Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(687,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, 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("1568.687");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.g (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: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.292213762624.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 687.3 | ||
Root | \(-1.05468 - 1.69931i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.687 |
Dual form | 1568.3.g.m.687.4 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −3.44128 | −1.14709 | −0.573546 | − | 0.819173i | \(-0.694433\pi\) | ||||
−0.573546 | + | 0.819173i | \(0.694433\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 4.88287i | − 0.976573i | −0.872683 | − | 0.488287i | \(-0.837622\pi\) | ||||
0.872683 | − | 0.488287i | \(-0.162378\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.84239 | 0.315821 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21.4776 | 1.95251 | 0.976253 | − | 0.216632i | \(-0.0695071\pi\) | ||||
0.976253 | + | 0.216632i | \(0.0695071\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 13.0760i | − 1.00585i | −0.864331 | − | 0.502924i | \(-0.832258\pi\) | ||||
0.864331 | − | 0.502924i | \(-0.167742\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 16.8033i | 1.12022i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.234889 | 0.0138170 | 0.00690851 | − | 0.999976i | \(-0.497801\pi\) | ||||
0.00690851 | + | 0.999976i | \(0.497801\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.55872 | 0.239933 | 0.119966 | − | 0.992778i | \(-0.461721\pi\) | ||||
0.119966 | + | 0.992778i | \(0.461721\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10.9523i | 0.476187i | 0.971242 | + | 0.238094i | \(0.0765225\pi\) | ||||
−0.971242 | + | 0.238094i | \(0.923478\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.15761 | 0.0463043 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 21.1900 | 0.784816 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 34.6435i | − 1.19460i | −0.802016 | − | 0.597302i | \(-0.796239\pi\) | ||||
0.802016 | − | 0.597302i | \(-0.203761\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.1079i | 1.10025i | 0.835081 | + | 0.550127i | \(0.185421\pi\) | ||||
−0.835081 | + | 0.550127i | \(0.814579\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −73.9103 | −2.23971 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 54.2370i | 1.46586i | 0.680302 | + | 0.732932i | \(0.261849\pi\) | ||||
−0.680302 | + | 0.732932i | \(0.738151\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 44.9982i | 1.15380i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 37.8300 | 0.922682 | 0.461341 | − | 0.887223i | \(-0.347368\pi\) | ||||
0.461341 | + | 0.887223i | \(0.347368\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.84714 | 0.112724 | 0.0563621 | − | 0.998410i | \(-0.482050\pi\) | ||||
0.0563621 | + | 0.998410i | \(0.482050\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 13.8790i | − 0.308423i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 72.3368i | 1.53908i | 0.638598 | + | 0.769541i | \(0.279515\pi\) | ||||
−0.638598 | + | 0.769541i | \(0.720485\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.808319 | −0.0158494 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 21.6707i | − 0.408881i | −0.978879 | − | 0.204440i | \(-0.934463\pi\) | ||||
0.978879 | − | 0.204440i | \(-0.0655374\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 104.872i | − 1.90677i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.6878 | −0.275225 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 34.9007 | 0.591537 | 0.295768 | − | 0.955260i | \(-0.404424\pi\) | ||||
0.295768 | + | 0.955260i | \(0.404424\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 63.6012i | 1.04264i | 0.853360 | + | 0.521321i | \(0.174561\pi\) | ||||
−0.853360 | + | 0.521321i | \(0.825439\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −63.8485 | −0.982284 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −18.4344 | −0.275140 | −0.137570 | − | 0.990492i | \(-0.543929\pi\) | ||||
−0.137570 | + | 0.990492i | \(0.543929\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 37.6899i | − 0.546231i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 47.5244i | − 0.669358i | −0.942332 | − | 0.334679i | \(-0.891372\pi\) | ||||
0.942332 | − | 0.334679i | \(-0.108628\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −55.9103 | −0.765894 | −0.382947 | − | 0.923770i | \(-0.625091\pi\) | ||||
−0.382947 | + | 0.923770i | \(0.625091\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.98365 | −0.0531153 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 95.0135i | − 1.20270i | −0.798985 | − | 0.601351i | \(-0.794629\pi\) | ||||
0.798985 | − | 0.601351i | \(-0.205371\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −98.5023 | −1.21608 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 71.5156 | 0.861634 | 0.430817 | − | 0.902439i | \(-0.358225\pi\) | ||||
0.430817 | + | 0.902439i | \(0.358225\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 1.14693i | − 0.0134933i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 119.218i | 1.37032i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 159.756 | 1.79501 | 0.897504 | − | 0.441006i | \(-0.145378\pi\) | ||||
0.897504 | + | 0.441006i | \(0.145378\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 117.375i | − 1.26209i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 22.2596i | − 0.234312i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 90.4794 | 0.932777 | 0.466389 | − | 0.884580i | \(-0.345555\pi\) | ||||
0.466389 | + | 0.884580i | \(0.345555\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 61.0477 | 0.616643 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 181.147i | − 1.79353i | −0.442503 | − | 0.896767i | \(-0.645909\pi\) | ||||
0.442503 | − | 0.896767i | \(-0.354091\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 39.3003i | − 0.381556i | −0.981633 | − | 0.190778i | \(-0.938899\pi\) | ||||
0.981633 | − | 0.190778i | \(-0.0611010\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −38.4498 | −0.359344 | −0.179672 | − | 0.983727i | \(-0.557504\pi\) | ||||
