Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,3,Mod(19,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("24.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.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: | \(0.653952634465\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.4752.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} - 6x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(0.866025 + 0.719687i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.19 |
Dual form | 24.3.b.a.19.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(13\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | + | 1.96622i | −0.183013 | + | 0.983111i | ||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −3.73205 | − | 1.43937i | −0.933013 | − | 0.359843i | ||||
\(5\) | 2.87875i | 0.575749i | 0.957668 | + | 0.287875i | \(0.0929487\pi\) | ||||
−0.957668 | + | 0.287875i | \(0.907051\pi\) | |||||||
\(6\) | −0.633975 | + | 3.40559i | −0.105662 | + | 0.567599i | ||||
\(7\) | − | 10.7436i | − | 1.53480i | −0.641166 | − | 0.767402i | \(-0.721549\pi\) | ||
0.641166 | − | 0.767402i | \(-0.278451\pi\) | |||||||
\(8\) | 4.19615 | − | 6.81119i | 0.524519 | − | 0.851399i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | −5.66025 | − | 1.05369i | −0.566025 | − | 0.105369i | ||||
\(11\) | −8.00000 | −0.727273 | −0.363636 | − | 0.931541i | \(-0.618465\pi\) | ||||
−0.363636 | + | 0.931541i | \(0.618465\pi\) | |||||||
\(12\) | −6.46410 | − | 2.49307i | −0.538675 | − | 0.207756i | ||||
\(13\) | 15.7298i | 1.20998i | 0.796232 | + | 0.604991i | \(0.206823\pi\) | ||||
−0.796232 | + | 0.604991i | \(0.793177\pi\) | |||||||
\(14\) | 21.1244 | + | 3.93244i | 1.50888 | + | 0.280889i | ||||
\(15\) | 4.98614i | 0.332409i | ||||||||
\(16\) | 11.8564 | + | 10.7436i | 0.741025 | + | 0.671477i | ||||
\(17\) | −15.8564 | −0.932730 | −0.466365 | − | 0.884592i | \(-0.654437\pi\) | ||||
−0.466365 | + | 0.884592i | \(0.654437\pi\) | |||||||
\(18\) | −1.09808 | + | 5.89866i | −0.0610042 | + | 0.327704i | ||||
\(19\) | 1.07180 | 0.0564104 | 0.0282052 | − | 0.999602i | \(-0.491021\pi\) | ||||
0.0282052 | + | 0.999602i | \(0.491021\pi\) | |||||||
\(20\) | 4.14359 | − | 10.7436i | 0.207180 | − | 0.537182i | ||||
\(21\) | − | 18.6085i | − | 0.886120i | ||||||
\(22\) | 2.92820 | − | 15.7298i | 0.133100 | − | 0.714989i | ||||
\(23\) | 21.4873i | 0.934229i | 0.884197 | + | 0.467114i | \(0.154706\pi\) | ||||
−0.884197 | + | 0.467114i | \(0.845294\pi\) | |||||||
\(24\) | 7.26795 | − | 11.7973i | 0.302831 | − | 0.491555i | ||||
\(25\) | 16.7128 | 0.668513 | ||||||||
\(26\) | −30.9282 | − | 5.75749i | −1.18955 | − | 0.221442i | ||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −15.4641 | + | 40.0958i | −0.552289 | + | 1.43199i | ||||
\(29\) | − | 40.0958i | − | 1.38261i | −0.722562 | − | 0.691307i | \(-0.757035\pi\) | ||
0.722562 | − | 0.691307i | \(-0.242965\pi\) | |||||||
\(30\) | −9.80385 | − | 1.82505i | −0.326795 | − | 0.0608351i | ||||
\(31\) | − | 9.20092i | − | 0.296804i | −0.988927 | − | 0.148402i | \(-0.952587\pi\) | ||
0.988927 | − | 0.148402i | \(-0.0474129\pi\) | |||||||
\(32\) | −25.4641 | + | 19.3799i | −0.795753 | + | 0.605621i | ||||
\(33\) | −13.8564 | −0.419891 | ||||||||
\(34\) | 5.80385 | − | 31.1772i | 0.170701 | − | 0.916976i | ||||
\(35\) | 30.9282 | 0.883663 | ||||||||
\(36\) | −11.1962 | − | 4.31812i | −0.311004 | − | 0.119948i | ||||
\(37\) | 9.97227i | 0.269521i | 0.990878 | + | 0.134760i | \(0.0430265\pi\) | ||||
−0.990878 | + | 0.134760i | \(0.956974\pi\) | |||||||
\(38\) | −0.392305 | + | 2.10739i | −0.0103238 | + | 0.0554576i | ||||
\(39\) | 27.2448i | 0.698584i | ||||||||
\(40\) | 19.6077 | + | 12.0797i | 0.490192 | + | 0.301992i | ||||
\(41\) | 51.5692 | 1.25779 | 0.628893 | − | 0.777492i | \(-0.283508\pi\) | ||||
0.628893 | + | 0.777492i | \(0.283508\pi\) | |||||||
\(42\) | 36.5885 | + | 6.81119i | 0.871154 | + | 0.162171i | ||||
\(43\) | −12.7846 | −0.297317 | −0.148658 | − | 0.988889i | \(-0.547495\pi\) | ||||
−0.148658 | + | 0.988889i | \(0.547495\pi\) | |||||||
\(44\) | 29.8564 | + | 11.5150i | 0.678555 | + | 0.261704i | ||||
\(45\) | 8.63624i | 0.191916i | ||||||||
\(46\) | −42.2487 | − | 7.86488i | −0.918450 | − | 0.170976i | ||||
\(47\) | − | 1.54272i | − | 0.0328237i | −0.999865 | − | 0.0164119i | \(-0.994776\pi\) | ||
0.999865 | − | 0.0164119i | \(-0.00522430\pi\) | |||||||
\(48\) | 20.5359 | + | 18.6085i | 0.427831 | + | 0.387677i | ||||
\(49\) | −66.4256 | −1.35563 | ||||||||
\(50\) | −6.11731 | + | 32.8611i | −0.122346 | + | 0.657222i | ||||
\(51\) | −27.4641 | −0.538512 | ||||||||
\(52\) | 22.6410 | − | 58.7043i | 0.435404 | − | 1.12893i | ||||
\(53\) | 28.5808i | 0.539260i | 0.962964 | + | 0.269630i | \(0.0869014\pi\) | ||||
−0.962964 | + | 0.269630i | \(0.913099\pi\) | |||||||
\(54\) | −1.90192 | + | 10.2168i | −0.0352208 | + | 0.189200i | ||||
\(55\) | − | 23.0300i | − | 0.418727i | ||||||
\(56\) | −73.1769 | − | 45.0819i | −1.30673 | − | 0.805034i | ||||
\(57\) | 1.85641 | 0.0325685 | ||||||||
\(58\) | 78.8372 | + | 14.6761i | 1.35926 | + | 0.253036i | ||||
\(59\) | −11.2154 | −0.190091 | −0.0950457 | − | 0.995473i | \(-0.530300\pi\) | ||||
−0.0950457 | + | 0.995473i | \(0.530300\pi\) | |||||||
\(60\) | 7.17691 | − | 18.6085i | 0.119615 | − | 0.310142i | ||||
\(61\) | 1.54272i | 0.0252904i | 0.999920 | + | 0.0126452i | \(0.00402520\pi\) | ||||
−0.999920 | + | 0.0126452i | \(0.995975\pi\) | |||||||
\(62\) | 18.0910 | + | 3.36777i | 0.291791 | + | 0.0543189i | ||||
\(63\) | − | 32.2309i | − | 0.511602i | ||||||
\(64\) | −28.7846 | − | 57.1616i | −0.449760 | − | 0.893150i | ||||
\(65\) | −45.2820 | −0.696647 | ||||||||
\(66\) | 5.07180 | − | 27.2448i | 0.0768454 | − | 0.412799i | ||||
\(67\) | −43.2154 | −0.645006 | −0.322503 | − | 0.946568i | \(-0.604524\pi\) | ||||
−0.322503 | + | 0.946568i | \(0.604524\pi\) | |||||||
\(68\) | 59.1769 | + | 22.8233i | 0.870249 | + | 0.335637i | ||||
\(69\) | 37.2170i | 0.539377i | ||||||||
\(70\) | −11.3205 | + | 60.8117i | −0.161722 | + | 0.868738i | ||||
\(71\) | − | 84.4063i | − | 1.18882i | −0.804162 | − | 0.594411i | \(-0.797385\pi\) | ||
0.804162 | − | 0.594411i | \(-0.202615\pi\) | |||||||
\(72\) | 12.5885 | − | 20.4336i | 0.174840 | − | 0.283800i | ||||
\(73\) | 105.426 | 1.44419 | 0.722093 | − | 0.691796i | \(-0.243180\pi\) | ||||
0.722093 | + | 0.691796i | \(0.243180\pi\) | |||||||
\(74\) | −19.6077 | − | 3.65011i | −0.264969 | − | 0.0493258i | ||||
\(75\) | 28.9474 | 0.385966 | ||||||||
\(76\) | −4.00000 | − | 1.54272i | −0.0526316 | − | 0.0202989i | ||||
\(77\) | 85.9491i | 1.11622i | ||||||||
\(78\) | −53.5692 | − | 9.97227i | −0.686785 | − | 0.127850i | ||||
\(79\) | 73.6627i | 0.932439i | 0.884669 | + | 0.466220i | \(0.154384\pi\) | ||||
−0.884669 | + | 0.466220i | \(0.845616\pi\) | |||||||
\(80\) | −30.9282 | + | 34.1316i | −0.386603 | + | 0.426645i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −18.8756 | + | 101.396i | −0.230191 | + | 1.23654i | ||||
\(83\) | 12.2872 | 0.148038 | 0.0740192 | − | 0.997257i | \(-0.476417\pi\) | ||||
0.0740192 | + | 0.997257i | \(0.476417\pi\) | |||||||
\(84\) | −26.7846 | + | 69.4479i | −0.318864 | + | 0.826761i | ||||
\(85\) | − | 45.6466i | − | 0.537019i | ||||||
\(86\) | 4.67949 | − | 25.1374i | 0.0544127 | − | 0.292295i | ||||
\(87\) | − | 69.4479i | − | 0.798252i | ||||||
\(88\) | −33.5692 | + | 54.4895i | −0.381468 | + | 0.619199i | ||||
\(89\) | 33.1384 | 0.372342 | 0.186171 | − | 0.982517i | \(-0.440392\pi\) | ||||
0.186171 | + | 0.982517i | \(0.440392\pi\) | |||||||
\(90\) | −16.9808 | − | 3.16108i | −0.188675 | − | 0.0351232i | ||||
\(91\) | 168.995 | 1.85709 | ||||||||
\(92\) | 30.9282 | − | 80.1916i | 0.336176 | − | 0.871647i | ||||
\(93\) | − | 15.9365i | − | 0.171360i | ||||||
\(94\) | 3.03332 | + | 0.564673i | 0.0322694 | + | 0.00600716i | ||||
\(95\) | 3.08543i | 0.0324782i | ||||||||
\(96\) | −44.1051 | + | 33.5669i | −0.459428 | + | 0.349655i | ||||
\(97\) | −69.1384 | −0.712767 | −0.356384 | − | 0.934340i | \(-0.615990\pi\) | ||||
−0.356384 | + | 0.934340i | \(0.615990\pi\) | |||||||
\(98\) | 24.3135 | − | 130.607i | 0.248097 | − | 1.33273i | ||||
\(99\) | −24.0000 | −0.242424 | ||||||||
\(100\) | −62.3731 | − | 24.0560i | −0.623731 | − | 0.240560i | ||||
\(101\) | − | 97.2574i | − | 0.962944i | −0.876461 | − | 0.481472i | \(-0.840102\pi\) | ||
0.876461 | − | 0.481472i | \(-0.159898\pi\) | |||||||
\(102\) | 10.0526 | − | 54.0005i | 0.0985545 | − | 0.529417i | ||||
\(103\) | 139.667i | 1.35599i | 0.735065 | + | 0.677996i | \(0.237151\pi\) | ||||
−0.735065 | + | 0.677996i | \(0.762849\pi\) | |||||||
\(104\) | 107.138 | + | 66.0045i | 1.03018 | + | 0.634659i | ||||
\(105\) | 53.5692 | 0.510183 | ||||||||
\(106\) | −56.1962 | − | 10.4613i | −0.530152 | − | 0.0986915i | ||||
\(107\) | −197.779 | −1.84841 | −0.924203 | − | 0.381901i | \(-0.875269\pi\) | ||||
−0.924203 | + | 0.381901i | \(0.875269\pi\) | |||||||
\(108\) | −19.3923 | − | 7.47921i | −0.179558 | − | 0.0692519i | ||||
\(109\) | − | 190.713i | − | 1.74966i | −0.484427 | − | 0.874832i | \(-0.660972\pi\) | ||
0.484427 | − | 0.874832i | \(-0.339028\pi\) | |||||||
\(110\) | 45.2820 | + | 8.42956i | 0.411655 | + | 0.0766323i | ||||
\(111\) | 17.2725i | 0.155608i | ||||||||
\(112\) | 115.426 | − | 127.381i | 1.03059 | − | 1.13733i | ||||
