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 | 145.10 | ||
Character | \(\chi\) | \(=\) | 684.145 |
Dual form | 684.5.y.f.217.10 |
$q$-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 | ||||||||
\(5\) | 18.6023 | + | 32.2201i | 0.744091 | + | 1.28880i | 0.950618 | + | 0.310362i | \(0.100450\pi\) |
−0.206527 | + | 0.978441i | \(0.566216\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −25.9074 | −0.528722 | −0.264361 | − | 0.964424i | \(-0.585161\pi\) | ||||
−0.264361 | + | 0.964424i | \(0.585161\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 189.278 | 1.56428 | 0.782141 | − | 0.623102i | \(-0.214128\pi\) | ||||
0.782141 | + | 0.623102i | \(0.214128\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 111.709 | + | 64.4949i | 0.660997 | + | 0.381627i | 0.792657 | − | 0.609668i | \(-0.208697\pi\) |
−0.131660 | + | 0.991295i | \(0.542031\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 160.296 | + | 277.640i | 0.554656 | + | 0.960692i | 0.997930 | + | 0.0643064i | \(0.0204835\pi\) |
−0.443274 | + | 0.896386i | \(0.646183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.91800 | − | 360.890i | −0.0247036 | − | 0.999695i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 294.572 | − | 510.213i | 0.556846 | − | 0.964486i | −0.440911 | − | 0.897551i | \(-0.645345\pi\) |
0.997757 | − | 0.0669351i | \(-0.0213220\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −379.589 | + | 657.467i | −0.607342 | + | 1.05195i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 788.932 | + | 455.490i | 0.938088 | + | 0.541605i | 0.889360 | − | 0.457207i | \(-0.151150\pi\) |
0.0487275 | + | 0.998812i | \(0.484483\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1657.55i | − | 1.72482i | −0.506209 | − | 0.862411i | \(-0.668953\pi\) | ||
0.506209 | − | 0.862411i | \(-0.331047\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −481.936 | − | 834.737i | −0.393417 | − | 0.681418i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1024.72i | 0.748516i | 0.927325 | + | 0.374258i | \(0.122102\pi\) | ||||
−0.927325 | + | 0.374258i | \(0.877898\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1389.77 | − | 802.383i | 0.826751 | − | 0.477325i | −0.0259880 | − | 0.999662i | \(-0.508273\pi\) |
0.852739 | + | 0.522337i | \(0.174940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 905.234 | + | 1567.91i | 0.489580 | + | 0.847978i | 0.999928 | − | 0.0119902i | \(-0.00381670\pi\) |
−0.510348 | + | 0.859968i | \(0.670483\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 516.200 | − | 894.084i | 0.233680 | − | 0.404746i | −0.725208 | − | 0.688530i | \(-0.758256\pi\) |
0.958888 | + | 0.283784i | \(0.0915898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1729.81 | −0.720453 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 656.643 | + | 379.113i | 0.233764 | + | 0.134964i | 0.612307 | − | 0.790620i | \(-0.290242\pi\) |
−0.378543 | + | 0.925584i | \(0.623575\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3521.00 | + | 6098.56i | 1.16397 | + | 2.01605i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −896.448 | + | 517.564i | −0.257526 | + | 0.148683i | −0.623205 | − | 0.782058i | \(-0.714170\pi\) |
0.365680 | + | 0.930741i | \(0.380837\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2769.93 | − | 4797.67i | 0.744406 | − | 1.28935i | −0.206066 | − | 0.978538i | \(-0.566066\pi\) |
0.950472 | − | 0.310810i | \(-0.100600\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4799.01i | 1.13586i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1014.94 | + | 585.977i | 0.226095 | + | 0.130536i | 0.608769 | − | 0.793347i | \(-0.291663\pi\) |
−0.382674 | + | 0.923883i | \(0.624997\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6058.10 | + | 3497.65i | −1.20177 | + | 0.693840i | −0.960948 | − | 0.276731i | \(-0.910749\pi\) |
−0.240818 | + | 0.970570i | \(0.577416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3097.26 | + | 5364.62i | 0.581209 | + | 1.00668i | 0.995336 | + | 0.0964646i | \(0.0307535\pi\) |
−0.414127 | + | 0.910219i | \(0.635913\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4903.70 | −0.827070 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4443.93 | − | 2565.70i | 0.712054 | − | 0.411105i | −0.0997669 | − | 0.995011i | \(-0.531810\pi\) |
0.811821 | + | 0.583906i | \(0.198476\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3973.43 | −0.576779 | −0.288390 | − | 0.957513i | \(-0.593120\pi\) | ||||
−0.288390 | + | 0.957513i | \(0.593120\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5963.72 | + | 10329.5i | −0.825429 | + | 1.42968i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7936.06 | − | 4581.89i | −1.00190 | − | 0.578448i | −0.0930914 | − | 0.995658i | \(-0.529675\pi\) |
−0.908810 | + | 0.417209i | \(0.863008\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2894.07 | − | 1670.89i | −0.349484 | − | 0.201774i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11462.0 | − | 7000.71i | 1.27003 | − | 0.775702i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9602.98 | + | 5544.28i | −1.02062 | + | 0.589253i | −0.914282 | − | 0.405077i | \(-0.867245\pi\) |
−0.106334 | + | 0.994330i | \(0.533911\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2172.57 | + | 3763.01i | −0.212977 | + | 0.368886i | −0.952645 | − | 0.304086i | \(-0.901649\pi\) |
0.739668 | + | 0.672972i | \(0.234982\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14532.9i | 1.36987i | 0.728606 | + | 0.684933i | \(0.240169\pi\) | ||||
−0.728606 | + | 0.684933i | \(0.759831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 16840.7i | − | 1.47093i | −0.677561 | − | 0.735467i | \(-0.736963\pi\) | ||
0.677561 | − | 0.735467i | \(-0.263037\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14906.5 | − | 8606.29i | 1.25465 | − | 0.724374i | 0.282623 | − | 0.959231i | \(-0.408795\pi\) |
