Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(1469,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.1469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.d (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1469.6 | ||
Root | \(-1.01575 - 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1469 |
Dual form | 1470.2.d.f.1469.7 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.707107 | − | 1.58114i | 0.408248 | − | 0.912871i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.41421 | + | 1.73205i | −0.632456 | + | 0.774597i | ||||
\(6\) | 0.707107 | − | 1.58114i | 0.288675 | − | 0.645497i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.00000 | − | 2.23607i | −0.666667 | − | 0.745356i | ||||
\(10\) | −1.41421 | + | 1.73205i | −0.447214 | + | 0.547723i | ||||
\(11\) | − | 4.68556i | − | 1.41275i | −0.707838 | − | 0.706374i | \(-0.750330\pi\) | ||
0.707838 | − | 0.706374i | \(-0.249670\pi\) | |||||||
\(12\) | 0.707107 | − | 1.58114i | 0.204124 | − | 0.456435i | ||||
\(13\) | −1.04456 | −0.289708 | −0.144854 | − | 0.989453i | \(-0.546271\pi\) | ||||
−0.144854 | + | 0.989453i | \(0.546271\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73861 | + | 3.46081i | 0.448908 | + | 0.893578i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.16228i | − | 0.766965i | −0.923548 | − | 0.383482i | \(-0.874725\pi\) | ||
0.923548 | − | 0.383482i | \(-0.125275\pi\) | |||||||
\(18\) | −2.00000 | − | 2.23607i | −0.471405 | − | 0.527046i | ||||
\(19\) | − | 1.43023i | − | 0.328117i | −0.986451 | − | 0.164058i | \(-0.947541\pi\) | ||
0.986451 | − | 0.164058i | \(-0.0524585\pi\) | |||||||
\(20\) | −1.41421 | + | 1.73205i | −0.316228 | + | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.68556i | − | 0.998964i | ||||||
\(23\) | 4.47723 | 0.933566 | 0.466783 | − | 0.884372i | \(-0.345413\pi\) | ||||
0.466783 | + | 0.884372i | \(0.345413\pi\) | |||||||
\(24\) | 0.707107 | − | 1.58114i | 0.144338 | − | 0.322749i | ||||
\(25\) | −1.00000 | − | 4.89898i | −0.200000 | − | 0.979796i | ||||
\(26\) | −1.04456 | −0.204854 | ||||||||
\(27\) | −4.94975 | + | 1.58114i | −0.952579 | + | 0.304290i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.92163i | − | 1.28531i | −0.766154 | − | 0.642657i | \(-0.777832\pi\) | ||
0.766154 | − | 0.642657i | \(-0.222168\pi\) | |||||||
\(30\) | 1.73861 | + | 3.46081i | 0.317426 | + | 0.631855i | ||||
\(31\) | 6.62638i | 1.19013i | 0.803677 | + | 0.595066i | \(0.202874\pi\) | ||||
−0.803677 | + | 0.595066i | \(0.797126\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −7.40852 | − | 3.31319i | −1.28966 | − | 0.576752i | ||||
\(34\) | − | 3.16228i | − | 0.542326i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | − | 2.23607i | −0.333333 | − | 0.372678i | ||||
\(37\) | − | 2.66291i | − | 0.437780i | −0.975750 | − | 0.218890i | \(-0.929756\pi\) | ||
0.975750 | − | 0.218890i | \(-0.0702436\pi\) | |||||||
\(38\) | − | 1.43023i | − | 0.232013i | ||||||
\(39\) | −0.738613 | + | 1.65159i | −0.118273 | + | 0.264466i | ||||
\(40\) | −1.41421 | + | 1.73205i | −0.223607 | + | 0.273861i | ||||
\(41\) | 1.04456 | 0.163132 | 0.0815661 | − | 0.996668i | \(-0.474008\pi\) | ||||
0.0815661 | + | 0.996668i | \(0.474008\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.92163i | − | 1.05554i | −0.849388 | − | 0.527769i | \(-0.823029\pi\) | ||
0.849388 | − | 0.527769i | \(-0.176971\pi\) | |||||||
\(44\) | − | 4.68556i | − | 0.706374i | ||||||
\(45\) | 6.70141 | − | 0.301824i | 0.998987 | − | 0.0449933i | ||||
\(46\) | 4.47723 | 0.660131 | ||||||||
\(47\) | − | 11.2189i | − | 1.63644i | −0.574904 | − | 0.818221i | \(-0.694960\pi\) | ||
0.574904 | − | 0.818221i | \(-0.305040\pi\) | |||||||
\(48\) | 0.707107 | − | 1.58114i | 0.102062 | − | 0.228218i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | − | 4.89898i | −0.141421 | − | 0.692820i | ||||
\(51\) | −5.00000 | − | 2.23607i | −0.700140 | − | 0.313112i | ||||
\(52\) | −1.04456 | −0.144854 | ||||||||
\(53\) | 5.00000 | 0.686803 | 0.343401 | − | 0.939189i | \(-0.388421\pi\) | ||||
0.343401 | + | 0.939189i | \(0.388421\pi\) | |||||||
\(54\) | −4.94975 | + | 1.58114i | −0.673575 | + | 0.215166i | ||||
\(55\) | 8.11562 | + | 6.62638i | 1.09431 | + | 0.893501i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.26139 | − | 1.01132i | −0.299528 | − | 0.133953i | ||||
\(58\) | − | 6.92163i | − | 0.908854i | ||||||
\(59\) | −10.5744 | −1.37667 | −0.688334 | − | 0.725394i | \(-0.741658\pi\) | ||||
−0.688334 | + | 0.725394i | \(0.741658\pi\) | |||||||
\(60\) | 1.73861 | + | 3.46081i | 0.224454 | + | 0.446789i | ||||
\(61\) | 3.46410i | 0.443533i | 0.975100 | + | 0.221766i | \(0.0711822\pi\) | ||||
−0.975100 | + | 0.221766i | \(0.928818\pi\) | |||||||
\(62\) | 6.62638i | 0.841551i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.47723 | − | 1.80922i | 0.183227 | − | 0.224407i | ||||
\(66\) | −7.40852 | − | 3.31319i | −0.911925 | − | 0.407825i | ||||
\(67\) | 14.2701i | 1.74337i | 0.490067 | + | 0.871685i | \(0.336972\pi\) | ||||
−0.490067 | + | 0.871685i | \(0.663028\pi\) | |||||||
\(68\) | − | 3.16228i | − | 0.383482i | ||||||
\(69\) | 3.16588 | − | 7.07912i | 0.381127 | − | 0.852225i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92163i | 0.821446i | 0.911760 | + | 0.410723i | \(0.134724\pi\) | ||||
−0.911760 | + | 0.410723i | \(0.865276\pi\) | |||||||
\(72\) | −2.00000 | − | 2.23607i | −0.235702 | − | 0.263523i | ||||
\(73\) | 3.50333 | 0.410033 | 0.205017 | − | 0.978758i | \(-0.434275\pi\) | ||||
0.205017 | + | 0.978758i | \(0.434275\pi\) | |||||||
\(74\) | − | 2.66291i | − | 0.309557i | ||||||
\(75\) | −8.45307 | − | 1.88296i | −0.976077 | − | 0.217426i | ||||
\(76\) | − | 1.43023i | − | 0.164058i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.738613 | + | 1.65159i | −0.0836314 | + | 0.187006i | ||||
\(79\) | 11.4772 | 1.29129 | 0.645644 | − | 0.763638i | \(-0.276589\pi\) | ||||
0.645644 | + | 0.763638i | \(0.276589\pi\) | |||||||
\(80\) | −1.41421 | + | 1.73205i | −0.158114 | + | 0.193649i | ||||
\(81\) | −1.00000 | + | 8.94427i | −0.111111 | + | 0.993808i | ||||
\(82\) | 1.04456 | 0.115352 | ||||||||
\(83\) | − | 4.06775i | − | 0.446494i | −0.974762 | − | 0.223247i | \(-0.928334\pi\) | ||
0.974762 | − | 0.223247i | \(-0.0716656\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.47723 | + | 4.47214i | 0.594089 | + | 0.485071i | ||||
\(86\) | − | 6.92163i | − | 0.746378i | ||||||
\(87\) | −10.9441 | − | 4.89433i | −1.17333 | − | 0.524727i | ||||
\(88\) | − | 4.68556i | − | 0.499482i | ||||||
\(89\) | −4.91754 | −0.521258 | −0.260629 | − | 0.965439i | \(-0.583930\pi\) | ||||
−0.260629 | + | 0.965439i | \(0.583930\pi\) | |||||||
\(90\) | 6.70141 | − | 0.301824i | 0.706391 | − | 0.0318150i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.47723 | 0.466783 | ||||||||
\(93\) | 10.4772 | + | 4.68556i | 1.08644 | + | 0.485870i | ||||
\(94\) | − | 11.2189i | − | 1.15714i | ||||||
\(95\) | 2.47723 | + | 2.02265i | 0.254158 | + | 0.207519i | ||||
\(96\) | 0.707107 | − | 1.58114i | 0.0721688 | − | 0.161374i | ||||
\(97\) | 11.9886 | 1.21726 | 0.608629 | − | 0.793455i | \(-0.291720\pi\) | ||||
0.608629 | + | 0.793455i | \(0.291720\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.4772 | + | 9.37112i | −1.05300 | + | 0.941833i | ||||
\(100\) | −1.00000 | − | 4.89898i | −0.100000 | − | 0.489898i | ||||
\(101\) | 11.3137 | 1.12576 | 0.562878 | − | 0.826540i | \(-0.309694\pi\) | ||||
0.562878 | + | 0.826540i | \(0.309694\pi\) | |||||||
\(102\) | −5.00000 | − | 2.23607i | −0.495074 | − | 0.221404i | ||||
\(103\) | −4.91754 | −0.484540 | −0.242270 | − | 0.970209i | \(-0.577892\pi\) | ||||
−0.242270 | + | 0.970209i | \(0.577892\pi\) | |||||||
\(104\) | −1.04456 | −0.102427 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.00000 | 0.485643 | ||||||||
\(107\) | −5.47723 | −0.529503 | −0.264752 | − | 0.964317i | \(-0.585290\pi\) | ||||
−0.264752 | + | 0.964317i | \(0.585290\pi\) | |||||||
\(108\) | −4.94975 | + | 1.58114i | −0.476290 | + | 0.152145i | ||||
\(109\) | −20.4317 | −1.95700 | −0.978500 | − | 0.206248i | \(-0.933875\pi\) | ||||
−0.978500 | + | 0.206248i | \(0.933875\pi\) | |||||||
\(110\) | 8.11562 | + | 6.62638i | 0.773794 | + | 0.631800i | ||||
\(111\) | −4.21043 | − | 1.88296i | −0.399637 | − | 0.178723i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.4772 | 1.64412 | 0.822060 | − | 0.569402i | \(-0.192825\pi\) | ||||
0.822060 | + | 0.569402i | \(0.192825\pi\) | |||||||
\(114\) | −2.26139 | − | 1.01132i | −0.211798 | − | 0.0947191i | ||||
\(115\) | −6.33175 | + | 7.75478i | −0.590439 | + | 0.723137i | ||||
\(116\) | − | 6.92163i | − | 0.642657i | ||||||
