Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (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: | \(5.08647060876\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 589.1 | ||
Root | \(-1.12906 + 0.851598i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.589 |
Dual form | 637.2.q.h.491.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | −0.974813 | − | 0.223022i | \(-0.928408\pi\) |
−0.680549 | − | 0.732702i | \(-0.738259\pi\) | |||||||
\(3\) | −0.172975 | + | 0.299601i | −0.0998669 | + | 0.172975i | −0.911629 | − | 0.411013i | \(-0.865175\pi\) |
0.811763 | + | 0.583988i | \(0.198508\pi\) | |||||||
\(4\) | 2.65363 | + | 4.59623i | 1.32682 | + | 2.29811i | ||||
\(5\) | − | 3.25812i | − | 1.45708i | −0.685005 | − | 0.728539i | \(-0.740200\pi\) | ||
0.685005 | − | 0.728539i | \(-0.259800\pi\) | |||||||
\(6\) | 0.809880 | − | 0.467584i | 0.330632 | − | 0.190890i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 8.94020i | − | 3.16084i | ||||||
\(9\) | 1.44016 | + | 2.49443i | 0.480053 | + | 0.831477i | ||||
\(10\) | −4.40367 | + | 7.62739i | −1.39256 | + | 2.41199i | ||||
\(11\) | −1.59871 | − | 0.923014i | −0.482028 | − | 0.278299i | 0.239233 | − | 0.970962i | \(-0.423104\pi\) |
−0.721261 | + | 0.692663i | \(0.756437\pi\) | |||||||
\(12\) | −1.83605 | −0.530021 | ||||||||
\(13\) | −3.60550 | + | 0.0186461i | −0.999987 | + | 0.00517151i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.976136 | + | 0.563573i | 0.252037 | + | 0.145514i | ||||
\(16\) | −6.77628 | + | 11.7369i | −1.69407 | + | 2.93422i | ||||
\(17\) | −1.07657 | − | 1.86467i | −0.261107 | − | 0.452250i | 0.705430 | − | 0.708780i | \(-0.250754\pi\) |
−0.966536 | + | 0.256530i | \(0.917421\pi\) | |||||||
\(18\) | − | 7.78607i | − | 1.83519i | ||||||
\(19\) | 2.07929 | − | 1.20048i | 0.477021 | − | 0.275408i | −0.242153 | − | 0.970238i | \(-0.577854\pi\) |
0.719174 | + | 0.694830i | \(0.244520\pi\) | |||||||
\(20\) | 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 | \(-0.772815\pi\) |
0.944910 | + | 0.327329i | \(0.106149\pi\) | |||||||
\(24\) | 2.67849 | + | 1.54643i | 0.546744 | + | 0.315663i | ||||
\(25\) | −5.61537 | −1.12307 | ||||||||
\(26\) | 8.46582 | + | 4.82954i | 1.66028 | + | 0.947151i | ||||
\(27\) | −2.03429 | −0.391500 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.36703 | − | 2.36777i | 0.253851 | − | 0.439683i | −0.710732 | − | 0.703463i | \(-0.751636\pi\) |
0.964583 | + | 0.263780i | \(0.0849693\pi\) | |||||||
\(30\) | −1.52345 | − | 2.63869i | −0.278142 | − | 0.481756i | ||||
\(31\) | − | 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 | ||||
\(33\) | 0.553071 | − | 0.319316i | 0.0962774 | − | 0.0555858i | ||||
\(34\) | 5.82036i | 0.998183i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.64331 | + | 13.2386i | −1.27389 | + | 2.20643i | ||||
\(37\) | −5.14042 | − | 2.96783i | −0.845081 | − | 0.487908i | 0.0139073 | − | 0.999903i | \(-0.495573\pi\) |
−0.858988 | + | 0.511996i | \(0.828906\pi\) | |||||||
\(38\) | −6.49025 | −1.05286 | ||||||||
\(39\) | 0.618074 | − | 1.08344i | 0.0989710 | − | 0.173489i | ||||
\(40\) | −29.1283 | −4.60558 | ||||||||
\(41\) | −3.65577 | − | 2.11066i | −0.570935 | − | 0.329629i | 0.186588 | − | 0.982438i | \(-0.440257\pi\) |
−0.757523 | + | 0.652809i | \(0.773590\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.34111 | − | 7.51903i | −0.662014 | − | 1.14664i | −0.980086 | − | 0.198575i | \(-0.936369\pi\) |
0.318072 | − | 0.948067i | \(-0.396965\pi\) | |||||||
\(44\) | − | 9.79737i | − | 1.47701i | ||||||
\(45\) | 8.12716 | − | 4.69222i | 1.21153 | − | 0.699475i | ||||
\(46\) | −4.24343 | + | 2.44994i | −0.625659 | + | 0.361224i | ||||
\(47\) | 5.87774i | 0.857357i | 0.903457 | + | 0.428678i | \(0.141021\pi\) | ||||
−0.903457 | + | 0.428678i | \(0.858979\pi\) | |||||||
\(48\) | −2.34425 | − | 4.06036i | −0.338363 | − | 0.586062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 13.1458 | + | 7.58972i | 1.85910 | + | 1.07335i | ||||
\(51\) | 0.744877 | 0.104304 | ||||||||
\(52\) | −9.65339 | − | 16.5222i | −1.33868 | − | 2.29122i | ||||
\(53\) | −9.30628 | −1.27832 | −0.639158 | − | 0.769076i | \(-0.720717\pi\) | ||||
−0.639158 | + | 0.769076i | \(0.720717\pi\) | |||||||
\(54\) | 4.76235 | + | 2.74954i | 0.648074 | + | 0.374166i | ||||
\(55\) | −3.00729 | + | 5.20878i | −0.405503 | + | 0.702352i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.830609i | 0.110017i | ||||||||
\(58\) | −6.40054 | + | 3.69535i | −0.840432 | + | 0.485224i | ||||
\(59\) | −9.31173 | + | 5.37613i | −1.21228 | + | 0.699912i | −0.963256 | − | 0.268584i | \(-0.913444\pi\) |
−0.249028 | + | 0.968496i | \(0.580111\pi\) | |||||||
\(60\) | 5.98206i | 0.772281i | ||||||||
\(61\) | 5.05504 | + | 8.75558i | 0.647231 | + | 1.12104i | 0.983781 | + | 0.179371i | \(0.0574064\pi\) |
−0.336550 | + | 0.941665i | \(0.609260\pi\) | |||||||
\(62\) | −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 | ||||
\(66\) | −1.72635 | −0.212499 | ||||||||
\(67\) | 0.716130 | + | 0.413458i | 0.0874892 | + | 0.0505119i | 0.543106 | − | 0.839664i | \(-0.317248\pi\) |
−0.455617 | + | 0.890176i | \(0.650581\pi\) | |||||||
\(68\) | 5.71365 | − | 9.89633i | 0.692881 | − | 1.20011i | ||||
\(69\) | 0.313538 | + | 0.543065i | 0.0377456 | + | 0.0653773i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.03884 | + | 1.17712i | −0.241965 | + | 0.139699i | −0.616080 | − | 0.787684i | \(-0.711280\pi\) |
0.374114 | + | 0.927383i | \(0.377947\pi\) | |||||||
\(72\) | 22.3007 | − | 12.8753i | 2.62816 | − | 1.51737i | ||||
\(73\) | 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 | ||||
\(75\) | 0.971316 | − | 1.68237i | 0.112158 | − | 0.194263i | ||||
\(76\) | 11.0353 | + | 6.37126i | 1.26584 | + | 0.730833i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.91130 | + | 1.70098i | −0.329640 | + | 0.192598i | ||||
\(79\) | 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 | ||||
\(81\) | −3.96860 | + | 6.87381i | −0.440955 | + | 0.763757i | ||||
\(82\) | 5.70552 | + | 9.88225i | 0.630069 | + | 1.09131i | ||||
\(83\) | − | 9.97031i | − | 1.09438i | −0.837007 | − | 0.547192i | \(-0.815697\pi\) | ||
0.837007 | − | 0.547192i | \(-0.184303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.07534 | + | 3.50760i | −0.658963 | + | 0.380452i | ||||
\(86\) | 23.4698i | 2.53081i | ||||||||
\(87\) | 0.472923 | + | 0.819127i | 0.0507027 | + | 0.0878196i | ||||
\(88\) | −8.25193 | + | 14.2928i | −0.879658 | + | 1.52361i | ||||
\(89\) | −13.0886 | − | 7.55674i | −1.38739 | − | 0.801012i | −0.394373 | − | 0.918950i | \(-0.629038\pi\) |
−0.993021 | + | 0.117938i | \(0.962372\pi\) | |||||||
\(90\) | −25.3680 | −2.67402 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.62010 | 1.00296 | ||||||||
\(93\) | 0.522012 | + | 0.301384i | 0.0541301 | + | 0.0312520i | ||||
\(94\) | 7.94435 | − | 13.7600i | 0.819397 | − | 1.41924i | ||||
\(95\) | −3.91130 | − | 6.77458i | −0.401291 | − | 0.695057i | ||||
\(96\) | 6.48823i | 0.662202i | ||||||||
\(97\) | −7.99489 | + | 4.61585i | −0.811758 | + | 0.468669i | −0.847566 | − | 0.530690i | \(-0.821933\pi\) |
0.0358079 | + | 0.999359i | \(0.488600\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.31715i | − | 0.534394i | ||||||
\(100\) | −14.9011 | − | 25.8095i | −1.49011 | − | 2.58095i | ||||
\(101\) | −7.41169 | + | 12.8374i | −0.737491 | + | 1.27737i | 0.216131 | + | 0.976364i | \(0.430656\pi\) |
−0.953622 | + | 0.301007i | \(0.902677\pi\) | |||||||
\(102\) | −1.74378 | − | 1.00677i | −0.172660 | − | 0.0996855i | ||||
\(103\) | −4.28286 | −0.422003 | −0.211001 | − | 0.977486i | \(-0.567672\pi\) | ||||
−0.211001 | + | 0.977486i | \(0.567672\pi\) | |||||||
\(104\) | 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 | 0.132082 | − | 0.991239i | \(-0.457834\pi\) |
0.792397 | − | 0.610006i | \(-0.208833\pi\) | |||||||
\(108\) | −5.39827 | − | 9.35007i | −0.519448 | − | 0.899711i | ||||
\(109\) | 4.27153i | 0.409139i | 0.978852 | + | 0.204569i | \(0.0655794\pi\) | ||||
−0.978852 | + | 0.204569i | \(0.934421\pi\) | |||||||
\(110\) | 14.0804 | − | 8.12930i | 1.34251 | − | 0.775099i | ||||
\(111\) | 1.77833 | − | 1.02672i | 0.168791 | − | 0.0974516i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.37488 | − | 2.38137i | −0.129338 | − | 0.224020i | 0.794082 | − | 0.607810i | \(-0.207952\pi\) |
−0.923420 | + | 0.383790i | \(0.874619\pi\) | |||||||
