Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(55,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, 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("252.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.b (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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.11 | ||
Root | \(-2.78362 + 0.501431i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.55 |
Dual form | 252.4.b.e.55.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.78362 | − | 0.501431i | 0.984160 | − | 0.177282i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.49713 | − | 2.79159i | 0.937142 | − | 0.348949i | ||||
\(5\) | 4.57514i | 0.409213i | 0.978844 | + | 0.204606i | \(0.0655914\pi\) | ||||
−0.978844 | + | 0.204606i | \(0.934409\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.93118 | − | 18.2868i | −0.158269 | − | 0.987396i | ||||
\(8\) | 19.4694 | − | 11.5300i | 0.860435 | − | 0.509560i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.29411 | + | 12.7355i | 0.0725462 | + | 0.402731i | ||||
\(11\) | − | 26.0206i | − | 0.713227i | −0.934252 | − | 0.356613i | \(-0.883931\pi\) | ||
0.934252 | − | 0.356613i | \(-0.116069\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 75.0905i | − | 1.60203i | −0.598647 | − | 0.801013i | \(-0.704295\pi\) | ||
0.598647 | − | 0.801013i | \(-0.295705\pi\) | |||||||
\(14\) | −17.3289 | − | 49.4339i | −0.330810 | − | 0.943697i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 48.4141 | − | 41.8578i | 0.756470 | − | 0.654029i | ||||
\(17\) | 115.976i | 1.65460i | 0.561758 | + | 0.827302i | \(0.310125\pi\) | ||||
−0.561758 | + | 0.827302i | \(0.689875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 119.051 | 1.43748 | 0.718739 | − | 0.695280i | \(-0.244720\pi\) | ||||
0.718739 | + | 0.695280i | \(0.244720\pi\) | |||||||
\(20\) | 12.7719 | + | 34.3004i | 0.142794 | + | 0.383490i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −13.0475 | − | 72.4315i | −0.126443 | − | 0.701929i | ||||
\(23\) | − | 61.4339i | − | 0.556950i | −0.960443 | − | 0.278475i | \(-0.910171\pi\) | ||
0.960443 | − | 0.278475i | \(-0.0898290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 104.068 | 0.832545 | ||||||||
\(26\) | −37.6527 | − | 209.024i | −0.284011 | − | 1.57665i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −73.0248 | − | 128.916i | −0.492871 | − | 0.870102i | ||||
\(29\) | 71.9146 | 0.460490 | 0.230245 | − | 0.973133i | \(-0.426047\pi\) | ||||
0.230245 | + | 0.973133i | \(0.426047\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −231.587 | −1.34175 | −0.670875 | − | 0.741571i | \(-0.734081\pi\) | ||||
−0.670875 | + | 0.741571i | \(0.734081\pi\) | |||||||
\(32\) | 113.778 | − | 140.793i | 0.628539 | − | 0.777778i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 58.1538 | + | 322.833i | 0.293332 | + | 1.62839i | ||||
\(35\) | 83.6647 | − | 13.4106i | 0.404055 | − | 0.0647657i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.3306 | 0.0592309 | 0.0296155 | − | 0.999561i | \(-0.490572\pi\) | ||||
0.0296155 | + | 0.999561i | \(0.490572\pi\) | |||||||
\(38\) | 331.392 | − | 59.6956i | 1.41471 | − | 0.254840i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 52.7515 | + | 89.0753i | 0.208518 | + | 0.352101i | ||||
\(41\) | − | 144.133i | − | 0.549018i | −0.961584 | − | 0.274509i | \(-0.911485\pi\) | ||
0.961584 | − | 0.274509i | \(-0.0885154\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 288.638i | 1.02365i | 0.859090 | + | 0.511825i | \(0.171030\pi\) | ||||
−0.859090 | + | 0.511825i | \(0.828970\pi\) | |||||||
\(44\) | −72.6387 | − | 195.080i | −0.248880 | − | 0.668395i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −30.8049 | − | 171.009i | −0.0987376 | − | 0.548128i | ||||
\(47\) | −343.549 | −1.06621 | −0.533104 | − | 0.846050i | \(-0.678975\pi\) | ||||
−0.533104 | + | 0.846050i | \(0.678975\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −325.816 | + | 107.204i | −0.949902 | + | 0.312548i | ||||
\(50\) | 289.687 | − | 52.1829i | 0.819357 | − | 0.147596i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −209.622 | − | 562.963i | −0.559025 | − | 1.50133i | ||||
\(53\) | −142.666 | −0.369749 | −0.184875 | − | 0.982762i | \(-0.559188\pi\) | ||||
−0.184875 | + | 0.982762i | \(0.559188\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 119.048 | 0.291861 | ||||||||
\(56\) | −267.916 | − | 322.237i | −0.639318 | − | 0.768943i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 200.183 | − | 36.0602i | 0.453196 | − | 0.0816368i | ||||
\(59\) | 403.919 | 0.891284 | 0.445642 | − | 0.895211i | \(-0.352975\pi\) | ||||
0.445642 | + | 0.895211i | \(0.352975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 21.7765i | − | 0.0457082i | −0.999739 | − | 0.0228541i | \(-0.992725\pi\) | ||
0.999739 | − | 0.0228541i | \(-0.00727532\pi\) | |||||||
\(62\) | −644.651 | + | 116.125i | −1.32050 | + | 0.237869i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 246.117 | − | 448.966i | 0.480697 | − | 0.876887i | ||||
\(65\) | 343.549 | 0.655570 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 598.674i | 1.09164i | 0.837904 | + | 0.545818i | \(0.183781\pi\) | ||||
−0.837904 | + | 0.545818i | \(0.816219\pi\) | |||||||
\(68\) | 323.757 | + | 869.486i | 0.577372 | + | 1.55060i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 226.167 | − | 79.2821i | 0.386173 | − | 0.135372i | ||||
\(71\) | 589.524i | 0.985403i | 0.870198 | + | 0.492701i | \(0.163991\pi\) | ||||
−0.870198 | + | 0.492701i | \(0.836009\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.85314i | 0.0109877i | 0.999985 | + | 0.00549383i | \(0.00174875\pi\) | ||||
−0.999985 | + | 0.00549383i | \(0.998251\pi\) | |||||||
\(74\) | 37.1075 | − | 6.68439i | 0.0582927 | − | 0.0105006i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 892.538 | − | 332.340i | 1.34712 | − | 0.501606i | ||||
\(77\) | −475.834 | + | 76.2711i | −0.704237 | + | 0.112882i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 972.231i | 1.38461i | 0.721603 | + | 0.692307i | \(0.243406\pi\) | ||||
−0.721603 | + | 0.692307i | \(0.756594\pi\) | |||||||
\(80\) | 191.505 | + | 221.501i | 0.267637 | + | 0.309557i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −72.2726 | − | 401.212i | −0.0973313 | − | 0.540322i | ||||
\(83\) | −429.745 | −0.568321 | −0.284161 | − | 0.958777i | \(-0.591715\pi\) | ||||
−0.284161 | + | 0.958777i | \(0.591715\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −530.605 | −0.677085 | ||||||||
\(86\) | 144.732 | + | 803.461i | 0.181475 | + | 1.00743i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −300.018 | − | 506.605i | −0.363432 | − | 0.613685i | ||||
\(89\) | − | 1083.91i | − | 1.29095i | −0.763781 | − | 0.645476i | \(-0.776659\pi\) | ||
0.763781 | − | 0.645476i | \(-0.223341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1373.17 | + | 220.104i | −1.58183 | + | 0.253551i | ||||
\(92\) | −171.498 | − | 460.578i | −0.194347 | − | 0.521942i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −956.312 | + | 172.266i | −1.04932 | + | 0.189020i | ||||
\(95\) | 544.673i | 0.588234i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1031.01i | 1.07921i | 0.841920 | + | 0.539603i | \(0.181426\pi\) | ||||
−0.841920 | + | 0.539603i | \(0.818574\pi\) | |||||||
\(98\) | −853.195 | + | 461.790i | −0.879446 | + | 0.475999i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 780.213 | − | 290.515i | 0.780213 | − | 0.290515i | ||||
\(101\) | 207.988i | 0.204907i | 0.994738 | + | 0.102454i | \(0.0326693\pi\) | ||||
−0.994738 | + | 0.102454i | \(0.967331\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1229.81 | 1.17647 | 0.588237 | − | 0.808689i | \(-0.299822\pi\) | ||||
0.588237 | + | 0.808689i | \(0.299822\pi\) | |||||||
\(104\) | −865.795 | − | 1461.97i | −0.816329 | − | 1.37844i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −397.129 | + | 71.5372i | −0.363892 | + | 0.0655500i | ||||
\(107\) | 1502.68i | 1.35766i | 0.734294 | + | 0.678832i | \(0.237513\pi\) | ||||
−0.734294 | + | 0.678832i | \(0.762487\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 579.301 | 0.509055 | 0.254527 | − | 0.967066i | \(-0.418080\pi\) | ||||
0.254527 | + | 0.967066i | \(0.418080\pi\) | |||||||
