Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,5,Mod(145,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.145");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.y (of order \(6\), degree \(2\), 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: | \(70.7050547493\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.12 | ||
Character | \(\chi\) | \(=\) | 684.145 |
Dual form | 684.5.y.f.217.12 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 22.6095 | + | 39.1607i | 0.904379 | + | 1.56643i | 0.821749 | + | 0.569850i | \(0.192999\pi\) |
0.0826297 | + | 0.996580i | \(0.473668\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 80.9352 | 1.65174 | 0.825870 | − | 0.563861i | \(-0.190685\pi\) | ||||
0.825870 | + | 0.563861i | \(0.190685\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −74.1039 | −0.612429 | −0.306214 | − | 0.951963i | \(-0.599062\pi\) | ||||
−0.306214 | + | 0.951963i | \(0.599062\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −249.736 | − | 144.185i | −1.47773 | − | 0.853168i | −0.478047 | − | 0.878335i | \(-0.658655\pi\) |
−0.999683 | + | 0.0251668i | \(0.991988\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 255.062 | + | 441.781i | 0.882568 | + | 1.52865i | 0.848475 | + | 0.529235i | \(0.177521\pi\) |
0.0340930 | + | 0.999419i | \(0.489146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −356.260 | + | 58.3104i | −0.986869 | + | 0.161525i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −122.424 | + | 212.044i | −0.231425 | + | 0.400839i | −0.958228 | − | 0.286007i | \(-0.907672\pi\) |
0.726803 | + | 0.686846i | \(0.241005\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −709.876 | + | 1229.54i | −1.13580 | + | 1.96727i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −932.845 | − | 538.578i | −1.10921 | − | 0.640402i | −0.170585 | − | 0.985343i | \(-0.554566\pi\) |
−0.938624 | + | 0.344941i | \(0.887899\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 96.0919i | − | 0.0999915i | −0.998749 | − | 0.0499958i | \(-0.984079\pi\) | ||
0.998749 | − | 0.0499958i | \(-0.0159208\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1829.90 | + | 3169.48i | 1.49380 | + | 2.58733i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1334.85i | 0.975058i | 0.873107 | + | 0.487529i | \(0.162102\pi\) | ||||
−0.873107 | + | 0.487529i | \(0.837898\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1755.03 | + | 1013.27i | −1.04404 | + | 0.602778i | −0.920975 | − | 0.389621i | \(-0.872606\pi\) |
−0.123066 | + | 0.992398i | \(0.539273\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1407.13 | − | 2437.22i | −0.761020 | − | 1.31813i | −0.942325 | − | 0.334699i | \(-0.891365\pi\) |
0.181305 | − | 0.983427i | \(-0.441968\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1409.02 | + | 2440.49i | −0.637854 | + | 1.10479i | 0.348049 | + | 0.937476i | \(0.386844\pi\) |
−0.985903 | + | 0.167319i | \(0.946489\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4149.51 | 1.72824 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −754.360 | − | 435.530i | −0.268551 | − | 0.155048i | 0.359678 | − | 0.933077i | \(-0.382887\pi\) |
−0.628229 | + | 0.778028i | \(0.716220\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1675.45 | − | 2901.96i | −0.553867 | − | 0.959326i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5311.50 | − | 3066.60i | 1.52586 | − | 0.880953i | 0.526326 | − | 0.850283i | \(-0.323569\pi\) |
0.999530 | − | 0.0306702i | \(-0.00976415\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.3481 | + | 24.8516i | −0.00385598 | + | 0.00667875i | −0.867947 | − | 0.496657i | \(-0.834561\pi\) |
0.864091 | + | 0.503336i | \(0.167894\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 13039.8i | − | 3.08635i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3618.21 | + | 2088.97i | 0.806016 | + | 0.465354i | 0.845571 | − | 0.533864i | \(-0.179260\pi\) |
−0.0395543 | + | 0.999217i | \(0.512594\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2892.44 | − | 1669.95i | 0.573783 | − | 0.331274i | −0.184876 | − | 0.982762i | \(-0.559188\pi\) |
0.758659 | + | 0.651488i | \(0.225855\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −457.115 | − | 791.747i | −0.0857788 | − | 0.148573i | 0.819944 | − | 0.572444i | \(-0.194005\pi\) |
−0.905723 | + | 0.423870i | \(0.860671\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5997.61 | −1.01157 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 413.941 | − | 238.989i | 0.0663261 | − | 0.0382934i | −0.466470 | − | 0.884537i | \(-0.654475\pi\) |
0.532796 | + | 0.846244i | \(0.321141\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1080.06 | −0.156781 | −0.0783903 | − | 0.996923i | \(-0.524978\pi\) | ||||
−0.0783903 | + | 0.996923i | \(0.524978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11533.6 | + | 19976.9i | −1.59635 | + | 2.76496i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10502.6 | + | 6063.65i | 1.32591 | + | 0.765516i | 0.984665 | − | 0.174457i | \(-0.0558171\pi\) |
0.341248 | + | 0.939973i | \(0.389150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20212.5 | − | 11669.7i | −2.44082 | − | 1.40921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10338.3 | − | 12633.0i | −1.14552 | − | 1.39978i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10463.6 | + | 6041.19i | −1.11209 | + | 0.642065i | −0.939370 | − | 0.342906i | \(-0.888589\pi\) |
−0.172719 | + | 0.984971i | \(0.555255\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1988.34 | + | 3443.91i | −0.194917 | + | 0.337606i | −0.946873 | − | 0.321607i | \(-0.895777\pi\) |
0.751957 | + | 0.659213i | \(0.229110\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11605.7i | 1.09395i | 0.837149 | + | 0.546975i | \(0.184221\pi\) | ||||
−0.837149 | + | 0.546975i | \(0.815779\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8776.07i | − | 0.766536i | −0.923637 | − | 0.383268i | \(-0.874799\pi\) | ||
