Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(783,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.783");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.12258833328.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 29x^{4} - 20x^{3} + 808x^{2} - 672x + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 783.1 | ||
Root | \(0.426664 - 0.739004i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.783 |
Dual form | 784.4.f.h.783.2 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −7.06258 | −1.35919 | −0.679597 | − | 0.733586i | \(-0.737845\pi\) | ||||
−0.679597 | + | 0.733586i | \(0.737845\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.22397i | − 0.109475i | −0.998501 | − | 0.0547374i | \(-0.982568\pi\) | ||||
0.998501 | − | 0.0547374i | \(-0.0174322\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 22.8800 | 0.847408 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.57968i | 0.125529i | 0.998028 | + | 0.0627647i | \(0.0199918\pi\) | ||||
−0.998028 | + | 0.0627647i | \(0.980008\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 41.0611i | 0.876024i | 0.898969 | + | 0.438012i | \(0.144317\pi\) | ||||
−0.898969 | + | 0.438012i | \(0.855683\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.64436i | 0.148798i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 119.455i | − 1.70424i | −0.523346 | − | 0.852120i | \(-0.675317\pi\) | ||||
0.523346 | − | 0.852120i | \(-0.324683\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −60.1826 | −0.726675 | −0.363337 | − | 0.931658i | \(-0.618363\pi\) | ||||
−0.363337 | + | 0.931658i | \(0.618363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.35305i | 0.0757275i | 0.999283 | + | 0.0378637i | \(0.0120553\pi\) | ||||
−0.999283 | + | 0.0378637i | \(0.987945\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 123.502 | 0.988015 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.0976 | 0.207401 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 164.382 | 1.05258 | 0.526292 | − | 0.850304i | \(-0.323582\pi\) | ||||
0.526292 | + | 0.850304i | \(0.323582\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −287.559 | −1.66604 | −0.833019 | − | 0.553244i | \(-0.813390\pi\) | ||||
−0.833019 | + | 0.553244i | \(0.813390\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 32.3443i | − 0.170619i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −148.742 | −0.660892 | −0.330446 | − | 0.943825i | \(-0.607199\pi\) | ||||
−0.330446 | + | 0.943825i | \(0.607199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 289.998i | − 1.19069i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 358.778i | − 1.36663i | −0.730125 | − | 0.683314i | \(-0.760538\pi\) | ||||
0.730125 | − | 0.683314i | \(-0.239462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 360.388i | − 1.27811i | −0.769161 | − | 0.639055i | \(-0.779326\pi\) | ||||
0.769161 | − | 0.639055i | \(-0.220674\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 28.0044i | − 0.0927699i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −225.434 | −0.699637 | −0.349819 | − | 0.936817i | \(-0.613757\pi\) | ||||
−0.349819 | + | 0.936817i | \(0.613757\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 843.660i | 2.31639i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 684.724 | 1.77460 | 0.887302 | − | 0.461189i | \(-0.152577\pi\) | ||||
0.887302 | + | 0.461189i | \(0.152577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.60537 | 0.0137423 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 425.044 | 0.987692 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −85.0522 | −0.187675 | −0.0938377 | − | 0.995588i | \(-0.529913\pi\) | ||||
−0.0938377 | + | 0.995588i | \(0.529913\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 209.127i | 0.438949i | 0.975618 | + | 0.219475i | \(0.0704344\pi\) | ||||
−0.975618 | + | 0.219475i | \(0.929566\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 50.2574 | 0.0959026 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 417.225i | 0.760778i | 0.924827 | + | 0.380389i | \(0.124210\pi\) | ||||
−0.924827 | + | 0.380389i | \(0.875790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 58.9941i | − 0.102928i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 982.974i | 1.64306i | 0.570162 | + | 0.821532i | \(0.306880\pi\) | ||||
−0.570162 | + | 0.821532i | \(0.693120\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 341.526i | 0.547570i | 0.961791 | + | 0.273785i | \(0.0882757\pi\) | ||||
−0.961791 | + | 0.273785i | \(0.911724\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −872.242 | −1.34290 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 76.2934i | − 0.108654i | −0.998523 | − | 0.0543271i | \(-0.982699\pi\) | ||||
0.998523 | − | 0.0543271i | \(-0.0173014\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −823.265 | −1.12931 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 523.643 | 0.692498 | 0.346249 | − | 0.938143i | \(-0.387455\pi\) | ||||
0.346249 | + | 0.938143i | \(0.387455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −146.209 | −0.186571 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1160.96 | −1.43067 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 972.055i | 1.15773i | 0.815425 | + | 0.578863i | \(0.196503\pi\) | ||||
−0.815425 | + | 0.578863i | \(0.803497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2030.91 | 2.26447 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 73.6614i | 0.0795526i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 676.730i | 0.708367i | 0.935176 | + | 0.354183i | \(0.115241\pi\) | ||||
−0.935176 | + | 0.354183i | \(0.884759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 104.783i | 0.106375i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 838.786i | 0.826360i | 0.910649 | + | 0.413180i | \(0.135582\pi\) | ||||
−0.910649 | + | 0.413180i | \(0.864418\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1515.20 | −1.44949 | −0.724744 | − | 0.689018i | \(-0.758042\pi\) | ||||
