Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,3,Mod(13,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.k (of order \(4\), degree \(2\), 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: | \(1.63488158616\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.13 |
Dual form | 60.3.k.a.37.1 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.22474 | − | 2.67423i | 0.844949 | − | 0.534847i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.44949 | − | 7.44949i | 1.06421 | − | 1.06421i | 0.0664211 | − | 0.997792i | \(-0.478842\pi\) |
0.997792 | − | 0.0664211i | \(-0.0211581\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.2474 | −1.47704 | −0.738520 | − | 0.674231i | \(-0.764475\pi\) | ||||
−0.738520 | + | 0.674231i | \(0.764475\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.2474 | + | 12.2474i | 0.942111 | + | 0.942111i | 0.998414 | − | 0.0563023i | \(-0.0179311\pi\) |
−0.0563023 | + | 0.998414i | \(0.517931\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.44949 | − | 1.89898i | −0.563299 | − | 0.126599i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.55051 | + | 7.55051i | −0.444148 | + | 0.444148i | −0.893403 | − | 0.449256i | \(-0.851689\pi\) |
0.449256 | + | 0.893403i | \(0.351689\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.4949i | 0.762889i | 0.924392 | + | 0.381445i | \(0.124573\pi\) | ||||
−0.924392 | + | 0.381445i | \(0.875427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −18.2474 | −0.868926 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.65153 | − | 2.65153i | −0.115284 | − | 0.115284i | 0.647111 | − | 0.762395i | \(-0.275977\pi\) |
−0.762395 | + | 0.647111i | \(0.775977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.6969 | − | 22.5959i | 0.427878 | − | 0.903837i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34.2474i | 1.18095i | 0.807057 | + | 0.590473i | \(0.201059\pi\) | ||||
−0.807057 | + | 0.590473i | \(0.798941\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.4949 | −0.661126 | −0.330563 | − | 0.943784i | \(-0.607239\pi\) | ||||
−0.330563 | + | 0.943784i | \(0.607239\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 19.8990 | + | 19.8990i | 0.602999 | + | 0.602999i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 11.5505 | − | 51.3939i | 0.330015 | − | 1.46840i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.34847 | − | 7.34847i | 0.198607 | − | 0.198607i | −0.600795 | − | 0.799403i | \(-0.705149\pi\) |
0.799403 | + | 0.600795i | \(0.205149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 30.0000i | − | 0.769231i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 25.5051 | 0.622076 | 0.311038 | − | 0.950398i | \(-0.399323\pi\) | ||||
0.311038 | + | 0.950398i | \(0.399323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 25.1010 | + | 25.1010i | 0.583745 | + | 0.583745i | 0.935930 | − | 0.352186i | \(-0.114561\pi\) |
−0.352186 | + | 0.935930i | \(0.614561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.02270 | + | 12.6742i | 0.178282 | + | 0.281650i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 22.0454 | − | 22.0454i | 0.469051 | − | 0.469051i | −0.432556 | − | 0.901607i | \(-0.642388\pi\) |
0.901607 | + | 0.432556i | \(0.142388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 61.9898i | − | 1.26510i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.4949 | 0.362645 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −35.3031 | − | 35.3031i | −0.666096 | − | 0.666096i | 0.290714 | − | 0.956810i | \(-0.406107\pi\) |
−0.956810 | + | 0.290714i | \(0.906107\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −68.6413 | + | 43.4495i | −1.24802 | + | 0.789991i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.7526 | − | 17.7526i | 0.311448 | − | 0.311448i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 88.7423i | 1.50411i | 0.659102 | + | 0.752054i | \(0.270937\pi\) | ||||
−0.659102 | + | 0.752054i | \(0.729063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −102.495 | −1.68024 | −0.840122 | − | 0.542397i | \(-0.817517\pi\) | ||||
−0.840122 | + | 0.542397i | \(0.817517\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 22.3485 | + | 22.3485i | 0.354738 | + | 0.354738i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 84.4949 | + | 18.9898i | 1.29992 | + | 0.292151i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24.6969 | + | 24.6969i | −0.368611 | + | 0.368611i | −0.866970 | − | 0.498359i | \(-0.833936\pi\) |
0.498359 | + | 0.866970i | \(0.333936\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.49490i | 0.0941289i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 77.9796 | 1.09830 | 0.549152 | − | 0.835722i | \(-0.314951\pi\) | ||||
0.549152 | + | 0.835722i | \(0.314951\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −44.1918 | − | 44.1918i | −0.605368 | − | 0.605368i | 0.336364 | − | 0.941732i | \(-0.390803\pi\) |
−0.941732 | + | 0.336364i | \(0.890803\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −40.7753 | + | 14.5732i | −0.543670 | + | 0.194310i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −121.035 | + | 121.035i | −1.57189 | + | 1.57189i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 48.4949i | 0.613859i | 0.951732 | + | 0.306930i | \(0.0993017\pi\) | ||||
−0.951732 | + | 0.306930i | \(0.900698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −101.641 | − | 101.641i | −1.22459 | − | 1.22459i | −0.965981 | − | 0.258613i | \(-0.916734\pi\) |
−0.258613 | − | 0.965981i | \(-0.583266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.7071 | + | 52.0908i | −0.137731 | + | 0.612833i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 41.9444 | − | 41.9444i | 0.482119 | − | 0.482119i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 156.969i | − | 1.76370i | −0.471529 | − | 0.881850i | \(-0.656298\pi\) | ||
0.471529 | − | 0.881850i | \(-0.343702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 182.474 | 2.00521 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 25.1010 | + | 25.1010i | 0.269903 | + | 0.269903i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 38.7628 | + | 61.2372i | 0.408029 | + | 0.644603i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 55.4041 | − | 55.4041i | 0.571176 | − | 0.571176i | −0.361281 | − | 0.932457i | \(-0.617660\pi\) |
0.932457 | + | 0.361281i | \(0.117660\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 48.7423i | − | 0.492347i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 45.7526 | 0.452996 | 0.226498 | − | 0.974012i | \(-0.427272\pi\) | ||||
0.226498 | + | 0.974012i | \(0.427272\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 23.1566 | + | 23.1566i | 0.224822 | + | 0.224822i | 0.810525 | − | 0.585704i | \(-0.199182\pi\) |
−0.585704 | + | 0.810525i | \(0.699182\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −77.0908 | + | 48.7980i | −0.734198 | + | 0.464742i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.3383 | − | 16.3383i | 0.152694 | − | 0.152694i | −0.626626 | − | 0.779320i | \(-0.715565\pi\) |
0.779320 | + | 0.626626i | \(0.215565\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 159.485i | − | 1.46316i | −0.681754 | − | 0.731581i | \(-0.738783\pi\) | ||
0.681754 | − | 0.731581i | \(-0.261217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.0000 | −0.162162 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0556 | + | 13.0556i | 0.115536 | + | 0.115536i | 0.762511 | − | 0.646975i | \(-0.223966\pi\) |
