Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), 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: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.j.199.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56155i | 0.905646i | 0.891601 | + | 0.452823i | \(0.149583\pi\) | ||||
−0.891601 | + | 0.452823i | \(0.850417\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 1.43845 | 0.179806 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −7.68466 | −0.522875 | ||||||||
\(7\) | − 6.24621i | − 0.337264i | −0.985679 | − | 0.168632i | \(-0.946065\pi\) | ||||
0.985679 | − | 0.168632i | \(-0.0539349\pi\) | |||||||
\(8\) | 24.1771i | 1.06849i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 4.31534i | 0.103811i | ||||||||
\(13\) | − 49.1231i | − 1.04802i | −0.851711 | − | 0.524011i | \(-0.824435\pi\) | ||||
0.851711 | − | 0.524011i | \(-0.175565\pi\) | |||||||
\(14\) | 16.0000 | 0.305441 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −50.4233 | −0.787864 | ||||||||
\(17\) | − 82.7083i | − 1.17998i | −0.807409 | − | 0.589992i | \(-0.799131\pi\) | ||||
0.807409 | − | 0.589992i | \(-0.200869\pi\) | |||||||
\(18\) | − 23.0540i | − 0.301882i | ||||||||
\(19\) | 130.354 | 1.57396 | 0.786981 | − | 0.616977i | \(-0.211643\pi\) | ||||
0.786981 | + | 0.616977i | \(0.211643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.7386 | 0.194719 | ||||||||
\(22\) | − 28.1771i | − 0.273062i | ||||||||
\(23\) | − 185.693i | − 1.68347i | −0.539895 | − | 0.841733i | \(-0.681536\pi\) | ||||
0.539895 | − | 0.841733i | \(-0.318464\pi\) | |||||||
\(24\) | −72.5312 | −0.616891 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 125.831 | 0.949137 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | − 8.98485i | − 0.0606420i | ||||||||
\(29\) | 8.90720 | 0.0570354 | 0.0285177 | − | 0.999593i | \(-0.490921\pi\) | ||||
0.0285177 | + | 0.999593i | \(0.490921\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.26137 | 0.0304829 | 0.0152414 | − | 0.999884i | \(-0.495148\pi\) | ||||
0.0152414 | + | 0.999884i | \(0.495148\pi\) | |||||||
\(32\) | 64.2547i | 0.354961i | ||||||||
\(33\) | − 33.0000i | − 0.174078i | ||||||||
\(34\) | 211.862 | 1.06865 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −12.9460 | −0.0599353 | ||||||||
\(37\) | 416.894i | 1.85235i | 0.377094 | + | 0.926175i | \(0.376923\pi\) | ||||
−0.377094 | + | 0.926175i | \(0.623077\pi\) | |||||||
\(38\) | 333.909i | 1.42545i | ||||||||
\(39\) | 147.369 | 0.605076 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −298.479 | −1.13694 | −0.568471 | − | 0.822703i | \(-0.692465\pi\) | ||||
−0.568471 | + | 0.822703i | \(0.692465\pi\) | |||||||
\(42\) | 48.0000i | 0.176347i | ||||||||
\(43\) | − 513.633i | − 1.82159i | −0.412863 | − | 0.910793i | \(-0.635471\pi\) | ||||
0.412863 | − | 0.910793i | \(-0.364529\pi\) | |||||||
\(44\) | −15.8229 | −0.0542135 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 475.663 | 1.52462 | ||||||||
\(47\) | − 557.295i | − 1.72957i | −0.502140 | − | 0.864786i | \(-0.667454\pi\) | ||||
0.502140 | − | 0.864786i | \(-0.332546\pi\) | |||||||
\(48\) | − 151.270i | − 0.454873i | ||||||||
\(49\) | 303.985 | 0.886253 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 248.125 | 0.681264 | ||||||||
\(52\) | − 70.6610i | − 0.188441i | ||||||||
\(53\) | − 168.064i | − 0.435574i | −0.975996 | − | 0.217787i | \(-0.930116\pi\) | ||||
0.975996 | − | 0.217787i | \(-0.0698838\pi\) | |||||||
\(54\) | 69.1619 | 0.174292 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 151.015 | 0.360362 | ||||||||
\(57\) | 391.062i | 0.908728i | ||||||||
\(58\) | 22.8163i | 0.0516539i | ||||||||
\(59\) | −618.773 | −1.36538 | −0.682689 | − | 0.730709i | \(-0.739190\pi\) | ||||
−0.682689 | + | 0.730709i | \(0.739190\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 786.405 | 1.65064 | 0.825319 | − | 0.564667i | \(-0.190996\pi\) | ||||
0.825319 | + | 0.564667i | \(0.190996\pi\) | |||||||
\(62\) | 13.4773i | 0.0276067i | ||||||||
\(63\) | 56.2159i | 0.112421i | ||||||||
\(64\) | −567.978 | −1.10933 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 84.5312 | 0.157653 | ||||||||
\(67\) | 339.015i | 0.618169i | 0.951035 | + | 0.309084i | \(0.100023\pi\) | ||||
−0.951035 | + | 0.309084i | \(0.899977\pi\) | |||||||
\(68\) | − 118.972i | − 0.212168i | ||||||||
\(69\) | 557.080 | 0.971949 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1120.71 | 1.87329 | 0.936645 | − | 0.350280i | \(-0.113913\pi\) | ||||
0.936645 | + | 0.350280i | \(0.113913\pi\) | |||||||
\(72\) | − 217.594i | − 0.356162i | ||||||||
\(73\) | − 123.430i | − 0.197896i | −0.995093 | − | 0.0989478i | \(-0.968452\pi\) | ||||
0.995093 | − | 0.0989478i | \(-0.0315477\pi\) | |||||||
\(74\) | −1067.90 | −1.67757 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 187.508 | 0.283008 | ||||||||
\(77\) | 68.7083i | 0.101689i | ||||||||
\(78\) | 377.494i | 0.547985i | ||||||||
\(79\) | 309.835 | 0.441255 | 0.220628 | − | 0.975358i | \(-0.429189\pi\) | ||||
0.220628 | + | 0.975358i | \(0.429189\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − 764.570i | − 1.02967i | ||||||||
\(83\) | − 1021.22i | − 1.35053i | −0.737577 | − | 0.675263i | \(-0.764030\pi\) | ||||
0.737577 | − | 0.675263i | \(-0.235970\pi\) | |||||||
\(84\) | 26.9545 | 0.0350117 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1315.70 | 1.64971 | ||||||||
\(87\) | 26.7216i | 0.0329294i | ||||||||
\(88\) | − 265.948i | − 0.322161i | ||||||||
\(89\) | 141.879 | 0.168979 | 0.0844894 | − | 0.996424i | \(-0.473074\pi\) | ||||
0.0844894 | + | 0.996424i | \(0.473074\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −306.833 | −0.353460 | ||||||||
\(92\) | − 267.110i | − 0.302697i | ||||||||
\(93\) | 15.7841i | 0.0175993i | ||||||||
\(94\) | 1427.54 | 1.56638 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −192.764 | −0.204937 | ||||||||
\(97\) | − 798.345i | − 0.835666i | −0.908524 | − | 0.417833i | \(-0.862790\pi\) | ||||
0.908524 | − | 0.417833i | \(-0.137210\pi\) | |||||||
\(98\) | 778.673i | 0.802631i | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 241.400 | 0.237823 | 0.118912 | − | 0.992905i | \(-0.462059\pi\) | ||||
0.118912 | + | 0.992905i | \(0.462059\pi\) | |||||||
\(102\) | 635.585i | 0.616983i | ||||||||
\(103\) | 1168.38i | 1.11771i | 0.829267 | + | 0.558853i | \(0.188758\pi\) | ||||
−0.829267 | + | 0.558853i | \(0.811242\pi\) | |||||||
\(104\) | 1187.65 | 1.11980 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 430.506 | 0.394476 | ||||||||
\(107\) | 2106.82i | 1.90350i | 0.306882 | + | 0.951748i | \(0.400714\pi\) | ||||
−0.306882 | + | 0.951748i | \(0.599286\pi\) | |||||||
\(108\) | − 38.8381i | − 0.0346037i | ||||||||
\(109\) | −493.792 | −0.433914 | −0.216957 | − | 0.976181i | \(-0.569613\pi\) | ||||
−0.216957 | + | 0.976181i | \(0.569613\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1250.68 | −1.06945 | ||||||||
\(112\) | 314.955i | 0.265718i | ||||||||
\(113\) | 170.000i | 0.141524i | 0.997493 | + | 0.0707622i | \(0.0225431\pi\) | ||||
−0.997493 | + | 0.0707622i | \(0.977457\pi\) | |||||||
