Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(91,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.h (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 91.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.91 |
Dual form | 450.2.h.b.361.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | − | 0.587785i | −0.572061 | − | 0.415627i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | −0.690983 | + | 2.12663i | −0.309017 | + | 0.951057i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 0.309017 | − | 0.951057i | 0.109254 | − | 0.336249i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.80902 | − | 1.31433i | 0.572061 | − | 0.415627i | ||||
\(11\) | −0.618034 | − | 0.449028i | −0.186344 | − | 0.135387i | 0.490702 | − | 0.871327i | \(-0.336740\pi\) |
−0.677046 | + | 0.735940i | \(0.736740\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | + | 1.08981i | −0.416025 | + | 0.302260i | −0.776037 | − | 0.630688i | \(-0.782773\pi\) |
0.360011 | + | 0.932948i | \(0.382773\pi\) | |||||||
\(14\) | −1.61803 | − | 1.17557i | −0.432438 | − | 0.314184i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | −0.354102 | + | 1.08981i | −0.0858823 | + | 0.264319i | −0.984770 | − | 0.173860i | \(-0.944376\pi\) |
0.898888 | + | 0.438178i | \(0.144376\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.23607 | + | 6.88191i | −0.512989 | + | 1.57882i | 0.273922 | + | 0.961752i | \(0.411679\pi\) |
−0.786911 | + | 0.617066i | \(0.788321\pi\) | |||||||
\(20\) | −2.23607 | −0.500000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.236068 | + | 0.726543i | 0.0503299 | + | 0.154899i | ||||
\(23\) | 4.85410 | + | 3.52671i | 1.01215 | + | 0.735370i | 0.964659 | − | 0.263501i | \(-0.0848774\pi\) |
0.0474912 | + | 0.998872i | \(0.484877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | − | 2.93893i | −0.809017 | − | 0.587785i | ||||
\(26\) | 1.85410 | 0.363619 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.618034 | + | 1.90211i | 0.116797 | + | 0.359466i | ||||
\(29\) | 1.11803 | + | 3.44095i | 0.207614 | + | 0.638969i | 0.999596 | + | 0.0284251i | \(0.00904922\pi\) |
−0.791982 | + | 0.610544i | \(0.790951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | + | 9.23305i | −0.538816 | + | 1.65830i | 0.196440 | + | 0.980516i | \(0.437062\pi\) |
−0.735256 | + | 0.677789i | \(0.762938\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.927051 | − | 0.673542i | 0.158988 | − | 0.115511i | ||||
\(35\) | −1.38197 | + | 4.25325i | −0.233595 | + | 0.718931i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.16312 | − | 5.20431i | 1.17761 | − | 0.855583i | 0.185710 | − | 0.982605i | \(-0.440542\pi\) |
0.991900 | + | 0.127021i | \(0.0405417\pi\) | |||||||
\(38\) | 5.85410 | − | 4.25325i | 0.949661 | − | 0.689969i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.80902 | + | 1.31433i | 0.286031 | + | 0.207813i | ||||
\(41\) | 4.11803 | − | 2.99193i | 0.643129 | − | 0.467260i | −0.217795 | − | 0.975995i | \(-0.569886\pi\) |
0.860924 | + | 0.508734i | \(0.169886\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.23607 | 0.493496 | 0.246748 | − | 0.969080i | \(-0.420638\pi\) | ||||
0.246748 | + | 0.969080i | \(0.420638\pi\) | |||||||
\(44\) | 0.236068 | − | 0.726543i | 0.0355886 | − | 0.109530i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.85410 | − | 5.70634i | −0.273372 | − | 0.841354i | ||||
\(47\) | −2.85410 | − | 8.78402i | −0.416314 | − | 1.28128i | −0.911071 | − | 0.412250i | \(-0.864743\pi\) |
0.494757 | − | 0.869031i | \(-0.335257\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 1.54508 | + | 4.75528i | 0.218508 | + | 0.672499i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.50000 | − | 1.08981i | −0.208013 | − | 0.151130i | ||||
\(53\) | 3.57295 | + | 10.9964i | 0.490782 | + | 1.51047i | 0.823428 | + | 0.567421i | \(0.192059\pi\) |
−0.332646 | + | 0.943052i | \(0.607941\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.38197 | − | 1.00406i | 0.186344 | − | 0.135387i | ||||
\(56\) | 0.618034 | − | 1.90211i | 0.0825883 | − | 0.254181i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.11803 | − | 3.44095i | 0.146805 | − | 0.451820i | ||||
\(59\) | −7.23607 | + | 5.25731i | −0.942056 | + | 0.684444i | −0.948915 | − | 0.315533i | \(-0.897817\pi\) |
0.00685884 | + | 0.999976i | \(0.497817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.73607 | + | 1.26133i | 0.222281 | + | 0.161496i | 0.693353 | − | 0.720598i | \(-0.256133\pi\) |
−0.471072 | + | 0.882095i | \(0.656133\pi\) | |||||||
\(62\) | 7.85410 | − | 5.70634i | 0.997472 | − | 0.724706i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | −1.28115 | − | 3.94298i | −0.158907 | − | 0.489067i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.14590 | − | 3.52671i | 0.139994 | − | 0.430856i | −0.856340 | − | 0.516413i | \(-0.827267\pi\) |
0.996333 | + | 0.0855568i | \(0.0272669\pi\) | |||||||
\(68\) | −1.14590 | −0.138961 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.61803 | − | 2.62866i | 0.432438 | − | 0.314184i | ||||
\(71\) | −2.52786 | − | 7.77997i | −0.300002 | − | 0.923312i | −0.981495 | − | 0.191487i | \(-0.938669\pi\) |
0.681493 | − | 0.731825i | \(-0.261331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.97214 | + | 5.79210i | 0.933068 | + | 0.677914i | 0.946742 | − | 0.321993i | \(-0.104353\pi\) |
−0.0136741 | + | 0.999907i | \(0.504353\pi\) | |||||||
\(74\) | −8.85410 | −1.02927 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.23607 | −0.830034 | ||||||||
\(77\) | −1.23607 | − | 0.898056i | −0.140863 | − | 0.102343i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(80\) | −0.690983 | − | 2.12663i | −0.0772542 | − | 0.237764i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.09017 | −0.562115 | ||||||||
\(83\) | −1.85410 | + | 5.70634i | −0.203514 | + | 0.626352i | 0.796257 | + | 0.604959i | \(0.206810\pi\) |
−0.999771 | + | 0.0213936i | \(0.993190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.07295 | − | 1.50609i | −0.224843 | − | 0.163358i | ||||
\(86\) | −2.61803 | − | 1.90211i | −0.282310 | − | 0.205110i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.618034 | + | 0.449028i | −0.0658826 | + | 0.0478665i | ||||
\(89\) | 2.92705 | + | 2.12663i | 0.310267 | + | 0.225422i | 0.732011 | − | 0.681293i | \(-0.238582\pi\) |
−0.421744 | + | 0.906715i | \(0.638582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | + | 2.17963i | −0.314485 | + | 0.228487i | ||||
\(92\) | −1.85410 | + | 5.70634i | −0.193303 | + | 0.594927i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.85410 | + | 8.78402i | −0.294378 | + | 0.906003i | ||||
\(95\) | −13.0902 | − | 9.51057i | −1.34302 | − | 0.975763i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.20820 | − | 6.79615i | −0.224209 | − | 0.690045i | −0.998371 | − | 0.0570570i | \(-0.981828\pi\) |
0.774162 | − | 0.632988i | \(-0.218172\pi\) | |||||||
\(98\) | 2.42705 | + | 1.76336i | 0.245169 | + | 0.178126i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.54508 | − | 4.75528i | 0.154508 | − | 0.475528i | ||||
\(101\) | −17.3262 | −1.72403 | −0.862013 | − | 0.506887i | \(-0.830796\pi\) | ||||
−0.862013 | + | 0.506887i | \(0.830796\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.85410 | − | 14.9394i | −0.478289 | − | 1.47202i | −0.841470 | − | 0.540303i | \(-0.818309\pi\) |
0.363181 | − | 0.931718i | \(-0.381691\pi\) | |||||||
\(104\) | 0.572949 | + | 1.76336i | 0.0561823 | + | 0.172911i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.57295 | − | 10.9964i | 0.347035 | − | 1.06807i | ||||
\(107\) | 6.94427 | 0.671328 | 0.335664 | − | 0.941982i | \(-0.391039\pi\) | ||||
0.335664 | + | 0.941982i | \(0.391039\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.2082 | − | 10.3229i | 1.36090 | − | 0.988751i | 0.362512 | − | 0.931979i | \(-0.381919\pi\) |
0.998387 | − | 0.0567720i | \(-0.0180808\pi\) | |||||||
\(110\) | −1.70820 | −0.162871 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.61803 | + | 1.17557i | −0.152890 | + | 0.111081i | ||||
\(113\) | 6.92705 | − | 5.03280i | 0.651642 | − | 0.473446i | −0.212188 | − | 0.977229i | \(-0.568059\pi\) |
0.863830 | + | 0.503783i | \(0.168059\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.8541 | + | 7.88597i | −1.01215 | + | 0.735370i | ||||
\(116\) | −2.92705 | + | 2.12663i | −0.271770 | + | 0.197452i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.94427 | 0.823387 | ||||||||
\(119\) | −0.708204 | + | 2.17963i | −0.0649209 | + | 0.199806i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.21885 | − | 9.90659i | −0.292622 | − | 0.900599i | ||||
