Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(127,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("2304.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.b (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: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.127 |
Dual form | 2304.3.b.o.127.4 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | − 8.92820i | − 1.78564i | −0.450413 | − | 0.892820i | \(-0.648723\pi\) | ||||
0.450413 | − | 0.892820i | \(-0.351277\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 10.9282i | − 1.56117i | −0.625048 | − | 0.780586i | \(-0.714921\pi\) | ||||
0.625048 | − | 0.780586i | \(-0.285079\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.07180 | 0.0974361 | 0.0487180 | − | 0.998813i | \(-0.484486\pi\) | ||||
0.0487180 | + | 0.998813i | \(0.484486\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.85641i | − 0.296647i | −0.988939 | − | 0.148323i | \(-0.952612\pi\) | ||||
0.988939 | − | 0.148323i | \(-0.0473876\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.85641 | −0.462142 | −0.231071 | − | 0.972937i | \(-0.574223\pi\) | ||||
−0.231071 | + | 0.972937i | \(0.574223\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.0718 | −0.898516 | −0.449258 | − | 0.893402i | \(-0.648312\pi\) | ||||
−0.449258 | + | 0.893402i | \(0.648312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.00000i | 0.347826i | 0.984761 | + | 0.173913i | \(0.0556412\pi\) | ||||
−0.984761 | + | 0.173913i | \(0.944359\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −54.7128 | −2.18851 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.07180i | 0.105924i | 0.998597 | + | 0.0529620i | \(0.0168662\pi\) | ||||
−0.998597 | + | 0.0529620i | \(0.983134\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 30.6410i | − 0.988420i | −0.869343 | − | 0.494210i | \(-0.835457\pi\) | ||||
0.869343 | − | 0.494210i | \(-0.164543\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −97.5692 | −2.78769 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 45.7128i | − 1.23548i | −0.786382 | − | 0.617741i | \(-0.788048\pi\) | ||||
0.786382 | − | 0.617741i | \(-0.211952\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −35.8564 | −0.874546 | −0.437273 | − | 0.899329i | \(-0.644056\pi\) | ||||
−0.437273 | + | 0.899329i | \(0.644056\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 74.6410 | 1.73584 | 0.867919 | − | 0.496706i | \(-0.165457\pi\) | ||||
0.867919 | + | 0.496706i | \(0.165457\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 42.1436i | − 0.896672i | −0.893865 | − | 0.448336i | \(-0.852017\pi\) | ||||
0.893865 | − | 0.448336i | \(-0.147983\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −70.4256 | −1.43726 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.9282i | 0.243928i | 0.992535 | + | 0.121964i | \(0.0389193\pi\) | ||||
−0.992535 | + | 0.121964i | \(0.961081\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 9.56922i | − 0.173986i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −44.2102 | −0.749326 | −0.374663 | − | 0.927161i | \(-0.622242\pi\) | ||||
−0.374663 | + | 0.927161i | \(0.622242\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 14.0000i | − 0.229508i | −0.993394 | − | 0.114754i | \(-0.963392\pi\) | ||||
0.993394 | − | 0.114754i | \(-0.0366080\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −34.4308 | −0.529704 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 80.4974 | 1.20145 | 0.600727 | − | 0.799454i | \(-0.294878\pi\) | ||||
0.600727 | + | 0.799454i | \(0.294878\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 123.138i | 1.73434i | 0.498009 | + | 0.867172i | \(0.334065\pi\) | ||||
−0.498009 | + | 0.867172i | \(0.665935\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 85.4256 | 1.17021 | 0.585107 | − | 0.810956i | \(-0.301052\pi\) | ||||
0.585107 | + | 0.810956i | \(0.301052\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 11.7128i | − 0.152114i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 55.2154i | − 0.698929i | −0.936950 | − | 0.349464i | \(-0.886364\pi\) | ||||
0.936950 | − | 0.349464i | \(-0.113636\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 49.0718 | 0.591226 | 0.295613 | − | 0.955308i | \(-0.404476\pi\) | ||||
0.295613 | + | 0.955308i | \(0.404476\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 70.1436i | 0.825219i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −105.713 | −1.18778 | −0.593892 | − | 0.804545i | \(-0.702409\pi\) | ||||
−0.593892 | + | 0.804545i | \(0.702409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −42.1436 | −0.463116 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 152.420i | 1.60443i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 21.1384 | 0.217922 | 0.108961 | − | 0.994046i | \(-0.465248\pi\) | ||||
0.108961 | + | 0.994046i | \(0.465248\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 172.928i | 1.71216i | 0.516843 | + | 0.856080i | \(0.327107\pi\) | ||||
−0.516843 | + | 0.856080i | \(0.672893\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 16.7846i | − 0.162957i | −0.996675 | − | 0.0814787i | \(-0.974036\pi\) | ||||
0.996675 | − | 0.0814787i | \(-0.0259643\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 138.067 | 1.29034 | 0.645171 | − | 0.764038i | \(-0.276786\pi\) | ||||
