Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(73,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.fn (of order \(12\), degree \(4\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 460.3 | ||
Character | \(\chi\) | \(=\) | 819.460 |
Dual form | 819.2.fn.e.73.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.423548 | − | 1.58070i | −0.299493 | − | 1.11772i | −0.937583 | − | 0.347762i | \(-0.886942\pi\) |
0.638089 | − | 0.769962i | \(-0.279725\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.587174 | + | 0.339005i | −0.293587 | + | 0.169502i | ||||
\(5\) | 2.77274 | − | 0.742954i | 1.24001 | − | 0.332259i | 0.421539 | − | 0.906810i | \(-0.361490\pi\) |
0.818469 | + | 0.574551i | \(0.194823\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.92960 | + | 1.81015i | 0.729321 | + | 0.684172i | ||||
\(8\) | −1.52975 | − | 1.52975i | −0.540847 | − | 0.540847i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.34878 | − | 4.06820i | −0.742749 | − | 1.28648i | ||||
\(11\) | −0.894725 | + | 3.33916i | −0.269770 | + | 1.00679i | 0.689496 | + | 0.724290i | \(0.257832\pi\) |
−0.959266 | + | 0.282505i | \(0.908835\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.29273 | − | 2.78269i | 0.635890 | − | 0.771780i | ||||
\(14\) | 2.04403 | − | 3.81681i | 0.546289 | − | 1.02008i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.44816 | + | 4.24034i | −0.612040 | + | 1.06008i | ||||
\(17\) | −3.22444 | − | 5.58489i | −0.782040 | − | 1.35453i | −0.930751 | − | 0.365653i | \(-0.880846\pi\) |
0.148711 | − | 0.988881i | \(-0.452488\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.93592 | − | 0.786677i | 0.673546 | − | 0.180476i | 0.0941943 | − | 0.995554i | \(-0.469973\pi\) |
0.579352 | + | 0.815078i | \(0.303306\pi\) | |||||||
\(20\) | −1.37622 | + | 1.37622i | −0.307731 | + | 0.307731i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.65717 | 1.20611 | ||||||||
\(23\) | 2.97203 | + | 1.71590i | 0.619712 | + | 0.357791i | 0.776757 | − | 0.629801i | \(-0.216863\pi\) |
−0.157045 | + | 0.987591i | \(0.550197\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.80599 | − | 1.62004i | 0.561198 | − | 0.324008i | ||||
\(26\) | −5.36969 | − | 2.44553i | −1.05308 | − | 0.479607i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.74666 | − | 0.408727i | −0.330088 | − | 0.0772422i | ||||
\(29\) | 4.40371 | 0.817748 | 0.408874 | − | 0.912591i | \(-0.365921\pi\) | ||||
0.408874 | + | 0.912591i | \(0.365921\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.868206 | − | 3.24019i | 0.155934 | − | 0.581955i | −0.843089 | − | 0.537774i | \(-0.819265\pi\) |
0.999024 | − | 0.0441812i | \(-0.0140679\pi\) | |||||||
\(32\) | 3.56028 | + | 0.953974i | 0.629374 | + | 0.168640i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.46233 | + | 7.46233i | −1.27978 | + | 1.27978i | ||||
\(35\) | 6.69515 | + | 3.58547i | 1.13169 | + | 0.606055i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.75982 | − | 1.00744i | 0.618110 | − | 0.165622i | 0.0638414 | − | 0.997960i | \(-0.479665\pi\) |
0.554268 | + | 0.832338i | \(0.312998\pi\) | |||||||
\(38\) | −2.48700 | − | 4.30762i | −0.403445 | − | 0.698787i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.37812 | − | 3.10506i | −0.850356 | − | 0.490953i | ||||
\(41\) | 3.03989 | + | 3.03989i | 0.474751 | + | 0.474751i | 0.903448 | − | 0.428697i | \(-0.141027\pi\) |
−0.428697 | + | 0.903448i | \(0.641027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.48958i | − | 0.684654i | −0.939581 | − | 0.342327i | \(-0.888785\pi\) | ||
0.939581 | − | 0.342327i | \(-0.111215\pi\) | |||||||
\(44\) | −0.606632 | − | 2.26398i | −0.0914533 | − | 0.341308i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.45353 | − | 5.42467i | 0.214312 | − | 0.799823i | ||||
\(47\) | 1.47790 | + | 5.51561i | 0.215574 | + | 0.804535i | 0.985964 | + | 0.166961i | \(0.0533953\pi\) |
−0.770389 | + | 0.637574i | \(0.779938\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.446725 | + | 6.98573i | 0.0638179 | + | 0.997962i | ||||
\(50\) | −3.74927 | − | 3.74927i | −0.530227 | − | 0.530227i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.402887 | + | 2.41117i | −0.0558704 | + | 0.334369i | ||||
\(53\) | −5.72526 | − | 9.91644i | −0.786425 | − | 1.36213i | −0.928144 | − | 0.372221i | \(-0.878596\pi\) |
0.141719 | − | 0.989907i | \(-0.454737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.92337i | 1.33807i | ||||||||
\(56\) | −0.182733 | − | 5.72087i | −0.0244187 | − | 0.764483i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.86518 | − | 6.96095i | −0.244910 | − | 0.914018i | ||||
\(59\) | −2.86050 | − | 0.766469i | −0.372405 | − | 0.0997857i | 0.0677619 | − | 0.997702i | \(-0.478414\pi\) |
−0.440167 | + | 0.897916i | \(0.645081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.03504 | − | 1.75228i | −0.388598 | − | 0.224357i | 0.292955 | − | 0.956126i | \(-0.405361\pi\) |
−0.681552 | + | 0.731769i | \(0.738695\pi\) | |||||||
\(62\) | −5.48950 | −0.697167 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.76085i | 0.470107i | ||||||||
\(65\) | 4.28975 | − | 9.41908i | 0.532078 | − | 1.16829i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.04645 | − | 1.88809i | −0.860861 | − | 0.230667i | −0.198729 | − | 0.980054i | \(-0.563681\pi\) |
−0.662132 | + | 0.749387i | \(0.730348\pi\) | |||||||
\(68\) | 3.78661 | + | 2.18620i | 0.459193 | + | 0.265115i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.83184 | − | 12.1016i | 0.338470 | − | 1.44642i | ||||
\(71\) | −8.31408 | + | 8.31408i | −0.986700 | + | 0.986700i | −0.999913 | − | 0.0132127i | \(-0.995794\pi\) |
0.0132127 | + | 0.999913i | \(0.495794\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.51174 | + | 1.20892i | 0.528059 | + | 0.141493i | 0.512992 | − | 0.858393i | \(-0.328537\pi\) |
0.0150673 | + | 0.999886i | \(0.495204\pi\) | |||||||
\(74\) | −3.18492 | − | 5.51645i | −0.370240 | − | 0.641274i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.45721 | + | 1.45721i | −0.167153 | + | 0.167153i | ||||
\(77\) | −7.77084 | + | 4.82366i | −0.885569 | + | 0.549708i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.543920 | + | 0.942097i | −0.0611957 | + | 0.105994i | −0.895000 | − | 0.446066i | \(-0.852825\pi\) |
0.833804 | + | 0.552060i | \(0.186158\pi\) | |||||||
\(80\) | −3.63774 | + | 13.5762i | −0.406712 | + | 1.51787i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.51762 | − | 6.09269i | 0.388456 | − | 0.672825i | ||||
\(83\) | −2.01261 | − | 2.01261i | −0.220913 | − | 0.220913i | 0.587970 | − | 0.808883i | \(-0.299927\pi\) |
−0.808883 | + | 0.587970i | \(0.799927\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.0898 | − | 13.0898i | −1.41979 | − | 1.41979i | ||||
\(86\) | −7.09668 | + | 1.90155i | −0.765255 | + | 0.205049i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.47677 | − | 3.73937i | 0.690426 | − | 0.398618i | ||||
\(89\) | −1.28423 | − | 4.79280i | −0.136128 | − | 0.508036i | −0.999991 | − | 0.00430871i | \(-0.998628\pi\) |
0.863863 | − | 0.503727i | \(-0.168038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.46115 | − | 1.21930i | 0.991798 | − | 0.127817i | ||||
\(92\) | −2.32680 | −0.242586 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.09257 | − | 4.67225i | 0.834685 | − | 0.481906i | ||||
\(95\) | 7.55608 | − | 4.36250i | 0.775237 | − | 0.447584i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.20816 | − | 3.20816i | −0.325739 | − | 0.325739i | 0.525225 | − | 0.850964i | \(-0.323981\pi\) |
−0.850964 | + | 0.525225i | \(0.823981\pi\) | |||||||
\(98\) | 10.8531 | − | 3.66493i | 1.09633 | − | 0.370214i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.09840 | + | 1.90249i | −0.109840 | + | 0.190249i | ||||
\(101\) | 4.57037 | + | 7.91611i | 0.454769 | + | 0.787682i | 0.998675 | − | 0.0514637i | \(-0.0163887\pi\) |
−0.543906 | + | 0.839146i | \(0.683055\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.56180 | + | 4.43716i | −0.252421 | + | 0.437207i | −0.964192 | − | 0.265205i | \(-0.914560\pi\) |
0.711771 | + | 0.702412i | \(0.247894\pi\) | |||||||
\(104\) | −7.76411 | + | 0.749511i | −0.761334 | + | 0.0734956i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.2500 | + | 13.2500i | −1.28696 | + | 1.28696i | ||||
\(107\) | −6.27683 | + | 10.8718i | −0.606804 | + | 1.05102i | 0.384960 | + | 0.922933i | \(0.374215\pi\) |
−0.991764 | + | 0.128082i | \(0.959118\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.8614 | − | 5.05389i | −1.80659 | − | 0.484075i | −0.811617 | − | 0.584190i | \(-0.801412\pi\) |
−0.994976 | + | 0.100114i | \(0.968079\pi\) | |||||||
\(110\) | 15.6859 | − | 4.20302i | 1.49559 | − | 0.400742i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.3996 | + | 3.75063i | −1.17165 | + | 0.354401i | ||||
\(113\) | −0.000230976 | 0 | −2.17284e−5 | 0 | −1.08642e−5 | − | 1.00000i | \(-0.500003\pi\) | ||