\(110\) | 331.384 | − | 59.6941i | 0.287238 | − | 0.0517419i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −907.358 | − | 762.647i | −0.765511 | − | 0.643423i | ||||
\(113\) | −614.637 | −0.511683 | −0.255842 | − | 0.966719i | \(-0.582353\pi\) | ||||
−0.255842 | + | 0.966719i | \(0.582353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 281.069 | 0.227911 | ||||||||
\(116\) | 539.153 | − | 200.756i | 0.431544 | − | 0.160687i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1124.36 | − | 202.537i | 0.877166 | − | 0.158009i | ||||
\(119\) | 2120.83 | − | 339.946i | 1.63375 | − | 0.261873i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 653.930 | 0.491308 | ||||||||
\(122\) | −10.9194 | − | 60.6177i | −0.00810327 | − | 0.0449842i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1736.24 | + | 646.496i | −1.25741 | + | 0.468202i | ||||
\(125\) | 1048.02i | 0.749901i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 273.874i | − | 0.191358i | −0.995412 | − | 0.0956788i | \(-0.969498\pi\) | ||
0.995412 | − | 0.0956788i | \(-0.0305022\pi\) | |||||||
\(128\) | 459.972 | − | 1373.16i | 0.317626 | − | 0.948216i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 956.312 | − | 172.266i | 0.645185 | − | 0.116221i | ||||
\(131\) | −2187.84 | −1.45918 | −0.729591 | − | 0.683884i | \(-0.760290\pi\) | ||||
−0.729591 | + | 0.683884i | \(0.760290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −348.959 | − | 2177.06i | −0.227508 | − | 1.41936i | ||||
\(134\) | 300.193 | + | 1666.48i | 0.193528 | + | 1.07434i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1337.20 | + | 2257.98i | 0.843120 | + | 1.42368i | ||||
\(137\) | 2535.39 | 1.58112 | 0.790558 | − | 0.612388i | \(-0.209791\pi\) | ||||
0.790558 | + | 0.612388i | \(0.209791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1007.32 | −0.614675 | −0.307338 | − | 0.951601i | \(-0.599438\pi\) | ||||
−0.307338 | + | 0.951601i | \(0.599438\pi\) | |||||||
\(140\) | 589.809 | − | 334.098i | 0.356057 | − | 0.201689i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 295.605 | + | 1641.01i | 0.174695 | + | 0.969794i | ||||
\(143\) | −1953.90 | −1.14261 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 329.019i | 0.188438i | ||||||||
\(146\) | 3.43637 | + | 19.0766i | 0.00194792 | + | 0.0108136i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 99.9416 | − | 37.2137i | 0.0555078 | − | 0.0206686i | ||||
\(149\) | −2342.59 | −1.28800 | −0.644002 | − | 0.765024i | \(-0.722727\pi\) | ||||
−0.644002 | + | 0.765024i | \(0.722727\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 561.022i | 0.302353i | 0.988507 | + | 0.151177i | \(0.0483062\pi\) | ||||
−0.988507 | + | 0.151177i | \(0.951694\pi\) | |||||||
\(152\) | 2317.85 | − | 1372.66i | 1.23686 | − | 0.732481i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1286.30 | + | 450.908i | −0.673070 | + | 0.235943i | ||||
\(155\) | − | 1059.54i | − | 0.549061i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 459.220i | − | 0.233438i | −0.993165 | − | 0.116719i | \(-0.962762\pi\) | ||
0.993165 | − | 0.116719i | \(-0.0372377\pi\) | |||||||
\(158\) | 487.506 | + | 2706.33i | 0.245468 | + | 1.36268i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 644.146 | + | 520.549i | 0.318277 | + | 0.257206i | ||||
\(161\) | −1123.43 | + | 180.074i | −0.549931 | + | 0.0881480i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 558.186i | 0.268224i | 0.990966 | + | 0.134112i | \(0.0428182\pi\) | ||||
−0.990966 | + | 0.134112i | \(0.957182\pi\) | |||||||
\(164\) | −402.359 | − | 1080.58i | −0.191579 | − | 0.514508i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1196.25 | + | 215.487i | −0.559319 | + | 0.100753i | ||||
\(167\) | 2494.32 | 1.15579 | 0.577893 | − | 0.816113i | \(-0.303875\pi\) | ||||
0.577893 | + | 0.816113i | \(0.303875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3441.58 | −1.56649 | ||||||||
\(170\) | −1477.01 | + | 266.062i | −0.666360 | + | 0.120035i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 805.760 | + | 2163.96i | 0.357201 | + | 0.959305i | ||||
\(173\) | 2881.62i | 1.26639i | 0.773993 | + | 0.633195i | \(0.218257\pi\) | ||||
−0.773993 | + | 0.633195i | \(0.781743\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −305.043 | − | 1903.08i | −0.131766 | − | 0.822052i | ||||
\(176\) | −1089.16 | − | 1259.76i | −0.466471 | − | 0.539534i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −543.508 | − | 3017.21i | −0.228863 | − | 1.27050i | ||||
\(179\) | 2072.63i | 0.865452i | 0.901525 | + | 0.432726i | \(0.142448\pi\) | ||||
−0.901525 | + | 0.432726i | \(0.857552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2764.12i | − | 1.13511i | −0.823335 | − | 0.567556i | \(-0.807889\pi\) | ||
0.823335 | − | 0.567556i | \(-0.192111\pi\) | |||||||
\(182\) | −3712.01 | + | 1301.23i | −1.51183 | + | 0.529967i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −708.335 | − | 1196.08i | −0.283800 | − | 0.479220i | ||||
\(185\) | 60.9895i | 0.0242380i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3017.76 | 1.18011 | ||||||||
\(188\) | −2575.63 | + | 959.048i | −0.999188 | + | 0.372052i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 273.115 | + | 1516.16i | 0.104284 | + | 0.578916i | ||||
\(191\) | − | 4118.94i | − | 1.56040i | −0.625530 | − | 0.780200i | \(-0.715117\pi\) | ||
0.625530 | − | 0.780200i | \(-0.284883\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4537.82 | 1.69243 | 0.846216 | − | 0.532840i | \(-0.178875\pi\) | ||||
0.846216 | + | 0.532840i | \(0.178875\pi\) | |||||||
\(194\) | 516.979 | + | 2869.94i | 0.191324 | + | 1.06211i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2143.42 | + | 1713.27i | −0.781129 | + | 0.624369i | ||||
\(197\) | −846.178 | −0.306029 | −0.153014 | − | 0.988224i | \(-0.548898\pi\) | ||||
−0.153014 | + | 0.988224i | \(0.548898\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1218.87 | 0.434188 | 0.217094 | − | 0.976151i | \(-0.430342\pi\) | ||||
0.217094 | + | 0.976151i | \(0.430342\pi\) | |||||||
\(200\) | 2026.15 | − | 1199.91i | 0.716351 | − | 0.424232i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 104.292 | + | 578.962i | 0.0363265 | + | 0.201661i | ||||
\(203\) | −210.795 | − | 1315.09i | −0.0728813 | − | 0.454686i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 659.427 | 0.224665 | ||||||||
\(206\) | 3423.33 | − | 616.664i | 1.15784 | − | 0.208568i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3143.12 | − | 3635.43i | −1.04777 | − | 1.21188i | ||||
\(209\) | − | 3097.76i | − | 1.02525i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5064.81i | − | 1.65249i | −0.563308 | − | 0.826247i | \(-0.690472\pi\) | ||
0.563308 | − | 0.826247i | \(-0.309528\pi\) | |||||||
\(212\) | −1069.59 | + | 398.265i | −0.346507 | + | 0.129023i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 753.492 | + | 4182.91i | 0.240690 | + | 1.33616i | ||||
\(215\) | −1320.56 | −0.418890 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 678.824 | + | 4234.99i | 0.212357 | + | 1.32484i | ||||
\(218\) | 1612.56 | − | 290.479i | 0.500992 | − | 0.0902465i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 892.516 | − | 332.332i | 0.273516 | − | 0.101845i | ||||
\(221\) | 8708.67 | 2.65072 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3894.06 | −1.16935 | −0.584676 | − | 0.811267i | \(-0.698778\pi\) | ||||
−0.584676 | + | 0.811267i | \(0.698778\pi\) | |||||||
\(224\) | −2908.16 | − | 1667.95i | −0.867453 | − | 0.497519i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1710.92 | + | 308.198i | −0.503578 | + | 0.0907124i | ||||
\(227\) | 1165.95 | 0.340910 | 0.170455 | − | 0.985365i | \(-0.445476\pi\) | ||||
0.170455 | + | 0.985365i | \(0.445476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2537.92i | 0.732361i | 0.930544 | + | 0.366181i | \(0.119335\pi\) | ||||
−0.930544 | + | 0.366181i | \(0.880665\pi\) | |||||||
\(230\) | 782.390 | − | 140.936i | 0.224301 | − | 0.0404047i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1400.14 | − | 829.177i | 0.396221 | − | 0.234647i | ||||
\(233\) | −1345.53 | −0.378321 | −0.189160 | − | 0.981946i | \(-0.560577\pi\) | ||||
−0.189160 | + | 0.981946i | \(0.560577\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1571.78i | − | 0.436306i | ||||||
