Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(1471,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1471");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.m (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.1 | ||
Root | \(-1.63746 + 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1471 |
Dual form | 2352.3.m.h.1471.3 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.27492 | −0.654983 | −0.327492 | − | 0.944854i | \(-0.606203\pi\) | ||||
−0.327492 | + | 0.944854i | \(0.606203\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.6915i | 1.69923i | 0.527407 | + | 0.849613i | \(0.323164\pi\) | ||||
−0.527407 | + | 0.849613i | \(0.676836\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.2749 | −0.790378 | −0.395189 | − | 0.918600i | \(-0.629321\pi\) | ||||
−0.395189 | + | 0.918600i | \(0.629321\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.67232i | 0.378155i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.0997 | 1.47645 | 0.738226 | − | 0.674554i | \(-0.235664\pi\) | ||||
0.738226 | + | 0.674554i | \(0.235664\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.9309i | 1.62794i | 0.580905 | + | 0.813972i | \(0.302699\pi\) | ||||
−0.580905 | + | 0.813972i | \(0.697301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 5.25370i | − 0.228422i | −0.993457 | − | 0.114211i | \(-0.963566\pi\) | ||||
0.993457 | − | 0.114211i | \(-0.0364339\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.2749 | −0.570997 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −42.0241 | −1.44911 | −0.724553 | − | 0.689219i | \(-0.757954\pi\) | ||||
−0.724553 | + | 0.689219i | \(0.757954\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 52.1342i | − 1.68175i | −0.541232 | − | 0.840873i | \(-0.682042\pi\) | ||||
0.541232 | − | 0.840873i | \(-0.317958\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 32.3746 | 0.981048 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 35.9244 | 0.970930 | 0.485465 | − | 0.874256i | \(-0.338650\pi\) | ||||
0.485465 | + | 0.874256i | \(0.338650\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17.7967i | 0.456325i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 38.7492 | 0.945102 | 0.472551 | − | 0.881303i | \(-0.343333\pi\) | ||||
0.472551 | + | 0.881303i | \(0.343333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 31.5380i | − 0.733442i | −0.930331 | − | 0.366721i | \(-0.880480\pi\) | ||||
0.930331 | − | 0.366721i | \(-0.119520\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.82475 | 0.218328 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 24.2487i | − 0.515930i | −0.966154 | − | 0.257965i | \(-0.916948\pi\) | ||||
0.966154 | − | 0.257965i | \(-0.0830519\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 43.4739i | − 0.852429i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −65.6254 | −1.23822 | −0.619108 | − | 0.785306i | \(-0.712506\pi\) | ||||
−0.619108 | + | 0.785306i | \(0.712506\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 61.2130i | − 1.11296i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 53.5739 | 0.939893 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 44.8449i | 0.760083i | 0.924970 | + | 0.380041i | \(0.124090\pi\) | ||||
−0.924970 | + | 0.380041i | \(0.875910\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 63.0997 | 1.03442 | 0.517210 | − | 0.855858i | \(-0.326970\pi\) | ||||
0.517210 | + | 0.855858i | \(0.326970\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 33.6495 | 0.517685 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 22.2131i | − 0.331539i | −0.986165 | − | 0.165770i | \(-0.946989\pi\) | ||||
0.986165 | − | 0.165770i | \(-0.0530108\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.09967 | −0.131879 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 97.5703i | − 1.37423i | −0.726549 | − | 0.687115i | \(-0.758877\pi\) | ||||
0.726549 | − | 0.687115i | \(-0.241123\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −91.7251 | −1.25651 | −0.628254 | − | 0.778008i | \(-0.716230\pi\) | ||||
−0.628254 | + | 0.778008i | \(0.716230\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 24.7249i | 0.329665i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 9.26733i | − 0.117308i | −0.998278 | − | 0.0586540i | \(-0.981319\pi\) | ||||
0.998278 | − | 0.0586540i | \(-0.0186809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 51.1976i | − 0.616839i | −0.951250 | − | 0.308419i | \(-0.900200\pi\) | ||||
0.951250 | − | 0.308419i | \(-0.0998000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −82.1993 | −0.967051 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 72.7879i | 0.836642i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 53.4502 | 0.600564 | 0.300282 | − | 0.953851i | \(-0.402919\pi\) | ||||
0.300282 | + | 0.953851i | \(0.402919\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −90.2990 | −0.970957 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 101.296i | − 1.06628i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −129.522 | −1.33528 | −0.667641 | − | 0.744483i | \(-0.732696\pi\) | ||||
−0.667641 | + | 0.744483i | \(0.732696\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 56.0744i | − 0.566408i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −53.6977 | −0.531660 | −0.265830 | − | 0.964020i | \(-0.585646\pi\) | ||||
−0.265830 | + | 0.964020i | \(0.585646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 32.1134i | − 0.311781i | −0.987774 | − | 0.155890i | \(-0.950175\pi\) | ||||
0.987774 | − | 0.155890i | \(-0.0498247\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 57.2569i | 0.535112i | 0.963542 | + | 0.267556i | \(0.0862160\pi\) | ||||
−0.963542 | + | 0.267556i | \(0.913784\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −141.375 | −1.29701 | −0.648507 | − | 0.761208i | \(-0.724606\pi\) | ||||
−0.648507 | + | 0.761208i | \(0.724606\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 62.2229i | − 0.560567i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −72.1512 | −0.638506 | −0.319253 | − | 0.947670i | \(-0.603432\pi\) | ||||
