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: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} + 11 x^{12} - 8 x^{11} + 88 x^{10} - 57 x^{9} + 270 x^{8} + 17 x^{7} + 458 x^{6} - 101 x^{5} + 189 x^{4} - 30 x^{3} + 54 x^{2} - 12 x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 3781.6 | ||
Root | \(-1.36264 - 2.36015i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.3781 |
Dual form | 4020.2.q.k.841.6 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(7\) | 1.26463 | + | 2.19041i | 0.477986 | + | 0.827896i | 0.999682 | − | 0.0252357i | \(-0.00803361\pi\) |
−0.521695 | + | 0.853132i | \(0.674700\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0636774 | + | 0.110293i | 0.0191995 | + | 0.0332544i | 0.875466 | − | 0.483281i | \(-0.160555\pi\) |
−0.856266 | + | 0.516535i | \(0.827222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.22527 | + | 3.85428i | −0.617179 | + | 1.06899i | 0.372819 | + | 0.927904i | \(0.378391\pi\) |
−0.989998 | + | 0.141081i | \(0.954942\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.129720 | − | 0.224682i | 0.0314618 | − | 0.0544935i | −0.849866 | − | 0.526999i | \(-0.823317\pi\) |
0.881328 | + | 0.472506i | \(0.156650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.21355 | − | 5.56603i | 0.737239 | − | 1.27694i | −0.216495 | − | 0.976284i | \(-0.569463\pi\) |
0.953734 | − | 0.300652i | \(-0.0972041\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.26463 | − | 2.19041i | −0.275965 | − | 0.477986i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.09212 | − | 5.35572i | 0.644753 | − | 1.11674i | −0.339606 | − | 0.940568i | \(-0.610294\pi\) |
0.984359 | − | 0.176176i | \(-0.0563729\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.920164 | − | 1.59377i | −0.170870 | − | 0.295956i | 0.767854 | − | 0.640625i | \(-0.221325\pi\) |
−0.938724 | + | 0.344669i | \(0.887991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.61911 | − | 4.53644i | −0.470407 | − | 0.814768i | 0.529021 | − | 0.848609i | \(-0.322559\pi\) |
−0.999427 | + | 0.0338409i | \(0.989226\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0636774 | − | 0.110293i | −0.0110848 | − | 0.0191995i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.26463 | + | 2.19041i | 0.213762 | + | 0.370246i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.92280 | − | 8.52654i | 0.809303 | − | 1.40175i | −0.104044 | − | 0.994573i | \(-0.533178\pi\) |
0.913347 | − | 0.407182i | \(-0.133488\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.22527 | − | 3.85428i | 0.356328 | − | 0.617179i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.579529 | + | 1.00377i | 0.0905072 | + | 0.156763i | 0.907725 | − | 0.419566i | \(-0.137818\pi\) |
−0.817217 | + | 0.576329i | \(0.804485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.35137 | 0.358580 | 0.179290 | − | 0.983796i | \(-0.442620\pi\) | ||||
0.179290 | + | 0.983796i | \(0.442620\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.48732 | + | 9.50432i | 0.800408 | + | 1.38635i | 0.919348 | + | 0.393446i | \(0.128717\pi\) |
−0.118940 | + | 0.992901i | \(0.537950\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.301411 | − | 0.522059i | 0.0430587 | − | 0.0745798i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.129720 | + | 0.224682i | −0.0181645 | + | 0.0314618i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.37847 | −0.326708 | −0.163354 | − | 0.986568i | \(-0.552231\pi\) | ||||
−0.163354 | + | 0.986568i | \(0.552231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0636774 | + | 0.110293i | 0.00858626 | + | 0.0148718i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.21355 | + | 5.56603i | −0.425645 | + | 0.737239i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.400614 | −0.0521555 | −0.0260777 | − | 0.999660i | \(-0.508302\pi\) | ||||
−0.0260777 | + | 0.999660i | \(0.508302\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.78302 | − | 4.82033i | 0.356329 | − | 0.617180i | −0.631015 | − | 0.775770i | \(-0.717362\pi\) |
0.987344 | + | 0.158590i | \(0.0506949\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.26463 | + | 2.19041i | 0.159329 | + | 0.275965i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.22527 | + | 3.85428i | −0.276011 | + | 0.478065i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.76655 | + | 2.58469i | 0.948836 | + | 0.315771i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.09212 | + | 5.35572i | −0.372248 | + | 0.644753i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.62714 | + | 6.28239i | 0.430462 | + | 0.745582i | 0.996913 | − | 0.0785133i | \(-0.0250173\pi\) |
−0.566451 | + | 0.824095i | \(0.691684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00399 | − | 1.73897i | 0.117509 | − | 0.203531i | −0.801271 | − | 0.598301i | \(-0.795843\pi\) |
0.918780 | + | 0.394770i | \(0.129176\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.161057 | + | 0.278959i | −0.0183542 | + | 0.0317903i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.753802 | + | 1.30562i | 0.0848094 | + | 0.146894i | 0.905310 | − | 0.424752i | \(-0.139639\pi\) |
−0.820501 | + | 0.571646i | \(0.806305\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.21009 | + | 5.56004i | −0.352353 | + | 0.610294i | −0.986661 | − | 0.162786i | \(-0.947952\pi\) |
0.634308 | + | 0.773081i | \(0.281285\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.129720 | − | 0.224682i | 0.0140702 | − | 0.0243702i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.920164 | + | 1.59377i | 0.0986520 | + | 0.170870i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.27157 | −0.134786 | −0.0673932 | − | 0.997726i | \(-0.521468\pi\) | ||||
−0.0673932 | + | 0.997726i | \(0.521468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.2566 | −1.18001 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.61911 | + | 4.53644i | 0.271589 | + | 0.470407i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.21355 | − | 5.56603i | 0.329703 | − | 0.571063i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.93224 | + | 5.07880i | −0.297724 | + | 0.515674i | −0.975615 | − | 0.219489i | \(-0.929561\pi\) |
0.677891 | + | 0.735163i | \(0.262894\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0636774 | + | 0.110293i | 0.00639982 | + | 0.0110848i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.52837 | + | 2.64722i | 0.152079 | + | 0.263408i | 0.931992 | − | 0.362480i | \(-0.118070\pi\) |
−0.779913 | + | 0.625888i | \(0.784737\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.62209 | + | 11.4698i | 0.652494 | + | 1.13015i | 0.982516 | + | 0.186180i | \(0.0596107\pi\) |
−0.330021 | + | 0.943973i | \(0.607056\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.26463 | − | 2.19041i | −0.123415 | − | 0.213762i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.51097 | 0.919460 | 0.459730 | − | 0.888059i | \(-0.347946\pi\) | ||||
0.459730 | + | 0.888059i | \(0.347946\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.74556 | 0.646107 | 0.323054 | − | 0.946381i | \(-0.395291\pi\) | ||||
0.323054 | + | 0.946381i | \(0.395291\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.92280 | + | 8.52654i | −0.467251 | + | 0.809303i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.56883 | − | 7.91345i | −0.429800 | − | 0.744435i | 0.567056 | − | 0.823679i | \(-0.308082\pi\) |