\(113\) | −113.713 | −1.00631 | −0.503154 | − | 0.864197i | \(-0.667827\pi\) | ||||
−0.503154 | + | 0.864197i | \(0.667827\pi\) | |||||||
\(114\) | −0.679492 | + | 3.65011i | −0.00596046 | + | 0.0320185i | ||||
\(115\) | −61.8564 | −0.537882 | ||||||||
\(116\) | −57.7128 | + | 149.639i | −0.497524 | + | 1.29000i | ||||
\(117\) | 47.1893i | 0.403327i | ||||||||
\(118\) | 4.10512 | − | 22.0519i | 0.0347891 | − | 0.186881i | ||||
\(119\) | 170.355i | 1.43156i | ||||||||
\(120\) | 33.9615 | + | 20.9226i | 0.283013 | + | 0.174355i | ||||
\(121\) | −57.0000 | −0.471074 | ||||||||
\(122\) | −3.03332 | − | 0.564673i | −0.0248633 | − | 0.00462847i | ||||
\(123\) | 89.3205 | 0.726183 | ||||||||
\(124\) | −13.2436 | + | 34.3383i | −0.106803 | + | 0.276922i | ||||
\(125\) | 120.081i | 0.960645i | ||||||||
\(126\) | 63.3731 | + | 11.7973i | 0.502961 | + | 0.0936296i | ||||
\(127\) | − | 36.8590i | − | 0.290229i | −0.989415 | − | 0.145114i | \(-0.953645\pi\) | ||
0.989415 | − | 0.145114i | \(-0.0463550\pi\) | |||||||
\(128\) | 122.928 | − | 35.6743i | 0.960377 | − | 0.278706i | ||||
\(129\) | −22.1436 | −0.171656 | ||||||||
\(130\) | 16.5744 | − | 89.0345i | 0.127495 | − | 0.684881i | ||||
\(131\) | 194.641 | 1.48581 | 0.742905 | − | 0.669397i | \(-0.233448\pi\) | ||||
0.742905 | + | 0.669397i | \(0.233448\pi\) | |||||||
\(132\) | 51.7128 | + | 19.9445i | 0.391764 | + | 0.151095i | ||||
\(133\) | − | 11.5150i | − | 0.0865789i | ||||||
\(134\) | 15.8179 | − | 84.9710i | 0.118044 | − | 0.634112i | ||||
\(135\) | 14.9584i | 0.110803i | ||||||||
\(136\) | −66.5359 | + | 108.001i | −0.489235 | + | 0.794125i | ||||
\(137\) | 16.4308 | 0.119933 | 0.0599664 | − | 0.998200i | \(-0.480901\pi\) | ||||
0.0599664 | + | 0.998200i | \(0.480901\pi\) | |||||||
\(138\) | −73.1769 | − | 13.6224i | −0.530267 | − | 0.0987129i | ||||
\(139\) | −113.492 | −0.816491 | −0.408246 | − | 0.912872i | \(-0.633859\pi\) | ||||
−0.408246 | + | 0.912872i | \(0.633859\pi\) | |||||||
\(140\) | −115.426 | − | 44.5172i | −0.824469 | − | 0.317980i | ||||
\(141\) | − | 2.67206i | − | 0.0189508i | ||||||
\(142\) | 165.962 | + | 30.8949i | 1.16874 | + | 0.217569i | ||||
\(143\) | − | 125.838i | − | 0.879987i | ||||||
\(144\) | 35.5692 | + | 32.2309i | 0.247008 | + | 0.223826i | ||||
\(145\) | 115.426 | 0.796039 | ||||||||
\(146\) | −38.5885 | + | 207.290i | −0.264305 | + | 1.41980i | ||||
\(147\) | −115.053 | −0.782670 | ||||||||
\(148\) | 14.3538 | − | 37.2170i | 0.0969853 | − | 0.251466i | ||||
\(149\) | − | 31.6662i | − | 0.212525i | −0.994338 | − | 0.106262i | \(-0.966112\pi\) | ||
0.994338 | − | 0.106262i | \(-0.0338884\pi\) | |||||||
\(150\) | −10.5955 | + | 56.9171i | −0.0706367 | + | 0.379447i | ||||
\(151\) | − | 90.5218i | − | 0.599482i | −0.954021 | − | 0.299741i | \(-0.903100\pi\) | ||
0.954021 | − | 0.299741i | \(-0.0969003\pi\) | |||||||
\(152\) | 4.49742 | − | 7.30021i | 0.0295883 | − | 0.0480277i | ||||
\(153\) | −47.5692 | −0.310910 | ||||||||
\(154\) | −168.995 | − | 31.4595i | −1.09737 | − | 0.204283i | ||||
\(155\) | 26.4871 | 0.170885 | ||||||||
\(156\) | 39.2154 | − | 101.679i | 0.251381 | − | 0.651787i | ||||
\(157\) | 231.016i | 1.47144i | 0.677287 | + | 0.735719i | \(0.263156\pi\) | ||||
−0.677287 | + | 0.735719i | \(0.736844\pi\) | |||||||
\(158\) | −144.837 | − | 26.9624i | −0.916691 | − | 0.170648i | ||||
\(159\) | 49.5034i | 0.311342i | ||||||||
\(160\) | −55.7898 | − | 73.3047i | −0.348686 | − | 0.458154i | ||||
\(161\) | 230.851 | 1.43386 | ||||||||
\(162\) | −3.29423 | + | 17.6960i | −0.0203347 | + | 0.109235i | ||||
\(163\) | 22.3538 | 0.137140 | 0.0685700 | − | 0.997646i | \(-0.478156\pi\) | ||||
0.0685700 | + | 0.997646i | \(0.478156\pi\) | |||||||
\(164\) | −192.459 | − | 74.2274i | −1.17353 | − | 0.452606i | ||||
\(165\) | − | 39.8891i | − | 0.241752i | ||||||
\(166\) | −4.49742 | + | 24.1593i | −0.0270929 | + | 0.145538i | ||||
\(167\) | − | 221.044i | − | 1.32361i | −0.749674 | − | 0.661807i | \(-0.769790\pi\) | ||
0.749674 | − | 0.661807i | \(-0.230210\pi\) | |||||||
\(168\) | −126.746 | − | 78.0842i | −0.754441 | − | 0.464787i | ||||
\(169\) | −78.4256 | −0.464057 | ||||||||
\(170\) | 89.7513 | + | 16.7078i | 0.527949 | + | 0.0982812i | ||||
\(171\) | 3.21539 | 0.0188035 | ||||||||
\(172\) | 47.7128 | + | 18.4018i | 0.277400 | + | 0.106987i | ||||
\(173\) | − | 231.525i | − | 1.33830i | −0.743130 | − | 0.669148i | \(-0.766659\pi\) | ||
0.743130 | − | 0.669148i | \(-0.233341\pi\) | |||||||
\(174\) | 136.550 | + | 25.4197i | 0.784770 | + | 0.146090i | ||||
\(175\) | − | 179.556i | − | 1.02604i | ||||||
\(176\) | −94.8513 | − | 85.9491i | −0.538928 | − | 0.488347i | ||||
\(177\) | −19.4256 | −0.109749 | ||||||||
\(178\) | −12.1295 | + | 65.1575i | −0.0681433 | + | 0.366053i | ||||
\(179\) | 193.646 | 1.08182 | 0.540911 | − | 0.841080i | \(-0.318080\pi\) | ||||
0.540911 | + | 0.841080i | \(0.318080\pi\) | |||||||
\(180\) | 12.4308 | − | 32.2309i | 0.0690599 | − | 0.179061i | ||||
\(181\) | 270.492i | 1.49443i | 0.664583 | + | 0.747214i | \(0.268609\pi\) | ||||
−0.664583 | + | 0.747214i | \(0.731391\pi\) | |||||||
\(182\) | −61.8564 | + | 332.281i | −0.339870 | + | 1.82572i | ||||
\(183\) | 2.67206i | 0.0146014i | ||||||||
\(184\) | 146.354 | + | 90.1638i | 0.795401 | + | 0.490021i | ||||
\(185\) | −28.7077 | −0.155177 | ||||||||
\(186\) | 31.3346 | + | 5.83315i | 0.168466 | + | 0.0313610i | ||||
\(187\) | 126.851 | 0.678349 | ||||||||
\(188\) | −2.22055 | + | 5.75749i | −0.0118114 | + | 0.0306250i | ||||
\(189\) | − | 55.8255i | − | 0.295373i | ||||||
\(190\) | −6.06664 | − | 1.12935i | −0.0319297 | − | 0.00594393i | ||||
\(191\) | 311.510i | 1.63094i | 0.578798 | + | 0.815471i | \(0.303522\pi\) | ||||
−0.578798 | + | 0.815471i | \(0.696478\pi\) | |||||||
\(192\) | −49.8564 | − | 99.0068i | −0.259669 | − | 0.515660i | ||||
\(193\) | 48.2769 | 0.250139 | 0.125070 | − | 0.992148i | \(-0.460085\pi\) | ||||
0.125070 | + | 0.992148i | \(0.460085\pi\) | |||||||
\(194\) | 25.3064 | − | 135.941i | 0.130445 | − | 0.700729i | ||||
\(195\) | −78.4308 | −0.402209 | ||||||||
\(196\) | 247.904 | + | 95.6113i | 1.26482 | + | 0.487813i | ||||
\(197\) | 251.883i | 1.27859i | 0.768960 | + | 0.639297i | \(0.220775\pi\) | ||||
−0.768960 | + | 0.639297i | \(0.779225\pi\) | |||||||
\(198\) | 8.78461 | − | 47.1893i | 0.0443667 | − | 0.238330i | ||||
\(199\) | − | 72.1200i | − | 0.362412i | −0.983445 | − | 0.181206i | \(-0.942000\pi\) | ||
0.983445 | − | 0.181206i | \(-0.0580001\pi\) | |||||||
\(200\) | 70.1295 | − | 113.834i | 0.350648 | − | 0.569171i | ||||
\(201\) | −74.8513 | −0.372394 | ||||||||
\(202\) | 191.229 | + | 35.5987i | 0.946681 | + | 0.176231i | ||||
\(203\) | −430.774 | −2.12204 | ||||||||
\(204\) | 102.497 | + | 39.5311i | 0.502438 | + | 0.193780i | ||||
\(205\) | 148.455i | 0.724170i | ||||||||
\(206\) | −274.617 | − | 51.1217i | −1.33309 | − | 0.248164i | ||||
\(207\) | 64.4618i | 0.311410i | ||||||||
\(208\) | −168.995 | + | 186.499i | −0.812475 | + | 0.896628i | ||||
\(209\) | −8.57437 | −0.0410257 | ||||||||
\(210\) | −19.6077 | + | 105.329i | −0.0933700 | + | 0.501566i | ||||
\(211\) | −264.918 | −1.25554 | −0.627768 | − | 0.778401i | \(-0.716031\pi\) | ||||
−0.627768 | + | 0.778401i | \(0.716031\pi\) | |||||||
\(212\) | 41.1384 | − | 106.665i | 0.194049 | − | 0.503137i | ||||
\(213\) | − | 146.196i | − | 0.686367i | ||||||
\(214\) | 72.3923 | − | 388.878i | 0.338282 | − | 1.81719i | ||||
\(215\) | − | 36.8037i | − | 0.171180i | ||||||
\(216\) | 21.8038 | − | 35.3920i | 0.100944 | − | 0.163852i | ||||
\(217\) | −98.8513 | −0.455536 | ||||||||
\(218\) | 374.985 | + | 69.8059i | 1.72011 | + | 0.320211i | ||||
\(219\) | 182.603 | 0.833802 | ||||||||
\(220\) | −33.1487 | + | 85.9491i | −0.150676 | + | 0.390678i | ||||
\(221\) | − | 249.418i | − | 1.12859i | ||||||
\(222\) | −33.9615 | − | 6.32217i | −0.152980 | − | 0.0284782i | ||||
\(223\) | − | 30.6882i | − | 0.137615i | −0.997630 | − | 0.0688076i | \(-0.978081\pi\) | ||
0.997630 | − | 0.0688076i | \(-0.0219195\pi\) | |||||||
\(224\) | 208.210 | + | 273.577i | 0.929510 | + | 1.22133i | ||||
\(225\) | 50.1384 | 0.222838 | ||||||||
\(226\) | 41.6218 | − | 223.585i | 0.184167 | − | 0.989312i | ||||
\(227\) | 295.846 | 1.30329 | 0.651643 | − | 0.758525i | \(-0.274080\pi\) | ||||
0.651643 | + | 0.758525i | \(0.274080\pi\) | |||||||
\(228\) | −6.92820 | − | 2.67206i | −0.0303869 | − | 0.0117196i | ||||
\(229\) | − | 256.718i | − | 1.12104i | −0.828141 | − | 0.560519i | \(-0.810602\pi\) | ||
0.828141 | − | 0.560519i | \(-0.189398\pi\) | |||||||
\(230\) | 22.6410 | − | 121.623i | 0.0984392 | − | 0.528797i | ||||
\(231\) | 148.868i | 0.644451i | ||||||||
\(232\) | −273.100 | − | 168.248i | −1.17716 | − | 0.725207i | ||||
\(233\) | −404.564 | −1.73633 | −0.868163 | − | 0.496279i | \(-0.834699\pi\) | ||||
−0.868163 | + | 0.496279i | \(0.834699\pi\) | |||||||
\(234\) | −92.7846 | − | 17.2725i | −0.396515 | − | 0.0738140i | ||||
\(235\) | 4.44109 | 0.0188983 | ||||||||
\(236\) | 41.8564 | + | 16.1431i | 0.177358 | + | 0.0684031i | ||||
\(237\) | 127.588i | 0.538344i | ||||||||
\(238\) | −334.956 | − | 62.3544i | −1.40738 | − | 0.261993i | ||||
\(239\) | 115.150i | 0.481799i | 0.970550 | + | 0.240899i | \(0.0774424\pi\) | ||||
−0.970550 | + | 0.240899i | \(0.922558\pi\) | |||||||
\(240\) | −53.5692 | + | 59.1177i | −0.223205 | + | 0.246324i | ||||