0.972030 | + | 0.234857i | \(0.0754620\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15278.5i | 1.19653i | 0.801299 | + | 0.598265i | \(0.204143\pi\) | ||||
−0.801299 | + | 0.598265i | \(0.795857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21918.8 | 1.65738 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4152.84 | − | 7192.92i | −0.293259 | − | 0.507939i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21185.2 | 1.44698 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4992.03 | −0.319490 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1191.50 | + | 687.911i | 0.0738729 | + | 0.0426506i | 0.536481 | − | 0.843912i | \(-0.319753\pi\) |
−0.462609 | + | 0.886563i | \(0.653086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2974.72 | + | 5152.37i | 0.173342 | + | 0.300237i | 0.939586 | − | 0.342312i | \(-0.111210\pi\) |
−0.766244 | + | 0.642549i | \(0.777877\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 231.042 | + | 9349.70i | 0.0130613 | + | 0.528560i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1771.01 | − | 3067.49i | 0.0943585 | − | 0.163434i | −0.814982 | − | 0.579486i | \(-0.803253\pi\) |
0.909341 | + | 0.416052i | \(0.136587\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15505.8 | + | 26856.9i | −0.802537 | + | 1.39003i | 0.115405 | + | 0.993319i | \(0.463183\pi\) |
−0.917942 | + | 0.396716i | \(0.870150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21144.0 | + | 12207.5i | 1.03399 | + | 0.596972i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 33892.6i | 1.61201i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16399.8 | + | 28405.3i | 0.738698 | + | 1.27946i | 0.953082 | + | 0.302713i | \(0.0978923\pi\) |
−0.214384 | + | 0.976749i | \(0.568774\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19290.6i | 0.846043i | 0.906120 | + | 0.423021i | \(0.139030\pi\) | ||||
−0.906120 | + | 0.423021i | \(0.860970\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 53406.5 | − | 30834.3i | 2.22296 | − | 1.28342i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13160.1 | + | 22794.0i | 0.533900 | + | 0.924742i | 0.999216 | + | 0.0395974i | \(0.0126075\pi\) |
−0.465316 | + | 0.885145i | \(0.654059\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7631.57 | + | 13218.3i | −0.294417 | + | 0.509945i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 37908.8 | 1.42680 | 0.713402 | − | 0.700755i | \(-0.247153\pi\) | ||||
0.713402 | + | 0.700755i | \(0.247153\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22176.3 | + | 12803.5i | 0.795163 | + | 0.459088i | 0.841777 | − | 0.539825i | \(-0.181510\pi\) |
−0.0466139 | + | 0.998913i | \(0.514843\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5961.30 | − | 10325.3i | −0.208722 | − | 0.361517i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20073.0 | − | 11589.1i | 0.670687 | − | 0.387221i | −0.125650 | − | 0.992075i | \(-0.540102\pi\) |
0.796337 | + | 0.604854i | \(0.206768\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9834.15 | − | 17033.2i | 0.321115 | − | 0.556188i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 34080.4i | − | 1.06365i | −0.846854 | − | 0.531826i | \(-0.821506\pi\) | ||
0.846854 | − | 0.531826i | \(-0.178494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9053.50 | − | 5227.04i | −0.276350 | − | 0.159551i | 0.355420 | − | 0.934707i | \(-0.384338\pi\) |
−0.631770 | + | 0.775156i | \(0.717671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −33016.5 | + | 19062.1i | −0.964689 | + | 0.556964i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30340.4 | + | 52551.2i | 0.867638 | + | 1.50279i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −28229.8 | −0.773822 | −0.386911 | − | 0.922117i | \(-0.626458\pi\) | ||||
−0.386911 | + | 0.922117i | \(0.626458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12133.7 | + | 7005.37i | −0.325744 | + | 0.188069i | −0.653950 | − | 0.756538i | \(-0.726889\pi\) |
0.328206 | + | 0.944606i | \(0.393556\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −60171.8 | −1.55046 | −0.775230 | − | 0.631679i | \(-0.782366\pi\) | ||||
−0.775230 | + | 0.631679i | \(0.782366\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4076.45 | − | 7060.62i | 0.102938 | − | 0.178294i | −0.809956 | − | 0.586491i | \(-0.800509\pi\) |
0.912894 | + | 0.408197i | \(0.133842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20439.1 | − | 11800.5i | −0.495987 | − | 0.286358i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 51705.7 | + | 29852.3i | 1.23036 | + | 0.710346i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1687.98 | − | 68308.5i | −0.0386434 | − | 1.56380i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 37338.0 | − | 21557.1i | 0.838660 | − | 0.484201i | −0.0181482 | − | 0.999835i | \(-0.505777\pi\) |
0.856809 | + | 0.515634i | \(0.172444\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −33678.8 | + | 58333.4i | −0.728584 | + | 1.26195i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 42942.9i | 0.911951i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 41353.0i | 0.846687i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −73783.8 | + | 42599.1i | −1.48372 | + | 0.856625i | −0.999829 | − | 0.0185052i | \(-0.994109\pi\) |
−0.483888 | + | 0.875130i | \(0.660776\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 51033.0i | − | 0.990374i | −0.868787 | − | 0.495187i | \(-0.835100\pi\) | ||
0.868787 | − | 0.495187i | \(-0.164900\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −69442.5 | −1.32420 | −0.662101 | − | 0.749414i | \(-0.730335\pi\) | ||||
−0.662101 | + | 0.749414i | \(0.730335\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6428.13 | + | 11133.8i | 0.118406 | + | 0.205085i | 0.919136 | − | 0.393940i | \(-0.128888\pi\) |