\(117\) | 2.08911 | + | 2.33570i | 0.193139 | + | 0.215935i | ||||
\(118\) | −10.5744 | −0.973452 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.73861 | + | 3.46081i | 0.158713 | + | 0.315928i | ||||
\(121\) | −10.9545 | −0.995859 | ||||||||
\(122\) | 3.46410i | 0.313625i | ||||||||
\(123\) | 0.738613 | − | 1.65159i | 0.0665985 | − | 0.148919i | ||||
\(124\) | 6.62638i | 0.595066i | ||||||||
\(125\) | 9.89949 | + | 5.19615i | 0.885438 | + | 0.464758i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.73085i | 0.774738i | 0.921925 | + | 0.387369i | \(0.126616\pi\) | ||||
−0.921925 | + | 0.387369i | \(0.873384\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −10.9441 | − | 4.89433i | −0.963570 | − | 0.430922i | ||||
\(130\) | 1.47723 | − | 1.80922i | 0.129561 | − | 0.158679i | ||||
\(131\) | −13.7725 | −1.20331 | −0.601654 | − | 0.798757i | \(-0.705491\pi\) | ||||
−0.601654 | + | 0.798757i | \(0.705491\pi\) | |||||||
\(132\) | −7.40852 | − | 3.31319i | −0.644829 | − | 0.288376i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.2701i | 1.23275i | ||||||||
\(135\) | 4.26139 | − | 10.8093i | 0.366762 | − | 0.930315i | ||||
\(136\) | − | 3.16228i | − | 0.271163i | ||||||
\(137\) | −3.47723 | −0.297079 | −0.148540 | − | 0.988906i | \(-0.547457\pi\) | ||||
−0.148540 | + | 0.988906i | \(0.547457\pi\) | |||||||
\(138\) | 3.16588 | − | 7.07912i | 0.269497 | − | 0.602614i | ||||
\(139\) | 20.1810i | 1.71173i | 0.517202 | + | 0.855863i | \(0.326974\pi\) | ||||
−0.517202 | + | 0.855863i | \(0.673026\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.7386 | − | 7.93295i | −1.49386 | − | 0.668075i | ||||
\(142\) | 6.92163i | 0.580850i | ||||||||
\(143\) | 4.89433i | 0.409284i | ||||||||
\(144\) | −2.00000 | − | 2.23607i | −0.166667 | − | 0.186339i | ||||
\(145\) | 11.9886 | + | 9.78866i | 0.995600 | + | 0.812904i | ||||
\(146\) | 3.50333 | 0.289937 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 2.66291i | − | 0.218890i | ||||||
\(149\) | 2.44949i | 0.200670i | 0.994954 | + | 0.100335i | \(0.0319915\pi\) | ||||
−0.994954 | + | 0.100335i | \(0.968009\pi\) | |||||||
\(150\) | −8.45307 | − | 1.88296i | −0.690191 | − | 0.153743i | ||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | − | 1.43023i | − | 0.116007i | ||||||
\(153\) | −7.07107 | + | 6.32456i | −0.571662 | + | 0.511310i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.4772 | − | 9.37112i | −0.921873 | − | 0.752706i | ||||
\(156\) | −0.738613 | + | 1.65159i | −0.0591364 | + | 0.132233i | ||||
\(157\) | 14.4474 | 1.15303 | 0.576513 | − | 0.817088i | \(-0.304413\pi\) | ||||
0.576513 | + | 0.817088i | \(0.304413\pi\) | |||||||
\(158\) | 11.4772 | 0.913079 | ||||||||
\(159\) | 3.53553 | − | 7.90569i | 0.280386 | − | 0.626962i | ||||
\(160\) | −1.41421 | + | 1.73205i | −0.111803 | + | 0.136931i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | + | 8.94427i | −0.0785674 | + | 0.702728i | ||||
\(163\) | − | 14.6969i | − | 1.15115i | −0.817748 | − | 0.575577i | \(-0.804778\pi\) | ||
0.817748 | − | 0.575577i | \(-0.195222\pi\) | |||||||
\(164\) | 1.04456 | 0.0815661 | ||||||||
\(165\) | 16.2158 | − | 8.14637i | 1.26240 | − | 0.634194i | ||||
\(166\) | − | 4.06775i | − | 0.315719i | ||||||
\(167\) | − | 4.29068i | − | 0.332023i | −0.986124 | − | 0.166011i | \(-0.946911\pi\) | ||
0.986124 | − | 0.166011i | \(-0.0530889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9089 | −0.916069 | ||||||||
\(170\) | 5.47723 | + | 4.47214i | 0.420084 | + | 0.342997i | ||||
\(171\) | −3.19808 | + | 2.86045i | −0.244564 | + | 0.218744i | ||||
\(172\) | − | 6.92163i | − | 0.527769i | ||||||
\(173\) | 1.12840i | 0.0857909i | 0.999080 | + | 0.0428954i | \(0.0136582\pi\) | ||||
−0.999080 | + | 0.0428954i | \(0.986342\pi\) | |||||||
\(174\) | −10.9441 | − | 4.89433i | −0.829666 | − | 0.371038i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.68556i | − | 0.353187i | ||||||
\(177\) | −7.47723 | + | 16.7196i | −0.562023 | + | 1.25672i | ||||
\(178\) | −4.91754 | −0.368585 | ||||||||
\(179\) | 19.3825i | 1.44872i | 0.689424 | + | 0.724358i | \(0.257864\pi\) | ||||
−0.689424 | + | 0.724358i | \(0.742136\pi\) | |||||||
\(180\) | 6.70141 | − | 0.301824i | 0.499494 | − | 0.0224966i | ||||
\(181\) | 3.16228i | 0.235050i | 0.993070 | + | 0.117525i | \(0.0374961\pi\) | ||||
−0.993070 | + | 0.117525i | \(0.962504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.47723 | + | 2.44949i | 0.404888 | + | 0.181071i | ||||
\(184\) | 4.47723 | 0.330065 | ||||||||
\(185\) | 4.61230 | + | 3.76593i | 0.339103 | + | 0.276876i | ||||
\(186\) | 10.4772 | + | 4.68556i | 0.768227 | + | 0.343562i | ||||
\(187\) | −14.8170 | −1.08353 | ||||||||
\(188\) | − | 11.2189i | − | 0.818221i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.47723 | + | 2.02265i | 0.179717 | + | 0.146738i | ||||
\(191\) | 16.2927i | 1.17890i | 0.807804 | + | 0.589451i | \(0.200656\pi\) | ||||
−0.807804 | + | 0.589451i | \(0.799344\pi\) | |||||||
\(192\) | 0.707107 | − | 1.58114i | 0.0510310 | − | 0.114109i | ||||
\(193\) | 7.34847i | 0.528954i | 0.964392 | + | 0.264477i | \(0.0851994\pi\) | ||||
−0.964392 | + | 0.264477i | \(0.914801\pi\) | |||||||
\(194\) | 11.9886 | 0.860732 | ||||||||
\(195\) | −1.81608 | − | 3.61501i | −0.130052 | − | 0.258877i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.00000 | 0.641223 | 0.320612 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320612 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(198\) | −10.4772 | + | 9.37112i | −0.744584 | + | 0.665976i | ||||
\(199\) | − | 15.5096i | − | 1.09944i | −0.835348 | − | 0.549722i | \(-0.814734\pi\) | ||
0.835348 | − | 0.549722i | \(-0.185266\pi\) | |||||||
\(200\) | −1.00000 | − | 4.89898i | −0.0707107 | − | 0.346410i | ||||
\(201\) | 22.5630 | + | 10.0905i | 1.59147 | + | 0.711728i | ||||
\(202\) | 11.3137 | 0.796030 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.00000 | − | 2.23607i | −0.350070 | − | 0.156556i | ||||
\(205\) | −1.47723 | + | 1.80922i | −0.103174 | + | 0.126362i | ||||
\(206\) | −4.91754 | −0.342621 | ||||||||
\(207\) | −8.95445 | − | 10.0114i | −0.622377 | − | 0.695839i | ||||
\(208\) | −1.04456 | −0.0724269 | ||||||||
\(209\) | −6.70141 | −0.463546 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.4772 | 1.68508 | 0.842541 | − | 0.538632i | \(-0.181059\pi\) | ||||
0.842541 | + | 0.538632i | \(0.181059\pi\) | |||||||
\(212\) | 5.00000 | 0.343401 | ||||||||
\(213\) | 10.9441 | + | 4.89433i | 0.749874 | + | 0.335354i | ||||
\(214\) | −5.47723 | −0.374415 | ||||||||
\(215\) | 11.9886 | + | 9.78866i | 0.817616 | + | 0.667581i | ||||
\(216\) | −4.94975 | + | 1.58114i | −0.336788 | + | 0.107583i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −20.4317 | −1.38381 | ||||||||
\(219\) | 2.47723 | − | 5.53924i | 0.167395 | − | 0.374307i | ||||
\(220\) | 8.11562 | + | 6.62638i | 0.547155 | + | 0.446750i | ||||
\(221\) | 3.30318i | 0.222196i | ||||||||
\(222\) | −4.21043 | − | 1.88296i | −0.282586 | − | 0.126376i | ||||
\(223\) | 21.8881 | 1.46574 | 0.732868 | − | 0.680371i | \(-0.238181\pi\) | ||||
0.732868 | + | 0.680371i | \(0.238181\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.95445 | + | 12.0340i | −0.596963 | + | 0.802268i | ||||
\(226\) | 17.4772 | 1.16257 | ||||||||
\(227\) | − | 10.3923i | − | 0.689761i | −0.938647 | − | 0.344881i | \(-0.887919\pi\) | ||
0.938647 | − | 0.344881i | \(-0.112081\pi\) | |||||||
\(228\) | −2.26139 | − | 1.01132i | −0.149764 | − | 0.0669765i | ||||
\(229\) | − | 13.5546i | − | 0.895712i | −0.894106 | − | 0.447856i | \(-0.852188\pi\) | ||
0.894106 | − | 0.447856i | \(-0.147812\pi\) | |||||||
\(230\) | −6.33175 | + | 7.75478i | −0.417503 | + | 0.511335i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.92163i | − | 0.454427i | ||||||
\(233\) | −4.00000 | −0.262049 | −0.131024 | − | 0.991379i | \(-0.541827\pi\) | ||||
−0.131024 | + | 0.991379i | \(0.541827\pi\) | |||||||
\(234\) | 2.08911 | + | 2.33570i | 0.136570 | + | 0.152689i | ||||
\(235\) | 19.4317 | + | 15.8659i | 1.26758 | + | 1.03498i | ||||
\(236\) | −10.5744 | −0.688334 | ||||||||
\(237\) | 8.11562 | − | 18.1471i | 0.527166 | − | 1.17878i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 1.73861 | + | 3.46081i | 0.112227 | + | 0.223395i | ||||
\(241\) | 21.3094i | 1.37266i | 0.727292 | + | 0.686328i | \(0.240779\pi\) | ||||
−0.727292 | + | 0.686328i | \(0.759221\pi\) | |||||||
\(242\) | −10.9545 | −0.704179 | ||||||||
\(243\) | 13.4350 | + | 7.90569i | 0.861858 | + | 0.507151i | ||||
\(244\) | 3.46410i | 0.221766i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.738613 | − | 1.65159i | 0.0470922 | − | 0.105301i | ||||
\(247\) | 1.49395i | 0.0950579i | ||||||||