\(241\) | 251.415 | 1.04322 | 0.521609 | − | 0.853185i | \(-0.325332\pi\) | ||||
0.521609 | + | 0.853185i | \(0.325332\pi\) | |||||||
\(242\) | 20.8634 | − | 112.075i | 0.0862126 | − | 0.463118i | ||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 2.22055 | − | 5.75749i | 0.00910059 | − | 0.0235963i | ||||
\(245\) | − | 191.223i | − | 0.780500i | ||||||
\(246\) | −32.6936 | + | 175.624i | −0.132901 | + | 0.713918i | ||||
\(247\) | 16.8591i | 0.0682555i | ||||||||
\(248\) | −62.6692 | − | 38.6084i | −0.252698 | − | 0.155679i | ||||
\(249\) | 21.2820 | 0.0854700 | ||||||||
\(250\) | −236.105 | − | 43.9526i | −0.944420 | − | 0.175810i | ||||
\(251\) | 6.85125 | 0.0272958 | 0.0136479 | − | 0.999907i | \(-0.495656\pi\) | ||||
0.0136479 | + | 0.999907i | \(0.495656\pi\) | |||||||
\(252\) | −46.3923 | + | 120.287i | −0.184096 | + | 0.477331i | ||||
\(253\) | − | 171.898i | − | 0.679439i | ||||||
\(254\) | 72.4730 | + | 13.4913i | 0.285327 | + | 0.0531155i | ||||
\(255\) | − | 79.0622i | − | 0.310048i | ||||||
\(256\) | 25.1487 | + | 254.762i | 0.0982373 | + | 0.995163i | ||||
\(257\) | 248.277 | 0.966058 | 0.483029 | − | 0.875604i | \(-0.339537\pi\) | ||||
0.483029 | + | 0.875604i | \(0.339537\pi\) | |||||||
\(258\) | 8.10512 | − | 43.5392i | 0.0314152 | − | 0.168757i | ||||
\(259\) | 107.138 | 0.413662 | ||||||||
\(260\) | 168.995 | + | 65.1778i | 0.649980 | + | 0.250684i | ||||
\(261\) | − | 120.287i | − | 0.460871i | ||||||
\(262\) | −71.2436 | + | 382.707i | −0.271922 | + | 1.46071i | ||||
\(263\) | 498.835i | 1.89671i | 0.317208 | + | 0.948356i | \(0.397255\pi\) | ||||
−0.317208 | + | 0.948356i | \(0.602745\pi\) | |||||||
\(264\) | −58.1436 | + | 94.3786i | −0.220241 | + | 0.357495i | ||||
\(265\) | −82.2769 | −0.310479 | ||||||||
\(266\) | 22.6410 | + | 4.21478i | 0.0851166 | + | 0.0158450i | ||||
\(267\) | 57.3975 | 0.214972 | ||||||||
\(268\) | 161.282 | + | 62.2031i | 0.601799 | + | 0.232101i | ||||
\(269\) | 234.611i | 0.872158i | 0.899908 | + | 0.436079i | \(0.143633\pi\) | ||||
−0.899908 | + | 0.436079i | \(0.856367\pi\) | |||||||
\(270\) | −29.4115 | − | 5.47516i | −0.108932 | − | 0.0202784i | ||||
\(271\) | 101.321i | 0.373878i | 0.982372 | + | 0.186939i | \(0.0598566\pi\) | ||||
−0.982372 | + | 0.186939i | \(0.940143\pi\) | |||||||
\(272\) | −188.000 | − | 170.355i | −0.691176 | − | 0.626307i | ||||
\(273\) | 292.708 | 1.07219 | ||||||||
\(274\) | −6.01408 | + | 32.3065i | −0.0219492 | + | 0.117907i | ||||
\(275\) | −133.703 | −0.486191 | ||||||||
\(276\) | 53.5692 | − | 138.896i | 0.194091 | − | 0.503246i | ||||
\(277\) | − | 169.942i | − | 0.613509i | −0.951789 | − | 0.306755i | \(-0.900757\pi\) | ||
0.951789 | − | 0.306755i | \(-0.0992431\pi\) | |||||||
\(278\) | 41.5411 | − | 223.151i | 0.149428 | − | 0.802701i | ||||
\(279\) | − | 27.6027i | − | 0.0989346i | ||||||
\(280\) | 129.779 | − | 210.658i | 0.463498 | − | 0.752349i | ||||
\(281\) | −111.128 | −0.395474 | −0.197737 | − | 0.980255i | \(-0.563359\pi\) | ||||
−0.197737 | + | 0.980255i | \(0.563359\pi\) | |||||||
\(282\) | 5.25387 | + | 0.978043i | 0.0186307 | + | 0.00346824i | ||||
\(283\) | 550.620 | 1.94566 | 0.972828 | − | 0.231531i | \(-0.0743734\pi\) | ||||
0.972828 | + | 0.231531i | \(0.0743734\pi\) | |||||||
\(284\) | −121.492 | + | 315.009i | −0.427790 | + | 1.10919i | ||||
\(285\) | 5.34413i | 0.0187513i | ||||||||
\(286\) | 247.426 | + | 46.0600i | 0.865125 | + | 0.161049i | ||||
\(287\) | − | 554.041i | − | 1.93046i | ||||||
\(288\) | −76.3923 | + | 58.1396i | −0.265251 | + | 0.201874i | ||||
\(289\) | −37.5744 | −0.130015 | ||||||||
\(290\) | −42.2487 | + | 226.952i | −0.145685 | + | 0.782594i | ||||
\(291\) | −119.751 | −0.411516 | ||||||||
\(292\) | −393.454 | − | 151.747i | −1.34744 | − | 0.519681i | ||||
\(293\) | 223.509i | 0.762829i | 0.924404 | + | 0.381414i | \(0.124563\pi\) | ||||
−0.924404 | + | 0.381414i | \(0.875437\pi\) | |||||||
\(294\) | 42.1122 | − | 226.219i | 0.143239 | − | 0.769452i | ||||
\(295\) | − | 32.2863i | − | 0.109445i | ||||||
\(296\) | 67.9230 | + | 41.8452i | 0.229470 | + | 0.141369i | ||||
\(297\) | −41.5692 | −0.139964 | ||||||||
\(298\) | 62.2628 | + | 11.5906i | 0.208936 | + | 0.0388948i | ||||
\(299\) | −337.990 | −1.13040 | ||||||||
\(300\) | −108.033 | − | 41.6662i | −0.360111 | − | 0.138887i | ||||
\(301\) | 137.353i | 0.456323i | ||||||||
\(302\) | 177.986 | + | 33.1333i | 0.589357 | + | 0.109713i | ||||
\(303\) | − | 168.455i | − | 0.555956i | ||||||
\(304\) | 12.7077 | + | 11.5150i | 0.0418015 | + | 0.0378783i | ||||
\(305\) | −4.44109 | −0.0145610 | ||||||||
\(306\) | 17.4115 | − | 93.5316i | 0.0569005 | − | 0.305659i | ||||
\(307\) | −371.790 | −1.21104 | −0.605521 | − | 0.795829i | \(-0.707035\pi\) | ||||
−0.605521 | + | 0.795829i | \(0.707035\pi\) | |||||||
\(308\) | 123.713 | − | 320.766i | 0.401665 | − | 1.04145i | ||||
\(309\) | 241.911i | 0.782883i | ||||||||
\(310\) | −9.69496 | + | 52.0795i | −0.0312741 | + | 0.167998i | ||||
\(311\) | − | 330.023i | − | 1.06117i | −0.847633 | − | 0.530583i | \(-0.821973\pi\) | ||
0.847633 | − | 0.530583i | \(-0.178027\pi\) | |||||||
\(312\) | 185.569 | + | 114.323i | 0.594773 | + | 0.366420i | ||||
\(313\) | −80.2769 | −0.256476 | −0.128238 | − | 0.991743i | \(-0.540932\pi\) | ||||
−0.128238 | + | 0.991743i | \(0.540932\pi\) | |||||||
\(314\) | −454.228 | − | 84.5576i | −1.44659 | − | 0.269292i | ||||
\(315\) | 92.7846 | 0.294554 | ||||||||
\(316\) | 106.028 | − | 274.913i | 0.335532 | − | 0.869978i | ||||
\(317\) | 68.8833i | 0.217297i | 0.994080 | + | 0.108649i | \(0.0346524\pi\) | ||||
−0.994080 | + | 0.108649i | \(0.965348\pi\) | |||||||
\(318\) | −97.3346 | − | 18.1195i | −0.306084 | − | 0.0569795i | ||||
\(319\) | 320.766i | 1.00554i | ||||||||
\(320\) | 164.554 | − | 82.8636i | 0.514230 | − | 0.258949i | ||||
\(321\) | −342.564 | −1.06718 | ||||||||
\(322\) | −84.4974 | + | 453.905i | −0.262414 | + | 1.40964i | ||||
\(323\) | −16.9948 | −0.0526156 | ||||||||
\(324\) | −33.5885 | − | 12.9544i | −0.103668 | − | 0.0399826i | ||||
\(325\) | 262.889i | 0.808888i | ||||||||
\(326\) | −8.18207 | + | 43.9526i | −0.0250984 | + | 0.134824i | ||||
\(327\) | − | 330.325i | − | 1.01017i | ||||||
\(328\) | 216.392 | − | 351.248i | 0.659733 | − | 1.07088i | ||||
\(329\) | −16.5744 | −0.0503780 | ||||||||
\(330\) | 78.4308 | + | 14.6004i | 0.237669 | + | 0.0442437i | ||||
\(331\) | −396.056 | −1.19654 | −0.598272 | − | 0.801293i | \(-0.704146\pi\) | ||||
−0.598272 | + | 0.801293i | \(0.704146\pi\) | |||||||
\(332\) | −45.8564 | − | 17.6859i | −0.138122 | − | 0.0532706i | ||||
\(333\) | 29.9168i | 0.0898403i | ||||||||
\(334\) | 434.620 | + | 80.9075i | 1.30126 | + | 0.242238i | ||||
\(335\) | − | 124.406i | − | 0.371362i | ||||||
\(336\) | 199.923 | − | 220.630i | 0.595009 | − | 0.656637i | ||||
\(337\) | 231.723 | 0.687606 | 0.343803 | − | 0.939042i | \(-0.388285\pi\) | ||||
0.343803 | + | 0.939042i | \(0.388285\pi\) | |||||||
\(338\) | 28.7058 | − | 154.202i | 0.0849283 | − | 0.456219i | ||||
\(339\) | −196.956 | −0.580992 | ||||||||
\(340\) | −65.7025 | + | 170.355i | −0.193243 | + | 0.501045i | ||||
\(341\) | 73.6073i | 0.215857i | ||||||||
\(342\) | −1.17691 | + | 6.32217i | −0.00344127 | + | 0.0184859i | ||||
\(343\) | 187.215i | 0.545815i | ||||||||
\(344\) | −53.6462 | + | 87.0784i | −0.155948 | + | 0.253135i | ||||
\(345\) | −107.138 | −0.310546 | ||||||||
\(346\) | 455.229 | + | 84.7441i | 1.31569 | + | 0.244925i | ||||
\(347\) | 462.123 | 1.33177 | 0.665883 | − | 0.746056i | \(-0.268055\pi\) | ||||
0.665883 | + | 0.746056i | \(0.268055\pi\) | |||||||
\(348\) | −99.9615 | + | 259.183i | −0.287246 | + | 0.744779i | ||||
\(349\) | − | 266.993i | − | 0.765022i | −0.923951 | − | 0.382511i | \(-0.875059\pi\) | ||
0.923951 | − | 0.382511i | \(-0.124941\pi\) | |||||||
\(350\) | 353.047 | + | 65.7222i | 1.00871 | + | 0.187778i | ||||
\(351\) | 81.7343i | 0.232861i | ||||||||
\(352\) | 203.713 | − | 155.039i | 0.578730 | − | 0.440452i | ||||
\(353\) | 262.862 | 0.744650 | 0.372325 | − | 0.928102i | \(-0.378561\pi\) | ||||
0.372325 | + | 0.928102i | \(0.378561\pi\) | |||||||
\(354\) | 7.11027 | − | 38.1951i | 0.0200855 | − | 0.107896i | ||||
\(355\) | 242.985 | 0.684463 | ||||||||
\(356\) | −123.674 | − | 47.6986i | −0.347400 | − | 0.133985i | ||||
\(357\) | 295.064i | 0.826510i | ||||||||
\(358\) | −70.8794 | + | 380.751i | −0.197987 | + | 1.06355i | ||||
\(359\) | − | 164.185i | − | 0.457339i | −0.973504 | − | 0.228669i | \(-0.926563\pi\) | ||
0.973504 | − | 0.228669i | \(-0.0734374\pi\) | |||||||
\(360\) | 58.8231 | + | 36.2390i | 0.163397 | + | 0.100664i | ||||
\(361\) | −359.851 | −0.996818 | ||||||||
\(362\) | −531.846 | − | 99.0068i | −1.46919 | − | 0.273499i | ||||
\(363\) | −98.7269 | −0.271975 | ||||||||
\(364\) | −630.697 | − | 243.247i | −1.73269 | − | 0.668260i | ||||
\(365\) | 303.494i | 0.831490i | ||||||||
\(366\) | −5.25387 | − | 0.978043i | −0.0143548 | − | 0.00267225i | ||||
\(367\) | 242.475i | 0.660696i | 0.943859 | + | 0.330348i | \(0.107166\pi\) | ||||
−0.943859 | + | 0.330348i | \(0.892834\pi\) | |||||||
\(368\) | −230.851 | + | 254.762i | −0.627313 | + | 0.692287i | ||||
\(369\) | 154.708 | 0.419262 | ||||||||
\(370\) | 10.5077 | − | 56.4456i | 0.0283993 | − | 0.152556i | ||||
\(371\) | 307.061 | 0.827659 | ||||||||
\(372\) | −22.9385 | + | 59.4757i | −0.0616627 | + | 0.159881i | ||||
