Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,5,Mod(145,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("336.145");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bh (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.7323075962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 241.2 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.241 |
Dual form | 336.5.bh.d.145.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 4.50000 | + | 2.59808i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.2574 | + | 7.07679i | −0.490294 | + | 0.283072i | −0.724697 | − | 0.689068i | \(-0.758020\pi\) |
0.234402 | + | 0.972140i | \(0.424687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.1985 | − | 47.4573i | −0.248949 | − | 0.968517i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 13.5000 | + | 23.3827i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 32.0147 | − | 55.4511i | 0.264584 | − | 0.458274i | −0.702870 | − | 0.711318i | \(-0.748099\pi\) |
0.967455 | + | 0.253044i | \(0.0814319\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 228.919i | 1.35455i | 0.735729 | + | 0.677276i | \(0.236839\pi\) | ||||
−0.735729 | + | 0.677276i | \(0.763161\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −73.5442 | −0.326863 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −195.250 | − | 112.728i | −0.675605 | − | 0.390061i | 0.122592 | − | 0.992457i | \(-0.460879\pi\) |
−0.798197 | + | 0.602397i | \(0.794213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 255.250 | − | 147.369i | 0.707063 | − | 0.408223i | −0.102910 | − | 0.994691i | \(-0.532815\pi\) |
0.809973 | + | 0.586468i | \(0.199482\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 68.4045 | − | 245.251i | 0.155112 | − | 0.556124i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 354.749 | + | 614.444i | 0.670604 | + | 1.16152i | 0.977733 | + | 0.209852i | \(0.0672982\pi\) |
−0.307129 | + | 0.951668i | \(0.599368\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −212.338 | + | 367.780i | −0.339741 | + | 0.588449i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 740.397 | 0.880377 | 0.440188 | − | 0.897905i | \(-0.354912\pi\) | ||||
0.440188 | + | 0.897905i | \(0.354912\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 577.390 | + | 333.356i | 0.600822 | + | 0.346885i | 0.769365 | − | 0.638809i | \(-0.220573\pi\) |
−0.168543 | + | 0.985694i | \(0.553906\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 288.132 | − | 166.353i | 0.264584 | − | 0.152758i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 485.367 | + | 495.375i | 0.396218 | + | 0.404388i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 416.882 | + | 722.061i | 0.304516 | + | 0.527437i | 0.977153 | − | 0.212535i | \(-0.0681720\pi\) |
−0.672638 | + | 0.739972i | \(0.734839\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −594.749 | + | 1030.14i | −0.391025 | + | 0.677276i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2817.60i | 1.67615i | 0.545558 | + | 0.838073i | \(0.316318\pi\) | ||||
−0.545558 | + | 0.838073i | \(0.683682\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3066.41 | −1.65841 | −0.829207 | − | 0.558942i | \(-0.811207\pi\) | ||||
−0.829207 | + | 0.558942i | \(0.811207\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −330.949 | − | 191.073i | −0.163431 | − | 0.0943572i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 531.502 | − | 306.863i | 0.240608 | − | 0.138915i | −0.374848 | − | 0.927086i | \(-0.622305\pi\) |
0.615456 | + | 0.788171i | \(0.288972\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2103.39 | + | 1157.81i | −0.876049 | + | 0.482222i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −585.749 | − | 1014.55i | −0.225202 | − | 0.390061i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 576.300 | − | 998.181i | 0.205162 | − | 0.355351i | −0.745022 | − | 0.667040i | \(-0.767561\pi\) |
0.950184 | + | 0.311688i | \(0.100895\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 906.246i | 0.299585i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1531.50 | 0.471375 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3024.67 | + | 1746.30i | 0.868909 | + | 0.501665i | 0.866986 | − | 0.498333i | \(-0.166054\pi\) |
0.00192348 | + | 0.999998i | \(0.499388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1967.79 | − | 1136.11i | 0.528834 | − | 0.305323i | −0.211707 | − | 0.977333i | \(-0.567902\pi\) |
0.740542 | + | 0.672010i | \(0.234569\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 945.000 | − | 925.907i | 0.238095 | − | 0.233285i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1620.01 | − | 2805.94i | −0.383435 | − | 0.664129i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4337.31 | + | 7512.44i | −0.966208 | + | 1.67352i | −0.259874 | + | 0.965642i | \(0.583681\pi\) |
−0.706334 | + | 0.707879i | \(0.749652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3686.66i | 0.774346i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 353.591 | 0.0701431 | 0.0350715 | − | 0.999385i | \(-0.488834\pi\) | ||||
0.0350715 | + | 0.999385i | \(0.488834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3524.68 | + | 2034.97i | 0.661415 | + | 0.381868i | 0.792816 | − | 0.609461i | \(-0.208614\pi\) |
−0.131401 | + | 0.991329i | \(0.541948\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1911.04 | + | 1103.34i | −0.339741 | + | 0.196150i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3022.09 | − | 842.913i | −0.509714 | − | 0.142168i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3236.41 | + | 5605.63i | 0.518573 | + | 0.898194i | 0.999767 | + | 0.0215805i | \(0.00686981\pi\) |
−0.481194 | + | 0.876614i | \(0.659797\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −364.500 | + | 631.333i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8225.83i | − | 1.19405i | −0.802222 | − | 0.597026i | \(-0.796349\pi\) | ||
0.802222 | − | 0.597026i | \(-0.203651\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3191.00 | 0.441660 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3331.79 | + | 1923.61i | 0.440188 | + | 0.254143i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13456.5 | + | 7769.13i | −1.69884 | + | 0.980828i | −0.751983 | + | 0.659183i | \(0.770902\pi\) |
−0.946860 | + | 0.321645i | \(0.895764\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10863.9 | − | 2792.47i | 1.31191 | − | 0.337214i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1732.17 | + | 3000.21i | 0.200274 | + | 0.346885i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2085.79 | + | 3612.70i | −0.231113 | + | 0.400299i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1558.61i | − | 0.165651i | −0.996564 | − | 0.0828254i | \(-0.973606\pi\) | ||
0.996564 | − | 0.0828254i | \(-0.0263944\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1728.79 | 0.176390 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13627.2 | + | 7867.66i | 1.33587 | + | 0.771264i | 0.986192 | − | 0.165607i | \(-0.0529583\pi\) |
0.349676 | + | 0.936871i | \(0.386292\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −29.2099 | + | 16.8644i | −0.00275332 | + | 0.00158963i | −0.501376 | − | 0.865229i | \(-0.667173\pi\) |
0.498623 | + | 0.866819i | \(0.333839\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 897.127 | + | 3490.21i | 0.0813721 | + | 0.316572i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2723.23 | − | 4716.78i | −0.237858 | − | 0.411981i | 0.722242 | − | 0.691641i | \(-0.243112\pi\) |
−0.960099 | + | 0.279659i | \(0.909778\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8348.89 | + | 14460.7i | −0.702709 | + | 1.21713i | 0.264803 | + | 0.964303i | \(0.414693\pi\) |
−0.967512 | + | 0.252825i | \(0.918640\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4332.37i | 0.351625i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9455.64 | 0.740515 | 0.370258 | − | 0.928929i | \(-0.379269\pi\) | ||||
