Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(223,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("1344.223");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.p (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.28 | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.d.223.27 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −15.6891 | −1.40328 | −0.701639 | − | 0.712532i | \(-0.747548\pi\) | ||||
−0.701639 | + | 0.712532i | \(0.747548\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.8361 | + | 15.0193i | −0.585094 | + | 0.810965i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 41.3237 | 1.13269 | 0.566344 | − | 0.824169i | \(-0.308357\pi\) | ||||
0.566344 | + | 0.824169i | \(0.308357\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.02995 | −0.171316 | −0.0856580 | − | 0.996325i | \(-0.527299\pi\) | ||||
−0.0856580 | + | 0.996325i | \(0.527299\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 47.0674i | − | 0.810183i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.2211i | 0.202889i | 0.994841 | + | 0.101444i | \(0.0323464\pi\) | ||||
−0.994841 | + | 0.101444i | \(0.967654\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 10.2063i | − | 0.123236i | −0.998100 | − | 0.0616182i | \(-0.980374\pi\) | ||
0.998100 | − | 0.0616182i | \(-0.0196261\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −45.0579 | − | 32.5083i | −0.468211 | − | 0.337804i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 203.033i | − | 1.84067i | −0.391135 | − | 0.920333i | \(-0.627917\pi\) | ||
0.391135 | − | 0.920333i | \(-0.372083\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 121.149 | 0.969190 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 82.6180i | − | 0.529027i | −0.964382 | − | 0.264513i | \(-0.914789\pi\) | ||
0.964382 | − | 0.264513i | \(-0.0852113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 156.241 | 0.905214 | 0.452607 | − | 0.891710i | \(-0.350494\pi\) | ||||
0.452607 | + | 0.891710i | \(0.350494\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 123.971i | 0.653958i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 170.009 | − | 235.640i | 0.821050 | − | 1.13801i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 106.169i | − | 0.471732i | −0.971786 | − | 0.235866i | \(-0.924207\pi\) | ||
0.971786 | − | 0.235866i | \(-0.0757927\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 24.0898i | − | 0.0989093i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 315.657i | 1.20238i | 0.799108 | + | 0.601188i | \(0.205306\pi\) | ||||
−0.799108 | + | 0.601188i | \(0.794694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 154.276 | 0.547137 | 0.273569 | − | 0.961853i | \(-0.411796\pi\) | ||||
0.273569 | + | 0.961853i | \(0.411796\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 141.202 | 0.467759 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −474.835 | −1.47365 | −0.736827 | − | 0.676081i | \(-0.763677\pi\) | ||||
−0.736827 | + | 0.676081i | \(0.763677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −108.158 | − | 325.501i | −0.315330 | − | 0.948982i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −42.6632 | −0.117138 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 266.866i | − | 0.691638i | −0.938301 | − | 0.345819i | \(-0.887601\pi\) | ||
0.938301 | − | 0.345819i | \(-0.112399\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −648.334 | −1.58948 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30.6190 | 0.0711506 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 425.632i | − | 0.939197i | −0.882880 | − | 0.469598i | \(-0.844399\pi\) | ||
0.882880 | − | 0.469598i | \(-0.155601\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.30642 | 0.0174349 | 0.00871744 | − | 0.999962i | \(-0.497225\pi\) | ||||
0.00871744 | + | 0.999962i | \(0.497225\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 97.5248 | − | 135.174i | 0.195031 | − | 0.270322i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 125.983 | 0.240404 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 820.303 | 1.49576 | 0.747880 | − | 0.663834i | \(-0.231072\pi\) | ||||
0.747880 | + | 0.663834i | \(0.231072\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 609.099 | 1.06271 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 109.956i | 0.183795i | 0.995768 | + | 0.0918974i | \(0.0292932\pi\) | ||||
−0.995768 | + | 0.0918974i | \(0.970707\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 53.8640i | − | 0.0863604i | −0.999067 | − | 0.0431802i | \(-0.986251\pi\) | ||
0.999067 | − | 0.0431802i | \(-0.0137490\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 363.446i | 0.559562i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −447.788 | + | 620.653i | −0.662730 | + | 0.918571i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1171.20i | 1.66798i | 0.551782 | + | 0.833988i | \(0.313948\pi\) | ||||
−0.551782 | + | 0.833988i | \(0.686052\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 507.294i | 0.670876i | 0.942062 | + | 0.335438i | \(0.108884\pi\) | ||||
−0.942062 | + | 0.335438i | \(0.891116\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 223.116i | − | 0.284710i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 247.854 | 0.305434 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1061.99i | 1.26484i | 0.774627 | + | 0.632418i | \(0.217938\pi\) | ||||
−0.774627 | + | 0.632418i | \(0.782062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 87.0133 | − | 120.604i | 0.100236 | − | 0.138931i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 468.722i | 0.522626i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 160.128i | 0.172935i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 573.319i | − | 0.600121i | −0.953920 | − | 0.300060i | \(-0.902993\pi\) | ||
0.953920 | − | 0.300060i | \(-0.0970068\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −371.914 | −0.377563 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1515.77 | 1.49331 | 0.746657 | − | 0.665209i | \(-0.231658\pi\) | ||||
0.746657 | + | 0.665209i | \(0.231658\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1642.32 | −1.57109 | −0.785545 | − | 0.618804i | \(-0.787618\pi\) | ||||
−0.785545 | + | 0.618804i | \(0.787618\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 706.919 | + | 510.027i | 0.657031 | + | 0.474033i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 900.675 | 0.813752 | 0.406876 | − | 0.913483i | \(-0.366618\pi\) | ||||
0.406876 | + | 0.913483i | \(0.366618\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1603.61i | 1.40915i | 0.709627 | + | 0.704577i | \(0.248863\pi\) | ||||
−0.709627 | + | 0.704577i | \(0.751137\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 318.507 | 0.272355 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 821.120 | 0.683580 | 0.341790 | − | 0.939776i | \(-0.388967\pi\) | ||||
