Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), 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: | \(6.76332905120\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 372.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.372 |
Dual form | 847.2.f.h.148.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(3\) | 2.42705 | − | 1.76336i | 1.40126 | − | 1.01807i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(4\) | 1.61803 | + | 1.17557i | 0.809017 | + | 0.587785i | ||||
\(5\) | −0.309017 | − | 0.951057i | −0.138197 | − | 0.425325i | 0.857877 | − | 0.513855i | \(-0.171783\pi\) |
−0.996074 | + | 0.0885298i | \(0.971783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.809017 | − | 0.587785i | −0.305780 | − | 0.222162i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.85410 | − | 5.70634i | 0.618034 | − | 1.90211i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 6.00000 | 1.73205 | ||||||||
\(13\) | 1.23607 | − | 3.80423i | 0.342824 | − | 1.05510i | −0.619915 | − | 0.784669i | \(-0.712833\pi\) |
0.962739 | − | 0.270434i | \(-0.0871670\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.42705 | − | 1.76336i | −0.626662 | − | 0.455296i | ||||
\(16\) | 1.23607 | + | 3.80423i | 0.309017 | + | 0.951057i | ||||
\(17\) | −0.618034 | − | 1.90211i | −0.149895 | − | 0.461330i | 0.847713 | − | 0.530456i | \(-0.177979\pi\) |
−0.997608 | + | 0.0691254i | \(0.977979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.85410 | + | 3.52671i | −1.11361 | + | 0.809083i | −0.983228 | − | 0.182381i | \(-0.941620\pi\) |
−0.130379 | + | 0.991464i | \(0.541620\pi\) | |||||||
\(20\) | 0.618034 | − | 1.90211i | 0.138197 | − | 0.425325i | ||||
\(21\) | −3.00000 | −0.654654 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.00000 | −1.04257 | −0.521286 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521286 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.23607 | − | 2.35114i | 0.647214 | − | 0.470228i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.78115 | − | 8.55951i | −0.535233 | − | 1.64728i | ||||
\(28\) | −0.618034 | − | 1.90211i | −0.116797 | − | 0.359466i | ||||
\(29\) | 8.09017 | + | 5.87785i | 1.50231 | + | 1.09149i | 0.969451 | + | 0.245284i | \(0.0788811\pi\) |
0.532855 | + | 0.846206i | \(0.321119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.309017 | − | 0.951057i | 0.0555011 | − | 0.170815i | −0.919463 | − | 0.393176i | \(-0.871376\pi\) |
0.974964 | + | 0.222361i | \(0.0713764\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.309017 | + | 0.951057i | −0.0522334 | + | 0.160758i | ||||
\(36\) | 9.70820 | − | 7.05342i | 1.61803 | − | 1.17557i | ||||
\(37\) | 4.04508 | + | 2.93893i | 0.665008 | + | 0.483157i | 0.868350 | − | 0.495951i | \(-0.165181\pi\) |
−0.203343 | + | 0.979108i | \(0.565181\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.70820 | − | 11.4127i | −0.593788 | − | 1.82749i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.61803 | + | 1.17557i | −0.252694 | + | 0.183593i | −0.706920 | − | 0.707293i | \(-0.749916\pi\) |
0.454226 | + | 0.890887i | \(0.349916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | −0.894427 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.47214 | + | 4.70228i | −0.944058 | + | 0.685898i | −0.949394 | − | 0.314087i | \(-0.898301\pi\) |
0.00533600 | + | 0.999986i | \(0.498301\pi\) | |||||||
\(48\) | 9.70820 | + | 7.05342i | 1.40126 | + | 1.01807i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.85410 | − | 3.52671i | −0.679710 | − | 0.493838i | ||||
\(52\) | 6.47214 | − | 4.70228i | 0.897524 | − | 0.652089i | ||||
\(53\) | −1.85410 | + | 5.70634i | −0.254680 | + | 0.783826i | 0.739212 | + | 0.673473i | \(0.235198\pi\) |
−0.993892 | + | 0.110353i | \(0.964802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.56231 | + | 17.1190i | −0.736745 | + | 2.26747i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.42705 | − | 1.76336i | −0.315975 | − | 0.229569i | 0.418481 | − | 0.908226i | \(-0.362563\pi\) |