−0.179672 | + | 0.983727i | \(0.557504\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 27.8786i | − 0.255767i | −0.991789 | − | 0.127883i | \(-0.959182\pi\) | ||||
0.991789 | − | 0.127883i | \(-0.0408183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 186.644i | − 1.68148i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 82.4419 | 0.729574 | 0.364787 | − | 0.931091i | \(-0.381142\pi\) | ||||
0.364787 | + | 0.931091i | \(0.381142\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 53.4786 | 0.465032 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 37.1672i | − 0.317668i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 340.286 | 2.81228 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −130.183 | −1.05840 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 127.724i | − 1.02179i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 25.1408i | 0.197959i | 0.995089 | + | 0.0989796i | \(0.0315579\pi\) | ||||
−0.995089 | + | 0.0989796i | \(0.968442\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.6804 | −0.129305 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −126.398 | −0.964872 | −0.482436 | − | 0.875931i | \(-0.660248\pi\) | ||||
−0.482436 | + | 0.875931i | \(0.660248\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 103.468i | − 0.766431i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 34.9456 | 0.255078 | 0.127539 | − | 0.991834i | \(-0.459292\pi\) | ||||
0.127539 | + | 0.991834i | \(0.459292\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −119.148 | −0.857177 | −0.428589 | − | 0.903500i | \(-0.640989\pi\) | ||||
−0.428589 | + | 0.903500i | \(0.640989\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 248.931i | − 1.76547i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 280.841i | − 1.96392i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −169.160 | −1.16662 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 121.932i | − 0.818334i | −0.912460 | − | 0.409167i | \(-0.865819\pi\) | ||||
0.912460 | − | 0.409167i | \(-0.134181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 220.404i | 1.45963i | 0.683645 | + | 0.729815i | \(0.260394\pi\) | ||||
−0.683645 | + | 0.729815i | \(0.739606\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.667647 | 0.00436371 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 166.544 | 1.07448 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.77014i | 0.0431219i | 0.999768 | + | 0.0215610i | \(0.00686360\pi\) | ||||
−0.999768 | + | 0.0215610i | \(0.993136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 74.5748i | 0.469024i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 207.243 | 1.27143 | 0.635715 | − | 0.771924i | \(-0.280706\pi\) | ||||
0.635715 | + | 0.771924i | \(0.280706\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 360.894i | 2.18724i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 165.529i | 0.991193i | 0.868553 | + | 0.495596i | \(0.165050\pi\) | ||||
−0.868553 | + | 0.495596i | \(0.834950\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.98237 | −0.0117300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.9577 | 0.0757759 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 88.8530i | 0.513601i | 0.966464 | + | 0.256800i | \(0.0826683\pi\) | ||||
−0.966464 | + | 0.256800i | \(0.917332\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −120.103 | −0.678548 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −80.3791 | −0.449045 | −0.224523 | − | 0.974469i | \(-0.572082\pi\) | ||||
−0.224523 | + | 0.974469i | \(0.572082\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 276.353i | − 1.52681i | −0.645919 | − | 0.763406i | \(-0.723526\pi\) | ||||
0.645919 | − | 0.763406i | \(-0.276474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 218.869i | − 1.19601i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 264.832 | 1.43152 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.04485 | 0.0269778 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 203.015i | − 1.06290i | −0.847088 | − | 0.531452i | \(-0.821647\pi\) | ||||
0.847088 | − | 0.531452i | \(-0.178353\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 87.3328 | 0.452502 | 0.226251 | − | 0.974069i | \(-0.427353\pi\) | ||||
0.226251 | + | 0.974069i | \(0.427353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 219.720 | 1.12677 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.6639i | 0.109969i | 0.998487 | + | 0.0549845i | \(0.0175109\pi\) | ||||
−0.998487 | + | 0.0549845i | \(0.982489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 181.933i | − 0.914235i | −0.889406 | − | 0.457118i | \(-0.848882\pi\) | ||||
0.889406 | − | 0.457118i | \(-0.151118\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 63.4378 | 0.315611 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 184.719i | − 0.901067i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 31.1307i | 0.150390i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 97.9103 | 0.468470 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.4204 | 0.101519 | 0.0507594 | − | 0.998711i | \(-0.483836\pi\) | ||||
0.0507594 | + | 0.998711i | \(0.483836\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 163.545i | 0.767815i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 23.6680i | − 0.110084i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 192.403 | 0.878552 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3.07142i | − 0.0138978i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 195.958i | − 0.878735i | −0.898307 | − | 0.439367i | \(-0.855203\pi\) | ||||
0.898307 | − | 0.439367i | \(-0.144797\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.29038 | 0.0146239 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.2652 | −0.120111 | −0.0600554 | − | 0.998195i | \(-0.519128\pi\) | ||||
−0.0600554 | + | 0.998195i | \(0.519128\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 176.347i | − 0.770076i | −0.922901 | − | 0.385038i | \(-0.874188\pi\) | ||||
0.922901 | − | 0.385038i | \(-0.125812\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 71.8366 | 0.308312 | 0.154156 | − | 0.988047i | \(-0.450734\pi\) | ||||