0.645171 | + | 0.764038i | \(0.276786\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.85641i | 0.0720771i | 0.999350 | + | 0.0360386i | \(0.0114739\pi\) | ||||
−0.999350 | + | 0.0360386i | \(0.988526\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −165.138 | −1.46140 | −0.730701 | − | 0.682698i | \(-0.760807\pi\) | ||||
−0.730701 | + | 0.682698i | \(0.760807\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 71.4256 | 0.621092 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 85.8564i | 0.721482i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119.851 | −0.990506 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 265.282i | 2.12226i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 147.349i | − 1.16023i | −0.814536 | − | 0.580113i | \(-0.803008\pi\) | ||||
0.814536 | − | 0.580113i | \(-0.196992\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 70.9282 | 0.541437 | 0.270718 | − | 0.962659i | \(-0.412739\pi\) | ||||
0.270718 | + | 0.962659i | \(0.412739\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 186.564i | 1.40274i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 206.133 | 1.50462 | 0.752311 | − | 0.658808i | \(-0.228939\pi\) | ||||
0.752311 | + | 0.658808i | \(0.228939\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 39.9230 | 0.287216 | 0.143608 | − | 0.989635i | \(-0.454130\pi\) | ||||
0.143608 | + | 0.989635i | \(0.454130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 4.13328i | − 0.0289041i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27.4256 | 0.189142 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 0.353829i | − 0.00237469i | −0.999999 | − | 0.00118735i | \(-0.999622\pi\) | ||||
0.999999 | − | 0.00118735i | \(-0.000377944\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 104.210i | 0.690134i | 0.938578 | + | 0.345067i | \(0.112144\pi\) | ||||
−0.938578 | + | 0.345067i | \(0.887856\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −273.569 | −1.76496 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 221.713i | 1.41218i | 0.708120 | + | 0.706092i | \(0.249543\pi\) | ||||
−0.708120 | + | 0.706092i | \(0.750457\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 87.4256 | 0.543016 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −175.923 | −1.07928 | −0.539641 | − | 0.841895i | \(-0.681440\pi\) | ||||
−0.539641 | + | 0.841895i | \(0.681440\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 237.856i | − 1.42429i | −0.702032 | − | 0.712145i | \(-0.747724\pi\) | ||||
0.702032 | − | 0.712145i | \(-0.252276\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 154.128 | 0.912001 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 71.7795i | 0.414910i | 0.978245 | + | 0.207455i | \(0.0665181\pi\) | ||||
−0.978245 | + | 0.207455i | \(0.933482\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 597.913i | 3.41664i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.93336 | −0.0331473 | −0.0165736 | − | 0.999863i | \(-0.505276\pi\) | ||||
−0.0165736 | + | 0.999863i | \(0.505276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 150.995i | 0.834226i | 0.908855 | + | 0.417113i | \(0.136958\pi\) | ||||
−0.908855 | + | 0.417113i | \(0.863042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −408.133 | −2.20613 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.42047 | −0.0450293 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.4256i | 0.122647i | 0.998118 | + | 0.0613236i | \(0.0195322\pi\) | ||||
−0.998118 | + | 0.0613236i | \(0.980468\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 137.426 | 0.712050 | 0.356025 | − | 0.934476i | \(-0.384132\pi\) | ||||
0.356025 | + | 0.934476i | \(0.384132\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 39.4923i | 0.200468i | 0.994964 | + | 0.100234i | \(0.0319592\pi\) | ||||
−0.994964 | + | 0.100234i | \(0.968041\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 275.923i | − 1.38655i | −0.720674 | − | 0.693274i | \(-0.756168\pi\) | ||||
0.720674 | − | 0.693274i | \(-0.243832\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 33.5692 | 0.165366 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 320.133i | 1.56163i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.2975 | −0.0875478 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 189.359 | 0.897436 | 0.448718 | − | 0.893673i | \(-0.351881\pi\) | ||||
0.448718 | + | 0.893673i | \(0.351881\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 666.410i | − 3.09958i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −334.851 | −1.54309 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.2975i | 0.137093i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 144.210i | − 0.646683i | −0.946282 | − | 0.323341i | \(-0.895194\pi\) | ||||
0.946282 | − | 0.323341i | \(-0.104806\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 225.072 | 0.991506 | 0.495753 | − | 0.868464i | \(-0.334892\pi\) | ||||
0.495753 | + | 0.868464i | \(0.334892\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 233.846i | − 1.02116i | −0.859830 | − | 0.510581i | \(-0.829430\pi\) | ||||
0.859830 | − | 0.510581i | \(-0.170570\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −218.862 | −0.939320 | −0.469660 | − | 0.882847i | \(-0.655623\pi\) | ||||
