Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
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, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
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.m (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: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.18 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.c.2157.17 |
$q$-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 | ||||||||
\(3\) | −0.722868 | −0.417348 | −0.208674 | − | 0.977985i | \(-0.566915\pi\) | ||||
−0.208674 | + | 0.977985i | \(0.566915\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.383791i | − | 0.171637i | −0.996311 | − | 0.0858183i | \(-0.972650\pi\) | ||
0.996311 | − | 0.0858183i | \(-0.0273505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.47746 | −0.825821 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.37304 | − | 1.27380i | 0.935514 | − | 0.353289i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.277430i | 0.0716322i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.43236 | −1.31754 | −0.658771 | − | 0.752344i | \(-0.728923\pi\) | ||||
−0.658771 | + | 0.752344i | \(0.728923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.21859i | − | 1.19723i | −0.801038 | − | 0.598614i | \(-0.795718\pi\) | ||
0.801038 | − | 0.598614i | \(-0.204282\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.722868i | − | 0.157743i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.81438 | 0.586838 | 0.293419 | − | 0.955984i | \(-0.405207\pi\) | ||||
0.293419 | + | 0.955984i | \(0.405207\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.85270 | 0.970541 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.95948 | 0.762002 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.99936 | 0.371272 | 0.185636 | − | 0.982619i | \(-0.440565\pi\) | ||||
0.185636 | + | 0.982619i | \(0.440565\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.19118i | 0.393548i | 0.980449 | + | 0.196774i | \(0.0630465\pi\) | ||||
−0.980449 | + | 0.196774i | \(0.936954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.722868i | 0.125835i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.383791 | 0.0648726 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.80912i | 1.44821i | 0.689690 | + | 0.724105i | \(0.257747\pi\) | ||||
−0.689690 | + | 0.724105i | \(0.742253\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.43827 | + | 0.920790i | −0.390435 | + | 0.147444i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.89210i | − | 0.920191i | −0.887869 | − | 0.460096i | \(-0.847815\pi\) | ||
0.887869 | − | 0.460096i | \(-0.152185\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.25357 | −1.41116 | −0.705578 | − | 0.708632i | \(-0.749313\pi\) | ||||
−0.705578 | + | 0.708632i | \(0.749313\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.950828i | 0.141741i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.28744i | 1.20885i | 0.796663 | + | 0.604424i | \(0.206597\pi\) | ||||
−0.796663 | + | 0.604424i | \(0.793403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.92688 | 0.549873 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.632174 | −0.0868358 | −0.0434179 | − | 0.999057i | \(-0.513825\pi\) | ||||
−0.0434179 | + | 0.999057i | \(0.513825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.383791 | −0.0517504 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.77235i | 0.499660i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.2980i | 1.73125i | 0.500694 | + | 0.865625i | \(0.333078\pi\) | ||||
−0.500694 | + | 0.865625i | \(0.666922\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.3069 | −1.70377 | −0.851884 | − | 0.523731i | \(-0.824540\pi\) | ||||
−0.851884 | + | 0.523731i | \(0.824540\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.47746i | − | 0.312131i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.488874 | − | 1.29454i | −0.0606373 | − | 0.160569i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.84695i | − | 0.958657i | −0.877636 | − | 0.479329i | \(-0.840880\pi\) | ||
0.877636 | − | 0.479329i | \(-0.159120\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.03442 | −0.244916 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.46182i | − | 1.00423i | −0.864800 | − | 0.502116i | \(-0.832555\pi\) | ||
0.864800 | − | 0.502116i | \(-0.167445\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.6678i | − | 1.59970i | −0.600203 | − | 0.799848i | \(-0.704914\pi\) | ||
0.600203 | − | 0.799848i | \(-0.295086\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.50786 | −0.405053 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.9841 | −1.57333 | −0.786666 | − | 0.617379i | \(-0.788195\pi\) | ||||
−0.786666 | + | 0.617379i | \(0.788195\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.57021 | 0.507801 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.5504i | − | 1.48735i | −0.668540 | − | 0.743677i | \(-0.733080\pi\) | ||
0.668540 | − | 0.743677i | \(-0.266920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.08489i | 0.226138i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.44528 | −0.154950 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.98493i | 0.422402i | 0.977443 | + | 0.211201i | \(0.0677374\pi\) | ||||
−0.977443 | + | 0.211201i | \(0.932263\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.27380 | + | 3.37304i | 0.133531 | + | 0.353591i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.58393i | − | 0.164246i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.00285 | −0.205488 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.98484i | − | 0.506134i | −0.967449 | − | 0.253067i | \(-0.918561\pi\) | ||
0.967449 | − | 0.253067i | \(-0.0814393\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.47746i | 0.248994i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.966532 | −0.0961735 | −0.0480867 | − | 0.998843i | \(-0.515312\pi\) | ||||
−0.0480867 | + | 0.998843i | \(0.515312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.4249 | −1.12573 | −0.562864 | − | 0.826550i | \(-0.690300\pi\) | ||||
−0.562864 | + | 0.826550i | \(0.690300\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.277430 | −0.0270744 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.2340 | 1.18271 | 0.591353 | − | 0.806413i | \(-0.298594\pi\) | ||||
0.591353 | + | 0.806413i | \(0.298594\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.65127i | 0.158163i | 0.996868 | + | 0.0790814i | \(0.0251987\pi\) | ||||
−0.996868 | + | 0.0790814i | \(0.974801\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6.36783i | − | 0.604407i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.25772 | −0.682749 | −0.341375 | − | 0.939927i | \(-0.610892\pi\) | ||||
