Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.2985670477\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.8 | ||
Root | \(-2.78362 + 0.501431i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.g.895.5 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 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 | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 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 | \(0.295705\pi\) | ||||
−0.598647 | + | 0.801013i | \(0.704295\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 13.7254i | − | 0.236259i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 115.976i | − | 1.65460i | −0.561758 | − | 0.827302i | \(-0.689875\pi\) | ||
0.561758 | − | 0.827302i | \(-0.310125\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −119.051 | −1.43748 | −0.718739 | − | 0.695280i | \(-0.755280\pi\) | ||||
−0.718739 | + | 0.695280i | \(0.755280\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.79355 | + | 54.8605i | 0.0913767 | + | 0.570073i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 61.4339i | 0.556950i | 0.960443 | + | 0.278475i | \(0.0898290\pi\) | ||||
−0.960443 | + | 0.278475i | \(0.910171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 104.068 | 0.832545 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 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 | \(0.734081\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 78.0617i | 0.411782i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 83.6647 | − | 13.4106i | 0.404055 | − | 0.0647657i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −13.3306 | −0.0592309 | −0.0296155 | − | 0.999561i | \(-0.509428\pi\) | ||||
−0.0296155 | + | 0.999561i | \(0.509428\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 225.271i | − | 0.924931i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 144.133i | 0.549018i | 0.961584 | + | 0.274509i | \(0.0885154\pi\) | ||||
−0.961584 | + | 0.274509i | \(0.911485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 288.638i | − | 1.02365i | −0.859090 | − | 0.511825i | \(-0.828970\pi\) | ||
0.859090 | − | 0.511825i | \(-0.171030\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 41.1762i | 0.136404i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 343.549 | 1.06621 | 0.533104 | − | 0.846050i | \(-0.321025\pi\) | ||||
0.533104 | + | 0.846050i | \(0.321025\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −325.816 | + | 107.204i | −0.949902 | + | 0.312548i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 347.927i | 0.955286i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −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 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 357.152 | 0.829928 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 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 | \(0.00727532\pi\) | ||||
−0.999739 | + | 0.0228541i | \(0.992725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −26.3807 | − | 164.581i | −0.0527564 | − | 0.329132i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −343.549 | −0.655570 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 598.674i | − | 1.09164i | −0.837904 | − | 0.545818i | \(-0.816219\pi\) | ||
0.837904 | − | 0.545818i | \(-0.183781\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 184.302i | − | 0.321555i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 589.524i | − | 0.985403i | −0.870198 | − | 0.492701i | \(-0.836009\pi\) | ||
0.870198 | − | 0.492701i | \(-0.163991\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.85314i | 0.0109877i | 0.999985 | + | 0.00549383i | \(0.00174875\pi\) | ||||
−0.999985 | + | 0.00549383i | \(0.998251\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −312.204 | −0.480670 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −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 | \(0.756594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −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 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −215.744 | −0.265864 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1083.91i | 1.29095i | 0.763781 | + | 0.645476i | \(0.223341\pi\) | ||||
−0.763781 | + | 0.645476i | \(0.776659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1373.17 | − | 220.104i | 1.58183 | − | 0.253551i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 694.761 | 0.774660 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 544.673i | − | 0.588234i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1031.01i | 1.07921i | 0.841920 | + | 0.539603i | \(0.181426\pi\) | ||||
−0.841920 | + | 0.539603i | \(0.818574\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 234.185i | − | 0.237742i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 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 | \(0.299822\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −250.994 | + | 40.2317i | −0.233281 | + | 0.0373925i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 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 | \(-0.581920\pi\) | ||||
−0.254527 | + | 0.967066i | \(0.581920\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 39.9919 | 0.0341970 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 614.637 | 0.511683 | 0.255842 | − | 0.966719i | \(-0.417647\pi\) | ||||
0.255842 | + | 0.966719i | \(0.417647\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −281.069 | −0.227911 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 675.814i | 0.534009i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2120.83 | + | 339.946i | −1.63375 | + | 0.261873i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 653.930 | 0.491308 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 432.398i | − | 0.316976i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1048.02i | 0.749901i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 273.874i | − | 0.191358i | −0.995412 | − | 0.0956788i | \(-0.969498\pi\) | ||
