 | + | 0.814409i | \(0.302939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.55842 | − | 7.89542i | −0.432666 | − | 0.749400i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.55842 | − | 11.3595i | 0.616964 | − | 1.06861i | −0.373072 | − | 0.927802i | \(-0.621696\pi\) |
0.990036 | − | 0.140811i | \(-0.0449711\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.813859 | + | 1.40965i | 0.0758928 | + | 0.131450i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | + | 0.866025i | 0.0462250 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.86141 | −0.353975 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.05842 | − | 7.02939i | −0.368947 | − | 0.639036i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.18614 | − | 8.98266i | 0.467619 | − | 0.809939i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.12772 | − | 3.68532i | 0.188805 | − | 0.327019i | −0.756047 | − | 0.654517i | \(-0.772872\pi\) |
0.944852 | + | 0.327498i | \(0.106205\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.37228 | 0.296913 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.4891 | 1.52803 | 0.764016 | − | 0.645197i | \(-0.223225\pi\) | ||||
0.764016 | + | 0.645197i | \(0.223225\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.1168 | −1.31080 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.7446 | −1.77233 | −0.886164 | − | 0.463372i | \(-0.846639\pi\) | ||||
−0.886164 | + | 0.463372i | \(0.846639\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.627719 | 0.0532424 | 0.0266212 | − | 0.999646i | \(-0.491525\pi\) | ||||
0.0266212 | + | 0.999646i | \(0.491525\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.813859 | − | 1.40965i | 0.0685393 | − | 0.118714i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.37228 | 0.365629 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.18614 | − | 3.78651i | 0.181549 | − | 0.314452i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.686141 | + | 1.18843i | 0.0565919 | + | 0.0980201i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.74456 | −0.716382 | −0.358191 | − | 0.933648i | \(-0.616606\pi\) | ||||
−0.358191 | + | 0.933648i | \(0.616606\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.500000 | + | 0.866025i | 0.0406894 | + | 0.0704761i | 0.885653 | − | 0.464348i | \(-0.153711\pi\) |
−0.844963 | + | 0.534824i | \(0.820378\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.813859 | − | 1.40965i | −0.0657966 | − | 0.113963i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.87228 | − | 6.70699i | 0.311029 | − | 0.538718i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.81386 | − | 3.14170i | −0.144762 | − | 0.250735i | 0.784522 | − | 0.620101i | \(-0.212908\pi\) |
−0.929284 | + | 0.369366i | \(0.879575\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.74456 | −0.693489 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.86141 | −0.304321 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.50000 | − | 6.06218i | 0.274141 | − | 0.474826i | −0.695777 | − | 0.718258i | \(-0.744940\pi\) |
0.969918 | + | 0.243432i | \(0.0782731\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.18614 | + | 3.78651i | −0.170191 | + | 0.294779i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.81386 | − | 11.8020i | 0.527272 | − | 0.913262i | −0.472223 | − | 0.881479i | \(-0.656548\pi\) |
0.999495 | − | 0.0317830i | \(-0.0101185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.18614 | − | 5.51856i | −0.243650 | − | 0.422015i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.558422 | + | 0.967215i | 0.0424560 | + | 0.0735360i | 0.886473 | − | 0.462781i | \(-0.153148\pi\) |
−0.844017 | + | 0.536317i | \(0.819815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.18614 | − | 2.05446i | 0.0896638 | − | 0.155302i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.74456 | −0.206294 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.7446 | −1.10206 | −0.551030 | − | 0.834485i | \(-0.685765\pi\) | ||||
−0.551030 | + | 0.834485i | \(0.685765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.87228 | + | 11.9031i | −0.510813 | + | 0.884753i | 0.489109 | + | 0.872223i | \(0.337322\pi\) |
−0.999921 | + | 0.0125307i | \(0.996011\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.50000 | − | 9.52628i | −0.406572 | − | 0.704203i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.55842 | + | 7.89542i | 0.335142 | + | 0.580483i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.11684 | −0.520435 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.18614 | − | 2.05446i | 0.0862790 | − | 0.149440i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.55842 | − | 16.5557i | −0.691623 | − | 1.19793i | −0.971306 | − | 0.237834i | \(-0.923563\pi\) |
0.279683 | − | 0.960092i | \(-0.409771\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.116844 | 0.00841061 | 0.00420531 | − | 0.999991i | \(-0.498661\pi\) | ||||
0.00420531 | + | 0.999991i | \(0.498661\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.500000 | − | 0.866025i | −0.0358057 | − | 0.0620174i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.18614 | − | 8.98266i | 0.369497 | − | 0.639988i | −0.619990 | − | 0.784610i | \(-0.712863\pi\) |
0.989487 | + | 0.144622i | \(0.0461966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.87228 | + | 3.24289i | 0.132723 | + | 0.229882i | 0.924725 | − | 0.380636i | \(-0.124295\pi\) |
−0.792003 | + | 0.610518i | \(0.790961\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.05842 | + | 8.11663i | −0.0746553 | + | 0.572503i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.18614 | + | 8.98266i | 0.363996 | + | 0.630459i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.18614 | + | 8.98266i | −0.362216 | + | 0.627376i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.813859 | − | 1.40965i | −0.0565671 | − | 0.0979772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.8614 | −1.92721 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.87228 | + | 3.24289i | 0.128893 | + | 0.223250i | 0.923248 | − | 0.384204i | \(-0.125524\pi\) |
−0.794355 | + | 0.607454i | \(0.792191\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.55842 | + | 11.3595i | −0.449376 | + | 0.778341i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.37228 | −0.229988 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.18614 | + | 15.9109i | 0.623596 | + | 1.08010i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.50000 | + | 11.2583i | 0.439229 | + | 0.760767i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.813859 | − | 1.40965i | 0.0547461 | − | 0.0948230i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.88316 | −0.393965 | −0.196983 | − | 0.980407i | \(-0.563114\pi\) | ||||
