Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(17,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1513609911\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.13 | ||
Character | \(\chi\) | \(=\) | 189.17 |
Dual form | 189.4.s.a.89.13 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.998155 | + | 0.576285i | 0.352901 | + | 0.203748i | 0.665962 | − | 0.745985i | \(-0.268021\pi\) |
−0.313061 | + | 0.949733i | \(0.601354\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.33579 | − | 5.77776i | −0.416974 | − | 0.722220i | ||||
\(5\) | −0.274718 | −0.0245716 | −0.0122858 | − | 0.999925i | \(-0.503911\pi\) | ||||
−0.0122858 | + | 0.999925i | \(0.503911\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.15344 | + | 16.1001i | −0.494239 | + | 0.869326i | ||||
\(8\) | − | 16.9100i | − | 0.747325i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.274212 | − | 0.158316i | −0.00867133 | − | 0.00500640i | ||||
\(11\) | 26.2387i | 0.719205i | 0.933106 | + | 0.359602i | \(0.117088\pi\) | ||||
−0.933106 | + | 0.359602i | \(0.882912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −39.6128 | − | 22.8704i | −0.845123 | − | 0.487932i | 0.0138792 | − | 0.999904i | \(-0.495582\pi\) |
−0.859002 | + | 0.511972i | \(0.828915\pi\) | |||||||
\(14\) | −18.4148 | + | 10.7954i | −0.351541 | + | 0.206086i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.9413 | + | 29.3432i | −0.264708 | + | 0.458488i | ||||
\(17\) | −30.2340 | + | 52.3669i | −0.431343 | + | 0.747108i | −0.996989 | − | 0.0775399i | \(-0.975293\pi\) |
0.565646 | + | 0.824648i | \(0.308627\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −38.8827 | + | 22.4489i | −0.469490 | + | 0.271060i | −0.716026 | − | 0.698074i | \(-0.754041\pi\) |
0.246536 | + | 0.969134i | \(0.420708\pi\) | |||||||
\(20\) | 0.916403 | + | 1.58726i | 0.0102457 | + | 0.0177461i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −15.1209 | + | 26.1902i | −0.146536 | + | 0.253808i | ||||
\(23\) | 127.767i | 1.15832i | 0.815214 | + | 0.579159i | \(0.196619\pi\) | ||||
−0.815214 | + | 0.579159i | \(0.803381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.925 | −0.999396 | ||||||||
\(26\) | −26.3598 | − | 45.6565i | −0.198830 | − | 0.344384i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 123.557 | − | 0.820329i | 0.833929 | − | 0.00553670i | ||||
\(29\) | −58.2779 | + | 33.6468i | −0.373170 | + | 0.215450i | −0.674843 | − | 0.737962i | \(-0.735788\pi\) |
0.301672 | + | 0.953412i | \(0.402455\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 85.6986 | − | 49.4781i | 0.496513 | − | 0.286662i | −0.230759 | − | 0.973011i | \(-0.574121\pi\) |
0.727273 | + | 0.686349i | \(0.240788\pi\) | |||||||
\(32\) | −150.976 | + | 87.1662i | −0.834034 | + | 0.481530i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −60.3565 | + | 34.8469i | −0.304443 | + | 0.175770i | ||||
\(35\) | 2.51462 | − | 4.42301i | 0.0121442 | − | 0.0213607i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −123.714 | − | 214.278i | −0.549686 | − | 0.952085i | −0.998296 | − | 0.0583567i | \(-0.981414\pi\) |
0.448610 | − | 0.893728i | \(-0.351919\pi\) | |||||||
\(38\) | −51.7480 | −0.220911 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.64550i | 0.0183629i | ||||||||
\(41\) | −134.234 | + | 232.500i | −0.511312 | + | 0.885618i | 0.488602 | + | 0.872507i | \(0.337507\pi\) |
−0.999914 | + | 0.0131112i | \(0.995826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −72.4990 | − | 125.572i | −0.257116 | − | 0.445338i | 0.708352 | − | 0.705859i | \(-0.249439\pi\) |
−0.965468 | + | 0.260521i | \(0.916106\pi\) | |||||||
\(44\) | 151.601 | − | 87.5267i | 0.519424 | − | 0.299890i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −73.6304 | + | 127.532i | −0.236005 | + | 0.408772i | ||||
\(47\) | 250.874 | − | 434.526i | 0.778589 | − | 1.34856i | −0.154166 | − | 0.988045i | \(-0.549269\pi\) |
0.932755 | − | 0.360511i | \(-0.117398\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −175.429 | − | 294.743i | −0.511455 | − | 0.859310i | ||||
\(50\) | −124.694 | − | 71.9922i | −0.352688 | − | 0.203625i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 305.164i | 0.813820i | ||||||||
\(53\) | 333.839 | + | 192.742i | 0.865213 | + | 0.499531i | 0.865755 | − | 0.500469i | \(-0.166839\pi\) |
−0.000541270 | 1.00000i | \(0.500172\pi\) | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.20824i | − | 0.0176720i | ||||||
\(56\) | 272.254 | + | 154.785i | 0.649669 | + | 0.369357i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −77.5605 | −0.175590 | ||||||||
\(59\) | −274.307 | − | 475.113i | −0.605283 | − | 1.04838i | −0.992007 | − | 0.126185i | \(-0.959727\pi\) |
0.386724 | − | 0.922195i | \(-0.373607\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 189.637 | + | 109.487i | 0.398041 | + | 0.229809i | 0.685638 | − | 0.727942i | \(-0.259523\pi\) |
−0.287597 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(62\) | 114.054 | 0.233627 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 70.1309 | 0.136974 | ||||||||
\(65\) | 10.8824 | + | 6.28293i | 0.0207660 | + | 0.0119893i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 378.858 | + | 656.202i | 0.690819 | + | 1.19653i | 0.971570 | + | 0.236753i | \(0.0760834\pi\) |
−0.280750 | + | 0.959781i | \(0.590583\pi\) | |||||||
\(68\) | 403.418 | 0.719435 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.05889 | − | 2.96571i | 0.00863790 | − | 0.00506386i | ||||
\(71\) | 1109.53i | 1.85461i | 0.374306 | + | 0.927305i | \(0.377881\pi\) | ||||
−0.374306 | + | 0.927305i | \(0.622119\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −125.762 | − | 72.6086i | −0.201634 | − | 0.116414i | 0.395783 | − | 0.918344i | \(-0.370473\pi\) |
−0.597418 | + | 0.801930i | \(0.703806\pi\) | |||||||
\(74\) | − | 285.177i | − | 0.447989i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 259.409 | + | 149.770i | 0.391530 | + | 0.226050i | ||||
\(77\) | −422.446 | − | 240.174i | −0.625223 | − | 0.355459i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 445.950 | − | 772.407i | 0.635104 | − | 1.10003i | −0.351389 | − | 0.936230i | \(-0.614290\pi\) |
0.986493 | − | 0.163803i | \(-0.0523763\pi\) | |||||||
\(80\) | 4.65409 | − | 8.06113i | 0.00650429 | − | 0.0112658i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −267.972 | + | 154.714i | −0.360885 | + | 0.208357i | ||||
\(83\) | −745.760 | − | 1291.69i | −0.986238 | − | 1.70821i | −0.636299 | − | 0.771442i | \(-0.719536\pi\) |
−0.349939 | − | 0.936772i | \(-0.613798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.30585 | − | 14.3862i | 0.0105988 | − | 0.0183576i | ||||
\(86\) | − | 167.120i | − | 0.209547i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 443.696 | 0.537480 | ||||||||
\(89\) | 145.205 | + | 251.503i | 0.172941 | + | 0.299542i | 0.939447 | − | 0.342695i | \(-0.111340\pi\) |
−0.766506 | + | 0.642237i | \(0.778006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 730.810 | − | 428.428i | 0.841865 | − | 0.493532i | ||||
\(92\) | 738.209 | − | 426.205i | 0.836561 | − | 0.482989i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 500.822 | − | 289.150i | 0.549530 | − | 0.317271i | ||||
\(95\) | 10.6818 | − | 6.16714i | 0.0115361 | − | 0.00666037i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 144.917 | − | 83.6676i | 0.151691 | − | 0.0875789i | −0.422233 | − | 0.906487i | \(-0.638754\pi\) |
0.573924 | + | 0.818908i | \(0.305420\pi\) | |||||||
\(98\) | −5.24921 | − | 395.297i | −0.00541072 | − | 0.407459i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 416.722 | + | 721.784i | 0.416722 | + | 0.721784i | ||||
\(101\) | −945.019 | −0.931019 | −0.465510 | − | 0.885043i | \(-0.654129\pi\) | ||||
−0.465510 | + | 0.885043i | \(0.654129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 836.645i | 0.800360i | 0.916437 | + | 0.400180i | \(0.131052\pi\) | ||||
−0.916437 | + | 0.400180i | \(0.868948\pi\) | |||||||
\(104\) | −386.740 | + | 669.853i | −0.364644 | + | 0.631582i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 222.149 | + | 384.773i | 0.203557 | + | 0.352570i | ||||
\(107\) | 1220.83 | − | 704.848i | 1.10301 | − | 0.636825i | 0.166002 | − | 0.986125i | \(-0.446914\pi\) |
0.937011 | + | 0.349301i | \(0.113581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.79612 | − | 13.5033i | 0.00685076 | − | 0.0118659i | −0.862580 | − | 0.505921i | \(-0.831153\pi\) |
0.869430 | + | 0.494055i | \(0.164486\pi\) | |||||||
\(110\) | 4.15400 | − | 7.19494i | 0.00360062 | − | 0.00623646i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −317.359 | − | 541.349i | −0.267746 | − | 0.456721i | ||||
