Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(127,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.ct (of order \(6\), degree \(2\), 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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.58891012706304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.6 | ||
Root | \(-1.12906 - 0.851598i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.127 |
Dual form | 819.2.ct.a.316.6 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.34104 | − | 1.35160i | 1.65536 | − | 0.955724i | 0.680549 | − | 0.732702i | \(-0.261741\pi\) |
0.974813 | − | 0.223022i | \(-0.0715921\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.65363 | − | 4.59623i | 1.32682 | − | 2.29811i | ||||
\(5\) | 3.25812i | 1.45708i | 0.685005 | + | 0.728539i | \(0.259800\pi\) | ||||
−0.685005 | + | 0.728539i | \(0.740200\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | ||||
\(8\) | − | 8.94020i | − | 3.16084i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.40367 | + | 7.62739i | 1.39256 | + | 2.41199i | ||||
\(11\) | 1.59871 | − | 0.923014i | 0.482028 | − | 0.278299i | −0.239233 | − | 0.970962i | \(-0.576896\pi\) |
0.721261 | + | 0.692663i | \(0.243563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.60550 | + | 0.0186461i | 0.999987 | + | 0.00517151i | ||||
\(14\) | 2.70320 | 0.722460 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.77628 | − | 11.7369i | −1.69407 | − | 2.93422i | ||||
\(17\) | −1.07657 | + | 1.86467i | −0.261107 | + | 0.452250i | −0.966536 | − | 0.256530i | \(-0.917421\pi\) |
0.705430 | + | 0.708780i | \(0.250754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.07929 | − | 1.20048i | −0.477021 | − | 0.275408i | 0.242153 | − | 0.970238i | \(-0.422146\pi\) |
−0.719174 | + | 0.694830i | \(0.755480\pi\) | |||||||
\(20\) | 14.9751 | + | 8.64587i | 3.34853 | + | 1.93328i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.49509 | − | 4.32162i | 0.531954 | − | 0.921372i | ||||
\(23\) | −0.906314 | − | 1.56978i | −0.188979 | − | 0.327322i | 0.755931 | − | 0.654652i | \(-0.227185\pi\) |
−0.944910 | + | 0.327329i | \(0.893851\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.61537 | −1.12307 | ||||||||
\(26\) | 8.46582 | − | 4.82954i | 1.66028 | − | 0.947151i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.59623 | − | 2.65363i | 0.868606 | − | 0.501490i | ||||
\(29\) | −1.36703 | − | 2.36777i | −0.253851 | − | 0.439683i | 0.710732 | − | 0.703463i | \(-0.248364\pi\) |
−0.964583 | + | 0.263780i | \(0.915031\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.74236i | − | 0.312937i | −0.987683 | − | 0.156468i | \(-0.949989\pi\) | ||
0.987683 | − | 0.156468i | \(-0.0500110\pi\) | |||||||
\(32\) | −16.2422 | − | 9.37743i | −2.87124 | − | 1.65771i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.82036i | 0.998183i | ||||||||
\(35\) | −1.62906 | + | 2.82162i | −0.275362 | + | 0.476940i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.14042 | + | 2.96783i | −0.845081 | + | 0.487908i | −0.858988 | − | 0.511996i | \(-0.828906\pi\) |
0.0139073 | + | 0.999903i | \(0.495573\pi\) | |||||||
\(38\) | −6.49025 | −1.05286 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 29.1283 | 4.60558 | ||||||||
\(41\) | −3.65577 | + | 2.11066i | −0.570935 | + | 0.329629i | −0.757523 | − | 0.652809i | \(-0.773590\pi\) |
0.186588 | + | 0.982438i | \(0.440257\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.34111 | + | 7.51903i | −0.662014 | + | 1.14664i | 0.318072 | + | 0.948067i | \(0.396965\pi\) |
−0.980086 | + | 0.198575i | \(0.936369\pi\) | |||||||
\(44\) | − | 9.79737i | − | 1.47701i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.24343 | − | 2.44994i | −0.625659 | − | 0.361224i | ||||
\(47\) | − | 5.87774i | − | 0.857357i | −0.903457 | − | 0.428678i | \(-0.858979\pi\) | ||
0.903457 | − | 0.428678i | \(-0.141021\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | −13.1458 | + | 7.58972i | −1.85910 | + | 1.07335i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.65339 | − | 16.5222i | 1.33868 | − | 2.29122i | ||||
\(53\) | 9.30628 | 1.27832 | 0.639158 | − | 0.769076i | \(-0.279283\pi\) | ||||
0.639158 | + | 0.769076i | \(0.279283\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00729 | + | 5.20878i | 0.405503 | + | 0.702352i | ||||
\(56\) | 4.47010 | − | 7.74244i | 0.597342 | − | 1.03463i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.40054 | − | 3.69535i | −0.840432 | − | 0.485224i | ||||
\(59\) | −9.31173 | − | 5.37613i | −1.21228 | − | 0.699912i | −0.249028 | − | 0.968496i | \(-0.580111\pi\) |
−0.963256 | + | 0.268584i | \(0.913444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.05504 | + | 8.75558i | −0.647231 | + | 1.12104i | 0.336550 | + | 0.941665i | \(0.390740\pi\) |
−0.983781 | + | 0.179371i | \(0.942594\pi\) | |||||||
\(62\) | −2.35497 | − | 4.07893i | −0.299081 | − | 0.518024i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −23.5929 | −2.94911 | ||||||||
\(65\) | −0.0607514 | + | 11.7472i | −0.00753529 | + | 1.45706i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.716130 | − | 0.413458i | 0.0874892 | − | 0.0505119i | −0.455617 | − | 0.890176i | \(-0.650581\pi\) |
0.543106 | + | 0.839664i | \(0.317248\pi\) | |||||||
\(68\) | 5.71365 | + | 9.89633i | 0.692881 | + | 1.20011i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.80735i | 1.05268i | ||||||||
\(71\) | 2.03884 | + | 1.17712i | 0.241965 | + | 0.139699i | 0.616080 | − | 0.787684i | \(-0.288720\pi\) |
−0.374114 | + | 0.927383i | \(0.622053\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.19482i | 0.373925i | 0.982367 | + | 0.186963i | \(0.0598644\pi\) | ||||
−0.982367 | + | 0.186963i | \(0.940136\pi\) | |||||||
\(74\) | −8.02261 | + | 13.8956i | −0.932610 | + | 1.61533i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.0353 | + | 6.37126i | −1.26584 | + | 0.730833i | ||||
\(77\) | 1.84603 | 0.210374 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.801911 | 0.0902220 | 0.0451110 | − | 0.998982i | \(-0.485636\pi\) | ||||
0.0451110 | + | 0.998982i | \(0.485636\pi\) | |||||||
\(80\) | 38.2402 | − | 22.0780i | 4.27538 | − | 2.46839i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.70552 | + | 9.88225i | −0.630069 | + | 1.09131i | ||||
\(83\) | 9.97031i | 1.09438i | 0.837007 | + | 0.547192i | \(0.184303\pi\) | ||||
−0.837007 | + | 0.547192i | \(0.815697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.07534 | − | 3.50760i | −0.658963 | − | 0.380452i | ||||
\(86\) | 23.4698i | 2.53081i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.25193 | − | 14.2928i | −0.879658 | − | 1.52361i | ||||
\(89\) | −13.0886 | + | 7.55674i | −1.38739 | + | 0.801012i | −0.993021 | − | 0.117938i | \(-0.962372\pi\) |
−0.394373 | + | 0.918950i | \(0.629038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.11313 | + | 1.81890i | 0.326345 | + | 0.190672i | ||||
\(92\) | −9.62010 | −1.00296 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.94435 | − | 13.7600i | −0.819397 | − | 1.41924i | ||||
\(95\) | 3.91130 | − | 6.77458i | 0.401291 | − | 0.695057i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.99489 | + | 4.61585i | 0.811758 | + | 0.468669i | 0.847566 | − | 0.530690i | \(-0.178067\pi\) |
−0.0358079 | + | 0.999359i | \(0.511400\pi\) | |||||||
\(98\) | 2.34104 | + | 1.35160i | 0.236480 | + | 0.136532i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.9011 | + | 25.8095i | −1.49011 | + | 2.58095i | ||||
\(101\) | −7.41169 | − | 12.8374i | −0.737491 | − | 1.27737i | −0.953622 | − | 0.301007i | \(-0.902677\pi\) |
0.216131 | − | 0.976364i | \(-0.430656\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.28286 | 0.422003 | 0.211001 | − | 0.977486i | \(-0.432328\pi\) | ||||
0.211001 | + | 0.977486i | \(0.432328\pi\) | |||||||
\(104\) | 0.166700 | − | 32.2339i | 0.0163463 | − | 3.16079i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.7863 | − | 12.5783i | 2.11608 | − | 1.22172i | ||||
\(107\) | −9.56289 | − | 16.5634i | −0.924479 | − | 1.60124i | −0.792397 | − | 0.610006i | \(-0.791167\pi\) |
−0.132082 | − | 0.991239i | \(-0.542166\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.27153i | − | 0.409139i | −0.978852 | − | 0.204569i | \(-0.934421\pi\) | ||
0.978852 | − | 0.204569i | \(-0.0655794\pi\) | |||||||
\(110\) | 14.0804 | + | 8.12930i | 1.34251 | + | 0.775099i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 13.5526i | − | 1.28060i | ||||||
\(113\) | 1.37488 | − | 2.38137i | 0.129338 | − | 0.224020i | −0.794082 | − | 0.607810i | \(-0.792048\pi\) |