\(114\) | 1.12265 | − | 1.94448i | 0.105146 | − | 0.182118i | ||||
\(115\) | −5.11454 | − | 2.95288i | −0.476934 | − | 0.275358i | ||||
\(116\) | 14.5104 | 1.34726 | ||||||||
\(117\) | −5.23901 | − | 8.96682i | −0.484347 | − | 0.828983i | ||||
\(118\) | 29.0655 | 2.67569 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.03845 | − | 8.72685i | 0.459945 | − | 0.796649i | ||||
\(121\) | −3.79609 | − | 6.57502i | −0.345099 | − | 0.597729i | ||||
\(122\) | − | 27.3295i | − | 2.47430i | ||||||
\(123\) | 1.26471 | − | 0.730180i | 0.114035 | − | 0.0658381i | ||||
\(124\) | 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 | −0.997036 | − | 0.0769320i | \(-0.975488\pi\) |
0.565143 | + | 0.824993i | \(0.308821\pi\) | |||||||
\(128\) | 22.7475 | + | 13.1333i | 2.01061 | + | 1.16083i | ||||
\(129\) | 3.00361 | 0.264453 | ||||||||
\(130\) | 15.7352 | − | 27.5827i | 1.38007 | − | 2.41916i | ||||
\(131\) | 18.6615 | 1.63046 | 0.815230 | − | 0.579138i | \(-0.196611\pi\) | ||||
0.815230 | + | 0.579138i | \(0.196611\pi\) | |||||||
\(132\) | 2.93530 | + | 1.69470i | 0.255485 | + | 0.147504i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.11766 | − | 1.93584i | −0.0965509 | − | 0.167231i | ||||
\(135\) | 6.62797i | 0.570445i | ||||||||
\(136\) | −16.6706 | + | 9.62475i | −1.42949 | + | 0.825315i | ||||
\(137\) | −7.29328 | + | 4.21078i | −0.623107 | + | 0.359751i | −0.778078 | − | 0.628168i | \(-0.783805\pi\) |
0.154971 | + | 0.987919i | \(0.450472\pi\) | |||||||
\(138\) | − | 1.69511i | − | 0.144298i | ||||||
\(139\) | −8.81809 | − | 15.2734i | −0.747941 | − | 1.29547i | −0.948808 | − | 0.315853i | \(-0.897709\pi\) |
0.200867 | − | 0.979619i | \(-0.435624\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.76098 | − | 1.01670i | −0.148301 | − | 0.0856216i | ||||
\(142\) | 6.36399 | 0.534054 | ||||||||
\(143\) | 5.78135 | + | 3.29812i | 0.483461 | + | 0.275803i | ||||
\(144\) | −39.0357 | −3.25298 | ||||||||
\(145\) | −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 | \(-0.719335\pi\) |
0.350530 | + | 0.936552i | \(0.386002\pi\) | |||||||
\(150\) | −4.54777 | + | 2.62566i | −0.371324 | + | 0.214384i | ||||
\(151\) | − | 18.9010i | − | 1.53814i | −0.639165 | − | 0.769069i | \(-0.720720\pi\) | ||
0.639165 | − | 0.769069i | \(-0.279280\pi\) | |||||||
\(152\) | −10.7325 | − | 18.5892i | −0.870521 | − | 1.50779i | ||||
\(153\) | 3.10086 | − | 5.37086i | 0.250690 | − | 0.434208i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.67682 | −0.455973 | ||||||||
\(156\) | 6.61987 | − | 0.0342352i | 0.530014 | − | 0.00274101i | ||||
\(157\) | 11.5735 | 0.923670 | 0.461835 | − | 0.886966i | \(-0.347191\pi\) | ||||
0.461835 | + | 0.886966i | \(0.347191\pi\) | |||||||
\(158\) | −1.87730 | − | 1.08386i | −0.149350 | − | 0.0862273i | ||||
\(159\) | 1.60975 | − | 2.78817i | 0.127661 | − | 0.221116i | ||||
\(160\) | −30.5528 | − | 52.9190i | −2.41541 | − | 4.18362i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 18.5813 | − | 10.7279i | 1.45988 | − | 0.842863i | ||||
\(163\) | −3.81520 | + | 2.20271i | −0.298830 | + | 0.172529i | −0.641917 | − | 0.766774i | \(-0.721861\pi\) |
0.343087 | + | 0.939304i | \(0.388527\pi\) | |||||||
\(164\) | − | 22.4037i | − | 1.74943i | ||||||
\(165\) | −1.04037 | − | 1.80197i | −0.0809927 | − | 0.140284i | ||||
\(166\) | −13.4759 | + | 23.3409i | −1.04593 | + | 1.81160i | ||||
\(167\) | 7.81076 | + | 4.50954i | 0.604415 | + | 0.348959i | 0.770776 | − | 0.637106i | \(-0.219869\pi\) |
−0.166362 | + | 0.986065i | \(0.553202\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9993 | − | 0.134457i | 0.999947 | − | 0.0103429i | ||||
\(170\) | 18.9635 | 1.45443 | ||||||||
\(171\) | 5.98901 | + | 3.45776i | 0.457991 | + | 0.264421i | ||||
\(172\) | 23.0395 | − | 39.9055i | 1.75674 | − | 3.04277i | ||||
\(173\) | −3.04600 | − | 5.27583i | −0.231583 | − | 0.401114i | 0.726691 | − | 0.686964i | \(-0.241057\pi\) |
−0.958274 | + | 0.285851i | \(0.907724\pi\) | |||||||
\(174\) | − | 2.55681i | − | 0.193831i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 21.6666 | − | 12.5092i | 1.63318 | − | 0.942917i | ||||
\(177\) | − | 3.71974i | − | 0.279592i | ||||||
\(178\) | 20.4273 | + | 35.3812i | 1.53109 | + | 2.65193i | ||||
\(179\) | 1.93982 | − | 3.35987i | 0.144989 | − | 0.251128i | −0.784380 | − | 0.620281i | \(-0.787019\pi\) |
0.929369 | + | 0.369152i | \(0.120352\pi\) | |||||||
\(180\) | 43.1330 | + | 24.9029i | 3.21495 | + | 1.85615i | ||||
\(181\) | 6.58392 | 0.489379 | 0.244690 | − | 0.969601i | \(-0.421314\pi\) | ||||
0.244690 | + | 0.969601i | \(0.421314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.49757 | −0.258548 | ||||||||
\(184\) | −14.0342 | − | 8.10262i | −1.03461 | − | 0.597333i | ||||
\(185\) | −9.66954 | + | 16.7481i | −0.710919 | + | 1.23135i | ||||
\(186\) | −0.814700 | − | 1.41110i | −0.0597367 | − | 0.103467i | ||||
\(187\) | 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 | \(-0.00102172\pi\) |
−0.502777 | + | 0.864416i | \(0.667688\pi\) | |||||||
\(192\) | 4.08097 | − | 7.06845i | 0.294519 | − | 0.510122i | ||||
\(193\) | 19.7047 | + | 11.3765i | 1.41838 | + | 0.818899i | 0.996156 | − | 0.0875946i | \(-0.0279180\pi\) |
0.422219 | + | 0.906494i | \(0.361251\pi\) | |||||||
\(194\) | 24.9551 | 1.79167 | ||||||||
\(195\) | −3.52997 | − | 2.01376i | −0.252786 | − | 0.144208i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.5809 | − | 7.26358i | −0.896352 | − | 0.517509i | −0.0203371 | − | 0.999793i | \(-0.506474\pi\) |
−0.876015 | + | 0.482284i | \(0.839807\pi\) | |||||||
\(198\) | −7.18665 | + | 12.4476i | −0.510733 | + | 0.884615i | ||||
\(199\) | −11.9202 | − | 20.6464i | −0.845001 | − | 1.46358i | −0.885620 | − | 0.464410i | \(-0.846266\pi\) |
0.0406192 | − | 0.999175i | \(-0.487067\pi\) | |||||||
\(200\) | 50.2025i | 3.54985i | ||||||||
\(201\) | −0.247745 | + | 0.143035i | −0.0174746 | + | 0.0100889i | ||||
\(202\) | 34.7021 | − | 20.0353i | 2.44163 | − | 1.40968i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.97663 | + | 3.42363i | 0.138392 | + | 0.239702i | ||||
\(205\) | −6.87678 | + | 11.9109i | −0.480295 | + | 0.831896i | ||||
\(206\) | 10.0263 | + | 5.78871i | 0.698568 | + | 0.403318i | ||||
\(207\) | 5.22095 | 0.362881 | ||||||||
\(208\) | 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 | −0.930687 | − | 0.365816i | \(-0.880790\pi\) |
0.782149 | + | 0.623091i | \(0.214123\pi\) | |||||||
\(212\) | −24.6955 | − | 42.7738i | −1.69609 | − | 2.93772i | ||||
\(213\) | − | 0.814450i | − | 0.0558052i | ||||||
\(214\) | −44.7741 | + | 25.8504i | −3.06070 | + | 1.76709i | ||||
\(215\) | −24.4979 | + | 14.1439i | −1.67075 | + | 0.964605i | ||||
\(216\) | 18.1870i | 1.23747i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.77339 | − | 9.99981i | 0.391024 | − | 0.677273i | ||||
\(219\) | −0.957171 | − | 0.552623i | −0.0646796 | − | 0.0373428i | ||||
\(220\) | −31.9210 | −2.15212 | ||||||||
\(221\) | 3.91635 | + | 6.70301i | 0.263442 | + | 0.450893i | ||||
\(222\) | −5.55083 | −0.372548 | ||||||||
\(223\) | 20.2604 | + | 11.6973i | 1.35674 | + | 0.783312i | 0.989182 | − | 0.146691i | \(-0.0468623\pi\) |
0.367553 | + | 0.930003i | \(0.380196\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.08703 | − | 14.0071i | −0.539135 | − | 0.933810i | ||||
\(226\) | 7.43315i | 0.494446i | ||||||||
\(227\) | 23.1427 | − | 13.3614i | 1.53603 | − | 0.886829i | 0.536968 | − | 0.843602i | \(-0.319569\pi\) |
0.999065 | − | 0.0432270i | \(-0.0137639\pi\) | |||||||
\(228\) | −3.81767 | + | 2.20413i | −0.252831 | + | 0.145972i | ||||
\(229\) | − | 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 | \(-0.374639\pi\) | ||||
0.383731 | + | 0.923445i | \(0.374639\pi\) | |||||||
\(234\) | 0.145180 | + | 28.0727i | 0.00949072 | + | 1.83517i | ||||
\(235\) | 19.1504 | 1.24924 | ||||||||
\(236\) | −49.4199 | − | 28.5326i | −3.21696 | − | 1.85731i | ||||
\(237\) | −0.138710 | + | 0.240253i | −0.00901019 | + | 0.0156061i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.42797i | − | 0.0923677i | −0.998933 | − | 0.0461838i | \(-0.985294\pi\) | ||
0.998933 | − | 0.0461838i | \(-0.0147060\pi\) | |||||||
\(240\) | −13.2292 | + | 7.63786i | −0.853938 | + | 0.493021i | ||||
\(241\) | 2.32068 | − | 1.33984i | 0.149488 | − | 0.0863069i | −0.423390 | − | 0.905947i | \(-0.639160\pi\) |
0.572878 | + | 0.819640i | \(0.305827\pi\) | |||||||