0.995412 | − | 0.0956788i | \(-0.0305022\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 865.915i | 0.591004i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −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 | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 123.529i | − | 0.0787530i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2535.39 | −1.58112 | −0.790558 | − | 0.612388i | \(-0.790209\pi\) | ||||
−0.790558 | + | 0.612388i | \(0.790209\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1007.32 | 0.614675 | 0.307338 | − | 0.951601i | \(-0.400562\pi\) | ||||
0.307338 | + | 0.951601i | \(0.400562\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1030.65 | −0.615576 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1953.90 | 1.14261 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 329.019i | 0.188438i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 977.449 | − | 321.612i | 0.548426 | − | 0.180450i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −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 | \(0.951694\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1043.78i | − | 0.551534i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1059.54i | − | 0.549061i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 459.220i | 0.233438i | 0.993165 | + | 0.116719i | \(0.0372377\pi\) | ||||
−0.993165 | + | 0.116719i | \(0.962762\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 427.998 | 0.213475 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1123.43 | − | 180.074i | 0.549931 | − | 0.0881480i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 558.186i | − | 0.268224i | −0.990966 | − | 0.134112i | \(-0.957182\pi\) | ||
0.990966 | − | 0.134112i | \(-0.0428182\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −357.143 | −0.168506 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2494.32 | −1.15579 | −0.577893 | − | 0.816113i | \(-0.696125\pi\) | ||||
−0.577893 | + | 0.816113i | \(0.696125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3441.58 | −1.56649 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1071.45 | −0.479159 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 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 | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1211.76 | −0.514583 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(0.192111\pi\) | ||||
−0.823335 | + | 0.567556i | \(0.807889\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 65.3296i | − | 0.0263896i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 60.9895i | − | 0.0242380i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3017.76 | −1.18011 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 79.1420 | + | 493.744i | 0.0304589 | + | 0.190024i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4118.94i | 1.56040i | 0.625530 | + | 0.780200i | \(0.284883\pi\) | ||||
−0.625530 | + | 0.780200i | \(0.715117\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4537.82 | 1.69243 | 0.846216 | − | 0.532840i | \(-0.178875\pi\) | ||||
0.846216 | + | 0.532840i | \(0.178875\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1030.65 | 0.378493 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −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 | \(0.430342\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1796.02i | 0.630257i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −210.795 | − | 1315.09i | −0.0728813 | − | 0.454686i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −659.427 | −0.224665 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 552.905i | 0.185650i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3097.76i | 1.02525i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5064.81i | 1.65249i | 0.563308 | + | 0.826247i | \(0.309528\pi\) | ||||
−0.563308 | + | 0.826247i | \(0.690472\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1768.57i | 0.568923i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1320.56 | 0.418890 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 678.824 | + | 4234.99i | 0.212357 | + | 1.32484i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 20.5594i | − | 0.00634373i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8708.67 | 2.65072 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3894.06 | −1.16935 | −0.584676 | − | 0.811267i | \(-0.698778\pi\) | ||||
−0.584676 | + | 0.811267i | \(0.698778\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 936.613 | 0.277515 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 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 | \(-0.880665\pi\) | ||
0.930544 | − | 0.366181i | \(-0.119335\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1427.50 | − | 228.813i | 0.406592 | − | 0.0651723i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1345.53 | 0.378321 | 0.189160 | − | 0.981946i | \(-0.439423\pi\) | ||||
0.189160 | + | 0.981946i | \(0.439423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1571.78i | 0.436306i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 2916.69i | − | 0.799408i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6239.81i | 1.68878i | 0.535725 | + | 0.844392i | \(0.320038\pi\) | ||||
−0.535725 | + | 0.844392i | \(0.679962\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4546.01i | 1.21508i | 0.794289 | + | 0.607540i | \(0.207844\pi\) | ||||
−0.794289 | + | 0.607540i | \(0.792156\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −490.474 | − | 1490.65i | −0.127899 | − | 0.388712i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8939.56i | − | 2.30288i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1289.24 | 0.328121 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1591.82 | −0.390915 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7170.16i | 1.74032i | 0.492770 | + | 0.870160i | \(0.335984\pi\) | ||||
−0.492770 | + | 0.870160i | \(0.664016\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 39.0746 | + | 243.775i | 0.00937442 | + | 0.0584844i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 647.231 | 0.153497 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2093.31i | 0.490795i | 0.969422 | + | 0.245398i | \(0.0789185\pi\) | ||||