\(114\) | −1001.73 | −0.822986 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.8125 | 0.0102553 | ||||||||
\(117\) | 442.108i | 0.349341i | ||||||||
\(118\) | − 1585.02i | − 1.23655i | ||||||||
\(119\) | −516.614 | −0.397966 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 2014.42i | 1.49489i | ||||||||
\(123\) | − 895.437i | − 0.656414i | ||||||||
\(124\) | 7.56820 | 0.00548100 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −144.000 | −0.101814 | ||||||||
\(127\) | 948.182i | 0.662500i | 0.943543 | + | 0.331250i | \(0.107470\pi\) | ||||
−0.943543 | + | 0.331250i | \(0.892530\pi\) | |||||||
\(128\) | − 940.868i | − 0.649702i | ||||||||
\(129\) | 1540.90 | 1.05169 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1484.84 | −0.990312 | −0.495156 | − | 0.868804i | \(-0.664889\pi\) | ||||
−0.495156 | + | 0.868804i | \(0.664889\pi\) | |||||||
\(132\) | − 47.4688i | − 0.0313002i | ||||||||
\(133\) | − 814.220i | − 0.530841i | ||||||||
\(134\) | −868.405 | −0.559842 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1999.65 | 1.26080 | ||||||||
\(137\) | − 684.928i | − 0.427134i | −0.976928 | − | 0.213567i | \(-0.931492\pi\) | ||||
0.976928 | − | 0.213567i | \(-0.0685082\pi\) | |||||||
\(138\) | 1426.99i | 0.880242i | ||||||||
\(139\) | −830.483 | −0.506767 | −0.253384 | − | 0.967366i | \(-0.581543\pi\) | ||||
−0.253384 | + | 0.967366i | \(0.581543\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1671.89 | 0.998569 | ||||||||
\(142\) | 2870.75i | 1.69654i | ||||||||
\(143\) | 540.354i | 0.315991i | ||||||||
\(144\) | 453.810 | 0.262621 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 316.172 | 0.179223 | ||||||||
\(147\) | 911.955i | 0.511679i | ||||||||
\(148\) | 599.680i | 0.333063i | ||||||||
\(149\) | 1213.64 | 0.667285 | 0.333642 | − | 0.942700i | \(-0.391722\pi\) | ||||
0.333642 | + | 0.942700i | \(0.391722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30.8466 | 0.0166242 | 0.00831212 | − | 0.999965i | \(-0.497354\pi\) | ||||
0.00831212 | + | 0.999965i | \(0.497354\pi\) | |||||||
\(152\) | 3151.58i | 1.68176i | ||||||||
\(153\) | 744.375i | 0.393328i | ||||||||
\(154\) | −176.000 | −0.0920941 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 211.983 | 0.108796 | ||||||||
\(157\) | − 345.239i | − 0.175497i | −0.996143 | − | 0.0877485i | \(-0.972033\pi\) | ||||
0.996143 | − | 0.0877485i | \(-0.0279672\pi\) | |||||||
\(158\) | 793.659i | 0.399621i | ||||||||
\(159\) | 504.193 | 0.251479 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1159.88 | −0.567772 | ||||||||
\(162\) | 207.486i | 0.100627i | ||||||||
\(163\) | 1921.49i | 0.923331i | 0.887054 | + | 0.461665i | \(0.152748\pi\) | ||||
−0.887054 | + | 0.461665i | \(0.847252\pi\) | |||||||
\(164\) | −429.346 | −0.204429 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2615.91 | 1.22310 | ||||||||
\(167\) | − 172.297i | − 0.0798369i | −0.999203 | − | 0.0399185i | \(-0.987290\pi\) | ||||
0.999203 | − | 0.0399185i | \(-0.0127098\pi\) | |||||||
\(168\) | 453.045i | 0.208055i | ||||||||
\(169\) | −216.080 | −0.0983521 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1173.19 | −0.524654 | ||||||||
\(172\) | − 738.833i | − 0.327532i | ||||||||
\(173\) | − 1025.29i | − 0.450587i | −0.974291 | − | 0.225293i | \(-0.927666\pi\) | ||||
0.974291 | − | 0.225293i | \(-0.0723340\pi\) | |||||||
\(174\) | −68.4488 | −0.0298224 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 554.656 | 0.237550 | ||||||||
\(177\) | − 1856.32i | − 0.788302i | ||||||||
\(178\) | 363.430i | 0.153035i | ||||||||
\(179\) | −1658.29 | −0.692437 | −0.346219 | − | 0.938154i | \(-0.612534\pi\) | ||||
−0.346219 | + | 0.938154i | \(0.612534\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2021.81 | −0.830275 | −0.415137 | − | 0.909759i | \(-0.636266\pi\) | ||||
−0.415137 | + | 0.909759i | \(0.636266\pi\) | |||||||
\(182\) | − 785.970i | − 0.320110i | ||||||||
\(183\) | 2359.22i | 0.952996i | ||||||||
\(184\) | 4489.52 | 1.79876 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −40.4318 | −0.0159387 | ||||||||
\(187\) | 909.792i | 0.355778i | ||||||||
\(188\) | − 801.640i | − 0.310987i | ||||||||
\(189\) | −168.648 | −0.0649064 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1440.22 | 0.545607 | 0.272803 | − | 0.962070i | \(-0.412049\pi\) | ||||
0.272803 | + | 0.962070i | \(0.412049\pi\) | |||||||
\(192\) | − 1703.93i | − 0.640473i | ||||||||
\(193\) | − 2798.05i | − 1.04356i | −0.853079 | − | 0.521782i | \(-0.825267\pi\) | ||||
0.853079 | − | 0.521782i | \(-0.174733\pi\) | |||||||
\(194\) | 2045.00 | 0.756817 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 437.266 | 0.159354 | ||||||||
\(197\) | − 458.943i | − 0.165982i | −0.996550 | − | 0.0829908i | \(-0.973553\pi\) | ||||
0.996550 | − | 0.0829908i | \(-0.0264472\pi\) | |||||||
\(198\) | 253.594i | 0.0910208i | ||||||||
\(199\) | 2371.04 | 0.844615 | 0.422308 | − | 0.906453i | \(-0.361220\pi\) | ||||
0.422308 | + | 0.906453i | \(0.361220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1017.05 | −0.356900 | ||||||||
\(202\) | 618.358i | 0.215384i | ||||||||
\(203\) | − 55.6363i | − 0.0192360i | ||||||||
\(204\) | 356.915 | 0.122495 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2992.86 | −1.01225 | ||||||||
\(207\) | 1671.24i | 0.561155i | ||||||||
\(208\) | 2476.95i | 0.825699i | ||||||||
\(209\) | −1433.90 | −0.474568 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4319.87 | 1.40944 | 0.704721 | − | 0.709484i | \(-0.251072\pi\) | ||||
0.704721 | + | 0.709484i | \(0.251072\pi\) | |||||||
\(212\) | − 241.752i | − 0.0783187i | ||||||||
\(213\) | 3362.12i | 1.08154i | ||||||||
\(214\) | −5396.73 | −1.72389 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 652.781 | 0.205630 | ||||||||
\(217\) | − 32.8636i | − 0.0102808i | ||||||||
\(218\) | − 1264.87i | − 0.392973i | ||||||||
\(219\) | 370.290 | 0.114255 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4062.89 | −1.23665 | ||||||||
\(222\) | − 3203.69i | − 0.968547i | ||||||||
\(223\) | − 3837.73i | − 1.15244i | −0.817295 | − | 0.576219i | \(-0.804527\pi\) | ||||
0.817295 | − | 0.576219i | \(-0.195473\pi\) | |||||||
\(224\) | 401.349 | 0.119715 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −435.464 | −0.128171 | ||||||||
\(227\) | 5003.71i | 1.46303i | 0.681825 | + | 0.731515i | \(0.261187\pi\) | ||||
−0.681825 | + | 0.731515i | \(0.738813\pi\) | |||||||
\(228\) | 562.523i | 0.163395i | ||||||||
\(229\) | 277.375 | 0.0800412 | 0.0400206 | − | 0.999199i | \(-0.487258\pi\) | ||||
0.0400206 | + | 0.999199i | \(0.487258\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −206.125 | −0.0587101 | ||||||||
\(232\) | 215.350i | 0.0609415i | ||||||||
\(233\) | 2269.91i | 0.638225i | 0.947717 | + | 0.319113i | \(0.103385\pi\) | ||||
−0.947717 | + | 0.319113i | \(0.896615\pi\) | |||||||
\(234\) | −1132.48 | −0.316379 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −890.072 | −0.245503 | ||||||||
\(237\) | 929.505i | 0.254759i | ||||||||
\(238\) | − 1323.33i | − 0.360416i | ||||||||
\(239\) | 1617.11 | 0.437665 | 0.218832 | − | 0.975762i | \(-0.429775\pi\) | ||||
