Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2300,2,Mod(1749,2300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2300.1749");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2300.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.3655924649\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 53x^{4} + 29x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1749.2 | ||
Root | \(-2.50653i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2300.1749 |
Dual form | 2300.2.c.j.1749.7 |
$q$-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 \(\left(\mathbb{Z}/2300\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(1151\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 2.50653i | − 1.44715i | −0.690247 | − | 0.723574i | \(-0.742498\pi\) | ||||
0.690247 | − | 0.723574i | \(-0.257502\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.797915i | 0.301583i | 0.988566 | + | 0.150792i | \(0.0481823\pi\) | ||||
−0.988566 | + | 0.150792i | \(0.951818\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.28271 | −1.09424 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.21515 | 1.27092 | 0.635458 | − | 0.772135i | \(-0.280811\pi\) | ||||
0.635458 | + | 0.772135i | \(0.280811\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.48479i | 0.411808i | 0.978572 | + | 0.205904i | \(0.0660134\pi\) | ||||
−0.978572 | + | 0.205904i | \(0.933987\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.01307i | 0.730776i | 0.930855 | + | 0.365388i | \(0.119064\pi\) | ||||
−0.930855 | + | 0.365388i | \(0.880936\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.21515 | 0.508191 | 0.254095 | − | 0.967179i | \(-0.418222\pi\) | ||||
0.254095 | + | 0.967179i | \(0.418222\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.708618i | 0.136374i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.57409 | 0.477997 | 0.238998 | − | 0.971020i | \(-0.423181\pi\) | ||||
0.238998 | + | 0.971020i | \(0.423181\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.78924 | 1.57859 | 0.789297 | − | 0.614011i | \(-0.210445\pi\) | ||||
0.789297 | + | 0.614011i | \(0.210445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 10.5654i | − 1.83920i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.57848i | 1.57469i | 0.616511 | + | 0.787346i | \(0.288546\pi\) | ||||
−0.616511 | + | 0.787346i | \(0.711454\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.72168 | 0.595946 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.26097 | −0.196930 | −0.0984651 | − | 0.995141i | \(-0.531393\pi\) | ||||
−0.0984651 | + | 0.995141i | \(0.531393\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.21515i | 0.337807i | 0.985633 | + | 0.168904i | \(0.0540227\pi\) | ||||
−0.985633 | + | 0.168904i | \(0.945977\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2.86547i | − 0.417972i | −0.977919 | − | 0.208986i | \(-0.932984\pi\) | ||||
0.977919 | − | 0.208986i | \(-0.0670163\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.36333 | 0.909047 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.55235 | 1.05754 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 5.41724i | − 0.744115i | −0.928210 | − | 0.372057i | \(-0.878652\pi\) | ||||
0.928210 | − | 0.372057i | \(-0.121348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 5.55235i | − 0.735427i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.21515 | 0.158199 | 0.0790996 | − | 0.996867i | \(-0.474795\pi\) | ||||
0.0790996 | + | 0.996867i | \(0.474795\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.58276 | 0.330689 | 0.165344 | − | 0.986236i | \(-0.447126\pi\) | ||||
0.165344 | + | 0.986236i | \(0.447126\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 2.61932i | − 0.330004i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.56542i | − 1.04643i | −0.852200 | − | 0.523216i | \(-0.824732\pi\) | ||||
0.852200 | − | 0.523216i | \(-0.175268\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.50653 | −0.301751 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.73036 | 0.798747 | 0.399373 | − | 0.916788i | \(-0.369228\pi\) | ||||
0.399373 | + | 0.916788i | \(0.369228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 3.02174i | − 0.353668i | −0.984241 | − | 0.176834i | \(-0.943414\pi\) | ||||
0.984241 | − | 0.176834i | \(-0.0565856\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.36333i | 0.383287i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.189019 | −0.0212663 | −0.0106331 | − | 0.999943i | \(-0.503385\pi\) | ||||
−0.0106331 | + | 0.999943i | \(0.503385\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.07195 | −0.896883 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.22822i | 0.793400i | 0.917948 | + | 0.396700i | \(0.129845\pi\) | ||||
−0.917948 | + | 0.396700i | \(0.870155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 6.45204i | − 0.691732i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.38682 | −0.677002 | −0.338501 | − | 0.940966i | \(-0.609920\pi\) | ||||
−0.338501 | + | 0.940966i | \(0.609920\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.18474 | −0.124194 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 22.0305i | − 2.28446i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 13.3999i | − 1.36055i | −0.732956 | − | 0.680276i | \(-0.761860\pi\) | ||||
0.732956 | − | 0.680276i | \(-0.238140\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.8371 | −1.39068 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.1978 | 1.71125 | 0.855623 | − | 0.517600i | \(-0.173174\pi\) | ||||
0.855623 | + | 0.517600i | \(0.173174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.393745i | 0.0387968i | 0.999812 | + | 0.0193984i | \(0.00617509\pi\) | ||||
