Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(49,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.h (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(0.587785 + 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.199 |
Dual form | 750.2.h.a.49.2 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.587785 | + | 0.809017i | 0.415627 | + | 0.572061i | ||||
\(3\) | 0.951057 | + | 0.309017i | 0.549093 | + | 0.178411i | ||||
\(4\) | −0.309017 | + | 0.951057i | −0.154508 | + | 0.475528i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.309017 | + | 0.951057i | 0.126156 | + | 0.388267i | ||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | −0.951057 | + | 0.309017i | −0.336249 | + | 0.109254i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.618034 | − | 0.449028i | 0.186344 | − | 0.135387i | −0.490702 | − | 0.871327i | \(-0.663260\pi\) |
0.677046 | + | 0.735940i | \(0.263260\pi\) | |||||||
\(12\) | −0.587785 | + | 0.809017i | −0.169679 | + | 0.233543i | ||||
\(13\) | −1.08981 | + | 1.50000i | −0.302260 | + | 0.416025i | −0.932948 | − | 0.360011i | \(-0.882773\pi\) |
0.630688 | + | 0.776037i | \(0.282773\pi\) | |||||||
\(14\) | −1.61803 | + | 1.17557i | −0.432438 | + | 0.314184i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −1.08981 | + | 0.354102i | −0.264319 | + | 0.0858823i | −0.438178 | − | 0.898888i | \(-0.644376\pi\) |
0.173860 | + | 0.984770i | \(0.444376\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 2.23607 | + | 6.88191i | 0.512989 | + | 1.57882i | 0.786911 | + | 0.617066i | \(0.211679\pi\) |
−0.273922 | + | 0.961752i | \(0.588321\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.618034 | + | 1.90211i | −0.134866 | + | 0.415075i | ||||
\(22\) | 0.726543 | + | 0.236068i | 0.154899 | + | 0.0503299i | ||||
\(23\) | 3.52671 | + | 4.85410i | 0.735370 | + | 1.01215i | 0.998872 | + | 0.0474912i | \(0.0151226\pi\) |
−0.263501 | + | 0.964659i | \(0.584877\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.85410 | −0.363619 | ||||||||
\(27\) | 0.587785 | + | 0.809017i | 0.113119 | + | 0.155695i | ||||
\(28\) | −1.90211 | − | 0.618034i | −0.359466 | − | 0.116797i | ||||
\(29\) | 1.11803 | − | 3.44095i | 0.207614 | − | 0.638969i | −0.791982 | − | 0.610544i | \(-0.790951\pi\) |
0.999596 | − | 0.0284251i | \(-0.00904922\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | − | 9.23305i | −0.538816 | − | 1.65830i | −0.735256 | − | 0.677789i | \(-0.762938\pi\) |
0.196440 | − | 0.980516i | \(-0.437062\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0.726543 | − | 0.236068i | 0.126475 | − | 0.0410942i | ||||
\(34\) | −0.927051 | − | 0.673542i | −0.158988 | − | 0.115511i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.809017 | + | 0.587785i | −0.134836 | + | 0.0979642i | ||||
\(37\) | −5.20431 | + | 7.16312i | −0.855583 | + | 1.17761i | 0.127021 | + | 0.991900i | \(0.459458\pi\) |
−0.982605 | + | 0.185710i | \(0.940542\pi\) | |||||||
\(38\) | −4.25325 | + | 5.85410i | −0.689969 | + | 0.949661i | ||||
\(39\) | −1.50000 | + | 1.08981i | −0.240192 | + | 0.174510i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.11803 | − | 2.99193i | −0.643129 | − | 0.467260i | 0.217795 | − | 0.975995i | \(-0.430114\pi\) |
−0.860924 | + | 0.508734i | \(0.830114\pi\) | |||||||
\(42\) | −1.90211 | + | 0.618034i | −0.293502 | + | 0.0953647i | ||||
\(43\) | − | 3.23607i | − | 0.493496i | −0.969080 | − | 0.246748i | \(-0.920638\pi\) | ||
0.969080 | − | 0.246748i | \(-0.0793619\pi\) | |||||||
\(44\) | 0.236068 | + | 0.726543i | 0.0355886 | + | 0.109530i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.85410 | + | 5.70634i | −0.273372 | + | 0.841354i | ||||
\(47\) | 8.78402 | + | 2.85410i | 1.28128 | + | 0.416314i | 0.869031 | − | 0.494757i | \(-0.164743\pi\) |
0.412250 | + | 0.911071i | \(0.364743\pi\) | |||||||
\(48\) | −0.587785 | − | 0.809017i | −0.0848395 | − | 0.116772i | ||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.14590 | −0.160458 | ||||||||
\(52\) | −1.08981 | − | 1.50000i | −0.151130 | − | 0.208013i | ||||
\(53\) | 10.9964 | + | 3.57295i | 1.51047 | + | 0.490782i | 0.943052 | − | 0.332646i | \(-0.107941\pi\) |
0.567421 | + | 0.823428i | \(0.307941\pi\) | |||||||
\(54\) | −0.309017 | + | 0.951057i | −0.0420519 | + | 0.129422i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.618034 | − | 1.90211i | −0.0825883 | − | 0.254181i | ||||
\(57\) | 7.23607i | 0.958441i | ||||||||
\(58\) | 3.44095 | − | 1.11803i | 0.451820 | − | 0.146805i | ||||
\(59\) | −7.23607 | − | 5.25731i | −0.942056 | − | 0.684444i | 0.00685884 | − | 0.999976i | \(-0.497817\pi\) |
−0.948915 | + | 0.315533i | \(0.897817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.73607 | − | 1.26133i | 0.222281 | − | 0.161496i | −0.471072 | − | 0.882095i | \(-0.656133\pi\) |
0.693353 | + | 0.720598i | \(0.256133\pi\) | |||||||
\(62\) | 5.70634 | − | 7.85410i | 0.724706 | − | 0.997472i | ||||
\(63\) | −1.17557 | + | 1.61803i | −0.148108 | + | 0.203853i | ||||
\(64\) | 0.809017 | − | 0.587785i | 0.101127 | − | 0.0734732i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.618034 | + | 0.449028i | 0.0760747 | + | 0.0552715i | ||||
\(67\) | −3.52671 | + | 1.14590i | −0.430856 | + | 0.139994i | −0.516413 | − | 0.856340i | \(-0.672733\pi\) |
0.0855568 | + | 0.996333i | \(0.472733\pi\) | |||||||
\(68\) | − | 1.14590i | − | 0.138961i | ||||||
\(69\) | 1.85410 | + | 5.70634i | 0.223208 | + | 0.686963i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.52786 | − | 7.77997i | 0.300002 | − | 0.923312i | −0.681493 | − | 0.731825i | \(-0.738669\pi\) |
0.981495 | − | 0.191487i | \(-0.0613311\pi\) | |||||||
\(72\) | −0.951057 | − | 0.309017i | −0.112083 | − | 0.0364180i | ||||
\(73\) | −5.79210 | − | 7.97214i | −0.677914 | − | 0.933068i | 0.321993 | − | 0.946742i | \(-0.395647\pi\) |
−0.999907 | + | 0.0136741i | \(0.995647\pi\) | |||||||
\(74\) | −8.85410 | −1.02927 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.23607 | −0.830034 | ||||||||
\(77\) | 0.898056 | + | 1.23607i | 0.102343 | + | 0.140863i | ||||
\(78\) | −1.76336 | − | 0.572949i | −0.199661 | − | 0.0648737i | ||||
\(79\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | − | 5.09017i | − | 0.562115i | ||||||
\(83\) | 5.70634 | − | 1.85410i | 0.626352 | − | 0.203514i | 0.0213936 | − | 0.999771i | \(-0.493190\pi\) |
0.604959 | + | 0.796257i | \(0.293190\pi\) | |||||||
\(84\) | −1.61803 | − | 1.17557i | −0.176542 | − | 0.128265i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.61803 | − | 1.90211i | 0.282310 | − | 0.205110i | ||||
\(87\) | 2.12663 | − | 2.92705i | 0.227998 | − | 0.313813i | ||||
\(88\) | −0.449028 | + | 0.618034i | −0.0478665 | + | 0.0658826i | ||||
\(89\) | 2.92705 | − | 2.12663i | 0.310267 | − | 0.225422i | −0.421744 | − | 0.906715i | \(-0.638582\pi\) |
0.732011 | + | 0.681293i | \(0.238582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | − | 2.17963i | −0.314485 | − | 0.228487i | ||||
\(92\) | −5.70634 | + | 1.85410i | −0.594927 | + | 0.193303i | ||||
\(93\) | − | 9.70820i | − | 1.00669i | ||||||
\(94\) | 2.85410 | + | 8.78402i | 0.294378 | + | 0.906003i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.309017 | − | 0.951057i | 0.0315389 | − | 0.0970668i | ||||
\(97\) | −6.79615 | − | 2.20820i | −0.690045 | − | 0.224209i | −0.0570570 | − | 0.998371i | \(-0.518172\pi\) |
−0.632988 | + | 0.774162i | \(0.718172\pi\) | |||||||
\(98\) | 1.76336 | + | 2.42705i | 0.178126 | + | 0.245169i | ||||
\(99\) | 0.763932 | 0.0767781 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.3262 | 1.72403 | 0.862013 | − | 0.506887i | \(-0.169204\pi\) | ||||
0.862013 | + | 0.506887i | \(0.169204\pi\) | |||||||
\(102\) | −0.673542 | − | 0.927051i | −0.0666906 | − | 0.0917917i | ||||
\(103\) | 14.9394 | + | 4.85410i | 1.47202 | + | 0.478289i | 0.931718 | − | 0.363181i | \(-0.118309\pi\) |
0.540303 | + | 0.841470i | \(0.318309\pi\) | |||||||
\(104\) | 0.572949 | − | 1.76336i | 0.0561823 | − | 0.172911i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.57295 | + | 10.9964i | 0.347035 | + | 1.06807i | ||||
\(107\) | − | 6.94427i | − | 0.671328i | −0.941982 | − | 0.335664i | \(-0.891039\pi\) | ||
0.941982 | − | 0.335664i | \(-0.108961\pi\) | |||||||
\(108\) | −0.951057 | + | 0.309017i | −0.0915155 | + | 0.0297352i | ||||
\(109\) | −14.2082 | − | 10.3229i | −1.36090 | − | 0.988751i | −0.998387 | − | 0.0567720i | \(-0.981919\pi\) |
−0.362512 | − | 0.931979i | \(-0.618081\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.16312 | + | 5.20431i | −0.679893 | + | 0.493971i | ||||
\(112\) | 1.17557 | − | 1.61803i | 0.111081 | − | 0.152890i | ||||
\(113\) | −5.03280 | + | 6.92705i | −0.473446 | + | 0.651642i | −0.977229 | − | 0.212188i | \(-0.931941\pi\) |
0.503783 | + | 0.863830i | \(0.331941\pi\) | |||||||
\(114\) | −5.85410 | + | 4.25325i | −0.548287 | + | 0.398354i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.92705 | + | 2.12663i | 0.271770 | + | 0.197452i | ||||
\(117\) | −1.76336 | + | 0.572949i | −0.163022 | + | 0.0529692i | ||||
\(118\) | − | 8.94427i | − | 0.823387i | ||||||