−0.319253 | + | 0.947670i | \(0.603432\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.2054i | 0.149612i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 30.8248 | 0.263459 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −228.371 | −1.88737 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 67.1155i | − 0.545655i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 128.622 | 1.02898 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 150.887i | 1.18809i | 0.804433 | + | 0.594043i | \(0.202469\pi\) | ||||
−0.804433 | + | 0.594043i | \(0.797531\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −54.6254 | −0.423453 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 140.741i | − 1.07436i | −0.843469 | − | 0.537178i | \(-0.819490\pi\) | ||||
0.843469 | − | 0.537178i | \(-0.180510\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 17.0170i | − 0.126052i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −45.0515 | −0.328843 | −0.164421 | − | 0.986390i | \(-0.552576\pi\) | ||||
−0.164421 | + | 0.986390i | \(0.552576\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 32.2285i | 0.231860i | 0.993257 | + | 0.115930i | \(0.0369848\pi\) | ||||
−0.993257 | + | 0.115930i | \(0.963015\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −42.0000 | −0.297872 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 192.053i | − 1.34303i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 137.625 | 0.949141 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 157.148 | 1.05468 | 0.527342 | − | 0.849653i | \(-0.323189\pi\) | ||||
0.527342 | + | 0.849653i | \(0.323189\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 8.67607i | − 0.0574574i | −0.999587 | − | 0.0287287i | \(-0.990854\pi\) | ||||
0.999587 | − | 0.0287287i | \(-0.00914589\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −75.2990 | −0.492150 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 170.735i | 1.10152i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 110.048 | 0.700944 | 0.350472 | − | 0.936573i | \(-0.386021\pi\) | ||||
0.350472 | + | 0.936573i | \(0.386021\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 113.667i | 0.714884i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 147.627i | 0.905688i | 0.891590 | + | 0.452844i | \(0.149591\pi\) | ||||
−0.891590 | + | 0.452844i | \(0.850409\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −106.024 | −0.642570 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 60.5642i | 0.362660i | 0.983422 | + | 0.181330i | \(0.0580402\pi\) | ||||
−0.983422 | + | 0.181330i | \(0.941960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −63.4261 | −0.375302 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 92.7928i | − 0.542648i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 90.8522 | 0.525157 | 0.262578 | − | 0.964911i | \(-0.415427\pi\) | ||||
0.262578 | + | 0.964911i | \(0.415427\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 77.6736 | 0.438834 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 318.666i | − 1.78026i | −0.455711 | − | 0.890128i | \(-0.650615\pi\) | ||||
0.455711 | − | 0.890128i | \(-0.349385\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −31.6769 | −0.175011 | −0.0875053 | − | 0.996164i | \(-0.527889\pi\) | ||||
−0.0875053 | + | 0.996164i | \(0.527889\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 109.292i | − 0.597223i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −117.650 | −0.635943 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 469.150i | 2.50882i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 241.011i | − 1.26184i | −0.775849 | − | 0.630919i | \(-0.782678\pi\) | ||||
0.775849 | − | 0.630919i | \(-0.217322\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −341.447 | −1.76915 | −0.884577 | − | 0.466394i | \(-0.845553\pi\) | ||||
−0.884577 | + | 0.466394i | \(0.845553\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 58.2826i | − 0.298885i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −142.550 | −0.723603 | −0.361802 | − | 0.932255i | \(-0.617838\pi\) | ||||
−0.361802 | + | 0.932255i | \(0.617838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 5.25370i | − 0.0264005i | −0.999913 | − | 0.0132002i | \(-0.995798\pi\) | ||||
0.999913 | − | 0.0132002i | \(-0.00420189\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −38.4743 | −0.191414 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −126.900 | −0.619026 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.7611i | 0.0761405i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −578.145 | −2.76624 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 271.267i | − 1.28563i | −0.766023 | − | 0.642814i | \(-0.777767\pi\) | ||||
0.766023 | − | 0.642814i | \(-0.222233\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −168.997 | −0.793412 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 103.284i | 0.480392i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 158.873i | 0.725445i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −257.897 | −1.16695 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 76.8907i | 0.344801i | 0.985027 | + | 0.172401i | \(0.0551524\pi\) | ||||
−0.985027 | + | 0.172401i | \(0.944848\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 42.8248 | 0.190332 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 138.292i | − 0.609217i | −0.952478 | − | 0.304608i | \(-0.901474\pi\) | ||||
0.952478 | − | 0.304608i | \(-0.0985256\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −134.371 | −0.586774 | −0.293387 | − | 0.955994i | \(-0.594782\pi\) | ||||
−0.293387 | + | 0.955994i | \(0.594782\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −71.8488 | −0.308364 | −0.154182 | − | 0.988042i | \(-0.549274\pi\) | ||||
−0.154182 | + | 0.988042i | \(0.549274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 79.4125i | 0.337926i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.0515 | −0.0677278 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 331.308i | − 1.38623i | −0.720829 | − | 0.693113i | \(-0.756239\pi\) | ||||