−0.999812 | + | 0.0193984i | \(0.993825\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.969587i | 0.0937336i | 0.998901 | + | 0.0468668i | \(0.0149236\pi\) | ||||
−0.998901 | + | 0.0468668i | \(0.985076\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1612 | −0.973271 | −0.486635 | − | 0.873605i | \(-0.661776\pi\) | ||||
−0.486635 | + | 0.873605i | \(0.661776\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.0088 | 2.27881 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.99572i | 0.658102i | 0.944312 | + | 0.329051i | \(0.106729\pi\) | ||||
−0.944312 | + | 0.329051i | \(0.893271\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 4.87414i | − 0.450615i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.40417 | −0.220390 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.76750 | 0.615227 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.16066i | 0.284987i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4.78924i | − 0.424976i | −0.977164 | − | 0.212488i | \(-0.931843\pi\) | ||||
0.977164 | − | 0.212488i | \(-0.0681567\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.55235 | 0.488857 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.11543 | −0.446937 | −0.223469 | − | 0.974711i | \(-0.571738\pi\) | ||||
−0.223469 | + | 0.974711i | \(0.571738\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.76750i | 0.153262i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 12.0261i | − 1.02746i | −0.857951 | − | 0.513731i | \(-0.828263\pi\) | ||||
0.857951 | − | 0.513731i | \(-0.171737\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1041 | −1.02666 | −0.513329 | − | 0.858192i | \(-0.671588\pi\) | ||||
−0.513329 | + | 0.858192i | \(0.671588\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.18240 | −0.604867 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.25863i | 0.523373i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 15.9499i | − 1.31553i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.7701 | −1.21002 | −0.605009 | − | 0.796219i | \(-0.706830\pi\) | ||||
−0.605009 | + | 0.796219i | \(0.706830\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.40048 | −0.520863 | −0.260432 | − | 0.965492i | \(-0.583865\pi\) | ||||
−0.260432 | + | 0.965492i | \(0.583865\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 9.89102i | − 0.799641i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 10.8780i | − 0.868155i | −0.900876 | − | 0.434078i | \(-0.857074\pi\) | ||||
0.900876 | − | 0.434078i | \(-0.142926\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.5785 | −1.07684 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.797915 | 0.0628845 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6237i | 1.22374i | 0.790957 | + | 0.611872i | \(0.209583\pi\) | ||||
−0.790957 | + | 0.611872i | \(0.790417\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.7502i | 0.986637i | 0.869849 | + | 0.493318i | \(0.164216\pi\) | ||||
−0.869849 | + | 0.493318i | \(0.835784\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.7954 | 0.830414 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.27170 | −0.556081 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 0.569697i | − 0.0433133i | −0.999765 | − | 0.0216566i | \(-0.993106\pi\) | ||||
0.999765 | − | 0.0216566i | \(-0.00689406\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 3.04582i | − 0.228938i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.99825 | −0.298843 | −0.149422 | − | 0.988774i | \(-0.547741\pi\) | ||||
−0.149422 | + | 0.988774i | \(0.547741\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.2178 | −0.833812 | −0.416906 | − | 0.908950i | \(-0.636886\pi\) | ||||
−0.416906 | + | 0.908950i | \(0.636886\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 6.47378i | − 0.478556i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.7005i | 0.928755i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.565417 | −0.0411280 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0365585 | −0.00264528 | −0.00132264 | − | 0.999999i | \(-0.500421\pi\) | ||||
−0.00132264 | + | 0.999999i | \(0.500421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 10.2201i | − 0.735661i | −0.929893 | − | 0.367831i | \(-0.880101\pi\) | ||||
0.929893 | − | 0.367831i | \(-0.119899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 17.4657i | − 1.24438i | −0.782867 | − | 0.622190i | \(-0.786243\pi\) | ||||
0.782867 | − | 0.622190i | \(-0.213757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.37640 | 0.310235 | 0.155117 | − | 0.987896i | \(-0.450424\pi\) | ||||
0.155117 | + | 0.987896i | \(0.450424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.4695 | −1.51434 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.05390i | 0.144156i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.28271i | 0.228164i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.33720 | 0.645868 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6455 | 0.801706 | 0.400853 | − | 0.916142i | \(-0.368714\pi\) | ||||
0.400853 | + | 0.916142i | \(0.368714\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 16.8699i | − 1.15590i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.01307i | 0.476078i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.57409 | −0.511810 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.47378 | −0.300939 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.4068i | 1.23261i | 0.787507 | + | 0.616306i | \(0.211371\pi\) | ||||
−0.787507 | + | 0.616306i | \(0.788629\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 27.2747i | − 1.81029i | −0.425105 | − | 0.905144i | \(-0.639763\pi\) | ||||