−0.196983 | + | 0.980407i | \(0.563114\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9307 | − | 18.9325i | 0.725496 | − | 1.25660i | −0.233273 | − | 0.972411i | \(-0.574944\pi\) |
0.958769 | − | 0.284185i | \(-0.0917230\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.61684 | − | 16.6569i | −0.635499 | − | 1.10072i | −0.986409 | − | 0.164307i | \(-0.947461\pi\) |
0.350910 | − | 0.936409i | \(-0.385872\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.18614 | − | 8.98266i | −0.341223 | − | 0.591016i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.81386 | − | 6.60580i | 0.249854 | − | 0.432760i | −0.713631 | − | 0.700522i | \(-0.752951\pi\) |
0.963485 | + | 0.267762i | \(0.0862840\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.813859 | + | 1.40965i | −0.0530903 | + | 0.0919551i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.12772 | − | 3.68532i | 0.138210 | − | 0.239387i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.44158 | − | 9.42509i | 0.351986 | − | 0.609658i | −0.634611 | − | 0.772832i | \(-0.718840\pi\) |
0.986597 | + | 0.163173i | \(0.0521730\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.1168 | 1.55350 | 0.776751 | − | 0.629808i | \(-0.216866\pi\) | ||||
0.776751 | + | 0.629808i | \(0.216866\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.686141 | − | 1.18843i | −0.0438359 | − | 0.0759260i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.18614 | − | 5.51856i | 0.202729 | − | 0.351137i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.55842 | − | 6.16337i | −0.225506 | − | 0.390588i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.55842 | − | 16.5557i | −0.603322 | − | 1.04498i | −0.992314 | − | 0.123744i | \(-0.960510\pi\) |
0.388992 | − | 0.921241i | \(-0.372823\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.11684 | −0.447432 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.813859 | + | 1.40965i | 0.0509658 | + | 0.0882754i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.18614 | − | 8.98266i | 0.323503 | − | 0.560323i | −0.657706 | − | 0.753275i | \(-0.728473\pi\) |
0.981208 | + | 0.192952i | \(0.0618062\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.6277 | −1.34388 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.18614 | + | 3.78651i | −0.135319 | + | 0.234379i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.48913 | 0.338474 | 0.169237 | − | 0.985575i | \(-0.445870\pi\) | ||||
0.169237 | + | 0.985575i | \(0.445870\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.74456 | 0.537174 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.4891 | −0.703123 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.7446 | 1.26482 | 0.632409 | − | 0.774635i | \(-0.282066\pi\) | ||||
0.632409 | + | 0.774635i | \(0.282066\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.1168 | −1.58649 | −0.793243 | − | 0.608906i | \(-0.791609\pi\) | ||||
−0.793243 | + | 0.608906i | \(0.791609\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.37228 | 0.143577 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.18614 | − | 3.78651i | 0.131829 | − | 0.228335i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8614 | 0.892935 | 0.446468 | − | 0.894800i | \(-0.352682\pi\) | ||||
0.446468 | + | 0.894800i | \(0.352682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.87228 | + | 6.70699i | −0.231827 | + | 0.401537i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.81386 | − | 11.8020i | −0.406481 | − | 0.704045i | 0.588012 | − | 0.808852i | \(-0.299911\pi\) |
−0.994493 | + | 0.104807i | \(0.966578\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4891 | 0.801845 | 0.400923 | − | 0.916112i | \(-0.368690\pi\) | ||||
0.400923 | + | 0.916112i | \(0.368690\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.18614 | + | 5.51856i | 0.188731 | + | 0.326891i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.3030 | − | 21.3094i | −0.726222 | − | 1.25785i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.17527 | − | 12.4279i | 0.422074 | − | 0.731054i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.500000 | + | 0.866025i | 0.0293105 | + | 0.0507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.74456 | 0.159795 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.18614 | − | 3.78651i | 0.126853 | − | 0.219715i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.813859 | − | 1.40965i | 0.0470667 | − | 0.0815219i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | − | 6.92820i | 0.230556 | − | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.93070 | − | 13.7364i | 0.455607 | − | 0.789134i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.50000 | + | 9.52628i | 0.314929 | + | 0.545473i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.500000 | + | 0.866025i | 0.0285365 | + | 0.0494267i | 0.879941 | − | 0.475083i | \(-0.157582\pi\) |
−0.851404 | + | 0.524510i | \(0.824249\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.55842 | + | 13.0916i | −0.429984 | + | 0.744753i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.2337 | 1.14735 | 0.573674 | − | 0.819084i | \(-0.305518\pi\) | ||||
0.573674 | + | 0.819084i | \(0.305518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.4891 | 1.10159 | 0.550795 | − | 0.834640i | \(-0.314325\pi\) | ||||
0.550795 | + | 0.834640i | \(0.314325\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.18614 | + | 2.05446i | −0.0668315 | + | 0.115755i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.558422 | + | 0.967215i | 0.0313641 | + | 0.0543242i | 0.881281 | − | 0.472592i | \(-0.156682\pi\) |
−0.849917 | + | 0.526916i | \(0.823348\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.55842 | + | 16.5557i | 0.535169 | + | 0.926940i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.18614 | + | 8.98266i | −0.288565 | + | 0.499809i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.500000 | + | 0.866025i | 0.0277350 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.1168 | 0.670063 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.93070 | − | 3.34408i | −0.106443 | − | 0.184365i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.98913 | + | 13.8376i | −0.439122 | + | 0.760582i | −0.997622 | − | 0.0689229i | \(-0.978044\pi\) |