−0.734456 | + | 0.678656i | \(0.762563\pi\) | |||||||
\(60\) | −1.85410 | − | 5.70634i | −0.239364 | − | 0.736685i | ||||
\(61\) | 0.618034 | + | 1.90211i | 0.0791311 | + | 0.243541i | 0.982794 | − | 0.184703i | \(-0.0591324\pi\) |
−0.903663 | + | 0.428244i | \(0.859132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.85410 | + | 3.52671i | −0.611559 | + | 0.444324i | ||||
\(64\) | −2.47214 | + | 7.60845i | −0.309017 | + | 0.951057i | ||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00000 | −0.366508 | −0.183254 | − | 0.983066i | \(-0.558663\pi\) | ||||
−0.183254 | + | 0.983066i | \(0.558663\pi\) | |||||||
\(68\) | 1.23607 | − | 3.80423i | 0.149895 | − | 0.461330i | ||||
\(69\) | −12.1353 | + | 8.81678i | −1.46091 | + | 1.06142i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.309017 | + | 0.951057i | 0.0366736 | + | 0.112870i | 0.967717 | − | 0.252038i | \(-0.0811007\pi\) |
−0.931044 | + | 0.364907i | \(0.881101\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.09017 | + | 5.87785i | 0.946883 | + | 0.687951i | 0.950068 | − | 0.312044i | \(-0.101014\pi\) |
−0.00318477 | + | 0.999995i | \(0.501014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.70820 | − | 11.4127i | 0.428187 | − | 1.31782i | ||||
\(76\) | −12.0000 | −1.37649 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.85410 | + | 5.70634i | −0.208603 | + | 0.642013i | 0.790943 | + | 0.611889i | \(0.209590\pi\) |
−0.999546 | + | 0.0301240i | \(0.990410\pi\) | |||||||
\(80\) | 3.23607 | − | 2.35114i | 0.361803 | − | 0.262866i | ||||
\(81\) | −7.28115 | − | 5.29007i | −0.809017 | − | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.70820 | − | 11.4127i | −0.407028 | − | 1.25270i | −0.919190 | − | 0.393815i | \(-0.871155\pi\) |
0.512161 | − | 0.858889i | \(-0.328845\pi\) | |||||||
\(84\) | −4.85410 | − | 3.52671i | −0.529626 | − | 0.384796i | ||||
\(85\) | −1.61803 | + | 1.17557i | −0.175500 | + | 0.127509i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 30.0000 | 3.21634 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.0000 | −1.59000 | −0.794998 | − | 0.606612i | \(-0.792528\pi\) | ||||
−0.794998 | + | 0.606612i | \(0.792528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23607 | + | 2.35114i | −0.339232 | + | 0.246467i | ||||
\(92\) | −8.09017 | − | 5.87785i | −0.843459 | − | 0.612808i | ||||
\(93\) | −0.927051 | − | 2.85317i | −0.0961307 | − | 0.295860i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.85410 | + | 3.52671i | 0.498020 | + | 0.361833i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.54508 | + | 4.75528i | −0.156880 | + | 0.482826i | −0.998346 | − | 0.0574829i | \(-0.981693\pi\) |
0.841467 | + | 0.540309i | \(0.181693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.00000 | 0.800000 | ||||||||
\(101\) | 3.70820 | − | 11.4127i | 0.368980 | − | 1.13560i | −0.578471 | − | 0.815703i | \(-0.696350\pi\) |
0.947451 | − | 0.319901i | \(-0.103650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.70820 | + | 7.05342i | 0.956578 | + | 0.694994i | 0.952353 | − | 0.304997i | \(-0.0986553\pi\) |
0.00422434 | + | 0.999991i | \(0.498655\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.927051 | + | 2.85317i | 0.0904709 | + | 0.278441i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.09017 | + | 5.87785i | −0.782106 | + | 0.568233i | −0.905610 | − | 0.424111i | \(-0.860587\pi\) |
0.123504 | + | 0.992344i | \(0.460587\pi\) | |||||||
\(108\) | 5.56231 | − | 17.1190i | 0.535233 | − | 1.64728i | ||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.0000 | 1.42374 | ||||||||
\(112\) | 1.23607 | − | 3.80423i | 0.116797 | − | 0.359466i | ||||
\(113\) | 15.3713 | − | 11.1679i | 1.44601 | − | 1.05059i | 0.459270 | − | 0.888297i | \(-0.348111\pi\) |