0.720829 | − | 0.693113i | \(-0.243761\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −106.526 | −0.442016 | −0.221008 | − | 0.975272i | \(-0.570935\pi\) | ||||
−0.221008 | + | 0.975272i | \(0.570935\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 317.813i | − 1.28669i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −88.6769 | −0.356132 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 251.100i | − 1.00040i | −0.865910 | − | 0.500199i | \(-0.833260\pi\) | ||||
0.865910 | − | 0.500199i | \(-0.166740\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 98.1993 | 0.388140 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 142.373i | 0.558327i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 406.399 | 1.58132 | 0.790659 | − | 0.612257i | \(-0.209738\pi\) | ||||
0.790659 | + | 0.612257i | \(0.209738\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 126.072 | 0.483036 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 56.4298i | 0.214562i | 0.994229 | + | 0.107281i | \(0.0342144\pi\) | ||||
−0.994229 | + | 0.107281i | \(0.965786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 214.918 | 0.811011 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 92.5784i | − 0.346736i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 136.471 | 0.507327 | 0.253663 | − | 0.967293i | \(-0.418364\pi\) | ||||
0.253663 | + | 0.967293i | \(0.418364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 0.617163i | − 0.00227735i | −0.999999 | − | 0.00113868i | \(-0.999638\pi\) | ||||
0.999999 | − | 0.00113868i | \(-0.000362452\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 266.819i | − 0.970252i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 391.265 | 1.41251 | 0.706254 | − | 0.707958i | \(-0.250383\pi\) | ||||
0.706254 | + | 0.707958i | \(0.250383\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 156.402i | 0.560582i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −534.248 | −1.90124 | −0.950618 | − | 0.310362i | \(-0.899550\pi\) | ||||
−0.950618 | + | 0.310362i | \(0.899550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 64.0442i | 0.226304i | 0.993578 | + | 0.113152i | \(0.0360948\pi\) | ||||
−0.993578 | + | 0.113152i | \(0.963905\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −175.450 | −0.615615 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 340.993 | 1.17991 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 224.339i | 0.770926i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −88.6703 | −0.302629 | −0.151314 | − | 0.988486i | \(-0.548351\pi\) | ||||
−0.151314 | + | 0.988486i | \(0.548351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 146.863i | − 0.497841i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −97.1238 | −0.327016 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 53.9813i | 0.180539i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 93.0071i | 0.306954i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −206.646 | −0.677528 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 147.004i | 0.478841i | 0.970916 | + | 0.239421i | \(0.0769575\pi\) | ||||
−0.970916 | + | 0.239421i | \(0.923043\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −55.6221 | −0.180007 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 184.204i | − 0.592297i | −0.955142 | − | 0.296149i | \(-0.904298\pi\) | ||||
0.955142 | − | 0.296149i | \(-0.0957024\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 223.042 | 0.712593 | 0.356296 | − | 0.934373i | \(-0.384039\pi\) | ||||
0.356296 | + | 0.934373i | \(0.384039\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −620.718 | −1.95810 | −0.979051 | − | 0.203614i | \(-0.934731\pi\) | ||||
−0.979051 | + | 0.203614i | \(0.934731\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 785.492i | − 2.46236i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 99.1719 | 0.308947 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 776.356i | 2.40358i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 146.674 | 0.451303 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 244.868i | 0.748832i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 363.485i | 1.09814i | 0.835776 | + | 0.549071i | \(0.185018\pi\) | ||||
−0.835776 | + | 0.549071i | \(0.814982\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −107.773 | −0.323643 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 72.7461i | 0.217153i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −322.093 | −0.955766 | −0.477883 | − | 0.878424i | \(-0.658596\pi\) | ||||
−0.477883 | + | 0.878424i | \(0.658596\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 124.969i | 0.368642i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 974.464 | 2.85767 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 29.8007 | 0.0863787 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 352.291i | − 1.01525i | −0.861579 | − | 0.507624i | \(-0.830524\pi\) | ||||
0.861579 | − | 0.507624i | \(-0.169476\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −221.395 | −0.634371 | −0.317185 | − | 0.948364i | \(-0.602738\pi\) | ||||
−0.317185 | + | 0.948364i | \(0.602738\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 53.3900i | − 0.152108i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 57.7459 | 0.163586 | 0.0817930 | − | 0.996649i | \(-0.473935\pi\) | ||||
0.0817930 | + | 0.996649i | \(0.473935\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 319.535i | 0.900097i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 280.727i | 0.781971i | 0.920397 | + | 0.390985i | \(0.127866\pi\) | ||||
−0.920397 | + | 0.390985i | \(0.872134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −595.722 | −1.65020 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 395.551i | 1.08967i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 300.392 | 0.822992 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 92.7194i | 0.252641i | 0.991989 | + | 0.126321i | \(0.0403168\pi\) | ||||
