Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(3849,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.3849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3849.15 | ||
Character | \(\chi\) | \(=\) | 4004.3849 |
Dual form | 4004.2.e.a.3849.34 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.12498i | − | 0.649505i | −0.945799 | − | 0.324753i | \(-0.894719\pi\) | ||
0.945799 | − | 0.324753i | \(-0.105281\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.542613i | − | 0.242664i | −0.992612 | − | 0.121332i | \(-0.961283\pi\) | ||
0.992612 | − | 0.121332i | \(-0.0387166\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.59076 | − | 2.11411i | 0.601251 | − | 0.799060i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.73443 | 0.578143 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.31290 | + | 0.157052i | −0.998878 | + | 0.0473529i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.610427 | −0.157612 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.02265 | 0.975636 | 0.487818 | − | 0.872945i | \(-0.337793\pi\) | ||||
0.487818 | + | 0.872945i | \(0.337793\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.33379 | −1.22366 | −0.611828 | − | 0.790991i | \(-0.709566\pi\) | ||||
−0.611828 | + | 0.790991i | \(0.709566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.37833 | − | 1.78957i | −0.518994 | − | 0.390516i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.782280 | −0.163117 | −0.0815583 | − | 0.996669i | \(-0.525990\pi\) | ||||
−0.0815583 | + | 0.996669i | \(0.525990\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.70557 | 0.941114 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.32612i | − | 1.02501i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.41746i | − | 0.263216i | −0.991302 | − | 0.131608i | \(-0.957986\pi\) | ||
0.991302 | − | 0.131608i | \(-0.0420140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.44439i | 0.259420i | 0.991552 | + | 0.129710i | \(0.0414047\pi\) | ||||
−0.991552 | + | 0.129710i | \(0.958595\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.176679 | + | 3.72694i | 0.0307559 | + | 0.648777i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.14715 | − | 0.863168i | −0.193903 | − | 0.145902i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.61353 | 1.25166 | 0.625828 | − | 0.779961i | \(-0.284761\pi\) | ||||
0.625828 | + | 0.779961i | \(0.284761\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.12498i | − | 0.180140i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.96215 | 0.462610 | 0.231305 | − | 0.972881i | \(-0.425700\pi\) | ||||
0.231305 | + | 0.972881i | \(0.425700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.89524i | − | 0.289022i | −0.989503 | − | 0.144511i | \(-0.953839\pi\) | ||
0.989503 | − | 0.144511i | \(-0.0461609\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 0.941124i | − | 0.140295i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 12.1838i | − | 1.77719i | −0.458695 | − | 0.888594i | \(-0.651683\pi\) | ||
0.458695 | − | 0.888594i | \(-0.348317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.93896 | − | 6.72610i | −0.276994 | − | 0.960872i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 4.52539i | − | 0.633681i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.00267 | −1.09925 | −0.549625 | − | 0.835411i | \(-0.685230\pi\) | ||||
−0.549625 | + | 0.835411i | \(0.685230\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0852184 | + | 1.79763i | 0.0114908 | + | 0.242392i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00039i | 0.794771i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 11.0063i | − | 1.43289i | −0.697642 | − | 0.716447i | \(-0.745767\pi\) | ||
0.697642 | − | 0.716447i | \(-0.254233\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.17603 | 0.278612 | 0.139306 | − | 0.990249i | \(-0.455513\pi\) | ||||
0.139306 | + | 0.990249i | \(0.455513\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.75906 | − | 3.66678i | 0.347609 | − | 0.461971i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.542613i | − | 0.0673029i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.82061 | −0.588931 | −0.294466 | − | 0.955662i | \(-0.595142\pi\) | ||||
−0.294466 | + | 0.955662i | \(0.595142\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.880046i | 0.105945i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.39107 | −0.877159 | −0.438579 | − | 0.898692i | \(-0.644518\pi\) | ||||
−0.438579 | + | 0.898692i | \(0.644518\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.62679 | −0.307442 | −0.153721 | − | 0.988114i | \(-0.549126\pi\) | ||||
−0.153721 | + | 0.988114i | \(0.549126\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 5.29365i | − | 0.611259i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.93801 | + | 7.25369i | −0.562739 | + | 0.826635i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.5302i | 1.29725i | 0.761107 | + | 0.648626i | \(0.224656\pi\) | ||||
−0.761107 | + | 0.648626i | \(0.775344\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.788469 | −0.0876076 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.51333 | 0.934460 | 0.467230 | − | 0.884136i | \(-0.345252\pi\) | ||||
0.467230 | + | 0.884136i | \(0.345252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.18274i | − | 0.236752i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.59461 | −0.170960 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.14290i | − | 0.439147i | −0.975596 | − | 0.219573i | \(-0.929533\pi\) | ||
0.975596 | − | 0.219573i | \(-0.0704665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.59076 | − | 2.11411i | 0.166757 | − | 0.221619i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.62491 | 0.168495 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.89419i | 0.296937i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.96598i | − | 0.301149i | −0.988599 | − | 0.150575i | \(-0.951888\pi\) | ||
0.988599 | − | 0.150575i | \(-0.0481124\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.74600 | + | 0.272395i | −0.577494 | + | 0.0273767i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.31205 | 0.528568 | 0.264284 | − | 0.964445i | \(-0.414864\pi\) | ||||
0.264284 | + | 0.964445i | \(0.414864\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.15611i | 0.113915i | 0.998377 | + | 0.0569577i | \(0.0181400\pi\) | ||||
−0.998377 | + | 0.0569577i | \(0.981860\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.971044 | + | 1.29051i | −0.0947641 | + | 0.125941i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.6495i | 1.22288i | 0.791292 | + | 0.611439i | \(0.209409\pi\) | ||||
−0.791292 | + | 0.611439i | \(0.790591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.8751i | − | 1.13743i | −0.822534 | − | 0.568716i | \(-0.807441\pi\) | ||
0.822534 | − | 0.568716i | \(-0.192559\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8.56503i | − | 0.812957i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.52126 | 0.425325 | 0.212662 | − | 0.977126i | \(-0.431787\pi\) | ||||