\(113\) | 382.754 | + | 220.983i | 0.318641 | + | 0.183968i | 0.650787 | − | 0.759261i | \(-0.274439\pi\) |
−0.332146 | + | 0.943228i | \(0.607773\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 35.1000i | − | 0.0284617i | ||||||
\(116\) | 388.806 | + | 224.477i | 0.311204 | + | 0.179674i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 632.315i | − | 0.493299i | ||||||
\(119\) | −566.369 | − | 966.110i | −0.436294 | − | 0.744228i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 642.533 | 0.482745 | ||||||||
\(122\) | 126.191 | + | 218.570i | 0.0936461 | + | 0.162200i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −571.745 | − | 330.097i | −0.414066 | − | 0.239061i | ||||
\(125\) | 68.6589 | 0.0491283 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2019.56 | −1.41108 | −0.705539 | − | 0.708671i | \(-0.749295\pi\) | ||||
−0.705539 | + | 0.708671i | \(0.749295\pi\) | |||||||
\(128\) | 1277.81 | + | 737.745i | 0.882372 | + | 0.509438i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.24152 | + | 12.5427i | 0.00488556 | + | 0.00846204i | ||||
\(131\) | −954.174 | −0.636386 | −0.318193 | − | 0.948026i | \(-0.603076\pi\) | ||||
−0.318193 | + | 0.948026i | \(0.603076\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.52058 | − | 831.502i | −0.00359921 | − | 0.542108i | ||||
\(134\) | 873.322i | 0.563011i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 885.526 | + | 511.259i | 0.558333 | + | 0.322353i | ||||
\(137\) | 1382.02i | 0.861857i | 0.902386 | + | 0.430928i | \(0.141814\pi\) | ||||
−0.902386 | + | 0.430928i | \(0.858186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2724.54 | − | 1573.02i | −1.66254 | − | 0.959867i | −0.971497 | − | 0.237052i | \(-0.923819\pi\) |
−0.691041 | − | 0.722815i | \(-0.742848\pi\) | |||||||
\(140\) | −33.9433 | + | 0.225359i | −0.0204909 | + | 0.000136045i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −639.407 | + | 1107.49i | −0.377872 | + | 0.654494i | ||||
\(143\) | 600.089 | − | 1039.39i | 0.350923 | − | 0.607817i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0100 | − | 9.24339i | 0.00916938 | − | 0.00529394i | ||||
\(146\) | −83.6865 | − | 144.949i | −0.0474380 | − | 0.0821650i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −825.365 | + | 1429.57i | −0.458410 | + | 0.793989i | ||||
\(149\) | 363.709i | 0.199975i | 0.994989 | + | 0.0999873i | \(0.0318802\pi\) | ||||
−0.994989 | + | 0.0999873i | \(0.968120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −516.508 | −0.278363 | −0.139181 | − | 0.990267i | \(-0.544447\pi\) | ||||
−0.139181 | + | 0.990267i | \(0.544447\pi\) | |||||||
\(152\) | 379.612 | + | 657.508i | 0.202570 | + | 0.350861i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −283.258 | − | 483.180i | −0.148218 | − | 0.252830i | ||||
\(155\) | −23.5430 | + | 13.5925i | −0.0122001 | + | 0.00704374i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1002.39 | + | 578.732i | −0.509552 | + | 0.294190i | −0.732650 | − | 0.680606i | \(-0.761717\pi\) |
0.223097 | + | 0.974796i | \(0.428383\pi\) | |||||||
\(158\) | 890.254 | − | 513.988i | 0.448258 | − | 0.258802i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 41.4760 | − | 23.9462i | 0.0204935 | − | 0.0118319i | ||||
\(161\) | −2057.07 | − | 1169.51i | −1.00696 | − | 0.572487i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1783.72 | + | 3089.49i | 0.857126 | + | 1.48459i | 0.874658 | + | 0.484740i | \(0.161086\pi\) |
−0.0175321 | + | 0.999846i | \(0.505581\pi\) | |||||||
\(164\) | 1791.10 | 0.852814 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 1719.08i | − | 0.803775i | ||||||
\(167\) | −1874.87 | + | 3247.37i | −0.868754 | + | 1.50473i | −0.00548318 | + | 0.999985i | \(0.501745\pi\) |
−0.863271 | + | 0.504741i | \(0.831588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −52.3864 | − | 90.7359i | −0.0238445 | − | 0.0412999i | ||||
\(170\) | 16.5811 | − | 9.57308i | 0.00748064 | − | 0.00431895i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −483.683 | + | 837.763i | −0.214421 | + | 0.371389i | ||||
\(173\) | −1176.24 | + | 2037.30i | −0.516922 | + | 0.895335i | 0.482885 | + | 0.875684i | \(0.339589\pi\) |
−0.999807 | + | 0.0196514i | \(0.993744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1143.49 | − | 2011.30i | 0.493941 | − | 0.868801i | ||||
\(176\) | −769.927 | − | 444.518i | −0.329747 | − | 0.190379i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 334.718i | 0.140945i | ||||||||
\(179\) | −1977.18 | − | 1141.53i | −0.825595 | − | 0.476657i | 0.0267473 | − | 0.999642i | \(-0.491485\pi\) |
−0.852342 | + | 0.522985i | \(0.824818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3446.80i | − | 1.41546i | −0.706482 | − | 0.707731i | \(-0.749719\pi\) | ||
0.706482 | − | 0.707731i | \(-0.250281\pi\) | |||||||
\(182\) | 976.359 | − | 6.48233i | 0.397651 | − | 0.00264012i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2160.55 | 0.865640 | ||||||||
\(185\) | 33.9864 | + | 58.8662i | 0.0135067 | + | 0.0233942i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1374.04 | − | 793.301i | −0.537324 | − | 0.310224i | ||||
\(188\) | −3347.45 | −1.29861 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.2161 | 0.00542814 | ||||||||
\(191\) | −1540.99 | − | 889.689i | −0.583780 | − | 0.337045i | 0.178854 | − | 0.983876i | \(-0.442761\pi\) |
−0.762634 | + | 0.646830i | \(0.776094\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 249.570 | + | 432.268i | 0.0930800 | + | 0.161219i | 0.908806 | − | 0.417220i | \(-0.136995\pi\) |
−0.815726 | + | 0.578439i | \(0.803662\pi\) | |||||||
\(194\) | 192.866 | 0.0713760 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1117.76 | + | 1996.79i | −0.407347 | + | 0.727693i | ||||
\(197\) | 4333.51i | 1.56726i | 0.621229 | + | 0.783629i | \(0.286634\pi\) | ||||
−0.621229 | + | 0.783629i | \(0.713366\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1426.57 | − | 823.632i | −0.508176 | − | 0.293396i | 0.223907 | − | 0.974610i | \(-0.428119\pi\) |
−0.732084 | + | 0.681215i | \(0.761452\pi\) | |||||||
\(200\) | 2112.48i | 0.746874i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −943.276 | − | 544.601i | −0.328558 | − | 0.189693i | ||||
\(203\) | −8.27433 | − | 1246.27i | −0.00286081 | − | 0.430890i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 36.8765 | − | 63.8719i | 0.0125637 | − | 0.0217610i | ||||
\(206\) | −482.146 | + | 835.102i | −0.163071 | + | 0.282448i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1342.19 | − | 774.911i | 0.447422 | − | 0.258319i | ||||
\(209\) | −589.030 | − | 1020.23i | −0.194948 | − | 0.337659i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1023.38 | + | 1772.54i | −0.333897 | + | 0.578327i | −0.983272 | − | 0.182141i | \(-0.941697\pi\) |
0.649375 | + | 0.760468i | \(0.275031\pi\) | |||||||
\(212\) | − | 2571.79i | − | 0.833166i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1624.77 | 0.519006 | ||||||||
\(215\) | 19.9168 | + | 34.4969i | 0.00631775 | + | 0.0109427i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.1675 | + | 1832.65i | 0.00380638 | + | 0.573312i | ||||
\(218\) | 15.5635 | − | 8.98558i | 0.00483528 | − | 0.00279165i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −41.6475 | + | 24.0452i | −0.0127631 | + | 0.00736876i | ||||
\(221\) | 2395.31 | − | 1382.93i | 0.729076 | − | 0.420932i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1682.84 | + | 971.590i | −0.505343 | + | 0.291760i | −0.730917 | − | 0.682466i | \(-0.760908\pi\) |
0.225574 | + | 0.974226i | \(0.427574\pi\) | |||||||
\(224\) | −21.4357 | − | 3228.61i | −0.00639389 | − | 0.963038i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 254.699 | + | 441.151i | 0.0749659 | + | 0.129845i | ||||
\(227\) | 3979.61 | 1.16359 | 0.581797 | − | 0.813334i | \(-0.302350\pi\) | ||||
0.581797 | + | 0.813334i | \(0.302350\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3742.04i | 1.07983i | 0.841720 | + | 0.539915i | \(0.181544\pi\) | ||||
−0.841720 | + | 0.539915i | \(0.818456\pi\) | |||||||
\(230\) | 20.2276 | − | 35.0353i | 0.00579900 | − | 0.0100442i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 568.968 | + | 985.481i | 0.161011 | + | 0.278879i | ||||
\(233\) | 4212.14 | − | 2431.88i | 1.18432 | − | 0.683767i | 0.227309 | − | 0.973823i | \(-0.427007\pi\) |
0.957010 | + | 0.290056i | \(0.0936739\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −68.9196 | + | 119.372i | −0.0191311 | + | 0.0331361i | ||||
