Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(3649,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3800.3649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 760) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3649.2 | ||
Root | \(0.432320 - 0.432320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.3649 |
Dual form | 3800.2.d.k.3649.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(951\) | \(1901\) | \(1977\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.76156i | − 1.01704i | −0.861052 | − | 0.508518i | \(-0.830194\pi\) | ||||
0.861052 | − | 0.508518i | \(-0.169806\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.62620i | − 1.74854i | −0.485441 | − | 0.874269i | \(-0.661341\pi\) | ||||
0.485441 | − | 0.874269i | \(-0.338659\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.103084 | −0.0343612 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.52311 | −1.66528 | −0.832641 | − | 0.553813i | \(-0.813172\pi\) | ||||
−0.832641 | + | 0.553813i | \(0.813172\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.49084i | − 1.52288i | −0.648233 | − | 0.761442i | \(-0.724492\pi\) | ||||
0.648233 | − | 0.761442i | \(-0.275508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.62620i | − 1.60709i | −0.595245 | − | 0.803545i | \(-0.702945\pi\) | ||||
0.595245 | − | 0.803545i | \(-0.297055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.14931 | −1.77833 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 4.14931i | − 0.865191i | −0.901588 | − | 0.432596i | \(-0.857598\pi\) | ||||
0.901588 | − | 0.432596i | \(-0.142402\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.10308i | − 0.982089i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.87859 | 1.46302 | 0.731509 | − | 0.681832i | \(-0.238816\pi\) | ||||
0.731509 | + | 0.681832i | \(0.238816\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25240 | 0.224937 | 0.112468 | − | 0.993655i | \(-0.464124\pi\) | ||||
0.112468 | + | 0.993655i | \(0.464124\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.72928i | 1.69365i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 0.387755i | − 0.0637466i | −0.999492 | − | 0.0318733i | \(-0.989853\pi\) | ||||
0.999492 | − | 0.0318733i | \(-0.0101473\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.67243 | −1.54883 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.77551 | 1.05816 | 0.529078 | − | 0.848573i | \(-0.322538\pi\) | ||||
0.529078 | + | 0.848573i | \(0.322538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9817i | 1.67469i | 0.546675 | + | 0.837345i | \(0.315893\pi\) | ||||
−0.546675 | + | 0.837345i | \(0.684107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.72928i | 0.252242i | 0.992015 | + | 0.126121i | \(0.0402527\pi\) | ||||
−0.992015 | + | 0.126121i | \(0.959747\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.4017 | −2.05739 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.6724 | −1.63447 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.49084i | − 0.204782i | −0.994744 | − | 0.102391i | \(-0.967351\pi\) | ||||
0.994744 | − | 0.102391i | \(-0.0326494\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 1.76156i | − 0.233324i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.626198 | −0.0815240 | −0.0407620 | − | 0.999169i | \(-0.512979\pi\) | ||||
−0.0407620 | + | 0.999169i | \(0.512979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.0462 | 1.92647 | 0.963236 | − | 0.268656i | \(-0.0865796\pi\) | ||||
0.963236 | + | 0.268656i | \(0.0865796\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.476886i | 0.0600819i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.22012i | 0.637739i | 0.947799 | + | 0.318870i | \(0.103303\pi\) | ||||
−0.947799 | + | 0.318870i | \(0.896697\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.30925 | −0.879930 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0462 | −1.31095 | −0.655473 | − | 0.755219i | \(-0.727531\pi\) | ||||
−0.655473 | + | 0.755219i | \(0.727531\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.83237i | 0.565586i | 0.959181 | + | 0.282793i | \(0.0912609\pi\) | ||||
−0.959181 | + | 0.282793i | \(0.908739\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 25.5510i | 2.91181i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.98168 | 0.335465 | 0.167732 | − | 0.985833i | \(-0.446356\pi\) | ||||
0.167732 | + | 0.985833i | \(0.446356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.29862 | −1.03318 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.74760i | 0.301589i | 0.988565 | + | 0.150794i | \(0.0481831\pi\) | ||||
−0.988565 | + | 0.150794i | \(0.951817\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 13.8786i | − 1.48794i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.27072 | −0.452695 | −0.226348 | − | 0.974047i | \(-0.572679\pi\) | ||||
−0.226348 | + | 0.974047i | \(0.572679\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.4017 | −2.66282 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 2.20617i | − 0.228769i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 13.7047i | − 1.39150i | −0.718283 | − | 0.695751i | \(-0.755072\pi\) | ||||
0.718283 | − | 0.695751i | \(-0.244928\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.569343 | 0.0572211 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.04623 | 0.701126 | 0.350563 | − | 0.936539i | \(-0.385990\pi\) | ||||
0.350563 | + | 0.936539i | \(0.385990\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 0.658473i | − 0.0648813i | −0.999474 | − | 0.0324407i | \(-0.989672\pi\) | ||||
