Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(289,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, 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("2016.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.s (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: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1156923.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.2 | ||
Root | \(0.500000 - 1.51496i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.865 |
Dual form | 2016.2.s.u.289.2 |
$q$-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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.227452 | + | 0.393958i | 0.101720 | + | 0.176184i | 0.912393 | − | 0.409315i | \(-0.134232\pi\) |
−0.810674 | + | 0.585498i | \(0.800899\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.16908 | − | 1.51496i | 0.819835 | − | 0.572600i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.89653 | + | 5.01694i | −0.873337 | + | 1.51266i | −0.0148132 | + | 0.999890i | \(0.504715\pi\) |
−0.858524 | + | 0.512774i | \(0.828618\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.88325 | −1.63172 | −0.815861 | − | 0.578249i | \(-0.803736\pi\) | ||||
−0.815861 | + | 0.578249i | \(0.803736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.45490 | − | 2.51997i | 0.352866 | − | 0.611182i | −0.633884 | − | 0.773428i | \(-0.718540\pi\) |
0.986750 | + | 0.162246i | \(0.0518738\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.94163 | − | 5.09505i | −0.674856 | − | 1.16888i | −0.976511 | − | 0.215467i | \(-0.930873\pi\) |
0.301656 | − | 0.953417i | \(-0.402461\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.45490 | − | 2.51997i | −0.303368 | − | 0.525450i | 0.673528 | − | 0.739161i | \(-0.264778\pi\) |
−0.976897 | + | 0.213712i | \(0.931445\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.39653 | − | 4.15091i | 0.479306 | − | 0.830183i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.54510 | −0.658308 | −0.329154 | − | 0.944276i | \(-0.606763\pi\) | ||||
−0.329154 | + | 0.944276i | \(0.606763\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.16908 | − | 3.75696i | 0.389578 | − | 0.674769i | −0.602815 | − | 0.797881i | \(-0.705954\pi\) |
0.992393 | + | 0.123112i | \(0.0392875\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.09019 | + | 0.509947i | 0.184276 | + | 0.0861968i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.85144 | − | 6.67088i | −0.633172 | − | 1.09669i | −0.986899 | − | 0.161338i | \(-0.948419\pi\) |
0.353727 | − | 0.935349i | \(-0.384914\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.58612 | −1.49710 | −0.748551 | − | 0.663078i | \(-0.769250\pi\) | ||||
−0.748551 | + | 0.663078i | \(0.769250\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7931 | 1.64593 | 0.822963 | − | 0.568095i | \(-0.192319\pi\) | ||||
0.822963 | + | 0.568095i | \(0.192319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.45490 | + | 4.25202i | 0.358085 | + | 0.620221i | 0.987641 | − | 0.156734i | \(-0.0500966\pi\) |
−0.629556 | + | 0.776955i | \(0.716763\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.40981 | − | 6.57212i | 0.344258 | − | 0.938875i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.56561 | − | 11.3720i | 0.901856 | − | 1.56206i | 0.0767730 | − | 0.997049i | \(-0.475538\pi\) |
0.825083 | − | 0.565012i | \(-0.191128\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.63529 | −0.355342 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.896531 | + | 1.55284i | −0.116718 | + | 0.202162i | −0.918465 | − | 0.395501i | \(-0.870571\pi\) |
0.801747 | + | 0.597664i | \(0.203904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.33816 | − | 4.04981i | −0.299370 | − | 0.518525i | 0.676622 | − | 0.736331i | \(-0.263443\pi\) |
−0.975992 | + | 0.217806i | \(0.930110\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.33816 | − | 2.31776i | −0.165978 | − | 0.287482i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.94163 | + | 6.82710i | −0.481546 | + | 0.834063i | −0.999776 | − | 0.0211789i | \(-0.993258\pi\) |
0.518229 | + | 0.855242i | \(0.326591\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.909808 | 0.107974 | 0.0539872 | − | 0.998542i | \(-0.482807\pi\) | ||||
0.0539872 | + | 0.998542i | \(0.482807\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.60347 | + | 4.50934i | −0.304713 | + | 0.527778i | −0.977197 | − | 0.212333i | \(-0.931894\pi\) |
0.672484 | + | 0.740111i | \(0.265227\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.31764 | + | 15.2703i | 0.150159 | + | 1.74021i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.37602 | + | 2.38333i | 0.154814 | + | 0.268146i | 0.932991 | − | 0.359899i | \(-0.117189\pi\) |
−0.778177 | + | 0.628045i | \(0.783856\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.97345 | −1.09473 | −0.547364 | − | 0.836895i | \(-0.684369\pi\) | ||||
−0.547364 | + | 0.836895i | \(0.684369\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.32368 | 0.143574 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.45490 | − | 4.25202i | −0.260219 | − | 0.450713i | 0.706081 | − | 0.708131i | \(-0.250462\pi\) |
−0.966300 | + | 0.257418i | \(0.917128\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.7612 | + | 8.91288i | −1.33774 | + | 0.934324i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.33816 | − | 2.31776i | 0.137292 | − | 0.237797i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.79306 | −0.588196 | −0.294098 | − | 0.955775i | \(-0.595019\pi\) | ||||
−0.294098 | + | 0.955775i | \(0.595019\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.33816 | − | 14.4421i | 0.829678 | − | 1.43704i | −0.0686134 | − | 0.997643i | \(-0.521858\pi\) |
0.898291 | − | 0.439401i | \(-0.144809\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.396531 | + | 0.686812i | 0.0390714 | + | 0.0676736i | 0.884900 | − | 0.465781i | \(-0.154227\pi\) |
−0.845828 | + | 0.533455i | \(0.820893\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.98672 | + | 10.3693i | 0.578758 | + | 1.00244i | 0.995622 | + | 0.0934699i | \(0.0297959\pi\) |