\(236\) | 3028.24 | − | 1127.58i | 0.835260 | − | 0.311012i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5733.13 | − | 2009.73i | 1.56144 | − | 0.547360i | ||||
\(239\) | − | 6239.81i | − | 1.68878i | −0.535725 | − | 0.844392i | \(-0.679962\pi\) | ||
0.535725 | − | 0.844392i | \(-0.320038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4546.01i | 1.21508i | 0.794289 | + | 0.607540i | \(0.207844\pi\) | ||||
−0.794289 | + | 0.607540i | \(0.792156\pi\) | |||||||
\(242\) | 1820.30 | − | 327.901i | 0.483525 | − | 0.0871002i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −60.7912 | − | 163.262i | −0.0159498 | − | 0.0428351i | ||||
\(245\) | −490.474 | − | 1490.65i | −0.127899 | − | 0.388712i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8939.56i | − | 2.30288i | ||||||
\(248\) | −4508.86 | + | 2670.20i | −1.15449 | + | 0.683702i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 525.508 | + | 2917.29i | 0.132944 | + | 0.738022i | ||||
\(251\) | 6775.91 | 1.70395 | 0.851976 | − | 0.523582i | \(-0.175404\pi\) | ||||
0.851976 | + | 0.523582i | \(0.175404\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1598.55 | −0.397232 | ||||||||
\(254\) | −137.329 | − | 762.363i | −0.0339243 | − | 0.188326i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 591.842 | − | 4053.02i | 0.144493 | − | 0.989506i | ||||
\(257\) | − | 7170.16i | − | 1.74032i | −0.492770 | − | 0.870160i | \(-0.664016\pi\) | ||
0.492770 | − | 0.870160i | \(-0.335984\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −39.0746 | − | 243.775i | −0.00937442 | − | 0.0584844i | ||||
\(260\) | 2575.63 | − | 959.048i | 0.614362 | − | 0.228760i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6090.14 | + | 1097.05i | −1.43607 | + | 0.258687i | ||||
\(263\) | − | 2093.31i | − | 0.490795i | −0.969422 | − | 0.245398i | \(-0.921081\pi\) | ||
0.969422 | − | 0.245398i | \(-0.0789185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 652.717i | − | 0.151306i | ||||||
\(266\) | −2063.01 | − | 5885.13i | −0.475532 | − | 1.35654i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1671.25 | + | 4488.34i | 0.380925 | + | 1.02302i | ||||
\(269\) | − | 1573.92i | − | 0.356742i | −0.983963 | − | 0.178371i | \(-0.942917\pi\) | ||
0.983963 | − | 0.178371i | \(-0.0570828\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1974.18 | 0.442519 | 0.221260 | − | 0.975215i | \(-0.428983\pi\) | ||||
0.221260 | + | 0.975215i | \(0.428983\pi\) | |||||||
\(272\) | 4854.50 | + | 5614.86i | 1.08216 | + | 1.25166i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7057.57 | − | 1271.32i | 1.55607 | − | 0.280304i | ||||
\(275\) | − | 2707.91i | − | 0.593793i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4758.46 | 1.03216 | 0.516079 | − | 0.856541i | \(-0.327391\pi\) | ||||
0.516079 | + | 0.856541i | \(0.327391\pi\) | |||||||
\(278\) | −2804.00 | + | 505.102i | −0.604939 | + | 0.108971i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1474.28 | − | 1225.75i | 0.314661 | − | 0.261617i | ||||
\(281\) | −1753.46 | −0.372252 | −0.186126 | − | 0.982526i | \(-0.559593\pi\) | ||||
−0.186126 | + | 0.982526i | \(0.559593\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3603.19 | 0.756846 | 0.378423 | − | 0.925633i | \(-0.376466\pi\) | ||||
0.378423 | + | 0.925633i | \(0.376466\pi\) | |||||||
\(284\) | 1645.71 | + | 4419.74i | 0.343855 | + | 0.923462i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5438.91 | + | 979.743i | −1.12451 | + | 0.202564i | ||||
\(287\) | −2635.73 | + | 422.480i | −0.542099 | + | 0.0868926i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8537.38 | −1.73771 | ||||||||
\(290\) | 164.980 | + | 915.865i | 0.0334068 | + | 0.185453i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.1311 | + | 51.3789i | 0.00383413 | + | 0.0102970i | ||||
\(293\) | 8854.04i | 1.76539i | 0.469949 | + | 0.882693i | \(0.344272\pi\) | ||||
−0.469949 | + | 0.882693i | \(0.655728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1847.98i | 0.364725i | ||||||||
\(296\) | 259.540 | − | 153.703i | 0.0509644 | − | 0.0301817i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6520.90 | + | 1174.65i | −1.26760 | + | 0.228341i | ||||
\(299\) | −4613.10 | −0.892249 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5278.28 | − | 846.052i | 1.01075 | − | 0.162012i | ||||
\(302\) | 281.314 | + | 1561.68i | 0.0536019 | + | 0.297564i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5763.72 | − | 4983.20i | 1.08741 | − | 0.940152i | ||||
\(305\) | 99.6307 | 0.0187044 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4372.30 | −0.812836 | −0.406418 | − | 0.913687i | \(-0.633222\pi\) | ||||
−0.406418 | + | 0.913687i | \(0.633222\pi\) | |||||||
\(308\) | −3354.47 | + | 1900.15i | −0.620580 | + | 0.351529i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −531.287 | − | 2949.37i | −0.0973389 | − | 0.540364i | ||||
\(311\) | −1956.21 | −0.356676 | −0.178338 | − | 0.983969i | \(-0.557072\pi\) | ||||
−0.178338 | + | 0.983969i | \(0.557072\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6314.07i | − | 1.14023i | −0.821565 | − | 0.570115i | \(-0.806899\pi\) | ||
0.821565 | − | 0.570115i | \(-0.193101\pi\) | |||||||
\(314\) | −230.267 | − | 1278.30i | −0.0413844 | − | 0.229740i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2714.07 | + | 7288.95i | 0.483159 | + | 1.29758i | ||||
\(317\) | −4962.78 | −0.879298 | −0.439649 | − | 0.898170i | \(-0.644897\pi\) | ||||
−0.439649 | + | 0.898170i | \(0.644897\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1871.26i | − | 0.328434i | ||||||
\(320\) | 2054.08 | + | 1126.02i | 0.358833 | + | 0.196707i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3036.92 | + | 1064.58i | −0.525593 | + | 0.184245i | ||||
\(323\) | 13807.0i | 2.37846i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 7814.52i | − | 1.33376i | ||||||
\(326\) | 279.892 | + | 1553.78i | 0.0475514 | + | 0.263976i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1661.86 | − | 2806.18i | −0.279758 | − | 0.472395i | ||||
\(329\) | 1007.01 | + | 6282.42i | 0.168748 | + | 1.05277i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6941.96i | 1.15276i | 0.817181 | + | 0.576381i | \(0.195536\pi\) | ||||
−0.817181 | + | 0.576381i | \(0.804464\pi\) | |||||||
\(332\) | −3221.86 | + | 1199.67i | −0.532598 | + | 0.198315i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6943.25 | − | 1250.73i | 1.13748 | − | 0.204900i | ||||
\(335\) | −2739.01 | −0.446711 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1809.91 | −0.292558 | −0.146279 | − | 0.989243i | \(-0.546730\pi\) | ||||
−0.146279 | + | 0.989243i | \(0.546730\pi\) | |||||||
\(338\) | −9580.06 | + | 1725.71i | −1.54168 | + | 0.277711i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3978.02 | + | 1481.23i | −0.634524 | + | 0.236268i | ||||
\(341\) | 6026.02i | 0.956972i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2915.45 | + | 5643.91i | 0.458949 | + | 0.888463i | ||||
\(344\) | 3328.01 | + | 5619.62i | 0.521611 | + | 0.880784i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1444.93 | + | 8021.34i | 0.224509 | + | 1.24633i | ||||
\(347\) | 3542.86i | 0.548100i | 0.961716 | + | 0.274050i | \(0.0883633\pi\) | ||||
−0.961716 | + | 0.274050i | \(0.911637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1318.04i | 0.202158i | 0.994878 | + | 0.101079i | \(0.0322295\pi\) | ||||
−0.994878 | + | 0.101079i | \(0.967771\pi\) | |||||||
\(350\) | −1803.39 | − | 5144.49i | −0.275414 | − | 0.785671i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3663.51 | − | 2960.56i | −0.554732 | − | 0.448291i | ||||
\(353\) | − | 1254.21i | − | 0.189107i | −0.995520 | − | 0.0945534i | \(-0.969858\pi\) | ||
0.995520 | − | 0.0945534i | \(-0.0301423\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2697.15 | −0.403239 | ||||||||
\(356\) | −3025.84 | − | 8126.25i | −0.450476 | − | 1.20980i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1039.28 | + | 5769.44i | 0.153430 | + | 0.851743i | ||||
\(359\) | 2350.70i | 0.345585i | 0.984958 | + | 0.172793i | \(0.0552791\pi\) | ||||
−0.984958 | + | 0.172793i | \(0.944721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7314.03 | 1.06634 | ||||||||
\(362\) | −1386.01 | − | 7694.26i | −0.201235 | − | 1.11713i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9680.37 | + | 5483.47i | −1.39393 | + | 0.789593i | ||||