0.370258 | + | 0.928929i | \(0.379269\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8696.58 | − | 5020.97i | −0.657586 | − | 0.379658i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5352.74 | + | 3090.41i | −0.391025 | + | 0.225759i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2967.99 | + | 10641.1i | −0.209589 | + | 0.751440i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5270.62 | + | 9128.97i | 0.359990 | + | 0.623521i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7320.35 | + | 12679.2i | −0.483862 | + | 0.838073i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 14856.7i | − | 0.950827i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2380.07 | 0.147564 | 0.0737822 | − | 0.997274i | \(-0.476493\pi\) | ||||
0.0737822 | + | 0.997274i | \(0.476493\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13798.8 | − | 7966.76i | −0.829207 | − | 0.478743i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3758.37 | − | 2169.90i | 0.219006 | − | 0.126443i | −0.386484 | − | 0.922296i | \(-0.626310\pi\) |
0.605490 | + | 0.795853i | \(0.292977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10107.4 | − | 10315.8i | −0.571393 | − | 0.583176i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −992.846 | − | 1719.66i | −0.0544772 | − | 0.0943572i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15379.6 | − | 26638.2i | 0.819414 | − | 1.41927i | −0.0867001 | − | 0.996234i | \(-0.527632\pi\) |
0.906114 | − | 0.423033i | \(-0.139034\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 27186.6i | 1.40710i | 0.710644 | + | 0.703551i | \(0.248404\pi\) | ||||
−0.710644 | + | 0.703551i | \(0.751596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3189.01 | 0.160405 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12693.8 | + | 7328.78i | 0.620755 | + | 0.358393i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9075.31 | + | 5239.63i | −0.431644 | + | 0.249210i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12473.4 | − | 254.611i | −0.577230 | − | 0.0117827i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2913.46 | + | 5046.26i | 0.131231 | + | 0.227299i | 0.924151 | − | 0.382027i | \(-0.124774\pi\) |
−0.792920 | + | 0.609325i | \(0.791440\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12593.4 | − | 21812.4i | 0.552317 | − | 0.956642i | −0.445789 | − | 0.895138i | \(-0.647077\pi\) |
0.998107 | − | 0.0615039i | \(-0.0195897\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6087.29i | − | 0.260040i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9436.37 | −0.392773 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20694.6 | + | 11948.0i | 0.839571 | + | 0.484726i | 0.857118 | − | 0.515120i | \(-0.172253\pi\) |
−0.0175475 | + | 0.999846i | \(0.505586\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5186.70 | − | 2994.54i | 0.205162 | − | 0.118450i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24832.5 | − | 24330.7i | 0.958005 | − | 0.938650i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21293.0 | − | 36880.5i | −0.801422 | − | 1.38810i | −0.918680 | − | 0.395001i | \(-0.870744\pi\) |
0.117259 | − | 0.993101i | \(-0.462589\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2354.50 | + | 4078.11i | −0.0864828 | + | 0.149793i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 26356.3i | − | 0.945043i | −0.881319 | − | 0.472521i | \(-0.843344\pi\) | ||
0.881319 | − | 0.472521i | \(-0.156656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23843.0 | −0.834809 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6891.74 | + | 3978.95i | 0.235688 | + | 0.136074i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24265.3 | − | 14009.6i | 0.810763 | − | 0.468094i | −0.0364578 | − | 0.999335i | \(-0.511607\pi\) |
0.847221 | + | 0.531241i | \(0.178274\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20044.1 | + | 5590.63i | 0.654500 | + | 0.182551i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9074.02 | + | 15716.7i | 0.289636 | + | 0.501665i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12699.2 | − | 21995.7i | 0.396343 | − | 0.686487i | −0.596928 | − | 0.802295i | \(-0.703612\pi\) |
0.993272 | + | 0.115808i | \(0.0369457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 44097.2i | − | 1.34603i | −0.739630 | − | 0.673014i | \(-0.764999\pi\) | ||
0.739630 | − | 0.673014i | \(-0.235001\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11806.8 | 0.352556 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10219.8 | − | 5900.38i | −0.298605 | − | 0.172400i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12501.7 | + | 7217.88i | −0.357509 | + | 0.206408i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6658.08 | − | 1711.40i | 0.186391 | − | 0.0479102i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −32279.6 | − | 55909.8i | −0.884832 | − | 1.53257i | −0.845906 | − | 0.533332i | \(-0.820940\pi\) |
−0.0389256 | − | 0.999242i | \(-0.512394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18337.3 | + | 31761.1i | −0.492290 | + | 0.852670i | −0.999961 | − | 0.00888055i | \(-0.997173\pi\) |
0.507671 | + | 0.861551i | \(0.330507\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 16835.7i | − | 0.442753i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −73147.0 | −1.88480 | −0.942398 | − | 0.334494i | \(-0.891434\pi\) | ||||
−0.942398 | + | 0.334494i | \(0.891434\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1213.33 | + | 700.514i | 0.0306387 | + | 0.0176893i | 0.515241 | − | 0.857045i | \(-0.327702\pi\) |
−0.484602 | + | 0.874735i | \(0.661036\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −39035.8 | + | 22537.3i | −0.966208 | + | 0.557840i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9031.72 | − | 35137.3i | −0.219169 | − | 0.852660i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19939.6 | − | 34536.4i | −0.474469 | − | 0.821805i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9578.23 | + | 16590.0i | −0.223535 | + | 0.387173i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 18871.8i | − | 0.432038i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −58231.7 | −1.30796 | −0.653980 | − | 0.756512i | \(-0.726902\pi\) | ||||
−0.653980 | + | 0.756512i | \(0.726902\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1591.16 | + | 918.657i | 0.0350715 | + | 0.0202486i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 37586.1 | − | 21700.3i | 0.813111 | − | 0.469450i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8776.92 | − | 31467.8i | 0.186390 | − | 0.668263i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10574.0 | + | 18314.8i | 0.220472 | + | 0.381868i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25805.5 | − | 44696.4i | 0.528357 | − | 0.915141i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 61050.9i | 1.22767i | 0.789434 | + | 0.613836i | \(0.210374\pi\) | ||||
−0.789434 | + | 0.613836i | \(0.789626\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11466.3 | −0.226494 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21645.2 | − | 12496.8i | −0.420058 | − | 0.242520i | 0.275044 | − | 0.961432i | \(-0.411307\pi\) |
−0.695102 | + | 0.718911i | \(0.744641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16392.9 | + | 9464.44i | −0.312597 | + | 0.180478i | −0.648088 | − | 0.761565i | \(-0.724431\pi\) |
0.335491 | + | 0.942043i | \(0.391098\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11409.5 | − | 11644.7i | −0.213817 | − | 0.218226i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3342.37 | − | 5789.15i | −0.0615662 | − | 0.106636i | 0.833599 | − | 0.552369i | \(-0.186276\pi\) |
−0.895166 | + | 0.445734i | \(0.852943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4343.21 | + | 7522.66i | −0.0786457 | + | 0.136218i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33633.8i | 0.598796i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 96461.0 | 1.68871 | 0.844356 | − | 0.535782i | \(-0.179983\pi\) | ||||