−0.416864 | + | 0.908969i | \(0.636871\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.30634 | − | 3.99470i | 0.220907 | − | 0.382623i | −0.734176 | − | 0.678959i | \(-0.762432\pi\) |
0.955084 | + | 0.296336i | \(0.0957649\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.00000 | −0.752577 | −0.376288 | − | 0.926503i | \(-0.622800\pi\) | ||||
−0.376288 | + | 0.926503i | \(0.622800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.661842 | − | 1.14634i | 0.0617171 | − | 0.106897i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.661842 | − | 7.67013i | −0.0606709 | − | 0.703119i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.2798 | − | 19.5372i | −1.02544 | − | 1.77611i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.45490 | 0.398459 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.24797 | −0.110739 | −0.0553696 | − | 0.998466i | \(-0.517634\pi\) | ||||
−0.0553696 | + | 0.998466i | \(0.517634\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.89653 | − | 5.01694i | −0.253071 | − | 0.438332i | 0.711299 | − | 0.702890i | \(-0.248107\pi\) |
−0.964370 | + | 0.264558i | \(0.914774\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.0994 | − | 6.59512i | −1.22257 | − | 0.571870i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.54510 | + | 2.67618i | −0.132006 | + | 0.228642i | −0.924450 | − | 0.381303i | \(-0.875475\pi\) |
0.792443 | + | 0.609945i | \(0.208809\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.70287 | −0.483711 | −0.241856 | − | 0.970312i | \(-0.577756\pi\) | ||||
−0.241856 | + | 0.970312i | \(0.577756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.0410 | − | 29.5159i | 1.42504 | − | 2.46825i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.806339 | − | 1.39662i | −0.0669628 | − | 0.115983i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.54510 | + | 2.67618i | 0.126579 | + | 0.219242i | 0.922349 | − | 0.386357i | \(-0.126267\pi\) |
−0.795770 | + | 0.605599i | \(0.792934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.862740 | − | 1.49431i | 0.0702088 | − | 0.121605i | −0.828784 | − | 0.559569i | \(-0.810967\pi\) |
0.898993 | + | 0.437964i | \(0.144300\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.97345 | 0.158511 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.79306 | − | 4.83773i | 0.222911 | − | 0.386093i | −0.732780 | − | 0.680466i | \(-0.761778\pi\) |
0.955691 | + | 0.294373i | \(0.0951109\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.97345 | − | 3.26189i | −0.549585 | − | 0.257073i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.42835 | + | 7.67013i | 0.346855 | + | 0.600771i | 0.985689 | − | 0.168574i | \(-0.0539162\pi\) |
−0.638834 | + | 0.769345i | \(0.720583\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4057 | 1.34690 | 0.673448 | − | 0.739234i | \(-0.264812\pi\) | ||||
0.673448 | + | 0.739234i | \(0.264812\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.6127 | 1.66251 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.33816 | − | 14.4421i | −0.633938 | − | 1.09801i | −0.986739 | − | 0.162315i | \(-0.948104\pi\) |
0.352801 | − | 0.935699i | \(-0.385229\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.09019 | − | 12.6343i | −0.0824108 | − | 0.955064i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.09019 | − | 5.35237i | 0.230972 | − | 0.400055i | −0.727123 | − | 0.686508i | \(-0.759143\pi\) |
0.958094 | + | 0.286453i | \(0.0924762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.20694 | −0.238370 | −0.119185 | − | 0.992872i | \(-0.538028\pi\) | ||||
−0.119185 | + | 0.992872i | \(0.538028\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.75203 | − | 3.03461i | 0.128812 | − | 0.223109i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.42835 | + | 14.5983i | 0.616342 | + | 1.06754i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.6763 | − | 18.4919i | −0.772511 | − | 1.33803i | −0.936183 | − | 0.351514i | \(-0.885667\pi\) |
0.163672 | − | 0.986515i | \(-0.447666\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.20287 | + | 14.2078i | −0.590456 | + | 1.02270i | 0.403716 | + | 0.914885i | \(0.367719\pi\) |
−0.994171 | + | 0.107814i | \(0.965615\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.6763 | −1.75811 | −0.879057 | − | 0.476716i | \(-0.841827\pi\) | ||||
−0.879057 | + | 0.476716i | \(0.841827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.90981 | − | 11.9681i | 0.489823 | − | 0.848399i | −0.510108 | − | 0.860110i | \(-0.670395\pi\) |
0.999931 | + | 0.0117114i | \(0.00372795\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.68959 | + | 5.37067i | −0.539704 | + | 0.376947i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.18038 | − | 3.77654i | −0.152285 | − | 0.263765i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 34.0821 | 2.35751 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5861 | −0.797622 | −0.398811 | − | 0.917033i | \(-0.630577\pi\) | ||||
−0.398811 | + | 0.917033i | \(0.630577\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.45490 | + | 4.25202i | 0.167423 | + | 0.289985i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.986723 | − | 11.4352i | −0.0669831 | − | 0.776272i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.55957 | + | 14.8256i | −0.575779 | + | 0.997279i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.4549 | −1.36976 | −0.684881 | − | 0.728655i | \(-0.740146\pi\) | ||||
−0.684881 | + | 0.728655i | \(0.740146\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.86998 | + | 15.3633i | −0.588721 | + | 1.01969i | 0.405679 | + | 0.914016i | \(0.367035\pi\) |
−0.994400 | + | 0.105679i | \(0.966298\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0994 | + | 20.9568i | 0.799551 | + | 1.38486i | 0.919909 | + | 0.392132i | \(0.128262\pi\) |
−0.120358 | + | 0.992731i | \(0.538404\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.3382 | + | 19.6383i | 0.742787 | + | 1.28655i | 0.951221 | + | 0.308509i | \(0.0998300\pi\) |
