Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 16x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.2 | ||
Root | \(-2.03151i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.d.485.3 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.03151i | − 1.01575i | −0.861430 | − | 0.507877i | \(-0.830431\pi\) | ||||
0.861430 | − | 0.507877i | \(-0.169569\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.127017 | −0.0317542 | ||||||||
\(5\) | 0.796921i | 0.159384i | 0.996820 | + | 0.0796921i | \(0.0253937\pi\) | ||||
−0.996820 | + | 0.0796921i | \(0.974606\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.12702 | 0.161002 | 0.0805012 | − | 0.996755i | \(-0.474348\pi\) | ||||
0.0805012 | + | 0.996755i | \(0.474348\pi\) | |||||||
\(8\) | − 7.86799i | − 0.983499i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.61895 | 0.161895 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.25403 | 0.711849 | 0.355924 | − | 0.934515i | \(-0.384166\pi\) | ||||
0.355924 | + | 0.934515i | \(0.384166\pi\) | |||||||
\(14\) | − 2.28954i | − 0.163539i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.4919 | −1.03075 | ||||||||
\(17\) | − 11.7514i | − 0.691257i | −0.938371 | − | 0.345629i | \(-0.887666\pi\) | ||||
0.938371 | − | 0.345629i | \(-0.112334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.2379 | 0.907258 | 0.453629 | − | 0.891191i | \(-0.350129\pi\) | ||||
0.453629 | + | 0.891191i | \(0.350129\pi\) | |||||||
\(20\) | − 0.101222i | − 0.00506111i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 5.11797i | − 0.222520i | −0.993791 | − | 0.111260i | \(-0.964511\pi\) | ||||
0.993791 | − | 0.111260i | \(-0.0354887\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.3649 | 0.974597 | ||||||||
\(26\) | − 18.7996i | − 0.723062i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.143150 | −0.00511250 | ||||||||
\(29\) | 29.0812i | 1.00280i | 0.865216 | + | 0.501400i | \(0.167181\pi\) | ||||
−0.865216 | + | 0.501400i | \(0.832819\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −52.7298 | −1.70096 | −0.850481 | − | 0.526005i | \(-0.823689\pi\) | ||||
−0.850481 | + | 0.526005i | \(0.823689\pi\) | |||||||
\(32\) | 2.03151i | 0.0634846i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −23.8730 | −0.702147 | ||||||||
\(35\) | 0.898143i | 0.0256612i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 37.3649 | 1.00986 | 0.504931 | − | 0.863160i | \(-0.331518\pi\) | ||||
0.504931 | + | 0.863160i | \(0.331518\pi\) | |||||||
\(38\) | − 35.0189i | − 0.921550i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.27017 | 0.156754 | ||||||||
\(41\) | − 75.0089i | − 1.82949i | −0.404037 | − | 0.914743i | \(-0.632393\pi\) | ||||
0.404037 | − | 0.914743i | \(-0.367607\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 68.8407 | 1.60095 | 0.800473 | − | 0.599368i | \(-0.204581\pi\) | ||||
0.800473 | + | 0.599368i | \(0.204581\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.3972 | −0.226026 | ||||||||
\(47\) | − 9.36061i | − 0.199162i | −0.995029 | − | 0.0995809i | \(-0.968250\pi\) | ||||
0.995029 | − | 0.0995809i | \(-0.0317502\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −47.7298 | −0.974078 | ||||||||
\(50\) | − 49.4975i | − 0.989949i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.17542 | −0.0226042 | ||||||||
\(53\) | 34.0195i | 0.641878i | 0.947100 | + | 0.320939i | \(0.103998\pi\) | ||||
−0.947100 | + | 0.320939i | \(0.896002\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 8.86735i | − 0.158346i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 59.0786 | 1.01860 | ||||||||
\(59\) | − 69.2965i | − 1.17452i | −0.809400 | − | 0.587258i | \(-0.800207\pi\) | ||||
0.809400 | − | 0.587258i | \(-0.199793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24.9839 | −0.409572 | −0.204786 | − | 0.978807i | \(-0.565650\pi\) | ||||
−0.204786 | + | 0.978807i | \(0.565650\pi\) | |||||||
\(62\) | 107.121i | 1.72776i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −61.8407 | −0.966261 | ||||||||
\(65\) | 7.37473i | 0.113457i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.8730 | −0.251836 | −0.125918 | − | 0.992041i | \(-0.540188\pi\) | ||||
−0.125918 | + | 0.992041i | \(0.540188\pi\) | |||||||
\(68\) | 1.49262i | 0.0219503i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.82458 | 0.0260655 | ||||||||
\(71\) | − 77.0632i | − 1.08540i | −0.839927 | − | 0.542699i | \(-0.817403\pi\) | ||||
0.839927 | − | 0.542699i | \(-0.182597\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 55.2379 | 0.756684 | 0.378342 | − | 0.925666i | \(-0.376494\pi\) | ||||
0.378342 | + | 0.925666i | \(0.376494\pi\) | |||||||
\(74\) | − 75.9071i | − 1.02577i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.18950 | −0.0288092 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 64.9839 | 0.822581 | 0.411290 | − | 0.911504i | \(-0.365078\pi\) | ||||
0.411290 | + | 0.911504i | \(0.365078\pi\) | |||||||
\(80\) | − 13.1428i | − 0.164285i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −152.381 | −1.85831 | ||||||||
\(83\) | − 120.342i | − 1.44991i | −0.688799 | − | 0.724953i | \(-0.741862\pi\) | ||||
0.688799 | − | 0.724953i | \(-0.258138\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.36492 | 0.110175 | ||||||||
\(86\) | − 139.850i | − 1.62617i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 110.926i | − 1.24636i | −0.782079 | − | 0.623179i | \(-0.785841\pi\) | ||||
0.782079 | − | 0.623179i | \(-0.214159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4294 | 0.114609 | ||||||||
\(92\) | 0.650067i | 0.00706595i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −19.0161 | −0.202299 | ||||||||
\(95\) | 13.7372i | 0.144603i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0948 | −0.145307 | −0.0726534 | − | 0.997357i | \(-0.523147\pi\) | ||||
−0.0726534 | + | 0.997357i | \(0.523147\pi\) | |||||||
\(98\) | 96.9634i | 0.989423i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.09475 | −0.0309475 | ||||||||
\(101\) | − 25.1194i | − 0.248707i | −0.992238 | − | 0.124353i | \(-0.960314\pi\) | ||||
0.992238 | − | 0.124353i | \(-0.0396857\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −56.3649 | −0.547232 | −0.273616 | − | 0.961839i | \(-0.588220\pi\) | ||||
−0.273616 | + | 0.961839i | \(0.588220\pi\) | |||||||
\(104\) | − 72.8106i | − 0.700102i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 69.1109 | 0.651989 | ||||||||
\(107\) | − 80.7670i | − 0.754832i | −0.926044 | − | 0.377416i | \(-0.876813\pi\) | ||||
0.926044 | − | 0.377416i | \(-0.123187\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 105.698 | 0.969702 | 0.484851 | − | 0.874597i | \(-0.338874\pi\) | ||||