0.341790 | + | 0.939776i | \(0.388967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3185.41i | 2.58297i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 72.2695 | 0.0571053 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −213.590 | − | 154.101i | −0.164536 | − | 0.118709i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 376.652 | 0.282984 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −946.972 | −0.694192 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 60.4223 | 0.0432347 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2459.21i | 1.71826i | 0.511754 | + | 0.859132i | \(0.328996\pi\) | ||||
−0.511754 | + | 0.859132i | \(0.671004\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 462.828i | 0.315890i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1027.71i | − | 0.685428i | −0.939440 | − | 0.342714i | \(-0.888654\pi\) | ||
0.939440 | − | 0.342714i | \(-0.111346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 153.292 | + | 110.597i | 0.0999405 | + | 0.0721049i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 423.606i | 0.270061i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1372.27 | 0.855771 | 0.427886 | − | 0.903833i | \(-0.359259\pi\) | ||||
0.427886 | + | 0.903833i | \(0.359259\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1161.76i | 0.708915i | 0.935072 | + | 0.354458i | \(0.115334\pi\) | ||||
−0.935072 | + | 0.354458i | \(0.884666\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 1424.50i | − | 0.850815i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −331.827 | −0.194048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1296.20i | 0.742372i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 976.503 | − | 324.474i | 0.547895 | − | 0.182056i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 647.153i | − | 0.355818i | −0.984047 | − | 0.177909i | \(-0.943067\pi\) | ||
0.984047 | − | 0.177909i | \(-0.0569332\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1459.53i | − | 0.786588i | −0.919413 | − | 0.393294i | \(-0.871336\pi\) | ||
0.919413 | − | 0.393294i | \(-0.128664\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 127.990i | − | 0.0676297i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2451.28 | −1.27027 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1989.05 | 1.01110 | 0.505552 | − | 0.862796i | \(-0.331289\pi\) | ||||
0.505552 | + | 0.862796i | \(0.331289\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 800.597 | 0.399317 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3049.41 | + | 2200.09i | 1.49272 | + | 1.07696i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3462.74 | −1.66395 | −0.831973 | − | 0.554817i | \(-0.812788\pi\) | ||||
−0.831973 | + | 0.554817i | \(0.812788\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 1945.00i | − | 0.917685i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −826.203 | −0.382835 | −0.191418 | − | 0.981509i | \(-0.561308\pi\) | ||||
−0.191418 | + | 0.981509i | \(0.561308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2132.52 | −0.970651 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 91.8570i | 0.0410788i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2511.03 | 1.10352 | 0.551762 | − | 0.834001i | \(-0.313956\pi\) | ||||
0.551762 | + | 0.834001i | \(0.313956\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1312.78 | + | 1819.57i | −0.567067 | + | 0.785980i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1276.90 | 0.542246 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3839.23 | 1.60312 | 0.801558 | − | 0.597917i | \(-0.204005\pi\) | ||||
0.801558 | + | 0.597917i | \(0.204005\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −641.534 | −0.263452 | −0.131726 | − | 0.991286i | \(-0.542052\pi\) | ||||
−0.131726 | + | 0.991286i | \(0.542052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.9193i | 0.0100660i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1665.70i | 0.661971i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 587.667i | 0.229810i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 405.521 | + | 292.575i | 0.156070 | + | 0.112601i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1641.13i | 0.621719i | 0.950456 | + | 0.310859i | \(0.100617\pi\) | ||||
−0.950456 | + | 0.310859i | \(0.899383\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2245.24 | 0.837390 | 0.418695 | − | 0.908127i | \(-0.362488\pi\) | ||||
0.418695 | + | 0.908127i | \(0.362488\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 377.949i | 0.138797i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3758.27i | − | 1.35922i | −0.733574 | − | 0.679609i | \(-0.762149\pi\) | ||
0.733574 | − | 0.679609i | \(-0.237851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4894.52 | −1.74353 | −0.871767 | − | 0.489921i | \(-0.837026\pi\) | ||||
−0.871767 | + | 0.489921i | \(0.837026\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2460.91i | 0.863577i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1240.86 | + | 895.256i | 0.429022 | + | 0.309530i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 4952.39i | − | 1.68727i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1827.30i | 0.613556i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 421.764i | − | 0.139589i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −34.5211 | −0.0112632 | −0.00563160 | − | 0.999984i | \(-0.501793\pi\) | ||||
−0.00563160 | + | 0.999984i | \(0.501793\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −329.869 | −0.106114 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2420.46 | −0.767786 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1693.04 | + | 2346.62i | −0.529635 | + | 0.734097i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 161.592 | 0.0498602 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 114.194i | − | 0.0347581i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2469.84 | −0.741671 | −0.370835 | − | 0.928699i | \(-0.620929\pi\) | ||||
−0.370835 | + | 0.928699i | \(0.620929\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1090.34 | −0.323063 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3287.81i | 0.961320i | 0.876907 | + | 0.480660i | \(0.159603\pi\) | ||||
−0.876907 | + | 0.480660i | \(0.840397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4047.39 | −1.16794 | −0.583972 | − | 0.811774i | \(-0.698502\pi\) | ||||
−0.583972 | + | 0.811774i | \(0.698502\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1861.96 | − | 1343.36i | −0.530337 | − | 0.382627i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.42114 | 0.00208659 | 0.00104329 | − | 0.999999i | \(-0.499668\pi\) | ||||
0.00104329 | + | 0.999999i | \(0.499668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7449.74 | 2.06795 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3513.60 | −0.963007 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2959.05i | 0.800858i | 0.916328 | + | 0.400429i | \(0.131139\pi\) | ||||