0.986743 | − | 0.162293i | \(-0.0518889\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.54508 | + | 4.75528i | 0.144080 | + | 0.443432i | ||||
\(116\) | 6.18034 | + | 19.0211i | 0.573830 | + | 1.76607i | ||||
\(117\) | −19.4164 | − | 14.1068i | −1.79505 | − | 1.30418i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.618034 | + | 1.90211i | −0.0566551 | + | 0.174366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.85410 | + | 5.70634i | −0.167179 | + | 0.514523i | ||||
\(124\) | 1.61803 | − | 1.17557i | 0.145304 | − | 0.105569i | ||||
\(125\) | −7.28115 | − | 5.29007i | −0.651246 | − | 0.473158i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.618034 | − | 1.90211i | −0.0548416 | − | 0.168785i | 0.919884 | − | 0.392191i | \(-0.128283\pi\) |
−0.974726 | + | 0.223405i | \(0.928283\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.4164 | − | 14.1068i | 1.70952 | − | 1.24204i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0000 | −1.57267 | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | 0.520266 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.28115 | + | 5.29007i | −0.626662 | + | 0.455296i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.927051 | − | 2.85317i | −0.0792033 | − | 0.243763i | 0.903613 | − | 0.428350i | \(-0.140905\pi\) |
−0.982816 | + | 0.184588i | \(0.940905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.09017 | − | 5.87785i | −0.686199 | − | 0.498553i | 0.189209 | − | 0.981937i | \(-0.439408\pi\) |
−0.875409 | + | 0.483384i | \(0.839408\pi\) | |||||||
\(140\) | −1.61803 | + | 1.17557i | −0.136749 | + | 0.0993538i | ||||
\(141\) | −7.41641 | + | 22.8254i | −0.624574 | + | 1.92224i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 24.0000 | 2.00000 | ||||||||
\(145\) | 3.09017 | − | 9.51057i | 0.256625 | − | 0.789809i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.42705 | + | 1.76336i | 0.200180 | + | 0.145439i | ||||
\(148\) | 3.09017 | + | 9.51057i | 0.254010 | + | 0.781764i | ||||
\(149\) | 6.79837 | + | 20.9232i | 0.556944 | + | 1.71410i | 0.690752 | + | 0.723092i | \(0.257280\pi\) |
−0.133808 | + | 0.991007i | \(0.542720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.85410 | − | 3.52671i | 0.395021 | − | 0.287000i | −0.372489 | − | 0.928037i | \(-0.621495\pi\) |
0.767510 | + | 0.641037i | \(0.221495\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 7.41641 | − | 22.8254i | 0.593788 | − | 1.82749i | ||||
\(157\) | −5.66312 | + | 4.11450i | −0.451966 | + | 0.328373i | −0.790372 | − | 0.612628i | \(-0.790112\pi\) |
0.338405 | + | 0.941000i | \(0.390112\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.56231 | + | 17.1190i | 0.441120 | + | 1.35763i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.04508 | + | 2.93893i | 0.318797 | + | 0.231620i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.23607 | − | 3.80423i | 0.0968163 | − | 0.297970i | −0.890906 | − | 0.454187i | \(-0.849930\pi\) |
0.987723 | + | 0.156217i | \(0.0499299\pi\) | |||||||
\(164\) | −4.00000 | −0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.618034 | − | 1.90211i | 0.0478249 | − | 0.147190i | −0.924292 | − | 0.381685i | \(-0.875344\pi\) |
0.972117 | + | 0.234495i | \(0.0753438\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.42705 | − | 1.76336i | −0.186696 | − | 0.135643i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.1246 | + | 34.2380i | 0.850720 | + | 2.61825i | ||||
\(172\) | 12.9443 | + | 9.40456i | 0.986991 | + | 0.717091i | ||||
\(173\) | 12.9443 | − | 9.40456i | 0.984135 | − | 0.715016i | 0.0255059 | − | 0.999675i | \(-0.491880\pi\) |
0.958629 | + | 0.284659i | \(0.0918803\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00000 | −0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.00000 | −0.676481 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.809017 | + | 0.587785i | −0.0604688 | + | 0.0439331i | −0.617609 | − | 0.786485i | \(-0.711899\pi\) |