0.484851 | + | 0.874597i | \(0.338874\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −18.5867 | −0.165953 | ||||||||
\(113\) | 182.444i | 1.61454i | 0.590179 | + | 0.807272i | \(0.299057\pi\) | ||||
−0.590179 | + | 0.807272i | \(0.700943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.07862 | 0.0354662 | ||||||||
\(116\) | − 3.69380i | − 0.0318431i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −140.776 | −1.19302 | ||||||||
\(119\) | − 13.2440i | − 0.111294i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 50.7549i | 0.416024i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.69757 | 0.0540126 | ||||||||
\(125\) | 39.3399i | 0.314720i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −143.492 | −1.12986 | −0.564929 | − | 0.825140i | \(-0.691096\pi\) | ||||
−0.564929 | + | 0.825140i | \(0.691096\pi\) | |||||||
\(128\) | 133.756i | 1.04497i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 14.9818 | 0.115245 | ||||||||
\(131\) | 69.8125i | 0.532920i | 0.963846 | + | 0.266460i | \(0.0858540\pi\) | ||||
−0.963846 | + | 0.266460i | \(0.914146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.4274 | 0.146071 | ||||||||
\(134\) | 34.2776i | 0.255803i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −92.4597 | −0.679850 | ||||||||
\(137\) | − 227.754i | − 1.66244i | −0.555946 | − | 0.831219i | \(-0.687644\pi\) | ||||
0.555946 | − | 0.831219i | \(-0.312356\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 102.808 | 0.739629 | 0.369815 | − | 0.929106i | \(-0.379421\pi\) | ||||
0.369815 | + | 0.929106i | \(0.379421\pi\) | |||||||
\(140\) | − 0.114079i | 0 0.000814851i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −156.554 | −1.10250 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.1754 | −0.159830 | ||||||||
\(146\) | − 112.216i | − 0.768604i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.74597 | −0.0320673 | ||||||||
\(149\) | − 2.27958i | − 0.0152992i | −0.999971 | − | 0.00764960i | \(-0.997565\pi\) | ||||
0.999971 | − | 0.00764960i | \(-0.00243497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −233.714 | −1.54777 | −0.773886 | − | 0.633324i | \(-0.781690\pi\) | ||||
−0.773886 | + | 0.633324i | \(0.781690\pi\) | |||||||
\(152\) | − 135.628i | − 0.892287i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 42.0215i | − 0.271107i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −170.157 | −1.08380 | −0.541902 | − | 0.840442i | \(-0.682296\pi\) | ||||
−0.541902 | + | 0.840442i | \(0.682296\pi\) | |||||||
\(158\) | − 132.015i | − 0.835539i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.61895 | −0.0101184 | ||||||||
\(161\) | − 5.76804i | − 0.0358263i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 118.333 | 0.725967 | 0.362984 | − | 0.931796i | \(-0.381758\pi\) | ||||
0.362984 | + | 0.931796i | \(0.381758\pi\) | |||||||
\(164\) | 9.52738i | 0.0580938i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −244.476 | −1.47275 | ||||||||
\(167\) | 195.857i | 1.17280i | 0.810023 | + | 0.586399i | \(0.199455\pi\) | ||||
−0.810023 | + | 0.586399i | \(0.800545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −83.3629 | −0.493271 | ||||||||
\(170\) | − 19.0249i | − 0.111911i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.74392 | −0.0508367 | ||||||||
\(173\) | 171.185i | 0.989511i | 0.869032 | + | 0.494755i | \(0.164742\pi\) | ||||
−0.869032 | + | 0.494755i | \(0.835258\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27.4597 | 0.156912 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −225.347 | −1.26599 | ||||||||
\(179\) | 215.228i | 1.20239i | 0.799101 | + | 0.601197i | \(0.205309\pi\) | ||||
−0.799101 | + | 0.601197i | \(0.794691\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 237.730 | 1.31342 | 0.656712 | − | 0.754141i | \(-0.271947\pi\) | ||||
0.656712 | + | 0.754141i | \(0.271947\pi\) | |||||||
\(182\) | − 21.1875i | − 0.116415i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −40.2681 | −0.218848 | ||||||||
\(185\) | 29.7769i | 0.160956i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.18895i | 0.00632422i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 27.9073 | 0.146881 | ||||||||
\(191\) | 337.929i | 1.76926i | 0.466294 | + | 0.884630i | \(0.345589\pi\) | ||||
−0.466294 | + | 0.884630i | \(0.654411\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −252.903 | −1.31038 | −0.655190 | − | 0.755464i | \(-0.727411\pi\) | ||||
−0.655190 | + | 0.755464i | \(0.727411\pi\) | |||||||
\(194\) | 28.6336i | 0.147596i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.06248 | 0.0309310 | ||||||||
\(197\) | 94.1578i | 0.477959i | 0.971025 | + | 0.238979i | \(0.0768128\pi\) | ||||
−0.971025 | + | 0.238979i | \(0.923187\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 179.571 | 0.902365 | 0.451182 | − | 0.892432i | \(-0.351002\pi\) | ||||
0.451182 | + | 0.892432i | \(0.351002\pi\) | |||||||
\(200\) | − 191.703i | − 0.958514i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −51.0302 | −0.252625 | ||||||||
\(203\) | 32.7750i | 0.161453i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 59.7762 | 0.291591 | ||||||||
\(206\) | 114.506i | 0.555853i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −152.617 | −0.733735 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 200.175 | 0.948699 | 0.474349 | − | 0.880337i | \(-0.342683\pi\) | ||||
0.474349 | + | 0.880337i | \(0.342683\pi\) | |||||||
\(212\) | − 4.32105i | − 0.0203823i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −164.079 | −0.766723 | ||||||||
\(215\) | 54.8606i | 0.255166i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −59.4274 | −0.273859 | ||||||||
\(218\) | − 214.725i | − 0.984978i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 108.748i | − 0.492071i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −182.984 | −0.820555 | −0.410278 | − | 0.911961i | \(-0.634568\pi\) | ||||
−0.410278 | + | 0.911961i | \(0.634568\pi\) | |||||||
\(224\) | 2.28954i | 0.0102212i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 370.635 | 1.63998 | ||||||||
\(227\) | − 321.608i | − 1.41678i | −0.705823 | − | 0.708388i | \(-0.749423\pi\) | ||||
0.705823 | − | 0.708388i | \(-0.250577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 201.000 | 0.877729 | 0.438865 | − | 0.898553i | \(-0.355381\pi\) | ||||
0.438865 | + | 0.898553i | \(0.355381\pi\) | |||||||
\(230\) | − 8.28573i | − 0.0360249i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 228.810 | 0.986252 | ||||||||