0.923420 | + | 0.383790i | \(0.125381\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.11454 | − | 2.95288i | 0.476934 | − | 0.275358i | ||||
\(116\) | −14.5104 | −1.34726 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.0655 | −2.67569 | ||||||||
\(119\) | −1.86467 | + | 1.07657i | −0.170934 | + | 0.0986890i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.79609 | + | 6.57502i | −0.345099 | + | 0.597729i | ||||
\(122\) | 27.3295i | 2.47430i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.00828 | − | 4.62358i | −0.719165 | − | 0.415210i | ||||
\(125\) | − | 2.00495i | − | 0.179329i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.86719 | − | 8.43022i | −0.431893 | − | 0.748061i | 0.565143 | − | 0.824993i | \(-0.308821\pi\) |
−0.997036 | + | 0.0769320i | \(0.975488\pi\) | |||||||
\(128\) | −22.7475 | + | 13.1333i | −2.01061 | + | 1.16083i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.7352 | + | 27.5827i | 1.38007 | + | 2.41916i | ||||
\(131\) | 18.6615 | 1.63046 | 0.815230 | − | 0.579138i | \(-0.196611\pi\) | ||||
0.815230 | + | 0.579138i | \(0.196611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.20048 | − | 2.07929i | −0.104095 | − | 0.180297i | ||||
\(134\) | 1.11766 | − | 1.93584i | 0.0965509 | − | 0.167231i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.6706 | + | 9.62475i | 1.42949 | + | 0.825315i | ||||
\(137\) | 7.29328 | + | 4.21078i | 0.623107 | + | 0.359751i | 0.778078 | − | 0.628168i | \(-0.216195\pi\) |
−0.154971 | + | 0.987919i | \(0.549528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.81809 | − | 15.2734i | 0.747941 | − | 1.29547i | −0.200867 | − | 0.979619i | \(-0.564376\pi\) |
0.948808 | − | 0.315853i | \(-0.102291\pi\) | |||||||
\(140\) | 8.64587 | + | 14.9751i | 0.730709 | + | 1.26563i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.36399 | 0.534054 | ||||||||
\(143\) | 5.78135 | − | 3.29812i | 0.483461 | − | 0.275803i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.71448 | − | 4.45396i | 0.640653 | − | 0.369881i | ||||
\(146\) | 4.31811 | + | 7.47919i | 0.357370 | + | 0.618982i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 31.5021i | 2.58946i | ||||||||
\(149\) | 3.48232 | + | 2.01052i | 0.285283 | + | 0.164708i | 0.635813 | − | 0.771843i | \(-0.280665\pi\) |
−0.350530 | + | 0.936552i | \(0.613998\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.9010i | 1.53814i | 0.639165 | + | 0.769069i | \(0.279280\pi\) | ||||
−0.639165 | + | 0.769069i | \(0.720720\pi\) | |||||||
\(152\) | −10.7325 | + | 18.5892i | −0.870521 | + | 1.50779i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.32162 | − | 2.49509i | 0.348246 | − | 0.201060i | ||||
\(155\) | 5.67682 | 0.455973 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5735 | −0.923670 | −0.461835 | − | 0.886966i | \(-0.652809\pi\) | ||||
−0.461835 | + | 0.886966i | \(0.652809\pi\) | |||||||
\(158\) | 1.87730 | − | 1.08386i | 0.149350 | − | 0.0862273i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 30.5528 | − | 52.9190i | 2.41541 | − | 4.18362i | ||||
\(161\) | − | 1.81263i | − | 0.142855i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.81520 | − | 2.20271i | −0.298830 | − | 0.172529i | 0.343087 | − | 0.939304i | \(-0.388527\pi\) |
−0.641917 | + | 0.766774i | \(0.721861\pi\) | |||||||
\(164\) | 22.4037i | 1.74943i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.4759 | + | 23.3409i | 1.04593 | + | 1.81160i | ||||
\(167\) | 7.81076 | − | 4.50954i | 0.604415 | − | 0.348959i | −0.166362 | − | 0.986065i | \(-0.553202\pi\) |
0.770776 | + | 0.637106i | \(0.219869\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9993 | + | 0.134457i | 0.999947 | + | 0.0103429i | ||||
\(170\) | −18.9635 | −1.45443 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 23.0395 | + | 39.9055i | 1.75674 | + | 3.04277i | ||||
\(173\) | −3.04600 | + | 5.27583i | −0.231583 | + | 0.401114i | −0.958274 | − | 0.285851i | \(-0.907724\pi\) |
0.726691 | + | 0.686964i | \(0.241057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.86305 | − | 2.80769i | −0.367612 | − | 0.212241i | ||||
\(176\) | −21.6666 | − | 12.5092i | −1.63318 | − | 0.942917i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −20.4273 | + | 35.3812i | −1.53109 | + | 2.65193i | ||||
\(179\) | −1.93982 | − | 3.35987i | −0.144989 | − | 0.251128i | 0.784380 | − | 0.620281i | \(-0.212981\pi\) |
−0.929369 | + | 0.369152i | \(0.879648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.58392 | −0.489379 | −0.244690 | − | 0.969601i | \(-0.578686\pi\) | ||||
−0.244690 | + | 0.969601i | \(0.578686\pi\) | |||||||
\(182\) | 9.74638 | + | 0.0504042i | 0.722450 | + | 0.00373621i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.0342 | + | 8.10262i | −1.03461 | + | 0.597333i | ||||
\(185\) | −9.66954 | − | 16.7481i | −0.710919 | − | 1.23135i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.97476i | 0.290663i | ||||||||
\(188\) | −27.0155 | − | 15.5974i | −1.97030 | − | 1.13756i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 21.1460i | − | 1.53410i | ||||||
\(191\) | −6.87168 | + | 11.9021i | −0.497218 | + | 0.861206i | −0.999995 | − | 0.00320983i | \(-0.998978\pi\) |
0.502777 | + | 0.864416i | \(0.332312\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.7047 | − | 11.3765i | 1.41838 | − | 0.818899i | 0.422219 | − | 0.906494i | \(-0.361251\pi\) |
0.996156 | + | 0.0875946i | \(0.0279180\pi\) | |||||||
\(194\) | 24.9551 | 1.79167 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.30727 | 0.379091 | ||||||||
\(197\) | 12.5809 | − | 7.26358i | 0.896352 | − | 0.517509i | 0.0203371 | − | 0.999793i | \(-0.493526\pi\) |
0.876015 | + | 0.482284i | \(0.160193\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.9202 | − | 20.6464i | 0.845001 | − | 1.46358i | −0.0406192 | − | 0.999175i | \(-0.512933\pi\) |
0.885620 | − | 0.464410i | \(-0.153734\pi\) | |||||||
\(200\) | 50.2025i | 3.54985i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −34.7021 | − | 20.0353i | −2.44163 | − | 1.40968i | ||||
\(203\) | − | 2.73406i | − | 0.191894i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.87678 | − | 11.9109i | −0.480295 | − | 0.831896i | ||||
\(206\) | 10.0263 | − | 5.78871i | 0.698568 | − | 0.403318i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −24.2131 | − | 42.4437i | −1.67887 | − | 2.94294i | ||||
\(209\) | −4.43223 | −0.306584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.15764 | − | 3.73714i | −0.148538 | − | 0.257275i | 0.782149 | − | 0.623091i | \(-0.214123\pi\) |
−0.930687 | + | 0.365816i | \(0.880790\pi\) | |||||||
\(212\) | 24.6955 | − | 42.7738i | 1.69609 | − | 2.93772i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −44.7741 | − | 25.8504i | −3.06070 | − | 1.76709i | ||||
\(215\) | −24.4979 | − | 14.1439i | −1.67075 | − | 0.964605i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.871180 | − | 1.50893i | 0.0591395 | − | 0.102433i | ||||
\(218\) | −5.77339 | − | 9.99981i | −0.391024 | − | 0.677273i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 31.9210 | 2.15212 | ||||||||
\(221\) | −3.91635 | + | 6.70301i | −0.263442 | + | 0.450893i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.2604 | + | 11.6973i | −1.35674 | + | 0.783312i | −0.989182 | − | 0.146691i | \(-0.953138\pi\) |
−0.367553 | + | 0.930003i | \(0.619804\pi\) | |||||||
\(224\) | −9.37743 | − | 16.2422i | −0.626556 | − | 1.08523i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 7.43315i | − | 0.494446i | ||||||
\(227\) | 23.1427 | + | 13.3614i | 1.53603 | + | 0.886829i | 0.999065 | + | 0.0432270i | \(0.0137639\pi\) |
0.536968 | + | 0.843602i | \(0.319569\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.00670i | − | 0.198688i | −0.995053 | − | 0.0993442i | \(-0.968326\pi\) | ||
0.995053 | − | 0.0993442i | \(-0.0316745\pi\) | |||||||
\(230\) | 7.98222 | − | 13.8256i | 0.526332 | − | 0.911634i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.1683 | + | 12.2215i | −1.38977 | + | 0.802383i | ||||
\(233\) | −11.7148 | −0.767462 | −0.383731 | − | 0.923445i | \(-0.625361\pi\) | ||||
−0.383731 | + | 0.923445i | \(0.625361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.1504 | 1.24924 | ||||||||
\(236\) | −49.4199 | + | 28.5326i | −3.21696 | + | 1.85731i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.91018 | + | 5.04058i | −0.188639 | + | 0.326732i | ||||
\(239\) | − | 1.42797i | − | 0.0923677i | −0.998933 | − | 0.0461838i | \(-0.985294\pi\) | ||
0.998933 | − | 0.0461838i | \(-0.0147060\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.32068 | − | 1.33984i | −0.149488 | − | 0.0863069i | 0.423390 | − | 0.905947i | \(-0.360840\pi\) |