−1.08642e−5 | 1.00000i | \(0.500003\pi\) | ||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.51552 | + | 2.54968i | 0.887327 | + | 0.237759i | ||||
\(116\) | −2.58574 | + | 1.49288i | −0.240080 | + | 0.138610i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.84623i | 0.446132i | ||||||||
\(119\) | 3.88760 | − | 16.6133i | 0.356375 | − | 1.52294i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.823180 | − | 0.475263i | −0.0748345 | − | 0.0432057i | ||||
\(122\) | −1.48435 | + | 5.53967i | −0.134387 | + | 0.501539i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.588652 | + | 2.19688i | 0.0528625 | + | 0.197286i | ||||
\(125\) | −3.57226 | + | 3.57226i | −0.319513 | + | 0.319513i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4887i | 1.10820i | 0.832452 | + | 0.554098i | \(0.186937\pi\) | ||||
−0.832452 | + | 0.554098i | \(0.813063\pi\) | |||||||
\(128\) | 13.0653 | − | 3.50085i | 1.15482 | − | 0.309434i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −16.7057 | − | 2.79138i | −1.46518 | − | 0.244820i | ||||
\(131\) | 11.7665 | + | 6.79340i | 1.02805 | + | 0.593542i | 0.916424 | − | 0.400209i | \(-0.131062\pi\) |
0.111621 | + | 0.993751i | \(0.464396\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.08915 | + | 3.79647i | 0.614708 | + | 0.329196i | ||||
\(134\) | 11.9380i | 1.03129i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.61089 | + | 13.4760i | −0.309631 | + | 1.15556i | ||||
\(137\) | −0.349865 | + | 1.30571i | −0.0298910 | + | 0.111555i | −0.979260 | − | 0.202610i | \(-0.935058\pi\) |
0.949369 | + | 0.314164i | \(0.101724\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.8190i | 1.59621i | 0.602521 | + | 0.798103i | \(0.294163\pi\) | ||||
−0.602521 | + | 0.798103i | \(0.705837\pi\) | |||||||
\(140\) | −5.14670 | + | 0.164393i | −0.434976 | + | 0.0138938i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.6635 | + | 9.62067i | 1.39837 | + | 0.807349i | ||||
\(143\) | 7.24049 | + | 10.1456i | 0.605480 | + | 0.848414i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.2104 | − | 3.27175i | 1.01401 | − | 0.271704i | ||||
\(146\) | − | 7.64375i | − | 0.632601i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.86614 | + | 1.86614i | −0.153396 | + | 0.153396i | ||||
\(149\) | 5.52045 | + | 20.6026i | 0.452253 | + | 1.68783i | 0.696040 | + | 0.718003i | \(0.254944\pi\) |
−0.243787 | + | 0.969829i | \(0.578390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.36658 | − | 16.2963i | 0.355348 | − | 1.32618i | −0.524699 | − | 0.851288i | \(-0.675822\pi\) |
0.880047 | − | 0.474887i | \(-0.157511\pi\) | |||||||
\(152\) | −5.69463 | − | 3.28779i | −0.461895 | − | 0.266675i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.9161 | + | 10.2403i | 0.879644 | + | 0.825189i | ||||
\(155\) | − | 9.62925i | − | 0.773440i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.46297 | + | 5.46345i | −0.755227 | + | 0.436031i | −0.827580 | − | 0.561348i | \(-0.810283\pi\) |
0.0723522 | + | 0.997379i | \(0.476949\pi\) | |||||||
\(158\) | 1.71955 | + | 0.460752i | 0.136800 | + | 0.0366554i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.5805 | 0.836462 | ||||||||
\(161\) | 2.62880 | + | 8.69084i | 0.207178 | + | 0.684934i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.37856 | − | 2.24503i | 0.656259 | − | 0.175844i | 0.0847019 | − | 0.996406i | \(-0.473006\pi\) |
0.571557 | + | 0.820562i | \(0.306340\pi\) | |||||||
\(164\) | −2.81548 | − | 0.754405i | −0.219852 | − | 0.0589091i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.32890 | + | 4.03377i | −0.180758 | + | 0.313082i | ||||
\(167\) | 8.00174 | − | 8.00174i | 0.619193 | − | 0.619193i | −0.326131 | − | 0.945324i | \(-0.605745\pi\) |
0.945324 | + | 0.326131i | \(0.105745\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.48674 | − | 12.7599i | −0.191288 | − | 0.981534i | ||||
\(170\) | −15.1470 | + | 26.2353i | −1.16172 | + | 2.01216i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.52199 | + | 2.63616i | 0.116050 | + | 0.201005i | ||||
\(173\) | −1.63833 | + | 2.83768i | −0.124560 | + | 0.215745i | −0.921561 | − | 0.388234i | \(-0.873085\pi\) |
0.797001 | + | 0.603978i | \(0.206419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.34696 | + | 1.95323i | 0.630971 | + | 0.147650i | ||||
\(176\) | −11.9687 | − | 11.9687i | −0.902178 | − | 0.902178i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.03205 | + | 4.05996i | −0.527075 | + | 0.304307i | ||||
\(179\) | 1.94863 | − | 1.12504i | 0.145648 | − | 0.0840897i | −0.425405 | − | 0.905003i | \(-0.639868\pi\) |
0.571053 | + | 0.820913i | \(0.306535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.5420 | −1.15523 | −0.577615 | − | 0.816310i | \(-0.696016\pi\) | ||||
−0.577615 | + | 0.816310i | \(0.696016\pi\) | |||||||
\(182\) | −5.93459 | − | 14.4388i | −0.439901 | − | 1.07028i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.92156 | − | 7.17136i | −0.141659 | − | 0.528679i | ||||
\(185\) | 9.67652 | − | 5.58674i | 0.711432 | − | 0.410745i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.5338 | − | 5.76997i | 1.57471 | − | 0.421942i | ||||
\(188\) | −2.73761 | − | 2.73761i | −0.199660 | − | 0.199660i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.0962 | − | 10.0962i | −0.732454 | − | 0.732454i | ||||
\(191\) | −1.18897 | + | 2.05936i | −0.0860308 | + | 0.149010i | −0.905830 | − | 0.423641i | \(-0.860752\pi\) |
0.819799 | + | 0.572651i | \(0.194085\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.02038 | + | 7.54017i | −0.145430 | + | 0.542753i | 0.854306 | + | 0.519771i | \(0.173983\pi\) |
−0.999736 | + | 0.0229822i | \(0.992684\pi\) | |||||||
\(194\) | −3.71233 | + | 6.42995i | −0.266530 | + | 0.461643i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.63050 | − | 3.95039i | −0.187893 | − | 0.282171i | ||||
\(197\) | 10.9402 | − | 10.9402i | 0.779454 | − | 0.779454i | −0.200284 | − | 0.979738i | \(-0.564187\pi\) |
0.979738 | + | 0.200284i | \(0.0641866\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0868 | − | 17.4708i | −0.715031 | − | 1.23847i | −0.962947 | − | 0.269689i | \(-0.913079\pi\) |
0.247916 | − | 0.968781i | \(-0.420254\pi\) | |||||||
\(200\) | −6.77070 | − | 1.81420i | −0.478761 | − | 0.128284i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.5772 | − | 10.5772i | 0.744212 | − | 0.744212i | ||||
\(203\) | 8.49741 | + | 7.97137i | 0.596401 | + | 0.559480i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.6873 | + | 6.17033i | 0.746435 | + | 0.430954i | ||||
\(206\) | 8.09887 | + | 2.17009i | 0.564275 | + | 0.151197i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.18657 | + | 16.5344i | 0.428962 | + | 1.14646i | ||||
\(209\) | 10.5074i | 0.726809i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.36943 | 0.163118 | 0.0815591 | − | 0.996669i | \(-0.474010\pi\) | ||||
0.0815591 | + | 0.996669i | \(0.474010\pi\) | |||||||
\(212\) | 6.72344 | + | 3.88178i | 0.461768 | + | 0.266602i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.8436 | + | 5.31707i | 1.35648 | + | 0.363468i | ||||
\(215\) | −3.33555 | − | 12.4484i | −0.227483 | − | 0.848976i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.54051 | − | 4.68069i | 0.511883 | − | 0.317746i | ||||
\(218\) | 31.9548i | 2.16425i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.36407 | − | 5.82674i | −0.226806 | − | 0.392839i | ||||
\(221\) | −22.9338 | − | 3.83205i | −1.54269 | − | 0.257771i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.67825 | + | 9.67825i | 0.648103 | + | 0.648103i | 0.952534 | − | 0.304431i | \(-0.0984663\pi\) |
−0.304431 | + | 0.952534i | \(0.598466\pi\) | |||||||
\(224\) | 5.14309 | + | 8.28542i | 0.343637 | + | 0.553593i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.78292e−5 | 0 | 0.000365104i | 6.50750e−6 | 0 | 2.42863e-5i | ||||
\(227\) | 3.37455 | − | 12.5940i | 0.223977 | − | 0.835894i | −0.758835 | − | 0.651283i | \(-0.774231\pi\) |
0.982812 | − | 0.184611i | \(-0.0591024\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.93373 | + | 14.6809i | 0.259948 | + | 0.970139i | 0.965270 | + | 0.261253i | \(0.0841356\pi\) |
−0.705322 | + | 0.708887i | \(0.749198\pi\) | |||||||
\(230\) | − | 16.1211i | − | 1.06299i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.73656 | − | 6.73656i | −0.442277 | − | 0.442277i | ||||
\(233\) | 6.69859 | + | 3.86743i | 0.438839 | + | 0.253364i | 0.703105 | − | 0.711086i | \(-0.251796\pi\) |
−0.264266 | + | 0.964450i | \(0.585130\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.19569 | + | 14.1954i | 0.534628 | + | 0.926003i | ||||
\(236\) | 1.93945 | − | 0.519673i | 0.126247 | − | 0.0338278i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −27.9073 | + | 0.891400i | −1.80896 | + | 0.0577809i | ||||
\(239\) | −2.10971 | + | 2.10971i | −0.136466 | + | 0.136466i | −0.772040 | − | 0.635574i | \(-0.780763\pi\) |
0.635574 | + | 0.772040i | \(0.280763\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.5066 | + | 6.83448i | 1.64303 | + | 0.440247i | 0.957648 | − | 0.287941i | \(-0.0929707\pi\) |