\(233\) | 39.3399i | 0.168841i | 0.996430 | + | 0.0844205i | \(0.0269039\pi\) | ||||
−0.996430 | + | 0.0844205i | \(0.973096\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.45967 | 0.0317433 | ||||||||
\(236\) | 8.80181i | 0.0372958i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −26.9052 | −0.113047 | ||||||||
\(239\) | − 23.7707i | − 0.0994592i | −0.998763 | − | 0.0497296i | \(-0.984164\pi\) | ||||
0.998763 | − | 0.0497296i | \(-0.0158359\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 166.952 | 0.692745 | 0.346373 | − | 0.938097i | \(-0.387413\pi\) | ||||
0.346373 | + | 0.938097i | \(0.387413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.17337 | 0.0130056 | ||||||||
\(245\) | − 38.0369i | − 0.155253i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 159.520 | 0.645830 | ||||||||
\(248\) | 414.878i | 1.67289i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 79.9193 | 0.319677 | ||||||||
\(251\) | 247.487i | 0.986005i | 0.870028 | + | 0.493003i | \(0.164101\pi\) | ||||
−0.870028 | + | 0.493003i | \(0.835899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 291.505i | 1.14766i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 24.3629 | 0.0951675 | ||||||||
\(257\) | − 69.1040i | − 0.268887i | −0.990921 | − | 0.134444i | \(-0.957075\pi\) | ||||
0.990921 | − | 0.134444i | \(-0.0429247\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 42.1109 | 0.162590 | ||||||||
\(260\) | − 0.936714i | − 0.00360275i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 141.825 | 0.541315 | ||||||||
\(263\) | − 162.520i | − 0.617949i | −0.951070 | − | 0.308974i | \(-0.900014\pi\) | ||||
0.951070 | − | 0.308974i | \(-0.0999857\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.1109 | −0.102305 | ||||||||
\(266\) | − 39.4669i | − 0.148372i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.14315 | 0.00799683 | ||||||||
\(269\) | 445.060i | 1.65450i | 0.561837 | + | 0.827248i | \(0.310095\pi\) | ||||
−0.561837 | + | 0.827248i | \(0.689905\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −177.317 | −0.654304 | −0.327152 | − | 0.944972i | \(-0.606089\pi\) | ||||
−0.327152 | + | 0.944972i | \(0.606089\pi\) | |||||||
\(272\) | 193.803i | 0.712510i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −462.683 | −1.68863 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 51.9193 | 0.187434 | 0.0937172 | − | 0.995599i | \(-0.470125\pi\) | ||||
0.0937172 | + | 0.995599i | \(0.470125\pi\) | |||||||
\(278\) | − 208.856i | − 0.751281i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.06658 | 0.0252378 | ||||||||
\(281\) | − 440.088i | − 1.56615i | −0.621927 | − | 0.783075i | \(-0.713650\pi\) | ||||
0.621927 | − | 0.783075i | \(-0.286350\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 402.490 | 1.42223 | 0.711113 | − | 0.703078i | \(-0.248191\pi\) | ||||
0.711113 | + | 0.703078i | \(0.248191\pi\) | |||||||
\(284\) | 9.78831i | 0.0344659i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 84.5363i | − 0.294552i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 150.905 | 0.522163 | ||||||||
\(290\) | 47.0810i | 0.162348i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.01613 | −0.0240279 | ||||||||
\(293\) | − 137.303i | − 0.468610i | −0.972163 | − | 0.234305i | \(-0.924719\pi\) | ||||
0.972163 | − | 0.234305i | \(-0.0752814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 55.2238 | 0.187199 | ||||||||
\(296\) | − 293.987i | − 0.993198i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.63098 | −0.0155402 | ||||||||
\(299\) | − 47.3618i | − 0.158401i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 77.5846 | 0.257756 | ||||||||
\(302\) | 474.791i | 1.57215i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −284.286 | −0.935152 | ||||||||
\(305\) | − 19.9102i | − 0.0652792i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 359.413 | 1.17073 | 0.585364 | − | 0.810771i | \(-0.300952\pi\) | ||||
0.585364 | + | 0.810771i | \(0.300952\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −85.3670 | −0.275377 | ||||||||
\(311\) | − 29.2965i | − 0.0942009i | −0.998890 | − | 0.0471005i | \(-0.985002\pi\) | ||||
0.998890 | − | 0.0471005i | \(-0.0149981\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 274.681 | 0.877576 | 0.438788 | − | 0.898591i | \(-0.355408\pi\) | ||||
0.438788 | + | 0.898591i | \(0.355408\pi\) | |||||||
\(314\) | 345.675i | 1.10088i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.25403 | −0.0261204 | ||||||||
\(317\) | 585.684i | 1.84758i | 0.382895 | + | 0.923792i | \(0.374927\pi\) | ||||
−0.382895 | + | 0.923792i | \(0.625073\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 49.2822i | − 0.154007i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.7178 | −0.0363907 | ||||||||
\(323\) | − 202.569i | − 0.627149i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 225.474 | 0.693765 | ||||||||
\(326\) | − 240.393i | − 0.737403i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −590.169 | −1.79930 | ||||||||
\(329\) | − 10.5496i | − 0.0320655i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −88.3831 | −0.267018 | −0.133509 | − | 0.991048i | \(-0.542625\pi\) | ||||
−0.133509 | + | 0.991048i | \(0.542625\pi\) | |||||||
\(332\) | 15.2855i | 0.0460405i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 397.885 | 1.19127 | ||||||||
\(335\) | − 13.4464i | − 0.0401386i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −335.429 | −0.995340 | −0.497670 | − | 0.867367i | \(-0.665811\pi\) | ||||
−0.497670 | + | 0.867367i | \(0.665811\pi\) | |||||||
\(338\) | 169.352i | 0.501042i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.18950 | −0.00349853 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −109.016 | −0.317831 | ||||||||
\(344\) | − 541.638i | − 1.57453i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 347.764 | 1.00510 | ||||||||
\(347\) | 440.046i | 1.26814i | 0.773274 | + | 0.634072i | \(0.218618\pi\) | ||||
−0.773274 | + | 0.634072i | \(0.781382\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 470.252 | 1.34743 | 0.673713 | − | 0.738993i | \(-0.264698\pi\) | ||||
0.673713 | + | 0.738993i | \(0.264698\pi\) | |||||||
\(350\) | − 55.7845i | − 0.159384i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 459.088i | 1.30053i | 0.759707 | + | 0.650266i | \(0.225342\pi\) | ||||
−0.759707 | + | 0.650266i | \(0.774658\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 61.4133 | 0.172995 | ||||||||
\(356\) | 14.0894i | 0.0395771i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 437.238 | 1.22133 | ||||||||
\(359\) | − 403.162i | − 1.12301i | −0.827472 | − | 0.561507i | \(-0.810222\pi\) | ||||