−0.800730 | + | 0.599025i | \(0.795555\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 38410.0 | 0.695518 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −80974.3 | −1.41759 | −0.708796 | − | 0.705414i | \(-0.750761\pi\) | ||||
−0.708796 | + | 0.705414i | \(0.750761\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20674.8 | + | 11936.6i | 0.355965 | + | 0.205516i | 0.667309 | − | 0.744781i | \(-0.267446\pi\) |
−0.311344 | + | 0.950297i | \(0.600779\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −32178.4 | − | 55734.6i | −0.536083 | − | 0.928523i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22279.4 | − | 40889.6i | 0.365181 | − | 0.670223i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18715.1 | + | 32415.5i | −0.297060 | + | 0.514523i | −0.975462 | − | 0.220168i | \(-0.929340\pi\) |
0.678402 | + | 0.734691i | \(0.262673\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 55756.0 | − | 96572.1i | 0.871064 | − | 1.50873i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 41785.0 | + | 24124.6i | 0.632636 | + | 0.365253i | 0.781772 | − | 0.623564i | \(-0.214316\pi\) |
−0.149136 | + | 0.988817i | \(0.547649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 26547.7i | − | 0.395756i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 34898.2 | + | 60445.5i | 0.504536 | + | 0.873882i | 0.999986 | + | 0.00524540i | \(0.00166967\pi\) |
−0.495450 | + | 0.868636i | \(0.664997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28209.5i | 0.401701i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 97588.6 | − | 56342.8i | 1.34864 | − | 0.778635i | 0.360579 | − | 0.932729i | \(-0.382579\pi\) |
0.988056 | + | 0.154093i | \(0.0492457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32603.7 | + | 56471.3i | 0.443944 | + | 0.768934i | 0.997978 | − | 0.0635601i | \(-0.0202455\pi\) |
−0.554034 | + | 0.832494i | \(0.686912\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −71847.9 | + | 124444.i | −0.950055 | + | 1.64554i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −148562. | −1.93620 | −0.968098 | − | 0.250573i | \(-0.919381\pi\) | ||||
−0.968098 | + | 0.250573i | \(0.919381\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 68337.5 | + | 39454.7i | 0.865459 | + | 0.499673i | 0.865837 | − | 0.500327i | \(-0.166787\pi\) |
−0.000377502 | 1.00000i | \(0.500120\pi\) | ||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27276.6 | − | 47244.4i | −0.340578 | − | 0.589899i | 0.643962 | − | 0.765058i | \(-0.277290\pi\) |
−0.984540 | + | 0.175158i | \(0.943956\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −36005.2 | + | 20787.6i | −0.437121 | + | 0.252372i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9628.86 | + | 16677.7i | −0.115287 | + | 0.199682i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 51381.0i | − | 0.598505i | −0.954174 | − | 0.299252i | \(-0.903263\pi\) | ||
0.954174 | − | 0.299252i | \(-0.0967372\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33351.9 | − | 19255.7i | −0.383245 | − | 0.221267i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 65812.3 | − | 37996.8i | 0.736147 | − | 0.425015i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23452.2 | − | 40620.4i | −0.258852 | − | 0.448344i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 206108. | 2.21562 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −38744.0 | + | 22368.9i | −0.411081 | + | 0.237338i | −0.691254 | − | 0.722612i | \(-0.742942\pi\) |
0.280173 | + | 0.959950i | \(0.409608\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −135143. | −1.39724 | −0.698622 | − | 0.715491i | \(-0.746203\pi\) | ||||
−0.698622 | + | 0.715491i | \(0.746203\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 63850.3 | − | 110592.i | 0.651739 | − | 1.12885i | −0.330961 | − | 0.943644i | \(-0.607373\pi\) |
0.982701 | − | 0.185201i | \(-0.0592937\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −121666. | − | 70243.6i | −1.21073 | − | 0.699018i | −0.247815 | − | 0.968807i | \(-0.579713\pi\) |
−0.962919 | + | 0.269789i | \(0.913046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 149328. | + | 86214.3i | 1.46743 | + | 0.847223i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 98768.0 | − | 60325.0i | 0.946697 | − | 0.578219i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −84806.7 | + | 48963.1i | −0.802903 | + | 0.463556i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13373.4 | + | 23163.4i | −0.123552 | + | 0.213998i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 119946.i | − | 1.09479i | −0.836874 | − | 0.547395i | \(-0.815619\pi\) | ||
0.836874 | − | 0.547395i | \(-0.184381\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 43602.0i | 0.388523i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 53966.2 | − | 31157.4i | 0.475184 | − | 0.274348i | −0.243223 | − | 0.969970i | \(-0.578205\pi\) |
0.718407 | + | 0.695623i | \(0.244871\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 313739.i | − | 2.69811i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 107018. | 0.909641 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5657.07 | + | 9798.33i | 0.0469821 | + | 0.0813754i | 0.888560 | − | 0.458760i | \(-0.151706\pi\) |
−0.841578 | + | 0.540136i | \(0.818373\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −143009. | −1.17412 | −0.587060 | − | 0.809543i | \(-0.699715\pi\) | ||||
−0.587060 | + | 0.809543i | \(0.699715\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 167076. | 1.34080 | 0.670400 | − | 0.742000i | \(-0.266122\pi\) | ||||
0.670400 | + | 0.742000i | \(0.266122\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −225389. | − | 130128.i | −1.78845 | − | 1.03256i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20058.8 | + | 34742.9i | 0.155638 | + | 0.269573i | 0.933291 | − | 0.359120i | \(-0.116923\pi\) |