\(373\) | − | 328.480i | − | 0.880643i | −0.897840 | − | 0.440321i | \(-0.854864\pi\) | ||
0.897840 | − | 0.440321i | \(-0.145136\pi\) | |||||||
\(374\) | −46.4308 | + | 249.418i | −0.124146 | + | 0.666892i | ||||
\(375\) | 207.986i | 0.554629i | ||||||||
\(376\) | −10.5077 | − | 6.47347i | −0.0279461 | − | 0.0172167i | ||||
\(377\) | 630.697 | 1.67294 | ||||||||
\(378\) | 109.765 | + | 20.4336i | 0.290385 | + | 0.0540571i | ||||
\(379\) | 36.2102 | 0.0955415 | 0.0477708 | − | 0.998858i | \(-0.484788\pi\) | ||||
0.0477708 | + | 0.998858i | \(0.484788\pi\) | |||||||
\(380\) | 4.44109 | − | 11.5150i | 0.0116871 | − | 0.0303026i | ||||
\(381\) | − | 63.8417i | − | 0.167564i | ||||||
\(382\) | −612.497 | − | 114.021i | −1.60340 | − | 0.298483i | ||||
\(383\) | 164.295i | 0.428969i | 0.976727 | + | 0.214485i | \(0.0688072\pi\) | ||||
−0.976727 | + | 0.214485i | \(0.931193\pi\) | |||||||
\(384\) | 212.918 | − | 61.7897i | 0.554474 | − | 0.160911i | ||||
\(385\) | −247.426 | −0.642664 | ||||||||
\(386\) | −17.6706 | + | 94.9230i | −0.0457787 | + | 0.245915i | ||||
\(387\) | −38.3538 | −0.0991055 | ||||||||
\(388\) | 258.028 | + | 99.5161i | 0.665021 | + | 0.256485i | ||||
\(389\) | − | 604.936i | − | 1.55510i | −0.628819 | − | 0.777552i | \(-0.716461\pi\) | ||
0.628819 | − | 0.777552i | \(-0.283539\pi\) | |||||||
\(390\) | 28.7077 | − | 154.212i | 0.0736094 | − | 0.395416i | ||||
\(391\) | − | 340.711i | − | 0.871383i | ||||||
\(392\) | −278.732 | + | 452.438i | −0.711051 | + | 1.15418i | ||||
\(393\) | 337.128 | 0.857832 | ||||||||
\(394\) | −495.258 | − | 92.1956i | −1.25700 | − | 0.233999i | ||||
\(395\) | −212.056 | −0.536851 | ||||||||
\(396\) | 89.5692 | + | 34.5450i | 0.226185 | + | 0.0872348i | ||||
\(397\) | − | 541.699i | − | 1.36448i | −0.731128 | − | 0.682241i | \(-0.761006\pi\) | ||
0.731128 | − | 0.682241i | \(-0.238994\pi\) | |||||||
\(398\) | 141.804 | + | 26.3977i | 0.356291 | + | 0.0663260i | ||||
\(399\) | − | 19.9445i | − | 0.0499863i | ||||||
\(400\) | 198.154 | + | 179.556i | 0.495385 | + | 0.448891i | ||||
\(401\) | −379.569 | −0.946557 | −0.473278 | − | 0.880913i | \(-0.656930\pi\) | ||||
−0.473278 | + | 0.880913i | \(0.656930\pi\) | |||||||
\(402\) | 27.3975 | − | 147.174i | 0.0681529 | − | 0.366105i | ||||
\(403\) | 144.728 | 0.359127 | ||||||||
\(404\) | −139.990 | + | 362.969i | −0.346509 | + | 0.898439i | ||||
\(405\) | 25.9087i | 0.0639722i | ||||||||
\(406\) | 157.674 | − | 846.998i | 0.388360 | − | 2.08620i | ||||
\(407\) | − | 79.7782i | − | 0.196015i | ||||||
\(408\) | −115.244 | + | 187.063i | −0.282460 | + | 0.458488i | ||||
\(409\) | 251.415 | 0.614707 | 0.307354 | − | 0.951595i | \(-0.400557\pi\) | ||||
0.307354 | + | 0.951595i | \(0.400557\pi\) | |||||||
\(410\) | −291.895 | − | 54.3382i | −0.711939 | − | 0.132532i | ||||
\(411\) | 28.4589 | 0.0692432 | ||||||||
\(412\) | 201.033 | − | 521.245i | 0.487945 | − | 1.26516i | ||||
\(413\) | 120.494i | 0.291753i | ||||||||
\(414\) | −126.746 | − | 23.5947i | −0.306150 | − | 0.0569919i | ||||
\(415\) | 35.3717i | 0.0852330i | ||||||||
\(416\) | −304.841 | − | 400.544i | −0.732791 | − | 0.962847i | ||||
\(417\) | −196.574 | −0.471401 | ||||||||
\(418\) | 3.13844 | − | 16.8591i | 0.00750823 | − | 0.0403328i | ||||
\(419\) | 268.133 | 0.639936 | 0.319968 | − | 0.947428i | \(-0.396328\pi\) | ||||
0.319968 | + | 0.947428i | \(0.396328\pi\) | |||||||
\(420\) | −199.923 | − | 77.1061i | −0.476007 | − | 0.183586i | ||||
\(421\) | 218.261i | 0.518434i | 0.965819 | + | 0.259217i | \(0.0834645\pi\) | ||||
−0.965819 | + | 0.259217i | \(0.916536\pi\) | |||||||
\(422\) | 96.9667 | − | 520.887i | 0.229779 | − | 1.23433i | ||||
\(423\) | − | 4.62815i | − | 0.0109412i | ||||||
\(424\) | 194.669 | + | 119.929i | 0.459125 | + | 0.282852i | ||||
\(425\) | −265.005 | −0.623542 | ||||||||
\(426\) | 287.454 | + | 53.5115i | 0.674774 | + | 0.125614i | ||||
\(427\) | 16.5744 | 0.0388159 | ||||||||
\(428\) | 738.123 | + | 284.679i | 1.72459 | + | 0.665137i | ||||
\(429\) | − | 217.958i | − | 0.508061i | ||||||
\(430\) | 72.3641 | + | 13.4711i | 0.168289 | + | 0.0313281i | ||||
\(431\) | 550.955i | 1.27832i | 0.769074 | + | 0.639159i | \(0.220718\pi\) | ||||
−0.769074 | + | 0.639159i | \(0.779282\pi\) | |||||||
\(432\) | 61.6077 | + | 55.8255i | 0.142610 | + | 0.129226i | ||||
\(433\) | −263.128 | −0.607686 | −0.303843 | − | 0.952722i | \(-0.598270\pi\) | ||||
−0.303843 | + | 0.952722i | \(0.598270\pi\) | |||||||
\(434\) | 36.1821 | − | 194.363i | 0.0833688 | − | 0.447842i | ||||
\(435\) | 199.923 | 0.459593 | ||||||||
\(436\) | −274.508 | + | 711.752i | −0.629605 | + | 1.63246i | ||||
\(437\) | 23.0300i | 0.0527002i | ||||||||
\(438\) | −66.8372 | + | 359.037i | −0.152596 | + | 0.819719i | ||||
\(439\) | 440.489i | 1.00339i | 0.865044 | + | 0.501696i | \(0.167290\pi\) | ||||
−0.865044 | + | 0.501696i | \(0.832710\pi\) | |||||||
\(440\) | −156.862 | − | 96.6373i | −0.356504 | − | 0.219630i | ||||
\(441\) | −199.277 | −0.451875 | ||||||||
\(442\) | 490.410 | + | 91.2932i | 1.10953 | + | 0.206546i | ||||
\(443\) | −228.708 | −0.516270 | −0.258135 | − | 0.966109i | \(-0.583108\pi\) | ||||
−0.258135 | + | 0.966109i | \(0.583108\pi\) | |||||||
\(444\) | 24.8616 | − | 64.4618i | 0.0559945 | − | 0.145184i | ||||
\(445\) | 95.3972i | 0.214376i | ||||||||
\(446\) | 60.3397 | + | 11.2327i | 0.135291 | + | 0.0251853i | ||||
\(447\) | − | 54.8475i | − | 0.122701i | ||||||
\(448\) | −614.123 | + | 309.251i | −1.37081 | + | 0.690293i | ||||
\(449\) | −108.410 | −0.241448 | −0.120724 | − | 0.992686i | \(-0.538522\pi\) | ||||
−0.120724 | + | 0.992686i | \(0.538522\pi\) | |||||||
\(450\) | −18.3519 | + | 98.5833i | −0.0407821 | + | 0.219074i | ||||
\(451\) | −412.554 | −0.914753 | ||||||||
\(452\) | 424.382 | + | 163.675i | 0.938898 | + | 0.362113i | ||||
\(453\) | − | 156.788i | − | 0.346111i | ||||||
\(454\) | −108.287 | + | 581.699i | −0.238518 | + | 1.28127i | ||||
\(455\) | 486.493i | 1.06922i | ||||||||
\(456\) | 7.78976 | − | 12.6443i | 0.0170828 | − | 0.0277288i | ||||
\(457\) | 561.692 | 1.22909 | 0.614543 | − | 0.788883i | \(-0.289340\pi\) | ||||
0.614543 | + | 0.788883i | \(0.289340\pi\) | |||||||
\(458\) | 504.764 | + | 93.9652i | 1.10210 | + | 0.205164i | ||||
\(459\) | −82.3923 | −0.179504 | ||||||||
\(460\) | 230.851 | + | 89.0345i | 0.501851 | + | 0.193553i | ||||
\(461\) | − | 335.160i | − | 0.727028i | −0.931589 | − | 0.363514i | \(-0.881577\pi\) | ||
0.931589 | − | 0.363514i | \(-0.118423\pi\) | |||||||
\(462\) | −292.708 | − | 54.4895i | −0.633566 | − | 0.117943i | ||||
\(463\) | − | 389.912i | − | 0.842142i | −0.907028 | − | 0.421071i | \(-0.861654\pi\) | ||
0.907028 | − | 0.421071i | \(-0.138346\pi\) | |||||||
\(464\) | 430.774 | − | 475.392i | 0.928393 | − | 1.02455i | ||||
\(465\) | 45.8770 | 0.0986603 | ||||||||
\(466\) | 148.081 | − | 795.462i | 0.317770 | − | 1.70700i | ||||
\(467\) | −546.410 | −1.17004 | −0.585022 | − | 0.811018i | \(-0.698914\pi\) | ||||
−0.585022 | + | 0.811018i | \(0.698914\pi\) | |||||||
\(468\) | 67.9230 | − | 176.113i | 0.145135 | − | 0.376310i | ||||
\(469\) | 464.290i | 0.989958i | ||||||||
\(470\) | −1.62555 | + | 8.73217i | −0.00345862 | + | 0.0185791i | ||||
\(471\) | 400.131i | 0.849535i | ||||||||
\(472\) | −47.0615 | + | 76.3902i | −0.0997065 | + | 0.161844i | ||||
\(473\) | 102.277 | 0.216230 | ||||||||
\(474\) | −250.865 | − | 46.7003i | −0.529252 | − | 0.0985238i | ||||
\(475\) | 17.9127 | 0.0377110 | ||||||||
\(476\) | 245.205 | − | 635.775i | 0.515137 | − | 1.33566i | ||||
\(477\) | 85.7424i | 0.179753i | ||||||||
\(478\) | −226.410 | − | 42.1478i | −0.473661 | − | 0.0881753i | ||||
\(479\) | − | 368.369i | − | 0.769037i | −0.923117 | − | 0.384519i | \(-0.874367\pi\) | ||
0.923117 | − | 0.384519i | \(-0.125633\pi\) | |||||||
\(480\) | −96.6307 | − | 126.967i | −0.201314 | − | 0.264516i | ||||
\(481\) | −156.862 | −0.326116 | ||||||||
\(482\) | −92.0244 | + | 494.338i | −0.190922 | + | 1.02560i | ||||
\(483\) | 399.846 | 0.827839 | ||||||||
\(484\) | 212.727 | + | 82.0443i | 0.439518 | + | 0.169513i | ||||
\(485\) | − | 199.032i | − | 0.410375i | ||||||
\(486\) | −5.70577 | + | 30.6504i | −0.0117403 | + | 0.0630666i | ||||
\(487\) | 90.6326i | 0.186104i | 0.995661 | + | 0.0930519i | \(0.0296623\pi\) | ||||
−0.995661 | + | 0.0930519i | \(0.970338\pi\) | |||||||
\(488\) | 10.5077 | + | 6.47347i | 0.0215322 | + | 0.0132653i | ||||
\(489\) | 38.7180 | 0.0791778 | ||||||||
\(490\) | 375.986 | + | 69.9923i | 0.767318 | + | 0.142841i | ||||
\(491\) | −17.6462 | −0.0359392 | −0.0179696 | − | 0.999839i | \(-0.505720\pi\) | ||||
−0.0179696 | + | 0.999839i | \(0.505720\pi\) | |||||||
\(492\) | −333.349 | − | 128.566i | −0.677538 | − | 0.261312i | ||||
\(493\) | 635.775i | 1.28960i | ||||||||
\(494\) | −33.1487 | − | 6.17086i | −0.0671027 | − | 0.0124916i | ||||
\(495\) | − | 69.0899i | − | 0.139576i | ||||||
\(496\) | 98.8513 | − | 109.090i | 0.199297 | − | 0.219939i | ||||
\(497\) | −906.831 | −1.82461 | ||||||||
\(498\) | −7.78976 | + | 41.8452i | −0.0156421 | + | 0.0840265i | ||||
\(499\) | 548.631 | 1.09946 | 0.549730 | − | 0.835342i | \(-0.314731\pi\) | ||||
0.549730 | + | 0.835342i | \(0.314731\pi\) | |||||||
\(500\) | 172.841 | − | 448.147i | 0.345682 | − | 0.896294i | ||||
\(501\) | − | 382.859i | − | 0.764189i | ||||||
\(502\) | −2.50773 | + | 13.4711i | −0.00499548 | + | 0.0268348i | ||||
