Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(257,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.257");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.e (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: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 32 x^{14} + 356 x^{13} + 1348 x^{12} - 8992 x^{11} + 22064 x^{10} + \cdots + 21479188203 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{54}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.7 | ||
Root | \(-3.40000 - 2.59434i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.257 |
Dual form | 384.5.e.c.257.8 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.622561 | − | 8.97844i | 0.0691735 | − | 0.997605i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.562050i | − | 0.0224820i | −0.999937 | − | 0.0112410i | \(-0.996422\pi\) | ||
0.999937 | − | 0.0112410i | \(-0.00357820\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 55.8203 | 1.13919 | 0.569595 | − | 0.821926i | \(-0.307100\pi\) | ||||
0.569595 | + | 0.821926i | \(0.307100\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −80.2248 | − | 11.1793i | −0.990430 | − | 0.138016i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 87.7824i | 0.725475i | 0.931891 | + | 0.362737i | \(0.118158\pi\) | ||||
−0.931891 | + | 0.362737i | \(0.881842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 71.5994 | 0.423665 | 0.211832 | − | 0.977306i | \(-0.432057\pi\) | ||||
0.211832 | + | 0.977306i | \(0.432057\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.04633 | − | 0.349910i | −0.0224281 | − | 0.00155516i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 334.017i | 1.15577i | 0.816119 | + | 0.577884i | \(0.196121\pi\) | ||||
−0.816119 | + | 0.577884i | \(0.803879\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 365.653 | 1.01289 | 0.506445 | − | 0.862272i | \(-0.330959\pi\) | ||||
0.506445 | + | 0.862272i | \(0.330959\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 34.7515 | − | 501.179i | 0.0788017 | − | 1.13646i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 789.593i | 1.49262i | 0.665601 | + | 0.746308i | \(0.268175\pi\) | ||||
−0.665601 | + | 0.746308i | \(0.731825\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 624.684 | 0.999495 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −150.317 | + | 713.334i | −0.206196 | + | 0.978511i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 236.473i | − | 0.281181i | −0.990068 | − | 0.140590i | \(-0.955100\pi\) | ||
0.990068 | − | 0.140590i | \(-0.0449000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1280.52 | −1.33249 | −0.666245 | − | 0.745733i | \(-0.732100\pi\) | ||||
−0.666245 | + | 0.745733i | \(0.732100\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 788.149 | + | 54.6499i | 0.723737 | + | 0.0501836i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 31.3738i | − | 0.0256112i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 513.856 | 0.375352 | 0.187676 | − | 0.982231i | \(-0.439905\pi\) | ||||
0.187676 | + | 0.982231i | \(0.439905\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 44.5750 | − | 642.851i | 0.0293064 | − | 0.422650i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1189.01i | 0.707323i | 0.935374 | + | 0.353661i | \(0.115063\pi\) | ||||
−0.935374 | + | 0.353661i | \(0.884937\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 204.172 | 0.110423 | 0.0552114 | − | 0.998475i | \(-0.482417\pi\) | ||||
0.0552114 | + | 0.998475i | \(0.482417\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.28330 | + | 45.0903i | −0.00310286 | + | 0.0222668i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1316.07i | 0.595779i | 0.954600 | + | 0.297889i | \(0.0962826\pi\) | ||||
−0.954600 | + | 0.297889i | \(0.903717\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 714.903 | 0.297752 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2998.95 | + | 207.946i | 1.15300 | + | 0.0799485i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 317.847i | − | 0.113153i | −0.998398 | − | 0.0565766i | \(-0.981981\pi\) | ||
0.998398 | − | 0.0565766i | \(-0.0180185\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 49.3381 | 0.0163101 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 227.641 | − | 3283.00i | 0.0700651 | − | 1.01046i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1274.33i | − | 0.366081i | −0.983105 | − | 0.183040i | \(-0.941406\pi\) | ||
0.983105 | − | 0.183040i | \(-0.0585939\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5771.27 | 1.55100 | 0.775500 | − | 0.631347i | \(-0.217498\pi\) | ||||
0.775500 | + | 0.631347i | \(0.217498\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4478.17 | − | 624.029i | −1.12829 | − | 0.157226i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 40.2424i | − | 0.00952483i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7246.66 | 1.61432 | 0.807158 | − | 0.590336i | \(-0.201005\pi\) | ||||
0.807158 | + | 0.590336i | \(0.201005\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7089.32 | + | 491.570i | 1.48904 | + | 0.103249i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4833.29i | − | 0.958796i | −0.877598 | − | 0.479398i | \(-0.840855\pi\) | ||
0.877598 | − | 0.479398i | \(-0.159145\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6984.08 | 1.31058 | 0.655290 | − | 0.755377i | \(-0.272546\pi\) | ||||
0.655290 | + | 0.755377i | \(0.272546\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 388.904 | − | 5608.69i | 0.0691385 | − | 0.997100i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4900.04i | 0.826453i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9332.37 | −1.49533 | −0.747666 | − | 0.664075i | \(-0.768826\pi\) | ||||
−0.747666 | + | 0.664075i | \(0.768826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6311.05 | + | 1793.71i | 0.961903 | + | 0.273389i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 838.939i | − | 0.121780i | −0.998144 | − | 0.0608898i | \(-0.980606\pi\) | ||
0.998144 | − | 0.0608898i | \(-0.0193938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 187.734 | 0.0259840 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2123.16 | − | 147.219i | −0.280507 | − | 0.0194502i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13943.2i | − | 1.76028i | −0.474715 | − | 0.880140i | \(-0.657449\pi\) | ||
0.474715 | − | 0.880140i | \(-0.342551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3996.70 | 0.482635 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −797.204 | + | 11497.1i | −0.0921730 | + | 1.32930i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 205.515i | − | 0.0227718i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6578.49 | 0.699170 | 0.349585 | − | 0.936905i | \(-0.386323\pi\) | ||||
0.349585 | + | 0.936905i | \(0.386323\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 981.342 | − | 7042.33i | 0.100127 | − | 0.718532i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 17934.3i | − | 1.75810i | −0.476732 | − | 0.879049i | \(-0.658179\pi\) | ||
0.476732 | − | 0.879049i | \(-0.341821\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13246.5 | −1.24861 | −0.624303 | − | 0.781182i | \(-0.714617\pi\) | ||||
−0.624303 | + | 0.781182i | \(0.714617\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −281.688 | − | 19.5321i | −0.0255499 | − | 0.00177162i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11912.3i | 1.04046i | 0.854025 | + | 0.520232i | \(0.174155\pi\) | ||||