−0.969422 | + | 0.245398i | \(0.921081\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 652.717i | − | 0.151306i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3251.74i | − | 0.745331i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 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 | \(0.428983\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4119.50 | + | 660.312i | −0.913273 | + | 0.146388i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2707.91i | − | 0.593793i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4758.46 | −1.03216 | −0.516079 | − | 0.856541i | \(-0.672609\pi\) | ||||
−0.516079 | + | 0.856541i | \(0.672609\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2084.28 | −0.447250 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1753.46 | 0.372252 | 0.186126 | − | 0.982526i | \(-0.440407\pi\) | ||||
0.186126 | + | 0.982526i | \(0.440407\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3603.19 | −0.756846 | −0.378423 | − | 0.925633i | \(-0.623534\pi\) | ||||
−0.378423 | + | 0.925633i | \(0.623534\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1634.02i | 0.339617i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2635.73 | − | 422.480i | 0.542099 | − | 0.0868926i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8537.38 | −1.73771 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 3093.02i | − | 0.623080i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 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 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 702.555i | 0.137261i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4613.10 | −0.892249 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5278.28 | + | 846.052i | −1.01075 | + | 0.162012i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 623.965i | − | 0.118303i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −99.6307 | −0.0187044 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4372.30 | 0.812836 | 0.406418 | − | 0.913687i | \(-0.366778\pi\) | ||||
0.406418 | + | 0.913687i | \(0.366778\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3689.43 | −0.679237 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1956.21 | 0.356676 | 0.178338 | − | 0.983969i | \(-0.442928\pi\) | ||||
0.178338 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6314.07i | − | 1.14023i | −0.821565 | − | 0.570115i | \(-0.806899\pi\) | ||
0.821565 | − | 0.570115i | \(-0.193101\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 752.983 | − | 120.695i | 0.134685 | − | 0.0215886i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −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 | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 4508.05i | − | 0.783848i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13807.0i | 2.37846i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7814.52i | 1.33376i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1737.90 | 0.293903 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1007.01 | − | 6282.42i | −0.168748 | − | 1.05277i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 6941.96i | − | 1.15276i | −0.817181 | − | 0.576381i | \(-0.804464\pi\) | ||
0.817181 | − | 0.576381i | \(-0.195536\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −119.976 | −0.0197436 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2739.01 | 0.446711 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1809.91 | −0.292558 | −0.146279 | − | 0.989243i | \(-0.546730\pi\) | ||||
−0.146279 | + | 0.989243i | \(0.546730\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1843.91 | −0.295420 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6026.02i | 0.956972i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2915.45 | + | 5643.91i | 0.458949 | + | 0.888463i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 843.206 | 0.131585 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 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 | \(-0.967771\pi\) | ||
0.994878 | − | 0.101079i | \(-0.0322295\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2027.44i | − | 0.308310i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1254.21i | 0.189107i | 0.995520 | + | 0.0945534i | \(0.0301423\pi\) | ||||
−0.995520 | + | 0.0945534i | \(0.969858\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2697.15 | 0.403239 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6362.49 | − | 1019.84i | 0.943245 | − | 0.151192i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2350.70i | − | 0.345585i | −0.984958 | − | 0.172793i | \(-0.944721\pi\) | ||
0.984958 | − | 0.172793i | \(-0.0552791\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7314.03 | 1.06634 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1961.79 | −0.283657 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.3540 | −0.00449629 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2941.18 | −0.418333 | −0.209167 | − | 0.977880i | \(-0.567075\pi\) | ||||
−0.209167 | + | 0.977880i | \(0.567075\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1297.19i | 0.183006i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 418.181 | + | 2608.91i | 0.0585198 | + | 0.365089i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7367.26 | 1.02269 | 0.511343 | − | 0.859377i | \(-0.329148\pi\) | ||||
0.511343 | + | 0.859377i | \(0.329148\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 3144.05i | − | 0.432955i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5400.10i | 0.737717i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8022.57i | − | 1.08731i | −0.839308 | − | 0.543657i | \(-0.817039\pi\) | ||
0.839308 | − | 0.543657i | \(-0.182961\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 821.623i | 0.110480i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13469.5 | −1.79702 | −0.898511 | − | 0.438950i | \(-0.855350\pi\) | ||||