0.844356 | + | 0.535782i | \(0.179983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 47371.8 | + | 27350.1i | 0.815616 | + | 0.470896i | 0.848902 | − | 0.528550i | \(-0.177264\pi\) |
−0.0332863 | + | 0.999446i | \(0.510597\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3280.50 | + | 1894.00i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17588.4 | − | 29077.0i | 0.293019 | − | 0.484415i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33735.5 | + | 58431.6i | 0.552959 | + | 0.957753i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21371.3 | − | 37016.2i | 0.344693 | − | 0.597026i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 108137.i | − | 1.71643i | −0.513286 | − | 0.858217i | \(-0.671572\pi\) | ||
0.513286 | − | 0.858217i | \(-0.328428\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 45428.8 | 0.709725 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14359.5 | + | 8290.45i | 0.220830 | + | 0.127496i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31078.3 | − | 17943.0i | 0.470533 | − | 0.271663i | −0.245930 | − | 0.969288i | \(-0.579093\pi\) |
0.716463 | + | 0.697625i | \(0.245760\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29181.8 | − | 28592.2i | 0.435023 | − | 0.426233i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9995.36 | + | 17312.5i | 0.146729 | + | 0.254143i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −32715.8 | + | 56665.4i | −0.472984 | + | 0.819232i | −0.999522 | − | 0.0309199i | \(-0.990156\pi\) |
0.526538 | + | 0.850151i | \(0.323490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16313.4i | 0.232302i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −80739.2 | −1.13256 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −59938.7 | − | 34605.6i | −0.828329 | − | 0.478236i | 0.0249511 | − | 0.999689i | \(-0.492057\pi\) |
−0.853280 | + | 0.521453i | \(0.825390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5672.94 | + | 3275.27i | −0.0772449 | + | 0.0445973i | −0.538125 | − | 0.842865i | \(-0.680867\pi\) |
0.460880 | + | 0.887462i | \(0.347534\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 56142.5 | + | 15659.1i | 0.753298 | + | 0.210108i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13595.9 | + | 23548.8i | 0.179780 | + | 0.311389i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −39551.6 | + | 68505.4i | −0.515471 | + | 0.892823i | 0.484367 | + | 0.874865i | \(0.339050\pi\) |
−0.999839 | + | 0.0179578i | \(0.994284\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18001.2i | 0.231257i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 34363.1 | 0.435191 | 0.217596 | − | 0.976039i | \(-0.430179\pi\) | ||||
0.217596 | + | 0.976039i | \(0.430179\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −79598.4 | − | 45956.1i | −0.993874 | − | 0.573813i | −0.0874439 | − | 0.996169i | \(-0.527870\pi\) |
−0.906430 | + | 0.422356i | \(0.861203\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18772.1 | + | 10838.1i | −0.231113 | + | 0.133433i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 133716. | − | 34370.5i | 1.62338 | − | 0.417274i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16345.5 | − | 28311.3i | −0.195705 | − | 0.338972i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4049.38 | − | 7013.74i | 0.0478193 | − | 0.0828254i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 23218.2i | − | 0.270453i | −0.990815 | − | 0.135227i | \(-0.956824\pi\) | ||
0.990815 | − | 0.135227i | \(-0.0431763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −49432.7 | −0.568028 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7779.58 | + | 4491.54i | 0.0881948 | + | 0.0509193i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −140658. | + | 81208.9i | −1.57334 | + | 0.908367i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 37405.5 | + | 145523.i | 0.412860 | + | 1.60620i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 40881.6 | + | 70808.9i | 0.445289 | + | 0.771264i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16080.0 | + | 27851.3i | −0.172856 | + | 0.299396i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 66385.9i | − | 0.704367i | −0.935931 | − | 0.352183i | \(-0.885439\pi\) | ||
0.935931 | − | 0.352183i | \(-0.114561\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −175.260 | −0.00183555 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 82879.0 | + | 47850.2i | 0.856888 | + | 0.494724i | 0.862969 | − | 0.505257i | \(-0.168602\pi\) |
−0.00608108 | + | 0.999982i | \(0.501936\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 41486.1 | − | 23952.0i | 0.423461 | − | 0.244486i | −0.273096 | − | 0.961987i | \(-0.588048\pi\) |
0.696557 | + | 0.717501i | \(0.254714\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5030.75 | + | 18036.7i | −0.0507005 | + | 0.181776i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17064.1 | + | 29555.9i | 0.169811 | + | 0.294121i | 0.938353 | − | 0.345678i | \(-0.112351\pi\) |
−0.768543 | + | 0.639799i | \(0.779018\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23703.6 | − | 41055.8i | 0.232934 | − | 0.403454i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 28300.7i | − | 0.274654i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −66450.0 | −0.636927 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −84192.0 | − | 48608.3i | −0.797084 | − | 0.460196i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −75140.0 | + | 43382.1i | −0.702709 | + | 0.405709i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21046.4 | − | 21480.4i | −0.194440 | − | 0.198450i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 66642.6 | + | 115428.i | 0.608270 | + | 1.05355i | 0.991526 | + | 0.129912i | \(0.0414694\pi\) |
−0.383256 | + | 0.923642i | \(0.625197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11255.8 | + | 19495.7i | −0.101505 | + | 0.175812i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 122777.i | − | 1.09402i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −49734.4 | −0.437922 | −0.218961 | − | 0.975734i | \(-0.570267\pi\) | ||||
−0.218961 | + | 0.975734i | \(0.570267\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 42550.4 | + | 24566.5i | 0.370258 | + | 0.213768i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36970.0 | − | 21344.6i | 0.317936 | − | 0.183561i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 80605.0 | + | 85697.8i | 0.685131 | + | 0.728420i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26089.7 | − | 45188.8i | −0.219195 | − | 0.379658i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9384.77 | − | 16254.9i | 0.0779408 | − | 0.134997i | −0.824421 | − | 0.565978i | \(-0.808499\pi\) |
0.902361 | + | 0.430980i | \(0.141832\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4574.17i | 0.0375545i | 0.999824 | + | 0.0187772i | \(0.00597733\pi\) | ||||
−0.999824 | + | 0.0187772i | \(0.994023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −32116.5 | −0.260683 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 52734.9 | + | 30446.5i | 0.423203 | + | 0.244336i | 0.696447 | − | 0.717608i | \(-0.254763\pi\) |
−0.273244 | + | 0.961945i | \(0.588097\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4334.10 | + | 2502.29i | −0.0343908 | + | 0.0198555i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −41002.5 | + | 40174.0i | −0.321717 | + | 0.315217i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 116059. | + | 201020.i | 0.900513 | + | 1.55973i | 0.826830 | + | 0.562452i | \(0.190142\pi\) |
0.0736826 | + | 0.997282i | \(0.476525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21725.5 | + | 37629.7i | −0.166708 | + | 0.288746i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 54773.8i | 0.415681i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −57604.4 | −0.432384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 125329. | + | 72358.9i | 0.930509 | + | 0.537229i | 0.886972 | − | 0.461822i | \(-0.152804\pi\) |