−0.996855 | + | 0.0792448i | \(0.974749\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.09212 | − | 5.35572i | 0.288342 | − | 0.499423i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.22527 | + | 3.85428i | −0.205726 | + | 0.356328i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.656194 | 0.0601532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.49189 | − | 9.51223i | 0.499263 | − | 0.864748i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.579529 | − | 1.00377i | −0.0522544 | − | 0.0905072i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.10991 | − | 1.92242i | −0.0984887 | − | 0.170587i | 0.812571 | − | 0.582863i | \(-0.198067\pi\) |
−0.911059 | + | 0.412275i | \(0.864734\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.35137 | −0.207026 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.0542 | −1.83952 | −0.919758 | − | 0.392487i | \(-0.871615\pi\) | ||||
−0.919758 | + | 0.392487i | \(0.871615\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.2558 | 1.40956 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.65782 | 0.654252 | 0.327126 | − | 0.944981i | \(-0.393920\pi\) | ||||
0.327126 | + | 0.944981i | \(0.393920\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0649 | 1.10815 | 0.554074 | − | 0.832467i | \(-0.313072\pi\) | ||||
0.554074 | + | 0.832467i | \(0.313072\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.48732 | − | 9.50432i | −0.462116 | − | 0.800408i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.566798 | −0.0473980 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.920164 | − | 1.59377i | −0.0764155 | − | 0.132355i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.301411 | + | 0.522059i | −0.0248599 | + | 0.0430587i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.39911 | −0.114619 | −0.0573096 | − | 0.998356i | \(-0.518252\pi\) | ||||
−0.0573096 | + | 0.998356i | \(0.518252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.77578 | + | 15.2001i | −0.714163 | + | 1.23697i | 0.249118 | + | 0.968473i | \(0.419859\pi\) |
−0.963281 | + | 0.268494i | \(0.913474\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.129720 | − | 0.224682i | 0.0104873 | − | 0.0181645i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.61911 | − | 4.53644i | −0.210372 | − | 0.364375i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.24823 | + | 3.89404i | −0.179428 | + | 0.310779i | −0.941685 | − | 0.336496i | \(-0.890758\pi\) |
0.762257 | + | 0.647275i | \(0.224091\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.37847 | 0.188625 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.6416 | 1.23273 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4296 | + | 18.0645i | 0.816907 | + | 1.41492i | 0.907951 | + | 0.419077i | \(0.137646\pi\) |
−0.0910440 | + | 0.995847i | \(0.529020\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0636774 | − | 0.110293i | −0.00495728 | − | 0.00858626i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.14610 | − | 10.6454i | −0.475600 | − | 0.823763i | 0.524010 | − | 0.851712i | \(-0.324436\pi\) |
−0.999609 | + | 0.0279497i | \(0.991102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.40366 | − | 5.89531i | −0.261820 | − | 0.453485i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.21355 | − | 5.56603i | 0.245746 | − | 0.425645i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.90299 | − | 6.76018i | 0.296739 | − | 0.513967i | −0.678649 | − | 0.734463i | \(-0.737434\pi\) |
0.975388 | + | 0.220496i | \(0.0707676\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.26463 | + | 2.19041i | 0.0955972 | + | 0.165579i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.400614 | 0.0301120 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.9995 | 1.19586 | 0.597929 | − | 0.801549i | \(-0.295990\pi\) | ||||
0.597929 | + | 0.801549i | \(0.295990\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8380 | − | 18.7720i | −0.805583 | − | 1.39531i | −0.915897 | − | 0.401414i | \(-0.868519\pi\) |
0.110314 | − | 0.993897i | \(-0.464814\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.78302 | + | 4.82033i | −0.205727 | + | 0.356329i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.92280 | − | 8.52654i | 0.361931 | − | 0.626884i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0330410 | 0.00241620 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.26463 | − | 2.19041i | −0.0919885 | − | 0.159329i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8281 | + | 22.2189i | −0.928207 | + | 1.60770i | −0.141888 | + | 0.989883i | \(0.545317\pi\) |
−0.786320 | + | 0.617820i | \(0.788016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.9337 | 1.29090 | 0.645449 | − | 0.763804i | \(-0.276670\pi\) | ||||
0.645449 | + | 0.763804i | \(0.276670\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.22527 | − | 3.85428i | 0.159355 | − | 0.276011i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.49225 | − | 6.04876i | −0.248813 | − | 0.430956i | 0.714384 | − | 0.699754i | \(-0.246707\pi\) |
−0.963197 | + | 0.268798i | \(0.913374\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.19684 | + | 2.07299i | −0.0848417 | + | 0.146950i | −0.905324 | − | 0.424722i | \(-0.860372\pi\) |
0.820482 | + | 0.571672i | \(0.193705\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.76655 | − | 2.58469i | −0.547810 | − | 0.182310i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.32734 | − | 4.03107i | 0.163347 | − | 0.282926i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.579529 | + | 1.00377i | 0.0404761 | + | 0.0701066i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.09212 | − | 5.35572i | 0.214918 | − | 0.372248i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.818522 | 0.0566184 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.40604 | − | 2.43533i | 0.0967959 | − | 0.167655i | −0.813561 | − | 0.581480i | \(-0.802474\pi\) |
0.910357 | + | 0.413824i | \(0.135807\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.62714 | − | 6.28239i | −0.248527 | − | 0.430462i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.35137 | 0.160362 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.62443 | − | 11.4738i | 0.449695 | − | 0.778895i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00399 | + | 1.73897i | −0.0678436 | + | 0.117509i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.577326 | + | 0.999958i | 0.0388352 | + | 0.0672645i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.8891 | −0.863117 | −0.431558 | − | 0.902085i | \(-0.642036\pi\) | ||||
−0.431558 | + | 0.902085i | \(0.642036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.67253 | + | 8.09306i | 0.310127 | + | 0.537155i | 0.978390 | − | 0.206770i | \(-0.0662952\pi\) |
−0.668263 | + | 0.743925i | \(0.732962\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.60442 | − | 2.77893i | 0.106023 | − | 0.183637i | −0.808133 | − | 0.589000i | \(-0.799522\pi\) |
0.914156 | + | 0.405363i | \(0.132855\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.161057 | − | 0.278959i | 0.0105968 | − | 0.0183542i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.73530 | + | 9.93383i | 0.375732 | + | 0.650787i | 0.990436 | − | 0.137971i | \(-0.0440580\pi\) |
−0.614704 | + | 0.788758i | \(0.710725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.48732 | + | 9.50432i | 0.357953 | + | 0.619993i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.753802 | − | 1.30562i | −0.0489647 | − | 0.0848094i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.95082 | − | 5.11096i | −0.190872 | − | 0.330601i | 0.754667 | − | 0.656108i | \(-0.227798\pi\) |
−0.945540 | + | 0.325507i | \(0.894465\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.02817 | 0.581556 | 0.290778 | − | 0.956791i | \(-0.406086\pi\) | ||||