\(242\) | 20.5232i | 1.31928i | ||||||||
\(243\) | −4.42437 | − | 7.66323i | −0.283824 | − | 0.491597i | ||||
\(244\) | −26.8284 | + | 46.4682i | −1.71751 | + | 2.97482i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.94764 | −0.251692 | ||||||||
\(247\) | −7.47450 | + | 4.36710i | −0.475591 | + | 0.277872i | ||||
\(248\) | −15.5770 | −0.989143 | ||||||||
\(249\) | 2.98711 | + | 1.72461i | 0.189301 | + | 0.109293i | ||||
\(250\) | 2.70989 | − | 4.69367i | 0.171389 | − | 0.296854i | ||||
\(251\) | −5.46696 | − | 9.46906i | −0.345072 | − | 0.597681i | 0.640295 | − | 0.768129i | \(-0.278812\pi\) |
−0.985367 | + | 0.170447i | \(0.945479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.89786 | + | 1.67308i | −0.182187 | + | 0.105186i | ||||
\(254\) | 22.7885 | − | 13.1570i | 1.42988 | − | 0.825541i | ||||
\(255\) | − | 2.42690i | − | 0.151978i | ||||||
\(256\) | −11.9089 | − | 20.6268i | −0.744307 | − | 1.28918i | ||||
\(257\) | −2.07569 | + | 3.59520i | −0.129478 | + | 0.224262i | −0.923474 | − | 0.383660i | \(-0.874663\pi\) |
0.793996 | + | 0.607922i | \(0.207997\pi\) | |||||||
\(258\) | −7.03156 | − | 4.05967i | −0.437766 | − | 0.252744i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −53.8315 | + | 31.4519i | −3.33849 | + | 1.95057i | ||||
\(261\) | 7.87497 | 0.487448 | ||||||||
\(262\) | −43.6872 | − | 25.2228i | −2.69900 | − | 1.55827i | ||||
\(263\) | −2.02680 | + | 3.51052i | −0.124978 | + | 0.216468i | −0.921724 | − | 0.387846i | \(-0.873219\pi\) |
0.796747 | + | 0.604314i | \(0.206553\pi\) | |||||||
\(264\) | −2.85475 | − | 4.94457i | −0.175698 | − | 0.304317i | ||||
\(265\) | 30.3210i | 1.86260i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.52801 | − | 2.61425i | 0.277110 | − | 0.159989i | ||||
\(268\) | 4.38866i | 0.268080i | ||||||||
\(269\) | 2.00011 | + | 3.46430i | 0.121949 | + | 0.211222i | 0.920536 | − | 0.390657i | \(-0.127752\pi\) |
−0.798587 | + | 0.601879i | \(0.794419\pi\) | |||||||
\(270\) | 8.95836 | − | 15.5163i | 0.545188 | − | 0.944294i | ||||
\(271\) | 2.41189 | + | 1.39251i | 0.146512 | + | 0.0845888i | 0.571464 | − | 0.820627i | \(-0.306376\pi\) |
−0.424952 | + | 0.905216i | \(0.639709\pi\) | |||||||
\(272\) | 29.1806 | 1.76933 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.7651 | 1.37529 | ||||||||
\(275\) | 8.97733 | + | 5.18306i | 0.541353 | + | 0.312551i | ||||
\(276\) | −1.66403 | + | 2.88219i | −0.100163 | + | 0.173487i | ||||
\(277\) | 8.34618 | + | 14.4560i | 0.501474 | + | 0.868578i | 0.999999 | + | 0.00170243i | \(0.000541901\pi\) |
−0.498525 | + | 0.866875i | \(0.666125\pi\) | |||||||
\(278\) | 47.6741i | 2.85930i | ||||||||
\(279\) | 4.34619 | − | 2.50928i | 0.260200 | − | 0.150226i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.3731i | − | 0.797774i | −0.917000 | − | 0.398887i | \(-0.869397\pi\) | ||
0.917000 | − | 0.398887i | \(-0.130603\pi\) | |||||||
\(282\) | 2.74834 | + | 4.76026i | 0.163661 | + | 0.283470i | ||||
\(283\) | 9.44312 | − | 16.3560i | 0.561335 | − | 0.972261i | −0.436045 | − | 0.899925i | \(-0.643621\pi\) |
0.997380 | − | 0.0723362i | \(-0.0230455\pi\) | |||||||
\(284\) | −10.8207 | − | 6.24731i | −0.642088 | − | 0.370710i | ||||
\(285\) | 2.70623 | 0.160303 | ||||||||
\(286\) | −9.07663 | − | 15.5351i | −0.536712 | − | 0.918609i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 46.7827 | + | 27.0100i | 2.75669 | + | 1.59158i | ||||
\(289\) | 6.18199 | − | 10.7075i | 0.363647 | − | 0.629855i | ||||
\(290\) | 12.0399 | + | 20.8537i | 0.707008 | + | 1.22457i | ||||
\(291\) | − | 3.19370i | − | 0.187218i | ||||||
\(292\) | −14.6841 | + | 8.47789i | −0.859324 | + | 0.496131i | ||||
\(293\) | 2.95999 | − | 1.70895i | 0.172925 | − | 0.0998380i | −0.411040 | − | 0.911617i | \(-0.634834\pi\) |
0.583964 | + | 0.811779i | \(0.301501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.5161 | + | 30.3388i | 1.01983 | + | 1.76639i | ||||
\(296\) | −26.5329 | + | 45.9564i | −1.54220 | + | 2.67116i | ||||
\(297\) | 3.25224 | + | 1.87768i | 0.188714 | + | 0.108954i | ||||
\(298\) | 10.8697 | 0.629663 | ||||||||
\(299\) | −3.23845 | + | 5.67675i | −0.187284 | + | 0.328295i | ||||
\(300\) | 10.3101 | 0.595252 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −25.5465 | + | 44.2479i | −1.47004 | + | 2.54618i | ||||
\(303\) | −2.56407 | − | 4.44110i | −0.147302 | − | 0.255134i | ||||
\(304\) | 32.5391i | 1.86625i | ||||||||
\(305\) | 28.5268 | − | 16.4699i | 1.63344 | − | 0.943066i | ||||
\(306\) | −14.5185 | + | 8.38225i | −0.829966 | + | 0.479181i | ||||
\(307\) | − | 16.3679i | − | 0.934165i | −0.884214 | − | 0.467083i | \(-0.845305\pi\) | ||
0.884214 | − | 0.467083i | \(-0.154695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.740826 | − | 1.28315i | 0.0421441 | − | 0.0729958i | ||||
\(310\) | 13.2896 | + | 7.67278i | 0.754801 | + | 0.435785i | ||||
\(311\) | 23.6979 | 1.34378 | 0.671891 | − | 0.740650i | \(-0.265482\pi\) | ||||
0.671891 | + | 0.740650i | \(0.265482\pi\) | |||||||
\(312\) | −9.68614 | − | 5.52570i | −0.548370 | − | 0.312831i | ||||
\(313\) | 5.18025 | 0.292805 | 0.146403 | − | 0.989225i | \(-0.453231\pi\) | ||||
0.146403 | + | 0.989225i | \(0.453231\pi\) | |||||||
\(314\) | −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 | \(0.945516\pi\) | |||||||
\(318\) | −7.53697 | + | 4.35147i | −0.422652 | + | 0.244018i | ||||
\(319\) | −4.37096 | + | 2.52358i | −0.244727 | + | 0.141293i | ||||
\(320\) | 76.8686i | 4.29709i | ||||||||
\(321\) | 3.30827 | + | 5.73010i | 0.184650 | + | 0.319823i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.47700 | − | 2.58480i | −0.249107 | − | 0.143822i | ||||
\(324\) | −42.1248 | −2.34027 | ||||||||
\(325\) | 20.2462 | − | 0.104705i | 1.12306 | − | 0.00580799i | ||||
\(326\) | 11.9087 | 0.659562 | ||||||||
\(327\) | −1.27975 | − | 0.738866i | −0.0707706 | − | 0.0408594i | ||||
\(328\) | −18.8697 | + | 32.6833i | −1.04190 | + | 1.80463i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.62465i | 0.309627i | ||||||||
\(331\) | 14.9605 | − | 8.63743i | 0.822301 | − | 0.474756i | −0.0289082 | − | 0.999582i | \(-0.509203\pi\) |
0.851209 | + | 0.524826i | \(0.175870\pi\) | |||||||
\(332\) | 45.8258 | − | 26.4576i | 2.51502 | − | 1.45205i | ||||
\(333\) | − | 17.0966i | − | 0.936886i | ||||||
\(334\) | −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 | ||||
\(339\) | 0.951279 | 0.0516664 | ||||||||
\(340\) | −32.2435 | − | 18.6158i | −1.74865 | − | 1.00958i | ||||
\(341\) | −1.60822 | + | 2.78552i | −0.0870901 | + | 0.150844i | ||||
\(342\) | −9.34700 | − | 16.1895i | −0.505428 | − | 0.875427i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −67.2216 | + | 38.8104i | −3.62435 | + | 2.09252i | ||||
\(345\) | 1.76937 | − | 1.02155i | 0.0952598 | − | 0.0549983i | ||||
\(346\) | 16.4679i | 0.885318i | ||||||||
\(347\) | −14.4110 | − | 24.9606i | −0.773623 | − | 1.33995i | −0.935565 | − | 0.353154i | \(-0.885109\pi\) |
0.161942 | − | 0.986800i | \(-0.448224\pi\) | |||||||
\(348\) | −2.50993 | + | 4.34733i | −0.134546 | + | 0.233041i | ||||
\(349\) | 10.1516 | + | 5.86103i | 0.543403 | + | 0.313734i | 0.746457 | − | 0.665434i | \(-0.231753\pi\) |
−0.203054 | + | 0.979167i | \(0.565087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.33464 | − | 0.0379317i | 0.391494 | − | 0.00202464i | ||||
\(352\) | −34.6220 | −1.84536 | ||||||||
\(353\) | −15.4466 | − | 8.91811i | −0.822141 | − | 0.474663i | 0.0290134 | − | 0.999579i | \(-0.490763\pi\) |
−0.851154 | + | 0.524916i | \(0.824097\pi\) | |||||||
\(354\) | −5.02759 | + | 8.70804i | −0.267213 | + | 0.462827i | ||||
\(355\) | 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 | \(0.952094\pi\) | |||||||
\(360\) | −41.9494 | − | 72.6584i | −2.21093 | − | 3.82943i | ||||
\(361\) | −6.61771 | + | 11.4622i | −0.348300 | + | 0.603274i | ||||
\(362\) | −15.4132 | − | 8.89882i | −0.810100 | − | 0.467712i | ||||
\(363\) | 2.62651 | 0.137856 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4091 | 0.544838 | ||||||||
\(366\) | 8.18794 | + | 4.72731i | 0.427991 | + | 0.247100i | ||||
\(367\) | −9.81580 | + | 17.0015i | −0.512381 | + | 0.887469i | 0.487516 | + | 0.873114i | \(0.337903\pi\) |
−0.999897 | + | 0.0143554i | \(0.995430\pi\) | |||||||
\(368\) | 12.2829 | + | 21.2746i | 0.640289 | + | 1.10901i | ||||
\(369\) | − | 12.1587i | − | 0.632958i | ||||||