0.0435362 | + | 0.999052i | \(0.486138\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −65883.1 | + | 38037.6i | −0.483862 | + | 0.279358i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −54401.0 | − | 15173.4i | −0.395238 | − | 0.110239i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 74441.6 | + | 128937.i | 0.535054 | + | 0.926741i | 0.999161 | + | 0.0409616i | \(0.0130421\pi\) |
−0.464107 | + | 0.885779i | \(0.653625\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 38598.8 | − | 66855.0i | 0.274480 | − | 0.475414i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 169491.i | 1.19252i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −140667. | −0.979299 | −0.489649 | − | 0.871919i | \(-0.662875\pi\) | ||||
−0.489649 | + | 0.871919i | \(0.662875\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10710.3 | + | 6183.59i | 0.0737822 | + | 0.0425982i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25393.9 | + | 14661.2i | −0.173114 | + | 0.0999473i | −0.584053 | − | 0.811715i | \(-0.698534\pi\) |
0.410939 | + | 0.911663i | \(0.365201\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 43008.0 | − | 11054.8i | 0.290153 | − | 0.0745814i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −41396.5 | − | 71700.8i | −0.276402 | − | 0.478743i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −66209.9 | + | 114679.i | −0.437546 | + | 0.757852i | −0.997500 | − | 0.0706723i | \(-0.977486\pi\) |
0.559954 | + | 0.828524i | \(0.310819\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 159960.i | − | 1.04630i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22550.2 | 0.146004 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −79339.7 | − | 45806.8i | −0.508507 | − | 0.293586i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29642.0 | − | 17113.8i | 0.188073 | − | 0.108584i | −0.403007 | − | 0.915197i | \(-0.632035\pi\) |
0.591080 | + | 0.806613i | \(0.298702\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18682.0 | − | 72680.8i | −0.117348 | − | 0.456535i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 89540.6 | + | 155089.i | 0.556841 | + | 0.964477i | 0.997758 | + | 0.0669288i | \(0.0213200\pi\) |
−0.440917 | + | 0.897548i | \(0.645347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −76311.7 | + | 132176.i | −0.469873 | + | 0.813845i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 10318.0i | − | 0.0629048i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 53385.5 | 0.322281 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 43099.3 | + | 24883.4i | 0.257646 | + | 0.148752i | 0.623260 | − | 0.782014i | \(-0.285808\pi\) |
−0.365614 | + | 0.930767i | \(0.619141\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 138416. | − | 79914.7i | 0.819414 | − | 0.473089i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45978.1 | − | 164845.i | 0.269557 | − | 0.966442i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 58212.4 | + | 100827.i | 0.338002 | + | 0.585437i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −70633.0 | + | 122340.i | −0.406196 | + | 0.703551i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 43951.2i | − | 0.250347i | −0.992135 | − | 0.125174i | \(-0.960051\pi\) | ||
0.992135 | − | 0.125174i | \(-0.0399488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −218257. | −1.23141 | −0.615707 | − | 0.787975i | \(-0.711129\pi\) | ||||
−0.615707 | + | 0.787975i | \(0.711129\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14350.6 | + | 8285.30i | 0.0802025 | + | 0.0463050i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 82917.9 | − | 47872.7i | 0.459061 | − | 0.265039i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −77920.6 | − | 79527.4i | −0.427363 | − | 0.436175i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 38081.5 | + | 65959.0i | 0.206918 | + | 0.358393i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38369.8 | + | 66458.5i | −0.206555 | + | 0.357763i | −0.950627 | − | 0.310336i | \(-0.899558\pi\) |
0.744072 | + | 0.668099i | \(0.232892\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 216713.i | − | 1.15587i | −0.816083 | − | 0.577935i | \(-0.803859\pi\) | ||
0.816083 | − | 0.577935i | \(-0.196141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −54451.9 | −0.287763 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 181099. | + | 104558.i | 0.948318 | + | 0.547512i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20578.6 | + | 11881.0i | −0.106779 | + | 0.0616489i | −0.552438 | − | 0.833554i | \(-0.686303\pi\) |
0.445659 | + | 0.895203i | \(0.352969\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −55468.6 | − | 33552.5i | −0.285214 | − | 0.172523i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 87432.4 | + | 151437.i | 0.445517 | + | 0.771659i | 0.998088 | − | 0.0618072i | \(-0.0196864\pi\) |
−0.552571 | + | 0.833466i | \(0.686353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 109961. | − | 190458.i | 0.555289 | − | 0.961788i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30277.6i | 0.151532i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −195154. | −0.968023 | −0.484011 | − | 0.875062i | \(-0.660821\pi\) | ||||
−0.484011 | + | 0.875062i | \(0.660821\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 156239. | + | 90204.7i | 0.768134 | + | 0.443482i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 113340. | − | 65437.2i | 0.552317 | − | 0.318881i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −113401. | + | 111110.i | −0.547764 | + | 0.536697i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29236.1 | − | 50638.5i | −0.139987 | − | 0.242464i | 0.787505 | − | 0.616309i | \(-0.211373\pi\) |
−0.927491 | + | 0.373844i | \(0.878039\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15815.2 | − | 27392.8i | 0.0750672 | − | 0.130020i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 307243.i | − | 1.44571i | −0.691002 | − | 0.722853i | \(-0.742831\pi\) | ||
0.691002 | − | 0.722853i | \(-0.257169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17772.2 | 0.0829049 | 0.0414524 | − | 0.999140i | \(-0.486801\pi\) | ||||
0.0414524 | + | 0.999140i | \(0.486801\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −42463.7 | − | 24516.4i | −0.196387 | − | 0.113384i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −56261.4 | + | 32482.5i | −0.257974 | + | 0.148942i | −0.623410 | − | 0.781895i | \(-0.714253\pi\) |
0.365436 | + | 0.930837i | \(0.380920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 409429. | + | 114197.i | 1.86137 | + | 0.519168i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 62083.7 | + | 107532.i | 0.279857 | + | 0.484726i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −98170.2 | + | 170036.i | −0.438790 | + | 0.760007i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 125168.i | 0.554760i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31120.2 | 0.136775 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −182677. | − | 105468.i | −0.796181 | − | 0.459675i | 0.0459530 | − | 0.998944i | \(-0.485368\pi\) |
−0.842134 | + | 0.539268i | \(0.818701\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −165294. | + | 95432.3i | −0.714440 | + | 0.412482i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 174959. | − | 44971.7i | 0.749967 | − | 0.192773i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11029.9 | + | 19104.4i | 0.0468910 | + | 0.0812177i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −114444. | + | 198223.i | −0.482542 | + | 0.835787i | −0.999799 | − | 0.0200431i | \(-0.993620\pi\) |
0.517257 | + | 0.855830i | \(0.326953\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 221283.i | − | 0.925402i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −140350. | −0.582169 | −0.291085 | − | 0.956697i | \(-0.594016\pi\) | ||||