−0.724744 | + | 0.689018i | \(0.758042\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1687.67i | 1.52480i | 0.647107 | + | 0.762399i | \(0.275979\pi\) | ||||
−0.647107 | + | 0.762399i | \(0.724021\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1576.23 | −1.38510 | −0.692550 | − | 0.721370i | \(-0.743513\pi\) | ||||
−0.692550 | + | 0.721370i | \(0.743513\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1050.50 | 0.898281 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2192.01 | −1.82484 | −0.912422 | − | 0.409251i | \(-0.865790\pi\) | ||||
−0.912422 | + | 0.409251i | \(0.865790\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.2239 | 0.00829025 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 939.480i | 0.742350i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1310.03 | 0.984242 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2533.90i | 1.85751i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 304.158i | − 0.217638i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1085.60i | 0.758515i | 0.925291 | + | 0.379258i | \(0.123821\pi\) | ||||
−0.925291 | + | 0.379258i | \(0.876179\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2545.27i | 1.73720i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1533.35 | 1.02267 | 0.511334 | − | 0.859382i | \(-0.329151\pi\) | ||||
0.511334 | + | 0.859382i | \(0.329151\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 35.6145i | − 0.0227052i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 920.175 | 0.573838 | 0.286919 | − | 0.957955i | \(-0.407369\pi\) | ||||
0.286919 | + | 0.957955i | \(0.407369\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1424.66 | 0.869339 | 0.434669 | − | 0.900590i | \(-0.356865\pi\) | ||||
0.434669 | + | 0.900590i | \(0.356865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1592.15 | 0.950943 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −188.047 | −0.109967 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 201.198i | − 0.115232i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1378.25 | −0.757791 | −0.378896 | − | 0.925439i | \(-0.623696\pi\) | ||||
−0.378896 | + | 0.925439i | \(0.623696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 1333.78i | − 0.718817i | −0.933180 | − | 0.359409i | \(-0.882978\pi\) | ||||
0.933180 | − | 0.359409i | \(-0.117022\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 2733.13i | − 1.44419i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 351.963i | 0.182389i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1255.89i | 0.638416i | 0.947685 | + | 0.319208i | \(0.103417\pi\) | ||||
−0.947685 | + | 0.319208i | \(0.896583\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4835.92 | −2.41203 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3254.58i | 1.56392i | 0.623330 | + | 0.781959i | \(0.285779\pi\) | ||||
−0.623330 | + | 0.781959i | \(0.714221\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −39.5884 | −0.0186785 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2736.24 | −1.26788 | −0.633941 | − | 0.773381i | \(-0.718564\pi\) | ||||
−0.633941 | + | 0.773381i | \(0.718564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 510.983 | 0.232582 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1376.98 | −0.615791 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3380.13i | 1.48547i | 0.669584 | + | 0.742737i | \(0.266473\pi\) | ||||
−0.669584 | + | 0.742737i | \(0.733527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 600.688 | 0.255087 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1217.98i | − 0.508584i | −0.967128 | − | 0.254292i | \(-0.918158\pi\) | ||||
0.967128 | − | 0.254292i | \(-0.0818423\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1757.61i | 0.721781i | 0.932608 | + | 0.360890i | \(0.117527\pi\) | ||||
−0.932608 | + | 0.360890i | \(0.882473\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 1476.97i | − 0.596618i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 182.055i | 0.0723511i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 547.065 | 0.213932 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 956.433i | 0.362330i | 0.983453 | + | 0.181165i | \(0.0579868\pi\) | ||||
−0.983453 | + | 0.181165i | \(0.942013\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1333.55 | 0.497362 | 0.248681 | − | 0.968585i | \(-0.420003\pi\) | ||||
0.248681 | + | 0.968585i | \(0.420003\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −354.947 | −0.130350 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1098.75 | 0.397373 | 0.198686 | − | 0.980063i | \(-0.436332\pi\) | ||||
0.198686 | + | 0.980063i | \(0.436332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 248.579 | 0.0885491 | 0.0442745 | − | 0.999019i | \(-0.485902\pi\) | ||||
0.0442745 | + | 0.999019i | \(0.485902\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 2946.68i | − 1.03405i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −439.132 | −0.149611 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 191.118i | 0.0641721i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 275.617i | − 0.0912191i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2029.24i | 0.662078i | 0.943617 | + | 0.331039i | \(0.107399\pi\) | ||||
−0.943617 | + | 0.331039i | \(0.892601\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 6942.33i | − 2.23324i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −441.103 | −0.139921 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2412.06i | − 0.744254i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4904.96 | 1.49295 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3904.24 | 1.17241 | 0.586204 | − | 0.810164i | \(-0.300622\pi\) | ||||
0.586204 | + | 0.810164i | \(0.300622\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2825.73 | 0.837253 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4255.75 | −1.24434 | −0.622168 | − | 0.782884i | \(-0.713748\pi\) | ||||
−0.622168 | + | 0.782884i | \(0.713748\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1732.25i | − 0.499871i | −0.968262 | − | 0.249936i | \(-0.919591\pi\) | ||||