0.923637 | − | 0.383268i | \(-0.125201\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7467.61 | + | 4311.42i | −0.628533 | + | 0.362884i | −0.780184 | − | 0.625550i | \(-0.784875\pi\) |
0.151650 | + | 0.988434i | \(0.451541\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10759.3i | − | 0.842609i | −0.906919 | − | 0.421305i | \(-0.861572\pi\) | ||
0.906919 | − | 0.421305i | \(-0.138428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11071.7 | −0.837182 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20643.5 | + | 35755.6i | 1.45777 | + | 2.52494i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9149.62 | −0.624931 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −35937.8 | −2.30002 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17433.4 | + | 10065.2i | 1.08087 | + | 0.624042i | 0.931132 | − | 0.364683i | \(-0.118823\pi\) |
0.149741 | + | 0.988725i | \(0.452156\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8527.03 | + | 14769.2i | 0.496884 | + | 0.860629i | 0.999994 | − | 0.00359405i | \(-0.00114402\pi\) |
−0.503109 | + | 0.864223i | \(0.667811\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −28833.9 | + | 4719.36i | −1.63005 | + | 0.266796i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1504.38 | − | 2605.67i | 0.0801526 | − | 0.138828i | −0.823163 | − | 0.567805i | \(-0.807793\pi\) |
0.903315 | + | 0.428977i | \(0.141126\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14478.5 | + | 25077.6i | −0.749368 | + | 1.29794i | 0.198758 | + | 0.980049i | \(0.436309\pi\) |
−0.948126 | + | 0.317895i | \(0.897024\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18506.4 | + | 10684.7i | 0.905004 | + | 0.522504i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 48707.9i | − | 2.31666i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2948.53 | − | 5107.00i | −0.132811 | − | 0.230035i | 0.791948 | − | 0.610588i | \(-0.209067\pi\) |
−0.924759 | + | 0.380553i | \(0.875734\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17146.3i | − | 0.752000i | −0.926620 | − | 0.376000i | \(-0.877299\pi\) | ||
0.926620 | − | 0.376000i | \(-0.122701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3763.03 | − | 2172.59i | 0.156630 | − | 0.0904302i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5645.97 | − | 9779.11i | −0.229055 | − | 0.396735i | 0.728473 | − | 0.685074i | \(-0.240230\pi\) |
−0.957528 | + | 0.288340i | \(0.906897\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9908.39 | + | 17161.8i | −0.382253 | + | 0.662082i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7367.31 | 0.277290 | 0.138645 | − | 0.990342i | \(-0.455725\pi\) | ||||
0.138645 | + | 0.990342i | \(0.455725\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11698.1 | + | 6753.93i | 0.419454 | + | 0.242172i | 0.694844 | − | 0.719161i | \(-0.255474\pi\) |
−0.275390 | + | 0.961333i | \(0.588807\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27298.3 | + | 47282.1i | 0.955790 | + | 1.65548i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3410.27 | − | 1968.92i | 0.113946 | − | 0.0657865i | −0.441944 | − | 0.897043i | \(-0.645711\pi\) |
0.555890 | + | 0.831256i | \(0.312378\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −57454.0 | + | 99513.2i | −1.87605 | + | 3.24941i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 54947.2i | 1.71490i | 0.514565 | + | 0.857451i | \(0.327953\pi\) | ||||
−0.514565 | + | 0.857451i | \(0.672047\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6115.34 | + | 3530.69i | 0.186665 | + | 0.107771i | 0.590420 | − | 0.807096i | \(-0.298962\pi\) |
−0.403755 | + | 0.914867i | \(0.632295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −52273.9 | + | 30180.4i | −1.52736 | + | 0.881822i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18901.1 | − | 32737.7i | −0.540510 | − | 0.936191i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25754.7 | 0.705975 | 0.352988 | − | 0.935628i | \(-0.385166\pi\) | ||||
0.352988 | + | 0.935628i | \(0.385166\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14871.2 | − | 8585.90i | 0.399238 | − | 0.230500i | −0.286917 | − | 0.957955i | \(-0.592630\pi\) |
0.686155 | + | 0.727455i | \(0.259297\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22172.8 | 0.571331 | 0.285666 | − | 0.958329i | \(-0.407785\pi\) | ||||
0.285666 | + | 0.958329i | \(0.407785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5574.48 | + | 9655.29i | −0.140766 | + | 0.243814i | −0.927785 | − | 0.373114i | \(-0.878290\pi\) |
0.787019 | + | 0.616929i | \(0.211623\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −75500.0 | − | 43590.0i | −1.83212 | − | 1.05778i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −79360.7 | − | 45818.9i | −1.88842 | − | 1.09028i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26400.2 | − | 4321.02i | 0.604387 | − | 0.0989222i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6725.42 | + | 3882.93i | −0.151062 | + | 0.0872156i | −0.573626 | − | 0.819118i | \(-0.694464\pi\) |
0.422564 | + | 0.906333i | \(0.361130\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 63628.8 | − | 110208.i | 1.37650 | − | 2.38417i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 7777.22i | − | 0.165160i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 147105.i | − | 3.01192i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9431.33 | + | 5445.18i | −0.189654 | + | 0.109497i | −0.591821 | − | 0.806070i | \(-0.701591\pi\) |
0.402166 | + | 0.915567i | \(0.368257\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 36261.1i | − | 0.703703i | −0.936056 | − | 0.351852i | \(-0.885552\pi\) | ||
0.936056 | − | 0.351852i | \(-0.114448\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −38554.9 | −0.735205 | −0.367603 | − | 0.929983i | \(-0.619821\pi\) | ||||