−0.291085 | + | 0.956697i | \(0.594016\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −144562. | − | 83463.1i | −0.594787 | − | 0.343400i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −21190.5 | + | 12234.3i | −0.0864828 | + | 0.0499309i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4313.28 | − | 16780.5i | −0.0174620 | − | 0.0679348i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −172663. | − | 299062.i | −0.693424 | − | 1.20105i | −0.970709 | − | 0.240258i | \(-0.922768\pi\) |
0.277285 | − | 0.960788i | \(-0.410566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 68475.7 | − | 118603.i | 0.272810 | − | 0.472521i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 58979.0i | − | 0.233110i | −0.993184 | − | 0.116555i | \(-0.962815\pi\) | ||
0.993184 | − | 0.116555i | \(-0.0371851\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −222711. | −0.873291 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −107293. | − | 61945.9i | −0.417404 | − | 0.240988i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20653.6 | − | 11924.3i | 0.0797186 | − | 0.0460255i | −0.459611 | − | 0.888120i | \(-0.652011\pi\) |
0.539329 | + | 0.842095i | \(0.318678\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 53578.7 | − | 192095.i | 0.205187 | − | 0.735657i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20675.2 | + | 35810.6i | 0.0785626 | + | 0.136074i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 238.691 | − | 413.425i | 0.000899957 | − | 0.00155877i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 39296.5i | − | 0.147019i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 145592. | 0.540509 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 417171. | + | 240854.i | 1.53688 | + | 0.887315i | 0.999019 | + | 0.0442788i | \(0.0140990\pi\) |
0.537856 | + | 0.843037i | \(0.319234\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 399593. | − | 230705.i | 1.46088 | − | 0.843438i | 0.461826 | − | 0.886970i | \(-0.347194\pi\) |
0.999052 | + | 0.0435320i | \(0.0138610\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 75673.4 | + | 77233.9i | 0.274552 | + | 0.280214i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −75156.9 | − | 130176.i | −0.270612 | − | 0.468714i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −111774. | + | 193598.i | −0.399419 | + | 0.691813i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 94299.9i | 0.334443i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −645003. | −2.27043 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 66759.3 | + | 38543.5i | 0.233240 | + | 0.134661i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 114293. | − | 65987.2i | 0.396343 | − | 0.228829i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3137.44 | + | 153703.i | −0.0107994 | + | 0.529059i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 254098. | + | 440111.i | 0.868174 | + | 1.50372i | 0.863861 | + | 0.503731i | \(0.168040\pi\) |
0.00431302 | + | 0.999991i | \(0.498627\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 114568. | − | 198438.i | 0.388565 | − | 0.673014i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 236333.i | − | 0.795668i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40170.8 | −0.134257 | −0.0671283 | − | 0.997744i | \(-0.521384\pi\) | ||||
−0.0671283 | + | 0.997744i | \(0.521384\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 53130.4 | + | 30674.9i | 0.176278 | + | 0.101774i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 188986. | − | 109111.i | 0.622482 | − | 0.359390i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 226549. | − | 221972.i | 0.740818 | − | 0.725851i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −30659.3 | − | 53103.4i | −0.0995350 | − | 0.172400i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39230.2 | − | 67948.7i | 0.126447 | − | 0.219013i | −0.795850 | − | 0.605493i | \(-0.792976\pi\) |
0.922298 | + | 0.386480i | \(0.126309\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 701959.i | − | 2.24641i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −75010.4 | −0.238339 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 355612. | + | 205312.i | 1.12191 | + | 0.647737i | 0.941889 | − | 0.335926i | \(-0.109049\pi\) |
0.180024 | + | 0.983662i | \(0.442382\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −115901. | + | 66915.6i | −0.363071 | + | 0.209619i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 34407.7 | + | 9596.89i | 0.107026 | + | 0.0298514i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 74404.3 | + | 128872.i | 0.229812 | + | 0.398047i | 0.957752 | − | 0.287594i | \(-0.0928554\pi\) |
−0.727940 | + | 0.685641i | \(0.759522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36146.3 | − | 62607.3i | 0.110864 | − | 0.192023i | −0.805255 | − | 0.592929i | \(-0.797971\pi\) |
0.916119 | + | 0.400906i | \(0.131305\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 335459.i | − | 1.02172i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −301307. | −0.911326 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −482666. | − | 278667.i | −1.44976 | − | 0.837018i | −0.451290 | − | 0.892377i | \(-0.649036\pi\) |
−0.998466 | + | 0.0553596i | \(0.982369\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −165036. | + | 95283.4i | −0.492290 | + | 0.284223i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −390376. | + | 100343.i | −1.15646 | + | 0.297258i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36900.2 | − | 63913.0i | −0.108565 | − | 0.188041i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 43740.3 | − | 75760.5i | 0.127812 | − | 0.221376i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 308119.i | − | 0.894217i | −0.894480 | − | 0.447109i | \(-0.852454\pi\) | ||
0.894480 | − | 0.447109i | \(-0.147546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 196505. | 0.566426 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −329162. | − | 190042.i | −0.942398 | − | 0.544094i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −200805. | + | 115935.i | −0.571038 | + | 0.329689i | −0.757564 | − | 0.652761i | \(-0.773611\pi\) |
0.186526 | + | 0.982450i | \(0.440277\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −38925.3 | − | 151436.i | −0.109951 | − | 0.427755i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3639.98 | + | 6304.62i | 0.0102129 | + | 0.0176893i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −167042. | + | 289325.i | −0.465555 | + | 0.806365i | −0.999226 | − | 0.0393269i | \(-0.987479\pi\) |
0.533671 | + | 0.845692i | \(0.320812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 645072.i | − | 1.78591i | −0.450147 | − | 0.892955i | \(-0.648628\pi\) | ||
0.450147 | − | 0.892955i | \(-0.351372\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −234215. | −0.644139 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −129208. | − | 74598.1i | −0.353002 | − | 0.203806i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −120643. | + | 69653.0i | −0.327433 | + | 0.189044i | −0.654701 | − | 0.755888i | \(-0.727205\pi\) |
0.327268 | + | 0.944932i | \(0.393872\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 50646.5 | − | 181583.i | 0.136557 | − | 0.489598i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 70246.8 | + | 121671.i | 0.188167 | + | 0.325915i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 203665. | − | 352759.i | 0.541997 | − | 0.938765i | −0.456793 | − | 0.889573i | \(-0.651002\pi\) |
0.998789 | − | 0.0491924i | \(-0.0156647\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 207218.i | − | 0.547870i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 276504. | 0.726325 | 0.363163 | − | 0.931726i | \(-0.381697\pi\) | ||||
0.363163 | + | 0.931726i | \(0.381697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −193904. | − | 111950.i | −0.506064 | − | 0.292176i | 0.225150 | − | 0.974324i | \(-0.427713\pi\) |