−0.341375 | + | 0.939927i | \(0.610892\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.08013i | − | 0.100723i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.35659 | + | 3.15579i | −0.772567 | + | 0.291753i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.43236i | − | 0.497984i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.25921i | 0.384040i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 3.78138i | − | 0.338217i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.03568 | −0.713052 | −0.356526 | − | 0.934285i | \(-0.616039\pi\) | ||||
−0.356526 | + | 0.934285i | \(0.616039\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.68911 | 0.588943 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.5041 | 1.26723 | 0.633616 | − | 0.773648i | \(-0.281570\pi\) | ||||
0.633616 | + | 0.773648i | \(0.281570\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.21859 | 0.452509 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.51961i | − | 0.130788i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.28927i | 0.366457i | 0.983070 | + | 0.183228i | \(0.0586548\pi\) | ||||
−0.983070 | + | 0.183228i | \(0.941345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.6819 | −1.41494 | −0.707469 | − | 0.706745i | \(-0.750163\pi\) | ||||
−0.707469 | + | 0.706745i | \(0.750163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 5.99073i | − | 0.504510i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.27380 | − | 3.37304i | −0.106521 | − | 0.282068i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.767338i | − | 0.0637240i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.722868 | 0.0596211 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.6040i | 1.60602i | 0.595967 | + | 0.803009i | \(0.296769\pi\) | ||||
−0.595967 | + | 0.803009i | \(0.703231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.47295i | − | 0.201246i | −0.994925 | − | 0.100623i | \(-0.967916\pi\) | ||
0.994925 | − | 0.100623i | \(-0.0320835\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.4585 | 1.08805 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.840956 | 0.0675472 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1146 | −0.807234 | −0.403617 | − | 0.914928i | \(-0.632247\pi\) | ||||
−0.403617 | + | 0.914928i | \(0.632247\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.456978 | 0.0362407 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.81438i | 0.221804i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 22.9361i | − | 1.79650i | −0.439488 | − | 0.898248i | \(-0.644840\pi\) | ||
0.439488 | − | 0.898248i | \(-0.355160\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.277430 | 0.0215979 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 20.6241i | − | 1.59594i | −0.602699 | − | 0.797969i | \(-0.705908\pi\) | ||
0.602699 | − | 0.797969i | \(-0.294092\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.75486 | − | 8.59318i | 0.750374 | − | 0.661014i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.9289i | 0.988695i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.66630 | −0.430801 | −0.215400 | − | 0.976526i | \(-0.569106\pi\) | ||||
−0.215400 | + | 0.976526i | \(0.569106\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.85270i | 0.366830i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 9.61268i | − | 0.722533i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.5552 | −0.938418 | −0.469209 | − | 0.883087i | \(-0.655461\pi\) | ||||
−0.469209 | + | 0.883087i | \(0.655461\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.9079 | −1.10810 | −0.554049 | − | 0.832484i | \(-0.686918\pi\) | ||||
−0.554049 | + | 0.832484i | \(0.686918\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.61909 | 0.711064 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.38086 | 0.248566 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.43236i | 0.397254i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.95948i | 0.288010i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.7347 | −1.28324 | −0.641618 | − | 0.767025i | \(-0.721736\pi\) | ||||
−0.641618 | + | 0.767025i | \(0.721736\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4927i | 1.11519i | 0.830115 | + | 0.557593i | \(0.188275\pi\) | ||||
−0.830115 | + | 0.557593i | \(0.811725\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.353391 | + | 0.935785i | 0.0253069 | + | 0.0670129i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.02539i | − | 0.358044i | −0.983845 | − | 0.179022i | \(-0.942707\pi\) | ||
0.983845 | − | 0.179022i | \(-0.0572934\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5290 | −1.17171 | −0.585855 | − | 0.810416i | \(-0.699241\pi\) | ||||
−0.585855 | + | 0.810416i | \(0.699241\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.67231i | 0.400094i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.99936i | 0.140328i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.26134 | −0.157939 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.97251 | −0.484623 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.21859 | −0.360978 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.0461 | −1.58656 | −0.793279 | − | 0.608859i | \(-0.791628\pi\) | ||||
−0.793279 | + | 0.608859i | \(0.791628\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.11677i | 0.419114i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.55144i | 0.242206i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.19118 | −0.148747 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.88001i | 0.667630i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.3236 | + | 6.91975i | −1.23258 | + | 0.465473i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.12458i | − | 0.209237i | −0.994512 | − | 0.104619i | \(-0.966638\pi\) | ||
0.994512 | − | 0.104619i | \(-0.0333622\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0224 | −0.801493 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 11.5176i | − | 0.764449i | −0.924069 | − | 0.382225i | \(-0.875158\pi\) | ||
0.924069 | − | 0.382225i | \(-0.124842\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.82300i | 0.252631i | 0.991990 | + | 0.126315i | \(0.0403151\pi\) | ||||
−0.991990 | + | 0.126315i | \(0.959685\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.722868 | −0.0475612 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.54901 | −0.298016 | −0.149008 | − | 0.988836i | \(-0.547608\pi\) | ||||