−0.777653 | + | 0.628694i | \(0.783590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −130162. | + | 6436.83i | −0.998779 | + | 0.0493921i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −115232. | + | 199588.i | −0.864945 | + | 1.49813i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10253.8 | − | 17760.2i | 0.0761298 | − | 0.131861i | −0.825447 | − | 0.564479i | \(-0.809077\pi\) |
0.901577 | + | 0.432619i | \(0.142410\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17011.9 | − | 9821.82i | −0.123596 | − | 0.0713582i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 86938.8i | 0.624879i | 0.949938 | + | 0.312440i | \(0.101146\pi\) | ||||
−0.949938 | + | 0.312440i | \(0.898854\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 58753.6 | + | 101764.i | 0.413382 | + | 0.715999i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 145646.i | − | 1.01396i | −0.861958 | − | 0.506980i | \(-0.830762\pi\) | ||
0.861958 | − | 0.506980i | \(-0.169238\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 165096. | − | 95318.3i | 1.12548 | − | 0.649799i | 0.182689 | − | 0.983171i | \(-0.441520\pi\) |
0.942795 | + | 0.333372i | \(0.108186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −91219.9 | − | 157997.i | −0.615415 | − | 1.06593i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 76712.0 | − | 132869.i | 0.506949 | − | 0.878062i | −0.493019 | − | 0.870019i | \(-0.664107\pi\) |
0.999968 | − | 0.00804280i | \(-0.00256013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 188874. | 1.23543 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 165334. | + | 95455.9i | 1.05967 | + | 0.611799i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17906.9 | − | 31015.7i | −0.113616 | − | 0.196789i | 0.803610 | − | 0.595157i | \(-0.202910\pi\) |
−0.917226 | + | 0.398368i | \(0.869577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −256007. | + | 147806.i | −1.59207 | + | 0.919185i | −0.599124 | + | 0.800657i | \(0.704484\pi\) |
−0.992951 | + | 0.118528i | \(0.962182\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 106904. | − | 185163.i | 0.658239 | − | 1.14010i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 193957.i | 1.17089i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −212656. | − | 122777.i | −1.27125 | − | 0.733957i | −0.296028 | − | 0.955179i | \(-0.595662\pi\) |
−0.975224 | + | 0.221222i | \(0.928996\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23224.6 | − | 13408.7i | 0.136160 | − | 0.0786117i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −73914.9 | − | 128024.i | −0.429176 | − | 0.743355i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17960.1 | 0.102301 | 0.0511505 | − | 0.998691i | \(-0.483711\pi\) | ||||
0.0511505 | + | 0.998691i | \(0.483711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24547.6 | + | 14172.5i | −0.138498 | + | 0.0799620i | −0.567648 | − | 0.823271i | \(-0.692147\pi\) |
0.429150 | + | 0.903233i | \(0.358813\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −243386. | −1.34746 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −71761.7 | + | 124295.i | −0.393583 | + | 0.681706i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −117302. | − | 67724.3i | −0.631467 | − | 0.364578i | 0.149853 | − | 0.988708i | \(-0.452120\pi\) |
−0.781320 | + | 0.624131i | \(0.785453\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −295101. | − | 170377.i | −1.57397 | − | 0.908729i | −0.995676 | − | 0.0928982i | \(-0.970387\pi\) |
−0.578290 | − | 0.815831i | \(-0.696280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −186758. | − | 101758.i | −0.977948 | − | 0.532850i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −176624. | + | 101974.i | −0.916477 | + | 0.529129i | −0.882510 | − | 0.470294i | \(-0.844148\pi\) |
−0.0339679 | + | 0.999423i | \(0.510814\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11724.2 | + | 20307.0i | −0.0597417 | + | 0.103476i | −0.894349 | − | 0.447369i | \(-0.852361\pi\) |
0.834608 | + | 0.550845i | \(0.185694\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 340934.i | − | 1.72167i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 239774.i | 1.18935i | 0.803966 | + | 0.594675i | \(0.202719\pi\) | ||||
−0.803966 | + | 0.594675i | \(0.797281\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 263053. | − | 151874.i | 1.29327 | − | 0.746671i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 124330.i | − | 0.600554i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −230624. | −1.10426 | −0.552130 | − | 0.833758i | \(-0.686185\pi\) | ||||
−0.552130 | + | 0.833758i | \(0.686185\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −193513. | − | 335175.i | −0.910561 | − | 1.57714i | −0.813273 | − | 0.581882i | \(-0.802316\pi\) |
−0.0972884 | − | 0.995256i | \(-0.531017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −84329.2 | −0.393383 | −0.196692 | − | 0.980465i | \(-0.563020\pi\) | ||||
−0.196692 | + | 0.980465i | \(0.563020\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −267364. | −1.22594 | −0.612971 | − | 0.790106i | \(-0.710026\pi\) | ||||
−0.612971 | + | 0.790106i | \(0.710026\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26294.4 | − | 15181.1i | −0.119541 | − | 0.0690173i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 171341. | + | 296771.i | 0.765841 | + | 1.32648i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 240659. | + | 131127.i | 1.06663 | + | 0.581170i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23830.8 | + | 41276.2i | −0.103865 | + | 0.179899i | −0.913274 | − | 0.407346i | \(-0.866454\pi\) |
0.809409 | + | 0.587245i | \(0.199788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −66089.1 | + | 114470.i | −0.285654 | + | 0.494767i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −357274. | − | 206272.i | −1.51886 | − | 0.876916i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 300808.i | − | 1.26833i | −0.773199 | − | 0.634163i | \(-0.781345\pi\) | ||