−0.916328 | + | 0.400429i | \(0.868861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5561.26i | 1.48644i | 0.669047 | + | 0.743220i | \(0.266702\pi\) | ||||
−0.669047 | + | 0.743220i | \(0.733298\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1696.91 | + | 5106.83i | 0.442495 | + | 1.33169i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 81.9563i | 0.0211124i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1521.88 | −0.387331 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 129.815i | 0.0326449i | 0.999867 | + | 0.0163224i | \(0.00519583\pi\) | ||||
−0.999867 | + | 0.0163224i | \(0.994804\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8390.09i | − | 2.08490i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 669.348 | 0.164377 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 341.353i | 0.0828521i | 0.999142 | + | 0.0414260i | \(0.0131901\pi\) | ||||
−0.999142 | + | 0.0414260i | \(0.986810\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1594.58 | + | 1150.46i | 0.382558 | + | 0.276008i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 743.562i | 0.176342i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 477.176i | − | 0.111878i | −0.998434 | − | 0.0559391i | \(-0.982185\pi\) | ||
0.998434 | − | 0.0559391i | \(-0.0178153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4186.89i | 0.970560i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3185.96 | −0.730254 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 147.535 | 0.0334399 | 0.0167200 | − | 0.999860i | \(-0.494678\pi\) | ||||
0.0167200 | + | 0.999860i | \(0.494678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6071.49 | 1.36095 | 0.680474 | − | 0.732773i | \(-0.261774\pi\) | ||||
0.680474 | + | 0.732773i | \(0.261774\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 361.812 | + | 261.040i | 0.0802120 | + | 0.0578712i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5006.32 | 1.09779 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 569.213i | 0.123468i | 0.998093 | + | 0.0617341i | \(0.0196631\pi\) | ||||
−0.998093 | + | 0.0617341i | \(0.980337\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1406.17 | −0.301738 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −784.629 | −0.166573 | −0.0832866 | − | 0.996526i | \(-0.526542\pi\) | ||||
−0.0832866 | + | 0.996526i | \(0.526542\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7125.60i | − | 1.49672i | −0.663290 | − | 0.748362i | \(-0.730840\pi\) | ||
0.663290 | − | 0.748362i | \(-0.269160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −480.385 | −0.0998441 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4740.95 | − | 3420.49i | −0.975085 | − | 0.703503i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4710.76 | 0.958836 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1719.96 | 0.346480 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6069.86 | 1.21026 | 0.605128 | − | 0.796129i | \(-0.293122\pi\) | ||||
0.605128 | + | 0.796129i | \(0.293122\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6677.80i | 1.31795i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1115.74i | − | 0.217986i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1630.35i | 0.315335i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1671.75 | + | 2317.12i | −0.320127 | + | 0.443709i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4547.31i | 0.862165i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −130.321 | −0.0244660 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4655.34i | 0.865453i | 0.901525 | + | 0.432727i | \(0.142448\pi\) | ||||
−0.901525 | + | 0.432727i | \(0.857552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4926.95i | − | 0.907070i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3077.49 | 0.561121 | 0.280560 | − | 0.959836i | \(-0.409480\pi\) | ||||
0.280560 | + | 0.959836i | \(0.409480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 485.087i | 0.0875999i | 0.999040 | + | 0.0437999i | \(0.0139464\pi\) | ||||
−0.999040 | + | 0.0437999i | \(0.986054\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1530.08 | + | 2120.76i | −0.273683 | + | 0.379337i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8675.14i | 1.53705i | 0.639821 | + | 0.768524i | \(0.279008\pi\) | ||||
−0.639821 | + | 0.768524i | \(0.720992\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3414.08i | − | 0.599223i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2702.02i | 0.469820i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 145.145 | 0.0250033 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −972.818 | −0.166038 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4810.83 | −0.813576 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5145.35 | − | 7131.68i | 0.862227 | − | 1.19508i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10094.7 | −1.67630 | −0.838152 | − | 0.545436i | \(-0.816364\pi\) | ||||
−0.838152 | + | 0.545436i | \(0.816364\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 955.522i | 0.157244i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12869.8 | −2.09897 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2044.06 | −0.330406 | −0.165203 | − | 0.986260i | \(-0.552828\pi\) | ||||
−0.165203 | + | 0.986260i | \(0.552828\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2463.36i | 0.394665i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6456.44 | 1.02533 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6060.80 | + | 1902.70i | 0.954089 | + | 0.299522i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9556.24 | −1.49128 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7094.50 | 1.09756 | 0.548779 | − | 0.835967i | \(-0.315093\pi\) | ||||
0.548779 | + | 0.835967i | \(0.315093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6628.07 | 1.01660 | 0.508299 | − | 0.861181i | \(-0.330275\pi\) | ||||
0.508299 | + | 0.861181i | \(0.330275\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 216.809i | 0.0329698i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6785.57i | − | 1.02311i | −0.859249 | − | 0.511557i | \(-0.829069\pi\) | ||
0.859249 | − | 0.511557i | \(-0.170931\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1725.12i | − | 0.257915i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 462.302 | − | 640.770i | 0.0685368 | − | 0.0949949i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3251.11i | 0.477959i | 0.971025 | + | 0.238979i | \(0.0768128\pi\) | ||||
−0.971025 | + | 0.238979i | \(0.923187\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6754.83 | 0.984813 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1129.95i | 0.163381i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 845.080i | 0.121188i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2278.93 | 0.324139 | 0.162070 | − | 0.986779i | \(-0.448183\pi\) | ||||