−0.149008 | + | 0.988836i | \(0.547608\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.18065 | 0.207483 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.1086 | 0.656627 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.3313i | − | 0.797644i | −0.917028 | − | 0.398822i | \(-0.869419\pi\) | ||
0.917028 | − | 0.398822i | \(-0.130581\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 21.7442i | − | 1.40067i | −0.713815 | − | 0.700335i | \(-0.753034\pi\) | ||
0.713815 | − | 0.700335i | \(-0.246966\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.1821 | −0.973932 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.383791i | 0.0245195i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.64745 | − | 17.6025i | −0.422967 | − | 1.12002i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.79517i | 0.620744i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3695 | 0.970115 | 0.485057 | − | 0.874482i | \(-0.338799\pi\) | ||||
0.485057 | + | 0.874482i | \(0.338799\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.81438i | − | 0.176938i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 1.50710i | − | 0.0943783i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.7666 | 0.796358 | 0.398179 | − | 0.917308i | \(-0.369642\pi\) | ||||
0.398179 | + | 0.917308i | \(0.369642\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.80912 | −0.547372 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.95335 | −0.306605 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.6129 | −1.70268 | −0.851342 | − | 0.524610i | \(-0.824211\pi\) | ||||
−0.851342 | + | 0.524610i | \(0.824211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.242623i | 0.0149042i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.88058i | − | 0.176289i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.1801 | 1.71817 | 0.859084 | − | 0.511835i | \(-0.171034\pi\) | ||||
0.859084 | + | 0.511835i | \(0.171034\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.96706i | 0.240981i | 0.992714 | + | 0.120491i | \(0.0384468\pi\) | ||||
−0.992714 | + | 0.120491i | \(0.961553\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.920790 | − | 2.43827i | −0.0557287 | − | 0.147571i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 4.85270i | − | 0.292629i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.0315 | 1.50400 | 0.751998 | − | 0.659166i | \(-0.229090\pi\) | ||||
0.751998 | + | 0.659166i | \(0.229090\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 5.42857i | − | 0.325000i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.59437i | − | 0.214422i | −0.994236 | − | 0.107211i | \(-0.965808\pi\) | ||
0.994236 | − | 0.107211i | \(-0.0341920\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.2143 | −0.666618 | −0.333309 | − | 0.942818i | \(-0.608165\pi\) | ||||
−0.333309 | + | 0.942818i | \(0.608165\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.44780 | 0.0857600 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.89210 | 0.347800 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.5105 | 0.735914 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.60338i | 0.211234i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2580i | 0.599279i | 0.954052 | + | 0.299640i | \(0.0968665\pi\) | ||||
−0.954052 | + | 0.299640i | \(0.903134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.10365 | 0.297146 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.95948i | − | 0.229752i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.49302 | − | 3.58496i | 0.548995 | − | 0.207323i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 9.25357i | − | 0.533367i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.698674 | 0.0401378 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.10705i | 0.292429i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.1345i | 1.03499i | 0.855687 | + | 0.517494i | \(0.173135\pi\) | ||||
−0.855687 | + | 0.517494i | \(0.826865\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.25868 | 0.469820 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.3181 | −1.20884 | −0.604420 | − | 0.796666i | \(-0.706595\pi\) | ||||
−0.604420 | + | 0.796666i | \(0.706595\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.529307 | −0.0299182 | −0.0149591 | − | 0.999888i | \(-0.504762\pi\) | ||||
−0.0149591 | + | 0.999888i | \(0.504762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.950828 | −0.0535731 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.03911i | − | 0.170693i | −0.996351 | − | 0.0853467i | \(-0.972800\pi\) | ||
0.996351 | − | 0.0853467i | \(-0.0271998\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.99936i | − | 0.111943i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.84356 | −0.493600 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.3493i | 1.57740i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.3684 | − | 6.18138i | 0.907955 | − | 0.342881i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.19365i | − | 0.0660089i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.28744 | −0.456902 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.8844i | 0.873087i | 0.899683 | + | 0.436543i | \(0.143797\pi\) | ||||
−0.899683 | + | 0.436543i | \(0.856203\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 21.8243i | − | 1.19596i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.01159 | −0.164541 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.1118 | 0.877667 | 0.438833 | − | 0.898568i | \(-0.355392\pi\) | ||||
0.438833 | + | 0.898568i | \(0.355392\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.24637 | 0.284944 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.19118 | 0.118659 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.780793i | 0.0420365i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.13479 | −0.114602 | −0.0573008 | − | 0.998357i | \(-0.518249\pi\) | ||||
−0.0573008 | + | 0.998357i | \(0.518249\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.3659i | 1.62545i | 0.582647 | + | 0.812725i | \(0.302017\pi\) | ||||
−0.582647 | + | 0.812725i | \(0.697983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.3555 | − | 5.04359i | 0.712864 | − | 0.269207i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.02651i | 0.107860i | 0.998545 | + | 0.0539301i | \(0.0171748\pi\) | ||||
−0.998545 | + | 0.0539301i | \(0.982825\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.24757 | −0.172363 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.92688i | 0.207832i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.8666i | 0.626295i | 0.949705 | + | 0.313147i | \(0.101383\pi\) | ||||