0.773199 | − | 0.634163i | \(-0.218655\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15562.0 | + | 26954.1i | 0.0645508 | + | 0.111805i | 0.896495 | − | 0.443055i | \(-0.146105\pi\) |
−0.831944 | + | 0.554860i | \(0.812772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 292052.i | 1.20162i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 156949. | − | 90614.8i | 0.635399 | − | 0.366848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 83695.1 | + | 144964.i | 0.336124 | + | 0.582183i | 0.983700 | − | 0.179817i | \(-0.0575507\pi\) |
−0.647576 | + | 0.762001i | \(0.724217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 193752. | − | 335589.i | 0.765793 | − | 1.32639i | −0.174034 | − | 0.984740i | \(-0.555680\pi\) |
0.939826 | − | 0.341652i | \(-0.110987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −161659. | −0.633896 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 49772.1 | + | 28735.9i | 0.192110 | + | 0.110915i | 0.592970 | − | 0.805225i | \(-0.297955\pi\) |
−0.400860 | + | 0.916139i | \(0.631289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −80241.9 | − | 138983.i | −0.307298 | − | 0.532255i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −468251. | + | 270345.i | −1.76549 | + | 1.01930i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 97705.3 | − | 169231.i | 0.365542 | − | 0.633137i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 253537.i | 0.934039i | 0.884247 | + | 0.467020i | \(0.154672\pi\) | ||||
−0.884247 | + | 0.467020i | \(0.845328\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 303436. | + | 175189.i | 1.10934 | + | 0.640477i | 0.938658 | − | 0.344850i | \(-0.112070\pi\) |
0.170680 | + | 0.985326i | \(0.445403\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 460204. | − | 265699.i | 1.65702 | − | 0.956683i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −33624.4 | − | 58239.1i | −0.120155 | − | 0.208115i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 206999. | 0.728640 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 542609. | − | 313276.i | 1.89574 | − | 1.09451i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −327415. | −1.12699 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −90974.1 | + | 157572.i | −0.310830 | + | 0.538374i | −0.978542 | − | 0.206046i | \(-0.933940\pi\) |
0.667712 | + | 0.744420i | \(0.267274\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 554591. | + | 320193.i | 1.86715 | + | 1.07800i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −65609.1 | − | 37879.4i | −0.219275 | − | 0.126598i | 0.386340 | − | 0.922357i | \(-0.373739\pi\) |
−0.605615 | + | 0.795758i | \(0.707073\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 157346. | − | 288780.i | 0.518266 | − | 0.951181i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −115131. | + | 66470.6i | −0.376478 | + | 0.217360i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12063.0 | − | 20893.8i | 0.0388818 | − | 0.0673453i | −0.845930 | − | 0.533295i | \(-0.820954\pi\) |
0.884811 | + | 0.465949i | \(0.154287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 233532.i | 0.747348i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 564081.i | − | 1.77961i | −0.456343 | − | 0.889804i | \(-0.650841\pi\) | ||
0.456343 | − | 0.889804i | \(-0.349159\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −492274. | + | 284214.i | −1.54209 | + | 0.890326i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 188598.i | − | 0.582521i | −0.956644 | − | 0.291261i | \(-0.905925\pi\) | ||
0.956644 | − | 0.291261i | \(-0.0940747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −168254. | −0.516052 | −0.258026 | − | 0.966138i | \(-0.583072\pi\) | ||||
−0.258026 | + | 0.966138i | \(0.583072\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 223632. | + | 387343.i | 0.676393 | + | 1.17155i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 346445. | 1.04060 | 0.520298 | − | 0.853985i | \(-0.325821\pi\) | ||||
0.520298 | + | 0.853985i | \(0.325821\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 102941. | 0.304956 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 124288. | + | 71757.8i | 0.365673 | + | 0.211121i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 303062. | + | 524919.i | 0.879539 | + | 1.52341i | 0.851847 | + | 0.523791i | \(0.175483\pi\) |
0.0276924 | + | 0.999616i | \(0.491184\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −598194. | + | 14782.1i | −1.72430 | + | 0.0426093i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −127645. | + | 221088.i | −0.362991 | + | 0.628719i | −0.988452 | − | 0.151537i | \(-0.951578\pi\) |
0.625460 | + | 0.780256i | \(0.284911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 154504. | − | 267609.i | 0.436422 | − | 0.755905i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −178869. | − | 103270.i | −0.498520 | − | 0.287821i | 0.229582 | − | 0.973289i | \(-0.426264\pi\) |
−0.728102 | + | 0.685469i | \(0.759597\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 580567.i | − | 1.60732i | −0.595086 | − | 0.803662i | \(-0.702882\pi\) | ||
0.595086 | − | 0.803662i | \(-0.297118\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 394093. | + | 682589.i | 1.07668 | + | 1.86487i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19201.3i | 0.0521140i | 0.999660 | + | 0.0260570i | \(0.00829514\pi\) | ||||
−0.999660 | + | 0.0260570i | \(0.991705\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 115328. | − | 66584.6i | 0.308924 | − | 0.178357i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 260010. | + | 450351.i | 0.691942 | + | 1.19848i | 0.971201 | + | 0.238262i | \(0.0765778\pi\) |
−0.279259 | + | 0.960216i | \(0.590089\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 305961. | − | 529939.i | 0.803702 | − | 1.39205i | −0.113462 | − | 0.993542i | \(-0.536194\pi\) |