0.557140 | + | 0.830418i | \(0.311899\pi\) | |||||||
\(180\) | −9.70820 | − | 7.05342i | −0.723607 | − | 0.525731i | ||||
\(181\) | 1.54508 | + | 4.75528i | 0.114845 | + | 0.353457i | 0.991915 | − | 0.126906i | \(-0.0405047\pi\) |
−0.877069 | + | 0.480364i | \(0.840505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.85410 | + | 3.52671i | 0.358826 | + | 0.260702i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.54508 | − | 4.75528i | 0.113597 | − | 0.349615i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −16.0000 | −1.16692 | ||||||||
\(189\) | −2.78115 | + | 8.55951i | −0.202299 | + | 0.622613i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.04508 | − | 2.93893i | −0.292692 | − | 0.212653i | 0.431742 | − | 0.901997i | \(-0.357899\pi\) |
−0.724434 | + | 0.689344i | \(0.757899\pi\) | |||||||
\(192\) | 7.41641 | + | 22.8254i | 0.535233 | + | 1.64728i | ||||
\(193\) | −4.32624 | − | 13.3148i | −0.311409 | − | 0.958420i | −0.977207 | − | 0.212287i | \(-0.931909\pi\) |
0.665798 | − | 0.746132i | \(-0.268091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.70820 | + | 7.05342i | −0.695219 | + | 0.505106i | ||||
\(196\) | −0.618034 | + | 1.90211i | −0.0441453 | + | 0.135865i | ||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.00000 | −0.567105 | −0.283552 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283552 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.28115 | + | 5.29007i | −0.513573 | + | 0.373133i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.09017 | − | 9.51057i | −0.216887 | − | 0.667511i | ||||
\(204\) | −3.70820 | − | 11.4127i | −0.259626 | − | 0.799047i | ||||
\(205\) | 1.61803 | + | 1.17557i | 0.113008 | + | 0.0821054i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.27051 | + | 28.5317i | −0.644345 | + | 1.98309i | ||||
\(208\) | 16.0000 | 1.10940 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.618034 | − | 1.90211i | 0.0425472 | − | 0.130947i | −0.927527 | − | 0.373757i | \(-0.878069\pi\) |
0.970074 | + | 0.242810i | \(0.0780693\pi\) | |||||||
\(212\) | −9.70820 | + | 7.05342i | −0.666762 | + | 0.484431i | ||||
\(213\) | 2.42705 | + | 1.76336i | 0.166299 | + | 0.120823i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.47214 | − | 7.60845i | −0.168598 | − | 0.518892i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.809017 | + | 0.587785i | −0.0549197 | + | 0.0399015i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30.0000 | 2.02721 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.809017 | + | 0.587785i | −0.0541758 | + | 0.0393610i | −0.614544 | − | 0.788883i | \(-0.710660\pi\) |
0.560368 | + | 0.828244i | \(0.310660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.41641 | − | 22.8254i | −0.494427 | − | 1.52169i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.23607 | + | 2.35114i | 0.214785 | + | 0.156051i | 0.689976 | − | 0.723832i | \(-0.257621\pi\) |
−0.475191 | + | 0.879883i | \(0.657621\pi\) | |||||||
\(228\) | −29.1246 | + | 21.1603i | −1.92882 | + | 1.40137i | ||||
\(229\) | −2.16312 | + | 6.65740i | −0.142943 | + | 0.439933i | −0.996741 | − | 0.0806717i | \(-0.974293\pi\) |
0.853798 | + | 0.520605i | \(0.174293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.85410 | + | 5.70634i | −0.121466 | + | 0.373835i | −0.993241 | − | 0.116073i | \(-0.962969\pi\) |
0.871774 | + | 0.489907i | \(0.162969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.47214 | + | 4.70228i | 0.422196 | + | 0.306743i | ||||
\(236\) | −1.85410 | − | 5.70634i | −0.120692 | − | 0.371451i | ||||
\(237\) | 5.56231 | + | 17.1190i | 0.361311 | + | 1.11200i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.23607 | − | 2.35114i | 0.209324 | − | 0.152083i | −0.478184 | − | 0.878260i | \(-0.658705\pi\) |