0.425105 | − | 0.905144i | \(-0.360237\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.8606 | −0.849853 | −0.424926 | − | 0.905228i | \(-0.639700\pi\) | ||||
−0.424926 | + | 0.905228i | \(0.639700\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.43030 | 0.554673 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 24.8847i | − 1.63025i | −0.579285 | − | 0.815125i | \(-0.696668\pi\) | ||||
0.579285 | − | 0.815125i | \(-0.303332\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.473782i | 0.0307754i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.8160 | 1.15242 | 0.576209 | − | 0.817302i | \(-0.304531\pi\) | ||||
0.576209 | + | 0.817302i | \(0.304531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.2004 | 0.850315 | 0.425158 | − | 0.905119i | \(-0.360219\pi\) | ||||
0.425158 | + | 0.905119i | \(0.360219\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3585i | 1.43430i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.28904i | 0.209277i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.1178 | 1.14817 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.1266 | −1.77533 | −0.887666 | − | 0.460488i | \(-0.847675\pi\) | ||||
−0.887666 | + | 0.460488i | \(0.847675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.21515i | − 0.265004i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 17.1416i | − 1.06926i | −0.845086 | − | 0.534631i | \(-0.820451\pi\) | ||||
0.845086 | − | 0.534631i | \(-0.179549\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.64281 | −0.474901 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.44999 | −0.523041 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.7093i | 1.40032i | 0.713988 | + | 0.700158i | \(0.246887\pi\) | ||||
−0.713988 | + | 0.700158i | \(0.753113\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.0088i | 0.979722i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.3758 | 1.18136 | 0.590682 | − | 0.806904i | \(-0.298859\pi\) | ||||
0.590682 | + | 0.806904i | \(0.298859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.0549 | 1.94720 | 0.973598 | − | 0.228268i | \(-0.0733061\pi\) | ||||
0.973598 | + | 0.228268i | \(0.0733061\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.96959i | 0.179728i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 6.36099i | − 0.382195i | −0.981571 | − | 0.191098i | \(-0.938795\pi\) | ||||
0.981571 | − | 0.191098i | \(-0.0612047\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −28.8525 | −1.72736 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.7440 | −0.879554 | −0.439777 | − | 0.898107i | \(-0.644943\pi\) | ||||
−0.439777 | + | 0.898107i | \(0.644943\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.76136i | 0.520809i | 0.965500 | + | 0.260404i | \(0.0838558\pi\) | ||||
−0.965500 | + | 0.260404i | \(0.916144\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.00615i | − 0.0593909i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.92143 | 0.465967 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −33.5873 | −1.96892 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2047i | 0.596166i | 0.954540 | + | 0.298083i | \(0.0963473\pi\) | ||||
−0.954540 | + | 0.298083i | \(0.903653\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.98693i | 0.173319i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.48479 | 0.0858678 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.76750 | −0.101877 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 43.1069i | − 2.47642i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.7267i | 1.52537i | 0.646769 | + | 0.762686i | \(0.276120\pi\) | ||||
−0.646769 | + | 0.762686i | \(0.723880\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.986934 | 0.0561447 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.7807 | 1.51859 | 0.759297 | − | 0.650745i | \(-0.225543\pi\) | ||||
0.759297 | + | 0.650745i | \(0.225543\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9214i | 0.730362i | 0.930936 | + | 0.365181i | \(0.118993\pi\) | ||||
−0.930936 | + | 0.365181i | \(0.881007\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 14.1717i | − 0.795960i | −0.917394 | − | 0.397980i | \(-0.869711\pi\) | ||||
0.917394 | − | 0.397980i | \(-0.130289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.8502 | 0.607493 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.43030 | 0.135646 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.67440i | 0.371373i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.4695i | 1.40847i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.28640 | 0.126053 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.6766 | 1.68614 | 0.843068 | − | 0.537807i | \(-0.180747\pi\) | ||||
0.843068 | + | 0.537807i | \(0.180747\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 31.4434i | − 1.72309i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.4260i | 1.60294i | 0.598037 | + | 0.801469i | \(0.295948\pi\) | ||||
−0.598037 | + | 0.801469i | \(0.704052\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.5350 | 0.952371 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.0480 | 2.00626 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.6628i | 0.575737i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.9157i | 0.747033i | 0.927624 | + | 0.373516i | \(0.121848\pi\) | ||||
−0.927624 | + | 0.373516i | \(0.878152\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.2931 | −0.550979 | −0.275489 | − | 0.961304i | \(-0.588840\pi\) | ||||
−0.275489 | + | 0.961304i | \(0.588840\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.05215 | −0.0561597 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.8960i | 0.739609i | 0.929110 | + | 0.369805i | \(0.120575\pi\) | ||||