0.917164 | − | 0.398510i | \(-0.130473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 561440. | 1.46528 | 0.732642 | − | 0.680614i | \(-0.238287\pi\) | ||||
0.732642 | + | 0.680614i | \(0.238287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 205602. | + | 118705.i | 0.529727 | + | 0.305838i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 144380. | + | 250073.i | 0.369613 | + | 0.640188i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −284503. | + | 164258.i | −0.719093 | + | 0.415169i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −330147. | + | 571831.i | −0.829179 | + | 1.43618i | 0.0695045 | + | 0.997582i | \(0.477858\pi\) |
−0.898683 | + | 0.438598i | \(0.855475\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 51186.8i | 0.126944i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −193234. | − | 111564.i | −0.476218 | − | 0.274944i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45344.7 | − | 26179.8i | 0.110360 | − | 0.0637162i | −0.443804 | − | 0.896124i | \(-0.646371\pi\) |
0.554164 | + | 0.832408i | \(0.313038\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 128987. | + | 223412.i | 0.311978 | + | 0.540362i | 0.978791 | − | 0.204864i | \(-0.0656751\pi\) |
−0.666812 | + | 0.745226i | \(0.732342\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −295878. | −0.706813 | −0.353407 | − | 0.935470i | \(-0.614977\pi\) | ||||
−0.353407 | + | 0.935470i | \(0.614977\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −169678. | + | 97963.6i | −0.402843 | + | 0.232582i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −605903. | −1.42094 | −0.710472 | − | 0.703726i | \(-0.751518\pi\) | ||||
−0.710472 | + | 0.703726i | \(0.751518\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −110673. | + | 191691.i | −0.257964 | + | 0.446807i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 512302. | + | 295778.i | 1.17965 | + | 0.681074i | 0.955935 | − | 0.293579i | \(-0.0948465\pi\) |
0.223720 | + | 0.974653i | \(0.428180\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 313351. | + | 180913.i | 0.717179 | + | 0.414063i | 0.813713 | − | 0.581266i | \(-0.197442\pi\) |
−0.0965345 | + | 0.995330i | \(0.530776\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −296950. | + | 181370.i | −0.671491 | + | 0.410130i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 464794. | − | 268349.i | 1.04474 | − | 0.603182i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 524288. | − | 908093.i | 1.16446 | − | 2.01690i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 172441.i | 0.380724i | 0.981714 | + | 0.190362i | \(0.0609661\pi\) | ||||
−0.981714 | + | 0.190362i | \(0.939034\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 708240.i | − | 1.54526i | −0.634854 | − | 0.772632i | \(-0.718940\pi\) | ||
0.634854 | − | 0.772632i | \(-0.281060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 248788. | − | 143638.i | 0.539622 | − | 0.311551i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 766639.i | − | 1.64342i | −0.569904 | − | 0.821712i | \(-0.693019\pi\) | ||
0.569904 | − | 0.821712i | \(-0.306981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 131780. | 0.280845 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 48901.8 | + | 84700.3i | 0.103012 | + | 0.178421i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41957.7 | 0.0878729 | 0.0439365 | − | 0.999034i | \(-0.486010\pi\) | ||||
0.0439365 | + | 0.999034i | \(0.486010\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.15377e6 | −2.38864 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 445547. | + | 257237.i | 0.917125 | + | 0.529502i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 397795. | + | 689002.i | 0.809513 | + | 1.40212i | 0.913202 | + | 0.407508i | \(0.133602\pi\) |
−0.103689 | + | 0.994610i | \(0.533065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 369810. | − | 9138.44i | 0.748287 | − | 0.0184910i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 56285.6 | − | 97489.6i | 0.112605 | − | 0.195038i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −104386. | + | 180802.i | −0.207659 | + | 0.359676i | −0.950977 | − | 0.309263i | \(-0.899918\pi\) |
0.743318 | + | 0.668939i | \(0.233251\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −845706. | − | 488268.i | −1.66357 | − | 0.960461i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 908347.i | 1.77681i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −121432. | − | 210327.i | −0.234897 | − | 0.406853i | 0.724346 | − | 0.689437i | \(-0.242142\pi\) |
−0.959243 | + | 0.282584i | \(0.908809\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 376509.i | − | 0.724278i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −598940. | + | 345798.i | −1.13948 | + | 0.657880i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −58207.6 | − | 100819.i | −0.110131 | − | 0.190753i | 0.805692 | − | 0.592335i | \(-0.201794\pi\) |
−0.915823 | + | 0.401582i | \(0.868461\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −290210. | + | 502658.i | −0.543097 | + | 0.940672i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 696231. | 1.29582 | 0.647911 | − | 0.761716i | \(-0.275643\pi\) | ||||
0.647911 | + | 0.761716i | \(0.275643\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 192106. | + | 110913.i | 0.353677 | + | 0.204195i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24355.4 | + | 42184.8i | 0.0445971 | + | 0.0772444i | 0.887462 | − | 0.460880i | \(-0.152466\pi\) |
−0.842865 | + | 0.538125i | \(0.819133\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −82349.9 | + | 47544.7i | −0.149171 | + | 0.0861241i | −0.572728 | − | 0.819746i | \(-0.694115\pi\) |