0.290778 | + | 0.956791i | \(0.406086\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.301411 | − | 0.522059i | 0.0192564 | − | 0.0333531i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.3020 | + | 24.7719i | 0.910017 | + | 1.57620i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.21009 | − | 5.56004i | 0.203431 | − | 0.352353i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.88177 | + | 4.99137i | −0.181896 | + | 0.315052i | −0.942526 | − | 0.334133i | \(-0.891557\pi\) |
0.760630 | + | 0.649185i | \(0.224890\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.787594 | 0.0495156 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.129720 | + | 0.224682i | −0.00812341 | + | 0.0140702i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.0716 | − | 24.3727i | −0.877761 | − | 1.52033i | −0.853792 | − | 0.520614i | \(-0.825703\pi\) |
−0.0239683 | − | 0.999713i | \(-0.507630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.9021 | 1.54734 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.920164 | − | 1.59377i | −0.0569567 | − | 0.0986520i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3621 | 0.885607 | 0.442803 | − | 0.896619i | \(-0.353984\pi\) | ||||
0.442803 | + | 0.896619i | \(0.353984\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.37847 | −0.146108 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.27157 | 0.0778190 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.7111 | 1.32375 | 0.661873 | − | 0.749616i | \(-0.269762\pi\) | ||||
0.661873 | + | 0.749616i | \(0.269762\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.7458 | 0.652758 | 0.326379 | − | 0.945239i | \(-0.394171\pi\) | ||||
0.326379 | + | 0.945239i | \(0.394171\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.2566 | 0.681280 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0636774 | + | 0.110293i | 0.00383989 | + | 0.00665089i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.2641 | 1.63814 | 0.819070 | − | 0.573693i | \(-0.194490\pi\) | ||||
0.819070 | + | 0.573693i | \(0.194490\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.61911 | − | 4.53644i | −0.156802 | − | 0.271589i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.30782 | + | 10.9255i | −0.376293 | + | 0.651758i | −0.990520 | − | 0.137371i | \(-0.956135\pi\) |
0.614227 | + | 0.789130i | \(0.289468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.7031 | 1.34956 | 0.674780 | − | 0.738019i | \(-0.264239\pi\) | ||||
0.674780 | + | 0.738019i | \(0.264239\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.21355 | + | 5.56603i | −0.190354 | + | 0.329703i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.46578 | + | 2.53881i | −0.0865224 | + | 0.149861i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.46635 | + | 14.6641i | 0.498020 | + | 0.862596i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.93224 | − | 5.07880i | 0.171891 | − | 0.297724i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.2730 | −0.600156 | −0.300078 | − | 0.953915i | \(-0.597013\pi\) | ||||
−0.300078 | + | 0.953915i | \(0.597013\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.400614 | −0.0233246 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.0636774 | − | 0.110293i | −0.00369494 | − | 0.00639982i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.7616 | + | 23.8358i | 0.795855 | + | 1.37846i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.97362 | + | 5.15045i | 0.171396 | + | 0.296867i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.52837 | − | 2.64722i | −0.0878028 | − | 0.152079i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.78302 | − | 4.82033i | 0.159355 | − | 0.276011i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.66618 | + | 9.81412i | −0.323386 | + | 0.560121i | −0.981184 | − | 0.193073i | \(-0.938155\pi\) |
0.657798 | + | 0.753194i | \(0.271488\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.62209 | − | 11.4698i | −0.376718 | − | 0.652494i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.3637 | 0.757784 | 0.378892 | − | 0.925441i | \(-0.376305\pi\) | ||||
0.378892 | + | 0.925441i | \(0.376305\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.3998 | 1.26611 | 0.633057 | − | 0.774105i | \(-0.281800\pi\) | ||||
0.633057 | + | 0.774105i | \(0.281800\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.26463 | + | 2.19041i | 0.0712540 | + | 0.123415i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.0809 | − | 22.6568i | 0.734699 | − | 1.27254i | −0.220157 | − | 0.975464i | \(-0.570657\pi\) |
0.954855 | − | 0.297071i | \(-0.0960097\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.117187 | − | 0.202974i | 0.00656123 | − | 0.0113644i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.51097 | −0.530850 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.833726 | − | 1.44406i | −0.0463898 | − | 0.0803494i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.22527 | + | 3.85428i | −0.123436 | + | 0.213797i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.74556 | −0.373030 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.8789 | + | 24.0389i | −0.765168 | + | 1.32531i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.5888 | + | 20.0723i | 0.636975 | + | 1.10327i | 0.986093 | + | 0.166195i | \(0.0531481\pi\) |
−0.349117 | + | 0.937079i | \(0.613519\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.92280 | − | 8.52654i | 0.269768 | − | 0.467251i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.76655 | + | 2.58469i | 0.424332 | + | 0.141217i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.8157 | + | 18.7333i | −0.589168 | + | 1.02047i | 0.405173 | + | 0.914240i | \(0.367211\pi\) |
−0.994342 | + | 0.106230i | \(0.966122\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.56883 | + | 7.91345i | 0.248145 | + | 0.429800i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.333557 | − | 0.577737i | 0.0180631 | − | 0.0312862i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.2295 | 1.03830 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.09212 | + | 5.35572i | −0.166474 | + | 0.288342i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.804179 | + | 1.39288i | 0.0431706 | + | 0.0747736i | 0.886803 | − | 0.462147i | \(-0.152921\pi\) |
−0.843633 | + | 0.536921i | \(0.819587\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.7156 | −0.787710 | −0.393855 | − | 0.919173i | \(-0.628859\pi\) | ||||
−0.393855 | + | 0.919173i | \(0.628859\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.22527 | − | 3.85428i | 0.118776 | − | 0.205726i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.3424 | + | 17.9136i | −0.550473 | + | 0.953447i | 0.447768 | + | 0.894150i | \(0.352219\pi\) |
−0.998240 | + | 0.0592968i | \(0.981114\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.62714 | + | 6.28239i | 0.192508 | + | 0.333434i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.656194 | −0.0347295 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.3344 | −0.756539 | −0.378269 | − | 0.925696i | \(-0.623481\pi\) | ||||
−0.378269 | + | 0.925696i | \(0.623481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.1538 | − | 19.3190i | −0.587043 | − | 1.01679i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.49189 | + | 9.51223i | −0.288249 | + | 0.499263i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.00399 | − | 1.73897i | 0.0525514 | − | 0.0910218i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.2343 | − | 22.9225i | −0.690825 | − | 1.19654i | −0.971568 | − | 0.236760i | \(-0.923914\pi\) |