0.218832 | + | 0.975762i | \(0.429775\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5646.63 | 1.50926 | 0.754629 | − | 0.656151i | \(-0.227817\pi\) | ||||
0.754629 | + | 0.656151i | \(0.227817\pi\) | |||||||
\(242\) | 309.948i | 0.0823314i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 1131.20 | 0.296794 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2293.71 | 0.594478 | ||||||||
\(247\) | − 6403.40i | − 1.64955i | ||||||||
\(248\) | 127.204i | 0.0325705i | ||||||||
\(249\) | 3063.66 | 0.779726 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6217.61 | −1.56355 | −0.781777 | − | 0.623558i | \(-0.785687\pi\) | ||||
−0.781777 | + | 0.623558i | \(0.785687\pi\) | |||||||
\(252\) | 80.8636i | 0.0202140i | ||||||||
\(253\) | 2042.62i | 0.507584i | ||||||||
\(254\) | −2428.82 | −0.599991 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2133.74 | −0.520933 | ||||||||
\(257\) | − 7712.75i | − 1.87202i | −0.351980 | − | 0.936008i | \(-0.614491\pi\) | ||||
0.351980 | − | 0.936008i | \(-0.385509\pi\) | |||||||
\(258\) | 3947.09i | 0.952462i | ||||||||
\(259\) | 2604.01 | 0.624730 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −80.1648 | −0.0190118 | ||||||||
\(262\) | − 3803.49i | − 0.896871i | ||||||||
\(263\) | 206.347i | 0.0483798i | 0.999707 | + | 0.0241899i | \(0.00770063\pi\) | ||||
−0.999707 | + | 0.0241899i | \(0.992299\pi\) | |||||||
\(264\) | 797.844 | 0.186000 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2085.67 | 0.480753 | ||||||||
\(267\) | 425.636i | 0.0975600i | ||||||||
\(268\) | 487.655i | 0.111150i | ||||||||
\(269\) | −1712.47 | −0.388146 | −0.194073 | − | 0.980987i | \(-0.562170\pi\) | ||||
−0.194073 | + | 0.980987i | \(0.562170\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −477.081 | −0.106940 | −0.0534698 | − | 0.998569i | \(-0.517028\pi\) | ||||
−0.0534698 | + | 0.998569i | \(0.517028\pi\) | |||||||
\(272\) | 4170.43i | 0.929666i | ||||||||
\(273\) | − 920.500i | − 0.204070i | ||||||||
\(274\) | 1754.48 | 0.386832 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 801.329 | 0.174762 | ||||||||
\(277\) | − 4283.48i | − 0.929130i | −0.885539 | − | 0.464565i | \(-0.846211\pi\) | ||||
0.885539 | − | 0.464565i | \(-0.153789\pi\) | |||||||
\(278\) | − 2127.33i | − 0.458952i | ||||||||
\(279\) | −47.3523 | −0.0101610 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3477.79 | 0.738319 | 0.369160 | − | 0.929366i | \(-0.379646\pi\) | ||||
0.369160 | + | 0.929366i | \(0.379646\pi\) | |||||||
\(282\) | 4282.62i | 0.904350i | ||||||||
\(283\) | − 6568.27i | − 1.37966i | −0.723973 | − | 0.689829i | \(-0.757686\pi\) | ||||
0.723973 | − | 0.689829i | \(-0.242314\pi\) | |||||||
\(284\) | 1612.08 | 0.336829 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1384.15 | −0.286176 | ||||||||
\(287\) | 1864.36i | 0.383449i | ||||||||
\(288\) | − 578.292i | − 0.118320i | ||||||||
\(289\) | −1927.67 | −0.392360 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2395.03 | 0.482472 | ||||||||
\(292\) | − 177.547i | − 0.0355828i | ||||||||
\(293\) | 8352.29i | 1.66534i | 0.553766 | + | 0.832672i | \(0.313190\pi\) | ||||
−0.553766 | + | 0.832672i | \(0.686810\pi\) | |||||||
\(294\) | −2336.02 | −0.463399 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10079.3 | −1.97921 | ||||||||
\(297\) | 297.000i | 0.0580259i | ||||||||
\(298\) | 3108.81i | 0.604324i | ||||||||
\(299\) | −9121.83 | −1.76431 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3208.26 | −0.614355 | ||||||||
\(302\) | 79.0152i | 0.0150557i | ||||||||
\(303\) | 724.199i | 0.137307i | ||||||||
\(304\) | −6572.89 | −1.24007 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1906.76 | −0.356216 | ||||||||
\(307\) | − 5383.89i | − 1.00090i | −0.865767 | − | 0.500448i | \(-0.833169\pi\) | ||||
0.865767 | − | 0.500448i | \(-0.166831\pi\) | |||||||
\(308\) | 98.8333i | 0.0182843i | ||||||||
\(309\) | −3505.14 | −0.645308 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1790.41 | −0.326447 | −0.163223 | − | 0.986589i | \(-0.552189\pi\) | ||||
−0.163223 | + | 0.986589i | \(0.552189\pi\) | |||||||
\(312\) | 3562.96i | 0.646516i | ||||||||
\(313\) | − 809.076i | − 0.146108i | −0.997328 | − | 0.0730538i | \(-0.976726\pi\) | ||||
0.997328 | − | 0.0730538i | \(-0.0232745\pi\) | |||||||
\(314\) | 884.347 | 0.158938 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 445.682 | 0.0793403 | ||||||||
\(317\) | − 10744.5i | − 1.90370i | −0.306567 | − | 0.951849i | \(-0.599180\pi\) | ||||
0.306567 | − | 0.951849i | \(-0.400820\pi\) | |||||||
\(318\) | 1291.52i | 0.227751i | ||||||||
\(319\) | −97.9792 | −0.0171968 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6320.46 | −1.09898 | ||||||||
\(322\) | − 2971.09i | − 0.514200i | ||||||||
\(323\) | − 10781.4i | − 1.85725i | ||||||||
\(324\) | 116.514 | 0.0199784 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4922.00 | −0.836210 | ||||||||
\(327\) | − 1481.37i | − 0.250521i | ||||||||
\(328\) | − 7216.35i | − 1.21481i | ||||||||
\(329\) | −3480.98 | −0.583322 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3399.12 | 0.564449 | 0.282224 | − | 0.959348i | \(-0.408928\pi\) | ||||
0.282224 | + | 0.959348i | \(0.408928\pi\) | |||||||
\(332\) | − 1468.97i | − 0.242832i | ||||||||
\(333\) | − 3752.05i | − 0.617450i | ||||||||
\(334\) | 441.349 | 0.0723039 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −944.864 | −0.153412 | ||||||||
\(337\) | 11840.0i | 1.91384i | 0.290356 | + | 0.956919i | \(0.406226\pi\) | ||||
−0.290356 | + | 0.956919i | \(0.593774\pi\) | |||||||
\(338\) | − 553.499i | − 0.0890721i | ||||||||
\(339\) | −510.000 | −0.0817091 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −57.8750 | −0.00919093 | ||||||||
\(342\) | − 3005.18i | − 0.475151i | ||||||||
\(343\) | − 4041.20i | − 0.636165i | ||||||||
\(344\) | 12418.1 | 1.94634 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2626.34 | 0.408072 | ||||||||
\(347\) | 2076.67i | 0.321272i | 0.987014 | + | 0.160636i | \(0.0513545\pi\) | ||||
−0.987014 | + | 0.160636i | \(0.948645\pi\) | |||||||
\(348\) | 38.4376i | 0.00592090i | ||||||||
\(349\) | −5837.37 | −0.895322 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1326.32 | −0.201692 | ||||||||
\(352\) | − 706.802i | − 0.107025i | ||||||||
\(353\) | − 2423.64i | − 0.365431i | −0.983166 | − | 0.182715i | \(-0.941511\pi\) | ||||
0.983166 | − | 0.182715i | \(-0.0584887\pi\) | |||||||
\(354\) | 4755.06 | 0.713922 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 204.085 | 0.0303834 | ||||||||
\(357\) | − 1549.84i | − 0.229765i | ||||||||
\(358\) | − 4247.79i | − 0.627103i | ||||||||
\(359\) | 3882.22 | 0.570740 | 0.285370 | − | 0.958417i | \(-0.407884\pi\) | ||||
0.285370 | + | 0.958417i | \(0.407884\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10133.2 | 1.47736 | ||||||||
\(362\) | − 5178.96i | − 0.751935i | ||||||||
\(363\) | 363.000i | 0.0524864i | ||||||||
\(364\) | −441.363 | −0.0635542 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6043.26 | −0.863077 | ||||||||
\(367\) | − 5666.65i | − 0.805986i | −0.915203 | − | 0.402993i | \(-0.867970\pi\) | ||||