0.162070 | + | 0.986779i | \(0.448183\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2840.92i | − | 0.400792i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4008.13 | + | 2891.78i | 0.560894 | + | 0.404673i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 711.350i | − | 0.0987461i | −0.998780 | − | 0.0493730i | \(-0.984278\pi\) | ||
0.998780 | − | 0.0493730i | \(-0.0157223\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 181.267i | 0.0249615i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 663.418i | 0.0906307i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11988.5 | −1.62482 | −0.812412 | − | 0.583084i | \(-0.801846\pi\) | ||||
−0.812412 | + | 0.583084i | \(0.801846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7377.63 | −0.992040 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2949.04 | 0.393443 | 0.196722 | − | 0.980459i | \(-0.436971\pi\) | ||||
0.196722 | + | 0.980459i | \(0.436971\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7025.40 | − | 9737.51i | 0.929994 | − | 1.28901i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1388.49 | −0.182379 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12522.4i | 1.63217i | 0.577934 | + | 0.816083i | \(0.303859\pi\) | ||||
−0.577934 | + | 0.816083i | \(0.696141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2887.35 | 0.373451 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3083.12 | 0.395732 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 18375.1i | − | 2.34064i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11913.8 | 1.50614 | 0.753069 | − | 0.657942i | \(-0.228573\pi\) | ||||
0.753069 | + | 0.657942i | \(0.228573\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −331.790 | + | 459.875i | −0.0416298 | + | 0.0577007i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7252.00 | 0.903111 | 0.451555 | − | 0.892243i | \(-0.350869\pi\) | ||||
0.451555 | + | 0.892243i | \(0.350869\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1254.60 | −0.155078 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1270.82 | −0.155920 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4387.30i | − | 0.534326i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13209.0i | 1.59693i | 0.602043 | + | 0.798464i | \(0.294354\pi\) | ||||
−0.602043 | + | 0.798464i | \(0.705646\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4116.80i | 0.494080i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6392.70 | + | 4612.19i | 0.761656 | + | 0.549519i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7959.00i | − | 0.941426i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3485.28 | −0.409292 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5362.97i | − | 0.625294i | −0.949869 | − | 0.312647i | \(-0.898784\pi\) | ||
0.949869 | − | 0.312647i | \(-0.101216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3238.08i | 0.374856i | 0.982278 | + | 0.187428i | \(0.0600151\pi\) | ||||
−0.982278 | + | 0.187428i | \(0.939985\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4273.51 | 0.491218 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1722.86i | 0.196638i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −90.0092 | + | 124.757i | −0.0102011 | + | 0.0141391i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 995.482i | − | 0.112033i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16968.0i | − | 1.89633i | −0.317779 | − | 0.948165i | \(-0.602937\pi\) | ||
0.317779 | − | 0.948165i | \(-0.397063\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 129.696i | 0.0143944i | 0.999974 | + | 0.00719722i | \(0.00229096\pi\) | ||||
−0.999974 | + | 0.00719722i | \(0.997709\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3888.61 | −0.428609 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2072.22 | −0.226837 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16075.4 | 1.74769 | 0.873847 | − | 0.486201i | \(-0.161618\pi\) | ||||
0.873847 | + | 0.486201i | \(0.161618\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 973.423 | + | 2929.51i | 0.105110 | + | 0.316327i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6218.21 | −0.666899 | −0.333449 | − | 0.942768i | \(-0.608213\pi\) | ||||
−0.333449 | + | 0.942768i | \(0.608213\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 16661.7i | − | 1.77492i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1941.46 | 0.205431 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4008.24 | −0.421293 | −0.210647 | − | 0.977562i | \(-0.567557\pi\) | ||||
−0.210647 | + | 0.977562i | \(0.567557\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13044.1i | 1.36192i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4378.58 | 0.454137 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1365.16 | + | 1892.17i | −0.140659 | + | 0.194959i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10539.9 | 1.07886 | 0.539429 | − | 0.842031i | \(-0.318640\pi\) | ||||
0.539429 | + | 0.842031i | \(0.318640\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 383.969 | 0.0390460 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9445.51 | −0.954276 | −0.477138 | − | 0.878828i | \(-0.658326\pi\) | ||||
−0.477138 | + | 0.878828i | \(0.658326\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3097.02i | − | 0.310865i | −0.987847 | − | 0.155433i | \(-0.950323\pi\) | ||
0.987847 | − | 0.155433i | \(-0.0496771\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 7353.84i | − | 0.733389i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 397.479i | 0.0393857i | 0.999806 | + | 0.0196929i | \(0.00626884\pi\) | ||||
−0.999806 | + | 0.0196929i | \(0.993731\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8888.88 | + | 12320.4i | −0.875160 | + | 1.21301i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5967.15i | 0.583761i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6375.27 | 0.619736 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1236.48i | − | 0.119440i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2401.79i | 0.230546i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7591.55 | −0.724148 | −0.362074 | − | 0.932149i | \(-0.617931\pi\) | ||||
−0.362074 | + | 0.932149i | \(0.617931\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 852.532i | 0.0808152i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6600.26 | + | 9148.24i | −0.621785 | + | 0.861821i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8994.87i | 0.842136i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4582.61i | − | 0.426403i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683890\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 10388.2i | − | 0.960679i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14345.7 | 1.31856 | 0.659280 | − | 0.751897i | \(-0.270861\pi\) | ||||