−0.208434 | + | 0.978036i | \(0.566837\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.11675 | + | 1.93426i | −0.0728485 | + | 0.126177i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.90981 | 0.188220 | 0.0941099 | − | 0.995562i | \(-0.469999\pi\) | ||||
0.0941099 | + | 0.995562i | \(0.469999\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8700 | + | 18.8274i | −0.700197 | + | 1.21278i | 0.268200 | + | 0.963363i | \(0.413571\pi\) |
−0.968397 | + | 0.249413i | \(0.919762\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.13726 | − | 0.545479i | 0.200432 | − | 0.0348494i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.3063 | + | 29.9755i | 1.10118 | + | 1.90729i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.02655 | −0.506632 | −0.253316 | − | 0.967384i | \(-0.581521\pi\) | ||||
−0.253316 | + | 0.967384i | \(0.581521\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.8567 | 1.05977 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.45490 | − | 11.1802i | −0.402646 | − | 0.697403i | 0.591398 | − | 0.806379i | \(-0.298576\pi\) |
−0.994044 | + | 0.108976i | \(0.965243\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.4602 | − | 8.63491i | −1.14706 | − | 0.536547i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.45490 | + | 7.71612i | −0.274701 | + | 0.475796i | −0.970060 | − | 0.242867i | \(-0.921912\pi\) |
0.695359 | + | 0.718663i | \(0.255246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.97345 | 0.366946 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.02051 | + | 5.23168i | −0.184164 | + | 0.318981i | −0.943295 | − | 0.331957i | \(-0.892291\pi\) |
0.759130 | + | 0.650938i | \(0.225624\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.68236 | + | 11.5742i | 0.405924 | + | 0.703081i | 0.994429 | − | 0.105413i | \(-0.0336164\pi\) |
−0.588504 | + | 0.808494i | \(0.700283\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.8833 | + | 24.0465i | 0.837192 | + | 1.45006i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.39653 | + | 4.15091i | −0.143994 | + | 0.249404i | −0.928997 | − | 0.370087i | \(-0.879328\pi\) |
0.785003 | + | 0.619491i | \(0.212661\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.32368 | −0.436894 | −0.218447 | − | 0.975849i | \(-0.570099\pi\) | ||||
−0.218447 | + | 0.975849i | \(0.570099\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.60347 | − | 11.4375i | 0.392535 | − | 0.679891i | −0.600248 | − | 0.799814i | \(-0.704931\pi\) |
0.992783 | + | 0.119923i | \(0.0382647\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.7931 | + | 14.5226i | −1.22738 | + | 0.857240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.26651 | + | 7.38981i | 0.250971 | + | 0.434695i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.54510 | −0.440789 | −0.220395 | − | 0.975411i | \(-0.570735\pi\) | ||||
−0.220395 | + | 0.975411i | \(0.570735\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.815671 | −0.0474902 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.55957 | + | 14.8256i | 0.495013 | + | 0.857387i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.4110 | − | 16.3510i | 1.34939 | − | 0.942458i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.06364 | − | 1.84227i | 0.0609037 | − | 0.105488i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.1086 | 1.31888 | 0.659439 | − | 0.751758i | \(-0.270794\pi\) | ||||
0.659439 | + | 0.751758i | \(0.270794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.70287 | + | 6.41356i | −0.209971 | + | 0.363680i | −0.951705 | − | 0.307014i | \(-0.900670\pi\) |
0.741734 | + | 0.670694i | \(0.234003\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.29306 | − | 12.6320i | −0.412228 | − | 0.714000i | 0.582905 | − | 0.812540i | \(-0.301916\pi\) |
−0.995133 | + | 0.0985402i | \(0.968583\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.682356 | + | 1.18188i | 0.0383249 | + | 0.0663807i | 0.884552 | − | 0.466442i | \(-0.154464\pi\) |
−0.846227 | + | 0.532823i | \(0.821131\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.2685 | − | 17.7855i | 0.574925 | − | 0.995799i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.1191 | −0.952534 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.0994 | + | 24.4209i | −0.782094 | + | 1.35463i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.7665 | + | 5.50389i | 0.648709 | + | 0.303439i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.48672 | − | 9.50328i | −0.301578 | − | 0.522348i | 0.674916 | − | 0.737895i | \(-0.264180\pi\) |
−0.976493 | + | 0.215547i | \(0.930847\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.58612 | −0.195931 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.1722 | −1.20780 | −0.603900 | − | 0.797060i | \(-0.706387\pi\) | ||||
−0.603900 | + | 0.797060i | \(0.706387\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.5656 | + | 21.7643i | 0.680466 | + | 1.17860i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.72942 | − | 17.9062i | −0.255365 | − | 0.966845i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.116746 | − | 0.202210i | 0.00626725 | − | 0.0108552i | −0.862875 | − | 0.505418i | \(-0.831338\pi\) |
0.869142 | + | 0.494563i | \(0.164672\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.35263 | 0.393577 | 0.196789 | − | 0.980446i | \(-0.436949\pi\) | ||||
0.196789 | + | 0.980446i | \(0.436949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.58612 | − | 16.6037i | 0.510218 | − | 0.883723i | −0.489712 | − | 0.871884i | \(-0.662898\pi\) |
0.999930 | − | 0.0118391i | \(-0.00376859\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.206938 | + | 0.358427i | 0.0109831 | + | 0.0190233i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.4694 | + | 18.1335i | 0.552553 | + | 0.957049i | 0.998089 | + | 0.0617857i | \(0.0196795\pi\) |
−0.445537 | + | 0.895264i | \(0.646987\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.80634 | + | 13.5210i | −0.410860 | + | 0.711630i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.36866 | −0.123981 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.5072 | − | 21.6632i | 0.652872 | − | 1.13081i | −0.329550 | − | 0.944138i | \(-0.606897\pi\) |