−0.469660 | + | 0.882847i | \(0.655623\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −376.267 | −1.60113 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 371.979i | − 1.55640i | −0.628017 | − | 0.778200i | \(-0.716133\pi\) | ||||
0.628017 | − | 0.778200i | \(-0.283867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −328.564 | −1.36334 | −0.681668 | − | 0.731661i | \(-0.738745\pi\) | ||||
−0.681668 | + | 0.731661i | \(0.738745\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 628.774i | 2.56643i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 65.8358i | 0.266542i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 148.210 | 0.590479 | 0.295240 | − | 0.955423i | \(-0.404601\pi\) | ||||
0.295240 | + | 0.955423i | \(0.404601\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.57437i | 0.0338908i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −351.703 | −1.36849 | −0.684246 | − | 0.729251i | \(-0.739869\pi\) | ||||
−0.684246 | + | 0.729251i | \(0.739869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −499.559 | −1.92880 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 242.144i | 0.920698i | 0.887738 | + | 0.460349i | \(0.152276\pi\) | ||||
−0.887738 | + | 0.460349i | \(0.847724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 115.426 | 0.435568 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 75.6462i | 0.281213i | 0.990066 | + | 0.140606i | \(0.0449052\pi\) | ||||
−0.990066 | + | 0.140606i | \(0.955095\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 150.795i | − 0.556439i | −0.960518 | − | 0.278219i | \(-0.910256\pi\) | ||||
0.960518 | − | 0.278219i | \(-0.0897442\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −58.6410 | −0.213240 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 213.559i | − 0.770971i | −0.922714 | − | 0.385485i | \(-0.874034\pi\) | ||||
0.922714 | − | 0.385485i | \(-0.125966\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 194.000 | 0.690391 | 0.345196 | − | 0.938531i | \(-0.387813\pi\) | ||||
0.345196 | + | 0.938531i | \(0.387813\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −179.790 | −0.635300 | −0.317650 | − | 0.948208i | \(-0.602894\pi\) | ||||
−0.317650 | + | 0.948208i | \(0.602894\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 391.846i | 1.36532i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −227.277 | −0.786425 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 517.902i | − 1.76759i | −0.467879 | − | 0.883793i | \(-0.654982\pi\) | ||||
0.467879 | − | 0.883793i | \(-0.345018\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 394.718i | 1.33803i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.8513 | 0.103181 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 815.692i | − 2.70994i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −124.995 | −0.409819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −407.769 | −1.32824 | −0.664119 | − | 0.747627i | \(-0.731193\pi\) | ||||
−0.664119 | + | 0.747627i | \(0.731193\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 368.995i | 1.18648i | 0.805026 | + | 0.593239i | \(0.202151\pi\) | ||||
−0.805026 | + | 0.593239i | \(0.797849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −341.979 | −1.09259 | −0.546293 | − | 0.837594i | \(-0.683961\pi\) | ||||
−0.546293 | + | 0.837594i | \(0.683961\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 396.487i | 1.25075i | 0.780325 | + | 0.625374i | \(0.215054\pi\) | ||||
−0.780325 | + | 0.625374i | \(0.784946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.29234i | 0.0103208i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 134.123 | 0.415241 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 210.995i | 0.649215i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −460.554 | −1.39986 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 267.061 | 0.806832 | 0.403416 | − | 0.915017i | \(-0.367823\pi\) | ||||
0.403416 | + | 0.915017i | \(0.367823\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 718.697i | − 2.14537i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −149.426 | −0.443399 | −0.221700 | − | 0.975115i | \(-0.571160\pi\) | ||||
−0.221700 | + | 0.975115i | \(0.571160\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 32.8409i | − 0.0963077i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 234.144i | 0.682634i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 529.913 | 1.52713 | 0.763563 | − | 0.645733i | \(-0.223448\pi\) | ||||
0.763563 | + | 0.645733i | \(0.223448\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 75.7025i | − 0.216913i | −0.994101 | − | 0.108456i | \(-0.965409\pi\) | ||||
0.994101 | − | 0.108456i | \(-0.0345908\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −325.138 | −0.921072 | −0.460536 | − | 0.887641i | \(-0.652343\pi\) | ||||
−0.460536 | + | 0.887641i | \(0.652343\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1099.41 | 3.09692 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 195.713i | 0.545161i | 0.962133 | + | 0.272581i | \(0.0878771\pi\) | ||||
−0.962133 | + | 0.272581i | \(0.912123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −69.5538 | −0.192670 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 762.697i | − 2.08958i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 257.051i | 0.700412i | 0.936673 | + | 0.350206i | \(0.113888\pi\) | ||||