−0.898511 | + | 0.438950i | \(0.855350\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −348.950 | − | 2177.00i | −0.0461926 | − | 0.288183i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2597.74i | − | 0.341216i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6563.53 | 0.842459 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4448.09 | −0.566602 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 6101.12i | − | 0.771301i | −0.922645 | − | 0.385650i | \(-0.873977\pi\) | ||
0.922645 | − | 0.385650i | \(-0.126023\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1046.88 | − | 6531.17i | −0.131352 | − | 0.819468i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6300.98 | 0.784679 | 0.392339 | − | 0.919821i | \(-0.371666\pi\) | ||||
0.392339 | + | 0.919821i | \(0.371666\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 17390.0i | − | 2.14952i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 370.586i | 0.0454681i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 346.871i | 0.0422451i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 897.858i | − | 0.108548i | −0.998526 | − | 0.0542741i | \(-0.982716\pi\) | ||
0.998526 | − | 0.0542741i | \(-0.0172845\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7606.16 | 0.912857 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1183.96 | − | 7386.40i | −0.141063 | − | 0.880051i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1966.14i | − | 0.232564i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3021.96 | −0.354883 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −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 | \(-0.219600\pi\) | ||||
0.771313 | + | 0.636456i | \(0.219600\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3091.94 | 0.355403 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 12069.4i | − | 1.37753i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 398.224 | − | 63.8311i | 0.0451321 | − | 0.00723420i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5861.69 | −0.659685 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4512.65i | − | 0.504332i | −0.967684 | − | 0.252166i | \(-0.918857\pi\) | ||
0.967684 | − | 0.252166i | \(-0.0811428\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4597.71i | 0.510282i | 0.966904 | + | 0.255141i | \(0.0821219\pi\) | ||||
−0.966904 | + | 0.255141i | \(0.917878\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 987.057i | − | 0.108795i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 7313.74i | − | 0.800604i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14584.7 | −1.58562 | −0.792811 | − | 0.609467i | \(-0.791383\pi\) | ||||
−0.792811 | + | 0.609467i | \(0.791383\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2932.35 | + | 964.837i | −0.316634 | + | 0.104183i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 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 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7027.78 | 0.743630 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −833.584 | −0.0876152 | −0.0438076 | − | 0.999040i | \(-0.513949\pi\) | ||||
−0.0438076 | + | 0.999040i | \(0.513949\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3750.42 | 0.391575 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1683.07i | − | 0.174564i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 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 | \(0.607300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3131.35i | 0.318429i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 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 | \(0.977161\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3178.63i | 0.317001i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 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 | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1377.66i | − | 0.134775i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7510.53 | −0.730094 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12389.4 | −1.19676 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1284.00 | −0.123250 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13044.0 | −1.24425 | −0.622126 | − | 0.782917i | \(-0.713731\pi\) | ||||
−0.622126 | + | 0.782917i | \(0.713731\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1001.00i | − | 0.0948895i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3370.30 | + | 540.222i | −0.317503 | + | 0.0508923i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4717.00 | −0.441625 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6444.14i | − | 0.599614i | −0.954000 | − | 0.299807i | \(-0.903078\pi\) | ||
0.954000 | − | 0.299807i | \(-0.0969223\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1674.56i | 0.154859i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 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 | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1071.43 | 0.0972871 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10780.5 | + | 1728.00i | −0.972983 | + | 0.155959i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1184.12i | 0.106230i | 0.998588 | + | 0.0531148i | \(0.0169149\pi\) | ||||
−0.998588 | + | 0.0531148i | \(0.983085\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7482.95 | 0.667293 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19759.9 | 1.75159 | 0.875794 | − | 0.482684i | \(-0.160338\pi\) | ||||
0.875794 | + | 0.482684i | \(0.160338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −951.576 | −0.0838506 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10324.7 | 0.904413 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 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 | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3214.36 | 0.276643 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5626.55i | 0.481428i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8939.34i | − | 0.760448i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8644.85i | − | 0.731150i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 18031.5i | − | 1.51626i | −0.652101 | − | 0.758132i | \(-0.726112\pi\) | ||