\(236\) | −1830.06 | + | 3169.75i | −0.504774 | + | 0.874294i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.56945 | − | 1290.72i | −0.00233393 | − | 0.351533i | ||||
\(239\) | 3994.45 | + | 2306.19i | 1.08108 | + | 0.624165i | 0.931189 | − | 0.364537i | \(-0.118773\pi\) |
0.149896 | + | 0.988702i | \(0.452106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 945.401i | − | 0.252691i | −0.991986 | − | 0.126346i | \(-0.959675\pi\) | ||
0.991986 | − | 0.126346i | \(-0.0403248\pi\) | |||||||
\(242\) | 641.348 | + | 370.282i | 0.170361 | + | 0.0983580i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1460.90i | − | 0.383297i | ||||||
\(245\) | 48.1936 | + | 80.9714i | 0.0125672 | + | 0.0211146i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2053.67 | 0.529036 | ||||||||
\(248\) | −836.676 | − | 1449.17i | −0.214230 | − | 0.371057i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 68.5322 | + | 39.5671i | 0.0173374 | + | 0.0100098i | ||||
\(251\) | 478.897 | 0.120429 | 0.0602146 | − | 0.998185i | \(-0.480822\pi\) | ||||
0.0602146 | + | 0.998185i | \(0.480822\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3352.44 | −0.833068 | ||||||||
\(254\) | −2015.83 | − | 1163.84i | −0.497971 | − | 0.287504i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 569.780 | + | 986.887i | 0.139106 | + | 0.240939i | ||||
\(257\) | 4135.57 | 1.00377 | 0.501887 | − | 0.864933i | \(-0.332639\pi\) | ||||
0.501887 | + | 0.864933i | \(0.332639\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4582.31 | − | 30.4233i | 1.09935 | − | 0.00729889i | ||||
\(260\) | − | 83.8342i | − | 0.0199968i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −952.414 | − | 549.876i | −0.224581 | − | 0.129662i | ||||
\(263\) | 1336.33i | 0.313315i | 0.987653 | + | 0.156658i | \(0.0500719\pi\) | ||||
−0.987653 | + | 0.156658i | \(0.949928\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −91.7117 | − | 52.9498i | −0.0212596 | − | 0.0122743i | ||||
\(266\) | 473.672 | − | 833.150i | 0.109183 | − | 0.192044i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2527.58 | − | 4377.90i | 0.576107 | − | 0.997847i | ||||
\(269\) | 1094.02 | − | 1894.90i | 0.247969 | − | 0.429494i | −0.714993 | − | 0.699131i | \(-0.753570\pi\) |
0.962962 | + | 0.269637i | \(0.0869037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3642.53 | − | 2103.02i | 0.816488 | − | 0.471400i | −0.0327159 | − | 0.999465i | \(-0.510416\pi\) |
0.849204 | + | 0.528065i | \(0.177082\pi\) | |||||||
\(272\) | −1024.41 | − | 1774.33i | −0.228360 | − | 0.395531i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −796.440 | + | 1379.48i | −0.175601 | + | 0.304150i | ||||
\(275\) | − | 3277.85i | − | 0.718770i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2108.80 | −0.457421 | −0.228710 | − | 0.973495i | \(-0.573451\pi\) | ||||
−0.228710 | + | 0.973495i | \(0.573451\pi\) | |||||||
\(278\) | −1813.01 | − | 3140.23i | −0.391141 | − | 0.677476i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −74.7932 | − | 42.5223i | −0.0159634 | − | 0.00907569i | ||||
\(281\) | −5062.18 | + | 2922.65i | −1.07468 | + | 0.620465i | −0.929455 | − | 0.368934i | \(-0.879723\pi\) |
−0.145221 | + | 0.989399i | \(0.546389\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6556.08 | − | 3785.15i | 1.37710 | − | 0.795067i | 0.385288 | − | 0.922796i | \(-0.374102\pi\) |
0.991809 | + | 0.127729i | \(0.0407688\pi\) | |||||||
\(284\) | 6410.61 | − | 3701.17i | 1.33944 | − | 0.773324i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1197.96 | − | 691.645i | 0.247682 | − | 0.142999i | ||||
\(287\) | −2514.58 | − | 4289.35i | −0.517180 | − | 0.882204i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 628.305 | + | 1088.26i | 0.127886 | + | 0.221505i | ||||
\(290\) | 21.3073 | 0.00431451 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 968.828i | 0.194166i | ||||||||
\(293\) | −92.9288 | + | 160.957i | −0.0185289 | + | 0.0320930i | −0.875141 | − | 0.483868i | \(-0.839232\pi\) |
0.856612 | + | 0.515961i | \(0.172565\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 75.3571 | + | 130.522i | 0.0148727 | + | 0.0257603i | ||||
\(296\) | −3623.45 | + | 2092.00i | −0.711516 | + | 0.410794i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −209.600 | + | 363.038i | −0.0407444 | + | 0.0705713i | ||||
\(299\) | 2922.09 | − | 5061.22i | 0.565181 | − | 0.978922i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2685.34 | − | 17.8288i | 0.514221 | − | 0.00341406i | ||||
\(302\) | −515.555 | − | 297.656i | −0.0982346 | − | 0.0567158i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 1521.26i | − | 0.287007i | ||||||
\(305\) | −52.0967 | − | 30.0780i | −0.00978049 | − | 0.00564677i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2608.06i | − | 0.484853i | −0.970170 | − | 0.242427i | \(-0.922057\pi\) | ||
0.970170 | − | 0.242427i | \(-0.0779434\pi\) | |||||||
\(308\) | 21.5243 | + | 3241.96i | 0.00398202 | + | 0.599766i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −31.3327 | −0.00574058 | ||||||||
\(311\) | −1846.85 | − | 3198.84i | −0.336738 | − | 0.583247i | 0.647079 | − | 0.762423i | \(-0.275990\pi\) |
−0.983817 | + | 0.179176i | \(0.942657\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5911.47 | + | 3412.99i | 1.06753 | + | 0.616337i | 0.927505 | − | 0.373811i | \(-0.121949\pi\) |
0.140023 | + | 0.990148i | \(0.455282\pi\) | |||||||
\(314\) | −1334.06 | −0.239762 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5950.38 | −1.05929 | ||||||||
\(317\) | 2657.16 | + | 1534.11i | 0.470791 | + | 0.271811i | 0.716571 | − | 0.697514i | \(-0.245711\pi\) |
−0.245780 | + | 0.969326i | \(0.579044\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −882.846 | − | 1529.13i | −0.154953 | − | 0.268386i | ||||
\(320\) | −19.2662 | −0.00336567 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1379.31 | − | 2352.81i | −0.238713 | − | 0.407196i | ||||
\(323\) | − | 2714.89i | − | 0.467680i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4948.60 | + | 2857.08i | 0.844613 | + | 0.487638i | ||||
\(326\) | 4111.72i | 0.698550i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3931.57 | + | 2269.90i | 0.661844 | + | 0.382116i | ||||
\(329\) | 4699.57 | + | 8016.51i | 0.787525 | + | 1.34336i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −455.469 | + | 788.896i | −0.0756340 | + | 0.131002i | −0.901362 | − | 0.433067i | \(-0.857431\pi\) |
0.825728 | + | 0.564069i | \(0.190765\pi\) | |||||||
\(332\) | −4975.40 | + | 8617.64i | −0.822471 | + | 1.42456i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3742.83 | + | 2160.92i | −0.613169 | + | 0.354013i | ||||
\(335\) | −104.079 | − | 180.271i | −0.0169745 | − | 0.0294007i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2379.71 | + | 4121.79i | −0.384663 | + | 0.666255i | −0.991722 | − | 0.128401i | \(-0.959016\pi\) |
0.607060 | + | 0.794656i | \(0.292349\pi\) | |||||||
\(338\) | − | 120.758i | − | 0.0194330i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −110.826 | −0.0176776 | ||||||||
\(341\) | 1298.24 | + | 2248.61i | 0.206169 | + | 0.357095i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6351.19 | − | 126.517i | 0.999802 | − | 0.0199163i | ||||
\(344\) | −2123.43 | + | 1225.96i | −0.332812 | + | 0.192149i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2348.13 | + | 1355.69i | −0.364845 | + | 0.210643i | ||||
\(347\) | −2185.79 | + | 1261.97i | −0.338154 | + | 0.195233i | −0.659455 | − | 0.751744i | \(-0.729213\pi\) |
0.321302 | + | 0.946977i | \(0.395880\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6370.82 | + | 3678.20i | −0.977142 | + | 0.564153i | −0.901406 | − | 0.432975i | \(-0.857464\pi\) |
−0.0757357 | + | 0.997128i | \(0.524131\pi\) | |||||||
\(350\) | 2300.46 | − | 1348.62i | 0.351328 | − | 0.205962i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2287.12 | − | 3961.41i | −0.346318 | − | 0.599841i | ||||
\(353\) | 192.834 | 0.0290752 | 0.0145376 | − | 0.999894i | \(-0.495372\pi\) | ||||
0.0145376 | + | 0.999894i | \(0.495372\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 304.809i | − | 0.0455707i | ||||||
\(356\) | 968.748 | − | 1677.92i | 0.144223 | − | 0.249802i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1315.69 | − | 2278.84i | −0.194236 | − | 0.336426i | ||||
\(359\) | 3707.83 | − | 2140.72i | 0.545103 | − | 0.314715i | −0.202042 | − | 0.979377i | \(-0.564758\pi\) |
0.747144 | + | 0.664662i | \(0.231424\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2421.59 | + | 4194.32i | −0.353053 | + | 0.611506i | ||||
\(362\) | 1986.34 | − | 3440.44i | 0.288397 | − | 0.499518i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4913.18 | − | 2793.30i | −0.707475 | − | 0.402222i | ||||