0.968262 | − | 0.249936i | \(-0.0804095\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −874.910 | −0.245997 | −0.122998 | − | 0.992407i | \(-0.539251\pi\) | ||||
−0.122998 | + | 0.992407i | \(0.539251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 275.924i | 0.0765927i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 538.828i | 0.147682i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 1842.84i | − 0.498760i | −0.968406 | − | 0.249380i | \(-0.919773\pi\) | ||||
0.968406 | − | 0.249380i | \(-0.0802269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 4683.60i | − 1.25185i | −0.779881 | − | 0.625927i | \(-0.784721\pi\) | ||||
0.779881 | − | 0.625927i | \(-0.215279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5028.74 | 1.32755 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2471.16i | − 0.636585i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3698.27 | −0.941239 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1015.59 | 0.255393 | 0.127696 | − | 0.991813i | \(-0.459242\pi\) | ||||
0.127696 | + | 0.991813i | \(0.459242\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.2543 | −0.00950603 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1032.61 | 0.253587 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 3016.56i | − 0.732171i | −0.930581 | − | 0.366085i | \(-0.880698\pi\) | ||||
0.930581 | − | 0.366085i | \(-0.119302\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3761.06 | 0.891969 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 2651.05i | − 0.621561i | −0.950482 | − | 0.310780i | \(-0.899410\pi\) | ||||
0.950482 | − | 0.310780i | \(-0.100590\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 838.078i | − 0.194275i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6865.21i | − 1.57357i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 452.582i | 0.102581i | 0.998684 | + | 0.0512907i | \(0.0163335\pi\) | ||||
−0.998684 | + | 0.0512907i | \(0.983666\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 164.726 | 0.0369239 | 0.0184620 | − | 0.999830i | \(-0.494123\pi\) | ||||
0.0184620 | + | 0.999830i | \(0.494123\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 565.599i | 0.124025i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1939.61 | 0.420721 | 0.210360 | − | 0.977624i | \(-0.432536\pi\) | ||||
0.210360 | + | 0.977624i | \(0.432536\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6579.37 | −1.41181 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7152.79 | −1.51850 | −0.759252 | − | 0.650796i | \(-0.774435\pi\) | ||||
−0.759252 | + | 0.650796i | \(0.774435\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3295.55 | 0.692226 | 0.346113 | − | 0.938193i | \(-0.387501\pi\) | ||||
0.346113 | + | 0.938193i | \(0.387501\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 520.239i | − 0.108127i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9356.49 | −1.90443 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 4779.46i | − 0.962808i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7368.65i | 1.46922i | 0.678491 | + | 0.734609i | \(0.262634\pi\) | ||||
−0.678491 | + | 0.734609i | \(0.737366\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 104.101i | 0.0205457i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 133.258i | 0.0260350i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −342.986 | −0.0663391 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 5923.99i | − 1.12318i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 255.964 | 0.0480539 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2692.96 | −0.500636 | −0.250318 | − | 0.968164i | \(-0.580535\pi\) | ||||
−0.250318 | + | 0.968164i | \(0.580535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10701.2 | 1.97014 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2971.99 | 0.541885 | 0.270943 | − | 0.962596i | \(-0.412665\pi\) | ||||
0.270943 | + | 0.962596i | \(0.412665\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1140.00i | 0.205868i | 0.994688 | + | 0.102934i | \(0.0328230\pi\) | ||||
−0.994688 | + | 0.102934i | \(0.967177\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5645.11 | −1.00019 | −0.500097 | − | 0.865970i | \(-0.666702\pi\) | ||||
−0.500097 | + | 0.865970i | \(0.666702\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 752.816i | 0.132130i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 11919.3i | − 2.07250i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7189.10i | 1.23843i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5071.13i | 0.865525i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11132.3 | 1.88262 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 7359.98i | − 1.22218i | −0.791562 | − | 0.611089i | \(-0.790732\pi\) | ||||
0.791562 | − | 0.611089i | \(-0.209268\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3403.22 | −0.560046 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 510.669 | 0.0832861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10163.9 | −1.64292 | −0.821459 | − | 0.570268i | \(-0.806839\pi\) | ||||
−0.821459 | + | 0.570268i | \(0.806839\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15481.3 | 2.48032 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1316.93i | − 0.209137i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −72.2068 | −0.0112681 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10544.8i | 1.63133i | 0.578522 | + | 0.815666i | \(0.303630\pi\) | ||||
−0.578522 | + | 0.815666i | \(0.696370\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6048.02i | 0.927631i | 0.885932 | + | 0.463816i | \(0.153520\pi\) | ||||
−0.885932 | + | 0.463816i | \(0.846480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1194.78i | 0.181689i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6289.12i | 0.948261i | 0.880454 | + | 0.474131i | \(0.157238\pi\) | ||||
−0.880454 | + | 0.474131i | \(0.842762\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1203.13 | 0.179874 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 154.662i | 0.0227375i | 0.999935 | + | 0.0113687i | \(0.00361886\pi\) | ||||