−0.646975 | + | 0.762511i | \(0.723966\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.2929 | − | 4.11123i | −0.159068 | − | 0.0357498i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −36.7423 | + | 36.7423i | −0.314037 | + | 0.314037i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 112.495i | 0.945335i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 142.980 | 1.18165 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −31.2372 | − | 31.2372i | −0.253961 | − | 0.253961i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15.2350 | − | 124.068i | −0.121880 | − | 0.992545i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.44949 | − | 7.44949i | 0.0586574 | − | 0.0586574i | −0.677170 | − | 0.735827i | \(-0.736794\pi\) |
0.735827 | + | 0.677170i | \(0.236794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 61.4847i | − | 0.476626i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.7526 | 0.150783 | 0.0753914 | − | 0.997154i | \(-0.475979\pi\) | ||||
0.0753914 | + | 0.997154i | \(0.475979\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 107.980 | + | 107.980i | 0.811877 | + | 0.811877i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.69694 | − | 25.3485i | 0.0421995 | − | 0.187766i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −101.641 | + | 101.641i | −0.741907 | + | 0.741907i | −0.972945 | − | 0.231037i | \(-0.925788\pi\) |
0.231037 | + | 0.972945i | \(0.425788\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 24.0204i | − | 0.172809i | −0.996260 | − | 0.0864044i | \(-0.972462\pi\) | ||
0.996260 | − | 0.0864044i | \(-0.0275377\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −54.0000 | −0.382979 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −198.990 | − | 198.990i | −1.39154 | − | 1.39154i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 91.5857 | + | 144.687i | 0.631626 | + | 0.997840i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −75.9217 | + | 75.9217i | −0.516474 | + | 0.516474i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 199.732i | 1.34048i | 0.742143 | + | 0.670242i | \(0.233810\pi\) | ||||
−0.742143 | + | 0.670242i | \(0.766190\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −158.990 | −1.05291 | −0.526456 | − | 0.850202i | \(-0.676480\pi\) | ||||
−0.526456 | + | 0.850202i | \(0.676480\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.6515 | − | 22.6515i | −0.148049 | − | 0.148049i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −86.5857 | + | 54.8082i | −0.558618 | + | 0.353601i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −37.3485 | + | 37.3485i | −0.237888 | + | 0.237888i | −0.815975 | − | 0.578087i | \(-0.803799\pi\) |
0.578087 | + | 0.815975i | \(0.303799\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 86.4745i | 0.543865i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −39.5051 | −0.245373 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.98979 | + | 8.98979i | 0.0551521 | + | 0.0551521i | 0.734145 | − | 0.678993i | \(-0.237583\pi\) |
−0.678993 | + | 0.734145i | \(0.737583\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 137.283 | + | 30.8536i | 0.832016 | + | 0.186991i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 88.3587 | − | 88.3587i | 0.529094 | − | 0.529094i | −0.391208 | − | 0.920302i | \(-0.627943\pi\) |
0.920302 | + | 0.391208i | \(0.127943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 131.000i | 0.775148i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −43.4847 | −0.254296 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 170.631 | + | 170.631i | 0.986307 | + | 0.986307i | 0.999908 | − | 0.0136005i | \(-0.00432929\pi\) |
−0.0136005 | + | 0.999908i | \(0.504329\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −88.6413 | − | 248.015i | −0.506522 | − | 1.41723i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 108.687 | − | 108.687i | 0.614049 | − | 0.614049i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 75.7526i | − | 0.423199i | −0.977357 | − | 0.211599i | \(-0.932133\pi\) | ||
0.977357 | − | 0.211599i | \(-0.0678672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −279.444 | −1.54389 | −0.771944 | − | 0.635690i | \(-0.780716\pi\) | ||||
−0.771944 | + | 0.635690i | \(0.780716\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 125.530 | + | 125.530i | 0.685957 | + | 0.685957i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.3939 | − | 50.6969i | 0.0615885 | − | 0.274038i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 122.677 | − | 122.677i | 0.656024 | − | 0.656024i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 54.7423i | − | 0.289642i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −69.4847 | −0.363794 | −0.181897 | − | 0.983318i | \(-0.558224\pi\) | ||||
−0.181897 | + | 0.983318i | \(0.558224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −53.5857 | − | 53.5857i | −0.277646 | − | 0.277646i | 0.554523 | − | 0.832169i | \(-0.312901\pi\) |
−0.832169 | + | 0.554523i | \(0.812901\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −80.2270 | − | 126.742i | −0.411421 | − | 0.649961i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 260.252 | − | 260.252i | 1.32108 | − | 1.32108i | 0.408171 | − | 0.912906i | \(-0.366167\pi\) |
0.912906 | − | 0.408171i | \(-0.133833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 65.0102i | 0.326684i | 0.986569 | + | 0.163342i | \(0.0522275\pi\) | ||||
−0.986569 | + | 0.163342i | \(0.947773\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 60.4949 | 0.300970 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 255.126 | + | 255.126i | 1.25678 | + | 1.25678i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 107.753 | − | 68.2066i | 0.525622 | − | 0.332715i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.95459 | − | 7.95459i | 0.0384280 | − | 0.0384280i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 235.505i | − | 1.12682i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0204 | 0.0569688 | 0.0284844 | − | 0.999594i | \(-0.490932\pi\) | ||||
0.0284844 | + | 0.999594i | \(0.490932\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −95.5051 | − | 95.5051i | −0.448381 | − | 0.448381i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 173.171 | + | 38.9194i | 0.805448 | + | 0.181020i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −152.677 | + | 152.677i | −0.703578 | + | 0.703578i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 108.247i | 0.494281i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −184.949 | −0.836873 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −239.722 | − | 239.722i | −1.07499 | − | 1.07499i | −0.996951 | − | 0.0780357i | \(-0.975135\pi\) |
−0.0780357 | − | 0.996951i | \(-0.524865\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 67.7878 | + | 32.0908i | 0.301279 | + | 0.142626i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.02041 | − | 2.02041i | 0.00890049 | − | 0.00890049i | −0.702643 | − | 0.711543i | \(-0.747997\pi\) |
0.711543 | + | 0.702643i | \(0.247997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 284.969i | 1.24441i | 0.782855 | + | 0.622204i | \(0.213763\pi\) | ||||
−0.782855 | + | 0.622204i | \(0.786237\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 296.474 | 1.28344 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 151.237 | + | 151.237i | 0.649087 | + | 0.649087i | 0.952772 | − | 0.303685i | \(-0.0982172\pi\) |
−0.303685 | + | 0.952772i | \(0.598217\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34.1816 | − | 152.091i | 0.145454 | − | 0.647195i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 59.3939 | − | 59.3939i | 0.250607 | − | 0.250607i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 50.9694i | 0.213261i | 0.994299 | + | 0.106631i | \(0.0340062\pi\) | ||||
−0.994299 | + | 0.106631i | \(0.965994\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −32.0000 | −0.132780 | −0.0663900 | − | 0.997794i | \(-0.521148\pi\) | ||||