0.827472 | − | 0.561507i | \(-0.189778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −63.8548 | −0.176883 | ||||||||
\(362\) | − 482.950i | − 1.33411i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.32471 | −0.00363932 | ||||||||
\(365\) | 44.0202i | 0.120603i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 634.458 | 1.72877 | 0.864384 | − | 0.502833i | \(-0.167709\pi\) | ||||
0.864384 | + | 0.502833i | \(0.167709\pi\) | |||||||
\(368\) | 84.4052i | 0.229362i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 60.4919 | 0.163492 | ||||||||
\(371\) | 38.3406i | 0.103344i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 43.3629 | 0.116254 | 0.0581272 | − | 0.998309i | \(-0.481487\pi\) | ||||
0.0581272 | + | 0.998309i | \(0.481487\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −73.6492 | −0.195875 | ||||||||
\(377\) | 269.118i | 0.713842i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −230.458 | −0.608068 | −0.304034 | − | 0.952661i | \(-0.598334\pi\) | ||||
−0.304034 | + | 0.952661i | \(0.598334\pi\) | |||||||
\(380\) | − 1.74486i | − 0.00459173i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 686.504 | 1.79713 | ||||||||
\(383\) | 715.367i | 1.86780i | 0.357536 | + | 0.933899i | \(0.383617\pi\) | ||||
−0.357536 | + | 0.933899i | \(0.616383\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 513.774i | 1.33102i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.79027 | 0.00461409 | ||||||||
\(389\) | 373.539i | 0.960255i | 0.877199 | + | 0.480127i | \(0.159410\pi\) | ||||
−0.877199 | + | 0.480127i | \(0.840590\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −60.1431 | −0.153819 | ||||||||
\(392\) | 375.538i | 0.958005i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 191.282 | 0.485488 | ||||||||
\(395\) | 51.7870i | 0.131106i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 265.429 | 0.668588 | 0.334294 | − | 0.942469i | \(-0.391502\pi\) | ||||
0.334294 | + | 0.942469i | \(0.391502\pi\) | |||||||
\(398\) | − 364.799i | − 0.916580i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −401.825 | −1.00456 | ||||||||
\(401\) | 634.698i | 1.58279i | 0.611306 | + | 0.791394i | \(0.290644\pi\) | ||||
−0.611306 | + | 0.791394i | \(0.709356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −487.964 | −1.21083 | ||||||||
\(404\) | 3.19058i | 0.00789748i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 66.5826 | 0.163997 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 483.014 | 1.18096 | 0.590482 | − | 0.807051i | \(-0.298938\pi\) | ||||
0.590482 | + | 0.807051i | \(0.298938\pi\) | |||||||
\(410\) | − 121.436i | − 0.296185i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.15928 | 0.0173769 | ||||||||
\(413\) | − 78.0983i | − 0.189100i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 95.9032 | 0.231092 | ||||||||
\(416\) | 18.7996i | 0.0451914i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 565.911i | − 1.35062i | −0.737533 | − | 0.675311i | \(-0.764009\pi\) | ||||
0.737533 | − | 0.675311i | \(-0.235991\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 632.871 | 1.50326 | 0.751628 | − | 0.659587i | \(-0.229269\pi\) | ||||
0.751628 | + | 0.659587i | \(0.229269\pi\) | |||||||
\(422\) | − 406.658i | − 0.963644i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 267.665 | 0.631286 | ||||||||
\(425\) | − 286.321i | − 0.673697i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.1572 | −0.0659420 | ||||||||
\(428\) | 10.2588i | 0.0239690i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 111.450 | 0.259185 | ||||||||
\(431\) | 325.762i | 0.755829i | 0.925840 | + | 0.377915i | \(0.123359\pi\) | ||||
−0.925840 | + | 0.377915i | \(0.876641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 242.427 | 0.559879 | 0.279939 | − | 0.960018i | \(-0.409686\pi\) | ||||
0.279939 | + | 0.960018i | \(0.409686\pi\) | |||||||
\(434\) | 120.727i | 0.278173i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.4254 | −0.0307921 | ||||||||
\(437\) | − 88.2230i | − 0.201883i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −43.2702 | −0.0985653 | −0.0492826 | − | 0.998785i | \(-0.515694\pi\) | ||||
−0.0492826 | + | 0.998785i | \(0.515694\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −220.921 | −0.499822 | ||||||||
\(443\) | − 650.758i | − 1.46898i | −0.678620 | − | 0.734490i | \(-0.737422\pi\) | ||||
0.678620 | − | 0.734490i | \(-0.262578\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 88.3992 | 0.198650 | ||||||||
\(446\) | 371.733i | 0.833482i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −69.6955 | −0.155570 | ||||||||
\(449\) | 18.7996i | 0.0418700i | 0.999781 | + | 0.0209350i | \(0.00666430\pi\) | ||||
−0.999781 | + | 0.0209350i | \(0.993336\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 23.1734i | − 0.0512685i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −653.349 | −1.43909 | ||||||||
\(455\) | 8.31145i | 0.0182669i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.4456 | 0.0447387 | 0.0223693 | − | 0.999750i | \(-0.492879\pi\) | ||||
0.0223693 | + | 0.999750i | \(0.492879\pi\) | |||||||
\(458\) | − 408.333i | − 0.891556i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.518052 | −0.00112620 | ||||||||
\(461\) | − 231.268i | − 0.501666i | −0.968030 | − | 0.250833i | \(-0.919295\pi\) | ||||
0.968030 | − | 0.250833i | \(-0.0807045\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −741.663 | −1.60186 | −0.800932 | − | 0.598755i | \(-0.795662\pi\) | ||||
−0.800932 | + | 0.598755i | \(0.795662\pi\) | |||||||
\(464\) | − 479.605i | − 1.03363i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 79.9193 | 0.171501 | ||||||||
\(467\) | 551.632i | 1.18122i | 0.806956 | + | 0.590612i | \(0.201114\pi\) | ||||
−0.806956 | + | 0.590612i | \(0.798886\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.0161 | −0.0405461 | ||||||||
\(470\) | − 15.1544i | − 0.0322433i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −545.224 | −1.15514 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 420.000 | 0.884211 | ||||||||
\(476\) | 1.68221i | 0.00353405i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −48.2904 | −0.101026 | ||||||||
\(479\) | − 659.380i | − 1.37658i | −0.725438 | − | 0.688288i | \(-0.758363\pi\) | ||||
0.725438 | − | 0.688288i | \(-0.241637\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 345.776 | 0.718869 | ||||||||
\(482\) | − 339.163i | − 0.703658i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 11.2324i | − 0.0231596i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.7480 | −0.0220698 | −0.0110349 | − | 0.999939i | \(-0.503513\pi\) | ||||