−0.367603 | + | 0.929983i | \(0.619821\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22940.1 | − | 39733.4i | −0.422555 | − | 0.731886i | 0.573634 | − | 0.819112i | \(-0.305533\pi\) |
−0.996189 | + | 0.0872256i | \(0.972200\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −127429. | −2.30744 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −44600.7 | −0.780812 | −0.390406 | − | 0.920643i | \(-0.627665\pi\) | ||||
−0.390406 | + | 0.920643i | \(0.627665\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 64615.1 | + | 37305.6i | 1.11250 | + | 0.642302i | 0.939476 | − | 0.342615i | \(-0.111313\pi\) |
0.173024 | + | 0.984918i | \(0.444646\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 93818.2 | + | 162498.i | 1.56299 | + | 2.70717i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 97378.5 | + | 36805.2i | 1.59613 | + | 0.603275i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −49554.2 | + | 85830.3i | −0.786562 | + | 1.36236i | 0.141500 | + | 0.989938i | \(0.454807\pi\) |
−0.928062 | + | 0.372426i | \(0.878526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9072.07 | − | 15713.3i | 0.141731 | − | 0.245485i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −79479.8 | − | 45887.7i | −1.20335 | − | 0.694752i | −0.242048 | − | 0.970264i | \(-0.577819\pi\) |
−0.961298 | + | 0.275512i | \(0.911153\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 108037.i | 1.61054i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1387.54 | − | 2403.29i | −0.0200602 | − | 0.0347452i | 0.855821 | − | 0.517272i | \(-0.173052\pi\) |
−0.875881 | + | 0.482527i | \(0.839719\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 39388.4i | − | 0.560889i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 109424. | − | 63175.9i | 1.51219 | − | 0.873065i | 0.512295 | − | 0.858810i | \(-0.328796\pi\) |
0.999898 | − | 0.0142555i | \(-0.00453783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −61390.2 | − | 106331.i | −0.835911 | − | 1.44784i | −0.893286 | − | 0.449488i | \(-0.851606\pi\) |
0.0573751 | − | 0.998353i | \(-0.481727\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 52604.6 | − | 91113.8i | 0.695597 | − | 1.20481i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32054.0 | −0.417756 | −0.208878 | − | 0.977942i | \(-0.566981\pi\) | ||||
−0.208878 | + | 0.977942i | \(0.566981\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 66717.7 | + | 38519.5i | 0.844945 | + | 0.487829i | 0.858942 | − | 0.512073i | \(-0.171122\pi\) |
−0.0139972 | + | 0.999902i | \(0.504456\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9079.82 | − | 15726.7i | −0.113372 | − | 0.196365i | 0.803756 | − | 0.594959i | \(-0.202832\pi\) |
−0.917128 | + | 0.398594i | \(0.869498\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −142044. | + | 82009.2i | −1.72448 | + | 0.995631i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −88353.0 | + | 153032.i | −1.05785 | + | 1.83226i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 63343.7i | 0.737850i | 0.929459 | + | 0.368925i | \(0.120274\pi\) | ||||
−0.929459 | + | 0.368925i | \(0.879726\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 240181. | + | 138668.i | 2.75990 | + | 1.59343i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 61147.3 | − | 35303.4i | 0.683966 | − | 0.394888i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −113886. | − | 197257.i | −1.25701 | − | 2.17720i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1297.61 | −0.0139491 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −43757.1 | + | 25263.2i | −0.464271 | + | 0.268047i | −0.713839 | − | 0.700310i | \(-0.753045\pi\) |
0.249567 | + | 0.968357i | \(0.419712\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −87150.9 | −0.901055 | −0.450527 | − | 0.892763i | \(-0.648764\pi\) | ||||
−0.450527 | + | 0.892763i | \(0.648764\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 43099.7 | − | 74650.9i | 0.439932 | − | 0.761985i | −0.557752 | − | 0.830008i | \(-0.688336\pi\) |
0.997684 | + | 0.0680232i | \(0.0216692\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 150310. | + | 86781.6i | 1.49579 | + | 0.863593i | 0.999988 | − | 0.00484511i | \(-0.00154225\pi\) |
0.495798 | + | 0.868438i | \(0.334876\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 69127.4 | + | 39910.7i | 0.679311 | + | 0.392201i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −116629. | − | 142516.i | −1.11789 | − | 1.36602i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 354564. | − | 204707.i | 3.35682 | − | 1.93806i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −114039. | + | 197522.i | −1.05357 | + | 1.82483i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 185379.i | − | 1.69201i | −0.533173 | − | 0.846006i | \(-0.679001\pi\) | ||
0.533173 | − | 0.846006i | \(-0.320999\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 188922.i | 1.68342i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 117923. | − | 68083.2i | 1.03834 | − | 0.599487i | 0.118979 | − | 0.992897i | \(-0.462038\pi\) |
0.919363 | + | 0.393410i | \(0.128705\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7120.78i | 0.0612377i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 141516. | 1.20287 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33006.4 | + | 57168.7i | 0.274119 | + | 0.474788i | 0.969912 | − | 0.243454i | \(-0.0782805\pi\) |
−0.695794 | + | 0.718242i | \(0.744947\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 88069.6 | 0.723061 | 0.361531 | − | 0.932360i | \(-0.382254\pi\) | ||||
0.361531 | + | 0.932360i | \(0.382254\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −46526.1 | −0.373377 | −0.186688 | − | 0.982419i | \(-0.559775\pi\) | ||||
−0.186688 | + | 0.982419i | \(0.559775\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 130793. | + | 75513.4i | 1.03783 | + | 0.599194i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1061.12 | − | 1837.91i | −0.00823333 | − | 0.0142606i | 0.861879 | − | 0.507113i | \(-0.169287\pi\) |
