Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(649,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.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: | \(79.6525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
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 | 649.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.649 |
Dual form | 1350.4.c.m.649.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 19.0000i | 1.02590i | 0.858417 | + | 0.512952i | \(0.171448\pi\) | ||||
−0.858417 | + | 0.512952i | \(0.828552\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 50.0000i | 1.06673i | 0.845885 | + | 0.533366i | \(0.179073\pi\) | ||||
−0.845885 | + | 0.533366i | \(0.820927\pi\) | |||||||
\(14\) | 38.0000 | 0.725423 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 126.000i | 1.79762i | 0.438342 | + | 0.898808i | \(0.355566\pi\) | ||||
−0.438342 | + | 0.898808i | \(0.644434\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −29.0000 | −0.350161 | −0.175080 | − | 0.984554i | \(-0.556019\pi\) | ||||
−0.175080 | + | 0.984554i | \(0.556019\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 24.0000i | − 0.232583i | ||||||||
\(23\) | 18.0000i | 0.163185i | 0.996666 | + | 0.0815926i | \(0.0260006\pi\) | ||||
−0.996666 | + | 0.0815926i | \(0.973999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 100.000 | 0.754293 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 76.0000i | − 0.512952i | ||||||||
\(29\) | −102.000 | −0.653135 | −0.326568 | − | 0.945174i | \(-0.605892\pi\) | ||||
−0.326568 | + | 0.945174i | \(0.605892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −265.000 | −1.53534 | −0.767668 | − | 0.640848i | \(-0.778583\pi\) | ||||
−0.767668 | + | 0.640848i | \(0.778583\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 252.000 | 1.27111 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 65.0000i | − 0.288809i | −0.989519 | − | 0.144405i | \(-0.953873\pi\) | ||||
0.989519 | − | 0.144405i | \(-0.0461267\pi\) | |||||||
\(38\) | 58.0000i | 0.247601i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 240.000 | 0.914188 | 0.457094 | − | 0.889418i | \(-0.348890\pi\) | ||||
0.457094 | + | 0.889418i | \(0.348890\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 367.000i | − 1.30156i | −0.759267 | − | 0.650779i | \(-0.774443\pi\) | ||||
0.759267 | − | 0.650779i | \(-0.225557\pi\) | |||||||
\(44\) | −48.0000 | −0.164461 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 36.0000 | 0.115389 | ||||||||
\(47\) | 72.0000i | 0.223453i | 0.993739 | + | 0.111726i | \(0.0356380\pi\) | ||||
−0.993739 | + | 0.111726i | \(0.964362\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18.0000 | −0.0524781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 200.000i | − 0.533366i | ||||||||
\(53\) | − 636.000i | − 1.64833i | −0.566352 | − | 0.824163i | \(-0.691646\pi\) | ||||
0.566352 | − | 0.824163i | \(-0.308354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −152.000 | −0.362712 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 204.000i | 0.461836i | ||||||||
\(59\) | −102.000 | −0.225072 | −0.112536 | − | 0.993648i | \(-0.535897\pi\) | ||||
−0.112536 | + | 0.993648i | \(0.535897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −103.000 | −0.216193 | −0.108097 | − | 0.994140i | \(-0.534476\pi\) | ||||
−0.108097 | + | 0.994140i | \(0.534476\pi\) | |||||||
\(62\) | 530.000i | 1.08565i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 52.0000i | 0.0948181i | 0.998876 | + | 0.0474090i | \(0.0150964\pi\) | ||||
−0.998876 | + | 0.0474090i | \(0.984904\pi\) | |||||||
\(68\) | − 504.000i | − 0.898808i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −582.000 | −0.972827 | −0.486413 | − | 0.873729i | \(-0.661695\pi\) | ||||
−0.486413 | + | 0.873729i | \(0.661695\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 65.0000i | 0.104215i | 0.998641 | + | 0.0521074i | \(0.0165938\pi\) | ||||
−0.998641 | + | 0.0521074i | \(0.983406\pi\) | |||||||
\(74\) | −130.000 | −0.204219 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 116.000 | 0.175080 | ||||||||
\(77\) | 228.000i | 0.337442i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −173.000 | −0.246380 | −0.123190 | − | 0.992383i | \(-0.539312\pi\) | ||||
−0.123190 | + | 0.992383i | \(0.539312\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 480.000i | − 0.646428i | ||||||||
\(83\) | 498.000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −734.000 | −0.920340 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 96.0000i | 0.116291i | ||||||||
\(89\) | 822.000 | 0.979009 | 0.489505 | − | 0.872001i | \(-0.337178\pi\) | ||||
0.489505 | + | 0.872001i | \(0.337178\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −950.000 | −1.09436 | ||||||||
\(92\) | − 72.0000i | − 0.0815926i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 144.000 | 0.158005 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 821.000i | − 0.859381i | −0.902976 | − | 0.429690i | \(-0.858623\pi\) | ||||
0.902976 | − | 0.429690i | \(-0.141377\pi\) | |||||||
\(98\) | 36.0000i | 0.0371076i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1200.00 | −1.18222 | −0.591111 | − | 0.806590i | \(-0.701311\pi\) | ||||
−0.591111 | + | 0.806590i | \(0.701311\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2041.00i | − 1.95248i | −0.216686 | − | 0.976241i | \(-0.569525\pi\) | ||||
0.216686 | − | 0.976241i | \(-0.430475\pi\) | |||||||
\(104\) | −400.000 | −0.377146 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1272.00 | −1.16554 | ||||||||
\(107\) | 1278.00i | 1.15466i | 0.816510 | + | 0.577331i | \(0.195906\pi\) | ||||
−0.816510 | + | 0.577331i | \(0.804094\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 205.000 | 0.180142 | 0.0900708 | − | 0.995935i | \(-0.471291\pi\) | ||||
0.0900708 | + | 0.995935i | \(0.471291\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 304.000i | 0.256476i | ||||||||
\(113\) | − 1500.00i | − 1.24874i | −0.781127 | − | 0.624372i | \(-0.785355\pi\) | ||||
0.781127 | − | 0.624372i | \(-0.214645\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 408.000 | 0.326568 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 204.000i | 0.159150i | ||||||||