0.154156 | + | 0.988047i | \(0.450734\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 353.211 | 1.50303 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 326.968i | 1.37961i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 71.0926i | − 0.297459i | −0.988878 | − | 0.148729i | \(-0.952482\pi\) | ||||
0.988878 | − | 0.148729i | \(-0.0475183\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −56.1113 | −0.232827 | −0.116413 | − | 0.993201i | \(-0.537140\pi\) | ||||
−0.116413 | + | 0.993201i | \(0.537140\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 148.264 | 0.610138 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 59.6100i | − 0.241336i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −246.105 | −0.988374 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 368.953 | 1.46993 | 0.734966 | − | 0.678104i | \(-0.237198\pi\) | ||||
0.734966 | + | 0.678104i | \(0.237198\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 235.229i | 0.929759i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.94691i | 0.0154781i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.7428 | −0.0923845 | −0.0461923 | − | 0.998933i | \(-0.514709\pi\) | ||||
−0.0461923 | + | 0.998933i | \(0.514709\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 98.4705i | − 0.377282i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 73.9707i | − 0.281257i | −0.990062 | − | 0.140629i | \(-0.955088\pi\) | ||||
0.990062 | − | 0.140629i | \(-0.0449124\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −105.815 | −0.399302 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −549.764 | −2.05904 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 335.593i | 1.24756i | 0.781601 | + | 0.623779i | \(0.214403\pi\) | ||||
−0.781601 | + | 0.623779i | \(0.785597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 187.276i | − 0.691054i | −0.938409 | − | 0.345527i | \(-0.887700\pi\) | ||||
0.938409 | − | 0.345527i | \(-0.112300\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.8626 | 0.0904095 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 132.592i | − 0.478670i | −0.970937 | − | 0.239335i | \(-0.923071\pi\) | ||||
0.970937 | − | 0.239335i | \(-0.0769294\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 96.9480i | 0.347484i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 331.520 | 1.17979 | 0.589894 | − | 0.807481i | \(-0.299170\pi\) | ||||
0.589894 | + | 0.807481i | \(0.299170\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −66.7158 | −0.235745 | −0.117873 | − | 0.993029i | \(-0.537607\pi\) | ||||
−0.117873 | + | 0.993029i | \(0.537607\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 76.6016i | 0.268778i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.945 | −0.999809 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −311.365 | −1.06998 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 289.215i | − 0.987082i | −0.869723 | − | 0.493541i | \(-0.835702\pi\) | ||||
0.869723 | − | 0.493541i | \(-0.164298\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 170.415i | − 0.577679i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 455.111 | 1.53236 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 143.213 | 0.478972 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 623.377i | 2.05735i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 310.556 | 1.01822 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.693177 | 0.00225790 | 0.00112895 | − | 0.999999i | \(-0.499641\pi\) | ||||
0.00112895 | + | 0.999999i | \(0.499641\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 135.243i | 0.437680i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 62.1583i | 0.199866i | 0.994994 | + | 0.0999330i | \(0.0318628\pi\) | ||||
−0.994994 | + | 0.0999330i | \(0.968137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −213.594 | −0.682408 | −0.341204 | − | 0.939989i | \(-0.610835\pi\) | ||||
−0.341204 | + | 0.939989i | \(0.610835\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.4577i | 0.0739990i | 0.999315 | + | 0.0369995i | \(0.0117800\pi\) | ||||
−0.999315 | + | 0.0369995i | \(0.988220\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 744.059i | − 2.33247i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 132.317 | 0.412201 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.07079 | 0.00331515 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 15.1369i | − 0.0465751i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 95.9380i | 0.293388i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −507.406 | −1.53295 | −0.766474 | − | 0.642275i | \(-0.777991\pi\) | ||||
−0.766474 | + | 0.642275i | \(0.777991\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 154.163i | 0.462951i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 90.0126i | 0.268694i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −342.726 | −1.01699 | −0.508495 | − | 0.861065i | \(-0.669798\pi\) | ||||
−0.508495 | + | 0.861065i | \(0.669798\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −283.705 | −0.836889 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 732.555i | 2.14825i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −184.035 | −0.533434 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −136.745 | −0.394079 | −0.197039 | − | 0.980396i | \(-0.563133\pi\) | ||||
−0.197039 | + | 0.980396i | \(0.563133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 82.0565i | − 0.235119i | −0.993066 | − | 0.117559i | \(-0.962493\pi\) | ||||
0.993066 | − | 0.117559i | \(-0.0375071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 277.081i | − 0.789406i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −507.367 | −1.43730 | −0.718651 | − | 0.695371i | \(-0.755240\pi\) | ||||
−0.718651 | + | 0.695371i | \(0.755240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −232.055 | −0.653677 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 560.809i | 1.56214i | 0.624442 | + | 0.781071i | \(0.285326\pi\) | ||||
−0.624442 | + | 0.781071i | \(0.714674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −340.218 | −0.942432 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1171.02 | −3.22595 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 273.003i | 0.747952i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 26.9431i | − 0.0734145i | −0.999326 | − | 0.0367072i | \(-0.988313\pi\) | ||||