0.558500 | + | 0.829505i | \(0.311377\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.55842 | − | 7.89542i | −0.249800 | − | 0.432666i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.05842 | − | 8.11663i | 0.0578278 | − | 0.443459i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.500000 | + | 0.866025i | 0.0272367 | + | 0.0471754i | 0.879322 | − | 0.476227i | \(-0.157996\pi\) |
−0.852086 | + | 0.523402i | \(0.824663\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.55842 | − | 11.3595i | 0.356205 | − | 0.616964i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9307 | + | 29.3248i | 0.916849 | + | 1.58803i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8614 | 1.07242 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.813859 | + | 1.40965i | 0.0438167 | + | 0.0758928i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.558422 | + | 0.967215i | −0.0299777 | + | 0.0519228i | −0.880625 | − | 0.473814i | \(-0.842877\pi\) |
0.850647 | + | 0.525737i | \(0.176210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.62772 | −0.140659 | −0.0703293 | − | 0.997524i | \(-0.522405\pi\) | ||||
−0.0703293 | + | 0.997524i | \(0.522405\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.500000 | + | 0.866025i | 0.0266880 | + | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.6753 | + | 28.8824i | 0.887535 | + | 1.53726i | 0.842780 | + | 0.538257i | \(0.180917\pi\) |
0.0447544 | + | 0.998998i | \(0.485749\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.55842 | − | 11.3595i | 0.348085 | − | 0.602901i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.86141 | −0.204367 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.8030 | + | 18.7113i | −0.568578 | + | 0.984806i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.05842 | − | 7.02939i | −0.213012 | − | 0.368947i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.50000 | − | 11.2583i | −0.340226 | − | 0.589288i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.55842 | + | 13.0916i | −0.394546 | + | 0.683374i | −0.993043 | − | 0.117751i | \(-0.962432\pi\) |
0.598497 | + | 0.801125i | \(0.295765\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.18614 | − | 8.98266i | 0.269980 | − | 0.467619i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.3723 | + | 17.9653i | −0.538502 | + | 0.932713i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.6168 | − | 18.3889i | 0.549719 | − | 0.952142i | −0.448574 | − | 0.893746i | \(-0.648068\pi\) |
0.998293 | − | 0.0583962i | \(-0.0185987\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.37228 | −0.225184 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.2446 | + | 26.4044i | 0.783061 | + | 1.35630i | 0.930151 | + | 0.367178i | \(0.119676\pi\) |
−0.147090 | + | 0.989123i | \(0.546991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.12772 | − | 3.68532i | 0.109006 | − | 0.188805i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.44158 | + | 14.6212i | 0.431344 | + | 0.747111i | 0.996989 | − | 0.0775384i | \(-0.0247060\pi\) |
−0.565645 | + | 0.824649i | \(0.691373\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.18614 | + | 8.98266i | 0.264310 | + | 0.457799i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.37228 | 0.171423 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.93070 | + | 3.34408i | 0.0978905 | + | 0.169551i | 0.910811 | − | 0.412823i | \(-0.135457\pi\) |
−0.812921 | + | 0.582374i | \(0.802124\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.32473 | + | 2.29451i | −0.0669947 | + | 0.116038i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.4891 | 0.882210 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.12772 | + | 3.68532i | −0.107057 | + | 0.185428i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.8832 | −0.596399 | −0.298199 | − | 0.954504i | \(-0.596386\pi\) | ||||
−0.298199 | + | 0.954504i | \(0.596386\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.1168 | −0.756789 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.7228 | −1.58416 | −0.792081 | − | 0.610416i | \(-0.791002\pi\) | ||||
−0.792081 | + | 0.610416i | \(0.791002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.74456 | −0.385784 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −39.8614 | −1.97586 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.3030 | + | 23.0414i | −0.657790 | + | 1.13933i | 0.323396 | + | 0.946264i | \(0.395175\pi\) |
−0.981186 | + | 0.193062i | \(0.938158\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.7446 | −1.02325 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.25544 | + | 5.63858i | −0.160190 | + | 0.277457i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.55842 | + | 6.16337i | 0.174676 | + | 0.302548i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.627719 | 0.0307395 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.67527 | − | 13.2940i | −0.374961 | − | 0.649452i | 0.615360 | − | 0.788246i | \(-0.289011\pi\) |
−0.990321 | + | 0.138794i | \(0.955677\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8723 | + | 24.0275i | 0.676094 | + | 1.17103i | 0.976148 | + | 0.217106i | \(0.0696619\pi\) |
−0.300054 | + | 0.953922i | \(0.597005\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.813859 | − | 1.40965i | 0.0395712 | − | 0.0685393i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.813859 | − | 1.40965i | −0.0394780 | − | 0.0683779i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.0951 | −1.26283 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.37228 | 0.211096 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0475 | + | 31.2593i | −0.869320 | + | 1.50571i | −0.00662675 | + | 0.999978i | \(0.502109\pi\) |
−0.862693 | + | 0.505728i | \(0.831224\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.81386 | + | 13.5340i | −0.375510 | + | 0.650403i | −0.990403 | − | 0.138208i | \(-0.955866\pi\) |
0.614893 | + | 0.788610i | \(0.289199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.18614 | − | 3.78651i | 0.104817 | − | 0.181549i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.18614 | + | 8.98266i | −0.248087 | + | 0.429699i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.500000 | + | 0.866025i | 0.0238637 | + | 0.0413331i | 0.877711 | − | 0.479191i | \(-0.159070\pi\) |
−0.853847 | + | 0.520524i | \(0.825737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.686141 | + | 1.18843i | 0.0326734 | + | 0.0565919i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.93070 | + | 13.7364i | −0.376799 | + | 0.652635i | −0.990595 | − | 0.136830i | \(-0.956309\pi\) |