\(122\) | −0.663119 | − | 2.04087i | −0.0600360 | − | 0.184772i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.70820 | −0.871822 | ||||||||
\(125\) | 9.04508 | − | 6.57164i | 0.809017 | − | 0.587785i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0902 | − | 8.05748i | −0.984093 | − | 0.714986i | −0.0254737 | − | 0.999675i | \(-0.508109\pi\) |
−0.958620 | + | 0.284690i | \(0.908109\pi\) | |||||||
\(128\) | 0.309017 | + | 0.951057i | 0.0273135 | + | 0.0840623i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.28115 | + | 3.94298i | −0.112365 | + | 0.345823i | ||||
\(131\) | 1.61803 | − | 4.97980i | 0.141368 | − | 0.435087i | −0.855158 | − | 0.518368i | \(-0.826540\pi\) |
0.996526 | + | 0.0832809i | \(0.0265399\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.47214 | + | 13.7638i | −0.387783 | + | 1.19347i | ||||
\(134\) | −3.00000 | + | 2.17963i | −0.259161 | + | 0.188291i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.927051 | + | 0.673542i | 0.0794940 | + | 0.0577557i | ||||
\(137\) | 11.3541 | − | 8.24924i | 0.970046 | − | 0.704780i | 0.0145842 | − | 0.999894i | \(-0.495358\pi\) |
0.955462 | + | 0.295114i | \(0.0953575\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8541 | − | 7.88597i | −0.920633 | − | 0.668879i | 0.0230486 | − | 0.999734i | \(-0.492663\pi\) |
−0.943681 | + | 0.330855i | \(0.892663\pi\) | |||||||
\(140\) | −4.47214 | −0.377964 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.52786 | + | 7.77997i | −0.212134 | + | 0.652880i | ||||
\(143\) | 1.41641 | 0.118446 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.09017 | −0.671852 | ||||||||
\(146\) | −3.04508 | − | 9.37181i | −0.252013 | − | 0.775616i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.16312 | + | 5.20431i | 0.588805 | + | 0.427792i | ||||
\(149\) | 22.0344 | 1.80513 | 0.902566 | − | 0.430552i | \(-0.141681\pi\) | ||||
0.902566 | + | 0.430552i | \(0.141681\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.9443 | 0.890632 | 0.445316 | − | 0.895373i | \(-0.353091\pi\) | ||||
0.445316 | + | 0.895373i | \(0.353091\pi\) | |||||||
\(152\) | 5.85410 | + | 4.25325i | 0.474830 | + | 0.344984i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.472136 | + | 1.45309i | 0.0380458 | + | 0.117093i | ||||
\(155\) | −17.5623 | − | 12.7598i | −1.41064 | − | 1.02489i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.1459 | 0.889540 | 0.444770 | − | 0.895645i | \(-0.353286\pi\) | ||||
0.444770 | + | 0.895645i | \(0.353286\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.690983 | + | 2.12663i | −0.0546270 | + | 0.168125i | ||||
\(161\) | 9.70820 | + | 7.05342i | 0.765114 | + | 0.555888i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.32624 | + | 6.77591i | −0.730487 | + | 0.530730i | −0.889718 | − | 0.456511i | \(-0.849099\pi\) |
0.159230 | + | 0.987241i | \(0.449099\pi\) | |||||||
\(164\) | 4.11803 | + | 2.99193i | 0.321564 | + | 0.233630i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.85410 | − | 3.52671i | 0.376751 | − | 0.273726i | ||||
\(167\) | 0.763932 | − | 2.35114i | 0.0591148 | − | 0.181937i | −0.917139 | − | 0.398569i | \(-0.869507\pi\) |
0.976253 | + | 0.216632i | \(0.0695071\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.95492 | + | 9.09429i | −0.227301 | + | 0.699561i | ||||
\(170\) | 0.791796 | + | 2.43690i | 0.0607280 | + | 0.186902i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.00000 | + | 3.07768i | 0.0762493 | + | 0.234671i | ||||
\(173\) | −17.8713 | − | 12.9843i | −1.35873 | − | 0.987176i | −0.998524 | − | 0.0543039i | \(-0.982706\pi\) |
−0.360207 | − | 0.932872i | \(-0.617294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.09017 | − | 5.87785i | −0.611559 | − | 0.444324i | ||||
\(176\) | 0.763932 | 0.0575835 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.11803 | − | 3.44095i | −0.0838002 | − | 0.257910i | ||||
\(179\) | 8.09017 | + | 24.8990i | 0.604688 | + | 1.86104i | 0.498923 | + | 0.866646i | \(0.333729\pi\) |
0.105764 | + | 0.994391i | \(0.466271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.79180 | − | 8.59226i | 0.207513 | − | 0.638658i | −0.792088 | − | 0.610407i | \(-0.791006\pi\) |
0.999601 | − | 0.0282515i | \(-0.00899392\pi\) | |||||||
\(182\) | 3.70820 | 0.274870 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.85410 | − | 3.52671i | 0.357849 | − | 0.259993i | ||||
\(185\) | 6.11803 | + | 18.8294i | 0.449807 | + | 1.38436i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.708204 | − | 0.514540i | 0.0517890 | − | 0.0376269i | ||||
\(188\) | 7.47214 | − | 5.42882i | 0.544962 | − | 0.395938i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.00000 | + | 15.3884i | 0.362738 | + | 1.11639i | ||||
\(191\) | −4.23607 | + | 3.07768i | −0.306511 | + | 0.222693i | −0.730398 | − | 0.683022i | \(-0.760665\pi\) |
0.423887 | + | 0.905715i | \(0.360665\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.61803 | 0.332413 | 0.166207 | − | 0.986091i | \(-0.446848\pi\) | ||||
0.166207 | + | 0.986091i | \(0.446848\pi\) | |||||||
\(194\) | −2.20820 | + | 6.79615i | −0.158540 | + | 0.487935i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.927051 | − | 2.85317i | −0.0662179 | − | 0.203798i | ||||
\(197\) | −0.718847 | − | 2.21238i | −0.0512157 | − | 0.157626i | 0.922177 | − | 0.386767i | \(-0.126408\pi\) |
−0.973393 | + | 0.229141i | \(0.926408\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.1803 | 1.14699 | 0.573497 | − | 0.819208i | \(-0.305586\pi\) | ||||
0.573497 | + | 0.819208i | \(0.305586\pi\) | |||||||
\(200\) | −4.04508 | + | 2.93893i | −0.286031 | + | 0.207813i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.0172 | + | 10.1841i | 0.986248 | + | 0.716551i | ||||
\(203\) | 2.23607 | + | 6.88191i | 0.156941 | + | 0.483015i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.51722 | + | 10.8249i | 0.245653 | + | 0.756043i | ||||
\(206\) | −4.85410 | + | 14.9394i | −0.338201 | + | 1.04088i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.572949 | − | 1.76336i | 0.0397269 | − | 0.122267i | ||||
\(209\) | 4.47214 | − | 3.24920i | 0.309344 | − | 0.224752i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.47214 | + | 4.70228i | 0.445560 | + | 0.323718i | 0.787840 | − | 0.615880i | \(-0.211199\pi\) |
−0.342280 | + | 0.939598i | \(0.611199\pi\) | |||||||
\(212\) | −9.35410 | + | 6.79615i | −0.642442 | + | 0.466762i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.61803 | − | 4.08174i | −0.384041 | − | 0.279022i | ||||
\(215\) | −2.23607 | + | 6.88191i | −0.152499 | + | 0.469342i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | + | 18.4661i | −0.407307 | + | 1.25356i | ||||
\(218\) | −17.5623 | −1.18947 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.38197 | + | 1.00406i | 0.0931721 | + | 0.0676935i | ||||
\(221\) | −0.656541 | − | 2.02063i | −0.0441637 | − | 0.135922i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7082 | + | 9.23305i | 0.851004 | + | 0.618291i | 0.925423 | − | 0.378936i | \(-0.123710\pi\) |
−0.0744185 | + | 0.997227i | \(0.523710\pi\) | |||||||
\(224\) | 2.00000 | 0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.56231 | −0.569556 | ||||||||
\(227\) | 0.763932 | + | 0.555029i | 0.0507039 | + | 0.0368386i | 0.612849 | − | 0.790200i | \(-0.290024\pi\) |
−0.562145 | + | 0.827039i | \(0.690024\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.86475 | + | 8.81678i | 0.189308 | + | 0.582629i | 0.999996 | − | 0.00284891i | \(-0.000906837\pi\) |
−0.810688 | + | 0.585478i | \(0.800907\pi\) | |||||||
\(230\) | 13.4164 | 0.884652 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.61803 | 0.237536 | ||||||||
\(233\) | 3.37132 | − | 10.3759i | 0.220863 | − | 0.679746i | −0.777823 | − | 0.628484i | \(-0.783676\pi\) |
0.998685 | − | 0.0512616i | \(-0.0163242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.6525 | 1.34722 | ||||||||
\(236\) | −7.23607 | − | 5.25731i | −0.471028 | − | 0.342222i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.85410 | − | 1.34708i | 0.120184 | − | 0.0873185i | ||||
\(239\) | −21.7082 | − | 15.7719i | −1.40419 | − | 1.02020i | −0.994136 | − | 0.108139i | \(-0.965511\pi\) |
−0.410051 | − | 0.912063i | \(-0.634489\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.78115 | − | 4.20025i | 0.372397 | − | 0.270562i | −0.385807 | − | 0.922579i | \(-0.626077\pi\) |
0.758204 | + | 0.652017i | \(0.226077\pi\) | |||||||
\(242\) | −3.21885 | + | 9.90659i | −0.206915 | + | 0.636820i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.663119 | + | 2.04087i | −0.0424518 | + | 0.130653i | ||||