\(503\) | − | 262.475i | − | 0.521820i | −0.965363 | − | 0.260910i | \(-0.915977\pi\) | ||
0.965363 | − | 0.260910i | \(-0.0840225\pi\) | |||||||
\(504\) | −219.531 | − | 135.246i | −0.435577 | − | 0.268345i | ||||
\(505\) | 279.979 | 0.554415 | ||||||||
\(506\) | 337.990 | + | 62.9191i | 0.667964 | + | 0.124346i | ||||
\(507\) | −135.837 | −0.267923 | ||||||||
\(508\) | −53.0539 | + | 137.560i | −0.104437 | + | 0.270787i | ||||
\(509\) | 230.093i | 0.452049i | 0.974122 | + | 0.226025i | \(0.0725730\pi\) | ||||
−0.974122 | + | 0.226025i | \(0.927427\pi\) | |||||||
\(510\) | 155.454 | + | 28.9388i | 0.304811 | + | 0.0567427i | ||||
\(511\) | − | 1132.65i | − | 2.21654i | ||||||
\(512\) | −510.123 | − | 43.8013i | −0.996334 | − | 0.0855493i | ||||
\(513\) | 5.56922 | 0.0108562 | ||||||||
\(514\) | −90.8756 | + | 488.167i | −0.176801 | + | 0.949742i | ||||
\(515\) | −402.067 | −0.780712 | ||||||||
\(516\) | 82.6410 | + | 31.8729i | 0.160157 | + | 0.0617692i | ||||
\(517\) | 12.3417i | 0.0238718i | ||||||||
\(518\) | −39.2154 | + | 210.658i | −0.0757054 | + | 0.406675i | ||||
\(519\) | − | 401.013i | − | 0.772665i | ||||||
\(520\) | −190.010 | + | 308.425i | −0.365404 | + | 0.593124i | ||||
\(521\) | 164.144 | 0.315055 | 0.157527 | − | 0.987515i | \(-0.449648\pi\) | ||||
0.157527 | + | 0.987515i | \(0.449648\pi\) | |||||||
\(522\) | 236.512 | + | 44.0282i | 0.453087 | + | 0.0843453i | ||||
\(523\) | −185.492 | −0.354670 | −0.177335 | − | 0.984151i | \(-0.556748\pi\) | ||||
−0.177335 | + | 0.984151i | \(0.556748\pi\) | |||||||
\(524\) | −726.410 | − | 280.161i | −1.38628 | − | 0.534659i | ||||
\(525\) | − | 311.001i | − | 0.592382i | ||||||
\(526\) | −980.820 | − | 182.586i | −1.86468 | − | 0.347122i | ||||
\(527\) | 145.893i | 0.276838i | ||||||||
\(528\) | −164.287 | − | 148.868i | −0.311150 | − | 0.281947i | ||||
\(529\) | 67.2975 | 0.127216 | ||||||||
\(530\) | 30.1154 | − | 161.775i | 0.0568216 | − | 0.305235i | ||||
\(531\) | −33.6462 | −0.0633638 | ||||||||
\(532\) | −16.5744 | + | 42.9745i | −0.0311548 | + | 0.0807792i | ||||
\(533\) | 811.172i | 1.52190i | ||||||||
\(534\) | −21.0089 | + | 112.856i | −0.0393426 | + | 0.211341i | ||||
\(535\) | − | 569.357i | − | 1.06422i | ||||||
\(536\) | −181.338 | + | 294.348i | −0.338318 | + | 0.549157i | ||||
\(537\) | 335.405 | 0.624590 | ||||||||
\(538\) | −461.296 | − | 85.8734i | −0.857428 | − | 0.159616i | ||||
\(539\) | 531.405 | 0.985909 | ||||||||
\(540\) | 21.5307 | − | 55.8255i | 0.0398717 | − | 0.103381i | ||||
\(541\) | 891.253i | 1.64742i | 0.567013 | + | 0.823709i | \(0.308099\pi\) | ||||
−0.567013 | + | 0.823709i | \(0.691901\pi\) | |||||||
\(542\) | −199.219 | − | 37.0860i | −0.367563 | − | 0.0684244i | ||||
\(543\) | 468.505i | 0.862809i | ||||||||
\(544\) | 403.769 | − | 307.295i | 0.742223 | − | 0.564881i | ||||
\(545\) | 549.015 | 1.00737 | ||||||||
\(546\) | −107.138 | + | 575.528i | −0.196224 | + | 1.05408i | ||||
\(547\) | 524.631 | 0.959105 | 0.479553 | − | 0.877513i | \(-0.340799\pi\) | ||||
0.479553 | + | 0.877513i | \(0.340799\pi\) | |||||||
\(548\) | −61.3205 | − | 23.6500i | −0.111899 | − | 0.0431570i | ||||
\(549\) | 4.62815i | 0.00843014i | ||||||||
\(550\) | 48.9385 | − | 262.889i | 0.0889791 | − | 0.477979i | ||||
\(551\) | − | 42.9745i | − | 0.0779937i | ||||||
\(552\) | 253.492 | + | 156.168i | 0.459225 | + | 0.282914i | ||||
\(553\) | 791.405 | 1.43111 | ||||||||
\(554\) | 334.144 | + | 62.2031i | 0.603147 | + | 0.112280i | ||||
\(555\) | −49.7231 | −0.0895912 | ||||||||
\(556\) | 423.559 | + | 163.358i | 0.761797 | + | 0.293809i | ||||
\(557\) | − | 570.804i | − | 1.02478i | −0.858752 | − | 0.512391i | \(-0.828760\pi\) | ||
0.858752 | − | 0.512391i | \(-0.171240\pi\) | |||||||
\(558\) | 54.2731 | + | 10.1033i | 0.0972636 | + | 0.0181063i | ||||
\(559\) | − | 201.099i | − | 0.359748i | ||||||
\(560\) | 366.697 | + | 332.281i | 0.654817 | + | 0.593359i | ||||
\(561\) | 219.713 | 0.391645 | ||||||||
\(562\) | 40.6757 | − | 218.502i | 0.0723767 | − | 0.388794i | ||||
\(563\) | −161.877 | −0.287526 | −0.143763 | − | 0.989612i | \(-0.545920\pi\) | ||||
−0.143763 | + | 0.989612i | \(0.545920\pi\) | |||||||
\(564\) | −3.84610 | + | 9.97227i | −0.00681932 | + | 0.0176813i | ||||
\(565\) | − | 327.350i | − | 0.579381i | ||||||
\(566\) | −201.541 | + | 1082.64i | −0.356080 | + | 1.91279i | ||||
\(567\) | − | 96.6927i | − | 0.170534i | ||||||
\(568\) | −574.908 | − | 354.182i | −1.01216 | − | 0.623560i | ||||
\(569\) | 624.123 | 1.09688 | 0.548438 | − | 0.836191i | \(-0.315222\pi\) | ||||
0.548438 | + | 0.836191i | \(0.315222\pi\) | |||||||
\(570\) | −10.5077 | − | 1.95609i | −0.0184346 | − | 0.00343173i | ||||
\(571\) | −593.031 | −1.03858 | −0.519291 | − | 0.854597i | \(-0.673804\pi\) | ||||
−0.519291 | + | 0.854597i | \(0.673804\pi\) | |||||||
\(572\) | −181.128 | + | 469.634i | −0.316658 | + | 0.821039i | ||||
\(573\) | 539.551i | 0.941625i | ||||||||
\(574\) | 1089.37 | + | 202.793i | 1.89785 | + | 0.353298i | ||||
\(575\) | 359.113i | 0.624544i | ||||||||
\(576\) | −86.3538 | − | 171.485i | −0.149920 | − | 0.297717i | ||||
\(577\) | −1003.68 | −1.73948 | −0.869742 | − | 0.493507i | \(-0.835715\pi\) | ||||
−0.869742 | + | 0.493507i | \(0.835715\pi\) | |||||||
\(578\) | 13.7532 | − | 73.8795i | 0.0237944 | − | 0.127819i | ||||
\(579\) | 83.6180 | 0.144418 | ||||||||
\(580\) | −430.774 | − | 166.141i | −0.742714 | − | 0.286449i | ||||
\(581\) | − | 132.009i | − | 0.227210i | ||||||
\(582\) | 43.8320 | − | 235.458i | 0.0753127 | − | 0.404566i | ||||
\(583\) | − | 228.646i | − | 0.392189i | ||||||
\(584\) | 442.382 | − | 718.074i | 0.757503 | − | 1.22958i | ||||
\(585\) | −135.846 | −0.232216 | ||||||||
\(586\) | −439.468 | − | 81.8099i | −0.749945 | − | 0.139607i | ||||
\(587\) | 859.215 | 1.46374 | 0.731870 | − | 0.681444i | \(-0.238648\pi\) | ||||
0.731870 | + | 0.681444i | \(0.238648\pi\) | |||||||
\(588\) | 429.382 | + | 165.604i | 0.730241 | + | 0.281639i | ||||
\(589\) | − | 9.86151i | − | 0.0167428i | ||||||
\(590\) | 63.4820 | + | 11.8176i | 0.107597 | + | 0.0200298i | ||||
\(591\) | 436.274i | 0.738196i | ||||||||
\(592\) | −107.138 | + | 118.235i | −0.180977 | + | 0.199722i | ||||
\(593\) | −1007.42 | −1.69885 | −0.849423 | − | 0.527713i | \(-0.823050\pi\) | ||||
−0.849423 | + | 0.527713i | \(0.823050\pi\) | |||||||
\(594\) | 15.2154 | − | 81.7343i | 0.0256151 | − | 0.137600i | ||||
\(595\) | −490.410 | −0.824219 | ||||||||
\(596\) | −45.5795 | + | 118.180i | −0.0764757 | + | 0.198289i | ||||
\(597\) | − | 124.915i | − | 0.209239i | ||||||
\(598\) | 123.713 | − | 664.562i | 0.206878 | − | 1.11131i | ||||
\(599\) | − | 86.0598i | − | 0.143672i | −0.997416 | − | 0.0718362i | \(-0.977114\pi\) | ||
0.997416 | − | 0.0718362i | \(-0.0228859\pi\) | |||||||
\(600\) | 121.468 | − | 197.167i | 0.202446 | − | 0.328611i | ||||
\(601\) | −406.000 | −0.675541 | −0.337770 | − | 0.941229i | \(-0.609673\pi\) | ||||
−0.337770 | + | 0.941229i | \(0.609673\pi\) | |||||||
\(602\) | −270.067 | − | 50.2747i | −0.448616 | − | 0.0835129i | ||||
\(603\) | −129.646 | −0.215002 | ||||||||
\(604\) | −130.295 | + | 337.832i | −0.215720 | + | 0.559325i | ||||
\(605\) | − | 164.089i | − | 0.271221i | ||||||
\(606\) | 331.219 | + | 61.6587i | 0.546566 | + | 0.101747i | ||||
\(607\) | 1187.80i | 1.95684i | 0.206617 | + | 0.978422i | \(0.433755\pi\) | ||||
−0.206617 | + | 0.978422i | \(0.566245\pi\) | |||||||
\(608\) | −27.2923 | + | 20.7713i | −0.0448887 | + | 0.0341633i | ||||
\(609\) | −746.123 | −1.22516 | ||||||||
\(610\) | 1.62555 | − | 8.73217i | 0.00266484 | − | 0.0143150i | ||||
\(611\) | 24.2666 | 0.0397162 | ||||||||
\(612\) | 177.531 | + | 68.4699i | 0.290083 | + | 0.111879i | ||||
\(613\) | − | 500.378i | − | 0.816277i | −0.912920 | − | 0.408139i | \(-0.866178\pi\) | ||
0.912920 | − | 0.408139i | \(-0.133822\pi\) | |||||||
\(614\) | 136.084 | − | 731.021i | 0.221636 | − | 1.19059i | ||||
\(615\) | 257.131i | 0.418099i | ||||||||
\(616\) | 585.415 | + | 360.655i | 0.950350 | + | 0.585479i | ||||
\(617\) | 88.8306 | 0.143972 | 0.0719859 | − | 0.997406i | \(-0.477066\pi\) | ||||
0.0719859 | + | 0.997406i | \(0.477066\pi\) | |||||||
\(618\) | −475.650 | − | 88.5455i | −0.769660 | − | 0.143277i | ||||
\(619\) | −424.231 | −0.685349 | −0.342674 | − | 0.939454i | \(-0.611333\pi\) | ||||
−0.342674 | + | 0.939454i | \(0.611333\pi\) | |||||||
\(620\) | −98.8513 | − | 38.1249i | −0.159438 | − | 0.0614917i | ||||
\(621\) | 111.651i | 0.179792i | ||||||||
\(622\) | 648.897 | + | 120.797i | 1.04324 | + | 0.194207i | ||||
\(623\) | − | 356.027i | − | 0.571472i | ||||||
\(624\) | −292.708 | + | 323.025i | −0.469083 | + | 0.517668i | ||||
\(625\) | 72.1384 | 0.115422 | ||||||||
\(626\) | 29.3834 | − | 157.842i | 0.0469383 | − | 0.252144i | ||||
\(627\) | −14.8513 | −0.0236862 | ||||||||
\(628\) | 332.518 | − | 862.163i | 0.529487 | − | 1.37287i | ||||
\(629\) | − | 158.124i | − | 0.251390i | ||||||
\(630\) | −33.9615 | + | 182.435i | −0.0539072 | + | 0.289579i | ||||
\(631\) | 90.6326i | 0.143633i | 0.997418 | + | 0.0718166i | \(0.0228796\pi\) | ||||
−0.997418 | + | 0.0718166i | \(0.977120\pi\) | |||||||
\(632\) | 501.731 | + | 309.100i | 0.793878 | + | 0.489082i | ||||
\(633\) | −458.851 | −0.724883 | ||||||||
\(634\) | −135.440 | − | 25.2130i | −0.213627 | − | 0.0397682i | ||||