0.685377 | + | 0.728188i | \(0.259637\pi\) | |||||||
\(242\) | −0.402593 | + | 1.50250i | −0.0258797 | + | 0.0965843i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.37613 | 0.152116 | ||||||||
\(245\) | 6.42873 | + | 19.0377i | 0.410717 | + | 1.21628i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.54220 | − | 9.97340i | 0.289013 | − | 0.634592i | ||||
\(248\) | −6.28480 | + | 3.62853i | −0.399085 | + | 0.230412i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.15971 | + | 4.13366i | 0.452820 | + | 0.261436i | ||||
\(251\) | −7.06132 | −0.445707 | −0.222853 | − | 0.974852i | \(-0.571537\pi\) | ||||
−0.222853 | + | 0.974852i | \(0.571537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.38884 | + | 8.38884i | −0.527402 | + | 0.527402i | ||||
\(254\) | 19.7409 | − | 5.28957i | 1.23866 | − | 0.331897i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.30674 | − | 12.6556i | −0.456671 | − | 0.790978i | ||||
\(257\) | −6.52671 | + | 11.3046i | −0.407125 | + | 0.705161i | −0.994566 | − | 0.104106i | \(-0.966802\pi\) |
0.587441 | + | 0.809267i | \(0.300135\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.07856 | + | 4.86187i | 0.564114 | + | 0.302102i | ||||
\(260\) | 0.674288 | + | 6.98488i | 0.0418175 | + | 0.433184i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.75466 | − | 21.4767i | 0.355524 | − | 1.32683i | ||||
\(263\) | 11.1673 | + | 19.3423i | 0.688606 | + | 1.19270i | 0.972289 | + | 0.233782i | \(0.0751101\pi\) |
−0.283684 | + | 0.958918i | \(0.591557\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.2421 | − | 23.2421i | −1.42775 | − | 1.42775i | ||||
\(266\) | 2.99850 | − | 12.8138i | 0.183850 | − | 0.785666i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.77756 | − | 1.28014i | 0.291836 | − | 0.0781972i | ||||
\(269\) | −2.71439 | + | 1.56715i | −0.165499 | + | 0.0955511i | −0.580462 | − | 0.814287i | \(-0.697128\pi\) |
0.414963 | + | 0.909838i | \(0.363795\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.09187 | − | 15.2711i | −0.248563 | − | 0.927651i | −0.971559 | − | 0.236798i | \(-0.923902\pi\) |
0.722995 | − | 0.690853i | \(-0.242765\pi\) | |||||||
\(272\) | 31.5757 | 1.91456 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.21213 | 0.133639 | ||||||||
\(275\) | 2.89898 | + | 10.8191i | 0.174815 | + | 0.652419i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.5340 | + | 14.7421i | −1.53419 | + | 0.885765i | −0.535028 | + | 0.844834i | \(0.679699\pi\) |
−0.999162 | + | 0.0409305i | \(0.986968\pi\) | |||||||
\(278\) | 29.7472 | − | 7.97074i | 1.78412 | − | 0.478053i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.75701 | − | 15.7267i | −0.284286 | − | 0.939852i | ||||
\(281\) | −16.8969 | − | 16.8969i | −1.00798 | − | 1.00798i | −0.999968 | − | 0.00801615i | \(-0.997448\pi\) |
−0.00801615 | − | 0.999968i | \(-0.502552\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.66719 | + | 8.08381i | 0.277436 | + | 0.480533i | 0.970747 | − | 0.240106i | \(-0.0771822\pi\) |
−0.693311 | + | 0.720638i | \(0.743849\pi\) | |||||||
\(284\) | 2.06330 | − | 7.70032i | 0.122434 | − | 0.456930i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.9704 | − | 15.7422i | 0.766956 | − | 0.930854i | ||||
\(287\) | 0.363124 | + | 11.3684i | 0.0214346 | + | 0.671057i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.2940 | + | 21.2938i | −0.723174 | + | 1.25257i | ||||
\(290\) | −10.3433 | − | 17.9152i | −0.607381 | − | 1.05202i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.05900 | + | 0.819657i | −0.179015 | + | 0.0479668i | ||||
\(293\) | −2.08232 | + | 2.08232i | −0.121650 | + | 0.121650i | −0.765311 | − | 0.643661i | \(-0.777415\pi\) |
0.643661 | + | 0.765311i | \(0.277415\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.50088 | −0.494940 | ||||||||
\(296\) | −7.29269 | − | 4.21044i | −0.423879 | − | 0.244727i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 30.2284 | − | 17.4524i | 1.75108 | − | 1.01099i | ||||
\(299\) | 11.5889 | − | 4.33614i | 0.670204 | − | 0.250766i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.12680 | − | 8.66309i | 0.468421 | − | 0.499332i | ||||
\(302\) | −27.6091 | −1.58872 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.85182 | + | 14.3752i | −0.220917 | + | 0.824474i | ||||
\(305\) | −9.71726 | − | 2.60373i | −0.556409 | − | 0.149089i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.85597 | + | 3.85597i | −0.220072 | + | 0.220072i | −0.808529 | − | 0.588457i | \(-0.799736\pi\) |
0.588457 | + | 0.808529i | \(0.299736\pi\) | |||||||
\(308\) | 2.92759 | − | 5.46668i | 0.166815 | − | 0.311493i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.2210 | + | 4.07844i | −0.864493 | + | 0.231640i | ||||
\(311\) | 7.03750 | + | 12.1893i | 0.399060 | + | 0.691192i | 0.993610 | − | 0.112866i | \(-0.0360032\pi\) |
−0.594550 | + | 0.804058i | \(0.702670\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.07599 | + | 2.35327i | 0.230388 | + | 0.133015i | 0.610751 | − | 0.791823i | \(-0.290868\pi\) |
−0.380363 | + | 0.924837i | \(0.624201\pi\) | |||||||
\(314\) | 12.6441 | + | 12.6441i | 0.713548 | + | 0.713548i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 0.737566i | − | 0.0414913i | ||||||
\(317\) | −7.57921 | − | 28.2860i | −0.425691 | − | 1.58870i | −0.762410 | − | 0.647094i | \(-0.775984\pi\) |
0.336720 | − | 0.941605i | \(-0.390683\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.94011 | + | 14.7047i | −0.220604 | + | 0.823305i | ||||
\(320\) | 2.79414 | + | 10.4279i | 0.156197 | + | 0.582936i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.6242 | − | 7.83633i | 0.703519 | − | 0.436702i | ||||
\(323\) | −13.8602 | − | 13.8602i | −0.771201 | − | 0.771201i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.92532 | − | 11.5225i | 0.106798 | − | 0.639155i | ||||
\(326\) | −7.09744 | − | 12.2931i | −0.393091 | − | 0.680853i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 9.30051i | − | 0.513535i | ||||||
\(329\) | −7.13231 | + | 13.3182i | −0.393217 | + | 0.734254i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.83537 | + | 14.3138i | 0.210811 | + | 0.786757i | 0.987599 | + | 0.156996i | \(0.0501808\pi\) |
−0.776788 | + | 0.629762i | \(0.783152\pi\) | |||||||
\(332\) | 1.86404 | + | 0.499467i | 0.102302 | + | 0.0274118i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.0375 | − | 9.25924i | −0.877532 | − | 0.506643i | ||||
\(335\) | −20.9408 | −1.14412 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.51919i | − | 0.518543i | −0.965804 | − | 0.259272i | \(-0.916518\pi\) | ||
0.965804 | − | 0.259272i | \(-0.0834825\pi\) | |||||||
\(338\) | −19.1164 | + | 9.33524i | −1.03980 | + | 0.507770i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.1235 | + | 3.24849i | 0.657491 | + | 0.176174i | ||||
\(341\) | 10.0427 | + | 5.79816i | 0.543843 | + | 0.313988i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.7832 | + | 14.2883i | −0.636233 | + | 0.771497i | ||||
\(344\) | −6.86791 | + | 6.86791i | −0.370293 | + | 0.370293i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.17944 | + | 1.38783i | 0.278448 | + | 0.0746100i | ||||
\(347\) | −17.5649 | − | 30.4233i | −0.942933 | − | 1.63321i | −0.759838 | − | 0.650112i | \(-0.774722\pi\) |
−0.183095 | − | 0.983095i | \(-0.558612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.64759 | + | 6.64759i | −0.355837 | + | 0.355837i | −0.862276 | − | 0.506439i | \(-0.830962\pi\) |
0.506439 | + | 0.862276i | \(0.330962\pi\) | |||||||
\(350\) | −0.447862 | − | 14.0213i | −0.0239393 | − | 0.749472i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.37094 | + | 11.0348i | −0.339572 | + | 0.588157i | ||||
\(353\) | −3.20243 | + | 11.9516i | −0.170448 | + | 0.636121i | 0.826834 | + | 0.562446i | \(0.190139\pi\) |
−0.997282 | + | 0.0736752i | \(0.976527\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.8758 | + | 29.2298i | −0.895676 | + | 1.55136i | ||||
\(356\) | 2.37885 | + | 2.37885i | 0.126079 | + | 0.126079i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.60370 | − | 2.60370i | −0.137610 | − | 0.137610i | ||||
\(359\) | −4.14143 | + | 1.10969i | −0.218576 | + | 0.0585673i | −0.366445 | − | 0.930440i | \(-0.619425\pi\) |
0.147869 | + | 0.989007i | \(0.452759\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.45373 | + | 4.88076i | −0.444933 | + | 0.256882i | ||||
\(362\) | 6.58279 | + | 24.5673i | 0.345984 | + | 1.29123i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.14199 | + | 3.92331i | −0.269513 | + | 0.205638i | ||||
\(365\) | 13.4081 | 0.701810 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.4207 | + | 12.3672i | −1.11815 | + | 0.645565i | −0.940928 | − | 0.338606i | \(-0.890045\pi\) |
−0.177223 | + | 0.984171i | \(0.556711\pi\) | |||||||
\(368\) | −14.5520 | + | 8.40162i | −0.758577 | + | 0.437965i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.9294 | − | 12.9294i | −0.672169 | − | 0.672169i | ||||