\(365\) | 34.5491 | + | 19.9469i | 0.00495447 | + | 0.00286046i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5775.69i | 0.821495i | 0.911749 | + | 0.410747i | \(0.134732\pi\) | ||||
−0.911749 | + | 0.410747i | \(0.865268\pi\) | |||||||
\(368\) | −3749.11 | − | 2164.55i | −0.531075 | − | 0.306616i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 78.3435i | 0.0110078i | ||||||||
\(371\) | −6158.95 | + | 3610.60i | −0.861878 | + | 0.505264i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12373.8 | −1.71767 | −0.858834 | − | 0.512255i | \(-0.828810\pi\) | ||||
−0.858834 | + | 0.512255i | \(0.828810\pi\) | |||||||
\(374\) | −914.335 | − | 1583.67i | −0.126415 | − | 0.218957i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7347.85 | − | 4242.28i | −1.00781 | − | 0.581859i | ||||
\(377\) | 3078.07 | 0.420500 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9640.94 | 1.30665 | 0.653327 | − | 0.757076i | \(-0.273373\pi\) | ||||
0.653327 | + | 0.757076i | \(0.273373\pi\) | |||||||
\(380\) | −71.2645 | − | 41.1446i | −0.00962050 | − | 0.00555440i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1025.43 | − | 1776.10i | −0.137344 | − | 0.237887i | ||||
\(383\) | −10541.8 | −1.40642 | −0.703212 | − | 0.710980i | \(-0.748252\pi\) | ||||
−0.703212 | + | 0.710980i | \(0.748252\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 116.054 | + | 65.9802i | 0.0153627 | + | 0.00873419i | ||||
\(386\) | 575.294i | 0.0758593i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −966.822 | − | 558.195i | −0.126503 | − | 0.0730363i | ||||
\(389\) | 1429.20i | 0.186281i | 0.995653 | + | 0.0931406i | \(0.0296906\pi\) | ||||
−0.995653 | + | 0.0931406i | \(0.970309\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6690.78 | − | 3862.92i | −0.865389 | − | 0.499633i | ||||
\(392\) | −4984.12 | + | 2966.51i | −0.642184 | + | 0.382223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2497.34 | + | 4325.52i | −0.319325 | + | 0.553087i | ||||
\(395\) | −122.511 | + | 212.195i | −0.0156055 | + | 0.0270295i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5532.85 | + | 3194.39i | −0.699460 | + | 0.403834i | −0.807146 | − | 0.590351i | \(-0.798989\pi\) |
0.107686 | + | 0.994185i | \(0.465656\pi\) | |||||||
\(398\) | −949.294 | − | 1644.23i | −0.119557 | − | 0.207079i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2116.39 | − | 3665.69i | 0.264548 | − | 0.458211i | ||||
\(401\) | 15077.6i | 1.87765i | 0.344396 | + | 0.938825i | \(0.388084\pi\) | ||||
−0.344396 | + | 0.938825i | \(0.611916\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4526.34 | −0.559487 | ||||||||
\(404\) | 3152.39 | + | 5460.09i | 0.388211 | + | 0.672401i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 709.946 | − | 1248.74i | 0.0867833 | − | 0.152645i | ||||
\(407\) | 5622.37 | − | 3246.08i | 0.684744 | − | 0.395337i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5666.97 | − | 3271.83i | 0.685119 | − | 0.395554i | −0.116662 | − | 0.993172i | \(-0.537219\pi\) |
0.801781 | + | 0.597618i | \(0.203886\pi\) | |||||||
\(410\) | 73.6169 | − | 42.5027i | 0.00886751 | − | 0.00511966i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4833.93 | − | 2790.87i | 0.578036 | − | 0.333729i | ||||
\(413\) | 10160.2 | − | 67.4567i | 1.21054 | − | 0.00803712i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 204.874 | + | 354.852i | 0.0242334 | + | 0.0419735i | ||||
\(416\) | 7974.12 | 0.939815 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1357.80i | − | 0.158880i | ||||||
\(419\) | −3808.29 | + | 6596.15i | −0.444027 | + | 0.769077i | −0.997984 | − | 0.0634684i | \(-0.979784\pi\) |
0.553957 | + | 0.832545i | \(0.313117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2874.27 | + | 4978.38i | 0.332739 | + | 0.576321i | 0.983048 | − | 0.183349i | \(-0.0586938\pi\) |
−0.650309 | + | 0.759670i | \(0.725360\pi\) | |||||||
\(422\) | −2042.98 | + | 1179.52i | −0.235665 | + | 0.136061i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3259.27 | − | 5645.23i | 0.373312 | − | 0.646595i | ||||
\(425\) | 3776.97 | − | 6541.91i | 0.431083 | − | 0.746657i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3498.58 | + | 2051.00i | −0.396506 | + | 0.232447i | ||||
\(428\) | −8144.89 | − | 4702.45i | −0.919855 | − | 0.531079i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 45.9111i | 0.00514890i | ||||||||
\(431\) | −11353.0 | − | 6554.64i | −1.26880 | − | 0.732543i | −0.294040 | − | 0.955793i | \(-0.595000\pi\) |
−0.974761 | + | 0.223251i | \(0.928333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12018.7i | 1.33390i | 0.745102 | + | 0.666951i | \(0.232401\pi\) | ||||
−0.745102 | + | 0.666951i | \(0.767599\pi\) | |||||||
\(434\) | −1043.99 | + | 1836.28i | −0.115468 | + | 0.203098i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −104.025 | −0.0114263 | ||||||||
\(437\) | −2868.24 | − | 4967.94i | −0.313974 | − | 0.543819i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3519.12 | − | 2031.76i | −0.382593 | − | 0.220890i | 0.296353 | − | 0.955079i | \(-0.404230\pi\) |
−0.678946 | + | 0.734188i | \(0.737563\pi\) | |||||||
\(440\) | −121.892 | −0.0132067 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3187.85 | 0.343056 | ||||||||
\(443\) | 5733.91 | + | 3310.47i | 0.614958 | + | 0.355046i | 0.774903 | − | 0.632080i | \(-0.217799\pi\) |
−0.159946 | + | 0.987126i | \(0.551132\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −39.8905 | − | 69.0924i | −0.00424942 | − | 0.00736021i | ||||
\(446\) | −2239.65 | −0.237782 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −641.939 | + | 1129.12i | −0.0676981 | + | 0.119075i | ||||
\(449\) | 3211.25i | 0.337524i | 0.985657 | + | 0.168762i | \(0.0539769\pi\) | ||||
−0.985657 | + | 0.168762i | \(0.946023\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6100.48 | − | 3522.11i | −0.636940 | − | 0.367738i | ||||
\(452\) | − | 2948.61i | − | 0.306839i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3972.26 | + | 2293.39i | 0.410634 | + | 0.237079i | ||||
\(455\) | −200.767 | + | 117.697i | −0.0206859 | + | 0.0121269i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3926.69 | − | 6801.23i | 0.401932 | − | 0.696166i | −0.592027 | − | 0.805918i | \(-0.701672\pi\) |
0.993959 | + | 0.109752i | \(0.0350056\pi\) | |||||||
\(458\) | −2156.48 | + | 3735.14i | −0.220013 | + | 0.381073i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −202.800 | + | 117.086i | −0.0205556 | + | 0.0118678i | ||||
\(461\) | −2992.54 | − | 5183.22i | −0.302335 | − | 0.523659i | 0.674330 | − | 0.738430i | \(-0.264433\pi\) |
−0.976664 | + | 0.214771i | \(0.931099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9378.59 | − | 16244.2i | 0.941383 | − | 1.63052i | 0.178546 | − | 0.983932i | \(-0.442861\pi\) |
0.762837 | − | 0.646591i | \(-0.223806\pi\) | |||||||
\(464\) | − | 2280.08i | − | 0.228125i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5605.82 | 0.557263 | ||||||||
\(467\) | 4572.53 | + | 7919.86i | 0.453087 | + | 0.784770i | 0.998576 | − | 0.0533484i | \(-0.0169894\pi\) |
−0.545489 | + | 0.838118i | \(0.683656\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14032.8 | + | 93.1678i | −1.38161 | + | 0.00917290i | ||||
\(470\) | −137.585 | + | 79.4347i | −0.0135028 | + | 0.00779585i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8034.17 | + | 4638.53i | −0.783480 | + | 0.452343i | ||||
\(473\) | 3294.84 | − | 1902.28i | 0.320289 | − | 0.184919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4857.40 | − | 2804.42i | 0.469206 | − | 0.270896i | ||||
\(476\) | −3692.66 | + | 6495.08i | −0.355573 | + | 0.625424i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2658.05 | + | 4603.88i | 0.254344 | + | 0.440537i | ||||
\(479\) | 40.6827 | 0.00388067 | 0.00194033 | − | 0.999998i | \(-0.499382\pi\) | ||||
0.00194033 | + | 0.999998i | \(0.499382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11317.5i | 1.07284i | ||||||||
\(482\) | 544.820 | − | 943.657i | 0.0514852 | − | 0.0891751i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2143.36 | − | 3712.40i | −0.201292 | − | 0.348648i | ||||
\(485\) | −39.8112 | + | 22.9850i | −0.00372729 | + | 0.00215195i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5493.67 | − | 9515.32i | 0.511174 | − | 0.885380i | −0.488742 | − | 0.872429i | \(-0.662544\pi\) |
0.999916 | − | 0.0129516i | \(-0.00412273\pi\) | |||||||
\(488\) | 1851.43 | − | 3206.76i | 0.171742 | − | 0.297466i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.44206 | + | 108.595i | 0.000132950 | + | 0.0100119i | ||||