−0.731214 | + | 0.682148i | \(0.761046\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −86204.1 | + | 49770.0i | −0.223535 | + | 0.129058i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 532852. | + | 543839.i | 1.37287 | + | 1.40118i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27573.7 | − | 47759.1i | −0.0705888 | − | 0.122263i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 49030.5 | − | 84923.3i | 0.124719 | − | 0.216019i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 187976.i | − | 0.475119i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −299528. | −0.752278 | −0.376139 | − | 0.926563i | \(-0.622749\pi\) | ||||
−0.376139 | + | 0.926563i | \(0.622749\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −262042. | − | 151290.i | −0.653980 | − | 0.377575i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29173.3 | + | 16843.2i | −0.0723500 | + | 0.0417713i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −265046. | − | 481507.i | −0.653194 | − | 1.18665i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4773.48 | + | 8267.92i | 0.0116905 | + | 0.0202486i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −288942. | + | 500462.i | −0.703226 | + | 1.21802i | 0.264102 | + | 0.964495i | \(0.414924\pi\) |
−0.967328 | + | 0.253528i | \(0.918409\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 135320.i | − | 0.327295i | −0.986519 | − | 0.163647i | \(-0.947674\pi\) | ||
0.986519 | − | 0.163647i | \(-0.0523259\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 225516. | 0.542074 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −188880. | − | 109050.i | −0.451209 | − | 0.260506i | 0.257132 | − | 0.966376i | \(-0.417223\pi\) |
−0.708341 | + | 0.705871i | \(0.750556\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 193668. | − | 111814.i | 0.459800 | − | 0.265465i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 121252. | − | 118802.i | 0.286106 | − | 0.280325i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −72127.2 | − | 124928.i | −0.169150 | − | 0.292977i | 0.768971 | − | 0.639284i | \(-0.220769\pi\) |
−0.938121 | + | 0.346307i | \(0.887436\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30711.8 | + | 53194.4i | −0.0715851 | + | 0.123989i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 109889.i | 0.254579i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 159392. | 0.367024 | 0.183512 | − | 0.983017i | \(-0.441253\pi\) | ||||
0.183512 | + | 0.983017i | \(0.441253\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 305674. | + | 176481.i | 0.699609 | + | 0.403919i | 0.807202 | − | 0.590276i | \(-0.200981\pi\) |
−0.107593 | + | 0.994195i | \(0.534314\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 232249. | − | 134089.i | 0.528357 | − | 0.305047i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 196892. | + | 54916.7i | 0.445231 | + | 0.124183i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 262655. | + | 454932.i | 0.590384 | + | 1.02258i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −158615. | + | 274729.i | −0.354398 | + | 0.613836i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 145488.i | − | 0.323135i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 504858. | 1.11465 | 0.557326 | − | 0.830294i | \(-0.311827\pi\) | ||||
0.557326 | + | 0.830294i | \(0.311827\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −51598.2 | − | 29790.2i | −0.113247 | − | 0.0653832i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −169486. | + | 97853.0i | −0.369792 | + | 0.213500i | −0.673368 | − | 0.739308i | \(-0.735153\pi\) |
0.303576 | + | 0.952807i | \(0.401820\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −73967.4 | + | 19012.7i | −0.160436 | + | 0.0412385i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −64935.5 | − | 112472.i | −0.140019 | − | 0.242520i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −117221. | + | 203032.i | −0.251283 | + | 0.435235i | −0.963879 | − | 0.266340i | \(-0.914186\pi\) |
0.712596 | + | 0.701574i | \(0.247519\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 435352.i | 0.927812i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −98357.4 | −0.208398 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 228503. | + | 131926.i | 0.481341 | + | 0.277902i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 77344.0 | − | 44654.6i | 0.161983 | − | 0.0935212i | −0.416817 | − | 0.908990i | \(-0.636854\pi\) |
0.578800 | + | 0.815469i | \(0.303521\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −21088.7 | − | 82044.0i | −0.0439120 | − | 0.170836i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −192394. | − | 333236.i | −0.398311 | − | 0.689895i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 317621. | − | 550136.i | 0.653799 | − | 1.13241i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 34734.9i | − | 0.0710905i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 122213. | 0.248704 | 0.124352 | − | 0.992238i | \(-0.460315\pi\) | ||||
0.124352 | + | 0.992238i | \(0.460315\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 212818. | + | 122871.i | 0.430624 | + | 0.248621i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −39088.9 | + | 22568.0i | −0.0786457 | + | 0.0454061i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 207147. | − | 742683.i | 0.414419 | − | 1.48582i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42009.9 | − | 72763.3i | −0.0835717 | − | 0.144750i | 0.821210 | − | 0.570626i | \(-0.193299\pi\) |
−0.904782 | + | 0.425876i | \(0.859966\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −87383.1 | + | 151352.i | −0.172858 | + | 0.299398i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 473032.i | 0.930489i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −207457. | −0.405804 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 434074. | + | 250613.i | 0.844356 | + | 0.487489i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −657416. | + | 379560.i | −1.27169 | + | 0.734213i | −0.975307 | − | 0.220855i | \(-0.929115\pi\) |
−0.296388 | + | 0.955068i | \(0.595782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1156.65 | + | 1180.51i | 0.00222502 | + | 0.00227090i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 142115. | + | 246151.i | 0.271872 | + | 0.470896i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −157214. | + | 272303.i | −0.299100 | + | 0.518057i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 92384.1i | 0.174795i | 0.996174 | + | 0.0873974i | \(0.0278550\pi\) | ||||
−0.996174 | + | 0.0873974i | \(0.972145\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 598715. | + | 345668.i | 1.12043 | + | 0.646882i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2903.50 | − | 1676.34i | 0.00540399 | − | 0.00312000i | −0.497296 | − | 0.867581i | \(-0.665674\pi\) |
0.502700 | + | 0.864461i | \(0.332340\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 154692. | − | 85150.5i | 0.286348 | − | 0.157620i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 277715. | + | 481017.i | 0.511287 | + | 0.885575i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13592.8 | + | 23543.4i | −0.0248897 | + | 0.0431103i | −0.878202 | − | 0.478290i | \(-0.841257\pi\) |
0.853312 | + | 0.521400i | \(0.174590\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 350589.i | 0.638502i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −773801. | −1.40169 | −0.700845 | − | 0.713314i | \(-0.747193\pi\) | ||||
−0.700845 | + | 0.713314i | \(0.747193\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −71422.6 | − | 41235.9i | −0.128684 | − | 0.0742955i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 192342. | − | 111049.i | 0.344693 | − | 0.199009i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −190626. | + | 186775.i | −0.339797 | + | 0.332931i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 98922.2 | + | 171338.i | 0.175394 | + | 0.303791i | 0.940297 | − | 0.340354i | \(-0.110547\pi\) |
−0.764904 | + | 0.644145i | \(0.777214\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 280948. | − | 486617.i | 0.495492 | − | 0.858217i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 356483.i | 0.625381i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −770706. | −1.34492 | −0.672461 | − | 0.740132i | \(-0.734763\pi\) | ||||
