Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(701,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.g (of order \(2\), degree \(1\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 701.2 | ||
Root | \(1.58114 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.701 |
Dual form | 900.3.g.d.701.1 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.48683 | −0.783833 | −0.391917 | − | 0.920001i | \(-0.628188\pi\) | ||||
−0.391917 | + | 0.920001i | \(0.628188\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.17377i | 0.833979i | 0.908911 | + | 0.416989i | \(0.136915\pi\) | ||||
−0.908911 | + | 0.416989i | \(0.863085\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.4868 | −0.883603 | −0.441801 | − | 0.897113i | \(-0.645660\pi\) | ||||
−0.441801 | + | 0.897113i | \(0.645660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 16.9706i | − 0.998268i | −0.866525 | − | 0.499134i | \(-0.833651\pi\) | ||||
0.866525 | − | 0.499134i | \(-0.166349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.9737 | 1.41967 | 0.709833 | − | 0.704370i | \(-0.248770\pi\) | ||||
0.709833 | + | 0.704370i | \(0.248770\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 4.93113i | − 0.214397i | −0.994238 | − | 0.107198i | \(-0.965812\pi\) | ||||
0.994238 | − | 0.107198i | \(-0.0341880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 20.5247i | − 0.707749i | −0.935293 | − | 0.353874i | \(-0.884864\pi\) | ||||
0.935293 | − | 0.353874i | \(-0.115136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.9737 | 0.676570 | 0.338285 | − | 0.941044i | \(-0.390153\pi\) | ||||
0.338285 | + | 0.941044i | \(0.390153\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 62.4605 | 1.68812 | 0.844061 | − | 0.536247i | \(-0.180159\pi\) | ||||
0.844061 | + | 0.536247i | \(0.180159\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 40.9377i | − 0.998481i | −0.866464 | − | 0.499240i | \(-0.833612\pi\) | ||||
0.866464 | − | 0.499240i | \(-0.166388\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.02633 | −0.0238682 | −0.0119341 | − | 0.999929i | \(-0.503799\pi\) | ||||
−0.0119341 | + | 0.999929i | \(0.503799\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 86.2298i | − 1.83468i | −0.398109 | − | 0.917338i | \(-0.630333\pi\) | ||||
0.398109 | − | 0.917338i | \(-0.369667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18.8947 | −0.385605 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 96.0920i | 1.81306i | 0.422144 | + | 0.906529i | \(0.361278\pi\) | ||||
−0.422144 | + | 0.906529i | \(0.638722\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 112.374i | − 1.90465i | −0.305092 | − | 0.952323i | \(-0.598687\pi\) | ||||
0.305092 | − | 0.952323i | \(-0.401313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −66.9210 | −1.09707 | −0.548533 | − | 0.836129i | \(-0.684813\pi\) | ||||
−0.548533 | + | 0.836129i | \(0.684813\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 76.0000 | 1.13433 | 0.567164 | − | 0.823605i | \(-0.308040\pi\) | ||||
0.567164 | + | 0.823605i | \(0.308040\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 24.0789i | − 0.339139i | −0.985518 | − | 0.169570i | \(-0.945762\pi\) | ||||
0.985518 | − | 0.169570i | \(-0.0542377\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 18.9210 | 0.259192 | 0.129596 | − | 0.991567i | \(-0.458632\pi\) | ||||
0.129596 | + | 0.991567i | \(0.458632\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 50.3349i | − 0.653700i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 106.921 | 1.35343 | 0.676715 | − | 0.736245i | \(-0.263403\pi\) | ||||
0.676715 | + | 0.736245i | \(0.263403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 45.1804i | − 0.544342i | −0.962249 | − | 0.272171i | \(-0.912258\pi\) | ||||
0.962249 | − | 0.272171i | \(-0.0877416\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 115.928i | − 1.30256i | −0.758835 | − | 0.651282i | \(-0.774231\pi\) | ||||
0.758835 | − | 0.651282i | \(-0.225769\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 63.0263 | 0.692597 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 87.0263 | 0.897179 | 0.448589 | − | 0.893738i | \(-0.351927\pi\) | ||||
0.448589 | + | 0.893738i | \(0.351927\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 129.233i | 1.27953i | 0.768569 | + | 0.639767i | \(0.220969\pi\) | ||||
−0.768569 | + | 0.639767i | \(0.779031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −114.302 | −1.10973 | −0.554866 | − | 0.831939i | \(-0.687231\pi\) | ||||
−0.554866 | + | 0.831939i | \(0.687231\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 93.3381i | − 0.872319i | −0.899869 | − | 0.436159i | \(-0.856338\pi\) | ||||