−0.854025 | + | 0.520232i | \(0.825845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12868.3 | 1.08310 | 0.541548 | − | 0.840670i | \(-0.317838\pi\) | ||||
0.541548 | + | 0.840670i | \(0.317838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 319.907 | − | 4613.63i | 0.0259644 | − | 0.374453i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 22368.0i | 1.75174i | 0.482544 | + | 0.875872i | \(0.339713\pi\) | ||||
−0.482544 | + | 0.875872i | \(0.660287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 443.791 | 0.0335570 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5744.05 | − | 800.428i | −0.419610 | − | 0.0584723i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18644.9i | 1.31664i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6935.25 | 0.473687 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10675.5 | + | 740.231i | 0.705628 | + | 0.0489280i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 702.385i | − | 0.0449526i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12221.9 | 0.757762 | 0.378881 | − | 0.925445i | \(-0.376309\pi\) | ||||
0.378881 | + | 0.925445i | \(0.376309\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 127.109 | − | 1833.14i | 0.00763832 | − | 0.110158i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15121.0i | 0.881125i | 0.897722 | + | 0.440563i | \(0.145221\pi\) | ||||
−0.897722 | + | 0.440563i | \(0.854779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20410.9 | 1.15387 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 400.929 | + | 84.4857i | 0.0219989 | + | 0.00463570i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2504.91i | 0.133460i | 0.997771 | + | 0.0667300i | \(0.0212566\pi\) | ||||
−0.997771 | + | 0.0667300i | \(0.978743\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 28510.7 | 1.47563 | 0.737815 | − | 0.675003i | \(-0.235858\pi\) | ||||
0.737815 | + | 0.675003i | \(0.235858\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11816.3 | + | 819.337i | 0.594351 | + | 0.0412121i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6285.17i | 0.307358i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −132.910 | −0.00632150 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 445.071 | − | 6418.71i | 0.0205965 | − | 0.297039i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 33444.1i | − | 1.50642i | −0.657778 | − | 0.753212i | \(-0.728504\pi\) | ||
0.657778 | − | 0.753212i | \(-0.271496\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13142.6 | −0.576404 | −0.288202 | − | 0.957570i | \(-0.593057\pi\) | ||||
−0.288202 | + | 0.957570i | \(0.593057\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3734.06 | − | 26796.5i | 0.159514 | − | 1.14471i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 719.718i | 0.0299570i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31662.0 | −1.28452 | −0.642258 | − | 0.766488i | \(-0.722002\pi\) | ||||
−0.642258 | + | 0.766488i | \(0.722002\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2853.77 | − | 197.879i | −0.112882 | − | 0.00782719i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 44075.3i | 1.70037i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −32147.7 | −1.20997 | −0.604985 | − | 0.796237i | \(-0.706821\pi\) | ||||
−0.604985 | + | 0.796237i | \(0.706821\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 30.7160 | − | 442.979i | 0.00112823 | − | 0.0162710i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13951.1i | 0.500238i | 0.968215 | + | 0.250119i | \(0.0804698\pi\) | ||||
−0.968215 | + | 0.250119i | \(0.919530\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23434.5 | −0.820508 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29334.5 | − | 4087.73i | −1.00320 | − | 0.139794i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 32861.5i | 1.09798i | 0.835828 | + | 0.548991i | \(0.184988\pi\) | ||||
−0.835828 | + | 0.548991i | \(0.815012\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 34870.0 | 1.13861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11441.5 | − | 793.347i | −0.365204 | − | 0.0253231i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20985.9i | 0.654971i | 0.944856 | + | 0.327486i | \(0.106201\pi\) | ||||
−0.944856 | + | 0.327486i | \(0.893799\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −56067.7 | −1.71142 | −0.855708 | − | 0.517459i | \(-0.826878\pi\) | ||||
−0.855708 | + | 0.517459i | \(0.826878\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3592.97 | − | 51817.0i | 0.107288 | − | 1.54728i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 288.813i | − | 0.00843865i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −29320.8 | −0.838480 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8390.74 | + | 39818.5i | −0.234897 | + | 1.11471i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 47798.6i | 1.31023i | 0.755529 | + | 0.655116i | \(0.227380\pi\) | ||||
−0.755529 | + | 0.655116i | \(0.772620\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 43.1516 | 0.00115846 | 0.000579232 | − | 1.00000i | \(-0.499816\pi\) | ||||
0.000579232 | 1.00000i | \(0.499816\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −361.314 | − | 25.0534i | −0.00950201 | − | 0.000658865i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 40137.0i | − | 1.03422i | −0.855920 | − | 0.517109i | \(-0.827008\pi\) | ||
0.855920 | − | 0.517109i | \(-0.172992\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23378.7 | 0.590355 | 0.295178 | − | 0.955442i | \(-0.404621\pi\) | ||||
0.295178 | + | 0.955442i | \(0.404621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4511.49 | − | 65063.7i | 0.111668 | − | 1.61045i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 13200.0i | − | 0.320318i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 668.282 | 0.0159020 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8827.07 | − | 63345.0i | 0.206004 | − | 1.47833i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32097.9i | 0.734826i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −54577.0 | −1.22587 | −0.612935 | − | 0.790133i | \(-0.710011\pi\) | ||||
−0.612935 | + | 0.790133i | \(0.710011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −43395.4 | − | 3009.02i | −0.956500 | − | 0.0663232i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 114.755i | − | 0.00248252i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −71479.2 | −1.51796 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4348.02 | − | 62706.2i | 0.0906573 | − | 1.30744i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23915.4i | 0.489658i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20007.6 | 0.402332 | 0.201166 | − | 0.979557i | \(-0.435527\pi\) | ||||
0.201166 | + | 0.979557i | \(0.435527\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −50115.2 | − | 6983.50i | −0.989929 | − | 0.137946i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 18082.4i | − | 0.350917i | −0.984487 | − | 0.175458i | \(-0.943859\pi\) | ||
0.984487 | − | 0.175458i | \(-0.0561407\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 56787.1 | 1.08288 | 0.541438 | − | 0.840741i | \(-0.317880\pi\) | ||||
0.541438 | + | 0.840741i | \(0.317880\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 43994.7 | + | 3050.57i | 0.824473 | + | 0.0571686i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 57688.8i | − | 1.06262i | −0.847176 | − | 0.531312i | \(-0.821699\pi\) | ||