\(119\) | −0.708204 | − | 2.17963i | −0.0649209 | − | 0.199806i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.21885 | + | 9.90659i | −0.292622 | + | 0.900599i | ||||
\(122\) | 2.04087 | + | 0.663119i | 0.184772 | + | 0.0600360i | ||||
\(123\) | −2.99193 | − | 4.11803i | −0.269773 | − | 0.371311i | ||||
\(124\) | 9.70820 | 0.871822 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | −8.05748 | − | 11.0902i | −0.714986 | − | 0.984093i | −0.999675 | − | 0.0254737i | \(-0.991891\pi\) |
0.284690 | − | 0.958620i | \(-0.408109\pi\) | |||||||
\(128\) | 0.951057 | + | 0.309017i | 0.0840623 | + | 0.0273135i | ||||
\(129\) | 1.00000 | − | 3.07768i | 0.0880451 | − | 0.270975i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.61803 | − | 4.97980i | −0.141368 | − | 0.435087i | 0.855158 | − | 0.518368i | \(-0.173460\pi\) |
−0.996526 | + | 0.0832809i | \(0.973460\pi\) | |||||||
\(132\) | 0.763932i | 0.0664917i | ||||||||
\(133\) | −13.7638 | + | 4.47214i | −1.19347 | + | 0.387783i | ||||
\(134\) | −3.00000 | − | 2.17963i | −0.259161 | − | 0.188291i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.927051 | − | 0.673542i | 0.0794940 | − | 0.0577557i | ||||
\(137\) | 8.24924 | − | 11.3541i | 0.704780 | − | 0.970046i | −0.295114 | − | 0.955462i | \(-0.595358\pi\) |
0.999894 | − | 0.0145842i | \(-0.00464248\pi\) | |||||||
\(138\) | −3.52671 | + | 4.85410i | −0.300214 | + | 0.413209i | ||||
\(139\) | 10.8541 | − | 7.88597i | 0.920633 | − | 0.668879i | −0.0230486 | − | 0.999734i | \(-0.507337\pi\) |
0.943681 | + | 0.330855i | \(0.107337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.47214 | + | 5.42882i | 0.629267 | + | 0.457190i | ||||
\(142\) | 7.77997 | − | 2.52786i | 0.652880 | − | 0.212134i | ||||
\(143\) | 1.41641i | 0.118446i | ||||||||
\(144\) | −0.309017 | − | 0.951057i | −0.0257514 | − | 0.0792547i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.04508 | − | 9.37181i | 0.252013 | − | 0.775616i | ||||
\(147\) | 2.85317 | + | 0.927051i | 0.235325 | + | 0.0764619i | ||||
\(148\) | −5.20431 | − | 7.16312i | −0.427792 | − | 0.588805i | ||||
\(149\) | 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 | \(0.353091\pi\) | |||||||
\(152\) | −4.25325 | − | 5.85410i | −0.344984 | − | 0.474830i | ||||
\(153\) | −1.08981 | − | 0.354102i | −0.0881062 | − | 0.0286274i | ||||
\(154\) | −0.472136 | + | 1.45309i | −0.0380458 | + | 0.117093i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.572949 | − | 1.76336i | −0.0458726 | − | 0.141181i | ||||
\(157\) | 11.1459i | 0.889540i | 0.895645 | + | 0.444770i | \(0.146714\pi\) | ||||
−0.895645 | + | 0.444770i | \(0.853286\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.35410 | + | 6.79615i | 0.741829 | + | 0.538970i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.70820 | + | 7.05342i | −0.765114 | + | 0.555888i | ||||
\(162\) | −0.587785 | + | 0.809017i | −0.0461808 | + | 0.0635624i | ||||
\(163\) | −6.77591 | + | 9.32624i | −0.530730 | + | 0.730487i | −0.987241 | − | 0.159230i | \(-0.949099\pi\) |
0.456511 | + | 0.889718i | \(0.349099\pi\) | |||||||
\(164\) | 4.11803 | − | 2.99193i | 0.321564 | − | 0.233630i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.85410 | + | 3.52671i | 0.376751 | + | 0.273726i | ||||
\(167\) | 2.35114 | − | 0.763932i | 0.181937 | − | 0.0591148i | −0.216632 | − | 0.976253i | \(-0.569507\pi\) |
0.398569 | + | 0.917139i | \(0.369507\pi\) | |||||||
\(168\) | − | 2.00000i | − | 0.154303i | ||||||
\(169\) | 2.95492 | + | 9.09429i | 0.227301 | + | 0.699561i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.23607 | + | 6.88191i | −0.170996 | + | 0.526273i | ||||
\(172\) | 3.07768 | + | 1.00000i | 0.234671 | + | 0.0762493i | ||||
\(173\) | −12.9843 | − | 17.8713i | −0.987176 | − | 1.35873i | −0.932872 | − | 0.360207i | \(-0.882706\pi\) |
−0.0543039 | − | 0.998524i | \(-0.517294\pi\) | |||||||
\(174\) | 3.61803 | 0.274282 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.763932 | −0.0575835 | ||||||||
\(177\) | −5.25731 | − | 7.23607i | −0.395164 | − | 0.543896i | ||||
\(178\) | 3.44095 | + | 1.11803i | 0.257910 | + | 0.0838002i | ||||
\(179\) | 8.09017 | − | 24.8990i | 0.604688 | − | 1.86104i | 0.105764 | − | 0.994391i | \(-0.466271\pi\) |
0.498923 | − | 0.866646i | \(-0.333729\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.79180 | + | 8.59226i | 0.207513 | + | 0.638658i | 0.999601 | + | 0.0282515i | \(0.00899392\pi\) |
−0.792088 | + | 0.610407i | \(0.791006\pi\) | |||||||
\(182\) | − | 3.70820i | − | 0.274870i | ||||||
\(183\) | 2.04087 | − | 0.663119i | 0.150865 | − | 0.0490192i | ||||
\(184\) | −4.85410 | − | 3.52671i | −0.357849 | − | 0.259993i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.85410 | − | 5.70634i | 0.575891 | − | 0.418409i | ||||
\(187\) | −0.514540 | + | 0.708204i | −0.0376269 | + | 0.0517890i | ||||
\(188\) | −5.42882 | + | 7.47214i | −0.395938 | + | 0.544962i | ||||
\(189\) | −1.61803 | + | 1.17557i | −0.117695 | + | 0.0855102i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.23607 | + | 3.07768i | 0.306511 | + | 0.222693i | 0.730398 | − | 0.683022i | \(-0.239335\pi\) |
−0.423887 | + | 0.905715i | \(0.639335\pi\) | |||||||
\(192\) | 0.951057 | − | 0.309017i | 0.0686366 | − | 0.0223014i | ||||
\(193\) | − | 4.61803i | − | 0.332413i | −0.986091 | − | 0.166207i | \(-0.946848\pi\) | ||
0.986091 | − | 0.166207i | \(-0.0531519\pi\) | |||||||
\(194\) | −2.20820 | − | 6.79615i | −0.158540 | − | 0.487935i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.927051 | + | 2.85317i | −0.0662179 | + | 0.203798i | ||||
\(197\) | 2.21238 | + | 0.718847i | 0.157626 | + | 0.0512157i | 0.386767 | − | 0.922177i | \(-0.373592\pi\) |
−0.229141 | + | 0.973393i | \(0.573592\pi\) | |||||||
\(198\) | 0.449028 | + | 0.618034i | 0.0319110 | + | 0.0439218i | ||||
\(199\) | −16.1803 | −1.14699 | −0.573497 | − | 0.819208i | \(-0.694414\pi\) | ||||
−0.573497 | + | 0.819208i | \(0.694414\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.70820 | −0.261557 | ||||||||
\(202\) | 10.1841 | + | 14.0172i | 0.716551 | + | 0.986248i | ||||
\(203\) | 6.88191 | + | 2.23607i | 0.483015 | + | 0.156941i | ||||
\(204\) | 0.354102 | − | 1.08981i | 0.0247921 | − | 0.0763022i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.85410 | + | 14.9394i | 0.338201 | + | 1.04088i | ||||
\(207\) | 6.00000i | 0.417029i | ||||||||
\(208\) | 1.76336 | − | 0.572949i | 0.122267 | − | 0.0397269i | ||||
\(209\) | 4.47214 | + | 3.24920i | 0.309344 | + | 0.224752i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.47214 | − | 4.70228i | 0.445560 | − | 0.323718i | −0.342280 | − | 0.939598i | \(-0.611199\pi\) |
0.787840 | + | 0.615880i | \(0.211199\pi\) | |||||||
\(212\) | −6.79615 | + | 9.35410i | −0.466762 | + | 0.642442i | ||||
\(213\) | 4.80828 | − | 6.61803i | 0.329458 | − | 0.453460i | ||||
\(214\) | 5.61803 | − | 4.08174i | 0.384041 | − | 0.279022i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.809017 | − | 0.587785i | −0.0550466 | − | 0.0399937i | ||||
\(217\) | 18.4661 | − | 6.00000i | 1.25356 | − | 0.407307i | ||||
\(218\) | − | 17.5623i | − | 1.18947i | ||||||
\(219\) | −3.04508 | − | 9.37181i | −0.205768 | − | 0.633288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.656541 | − | 2.02063i | 0.0441637 | − | 0.135922i | ||||
\(222\) | −8.42075 | − | 2.73607i | −0.565164 | − | 0.183633i | ||||
\(223\) | −9.23305 | − | 12.7082i | −0.618291 | − | 0.851004i | 0.378936 | − | 0.925423i | \(-0.376290\pi\) |
−0.997227 | + | 0.0744185i | \(0.976290\pi\) | |||||||
\(224\) | 2.00000 | 0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.56231 | −0.569556 | ||||||||
\(227\) | −0.555029 | − | 0.763932i | −0.0368386 | − | 0.0507039i | 0.790200 | − | 0.612849i | \(-0.209976\pi\) |
−0.827039 | + | 0.562145i | \(0.809976\pi\) | |||||||
\(228\) | −6.88191 | − | 2.23607i | −0.455766 | − | 0.148087i | ||||
\(229\) | −2.86475 | + | 8.81678i | −0.189308 | + | 0.582629i | −0.999996 | − | 0.00284891i | \(-0.999093\pi\) |
0.810688 | + | 0.585478i | \(0.199093\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.472136 | + | 1.45309i | 0.0310643 | + | 0.0956060i | ||||
\(232\) | 3.61803i | 0.237536i | ||||||||
\(233\) | −10.3759 | + | 3.37132i | −0.679746 | + | 0.220863i | −0.628484 | − | 0.777823i | \(-0.716324\pi\) |
−0.0512616 | + | 0.998685i | \(0.516324\pi\) | |||||||
\(234\) | −1.50000 | − | 1.08981i | −0.0980581 | − | 0.0712434i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.23607 | − | 5.25731i | 0.471028 | − | 0.342222i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.34708 | − | 1.85410i | 0.0873185 | − | 0.120184i | ||||
\(239\) | −21.7082 | + | 15.7719i | −1.40419 | + | 1.02020i | −0.410051 | + | 0.912063i | \(0.634489\pi\) |
−0.994136 | + | 0.108139i | \(0.965511\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.78115 | + | 4.20025i | 0.372397 | + | 0.270562i | 0.758204 | − | 0.652017i | \(-0.226077\pi\) |
−0.385807 | + | 0.922579i | \(0.626077\pi\) | |||||||
\(242\) | −9.90659 | + | 3.21885i | −0.636820 | + | 0.206915i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0.663119 | + | 2.04087i | 0.0424518 | + | 0.130653i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.57295 | − | 4.84104i | 0.100288 | − | 0.308653i | ||||