0.212662 | + | 0.977126i | \(0.431787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.424476i | 0.0395825i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.73443 | 0.160348 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.39908 | − | 8.50435i | 0.586603 | − | 0.779592i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9507 | − | 1.04059i | 0.995515 | − | 0.0945995i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.33235i | − | 0.300468i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.26637i | − | 0.471039i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.87244i | 0.698566i | 0.937017 | + | 0.349283i | \(0.113575\pi\) | ||||
−0.937017 | + | 0.349283i | \(0.886425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.13210 | −0.187721 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.78032 | −0.505029 | −0.252514 | − | 0.967593i | \(-0.581257\pi\) | ||||
−0.252514 | + | 0.967593i | \(0.581257\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.48479 | + | 11.2762i | −0.735725 | + | 0.977775i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.89002 | −0.248734 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.88191 | −0.160783 | −0.0803913 | − | 0.996763i | \(-0.525617\pi\) | ||||
−0.0803913 | + | 0.996763i | \(0.525617\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.06829 | −0.769162 | −0.384581 | − | 0.923091i | \(-0.625654\pi\) | ||||
−0.384581 | + | 0.923091i | \(0.625654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.7065 | −1.15429 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.31290 | + | 0.157052i | −0.277039 | + | 0.0131333i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.769133 | −0.0638730 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.56670 | + | 2.18128i | −0.624091 | + | 0.179909i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.7787i | − | 0.964948i | −0.875910 | − | 0.482474i | \(-0.839738\pi\) | ||
0.875910 | − | 0.482474i | \(-0.160262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.6944i | 1.35857i | 0.733873 | + | 0.679287i | \(0.237711\pi\) | ||||
−0.733873 | + | 0.679287i | \(0.762289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.97700 | 0.564057 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.783746 | 0.0629520 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.0692i | − | 1.36227i | −0.732158 | − | 0.681135i | \(-0.761487\pi\) | ||
0.732158 | − | 0.681135i | \(-0.238513\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.00281i | 0.713969i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.24442 | + | 1.65383i | −0.0980741 | + | 0.130340i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7898 | −0.923446 | −0.461723 | − | 0.887024i | \(-0.652769\pi\) | ||||
−0.461723 | + | 0.887024i | \(0.652769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.02229 | − | 0.0958686i | 0.157435 | − | 0.00746336i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.9134 | 0.844501 | 0.422250 | − | 0.906479i | \(-0.361240\pi\) | ||||
0.422250 | + | 0.906479i | \(0.361240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.25109 | −0.707448 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.00506 | −0.532585 | −0.266293 | − | 0.963892i | \(-0.585799\pi\) | ||||
−0.266293 | + | 0.963892i | \(0.585799\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.48544 | − | 9.94811i | 0.565846 | − | 0.752007i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.3818 | −0.930672 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.5303 | −0.936560 | −0.468280 | − | 0.883580i | \(-0.655126\pi\) | ||||
−0.468280 | + | 0.883580i | \(0.655126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.912460i | 0.0678226i | 0.999425 | + | 0.0339113i | \(0.0107964\pi\) | ||||
−0.999425 | + | 0.0339113i | \(0.989204\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.44798i | − | 0.180960i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4.13120i | − | 0.303732i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.3267 | + | 0.631764i | −0.974542 | + | 0.0461992i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.2600 | − | 8.47258i | −0.819046 | − | 0.616290i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.07399 | −0.439498 | −0.219749 | − | 0.975556i | \(-0.570524\pi\) | ||||
−0.219749 | + | 0.975556i | \(0.570524\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.1088i | 1.37548i | 0.725955 | + | 0.687742i | \(0.241398\pi\) | ||||
−0.725955 | + | 0.687742i | \(0.758602\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.610427 | −0.0437136 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 26.7361i | − | 1.90487i | −0.304741 | − | 0.952435i | \(-0.598570\pi\) | ||
0.304741 | − | 0.952435i | \(-0.401430\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.99775i | − | 0.354281i | −0.984186 | − | 0.177141i | \(-0.943315\pi\) | ||
0.984186 | − | 0.177141i | \(-0.0566847\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.42307i | 0.382514i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.99667 | − | 2.25484i | −0.210325 | − | 0.158259i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.60730i | − | 0.112259i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.35681 | −0.0943048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.6703 | − | 0.837682i | 1.22228 | − | 0.0579436i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.87824i | 0.266989i | 0.991050 | + | 0.133495i | \(0.0426199\pi\) | ||||
−0.991050 | + | 0.133495i | \(0.957380\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.31478i | 0.569719i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.02838 | −0.0701352 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.05361 | + | 2.29768i | 0.207292 | + | 0.155977i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.95508i | 0.199685i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.02265 | 0.270593 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.18192i | 0.614867i | 0.951570 | + | 0.307434i | \(0.0994702\pi\) | ||||
−0.951570 | + | 0.307434i | \(0.900530\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.16148 | 0.544099 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.46700 | 0.429230 | 0.214615 | − | 0.976699i | \(-0.431150\pi\) | ||||
0.214615 | + | 0.976699i | \(0.431150\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 24.5452i | − | 1.62199i | −0.585052 | − | 0.810996i | \(-0.698926\pi\) | ||
0.585052 | − | 0.810996i | \(-0.301074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.16023 | + | 5.55515i | 0.536903 | + | 0.365502i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.2225i | 1.32482i | 0.749141 | + | 0.662410i | \(0.230466\pi\) | ||||
−0.749141 | + | 0.662410i | \(0.769534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.61108 | −0.431260 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.9712 | 0.842572 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.1695i | − | 1.43403i | −0.697060 | − | 0.717013i | \(-0.745509\pi\) | ||