0.847176 | − | 0.531312i | \(-0.178301\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 739.700 | 0.0133943 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5809.97 | + | 83790.1i | −0.103437 | + | 1.49175i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 31777.3i | − | 0.556315i | −0.960535 | − | 0.278158i | \(-0.910276\pi\) | ||
0.960535 | − | 0.278158i | \(-0.0897238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28106.4 | −0.483918 | −0.241959 | − | 0.970286i | \(-0.577790\pi\) | ||||
−0.241959 | + | 0.970286i | \(0.577790\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20033.7 | − | 55546.7i | 0.339273 | − | 0.940688i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 401.811i | − | 0.00669406i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26180.5 | 0.429126 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7532.37 | − | 522.291i | −0.121488 | − | 0.00842391i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 114789.i | 1.82202i | 0.412386 | + | 0.911009i | \(0.364696\pi\) | ||||
−0.412386 | + | 0.911009i | \(0.635304\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −69312.4 | −1.08285 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 116.876 | − | 1685.56i | 0.00179740 | − | 0.0259217i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 50929.0i | 0.771079i | 0.922691 | + | 0.385539i | \(0.125985\pi\) | ||||
−0.922691 | + | 0.385539i | \(0.874015\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28683.6 | 0.427597 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2643.59 | + | 18971.0i | −0.0388073 | + | 0.278490i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2156.83i | − | 0.0311820i | −0.999878 | − | 0.0155910i | \(-0.995037\pi\) | ||
0.999878 | − | 0.0155910i | \(-0.00496297\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −178.646 | −0.00254391 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −125188. | − | 8680.48i | −1.75606 | − | 0.121765i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 121224.i | − | 1.67527i | −0.546230 | − | 0.837635i | \(-0.683938\pi\) | ||
0.546230 | − | 0.837635i | \(-0.316062\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21224.3 | 0.288998 | 0.144499 | − | 0.989505i | \(-0.453843\pi\) | ||||
0.144499 | + | 0.989505i | \(0.453843\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2488.19 | − | 35884.1i | 0.0333855 | − | 0.481478i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 54836.3i | 0.725108i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −116163. | −1.51394 | −0.756970 | − | 0.653450i | \(-0.773321\pi\) | ||||
−0.756970 | + | 0.653450i | \(0.773321\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 102730. | + | 14315.3i | 1.31974 | + | 0.183904i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 117518.i | 1.48830i | 0.668011 | + | 0.744151i | \(0.267146\pi\) | ||||
−0.668011 | + | 0.744151i | \(0.732854\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −73183.7 | −0.913780 | −0.456890 | − | 0.889523i | \(-0.651037\pi\) | ||||
−0.456890 | + | 0.889523i | \(0.651037\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1845.21 | − | 127.946i | −0.0227172 | − | 0.00157520i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 66370.8i | 0.805774i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −28046.3 | −0.335799 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4095.51 | − | 59064.6i | 0.0483640 | − | 0.697495i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 90550.0i | − | 1.05476i | −0.849630 | − | 0.527380i | \(-0.823175\pi\) | ||
0.849630 | − | 0.527380i | \(-0.176825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −716.235 | −0.00823023 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −62618.2 | − | 13195.2i | −0.709885 | − | 0.149590i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 56534.4i | 0.632369i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11396.9 | 0.125792 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −161023. | − | 11165.2i | −1.75389 | − | 0.121614i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3243.74i | − | 0.0348696i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −47033.7 | −0.499036 | −0.249518 | − | 0.968370i | \(-0.580272\pi\) | ||||
−0.249518 | + | 0.968370i | \(0.580272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8246.73 | + | 118933.i | −0.0863704 | + | 1.24562i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 166222.i | 1.71857i | 0.511495 | + | 0.859286i | \(0.329092\pi\) | ||||
−0.511495 | + | 0.859286i | \(0.670908\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 114083. | 1.16448 | 0.582241 | − | 0.813016i | \(-0.302176\pi\) | ||||
0.582241 | + | 0.813016i | \(0.302176\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −350.735 | + | 2516.96i | −0.00353475 | + | 0.0253661i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 32769.6i | − | 0.326101i | −0.986618 | − | 0.163051i | \(-0.947867\pi\) | ||
0.986618 | − | 0.163051i | \(-0.0521334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20758.2 | 0.203989 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 106954. | + | 7416.12i | 1.03797 | + | 0.0719725i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 122134.i | 1.17067i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 44727.0 | 0.423451 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8011.28 | − | 115537.i | 0.0749215 | − | 1.08050i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 73463.7i | 0.678705i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 137589. | 1.25582 | 0.627912 | − | 0.778285i | \(-0.283910\pi\) | ||||
0.627912 | + | 0.778285i | \(0.283910\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −41224.0 | − | 5744.53i | −0.371760 | − | 0.0518043i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4072.98i | − | 0.0362930i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8517.04 | −0.0749944 | −0.0374972 | − | 0.999297i | \(-0.511939\pi\) | ||||
−0.0374972 | + | 0.999297i | \(0.511939\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 200830. | + | 13925.5i | 1.74755 | + | 0.121174i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 112407.i | − | 0.966688i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −94118.4 | −0.799993 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 276.287 | − | 3984.55i | 0.00232125 | − | 0.0334766i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 83527.7i | − | 0.693699i | −0.937921 | − | 0.346850i | \(-0.887251\pi\) | ||
0.937921 | − | 0.346850i | \(-0.112749\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 133537. | 1.09635 | 0.548177 | − | 0.836363i | \(-0.315322\pi\) | ||||
0.548177 | + | 0.836363i | \(0.315322\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10762.6 | + | 51074.3i | −0.0873582 | + | 0.414561i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4971.02i | 0.0398929i | 0.999801 | + | 0.0199465i | \(0.00634958\pi\) | ||||
−0.999801 | + | 0.0199465i | \(0.993650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2716.55 | −0.0215556 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 167402. | + | 11607.6i | 1.31348 | + | 0.0910764i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 101188.i | − | 0.785125i | −0.919725 | − | 0.392562i | \(-0.871589\pi\) | ||