\(370\) | 45.2735 | − | 26.1387i | 2.35366 | − | 1.35888i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.19905i | 0.165863i | ||||||||
\(373\) | −16.0323 | − | 27.7687i | −0.830119 | − | 1.43781i | −0.897943 | − | 0.440111i | \(-0.854939\pi\) |
0.0678240 | − | 0.997697i | \(-0.478394\pi\) | |||||||
\(374\) | 5.37227 | − | 9.30505i | 0.277794 | − | 0.481153i | ||||
\(375\) | −0.600686 | − | 0.346806i | −0.0310193 | − | 0.0179090i | ||||
\(376\) | 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 | 0.0131425 | − | 0.999914i | \(-0.495816\pi\) |
−0.859379 | + | 0.511339i | \(0.829150\pi\) | |||||||
\(380\) | 20.7583 | − | 35.9545i | 1.06488 | − | 1.84443i | ||||
\(381\) | −1.68380 | − | 2.91643i | −0.0862637 | − | 0.149413i | ||||
\(382\) | − | 37.1510i | − | 1.90081i | ||||||
\(383\) | −0.606070 | + | 0.349915i | −0.0309687 | + | 0.0178798i | −0.515404 | − | 0.856947i | \(-0.672358\pi\) |
0.484436 | + | 0.874827i | \(0.339025\pi\) | |||||||
\(384\) | −7.86948 | + | 4.54345i | −0.401588 | + | 0.231857i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −30.7529 | − | 53.2657i | −1.56528 | − | 2.71115i | ||||
\(387\) | 12.5038 | − | 21.6572i | 0.635604 | − | 1.10090i | ||||
\(388\) | −42.4310 | − | 24.4976i | −2.15411 | − | 1.24368i | ||||
\(389\) | 20.0547 | 1.01681 | 0.508407 | − | 0.861117i | \(-0.330235\pi\) | ||||
0.508407 | + | 0.861117i | \(0.330235\pi\) | |||||||
\(390\) | 5.54200 | + | 9.48539i | 0.280630 | + | 0.480311i | ||||
\(391\) | −3.90284 | −0.197375 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.22796 | + | 5.59099i | −0.162829 | + | 0.282028i | ||||
\(394\) | 19.6349 | + | 34.0086i | 0.989192 | + | 1.71333i | ||||
\(395\) | − | 2.61272i | − | 0.131460i | ||||||
\(396\) | 24.4388 | − | 14.1098i | 1.22810 | − | 0.709043i | ||||
\(397\) | 19.2953 | − | 11.1401i | 0.968403 | − | 0.559108i | 0.0696541 | − | 0.997571i | \(-0.477810\pi\) |
0.898749 | + | 0.438463i | \(0.144477\pi\) | |||||||
\(398\) | 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 | \(-0.371635\pi\) |
−0.600340 | + | 0.799745i | \(0.704968\pi\) | |||||||
\(402\) | 0.773306 | 0.0385690 | ||||||||
\(403\) | 0.0324883 | + | 6.28208i | 0.00161836 | + | 0.312933i | ||||
\(404\) | −78.6717 | −3.91406 | ||||||||
\(405\) | 22.3957 | + | 12.9302i | 1.11285 | + | 0.642506i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.47869 | + | 9.48937i | 0.271568 | + | 0.470370i | ||||
\(408\) | − | 6.65935i | − | 0.329687i | ||||||
\(409\) | −31.8727 | + | 18.4017i | −1.57601 | + | 0.909907i | −0.580597 | + | 0.814191i | \(0.697181\pi\) |
−0.995409 | + | 0.0957164i | \(0.969486\pi\) | |||||||
\(410\) | 32.1976 | − | 18.5893i | 1.59013 | − | 0.918060i | ||||
\(411\) | − | 2.91343i | − | 0.143709i | ||||||
\(412\) | −11.3651 | − | 19.6850i | −0.559921 | − | 0.969811i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.2224 | − | 7.05662i | −0.600699 | − | 0.346814i | ||||
\(415\) | −32.4845 | −1.59460 | ||||||||
\(416\) | −58.3864 | + | 34.1132i | −2.86263 | + | 1.67254i | ||||
\(417\) | 6.10122 | 0.298778 | ||||||||
\(418\) | 10.3760 | + | 5.99059i | 0.507507 | + | 0.293009i | ||||
\(419\) | 14.6334 | − | 25.3457i | 0.714887 | − | 1.23822i | −0.248116 | − | 0.968730i | \(-0.579812\pi\) |
0.963003 | − | 0.269490i | \(-0.0868552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.53862i | 0.367410i | 0.982981 | + | 0.183705i | \(0.0588091\pi\) | ||||
−0.982981 | + | 0.183705i | \(0.941191\pi\) | |||||||
\(422\) | 10.1022 | − | 5.83251i | 0.491768 | − | 0.283922i | ||||
\(423\) | −14.6616 | + | 8.46489i | −0.712872 | + | 0.411577i | ||||
\(424\) | 83.2000i | 4.04055i | ||||||||
\(425\) | 6.04534 | + | 10.4708i | 0.293242 | + | 0.507910i | ||||
\(426\) | −1.10081 | + | 1.90666i | −0.0533343 | + | 0.0923778i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 101.506 | 4.90646 | ||||||||
\(429\) | −1.98815 | + | 1.16161i | −0.0959886 | + | 0.0560829i | ||||
\(430\) | 76.4674 | 3.68759 | ||||||||
\(431\) | −27.0426 | − | 15.6131i | −1.30260 | − | 0.752055i | −0.321748 | − | 0.946825i | \(-0.604270\pi\) |
−0.980849 | + | 0.194771i | \(0.937604\pi\) | |||||||
\(432\) | 13.7849 | − | 23.8762i | 0.663228 | − | 1.14874i | ||||
\(433\) | −2.94202 | − | 5.09573i | −0.141384 | − | 0.244885i | 0.786634 | − | 0.617420i | \(-0.211822\pi\) |
−0.928018 | + | 0.372535i | \(0.878489\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.66882 | − | 1.54084i | 0.127960 | − | 0.0738777i | ||||
\(436\) | −19.6329 | + | 11.3351i | −0.940247 | + | 0.542852i | ||||
\(437\) | − | 4.35204i | − | 0.208186i | ||||||
\(438\) | 1.49385 | + | 2.58742i | 0.0713788 | + | 0.123632i | ||||
\(439\) | 4.97821 | − | 8.62251i | 0.237597 | − | 0.411530i | −0.722427 | − | 0.691447i | \(-0.756974\pi\) |
0.960024 | + | 0.279917i | \(0.0903069\pi\) | |||||||
\(440\) | 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 | \(-0.824845\pi\) | ||||
−0.852385 | + | 0.522915i | \(0.824845\pi\) | |||||||
\(444\) | 9.43805 | + | 5.44906i | 0.447910 | + | 0.258601i | ||||
\(445\) | −24.6208 | + | 42.6444i | −1.16714 | + | 2.02154i | ||||
\(446\) | −31.6202 | − | 54.7678i | −1.49726 | − | 2.59333i | ||||
\(447\) | − | 1.39108i | − | 0.0657956i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.46001 | − | 1.99764i | 0.163288 | − | 0.0942744i | −0.416129 | − | 0.909306i | \(-0.636614\pi\) |
0.579417 | + | 0.815031i | \(0.303280\pi\) | |||||||
\(450\) | 43.7217i | 2.06106i | ||||||||
\(451\) | 3.89633 | + | 6.74864i | 0.183471 | + | 0.317781i | ||||
\(452\) | 7.29687 | − | 12.6386i | 0.343216 | − | 0.594467i | ||||
\(453\) | 5.66274 | + | 3.26939i | 0.266059 | + | 0.153609i | ||||
\(454\) | −72.2371 | −3.39026 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.42580 | 0.347745 | ||||||||
\(457\) | 35.6995 | + | 20.6111i | 1.66995 | + | 0.964147i | 0.967660 | + | 0.252257i | \(0.0811729\pi\) |
0.702291 | + | 0.711890i | \(0.252160\pi\) | |||||||
\(458\) | −4.06385 | + | 7.03880i | −0.189891 | + | 0.328901i | ||||
\(459\) | 2.19006 | + | 3.79329i | 0.102223 | + | 0.177056i | ||||
\(460\) | − | 31.3435i | − | 1.46140i | ||||||
\(461\) | −21.4139 | + | 12.3633i | −0.997343 | + | 0.575816i | −0.907461 | − | 0.420136i | \(-0.861982\pi\) |
−0.0898818 | + | 0.995952i | \(0.528649\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.4057i | 1.13423i | 0.823639 | + | 0.567115i | \(0.191940\pi\) | ||||
−0.823639 | + | 0.567115i | \(0.808060\pi\) | |||||||
\(464\) | 18.5268 | + | 32.0893i | 0.860084 | + | 1.48971i | ||||
\(465\) | 0.981946 | − | 1.70078i | 0.0455366 | − | 0.0788718i | ||||
\(466\) | −27.4248 | − | 15.8337i | −1.27043 | − | 0.733482i | ||||
\(467\) | −4.44860 | −0.205857 | −0.102928 | − | 0.994689i | \(-0.532821\pi\) | ||||
−0.102928 | + | 0.994689i | \(0.532821\pi\) | |||||||
\(468\) | 27.3111 | − | 47.8744i | 1.26246 | − | 2.21299i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −44.8318 | − | 25.8837i | −2.06794 | − | 1.19392i | ||||
\(471\) | −2.00193 | + | 3.46744i | −0.0922441 | + | 0.159771i | ||||
\(472\) | 48.0637 | + | 83.2487i | 2.21231 | + | 3.83183i | ||||
\(473\) | 16.0276i | 0.736951i | ||||||||
\(474\) | 0.649451 | − | 0.374961i | 0.0298303 | − | 0.0172225i | ||||
\(475\) | −11.6760 | + | 6.74113i | −0.535730 | + | 0.309304i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.4025 | − | 23.2139i | −0.613660 | − | 1.06289i | ||||
\(478\) | −1.93004 | + | 3.34293i | −0.0882780 | + | 0.152902i | ||||
\(479\) | 27.4328 | + | 15.8383i | 1.25343 | + | 0.723671i | 0.971790 | − | 0.235848i | \(-0.0757868\pi\) |
0.281645 | + | 0.959519i | \(0.409120\pi\) | |||||||
\(480\) | 21.1394 | 0.964879 | ||||||||
\(481\) | 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 | ||||
\(486\) | 23.9199i | 1.08503i | ||||||||
\(487\) | 23.3096 | − | 13.4578i | 1.05626 | − | 0.609832i | 0.131864 | − | 0.991268i | \(-0.457904\pi\) |
0.924395 | + | 0.381436i | \(0.124570\pi\) | |||||||
\(488\) | 78.2766 | − | 45.1930i | 3.54341 | − | 2.04579i | ||||
\(489\) | − | 1.52405i | − | 0.0689200i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.86358 | − | 8.42396i | 0.219490 | − | 0.380168i | −0.735162 | − | 0.677891i | \(-0.762894\pi\) |
0.954652 | + | 0.297723i | \(0.0962273\pi\) | |||||||
\(492\) | 6.71215 | + | 3.87526i | 0.302607 | + | 0.174710i | ||||
\(493\) | −5.88682 | −0.265129 | ||||||||
\(494\) | 23.4006 | − | 0.121018i | 1.05284 | − | 0.00544487i | ||||