−0.929110 | + | 0.369805i | \(0.879425\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.02613i | 0.318937i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.8328 | 1.73285 | 0.866425 | − | 0.499307i | \(-0.166412\pi\) | ||||
0.866425 | + | 0.499307i | \(0.166412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0931 | −0.741742 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 16.9630i | − 0.890325i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.47114i | 0.181192i | 0.995888 | + | 0.0905961i | \(0.0288772\pi\) | ||||
−0.995888 | + | 0.0905961i | \(0.971123\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.13939 | 0.215488 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.32249 | 0.224413 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.7440i | 1.28120i | 0.767876 | + | 0.640598i | \(0.221314\pi\) | ||||
−0.767876 | + | 0.640598i | \(0.778686\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.82199i | 0.196843i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.7832 | −1.94079 | −0.970397 | − | 0.241517i | \(-0.922355\pi\) | ||||
−0.970397 | + | 0.241517i | \(0.922355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.0044 | −0.615004 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 8.51151i | − 0.434918i | −0.976069 | − | 0.217459i | \(-0.930223\pi\) | ||||
0.976069 | − | 0.217459i | \(-0.0697768\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 7.27170i | − 0.369641i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.2309 | 1.43136 | 0.715681 | − | 0.698428i | \(-0.246117\pi\) | ||||
0.715681 | + | 0.698428i | \(0.246117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.01307 | 0.152377 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.8220i | 0.646784i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.0714i | 0.605844i | 0.953015 | + | 0.302922i | \(0.0979622\pi\) | ||||
−0.953015 | + | 0.302922i | \(0.902038\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.43030 | 0.221793 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.1612 | −1.60606 | −0.803028 | − | 0.595941i | \(-0.796779\pi\) | ||||
−0.803028 | + | 0.595941i | \(0.796779\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0502i | 0.650077i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.3748i | 2.00130i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.6704 | −0.873746 | −0.436873 | − | 0.899523i | \(-0.643914\pi\) | ||||
−0.436873 | + | 0.899523i | \(0.643914\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.1439 | −1.48689 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.969587i | 0.0477103i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.3394i | 1.48573i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.8710 | 0.824204 | 0.412102 | − | 0.911138i | \(-0.364795\pi\) | ||||
0.412102 | + | 0.911138i | \(0.364795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.29519 | 0.404283 | 0.202141 | − | 0.979356i | \(-0.435210\pi\) | ||||
0.202141 | + | 0.979356i | \(0.435210\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.40651i | 0.457360i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.06083i | 0.0997303i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.6875 | 0.757398 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.3213 | −0.882507 | −0.441254 | − | 0.897382i | \(-0.645466\pi\) | ||||
−0.441254 | + | 0.897382i | \(0.645466\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.39538i | 0.115115i | 0.998342 | + | 0.0575574i | \(0.0183312\pi\) | ||||
−0.998342 | + | 0.0575574i | \(0.981669\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2.21515i | − 0.105965i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.00234 | −0.143294 | −0.0716469 | − | 0.997430i | \(-0.522825\pi\) | ||||
−0.0716469 | + | 0.997430i | \(0.522825\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.8890 | −0.994713 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 17.0790i | − 0.811447i | −0.913996 | − | 0.405724i | \(-0.867020\pi\) | ||||
0.913996 | − | 0.405724i | \(-0.132980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 37.0219i | 1.75107i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.01999 | 0.378487 | 0.189243 | − | 0.981930i | \(-0.439397\pi\) | ||||
0.189243 | + | 0.981930i | \(0.439397\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.31518 | −0.250282 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.0430i | 0.753766i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.7081i | 1.24935i | 0.780883 | + | 0.624677i | \(0.214769\pi\) | ||||
−0.780883 | + | 0.624677i | \(0.785231\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.13511 | −0.0996586 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.7895 | 0.688818 | 0.344409 | − | 0.938820i | \(-0.388079\pi\) | ||||
0.344409 | + | 0.938820i | \(0.388079\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.64545i | 0.0764708i | 0.999269 | + | 0.0382354i | \(0.0121737\pi\) | ||||
−0.999269 | + | 0.0382354i | \(0.987826\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 22.3591i | − 1.03465i | −0.855788 | − | 0.517327i | \(-0.826927\pi\) | ||||
0.855788 | − | 0.517327i | \(-0.173073\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.83447 | 0.315587 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.2659 | −1.25635 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.33720i | 0.429325i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.7832i | 0.814237i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.9245 | −0.681916 | −0.340958 | − | 0.940078i | \(-0.610751\pi\) | ||||