0.659280 | + | 0.751897i | \(0.270861\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1174.91 | 0.107334 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5835.00 | 0.529826 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1651.47 | − | 1191.50i | −0.149051 | − | 0.107537i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5091.08 | 0.456729 | 0.228365 | − | 0.973576i | \(-0.426662\pi\) | ||||
0.228365 | + | 0.973576i | \(0.426662\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 2478.61i | − | 0.221030i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13924.4 | 1.23431 | 0.617155 | − | 0.786842i | \(-0.288285\pi\) | ||||
0.617155 | + | 0.786842i | \(0.288285\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23781.1 | −2.09554 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 6397.56i | − | 0.560406i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −404.309 | −0.0352076 | −0.0176038 | − | 0.999845i | \(-0.505604\pi\) | ||||
−0.0176038 | + | 0.999845i | \(0.505604\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 809.000 | + | 583.676i | 0.0700353 | + | 0.0505290i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −275.571 | −0.0237169 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25766.5 | 2.20468 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19621.9 | −1.66919 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7533.08i | 0.637120i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 14904.9i | − | 1.25335i | −0.779279 | − | 0.626677i | \(-0.784415\pi\) | ||
0.779279 | − | 0.626677i | \(-0.215585\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20930.9i | − | 1.74999i | −0.484136 | − | 0.874993i | \(-0.660866\pi\) | ||
0.484136 | − | 0.874993i | \(-0.339134\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5458.71 | − | 3938.34i | −0.453786 | − | 0.327397i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2221.91i | 0.183658i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29055.4 | −2.38805 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3830.69i | 0.313066i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2534.71i | − | 0.205986i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14130.8 | −1.14192 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11517.7i | 0.925559i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4469.50 | − | 13450.9i | −0.357171 | − | 1.07490i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 903.665i | 0.0718144i | 0.999355 | + | 0.0359072i | \(0.0114321\pi\) | ||||
−0.999355 | + | 0.0359072i | \(0.988568\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1924.60i | − | 0.152104i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 25159.2i | − | 1.97744i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −390.629 | −0.0305340 | −0.0152670 | − | 0.999883i | \(-0.504860\pi\) | ||||
−0.0152670 | + | 0.999883i | \(0.504860\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −74.7578 | −0.00581163 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −843.226 | −0.0651954 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17590.6 | − | 12691.2i | −1.35267 | − | 0.975923i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4997.10 | −0.382189 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9201.82i | 0.699989i | 0.936752 | + | 0.349994i | \(0.113816\pi\) | ||||
−0.936752 | + | 0.349994i | \(0.886184\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1238.83 | −0.0937333 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1763.00 | −0.132681 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 12105.2i | − | 0.906169i | −0.891468 | − | 0.453084i | \(-0.850324\pi\) | ||
0.891468 | − | 0.453084i | \(-0.149676\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12882.7 | −0.959252 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −877.724 | + | 1216.56i | −0.0650105 | + | 0.0901073i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20681.2 | −1.52373 | −0.761864 | − | 0.647737i | \(-0.775716\pi\) | ||||
−0.761864 | + | 0.647737i | \(0.775716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25231.2 | −1.84920 | −0.924599 | − | 0.380943i | \(-0.875600\pi\) | ||||
−0.924599 | + | 0.380943i | \(0.875600\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4923.40 | −0.358950 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 24597.2i | − | 1.78396i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6102.77i | 0.440314i | 0.975464 | + | 0.220157i | \(0.0706570\pi\) | ||||
−0.975464 | + | 0.220157i | \(0.929343\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6735.73i | 0.483467i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7619.20 | − | 5497.09i | −0.544058 | − | 0.392526i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11027.9i | − | 0.783410i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1133.85 | −0.0801346 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 18315.2i | − | 1.28781i | −0.765103 | − | 0.643907i | \(-0.777312\pi\) | ||
0.765103 | − | 0.643907i | \(-0.222688\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1594.64i | − | 0.111555i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11274.8 | 0.784745 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19068.9i | 1.32052i | 0.751038 | + | 0.660259i | \(0.229553\pi\) | ||||
−0.751038 | + | 0.660259i | \(0.770447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3351.04 | + | 2417.71i | 0.230890 | + | 0.166582i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 14683.6i | − | 1.00663i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 909.641i | 0.0620483i | 0.999519 | + | 0.0310241i | \(0.00987688\pi\) | ||||
−0.999519 | + | 0.0310241i | \(0.990123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 16132.6i | − | 1.09494i | −0.836824 | − | 0.547471i | \(-0.815590\pi\) | ||
0.836824 | − | 0.547471i | \(-0.184410\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7382.72 | −0.498587 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5909.33 | −0.397105 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23364.8 | 1.56235 | 0.781177 | − | 0.624309i | \(-0.214620\pi\) | ||||
0.781177 | + | 0.624309i | \(0.214620\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2685.77 | + | 3722.59i | −0.178707 | + | 0.247696i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3812.90 | 0.252461 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 25176.1i | − | 1.65882i | −0.558643 | − | 0.829408i | \(-0.688678\pi\) | ||
0.558643 | − | 0.829408i | \(-0.311322\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14857.2 | 0.974144 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28030.4 | 1.82895 | 0.914474 | − | 0.404645i | \(-0.132605\pi\) | ||||
0.914474 | + | 0.404645i | \(0.132605\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24278.8i | 1.57649i | 0.615361 | + | 0.788245i | \(0.289010\pi\) | ||||