−0.572878 | + | 0.819640i | \(0.694173\pi\) | |||||||
\(242\) | 20.5232i | 1.31928i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 26.8284 | + | 46.4682i | 1.71751 | + | 2.97482i | ||||
\(245\) | −2.82162 | + | 1.62906i | −0.180267 | + | 0.104077i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.47450 | − | 4.36710i | −0.475591 | − | 0.277872i | ||||
\(248\) | −15.5770 | −0.989143 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.70989 | − | 4.69367i | −0.171389 | − | 0.296854i | ||||
\(251\) | −5.46696 | + | 9.46906i | −0.345072 | + | 0.597681i | −0.985367 | − | 0.170447i | \(-0.945479\pi\) |
0.640295 | + | 0.768129i | \(0.278812\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.89786 | − | 1.67308i | −0.182187 | − | 0.105186i | ||||
\(254\) | −22.7885 | − | 13.1570i | −1.42988 | − | 0.825541i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.9089 | + | 20.6268i | −0.744307 | + | 1.28918i | ||||
\(257\) | −2.07569 | − | 3.59520i | −0.129478 | − | 0.224262i | 0.793996 | − | 0.607922i | \(-0.207997\pi\) |
−0.923474 | + | 0.383660i | \(0.874663\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.93565 | −0.368823 | ||||||||
\(260\) | 53.8315 | + | 31.4519i | 3.33849 | + | 1.95057i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 43.6872 | − | 25.2228i | 2.69900 | − | 1.55827i | ||||
\(263\) | 2.02680 | + | 3.51052i | 0.124978 | + | 0.216468i | 0.921724 | − | 0.387846i | \(-0.126781\pi\) |
−0.796747 | + | 0.604314i | \(0.793447\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.3210i | 1.86260i | ||||||||
\(266\) | −5.62072 | − | 3.24513i | −0.344629 | − | 0.198971i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 4.38866i | − | 0.268080i | ||||||
\(269\) | 2.00011 | − | 3.46430i | 0.121949 | − | 0.211222i | −0.798587 | − | 0.601879i | \(-0.794419\pi\) |
0.920536 | + | 0.390657i | \(0.127752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.41189 | + | 1.39251i | −0.146512 | + | 0.0845888i | −0.571464 | − | 0.820627i | \(-0.693624\pi\) |
0.424952 | + | 0.905216i | \(0.360291\pi\) | |||||||
\(272\) | 29.1806 | 1.76933 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.7651 | 1.37529 | ||||||||
\(275\) | −8.97733 | + | 5.18306i | −0.541353 | + | 0.312551i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.34618 | − | 14.4560i | 0.501474 | − | 0.868578i | −0.498525 | − | 0.866875i | \(-0.666125\pi\) |
0.999999 | − | 0.00170243i | \(-0.000541901\pi\) | |||||||
\(278\) | − | 47.6741i | − | 2.85930i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 25.2258 | + | 14.5641i | 1.50753 | + | 0.870373i | ||||
\(281\) | − | 13.3731i | − | 0.797774i | −0.917000 | − | 0.398887i | \(-0.869397\pi\) | ||
0.917000 | − | 0.398887i | \(-0.130603\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.44312 | − | 16.3560i | −0.561335 | − | 0.972261i | −0.997380 | − | 0.0723362i | \(-0.976955\pi\) |
0.436045 | − | 0.899925i | \(-0.356379\pi\) | |||||||
\(284\) | 10.8207 | − | 6.24731i | 0.642088 | − | 0.370710i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.07663 | − | 15.5351i | 0.536712 | − | 0.918609i | ||||
\(287\) | −4.22131 | −0.249176 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.18199 | + | 10.7075i | 0.363647 | + | 0.629855i | ||||
\(290\) | 12.0399 | − | 20.8537i | 0.707008 | − | 1.22457i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.6841 | + | 8.47789i | 0.859324 | + | 0.496131i | ||||
\(293\) | 2.95999 | + | 1.70895i | 0.172925 | + | 0.0998380i | 0.583964 | − | 0.811779i | \(-0.301501\pi\) |
−0.411040 | + | 0.911617i | \(0.634834\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.5161 | − | 30.3388i | 1.01983 | − | 1.76639i | ||||
\(296\) | 26.5329 | + | 45.9564i | 1.54220 | + | 2.67116i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.8697 | 0.629663 | ||||||||
\(299\) | −3.23845 | − | 5.67675i | −0.187284 | − | 0.328295i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.51903 | + | 4.34111i | −0.433390 | + | 0.250218i | ||||
\(302\) | 25.5465 | + | 44.2479i | 1.47004 | + | 2.54618i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 32.5391i | 1.86625i | ||||||||
\(305\) | −28.5268 | − | 16.4699i | −1.63344 | − | 0.943066i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.3679i | − | 0.934165i | −0.884214 | − | 0.467083i | \(-0.845305\pi\) | ||
0.884214 | − | 0.467083i | \(-0.154695\pi\) | |||||||
\(308\) | 4.89868 | − | 8.48477i | 0.279128 | − | 0.483464i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.2896 | − | 7.67278i | 0.754801 | − | 0.435785i | ||||
\(311\) | 23.6979 | 1.34378 | 0.671891 | − | 0.740650i | \(-0.265482\pi\) | ||||
0.671891 | + | 0.740650i | \(0.265482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.18025 | −0.292805 | −0.146403 | − | 0.989225i | \(-0.546769\pi\) | ||||
−0.146403 | + | 0.989225i | \(0.546769\pi\) | |||||||
\(314\) | −27.0941 | + | 15.6428i | −1.52901 | + | 0.882774i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.12798 | − | 3.68577i | 0.119708 | − | 0.207341i | ||||
\(317\) | 6.06537i | 0.340665i | 0.985387 | + | 0.170332i | \(0.0544842\pi\) | ||||
−0.985387 | + | 0.170332i | \(0.945516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.37096 | − | 2.52358i | −0.244727 | − | 0.141293i | ||||
\(320\) | − | 76.8686i | − | 4.29709i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.44994 | − | 4.24343i | −0.136530 | − | 0.236477i | ||||
\(323\) | 4.47700 | − | 2.58480i | 0.249107 | − | 0.143822i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.2462 | − | 0.104705i | −1.12306 | − | 0.00580799i | ||||
\(326\) | −11.9087 | −0.659562 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.8697 | + | 32.6833i | 1.04190 | + | 1.80463i | ||||
\(329\) | 2.93887 | − | 5.09027i | 0.162025 | − | 0.280636i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9605 | + | 8.63743i | 0.822301 | + | 0.474756i | 0.851209 | − | 0.524826i | \(-0.175870\pi\) |
−0.0289082 | + | 0.999582i | \(0.509203\pi\) | |||||||
\(332\) | 45.8258 | + | 26.4576i | 2.51502 | + | 1.45205i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.1902 | − | 21.1140i | 0.667017 | − | 1.15531i | ||||
\(335\) | 1.34710 | + | 2.33324i | 0.0735998 | + | 0.127479i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.35464 | −0.455106 | −0.227553 | − | 0.973766i | \(-0.573073\pi\) | ||||
−0.227553 | + | 0.973766i | \(0.573073\pi\) | |||||||
\(338\) | 30.6136 | − | 17.2551i | 1.66516 | − | 0.938552i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −32.2435 | + | 18.6158i | −1.74865 | + | 1.00958i | ||||
\(341\) | −1.60822 | − | 2.78552i | −0.0870901 | − | 0.150844i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 67.2216 | + | 38.8104i | 3.62435 | + | 2.09252i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.4679i | 0.885318i | ||||||||
\(347\) | 14.4110 | − | 24.9606i | 0.773623 | − | 1.33995i | −0.161942 | − | 0.986800i | \(-0.551776\pi\) |
0.935565 | − | 0.353154i | \(-0.114891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1516 | + | 5.86103i | −0.543403 | + | 0.313734i | −0.746457 | − | 0.665434i | \(-0.768247\pi\) |
0.203054 | + | 0.979167i | \(0.434913\pi\) | |||||||
\(350\) | −15.1794 | −0.811376 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −34.6220 | −1.84536 | ||||||||
\(353\) | −15.4466 | + | 8.91811i | −0.822141 | + | 0.474663i | −0.851154 | − | 0.524916i | \(-0.824097\pi\) |
0.0290134 | + | 0.999579i | \(0.490763\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.83521 | + | 6.64278i | −0.203552 | + | 0.352562i | ||||
\(356\) | 80.2113i | 4.25119i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.08239 | − | 5.24372i | −0.480019 | − | 0.277139i | ||||
\(359\) | 5.68162i | 0.299864i | 0.988696 | + | 0.149932i | \(0.0479055\pi\) | ||||
−0.988696 | + | 0.149932i | \(0.952094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.61771 | − | 11.4622i | −0.348300 | − | 0.603274i | ||||
\(362\) | −15.4132 | + | 8.89882i | −0.810100 | + | 0.467712i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.6212 | − | 9.48199i | 0.871188 | − | 0.496991i | ||||
\(365\) | −10.4091 | −0.544838 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.81580 | + | 17.0015i | 0.512381 | + | 0.887469i | 0.999897 | + | 0.0143554i | \(0.00456964\pi\) |
−0.487516 | + | 0.873114i | \(0.662097\pi\) | |||||||
\(368\) | −12.2829 | + | 21.2746i | −0.640289 | + | 1.10901i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −45.2735 | − | 26.1387i | −2.35366 | − | 1.35888i | ||||
\(371\) | 8.05947 | + | 4.65314i | 0.418427 | + | 0.241579i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0323 | + | 27.7687i | −0.830119 | + | 1.43781i | 0.0678240 | + | 0.997697i | \(0.478394\pi\) |