−0.949705 | + | 0.313147i | \(0.898617\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.23372 | −0.433354 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.722868 | 0.0379407 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.24558 | −0.274566 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.2420 | −1.10882 | −0.554412 | − | 0.832242i | \(-0.687057\pi\) | ||||
−0.554412 | + | 0.832242i | \(0.687057\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.5975i | 0.759913i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.632174i | − | 0.0328209i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.6162 | −0.912131 | −0.456066 | − | 0.889946i | \(-0.650742\pi\) | ||||
−0.456066 | + | 0.889946i | \(0.650742\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.73344i | 0.141154i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.74394 | − | 2.54679i | 0.347331 | − | 0.131166i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.5983i | − | 0.852595i | −0.904583 | − | 0.426298i | \(-0.859818\pi\) | ||
0.904583 | − | 0.426298i | \(-0.140182\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.80874 | 0.297591 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 18.4942i | − | 0.945008i | −0.881329 | − | 0.472504i | \(-0.843350\pi\) | ||
0.881329 | − | 0.472504i | \(-0.156650\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.383791i | − | 0.0195598i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.9254 | 1.16536 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.1720 | −0.870653 | −0.435327 | − | 0.900273i | \(-0.643367\pi\) | ||||
−0.435327 | + | 0.900273i | \(0.643367\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.2887 | −0.773183 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.4846 | −0.528877 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.36697i | 0.270041i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.69929i | 0.0852847i | 0.999090 | + | 0.0426424i | \(0.0135776\pi\) | ||||
−0.999090 | + | 0.0426424i | \(0.986422\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.77235 | −0.188854 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 16.0941i | − | 0.803703i | −0.915705 | − | 0.401851i | \(-0.868367\pi\) | ||
0.915705 | − | 0.401851i | \(-0.131633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.79113 | + | 7.39095i | 0.139036 | + | 0.368169i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.75400i | − | 0.0871572i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.80912 | 0.436652 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 23.5297i | − | 1.16347i | −0.813379 | − | 0.581734i | \(-0.802374\pi\) | ||
0.813379 | − | 0.581734i | \(-0.197626\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 3.10057i | − | 0.152940i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.2980 | −0.654351 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.20054 | −0.255284 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0588 | 0.590521 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.71087 | 0.327847 | 0.163924 | − | 0.986473i | \(-0.447585\pi\) | ||||
0.163924 | + | 0.986473i | \(0.447585\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.7391i | 0.620864i | 0.950596 | + | 0.310432i | \(0.100474\pi\) | ||||
−0.950596 | + | 0.310432i | \(0.899526\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 20.5318i | − | 0.998292i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.3616 | −1.27873 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 13.3069i | − | 0.643964i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.920790 | + | 2.43827i | 0.0444562 | + | 0.117721i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.34857i | 0.402137i | 0.979577 | + | 0.201068i | \(0.0644413\pi\) | ||||
−0.979577 | + | 0.201068i | \(0.935559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.00531 | −0.144426 | −0.0722130 | − | 0.997389i | \(-0.523006\pi\) | ||||
−0.0722130 | + | 0.997389i | \(0.523006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.554684i | 0.0265951i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 14.6871i | − | 0.702579i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.5404 | 0.741704 | 0.370852 | − | 0.928692i | \(-0.379066\pi\) | ||||
0.370852 | + | 0.928692i | \(0.379066\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.47746 | 0.117974 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.6406 | −1.21822 | −0.609111 | − | 0.793085i | \(-0.708473\pi\) | ||||
−0.609111 | + | 0.793085i | \(0.708473\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.52938 | 0.0724996 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 14.1711i | − | 0.670268i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9.03275i | − | 0.426282i | −0.977021 | − | 0.213141i | \(-0.931631\pi\) | ||
0.977021 | − | 0.213141i | \(-0.0683694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.89210 | −0.277448 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.78761i | 0.0839894i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.29454 | − | 0.488874i | 0.0606892 | − | 0.0229188i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.1393i | 0.474295i | 0.971474 | + | 0.237148i | \(0.0762125\pi\) | ||||
−0.971474 | + | 0.237148i | \(0.923787\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.5093 | −1.00397 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 37.1766i | − | 1.73149i | −0.500486 | − | 0.865745i | \(-0.666845\pi\) | ||
0.500486 | − | 0.865745i | \(-0.333155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.4199i | 0.856046i | 0.903768 | + | 0.428023i | \(0.140790\pi\) | ||||
−0.903768 | + | 0.428023i | \(0.859210\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.607900 | −0.0281907 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.7425 | −0.867298 | −0.433649 | − | 0.901082i | \(-0.642774\pi\) | ||||
−0.433649 | + | 0.901082i | \(0.642774\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.84695 | 0.362338 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.31153 | 0.336897 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.25357i | 0.425480i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 25.3243i | − | 1.16196i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.56619 | 0.0717108 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 10.2727i | − | 0.469373i | −0.972071 | − | 0.234686i | \(-0.924594\pi\) | ||
0.972071 | − | 0.234686i | \(-0.0754063\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.2211 | + | 29.7135i | 0.511636 | + | 1.35482i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 2.03442i | − | 0.0925694i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.91314 | −0.0868711 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.0239i | 1.76834i | 0.467162 | + | 0.884172i | \(0.345276\pi\) | ||||