−0.0663900 | + | 0.997794i | \(0.521148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −165.775 | − | 261.891i | −0.676634 | − | 1.06894i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −177.526 | + | 177.526i | −0.718727 | + | 0.718727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 248.969i | 0.999877i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −373.237 | −1.48700 | −0.743500 | − | 0.668735i | \(-0.766836\pi\) | ||||
−0.743500 | + | 0.668735i | \(0.766836\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 43.0806 | + | 43.0806i | 0.170279 | + | 0.170279i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 78.1362 | − | 49.4597i | 0.306417 | − | 0.193960i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −206.136 | + | 206.136i | −0.802086 | + | 0.802086i | −0.983421 | − | 0.181335i | \(-0.941958\pi\) |
0.181335 | + | 0.983421i | \(0.441958\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 109.485i | − | 0.422721i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −102.742 | −0.393649 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 210.833 | + | 210.833i | 0.801647 | + | 0.801647i | 0.983353 | − | 0.181706i | \(-0.0581619\pi\) |
−0.181706 | + | 0.983353i | \(0.558162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −243.555 | − | 54.7378i | −0.919076 | − | 0.206558i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −192.247 | + | 192.247i | −0.720028 | + | 0.720028i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 205.258i | − | 0.763040i | −0.924361 | − | 0.381520i | \(-0.875401\pi\) | ||
0.924361 | − | 0.381520i | \(-0.124599\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −66.0000 | −0.243542 | −0.121771 | − | 0.992558i | \(-0.538857\pi\) | ||||
−0.121771 | + | 0.992558i | \(0.538857\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −223.485 | − | 223.485i | −0.818625 | − | 0.818625i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −173.798 | + | 367.126i | −0.631993 | + | 1.33500i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 148.157 | − | 148.157i | 0.534861 | − | 0.534861i | −0.387154 | − | 0.922015i | \(-0.626542\pi\) |
0.922015 | + | 0.387154i | \(0.126542\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 61.4847i | − | 0.220375i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 324.434 | 1.15457 | 0.577284 | − | 0.816543i | \(-0.304113\pi\) | ||||
0.577284 | + | 0.816543i | \(0.304113\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 304.747 | + | 304.747i | 1.07684 | + | 1.07684i | 0.996791 | + | 0.0800537i | \(0.0255092\pi\) |
0.0800537 | + | 0.996791i | \(0.474491\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 27.5255 | − | 122.474i | 0.0965807 | − | 0.429735i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 190.000 | − | 190.000i | 0.662021 | − | 0.662021i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 174.980i | 0.605466i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −135.712 | −0.466363 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −145.151 | − | 145.151i | −0.495396 | − | 0.495396i | 0.414605 | − | 0.910001i | \(-0.363920\pi\) |
−0.910001 | + | 0.414605i | \(0.863920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 237.318 | + | 374.914i | 0.804467 | + | 1.27089i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −59.6969 | + | 59.6969i | −0.201000 | + | 0.201000i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 64.9490i | − | 0.217221i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 373.980 | 1.24246 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −56.0352 | − | 56.0352i | −0.184935 | − | 0.184935i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −433.015 | + | 274.095i | −1.41972 | + | 0.898673i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 120.606 | − | 120.606i | 0.392854 | − | 0.392854i | −0.482850 | − | 0.875703i | \(-0.660398\pi\) |
0.875703 | + | 0.482850i | \(0.160398\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 56.7219i | − | 0.183566i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0204 | −0.0579434 | −0.0289717 | − | 0.999580i | \(-0.509223\pi\) | ||||
−0.0289717 | + | 0.999580i | \(0.509223\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −323.586 | − | 323.586i | −1.03382 | − | 1.03382i | −0.999408 | − | 0.0344125i | \(-0.989044\pi\) |
−0.0344125 | − | 0.999408i | \(-0.510956\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 154.182 | + | 34.6515i | 0.489465 | + | 0.110005i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 62.4495 | − | 62.4495i | 0.197002 | − | 0.197002i | −0.601712 | − | 0.798713i | \(-0.705514\pi\) |
0.798713 | + | 0.601712i | \(0.205514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 556.434i | − | 1.74431i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −40.0204 | −0.124674 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −109.444 | − | 109.444i | −0.338836 | − | 0.338836i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 407.753 | − | 145.732i | 1.25462 | − | 0.448407i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −195.328 | + | 195.328i | −0.597334 | + | 0.597334i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 328.454i | − | 0.998341i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 618.413 | 1.86832 | 0.934159 | − | 0.356857i | \(-0.116152\pi\) | ||||
0.934159 | + | 0.356857i | \(0.116152\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.0454 | + | 22.0454i | 0.0662024 | + | 0.0662024i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −38.2929 | + | 170.384i | −0.114307 | + | 0.508608i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −55.4041 | + | 55.4041i | −0.164404 | + | 0.164404i | −0.784514 | − | 0.620111i | \(-0.787088\pi\) |
0.620111 | + | 0.784514i | \(0.287088\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 31.9796i | − | 0.0943351i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 332.990 | 0.976510 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −96.7673 | − | 96.7673i | −0.282121 | − | 0.282121i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.3689 | + | 27.4393i | 0.0503446 | + | 0.0795342i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 413.081 | − | 413.081i | 1.19043 | − | 1.19043i | 0.213488 | − | 0.976946i | \(-0.431517\pi\) |
0.976946 | − | 0.213488i | \(-0.0684826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 258.454i | 0.740556i | 0.928921 | + | 0.370278i | \(0.120738\pi\) | ||||
−0.928921 | + | 0.370278i | \(0.879262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 90.0000 | 0.256410 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −83.9138 | − | 83.9138i | −0.237716 | − | 0.237716i | 0.578188 | − | 0.815904i | \(-0.303760\pi\) |
−0.815904 | + | 0.578188i | \(0.803760\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 329.444 | − | 208.536i | 0.928011 | − | 0.587425i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 137.778 | − | 137.778i | 0.385932 | − | 0.385932i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 138.515i | 0.385837i | 0.981215 | + | 0.192918i | \(0.0617952\pi\) | ||||
−0.981215 | + | 0.192918i | \(0.938205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 150.898 | 0.418000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −175.114 | − | 175.114i | −0.482406 | − | 0.482406i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −304.879 | − | 68.5199i | −0.835284 | − | 0.187726i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −408.964 | + | 408.964i | −1.11434 | + | 1.11434i | −0.121786 | + | 0.992556i | \(0.538862\pi\) |
−0.992556 | + | 0.121786i | \(0.961138\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 76.5153i | 0.207359i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −525.980 | −1.41773 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −143.106 | − | 143.106i | −0.383661 | − | 0.383661i | 0.488758 | − | 0.872419i | \(-0.337450\pi\) |