0.652101 | − | 0.758132i | \(-0.273888\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5733.64 | 0.479378 | 0.239689 | − | 0.970850i | \(-0.422955\pi\) | ||||
0.239689 | + | 0.970850i | \(0.422955\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 915.128 | + | 5709.23i | 0.0760752 | + | 0.474612i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26858.5i | 2.22006i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8392.87 | 0.689806 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3635.27 | 0.297095 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10823.0 | −0.879542 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6874.99 | −0.555573 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 6217.90i | − | 0.499669i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2789.51 | + | 8477.92i | 0.222918 | + | 0.677495i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3887.89 | 0.308971 | 0.154486 | − | 0.987995i | \(-0.450628\pi\) | ||||
0.154486 | + | 0.987995i | \(0.450628\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8292.35i | − | 0.655357i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2650.38i | − | 0.208312i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4722.04i | 0.369104i | 0.982823 | + | 0.184552i | \(0.0590834\pi\) | ||||
−0.982823 | + | 0.184552i | \(0.940917\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 195.989i | 0.0152361i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8561.47 | −0.661943 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17779.0 | − | 2849.79i | 1.36716 | − | 0.219142i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 182.969i | 0.0139938i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 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 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9053.27 | 0.681335 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 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 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −237.426 | − | 1481.23i | −0.0175855 | − | 0.109711i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7220.86 | −0.532011 | −0.266005 | − | 0.963972i | \(-0.585704\pi\) | ||||
−0.266005 | + | 0.963972i | \(0.585704\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 365.261i | − | 0.0267700i | −0.999910 | − | 0.0133850i | \(-0.995739\pi\) | ||
0.999910 | − | 0.0133850i | \(-0.00426071\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 12356.8i | − | 0.900897i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6393.31i | 0.463686i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2258.22i | 0.162931i | 0.996676 | + | 0.0814653i | \(0.0259600\pi\) | ||||
−0.996676 | + | 0.0814653i | \(0.974040\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13613.5 | −0.977126 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1259.66 | + | 7858.68i | 0.0899477 | + | 0.561158i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3712.25i | 0.263715i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3091.94 | −0.218523 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 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 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2538.53 | 0.176686 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7013.68i | 0.485695i | 0.970064 | + | 0.242848i | \(0.0780815\pi\) | ||||
−0.970064 | + | 0.242848i | \(0.921919\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1555.30 | − | 9703.08i | −0.107162 | − | 0.668551i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3656.61 | −0.250679 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25452.7i | 1.73618i | 0.496409 | + | 0.868089i | \(0.334652\pi\) | ||||
−0.496409 | + | 0.868089i | \(0.665348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 26422.8i | − | 1.79336i | −0.442682 | − | 0.896679i | \(-0.645973\pi\) | ||
0.442682 | − | 0.896679i | \(-0.354027\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 5388.06i | − | 0.363879i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2991.82i | 0.201049i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6179.28 | −0.413195 | −0.206597 | − | 0.978426i | \(-0.566239\pi\) | ||||
−0.206597 | + | 0.978426i | \(0.566239\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 632.384 | + | 3945.27i | 0.0420780 | + | 0.262513i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25797.3i | 1.70809i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6512.10 | 0.429072 | 0.214536 | − | 0.976716i | \(-0.431176\pi\) | ||||
0.214536 | + | 0.976716i | \(0.431176\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1978.28 | 0.129711 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15211.8 | 0.992551 | 0.496275 | − | 0.868165i | \(-0.334701\pi\) | ||||
0.496275 | + | 0.868165i | \(0.334701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11712.0 | 0.760496 | 0.380248 | − | 0.924885i | \(-0.375839\pi\) | ||||
0.380248 | + | 0.924885i | \(0.375839\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1658.72i | − | 0.107185i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19821.4 | − | 3177.15i | 1.27468 | − | 0.204318i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8213.69 | 0.525676 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 9293.29i | − | 0.591927i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1546.03i | 0.0980037i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16130.7i | − | 1.01768i | −0.860862 | − | 0.508839i | \(-0.830075\pi\) | ||
0.860862 | − | 0.508839i | \(-0.169925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 15194.4i | − | 0.954068i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1253.01 | 0.0783059 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8050.01 | − | 24465.7i | −0.500711 | − | 1.52177i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 5305.71i | − | 0.328468i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20295.1 | 1.25056 | 0.625280 | − | 0.780401i | \(-0.284985\pi\) | ||||