0.697060 | − | 0.717013i | \(-0.254491\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.2847 | −1.82198 | −0.910990 | − | 0.412428i | \(-0.864681\pi\) | ||||
−0.910990 | + | 0.412428i | \(0.864681\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.0913i | − | 0.968110i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.64967 | + | 1.05210i | −0.233169 | + | 0.0672165i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.33379 | −0.339381 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 9.57729i | − | 0.606936i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 25.7507i | − | 1.62537i | −0.582703 | − | 0.812685i | \(-0.698005\pi\) | ||
0.582703 | − | 0.812685i | \(-0.301995\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.59162 | − | 0.122858i | 0.162934 | − | 0.00772404i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.45554 | −0.153772 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5.71650i | − | 0.356586i | −0.983977 | − | 0.178293i | \(-0.942943\pi\) | ||
0.983977 | − | 0.178293i | \(-0.0570574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.1113 | − | 16.0959i | 0.752560 | − | 1.00015i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2.45848i | − | 0.152176i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.0902i | 1.60879i | 0.594096 | + | 0.804394i | \(0.297510\pi\) | ||||
−0.594096 | + | 0.804394i | \(0.702490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.34235i | 0.266749i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.66066 | −0.285228 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.47981i | 0.212168i | 0.994357 | + | 0.106084i | \(0.0338312\pi\) | ||||
−0.994357 | + | 0.106084i | \(0.966169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.53591 | 0.457774 | 0.228887 | − | 0.973453i | \(-0.426491\pi\) | ||||
0.228887 | + | 0.973453i | \(0.426491\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.37833 | − | 1.78957i | −0.143943 | − | 0.108310i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.5891 | + | 0.739018i | −0.940058 | + | 0.0445645i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.04518i | 0.423304i | 0.977345 | + | 0.211652i | \(0.0678843\pi\) | ||||
−0.977345 | + | 0.211652i | \(0.932116\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.50519i | 0.149982i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.8849i | − | 0.887958i | −0.896037 | − | 0.443979i | \(-0.853566\pi\) | ||
0.896037 | − | 0.443979i | \(-0.146434\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0845 | 0.837240 | 0.418620 | − | 0.908162i | \(-0.362514\pi\) | ||||
0.418620 | + | 0.908162i | \(0.362514\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.25589 | 0.192862 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.71207 | − | 6.26232i | 0.278145 | − | 0.369653i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.818271 | −0.0481336 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.33665 | −0.195598 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.36150 | −0.430064 | −0.215032 | − | 0.976607i | \(-0.568986\pi\) | ||||
−0.215032 | + | 0.976607i | \(0.568986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.97215 | −0.347712 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.836476 | + | 17.6449i | 0.0485373 | + | 1.02386i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.782280 | −0.0452404 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00676 | − | 3.01488i | −0.230946 | − | 0.173775i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5.97592i | − | 0.343308i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.18074i | − | 0.0676091i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.1790 | 1.72241 | 0.861204 | − | 0.508260i | \(-0.169711\pi\) | ||||
0.861204 | + | 0.508260i | \(0.169711\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.30060 | 0.0739886 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.09899i | 0.289137i | 0.989495 | + | 0.144569i | \(0.0461794\pi\) | ||||
−0.989495 | + | 0.144569i | \(0.953821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.00608i | − | 0.113390i | −0.998392 | − | 0.0566952i | \(-0.981944\pi\) | ||
0.998392 | − | 0.0566952i | \(-0.0180563\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.98964 | − | 1.49710i | −0.112104 | − | 0.0843523i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.3106 | −1.64625 | −0.823123 | − | 0.567864i | \(-0.807770\pi\) | ||||
−0.823123 | + | 0.567864i | \(0.807770\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.222615 | + | 4.69591i | 0.0124640 | + | 0.262921i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.2304 | 0.794266 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.4560 | −1.19384 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.70557 | 0.261018 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.3592 | −0.738767 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.7579 | − | 19.3815i | −1.42008 | − | 1.06854i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.3434 | −1.44796 | −0.723981 | − | 0.689820i | \(-0.757690\pi\) | ||||
−0.723981 | + | 0.689820i | \(0.757690\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.2051 | 0.723636 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.61573i | 0.142912i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.6781i | 0.854041i | 0.904242 | + | 0.427021i | \(0.140437\pi\) | ||||
−0.904242 | + | 0.427021i | \(0.859563\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 5.08631i | − | 0.276251i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.226844 | − | 4.78513i | −0.0122843 | − | 0.259129i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.3042 | − | 6.60045i | −0.934337 | − | 0.356391i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.477525 | 0.0257091 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.5310i | − | 0.994797i | −0.867522 | − | 0.497399i | \(-0.834289\pi\) | ||
0.867522 | − | 0.497399i | \(-0.165711\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.8196 | 0.632687 | 0.316343 | − | 0.948645i | \(-0.397545\pi\) | ||||
0.316343 | + | 0.948645i | \(0.397545\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.32612i | − | 0.284287i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6.15971i | − | 0.327848i | −0.986473 | − | 0.163924i | \(-0.947585\pi\) | ||
0.986473 | − | 0.163924i | \(-0.0524153\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.01049i | 0.212855i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.56718 | − | 7.19881i | −0.506349 | − | 0.381001i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.9343i | − | 0.999313i | −0.866224 | − | 0.499656i | \(-0.833460\pi\) | ||