−0.897943 | + | 0.440111i | \(0.854939\pi\) | |||||||
\(374\) | 5.37227 | + | 9.30505i | 0.277794 | + | 0.481153i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −52.5482 | −2.70997 | ||||||||
\(377\) | −4.88468 | − | 8.56248i | −0.251574 | − | 0.440990i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4745 | + | 9.51154i | −0.846237 | + | 0.488575i | −0.859379 | − | 0.511339i | \(-0.829150\pi\) |
0.0131425 | + | 0.999914i | \(0.495816\pi\) | |||||||
\(380\) | −20.7583 | − | 35.9545i | −1.06488 | − | 1.84443i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 37.1510i | 1.90081i | ||||||||
\(383\) | −0.606070 | − | 0.349915i | −0.0309687 | − | 0.0178798i | 0.484436 | − | 0.874827i | \(-0.339025\pi\) |
−0.515404 | + | 0.856947i | \(0.672358\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.01459i | 0.306532i | ||||||||
\(386\) | 30.7529 | − | 53.2657i | 1.56528 | − | 2.71115i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 42.4310 | − | 24.4976i | 2.15411 | − | 1.24368i | ||||
\(389\) | −20.0547 | −1.01681 | −0.508407 | − | 0.861117i | \(-0.669765\pi\) | ||||
−0.508407 | + | 0.861117i | \(0.669765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.90284 | 0.197375 | ||||||||
\(392\) | 7.74244 | − | 4.47010i | 0.391052 | − | 0.225774i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.6349 | − | 34.0086i | 0.989192 | − | 1.71333i | ||||
\(395\) | 2.61272i | 0.131460i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.2953 | − | 11.1401i | −0.968403 | − | 0.559108i | −0.0696541 | − | 0.997571i | \(-0.522190\pi\) |
−0.898749 | + | 0.438463i | \(0.855523\pi\) | |||||||
\(398\) | − | 64.4453i | − | 3.23035i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 38.0513 | + | 65.9069i | 1.90257 | + | 3.29534i | ||||
\(401\) | 4.16341 | − | 2.40374i | 0.207911 | − | 0.120037i | −0.392429 | − | 0.919782i | \(-0.628365\pi\) |
0.600340 | + | 0.799745i | \(0.295032\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0324883 | − | 6.28208i | 0.00161836 | − | 0.312933i | ||||
\(404\) | −78.6717 | −3.91406 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.69535 | − | 6.40054i | −0.183397 | − | 0.317653i | ||||
\(407\) | −5.47869 | + | 9.48937i | −0.271568 | + | 0.470370i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.8727 | + | 18.4017i | 1.57601 | + | 0.909907i | 0.995409 | + | 0.0957164i | \(0.0305142\pi\) |
0.580597 | + | 0.814191i | \(0.302819\pi\) | |||||||
\(410\) | −32.1976 | − | 18.5893i | −1.59013 | − | 0.918060i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.3651 | − | 19.6850i | 0.559921 | − | 0.969811i | ||||
\(413\) | −5.37613 | − | 9.31173i | −0.264542 | − | 0.458200i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.4845 | −1.59460 | ||||||||
\(416\) | −58.3864 | − | 34.1132i | −2.86263 | − | 1.67254i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.3760 | + | 5.99059i | −0.507507 | + | 0.293009i | ||||
\(419\) | 14.6334 | + | 25.3457i | 0.714887 | + | 1.23822i | 0.963003 | + | 0.269490i | \(0.0868552\pi\) |
−0.248116 | + | 0.968730i | \(0.579812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 7.53862i | − | 0.367410i | −0.982981 | − | 0.183705i | \(-0.941191\pi\) | ||
0.982981 | − | 0.183705i | \(-0.0588091\pi\) | |||||||
\(422\) | −10.1022 | − | 5.83251i | −0.491768 | − | 0.283922i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 83.2000i | − | 4.04055i | ||||||
\(425\) | 6.04534 | − | 10.4708i | 0.293242 | − | 0.507910i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.75558 | + | 5.05504i | −0.423712 | + | 0.244630i | ||||
\(428\) | −101.506 | −4.90646 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −76.4674 | −3.68759 | ||||||||
\(431\) | 27.0426 | − | 15.6131i | 1.30260 | − | 0.752055i | 0.321748 | − | 0.946825i | \(-0.395730\pi\) |
0.980849 | + | 0.194771i | \(0.0623963\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.94202 | − | 5.09573i | 0.141384 | − | 0.244885i | −0.786634 | − | 0.617420i | \(-0.788178\pi\) |
0.928018 | + | 0.372535i | \(0.121511\pi\) | |||||||
\(434\) | − | 4.70994i | − | 0.226084i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.6329 | − | 11.3351i | −0.940247 | − | 0.542852i | ||||
\(437\) | 4.35204i | 0.208186i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.97821 | − | 8.62251i | −0.237597 | − | 0.411530i | 0.722427 | − | 0.691447i | \(-0.243026\pi\) |
−0.960024 | + | 0.279917i | \(0.909693\pi\) | |||||||
\(440\) | 46.5676 | − | 26.8858i | 2.22002 | − | 1.28173i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.108527 | + | 20.9853i | −0.00516212 | + | 0.998170i | ||||
\(443\) | 35.8813 | 1.70477 | 0.852385 | − | 0.522915i | \(-0.175155\pi\) | ||||
0.852385 | + | 0.522915i | \(0.175155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.6208 | − | 42.6444i | −1.16714 | − | 2.02154i | ||||
\(446\) | −31.6202 | + | 54.7678i | −1.49726 | + | 2.59333i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.4321 | − | 11.7965i | −0.965324 | − | 0.557330i | ||||
\(449\) | −3.46001 | − | 1.99764i | −0.163288 | − | 0.0942744i | 0.416129 | − | 0.909306i | \(-0.363386\pi\) |
−0.579417 | + | 0.815031i | \(0.696720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.89633 | + | 6.74864i | −0.183471 | + | 0.317781i | ||||
\(452\) | −7.29687 | − | 12.6386i | −0.343216 | − | 0.594467i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 72.2371 | 3.39026 | ||||||||
\(455\) | −5.92620 | + | 10.1430i | −0.277825 | + | 0.475510i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.6995 | − | 20.6111i | 1.66995 | − | 0.964147i | 0.702291 | − | 0.711890i | \(-0.252160\pi\) |
0.967660 | − | 0.252257i | \(-0.0811729\pi\) | |||||||
\(458\) | −4.06385 | − | 7.03880i | −0.189891 | − | 0.328901i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 31.3435i | − | 1.46140i | ||||||
\(461\) | −21.4139 | − | 12.3633i | −0.997343 | − | 0.575816i | −0.0898818 | − | 0.995952i | \(-0.528649\pi\) |
−0.907461 | + | 0.420136i | \(0.861982\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.4057i | − | 1.13423i | −0.823639 | − | 0.567115i | \(-0.808060\pi\) | ||
0.823639 | − | 0.567115i | \(-0.191940\pi\) | |||||||
\(464\) | −18.5268 | + | 32.0893i | −0.860084 | + | 1.48971i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.4248 | + | 15.8337i | −1.27043 | + | 0.733482i | ||||
\(467\) | −4.44860 | −0.205857 | −0.102928 | − | 0.994689i | \(-0.532821\pi\) | ||||
−0.102928 | + | 0.994689i | \(0.532821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.826916 | 0.0381834 | ||||||||
\(470\) | 44.8318 | − | 25.8837i | 2.06794 | − | 1.19392i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −48.0637 | + | 83.2487i | −2.21231 | + | 3.83183i | ||||
\(473\) | 16.0276i | 0.736951i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.6760 | + | 6.74113i | 0.535730 | + | 0.309304i | ||||
\(476\) | 11.4273i | 0.523769i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.93004 | − | 3.34293i | −0.0882780 | − | 0.152902i | ||||
\(479\) | 27.4328 | − | 15.8383i | 1.25343 | − | 0.723671i | 0.281645 | − | 0.959519i | \(-0.409120\pi\) |
0.971790 | + | 0.235848i | \(0.0757868\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.5892 | + | 10.6047i | −0.847593 | + | 0.483531i | ||||
\(482\) | −7.24372 | −0.329942 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.1469 | + | 34.8954i | 0.915767 | + | 1.58616i | ||||
\(485\) | −15.0390 | + | 26.0483i | −0.682887 | + | 1.18279i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.3096 | + | 13.4578i | 1.05626 | + | 0.609832i | 0.924395 | − | 0.381436i | \(-0.124570\pi\) |
0.131864 | + | 0.991268i | \(0.457904\pi\) | |||||||
\(488\) | 78.2766 | + | 45.1930i | 3.54341 | + | 2.04579i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.40367 | + | 7.62739i | −0.198938 | + | 0.344570i | ||||
\(491\) | −4.86358 | − | 8.42396i | −0.219490 | − | 0.380168i | 0.735162 | − | 0.677891i | \(-0.237106\pi\) |
−0.954652 | + | 0.297723i | \(0.903773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.88682 | 0.265129 | ||||||||
\(494\) | −23.4006 | − | 0.121018i | −1.05284 | − | 0.00544487i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.4498 | + | 11.8067i | −0.918225 | + | 0.530137i | ||||
\(497\) | 1.17712 | + | 2.03884i | 0.0528012 | + | 0.0914543i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.87525i | 0.352545i | 0.984341 | + | 0.176272i | \(0.0564039\pi\) | ||||
−0.984341 | + | 0.176272i | \(0.943596\pi\) | |||||||
\(500\) | −9.21523 | − | 5.32042i | −0.412118 | − | 0.237936i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29.5565i | 1.31917i | ||||||||