0.999474 | − | 0.0324407i | \(-0.0103280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 5.22012i | − 0.504648i | −0.967643 | − | 0.252324i | \(-0.918805\pi\) | ||||
0.967643 | − | 0.252324i | \(-0.0811949\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.8140 | 1.13158 | 0.565790 | − | 0.824549i | \(-0.308571\pi\) | ||||
0.565790 | + | 0.824549i | \(0.308571\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.683053 | −0.0648325 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0891304i | 0.00838468i | 0.999991 | + | 0.00419234i | \(0.00133447\pi\) | ||||
−0.999991 | + | 0.00419234i | \(0.998666\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.566016i | 0.0523282i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −30.6541 | −2.81006 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.5048 | 1.77316 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 11.9354i | − 1.07618i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3694i | 1.18635i | 0.805075 | + | 0.593173i | \(0.202125\pi\) | ||||
−0.805075 | + | 0.593173i | \(0.797875\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.3449 | 1.70322 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.62620i | − 0.401142i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 10.6262i | − 0.907857i | −0.891038 | − | 0.453929i | \(-0.850022\pi\) | ||||
0.891038 | − | 0.453929i | \(-0.149978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.5693 | 1.06612 | 0.533059 | − | 0.846078i | \(-0.321042\pi\) | ||||
0.533059 | + | 0.846078i | \(0.321042\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.04623 | 0.256539 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 30.3265i | 2.53603i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 25.3694i | 2.09244i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.04623 | −0.577250 | −0.288625 | − | 0.957442i | \(-0.593198\pi\) | ||||
−0.288625 | + | 0.957442i | \(0.593198\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.47689 | 0.364324 | 0.182162 | − | 0.983269i | \(-0.441691\pi\) | ||||
0.182162 | + | 0.983269i | \(0.441691\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.683053i | 0.0552216i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.27072i | 0.660075i | 0.943968 | + | 0.330038i | \(0.107061\pi\) | ||||
−0.943968 | + | 0.330038i | \(0.892939\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.62620 | −0.208271 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.1955 | −1.51282 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.5693i | 1.45446i | 0.686392 | + | 0.727232i | \(0.259193\pi\) | ||||
−0.686392 | + | 0.727232i | \(0.740807\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 21.3694i | − 1.65362i | −0.562484 | − | 0.826808i | \(-0.690154\pi\) | ||||
0.562484 | − | 0.826808i | \(-0.309846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.1493 | −1.31918 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.103084 | −0.00788301 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3878i | 0.941824i | 0.882180 | + | 0.470912i | \(0.156075\pi\) | ||||
−0.882180 | + | 0.470912i | \(0.843925\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.10308i | 0.0829128i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.7755 | −0.954886 | −0.477443 | − | 0.878663i | \(-0.658436\pi\) | ||||
−0.477443 | + | 0.878663i | \(0.658436\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 26.5048i | − 1.95929i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 36.5972i | 2.67626i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.6079 | −1.71722 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.1955 | −1.38894 | −0.694470 | − | 0.719521i | \(-0.744361\pi\) | ||||
−0.694470 | + | 0.719521i | \(0.744361\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7047i | 0.986486i | 0.869892 | + | 0.493243i | \(0.164189\pi\) | ||||
−0.869892 | + | 0.493243i | \(0.835811\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2.00000i | − 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.561647 | 0.0398141 | 0.0199071 | − | 0.999802i | \(-0.493663\pi\) | ||||
0.0199071 | + | 0.999802i | \(0.493663\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.19554 | 0.648603 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 36.4479i | − 2.55814i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.427726i | 0.0297290i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.52311 | −0.382042 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6724 | 1.07893 | 0.539467 | − | 0.842007i | \(-0.318626\pi\) | ||||
0.539467 | + | 0.842007i | \(0.318626\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.4586i | 1.33328i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 5.79383i | − 0.393311i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.51249 | 0.575221 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −36.3834 | −2.44741 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 12.0525i | − 0.807094i | −0.914959 | − | 0.403547i | \(-0.867777\pi\) | ||||
0.914959 | − | 0.403547i | \(-0.132223\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.07850i | 0.204327i | 0.994768 | + | 0.102164i | \(0.0325766\pi\) | ||||
−0.994768 | + | 0.102164i | \(0.967423\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.7938 | −1.17585 | −0.587925 | − | 0.808916i | \(-0.700055\pi\) | ||||
−0.587925 | + | 0.808916i | \(0.700055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 45.0096 | 2.96141 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 8.50479i | − 0.557167i | −0.960412 | − | 0.278584i | \(-0.910135\pi\) | ||||
0.960412 | − | 0.278584i | \(-0.0898650\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 5.25240i | − 0.341180i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.6079 | 1.52707 | 0.763533 | − | 0.645768i | \(-0.223463\pi\) | ||||