−0.872419 | + | 0.488758i | \(0.837450\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −133.293 | + | 170.611i | −0.355448 | + | 0.454962i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −419.444 | + | 419.444i | −1.11258 | + | 1.11258i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 194.000i | 0.511873i | 0.966694 | + | 0.255937i | \(0.0823839\pi\) | ||||
−0.966694 | + | 0.255937i | \(0.917616\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.2474 | −0.0478936 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 51.4893 | + | 51.4893i | 0.134437 | + | 0.134437i | 0.771123 | − | 0.636686i | \(-0.219695\pi\) |
−0.636686 | + | 0.771123i | \(0.719695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −187.666 | + | 835.019i | −0.487445 | + | 2.16888i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −75.3031 | + | 75.3031i | −0.194582 | + | 0.194582i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.1964i | 0.0904792i | 0.998976 | + | 0.0452396i | \(0.0144051\pi\) | ||||
−0.998976 | + | 0.0452396i | \(0.985595\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.0408 | 0.102406 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.1918 | − | 24.1918i | −0.0615568 | − | 0.0615568i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 129.687 | + | 204.879i | 0.328321 | + | 0.518680i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 409.267 | − | 409.267i | 1.03090 | − | 1.03090i | 0.0313917 | − | 0.999507i | \(-0.490006\pi\) |
0.999507 | − | 0.0313917i | \(-0.00999391\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 264.495i | − | 0.662894i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 375.898 | 0.937401 | 0.468701 | − | 0.883357i | \(-0.344722\pi\) | ||||
0.468701 | + | 0.883357i | \(0.344722\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −251.010 | − | 251.010i | −0.622854 | − | 0.622854i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −38.0227 | + | 24.0681i | −0.0938832 | + | 0.0594274i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −119.394 | + | 119.394i | −0.293351 | + | 0.293351i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 207.959i | − | 0.508458i | −0.967144 | − | 0.254229i | \(-0.918178\pi\) | ||
0.967144 | − | 0.254229i | \(-0.0818216\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 248.969 | 0.605765 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 661.085 | + | 661.085i | 1.60069 | + | 1.60069i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −701.221 | − | 157.596i | −1.68969 | − | 0.379749i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.4189 | + | 29.4189i | −0.0705489 | + | 0.0705489i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 810.186i | − | 1.93362i | −0.255499 | − | 0.966809i | \(-0.582240\pi\) | ||
0.255499 | − | 0.966809i | \(-0.417760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −505.959 | −1.20180 | −0.600902 | − | 0.799323i | \(-0.705192\pi\) | ||||
−0.600902 | + | 0.799323i | \(0.705192\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 66.1362 | + | 66.1362i | 0.156350 | + | 0.156350i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 89.8434 | + | 251.378i | 0.211396 | + | 0.591478i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −763.535 | + | 763.535i | −1.78814 | + | 1.78814i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 487.423i | 1.13619i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −92.4541 | −0.214511 | −0.107255 | − | 0.994232i | \(-0.534206\pi\) | ||||
−0.107255 | + | 0.994232i | \(0.534206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 69.8990 | + | 69.8990i | 0.161430 | + | 0.161430i | 0.783200 | − | 0.621770i | \(-0.213586\pi\) |
−0.621770 | + | 0.783200i | \(0.713586\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 65.0352 | − | 289.373i | 0.149506 | − | 0.665226i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 38.4337 | − | 38.4337i | 0.0879489 | − | 0.0879489i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 128.929i | − | 0.293687i | −0.989160 | − | 0.146843i | \(-0.953089\pi\) | ||
0.989160 | − | 0.146843i | \(-0.0469114\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 185.969 | 0.421699 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −335.555 | − | 335.555i | −0.757461 | − | 0.757461i | 0.218399 | − | 0.975860i | \(-0.429917\pi\) |
−0.975860 | + | 0.218399i | \(0.929917\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −419.773 | − | 663.156i | −0.943310 | − | 1.49024i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 244.621 | − | 244.621i | 0.547250 | − | 0.547250i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 521.423i | 1.16130i | 0.814153 | + | 0.580650i | \(0.197201\pi\) | ||||
−0.814153 | + | 0.580650i | \(0.802799\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −414.393 | −0.918831 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 194.722 | + | 194.722i | 0.429850 | + | 0.429850i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 770.908 | − | 487.980i | 1.69430 | − | 1.07248i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 548.939 | − | 548.939i | 1.20118 | − | 1.20118i | 0.227371 | − | 0.973808i | \(-0.426987\pi\) |
0.973808 | − | 0.227371i | \(-0.0730129\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 55.4847i | 0.120882i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 142.288 | 0.308651 | 0.154326 | − | 0.988020i | \(-0.450680\pi\) | ||||
0.154326 | + | 0.988020i | \(0.450680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 537.045 | + | 537.045i | 1.15993 | + | 1.15993i | 0.984491 | + | 0.175434i | \(0.0561329\pi\) |
0.175434 | + | 0.984491i | \(0.443867\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 173.171 | + | 38.9194i | 0.372412 | + | 0.0836976i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −367.044 | + | 367.044i | −0.785962 | + | 0.785962i | −0.980830 | − | 0.194867i | \(-0.937572\pi\) |
0.194867 | + | 0.980830i | \(0.437572\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 367.959i | 0.784561i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 91.4847 | 0.194235 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −407.828 | − | 407.828i | −0.862215 | − | 0.862215i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 327.526 | + | 155.051i | 0.689527 | + | 0.326423i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 105.909 | − | 105.909i | 0.222032 | − | 0.222032i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 94.9694i | − | 0.198266i | −0.995074 | − | 0.0991330i | \(-0.968393\pi\) | ||
0.995074 | − | 0.0991330i | \(-0.0316069\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 180.000 | 0.374220 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 48.3837 | + | 48.3837i | 0.100173 | + | 0.100173i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 85.9046 | − | 382.232i | 0.177123 | − | 0.788106i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 244.621 | − | 244.621i | 0.502302 | − | 0.502302i | −0.409851 | − | 0.912153i | \(-0.634419\pi\) |
0.912153 | + | 0.409851i | \(0.134419\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 22.0204i | − | 0.0450315i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 163.217 | 0.332417 | 0.166209 | − | 0.986091i | \(-0.446847\pi\) | ||||
0.166209 | + | 0.986091i | \(0.446847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −258.586 | − | 258.586i | −0.524515 | − | 0.524515i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −130.348 | − | 205.924i | −0.263330 | − | 0.416008i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 580.908 | − | 580.908i | 1.16883 | − | 1.16883i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.55613i | − | 0.0171465i | −0.999963 | − | 0.00857327i | \(-0.997271\pi\) | ||