−0.870113 | + | 0.492853i | \(0.835954\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 123521. | − | 41547.2i | 0.947820 | − | 0.318807i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20670.3 | − | 35802.0i | 0.155153 | − | 0.268733i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −85852.7 | + | 148701.i | −0.637415 | + | 1.10403i | 0.348583 | + | 0.937278i | \(0.386663\pi\) |
−0.985998 | + | 0.166757i | \(0.946671\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −61054.3 | − | 35249.7i | −0.443576 | − | 0.256099i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 197021.i | − | 1.41611i | −0.706160 | − | 0.708053i | \(-0.749574\pi\) | ||
0.706160 | − | 0.708053i | \(-0.250426\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 155310. | + | 269005.i | 1.09274 | + | 1.89268i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 77106.2i | 0.536798i | 0.963308 | + | 0.268399i | \(0.0864946\pi\) | ||||
−0.963308 | + | 0.268399i | \(0.913505\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −78369.6 | + | 45246.7i | −0.534257 | + | 0.308453i | −0.742748 | − | 0.669571i | \(-0.766478\pi\) |
0.208491 | + | 0.978024i | \(0.433145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −135603. | − | 234871.i | −0.914844 | − | 1.58456i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 146861. | − | 254371.i | 0.970525 | − | 1.68100i | 0.276552 | − | 0.960999i | \(-0.410808\pi\) |
0.693974 | − | 0.720000i | \(-0.255858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −124903. | −0.816993 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18718.0 | + | 10806.8i | 0.119968 | + | 0.0692635i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 150469. | + | 260620.i | 0.954700 | + | 1.65359i | 0.735054 | + | 0.678009i | \(0.237157\pi\) |
0.219646 | + | 0.975580i | \(0.429510\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −183175. | + | 105756.i | −1.13914 | + | 0.657682i | −0.946217 | − | 0.323532i | \(-0.895130\pi\) |
−0.192921 | + | 0.981214i | \(0.561796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13855.0 | + | 23997.6i | −0.0853095 | + | 0.147760i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 98917.9i | − | 0.597154i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −104736. | − | 60469.2i | −0.626107 | − | 0.361483i | 0.153136 | − | 0.988205i | \(-0.451063\pi\) |
−0.779243 | + | 0.626722i | \(0.784396\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 429888. | − | 248196.i | 2.52032 | − | 1.45510i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24419.6 | − | 42296.0i | −0.141789 | − | 0.245586i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 63415.7 | 0.361218 | 0.180609 | − | 0.983555i | \(-0.442193\pi\) | ||||
0.180609 | + | 0.983555i | \(0.442193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −138630. | + | 80038.0i | −0.782155 | + | 0.451577i | −0.837194 | − | 0.546907i | \(-0.815805\pi\) |
0.0550384 | + | 0.998484i | \(0.482472\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −724250. | −4.00969 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1161.27 | + | 2011.37i | −0.00636907 | + | 0.0110316i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 281898. | + | 162754.i | 1.51753 | + | 0.876147i | 0.999788 | + | 0.0206104i | \(0.00656095\pi\) |
0.517743 | + | 0.855536i | \(0.326772\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −225615. | − | 130259.i | −1.20335 | − | 0.694755i | −0.242053 | − | 0.970263i | \(-0.577821\pi\) |
−0.961299 | + | 0.275508i | \(0.911154\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31250.2 | − | 82681.3i | 0.163640 | − | 0.432957i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 156044. | − | 90092.1i | 0.809689 | − | 0.467474i | −0.0371590 | − | 0.999309i | \(-0.511831\pi\) |
0.846848 | + | 0.531835i | \(0.178497\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 121785. | − | 210938.i | 0.620564 | − | 1.07485i | −0.368817 | − | 0.929502i | \(-0.620237\pi\) |
0.989381 | − | 0.145346i | \(-0.0464297\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 548384.i | 2.76927i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 108921.i | − | 0.540280i | −0.962821 | − | 0.270140i | \(-0.912930\pi\) | ||
0.962821 | − | 0.270140i | \(-0.0870699\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 130055. | − | 75087.1i | 0.639401 | − | 0.369158i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.05538e6i | − | 5.09784i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 243509. | 1.16596 | 0.582979 | − | 0.812488i | \(-0.301887\pi\) | ||||
0.582979 | + | 0.812488i | \(0.301887\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15578.6 | − | 26982.9i | −0.0733038 | − | 0.126966i | 0.827044 | − | 0.562138i | \(-0.190021\pi\) |
−0.900347 | + | 0.435172i | \(0.856688\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 281050. | 1.31106 | 0.655529 | − | 0.755170i | \(-0.272446\pi\) | ||||
0.655529 | + | 0.755170i | \(0.272446\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 69672.6 | 0.319469 | 0.159734 | − | 0.987160i | \(-0.448936\pi\) | ||||
0.159734 | + | 0.987160i | \(0.448936\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 292840. | + | 169071.i | 1.33133 | + | 0.768643i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 104274. | + | 180607.i | 0.466071 | + | 0.807258i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 181205. | − | 479429.i | 0.803125 | − | 2.12489i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −139152. | + | 241019.i | −0.606485 | + | 1.05046i | 0.385330 | + | 0.922779i | \(0.374088\pi\) |
−0.991815 | + | 0.127684i | \(0.959246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 192466. | − | 333362.i | 0.831888 | − | 1.44087i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −473155. | − | 273176.i | −2.01150 | − | 1.16134i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 189370.i | 0.798460i | 0.916851 | + | 0.399230i | \(0.130723\pi\) | ||||