\(491\) | 2232.83 | + | 1289.12i | 0.205226 | + | 0.118488i | 0.599091 | − | 0.800681i | \(-0.295529\pi\) |
−0.393865 | + | 0.919168i | \(0.628862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4069.11i | − | 0.371731i | ||||||
\(494\) | 2049.88 | + | 1183.50i | 0.186697 | + | 0.107790i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3352.90i | 0.303527i | ||||||||
\(497\) | −17863.6 | − | 10156.0i | −1.61226 | − | 0.916621i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1096.63 | −0.0983809 | −0.0491904 | − | 0.998789i | \(-0.515664\pi\) | ||||
−0.0491904 | + | 0.998789i | \(0.515664\pi\) | |||||||
\(500\) | −229.032 | − | 396.694i | −0.0204852 | − | 0.0354814i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 478.014 | + | 275.981i | 0.0424996 | + | 0.0245372i | ||||
\(503\) | 22314.6 | 1.97805 | 0.989024 | − | 0.147755i | \(-0.0472046\pi\) | ||||
0.989024 | + | 0.147755i | \(0.0472046\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 259.614 | 0.0228766 | ||||||||
\(506\) | −3346.26 | − | 1931.96i | −0.293991 | − | 0.169736i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6736.82 | + | 11668.5i | 0.588382 | + | 1.01911i | ||||
\(509\) | −5432.23 | −0.473044 | −0.236522 | − | 0.971626i | \(-0.576007\pi\) | ||||
−0.236522 | + | 0.971626i | \(0.576007\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2320.16 | − | 1360.16i | 0.200857 | − | 0.117750i | ||||
\(512\) | − | 10490.5i | − | 0.905506i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4127.94 | + | 2383.27i | 0.354233 | + | 0.204516i | ||||
\(515\) | − | 229.842i | − | 0.0196661i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11401.4 | + | 6582.59i | 0.969888 | + | 0.559965i | ||||
\(518\) | 4591.39 | + | 2610.35i | 0.389448 | + | 0.221414i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 106.245 | − | 184.021i | 0.00895987 | − | 0.0155189i | ||||
\(521\) | −5784.74 | + | 10019.5i | −0.486438 | + | 0.842535i | −0.999878 | − | 0.0155903i | \(-0.995037\pi\) |
0.513441 | + | 0.858125i | \(0.328371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9256.60 | − | 5344.30i | 0.773925 | − | 0.446826i | −0.0603481 | − | 0.998177i | \(-0.519221\pi\) |
0.834273 | + | 0.551352i | \(0.185888\pi\) | |||||||
\(524\) | 3182.93 | + | 5512.99i | 0.265356 | + | 0.459611i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −770.110 | + | 1333.87i | −0.0638372 | + | 0.110569i | ||||
\(527\) | 5983.69i | 0.494599i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4157.49 | −0.341702 | ||||||||
\(530\) | −61.0284 | − | 105.704i | −0.00500170 | − | 0.00866320i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4785.80 | + | 2805.61i | −0.390020 | + | 0.228644i | ||||
\(533\) | 10634.7 | − | 6139.97i | 0.864243 | − | 0.498971i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −335.385 | + | 193.635i | −0.0271028 | + | 0.0156478i | ||||
\(536\) | 11096.4 | − | 6406.50i | 0.894200 | − | 0.516266i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2184.00 | − | 1260.94i | 0.175017 | − | 0.101046i | ||||
\(539\) | 7733.67 | − | 4603.02i | 0.618020 | − | 0.367841i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6142.32 | − | 10638.8i | −0.488131 | − | 0.845468i | 0.511776 | − | 0.859119i | \(-0.328988\pi\) |
−0.999907 | + | 0.0136513i | \(0.995655\pi\) | |||||||
\(542\) | 4847.75 | 0.384186 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 10541.5i | − | 0.830818i | ||||||
\(545\) | −2.14174 | + | 3.70960i | −0.000168334 | + | 0.000291563i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2319.96 | + | 4018.29i | 0.181342 | + | 0.314094i | 0.942338 | − | 0.334663i | \(-0.108622\pi\) |
−0.760996 | + | 0.648757i | \(0.775289\pi\) | |||||||
\(548\) | 7985.01 | − | 4610.15i | 0.622450 | − | 0.359372i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1888.98 | − | 3271.80i | 0.146448 | − | 0.253655i | ||||
\(551\) | 1510.67 | − | 2616.56i | 0.116800 | − | 0.202303i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8353.89 | + | 14250.0i | 0.642394 | + | 1.09579i | ||||
\(554\) | −2104.91 | − | 1215.27i | −0.161424 | − | 0.0931983i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20989.0i | 1.60096i | ||||||||
\(557\) | 918.666 | + | 530.392i | 0.0698835 | + | 0.0403473i | 0.534535 | − | 0.845147i | \(-0.320487\pi\) |
−0.464651 | + | 0.885494i | \(0.653820\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6632.33i | 0.501821i | ||||||||
\(560\) | 87.1843 | + | 148.719i | 0.00657895 | + | 0.0112223i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6737.12 | −0.505673 | ||||||||
\(563\) | −9805.04 | − | 16982.8i | −0.733984 | − | 1.27130i | −0.955168 | − | 0.296066i | \(-0.904325\pi\) |
0.221183 | − | 0.975232i | \(-0.429008\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −105.150 | − | 60.7081i | −0.00782951 | − | 0.00452037i | ||||
\(566\) | 8725.31 | 0.647972 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18762.2 | 1.38600 | ||||||||
\(569\) | −18029.9 | − | 10409.6i | −1.32839 | − | 0.766945i | −0.343337 | − | 0.939212i | \(-0.611557\pi\) |
−0.985050 | + | 0.172267i | \(0.944891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7362.92 | − | 12753.0i | −0.539630 | − | 0.934667i | −0.998924 | − | 0.0463823i | \(-0.985231\pi\) |
0.459294 | − | 0.888285i | \(-0.348103\pi\) | |||||||
\(572\) | −8007.09 | −0.585303 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −38.0468 | − | 5730.55i | −0.00276663 | − | 0.416705i | ||||
\(575\) | − | 15961.3i | − | 1.15762i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14296.1 | − | 8253.86i | −1.03146 | − | 0.595516i | −0.114060 | − | 0.993474i | \(-0.536386\pi\) |
−0.917404 | + | 0.397958i | \(0.869719\pi\) | |||||||
\(578\) | 1448.33i | 0.104226i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −106.812 | − | 61.6680i | −0.00764678 | − | 0.00441487i | ||||
\(581\) | 27622.7 | − | 183.395i | 1.97243 | − | 0.0130956i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5057.29 | + | 8759.48i | −0.359265 | + | 0.622266i | ||||
\(584\) | −1227.81 | + | 2126.64i | −0.0869988 | + | 0.150686i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −185.515 | + | 107.107i | −0.0130777 | + | 0.00755043i | ||||
\(587\) | −6104.52 | − | 10573.3i | −0.429234 | − | 0.743456i | 0.567571 | − | 0.823324i | \(-0.307883\pi\) |
−0.996805 | + | 0.0798686i | \(0.974550\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2221.46 | + | 3847.68i | −0.155405 | + | 0.269170i | ||||
\(590\) | 173.709i | 0.0121211i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8383.49 | 0.582026 | ||||||||
\(593\) | 4385.09 | + | 7595.19i | 0.303666 | + | 0.525965i | 0.976963 | − | 0.213407i | \(-0.0684560\pi\) |
−0.673298 | + | 0.739372i | \(0.735123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 155.592 | + | 265.408i | 0.0107204 | + | 0.0182868i | ||||
\(596\) | 2101.42 | − | 1213.26i | 0.144426 | − | 0.0833842i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5833.41 | − | 3367.92i | 0.398906 | − | 0.230308i | ||||
\(599\) | −19136.2 | + | 11048.3i | −1.30531 | + | 0.753623i | −0.981310 | − | 0.192433i | \(-0.938362\pi\) |
−0.324003 | + | 0.946056i | \(0.605029\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10189.4 | − | 5882.86i | 0.691572 | − | 0.399279i | −0.112629 | − | 0.993637i | \(-0.535927\pi\) |
0.804201 | + | 0.594358i | \(0.202594\pi\) | |||||||
\(602\) | 2690.66 | + | 1529.73i | 0.182165 | + | 0.103566i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1722.96 | + | 2984.26i | 0.116070 | + | 0.201039i | ||||
\(605\) | −176.516 | −0.0118618 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8352.53i | − | 0.558515i | −0.960216 | − | 0.279258i | \(-0.909912\pi\) | ||
0.960216 | − | 0.279258i | \(-0.0900884\pi\) | |||||||
\(608\) | 3913.58 | − | 6778.52i | 0.261047 | − | 0.452147i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −34.6671 | − | 60.0451i | −0.00230103 | − | 0.00398550i | ||||
\(611\) | −19875.6 | + | 11475.2i | −1.31601 | + | 0.759797i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6844.06 | + | 11854.3i | −0.450945 | + | 0.781059i | −0.998445 | − | 0.0557466i | \(-0.982246\pi\) |
0.547500 | + | 0.836805i | \(0.315579\pi\) | |||||||
\(614\) | 1502.99 | − | 2603.25i | 0.0987877 | − | 0.171105i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4061.35 | + | 7143.58i | −0.265644 | + | 0.467245i | ||||
\(617\) | −2227.88 | − | 1286.27i | −0.145366 | − | 0.0839274i | 0.425553 | − | 0.904934i | \(-0.360080\pi\) |
−0.570919 | + | 0.821006i | \(0.693413\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 27393.3i | − | 1.77872i | −0.457206 | − | 0.889361i | \(-0.651150\pi\) | ||