−0.991989 | + | 0.126321i | \(0.959683\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −116.248 | −0.315034 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −156.873 | −0.420571 | −0.210285 | − | 0.977640i | \(-0.567439\pi\) | ||||
−0.210285 | + | 0.977640i | \(0.567439\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 222.780i | − 0.594080i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 431.794 | 1.14534 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 466.559i | − 1.23103i | −0.788127 | − | 0.615513i | \(-0.788949\pi\) | ||||
0.788127 | − | 0.615513i | \(-0.211051\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 261.344 | 0.685942 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 496.089i | − 1.29527i | −0.761950 | − | 0.647635i | \(-0.775758\pi\) | ||||
0.761950 | − | 0.647635i | \(-0.224242\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 94.6140i | 0.244481i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 648.296 | 1.66657 | 0.833285 | − | 0.552844i | \(-0.186457\pi\) | ||||
0.833285 | + | 0.552844i | \(0.186457\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 131.866i | − 0.337253i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −243.770 | −0.620280 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.3497i | 0.0768348i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −312.419 | −0.786951 | −0.393475 | − | 0.919335i | \(-0.628727\pi\) | ||||
−0.393475 | + | 0.919335i | \(0.628727\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.0000 | 0.0798005 | 0.0399002 | − | 0.999204i | \(-0.487296\pi\) | ||||
0.0399002 | + | 0.999204i | \(0.487296\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 535.674i | 1.32922i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −29.4743 | −0.0727759 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 671.480i | 1.64983i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −610.739 | −1.49325 | −0.746625 | − | 0.665245i | \(-0.768327\pi\) | ||||
−0.746625 | + | 0.665245i | \(0.768327\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 78.0315i | 0.189858i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 167.668i | 0.404019i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 55.8214 | 0.133864 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 674.432i | − 1.60962i | −0.593530 | − | 0.804812i | \(-0.702266\pi\) | ||||
0.593530 | − | 0.804812i | \(-0.297734\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −97.9792 | −0.232730 | −0.116365 | − | 0.993207i | \(-0.537124\pi\) | ||||
−0.116365 | + | 0.993207i | \(0.537124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 72.7461i | 0.171977i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −358.296 | −0.843049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −332.646 | −0.775399 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 2.45995i | − 0.00570755i | −0.999996 | − | 0.00285377i | \(-0.999092\pi\) | ||||
0.999996 | − | 0.00285377i | \(-0.000908385\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −475.670 | −1.09855 | −0.549273 | − | 0.835643i | \(-0.685095\pi\) | ||||
−0.549273 | + | 0.835643i | \(0.685095\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 238.374i | − 0.547987i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 162.502 | 0.371857 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 137.046i | − 0.312179i | −0.987743 | − | 0.156089i | \(-0.950111\pi\) | ||||
0.987743 | − | 0.156089i | \(-0.0498888\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 161.033i | 0.363506i | 0.983344 | + | 0.181753i | \(0.0581772\pi\) | ||||
−0.983344 | + | 0.181753i | \(0.941823\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −175.045 | −0.393359 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 272.188i | − 0.608922i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 279.643 | 0.622813 | 0.311406 | − | 0.950277i | \(-0.399200\pi\) | ||||
0.311406 | + | 0.950277i | \(0.399200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 724.279i | 1.60594i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.0274 | −0.0331731 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 469.350 | 1.02703 | 0.513513 | − | 0.858082i | \(-0.328344\pi\) | ||||
0.513513 | + | 0.858082i | \(0.328344\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 130.422i | 0.284143i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −234.440 | −0.508547 | −0.254274 | − | 0.967132i | \(-0.581836\pi\) | ||||
−0.254274 | + | 0.967132i | \(0.581836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 515.120i | − 1.11257i | −0.830992 | − | 0.556285i | \(-0.812226\pi\) | ||||
0.830992 | − | 0.556285i | \(-0.187774\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 295.722 | 0.635961 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 140.500i | − 0.300857i | −0.988621 | − | 0.150429i | \(-0.951935\pi\) | ||||
0.988621 | − | 0.150429i | \(-0.0480654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 190.609i | − 0.404690i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 589.492 | 1.24628 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 441.536i | − 0.929550i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 196.876 | 0.412738 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 907.091i | − 1.89372i | −0.321648 | − | 0.946859i | \(-0.604237\pi\) | ||||
0.321648 | − | 0.946859i | \(-0.395763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −369.120 | −0.767402 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 424.175 | 0.874588 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 290.006i | 0.595495i | 0.954645 | + | 0.297748i | \(0.0962354\pi\) | ||||
−0.954645 | + | 0.297748i | \(0.903765\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 255.698 | 0.522899 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 353.412i | 0.719779i | 0.932995 | + | 0.359890i | \(0.117186\pi\) | ||||