\(247\) | −12.7598 | − | 4.14590i | −0.811884 | − | 0.263797i | ||||
\(248\) | 5.70634 | + | 7.85410i | 0.362353 | + | 0.498736i | ||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.52786 | −0.222677 | −0.111338 | − | 0.993783i | \(-0.535514\pi\) | ||||
−0.111338 | + | 0.993783i | \(0.535514\pi\) | |||||||
\(252\) | −1.17557 | − | 1.61803i | −0.0740540 | − | 0.101927i | ||||
\(253\) | 4.35926 | + | 1.41641i | 0.274064 | + | 0.0890488i | ||||
\(254\) | 4.23607 | − | 13.0373i | 0.265795 | − | 0.818031i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | − | 9.38197i | − | 0.585231i | −0.956230 | − | 0.292615i | \(-0.905474\pi\) | ||
0.956230 | − | 0.292615i | \(-0.0945256\pi\) | |||||||
\(258\) | 3.07768 | − | 1.00000i | 0.191608 | − | 0.0622573i | ||||
\(259\) | −14.3262 | − | 10.4086i | −0.890189 | − | 0.646760i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.92705 | − | 2.12663i | 0.181180 | − | 0.131635i | ||||
\(262\) | 3.07768 | − | 4.23607i | 0.190140 | − | 0.261705i | ||||
\(263\) | 4.97980 | − | 6.85410i | 0.307067 | − | 0.422642i | −0.627396 | − | 0.778700i | \(-0.715879\pi\) |
0.934464 | + | 0.356058i | \(0.115879\pi\) | |||||||
\(264\) | −0.618034 | + | 0.449028i | −0.0380374 | + | 0.0276358i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −11.7082 | − | 8.50651i | −0.717876 | − | 0.521567i | ||||
\(267\) | 3.44095 | − | 1.11803i | 0.210583 | − | 0.0684226i | ||||
\(268\) | − | 3.70820i | − | 0.226515i | ||||||
\(269\) | 4.04508 | + | 12.4495i | 0.246633 | + | 0.759059i | 0.995364 | + | 0.0961842i | \(0.0306638\pi\) |
−0.748730 | + | 0.662875i | \(0.769336\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.79837 | − | 5.53483i | 0.109243 | − | 0.336217i | −0.881460 | − | 0.472260i | \(-0.843438\pi\) |
0.990703 | + | 0.136043i | \(0.0434385\pi\) | |||||||
\(272\) | 1.08981 | + | 0.354102i | 0.0660797 | + | 0.0214706i | ||||
\(273\) | −2.17963 | − | 3.00000i | −0.131917 | − | 0.181568i | ||||
\(274\) | 14.0344 | 0.847852 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | 16.9600 | + | 23.3435i | 1.01903 | + | 1.40257i | 0.912883 | + | 0.408222i | \(0.133851\pi\) |
0.106146 | + | 0.994351i | \(0.466149\pi\) | |||||||
\(278\) | 12.7598 | + | 4.14590i | 0.765280 | + | 0.248654i | ||||
\(279\) | 3.00000 | − | 9.23305i | 0.179605 | − | 0.552768i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.57295 | + | 4.84104i | 0.0938343 | + | 0.288792i | 0.986948 | − | 0.161038i | \(-0.0514843\pi\) |
−0.893114 | + | 0.449831i | \(0.851484\pi\) | |||||||
\(282\) | 9.23607i | 0.550000i | ||||||||
\(283\) | −1.17557 | + | 0.381966i | −0.0698804 | + | 0.0227055i | −0.343749 | − | 0.939062i | \(-0.611697\pi\) |
0.273868 | + | 0.961767i | \(0.411697\pi\) | |||||||
\(284\) | 6.61803 | + | 4.80828i | 0.392708 | + | 0.285319i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.14590 | + | 0.832544i | −0.0677584 | + | 0.0492293i | ||||
\(287\) | 5.98385 | − | 8.23607i | 0.353216 | − | 0.486160i | ||||
\(288\) | 0.587785 | − | 0.809017i | 0.0346356 | − | 0.0476718i | ||||
\(289\) | −12.6910 | + | 9.22054i | −0.746528 | + | 0.542385i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.78115 | − | 4.20025i | −0.338897 | − | 0.246223i | ||||
\(292\) | 9.37181 | − | 3.04508i | 0.548444 | − | 0.178200i | ||||
\(293\) | 4.20163i | 0.245462i | 0.992440 | + | 0.122731i | \(0.0391652\pi\) | ||||
−0.992440 | + | 0.122731i | \(0.960835\pi\) | |||||||
\(294\) | 0.927051 | + | 2.85317i | 0.0540667 | + | 0.166400i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.73607 | − | 8.42075i | 0.159031 | − | 0.489446i | ||||
\(297\) | 0.726543 | + | 0.236068i | 0.0421583 | + | 0.0136981i | ||||
\(298\) | 12.9515 | + | 17.8262i | 0.750261 | + | 1.03265i | ||||
\(299\) | −11.1246 | −0.643353 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.47214 | 0.373048 | ||||||||
\(302\) | 6.43288 | + | 8.85410i | 0.370171 | + | 0.509496i | ||||
\(303\) | 16.4782 | + | 5.35410i | 0.946650 | + | 0.307585i | ||||
\(304\) | 2.23607 | − | 6.88191i | 0.128247 | − | 0.394705i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.354102 | − | 1.08981i | −0.0202427 | − | 0.0623005i | ||||
\(307\) | − | 29.7082i | − | 1.69554i | −0.530367 | − | 0.847768i | \(-0.677946\pi\) | ||
0.530367 | − | 0.847768i | \(-0.322054\pi\) | |||||||
\(308\) | −1.45309 | + | 0.472136i | −0.0827972 | + | 0.0269024i | ||||
\(309\) | 12.7082 | + | 9.23305i | 0.722944 | + | 0.525250i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.2361 | + | 7.43694i | −0.580434 | + | 0.421710i | −0.838881 | − | 0.544315i | \(-0.816789\pi\) |
0.258446 | + | 0.966026i | \(0.416789\pi\) | |||||||
\(312\) | 1.08981 | − | 1.50000i | 0.0616986 | − | 0.0849208i | ||||
\(313\) | −10.7921 | + | 14.8541i | −0.610008 | + | 0.839603i | −0.996578 | − | 0.0826564i | \(-0.973660\pi\) |
0.386570 | + | 0.922260i | \(0.373660\pi\) | |||||||
\(314\) | −9.01722 | + | 6.55139i | −0.508871 | + | 0.369717i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.4086 | + | 3.38197i | −0.584606 | + | 0.189950i | −0.586363 | − | 0.810048i | \(-0.699441\pi\) |
0.00175672 | + | 0.999998i | \(0.499441\pi\) | |||||||
\(318\) | 11.5623i | 0.648382i | ||||||||
\(319\) | −0.854102 | − | 2.62866i | −0.0478205 | − | 0.147176i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.14590 | − | 6.60440i | 0.119772 | − | 0.368621i | ||||
\(322\) | −11.4127 | − | 3.70820i | −0.636004 | − | 0.206650i | ||||
\(323\) | −4.87380 | − | 6.70820i | −0.271185 | − | 0.373254i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.5279 | −0.638469 | ||||||||
\(327\) | −10.3229 | − | 14.2082i | −0.570856 | − | 0.785715i | ||||
\(328\) | 4.84104 | + | 1.57295i | 0.267302 | + | 0.0868516i | ||||
\(329\) | −5.70820 | + | 17.5680i | −0.314703 | + | 0.968558i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.27051 | − | 22.3763i | −0.399623 | − | 1.22991i | −0.925302 | − | 0.379231i | \(-0.876189\pi\) |
0.525679 | − | 0.850683i | \(-0.323811\pi\) | |||||||
\(332\) | 6.00000i | 0.329293i | ||||||||
\(333\) | −8.42075 | + | 2.73607i | −0.461454 | + | 0.149936i | ||||
\(334\) | 2.00000 | + | 1.45309i | 0.109435 | + | 0.0795093i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.61803 | − | 1.17557i | 0.0882710 | − | 0.0641326i | ||||
\(337\) | −14.5964 | + | 20.0902i | −0.795115 | + | 1.09438i | 0.198338 | + | 0.980134i | \(0.436446\pi\) |
−0.993452 | + | 0.114248i | \(0.963554\pi\) | |||||||
\(338\) | −5.62058 | + | 7.73607i | −0.305719 | + | 0.420787i | ||||
\(339\) | −6.92705 | + | 5.03280i | −0.376226 | + | 0.273344i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | − | 4.35926i | −0.324918 | − | 0.236067i | ||||
\(342\) | −6.88191 | + | 2.23607i | −0.372131 | + | 0.120913i | ||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 1.00000 | + | 3.07768i | 0.0539164 | + | 0.165938i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.82624 | − | 21.0090i | 0.366981 | − | 1.12945i | ||||
\(347\) | −0.726543 | − | 0.236068i | −0.0390028 | − | 0.0126728i | 0.289451 | − | 0.957193i | \(-0.406527\pi\) |
−0.328453 | + | 0.944520i | \(0.606527\pi\) | |||||||
\(348\) | 2.12663 | + | 2.92705i | 0.113999 | + | 0.156906i | ||||
\(349\) | 9.79837 | 0.524495 | 0.262247 | − | 0.965001i | \(-0.415536\pi\) | ||||
0.262247 | + | 0.965001i | \(0.415536\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.85410 | −0.0989646 | ||||||||
\(352\) | −0.449028 | − | 0.618034i | −0.0239333 | − | 0.0329413i | ||||
\(353\) | −10.9637 | − | 3.56231i | −0.583536 | − | 0.189602i | 0.00234791 | − | 0.999997i | \(-0.499253\pi\) |
−0.585884 | + | 0.810395i | \(0.699253\pi\) | |||||||
\(354\) | 2.76393 | − | 8.50651i | 0.146901 | − | 0.452116i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.11803 | + | 3.44095i | 0.0592557 | + | 0.182370i | ||||
\(357\) | − | 2.29180i | − | 0.121295i | ||||||
\(358\) | 24.8990 | − | 8.09017i | 1.31595 | − | 0.427579i | ||||
\(359\) | 6.38197 | + | 4.63677i | 0.336827 | + | 0.244719i | 0.743322 | − | 0.668934i | \(-0.233249\pi\) |
−0.406495 | + | 0.913653i | \(0.633249\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −26.9894 | + | 19.6089i | −1.42049 | + | 1.03205i | ||||
\(362\) | −5.31031 | + | 7.30902i | −0.279104 | + | 0.384153i | ||||
\(363\) | −6.12261 | + | 8.42705i | −0.321354 | + | 0.442305i | ||||
\(364\) | 3.00000 | − | 2.17963i | 0.157243 | − | 0.114244i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.73607 | + | 1.26133i | 0.0907457 | + | 0.0659306i | ||||
\(367\) | 3.35520 | − | 1.09017i | 0.175140 | − | 0.0569064i | −0.220134 | − | 0.975470i | \(-0.570650\pi\) |
0.395274 | + | 0.918563i | \(0.370650\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | −1.57295 | − | 4.84104i | −0.0818845 | − | 0.252014i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.14590 | + | 21.9928i | −0.370997 | + | 1.14181i | ||||
\(372\) | 9.23305 | + | 3.00000i | 0.478711 | + | 0.155543i | ||||
\(373\) | 17.2905 | + | 23.7984i | 0.895270 | + | 1.23223i | 0.971952 | + | 0.235178i | \(0.0755672\pi\) |
−0.0766827 | + | 0.997056i | \(0.524433\pi\) | |||||||