\(248\) | 6.62638i | 0.420776i | ||||||||
\(249\) | −6.43168 | − | 2.87633i | −0.407591 | − | 0.182280i | ||||
\(250\) | 9.89949 | + | 5.19615i | 0.626099 | + | 0.328634i | ||||
\(251\) | 8.85494 | 0.558919 | 0.279459 | − | 0.960158i | \(-0.409845\pi\) | ||||
0.279459 | + | 0.960158i | \(0.409845\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 20.9783i | − | 1.31889i | ||||||
\(254\) | 8.73085i | 0.547822i | ||||||||
\(255\) | 10.9441 | − | 5.49798i | 0.685343 | − | 0.344297i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 10.9960i | − | 0.685909i | −0.939352 | − | 0.342954i | \(-0.888572\pi\) | ||
0.939352 | − | 0.342954i | \(-0.111428\pi\) | |||||||
\(258\) | −10.9441 | − | 4.89433i | −0.681347 | − | 0.304708i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.47723 | − | 1.80922i | 0.0916136 | − | 0.112203i | ||||
\(261\) | −15.4772 | + | 13.8433i | −0.958016 | + | 0.856876i | ||||
\(262\) | −13.7725 | −0.850867 | ||||||||
\(263\) | −2.00000 | −0.123325 | −0.0616626 | − | 0.998097i | \(-0.519640\pi\) | ||||
−0.0616626 | + | 0.998097i | \(0.519640\pi\) | |||||||
\(264\) | −7.40852 | − | 3.31319i | −0.455963 | − | 0.203913i | ||||
\(265\) | −7.07107 | + | 8.66025i | −0.434372 | + | 0.531995i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.47723 | + | 7.77531i | −0.212803 | + | 0.475841i | ||||
\(268\) | 14.2701i | 0.871685i | ||||||||
\(269\) | 17.5810 | 1.07194 | 0.535968 | − | 0.844239i | \(-0.319947\pi\) | ||||
0.535968 | + | 0.844239i | \(0.319947\pi\) | |||||||
\(270\) | 4.26139 | − | 10.8093i | 0.259340 | − | 0.657832i | ||||
\(271\) | − | 6.32456i | − | 0.384189i | −0.981376 | − | 0.192095i | \(-0.938472\pi\) | ||
0.981376 | − | 0.192095i | \(-0.0615281\pi\) | |||||||
\(272\) | − | 3.16228i | − | 0.191741i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.47723 | −0.210067 | ||||||||
\(275\) | −22.9545 | + | 4.68556i | −1.38421 | + | 0.282550i | ||||
\(276\) | 3.16588 | − | 7.07912i | 0.190563 | − | 0.426113i | ||||
\(277\) | − | 9.79796i | − | 0.588702i | −0.955697 | − | 0.294351i | \(-0.904896\pi\) | ||
0.955697 | − | 0.294351i | \(-0.0951035\pi\) | |||||||
\(278\) | 20.1810i | 1.21037i | ||||||||
\(279\) | 14.8170 | − | 13.2528i | 0.887073 | − | 0.793422i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.80922i | 0.107929i | 0.998543 | + | 0.0539646i | \(0.0171858\pi\) | ||||
−0.998543 | + | 0.0539646i | \(0.982814\pi\) | |||||||
\(282\) | −17.7386 | − | 7.93295i | −1.05632 | − | 0.472400i | ||||
\(283\) | 9.22460 | 0.548345 | 0.274173 | − | 0.961680i | \(-0.411596\pi\) | ||||
0.274173 | + | 0.961680i | \(0.411596\pi\) | |||||||
\(284\) | 6.92163i | 0.410723i | ||||||||
\(285\) | 4.94975 | − | 2.48661i | 0.293198 | − | 0.147294i | ||||
\(286\) | 4.89433i | 0.289408i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.00000 | − | 2.23607i | −0.117851 | − | 0.131762i | ||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 11.9886 | + | 9.78866i | 0.703995 | + | 0.574810i | ||||
\(291\) | 8.47723 | − | 18.9557i | 0.496944 | − | 1.11120i | ||||
\(292\) | 3.50333 | 0.205017 | ||||||||
\(293\) | 8.05661i | 0.470672i | 0.971914 | + | 0.235336i | \(0.0756190\pi\) | ||||
−0.971914 | + | 0.235336i | \(0.924381\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.9545 | − | 18.3154i | 0.870682 | − | 1.06636i | ||||
\(296\) | − | 2.66291i | − | 0.154779i | ||||||
\(297\) | 7.40852 | + | 23.1923i | 0.429886 | + | 1.34576i | ||||
\(298\) | 2.44949i | 0.141895i | ||||||||
\(299\) | −4.67671 | −0.270461 | ||||||||
\(300\) | −8.45307 | − | 1.88296i | −0.488038 | − | 0.108713i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.00000 | −0.115087 | ||||||||
\(303\) | 8.00000 | − | 17.8885i | 0.459588 | − | 1.02767i | ||||
\(304\) | − | 1.43023i | − | 0.0820291i | ||||||
\(305\) | −6.00000 | − | 4.89898i | −0.343559 | − | 0.280515i | ||||
\(306\) | −7.07107 | + | 6.32456i | −0.404226 | + | 0.361551i | ||||
\(307\) | −11.9886 | −0.684226 | −0.342113 | − | 0.939659i | \(-0.611143\pi\) | ||||
−0.342113 | + | 0.939659i | \(0.611143\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.47723 | + | 7.77531i | −0.197812 | + | 0.442322i | ||||
\(310\) | −11.4772 | − | 9.37112i | −0.651863 | − | 0.532244i | ||||
\(311\) | 17.5810 | 0.996930 | 0.498465 | − | 0.866910i | \(-0.333897\pi\) | ||||
0.498465 | + | 0.866910i | \(0.333897\pi\) | |||||||
\(312\) | −0.738613 | + | 1.65159i | −0.0418157 | + | 0.0935028i | ||||
\(313\) | 23.2379 | 1.31348 | 0.656742 | − | 0.754115i | \(-0.271934\pi\) | ||||
0.656742 | + | 0.754115i | \(0.271934\pi\) | |||||||
\(314\) | 14.4474 | 0.815313 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.4772 | 0.645644 | ||||||||
\(317\) | −9.90890 | −0.556539 | −0.278270 | − | 0.960503i | \(-0.589761\pi\) | ||||
−0.278270 | + | 0.960503i | \(0.589761\pi\) | |||||||
\(318\) | 3.53553 | − | 7.90569i | 0.198263 | − | 0.443329i | ||||
\(319\) | −32.4317 | −1.81583 | ||||||||
\(320\) | −1.41421 | + | 1.73205i | −0.0790569 | + | 0.0968246i | ||||
\(321\) | −3.87298 | + | 8.66025i | −0.216169 | + | 0.483368i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.52277 | −0.251654 | ||||||||
\(324\) | −1.00000 | + | 8.94427i | −0.0555556 | + | 0.496904i | ||||
\(325\) | 1.04456 | + | 5.11726i | 0.0579416 | + | 0.283854i | ||||
\(326\) | − | 14.6969i | − | 0.813988i | ||||||
\(327\) | −14.4474 | + | 32.3053i | −0.798942 | + | 1.78649i | ||||
\(328\) | 1.04456 | 0.0576760 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 16.2158 | − | 8.14637i | 0.892653 | − | 0.448443i | ||||
\(331\) | 21.4317 | 1.17799 | 0.588996 | − | 0.808136i | \(-0.299523\pi\) | ||||
0.588996 | + | 0.808136i | \(0.299523\pi\) | |||||||
\(332\) | − | 4.06775i | − | 0.223247i | ||||||
\(333\) | −5.95445 | + | 5.32582i | −0.326302 | + | 0.291853i | ||||
\(334\) | − | 4.29068i | − | 0.234776i | ||||||
\(335\) | −24.7165 | − | 20.1810i | −1.35041 | − | 1.10260i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.1464i | − | 0.934025i | −0.884251 | − | 0.467013i | \(-0.845330\pi\) | ||
0.884251 | − | 0.467013i | \(-0.154670\pi\) | |||||||
\(338\) | −11.9089 | −0.647759 | ||||||||
\(339\) | 12.3583 | − | 27.6339i | 0.671209 | − | 1.50087i | ||||
\(340\) | 5.47723 | + | 4.47214i | 0.297044 | + | 0.242536i | ||||
\(341\) | 31.0483 | 1.68136 | ||||||||
\(342\) | −3.19808 | + | 2.86045i | −0.172933 | + | 0.154676i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 6.92163i | − | 0.373189i | ||||||
\(345\) | 7.78416 | + | 15.4948i | 0.419085 | + | 0.834214i | ||||
\(346\) | 1.12840i | 0.0606633i | ||||||||
\(347\) | −17.4772 | −0.938227 | −0.469113 | − | 0.883138i | \(-0.655426\pi\) | ||||
−0.469113 | + | 0.883138i | \(0.655426\pi\) | |||||||
\(348\) | −10.9441 | − | 4.89433i | −0.586663 | − | 0.262364i | ||||
\(349\) | − | 11.7436i | − | 0.628623i | −0.949320 | − | 0.314311i | \(-0.898226\pi\) | ||
0.949320 | − | 0.314311i | \(-0.101774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.17029 | − | 1.65159i | 0.275970 | − | 0.0881553i | ||||
\(352\) | − | 4.68556i | − | 0.249741i | ||||||
\(353\) | − | 0.603648i | − | 0.0321289i | −0.999871 | − | 0.0160645i | \(-0.994886\pi\) | ||
0.999871 | − | 0.0160645i | \(-0.00511370\pi\) | |||||||
\(354\) | −7.47723 | + | 16.7196i | −0.397410 | + | 0.888636i | ||||
\(355\) | −11.9886 | − | 9.78866i | −0.636289 | − | 0.519528i | ||||
\(356\) | −4.91754 | −0.260629 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.3825i | 1.02440i | ||||||||
\(359\) | − | 11.3938i | − | 0.601340i | −0.953728 | − | 0.300670i | \(-0.902790\pi\) | ||
0.953728 | − | 0.300670i | \(-0.0972102\pi\) | |||||||
\(360\) | 6.70141 | − | 0.301824i | 0.353195 | − | 0.0159075i | ||||
\(361\) | 16.9545 | 0.892340 | ||||||||
\(362\) | 3.16228i | 0.166206i | ||||||||
\(363\) | −7.74597 | + | 17.3205i | −0.406558 | + | 0.909091i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.95445 | + | 6.06794i | −0.259328 | + | 0.317610i | ||||
\(366\) | 5.47723 | + | 2.44949i | 0.286299 | + | 0.128037i | ||||
\(367\) | 0.369657 | 0.0192960 | 0.00964798 | − | 0.999953i | \(-0.496929\pi\) | ||||
0.00964798 | + | 0.999953i | \(0.496929\pi\) | |||||||
\(368\) | 4.47723 | 0.233392 | ||||||||
\(369\) | −2.08911 | − | 2.33570i | −0.108755 | − | 0.121592i | ||||
\(370\) | 4.61230 | + | 3.76593i | 0.239782 | + | 0.195781i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.4772 | + | 4.68556i | 0.543219 | + | 0.242935i | ||||
\(373\) | 23.2144i | 1.20199i | 0.799251 | + | 0.600997i | \(0.205230\pi\) | ||||
−0.799251 | + | 0.600997i | \(0.794770\pi\) | |||||||
\(374\) | −14.8170 | −0.766171 | ||||||||
\(375\) | 15.2158 | − | 11.9782i | 0.785743 | − | 0.618554i | ||||