−0.0110349 | + | 0.999939i | \(0.503513\pi\) | |||||||
\(488\) | 196.573i | 0.402813i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −77.2722 | −0.157698 | ||||||||
\(491\) | 186.899i | 0.380649i | 0.981721 | + | 0.190324i | \(0.0609540\pi\) | ||||
−0.981721 | + | 0.190324i | \(0.939046\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 341.744 | 0.693193 | ||||||||
\(494\) | − 324.066i | − 0.656004i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 869.617 | 1.75326 | ||||||||
\(497\) | − 86.8515i | − 0.174752i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −433.631 | −0.869000 | −0.434500 | − | 0.900672i | \(-0.643075\pi\) | ||||
−0.434500 | + | 0.900672i | \(0.643075\pi\) | |||||||
\(500\) | − 4.99683i | − 0.00999366i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 502.772 | 1.00154 | ||||||||
\(503\) | − 72.8434i | − 0.144818i | −0.997375 | − | 0.0724090i | \(-0.976931\pi\) | ||||
0.997375 | − | 0.0724090i | \(-0.0230687\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0182 | 0.0396400 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.2259 | 0.0358777 | ||||||||
\(509\) | 665.644i | 1.30775i | 0.756603 | + | 0.653874i | \(0.226858\pi\) | ||||
−0.756603 | + | 0.653874i | \(0.773142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 62.2540 | 0.121828 | ||||||||
\(512\) | 485.530i | 0.948301i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −140.385 | −0.273123 | ||||||||
\(515\) | − 44.9184i | − 0.0872202i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 85.5485i | − 0.165152i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 58.0243 | 0.111585 | ||||||||
\(521\) | − 30.7763i | − 0.0590715i | −0.999564 | − | 0.0295358i | \(-0.990597\pi\) | ||||
0.999564 | − | 0.0295358i | \(-0.00940289\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 77.4274 | 0.148045 | 0.0740224 | − | 0.997257i | \(-0.476416\pi\) | ||||
0.0740224 | + | 0.997257i | \(0.476416\pi\) | |||||||
\(524\) | − 8.86735i | − 0.0169224i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −330.161 | −0.627683 | ||||||||
\(527\) | 619.648i | 1.17580i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 502.806 | 0.950485 | ||||||||
\(530\) | 55.0759i | 0.103917i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.46760 | −0.00463835 | ||||||||
\(533\) | − 694.135i | − 1.30232i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 64.3649 | 0.120308 | ||||||||
\(536\) | 132.756i | 0.247680i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 904.141 | 1.68056 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −574.375 | −1.06169 | −0.530846 | − | 0.847469i | \(-0.678126\pi\) | ||||
−0.530846 | + | 0.847469i | \(0.678126\pi\) | |||||||
\(542\) | 360.220i | 0.664612i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 23.8730 | 0.0438842 | ||||||||
\(545\) | 84.2326i | 0.154555i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1018.85 | −1.86262 | −0.931312 | − | 0.364224i | \(-0.881334\pi\) | ||||
−0.931312 | + | 0.364224i | \(0.881334\pi\) | |||||||
\(548\) | 28.9285i | 0.0527893i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 501.299i | 0.909798i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 73.2379 | 0.132437 | ||||||||
\(554\) | − 105.474i | − 0.190387i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.0584 | −0.0234863 | ||||||||
\(557\) | 373.330i | 0.670251i | 0.942174 | + | 0.335125i | \(0.108779\pi\) | ||||
−0.942174 | + | 0.335125i | \(0.891221\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 637.054 | 1.13963 | ||||||||
\(560\) | − 14.8121i | − 0.0264502i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −894.042 | −1.59082 | ||||||||
\(563\) | 1014.70i | 1.80232i | 0.433491 | + | 0.901158i | \(0.357282\pi\) | ||||
−0.433491 | + | 0.901158i | \(0.642718\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −145.393 | −0.257333 | ||||||||
\(566\) | − 817.661i | − 1.44463i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −606.333 | −1.06749 | ||||||||
\(569\) | 580.458i | 1.02014i | 0.860134 | + | 0.510068i | \(0.170380\pi\) | ||||
−0.860134 | + | 0.510068i | \(0.829620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −604.454 | −1.05859 | −0.529294 | − | 0.848439i | \(-0.677543\pi\) | ||||
−0.529294 | + | 0.848439i | \(0.677543\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −171.736 | −0.299192 | ||||||||
\(575\) | − 124.699i | − 0.216868i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.90320 | −0.0154302 | −0.00771508 | − | 0.999970i | \(-0.502456\pi\) | ||||
−0.00771508 | + | 0.999970i | \(0.502456\pi\) | |||||||
\(578\) | − 306.565i | − 0.530389i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.94366 | 0.00507528 | ||||||||
\(581\) | − 135.628i | − 0.233438i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − 434.611i | − 0.744197i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −278.931 | −0.475992 | ||||||||
\(587\) | 680.972i | 1.16009i | 0.814585 | + | 0.580045i | \(0.196965\pi\) | ||||
−0.814585 | + | 0.580045i | \(0.803035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −908.952 | −1.54321 | ||||||||
\(590\) | − 112.188i | − 0.190148i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −616.220 | −1.04091 | ||||||||
\(593\) | 855.518i | 1.44269i | 0.692574 | + | 0.721347i | \(0.256477\pi\) | ||||
−0.692574 | + | 0.721347i | \(0.743523\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.5544 | 0.0177385 | ||||||||
\(596\) | 0.289545i | 0 0.000485814i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −96.2159 | −0.160896 | ||||||||
\(599\) | − 186.251i | − 0.310937i | −0.987841 | − | 0.155469i | \(-0.950311\pi\) | ||||
0.987841 | − | 0.155469i | \(-0.0496887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 362.843 | 0.603732 | 0.301866 | − | 0.953350i | \(-0.402391\pi\) | ||||
0.301866 | + | 0.953350i | \(0.402391\pi\) | |||||||
\(602\) | − 157.614i | − 0.261817i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 29.6855 | 0.0491482 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.0000 | 0.0263591 | 0.0131796 | − | 0.999913i | \(-0.495805\pi\) | ||||
0.0131796 | + | 0.999913i | \(0.495805\pi\) | |||||||
\(608\) | 35.0189i | 0.0575969i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −40.4476 | −0.0663076 | ||||||||
\(611\) | − 86.6234i | − 0.141773i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1161.74 | −1.89517 | −0.947585 | − | 0.319502i | \(-0.896484\pi\) | ||||
−0.947585 | + | 0.319502i | \(0.896484\pi\) | |||||||
\(614\) | − 730.150i | − 1.18917i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 163.905i | 0.265648i | 0.991140 | + | 0.132824i | \(0.0424045\pi\) | ||||