\(245\) | 2.07295 | − | 6.37988i | 0.132436 | − | 0.407596i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.14590 | − | 12.7598i | −0.263797 | − | 0.811884i | ||||
\(248\) | 7.85410 | + | 5.70634i | 0.498736 | + | 0.362353i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.1803 | −0.707107 | ||||||||
\(251\) | 3.52786 | 0.222677 | 0.111338 | − | 0.993783i | \(-0.464486\pi\) | ||||
0.111338 | + | 0.993783i | \(0.464486\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.41641 | − | 4.35926i | −0.0890488 | − | 0.274064i | ||||
\(254\) | 4.23607 | + | 13.0373i | 0.265795 | + | 0.818031i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 9.38197 | 0.585231 | 0.292615 | − | 0.956230i | \(-0.405474\pi\) | ||||
0.292615 | + | 0.956230i | \(0.405474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.3262 | − | 10.4086i | 0.890189 | − | 0.646760i | ||||
\(260\) | 3.35410 | − | 2.43690i | 0.208013 | − | 0.151130i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.23607 | + | 3.07768i | −0.261705 | + | 0.190140i | ||||
\(263\) | −6.85410 | + | 4.97980i | −0.422642 | + | 0.307067i | −0.778700 | − | 0.627396i | \(-0.784121\pi\) |
0.356058 | + | 0.934464i | \(0.384121\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.8541 | −1.58820 | ||||||||
\(266\) | 11.7082 | − | 8.50651i | 0.717876 | − | 0.521567i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.70820 | 0.226515 | ||||||||
\(269\) | 4.04508 | − | 12.4495i | 0.246633 | − | 0.759059i | −0.748730 | − | 0.662875i | \(-0.769336\pi\) |
0.995364 | − | 0.0961842i | \(-0.0306638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.79837 | + | 5.53483i | 0.109243 | + | 0.336217i | 0.990703 | − | 0.136043i | \(-0.0434385\pi\) |
−0.881460 | + | 0.472260i | \(0.843438\pi\) | |||||||
\(272\) | −0.354102 | − | 1.08981i | −0.0214706 | − | 0.0660797i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.0344 | −0.847852 | ||||||||
\(275\) | 1.18034 | + | 3.63271i | 0.0711772 | + | 0.219061i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.3435 | + | 16.9600i | 1.40257 | + | 1.01903i | 0.994351 | + | 0.106146i | \(0.0338510\pi\) |
0.408222 | + | 0.912883i | \(0.366149\pi\) | |||||||
\(278\) | 4.14590 | + | 12.7598i | 0.248654 | + | 0.765280i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.61803 | + | 2.62866i | 0.216219 | + | 0.157092i | ||||
\(281\) | −1.57295 | + | 4.84104i | −0.0938343 | + | 0.288792i | −0.986948 | − | 0.161038i | \(-0.948516\pi\) |
0.893114 | + | 0.449831i | \(0.148516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.381966 | + | 1.17557i | −0.0227055 | + | 0.0698804i | −0.961767 | − | 0.273868i | \(-0.911697\pi\) |
0.939062 | + | 0.343749i | \(0.111697\pi\) | |||||||
\(284\) | 6.61803 | − | 4.80828i | 0.392708 | − | 0.285319i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.14590 | − | 0.832544i | −0.0677584 | − | 0.0492293i | ||||
\(287\) | 8.23607 | − | 5.98385i | 0.486160 | − | 0.353216i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6910 | + | 9.22054i | 0.746528 | + | 0.542385i | ||||
\(290\) | 6.54508 | + | 4.75528i | 0.384341 | + | 0.279240i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.04508 | + | 9.37181i | −0.178200 | + | 0.548444i | ||||
\(293\) | 4.20163 | 0.245462 | 0.122731 | − | 0.992440i | \(-0.460835\pi\) | ||||
0.122731 | + | 0.992440i | \(0.460835\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.18034 | − | 19.0211i | −0.359833 | − | 1.10745i | ||||
\(296\) | −2.73607 | − | 8.42075i | −0.159031 | − | 0.489446i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.8262 | − | 12.9515i | −1.03265 | − | 0.750261i | ||||
\(299\) | −11.1246 | −0.643353 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.47214 | 0.373048 | ||||||||
\(302\) | −8.85410 | − | 6.43288i | −0.509496 | − | 0.370171i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.23607 | − | 6.88191i | −0.128247 | − | 0.394705i | ||||
\(305\) | −3.88197 | + | 2.82041i | −0.222281 | + | 0.161496i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.7082 | −1.69554 | −0.847768 | − | 0.530367i | \(-0.822054\pi\) | ||||
−0.847768 | + | 0.530367i | \(0.822054\pi\) | |||||||
\(308\) | 0.472136 | − | 1.45309i | 0.0269024 | − | 0.0827972i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.70820 | + | 20.6457i | 0.381000 | + | 1.17260i | ||||
\(311\) | 10.2361 | + | 7.43694i | 0.580434 | + | 0.421710i | 0.838881 | − | 0.544315i | \(-0.183211\pi\) |
−0.258446 | + | 0.966026i | \(0.583211\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.8541 | + | 10.7921i | −0.839603 | + | 0.610008i | −0.922260 | − | 0.386570i | \(-0.873660\pi\) |
0.0826564 | + | 0.996578i | \(0.473660\pi\) | |||||||
\(314\) | −9.01722 | − | 6.55139i | −0.508871 | − | 0.369717i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.38197 | + | 10.4086i | −0.189950 | + | 0.584606i | −0.999998 | − | 0.00175672i | \(-0.999441\pi\) |
0.810048 | + | 0.586363i | \(0.199441\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.854102 | − | 2.62866i | 0.0478205 | − | 0.147176i | ||||
\(320\) | 1.80902 | − | 1.31433i | 0.101127 | − | 0.0734732i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.70820 | − | 11.4127i | −0.206650 | − | 0.636004i | ||||
\(323\) | −6.70820 | − | 4.87380i | −0.373254 | − | 0.271185i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.27051 | 0.514235 | ||||||||
\(326\) | 11.5279 | 0.638469 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.57295 | − | 4.84104i | −0.0868516 | − | 0.267302i | ||||
\(329\) | −5.70820 | − | 17.5680i | −0.314703 | − | 0.968558i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.27051 | + | 22.3763i | −0.399623 | + | 1.22991i | 0.525679 | + | 0.850683i | \(0.323811\pi\) |
−0.925302 | + | 0.379231i | \(0.876189\pi\) | |||||||
\(332\) | −6.00000 | −0.329293 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.00000 | + | 1.45309i | −0.109435 | + | 0.0795093i | ||||
\(335\) | 6.70820 | + | 4.87380i | 0.366508 | + | 0.266284i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0902 | − | 14.5964i | 1.09438 | − | 0.795115i | 0.114248 | − | 0.993452i | \(-0.463554\pi\) |
0.980134 | + | 0.198338i | \(0.0635543\pi\) | |||||||
\(338\) | 7.73607 | − | 5.62058i | 0.420787 | − | 0.305719i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.791796 | − | 2.43690i | 0.0429412 | − | 0.132159i | ||||
\(341\) | 6.00000 | − | 4.35926i | 0.324918 | − | 0.236067i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 1.00000 | − | 3.07768i | 0.0539164 | − | 0.165938i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.82624 | + | 21.0090i | 0.366981 | + | 1.12945i | ||||
\(347\) | 0.236068 | + | 0.726543i | 0.0126728 | + | 0.0390028i | 0.957193 | − | 0.289451i | \(-0.0934726\pi\) |
−0.944520 | + | 0.328453i | \(0.893473\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.79837 | −0.524495 | −0.262247 | − | 0.965001i | \(-0.584464\pi\) | ||||
−0.262247 | + | 0.965001i | \(0.584464\pi\) | |||||||
\(350\) | 3.09017 | + | 9.51057i | 0.165177 | + | 0.508361i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.618034 | − | 0.449028i | −0.0329413 | − | 0.0239333i | ||||
\(353\) | −3.56231 | − | 10.9637i | −0.189602 | − | 0.583536i | 0.810395 | − | 0.585884i | \(-0.199253\pi\) |
−0.999997 | + | 0.00234791i | \(0.999253\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.2918 | 0.970828 | ||||||||
\(356\) | −1.11803 | + | 3.44095i | −0.0592557 | + | 0.182370i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.09017 | − | 24.8990i | 0.427579 | − | 1.31595i | ||||
\(359\) | 6.38197 | − | 4.63677i | 0.336827 | − | 0.244719i | −0.406495 | − | 0.913653i | \(-0.633249\pi\) |
0.743322 | + | 0.668934i | \(0.233249\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −26.9894 | − | 19.6089i | −1.42049 | − | 1.03205i | ||||
\(362\) | −7.30902 | + | 5.31031i | −0.384153 | + | 0.279104i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.00000 | − | 2.17963i | −0.157243 | − | 0.114244i | ||||
\(365\) | −17.8262 | + | 12.9515i | −0.933068 | + | 0.677914i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.09017 | + | 3.35520i | −0.0569064 | + | 0.175140i | −0.975470 | − | 0.220134i | \(-0.929350\pi\) |
0.918563 | + | 0.395274i | \(0.129350\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.11803 | − | 18.8294i | 0.318061 | − | 0.978892i | ||||
\(371\) | 7.14590 | + | 21.9928i | 0.370997 | + | 1.14181i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.7984 | − | 17.2905i | −1.23223 | − | 0.895270i | −0.235178 | − | 0.971952i | \(-0.575567\pi\) |
−0.997056 | + | 0.0766827i | \(0.975567\pi\) | |||||||