\(503\) | −4.87603 | + | 8.44553i | −0.217411 | + | 0.376568i | −0.954016 | − | 0.299756i | \(-0.903095\pi\) |
0.736604 | + | 0.676324i | \(0.236428\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.8259 | − | 24.1482i | 1.86123 | − | 1.07458i | ||||
\(506\) | −9.04533 | −0.402114 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −51.6630 | −2.29217 | ||||||||
\(509\) | 19.9407 | − | 11.5128i | 0.883857 | − | 0.510295i | 0.0119288 | − | 0.999929i | \(-0.496203\pi\) |
0.871928 | + | 0.489634i | \(0.162870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.59741 | + | 2.76680i | −0.0706653 | + | 0.122396i | ||||
\(512\) | 11.8512i | 0.523752i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.71853 | − | 5.61100i | −0.428666 | − | 0.247490i | ||||
\(515\) | 13.9541i | 0.614891i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.42524 | − | 9.39679i | −0.238602 | − | 0.413270i | ||||
\(518\) | −13.8956 | + | 8.02261i | −0.610537 | + | 0.352493i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 105.022 | + | 0.543130i | 4.60552 | + | 0.0238178i | ||||
\(521\) | −0.486481 | −0.0213131 | −0.0106566 | − | 0.999943i | \(-0.503392\pi\) | ||||
−0.0106566 | + | 0.999943i | \(0.503392\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3135 | + | 29.9878i | 0.757065 | + | 1.31128i | 0.944341 | + | 0.328968i | \(0.106701\pi\) |
−0.187275 | + | 0.982307i | \(0.559966\pi\) | |||||||
\(524\) | 49.5207 | − | 85.7724i | 2.16332 | − | 3.74698i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.48962 | + | 5.47883i | 0.413767 | + | 0.238888i | ||||
\(527\) | 3.24893 | + | 1.87577i | 0.141526 | + | 0.0817099i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.85719 | − | 17.0732i | 0.428574 | − | 0.742311i | ||||
\(530\) | 40.9818 | + | 70.9826i | 1.78014 | + | 3.08329i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.7425 | −0.552458 | ||||||||
\(533\) | −13.2202 | + | 7.54182i | −0.572632 | + | 0.326672i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 53.9656 | − | 31.1571i | 2.33314 | − | 1.34704i | ||||
\(536\) | −3.69639 | − | 6.40234i | −0.159660 | − | 0.276539i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 10.8134i | − | 0.466198i | ||||||
\(539\) | 1.59871 | + | 0.923014i | 0.0688612 | + | 0.0397570i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.5384i | 0.969002i | 0.874791 | + | 0.484501i | \(0.160999\pi\) | ||||
−0.874791 | + | 0.484501i | \(0.839001\pi\) | |||||||
\(542\) | −3.76422 | + | 6.51982i | −0.161687 | + | 0.280050i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 34.9717 | − | 20.1909i | 1.49940 | − | 0.865678i | ||||
\(545\) | 13.9172 | 0.596146 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.3716 | 1.68341 | 0.841704 | − | 0.539940i | \(-0.181553\pi\) | ||||
0.841704 | + | 0.539940i | \(0.181553\pi\) | |||||||
\(548\) | 38.7074 | − | 22.3477i | 1.65350 | − | 0.954648i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.0108 | + | 24.2675i | −0.597424 | + | 1.03477i | ||||
\(551\) | 6.56436i | 0.279651i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.694475 | + | 0.400955i | 0.0295321 | + | 0.0170504i | ||||
\(554\) | − | 45.1227i | − | 1.91708i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −46.8000 | − | 81.0600i | −1.98476 | − | 3.43771i | ||||
\(557\) | −0.629579 | + | 0.363487i | −0.0266761 | + | 0.0154015i | −0.513279 | − | 0.858222i | \(-0.671569\pi\) |
0.486603 | + | 0.873623i | \(0.338236\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.7921 | + | 27.0289i | −0.667935 | + | 1.14320i | ||||
\(560\) | 44.1559 | 1.86593 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0751 | − | 31.3070i | −0.762452 | − | 1.32061i | ||||
\(563\) | −20.8038 | + | 36.0333i | −0.876777 | + | 1.51862i | −0.0219200 | + | 0.999760i | \(0.506978\pi\) |
−0.854857 | + | 0.518863i | \(0.826355\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.75879 | + | 4.47954i | 0.326415 | + | 0.188456i | ||||
\(566\) | −44.2134 | − | 25.5266i | −1.85843 | − | 1.07296i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.5237 | − | 18.2276i | 0.441565 | − | 0.764813i | ||||
\(569\) | 12.6944 | + | 21.9873i | 0.532177 | + | 0.921757i | 0.999294 | + | 0.0375618i | \(0.0119591\pi\) |
−0.467118 | + | 0.884195i | \(0.654708\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.9992 | −0.711393 | −0.355697 | − | 0.934602i | \(-0.615756\pi\) | ||||
−0.355697 | + | 0.934602i | \(0.615756\pi\) | |||||||
\(572\) | 0.182683 | − | 35.3244i | 0.00763836 | − | 1.47699i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.88225 | + | 5.70552i | −0.412477 | + | 0.238144i | ||||
\(575\) | 5.08929 | + | 8.81490i | 0.212238 | + | 0.367607i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 15.9759i | − | 0.665084i | −0.943088 | − | 0.332542i | \(-0.892094\pi\) | ||
0.943088 | − | 0.332542i | \(-0.107906\pi\) | |||||||
\(578\) | 28.9445 | + | 16.7111i | 1.20393 | + | 0.695092i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 47.2767i | − | 1.96306i | ||||||
\(581\) | −4.98516 | + | 8.63454i | −0.206819 | + | 0.358221i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.8780 | − | 8.58982i | 0.616184 | − | 0.355754i | ||||
\(584\) | 28.5623 | 1.18192 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.23926 | 0.381670 | ||||||||
\(587\) | 13.8404 | − | 7.99075i | 0.571254 | − | 0.329814i | −0.186396 | − | 0.982475i | \(-0.559681\pi\) |
0.757650 | + | 0.652661i | \(0.226347\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.09166 | + | 3.62287i | −0.0861855 | + | 0.149278i | ||||
\(590\) | − | 94.6989i | − | 3.89869i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 69.6660 | + | 40.2217i | 2.86325 | + | 1.65310i | ||||
\(593\) | 29.0532i | 1.19307i | 0.802586 | + | 0.596536i | \(0.203457\pi\) | ||||
−0.802586 | + | 0.596536i | \(0.796543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.50760 | − | 6.07534i | −0.143797 | − | 0.249065i | ||||
\(596\) | 18.4816 | − | 10.6704i | 0.757037 | − | 0.437075i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.2540 | − | 8.91240i | −0.623783 | − | 0.364455i | ||||
\(599\) | −3.45554 | −0.141190 | −0.0705948 | − | 0.997505i | \(-0.522490\pi\) | ||||
−0.0705948 | + | 0.997505i | \(0.522490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.76518 | − | 13.4497i | −0.316748 | − | 0.548624i | 0.663059 | − | 0.748567i | \(-0.269258\pi\) |
−0.979808 | + | 0.199943i | \(0.935924\pi\) | |||||||
\(602\) | −11.7349 | + | 20.3254i | −0.478278 | + | 0.828402i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 86.8732 | + | 50.1563i | 3.53482 | + | 2.04083i | ||||
\(605\) | −21.4222 | − | 12.3681i | −0.870938 | − | 0.502836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.73922 | + | 13.4047i | −0.314125 | + | 0.544081i | −0.979251 | − | 0.202650i | \(-0.935044\pi\) |
0.665126 | + | 0.746731i | \(0.268378\pi\) | |||||||
\(608\) | 22.5148 | + | 38.9967i | 0.913095 | + | 1.58153i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −89.0429 | −3.60524 | ||||||||
\(611\) | 0.109597 | − | 21.1922i | 0.00443383 | − | 0.857345i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.17669 | + | 3.56611i | −0.249474 | + | 0.144034i | −0.619523 | − | 0.784978i | \(-0.712674\pi\) |
0.370049 | + | 0.929012i | \(0.379341\pi\) | |||||||
\(614\) | −22.1228 | − | 38.3178i | −0.892804 | − | 1.54638i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 16.5039i | − | 0.664959i | ||||||
\(617\) | 4.30142 | + | 2.48342i | 0.173168 | + | 0.0999789i | 0.584079 | − | 0.811697i | \(-0.301456\pi\) |
−0.410911 | + | 0.911676i | \(0.634789\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 42.3570i | − | 1.70247i | −0.524784 | − | 0.851235i | \(-0.675854\pi\) | ||
0.524784 | − | 0.851235i | \(-0.324146\pi\) | |||||||
\(620\) | 15.0642 | − | 26.0920i | 0.604993 | − | 1.04788i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 55.4776 | − | 32.0300i | 2.22445 | − | 1.28429i | ||||
\(623\) | −15.1135 | −0.605508 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.5445 | −0.861779 | ||||||||
\(626\) | −12.1272 | + | 7.00162i | −0.484699 | + | 0.279841i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30.7120 | + | 53.1947i | −1.22554 | + | 2.12270i | ||||
\(629\) | − | 12.7803i | − | 0.509583i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.42803 | − | 3.13387i | −0.216086 | − | 0.124758i | 0.388050 | − | 0.921638i | \(-0.373149\pi\) |
−0.604137 | + | 0.796881i | \(0.706482\pi\) | |||||||