0.763533 | + | 0.645768i | \(0.223463\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.11078 | 0.586877 | 0.293438 | − | 0.955978i | \(-0.405200\pi\) | ||||
0.293438 | + | 0.955978i | \(0.405200\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.07081i | 0.0686924i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 5.49084i | − 0.349374i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.84006 | 0.306726 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5510 | 0.855333 | 0.427666 | − | 0.903937i | \(-0.359336\pi\) | ||||
0.427666 | + | 0.903937i | \(0.359336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.9171i | 1.44079i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.6585i | 0.664857i | 0.943128 | + | 0.332429i | \(0.107868\pi\) | ||||
−0.943128 | + | 0.332429i | \(0.892132\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.79383 | −0.111463 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.812155 | −0.0502711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.9634i | 1.10767i | 0.832627 | + | 0.553834i | \(0.186836\pi\) | ||||
−0.832627 | + | 0.553834i | \(0.813164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.52311i | 0.460407i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.5510 | −0.948162 | −0.474081 | − | 0.880481i | \(-0.657220\pi\) | ||||
−0.474081 | + | 0.880481i | \(0.657220\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.29093 | 0.503638 | 0.251819 | − | 0.967774i | \(-0.418971\pi\) | ||||
0.251819 | + | 0.967774i | \(0.418971\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 44.7466i | 2.70819i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 28.5693i | − 1.71657i | −0.513177 | − | 0.858283i | \(-0.671532\pi\) | ||||
0.513177 | − | 0.858283i | \(-0.328468\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.129102 | −0.00772911 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.3169 | −1.15235 | −0.576176 | − | 0.817325i | \(-0.695456\pi\) | ||||
−0.576176 | + | 0.817325i | \(0.695456\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 16.2986i | − 0.968853i | −0.874832 | − | 0.484426i | \(-0.839028\pi\) | ||||
0.874832 | − | 0.484426i | \(-0.160972\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 31.3449i | − 1.85023i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −26.9065 | −1.58274 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.1416 | −1.41521 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.3955i | 1.54204i | 0.636812 | + | 0.771019i | \(0.280253\pi\) | ||||
−0.636812 | + | 0.771019i | \(0.719747\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.1849i | 1.63545i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.7832 | −1.31759 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50.8034 | 2.92826 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 12.4123i | − 0.713070i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 30.2095i | − 1.72415i | −0.506783 | − | 0.862073i | \(-0.669166\pi\) | ||||
0.506783 | − | 0.862073i | \(-0.330834\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.15994 | −0.0659866 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.12141 | −0.233703 | −0.116852 | − | 0.993149i | \(-0.537280\pi\) | ||||
−0.116852 | + | 0.993149i | \(0.537280\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1031i | 0.853677i | 0.904328 | + | 0.426838i | \(0.140373\pi\) | ||||
−0.904328 | + | 0.426838i | \(0.859627\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 13.3126i | − 0.747709i | −0.927487 | − | 0.373854i | \(-0.878036\pi\) | ||||
0.927487 | − | 0.373854i | \(-0.121964\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.5144 | −2.43634 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.19554 | −0.513245 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 6.62620i | − 0.368692i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 20.8111i | − 1.15086i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.9248 | 0.930272 | 0.465136 | − | 0.885239i | \(-0.346005\pi\) | ||||
0.465136 | + | 0.885239i | \(0.346005\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0399712i | 0.00219041i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.16327i | 0.0633671i | 0.999498 | + | 0.0316836i | \(0.0100869\pi\) | ||||
−0.999498 | + | 0.0316836i | \(0.989913\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.157008 | 0.00852752 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.91713 | −0.374583 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 34.2418i | 1.84888i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.70138i | 0.198700i | 0.995053 | + | 0.0993501i | \(0.0316764\pi\) | ||||
−0.995053 | + | 0.0993501i | \(0.968324\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.54144 | 0.136040 | 0.0680200 | − | 0.997684i | \(-0.478332\pi\) | ||||
0.0680200 | + | 0.997684i | \(0.478332\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.0202 | −1.49561 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.3738i | 1.13761i | 0.822471 | + | 0.568806i | \(0.192595\pi\) | ||||
−0.822471 | + | 0.568806i | \(0.807405\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 53.9990i | 2.85793i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.42003 | 0.233280 | 0.116640 | − | 0.993174i | \(-0.462788\pi\) | ||||
0.116640 | + | 0.993174i | \(0.462788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 34.3588i | − 1.80337i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.28030i | 0.171230i | 0.996328 | + | 0.0856152i | \(0.0272856\pi\) | ||||