−0.932995 | + | 0.359890i | \(0.882814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1054.79 | −2.13953 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 183.639i | 0.370988i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 328.562i | 0.658440i | 0.944253 | + | 0.329220i | \(0.106786\pi\) | ||||
−0.944253 | + | 0.329220i | \(0.893214\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 104.900 | 0.209382 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 791.625i | 1.57381i | 0.617076 | + | 0.786904i | \(0.288317\pi\) | ||||
−0.617076 | + | 0.786904i | \(0.711683\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 175.855 | 0.348229 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 109.857i | 0.216681i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 435.275 | 0.855157 | 0.427579 | − | 0.903978i | \(-0.359367\pi\) | ||||
0.427579 | + | 0.903978i | \(0.359367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −160.722 | −0.313298 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 105.169i | 0.204211i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 453.244 | 0.876681 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 157.361i | − 0.303200i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 258.756 | 0.496652 | 0.248326 | − | 0.968676i | \(-0.420120\pi\) | ||||
0.248326 | + | 0.968676i | \(0.420120\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 934.757i | − 1.78730i | −0.448767 | − | 0.893649i | \(-0.648137\pi\) | ||||
0.448767 | − | 0.893649i | \(-0.351863\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1308.55i | − 2.48302i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 501.399 | 0.947824 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 134.535i | − 0.253361i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −398.145 | −0.746988 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 187.512i | − 0.350489i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −551.945 | −1.02783 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 106.914 | 0.197624 | 0.0988119 | − | 0.995106i | \(-0.468496\pi\) | ||||
0.0988119 | + | 0.995106i | \(0.468496\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 54.8660i | 0.101042i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 462.990 | 0.849523 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 33.5534i | − 0.0613408i | −0.999530 | − | 0.0306704i | \(-0.990236\pi\) | ||||
0.999530 | − | 0.0306704i | \(-0.00976422\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −189.299 | −0.344807 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1299.84i | − 2.35906i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 203.775i | 0.367162i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −969.908 | −1.74131 | −0.870653 | − | 0.491897i | \(-0.836304\pi\) | ||||
−0.870653 | + | 0.491897i | \(0.836304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 324.050i | 0.579696i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 812.591 | 1.44847 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 114.619i | 0.203586i | 0.994806 | + | 0.101793i | \(0.0324579\pi\) | ||||
−0.994806 | + | 0.101793i | \(0.967542\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 236.289 | 0.418211 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 304.550 | 0.535237 | 0.267618 | − | 0.963525i | \(-0.413763\pi\) | ||||
0.267618 | + | 0.963525i | \(0.413763\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 819.417i | 1.43506i | 0.696530 | + | 0.717528i | \(0.254726\pi\) | ||||
−0.696530 | + | 0.717528i | \(0.745274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −417.444 | −0.728523 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 74.9961i | 0.130428i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1035.79 | 1.79513 | 0.897566 | − | 0.440881i | \(-0.145334\pi\) | ||||
0.897566 | + | 0.440881i | \(0.145334\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 591.403i | 1.02142i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1226.64i | − 2.10401i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −100.949 | −0.172562 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 991.224i | − 1.68863i | −0.535850 | − | 0.844313i | \(-0.680009\pi\) | ||||
0.535850 | − | 0.844313i | \(-0.319991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1612.56 | 2.73779 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 246.904i | 0.417773i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −546.736 | −0.921983 | −0.460992 | − | 0.887405i | \(-0.652506\pi\) | ||||
−0.460992 | + | 0.887405i | \(0.652506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.09967 | −0.0152423 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 449.726i | − 0.750795i | −0.926864 | − | 0.375397i | \(-0.877506\pi\) | ||||
0.926864 | − | 0.375397i | \(-0.122494\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 392.106 | 0.652423 | 0.326212 | − | 0.945297i | \(-0.394228\pi\) | ||||
0.326212 | + | 0.945297i | \(0.394228\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 66.6394i | 0.110513i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 747.897 | 1.23619 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 758.684i | 1.24989i | 0.780668 | + | 0.624946i | \(0.214879\pi\) | ||||
−0.780668 | + | 0.624946i | \(0.785121\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 249.154i | 0.407780i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −435.341 | −0.710180 | −0.355090 | − | 0.934832i | \(-0.615550\pi\) | ||||
−0.355090 | + | 0.934832i | \(0.615550\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 219.798i | 0.357395i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −145.189 | −0.235315 | −0.117658 | − | 0.993054i | \(-0.537539\pi\) | ||||
−0.117658 | + | 0.993054i | \(0.537539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 510.839i | − 0.825264i | −0.910898 | − | 0.412632i | \(-0.864610\pi\) | ||||