\(632\) | − | 7.16924i | − | 0.285177i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.19794 | + | 14.1992i | 0.325582 | + | 0.563924i | ||||
\(635\) | 27.4667 | − | 15.8579i | 1.08998 | − | 0.629302i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.78660 | + | 3.13178i | 0.0707878 | + | 0.124086i | ||||
\(638\) | −13.6434 | −0.540149 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −42.7898 | − | 74.1142i | −1.69142 | − | 2.92962i | ||||
\(641\) | 15.7818 | − | 27.3350i | 0.623345 | − | 1.07967i | −0.365513 | − | 0.930806i | \(-0.619106\pi\) |
0.988858 | − | 0.148860i | \(-0.0475602\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.8053 | + | 9.12520i | 0.623300 | + | 0.359863i | 0.778153 | − | 0.628075i | \(-0.216157\pi\) |
−0.154852 | + | 0.987938i | \(0.549490\pi\) | |||||||
\(644\) | −8.33125 | − | 4.81005i | −0.328297 | − | 0.189543i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.98721 | − | 12.1022i | 0.274908 | − | 0.476155i | ||||
\(647\) | −11.5137 | − | 19.9423i | −0.452649 | − | 0.784011i | 0.545901 | − | 0.837850i | \(-0.316188\pi\) |
−0.998550 | + | 0.0538387i | \(0.982854\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.8490 | −0.779140 | ||||||||
\(650\) | −47.5387 | + | 27.1197i | −1.86462 | + | 1.06372i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.2483 | + | 11.6904i | −0.792985 | + | 0.457830i | ||||
\(653\) | 14.4062 | + | 24.9523i | 0.563759 | + | 0.976459i | 0.997164 | + | 0.0752597i | \(0.0239786\pi\) |
−0.433405 | + | 0.901199i | \(0.642688\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 60.8014i | 2.37571i | ||||||||
\(656\) | 49.5450 | + | 28.6048i | 1.93441 | + | 1.11683i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 15.8887i | − | 0.619406i | ||||||
\(659\) | −15.6114 | + | 27.0397i | −0.608134 | + | 1.05332i | 0.383414 | + | 0.923577i | \(0.374748\pi\) |
−0.991548 | + | 0.129742i | \(0.958585\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.0000 | + | 13.2791i | −0.894598 | + | 0.516496i | −0.875444 | − | 0.483320i | \(-0.839431\pi\) |
−0.0191541 | + | 0.999817i | \(0.506097\pi\) | |||||||
\(662\) | 46.6973 | 1.81494 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 89.1366 | 3.45917 | ||||||||
\(665\) | 6.77458 | − | 3.91130i | 0.262707 | − | 0.151674i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.47792 | + | 4.29188i | −0.0959454 | + | 0.166182i | ||||
\(668\) | − | 47.8667i | − | 1.85202i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.30721 | + | 3.64147i | 0.243669 | + | 0.140682i | ||||
\(671\) | 18.6635i | 0.720495i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.86930 | − | 17.0941i | −0.380434 | − | 0.658930i | 0.610691 | − | 0.791869i | \(-0.290892\pi\) |
−0.991124 | + | 0.132939i | \(0.957559\pi\) | |||||||
\(674\) | −19.5585 | + | 11.2921i | −0.753366 | + | 0.434956i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 35.1134 | − | 59.3910i | 1.35052 | − | 2.28427i | ||||
\(677\) | 13.1440 | 0.505163 | 0.252582 | − | 0.967576i | \(-0.418720\pi\) | ||||
0.252582 | + | 0.967576i | \(0.418720\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.61585 | + | 7.99489i | 0.177140 | + | 0.306816i | ||||
\(680\) | −31.3586 | + | 54.3147i | −1.20255 | + | 2.08287i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.52981 | − | 4.34734i | −0.288331 | − | 0.166468i | ||||
\(683\) | 5.85654 | + | 3.38128i | 0.224094 | + | 0.129381i | 0.607845 | − | 0.794056i | \(-0.292034\pi\) |
−0.383750 | + | 0.923437i | \(0.625368\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.7192 | + | 23.7624i | −0.524185 | + | 0.907915i | ||||
\(686\) | 1.35160 | + | 2.34104i | 0.0516043 | + | 0.0893812i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 117.666 | 4.48599 | ||||||||
\(689\) | 33.5538 | + | 0.173526i | 1.27830 | + | 0.00661082i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.94223 | − | 4.58545i | 0.302137 | − | 0.174439i | −0.341266 | − | 0.939967i | \(-0.610856\pi\) |
0.643402 | + | 0.765528i | \(0.277522\pi\) | |||||||
\(692\) | 16.1659 | + | 28.0002i | 0.614537 | + | 1.06441i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 77.9115i | − | 2.95748i | ||||||
\(695\) | 49.7626 | + | 28.7304i | 1.88760 | + | 1.08981i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 9.08908i | − | 0.344273i | ||||||
\(698\) | −15.8435 | + | 27.4418i | −0.599686 | + | 1.03869i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −25.8095 | + | 14.9011i | −0.975509 | + | 0.563210i | ||||
\(701\) | −47.4700 | −1.79292 | −0.896459 | − | 0.443127i | \(-0.853869\pi\) | ||||
−0.896459 | + | 0.443127i | \(0.853869\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.2512 | 0.537495 | ||||||||
\(704\) | −37.7181 | + | 21.7766i | −1.42156 | + | 0.820736i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.1074 | + | 41.7552i | −0.907294 | + | 1.57148i | ||||
\(707\) | − | 14.8234i | − | 0.557491i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.2866 | + | 17.4860i | 1.13744 | + | 0.656699i | 0.945795 | − | 0.324766i | \(-0.105285\pi\) |
0.191642 | + | 0.981465i | \(0.438619\pi\) | |||||||
\(710\) | 20.7347i | 0.778158i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 67.5587 | + | 117.015i | 2.53187 | + | 4.38533i | ||||
\(713\) | −2.73512 | + | 1.57912i | −0.102431 | + | 0.0591387i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7457 | + | 18.8364i | 0.401866 | + | 0.704440i | ||||
\(716\) | −20.5903 | −0.769496 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.67926 | + | 13.3009i | 0.286588 | + | 0.496384i | ||||
\(719\) | 4.18051 | − | 7.24085i | 0.155907 | − | 0.270038i | −0.777482 | − | 0.628905i | \(-0.783503\pi\) |
0.933389 | + | 0.358867i | \(0.116837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.70907 | + | 2.14143i | 0.138133 | + | 0.0797511i | ||||
\(722\) | −30.9846 | − | 17.8890i | −1.15313 | − | 0.665758i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.4713 | + | 30.2612i | −0.649317 | + | 1.12465i | ||||
\(725\) | 7.67639 | + | 13.2959i | 0.285094 | + | 0.493797i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.4014 | −1.01626 | −0.508131 | − | 0.861280i | \(-0.669663\pi\) | ||||
−0.508131 | + | 0.861280i | \(0.669663\pi\) | |||||||
\(728\) | 16.2613 | − | 27.8320i | 0.602685 | − | 1.03152i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24.3681 | + | 14.0689i | −0.901905 | + | 0.520715i | ||||
\(731\) | −9.34703 | − | 16.1895i | −0.345712 | − | 0.598791i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12.1569i | − | 0.449026i | −0.974471 | − | 0.224513i | \(-0.927921\pi\) | ||
0.974471 | − | 0.224513i | \(-0.0720792\pi\) | |||||||
\(734\) | 45.9583 | + | 26.5340i | 1.69635 | + | 0.979389i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33.9956i | 1.25309i | ||||||||
\(737\) | 0.763255 | − | 1.32200i | 0.0281148 | − | 0.0486963i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.9537 | + | 24.2220i | −1.54329 | + | 0.891019i | −0.544662 | + | 0.838656i | \(0.683342\pi\) |
−0.998628 | + | 0.0523634i | \(0.983325\pi\) | |||||||
\(740\) | −102.638 | −3.77304 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25.1567 | 0.923531 | ||||||||
\(743\) | 14.7143 | − | 8.49532i | 0.539816 | − | 0.311663i | −0.205188 | − | 0.978722i | \(-0.565781\pi\) |
0.745004 | + | 0.667060i | \(0.232447\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.55052 | + | 11.3458i | −0.239993 | + | 0.415679i | ||||
\(746\) | 86.6767i | 3.17346i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.2689 | + | 10.5475i | 0.667977 | + | 0.385657i | ||||
\(749\) | − | 19.1258i | − | 0.698841i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.5162 | + | 37.2671i | 0.785136 | + | 1.35990i | 0.928918 | + | 0.370287i | \(0.120741\pi\) |
−0.143781 | + | 0.989610i | \(0.545926\pi\) | |||||||
\(752\) | −68.9863 | + | 39.8292i | −2.51567 | + | 1.45242i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −23.0083 | − | 13.4430i | −0.837911 | − | 0.489563i | ||||
\(755\) | −61.5817 | −2.24119 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5892 | − | 25.2693i | −0.530255 | − | 0.918428i | −0.999377 | − | 0.0352949i | \(-0.988763\pi\) |
0.469122 | − | 0.883133i | \(-0.344570\pi\) | |||||||
\(758\) | −25.7116 | + | 44.5337i | −0.933886 | + | 1.61754i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −60.5661 | − | 34.9678i | −2.19696 | − | 1.26842i | ||||
\(761\) | 25.4829 | + | 14.7126i | 0.923754 | + | 0.533330i | 0.884831 | − | 0.465912i | \(-0.154274\pi\) |
0.0389234 | + | 0.999242i | \(0.487607\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.13577 | − | 3.69925i | 0.0773199 | − | 0.133922i | ||||