\(495\) | −17.3239 | −0.778653 | ||||||||
\(496\) | 20.4498 | + | 11.8067i | 0.918225 | + | 0.530137i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.66196 | − | 8.07475i | −0.208907 | − | 0.361838i | ||||
\(499\) | − | 7.87525i | − | 0.352545i | −0.984341 | − | 0.176272i | \(-0.943596\pi\) | ||
0.984341 | − | 0.176272i | \(-0.0564039\pi\) | |||||||
\(500\) | −9.21523 | + | 5.32042i | −0.412118 | + | 0.237936i | ||||
\(501\) | −2.70213 | + | 1.56007i | −0.120722 | + | 0.0696989i | ||||
\(502\) | 29.5565i | 1.31917i | ||||||||
\(503\) | −4.87603 | − | 8.44553i | −0.217411 | − | 0.376568i | 0.736604 | − | 0.676324i | \(-0.236428\pi\) |
−0.954016 | + | 0.299756i | \(0.903095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.8259 | + | 24.1482i | 1.86123 | + | 1.07458i | ||||
\(506\) | 9.04533 | 0.402114 | ||||||||
\(507\) | −2.20827 | + | 3.91786i | −0.0980725 | + | 0.173998i | ||||
\(508\) | −51.6630 | −2.29217 | ||||||||
\(509\) | 19.9407 | + | 11.5128i | 0.883857 | + | 0.510295i | 0.871928 | − | 0.489634i | \(-0.162870\pi\) |
0.0119288 | + | 0.999929i | \(0.496203\pi\) | |||||||
\(510\) | −3.28019 | + | 5.68146i | −0.145249 | + | 0.251579i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.8512i | 0.523752i | ||||||||
\(513\) | −4.22988 | + | 2.44212i | −0.186754 | + | 0.107822i | ||||
\(514\) | 9.71853 | − | 5.61100i | 0.428666 | − | 0.247490i | ||||
\(515\) | 13.9541i | 0.614891i | ||||||||
\(516\) | 7.97048 | + | 13.8053i | 0.350881 | + | 0.607744i | ||||
\(517\) | 5.42524 | − | 9.39679i | 0.238602 | − | 0.413270i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.10752 | 0.0925100 | ||||||||
\(520\) | 105.022 | − | 0.543130i | 4.60552 | − | 0.0238178i | ||||
\(521\) | −0.486481 | −0.0213131 | −0.0106566 | − | 0.999943i | \(-0.503392\pi\) | ||||
−0.0106566 | + | 0.999943i | \(0.503392\pi\) | |||||||
\(522\) | −18.4356 | − | 10.6438i | −0.806904 | − | 0.465866i | ||||
\(523\) | −17.3135 | + | 29.9878i | −0.757065 | + | 1.31128i | 0.187275 | + | 0.982307i | \(0.440034\pi\) |
−0.944341 | + | 0.328968i | \(0.893299\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 8.65510i | 0.376665i | ||||||||
\(529\) | 9.85719 | + | 17.0732i | 0.428574 | + | 0.742311i | ||||
\(530\) | 40.9818 | − | 70.9826i | 1.78014 | − | 3.08329i | ||||
\(531\) | −26.8208 | − | 15.4850i | −1.16392 | − | 0.671990i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.2202 | + | 7.54182i | 0.572632 | + | 0.326672i | ||||
\(534\) | −14.1336 | −0.611622 | ||||||||
\(535\) | −53.9656 | − | 31.1571i | −2.33314 | − | 1.34704i | ||||
\(536\) | 3.69639 | − | 6.40234i | 0.159660 | − | 0.276539i | ||||
\(537\) | 0.671080 | + | 1.16234i | 0.0289592 | + | 0.0501589i | ||||
\(538\) | − | 10.8134i | − | 0.466198i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −30.4637 | + | 17.5882i | −1.31095 | + | 0.756876i | ||||
\(541\) | − | 22.5384i | − | 0.969002i | −0.874791 | − | 0.484501i | \(-0.839001\pi\) | ||
0.874791 | − | 0.484501i | \(-0.160999\pi\) | |||||||
\(542\) | −3.76422 | − | 6.51982i | −0.161687 | − | 0.280050i | ||||
\(543\) | −1.13885 | + | 1.97255i | −0.0488728 | + | 0.0846502i | ||||
\(544\) | −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 | ||||
\(549\) | −14.5601 | + | 25.2189i | −0.621411 | + | 1.07631i | ||||
\(550\) | −14.0108 | − | 24.2675i | −0.597424 | − | 1.03477i | ||||
\(551\) | − | 6.56436i | − | 0.279651i | ||||||
\(552\) | 4.85510 | − | 2.80310i | 0.206647 | − | 0.119308i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 45.1227i | − | 1.91708i | ||||||
\(555\) | −3.34517 | − | 5.79401i | −0.141995 | − | 0.245942i | ||||
\(556\) | 46.8000 | − | 81.0600i | 1.98476 | − | 3.43771i | ||||
\(557\) | 0.629579 | + | 0.363487i | 0.0266761 | + | 0.0154015i | 0.513279 | − | 0.858222i | \(-0.328431\pi\) |
−0.486603 | + | 0.873623i | \(0.661764\pi\) | |||||||
\(558\) | −13.5661 | −0.574300 | ||||||||
\(559\) | 15.7921 | + | 27.0289i | 0.667935 | + | 1.14320i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.19084 | − | 0.687532i | −0.0502773 | − | 0.0290276i | ||||
\(562\) | −18.0751 | + | 31.3070i | −0.762452 | + | 1.32061i | ||||
\(563\) | −20.8038 | − | 36.0333i | −0.876777 | − | 1.51862i | −0.854857 | − | 0.518863i | \(-0.826355\pi\) |
−0.0219200 | − | 0.999760i | \(-0.506978\pi\) | |||||||
\(564\) | − | 10.7918i | − | 0.454417i | ||||||
\(565\) | −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 | 0.467118 | + | 0.884195i | \(0.345292\pi\) |
−0.999294 | + | 0.0375618i | \(0.988041\pi\) | |||||||
\(570\) | −6.33537 | − | 3.65773i | −0.265360 | − | 0.153205i | ||||
\(571\) | −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 | ||||
\(573\) | −4.75451 | −0.198622 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.08929 | + | 8.81490i | −0.212238 | + | 0.367607i | ||||
\(576\) | −33.9776 | − | 58.8508i | −1.41573 | − | 2.45212i | ||||
\(577\) | − | 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 | ||||
\(579\) | −6.81682 | + | 3.93570i | −0.283298 | + | 0.163562i | ||||
\(580\) | − | 47.2767i | − | 1.96306i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.31660 | + | 7.47657i | −0.178929 | + | 0.309914i | ||||
\(583\) | 14.8780 | + | 8.58982i | 0.616184 | + | 0.355754i | ||||
\(584\) | 28.5623 | 1.18192 | ||||||||
\(585\) | −29.2150 | + | 17.0693i | −1.20789 | + | 0.705731i | ||||
\(586\) | −9.23926 | −0.381670 | ||||||||
\(587\) | 13.8404 | + | 7.99075i | 0.571254 | + | 0.329814i | 0.757650 | − | 0.652661i | \(-0.226347\pi\) |
−0.186396 | + | 0.982475i | \(0.559681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.09166 | − | 3.62287i | −0.0861855 | − | 0.149278i | ||||
\(590\) | − | 94.6989i | − | 3.89869i | ||||||
\(591\) | 4.35235 | − | 2.51283i | 0.179032 | − | 0.103364i | ||||
\(592\) | 69.6660 | − | 40.2217i | 2.86325 | − | 1.65310i | ||||
\(593\) | − | 29.0532i | − | 1.19307i | −0.802586 | − | 0.596536i | \(-0.796543\pi\) | ||
0.802586 | − | 0.596536i | \(-0.203457\pi\) | |||||||
\(594\) | −5.07574 | − | 8.79143i | −0.208260 | − | 0.360717i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.4816 | − | 10.6704i | −0.757037 | − | 0.437075i | ||||
\(597\) | 8.24757 | 0.337551 | ||||||||
\(598\) | 15.2540 | − | 8.91240i | 0.623783 | − | 0.364455i | ||||
\(599\) | 3.45554 | 0.141190 | 0.0705948 | − | 0.997505i | \(-0.477510\pi\) | ||||
0.0705948 | + | 0.997505i | \(0.477510\pi\) | |||||||
\(600\) | −15.0407 | − | 8.68376i | −0.614035 | − | 0.354513i | ||||
\(601\) | 7.76518 | − | 13.4497i | 0.316748 | − | 0.548624i | −0.663059 | − | 0.748567i | \(-0.730742\pi\) |
0.979808 | + | 0.199943i | \(0.0640756\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.38178i | 0.0969936i | ||||||||
\(604\) | 86.8732 | − | 50.1563i | 3.53482 | − | 2.04083i | ||||
\(605\) | −21.4222 | + | 12.3681i | −0.870938 | + | 0.502836i | ||||
\(606\) | 13.8624i | 0.563120i | ||||||||
\(607\) | 7.73922 | + | 13.4047i | 0.314125 | + | 0.544081i | 0.979251 | − | 0.202650i | \(-0.0649555\pi\) |
−0.665126 | + | 0.746731i | \(0.731622\pi\) | |||||||
\(608\) | 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 | ||||
\(612\) | 32.9142 | 1.33048 | ||||||||
\(613\) | −6.17669 | − | 3.56611i | −0.249474 | − | 0.144034i | 0.370049 | − | 0.929012i | \(-0.379341\pi\) |
−0.619523 | + | 0.784978i | \(0.712674\pi\) | |||||||
\(614\) | −22.1228 | + | 38.3178i | −0.892804 | + | 1.54638i | ||||
\(615\) | −2.37902 | − | 4.12058i | −0.0959312 | − | 0.166158i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.30142 | + | 2.48342i | −0.173168 | + | 0.0999789i | −0.584079 | − | 0.811697i | \(-0.698544\pi\) |
0.410911 | + | 0.911676i | \(0.365211\pi\) | |||||||
\(618\) | −3.46860 | + | 2.00260i | −0.139528 | + | 0.0805563i | ||||
\(619\) | − | 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 | ||||
\(621\) | −1.84371 | + | 3.19339i | −0.0739854 | + | 0.128146i | ||||
\(622\) | −55.4776 | − | 32.0300i | −2.22445 | − | 1.28429i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.52791 | + | 14.5959i | 0.341390 | + | 0.584305i | ||||
\(625\) | −21.5445 | −0.861779 | ||||||||
\(626\) | −12.1272 | − | 7.00162i | −0.484699 | − | 0.279841i | ||||
\(627\) | 0.766663 | − | 1.32790i | 0.0306176 | − | 0.0530312i | ||||
\(628\) | 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 | −0.604137 | − | 0.796881i | \(-0.706482\pi\) |
0.388050 | + | 0.921638i | \(0.373149\pi\) | |||||||