\(376\) | − | 11.2189i | − | 0.578570i | ||||||
\(377\) | 7.23003i | 0.372365i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.4772 | −1.05184 | −0.525922 | − | 0.850533i | \(-0.676280\pi\) | ||||
−0.525922 | + | 0.850533i | \(0.676280\pi\) | |||||||
\(380\) | 2.47723 | + | 2.02265i | 0.127079 | + | 0.103760i | ||||
\(381\) | 13.8047 | + | 6.17364i | 0.707235 | + | 0.316285i | ||||
\(382\) | 16.2927i | 0.833609i | ||||||||
\(383\) | 18.1471i | 0.927273i | 0.886026 | + | 0.463636i | \(0.153456\pi\) | ||||
−0.886026 | + | 0.463636i | \(0.846544\pi\) | |||||||
\(384\) | 0.707107 | − | 1.58114i | 0.0360844 | − | 0.0806872i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.34847i | 0.374027i | ||||||||
\(387\) | −15.4772 | + | 13.8433i | −0.786752 | + | 0.703692i | ||||
\(388\) | 11.9886 | 0.608629 | ||||||||
\(389\) | 7.34847i | 0.372582i | 0.982495 | + | 0.186291i | \(0.0596468\pi\) | ||||
−0.982495 | + | 0.186291i | \(0.940353\pi\) | |||||||
\(390\) | −1.81608 | − | 3.61501i | −0.0919607 | − | 0.183053i | ||||
\(391\) | − | 14.1582i | − | 0.716012i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.73861 | + | 21.7762i | −0.491248 | + | 1.09846i | ||||
\(394\) | 9.00000 | 0.453413 | ||||||||
\(395\) | −16.2312 | + | 19.8791i | −0.816683 | + | 1.00023i | ||||
\(396\) | −10.4772 | + | 9.37112i | −0.526500 | + | 0.470916i | ||||
\(397\) | 14.8815 | 0.746879 | 0.373439 | − | 0.927655i | \(-0.378178\pi\) | ||||
0.373439 | + | 0.927655i | \(0.378178\pi\) | |||||||
\(398\) | − | 15.5096i | − | 0.777424i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | − | 4.89898i | −0.0500000 | − | 0.244949i | ||||
\(401\) | 0.955537i | 0.0477173i | 0.999715 | + | 0.0238586i | \(0.00759516\pi\) | ||||
−0.999715 | + | 0.0238586i | \(0.992405\pi\) | |||||||
\(402\) | 22.5630 | + | 10.0905i | 1.12534 | + | 0.503267i | ||||
\(403\) | − | 6.92163i | − | 0.344791i | ||||||
\(404\) | 11.3137 | 0.562878 | ||||||||
\(405\) | −14.0777 | − | 14.3812i | −0.699528 | − | 0.714606i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.4772 | −0.618473 | ||||||||
\(408\) | −5.00000 | − | 2.23607i | −0.247537 | − | 0.110702i | ||||
\(409\) | − | 15.5096i | − | 0.766899i | −0.923562 | − | 0.383449i | \(-0.874736\pi\) | ||
0.923562 | − | 0.383449i | \(-0.125264\pi\) | |||||||
\(410\) | −1.47723 | + | 1.80922i | −0.0729550 | + | 0.0893512i | ||||
\(411\) | −2.45877 | + | 5.49798i | −0.121282 | + | 0.271195i | ||||
\(412\) | −4.91754 | −0.242270 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.95445 | − | 10.0114i | −0.440087 | − | 0.492033i | ||||
\(415\) | 7.04555 | + | 5.75267i | 0.345852 | + | 0.282387i | ||||
\(416\) | −1.04456 | −0.0512136 | ||||||||
\(417\) | 31.9089 | + | 14.2701i | 1.56259 | + | 0.698810i | ||||
\(418\) | −6.70141 | −0.327777 | ||||||||
\(419\) | −8.85494 | −0.432592 | −0.216296 | − | 0.976328i | \(-0.569398\pi\) | ||||
−0.216296 | + | 0.976328i | \(0.569398\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9545 | 0.923783 | 0.461892 | − | 0.886936i | \(-0.347171\pi\) | ||||
0.461892 | + | 0.886936i | \(0.347171\pi\) | |||||||
\(422\) | 24.4772 | 1.19153 | ||||||||
\(423\) | −25.0862 | + | 22.4378i | −1.21973 | + | 1.09096i | ||||
\(424\) | 5.00000 | 0.242821 | ||||||||
\(425\) | −15.4919 | + | 3.16228i | −0.751469 | + | 0.153393i | ||||
\(426\) | 10.9441 | + | 4.89433i | 0.530241 | + | 0.237131i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.47723 | −0.264752 | ||||||||
\(429\) | 7.73861 | + | 3.46081i | 0.373624 | + | 0.167090i | ||||
\(430\) | 11.9886 | + | 9.78866i | 0.578142 | + | 0.472051i | ||||
\(431\) | 7.66374i | 0.369149i | 0.982818 | + | 0.184575i | \(0.0590908\pi\) | ||||
−0.982818 | + | 0.184575i | \(0.940909\pi\) | |||||||
\(432\) | −4.94975 | + | 1.58114i | −0.238145 | + | 0.0760726i | ||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.9545 | − | 12.0340i | 1.14853 | − | 0.576987i | ||||
\(436\) | −20.4317 | −0.978500 | ||||||||
\(437\) | − | 6.40345i | − | 0.306318i | ||||||
\(438\) | 2.47723 | − | 5.53924i | 0.118366 | − | 0.264675i | ||||
\(439\) | − | 8.88319i | − | 0.423971i | −0.977273 | − | 0.211986i | \(-0.932007\pi\) | ||
0.977273 | − | 0.211986i | \(-0.0679930\pi\) | |||||||
\(440\) | 8.11562 | + | 6.62638i | 0.386897 | + | 0.315900i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.30318i | 0.157116i | ||||||||
\(443\) | −15.0455 | −0.714836 | −0.357418 | − | 0.933945i | \(-0.616343\pi\) | ||||
−0.357418 | + | 0.933945i | \(0.616343\pi\) | |||||||
\(444\) | −4.21043 | − | 1.88296i | −0.199818 | − | 0.0893615i | ||||
\(445\) | 6.95445 | − | 8.51743i | 0.329673 | − | 0.403765i | ||||
\(446\) | 21.8881 | 1.03643 | ||||||||
\(447\) | 3.87298 | + | 1.73205i | 0.183186 | + | 0.0819232i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.8773i | 1.22122i | 0.791930 | + | 0.610612i | \(0.209077\pi\) | ||||
−0.791930 | + | 0.610612i | \(0.790923\pi\) | |||||||
\(450\) | −8.95445 | + | 12.0340i | −0.422117 | + | 0.567289i | ||||
\(451\) | − | 4.89433i | − | 0.230465i | ||||||
\(452\) | 17.4772 | 0.822060 | ||||||||
\(453\) | −1.41421 | + | 3.16228i | −0.0664455 | + | 0.148577i | ||||
\(454\) | − | 10.3923i | − | 0.487735i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.26139 | − | 1.01132i | −0.105899 | − | 0.0473595i | ||||
\(457\) | − | 11.0785i | − | 0.518230i | −0.965846 | − | 0.259115i | \(-0.916569\pi\) | ||
0.965846 | − | 0.259115i | \(-0.0834308\pi\) | |||||||
\(458\) | − | 13.5546i | − | 0.633364i | ||||||
\(459\) | 5.00000 | + | 15.6525i | 0.233380 | + | 0.730595i | ||||
\(460\) | −6.33175 | + | 7.75478i | −0.295220 | + | 0.361569i | ||||
\(461\) | −31.7876 | −1.48050 | −0.740248 | − | 0.672334i | \(-0.765292\pi\) | ||||
−0.740248 | + | 0.672334i | \(0.765292\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.5741i | 1.04911i | 0.851377 | + | 0.524554i | \(0.175768\pi\) | ||||
−0.851377 | + | 0.524554i | \(0.824232\pi\) | |||||||
\(464\) | − | 6.92163i | − | 0.321328i | ||||||
\(465\) | −22.9327 | + | 11.5207i | −1.06348 | + | 0.534260i | ||||
\(466\) | −4.00000 | −0.185296 | ||||||||
\(467\) | − | 28.0146i | − | 1.29636i | −0.761486 | − | 0.648181i | \(-0.775530\pi\) | ||
0.761486 | − | 0.648181i | \(-0.224470\pi\) | |||||||
\(468\) | 2.08911 | + | 2.33570i | 0.0965693 | + | 0.107968i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 19.4317 | + | 15.8659i | 0.896316 | + | 0.731839i | ||||
\(471\) | 10.2158 | − | 22.8433i | 0.470721 | − | 1.05256i | ||||
\(472\) | −10.5744 | −0.486726 | ||||||||
\(473\) | −32.4317 | −1.49121 | ||||||||
\(474\) | 8.11562 | − | 18.1471i | 0.372763 | − | 0.833523i | ||||
\(475\) | −7.00665 | + | 1.43023i | −0.321487 | + | 0.0656233i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.0000 | − | 11.1803i | −0.457869 | − | 0.511913i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −42.3620 | −1.93557 | −0.967784 | − | 0.251780i | \(-0.918984\pi\) | ||||
−0.967784 | + | 0.251780i | \(0.918984\pi\) | |||||||
\(480\) | 1.73861 | + | 3.46081i | 0.0793565 | + | 0.157964i | ||||
\(481\) | 2.78156i | 0.126828i | ||||||||
\(482\) | 21.3094i | 0.970615i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9545 | −0.497930 | ||||||||
\(485\) | −16.9545 | + | 20.7649i | −0.769862 | + | 0.942884i | ||||
\(486\) | 13.4350 | + | 7.90569i | 0.609425 | + | 0.358610i | ||||
\(487\) | − | 17.0349i | − | 0.771923i | −0.922515 | − | 0.385962i | \(-0.873870\pi\) | ||
0.922515 | − | 0.385962i | \(-0.126130\pi\) | |||||||
\(488\) | 3.46410i | 0.156813i | ||||||||
\(489\) | −23.2379 | − | 10.3923i | −1.05085 | − | 0.469956i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13.8433i | − | 0.624737i | −0.949961 | − | 0.312369i | \(-0.898878\pi\) | ||
0.949961 | − | 0.312369i | \(-0.101122\pi\) | |||||||
\(492\) | 0.738613 | − | 1.65159i | 0.0332992 | − | 0.0744594i | ||||
\(493\) | −21.8881 | −0.985791 | ||||||||
\(494\) | 1.49395i | 0.0672161i | ||||||||
\(495\) | −1.41421 | − | 31.3998i | −0.0635642 | − | 1.41132i | ||||
\(496\) | 6.62638i | 0.297533i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.43168 | − | 2.87633i | −0.288210 | − | 0.128892i | ||||
\(499\) | 1.90890 | 0.0854542 | 0.0427271 | − | 0.999087i | \(-0.486395\pi\) | ||||
0.0427271 | + | 0.999087i | \(0.486395\pi\) | |||||||
\(500\) | 9.89949 | + | 5.19615i | 0.442719 | + | 0.232379i | ||||
\(501\) | −6.78416 | − | 3.03397i | −0.303094 | − | 0.135548i | ||||
\(502\) | 8.85494 | 0.395215 | ||||||||
\(503\) | 15.5096i | 0.691537i | 0.938320 | + | 0.345769i | \(0.112382\pi\) | ||||
−0.938320 | + | 0.345769i | \(0.887618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.0000 | + | 19.5959i | −0.711991 | + | 0.872007i | ||||