0.999963 | − | 0.00857327i | \(-0.00272899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −216.434 | −0.432003 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 46.5903 | + | 46.5903i | 0.0926249 | + | 0.0926249i | 0.751901 | − | 0.659276i | \(-0.229137\pi\) |
−0.659276 | + | 0.751901i | \(0.729137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 193.293 | − | 122.353i | 0.382758 | − | 0.242283i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 160.442 | − | 160.442i | 0.316453 | − | 0.316453i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 336.227i | 0.660564i | 0.943882 | + | 0.330282i | \(0.107144\pi\) | ||||
−0.943882 | + | 0.330282i | \(0.892856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −658.413 | −1.28848 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 53.2577 | + | 53.2577i | 0.103816 | + | 0.103816i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 159.757 | + | 35.9046i | 0.310208 | + | 0.0697177i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −358.182 | + | 358.182i | −0.692808 | + | 0.692808i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 417.959i | − | 0.805316i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 252.556 | 0.484753 | 0.242376 | − | 0.970182i | \(-0.422073\pi\) | ||||
0.242376 | + | 0.970182i | \(0.422073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.6867 | − | 33.6867i | −0.0644106 | − | 0.0644106i | 0.674168 | − | 0.738578i | \(-0.264502\pi\) |
−0.738578 | + | 0.674168i | \(0.764502\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −195.192 | + | 412.318i | −0.371794 | + | 0.785367i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 154.747 | − | 154.747i | 0.293637 | − | 0.293637i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 514.939i | − | 0.973419i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −266.227 | −0.501369 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 312.372 | + | 312.372i | 0.586065 | + | 0.586065i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.3326 | − | 112.717i | 0.0473507 | − | 0.210687i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −92.7775 | + | 92.7775i | −0.172770 | + | 0.172770i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1007.18i | 1.86860i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −604.474 | −1.11733 | −0.558664 | − | 0.829394i | \(-0.688686\pi\) | ||||
−0.558664 | + | 0.829394i | \(0.688686\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 342.247 | + | 342.247i | 0.630290 | + | 0.630290i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −426.499 | − | 673.782i | −0.782568 | − | 1.23630i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 615.353 | − | 615.353i | 1.12496 | − | 1.12496i | 0.133975 | − | 0.990985i | \(-0.457226\pi\) |
0.990985 | − | 0.133975i | \(-0.0427742\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 307.485i | − | 0.560081i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −496.413 | −0.900931 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 361.262 | + | 361.262i | 0.653277 | + | 0.653277i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −76.0454 | + | 48.1362i | −0.137019 | + | 0.0867319i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −439.040 | + | 439.040i | −0.788222 | + | 0.788222i | −0.981203 | − | 0.192980i | \(-0.938185\pi\) |
0.192980 | + | 0.981203i | \(0.438185\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 614.847i | 1.09991i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −300.495 | −0.535642 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −52.5765 | − | 52.5765i | −0.0933864 | − | 0.0933864i | 0.658870 | − | 0.752257i | \(-0.271035\pi\) |
−0.752257 | + | 0.658870i | \(0.771035\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 90.0704 | + | 20.2429i | 0.159417 | + | 0.0358281i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −67.0454 | + | 67.0454i | −0.118246 | + | 0.118246i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 680.929i | 1.19671i | 0.801231 | + | 0.598356i | \(0.204179\pi\) | ||||
−0.801231 | + | 0.598356i | \(0.795821\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 254.495 | 0.445700 | 0.222850 | − | 0.974853i | \(-0.428464\pi\) | ||||
0.222850 | + | 0.974853i | \(0.428464\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 85.1010 | + | 85.1010i | 0.148518 | + | 0.148518i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −88.2770 | + | 31.5505i | −0.153525 | + | 0.0548705i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −279.999 | + | 279.999i | −0.485267 | + | 0.485267i | −0.906809 | − | 0.421542i | \(-0.861489\pi\) |
0.421542 | + | 0.906809i | \(0.361489\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 131.258i | 0.226697i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1514.35 | −2.60646 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 573.585 | + | 573.585i | 0.983850 | + | 0.983850i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −56.9694 | + | 253.485i | −0.0973836 | + | 0.433307i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 312.347 | − | 312.347i | 0.532108 | − | 0.532108i | −0.389091 | − | 0.921199i | \(-0.627211\pi\) |
0.921199 | + | 0.389091i | \(0.127211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 297.071i | − | 0.504366i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −637.485 | −1.07865 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −424.570 | − | 424.570i | −0.715969 | − | 0.715969i | 0.251808 | − | 0.967777i | \(-0.418975\pi\) |
−0.967777 | + | 0.251808i | \(0.918975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 300.838 | + | 475.262i | 0.505610 | + | 0.798760i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 79.6209 | − | 79.6209i | 0.133368 | − | 0.133368i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 396.536i | 0.661996i | 0.943631 | + | 0.330998i | \(0.107385\pi\) | ||||
−0.943631 | + | 0.330998i | \(0.892615\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 238.908 | 0.397518 | 0.198759 | − | 0.980048i | \(-0.436309\pi\) | ||||
0.198759 | + | 0.980048i | \(0.436309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −74.0908 | − | 74.0908i | −0.122870 | − | 0.122870i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 604.052 | − | 382.361i | 0.998434 | − | 0.632002i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 92.8025 | − | 92.8025i | 0.152887 | − | 0.152887i | −0.626519 | − | 0.779406i | \(-0.715521\pi\) |
0.779406 | + | 0.626519i | \(0.215521\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 624.929i | − | 1.02616i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 540.000 | 0.883797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 301.943 | + | 301.943i | 0.492567 | + | 0.492567i | 0.909114 | − | 0.416547i | \(-0.136760\pi\) |
−0.416547 | + | 0.909114i | \(0.636760\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −215.505 | − | 48.4337i | −0.350415 | − | 0.0787539i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −372.904 | + | 372.904i | −0.604382 | + | 0.604382i | −0.941472 | − | 0.337090i | \(-0.890557\pi\) |
0.337090 | + | 0.941472i | \(0.390557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 815.939i | 1.31816i | 0.752074 | + | 0.659078i | \(0.229053\pi\) | ||||
−0.752074 | + | 0.659078i | \(0.770947\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.4847 | −0.0313763 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1169.34 | − | 1169.34i | −1.87695 | − | 1.87695i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −396.151 | − | 483.414i | −0.633842 | − | 0.773463i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −288.434 | + | 288.434i | −0.460022 | + | 0.460022i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 110.969i | 0.176422i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 550.434 | 0.872320 | 0.436160 | − | 0.899869i | \(-0.356338\pi\) | ||||