0.910898 | − | 0.412632i | \(-0.135390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.2990 | 0.0439598 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −64.3538 | −0.102966 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1001.38i | 1.59709i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 901.691 | 1.43353 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 345.666i | 0.547807i | 0.961757 | + | 0.273904i | \(0.0883150\pi\) | ||||
−0.961757 | + | 0.273904i | \(0.911685\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −469.849 | −0.742257 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 494.142i | − 0.778177i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 292.711i | 0.458076i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 904.145 | 1.41052 | 0.705261 | − | 0.708948i | \(-0.250830\pi\) | ||||
0.705261 | + | 0.708948i | \(0.250830\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 265.621i | − 0.413096i | −0.978436 | − | 0.206548i | \(-0.933777\pi\) | ||||
0.978436 | − | 0.206548i | \(-0.0662230\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 178.894 | 0.277355 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 354.271i | − 0.547559i | −0.961793 | − | 0.273779i | \(-0.911726\pi\) | ||||
0.961793 | − | 0.273779i | \(-0.0882738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −838.217 | −1.29155 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 780.966 | 1.19597 | 0.597983 | − | 0.801509i | \(-0.295969\pi\) | ||||
0.597983 | + | 0.801509i | \(0.295969\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 460.914i | 0.703685i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 275.175 | 0.418836 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 309.905i | − 0.470265i | −0.971963 | − | 0.235133i | \(-0.924448\pi\) | ||||
0.971963 | − | 0.235133i | \(-0.0755524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 690.117 | 1.04405 | 0.522025 | − | 0.852930i | \(-0.325177\pi\) | ||||
0.522025 | + | 0.852930i | \(0.325177\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 446.691i | 0.673742i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 220.782i | 0.331007i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 133.179 | 0.199071 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1179.43i | 1.75771i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 714.238 | 1.06127 | 0.530637 | − | 0.847599i | \(-0.321953\pi\) | ||||
0.530637 | + | 0.847599i | \(0.321953\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 74.1746i | − 0.109888i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1178.41 | −1.74063 | −0.870317 | − | 0.492492i | \(-0.836086\pi\) | ||||
−0.870317 | + | 0.492492i | \(0.836086\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −239.529 | −0.351731 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 845.501i | 1.23792i | 0.785421 | + | 0.618961i | \(0.212446\pi\) | ||||
−0.785421 | + | 0.618961i | \(0.787554\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 147.540 | 0.215387 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 232.738i | 0.338774i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 674.296 | 0.978658 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1006.44i | 1.45649i | 0.685316 | + | 0.728245i | \(0.259664\pi\) | ||||
−0.685316 | + | 0.728245i | \(0.740336\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 105.546i | − 0.151864i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 972.591 | 1.39540 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 124.446i | 0.178034i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1047.00 | −1.49358 | −0.746791 | − | 0.665059i | \(-0.768406\pi\) | ||||
−0.746791 | + | 0.665059i | \(0.768406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1111.18i | 1.58062i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 137.547 | 0.195101 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1328.97 | −1.87443 | −0.937215 | − | 0.348753i | \(-0.886605\pi\) | ||||
−0.937215 | + | 0.348753i | \(0.886605\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.8020i | 0.0391027i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −273.897 | −0.384147 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 628.959i | 0.879663i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −573.842 | −0.800338 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1301.17i | − 1.80970i | −0.425732 | − | 0.904849i | \(-0.639984\pi\) | ||||
0.425732 | − | 0.904849i | \(-0.360016\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 184.508i | 0.255198i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 599.890 | 0.827435 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 951.043i | 1.30817i | 0.756419 | + | 0.654087i | \(0.226947\pi\) | ||||
−0.756419 | + | 0.654087i | \(0.773053\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 791.593i | − 1.08289i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −730.625 | −0.996760 | −0.498380 | − | 0.866959i | \(-0.666072\pi\) | ||||
−0.498380 | + | 0.866959i | \(0.666072\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 415.196 | 0.563360 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 227.599i | − 0.307983i | −0.988072 | − | 0.153991i | \(-0.950787\pi\) | ||||
0.988072 | − | 0.153991i | \(-0.0492128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −550.468 | −0.742871 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1129.94i | 1.52078i | 0.649470 | + | 0.760388i | \(0.274991\pi\) | ||||
−0.649470 | + | 0.760388i | \(0.725009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −514.646 | −0.690800 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 153.593i | 0.205613i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 991.605i | 1.32038i | 0.751099 | + | 0.660190i | \(0.229524\pi\) | ||||
−0.751099 | + | 0.660190i | \(0.770476\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −434.918 | −0.577580 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.4134i | 0.0376337i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −373.286 | −0.493112 | −0.246556 | − | 0.969129i | \(-0.579299\pi\) | ||||