−0.936673 | + | 0.350206i | \(0.886112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 141.282 | 0.380814 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 339.128i | 0.909191i | 0.890698 | + | 0.454595i | \(0.150216\pi\) | ||||
−0.890698 | + | 0.454595i | \(0.849784\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.8461 | 0.0314220 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 163.215 | 0.430647 | 0.215324 | − | 0.976543i | \(-0.430919\pi\) | ||||
0.215324 | + | 0.976543i | \(0.430919\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 76.5538i | 0.199879i | 0.994994 | + | 0.0999396i | \(0.0318650\pi\) | ||||
−0.994994 | + | 0.0999396i | \(0.968135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −104.574 | −0.271622 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 338.477i | 0.870120i | 0.900401 | + | 0.435060i | \(0.143273\pi\) | ||||
−0.900401 | + | 0.435060i | \(0.856727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 62.8513i | − 0.160745i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −492.974 | −1.24804 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 7.72312i | − 0.0194537i | −0.999953 | − | 0.00972685i | \(-0.996904\pi\) | ||||
0.999953 | − | 0.00972685i | \(-0.00309620\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −448.123 | −1.11751 | −0.558757 | − | 0.829332i | \(-0.688721\pi\) | ||||
−0.558757 | + | 0.829332i | \(0.688721\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −118.164 | −0.293211 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 48.9948i | − 0.120380i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 317.692 | 0.776754 | 0.388377 | − | 0.921501i | \(-0.373036\pi\) | ||||
0.388377 | + | 0.921501i | \(0.373036\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 483.138i | 1.16983i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 438.123i | − 1.05572i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −660.056 | −1.57531 | −0.787657 | − | 0.616114i | \(-0.788706\pi\) | ||||
−0.787657 | + | 0.616114i | \(0.788706\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 42.4411i | 0.100810i | 0.998729 | + | 0.0504051i | \(0.0160512\pi\) | ||||
−0.998729 | + | 0.0504051i | \(0.983949\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 429.846 | 1.01140 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −152.995 | −0.358302 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 302.123i | 0.700981i | 0.936566 | + | 0.350491i | \(0.113985\pi\) | ||||
−0.936566 | + | 0.350491i | \(0.886015\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 376.277 | 0.869000 | 0.434500 | − | 0.900672i | \(-0.356925\pi\) | ||||
0.434500 | + | 0.900672i | \(0.356925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 136.574i | − 0.312527i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 394.928i | 0.899609i | 0.893127 | + | 0.449804i | \(0.148506\pi\) | ||||
−0.893127 | + | 0.449804i | \(0.851494\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 666.487 | 1.50449 | 0.752243 | − | 0.658886i | \(-0.228972\pi\) | ||||
0.752243 | + | 0.658886i | \(0.228972\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 943.825i | 2.12096i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 793.825 | 1.76799 | 0.883993 | − | 0.467501i | \(-0.154845\pi\) | ||||
0.883993 | + | 0.467501i | \(0.154845\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.4308 | −0.0852124 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 376.267i | 0.826959i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −693.138 | −1.51671 | −0.758357 | − | 0.651839i | \(-0.773998\pi\) | ||||
−0.758357 | + | 0.651839i | \(0.773998\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 99.0924i | − 0.214951i | −0.994208 | − | 0.107476i | \(-0.965723\pi\) | ||||
0.994208 | − | 0.107476i | \(-0.0342767\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 308.077i | 0.665393i | 0.943034 | + | 0.332696i | \(0.107958\pi\) | ||||
−0.943034 | + | 0.332696i | \(0.892042\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −295.195 | −0.632109 | −0.316054 | − | 0.948741i | \(-0.602358\pi\) | ||||
−0.316054 | + | 0.948741i | \(0.602358\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 879.692i | − 1.87568i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 80.0000 | 0.169133 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 934.046 | 1.96641 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 291.559i | 0.608682i | 0.952563 | + | 0.304341i | \(0.0984363\pi\) | ||||
−0.952563 | + | 0.304341i | \(0.901564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −176.287 | −0.366501 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 188.728i | − 0.389130i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 729.779i | − 1.49852i | −0.662276 | − | 0.749260i | \(-0.730409\pi\) | ||||
0.662276 | − | 0.749260i | \(-0.269591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −258.487 | −0.526450 | −0.263225 | − | 0.964734i | \(-0.584786\pi\) | ||||
−0.263225 | + | 0.964734i | \(0.584786\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 24.1333i | − 0.0489519i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1345.68 | 2.70761 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −495.195 | −0.992374 | −0.496187 | − | 0.868216i | \(-0.665267\pi\) | ||||