0.899869 | − | 0.436159i | \(-0.143662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 120.868 | 1.10888 | 0.554442 | − | 0.832222i | \(-0.312932\pi\) | ||||
0.554442 | + | 0.832222i | \(0.312932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 110.309i | 0.976183i | 0.872793 | + | 0.488091i | \(0.162307\pi\) | ||||
−0.872793 | + | 0.488091i | \(0.837693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 93.1146i | 0.782476i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 36.8420 | 0.304479 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −105.381 | −0.829776 | −0.414888 | − | 0.909873i | \(-0.636179\pi\) | ||||
−0.414888 | + | 0.909873i | \(0.636179\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 140.584i | − 1.07316i | −0.843850 | − | 0.536580i | \(-0.819716\pi\) | ||||
0.843850 | − | 0.536580i | \(-0.180284\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −148.000 | −1.11278 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 266.951i | − 1.94855i | −0.225365 | − | 0.974274i | \(-0.572357\pi\) | ||||
0.225365 | − | 0.974274i | \(-0.427643\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.8420 | −0.113971 | −0.0569856 | − | 0.998375i | \(-0.518149\pi\) | ||||
−0.0569856 | + | 0.998375i | \(0.518149\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 105.378i | − 0.736906i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 41.6262i | − 0.279370i | −0.990196 | − | 0.139685i | \(-0.955391\pi\) | ||||
0.990196 | − | 0.139685i | \(-0.0446091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 103.842 | 0.687695 | 0.343848 | − | 0.939025i | \(-0.388270\pi\) | ||||
0.343848 | + | 0.939025i | \(0.388270\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.5132 | 0.0797017 | 0.0398509 | − | 0.999206i | \(-0.487312\pi\) | ||||
0.0398509 | + | 0.999206i | \(0.487312\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.0563i | 0.168051i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 290.868 | 1.78447 | 0.892234 | − | 0.451573i | \(-0.149137\pi\) | ||||
0.892234 | + | 0.451573i | \(0.149137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 174.637i | 1.04573i | 0.852416 | + | 0.522865i | \(0.175137\pi\) | ||||
−0.852416 | + | 0.522865i | \(0.824863\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −37.0527 | −0.219247 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 43.5799i | − 0.251907i | −0.992036 | − | 0.125954i | \(-0.959801\pi\) | ||||
0.992036 | − | 0.125954i | \(-0.0401990\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 88.2952i | − 0.493270i | −0.969109 | − | 0.246635i | \(-0.920675\pi\) | ||||
0.969109 | − | 0.246635i | \(-0.0793248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −56.8683 | −0.314190 | −0.157095 | − | 0.987584i | \(-0.550213\pi\) | ||||
−0.157095 | + | 0.987584i | \(0.550213\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 155.684 | 0.832535 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 56.6430i | − 0.296560i | −0.988945 | − | 0.148280i | \(-0.952626\pi\) | ||||
0.988945 | − | 0.148280i | \(-0.0473737\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −110.000 | −0.569948 | −0.284974 | − | 0.958535i | \(-0.591985\pi\) | ||||
−0.284974 | + | 0.958535i | \(0.591985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 245.049i | 1.24391i | 0.783055 | + | 0.621953i | \(0.213661\pi\) | ||||
−0.783055 | + | 0.621953i | \(0.786339\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −169.895 | −0.853742 | −0.426871 | − | 0.904313i | \(-0.640384\pi\) | ||||
−0.426871 | + | 0.904313i | \(0.640384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 112.616i | 0.554757i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 247.450i | 1.18397i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −265.579 | −1.25867 | −0.629333 | − | 0.777136i | \(-0.716672\pi\) | ||||
−0.629333 | + | 0.777136i | \(0.716672\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −115.079 | −0.530318 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 194.938i | 0.882072i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 187.329 | 0.840040 | 0.420020 | − | 0.907515i | \(-0.362023\pi\) | ||||
0.420020 | + | 0.907515i | \(0.362023\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 421.063i | 1.85490i | 0.373942 | + | 0.927452i | \(0.378006\pi\) | ||||
−0.373942 | + | 0.927452i | \(0.621994\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −102.105 | −0.445875 | −0.222937 | − | 0.974833i | \(-0.571565\pi\) | ||||
−0.222937 | + | 0.974833i | \(0.571565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 99.0694i | 0.425191i | 0.977140 | + | 0.212595i | \(0.0681916\pi\) | ||||