0.866224 | − | 0.499656i | \(-0.166540\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.44936 | 0.497335 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.17064 | − | 12.3192i | −0.0614429 | − | 0.646592i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.42533i | 0.0746052i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.56290i | − | 0.0815825i | −0.999168 | − | 0.0407912i | \(-0.987012\pi\) | ||
0.999168 | − | 0.0407912i | \(-0.0129879\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.13764 | 0.267455 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.7303 | + | 16.9186i | −0.660926 | + | 0.878367i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.2673i | 1.10118i | 0.834776 | + | 0.550590i | \(0.185597\pi\) | ||||
−0.834776 | + | 0.550590i | \(0.814403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.92454 | −0.305942 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1.41746i | − | 0.0730029i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.1466 | 1.24033 | 0.620163 | − | 0.784473i | \(-0.287066\pi\) | ||||
0.620163 | + | 0.784473i | \(0.287066\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.85631 | 0.453722 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.3252i | 1.24296i | 0.783431 | + | 0.621479i | \(0.213468\pi\) | ||||
−0.783431 | + | 0.621479i | \(0.786532\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.93595 | + | 2.67943i | 0.200595 | + | 0.136557i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 3.28717i | − | 0.167096i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.68893 | −0.0856322 | −0.0428161 | − | 0.999083i | \(-0.513633\pi\) | ||||
−0.0428161 | + | 0.999083i | \(0.513633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.14684 | −0.159143 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.50272i | 0.328019i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.25645 | 0.314796 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.7448i | 1.44266i | 0.692591 | + | 0.721331i | \(0.256469\pi\) | ||||
−0.692591 | + | 0.721331i | \(0.743531\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.6855 | + | 9.54519i | 0.635070 | + | 0.477857i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.5750 | 1.62672 | 0.813360 | − | 0.581761i | \(-0.197636\pi\) | ||||
0.813360 | + | 0.581761i | \(0.197636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.44439i | 0.0719502i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.427834i | 0.0212592i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.2229 | + | 1.19572i | −1.25025 | + | 0.0592695i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.2013 | −1.79004 | −0.895021 | − | 0.446025i | \(-0.852839\pi\) | ||||
−0.895021 | + | 0.446025i | \(0.852839\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.11711i | 0.104429i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.2685 | − | 17.5083i | −1.14497 | − | 0.861529i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.61945i | − | 0.226760i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.2016i | 0.499575i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.8643i | 1.55667i | 0.627848 | + | 0.778336i | \(0.283936\pi\) | ||||
−0.627848 | + | 0.778336i | \(0.716064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.1231 | 1.46811 | 0.734054 | − | 0.679091i | \(-0.237626\pi\) | ||||
0.734054 | + | 0.679091i | \(0.237626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 21.1319i | − | 1.02747i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.9289 | 0.918185 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.46154 | − | 4.60037i | 0.167516 | − | 0.222628i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.176679 | + | 3.72694i | 0.00853016 | + | 0.179938i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 19.7786i | − | 0.952701i | −0.879255 | − | 0.476351i | \(-0.841959\pi\) | ||
0.879255 | − | 0.476351i | \(-0.158041\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.8404i | − | 0.761242i | −0.924731 | − | 0.380621i | \(-0.875710\pi\) | ||
0.924731 | − | 0.380621i | \(-0.124290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.865256i | 0.0414859i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.17252 | 0.199599 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.3796 | 0.924937 | 0.462469 | − | 0.886636i | \(-0.346964\pi\) | ||||
0.462469 | + | 0.886636i | \(0.346964\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.36298 | − | 11.6659i | −0.160142 | − | 0.555521i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.9332 | 1.04208 | 0.521039 | − | 0.853533i | \(-0.325545\pi\) | ||||
0.521039 | + | 0.853533i | \(0.325545\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.24799 | −0.106565 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.2507 | −0.626739 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.75505 | 0.318790 | 0.159395 | − | 0.987215i | \(-0.449046\pi\) | ||||
0.159395 | + | 0.987215i | \(0.449046\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.81332 | + | 0.465211i | −0.462091 | + | 0.0219059i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.7808 | 0.882400 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.14715 | − | 0.863168i | −0.0537791 | − | 0.0404660i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.24446i | − | 0.0582135i | −0.999576 | − | 0.0291068i | \(-0.990734\pi\) | ||
0.999576 | − | 0.0291068i | \(-0.00926628\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 21.4251i | − | 1.00004i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.1607 | 0.752680 | 0.376340 | − | 0.926482i | \(-0.377182\pi\) | ||||
0.376340 | + | 0.926482i | \(0.377182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.2427 | 1.08018 | 0.540090 | − | 0.841607i | \(-0.318390\pi\) | ||||
0.540090 | + | 0.841607i | \(0.318390\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 0.881695i | − | 0.0408876i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 37.1943i | − | 1.72115i | −0.509324 | − | 0.860575i | \(-0.670105\pi\) | ||
0.509324 | − | 0.860575i | \(-0.329895\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.66844 | + | 10.1913i | −0.354096 | + | 0.470591i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.2024 | −0.884801 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.297651 | + | 6.27876i | 0.0136860 | + | 0.288698i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.0985 | −1.15160 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.8801 | −0.635524 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.2609 | −1.10851 | −0.554254 | − | 0.832347i | \(-0.686996\pi\) | ||||
−0.554254 | + | 0.832347i | \(0.686996\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.61353 | 0.347147 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.86052 | + | 1.39994i | 0.0846565 | + | 0.0636996i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.60938 | −0.0730781 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.7210 | 1.48273 | 0.741365 | − | 0.671102i | \(-0.234179\pi\) | ||||