\(371\) | 6.90276 | − | 29.4984i | 0.358373 | − | 1.53148i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.95677 | − | 6.85332i | 0.204874 | − | 0.354852i | −0.745219 | − | 0.666820i | \(-0.767655\pi\) |
0.950092 | + | 0.311968i | \(0.100988\pi\) | |||||||
\(374\) | −18.2412 | − | 31.5947i | −0.943230 | − | 1.63372i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.17667 | − | 10.6983i | 0.318537 | − | 0.551723i | ||||
\(377\) | 10.0965 | − | 12.2542i | 0.519998 | − | 0.631122i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.32389 | − | 3.32389i | 0.170737 | − | 0.170737i | −0.616566 | − | 0.787303i | \(-0.711477\pi\) |
0.787303 | + | 0.616566i | \(0.211477\pi\) | |||||||
\(380\) | −2.95782 | + | 5.12309i | −0.151733 | + | 0.262809i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.75881 | + | 1.00717i | 0.192318 | + | 0.0515313i | ||||
\(383\) | 8.74833 | − | 2.34411i | 0.447019 | − | 0.119778i | −0.0282852 | − | 0.999600i | \(-0.509005\pi\) |
0.475304 | + | 0.879822i | \(0.342338\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.9628 | + | 19.1482i | −0.915468 | + | 0.975880i | ||||
\(386\) | 12.7745 | 0.650204 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.97133 | + | 0.796165i | 0.150846 | + | 0.0404191i | ||||
\(389\) | −18.5856 | + | 10.7304i | −0.942328 | + | 0.544053i | −0.890689 | − | 0.454612i | \(-0.849778\pi\) |
−0.0516387 | + | 0.998666i | \(0.516444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 22.1313i | − | 1.11923i | ||||||
\(392\) | 10.0030 | − | 11.3698i | 0.505229 | − | 0.574260i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.9268 | − | 12.6594i | −1.10466 | − | 0.637773i | ||||
\(395\) | −0.808215 | + | 3.01630i | −0.0406657 | + | 0.151766i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.38387 | − | 12.6288i | −0.169831 | − | 0.633819i | −0.997374 | − | 0.0724172i | \(-0.976929\pi\) |
0.827543 | − | 0.561402i | \(-0.189738\pi\) | |||||||
\(398\) | −23.3439 | + | 23.3439i | −1.17012 | + | 1.17012i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.8645i | 0.793224i | ||||||||
\(401\) | −20.5002 | + | 5.49301i | −1.02373 | + | 0.274308i | −0.731356 | − | 0.681996i | \(-0.761112\pi\) |
−0.292375 | + | 0.956304i | \(0.594445\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.02588 | − | 9.84484i | −0.349984 | − | 0.490406i | ||||
\(404\) | −5.36720 | − | 3.09875i | −0.267028 | − | 0.154169i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.00130 | − | 16.8081i | 0.446727 | − | 0.834173i | ||||
\(407\) | 13.4560i | 0.666990i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.20463 | + | 8.22781i | −0.109012 | + | 0.406839i | −0.998769 | − | 0.0495951i | \(-0.984207\pi\) |
0.889757 | + | 0.456434i | \(0.150874\pi\) | |||||||
\(410\) | 5.22686 | − | 19.5069i | 0.258136 | − | 0.963377i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 3.47385i | − | 0.171144i | ||||||
\(413\) | −4.13220 | − | 6.65691i | −0.203332 | − | 0.327565i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.07573 | − | 4.08517i | −0.347334 | − | 0.200533i | ||||
\(416\) | 10.8174 | − | 7.71995i | 0.530366 | − | 0.378502i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.6090 | − | 4.45037i | 0.812373 | − | 0.217675i | ||||
\(419\) | 8.39090i | 0.409922i | 0.978770 | + | 0.204961i | \(0.0657068\pi\) | ||||
−0.978770 | + | 0.204961i | \(0.934293\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5414 | − | 20.5414i | 1.00113 | − | 1.00113i | 0.00112764 | − | 0.999999i | \(-0.499641\pi\) |
0.999999 | − | 0.00112764i | \(-0.000358939\pi\) | |||||||
\(422\) | −1.00357 | − | 3.74536i | −0.0488528 | − | 0.182321i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.41144 | + | 23.9278i | −0.311367 | + | 1.16204i | ||||
\(425\) | −18.0955 | − | 10.4474i | −0.877760 | − | 0.506775i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.68453 | − | 8.87509i | −0.129914 | − | 0.429496i | ||||
\(428\) | − | 8.51150i | − | 0.411419i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.2645 | + | 10.5450i | −0.880792 | + | 0.508526i | ||||
\(431\) | 9.66314 | + | 2.58923i | 0.465457 | + | 0.124719i | 0.483923 | − | 0.875111i | \(-0.339212\pi\) |
−0.0184658 | + | 0.999829i | \(0.505878\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 41.3846 | 1.98882 | 0.994409 | − | 0.105595i | \(-0.0336746\pi\) | ||||
0.994409 | + | 0.105595i | \(0.0336746\pi\) | |||||||
\(434\) | −10.5925 | − | 9.93681i | −0.508458 | − | 0.476982i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.7882 | − | 3.42659i | 0.612444 | − | 0.164104i | ||||
\(437\) | 10.0755 | + | 2.69973i | 0.481977 | + | 0.129145i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.0712884 | + | 0.123475i | −0.00340241 | + | 0.00589314i | −0.867722 | − | 0.497051i | \(-0.834416\pi\) |
0.864319 | + | 0.502944i | \(0.167750\pi\) | |||||||
\(440\) | 15.1802 | − | 15.1802i | 0.723689 | − | 0.723689i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.65623 | + | 37.8745i | 0.173909 | + | 1.80151i | ||||
\(443\) | 12.9368 | − | 22.4072i | 0.614647 | − | 1.06460i | −0.375800 | − | 0.926701i | \(-0.622632\pi\) |
0.990446 | − | 0.137898i | \(-0.0440347\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.12166 | − | 12.3351i | −0.337599 | − | 0.584738i | ||||
\(446\) | 11.1992 | − | 19.3976i | 0.530298 | − | 0.918504i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.80770 | + | 7.25695i | −0.321634 | + | 0.342859i | ||||
\(449\) | −1.26645 | − | 1.26645i | −0.0597675 | − | 0.0597675i | 0.676591 | − | 0.736359i | \(-0.263456\pi\) |
−0.736359 | + | 0.676591i | \(0.763456\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8705 | + | 7.43081i | −0.606050 | + | 0.349903i | ||||
\(452\) | 0.000135623 | 0 | 7.83019e-5i | 6.37916e−6 | 0 | 3.68301e-6i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.3367 | −1.00138 | ||||||||
\(455\) | 25.3274 | − | 10.4100i | 1.18737 | − | 0.488028i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.20672 | − | 4.50353i | −0.0564479 | − | 0.210666i | 0.931941 | − | 0.362609i | \(-0.118114\pi\) |
−0.988389 | + | 0.151942i | \(0.951447\pi\) | |||||||
\(458\) | 21.5400 | − | 12.4361i | 1.00650 | − | 0.581101i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.45162 | + | 1.72871i | −0.300808 | + | 0.0806013i | ||||
\(461\) | −3.60896 | − | 3.60896i | −0.168086 | − | 0.168086i | 0.618052 | − | 0.786137i | \(-0.287922\pi\) |
−0.786137 | + | 0.618052i | \(0.787922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00230 | − | 4.00230i | −0.186003 | − | 0.186003i | 0.607963 | − | 0.793965i | \(-0.291987\pi\) |
−0.793965 | + | 0.607963i | \(0.791987\pi\) | |||||||
\(464\) | −10.7810 | + | 18.6732i | −0.500495 | + | 0.866883i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.27608 | − | 12.2265i | 0.151762 | − | 0.566382i | ||||
\(467\) | 20.0309 | − | 34.6946i | 0.926921 | − | 1.60547i | 0.138479 | − | 0.990365i | \(-0.455779\pi\) |
0.788442 | − | 0.615109i | \(-0.210888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.1791 | − | 16.3984i | −0.470028 | − | 0.757207i | ||||
\(470\) | 18.9674 | − | 18.9674i | 0.874899 | − | 0.874899i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.20334 | + | 5.54834i | 0.147446 | + | 0.255383i | ||||
\(473\) | 14.9914 | + | 4.01694i | 0.689306 | + | 0.184699i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.96371 | − | 6.96371i | 0.319517 | − | 0.319517i | ||||
\(476\) | 3.34930 | + | 11.0728i | 0.153515 | + | 0.507521i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.22838 | + | 2.44126i | 0.193402 | + | 0.111661i | ||||
\(479\) | −11.3889 | − | 3.05163i | −0.520370 | − | 0.139433i | −0.0109323 | − | 0.999940i | \(-0.503480\pi\) |
−0.509438 | + | 0.860508i | \(0.670147\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.81686 | − | 12.7722i | 0.265226 | − | 0.582362i | ||||
\(482\) | − | 43.2131i | − | 1.96830i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.644466 | 0.0292939 | ||||||||
\(485\) | −11.2789 | − | 6.51188i | −0.512149 | − | 0.295689i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.531550 | − | 0.142428i | −0.0240868 | − | 0.00645405i | 0.246756 | − | 0.969078i | \(-0.420636\pi\) |
−0.270842 | + | 0.962624i | \(0.587302\pi\) | |||||||
\(488\) | 1.96230 | + | 7.32340i | 0.0888291 | + | 0.331515i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 27.3701 | − | 18.2253i | 1.23646 | − | 0.823335i | ||||
\(491\) | − | 3.02403i | − | 0.136472i | −0.997669 | − | 0.0682362i | \(-0.978263\pi\) | ||
0.997669 | − | 0.0682362i | \(-0.0217372\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.1995 | − | 24.5942i | −0.639512 | − | 1.10767i | ||||
\(494\) | −17.6888 | − | 2.95565i | −0.795857 | − | 0.132981i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.6140 | + | 11.6140i | 0.521484 | + | 0.521484i | ||||