\(374\) | −0.875388 | −0.0452652 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.23607 | −0.476314 | ||||||||
\(377\) | −5.42705 | − | 3.94298i | −0.279507 | − | 0.203074i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.23607 | + | 22.2703i | 0.371692 | + | 1.14395i | 0.945684 | + | 0.325089i | \(0.105394\pi\) |
−0.573992 | + | 0.818861i | \(0.694606\pi\) | |||||||
\(380\) | 5.00000 | − | 15.3884i | 0.256495 | − | 0.789409i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.23607 | 0.267901 | ||||||||
\(383\) | −3.56231 | + | 10.9637i | −0.182025 | + | 0.560216i | −0.999884 | − | 0.0152022i | \(-0.995161\pi\) |
0.817859 | + | 0.575419i | \(0.195161\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.76393 | − | 2.00811i | 0.140863 | − | 0.102343i | ||||
\(386\) | −3.73607 | − | 2.71441i | −0.190161 | − | 0.138160i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.78115 | − | 4.20025i | 0.293494 | − | 0.213236i | ||||
\(389\) | −25.0623 | − | 18.2088i | −1.27071 | − | 0.923224i | −0.271479 | − | 0.962444i | \(-0.587513\pi\) |
−0.999231 | + | 0.0392200i | \(0.987513\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.56231 | + | 4.04125i | −0.281298 | + | 0.204375i | ||||
\(392\) | −0.927051 | + | 2.85317i | −0.0468231 | + | 0.144107i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.718847 | + | 2.21238i | −0.0362150 | + | 0.111458i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.67376 | − | 23.6174i | −0.385135 | − | 1.18532i | −0.936382 | − | 0.350982i | \(-0.885848\pi\) |
0.551247 | − | 0.834342i | \(-0.314152\pi\) | |||||||
\(398\) | −13.0902 | − | 9.51057i | −0.656151 | − | 0.476722i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | 14.9098 | 0.744561 | 0.372281 | − | 0.928120i | \(-0.378576\pi\) | ||||
0.372281 | + | 0.928120i | \(0.378576\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.56231 | − | 17.1190i | −0.277078 | − | 0.852759i | ||||
\(404\) | −5.35410 | − | 16.4782i | −0.266377 | − | 0.819823i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.23607 | − | 6.88191i | 0.110974 | − | 0.341543i | ||||
\(407\) | −6.76393 | −0.335276 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.0172 | − | 15.2699i | 1.03923 | − | 0.755048i | 0.0690987 | − | 0.997610i | \(-0.477988\pi\) |
0.970136 | + | 0.242562i | \(0.0779877\pi\) | |||||||
\(410\) | 3.51722 | − | 10.8249i | 0.173703 | − | 0.534603i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.7082 | − | 9.23305i | 0.626088 | − | 0.454880i | ||||
\(413\) | −14.4721 | + | 10.5146i | −0.712127 | + | 0.517391i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.8541 | − | 7.88597i | −0.532807 | − | 0.387107i | ||||
\(416\) | −1.50000 | + | 1.08981i | −0.0735436 | + | 0.0534325i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.52786 | −0.270377 | ||||||||
\(419\) | 0.652476 | − | 2.00811i | 0.0318755 | − | 0.0981028i | −0.933853 | − | 0.357657i | \(-0.883576\pi\) |
0.965729 | + | 0.259554i | \(0.0835757\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.0278640 | + | 0.0857567i | 0.00135801 | + | 0.00417953i | 0.951733 | − | 0.306926i | \(-0.0993006\pi\) |
−0.950375 | + | 0.311106i | \(0.899301\pi\) | |||||||
\(422\) | −2.47214 | − | 7.60845i | −0.120342 | − | 0.370374i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.5623 | 0.561515 | ||||||||
\(425\) | 4.63525 | − | 3.36771i | 0.224843 | − | 0.163358i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.47214 | + | 2.52265i | 0.168028 | + | 0.122080i | ||||
\(428\) | 2.14590 | + | 6.60440i | 0.103726 | + | 0.319235i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.85410 | − | 4.25325i | 0.282310 | − | 0.205110i | ||||
\(431\) | 3.00000 | − | 9.23305i | 0.144505 | − | 0.444740i | −0.852442 | − | 0.522822i | \(-0.824879\pi\) |
0.996947 | + | 0.0780813i | \(0.0248794\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.22542 | + | 28.3929i | −0.443346 | + | 1.36448i | 0.440942 | + | 0.897535i | \(0.354644\pi\) |
−0.884288 | + | 0.466942i | \(0.845356\pi\) | |||||||
\(434\) | 15.7082 | − | 11.4127i | 0.754018 | − | 0.547826i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.2082 | + | 10.3229i | 0.680450 | + | 0.494376i | ||||
\(437\) | −35.1246 | + | 25.5195i | −1.68024 | + | 1.22076i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.2361 | − | 8.89002i | −0.583996 | − | 0.424298i | 0.256167 | − | 0.966633i | \(-0.417540\pi\) |
−0.840162 | + | 0.542335i | \(0.817540\pi\) | |||||||
\(440\) | −0.527864 | − | 1.62460i | −0.0251649 | − | 0.0774497i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.656541 | + | 2.02063i | −0.0312285 | + | 0.0961114i | ||||
\(443\) | 28.0689 | 1.33359 | 0.666796 | − | 0.745240i | \(-0.267665\pi\) | ||||
0.666796 | + | 0.745240i | \(0.267665\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.54508 | + | 4.75528i | −0.310267 | + | 0.225422i | ||||
\(446\) | −4.85410 | − | 14.9394i | −0.229848 | − | 0.707401i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.61803 | − | 1.17557i | −0.0764449 | − | 0.0555405i | ||||
\(449\) | 19.7984 | 0.934343 | 0.467172 | − | 0.884167i | \(-0.345273\pi\) | ||||
0.467172 | + | 0.884167i | \(0.345273\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.88854 | −0.183104 | ||||||||
\(452\) | 6.92705 | + | 5.03280i | 0.325821 | + | 0.236723i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.291796 | − | 0.898056i | −0.0136947 | − | 0.0421479i | ||||
\(455\) | −2.56231 | − | 7.88597i | −0.120123 | − | 0.369700i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.52786 | −0.165027 | −0.0825133 | − | 0.996590i | \(-0.526295\pi\) | ||||
−0.0825133 | + | 0.996590i | \(0.526295\pi\) | |||||||
\(458\) | 2.86475 | − | 8.81678i | 0.133861 | − | 0.411981i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.8541 | − | 7.88597i | −0.506075 | − | 0.367685i | ||||
\(461\) | 11.2533 | + | 8.17599i | 0.524118 | + | 0.380794i | 0.818153 | − | 0.575001i | \(-0.194998\pi\) |
−0.294035 | + | 0.955795i | \(0.594998\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.7984 | − | 15.1109i | 0.966582 | − | 0.702263i | 0.0119123 | − | 0.999929i | \(-0.496208\pi\) |
0.954670 | + | 0.297666i | \(0.0962081\pi\) | |||||||
\(464\) | −2.92705 | − | 2.12663i | −0.135885 | − | 0.0987262i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.82624 | + | 6.41264i | −0.408868 | + | 0.297060i | ||||
\(467\) | −11.7984 | + | 36.3117i | −0.545964 | + | 1.68030i | 0.172724 | + | 0.984970i | \(0.444743\pi\) |
−0.718688 | + | 0.695333i | \(0.755257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.29180 | − | 7.05342i | 0.105825 | − | 0.325697i | ||||
\(470\) | −16.7082 | − | 12.1392i | −0.770692 | − | 0.559940i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.76393 | + | 8.50651i | 0.127220 | + | 0.391544i | ||||
\(473\) | −2.00000 | − | 1.45309i | −0.0919601 | − | 0.0668129i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.2705 | − | 21.2663i | 1.34302 | − | 0.975763i | ||||
\(476\) | −2.29180 | −0.105044 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.29180 | + | 25.5195i | 0.379258 | + | 1.16724i | ||||
\(479\) | 1.38197 | + | 4.25325i | 0.0631436 | + | 0.194336i | 0.977652 | − | 0.210232i | \(-0.0674219\pi\) |
−0.914508 | + | 0.404568i | \(0.867422\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.07295 | + | 15.6129i | −0.231307 | + | 0.711888i | ||||
\(482\) | −7.14590 | −0.325487 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.42705 | − | 6.12261i | 0.383048 | − | 0.278300i | ||||
\(485\) | 15.9787 | 0.725556 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.1803 | + | 13.9353i | −0.869144 | + | 0.631470i | −0.930357 | − | 0.366655i | \(-0.880503\pi\) |
0.0612130 | + | 0.998125i | \(0.480503\pi\) | |||||||
\(488\) | 1.73607 | − | 1.26133i | 0.0785881 | − | 0.0570976i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.42705 | + | 3.94298i | −0.245169 | + | 0.178126i | ||||
\(491\) | −4.76393 | + | 3.46120i | −0.214993 | + | 0.156202i | −0.690070 | − | 0.723743i | \(-0.742420\pi\) |
0.475077 | + | 0.879944i | \(0.342420\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.14590 | −0.186722 | ||||||||
\(494\) | −4.14590 | + | 12.7598i | −0.186533 | + | 0.574089i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | − | 9.23305i | −0.134704 | − | 0.414576i | ||||
\(497\) | −5.05573 | − | 15.5599i | −0.226780 | − | 0.697958i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.58359 | −0.294722 | −0.147361 | − | 0.989083i | \(-0.547078\pi\) | ||||
−0.147361 | + | 0.989083i | \(0.547078\pi\) | |||||||