−0.996328 | + | 0.0856152i | \(0.972714\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.698445 | −0.0363596 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.89692 | −0.358070 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.8078i | 0.766718i | 0.923599 | + | 0.383359i | \(0.125233\pi\) | ||||
−0.923599 | + | 0.383359i | \(0.874767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 43.2601i | − 2.22801i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.7370 | 1.01382 | 0.506910 | − | 0.861999i | \(-0.330788\pi\) | ||||
0.506910 | + | 0.861999i | \(0.330788\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.5510 | 1.20656 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.2095i | 0.521681i | 0.965382 | + | 0.260840i | \(0.0839996\pi\) | ||||
−0.965382 | + | 0.260840i | \(0.916000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.13203i | − 0.0575444i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.7110 | −0.543067 | −0.271534 | − | 0.962429i | \(-0.587531\pi\) | ||||
−0.271534 | + | 0.962429i | \(0.587531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.4942 | −1.39044 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.04623i | 0.355435i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.5693i | 1.03235i | 0.856484 | + | 0.516173i | \(0.172644\pi\) | ||||
−0.856484 | + | 0.516173i | \(0.827356\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.14931 | −0.407976 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.9634 | −1.19667 | −0.598336 | − | 0.801245i | \(-0.704171\pi\) | ||||
−0.598336 | + | 0.801245i | \(0.704171\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6.87671i | − 0.342553i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.14162i | 0.106156i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.50479 | 0.222748 | 0.111374 | − | 0.993779i | \(-0.464475\pi\) | ||||
0.111374 | + | 0.993779i | \(0.464475\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.7187 | −0.923323 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.89692i | 0.142548i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 22.1416i | − 1.08428i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.7572 | 1.55144 | 0.775720 | − | 0.631077i | \(-0.217387\pi\) | ||||
0.775720 | + | 0.631077i | \(0.217387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.4296 | −1.04442 | −0.522208 | − | 0.852818i | \(-0.674891\pi\) | ||||
−0.522208 | + | 0.852818i | \(0.674891\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 0.178261i | − 0.00866734i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 69.6068i | − 3.36851i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 53.4219 | 2.57923 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.6831 | −0.514585 | −0.257292 | − | 0.966334i | \(-0.582830\pi\) | ||||
−0.257292 | + | 0.966334i | \(0.582830\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.6864i | 1.18635i | 0.805073 | + | 0.593176i | \(0.202126\pi\) | ||||
−0.805073 | + | 0.593176i | \(0.797874\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4.14931i | − 0.198489i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.9817 | 0.715036 | 0.357518 | − | 0.933906i | \(-0.383623\pi\) | ||||
0.357518 | + | 0.933906i | \(0.383623\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.48458 | 0.0706944 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.54144i | 0.215770i | 0.994163 | + | 0.107885i | \(0.0344079\pi\) | ||||
−0.994163 | + | 0.107885i | \(0.965592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4123i | 0.587083i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0925 | 0.759450 | 0.379725 | − | 0.925099i | \(-0.376019\pi\) | ||||
0.379725 | + | 0.925099i | \(0.376019\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.4219 | −1.76213 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 7.88629i | − 0.370530i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 4.65410i | − 0.217710i | −0.994058 | − | 0.108855i | \(-0.965282\pi\) | ||||
0.994058 | − | 0.108855i | \(-0.0347184\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −33.8140 | −1.57830 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.0096 | 0.885365 | 0.442682 | − | 0.896679i | \(-0.354027\pi\) | ||||
0.442682 | + | 0.896679i | \(0.354027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6339i | 0.494199i | 0.968990 | + | 0.247099i | \(0.0794774\pi\) | ||||
−0.968990 | + | 0.247099i | \(0.920523\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.8805i | 1.52153i | 0.649029 | + | 0.760764i | \(0.275175\pi\) | ||||
−0.649029 | + | 0.760764i | \(0.724825\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.1493 | 1.11511 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.5693 | 0.671320 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 60.6531i | − 2.78883i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.153681i | 0.00703658i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.4402 | −0.568409 | −0.284205 | − | 0.958764i | \(-0.591729\pi\) | ||||
−0.284205 | + | 0.958764i | \(0.591729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.12910 | −0.0970787 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 33.8140i | 1.53859i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.9571i | 1.85594i | 0.372651 | + | 0.927972i | \(0.378449\pi\) | ||||
−0.372651 | + | 0.927972i | \(0.621551\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.7110 | 1.47924 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.3449 | 1.95613 | 0.978063 | − | 0.208310i | \(-0.0667962\pi\) | ||||