\(497\) | −31.0926 | + | 0.993144i | −1.39469 | + | 0.0445486i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.92557 | − | 37.0427i | −0.444330 | − | 1.65826i | −0.717701 | − | 0.696352i | \(-0.754805\pi\) |
0.273371 | − | 0.961909i | \(-0.411861\pi\) | |||||||
\(500\) | 0.886524 | − | 3.30855i | 0.0396466 | − | 0.147963i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.99081 | + | 11.1618i | 0.133486 | + | 0.498178i | ||||
\(503\) | 27.2615i | 1.21553i | 0.794117 | + | 0.607765i | \(0.207934\pi\) | ||||
−0.794117 | + | 0.607765i | \(0.792066\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.5538 | + | 18.5538i | 0.825631 | + | 0.825631i | ||||
\(506\) | 16.8133 | + | 9.70717i | 0.747443 | + | 0.431536i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.23374 | − | 7.33305i | −0.187842 | − | 0.325351i | ||||
\(509\) | 17.4575 | − | 4.67772i | 0.773790 | − | 0.207336i | 0.149745 | − | 0.988725i | \(-0.452155\pi\) |
0.624045 | + | 0.781388i | \(0.285488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.51754 | + | 10.4996i | 0.288319 | + | 0.464477i | ||||
\(512\) | 2.21895 | − | 2.21895i | 0.0980646 | − | 0.0980646i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.6336 | + | 5.52874i | 0.910107 | + | 0.243862i | ||||
\(515\) | −3.80660 | + | 14.2064i | −0.167739 | + | 0.626009i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.7398 | −0.868157 | ||||||||
\(518\) | 3.83996 | − | 16.4097i | 0.168718 | − | 0.721002i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −20.9710 | + | 7.84658i | −0.919640 | + | 0.344095i | ||||
\(521\) | −10.0266 | + | 5.78888i | −0.439275 | + | 0.253616i | −0.703290 | − | 0.710903i | \(-0.748286\pi\) |
0.264015 | + | 0.964519i | \(0.414953\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.36503 | − | 4.82955i | −0.365777 | − | 0.211182i | 0.305835 | − | 0.952085i | \(-0.401065\pi\) |
−0.671612 | + | 0.740903i | \(0.734398\pi\) | |||||||
\(524\) | −9.21198 | −0.402427 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.8446 | − | 25.8446i | 1.12688 | − | 1.12688i | ||||
\(527\) | −20.8956 | + | 5.59895i | −0.910225 | + | 0.243894i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.61134 | − | 9.71913i | −0.243971 | − | 0.422571i | ||||
\(530\) | −26.8947 | + | 46.5830i | −1.16823 | + | 2.02344i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.44959 | + | 0.174068i | −0.236270 | + | 0.00754680i | ||||
\(533\) | 15.4287 | − | 1.48942i | 0.668292 | − | 0.0645138i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.32679 | + | 34.8081i | −0.403232 | + | 1.50488i | ||||
\(536\) | 7.89098 | + | 13.6676i | 0.340839 | + | 0.590350i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.62688 | + | 3.62688i | 0.156366 | + | 0.156366i | ||||
\(539\) | −23.7262 | − | 4.75862i | −1.02196 | − | 0.204968i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.4151 | + | 7.88175i | −1.26465 | + | 0.338863i | −0.827980 | − | 0.560757i | \(-0.810510\pi\) |
−0.436673 | + | 0.899620i | \(0.643843\pi\) | |||||||
\(542\) | −22.4059 | + | 12.9360i | −0.962415 | + | 0.555651i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.15205 | − | 22.9598i | −0.263767 | − | 0.984392i | ||||
\(545\) | −56.0526 | −2.40103 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.0288 | 1.75427 | 0.877133 | − | 0.480247i | \(-0.159453\pi\) | ||||
0.877133 | + | 0.480247i | \(0.159453\pi\) | |||||||
\(548\) | −0.237212 | − | 0.885286i | −0.0101332 | − | 0.0378176i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15.8740 | − | 9.16485i | 0.676869 | − | 0.390790i | ||||
\(551\) | 12.9289 | − | 3.46430i | 0.550791 | − | 0.147584i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.75488 | + | 0.833296i | −0.117150 | + | 0.0354353i | ||||
\(554\) | 34.1177 | + | 34.1177i | 1.44952 | + | 1.44952i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.37973 | − | 11.0500i | −0.270561 | − | 0.468625i | ||||
\(557\) | −1.02281 | + | 3.81720i | −0.0433381 | + | 0.161740i | −0.984204 | − | 0.177040i | \(-0.943348\pi\) |
0.940866 | + | 0.338780i | \(0.110014\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.4931 | − | 10.2934i | −0.528402 | − | 0.435365i | ||||
\(560\) | −31.5944 | + | 19.6119i | −1.33511 | + | 0.828753i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.5523 | + | 33.8656i | −0.824764 | + | 1.42853i | ||||
\(563\) | 14.8777 | + | 25.7689i | 0.627018 | + | 1.08603i | 0.988147 | + | 0.153512i | \(0.0490583\pi\) |
−0.361128 | + | 0.932516i | \(0.617608\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.000640436 | 0 | 0.000171604i | −2.69433e−5 | 0 | 7.21945e-6i | ||||
\(566\) | 10.8013 | − | 10.8013i | 0.454013 | − | 0.454013i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.4369 | 1.06731 | ||||||||
\(569\) | 10.3301 | + | 5.96411i | 0.433062 | + | 0.250028i | 0.700650 | − | 0.713505i | \(-0.252893\pi\) |
−0.267588 | + | 0.963533i | \(0.586227\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.93851 | + | 5.73800i | −0.415914 | + | 0.240128i | −0.693328 | − | 0.720623i | \(-0.743856\pi\) |
0.277414 | + | 0.960751i | \(0.410523\pi\) | |||||||
\(572\) | −7.69081 | − | 3.50264i | −0.321569 | − | 0.146453i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.8163 | − | 5.38906i | 0.743637 | − | 0.224935i | ||||
\(575\) | 11.1193 | 0.463708 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.995790 | − | 3.71634i | 0.0414553 | − | 0.154713i | −0.942096 | − | 0.335344i | \(-0.891147\pi\) |
0.983551 | + | 0.180631i | \(0.0578140\pi\) | |||||||
\(578\) | 38.8662 | + | 10.4142i | 1.61662 | + | 0.433172i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.06046 | + | 6.06046i | −0.251647 | + | 0.251647i | ||||
\(581\) | −0.240413 | − | 7.52666i | −0.00997401 | − | 0.312259i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.2351 | − | 10.2451i | 1.58354 | − | 0.424308i | ||||
\(584\) | −5.05248 | − | 8.75115i | −0.209073 | − | 0.362125i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.17348 | + | 2.40956i | 0.172405 | + | 0.0995380i | ||||
\(587\) | 26.9080 | + | 26.9080i | 1.11061 | + | 1.11061i | 0.993068 | + | 0.117543i | \(0.0375018\pi\) |
0.117543 | + | 0.993068i | \(0.462498\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 10.1959i | − | 0.420116i | ||||||
\(590\) | 3.60053 | + | 13.4374i | 0.148231 | + | 0.553207i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.93275 | + | 18.4093i | −0.202735 | + | 0.756616i | ||||
\(593\) | −2.64245 | − | 9.86174i | −0.108512 | − | 0.404973i | 0.890208 | − | 0.455555i | \(-0.150559\pi\) |
−0.998720 | + | 0.0505817i | \(0.983892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.56362 | − | 48.9527i | −0.0641023 | − | 2.00687i | ||||
\(596\) | −10.2258 | − | 10.2258i | −0.418867 | − | 0.418867i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.7626 | − | 16.4821i | −0.481009 | − | 0.674001i | ||||
\(599\) | −11.3254 | − | 19.6162i | −0.462745 | − | 0.801498i | 0.536352 | − | 0.843995i | \(-0.319802\pi\) |
−0.999097 | + | 0.0424970i | \(0.986469\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.02946i | 0.327529i | 0.986499 | + | 0.163764i | \(0.0523637\pi\) | ||||
−0.986499 | + | 0.163764i | \(0.947636\pi\) | |||||||
\(602\) | −17.1359 | − | 9.17681i | −0.698405 | − | 0.374019i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.96059 | + | 11.0491i | 0.120465 | + | 0.449580i | ||||
\(605\) | −2.63556 | − | 0.706197i | −0.107151 | − | 0.0287110i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.91774 | + | 1.68456i | 0.118427 | + | 0.0683741i | 0.558044 | − | 0.829812i | \(-0.311552\pi\) |
−0.439616 | + | 0.898186i | \(0.644886\pi\) | |||||||
\(608\) | 11.2032 | 0.454348 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.4629i | 0.666563i | ||||||||
\(611\) | 18.7367 | + | 8.53328i | 0.758005 | + | 0.345220i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.4399 | + | 8.42429i | 1.26984 | + | 0.340254i | 0.829971 | − | 0.557806i | \(-0.188357\pi\) |
0.439873 | + | 0.898060i | \(0.355023\pi\) | |||||||
\(614\) | 7.72832 | + | 4.46195i | 0.311889 | + | 0.180069i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.2664 | + | 4.50843i | 0.776265 | + | 0.181650i | ||||
\(617\) | 24.9178 | − | 24.9178i | 1.00315 | − | 1.00315i | 0.00315687 | − | 0.999995i | \(-0.498995\pi\) |
0.999995 | − | 0.00315687i | \(-0.00100487\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.3745 | + | 4.11957i | 0.617951 | + | 0.165580i | 0.554196 | − | 0.832386i | \(-0.313026\pi\) |
0.0637551 | + | 0.997966i | \(0.479692\pi\) | |||||||
\(620\) | 3.26436 | + | 5.65404i | 0.131100 | + | 0.227072i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.2869 | − | 16.2869i | 0.653047 | − | 0.653047i | ||||
\(623\) | 6.19763 | − | 11.5728i | 0.248303 | − | 0.463656i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.3511 | + | 26.5890i | −0.614046 | + | 1.06356i | ||||
\(626\) | 1.99345 | − | 7.43964i | 0.0796741 | − | 0.297348i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.70427 | − | 6.41599i | 0.147817 | − | 0.256026i | ||||