0.982423 | − | 0.186670i | \(-0.0597696\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.98672 | − | 34.6133i | −0.155063 | − | 1.79703i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1630 | + | 17.6029i | 0.526222 | + | 0.911444i | 0.999533 | + | 0.0305483i | \(0.00972533\pi\) |
−0.473311 | + | 0.880895i | \(0.656941\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.8567 | 1.07417 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.7931 | 1.06807 | 0.534034 | − | 0.845463i | \(-0.320675\pi\) | ||||
0.534034 | + | 0.845463i | \(0.320675\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.5861 | − | 21.7998i | −0.643121 | − | 1.11392i | −0.984732 | − | 0.174077i | \(-0.944306\pi\) |
0.341611 | − | 0.939841i | \(-0.389027\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.71615 | + | 3.99235i | −0.291322 | + | 0.203469i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.2214 | − | 21.1681i | 0.619650 | − | 1.07327i | −0.369899 | − | 0.929072i | \(-0.620608\pi\) |
0.989549 | − | 0.144194i | \(-0.0460589\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.46698 | −0.428194 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.625956 | + | 1.08419i | −0.0314952 | + | 0.0545514i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.39653 | + | 7.61502i | 0.220656 | + | 0.382187i | 0.955007 | − | 0.296583i | \(-0.0958470\pi\) |
−0.734352 | + | 0.678769i | \(0.762514\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5596 | + | 28.6820i | 0.826945 | + | 1.43231i | 0.900423 | + | 0.435015i | \(0.143257\pi\) |
−0.0734778 | + | 0.997297i | \(0.523410\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.7612 | + | 22.1031i | −0.635683 | + | 1.10103i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.6232 | 2.21189 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.47345 | − | 6.01618i | 0.171751 | − | 0.297481i | −0.767281 | − | 0.641311i | \(-0.778391\pi\) |
0.939032 | + | 0.343830i | \(0.111724\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.407836 | + | 4.72643i | 0.0200683 | + | 0.232573i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.26848 | − | 3.92912i | −0.111355 | − | 0.192873i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.2254 | −1.42775 | −0.713876 | − | 0.700272i | \(-0.753062\pi\) | ||||
−0.713876 | + | 0.700272i | \(0.753062\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.2359 | 1.61982 | 0.809909 | − | 0.586556i | \(-0.199516\pi\) | ||||
0.809909 | + | 0.586556i | \(0.199516\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.97345 | − | 12.0784i | −0.338262 | − | 0.585887i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.2069 | − | 5.24215i | −0.542342 | − | 0.253685i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.09019 | + | 5.35237i | −0.148849 | + | 0.257815i | −0.930802 | − | 0.365523i | \(-0.880890\pi\) |
0.781953 | + | 0.623337i | \(0.214224\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.6127 | 0.798354 | 0.399177 | − | 0.916874i | \(-0.369296\pi\) | ||||
0.399177 | + | 0.916874i | \(0.369296\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.55957 | + | 14.8256i | −0.409460 | + | 0.709205i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8136 | − | 23.9258i | −0.659286 | − | 1.14192i | −0.980801 | − | 0.195012i | \(-0.937525\pi\) |
0.321515 | − | 0.946905i | \(-0.395808\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0133 | + | 17.3435i | 0.475745 | + | 0.824015i | 0.999614 | − | 0.0277842i | \(-0.00884512\pi\) |
−0.523869 | + | 0.851799i | \(0.675512\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.11675 | − | 1.93426i | 0.0529388 | − | 0.0916927i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0371 | −0.709644 | −0.354822 | − | 0.934934i | \(-0.615459\pi\) | ||||
−0.354822 | + | 0.934934i | \(0.615459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.7665 | − | 48.0930i | 1.30747 | − | 2.26461i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.41388 | − | 3.00015i | −0.300687 | − | 0.140649i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.0596 | + | 36.4762i | 0.985125 | + | 1.70629i | 0.641379 | + | 0.767224i | \(0.278363\pi\) |
0.343746 | + | 0.939063i | \(0.388304\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.9098 | −0.973867 | −0.486933 | − | 0.873439i | \(-0.661885\pi\) | ||||
−0.486933 | + | 0.873439i | \(0.661885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.1457 | 1.77278 | 0.886390 | − | 0.462939i | \(-0.153205\pi\) | ||||
0.886390 | + | 0.462939i | \(0.153205\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.76651 | − | 9.98789i | −0.266842 | − | 0.462184i | 0.701202 | − | 0.712962i | \(-0.252647\pi\) |
−0.968045 | + | 0.250778i | \(0.919314\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.79306 | + | 20.7799i | 0.0827959 | + | 0.959527i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.2624 | + | 54.1481i | −1.43745 | + | 2.48973i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.1988 | −1.29385 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.66184 | − | 6.34250i | 0.167314 | − | 0.289796i | −0.770161 | − | 0.637850i | \(-0.779824\pi\) |
0.937475 | + | 0.348054i | \(0.113157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.6590 | + | 39.2465i | 1.03316 | + | 1.78949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.31764 | − | 2.28223i | −0.0598311 | − | 0.103631i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.0258 | + | 22.5613i | −0.590254 | + | 1.02235i | 0.403943 | + | 0.914784i | \(0.367639\pi\) |
−0.994198 | + | 0.107567i | \(0.965694\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.37919 | 0.333018 | 0.166509 | − | 0.986040i | \(-0.446751\pi\) | ||||
0.166509 | + | 0.986040i | \(0.446751\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.15777 | + | 8.93353i | −0.232294 | + | 0.402346i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.97345 | − | 1.37832i | 0.0885211 | − | 0.0618261i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.175119 | + | 0.303315i | 0.00783940 | + | 0.0135782i | 0.869918 | − | 0.493196i | \(-0.164171\pi\) |