\(500\) | 9.04508 | + | 6.57164i | 0.404508 | + | 0.293893i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.85410 | − | 2.07363i | −0.127385 | − | 0.0925505i | ||||
\(503\) | −9.41641 | − | 28.9807i | −0.419857 | − | 1.29219i | −0.907834 | − | 0.419330i | \(-0.862265\pi\) |
0.487977 | − | 0.872857i | \(-0.337735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.9721 | − | 36.8464i | 0.532753 | − | 1.63965i | ||||
\(506\) | −1.41641 | + | 4.35926i | −0.0629670 | + | 0.193793i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.23607 | − | 13.0373i | 0.187945 | − | 0.578436i | ||||
\(509\) | 23.2533 | − | 16.8945i | 1.03068 | − | 0.748836i | 0.0622385 | − | 0.998061i | \(-0.480176\pi\) |
0.968445 | + | 0.249226i | \(0.0801761\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.9443 | + | 11.5842i | 0.705333 | + | 0.512454i | ||||
\(512\) | −0.809017 | + | 0.587785i | −0.0357538 | + | 0.0259767i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.59017 | − | 5.51458i | −0.334788 | − | 0.243238i | ||||
\(515\) | 35.1246 | 1.54778 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.18034 | + | 6.71040i | −0.0958912 | + | 0.295123i | ||||
\(518\) | −17.7082 | −0.778054 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.14590 | −0.181810 | ||||||||
\(521\) | 8.42705 | + | 25.9358i | 0.369196 | + | 1.13627i | 0.947312 | + | 0.320313i | \(0.103788\pi\) |
−0.578116 | + | 0.815955i | \(0.696212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.7082 | + | 9.23305i | 0.555691 | + | 0.403733i | 0.829879 | − | 0.557943i | \(-0.188409\pi\) |
−0.274188 | + | 0.961676i | \(0.588409\pi\) | |||||||
\(524\) | 5.23607 | 0.228739 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.47214 | 0.369403 | ||||||||
\(527\) | −9.00000 | − | 6.53888i | −0.392046 | − | 0.284838i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.01722 | + | 12.3637i | 0.174662 | + | 0.537554i | ||||
\(530\) | 20.9164 | + | 15.1967i | 0.908551 | + | 0.660101i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.4721 | −0.627447 | ||||||||
\(533\) | −2.91641 | + | 8.97578i | −0.126324 | + | 0.388784i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.79837 | + | 14.7679i | −0.207452 | + | 0.638471i | ||||
\(536\) | −3.00000 | − | 2.17963i | −0.129580 | − | 0.0941456i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.5902 | + | 7.69421i | −0.456575 | + | 0.331721i | ||||
\(539\) | 1.85410 | + | 1.34708i | 0.0798618 | + | 0.0580230i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.92705 | − | 7.21242i | 0.426797 | − | 0.310086i | −0.353570 | − | 0.935408i | \(-0.615032\pi\) |
0.780367 | + | 0.625322i | \(0.215032\pi\) | |||||||
\(542\) | 1.79837 | − | 5.53483i | 0.0772468 | − | 0.237741i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.354102 | + | 1.08981i | −0.0151820 | + | 0.0467254i | ||||
\(545\) | 12.1353 | + | 37.3485i | 0.519817 | + | 1.59983i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.618034 | + | 1.90211i | 0.0264252 | + | 0.0813285i | 0.963399 | − | 0.268070i | \(-0.0863859\pi\) |
−0.936974 | + | 0.349399i | \(0.886386\pi\) | |||||||
\(548\) | 11.3541 | + | 8.24924i | 0.485023 | + | 0.352390i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.18034 | − | 3.63271i | 0.0503299 | − | 0.154899i | ||||
\(551\) | −26.1803 | −1.11532 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.91641 | − | 27.4419i | −0.378822 | − | 1.16589i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.14590 | − | 12.7598i | 0.175825 | − | 0.541134i | ||||
\(557\) | −6.27051 | −0.265690 | −0.132845 | − | 0.991137i | \(-0.542411\pi\) | ||||
−0.132845 | + | 0.991137i | \(0.542411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.85410 | + | 3.52671i | −0.205307 | + | 0.149164i | ||||
\(560\) | −1.38197 | − | 4.25325i | −0.0583987 | − | 0.179733i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.11803 | − | 2.99193i | 0.173709 | − | 0.126207i | ||||
\(563\) | 1.23607 | − | 0.898056i | 0.0520941 | − | 0.0378485i | −0.561434 | − | 0.827522i | \(-0.689750\pi\) |
0.613528 | + | 0.789673i | \(0.289750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.91641 | + | 18.2088i | 0.248905 | + | 0.766051i | ||||
\(566\) | 1.00000 | − | 0.726543i | 0.0420331 | − | 0.0305389i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.18034 | −0.343239 | ||||||||
\(569\) | −7.29837 | + | 22.4621i | −0.305964 | + | 0.941660i | 0.673352 | + | 0.739322i | \(0.264854\pi\) |
−0.979316 | + | 0.202338i | \(0.935146\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.27051 | + | 19.2986i | 0.262413 | + | 0.807623i | 0.992278 | + | 0.124032i | \(0.0395827\pi\) |
−0.729866 | + | 0.683591i | \(0.760417\pi\) | |||||||
\(572\) | 0.437694 | + | 1.34708i | 0.0183009 | + | 0.0563244i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.1803 | −0.424919 | ||||||||
\(575\) | −9.27051 | − | 28.5317i | −0.386607 | − | 1.18985i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.0902 | + | 14.5964i | 0.836365 | + | 0.607655i | 0.921353 | − | 0.388727i | \(-0.127085\pi\) |
−0.0849881 | + | 0.996382i | \(0.527085\pi\) | |||||||
\(578\) | −4.84752 | − | 14.9191i | −0.201630 | − | 0.620555i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.50000 | − | 7.69421i | −0.103807 | − | 0.319485i | ||||
\(581\) | −3.70820 | + | 11.4127i | −0.153842 | + | 0.473478i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.72949 | − | 8.40051i | 0.113044 | − | 0.347913i | ||||
\(584\) | 7.97214 | − | 5.79210i | 0.329889 | − | 0.239679i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.39919 | − | 2.46965i | −0.140419 | − | 0.102020i | ||||
\(587\) | 16.0902 | − | 11.6902i | 0.664112 | − | 0.482506i | −0.203937 | − | 0.978984i | \(-0.565374\pi\) |
0.868049 | + | 0.496478i | \(0.165374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −56.8328 | − | 41.2915i | −2.34176 | − | 1.70138i | ||||
\(590\) | −6.18034 | + | 19.0211i | −0.254441 | + | 0.783088i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.73607 | + | 8.42075i | −0.112452 | + | 0.346091i | ||||
\(593\) | −23.0344 | −0.945911 | −0.472956 | − | 0.881086i | \(-0.656813\pi\) | ||||
−0.472956 | + | 0.881086i | \(0.656813\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.14590 | − | 3.01217i | −0.169965 | − | 0.123487i | ||||
\(596\) | 6.80902 | + | 20.9560i | 0.278908 | + | 0.858391i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.00000 | + | 6.53888i | 0.368037 | + | 0.267395i | ||||
\(599\) | −18.9443 | −0.774042 | −0.387021 | − | 0.922071i | \(-0.626496\pi\) | ||||
−0.387021 | + | 0.922071i | \(0.626496\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.32624 | −0.339634 | −0.169817 | − | 0.985476i | \(-0.554318\pi\) | ||||
−0.169817 | + | 0.985476i | \(0.554318\pi\) | |||||||
\(602\) | −5.23607 | − | 3.80423i | −0.213406 | − | 0.155049i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.38197 | + | 10.4086i | 0.137610 | + | 0.423521i | ||||
\(605\) | 23.2918 | 0.946946 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.1803 | −0.981450 | −0.490725 | − | 0.871315i | \(-0.663268\pi\) | ||||
−0.490725 | + | 0.871315i | \(0.663268\pi\) | |||||||
\(608\) | −2.23607 | + | 6.88191i | −0.0906845 | + | 0.279098i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.79837 | 0.194280 | ||||||||
\(611\) | 13.8541 | + | 10.0656i | 0.560477 | + | 0.407210i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.16312 | − | 0.845055i | 0.0469779 | − | 0.0341315i | −0.564048 | − | 0.825742i | \(-0.690757\pi\) |
0.611026 | + | 0.791610i | \(0.290757\pi\) | |||||||
\(614\) | 24.0344 | + | 17.4620i | 0.969951 | + | 0.704711i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.23607 | + | 0.898056i | −0.0498026 | + | 0.0361837i | ||||
\(617\) | −3.28115 | + | 10.0984i | −0.132094 | + | 0.406544i | −0.995127 | − | 0.0986041i | \(-0.968562\pi\) |
0.863032 | + | 0.505148i | \(0.168562\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.23607 | + | 22.2703i | −0.290842 | + | 0.895120i | 0.693744 | + | 0.720221i | \(0.255960\pi\) |
−0.984586 | + | 0.174899i | \(0.944040\pi\) | |||||||
\(620\) | 6.70820 | − | 20.6457i | 0.269408 | − | 0.829152i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.90983 | − | 12.0332i | −0.156770 | − | 0.482488i | ||||
\(623\) | 5.85410 | + | 4.25325i | 0.234540 | + | 0.170403i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.72542 | + | 23.7764i | 0.309017 | + | 0.951057i | ||||
\(626\) | 18.3607 | 0.733840 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.44427 | + | 10.6004i | 0.137441 | + | 0.423001i | ||||