−0.615361 | + | 0.788245i | \(0.710990\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5481.89 | −0.354236 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15950.3 | − | 11507.8i | −1.02574 | − | 0.740048i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16091.6 | −1.02986 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1265.29 | 0.0805915 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1509.84 | 0.0957093 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9973.29i | 0.629208i | 0.949223 | + | 0.314604i | \(0.101872\pi\) | ||||
−0.949223 | + | 0.314604i | \(0.898128\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 103.563i | − | 0.00650281i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 38582.9i | − | 2.41120i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 868.504 | + | 2613.76i | 0.0540210 | + | 0.162576i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 989.608i | − | 0.0612650i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17715.9 | −1.09163 | −0.545815 | − | 0.837906i | \(-0.683780\pi\) | ||||
−0.545815 | + | 0.837906i | \(0.683780\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3370.63i | 0.206726i | 0.994644 | + | 0.103363i | \(0.0329603\pi\) | ||||
−0.994644 | + | 0.103363i | \(0.967040\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 7261.38i | − | 0.443281i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22938.8 | 1.39385 | 0.696923 | − | 0.717146i | \(-0.254552\pi\) | ||||
0.696923 | + | 0.717146i | \(0.254552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 17588.7i | − | 1.06382i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7039.87 | − | 5079.11i | −0.423831 | − | 0.305785i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21021.4i | 1.25977i | 0.776688 | + | 0.629885i | \(0.216898\pi\) | ||||
−0.776688 | + | 0.629885i | \(0.783102\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16123.8i | 0.961847i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 484.776i | 0.0287868i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21351.4 | 1.26211 | 0.631055 | − | 0.775738i | \(-0.282622\pi\) | ||||
0.631055 | + | 0.775738i | \(0.282622\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5778.37 | 0.340019 | 0.170010 | − | 0.985442i | \(-0.445620\pi\) | ||||
0.170010 | + | 0.985442i | \(0.445620\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 342.583 | 0.0200676 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2405.02 | − | 1735.17i | −0.140244 | − | 0.101183i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16774.2 | −0.973762 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 7409.51i | − | 0.428204i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 343.252 | 0.0197483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9562.36 | 0.547700 | 0.273850 | − | 0.961772i | \(-0.411703\pi\) | ||||
0.273850 | + | 0.961772i | \(0.411703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 3271.02i | − | 0.186521i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25060.1 | 1.42266 | 0.711329 | − | 0.702860i | \(-0.248094\pi\) | ||||
0.711329 | + | 0.702860i | \(0.248094\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8610.84 | + | 6212.54i | 0.486677 | + | 0.351127i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9863.43 | −0.555018 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16236.9 | −0.909644 | −0.454822 | − | 0.890582i | \(-0.650297\pi\) | ||||
−0.454822 | + | 0.890582i | \(0.650297\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21529.7 | −1.20089 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 12142.2i | − | 0.674313i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2142.92i | 0.118489i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15848.6i | 0.872516i | 0.899822 | + | 0.436258i | \(0.143696\pi\) | ||||
−0.899822 | + | 0.436258i | \(0.856304\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4030.09 | − | 5585.88i | 0.220910 | − | 0.306190i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 18227.0i | − | 0.994805i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4488.98 | −0.243949 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.2634i | 0.00120469i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21638.9i | 1.16589i | 0.812511 | + | 0.582946i | \(0.198100\pi\) | ||||
−0.812511 | + | 0.582946i | \(0.801900\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1083.60 | −0.0581346 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22349.2i | 1.19393i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16425.0 | + | 22765.8i | −0.873729 | + | 1.21103i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15659.1i | 0.829462i | 0.909944 | + | 0.414731i | \(0.136124\pi\) | ||||
−0.909944 | + | 0.414731i | \(0.863876\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 10540.8i | − | 0.555992i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 31722.0i | − | 1.66620i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5206.08 | 0.272303 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8877.15 | −0.462376 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26401.4 | 1.36941 | 0.684705 | − | 0.728820i | \(-0.259931\pi\) | ||||
0.684705 | + | 0.728820i | \(0.259931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17796.3 | − | 24666.4i | 0.919236 | − | 1.27410i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16683.8 | −0.858197 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 10009.1i | − | 0.512728i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12097.7 | −0.617164 | −0.308582 | − | 0.951198i | \(-0.599854\pi\) | ||||
−0.308582 | + | 0.951198i | \(0.599854\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2193.97i | 0.111008i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32395.5 | −1.63241 | −0.816205 | − | 0.577762i | \(-0.803926\pi\) | ||||
−0.816205 | + | 0.577762i | \(0.803926\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15320.5 | + | 5090.72i | −0.768849 | + | 0.255475i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33898.0 | 1.69423 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3055.66 | 0.152103 | 0.0760516 | − | 0.997104i | \(-0.475769\pi\) | ||||
0.0760516 | + | 0.997104i | \(0.475769\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −245.869 | −0.0121892 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 31219.4i | − | 1.54149i | −0.637143 | − | 0.770746i | \(-0.719884\pi\) | ||
0.637143 | − | 0.770746i | \(-0.280116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10153.3i | 0.499311i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 4565.65i | − | 0.223625i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9759.79 | + | 13527.5i | −0.476122 | + | 0.659925i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19939.2i | 0.968830i | 0.874838 | + | 0.484415i | \(0.160968\pi\) | ||||