\(374\) | −0.875388 | −0.0452652 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.23607 | −0.476314 | ||||||||
\(377\) | 3.94298 | + | 5.42705i | 0.203074 | + | 0.279507i | ||||
\(378\) | −1.90211 | − | 0.618034i | −0.0978341 | − | 0.0317882i | ||||
\(379\) | −7.23607 | + | 22.2703i | −0.371692 | + | 1.14395i | 0.573992 | + | 0.818861i | \(0.305394\pi\) |
−0.945684 | + | 0.325089i | \(0.894606\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.23607 | − | 13.0373i | −0.217020 | − | 0.667920i | ||||
\(382\) | 5.23607i | 0.267901i | ||||||||
\(383\) | 10.9637 | − | 3.56231i | 0.560216 | − | 0.182025i | −0.0152022 | − | 0.999884i | \(-0.504839\pi\) |
0.575419 | + | 0.817859i | \(0.304839\pi\) | |||||||
\(384\) | 0.809017 | + | 0.587785i | 0.0412850 | + | 0.0299953i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.73607 | − | 2.71441i | 0.190161 | − | 0.138160i | ||||
\(387\) | 1.90211 | − | 2.61803i | 0.0966898 | − | 0.133082i | ||||
\(388\) | 4.20025 | − | 5.78115i | 0.213236 | − | 0.293494i | ||||
\(389\) | −25.0623 | + | 18.2088i | −1.27071 | + | 0.923224i | −0.999231 | − | 0.0392200i | \(-0.987513\pi\) |
−0.271479 | + | 0.962444i | \(0.587513\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.56231 | − | 4.04125i | −0.281298 | − | 0.204375i | ||||
\(392\) | −2.85317 | + | 0.927051i | −0.144107 | + | 0.0468231i | ||||
\(393\) | − | 5.23607i | − | 0.264125i | ||||||
\(394\) | 0.718847 | + | 2.21238i | 0.0362150 | + | 0.111458i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.236068 | + | 0.726543i | −0.0118629 | + | 0.0365101i | ||||
\(397\) | −23.6174 | − | 7.67376i | −1.18532 | − | 0.385135i | −0.350982 | − | 0.936382i | \(-0.614152\pi\) |
−0.834342 | + | 0.551247i | \(0.814152\pi\) | |||||||
\(398\) | −9.51057 | − | 13.0902i | −0.476722 | − | 0.656151i | ||||
\(399\) | −14.4721 | −0.724513 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.9098 | −0.744561 | −0.372281 | − | 0.928120i | \(-0.621424\pi\) | ||||
−0.372281 | + | 0.928120i | \(0.621424\pi\) | |||||||
\(402\) | −2.17963 | − | 3.00000i | −0.108710 | − | 0.149626i | ||||
\(403\) | 17.1190 | + | 5.56231i | 0.852759 | + | 0.277078i | ||||
\(404\) | −5.35410 | + | 16.4782i | −0.266377 | + | 0.819823i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.23607 | + | 6.88191i | 0.110974 | + | 0.341543i | ||||
\(407\) | 6.76393i | 0.335276i | ||||||||
\(408\) | 1.08981 | − | 0.354102i | 0.0539538 | − | 0.0175307i | ||||
\(409\) | −21.0172 | − | 15.2699i | −1.03923 | − | 0.755048i | −0.0690987 | − | 0.997610i | \(-0.522012\pi\) |
−0.970136 | + | 0.242562i | \(0.922012\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.3541 | − | 8.24924i | 0.560057 | − | 0.406905i | ||||
\(412\) | −9.23305 | + | 12.7082i | −0.454880 | + | 0.626088i | ||||
\(413\) | 10.5146 | − | 14.4721i | 0.517391 | − | 0.712127i | ||||
\(414\) | −4.85410 | + | 3.52671i | −0.238566 | + | 0.173328i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.50000 | + | 1.08981i | 0.0735436 | + | 0.0534325i | ||||
\(417\) | 12.7598 | − | 4.14590i | 0.624848 | − | 0.203026i | ||||
\(418\) | 5.52786i | 0.270377i | ||||||||
\(419\) | 0.652476 | + | 2.00811i | 0.0318755 | + | 0.0981028i | 0.965729 | − | 0.259554i | \(-0.0835757\pi\) |
−0.933853 | + | 0.357657i | \(0.883576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.0278640 | − | 0.0857567i | 0.00135801 | − | 0.00417953i | −0.950375 | − | 0.311106i | \(-0.899301\pi\) |
0.951733 | + | 0.306926i | \(0.0993006\pi\) | |||||||
\(422\) | 7.60845 | + | 2.47214i | 0.370374 | + | 0.120342i | ||||
\(423\) | 5.42882 | + | 7.47214i | 0.263958 | + | 0.363308i | ||||
\(424\) | −11.5623 | −0.561515 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.18034 | 0.396339 | ||||||||
\(427\) | 2.52265 | + | 3.47214i | 0.122080 | + | 0.168028i | ||||
\(428\) | 6.60440 | + | 2.14590i | 0.319235 | + | 0.103726i | ||||
\(429\) | −0.437694 | + | 1.34708i | −0.0211321 | + | 0.0650378i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | − | 9.23305i | −0.144505 | − | 0.444740i | 0.852442 | − | 0.522822i | \(-0.175121\pi\) |
−0.996947 | + | 0.0780813i | \(0.975121\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | −28.3929 | + | 9.22542i | −1.36448 | + | 0.443346i | −0.897535 | − | 0.440942i | \(-0.854644\pi\) |
−0.466942 | + | 0.884288i | \(0.654644\pi\) | |||||||
\(434\) | 15.7082 | + | 11.4127i | 0.754018 | + | 0.547826i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.2082 | − | 10.3229i | 0.680450 | − | 0.494376i | ||||
\(437\) | −25.5195 | + | 35.1246i | −1.22076 | + | 1.68024i | ||||
\(438\) | 5.79210 | − | 7.97214i | 0.276757 | − | 0.380923i | ||||
\(439\) | 12.2361 | − | 8.89002i | 0.583996 | − | 0.424298i | −0.256167 | − | 0.966633i | \(-0.582460\pi\) |
0.840162 | + | 0.542335i | \(0.182460\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.42705 | + | 1.76336i | 0.115574 | + | 0.0839693i | ||||
\(442\) | 2.02063 | − | 0.656541i | 0.0961114 | − | 0.0312285i | ||||
\(443\) | 28.0689i | 1.33359i | 0.745240 | + | 0.666796i | \(0.232335\pi\) | ||||
−0.745240 | + | 0.666796i | \(0.767665\pi\) | |||||||
\(444\) | −2.73607 | − | 8.42075i | −0.129848 | − | 0.399631i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.85410 | − | 14.9394i | 0.229848 | − | 0.707401i | ||||
\(447\) | 20.9560 | + | 6.80902i | 0.991185 | + | 0.322055i | ||||
\(448\) | 1.17557 | + | 1.61803i | 0.0555405 | + | 0.0764449i | ||||
\(449\) | 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 | ||||||||
\(452\) | −5.03280 | − | 6.92705i | −0.236723 | − | 0.325821i | ||||
\(453\) | 10.4086 | + | 3.38197i | 0.489040 | + | 0.158899i | ||||
\(454\) | 0.291796 | − | 0.898056i | 0.0136947 | − | 0.0421479i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.23607 | − | 6.88191i | −0.104713 | − | 0.322275i | ||||
\(457\) | − | 3.52786i | − | 0.165027i | −0.996590 | − | 0.0825133i | \(-0.973705\pi\) | ||
0.996590 | − | 0.0825133i | \(-0.0262947\pi\) | |||||||
\(458\) | −8.81678 | + | 2.86475i | −0.411981 | + | 0.133861i | ||||
\(459\) | −0.927051 | − | 0.673542i | −0.0432710 | − | 0.0314382i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.2533 | + | 8.17599i | −0.524118 | + | 0.380794i | −0.818153 | − | 0.575001i | \(-0.805002\pi\) |
0.294035 | + | 0.955795i | \(0.405002\pi\) | |||||||
\(462\) | −0.898056 | + | 1.23607i | −0.0417813 | + | 0.0575071i | ||||
\(463\) | 15.1109 | − | 20.7984i | 0.702263 | − | 0.966582i | −0.297666 | − | 0.954670i | \(-0.596208\pi\) |
0.999929 | − | 0.0119123i | \(-0.00379188\pi\) | |||||||
\(464\) | −2.92705 | + | 2.12663i | −0.135885 | + | 0.0987262i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.82624 | − | 6.41264i | −0.408868 | − | 0.297060i | ||||
\(467\) | −36.3117 | + | 11.7984i | −1.68030 | + | 0.545964i | −0.984970 | − | 0.172724i | \(-0.944743\pi\) |
−0.695333 | + | 0.718688i | \(0.744743\pi\) | |||||||
\(468\) | − | 1.85410i | − | 0.0857059i | ||||||
\(469\) | −2.29180 | − | 7.05342i | −0.105825 | − | 0.325697i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.44427 | + | 10.6004i | −0.158704 | + | 0.488440i | ||||
\(472\) | 8.50651 | + | 2.76393i | 0.391544 | + | 0.127220i | ||||
\(473\) | −1.45309 | − | 2.00000i | −0.0668129 | − | 0.0919601i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.29180 | 0.105044 | ||||||||
\(477\) | 6.79615 | + | 9.35410i | 0.311174 | + | 0.428295i | ||||
\(478\) | −25.5195 | − | 8.29180i | −1.16724 | − | 0.379258i | ||||
\(479\) | 1.38197 | − | 4.25325i | 0.0631436 | − | 0.194336i | −0.914508 | − | 0.404568i | \(-0.867422\pi\) |
0.977652 | + | 0.210232i | \(0.0674219\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.07295 | − | 15.6129i | −0.231307 | − | 0.711888i | ||||
\(482\) | 7.14590i | 0.325487i | ||||||||
\(483\) | −11.4127 | + | 3.70820i | −0.519295 | + | 0.168729i | ||||
\(484\) | −8.42705 | − | 6.12261i | −0.383048 | − | 0.278300i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.809017 | + | 0.587785i | −0.0366978 | + | 0.0266625i | ||||
\(487\) | 13.9353 | − | 19.1803i | 0.631470 | − | 0.869144i | −0.366655 | − | 0.930357i | \(-0.619497\pi\) |
0.998125 | + | 0.0612130i | \(0.0194969\pi\) | |||||||
\(488\) | −1.26133 | + | 1.73607i | −0.0570976 | + | 0.0785881i | ||||
\(489\) | −9.32624 | + | 6.77591i | −0.421747 | + | 0.306417i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.76393 | + | 3.46120i | 0.214993 | + | 0.156202i | 0.690070 | − | 0.723743i | \(-0.257580\pi\) |
−0.475077 | + | 0.879944i | \(0.657580\pi\) | |||||||
\(492\) | 4.84104 | − | 1.57295i | 0.218251 | − | 0.0709140i | ||||
\(493\) | 4.14590i | 0.186722i | ||||||||
\(494\) | −4.14590 | − | 12.7598i | −0.186533 | − | 0.574089i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | + | 9.23305i | −0.134704 | + | 0.414576i | ||||
\(497\) | 15.5599 | + | 5.05573i | 0.697958 | + | 0.226780i | ||||
\(498\) | 3.52671 | + | 4.85410i | 0.158036 | + | 0.217518i | ||||
\(499\) | 6.58359 | 0.294722 | 0.147361 | − | 0.989083i | \(-0.452922\pi\) | ||||
0.147361 | + | 0.989083i | \(0.452922\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.47214 | 0.110447 | ||||||||