−0.916851 | + | 0.399230i | \(0.869277\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 201087. | + | 348293.i | 0.834105 | + | 1.44471i | 0.894757 | + | 0.446554i | \(0.147349\pi\) |
−0.0606517 | + | 0.998159i | \(0.519318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 549484.i | − | 2.26080i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 234100. | − | 135158.i | 0.947740 | − | 0.547178i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16839.7 | + | 29167.2i | 0.0676290 | + | 0.117137i | 0.897857 | − | 0.440287i | \(-0.145123\pi\) |
−0.830228 | + | 0.557424i | \(0.811790\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −186494. | + | 323016.i | −0.737102 | + | 1.27670i | 0.216692 | + | 0.976240i | \(0.430473\pi\) |
−0.953795 | + | 0.300459i | \(0.902860\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −179822. | −0.705114 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 322491. | + | 186190.i | 1.24475 | + | 0.718656i | 0.970057 | − | 0.242877i | \(-0.0780912\pi\) |
0.274691 | + | 0.961533i | \(0.411425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36996.7 | − | 64080.2i | −0.141684 | − | 0.245404i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −454489. | + | 262399.i | −1.71360 | + | 0.989345i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 104414. | − | 180850.i | 0.390640 | − | 0.676608i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 158791.i | 0.584994i | 0.956266 | + | 0.292497i | \(0.0944861\pi\) | ||||
−0.956266 | + | 0.292497i | \(0.905514\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −87644.1 | − | 50601.4i | −0.320420 | − | 0.184994i | 0.331160 | − | 0.943575i | \(-0.392560\pi\) |
−0.651580 | + | 0.758580i | \(0.725893\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42451.5 | − | 24509.4i | 0.152852 | − | 0.0882494i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 109945. | + | 190431.i | 0.392885 | + | 0.680497i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 584394. | 2.05708 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 343678. | − | 198422.i | 1.20073 | − | 0.693239i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −307495. | −1.05842 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16520.2 | + | 28613.8i | −0.0564443 | + | 0.0977644i | −0.892867 | − | 0.450321i | \(-0.851310\pi\) |
0.836423 | + | 0.548085i | \(0.184643\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −337677. | − | 194958.i | −1.13686 | − | 0.656369i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −346166. | − | 199859.i | −1.15694 | − | 0.667959i | −0.206370 | − | 0.978474i | \(-0.566165\pi\) |
−0.950568 | + | 0.310515i | \(0.899498\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 363740. | + | 137479.i | 1.19808 | + | 0.452828i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33502.4 | − | 19342.6i | 0.109553 | − | 0.0632507i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −154975. | + | 268425.i | −0.499520 | + | 0.865193i | −1.00000 | 0.000554526i | \(-0.999823\pi\) | |
0.500480 | + | 0.865748i | \(0.333157\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 811548.i | 2.59711i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 333661.i | 1.05266i | 0.850280 | + | 0.526330i | \(0.176432\pi\) | ||||
−0.850280 | + | 0.526330i | \(0.823568\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 421341. | − | 243262.i | 1.31989 | − | 0.762038i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 199994.i | − | 0.617720i | −0.951107 | − | 0.308860i | \(-0.900053\pi\) | ||
0.951107 | − | 0.308860i | \(-0.0999475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −57688.4 | −0.176936 | −0.0884680 | − | 0.996079i | \(-0.528197\pi\) | ||||
−0.0884680 | + | 0.996079i | \(0.528197\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −173811. | − | 301050.i | −0.525705 | − | 0.910548i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 309540. | 0.929748 | 0.464874 | − | 0.885377i | \(-0.346100\pi\) | ||||
0.464874 | + | 0.885377i | \(0.346100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −87415.0 | −0.258961 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 55901.0 | + | 32274.5i | 0.164468 | + | 0.0949559i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 135516. | + | 234721.i | 0.393292 | + | 0.681201i | 0.992882 | − | 0.119106i | \(-0.0380029\pi\) |
−0.599590 | + | 0.800307i | \(0.704670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5603.15 | + | 34233.6i | 0.0161511 | + | 0.0986785i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −237698. | + | 411705.i | −0.675952 | + | 1.17078i | 0.300237 | + | 0.953865i | \(0.402934\pi\) |
−0.976190 | + | 0.216919i | \(0.930399\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −933478. | + | 1.61683e6i | −2.63676 | + | 4.56700i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 107867. | + | 62276.8i | 0.300631 | + | 0.173569i | 0.642726 | − | 0.766096i | \(-0.277803\pi\) |
−0.342095 | + | 0.939665i | \(0.611137\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 227894.i | − | 0.630934i | −0.948937 | − | 0.315467i | \(-0.897839\pi\) | ||
0.948937 | − | 0.315467i | \(-0.102161\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −206868. | − | 358306.i | −0.565175 | − | 0.978911i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16725.2i | 0.0453936i | 0.999742 | + | 0.0226968i | \(0.00722523\pi\) | ||||
−0.999742 | + | 0.0226968i | \(0.992775\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 703766. | − | 406320.i | 1.88515 | − | 1.08839i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −265181. | − | 459308.i | −0.705703 | − | 1.22231i | −0.966437 | − | 0.256903i | \(-0.917298\pi\) |