0.280744 | − | 0.959783i | \(-0.409419\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.579529 | + | 1.00377i | 0.0301691 | + | 0.0522544i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00789 | − | 5.20981i | −0.156162 | − | 0.270480i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0974 | − | 33.0776i | −0.988824 | − | 1.71269i | −0.623526 | − | 0.781803i | \(-0.714300\pi\) |
−0.365298 | − | 0.930891i | \(-0.619033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.19046 | 0.421830 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6683 | − | 20.2101i | 0.599361 | − | 1.03812i | −0.393555 | − | 0.919301i | \(-0.628755\pi\) |
0.992916 | − | 0.118822i | \(-0.0379119\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.10991 | + | 1.92242i | 0.0568625 | + | 0.0984887i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.37068 | − | 11.0343i | 0.325526 | − | 0.563828i | −0.656092 | − | 0.754681i | \(-0.727792\pi\) |
0.981619 | + | 0.190852i | \(0.0611251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.161057 | + | 0.278959i | −0.00820823 | + | 0.0142171i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.35137 | 0.119527 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.79864 | − | 6.57944i | 0.192599 | − | 0.333591i | −0.753512 | − | 0.657434i | \(-0.771642\pi\) |
0.946111 | + | 0.323843i | \(0.104975\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.802223 | − | 1.38949i | −0.0405702 | − | 0.0702696i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.0542 | 1.06204 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.753802 | + | 1.30562i | 0.0379279 | + | 0.0656931i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.30752 | −0.467131 | −0.233565 | − | 0.972341i | \(-0.575039\pi\) | ||||
−0.233565 | + | 0.972341i | \(0.575039\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.2558 | −0.813810 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.38966 | −0.0693961 | −0.0346980 | − | 0.999398i | \(-0.511047\pi\) | ||||
−0.0346980 | + | 0.999398i | \(0.511047\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.3129 | 1.16130 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.25388 | 0.0621528 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.77429 | − | 8.26931i | −0.236073 | − | 0.408891i | 0.723511 | − | 0.690313i | \(-0.242527\pi\) |
−0.959584 | + | 0.281422i | \(0.909194\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.65782 | −0.377732 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.506629 | − | 0.877508i | −0.0249296 | − | 0.0431793i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.21009 | + | 5.56004i | −0.157577 | + | 0.272932i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.0649 | −0.639790 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.84344 | − | 13.5852i | 0.383177 | − | 0.663683i | −0.608337 | − | 0.793679i | \(-0.708163\pi\) |
0.991515 | + | 0.129996i | \(0.0414965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.83514 | + | 17.0350i | −0.479336 | + | 0.830233i | −0.999719 | − | 0.0236991i | \(-0.992456\pi\) |
0.520384 | + | 0.853933i | \(0.325789\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.48732 | + | 9.50432i | 0.266803 | + | 0.462116i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.129720 | − | 0.224682i | 0.00629236 | − | 0.0108987i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.0780 | 0.681281 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.566798 | 0.0273653 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.2820 | − | 28.2012i | −0.784275 | − | 1.35840i | −0.929431 | − | 0.368996i | \(-0.879702\pi\) |
0.145156 | − | 0.989409i | \(-0.453632\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.6446 | + | 21.9010i | 0.607659 | + | 1.05250i | 0.991625 | + | 0.129149i | \(0.0412246\pi\) |
−0.383966 | + | 0.923347i | \(0.625442\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.920164 | + | 1.59377i | 0.0441185 | + | 0.0764155i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.8734 | − | 34.4217i | −0.950673 | − | 1.64661i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.23674 | − | 2.14209i | 0.0590263 | − | 0.102237i | −0.835002 | − | 0.550247i | \(-0.814534\pi\) |
0.894029 | + | 0.448010i | \(0.147867\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.301411 | − | 0.522059i | 0.0143529 | − | 0.0248599i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.3001 | − | 19.5724i | −0.536885 | − | 0.929913i | −0.999070 | − | 0.0431289i | \(-0.986267\pi\) |
0.462184 | − | 0.886784i | \(-0.347066\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.27157 | −0.0602783 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.39911 | 0.0661755 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.22258 | − | 7.31373i | −0.199276 | − | 0.345156i | 0.749018 | − | 0.662550i | \(-0.230526\pi\) |
−0.948294 | + | 0.317394i | \(0.897192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0738058 | + | 0.127835i | −0.00347538 | + | 0.00601954i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.77578 | − | 15.2001i | 0.412322 | − | 0.714163i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.2566 | −0.527717 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.9230 | − | 22.3833i | −0.604512 | − | 1.04705i | −0.992128 | − | 0.125225i | \(-0.960035\pi\) |
0.387616 | − | 0.921821i | \(-0.373299\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.129720 | + | 0.224682i | −0.00605483 | + | 0.0104873i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0486 | −0.840605 | −0.420302 | − | 0.907384i | \(-0.638076\pi\) | ||||
−0.420302 | + | 0.907384i | \(0.638076\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.34724 | − | 7.52964i | 0.202033 | − | 0.349932i | −0.747150 | − | 0.664655i | \(-0.768578\pi\) |
0.949183 | + | 0.314723i | \(0.101912\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.61911 | + | 4.53644i | 0.121458 | + | 0.210372i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.0554 | − | 26.0767i | 0.696681 | − | 1.20669i | −0.272929 | − | 0.962034i | \(-0.587993\pi\) |
0.969611 | − | 0.244653i | \(-0.0786741\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.16030 | + | 20.2806i | 0.192105 | + | 0.936471i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.24823 | − | 3.89404i | 0.103593 | − | 0.179428i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.149729 | + | 0.259338i | 0.00688455 | + | 0.0119244i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.21355 | − | 5.56603i | 0.147448 | − | 0.255387i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.37847 | −0.108903 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.45632 | + | 14.6468i | −0.386379 | + | 0.669228i | −0.991959 | − | 0.126556i | \(-0.959608\pi\) |
0.605580 | + | 0.795784i | \(0.292941\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.9091 | + | 37.9477i | 0.998970 | + | 1.73027i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.6416 | −0.711717 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.93224 | + | 5.07880i | −0.133146 | + | 0.230616i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.89964 | + | 15.4146i | −0.403281 | + | 0.698503i | −0.994120 | − | 0.108286i | \(-0.965464\pi\) |
0.590839 | + | 0.806790i | \(0.298797\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.4296 | − | 18.0645i | −0.471641 | − | 0.816907i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.3667 | −1.37043 | −0.685216 | − | 0.728340i | \(-0.740292\pi\) | ||||