0.999326 | − | 0.0367072i | \(-0.0116869\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 107.528 | 0.291403 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 538.034i | 1.44245i | 0.692701 | + | 0.721225i | \(0.256421\pi\) | ||||
−0.692701 | + | 0.721225i | \(0.743579\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 439.534i | 1.17209i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −453.000 | −1.20159 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 182.132 | 0.480560 | 0.240280 | − | 0.970704i | \(-0.422761\pi\) | ||||
0.240280 | + | 0.970704i | \(0.422761\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 86.5166i | − 0.227078i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 333.271i | 0.870160i | 0.900392 | + | 0.435080i | \(0.143280\pi\) | ||||
−0.900392 | + | 0.435080i | \(0.856720\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.7775 | 0.0356007 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 109.639i | − 0.281847i | −0.990020 | − | 0.140924i | \(-0.954993\pi\) | ||||
0.990020 | − | 0.140924i | \(-0.0450072\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.57258i | 0.00657948i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 434.971 | 1.10680 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −463.938 | −1.17453 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 310.938i | − 0.783219i | −0.920131 | − | 0.391610i | \(-0.871918\pi\) | ||||
0.920131 | − | 0.391610i | \(-0.128082\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −423.903 | −1.05711 | −0.528557 | − | 0.848898i | \(-0.677267\pi\) | ||||
−0.528557 | + | 0.848898i | \(0.677267\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 445.995 | 1.10669 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 480.974i | 1.18759i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1164.88i | 2.86211i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −444.543 | −1.08690 | −0.543451 | − | 0.839441i | \(-0.682883\pi\) | ||||
−0.543451 | + | 0.839441i | \(0.682883\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −120.258 | −0.292598 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 349.201i | − 0.841449i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 410.020 | 0.983261 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 457.129 | 1.09100 | 0.545500 | − | 0.838111i | \(-0.316340\pi\) | ||||
0.545500 | + | 0.838111i | \(0.316340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 25.4812i | − 0.0605255i | −0.999542 | − | 0.0302628i | \(-0.990366\pi\) | ||||
0.999542 | − | 0.0302628i | \(-0.00963441\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 205.610i | 0.486075i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.271910 | 0.000639787 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 966.453i | 2.25280i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 124.595i | − 0.289084i | −0.989499 | − | 0.144542i | \(-0.953829\pi\) | ||||
0.989499 | − | 0.144542i | \(-0.0461709\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 272.271 | 0.628802 | 0.314401 | − | 0.949290i | \(-0.398196\pi\) | ||||
0.314401 | + | 0.949290i | \(0.398196\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 582.126 | 1.33822 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 49.9285i | 0.114253i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 255.069i | − 0.581023i | −0.956871 | − | 0.290512i | \(-0.906174\pi\) | ||||
0.956871 | − | 0.290512i | \(-0.0938255\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −131.274 | −0.296330 | −0.148165 | − | 0.988963i | \(-0.547337\pi\) | ||||
−0.148165 | + | 0.988963i | \(0.547337\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 780.066i | − 1.75296i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 419.601i | 0.938704i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −642.824 | −1.43168 | −0.715839 | − | 0.698265i | \(-0.753956\pi\) | ||||
−0.715839 | + | 0.698265i | \(0.753956\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 812.496 | 1.80154 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 758.472i | − 1.67433i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 693.088 | 1.51660 | 0.758302 | − | 0.651903i | \(-0.226029\pi\) | ||||
0.758302 | + | 0.651903i | \(0.226029\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.97731 | 0.0108438 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 258.699i | − 0.561170i | −0.959829 | − | 0.280585i | \(-0.909472\pi\) | ||||
0.959829 | − | 0.280585i | \(-0.0905285\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 637.226i | 1.37630i | 0.725569 | + | 0.688150i | \(0.241577\pi\) | ||||
−0.725569 | + | 0.688150i | \(0.758423\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −573.125 | −1.23253 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −199.483 | −0.427159 | −0.213580 | − | 0.976926i | \(-0.568512\pi\) | ||||
−0.213580 | + | 0.976926i | \(0.568512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 23.2979i | − 0.0494648i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 104.105 | 0.220095 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.27721 | 0.0111099 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 61.5966i | − 0.129133i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 674.160i | 1.40743i | 0.710481 | + | 0.703716i | \(0.248477\pi\) | ||||
−0.710481 | + | 0.703716i | \(0.751523\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 709.204 | 1.47444 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 441.799i | − 0.910926i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 401.718i | − 0.824883i | −0.910984 | − | 0.412442i | \(-0.864676\pi\) | ||||
0.910984 | − | 0.412442i | \(-0.135324\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −713.181 | −1.45845 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −428.880 | −0.873482 | −0.436741 | − | 0.899587i | \(-0.643867\pi\) | ||||
−0.436741 | + | 0.899587i | \(0.643867\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8.13739i | − 0.0165059i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 298.088i | − 0.602198i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −182.619 | −0.365970 | −0.182985 | − | 0.983116i | \(-0.558576\pi\) | ||||