\(119\) | −2394.00 | −1.84418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 206.000i | 0.152872i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1060.00 | 0.767668 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 416.000i | − 0.290662i | −0.989383 | − | 0.145331i | \(-0.953575\pi\) | ||||
0.989383 | − | 0.145331i | \(-0.0464247\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1902.00 | −1.26854 | −0.634269 | − | 0.773112i | \(-0.718699\pi\) | ||||
−0.634269 | + | 0.773112i | \(0.718699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 551.000i | − 0.359231i | ||||||||
\(134\) | 104.000 | 0.0670465 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1008.00 | −0.635554 | ||||||||
\(137\) | 2712.00i | 1.69125i | 0.533774 | + | 0.845627i | \(0.320773\pi\) | ||||
−0.533774 | + | 0.845627i | \(0.679227\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 367.000 | 0.223946 | 0.111973 | − | 0.993711i | \(-0.464283\pi\) | ||||
0.111973 | + | 0.993711i | \(0.464283\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1164.00i | 0.687892i | ||||||||
\(143\) | 600.000i | 0.350871i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 130.000 | 0.0736909 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 260.000i | 0.144405i | ||||||||
\(149\) | −3006.00 | −1.65276 | −0.826380 | − | 0.563113i | \(-0.809603\pi\) | ||||
−0.826380 | + | 0.563113i | \(0.809603\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2651.00 | 1.42871 | 0.714355 | − | 0.699783i | \(-0.246720\pi\) | ||||
0.714355 | + | 0.699783i | \(0.246720\pi\) | |||||||
\(152\) | − 232.000i | − 0.123801i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 456.000 | 0.238607 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2801.00i | − 1.42385i | −0.702257 | − | 0.711924i | \(-0.747824\pi\) | ||||
0.702257 | − | 0.711924i | \(-0.252176\pi\) | |||||||
\(158\) | 346.000i | 0.174217i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −342.000 | −0.167412 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1412.00i | 0.678505i | 0.940695 | + | 0.339253i | \(0.110174\pi\) | ||||
−0.940695 | + | 0.339253i | \(0.889826\pi\) | |||||||
\(164\) | −960.000 | −0.457094 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 996.000 | 0.465690 | ||||||||
\(167\) | 2154.00i | 0.998093i | 0.866575 | + | 0.499046i | \(0.166316\pi\) | ||||
−0.866575 | + | 0.499046i | \(0.833684\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −303.000 | −0.137915 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1468.00i | 0.650779i | ||||||||
\(173\) | 234.000i | 0.102836i | 0.998677 | + | 0.0514182i | \(0.0163741\pi\) | ||||
−0.998677 | + | 0.0514182i | \(0.983626\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 192.000 | 0.0822304 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 1644.00i | − 0.692264i | ||||||||
\(179\) | −2472.00 | −1.03221 | −0.516106 | − | 0.856525i | \(-0.672619\pi\) | ||||
−0.516106 | + | 0.856525i | \(0.672619\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −190.000 | −0.0780254 | −0.0390127 | − | 0.999239i | \(-0.512421\pi\) | ||||
−0.0390127 | + | 0.999239i | \(0.512421\pi\) | |||||||
\(182\) | 1900.00i | 0.773832i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −144.000 | −0.0576947 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1512.00i | 0.591275i | ||||||||
\(188\) | − 288.000i | − 0.111726i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1524.00 | 0.577344 | 0.288672 | − | 0.957428i | \(-0.406786\pi\) | ||||
0.288672 | + | 0.957428i | \(0.406786\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3335.00i | 1.24383i | 0.783086 | + | 0.621913i | \(0.213644\pi\) | ||||
−0.783086 | + | 0.621913i | \(0.786356\pi\) | |||||||
\(194\) | −1642.00 | −0.607674 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 72.0000 | 0.0262391 | ||||||||
\(197\) | 4440.00i | 1.60577i | 0.596133 | + | 0.802886i | \(0.296703\pi\) | ||||
−0.596133 | + | 0.802886i | \(0.703297\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2192.00 | −0.780838 | −0.390419 | − | 0.920637i | \(-0.627670\pi\) | ||||
−0.390419 | + | 0.920637i | \(0.627670\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2400.00i | 0.835957i | ||||||||
\(203\) | − 1938.00i | − 0.670054i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4082.00 | −1.38061 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 800.000i | 0.266683i | ||||||||
\(209\) | −348.000 | −0.115175 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1732.00 | −0.565099 | −0.282549 | − | 0.959253i | \(-0.591180\pi\) | ||||
−0.282549 | + | 0.959253i | \(0.591180\pi\) | |||||||
\(212\) | 2544.00i | 0.824163i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2556.00 | 0.816470 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 5035.00i | − 1.57511i | ||||||||
\(218\) | − 410.000i | − 0.127379i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6300.00 | −1.91757 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5989.00i | − 1.79844i | −0.437492 | − | 0.899222i | \(-0.644133\pi\) | ||||
0.437492 | − | 0.899222i | \(-0.355867\pi\) | |||||||
\(224\) | 608.000 | 0.181356 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3000.00 | −0.882996 | ||||||||
\(227\) | 3300.00i | 0.964884i | 0.875928 | + | 0.482442i | \(0.160250\pi\) | ||||
−0.875928 | + | 0.482442i | \(0.839750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4379.00 | −1.26364 | −0.631818 | − | 0.775117i | \(-0.717691\pi\) | ||||
−0.631818 | + | 0.775117i | \(0.717691\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 816.000i | − 0.230918i | ||||||||
\(233\) | 2958.00i | 0.831695i | 0.909434 | + | 0.415848i | \(0.136515\pi\) | ||||
−0.909434 | + | 0.415848i | \(0.863485\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 408.000 | 0.112536 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4788.00i | 1.30403i | ||||||||
\(239\) | 2676.00 | 0.724251 | 0.362126 | − | 0.932129i | \(-0.382051\pi\) | ||||
0.362126 | + | 0.932129i | \(0.382051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3626.00 | 0.969175 | 0.484588 | − | 0.874743i | \(-0.338970\pi\) | ||||