\(506\) | − | 20.9783i | − | 0.932599i | ||||||
\(507\) | −8.42087 | + | 18.8296i | −0.373984 | + | 0.836253i | ||||
\(508\) | 8.73085i | 0.387369i | ||||||||
\(509\) | −24.7165 | −1.09554 | −0.547770 | − | 0.836629i | \(-0.684523\pi\) | ||||
−0.547770 | + | 0.836629i | \(0.684523\pi\) | |||||||
\(510\) | 10.9441 | − | 5.49798i | 0.484611 | − | 0.243454i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.26139 | + | 7.07926i | 0.0998427 | + | 0.312557i | ||||
\(514\) | − | 10.9960i | − | 0.485011i | ||||||
\(515\) | 6.95445 | − | 8.51743i | 0.306450 | − | 0.375323i | ||||
\(516\) | −10.9441 | − | 4.89433i | −0.481785 | − | 0.215461i | ||||
\(517\) | −52.5667 | −2.31188 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.78416 | + | 0.797901i | 0.0783160 | + | 0.0350240i | ||||
\(520\) | 1.47723 | − | 1.80922i | 0.0647806 | − | 0.0793397i | ||||
\(521\) | −35.5962 | −1.55950 | −0.779748 | − | 0.626093i | \(-0.784653\pi\) | ||||
−0.779748 | + | 0.626093i | \(0.784653\pi\) | |||||||
\(522\) | −15.4772 | + | 13.8433i | −0.677420 | + | 0.605903i | ||||
\(523\) | −16.9061 | −0.739254 | −0.369627 | − | 0.929180i | \(-0.620515\pi\) | ||||
−0.369627 | + | 0.929180i | \(0.620515\pi\) | |||||||
\(524\) | −13.7725 | −0.601654 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.00000 | −0.0872041 | ||||||||
\(527\) | 20.9545 | 0.912790 | ||||||||
\(528\) | −7.40852 | − | 3.31319i | −0.322414 | − | 0.144188i | ||||
\(529\) | −2.95445 | −0.128454 | ||||||||
\(530\) | −7.07107 | + | 8.66025i | −0.307148 | + | 0.376177i | ||||
\(531\) | 21.1488 | + | 23.6451i | 0.917779 | + | 1.02611i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.09110 | −0.0472607 | ||||||||
\(534\) | −3.47723 | + | 7.77531i | −0.150474 | + | 0.336471i | ||||
\(535\) | 7.74597 | − | 9.48683i | 0.334887 | − | 0.410152i | ||||
\(536\) | 14.2701i | 0.616374i | ||||||||
\(537\) | 30.6464 | + | 13.7055i | 1.32249 | + | 0.591436i | ||||
\(538\) | 17.5810 | 0.757973 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.26139 | − | 10.8093i | 0.183381 | − | 0.465157i | ||||
\(541\) | 8.52277 | 0.366423 | 0.183211 | − | 0.983074i | \(-0.441351\pi\) | ||||
0.183211 | + | 0.983074i | \(0.441351\pi\) | |||||||
\(542\) | − | 6.32456i | − | 0.271663i | ||||||
\(543\) | 5.00000 | + | 2.23607i | 0.214571 | + | 0.0959589i | ||||
\(544\) | − | 3.16228i | − | 0.135582i | ||||||
\(545\) | 28.8948 | − | 35.3887i | 1.23772 | − | 1.51589i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.61845i | − | 0.154714i | −0.997003 | − | 0.0773569i | \(-0.975352\pi\) | ||
0.997003 | − | 0.0773569i | \(-0.0246481\pi\) | |||||||
\(548\) | −3.47723 | −0.148540 | ||||||||
\(549\) | 7.74597 | − | 6.92820i | 0.330590 | − | 0.295689i | ||||
\(550\) | −22.9545 | + | 4.68556i | −0.978781 | + | 0.199793i | ||||
\(551\) | −9.89949 | −0.421733 | ||||||||
\(552\) | 3.16588 | − | 7.07912i | 0.134749 | − | 0.301307i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 9.79796i | − | 0.416275i | ||||||
\(555\) | 9.21584 | − | 4.62977i | 0.391191 | − | 0.196523i | ||||
\(556\) | 20.1810i | 0.855863i | ||||||||
\(557\) | 27.8634 | 1.18061 | 0.590304 | − | 0.807181i | \(-0.299008\pi\) | ||||
0.590304 | + | 0.807181i | \(0.299008\pi\) | |||||||
\(558\) | 14.8170 | − | 13.2528i | 0.627255 | − | 0.561034i | ||||
\(559\) | 7.23003i | 0.305798i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.4772 | + | 23.4278i | −0.442349 | + | 0.989122i | ||||
\(562\) | 1.80922i | 0.0763175i | ||||||||
\(563\) | − | 10.3923i | − | 0.437983i | −0.975727 | − | 0.218992i | \(-0.929723\pi\) | ||
0.975727 | − | 0.218992i | \(-0.0702768\pi\) | |||||||
\(564\) | −17.7386 | − | 7.93295i | −0.746930 | − | 0.334037i | ||||
\(565\) | −24.7165 | + | 30.2714i | −1.03983 | + | 1.27353i | ||||
\(566\) | 9.22460 | 0.387739 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.92163i | 0.290425i | ||||||||
\(569\) | 7.56189i | 0.317011i | 0.987358 | + | 0.158505i | \(0.0506676\pi\) | ||||
−0.987358 | + | 0.158505i | \(0.949332\pi\) | |||||||
\(570\) | 4.94975 | − | 2.48661i | 0.207322 | − | 0.104153i | ||||
\(571\) | 14.9545 | 0.625824 | 0.312912 | − | 0.949782i | \(-0.398695\pi\) | ||||
0.312912 | + | 0.949782i | \(0.398695\pi\) | |||||||
\(572\) | 4.89433i | 0.204642i | ||||||||
\(573\) | 25.7611 | + | 11.5207i | 1.07618 | + | 0.481284i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.47723 | − | 21.9338i | −0.186713 | − | 0.914704i | ||||
\(576\) | −2.00000 | − | 2.23607i | −0.0833333 | − | 0.0931695i | ||||
\(577\) | −0.674899 | −0.0280964 | −0.0140482 | − | 0.999901i | \(-0.504472\pi\) | ||||
−0.0140482 | + | 0.999901i | \(0.504472\pi\) | |||||||
\(578\) | 7.00000 | 0.291162 | ||||||||
\(579\) | 11.6190 | + | 5.19615i | 0.482867 | + | 0.215945i | ||||
\(580\) | 11.9886 | + | 9.78866i | 0.497800 | + | 0.406452i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.47723 | − | 18.9557i | 0.351392 | − | 0.785737i | ||||
\(583\) | − | 23.4278i | − | 0.970280i | ||||||
\(584\) | 3.50333 | 0.144969 | ||||||||
\(585\) | −7.00000 | + | 0.315272i | −0.289414 | + | 0.0130349i | ||||
\(586\) | 8.05661i | 0.332815i | ||||||||
\(587\) | − | 21.0864i | − | 0.870330i | −0.900351 | − | 0.435165i | \(-0.856690\pi\) | ||
0.900351 | − | 0.435165i | \(-0.143310\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.47723 | 0.390502 | ||||||||
\(590\) | 14.9545 | − | 18.3154i | 0.615665 | − | 0.754033i | ||||
\(591\) | 6.36396 | − | 14.2302i | 0.261778 | − | 0.585354i | ||||
\(592\) | − | 2.66291i | − | 0.109445i | ||||||
\(593\) | − | 1.65316i | − | 0.0678871i | −0.999424 | − | 0.0339435i | \(-0.989193\pi\) | ||
0.999424 | − | 0.0339435i | \(-0.0108066\pi\) | |||||||
\(594\) | 7.40852 | + | 23.1923i | 0.303975 | + | 0.951593i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.44949i | 0.100335i | ||||||||
\(597\) | −24.5228 | − | 10.9669i | −1.00365 | − | 0.448846i | ||||
\(598\) | −4.67671 | −0.191245 | ||||||||
\(599\) | − | 23.6412i | − | 0.965954i | −0.875633 | − | 0.482977i | \(-0.839556\pi\) | ||
0.875633 | − | 0.482977i | \(-0.160444\pi\) | |||||||
\(600\) | −8.45307 | − | 1.88296i | −0.345095 | − | 0.0768716i | ||||
\(601\) | − | 4.06775i | − | 0.165927i | −0.996553 | − | 0.0829635i | \(-0.973562\pi\) | ||
0.996553 | − | 0.0829635i | \(-0.0264385\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.9089 | − | 28.5402i | 1.29943 | − | 1.16225i | ||||
\(604\) | −2.00000 | −0.0813788 | ||||||||
\(605\) | 15.4919 | − | 18.9737i | 0.629837 | − | 0.771389i | ||||
\(606\) | 8.00000 | − | 17.8885i | 0.324978 | − | 0.726672i | ||||
\(607\) | 12.2938 | 0.498992 | 0.249496 | − | 0.968376i | \(-0.419735\pi\) | ||||
0.249496 | + | 0.968376i | \(0.419735\pi\) | |||||||
\(608\) | − | 1.43023i | − | 0.0580034i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.00000 | − | 4.89898i | −0.242933 | − | 0.198354i | ||||
\(611\) | 11.7188i | 0.474090i | ||||||||
\(612\) | −7.07107 | + | 6.32456i | −0.285831 | + | 0.255655i | ||||
\(613\) | 5.85452i | 0.236462i | 0.992986 | + | 0.118231i | \(0.0377223\pi\) | ||||
−0.992986 | + | 0.118231i | \(0.962278\pi\) | |||||||
\(614\) | −11.9886 | −0.483821 | ||||||||
\(615\) | 1.81608 | + | 3.61501i | 0.0732314 | + | 0.145771i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.5228 | 0.584665 | 0.292332 | − | 0.956317i | \(-0.405569\pi\) | ||||
0.292332 | + | 0.956317i | \(0.405569\pi\) | |||||||
\(618\) | −3.47723 | + | 7.77531i | −0.139875 | + | 0.312769i | ||||
\(619\) | − | 30.1925i | − | 1.21354i | −0.794877 | − | 0.606771i | \(-0.792465\pi\) | ||
0.794877 | − | 0.606771i | \(-0.207535\pi\) | |||||||
\(620\) | −11.4772 | − | 9.37112i | −0.460936 | − | 0.376353i | ||||
\(621\) | −22.1611 | + | 7.07912i | −0.889296 | + | 0.284075i | ||||
\(622\) | 17.5810 | 0.704936 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.738613 | + | 1.65159i | −0.0295682 | + | 0.0661165i | ||||
\(625\) | −23.0000 | + | 9.79796i | −0.920000 | + | 0.391918i | ||||
\(626\) | 23.2379 | 0.928773 | ||||||||
\(627\) | −4.73861 | + | 10.5959i | −0.189242 | + | 0.423158i | ||||
\(628\) | 14.4474 | 0.576513 | ||||||||
\(629\) | −8.42087 | −0.335762 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.47723 | 0.138426 | 0.0692131 | − | 0.997602i | \(-0.477951\pi\) | ||||
0.0692131 | + | 0.997602i | \(0.477951\pi\) | |||||||
\(632\) | 11.4772 | 0.456540 | ||||||||
\(633\) | 17.3080 | − | 38.7019i | 0.687932 | − | 1.53826i | ||||
\(634\) | −9.90890 | −0.393533 | ||||||||
\(635\) | −15.1223 | − | 12.3473i | −0.600109 | − | 0.489987i | ||||
\(636\) | 3.53553 | − | 7.90569i | 0.140193 | − | 0.313481i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −32.4317 | −1.28398 | ||||||||