−0.977140 | + | 0.212595i | \(0.931808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 77.9680i | 0.326226i | 0.986607 | + | 0.163113i | \(0.0521535\pi\) | ||||
−0.986607 | + | 0.163113i | \(0.947847\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −257.947 | −1.07032 | −0.535160 | − | 0.844750i | \(-0.679749\pi\) | ||||
−0.535160 | + | 0.844750i | \(0.679749\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −309.842 | −1.25442 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 274.971i | − 1.09550i | −0.836641 | − | 0.547752i | \(-0.815484\pi\) | ||||
0.836641 | − | 0.547752i | \(-0.184516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 45.2370 | 0.178802 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 131.634i | 0.512193i | 0.966651 | + | 0.256096i | \(0.0824365\pi\) | ||||
−0.966651 | + | 0.256096i | \(0.917564\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −342.710 | −1.32321 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 458.782i | − 1.74442i | −0.489133 | − | 0.872209i | \(-0.662687\pi\) | ||||
0.489133 | − | 0.872209i | \(-0.337313\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 301.916i | 1.12236i | 0.827692 | + | 0.561182i | \(0.189653\pi\) | ||||
−0.827692 | + | 0.561182i | \(0.810347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 475.842 | 1.75587 | 0.877937 | − | 0.478776i | \(-0.158919\pi\) | ||||
0.877937 | + | 0.478776i | \(0.158919\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −322.039 | −1.16260 | −0.581298 | − | 0.813691i | \(-0.697455\pi\) | ||||
−0.581298 | + | 0.813691i | \(0.697455\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 352.139i | 1.25316i | 0.779355 | + | 0.626582i | \(0.215547\pi\) | ||||
−0.779355 | + | 0.626582i | \(0.784453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 281.631 | 0.995164 | 0.497582 | − | 0.867417i | \(-0.334221\pi\) | ||||
0.497582 | + | 0.867417i | \(0.334221\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 224.618i | 0.782642i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.00346021 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 64.3281i | 0.219550i | 0.993956 | + | 0.109775i | \(0.0350130\pi\) | ||||
−0.993956 | + | 0.109775i | \(0.964987\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 56.6430i | 0.189442i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.63132 | 0.0187087 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −230.158 | −0.749700 | −0.374850 | − | 0.927085i | \(-0.622306\pi\) | ||||
−0.374850 | + | 0.927085i | \(0.622306\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 8.48528i | − 0.0272839i | −0.999907 | − | 0.0136419i | \(-0.995658\pi\) | ||||
0.999907 | − | 0.0136419i | \(-0.00434250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −605.579 | −1.93476 | −0.967378 | − | 0.253337i | \(-0.918472\pi\) | ||||
−0.967378 | + | 0.253337i | \(0.918472\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 87.9601i | − 0.277477i | −0.990329 | − | 0.138738i | \(-0.955695\pi\) | ||||
0.990329 | − | 0.138738i | \(-0.0443047\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 188.289 | 0.590248 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 457.758i | − 1.41721i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 473.128i | 1.43808i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −49.2370 | −0.148752 | −0.0743761 | − | 0.997230i | \(-0.523697\pi\) | ||||
−0.0743761 | + | 0.997230i | \(0.523697\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.71033 | 0.00804251 | 0.00402125 | − | 0.999992i | \(-0.498720\pi\) | ||||
0.00402125 | + | 0.999992i | \(0.498720\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 192.408i | 0.564245i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 372.527 | 1.08608 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 74.9906i | 0.216111i | 0.994145 | + | 0.108056i | \(0.0344624\pi\) | ||||
−0.994145 | + | 0.108056i | \(0.965538\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −150.921 | −0.432438 | −0.216219 | − | 0.976345i | \(-0.569373\pi\) | ||||
−0.216219 | + | 0.976345i | \(0.569373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 292.407i | 0.828349i | 0.910198 | + | 0.414174i | \(0.135930\pi\) | ||||
−0.910198 | + | 0.414174i | \(0.864070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 576.776i | 1.60662i | 0.595563 | + | 0.803309i | \(0.296929\pi\) | ||||
−0.595563 | + | 0.803309i | \(0.703071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 366.579 | 1.01545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −243.540 | −0.663595 | −0.331798 | − | 0.943351i | \(-0.607655\pi\) | ||||
−0.331798 | + | 0.943351i | \(0.607655\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 527.241i | − 1.42113i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −115.908 | −0.310746 | −0.155373 | − | 0.987856i | \(-0.549658\pi\) | ||||