\(502\) | −2.07363 | − | 2.85410i | −0.0925505 | − | 0.127385i | ||||
\(503\) | −28.9807 | − | 9.41641i | −1.29219 | − | 0.419857i | −0.419330 | − | 0.907834i | \(-0.637735\pi\) |
−0.872857 | + | 0.487977i | \(0.837735\pi\) | |||||||
\(504\) | 0.618034 | − | 1.90211i | 0.0275294 | − | 0.0847268i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.41641 | + | 4.35926i | 0.0629670 | + | 0.193793i | ||||
\(507\) | 9.56231i | 0.424677i | ||||||||
\(508\) | 13.0373 | − | 4.23607i | 0.578436 | − | 0.187945i | ||||
\(509\) | 23.2533 | + | 16.8945i | 1.03068 | + | 0.748836i | 0.968445 | − | 0.249226i | \(-0.0801761\pi\) |
0.0622385 | + | 0.998061i | \(0.480176\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.9443 | − | 11.5842i | 0.705333 | − | 0.512454i | ||||
\(512\) | −0.587785 | + | 0.809017i | −0.0259767 | + | 0.0357538i | ||||
\(513\) | −4.25325 | + | 5.85410i | −0.187786 | + | 0.258465i | ||||
\(514\) | 7.59017 | − | 5.51458i | 0.334788 | − | 0.243238i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.61803 | + | 1.90211i | 0.115253 | + | 0.0837359i | ||||
\(517\) | 6.71040 | − | 2.18034i | 0.295123 | − | 0.0958912i | ||||
\(518\) | − | 17.7082i | − | 0.778054i | ||||||
\(519\) | −6.82624 | − | 21.0090i | −0.299639 | − | 0.922193i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.42705 | + | 25.9358i | −0.369196 | + | 1.13627i | 0.578116 | + | 0.815955i | \(0.303788\pi\) |
−0.947312 | + | 0.320313i | \(0.896212\pi\) | |||||||
\(522\) | 3.44095 | + | 1.11803i | 0.150607 | + | 0.0489350i | ||||
\(523\) | −9.23305 | − | 12.7082i | −0.403733 | − | 0.555691i | 0.557943 | − | 0.829879i | \(-0.311591\pi\) |
−0.961676 | + | 0.274188i | \(0.911591\pi\) | |||||||
\(524\) | 5.23607 | 0.228739 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.47214 | 0.369403 | ||||||||
\(527\) | 6.53888 | + | 9.00000i | 0.284838 | + | 0.392046i | ||||
\(528\) | −0.726543 | − | 0.236068i | −0.0316187 | − | 0.0102735i | ||||
\(529\) | −4.01722 | + | 12.3637i | −0.174662 | + | 0.537554i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.76393 | − | 8.50651i | −0.119944 | − | 0.369151i | ||||
\(532\) | − | 14.4721i | − | 0.627447i | ||||||
\(533\) | 8.97578 | − | 2.91641i | 0.388784 | − | 0.126324i | ||||
\(534\) | 2.92705 | + | 2.12663i | 0.126666 | + | 0.0920282i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.00000 | − | 2.17963i | 0.129580 | − | 0.0941456i | ||||
\(537\) | 15.3884 | − | 21.1803i | 0.664059 | − | 0.913999i | ||||
\(538\) | −7.69421 | + | 10.5902i | −0.331721 | + | 0.456575i | ||||
\(539\) | 1.85410 | − | 1.34708i | 0.0798618 | − | 0.0580230i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.92705 | + | 7.21242i | 0.426797 | + | 0.310086i | 0.780367 | − | 0.625322i | \(-0.215032\pi\) |
−0.353570 | + | 0.935408i | \(0.615032\pi\) | |||||||
\(542\) | 5.53483 | − | 1.79837i | 0.237741 | − | 0.0772468i | ||||
\(543\) | 9.03444i | 0.387705i | ||||||||
\(544\) | 0.354102 | + | 1.08981i | 0.0151820 | + | 0.0467254i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.14590 | − | 3.52671i | 0.0490399 | − | 0.150929i | ||||
\(547\) | 1.90211 | + | 0.618034i | 0.0813285 | + | 0.0264252i | 0.349399 | − | 0.936974i | \(-0.386386\pi\) |
−0.268070 | + | 0.963399i | \(0.586386\pi\) | |||||||
\(548\) | 8.24924 | + | 11.3541i | 0.352390 | + | 0.485023i | ||||
\(549\) | 2.14590 | 0.0915847 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.1803 | 1.11532 | ||||||||
\(552\) | −3.52671 | − | 4.85410i | −0.150107 | − | 0.206604i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.91641 | + | 27.4419i | −0.378822 | + | 1.16589i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.14590 | + | 12.7598i | 0.175825 | + | 0.541134i | ||||
\(557\) | 6.27051i | 0.265690i | 0.991137 | + | 0.132845i | \(0.0424113\pi\) | ||||
−0.991137 | + | 0.132845i | \(0.957589\pi\) | |||||||
\(558\) | 9.23305 | − | 3.00000i | 0.390866 | − | 0.127000i | ||||
\(559\) | 4.85410 | + | 3.52671i | 0.205307 | + | 0.149164i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.708204 | + | 0.514540i | −0.0299004 | + | 0.0217239i | ||||
\(562\) | −2.99193 | + | 4.11803i | −0.126207 | + | 0.173709i | ||||
\(563\) | −0.898056 | + | 1.23607i | −0.0378485 | + | 0.0520941i | −0.827522 | − | 0.561434i | \(-0.810250\pi\) |
0.789673 | + | 0.613528i | \(0.210250\pi\) | |||||||
\(564\) | −7.47214 | + | 5.42882i | −0.314634 | + | 0.228595i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.00000 | − | 0.726543i | −0.0420331 | − | 0.0305389i | ||||
\(567\) | −1.90211 | + | 0.618034i | −0.0798812 | + | 0.0259550i | ||||
\(568\) | 8.18034i | 0.343239i | ||||||||
\(569\) | −7.29837 | − | 22.4621i | −0.305964 | − | 0.941660i | −0.979316 | − | 0.202338i | \(-0.935146\pi\) |
0.673352 | − | 0.739322i | \(-0.264854\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.27051 | − | 19.2986i | 0.262413 | − | 0.807623i | −0.729866 | − | 0.683591i | \(-0.760417\pi\) |
0.992278 | − | 0.124032i | \(-0.0395827\pi\) | |||||||
\(572\) | −1.34708 | − | 0.437694i | −0.0563244 | − | 0.0183009i | ||||
\(573\) | 3.07768 | + | 4.23607i | 0.128572 | + | 0.176964i | ||||
\(574\) | 10.1803 | 0.424919 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 14.5964 | + | 20.0902i | 0.607655 | + | 0.836365i | 0.996382 | − | 0.0849881i | \(-0.0270852\pi\) |
−0.388727 | + | 0.921353i | \(0.627085\pi\) | |||||||
\(578\) | −14.9191 | − | 4.84752i | −0.620555 | − | 0.201630i | ||||
\(579\) | 1.42705 | − | 4.39201i | 0.0593062 | − | 0.182526i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.70820 | + | 11.4127i | 0.153842 | + | 0.473478i | ||||
\(582\) | − | 7.14590i | − | 0.296207i | ||||||
\(583\) | 8.40051 | − | 2.72949i | 0.347913 | − | 0.113044i | ||||
\(584\) | 7.97214 | + | 5.79210i | 0.329889 | + | 0.239679i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.39919 | + | 2.46965i | −0.140419 | + | 0.102020i | ||||
\(587\) | 11.6902 | − | 16.0902i | 0.482506 | − | 0.664112i | −0.496478 | − | 0.868049i | \(-0.665374\pi\) |
0.978984 | + | 0.203937i | \(0.0653737\pi\) | |||||||
\(588\) | −1.76336 | + | 2.42705i | −0.0727196 | + | 0.100090i | ||||
\(589\) | 56.8328 | − | 41.2915i | 2.34176 | − | 1.70138i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.88197 | + | 1.36733i | 0.0774137 | + | 0.0562444i | ||||
\(592\) | 8.42075 | − | 2.73607i | 0.346091 | − | 0.112452i | ||||
\(593\) | − | 23.0344i | − | 0.945911i | −0.881086 | − | 0.472956i | \(-0.843187\pi\) | ||
0.881086 | − | 0.472956i | \(-0.156813\pi\) | |||||||
\(594\) | 0.236068 | + | 0.726543i | 0.00968599 | + | 0.0298104i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.80902 | + | 20.9560i | −0.278908 | + | 0.858391i | ||||
\(597\) | −15.3884 | − | 5.00000i | −0.629806 | − | 0.204636i | ||||
\(598\) | −6.53888 | − | 9.00000i | −0.267395 | − | 0.368037i | ||||
\(599\) | −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 | \(0.554318\pi\) | |||||||
\(602\) | 3.80423 | + | 5.23607i | 0.155049 | + | 0.213406i | ||||
\(603\) | −3.52671 | − | 1.14590i | −0.143619 | − | 0.0466646i | ||||
\(604\) | −3.38197 | + | 10.4086i | −0.137610 | + | 0.423521i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.35410 | + | 16.4782i | 0.217496 | + | 0.669382i | ||||
\(607\) | − | 24.1803i | − | 0.981450i | −0.871315 | − | 0.490725i | \(-0.836732\pi\) | ||
0.871315 | − | 0.490725i | \(-0.163268\pi\) | |||||||
\(608\) | 6.88191 | − | 2.23607i | 0.279098 | − | 0.0906845i | ||||
\(609\) | 5.85410 | + | 4.25325i | 0.237220 | + | 0.172351i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.8541 | + | 10.0656i | −0.560477 | + | 0.407210i | ||||
\(612\) | 0.673542 | − | 0.927051i | 0.0272263 | − | 0.0374738i | ||||
\(613\) | 0.845055 | − | 1.16312i | 0.0341315 | − | 0.0469779i | −0.791610 | − | 0.611026i | \(-0.790757\pi\) |
0.825742 | + | 0.564048i | \(0.190757\pi\) | |||||||
\(614\) | 24.0344 | − | 17.4620i | 0.969951 | − | 0.704711i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.23607 | − | 0.898056i | −0.0498026 | − | 0.0361837i | ||||
\(617\) | −10.0984 | + | 3.28115i | −0.406544 | + | 0.132094i | −0.505148 | − | 0.863032i | \(-0.668562\pi\) |
0.0986041 | + | 0.995127i | \(0.468562\pi\) | |||||||
\(618\) | 15.7082i | 0.631877i | ||||||||
\(619\) | 7.23607 | + | 22.2703i | 0.290842 | + | 0.895120i | 0.984586 | + | 0.174899i | \(0.0559598\pi\) |
−0.693744 | + | 0.720221i | \(0.744040\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.85410 | + | 5.70634i | −0.0744025 | + | 0.228988i | ||||
\(622\) | −12.0332 | − | 3.90983i | −0.482488 | − | 0.156770i | ||||
\(623\) | 4.25325 | + | 5.85410i | 0.170403 | + | 0.234540i | ||||
\(624\) | 1.85410 | 0.0742235 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18.3607 | −0.733840 | ||||||||
\(627\) | 3.24920 | + | 4.47214i | 0.129760 | + | 0.178600i | ||||
\(628\) | −10.6004 | − | 3.44427i | −0.423001 | − | 0.137441i | ||||
\(629\) | 3.13525 | − | 9.64932i | 0.125011 | − | 0.384744i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.888544 | − | 2.73466i | −0.0353724 | − | 0.108865i | 0.931811 | − | 0.362943i | \(-0.118228\pi\) |