0.978063 | + | 0.208310i | \(0.0667962\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 52.2051i | − 2.35120i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 51.1020i | 2.29224i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.4094 | −1.13748 | −0.568741 | − | 0.822517i | \(-0.692569\pi\) | ||||
−0.568741 | + | 0.822517i | \(0.692569\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −37.6435 | −1.68179 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 34.1127i | − 1.52101i | −0.649333 | − | 0.760504i | \(-0.724952\pi\) | ||||
0.649333 | − | 0.760504i | \(-0.275048\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.2095i | 1.34165i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.3632 | 0.991230 | 0.495615 | − | 0.868542i | \(-0.334943\pi\) | ||||
0.495615 | + | 0.868542i | \(0.334943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.3555 | 0.988948 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 5.10308i | − 0.225307i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 9.55102i | − 0.420053i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.8217 | 0.957868 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.29862 | 0.100705 | 0.0503523 | − | 0.998732i | \(-0.483966\pi\) | ||||
0.0503523 | + | 0.998732i | \(0.483966\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 27.3771i | − 1.19712i | −0.801079 | − | 0.598559i | \(-0.795740\pi\) | ||||
0.801079 | − | 0.598559i | \(-0.204260\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 8.29862i | − 0.361494i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.78321 | 0.251444 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0645508 | 0.00280127 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 37.2032i | − 1.61145i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.5048i | 0.971153i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 79.5423 | 3.42613 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.4586 | 0.664616 | 0.332308 | − | 0.943171i | \(-0.392173\pi\) | ||||
0.332308 | + | 0.943171i | \(0.392173\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 38.7543i | − 1.66310i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 13.9754i | − 0.597546i | −0.954324 | − | 0.298773i | \(-0.903423\pi\) | ||||
0.954324 | − | 0.298773i | \(-0.0965773\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.55102 | −0.0661960 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.87859 | 0.335639 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 13.7938i | − 0.586573i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.6618i | 1.29918i | 0.760284 | + | 0.649591i | \(0.225060\pi\) | ||||
−0.760284 | + | 0.649591i | \(0.774940\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 60.2986 | 2.55036 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 64.4681 | 2.72185 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.02458i | 0.0853259i | 0.999090 | + | 0.0426629i | \(0.0135842\pi\) | ||||
−0.999090 | + | 0.0426629i | \(0.986416\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 43.0173i | 1.80656i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.2620 | 1.18480 | 0.592402 | − | 0.805643i | \(-0.298180\pi\) | ||||
0.592402 | + | 0.805643i | \(0.298180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.6464 | 0.445538 | 0.222769 | − | 0.974871i | \(-0.428490\pi\) | ||||
0.222769 | + | 0.974871i | \(0.428490\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.8140i | 1.41260i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 9.30925i | − 0.387549i | −0.981046 | − | 0.193775i | \(-0.937927\pi\) | ||||
0.981046 | − | 0.193775i | \(-0.0620730\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.1416 | 1.00329 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.7110 | 0.527339 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.23407i | 0.341021i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 42.3911i | − 1.74967i | −0.484424 | − | 0.874834i | \(-0.660971\pi\) | ||||
0.484424 | − | 0.874834i | \(-0.339029\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.25240 | 0.0516041 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.52311 | −0.144922 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 28.5048i | − 1.17055i | −0.810834 | − | 0.585276i | \(-0.800986\pi\) | ||||
0.810834 | − | 0.585276i | \(-0.199014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 0.989374i | − 0.0404924i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.6156 | −1.04662 | −0.523312 | − | 0.852141i | \(-0.675304\pi\) | ||||
−0.523312 | + | 0.852141i | \(0.675304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.2803 | −1.19437 | −0.597184 | − | 0.802104i | \(-0.703714\pi\) | ||||
−0.597184 | + | 0.802104i | \(0.703714\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 0.538109i | − 0.0219135i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 20.0525i | − 0.813905i | −0.913449 | − | 0.406953i | \(-0.866591\pi\) | ||||
0.913449 | − | 0.406953i | \(-0.133409\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −64.2051 | −2.60172 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.49521 | 0.384135 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.89881i | 0.319030i | 0.987196 | + | 0.159515i | \(0.0509930\pi\) | ||||
−0.987196 | + | 0.159515i | \(0.949007\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 41.4094i | − 1.66708i | −0.552459 | − | 0.833540i | \(-0.686311\pi\) | ||||
0.552459 | − | 0.833540i | \(-0.313689\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.9450 | −1.08301 | −0.541506 | − | 0.840697i | \(-0.682146\pi\) | ||||