−0.685216 | + | 0.728340i | \(0.740292\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.477456 | −0.0215036 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0636774 | + | 0.110293i | 0.00286209 | + | 0.00495728i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.17399 | + | 15.8898i | −0.411510 | + | 0.712756i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.87126 | − | 10.1693i | 0.262834 | − | 0.455242i | −0.704160 | − | 0.710041i | \(-0.748676\pi\) |
0.966994 | + | 0.254800i | \(0.0820096\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.14610 | + | 10.6454i | 0.274588 | + | 0.475600i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.0945 | + | 31.3406i | 0.806793 | + | 1.39741i | 0.915074 | + | 0.403287i | \(0.132132\pi\) |
−0.108280 | + | 0.994120i | \(0.534534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.52837 | + | 2.64722i | 0.0680117 | + | 0.117800i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.40366 | + | 5.89531i | 0.151162 | + | 0.261820i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.6125 | −0.736335 | −0.368167 | − | 0.929759i | \(-0.620015\pi\) | ||||
−0.368167 | + | 0.929759i | \(0.620015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.07873 | 0.224670 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.21355 | + | 5.56603i | −0.141882 | + | 0.245746i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.62209 | + | 11.4698i | 0.291804 | + | 0.505420i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.698837 | + | 1.21042i | −0.0307348 | + | 0.0532342i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.90299 | + | 6.76018i | −0.171322 | + | 0.296739i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.82684 | 0.0800353 | 0.0400176 | − | 0.999199i | \(-0.487259\pi\) | ||||
0.0400176 | + | 0.999199i | \(0.487259\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.41000 | − | 4.17424i | 0.105382 | − | 0.182527i | −0.808512 | − | 0.588479i | \(-0.799727\pi\) |
0.913894 | + | 0.405953i | \(0.133060\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.26463 | − | 2.19041i | −0.0551931 | − | 0.0955972i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.35901 | −0.0591994 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.62247 | − | 13.2025i | −0.331412 | − | 0.574022i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.400614 | −0.0173852 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.15844 | −0.223437 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.51097 | 0.411195 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.9995 | −0.690429 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0767722 | 0.00330681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.4880 | −0.579895 | −0.289948 | − | 0.957043i | \(-0.593638\pi\) | ||||
−0.289948 | + | 0.957043i | \(0.593638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.8380 | + | 18.7720i | 0.465104 | + | 0.805583i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.74556 | 0.288948 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.28593 | + | 16.0837i | 0.397038 | + | 0.687690i | 0.993359 | − | 0.115056i | \(-0.0367048\pi\) |
−0.596321 | + | 0.802746i | \(0.703372\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.78302 | − | 4.82033i | 0.118776 | − | 0.205727i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.8280 | −0.503889 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.90657 | + | 3.30227i | −0.0810754 | + | 0.140427i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.92280 | + | 8.52654i | −0.208961 | + | 0.361931i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.3068 | + | 17.8518i | 0.436711 | + | 0.756406i | 0.997434 | − | 0.0715977i | \(-0.0228098\pi\) |
−0.560722 | + | 0.828004i | \(0.689476\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.23243 | + | 9.06284i | −0.221308 | + | 0.383317i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0330410 | −0.00139499 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.6923 | 0.956365 | 0.478182 | − | 0.878261i | \(-0.341296\pi\) | ||||
0.478182 | + | 0.878261i | \(0.341296\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.56883 | − | 7.91345i | −0.192212 | − | 0.332921i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.26463 | + | 2.19041i | 0.0531096 | + | 0.0919885i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.4285 | − | 28.4550i | −0.688720 | − | 1.19290i | −0.972252 | − | 0.233935i | \(-0.924840\pi\) |
0.283532 | − | 0.958963i | \(-0.408494\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.7995 | − | 18.7053i | −0.451944 | − | 0.782791i | 0.546562 | − | 0.837418i | \(-0.315936\pi\) |
−0.998507 | + | 0.0546277i | \(0.982603\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8281 | − | 22.2189i | 0.535901 | − | 0.928207i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.09212 | − | 5.35572i | 0.128951 | − | 0.223349i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.03957 | + | 1.80059i | 0.0432780 | + | 0.0749596i | 0.886853 | − | 0.462052i | \(-0.152887\pi\) |
−0.843575 | + | 0.537011i | \(0.819553\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.9337 | −0.745300 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.2383 | −0.673680 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.151455 | − | 0.262327i | −0.00627261 | − | 0.0108645i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.22527 | + | 3.85428i | −0.0920036 | + | 0.159355i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.6645 | + | 28.8637i | −0.687817 | + | 1.19133i | 0.284726 | + | 0.958609i | \(0.408097\pi\) |
−0.972543 | + | 0.232725i | \(0.925236\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.6666 | −1.38721 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.49225 | + | 6.04876i | 0.143652 | + | 0.248813i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.1056 | + | 26.1636i | −0.620311 | + | 1.07441i | 0.369117 | + | 0.929383i | \(0.379660\pi\) |
−0.989428 | + | 0.145027i | \(0.953673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.656194 | 0.0269013 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.19684 | − | 2.07299i | 0.0489834 | − | 0.0848417i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.0034 | + | 36.3789i | 0.858175 | + | 1.48640i | 0.873668 | + | 0.486523i | \(0.161735\pi\) |
−0.0154922 | + | 0.999880i | \(0.504932\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.98941 | + | 12.1060i | −0.285104 | + | 0.493815i | −0.972634 | − | 0.232341i | \(-0.925361\pi\) |
0.687530 | + | 0.726156i | \(0.258695\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.76655 | + | 2.58469i | 0.316279 | + | 0.105257i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.49189 | − | 9.51223i | 0.223277 | − | 0.386727i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.38323 | + | 7.59197i | 0.177910 | + | 0.308149i | 0.941164 | − | 0.337949i | \(-0.109733\pi\) |
−0.763255 | + | 0.646098i | \(0.776400\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.32734 | + | 4.03107i | −0.0943085 | + | 0.163347i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.8431 | −1.97598 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.8529 | − | 18.7977i | 0.438343 | − | 0.759233i | −0.559219 | − | 0.829020i | \(-0.688899\pi\) |
0.997562 | + | 0.0697873i | \(0.0222321\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.579529 | − | 1.00377i | −0.0233689 | − | 0.0404761i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.0856 | −0.526805 | −0.263403 | − | 0.964686i | \(-0.584845\pi\) | ||||