−0.496187 | + | 0.868216i | \(0.665267\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 698.831i | 1.38933i | 0.719336 | + | 0.694663i | \(0.244446\pi\) | ||||
−0.719336 | + | 0.694663i | \(0.755554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1543.94 | 3.05730 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 21.1948i | − 0.0416400i | −0.999783 | − | 0.0208200i | \(-0.993372\pi\) | ||||
0.999783 | − | 0.0208200i | \(-0.00662769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 933.549i | − 1.82691i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −149.856 | −0.290983 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 45.1694i | − 0.0873682i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 167.015 | 0.320567 | 0.160284 | − | 0.987071i | \(-0.448759\pi\) | ||||
0.160284 | + | 0.987071i | \(0.448759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 450.908 | 0.862156 | 0.431078 | − | 0.902315i | \(-0.358133\pi\) | ||||
0.431078 | + | 0.902315i | \(0.358133\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 240.728i | 0.456790i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 465.000 | 0.879017 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 138.277i | 0.259431i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1232.69i | − 2.30409i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −75.4820 | −0.140041 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 79.5692i | − 0.147078i | −0.997292 | − | 0.0735390i | \(-0.976571\pi\) | ||||
0.997292 | − | 0.0735390i | \(-0.0234293\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 70.1436 | 0.128704 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −349.933 | −0.639732 | −0.319866 | − | 0.947463i | \(-0.603638\pi\) | ||||
−0.319866 | + | 0.947463i | \(0.603638\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 52.4411i | − 0.0951744i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −603.405 | −1.09115 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 874.210i | − 1.56950i | −0.619814 | − | 0.784749i | \(-0.712792\pi\) | ||||
0.619814 | − | 0.784749i | \(-0.287208\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 287.846i | − 0.514930i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 104.497 | 0.185608 | 0.0928041 | − | 0.995684i | \(-0.470417\pi\) | ||||
0.0928041 | + | 0.995684i | \(0.470417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1474.39i | 2.60954i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 136.697 | 0.240241 | 0.120121 | − | 0.992759i | \(-0.461672\pi\) | ||||
0.120121 | + | 0.992759i | \(0.461672\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −566.928 | −0.992869 | −0.496435 | − | 0.868074i | \(-0.665358\pi\) | ||||
−0.496435 | + | 0.868074i | \(0.665358\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 437.703i | − 0.761222i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 778.574 | 1.34935 | 0.674675 | − | 0.738115i | \(-0.264284\pi\) | ||||
0.674675 | + | 0.738115i | \(0.264284\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 536.267i | − 0.923006i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.8564i | 0.0237674i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1053.89 | −1.79539 | −0.897693 | − | 0.440621i | \(-0.854758\pi\) | ||||
−0.897693 | + | 0.440621i | \(0.854758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 523.097i | 0.888111i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −544.543 | −0.918286 | −0.459143 | − | 0.888362i | \(-0.651843\pi\) | ||||
−0.459143 | + | 0.888362i | \(0.651843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 766.543 | 1.28831 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 948.246i | − 1.58305i | −0.611138 | − | 0.791524i | \(-0.709288\pi\) | ||||
0.611138 | − | 0.791524i | \(-0.290712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 542.000 | 0.901830 | 0.450915 | − | 0.892567i | \(-0.351098\pi\) | ||||
0.450915 | + | 0.892567i | \(0.351098\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1070.06i | 1.76869i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1096.06i | 1.80569i | 0.429962 | + | 0.902847i | \(0.358527\pi\) | ||||
−0.429962 | + | 0.902847i | \(0.641473\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −162.523 | −0.265995 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 738.000i | − 1.20392i | −0.798528 | − | 0.601958i | \(-0.794388\pi\) | ||||
0.798528 | − | 0.601958i | \(-0.205612\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −385.979 | −0.625574 | −0.312787 | − | 0.949823i | \(-0.601263\pi\) | ||||
−0.312787 | + | 0.949823i | \(0.601263\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −558.887 | −0.902887 | −0.451443 | − | 0.892300i | \(-0.649091\pi\) | ||||
−0.451443 | + | 0.892300i | \(0.649091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1155.25i | 1.85434i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1000.67 | 1.60107 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 359.138i | 0.570967i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 420.231i | 0.665976i | 0.942931 | + | 0.332988i | \(0.108057\pi\) | ||||
−0.942931 | + | 0.332988i | \(0.891943\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1315.56 | −2.07175 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 271.590i | 0.426358i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −256.964 | −0.400880 | −0.200440 | − | 0.979706i | \(-0.564237\pi\) | ||||