−0.541506 | + | 0.840697i | \(0.682146\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.1743 | −0.849695 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.7572i | 0.791555i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.72928i | 0.388550i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.56934 | −0.102446 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.4865 | −0.616507 | −0.308253 | − | 0.951304i | \(-0.599744\pi\) | ||||
−0.308253 | + | 0.951304i | \(0.599744\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 27.6079i | − 1.09731i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 79.0775i | 3.13316i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.13869 | 0.0450457 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.93545 | 0.392427 | 0.196213 | − | 0.980561i | \(-0.437135\pi\) | ||||
0.196213 | + | 0.980561i | \(0.437135\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.25240i | − 0.207134i | −0.994622 | − | 0.103567i | \(-0.966974\pi\) | ||||
0.994622 | − | 0.103567i | \(-0.0330257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.64452i | 0.0646528i | 0.999477 | + | 0.0323264i | \(0.0102916\pi\) | ||||
−0.999477 | + | 0.0323264i | \(0.989708\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.45856 | 0.135760 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.2062 | −0.400011 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.9450i | 1.21097i | 0.795856 | + | 0.605486i | \(0.207021\pi\) | ||||
−0.795856 | + | 0.605486i | \(0.792979\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 0.498138i | − 0.0194342i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.3372 | −0.675360 | −0.337680 | − | 0.941261i | \(-0.609642\pi\) | ||||
−0.337680 | + | 0.941261i | \(0.609642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.83237 | 0.343539 | 0.171770 | − | 0.985137i | \(-0.445052\pi\) | ||||
0.171770 | + | 0.985137i | \(0.445052\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 64.0914i | 2.48910i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 32.6907i | − 1.26579i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.2311 | −0.820843 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −83.1020 | −3.20812 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 29.6402i | − 1.14254i | −0.820761 | − | 0.571272i | \(-0.806450\pi\) | ||||
0.820761 | − | 0.571272i | \(-0.193550\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.2847i | 0.894903i | 0.894308 | + | 0.447451i | \(0.147668\pi\) | ||||
−0.894308 | + | 0.447451i | \(0.852332\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −63.4007 | −2.43309 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.42296 | 0.207808 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 27.3415i | − 1.04619i | −0.852273 | − | 0.523097i | \(-0.824776\pi\) | ||||
0.852273 | − | 0.523097i | \(-0.175224\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.3449i | 1.19588i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.18596 | −0.311860 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.8313 | 1.47721 | 0.738607 | − | 0.674137i | \(-0.235484\pi\) | ||||
0.738607 | + | 0.674137i | \(0.235484\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2.63389i | − 0.100053i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 44.8959i | − 1.70055i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.9817 | −0.566659 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.5144 | −0.737048 | −0.368524 | − | 0.929618i | \(-0.620137\pi\) | ||||
−0.368524 | + | 0.929618i | \(0.620137\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 0.387755i | − 0.0146245i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 32.5972i | − 1.22595i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.1387 | 0.418322 | 0.209161 | − | 0.977881i | \(-0.432927\pi\) | ||||
0.209161 | + | 0.977881i | \(0.432927\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.307362 | −0.0115270 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 5.19658i | − 0.194614i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 41.5866i | − 1.55308i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.1214 | 0.601227 | 0.300613 | − | 0.953746i | \(-0.402809\pi\) | ||||
0.300613 | + | 0.953746i | \(0.402809\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.04623 | −0.113447 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 16.0492i | − 0.596875i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8.21386i | − 0.304635i | −0.988332 | − | 0.152318i | \(-0.951326\pi\) | ||||
0.988332 | − | 0.152318i | \(-0.0486737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.0096 | −0.963318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 72.7668 | 2.69138 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 28.6743i | − 1.05911i | −0.848276 | − | 0.529555i | \(-0.822359\pi\) | ||||
0.848276 | − | 0.529555i | \(-0.177641\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 28.8313i | − 1.06202i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.7014 | 0.430442 | 0.215221 | − | 0.976565i | \(-0.430953\pi\) | ||||
0.215221 | + | 0.976565i | \(0.430953\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.67243 | −0.355325 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.91087i | − 0.0701030i | −0.999386 | − | 0.0350515i | \(-0.988840\pi\) | ||||
0.999386 | − | 0.0350515i | \(-0.0111595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 0.283233i | − 0.0103630i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.1493 | −0.882397 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.55976 | 0.348841 | 0.174420 | − | 0.984671i | \(-0.444195\pi\) | ||||
0.174420 | + | 0.984671i | \(0.444195\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 23.8709i | − 0.869904i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 33.6435i | − 1.22279i | −0.791324 | − | 0.611397i | \(-0.790608\pi\) | ||||