\(629\) | 3.13525 | + | 9.64932i | 0.125011 | + | 0.384744i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.888544 | + | 2.73466i | −0.0353724 | + | 0.108865i | −0.967184 | − | 0.254078i | \(-0.918228\pi\) |
0.931811 | + | 0.362943i | \(0.118228\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.85410 | − | 6.43288i | 0.351641 | − | 0.255482i | ||||
\(635\) | 24.7984 | − | 18.0171i | 0.984093 | − | 0.714986i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.50000 | − | 3.26944i | 0.178296 | − | 0.129540i | ||||
\(638\) | −2.23607 | + | 1.62460i | −0.0885268 | + | 0.0643185i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.23607 | −0.0883883 | ||||||||
\(641\) | −7.32624 | + | 5.32282i | −0.289369 | + | 0.210239i | −0.722994 | − | 0.690855i | \(-0.757234\pi\) |
0.433625 | + | 0.901094i | \(0.357234\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.7771 | 1.25317 | 0.626583 | − | 0.779355i | \(-0.284453\pi\) | ||||
0.626583 | + | 0.779355i | \(0.284453\pi\) | |||||||
\(644\) | −3.70820 | + | 11.4127i | −0.146124 | + | 0.449723i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.56231 | + | 7.88597i | 0.100813 | + | 0.310269i | ||||
\(647\) | 0.0344419 | + | 0.106001i | 0.00135405 | + | 0.00416733i | 0.951731 | − | 0.306933i | \(-0.0993026\pi\) |
−0.950377 | + | 0.311100i | \(0.899303\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.83282 | 0.268211 | ||||||||
\(650\) | −7.50000 | − | 5.44907i | −0.294174 | − | 0.213730i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.32624 | − | 6.77591i | −0.365244 | − | 0.265365i | ||||
\(653\) | −5.93769 | − | 18.2743i | −0.232360 | − | 0.715130i | −0.997461 | − | 0.0712197i | \(-0.977311\pi\) |
0.765101 | − | 0.643911i | \(-0.222689\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.47214 | + | 6.88191i | 0.370107 | + | 0.268898i | ||||
\(656\) | −1.57295 | + | 4.84104i | −0.0614133 | + | 0.189011i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.70820 | + | 17.5680i | −0.222529 | + | 0.684874i | ||||
\(659\) | 17.0344 | − | 12.3762i | 0.663568 | − | 0.482110i | −0.204298 | − | 0.978909i | \(-0.565491\pi\) |
0.867866 | + | 0.496799i | \(0.165491\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.2705 | + | 19.0866i | 1.02180 | + | 0.742384i | 0.966652 | − | 0.256094i | \(-0.0824355\pi\) |
0.0551524 | + | 0.998478i | \(0.482436\pi\) | |||||||
\(662\) | 19.0344 | − | 13.8293i | 0.739795 | − | 0.537492i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.85410 | + | 3.52671i | 0.188376 | + | 0.136863i | ||||
\(665\) | −26.1803 | − | 19.0211i | −1.01523 | − | 0.737608i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.70820 | + | 20.6457i | −0.259743 | + | 0.799406i | ||||
\(668\) | 2.47214 | 0.0956498 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.56231 | − | 7.88597i | −0.0989905 | − | 0.304661i | ||||
\(671\) | −0.506578 | − | 1.55909i | −0.0195562 | − | 0.0601879i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.69098 | − | 3.40820i | −0.180824 | − | 0.131376i | 0.493691 | − | 0.869637i | \(-0.335647\pi\) |
−0.674515 | + | 0.738261i | \(0.735647\pi\) | |||||||
\(674\) | −24.8328 | −0.956524 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.56231 | −0.367781 | ||||||||
\(677\) | 22.2705 | + | 16.1805i | 0.855925 | + | 0.621866i | 0.926773 | − | 0.375621i | \(-0.122571\pi\) |
−0.0708481 | + | 0.997487i | \(0.522571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.41641 | − | 13.5923i | −0.169486 | − | 0.521625i | ||||
\(680\) | −2.07295 | + | 1.50609i | −0.0794940 | + | 0.0577557i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.41641 | −0.283989 | ||||||||
\(683\) | 2.29180 | − | 7.05342i | 0.0876931 | − | 0.269892i | −0.897588 | − | 0.440836i | \(-0.854682\pi\) |
0.985281 | + | 0.170945i | \(0.0546819\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.69756 | + | 29.8460i | 0.370525 | + | 1.14036i | ||||
\(686\) | 16.1803 | + | 11.7557i | 0.617768 | + | 0.448835i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.61803 | + | 1.90211i | −0.0998116 | + | 0.0725174i | ||||
\(689\) | −17.3435 | − | 12.6008i | −0.660733 | − | 0.480051i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.47214 | − | 1.06957i | 0.0560027 | − | 0.0406883i | −0.559432 | − | 0.828876i | \(-0.688981\pi\) |
0.615434 | + | 0.788188i | \(0.288981\pi\) | |||||||
\(692\) | 6.82624 | − | 21.0090i | 0.259495 | − | 0.798642i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.236068 | − | 0.726543i | 0.00896102 | − | 0.0275792i | ||||
\(695\) | 24.2705 | − | 17.6336i | 0.920633 | − | 0.668879i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.80244 | + | 5.54734i | 0.0682723 | + | 0.210120i | ||||
\(698\) | 7.92705 | + | 5.75934i | 0.300043 | + | 0.217994i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.09017 | − | 9.51057i | 0.116797 | − | 0.359466i | ||||
\(701\) | −49.1591 | −1.85671 | −0.928356 | − | 0.371692i | \(-0.878778\pi\) | ||||
−0.928356 | + | 0.371692i | \(0.878778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.7984 | + | 60.9331i | 0.746710 | + | 2.29814i | ||||
\(704\) | 0.236068 | + | 0.726543i | 0.00889715 | + | 0.0273826i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.56231 | + | 10.9637i | −0.134069 | + | 0.412622i | ||||
\(707\) | −34.6525 | −1.30324 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.20820 | − | 3.05744i | 0.158042 | − | 0.114825i | −0.505953 | − | 0.862561i | \(-0.668859\pi\) |
0.663996 | + | 0.747736i | \(0.268859\pi\) | |||||||
\(710\) | −14.7984 | − | 10.7516i | −0.555373 | − | 0.403502i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.92705 | − | 2.12663i | 0.109696 | − | 0.0796987i | ||||
\(713\) | −47.1246 | + | 34.2380i | −1.76483 | + | 1.28222i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.978714 | + | 3.01217i | −0.0366018 | + | 0.112649i | ||||
\(716\) | −21.1803 | + | 15.3884i | −0.791546 | + | 0.575092i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.88854 | −0.294398 | ||||||||
\(719\) | 6.90983 | − | 21.2663i | 0.257693 | − | 0.793098i | −0.735594 | − | 0.677423i | \(-0.763097\pi\) |
0.993287 | − | 0.115675i | \(-0.0369032\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.70820 | − | 29.8788i | −0.361552 | − | 1.11274i | ||||
\(722\) | 10.3090 | + | 31.7279i | 0.383662 | + | 1.18079i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.03444 | 0.335762 | ||||||||
\(725\) | 5.59017 | − | 17.2048i | 0.207614 | − | 0.638969i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.1803 | − | 13.9353i | −0.711359 | − | 0.516833i | 0.172253 | − | 0.985053i | \(-0.444895\pi\) |
−0.883612 | + | 0.468220i | \(0.844895\pi\) | |||||||
\(728\) | 1.14590 | + | 3.52671i | 0.0424698 | + | 0.130709i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 22.0344 | 0.815531 | ||||||||
\(731\) | −1.14590 | + | 3.52671i | −0.0423826 | + | 0.130440i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.8541 | − | 36.4832i | 0.437841 | − | 1.34754i | −0.452306 | − | 0.891863i | \(-0.649398\pi\) |
0.890147 | − | 0.455674i | \(-0.150602\pi\) | |||||||
\(734\) | 2.85410 | − | 2.07363i | 0.105347 | − | 0.0765389i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.85410 | + | 3.52671i | 0.178925 | + | 0.129996i | ||||
\(737\) | −2.29180 | + | 1.66509i | −0.0844194 | + | 0.0613343i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.5623 | − | 12.7598i | −0.646040 | − | 0.469375i | 0.215880 | − | 0.976420i | \(-0.430738\pi\) |
−0.861920 | + | 0.507044i | \(0.830738\pi\) | |||||||
\(740\) | −16.0172 | + | 11.6372i | −0.588805 | + | 0.427792i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.14590 | − | 21.9928i | 0.262334 | − | 0.807382i | ||||
\(743\) | 24.6525 | 0.904412 | 0.452206 | − | 0.891914i | \(-0.350637\pi\) | ||||
0.452206 | + | 0.891914i | \(0.350637\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.2254 | + | 46.8590i | −0.557816 | + | 1.71678i | ||||
\(746\) | 9.09017 | + | 27.9767i | 0.332815 | + | 1.02430i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.708204 | + | 0.514540i | 0.0258945 | + | 0.0188135i | ||||
\(749\) | 13.8885 | 0.507476 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.2361 | 0.701934 | 0.350967 | − | 0.936388i | \(-0.385853\pi\) | ||||
0.350967 | + | 0.936388i | \(0.385853\pi\) | |||||||
\(752\) | 7.47214 | + | 5.42882i | 0.272481 | + | 0.197969i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.07295 | + | 6.37988i | 0.0754924 | + | 0.232342i | ||||
\(755\) | −7.56231 | + | 23.2744i | −0.275220 | + | 0.847042i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.1459 | −0.804906 | −0.402453 | − | 0.915441i | \(-0.631842\pi\) | ||||