−0.182985 | + | 0.983116i | \(0.558576\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 569.632i | − 1.13699i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 380.158i | 0.755781i | 0.925850 | + | 0.377891i | \(0.123350\pi\) | ||||
−0.925850 | + | 0.377891i | \(0.876650\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −884.516 | −1.75152 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.82188 | 0.0134554 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 289.538i | − 0.568836i | −0.958700 | − | 0.284418i | \(-0.908200\pi\) | ||||
0.958700 | − | 0.284418i | \(-0.0918004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 96.5995 | 0.188303 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −191.898 | −0.372617 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1553.62i | 3.00507i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 305.768i | − 0.589148i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 738.899 | 1.41823 | 0.709116 | − | 0.705092i | \(-0.249094\pi\) | ||||
0.709116 | + | 0.705092i | \(0.249094\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 647.126 | 1.23734 | 0.618668 | − | 0.785653i | \(-0.287673\pi\) | ||||
0.618668 | + | 0.785653i | \(0.287673\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.01157i | 0.0152022i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 409.047 | 0.773246 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 99.2014 | 0.186820 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 494.666i | − 0.928078i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 187.745i | 0.350926i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 276.607 | 0.515097 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 178.722i | − 0.330355i | −0.986264 | − | 0.165178i | \(-0.947180\pi\) | ||||
0.986264 | − | 0.165178i | \(-0.0528198\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 951.008i | 1.75140i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −136.127 | −0.249775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −452.236 | −0.826758 | −0.413379 | − | 0.910559i | \(-0.635651\pi\) | ||||
−0.413379 | + | 0.910559i | \(0.635651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 180.780i | 0.329289i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 157.930i | − 0.286625i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −911.360 | −1.64209 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 854.108i | 1.53341i | 0.642001 | + | 0.766704i | \(0.278105\pi\) | ||||
−0.642001 | + | 0.766704i | \(0.721895\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 63.3814i | − 0.113383i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.3607 | −0.0309460 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 249.654 | 0.443436 | 0.221718 | − | 0.975111i | \(-0.428834\pi\) | ||||
0.221718 | + | 0.975111i | \(0.428834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 402.553i | − 0.712483i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 104.353 | 0.183396 | 0.0916982 | − | 0.995787i | \(-0.470771\pi\) | ||||
0.0916982 | + | 0.995787i | \(0.470771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 649.705 | 1.13784 | 0.568919 | − | 0.822394i | \(-0.307362\pi\) | ||||
0.568919 | + | 0.822394i | \(0.307362\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 698.630i | 1.21925i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.6785i | 0.0220495i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 346.022 | 0.599692 | 0.299846 | − | 0.953988i | \(-0.403065\pi\) | ||||
0.299846 | + | 0.953988i | \(0.403065\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −300.537 | −0.519061 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 465.434i | − 0.798342i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −181.482 | −0.310226 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1153.54 | −1.96514 | −0.982572 | − | 0.185885i | \(-0.940485\pi\) | ||||
−0.982572 | + | 0.185885i | \(0.940485\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 155.488i | 0.263987i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 74.5515i | − 0.126145i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −880.135 | −1.48421 | −0.742104 | − | 0.670285i | \(-0.766172\pi\) | ||||
−0.742104 | + | 0.670285i | \(0.766172\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 626.081i | 1.04871i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 554.939i | − 0.926442i | −0.886243 | − | 0.463221i | \(-0.846694\pi\) | ||||
0.886243 | − | 0.463221i | \(-0.153306\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 666.057 | 1.10825 | 0.554124 | − | 0.832434i | \(-0.313054\pi\) | ||||
0.554124 | + | 0.832434i | \(0.313054\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −52.3977 | −0.0868950 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1661.57i | − 2.74640i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 192.927i | 0.317836i | 0.987292 | + | 0.158918i | \(0.0508006\pi\) | ||||
−0.987292 | + | 0.158918i | \(0.949199\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 945.878 | 1.54808 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 608.234i | − 0.992226i | −0.868258 | − | 0.496113i | \(-0.834760\pi\) | ||||
0.868258 | − | 0.496113i | \(-0.165240\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 635.668i | 1.03361i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.884056 | 0.00143283 | 0.000716415 | − | 1.00000i | \(-0.499772\pi\) | ||||
0.000716415 | 1.00000i | \(0.499772\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 358.525 | 0.579200 | 0.289600 | − | 0.957148i | \(-0.406478\pi\) | ||||
0.289600 | + | 0.957148i | \(0.406478\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 232.080i | 0.373719i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −594.720 | −0.951552 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −336.937 | −0.537379 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.7397i | 0.0202539i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 390.515i | − 0.618883i | −0.950918 | − | 0.309442i | \(-0.899858\pi\) | ||||
0.950918 | − | 0.309442i | \(-0.100142\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −73.7137 | −0.116451 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 122.759 | 0.193322 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 135.083i | − 0.211397i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −431.936 | −0.673848 | −0.336924 | − | 0.941532i | \(-0.609386\pi\) | ||||