0.457206 | − | 0.889361i | \(-0.348850\pi\) | |||||||
\(620\) | 157.069 | + | 90.6838i | 0.0101743 | + | 0.00587411i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 4257.26i | − | 0.274438i | ||||||
\(623\) | −5378.36 | + | 35.7085i | −0.345874 | + | 0.00229636i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15596.7 | 0.998189 | ||||||||
\(626\) | 3933.71 | + | 6813.39i | 0.251154 | + | 0.435012i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6687.55 | + | 3861.06i | 0.424940 | + | 0.245339i | ||||
\(629\) | 14961.5 | 0.948414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15166.2 | −0.956822 | −0.478411 | − | 0.878136i | \(-0.658787\pi\) | ||||
−0.478411 | + | 0.878136i | \(0.658787\pi\) | |||||||
\(632\) | −13061.4 | − | 7541.02i | −0.822082 | − | 0.474629i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1768.17 | + | 3062.56i | 0.110762 | + | 0.191845i | ||||
\(635\) | 554.810 | 0.0346724 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 208.320 | + | 15687.7i | 0.0129575 | + | 0.975778i | ||||
\(638\) | − | 2035.08i | − | 0.126285i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −351.038 | − | 202.672i | −0.0216813 | − | 0.0125177i | ||||
\(641\) | 22415.6i | 1.38122i | 0.723226 | + | 0.690612i | \(0.242659\pi\) | ||||
−0.723226 | + | 0.690612i | \(0.757341\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14768.9 | + | 8526.82i | 0.905798 | + | 0.522963i | 0.879077 | − | 0.476680i | \(-0.158160\pi\) |
0.0267213 | + | 0.999643i | \(0.491493\pi\) | |||||||
\(644\) | 104.811 | + | 15786.5i | 0.00641326 | + | 0.965956i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1564.55 | − | 2709.88i | 0.0952886 | − | 0.165045i | ||||
\(647\) | −13132.8 | + | 22746.6i | −0.797995 | + | 1.38217i | 0.122925 | + | 0.992416i | \(0.460773\pi\) |
−0.920920 | + | 0.389752i | \(0.872561\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12466.3 | − | 7197.43i | 0.754000 | − | 0.435322i | ||||
\(650\) | 3292.98 | + | 5703.62i | 0.198710 | + | 0.344176i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11900.2 | − | 20611.8i | 0.714798 | − | 1.23807i | ||||
\(653\) | 153.742i | 0.00921345i | 0.999989 | + | 0.00460672i | \(0.00146637\pi\) | ||||
−0.999989 | + | 0.00460672i | \(0.998534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 262.129 | 0.0156370 | ||||||||
\(656\) | −4548.19 | − | 7877.70i | −0.270697 | − | 0.468861i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 71.1069 | + | 10710.0i | 0.00421282 | + | 0.634529i | ||||
\(659\) | 9292.80 | − | 5365.20i | 0.549311 | − | 0.317145i | −0.199533 | − | 0.979891i | \(-0.563942\pi\) |
0.748844 | + | 0.662746i | \(0.230609\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27734.8 | + | 16012.7i | −1.63201 | + | 0.942243i | −0.648541 | + | 0.761180i | \(0.724621\pi\) |
−0.983471 | + | 0.181063i | \(0.942046\pi\) | |||||||
\(662\) | −909.258 | + | 524.960i | −0.0533826 | + | 0.0308205i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21842.6 | + | 12610.8i | −1.27659 | + | 0.737040i | ||||
\(665\) | 1.51661 | + | 228.429i | 8.84383e−5 | + | 0.0133204i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4298.96 | − | 7446.01i | −0.249560 | − | 0.432250i | ||||
\(668\) | 25016.7 | 1.44899 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 239.918i | − | 0.0138341i | ||||||
\(671\) | −2872.79 | + | 4975.81i | −0.165280 | + | 0.286273i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6229.97 | − | 10790.6i | −0.356831 | − | 0.618050i | 0.630598 | − | 0.776110i | \(-0.282810\pi\) |
−0.987430 | + | 0.158059i | \(0.949476\pi\) | |||||||
\(674\) | −4750.65 | + | 2742.79i | −0.271496 | + | 0.156748i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −349.500 | + | 605.352i | −0.0198851 | + | 0.0344420i | ||||
\(677\) | −4805.25 | + | 8322.94i | −0.272793 | + | 0.472491i | −0.969576 | − | 0.244791i | \(-0.921281\pi\) |
0.696783 | + | 0.717282i | \(0.254614\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.5753 | + | 3099.02i | 0.00116290 | + | 0.175154i | ||||
\(680\) | −243.270 | − | 140.452i | −0.0137191 | − | 0.00792073i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2992.62i | 0.168026i | ||||||||
\(683\) | −24434.5 | − | 14107.2i | −1.36890 | − | 0.790335i | −0.378113 | − | 0.925760i | \(-0.623427\pi\) |
−0.990788 | + | 0.135425i | \(0.956760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 379.668i | − | 0.0211772i | ||||||
\(686\) | 6412.38 | + | 3533.81i | 0.356889 | + | 0.196679i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4912.92 | 0.272243 | ||||||||
\(689\) | −8816.19 | − | 15270.1i | −0.487475 | − | 0.844331i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2458.51 | + | 1419.42i | 0.135349 | + | 0.0781439i | 0.566146 | − | 0.824305i | \(-0.308434\pi\) |
−0.430796 | + | 0.902449i | \(0.641767\pi\) | |||||||
\(692\) | 15694.7 | 0.862172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2909.01 | −0.159113 | ||||||||
\(695\) | 748.483 | + | 432.137i | 0.0408512 | + | 0.0235854i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8116.85 | − | 14058.8i | −0.441102 | − | 0.764010i | ||||
\(698\) | −8478.76 | −0.459779 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15435.3 | + | 102.479i | −0.833426 | + | 0.00553336i | ||||
\(701\) | − | 5765.47i | − | 0.310640i | −0.987864 | − | 0.155320i | \(-0.950359\pi\) | ||
0.987864 | − | 0.155320i | \(-0.0496409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9620.64 | + | 5554.48i | 0.516144 | + | 0.297996i | ||||
\(704\) | 1840.14i | 0.0985126i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 192.479 | + | 111.128i | 0.0102607 | + | 0.00592399i | ||||
\(707\) | 8650.18 | − | 15214.9i | 0.460146 | − | 0.809359i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2400.73 | + | 4158.18i | −0.127167 | + | 0.220259i | −0.922578 | − | 0.385811i | \(-0.873922\pi\) |
0.795411 | + | 0.606070i | \(0.207255\pi\) | |||||||
\(710\) | 175.657 | − | 304.247i | 0.00928492 | − | 0.0160819i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4252.92 | − | 2455.42i | 0.223855 | − | 0.129243i | ||||
\(713\) | 6321.68 | + | 10949.5i | 0.332046 | + | 0.575121i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −164.856 | + | 285.538i | −0.00862273 | + | 0.0149350i | ||||
\(716\) | 15231.6i | 0.795014i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4934.65 | 0.256490 | ||||||||
\(719\) | −2528.38 | − | 4379.29i | −0.131144 | − | 0.227149i | 0.792974 | − | 0.609256i | \(-0.208532\pi\) |
−0.924118 | + | 0.382107i | \(0.875198\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13470.1 | − | 7658.18i | −0.695774 | − | 0.395569i | ||||
\(722\) | −4834.25 | + | 2791.05i | −0.249186 | + | 0.143867i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19914.8 | + | 11497.8i | −1.02228 | + | 0.590211i | ||||
\(725\) | 7280.34 | − | 4203.31i | 0.372945 | − | 0.215320i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8680.56 | + | 5011.72i | −0.442839 | + | 0.255673i | −0.704801 | − | 0.709405i | \(-0.748964\pi\) |
0.261962 | + | 0.965078i | \(0.415630\pi\) | |||||||
\(728\) | −7244.73 | − | 12358.0i | −0.368829 | − | 0.629147i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 22.9902 | + | 39.8202i | 0.00116563 | + | 0.00201892i | ||||
\(731\) | 8767.75 | 0.443621 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31917.2i | − | 1.60831i | −0.594422 | − | 0.804153i | \(-0.702619\pi\) | ||
0.594422 | − | 0.804153i | \(-0.297381\pi\) | |||||||
\(734\) | −3328.44 | + | 5765.03i | −0.167378 | + | 0.289906i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11137.0 | − | 19289.8i | −0.557765 | − | 0.966077i | ||||
\(737\) | −17217.8 | + | 9940.73i | −0.860553 | + | 0.496841i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4191.82 | − | 7260.45i | 0.208659 | − | 0.361407i | −0.742634 | − | 0.669698i | \(-0.766424\pi\) |
0.951292 | + | 0.308291i | \(0.0997569\pi\) | |||||||
\(740\) | 226.743 | − | 392.731i | 0.0112638 | − | 0.0195095i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8228.32 | + | 54.6302i | −0.407104 | + | 0.00270288i | ||||
\(743\) | −14035.0 | − | 8103.09i | −0.692992 | − | 0.400099i | 0.111740 | − | 0.993737i | \(-0.464358\pi\) |
−0.804732 | + | 0.593638i | \(0.797691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 99.9176i | − | 0.00491369i | ||||||
\(746\) | −12351.0 | − | 7130.82i | −0.606167 | − | 0.349971i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10585.1i | 0.517421i | ||||||||