0.625280 | + | 0.780401i | \(0.284985\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10255.3 | 0.628976 | 0.314488 | − | 0.949262i | \(-0.398167\pi\) | ||||
0.314488 | + | 0.949262i | \(0.398167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3961.68 | −0.241846 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15162.9 | −0.921352 | −0.460676 | − | 0.887568i | \(-0.652393\pi\) | ||||
−0.460676 | + | 0.887568i | \(0.652393\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10510.2i | − | 0.635688i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2036.47 | − | 12705.0i | −0.122605 | − | 0.764896i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 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 | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 61.6783i | 0.00366255i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 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 | \(0.133492\pi\) | ||||
−0.913343 | + | 0.407191i | \(0.866508\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26126.0 | −1.53039 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9960.33 | + | 1596.54i | −0.580820 | + | 0.0930992i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4417.99i | 0.256470i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11682.2 | 0.675126 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 566.638 | 0.0326003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32235.3 | −1.84633 | −0.923165 | − | 0.384404i | \(-0.874407\pi\) | ||||
−0.923165 | + | 0.384404i | \(0.874407\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2809.84 | −0.160223 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 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 | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3497.84 | −0.196825 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 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 | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7613.77i | 0.422829i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 10712.9i | − | 0.592348i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20064.5 | −1.10462 | −0.552309 | − | 0.833639i | \(-0.686253\pi\) | ||||
−0.552309 | + | 0.833639i | \(0.686253\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4282.50 | + | 686.439i | −0.234746 | + | 0.0376272i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4608.63i | 0.251533i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16715.9 | 0.908408 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4036.60 | −0.218424 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −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 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 4715.35i | − | 0.251901i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3803.45 | − | 609.652i | 0.202325 | − | 0.0324305i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34258.5 | −1.81468 | −0.907338 | − | 0.420403i | \(-0.861889\pi\) | ||||
−0.907338 | + | 0.420403i | \(0.861889\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8750.08i | 0.461538i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 14227.3i | − | 0.747288i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8939.34i | 0.467570i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 18719.4i | − | 0.975020i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10303.7 | −0.534443 | −0.267221 | − | 0.963635i | \(-0.586105\pi\) | ||||
−0.267221 | + | 0.963635i | \(0.586105\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3604.80 | − | 22489.3i | −0.186199 | − | 1.16165i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 13638.0i | − | 0.701527i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7484.01 | 0.383378 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1468.60 | 0.0749209 | 0.0374605 | − | 0.999298i | \(-0.488073\pi\) | ||||
0.0374605 | + | 0.999298i | \(0.488073\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33475.1 | −1.69373 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5917.44i | 0.298179i | 0.988824 | + | 0.149090i | \(0.0476343\pi\) | ||||
−0.988824 | + | 0.149090i | \(0.952366\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1471.42 | + | 4471.96i | 0.0738424 | + | 0.224423i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15577.8 | −0.778584 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8120.94i | 0.404240i | 0.979361 | + | 0.202120i | \(0.0647831\pi\) | ||||
−0.979361 | + | 0.202120i | \(0.935217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26818.7i | 1.32957i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7975.20i | 0.393784i | 0.980425 | + | 0.196892i | \(0.0630849\pi\) | ||||
−0.980425 | + | 0.196892i | \(0.936915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 10717.7i | − | 0.527068i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3867.71 | −0.189440 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 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 | \(-0.0576723\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20327.7 | −0.983777 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2566.75 | −0.123727 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2056.45 | −0.0987358 | −0.0493679 | − | 0.998781i | \(-0.515721\pi\) | ||||
−0.0493679 | + | 0.998781i | \(0.515721\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4795.64 | −0.229342 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 28244.9i | − | 1.34544i | −0.739898 | − | 0.672719i | \(-0.765126\pi\) | ||
0.739898 | − | 0.672719i | \(-0.234874\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1698.04 | + | 10593.6i | 0.0805676 | + | 0.502639i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4775.45 | 0.225695 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30330.5i | 1.42786i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27026.1i | 1.26734i | 0.773603 | + | 0.633671i | \(0.218453\pi\) | ||||