0.915203 | − | 0.402993i | \(-0.132030\pi\) | |||||||
\(368\) | 9363.26i | 1.32634i | ||||||||
\(369\) | 2686.31 | 0.378981 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1049.77 | −0.146903 | ||||||||
\(372\) | 22.7046i | 0.00316446i | ||||||||
\(373\) | 174.771i | 0.0242608i | 0.999926 | + | 0.0121304i | \(0.00386132\pi\) | ||||
−0.999926 | + | 0.0121304i | \(0.996139\pi\) | |||||||
\(374\) | −2330.48 | −0.322209 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13473.8 | 1.84802 | ||||||||
\(377\) | − 437.550i | − 0.0597744i | ||||||||
\(378\) | − 432.000i | − 0.0587822i | ||||||||
\(379\) | −252.686 | −0.0342470 | −0.0171235 | − | 0.999853i | \(-0.505451\pi\) | ||||
−0.0171235 | + | 0.999853i | \(0.505451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2844.55 | −0.382495 | ||||||||
\(382\) | 3689.21i | 0.494126i | ||||||||
\(383\) | − 11014.5i | − 1.46950i | −0.678340 | − | 0.734748i | \(-0.737300\pi\) | ||||
0.678340 | − | 0.734748i | \(-0.262700\pi\) | |||||||
\(384\) | 2822.61 | 0.375105 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7167.35 | 0.945099 | ||||||||
\(387\) | 4622.69i | 0.607196i | ||||||||
\(388\) | − 1148.38i | − 0.150258i | ||||||||
\(389\) | −8099.40 | −1.05567 | −0.527835 | − | 0.849347i | \(-0.676996\pi\) | ||||
−0.527835 | + | 0.849347i | \(0.676996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15358.4 | −1.98646 | ||||||||
\(392\) | 7349.47i | 0.946949i | ||||||||
\(393\) | − 4454.51i | − 0.571757i | ||||||||
\(394\) | 1175.61 | 0.150320 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 142.406 | 0.0180712 | ||||||||
\(397\) | 424.353i | 0.0536465i | 0.999640 | + | 0.0268232i | \(0.00853912\pi\) | ||||
−0.999640 | + | 0.0268232i | \(0.991461\pi\) | |||||||
\(398\) | 6073.54i | 0.764922i | ||||||||
\(399\) | 2442.66 | 0.306481 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5904.18 | −0.735263 | −0.367632 | − | 0.929972i | \(-0.619831\pi\) | ||||
−0.367632 | + | 0.929972i | \(0.619831\pi\) | |||||||
\(402\) | − 2605.22i | − 0.323225i | ||||||||
\(403\) | − 258.455i | − 0.0319468i | ||||||||
\(404\) | 347.241 | 0.0427620 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 142.515 | 0.0174210 | ||||||||
\(407\) | − 4585.83i | − 0.558504i | ||||||||
\(408\) | 5998.94i | 0.727921i | ||||||||
\(409\) | −1370.47 | −0.165686 | −0.0828430 | − | 0.996563i | \(-0.526400\pi\) | ||||
−0.0828430 | + | 0.996563i | \(0.526400\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2054.78 | 0.246606 | ||||||||
\(412\) | 1680.65i | 0.200970i | ||||||||
\(413\) | 3864.98i | 0.460493i | ||||||||
\(414\) | −4280.97 | −0.508208 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3156.39 | 0.372007 | ||||||||
\(417\) | − 2491.45i | − 0.292582i | ||||||||
\(418\) | − 3673.00i | − 0.429790i | ||||||||
\(419\) | −1268.73 | −0.147927 | −0.0739635 | − | 0.997261i | \(-0.523565\pi\) | ||||
−0.0739635 | + | 0.997261i | \(0.523565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12241.9 | −1.41719 | −0.708594 | − | 0.705617i | \(-0.750670\pi\) | ||||
−0.708594 | + | 0.705617i | \(0.750670\pi\) | |||||||
\(422\) | 11065.6i | 1.27646i | ||||||||
\(423\) | 5015.66i | 0.576524i | ||||||||
\(424\) | 4063.31 | 0.465405 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8612.26 | −0.979496 | ||||||||
\(427\) | − 4912.05i | − 0.556700i | ||||||||
\(428\) | 3030.55i | 0.342260i | ||||||||
\(429\) | −1621.06 | −0.182437 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8050.11 | 0.899675 | 0.449838 | − | 0.893110i | \(-0.351482\pi\) | ||||
0.449838 | + | 0.893110i | \(0.351482\pi\) | |||||||
\(432\) | 1361.43i | 0.151624i | ||||||||
\(433\) | − 16565.7i | − 1.83856i | −0.393600 | − | 0.919282i | \(-0.628770\pi\) | ||||
0.393600 | − | 0.919282i | \(-0.371230\pi\) | |||||||
\(434\) | 84.1819 | 0.00931073 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −710.293 | −0.0780203 | ||||||||
\(437\) | − 24205.9i | − 2.64971i | ||||||||
\(438\) | 948.517i | 0.103475i | ||||||||
\(439\) | −4705.80 | −0.511607 | −0.255804 | − | 0.966729i | \(-0.582340\pi\) | ||||
−0.255804 | + | 0.966729i | \(0.582340\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2735.86 | −0.295418 | ||||||||
\(442\) | − 10407.3i | − 1.11997i | ||||||||
\(443\) | 15094.0i | 1.61882i | 0.587246 | + | 0.809408i | \(0.300212\pi\) | ||||
−0.587246 | + | 0.809408i | \(0.699788\pi\) | |||||||
\(444\) | −1799.04 | −0.192294 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9830.56 | 1.04370 | ||||||||
\(447\) | 3640.93i | 0.385257i | ||||||||
\(448\) | 3547.71i | 0.374138i | ||||||||
\(449\) | −973.478 | −0.102319 | −0.0511595 | − | 0.998690i | \(-0.516292\pi\) | ||||
−0.0511595 | + | 0.998690i | \(0.516292\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3283.27 | 0.342801 | ||||||||
\(452\) | 244.536i | 0.0254469i | ||||||||
\(453\) | 92.5398i | 0.00959801i | ||||||||
\(454\) | −12817.3 | −1.32499 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9454.75 | −0.970963 | ||||||||
\(457\) | − 62.6577i | − 0.00641358i | −0.999995 | − | 0.00320679i | \(-0.998979\pi\) | ||||
0.999995 | − | 0.00320679i | \(-0.00102075\pi\) | |||||||
\(458\) | 710.510i | 0.0724890i | ||||||||
\(459\) | −2233.12 | −0.227088 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11866.2 | −1.19884 | −0.599419 | − | 0.800436i | \(-0.704602\pi\) | ||||
−0.599419 | + | 0.800436i | \(0.704602\pi\) | |||||||
\(462\) | − 528.000i | − 0.0531705i | ||||||||
\(463\) | − 13144.8i | − 1.31942i | −0.751519 | − | 0.659711i | \(-0.770679\pi\) | ||||
0.751519 | − | 0.659711i | \(-0.229321\pi\) | |||||||
\(464\) | −449.131 | −0.0449361 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5814.48 | −0.578006 | ||||||||
\(467\) | 10176.8i | 1.00840i | 0.863586 | + | 0.504201i | \(0.168213\pi\) | ||||
−0.863586 | + | 0.504201i | \(0.831787\pi\) | |||||||
\(468\) | 635.949i | 0.0628136i | ||||||||
\(469\) | 2117.56 | 0.208486 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1035.72 | 0.101323 | ||||||||
\(472\) | − 14960.1i | − 1.45889i | ||||||||
\(473\) | 5649.96i | 0.549229i | ||||||||
\(474\) | −2380.98 | −0.230721 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −743.121 | −0.0715565 | ||||||||
\(477\) | 1512.58i | 0.145191i | ||||||||
\(478\) | 4142.30i | 0.396369i | ||||||||
\(479\) | −3431.25 | −0.327302 | −0.163651 | − | 0.986518i | \(-0.552327\pi\) | ||||
−0.163651 | + | 0.986518i | \(0.552327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20479.1 | 1.94130 | ||||||||
\(482\) | 14464.1i | 1.36685i | ||||||||
\(483\) | − 3479.64i | − 0.327803i | ||||||||
\(484\) | 174.052 | 0.0163460 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −622.457 | −0.0580972 | ||||||||
\(487\) | 2833.20i | 0.263624i | 0.991275 | + | 0.131812i | \(0.0420795\pi\) | ||||
−0.991275 | + | 0.131812i | \(0.957921\pi\) | |||||||
\(488\) | 19013.0i | 1.76368i | ||||||||
\(489\) | −5764.48 | −0.533085 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2667.29 | −0.245159 | −0.122580 | − | 0.992459i | \(-0.539117\pi\) | ||||