−0.155373 | + | 0.987856i | \(0.549658\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 235.764i | 0.625369i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.2107 | 0.0797115 | 0.0398558 | − | 0.999205i | \(-0.487310\pi\) | ||||
0.0398558 | + | 0.999205i | \(0.487310\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 651.319i | − 1.70057i | −0.526320 | − | 0.850286i | \(-0.676429\pi\) | ||||
0.526320 | − | 0.850286i | \(-0.323571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 205.600i | − 0.528536i | −0.964449 | − | 0.264268i | \(-0.914870\pi\) | ||||
0.964449 | − | 0.264268i | \(-0.0851303\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −83.6840 | −0.214026 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −118.355 | −0.298124 | −0.149062 | − | 0.988828i | \(-0.547625\pi\) | ||||
−0.149062 | + | 0.988828i | \(0.547625\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 170.971i | 0.426361i | 0.977013 | + | 0.213181i | \(0.0683823\pi\) | ||||
−0.977013 | + | 0.213181i | \(0.931618\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −240.921 | −0.597819 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 572.998i | 1.40786i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −335.947 | −0.821387 | −0.410694 | − | 0.911773i | \(-0.634713\pi\) | ||||
−0.410694 | + | 0.911773i | \(0.634713\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 616.578i | 1.49292i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 407.535i | − 0.972637i | −0.873781 | − | 0.486319i | \(-0.838339\pi\) | ||||
0.873781 | − | 0.486319i | \(-0.161661\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −771.210 | −1.83185 | −0.915926 | − | 0.401346i | \(-0.868542\pi\) | ||||
−0.915926 | + | 0.401346i | \(0.868542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 367.184 | 0.859916 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 436.210i | 1.01209i | 0.862508 | + | 0.506044i | \(0.168893\pi\) | ||||
−0.862508 | + | 0.506044i | \(0.831107\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 838.500 | 1.93649 | 0.968244 | − | 0.250006i | \(-0.0804324\pi\) | ||||
0.968244 | + | 0.250006i | \(0.0804324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 133.011i | − 0.304372i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 50.0000 | 0.113895 | 0.0569476 | − | 0.998377i | \(-0.481863\pi\) | ||||
0.0569476 | + | 0.998377i | \(0.481863\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 492.853i | 1.11253i | 0.831003 | + | 0.556267i | \(0.187767\pi\) | ||||
−0.831003 | + | 0.556267i | \(0.812233\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 483.102i | − 1.07595i | −0.842960 | − | 0.537976i | \(-0.819189\pi\) | ||||
0.842960 | − | 0.537976i | \(-0.180811\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 375.553 | 0.832712 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 546.921 | 1.19676 | 0.598382 | − | 0.801211i | \(-0.295811\pi\) | ||||
0.598382 | + | 0.801211i | \(0.295811\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 130.386i | − 0.282834i | −0.989950 | − | 0.141417i | \(-0.954834\pi\) | ||||
0.989950 | − | 0.141417i | \(-0.0451658\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.7765 | −0.0535130 | −0.0267565 | − | 0.999642i | \(-0.508518\pi\) | ||||
−0.0267565 | + | 0.999642i | \(0.508518\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 671.491i | − 1.43788i | −0.695071 | − | 0.718941i | \(-0.744627\pi\) | ||||
0.695071 | − | 0.718941i | \(-0.255373\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −416.999 | −0.889124 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.41535i | − 0.0199056i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 538.257i | − 1.12371i | −0.827236 | − | 0.561855i | \(-0.810088\pi\) | ||||
0.827236 | − | 0.561855i | \(-0.189912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −717.473 | −1.49163 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −608.250 | −1.24897 | −0.624486 | − | 0.781036i | \(-0.714692\pi\) | ||||
−0.624486 | + | 0.781036i | \(0.714692\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 143.561i | − 0.292386i | −0.989256 | − | 0.146193i | \(-0.953298\pi\) | ||||
0.989256 | − | 0.146193i | \(-0.0467020\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −348.316 | −0.706523 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 132.117i | 0.265828i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 616.605 | 1.23568 | 0.617841 | − | 0.786303i | \(-0.288008\pi\) | ||||
0.617841 | + | 0.786303i | \(0.288008\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 374.729i | − 0.744989i | −0.928034 | − | 0.372494i | \(-0.878503\pi\) | ||||