−0.340958 | + | 0.940078i | \(0.610751\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.2221 | −0.648471 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.00000i | − 0.0910032i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.9994i | 0.951574i | 0.879560 | + | 0.475787i | \(0.157837\pi\) | ||||
−0.879560 | + | 0.475787i | \(0.842163\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 39.1614 | 1.77094 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.9743 | −1.71376 | −0.856878 | − | 0.515520i | \(-0.827599\pi\) | ||||
−0.856878 | + | 0.515520i | \(0.827599\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.75590i | 0.349308i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.37025i | 0.240889i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.9630 | −0.938431 | −0.469216 | − | 0.883084i | \(-0.655463\pi\) | ||||
−0.469216 | + | 0.883084i | \(0.655463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.9587 | 1.42781 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 10.9157i | − 0.486706i | −0.969938 | − | 0.243353i | \(-0.921753\pi\) | ||||
0.969938 | − | 0.243353i | \(-0.0782474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 27.0590i | − 1.20173i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.0068 | 1.59598 | 0.797988 | − | 0.602674i | \(-0.205898\pi\) | ||||
0.797988 | + | 0.602674i | \(0.205898\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.41109 | 0.106660 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.56970i | 0.0693038i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 12.0784i | − 0.531207i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.42796 | −0.0626807 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.73973 | 0.426705 | 0.213353 | − | 0.976975i | \(-0.431562\pi\) | ||||
0.213353 | + | 0.976975i | \(0.431562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.8414i | 0.998784i | 0.866376 | + | 0.499392i | \(0.166443\pi\) | ||||
−0.866376 | + | 0.499392i | \(0.833557\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.4826i | 1.15360i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.98899 | −0.173107 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.87228i | − 0.0810974i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.0217i | 0.432470i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.8224 | 1.15532 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.1869 | −1.85675 | −0.928375 | − | 0.371645i | \(-0.878794\pi\) | ||||
−0.928375 | + | 0.371645i | \(0.878794\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.1178i | 1.20665i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 28.3438i | − 1.21189i | −0.795506 | − | 0.605946i | \(-0.792795\pi\) | ||||
0.795506 | − | 0.605946i | \(-0.207205\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.47846 | −0.361852 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.70200 | 0.242913 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 0.150821i | − 0.00641356i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 19.8214i | − 0.839860i | −0.907557 | − | 0.419930i | \(-0.862055\pi\) | ||||
0.907557 | − | 0.419930i | \(-0.137945\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.28904 | −0.139112 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.8343 | 1.34405 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 35.2109i | − 1.48396i | −0.670421 | − | 0.741981i | \(-0.733887\pi\) | ||||
0.670421 | − | 0.741981i | \(-0.266113\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 6.44073i | − 0.270485i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.83875 | 0.412462 | 0.206231 | − | 0.978503i | \(-0.433880\pi\) | ||||
0.206231 | + | 0.978503i | \(0.433880\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.5434 | 1.36190 | 0.680949 | − | 0.732331i | \(-0.261567\pi\) | ||||
0.680949 | + | 0.732331i | \(0.261567\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.0916351i | 0.00382811i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 16.7305i | − 0.696499i | −0.937402 | − | 0.348249i | \(-0.886776\pi\) | ||||
0.937402 | − | 0.348249i | \(-0.113224\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.6171 | −1.06461 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.76750 | −0.239276 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 22.8345i | − 0.945707i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.51257i | 0.227528i | 0.993508 | + | 0.113764i | \(0.0362908\pi\) | ||||
−0.993508 | + | 0.113764i | \(0.963709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.4695 | 0.802227 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43.7783 | −1.80080 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.61582i | 0.107419i | 0.998557 | + | 0.0537094i | \(0.0171044\pi\) | ||||
−0.998557 | + | 0.0537094i | \(0.982896\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 10.9696i | − 0.448955i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.72402 | 0.274736 | 0.137368 | − | 0.990520i | \(-0.456136\pi\) | ||||
0.137368 | + | 0.990520i | \(0.456136\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.7249 | −1.57962 | −0.789811 | − | 0.613350i | \(-0.789821\pi\) | ||||
−0.789811 | + | 0.613350i | \(0.789821\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.1178i | 1.14504i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24.4095i | − 0.990749i | −0.868679 | − | 0.495375i | \(-0.835031\pi\) | ||||
0.868679 | − | 0.495375i | \(-0.164969\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.14818 | 0.208615 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.25463 | 0.172124 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.8224i | 1.72958i | 0.502133 | + | 0.864790i | \(0.332549\pi\) | ||||