\(764\) | 36.4699 | + | 63.1677i | 1.31943 | + | 2.28533i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.89178 | −0.0683526 | ||||||||
\(767\) | −33.4732 | − | 19.5573i | −1.20865 | − | 0.706172i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.8839 | − | 8.59322i | 0.536727 | − | 0.309879i | −0.207024 | − | 0.978336i | \(-0.566378\pi\) |
0.743751 | + | 0.668456i | \(0.233045\pi\) | |||||||
\(770\) | 8.12930 | + | 14.0804i | 0.292960 | + | 0.507421i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 120.756i | − | 4.34612i | ||||||
\(773\) | −19.0180 | − | 10.9801i | −0.684031 | − | 0.394926i | 0.117341 | − | 0.993092i | \(-0.462563\pi\) |
−0.801372 | + | 0.598166i | \(0.795896\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.78399i | 0.351451i | ||||||||
\(776\) | 41.2666 | − | 71.4759i | 1.48139 | − | 2.56584i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −46.9488 | + | 27.1059i | −1.68320 | + | 0.971794i | ||||
\(779\) | 10.1352 | 0.363131 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.34600 | 0.155512 | ||||||||
\(782\) | 9.13669 | − | 5.27507i | 0.326727 | − | 0.188636i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.77628 | − | 11.7369i | 0.242010 | − | 0.419174i | ||||
\(785\) | − | 37.7081i | − | 1.34586i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.02275 | − | 1.16784i | −0.0721033 | − | 0.0416289i | 0.463515 | − | 0.886089i | \(-0.346588\pi\) |
−0.535618 | + | 0.844460i | \(0.679921\pi\) | |||||||
\(788\) | − | 77.0996i | − | 2.74656i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.53135 | + | 6.11648i | 0.125640 | + | 0.217615i | ||||
\(791\) | 2.38137 | − | 1.37488i | 0.0846716 | − | 0.0488852i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.3892 | + | 31.4740i | −0.653020 | + | 1.11767i | ||||
\(794\) | −60.2280 | −2.13741 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −63.2637 | − | 109.576i | −2.24232 | − | 3.88382i | ||||
\(797\) | −13.9020 | + | 24.0790i | −0.492434 | + | 0.852921i | −0.999962 | − | 0.00871411i | \(-0.997226\pi\) |
0.507528 | + | 0.861635i | \(0.330560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.9601 | + | 6.32780i | 0.387739 | + | 0.223861i | ||||
\(800\) | 91.2059 | + | 52.6577i | 3.22461 | + | 1.86173i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.49779 | − | 11.2545i | 0.229445 | − | 0.397410i | ||||
\(803\) | 2.94886 | + | 5.10758i | 0.104063 | + | 0.180243i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.90576 | 0.208151 | ||||||||
\(806\) | −8.41479 | − | 14.7505i | −0.296398 | − | 0.519564i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −114.769 | + | 66.2620i | −4.03756 | + | 2.33109i | ||||
\(809\) | 7.51017 | + | 13.0080i | 0.264043 | + | 0.457337i | 0.967313 | − | 0.253587i | \(-0.0816104\pi\) |
−0.703269 | + | 0.710924i | \(0.748277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.6933i | 1.53428i | 0.641481 | + | 0.767139i | \(0.278320\pi\) | ||||
−0.641481 | + | 0.767139i | \(0.721680\pi\) | |||||||
\(812\) | −12.5664 | − | 7.25520i | −0.440993 | − | 0.254608i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.6199i | 1.03818i | ||||||||
\(815\) | 7.17670 | − | 12.4304i | 0.251389 | − | 0.435418i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.0529 | − | 10.4228i | 0.631590 | − | 0.364648i | ||||
\(818\) | 99.4870 | 3.47848 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −72.9939 | −2.54906 | ||||||||
\(821\) | −15.6492 | + | 9.03506i | −0.546160 | + | 0.315326i | −0.747572 | − | 0.664181i | \(-0.768780\pi\) |
0.201412 | + | 0.979507i | \(0.435447\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.22775 | − | 3.85857i | 0.0776544 | − | 0.134501i | −0.824583 | − | 0.565741i | \(-0.808590\pi\) |
0.902238 | + | 0.431239i | \(0.141924\pi\) | |||||||
\(824\) | − | 38.2896i | − | 1.33388i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25.1714 | − | 14.5327i | −0.875826 | − | 0.505658i | ||||
\(827\) | − | 11.8352i | − | 0.411549i | −0.978599 | − | 0.205774i | \(-0.934029\pi\) | ||
0.978599 | − | 0.205774i | \(-0.0659713\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.76947 | − | 3.06482i | −0.0614563 | − | 0.106445i | 0.833660 | − | 0.552278i | \(-0.186241\pi\) |
−0.895117 | + | 0.445832i | \(0.852908\pi\) | |||||||
\(830\) | −76.0474 | + | 43.9060i | −2.63964 | + | 1.52400i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −85.0643 | − | 0.439917i | −2.94907 | − | 0.0152514i | ||||
\(833\) | −2.15314 | −0.0746019 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.6927 | + | 25.4484i | 0.508460 | + | 0.880679i | ||||
\(836\) | −11.7615 | + | 20.3715i | −0.406781 | + | 0.704565i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 68.5145 | + | 39.5569i | 2.36679 | + | 1.36647i | ||||
\(839\) | 28.9991 | + | 16.7426i | 1.00116 | + | 0.578020i | 0.908591 | − | 0.417686i | \(-0.137159\pi\) |
0.0925687 | + | 0.995706i | \(0.470492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7625 | − | 18.6411i | 0.371119 | − | 0.642797i | ||||
\(842\) | −10.1892 | − | 17.6482i | −0.351143 | − | 0.608197i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.9023 | −0.788330 | ||||||||
\(845\) | −0.438079 | + | 42.3533i | −0.0150704 | + | 1.45700i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.57502 | + | 3.79609i | −0.225920 | + | 0.130435i | ||||
\(848\) | −63.0620 | − | 109.227i | −2.16556 | − | 3.75086i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 32.6835i | − | 1.12103i | ||||||
\(851\) | 9.31768 | + | 5.37956i | 0.319406 | + | 0.184409i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0871i | 0.756248i | 0.925755 | + | 0.378124i | \(0.123431\pi\) | ||||
−0.925755 | + | 0.378124i | \(0.876569\pi\) | |||||||
\(854\) | −13.6648 | + | 23.6680i | −0.467598 | + | 0.809904i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −148.080 | + | 85.4941i | −5.06127 | + | 2.92213i | ||||
\(857\) | −6.89363 | −0.235482 | −0.117741 | − | 0.993044i | \(-0.537565\pi\) | ||||
−0.117741 | + | 0.993044i | \(0.537565\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.4834 | −1.27892 | −0.639459 | − | 0.768825i | \(-0.720842\pi\) | ||||
−0.639459 | + | 0.768825i | \(0.720842\pi\) | |||||||
\(860\) | −130.017 | + | 75.0654i | −4.43355 | + | 2.55971i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.2052 | − | 73.1015i | 1.43751 | − | 2.48985i | ||||
\(863\) | 17.5248i | 0.596552i | 0.954480 | + | 0.298276i | \(0.0964115\pi\) | ||||
−0.954480 | + | 0.298276i | \(0.903588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.1893 | − | 9.92425i | −0.584454 | − | 0.337435i | ||||
\(866\) | − | 15.9057i | − | 0.540498i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.62358 | − | 8.00828i | −0.156935 | − | 0.271819i | ||||
\(869\) | 1.28202 | − | 0.740175i | 0.0434896 | − | 0.0251087i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.58972 | − | 1.47737i | 0.0877493 | − | 0.0500588i | ||||
\(872\) | −38.1883 | −1.29322 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.88221 | + | 10.1883i | 0.198969 | + | 0.344624i | ||||
\(875\) | 1.00248 | − | 1.73634i | 0.0338899 | − | 0.0586990i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.4859 | − | 23.3745i | −1.36711 | − | 0.789302i | −0.376553 | − | 0.926395i | \(-0.622891\pi\) |
−0.990558 | + | 0.137093i | \(0.956224\pi\) | |||||||
\(878\) | −23.3083 | − | 13.4571i | −0.786618 | − | 0.454154i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 40.7565 | − | 70.5924i | 1.37390 | − | 2.37967i | ||||
\(881\) | 1.45937 | + | 2.52771i | 0.0491675 | + | 0.0851606i | 0.889562 | − | 0.456815i | \(-0.151010\pi\) |
−0.840394 | + | 0.541976i | \(0.817677\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.5505 | 0.960801 | 0.480400 | − | 0.877049i | \(-0.340491\pi\) | ||||
0.480400 | + | 0.877049i | \(0.340491\pi\) | |||||||
\(884\) | 20.4160 | + | 35.7878i | 0.686666 | + | 1.20367i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 83.9993 | − | 48.4970i | 2.82201 | − | 1.62929i | ||||
\(887\) | 0.211457 | + | 0.366254i | 0.00710004 | + | 0.0122976i | 0.869554 | − | 0.493839i | \(-0.164407\pi\) |
−0.862454 | + | 0.506136i | \(0.831073\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 9.73438i | − | 0.326480i | ||||||
\(890\) | −115.276 | − | 66.5548i | −3.86407 | − | 2.23092i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 124.162i | 4.15725i | ||||||||
\(893\) | −7.05610 | + | 12.2215i | −0.236123 | + | 0.408978i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.9469 | − | 6.32018i | 0.365914 | − | 0.211260i | ||||
\(896\) | −26.2666 | −0.877504 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.8000 | −0.360401 | ||||||||