0.260734 | − | 0.965411i | \(-0.416036\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 88813.7 | − | 153830.i | 0.233297 | − | 0.404083i | −0.725479 | − | 0.688244i | \(-0.758382\pi\) |
0.958776 | + | 0.284161i | \(0.0917152\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −152148. | −0.397086 | −0.198543 | − | 0.980092i | \(-0.563621\pi\) | ||||
−0.198543 | + | 0.980092i | \(0.563621\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 850026. | + | 490763.i | 2.19006 | + | 1.26443i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −368863. | − | 638890.i | −0.944289 | − | 1.63556i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −589713. | + | 340471.i | −1.49053 | + | 0.860556i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −124898. | + | 216329.i | −0.313686 | + | 0.543320i | −0.979157 | − | 0.203103i | \(-0.934897\pi\) |
0.665471 | + | 0.746423i | \(0.268231\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 910273.i | 2.25748i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.03628e6 | − | 598298.i | −2.55388 | − | 1.47448i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −614771. | + | 354938.i | −1.49623 | + | 0.863846i | −0.999991 | − | 0.00434221i | \(-0.998618\pi\) |
−0.496235 | + | 0.868188i | \(0.665284\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 233098. | + | 403737.i | 0.563788 | + | 0.976510i | 0.997161 | + | 0.0752955i | \(0.0239900\pi\) |
−0.433373 | + | 0.901215i | \(0.642677\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 564612. | 1.34878 | 0.674391 | − | 0.738375i | \(-0.264406\pi\) | ||||
0.674391 | + | 0.738375i | \(0.264406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −393603. | + | 227247.i | −0.934478 | + | 0.539521i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 270597. | 0.634595 | 0.317298 | − | 0.948326i | \(-0.397225\pi\) | ||||
0.317298 | + | 0.948326i | \(0.397225\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −385583. | + | 667850.i | −0.898743 | + | 1.55667i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −226186. | − | 130588.i | −0.520828 | − | 0.300700i | 0.216445 | − | 0.976295i | \(-0.430554\pi\) |
−0.737274 | + | 0.675594i | \(0.763887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 155129. | + | 89564.0i | 0.355051 | + | 0.204989i | 0.666908 | − | 0.745140i | \(-0.267617\pi\) |
−0.311856 | + | 0.950129i | \(0.600951\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −836734. | − | 1.02246e6i | −1.89210 | − | 2.31207i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 228405. | − | 131869.i | 0.513397 | − | 0.296410i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1063.25 | − | 1841.60i | 0.00236151 | − | 0.00409026i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 42358.2i | − | 0.0935207i | −0.998906 | − | 0.0467603i | \(-0.985110\pi\) | ||
0.998906 | − | 0.0467603i | \(-0.0148897\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 517746.i | − | 1.12964i | −0.825215 | − | 0.564819i | \(-0.808946\pi\) | ||
0.825215 | − | 0.564819i | \(-0.191054\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −846877. | + | 488945.i | −1.83688 | + | 1.06052i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 342764.i | − | 0.734775i | −0.930068 | − | 0.367387i | \(-0.880252\pi\) | ||
0.930068 | − | 0.367387i | \(-0.119748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 136053. | 0.289953 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 125594. | + | 217535.i | 0.264564 | + | 0.458238i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 322926. | 0.676311 | 0.338156 | − | 0.941090i | \(-0.390197\pi\) | ||||
0.338156 | + | 0.941090i | \(0.390197\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.30941e6 | −2.71085 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −895286. | − | 516893.i | −1.84288 | − | 1.06398i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 359397. | + | 622494.i | 0.731372 | + | 1.26677i | 0.956297 | + | 0.292398i | \(0.0944532\pi\) |
−0.224924 | + | 0.974376i | \(0.572214\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −77835.9 | − | 475555.i | −0.157496 | − | 0.962255i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −160927. | + | 278734.i | −0.321951 | + | 0.557636i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 394995. | − | 684151.i | 0.785776 | − | 1.36100i | −0.142759 | − | 0.989758i | \(-0.545597\pi\) |
0.928535 | − | 0.371246i | \(-0.121069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20375.7 | + | 11763.9i | 0.0400805 | + | 0.0231405i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 966301.i | 1.89017i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 188294. | + | 326135.i | 0.364233 | + | 0.630869i | 0.988653 | − | 0.150219i | \(-0.0479980\pi\) |
−0.624420 | + | 0.781089i | \(0.714665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 939311.i | 1.80692i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.32441e6 | − | 764648.i | 2.51968 | − | 1.45474i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 310749. | + | 538233.i | 0.587950 | + | 1.01836i | 0.994501 | + | 0.104731i | \(0.0333983\pi\) |
−0.406550 | + | 0.913628i | \(0.633268\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 717810. | − | 1.24328e6i | 1.34331 | − | 2.32667i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −409694. | −0.762521 | −0.381261 | − | 0.924468i | \(-0.624510\pi\) | ||||
−0.381261 | + | 0.924468i | \(0.624510\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −268123. | − | 154801.i | −0.493627 | − | 0.284996i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6909.45 | + | 11967.5i | 0.0126519 | + | 0.0219137i | 0.872282 | − | 0.489003i | \(-0.162639\pi\) |
−0.859630 | + | 0.510917i | \(0.829306\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −66341.6 | + | 38302.4i | −0.120173 | + | 0.0693822i | −0.558882 | − | 0.829247i | \(-0.688769\pi\) |