−0.862079 | + | 0.506774i | \(0.830838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.9098 | −0.664795 | −0.332398 | − | 0.943139i | \(-0.607858\pi\) | ||||
−0.332398 | + | 0.943139i | \(0.607858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.58612 | 0.337578 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.44886 | + | 14.6339i | 0.374489 | + | 0.648635i | 0.990250 | − | 0.139298i | \(-0.0444847\pi\) |
−0.615761 | + | 0.787933i | \(0.711151\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.18433 | + | 13.7253i | 0.0523916 | + | 0.607170i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.180384 | + | 0.312434i | −0.00794865 | + | 0.0137675i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.4428 | −1.25091 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.79306 | − | 6.56978i | 0.166177 | − | 0.287827i | −0.770896 | − | 0.636962i | \(-0.780191\pi\) |
0.937073 | + | 0.349134i | \(0.113524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.2572 | + | 36.8185i | 0.929511 | + | 1.60996i | 0.784140 | + | 0.620584i | \(0.213104\pi\) |
0.145371 | + | 0.989377i | \(0.453562\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.31160 | − | 10.9320i | −0.274938 | − | 0.476206i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.26651 | − | 12.5860i | 0.315935 | − | 0.547216i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 56.3976 | 2.44285 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.72338 | + | 4.71704i | −0.117742 | + | 0.203935i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.9919 | + | 31.1262i | 1.11955 | + | 1.34070i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.03182 | − | 12.1795i | −0.302322 | − | 0.523636i | 0.674340 | − | 0.738421i | \(-0.264428\pi\) |
−0.976661 | + | 0.214785i | \(0.931095\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.09833 | 0.0898824 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.49593 | −0.192232 | −0.0961161 | − | 0.995370i | \(-0.530642\pi\) | ||||
−0.0961161 | + | 0.995370i | \(0.530642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.4283 | + | 18.0624i | 0.444263 | + | 0.769485i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.59533 | + | 3.08503i | 0.280462 | + | 0.131189i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.9303 | − | 27.5921i | 0.674989 | − | 1.16912i | −0.301483 | − | 0.953472i | \(-0.597482\pi\) |
0.976472 | − | 0.215644i | \(-0.0691852\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −63.4983 | −2.68569 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.0688 | − | 39.9563i | 0.972233 | − | 1.68396i | 0.283454 | − | 0.958986i | \(-0.408520\pi\) |
0.688779 | − | 0.724972i | \(-0.258147\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.81962 | − | 3.15167i | −0.0765518 | − | 0.132592i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.31160 | − | 14.3961i | −0.348441 | − | 0.603517i | 0.637532 | − | 0.770424i | \(-0.279955\pi\) |
−0.985973 | + | 0.166907i | \(0.946622\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.2532 | + | 31.6155i | −0.763874 | + | 1.32307i | 0.176966 | + | 0.984217i | \(0.443372\pi\) |
−0.940840 | + | 0.338852i | \(0.889962\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.9469 | −0.581626 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.59019 | − | 13.1466i | 0.315984 | − | 0.547300i | −0.663662 | − | 0.748032i | \(-0.730999\pi\) |
0.979646 | + | 0.200732i | \(0.0643321\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.6332 | + | 15.1093i | −0.897496 | + | 0.626841i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.0350 | + | 65.8785i | 1.57525 | + | 2.72841i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.20694 | −0.338737 | −0.169368 | − | 0.985553i | \(-0.554173\pi\) | ||||
−0.169368 | + | 0.985553i | \(0.554173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.5225 | −1.05164 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.77859 | − | 4.81266i | −0.114103 | − | 0.197632i | 0.803318 | − | 0.595550i | \(-0.203066\pi\) |
−0.917421 | + | 0.397918i | \(0.869733\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.87117 | − | 2.00532i | 0.117707 | − | 0.0822103i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.7931 | + | 30.8185i | −0.727005 | + | 1.25921i | 0.231139 | + | 0.972921i | \(0.425755\pi\) |
−0.958143 | + | 0.286288i | \(0.907578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.18038 | 0.0481489 | 0.0240744 | − | 0.999710i | \(-0.492336\pi\) | ||||
0.0240744 | + | 0.999710i | \(0.492336\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.13122 | − | 8.88753i | 0.208614 | − | 0.361330i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.16908 | − | 10.6852i | −0.250395 | − | 0.433697i | 0.713239 | − | 0.700920i | \(-0.247227\pi\) |
−0.963635 | + | 0.267223i | \(0.913894\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.4428 | − | 25.0157i | −0.584294 | − | 1.01203i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.5451 | − | 18.2646i | 0.425912 | − | 0.737702i | −0.570593 | − | 0.821233i | \(-0.693287\pi\) |
0.996505 | + | 0.0835312i | \(0.0266198\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.3526 | −0.618074 | −0.309037 | − | 0.951050i | \(-0.600007\pi\) | ||||
−0.309037 | + | 0.951050i | \(0.600007\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.21615 | − | 15.9628i | 0.370428 | − | 0.641601i | −0.619203 | − | 0.785231i | \(-0.712544\pi\) |
0.989631 | + | 0.143630i | \(0.0458776\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.7665 | − | 5.50389i | −0.471415 | − | 0.220509i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.9694 | − | 18.9995i | −0.438775 | − | 0.759981i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.4139 | −0.893700 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.91375 | −0.235423 | −0.117711 | − | 0.993048i | \(-0.537556\pi\) | ||||