\(899\) | −4.12550 | + | 2.38186i | −0.137593 | + | 0.0794394i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0189 | + | 17.3532i | −0.333777 | + | 0.578118i | ||||
\(902\) | 21.0651i | 0.701391i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.2899 | − | 12.2917i | −0.708091 | − | 0.408816i | ||||
\(905\) | − | 21.4512i | − | 0.713063i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.2142 | − | 19.4236i | −0.372361 | − | 0.644949i | 0.617567 | − | 0.786518i | \(-0.288118\pi\) |
−0.989928 | + | 0.141570i | \(0.954785\pi\) | |||||||
\(908\) | 122.824 | − | 70.9127i | 4.07607 | − | 2.35332i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.164223 | + | 31.7549i | −0.00544394 | + | 1.05267i | ||||
\(911\) | 32.5788 | 1.07938 | 0.539692 | − | 0.841863i | \(-0.318541\pi\) | ||||
0.539692 | + | 0.841863i | \(0.318541\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.20274 | + | 15.9396i | 0.304566 | + | 0.527524i | ||||
\(914\) | 55.7159 | − | 96.5027i | 1.84292 | − | 3.19203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.8195 | − | 7.97869i | −0.456609 | − | 0.263623i | ||||
\(917\) | 16.1613 | + | 9.33073i | 0.533693 | + | 0.308128i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.93957 | − | 8.55558i | 0.162941 | − | 0.282223i | −0.772981 | − | 0.634429i | \(-0.781235\pi\) |
0.935922 | + | 0.352207i | \(0.114569\pi\) | |||||||
\(920\) | −26.3993 | − | 45.7250i | −0.870361 | − | 1.50751i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −66.8408 | −2.20129 | ||||||||
\(923\) | 7.32908 | + | 4.28214i | 0.241240 | + | 0.140948i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.8654 | − | 16.6654i | 0.949088 | − | 0.547956i | ||||
\(926\) | −32.9867 | − | 57.1346i | −1.08401 | − | 1.87756i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 51.2769i | 1.68325i | ||||||||
\(929\) | −25.9060 | − | 14.9568i | −0.849947 | − | 0.490717i | 0.0106859 | − | 0.999943i | \(-0.496599\pi\) |
−0.860633 | + | 0.509226i | \(0.829932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.40096i | − | 0.0786881i | ||||||
\(932\) | −31.0868 | + | 53.8439i | −1.01828 | + | 1.76371i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.4143 | + | 6.01273i | −0.340768 | + | 0.196742i | ||||
\(935\) | −12.9502 | −0.423518 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.8296 | −1.03983 | −0.519914 | − | 0.854219i | \(-0.674036\pi\) | ||||
−0.519914 | + | 0.854219i | \(0.674036\pi\) | |||||||
\(938\) | 1.93584 | − | 1.11766i | 0.0632074 | − | 0.0364928i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 50.8182 | − | 88.0197i | 1.65751 | − | 2.87089i | ||||
\(941\) | 42.0885i | 1.37205i | 0.727580 | + | 0.686023i | \(0.240645\pi\) | ||||
−0.727580 | + | 0.686023i | \(0.759355\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.62654 | + | 3.82584i | 0.215790 | + | 0.124586i | ||||
\(944\) | 145.721i | 4.74280i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.6629 | + | 37.5213i | 0.704322 | + | 1.21992i | ||||
\(947\) | −52.2540 | + | 30.1689i | −1.69803 | + | 0.980357i | −0.750397 | + | 0.660988i | \(0.770138\pi\) |
−0.947630 | + | 0.319369i | \(0.896529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0595711 | + | 11.5189i | −0.00193376 | + | 0.373920i | ||||
\(950\) | 36.4452 | 1.18244 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.62475 | + | 16.6706i | 0.311940 | + | 0.540296i | ||||
\(953\) | 8.68770 | − | 15.0475i | 0.281422 | − | 0.487438i | −0.690313 | − | 0.723511i | \(-0.742527\pi\) |
0.971735 | + | 0.236073i | \(0.0758605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.7785 | − | 22.3888i | −1.25484 | − | 0.724484i | ||||
\(956\) | −6.56328 | − | 3.78931i | −0.212272 | − | 0.122555i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 42.8140 | − | 74.1561i | 1.38326 | − | 2.39588i | ||||
\(959\) | 4.21078 | + | 7.29328i | 0.135973 | + | 0.235512i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.9642 | 0.902070 | ||||||||
\(962\) | −29.1847 | + | 49.9510i | −0.940951 | + | 1.61048i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.3165 | + | 7.11091i | −0.396686 | + | 0.229027i | ||||
\(965\) | 37.0661 | + | 64.2003i | 1.19320 | + | 2.06668i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.8630i | 0.606594i | 0.952896 | + | 0.303297i | \(0.0980874\pi\) | ||||
−0.952896 | + | 0.303297i | \(0.901913\pi\) | |||||||
\(968\) | 58.7820 | + | 33.9378i | 1.88932 | + | 1.09080i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 81.3068i | 2.61061i | ||||||||
\(971\) | −0.782231 | + | 1.35486i | −0.0251030 | + | 0.0434797i | −0.878304 | − | 0.478103i | \(-0.841325\pi\) |
0.853201 | + | 0.521582i | \(0.174658\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.2734 | − | 8.81809i | 0.489642 | − | 0.282695i | ||||
\(974\) | 72.7582 | 2.33132 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 137.017 | 4.38582 | ||||||||
\(977\) | 24.1409 | − | 13.9378i | 0.772336 | − | 0.445909i | −0.0613710 | − | 0.998115i | \(-0.519547\pi\) |
0.833707 | + | 0.552206i | \(0.186214\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.9499 | + | 24.1620i | −0.445842 | + | 0.772221i | ||||
\(980\) | 17.2917i | 0.552364i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.7716 | − | 13.1472i | −0.726672 | − | 0.419544i | ||||
\(983\) | − | 33.4239i | − | 1.06606i | −0.846097 | − | 0.533029i | \(-0.821054\pi\) | ||
0.846097 | − | 0.533029i | \(-0.178946\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.6657 | + | 40.9901i | 0.754051 | + | 1.30605i | ||||
\(986\) | 13.7813 | − | 7.95661i | 0.438885 | − | 0.253390i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −39.9068 | + | 22.7658i | −1.26960 | + | 0.724277i | ||||
\(989\) | 15.7376 | 0.500428 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.45548 | + | 16.3774i | 0.300363 | + | 0.520244i | 0.976218 | − | 0.216790i | \(-0.0695588\pi\) |
−0.675855 | + | 0.737035i | \(0.736225\pi\) | |||||||
\(992\) | −16.3388 | + | 28.2997i | −0.518759 | + | 0.898517i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.51138 | + | 3.18199i | 0.174810 | + | 0.100927i | ||||
\(995\) | 67.2685 | + | 38.8375i | 2.13256 | + | 1.23123i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.7888 | + | 37.7393i | −0.690057 | + | 1.19521i | 0.281762 | + | 0.959484i | \(0.409081\pi\) |
−0.971819 | + | 0.235730i | \(0.924252\pi\) | |||||||
\(998\) | 10.6442 | + | 18.4363i | 0.336936 | + | 0.583589i | ||||
\(999\) | 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.ct.a.127.6 | 12 | ||
3.2 | odd | 2 | 91.2.q.a.36.1 | ✓ | 12 | ||
12.11 | even | 2 | 1456.2.cc.c.673.4 | 12 | |||
13.4 | even | 6 | inner | 819.2.ct.a.316.6 | 12 | ||
21.2 | odd | 6 | 637.2.u.h.361.6 | 12 | |||
21.5 | even | 6 | 637.2.u.i.361.6 | 12 | |||
21.11 | odd | 6 | 637.2.k.h.569.1 | 12 | |||
21.17 | even | 6 | 637.2.k.g.569.1 | 12 | |||
21.20 | even | 2 | 637.2.q.h.491.1 | 12 | |||
39.2 | even | 12 | 1183.2.a.m.1.1 | 6 | |||
39.11 | even | 12 | 1183.2.a.p.1.6 | 6 | |||
39.17 | odd | 6 | 91.2.q.a.43.1 | yes | 12 | ||
39.23 | odd | 6 | 1183.2.c.i.337.12 | 12 | |||
39.29 | odd | 6 | 1183.2.c.i.337.1 | 12 | |||
156.95 | even | 6 | 1456.2.cc.c.225.4 | 12 | |||
273.17 | even | 6 | 637.2.u.i.30.6 | 12 | |||
273.41 | odd | 12 | 8281.2.a.by.1.1 | 6 | |||
273.95 | odd | 6 | 637.2.u.h.30.6 | 12 | |||
273.167 | odd | 12 | 8281.2.a.ch.1.6 | 6 | |||
273.173 | even | 6 | 637.2.k.g.459.6 | 12 | |||
273.212 | odd | 6 | 637.2.k.h.459.6 | 12 | |||
273.251 | even | 6 | 637.2.q.h.589.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.1 | ✓ | 12 | 3.2 | odd | 2 | ||
91.2.q.a.43.1 | yes | 12 | 39.17 | odd | 6 | ||
637.2.k.g.459.6 | 12 | 273.173 | even | 6 | |||
637.2.k.g.569.1 | 12 | 21.17 | even | 6 | |||
637.2.k.h.459.6 | 12 | 273.212 | odd | 6 | |||
637.2.k.h.569.1 | 12 | 21.11 | odd | 6 | |||
637.2.q.h.491.1 | 12 | 21.20 | even | 2 | |||
637.2.q.h.589.1 | 12 | 273.251 | even | 6 | |||
637.2.u.h.30.6 | 12 | 273.95 | odd | 6 | |||
637.2.u.h.361.6 | 12 | 21.2 | odd | 6 | |||
637.2.u.i.30.6 | 12 | 273.17 | even | 6 | |||
637.2.u.i.361.6 | 12 | 21.5 | even | 6 | |||
819.2.ct.a.127.6 | 12 | 1.1 | even | 1 | trivial | ||
819.2.ct.a.316.6 | 12 | 13.4 | even | 6 | inner | ||
1183.2.a.m.1.1 | 6 | 39.2 | even | 12 | |||
1183.2.a.p.1.6 | 6 | 39.11 | even | 12 | |||
1183.2.c.i.337.1 | 12 | 39.29 | odd | 6 | |||
1183.2.c.i.337.12 | 12 | 39.23 | odd | 6 | |||
1456.2.cc.c.225.4 | 12 | 156.95 | even | 6 | |||
1456.2.cc.c.673.4 | 12 | 12.11 | even | 2 | |||
8281.2.a.by.1.1 | 6 | 273.41 | odd | 12 | |||
8281.2.a.ch.1.6 | 6 | 273.167 | odd | 12 |