0.613795 | + | 0.789465i | \(0.289642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.4891 | 0.544637 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.74456 | −0.413604 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.9307 | − | 34.5210i | 0.940588 | − | 1.62915i | 0.176235 | − | 0.984348i | \(-0.443608\pi\) |
0.764353 | − | 0.644798i | \(-0.223059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.6753 | − | 39.2747i | −1.06774 | − | 1.84937i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.500000 | + | 0.866025i | 0.0234920 | + | 0.0406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.37228 | −0.111214 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9891 | − | 31.1581i | 0.841496 | − | 1.45751i | −0.0471342 | − | 0.998889i | \(-0.515009\pi\) |
0.888630 | − | 0.458625i | \(-0.151658\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.813859 | − | 1.40965i | −0.0379877 | − | 0.0657966i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.510875 | 0.0237938 | 0.0118969 | − | 0.999929i | \(-0.496213\pi\) | ||||
0.0118969 | + | 0.999929i | \(0.496213\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.55842 | + | 9.62747i | 0.258322 | + | 0.447426i | 0.965792 | − | 0.259316i | \(-0.0834972\pi\) |
−0.707471 | + | 0.706743i | \(0.750164\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.87228 | − | 6.70699i | 0.179573 | − | 0.311029i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.93070 | + | 3.34408i | 0.0893423 | + | 0.154745i | 0.907233 | − | 0.420628i | \(-0.138190\pi\) |
−0.817891 | + | 0.575373i | \(0.804857\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.4198 | + | 11.8020i | 0.712022 | + | 0.544963i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.81386 | − | 3.14170i | −0.0835782 | − | 0.144762i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.37228 | − | 12.7692i | 0.338978 | − | 0.587127i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.18614 | − | 5.51856i | −0.146190 | − | 0.253209i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.74456 | −0.400386 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.67527 | + | 8.09780i | 0.213618 | + | 0.369998i | 0.952844 | − | 0.303460i | \(-0.0981418\pi\) |
−0.739226 | + | 0.673458i | \(0.764808\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.55842 | − | 7.89542i | 0.207846 | − | 0.360000i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.86141 | −0.175700 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.500000 | − | 0.866025i | −0.0227038 | − | 0.0393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.75544 | + | 6.50461i | 0.170175 | + | 0.294752i | 0.938481 | − | 0.345331i | \(-0.112233\pi\) |
−0.768306 | + | 0.640083i | \(0.778900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.50000 | − | 6.06218i | 0.158275 | − | 0.274141i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.74456 | 0.123860 | 0.0619302 | − | 0.998080i | \(-0.480274\pi\) | ||||
0.0619302 | + | 0.998080i | \(0.480274\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.11684 | 0.320527 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.18614 | + | 3.78651i | −0.0982597 | + | 0.170191i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.5584 | + | 26.9480i | 0.697891 | + | 1.20878i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.44158 | − | 11.1571i | −0.288365 | − | 0.499462i | 0.685055 | − | 0.728491i | \(-0.259778\pi\) |
−0.973420 | + | 0.229029i | \(0.926445\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.81386 | − | 11.8020i | 0.304421 | − | 0.527272i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.44158 | + | 4.22894i | −0.108865 | + | 0.188559i | −0.915311 | − | 0.402749i | \(-0.868055\pi\) |
0.806446 | + | 0.591308i | \(0.201388\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.93070 | + | 13.7364i | −0.352912 | + | 0.611261i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.7446 | 0.919487 | 0.459743 | − | 0.888052i | \(-0.347941\pi\) | ||||
0.459743 | + | 0.888052i | \(0.347941\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.8397 | 1.36427 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.18614 | − | 5.51856i | −0.140672 | − | 0.243650i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.55842 | − | 13.0916i | 0.333064 | − | 0.576884i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.55842 | − | 6.16337i | −0.156499 | − | 0.271065i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.558422 | + | 0.967215i | 0.0245120 | + | 0.0424560i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.7228 | −1.38980 | −0.694901 | − | 0.719106i | \(-0.744552\pi\) | ||||
−0.694901 | + | 0.719106i | \(0.744552\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.5584 | + | 20.0198i | 0.505415 | + | 0.875404i | 0.999980 | + | 0.00626346i | \(0.00199373\pi\) |
−0.494566 | + | 0.869140i | \(0.664673\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.18614 | − | 2.05446i | 0.0517674 | − | 0.0896638i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.6060 | 0.549125 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.1753 | − | 17.6241i | 0.442403 | − | 0.766264i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.74456 | −0.119104 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3723 | 0.449273 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.7446 | −0.636275 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.00000 | 0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.6060 | 1.27286 | 0.636430 | − | 0.771334i | \(-0.280410\pi\) | ||||
0.636430 | + | 0.771334i | \(0.280410\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.87228 | + | 11.9031i | −0.294918 | + | 0.510813i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.1168 | −0.519029 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.5000 | − | 37.2391i | 0.919274 | − | 1.59223i | 0.118753 | − | 0.992924i | \(-0.462110\pi\) |
0.800521 | − | 0.599305i | \(-0.204556\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.50000 | − | 9.52628i | −0.234734 | − | 0.406572i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.8614 | 1.18694 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.04755 | − | 8.74261i | −0.214644 | − | 0.371774i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.55842 | + | 7.89542i | 0.193494 | + | 0.335142i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.81386 | − | 6.60580i | 0.161598 | − | 0.279897i | −0.773844 | − | 0.633377i | \(-0.781668\pi\) |