−0.874838 | + | 0.484415i | \(0.839032\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −389.446 | −0.0188475 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22898.7i | 1.10380i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27284.6i | 1.31001i | 0.755626 | + | 0.655004i | \(0.227333\pi\) | ||||
−0.755626 | + | 0.655004i | \(0.772667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25170.3 | 1.20372 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13346.7i | 0.635765i | 0.948130 | + | 0.317883i | \(0.102972\pi\) | ||||
−0.948130 | + | 0.317883i | \(0.897028\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24085.1 | − | 17376.9i | −1.14278 | − | 0.824488i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2008.04i | 0.0949032i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3417.81i | 0.160899i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 7158.77i | − | 0.335698i | −0.985813 | − | 0.167849i | \(-0.946318\pi\) | ||
0.985813 | − | 0.167849i | \(-0.0536821\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1024.06 | −0.0478347 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32460.8 | 1.51039 | 0.755196 | − | 0.655499i | \(-0.227542\pi\) | ||||
0.755196 | + | 0.655499i | \(0.227542\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18928.4 | 0.877325 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3451.37 | + | 4783.75i | −0.159353 | + | 0.220870i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3221.70 | 0.148176 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4543.81i | 0.208182i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2230.69 | −0.101811 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31206.4 | −1.41886 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4441.50i | 0.201172i | 0.994928 | + | 0.100586i | \(0.0320717\pi\) | ||||
−0.994928 | + | 0.100586i | \(0.967928\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1431.53 | 0.0645929 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8897.74 | + | 12332.6i | −0.399958 | + | 0.554359i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −66.7001 | −0.00298687 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12560.7 | −0.560353 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24575.5 | 1.09223 | 0.546115 | − | 0.837710i | \(-0.316106\pi\) | ||||
0.546115 | + | 0.837710i | \(0.316106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6752.65i | − | 0.298988i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 9557.89i | − | 0.421612i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2225.86i | − | 0.0978195i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −47842.6 | − | 34517.4i | −2.09470 | − | 1.51128i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 442.604i | 0.0193066i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41963.2 | 1.82367 | 0.911834 | − | 0.410560i | \(-0.134667\pi\) | ||||
0.911834 | + | 0.410560i | \(0.134667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22726.5i | 0.984015i | 0.870591 | + | 0.492007i | \(0.163737\pi\) | ||||
−0.870591 | + | 0.492007i | \(0.836263\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18214.5i | 0.785743i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 54327.4 | 2.33498 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1574.59i | − | 0.0674272i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −783.119 | + | 1085.44i | −0.0334120 | + | 0.0463104i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6589.44i | 0.280113i | 0.990143 | + | 0.140057i | \(0.0447285\pi\) | ||||
−0.990143 | + | 0.140057i | \(0.955272\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2131.91i | 0.0902961i | 0.998980 | + | 0.0451480i | \(0.0143760\pi\) | ||||
−0.998980 | + | 0.0451480i | \(0.985624\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15019.0i | 0.633810i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7776.80 | 0.326996 | 0.163498 | − | 0.986544i | \(-0.447722\pi\) | ||||
0.163498 | + | 0.986544i | \(0.447722\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35269.2 | 1.47762 | 0.738812 | − | 0.673911i | \(-0.235387\pi\) | ||||
0.738812 | + | 0.673911i | \(0.235387\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1707.64 | −0.0712844 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4628.97 | − | 1538.12i | 0.192538 | − | 0.0639769i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12962.4 | 0.537225 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 4218.50i | − | 0.174209i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40184.4 | −1.65354 | −0.826770 | − | 0.562540i | \(-0.809824\pi\) | ||||
−0.826770 | + | 0.562540i | \(0.809824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17563.3 | 0.720131 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 2353.89i | − | 0.0961711i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33457.4 | 1.36209 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4081.43 | + | 5657.04i | −0.165572 | + | 0.229490i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21376.8 | 0.864135 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21555.8 | −0.868302 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22397.6 | 0.899037 | 0.449518 | − | 0.893271i | \(-0.351596\pi\) | ||||
0.449518 | + | 0.893271i | \(0.351596\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1441.16i | − | 0.0576450i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 45332.7i | − | 1.80693i | −0.428665 | − | 0.903464i | \(-0.641016\pi\) | ||
0.428665 | − | 0.903464i | \(-0.358984\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 43758.8i | − | 1.73811i | −0.494720 | − | 0.869053i | \(-0.664729\pi\) | ||
0.494720 | − | 0.869053i | \(-0.335271\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10261.5 | − | 14222.8i | 0.406167 | − | 0.562965i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12274.9i | − | 0.484173i | −0.970255 | − | 0.242086i | \(-0.922168\pi\) | ||
0.970255 | − | 0.242086i | \(-0.0778317\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39395.8 | −1.54855 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14132.3i | 0.553584i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48398.3i | 1.88930i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6586.99 | −0.256248 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5159.87i | 0.200040i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −654.741 | + | 907.499i | −0.0252963 | + | 0.0350618i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 7854.33i | − | 0.302419i | −0.988502 | − | 0.151210i | \(-0.951683\pi\) | ||
0.988502 | − | 0.151210i | \(-0.0483169\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18209.6i | 0.698741i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18653.7i | 0.713347i | 0.934229 | + | 0.356673i | \(0.116089\pi\) | ||||
−0.934229 | + | 0.356673i | \(0.883911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33024.4 | 1.25862 | 0.629308 | − | 0.777156i | \(-0.283338\pi\) | ||||