−0.502133 | + | 0.864790i | \(0.667451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 40.6177i | − 1.63521i | −0.575782 | − | 0.817603i | \(-0.695302\pi\) | ||||
0.575782 | − | 0.817603i | \(-0.304698\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.6132 | −0.547160 | −0.273580 | − | 0.961849i | \(-0.588208\pi\) | ||||
−0.273580 | + | 0.961849i | \(0.588208\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.708618 | 0.0284359 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 5.09614i | − 0.204173i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 23.4040i | − 0.934666i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.8606 | −1.15075 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.7108 | −1.50124 | −0.750621 | − | 0.660733i | \(-0.770246\pi\) | ||||
−0.750621 | + | 0.660733i | \(0.770246\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 29.1897i | − 1.16019i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.44824i | 0.374353i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.0938 | −0.874017 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.0261 | −1.18596 | −0.592980 | − | 0.805217i | \(-0.702049\pi\) | ||||
−0.592980 | + | 0.805217i | \(0.702049\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 24.5030i | − 0.966302i | −0.875537 | − | 0.483151i | \(-0.839492\pi\) | ||||
0.875537 | − | 0.483151i | \(-0.160508\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.3535i | 0.760864i | 0.924809 | + | 0.380432i | \(0.124225\pi\) | ||||
−0.924809 | + | 0.380432i | \(0.875775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.12205 | 0.201058 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.5785 | 0.688955 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 36.2953i | − 1.42034i | −0.704028 | − | 0.710172i | \(-0.748617\pi\) | ||||
0.704028 | − | 0.710172i | \(-0.251383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.91949i | 0.386996i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.0553 | −1.17079 | −0.585394 | − | 0.810749i | \(-0.699060\pi\) | ||||
−0.585394 | + | 0.810749i | \(0.699060\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.29947 | 0.0505435 | 0.0252717 | − | 0.999681i | \(-0.491955\pi\) | ||||
0.0252717 | + | 0.999681i | \(0.491955\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.2137i | 0.435503i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.57409i | − 0.0996692i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 46.1373 | 1.78377 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.8867 | 0.420278 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.4441i | 1.94448i | 0.233994 | + | 0.972238i | \(0.424820\pi\) | ||||
−0.233994 | + | 0.972238i | \(0.575180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.84754i | 0.0710067i | 0.999370 | + | 0.0355034i | \(0.0113034\pi\) | ||||
−0.999370 | + | 0.0355034i | \(0.988697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.6920 | 0.410320 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −68.3650 | −2.61975 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.0332i | 1.22572i | 0.790193 | + | 0.612858i | \(0.209980\pi\) | ||||
−0.790193 | + | 0.612858i | \(0.790020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.2355i | 1.22986i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.04348 | 0.306432 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.5585 | 0.972291 | 0.486146 | − | 0.873878i | \(-0.338402\pi\) | ||||
0.486146 | + | 0.873878i | \(0.338402\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 11.0408i | − 0.419407i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 3.79938i | − 0.143912i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −62.3743 | −2.35921 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.5707 | 0.852484 | 0.426242 | − | 0.904609i | \(-0.359837\pi\) | ||||
0.426242 | + | 0.904609i | \(0.359837\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.2178i | 0.800244i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.7224i | 0.516083i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.6916 | −0.514198 | −0.257099 | − | 0.966385i | \(-0.582767\pi\) | ||||
−0.257099 | + | 0.966385i | \(0.582767\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.620494 | 0.0232703 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 8.78924i | − 0.329160i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 44.6563i | − 1.66772i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.5003 | −0.727239 | −0.363619 | − | 0.931548i | \(-0.618459\pi\) | ||||
−0.363619 | + | 0.931548i | \(0.618459\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.314175 | −0.0117005 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 33.0874i | − 1.23053i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.2432i | 1.86342i | 0.363209 | + | 0.931708i | \(0.381681\pi\) | ||||
−0.363209 | + | 0.931708i | \(0.618319\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 31.8264 | 1.17876 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.67440 | −0.246862 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.7355i | 0.765881i | 0.923773 | + | 0.382941i | \(0.125089\pi\) | ||||
−0.923773 | + | 0.382941i | \(0.874911\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 36.1045i | − 1.32993i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.6672 | −1.23847 | −0.619234 | − | 0.785207i | \(-0.712557\pi\) | ||||
−0.619234 | + | 0.785207i | \(0.712557\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.24410 | 0.302854 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.5412i | 1.34056i | 0.742106 | + | 0.670282i | \(0.233827\pi\) | ||||