−0.336924 | + | 0.941532i | \(0.609386\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 49.9370 | 0.0776625 | 0.0388313 | − | 0.999246i | \(-0.487637\pi\) | ||||
0.0388313 | + | 0.999246i | \(0.487637\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 81.4480i | 0.126276i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 224.141i | 0.346431i | 0.984884 | + | 0.173216i | \(0.0554157\pi\) | ||||
−0.984884 | + | 0.173216i | \(0.944584\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 749.582 | 1.15498 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 80.7637i | − 0.123681i | −0.998086 | − | 0.0618405i | \(-0.980303\pi\) | ||||
0.998086 | − | 0.0618405i | \(-0.0196970\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 617.186i | 0.942268i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −158.919 | −0.241886 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 940.466 | 1.42711 | 0.713555 | − | 0.700599i | \(-0.247084\pi\) | ||||
0.713555 | + | 0.700599i | \(0.247084\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 119.930i | 0.181437i | 0.995877 | + | 0.0907184i | \(0.0289163\pi\) | ||||
−0.995877 | + | 0.0907184i | \(0.971084\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.5696i | 0.0159421i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 379.426 | 0.568855 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 674.346i | 1.00799i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1366.00i | 2.03577i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1085.06 | 1.61227 | 0.806136 | − | 0.591731i | \(-0.201555\pi\) | ||||
0.806136 | + | 0.591731i | \(0.201555\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.5298 | 0.0363404 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 949.901i | 1.40310i | 0.712618 | + | 0.701552i | \(0.247509\pi\) | ||||
−0.712618 | + | 0.701552i | \(0.752491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 93.8270 | 0.137778 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 893.785 | 1.30862 | 0.654308 | − | 0.756228i | \(-0.272960\pi\) | ||||
0.654308 | + | 0.756228i | \(0.272960\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 170.635i | − 0.249102i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 606.861i | 0.883349i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −283.366 | −0.411272 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1208.56 | 1.74901 | 0.874504 | − | 0.485019i | \(-0.161187\pi\) | ||||
0.874504 | + | 0.485019i | \(0.161187\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 581.782i | 0.837096i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.88585 | 0.0127487 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −247.210 | −0.353662 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 219.477i | − 0.313091i | −0.987671 | − | 0.156546i | \(-0.949964\pi\) | ||||
0.987671 | − | 0.156546i | \(-0.0500358\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 247.251i | 0.351709i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1215.50 | −1.72411 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1265.13i | − 1.78439i | −0.451651 | − | 0.892195i | \(-0.649165\pi\) | ||||
0.451651 | − | 0.892195i | \(-0.350835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 270.066i | − 0.379839i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −373.560 | −0.523927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1371.31 | −1.91792 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 244.650i | 0.341213i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1163.47i | − 1.61818i | −0.587687 | − | 0.809089i | \(-0.699961\pi\) | ||||
0.587687 | − | 0.809089i | \(-0.300039\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 193.094 | 0.267074 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 40.1036i | − 0.0553153i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1303.68i | − 1.79324i | −0.442803 | − | 0.896619i | \(-0.646016\pi\) | ||||
0.442803 | − | 0.896619i | \(-0.353984\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 376.305 | 0.516193 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.13854 | 0.00155751 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1256.12i | − 1.71367i | −0.515589 | − | 0.856836i | \(-0.672427\pi\) | ||||
0.515589 | − | 0.856836i | \(-0.327573\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −395.925 | −0.537212 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −687.168 | −0.929862 | −0.464931 | − | 0.885347i | \(-0.653921\pi\) | ||||
−0.464931 | + | 0.885347i | \(0.653921\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 205.134i | 0.276835i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 362.628i | − 0.488059i | −0.969768 | − | 0.244030i | \(-0.921531\pi\) | ||||
0.969768 | − | 0.244030i | \(-0.0784694\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −595.376 | −0.799163 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 203.275 | 0.272122 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 261.366i | 0.348024i | 0.984744 | + | 0.174012i | \(0.0556732\pi\) | ||||
−0.984744 | + | 0.174012i | \(0.944327\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1269.67 | −1.68615 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1076.20 | 1.42544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1395.34i | 1.84325i | 0.388081 | + | 0.921625i | \(0.373138\pi\) | ||||
−0.388081 | + | 0.921625i | \(0.626862\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 809.488i | − 1.06652i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 319.500 | 0.419843 | 0.209921 | − | 0.977718i | \(-0.432679\pi\) | ||||
0.209921 | + | 0.977718i | \(0.432679\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 3.26003i | − 0.00426148i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 456.362i | − 0.594996i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −634.936 | −0.825664 | −0.412832 | − | 0.910807i | \(-0.635460\pi\) | ||||
−0.412832 | + | 0.910807i | \(0.635460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 81.7056 | 0.105974 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 96.1663i | 0.124407i | 0.998063 | + | 0.0622033i | \(0.0198127\pi\) | ||||