0.928034 | − | 0.372494i | \(-0.121497\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 173.036i | 0.339953i | 0.985448 | + | 0.169977i | \(0.0543693\pi\) | ||||
−0.985448 | + | 0.169977i | \(0.945631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −103.816 | −0.203163 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 791.052 | 1.53008 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 455.116i | − 0.873543i | −0.899572 | − | 0.436772i | \(-0.856122\pi\) | ||||
0.899572 | − | 0.436772i | \(-0.143878\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 295.395 | 0.564809 | 0.282404 | − | 0.959295i | \(-0.408868\pi\) | ||||
0.282404 | + | 0.959295i | \(0.408868\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 355.935i | − 0.675398i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 504.684 | 0.954034 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 470.245i | 0.882260i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 173.335i | − 0.321587i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 906.394 | 1.67541 | 0.837703 | − | 0.546127i | \(-0.183898\pi\) | ||||
0.837703 | + | 0.546127i | \(0.183898\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 672.921 | 1.23020 | 0.615101 | − | 0.788448i | \(-0.289115\pi\) | ||||
0.615101 | + | 0.788448i | \(0.289115\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 553.627i | − 1.00477i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −586.658 | −1.06086 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 870.336i | − 1.56254i | −0.624192 | − | 0.781271i | \(-0.714572\pi\) | ||||
0.624192 | − | 0.781271i | \(-0.285428\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.7893 | 0.0210900 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 23.6320i | − 0.0419751i | −0.999780 | − | 0.0209875i | \(-0.993319\pi\) | ||||
0.999780 | − | 0.0209875i | \(-0.00668103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 295.273i | − 0.518933i | −0.965752 | − | 0.259466i | \(-0.916453\pi\) | ||||
0.965752 | − | 0.259466i | \(-0.0835467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 893.920 | 1.56553 | 0.782767 | − | 0.622314i | \(-0.213807\pi\) | ||||
0.782767 | + | 0.622314i | \(0.213807\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 264.763 | 0.458861 | 0.229431 | − | 0.973325i | \(-0.426314\pi\) | ||||
0.229431 | + | 0.973325i | \(0.426314\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 247.897i | 0.426673i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −881.526 | −1.51205 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 791.885i | − 1.34904i | −0.738258 | − | 0.674519i | \(-0.764351\pi\) | ||||
0.738258 | − | 0.674519i | \(-0.235649\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 565.737 | 0.960504 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.82388i | 0.00307567i | 0.999999 | + | 0.00153784i | \(0.000489509\pi\) | ||||
−0.999999 | + | 0.00153784i | \(0.999510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 758.204i | 1.26578i | 0.774241 | + | 0.632891i | \(0.218132\pi\) | ||||
−0.774241 | + | 0.632891i | \(0.781868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −283.579 | −0.471845 | −0.235922 | − | 0.971772i | \(-0.575811\pi\) | ||||
−0.235922 | + | 0.971772i | \(0.575811\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −167.828 | −0.276488 | −0.138244 | − | 0.990398i | \(-0.544146\pi\) | ||||
−0.138244 | + | 0.990398i | \(0.544146\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 990.507i | 1.62112i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 395.698 | 0.645510 | 0.322755 | − | 0.946483i | \(-0.395391\pi\) | ||||
0.322755 | + | 0.946483i | \(0.395391\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 855.190i | − 1.38604i | −0.720916 | − | 0.693022i | \(-0.756279\pi\) | ||||
0.720916 | − | 0.693022i | \(-0.243721\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 308.158 | 0.497832 | 0.248916 | − | 0.968525i | \(-0.419926\pi\) | ||||
0.248916 | + | 0.968525i | \(0.419926\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 636.079i | 1.02099i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1059.99i | − 1.68520i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 344.974 | 0.546709 | 0.273355 | − | 0.961913i | \(-0.411867\pi\) | ||||
0.273355 | + | 0.961913i | \(0.411867\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 217.040 | 0.340722 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 202.641i | 0.316133i | 0.987428 | + | 0.158066i | \(0.0505260\pi\) | ||||
−0.987428 | + | 0.158066i | \(0.949474\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −724.605 | −1.12691 | −0.563456 | − | 0.826146i | \(-0.690529\pi\) | ||||