0.436160 | + | 0.899869i | \(0.356338\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.7219 | − | 14.7219i | −0.0232574 | − | 0.0232574i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.5505 | − | 51.3939i | 0.0181898 | − | 0.0809352i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 759.217 | − | 759.217i | 1.19186 | − | 1.19186i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 233.939i | 0.366101i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 927.939 | 1.44764 | 0.723821 | − | 0.689988i | \(-0.242384\pi\) | ||||
0.723821 | + | 0.689988i | \(0.242384\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 190.960 | + | 190.960i | 0.296983 | + | 0.296983i | 0.839831 | − | 0.542848i | \(-0.182654\pi\) |
−0.542848 | + | 0.839831i | \(0.682654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −164.424 | − | 259.757i | −0.254922 | − | 0.402724i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −637.146 | + | 637.146i | −0.984770 | + | 0.984770i | −0.999886 | − | 0.0151154i | \(-0.995188\pi\) |
0.0151154 | + | 0.999886i | \(0.495188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1441.84i | − | 2.22163i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 373.980 | 0.574469 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −404.116 | − | 404.116i | −0.618860 | − | 0.618860i | 0.326379 | − | 0.945239i | \(-0.394172\pi\) |
−0.945239 | + | 0.326379i | \(0.894172\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 83.4495 | − | 52.8230i | 0.127404 | − | 0.0806457i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 132.576 | − | 132.576i | 0.201789 | − | 0.201789i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 453.196i | − | 0.687703i | −0.939024 | − | 0.343852i | \(-0.888268\pi\) | ||
0.939024 | − | 0.343852i | \(-0.111732\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 717.546 | 1.08555 | 0.542773 | − | 0.839879i | \(-0.317374\pi\) | ||||
0.542773 | + | 0.839879i | \(0.317374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 226.515 | + | 226.515i | 0.341652 | + | 0.341652i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 744.949 | + | 167.423i | 1.12022 | + | 0.251765i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 90.8082 | − | 90.8082i | 0.136144 | − | 0.136144i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 587.196i | 0.877723i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1665.28 | 2.48179 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −121.413 | − | 121.413i | −0.180406 | − | 0.180406i | 0.611127 | − | 0.791533i | \(-0.290717\pi\) |
−0.791533 | + | 0.611127i | \(0.790717\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −43.7196 | − | 122.326i | −0.0647698 | − | 0.181223i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −671.943 | + | 671.943i | −0.992531 | + | 0.992531i | −0.999972 | − | 0.00744150i | \(-0.997631\pi\) |
0.00744150 | + | 0.999972i | \(0.497631\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 825.464i | − | 1.21571i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.94897 | −0.00726722 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 802.095 | + | 802.095i | 1.17437 | + | 1.17437i | 0.981157 | + | 0.193214i | \(0.0618913\pi\) |
0.193214 | + | 0.981157i | \(0.438109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −157.596 | + | 701.221i | −0.230067 | + | 1.02368i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 349.015 | − | 349.015i | 0.508027 | − | 0.508027i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 864.745i | − | 1.25507i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1146.49 | −1.65918 | −0.829591 | − | 0.558371i | \(-0.811426\pi\) | ||||
−0.829591 | + | 0.558371i | \(0.811426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −363.106 | − | 363.106i | −0.523962 | − | 0.523962i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −64.2362 | − | 101.480i | −0.0924262 | − | 0.146015i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −192.577 | + | 192.577i | −0.276293 | + | 0.276293i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 370.454i | − | 0.529977i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −673.217 | −0.960366 | −0.480183 | − | 0.877168i | \(-0.659430\pi\) | ||||
−0.480183 | + | 0.877168i | \(0.659430\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 106.515 | + | 106.515i | 0.151515 | + | 0.151515i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −228.136 | + | 144.409i | −0.323597 | + | 0.204835i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 340.833 | − | 340.833i | 0.482084 | − | 0.482084i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 955.939i | 1.34829i | 0.738598 | + | 0.674146i | \(0.235488\pi\) | ||||
−0.738598 | + | 0.674146i | \(0.764512\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −145.485 | −0.204620 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 54.3429 | + | 54.3429i | 0.0762172 | + | 0.0762172i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1372.83 | − | 308.536i | −1.92004 | − | 0.431518i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 62.4245 | − | 62.4245i | 0.0870634 | − | 0.0870634i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 89.0306i | − | 0.123826i | −0.998082 | − | 0.0619128i | \(-0.980280\pi\) | ||
0.998082 | − | 0.0619128i | \(-0.0197201\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 345.010 | 0.478516 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.1918 | + | 39.1918i | 0.0542072 | + | 0.0542072i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 773.853 | + | 366.343i | 1.06738 | + | 0.505300i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 332.703 | − | 332.703i | 0.457638 | − | 0.457638i | −0.440242 | − | 0.897879i | \(-0.645107\pi\) |
0.897879 | + | 0.440242i | \(0.145107\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −379.051 | −0.518538 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 229.823 | + | 229.823i | 0.313537 | + | 0.313537i | 0.846278 | − | 0.532741i | \(-0.178838\pi\) |
−0.532741 | + | 0.846278i | \(0.678838\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −117.717 | + | 523.782i | −0.160160 | + | 0.712629i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 401.262 | − | 401.262i | 0.544454 | − | 0.544454i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 923.281i | − | 1.24936i | −0.780879 | − | 0.624682i | \(-0.785228\pi\) | ||
0.780879 | − | 0.624682i | \(-0.214772\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 434.847 | 0.586838 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −585.782 | − | 585.782i | −0.788401 | − | 0.788401i | 0.192831 | − | 0.981232i | \(-0.438233\pi\) |
−0.981232 | + | 0.192831i | \(0.938233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 534.131 | + | 843.817i | 0.716954 | + | 1.13264i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 304.924 | − | 304.924i | 0.408198 | − | 0.408198i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 243.423i | − | 0.324998i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1354.27 | 1.80329 | 0.901645 | − | 0.432477i | \(-0.142361\pi\) | ||||
0.901645 | + | 0.432477i | \(0.142361\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 457.120 | + | 457.120i | 0.607066 | + | 0.607066i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −671.691 | + | 425.176i | −0.889657 | + | 0.563147i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −985.832 | + | 985.832i | −1.30229 | + | 1.30229i | −0.375442 | + | 0.926846i | \(0.622509\pi\) |
−0.926846 | + | 0.375442i | \(0.877491\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 105.526i | − | 0.139032i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 206.495 | 0.271347 | 0.135673 | − | 0.990754i | \(-0.456680\pi\) | ||||