\(365\) | −31.3540 | −0.00449629 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2941.18 | −0.418333 | −0.209167 | − | 0.977880i | \(-0.567075\pi\) | ||||
−0.209167 | + | 0.977880i | \(0.567075\pi\) | |||||||
\(368\) | −2571.49 | − | 2974.27i | −0.364262 | − | 0.421316i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 30.5820 | + | 169.772i | 0.00429698 | + | 0.0238541i | ||||
\(371\) | 418.181 | + | 2608.91i | 0.0585198 | + | 0.365089i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7367.26 | −1.02269 | −0.511343 | − | 0.859377i | \(-0.670852\pi\) | ||||
−0.511343 | + | 0.859377i | \(0.670852\pi\) | |||||||
\(374\) | 8400.30 | − | 1513.19i | 1.16141 | − | 0.209212i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6688.70 | + | 3961.13i | −0.917403 | + | 0.543297i | ||||
\(377\) | − | 5400.10i | − | 0.737717i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8022.57i | 1.08731i | 0.839308 | + | 0.543657i | \(0.182961\pi\) | ||||
−0.839308 | + | 0.543657i | \(0.817039\pi\) | |||||||
\(380\) | 1520.50 | + | 4083.48i | 0.205263 | + | 0.551259i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2065.36 | − | 11465.6i | −0.276632 | − | 1.53568i | ||||
\(383\) | 13469.5 | 1.79702 | 0.898511 | − | 0.438950i | \(-0.144650\pi\) | ||||
0.898511 | + | 0.438950i | \(0.144650\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −348.950 | − | 2177.00i | −0.0461926 | − | 0.288183i | ||||
\(386\) | 12631.6 | − | 2275.40i | 1.66562 | − | 0.300039i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2878.15 | + | 7729.61i | 0.376588 | + | 1.01137i | ||||
\(389\) | 642.221 | 0.0837067 | 0.0418533 | − | 0.999124i | \(-0.486674\pi\) | ||||
0.0418533 | + | 0.999124i | \(0.486674\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7124.85 | 0.921532 | ||||||||
\(392\) | −5107.39 | + | 5843.87i | −0.658067 | + | 0.752960i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2355.44 | + | 424.299i | −0.301181 | + | 0.0542535i | ||||
\(395\) | −4448.09 | −0.566602 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6101.12i | 0.771301i | 0.922645 | + | 0.385650i | \(0.126023\pi\) | ||||
−0.922645 | + | 0.385650i | \(0.873977\pi\) | |||||||
\(398\) | 3392.88 | − | 611.179i | 0.427311 | − | 0.0769740i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5038.36 | − | 4356.07i | 0.629795 | − | 0.544508i | ||||
\(401\) | −6300.98 | −0.784679 | −0.392339 | − | 0.919821i | \(-0.628334\pi\) | ||||
−0.392339 | + | 0.919821i | \(0.628334\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17390.0i | 2.14952i | ||||||||
\(404\) | 580.618 | + | 1559.32i | 0.0715021 | + | 0.192027i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1246.20 | − | 3555.02i | −0.152335 | − | 0.434563i | ||||
\(407\) | − | 346.871i | − | 0.0422451i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 897.858i | − | 0.108548i | −0.998526 | − | 0.0542741i | \(-0.982716\pi\) | ||
0.998526 | − | 0.0542741i | \(-0.0172845\pi\) | |||||||
\(410\) | 1835.60 | − | 330.657i | 0.221107 | − | 0.0398292i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9220.05 | − | 3433.12i | 1.10252 | − | 0.410529i | ||||
\(413\) | −1183.96 | − | 7386.40i | −0.141063 | − | 0.880051i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1966.14i | − | 0.232564i | ||||||
\(416\) | −10572.2 | − | 8543.63i | −1.24602 | − | 1.00694i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1553.31 | − | 8623.01i | −0.181758 | − | 1.00901i | ||||
\(419\) | −8654.42 | −1.00906 | −0.504530 | − | 0.863394i | \(-0.668334\pi\) | ||||
−0.504530 | + | 0.863394i | \(0.668334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13325.5 | −1.54263 | −0.771313 | − | 0.636456i | \(-0.780400\pi\) | ||||
−0.771313 | + | 0.636456i | \(0.780400\pi\) | |||||||
\(422\) | −2539.65 | − | 14098.5i | −0.292958 | − | 1.62632i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2777.63 | + | 1644.94i | −0.318145 | + | 0.188409i | ||||
\(425\) | 12069.4i | 1.37753i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −398.224 | + | 63.8311i | −0.0451321 | + | 0.00723420i | ||||
\(428\) | 4194.88 | + | 11265.8i | 0.473755 | + | 1.27232i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3675.94 | + | 662.169i | −0.412255 | + | 0.0742619i | ||||
\(431\) | 4512.65i | 0.504332i | 0.967684 | + | 0.252166i | \(0.0811428\pi\) | ||||
−0.967684 | + | 0.252166i | \(0.918857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4597.71i | 0.510282i | 0.966904 | + | 0.255141i | \(0.0821219\pi\) | ||||
−0.966904 | + | 0.255141i | \(0.917878\pi\) | |||||||
\(434\) | 4013.15 | + | 11448.2i | 0.443864 | + | 1.26621i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4343.10 | − | 1617.17i | 0.477057 | − | 0.177634i | ||||
\(437\) | − | 7313.74i | − | 0.800604i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14584.7 | −1.58562 | −0.792811 | − | 0.609467i | \(-0.791383\pi\) | ||||
−0.792811 | + | 0.609467i | \(0.791383\pi\) | |||||||
\(440\) | 2317.79 | − | 1372.62i | 0.251128 | − | 0.148721i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24241.7 | − | 4366.80i | 2.60873 | − | 0.469926i | ||||
\(443\) | 10578.3i | 1.13452i | 0.823539 | + | 0.567259i | \(0.191996\pi\) | ||||
−0.823539 | + | 0.567259i | \(0.808004\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4959.06 | 0.528274 | ||||||||
\(446\) | −10839.6 | + | 1952.60i | −1.15083 | + | 0.207306i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8931.58 | − | 3184.69i | −0.941914 | − | 0.335854i | ||||
\(449\) | 833.584 | 0.0876152 | 0.0438076 | − | 0.999040i | \(-0.486051\pi\) | ||||
0.0438076 | + | 0.999040i | \(0.486051\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3750.42 | −0.391575 | ||||||||
\(452\) | −4608.02 | + | 1715.81i | −0.479520 | + | 0.178551i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3245.56 | − | 584.642i | 0.335510 | − | 0.0604375i | ||||
\(455\) | −1007.01 | − | 6282.42i | −0.103756 | − | 0.647307i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6462.47 | −0.661492 | −0.330746 | − | 0.943720i | \(-0.607300\pi\) | ||||
−0.330746 | + | 0.943720i | \(0.607300\pi\) | |||||||
\(458\) | 1272.59 | + | 7064.63i | 0.129835 | + | 0.720761i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2107.21 | − | 784.628i | 0.213585 | − | 0.0795293i | ||||
\(461\) | − | 10142.3i | − | 1.02467i | −0.858786 | − | 0.512334i | \(-0.828781\pi\) | ||
0.858786 | − | 0.512334i | \(-0.171219\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1428.43i | 0.143380i | 0.997427 | + | 0.0716898i | \(0.0228391\pi\) | ||||
−0.997427 | + | 0.0716898i | \(0.977161\pi\) | |||||||
\(464\) | 3481.68 | − | 3010.19i | 0.348346 | − | 0.301173i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3745.46 | + | 674.691i | −0.372328 | + | 0.0670697i | ||||
\(467\) | 2039.86 | 0.202128 | 0.101064 | − | 0.994880i | \(-0.467775\pi\) | ||||
0.101064 | + | 0.994880i | \(0.467775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10947.8 | − | 1754.82i | 1.07788 | − | 0.172772i | ||||
\(470\) | −788.141 | − | 4375.26i | −0.0773494 | − | 0.429395i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7864.07 | − | 4657.20i | 0.766892 | − | 0.454163i | ||||
\(473\) | 7510.53 | 0.730094 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12389.4 | 1.19676 | ||||||||
\(476\) | 14951.2 | − | 8469.11i | 1.43967 | − | 0.815506i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3128.83 | − | 17369.3i | −0.299392 | − | 1.66203i | ||||
\(479\) | 13044.0 | 1.24425 | 0.622126 | − | 0.782917i | \(-0.286269\pi\) | ||||
0.622126 | + | 0.782917i | \(0.286269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1001.00i | − | 0.0948895i | ||||||
\(482\) | 2279.51 | + | 12654.4i | 0.215412 | + | 1.19583i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4902.60 | − | 1825.51i | 0.460425 | − | 0.171441i | ||||
\(485\) | −4717.00 | −0.441625 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6444.14i | − | 0.599614i | −0.954000 | − | 0.299807i | \(-0.903078\pi\) | ||
0.954000 | − | 0.299807i | \(-0.0969223\pi\) | |||||||
\(488\) | −251.084 | − | 423.977i | −0.0232911 | − | 0.0393289i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2112.75 | − | 3903.48i | −0.194785 | − | 0.359880i | ||||
\(491\) | − | 8032.35i | − | 0.738279i | −0.929374 | − | 0.369140i | \(-0.879652\pi\) | ||