−0.991140 | + | 0.132824i | \(0.957595\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −305.982 | −0.494316 | −0.247158 | − | 0.968975i | \(-0.579497\pi\) | ||||
−0.247158 | + | 0.968975i | \(0.579497\pi\) | |||||||
\(620\) | 5.33743i | 0.00860876i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −59.5160 | −0.0956849 | ||||||||
\(623\) | − 125.015i | − 0.200667i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 577.772 | 0.924435 | ||||||||
\(626\) | − 558.017i | − 0.891401i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.6128 | 0.0344153 | ||||||||
\(629\) | − 439.089i | − 0.698075i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 123.764 | 0.196140 | 0.0980698 | − | 0.995180i | \(-0.468733\pi\) | ||||
0.0980698 | + | 0.995180i | \(0.468733\pi\) | |||||||
\(632\) | − 511.292i | − 0.809007i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1189.82 | 1.87669 | ||||||||
\(635\) | − 114.352i | − 0.180081i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −441.693 | −0.693396 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −106.593 | −0.166551 | ||||||||
\(641\) | 261.417i | 0.407827i | 0.978989 | + | 0.203913i | \(0.0653661\pi\) | ||||
−0.978989 | + | 0.203913i | \(0.934634\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 218.000 | 0.339036 | 0.169518 | − | 0.985527i | \(-0.445779\pi\) | ||||
0.169518 | + | 0.985527i | \(0.445779\pi\) | |||||||
\(644\) | 0.732637i | 0.00113763i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −411.520 | −0.637028 | ||||||||
\(647\) | − 858.262i | − 1.32653i | −0.748387 | − | 0.663263i | \(-0.769171\pi\) | ||||
0.748387 | − | 0.663263i | \(-0.230829\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − 458.051i | − 0.704694i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.0302 | −0.0230525 | ||||||||
\(653\) | − 968.691i | − 1.48345i | −0.670706 | − | 0.741723i | \(-0.734009\pi\) | ||||
0.670706 | − | 0.741723i | \(-0.265991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −55.6351 | −0.0849391 | ||||||||
\(656\) | 1237.04i | 1.88573i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −21.4315 | −0.0325707 | ||||||||
\(659\) | 690.156i | 1.04728i | 0.851940 | + | 0.523639i | \(0.175426\pi\) | ||||
−0.851940 | + | 0.523639i | \(0.824574\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1183.04 | −1.78977 | −0.894885 | − | 0.446297i | \(-0.852743\pi\) | ||||
−0.894885 | + | 0.446297i | \(0.852743\pi\) | |||||||
\(662\) | 179.551i | 0.271225i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −946.851 | −1.42598 | ||||||||
\(665\) | 15.4821i | 0.0232814i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 148.837 | 0.223143 | ||||||||
\(668\) | − 24.8771i | − 0.0372412i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −27.3165 | −0.0407709 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1006.88 | −1.49611 | −0.748056 | − | 0.663636i | \(-0.769012\pi\) | ||||
−0.748056 | + | 0.663636i | \(0.769012\pi\) | |||||||
\(674\) | 681.427i | 1.01102i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.5885 | 0.0156634 | ||||||||
\(677\) | − 907.102i | − 1.33989i | −0.742413 | − | 0.669943i | \(-0.766319\pi\) | ||||
0.742413 | − | 0.669943i | \(-0.233681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.8850 | −0.0233947 | ||||||||
\(680\) | − 73.6831i | − 0.108357i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 687.644i | − 1.00680i | −0.864054 | − | 0.503400i | \(-0.832082\pi\) | ||||
0.864054 | − | 0.503400i | \(-0.167918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 181.502 | 0.264966 | ||||||||
\(686\) | 221.467i | 0.322838i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1135.32 | −1.65017 | ||||||||
\(689\) | 314.818i | 0.456920i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 199.099 | 0.288131 | 0.144066 | − | 0.989568i | \(-0.453982\pi\) | ||||
0.144066 | + | 0.989568i | \(0.453982\pi\) | |||||||
\(692\) | − 21.7434i | − 0.0314211i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 893.955 | 1.28812 | ||||||||
\(695\) | 81.9302i | 0.117885i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −881.458 | −1.26465 | ||||||||
\(698\) | − 955.320i | − 1.36865i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.48784 | −0.00498262 | ||||||||
\(701\) | 81.6124i | 0.116423i | 0.998304 | + | 0.0582114i | \(0.0185398\pi\) | ||||
−0.998304 | + | 0.0582114i | \(0.981460\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 644.093 | 0.916206 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 932.639 | 1.32102 | ||||||||
\(707\) | − 28.3100i | − 0.0400424i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1014.66 | −1.43112 | −0.715558 | − | 0.698553i | \(-0.753827\pi\) | ||||
−0.715558 | + | 0.698553i | \(0.753827\pi\) | |||||||
\(710\) | − 124.762i | − 0.175720i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −872.764 | −1.22579 | ||||||||
\(713\) | 269.870i | 0.378499i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 27.3376i | − 0.0381810i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −819.026 | −1.14070 | ||||||||
\(719\) | 613.361i | 0.853075i | 0.904470 | + | 0.426537i | \(0.140267\pi\) | ||||
−0.904470 | + | 0.426537i | \(0.859733\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −63.5242 | −0.0881057 | ||||||||
\(722\) | 129.721i | 0.179670i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −30.1956 | −0.0417067 | ||||||||
\(725\) | 708.561i | 0.977325i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 169.163 | 0.232687 | 0.116343 | − | 0.993209i | \(-0.462883\pi\) | ||||
0.116343 | + | 0.993209i | \(0.462883\pi\) | |||||||
\(728\) | − 82.0588i | − 0.112718i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 89.4274 | 0.122503 | ||||||||
\(731\) | − 808.973i | − 1.10667i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 165.734 | 0.226104 | 0.113052 | − | 0.993589i | \(-0.463937\pi\) | ||||
0.113052 | + | 0.993589i | \(0.463937\pi\) | |||||||
\(734\) | − 1288.90i | − 1.75600i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.3972 | 0.0141266 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1001.21 | 1.35481 | 0.677406 | − | 0.735610i | \(-0.263104\pi\) | ||||
0.677406 | + | 0.735610i | \(0.263104\pi\) | |||||||
\(740\) | − 3.78216i | − 0.00511103i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 77.8891 | 0.104972 | ||||||||
\(743\) | 110.639i | 0.148909i | 0.997224 | + | 0.0744544i | \(0.0237215\pi\) | ||||
−0.997224 | + | 0.0744544i | \(0.976278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.81665 | 0.00243845 | ||||||||