\(629\) | −17.7497 | − | 17.7497i | −0.707727 | − | 0.707727i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.7103 | − | 31.7103i | −1.26237 | − | 1.26237i | −0.949942 | − | 0.312427i | \(-0.898858\pi\) |
−0.312427 | − | 0.949942i | \(-0.601142\pi\) | |||||||
\(632\) | 2.27323 | − | 0.609110i | 0.0904241 | − | 0.0242291i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −41.5015 | + | 23.9609i | −1.64824 | + | 0.951610i | ||||
\(635\) | 9.27855 | + | 34.6280i | 0.368208 | + | 1.37417i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.4634 | + | 14.7733i | 0.810788 | + | 0.585340i | ||||
\(638\) | 24.9126 | 0.986298 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 33.6259 | − | 19.4139i | 1.32918 | − | 0.767402i | ||||
\(641\) | 3.56700 | − | 2.05941i | 0.140888 | − | 0.0813418i | −0.427899 | − | 0.903827i | \(-0.640746\pi\) |
0.568787 | + | 0.822485i | \(0.307413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.89221 | + | 6.89221i | 0.271802 | + | 0.271802i | 0.829825 | − | 0.558023i | \(-0.188440\pi\) |
−0.558023 | + | 0.829825i | \(0.688440\pi\) | |||||||
\(644\) | −4.48980 | − | 4.21185i | −0.176923 | − | 0.165970i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.0384 | + | 27.7793i | −0.631021 | + | 1.09296i | ||||
\(647\) | 6.39418 | + | 11.0750i | 0.251381 | + | 0.435405i | 0.963906 | − | 0.266242i | \(-0.0857820\pi\) |
−0.712525 | + | 0.701646i | \(0.752449\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.11872 | − | 8.86589i | 0.200927 | − | 0.348017i | ||||
\(650\) | −19.0291 | + | 1.83698i | −0.746384 | + | 0.0720524i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.15859 | + | 4.15859i | −0.162863 | + | 0.162863i | ||||
\(653\) | 7.12903 | − | 12.3479i | 0.278981 | − | 0.483209i | −0.692151 | − | 0.721753i | \(-0.743337\pi\) |
0.971132 | + | 0.238544i | \(0.0766701\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.6727 | + | 10.0944i | 1.47199 | + | 0.394420i | ||||
\(656\) | −20.3323 | + | 5.44802i | −0.793842 | + | 0.212709i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.0729 | + | 5.63318i | 0.938460 | + | 0.219604i | ||||
\(659\) | −18.4714 | −0.719542 | −0.359771 | − | 0.933041i | \(-0.617145\pi\) | ||||
−0.359771 | + | 0.933041i | \(0.617145\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.6076 | − | 8.46923i | −1.22939 | − | 0.329415i | −0.415050 | − | 0.909799i | \(-0.636236\pi\) |
−0.814343 | + | 0.580384i | \(0.802903\pi\) | |||||||
\(662\) | 21.0014 | − | 12.1251i | 0.816242 | − | 0.471257i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.15757i | 0.238960i | ||||||||
\(665\) | 22.4770 | + | 5.25973i | 0.871621 | + | 0.203964i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.0880 | + | 7.55635i | 0.506768 | + | 0.292583i | ||||
\(668\) | −1.98578 | + | 7.41104i | −0.0768322 | + | 0.286742i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.86941 | + | 33.1011i | 0.342655 | + | 1.27881i | ||||
\(671\) | 8.56669 | − | 8.56669i | 0.330713 | − | 0.330713i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.6367i | 1.37370i | 0.726801 | + | 0.686848i | \(0.241006\pi\) | ||||
−0.726801 | + | 0.686848i | \(0.758994\pi\) | |||||||
\(674\) | −15.0470 | + | 4.03183i | −0.579588 | + | 0.155300i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.78583 | + | 6.64928i | 0.222532 | + | 0.255742i | ||||
\(677\) | −23.9548 | − | 13.8303i | −0.920657 | − | 0.531542i | −0.0368124 | − | 0.999322i | \(-0.511720\pi\) |
−0.883845 | + | 0.467781i | \(0.845054\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.383225 | − | 11.9977i | −0.0147068 | − | 0.460430i | ||||
\(680\) | 40.0483i | 1.53578i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.91159 | − | 18.3303i | 0.188075 | − | 0.701904i | ||||
\(683\) | 0.418104 | − | 1.56039i | 0.0159983 | − | 0.0597065i | −0.957465 | − | 0.288549i | \(-0.906827\pi\) |
0.973464 | + | 0.228842i | \(0.0734940\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.88034i | 0.148260i | ||||||||
\(686\) | 27.5763 | + | 12.5740i | 1.05287 | + | 0.480076i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.0373 | + | 10.9912i | 0.725791 | + | 0.419036i | ||||
\(689\) | −40.7209 | − | 6.80413i | −1.55134 | − | 0.259217i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.7402 | + | 6.89707i | −0.979204 | + | 0.262377i | −0.712709 | − | 0.701460i | \(-0.752532\pi\) |
−0.266494 | + | 0.963836i | \(0.585865\pi\) | |||||||
\(692\) | − | 2.22161i | − | 0.0844531i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −40.6506 | + | 40.6506i | −1.54307 | + | 1.54307i | ||||
\(695\) | 13.9816 | + | 52.1802i | 0.530354 | + | 1.97931i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.17550 | − | 26.7793i | 0.271792 | − | 1.01434i | ||||
\(698\) | 13.3234 | + | 7.69228i | 0.504299 | + | 0.291157i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.56327 | + | 1.68277i | −0.210272 | + | 0.0636029i | ||||
\(701\) | − | 5.72322i | − | 0.216163i | −0.994142 | − | 0.108081i | \(-0.965529\pi\) | ||
0.994142 | − | 0.108081i | \(-0.0344707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.2460 | − | 5.91552i | 0.386434 | − | 0.223108i | ||||
\(704\) | −12.5581 | − | 3.36493i | −0.473301 | − | 0.126821i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.2483 | 0.762056 | ||||||||
\(707\) | −5.51034 | + | 23.5480i | −0.207238 | + | 0.885613i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5808 | − | 3.10307i | 0.434927 | − | 0.116538i | −0.0347112 | − | 0.999397i | \(-0.511051\pi\) |
0.469638 | + | 0.882859i | \(0.344384\pi\) | |||||||
\(710\) | 53.3513 | + | 14.2954i | 2.00224 | + | 0.536498i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.36722 | + | 9.29630i | −0.201145 | + | 0.348394i | ||||
\(713\) | 8.14019 | − | 8.14019i | 0.304853 | − | 0.304853i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.6137 | + | 22.7516i | 1.03269 | + | 0.850863i | ||||
\(716\) | −0.762791 | + | 1.32119i | −0.0285068 | + | 0.0493753i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.50818 | + | 6.07635i | 0.130924 | + | 0.226767i | ||||
\(719\) | 7.61939 | − | 13.1972i | 0.284155 | − | 0.492172i | −0.688249 | − | 0.725475i | \(-0.741620\pi\) |
0.972404 | + | 0.233303i | \(0.0749535\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.9752 | + | 3.92472i | −0.483221 | + | 0.146164i | ||||
\(722\) | 11.2956 | + | 11.2956i | 0.420378 | + | 0.420378i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.12586 | − | 5.26882i | 0.339160 | − | 0.195814i | ||||
\(725\) | 12.3568 | − | 7.13419i | 0.458919 | − | 0.264957i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.4937 | −0.722981 | −0.361491 | − | 0.932376i | \(-0.617732\pi\) | ||||
−0.361491 | + | 0.932376i | \(0.617732\pi\) | |||||||
\(728\) | −16.3384 | − | 12.6079i | −0.605540 | − | 0.467281i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.67895 | − | 21.1941i | −0.210187 | − | 0.784430i | ||||
\(731\) | −25.0738 | + | 14.4763i | −0.927387 | + | 0.535427i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.6716 | − | 7.68254i | 1.05901 | − | 0.283761i | 0.313040 | − | 0.949740i | \(-0.398652\pi\) |
0.745971 | + | 0.665979i | \(0.231986\pi\) | |||||||
\(734\) | 28.6216 | + | 28.6216i | 1.05644 | + | 1.05644i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.94434 | + | 8.94434i | 0.329693 | + | 0.329693i | ||||
\(737\) | 12.6093 | − | 21.8399i | 0.464469 | − | 0.804484i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.217474 | + | 0.811625i | −0.00799992 | + | 0.0298561i | −0.969810 | − | 0.243860i | \(-0.921586\pi\) |
0.961811 | + | 0.273716i | \(0.0882529\pi\) | |||||||
\(740\) | −3.78786 | + | 6.56077i | −0.139245 | + | 0.241179i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −49.5517 | + | 1.58276i | −1.81910 | + | 0.0581048i | ||||
\(743\) | −22.5891 | + | 22.5891i | −0.828715 | + | 0.828715i | −0.987339 | − | 0.158624i | \(-0.949294\pi\) |
0.158624 | + | 0.987339i | \(0.449294\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.6136 | + | 53.0243i | 1.12160 | + | 1.94266i | ||||
\(746\) | −12.5089 | − | 3.35176i | −0.457985 | − | 0.122717i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.6880 | + | 10.6880i | −0.390793 | + | 0.390793i | ||||
\(749\) | −31.7913 | + | 9.61623i | −1.16163 | + | 0.351369i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.9789 | − | 7.49334i | −0.473605 | − | 0.273436i | 0.244143 | − | 0.969739i | \(-0.421494\pi\) |
−0.717748 | + | 0.696303i | \(0.754827\pi\) | |||||||
\(752\) | −27.0062 | − | 7.23629i | −0.984815 | − | 0.263880i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −23.6465 | − | 10.7694i | −0.861156 | − | 0.392198i | ||||
\(755\) | − | 48.4296i | − | 1.76254i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.27355 | −0.155325 | −0.0776624 | − | 0.996980i | \(-0.524746\pi\) | ||||
−0.0776624 | + | 0.996980i | \(0.524746\pi\) | |||||||