−0.467162 | + | 0.884172i | \(0.654724\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.5798i | 0.749764i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.02434 | 0.181616 | 0.0908079 | − | 0.995868i | \(-0.471055\pi\) | ||||
0.0908079 | + | 0.995868i | \(0.471055\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.8613 | −0.489167 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.950828 | 0.0427365 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.46182 | 0.379564 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.7324i | 0.525212i | 0.964903 | + | 0.262606i | \(0.0845820\pi\) | ||||
−0.964903 | + | 0.262606i | \(0.915418\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.9085i | 0.666061i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.52353 | 0.424633 | 0.212317 | − | 0.977201i | \(-0.431899\pi\) | ||||
0.212317 | + | 0.977201i | \(0.431899\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.370946i | 0.0165069i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.05147 | + | 6.21173i | −0.313167 | + | 0.275873i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 4.56408i | − | 0.202299i | −0.994871 | − | 0.101150i | \(-0.967748\pi\) | ||
0.994871 | − | 0.101150i | \(-0.0322521\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.6678 | 0.604628 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 20.6629i | − | 0.912290i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.38477i | 0.193216i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.28744 | 0.364481 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.09599 | 0.179794 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.7904 | 1.21752 | 0.608759 | − | 0.793355i | \(-0.291668\pi\) | ||||
0.608759 | + | 0.793355i | \(0.291668\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.8738 | −1.35002 | −0.675009 | − | 0.737809i | \(-0.735860\pi\) | ||||
−0.675009 | + | 0.737809i | \(0.735860\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 3.50786i | − | 0.153096i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 11.9033i | − | 0.518515i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0793 | −0.655621 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 32.9452i | − | 1.42970i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.50536 | − | 19.8743i | −0.325093 | − | 0.860852i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.69530i | − | 0.202996i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.07573 | 0.391647 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.6566i | 1.10306i | 0.834154 | + | 0.551532i | \(0.185957\pi\) | ||||
−0.834154 | + | 0.551532i | \(0.814043\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.7765 | 0.462462 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.633742 | 0.0271465 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.7340 | −0.758251 | −0.379126 | − | 0.925345i | \(-0.623775\pi\) | ||||
−0.379126 | + | 0.925345i | \(0.623775\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 32.9672 | 1.40701 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.4339i | − | 0.444498i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 13.9841i | − | 0.594664i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.44392 | −0.103738 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 4.60249i | − | 0.195014i | −0.995235 | − | 0.0975069i | \(-0.968913\pi\) | ||
0.995235 | − | 0.0975069i | \(-0.0310868\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.2127 | + | 11.7872i | −1.32016 | + | 0.498546i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 3.92688i | − | 0.165793i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.6375 | 0.659041 | 0.329521 | − | 0.944148i | \(-0.393113\pi\) | ||||
0.329521 | + | 0.944148i | \(0.393113\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.78545i | 0.117185i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.57021i | 0.191931i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.8266 | 1.16655 | 0.583276 | − | 0.812274i | \(-0.301771\pi\) | ||||
0.583276 | + | 0.812274i | \(0.301771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.8460 | −1.37456 | −0.687280 | − | 0.726392i | \(-0.741196\pi\) | ||||
−0.687280 | + | 0.726392i | \(0.741196\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8198 | 0.535555 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.6573 | 0.569550 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.7664i | 0.573102i | 0.958065 | + | 0.286551i | \(0.0925088\pi\) | ||||
−0.958065 | + | 0.286551i | \(0.907491\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 11.1991i | − | 0.465420i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.5504 | 0.562167 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.632174i | 0.0261820i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.21117 | + | 3.20719i | 0.0500756 | + | 0.132601i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 19.0750i | − | 0.787310i | −0.919258 | − | 0.393655i | \(-0.871211\pi\) | ||
0.919258 | − | 0.393655i | \(-0.128789\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.4349 | 0.471166 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.63269i | 0.149429i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.8115i | 0.895690i | 0.894111 | + | 0.447845i | \(0.147808\pi\) | ||||
−0.894111 | + | 0.447845i | \(0.852192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.08489 | −0.0854722 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.9483 | 0.489011 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.30419 | 0.0532880 | 0.0266440 | − | 0.999645i | \(-0.491518\pi\) | ||||
0.0266440 | + | 0.999645i | \(0.491518\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.8904 | 1.83112 | 0.915559 | − | 0.402183i | \(-0.131748\pi\) | ||||
0.915559 | + | 0.402183i | \(0.131748\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.4405i | 0.791679i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.383791i | 0.0156033i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.20928 | −0.170849 | −0.0854247 | − | 0.996345i | \(-0.527225\pi\) | ||||
−0.0854247 | + | 0.996345i | \(0.527225\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 1.44528i | − | 0.0585655i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.5566 | + | 27.9539i | 0.427073 | + | 1.13089i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.2079i | 0.735411i | 0.929942 | + | 0.367706i | \(0.119857\pi\) | ||||