\(639\) | 15.4772 | − | 13.8433i | 0.612270 | − | 0.547631i | ||||
\(640\) | −1.41421 | + | 1.73205i | −0.0559017 | + | 0.0684653i | ||||
\(641\) | 16.0793i | 0.635095i | 0.948242 | + | 0.317547i | \(0.102859\pi\) | ||||
−0.948242 | + | 0.317547i | \(0.897141\pi\) | |||||||
\(642\) | −3.87298 | + | 8.66025i | −0.152854 | + | 0.341793i | ||||
\(643\) | 26.0663 | 1.02796 | 0.513978 | − | 0.857803i | \(-0.328171\pi\) | ||||
0.513978 | + | 0.857803i | \(0.328171\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.9545 | − | 12.0340i | 0.943206 | − | 0.473839i | ||||
\(646\) | −4.52277 | −0.177946 | ||||||||
\(647\) | − | 20.4039i | − | 0.802160i | −0.916043 | − | 0.401080i | \(-0.868635\pi\) | ||
0.916043 | − | 0.401080i | \(-0.131365\pi\) | |||||||
\(648\) | −1.00000 | + | 8.94427i | −0.0392837 | + | 0.351364i | ||||
\(649\) | 49.5469i | 1.94489i | ||||||||
\(650\) | 1.04456 | + | 5.11726i | 0.0409709 | + | 0.200715i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 14.6969i | − | 0.575577i | ||||||
\(653\) | 39.8634 | 1.55997 | 0.779987 | − | 0.625796i | \(-0.215226\pi\) | ||||
0.779987 | + | 0.625796i | \(0.215226\pi\) | |||||||
\(654\) | −14.4474 | + | 32.3053i | −0.564937 | + | 1.26324i | ||||
\(655\) | 19.4772 | − | 23.8546i | 0.761038 | − | 0.932078i | ||||
\(656\) | 1.04456 | 0.0407831 | ||||||||
\(657\) | −7.00665 | − | 7.83368i | −0.273356 | − | 0.305621i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.2929i | 1.33586i | 0.744224 | + | 0.667930i | \(0.232819\pi\) | ||||
−0.744224 | + | 0.667930i | \(0.767181\pi\) | |||||||
\(660\) | 16.2158 | − | 8.14637i | 0.631201 | − | 0.317097i | ||||
\(661\) | − | 0.603648i | − | 0.0234792i | −0.999931 | − | 0.0117396i | \(-0.996263\pi\) | ||
0.999931 | − | 0.0117396i | \(-0.00373691\pi\) | |||||||
\(662\) | 21.4317 | 0.832966 | ||||||||
\(663\) | 5.22278 | + | 2.33570i | 0.202836 | + | 0.0907110i | ||||
\(664\) | − | 4.06775i | − | 0.157859i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.95445 | + | 5.32582i | −0.230730 | + | 0.206371i | ||||
\(667\) | − | 30.9897i | − | 1.19993i | ||||||
\(668\) | − | 4.29068i | − | 0.166011i | ||||||
\(669\) | 15.4772 | − | 34.6081i | 0.598384 | − | 1.33803i | ||||
\(670\) | −24.7165 | − | 20.1810i | −0.954883 | − | 0.779659i | ||||
\(671\) | 16.2312 | 0.626600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.1585i | 0.545771i | 0.962047 | + | 0.272885i | \(0.0879780\pi\) | ||||
−0.962047 | + | 0.272885i | \(0.912022\pi\) | |||||||
\(674\) | − | 17.1464i | − | 0.660456i | ||||||
\(675\) | 12.6957 | + | 22.6676i | 0.488658 | + | 0.872475i | ||||
\(676\) | −11.9089 | −0.458035 | ||||||||
\(677\) | − | 32.9090i | − | 1.26479i | −0.774644 | − | 0.632397i | \(-0.782071\pi\) | ||
0.774644 | − | 0.632397i | \(-0.217929\pi\) | |||||||
\(678\) | 12.3583 | − | 27.6339i | 0.474616 | − | 1.06127i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.47723 | + | 4.47214i | 0.210042 | + | 0.171499i | ||||
\(681\) | −16.4317 | − | 7.34847i | −0.629663 | − | 0.281594i | ||||
\(682\) | 31.0483 | 1.18890 | ||||||||
\(683\) | −18.9545 | −0.725272 | −0.362636 | − | 0.931931i | \(-0.618123\pi\) | ||||
−0.362636 | + | 0.931931i | \(0.618123\pi\) | |||||||
\(684\) | −3.19808 | + | 2.86045i | −0.122282 | + | 0.109372i | ||||
\(685\) | 4.91754 | − | 6.02273i | 0.187890 | − | 0.230117i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.4317 | − | 9.58454i | −0.817669 | − | 0.365673i | ||||
\(688\) | − | 6.92163i | − | 0.263885i | ||||||
\(689\) | −5.22278 | −0.198972 | ||||||||
\(690\) | 7.78416 | + | 15.4948i | 0.296338 | + | 0.589878i | ||||
\(691\) | 3.46410i | 0.131781i | 0.997827 | + | 0.0658903i | \(0.0209887\pi\) | ||||
−0.997827 | + | 0.0658903i | \(0.979011\pi\) | |||||||
\(692\) | 1.12840i | 0.0428954i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.4772 | −0.663426 | ||||||||
\(695\) | −34.9545 | − | 28.5402i | −1.32590 | − | 1.08259i | ||||
\(696\) | −10.9441 | − | 4.89433i | −0.414833 | − | 0.185519i | ||||
\(697\) | − | 3.30318i | − | 0.125117i | ||||||
\(698\) | − | 11.7436i | − | 0.444503i | ||||||
\(699\) | −2.82843 | + | 6.32456i | −0.106981 | + | 0.239217i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 51.7546i | − | 1.95474i | −0.211531 | − | 0.977371i | \(-0.567845\pi\) | ||
0.211531 | − | 0.977371i | \(-0.432155\pi\) | |||||||
\(702\) | 5.17029 | − | 1.65159i | 0.195140 | − | 0.0623352i | ||||
\(703\) | −3.80857 | −0.143643 | ||||||||
\(704\) | − | 4.68556i | − | 0.176594i | ||||||
\(705\) | 38.8265 | − | 19.5053i | 1.46229 | − | 0.734612i | ||||
\(706\) | − | 0.603648i | − | 0.0227186i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.47723 | + | 16.7196i | −0.281011 | + | 0.628360i | ||||
\(709\) | −22.4317 | −0.842439 | −0.421220 | − | 0.906959i | \(-0.638398\pi\) | ||||
−0.421220 | + | 0.906959i | \(0.638398\pi\) | |||||||
\(710\) | −11.9886 | − | 9.78866i | −0.449924 | − | 0.367362i | ||||
\(711\) | −22.9545 | − | 25.6639i | −0.860859 | − | 0.962470i | ||||
\(712\) | −4.91754 | −0.184293 | ||||||||
\(713\) | 29.6678i | 1.11107i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.47723 | − | 6.92163i | −0.317030 | − | 0.258854i | ||||
\(716\) | 19.3825i | 0.724358i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 11.3938i | − | 0.425211i | ||||||
\(719\) | 0.803730 | 0.0299741 | 0.0149870 | − | 0.999888i | \(-0.495229\pi\) | ||||
0.0149870 | + | 0.999888i | \(0.495229\pi\) | |||||||
\(720\) | 6.70141 | − | 0.301824i | 0.249747 | − | 0.0112483i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.9545 | 0.630979 | ||||||||
\(723\) | 33.6931 | + | 15.0680i | 1.25306 | + | 0.560385i | ||||
\(724\) | 3.16228i | 0.117525i | ||||||||
\(725\) | −33.9089 | + | 6.92163i | −1.25935 | + | 0.257063i | ||||
\(726\) | −7.74597 | + | 17.3205i | −0.287480 | + | 0.642824i | ||||
\(727\) | 15.1223 | 0.560854 | 0.280427 | − | 0.959875i | \(-0.409524\pi\) | ||||
0.280427 | + | 0.959875i | \(0.409524\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.0000 | − | 15.6525i | 0.814815 | − | 0.579721i | ||||
\(730\) | −4.95445 | + | 6.06794i | −0.183372 | + | 0.224584i | ||||
\(731\) | −21.8881 | −0.809561 | ||||||||
\(732\) | 5.47723 | + | 2.44949i | 0.202444 | + | 0.0905357i | ||||
\(733\) | 2.39435 | 0.0884375 | 0.0442187 | − | 0.999022i | \(-0.485920\pi\) | ||||
0.0442187 | + | 0.999022i | \(0.485920\pi\) | |||||||
\(734\) | 0.369657 | 0.0136443 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.47723 | 0.165033 | ||||||||
\(737\) | 66.8634 | 2.46294 | ||||||||
\(738\) | −2.08911 | − | 2.33570i | −0.0769013 | − | 0.0859783i | ||||
\(739\) | 6.47723 | 0.238269 | 0.119134 | − | 0.992878i | \(-0.461988\pi\) | ||||
0.119134 | + | 0.992878i | \(0.461988\pi\) | |||||||
\(740\) | 4.61230 | + | 3.76593i | 0.169551 | + | 0.138438i | ||||
\(741\) | 2.36215 | + | 1.05638i | 0.0867756 | + | 0.0388072i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.4317 | 0.492760 | 0.246380 | − | 0.969173i | \(-0.420759\pi\) | ||||
0.246380 | + | 0.969173i | \(0.420759\pi\) | |||||||
\(744\) | 10.4772 | + | 4.68556i | 0.384114 | + | 0.171781i | ||||
\(745\) | −4.24264 | − | 3.46410i | −0.155438 | − | 0.126915i | ||||
\(746\) | 23.2144i | 0.849938i | ||||||||
\(747\) | −9.09576 | + | 8.13550i | −0.332797 | + | 0.297662i | ||||
\(748\) | −14.8170 | −0.541764 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 15.2158 | − | 11.9782i | 0.555604 | − | 0.437384i | ||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | − | 11.2189i | − | 0.409111i | ||||||
\(753\) | 6.26139 | − | 14.0009i | 0.228178 | − | 0.510221i | ||||
\(754\) | 7.23003i | 0.263302i | ||||||||
\(755\) | 2.82843 | − | 3.46410i | 0.102937 | − | 0.126072i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.1361i | 1.74954i | 0.484541 | + | 0.874768i | \(0.338986\pi\) | ||||
−0.484541 | + | 0.874768i | \(0.661014\pi\) | |||||||
\(758\) | −20.4772 | −0.743766 | ||||||||
\(759\) | −33.1696 | − | 14.8339i | −1.20398 | − | 0.538436i | ||||
\(760\) | 2.47723 | + | 2.02265i | 0.0898584 | + | 0.0733691i | ||||
\(761\) | −1.78387 | −0.0646653 | −0.0323326 | − | 0.999477i | \(-0.510294\pi\) | ||||
−0.0323326 | + | 0.999477i | \(0.510294\pi\) | |||||||
\(762\) | 13.8047 | + | 6.17364i | 0.500091 | + | 0.223648i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.2927i | 0.589451i | ||||||||
\(765\) | −0.954451 | − | 21.1917i | −0.0345083 | − | 0.766188i | ||||
\(766\) | 18.1471i | 0.655681i | ||||||||
\(767\) | 11.0455 | 0.398832 | ||||||||
\(768\) | 0.707107 | − | 1.58114i | 0.0255155 | − | 0.0570544i | ||||
\(769\) | − | 16.1921i | − | 0.583902i | −0.956433 | − | 0.291951i | \(-0.905696\pi\) | ||