\(758\) | −6.66191 | − | 3.84626i | −0.241971 | − | 0.139702i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.2324 | − | 4.88536i | −0.661359 | − | 0.177211i | ||||
\(761\) | 2.03075 | + | 7.57885i | 0.0736145 | + | 0.274733i | 0.992916 | − | 0.118822i | \(-0.0379118\pi\) |
−0.919301 | + | 0.393555i | \(0.871245\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.2467 | − | 43.8939i | −0.986396 | − | 1.58907i | ||||
\(764\) | − | 1.61227i | − | 0.0583297i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.41067 | − | 12.8357i | −0.267758 | − | 0.463771i | ||||
\(767\) | −8.69121 | + | 6.20258i | −0.313821 | + | 0.223962i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.34450 | − | 5.34450i | −0.192727 | − | 0.192727i | 0.604146 | − | 0.796874i | \(-0.293514\pi\) |
−0.796874 | + | 0.604146i | \(0.793514\pi\) | |||||||
\(770\) | 37.8756 | + | 20.2836i | 1.36494 | + | 0.730971i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.36984 | − | 5.11231i | −0.0493016 | − | 0.183996i | ||||
\(773\) | 7.88945 | − | 29.4438i | 0.283764 | − | 1.05902i | −0.665974 | − | 0.745975i | \(-0.731984\pi\) |
0.949738 | − | 0.313046i | \(-0.101349\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.81306 | − | 10.4985i | −0.101048 | − | 0.377116i | ||||
\(776\) | 9.81534i | 0.352350i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.8335 | + | 24.8335i | 0.890323 | + | 0.890323i | ||||
\(779\) | 11.3163 | + | 6.53345i | 0.405447 | + | 0.234085i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.3232 | − | 35.2009i | −0.727222 | − | 1.25959i | ||||
\(782\) | −34.9830 | + | 9.37366i | −1.25099 | + | 0.335201i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −30.7155 | − | 15.2079i | −1.09698 | − | 0.543140i | ||||
\(785\) | −22.1793 | + | 22.1793i | −0.791613 | + | 0.791613i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.3495 | − | 14.0270i | −1.86606 | − | 0.500008i | −1.00000 | 6.28799e-5i | \(-0.999980\pi\) | |
−0.866057 | − | 0.499946i | \(-0.833353\pi\) | |||||||
\(788\) | −2.71500 | + | 10.1325i | −0.0967180 | + | 0.360957i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.11018 | 0.181812 | ||||||||
\(791\) | −0.000445691 | 0 | 0.000418100i | −1.58470e−5 | 0 | 1.48659e-5i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.8346 | + | 4.42807i | −0.420259 | + | 0.157245i | ||||
\(794\) | −18.5291 | + | 10.6978i | −0.657572 | + | 0.379650i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.8454 | + | 6.83892i | 0.419847 | + | 0.242399i | ||||
\(797\) | 28.0843 | 0.994797 | 0.497399 | − | 0.867522i | \(-0.334289\pi\) | ||||
0.497399 | + | 0.867522i | \(0.334289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.0387 | − | 26.0387i | 0.921181 | − | 0.921181i | ||||
\(800\) | 11.5356 | − | 3.09095i | 0.407845 | − | 0.109282i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.3656 | + | 30.0781i | 0.613201 | + | 1.06210i | ||||
\(803\) | −8.07354 | + | 13.9838i | −0.284909 | + | 0.493477i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.7459 | + | 22.1444i | 0.484478 | + | 0.780487i | ||||
\(806\) | −12.5860 | + | 15.2756i | −0.443321 | + | 0.538059i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.11813 | − | 19.1011i | 0.180055 | − | 0.671976i | ||||
\(809\) | −6.38747 | − | 11.0634i | −0.224572 | − | 0.388969i | 0.731619 | − | 0.681714i | \(-0.238765\pi\) |
−0.956191 | + | 0.292744i | \(0.905432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.6613 | + | 20.6613i | 0.725515 | + | 0.725515i | 0.969723 | − | 0.244208i | \(-0.0785279\pi\) |
−0.244208 | + | 0.969723i | \(0.578528\pi\) | |||||||
\(812\) | −7.69178 | − | 1.79992i | −0.269929 | − | 0.0631646i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.2699 | − | 5.69926i | 0.745511 | − | 0.199759i | ||||
\(815\) | 21.5636 | − | 12.4498i | 0.755341 | − | 0.436096i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.53185 | − | 13.1810i | −0.123564 | − | 0.461146i | ||||
\(818\) | 13.9395 | 0.487382 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.36708 | −0.292191 | ||||||||
\(821\) | −0.330074 | − | 1.23185i | −0.0115197 | − | 0.0429920i | 0.959927 | − | 0.280251i | \(-0.0904177\pi\) |
−0.971446 | + | 0.237259i | \(0.923751\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.1222 | − | 11.0402i | 0.666559 | − | 0.384838i | −0.128213 | − | 0.991747i | \(-0.540924\pi\) |
0.794771 | + | 0.606909i | \(0.207591\pi\) | |||||||
\(824\) | 10.7066 | − | 2.86883i | 0.372983 | − | 0.0999406i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.77240 | + | 9.35130i | −0.305231 | + | 0.325373i | ||||
\(827\) | −9.30639 | − | 9.30639i | −0.323615 | − | 0.323615i | 0.526537 | − | 0.850152i | \(-0.323490\pi\) |
−0.850152 | + | 0.526537i | \(0.823490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.4841 | + | 26.8192i | 0.537784 | + | 0.931469i | 0.999023 | + | 0.0441933i | \(0.0140718\pi\) |
−0.461239 | + | 0.887276i | \(0.652595\pi\) | |||||||
\(830\) | −3.46053 | + | 12.9149i | −0.120117 | + | 0.448282i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10.4653 | + | 8.62263i | 0.362819 | + | 0.298936i | ||||
\(833\) | 37.5741 | − | 25.0199i | 1.30186 | − | 0.866890i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.2418 | − | 28.1317i | 0.562072 | − | 0.973537i | ||||
\(836\) | −3.56205 | − | 6.16965i | −0.123196 | − | 0.213382i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.2635 | − | 3.55395i | 0.458180 | − | 0.122769i | ||||
\(839\) | 22.1620 | − | 22.1620i | 0.765116 | − | 0.765116i | −0.212126 | − | 0.977242i | \(-0.568039\pi\) |
0.977242 | + | 0.212126i | \(0.0680389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.60734 | −0.331288 | ||||||||
\(842\) | −41.1701 | − | 23.7696i | −1.41882 | − | 0.819153i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.39127 | + | 0.803248i | −0.0478893 | + | 0.0276489i | ||||
\(845\) | −16.3751 | − | 33.5325i | −0.563322 | − | 1.15355i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.728113 | − | 2.40715i | −0.0250182 | − | 0.0827105i | ||||
\(848\) | 56.0654 | 1.92530 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.84997 | + | 33.0285i | −0.303551 | + | 1.13287i | ||||
\(851\) | 12.9030 | + | 3.45734i | 0.442308 | + | 0.118516i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0740 | − | 15.0740i | 0.516125 | − | 0.516125i | −0.400271 | − | 0.916397i | \(-0.631084\pi\) |
0.916397 | + | 0.400271i | \(0.131084\pi\) | |||||||
\(854\) | −12.8918 | + | 8.00247i | −0.441150 | + | 0.273839i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.2330 | − | 7.02912i | 0.896627 | − | 0.240250i | ||||
\(857\) | 18.8426 | + | 32.6363i | 0.643650 | + | 1.11483i | 0.984612 | + | 0.174757i | \(0.0559141\pi\) |
−0.340961 | + | 0.940077i | \(0.610753\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.05583 | + | 4.65104i | 0.274861 | + | 0.158691i | 0.631095 | − | 0.775706i | \(-0.282606\pi\) |
−0.356233 | + | 0.934397i | \(0.615939\pi\) | |||||||
\(860\) | 6.17863 | + | 6.17863i | 0.210689 | + | 0.210689i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 16.3712i | − | 0.557605i | ||||||
\(863\) | −5.95141 | − | 22.2110i | −0.202588 | − | 0.756070i | −0.990171 | − | 0.139861i | \(-0.955334\pi\) |
0.787583 | − | 0.616209i | \(-0.211332\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.43441 | + | 9.08536i | −0.0827726 | + | 0.308911i | ||||
\(866\) | −17.5284 | − | 65.4167i | −0.595638 | − | 2.22295i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.84081 | + | 5.30465i | −0.0964235 | + | 0.180052i | ||||
\(869\) | −2.65915 | − | 2.65915i | −0.0902056 | − | 0.0902056i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.4096 | + | 15.2792i | −0.725437 | + | 0.517716i | ||||
\(872\) | 21.1220 | + | 36.5843i | 0.715280 | + | 1.23890i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 17.0698i | − | 0.577396i | ||||||
\(875\) | −13.3594 | + | 0.426719i | −0.451629 | + | 0.0144257i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.73667 | − | 10.2134i | −0.0924108 | − | 0.344882i | 0.904203 | − | 0.427102i | \(-0.140466\pi\) |
−0.996614 | + | 0.0822203i | \(0.973799\pi\) | |||||||
\(878\) | 0.225371 | + | 0.0603880i | 0.00760591 | + | 0.00203800i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −42.0785 | − | 24.2940i | −1.41846 | − | 0.818951i | ||||
\(881\) | −19.0687 | −0.642440 | −0.321220 | − | 0.947005i | \(-0.604093\pi\) | ||||
−0.321220 | + | 0.947005i | \(0.604093\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.27586i | 0.143894i | 0.997408 | + | 0.0719471i | \(0.0229213\pi\) | ||||
−0.997408 | + | 0.0719471i | \(0.977079\pi\) | |||||||
\(884\) | 14.7652 | − | 5.52459i | 0.496607 | − | 0.185812i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40.8985 | − | 10.9587i | −1.37401 | − | 0.368165i | ||||
\(887\) | −5.75705 | − | 3.32383i | −0.193303 | − | 0.111603i | 0.400225 | − | 0.916417i | \(-0.368932\pi\) |
−0.593528 | + | 0.804813i | \(0.702265\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.6064 | + | 24.0983i | −0.758196 | + | 0.808230i | ||||