\(746\) | − 88.0919i | − 0.118086i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 91.0257i | − 0.121530i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −80.0827 | −0.106635 | −0.0533174 | − | 0.998578i | \(-0.516980\pi\) | ||||
−0.0533174 | + | 0.998578i | \(0.516980\pi\) | |||||||
\(752\) | 154.375i | 0.205285i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 546.715 | 0.725087 | ||||||||
\(755\) | − 186.251i | − 0.246691i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 254.464 | 0.336148 | 0.168074 | − | 0.985774i | \(-0.446245\pi\) | ||||
0.168074 | + | 0.985774i | \(0.446245\pi\) | |||||||
\(758\) | 468.176i | 0.617646i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 108.085 | 0.142216 | ||||||||
\(761\) | 280.475i | 0.368561i | 0.982874 | + | 0.184280i | \(0.0589954\pi\) | ||||
−0.982874 | + | 0.184280i | \(0.941005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 119.123 | 0.156124 | ||||||||
\(764\) | − 42.9226i | − 0.0561814i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1453.27 | 1.89722 | ||||||||
\(767\) | − 641.272i | − 0.836078i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −788.423 | −1.02526 | −0.512629 | − | 0.858610i | \(-0.671328\pi\) | ||||
−0.512629 | + | 0.858610i | \(0.671328\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 32.1229 | 0.0416100 | ||||||||
\(773\) | 420.198i | 0.543594i | 0.962355 | + | 0.271797i | \(0.0876179\pi\) | ||||
−0.962355 | + | 0.271797i | \(0.912382\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1284.76 | −1.65775 | ||||||||
\(776\) | 110.897i | 0.142909i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 758.847 | 0.975382 | ||||||||
\(779\) | − 1293.00i | − 1.65982i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 122.181i | 0.156242i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 787.157 | 1.00403 | ||||||||
\(785\) | − 135.602i | − 0.172741i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −246.730 | −0.313507 | −0.156753 | − | 0.987638i | \(-0.550103\pi\) | ||||
−0.156753 | + | 0.987638i | \(0.550103\pi\) | |||||||
\(788\) | − 11.9596i | − 0.0151772i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 105.206 | 0.133172 | ||||||||
\(791\) | 205.617i | 0.259945i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −231.202 | −0.291553 | ||||||||
\(794\) | − 539.222i | − 0.679120i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.8085 | −0.0286538 | ||||||||
\(797\) | − 166.005i | − 0.208287i | −0.994562 | − | 0.104144i | \(-0.966790\pi\) | ||||
0.994562 | − | 0.104144i | \(-0.0332101\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −110.000 | −0.137672 | ||||||||
\(800\) | 49.4975i | 0.0618718i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1289.39 | 1.60772 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.59667 | 0.00571015 | ||||||||
\(806\) | 991.301i | 1.22990i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −197.639 | −0.244603 | ||||||||
\(809\) | − 447.222i | − 0.552809i | −0.961041 | − | 0.276404i | \(-0.910857\pi\) | ||||
0.961041 | − | 0.276404i | \(-0.0891429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −885.903 | −1.09236 | −0.546180 | − | 0.837668i | \(-0.683918\pi\) | ||||
−0.546180 | + | 0.837668i | \(0.683918\pi\) | |||||||
\(812\) | − 4.16297i | − 0.00512681i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 94.3018i | 0.115708i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1186.67 | 1.45247 | ||||||||
\(818\) | − 981.246i | − 1.19957i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.59257 | −0.00925923 | ||||||||
\(821\) | 1575.63i | 1.91916i | 0.281430 | + | 0.959582i | \(0.409191\pi\) | ||||
−0.281430 | + | 0.959582i | \(0.590809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1433.92 | −1.74231 | −0.871153 | − | 0.491012i | \(-0.836627\pi\) | ||||
−0.871153 | + | 0.491012i | \(0.836627\pi\) | |||||||
\(824\) | 443.479i | 0.538202i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −158.657 | −0.192079 | ||||||||
\(827\) | 9.09551i | 0.0109982i | 0.999985 | + | 0.00549910i | \(0.00175043\pi\) | ||||
−0.999985 | + | 0.00549910i | \(0.998250\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 206.996 | 0.249693 | 0.124847 | − | 0.992176i | \(-0.460156\pi\) | ||||
0.124847 | + | 0.992176i | \(0.460156\pi\) | |||||||
\(830\) | − 194.828i | − 0.234732i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −572.276 | −0.687832 | ||||||||
\(833\) | 560.891i | 0.673339i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −156.083 | −0.186925 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1149.65 | −1.37190 | ||||||||
\(839\) | − 924.237i | − 1.10159i | −0.834639 | − | 0.550797i | \(-0.814324\pi\) | ||||
0.834639 | − | 0.550797i | \(-0.185676\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.71575 | −0.00560731 | ||||||||
\(842\) | − 1285.68i | − 1.52694i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.4256 | −0.0301251 | ||||||||
\(845\) | − 66.4336i | − 0.0786197i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 561.048i | − 0.661613i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −581.663 | −0.684310 | ||||||||
\(851\) | − 191.232i | − 0.224715i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −215.111 | −0.252182 | −0.126091 | − | 0.992019i | \(-0.540243\pi\) | ||||
−0.126091 | + | 0.992019i | \(0.540243\pi\) | |||||||
\(854\) | 57.2016i | 0.0669808i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −635.474 | −0.742376 | ||||||||
\(857\) | − 775.528i | − 0.904933i | −0.891781 | − | 0.452467i | \(-0.850544\pi\) | ||||
0.891781 | − | 0.452467i | \(-0.149456\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1070.94 | −1.24673 | −0.623363 | − | 0.781933i | \(-0.714234\pi\) | ||||
−0.623363 | + | 0.781933i | \(0.714234\pi\) | |||||||
\(860\) | − 6.96821i | − 0.00810257i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 661.788 | 0.767736 | ||||||||
\(863\) | − 698.664i | − 0.809576i | −0.914411 | − | 0.404788i | \(-0.867345\pi\) | ||||
0.914411 | − | 0.404788i | \(-0.132655\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −136.421 | −0.157712 | ||||||||
\(866\) | − 492.493i | − 0.568698i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.54827 | 0.00869616 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −156.143 | −0.179269 | ||||||||
\(872\) | − 831.627i | − 0.953701i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −179.226 | −0.205064 | ||||||||
\(875\) | 44.3368i | 0.0506706i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1205.04 | 1.37405 | 0.687023 | − | 0.726636i | \(-0.258917\pi\) | ||||