0.935442 | + | 0.353480i | \(0.115002\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.68614 | + | 2.92048i | 0.0713162 | + | 0.123523i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.11684 | −0.300473 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.7228 | −1.08409 | −0.542044 | − | 0.840350i | \(-0.682349\pi\) | ||||
−0.542044 | + | 0.840350i | \(0.682349\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.55842 | + | 11.3595i | −0.275915 | + | 0.477899i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.18614 | − | 2.05446i | 0.0498132 | − | 0.0862790i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.06930 | + | 7.04823i | −0.170594 | + | 0.295477i | −0.938628 | − | 0.344932i | \(-0.887902\pi\) |
0.768034 | + | 0.640409i | \(0.221235\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.75544 | − | 11.7008i | 0.282706 | − | 0.489662i | −0.689344 | − | 0.724434i | \(-0.742101\pi\) |
0.972050 | + | 0.234772i | \(0.0754345\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.55842 | − | 16.5557i | −0.399309 | − | 0.691623i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.813859 | − | 1.40965i | −0.0339403 | − | 0.0587863i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.6168 | + | 37.4415i | −0.899921 | + | 1.55871i | −0.0723275 | + | 0.997381i | \(0.523043\pi\) |
−0.827593 | + | 0.561328i | \(0.810291\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.116844 | 0.00485587 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.8832 | −0.700431 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.1168 | + | 33.1113i | −0.791739 | + | 1.37133i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.500000 | − | 0.866025i | −0.0206725 | − | 0.0358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.302985 | − | 0.524785i | −0.0125055 | − | 0.0216602i | 0.859705 | − | 0.510791i | \(-0.170647\pi\) |
−0.872210 | + | 0.489131i | \(0.837314\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.3505 | 2.03345 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.18614 | − | 8.98266i | 0.213329 | − | 0.369497i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.1861 | + | 19.3750i | 0.459360 | + | 0.795634i | 0.998927 | − | 0.0463080i | \(-0.0147456\pi\) |
−0.539567 | + | 0.841942i | \(0.681412\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.86141 | 0.158302 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.87228 | + | 3.24289i | 0.0766274 | + | 0.132723i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.55842 | − | 6.16337i | 0.145393 | − | 0.251828i | −0.784126 | − | 0.620601i | \(-0.786889\pi\) |
0.929520 | + | 0.368773i | \(0.120222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.2446 | − | 24.6723i | −0.581048 | − | 1.00640i | −0.995356 | − | 0.0962675i | \(-0.969310\pi\) |
0.414308 | − | 0.910137i | \(-0.364024\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.05842 | + | 8.11663i | −0.0431023 | + | 0.330535i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.05842 | + | 7.02939i | 0.164998 | + | 0.285785i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9891 | + | 34.6222i | −0.811334 | + | 1.40527i | 0.100597 | + | 0.994927i | \(0.467925\pi\) |
−0.911931 | + | 0.410344i | \(0.865409\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.18614 | + | 8.98266i | 0.210153 | + | 0.363996i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.62772 | 0.0658504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6168 | + | 28.7812i | 0.671148 | + | 1.16246i | 0.977579 | + | 0.210570i | \(0.0675318\pi\) |
−0.306431 | + | 0.951893i | \(0.599135\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.18614 | + | 8.98266i | −0.209125 | + | 0.362216i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.97825 | −0.200417 | −0.100208 | − | 0.994966i | \(-0.531951\pi\) | ||||
−0.100208 | + | 0.994966i | \(0.531951\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.38316 | − | 12.7880i | −0.296754 | − | 0.513993i | 0.678637 | − | 0.734474i | \(-0.262571\pi\) |
−0.975391 | + | 0.220480i | \(0.929238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.813859 | − | 1.40965i | −0.0326591 | − | 0.0565671i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.6277 | + | 23.6039i | −0.545983 | + | 0.945670i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −27.8614 | −1.11268 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.41983 | + | 12.8515i | −0.295848 | + | 0.512424i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.4198 | − | 40.5643i | −0.932329 | − | 1.61484i | −0.779330 | − | 0.626614i | \(-0.784440\pi\) |
−0.152999 | − | 0.988226i | \(-0.548893\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.87228 | + | 3.24289i | 0.0744165 | + | 0.128893i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.12772 | + | 3.68532i | −0.0844359 | + | 0.146247i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.686141 | + | 1.18843i | −0.0271859 | + | 0.0470873i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.55842 | + | 11.3595i | −0.259447 | + | 0.449376i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.6753 | − | 39.2747i | 0.895619 | − | 1.55126i | 0.0625827 | − | 0.998040i | \(-0.480066\pi\) |
0.833036 | − | 0.553218i | \(-0.186600\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.4674 | 1.43813 | 0.719066 | − | 0.694941i | \(-0.244570\pi\) | ||||
0.719066 | + | 0.694941i | \(0.244570\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.37228 | −0.132783 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.3030 | − | 21.3094i | −0.483680 | − | 0.837759i | 0.516144 | − | 0.856502i | \(-0.327367\pi\) |
−0.999824 | + | 0.0187430i | \(0.994034\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | + | 10.3923i | −0.235521 | + | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.18614 | + | 15.9109i | 0.360033 | + | 0.623596i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.4416 | + | 25.0135i | 0.565143 | + | 0.978856i | 0.997036 | + | 0.0769313i | \(0.0245122\pi\) |
−0.431894 | + | 0.901924i | \(0.642154\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.4891 | −0.683357 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.50000 | + | 11.2583i | 0.253589 | + | 0.439229i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.81386 | − | 11.8020i | 0.265430 | − | 0.459739i | −0.702246 | − | 0.711934i | \(-0.747819\pi\) |
0.967676 | + | 0.252196i | \(0.0811527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.8832 | 0.617783 | 0.308892 | − | 0.951097i | \(-0.400042\pi\) | ||||