0.956433 | − | 0.291951i | \(-0.0943045\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.3861 | − | 7.77531i | −0.626146 | − | 0.280021i | ||||
\(772\) | 7.34847i | 0.264477i | ||||||||
\(773\) | 16.1921i | 0.582390i | 0.956664 | + | 0.291195i | \(0.0940528\pi\) | ||||
−0.956664 | + | 0.291195i | \(0.905947\pi\) | |||||||
\(774\) | −15.4772 | + | 13.8433i | −0.556317 | + | 0.497585i | ||||
\(775\) | 32.4625 | − | 6.62638i | 1.16609 | − | 0.238027i | ||||
\(776\) | 11.9886 | 0.430366 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.34847i | 0.263455i | ||||||||
\(779\) | − | 1.49395i | − | 0.0535264i | ||||||
\(780\) | −1.81608 | − | 3.61501i | −0.0650261 | − | 0.129438i | ||||
\(781\) | 32.4317 | 1.16050 | ||||||||
\(782\) | − | 14.1582i | − | 0.506297i | ||||||
\(783\) | 10.9441 | + | 34.2603i | 0.391108 | + | 1.22436i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.4317 | + | 25.0236i | −0.729238 | + | 0.893130i | ||||
\(786\) | −9.73861 | + | 21.7762i | −0.347365 | + | 0.776731i | ||||
\(787\) | −50.1724 | −1.78845 | −0.894226 | − | 0.447616i | \(-0.852273\pi\) | ||||
−0.894226 | + | 0.447616i | \(0.852273\pi\) | |||||||
\(788\) | 9.00000 | 0.320612 | ||||||||
\(789\) | −1.41421 | + | 3.16228i | −0.0503473 | + | 0.112580i | ||||
\(790\) | −16.2312 | + | 19.8791i | −0.577482 | + | 0.707268i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.4772 | + | 9.37112i | −0.372292 | + | 0.332988i | ||||
\(793\) | − | 3.61845i | − | 0.128495i | ||||||
\(794\) | 14.8815 | 0.528123 | ||||||||
\(795\) | 8.69306 | + | 17.3041i | 0.308311 | + | 0.613712i | ||||
\(796\) | − | 15.5096i | − | 0.549722i | ||||||
\(797\) | 54.2183i | 1.92051i | 0.279121 | + | 0.960256i | \(0.409957\pi\) | ||||
−0.279121 | + | 0.960256i | \(0.590043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.4772 | −1.25509 | ||||||||
\(800\) | −1.00000 | − | 4.89898i | −0.0353553 | − | 0.173205i | ||||
\(801\) | 9.83508 | + | 10.9960i | 0.347505 | + | 0.388523i | ||||
\(802\) | 0.955537i | 0.0337412i | ||||||||
\(803\) | − | 16.4150i | − | 0.579274i | ||||||
\(804\) | 22.5630 | + | 10.0905i | 0.795736 | + | 0.355864i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 6.92163i | − | 0.243804i | ||||||
\(807\) | 12.4317 | − | 27.7981i | 0.437616 | − | 0.978539i | ||||
\(808\) | 11.3137 | 0.398015 | ||||||||
\(809\) | 8.84242i | 0.310883i | 0.987845 | + | 0.155441i | \(0.0496800\pi\) | ||||
−0.987845 | + | 0.155441i | \(0.950320\pi\) | |||||||
\(810\) | −14.0777 | − | 14.3812i | −0.494641 | − | 0.505303i | ||||
\(811\) | − | 38.3280i | − | 1.34588i | −0.739697 | − | 0.672940i | \(-0.765031\pi\) | ||
0.739697 | − | 0.672940i | \(-0.234969\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.0000 | − | 4.47214i | −0.350715 | − | 0.156845i | ||||
\(814\) | −12.4772 | −0.437327 | ||||||||
\(815\) | 25.4558 | + | 20.7846i | 0.891679 | + | 0.728053i | ||||
\(816\) | −5.00000 | − | 2.23607i | −0.175035 | − | 0.0782780i | ||||
\(817\) | −9.89949 | −0.346339 | ||||||||
\(818\) | − | 15.5096i | − | 0.542279i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.47723 | + | 1.80922i | −0.0515870 | + | 0.0631809i | ||||
\(821\) | − | 11.7090i | − | 0.408648i | −0.978903 | − | 0.204324i | \(-0.934500\pi\) | ||
0.978903 | − | 0.204324i | \(-0.0654996\pi\) | |||||||
\(822\) | −2.45877 | + | 5.49798i | −0.0857594 | + | 0.191764i | ||||
\(823\) | − | 3.19161i | − | 0.111252i | −0.998452 | − | 0.0556262i | \(-0.982284\pi\) | ||
0.998452 | − | 0.0556262i | \(-0.0177155\pi\) | |||||||
\(824\) | −4.91754 | −0.171311 | ||||||||
\(825\) | −8.82273 | + | 39.6074i | −0.307168 | + | 1.37895i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.90890 | −0.135926 | −0.0679629 | − | 0.997688i | \(-0.521650\pi\) | ||||
−0.0679629 | + | 0.997688i | \(0.521650\pi\) | |||||||
\(828\) | −8.95445 | − | 10.0114i | −0.311189 | − | 0.347920i | ||||
\(829\) | 50.4524i | 1.75228i | 0.482053 | + | 0.876142i | \(0.339891\pi\) | ||||
−0.482053 | + | 0.876142i | \(0.660109\pi\) | |||||||
\(830\) | 7.04555 | + | 5.75267i | 0.244555 | + | 0.199678i | ||||
\(831\) | −15.4919 | − | 6.92820i | −0.537409 | − | 0.240337i | ||||
\(832\) | −1.04456 | −0.0362135 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 31.9089 | + | 14.2701i | 1.10491 | + | 0.494133i | ||||
\(835\) | 7.43168 | + | 6.06794i | 0.257184 | + | 0.209990i | ||||
\(836\) | −6.70141 | −0.231773 | ||||||||
\(837\) | −10.4772 | − | 32.7989i | −0.362146 | − | 1.13370i | ||||
\(838\) | −8.85494 | −0.305889 | ||||||||
\(839\) | 40.1440 | 1.38593 | 0.692963 | − | 0.720973i | \(-0.256305\pi\) | ||||
0.692963 | + | 0.720973i | \(0.256305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9089 | −0.652031 | ||||||||
\(842\) | 18.9545 | 0.653214 | ||||||||
\(843\) | 2.86064 | + | 1.27931i | 0.0985255 | + | 0.0440619i | ||||
\(844\) | 24.4772 | 0.842541 | ||||||||
\(845\) | 16.8417 | − | 20.6268i | 0.579373 | − | 0.709584i | ||||
\(846\) | −25.0862 | + | 22.4378i | −0.862481 | + | 0.771426i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.00000 | 0.171701 | ||||||||
\(849\) | 6.52277 | − | 14.5854i | 0.223861 | − | 0.500569i | ||||
\(850\) | −15.4919 | + | 3.16228i | −0.531369 | + | 0.108465i | ||||
\(851\) | − | 11.9225i | − | 0.408697i | ||||||
\(852\) | 10.9441 | + | 4.89433i | 0.374937 | + | 0.167677i | ||||
\(853\) | −31.2891 | −1.07132 | −0.535659 | − | 0.844434i | \(-0.679937\pi\) | ||||
−0.535659 | + | 0.844434i | \(0.679937\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.431677 | − | 9.58454i | −0.0147630 | − | 0.327784i | ||||
\(856\) | −5.47723 | −0.187208 | ||||||||
\(857\) | − | 15.0637i | − | 0.514566i | −0.966336 | − | 0.257283i | \(-0.917173\pi\) | ||
0.966336 | − | 0.257283i | \(-0.0828273\pi\) | |||||||
\(858\) | 7.73861 | + | 3.46081i | 0.264192 | + | 0.118150i | ||||
\(859\) | − | 30.5733i | − | 1.04315i | −0.853207 | − | 0.521573i | \(-0.825345\pi\) | ||
0.853207 | − | 0.521573i | \(-0.174655\pi\) | |||||||
\(860\) | 11.9886 | + | 9.78866i | 0.408808 | + | 0.333790i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.66374i | 0.261028i | ||||||||
\(863\) | −26.4772 | −0.901295 | −0.450648 | − | 0.892702i | \(-0.648807\pi\) | ||||
−0.450648 | + | 0.892702i | \(0.648807\pi\) | |||||||
\(864\) | −4.94975 | + | 1.58114i | −0.168394 | + | 0.0537914i | ||||
\(865\) | −1.95445 | − | 1.59580i | −0.0664533 | − | 0.0542589i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.94975 | − | 11.0680i | 0.168102 | − | 0.375888i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 53.7772i | − | 1.82427i | ||||||
\(870\) | 23.9545 | − | 12.0340i | 0.812132 | − | 0.407992i | ||||
\(871\) | − | 14.9059i | − | 0.505068i | ||||||
\(872\) | −20.4317 | −0.691904 | ||||||||
\(873\) | −23.9772 | − | 26.8073i | −0.811506 | − | 0.907291i | ||||
\(874\) | − | 6.40345i | − | 0.216600i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.47723 | − | 5.53924i | 0.0836977 | − | 0.187154i | ||||
\(877\) | 55.6980i | 1.88079i | 0.340087 | + | 0.940394i | \(0.389543\pi\) | ||||
−0.340087 | + | 0.940394i | \(0.610457\pi\) | |||||||
\(878\) | − | 8.88319i | − | 0.299793i | ||||||
\(879\) | 12.7386 | + | 5.69688i | 0.429663 | + | 0.192151i | ||||
\(880\) | 8.11562 | + | 6.62638i | 0.273578 | + | 0.223375i | ||||
\(881\) | 18.7544 | 0.631853 | 0.315926 | − | 0.948784i | \(-0.397685\pi\) | ||||
0.315926 | + | 0.948784i | \(0.397685\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 24.3833i | − | 0.820564i | −0.911959 | − | 0.410282i | \(-0.865430\pi\) | ||
0.911959 | − | 0.410282i | \(-0.134570\pi\) | |||||||
\(884\) | 3.30318i | 0.111098i | ||||||||
\(885\) | −18.3848 | − | 36.5960i | −0.617997 | − | 1.23016i | ||||
\(886\) | −15.0455 | −0.505465 | ||||||||
\(887\) | 3.46410i | 0.116313i | 0.998307 | + | 0.0581566i | \(0.0185223\pi\) | ||||
−0.998307 | + | 0.0581566i | \(0.981478\pi\) | |||||||
\(888\) | −4.21043 | − | 1.88296i | −0.141293 | − | 0.0631881i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.95445 | − | 8.51743i | 0.233114 | − | 0.285505i | ||||
\(891\) | 41.9089 | + | 4.68556i | 1.40400 | + | 0.156972i | ||||
\(892\) | 21.8881 | 0.732868 | ||||||||
\(893\) | −16.0455 | −0.536944 | ||||||||
\(894\) | 3.87298 | + | 1.73205i | 0.129532 | + | 0.0579284i | ||||
\(895\) | −33.5715 | − | 27.4110i | −1.12217 | − | 0.916248i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.30694 | + | 7.39453i | −0.110415 | + | 0.246896i | ||||
\(898\) | 25.8773i | 0.863536i | ||||||||
\(899\) | 45.8653 | 1.52969 | ||||||||
\(900\) | −8.95445 | + | 12.0340i | −0.298482 | + | 0.401134i | ||||
\(901\) | − | 15.8114i | − | 0.526754i | ||||||
\(902\) | − | 4.89433i | − | 0.162963i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.4772 | 0.581284 | ||||||||