\(635\) | 106.108 | 0.167099 | ||||||||
\(636\) | 71.2539 | − | 184.749i | 0.112034 | − | 0.290486i | ||||
\(637\) | − | 1044.86i | − | 1.64028i | ||||||
\(638\) | −630.697 | − | 117.409i | −0.988554 | − | 0.184026i | ||||
\(639\) | − | 253.219i | − | 0.396274i | ||||||
\(640\) | 102.697 | + | 353.879i | 0.160465 | + | 0.552936i | ||||
\(641\) | 1090.40 | 1.70109 | 0.850546 | − | 0.525901i | \(-0.176272\pi\) | ||||
0.850546 | + | 0.525901i | \(0.176272\pi\) | |||||||
\(642\) | 125.387 | − | 673.557i | 0.195307 | − | 1.04915i | ||||
\(643\) | −454.200 | −0.706376 | −0.353188 | − | 0.935552i | \(-0.614902\pi\) | ||||
−0.353188 | + | 0.935552i | \(0.614902\pi\) | |||||||
\(644\) | −861.549 | − | 332.281i | −1.33781 | − | 0.515965i | ||||
\(645\) | − | 63.7458i | − | 0.0988307i | ||||||
\(646\) | 6.22055 | − | 33.4156i | 0.00962933 | − | 0.0517270i | ||||
\(647\) | 610.789i | 0.944032i | 0.881590 | + | 0.472016i | \(0.156474\pi\) | ||||
−0.881590 | + | 0.472016i | \(0.843526\pi\) | |||||||
\(648\) | 37.7654 | − | 61.3007i | 0.0582799 | − | 0.0945999i | ||||
\(649\) | 89.7231 | 0.138248 | ||||||||
\(650\) | −516.897 | − | 96.2239i | −0.795227 | − | 0.148037i | ||||
\(651\) | −171.215 | −0.263004 | ||||||||
\(652\) | −83.4256 | − | 32.1755i | −0.127953 | − | 0.0493489i | ||||
\(653\) | − | 673.612i | − | 1.03157i | −0.856720 | − | 0.515783i | \(-0.827501\pi\) | ||
0.856720 | − | 0.515783i | \(-0.172499\pi\) | |||||||
\(654\) | 649.492 | + | 120.907i | 0.993107 | + | 0.184874i | ||||
\(655\) | 560.322i | 0.855454i | ||||||||
\(656\) | 611.426 | + | 554.041i | 0.932051 | + | 0.844574i | ||||
\(657\) | 316.277 | 0.481396 | ||||||||
\(658\) | 6.06664 | − | 32.5889i | 0.00921982 | − | 0.0495272i | ||||
\(659\) | −819.328 | −1.24329 | −0.621645 | − | 0.783299i | \(-0.713535\pi\) | ||||
−0.621645 | + | 0.783299i | \(0.713535\pi\) | |||||||
\(660\) | −57.4153 | + | 148.868i | −0.0869929 | + | 0.225558i | ||||
\(661\) | 370.628i | 0.560707i | 0.959897 | + | 0.280354i | \(0.0904518\pi\) | ||||
−0.959897 | + | 0.280354i | \(0.909548\pi\) | |||||||
\(662\) | 144.967 | − | 778.734i | 0.218983 | − | 1.17634i | ||||
\(663\) | − | 432.004i | − | 0.651590i | ||||||
\(664\) | 51.5589 | − | 83.6904i | 0.0776490 | − | 0.126040i | ||||
\(665\) | 33.1487 | 0.0498477 | ||||||||
\(666\) | −58.8231 | − | 10.9503i | −0.0883230 | − | 0.0164419i | ||||
\(667\) | 861.549 | 1.29168 | ||||||||
\(668\) | −318.164 | + | 824.946i | −0.476294 | + | 1.23495i | ||||
\(669\) | − | 53.1535i | − | 0.0794521i | ||||||
\(670\) | 244.610 | + | 45.5358i | 0.365090 | + | 0.0679639i | ||||
\(671\) | − | 12.3417i | − | 0.0183930i | ||||||
\(672\) | 360.631 | + | 473.849i | 0.536653 | + | 0.705133i | ||||
\(673\) | −255.703 | −0.379944 | −0.189972 | − | 0.981789i | \(-0.560840\pi\) | ||||
−0.189972 | + | 0.981789i | \(0.560840\pi\) | |||||||
\(674\) | −84.8165 | + | 455.619i | −0.125841 | + | 0.675992i | ||||
\(675\) | 86.8423 | 0.128655 | ||||||||
\(676\) | 292.688 | + | 112.884i | 0.432971 | + | 0.166988i | ||||
\(677\) | 934.323i | 1.38009i | 0.723765 | + | 0.690047i | \(0.242410\pi\) | ||||
−0.723765 | + | 0.690047i | \(0.757590\pi\) | |||||||
\(678\) | 72.0910 | − | 387.260i | 0.106329 | − | 0.571180i | ||||
\(679\) | 742.798i | 1.09396i | ||||||||
\(680\) | −310.908 | − | 191.540i | −0.457217 | − | 0.281677i | ||||
\(681\) | 512.420 | 0.752453 | ||||||||
\(682\) | −144.728 | − | 26.9422i | −0.212212 | − | 0.0395046i | ||||
\(683\) | 1142.54 | 1.67283 | 0.836415 | − | 0.548096i | \(-0.184647\pi\) | ||||
0.836415 | + | 0.548096i | \(0.184647\pi\) | |||||||
\(684\) | −12.0000 | − | 4.62815i | −0.0175439 | − | 0.00676630i | ||||
\(685\) | 47.3001i | 0.0690512i | ||||||||
\(686\) | −368.105 | − | 68.5253i | −0.536596 | − | 0.0998911i | ||||
\(687\) | − | 444.648i | − | 0.647232i | ||||||
\(688\) | −151.580 | − | 137.353i | −0.220319 | − | 0.199641i | ||||
\(689\) | −449.569 | −0.652495 | ||||||||
\(690\) | 39.2154 | − | 210.658i | 0.0568339 | − | 0.305301i | ||||
\(691\) | 1316.90 | 1.90578 | 0.952892 | − | 0.303309i | \(-0.0980913\pi\) | ||||
0.952892 | + | 0.303309i | \(0.0980913\pi\) | |||||||
\(692\) | −333.251 | + | 864.063i | −0.481577 | + | 1.24865i | ||||
\(693\) | 257.847i | 0.372074i | ||||||||
\(694\) | −169.149 | + | 908.636i | −0.243730 | + | 1.30927i | ||||
\(695\) | − | 326.716i | − | 0.470094i | ||||||
\(696\) | −473.023 | − | 291.414i | −0.679631 | − | 0.418698i | ||||
\(697\) | −817.703 | −1.17317 | ||||||||
\(698\) | 524.967 | + | 97.7261i | 0.752101 | + | 0.140009i | ||||
\(699\) | −700.726 | −1.00247 | ||||||||
\(700\) | −258.449 | + | 670.113i | −0.369212 | + | 0.957305i | ||||
\(701\) | − | 318.493i | − | 0.454341i | −0.973855 | − | 0.227170i | \(-0.927053\pi\) | ||
0.973855 | − | 0.227170i | \(-0.0729474\pi\) | |||||||
\(702\) | −160.708 | − | 29.9168i | −0.228928 | − | 0.0426166i | ||||
\(703\) | 10.6883i | 0.0152038i | ||||||||
\(704\) | 230.277 | + | 457.293i | 0.327098 | + | 0.649563i | ||||
\(705\) | 7.69219 | 0.0109109 | ||||||||
\(706\) | −96.2140 | + | 516.844i | −0.136280 | + | 0.732074i | ||||
\(707\) | −1044.90 | −1.47793 | ||||||||
\(708\) | 72.4974 | + | 27.9607i | 0.102397 | + | 0.0394926i | ||||
\(709\) | 289.831i | 0.408788i | 0.978889 | + | 0.204394i | \(0.0655224\pi\) | ||||
−0.978889 | + | 0.204394i | \(0.934478\pi\) | |||||||
\(710\) | −88.9385 | + | 477.761i | −0.125266 | + | 0.672903i | ||||
\(711\) | 220.988i | 0.310813i | ||||||||
\(712\) | 139.054 | − | 225.712i | 0.195300 | − | 0.317012i | ||||
\(713\) | 197.703 | 0.277283 | ||||||||
\(714\) | −580.161 | − | 108.001i | −0.812551 | − | 0.151262i | ||||
\(715\) | 362.256 | 0.506652 | ||||||||
\(716\) | −722.697 | − | 278.729i | −1.00935 | − | 0.389287i | ||||
\(717\) | 199.445i | 0.278167i | ||||||||
\(718\) | 322.823 | + | 60.0957i | 0.449614 | + | 0.0836988i | ||||
\(719\) | − | 491.122i | − | 0.683062i | −0.939870 | − | 0.341531i | \(-0.889055\pi\) | ||
0.939870 | − | 0.341531i | \(-0.110945\pi\) | |||||||
\(720\) | −92.7846 | + | 102.395i | −0.128868 | + | 0.142215i | ||||
\(721\) | 1500.53 | 2.08118 | ||||||||
\(722\) | 131.715 | − | 707.547i | 0.182430 | − | 0.979982i | ||||
\(723\) | 435.464 | 0.602302 | ||||||||
\(724\) | 389.338 | − | 1009.49i | 0.537760 | − | 1.39432i | ||||
\(725\) | − | 670.113i | − | 0.924294i | ||||||
\(726\) | 36.1366 | − | 194.119i | 0.0497749 | − | 0.267381i | ||||
\(727\) | 774.918i | 1.06591i | 0.846143 | + | 0.532956i | \(0.178919\pi\) | ||||
−0.846143 | + | 0.532956i | \(0.821081\pi\) | |||||||
\(728\) | 709.128 | − | 1151.06i | 0.974077 | − | 1.58112i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −596.736 | − | 111.086i | −0.817446 | − | 0.152173i | ||||
\(731\) | 202.718 | 0.277316 | ||||||||
\(732\) | 3.84610 | − | 9.97227i | 0.00525423 | − | 0.0136233i | ||||
\(733\) | − | 858.966i | − | 1.17185i | −0.810365 | − | 0.585925i | \(-0.800731\pi\) | ||
0.810365 | − | 0.585925i | \(-0.199269\pi\) | |||||||
\(734\) | −476.760 | − | 88.7522i | −0.649537 | − | 0.120916i | ||||
\(735\) | − | 331.207i | − | 0.450622i | ||||||
\(736\) | −416.420 | − | 547.154i | −0.565789 | − | 0.743416i | ||||
\(737\) | 345.723 | 0.469095 | ||||||||
\(738\) | −56.6269 | + | 304.189i | −0.0767303 | + | 0.412181i | ||||
\(739\) | 63.1948 | 0.0855139 | 0.0427569 | − | 0.999086i | \(-0.486386\pi\) | ||||
0.0427569 | + | 0.999086i | \(0.486386\pi\) | |||||||
\(740\) | 107.138 | + | 41.3210i | 0.144782 | + | 0.0558393i | ||||
\(741\) | 29.2008i | 0.0394073i | ||||||||
\(742\) | −112.392 | + | 603.751i | −0.151472 | + | 0.813680i | ||||
\(743\) | − | 1105.00i | − | 1.48721i | −0.668620 | − | 0.743604i | \(-0.733115\pi\) | ||
0.668620 | − | 0.743604i | \(-0.266885\pi\) | |||||||
\(744\) | −108.546 | − | 66.8718i | −0.145895 | − | 0.0898814i | ||||
\(745\) | 91.1591 | 0.122361 | ||||||||
\(746\) | 645.864 | + | 120.232i | 0.865769 | + | 0.161169i | ||||
\(747\) | 36.8616 | 0.0493461 | ||||||||
\(748\) | −473.415 | − | 182.586i | −0.632908 | − | 0.244099i | ||||
\(749\) | 2124.87i | 2.83694i | ||||||||
\(750\) | −408.946 | − | 76.1281i | −0.545261 | − | 0.101504i | ||||
\(751\) | − | 804.119i | − | 1.07073i | −0.844621 | − | 0.535365i | \(-0.820174\pi\) | ||
0.844621 | − | 0.535365i | \(-0.179826\pi\) | |||||||
\(752\) | 16.5744 | − | 18.2911i | 0.0220404 | − | 0.0243232i | ||||
\(753\) | 11.8667 | 0.0157593 | ||||||||
\(754\) | −230.851 | + | 1240.09i | −0.306169 | + | 1.64468i | ||||
\(755\) | 260.589 | 0.345152 | ||||||||
\(756\) | −80.3538 | + | 208.344i | −0.106288 | + | 0.275587i | ||||
\(757\) | − | 1351.03i | − | 1.78471i | −0.451334 | − | 0.892355i | \(-0.649052\pi\) | ||
0.451334 | − | 0.892355i | \(-0.350948\pi\) | |||||||
\(758\) | −13.2539 | + | 71.1973i | −0.0174853 | + | 0.0939279i | ||||
\(759\) | − | 297.736i | − | 0.392274i | ||||||
\(760\) | 21.0155 | + | 12.9469i | 0.0276519 | + | 0.0170355i | ||||
\(761\) | −709.805 | −0.932726 | −0.466363 | − | 0.884593i | \(-0.654436\pi\) | ||||
−0.466363 | + | 0.884593i | \(0.654436\pi\) | |||||||
\(762\) | 125.527 | + | 23.3677i | 0.164734 | + | 0.0306663i | ||||
\(763\) | −2048.95 | −2.68539 | ||||||||
\(764\) | 448.379 | − | 1162.57i | 0.586884 | − | 1.52169i | ||||
\(765\) | − | 136.940i | − | 0.179006i | ||||||
\(766\) | −323.041 | − | 60.1363i | −0.421724 | − | 0.0785069i | ||||
\(767\) | − | 176.415i | − | 0.230007i | ||||||