0.919725 | − | 0.392562i | \(-0.128411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3381.22 | 0.0259453 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4317.61 | − | 62267.7i | 0.0327665 | − | 0.472552i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3925.40i | − | 0.0294644i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 72491.9 | 0.538217 | 0.269108 | − | 0.963110i | \(-0.413271\pi\) | ||||
0.269108 | + | 0.963110i | \(0.413271\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13292.2 | − | 95388.1i | 0.0976215 | − | 0.700554i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 17742.3i | − | 0.128903i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 91510.6 | 0.657739 | 0.328870 | − | 0.944375i | \(-0.393332\pi\) | ||||
0.328870 | + | 0.944375i | \(0.393332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6306.32 | − | 437.277i | −0.0448449 | − | 0.00310953i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 16931.3i | − | 0.119126i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 150530. | 1.04796 | 0.523981 | − | 0.851730i | \(-0.324446\pi\) | ||||
0.523981 | + | 0.851730i | \(0.324446\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7608.91 | − | 109734.i | 0.0524170 | − | 0.755947i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 228289.i | 1.55628i | 0.628091 | + | 0.778140i | \(0.283837\pi\) | ||||
−0.628091 | + | 0.778140i | \(0.716163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2754.07 | 0.0185803 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16379.6 | − | 2282.49i | −0.109366 | − | 0.0152400i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 280509.i | 1.85374i | 0.375385 | + | 0.926869i | \(0.377510\pi\) | ||||
−0.375385 | + | 0.926869i | \(0.622490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −263738. | −1.72512 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 135763. | + | 9413.74i | 0.879015 | + | 0.0609505i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5245.25i | 0.0336180i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 119440. | 0.757827 | 0.378913 | − | 0.925432i | \(-0.376298\pi\) | ||||
0.378913 | + | 0.925432i | \(0.376298\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12707.0 | − | 183258.i | 0.0798174 | − | 1.15111i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1318.85i | 0.00820176i | 0.999992 | + | 0.00410088i | \(0.00130535\pi\) | ||||
−0.999992 | + | 0.00410088i | \(0.998695\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −91684.7 | −0.564530 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1008.15 | − | 3547.12i | 0.00614634 | − | 0.0216255i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45107.6i | 0.272308i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38558.7 | 0.230503 | 0.115251 | − | 0.993336i | \(-0.463233\pi\) | ||||
0.115251 | + | 0.993336i | \(0.463233\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22490.2 | + | 1559.46i | 0.133140 | + | 0.00923188i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 71133.3i | − | 0.417035i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −471.526 | −0.00273785 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17749.6 | − | 255981.i | 0.102074 | − | 1.47210i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 99777.3i | − | 0.568334i | −0.958775 | − | 0.284167i | \(-0.908283\pi\) | ||
0.958775 | − | 0.284167i | \(-0.0917170\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −109123. | −0.615674 | −0.307837 | − | 0.951439i | \(-0.599605\pi\) | ||||
−0.307837 | + | 0.951439i | \(0.599605\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14712.7 | − | 105582.i | 0.0822267 | − | 0.590077i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 208655.i | 1.15518i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 322154. | 1.76688 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 56431.0 | + | 3912.90i | 0.306622 | + | 0.0212610i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 340800.i | − | 1.83462i | −0.398178 | − | 0.917308i | \(-0.630357\pi\) | ||
0.398178 | − | 0.917308i | \(-0.369643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 255345. | 1.36192 | 0.680959 | − | 0.732321i | \(-0.261563\pi\) | ||||
0.680959 | + | 0.732321i | \(0.261563\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −82.7443 | + | 1193.32i | −0.000437280 | + | 0.00630636i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 288717.i | 1.51185i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −257441. | −1.33582 | −0.667912 | − | 0.744240i | \(-0.732812\pi\) | ||||
−0.667912 | + | 0.744240i | \(0.732812\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −57353.0 | − | 7992.08i | −0.294903 | − | 0.0410944i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 118677.i | − | 0.604729i | −0.953192 | − | 0.302364i | \(-0.902224\pi\) | ||
0.953192 | − | 0.302364i | \(-0.0977759\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7836.76 | −0.0395746 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −300276. | − | 20821.0i | −1.50282 | − | 0.104205i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 351950.i | − | 1.74578i | −0.487919 | − | 0.872889i | \(-0.662244\pi\) | ||
0.487919 | − | 0.872889i | \(-0.337756\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −104374. | −0.513145 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8182.06 | + | 118000.i | −0.0398718 | + | 0.575023i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 2246.34i | − | 0.0108506i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 279904. | 1.34022 | 0.670110 | − | 0.742261i | \(-0.266247\pi\) | ||||
0.670110 | + | 0.742261i | \(0.266247\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −238266. | − | 50208.5i | −1.13093 | − | 0.238315i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 239756.i | − | 1.12815i | −0.825723 | − | 0.564076i | \(-0.809233\pi\) | ||
0.825723 | − | 0.564076i | \(-0.190767\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7111.21 | 0.0331728 | 0.0165864 | − | 0.999862i | \(-0.494720\pi\) | ||||
0.0165864 | + | 0.999862i | \(0.494720\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6461.95 | + | 448.068i | 0.0298853 | + | 0.00207223i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 174901.i | − | 0.801969i | −0.916085 | − | 0.400984i | \(-0.868668\pi\) | ||
0.916085 | − | 0.400984i | \(-0.131332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 404511. | 1.83901 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19711.6 | + | 284276.i | −0.0888544 | + | 1.28144i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17922.7i | 0.0801089i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 228418. | 1.01238 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3553.30 | + | 25499.2i | −0.0156169 | + | 0.112070i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 227873.i | 0.993166i | 0.867989 | + | 0.496583i | \(0.165412\pi\) | ||||
−0.867989 | + | 0.496583i | \(0.834588\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36791.8 | 0.159023 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 395728. | + | 27439.6i | 1.69630 | + | 0.117621i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 3697.44i | − | 0.0157187i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −151441. | −0.638537 | −0.319268 | − | 0.947664i | \(-0.603437\pi\) | ||||