−0.200440 | + | 0.979706i | \(0.564237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 467.215 | 0.726618 | 0.363309 | − | 0.931669i | \(-0.381647\pi\) | ||||
0.363309 | + | 0.931669i | \(0.381647\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 971.138i | − 1.50099i | −0.660878 | − | 0.750493i | \(-0.729816\pi\) | ||||
0.660878 | − | 0.750493i | \(-0.270184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.3844 | −0.0730114 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 439.380i | − 0.672863i | −0.941708 | − | 0.336432i | \(-0.890780\pi\) | ||||
0.941708 | − | 0.336432i | \(-0.109220\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 633.261i | − 0.966811i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1092.48 | −1.65778 | −0.828890 | − | 0.559412i | \(-0.811027\pi\) | ||||
−0.828890 | + | 0.559412i | \(0.811027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 122.267i | − 0.184972i | −0.995714 | − | 0.0924861i | \(-0.970519\pi\) | ||||
0.995714 | − | 0.0924861i | \(-0.0294814\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1665.68 | 2.50478 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.5744 | −0.0368431 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 15.0052i | − 0.0223624i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −796.851 | −1.18403 | −0.592014 | − | 0.805927i | \(-0.701667\pi\) | ||||
−0.592014 | + | 0.805927i | \(0.701667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1185.19i | − 1.75066i | −0.483529 | − | 0.875328i | \(-0.660645\pi\) | ||||
0.483529 | − | 0.875328i | \(-0.339355\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 231.005i | − 0.340214i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 850.446 | 1.24516 | 0.622581 | − | 0.782555i | \(-0.286084\pi\) | ||||
0.622581 | + | 0.782555i | \(0.286084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1840.40i | − 2.68672i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 49.8564 | 0.0723605 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1161.49 | 1.68089 | 0.840443 | − | 0.541900i | \(-0.182295\pi\) | ||||
0.840443 | + | 0.541900i | \(0.182295\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 356.441i | − 0.512865i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 281.703 | 0.404164 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 177.215i | − 0.252804i | −0.991979 | − | 0.126402i | \(-0.959657\pi\) | ||||
0.991979 | − | 0.126402i | \(-0.0403429\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 780.400i | 1.11010i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1889.79 | 2.67298 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 329.846i | − 0.465227i | −0.972569 | − | 0.232614i | \(-0.925272\pi\) | ||||
0.972569 | − | 0.232614i | \(-0.0747277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 245.128 | 0.343798 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.9028 | −0.0516123 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1343.27i | − 1.86825i | −0.356946 | − | 0.934125i | \(-0.616182\pi\) | ||||
0.356946 | − | 0.934125i | \(-0.383818\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −183.426 | −0.254404 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 168.067i | − 0.231816i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 6.64102i | − 0.00913482i | −0.999990 | − | 0.00456741i | \(-0.998546\pi\) | ||||
0.999990 | − | 0.00456741i | \(-0.00145386\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −586.410 | −0.802203 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1396.39i | − 1.90503i | −0.304486 | − | 0.952517i | \(-0.598485\pi\) | ||||
0.304486 | − | 0.952517i | \(-0.401515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 86.2769 | 0.117065 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −276.939 | −0.374748 | −0.187374 | − | 0.982289i | \(-0.559998\pi\) | ||||
−0.187374 | + | 0.982289i | \(0.559998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 424.728i | 0.571640i | 0.958283 | + | 0.285820i | \(0.0922659\pi\) | ||||
−0.958283 | + | 0.285820i | \(0.907734\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.15906 | −0.00424035 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1508.82i | − 2.01445i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1008.32i | − 1.34264i | −0.741167 | − | 0.671320i | \(-0.765728\pi\) | ||||
0.741167 | − | 0.671320i | \(-0.234272\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 930.410 | 1.23233 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.70766i | 0.00357683i | 0.999998 | + | 0.00178841i | \(0.000569270\pi\) | ||||
−0.999998 | + | 0.00178841i | \(0.999431\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 656.431 | 0.862590 | 0.431295 | − | 0.902211i | \(-0.358057\pi\) | ||||
0.431295 | + | 0.902211i | \(0.358057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 85.8564 | 0.112525 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 170.493i | 0.222285i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −533.959 | −0.694355 | −0.347177 | − | 0.937799i | \(-0.612860\pi\) | ||||
−0.347177 | + | 0.937799i | \(0.612860\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 350.918i | 0.453969i | 0.973898 | + | 0.226984i | \(0.0728866\pi\) | ||||