−0.999935 | + | 0.0113687i | \(0.996381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3237.06 | −0.471944 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9252.17 | −1.33778 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 418.016 | 0.0599451 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5890.42 | 0.837813 | 0.418907 | − | 0.908029i | \(-0.362413\pi\) | ||||
0.418907 | + | 0.908029i | \(0.362413\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 8208.86i | − 1.15809i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 350.300 | 0.0486270 | 0.0243135 | − | 0.999704i | \(-0.492260\pi\) | ||||
0.0243135 | + | 0.999704i | \(0.492260\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2148.14i | 0.295812i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6749.71i | 0.922089i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 8247.17i | − 1.11775i | −0.829251 | − | 0.558877i | \(-0.811233\pi\) | ||||
0.829251 | − | 0.558877i | \(-0.188767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 7667.14i | − 1.03097i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12680.2 | 1.69171 | 0.845856 | − | 0.533411i | \(-0.179090\pi\) | ||||
0.845856 | + | 0.533411i | \(0.179090\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 8245.69i | − 1.08308i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7727.53 | −1.00720 | −0.503601 | − | 0.863937i | \(-0.667992\pi\) | ||||
−0.503601 | + | 0.863937i | \(0.667992\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 997.814 | 0.129058 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10829.4 | −1.39000 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −93.3806 | −0.0118949 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10096.2i | 1.27636i | 0.769889 | + | 0.638178i | \(0.220312\pi\) | ||||
−0.769889 | + | 0.638178i | \(0.779688\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7678.50 | 0.956224 | 0.478112 | − | 0.878299i | \(-0.341321\pi\) | ||||
0.478112 | + | 0.878299i | \(0.341321\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 11807.5i | − 1.45949i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1007.65i | 0.123631i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 681.190i | − 0.0829615i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3711.55i | 0.448715i | 0.974507 | + | 0.224358i | \(0.0720284\pi\) | ||||
−0.974507 | + | 0.224358i | \(0.927972\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6498.81 | −0.779957 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 640.921i | − 0.0758111i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10061.8 | −1.18160 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8868.09 | 1.03397 | 0.516986 | − | 0.855994i | \(-0.327054\pi\) | ||||
0.516986 | + | 0.855994i | \(0.327054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9571.99 | −1.10810 | −0.554050 | − | 0.832483i | \(-0.686919\pi\) | ||||
−0.554050 | + | 0.832483i | \(0.686919\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5157.94 | −0.592879 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 14752.9i | − 1.68382i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1328.09 | 0.149466 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7712.13i | 0.861903i | 0.902375 | + | 0.430952i | \(0.141822\pi\) | ||||
−0.902375 | + | 0.430952i | \(0.858178\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2222.71i | 0.246690i | 0.992364 | + | 0.123345i | \(0.0393622\pi\) | ||||
−0.992364 | + | 0.123345i | \(0.960638\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1420.98i | 0.156622i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 502.708i | − 0.0550293i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10612.6 | 1.15378 | 0.576890 | − | 0.816822i | \(-0.304266\pi\) | ||||
0.576890 | + | 0.816822i | \(0.304266\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 15591.1i | − 1.67213i | −0.548630 | − | 0.836065i | \(-0.684851\pi\) | ||||
0.548630 | − | 0.836065i | \(-0.315149\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1189.76 | 0.126742 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9734.03 | 1.02999 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2759.74 | 0.290067 | 0.145033 | − | 0.989427i | \(-0.453671\pi\) | ||||
0.145033 | + | 0.989427i | \(0.453671\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1643.09 | 0.171552 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9419.92i | 0.977012i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7672.29 | −0.785327 | −0.392664 | − | 0.919682i | \(-0.628446\pi\) | ||||
−0.392664 | + | 0.919682i | \(0.628446\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 3475.86i | − 0.353462i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13864.8i | 1.40076i | 0.713771 | + | 0.700379i | \(0.246986\pi\) | ||||
−0.713771 | + | 0.700379i | \(0.753014\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11518.3i | 1.15616i | 0.815981 | + | 0.578079i | \(0.196197\pi\) | ||||
−0.815981 | + | 0.578079i | \(0.803803\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 2485.77i | − 0.247902i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2815.92 | −0.279027 | −0.139513 | − | 0.990220i | \(-0.544554\pi\) | ||||
−0.139513 | + | 0.990220i | \(0.544554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 8869.86i | − 0.867731i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1650.46 | 0.160440 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7432.66 | −0.717966 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15666.5 | 1.50381 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3120.15 | 0.297627 | 0.148813 | − | 0.988865i | \(-0.452455\pi\) | ||||
0.148813 | + | 0.988865i | \(0.452455\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 6107.51i | − 0.578957i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 828.295 | 0.0775483 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1988.38i | 0.185015i | 0.995712 | + | 0.0925074i | \(0.0294882\pi\) | ||||