0.135673 | + | 0.990754i | \(0.456680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1188.08 | − | 1188.08i | −1.55712 | − | 1.55712i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −156.272 | − | 35.1214i | −0.204278 | − | 0.0459104i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1086.87 | + | 1086.87i | −1.41704 | + | 1.41704i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 852.969i | 1.10919i | 0.832119 | + | 0.554596i | \(0.187127\pi\) | ||||
−0.832119 | + | 0.554596i | \(0.812873\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 504.929 | 0.654901 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −491.035 | − | 491.035i | −0.635233 | − | 0.635233i | 0.314143 | − | 0.949376i | \(-0.398283\pi\) |
−0.949376 | + | 0.314143i | \(0.898283\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −219.233 | + | 463.101i | −0.282881 | + | 0.597550i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −134.091 | + | 134.091i | −0.172575 | + | 0.172575i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 369.694i | 0.474575i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1266.97 | −1.62224 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 125.833 | + | 125.833i | 0.160706 | + | 0.160706i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −57.9092 | + | 257.666i | −0.0737697 | + | 0.328237i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −958.586 | + | 958.586i | −1.21803 | + | 1.21803i | −0.249702 | + | 0.968323i | \(0.580333\pi\) |
−0.968323 | + | 0.249702i | \(0.919667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 516.434i | − | 0.654542i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 194.515 | 0.245911 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1255.30 | − | 1255.30i | −1.58298 | − | 1.58298i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 231.253 | + | 365.333i | 0.290884 | + | 0.459538i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 169.065 | − | 169.065i | 0.212126 | − | 0.212126i | −0.593044 | − | 0.805170i | \(-0.702074\pi\) |
0.805170 | + | 0.593044i | \(0.202074\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 332.908i | 0.416656i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 470.908 | 0.587900 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 718.005 | + | 718.005i | 0.894153 | + | 0.894153i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −166.899 | + | 105.646i | −0.207328 | + | 0.131237i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −251.388 | + | 251.388i | −0.311510 | + | 0.311510i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 126.082i | 0.155849i | 0.996959 | + | 0.0779244i | \(0.0248293\pi\) | ||||
−0.996959 | + | 0.0779244i | \(0.975171\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.9286 | 0.0406024 | 0.0203012 | − | 0.999794i | \(-0.493537\pi\) | ||||
0.0203012 | + | 0.999794i | \(0.493537\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 80.8332 | + | 80.8332i | 0.0994258 | + | 0.0994258i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 62.0204 | + | 13.9388i | 0.0760987 | + | 0.0171028i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −363.837 | + | 363.837i | −0.445333 | + | 0.445333i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 547.423i | 0.668405i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 980.064 | 1.19374 | 0.596872 | − | 0.802337i | \(-0.296410\pi\) | ||||
0.596872 | + | 0.802337i | \(0.296410\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −503.863 | − | 503.863i | −0.612227 | − | 0.612227i | 0.331299 | − | 0.943526i | \(-0.392513\pi\) |
−0.943526 | + | 0.331299i | \(0.892513\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 662.494 | − | 236.778i | 0.803023 | − | 0.287003i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1078.84 | − | 1078.84i | 1.30452 | − | 1.30452i | 0.379208 | − | 0.925311i | \(-0.376196\pi\) |
0.925311 | − | 0.379208i | \(-0.123804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 124.352i | − | 0.150002i | −0.997183 | − | 0.0750012i | \(-0.976104\pi\) | ||
0.997183 | − | 0.0750012i | \(-0.0238961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −362.908 | −0.436713 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 468.055 | + | 468.055i | 0.561890 | + | 0.561890i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 137.001 | − | 609.585i | 0.164073 | − | 0.730042i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −75.3031 | + | 75.3031i | −0.0899678 | + | 0.0899678i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1125.48i | 1.34146i | 0.741702 | + | 0.670730i | \(0.234019\pi\) | ||||
−0.741702 | + | 0.670730i | \(0.765981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −331.888 | −0.394635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −397.348 | − | 397.348i | −0.471350 | − | 0.471350i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 350.325 | + | 553.442i | 0.414585 | + | 0.654960i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1065.12 | − | 1065.12i | 1.25753 | − | 1.25753i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 746.474i | − | 0.879240i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.9694 | −0.0457925 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1039.87 | + | 1039.87i | 1.21908 | + | 1.21908i | 0.967955 | + | 0.251122i | \(0.0807995\pi\) |
0.251122 | + | 0.967955i | \(0.419201\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −183.712 | + | 116.288i | −0.214868 | + | 0.136010i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 620.177 | − | 620.177i | 0.723660 | − | 0.723660i | −0.245688 | − | 0.969349i | \(-0.579014\pi\) |
0.969349 | + | 0.245688i | \(0.0790140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 948.888i | − | 1.10464i | −0.833631 | − | 0.552321i | \(-0.813742\pi\) | ||
0.833631 | − | 0.552321i | \(-0.186258\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −465.403 | −0.540538 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1064.42 | − | 1064.42i | −1.23339 | − | 1.23339i | −0.962652 | − | 0.270740i | \(-0.912732\pi\) |
−0.270740 | − | 0.962652i | \(-0.587268\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1177.18 | + | 264.565i | 1.36090 | + | 0.305856i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 214.305 | − | 214.305i | 0.247180 | − | 0.247180i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 787.918i | − | 0.906695i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −604.949 | −0.694545 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 166.212 | + | 166.212i | 0.190392 | + | 0.190392i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1037.74 | − | 810.752i | −1.18598 | − | 0.926573i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −329.975 | + | 329.975i | −0.376254 | + | 0.376254i | −0.869749 | − | 0.493495i | \(-0.835719\pi\) |
0.493495 | + | 0.869749i | \(0.335719\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 355.546i | 0.404489i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 135.857 | 0.154208 | 0.0771039 | − | 0.997023i | \(-0.475433\pi\) | ||||
0.0771039 | + | 0.997023i | \(0.475433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.8694 | − | 46.8694i | −0.0530797 | − | 0.0530797i | 0.680069 | − | 0.733148i | \(-0.261950\pi\) |
−0.733148 | + | 0.680069i | \(0.761950\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 168.520 | − | 749.828i | 0.190418 | − | 0.847263i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.5097 | + | 43.5097i | −0.0490526 | + | 0.0490526i | −0.731208 | − | 0.682155i | \(-0.761043\pi\) |