−0.122580 | + | 0.992459i | \(0.539117\pi\) | |||||||
\(492\) | − 1288.04i | − 0.118027i | ||||||||
\(493\) | − 736.700i | − 0.0673008i | ||||||||
\(494\) | 16402.7 | 1.49391 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −265.295 | −0.0240164 | ||||||||
\(497\) | − 7000.18i | − 0.631793i | ||||||||
\(498\) | 7847.74i | 0.706156i | ||||||||
\(499\) | 11137.0 | 0.999120 | 0.499560 | − | 0.866279i | \(-0.333495\pi\) | ||||
0.499560 | + | 0.866279i | \(0.333495\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 516.892 | 0.0460939 | ||||||||
\(502\) | − 15926.7i | − 1.41603i | ||||||||
\(503\) | 8780.30i | 0.778319i | 0.921170 | + | 0.389159i | \(0.127234\pi\) | ||||
−0.921170 | + | 0.389159i | \(0.872766\pi\) | |||||||
\(504\) | −1359.14 | −0.120121 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5232.29 | −0.459691 | ||||||||
\(507\) | − 648.239i | − 0.0567836i | ||||||||
\(508\) | 1363.91i | 0.119121i | ||||||||
\(509\) | −13597.4 | −1.18408 | −0.592039 | − | 0.805910i | \(-0.701677\pi\) | ||||
−0.592039 | + | 0.805910i | \(0.701677\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −770.969 | −0.0667430 | ||||||||
\(512\) | − 12992.6i | − 1.12148i | ||||||||
\(513\) | − 3519.56i | − 0.302909i | ||||||||
\(514\) | 19756.6 | 1.69538 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2216.50 | 0.189101 | ||||||||
\(517\) | 6130.25i | 0.521486i | ||||||||
\(518\) | 6670.30i | 0.565784i | ||||||||
\(519\) | 3075.88 | 0.260146 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14001.3 | 1.17736 | 0.588682 | − | 0.808364i | \(-0.299647\pi\) | ||||
0.588682 | + | 0.808364i | \(0.299647\pi\) | |||||||
\(522\) | − 205.346i | − 0.0172180i | ||||||||
\(523\) | − 14749.8i | − 1.23320i | −0.787275 | − | 0.616602i | \(-0.788509\pi\) | ||||
0.787275 | − | 0.616602i | \(-0.211491\pi\) | |||||||
\(524\) | −2135.86 | −0.178064 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −528.568 | −0.0438149 | ||||||||
\(527\) | − 435.159i | − 0.0359693i | ||||||||
\(528\) | 1663.97i | 0.137150i | ||||||||
\(529\) | −22315.0 | −1.83406 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5568.95 | 0.455126 | ||||||||
\(532\) | − 1171.21i | − 0.0954483i | ||||||||
\(533\) | 14662.2i | 1.19154i | ||||||||
\(534\) | −1090.29 | −0.0883548 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8196.40 | −0.660505 | ||||||||
\(537\) | − 4974.86i | − 0.399779i | ||||||||
\(538\) | − 4386.59i | − 0.351523i | ||||||||
\(539\) | −3343.83 | −0.267215 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1484.06 | 0.117939 | 0.0589694 | − | 0.998260i | \(-0.481219\pi\) | ||||
0.0589694 | + | 0.998260i | \(0.481219\pi\) | |||||||
\(542\) | − 1222.07i | − 0.0968493i | ||||||||
\(543\) | − 6065.42i | − 0.479359i | ||||||||
\(544\) | 5314.40 | 0.418847 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2357.91 | 0.184815 | ||||||||
\(547\) | 16562.2i | 1.29460i | 0.762234 | + | 0.647302i | \(0.224103\pi\) | ||||
−0.762234 | + | 0.647302i | \(0.775897\pi\) | |||||||
\(548\) | − 985.233i | − 0.0768012i | ||||||||
\(549\) | −7077.65 | −0.550212 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1161.09 | 0.0897716 | ||||||||
\(552\) | 13468.6i | 1.03851i | ||||||||
\(553\) | − 1935.30i | − 0.148819i | ||||||||
\(554\) | 10972.3 | 0.841463 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1194.61 | −0.0911197 | ||||||||
\(557\) | 8821.52i | 0.671059i | 0.942030 | + | 0.335529i | \(0.108915\pi\) | ||||
−0.942030 | + | 0.335529i | \(0.891085\pi\) | |||||||
\(558\) | − 121.295i | − 0.00920223i | ||||||||
\(559\) | −25231.2 | −1.90906 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2729.37 | −0.205409 | ||||||||
\(562\) | 8908.55i | 0.668656i | ||||||||
\(563\) | − 5985.53i | − 0.448064i | −0.974582 | − | 0.224032i | \(-0.928078\pi\) | ||||
0.974582 | − | 0.224032i | \(-0.0719220\pi\) | |||||||
\(564\) | 2404.92 | 0.179549 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16825.0 | 1.24948 | ||||||||
\(567\) | − 505.943i | − 0.0374737i | ||||||||
\(568\) | 27095.5i | 2.00158i | ||||||||
\(569\) | 3453.08 | 0.254413 | 0.127206 | − | 0.991876i | \(-0.459399\pi\) | ||||
0.127206 | + | 0.991876i | \(0.459399\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21484.5 | −1.57460 | −0.787302 | − | 0.616568i | \(-0.788523\pi\) | ||||
−0.787302 | + | 0.616568i | \(0.788523\pi\) | |||||||
\(572\) | 777.271i | 0.0568170i | ||||||||
\(573\) | 4320.67i | 0.315006i | ||||||||
\(574\) | −4775.67 | −0.347269 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5111.80 | 0.369777 | ||||||||
\(577\) | 13294.4i | 0.959189i | 0.877490 | + | 0.479594i | \(0.159216\pi\) | ||||
−0.877490 | + | 0.479594i | \(0.840784\pi\) | |||||||
\(578\) | − 4937.82i | − 0.355340i | ||||||||
\(579\) | 8394.14 | 0.602502 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6378.77 | −0.455483 | ||||||||
\(582\) | 6135.01i | 0.436949i | ||||||||
\(583\) | 1848.71i | 0.131330i | ||||||||
\(584\) | 2984.18 | 0.211449 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21394.8 | −1.50821 | ||||||||
\(587\) | − 6695.73i | − 0.470805i | −0.971898 | − | 0.235402i | \(-0.924359\pi\) | ||||
0.971898 | − | 0.235402i | \(-0.0756408\pi\) | |||||||
\(588\) | 1311.80i | 0.0920028i | ||||||||
\(589\) | 685.841 | 0.0479789 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1376.83 | 0.0958295 | ||||||||
\(592\) | − 21021.2i | − 1.45940i | ||||||||
\(593\) | − 10239.6i | − 0.709088i | −0.935039 | − | 0.354544i | \(-0.884636\pi\) | ||||
0.935039 | − | 0.354544i | \(-0.115364\pi\) | |||||||
\(594\) | −760.781 | −0.0525509 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1745.76 | 0.119982 | ||||||||
\(597\) | 7113.11i | 0.487639i | ||||||||
\(598\) | − 23366.0i | − 1.59784i | ||||||||
\(599\) | 23890.8 | 1.62963 | 0.814817 | − | 0.579719i | \(-0.196838\pi\) | ||||
0.814817 | + | 0.579719i | \(0.196838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11343.8 | −0.769920 | −0.384960 | − | 0.922933i | \(-0.625785\pi\) | ||||
−0.384960 | + | 0.922933i | \(0.625785\pi\) | |||||||
\(602\) | − 8218.12i | − 0.556388i | ||||||||
\(603\) | − 3051.14i | − 0.206056i | ||||||||
\(604\) | 44.3712 | 0.00298914 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1855.07 | −0.124352 | ||||||||
\(607\) | 26032.5i | 1.74074i | 0.492399 | + | 0.870369i | \(0.336120\pi\) | ||||
−0.492399 | + | 0.870369i | \(0.663880\pi\) | |||||||
\(608\) | 8375.87i | 0.558695i | ||||||||
\(609\) | 166.909 | 0.0111059 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27376.1 | −1.81263 | ||||||||
\(612\) | 1070.74i | 0.0707226i | ||||||||
\(613\) | − 4568.13i | − 0.300987i | −0.988611 | − | 0.150493i | \(-0.951914\pi\) | ||||
0.988611 | − | 0.150493i | \(-0.0480863\pi\) | |||||||
\(614\) | 13791.1 | 0.906457 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1661.17 | −0.108653 | ||||||||
\(617\) | 12755.9i | 0.832308i | 0.909294 | + | 0.416154i | \(0.136622\pi\) | ||||
−0.909294 | + | 0.416154i | \(0.863378\pi\) | |||||||
\(618\) | − 8978.59i | − 0.584421i | ||||||||
\(619\) | 1138.94 | 0.0739545 | 0.0369772 | − | 0.999316i | \(-0.488227\pi\) | ||||