0.687508 | + | 0.726177i | \(0.258705\pi\) | |||||||
\(240\) | 3.70820 | − | 11.4127i | 0.239364 | − | 0.736685i | ||||
\(241\) | 12.0000 | 0.772988 | 0.386494 | − | 0.922292i | \(-0.373686\pi\) | ||||
0.386494 | + | 0.922292i | \(0.373686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.23607 | + | 3.80423i | −0.0791311 | + | 0.243541i | ||||
\(245\) | 0.809017 | − | 0.587785i | 0.0516862 | − | 0.0375522i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.41641 | + | 22.8254i | 0.471895 | + | 1.45234i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.1246 | − | 21.1603i | −1.84570 | − | 1.34098i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.48936 | + | 19.9722i | −0.409605 | + | 1.26063i | 0.507384 | + | 0.861720i | \(0.330613\pi\) |
−0.916989 | + | 0.398913i | \(0.869387\pi\) | |||||||
\(252\) | −12.0000 | −0.755929 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.85410 | + | 5.70634i | −0.116108 | + | 0.357345i | ||||
\(256\) | −12.9443 | + | 9.40456i | −0.809017 | + | 0.587785i | ||||
\(257\) | 4.85410 | + | 3.52671i | 0.302791 | + | 0.219990i | 0.728797 | − | 0.684730i | \(-0.240080\pi\) |
−0.426006 | + | 0.904720i | \(0.640080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.54508 | − | 4.75528i | −0.0960069 | − | 0.295479i | ||||
\(260\) | −6.47214 | − | 4.70228i | −0.401385 | − | 0.291623i | ||||
\(261\) | 48.5410 | − | 35.2671i | 3.00461 | − | 2.18298i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.0000 | −1.10993 | −0.554964 | − | 0.831875i | \(-0.687268\pi\) | ||||
−0.554964 | + | 0.831875i | \(0.687268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36.4058 | + | 26.4503i | −2.22800 | + | 1.61873i | ||||
\(268\) | −4.85410 | − | 3.52671i | −0.296511 | − | 0.215428i | ||||
\(269\) | −5.56231 | − | 17.1190i | −0.339140 | − | 1.04376i | −0.964647 | − | 0.263546i | \(-0.915108\pi\) |
0.625507 | − | 0.780219i | \(-0.284892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.9443 | + | 9.40456i | 0.786309 | + | 0.571287i | 0.906866 | − | 0.421420i | \(-0.138468\pi\) |
−0.120557 | + | 0.992706i | \(0.538468\pi\) | |||||||
\(272\) | 6.47214 | − | 4.70228i | 0.392431 | − | 0.285118i | ||||
\(273\) | −3.70820 | + | 11.4127i | −0.224431 | + | 0.690727i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −30.0000 | −1.80579 | ||||||||
\(277\) | −7.41641 | + | 22.8254i | −0.445609 | + | 1.37144i | 0.436206 | + | 0.899847i | \(0.356322\pi\) |
−0.881815 | + | 0.471596i | \(0.843678\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.85410 | − | 3.52671i | −0.290607 | − | 0.211139i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.23607 | + | 3.80423i | 0.0737376 | + | 0.226941i | 0.981132 | − | 0.193339i | \(-0.0619318\pi\) |
−0.907394 | + | 0.420280i | \(0.861932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(284\) | −0.618034 | + | 1.90211i | −0.0366736 | + | 0.112870i | ||||
\(285\) | 18.0000 | 1.06623 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.5172 | − | 7.64121i | 0.618660 | − | 0.449483i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.63525 | + | 14.2658i | 0.271723 | + | 0.836279i | ||||
\(292\) | 6.18034 | + | 19.0211i | 0.361677 | + | 1.11313i | ||||
\(293\) | −4.85410 | − | 3.52671i | −0.283580 | − | 0.206033i | 0.436898 | − | 0.899511i | \(-0.356077\pi\) |
−0.720477 | + | 0.693479i | \(0.756077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.927051 | + | 2.85317i | −0.0539750 | + | 0.166118i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.18034 | + | 19.0211i | −0.357418 | + | 1.10002i | ||||
\(300\) | 19.4164 | − | 14.1068i | 1.12101 | − | 0.814459i | ||||
\(301\) | −6.47214 | − | 4.70228i | −0.373048 | − | 0.271035i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.1246 | − | 34.2380i | −0.639092 | − | 1.96692i | ||||
\(304\) | −19.4164 | − | 14.1068i | −1.11361 | − | 0.809083i | ||||