0.484588 | + | 0.874743i | \(0.338970\pi\) | |||||||
\(242\) | 2374.00i | 0.630605i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 412.000 | 0.108097 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1450.00i | − 0.373527i | ||||||||
\(248\) | − 2120.00i | − 0.542823i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2046.00 | −0.514511 | −0.257256 | − | 0.966343i | \(-0.582818\pi\) | ||||
−0.257256 | + | 0.966343i | \(0.582818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 216.000i | 0.0536751i | ||||||||
\(254\) | −832.000 | −0.205529 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − 5700.00i | − 1.38349i | −0.722143 | − | 0.691744i | \(-0.756843\pi\) | ||||
0.722143 | − | 0.691744i | \(-0.243157\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1235.00 | 0.296290 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3804.00i | 0.896992i | ||||||||
\(263\) | − 7674.00i | − 1.79924i | −0.436678 | − | 0.899618i | \(-0.643845\pi\) | ||||
0.436678 | − | 0.899618i | \(-0.356155\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1102.00 | −0.254015 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 208.000i | − 0.0474090i | ||||||||
\(269\) | −4326.00 | −0.980524 | −0.490262 | − | 0.871575i | \(-0.663099\pi\) | ||||
−0.490262 | + | 0.871575i | \(0.663099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6473.00 | 1.45095 | 0.725474 | − | 0.688250i | \(-0.241621\pi\) | ||||
0.725474 | + | 0.688250i | \(0.241621\pi\) | |||||||
\(272\) | 2016.00i | 0.449404i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5424.00 | 1.19590 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7825.00i | 1.69732i | 0.528936 | + | 0.848662i | \(0.322591\pi\) | ||||
−0.528936 | + | 0.848662i | \(0.677409\pi\) | |||||||
\(278\) | − 734.000i | − 0.158354i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2760.00 | 0.585935 | 0.292968 | − | 0.956122i | \(-0.405357\pi\) | ||||
0.292968 | + | 0.956122i | \(0.405357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4801.00i | − 1.00844i | −0.863574 | − | 0.504222i | \(-0.831779\pi\) | ||||
0.863574 | − | 0.504222i | \(-0.168221\pi\) | |||||||
\(284\) | 2328.00 | 0.486413 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1200.00 | 0.248103 | ||||||||
\(287\) | 4560.00i | 0.937869i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10963.0 | −2.23143 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 260.000i | − 0.0521074i | ||||||||
\(293\) | − 8166.00i | − 1.62820i | −0.580724 | − | 0.814100i | \(-0.697231\pi\) | ||||
0.580724 | − | 0.814100i | \(-0.302769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 520.000 | 0.102109 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6012.00i | 1.16868i | ||||||||
\(299\) | −900.000 | −0.174075 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6973.00 | 1.33527 | ||||||||
\(302\) | − 5302.00i | − 1.01025i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −464.000 | −0.0875402 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 577.000i | 0.107268i | 0.998561 | + | 0.0536338i | \(0.0170804\pi\) | ||||
−0.998561 | + | 0.0536338i | \(0.982920\pi\) | |||||||
\(308\) | − 912.000i | − 0.168721i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7656.00 | −1.39592 | −0.697961 | − | 0.716135i | \(-0.745909\pi\) | ||||
−0.697961 | + | 0.716135i | \(0.745909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2726.00i | 0.492277i | 0.969235 | + | 0.246138i | \(0.0791618\pi\) | ||||
−0.969235 | + | 0.246138i | \(0.920838\pi\) | |||||||
\(314\) | −5602.00 | −1.00681 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 692.000 | 0.123190 | ||||||||
\(317\) | 9450.00i | 1.67434i | 0.546945 | + | 0.837169i | \(0.315791\pi\) | ||||
−0.546945 | + | 0.837169i | \(0.684209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1224.00 | −0.214830 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 684.000i | 0.118378i | ||||||||
\(323\) | − 3654.00i | − 0.629455i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2824.00 | 0.479776 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1920.00i | 0.323214i | ||||||||
\(329\) | −1368.00 | −0.229241 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3089.00 | 0.512951 | 0.256476 | − | 0.966551i | \(-0.417439\pi\) | ||||
0.256476 | + | 0.966551i | \(0.417439\pi\) | |||||||
\(332\) | − 1992.00i | − 0.329293i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4308.00 | 0.705758 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7894.00i | 1.27600i | 0.770034 | + | 0.638002i | \(0.220239\pi\) | ||||
−0.770034 | + | 0.638002i | \(0.779761\pi\) | |||||||
\(338\) | 606.000i | 0.0975209i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3180.00 | −0.505005 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6175.00i | 0.972066i | ||||||||
\(344\) | 2936.00 | 0.460170 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 468.000 | 0.0727163 | ||||||||
\(347\) | 3450.00i | 0.533734i | 0.963733 | + | 0.266867i | \(0.0859884\pi\) | ||||
−0.963733 | + | 0.266867i | \(0.914012\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2261.00 | −0.346787 | −0.173393 | − | 0.984853i | \(-0.555473\pi\) | ||||
−0.173393 | + | 0.984853i | \(0.555473\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 384.000i | − 0.0581456i | ||||||||
\(353\) | 11544.0i | 1.74058i | 0.492539 | + | 0.870291i | \(0.336069\pi\) | ||||
−0.492539 | + | 0.870291i | \(0.663931\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3288.00 | −0.489505 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4944.00i | 0.729884i | ||||||||
\(359\) | 198.000 | 0.0291087 | 0.0145544 | − | 0.999894i | \(-0.495367\pi\) | ||||
0.0145544 | + | 0.999894i | \(0.495367\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6018.00 | −0.877387 | ||||||||
\(362\) | 380.000i | 0.0551723i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3800.00 | 0.547182 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 10388.0i | − 1.47752i | −0.673970 | − | 0.738759i | \(-0.735412\pi\) | ||||
0.673970 | − | 0.738759i | \(-0.264588\pi\) | |||||||