−0.929942 | + | 0.367706i | \(0.880143\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.63465 | 0.0659153 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.2443i | 0.573455i | 0.958012 | + | 0.286727i | \(0.0925673\pi\) | ||||
−0.958012 | + | 0.286727i | \(0.907433\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 30.1836i | − | 1.21318i | −0.795014 | − | 0.606591i | \(-0.792537\pi\) | ||
0.795014 | − | 0.606591i | \(-0.207463\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.1435 | 0.447172 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.98493 | −0.159653 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.8123 | 0.912490 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.77235 | 0.150653 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 47.8543i | − | 1.90808i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.93512i | 0.0770358i | 0.999258 | + | 0.0385179i | \(0.0122637\pi\) | ||||
−0.999258 | + | 0.0385179i | \(0.987736\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.6593 | 0.662146 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.08402i | 0.122386i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.37304 | + | 1.27380i | −0.133645 | + | 0.0504698i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.9638i | 0.829316i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.5002 | 1.79715 | 0.898574 | − | 0.438821i | \(-0.144604\pi\) | ||||
0.898574 | + | 0.438821i | \(0.144604\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 18.6451i | − | 0.735292i | −0.929966 | − | 0.367646i | \(-0.880164\pi\) | ||
0.929966 | − | 0.367646i | \(-0.119836\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 2.56722i | − | 0.101084i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.6333 | 1.08638 | 0.543189 | − | 0.839611i | \(-0.317217\pi\) | ||||
0.543189 | + | 0.839611i | \(0.317217\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.2980 | 0.521991 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.58393 | 0.0620793 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.6935 | 0.418468 | 0.209234 | − | 0.977866i | \(-0.432903\pi\) | ||||
0.209234 | + | 0.977866i | \(0.432903\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 5.56656i | − | 0.217503i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 33.8615i | 1.32106i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.1509 | −0.434376 | −0.217188 | − | 0.976130i | \(-0.569688\pi\) | ||||
−0.217188 | + | 0.976130i | \(0.569688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.18156i | − | 0.240435i | −0.992748 | − | 0.120217i | \(-0.961641\pi\) | ||
0.992748 | − | 0.120217i | \(-0.0383591\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.2455 | − | 5.00206i | 0.514414 | − | 0.194264i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.00285i | − | 0.0776672i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.62696 | 0.217877 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.25866i | 0.0873247i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.3069i | 0.513705i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.1526 | 0.931015 | 0.465507 | − | 0.885044i | \(-0.345872\pi\) | ||||
0.465507 | + | 0.885044i | \(0.345872\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.2142 | 0.739554 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.1643 | 0.967143 | 0.483571 | − | 0.875305i | \(-0.339339\pi\) | ||||
0.483571 | + | 0.875305i | \(0.339339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.98484 | 0.191301 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.32569i | 0.319041i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.7812i | 1.48392i | 0.670443 | + | 0.741961i | \(0.266104\pi\) | ||||
−0.670443 | + | 0.741961i | \(0.733896\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.64618 | 0.0628974 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.76352i | − | 0.105435i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.13235 | + | 0.805265i | −0.0812362 | + | 0.0306781i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.27158i | − | 0.124457i | −0.998062 | − | 0.0622283i | \(-0.980179\pi\) | ||
0.998062 | − | 0.0622283i | \(-0.0198207\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.47746 | −0.0941110 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.40235i | 0.242855i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.0080i | 1.21239i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.28833 | 0.124376 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.2566 | −1.82263 | −0.911313 | − | 0.411715i | \(-0.864930\pi\) | ||||
−0.911313 | + | 0.411715i | \(0.864930\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45.9712 | 1.73384 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.29919 | −0.0865924 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 0.966532i | − | 0.0363502i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.1828i | 1.77199i | 0.463698 | + | 0.885993i | \(0.346522\pi\) | ||||
−0.463698 | + | 0.885993i | \(0.653478\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.6450 | 1.29929 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.16681i | 0.230949i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.29454 | + | 0.488874i | −0.0484132 | + | 0.0182828i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.91388i | 0.332895i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.56804 | −0.133066 | −0.0665328 | − | 0.997784i | \(-0.521194\pi\) | ||||
−0.0665328 | + | 0.997784i | \(0.521194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 11.4249i | − | 0.425485i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.7182i | 0.584566i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.70232 | 0.360335 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.6748 | 1.02640 | 0.513202 | − | 0.858268i | \(-0.328459\pi\) | ||||
0.513202 | + | 0.858268i | \(0.328459\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.73597 | −0.101332 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.2687 | 1.85926 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 37.6774i | − | 1.39165i | −0.718212 | − | 0.695824i | \(-0.755039\pi\) | ||
0.718212 | − | 0.695824i | \(-0.244961\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 0.277430i | − | 0.0102332i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.84695 | −0.289046 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 24.3642i | − | 0.896252i | −0.893970 | − | 0.448126i | \(-0.852092\pi\) | ||
0.893970 | − | 0.448126i | \(-0.147908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.80523 | + | 12.7243i | 0.176524 | + | 0.467439i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.4463i | 1.52052i | 0.649622 | + | 0.760258i | \(0.274927\pi\) | ||||