\(632\) | − | 7.16924i | − | 0.285177i | ||||||
\(633\) | −0.746432 | − | 1.29286i | −0.0296680 | − | 0.0513865i | ||||
\(634\) | 8.19794 | − | 14.1992i | 0.325582 | − | 0.563924i | ||||
\(635\) | 27.4667 | + | 15.8579i | 1.08998 | + | 0.629302i | ||||
\(636\) | 17.0868 | 0.677534 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.6434 | 0.540149 | ||||||||
\(639\) | −5.87250 | − | 3.39049i | −0.232313 | − | 0.134126i | ||||
\(640\) | 42.7898 | − | 74.1142i | 1.69142 | − | 2.92962i | ||||
\(641\) | −15.7818 | − | 27.3350i | −0.623345 | − | 1.07967i | −0.988858 | − | 0.148860i | \(-0.952440\pi\) |
0.365513 | − | 0.930806i | \(-0.380894\pi\) | |||||||
\(642\) | − | 17.8858i | − | 0.705897i | ||||||
\(643\) | −15.8053 | + | 9.12520i | −0.623300 | + | 0.359863i | −0.778153 | − | 0.628075i | \(-0.783843\pi\) |
0.154852 | + | 0.987938i | \(0.450510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 9.78613i | − | 0.385329i | ||||||
\(646\) | 6.98721 | + | 12.1022i | 0.274908 | + | 0.476155i | ||||
\(647\) | −11.5137 | + | 19.9423i | −0.452649 | + | 0.784011i | −0.998550 | − | 0.0538387i | \(-0.982854\pi\) |
0.545901 | + | 0.837850i | \(0.316188\pi\) | |||||||
\(648\) | 61.4532 | + | 35.4800i | 2.41411 | + | 1.39379i | ||||
\(649\) | 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 | 0.433405 | + | 0.901199i | \(0.357312\pi\) |
−0.997164 | + | 0.0752597i | \(0.976021\pi\) | |||||||
\(654\) | 1.99730 | + | 3.45943i | 0.0781006 | + | 0.135274i | ||||
\(655\) | − | 60.8014i | − | 2.37571i | ||||||
\(656\) | 49.5450 | − | 28.6048i | 1.93441 | − | 1.11683i | ||||
\(657\) | −7.96926 | + | 4.60105i | −0.310910 | + | 0.179504i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.6114 | + | 27.0397i | 0.608134 | + | 1.05332i | 0.991548 | + | 0.129742i | \(0.0414149\pi\) |
−0.383414 | + | 0.923577i | \(0.625252\pi\) | |||||||
\(660\) | 5.52153 | − | 9.56356i | 0.214925 | − | 0.372261i | ||||
\(661\) | 23.0000 | + | 13.2791i | 0.894598 | + | 0.516496i | 0.875444 | − | 0.483320i | \(-0.160569\pi\) |
0.0191541 | + | 0.999817i | \(0.493903\pi\) | |||||||
\(662\) | −46.6973 | −1.81494 | ||||||||
\(663\) | −2.68566 | + | 0.0138891i | −0.104302 | + | 0.000539407i | ||||
\(664\) | −89.1366 | −3.45917 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23.1077 | + | 40.0237i | −0.895405 | + | 1.55089i | ||||
\(667\) | −2.47792 | − | 4.29188i | −0.0959454 | − | 0.166182i | ||||
\(668\) | 47.8667i | 1.85202i | ||||||||
\(669\) | −7.00906 | + | 4.04668i | −0.270986 | + | 0.156454i | ||||
\(670\) | −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 | −0.991124 | − | 0.132939i | \(-0.957559\pi\) |
0.610691 | + | 0.791869i | \(0.290892\pi\) | |||||||
\(674\) | 19.5585 | + | 11.2921i | 0.753366 | + | 0.434956i | ||||
\(675\) | 11.4233 | 0.439683 | ||||||||
\(676\) | 35.1134 | + | 59.3910i | 1.35052 | + | 2.28427i | ||||
\(677\) | 13.1440 | 0.505163 | 0.252582 | − | 0.967576i | \(-0.418720\pi\) | ||||
0.252582 | + | 0.967576i | \(0.418720\pi\) | |||||||
\(678\) | −2.22698 | − | 1.28575i | −0.0855266 | − | 0.0493788i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 31.3586 | + | 54.3147i | 1.20255 | + | 2.08287i | ||||
\(681\) | 9.24475i | 0.354260i | ||||||||
\(682\) | 7.52981 | − | 4.34734i | 0.288331 | − | 0.166468i | ||||
\(683\) | −5.85654 | + | 3.38128i | −0.224094 | + | 0.129381i | −0.607845 | − | 0.794056i | \(-0.707966\pi\) |
0.383750 | + | 0.923437i | \(0.374632\pi\) | |||||||
\(684\) | 36.7025i | 1.40336i | ||||||||
\(685\) | 13.7192 | + | 23.7624i | 0.524185 | + | 0.907915i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.900810 | + | 0.520083i | 0.0343681 | + | 0.0198424i | ||||
\(688\) | 117.666 | 4.48599 | ||||||||
\(689\) | 33.5538 | − | 0.173526i | 1.27830 | − | 0.00661082i | ||||
\(690\) | −5.52288 | −0.210253 | ||||||||
\(691\) | −7.94223 | − | 4.58545i | −0.302137 | − | 0.174439i | 0.341266 | − | 0.939967i | \(-0.389144\pi\) |
−0.643402 | + | 0.765528i | \(0.722478\pi\) | |||||||
\(692\) | 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 | ||||
\(696\) | 7.32316 | − | 4.22803i | 0.277584 | − | 0.160263i | ||||
\(697\) | 9.08908i | 0.344273i | ||||||||
\(698\) | −15.8435 | − | 27.4418i | −0.599686 | − | 1.03869i | ||||
\(699\) | −2.02636 | + | 3.50976i | −0.0766440 | + | 0.132751i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.4700 | 1.79292 | 0.896459 | − | 0.443127i | \(-0.146131\pi\) | ||||
0.896459 | + | 0.443127i | \(0.146131\pi\) | |||||||
\(702\) | −17.2219 | − | 9.82469i | −0.650000 | − | 0.370809i | ||||
\(703\) | −14.2512 | −0.537495 | ||||||||
\(704\) | 37.7181 | + | 21.7766i | 1.42156 | + | 0.820736i | ||||
\(705\) | −3.31253 | + | 5.73748i | −0.124757 | + | 0.216086i | ||||
\(706\) | 24.1074 | + | 41.7552i | 0.907294 | + | 1.57148i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17.0968 | − | 9.87082i | 0.642535 | − | 0.370968i | ||||
\(709\) | 30.2866 | − | 17.4860i | 1.13744 | − | 0.656699i | 0.191642 | − | 0.981465i | \(-0.438619\pi\) |
0.945795 | + | 0.324766i | \(0.105285\pi\) | |||||||
\(710\) | − | 20.7347i | − | 0.778158i | ||||||
\(711\) | 1.15488 | + | 2.00031i | 0.0433114 | + | 0.0750175i | ||||
\(712\) | −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 | ||||||||
\(717\) | 0.427821 | + | 0.247002i | 0.0159773 | + | 0.00922448i | ||||
\(718\) | 7.67926 | − | 13.3009i | 0.286588 | − | 0.496384i | ||||
\(719\) | 4.18051 | + | 7.24085i | 0.155907 | + | 0.270038i | 0.933389 | − | 0.358867i | \(-0.116837\pi\) |
−0.777482 | + | 0.628905i | \(0.783503\pi\) | |||||||
\(720\) | 127.183i | 4.73984i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 30.9846 | − | 17.8890i | 1.15313 | − | 0.665758i | ||||
\(723\) | 0.927035i | 0.0344768i | ||||||||
\(724\) | 17.4713 | + | 30.2612i | 0.649317 | + | 1.12465i | ||||
\(725\) | −7.67639 | + | 13.2959i | −0.285094 | + | 0.493797i | ||||
\(726\) | −6.14875 | − | 3.54998i | −0.228202 | − | 0.131752i | ||||
\(727\) | 27.4014 | 1.01626 | 0.508131 | − | 0.861280i | \(-0.330337\pi\) | ||||
0.508131 | + | 0.861280i | \(0.330337\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.7504 | −0.768532 | ||||||||
\(730\) | −24.3681 | − | 14.0689i | −0.901905 | − | 0.520715i | ||||
\(731\) | −9.34703 | + | 16.1895i | −0.345712 | + | 0.598791i | ||||
\(732\) | −9.28127 | − | 16.0756i | −0.343046 | − | 0.594173i | ||||
\(733\) | − | 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 | ||||
\(738\) | −16.4337 | + | 28.4640i | −0.604934 | + | 1.04778i | ||||
\(739\) | −41.9537 | − | 24.2220i | −1.54329 | − | 0.891019i | −0.998628 | − | 0.0523634i | \(-0.983325\pi\) |
−0.544662 | − | 0.838656i | \(-0.683342\pi\) | |||||||
\(740\) | −102.638 | −3.77304 | ||||||||
\(741\) | −0.0154876 | − | 2.99476i | −0.000568953 | − | 0.110015i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.7143 | − | 8.49532i | −0.539816 | − | 0.311663i | 0.205188 | − | 0.978722i | \(-0.434219\pi\) |
−0.745004 | + | 0.667060i | \(0.767553\pi\) | |||||||
\(744\) | 2.69443 | − | 4.66689i | 0.0987826 | − | 0.171097i | ||||
\(745\) | 6.55052 | + | 11.3458i | 0.239993 | + | 0.415679i | ||||
\(746\) | 86.6767i | 3.17346i | ||||||||
\(747\) | 24.8702 | − | 14.3588i | 0.909955 | − | 0.525363i | ||||
\(748\) | −18.2689 | + | 10.5475i | −0.667977 | + | 0.385657i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.937485 | + | 1.62377i | 0.0342321 | + | 0.0592917i | ||||
\(751\) | 21.5162 | − | 37.2671i | 0.785136 | − | 1.35990i | −0.143781 | − | 0.989610i | \(-0.545926\pi\) |
0.928918 | − | 0.370287i | \(-0.120741\pi\) | |||||||
\(752\) | −68.9863 | − | 39.8292i | −2.51567 | − | 1.45242i | ||||
\(753\) | 3.78258 | 0.137845 | ||||||||
\(754\) | 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 | 0.469122 | + | 0.883133i | \(0.344570\pi\) |
−0.999377 | + | 0.0352949i | \(0.988763\pi\) | |||||||
\(758\) | 25.7116 | + | 44.5337i | 0.933886 | + | 1.61754i | ||||
\(759\) | − | 1.15760i | − | 0.0420183i | ||||||
\(760\) | −60.5661 | + | 34.9678i | −2.19696 | + | 1.26842i | ||||
\(761\) | 25.4829 | − | 14.7126i | 0.923754 | − | 0.533330i | 0.0389234 | − | 0.999242i | \(-0.487607\pi\) |
0.884831 | + | 0.465912i | \(0.154274\pi\) | |||||||
\(762\) | 9.10328i | 0.329777i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −36.4699 | + | 63.1677i | −1.31943 | + | 2.28533i | ||||
\(765\) | −17.4989 | − | 10.1030i | −0.632675 | − | 0.365275i | ||||