\(768\) | 43.5589 | + | 441.260i | 0.0567173 | + | 0.574558i | ||||
\(769\) | −195.703 | −0.254490 | −0.127245 | − | 0.991871i | \(-0.540613\pi\) | ||||
−0.127245 | + | 0.991871i | \(0.540613\pi\) | |||||||
\(770\) | 90.5641 | − | 486.493i | 0.117616 | − | 0.631810i | ||||
\(771\) | 430.028 | 0.557754 | ||||||||
\(772\) | −180.172 | − | 69.4885i | −0.233383 | − | 0.0900110i | ||||
\(773\) | 12.5484i | 0.0162334i | 0.999967 | + | 0.00811670i | \(0.00258365\pi\) | ||||
−0.999967 | + | 0.00811670i | \(0.997416\pi\) | |||||||
\(774\) | 14.0385 | − | 75.4121i | 0.0181376 | − | 0.0974317i | ||||
\(775\) | − | 153.773i | − | 0.198417i | ||||||
\(776\) | −290.115 | + | 470.915i | −0.373860 | + | 0.606849i | ||||
\(777\) | 185.569 | 0.238828 | ||||||||
\(778\) | 1189.44 | + | 221.422i | 1.52884 | + | 0.284604i | ||||
\(779\) | 55.2717 | 0.0709521 | ||||||||
\(780\) | 292.708 | + | 112.891i | 0.375266 | + | 0.144732i | ||||
\(781\) | 675.251i | 0.864598i | ||||||||
\(782\) | 669.913 | + | 124.709i | 0.856666 | + | 0.159474i | ||||
\(783\) | − | 208.344i | − | 0.266084i | ||||||
\(784\) | −787.569 | − | 713.652i | −1.00455 | − | 0.910271i | ||||
\(785\) | −665.036 | −0.847180 | ||||||||
\(786\) | −123.397 | + | 662.868i | −0.156994 | + | 0.843344i | ||||
\(787\) | −432.918 | −0.550086 | −0.275043 | − | 0.961432i | \(-0.588692\pi\) | ||||
−0.275043 | + | 0.961432i | \(0.588692\pi\) | |||||||
\(788\) | 362.554 | − | 940.040i | 0.460094 | − | 1.19294i | ||||
\(789\) | 864.008i | 1.09507i | ||||||||
\(790\) | 77.6180 | − | 416.950i | 0.0982506 | − | 0.527784i | ||||
\(791\) | 1221.69i | 1.54449i | ||||||||
\(792\) | −100.708 | + | 163.469i | −0.127156 | + | 0.206400i | ||||
\(793\) | −24.2666 | −0.0306010 | ||||||||
\(794\) | 1065.10 | + | 198.276i | 1.34144 | + | 0.249717i | ||||
\(795\) | −142.508 | −0.179255 | ||||||||
\(796\) | −103.808 | + | 269.155i | −0.130412 | + | 0.338135i | ||||
\(797\) | 700.746i | 0.879230i | 0.898186 | + | 0.439615i | \(0.144885\pi\) | ||||
−0.898186 | + | 0.439615i | \(0.855115\pi\) | |||||||
\(798\) | 39.2154 | + | 7.30021i | 0.0491421 | + | 0.00914813i | ||||
\(799\) | 24.4619i | 0.0306157i | ||||||||
\(800\) | −425.577 | + | 323.892i | −0.531971 | + | 0.404865i | ||||
\(801\) | 99.4153 | 0.124114 | ||||||||
\(802\) | 138.932 | − | 746.317i | 0.173232 | − | 0.930570i | ||||
\(803\) | −843.405 | −1.05032 | ||||||||
\(804\) | 279.349 | + | 107.739i | 0.347449 | + | 0.134004i | ||||
\(805\) | 664.562i | 0.825543i | ||||||||
\(806\) | −52.9742 | + | 284.568i | −0.0657248 | + | 0.353062i | ||||
\(807\) | 406.357i | 0.503541i | ||||||||
\(808\) | −662.438 | − | 408.107i | −0.819849 | − | 0.505083i | ||||
\(809\) | −848.102 | −1.04833 | −0.524167 | − | 0.851615i | \(-0.675623\pi\) | ||||
−0.524167 | + | 0.851615i | \(0.675623\pi\) | |||||||
\(810\) | −50.9423 | − | 9.48325i | −0.0628917 | − | 0.0117077i | ||||
\(811\) | 1242.18 | 1.53166 | 0.765832 | − | 0.643041i | \(-0.222327\pi\) | ||||
0.765832 | + | 0.643041i | \(0.222327\pi\) | |||||||
\(812\) | 1607.67 | + | 620.045i | 1.97989 | + | 0.763602i | ||||
\(813\) | 175.493i | 0.215858i | ||||||||
\(814\) | 156.862 | + | 29.2008i | 0.192705 | + | 0.0358733i | ||||
\(815\) | 64.3510i | 0.0789583i | ||||||||
\(816\) | −325.626 | − | 295.064i | −0.399051 | − | 0.361598i | ||||
\(817\) | −13.7025 | −0.0167717 | ||||||||
\(818\) | −92.0244 | + | 494.338i | −0.112499 | + | 0.604325i | ||||
\(819\) | 506.985 | 0.619029 | ||||||||
\(820\) | 213.682 | − | 554.041i | 0.260588 | − | 0.675659i | ||||
\(821\) | 208.303i | 0.253719i | 0.991921 | + | 0.126859i | \(0.0404897\pi\) | ||||
−0.991921 | + | 0.126859i | \(0.959510\pi\) | |||||||
\(822\) | −10.4167 | + | 55.9566i | −0.0126724 | + | 0.0680737i | ||||
\(823\) | − | 778.114i | − | 0.945461i | −0.881207 | − | 0.472730i | \(-0.843268\pi\) | ||
0.881207 | − | 0.472730i | \(-0.156732\pi\) | |||||||
\(824\) | 951.300 | + | 586.065i | 1.15449 | + | 0.711244i | ||||
\(825\) | −231.580 | −0.280702 | ||||||||
\(826\) | −236.918 | − | 44.1039i | −0.286826 | − | 0.0533945i | ||||
\(827\) | −1280.57 | −1.54845 | −0.774225 | − | 0.632910i | \(-0.781860\pi\) | ||||
−0.774225 | + | 0.632910i | \(0.781860\pi\) | |||||||
\(828\) | 92.7846 | − | 240.575i | 0.112059 | − | 0.290549i | ||||
\(829\) | − | 9.78043i | − | 0.0117979i | −0.999983 | − | 0.00589893i | \(-0.998122\pi\) | ||
0.999983 | − | 0.00589893i | \(-0.00187770\pi\) | |||||||
\(830\) | −69.5486 | − | 12.9469i | −0.0837935 | − | 0.0155987i | ||||
\(831\) | − | 294.348i | − | 0.354210i | ||||||
\(832\) | 899.138 | − | 452.775i | 1.08070 | − | 0.544201i | ||||
\(833\) | 1053.27 | 1.26443 | ||||||||
\(834\) | 71.9512 | − | 386.509i | 0.0862724 | − | 0.463440i | ||||
\(835\) | 636.328 | 0.762070 | ||||||||
\(836\) | 32.0000 | + | 12.3417i | 0.0382775 | + | 0.0147628i | ||||
\(837\) | − | 47.8094i | − | 0.0571199i | ||||||
\(838\) | −98.1436 | + | 527.209i | −0.117116 | + | 0.629128i | ||||
\(839\) | − | 1232.38i | − | 1.46886i | −0.678682 | − | 0.734432i | \(-0.737449\pi\) | ||
0.678682 | − | 0.734432i | \(-0.262551\pi\) | |||||||
\(840\) | 224.785 | − | 364.870i | 0.267601 | − | 0.434369i | ||||
\(841\) | −766.672 | −0.911619 | ||||||||
\(842\) | −429.149 | − | 79.8890i | −0.509678 | − | 0.0948800i | ||||
\(843\) | −192.480 | −0.228327 | ||||||||
\(844\) | 988.687 | + | 381.316i | 1.17143 | + | 0.451796i | ||||
\(845\) | − | 225.768i | − | 0.267181i | ||||||
\(846\) | 9.09996 | + | 1.69402i | 0.0107565 | + | 0.00200239i | ||||
\(847\) | 612.387i | 0.723007i | ||||||||
\(848\) | −307.061 | + | 338.865i | −0.362101 | + | 0.399606i | ||||
\(849\) | 953.703 | 1.12332 | ||||||||
\(850\) | 96.9986 | − | 521.059i | 0.114116 | − | 0.613010i | ||||
\(851\) | −214.277 | −0.251794 | ||||||||
\(852\) | −210.431 | + | 545.611i | −0.246984 | + | 0.640389i | ||||
\(853\) | 412.170i | 0.483201i | 0.970376 | + | 0.241600i | \(0.0776723\pi\) | ||||
−0.970376 | + | 0.241600i | \(0.922328\pi\) | |||||||
\(854\) | −6.06664 | + | 32.5889i | −0.00710380 | + | 0.0381603i | ||||
\(855\) | 9.25630i | 0.0108261i | ||||||||
\(856\) | −829.913 | + | 1347.11i | −0.969524 | + | 1.57373i | ||||
\(857\) | −136.451 | −0.159220 | −0.0796099 | − | 0.996826i | \(-0.525367\pi\) | ||||
−0.0796099 | + | 0.996826i | \(0.525367\pi\) | |||||||
\(858\) | 428.554 | + | 79.7782i | 0.499480 | + | 0.0929816i | ||||
\(859\) | −649.646 | −0.756282 | −0.378141 | − | 0.925748i | \(-0.623437\pi\) | ||||
−0.378141 | + | 0.925748i | \(0.623437\pi\) | |||||||
\(860\) | −52.9742 | + | 137.353i | −0.0615979 | + | 0.159713i | ||||
\(861\) | − | 959.627i | − | 1.11455i | ||||||
\(862\) | −1083.30 | − | 201.664i | −1.25673 | − | 0.233949i | ||||
\(863\) | 1192.38i | 1.38167i | 0.723015 | + | 0.690833i | \(0.242756\pi\) | ||||
−0.723015 | + | 0.690833i | \(0.757244\pi\) | |||||||
\(864\) | −132.315 | + | 100.701i | −0.153143 | + | 0.116552i | ||||
\(865\) | 666.502 | 0.770523 | ||||||||
\(866\) | 96.3116 | − | 517.368i | 0.111214 | − | 0.597423i | ||||
\(867\) | −65.0807 | −0.0750643 | ||||||||
\(868\) | 368.918 | + | 142.284i | 0.425021 | + | 0.163922i | ||||
\(869\) | − | 589.302i | − | 0.678138i | ||||||
\(870\) | −73.1769 | + | 393.093i | −0.0841114 | + | 0.451831i | ||||
\(871\) | − | 679.768i | − | 0.780446i | ||||||
\(872\) | −1298.98 | − | 800.262i | −1.48966 | − | 0.917732i | ||||
\(873\) | −207.415 | −0.237589 | ||||||||
\(874\) | −45.2820 | − | 8.42956i | −0.0518101 | − | 0.00964480i | ||||
\(875\) | 1290.10 | 1.47440 | ||||||||
\(876\) | −681.482 | − | 262.833i | −0.777947 | − | 0.300038i | ||||
\(877\) | − | 744.451i | − | 0.848861i | −0.905460 | − | 0.424431i | \(-0.860474\pi\) | ||
0.905460 | − | 0.424431i | \(-0.139526\pi\) | |||||||
\(878\) | −866.099 | − | 161.230i | −0.986445 | − | 0.183633i | ||||
\(879\) | 387.129i | 0.440419i | ||||||||
\(880\) | 247.426 | − | 273.053i | 0.281165 | − | 0.310287i | ||||
\(881\) | 651.108 | 0.739055 | 0.369528 | − | 0.929220i | \(-0.379520\pi\) | ||||
0.369528 | + | 0.929220i | \(0.379520\pi\) | |||||||
\(882\) | 72.9404 | − | 391.822i | 0.0826989 | − | 0.444243i | ||||
\(883\) | 1171.44 | 1.32666 | 0.663330 | − | 0.748327i | \(-0.269143\pi\) | ||||
0.663330 | + | 0.748327i | \(0.269143\pi\) | |||||||
\(884\) | −359.005 | + | 930.839i | −0.406114 | + | 1.05299i | ||||
\(885\) | − | 55.9215i | − | 0.0631881i | ||||||
\(886\) | 83.7128 | − | 449.690i | 0.0944840 | − | 0.507551i | ||||
\(887\) | 1026.87i | 1.15769i | 0.815437 | + | 0.578845i | \(0.196496\pi\) | ||||
−0.815437 | + | 0.578845i | \(0.803504\pi\) | |||||||
\(888\) | 117.646 | + | 72.4780i | 0.132484 | + | 0.0816193i | ||||
\(889\) | −396.000 | −0.445444 | ||||||||
\(890\) | −187.572 | − | 34.9178i | −0.210755 | − | 0.0392335i | ||||
\(891\) | −72.0000 | −0.0808081 | ||||||||
\(892\) | −44.1718 | + | 114.530i | −0.0495199 | + | 0.128397i | ||||
\(893\) | − | 1.65348i | − | 0.00185160i | ||||||
\(894\) | 107.842 | + | 20.0756i | 0.120629 | + | 0.0224559i | ||||
\(895\) | 557.458i | 0.622859i | ||||||||
\(896\) | −383.272 | − | 1320.70i | −0.427759 | − | 1.47399i | ||||
\(897\) | −585.415 | −0.652637 | ||||||||
\(898\) | 39.6809 | − | 213.158i | 0.0441881 | − | 0.237370i | ||||
\(899\) | −368.918 | −0.410365 | ||||||||
\(900\) | −187.119 | − | 72.1680i | −0.207910 | − | 0.0801866i | ||||
\(901\) | − | 453.189i | − | 0.502984i | ||||||
\(902\) | 151.005 | − | 811.172i | 0.167411 | − | 0.899304i | ||||