\(368\) | 288.000i | 0.0407963i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12084.0 | 1.69102 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4867.00i | − 0.675613i | −0.941216 | − | 0.337807i | \(-0.890315\pi\) | ||||
0.941216 | − | 0.337807i | \(-0.109685\pi\) | |||||||
\(374\) | 3024.00 | 0.418094 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −576.000 | −0.0790025 | ||||||||
\(377\) | − 5100.00i | − 0.696720i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −656.000 | −0.0889089 | −0.0444544 | − | 0.999011i | \(-0.514155\pi\) | ||||
−0.0444544 | + | 0.999011i | \(0.514155\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 3048.00i | − 0.408244i | ||||||||
\(383\) | 3078.00i | 0.410649i | 0.978694 | + | 0.205324i | \(0.0658249\pi\) | ||||
−0.978694 | + | 0.205324i | \(0.934175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6670.00 | 0.879518 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3284.00i | 0.429690i | ||||||||
\(389\) | −1644.00 | −0.214278 | −0.107139 | − | 0.994244i | \(-0.534169\pi\) | ||||
−0.107139 | + | 0.994244i | \(0.534169\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2268.00 | −0.293344 | ||||||||
\(392\) | − 144.000i | − 0.0185538i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8880.00 | 1.13545 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5729.00i | − 0.724258i | −0.932128 | − | 0.362129i | \(-0.882050\pi\) | ||||
0.932128 | − | 0.362129i | \(-0.117950\pi\) | |||||||
\(398\) | 4384.00i | 0.552136i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1776.00 | −0.221170 | −0.110585 | − | 0.993867i | \(-0.535272\pi\) | ||||
−0.110585 | + | 0.993867i | \(0.535272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 13250.0i | − 1.63779i | ||||||||
\(404\) | 4800.00 | 0.591111 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3876.00 | −0.473800 | ||||||||
\(407\) | − 780.000i | − 0.0949955i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12842.0 | −1.55256 | −0.776279 | − | 0.630390i | \(-0.782895\pi\) | ||||
−0.776279 | + | 0.630390i | \(0.782895\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8164.00i | 0.976241i | ||||||||
\(413\) | − 1938.00i | − 0.230903i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1600.00 | 0.188573 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 696.000i | 0.0814413i | ||||||||
\(419\) | 11298.0 | 1.31729 | 0.658644 | − | 0.752455i | \(-0.271130\pi\) | ||||
0.658644 | + | 0.752455i | \(0.271130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3431.00 | 0.397189 | 0.198595 | − | 0.980082i | \(-0.436362\pi\) | ||||
0.198595 | + | 0.980082i | \(0.436362\pi\) | |||||||
\(422\) | 3464.00i | 0.399585i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5088.00 | 0.582772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1957.00i | − 0.221794i | ||||||||
\(428\) | − 5112.00i | − 0.577331i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10530.0 | 1.17683 | 0.588413 | − | 0.808560i | \(-0.299753\pi\) | ||||
0.588413 | + | 0.808560i | \(0.299753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3179.00i | 0.352824i | 0.984316 | + | 0.176412i | \(0.0564492\pi\) | ||||
−0.984316 | + | 0.176412i | \(0.943551\pi\) | |||||||
\(434\) | −10070.0 | −1.11377 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −820.000 | −0.0900708 | ||||||||
\(437\) | − 522.000i | − 0.0571411i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6047.00 | −0.657420 | −0.328710 | − | 0.944431i | \(-0.606614\pi\) | ||||
−0.328710 | + | 0.944431i | \(0.606614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12600.0i | 1.35593i | ||||||||
\(443\) | 16554.0i | 1.77540i | 0.460418 | + | 0.887702i | \(0.347700\pi\) | ||||
−0.460418 | + | 0.887702i | \(0.652300\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11978.0 | −1.27169 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 1216.00i | − 0.128238i | ||||||||
\(449\) | 4446.00 | 0.467304 | 0.233652 | − | 0.972320i | \(-0.424932\pi\) | ||||
0.233652 | + | 0.972320i | \(0.424932\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2880.00 | 0.300696 | ||||||||
\(452\) | 6000.00i | 0.624372i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6600.00 | 0.682276 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 146.000i | − 0.0149444i | −0.999972 | − | 0.00747220i | \(-0.997622\pi\) | ||||
0.999972 | − | 0.00747220i | \(-0.00237850\pi\) | |||||||
\(458\) | 8758.00i | 0.893525i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9822.00 | 0.992313 | 0.496156 | − | 0.868233i | \(-0.334744\pi\) | ||||
0.496156 | + | 0.868233i | \(0.334744\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7931.00i | 0.796080i | 0.917368 | + | 0.398040i | \(0.130309\pi\) | ||||
−0.917368 | + | 0.398040i | \(0.869691\pi\) | |||||||
\(464\) | −1632.00 | −0.163284 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5916.00 | 0.588097 | ||||||||
\(467\) | − 18714.0i | − 1.85435i | −0.374631 | − | 0.927174i | \(-0.622230\pi\) | ||||
0.374631 | − | 0.927174i | \(-0.377770\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −988.000 | −0.0972742 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 816.000i | − 0.0795751i | ||||||||
\(473\) | − 4404.00i | − 0.428110i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9576.00 | 0.922091 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 5352.00i | − 0.512123i | ||||||||
\(479\) | −12786.0 | −1.21964 | −0.609820 | − | 0.792540i | \(-0.708758\pi\) | ||||
−0.609820 | + | 0.792540i | \(0.708758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3250.00 | 0.308082 | ||||||||
\(482\) | − 7252.00i | − 0.685310i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4748.00 | 0.445905 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 10400.0i | − 0.967698i | −0.875151 | − | 0.483849i | \(-0.839238\pi\) | ||||
0.875151 | − | 0.483849i | \(-0.160762\pi\) | |||||||
\(488\) | − 824.000i | − 0.0764359i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19548.0 | −1.79672 | −0.898359 | − | 0.439261i | \(-0.855240\pi\) | ||||
−0.898359 | + | 0.439261i | \(0.855240\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 12852.0i | − 1.17409i | ||||||||