−0.995712 | + | 0.0925074i | \(0.970512\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 22985.8i | − 2.12567i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 3035.51i | − 0.279003i | −0.990222 | − | 0.139502i | \(-0.955450\pi\) | ||||
0.990222 | − | 0.139502i | \(-0.0445501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 19636.2i | − 1.79386i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 128.251 | 0.0116454 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16519.7i | 1.48201i | 0.671498 | + | 0.741007i | \(0.265651\pi\) | ||||
−0.671498 | + | 0.741007i | \(0.734349\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19324.9 | 1.72330 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16446.0 | −1.45783 | −0.728917 | − | 0.684602i | \(-0.759976\pi\) | ||||
−0.728917 | + | 0.684602i | \(0.759976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1026.65 | 0.0904656 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3608.86 | −0.316124 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 4685.12i | − 0.407985i | −0.978972 | − | 0.203992i | \(-0.934608\pi\) | ||||
0.978972 | − | 0.203992i | \(-0.0653917\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1751.17 | −0.150713 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1854.56i | 0.158682i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1032.42i | − 0.0878251i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 23872.5i | − 2.01905i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2199.68i | 0.184971i | 0.995714 | + | 0.0924853i | \(0.0294811\pi\) | ||||
−0.995714 | + | 0.0924853i | \(0.970519\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10465.4 | −0.874988 | −0.437494 | − | 0.899221i | \(-0.644134\pi\) | ||||
−0.437494 | + | 0.899221i | \(0.644134\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34350.4i | 2.83933i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12097.2 | 0.994265 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1946.00 | −0.159038 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14731.8 | 1.19720 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2065.65 | 0.166927 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8602.11i | 0.691264i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2934.94 | −0.233240 | −0.116620 | − | 0.993177i | \(-0.537206\pi\) | ||||
−0.116620 | + | 0.993177i | \(0.537206\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 12413.3i | − 0.981040i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1929.26i | 0.151634i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9168.13i | 0.716638i | 0.933599 | + | 0.358319i | \(0.116650\pi\) | ||||
−0.933599 | + | 0.358319i | \(0.883350\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4784.82i | 0.371970i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9892.92 | −0.764887 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1285.78i | − 0.0983391i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4618.14 | 0.351305 | 0.175652 | − | 0.984452i | \(-0.443797\pi\) | ||||
0.175652 | + | 0.984452i | \(0.443797\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14797.9 | 1.11965 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3863.69 | −0.290776 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23789.6 | −1.78084 | −0.890418 | − | 0.455144i | \(-0.849588\pi\) | ||||
−0.890418 | + | 0.455144i | \(0.849588\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2682.95i | 0.199775i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14772.6 | −1.08840 | −0.544200 | − | 0.838955i | \(-0.683167\pi\) | ||||
−0.544200 | + | 0.838955i | \(0.683167\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 24295.7i | − 1.78064i | −0.455339 | − | 0.890318i | \(-0.650482\pi\) | ||||
0.455339 | − | 0.890318i | \(-0.349518\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 6754.88i | − 0.492477i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1031.62i | 0.0748199i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10024.6i | 0.723275i | 0.932319 | + | 0.361638i | \(0.117782\pi\) | ||||
−0.932319 | + | 0.361638i | \(0.882218\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9418.30 | −0.676012 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3135.81i | 0.222765i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1149.89 | 0.0812686 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10134.7 | −0.712613 | −0.356306 | − | 0.934369i | \(-0.615964\pi\) | ||||
−0.356306 | + | 0.934369i | \(0.615964\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17306.1 | 1.21067 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7759.98 | −0.540107 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2197.51i | 0.152177i | 0.997101 | + | 0.0760885i | \(0.0242431\pi\) | ||||
−0.997101 | + | 0.0760885i | \(0.975757\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1755.61 | −0.120355 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24663.6i | 1.68235i | 0.540765 | + | 0.841174i | \(0.318135\pi\) | ||||
−0.540765 | + | 0.841174i | \(0.681865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 21532.0i | − 1.46142i | −0.682691 | − | 0.730708i | \(-0.739190\pi\) | ||||
0.682691 | − | 0.730708i | \(-0.260810\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9546.12i | 0.644690i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 1603.43i | − 0.107750i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −987.430 | −0.0660273 | −0.0330136 | − | 0.999455i | \(-0.510510\pi\) | ||||
−0.0330136 | + | 0.999455i | \(0.510510\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 9256.58i | − 0.612899i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7278.51 | 0.479570 | 0.239785 | − | 0.970826i | \(-0.422923\pi\) | ||||
0.239785 | + | 0.970826i | \(0.422923\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3101.41 | 0.203351 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2543.97 | −0.165991 | −0.0829953 | − | 0.996550i | \(-0.526449\pi\) | ||||
−0.0829953 | + | 0.996550i | \(0.526449\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7853.15 | −0.509927 | −0.254963 | − | 0.966951i | \(-0.582063\pi\) | ||||