−0.117711 | + | 0.993048i | \(0.537556\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.283853 | − | 0.491647i | −0.0112643 | − | 0.0195104i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.1775 | + | 38.6655i | −0.561734 | + | 1.53198i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.0821 | − | 39.9793i | 0.911686 | − | 1.57909i | 0.100005 | − | 0.994987i | \(-0.468114\pi\) |
0.811681 | − | 0.584100i | \(-0.198553\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.0555 | −1.22471 | −0.612355 | − | 0.790583i | \(-0.709778\pi\) | ||||
−0.612355 | + | 0.790583i | \(0.709778\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.51854 | − | 14.7545i | 0.334898 | − | 0.580061i | −0.648567 | − | 0.761158i | \(-0.724631\pi\) |
0.983465 | + | 0.181097i | \(0.0579647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.19366 | − | 8.99568i | −0.203869 | − | 0.353111i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.06968 | − | 7.04889i | −0.159259 | − | 0.275844i | 0.775343 | − | 0.631541i | \(-0.217577\pi\) |
−0.934602 | + | 0.355696i | \(0.884244\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.31764 | − | 2.28223i | 0.0514846 | − | 0.0891740i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.1191 | 1.60177 | 0.800887 | − | 0.598815i | \(-0.204362\pi\) | ||||
0.800887 | + | 0.598815i | \(0.204362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.67105 | − | 11.5546i | 0.259474 | − | 0.449422i | −0.706627 | − | 0.707586i | \(-0.749784\pi\) |
0.966101 | + | 0.258164i | \(0.0831175\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.608734 | − | 7.05465i | −0.0236057 | − | 0.273568i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.15777 | + | 8.93353i | 0.199710 | + | 0.345908i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.0902 | 1.04581 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.75837 | 0.376158 | 0.188079 | − | 0.982154i | \(-0.439774\pi\) | ||||
0.188079 | + | 0.982154i | \(0.439774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.2275 | + | 28.1068i | 0.623672 | + | 1.08023i | 0.988796 | + | 0.149272i | \(0.0476931\pi\) |
−0.365124 | + | 0.930959i | \(0.618974\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.5656 | + | 8.77624i | −0.482224 | + | 0.336801i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.4827 | − | 32.0129i | 0.707219 | − | 1.22494i | −0.258666 | − | 0.965967i | \(-0.583283\pi\) |
0.965885 | − | 0.258973i | \(-0.0833839\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.40574 | −0.0537106 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.6272 | + | 66.9042i | −1.47158 | + | 2.54885i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.12596 | − | 12.3425i | −0.271084 | − | 0.469531i | 0.698056 | − | 0.716044i | \(-0.254049\pi\) |
−0.969140 | + | 0.246512i | \(0.920715\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.29713 | − | 2.24669i | −0.0492029 | − | 0.0852220i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.9469 | + | 24.1567i | −0.528276 | + | 0.915001i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.3937 | 1.94111 | 0.970556 | − | 0.240876i | \(-0.0774347\pi\) | ||||
0.970556 | + | 0.240876i | \(0.0774347\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.6590 | + | 39.2465i | −0.854599 | + | 1.48021i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.79306 | − | 43.9580i | −0.142653 | − | 1.65321i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.5861 | − | 21.7998i | −0.472682 | − | 0.818709i | 0.526829 | − | 0.849971i | \(-0.323381\pi\) |
−0.999511 | + | 0.0312621i | \(0.990047\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.6232 | −0.472743 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.5041 | 0.579819 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.09019 | + | 7.08442i | 0.152538 | + | 0.264204i | 0.932160 | − | 0.362047i | \(-0.117922\pi\) |
−0.779622 | + | 0.626251i | \(0.784589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.90060 | + | 0.889022i | 0.0707820 | + | 0.0331089i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.49593 | + | 14.7154i | −0.315531 | + | 0.546516i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.9614 | 0.999942 | 0.499971 | − | 0.866042i | \(-0.333344\pi\) | ||||
0.499971 | + | 0.866042i | \(0.333344\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.7029 | − | 27.1982i | 0.580792 | − | 1.00596i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.7347 | + | 18.5930i | 0.396495 | + | 0.686749i | 0.993291 | − | 0.115644i | \(-0.0368931\pi\) |
−0.596796 | + | 0.802393i | \(0.703560\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.8341 | − | 39.5498i | −0.841105 | − | 1.45684i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.671052 | − | 1.16230i | 0.0246850 | − | 0.0427557i | −0.853419 | − | 0.521226i | \(-0.825475\pi\) |
0.878104 | + | 0.478470i | \(0.158808\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.9919 | −0.990236 | −0.495118 | − | 0.868826i | \(-0.664875\pi\) | ||||
−0.495118 | + | 0.868826i | \(0.664875\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.702870 | + | 1.21741i | −0.0257512 | + | 0.0446024i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.6947 | + | 13.4222i | 1.04848 | + | 0.490437i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.44360 | + | 11.1606i | 0.235130 | + | 0.407258i | 0.959311 | − | 0.282353i | \(-0.0911150\pi\) |
−0.724180 | + | 0.689611i | \(0.757782\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.784928 | 0.0285664 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.3897 | −0.959151 | −0.479575 | − | 0.877501i | \(-0.659209\pi\) | ||||
−0.479575 | + | 0.877501i | \(0.659209\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.2214 | + | 26.3643i | 0.551776 | + | 0.955704i | 0.998147 | + | 0.0608556i | \(0.0193829\pi\) |
−0.446371 | + | 0.894848i | \(0.647284\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.04916 | − | 12.1588i | −0.0379823 | − | 0.440179i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.27452 | − | 9.13574i | 0.190452 | − | 0.329872i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.1191 | 1.51886 | 0.759428 | − | 0.650592i | \(-0.225479\pi\) | ||||