−0.649622 | + | 0.760258i | \(0.725073\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.52382 | 0.275652 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 33.5707i | 1.22829i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.2340i | 0.447021i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.2124 | −1.32141 | −0.660705 | − | 0.750645i | \(-0.729743\pi\) | ||||
−0.660705 | + | 0.750645i | \(0.729743\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.1101 | −0.404875 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.949095 | −0.0345411 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.6886 | 1.47885 | 0.739426 | − | 0.673238i | \(-0.235097\pi\) | ||||
0.739426 | + | 0.673238i | \(0.235097\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.03442i | 0.0738448i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 30.1176i | − | 1.09176i | −0.837863 | − | 0.545881i | \(-0.816195\pi\) | ||
0.837863 | − | 0.545881i | \(-0.183805\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.65127 | −0.0597799 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 5.16524i | − | 0.186750i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.9390 | + | 44.8547i | 0.611631 | + | 1.61961i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 26.4775i | − | 0.954803i | −0.878685 | − | 0.477401i | \(-0.841579\pi\) | ||
0.878685 | − | 0.477401i | \(-0.158421\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.22856 | −0.332358 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 24.1869i | − | 0.869944i | −0.900444 | − | 0.434972i | \(-0.856758\pi\) | ||
0.900444 | − | 0.434972i | \(-0.143242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.6332i | 0.381954i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.36783 | 0.228444 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.7485 | −1.10168 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.46182 | −0.302788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.91644 | 0.282911 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.88190i | 0.138551i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.31299i | 0.0824493i | 0.999150 | + | 0.0412247i | \(0.0131259\pi\) | ||||
−0.999150 | + | 0.0412247i | \(0.986874\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.9605 | 0.710612 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.25772i | − | 0.258055i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.8846 | + | 16.9503i | −1.59390 | + | 0.601922i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 0.175384i | − | 0.00622024i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.77307 | 0.133649 | 0.0668245 | − | 0.997765i | \(-0.478713\pi\) | ||||
0.0668245 | + | 0.997765i | \(0.478713\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 45.0204i | − | 1.59271i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 9.87252i | − | 0.348828i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.6678 | −0.482326 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.08013 | 0.0380697 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.3704 | −0.717074 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.8667 | 0.909425 | 0.454712 | − | 0.890638i | \(-0.349742\pi\) | ||||
0.454712 | + | 0.890638i | \(0.349742\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 48.4744i | − | 1.70217i | −0.525030 | − | 0.851084i | \(-0.675946\pi\) | ||
0.525030 | − | 0.851084i | \(-0.324054\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 2.86766i | − | 0.100573i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.80269 | −0.308345 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.2906i | 1.68948i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.15579 | − | 8.35659i | −0.110272 | − | 0.292003i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.5115i | 1.79776i | 0.438191 | + | 0.898882i | \(0.355619\pi\) | ||||
−0.438191 | + | 0.898882i | \(0.644381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.5098 | −0.366350 | −0.183175 | − | 0.983080i | \(-0.558638\pi\) | ||||
−0.183175 | + | 0.983080i | \(0.558638\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.50786i | 0.122128i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32.7724i | − | 1.13961i | −0.821781 | − | 0.569804i | \(-0.807019\pi\) | ||
0.821781 | − | 0.569804i | \(-0.192981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.0578 | −1.00922 | −0.504609 | − | 0.863348i | \(-0.668363\pi\) | ||||
−0.504609 | + | 0.863348i | \(0.668363\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.0944 | −0.627689 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.43236 | 0.188220 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.91533 | −0.273921 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.67594i | 0.299884i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.8360i | 1.13362i | 0.823847 | + | 0.566812i | \(0.191823\pi\) | ||||
−0.823847 | + | 0.566812i | \(0.808177\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0025 | −0.862157 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.59825i | 0.0894886i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.29799 | − | 3.74383i | −0.113454 | − | 0.128792i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.10642 | 0.278212 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.7922i | 0.849865i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12.7512i | − | 0.436592i | −0.975883 | − | 0.218296i | \(-0.929950\pi\) | ||
0.975883 | − | 0.218296i | \(-0.0700498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.96199 | 0.169696 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.6957 | −0.946068 | −0.473034 | − | 0.881044i | \(-0.656841\pi\) | ||||
−0.473034 | + | 0.881044i | \(0.656841\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3531 | 0.592080 | 0.296040 | − | 0.955176i | \(-0.404334\pi\) | ||||
0.296040 | + | 0.955176i | \(0.404334\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.25921 | −0.145153 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.9484i | 1.05350i | 0.850022 | + | 0.526748i | \(0.176589\pi\) | ||||
−0.850022 | + | 0.526748i | \(0.823411\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.17468i | 0.0739412i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.04347 | −0.307132 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.9841i | 0.474378i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.99545 | − | 26.4681i | −0.338683 | − | 0.896838i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.3498i | 0.417976i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.78138 | 0.127834 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.39890i | 0.114773i | 0.998352 | + | 0.0573863i | \(0.0182767\pi\) | ||||