\(749\) | 173.334 | + | 26107.4i | 0.00845594 | + | 1.27362i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29812.4 | −1.44856 | −0.724281 | − | 0.689505i | \(-0.757828\pi\) | ||||
−0.724281 | + | 0.689505i | \(0.757828\pi\) | |||||||
\(752\) | 8500.26 | + | 14722.9i | 0.412198 | + | 0.713948i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3072.39 | + | 1773.84i | 0.148395 | + | 0.0856758i | ||||
\(755\) | 141.894 | 0.00683981 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29462.2 | 1.41456 | 0.707281 | − | 0.706933i | \(-0.249922\pi\) | ||||
0.707281 | + | 0.706933i | \(0.249922\pi\) | |||||||
\(758\) | 9623.15 | + | 5555.93i | 0.461120 | + | 0.266227i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −104.286 | − | 180.630i | −0.00497746 | − | 0.00862121i | ||||
\(761\) | 1305.63 | 0.0621931 | 0.0310965 | − | 0.999516i | \(-0.490100\pi\) | ||||
0.0310965 | + | 0.999516i | \(0.490100\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 146.043 | + | 249.120i | 0.00692939 | + | 0.0118201i | ||||
\(764\) | 11871.3i | 0.562156i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10522.3 | − | 6075.08i | −0.496329 | − | 0.286556i | ||||
\(767\) | 25094.0i | 1.18135i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1387.38 | − | 801.002i | −0.0650586 | − | 0.0375616i | 0.467118 | − | 0.884195i | \(-0.345292\pi\) |
−0.532176 | + | 0.846633i | \(0.678626\pi\) | |||||||
\(770\) | 77.8162 | + | 132.739i | 0.00364195 | + | 0.00621242i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1665.03 | − | 2883.91i | 0.0776239 | − | 0.134449i | ||||
\(773\) | 9429.57 | − | 16332.5i | 0.438755 | − | 0.759947i | −0.558838 | − | 0.829277i | \(-0.688753\pi\) |
0.997594 | + | 0.0693300i | \(0.0220861\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10705.9 | + | 6181.03i | −0.496214 | + | 0.286489i | ||||
\(776\) | −1414.82 | − | 2450.54i | −0.0654499 | − | 0.113363i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −823.627 | + | 1426.56i | −0.0379543 | + | 0.0657388i | ||||
\(779\) | − | 12053.6i | − | 0.554385i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29112.7 | −1.33384 | ||||||||
\(782\) | −4452.29 | − | 7711.59i | −0.203598 | − | 0.352642i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11620.7 | − | 154.314i | 0.529370 | − | 0.00702959i | ||||
\(785\) | 275.376 | − | 158.988i | 0.0125205 | − | 0.00722872i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20329.8 | − | 11737.4i | 0.920810 | − | 0.531630i | 0.0369165 | − | 0.999318i | \(-0.488246\pi\) |
0.883893 | + | 0.467689i | \(0.154913\pi\) | |||||||
\(788\) | 25038.0 | − | 14455.7i | 1.13190 | − | 0.653506i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −244.569 | + | 141.202i | −0.0110144 | + | 0.00635917i | ||||
\(791\) | −7061.37 | + | 4139.64i | −0.317413 | + | 0.186079i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5008.02 | − | 8674.15i | −0.224262 | − | 0.388434i | ||||
\(794\) | −7363.52 | −0.329120 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10989.9i | 0.489353i | ||||||||
\(797\) | −15759.6 | + | 27296.5i | −0.700420 | + | 1.21316i | 0.267900 | + | 0.963447i | \(0.413670\pi\) |
−0.968319 | + | 0.249715i | \(0.919663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15169.9 | + | 26275.0i | 0.671678 | + | 1.16338i | ||||
\(800\) | 18860.6 | − | 10889.2i | 0.833530 | − | 0.481239i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8688.97 | + | 15049.7i | −0.382566 | + | 0.662625i | ||||
\(803\) | 1905.15 | − | 3299.82i | 0.0837252 | − | 0.145016i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 565.116 | + | 321.286i | 0.0247425 | + | 0.0140669i | ||||
\(806\) | −4517.99 | − | 2608.46i | −0.197444 | − | 0.113994i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15980.3i | 0.695774i | ||||||||
\(809\) | −14756.8 | − | 8519.85i | −0.641312 | − | 0.370262i | 0.143807 | − | 0.989606i | \(-0.454065\pi\) |
−0.785120 | + | 0.619344i | \(0.787399\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9916.81i | 0.429379i | 0.976682 | + | 0.214689i | \(0.0688739\pi\) | ||||
−0.976682 | + | 0.214689i | \(0.931126\pi\) | |||||||
\(812\) | −7173.03 | + | 4205.09i | −0.310005 | + | 0.181736i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7482.67 | 0.322196 | ||||||||
\(815\) | −490.020 | − | 848.740i | −0.0210609 | − | 0.0364786i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5637.91 | + | 3255.05i | 0.241427 | + | 0.139388i | ||||
\(818\) | 7542.02 | 0.322372 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −492.049 | −0.0209550 | ||||||||
\(821\) | −1740.83 | − | 1005.07i | −0.0740018 | − | 0.0427250i | 0.462543 | − | 0.886597i | \(-0.346937\pi\) |
−0.536544 | + | 0.843872i | \(0.680271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5316.32 | − | 9208.13i | −0.225170 | − | 0.390006i | 0.731200 | − | 0.682163i | \(-0.238961\pi\) |
−0.956371 | + | 0.292157i | \(0.905627\pi\) | |||||||
\(824\) | 14147.7 | 0.598129 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10180.4 | + | 5787.86i | 0.428838 | + | 0.243808i | ||||
\(827\) | 5725.20i | 0.240731i | 0.992730 | + | 0.120366i | \(0.0384067\pi\) | ||||
−0.992730 | + | 0.120366i | \(0.961593\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16983.1 | + | 9805.21i | 0.711517 | + | 0.410795i | 0.811623 | − | 0.584182i | \(-0.198585\pi\) |
−0.100105 | + | 0.994977i | \(0.531918\pi\) | |||||||
\(830\) | 472.263i | 0.0197500i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2778.08 | − | 1603.92i | −0.115760 | − | 0.0668342i | ||||
\(833\) | 20738.7 | − | 275.393i | 0.862610 | − | 0.0114547i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 515.062 | − | 892.113i | 0.0213466 | − | 0.0369735i | ||||
\(836\) | −3929.76 | + | 6806.55i | −0.162576 | + | 0.281590i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7602.53 | + | 4389.32i | −0.313395 | + | 0.180939i | ||||
\(839\) | −14243.5 | − | 24670.5i | −0.586104 | − | 1.01516i | −0.994737 | − | 0.102462i | \(-0.967328\pi\) |
0.408633 | − | 0.912699i | \(-0.366005\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9930.29 | + | 17199.8i | −0.407163 | + | 0.705226i | ||||
\(842\) | 6625.59i | 0.271179i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13655.1 | 0.556906 | ||||||||
\(845\) | 14.3915 | + | 24.9268i | 0.000585897 | + | 0.00101480i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5881.39 | + | 10344.9i | −0.238591 | + | 0.419662i | ||||
\(848\) | −11311.3 | + | 6530.61i | −0.458058 | + | 0.264460i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7540.01 | − | 4353.23i | 0.304259 | − | 0.175664i | ||||
\(851\) | 27377.8 | − | 15806.6i | 1.10282 | − | 0.636712i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20170.8 | − | 11645.6i | 0.809652 | − | 0.467453i | −0.0371829 | − | 0.999308i | \(-0.511838\pi\) |
0.846835 | + | 0.531856i | \(0.178505\pi\) | |||||||
\(854\) | −4674.09 | + | 31.0326i | −0.187288 | + | 0.00124346i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11919.0 | − | 20644.3i | −0.475915 | − | 0.824309i | ||||
\(857\) | −34729.8 | −1.38430 | −0.692152 | − | 0.721752i | \(-0.743337\pi\) | ||||
−0.692152 | + | 0.721752i | \(0.743337\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38761.1i | 1.53960i | 0.638288 | + | 0.769798i | \(0.279643\pi\) | ||||
−0.638288 | + | 0.769798i | \(0.720357\pi\) | |||||||
\(860\) | 132.877 | − | 230.149i | 0.00526867 | − | 0.00912560i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7554.68 | − | 13085.1i | −0.298508 | − | 0.517030i | ||||
\(863\) | 6375.08 | − | 3680.65i | 0.251460 | − | 0.145181i | −0.368972 | − | 0.929440i | \(-0.620290\pi\) |
0.620433 | + | 0.784260i | \(0.286957\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 323.134 | − | 559.684i | 0.0127016 | − | 0.0219998i | ||||
\(866\) | −6926.17 | + | 11996.5i | −0.271779 | + | 0.470736i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10548.0 | − | 6183.65i | 0.412470 | − | 0.241805i | ||||
\(869\) | 20266.9 | + | 11701.1i | 0.791149 | + | 0.456770i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 34658.6i | − | 1.34829i | ||||||
\(872\) | −228.341 | − | 131.833i | −0.00886765 | − | 0.00511974i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 6611.70i | − | 0.255886i | ||||||
\(875\) | −628.465 | + | 1105.42i | −0.0242811 | + | 0.0427085i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1980.37 | −0.0762512 | −0.0381256 | − | 0.999273i | \(-0.512139\pi\) | ||||
−0.0381256 | + | 0.999273i | \(0.512139\pi\) | |||||||
\(878\) | −2341.75 | − | 4056.03i | −0.0900117 | − | 0.155905i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 211.513 | + | 122.117i | 0.00810239 | + | 0.00467792i | ||||