−0.263403 | + | 0.964686i | \(0.584845\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.59657 | − | 4.49739i | 0.104365 | − | 0.180766i | −0.809114 | − | 0.587652i | \(-0.800052\pi\) |
0.913479 | + | 0.406887i | \(0.133386\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.09212 | + | 5.35572i | −0.124083 | + | 0.214918i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.60807 | − | 2.78526i | −0.0644261 | − | 0.111589i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.818522 | −0.0326886 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.27718 | − | 2.21213i | −0.0509243 | − | 0.0882035i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.6639 | − | 34.0589i | 0.782807 | − | 1.35586i | −0.147493 | − | 0.989063i | \(-0.547120\pi\) |
0.930300 | − | 0.366799i | \(-0.119546\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.40604 | + | 2.43533i | −0.0558851 | + | 0.0967959i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.10991 | − | 1.92242i | −0.0440455 | − | 0.0762890i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.34144 | + | 2.32344i | 0.0531498 | + | 0.0920582i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.62714 | + | 6.28239i | 0.143487 | + | 0.248527i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.2916 | − | 17.8256i | −0.406495 | − | 0.704071i | 0.587999 | − | 0.808862i | \(-0.299916\pi\) |
−0.994494 | + | 0.104791i | \(0.966583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.1661 | 0.519221 | 0.259611 | − | 0.965713i | \(-0.416406\pi\) | ||||
0.259611 | + | 0.965713i | \(0.416406\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.35137 | −0.0925851 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.8290 | + | 37.8089i | −0.858185 | + | 1.48642i | 0.0154731 | + | 0.999880i | \(0.495075\pi\) |
−0.873658 | + | 0.486540i | \(0.838259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.0255101 | − | 0.0441847i | −0.00100136 | − | 0.00173440i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.62443 | + | 11.4738i | −0.259632 | + | 0.449695i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.06309 | + | 10.5016i | −0.237267 | + | 0.410959i | −0.959929 | − | 0.280243i | \(-0.909585\pi\) |
0.722662 | + | 0.691202i | \(0.242918\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.0542 | −0.822656 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.00399 | − | 1.73897i | 0.0391695 | − | 0.0678436i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.16250 | − | 8.94172i | −0.201103 | − | 0.348320i | 0.747781 | − | 0.663945i | \(-0.231119\pi\) |
−0.948884 | + | 0.315625i | \(0.897786\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.49081 | −0.291359 | −0.145679 | − | 0.989332i | \(-0.546537\pi\) | ||||
−0.145679 | + | 0.989332i | \(0.546537\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.577326 | − | 0.999958i | −0.0224215 | − | 0.0388352i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.2558 | 0.630374 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.3810 | −0.440676 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.8891 | 0.498321 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.708862 | 0.0273653 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.6286 | 1.41193 | 0.705964 | − | 0.708248i | \(-0.250514\pi\) | ||||
0.705964 | + | 0.708248i | \(0.250514\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.846703 | + | 1.46653i | 0.0325415 | + | 0.0563634i | 0.881837 | − | 0.471553i | \(-0.156307\pi\) |
−0.849296 | + | 0.527917i | \(0.822973\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.8328 | −0.569232 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.67253 | − | 8.09306i | −0.179052 | − | 0.310127i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.70767 | − | 2.95778i | 0.0653423 | − | 0.113176i | −0.831503 | − | 0.555520i | \(-0.812519\pi\) |
0.896846 | + | 0.442343i | \(0.145853\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.65782 | 0.292590 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.60442 | + | 2.77893i | −0.0612123 | + | 0.106023i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.29274 | − | 9.16729i | 0.201637 | − | 0.349246i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.242076 | − | 0.419288i | −0.00920901 | − | 0.0159505i | 0.861384 | − | 0.507954i | \(-0.169598\pi\) |
−0.870593 | + | 0.492004i | \(0.836265\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.161057 | + | 0.278959i | −0.00611805 | + | 0.0105968i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.0649 | 0.495579 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.300707 | 0.0113901 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.73530 | − | 9.93383i | −0.216929 | − | 0.375732i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4531 | − | 35.4258i | −0.772503 | − | 1.33801i | −0.936187 | − | 0.351502i | \(-0.885671\pi\) |
0.163684 | − | 0.986513i | \(-0.447662\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.6393 | − | 54.8009i | −1.19330 | − | 2.06686i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.48732 | − | 9.50432i | −0.206664 | − | 0.357953i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.86566 | + | 6.69552i | −0.145383 | + | 0.251811i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0717 | + | 17.4447i | −0.378250 | + | 0.655148i | −0.990808 | − | 0.135278i | \(-0.956807\pi\) |
0.612558 | + | 0.790426i | \(0.290141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.753802 | + | 1.30562i | 0.0282698 | + | 0.0489647i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.3945 | −1.21318 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.566798 | −0.0211970 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.95082 | + | 5.11096i | 0.110200 | + | 0.190872i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.2608 | + | 24.7005i | −0.531839 | + | 0.921173i | 0.467470 | + | 0.884009i | \(0.345166\pi\) |
−0.999309 | + | 0.0371636i | \(0.988168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.7490 | + | 29.0102i | −0.623766 | + | 1.08040i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.02817 | −0.335761 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.920164 | − | 1.59377i | −0.0341740 | − | 0.0591912i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.10936 | − | 5.38557i | 0.115320 | − | 0.199740i | −0.802588 | − | 0.596534i | \(-0.796544\pi\) |
0.917908 | + | 0.396794i | \(0.129877\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.305021 | − | 0.528311i | 0.0112816 | − | 0.0195403i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.23190 | + | 5.59782i | 0.119373 | + | 0.206760i | 0.919519 | − | 0.393045i | \(-0.128578\pi\) |
−0.800146 | + | 0.599805i | \(0.795245\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.301411 | + | 0.522059i | −0.0111177 | + | 0.0192564i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.209482 | + | 1.02118i | 0.00771636 | + | 0.0376156i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.6691 | + | 28.8717i | −0.613183 | + | 1.06206i | 0.377518 | + | 0.926002i | \(0.376778\pi\) |
−0.990700 | + | 0.136061i | \(0.956556\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.3020 | − | 24.7719i | −0.525398 | − | 0.910017i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.72772 | − | 8.18865i | 0.173443 | − | 0.300412i | −0.766178 | − | 0.642628i | \(-0.777844\pi\) |
0.939621 | + | 0.342216i | \(0.111177\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.39911 | −0.0512593 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.21009 | + | 5.56004i | −0.117451 | + | 0.203431i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0279 | + | 20.8329i | 0.439489 | + | 0.761217i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.14643 | 0.114815 | 0.0574074 | − | 0.998351i | \(-0.481717\pi\) | ||||