\(494\) | −2900.00 | −0.264124 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4240.00 | −0.383834 | ||||||||
\(497\) | − 11058.0i | − 0.998026i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14939.0 | −1.34020 | −0.670102 | − | 0.742269i | \(-0.733750\pi\) | ||||
−0.670102 | + | 0.742269i | \(0.733750\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4092.00i | 0.363815i | ||||||||
\(503\) | 4098.00i | 0.363262i | 0.983367 | + | 0.181631i | \(0.0581376\pi\) | ||||
−0.983367 | + | 0.181631i | \(0.941862\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 432.000 | 0.0379540 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1664.00i | 0.145331i | ||||||||
\(509\) | 12216.0 | 1.06378 | 0.531891 | − | 0.846813i | \(-0.321482\pi\) | ||||
0.531891 | + | 0.846813i | \(0.321482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1235.00 | −0.106914 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11400.0 | −0.978273 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 864.000i | 0.0734984i | ||||||||
\(518\) | − 2470.00i | − 0.209509i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18492.0 | 1.55499 | 0.777494 | − | 0.628890i | \(-0.216490\pi\) | ||||
0.777494 | + | 0.628890i | \(0.216490\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 5467.00i | − 0.457085i | −0.973534 | − | 0.228542i | \(-0.926604\pi\) | ||||
0.973534 | − | 0.228542i | \(-0.0733959\pi\) | |||||||
\(524\) | 7608.00 | 0.634269 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15348.0 | −1.27225 | ||||||||
\(527\) | − 33390.0i | − 2.75995i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11843.0 | 0.973371 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2204.00i | 0.179616i | ||||||||
\(533\) | 12000.0i | 0.975193i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −416.000 | −0.0335233 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8652.00i | 0.693335i | ||||||||
\(539\) | −216.000 | −0.0172612 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6983.00 | 0.554940 | 0.277470 | − | 0.960734i | \(-0.410504\pi\) | ||||
0.277470 | + | 0.960734i | \(0.410504\pi\) | |||||||
\(542\) | − 12946.0i | − 1.02597i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4032.00 | 0.317777 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 9281.00i | − 0.725461i | −0.931894 | − | 0.362730i | \(-0.881845\pi\) | ||||
0.931894 | − | 0.362730i | \(-0.118155\pi\) | |||||||
\(548\) | − 10848.0i | − 0.845627i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2958.00 | 0.228702 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 3287.00i | − 0.252762i | ||||||||
\(554\) | 15650.0 | 1.20019 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1468.00 | −0.111973 | ||||||||
\(557\) | 1986.00i | 0.151076i | 0.997143 | + | 0.0755382i | \(0.0240675\pi\) | ||||
−0.997143 | + | 0.0755382i | \(0.975933\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18350.0 | 1.38841 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 5520.00i | − 0.414319i | ||||||||
\(563\) | − 12672.0i | − 0.948599i | −0.880364 | − | 0.474299i | \(-0.842701\pi\) | ||||
0.880364 | − | 0.474299i | \(-0.157299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9602.00 | −0.713078 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 4656.00i | − 0.343946i | ||||||||
\(569\) | 8370.00 | 0.616676 | 0.308338 | − | 0.951277i | \(-0.400227\pi\) | ||||
0.308338 | + | 0.951277i | \(0.400227\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19675.0 | −1.44198 | −0.720992 | − | 0.692943i | \(-0.756314\pi\) | ||||
−0.720992 | + | 0.692943i | \(0.756314\pi\) | |||||||
\(572\) | − 2400.00i | − 0.175435i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9120.00 | 0.663173 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 26951.0i | − 1.94451i | −0.233914 | − | 0.972257i | \(-0.575154\pi\) | ||||
0.233914 | − | 0.972257i | \(-0.424846\pi\) | |||||||
\(578\) | 21926.0i | 1.57786i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9462.00 | −0.675645 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 7632.00i | − 0.542170i | ||||||||
\(584\) | −520.000 | −0.0368455 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16332.0 | −1.15131 | ||||||||
\(587\) | 10986.0i | 0.772471i | 0.922400 | + | 0.386236i | \(0.126225\pi\) | ||||
−0.922400 | + | 0.386236i | \(0.873775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7685.00 | 0.537614 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 1040.00i | − 0.0722023i | ||||||||
\(593\) | − 11226.0i | − 0.777397i | −0.921365 | − | 0.388699i | \(-0.872925\pi\) | ||||
0.921365 | − | 0.388699i | \(-0.127075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12024.0 | 0.826380 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1800.00i | 0.123089i | ||||||||
\(599\) | 11400.0 | 0.777615 | 0.388807 | − | 0.921319i | \(-0.372887\pi\) | ||||
0.388807 | + | 0.921319i | \(0.372887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6469.00 | −0.439062 | −0.219531 | − | 0.975606i | \(-0.570453\pi\) | ||||
−0.219531 | + | 0.975606i | \(0.570453\pi\) | |||||||
\(602\) | − 13946.0i | − 0.944180i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10604.0 | −0.714355 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 6383.00i | − 0.426817i | −0.976963 | − | 0.213409i | \(-0.931543\pi\) | ||||
0.976963 | − | 0.213409i | \(-0.0684565\pi\) | |||||||
\(608\) | 928.000i | 0.0619003i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3600.00 | −0.238364 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 10843.0i | − 0.714428i | −0.934022 | − | 0.357214i | \(-0.883727\pi\) | ||||
0.934022 | − | 0.357214i | \(-0.116273\pi\) | |||||||
\(614\) | 1154.00 | 0.0758496 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1824.00 | −0.119304 | ||||||||
\(617\) | − 25236.0i | − 1.64662i | −0.567594 | − | 0.823309i | \(-0.692126\pi\) | ||||
0.567594 | − | 0.823309i | \(-0.307874\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24809.0 | −1.61092 | −0.805459 | − | 0.592652i | \(-0.798081\pi\) | ||||
−0.805459 | + | 0.592652i | \(0.798081\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15312.0i | 0.987066i | ||||||||