\(890\) | −16.4817 | + | 16.4817i | −0.552468 | + | 0.552468i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.96378 | − | 2.40184i | −0.300130 | − | 0.0804195i | ||||
\(893\) | 8.67801 | + | 15.0308i | 0.290399 | + | 0.502985i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.56720 | − | 4.56720i | 0.152665 | − | 0.152665i | ||||
\(896\) | 31.5480 | + | 16.8950i | 1.05394 | + | 0.564421i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.46548 | + | 2.53828i | −0.0489036 | + | 0.0847036i | ||||
\(899\) | 3.82333 | − | 14.2689i | 0.127515 | − | 0.475893i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.9215 | + | 63.9499i | −1.23003 | + | 2.13048i | ||||
\(902\) | 17.1972 | + | 17.1972i | 0.572603 | + | 0.572603i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.000353334 | 0 | 0.000353334i | 1.17517e−5 | 0 | 1.17517e-5i | ||||
\(905\) | −43.0940 | + | 11.5470i | −1.43249 | + | 0.383835i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.7208 | + | 7.34433i | −0.422386 | + | 0.243865i | −0.696098 | − | 0.717947i | \(-0.745082\pi\) |
0.273712 | + | 0.961812i | \(0.411749\pi\) | |||||||
\(908\) | 2.28798 | + | 8.53886i | 0.0759293 | + | 0.283372i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −27.1825 | − | 35.6260i | −0.901090 | − | 1.18099i | ||||
\(911\) | −17.7868 | −0.589301 | −0.294651 | − | 0.955605i | \(-0.595203\pi\) | ||||
−0.294651 | + | 0.955605i | \(0.595203\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.52117 | − | 4.91970i | 0.282009 | − | 0.162818i | ||||
\(914\) | −6.60764 | + | 3.81492i | −0.218561 | + | 0.126186i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.28667 | − | 7.28667i | −0.240758 | − | 0.240758i | ||||
\(917\) | 10.4076 | + | 34.4077i | 0.343690 | + | 1.13624i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.1432 | + | 19.3006i | −0.367581 | + | 0.636670i | −0.989187 | − | 0.146661i | \(-0.953147\pi\) |
0.621605 | + | 0.783331i | \(0.286481\pi\) | |||||||
\(920\) | −10.6560 | − | 18.4567i | −0.351317 | − | 0.608499i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.17612 | + | 7.23325i | −0.137533 | + | 0.238214i | ||||
\(923\) | 4.07355 | + | 42.1975i | 0.134082 | + | 1.38895i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.91792 | − | 8.91792i | 0.293219 | − | 0.293219i | ||||
\(926\) | −4.63127 | + | 8.02160i | −0.152193 | + | 0.263606i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.6784 | + | 4.20102i | 0.514670 | + | 0.137905i | ||||
\(929\) | −41.4886 | + | 11.1168i | −1.36120 | + | 0.364731i | −0.864255 | − | 0.503054i | \(-0.832210\pi\) |
−0.496940 | + | 0.867785i | \(0.665543\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.80706 | + | 20.1581i | 0.223092 | + | 0.660655i | ||||
\(932\) | −5.24431 | −0.171783 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −63.3258 | − | 16.9681i | −2.07208 | − | 0.555213i | ||||
\(935\) | 55.4209 | − | 31.9973i | 1.81246 | − | 1.04642i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 52.3733i | − | 1.71096i | −0.517835 | − | 0.855481i | \(-0.673262\pi\) | ||
0.517835 | − | 0.855481i | \(-0.326738\pi\) | |||||||
\(938\) | −21.6096 | + | 23.0357i | −0.705579 | + | 0.752141i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.62459 | − | 5.55676i | −0.313919 | − | 0.181241i | ||||
\(941\) | −4.03247 | + | 15.0494i | −0.131455 | + | 0.490596i | −0.999987 | − | 0.00503603i | \(-0.998397\pi\) |
0.868532 | + | 0.495632i | \(0.165064\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.81849 | + | 14.2508i | 0.124347 | + | 0.464070i | ||||
\(944\) | 10.2531 | − | 10.2531i | 0.333708 | − | 0.333708i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 25.3983i | − | 0.825771i | ||||||
\(947\) | 41.1510 | − | 11.0264i | 1.33723 | − | 0.358309i | 0.481822 | − | 0.876269i | \(-0.339975\pi\) |
0.855405 | + | 0.517960i | \(0.173308\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.7083 | − | 9.78306i | 0.444989 | − | 0.317571i | ||||
\(950\) | −13.9570 | − | 8.05809i | −0.452825 | − | 0.261439i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −31.3612 | + | 19.4671i | −1.01642 | + | 0.630933i | ||||
\(953\) | − | 35.9437i | − | 1.16433i | −0.813070 | − | 0.582165i | \(-0.802206\pi\) | ||
0.813070 | − | 0.582165i | \(-0.197794\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.76670 | + | 6.59341i | −0.0571690 | + | 0.213358i | ||||
\(956\) | 0.523564 | − | 1.95397i | 0.0169333 | − | 0.0631958i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.2949i | 0.623390i | ||||||||
\(959\) | −3.03863 | + | 1.88620i | −0.0981226 | + | 0.0609086i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1017 | + | 9.87370i | 0.551669 | + | 0.318506i | ||||
\(962\) | −22.6527 | − | 3.78509i | −0.730354 | − | 0.122036i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.2937 | + | 4.63384i | −0.556993 | + | 0.149246i | ||||
\(965\) | 22.4080i | 0.721339i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.7209 | + | 31.7209i | −1.02008 | + | 1.02008i | −0.0202813 | + | 0.999794i | \(0.506456\pi\) |
−0.999794 | + | 0.0202813i | \(0.993544\pi\) | |||||||
\(968\) | 0.532224 | + | 1.98629i | 0.0171063 | + | 0.0638417i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.51618 | + | 20.5867i | −0.177114 | + | 0.660998i | ||||
\(971\) | −20.7204 | − | 11.9629i | −0.664950 | − | 0.383909i | 0.129210 | − | 0.991617i | \(-0.458756\pi\) |
−0.794161 | + | 0.607708i | \(0.792089\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.0652 | + | 36.3132i | −1.09208 | + | 1.16415i | ||||
\(974\) | 0.900548i | 0.0288554i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.8606 | − | 8.57975i | 0.475675 | − | 0.274631i | ||||
\(977\) | −42.6772 | − | 11.4353i | −1.36537 | − | 0.365849i | −0.499582 | − | 0.866267i | \(-0.666513\pi\) |
−0.865784 | + | 0.500418i | \(0.833180\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.1530 | 0.548211 | ||||||||
\(980\) | −10.2287 | − | 8.99908i | −0.326743 | − | 0.287465i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.78009 | + | 1.28082i | −0.152539 | + | 0.0408726i | ||||
\(983\) | 3.90158 | + | 1.04542i | 0.124441 | + | 0.0333439i | 0.320502 | − | 0.947248i | \(-0.396148\pi\) |
−0.196061 | + | 0.980592i | \(0.562815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.2062 | − | 38.4623i | 0.707548 | − | 1.22551i | ||||
\(986\) | −32.8620 | + | 32.8620i | −1.04654 | + | 1.04654i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.713969 | + | 7.39594i | 0.0227144 | + | 0.235296i | ||||
\(989\) | 7.70369 | − | 13.3432i | 0.244963 | − | 0.424288i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.4084 | + | 26.6881i | 0.489463 | + | 0.847774i | 0.999926 | − | 0.0121250i | \(-0.00385960\pi\) |
−0.510464 | + | 0.859899i | \(0.670526\pi\) | |||||||
\(992\) | 6.18211 | − | 10.7077i | 0.196282 | − | 0.339971i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.7391 | + | 48.7275i | 0.467495 | + | 1.54554i | ||||
\(995\) | −40.9480 | − | 40.9480i | −1.29814 | − | 1.29814i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.9509 | − | 20.1789i | 1.10691 | − | 0.639072i | 0.168879 | − | 0.985637i | \(-0.445985\pi\) |
0.938026 | + | 0.346565i | \(0.112652\pi\) | |||||||
\(998\) | −54.3496 | + | 31.3787i | −1.72040 | + | 0.993276i | ||||
\(999\) | 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 | 819.2.fn.e.460.3 | 32 | ||
3.2 | odd | 2 | 91.2.bb.a.5.6 | ✓ | 32 | ||
7.3 | odd | 6 | inner | 819.2.fn.e.577.6 | 32 | ||
13.8 | odd | 4 | inner | 819.2.fn.e.775.6 | 32 | ||
21.2 | odd | 6 | 637.2.i.a.538.11 | 32 | |||
21.5 | even | 6 | 637.2.i.a.538.12 | 32 | |||
21.11 | odd | 6 | 637.2.bc.b.31.3 | 32 | |||
21.17 | even | 6 | 91.2.bb.a.31.3 | yes | 32 | ||
21.20 | even | 2 | 637.2.bc.b.460.6 | 32 | |||
39.8 | even | 4 | 91.2.bb.a.47.3 | yes | 32 | ||
91.73 | even | 12 | inner | 819.2.fn.e.73.3 | 32 | ||
273.47 | odd | 12 | 637.2.i.a.489.12 | 32 | |||
273.86 | even | 12 | 637.2.i.a.489.11 | 32 | |||
273.125 | odd | 4 | 637.2.bc.b.411.3 | 32 | |||
273.164 | odd | 12 | 91.2.bb.a.73.6 | yes | 32 | ||
273.242 | even | 12 | 637.2.bc.b.619.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.bb.a.5.6 | ✓ | 32 | 3.2 | odd | 2 | ||
91.2.bb.a.31.3 | yes | 32 | 21.17 | even | 6 | ||
91.2.bb.a.47.3 | yes | 32 | 39.8 | even | 4 | ||
91.2.bb.a.73.6 | yes | 32 | 273.164 | odd | 12 | ||
637.2.i.a.489.11 | 32 | 273.86 | even | 12 | |||
637.2.i.a.489.12 | 32 | 273.47 | odd | 12 | |||
637.2.i.a.538.11 | 32 | 21.2 | odd | 6 | |||
637.2.i.a.538.12 | 32 | 21.5 | even | 6 | |||
637.2.bc.b.31.3 | 32 | 21.11 | odd | 6 | |||
637.2.bc.b.411.3 | 32 | 273.125 | odd | 4 | |||
637.2.bc.b.460.6 | 32 | 21.20 | even | 2 | |||
637.2.bc.b.619.6 | 32 | 273.242 | even | 12 | |||
819.2.fn.e.73.3 | 32 | 91.73 | even | 12 | inner | ||
819.2.fn.e.460.3 | 32 | 1.1 | even | 1 | trivial | ||
819.2.fn.e.577.6 | 32 | 7.3 | odd | 6 | inner | ||
819.2.fn.e.775.6 | 32 | 13.8 | odd | 4 | inner |