0.438708 | + | 0.898629i | \(0.355436\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 133329. | − | 230933.i | 0.240222 | − | 0.416077i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 710294.i | − | 1.26612i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 462729. | + | 267157.i | 0.820440 | + | 0.473681i | 0.850568 | − | 0.525865i | \(-0.176258\pi\) |
−0.0301283 | + | 0.999546i | \(0.509592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 671464. | − | 387670.i | 1.17795 | − | 0.680093i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −386193. | − | 668905.i | −0.673926 | − | 1.16727i | −0.976782 | − | 0.214237i | \(-0.931273\pi\) |
0.302856 | − | 0.953036i | \(-0.402060\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 134628. | 0.232469 | 0.116235 | − | 0.993222i | \(-0.462918\pi\) | ||||
0.116235 | + | 0.993222i | \(0.462918\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −604392. | + | 348946.i | −1.03817 | + | 0.599390i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.76863e6 | −3.00640 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14900.5 | − | 25808.5i | 0.0251970 | − | 0.0436425i | −0.853152 | − | 0.521663i | \(-0.825312\pi\) |
0.878349 | + | 0.478020i | \(0.158645\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −789192. | − | 455640.i | −1.32076 | − | 0.762541i | −0.336910 | − | 0.941537i | \(-0.609382\pi\) |
−0.983850 | + | 0.178996i | \(0.942715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 118149. | + | 68213.3i | 0.196710 | + | 0.113571i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 566163. | − | 463323.i | 0.932968 | − | 0.763501i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −214341. | + | 123750.i | −0.351401 | + | 0.202881i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 255305. | − | 442201.i | 0.414305 | − | 0.717597i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 398175.i | − | 0.642872i | −0.946931 | − | 0.321436i | \(-0.895834\pi\) | ||
0.946931 | − | 0.321436i | \(-0.104166\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 870805.i | − | 1.39177i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7166.48 | − | 4137.57i | 0.0113962 | − | 0.00657959i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 85943.7i | 0.135300i | 0.997709 | + | 0.0676499i | \(0.0215501\pi\) | ||||
−0.997709 | + | 0.0676499i | \(0.978450\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.43755e6 | −2.25180 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33874.0 | + | 58671.5i | 0.0525334 | + | 0.0909905i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −896093. | −1.38281 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 593956. | 0.907522 | 0.453761 | − | 0.891123i | \(-0.350082\pi\) | ||||
0.453761 | + | 0.891123i | \(0.350082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 801583. | + | 462794.i | 1.21873 | + | 0.703633i | 0.964646 | − | 0.263550i | \(-0.0848933\pi\) |
0.254082 | + | 0.967183i | \(0.418227\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 166571. | + | 288509.i | 0.250775 | + | 0.434355i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 643417. | + | 786231.i | 0.963937 | + | 1.17789i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −434476. | + | 752534.i | −0.644584 | + | 1.11645i | 0.339814 | + | 0.940493i | \(0.389636\pi\) |
−0.984398 | + | 0.175959i | \(0.943697\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 510698. | − | 884555.i | 0.753988 | − | 1.30595i | −0.191888 | − | 0.981417i | \(-0.561461\pi\) |
0.945876 | − | 0.324529i | \(-0.105206\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 799326. | + | 461491.i | 1.16873 | + | 0.674765i | 0.953380 | − | 0.301773i | \(-0.0975785\pi\) |
0.215347 | + | 0.976538i | \(0.430912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 390005.i | − | 0.567494i | −0.958899 | − | 0.283747i | \(-0.908422\pi\) | ||
0.958899 | − | 0.283747i | \(-0.0915776\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.05838e6 | + | 1.83317e6i | 1.52529 | + | 2.64188i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 610811.i | 0.876060i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −361978. | + | 208988.i | −0.514232 | + | 0.296892i | −0.734571 | − | 0.678531i | \(-0.762617\pi\) |
0.220340 | + | 0.975423i | \(0.429283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 226493. | + | 392297.i | 0.320230 | + | 0.554655i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.23440e6 | + | 2.13805e6i | −1.72879 | + | 2.99436i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −740526. | −1.03222 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −283048. | − | 163418.i | −0.390842 | − | 0.225653i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 203831. | + | 353045.i | 0.280138 | + | 0.485213i | 0.971419 | − | 0.237373i | \(-0.0762865\pi\) |
−0.691281 | + | 0.722586i | \(0.742953\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 959729. | − | 554100.i | 1.30673 | − | 0.754443i | 0.325184 | − | 0.945651i | \(-0.394574\pi\) |
0.981550 | + | 0.191208i | \(0.0612405\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 104151. | − | 180394.i | 0.141148 | − | 0.244476i | −0.786781 | − | 0.617232i | \(-0.788254\pi\) |
0.927929 | + | 0.372756i | \(0.121587\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 90149.7i | − | 0.121044i | −0.998167 | − | 0.0605219i | \(-0.980723\pi\) | ||
0.998167 | − | 0.0605219i | \(-0.0192765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 154209. | + | 89032.6i | 0.206100 | + | 0.118992i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30674.7 | + | 17710.0i | −0.0406200 | + | 0.0234520i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −602398. | − | 1.04338e6i | −0.794049 | − | 1.37533i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.90864e6 | −3.79904 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −311539. | + | 179867.i | −0.405055 | + | 0.233858i | −0.688663 | − | 0.725082i | \(-0.741802\pi\) |