−0.319268 | + | 0.947664i | \(0.603437\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20013.9 | + | 288636.i | −0.0836978 | + | 1.20707i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 187262.i | 0.776758i | 0.921500 | + | 0.388379i | \(0.126965\pi\) | ||||
−0.921500 | + | 0.388379i | \(0.873035\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 78985.9 | 0.324979 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3958.14 | − | 551.563i | −0.0161540 | − | 0.00225105i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 269796.i | − | 1.09225i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −67671.2 | −0.271771 | −0.135885 | − | 0.990725i | \(-0.543388\pi\) | ||||
−0.135885 | + | 0.990725i | \(0.543388\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 125260. | + | 8685.44i | 0.499040 | + | 0.0346032i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 20555.7i | − | 0.0812450i | −0.999175 | − | 0.0406225i | \(-0.987066\pi\) | ||
0.999175 | − | 0.0406225i | \(-0.0129341\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10080.0 | −0.0395255 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14589.4 | + | 210406.i | −0.0567574 | + | 0.818543i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 246028.i | − | 0.949620i | −0.880088 | − | 0.474810i | \(-0.842517\pi\) | ||
0.880088 | − | 0.474810i | \(-0.157483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 389853. | 1.49300 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −54963.9 | + | 260833.i | −0.208854 | + | 0.991123i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7445.17i | 0.0280712i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −115528. | −0.432222 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 295045. | + | 20458.3i | 1.09535 | + | 0.0759512i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 310680.i | 1.14456i | 0.820059 | + | 0.572278i | \(0.193940\pi\) | ||||
−0.820059 | + | 0.572278i | \(0.806060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 87436.7 | 0.319662 | 0.159831 | − | 0.987144i | \(-0.448905\pi\) | ||||
0.159831 | + | 0.987144i | \(0.448905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21708.7 | − | 313079.i | 0.0787618 | − | 1.13589i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 427717.i | − | 1.54005i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −343617. | −1.22790 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14246.0 | + | 102233.i | −0.0505248 | + | 0.362577i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 85132.3i | 0.299668i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6695.29 | 0.0233917 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 188421. | + | 13065.0i | 0.653402 | + | 0.0453066i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 62755.9i | 0.216012i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −259352. | −0.886125 | −0.443063 | − | 0.896491i | \(-0.646108\pi\) | ||||
−0.443063 | + | 0.896491i | \(0.646108\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −34905.6 | + | 503401.i | −0.118385 | + | 1.70732i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7232.61i | − | 0.0243502i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −301313. | −1.00703 | −0.503515 | − | 0.863986i | \(-0.667960\pi\) | ||||
−0.503515 | + | 0.863986i | \(0.667960\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −462999. | − | 64518.5i | −1.53616 | − | 0.214062i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 86467.0i | − | 0.284805i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −520935. | −1.70347 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2593.09 | − | 179.804i | −0.00841844 | − | 0.000583731i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 213353.i | 0.687682i | 0.939028 | + | 0.343841i | \(0.111728\pi\) | ||||
−0.939028 | + | 0.343841i | \(0.888272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14618.6 | 0.0467822 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18254.0 | + | 263255.i | −0.0580006 | + | 0.836472i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 372694.i | 1.17581i | 0.808931 | + | 0.587904i | \(0.200047\pi\) | ||||
−0.808931 | + | 0.587904i | \(0.799953\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12571.9 | 0.0393827 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 352284. | + | 100125.i | 1.09579 | + | 0.311442i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 181871.i | − | 0.561744i | −0.959745 | − | 0.280872i | \(-0.909376\pi\) | ||
0.959745 | − | 0.280872i | \(-0.0906236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −166399. | −0.510361 | −0.255180 | − | 0.966893i | \(-0.582135\pi\) | ||||
−0.255180 | + | 0.966893i | \(0.582135\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 429157. | + | 29757.5i | 1.30709 | + | 0.0906332i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 493246.i | 1.49186i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 124612. | 0.374289 | 0.187145 | − | 0.982332i | \(-0.440077\pi\) | ||||
0.187145 | + | 0.982332i | \(0.440077\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.8645 | − | 387.434i | 8.01350e−5 | − | 0.00115569i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 46829.8i | − | 0.138730i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27901.4 | 0.0820897 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −449.880 | + | 3228.44i | −0.00131457 | + | 0.00943368i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 412727.i | − | 1.19781i | −0.800821 | − | 0.598904i | \(-0.795603\pi\) | ||
0.800821 | − | 0.598904i | \(-0.204397\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −468228. | −1.34967 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −360367. | − | 24987.7i | −1.03174 | − | 0.0715404i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 26644.9i | − | 0.0757714i | −0.999282 | − | 0.0378857i | \(-0.987938\pi\) | ||
0.999282 | − | 0.0378857i | \(-0.0120623\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10479.4 | 0.0296006 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14554.6 | − | 209904.i | 0.0408369 | − | 0.588941i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 227404.i | − | 0.633789i | −0.948461 | − | 0.316895i | \(-0.897360\pi\) | ||
0.948461 | − | 0.316895i | \(-0.102640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −152020. | −0.420873 | −0.210437 | − | 0.977607i | \(-0.567489\pi\) | ||||
−0.210437 | + | 0.977607i | \(0.567489\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −581362. | − | 81012.3i | −1.59887 | − | 0.222801i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3897.95i | − | 0.0106494i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 249269. | 0.676535 | 0.338267 | − | 0.941050i | \(-0.390159\pi\) | ||||
0.338267 | + | 0.941050i | \(0.390159\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −118515. | − | 8217.79i | −0.319551 | − | 0.0221575i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 94230.1i | 0.252410i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −351135. | −0.934443 | −0.467221 | − | 0.884140i | \(-0.654745\pi\) | ||||
−0.467221 | + | 0.884140i | \(0.654745\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 416.047 | − | 6000.14i | 0.00110000 | − | 0.0158639i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 362003.i | − | 0.950915i | −0.879739 | − | 0.475458i | \(-0.842282\pi\) | ||