−0.254963 | + | 0.966951i | \(0.582063\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 243.054i | 0.0157060i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15065.5 | 0.964189 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1946.56i | 0.123985i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17768.0i | 1.12632i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 16369.0i | − 1.03271i | −0.856375 | − | 0.516355i | \(-0.827289\pi\) | ||||
0.856375 | − | 0.516355i | \(-0.172711\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 14331.7i | − 0.899893i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1328.74 | 0.0830383 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22490.5i | 1.39235i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14497.2 | 0.893302 | 0.446651 | − | 0.894708i | \(-0.352617\pi\) | ||||
0.446651 | + | 0.894708i | \(0.352617\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29771.6 | 1.82594 | 0.912969 | − | 0.408029i | \(-0.133784\pi\) | ||||
0.912969 | + | 0.408029i | \(0.133784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3115.32 | 0.190179 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11215.5 | −0.681496 | −0.340748 | − | 0.940155i | \(-0.610680\pi\) | ||||
−0.340748 | + | 0.940155i | \(0.610680\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 389.512i | − 0.0235588i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20401.0 | 1.22259 | 0.611295 | − | 0.791403i | \(-0.290649\pi\) | ||||
0.611295 | + | 0.791403i | \(0.290649\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1876.77i | − 0.111956i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7814.13i | 0.464016i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13427.1i | 0.793693i | 0.917885 | + | 0.396846i | \(0.129895\pi\) | ||||
−0.917885 | + | 0.396846i | \(0.870105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 2313.84i | − 0.136154i | −0.997680 | − | 0.0680771i | \(-0.978314\pi\) | ||||
0.997680 | − | 0.0680771i | \(-0.0216864\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −34641.6 | −2.02922 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1373.09i | 0.0797096i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27574.0 | −1.59353 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −957.732 | −0.0551011 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16395.5 | −0.939081 | −0.469540 | − | 0.882911i | \(-0.655580\pi\) | ||||
−0.469540 | + | 0.882911i | \(0.655580\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3593.61 | 0.204916 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24962.8i | 1.41713i | 0.705645 | + | 0.708566i | \(0.250658\pi\) | ||||
−0.705645 | + | 0.708566i | \(0.749342\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30056.6 | 1.69129 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20374.5i | 1.14145i | 0.821142 | + | 0.570724i | \(0.193337\pi\) | ||||
−0.821142 | + | 0.570724i | \(0.806663\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1126.26i | − 0.0628208i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12234.2i | 0.679422i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28115.5i | 1.55460i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6393.32 | −0.351973 | −0.175986 | − | 0.984393i | \(-0.556311\pi\) | ||||
−0.175986 | + | 0.984393i | \(0.556311\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1743.74i | − 0.0951707i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42857.8 | −2.32906 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6179.12 | 0.334357 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19401.6 | −1.04535 | −0.522674 | − | 0.852533i | \(-0.675066\pi\) | ||||
−0.522674 | + | 0.852533i | \(0.675066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8951.66 | 0.480254 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 1948.73i | − 0.104104i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14777.7 | 0.782776 | 0.391388 | − | 0.920226i | \(-0.371995\pi\) | ||||
0.391388 | + | 0.920226i | \(0.371995\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 1745.60i | − 0.0920745i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2402.00i | − 0.126165i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 230.163i | 0.0120386i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13015.2i | 0.677912i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6437.04 | 0.333882 | 0.166941 | − | 0.985967i | \(-0.446611\pi\) | ||||
0.166941 | + | 0.985967i | \(0.446611\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 33078.3i | 1.70151i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20301.5 | 1.03997 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13490.8 | 0.688235 | 0.344118 | − | 0.938927i | \(-0.388178\pi\) | ||||
0.344118 | + | 0.938927i | \(0.388178\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13287.7 | −0.675086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −43050.2 | −2.17820 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20806.6i | 1.04844i | 0.851582 | + | 0.524221i | \(0.175644\pi\) | ||||
−0.851582 | + | 0.524221i | \(0.824356\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1910.75 | −0.0955001 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17283.7i | 0.860342i | 0.902747 | + | 0.430171i | \(0.141547\pi\) | ||||
−0.902747 | + | 0.430171i | \(0.858453\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17452.8i | 0.865242i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11763.6i | 0.580839i | 0.956899 | + | 0.290420i | \(0.0937948\pi\) | ||||
−0.956899 | + | 0.290420i | \(0.906205\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1686.94i | 0.0829591i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11981.0 | 0.586828 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 12377.8i | − 0.601427i | −0.953715 | − | 0.300713i | \(-0.902775\pi\) | ||||
0.953715 | − | 0.300713i | \(-0.0972247\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7172.70 | −0.347129 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1632.50 | −0.0786924 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18350.8 | 0.881071 | 0.440536 | − | 0.897735i | \(-0.354789\pi\) | ||||