0.741365 | + | 0.671102i | \(0.234179\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.2632i | 0.599783i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.33499i | 0.105377i | 0.998611 | + | 0.0526884i | \(0.0167790\pi\) | ||||
−0.998611 | + | 0.0526884i | \(0.983221\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.70195i | − | 0.256803i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.147805 | + | 3.11785i | 0.00664335 | + | 0.140137i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.7574 | + | 15.6256i | −0.527393 | + | 0.700903i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.74831 | −0.346862 | −0.173431 | − | 0.984846i | \(-0.555485\pi\) | ||||
−0.173431 | + | 0.984846i | \(0.555485\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 12.2773i | − | 0.548508i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.0916 | 0.583728 | 0.291864 | − | 0.956460i | \(-0.405725\pi\) | ||||
0.291864 | + | 0.956460i | \(0.405725\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.88239i | − | 0.128265i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.12498i | − | 0.0499619i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.92323i | 0.395515i | 0.980251 | + | 0.197758i | \(0.0633659\pi\) | ||||
−0.980251 | + | 0.197758i | \(0.936634\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.17860 | + | 5.55333i | −0.184850 | + | 0.245665i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 28.4084i | 1.25426i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.627323 | 0.0276431 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.91348 | + | 40.3637i | 0.0841550 | + | 1.77519i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.88053i | 0.345917i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.24530i | − | 0.405044i | −0.979278 | − | 0.202522i | \(-0.935086\pi\) | ||
0.979278 | − | 0.202522i | \(-0.0649138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.70462 | 0.336899 | 0.168450 | − | 0.985710i | \(-0.446124\pi\) | ||||
0.168450 | + | 0.985710i | \(0.446124\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.1914 | − | 8.42094i | −0.488432 | − | 0.367520i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.81028i | 0.253100i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3880 | −0.973393 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 19.0896i | − | 0.828417i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.96215 | 0.128305 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.86381 | 0.296749 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.0963i | 0.608301i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.47992 | + | 21.9784i | 0.322183 | + | 0.946677i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.1488i | 1.46817i | 0.679057 | + | 0.734086i | \(0.262389\pi\) | ||||
−0.679057 | + | 0.734086i | \(0.737611\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.02650 | 0.0440511 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.44360 | −0.276014 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.98549i | 0.384192i | 0.981376 | + | 0.192096i | \(0.0615285\pi\) | ||||
−0.981376 | + | 0.192096i | \(0.938472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.77417 | 0.161077 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.56044i | 0.322086i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.3762 | + | 18.3418i | 1.03658 | + | 0.779974i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.64750 | −0.197275 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.5296i | 0.700380i | 0.936679 | + | 0.350190i | \(0.113883\pi\) | ||||
−0.936679 | + | 0.350190i | \(0.886117\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.89524i | − | 0.0801603i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.710720 | + | 14.9922i | 0.0300066 | + | 0.632970i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.31919 | −0.308467 | −0.154233 | − | 0.988034i | \(-0.549291\pi\) | ||||
−0.154233 | + | 0.988034i | \(0.549291\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.45330i | − | 0.103211i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.25427 | + | 1.66691i | −0.0526742 | + | 0.0700037i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.1180i | 0.843390i | 0.906738 | + | 0.421695i | \(0.138565\pi\) | ||||
−0.906738 | + | 0.421695i | \(0.861435\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.80273i | 0.410232i | 0.978738 | + | 0.205116i | \(0.0657571\pi\) | ||||
−0.978738 | + | 0.205116i | \(0.934243\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.83309i | 0.285456i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.68107 | −0.153511 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.6553i | 1.15131i | 0.817694 | + | 0.575653i | \(0.195252\pi\) | ||||
−0.817694 | + | 0.575653i | \(0.804748\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.4970 | 0.893384 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.5427 | − | 17.9982i | 0.561845 | − | 0.746689i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.5121 | − | 1.25683i | 1.09802 | − | 0.0520527i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 0.941124i | − | 0.0389107i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.43464i | 0.100488i | 0.998737 | + | 0.0502442i | \(0.0160000\pi\) | ||||
−0.998737 | + | 0.0502442i | \(0.984000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 7.70408i | − | 0.317441i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.0775 | −1.23722 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.1067 | 1.23634 | 0.618168 | − | 0.786046i | \(-0.287875\pi\) | ||||
0.618168 | + | 0.786046i | \(0.287875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.61457 | − | 3.47223i | −0.189179 | − | 0.142347i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.62235 | −0.230107 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.06062 | −0.0433358 | −0.0216679 | − | 0.999765i | \(-0.506898\pi\) | ||||
−0.0216679 | + | 0.999765i | \(0.506898\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.46521 | −0.182140 | −0.0910698 | − | 0.995845i | \(-0.529029\pi\) | ||||
−0.0910698 | + | 0.995845i | \(0.529029\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.36100 | −0.340486 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.564641 | − | 5.94198i | −0.0229559 | − | 0.241576i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.2106 | 1.87563 | 0.937816 | − | 0.347134i | \(-0.112845\pi\) | ||||
0.937816 | + | 0.347134i | \(0.112845\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.53664 | + | 3.37119i | −0.102790 | + | 0.136607i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 12.1838i | − | 0.492903i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.8369i | 0.801204i | 0.916252 | + | 0.400602i | \(0.131199\pi\) | ||||
−0.916252 | + | 0.400602i | \(0.868801\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.80818 | −0.0729127 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.7739 | 0.957102 | 0.478551 | − | 0.878060i | \(-0.341162\pi\) | ||||