−0.672461 | + | 0.740132i | \(0.734763\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 204430. | + | 118027.i | 0.354863 | + | 0.204880i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −131757. | + | 76069.9i | −0.227512 | + | 0.131354i | −0.609424 | − | 0.792845i | \(-0.708599\pi\) |
0.381912 | + | 0.924199i | \(0.375266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 788109. | + | 219817.i | 1.35375 | + | 0.377583i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 43078.4 | + | 74614.0i | 0.0736100 | + | 0.127496i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −399760. | + | 692405.i | −0.679531 | + | 1.17698i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 961897.i | 1.62658i | 0.581857 | + | 0.813291i | \(0.302326\pi\) | ||||
−0.581857 | + | 0.813291i | \(0.697674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 186470. | 0.313689 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −130829. | − | 75534.4i | −0.218951 | − | 0.126411i | 0.386514 | − | 0.922284i | \(-0.373679\pi\) |
−0.605464 | + | 0.795872i | \(0.707013\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −245204. | + | 141569.i | −0.408248 | + | 0.235702i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 205603. | − | 52848.3i | 0.340554 | − | 0.0875365i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 415226. | + | 719192.i | 0.684242 | + | 1.18514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11320.1 | − | 19607.0i | 0.0185588 | − | 0.0321447i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 103875.i | 0.169429i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −338215. | −0.548849 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 172244. | + | 99445.4i | 0.278097 | + | 0.160559i | 0.632561 | − | 0.774510i | \(-0.282004\pi\) |
−0.354465 | + | 0.935069i | \(0.615337\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −294442. | + | 169996.i | −0.472984 | + | 0.273077i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −115344. | − | 448739.i | −0.184350 | − | 0.717202i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 260076. | + | 450465.i | 0.413575 | + | 0.716333i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −42383.5 | + | 73410.4i | −0.0670599 | + | 0.116151i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 990756.i | − | 1.55973i | −0.625947 | − | 0.779866i | \(-0.715287\pi\) | ||
0.625947 | − | 0.779866i | \(-0.284713\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −138368. | −0.216741 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −363326. | − | 209767.i | −0.566281 | − | 0.326943i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 225683. | − | 130298.i | 0.350000 | − | 0.202073i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −132197. | + | 473965.i | −0.204000 | + | 0.731399i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −179816. | − | 311451.i | −0.276110 | − | 0.478236i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46144.3 | − | 79924.3i | 0.0705052 | − | 0.122119i | −0.828618 | − | 0.559815i | \(-0.810872\pi\) |
0.899123 | + | 0.437696i | \(0.144206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 617125.i | 0.938277i | 0.883125 | + | 0.469139i | \(0.155436\pi\) | ||||
−0.883125 | + | 0.469139i | \(0.844564\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34037.6 | −0.0514966 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 521991. | + | 301372.i | 0.785865 | + | 0.453719i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −782700. | + | 451892.i | −1.17260 | + | 0.677003i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 211958. | + | 216329.i | 0.315996 | + | 0.322512i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −153533. | − | 265927.i | −0.227780 | − | 0.394526i | 0.729370 | − | 0.684119i | \(-0.239813\pi\) |
−0.957150 | + | 0.289593i | \(0.906480\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 423429. | − | 733401.i | 0.625146 | − | 1.08278i | −0.363367 | − | 0.931646i | \(-0.618373\pi\) |
0.988513 | − | 0.151138i | \(-0.0482937\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 141293.i | 0.207592i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −294059. | −0.429956 | −0.214978 | − | 0.976619i | \(-0.568968\pi\) | ||||
−0.214978 | + | 0.976619i | \(0.568968\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 895803. | + | 517192.i | 1.30348 | + | 0.752563i | 0.980999 | − | 0.194013i | \(-0.0621506\pi\) |
0.322479 | + | 0.946577i | \(0.395484\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −355964. | + | 205516.i | −0.515471 | + | 0.297608i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 541205. | + | 11047.3i | 0.779959 | + | 0.0159208i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 186518. | + | 323059.i | 0.267515 | + | 0.463349i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −46768.6 | + | 81005.6i | −0.0667580 | + | 0.115628i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 307258.i | − | 0.436495i | −0.975893 | − | 0.218248i | \(-0.929966\pi\) | ||
0.975893 | − | 0.218248i | \(-0.0700340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −159093. | −0.224937 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 154634. | + | 89278.1i | 0.217596 | + | 0.125629i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 292252. | − | 168732.i | 0.409302 | − | 0.236311i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 368943. | − | 361489.i | 0.514272 | − | 0.503881i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −238795. | − | 413605.i | −0.331291 | − | 0.573813i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −295777. | + | 512302.i | −0.408419 | + | 0.707402i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 70737.4i | 0.0972190i | 0.998818 | + | 0.0486095i | \(0.0154790\pi\) | ||||
−0.998818 | + | 0.0486095i | \(0.984521\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −112633. | −0.154075 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 285670. | + | 164932.i | 0.388958 | + | 0.224565i | 0.681709 | − | 0.731624i | \(-0.261237\pi\) |
−0.292751 | + | 0.956189i | \(0.594571\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 60589.3 | − | 34981.2i | 0.0821125 | − | 0.0474077i | −0.458382 | − | 0.888756i | \(-0.651571\pi\) |
0.540494 | + | 0.841348i | \(0.318237\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 691018. | + | 192737.i | 0.932145 | + | 0.259991i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −386112. | − | 668765.i | −0.518431 | − | 0.897949i | −0.999771 | − | 0.0214151i | \(-0.993183\pi\) |
0.481339 | − | 0.876534i | \(-0.340150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −198286. | + | 343441.i | −0.265008 | + | 0.459008i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 169868.i | − | 0.225981i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 414451. | 0.548825 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.71974e6 | − | 992893.i | −2.26687 | − | 1.30878i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36444.4 | − | 21041.2i | 0.0478193 | − | 0.0276085i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −705058. | + | 181229.i | −0.920892 | + | 0.236707i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −121260. | − | 210028.i | −0.157659 | − | 0.273073i | 0.776365 | − | 0.630283i | \(-0.217061\pi\) |
−0.934024 | + | 0.357211i | \(0.883728\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 60322.5 | − | 104482.i | 0.0780732 | − | 0.135227i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 646528.i | 0.832982i | 0.909140 | + | 0.416491i | \(0.136740\pi\) | ||||
−0.909140 | + | 0.416491i | \(0.863260\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 461877. | 0.592387 | 0.296193 | − | 0.955128i | \(-0.404283\pi\) | ||||