−0.967184 | + | 0.254078i | \(0.918228\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.60845 | − | 2.47214i | 0.302409 | − | 0.0982586i | ||||
\(634\) | −8.85410 | − | 6.43288i | −0.351641 | − | 0.255482i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.35410 | + | 6.79615i | −0.370914 | + | 0.269485i | ||||
\(637\) | −3.26944 | + | 4.50000i | −0.129540 | + | 0.178296i | ||||
\(638\) | 1.62460 | − | 2.23607i | 0.0643185 | − | 0.0885268i | ||||
\(639\) | 6.61803 | − | 4.80828i | 0.261805 | − | 0.190213i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.32624 | + | 5.32282i | 0.289369 | + | 0.210239i | 0.722994 | − | 0.690855i | \(-0.242766\pi\) |
−0.433625 | + | 0.901094i | \(0.642766\pi\) | |||||||
\(642\) | 6.60440 | − | 2.14590i | 0.260655 | − | 0.0846918i | ||||
\(643\) | − | 31.7771i | − | 1.25317i | −0.779355 | − | 0.626583i | \(-0.784453\pi\) | ||
0.779355 | − | 0.626583i | \(-0.215547\pi\) | |||||||
\(644\) | −3.70820 | − | 11.4127i | −0.146124 | − | 0.449723i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.56231 | − | 7.88597i | 0.100813 | − | 0.310269i | ||||
\(647\) | −0.106001 | − | 0.0344419i | −0.00416733 | − | 0.00135405i | 0.306933 | − | 0.951731i | \(-0.400697\pi\) |
−0.311100 | + | 0.950377i | \(0.600697\pi\) | |||||||
\(648\) | −0.587785 | − | 0.809017i | −0.0230904 | − | 0.0317812i | ||||
\(649\) | −6.83282 | −0.268211 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.4164 | 0.760989 | ||||||||
\(652\) | −6.77591 | − | 9.32624i | −0.265365 | − | 0.365244i | ||||
\(653\) | −18.2743 | − | 5.93769i | −0.715130 | − | 0.232360i | −0.0712197 | − | 0.997461i | \(-0.522689\pi\) |
−0.643911 | + | 0.765101i | \(0.722689\pi\) | |||||||
\(654\) | 5.42705 | − | 16.7027i | 0.212214 | − | 0.653129i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.57295 | + | 4.84104i | 0.0614133 | + | 0.189011i | ||||
\(657\) | − | 9.85410i | − | 0.384445i | ||||||
\(658\) | −17.5680 | + | 5.70820i | −0.684874 | + | 0.222529i | ||||
\(659\) | 17.0344 | + | 12.3762i | 0.663568 | + | 0.482110i | 0.867866 | − | 0.496799i | \(-0.165491\pi\) |
−0.204298 | + | 0.978909i | \(0.565491\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.2705 | − | 19.0866i | 1.02180 | − | 0.742384i | 0.0551524 | − | 0.998478i | \(-0.482436\pi\) |
0.966652 | + | 0.256094i | \(0.0824355\pi\) | |||||||
\(662\) | 13.8293 | − | 19.0344i | 0.537492 | − | 0.739795i | ||||
\(663\) | 1.24882 | − | 1.71885i | 0.0485000 | − | 0.0667545i | ||||
\(664\) | −4.85410 | + | 3.52671i | −0.188376 | + | 0.136863i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.16312 | − | 5.20431i | −0.277565 | − | 0.201663i | ||||
\(667\) | 20.6457 | − | 6.70820i | 0.799406 | − | 0.259743i | ||||
\(668\) | 2.47214i | 0.0956498i | ||||||||
\(669\) | −4.85410 | − | 14.9394i | −0.187670 | − | 0.577590i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.506578 | − | 1.55909i | 0.0195562 | − | 0.0601879i | ||||
\(672\) | 1.90211 | + | 0.618034i | 0.0733756 | + | 0.0238412i | ||||
\(673\) | 3.40820 | + | 4.69098i | 0.131376 | + | 0.180824i | 0.869637 | − | 0.493691i | \(-0.164353\pi\) |
−0.738261 | + | 0.674515i | \(0.764353\pi\) | |||||||
\(674\) | −24.8328 | −0.956524 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.56231 | −0.367781 | ||||||||
\(677\) | −16.1805 | − | 22.2705i | −0.621866 | − | 0.855925i | 0.375621 | − | 0.926773i | \(-0.377429\pi\) |
−0.997487 | + | 0.0708481i | \(0.977429\pi\) | |||||||
\(678\) | −8.14324 | − | 2.64590i | −0.312739 | − | 0.101615i | ||||
\(679\) | 4.41641 | − | 13.5923i | 0.169486 | − | 0.521625i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.291796 | − | 0.898056i | −0.0111816 | − | 0.0344136i | ||||
\(682\) | − | 7.41641i | − | 0.283989i | ||||||
\(683\) | −7.05342 | + | 2.29180i | −0.269892 | + | 0.0876931i | −0.440836 | − | 0.897588i | \(-0.645318\pi\) |
0.170945 | + | 0.985281i | \(0.445318\pi\) | |||||||
\(684\) | −5.85410 | − | 4.25325i | −0.223837 | − | 0.162627i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.1803 | + | 11.7557i | −0.617768 | + | 0.448835i | ||||
\(687\) | −5.44907 | + | 7.50000i | −0.207895 | + | 0.286143i | ||||
\(688\) | −1.90211 | + | 2.61803i | −0.0725174 | + | 0.0998116i | ||||
\(689\) | −17.3435 | + | 12.6008i | −0.660733 | + | 0.480051i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.47214 | + | 1.06957i | 0.0560027 | + | 0.0406883i | 0.615434 | − | 0.788188i | \(-0.288981\pi\) |
−0.559432 | + | 0.828876i | \(0.688981\pi\) | |||||||
\(692\) | 21.0090 | − | 6.82624i | 0.798642 | − | 0.259495i | ||||
\(693\) | 1.52786i | 0.0580388i | ||||||||
\(694\) | −0.236068 | − | 0.726543i | −0.00896102 | − | 0.0275792i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.11803 | + | 3.44095i | −0.0423790 | + | 0.130429i | ||||
\(697\) | 5.54734 | + | 1.80244i | 0.210120 | + | 0.0682723i | ||||
\(698\) | 5.75934 | + | 7.92705i | 0.217994 | + | 0.300043i | ||||
\(699\) | −10.9098 | −0.412648 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.1591 | 1.85671 | 0.928356 | − | 0.371692i | \(-0.121222\pi\) | ||||
0.928356 | + | 0.371692i | \(0.121222\pi\) | |||||||
\(702\) | −1.08981 | − | 1.50000i | −0.0411324 | − | 0.0566139i | ||||
\(703\) | −60.9331 | − | 19.7984i | −2.29814 | − | 0.746710i | ||||
\(704\) | 0.236068 | − | 0.726543i | 0.00889715 | − | 0.0273826i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.56231 | − | 10.9637i | −0.134069 | − | 0.412622i | ||||
\(707\) | 34.6525i | 1.30324i | ||||||||
\(708\) | 8.50651 | − | 2.76393i | 0.319694 | − | 0.103875i | ||||
\(709\) | −4.20820 | − | 3.05744i | −0.158042 | − | 0.114825i | 0.505953 | − | 0.862561i | \(-0.331141\pi\) |
−0.663996 | + | 0.747736i | \(0.731141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.12663 | + | 2.92705i | −0.0796987 | + | 0.109696i | ||||
\(713\) | 34.2380 | − | 47.1246i | 1.28222 | − | 1.76483i | ||||
\(714\) | 1.85410 | − | 1.34708i | 0.0693880 | − | 0.0504133i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.1803 | + | 15.3884i | 0.791546 | + | 0.575092i | ||||
\(717\) | −25.5195 | + | 8.29180i | −0.953044 | + | 0.309663i | ||||
\(718\) | 7.88854i | 0.294398i | ||||||||
\(719\) | 6.90983 | + | 21.2663i | 0.257693 | + | 0.793098i | 0.993287 | + | 0.115675i | \(0.0369032\pi\) |
−0.735594 | + | 0.677423i | \(0.763097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.70820 | + | 29.8788i | −0.361552 | + | 1.11274i | ||||
\(722\) | −31.7279 | − | 10.3090i | −1.18079 | − | 0.383662i | ||||
\(723\) | 4.20025 | + | 5.78115i | 0.156209 | + | 0.215003i | ||||
\(724\) | −9.03444 | −0.335762 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.4164 | −0.386589 | ||||||||
\(727\) | −13.9353 | − | 19.1803i | −0.516833 | − | 0.711359i | 0.468220 | − | 0.883612i | \(-0.344895\pi\) |
−0.985053 | + | 0.172253i | \(0.944895\pi\) | |||||||
\(728\) | 3.52671 | + | 1.14590i | 0.130709 | + | 0.0424698i | ||||
\(729\) | −0.309017 | + | 0.951057i | −0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.14590 | + | 3.52671i | 0.0423826 | + | 0.130440i | ||||
\(732\) | 2.14590i | 0.0793147i | ||||||||
\(733\) | 36.4832 | − | 11.8541i | 1.34754 | − | 0.437841i | 0.455674 | − | 0.890147i | \(-0.349398\pi\) |
0.891863 | + | 0.452306i | \(0.149398\pi\) | |||||||
\(734\) | 2.85410 | + | 2.07363i | 0.105347 | + | 0.0765389i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.85410 | − | 3.52671i | 0.178925 | − | 0.129996i | ||||
\(737\) | −1.66509 | + | 2.29180i | −0.0613343 | + | 0.0844194i | ||||
\(738\) | 2.99193 | − | 4.11803i | 0.110134 | − | 0.151587i | ||||
\(739\) | 17.5623 | − | 12.7598i | 0.646040 | − | 0.469375i | −0.215880 | − | 0.976420i | \(-0.569262\pi\) |
0.861920 | + | 0.507044i | \(0.169262\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.8541 | − | 7.88597i | −0.398735 | − | 0.289698i | ||||
\(742\) | −21.9928 | + | 7.14590i | −0.807382 | + | 0.262334i | ||||
\(743\) | 24.6525i | 0.904412i | 0.891914 | + | 0.452206i | \(0.149363\pi\) | ||||
−0.891914 | + | 0.452206i | \(0.850637\pi\) | |||||||
\(744\) | 3.00000 | + | 9.23305i | 0.109985 | + | 0.338500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.09017 | + | 27.9767i | −0.332815 | + | 1.02430i | ||||
\(747\) | 5.70634 | + | 1.85410i | 0.208784 | + | 0.0678380i | ||||
\(748\) | −0.514540 | − | 0.708204i | −0.0188135 | − | 0.0258945i | ||||
\(749\) | 13.8885 | 0.507476 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.2361 | 0.701934 | 0.350967 | − | 0.936388i | \(-0.385853\pi\) | ||||
0.350967 | + | 0.936388i | \(0.385853\pi\) | |||||||
\(752\) | −5.42882 | − | 7.47214i | −0.197969 | − | 0.272481i | ||||
\(753\) | −3.35520 | − | 1.09017i | −0.122270 | − | 0.0397280i | ||||
\(754\) | −2.07295 | + | 6.37988i | −0.0754924 | + | 0.232342i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.618034 | − | 1.90211i | −0.0224777 | − | 0.0691792i | ||||
\(757\) | − | 22.1459i | − | 0.804906i | −0.915441 | − | 0.402453i | \(-0.868158\pi\) | ||
0.915441 | − | 0.402453i | \(-0.131842\pi\) | |||||||
\(758\) | −22.2703 | + | 7.23607i | −0.808895 | + | 0.262826i | ||||
\(759\) | 3.70820 | + | 2.69417i | 0.134599 | + | 0.0977921i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.5344 | − | 26.5438i | 1.32437 | − | 0.962213i | 0.324506 | − | 0.945884i | \(-0.394802\pi\) |