0.759428 | + | 0.650592i | \(0.225479\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.0145 | − | 32.9340i | 0.683903 | − | 1.18455i | −0.289877 | − | 0.957064i | \(-0.593614\pi\) |
0.973780 | − | 0.227491i | \(-0.0730522\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.3965 | − | 18.0073i | −0.373454 | − | 0.646842i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.1988 | + | 48.8418i | 1.01033 | + | 1.74994i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.63529 | + | 4.56445i | −0.0942980 | + | 0.163329i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.54115 | 0.0906976 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.7931 | − | 27.3544i | 0.562962 | − | 0.975079i | −0.434274 | − | 0.900781i | \(-0.642995\pi\) |
0.997236 | − | 0.0742978i | \(-0.0236716\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.3526 | + | 12.1197i | −0.616989 | + | 0.430925i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.7560 | + | 23.8261i | 0.488489 | + | 0.846088i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −45.2133 | −1.60154 | −0.800768 | − | 0.598974i | \(-0.795575\pi\) | ||||
−0.800768 | + | 0.598974i | \(0.795575\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.2866 | 0.505424 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.0821 | − | 26.1229i | −0.532234 | − | 0.921857i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.301075 | − | 3.48917i | −0.0106115 | − | 0.122977i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.495933 | − | 0.858981i | 0.0174361 | − | 0.0302002i | −0.857176 | − | 0.515024i | \(-0.827783\pi\) |
0.874612 | + | 0.484824i | \(0.161116\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.6151 | 0.829237 | 0.414619 | − | 0.909995i | \(-0.363915\pi\) | ||||
0.414619 | + | 0.909995i | \(0.363915\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.01447 | + | 3.48917i | −0.0705640 | + | 0.122220i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.7492 | − | 54.9912i | −1.11076 | − | 1.92390i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.6332 | − | 30.5416i | −0.615403 | − | 1.06591i | −0.990314 | − | 0.138848i | \(-0.955660\pi\) |
0.374911 | − | 0.927061i | \(-0.377673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.27058 | − | 9.12890i | 0.183721 | − | 0.318214i | −0.759424 | − | 0.650596i | \(-0.774519\pi\) |
0.943145 | + | 0.332382i | \(0.107852\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.4323 | −1.09301 | −0.546504 | − | 0.837456i | \(-0.684042\pi\) | ||||
−0.546504 | + | 0.837456i | \(0.684042\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.7612 | − | 22.1031i | 0.443216 | − | 0.767673i | −0.554710 | − | 0.832044i | \(-0.687171\pi\) |
0.997926 | + | 0.0643708i | \(0.0205040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.0555 | − | 15.6345i | −0.452346 | − | 0.541702i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.95897 | + | 6.85714i | 0.137006 | + | 0.237301i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.78253 | −0.0960637 | −0.0480318 | − | 0.998846i | \(-0.515295\pi\) | ||||
−0.0480318 | + | 0.998846i | \(0.515295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.4323 | −0.566631 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.91585 | + | 8.51450i | 0.169110 | + | 0.292908i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −54.0647 | − | 25.2893i | −1.85769 | − | 0.868949i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.2069 | + | 19.4110i | −0.384169 | + | 0.665400i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.7931 | 0.643462 | 0.321731 | − | 0.946831i | \(-0.395735\pi\) | ||||
0.321731 | + | 0.946831i | \(0.395735\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.4694 | − | 18.1335i | 0.357627 | − | 0.619428i | −0.629937 | − | 0.776646i | \(-0.716919\pi\) |
0.987564 | + | 0.157218i | \(0.0502525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.79306 | − | 10.0339i | −0.197657 | − | 0.342352i | 0.750111 | − | 0.661311i | \(-0.230000\pi\) |
−0.947768 | + | 0.318960i | \(0.896666\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.7665 | + | 25.5763i | 0.502658 | + | 0.870629i | 0.999995 | + | 0.00307167i | \(0.000977744\pi\) |
−0.497337 | + | 0.867557i | \(0.665689\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.79306 | − | 6.56978i | 0.128968 | − | 0.223379i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.9427 | −0.540819 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.1896 | − | 40.1656i | 0.785749 | − | 1.36096i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.66304 | − | 6.74899i | 0.326670 | − | 0.228158i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.61268 | − | 4.52529i | −0.0882239 | − | 0.152808i | 0.818537 | − | 0.574454i | \(-0.194786\pi\) |
−0.906760 | + | 0.421646i | \(0.861452\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.1433 | 0.442809 | 0.221405 | − | 0.975182i | \(-0.428936\pi\) | ||||
0.221405 | + | 0.975182i | \(0.428936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.96531 | 0.268054 | 0.134027 | − | 0.990978i | \(-0.457209\pi\) | ||||
0.134027 | + | 0.990978i | \(0.457209\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.8977 | + | 34.4639i | 0.668100 | + | 1.15718i | 0.978435 | + | 0.206556i | \(0.0662256\pi\) |
−0.310334 | + | 0.950627i | \(0.600441\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.70694 | + | 1.89062i | −0.0907878 | + | 0.0634092i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.4428 | − | 25.0157i | 0.483311 | − | 0.837119i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.81148 | 0.0939775 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.68959 | + | 13.3188i | −0.256462 | + | 0.444206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.1047 | − | 33.0903i | −0.636469 | − | 1.10240i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.729425 | − | 1.26340i | −0.0242469 | − | 0.0419968i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.79833 | − | 10.0430i | 0.192530 | − | 0.333472i | −0.753558 | − | 0.657382i | \(-0.771664\pi\) |