−0.773603 | + | 0.633671i | \(0.781547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 21510.5i | − | 1.00477i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 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 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −117.224 | − | 731.326i | −0.00541233 | − | 0.0337660i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 17159.1i | − | 0.789202i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15339.7 | −0.702816 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1941.69 | −0.0886213 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2100.99 | −0.0955257 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13905.7 | −0.629843 | −0.314921 | − | 0.949118i | \(-0.601978\pi\) | ||||
−0.314921 | + | 0.949118i | \(0.601978\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 6279.94i | − | 0.283361i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1801.61 | − | 11239.8i | −0.0809836 | − | 0.505234i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1635.21 | −0.0732258 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1958.15i | 0.0873566i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 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 | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9755.23i | 0.430317i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 178.323 | 0.00783669 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 823.864 | + | 5139.85i | 0.0360713 | + | 0.225039i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4721.77i | 0.205965i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33518.7 | 1.45668 | 0.728339 | − | 0.685217i | \(-0.240292\pi\) | ||||
0.728339 | + | 0.685217i | \(0.240292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35133.3 | 1.52120 | 0.760602 | − | 0.649218i | \(-0.224904\pi\) | ||||
0.760602 | + | 0.649218i | \(0.224904\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5922.53 | −0.255489 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2553.78 | 0.109761 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34362.5i | 1.47147i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12358.5 | − | 1980.94i | 0.527278 | − | 0.0845171i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 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 | \(0.857120\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8123.73i | 0.342827i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 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 | \(-0.699483\pi\) | ||
0.586471 | − | 0.809970i | \(-0.300517\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14275.4 | 0.595917 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12433.1 | + | 37786.8i | 0.517144 | + | 1.57171i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 11411.8i | − | 0.472962i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6252.85 | 0.258220 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36214.5 | −1.49018 | −0.745091 | − | 0.666962i | \(-0.767594\pi\) | ||||
−0.745091 | + | 0.666962i | \(0.767594\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19217.3 | −0.787949 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5260.39 | −0.214920 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 15745.7i | − | 0.641027i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1916.79 | − | 11958.3i | −0.0777588 | − | 0.485115i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10809.6 | 0.436965 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 818.954i | − | 0.0329887i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1180.57i | 0.0473881i | 0.999719 | + | 0.0236941i | \(0.00754276\pi\) | ||||
−0.999719 | + | 0.0236941i | \(0.992457\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4902.05i | − | 0.196078i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29570.1i | 1.17864i | 0.807900 | + | 0.589320i | \(0.200604\pi\) | ||||
−0.807900 | + | 0.589320i | \(0.799396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18516.7 | −0.735483 | −0.367742 | − | 0.929928i | \(-0.619869\pi\) | ||||
−0.367742 | + | 0.929928i | \(0.619869\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7907.19 | + | 1267.44i | −0.312981 | + | 0.0501675i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 35215.9i | − | 1.38907i | −0.719461 | − | 0.694533i | \(-0.755611\pi\) | ||
0.719461 | − | 0.694533i | \(-0.244389\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13183.8 | −0.518223 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25612.1 | 1.00327 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25298.0 | 0.987544 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44954.7 | 1.74883 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9279.07i | 0.359735i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19164.9 | − | 3071.93i | 0.740449 | − | 0.118686i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20910.2 | 0.805115 | 0.402558 | − | 0.915395i | \(-0.368121\pi\) | ||||
0.402558 | + | 0.915395i | \(0.368121\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 26562.1i | − | 1.01925i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 19841.3i | − | 0.758762i | −0.925241 | − | 0.379381i | \(-0.876137\pi\) | ||
0.925241 | − | 0.379381i | \(-0.123863\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 37682.4i | − | 1.43614i | −0.695971 | − | 0.718070i | \(-0.745026\pi\) | ||
0.695971 | − | 0.718070i | \(-0.254974\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 5543.95i | − | 0.210574i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16665.2 | 0.630850 | 0.315425 | − | 0.948950i | \(-0.397853\pi\) | ||||