0.999867 | − | 0.0163292i | \(-0.00519799\pi\) | |||||||
\(762\) | 8.05748 | − | 11.0902i | 0.291892 | − | 0.401754i | ||||
\(763\) | 20.6457 | − | 28.4164i | 0.747426 | − | 1.02874i | ||||
\(764\) | −4.23607 | + | 3.07768i | −0.153256 | + | 0.111347i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.32624 | + | 6.77591i | 0.336971 | + | 0.244824i | ||||
\(767\) | 15.7719 | − | 5.12461i | 0.569492 | − | 0.185039i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −13.0902 | − | 40.2874i | −0.472044 | − | 1.45280i | −0.849904 | − | 0.526938i | \(-0.823340\pi\) |
0.377860 | − | 0.925863i | \(-0.376660\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.89919 | − | 8.92278i | 0.104412 | − | 0.321346i | ||||
\(772\) | 4.39201 | + | 1.42705i | 0.158072 | + | 0.0513607i | ||||
\(773\) | 1.71036 | + | 2.35410i | 0.0615172 | + | 0.0846712i | 0.838667 | − | 0.544644i | \(-0.183335\pi\) |
−0.777150 | + | 0.629315i | \(0.783335\pi\) | |||||||
\(774\) | 3.23607 | 0.116318 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.14590 | 0.256523 | ||||||||
\(777\) | −10.4086 | − | 14.3262i | −0.373407 | − | 0.513951i | ||||
\(778\) | −29.4625 | − | 9.57295i | −1.05628 | − | 0.343207i | ||||
\(779\) | 11.3820 | − | 35.0301i | 0.407801 | − | 1.25508i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.93112 | − | 5.94336i | −0.0691008 | − | 0.212670i | ||||
\(782\) | − | 6.87539i | − | 0.245863i | ||||||
\(783\) | 3.44095 | − | 1.11803i | 0.122970 | − | 0.0399553i | ||||
\(784\) | −2.42705 | − | 1.76336i | −0.0866804 | − | 0.0629770i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.23607 | − | 3.07768i | 0.151096 | − | 0.109777i | ||||
\(787\) | −21.4783 | + | 29.5623i | −0.765618 | + | 1.05378i | 0.231108 | + | 0.972928i | \(0.425765\pi\) |
−0.996726 | + | 0.0808543i | \(0.974235\pi\) | |||||||
\(788\) | −1.36733 | + | 1.88197i | −0.0487091 | + | 0.0670423i | ||||
\(789\) | 6.85410 | − | 4.97980i | 0.244012 | − | 0.177285i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.8541 | − | 10.0656i | −0.492595 | − | 0.357891i | ||||
\(792\) | −0.726543 | + | 0.236068i | −0.0258166 | + | 0.00838831i | ||||
\(793\) | 3.97871i | 0.141288i | ||||||||
\(794\) | −7.67376 | − | 23.6174i | −0.272332 | − | 0.838151i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.00000 | − | 15.3884i | 0.177220 | − | 0.545428i | ||||
\(797\) | 2.21238 | + | 0.718847i | 0.0783667 | + | 0.0254629i | 0.347938 | − | 0.937518i | \(-0.386882\pi\) |
−0.269571 | + | 0.962980i | \(0.586882\pi\) | |||||||
\(798\) | −8.50651 | − | 11.7082i | −0.301127 | − | 0.414466i | ||||
\(799\) | −10.5836 | −0.374421 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.61803 | 0.127837 | ||||||||
\(802\) | −8.76378 | − | 12.0623i | −0.309460 | − | 0.425935i | ||||
\(803\) | −7.15942 | − | 2.32624i | −0.252651 | − | 0.0820912i | ||||
\(804\) | 1.14590 | − | 3.52671i | 0.0404127 | − | 0.124378i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.56231 | + | 17.1190i | 0.195924 | + | 0.602992i | ||||
\(807\) | 13.0902i | 0.460796i | ||||||||
\(808\) | −16.4782 | + | 5.35410i | −0.579702 | + | 0.188357i | ||||
\(809\) | −34.9615 | − | 25.4010i | −1.22918 | − | 0.893052i | −0.232352 | − | 0.972632i | \(-0.574642\pi\) |
−0.996829 | + | 0.0795797i | \(0.974642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.1803 | + | 13.9353i | −0.673513 | + | 0.489336i | −0.871199 | − | 0.490930i | \(-0.836657\pi\) |
0.197686 | + | 0.980265i | \(0.436657\pi\) | |||||||
\(812\) | −4.25325 | + | 5.85410i | −0.149260 | + | 0.205439i | ||||
\(813\) | 3.42071 | − | 4.70820i | 0.119970 | − | 0.165124i | ||||
\(814\) | −5.47214 | + | 3.97574i | −0.191798 | + | 0.139350i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.927051 | + | 0.673542i | 0.0324533 | + | 0.0235787i | ||||
\(817\) | 22.2703 | − | 7.23607i | 0.779140 | − | 0.253158i | ||||
\(818\) | − | 25.9787i | − | 0.908324i | ||||||
\(819\) | −1.14590 | − | 3.52671i | −0.0400409 | − | 0.123233i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.72949 | − | 8.40051i | 0.0952599 | − | 0.293180i | −0.892061 | − | 0.451914i | \(-0.850741\pi\) |
0.987321 | + | 0.158734i | \(0.0507413\pi\) | |||||||
\(822\) | 13.3475 | + | 4.33688i | 0.465549 | + | 0.151266i | ||||
\(823\) | 15.0454 | + | 20.7082i | 0.524449 | + | 0.721843i | 0.986272 | − | 0.165130i | \(-0.0528043\pi\) |
−0.461822 | + | 0.886972i | \(0.652804\pi\) | |||||||
\(824\) | −15.7082 | −0.547221 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.8885 | 0.622422 | ||||||||
\(827\) | −11.3067 | − | 15.5623i | −0.393172 | − | 0.541154i | 0.565842 | − | 0.824514i | \(-0.308551\pi\) |
−0.959014 | + | 0.283359i | \(0.908551\pi\) | |||||||
\(828\) | −5.70634 | − | 1.85410i | −0.198309 | − | 0.0644345i | ||||
\(829\) | −14.1697 | + | 43.6098i | −0.492134 | + | 1.51463i | 0.329242 | + | 0.944245i | \(0.393207\pi\) |
−0.821376 | + | 0.570387i | \(0.806793\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.91641 | + | 27.4419i | 0.309307 | + | 0.951948i | ||||
\(832\) | 1.85410i | 0.0642794i | ||||||||
\(833\) | −3.26944 | + | 1.06231i | −0.113279 | + | 0.0368067i | ||||
\(834\) | 10.8541 | + | 7.88597i | 0.375847 | + | 0.273069i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.47214 | + | 3.24920i | −0.154672 | + | 0.112376i | ||||
\(837\) | 5.70634 | − | 7.85410i | 0.197240 | − | 0.271477i | ||||
\(838\) | −1.24108 | + | 1.70820i | −0.0428725 | + | 0.0590089i | ||||
\(839\) | 28.4164 | − | 20.6457i | 0.981043 | − | 0.712770i | 0.0231018 | − | 0.999733i | \(-0.492646\pi\) |
0.957942 | + | 0.286963i | \(0.0926458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8713 | + | 9.35156i | 0.443839 | + | 0.322468i | ||||
\(842\) | 0.0857567 | − | 0.0278640i | 0.00295537 | − | 0.000960258i | ||||
\(843\) | 5.09017i | 0.175315i | ||||||||
\(844\) | 2.47214 | + | 7.60845i | 0.0850944 | + | 0.261894i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.85410 | + | 8.78402i | −0.0981260 | + | 0.302001i | ||||
\(847\) | −19.8132 | − | 6.43769i | −0.680789 | − | 0.221202i | ||||
\(848\) | −6.79615 | − | 9.35410i | −0.233381 | − | 0.321221i | ||||
\(849\) | −1.23607 | −0.0424217 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −53.1246 | −1.82109 | ||||||||
\(852\) | 4.80828 | + | 6.61803i | 0.164729 | + | 0.226730i | ||||
\(853\) | 37.5200 | + | 12.1910i | 1.28466 | + | 0.417411i | 0.870219 | − | 0.492665i | \(-0.163977\pi\) |
0.414441 | + | 0.910076i | \(0.363977\pi\) | |||||||
\(854\) | −1.32624 | + | 4.08174i | −0.0453829 | + | 0.139674i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.14590 | + | 6.60440i | 0.0733453 | + | 0.225734i | ||||
\(857\) | − | 39.3050i | − | 1.34263i | −0.741171 | − | 0.671316i | \(-0.765729\pi\) | ||
0.741171 | − | 0.671316i | \(-0.234271\pi\) | |||||||
\(858\) | −1.34708 | + | 0.437694i | −0.0459887 | + | 0.0149426i | ||||
\(859\) | 44.0689 | + | 32.0179i | 1.50361 | + | 1.09244i | 0.968915 | + | 0.247393i | \(0.0795737\pi\) |
0.534696 | + | 0.845045i | \(0.320426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.23607 | − | 5.98385i | 0.280684 | − | 0.203929i | ||||
\(862\) | 5.70634 | − | 7.85410i | 0.194359 | − | 0.267512i | ||||
\(863\) | 5.98385 | − | 8.23607i | 0.203693 | − | 0.280359i | −0.694934 | − | 0.719074i | \(-0.744566\pi\) |
0.898626 | + | 0.438715i | \(0.144566\pi\) | |||||||
\(864\) | 0.809017 | − | 0.587785i | 0.0275233 | − | 0.0199969i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −24.1525 | − | 17.5478i | −0.820735 | − | 0.596299i | ||||
\(867\) | −14.9191 | + | 4.84752i | −0.506681 | + | 0.164631i | ||||
\(868\) | 19.4164i | 0.659036i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.12461 | − | 6.53888i | 0.0719897 | − | 0.221562i | ||||
\(872\) | 16.7027 | + | 5.42705i | 0.565626 | + | 0.183783i | ||||
\(873\) | −4.20025 | − | 5.78115i | −0.142157 | − | 0.195662i | ||||
\(874\) | −43.4164 | −1.46858 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.85410 | 0.332939 | ||||||||
\(877\) | 17.0333 | + | 23.4443i | 0.575172 | + | 0.791657i | 0.993156 | − | 0.116798i | \(-0.0372630\pi\) |
−0.417983 | + | 0.908455i | \(0.637263\pi\) | |||||||
\(878\) | 14.3844 | + | 4.67376i | 0.485449 | + | 0.157732i | ||||
\(879\) | −1.29837 | + | 3.99598i | −0.0437931 | + | 0.134781i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.2016 | − | 40.6304i | −0.444774 | − | 1.36887i | −0.882731 | − | 0.469878i | \(-0.844298\pi\) |
0.437957 | − | 0.898996i | \(-0.355702\pi\) | |||||||
\(882\) | 3.00000i | 0.101015i | ||||||||
\(883\) | 18.8496 | − | 6.12461i | 0.634340 | − | 0.206110i | 0.0258434 | − | 0.999666i | \(-0.491773\pi\) |
0.608497 | + | 0.793556i | \(0.291773\pi\) | |||||||
\(884\) | 1.71885 | + | 1.24882i | 0.0578111 | + | 0.0420022i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.7082 | + | 16.4985i | −0.762897 | + | 0.554277i | ||||
\(887\) | 28.3197 | − | 38.9787i | 0.950882 | − | 1.30878i | −0.000252175 | − | 1.00000i | \(-0.500080\pi\) |
0.951134 | − | 0.308777i | \(-0.0999197\pi\) | |||||||