−0.563456 | + | 0.826146i | \(0.690529\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 125.679i | − 0.194249i | −0.995272 | − | 0.0971243i | \(-0.969036\pi\) | ||||
0.995272 | − | 0.0971243i | \(-0.0309644\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1030.89 | 1.58843 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 551.226i | − 0.844144i | −0.906562 | − | 0.422072i | \(-0.861303\pi\) | ||||
0.906562 | − | 0.422072i | \(-0.138697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 801.765i | − 1.21664i | −0.793692 | − | 0.608320i | \(-0.791844\pi\) | ||||
0.793692 | − | 0.608320i | \(-0.208156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −529.079 | −0.800422 | −0.400211 | − | 0.916423i | \(-0.631063\pi\) | ||||
−0.400211 | + | 0.916423i | \(0.631063\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −101.210 | −0.151739 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 613.918i | − 0.914929i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −413.395 | −0.614257 | −0.307129 | − | 0.951668i | \(-0.599368\pi\) | ||||
−0.307129 | + | 0.951668i | \(0.599368\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 359.936i | − 0.531663i | −0.964019 | − | 0.265832i | \(-0.914353\pi\) | ||||
0.964019 | − | 0.265832i | \(-0.0856465\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −477.499 | −0.703239 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.5484i | 0.0315496i | 0.999876 | + | 0.0157748i | \(0.00502148\pi\) | ||||
−0.999876 | + | 0.0157748i | \(0.994979\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1103.79i | − 1.60202i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −384.921 | −0.557049 | −0.278525 | − | 0.960429i | \(-0.589845\pi\) | ||||
−0.278525 | + | 0.960429i | \(0.589845\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −694.736 | −0.996752 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 439.057i | − 0.626330i | −0.949699 | − | 0.313165i | \(-0.898611\pi\) | ||||
0.949699 | − | 0.313165i | \(-0.101389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1684.79 | 2.39657 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 709.080i | − 1.00294i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −126.421 | −0.178309 | −0.0891547 | − | 0.996018i | \(-0.528417\pi\) | ||||
−0.0891547 | + | 0.996018i | \(0.528417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 103.424i | − 0.145054i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 571.715i | 0.795153i | 0.917569 | + | 0.397576i | \(0.130149\pi\) | ||||
−0.917569 | + | 0.397576i | \(0.869851\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 627.159 | 0.869846 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 841.038 | 1.15686 | 0.578431 | − | 0.815731i | \(-0.303665\pi\) | ||||
0.578431 | + | 0.815731i | \(0.303665\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.4175i | 0.0238269i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −494.749 | −0.674965 | −0.337483 | − | 0.941332i | \(-0.609575\pi\) | ||||
−0.337483 | + | 0.941332i | \(0.609575\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 697.206i | 0.946006i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1263.97 | 1.71038 | 0.855191 | − | 0.518312i | \(-0.173439\pi\) | ||||
0.855191 | + | 0.518312i | \(0.173439\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 956.343i | 1.28714i | 0.765389 | + | 0.643568i | \(0.222547\pi\) | ||||
−0.765389 | + | 0.643568i | \(0.777453\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 512.131i | 0.683752i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1121.66 | −1.49355 | −0.746776 | − | 0.665076i | \(-0.768399\pi\) | ||||
−0.746776 | + | 0.665076i | \(0.768399\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 466.433 | 0.616160 | 0.308080 | − | 0.951360i | \(-0.400313\pi\) | ||||
0.308080 | + | 0.951360i | \(0.400313\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1223.41i | 1.60763i | 0.594880 | + | 0.803814i | \(0.297199\pi\) | ||||
−0.594880 | + | 0.803814i | \(0.702801\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −663.184 | −0.869180 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1290.82i | 1.68295i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1290.63 | −1.67832 | −0.839162 | − | 0.543882i | \(-0.816954\pi\) | ||||
−0.839162 | + | 0.543882i | \(0.816954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 329.455i | 0.426204i | 0.977030 | + | 0.213102i | \(0.0683566\pi\) | ||||
−0.977030 | + | 0.213102i | \(0.931643\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1104.24i | − 1.41751i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 220.894 | 0.282835 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1506.13 | 1.91376 | 0.956881 | − | 0.290480i | \(-0.0938148\pi\) | ||||