0.682155 | + | 0.731208i | \(0.261043\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 110.990i | − | 0.124848i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 146.227 | 0.164116 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 319.546 | + | 319.546i | 0.357834 | + | 0.357834i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −202.580 | − | 320.035i | −0.226346 | − | 0.357581i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −79.5459 | + | 79.5459i | −0.0886800 | + | 0.0886800i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 701.898i | − | 0.780754i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 533.112 | 0.591690 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −458.030 | − | 458.030i | −0.507231 | − | 0.507231i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1180.58 | + | 747.298i | −1.30451 | + | 0.825744i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 638.938 | − | 638.938i | 0.704452 | − | 0.704452i | −0.260911 | − | 0.965363i | \(-0.584023\pi\) |
0.965363 | + | 0.260911i | \(0.0840229\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 137.258i | 0.150999i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 347.546 | 0.381499 | 0.190750 | − | 0.981639i | \(-0.438908\pi\) | ||||
0.190750 | + | 0.981639i | \(0.438908\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1651.41 | + | 1651.41i | 1.80878 | + | 1.80878i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 866.030 | + | 194.636i | 0.946480 | + | 0.212717i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 147.146 | − | 147.146i | 0.160465 | − | 0.160465i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.6684i | − | 0.0301071i | −0.999887 | − | 0.0150535i | \(-0.995208\pi\) | ||
0.999887 | − | 0.0150535i | \(-0.00479187\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −295.423 | −0.320764 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 955.051 | + | 955.051i | 1.03472 | + | 1.03472i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −87.4393 | − | 244.652i | −0.0945290 | − | 0.264488i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −69.4699 | + | 69.4699i | −0.0749406 | + | 0.0749406i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1070.49i | − | 1.15231i | −0.817341 | − | 0.576154i | \(-0.804553\pi\) | ||
0.817341 | − | 0.576154i | \(-0.195447\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 898.536 | 0.965130 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.0704 | + | 22.0704i | 0.0236553 | + | 0.0236553i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 190.211 | − | 846.343i | 0.203434 | − | 0.905180i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 60.5551 | − | 60.5551i | 0.0646266 | − | 0.0646266i | −0.674055 | − | 0.738681i | \(-0.735449\pi\) |
0.738681 | + | 0.674055i | \(0.235449\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 792.620i | 0.844111i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −264.064 | −0.280620 | −0.140310 | − | 0.990108i | \(-0.544810\pi\) | ||||
−0.140310 | + | 0.990108i | \(0.544810\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −67.6276 | − | 67.6276i | −0.0717153 | − | 0.0717153i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −146.394 | − | 231.272i | −0.154914 | − | 0.244733i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −115.455 | + | 115.455i | −0.121917 | + | 0.121917i | −0.765433 | − | 0.643516i | \(-0.777475\pi\) |
0.643516 | + | 0.765433i | \(0.277475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1082.47i | − | 1.14065i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −152.969 | −0.160851 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −378.359 | − | 378.359i | −0.397019 | − | 0.397019i | 0.480162 | − | 0.877180i | \(-0.340578\pi\) |
−0.877180 | + | 0.480162i | \(0.840578\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −293.555 | + | 185.818i | −0.307388 | + | 0.194574i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −681.489 | + | 681.489i | −0.712110 | + | 0.712110i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1514.35i | 1.57909i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −540.959 | −0.562913 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 49.0148 | + | 49.0148i | 0.0508980 | + | 0.0508980i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −369.687 | − | 83.0852i | −0.383095 | − | 0.0860987i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.1964 | + | 52.1964i | −0.0539777 | + | 0.0539777i | −0.733580 | − | 0.679603i | \(-0.762152\pi\) |
0.679603 | + | 0.733580i | \(0.262152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 268.082i | 0.276658i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1545.61 | −1.59177 | −0.795886 | − | 0.605447i | \(-0.792994\pi\) | ||||
−0.795886 | + | 0.605447i | \(0.792994\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −178.940 | − | 178.940i | −0.183905 | − | 0.183905i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −677.878 | − | 320.908i | −0.695259 | − | 0.329137i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −843.206 | + | 843.206i | −0.863056 | + | 0.863056i | −0.991692 | − | 0.128636i | \(-0.958940\pi\) |
0.128636 | + | 0.991692i | \(0.458940\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2550.35i | 2.60506i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 478.454 | 0.487721 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1241.39 | + | 1241.39i | 1.26286 | + | 1.26286i | 0.949703 | + | 0.313153i | \(0.101385\pi\) |
0.313153 | + | 0.949703i | \(0.398615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 403.523 | − | 1795.47i | 0.409668 | − | 1.82282i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −402.272 | + | 402.272i | −0.407571 | + | 0.407571i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 133.112i | − | 0.134593i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 219.816 | 0.221813 | 0.110906 | − | 0.993831i | \(-0.464625\pi\) | ||||
0.110906 | + | 0.993831i | \(0.464625\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −757.398 | − | 757.398i | −0.762738 | − | 0.762738i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 173.853 | + | 274.652i | 0.174726 | + | 0.276032i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 599.571 | − | 599.571i | 0.601375 | − | 0.601375i | −0.339302 | − | 0.940677i | \(-0.610191\pi\) |
0.940677 | + | 0.339302i | \(0.110191\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 54.0000i | − | 0.0540541i |
(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 | 60.3.k.a.13.1 | ✓ | 4 | |
3.2 | odd | 2 | 180.3.l.b.73.1 | 4 | |||
4.3 | odd | 2 | 240.3.bg.d.193.2 | 4 | |||
5.2 | odd | 4 | inner | 60.3.k.a.37.1 | yes | 4 | |
5.3 | odd | 4 | 300.3.k.a.157.2 | 4 | |||
5.4 | even | 2 | 300.3.k.a.193.2 | 4 | |||
8.3 | odd | 2 | 960.3.bg.a.193.1 | 4 | |||
8.5 | even | 2 | 960.3.bg.b.193.2 | 4 | |||
12.11 | even | 2 | 720.3.bh.f.433.1 | 4 | |||
15.2 | even | 4 | 180.3.l.b.37.1 | 4 | |||
15.8 | even | 4 | 900.3.l.b.757.1 | 4 | |||
15.14 | odd | 2 | 900.3.l.b.793.1 | 4 | |||
20.3 | even | 4 | 1200.3.bg.o.1057.1 | 4 | |||
20.7 | even | 4 | 240.3.bg.d.97.2 | 4 | |||
20.19 | odd | 2 | 1200.3.bg.o.193.1 | 4 | |||
40.27 | even | 4 | 960.3.bg.a.577.1 | 4 | |||
40.37 | odd | 4 | 960.3.bg.b.577.2 | 4 | |||
60.47 | odd | 4 | 720.3.bh.f.577.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.k.a.13.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
60.3.k.a.37.1 | yes | 4 | 5.2 | odd | 4 | inner | |
180.3.l.b.37.1 | 4 | 15.2 | even | 4 | |||
180.3.l.b.73.1 | 4 | 3.2 | odd | 2 | |||
240.3.bg.d.97.2 | 4 | 20.7 | even | 4 | |||
240.3.bg.d.193.2 | 4 | 4.3 | odd | 2 | |||
300.3.k.a.157.2 | 4 | 5.3 | odd | 4 | |||
300.3.k.a.193.2 | 4 | 5.4 | even | 2 | |||
720.3.bh.f.433.1 | 4 | 12.11 | even | 2 | |||
720.3.bh.f.577.1 | 4 | 60.47 | odd | 4 | |||
900.3.l.b.757.1 | 4 | 15.8 | even | 4 | |||
900.3.l.b.793.1 | 4 | 15.14 | odd | 2 | |||
960.3.bg.a.193.1 | 4 | 8.3 | odd | 2 | |||
960.3.bg.a.577.1 | 4 | 40.27 | even | 4 | |||
960.3.bg.b.193.2 | 4 | 8.5 | even | 2 | |||
960.3.bg.b.577.2 | 4 | 40.37 | odd | 4 | |||
1200.3.bg.o.193.1 | 4 | 20.19 | odd | 2 | |||
1200.3.bg.o.1057.1 | 4 | 20.3 | even | 4 |