0.478551 | + | 0.878060i | \(0.341162\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.3290i | 1.13864i | 0.822117 | + | 0.569319i | \(0.192793\pi\) | ||||
−0.822117 | + | 0.569319i | \(0.807207\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.16652i | 0.167197i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.75857 | − | 6.59037i | −0.350905 | − | 0.264037i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.6703 | 0.826810 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.942372 | − | 19.8787i | −0.0376347 | − | 0.793880i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.6266 | 1.22116 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.08124 | 0.361519 | 0.180759 | − | 0.983527i | \(-0.442144\pi\) | ||||
0.180759 | + | 0.983527i | \(0.442144\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.36293 | 0.173411 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.27169 | 0.169517 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.93896 | − | 6.72610i | −0.0768243 | − | 0.266498i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.8193 | −0.507123 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.0837 | 1.34622 | 0.673112 | − | 0.739541i | \(-0.264957\pi\) | ||||
0.673112 | + | 0.739541i | \(0.264957\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.8023i | − | 0.978108i | −0.872254 | − | 0.489054i | \(-0.837342\pi\) | ||
0.872254 | − | 0.489054i | \(-0.162658\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.15691i | 0.0455532i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.05031i | − | 0.237862i | −0.992902 | − | 0.118931i | \(-0.962053\pi\) | ||
0.992902 | − | 0.118931i | \(-0.0379468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.72855 | + | 36.4627i | 0.0678516 | + | 1.43129i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.58484 | − | 3.43523i | 0.101308 | − | 0.134637i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.8955 | 0.974235 | 0.487118 | − | 0.873336i | \(-0.338048\pi\) | ||||
0.487118 | + | 0.873336i | \(0.338048\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.13648i | 0.122552i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.55598 | −0.177746 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.3881i | 1.26166i | 0.775921 | + | 0.630830i | \(0.217285\pi\) | ||||
−0.775921 | + | 0.630830i | \(0.782715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.7723i | 1.23580i | 0.786257 | + | 0.617899i | \(0.212016\pi\) | ||||
−0.786257 | + | 0.617899i | \(0.787984\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 4.52539i | − | 0.175751i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.11864 | + | 4.60396i | 0.237271 | + | 0.178534i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.10885i | 0.0429349i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.3294 | 0.399359 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.20897 | + | 0.341749i | −0.278299 | + | 0.0131931i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 49.3140i | − | 1.90091i | −0.310857 | − | 0.950457i | \(-0.600616\pi\) | ||
0.310857 | − | 0.950457i | \(-0.399384\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 25.0624i | − | 0.964653i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.4625 | −1.63196 | −0.815982 | − | 0.578077i | \(-0.803803\pi\) | ||||
−0.815982 | + | 0.578077i | \(0.803803\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.27041 | − | 4.71816i | −0.240636 | − | 0.181066i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 7.27522i | − | 0.278787i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.5517 | −0.709862 | −0.354931 | − | 0.934892i | \(-0.615496\pi\) | ||||
−0.354931 | + | 0.934892i | \(0.615496\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.02115i | 0.0390162i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.6128 | −1.05349 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.00267 | −0.304877 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 29.6112i | − | 1.12646i | −0.826300 | − | 0.563231i | \(-0.809558\pi\) | ||
0.826300 | − | 0.563231i | \(-0.190442\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.56464 | + | 12.5810i | −0.325344 | + | 0.477913i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.92057i | 0.186648i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.9157 | 0.451339 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.7498 | 0.860478 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12.2153i | − | 0.461366i | −0.973029 | − | 0.230683i | \(-0.925904\pi\) | ||
0.973029 | − | 0.230683i | \(-0.0740960\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.6090 | −1.53160 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.43731i | 0.280105i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.45020 | − | 11.2303i | 0.317802 | − | 0.422358i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.0916 | 0.792112 | 0.396056 | − | 0.918226i | \(-0.370379\pi\) | ||||
0.396056 | + | 0.918226i | \(0.370379\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.9984i | 0.749997i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.12992i | − | 0.0423158i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0852184 | + | 1.79763i | 0.00318699 | + | 0.0672274i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.9401 | −0.931407 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 16.1610i | − | 0.602702i | −0.953513 | − | 0.301351i | \(-0.902562\pi\) | ||
0.953513 | − | 0.301351i | \(-0.0974376\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.44416 | + | 1.83910i | 0.0910252 | + | 0.0684917i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.8197i | 1.18339i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 6.66996i | − | 0.247716i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.50393i | − | 0.0928655i | −0.998921 | − | 0.0464327i | \(-0.985215\pi\) | ||
0.998921 | − | 0.0464327i | \(-0.0147853\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.3428 | −0.716400 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.62391i | − | 0.281980i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0670 | 0.371835 | 0.185917 | − | 0.982565i | \(-0.440474\pi\) | ||||
0.185917 | + | 0.982565i | \(0.440474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.18359 | + | 4.10579i | 0.0436574 | + | 0.151444i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.9702 | − | 0.757085i | 0.588270 | − | 0.0278876i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 52.1934i | − | 1.91997i | −0.280058 | − | 0.959983i | \(-0.590354\pi\) | ||
0.280058 | − | 0.959983i | \(-0.409646\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00039i | 0.220430i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.8058i | − | 0.506485i | −0.967403 | − | 0.253242i | \(-0.918503\pi\) | ||