0.0574074 | + | 0.998351i | \(0.481717\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.88177 | − | 4.99137i | 0.105017 | − | 0.181896i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.77578 | + | 15.2001i | −0.319383 | + | 0.553188i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.64743 | − | 16.7098i | −0.350642 | − | 0.607329i | 0.635720 | − | 0.771919i | \(-0.280703\pi\) |
−0.986362 | + | 0.164590i | \(0.947370\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.787594 | −0.0285879 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.2180 | −1.45790 | −0.728951 | − | 0.684566i | \(-0.759992\pi\) | ||||
−0.728951 | + | 0.684566i | \(0.759992\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.53065 | + | 14.7755i | 0.308830 | + | 0.534910i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.129720 | − | 0.224682i | 0.00469005 | − | 0.00812341i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.891474 | − | 1.54408i | 0.0321893 | − | 0.0557535i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.67851 | + | 6.37137i | 0.132650 | + | 0.229757i | 0.924697 | − | 0.380703i | \(-0.124318\pi\) |
−0.792047 | + | 0.610460i | \(0.790985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0716 | + | 24.3727i | 0.506775 | + | 0.877761i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.8282 | − | 41.2717i | −0.857042 | − | 1.48444i | −0.874738 | − | 0.484597i | \(-0.838966\pi\) |
0.0176957 | − | 0.999843i | \(-0.494367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.61911 | − | 4.53644i | −0.0940813 | − | 0.162954i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.9021 | −0.893359 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.44938 | 0.266902 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.461933 | + | 0.800092i | −0.0165293 | + | 0.0286296i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.920164 | + | 1.59377i | 0.0328840 | + | 0.0569567i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.24823 | + | 3.89404i | −0.0802427 | + | 0.138984i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.3590 | − | 42.1911i | 0.868305 | − | 1.50395i | 0.00457767 | − | 0.999990i | \(-0.498543\pi\) |
0.863727 | − | 0.503959i | \(-0.168124\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.3621 | −0.511305 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.5558 | − | 20.0152i | 0.410876 | − | 0.711659i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3859 | + | 21.4531i | 0.439838 | + | 0.761821i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.37847 | 0.0843556 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.99411 | + | 5.18595i | 0.106057 | + | 0.183696i | 0.914169 | − | 0.405332i | \(-0.132844\pi\) |
−0.808113 | + | 0.589028i | \(0.799511\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.84727 | 0.100729 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.27157 | −0.0449288 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.255727 | 0.00902441 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.6416 | 0.551294 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.7111 | −0.764265 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.20123 | 0.147707 | 0.0738537 | − | 0.997269i | \(-0.476470\pi\) | ||||
0.0738537 | + | 0.997269i | \(0.476470\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.5830 | − | 37.3828i | −0.757880 | − | 1.31269i | −0.943930 | − | 0.330147i | \(-0.892902\pi\) |
0.186049 | − | 0.982540i | \(-0.440432\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.7458 | −0.376870 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.4296 | + | 18.0645i | 0.365332 | + | 0.632773i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.55624 | − | 13.0878i | 0.264359 | − | 0.457884i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.2566 | −0.393337 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5317 | − | 21.7055i | 0.437359 | − | 0.757527i | −0.560126 | − | 0.828407i | \(-0.689247\pi\) |
0.997485 | + | 0.0708800i | \(0.0225807\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5534 | − | 26.9393i | 0.542158 | − | 0.939046i | −0.456622 | − | 0.889661i | \(-0.650941\pi\) |
0.998780 | − | 0.0493847i | \(-0.0157260\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0636774 | − | 0.110293i | −0.00221696 | − | 0.00383989i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.4403 | + | 30.2076i | −0.606460 | + | 1.05042i | 0.385359 | + | 0.922767i | \(0.374078\pi\) |
−0.991819 | + | 0.127653i | \(0.959256\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.6255 | −0.646890 | −0.323445 | − | 0.946247i | \(-0.604841\pi\) | ||||
−0.323445 | + | 0.946247i | \(0.604841\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.2641 | −0.945781 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.0781983 | − | 0.135443i | −0.00270941 | − | 0.00469283i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.14610 | − | 10.6454i | −0.212695 | − | 0.368398i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.61911 | + | 4.53644i | 0.0905298 | + | 0.156802i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.964584 | − | 1.67071i | −0.0333011 | − | 0.0576792i | 0.848895 | − | 0.528562i | \(-0.177269\pi\) |
−0.882196 | + | 0.470883i | \(0.843935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8066 | − | 22.1817i | 0.441607 | − | 0.764885i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.30782 | − | 10.9255i | 0.217253 | − | 0.376293i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.40366 | − | 5.89531i | −0.117089 | − | 0.202805i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.7809 | 0.954563 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.7031 | −0.779168 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.4438 | − | 52.7302i | −1.04360 | − | 1.80757i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.9753 | − | 29.4021i | 0.581224 | − | 1.00671i | −0.414111 | − | 0.910226i | \(-0.635907\pi\) |
0.995335 | − | 0.0964828i | \(-0.0307593\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.21355 | − | 5.56603i | 0.109901 | − | 0.190354i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.6154 | −1.66067 | −0.830334 | − | 0.557265i | \(-0.811851\pi\) | ||||
−0.830334 | + | 0.557265i | \(0.811851\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.1749 | + | 17.6234i | 0.347162 | + | 0.601302i | 0.985744 | − | 0.168251i | \(-0.0538120\pi\) |
−0.638582 | + | 0.769554i | \(0.720479\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.46578 | − | 2.53881i | 0.0499537 | − | 0.0865224i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.5329 | 0.664907 | 0.332454 | − | 0.943120i | \(-0.392123\pi\) | ||||
0.332454 | + | 0.943120i | \(0.392123\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.90299 | − | 6.76018i | 0.132706 | − | 0.229853i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.46635 | − | 14.6641i | −0.287532 | − | 0.498020i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.0960004 | + | 0.166278i | −0.00325659 | + | 0.00564058i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.2448 | + | 24.1828i | −0.923156 | + | 0.819404i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.93224 | + | 5.07880i | −0.0992414 | + | 0.171891i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.26463 | + | 2.19041i | 0.0427524 | + | 0.0740493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.3691 | + | 19.6918i | −0.383906 | + | 0.664945i | −0.991617 | − | 0.129214i | \(-0.958755\pi\) |