0.929374 | − | 0.369140i | \(-0.120348\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8340.35i | 0.761928i | ||||||||
\(494\) | −4482.57 | − | 24884.4i | −0.408260 | − | 2.26640i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11212.1 | + | 9693.73i | −1.01499 | + | 0.877543i | ||||
\(497\) | 10780.5 | − | 1728.00i | 0.972983 | − | 0.155959i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1184.12i | − | 0.106230i | −0.998588 | − | 0.0531148i | \(-0.983085\pi\) | ||
0.998588 | − | 0.0531148i | \(-0.0169149\pi\) | |||||||
\(500\) | 2925.64 | + | 7857.13i | 0.261677 | + | 0.702763i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18861.6 | − | 3397.65i | 1.67696 | − | 0.302081i | ||||
\(503\) | −19759.9 | −1.75159 | −0.875794 | − | 0.482684i | \(-0.839662\pi\) | ||||
−0.875794 | + | 0.482684i | \(0.839662\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −951.576 | −0.0838506 | ||||||||
\(506\) | −4449.75 | + | 801.560i | −0.390940 | + | 0.0704223i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −764.544 | − | 2053.27i | −0.0667740 | − | 0.179329i | ||||
\(509\) | − | 14150.4i | − | 1.23223i | −0.787654 | − | 0.616117i | \(-0.788705\pi\) | ||
0.787654 | − | 0.616117i | \(-0.211295\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 125.322 | − | 20.0878i | 0.0108492 | − | 0.00173901i | ||||
\(512\) | −384.840 | − | 11578.8i | −0.0332182 | − | 0.999448i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3595.34 | − | 19959.0i | −0.308528 | − | 1.71275i | ||||
\(515\) | 5626.55i | 0.481428i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8939.34i | 0.760448i | ||||||||
\(518\) | −231.005 | − | 658.986i | −0.0195942 | − | 0.0558961i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6688.70 | − | 3961.13i | 0.564075 | − | 0.334052i | ||||
\(521\) | 18031.5i | 1.51626i | 0.652101 | + | 0.758132i | \(0.273888\pi\) | ||||
−0.652101 | + | 0.758132i | \(0.726112\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5733.64 | −0.479378 | −0.239689 | − | 0.970850i | \(-0.577045\pi\) | ||||
−0.239689 | + | 0.970850i | \(0.577045\pi\) | |||||||
\(524\) | −16402.6 | + | 6107.56i | −1.36746 | + | 0.509180i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1049.65 | − | 5827.00i | −0.0870094 | − | 0.483021i | ||||
\(527\) | − | 26858.5i | − | 2.22006i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8392.87 | 0.689806 | ||||||||
\(530\) | −327.292 | − | 1816.92i | −0.0268239 | − | 0.148909i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8693.64 | − | 15347.5i | −0.708491 | − | 1.25075i | ||||
\(533\) | −10823.0 | −0.879542 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6874.99 | −0.555573 | ||||||||
\(536\) | 6902.73 | + | 11655.8i | 0.556254 | + | 0.939282i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −789.213 | − | 4381.21i | −0.0632442 | − | 0.351092i | ||||
\(539\) | 2789.51 | + | 8477.92i | 0.222918 | + | 0.677495i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3887.89 | −0.308971 | −0.154486 | − | 0.987995i | \(-0.549372\pi\) | ||||
−0.154486 | + | 0.987995i | \(0.549372\pi\) | |||||||
\(542\) | 5495.37 | − | 989.913i | 0.435510 | − | 0.0784509i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16328.6 | + | 13195.5i | 1.28691 | + | 1.03998i | ||||
\(545\) | 2650.38i | 0.208312i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4722.04i | − | 0.369104i | −0.982823 | − | 0.184552i | \(-0.940917\pi\) | ||
0.982823 | − | 0.184552i | \(-0.0590834\pi\) | |||||||
\(548\) | 19008.1 | − | 7077.76i | 1.48173 | − | 0.551728i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1357.83 | − | 7537.81i | −0.105269 | − | 0.584388i | ||||
\(551\) | 8561.47 | 0.661943 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17779.0 | − | 2849.79i | 1.36716 | − | 0.219142i | ||||
\(554\) | 13245.8 | − | 2386.04i | 1.01581 | − | 0.182984i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7552.02 | + | 2812.03i | −0.576038 | + | 0.214490i | ||||
\(557\) | 13987.0 | 1.06400 | 0.532000 | − | 0.846745i | \(-0.321441\pi\) | ||||
0.532000 | + | 0.846745i | \(0.321441\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21674.0 | 1.63991 | ||||||||
\(560\) | 3489.21 | − | 4151.29i | 0.263297 | − | 0.313257i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4880.98 | + | 879.240i | −0.366356 | + | 0.0659938i | ||||
\(563\) | 6757.50 | 0.505852 | 0.252926 | − | 0.967486i | \(-0.418607\pi\) | ||||
0.252926 | + | 0.967486i | \(0.418607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2812.05i | − | 0.209387i | ||||||
\(566\) | 10029.9 | − | 1806.75i | 0.744858 | − | 0.134176i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6797.23 | + | 11477.7i | 0.502122 | + | 0.847875i | ||||
\(569\) | 7220.86 | 0.532011 | 0.266005 | − | 0.963972i | \(-0.414296\pi\) | ||||
0.266005 | + | 0.963972i | \(0.414296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 365.261i | 0.0267700i | 0.999910 | + | 0.0133850i | \(0.00426071\pi\) | ||||
−0.999910 | + | 0.0133850i | \(0.995739\pi\) | |||||||
\(572\) | −14648.6 | + | 5454.48i | −1.07079 | + | 0.398712i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7125.04 | + | 2497.66i | −0.518107 | + | 0.181621i | ||||
\(575\) | − | 6393.31i | − | 0.463686i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2258.22i | 0.162931i | 0.996676 | + | 0.0814653i | \(0.0259600\pi\) | ||||
−0.996676 | + | 0.0814653i | \(0.974040\pi\) | |||||||
\(578\) | −23764.9 | + | 4280.90i | −1.71019 | + | 0.308066i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 918.486 | + | 2466.70i | 0.0657553 | + | 0.176593i | ||||
\(581\) | 1259.66 | + | 7858.68i | 0.0899477 | + | 0.561158i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3712.25i | 0.263715i | ||||||||
\(584\) | 79.0169 | + | 133.427i | 0.00559887 | + | 0.00945417i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4439.69 | + | 24646.3i | 0.312972 | + | 1.73742i | ||||
\(587\) | 1086.09 | 0.0763677 | 0.0381839 | − | 0.999271i | \(-0.487843\pi\) | ||||
0.0381839 | + | 0.999271i | \(0.487843\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27570.6 | −1.92873 | ||||||||
\(590\) | 926.636 | + | 5144.10i | 0.0646593 | + | 0.358948i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 645.391 | − | 557.992i | 0.0448064 | − | 0.0387387i | ||||
\(593\) | − | 7013.68i | − | 0.485695i | −0.970064 | − | 0.242848i | \(-0.921919\pi\) | ||
0.970064 | − | 0.242848i | \(-0.0780815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1555.30 | + | 9703.08i | 0.107162 | + | 0.668551i | ||||
\(596\) | −17562.7 | + | 6539.56i | −1.20704 | + | 0.449447i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12841.1 | + | 2313.15i | −0.878116 | + | 0.158180i | ||||
\(599\) | − | 25452.7i | − | 1.73618i | −0.496409 | − | 0.868089i | \(-0.665348\pi\) | ||
0.496409 | − | 0.868089i | \(-0.334652\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 26422.8i | − | 1.79336i | −0.442682 | − | 0.896679i | \(-0.645973\pi\) | ||
0.442682 | − | 0.896679i | \(-0.354027\pi\) | |||||||
\(602\) | 14268.5 | − | 5001.78i | 0.966015 | − | 0.338634i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1566.14 | + | 4206.06i | 0.105506 | + | 0.283348i | ||||
\(605\) | 2991.82i | 0.201049i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6179.28 | −0.413195 | −0.206597 | − | 0.978426i | \(-0.566239\pi\) | ||||
−0.206597 | + | 0.978426i | \(0.566239\pi\) | |||||||
\(608\) | 13545.3 | − | 16761.5i | 0.903511 | − | 1.11804i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 277.334 | − | 49.9579i | 0.0184081 | − | 0.00331596i | ||||
\(611\) | 25797.3i | 1.70809i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6512.10 | −0.429072 | −0.214536 | − | 0.976716i | \(-0.568824\pi\) | ||||
−0.214536 | + | 0.976716i | \(0.568824\pi\) | |||||||
\(614\) | −12170.9 | + | 2192.41i | −0.799960 | + | 0.144102i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8384.80 | + | 6971.33i | −0.548430 | + | 0.455979i | ||||
\(617\) | −15211.8 | −0.992551 | −0.496275 | − | 0.868165i | \(-0.665299\pi\) | ||||
−0.496275 | + | 0.868165i | \(0.665299\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11712.0 | −0.760496 | −0.380248 | − | 0.924885i | \(-0.624161\pi\) | ||||
−0.380248 | + | 0.924885i | \(0.624161\pi\) | |||||||
\(620\) | −2957.81 | − | 7943.53i | −0.191594 | − | 0.514548i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5445.35 | + | 980.902i | −0.351027 | + | 0.0632325i | ||||