0.956881 | + | 0.290480i | \(0.0938148\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 605.245i | − 0.765165i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 768.710 | 0.969370 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 250.874i | 0.314773i | 0.987537 | + | 0.157387i | \(0.0503069\pi\) | ||||
−0.987537 | + | 0.157387i | \(0.949693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1463.37 | −1.83150 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 173.577i | 0.216160i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1097.02i | 1.35602i | 0.735053 | + | 0.678010i | \(0.237157\pi\) | ||||
−0.735053 | + | 0.678010i | \(0.762843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −221.473 | −0.273087 | −0.136543 | − | 0.990634i | \(-0.543599\pi\) | ||||
−0.136543 | + | 0.990634i | \(0.543599\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.6840 | −0.0338849 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1003.92i | − 1.22281i | −0.791319 | − | 0.611403i | \(-0.790605\pi\) | ||||
0.791319 | − | 0.611403i | \(-0.209395\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −335.013 | −0.407063 | −0.203531 | − | 0.979068i | \(-0.565242\pi\) | ||||
−0.203531 | + | 0.979068i | \(0.565242\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1004.72i | − 1.21490i | −0.794357 | − | 0.607451i | \(-0.792192\pi\) | ||||
0.794357 | − | 0.607451i | \(-0.207808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 676.763 | 0.816361 | 0.408180 | − | 0.912901i | \(-0.366163\pi\) | ||||
0.408180 | + | 0.912901i | \(0.366163\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 320.653i | 0.384938i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 621.286i | − 0.740507i | −0.928931 | − | 0.370254i | \(-0.879271\pi\) | ||||
0.928931 | − | 0.370254i | \(-0.120729\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 419.736 | 0.499092 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −202.146 | −0.238661 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 308.001i | − 0.361928i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 544.591 | 0.638443 | 0.319221 | − | 0.947680i | \(-0.396579\pi\) | ||||
0.319221 | + | 0.947680i | \(0.396579\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 362.149i | − 0.422578i | −0.977424 | − | 0.211289i | \(-0.932234\pi\) | ||||
0.977424 | − | 0.211289i | \(-0.0677661\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.6840 | −0.0252433 | −0.0126216 | − | 0.999920i | \(-0.504018\pi\) | ||||
−0.0126216 | + | 0.999920i | \(0.504018\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 220.300i | − 0.255273i | −0.991821 | − | 0.127636i | \(-0.959261\pi\) | ||||
0.991821 | − | 0.127636i | \(-0.0407390\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 980.868i | 1.12873i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −872.999 | −1.00230 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1136.41 | −1.29579 | −0.647895 | − | 0.761730i | \(-0.724350\pi\) | ||||
−0.647895 | + | 0.761730i | \(0.724350\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 711.758i | − 0.807898i | −0.914782 | − | 0.403949i | \(-0.867637\pi\) | ||||
0.914782 | − | 0.403949i | \(-0.132363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 536.394 | 0.607468 | 0.303734 | − | 0.952757i | \(-0.401767\pi\) | ||||
0.303734 | + | 0.952757i | \(0.401767\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1463.95i | 1.65045i | 0.564801 | + | 0.825227i | \(0.308953\pi\) | ||||
−0.564801 | + | 0.825227i | \(0.691047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 578.211 | 0.650406 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2325.93i | − 2.60463i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 430.479i | − 0.478842i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1630.74 | 1.80992 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −855.657 | −0.943392 | −0.471696 | − | 0.881761i | \(-0.656358\pi\) | ||||
−0.471696 | + | 0.881761i | \(0.656358\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1581.02i | 1.73547i | 0.497024 | + | 0.867737i | \(0.334426\pi\) | ||||
−0.497024 | + | 0.867737i | \(0.665574\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 414.474 | 0.453969 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 771.360i | 0.841178i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1489.08 | −1.62033 | −0.810163 | − | 0.586205i | \(-0.800621\pi\) | ||||
−0.810163 | + | 0.586205i | \(0.800621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 276.590i | 0.299664i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 736.990i | 0.793316i | 0.917966 | + | 0.396658i | \(0.129830\pi\) | ||||