−0.742106 | + | 0.670282i | \(0.766173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 23.7281i | − 0.868167i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.773648 | −0.0282685 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.3495 | 0.925016 | 0.462508 | − | 0.886615i | \(-0.346950\pi\) | ||||
0.462508 | + | 0.886615i | \(0.346950\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 70.5001i | 2.56917i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 9.14818i | − 0.332496i | −0.986084 | − | 0.166248i | \(-0.946835\pi\) | ||||
0.986084 | − | 0.166248i | \(-0.0531653\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.5654 | −0.383500 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.9609 | 0.759833 | 0.379916 | − | 0.925021i | \(-0.375953\pi\) | ||||
0.379916 | + | 0.925021i | \(0.375953\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8.10781i | − 0.293522i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.80425i | 0.0651477i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.5915 | −1.31953 | −0.659763 | − | 0.751474i | \(-0.729343\pi\) | ||||
−0.659763 | + | 0.751474i | \(0.729343\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.9659 | −1.54738 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.1219i | 1.37115i | 0.728003 | + | 0.685574i | \(0.240449\pi\) | ||||
−0.728003 | + | 0.685574i | \(0.759551\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.1570i | 0.687252i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.79324 | −0.100078 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.3695 | 1.01514 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.82405i | 0.0651861i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.4495i | 0.728946i | 0.931214 | + | 0.364473i | \(0.118751\pi\) | ||||
−0.931214 | + | 0.364473i | \(0.881249\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 56.9217 | 2.02646 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.58199 | −0.198473 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.83487i | 0.136180i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 27.5177i | − 0.974725i | −0.873200 | − | 0.487363i | \(-0.837959\pi\) | ||||
0.873200 | − | 0.487363i | \(-0.162041\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.63386 | 0.305444 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.9661 | 0.740800 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 12.7371i | − 0.449482i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 48.5661i | − 1.70961i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.1917 | −0.569268 | −0.284634 | − | 0.958636i | \(-0.591872\pi\) | ||||
−0.284634 | + | 0.958636i | \(0.591872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.2872 | −0.607036 | −0.303518 | − | 0.952826i | \(-0.598161\pi\) | ||||
−0.303518 | + | 0.952826i | \(0.598161\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 80.3467i | − 2.81788i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.90690i | 0.171671i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.88915 | 0.135898 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.6395 | −1.13913 | −0.569564 | − | 0.821947i | \(-0.692888\pi\) | ||||
−0.569564 | + | 0.821947i | \(0.692888\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 39.7419i | − 1.38532i | −0.721266 | − | 0.692658i | \(-0.756440\pi\) | ||||
0.721266 | − | 0.692658i | \(-0.243560\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 9.46764i | − 0.329222i | −0.986359 | − | 0.164611i | \(-0.947363\pi\) | ||||
0.986359 | − | 0.164611i | \(-0.0526369\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.6920 | −1.51748 | −0.758742 | − | 0.651391i | \(-0.774186\pi\) | ||||
−0.758742 | + | 0.651391i | \(0.774186\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.9440 | −0.553093 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.1731i | 0.664310i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.22822i | 0.215279i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.37212 | 0.0473708 | 0.0236854 | − | 0.999719i | \(-0.492460\pi\) | ||||
0.0236854 | + | 0.999719i | \(0.492460\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3741 | −0.771519 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 36.9564i | 1.27284i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.39989i | 0.185542i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.9606 | 0.753687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.57848 | 0.328346 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.6367i | 0.638107i | 0.947737 | + | 0.319054i | \(0.103365\pi\) | ||||
−0.947737 | + | 0.319054i | \(0.896635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 21.9201i | − 0.748776i | −0.927272 | − | 0.374388i | \(-0.877853\pi\) | ||||
0.927272 | − | 0.374388i | \(-0.122147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.1587 | −1.47256 | −0.736278 | − | 0.676679i | \(-0.763419\pi\) | ||||
−0.736278 | + | 0.676679i | \(0.763419\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.52194 | −0.0859474 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 38.0107i | − 1.29390i | −0.762532 | − | 0.646950i | \(-0.776044\pi\) | ||||
0.762532 | − | 0.646950i | \(-0.223956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 19.8553i | − 0.674322i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.796743 | −0.0270277 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.7179 | 0.430929 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 43.9879i | 1.48877i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 27.9976i | − 0.945411i | −0.881220 | − | 0.472706i | \(-0.843277\pi\) | ||||
0.881220 | − | 0.472706i | \(-0.156723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.5785 | 0.862741 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.84326 | −0.297937 | −0.148968 | − | 0.988842i | \(-0.547595\pi\) | ||||