\(623\) | −19821.4 | + | 3177.15i | −1.27468 | + | 0.204318i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8213.69 | 0.525676 | ||||||||
\(626\) | −3166.07 | − | 17576.0i | −0.202143 | − | 1.12217i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1281.95 | − | 3442.83i | −0.0814578 | − | 0.218764i | ||||
\(629\) | 1546.03i | 0.0980037i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16130.7i | − | 1.01768i | −0.860862 | − | 0.508839i | \(-0.830075\pi\) | ||
0.860862 | − | 0.508839i | \(-0.169925\pi\) | |||||||
\(632\) | 11209.9 | + | 18928.8i | 0.705544 | + | 1.19137i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13814.5 | + | 2488.49i | −0.865370 | + | 0.155884i | ||||
\(635\) | 1253.01 | 0.0783059 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8050.01 | + | 24465.7i | 0.500711 | + | 1.52177i | ||||
\(638\) | −938.306 | − | 5208.88i | −0.0582255 | − | 0.323231i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6282.41 | + | 2104.43i | 0.388022 | + | 0.129977i | ||||
\(641\) | −20295.1 | −1.25056 | −0.625280 | − | 0.780401i | \(-0.715015\pi\) | ||||
−0.625280 | + | 0.780401i | \(0.715015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10255.3 | −0.628976 | −0.314488 | − | 0.949262i | \(-0.601833\pi\) | ||||
−0.314488 | + | 0.949262i | \(0.601833\pi\) | |||||||
\(644\) | −7919.83 | + | 4486.20i | −0.484604 | + | 0.274505i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6923.24 | + | 38433.5i | 0.421658 | + | 2.34078i | ||||
\(647\) | 15162.9 | 0.921352 | 0.460676 | − | 0.887568i | \(-0.347607\pi\) | ||||
0.460676 | + | 0.887568i | \(0.347607\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10510.2i | − | 0.635688i | ||||||
\(650\) | −3918.44 | − | 21752.7i | −0.236452 | − | 1.31263i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1558.23 | + | 4184.80i | 0.0935965 | + | 0.251364i | ||||
\(653\) | 7126.05 | 0.427050 | 0.213525 | − | 0.976938i | \(-0.431505\pi\) | ||||
0.213525 | + | 0.976938i | \(0.431505\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 10009.7i | − | 0.597116i | ||||||
\(656\) | −6033.09 | − | 6978.05i | −0.359074 | − | 0.415316i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5953.33 | + | 16983.0i | 0.352712 | + | 1.00618i | ||||
\(659\) | − | 2646.23i | − | 0.156422i | −0.996937 | − | 0.0782112i | \(-0.975079\pi\) | ||
0.996937 | − | 0.0782112i | \(-0.0249208\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 13839.8i | − | 0.814381i | −0.913343 | − | 0.407191i | \(-0.866508\pi\) | ||
0.913343 | − | 0.407191i | \(-0.133492\pi\) | |||||||
\(662\) | 3480.91 | + | 19323.8i | 0.204365 | + | 1.13450i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8366.89 | + | 4954.98i | −0.489004 | + | 0.289594i | ||||
\(665\) | 9960.33 | − | 1596.54i | 0.580820 | − | 0.0930992i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4417.99i | − | 0.256470i | ||||||
\(668\) | 18700.2 | − | 6963.11i | 1.08313 | − | 0.403310i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7624.39 | + | 1373.43i | −0.439636 | + | 0.0791941i | ||||
\(671\) | −566.638 | −0.0326003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32235.3 | −1.84633 | −0.923165 | − | 0.384404i | \(-0.874407\pi\) | ||||
−0.923165 | + | 0.384404i | \(0.874407\pi\) | |||||||
\(674\) | −5038.11 | + | 907.544i | −0.287924 | + | 0.0518654i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25802.0 | + | 9607.47i | −1.46802 | + | 0.546624i | ||||
\(677\) | 9.30221i | 0.000528084i | 1.00000 | 0.000264042i | \(8.40472e-5\pi\) | |||||
−1.00000 | 0.000264042i | \(0.999916\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18853.9 | − | 3022.07i | 1.06560 | − | 0.170805i | ||||
\(680\) | −10330.6 | + | 6117.89i | −0.582587 | + | 0.345015i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3021.63 | + | 16774.2i | 0.169654 | + | 0.941813i | ||||
\(683\) | 26622.3i | 1.49147i | 0.666244 | + | 0.745734i | \(0.267901\pi\) | ||||
−0.666244 | + | 0.745734i | \(0.732099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11599.7i | 0.647012i | ||||||||
\(686\) | 10945.6 | + | 14248.6i | 0.609188 | + | 0.793026i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12081.8 | + | 13974.2i | 0.669496 | + | 0.774360i | ||||
\(689\) | 10712.9i | 0.592348i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20064.5 | 1.10462 | 0.552309 | − | 0.833639i | \(-0.313747\pi\) | ||||
0.552309 | + | 0.833639i | \(0.313747\pi\) | |||||||
\(692\) | 8044.29 | + | 21603.9i | 0.441905 | + | 1.18679i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1776.50 | + | 9861.98i | 0.0971684 | + | 0.539418i | ||||
\(695\) | − | 4608.63i | − | 0.251533i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16715.9 | 0.908408 | ||||||||
\(698\) | 660.906 | + | 3668.93i | 0.0358390 | + | 0.198956i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7599.55 | − | 13416.1i | −0.410337 | − | 0.724399i | ||||
\(701\) | −32384.8 | −1.74487 | −0.872436 | − | 0.488728i | \(-0.837461\pi\) | ||||
−0.872436 | + | 0.488728i | \(0.837461\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1587.02 | 0.0851431 | ||||||||
\(704\) | −11682.3 | − | 6404.10i | −0.625419 | − | 0.342846i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −628.898 | − | 3491.24i | −0.0335253 | − | 0.186111i | ||||
\(707\) | 3803.45 | − | 609.652i | 0.202325 | − | 0.0324305i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34258.5 | 1.81468 | 0.907338 | − | 0.420403i | \(-0.138111\pi\) | ||||
0.907338 | + | 0.420403i | \(0.138111\pi\) | |||||||
\(710\) | −7507.86 | + | 1352.43i | −0.396852 | + | 0.0714873i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12497.6 | − | 21103.2i | −0.657818 | − | 1.11078i | ||||
\(713\) | 14227.3i | 0.747288i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 8939.34i | − | 0.467570i | ||||||
\(716\) | 5785.94 | + | 15538.8i | 0.301998 | + | 0.811051i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1178.71 | + | 6543.46i | 0.0612662 | + | 0.340111i | ||||
\(719\) | 10303.7 | 0.534443 | 0.267221 | − | 0.963635i | \(-0.413895\pi\) | ||||
0.267221 | + | 0.963635i | \(0.413895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3604.80 | − | 22489.3i | −0.186199 | − | 1.16165i | ||||
\(722\) | 20359.5 | − | 3667.48i | 1.04945 | − | 0.189044i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7716.28 | − | 20722.9i | −0.396095 | − | 1.06376i | ||||
\(725\) | 7484.01 | 0.383378 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1468.60 | 0.0749209 | 0.0374605 | − | 0.999298i | \(-0.488073\pi\) | ||||
0.0374605 | + | 0.999298i | \(0.488073\pi\) | |||||||
\(728\) | −24197.0 | + | 20117.9i | −1.23187 | + | 1.02420i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −87.2779 | + | 15.7219i | −0.00442507 | + | 0.000797113i | ||||
\(731\) | −33475.1 | −1.69373 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 5917.44i | − | 0.298179i | −0.988824 | − | 0.149090i | \(-0.952366\pi\) | ||
0.988824 | − | 0.149090i | \(-0.0476343\pi\) | |||||||
\(734\) | −8187.14 | + | 1474.80i | −0.411707 | + | 0.0741631i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8649.46 | − | 6989.82i | −0.433184 | − | 0.350065i | ||||
\(737\) | 15577.8 | 0.778584 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 8120.94i | − | 0.404240i | −0.979361 | − | 0.202120i | \(-0.935217\pi\) | ||
0.979361 | − | 0.202120i | \(-0.0647831\pi\) | |||||||
\(740\) | 170.258 | + | 457.247i | 0.00845783 | + | 0.0227145i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2472.25 | + | 7052.54i | 0.122317 | + | 0.348931i | ||||
\(743\) | − | 7975.20i | − | 0.393784i | −0.980425 | − | 0.196892i | \(-0.936915\pi\) | ||
0.980425 | − | 0.196892i | \(-0.0630849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 10717.7i | − | 0.527068i | ||||||
\(746\) | −20507.7 | + | 3694.17i | −1.00649 | + | 0.181304i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 22624.5 | − | 8424.33i | 1.10593 | − | 0.411797i | ||||
\(749\) | 27479.3 | − | 4404.65i | 1.34055 | − | 0.214876i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 7417.00i | − | 0.360387i | −0.983631 | − | 0.180193i | \(-0.942328\pi\) | ||
0.983631 | − | 0.180193i | \(-0.0576723\pi\) | |||||||