0.423557 | + | 0.905870i | \(0.360782\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −610148. | + | 1.05681e6i | −1.09932 | + | 1.90407i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 436298.i | 0.777714i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 120915. | + | 69810.4i | 0.214388 | + | 0.123777i | 0.603349 | − | 0.797477i | \(-0.293833\pi\) |
−0.388961 | + | 0.921254i | \(0.627166\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −621545. | + | 358849.i | −1.09038 | + | 0.629533i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43704.0 | − | 75697.5i | −0.0762657 | − | 0.132096i | 0.825370 | − | 0.564592i | \(-0.190966\pi\) |
−0.901636 | + | 0.432496i | \(0.857633\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 510619. | 0.881714 | 0.440857 | − | 0.897577i | \(-0.354675\pi\) | ||||
0.440857 | + | 0.897577i | \(0.354675\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −386189. | + | 222966.i | −0.663362 | + | 0.382992i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −133521. | −0.226965 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12429.1 | − | 21527.9i | 0.0210178 | − | 0.0364039i | −0.855325 | − | 0.518092i | \(-0.826643\pi\) |
0.876343 | + | 0.481688i | \(0.159976\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7645.09 | + | 4413.89i | 0.0127945 | + | 0.00738691i | 0.506384 | − | 0.862308i | \(-0.330982\pi\) |
−0.493589 | + | 0.869695i | \(0.664315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.08979e6 | + | 629189.i | 1.81442 | + | 1.04756i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −301966. | − | 494398.i | −0.497603 | − | 0.814707i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.14667e6 | + | 662028.i | −1.87990 | + | 1.08536i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −489616. | + | 848039.i | −0.794540 | + | 1.37618i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 209129.i | 0.337649i | 0.985646 | + | 0.168824i | \(0.0539971\pi\) | ||||
−0.985646 | + | 0.168824i | \(0.946003\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 395825.i | − | 0.632631i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 618850. | − | 357293.i | 0.984100 | − | 0.568170i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 975546.i | − | 1.53579i | −0.640578 | − | 0.767894i | \(-0.721305\pi\) | ||
0.640578 | − | 0.767894i | \(-0.278695\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 330978. | 0.518449 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 586244. | + | 1.01540e6i | 0.909175 | + | 1.57474i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −567858. | −0.876291 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −219203. | −0.334926 | −0.167463 | − | 0.985878i | \(-0.553557\pi\) | ||||
−0.167463 | + | 0.985878i | \(0.553557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 804012. | + | 464197.i | 1.22242 | + | 0.705765i | 0.965434 | − | 0.260649i | \(-0.0839366\pi\) |
0.256988 | + | 0.966415i | \(0.417270\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 705189. | + | 1.22142e6i | 1.06167 | + | 1.83887i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 557770. | − | 340672.i | 0.835625 | − | 0.510379i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 213229. | − | 369324.i | 0.316344 | − | 0.547925i | −0.663378 | − | 0.748284i | \(-0.730878\pi\) |
0.979722 | + | 0.200360i | \(0.0642112\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 250617. | − | 434082.i | 0.370008 | − | 0.640873i | −0.619558 | − | 0.784951i | \(-0.712688\pi\) |
0.989566 | + | 0.144078i | \(0.0460216\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 367431. | + | 212137.i | 0.537236 | + | 0.310173i | 0.743958 | − | 0.668226i | \(-0.232946\pi\) |
−0.206722 | + | 0.978400i | \(0.566280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 653309.i | 0.950626i | 0.879817 | + | 0.475313i | \(0.157665\pi\) | ||||
−0.879817 | + | 0.475313i | \(0.842335\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −277281. | − | 480264.i | −0.399604 | − | 0.692134i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 952696.i | 1.36641i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 382493. | − | 220833.i | 0.543376 | − | 0.313718i | −0.203070 | − | 0.979164i | \(-0.565092\pi\) |
0.746446 | + | 0.665446i | \(0.231759\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61302.0 | + | 106178.i | 0.0866727 | + | 0.150122i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 221788. | − | 384147.i | 0.310616 | − | 0.538003i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −548853. | −0.765048 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 522824. | + | 301853.i | 0.721933 | + | 0.416808i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −407216. | − | 705318.i | −0.559663 | − | 0.969364i | −0.997524 | − | 0.0703220i | \(-0.977597\pi\) |
0.437862 | − | 0.899042i | \(-0.355736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −193851. | + | 111920.i | −0.263940 | + | 0.152386i | −0.626131 | − | 0.779718i | \(-0.715362\pi\) |
0.362190 | + | 0.932104i | \(0.382029\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 393015. | − | 680722.i | 0.532627 | − | 0.922537i | −0.466647 | − | 0.884443i | \(-0.654538\pi\) |
0.999274 | − | 0.0380933i | \(-0.0121284\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 21594.6i | − | 0.0289950i | −0.999895 | − | 0.0144975i | \(-0.995385\pi\) | ||
0.999895 | − | 0.0144975i | \(-0.00461487\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 746806. | + | 431169.i | 0.998104 | + | 0.576255i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 841139. | − | 485632.i | 1.11385 | − | 0.643084i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 75585.0 | + | 130917.i | 0.0996322 | + | 0.172568i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 129330. | 0.168921 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −71775.7 | + | 41439.7i | −0.0933208 | + | 0.0538788i | −0.545934 | − | 0.837828i | \(-0.683825\pi\) |