\(623\) | 15618.0i | 1.00437i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5452.00 | 0.348092 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11204.0i | 0.711924i | ||||||||
\(629\) | 8190.00 | 0.519168 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11476.0 | −0.724013 | −0.362007 | − | 0.932176i | \(-0.617908\pi\) | ||||
−0.362007 | + | 0.932176i | \(0.617908\pi\) | |||||||
\(632\) | − 1384.00i | − 0.0871085i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18900.0 | 1.18394 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 900.000i | − 0.0559801i | ||||||||
\(638\) | 2448.00i | 0.151908i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25350.0 | 1.56204 | 0.781018 | − | 0.624509i | \(-0.214701\pi\) | ||||
0.781018 | + | 0.624509i | \(0.214701\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 14164.0i | − 0.868699i | −0.900744 | − | 0.434350i | \(-0.856978\pi\) | ||||
0.900744 | − | 0.434350i | \(-0.143022\pi\) | |||||||
\(644\) | 1368.00 | 0.0837061 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7308.00 | −0.445092 | ||||||||
\(647\) | 7536.00i | 0.457915i | 0.973436 | + | 0.228957i | \(0.0735316\pi\) | ||||
−0.973436 | + | 0.228957i | \(0.926468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1224.00 | −0.0740311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 5648.00i | − 0.339253i | ||||||||
\(653\) | − 432.000i | − 0.0258889i | −0.999916 | − | 0.0129445i | \(-0.995880\pi\) | ||||
0.999916 | − | 0.0129445i | \(-0.00412047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3840.00 | 0.228547 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2736.00i | 0.162098i | ||||||||
\(659\) | 10782.0 | 0.637340 | 0.318670 | − | 0.947866i | \(-0.396764\pi\) | ||||
0.318670 | + | 0.947866i | \(0.396764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26057.0 | 1.53328 | 0.766641 | − | 0.642076i | \(-0.221926\pi\) | ||||
0.766641 | + | 0.642076i | \(0.221926\pi\) | |||||||
\(662\) | − 6178.00i | − 0.362711i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3984.00 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1836.00i | − 0.106582i | ||||||||
\(668\) | − 8616.00i | − 0.499046i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1236.00 | −0.0711107 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19091.0i | 1.09347i | 0.837306 | + | 0.546734i | \(0.184129\pi\) | ||||
−0.837306 | + | 0.546734i | \(0.815871\pi\) | |||||||
\(674\) | 15788.0 | 0.902272 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1212.00 | 0.0689577 | ||||||||
\(677\) | − 1044.00i | − 0.0592676i | −0.999561 | − | 0.0296338i | \(-0.990566\pi\) | ||||
0.999561 | − | 0.0296338i | \(-0.00943412\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15599.0 | 0.881642 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6360.00i | 0.357092i | ||||||||
\(683\) | 26046.0i | 1.45918i | 0.683883 | + | 0.729592i | \(0.260290\pi\) | ||||
−0.683883 | + | 0.729592i | \(0.739710\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12350.0 | 0.687355 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 5872.00i | − 0.325389i | ||||||||
\(689\) | 31800.0 | 1.75832 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28060.0 | −1.54479 | −0.772397 | − | 0.635140i | \(-0.780942\pi\) | ||||
−0.772397 | + | 0.635140i | \(0.780942\pi\) | |||||||
\(692\) | − 936.000i | − 0.0514182i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6900.00 | 0.377407 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30240.0i | 1.64336i | ||||||||
\(698\) | 4522.00i | 0.245215i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16794.0 | 0.904851 | 0.452426 | − | 0.891802i | \(-0.350559\pi\) | ||||
0.452426 | + | 0.891802i | \(0.350559\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1885.00i | 0.101130i | ||||||||
\(704\) | −768.000 | −0.0411152 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23088.0 | 1.23078 | ||||||||
\(707\) | − 22800.0i | − 1.21285i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2495.00 | −0.132160 | −0.0660802 | − | 0.997814i | \(-0.521049\pi\) | ||||
−0.0660802 | + | 0.997814i | \(0.521049\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6576.00i | 0.346132i | ||||||||
\(713\) | − 4770.00i | − 0.250544i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9888.00 | 0.516106 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 396.000i | − 0.0205830i | ||||||||
\(719\) | −1950.00 | −0.101144 | −0.0505721 | − | 0.998720i | \(-0.516104\pi\) | ||||
−0.0505721 | + | 0.998720i | \(0.516104\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38779.0 | 2.00306 | ||||||||
\(722\) | 12036.0i | 0.620407i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 760.000 | 0.0390127 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 16127.0i | − 0.822720i | −0.911473 | − | 0.411360i | \(-0.865054\pi\) | ||||
0.911473 | − | 0.411360i | \(-0.134946\pi\) | |||||||
\(728\) | − 7600.00i | − 0.386916i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46242.0 | 2.33970 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 12634.0i | − 0.636627i | −0.947986 | − | 0.318313i | \(-0.896884\pi\) | ||||
0.947986 | − | 0.318313i | \(-0.103116\pi\) | |||||||
\(734\) | −20776.0 | −1.04476 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 576.000 | 0.0288473 | ||||||||
\(737\) | 624.000i | 0.0311877i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10420.0 | 0.518682 | 0.259341 | − | 0.965786i | \(-0.416495\pi\) | ||||
0.259341 | + | 0.965786i | \(0.416495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 24168.0i | − 1.19573i | ||||||||
\(743\) | − 21936.0i | − 1.08311i | −0.840664 | − | 0.541557i | \(-0.817835\pi\) | ||||
0.840664 | − | 0.541557i | \(-0.182165\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9734.00 | −0.477731 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 6048.00i | − 0.295637i | ||||||||
\(749\) | −24282.0 | −1.18457 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21715.0 | −1.05512 | −0.527558 | − | 0.849519i | \(-0.676892\pi\) | ||||
−0.527558 | + | 0.849519i | \(0.676892\pi\) | |||||||