\(905\) | −5.47723 | − | 4.47214i | −0.182069 | − | 0.148659i | ||||
\(906\) | −1.41421 | + | 3.16228i | −0.0469841 | + | 0.105060i | ||||
\(907\) | − | 9.79796i | − | 0.325336i | −0.986681 | − | 0.162668i | \(-0.947990\pi\) | ||
0.986681 | − | 0.162668i | \(-0.0520099\pi\) | |||||||
\(908\) | − | 10.3923i | − | 0.344881i | ||||||
\(909\) | −22.6274 | − | 25.2982i | −0.750504 | − | 0.839089i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0681i | 0.797410i | 0.917079 | + | 0.398705i | \(0.130540\pi\) | ||||
−0.917079 | + | 0.398705i | \(0.869460\pi\) | |||||||
\(912\) | −2.26139 | − | 1.01132i | −0.0748820 | − | 0.0334883i | ||||
\(913\) | −19.0597 | −0.630783 | ||||||||
\(914\) | − | 11.0785i | − | 0.366444i | ||||||
\(915\) | −11.9886 | + | 6.02273i | −0.396331 | + | 0.199105i | ||||
\(916\) | − | 13.5546i | − | 0.447856i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.00000 | + | 15.6525i | 0.165025 | + | 0.516609i | ||||
\(919\) | 0.431677 | 0.0142397 | 0.00711985 | − | 0.999975i | \(-0.497734\pi\) | ||||
0.00711985 | + | 0.999975i | \(0.497734\pi\) | |||||||
\(920\) | −6.33175 | + | 7.75478i | −0.208752 | + | 0.255668i | ||||
\(921\) | −8.47723 | + | 18.9557i | −0.279334 | + | 0.624610i | ||||
\(922\) | −31.7876 | −1.04687 | ||||||||
\(923\) | − | 7.23003i | − | 0.237979i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.0455 | + | 2.66291i | −0.428935 | + | 0.0875560i | ||||
\(926\) | 22.5741i | 0.741831i | ||||||||
\(927\) | 9.83508 | + | 10.9960i | 0.323026 | + | 0.361154i | ||||
\(928\) | − | 6.92163i | − | 0.227213i | ||||||
\(929\) | 15.9260 | 0.522515 | 0.261258 | − | 0.965269i | \(-0.415863\pi\) | ||||
0.261258 | + | 0.965269i | \(0.415863\pi\) | |||||||
\(930\) | −22.9327 | + | 11.5207i | −0.751991 | + | 0.377779i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.00000 | −0.131024 | ||||||||
\(933\) | 12.4317 | − | 27.7981i | 0.406995 | − | 0.910068i | ||||
\(934\) | − | 28.0146i | − | 0.916667i | ||||||
\(935\) | 20.9545 | − | 25.6639i | 0.685284 | − | 0.839298i | ||||
\(936\) | 2.08911 | + | 2.33570i | 0.0682848 | + | 0.0763447i | ||||
\(937\) | 53.6757 | 1.75351 | 0.876754 | − | 0.480938i | \(-0.159704\pi\) | ||||
0.876754 | + | 0.480938i | \(0.159704\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.4317 | − | 36.7423i | 0.536228 | − | 1.19904i | ||||
\(940\) | 19.4317 | + | 15.8659i | 0.633791 | + | 0.517489i | ||||
\(941\) | −20.4739 | −0.667430 | −0.333715 | − | 0.942674i | \(-0.608302\pi\) | ||||
−0.333715 | + | 0.942674i | \(0.608302\pi\) | |||||||
\(942\) | 10.2158 | − | 22.8433i | 0.332850 | − | 0.744275i | ||||
\(943\) | 4.67671 | 0.152295 | ||||||||
\(944\) | −10.5744 | −0.344167 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.4317 | −1.05444 | ||||||||
\(947\) | 32.8634 | 1.06792 | 0.533958 | − | 0.845511i | \(-0.320704\pi\) | ||||
0.533958 | + | 0.845511i | \(0.320704\pi\) | |||||||
\(948\) | 8.11562 | − | 18.1471i | 0.263583 | − | 0.589390i | ||||
\(949\) | −3.65942 | −0.118790 | ||||||||
\(950\) | −7.00665 | + | 1.43023i | −0.227326 | + | 0.0464027i | ||||
\(951\) | −7.00665 | + | 15.6674i | −0.227206 | + | 0.508049i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.9545 | 1.52100 | 0.760502 | − | 0.649336i | \(-0.224953\pi\) | ||||
0.760502 | + | 0.649336i | \(0.224953\pi\) | |||||||
\(954\) | −10.0000 | − | 11.1803i | −0.323762 | − | 0.361977i | ||||
\(955\) | −28.2199 | − | 23.0414i | −0.913173 | − | 0.745603i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22.9327 | + | 51.2790i | −0.741308 | + | 1.65761i | ||||
\(958\) | −42.3620 | −1.36865 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.73861 | + | 3.46081i | 0.0561135 | + | 0.111697i | ||||
\(961\) | −12.9089 | −0.416416 | ||||||||
\(962\) | 2.78156i | 0.0896811i | ||||||||
\(963\) | 10.9545 | + | 12.2474i | 0.353002 | + | 0.394669i | ||||
\(964\) | 21.3094i | 0.686328i | ||||||||
\(965\) | −12.7279 | − | 10.3923i | −0.409726 | − | 0.334540i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 7.23690i | − | 0.232723i | −0.993207 | − | 0.116361i | \(-0.962877\pi\) | ||
0.993207 | − | 0.116361i | \(-0.0371231\pi\) | |||||||
\(968\) | −10.9545 | −0.352089 | ||||||||
\(969\) | −3.19808 | + | 7.15113i | −0.102737 | + | 0.229728i | ||||
\(970\) | −16.9545 | + | 20.7649i | −0.544375 | + | 0.666720i | ||||
\(971\) | −37.7497 | −1.21145 | −0.605723 | − | 0.795676i | \(-0.707116\pi\) | ||||
−0.605723 | + | 0.795676i | \(0.707116\pi\) | |||||||
\(972\) | 13.4350 | + | 7.90569i | 0.430929 | + | 0.253575i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 17.0349i | − | 0.545832i | ||||||
\(975\) | 8.82971 | + | 1.96686i | 0.282777 | + | 0.0629899i | ||||
\(976\) | 3.46410i | 0.110883i | ||||||||
\(977\) | 3.90890 | 0.125057 | 0.0625284 | − | 0.998043i | \(-0.480084\pi\) | ||||
0.0625284 | + | 0.998043i | \(0.480084\pi\) | |||||||
\(978\) | −23.2379 | − | 10.3923i | −0.743066 | − | 0.332309i | ||||
\(979\) | 23.0414i | 0.736407i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 40.8634 | + | 45.6866i | 1.30467 | + | 1.45866i | ||||
\(982\) | − | 13.8433i | − | 0.441756i | ||||||
\(983\) | 52.7881i | 1.68368i | 0.539728 | + | 0.841840i | \(0.318527\pi\) | ||||
−0.539728 | + | 0.841840i | \(0.681473\pi\) | |||||||
\(984\) | 0.738613 | − | 1.65159i | 0.0235461 | − | 0.0526507i | ||||
\(985\) | −12.7279 | + | 15.5885i | −0.405545 | + | 0.496690i | ||||
\(986\) | −21.8881 | −0.697059 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.49395i | 0.0475290i | ||||||||
\(989\) | − | 30.9897i | − | 0.985414i | ||||||
\(990\) | −1.41421 | − | 31.3998i | −0.0449467 | − | 0.997953i | ||||
\(991\) | 10.5228 | 0.334267 | 0.167133 | − | 0.985934i | \(-0.446549\pi\) | ||||
0.167133 | + | 0.985934i | \(0.446549\pi\) | |||||||
\(992\) | 6.62638i | 0.210388i | ||||||||
\(993\) | 15.1545 | − | 33.8865i | 0.480913 | − | 1.07535i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.8634 | + | 21.9338i | 0.851626 | + | 0.695349i | ||||
\(996\) | −6.43168 | − | 2.87633i | −0.203795 | − | 0.0911401i | ||||
\(997\) | 15.4919 | 0.490634 | 0.245317 | − | 0.969443i | \(-0.421108\pi\) | ||||
0.245317 | + | 0.969443i | \(0.421108\pi\) | |||||||
\(998\) | 1.90890 | 0.0604252 | ||||||||
\(999\) | 4.21043 | + | 13.1807i | 0.133212 | + | 0.417020i |
(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 | 1470.2.d.f.1469.6 | 8 | ||
3.2 | odd | 2 | 1470.2.d.e.1469.7 | 8 | |||
5.4 | even | 2 | 1470.2.d.e.1469.3 | 8 | |||
7.2 | even | 3 | 210.2.t.e.59.3 | ✓ | 8 | ||
7.3 | odd | 6 | 210.2.t.e.89.4 | yes | 8 | ||
7.6 | odd | 2 | inner | 1470.2.d.f.1469.3 | 8 | ||
15.14 | odd | 2 | inner | 1470.2.d.f.1469.2 | 8 | ||
21.2 | odd | 6 | 210.2.t.f.59.1 | yes | 8 | ||
21.17 | even | 6 | 210.2.t.f.89.2 | yes | 8 | ||
21.20 | even | 2 | 1470.2.d.e.1469.2 | 8 | |||
35.2 | odd | 12 | 1050.2.s.i.101.8 | 16 | |||
35.3 | even | 12 | 1050.2.s.i.551.7 | 16 | |||
35.9 | even | 6 | 210.2.t.f.59.2 | yes | 8 | ||
35.17 | even | 12 | 1050.2.s.i.551.2 | 16 | |||
35.23 | odd | 12 | 1050.2.s.i.101.1 | 16 | |||
35.24 | odd | 6 | 210.2.t.f.89.1 | yes | 8 | ||
35.34 | odd | 2 | 1470.2.d.e.1469.6 | 8 | |||
105.2 | even | 12 | 1050.2.s.i.101.2 | 16 | |||
105.17 | odd | 12 | 1050.2.s.i.551.8 | 16 | |||
105.23 | even | 12 | 1050.2.s.i.101.7 | 16 | |||
105.38 | odd | 12 | 1050.2.s.i.551.1 | 16 | |||
105.44 | odd | 6 | 210.2.t.e.59.4 | yes | 8 | ||
105.59 | even | 6 | 210.2.t.e.89.3 | yes | 8 | ||
105.104 | even | 2 | inner | 1470.2.d.f.1469.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.e.59.3 | ✓ | 8 | 7.2 | even | 3 | ||
210.2.t.e.59.4 | yes | 8 | 105.44 | odd | 6 | ||
210.2.t.e.89.3 | yes | 8 | 105.59 | even | 6 | ||
210.2.t.e.89.4 | yes | 8 | 7.3 | odd | 6 | ||
210.2.t.f.59.1 | yes | 8 | 21.2 | odd | 6 | ||
210.2.t.f.59.2 | yes | 8 | 35.9 | even | 6 | ||
210.2.t.f.89.1 | yes | 8 | 35.24 | odd | 6 | ||
210.2.t.f.89.2 | yes | 8 | 21.17 | even | 6 | ||
1050.2.s.i.101.1 | 16 | 35.23 | odd | 12 | |||
1050.2.s.i.101.2 | 16 | 105.2 | even | 12 | |||
1050.2.s.i.101.7 | 16 | 105.23 | even | 12 | |||
1050.2.s.i.101.8 | 16 | 35.2 | odd | 12 | |||
1050.2.s.i.551.1 | 16 | 105.38 | odd | 12 | |||
1050.2.s.i.551.2 | 16 | 35.17 | even | 12 | |||
1050.2.s.i.551.7 | 16 | 35.3 | even | 12 | |||
1050.2.s.i.551.8 | 16 | 105.17 | odd | 12 | |||
1470.2.d.e.1469.2 | 8 | 21.20 | even | 2 | |||
1470.2.d.e.1469.3 | 8 | 5.4 | even | 2 | |||
1470.2.d.e.1469.6 | 8 | 35.34 | odd | 2 | |||
1470.2.d.e.1469.7 | 8 | 3.2 | odd | 2 | |||
1470.2.d.f.1469.2 | 8 | 15.14 | odd | 2 | inner | ||
1470.2.d.f.1469.3 | 8 | 7.6 | odd | 2 | inner | ||
1470.2.d.f.1469.6 | 8 | 1.1 | even | 1 | trivial | ||
1470.2.d.f.1469.7 | 8 | 105.104 | even | 2 | inner |