0.879739 | − | 0.475458i | \(-0.157718\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −599882. | −1.56561 | −0.782807 | − | 0.622265i | \(-0.786213\pi\) | ||||
−0.782807 | + | 0.622265i | \(0.786213\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −563244. | − | 118689.i | −1.46054 | − | 0.307772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 778312.i | − | 2.00529i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390033. | 0.998484 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 288189. | + | 19982.9i | 0.733065 | + | 0.0508304i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 171637.i | 0.433819i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 332404. | 0.834847 | 0.417424 | − | 0.908712i | \(-0.362933\pi\) | ||||
0.417424 | + | 0.908712i | \(0.362933\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −33977.5 | + | 490016.i | −0.0847977 | + | 1.22293i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 6869.34i | − | 0.0170360i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 51186.6 | 0.126147 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −54032.6 | + | 387750.i | −0.132329 | + | 0.949621i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 196470.i | − | 0.478166i | −0.970999 | − | 0.239083i | \(-0.923153\pi\) | ||
0.970999 | − | 0.239083i | \(-0.0768469\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −79225.2 | −0.191620 | −0.0958102 | − | 0.995400i | \(-0.530544\pi\) | ||||
−0.0958102 | + | 0.995400i | \(0.530544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1030.32 | − | 71.4417i | −0.00247658 | − | 0.000171725i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 222500.i | − | 0.531523i | −0.964039 | − | 0.265762i | \(-0.914377\pi\) | ||
0.964039 | − | 0.265762i | \(-0.0856234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 111864. | 0.265582 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −44500.2 | + | 641772.i | −0.105002 | + | 1.51432i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 456863.i | 1.07142i | 0.844402 | + | 0.535710i | \(0.179956\pi\) | ||||
−0.844402 | + | 0.535710i | \(0.820044\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8498.75 | 0.0198094 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −560297. | − | 78076.8i | −1.29804 | − | 0.180880i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 681304.i | − | 1.56881i | −0.620249 | − | 0.784405i | \(-0.712969\pi\) | ||
0.620249 | − | 0.784405i | \(-0.287031\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 107338. | 0.245670 | 0.122835 | − | 0.992427i | \(-0.460801\pi\) | ||||
0.122835 | + | 0.992427i | \(0.460801\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 214723. | + | 14888.8i | 0.488485 | + | 0.0338714i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 11471.9i | − | 0.0259414i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 186717. | 0.419694 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12455.9 | − | 179637.i | 0.0278307 | − | 0.401368i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 506616.i | 1.12521i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −650619. | −1.43647 | −0.718235 | − | 0.695800i | \(-0.755050\pi\) | ||||
−0.718235 | + | 0.695800i | \(0.755050\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −93900.7 | + | 445609.i | −0.206092 | + | 0.978016i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 549716.i | 1.19939i | 0.800228 | + | 0.599695i | \(0.204712\pi\) | ||||
−0.800228 | + | 0.599695i | \(0.795288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 367213. | 0.796487 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −162352. | − | 11257.4i | −0.350076 | − | 0.0242741i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 525635.i | − | 1.12679i | −0.826188 | − | 0.563395i | \(-0.809495\pi\) | ||
0.826188 | − | 0.563395i | \(-0.190505\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1407.88 | 0.00300044 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 35353.5 | − | 509860.i | 0.0749063 | − | 1.08028i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 22757.7i | − | 0.0479390i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −269536. | −0.564495 | −0.282247 | − | 0.959342i | \(-0.591080\pi\) | ||||
−0.282247 | + | 0.959342i | \(0.591080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 54778.8 | − | 393105.i | 0.114063 | − | 0.818544i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 16024.4i | − | 0.0331751i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −397149. | −0.817501 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −517955. | − | 35914.8i | −1.06008 | − | 0.0735054i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 535305.i | 1.08935i | 0.838649 | + | 0.544673i | \(0.183346\pi\) | ||||
−0.838649 | + | 0.544673i | \(0.816654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 187893. | 0.380190 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 460.508 | − | 6641.35i | 0.000926529 | − | 0.0133622i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.00110e6i | − | 2.00281i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −601177. | −1.19594 | −0.597971 | − | 0.801518i | \(-0.704026\pi\) | ||||
−0.597971 | + | 0.801518i | \(0.704026\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 748688. | + | 104329.i | 1.48102 | + | 0.206379i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.01109e6i | − | 1.98890i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3532.58 | 0.00691002 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −285311. | − | 19783.3i | −0.554983 | − | 0.0384823i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 794011.i | − | 1.53592i | −0.640497 | − | 0.767960i | \(-0.721272\pi\) | ||
0.640497 | − | 0.767960i | \(-0.278728\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −739421. | −1.42240 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17498.0 | + | 252352.i | −0.0334743 | + | 0.482759i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 147721.i | − | 0.281038i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −257472. | −0.487149 | −0.243574 | − | 0.969882i | \(-0.578320\pi\) | ||||
−0.243574 | + | 0.969882i | \(0.578320\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −486251. | − | 214453.i | −0.914966 | − | 0.403531i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 68196.8i | 0.127623i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 113268. | 0.210813 | 0.105407 | − | 0.994429i | \(-0.466386\pi\) | ||||
0.105407 | + | 0.994429i | \(0.466386\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3607.64 | − | 250.152i | −0.00667802 | − | 0.000463051i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 636129.i | 1.17114i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −309173. | −0.566125 | −0.283062 | − | 0.959102i | \(-0.591350\pi\) | ||||
−0.283062 | + | 0.959102i | \(0.591350\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16299.0 | − | 235060.i | 0.0296841 | − | 0.428098i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 693611.i | − | 1.25643i | −0.778040 | − | 0.628215i | \(-0.783786\pi\) | ||
0.778040 | − | 0.628215i | \(-0.216214\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18797.3 | −0.0338674 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9378.72 | + | 67303.8i | −0.0168075 | + | 0.120614i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 664947.i | 1.18529i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 642817. | 1.13974 | 0.569872 | − | 0.821733i | \(-0.306993\pi\) | ||||