0.308892 | + | 0.951097i | \(0.400042\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.813859 | − | 1.40965i | 0.0316077 | − | 0.0547461i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.1168 | 0.586206 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.11684 | 0.275565 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.88316 | −0.227456 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −48.0951 | −1.85669 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.6060 | 1.14123 | 0.570613 | − | 0.821219i | \(-0.306706\pi\) | ||||
0.570613 | + | 0.821219i | \(0.306706\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.6753 | − | 39.2747i | 0.871481 | − | 1.50945i | 0.0110168 | − | 0.999939i | \(-0.496493\pi\) |
0.860464 | − | 0.509511i | \(-0.170174\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.37228 | 0.0910398 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.9307 | − | 18.9325i | 0.418865 | − | 0.725496i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.4416 | + | 25.0135i | 0.552592 | + | 0.957117i | 0.998087 | + | 0.0618323i | \(0.0196944\pi\) |
−0.445495 | + | 0.895284i | \(0.646972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7446 | 0.792609 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.61684 | − | 16.6569i | −0.366905 | − | 0.635499i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.37228 | − | 7.57301i | −0.166571 | − | 0.288509i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.6753 | − | 32.3465i | 0.710441 | − | 1.23052i | −0.254251 | − | 0.967138i | \(-0.581829\pi\) |
0.964692 | − | 0.263381i | \(-0.0848376\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.18614 | − | 8.98266i | −0.197005 | − | 0.341223i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.627719 | −0.0238107 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.8832 | −0.639495 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.81386 | − | 6.60580i | 0.144253 | − | 0.249854i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.81386 | + | 11.8020i | −0.257356 | + | 0.445754i | −0.965533 | − | 0.260282i | \(-0.916185\pi\) |
0.708177 | + | 0.706035i | \(0.249518\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.0475 | + | 50.3118i | −1.09555 | + | 1.89755i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.813859 | + | 1.40965i | −0.0306517 | + | 0.0530903i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.8139 | − | 32.5866i | −0.707568 | − | 1.22554i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.69702 | + | 8.13547i | 0.176400 | + | 0.305534i | 0.940645 | − | 0.339392i | \(-0.110221\pi\) |
−0.764245 | + | 0.644926i | \(0.776888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.12772 | − | 3.68532i | 0.0797957 | − | 0.138210i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.6060 | 0.472097 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.37228 | −0.163514 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.44158 | − | 9.42509i | 0.203219 | − | 0.351986i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.4416 | − | 30.2097i | −0.650461 | − | 1.12663i | −0.983011 | − | 0.183546i | \(-0.941242\pi\) |
0.332550 | − | 0.943086i | \(-0.392091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.9307 | + | 31.0569i | 0.667774 | + | 1.15662i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.1168 | 0.896915 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.18614 | + | 3.78651i | −0.0811912 | + | 0.140627i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.6168 | + | 18.3889i | 0.393757 | + | 0.682007i | 0.992942 | − | 0.118604i | \(-0.0378418\pi\) |
−0.599185 | + | 0.800611i | \(0.704508\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.74456 | − | 4.75372i | −0.101511 | − | 0.175823i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.5584 | + | 39.0723i | −0.833214 | + | 1.44317i | 0.0622617 | + | 0.998060i | \(0.480169\pi\) |
−0.895476 | + | 0.445110i | \(0.853165\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.686141 | − | 1.18843i | −0.0253087 | − | 0.0438359i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.4198 | + | 21.7518i | 1.04686 | + | 0.801239i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.24456 | − | 3.88770i | −0.0825676 | − | 0.143011i | 0.821785 | − | 0.569798i | \(-0.192979\pi\) |
−0.904352 | + | 0.426787i | \(0.859645\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.18614 | − | 5.51856i | 0.117046 | − | 0.202729i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.30298 | + | 16.1132i | 0.341293 | + | 0.591138i | 0.984673 | − | 0.174410i | \(-0.0558017\pi\) |
−0.643380 | + | 0.765547i | \(0.722468\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.74456 | 0.320376 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.55842 | − | 6.16337i | −0.130196 | − | 0.225506i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.4674 | −0.746865 | −0.373433 | − | 0.927657i | \(-0.621819\pi\) | ||||
−0.373433 | + | 0.927657i | \(0.621819\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.55842 | − | 16.5557i | −0.348328 | − | 0.603322i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.500000 | − | 0.866025i | −0.0181969 | − | 0.0315179i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.7337 | + | 23.7874i | −0.499159 | + | 0.864569i | −1.00000 | 0.000970394i | \(-0.999691\pi\) | |
0.500840 | + | 0.865540i | \(0.333024\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.11684 | −0.258325 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.3723 | − | 24.8935i | 0.520312 | − | 0.901206i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.813859 | + | 1.40965i | 0.0294251 | + | 0.0509658i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.37228 | − | 2.37686i | −0.0495502 | − | 0.0858235i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.9891 | − | 20.7658i | 0.432339 | − | 0.748833i | −0.564735 | − | 0.825272i | \(-0.691022\pi\) |
0.997074 | + | 0.0764391i | \(0.0243551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.18614 | − | 8.98266i | 0.186774 | − | 0.323503i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.1861 | + | 24.5711i | −0.510240 | + | 0.883762i | 0.489690 | + | 0.871897i | \(0.337110\pi\) |