\(766\) | 1.89178 | 0.0683526 | ||||||||
\(767\) | 33.4732 | − | 19.5573i | 1.20865 | − | 0.706172i | ||||
\(768\) | 8.23976 | 0.297327 | ||||||||
\(769\) | −14.8839 | − | 8.59322i | −0.536727 | − | 0.309879i | 0.207024 | − | 0.978336i | \(-0.433622\pi\) |
−0.743751 | + | 0.668456i | \(0.766955\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.718083 | − | 1.24376i | −0.0258611 | − | 0.0447928i | ||||
\(772\) | 120.756i | 4.34612i | ||||||||
\(773\) | −19.0180 | + | 10.9801i | −0.684031 | + | 0.394926i | −0.801372 | − | 0.598166i | \(-0.795896\pi\) |
0.117341 | + | 0.993092i | \(0.462563\pi\) | |||||||
\(774\) | −58.5437 | + | 33.8002i | −2.10431 | + | 1.21492i | ||||
\(775\) | 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 | ||||||||
\(780\) | −0.111542 | − | 21.5683i | −0.00399386 | − | 0.772271i | ||||
\(781\) | 4.34600 | 0.155512 | ||||||||
\(782\) | 9.13669 | + | 5.27507i | 0.326727 | + | 0.188636i | ||||
\(783\) | −2.78094 | + | 4.81673i | −0.0993827 | + | 0.172136i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 37.7081i | − | 1.34586i | ||||||
\(786\) | 15.1135 | − | 8.72581i | 0.539082 | − | 0.311239i | ||||
\(787\) | 2.02275 | − | 1.16784i | 0.0721033 | − | 0.0416289i | −0.463515 | − | 0.886089i | \(-0.653412\pi\) |
0.535618 | + | 0.844460i | \(0.320079\pi\) | |||||||
\(788\) | − | 77.0996i | − | 2.74656i | ||||||
\(789\) | −0.701169 | − | 1.21446i | −0.0249623 | − | 0.0432359i | ||||
\(790\) | −3.53135 | + | 6.11648i | −0.125640 | + | 0.217615i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −47.5364 | −1.68913 | ||||||||
\(793\) | −18.3892 | − | 31.4740i | −0.653020 | − | 1.11767i | ||||
\(794\) | −60.2280 | −2.13741 | ||||||||
\(795\) | −9.08420 | − | 5.24476i | −0.322183 | − | 0.186013i | ||||
\(796\) | 63.2637 | − | 109.576i | 2.24232 | − | 3.88382i | ||||
\(797\) | −13.9020 | − | 24.0790i | −0.492434 | − | 0.852921i | 0.507528 | − | 0.861635i | \(-0.330560\pi\) |
−0.999962 | + | 0.00871411i | \(0.997226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.9601 | − | 6.32780i | 0.387739 | − | 0.223861i | ||||
\(800\) | −91.2059 | + | 52.6577i | −3.22461 | + | 1.86173i | ||||
\(801\) | − | 43.5316i | − | 1.53811i | ||||||
\(802\) | 6.49779 | + | 11.2545i | 0.229445 | + | 0.397410i | ||||
\(803\) | 2.94886 | − | 5.10758i | 0.104063 | − | 0.180243i | ||||
\(804\) | −1.31485 | − | 0.759127i | −0.0463711 | − | 0.0267724i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.41479 | − | 14.7505i | 0.296398 | − | 0.519564i | ||||
\(807\) | −1.38387 | −0.0487147 | ||||||||
\(808\) | 114.769 | + | 66.2620i | 4.03756 | + | 2.33109i | ||||
\(809\) | −7.51017 | + | 13.0080i | −0.264043 | + | 0.457337i | −0.967313 | − | 0.253587i | \(-0.918390\pi\) |
0.703269 | + | 0.710924i | \(0.251723\pi\) | |||||||
\(810\) | −34.9528 | − | 60.5401i | −1.22812 | − | 2.12716i | ||||
\(811\) | 43.6933i | 1.53428i | 0.641481 | + | 0.767139i | \(0.278320\pi\) | ||||
−0.641481 | + | 0.767139i | \(0.721680\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.834393 | + | 0.481737i | −0.0292634 | + | 0.0168953i | ||||
\(814\) | − | 29.6199i | − | 1.03818i | ||||||
\(815\) | 7.17670 | + | 12.4304i | 0.251389 | + | 0.435418i | ||||
\(816\) | −5.04750 | + | 8.74252i | −0.176698 | + | 0.306049i | ||||
\(817\) | −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 | \(-0.231220\pi\) |
−0.201412 | + | 0.979507i | \(0.564553\pi\) | |||||||
\(822\) | −3.93779 | + | 6.82045i | −0.137346 | + | 0.237890i | ||||
\(823\) | 2.22775 | + | 3.85857i | 0.0776544 | + | 0.134501i | 0.902238 | − | 0.431239i | \(-0.141924\pi\) |
−0.824583 | + | 0.565741i | \(0.808590\pi\) | |||||||
\(824\) | 38.2896i | 1.33388i | ||||||||
\(825\) | −3.10570 | + | 1.79308i | −0.108127 | + | 0.0624269i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11.8352i | − | 0.411549i | −0.978599 | − | 0.205774i | \(-0.934029\pi\) | ||
0.978599 | − | 0.205774i | \(-0.0659713\pi\) | |||||||
\(828\) | 13.8545 | + | 23.9967i | 0.481477 | + | 0.833942i | ||||
\(829\) | 1.76947 | − | 3.06482i | 0.0614563 | − | 0.106445i | −0.833660 | − | 0.552278i | \(-0.813759\pi\) |
0.895117 | + | 0.445832i | \(0.147092\pi\) | |||||||
\(830\) | 76.0474 | + | 43.9060i | 2.63964 | + | 1.52400i | ||||
\(831\) | −5.77471 | −0.200323 | ||||||||
\(832\) | 85.0643 | − | 0.439917i | 2.94907 | − | 0.0152514i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.2832 | − | 8.24640i | −0.494586 | − | 0.285550i | ||||
\(835\) | 14.6927 | − | 25.4484i | 0.508460 | − | 0.880679i | ||||
\(836\) | −11.7615 | − | 20.3715i | −0.406781 | − | 0.704565i | ||||
\(837\) | 3.54447i | 0.122515i | ||||||||
\(838\) | −68.5145 | + | 39.5569i | −2.36679 | + | 1.36647i | ||||
\(839\) | 28.9991 | − | 16.7426i | 1.00116 | − | 0.578020i | 0.0925687 | − | 0.995706i | \(-0.470492\pi\) |
0.908591 | + | 0.417686i | \(0.137159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7625 | + | 18.6411i | 0.371119 | + | 0.642797i | ||||
\(842\) | 10.1892 | − | 17.6482i | 0.351143 | − | 0.608197i | ||||
\(843\) | 4.00660 | + | 2.31321i | 0.137995 | + | 0.0796713i | ||||
\(844\) | −22.9023 | −0.788330 | ||||||||
\(845\) | −0.438079 | − | 42.3533i | −0.0150704 | − | 1.45700i | ||||
\(846\) | 45.7645 | 1.57342 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 63.0620 | − | 109.227i | 2.16556 | − | 3.75086i | ||||
\(849\) | 3.26684 | + | 5.65833i | 0.112118 | + | 0.194193i | ||||
\(850\) | − | 32.6835i | − | 1.12103i | ||||||
\(851\) | −9.31768 | + | 5.37956i | −0.319406 | + | 0.184409i | ||||
\(852\) | 3.74340 | − | 2.16125i | 0.128247 | − | 0.0740433i | ||||
\(853\) | 22.0871i | 0.756248i | 0.925755 | + | 0.378124i | \(0.123431\pi\) | ||||
−0.925755 | + | 0.378124i | \(0.876569\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.2658 | − | 19.5129i | 0.385282 | − | 0.667329i | ||||
\(856\) | −148.080 | − | 85.4941i | −5.06127 | − | 2.92213i | ||||
\(857\) | −6.89363 | −0.235482 | −0.117741 | − | 0.993044i | \(-0.537565\pi\) | ||||
−0.117741 | + | 0.993044i | \(0.537565\pi\) | |||||||
\(858\) | 6.22435 | − | 0.0321897i | 0.212496 | − | 0.00109894i | ||||
\(859\) | 37.4834 | 1.27892 | 0.639459 | − | 0.768825i | \(-0.279158\pi\) | ||||
0.639459 | + | 0.768825i | \(0.279158\pi\) | |||||||
\(860\) | −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 | \(0.903588\pi\) | |||||||
\(864\) | −33.0413 | + | 19.0764i | −1.12409 | + | 0.648993i | ||||
\(865\) | −17.1893 | + | 9.92425i | −0.584454 | + | 0.337435i | ||||
\(866\) | 15.9057i | 0.540498i | ||||||||
\(867\) | 2.13866 | + | 3.70426i | 0.0726326 | + | 0.125803i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.28202 | − | 0.740175i | −0.0434896 | − | 0.0251087i | ||||
\(870\) | −8.33040 | −0.282427 | ||||||||
\(871\) | −2.58972 | − | 1.47737i | −0.0877493 | − | 0.0500588i | ||||
\(872\) | 38.1883 | 1.29322 | ||||||||
\(873\) | −23.0278 | − | 13.2951i | −0.779374 | − | 0.449972i | ||||
\(874\) | −5.88221 | + | 10.1883i | −0.198969 | + | 0.344624i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 5.86584i | − | 0.198188i | ||||||
\(877\) | −40.4859 | + | 23.3745i | −1.36711 | + | 0.789302i | −0.990558 | − | 0.137093i | \(-0.956224\pi\) |
−0.376553 | + | 0.926395i | \(0.622891\pi\) | |||||||
\(878\) | −23.3083 | + | 13.4571i | −0.786618 | + | 0.454154i | ||||
\(879\) | 1.18242i | 0.0398821i | ||||||||
\(880\) | −40.7565 | − | 70.5924i | −1.37390 | − | 2.37967i | ||||
\(881\) | 1.45937 | − | 2.52771i | 0.0491675 | − | 0.0851606i | −0.840394 | − | 0.541976i | \(-0.817677\pi\) |
0.889562 | + | 0.456815i | \(0.151010\pi\) | |||||||
\(882\) | 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 | ||||
\(885\) | −12.1194 | −0.407388 | ||||||||
\(886\) | 83.9993 | + | 48.4970i | 2.82201 | + | 1.62929i | ||||
\(887\) | 0.211457 | − | 0.366254i | 0.00710004 | − | 0.0122976i | −0.862454 | − | 0.506136i | \(-0.831073\pi\) |
0.869554 | + | 0.493839i | \(0.164407\pi\) | |||||||
\(888\) | −9.17905 | − | 15.8986i | −0.308029 | − | 0.533521i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 115.276 | − | 66.5548i | 3.86407 | − | 2.23092i | ||||
\(891\) | 12.6892 | − | 7.32614i | 0.425106 | − | 0.245435i | ||||
\(892\) | 124.162i | 4.15725i | ||||||||
\(893\) | 7.05610 | + | 12.2215i | 0.236123 | + | 0.408978i | ||||
\(894\) | −1.88018 | + | 3.25656i | −0.0628825 | + | 0.108916i | ||||