0.967403 | − | 0.253242i | \(-0.0814970\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.39127 | −0.234158 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.7658 | 0.540251 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.7426 | + | 20.1224i | 0.977153 | + | 0.735257i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.9560 | 1.67696 | 0.838479 | − | 0.544934i | \(-0.183445\pi\) | ||||
0.838479 | + | 0.544934i | \(0.183445\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.9689 | −1.05569 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.05862 | 0.329677 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.79515 | −0.0652459 | −0.0326230 | − | 0.999468i | \(-0.510386\pi\) | ||||
−0.0326230 | + | 0.999468i | \(0.510386\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.138213 | − | 2.91551i | −0.00501681 | − | 0.105826i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.0229 | −0.689581 | −0.344790 | − | 0.938680i | \(-0.612050\pi\) | ||||
−0.344790 | + | 0.938680i | \(0.612050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.1054 | − | 18.8905i | −0.908876 | − | 0.683882i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 3.78582i | − | 0.136876i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11.0063i | − | 0.397413i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.7707 | 1.03750 | 0.518750 | − | 0.854926i | \(-0.326398\pi\) | ||||
0.518750 | + | 0.854926i | \(0.326398\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.43093 | −0.231604 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.4193i | 0.770397i | 0.922834 | + | 0.385199i | \(0.125867\pi\) | ||||
−0.922834 | + | 0.385199i | \(0.874133\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.79668i | 0.244144i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.1075 | − | 13.6249i | −0.649601 | − | 0.488791i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.7995 | −0.566076 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.4859 | − | 1.16078i | 0.876175 | − | 0.0415360i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.54956 | −0.269799 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.26197 | −0.330574 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.0125 | −1.39065 | −0.695323 | − | 0.718697i | \(-0.744739\pi\) | ||||
−0.695323 | + | 0.718697i | \(0.744739\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.3508 | 1.04492 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.19225 | − | 9.55846i | 0.255727 | − | 0.339860i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.17603 | 0.0772730 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.88504 | 0.173255 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 9.16026i | − | 0.324473i | −0.986752 | − | 0.162237i | \(-0.948129\pi\) | ||
0.986752 | − | 0.162237i | \(-0.0518708\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 49.0111i | − | 1.73389i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 7.18557i | − | 0.253890i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.70230 | − | 0.412542i | 0.307098 | − | 0.0145583i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.897390 | + | 0.675239i | 0.0316288 | + | 0.0237991i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.91470 | 0.137804 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.3689i | 1.24350i | 0.783215 | + | 0.621751i | \(0.213579\pi\) | ||||
−0.783215 | + | 0.621751i | \(0.786421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.3648 | 1.27694 | 0.638470 | − | 0.769647i | \(-0.279568\pi\) | ||||
0.638470 | + | 0.769647i | \(0.279568\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8.47772i | − | 0.297327i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.39728i | 0.224087i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.1088i | 0.353663i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.75906 | − | 3.66678i | 0.0964095 | − | 0.128128i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 4.66901i | − | 0.162950i | −0.996675 | − | 0.0814748i | \(-0.974037\pi\) | ||
0.996675 | − | 0.0814748i | \(-0.0259630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3486 | −0.360728 | −0.180364 | − | 0.983600i | \(-0.557728\pi\) | ||||
−0.180364 | + | 0.983600i | \(0.557728\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.831378 | + | 17.5374i | 0.0289449 | + | 0.610573i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.1288i | 1.70837i | 0.519966 | + | 0.854187i | \(0.325945\pi\) | ||||
−0.519966 | + | 0.854187i | \(0.674055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.3148i | 0.775026i | 0.921864 | + | 0.387513i | \(0.126666\pi\) | ||||
−0.921864 | + | 0.387513i | \(0.873334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.92566 | 0.274938 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.79975 | − | 27.0568i | −0.270245 | − | 0.937461i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 5.92173i | − | 0.204930i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.69300 | 0.265909 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.00657i | 0.103798i | 0.998652 | + | 0.0518991i | \(0.0165274\pi\) | ||||
−0.998652 | + | 0.0518991i | \(0.983473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.9908 | 0.930717 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.7451 | −0.576734 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 0.542613i | − | 0.0186665i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.2200 | − | 24.8063i | 0.522964 | − | 0.852355i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 15.8448i | − | 0.543791i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.95591 | −0.204166 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.6544 | 0.707193 | 0.353596 | − | 0.935398i | \(-0.384959\pi\) | ||||
0.353596 | + | 0.935398i | \(0.384959\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.01976i | 0.171672i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.4847 | −0.836382 | −0.418191 | − | 0.908359i | \(-0.637336\pi\) | ||||
−0.418191 | + | 0.908359i | \(0.637336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.5758i | 0.838515i | 0.907867 | + | 0.419258i | \(0.137710\pi\) | ||||
−0.907867 | + | 0.419258i | \(0.862290\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.04496 | − | 5.30097i | −0.240092 | − | 0.180657i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4854 | 0.595209 | 0.297605 | − | 0.954689i | \(-0.403812\pi\) | ||||
0.297605 | + | 0.954689i | \(0.403812\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.80104i | 0.129239i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.920535i | 0.0312630i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.81084 | − | 38.1985i | −0.0614286 | − | 1.29580i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.82061 | −0.163340 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5.14428i | − | 0.174107i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1337 | − | 8.37754i | −0.376388 | − | 0.283213i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 54.7318i | − | 1.84816i | −0.382198 | − | 0.924081i | \(-0.624833\pi\) | ||