−0.998063 | + | 0.0622033i | \(0.980187\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.4836i | 0.0509465i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 172.456 | 0.221382 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1020.71i | − 1.30693i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 734.098i | − 0.937545i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33.0577 | 0.0421117 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1319.25 | −1.67630 | −0.838148 | − | 0.545442i | \(-0.816362\pi\) | ||||
−0.838148 | + | 0.545442i | \(0.816362\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 254.554i | 0.322628i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 831.651 | 1.04874 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 364.139 | 0.458036 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 818.575i | − 1.02707i | −0.858068 | − | 0.513535i | \(-0.828336\pi\) | ||||
0.858068 | − | 0.513535i | \(-0.171664\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.9911i | 0.0212655i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 454.088 | 0.566902 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1200.82 | −1.49541 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1154.87i | − 1.43106i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1232.72 | 1.52376 | 0.761881 | − | 0.647717i | \(-0.224276\pi\) | ||||
0.761881 | + | 0.647717i | \(0.224276\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1009.05 | −1.24421 | −0.622103 | − | 0.782935i | \(-0.713722\pi\) | ||||
−0.622103 | + | 0.782935i | \(0.713722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 644.468i | 0.792703i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1011.94i | − 1.24164i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.0968 | 0.0270462 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 939.093i | 1.14384i | 0.820309 | + | 0.571920i | \(0.193801\pi\) | ||||
−0.820309 | + | 0.571920i | \(0.806199\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 911.100i | − 1.10705i | −0.832833 | − | 0.553524i | \(-0.813283\pi\) | ||||
0.832833 | − | 0.553524i | \(-0.186717\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −85.5591 | −0.103708 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 65.6564 | 0.0793910 | 0.0396955 | − | 0.999212i | \(-0.487361\pi\) | ||||
0.0396955 | + | 0.999212i | \(0.487361\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1515.94i | 1.82864i | 0.404997 | + | 0.914318i | \(0.367272\pi\) | ||||
−0.404997 | + | 0.914318i | \(0.632728\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 456.285i | 0.549079i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 808.257 | 0.967972 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 722.747i | 0.863497i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 869.972i | − 1.03692i | −0.855103 | − | 0.518458i | \(-0.826506\pi\) | ||||
0.855103 | − | 0.518458i | \(-0.173494\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −359.174 | −0.427080 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1140.85 | −1.35333 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.67964i | 0.0114552i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 229.588 | 0.270421 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −594.020 | −0.698026 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1643.91i | − 1.92721i | −0.267322 | − | 0.963607i | \(-0.586139\pi\) | ||||
0.267322 | − | 0.963607i | \(-0.413861\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 63.2706i | − 0.0740007i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −286.059 | −0.333791 | −0.166895 | − | 0.985975i | \(-0.553374\pi\) | ||||
−0.166895 | + | 0.985975i | \(0.553374\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 719.782 | 0.837930 | 0.418965 | − | 0.908002i | \(-0.362393\pi\) | ||||
0.418965 | + | 0.908002i | \(0.362393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1120.47i | 1.29835i | 0.760641 | + | 0.649173i | \(0.224885\pi\) | ||||
−0.760641 | + | 0.649173i | \(0.775115\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 433.857 | 0.501569 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 994.339 | 1.14687 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2040.66i | − 2.34828i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 241.048i | 0.276749i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 257.178 | 0.294591 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 145.400i | − 0.165792i | −0.996558 | − | 0.0828960i | \(-0.973583\pi\) | ||||
0.996558 | − | 0.0828960i | \(-0.0264169\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 995.269i | 1.13227i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −476.080 | −0.540386 | −0.270193 | − | 0.962806i | \(-0.587087\pi\) | ||||
−0.270193 | + | 0.962806i | \(0.587087\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1101.22 | 1.24714 | 0.623568 | − | 0.781769i | \(-0.285682\pi\) | ||||
0.623568 | + | 0.781769i | \(0.285682\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 586.447i | 0.662652i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1491.49i | 1.68150i | 0.541427 | + | 0.840748i | \(0.317884\pi\) | ||||
−0.541427 | + | 0.840748i | \(0.682116\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2115.59 | −2.37440 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 329.764i | 0.369276i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 392.481i | 0.438526i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −492.834 | −0.549425 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1181.62 | 1.31437 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 5.09021i | − 0.00564951i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1349.40 | −1.49104 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1155.46 | −1.27394 | −0.636969 | − | 0.770889i | \(-0.719812\pi\) | ||||
−0.636969 | + | 0.770889i | \(0.719812\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 514.891i | − 0.566436i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 944.690i | − 1.03698i | −0.855083 | − | 0.518491i | \(-0.826494\pi\) | ||||