−0.973898 | + | 0.226984i | \(0.927113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1676.46i | 2.16317i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 612.133 | 0.785794 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 131.979i | 0.168988i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1979.50 | 2.52165 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −391.041 | −0.496875 | −0.248438 | − | 0.968648i | \(-0.579917\pi\) | ||||
−0.248438 | + | 0.968648i | \(0.579917\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1804.67i | 2.28150i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53.9897 | −0.0680828 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 138.210i | − 0.173413i | −0.996234 | − | 0.0867065i | \(-0.972366\pi\) | ||||
0.996234 | − | 0.0867065i | \(-0.0276343\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 331.097i | 0.414389i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 91.5589 | 0.114021 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 780.554i | − 0.969632i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −919.528 | −1.13662 | −0.568311 | − | 0.822814i | \(-0.692403\pi\) | ||||
−0.568311 | + | 0.822814i | \(0.692403\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −181.359 | −0.223624 | −0.111812 | − | 0.993729i | \(-0.535665\pi\) | ||||
−0.111812 | + | 0.993729i | \(0.535665\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1570.68i | 1.92721i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1274.26 | −1.55968 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 839.359i | − 1.02236i | −0.859473 | − | 0.511181i | \(-0.829208\pi\) | ||||
0.859473 | − | 0.511181i | \(-0.170792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.1999i | 0.0318347i | 0.999873 | + | 0.0159173i | \(0.00506686\pi\) | ||||
−0.999873 | + | 0.0159173i | \(0.994933\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.38991 | −0.00893581 | −0.00446790 | − | 0.999990i | \(-0.501422\pi\) | ||||
−0.00446790 | + | 0.999990i | \(0.501422\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 340.410i | 0.410627i | 0.978696 | + | 0.205314i | \(0.0658215\pi\) | ||||
−0.978696 | + | 0.205314i | \(0.934179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 553.292 | 0.664216 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2123.63 | −2.54327 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 734.810i | − 0.875816i | −0.899020 | − | 0.437908i | \(-0.855719\pi\) | ||||
0.899020 | − | 0.437908i | \(-0.144281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 831.564 | 0.988780 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1376.09i | − 1.62851i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1309.76i | 1.54635i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 365.703 | 0.429733 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 778.800i | − 0.913013i | −0.889720 | − | 0.456506i | \(-0.849101\pi\) | ||||
0.889720 | − | 0.456506i | \(-0.150899\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1129.52 | −1.31799 | −0.658995 | − | 0.752147i | \(-0.729018\pi\) | ||||
−0.658995 | + | 0.752147i | \(0.729018\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1373.85 | −1.59936 | −0.799680 | − | 0.600426i | \(-0.794998\pi\) | ||||
−0.799680 | + | 0.600426i | \(0.794998\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 539.405i | − 0.625035i | −0.949912 | − | 0.312517i | \(-0.898828\pi\) | ||||
0.949912 | − | 0.312517i | \(-0.101172\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 640.862 | 0.740880 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 59.1797i | − 0.0681009i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 310.431i | − 0.356407i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2899.06 | 3.31321 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 668.236i | − 0.761956i | −0.924584 | − | 0.380978i | \(-0.875587\pi\) | ||||
0.924584 | − | 0.380978i | \(-0.124413\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1170.53 | −1.32864 | −0.664321 | − | 0.747448i | \(-0.731279\pi\) | ||||
−0.664321 | + | 0.747448i | \(0.731279\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.9179 | 0.0372796 | 0.0186398 | − | 0.999826i | \(-0.494066\pi\) | ||||
0.0186398 | + | 0.999826i | \(0.494066\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 655.846i | − 0.739398i | −0.929152 | − | 0.369699i | \(-0.879461\pi\) | ||||
0.929152 | − | 0.369699i | \(-0.120539\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1610.26 | −1.81131 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 719.467i | 0.805674i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.9742i | 0.0591891i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 94.1230 | 0.104697 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 101.569i | − 0.112729i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1348.11 | 1.48963 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 378.949 | 0.417805 | 0.208902 | − | 0.977937i | \(-0.433011\pi\) | ||||
0.208902 | + | 0.977937i | \(0.433011\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 571.938i | 0.627814i | 0.949454 | + | 0.313907i | \(0.101638\pi\) | ||||