−0.999930 | + | 0.0118648i | \(0.996223\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.87228 | + | 6.70699i | −0.139096 | + | 0.240922i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.6277 | −0.775890 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −66.0951 | −2.36810 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.6753 | + | 49.6670i | 1.02608 | + | 1.77723i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.18614 | + | 3.78651i | −0.0781263 | + | 0.135319i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.81386 | + | 3.14170i | 0.0647394 | + | 0.112132i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.55842 | + | 9.62747i | 0.198136 | + | 0.343182i | 0.947924 | − | 0.318496i | \(-0.103178\pi\) |
−0.749788 | + | 0.661678i | \(0.769844\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.48913 | 0.195418 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.5584 | − | 26.9480i | −0.553194 | − | 0.958160i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.50000 | − | 9.52628i | 0.195311 | − | 0.338288i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.74456 | 0.310138 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.06930 | − | 1.85208i | 0.0378764 | − | 0.0656039i | −0.846466 | − | 0.532443i | \(-0.821274\pi\) |
0.884342 | + | 0.466839i | \(0.154607\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.64947 | −0.0937314 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.4891 | −0.405948 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56.8397 | 2.00583 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.86141 | 0.136097 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.7446 | 0.730243 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.4891 | −0.825834 | −0.412917 | − | 0.910769i | \(-0.635490\pi\) | ||||
−0.412917 | + | 0.910769i | \(0.635490\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.9891 | + | 34.6222i | −0.701913 | + | 1.21575i | 0.265881 | + | 0.964006i | \(0.414337\pi\) |
−0.967794 | + | 0.251743i | \(0.918996\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.1168 | −0.915958 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.50000 | + | 6.06218i | −0.122600 | + | 0.212349i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.7446 | − | 18.6101i | −0.375905 | − | 0.651086i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.37228 | 0.0828942 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.55842 | + | 11.3595i | 0.228891 | + | 0.396450i | 0.957480 | − | 0.288501i | \(-0.0931569\pi\) |
−0.728589 | + | 0.684951i | \(0.759824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.87228 | + | 13.6352i | 0.274410 | + | 0.475293i | 0.969986 | − | 0.243160i | \(-0.0781840\pi\) |
−0.695576 | + | 0.718453i | \(0.744851\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.18614 | − | 3.78651i | 0.0761116 | − | 0.131829i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.30298 | + | 16.1132i | 0.323496 | + | 0.560312i | 0.981207 | − | 0.192959i | \(-0.0618083\pi\) |
−0.657710 | + | 0.753271i | \(0.728475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.6060 | 1.44504 | 0.722518 | − | 0.691353i | \(-0.242985\pi\) | ||||
0.722518 | + | 0.691353i | \(0.242985\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.8614 | 0.515536 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.11684 | − | 1.93443i | 0.0386964 | − | 0.0670240i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.81386 | + | 11.8020i | −0.235803 | + | 0.408423i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.87228 | + | 6.70699i | −0.133846 | + | 0.231827i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.30298 | + | 16.1132i | −0.321175 | + | 0.556291i | −0.980731 | − | 0.195365i | \(-0.937411\pi\) |
0.659556 | + | 0.751655i | \(0.270744\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.94158 | + | 8.55906i | 0.170399 | + | 0.295140i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.81386 | − | 11.8020i | −0.234682 | − | 0.406481i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | + | 10.3923i | −0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.2554 | −0.661625 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.4891 | 0.462946 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.41983 | + | 12.8515i | −0.254348 | + | 0.440544i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.38316 | + | 4.12775i | 0.0815977 | + | 0.141331i | 0.903936 | − | 0.427667i | \(-0.140664\pi\) |
−0.822339 | + | 0.568998i | \(0.807331\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.18614 | + | 5.51856i | 0.108964 | + | 0.188731i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.2337 | 0.486214 | 0.243107 | − | 0.970000i | \(-0.421833\pi\) | ||||
0.243107 | + | 0.970000i | \(0.421833\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.87228 | + | 17.0993i | −0.336838 | + | 0.583420i | −0.983836 | − | 0.179071i | \(-0.942691\pi\) |
0.646998 | + | 0.762491i | \(0.276024\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.3030 | − | 21.3094i | −0.419285 | − | 0.726222i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.2119 | 1.06247 | 0.531233 | − | 0.847226i | \(-0.321729\pi\) | ||||
0.531233 | + | 0.847226i | \(0.321729\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.558422 | − | 0.967215i | −0.0189869 | − | 0.0328863i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.17527 | − | 12.4279i | 0.243685 | − | 0.422074i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.30298 | − | 16.1132i | −0.315582 | − | 0.546604i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.55842 | + | 3.14170i | −0.256107 | + | 0.106452i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.500000 | + | 0.866025i | 0.0169224 | + | 0.0293105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.18614 | + | 2.05446i | −0.0400989 | + | 0.0694533i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.3614 | − | 31.8029i | −0.620021 | − | 1.07391i | −0.989481 | − | 0.144661i | \(-0.953791\pi\) |
0.369461 | − | 0.929246i | \(-0.379542\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00000 | −0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.1861 | − | 24.5711i | −0.477943 | − | 0.827822i | 0.521737 | − | 0.853106i | \(-0.325284\pi\) |
−0.999680 | + | 0.0252844i | \(0.991951\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.3030 | + | 28.2376i | −0.548639 | + | 0.950271i | 0.449729 | + | 0.893165i | \(0.351521\pi\) |
−0.998368 | + | 0.0571058i | \(0.981813\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.74456 | 0.0922575 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.0475 | + | 31.2593i | 0.605977 | + | 1.04958i | 0.991896 | + | 0.127051i | \(0.0405511\pi\) |