0.791324 | − | 0.611397i | \(-0.209392\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 40.3698 | 1.46533 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.4113 | −0.812409 | −0.406204 | − | 0.913782i | \(-0.633148\pi\) | ||||
−0.406204 | + | 0.913782i | \(0.633148\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 54.6541i | − 1.97861i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.43835i | 0.124152i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.98937 | −0.179921 | −0.0899607 | − | 0.995945i | \(-0.528674\pi\) | ||||
−0.0899607 | + | 0.995945i | \(0.528674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.7755 | 0.676183 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 16.6508i | − 0.598887i | −0.954114 | − | 0.299443i | \(-0.903199\pi\) | ||||
0.954114 | − | 0.299443i | \(-0.0968010\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.15994i | 0.113362i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.77551 | 0.242758 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 61.0096 | 2.18309 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 40.2051i | − 1.43681i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 43.8453i | − 1.56292i | −0.623958 | − | 0.781458i | \(-0.714476\pi\) | ||||
0.623958 | − | 0.781458i | \(-0.285524\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.6435 | 1.12654 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.412335 | 0.0146609 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 82.6164i | − 2.93380i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.0052i | 1.73585i | 0.496692 | + | 0.867927i | \(0.334548\pi\) | ||||
−0.496692 | + | 0.867927i | \(0.665452\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.4586 | 0.405375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.440241 | 0.0155552 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 26.6897i | − 0.941859i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.3940i | 0.964315i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.19554 | −0.323298 | −0.161649 | − | 0.986848i | \(-0.551681\pi\) | ||||
−0.161649 | + | 0.986848i | \(0.551681\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.9527 | −0.665520 | −0.332760 | − | 0.943011i | \(-0.607980\pi\) | ||||
−0.332760 | + | 0.943011i | \(0.607980\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 14.6049i | − 0.512218i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.9817i | 0.384200i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.61850 | 0.0914979 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.7572 | −1.59694 | −0.798468 | − | 0.602037i | \(-0.794356\pi\) | ||||
−0.798468 | + | 0.602037i | \(0.794356\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.3738i | 0.396466i | 0.980155 | + | 0.198233i | \(0.0635202\pi\) | ||||
−0.980155 | + | 0.198233i | \(0.936480\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 11.8386i | − 0.411669i | −0.978587 | − | 0.205835i | \(-0.934009\pi\) | ||||
0.978587 | − | 0.205835i | \(-0.0659909\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.9894 | 0.937380 | 0.468690 | − | 0.883363i | \(-0.344726\pi\) | ||||
0.468690 | + | 0.883363i | \(0.344726\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.3265 | −1.74581 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 95.4286i | 3.30640i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6.39108i | − 0.220908i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.81215 | −0.0970864 | −0.0485432 | − | 0.998821i | \(-0.515458\pi\) | ||||
−0.0485432 | + | 0.998821i | \(0.515458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.0722 | 1.14042 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.0279i | 1.17198i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 90.2330i | − 3.10044i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.7110 | −0.985358 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.60892 | −0.0551530 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.6068i | 1.35611i | 0.735010 | + | 0.678056i | \(0.237177\pi\) | ||||
−0.735010 | + | 0.678056i | \(0.762823\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.8742i | 0.610572i | 0.952261 | + | 0.305286i | \(0.0987520\pi\) | ||||
−0.952261 | + | 0.305286i | \(0.901248\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.12910 | −0.140883 | −0.0704416 | − | 0.997516i | \(-0.522441\pi\) | ||||
−0.0704416 | + | 0.997516i | \(0.522441\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −55.2158 | −1.88175 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 14.7509i | − 0.502128i | −0.967971 | − | 0.251064i | \(-0.919220\pi\) | ||||
0.967971 | − | 0.251064i | \(-0.0807804\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 47.3973i | 1.60970i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.4681 | −0.558644 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.6628 | 0.971203 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.41273i | 0.0478137i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.8357i | 0.568501i | 0.958750 | + | 0.284250i | \(0.0917447\pi\) | ||||
−0.958750 | + | 0.284250i | \(0.908255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 46.4971 | 1.56831 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.4373 | 1.53082 | 0.765411 | − | 0.643542i | \(-0.222536\pi\) | ||||
0.765411 | + | 0.643542i | \(0.222536\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 38.0837i | − 1.28162i | −0.767700 | − | 0.640810i | \(-0.778599\pi\) | ||||