0.452613 | + | 0.891707i | \(0.350492\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.09279e6 | 1.40794 | 0.703970 | − | 0.710230i | \(-0.251409\pi\) | ||||
0.703970 | + | 0.710230i | \(0.251409\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 169370. | − | 293358.i | 0.217228 | − | 0.376250i | −0.736732 | − | 0.676185i | \(-0.763632\pi\) |
0.953959 | + | 0.299936i | \(0.0969652\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −117292. | − | 67718.4i | −0.149080 | − | 0.0860715i | 0.423604 | − | 0.905847i | \(-0.360765\pi\) |
−0.572685 | + | 0.819776i | \(0.694098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30868.5 | − | 17822.0i | −0.0390582 | − | 0.0225503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −327269. | − | 178318.i | −0.410395 | − | 0.223610i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.09807e6 | − | 633974.i | 1.37084 | − | 0.791453i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 755000. | − | 1.30770e6i | 0.934173 | − | 1.61803i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 243081.i | 0.299434i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 388939.i | − | 0.474881i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4012.56 | + | 2316.65i | −0.00487761 | + | 0.00281609i | −0.502437 | − | 0.864614i | \(-0.667563\pi\) |
0.497559 | + | 0.867430i | \(0.334230\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 228474.i | 0.275296i | 0.990481 | + | 0.137648i | \(0.0439543\pi\) | ||||
−0.990481 | + | 0.137648i | \(0.956046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −752084. | −0.902245 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −77067.1 | − | 133484.i | −0.0916496 | − | 0.158742i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 252976. | 0.299535 | 0.149768 | − | 0.988721i | \(-0.452147\pi\) | ||||
0.149768 | + | 0.988721i | \(0.452147\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −902322. | −1.05915 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −673719. | − | 388972.i | −0.787399 | − | 0.454605i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −308399. | − | 534163.i | −0.357340 | − | 0.618931i | 0.630176 | − | 0.776453i | \(-0.282983\pi\) |
−0.987516 | + | 0.157522i | \(0.949650\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15426.4 | + | 624270.i | 0.0177978 | + | 0.720234i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.12880e6 | + | 1.95514e6i | −1.29120 | + | 2.23643i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −698080. | + | 1.20911e6i | −0.795108 | + | 1.37717i | 0.127663 | + | 0.991818i | \(0.459253\pi\) |
−0.922771 | + | 0.385350i | \(0.874081\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −119887. | − | 69216.8i | −0.135392 | − | 0.0781686i | 0.430774 | − | 0.902460i | \(-0.358241\pi\) |
−0.566166 | + | 0.824291i | \(0.691574\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 945437.i | − | 1.06319i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 171569. | + | 297167.i | 0.191311 | + | 0.331360i | 0.945685 | − | 0.325085i | \(-0.105393\pi\) |
−0.754374 | + | 0.656445i | \(0.772059\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 799031.i | 0.887220i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.06953e6 | − | 617492.i | 1.17762 | − | 0.679901i | 0.222160 | − | 0.975010i | \(-0.428689\pi\) |
0.955464 | + | 0.295109i | \(0.0953560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −525139. | − | 909567.i | −0.575794 | − | 0.997305i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45882.3 | + | 79470.5i | −0.0498894 | + | 0.0864109i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.82396e6 | −1.97501 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −451427. | − | 260632.i | −0.484767 | − | 0.279880i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 847953. | + | 1.46870e6i | 0.906815 | + | 1.57065i | 0.818462 | + | 0.574561i | \(0.194827\pi\) |
0.0883534 | + | 0.996089i | \(0.471840\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 699151. | − | 403655.i | 0.741536 | − | 0.428126i | −0.0810915 | − | 0.996707i | \(-0.525841\pi\) |
0.822628 | + | 0.568581i | \(0.192507\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 401715. | − | 695790.i | 0.424318 | − | 0.734941i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 90445.0i | − | 0.0947536i | −0.998877 | − | 0.0473768i | \(-0.984914\pi\) | ||
0.998877 | − | 0.0473768i | \(-0.0150861\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.50212e6 | − | 867251.i | −1.56726 | − | 0.904856i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −947240. | + | 546889.i | −0.980286 | + | 0.565968i | −0.902356 | − | 0.430990i | \(-0.858164\pi\) |
−0.0779295 | + | 0.996959i | \(0.524831\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.11933e6 | − | 1.93874e6i | −1.15368 | − | 1.99824i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.06662e6 | 1.09048 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 718383. | − | 414759.i | 0.731491 | − | 0.422326i | −0.0874766 | − | 0.996167i | \(-0.527880\pi\) |
0.818967 | + | 0.573840i | \(0.194547\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 303325. | 0.306381 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −619962. | + | 1.07381e6i | −0.623699 | + | 1.08028i | 0.365092 | + | 0.930972i | \(0.381038\pi\) |
−0.988791 | + | 0.149307i | \(0.952296\pi\) | |||||||
\(998\) | 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.145.10 | yes | 24 | |
3.2 | odd | 2 | inner | 684.5.y.f.145.3 | ✓ | 24 | |
19.8 | odd | 6 | inner | 684.5.y.f.217.10 | yes | 24 | |
57.8 | even | 6 | inner | 684.5.y.f.217.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.5.y.f.145.3 | ✓ | 24 | 3.2 | odd | 2 | inner | |
684.5.y.f.145.10 | yes | 24 | 1.1 | even | 1 | trivial | |
684.5.y.f.217.3 | yes | 24 | 57.8 | even | 6 | inner | |
684.5.y.f.217.10 | yes | 24 | 19.8 | odd | 6 | inner |