−0.402453 | + | 0.915441i | \(0.631842\pi\) | |||||||
\(758\) | 7.23607 | − | 22.2703i | 0.262826 | − | 0.808895i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.0902 | + | 9.51057i | −0.474830 | + | 0.344984i | ||||
\(761\) | −36.5344 | − | 26.5438i | −1.32437 | − | 0.962213i | −0.999867 | − | 0.0163292i | \(-0.994802\pi\) |
−0.324506 | − | 0.945884i | \(-0.605198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.4164 | − | 20.6457i | 1.02874 | − | 0.747426i | ||||
\(764\) | −4.23607 | − | 3.07768i | −0.153256 | − | 0.111347i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.32624 | − | 6.77591i | 0.336971 | − | 0.244824i | ||||
\(767\) | 5.12461 | − | 15.7719i | 0.185039 | − | 0.569492i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.0902 | − | 40.2874i | 0.472044 | − | 1.45280i | −0.377860 | − | 0.925863i | \(-0.623340\pi\) |
0.849904 | − | 0.526938i | \(-0.176660\pi\) | |||||||
\(770\) | −3.41641 | −0.123119 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.42705 | + | 4.39201i | 0.0513607 | + | 0.158072i | ||||
\(773\) | 2.35410 | + | 1.71036i | 0.0846712 | + | 0.0615172i | 0.629315 | − | 0.777150i | \(-0.283335\pi\) |
−0.544644 | + | 0.838667i | \(0.683335\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.2705 | − | 28.5317i | 1.41064 | − | 1.02489i | ||||
\(776\) | −7.14590 | −0.256523 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.57295 | + | 29.4625i | 0.343207 | + | 1.05628i | ||||
\(779\) | 11.3820 | + | 35.0301i | 0.407801 | + | 1.25508i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.93112 | + | 5.94336i | −0.0691008 | + | 0.212670i | ||||
\(782\) | 6.87539 | 0.245863 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.42705 | − | 1.76336i | 0.0866804 | − | 0.0629770i | ||||
\(785\) | −7.70163 | + | 23.7032i | −0.274883 | + | 0.846002i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.5623 | − | 21.4783i | 1.05378 | − | 0.765618i | 0.0808543 | − | 0.996726i | \(-0.474235\pi\) |
0.972928 | + | 0.231108i | \(0.0742351\pi\) | |||||||
\(788\) | 1.88197 | − | 1.36733i | 0.0670423 | − | 0.0487091i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.8541 | − | 10.0656i | 0.492595 | − | 0.357891i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.97871 | −0.141288 | ||||||||
\(794\) | −7.67376 | + | 23.6174i | −0.272332 | + | 0.838151i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.00000 | + | 15.3884i | 0.177220 | + | 0.545428i | ||||
\(797\) | −0.718847 | − | 2.21238i | −0.0254629 | − | 0.0783667i | 0.937518 | − | 0.347938i | \(-0.113118\pi\) |
−0.962980 | + | 0.269571i | \(0.913118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.5836 | 0.374421 | ||||||||
\(800\) | −4.04508 | − | 2.93893i | −0.143015 | − | 0.103907i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.0623 | − | 8.76378i | −0.425935 | − | 0.309460i | ||||
\(803\) | −2.32624 | − | 7.15942i | −0.0820912 | − | 0.252651i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.7082 | + | 15.7719i | −0.765114 | + | 0.555888i | ||||
\(806\) | −5.56231 | + | 17.1190i | −0.195924 | + | 0.602992i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.35410 | + | 16.4782i | −0.188357 | + | 0.579702i | ||||
\(809\) | −34.9615 | + | 25.4010i | −1.22918 | + | 0.893052i | −0.996829 | − | 0.0795797i | \(-0.974642\pi\) |
−0.232352 | + | 0.972632i | \(0.574642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.1803 | − | 13.9353i | −0.673513 | − | 0.489336i | 0.197686 | − | 0.980265i | \(-0.436657\pi\) |
−0.871199 | + | 0.490930i | \(0.836657\pi\) | |||||||
\(812\) | −5.85410 | + | 4.25325i | −0.205439 | + | 0.149260i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.47214 | + | 3.97574i | 0.191798 | + | 0.139350i | ||||
\(815\) | −7.96556 | − | 24.5155i | −0.279021 | − | 0.858739i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.23607 | + | 22.2703i | −0.253158 | + | 0.779140i | ||||
\(818\) | −25.9787 | −0.908324 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.20820 | + | 6.69015i | −0.321564 | + | 0.233630i | ||||
\(821\) | −2.72949 | − | 8.40051i | −0.0952599 | − | 0.293180i | 0.892061 | − | 0.451914i | \(-0.149259\pi\) |
−0.987321 | + | 0.158734i | \(0.949259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.7082 | − | 15.0454i | −0.721843 | − | 0.524449i | 0.165130 | − | 0.986272i | \(-0.447196\pi\) |
−0.886972 | + | 0.461822i | \(0.847196\pi\) | |||||||
\(824\) | −15.7082 | −0.547221 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.8885 | 0.622422 | ||||||||
\(827\) | 15.5623 | + | 11.3067i | 0.541154 | + | 0.393172i | 0.824514 | − | 0.565842i | \(-0.191449\pi\) |
−0.283359 | + | 0.959014i | \(0.591449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.1697 | + | 43.6098i | 0.492134 | + | 1.51463i | 0.821376 | + | 0.570387i | \(0.193207\pi\) |
−0.329242 | + | 0.944245i | \(0.606793\pi\) | |||||||
\(830\) | 4.14590 | + | 12.7598i | 0.143906 | + | 0.442898i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.85410 | 0.0642794 | ||||||||
\(833\) | 1.06231 | − | 3.26944i | 0.0368067 | − | 0.113279i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.47214 | + | 3.24920i | 0.154765 | + | 0.112443i | ||||
\(836\) | 4.47214 | + | 3.24920i | 0.154672 | + | 0.112376i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.70820 | + | 1.24108i | −0.0590089 | + | 0.0428725i | ||||
\(839\) | 28.4164 | + | 20.6457i | 0.981043 | + | 0.712770i | 0.957942 | − | 0.286963i | \(-0.0926458\pi\) |
0.0231018 | + | 0.999733i | \(0.492646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8713 | − | 9.35156i | 0.443839 | − | 0.322468i | ||||
\(842\) | 0.0278640 | − | 0.0857567i | 0.000960258 | − | 0.00295537i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.47214 | + | 7.60845i | −0.0850944 | + | 0.261894i | ||||
\(845\) | −17.2984 | − | 12.5680i | −0.595082 | − | 0.432352i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.43769 | − | 19.8132i | −0.221202 | − | 0.680789i | ||||
\(848\) | −9.35410 | − | 6.79615i | −0.321221 | − | 0.233381i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.72949 | −0.196520 | ||||||||
\(851\) | 53.1246 | 1.82109 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.1910 | − | 37.5200i | −0.417411 | − | 1.28466i | −0.910076 | − | 0.414441i | \(-0.863977\pi\) |
0.492665 | − | 0.870219i | \(-0.336023\pi\) | |||||||
\(854\) | −1.32624 | − | 4.08174i | −0.0453829 | − | 0.139674i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.14590 | − | 6.60440i | 0.0733453 | − | 0.225734i | ||||
\(857\) | 39.3050 | 1.34263 | 0.671316 | − | 0.741171i | \(-0.265729\pi\) | ||||
0.671316 | + | 0.741171i | \(0.265729\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0689 | + | 32.0179i | −1.50361 | + | 1.09244i | −0.534696 | + | 0.845045i | \(0.679574\pi\) |
−0.968915 | + | 0.247393i | \(0.920426\pi\) | |||||||
\(860\) | −7.23607 | −0.246748 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.85410 | + | 5.70634i | −0.267512 | + | 0.194359i | ||||
\(863\) | −8.23607 | + | 5.98385i | −0.280359 | + | 0.203693i | −0.719074 | − | 0.694934i | \(-0.755434\pi\) |
0.438715 | + | 0.898626i | \(0.355434\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.9615 | − | 29.0337i | 1.35873 | − | 0.987176i | ||||
\(866\) | 24.1525 | − | 17.5478i | 0.820735 | − | 0.596299i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −19.4164 | −0.659036 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.12461 | + | 6.53888i | 0.0719897 | + | 0.221562i | ||||
\(872\) | −5.42705 | − | 16.7027i | −0.183783 | − | 0.565626i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 43.4164 | 1.46858 | ||||||||
\(875\) | 18.0902 | − | 13.1433i | 0.611559 | − | 0.444324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.4443 | + | 17.0333i | 0.791657 | + | 0.575172i | 0.908455 | − | 0.417983i | \(-0.137263\pi\) |
−0.116798 | + | 0.993156i | \(0.537263\pi\) | |||||||
\(878\) | 4.67376 | + | 14.3844i | 0.157732 | + | 0.485449i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.527864 | + | 1.62460i | −0.0177943 | + | 0.0547652i | ||||
\(881\) | 13.2016 | − | 40.6304i | 0.444774 | − | 1.36887i | −0.437957 | − | 0.898996i | \(-0.644298\pi\) |
0.882731 | − | 0.469878i | \(-0.155702\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.12461 | − | 18.8496i | 0.206110 | − | 0.634340i | −0.793556 | − | 0.608497i | \(-0.791773\pi\) |
0.999666 | − | 0.0258434i | \(-0.00822713\pi\) | |||||||
\(884\) | 1.71885 | − | 1.24882i | 0.0578111 | − | 0.0420022i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.7082 | − | 16.4985i | −0.762897 | − | 0.554277i | ||||