0.569872 | + | 0.821733i | \(0.306993\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.03063e6 | + | 71463.2i | 1.81765 | + | 0.126035i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7386.79i | 0.0129587i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 127284. | 0.222117 | 0.111058 | − | 0.993814i | \(-0.464576\pi\) | ||||
0.111058 | + | 0.993814i | \(0.464576\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −43151.2 | + | 622318.i | −0.0749048 | + | 1.08026i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 125775.i | 0.217183i | 0.994086 | + | 0.108592i | \(0.0346341\pi\) | ||||
−0.994086 | + | 0.108592i | \(0.965366\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 718310. | 1.23385 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15060.9 | − | 2098.73i | −0.0257353 | − | 0.00358619i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 91241.0i | − | 0.155096i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 636165. | 1.07576 | 0.537882 | − | 0.843020i | \(-0.319225\pi\) | ||||
0.537882 | + | 0.843020i | \(0.319225\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 457263. | + | 31706.4i | 0.769231 | + | 0.0533382i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 346515.i | − | 0.579913i | −0.957040 | − | 0.289957i | \(-0.906359\pi\) | ||
0.957040 | − | 0.289957i | \(-0.0936409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −799923. | −1.33182 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17857.3 | − | 257534.i | 0.0295783 | − | 0.426572i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 434765.i | 0.716440i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 424278. | 0.695582 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 168684. | + | 35545.9i | 0.275138 | + | 0.0579784i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17795.6i | 0.0288785i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −666749. | −1.07650 | −0.538249 | − | 0.842786i | \(-0.680914\pi\) | ||||
−0.538249 | + | 0.842786i | \(0.680914\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19364.9 | − | 1342.76i | −0.0311073 | − | 0.00215697i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.24859e6i | 1.99557i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 413219. | 0.657104 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −111.218 | + | 1603.96i | −0.000175971 | + | 0.00253781i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 512411.i | 0.806681i | 0.915050 | + | 0.403341i | \(0.132151\pi\) | ||||
−0.915050 | + | 0.403341i | \(0.867849\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −439591. | −0.688582 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −155874. | + | 1.11859e6i | −0.242946 | + | 1.74343i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 613080.i | 0.950792i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24772.5 | 0.0382277 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.08840e6 | − | 75469.5i | −1.67126 | − | 0.115884i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 450334.i | − | 0.688079i | −0.938955 | − | 0.344039i | \(-0.888205\pi\) | ||
0.938955 | − | 0.344039i | \(-0.111795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −128497. | −0.195367 | −0.0976833 | − | 0.995218i | \(-0.531143\pi\) | ||||
−0.0976833 | + | 0.995218i | \(0.531143\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13213.4 | − | 190561.i | 0.0199910 | − | 0.288305i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18068.6i | 0.0272025i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 74656.0 | 0.111846 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −320634. | − | 44680.1i | −0.478016 | − | 0.0666110i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.03116e6i | − | 1.52982i | −0.644140 | − | 0.764908i | \(-0.722785\pi\) | ||
0.644140 | − | 0.764908i | \(-0.277215\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −456962. | −0.674652 | −0.337326 | − | 0.941388i | \(-0.609523\pi\) | ||||
−0.337326 | + | 0.941388i | \(0.609523\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 492344. | + | 34138.9i | 0.723371 | + | 0.0501582i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 476279.i | − | 0.696386i | −0.937423 | − | 0.348193i | \(-0.886795\pi\) | ||
0.937423 | − | 0.348193i | \(-0.113205\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −527555. | −0.767641 | −0.383821 | − | 0.923408i | \(-0.625392\pi\) | ||||
−0.383821 | + | 0.923408i | \(0.625392\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −72318.6 | + | 1.04296e6i | −0.104724 | + | 1.51031i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 238790.i | 0.344132i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7841.24 | 0.0112464 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 192485. | − | 913441.i | 0.274755 | − | 1.30386i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.17995e6i | − | 1.67626i | −0.545472 | − | 0.838129i | \(-0.683650\pi\) | ||
0.545472 | − | 0.838129i | \(-0.316350\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 651362. | 0.920937 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.05513e6 | + | 73162.0i | 1.48474 | + | 0.102951i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13171.4i | 0.0184467i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 387127. | 0.539619 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −45561.3 | + | 657076.i | −0.0632093 | + | 0.911591i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 405738.i | 0.560256i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 105304. | 0.144727 | 0.0723633 | − | 0.997378i | \(-0.476946\pi\) | ||||
0.0723633 | + | 0.997378i | \(0.476946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2297.51 | + | 16487.4i | −0.00314286 | + | 0.0225538i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 610982.i | − | 0.831891i | −0.909389 | − | 0.415946i | \(-0.863451\pi\) | ||
0.909389 | − | 0.415946i | \(-0.136549\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 732588. | 0.992827 | 0.496413 | − | 0.868086i | \(-0.334650\pi\) | ||||
0.496413 | + | 0.868086i | \(0.334650\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 595907. | + | 41319.9i | 0.803844 | + | 0.0557382i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 956613.i | 1.28444i | 0.766519 | + | 0.642222i | \(0.221987\pi\) | ||||
−0.766519 | + | 0.642222i | \(0.778013\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18469.8 | 0.0246848 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17460.5 | + | 251812.i | −0.0232284 | + | 0.334995i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 819218.i | − | 1.08483i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 518856. | 0.683929 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −527758. | − | 73542.6i | −0.692479 | − | 0.0964963i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 39207.3i | − | 0.0512095i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 778581. | 1.01229 | 0.506144 | − | 0.862449i | \(-0.331070\pi\) | ||||
0.506144 | + | 0.862449i | \(0.331070\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −812998. | − | 56372.9i | −1.05223 | − | 0.0729613i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 431230.i | 0.555594i | 0.960640 | + | 0.277797i | \(0.0896042\pi\) | ||||