\(888\) | 5.20431 | − | 7.16312i | 0.174645 | − | 0.240379i | ||||
\(889\) | 22.1803 | − | 16.1150i | 0.743905 | − | 0.540478i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.618034 | + | 0.449028i | 0.0207049 | + | 0.0150430i | ||||
\(892\) | 14.9394 | − | 4.85410i | 0.500208 | − | 0.162527i | ||||
\(893\) | 66.8328i | 2.23647i | ||||||||
\(894\) | 6.80902 | + | 20.9560i | 0.227728 | + | 0.700873i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.618034 | + | 1.90211i | −0.0206471 | + | 0.0635451i | ||||
\(897\) | −10.5801 | − | 3.43769i | −0.353260 | − | 0.114781i | ||||
\(898\) | 11.6372 | + | 16.0172i | 0.388338 | + | 0.534502i | ||||
\(899\) | −35.1246 | −1.17147 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.2492 | −0.441396 | ||||||||
\(902\) | −2.28563 | − | 3.14590i | −0.0761031 | − | 0.104747i | ||||
\(903\) | 6.15537 | + | 2.00000i | 0.204838 | + | 0.0665558i | ||||
\(904\) | 2.64590 | − | 8.14324i | 0.0880013 | − | 0.270840i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.38197 | + | 10.4086i | 0.112358 | + | 0.345803i | ||||
\(907\) | 33.7082i | 1.11926i | 0.828742 | + | 0.559631i | \(0.189057\pi\) | ||||
−0.828742 | + | 0.559631i | \(0.810943\pi\) | |||||||
\(908\) | 0.898056 | − | 0.291796i | 0.0298030 | − | 0.00968359i | ||||
\(909\) | 14.0172 | + | 10.1841i | 0.464922 | + | 0.337786i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.67376 | − | 1.21606i | 0.0554542 | − | 0.0402898i | −0.559713 | − | 0.828687i | \(-0.689089\pi\) |
0.615167 | + | 0.788397i | \(0.289089\pi\) | |||||||
\(912\) | 4.25325 | − | 5.85410i | 0.140839 | − | 0.193849i | ||||
\(913\) | 2.69417 | − | 3.70820i | 0.0891639 | − | 0.122724i | ||||
\(914\) | 2.85410 | − | 2.07363i | 0.0944053 | − | 0.0685895i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.50000 | − | 5.44907i | −0.247807 | − | 0.180042i | ||||
\(917\) | 9.95959 | − | 3.23607i | 0.328895 | − | 0.106864i | ||||
\(918\) | − | 1.14590i | − | 0.0378203i | ||||||
\(919\) | 5.85410 | + | 18.0171i | 0.193109 | + | 0.594328i | 0.999993 | + | 0.00361909i | \(0.00115200\pi\) |
−0.806884 | + | 0.590709i | \(0.798848\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.18034 | − | 28.2542i | 0.302502 | − | 0.931007i | ||||
\(922\) | −13.2290 | − | 4.29837i | −0.435675 | − | 0.141559i | ||||
\(923\) | 8.91505 | + | 12.2705i | 0.293442 | + | 0.403889i | ||||
\(924\) | −1.52786 | −0.0502630 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 25.7082 | 0.844824 | ||||||||
\(927\) | 9.23305 | + | 12.7082i | 0.303253 | + | 0.417392i | ||||
\(928\) | −3.44095 | − | 1.11803i | −0.112955 | − | 0.0367013i | ||||
\(929\) | −4.93769 | + | 15.1967i | −0.162000 | + | 0.498586i | −0.998803 | − | 0.0489190i | \(-0.984422\pi\) |
0.836802 | + | 0.547505i | \(0.184422\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.70820 | + | 20.6457i | 0.219853 | + | 0.676636i | ||||
\(932\) | − | 10.9098i | − | 0.357363i | ||||||
\(933\) | −12.0332 | + | 3.90983i | −0.393950 | + | 0.128002i | ||||
\(934\) | −30.8885 | − | 22.4418i | −1.01070 | − | 0.734319i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.50000 | − | 1.08981i | 0.0490290 | − | 0.0356217i | ||||
\(937\) | 14.0538 | − | 19.3435i | 0.459119 | − | 0.631923i | −0.515207 | − | 0.857066i | \(-0.672285\pi\) |
0.974326 | + | 0.225143i | \(0.0722848\pi\) | |||||||
\(938\) | 4.35926 | − | 6.00000i | 0.142335 | − | 0.195907i | ||||
\(939\) | −14.8541 | + | 10.7921i | −0.484745 | + | 0.352188i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.1976 | − | 21.9398i | −0.984412 | − | 0.715217i | −0.0257220 | − | 0.999669i | \(-0.508188\pi\) |
−0.958690 | + | 0.284452i | \(0.908188\pi\) | |||||||
\(942\) | −10.6004 | + | 3.44427i | −0.345379 | + | 0.112220i | ||||
\(943\) | − | 30.5410i | − | 0.994552i | ||||||
\(944\) | 2.76393 | + | 8.50651i | 0.0899583 | + | 0.276863i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.763932 | − | 2.35114i | 0.0248376 | − | 0.0764422i | ||||
\(947\) | −6.60440 | − | 2.14590i | −0.214614 | − | 0.0697323i | 0.199737 | − | 0.979850i | \(-0.435991\pi\) |
−0.414351 | + | 0.910117i | \(0.635991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.2705 | 0.593086 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.9443 | −0.354892 | ||||||||
\(952\) | 1.34708 | + | 1.85410i | 0.0436592 | + | 0.0600918i | ||||
\(953\) | −47.4266 | − | 15.4098i | −1.53630 | − | 0.499173i | −0.585946 | − | 0.810350i | \(-0.699277\pi\) |
−0.950352 | + | 0.311177i | \(0.899277\pi\) | |||||||
\(954\) | −3.57295 | + | 10.9964i | −0.115678 | + | 0.356022i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.29180 | − | 25.5195i | −0.268176 | − | 0.825360i | ||||
\(957\) | − | 2.76393i | − | 0.0893452i | ||||||
\(958\) | 4.25325 | − | 1.38197i | 0.137416 | − | 0.0446493i | ||||
\(959\) | 22.7082 | + | 16.4985i | 0.733286 | + | 0.532764i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −51.1697 | + | 37.1770i | −1.65064 | + | 1.19926i | ||||
\(962\) | 9.64932 | − | 13.2812i | 0.311107 | − | 0.428202i | ||||
\(963\) | 4.08174 | − | 5.61803i | 0.131532 | − | 0.181039i | ||||
\(964\) | −5.78115 | + | 4.20025i | −0.186198 | + | 0.135281i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.70820 | − | 7.05342i | −0.312356 | − | 0.226940i | ||||
\(967\) | −21.9273 | + | 7.12461i | −0.705134 | + | 0.229112i | −0.639566 | − | 0.768736i | \(-0.720886\pi\) |
−0.0655682 | + | 0.997848i | \(0.520886\pi\) | |||||||
\(968\) | − | 10.4164i | − | 0.334796i | ||||||
\(969\) | −2.56231 | − | 7.88597i | −0.0823131 | − | 0.253334i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.6738 | − | 35.9281i | 0.374629 | − | 1.15299i | −0.569100 | − | 0.822268i | \(-0.692708\pi\) |
0.943729 | − | 0.330721i | \(-0.107292\pi\) | |||||||
\(972\) | −0.951057 | − | 0.309017i | −0.0305052 | − | 0.00991172i | ||||
\(973\) | 15.7719 | + | 21.7082i | 0.505625 | + | 0.695933i | ||||
\(974\) | 23.7082 | 0.759660 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.14590 | −0.0686885 | ||||||||
\(977\) | 0.257270 | + | 0.354102i | 0.00823080 | + | 0.0113287i | 0.813113 | − | 0.582106i | \(-0.197771\pi\) |
−0.804882 | + | 0.593435i | \(0.797771\pi\) | |||||||
\(978\) | −10.9637 | − | 3.56231i | −0.350579 | − | 0.113910i | ||||
\(979\) | 0.854102 | − | 2.62866i | 0.0272972 | − | 0.0840122i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.42705 | − | 16.7027i | −0.173272 | − | 0.533278i | ||||
\(982\) | 5.88854i | 0.187911i | ||||||||
\(983\) | 23.3399 | − | 7.58359i | 0.744427 | − | 0.241879i | 0.0878456 | − | 0.996134i | \(-0.472002\pi\) |
0.656582 | + | 0.754255i | \(0.272002\pi\) | |||||||
\(984\) | 4.11803 | + | 2.99193i | 0.131278 | + | 0.0953791i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.35410 | + | 2.43690i | −0.106816 | + | 0.0776066i | ||||
\(987\) | −10.8576 | + | 14.9443i | −0.345603 | + | 0.475681i | ||||
\(988\) | 7.88597 | − | 10.8541i | 0.250886 | − | 0.345315i | ||||
\(989\) | 15.7082 | − | 11.4127i | 0.499492 | − | 0.362902i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.29180 | + | 3.84471i | 0.168099 | + | 0.122131i | 0.668654 | − | 0.743573i | \(-0.266871\pi\) |
−0.500555 | + | 0.865705i | \(0.666871\pi\) | |||||||
\(992\) | −9.23305 | + | 3.00000i | −0.293150 | + | 0.0952501i | ||||
\(993\) | − | 23.5279i | − | 0.746634i | ||||||
\(994\) | 5.05573 | + | 15.5599i | 0.160358 | + | 0.493531i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.85410 | + | 5.70634i | −0.0587495 | + | 0.180812i | ||||
\(997\) | 24.1724 | + | 7.85410i | 0.765549 | + | 0.248742i | 0.665658 | − | 0.746257i | \(-0.268151\pi\) |
0.0998904 | + | 0.994998i | \(0.468151\pi\) | |||||||
\(998\) | 3.86974 | + | 5.32624i | 0.122494 | + | 0.168599i | ||||
\(999\) | −8.85410 | −0.280131 |
(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 | 750.2.h.a.199.2 | 8 | ||
5.2 | odd | 4 | 750.2.g.a.301.1 | 4 | |||
5.3 | odd | 4 | 150.2.g.b.61.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 750.2.h.a.199.1 | 8 | ||
15.8 | even | 4 | 450.2.h.b.361.1 | 4 | |||
25.3 | odd | 20 | 3750.2.a.b.1.2 | 2 | |||
25.4 | even | 10 | 3750.2.c.c.1249.4 | 4 | |||
25.9 | even | 10 | inner | 750.2.h.a.49.2 | 8 | ||
25.12 | odd | 20 | 750.2.g.a.451.1 | 4 | |||
25.13 | odd | 20 | 150.2.g.b.91.1 | yes | 4 | ||
25.16 | even | 5 | inner | 750.2.h.a.49.1 | 8 | ||
25.21 | even | 5 | 3750.2.c.c.1249.2 | 4 | |||
25.22 | odd | 20 | 3750.2.a.g.1.2 | 2 | |||
75.38 | even | 20 | 450.2.h.b.91.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.b.61.1 | ✓ | 4 | 5.3 | odd | 4 | ||
150.2.g.b.91.1 | yes | 4 | 25.13 | odd | 20 | ||
450.2.h.b.91.1 | 4 | 75.38 | even | 20 | |||
450.2.h.b.361.1 | 4 | 15.8 | even | 4 | |||
750.2.g.a.301.1 | 4 | 5.2 | odd | 4 | |||
750.2.g.a.451.1 | 4 | 25.12 | odd | 20 | |||
750.2.h.a.49.1 | 8 | 25.16 | even | 5 | inner | ||
750.2.h.a.49.2 | 8 | 25.9 | even | 10 | inner | ||
750.2.h.a.199.1 | 8 | 5.4 | even | 2 | inner | ||
750.2.h.a.199.2 | 8 | 1.1 | even | 1 | trivial | ||
3750.2.a.b.1.2 | 2 | 25.3 | odd | 20 | |||
3750.2.a.g.1.2 | 2 | 25.22 | odd | 20 | |||
3750.2.c.c.1249.2 | 4 | 25.21 | even | 5 | |||
3750.2.c.c.1249.4 | 4 | 25.4 | even | 10 |