0.607711 | + | 0.794159i | \(0.292088\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.2730 | 0.346500 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.97368 | + | 3.41852i | −0.0664950 | + | 0.115173i | −0.897356 | − | 0.441307i | \(-0.854515\pi\) |
0.830861 | + | 0.556480i | \(0.187848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8940 | + | 22.3331i | 0.433918 | + | 0.751568i | 0.997207 | − | 0.0746919i | \(-0.0237973\pi\) |
−0.563288 | + | 0.826260i | \(0.690464\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.400614 | 0.0134665 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.63446 | − | 6.29508i | 0.122033 | − | 0.211368i | −0.798536 | − | 0.601947i | \(-0.794392\pi\) |
0.920569 | + | 0.390579i | \(0.127725\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.80726 | − | 4.86231i | 0.0941524 | − | 0.163077i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0636774 | + | 0.110293i | 0.00213327 | + | 0.00369494i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 70.5351 | 2.36037 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.9995 | 0.534804 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.7616 | − | 23.8358i | −0.459487 | − | 0.795855i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.82003 | + | 8.34853i | −0.160757 | + | 0.278439i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.308536 | + | 0.534400i | −0.0102788 | + | 0.0178034i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.97362 | − | 5.15045i | −0.0989558 | − | 0.171396i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.8380 | − | 18.7720i | −0.360268 | − | 0.624002i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.9180 | + | 22.3746i | 0.428934 | + | 0.742936i | 0.996779 | − | 0.0801999i | \(-0.0255559\pi\) |
−0.567845 | + | 0.823136i | \(0.692223\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.52837 | + | 2.64722i | 0.0506930 | + | 0.0878028i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.4490 | −1.73771 | −0.868857 | − | 0.495064i | \(-0.835145\pi\) | ||||
−0.868857 | + | 0.495064i | \(0.835145\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.817642 | −0.0270600 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.78302 | + | 4.82033i | −0.0920038 | + | 0.159355i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.6258 | − | 46.1173i | −0.879263 | − | 1.52293i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.72068 | − | 2.98031i | 0.0567600 | − | 0.0983112i | −0.836249 | − | 0.548350i | \(-0.815256\pi\) |
0.893009 | + | 0.450038i | \(0.148590\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.66618 | − | 9.81412i | 0.186707 | − | 0.323386i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.2855 | −1.06269 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.92280 | − | 8.52654i | 0.161861 | − | 0.280351i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.62209 | + | 11.4698i | 0.217498 | + | 0.376718i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.69058 | 0.285129 | 0.142564 | − | 0.989786i | \(-0.454465\pi\) | ||||
0.142564 | + | 0.989786i | \(0.454465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.93720 | − | 3.35532i | −0.0634891 | − | 0.109966i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.3637 | −0.437507 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0330410 | 0.00108056 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.0064 | −1.14361 | −0.571805 | − | 0.820390i | \(-0.693757\pi\) | ||||
−0.571805 | + | 0.820390i | \(0.693757\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.3998 | −0.730991 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.2468 | −1.24681 | −0.623404 | − | 0.781900i | \(-0.714251\pi\) | ||||
−0.623404 | + | 0.781900i | \(0.714251\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.16790 | 0.233419 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.26463 | − | 2.19041i | −0.0411385 | − | 0.0712540i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.23043 | 0.267453 | 0.133726 | − | 0.991018i | \(-0.457306\pi\) | ||||
0.133726 | + | 0.991018i | \(0.457306\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.46832 | + | 7.73935i | 0.145048 | + | 0.251230i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.0809 | + | 22.6568i | −0.424178 | + | 0.734699i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.94687 | 0.160245 | 0.0801224 | − | 0.996785i | \(-0.474469\pi\) | ||||
0.0801224 | + | 0.996785i | \(0.474469\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.8281 | + | 22.2189i | −0.415107 | + | 0.718986i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.117187 | + | 0.202974i | −0.00378813 | + | 0.00656123i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.68433 | + | 16.7737i | 0.312723 | + | 0.541652i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.78050 | − | 3.08391i | 0.0574354 | − | 0.0994811i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.51097 | 0.306487 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.9337 | 0.577307 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.598311 | + | 1.03631i | 0.0192404 | + | 0.0333254i | 0.875485 | − | 0.483245i | \(-0.160542\pi\) |
−0.856245 | + | 0.516570i | \(0.827209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.833726 | + | 1.44406i | 0.0267831 | + | 0.0463898i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.0105 | − | 34.6592i | −0.642167 | − | 1.11227i | −0.984948 | − | 0.172851i | \(-0.944702\pi\) |
0.342781 | − | 0.939415i | \(-0.388631\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.5223 | + | 28.6174i | 0.529680 | + | 0.917432i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.22527 | − | 3.85428i | 0.0712657 | − | 0.123436i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.18689 | + | 8.98396i | −0.165943 | + | 0.287422i | −0.936990 | − | 0.349357i | \(-0.886400\pi\) |
0.771047 | + | 0.636779i | \(0.219734\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0809705 | − | 0.140245i | −0.00258783 | − | 0.00448225i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.74556 | 0.215369 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.64691 | −0.0844233 | −0.0422117 | − | 0.999109i | \(-0.513440\pi\) | ||||
−0.0422117 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.49225 | − | 6.04876i | −0.111272 | − | 0.192729i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.8789 | − | 24.0389i | 0.441770 | − | 0.765168i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.27072 | − | 12.5933i | 0.231196 | − | 0.400442i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.365907 | 0.0116234 | 0.00581172 | − | 0.999983i | \(-0.498150\pi\) | ||||
0.00581172 | + | 0.999983i | \(0.498150\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.5888 | − | 20.0723i | −0.367758 | − | 0.636975i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.19684 | + | 2.07299i | −0.0379424 | + | 0.0657181i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.2282 | −0.608964 | −0.304482 | − | 0.952518i | \(-0.598483\pi\) | ||||
−0.304482 | + | 0.952518i | \(0.598483\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.92280 | + | 8.52654i | −0.155750 | + | 0.269768i |
(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.k.3781.6 | yes | 14 | |
67.37 | even | 3 | inner | 4020.2.q.k.841.6 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.q.k.841.6 | ✓ | 14 | 67.37 | even | 3 | inner | |
4020.2.q.k.3781.6 | yes | 14 | 1.1 | even | 1 | trivial |