\(752\) | 1152.00i | 0.0558632i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10200.0 | −0.492655 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19849.0i | 0.953004i | 0.879173 | + | 0.476502i | \(0.158096\pi\) | ||||
−0.879173 | + | 0.476502i | \(0.841904\pi\) | |||||||
\(758\) | 1312.00i | 0.0628681i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29952.0 | −1.42675 | −0.713377 | − | 0.700781i | \(-0.752835\pi\) | ||||
−0.713377 | + | 0.700781i | \(0.752835\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3895.00i | 0.184808i | ||||||||
\(764\) | −6096.00 | −0.288672 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6156.00 | 0.290372 | ||||||||
\(767\) | − 5100.00i | − 0.240092i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17582.0 | −0.824477 | −0.412239 | − | 0.911076i | \(-0.635253\pi\) | ||||
−0.412239 | + | 0.911076i | \(0.635253\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 13340.0i | − 0.621913i | ||||||||
\(773\) | 19194.0i | 0.893092i | 0.894761 | + | 0.446546i | \(0.147346\pi\) | ||||
−0.894761 | + | 0.446546i | \(0.852654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6568.00 | 0.303837 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3288.00i | 0.151517i | ||||||||
\(779\) | −6960.00 | −0.320113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6984.00 | −0.319984 | ||||||||
\(782\) | 4536.00i | 0.207426i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −288.000 | −0.0131195 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9823.00i | 0.444920i | 0.974942 | + | 0.222460i | \(0.0714087\pi\) | ||||
−0.974942 | + | 0.222460i | \(0.928591\pi\) | |||||||
\(788\) | − 17760.0i | − 0.802886i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28500.0 | 1.28109 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 5150.00i | − 0.230620i | ||||||||
\(794\) | −11458.0 | −0.512127 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8768.00 | 0.390419 | ||||||||
\(797\) | − 22188.0i | − 0.986122i | −0.869995 | − | 0.493061i | \(-0.835878\pi\) | ||||
0.869995 | − | 0.493061i | \(-0.164122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9072.00 | −0.401682 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3552.00i | 0.156391i | ||||||||
\(803\) | 780.000i | 0.0342785i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26500.0 | −1.15809 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 9600.00i | − 0.417979i | ||||||||
\(809\) | −9654.00 | −0.419551 | −0.209775 | − | 0.977750i | \(-0.567273\pi\) | ||||
−0.209775 | + | 0.977750i | \(0.567273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32377.0 | −1.40186 | −0.700931 | − | 0.713229i | \(-0.747232\pi\) | ||||
−0.700931 | + | 0.713229i | \(0.747232\pi\) | |||||||
\(812\) | 7752.00i | 0.335027i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1560.00 | −0.0671720 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10643.0i | 0.455755i | ||||||||
\(818\) | 25684.0i | 1.09782i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23952.0 | 1.01819 | 0.509093 | − | 0.860712i | \(-0.329981\pi\) | ||||
0.509093 | + | 0.860712i | \(0.329981\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5072.00i | 0.214822i | 0.994215 | + | 0.107411i | \(0.0342561\pi\) | ||||
−0.994215 | + | 0.107411i | \(0.965744\pi\) | |||||||
\(824\) | 16328.0 | 0.690307 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3876.00 | −0.163273 | ||||||||
\(827\) | 3024.00i | 0.127152i | 0.997977 | + | 0.0635760i | \(0.0202505\pi\) | ||||
−0.997977 | + | 0.0635760i | \(0.979749\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3049.00 | 0.127740 | 0.0638698 | − | 0.997958i | \(-0.479656\pi\) | ||||
0.0638698 | + | 0.997958i | \(0.479656\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 3200.00i | − 0.133341i | ||||||||
\(833\) | − 2268.00i | − 0.0943356i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1392.00 | 0.0575877 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 22596.0i | − 0.931463i | ||||||||
\(839\) | 40374.0 | 1.66134 | 0.830671 | − | 0.556764i | \(-0.187957\pi\) | ||||
0.830671 | + | 0.556764i | \(0.187957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13985.0 | −0.573414 | ||||||||
\(842\) | − 6862.00i | − 0.280855i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6928.00 | 0.282549 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 22553.0i | − 0.914912i | ||||||||
\(848\) | − 10176.0i | − 0.412082i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1170.00 | 0.0471294 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40322.0i | 1.61852i | 0.587449 | + | 0.809261i | \(0.300132\pi\) | ||||
−0.587449 | + | 0.809261i | \(0.699868\pi\) | |||||||
\(854\) | −3914.00 | −0.156832 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10224.0 | −0.408235 | ||||||||
\(857\) | 19932.0i | 0.794474i | 0.917716 | + | 0.397237i | \(0.130031\pi\) | ||||
−0.917716 | + | 0.397237i | \(0.869969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34553.0 | −1.37245 | −0.686224 | − | 0.727390i | \(-0.740733\pi\) | ||||
−0.686224 | + | 0.727390i | \(0.740733\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 21060.0i | − 0.832142i | ||||||||
\(863\) | 6918.00i | 0.272875i | 0.990649 | + | 0.136438i | \(0.0435653\pi\) | ||||
−0.990649 | + | 0.136438i | \(0.956435\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6358.00 | 0.249485 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20140.0i | 0.787553i | ||||||||
\(869\) | −2076.00 | −0.0810397 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2600.00 | −0.101145 | ||||||||
\(872\) | 1640.00i | 0.0636897i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1044.00 | −0.0404048 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 6497.00i | − 0.250157i | −0.992147 | − | 0.125079i | \(-0.960082\pi\) | ||||
0.992147 | − | 0.125079i | \(-0.0399183\pi\) | |||||||
\(878\) | 12094.0i | 0.464866i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44082.0 | −1.68577 | −0.842883 | − | 0.538096i | \(-0.819144\pi\) | ||||
−0.842883 | + | 0.538096i | \(0.819144\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10127.0i | 0.385958i | 0.981203 | + | 0.192979i | \(0.0618149\pi\) | ||||