\(895\) | −10.9469 | − | 6.32018i | −0.365914 | − | 0.211260i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.14059 | − | 1.95217i | −0.0380832 | − | 0.0651812i | ||||
\(898\) | −10.8000 | −0.360401 | ||||||||
\(899\) | −4.12550 | − | 2.38186i | −0.137593 | − | 0.0794394i | ||||
\(900\) | 42.9200 | − | 74.3397i | 1.43067 | − | 2.47799i | ||||
\(901\) | 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 | ||||||
\(906\) | −8.83779 | − | 15.3075i | −0.293616 | − | 0.508558i | ||||
\(907\) | −11.2142 | + | 19.4236i | −0.372361 | + | 0.644949i | −0.989928 | − | 0.141570i | \(-0.954785\pi\) |
0.617567 | + | 0.786518i | \(0.288118\pi\) | |||||||
\(908\) | 122.824 | + | 70.9127i | 4.07607 | + | 2.35332i | ||||
\(909\) | −42.6961 | −1.41614 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.5788 | −1.07938 | −0.539692 | − | 0.841863i | \(-0.681459\pi\) | ||||
−0.539692 | + | 0.841863i | \(0.681459\pi\) | |||||||
\(912\) | −9.74874 | − | 5.62844i | −0.322813 | − | 0.186376i | ||||
\(913\) | −9.20274 | + | 15.9396i | −0.304566 | + | 0.527524i | ||||
\(914\) | −55.7159 | − | 96.5027i | −1.84292 | − | 3.19203i | ||||
\(915\) | 11.3955i | 0.376724i | ||||||||
\(916\) | 13.8195 | − | 7.97869i | 0.456609 | − | 0.263623i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 11.8403i | − | 0.390788i | ||||||
\(919\) | 4.93957 | + | 8.55558i | 0.162941 | + | 0.282223i | 0.935922 | − | 0.352207i | \(-0.114569\pi\) |
−0.772981 | + | 0.634429i | \(0.781235\pi\) | |||||||
\(920\) | −26.3993 | + | 45.7250i | −0.870361 | + | 1.50751i | ||||
\(921\) | 4.90383 | + | 2.83123i | 0.161587 | + | 0.0932922i | ||||
\(922\) | 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 | ||||
\(927\) | −6.16800 | − | 10.6833i | −0.202584 | − | 0.350886i | ||||
\(928\) | − | 51.2769i | − | 1.68325i | ||||||
\(929\) | −25.9060 | + | 14.9568i | −0.849947 | + | 0.490717i | −0.860633 | − | 0.509226i | \(-0.829932\pi\) |
0.0106859 | + | 0.999943i | \(0.496599\pi\) | |||||||
\(930\) | −4.59754 | + | 2.65439i | −0.150759 | + | 0.0870409i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 31.0868 | + | 53.8439i | 1.01828 | + | 1.76371i | ||||
\(933\) | −4.09913 | + | 7.09990i | −0.134199 | + | 0.232440i | ||||
\(934\) | 10.4143 | + | 6.01273i | 0.340768 | + | 0.196742i | ||||
\(935\) | 12.9502 | 0.423518 | ||||||||
\(936\) | −80.1651 | + | 46.8378i | −2.62028 | + | 1.53094i | ||||
\(937\) | 31.8296 | 1.03983 | 0.519914 | − | 0.854219i | \(-0.325964\pi\) | ||||
0.519914 | + | 0.854219i | \(0.325964\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.896052 | + | 1.55201i | −0.0292416 | + | 0.0506479i | ||||
\(940\) | 50.8182 | + | 88.0197i | 1.65751 | + | 2.87089i | ||||
\(941\) | − | 42.0885i | − | 1.37205i | −0.727580 | − | 0.686023i | \(-0.759355\pi\) | ||
0.727580 | − | 0.686023i | \(-0.240645\pi\) | |||||||
\(942\) | 9.37318 | − | 5.41161i | 0.305395 | − | 0.176320i | ||||
\(943\) | −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 | 0.947630 | + | 0.319369i | \(0.103471\pi\) |
0.750397 | + | 0.660988i | \(0.229862\pi\) | |||||||
\(948\) | −1.47234 | −0.0478195 | ||||||||
\(949\) | −0.0595711 | − | 11.5189i | −0.00193376 | − | 0.373920i | ||||
\(950\) | 36.4452 | 1.18244 | ||||||||
\(951\) | −1.81719 | − | 1.04915i | −0.0589264 | − | 0.0340212i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.68770 | − | 15.0475i | −0.281422 | − | 0.487438i | 0.690313 | − | 0.723511i | \(-0.257473\pi\) |
−0.971735 | + | 0.236073i | \(0.924139\pi\) | |||||||
\(954\) | 72.4593i | 2.34596i | ||||||||
\(955\) | 38.7785 | − | 22.3888i | 1.25484 | − | 0.724484i | ||||
\(956\) | 6.56328 | − | 3.78931i | 0.212272 | − | 0.122555i | ||||
\(957\) | − | 1.74606i | − | 0.0564421i | ||||||
\(958\) | −42.8140 | − | 74.1561i | −1.38326 | − | 2.39588i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −23.0299 | − | 13.2963i | −0.743287 | − | 0.429137i | ||||
\(961\) | 27.9642 | 0.902070 | ||||||||
\(962\) | −29.1847 | − | 49.9510i | −0.940951 | − | 1.61048i | ||||
\(963\) | 55.0883 | 1.77520 | ||||||||
\(964\) | 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 | \(-0.901913\pi\) | ||
0.952896 | − | 0.303297i | \(-0.0980874\pi\) | |||||||
\(968\) | −58.7820 | + | 33.9378i | −1.88932 | + | 1.09080i | ||||
\(969\) | 1.54881 | − | 0.894208i | 0.0497551 | − | 0.0287261i | ||||
\(970\) | − | 81.3068i | − | 2.61061i | ||||||
\(971\) | −0.782231 | − | 1.35486i | −0.0251030 | − | 0.0434797i | 0.853201 | − | 0.521582i | \(-0.174658\pi\) |
−0.878304 | + | 0.478103i | \(0.841325\pi\) | |||||||
\(972\) | 23.4813 | − | 40.6708i | 0.753164 | − | 1.30452i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −72.7582 | −2.33132 | ||||||||
\(975\) | −3.47071 | + | 6.08390i | −0.111152 | + | 0.194841i | ||||
\(976\) | −137.017 | −4.38582 | ||||||||
\(977\) | −24.1409 | − | 13.9378i | −0.772336 | − | 0.445909i | 0.0613710 | − | 0.998115i | \(-0.480453\pi\) |
−0.833707 | + | 0.552206i | \(0.813786\pi\) | |||||||
\(978\) | −2.05990 | + | 3.56786i | −0.0658685 | + | 0.114088i | ||||
\(979\) | 13.9499 | + | 24.1620i | 0.445842 | + | 0.772221i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.6550 | + | 6.15169i | −0.340189 | + | 0.196408i | ||||
\(982\) | −22.7716 | + | 13.1472i | −0.726672 | + | 0.419544i | ||||
\(983\) | 33.4239i | 1.06606i | 0.846097 | + | 0.533029i | \(0.178946\pi\) | ||||
−0.846097 | + | 0.533029i | \(0.821054\pi\) | |||||||
\(984\) | −6.52795 | − | 11.3067i | −0.208104 | − | 0.360446i | ||||
\(985\) | −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 | ||||||||
\(990\) | 40.5559 | + | 23.4150i | 1.28895 | + | 0.744177i | ||||
\(991\) | 9.45548 | − | 16.3774i | 0.300363 | − | 0.520244i | −0.675855 | − | 0.737035i | \(-0.736225\pi\) |
0.976218 | + | 0.216790i | \(0.0695588\pi\) | |||||||
\(992\) | −16.3388 | − | 28.2997i | −0.518759 | − | 0.898517i | ||||
\(993\) | 5.97622i | 0.189650i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −67.2685 | + | 38.8375i | −2.13256 | + | 1.23123i | ||||
\(996\) | 18.3059i | 0.580046i | ||||||||
\(997\) | 21.7888 | + | 37.7393i | 0.690057 | + | 1.19521i | 0.971819 | + | 0.235730i | \(0.0757480\pi\) |
−0.281762 | + | 0.959484i | \(0.590919\pi\) | |||||||
\(998\) | −10.6442 | + | 18.4363i | −0.336936 | + | 0.583589i | ||||
\(999\) | 10.4571 | + | 6.03742i | 0.330849 | + | 0.191016i |
(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 | 637.2.q.h.589.1 | 12 | ||
7.2 | even | 3 | 637.2.k.g.459.6 | 12 | |||
7.3 | odd | 6 | 637.2.u.h.30.6 | 12 | |||
7.4 | even | 3 | 637.2.u.i.30.6 | 12 | |||
7.5 | odd | 6 | 637.2.k.h.459.6 | 12 | |||
7.6 | odd | 2 | 91.2.q.a.43.1 | yes | 12 | ||
13.6 | odd | 12 | 8281.2.a.ch.1.6 | 6 | |||
13.7 | odd | 12 | 8281.2.a.by.1.1 | 6 | |||
13.10 | even | 6 | inner | 637.2.q.h.491.1 | 12 | ||
21.20 | even | 2 | 819.2.ct.a.316.6 | 12 | |||
28.27 | even | 2 | 1456.2.cc.c.225.4 | 12 | |||
91.6 | even | 12 | 1183.2.a.p.1.6 | 6 | |||
91.10 | odd | 6 | 637.2.k.h.569.1 | 12 | |||
91.20 | even | 12 | 1183.2.a.m.1.1 | 6 | |||
91.23 | even | 6 | 637.2.u.i.361.6 | 12 | |||
91.48 | odd | 6 | 1183.2.c.i.337.12 | 12 | |||
91.62 | odd | 6 | 91.2.q.a.36.1 | ✓ | 12 | ||
91.69 | odd | 6 | 1183.2.c.i.337.1 | 12 | |||
91.75 | odd | 6 | 637.2.u.h.361.6 | 12 | |||
91.88 | even | 6 | 637.2.k.g.569.1 | 12 | |||
273.62 | even | 6 | 819.2.ct.a.127.6 | 12 | |||
364.335 | even | 6 | 1456.2.cc.c.673.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.1 | ✓ | 12 | 91.62 | odd | 6 | ||
91.2.q.a.43.1 | yes | 12 | 7.6 | odd | 2 | ||
637.2.k.g.459.6 | 12 | 7.2 | even | 3 | |||
637.2.k.g.569.1 | 12 | 91.88 | even | 6 | |||
637.2.k.h.459.6 | 12 | 7.5 | odd | 6 | |||
637.2.k.h.569.1 | 12 | 91.10 | odd | 6 | |||
637.2.q.h.491.1 | 12 | 13.10 | even | 6 | inner | ||
637.2.q.h.589.1 | 12 | 1.1 | even | 1 | trivial | ||
637.2.u.h.30.6 | 12 | 7.3 | odd | 6 | |||
637.2.u.h.361.6 | 12 | 91.75 | odd | 6 | |||
637.2.u.i.30.6 | 12 | 7.4 | even | 3 | |||
637.2.u.i.361.6 | 12 | 91.23 | even | 6 | |||
819.2.ct.a.127.6 | 12 | 273.62 | even | 6 | |||
819.2.ct.a.316.6 | 12 | 21.20 | even | 2 | |||
1183.2.a.m.1.1 | 6 | 91.20 | even | 12 | |||
1183.2.a.p.1.6 | 6 | 91.6 | even | 12 | |||
1183.2.c.i.337.1 | 12 | 91.69 | odd | 6 | |||
1183.2.c.i.337.12 | 12 | 91.48 | odd | 6 | |||
1456.2.cc.c.225.4 | 12 | 28.27 | even | 2 | |||
1456.2.cc.c.673.4 | 12 | 364.335 | even | 6 | |||
8281.2.a.by.1.1 | 6 | 13.7 | odd | 12 | |||
8281.2.a.ch.1.6 | 6 | 13.6 | odd | 12 |