0.0369772 | + | 0.999316i | \(0.488227\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5013.72 | −0.323983 | ||||||||
\(622\) | − 4586.24i | − 0.295645i | ||||||||
\(623\) | − 886.205i | − 0.0569904i | ||||||||
\(624\) | −7430.85 | −0.476718 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2072.49 | 0.132322 | ||||||||
\(627\) | − 4301.69i | − 0.273992i | ||||||||
\(628\) | − 496.607i | − 0.0315554i | ||||||||
\(629\) | 34480.6 | 2.18574 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7997.36 | 0.504548 | 0.252274 | − | 0.967656i | \(-0.418822\pi\) | ||||
0.252274 | + | 0.967656i | \(0.418822\pi\) | |||||||
\(632\) | 7490.91i | 0.471475i | ||||||||
\(633\) | 12959.6i | 0.813742i | ||||||||
\(634\) | 27522.7 | 1.72408 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 725.255 | 0.0452173 | ||||||||
\(637\) | − 14932.7i | − 0.928814i | ||||||||
\(638\) | − 250.979i | − 0.0155742i | ||||||||
\(639\) | −10086.4 | −0.624430 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −573.115 | −0.0353146 | −0.0176573 | − | 0.999844i | \(-0.505621\pi\) | ||||
−0.0176573 | + | 0.999844i | \(0.505621\pi\) | |||||||
\(642\) | − 16190.2i | − 0.995290i | ||||||||
\(643\) | − 16027.8i | − 0.983009i | −0.870875 | − | 0.491504i | \(-0.836447\pi\) | ||||
0.870875 | − | 0.491504i | \(-0.163553\pi\) | |||||||
\(644\) | −1668.42 | −0.102089 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27617.1 | 1.68201 | ||||||||
\(647\) | 2622.74i | 0.159367i | 0.996820 | + | 0.0796837i | \(0.0253910\pi\) | ||||
−0.996820 | + | 0.0796837i | \(0.974609\pi\) | |||||||
\(648\) | 1958.34i | 0.118721i | ||||||||
\(649\) | 6806.50 | 0.411677 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 98.5908 | 0.00593560 | ||||||||
\(652\) | 2763.97i | 0.166020i | ||||||||
\(653\) | 3102.00i | 0.185897i | 0.995671 | + | 0.0929484i | \(0.0296292\pi\) | ||||
−0.995671 | + | 0.0929484i | \(0.970371\pi\) | |||||||
\(654\) | 3794.62 | 0.226883 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15050.3 | 0.895755 | ||||||||
\(657\) | 1110.87i | 0.0659652i | ||||||||
\(658\) | − 8916.73i | − 0.528283i | ||||||||
\(659\) | 20840.2 | 1.23190 | 0.615948 | − | 0.787787i | \(-0.288773\pi\) | ||||
0.615948 | + | 0.787787i | \(0.288773\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18242.9 | 1.07348 | 0.536738 | − | 0.843749i | \(-0.319657\pi\) | ||||
0.536738 | + | 0.843749i | \(0.319657\pi\) | |||||||
\(662\) | 8707.03i | 0.511191i | ||||||||
\(663\) | − 12188.7i | − 0.713980i | ||||||||
\(664\) | 24690.2 | 1.44302 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9611.06 | 0.559191 | ||||||||
\(667\) | − 1654.01i | − 0.0960171i | ||||||||
\(668\) | − 247.841i | − 0.0143551i | ||||||||
\(669\) | 11513.2 | 0.665361 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8650.46 | −0.497686 | ||||||||
\(672\) | 1204.05i | 0.0691177i | ||||||||
\(673\) | − 12746.6i | − 0.730084i | −0.930991 | − | 0.365042i | \(-0.881055\pi\) | ||||
0.930991 | − | 0.365042i | \(-0.118945\pi\) | |||||||
\(674\) | −30328.7 | −1.73326 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −310.819 | −0.0176843 | ||||||||
\(677\) | 7683.11i | 0.436168i | 0.975930 | + | 0.218084i | \(0.0699807\pi\) | ||||
−0.975930 | + | 0.218084i | \(0.930019\pi\) | |||||||
\(678\) | − 1306.39i | − 0.0739995i | ||||||||
\(679\) | −4986.63 | −0.281840 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15011.1 | −0.844681 | ||||||||
\(682\) | − 148.250i | − 0.00832373i | ||||||||
\(683\) | − 21397.1i | − 1.19874i | −0.800473 | − | 0.599368i | \(-0.795418\pi\) | ||||
0.800473 | − | 0.599368i | \(-0.204582\pi\) | |||||||
\(684\) | −1687.57 | −0.0943359 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10351.8 | 0.576140 | ||||||||
\(687\) | 832.124i | 0.0462118i | ||||||||
\(688\) | 25899.0i | 1.43516i | ||||||||
\(689\) | −8255.84 | −0.456491 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26137.5 | 1.43895 | 0.719477 | − | 0.694516i | \(-0.244381\pi\) | ||||
0.719477 | + | 0.694516i | \(0.244381\pi\) | |||||||
\(692\) | − 1474.83i | − 0.0810181i | ||||||||
\(693\) | − 618.375i | − 0.0338963i | ||||||||
\(694\) | −5319.50 | −0.290959 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −646.051 | −0.0351846 | ||||||||
\(697\) | 24686.7i | 1.34157i | ||||||||
\(698\) | − 14952.7i | − 0.810845i | ||||||||
\(699\) | −6809.72 | −0.368479 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13382.4 | 0.721036 | 0.360518 | − | 0.932752i | \(-0.382600\pi\) | ||||
0.360518 | + | 0.932752i | \(0.382600\pi\) | |||||||
\(702\) | − 3397.45i | − 0.182662i | ||||||||
\(703\) | 54343.9i | 2.91553i | ||||||||
\(704\) | 6247.76 | 0.334476 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6208.27 | 0.330951 | ||||||||
\(707\) | − 1507.83i | − 0.0802092i | ||||||||
\(708\) | − 2670.22i | − 0.141741i | ||||||||
\(709\) | −18164.6 | −0.962179 | −0.481090 | − | 0.876671i | \(-0.659759\pi\) | ||||
−0.481090 | + | 0.876671i | \(0.659759\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2788.52 | −0.147085 | ||||||||
\(712\) | 3430.21i | 0.180552i | ||||||||
\(713\) | − 977.000i | − 0.0513169i | ||||||||
\(714\) | 3970.00 | 0.208086 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2385.36 | −0.124504 | ||||||||
\(717\) | 4851.32i | 0.252686i | ||||||||
\(718\) | 9944.50i | 0.516888i | ||||||||
\(719\) | −9665.62 | −0.501344 | −0.250672 | − | 0.968072i | \(-0.580652\pi\) | ||||
−0.250672 | + | 0.968072i | \(0.580652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7297.94 | 0.376962 | ||||||||
\(722\) | 25956.7i | 1.33796i | ||||||||
\(723\) | 16939.9i | 0.871371i | ||||||||
\(724\) | −2908.26 | −0.149288 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −929.844 | −0.0475341 | ||||||||
\(727\) | 29779.6i | 1.51921i | 0.650385 | + | 0.759605i | \(0.274608\pi\) | ||||
−0.650385 | + | 0.759605i | \(0.725392\pi\) | |||||||
\(728\) | − 7418.33i | − 0.377667i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42481.7 | −2.14944 | ||||||||
\(732\) | 3393.61i | 0.171354i | ||||||||
\(733\) | 35029.5i | 1.76513i | 0.470187 | + | 0.882567i | \(0.344186\pi\) | ||||
−0.470187 | + | 0.882567i | \(0.655814\pi\) | |||||||
\(734\) | 14515.4 | 0.729937 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11931.7 | 0.597564 | ||||||||
\(737\) | − 3729.17i | − 0.186385i | ||||||||
\(738\) | 6881.13i | 0.343222i | ||||||||
\(739\) | −23297.3 | −1.15968 | −0.579842 | − | 0.814729i | \(-0.696886\pi\) | ||||
−0.579842 | + | 0.814729i | \(0.696886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19210.2 | 0.952368 | ||||||||
\(742\) | − 2689.03i | − 0.133042i | ||||||||
\(743\) | 21570.4i | 1.06506i | 0.846411 | + | 0.532530i | \(0.178759\pi\) | ||||
−0.846411 | + | 0.532530i | \(0.821241\pi\) | |||||||
\(744\) | −381.613 | −0.0188046 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −447.684 | −0.0219717 | ||||||||
\(747\) | 9190.99i | 0.450175i | ||||||||
\(748\) | 1308.69i | 0.0639710i | ||||||||
\(749\) | 13159.6 | 0.641980 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28554.8 | 1.38746 | 0.693729 | − | 0.720236i | \(-0.255966\pi\) | ||||