0.283608 | + | 0.958940i | \(0.408469\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 671185. | 0.864750 | 0.432375 | − | 0.901694i | \(-0.357676\pi\) | ||||
0.432375 | + | 0.901694i | \(0.357676\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 347001. | − | 601024.i | 0.445051 | − | 0.770851i | −0.553005 | − | 0.833178i | \(-0.686519\pi\) |
0.998056 | + | 0.0623271i | \(0.0198522\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 520884. | + | 300732.i | 0.662054 | + | 0.382237i | 0.793059 | − | 0.609145i | \(-0.208487\pi\) |
−0.131005 | + | 0.991382i | \(0.541820\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.41098e6 | + | 814627.i | 1.78532 | + | 1.03075i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 359670. | − | 951609.i | 0.451026 | − | 1.19332i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.15177e6 | + | 1.24233e6i | −2.68628 | + | 1.55092i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −51753.0 | + | 89638.8i | −0.0640348 | + | 0.110912i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 444349.i | − | 0.547362i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 319308.i | 0.389864i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.25753e6 | − | 726034.i | 1.52863 | − | 0.882556i | 0.529212 | − | 0.848490i | \(-0.322488\pi\) |
0.999420 | − | 0.0340662i | \(-0.0108457\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 405570.i | 0.488685i | 0.969689 | + | 0.244343i | \(0.0785721\pi\) | ||||
−0.969689 | + | 0.244343i | \(0.921428\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 80036.8 | 0.0960169 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 690137. | + | 1.19535e6i | 0.820723 | + | 1.42153i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −567985. | −0.672521 | −0.336260 | − | 0.941769i | \(-0.609162\pi\) | ||||
−0.336260 | + | 0.941769i | \(0.609162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −963130. | −1.13053 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.64126e6 | − | 947581.i | −1.91820 | − | 1.10747i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 548586. | + | 950180.i | 0.635643 | + | 1.10097i | 0.986378 | + | 0.164492i | \(0.0525985\pi\) |
−0.350735 | + | 0.936475i | \(0.614068\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.47830e6 | + | 241959.i | −1.70555 | + | 0.279154i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 854688. | − | 1.48036e6i | 0.977652 | − | 1.69334i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 243059. | − | 420990.i | 0.276842 | − | 0.479505i | −0.693756 | − | 0.720210i | \(-0.744045\pi\) |
0.970598 | + | 0.240705i | \(0.0773787\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −594241. | − | 343085.i | −0.671094 | − | 0.387456i | 0.125397 | − | 0.992107i | \(-0.459980\pi\) |
−0.796491 | + | 0.604650i | \(0.793313\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 496193.i | − | 0.557991i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 144312. | + | 249956.i | 0.160918 | + | 0.278717i | 0.935198 | − | 0.354125i | \(-0.115221\pi\) |
−0.774280 | + | 0.632843i | \(0.781888\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 263637.i | 0.292735i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.39296e6 | + | 804224.i | −1.53374 | + | 0.885505i | −0.534556 | + | 0.845133i | \(0.679521\pi\) |
−0.999185 | + | 0.0403720i | \(0.987146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 582300. | + | 1.00857e6i | 0.638469 | + | 1.10586i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 121758. | − | 210890.i | 0.132391 | − | 0.229308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 914287. | 0.990002 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 672460. | + | 388245.i | 0.722124 | + | 0.416919i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 84060.1 | + | 145596.i | 0.0898953 | + | 0.155703i | 0.907467 | − | 0.420124i | \(-0.138013\pi\) |
−0.817571 | + | 0.575827i | \(0.804680\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −745165. | + | 430221.i | −0.790340 | + | 0.456303i | −0.840082 | − | 0.542459i | \(-0.817493\pi\) |
0.0497423 | + | 0.998762i | \(0.484160\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.17182e6 | + | 2.02966e6i | −1.23776 | + | 2.14386i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 612468.i | − | 0.641644i | −0.947140 | − | 0.320822i | \(-0.896041\pi\) | ||
0.947140 | − | 0.320822i | \(-0.103959\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −778280. | − | 449340.i | −0.812027 | − | 0.468824i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −335085. | + | 193461.i | −0.346775 | + | 0.200211i | −0.663264 | − | 0.748386i | \(-0.730829\pi\) |
0.316489 | + | 0.948596i | \(0.397496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 501315. | + | 868303.i | 0.516700 | + | 0.894950i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 689063. | 0.704476 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22518.6 | − | 13001.1i | 0.0229295 | − | 0.0132384i | −0.488491 | − | 0.872569i | \(-0.662453\pi\) |
0.511421 | + | 0.859330i | \(0.329119\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −504144. | −0.509224 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40472.2 | + | 70100.0i | −0.0407162 | + | 0.0705225i | −0.885665 | − | 0.464324i | \(-0.846297\pi\) |
0.844949 | + | 0.534847i | \(0.179631\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.5.y.f.145.12 | yes | 24 | |
3.2 | odd | 2 | inner | 684.5.y.f.145.1 | ✓ | 24 | |
19.8 | odd | 6 | inner | 684.5.y.f.217.12 | yes | 24 | |
57.8 | even | 6 | inner | 684.5.y.f.217.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.5.y.f.145.1 | ✓ | 24 | 3.2 | odd | 2 | inner | |
684.5.y.f.145.12 | yes | 24 | 1.1 | even | 1 | trivial | |
684.5.y.f.217.1 | yes | 24 | 57.8 | even | 6 | inner | |
684.5.y.f.217.12 | yes | 24 | 19.8 | odd | 6 | inner |