0.382198 | − | 0.924081i | \(-0.375167\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.28151i | 0.279329i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.616267i | 0.0207626i | 0.999946 | + | 0.0103813i | \(0.00330453\pi\) | ||||
−0.999946 | + | 0.0103813i | \(0.996695\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.8811 | 1.03923 | 0.519616 | − | 0.854400i | \(-0.326075\pi\) | ||||
0.519616 | + | 0.854400i | \(0.326075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.71852i | 0.225841i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.5326 | 0.689419 | 0.344709 | − | 0.938709i | \(-0.387977\pi\) | ||||
0.344709 | + | 0.938709i | \(0.387977\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.6432 | + | 12.5232i | 0.558196 | + | 0.420014i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.61212 | − | 0.123830i | 0.0875093 | − | 0.00414847i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 64.9858i | 2.17467i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.79912i | 0.227269i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.880046i | 0.0293839i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.04737 | 0.0682835 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.1919 | −1.07247 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.39167 | + | 4.50751i | −0.112868 | + | 0.150001i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.495113 | 0.0164581 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.2872 | −0.773239 | −0.386620 | − | 0.922239i | \(-0.626357\pi\) | ||||
−0.386620 | + | 0.922239i | \(0.626357\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.21337 | 0.305588 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.0093 | −0.364753 | −0.182377 | − | 0.983229i | \(-0.558379\pi\) | ||||
−0.182377 | + | 0.983229i | \(0.558379\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.2039 | + | 1.33703i | −0.933411 | + | 0.0442494i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.32831 | −0.0439124 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.19511 | + | 12.2203i | −0.303649 | + | 0.403548i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.1893i | 1.29274i | 0.763025 | + | 0.646368i | \(0.223713\pi\) | ||||
−0.763025 | + | 0.646368i | \(0.776287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 33.9507i | − | 1.11871i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.39107 | −0.243280 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.8260 | 1.17795 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.00520i | 0.0658593i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 9.17997i | − | 0.301185i | −0.988596 | − | 0.150593i | \(-0.951882\pi\) | ||
0.988596 | − | 0.150593i | \(-0.0481182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.3420 | + | 35.8756i | 0.338945 | + | 1.17578i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.73624 | 0.187796 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.342804 | + | 7.23122i | 0.0112109 | + | 0.236486i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.3221 | 0.957910 | 0.478955 | − | 0.877839i | \(-0.341016\pi\) | ||||
0.478955 | + | 0.877839i | \(0.341016\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.25679 | −0.0736477 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.0781 | 1.82810 | 0.914048 | − | 0.405607i | \(-0.132940\pi\) | ||||
0.914048 | + | 0.405607i | \(0.132940\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.31723 | −0.0754594 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.59734 | + | 6.10984i | −0.149551 | + | 0.198753i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.6490 | 1.35341 | 0.676705 | − | 0.736254i | \(-0.263407\pi\) | ||||
0.676705 | + | 0.736254i | \(0.263407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.62679 | −0.0852692 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.9737i | 1.06924i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 30.8813i | − | 1.00034i | −0.865927 | − | 0.500171i | \(-0.833271\pi\) | ||
0.865927 | − | 0.500171i | \(-0.166729\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.29583i | 0.106650i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.28279 | − | 0.250436i | 0.170768 | − | 0.00809545i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.99367 | + | 3.97858i | −0.0966707 | + | 0.128475i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.9137 | 0.932701 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.9397i | 0.706998i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.3687 | 0.333780 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.1191i | 1.12936i | 0.825311 | + | 0.564678i | \(0.191000\pi\) | ||||
−0.825311 | + | 0.564678i | \(0.809000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.1375i | 0.775408i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.3833i | 1.26387i | 0.775022 | + | 0.631934i | \(0.217739\pi\) | ||||
−0.775022 | + | 0.631934i | \(0.782261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.4255 | + | 19.1714i | −0.462460 | + | 0.614607i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 5.29365i | − | 0.169533i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.3910 | −0.812331 | −0.406166 | − | 0.913799i | \(-0.633134\pi\) | ||||
−0.406166 | + | 0.913799i | \(0.633134\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.650650 | + | 13.7250i | 0.0207949 | + | 0.438654i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 20.5966i | − | 0.657598i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.84305i | 0.313944i | 0.987603 | + | 0.156972i | \(0.0501733\pi\) | ||||
−0.987603 | + | 0.156972i | \(0.949827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.5074 | −0.462244 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.8037 | + | 28.9770i | −0.694020 | + | 0.922349i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.48261i | 0.0471443i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.9082 | 1.42656 | 0.713278 | − | 0.700881i | \(-0.247209\pi\) | ||||
0.713278 | + | 0.700881i | \(0.247209\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.6357i | 0.940459i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.71185 | −0.0859713 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.6119 | −0.842806 | −0.421403 | − | 0.906873i | \(-0.638462\pi\) | ||||
−0.421403 | + | 0.906873i | \(0.638462\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 40.5505i | − | 1.28296i |
(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 | 4004.2.e.a.3849.15 | ✓ | 48 | |
7.6 | odd | 2 | 4004.2.e.b.3849.34 | yes | 48 | ||
11.10 | odd | 2 | 4004.2.e.b.3849.15 | yes | 48 | ||
77.76 | even | 2 | inner | 4004.2.e.a.3849.34 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.e.a.3849.15 | ✓ | 48 | 1.1 | even | 1 | trivial | |
4004.2.e.a.3849.34 | yes | 48 | 77.76 | even | 2 | inner | |
4004.2.e.b.3849.15 | yes | 48 | 11.10 | odd | 2 | ||
4004.2.e.b.3849.34 | yes | 48 | 7.6 | odd | 2 |