0.296193 | + | 0.955128i | \(0.404283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −222447. | − | 128430.i | −0.284014 | − | 0.163976i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 186391. | − | 107613.i | 0.236907 | − | 0.136778i | −0.376847 | − | 0.926275i | \(-0.622992\pi\) |
0.613754 | + | 0.789497i | \(0.289658\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29033.2 | − | 112952.i | −0.0367359 | − | 0.142919i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23338.7 | + | 40423.9i | 0.0293983 | + | 0.0509193i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 90443.9 | − | 156653.i | 0.113417 | − | 0.196443i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 359479.i | 0.448774i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −843948. | −1.04889 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 427498. | + | 246816.i | 0.528950 | + | 0.305389i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −225045. | + | 129930.i | −0.277217 | + | 0.160051i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −209756. | + | 752038.i | −0.257240 | + | 0.922283i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 312067. | + | 540516.i | 0.381022 | + | 0.659950i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 549134. | − | 951128.i | 0.667519 | − | 1.15618i | −0.311076 | − | 0.950385i | \(-0.600689\pi\) |
0.978596 | − | 0.205793i | \(-0.0659773\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 424854.i | 0.514176i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.32312e6 | 1.59427 | 0.797133 | − | 0.603803i | \(-0.206349\pi\) | ||||
0.797133 | + | 0.603803i | \(0.206349\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −456131. | − | 263348.i | −0.547203 | − | 0.315928i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −144720. | + | 83553.9i | −0.172856 | + | 0.0997987i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −148824. | − | 151893.i | −0.176984 | − | 0.180633i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 258264. | + | 447326.i | 0.305797 | + | 0.529656i | 0.977438 | − | 0.211221i | \(-0.0677438\pi\) |
−0.671642 | + | 0.740876i | \(0.734411\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 172476. | − | 298736.i | 0.203333 | − | 0.352183i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 80943.8i | 0.0950124i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −354080. | −0.413826 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −788.669 | − | 455.338i | −0.000917773 | − | 0.000529876i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.07335e6 | − | 619697.i | 1.24368 | − | 0.718039i | 0.273838 | − | 0.961776i | \(-0.411707\pi\) |
0.969841 | + | 0.243737i | \(0.0783734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −366265. | + | 605506.i | −0.422568 | + | 0.698585i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 248637. | + | 430652.i | 0.285629 | + | 0.494724i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 102159. | − | 176944.i | 0.116856 | − | 0.202401i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.15260e6i | − | 1.31281i | −0.754411 | − | 0.656403i | \(-0.772077\pi\) | ||
0.754411 | − | 0.656403i | \(-0.227923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 248917. | 0.282308 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 93104.2 | + | 53753.7i | 0.105145 | + | 0.0607057i | 0.551650 | − | 0.834075i | \(-0.313998\pi\) |
−0.446505 | + | 0.894781i | \(0.647332\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.73126e6 | + | 999543.i | −1.94688 | + | 1.12403i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −69499.2 | + | 68095.1i | −0.0778245 | + | 0.0762521i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −206307. | − | 357335.i | −0.230046 | − | 0.398451i | 0.727775 | − | 0.685815i | \(-0.240554\pi\) |
−0.957821 | + | 0.287364i | \(0.907221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −465845. | + | 806867.i | −0.517260 | + | 0.895920i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 177335.i | 0.196080i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.43052e6 | 1.57510 | 0.787550 | − | 0.616251i | \(-0.211349\pi\) | ||||
0.787550 | + | 0.616251i | \(0.211349\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 791324. | + | 456871.i | 0.867656 | + | 0.500942i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 213332. | − | 123168.i | 0.232934 | − | 0.134485i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.45179e6 | − | 404928.i | −1.57858 | − | 0.440292i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −239507. | − | 414839.i | −0.259342 | − | 0.449193i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 73527.3 | − | 127353.i | 0.0792859 | − | 0.137327i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 519077.i | − | 0.557413i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 344533. | 0.368449 | 0.184225 | − | 0.982884i | \(-0.441023\pi\) | ||||
0.184225 | + | 0.982884i | \(0.441023\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −299025. | − | 172642.i | −0.318463 | − | 0.183865i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.25848e6 | − | 726581.i | 1.33477 | − | 0.770630i | 0.348744 | − | 0.937218i | \(-0.386608\pi\) |
0.986027 | + | 0.166588i | \(0.0532751\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.29020e6 | − | 331636.i | 1.36280 | − | 0.350296i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −252576. | − | 437474.i | −0.265695 | − | 0.460196i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −772853. | + | 1.33862e6i | −0.809669 | + | 1.40239i | 0.103424 | + | 0.994637i | \(0.467020\pi\) |
−0.913093 | + | 0.407751i | \(0.866313\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 994907.i | 1.03805i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −450840. | −0.468473 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −116280. | − | 67134.0i | −0.120336 | − | 0.0694761i | 0.438624 | − | 0.898671i | \(-0.355466\pi\) |
−0.558960 | + | 0.829195i | \(0.688799\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 896589. | − | 517646.i | 0.924105 | − | 0.533532i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −38901.1 | − | 151342.i | −0.0399326 | − | 0.155355i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.08781e6 | − | 1.88414e6i | −1.11214 | − | 1.92628i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −395596. | + | 685192.i | −0.402814 | + | 0.697694i | −0.994064 | − | 0.108794i | \(-0.965301\pi\) |
0.591251 | + | 0.806488i | \(0.298634\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 692571.i | 0.702369i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19829.5 | −0.0200293 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 582624. | + | 336378.i | 0.586136 | + | 0.338406i | 0.763568 | − | 0.645727i | \(-0.223446\pi\) |
−0.177432 | + | 0.984133i | \(0.556779\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −101302. | + | 58487.0i | −0.101505 | + | 0.0586041i |
(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 | 336.5.bh.d.241.2 | 4 | ||
4.3 | odd | 2 | 42.5.g.a.31.1 | yes | 4 | ||
7.5 | odd | 6 | inner | 336.5.bh.d.145.2 | 4 | ||
12.11 | even | 2 | 126.5.n.b.73.2 | 4 | |||
28.3 | even | 6 | 294.5.c.a.97.3 | 4 | |||
28.11 | odd | 6 | 294.5.c.a.97.4 | 4 | |||
28.19 | even | 6 | 42.5.g.a.19.1 | ✓ | 4 | ||
28.23 | odd | 6 | 294.5.g.c.19.1 | 4 | |||
28.27 | even | 2 | 294.5.g.c.31.1 | 4 | |||
84.11 | even | 6 | 882.5.c.a.685.2 | 4 | |||
84.47 | odd | 6 | 126.5.n.b.19.2 | 4 | |||
84.59 | odd | 6 | 882.5.c.a.685.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.5.g.a.19.1 | ✓ | 4 | 28.19 | even | 6 | ||
42.5.g.a.31.1 | yes | 4 | 4.3 | odd | 2 | ||
126.5.n.b.19.2 | 4 | 84.47 | odd | 6 | |||
126.5.n.b.73.2 | 4 | 12.11 | even | 2 | |||
294.5.c.a.97.3 | 4 | 28.3 | even | 6 | |||
294.5.c.a.97.4 | 4 | 28.11 | odd | 6 | |||
294.5.g.c.19.1 | 4 | 28.23 | odd | 6 | |||
294.5.g.c.31.1 | 4 | 28.27 | even | 2 | |||
336.5.bh.d.145.2 | 4 | 7.5 | odd | 6 | inner | ||
336.5.bh.d.241.2 | 4 | 1.1 | even | 1 | trivial | ||
882.5.c.a.685.1 | 4 | 84.59 | odd | 6 | |||
882.5.c.a.685.2 | 4 | 84.11 | even | 6 |