0.440536 | + | 0.897735i | \(0.354789\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 270.174 | 0.0129205 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 16558.4i | − 0.788754i | −0.918949 | − | 0.394377i | \(-0.870960\pi\) | ||||
0.918949 | − | 0.394377i | \(-0.129040\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3345.26 | −0.158102 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 3492.34i | − 0.164408i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 3663.72i | − 0.171804i | −0.996304 | − | 0.0859019i | \(-0.972623\pi\) | ||||
0.996304 | − | 0.0859019i | \(-0.0273772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21304.7i | 0.995162i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39653.9i | 1.84509i | 0.385893 | + | 0.922544i | \(0.373894\pi\) | ||||
−0.385893 | + | 0.922544i | \(0.626106\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35514.1 | −1.64607 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21592.2i | 0.993094i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4501.70 | −0.206253 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4783.12 | 0.218308 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1537.17 | 0.0698905 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35468.7 | 1.60651 | 0.803254 | − | 0.595637i | \(-0.203100\pi\) | ||||
0.803254 | + | 0.595637i | \(0.203100\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18723.2i | 0.844821i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8586.98 | −0.384530 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5919.00i | 0.264057i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 32026.0i | − 1.42336i | −0.702503 | − | 0.711681i | \(-0.747934\pi\) | ||||
0.702503 | − | 0.711681i | \(-0.252066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26929.2i | 1.19235i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22240.6i | 0.981067i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1564.08 | −0.0687362 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 3196.39i | − 0.139428i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3417.20 | 0.148507 | 0.0742537 | − | 0.997239i | \(-0.476343\pi\) | ||||
0.0742537 | + | 0.997239i | \(0.476343\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27667.8 | −1.19796 | −0.598982 | − | 0.800763i | \(-0.704428\pi\) | ||||
−0.598982 | + | 0.800763i | \(0.704428\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1163.39 | −0.0501868 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3983.50 | 0.171210 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21689.1i | 0.928770i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28684.9 | 1.21938 | 0.609690 | − | 0.792640i | \(-0.291294\pi\) | ||||
0.609690 | + | 0.792640i | \(0.291294\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21516.6i | 0.911326i | 0.890152 | + | 0.455663i | \(0.150598\pi\) | ||||
−0.890152 | + | 0.455663i | \(0.849402\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 3994.59i | − 0.168574i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 28539.8i | − 1.20003i | −0.799988 | − | 0.600016i | \(-0.795161\pi\) | ||||
0.799988 | − | 0.600016i | \(-0.204839\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 4362.57i | − 0.182772i | −0.995816 | − | 0.0913862i | \(-0.970870\pi\) | ||||
0.995816 | − | 0.0913862i | \(-0.0291298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13698.6 | −0.571841 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3349.06i | 0.138801i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8367.29 | −0.345539 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34373.2 | −1.41442 | −0.707208 | − | 0.707006i | \(-0.750045\pi\) | ||||
−0.707208 | + | 0.707006i | \(0.750045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2632.42 | 0.107935 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 50517.2 | 2.06394 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 625.426i | − 0.0254619i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23275.1 | −0.940869 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1242.45i | − 0.0500477i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9468.45i | 0.380063i | 0.981778 | + | 0.190031i | \(0.0608590\pi\) | ||||
−0.981778 | + | 0.190031i | \(0.939141\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1685.37i | 0.0674136i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 11389.0i | − 0.453957i | −0.973900 | − | 0.226978i | \(-0.927115\pi\) | ||||
0.973900 | − | 0.226978i | \(-0.0728847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8455.90 | 0.335869 | 0.167935 | − | 0.985798i | \(-0.446290\pi\) | ||||
0.167935 | + | 0.985798i | \(0.446290\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7474.49i | 0.294826i | 0.989075 | + | 0.147413i | \(0.0470946\pi\) | ||||
−0.989075 | + | 0.147413i | \(0.952905\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4137.17 | 0.162622 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 66080.9 | 2.58850 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 349.399 | 0.0136393 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17131.7 | −0.666460 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15483.6i | 0.600276i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32056.6 | −1.23429 | −0.617147 | − | 0.786848i | \(-0.711712\pi\) | ||||
−0.617147 | + | 0.786848i | \(0.711712\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 52041.7i | − 1.99695i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 27139.7i | − 1.03787i | −0.854815 | − | 0.518933i | \(-0.826329\pi\) | ||||
0.854815 | − | 0.518933i | \(-0.173671\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 43490.8i | − 1.65751i | −0.559611 | − | 0.828755i | \(-0.689049\pi\) | ||||
0.559611 | − | 0.828755i | \(-0.310951\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 735.222i | − 0.0279257i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33511.2 | 1.26854 | 0.634271 | − | 0.773111i | \(-0.281300\pi\) | ||||