0.693729 | + | 0.720236i | \(0.255966\pi\) | |||||||
\(752\) | 28100.7i | 1.36267i | ||||||||
\(753\) | − 18652.8i | − 0.902719i | ||||||||
\(754\) | 1120.81 | 0.0541344 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −242.591 | −0.0116706 | ||||||||
\(757\) | − 7812.81i | − 0.375114i | −0.982254 | − | 0.187557i | \(-0.939943\pi\) | ||||
0.982254 | − | 0.187557i | \(-0.0600570\pi\) | |||||||
\(758\) | − 647.268i | − 0.0310156i | ||||||||
\(759\) | −6127.87 | −0.293054 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2875.13 | 0.136956 | 0.0684778 | − | 0.997653i | \(-0.478186\pi\) | ||||
0.0684778 | + | 0.997653i | \(0.478186\pi\) | |||||||
\(762\) | − 7286.45i | − 0.346405i | ||||||||
\(763\) | 3084.33i | 0.146344i | ||||||||
\(764\) | 2071.69 | 0.0981033 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28214.3 | 1.33084 | ||||||||
\(767\) | 30396.0i | 1.43095i | ||||||||
\(768\) | − 6401.22i | − 0.300761i | ||||||||
\(769\) | 27657.7 | 1.29696 | 0.648479 | − | 0.761233i | \(-0.275406\pi\) | ||||
0.648479 | + | 0.761233i | \(0.275406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23138.2 | 1.08081 | ||||||||
\(772\) | − 4024.84i | − 0.187639i | ||||||||
\(773\) | − 3929.35i | − 0.182832i | −0.995813 | − | 0.0914160i | \(-0.970861\pi\) | ||||
0.995813 | − | 0.0914160i | \(-0.0291393\pi\) | |||||||
\(774\) | −11841.3 | −0.549904 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 19301.6 | 0.892898 | ||||||||
\(777\) | 7812.02i | 0.360688i | ||||||||
\(778\) | − 20747.0i | − 0.956064i | ||||||||
\(779\) | −38908.0 | −1.78950 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12327.8 | −0.564818 | ||||||||
\(782\) | − 39341.3i | − 1.79903i | ||||||||
\(783\) | − 240.495i | − 0.0109765i | ||||||||
\(784\) | −15327.9 | −0.698247 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 11410.5 | 0.517809 | ||||||||
\(787\) | 21125.7i | 0.956860i | 0.878126 | + | 0.478430i | \(0.158794\pi\) | ||||
−0.878126 | + | 0.478430i | \(0.841206\pi\) | |||||||
\(788\) | − 660.166i | − 0.0298445i | ||||||||
\(789\) | −619.040 | −0.0279321 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1061.86 | 0.0477310 | ||||||||
\(792\) | 2393.53i | 0.107387i | ||||||||
\(793\) | − 38630.7i | − 1.72991i | ||||||||
\(794\) | −1087.00 | −0.0485847 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3410.61 | 0.151867 | ||||||||
\(797\) | − 11696.3i | − 0.519828i | −0.965632 | − | 0.259914i | \(-0.916306\pi\) | ||||
0.965632 | − | 0.259914i | \(-0.0836942\pi\) | |||||||
\(798\) | 6257.00i | 0.277563i | ||||||||
\(799\) | −46093.0 | −2.04087 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1276.91 | −0.0563263 | ||||||||
\(802\) | − 15123.9i | − 0.665888i | ||||||||
\(803\) | 1357.73i | 0.0596678i | ||||||||
\(804\) | −1462.97 | −0.0641727 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 662.045 | 0.0289324 | ||||||||
\(807\) | − 5137.42i | − 0.224096i | ||||||||
\(808\) | 5836.34i | 0.254111i | ||||||||
\(809\) | −14310.2 | −0.621902 | −0.310951 | − | 0.950426i | \(-0.600648\pi\) | ||||
−0.310951 | + | 0.950426i | \(0.600648\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21697.9 | 0.939477 | 0.469739 | − | 0.882806i | \(-0.344348\pi\) | ||||
0.469739 | + | 0.882806i | \(0.344348\pi\) | |||||||
\(812\) | − 80.0299i | − 0.00345874i | ||||||||
\(813\) | − 1431.24i | − 0.0617416i | ||||||||
\(814\) | 11746.9 | 0.505807 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −12511.3 | −0.536743 | ||||||||
\(817\) | − 66954.1i | − 2.86711i | ||||||||
\(818\) | − 3510.54i | − 0.150053i | ||||||||
\(819\) | 2761.50 | 0.117820 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3613.00 | 0.153587 | 0.0767934 | − | 0.997047i | \(-0.475532\pi\) | ||||
0.0767934 | + | 0.997047i | \(0.475532\pi\) | |||||||
\(822\) | 5263.44i | 0.223338i | ||||||||
\(823\) | − 4763.98i | − 0.201776i | −0.994898 | − | 0.100888i | \(-0.967832\pi\) | ||||
0.994898 | − | 0.100888i | \(-0.0321684\pi\) | |||||||
\(824\) | −28248.0 | −1.19425 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9900.36 | −0.417043 | ||||||||
\(827\) | 33571.7i | 1.41161i | 0.708405 | + | 0.705806i | \(0.249415\pi\) | ||||
−0.708405 | + | 0.705806i | \(0.750585\pi\) | |||||||
\(828\) | 2403.99i | 0.100899i | ||||||||
\(829\) | −17980.5 | −0.753303 | −0.376652 | − | 0.926355i | \(-0.622925\pi\) | ||||
−0.376652 | + | 0.926355i | \(0.622925\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12850.4 | 0.536434 | ||||||||
\(832\) | 27900.9i | 1.16261i | ||||||||
\(833\) | − 25142.1i | − 1.04576i | ||||||||
\(834\) | 6381.98 | 0.264976 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2062.58 | −0.0853301 | ||||||||
\(837\) | − 142.057i | − 0.00586643i | ||||||||
\(838\) | − 3249.91i | − 0.133969i | ||||||||
\(839\) | 40139.5 | 1.65169 | 0.825847 | − | 0.563895i | \(-0.190698\pi\) | ||||
0.825847 | + | 0.563895i | \(0.190698\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24309.7 | −0.996747 | ||||||||
\(842\) | − 31358.4i | − 1.28347i | ||||||||
\(843\) | 10433.4i | 0.426269i | ||||||||
\(844\) | 6213.91 | 0.253426 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12847.9 | −0.522127 | ||||||||
\(847\) | − 755.792i | − 0.0306603i | ||||||||
\(848\) | 8474.36i | 0.343173i | ||||||||
\(849\) | 19704.8 | 0.796546 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 77414.4 | 3.11837 | ||||||||
\(852\) | 4836.24i | 0.194468i | ||||||||
\(853\) | − 15369.2i | − 0.616919i | −0.951237 | − | 0.308459i | \(-0.900187\pi\) | ||||
0.951237 | − | 0.308459i | \(-0.0998134\pi\) | |||||||
\(854\) | 12582.5 | 0.504173 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −50936.8 | −2.03386 | ||||||||
\(857\) | − 10324.9i | − 0.411541i | −0.978600 | − | 0.205770i | \(-0.934030\pi\) | ||||
0.978600 | − | 0.205770i | \(-0.0659700\pi\) | |||||||
\(858\) | − 4152.44i | − 0.165224i | ||||||||
\(859\) | 27112.5 | 1.07691 | 0.538455 | − | 0.842655i | \(-0.319008\pi\) | ||||
0.538455 | + | 0.842655i | \(0.319008\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5593.09 | −0.221384 | ||||||||
\(862\) | 20620.8i | 0.814787i | ||||||||
\(863\) | 30463.6i | 1.20161i | 0.799394 | + | 0.600807i | \(0.205154\pi\) | ||||
−0.799394 | + | 0.600807i | \(0.794846\pi\) | |||||||
\(864\) | 1734.88 | 0.0683122 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 42434.0 | 1.66509 | ||||||||
\(867\) | − 5783.00i | − 0.226529i | ||||||||
\(868\) | − 47.2726i | − 0.00184854i | ||||||||
\(869\) | −3408.19 | −0.133044 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16653.5 | 0.647855 | ||||||||
\(872\) | − 11938.4i | − 0.463631i | ||||||||
\(873\) | 7185.10i | 0.278555i | ||||||||
\(874\) | 62004.6 | 2.39970 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 532.642 | 0.0205437 | ||||||||
\(877\) | 5086.12i | 0.195833i | 0.995195 | + | 0.0979167i | \(0.0312179\pi\) | ||||
−0.995195 | + | 0.0979167i | \(0.968782\pi\) | |||||||
\(878\) | − 12054.2i | − 0.463335i | ||||||||
\(879\) | −25056.9 | −0.961487 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10625.5 | −0.406338 | −0.203169 | − | 0.979144i | \(-0.565124\pi\) | ||||