0.315425 | + | 0.948950i | \(0.397853\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5008.29 | + | 802.776i | −0.188946 | + | 0.0302860i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2107.67i | − | 0.0792474i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −40899.7 | −1.53265 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9482.58 | −0.354154 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13839.3 | 0.515140 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16654.5 | −0.617862 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16545.8i | 0.611788i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15834.8 | − | 2538.16i | 0.583555 | − | 0.0935377i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12646.2 | −0.464502 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20577.7i | 0.753331i | 0.926349 | + | 0.376665i | \(0.122929\pi\) | ||||
−0.926349 | + | 0.376665i | \(0.877071\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1871.90i | 0.0683024i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35684.4i | 1.29778i | 0.760883 | + | 0.648889i | \(0.224766\pi\) | ||||
−0.760883 | + | 0.648889i | \(0.775234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11182.2i | 0.405342i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 298.892 | 0.0107990 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 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 | \(0.985429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13116.9 | −0.469291 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44267.6 | 1.57864 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1387.30 | −0.0493124 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11068.3 | 0.392158 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24991.8i | 0.882620i | 0.897355 | + | 0.441310i | \(0.145486\pi\) | ||||
−0.897355 | + | 0.441310i | \(0.854514\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38788.6 | − | 12762.7i | 1.36546 | − | 0.449281i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5868.62 | −0.205927 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 13806.6i | − | 0.482915i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36329.3i | − | 1.26662i | −0.773896 | − | 0.633312i | \(-0.781695\pi\) | ||
0.773896 | − | 0.633312i | \(-0.218305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18942.2i | 0.658312i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 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 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2258.95 | + | 362.085i | −0.0777604 | + | 0.0124642i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 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 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14888.3 | 0.507663 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22686.6 | 0.771133 | 0.385566 | − | 0.922680i | \(-0.374006\pi\) | ||||
0.385566 | + | 0.922680i | \(0.374006\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18844.7 | −0.638535 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5613.77i | 0.189621i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7431.69 | + | 46364.2i | 0.250242 | + | 1.56119i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23841.5 | 0.800293 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13524.2i | 0.452555i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20761.1i | 0.692565i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30178.5i | 1.00359i | 0.864985 | + | 0.501797i | \(0.167328\pi\) | ||||
−0.864985 | + | 0.501797i | \(0.832672\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 41420.9i | − | 1.37320i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −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 | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 23443.6i | − | 0.770046i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29860.7 | −0.977817 | −0.488908 | − | 0.872335i | \(-0.662605\pi\) | ||||
−0.488908 | + | 0.872335i | \(0.662605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28204.1 | 0.920741 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5213.71 | −0.169685 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10417.7 | 0.338018 | 0.169009 | − | 0.985615i | \(-0.445943\pi\) | ||||
0.169009 | + | 0.985615i | \(0.445943\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 3871.38i | − | 0.125231i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3021.02 | + | 18847.3i | 0.0974266 | + | 0.607817i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17732.2 | 0.570122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3803.09i | − | 0.121906i | −0.998141 | − | 0.0609531i | \(-0.980586\pi\) | ||
0.998141 | − | 0.0609531i | \(-0.0194140\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20825.9i | 0.665548i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5576.50i | 0.177675i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53386.9i | 1.69587i | 0.530103 | + | 0.847933i | \(0.322153\pi\) | ||||
−0.530103 | + | 0.847933i | \(0.677847\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 359.927 | 0.0113990 |
(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 | 1344.4.b.g.895.8 | 12 | ||
4.3 | odd | 2 | 1344.4.b.h.895.8 | 12 | |||
7.6 | odd | 2 | 1344.4.b.h.895.5 | 12 | |||
8.3 | odd | 2 | 84.4.b.a.55.1 | ✓ | 12 | ||
8.5 | even | 2 | 84.4.b.b.55.2 | yes | 12 | ||
24.5 | odd | 2 | 252.4.b.e.55.11 | 12 | |||
24.11 | even | 2 | 252.4.b.f.55.12 | 12 | |||
28.27 | even | 2 | inner | 1344.4.b.g.895.5 | 12 | ||
56.13 | odd | 2 | 84.4.b.a.55.2 | yes | 12 | ||
56.27 | even | 2 | 84.4.b.b.55.1 | yes | 12 | ||
168.83 | odd | 2 | 252.4.b.e.55.12 | 12 | |||
168.125 | even | 2 | 252.4.b.f.55.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.b.a.55.1 | ✓ | 12 | 8.3 | odd | 2 | ||
84.4.b.a.55.2 | yes | 12 | 56.13 | odd | 2 | ||
84.4.b.b.55.1 | yes | 12 | 56.27 | even | 2 | ||
84.4.b.b.55.2 | yes | 12 | 8.5 | even | 2 | ||
252.4.b.e.55.11 | 12 | 24.5 | odd | 2 | |||
252.4.b.e.55.12 | 12 | 168.83 | odd | 2 | |||
252.4.b.f.55.11 | 12 | 168.125 | even | 2 | |||
252.4.b.f.55.12 | 12 | 24.11 | even | 2 | |||
1344.4.b.g.895.5 | 12 | 28.27 | even | 2 | inner | ||
1344.4.b.g.895.8 | 12 | 1.1 | even | 1 | trivial | ||
1344.4.b.h.895.5 | 12 | 7.6 | odd | 2 | |||
1344.4.b.h.895.8 | 12 | 4.3 | odd | 2 |