0.687023 | + | 0.726636i | \(0.258917\pi\) | |||||||
\(878\) | 87.9036i | 0.100118i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 37.9228i | − 0.0430452i | −0.999768 | − | 0.0215226i | \(-0.993149\pi\) | ||||
0.999768 | − | 0.0215226i | \(-0.00685139\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 444.786 | 0.503722 | 0.251861 | − | 0.967763i | \(-0.418957\pi\) | ||||
0.251861 | + | 0.967763i | \(0.418957\pi\) | |||||||
\(884\) | 13.8128i | 0.0156253i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1322.02 | −1.49212 | ||||||||
\(887\) | − 238.917i | − 0.269354i | −0.990890 | − | 0.134677i | \(-0.957000\pi\) | ||||
0.990890 | − | 0.134677i | \(-0.0429996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −161.718 | −0.181910 | ||||||||
\(890\) | − 179.584i | − 0.201779i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.2420 | 0.0260561 | ||||||||
\(893\) | − 161.357i | − 0.180691i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −171.520 | −0.191643 | ||||||||
\(896\) | 150.745i | 0.168242i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 38.1915 | 0.0425296 | ||||||||
\(899\) | − 1533.45i | − 1.70572i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 399.776 | 0.443703 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1435.46 | 1.58790 | ||||||||
\(905\) | 189.452i | 0.209339i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 83.7360 | 0.0923219 | 0.0461610 | − | 0.998934i | \(-0.485301\pi\) | ||||
0.0461610 | + | 0.998934i | \(0.485301\pi\) | |||||||
\(908\) | 40.8496i | 0.0449885i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 16.8848 | 0.0185547 | ||||||||
\(911\) | 682.361i | 0.749024i | 0.927222 | + | 0.374512i | \(0.122190\pi\) | ||||
−0.927222 | + | 0.374512i | \(0.877810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − 41.5353i | − 0.0454435i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −25.5303 | −0.0278716 | ||||||||
\(917\) | 78.6799i | 0.0858014i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1516.74 | 1.65043 | 0.825214 | − | 0.564820i | \(-0.191054\pi\) | ||||
0.825214 | + | 0.564820i | \(0.191054\pi\) | |||||||
\(920\) | − 32.0905i | − 0.0348810i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −469.823 | −0.509569 | ||||||||
\(923\) | − 713.146i | − 0.772639i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 910.393 | 0.984209 | ||||||||
\(926\) | 1506.69i | 1.62710i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −59.0786 | −0.0636623 | ||||||||
\(929\) | 901.919i | 0.970849i | 0.874279 | + | 0.485425i | \(0.161335\pi\) | ||||
−0.874279 | + | 0.485425i | \(0.838665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −822.762 | −0.883740 | ||||||||
\(932\) | − 4.99683i | − 0.00536140i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1120.64 | 1.19983 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −389.472 | −0.415658 | −0.207829 | − | 0.978165i | \(-0.566640\pi\) | ||||
−0.207829 | + | 0.978165i | \(0.566640\pi\) | |||||||
\(938\) | 38.6314i | 0.0411848i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.947502 | −0.00100798 | ||||||||
\(941\) | − 372.011i | − 0.395336i | −0.980269 | − | 0.197668i | \(-0.936663\pi\) | ||||
0.980269 | − | 0.197668i | \(-0.0633367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −383.893 | −0.407098 | ||||||||
\(944\) | 1142.83i | 1.21063i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 301.071i | 0.317920i | 0.987285 | + | 0.158960i | \(0.0508142\pi\) | ||||
−0.987285 | + | 0.158960i | \(0.949186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 511.173 | 0.538644 | ||||||||
\(950\) | − 853.233i | − 0.898139i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −104.204 | −0.109458 | ||||||||
\(953\) | 1174.88i | 1.23283i | 0.787422 | + | 0.616414i | \(0.211415\pi\) | ||||
−0.787422 | + | 0.616414i | \(0.788585\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −269.302 | −0.281992 | ||||||||
\(956\) | 3.01928i | 0.00315824i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1339.53 | −1.39826 | ||||||||
\(959\) | − 256.682i | − 0.267656i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1819.44 | 1.89327 | ||||||||
\(962\) | − 702.446i | − 0.730194i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.2056 | −0.0219975 | ||||||||
\(965\) | − 201.544i | − 0.208854i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −293.663 | −0.303685 | −0.151842 | − | 0.988405i | \(-0.548521\pi\) | ||||
−0.151842 | + | 0.988405i | \(0.548521\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.8187 | −0.0235244 | ||||||||
\(971\) | − 787.038i | − 0.810544i | −0.914196 | − | 0.405272i | \(-0.867177\pi\) | ||||
0.914196 | − | 0.405272i | \(-0.132823\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 115.867 | 0.119082 | ||||||||
\(974\) | 21.8347i | 0.0224175i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 412.032 | 0.422164 | ||||||||
\(977\) | 692.629i | 0.708935i | 0.935068 | + | 0.354467i | \(0.115338\pi\) | ||||
−0.935068 | + | 0.354467i | \(0.884662\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.83132i | 0.00492992i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 379.686 | 0.386645 | ||||||||
\(983\) | − 1798.69i | − 1.82979i | −0.403690 | − | 0.914896i | \(-0.632272\pi\) | ||||
0.403690 | − | 0.914896i | \(-0.367728\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −75.0364 | −0.0761791 | ||||||||
\(986\) | − 694.255i | − 0.704112i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.2617 | −0.0205078 | ||||||||
\(989\) | − 352.325i | − 0.356243i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 736.790 | 0.743482 | 0.371741 | − | 0.928337i | \(-0.378761\pi\) | ||||
0.371741 | + | 0.928337i | \(0.378761\pi\) | |||||||
\(992\) | − 107.121i | − 0.107985i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −176.439 | −0.177504 | ||||||||
\(995\) | 143.104i | 0.143823i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1277.49 | 1.28133 | 0.640667 | − | 0.767819i | \(-0.278658\pi\) | ||||
0.640667 | + | 0.767819i | \(0.278658\pi\) | |||||||
\(998\) | 880.924i | 0.882689i | ||||||||
\(999\) | 0 | 0 |
(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 | 1089.3.b.d.485.2 | yes | 4 | |
3.2 | odd | 2 | inner | 1089.3.b.d.485.3 | yes | 4 | |
11.10 | odd | 2 | 1089.3.b.c.485.3 | yes | 4 | ||
33.32 | even | 2 | 1089.3.b.c.485.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1089.3.b.c.485.2 | ✓ | 4 | 33.32 | even | 2 | ||
1089.3.b.c.485.3 | yes | 4 | 11.10 | odd | 2 | ||
1089.3.b.d.485.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1089.3.b.d.485.3 | yes | 4 | 3.2 | odd | 2 | inner |