\(752\) | −16632.6 | + | 14380.2i | −0.806554 | + | 0.697331i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2707.77 | − | 15031.8i | −0.130784 | − | 0.726031i | ||||
\(755\) | −2566.75 | −0.123727 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2056.45 | 0.0987358 | 0.0493679 | − | 0.998781i | \(-0.484279\pi\) | ||||
0.0493679 | + | 0.998781i | \(0.484279\pi\) | |||||||
\(758\) | 4022.76 | + | 22331.8i | 0.192762 | + | 1.07009i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6280.09 | + | 10604.5i | 0.299741 | + | 0.506137i | ||||
\(761\) | 28244.9i | 1.34544i | 0.739898 | + | 0.672719i | \(0.234874\pi\) | ||||
−0.739898 | + | 0.672719i | \(0.765126\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1698.04 | − | 10593.6i | −0.0805676 | − | 0.502639i | ||||
\(764\) | −11498.4 | − | 30880.3i | −0.544499 | − | 1.46232i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37494.1 | − | 6754.02i | 1.76856 | − | 0.318581i | ||||
\(767\) | − | 30330.5i | − | 1.42786i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27026.1i | 1.26734i | 0.773603 | + | 0.633671i | \(0.218453\pi\) | ||||
−0.773603 | + | 0.633671i | \(0.781547\pi\) | |||||||
\(770\) | −2062.96 | − | 5884.99i | −0.0965507 | − | 0.275429i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 34020.6 | − | 12667.7i | 1.58605 | − | 0.590572i | ||||
\(773\) | − | 21487.5i | − | 0.999810i | −0.866080 | − | 0.499905i | \(-0.833368\pi\) | ||
0.866080 | − | 0.499905i | \(-0.166632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24100.8 | −1.11707 | ||||||||
\(776\) | 11887.6 | + | 20073.1i | 0.549921 | + | 0.928587i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1787.70 | − | 322.029i | 0.0823808 | − | 0.0148397i | ||||
\(779\) | − | 17159.1i | − | 0.789202i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15339.7 | 0.702816 | ||||||||
\(782\) | 19832.9 | − | 3572.62i | 0.906935 | − | 0.163372i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −11286.8 | + | 18828.2i | −0.514156 | + | 0.857697i | ||||
\(785\) | 2100.99 | 0.0955257 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13905.7 | 0.629843 | 0.314921 | − | 0.949118i | \(-0.398022\pi\) | ||||
0.314921 | + | 0.949118i | \(0.398022\pi\) | |||||||
\(788\) | −6343.91 | + | 2362.18i | −0.286792 | + | 0.106788i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12381.8 | + | 2230.41i | −0.557627 | + | 0.100449i | ||||
\(791\) | 1801.61 | + | 11239.8i | 0.0809836 | + | 0.505234i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1635.21 | −0.0732258 | ||||||||
\(794\) | 3059.29 | + | 16983.2i | 0.136738 | + | 0.759083i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9138.04 | − | 3402.59i | 0.406896 | − | 0.151509i | ||||
\(797\) | − | 21571.7i | − | 0.958730i | −0.877616 | − | 0.479365i | \(-0.840867\pi\) | ||
0.877616 | − | 0.479365i | \(-0.159133\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 39843.4i | − | 1.76415i | ||||||
\(800\) | 11840.6 | − | 14652.0i | 0.523287 | − | 0.647535i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17539.6 | + | 3159.51i | −0.772249 | + | 0.139110i | ||||
\(803\) | 178.323 | 0.00783669 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −823.864 | − | 5139.85i | −0.0360713 | − | 0.225039i | ||||
\(806\) | 8719.86 | + | 48407.2i | 0.381072 | + | 2.11547i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2398.11 | + | 4049.42i | 0.104413 | + | 0.176309i | ||||
\(809\) | −33518.7 | −1.45668 | −0.728339 | − | 0.685217i | \(-0.759708\pi\) | ||||
−0.728339 | + | 0.685217i | \(0.759708\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35133.3 | −1.52120 | −0.760602 | − | 0.649218i | \(-0.775096\pi\) | ||||
−0.760602 | + | 0.649218i | \(0.775096\pi\) | |||||||
\(812\) | −5251.55 | − | 9270.95i | −0.226962 | − | 0.400673i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −173.932 | − | 965.558i | −0.00748931 | − | 0.0415759i | ||||
\(815\) | −2553.78 | −0.109761 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34362.5i | 1.47147i | ||||||||
\(818\) | −450.214 | − | 2499.30i | −0.0192437 | − | 0.106829i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4943.81 | − | 1840.85i | 0.210543 | − | 0.0783967i | ||||
\(821\) | 21025.2 | 0.893768 | 0.446884 | − | 0.894592i | \(-0.352534\pi\) | ||||
0.446884 | + | 0.894592i | \(0.352534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20491.2i | 0.867894i | 0.900938 | + | 0.433947i | \(0.142880\pi\) | ||||
−0.900938 | + | 0.433947i | \(0.857120\pi\) | |||||||
\(824\) | 23943.7 | − | 14179.7i | 1.01228 | − | 0.599484i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6999.47 | − | 19967.3i | −0.294846 | − | 0.841103i | ||||
\(827\) | 18080.6i | 0.760245i | 0.924936 | + | 0.380122i | \(0.124118\pi\) | ||||
−0.924936 | + | 0.380122i | \(0.875882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38666.1i | 1.61994i | 0.586471 | + | 0.809970i | \(0.300517\pi\) | ||||
−0.586471 | + | 0.809970i | \(0.699483\pi\) | |||||||
\(830\) | −985.885 | − | 5473.01i | −0.0412296 | − | 0.228881i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −33713.1 | − | 18481.0i | −1.40480 | − | 0.770089i | ||||
\(833\) | −12433.1 | − | 37786.8i | −0.517144 | − | 1.57171i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11411.8i | 0.472962i | ||||||||
\(836\) | −8647.68 | − | 23224.3i | −0.357759 | − | 0.960802i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24090.6 | + | 4339.59i | −0.993076 | + | 0.178889i | ||||
\(839\) | 36214.5 | 1.49018 | 0.745091 | − | 0.666962i | \(-0.232406\pi\) | ||||
0.745091 | + | 0.666962i | \(0.232406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19217.3 | −0.787949 | ||||||||
\(842\) | −37093.2 | + | 6681.82i | −1.51819 | + | 0.273481i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14138.9 | − | 37971.6i | −0.576635 | − | 1.54862i | ||||
\(845\) | − | 15745.7i | − | 0.641027i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1916.79 | − | 11958.3i | −0.0777588 | − | 0.485115i | ||||
\(848\) | −6907.05 | + | 5971.70i | −0.279704 | + | 0.241827i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6051.96 | + | 33596.6i | 0.244212 | + | 1.35571i | ||||
\(851\) | − | 818.954i | − | 0.0329887i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1180.57i | − | 0.0473881i | −0.999719 | − | 0.0236941i | \(-0.992457\pi\) | ||
0.999719 | − | 0.0236941i | \(-0.00754276\pi\) | |||||||
\(854\) | −1076.50 | + | 377.363i | −0.0431347 | + | 0.0151207i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17326.0 | + | 29256.4i | 0.691811 | + | 1.16818i | ||||
\(857\) | − | 29570.1i | − | 1.17864i | −0.807900 | − | 0.589320i | \(-0.799396\pi\) | ||
0.807900 | − | 0.589320i | \(-0.200604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18516.7 | 0.735483 | 0.367742 | − | 0.929928i | \(-0.380131\pi\) | ||||
0.367742 | + | 0.929928i | \(0.380131\pi\) | |||||||
\(860\) | −9900.41 | + | 3686.46i | −0.392560 | + | 0.146171i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2262.78 | + | 12561.5i | 0.0894092 | + | 0.496343i | ||||
\(863\) | 35215.9i | 1.38907i | 0.719461 | + | 0.694533i | \(0.244389\pi\) | ||||
−0.719461 | + | 0.694533i | \(0.755611\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13183.8 | −0.518223 | ||||||||
\(866\) | 2305.43 | + | 12798.3i | 0.0904640 | + | 0.502199i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16911.6 | + | 29855.3i | 0.661310 | + | 1.16746i | ||||
\(869\) | 25298.0 | 0.987544 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44954.7 | 1.74883 | ||||||||
\(872\) | 11278.7 | − | 6679.36i | 0.438009 | − | 0.259394i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3667.33 | − | 20358.7i | −0.141933 | − | 0.787922i | ||||
\(875\) | 19164.9 | − | 3071.93i | 0.740449 | − | 0.118686i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20910.2 | −0.805115 | −0.402558 | − | 0.915395i | \(-0.631879\pi\) | ||||
−0.402558 | + | 0.915395i | \(0.631879\pi\) | |||||||
\(878\) | −40598.3 | + | 7313.20i | −1.56051 | + | 0.281103i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5763.58 | − | 4983.08i | 0.220784 | − | 0.190886i | ||||
\(881\) | 19841.3i | 0.758762i | 0.925241 | + | 0.379381i | \(0.123863\pi\) | ||||
−0.925241 | + | 0.379381i | \(0.876137\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37682.4i | 1.43614i | 0.695971 | + | 0.718070i | \(0.254974\pi\) | ||||