0.767700 | − | 0.640810i | \(-0.221401\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.3049i | 0.715348i | 0.933847 | + | 0.357674i | \(0.116430\pi\) | ||||
−0.933847 | + | 0.357674i | \(0.883570\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 61.8496 | 2.07437 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 51.3574 | 1.72054 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.72928i | 0.0578682i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40.1339i | 1.34003i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.86712 | 0.329087 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.87859 | −0.329104 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 89.4931i | − 2.97814i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.4600i | 0.413728i | 0.978370 | + | 0.206864i | \(0.0663257\pi\) | ||||
−0.978370 | + | 0.206864i | \(0.933674\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.726351 | −0.0240916 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.2803 | 1.16889 | 0.584444 | − | 0.811434i | \(-0.301313\pi\) | ||||
0.584444 | + | 0.811434i | \(0.301313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 15.1753i | − 0.502230i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.5048i | 0.611082i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.392124 | 0.0129350 | 0.00646749 | − | 0.999979i | \(-0.497941\pi\) | ||||
0.00646749 | + | 0.999979i | \(0.497941\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −53.2158 | −1.75352 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 60.6531i | 1.99642i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0678779i | 0.00222940i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.4942 | 0.442729 | 0.221365 | − | 0.975191i | \(-0.428949\pi\) | ||||
0.221365 | + | 0.975191i | \(0.428949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.4017 | −0.471997 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.26009i | 0.237685i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 53.4296i | − 1.74547i | −0.488195 | − | 0.872735i | \(-0.662344\pi\) | ||||
0.488195 | − | 0.872735i | \(-0.337656\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.6049 | 0.868220 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.0568550 | −0.00185342 | −0.000926710 | − | 1.00000i | \(-0.500295\pi\) | ||||
−0.000926710 | 1.00000i | \(0.500295\pi\) | ||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 28.1137i | − 0.915508i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.03664i | 0.0661820i | 0.999452 | + | 0.0330910i | \(0.0105351\pi\) | ||||
−0.999452 | + | 0.0330910i | \(0.989465\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.5337 | 0.861322 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.4509 | −0.760446 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 17.5352i | − 0.568020i | −0.958821 | − | 0.284010i | \(-0.908335\pi\) | ||||
0.958821 | − | 0.284010i | \(-0.0916649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 76.6531i | 2.47784i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49.1589 | −1.58742 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4315 | −0.949403 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.538109i | 0.0173403i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 14.9904i | − 0.482059i | −0.970518 | − | 0.241030i | \(-0.922515\pi\) | ||||
0.970518 | − | 0.241030i | \(-0.0774851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.6724 | −0.374972 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.8805 | −0.670087 | −0.335043 | − | 0.942203i | \(-0.608751\pi\) | ||||
−0.335043 | + | 0.942203i | \(0.608751\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 58.1483i | − 1.86415i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 24.0246i | − 0.768614i | −0.923205 | − | 0.384307i | \(-0.874440\pi\) | ||||
0.923205 | − | 0.384307i | \(-0.125560\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.5877 | 0.753865 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.21784 | −0.0388825 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.9205i | 0.986209i | 0.869970 | + | 0.493105i | \(0.164138\pi\) | ||||
−0.869970 | + | 0.493105i | \(0.835862\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 14.0925i | − 0.448568i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45.5664 | 1.44893 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.56934 | 0.0816179 | 0.0408089 | − | 0.999167i | \(-0.487007\pi\) | ||||
0.0408089 | + | 0.999167i | \(0.487007\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 29.8140i | − 0.946120i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.1878i | 1.11441i | 0.830375 | + | 0.557205i | \(0.188126\pi\) | ||||
−0.830375 | + | 0.557205i | \(0.811874\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.97875 | −0.0626048 |
(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 | 3800.2.d.k.3649.2 | 6 | ||
5.2 | odd | 4 | 3800.2.a.y.1.1 | 3 | |||
5.3 | odd | 4 | 760.2.a.h.1.3 | ✓ | 3 | ||
5.4 | even | 2 | inner | 3800.2.d.k.3649.5 | 6 | ||
15.8 | even | 4 | 6840.2.a.bj.1.1 | 3 | |||
20.3 | even | 4 | 1520.2.a.r.1.1 | 3 | |||
20.7 | even | 4 | 7600.2.a.bo.1.3 | 3 | |||
40.3 | even | 4 | 6080.2.a.bs.1.3 | 3 | |||
40.13 | odd | 4 | 6080.2.a.bw.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.a.h.1.3 | ✓ | 3 | 5.3 | odd | 4 | ||
1520.2.a.r.1.1 | 3 | 20.3 | even | 4 | |||
3800.2.a.y.1.1 | 3 | 5.2 | odd | 4 | |||
3800.2.d.k.3649.2 | 6 | 1.1 | even | 1 | trivial | ||
3800.2.d.k.3649.5 | 6 | 5.4 | even | 2 | inner | ||
6080.2.a.bs.1.3 | 3 | 40.3 | even | 4 | |||
6080.2.a.bw.1.1 | 3 | 40.13 | odd | 4 | |||
6840.2.a.bj.1.1 | 3 | 15.8 | even | 4 | |||
7600.2.a.bo.1.3 | 3 | 20.7 | even | 4 |