0.946088 | + | 0.323909i | \(0.104997\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.4959 | −1.14290 | −0.571451 | − | 0.820636i | \(-0.693619\pi\) | ||||
−0.571451 | + | 0.820636i | \(0.693619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.8884 | − | 50.0362i | 0.956066 | − | 1.65596i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.8833 | − | 6.49402i | −0.458465 | − | 0.214451i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.927153 | + | 1.60588i | 0.0305839 | + | 0.0529729i | 0.880912 | − | 0.473280i | \(-0.156930\pi\) |
−0.850328 | + | 0.526253i | \(0.823597\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.35263 | −0.176184 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.9203 | −1.21393 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.5596 | − | 20.0218i | −0.379257 | − | 0.656893i | 0.611697 | − | 0.791092i | \(-0.290487\pi\) |
−0.990954 | + | 0.134199i | \(0.957154\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.5740 | + | 7.05465i | −1.32976 | + | 0.231207i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.83409 | + | 6.64084i | −0.125388 | + | 0.217179i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.3445 | −1.41600 | −0.708002 | − | 0.706211i | \(-0.750403\pi\) | ||||
−0.708002 | + | 0.706211i | \(0.750403\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.5656 | + | 25.2284i | −0.474825 | + | 0.822422i | −0.999584 | − | 0.0288292i | \(-0.990822\pi\) |
0.524759 | + | 0.851251i | \(0.324155\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.9469 | + | 24.1567i | 0.454173 | + | 0.786651i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.97345 | − | 12.0784i | −0.226607 | − | 0.392494i | 0.730194 | − | 0.683240i | \(-0.239430\pi\) |
−0.956800 | + | 0.290746i | \(0.906096\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.3169 | − | 26.5296i | 0.497207 | − | 0.861187i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.7134 | 1.28644 | 0.643222 | − | 0.765680i | \(-0.277597\pi\) | ||||
0.643222 | + | 0.765680i | \(0.277597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.85670 | − | 8.41205i | 0.157159 | − | 0.272208i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.702870 | + | 8.14561i | 0.0226969 | + | 0.263035i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.09019 | + | 10.5485i | 0.196458 | + | 0.340275i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.46304 | −0.240244 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.5717 | −0.404277 | −0.202139 | − | 0.979357i | \(-0.564789\pi\) | ||||
−0.202139 | + | 0.979357i | \(0.564789\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.07691 | + | 12.2576i | 0.227109 | + | 0.393364i | 0.956950 | − | 0.290253i | \(-0.0937393\pi\) |
−0.729841 | + | 0.683617i | \(0.760406\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.3700 | + | 8.63961i | −0.396563 | + | 0.276973i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.2624 | + | 40.2917i | −0.744231 | + | 1.28905i | 0.206322 | + | 0.978484i | \(0.433851\pi\) |
−0.950553 | + | 0.310562i | \(0.899483\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.4428 | 0.909037 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.2359 | + | 43.7098i | −0.804900 | + | 1.39413i | 0.111459 | + | 0.993769i | \(0.464448\pi\) |
−0.916359 | + | 0.400358i | \(0.868886\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.61268 | − | 9.72144i | −0.178835 | − | 0.309751i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.7029 | − | 27.1982i | −0.499322 | − | 0.864851i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.98870 | − | 3.44452i | 0.0631730 | − | 0.109419i | −0.832709 | − | 0.553711i | \(-0.813211\pi\) |
0.895882 | + | 0.444292i | \(0.146545\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.28660 | 0.199299 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.0092 | − | 38.1211i | 0.697039 | − | 1.20731i | −0.272450 | − | 0.962170i | \(-0.587834\pi\) |
0.969489 | − | 0.245136i | \(-0.0788328\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2016.2.s.u.865.2 | 6 | ||
3.2 | odd | 2 | 672.2.q.k.193.2 | ✓ | 6 | ||
4.3 | odd | 2 | 2016.2.s.v.865.2 | 6 | |||
7.2 | even | 3 | inner | 2016.2.s.u.289.2 | 6 | ||
12.11 | even | 2 | 672.2.q.l.193.2 | yes | 6 | ||
21.2 | odd | 6 | 672.2.q.k.289.2 | yes | 6 | ||
21.11 | odd | 6 | 4704.2.a.bu.1.2 | 3 | |||
21.17 | even | 6 | 4704.2.a.bt.1.2 | 3 | |||
24.5 | odd | 2 | 1344.2.q.z.193.2 | 6 | |||
24.11 | even | 2 | 1344.2.q.y.193.2 | 6 | |||
28.23 | odd | 6 | 2016.2.s.v.289.2 | 6 | |||
84.11 | even | 6 | 4704.2.a.bs.1.2 | 3 | |||
84.23 | even | 6 | 672.2.q.l.289.2 | yes | 6 | ||
84.59 | odd | 6 | 4704.2.a.bv.1.2 | 3 | |||
168.11 | even | 6 | 9408.2.a.ej.1.2 | 3 | |||
168.53 | odd | 6 | 9408.2.a.eh.1.2 | 3 | |||
168.59 | odd | 6 | 9408.2.a.eg.1.2 | 3 | |||
168.101 | even | 6 | 9408.2.a.ei.1.2 | 3 | |||
168.107 | even | 6 | 1344.2.q.y.961.2 | 6 | |||
168.149 | odd | 6 | 1344.2.q.z.961.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.q.k.193.2 | ✓ | 6 | 3.2 | odd | 2 | ||
672.2.q.k.289.2 | yes | 6 | 21.2 | odd | 6 | ||
672.2.q.l.193.2 | yes | 6 | 12.11 | even | 2 | ||
672.2.q.l.289.2 | yes | 6 | 84.23 | even | 6 | ||
1344.2.q.y.193.2 | 6 | 24.11 | even | 2 | |||
1344.2.q.y.961.2 | 6 | 168.107 | even | 6 | |||
1344.2.q.z.193.2 | 6 | 24.5 | odd | 2 | |||
1344.2.q.z.961.2 | 6 | 168.149 | odd | 6 | |||
2016.2.s.u.289.2 | 6 | 7.2 | even | 3 | inner | ||
2016.2.s.u.865.2 | 6 | 1.1 | even | 1 | trivial | ||
2016.2.s.v.289.2 | 6 | 28.23 | odd | 6 | |||
2016.2.s.v.865.2 | 6 | 4.3 | odd | 2 | |||
4704.2.a.bs.1.2 | 3 | 84.11 | even | 6 | |||
4704.2.a.bt.1.2 | 3 | 21.17 | even | 6 | |||
4704.2.a.bu.1.2 | 3 | 21.11 | odd | 6 | |||
4704.2.a.bv.1.2 | 3 | 84.59 | odd | 6 | |||
9408.2.a.eg.1.2 | 3 | 168.59 | odd | 6 | |||
9408.2.a.eh.1.2 | 3 | 168.53 | odd | 6 | |||
9408.2.a.ei.1.2 | 3 | 168.101 | even | 6 | |||
9408.2.a.ej.1.2 | 3 | 168.11 | even | 6 |