\(887\) | 38.9787 | − | 28.3197i | 1.30878 | − | 0.950882i | 0.308777 | − | 0.951134i | \(-0.400080\pi\) |
1.00000 | 0.000252175i | \(8.02698e-5\pi\) | ||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.1803 | − | 16.1150i | −0.743905 | − | 0.540478i | ||||
\(890\) | 8.09017 | 0.271183 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.85410 | + | 14.9394i | −0.162527 | + | 0.500208i | ||||
\(893\) | 66.8328 | 2.23647 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −58.5410 | −1.95681 | ||||||||
\(896\) | 0.618034 | + | 1.90211i | 0.0206471 | + | 0.0635451i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.0172 | − | 11.6372i | −0.534502 | − | 0.388338i | ||||
\(899\) | −35.1246 | −1.17147 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.2492 | −0.441396 | ||||||||
\(902\) | 3.14590 | + | 2.28563i | 0.104747 | + | 0.0761031i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.64590 | − | 8.14324i | −0.0880013 | − | 0.270840i | ||||
\(905\) | 16.3435 | + | 11.8742i | 0.543275 | + | 0.394712i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.7082 | 1.11926 | 0.559631 | − | 0.828742i | \(-0.310943\pi\) | ||||
0.559631 | + | 0.828742i | \(0.310943\pi\) | |||||||
\(908\) | −0.291796 | + | 0.898056i | −0.00968359 | + | 0.0298030i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.56231 | + | 7.88597i | −0.0849396 | + | 0.261417i | ||||
\(911\) | −1.67376 | − | 1.21606i | −0.0554542 | − | 0.0402898i | 0.559713 | − | 0.828687i | \(-0.310911\pi\) |
−0.615167 | + | 0.788397i | \(0.710911\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.70820 | − | 2.69417i | 0.122724 | − | 0.0891639i | ||||
\(914\) | 2.85410 | + | 2.07363i | 0.0944053 | + | 0.0685895i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.50000 | + | 5.44907i | −0.247807 | + | 0.180042i | ||||
\(917\) | 3.23607 | − | 9.95959i | 0.106864 | − | 0.328895i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.85410 | + | 18.0171i | −0.193109 | + | 0.594328i | 0.806884 | + | 0.590709i | \(0.201152\pi\) |
−0.999993 | + | 0.00361909i | \(0.998848\pi\) | |||||||
\(920\) | 4.14590 | + | 12.7598i | 0.136686 | + | 0.420677i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.29837 | − | 13.2290i | −0.141559 | − | 0.435675i | ||||
\(923\) | 12.2705 | + | 8.91505i | 0.403889 | + | 0.293442i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.2705 | −1.45561 | ||||||||
\(926\) | −25.7082 | −0.844824 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.11803 | + | 3.44095i | 0.0367013 | + | 0.112955i | ||||
\(929\) | −4.93769 | − | 15.1967i | −0.162000 | − | 0.498586i | 0.836802 | − | 0.547505i | \(-0.184422\pi\) |
−0.998803 | + | 0.0489190i | \(0.984422\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.70820 | − | 20.6457i | 0.219853 | − | 0.676636i | ||||
\(932\) | 10.9098 | 0.357363 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.8885 | − | 22.4418i | 1.01070 | − | 0.734319i | ||||
\(935\) | 0.604878 | + | 1.86162i | 0.0197816 | + | 0.0608816i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.3435 | + | 14.0538i | −0.631923 | + | 0.459119i | −0.857066 | − | 0.515207i | \(-0.827715\pi\) |
0.225143 | + | 0.974326i | \(0.427715\pi\) | |||||||
\(938\) | −6.00000 | + | 4.35926i | −0.195907 | + | 0.142335i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.38197 | + | 19.6417i | 0.208157 | + | 0.640641i | ||||
\(941\) | 30.1976 | − | 21.9398i | 0.984412 | − | 0.715217i | 0.0257220 | − | 0.999669i | \(-0.491812\pi\) |
0.958690 | + | 0.284452i | \(0.0918115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.5410 | 0.994552 | ||||||||
\(944\) | 2.76393 | − | 8.50651i | 0.0899583 | − | 0.276863i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.763932 | + | 2.35114i | 0.0248376 | + | 0.0764422i | ||||
\(947\) | 2.14590 | + | 6.60440i | 0.0697323 | + | 0.214614i | 0.979850 | − | 0.199737i | \(-0.0640087\pi\) |
−0.910117 | + | 0.414351i | \(0.864009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.2705 | −0.593086 | ||||||||
\(950\) | −36.1803 | −1.17385 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.85410 | + | 1.34708i | 0.0600918 | + | 0.0436592i | ||||
\(953\) | −15.4098 | − | 47.4266i | −0.499173 | − | 1.53630i | −0.810350 | − | 0.585946i | \(-0.800723\pi\) |
0.311177 | − | 0.950352i | \(-0.399277\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.61803 | − | 11.1352i | −0.117077 | − | 0.360325i | ||||
\(956\) | 8.29180 | − | 25.5195i | 0.268176 | − | 0.825360i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.38197 | − | 4.25325i | 0.0446493 | − | 0.137416i | ||||
\(959\) | 22.7082 | − | 16.4985i | 0.733286 | − | 0.532764i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −51.1697 | − | 37.1770i | −1.65064 | − | 1.19926i | ||||
\(962\) | 13.2812 | − | 9.64932i | 0.428202 | − | 0.311107i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.78115 | + | 4.20025i | 0.186198 | + | 0.135281i | ||||
\(965\) | −3.19098 | + | 9.82084i | −0.102721 | + | 0.316144i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.12461 | − | 21.9273i | 0.229112 | − | 0.705134i | −0.768736 | − | 0.639566i | \(-0.779114\pi\) |
0.997848 | − | 0.0655682i | \(-0.0208860\pi\) | |||||||
\(968\) | −10.4164 | −0.334796 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.9271 | − | 9.39205i | −0.415063 | − | 0.301561i | ||||
\(971\) | −11.6738 | − | 35.9281i | −0.374629 | − | 1.15299i | −0.943729 | − | 0.330721i | \(-0.892708\pi\) |
0.569100 | − | 0.822268i | \(-0.307292\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.7082 | − | 15.7719i | −0.695933 | − | 0.505625i | ||||
\(974\) | 23.7082 | 0.759660 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.14590 | −0.0686885 | ||||||||
\(977\) | −0.354102 | − | 0.257270i | −0.0113287 | − | 0.00823080i | 0.582106 | − | 0.813113i | \(-0.302229\pi\) |
−0.593435 | + | 0.804882i | \(0.702229\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.854102 | − | 2.62866i | −0.0272972 | − | 0.0840122i | ||||
\(980\) | 6.70820 | 0.214286 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.88854 | 0.187911 | ||||||||
\(983\) | −7.58359 | + | 23.3399i | −0.241879 | + | 0.744427i | 0.754255 | + | 0.656582i | \(0.227998\pi\) |
−0.996134 | + | 0.0878456i | \(0.972002\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.20163 | 0.165738 | ||||||||
\(986\) | 3.35410 | + | 2.43690i | 0.106816 | + | 0.0776066i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.8541 | − | 7.88597i | 0.345315 | − | 0.250886i | ||||
\(989\) | 15.7082 | + | 11.4127i | 0.499492 | + | 0.362902i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.29180 | − | 3.84471i | 0.168099 | − | 0.122131i | −0.500555 | − | 0.865705i | \(-0.666871\pi\) |
0.668654 | + | 0.743573i | \(0.266871\pi\) | |||||||
\(992\) | −3.00000 | + | 9.23305i | −0.0952501 | + | 0.293150i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.05573 | + | 15.5599i | −0.160358 | + | 0.493531i | ||||
\(995\) | −11.1803 | + | 34.4095i | −0.354441 | + | 1.09086i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.85410 | + | 24.1724i | 0.248742 | + | 0.765549i | 0.994998 | + | 0.0998904i | \(0.0318492\pi\) |
−0.746257 | + | 0.665658i | \(0.768151\pi\) | |||||||
\(998\) | 5.32624 | + | 3.86974i | 0.168599 | + | 0.122494i | ||||
\(999\) | 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 | 450.2.h.b.91.1 | 4 | ||
3.2 | odd | 2 | 150.2.g.b.91.1 | yes | 4 | ||
15.2 | even | 4 | 750.2.h.a.49.1 | 8 | |||
15.8 | even | 4 | 750.2.h.a.49.2 | 8 | |||
15.14 | odd | 2 | 750.2.g.a.451.1 | 4 | |||
25.11 | even | 5 | inner | 450.2.h.b.361.1 | 4 | ||
75.2 | even | 20 | 750.2.h.a.199.2 | 8 | |||
75.8 | even | 20 | 3750.2.c.c.1249.4 | 4 | |||
75.11 | odd | 10 | 150.2.g.b.61.1 | ✓ | 4 | ||
75.14 | odd | 10 | 750.2.g.a.301.1 | 4 | |||
75.17 | even | 20 | 3750.2.c.c.1249.2 | 4 | |||
75.23 | even | 20 | 750.2.h.a.199.1 | 8 | |||
75.44 | odd | 10 | 3750.2.a.g.1.2 | 2 | |||
75.56 | odd | 10 | 3750.2.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.b.61.1 | ✓ | 4 | 75.11 | odd | 10 | ||
150.2.g.b.91.1 | yes | 4 | 3.2 | odd | 2 | ||
450.2.h.b.91.1 | 4 | 1.1 | even | 1 | trivial | ||
450.2.h.b.361.1 | 4 | 25.11 | even | 5 | inner | ||
750.2.g.a.301.1 | 4 | 75.14 | odd | 10 | |||
750.2.g.a.451.1 | 4 | 15.14 | odd | 2 | |||
750.2.h.a.49.1 | 8 | 15.2 | even | 4 | |||
750.2.h.a.49.2 | 8 | 15.8 | even | 4 | |||
750.2.h.a.199.1 | 8 | 75.23 | even | 20 | |||
750.2.h.a.199.2 | 8 | 75.2 | even | 20 | |||
3750.2.a.b.1.2 | 2 | 75.56 | odd | 10 | |||
3750.2.a.g.1.2 | 2 | 75.44 | odd | 10 | |||
3750.2.c.c.1249.2 | 4 | 75.17 | even | 20 | |||
3750.2.c.c.1249.4 | 4 | 75.8 | even | 20 |