\(881\) | −30117.5 | −1.15174 | −0.575870 | − | 0.817541i | \(-0.695337\pi\) | ||||
−0.575870 | + | 0.817541i | \(0.695337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3739.43 | 0.142516 | 0.0712580 | − | 0.997458i | \(-0.477299\pi\) | ||||
0.0712580 | + | 0.997458i | \(0.477299\pi\) | |||||||
\(884\) | −15980.5 | − | 9226.34i | −0.608011 | − | 0.351036i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3815.55 | + | 6608.73i | 0.144680 | + | 0.250592i | ||||
\(887\) | 35778.8 | 1.35438 | 0.677190 | − | 0.735809i | \(-0.263198\pi\) | ||||
0.677190 | + | 0.735809i | \(0.263198\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18485.9 | − | 32515.2i | 0.697410 | − | 1.22669i | ||||
\(890\) | − | 91.9533i | − | 0.00346324i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11227.2 | + | 6482.04i | 0.421430 | + | 0.243313i | ||||
\(893\) | 22527.4i | 0.844177i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 543.168 | + | 313.598i | 0.0202861 | + | 0.0117122i | ||||
\(896\) | −23574.2 | + | 13820.0i | −0.878971 | + | 0.515285i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1850.60 | + | 3205.33i | −0.0687697 | + | 0.119113i | ||||
\(899\) | −3329.56 | + | 5766.96i | −0.123523 | + | 0.213948i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20186.6 | + | 11654.7i | −0.746408 | + | 0.430939i | ||||
\(902\) | −4059.48 | − | 7031.23i | −0.149851 | − | 0.259550i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3736.83 | − | 6472.38i | 0.137484 | − | 0.238128i | ||||
\(905\) | 946.900i | 0.0347801i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30813.7 | 1.12806 | 0.564031 | − | 0.825753i | \(-0.309250\pi\) | ||||
0.564031 | + | 0.825753i | \(0.309250\pi\) | |||||||
\(908\) | −13275.1 | − | 22993.2i | −0.485188 | − | 0.840370i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −268.224 | + | 1.78082i | −0.00977091 | + | 6.48719e-5i | ||||
\(911\) | 10135.1 | − | 5851.50i | 0.368595 | − | 0.212809i | −0.304249 | − | 0.952592i | \(-0.598406\pi\) |
0.672845 | + | 0.739784i | \(0.265072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33892.3 | − | 19567.7i | 1.22856 | − | 0.709307i | ||||
\(914\) | 7838.89 | − | 4525.79i | 0.283684 | − | 0.163785i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21620.6 | − | 12482.7i | 0.779875 | − | 0.450261i | ||||
\(917\) | 8733.98 | − | 15362.3i | 0.314527 | − | 0.553227i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9866.32 | + | 17089.0i | 0.354146 | + | 0.613398i | 0.986971 | − | 0.160896i | \(-0.0514384\pi\) |
−0.632826 | + | 0.774294i | \(0.718105\pi\) | |||||||
\(920\) | −593.543 | −0.0212701 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 6898.22i | − | 0.246400i | ||||||
\(923\) | 25375.5 | − | 43951.7i | 0.904924 | − | 1.56737i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15454.9 | + | 26768.6i | 0.549354 | + | 0.951510i | ||||
\(926\) | 18722.6 | − | 10809.5i | 0.664430 | − | 0.383609i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5865.72 | − | 10159.7i | 0.207491 | − | 0.359385i | ||||
\(929\) | 8592.29 | − | 14882.3i | 0.303449 | − | 0.525589i | −0.673466 | − | 0.739218i | \(-0.735195\pi\) |
0.976915 | + | 0.213629i | \(0.0685285\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13437.8 | + | 7522.22i | 0.473047 | + | 0.264802i | ||||
\(932\) | −28101.6 | − | 16224.5i | −0.987660 | − | 0.570226i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10540.3i | 0.369261i | ||||||||
\(935\) | 377.473 | + | 217.934i | 0.0132029 | + | 0.00762269i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16777.3i | − | 0.584940i | −0.956275 | − | 0.292470i | \(-0.905523\pi\) | ||
0.956275 | − | 0.292470i | \(-0.0944772\pi\) | |||||||
\(938\) | −14060.6 | − | 7993.90i | −0.489440 | − | 0.278262i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 919.606 | 0.0319088 | ||||||||
\(941\) | −4512.78 | − | 7816.36i | −0.156336 | − | 0.270782i | 0.777209 | − | 0.629243i | \(-0.216635\pi\) |
−0.933545 | + | 0.358461i | \(0.883302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29705.8 | − | 17150.7i | −1.02583 | − | 0.592262i | ||||
\(944\) | 18588.5 | 0.640893 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4385.01 | 0.150707 | ||||||||
\(947\) | 49093.6 | + | 28344.2i | 1.68461 | + | 0.972611i | 0.958525 | + | 0.285009i | \(0.0919967\pi\) |
0.726088 | + | 0.687602i | \(0.241337\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3321.18 | + | 5752.45i | 0.113604 | + | 0.196768i | ||||
\(950\) | 6464.59 | 0.220778 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16336.9 | + | 9577.32i | −0.556180 | + | 0.326053i | ||||
\(953\) | − | 2869.91i | − | 0.0975503i | −0.998810 | − | 0.0487751i | \(-0.984468\pi\) | ||
0.998810 | − | 0.0487751i | \(-0.0155318\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 423.338 | + | 244.414i | 0.0143444 | + | 0.00828173i | ||||
\(956\) | − | 30771.9i | − | 1.04104i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.6077 | + | 23.4448i | 0.00136949 | + | 0.000790677i | ||||
\(959\) | −22250.8 | − | 12650.3i | −0.749234 | − | 0.425963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9999.34 | + | 17319.4i | −0.335650 | + | 0.581362i | ||||
\(962\) | −6522.13 | + | 11296.7i | −0.218588 | + | 0.378606i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5462.30 | + | 3153.66i | −0.182499 | + | 0.105366i | ||||
\(965\) | −68.5615 | − | 118.752i | −0.00228712 | − | 0.00396141i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20201.6 | + | 34990.2i | −0.671810 | + | 1.16361i | 0.305580 | + | 0.952166i | \(0.401150\pi\) |
−0.977390 | + | 0.211443i | \(0.932184\pi\) | |||||||
\(968\) | − | 10865.3i | − | 0.360767i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −52.9837 | −0.00175382 | ||||||||
\(971\) | 15681.9 | + | 27161.9i | 0.518288 | + | 0.897701i | 0.999774 | + | 0.0212472i | \(0.00676372\pi\) |
−0.481486 | + | 0.876454i | \(0.659903\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50264.7 | − | 29467.0i | 1.65613 | − | 0.970884i | ||||
\(974\) | 10967.1 | − | 6331.84i | 0.360788 | − | 0.208301i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6425.39 | + | 3709.70i | −0.210729 | + | 0.121665i | ||||
\(977\) | 20718.0 | − | 11961.5i | 0.678430 | − | 0.391692i | −0.120833 | − | 0.992673i | \(-0.538557\pi\) |
0.799263 | + | 0.600981i | \(0.205223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6599.09 | + | 3809.99i | −0.215432 | + | 0.124380i | ||||
\(980\) | 307.070 | − | 548.555i | 0.0100092 | − | 0.0178805i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1485.81 | + | 2573.49i | 0.0482831 | + | 0.0836288i | ||||
\(983\) | 39291.6 | 1.27488 | 0.637440 | − | 0.770500i | \(-0.279993\pi\) | ||||
0.637440 | + | 0.770500i | \(0.279993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1190.50i | − | 0.0385100i | ||||||
\(986\) | 2344.97 | − | 4061.61i | 0.0757394 | − | 0.131184i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6850.61 | − | 11865.6i | −0.220594 | − | 0.382080i | ||||
\(989\) | 16044.0 | − | 9263.00i | 0.515844 | − | 0.297822i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12281.2 | − | 21271.6i | 0.393667 | − | 0.681852i | −0.599263 | − | 0.800552i | \(-0.704539\pi\) |
0.992930 | + | 0.118700i | \(0.0378728\pi\) | |||||||
\(992\) | −8625.63 | + | 14940.0i | −0.276073 | + | 0.478172i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11977.9 | − | 20431.9i | −0.382209 | − | 0.651971i | ||||
\(995\) | 391.906 | + | 226.267i | 0.0124867 | + | 0.00720919i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 10337.6i | − | 0.328379i | −0.986429 | − | 0.164190i | \(-0.947499\pi\) | ||
0.986429 | − | 0.164190i | \(-0.0525009\pi\) | |||||||
\(998\) | −1094.61 | − | 631.974i | −0.0347187 | − | 0.0200449i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 189.4.s.a.17.13 | 44 | ||
3.2 | odd | 2 | 63.4.s.a.59.10 | yes | 44 | ||
7.5 | odd | 6 | 189.4.i.a.152.10 | 44 | |||
9.2 | odd | 6 | 189.4.i.a.143.13 | 44 | |||
9.7 | even | 3 | 63.4.i.a.38.10 | yes | 44 | ||
21.5 | even | 6 | 63.4.i.a.5.13 | ✓ | 44 | ||
63.47 | even | 6 | inner | 189.4.s.a.89.13 | 44 | ||
63.61 | odd | 6 | 63.4.s.a.47.10 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.13 | ✓ | 44 | 21.5 | even | 6 | ||
63.4.i.a.38.10 | yes | 44 | 9.7 | even | 3 | ||
63.4.s.a.47.10 | yes | 44 | 63.61 | odd | 6 | ||
63.4.s.a.59.10 | yes | 44 | 3.2 | odd | 2 | ||
189.4.i.a.143.13 | 44 | 9.2 | odd | 6 | |||
189.4.i.a.152.10 | 44 | 7.5 | odd | 6 | |||
189.4.s.a.17.13 | 44 | 1.1 | even | 1 | trivial | ||
189.4.s.a.89.13 | 44 | 63.47 | even | 6 | inner |