−0.385919 | + | 0.922533i | \(0.626116\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.04755 | − | 8.74261i | −0.169289 | − | 0.293218i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.18614 | − | 3.78651i | 0.0732385 | − | 0.126853i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.3723 | −0.347095 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.7446 | 0.492856 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.813859 | − | 1.40965i | 0.0271740 | − | 0.0470667i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.9307 | − | 29.3248i | −0.564671 | − | 0.978038i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.11684 | + | 12.3267i | 0.237096 | + | 0.410663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.00000 | − | 6.92820i | 0.133112 | − | 0.230556i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.87228 | − | 11.9031i | 0.228442 | − | 0.395674i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.6753 | − | 21.9542i | 0.420875 | − | 0.728977i | −0.575150 | − | 0.818048i | \(-0.695056\pi\) |
0.996025 | + | 0.0890706i | \(0.0283897\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.93070 | − | 13.7364i | 0.263045 | − | 0.455607i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 58.9783 | 1.95404 | 0.977018 | − | 0.213155i | \(-0.0683741\pi\) | ||||
0.977018 | + | 0.213155i | \(0.0683741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.1168 | −1.02982 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.50000 | + | 9.52628i | 0.181824 | + | 0.314929i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.7446 | − | 35.9306i | 0.685046 | − | 1.18653i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.441578 | − | 0.764836i | −0.0145663 | − | 0.0252296i | 0.858650 | − | 0.512562i | \(-0.171303\pi\) |
−0.873217 | + | 0.487332i | \(0.837970\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.500000 | + | 0.866025i | 0.0164756 | + | 0.0285365i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.1168 | −0.431746 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.55842 | − | 7.89542i | −0.149880 | − | 0.259600i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.55842 | + | 13.0916i | −0.248251 | + | 0.429984i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.2337 | 1.64811 | 0.824057 | − | 0.566507i | \(-0.191706\pi\) | ||||
0.824057 | + | 0.566507i | \(0.191706\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.37228 | − | 7.57301i | 0.143296 | − | 0.248195i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.2337 | 0.662421 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.11684 | 0.232746 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.1168 | 0.787863 | 0.393931 | − | 0.919140i | \(-0.371115\pi\) | ||||
0.393931 | + | 0.919140i | \(0.371115\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.4891 | 0.636004 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.5109 | −0.407843 | −0.203921 | − | 0.978987i | \(-0.565369\pi\) | ||||
−0.203921 | + | 0.978987i | \(0.565369\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.8832 | −0.549791 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.18614 | + | 2.05446i | −0.0385852 | + | 0.0668315i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.9565 | 1.88333 | 0.941667 | − | 0.336547i | \(-0.109259\pi\) | ||||
0.941667 | + | 0.336547i | \(0.109259\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.50000 | + | 11.2583i | −0.210999 | + | 0.365461i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.558422 | + | 0.967215i | 0.0181081 | + | 0.0313641i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.25544 | −0.105454 | −0.0527270 | − | 0.998609i | \(-0.516791\pi\) | ||||
−0.0527270 | + | 0.998609i | \(0.516791\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.55842 | + | 16.5557i | 0.309303 | + | 0.535729i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.55842 | + | 16.5557i | 0.308980 | + | 0.535169i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.6060 | + | 42.6188i | −0.794568 | + | 1.37623i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.4891 | − | 25.0959i | −0.467391 | − | 0.809545i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.116844 | −0.00376134 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.7337 | + | 39.3759i | −0.731066 | + | 1.26624i | 0.225362 | + | 0.974275i | \(0.427644\pi\) |
−0.956428 | + | 0.291969i | \(0.905690\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.18614 | + | 8.98266i | −0.166603 | + | 0.288565i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.18614 | − | 3.78651i | 0.0701566 | − | 0.121515i | −0.828813 | − | 0.559525i | \(-0.810983\pi\) |
0.898970 | + | 0.438011i | \(0.144317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.744563 | − | 1.28962i | 0.0238696 | − | 0.0413433i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.500000 | + | 0.866025i | 0.0160128 | + | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.9307 | − | 18.9325i | −0.349704 | − | 0.605705i | 0.636493 | − | 0.771283i | \(-0.280385\pi\) |
−0.986197 | + | 0.165577i | \(0.947051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.1168 | + | 43.5036i | −0.802738 | + | 1.39038i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.1168 | 0.386861 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0217 | −0.415329 | −0.207665 | − | 0.978200i | \(-0.566586\pi\) | ||||
−0.207665 | + | 0.978200i | \(0.566586\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.18614 | + | 8.98266i | −0.165244 | + | 0.286211i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.93070 | − | 3.34408i | −0.0614550 | − | 0.106443i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.74456 | − | 4.75372i | −0.0872720 | − | 0.151160i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.4674 | −1.79375 | −0.896873 | − | 0.442289i | \(-0.854167\pi\) | ||||
−0.896873 | + | 0.442289i | \(0.854167\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.98913 | + | 13.8376i | −0.253527 | + | 0.439122i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.87228 | − | 3.24289i | −0.0593553 | − | 0.102806i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.4674 | −1.21827 | −0.609137 | − | 0.793065i | \(-0.708484\pi\) | ||||
−0.609137 | + | 0.793065i | \(0.708484\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.55842 | − | 7.89542i | −0.144222 | − | 0.249800i |
(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 | 4020.2.q.i.841.2 | ✓ | 4 | |
67.29 | even | 3 | inner | 4020.2.q.i.3781.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.i.841.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4020.2.q.i.3781.2 | yes | 4 | 67.29 | even | 3 | inner |