−0.998352 | + | 0.0573863i | \(0.981723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 7.41519i | − | 0.250108i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.97084 | 0.268544 | 0.134272 | − | 0.990944i | \(-0.457130\pi\) | ||||
0.134272 | + | 0.990944i | \(0.457130\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.74983 | 0.294455 | 0.147228 | − | 0.989103i | \(-0.452965\pi\) | ||||
0.147228 | + | 0.989103i | \(0.452965\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.68926 | −0.124013 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.8797 | −0.600341 | −0.300170 | − | 0.953886i | \(-0.597043\pi\) | ||||
−0.300170 | + | 0.953886i | \(0.597043\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.03568i | − | 0.269508i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 4.57021i | − | 0.153108i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43.2488 | 1.44727 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.81857i | 0.161067i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.86220 | + | 2.59145i | −0.229122 | + | 0.0865260i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.38097i | 0.146113i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.43420 | 0.114410 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.68911i | 0.222600i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.72153i | 0.190190i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.3274 | −0.641757 | −0.320879 | − | 0.947120i | \(-0.603978\pi\) | ||||
−0.320879 | + | 0.947120i | \(0.603978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.39455 | 0.0794221 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.0603 | 0.830286 | 0.415143 | − | 0.909756i | \(-0.363732\pi\) | ||||
0.415143 | + | 0.909756i | \(0.363732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5504 | −0.448454 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 3.69172i | − | 0.122045i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.5041i | 0.478969i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.5914 | 1.53691 | 0.768454 | − | 0.639905i | \(-0.221026\pi\) | ||||
0.768454 | + | 0.639905i | \(0.221026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 13.1088i | − | 0.431950i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.7787 | − | 28.5421i | −0.354784 | − | 0.939474i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.7480i | 1.40555i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.3047 | 0.929649 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53.2838i | 1.74818i | 0.485760 | + | 0.874092i | \(0.338543\pi\) | ||||
−0.485760 | + | 0.874092i | \(0.661457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.21859i | 0.171032i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.4102 | 0.504506 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.08489 | 0.0681833 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.72228 | 0.186939 | 0.0934693 | − | 0.995622i | \(-0.470204\pi\) | ||||
0.0934693 | + | 0.995622i | \(0.470204\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.382619 | 0.0124863 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.7898i | 0.351739i | 0.984414 | + | 0.175869i | \(0.0562736\pi\) | ||||
−0.984414 | + | 0.175869i | \(0.943726\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 16.5826i | − | 0.540003i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.51961 | 0.0494330 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 5.73552i | − | 0.186379i | −0.995648 | − | 0.0931896i | \(-0.970294\pi\) | ||
0.995648 | − | 0.0931896i | \(-0.0297063\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.4101 | − | 46.1021i | −0.565155 | − | 1.49654i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.19687i | 0.0712385i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.9541 | 1.00270 | 0.501351 | − | 0.865244i | \(-0.332836\pi\) | ||||
0.501351 | + | 0.865244i | \(0.332836\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.80641i | 0.220250i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.44528i | 0.0467191i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.28927 | −0.138508 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.1987 | 0.845120 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.3093 | −0.976703 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.94594 | 0.191407 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.27307i | 0.201728i | 0.994900 | + | 0.100864i | \(0.0321608\pi\) | ||||
−0.994900 | + | 0.100864i | \(0.967839\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 20.4928i | − | 0.658323i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.2312 | 0.552974 | 0.276487 | − | 0.961018i | \(-0.410830\pi\) | ||||
0.276487 | + | 0.961018i | \(0.410830\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 16.6819i | − | 0.534796i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.8322 | + | 4.46832i | −0.378933 | + | 0.143101i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.94006i | 0.126054i | 0.998012 | + | 0.0630269i | \(0.0200754\pi\) | ||||
−0.998012 | + | 0.0630269i | \(0.979925\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.98493 | 0.127359 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 4.09095i | − | 0.130614i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 36.4023i | − | 1.16105i | −0.814241 | − | 0.580527i | \(-0.802847\pi\) | ||
0.814241 | − | 0.580527i | \(-0.197153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.92870 | −0.0614535 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.99073 | 0.190687 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.0430 | −0.828121 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.8466 | 1.29754 | 0.648768 | − | 0.760986i | \(-0.275285\pi\) | ||||
0.648768 | + | 0.760986i | \(0.275285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 11.4823i | − | 0.364381i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.34368i | 0.201108i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.3419 | −1.15096 | −0.575480 | − | 0.817816i | \(-0.695185\pi\) | ||||
−0.575480 | + | 0.817816i | \(0.695185\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34.8795i | 1.10354i |
(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.m.c.2157.18 | yes | 36 | |
13.12 | even | 2 | inner | 4004.2.m.c.2157.17 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.c.2157.17 | ✓ | 36 | 13.12 | even | 2 | inner | |
4004.2.m.c.2157.18 | yes | 36 | 1.1 | even | 1 | trivial |