−0.246556 | + | 0.969129i | \(0.579299\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 170.086i | − 0.224093i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −226.213 | −0.297257 | −0.148629 | − | 0.988893i | \(-0.547486\pi\) | ||||
−0.148629 | + | 0.988893i | \(0.547486\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 246.598 | 0.322350 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 460.777i | − 0.600753i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −100.836 | −0.131126 | −0.0655628 | − | 0.997848i | \(-0.520884\pi\) | ||||
−0.0655628 | + | 0.997848i | \(0.520884\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 703.903i | − 0.912974i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 71.6079 | 0.0926364 | 0.0463182 | − | 0.998927i | \(-0.485251\pi\) | ||||
0.0463182 | + | 0.998927i | \(0.485251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 744.211i | 0.960272i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1198.55i | 1.53857i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1823.73 | 2.33512 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 218.364i | − 0.278881i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −360.399 | −0.459107 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 484.534i | 0.615672i | 0.951439 | + | 0.307836i | \(0.0996048\pi\) | ||||
−0.951439 | + | 0.307836i | \(0.900395\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 97.7392 | 0.123877 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −648.344 | −0.817584 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 372.249i | − 0.468237i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 189.275 | 0.237484 | 0.118742 | − | 0.992925i | \(-0.462114\pi\) | ||||
0.118742 | + | 0.992925i | \(0.462114\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 608.635i | − 0.761745i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −160.350 | −0.200188 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1714.48i | − 2.13509i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 236.375i | − 0.292905i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1117.95 | 1.38189 | 0.690947 | − | 0.722906i | \(-0.257194\pi\) | ||||
0.690947 | + | 0.722906i | \(0.257194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 706.070i | − 0.870616i | −0.900282 | − | 0.435308i | \(-0.856639\pi\) | ||||
0.900282 | − | 0.435308i | \(-0.143361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.06896 | −0.00131483 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 483.467i | − 0.593211i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 975.499 | 1.19400 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 848.423 | 1.03340 | 0.516701 | − | 0.856166i | \(-0.327160\pi\) | ||||
0.516701 | + | 0.856166i | \(0.327160\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.5938i | 0.0408187i | 0.999792 | + | 0.0204093i | \(0.00649694\pi\) | ||||
−0.999792 | + | 0.0204093i | \(0.993503\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −462.145 | −0.560175 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1246.59i | 1.50737i | 0.657236 | + | 0.753685i | \(0.271725\pi\) | ||||
−0.657236 | + | 0.753685i | \(0.728275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 769.107 | 0.927753 | 0.463876 | − | 0.885900i | \(-0.346458\pi\) | ||||
0.463876 | + | 0.885900i | \(0.346458\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 677.691i | − 0.815512i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 198.343i | − 0.237536i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 270.897 | 0.323652 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 244.162i | − 0.291015i | −0.989357 | − | 0.145508i | \(-0.953519\pi\) | ||||
0.989357 | − | 0.145508i | \(-0.0464815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 925.024 | 1.09991 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 925.344i | 1.09768i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 207.715 | 0.245817 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 110.928 | 0.130657 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 188.736i | − 0.221781i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 594.722 | 0.697212 | 0.348606 | − | 0.937269i | \(-0.386655\pi\) | ||||
0.348606 | + | 0.937269i | \(0.386655\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 303.889i | 0.355425i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −302.344 | −0.352793 | −0.176397 | − | 0.984319i | \(-0.556444\pi\) | ||||
−0.176397 | + | 0.984319i | \(0.556444\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 585.966i | − 0.682148i | −0.940036 | − | 0.341074i | \(-0.889209\pi\) | ||||
0.940036 | − | 0.341074i | \(-0.110791\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 43.5487i | − 0.0504619i | −0.999682 | − | 0.0252310i | \(-0.991968\pi\) | ||||
0.999682 | − | 0.0252310i | \(-0.00803212\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −297.533 | −0.343969 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 590.618i | − 0.681220i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 173.220 | 0.199333 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 228.238i | 0.262041i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 388.567 | 0.445094 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1404.03 | 1.60094 | 0.800472 | − | 0.599370i | \(-0.204582\pi\) | ||||
0.800472 | + | 0.599370i | \(0.204582\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 153.581i | 0.174723i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 507.842 | 0.576438 | 0.288219 | − | 0.957564i | \(-0.406937\pi\) | ||||
0.288219 | + | 0.957564i | \(0.406937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 438.774i | 0.496913i | 0.968643 | + | 0.248457i | \(0.0799233\pi\) | ||||
−0.968643 | + | 0.248457i | \(0.920077\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −254.375 | −0.287429 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 205.616i | − 0.231811i | −0.993260 | − | 0.115905i | \(-0.963023\pi\) | ||||