−0.203169 | + | 0.979144i | \(0.565124\pi\) | |||||||
\(882\) | − 7008.06i | − 0.267544i | ||||||||
\(883\) | 13112.2i | 0.499728i | 0.968281 | + | 0.249864i | \(0.0803859\pi\) | ||||
−0.968281 | + | 0.249864i | \(0.919614\pi\) | |||||||
\(884\) | −5844.25 | −0.222357 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38664.0 | −1.46607 | ||||||||
\(887\) | 14442.8i | 0.546719i | 0.961912 | + | 0.273360i | \(0.0881349\pi\) | ||||
−0.961912 | + | 0.273360i | \(0.911865\pi\) | |||||||
\(888\) | − 30237.8i | − 1.14270i | ||||||||
\(889\) | 5922.54 | 0.223437 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | − 5520.38i | − 0.207215i | ||||||||
\(893\) | − 72645.8i | − 2.72228i | ||||||||
\(894\) | −9326.43 | −0.348906 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5876.86 | −0.219121 | ||||||||
\(897\) | − 27365.5i | − 1.01863i | ||||||||
\(898\) | − 2493.61i | − 0.0926648i | ||||||||
\(899\) | 46.8641 | 0.00173860 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13900.3 | −0.513970 | ||||||||
\(902\) | 8410.27i | 0.310456i | ||||||||
\(903\) | − 9624.77i | − 0.354698i | ||||||||
\(904\) | −4110.10 | −0.151217 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −237.045 | −0.00869239 | ||||||||
\(907\) | 44981.9i | 1.64675i | 0.567499 | + | 0.823374i | \(0.307911\pi\) | ||||
−0.567499 | + | 0.823374i | \(0.692089\pi\) | |||||||
\(908\) | 7197.57i | 0.263062i | ||||||||
\(909\) | −2172.60 | −0.0792745 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6841.96 | 0.248830 | 0.124415 | − | 0.992230i | \(-0.460295\pi\) | ||||
0.124415 | + | 0.992230i | \(0.460295\pi\) | |||||||
\(912\) | − 19718.7i | − 0.715954i | ||||||||
\(913\) | 11233.4i | 0.407199i | ||||||||
\(914\) | 160.501 | 0.00580843 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 398.989 | 0.0143919 | ||||||||
\(917\) | 9274.61i | 0.333996i | ||||||||
\(918\) | − 5720.27i | − 0.205661i | ||||||||
\(919\) | 4753.54 | 0.170625 | 0.0853127 | − | 0.996354i | \(-0.472811\pi\) | ||||
0.0853127 | + | 0.996354i | \(0.472811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16151.7 | 0.577868 | ||||||||
\(922\) | − 30395.9i | − 1.08572i | ||||||||
\(923\) | − 55052.7i | − 1.96325i | ||||||||
\(924\) | −296.500 | −0.0105564 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 33671.2 | 1.19493 | ||||||||
\(927\) | − 10515.4i | − 0.372569i | ||||||||
\(928\) | 572.330i | 0.0202453i | ||||||||
\(929\) | 7507.93 | 0.265153 | 0.132576 | − | 0.991173i | \(-0.457675\pi\) | ||||
0.132576 | + | 0.991173i | \(0.457675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39625.7 | 1.39493 | ||||||||
\(932\) | 3265.14i | 0.114757i | ||||||||
\(933\) | − 5371.24i | − 0.188474i | ||||||||
\(934\) | −26068.3 | −0.913256 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10688.9 | −0.373266 | ||||||||
\(937\) | − 8540.47i | − 0.297764i | −0.988855 | − | 0.148882i | \(-0.952433\pi\) | ||||
0.988855 | − | 0.148882i | \(-0.0475675\pi\) | |||||||
\(938\) | 5424.24i | 0.188814i | ||||||||
\(939\) | 2427.23 | 0.0843552 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9101.13 | 0.315290 | 0.157645 | − | 0.987496i | \(-0.449610\pi\) | ||||
0.157645 | + | 0.987496i | \(0.449610\pi\) | |||||||
\(942\) | 2653.04i | 0.0917630i | ||||||||
\(943\) | 55425.5i | 1.91400i | ||||||||
\(944\) | 31200.6 | 1.07573 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14472.7 | −0.497407 | ||||||||
\(947\) | − 47540.0i | − 1.63130i | −0.578546 | − | 0.815650i | \(-0.696380\pi\) | ||||
0.578546 | − | 0.815650i | \(-0.303620\pi\) | |||||||
\(948\) | 1337.04i | 0.0458072i | ||||||||
\(949\) | −6063.26 | −0.207399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32233.6 | 1.09910 | ||||||||
\(952\) | − 12490.2i | − 0.425221i | ||||||||
\(953\) | 47370.7i | 1.61016i | 0.593164 | + | 0.805082i | \(0.297879\pi\) | ||||
−0.593164 | + | 0.805082i | \(0.702121\pi\) | |||||||
\(954\) | −3874.55 | −0.131492 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2326.12 | 0.0786947 | ||||||||
\(957\) | − 293.938i | − 0.00992859i | ||||||||
\(958\) | − 8789.33i | − 0.296420i | ||||||||
\(959\) | −4278.20 | −0.144057 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29763.3 | −0.999071 | ||||||||
\(962\) | 52458.4i | 1.75813i | ||||||||
\(963\) | − 18961.4i | − 0.634498i | ||||||||
\(964\) | 8122.38 | 0.271374 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8913.27 | 0.296874 | ||||||||
\(967\) | 36171.6i | 1.20290i | 0.798912 | + | 0.601448i | \(0.205409\pi\) | ||||
−0.798912 | + | 0.601448i | \(0.794591\pi\) | |||||||
\(968\) | 2925.43i | 0.0971351i | ||||||||
\(969\) | 32344.1 | 1.07228 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31713.2 | −1.04812 | −0.524060 | − | 0.851681i | \(-0.675583\pi\) | ||||
−0.524060 | + | 0.851681i | \(0.675583\pi\) | |||||||
\(972\) | 349.543i | 0.0115346i | ||||||||
\(973\) | 5187.37i | 0.170914i | ||||||||
\(974\) | −7257.40 | −0.238750 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39653.1 | −1.30048 | ||||||||
\(977\) | − 22800.5i | − 0.746626i | −0.927706 | − | 0.373313i | \(-0.878222\pi\) | ||||
0.927706 | − | 0.373313i | \(-0.121778\pi\) | |||||||
\(978\) | − 14766.0i | − 0.482786i | ||||||||
\(979\) | −1560.67 | −0.0509490 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4444.12 | 0.144638 | ||||||||
\(982\) | − 6832.41i | − 0.222027i | ||||||||
\(983\) | − 44597.4i | − 1.44704i | −0.690305 | − | 0.723518i | \(-0.742524\pi\) | ||||
0.690305 | − | 0.723518i | \(-0.257476\pi\) | |||||||
\(984\) | 21649.1 | 0.701369 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1887.10 | 0.0609507 | ||||||||
\(987\) | − 10443.0i | − 0.336781i | ||||||||
\(988\) | − 9210.95i | − 0.296599i | ||||||||
\(989\) | −95378.1 | −3.06658 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34788.1 | −1.11512 | −0.557558 | − | 0.830138i | \(-0.688261\pi\) | ||||
−0.557558 | + | 0.830138i | \(0.688261\pi\) | |||||||
\(992\) | 338.068i | 0.0108202i | ||||||||
\(993\) | 10197.4i | 0.325885i | ||||||||
\(994\) | 17931.3 | 0.572180 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4406.92 | 0.140199 | ||||||||
\(997\) | 20360.5i | 0.646765i | 0.946268 | + | 0.323383i | \(0.104820\pi\) | ||||
−0.946268 | + | 0.323383i | \(0.895180\pi\) | |||||||
\(998\) | 28528.0i | 0.904849i | ||||||||
\(999\) | 11256.1 | 0.356485 |
(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 | 825.4.c.j.199.4 | 4 | ||
5.2 | odd | 4 | 165.4.a.c.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 825.4.a.m.1.2 | 2 | |||
5.4 | even | 2 | inner | 825.4.c.j.199.1 | 4 | ||
15.2 | even | 4 | 495.4.a.d.1.2 | 2 | |||
15.8 | even | 4 | 2475.4.a.n.1.1 | 2 | |||
55.32 | even | 4 | 1815.4.a.n.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.c.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
495.4.a.d.1.2 | 2 | 15.2 | even | 4 | |||
825.4.a.m.1.2 | 2 | 5.3 | odd | 4 | |||
825.4.c.j.199.1 | 4 | 5.4 | even | 2 | inner | ||
825.4.c.j.199.4 | 4 | 1.1 | even | 1 | trivial | ||
1815.4.a.n.1.2 | 2 | 55.32 | even | 4 | |||
2475.4.a.n.1.1 | 2 | 15.8 | even | 4 |