0.634271 | + | 0.773111i | \(0.281300\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 3770.29i | − 0.141761i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13567.2 | 0.508409 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1490.77 | −0.0556771 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2422.36 | 0.0901677 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −47269.6 | −1.75365 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 81793.6i | − 3.02435i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2151.26 | 0.0790168 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 7530.44i | − 0.275683i | −0.990454 | − | 0.137841i | \(-0.955984\pi\) | ||||
0.990454 | − | 0.137841i | \(-0.0440164\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19191.4i | 0.700264i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19971.6i | 0.726332i | 0.931724 | + | 0.363166i | \(0.118304\pi\) | ||||
−0.931724 | + | 0.363166i | \(0.881696\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2398.12i | 0.0869289i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1807.76 | −0.0653146 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 46751.5i | − 1.67812i | −0.544041 | − | 0.839059i | \(-0.683106\pi\) | ||||
0.544041 | − | 0.839059i | \(-0.316894\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19019.2 | 0.680461 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40362.0 | −1.43936 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18369.9 | −0.652972 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −34667.9 | −1.22831 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18772.2i | 0.662968i | 0.943461 | + | 0.331484i | \(0.107549\pi\) | ||||
−0.943461 | + | 0.331484i | \(0.892451\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20989.9 | −0.736527 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 669.589i | − 0.0234202i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13717.6i | 0.478263i | 0.970987 | + | 0.239132i | \(0.0768628\pi\) | ||||
−0.970987 | + | 0.239132i | \(0.923137\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 8051.34i | − 0.279814i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 18443.8i | − 0.638949i | −0.947595 | − | 0.319475i | \(-0.896494\pi\) | ||||
0.947595 | − | 0.319475i | \(-0.103506\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2996.89 | 0.103491 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33239.1i | 1.14058i | 0.821444 | + | 0.570289i | \(0.193169\pi\) | ||||
−0.821444 | + | 0.570289i | \(0.806831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14023.5 | −0.479684 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39869.1 | 1.35946 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32914.7 | 1.11880 | 0.559398 | − | 0.828899i | \(-0.311033\pi\) | ||||
0.559398 | + | 0.828899i | \(0.311033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1170.64 | 0.0396660 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 5316.82i | − 0.179591i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52899.4 | 1.77568 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38614.0i | 1.29213i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1632.22i | − 0.0544487i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 29368.7i | − 0.976663i | −0.872658 | − | 0.488332i | \(-0.837606\pi\) | ||||
0.872658 | − | 0.488332i | \(-0.162394\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 50773.6i | − 1.68326i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31567.2 | 1.04329 | 0.521647 | − | 0.853161i | \(-0.325318\pi\) | ||||
0.521647 | + | 0.853161i | \(0.325318\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 35815.2i | − 1.17642i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23250.0 | 0.761344 | 0.380672 | − | 0.924710i | \(-0.375693\pi\) | ||||
0.380672 | + | 0.924710i | \(0.375693\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4451.70 | −0.145329 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −36064.3 | −1.17374 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4057.54 | −0.131654 | −0.0658268 | − | 0.997831i | \(-0.520968\pi\) | ||||
−0.0658268 | + | 0.997831i | \(0.520968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 1344.83i | − 0.0435023i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3010.34 | 0.0967880 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 42406.5i | − 1.35932i | −0.733526 | − | 0.679661i | \(-0.762127\pi\) | ||||
0.733526 | − | 0.679661i | \(-0.237873\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 51980.4i | 1.66118i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 304.252i | − 0.00969389i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 57689.0i | − 1.83253i | −0.400576 | − | 0.916263i | \(-0.631190\pi\) | ||||
0.400576 | − | 0.916263i | \(-0.368810\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4328.03 | −0.137070 |
(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 | 784.4.f.h.783.1 | 6 | ||
4.3 | odd | 2 | 784.4.f.g.783.5 | 6 | |||
7.4 | even | 3 | 112.4.p.f.47.3 | yes | 6 | ||
7.5 | odd | 6 | 112.4.p.g.31.1 | yes | 6 | ||
7.6 | odd | 2 | 784.4.f.g.783.6 | 6 | |||
28.11 | odd | 6 | 112.4.p.g.47.1 | yes | 6 | ||
28.19 | even | 6 | 112.4.p.f.31.3 | ✓ | 6 | ||
28.27 | even | 2 | inner | 784.4.f.h.783.2 | 6 | ||
56.5 | odd | 6 | 448.4.p.f.255.3 | 6 | |||
56.11 | odd | 6 | 448.4.p.f.383.3 | 6 | |||
56.19 | even | 6 | 448.4.p.g.255.1 | 6 | |||
56.53 | even | 6 | 448.4.p.g.383.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.4.p.f.31.3 | ✓ | 6 | 28.19 | even | 6 | ||
112.4.p.f.47.3 | yes | 6 | 7.4 | even | 3 | ||
112.4.p.g.31.1 | yes | 6 | 7.5 | odd | 6 | ||
112.4.p.g.47.1 | yes | 6 | 28.11 | odd | 6 | ||
448.4.p.f.255.3 | 6 | 56.5 | odd | 6 | |||
448.4.p.f.383.3 | 6 | 56.11 | odd | 6 | |||
448.4.p.g.255.1 | 6 | 56.19 | even | 6 | |||
448.4.p.g.383.1 | 6 | 56.53 | even | 6 | |||
784.4.f.g.783.5 | 6 | 4.3 | odd | 2 | |||
784.4.f.g.783.6 | 6 | 7.6 | odd | 2 | |||
784.4.f.h.783.1 | 6 | 1.1 | even | 1 | trivial | ||
784.4.f.h.783.2 | 6 | 28.27 | even | 2 | inner |