0.855083 | − | 0.518491i | \(-0.173506\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1535.98 | 1.68235 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1068.71 | −1.16799 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 149.150i | 0.162296i | 0.996702 | + | 0.0811478i | \(0.0258586\pi\) | ||||
−0.996702 | + | 0.0811478i | \(0.974141\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.38541 | −0.00259003 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −621.430 | −0.673272 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 62.7851i | 0.0678758i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 111.707i | − 0.120503i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 58.8399 | 0.0633368 | 0.0316684 | − | 0.999498i | \(-0.489918\pi\) | ||||
0.0316684 | + | 0.999498i | \(0.489918\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 213.904i | − 0.229265i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 24.6333i | − 0.0263458i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1700.18 | 1.81449 | 0.907246 | − | 0.420601i | \(-0.138181\pi\) | ||||
0.907246 | + | 0.420601i | \(0.138181\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 735.036 | 0.782786 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 56.6116i | − 0.0601611i | −0.999547 | − | 0.0300805i | \(-0.990424\pi\) | ||||
0.999547 | − | 0.0300805i | \(-0.00957637\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 414.325i | 0.439369i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −242.533 | −0.256107 | −0.128053 | − | 0.991767i | \(-0.540873\pi\) | ||||
−0.128053 | + | 0.991767i | \(0.540873\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 731.084i | 0.770373i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 80.7244i | − 0.0848837i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −364.070 | −0.382025 | −0.191013 | − | 0.981588i | \(-0.561177\pi\) | ||||
−0.191013 | + | 0.981588i | \(0.561177\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −991.294 | −1.03800 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2560.51i | 2.67556i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −202.348 | −0.210560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −109.290 | −0.113489 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 426.435i | − 0.441901i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1221.99i | 1.26369i | 0.775093 | + | 0.631847i | \(0.217703\pi\) | ||||
−0.775093 | + | 0.631847i | \(0.782297\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.68490 | −0.00380279 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1088.53 | −1.12104 | −0.560521 | − | 0.828140i | \(-0.689399\pi\) | ||||
−0.560521 | + | 0.828140i | \(0.689399\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 52.0903i | 0.0534259i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1061.51 | −1.08650 | −0.543252 | − | 0.839570i | \(-0.682807\pi\) | ||||
−0.543252 | + | 0.839570i | \(0.682807\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3431.17 | 3.50477 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 79.2419i | − 0.0807766i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1322.61i | − 1.34549i | −0.739877 | − | 0.672743i | \(-0.765116\pi\) | ||||
0.739877 | − | 0.672743i | \(-0.234884\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 105.782 | 0.107393 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 53.0874i | 0.0536778i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 675.806i | − 0.681944i | −0.940073 | − | 0.340972i | \(-0.889244\pi\) | ||||
0.940073 | − | 0.340972i | \(-0.110756\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1746.12 | 1.75843 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −888.354 | −0.892818 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 409.220i | − 0.410452i | −0.978715 | − | 0.205226i | \(-0.934207\pi\) | ||||
0.978715 | − | 0.205226i | \(-0.0657929\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1149.28i | 1.15043i |
(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 | 1568.3.g.m.687.3 | 8 | ||
4.3 | odd | 2 | 392.3.g.m.99.3 | 8 | |||
7.6 | odd | 2 | 224.3.g.b.15.6 | 8 | |||
8.3 | odd | 2 | inner | 1568.3.g.m.687.4 | 8 | ||
8.5 | even | 2 | 392.3.g.m.99.4 | 8 | |||
21.20 | even | 2 | 2016.3.g.b.1135.3 | 8 | |||
28.3 | even | 6 | 392.3.k.o.275.8 | 16 | |||
28.11 | odd | 6 | 392.3.k.n.275.8 | 16 | |||
28.19 | even | 6 | 392.3.k.o.67.3 | 16 | |||
28.23 | odd | 6 | 392.3.k.n.67.3 | 16 | |||
28.27 | even | 2 | 56.3.g.b.43.3 | ✓ | 8 | ||
56.5 | odd | 6 | 392.3.k.o.67.8 | 16 | |||
56.13 | odd | 2 | 56.3.g.b.43.4 | yes | 8 | ||
56.27 | even | 2 | 224.3.g.b.15.5 | 8 | |||
56.37 | even | 6 | 392.3.k.n.67.8 | 16 | |||
56.45 | odd | 6 | 392.3.k.o.275.3 | 16 | |||
56.53 | even | 6 | 392.3.k.n.275.3 | 16 | |||
84.83 | odd | 2 | 504.3.g.b.379.6 | 8 | |||
112.13 | odd | 4 | 1792.3.d.j.1023.12 | 16 | |||
112.27 | even | 4 | 1792.3.d.j.1023.11 | 16 | |||
112.69 | odd | 4 | 1792.3.d.j.1023.5 | 16 | |||
112.83 | even | 4 | 1792.3.d.j.1023.6 | 16 | |||
168.83 | odd | 2 | 2016.3.g.b.1135.6 | 8 | |||
168.125 | even | 2 | 504.3.g.b.379.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.3 | ✓ | 8 | 28.27 | even | 2 | ||
56.3.g.b.43.4 | yes | 8 | 56.13 | odd | 2 | ||
224.3.g.b.15.5 | 8 | 56.27 | even | 2 | |||
224.3.g.b.15.6 | 8 | 7.6 | odd | 2 | |||
392.3.g.m.99.3 | 8 | 4.3 | odd | 2 | |||
392.3.g.m.99.4 | 8 | 8.5 | even | 2 | |||
392.3.k.n.67.3 | 16 | 28.23 | odd | 6 | |||
392.3.k.n.67.8 | 16 | 56.37 | even | 6 | |||
392.3.k.n.275.3 | 16 | 56.53 | even | 6 | |||
392.3.k.n.275.8 | 16 | 28.11 | odd | 6 | |||
392.3.k.o.67.3 | 16 | 28.19 | even | 6 | |||
392.3.k.o.67.8 | 16 | 56.5 | odd | 6 | |||
392.3.k.o.275.3 | 16 | 56.45 | odd | 6 | |||
392.3.k.o.275.8 | 16 | 28.3 | even | 6 | |||
504.3.g.b.379.5 | 8 | 168.125 | even | 2 | |||
504.3.g.b.379.6 | 8 | 84.83 | odd | 2 | |||
1568.3.g.m.687.3 | 8 | 1.1 | even | 1 | trivial | ||
1568.3.g.m.687.4 | 8 | 8.3 | odd | 2 | inner | ||
1792.3.d.j.1023.5 | 16 | 112.69 | odd | 4 | |||
1792.3.d.j.1023.6 | 16 | 112.83 | even | 4 | |||
1792.3.d.j.1023.11 | 16 | 112.27 | even | 4 | |||
1792.3.d.j.1023.12 | 16 | 112.13 | odd | 4 | |||
2016.3.g.b.1135.3 | 8 | 21.20 | even | 2 | |||
2016.3.g.b.1135.6 | 8 | 168.83 | odd | 2 |