−0.148968 | + | 0.988842i | \(0.547595\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 19.3282i | − 0.650447i | −0.945637 | − | 0.325224i | \(-0.894560\pi\) | ||||
0.945637 | − | 0.325224i | \(-0.105440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.4857i | 0.754995i | 0.926011 | + | 0.377498i | \(0.123215\pi\) | ||||
−0.926011 | + | 0.377498i | \(0.876785\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.82141 | 0.128166 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.0245 | −1.13986 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 6.34745i | − 0.212409i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 3.72168i | − 0.124263i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.6243 | 0.754563 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.3225 | 0.543781 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.43030i | 0.147431i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 28.5934i | − 0.949429i | −0.880140 | − | 0.474714i | \(-0.842551\pi\) | ||||
0.880140 | − | 0.474714i | \(-0.157449\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −56.4554 | −1.87251 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2774 | −1.40071 | −0.700356 | − | 0.713794i | \(-0.746975\pi\) | ||||
−0.700356 | + | 0.713794i | \(0.746975\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.4680i | 1.00834i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.08168i | − 0.134789i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.3783 | 1.20001 | 0.600004 | − | 0.799997i | \(-0.295166\pi\) | ||||
0.600004 | + | 0.799997i | \(0.295166\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 66.9913 | 2.20744 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.99319i | 0.328930i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 1.29255i | − 0.0424529i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.0567 | −0.362757 | −0.181379 | − | 0.983413i | \(-0.558056\pi\) | ||||
−0.181379 | + | 0.983413i | \(0.558056\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.0957 | 0.461969 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 67.1267i | − 2.19763i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.7081i | 1.46055i | 0.683153 | + | 0.730276i | \(0.260608\pi\) | ||||
−0.683153 | + | 0.730276i | \(0.739392\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.3880 | 1.05694 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.1343 | 0.819356 | 0.409678 | − | 0.912230i | \(-0.365641\pi\) | ||||
0.409678 | + | 0.912230i | \(0.365641\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.26097i | 0.0410628i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.2426i | 1.63266i | 0.577583 | + | 0.816332i | \(0.303996\pi\) | ||||
−0.577583 | + | 0.816332i | \(0.696004\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.48666 | 0.145643 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −35.5218 | −1.15187 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 37.2648i | − 1.20712i | −0.797316 | − | 0.603562i | \(-0.793747\pi\) | ||||
0.797316 | − | 0.603562i | \(-0.206253\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 27.1963i | − 0.879133i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.59583 | 0.309866 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.2508 | 1.49196 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 3.18287i | − 0.102567i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.29267i | 0.202359i | 0.994868 | + | 0.101179i | \(0.0322616\pi\) | ||||
−0.994868 | + | 0.101179i | \(0.967738\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.7296 | 0.537432 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.1451 | 0.357665 | 0.178832 | − | 0.983880i | \(-0.442768\pi\) | ||||
0.178832 | + | 0.983880i | \(0.442768\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9.65805i | − 0.309623i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.1605i | 0.996912i | 0.866915 | + | 0.498456i | \(0.166099\pi\) | ||||
−0.866915 | + | 0.498456i | \(0.833901\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.9214 | −0.860413 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.3564 | 1.06499 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.4322i | 1.09822i | 0.835752 | + | 0.549108i | \(0.185032\pi\) | ||||
−0.835752 | + | 0.549108i | \(0.814968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 5.73094i | − 0.182418i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.21515 | 0.0704377 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.54092 | 0.176013 | 0.0880066 | − | 0.996120i | \(-0.471950\pi\) | ||||
0.0880066 | + | 0.996120i | \(0.471950\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 76.8918i | − 2.44009i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 12.0230i | − 0.380773i | −0.981709 | − | 0.190387i | \(-0.939026\pi\) | ||||
0.981709 | − | 0.190387i | \(-0.0609741\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.78749 | −0.214747 |
(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 | 2300.2.c.j.1749.2 | 8 | ||
5.2 | odd | 4 | 2300.2.a.m.1.1 | yes | 4 | ||
5.3 | odd | 4 | 2300.2.a.l.1.4 | ✓ | 4 | ||
5.4 | even | 2 | inner | 2300.2.c.j.1749.7 | 8 | ||
20.3 | even | 4 | 9200.2.a.co.1.1 | 4 | |||
20.7 | even | 4 | 9200.2.a.cm.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2300.2.a.l.1.4 | ✓ | 4 | 5.3 | odd | 4 | ||
2300.2.a.m.1.1 | yes | 4 | 5.2 | odd | 4 | ||
2300.2.c.j.1749.2 | 8 | 1.1 | even | 1 | trivial | ||
2300.2.c.j.1749.7 | 8 | 5.4 | even | 2 | inner | ||
9200.2.a.cm.1.4 | 4 | 20.7 | even | 4 | |||
9200.2.a.co.1.1 | 4 | 20.3 | even | 4 |