−0.695971 | + | 0.718070i | \(0.745026\pi\) | |||||||
\(884\) | 65290.1 | − | 24311.0i | 2.48410 | − | 0.924965i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5304.30 | + | 29446.1i | 0.201130 | + | 1.11655i | ||||
\(887\) | −16665.2 | −0.630850 | −0.315425 | − | 0.948950i | \(-0.602147\pi\) | ||||
−0.315425 | + | 0.948950i | \(0.602147\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5008.29 | + | 802.776i | −0.188946 | + | 0.0302860i | ||||
\(890\) | 13804.2 | − | 2486.62i | 0.519906 | − | 0.0936537i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −29194.3 | + | 10870.6i | −1.09585 | + | 0.408044i | ||||
\(893\) | −40899.7 | −1.53265 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9482.58 | −0.354154 | ||||||||
\(896\) | −26459.1 | − | 4386.43i | −0.986535 | − | 0.163549i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2320.38 | − | 417.984i | 0.0862274 | − | 0.0155326i | ||||
\(899\) | −16654.5 | −0.617862 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 16545.8i | − | 0.611788i | ||||||
\(902\) | −10439.7 | + | 1880.57i | −0.385372 | + | 0.0694193i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11966.6 | + | 7086.78i | −0.440270 | + | 0.260733i | ||||
\(905\) | 12646.2 | 0.464502 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 20577.7i | − | 0.753331i | −0.926349 | − | 0.376665i | \(-0.877071\pi\) | ||
0.926349 | − | 0.376665i | \(-0.122929\pi\) | |||||||
\(908\) | 8741.27 | − | 3254.85i | 0.319481 | − | 0.118960i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5953.33 | − | 16983.0i | −0.216869 | − | 0.618659i | ||||
\(911\) | − | 35684.4i | − | 1.29778i | −0.760883 | − | 0.648889i | \(-0.775234\pi\) | ||
0.760883 | − | 0.648889i | \(-0.224766\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11182.2i | 0.405342i | ||||||||
\(914\) | −17989.1 | + | 3240.48i | −0.651013 | + | 0.117271i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7084.84 | + | 19027.2i | 0.255556 | + | 0.686326i | ||||
\(917\) | 6412.97 | + | 40008.7i | 0.230943 | + | 1.44079i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2549.71i | 0.0915205i | 0.998952 | + | 0.0457602i | \(0.0145710\pi\) | ||||
−0.998952 | + | 0.0457602i | \(0.985429\pi\) | |||||||
\(920\) | 5472.24 | − | 3240.73i | 0.196103 | − | 0.116134i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5085.64 | − | 28232.2i | −0.181656 | − | 1.00844i | ||||
\(923\) | 44267.6 | 1.57864 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1387.30 | 0.0493124 | ||||||||
\(926\) | 716.258 | + | 3976.21i | 0.0254187 | + | 0.141108i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8182.28 | − | 10125.1i | 0.289436 | − | 0.358159i | ||||
\(929\) | − | 24991.8i | − | 0.882620i | −0.897355 | − | 0.441310i | \(-0.854514\pi\) | ||
0.897355 | − | 0.441310i | \(-0.145486\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38788.6 | + | 12762.7i | −1.36546 | + | 0.449281i | ||||
\(932\) | −10087.6 | + | 3756.18i | −0.354540 | + | 0.132015i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5678.21 | − | 1022.85i | 0.198926 | − | 0.0358337i | ||||
\(935\) | 13806.6i | 0.482915i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36329.3i | − | 1.26662i | −0.773896 | − | 0.633312i | \(-0.781695\pi\) | ||
0.773896 | − | 0.633312i | \(-0.218305\pi\) | |||||||
\(938\) | 29594.8 | − | 10374.4i | 1.03017 | − | 0.361124i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4387.78 | − | 11783.9i | −0.152248 | − | 0.408881i | ||||
\(941\) | 21505.5i | 0.745015i | 0.928029 | + | 0.372507i | \(0.121502\pi\) | ||||
−0.928029 | + | 0.372507i | \(0.878498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8854.64 | −0.305776 | ||||||||
\(944\) | 19555.4 | − | 16907.2i | 0.674230 | − | 0.582926i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20906.5 | − | 3766.01i | 0.718530 | − | 0.129433i | ||||
\(947\) | 17365.5i | 0.595886i | 0.954584 | + | 0.297943i | \(0.0963005\pi\) | ||||
−0.954584 | + | 0.297943i | \(0.903699\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 514.605 | 0.0176025 | ||||||||
\(950\) | 34487.4 | − | 6212.41i | 1.17781 | − | 0.212165i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 37371.7 | − | 31071.8i | 1.27229 | − | 1.05782i | ||||
\(953\) | −22686.6 | −0.771133 | −0.385566 | − | 0.922680i | \(-0.625994\pi\) | ||||
−0.385566 | + | 0.922680i | \(0.625994\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18844.7 | 0.638535 | ||||||||
\(956\) | −17419.0 | − | 46780.7i | −0.589299 | − | 1.58263i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36309.7 | − | 6540.68i | 1.22454 | − | 0.220584i | ||||
\(959\) | −7431.69 | − | 46364.2i | −0.250242 | − | 1.56119i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23841.5 | 0.800293 | ||||||||
\(962\) | −501.934 | − | 2786.42i | −0.0168222 | − | 0.0933865i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12690.6 | + | 34082.1i | 0.424001 | + | 1.13870i | ||||
\(965\) | 20761.1i | 0.692565i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30178.5i | 1.00359i | 0.864985 | + | 0.501797i | \(0.167328\pi\) | ||||
−0.864985 | + | 0.501797i | \(0.832672\pi\) | |||||||
\(968\) | 12731.6 | − | 7539.84i | 0.422738 | − | 0.250351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13130.4 | + | 2365.25i | −0.434630 | + | 0.0782924i | ||||
\(971\) | −54731.9 | −1.80889 | −0.904445 | − | 0.426591i | \(-0.859714\pi\) | ||||
−0.904445 | + | 0.426591i | \(0.859714\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2952.64 | + | 18420.7i | 0.0972841 | + | 0.606928i | ||||
\(974\) | −3231.29 | − | 17938.1i | −0.106301 | − | 0.590116i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −911.519 | − | 1054.29i | −0.0298945 | − | 0.0345769i | ||||
\(977\) | 29860.7 | 0.977817 | 0.488908 | − | 0.872335i | \(-0.337395\pi\) | ||||
0.488908 | + | 0.872335i | \(0.337395\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28204.1 | −0.920741 | ||||||||
\(980\) | −7838.44 | − | 9806.43i | −0.255500 | − | 0.319648i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4027.67 | − | 22359.1i | −0.130884 | − | 0.726585i | ||||
\(983\) | −10417.7 | −0.338018 | −0.169009 | − | 0.985615i | \(-0.554057\pi\) | ||||
−0.169009 | + | 0.985615i | \(0.554057\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 3871.38i | − | 0.125231i | ||||||
\(986\) | 4182.11 | + | 23216.4i | 0.135076 | + | 0.749859i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24955.6 | − | 67021.1i | −0.803586 | − | 2.15812i | ||||
\(989\) | 17732.2 | 0.570122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3803.09i | − | 0.121906i | −0.998141 | − | 0.0609531i | \(-0.980586\pi\) | ||
0.998141 | − | 0.0609531i | \(-0.0194140\pi\) | |||||||
\(992\) | −26349.4 | + | 32605.8i | −0.843343 | + | 1.04358i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 29142.5 | − | 10215.8i | 0.929922 | − | 0.325981i | ||||
\(995\) | 5576.50i | 0.177675i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 53386.9i | − | 1.69587i | −0.530103 | − | 0.847933i | \(-0.677847\pi\) | ||
0.530103 | − | 0.847933i | \(-0.322153\pi\) | |||||||
\(998\) | −593.755 | − | 3296.15i | −0.0188327 | − | 0.104547i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.4.b.e.55.11 | 12 | ||
3.2 | odd | 2 | 84.4.b.b.55.2 | yes | 12 | ||
4.3 | odd | 2 | 252.4.b.f.55.12 | 12 | |||
7.6 | odd | 2 | 252.4.b.f.55.11 | 12 | |||
12.11 | even | 2 | 84.4.b.a.55.1 | ✓ | 12 | ||
21.20 | even | 2 | 84.4.b.a.55.2 | yes | 12 | ||
24.5 | odd | 2 | 1344.4.b.g.895.8 | 12 | |||
24.11 | even | 2 | 1344.4.b.h.895.8 | 12 | |||
28.27 | even | 2 | inner | 252.4.b.e.55.12 | 12 | ||
84.83 | odd | 2 | 84.4.b.b.55.1 | yes | 12 | ||
168.83 | odd | 2 | 1344.4.b.g.895.5 | 12 | |||
168.125 | even | 2 | 1344.4.b.h.895.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.b.a.55.1 | ✓ | 12 | 12.11 | even | 2 | ||
84.4.b.a.55.2 | yes | 12 | 21.20 | even | 2 | ||
84.4.b.b.55.1 | yes | 12 | 84.83 | odd | 2 | ||
84.4.b.b.55.2 | yes | 12 | 3.2 | odd | 2 | ||
252.4.b.e.55.11 | 12 | 1.1 | even | 1 | trivial | ||
252.4.b.e.55.12 | 12 | 28.27 | even | 2 | inner | ||
252.4.b.f.55.11 | 12 | 7.6 | odd | 2 | |||
252.4.b.f.55.12 | 12 | 4.3 | odd | 2 | |||
1344.4.b.g.895.5 | 12 | 168.83 | odd | 2 | |||
1344.4.b.g.895.8 | 12 | 24.5 | odd | 2 | |||
1344.4.b.h.895.5 | 12 | 168.125 | even | 2 | |||
1344.4.b.h.895.8 | 12 | 24.11 | even | 2 |