0.629308 | + | 0.777156i | \(0.283338\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20033.4 | −0.760922 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17284.0 | −0.654272 | −0.327136 | − | 0.944977i | \(-0.606084\pi\) | ||||
−0.327136 | + | 0.944977i | \(0.606084\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36935.6 | − | 26648.2i | −1.39345 | − | 1.00535i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3347.22 | 0.125854 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4846.32i | 0.181608i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −60234.2 | −2.24962 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4891.04 | −0.182059 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 12908.3i | − | 0.478882i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3795.11 | 0.140326 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6951.35 | − | 5015.25i | −0.256176 | − | 0.184825i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10065.1 | 0.369697 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4574.90 | −0.167483 | −0.0837415 | − | 0.996488i | \(-0.526687\pi\) | ||||
−0.0837415 | + | 0.996488i | \(0.526687\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13641.9 | −0.497771 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33458.3i | 1.21682i | 0.793623 | + | 0.608410i | \(0.208192\pi\) | ||||
−0.793623 | + | 0.608410i | \(0.791808\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20963.3i | 0.759894i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 390.962i | − | 0.0141255i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15435.4 | + | 11136.3i | 0.555859 | + | 0.401040i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16910.7i | 0.607000i | 0.952832 | + | 0.303500i | \(0.0981552\pi\) | ||||
−0.952832 | + | 0.303500i | \(0.901845\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13966.0 | −0.499670 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 882.945i | − | 0.0314870i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 12862.3i | − | 0.457198i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14780.9 | 0.523697 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2636.58i | 0.0931145i | 0.998916 | + | 0.0465572i | \(0.0148250\pi\) | ||||
−0.998916 | + | 0.0465572i | \(0.985175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3322.17 | + | 1103.90i | −0.116949 | + | 0.0388601i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9232.48i | 0.323963i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 9219.99i | − | 0.322488i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 439.397i | − | 0.0153196i | −0.999971 | − | 0.00765980i | \(-0.997562\pi\) | ||
0.999971 | − | 0.00765980i | \(-0.00243822\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1455.26 | −0.0505758 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2110.06 | −0.0730989 | −0.0365494 | − | 0.999332i | \(-0.511637\pi\) | ||||
−0.0365494 | + | 0.999332i | \(0.511637\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 64088.9 | 2.21317 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6362.27 | − | 4590.24i | −0.219010 | − | 0.158011i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43359.1 | 1.48784 | 0.743919 | − | 0.668270i | \(-0.232965\pi\) | ||||
0.743919 | + | 0.668270i | \(0.232965\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 432.526i | 0.0147949i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26025.4 | −0.887415 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35158.7 | 1.19507 | 0.597535 | − | 0.801843i | \(-0.296147\pi\) | ||||
0.597535 | + | 0.801843i | \(0.296147\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 25748.0i | − | 0.872445i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10242.3 | 0.345961 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14870.0 | + | 20610.5i | −0.500707 | + | 0.694001i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5379.89 | −0.180588 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8106.07 | −0.271251 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35225.9 | −1.17509 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 20198.4i | − | 0.671702i | −0.941915 | − | 0.335851i | \(-0.890976\pi\) | ||
0.941915 | − | 0.335851i | \(-0.109024\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 435.434i | 0.0144357i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 30514.4i | − | 1.00850i | −0.863558 | − | 0.504250i | \(-0.831769\pi\) | ||
0.863558 | − | 0.504250i | \(-0.168231\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17448.8 | − | 12588.9i | −0.574906 | − | 0.414782i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 2918.46i | − | 0.0958619i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52407.4 | −1.71613 | −0.858067 | − | 0.513538i | \(-0.828334\pi\) | ||||
−0.858067 | + | 0.513538i | \(0.828334\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43885.3i | 1.43267i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 14432.5i | − | 0.469718i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33283.3 | −1.07993 | −0.539965 | − | 0.841687i | \(-0.681563\pi\) | ||||
−0.539965 | + | 0.841687i | \(0.681563\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 58964.1i | 1.90736i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21395.0 | + | 15436.1i | 0.689981 | + | 0.497807i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 31323.2i | − | 1.00710i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 7128.73i | − | 0.228508i | −0.993452 | − | 0.114254i | \(-0.963552\pi\) | ||
0.993452 | − | 0.114254i | \(-0.0364478\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 30284.2i | − | 0.967815i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 76790.7 | 2.44666 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9171.17 | 0.291328 | 0.145664 | − | 0.989334i | \(-0.453468\pi\) | ||||
0.145664 | + | 0.989334i | \(0.453468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2866.56 | −0.0907849 |
(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 | 1344.4.p.d.223.28 | yes | 32 | |
4.3 | odd | 2 | inner | 1344.4.p.d.223.23 | yes | 32 | |
7.6 | odd | 2 | 1344.4.p.c.223.21 | ✓ | 32 | ||
8.3 | odd | 2 | 1344.4.p.c.223.22 | yes | 32 | ||
8.5 | even | 2 | 1344.4.p.c.223.25 | yes | 32 | ||
28.27 | even | 2 | 1344.4.p.c.223.26 | yes | 32 | ||
56.13 | odd | 2 | inner | 1344.4.p.d.223.24 | yes | 32 | |
56.27 | even | 2 | inner | 1344.4.p.d.223.27 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.c.223.21 | ✓ | 32 | 7.6 | odd | 2 | ||
1344.4.p.c.223.22 | yes | 32 | 8.3 | odd | 2 | ||
1344.4.p.c.223.25 | yes | 32 | 8.5 | even | 2 | ||
1344.4.p.c.223.26 | yes | 32 | 28.27 | even | 2 | ||
1344.4.p.d.223.23 | yes | 32 | 4.3 | odd | 2 | inner | |
1344.4.p.d.223.24 | yes | 32 | 56.13 | odd | 2 | inner | |
1344.4.p.d.223.27 | yes | 32 | 56.27 | even | 2 | inner | |
1344.4.p.d.223.28 | yes | 32 | 1.1 | even | 1 | trivial |