0.993260 | − | 0.115905i | \(-0.0369770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 168.223i | 0.188803i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 750.035 | 0.839905 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1043.60i | 1.16604i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 93.4983 | 0.104234 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2190.89i | 2.43703i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1647.18 | −1.82816 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 103.739 | 0.114629 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 703.490i | 0.775623i | 0.921739 | + | 0.387812i | \(0.126769\pi\) | ||||
−0.921739 | + | 0.387812i | \(0.873231\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 161.093 | 0.177220 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 372.699i | − 0.409110i | −0.978855 | − | 0.204555i | \(-0.934425\pi\) | ||||
0.978855 | − | 0.204555i | \(-0.0655747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 956.959 | 1.04815 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 357.922i | 0.391171i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 295.584i | 0.321636i | 0.986984 | + | 0.160818i | \(0.0514133\pi\) | ||||
−0.986984 | + | 0.160818i | \(0.948587\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 254.619 | 0.276459 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1002.53i | 1.08616i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −512.818 | −0.554398 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 96.3403i | 0.103927i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1694.58 | 1.82409 | 0.912044 | − | 0.410092i | \(-0.134503\pi\) | ||||
0.912044 | + | 0.410092i | \(0.134503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −319.051 | −0.341963 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1536.43i | − 1.64324i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 246.691 | 0.263278 | 0.131639 | − | 0.991298i | \(-0.457976\pi\) | ||||
0.131639 | + | 0.991298i | \(0.457976\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 386.319i | − 0.411416i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −327.715 | −0.348263 | −0.174131 | − | 0.984722i | \(-0.555712\pi\) | ||||
−0.174131 | + | 0.984722i | \(0.555712\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 203.576i | − 0.215882i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 9.26160i | − 0.00977993i | −0.999988 | − | 0.00488997i | \(-0.998443\pi\) | ||||
0.999988 | − | 0.00488997i | \(-0.00155653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 942.468 | 0.993117 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1075.12i | 1.13051i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1300.02 | 1.36414 | 0.682068 | − | 0.731289i | \(-0.261081\pi\) | ||||
0.682068 | + | 0.731289i | \(0.261081\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 789.292i | 0.826483i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1360.51 | −1.42164 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1756.97 | −1.82827 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 171.771i | − 0.178371i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1118.21 | 1.15877 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 669.581i | − 0.692432i | −0.938155 | − | 0.346216i | \(-0.887466\pi\) | ||||
0.938155 | − | 0.346216i | \(-0.112534\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1344.69 | 1.38771 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1245.39i | 1.28258i | 0.767297 | + | 0.641292i | \(0.221601\pi\) | ||||
−0.767297 | + | 0.641292i | \(0.778399\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 254.046i | − 0.260560i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 216.515 | 0.221612 | 0.110806 | − | 0.993842i | \(-0.464657\pi\) | ||||
0.110806 | + | 0.993842i | \(0.464657\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 999.062i | 1.02049i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 424.124 | 0.432338 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 818.489i | 0.832644i | 0.909217 | + | 0.416322i | \(0.136681\pi\) | ||||
−0.909217 | + | 0.416322i | \(0.863319\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 466.839 | 0.473948 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −165.691 | −0.167534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 711.643i | − 0.718106i | −0.933317 | − | 0.359053i | \(-0.883100\pi\) | ||||
0.933317 | − | 0.359053i | \(-0.116900\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 629.574 | 0.634012 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.2054i | 0.0172919i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1089.16 | −1.09243 | −0.546216 | − | 0.837644i | \(-0.683932\pi\) | ||||
−0.546216 | + | 0.837644i | \(0.683932\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 186.669i | 0.186856i |
(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 | 2352.3.m.h.1471.1 | 4 | ||
4.3 | odd | 2 | inner | 2352.3.m.h.1471.3 | 4 | ||
7.3 | odd | 6 | 336.3.be.b.79.1 | yes | 4 | ||
7.5 | odd | 6 | 336.3.be.a.319.1 | yes | 4 | ||
7.6 | odd | 2 | 2352.3.m.g.1471.4 | 4 | |||
21.5 | even | 6 | 1008.3.cd.g.991.2 | 4 | |||
21.17 | even | 6 | 1008.3.cd.f.415.2 | 4 | |||
28.3 | even | 6 | 336.3.be.a.79.1 | ✓ | 4 | ||
28.19 | even | 6 | 336.3.be.b.319.1 | yes | 4 | ||
28.27 | even | 2 | 2352.3.m.g.1471.2 | 4 | |||
84.47 | odd | 6 | 1008.3.cd.f.991.2 | 4 | |||
84.59 | odd | 6 | 1008.3.cd.g.415.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.3.be.a.79.1 | ✓ | 4 | 28.3 | even | 6 | ||
336.3.be.a.319.1 | yes | 4 | 7.5 | odd | 6 | ||
336.3.be.b.79.1 | yes | 4 | 7.3 | odd | 6 | ||
336.3.be.b.319.1 | yes | 4 | 28.19 | even | 6 | ||
1008.3.cd.f.415.2 | 4 | 21.17 | even | 6 | |||
1008.3.cd.f.991.2 | 4 | 84.47 | odd | 6 | |||
1008.3.cd.g.415.2 | 4 | 84.59 | odd | 6 | |||
1008.3.cd.g.991.2 | 4 | 21.5 | even | 6 | |||
2352.3.m.g.1471.2 | 4 | 28.27 | even | 2 | |||
2352.3.m.g.1471.4 | 4 | 7.6 | odd | 2 | |||
2352.3.m.h.1471.1 | 4 | 1.1 | even | 1 | trivial | ||
2352.3.m.h.1471.3 | 4 | 4.3 | odd | 2 | inner |