−0.917966 | + | 0.396658i | \(0.870170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −509.658 | −0.547431 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1550.05 | −1.65427 | −0.827135 | − | 0.562003i | \(-0.810031\pi\) | ||||
−0.827135 | + | 0.562003i | \(0.810031\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 628.711i | − 0.668131i | −0.942550 | − | 0.334065i | \(-0.891579\pi\) | ||||
0.942550 | − | 0.334065i | \(-0.108421\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −201.869 | −0.214071 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1498.73i | − 1.58261i | −0.611423 | − | 0.791304i | \(-0.709402\pi\) | ||||
0.611423 | − | 0.791304i | \(-0.290598\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −217.342 | −0.229022 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 224.748i | − 0.235832i | −0.993024 | − | 0.117916i | \(-0.962379\pi\) | ||||
0.993024 | − | 0.117916i | \(-0.0376214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1464.72i | 1.52734i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −521.105 | −0.542253 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −233.986 | −0.241972 | −0.120986 | − | 0.992654i | \(-0.538606\pi\) | ||||
−0.120986 | + | 0.992654i | \(0.538606\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 691.940i | 0.712606i | 0.934371 | + | 0.356303i | \(0.115963\pi\) | ||||
−0.934371 | + | 0.356303i | \(0.884037\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 86.9224 | 0.0893344 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 395.571i | 0.404883i | 0.979294 | + | 0.202442i | \(0.0648877\pi\) | ||||
−0.979294 | + | 0.202442i | \(0.935112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1063.50 | 1.08631 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.82388i | − 0.00185542i | −1.00000 | 0.000927709i | \(-0.999705\pi\) | |||||
1.00000 | 0.000927709i | \(-0.000295299\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.06098i | 0.00511727i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 506.316 | 0.510914 | 0.255457 | − | 0.966820i | \(-0.417774\pi\) | ||||
0.255457 | + | 0.966820i | \(0.417774\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 295.670 | 0.296560 | 0.148280 | − | 0.988945i | \(-0.452626\pi\) | ||||
0.148280 | + | 0.988945i | \(0.452626\pi\) | |||||||
\(998\) | 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 | 900.3.g.d.701.2 | 4 | ||
3.2 | odd | 2 | inner | 900.3.g.d.701.1 | 4 | ||
4.3 | odd | 2 | 3600.3.l.n.1601.3 | 4 | |||
5.2 | odd | 4 | 900.3.b.b.449.4 | 8 | |||
5.3 | odd | 4 | 900.3.b.b.449.6 | 8 | |||
5.4 | even | 2 | 180.3.g.a.161.4 | yes | 4 | ||
12.11 | even | 2 | 3600.3.l.n.1601.4 | 4 | |||
15.2 | even | 4 | 900.3.b.b.449.3 | 8 | |||
15.8 | even | 4 | 900.3.b.b.449.5 | 8 | |||
15.14 | odd | 2 | 180.3.g.a.161.2 | ✓ | 4 | ||
20.3 | even | 4 | 3600.3.c.k.449.3 | 8 | |||
20.7 | even | 4 | 3600.3.c.k.449.5 | 8 | |||
20.19 | odd | 2 | 720.3.l.c.161.3 | 4 | |||
40.19 | odd | 2 | 2880.3.l.f.1601.1 | 4 | |||
40.29 | even | 2 | 2880.3.l.b.1601.2 | 4 | |||
45.4 | even | 6 | 1620.3.o.f.1241.3 | 8 | |||
45.14 | odd | 6 | 1620.3.o.f.1241.1 | 8 | |||
45.29 | odd | 6 | 1620.3.o.f.701.3 | 8 | |||
45.34 | even | 6 | 1620.3.o.f.701.1 | 8 | |||
60.23 | odd | 4 | 3600.3.c.k.449.4 | 8 | |||
60.47 | odd | 4 | 3600.3.c.k.449.6 | 8 | |||
60.59 | even | 2 | 720.3.l.c.161.1 | 4 | |||
120.29 | odd | 2 | 2880.3.l.b.1601.4 | 4 | |||
120.59 | even | 2 | 2880.3.l.f.1601.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.g.a.161.2 | ✓ | 4 | 15.14 | odd | 2 | ||
180.3.g.a.161.4 | yes | 4 | 5.4 | even | 2 | ||
720.3.l.c.161.1 | 4 | 60.59 | even | 2 | |||
720.3.l.c.161.3 | 4 | 20.19 | odd | 2 | |||
900.3.b.b.449.3 | 8 | 15.2 | even | 4 | |||
900.3.b.b.449.4 | 8 | 5.2 | odd | 4 | |||
900.3.b.b.449.5 | 8 | 15.8 | even | 4 | |||
900.3.b.b.449.6 | 8 | 5.3 | odd | 4 | |||
900.3.g.d.701.1 | 4 | 3.2 | odd | 2 | inner | ||
900.3.g.d.701.2 | 4 | 1.1 | even | 1 | trivial | ||
1620.3.o.f.701.1 | 8 | 45.34 | even | 6 | |||
1620.3.o.f.701.3 | 8 | 45.29 | odd | 6 | |||
1620.3.o.f.1241.1 | 8 | 45.14 | odd | 6 | |||
1620.3.o.f.1241.3 | 8 | 45.4 | even | 6 | |||
2880.3.l.b.1601.2 | 4 | 40.29 | even | 2 | |||
2880.3.l.b.1601.4 | 4 | 120.29 | odd | 2 | |||
2880.3.l.f.1601.1 | 4 | 40.19 | odd | 2 | |||
2880.3.l.f.1601.3 | 4 | 120.59 | even | 2 | |||
3600.3.c.k.449.3 | 8 | 20.3 | even | 4 | |||
3600.3.c.k.449.4 | 8 | 60.23 | odd | 4 | |||
3600.3.c.k.449.5 | 8 | 20.7 | even | 4 | |||
3600.3.c.k.449.6 | 8 | 60.47 | odd | 4 | |||
3600.3.l.n.1601.3 | 4 | 4.3 | odd | 2 | |||
3600.3.l.n.1601.4 | 4 | 12.11 | even | 2 |