−0.960640 | + | 0.277797i | \(0.910396\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.05031e6 | 1.34708 | 0.673541 | − | 0.739150i | \(-0.264772\pi\) | ||||
0.673541 | + | 0.739150i | \(0.264772\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −445.900 | + | 6430.68i | −0.000569313 | + | 0.00821051i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 422335.i | 0.536797i | 0.963308 | + | 0.268398i | \(0.0864944\pi\) | ||||
−0.963308 | + | 0.268398i | \(0.913506\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 682232. | 0.863234 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −157456. | + | 553999.i | −0.198337 | + | 0.697837i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 481227.i | 0.603458i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11795.1 | 0.0147251 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 507591. | + | 35196.1i | 0.630854 | + | 0.0437431i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 302809.i | 0.374671i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 106166. | 0.130779 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7095.28 | − | 102327.i | 0.00870149 | − | 0.125491i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31512.8i | 0.0384760i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 268248. | 0.326078 | 0.163039 | − | 0.986620i | \(-0.447870\pi\) | ||||
0.163039 | + | 0.986620i | \(0.447870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −200493. | + | 1.43878e6i | −0.242645 | + | 1.74127i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.04830e6i | − | 1.26313i | −0.775324 | − | 0.631564i | \(-0.782413\pi\) | ||
0.775324 | − | 0.631564i | \(-0.217587\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 73644.1 | 0.0883480 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29123.7 | − | 2019.43i | −0.0347860 | − | 0.00241205i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 844058.i | 1.00377i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −220409. | −0.260975 | −0.130487 | − | 0.991450i | \(-0.541654\pi\) | ||||
−0.130487 | + | 0.991450i | \(0.541654\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29281.3 | + | 422289.i | −0.0345201 | + | 0.497841i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 346061.i | − | 0.406208i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 320998. | 0.375162 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.06270e6 | + | 148086.i | 1.23666 | + | 0.172327i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 510188.i | − | 0.591152i | −0.955319 | − | 0.295576i | \(-0.904489\pi\) | ||
0.955319 | − | 0.295576i | \(-0.0955115\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 261406. | 0.301590 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.49242e6 | + | 103483.i | 1.71446 | + | 0.118880i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16479.8i | 0.0188507i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −899577. | −1.02461 | −0.512306 | − | 0.858803i | \(-0.671208\pi\) | ||||
−0.512306 | + | 0.858803i | \(0.671208\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 71023.7 | − | 1.02429e6i | 0.0805512 | − | 1.16169i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.71356e6i | − | 1.93517i | −0.252546 | − | 0.967585i | \(-0.581268\pi\) | ||
0.252546 | − | 0.967585i | \(-0.418732\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −938834. | −1.05576 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 22380.0 | + | 4716.02i | 0.0250609 | + | 0.00528095i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 149981.i | 0.167239i | 0.996498 | + | 0.0836193i | \(0.0266480\pi\) | ||||
−0.996498 | + | 0.0836193i | \(0.973352\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 500056. | 0.555247 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −294220. | − | 20401.1i | −0.325320 | − | 0.0225575i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 530581.i | − | 0.584206i | −0.956387 | − | 0.292103i | \(-0.905645\pi\) | ||
0.956387 | − | 0.292103i | \(-0.0943549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26865.2 | 0.0294566 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12923.2 | − | 186376.i | 0.0141106 | − | 0.203501i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 139825.i | 0.152036i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 716220. | 0.775532 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 133170. | − | 955661.i | 0.143600 | − | 1.03051i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 24.2534i | − | 2.60446e-5i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.45353e6 | −1.55443 | −0.777216 | − | 0.629233i | \(-0.783369\pi\) | ||||
−0.777216 | + | 0.629233i | \(0.783369\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.09658e6 | + | 76036.1i | 1.16786 | + | 0.0809790i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 177413.i | 0.188169i | 0.995564 | + | 0.0940845i | \(0.0299924\pi\) | ||||
−0.995564 | + | 0.0940845i | \(0.970008\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.59147e6 | 1.68102 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27845.3 | − | 401579.i | 0.0292916 | − | 0.422436i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 301481.i | 0.315842i | 0.987452 | + | 0.157921i | \(0.0504792\pi\) | ||||
−0.987452 | + | 0.157921i | \(0.949521\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.22397e6 | 1.27704 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.03235e6 | − | 143858.i | −1.07273 | − | 0.149484i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 178724.i | − | 0.184959i | −0.995715 | − | 0.0924795i | \(-0.970521\pi\) | ||
0.995715 | − | 0.0924795i | \(-0.0294793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22559.0 | −0.0232513 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 659589. | + | 45735.6i | 0.677079 | + | 0.0469483i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 161213.i | 0.164819i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −630243. | −0.641743 | −0.320871 | − | 0.947123i | \(-0.603976\pi\) | ||||
−0.320871 | + | 0.947123i | \(0.603976\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 85657.7 | − | 1.23534e6i | 0.0868696 | − | 1.25282i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 13140.0i | − | 0.0132724i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 544850. | 0.548134 | 0.274067 | − | 0.961711i | \(-0.411631\pi\) | ||||
0.274067 | + | 0.961711i | \(0.411631\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −77241.4 | + | 366551.i | −0.0773961 | + | 0.367286i |
(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 | 384.5.e.c.257.7 | yes | 16 | |
3.2 | odd | 2 | inner | 384.5.e.c.257.8 | yes | 16 | |
4.3 | odd | 2 | 384.5.e.b.257.10 | yes | 16 | ||
8.3 | odd | 2 | 384.5.e.d.257.7 | yes | 16 | ||
8.5 | even | 2 | 384.5.e.a.257.10 | yes | 16 | ||
12.11 | even | 2 | 384.5.e.b.257.9 | yes | 16 | ||
24.5 | odd | 2 | 384.5.e.a.257.9 | ✓ | 16 | ||
24.11 | even | 2 | 384.5.e.d.257.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.e.a.257.9 | ✓ | 16 | 24.5 | odd | 2 | ||
384.5.e.a.257.10 | yes | 16 | 8.5 | even | 2 | ||
384.5.e.b.257.9 | yes | 16 | 12.11 | even | 2 | ||
384.5.e.b.257.10 | yes | 16 | 4.3 | odd | 2 | ||
384.5.e.c.257.7 | yes | 16 | 1.1 | even | 1 | trivial | |
384.5.e.c.257.8 | yes | 16 | 3.2 | odd | 2 | inner | |
384.5.e.d.257.7 | yes | 16 | 8.3 | odd | 2 | ||
384.5.e.d.257.8 | yes | 16 | 24.11 | even | 2 |