\(903\) | 237.903i | 0.263458i | ||||||||
\(904\) | −477.156 | + | 774.520i | −0.527828 | + | 0.856769i | ||||
\(905\) | −778.677 | −0.860416 | ||||||||
\(906\) | 308.281 | + | 57.3885i | 0.340266 | + | 0.0633428i | ||||
\(907\) | −470.508 | −0.518752 | −0.259376 | − | 0.965776i | \(-0.583517\pi\) | ||||
−0.259376 | + | 0.965776i | \(0.583517\pi\) | |||||||
\(908\) | −1104.11 | − | 425.833i | −1.21598 | − | 0.468979i | ||||
\(909\) | − | 291.772i | − | 0.320981i | ||||||
\(910\) | −956.554 | − | 178.069i | −1.05116 | − | 0.195680i | ||||
\(911\) | − | 553.930i | − | 0.608046i | −0.952665 | − | 0.304023i | \(-0.901670\pi\) | ||
0.952665 | − | 0.304023i | \(-0.0983300\pi\) | |||||||
\(912\) | 22.0103 | + | 19.9445i | 0.0241341 | + | 0.0218690i | ||||
\(913\) | −98.2975 | −0.107664 | ||||||||
\(914\) | −205.594 | + | 1104.41i | −0.224938 | + | 1.20833i | ||||
\(915\) | −7.69219 | −0.00840677 | ||||||||
\(916\) | −369.513 | + | 958.084i | −0.403398 | + | 1.04594i | ||||
\(917\) | − | 2091.15i | − | 2.28043i | ||||||
\(918\) | 30.1577 | − | 162.001i | 0.0328515 | − | 0.176472i | ||||
\(919\) | − | 910.123i | − | 0.990341i | −0.868796 | − | 0.495170i | \(-0.835106\pi\) | ||
0.868796 | − | 0.495170i | \(-0.164894\pi\) | |||||||
\(920\) | −259.559 | + | 421.316i | −0.282129 | + | 0.457952i | ||||
\(921\) | −643.959 | −0.699195 | ||||||||
\(922\) | 658.999 | + | 122.677i | 0.714749 | + | 0.133055i | ||||
\(923\) | 1327.69 | 1.43845 | ||||||||
\(924\) | 214.277 | − | 555.583i | 0.231901 | − | 0.601281i | ||||
\(925\) | 166.665i | 0.180178i | ||||||||
\(926\) | 766.652 | + | 142.718i | 0.827918 | + | 0.154123i | ||||
\(927\) | 419.002i | 0.451997i | ||||||||
\(928\) | 777.051 | + | 1021.00i | 0.837340 | + | 1.10022i | ||||
\(929\) | 1278.69 | 1.37641 | 0.688206 | − | 0.725515i | \(-0.258398\pi\) | ||||
0.688206 | + | 0.725515i | \(0.258398\pi\) | |||||||
\(930\) | −16.7922 | + | 90.2044i | −0.0180561 | + | 0.0969940i | ||||
\(931\) | −71.1948 | −0.0764713 | ||||||||
\(932\) | 1509.85 | + | 582.319i | 1.62001 | + | 0.624806i | ||||
\(933\) | − | 571.616i | − | 0.612664i | ||||||
\(934\) | 200.000 | − | 1074.36i | 0.214133 | − | 1.15028i | ||||
\(935\) | 365.173i | 0.390559i | ||||||||
\(936\) | 321.415 | + | 198.014i | 0.343392 | + | 0.211553i | ||||
\(937\) | 634.554 | 0.677219 | 0.338609 | − | 0.940927i | \(-0.390044\pi\) | ||||
0.338609 | + | 0.940927i | \(0.390044\pi\) | |||||||
\(938\) | −912.897 | − | 169.942i | −0.973238 | − | 0.181175i | ||||
\(939\) | −139.044 | −0.148076 | ||||||||
\(940\) | −16.5744 | − | 6.39239i | −0.0176323 | − | 0.00680041i | ||||
\(941\) | − | 1136.25i | − | 1.20749i | −0.797177 | − | 0.603745i | \(-0.793674\pi\) | ||
0.797177 | − | 0.603745i | \(-0.206326\pi\) | |||||||
\(942\) | −786.746 | − | 146.458i | −0.835187 | − | 0.155476i | ||||
\(943\) | 1108.08i | 1.17506i | ||||||||
\(944\) | −132.974 | − | 120.494i | −0.140863 | − | 0.127642i | ||||
\(945\) | 160.708 | 0.170061 | ||||||||
\(946\) | −37.4359 | + | 201.099i | −0.0395729 | + | 0.212578i | ||||
\(947\) | 775.615 | 0.819023 | 0.409512 | − | 0.912305i | \(-0.365699\pi\) | ||||
0.409512 | + | 0.912305i | \(0.365699\pi\) | |||||||
\(948\) | 183.646 | − | 476.163i | 0.193720 | − | 0.502282i | ||||
\(949\) | 1658.32i | 1.74744i | ||||||||
\(950\) | −6.55652 | + | 35.2204i | −0.00690160 | + | 0.0370741i | ||||
\(951\) | 119.309i | 0.125457i | ||||||||
\(952\) | 1160.32 | + | 714.837i | 1.21883 | + | 0.750879i | ||||
\(953\) | 599.590 | 0.629160 | 0.314580 | − | 0.949231i | \(-0.398136\pi\) | ||||
0.314580 | + | 0.949231i | \(0.398136\pi\) | |||||||
\(954\) | −168.588 | − | 31.3839i | −0.176717 | − | 0.0328972i | ||||
\(955\) | −896.758 | −0.939014 | ||||||||
\(956\) | 165.744 | − | 429.745i | 0.173372 | − | 0.449524i | ||||
\(957\) | 555.583i | 0.580547i | ||||||||
\(958\) | 724.295 | + | 134.832i | 0.756049 | + | 0.140744i | ||||
\(959\) | − | 176.526i | − | 0.184073i | ||||||
\(960\) | 285.015 | − | 143.524i | 0.296891 | − | 0.149504i | ||||
\(961\) | 876.343 | 0.911908 | ||||||||
\(962\) | 57.4153 | − | 308.425i | 0.0596833 | − | 0.320608i | ||||
\(963\) | −593.338 | −0.616135 | ||||||||
\(964\) | −938.295 | − | 361.881i | −0.973335 | − | 0.375395i | ||||
\(965\) | 138.977i | 0.144018i | ||||||||
\(966\) | −146.354 | + | 786.186i | −0.151505 | + | 0.813857i | ||||
\(967\) | 1407.53i | 1.45556i | 0.685811 | + | 0.727780i | \(0.259448\pi\) | ||||
−0.685811 | + | 0.727780i | \(0.740552\pi\) | |||||||
\(968\) | −239.181 | + | 388.238i | −0.247087 | + | 0.401072i | ||||
\(969\) | −29.4359 | −0.0303776 | ||||||||
\(970\) | 391.341 | + | 72.8508i | 0.403444 | + | 0.0751039i | ||||
\(971\) | 653.661 | 0.673184 | 0.336592 | − | 0.941651i | \(-0.390726\pi\) | ||||
0.336592 | + | 0.941651i | \(0.390726\pi\) | |||||||
\(972\) | −58.1769 | − | 22.4376i | −0.0598528 | − | 0.0230840i | ||||
\(973\) | 1219.32i | 1.25315i | ||||||||
\(974\) | −178.204 | − | 33.1738i | −0.182961 | − | 0.0340594i | ||||
\(975\) | 455.337i | 0.467012i | ||||||||
\(976\) | −16.5744 | + | 18.2911i | −0.0169819 | + | 0.0187408i | ||||
\(977\) | −1003.57 | −1.02719 | −0.513597 | − | 0.858031i | \(-0.671687\pi\) | ||||
−0.513597 | + | 0.858031i | \(0.671687\pi\) | |||||||
\(978\) | −14.1718 | + | 76.1281i | −0.0144906 | + | 0.0778406i | ||||
\(979\) | −265.108 | −0.270794 | ||||||||
\(980\) | −275.241 | + | 713.652i | −0.280858 | + | 0.728217i | ||||
\(981\) | − | 572.140i | − | 0.583221i | ||||||
\(982\) | 6.45895 | − | 34.6963i | 0.00657734 | − | 0.0353323i | ||||
\(983\) | 105.672i | 0.107500i | 0.998554 | + | 0.0537498i | \(0.0171173\pi\) | ||||
−0.998554 | + | 0.0537498i | \(0.982883\pi\) | |||||||
\(984\) | 374.802 | − | 608.379i | 0.380897 | − | 0.618271i | ||||
\(985\) | −725.108 | −0.736150 | ||||||||
\(986\) | −1250.07 | − | 232.710i | −1.26782 | − | 0.236014i | ||||
\(987\) | −28.7077 | −0.0290858 | ||||||||
\(988\) | 24.2666 | − | 62.9191i | 0.0245613 | − | 0.0636833i | ||||
\(989\) | − | 274.706i | − | 0.277762i | ||||||
\(990\) | 135.846 | + | 25.2887i | 0.137218 | + | 0.0255441i | ||||
\(991\) | − | 1728.18i | − | 1.74388i | −0.489615 | − | 0.871938i | \(-0.662863\pi\) | ||
0.489615 | − | 0.871938i | \(-0.337137\pi\) | |||||||
\(992\) | 178.313 | + | 234.293i | 0.179751 | + | 0.236183i | ||||
\(993\) | −685.990 | −0.690825 | ||||||||
\(994\) | 331.923 | − | 1783.03i | 0.333927 | − | 1.79379i | ||||
\(995\) | 207.615 | 0.208659 | ||||||||
\(996\) | −79.4256 | − | 30.6328i | −0.0797446 | − | 0.0307558i | ||||
\(997\) | − | 135.205i | − | 0.135612i | −0.997699 | − | 0.0678060i | \(-0.978400\pi\) | ||
0.997699 | − | 0.0678060i | \(-0.0215999\pi\) | |||||||
\(998\) | −200.813 | + | 1078.73i | −0.201215 | + | 1.08089i | ||||
\(999\) | 51.8175i | 0.0518693i |
(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 | 24.3.b.a.19.2 | yes | 4 | |
3.2 | odd | 2 | 72.3.b.b.19.3 | 4 | |||
4.3 | odd | 2 | 96.3.b.a.79.2 | 4 | |||
5.2 | odd | 4 | 600.3.p.a.499.1 | 8 | |||
5.3 | odd | 4 | 600.3.p.a.499.8 | 8 | |||
5.4 | even | 2 | 600.3.g.a.451.3 | 4 | |||
8.3 | odd | 2 | inner | 24.3.b.a.19.1 | ✓ | 4 | |
8.5 | even | 2 | 96.3.b.a.79.1 | 4 | |||
12.11 | even | 2 | 288.3.b.b.271.2 | 4 | |||
16.3 | odd | 4 | 768.3.g.h.511.3 | 8 | |||
16.5 | even | 4 | 768.3.g.h.511.2 | 8 | |||
16.11 | odd | 4 | 768.3.g.h.511.6 | 8 | |||
16.13 | even | 4 | 768.3.g.h.511.7 | 8 | |||
20.3 | even | 4 | 2400.3.p.a.1999.4 | 8 | |||
20.7 | even | 4 | 2400.3.p.a.1999.5 | 8 | |||
20.19 | odd | 2 | 2400.3.g.a.751.3 | 4 | |||
24.5 | odd | 2 | 288.3.b.b.271.3 | 4 | |||
24.11 | even | 2 | 72.3.b.b.19.4 | 4 | |||
40.3 | even | 4 | 600.3.p.a.499.2 | 8 | |||
40.13 | odd | 4 | 2400.3.p.a.1999.1 | 8 | |||
40.19 | odd | 2 | 600.3.g.a.451.4 | 4 | |||
40.27 | even | 4 | 600.3.p.a.499.7 | 8 | |||
40.29 | even | 2 | 2400.3.g.a.751.4 | 4 | |||
40.37 | odd | 4 | 2400.3.p.a.1999.8 | 8 | |||
48.5 | odd | 4 | 2304.3.g.z.1279.6 | 8 | |||
48.11 | even | 4 | 2304.3.g.z.1279.5 | 8 | |||
48.29 | odd | 4 | 2304.3.g.z.1279.4 | 8 | |||
48.35 | even | 4 | 2304.3.g.z.1279.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.3.b.a.19.1 | ✓ | 4 | 8.3 | odd | 2 | inner | |
24.3.b.a.19.2 | yes | 4 | 1.1 | even | 1 | trivial | |
72.3.b.b.19.3 | 4 | 3.2 | odd | 2 | |||
72.3.b.b.19.4 | 4 | 24.11 | even | 2 | |||
96.3.b.a.79.1 | 4 | 8.5 | even | 2 | |||
96.3.b.a.79.2 | 4 | 4.3 | odd | 2 | |||
288.3.b.b.271.2 | 4 | 12.11 | even | 2 | |||
288.3.b.b.271.3 | 4 | 24.5 | odd | 2 | |||
600.3.g.a.451.3 | 4 | 5.4 | even | 2 | |||
600.3.g.a.451.4 | 4 | 40.19 | odd | 2 | |||
600.3.p.a.499.1 | 8 | 5.2 | odd | 4 | |||
600.3.p.a.499.2 | 8 | 40.3 | even | 4 | |||
600.3.p.a.499.7 | 8 | 40.27 | even | 4 | |||
600.3.p.a.499.8 | 8 | 5.3 | odd | 4 | |||
768.3.g.h.511.2 | 8 | 16.5 | even | 4 | |||
768.3.g.h.511.3 | 8 | 16.3 | odd | 4 | |||
768.3.g.h.511.6 | 8 | 16.11 | odd | 4 | |||
768.3.g.h.511.7 | 8 | 16.13 | even | 4 | |||
2304.3.g.z.1279.3 | 8 | 48.35 | even | 4 | |||
2304.3.g.z.1279.4 | 8 | 48.29 | odd | 4 | |||
2304.3.g.z.1279.5 | 8 | 48.11 | even | 4 | |||
2304.3.g.z.1279.6 | 8 | 48.5 | odd | 4 | |||
2400.3.g.a.751.3 | 4 | 20.19 | odd | 2 | |||
2400.3.g.a.751.4 | 4 | 40.29 | even | 2 | |||
2400.3.p.a.1999.1 | 8 | 40.13 | odd | 4 | |||
2400.3.p.a.1999.4 | 8 | 20.3 | even | 4 | |||
2400.3.p.a.1999.5 | 8 | 20.7 | even | 4 | |||
2400.3.p.a.1999.8 | 8 | 40.37 | odd | 4 |