−0.981203 | + | 0.192979i | \(0.938185\pi\) | |||||||
\(884\) | 25200.0 | 0.958787 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33108.0 | 1.25540 | ||||||||
\(887\) | 12936.0i | 0.489682i | 0.969563 | + | 0.244841i | \(0.0787358\pi\) | ||||
−0.969563 | + | 0.244841i | \(0.921264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7904.00 | 0.298191 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23956.0i | 0.899222i | ||||||||
\(893\) | − 2088.00i | − 0.0782444i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2432.00 | −0.0906779 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 8892.00i | − 0.330434i | ||||||||
\(899\) | 27030.0 | 1.00278 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 80136.0 | 2.96306 | ||||||||
\(902\) | − 5760.00i | − 0.212624i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12000.0 | 0.441498 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45853.0i | 1.67864i | 0.543640 | + | 0.839319i | \(0.317046\pi\) | ||||
−0.543640 | + | 0.839319i | \(0.682954\pi\) | |||||||
\(908\) | − 13200.0i | − 0.482442i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34530.0 | −1.25580 | −0.627898 | − | 0.778296i | \(-0.716084\pi\) | ||||
−0.627898 | + | 0.778296i | \(0.716084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5976.00i | 0.216623i | ||||||||
\(914\) | −292.000 | −0.0105673 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17516.0 | 0.631818 | ||||||||
\(917\) | − 36138.0i | − 1.30140i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31015.0 | 1.11326 | 0.556632 | − | 0.830759i | \(-0.312093\pi\) | ||||
0.556632 | + | 0.830759i | \(0.312093\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 19644.0i | − 0.701671i | ||||||||
\(923\) | − 29100.0i | − 1.03774i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15862.0 | 0.562913 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3264.00i | 0.115459i | ||||||||
\(929\) | −36186.0 | −1.27796 | −0.638980 | − | 0.769224i | \(-0.720643\pi\) | ||||
−0.638980 | + | 0.769224i | \(0.720643\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 522.000 | 0.0183758 | ||||||||
\(932\) | − 11832.0i | − 0.415848i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −37428.0 | −1.31122 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1441.00i | 0.0502406i | 0.999684 | + | 0.0251203i | \(0.00799688\pi\) | ||||
−0.999684 | + | 0.0251203i | \(0.992003\pi\) | |||||||
\(938\) | 1976.00i | 0.0687832i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33168.0 | −1.14904 | −0.574520 | − | 0.818491i | \(-0.694811\pi\) | ||||
−0.574520 | + | 0.818491i | \(0.694811\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4320.00i | 0.149182i | ||||||||
\(944\) | −1632.00 | −0.0562681 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8808.00 | −0.302720 | ||||||||
\(947\) | 42054.0i | 1.44305i | 0.692387 | + | 0.721527i | \(0.256559\pi\) | ||||
−0.692387 | + | 0.721527i | \(0.743441\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3250.00 | −0.111169 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 19152.0i | − 0.652017i | ||||||||
\(953\) | 26460.0i | 0.899395i | 0.893181 | + | 0.449698i | \(0.148468\pi\) | ||||
−0.893181 | + | 0.449698i | \(0.851532\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10704.0 | −0.362126 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25572.0i | 0.862415i | ||||||||
\(959\) | −51528.0 | −1.73506 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40434.0 | 1.35726 | ||||||||
\(962\) | − 6500.00i | − 0.217847i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14504.0 | −0.484588 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29239.0i | 0.972350i | 0.873861 | + | 0.486175i | \(0.161608\pi\) | ||||
−0.873861 | + | 0.486175i | \(0.838392\pi\) | |||||||
\(968\) | − 9496.00i | − 0.315303i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54288.0 | −1.79422 | −0.897109 | − | 0.441810i | \(-0.854336\pi\) | ||||
−0.897109 | + | 0.441810i | \(0.854336\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6973.00i | 0.229747i | ||||||||
\(974\) | −20800.0 | −0.684266 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1648.00 | −0.0540484 | ||||||||
\(977\) | 38634.0i | 1.26511i | 0.774516 | + | 0.632554i | \(0.217993\pi\) | ||||
−0.774516 | + | 0.632554i | \(0.782007\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9864.00 | 0.322017 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39096.0i | 1.27047i | ||||||||
\(983\) | − 19548.0i | − 0.634267i | −0.948381 | − | 0.317133i | \(-0.897280\pi\) | ||||
0.948381 | − | 0.317133i | \(-0.102720\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −25704.0 | −0.830205 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5800.00i | 0.186764i | ||||||||
\(989\) | 6606.00 | 0.212395 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28445.0 | 0.911791 | 0.455896 | − | 0.890033i | \(-0.349319\pi\) | ||||
0.455896 | + | 0.890033i | \(0.349319\pi\) | |||||||
\(992\) | 8480.00i | 0.271412i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22116.0 | −0.705711 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48706.0i | 1.54718i | 0.633689 | + | 0.773588i | \(0.281540\pi\) | ||||
−0.633689 | + | 0.773588i | \(0.718460\pi\) | |||||||
\(998\) | 29878.0i | 0.947667i | ||||||||
\(999\) | 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 | 1350.4.c.m.649.1 | 2 | ||
3.2 | odd | 2 | 1350.4.c.h.649.2 | 2 | |||
5.2 | odd | 4 | 1350.4.a.q.1.1 | yes | 1 | ||
5.3 | odd | 4 | 1350.4.a.k.1.1 | yes | 1 | ||
5.4 | even | 2 | inner | 1350.4.c.m.649.2 | 2 | ||
15.2 | even | 4 | 1350.4.a.c.1.1 | ✓ | 1 | ||
15.8 | even | 4 | 1350.4.a.y.1.1 | yes | 1 | ||
15.14 | odd | 2 | 1350.4.c.h.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.4.a.c.1.1 | ✓ | 1 | 15.2 | even | 4 | ||
1350.4.a.k.1.1 | yes | 1 | 5.3 | odd | 4 | ||
1350.4.a.q.1.1 | yes | 1 | 5.2 | odd | 4 | ||
1350.4.a.y.1.1 | yes | 1 | 15.8 | even | 4 | ||
1350.4.c.h.649.1 | 2 | 15.14 | odd | 2 | |||
1350.4.c.h.649.2 | 2 | 3.2 | odd | 2 | |||
1350.4.c.m.649.1 | 2 | 1.1 | even | 1 | trivial | ||
1350.4.c.m.649.2 | 2 | 5.4 | even | 2 | inner |