−0.949454 | + | 0.313907i | \(0.898362\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.5950 | 0.0576068 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 775.118i | − 0.845276i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 97.8207i | − 0.106443i | −0.998583 | − | 0.0532213i | \(-0.983051\pi\) | ||||
0.998583 | − | 0.0532213i | \(-0.0169489\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 474.872 | 0.514487 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2501.08i | 2.70387i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1228.06 | −1.32192 | −0.660959 | − | 0.750422i | \(-0.729850\pi\) | ||||
−0.660959 | + | 0.750422i | \(0.729850\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1202.29 | 1.29140 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 75.1797i | 0.0804061i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −494.554 | −0.527806 | −0.263903 | − | 0.964549i | \(-0.585010\pi\) | ||||
−0.263903 | + | 0.964549i | \(0.585010\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1154.48i | − 1.22686i | −0.789748 | − | 0.613431i | \(-0.789789\pi\) | ||||
0.789748 | − | 0.613431i | \(-0.210211\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 286.851i | − 0.304190i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1085.43 | 1.14618 | 0.573089 | − | 0.819493i | \(-0.305745\pi\) | ||||
0.573089 | + | 0.819493i | \(0.305745\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 329.436i | − 0.347140i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.8667 | 0.0565233 | 0.0282617 | − | 0.999601i | \(-0.491003\pi\) | ||||
0.0282617 | + | 0.999601i | \(0.491003\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 209.149 | 0.219004 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2252.67i | − 2.34897i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.1281 | 0.0230261 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1226.96i | − 1.27147i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 172.918i | 0.178819i | 0.995995 | + | 0.0894095i | \(0.0284980\pi\) | ||||
−0.995995 | + | 0.0894095i | \(0.971502\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −984.877 | −1.01429 | −0.507146 | − | 0.861860i | \(-0.669299\pi\) | ||||
−0.507146 | + | 0.861860i | \(0.669299\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 436.287i | − 0.448394i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 675.856 | 0.691767 | 0.345884 | − | 0.938277i | \(-0.387579\pi\) | ||||
0.345884 | + | 0.938277i | \(0.387579\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −113.303 | −0.115733 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 564.441i | − 0.574203i | −0.957900 | − | 0.287101i | \(-0.907308\pi\) | ||||
0.957900 | − | 0.287101i | \(-0.0926916\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 352.595 | 0.357964 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 597.128i | 0.603770i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1392.44i | 1.40508i | 0.711644 | + | 0.702541i | \(0.247951\pi\) | ||||
−0.711644 | + | 0.702541i | \(0.752049\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2463.50 | −2.47588 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 123.723i | − 0.124095i | −0.998073 | − | 0.0620477i | \(-0.980237\pi\) | ||||
0.998073 | − | 0.0620477i | \(-0.0197631\pi\) | |||||||
\(998\) | 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 | 2304.3.b.o.127.1 | 4 | ||
3.2 | odd | 2 | 768.3.b.a.127.2 | 4 | |||
4.3 | odd | 2 | 2304.3.b.k.127.1 | 4 | |||
8.3 | odd | 2 | inner | 2304.3.b.o.127.4 | 4 | ||
8.5 | even | 2 | 2304.3.b.k.127.4 | 4 | |||
12.11 | even | 2 | 768.3.b.d.127.4 | 4 | |||
16.3 | odd | 4 | 576.3.g.j.127.1 | 4 | |||
16.5 | even | 4 | 288.3.g.d.127.4 | 4 | |||
16.11 | odd | 4 | 288.3.g.d.127.3 | 4 | |||
16.13 | even | 4 | 576.3.g.j.127.2 | 4 | |||
24.5 | odd | 2 | 768.3.b.d.127.3 | 4 | |||
24.11 | even | 2 | 768.3.b.a.127.1 | 4 | |||
48.5 | odd | 4 | 96.3.g.a.31.3 | yes | 4 | ||
48.11 | even | 4 | 96.3.g.a.31.1 | ✓ | 4 | ||
48.29 | odd | 4 | 192.3.g.c.127.2 | 4 | |||
48.35 | even | 4 | 192.3.g.c.127.4 | 4 | |||
240.53 | even | 4 | 2400.3.j.b.799.1 | 4 | |||
240.59 | even | 4 | 2400.3.e.a.1951.4 | 4 | |||
240.107 | odd | 4 | 2400.3.j.b.799.2 | 4 | |||
240.149 | odd | 4 | 2400.3.e.a.1951.1 | 4 | |||
240.197 | even | 4 | 2400.3.j.a.799.3 | 4 | |||
240.203 | odd | 4 | 2400.3.j.a.799.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.3.g.a.31.1 | ✓ | 4 | 48.11 | even | 4 | ||
96.3.g.a.31.3 | yes | 4 | 48.5 | odd | 4 | ||
192.3.g.c.127.2 | 4 | 48.29 | odd | 4 | |||
192.3.g.c.127.4 | 4 | 48.35 | even | 4 | |||
288.3.g.d.127.3 | 4 | 16.11 | odd | 4 | |||
288.3.g.d.127.4 | 4 | 16.5 | even | 4 | |||
576.3.g.j.127.1 | 4 | 16.3 | odd | 4 | |||
576.3.g.j.127.2 | 4 | 16.13 | even | 4 | |||
768.3.b.a.127.1 | 4 | 24.11 | even | 2 | |||
768.3.b.a.127.2 | 4 | 3.2 | odd | 2 | |||
768.3.b.d.127.3 | 4 | 24.5 | odd | 2 | |||
768.3.b.d.127.4 | 4 | 12.11 | even | 2 | |||
2304.3.b.k.127.1 | 4 | 4.3 | odd | 2 | |||
2304.3.b.k.127.4 | 4 | 8.5 | even | 2 | |||
2304.3.b.o.127.1 | 4 | 1.1 | even | 1 | trivial | ||
2304.3.b.o.127.4 | 4 | 8.3 | odd | 2 | inner | ||
2400.3.e.a.1951.1 | 4 | 240.149 | odd | 4 | |||
2400.3.e.a.1951.4 | 4 | 240.59 | even | 4 | |||
2400.3.j.a.799.3 | 4 | 240.197 | even | 4 | |||
2400.3.j.a.799.4 | 4 | 240.203 | odd | 4 | |||
2400.3.j.b.799.1 | 4 | 240.53 | even | 4 | |||
2400.3.j.b.799.2 | 4 | 240.107 | odd | 4 |