\(305\) | 1.61803 | − | 1.17557i | 0.0926484 | − | 0.0673130i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 36.0000 | 2.04797 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.47214 | + | 4.70228i | −0.367001 | + | 0.266642i | −0.755966 | − | 0.654611i | \(-0.772833\pi\) |
0.388965 | + | 0.921252i | \(0.372833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.10739 | − | 21.8743i | −0.401733 | − | 1.23641i | −0.923592 | − | 0.383377i | \(-0.874761\pi\) |
0.521859 | − | 0.853032i | \(-0.325239\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.85410 | + | 3.52671i | 0.273498 | + | 0.198708i | ||||
\(316\) | −9.70820 | + | 7.05342i | −0.546129 | + | 0.396786i | ||||
\(317\) | 2.78115 | − | 8.55951i | 0.156205 | − | 0.480750i | −0.842076 | − | 0.539359i | \(-0.818667\pi\) |
0.998281 | + | 0.0586092i | \(0.0186666\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.00000 | 0.447214 | ||||||||
\(321\) | −9.27051 | + | 28.5317i | −0.517429 | + | 1.59248i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.70820 | + | 7.05342i | 0.540179 | + | 0.392463i | ||||
\(324\) | −5.56231 | − | 17.1190i | −0.309017 | − | 0.951057i | ||||
\(325\) | −4.94427 | − | 15.2169i | −0.274259 | − | 0.844082i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.70820 | + | 7.05342i | −0.536865 | + | 0.390055i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.0000 | −0.934405 | −0.467202 | − | 0.884150i | \(-0.654738\pi\) | ||||
−0.467202 | + | 0.884150i | \(0.654738\pi\) | |||||||
\(332\) | 7.41641 | − | 22.8254i | 0.407028 | − | 1.25270i | ||||
\(333\) | 24.2705 | − | 17.6336i | 1.33002 | − | 0.966313i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.927051 | + | 2.85317i | 0.0506502 | + | 0.155885i | ||||
\(336\) | −3.70820 | − | 11.4127i | −0.202299 | − | 0.622613i | ||||
\(337\) | −14.5623 | − | 10.5801i | −0.793259 | − | 0.576337i | 0.115670 | − | 0.993288i | \(-0.463099\pi\) |
−0.908929 | + | 0.416951i | \(0.863099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.6140 | − | 54.2102i | 0.956659 | − | 2.94430i | ||||
\(340\) | −4.00000 | −0.216930 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.309017 | − | 0.951057i | 0.0166853 | − | 0.0513522i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.1353 | + | 8.81678i | 0.653340 | + | 0.474679i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.32624 | − | 13.3148i | −0.232245 | − | 0.714775i | −0.997475 | − | 0.0710189i | \(-0.977375\pi\) |
0.765230 | − | 0.643757i | \(-0.222625\pi\) | |||||||
\(348\) | 48.5410 | + | 35.2671i | 2.60207 | + | 1.89052i | ||||
\(349\) | −27.5066 | + | 19.9847i | −1.47239 | + | 1.06976i | −0.492482 | + | 0.870323i | \(0.663910\pi\) |
−0.979911 | + | 0.199434i | \(0.936090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −36.0000 | −1.92154 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.00000 | 0.479022 | 0.239511 | − | 0.970894i | \(-0.423013\pi\) | ||||
0.239511 | + | 0.970894i | \(0.423013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.809017 | − | 0.587785i | 0.0429382 | − | 0.0311964i | ||||
\(356\) | −24.2705 | − | 17.6336i | −1.28633 | − | 0.934577i | ||||
\(357\) | 1.85410 | + | 5.70634i | 0.0981295 | + | 0.302011i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.47214 | + | 4.70228i | 0.341586 | + | 0.248177i | 0.745331 | − | 0.666695i | \(-0.232292\pi\) |
−0.403745 | + | 0.914872i | \(0.632292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.25329 | − | 16.1680i | 0.276489 | − | 0.850945i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.00000 | −0.419314 | ||||||||
\(365\) | 3.09017 | − | 9.51057i | 0.161747 | − | 0.497806i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.89919 | + | 6.46564i | 0.464534 | + | 0.337504i | 0.795307 | − | 0.606207i | \(-0.207310\pi\) |
−0.330773 | + | 0.943710i | \(0.607310\pi\) | |||||||
\(368\) | −6.18034 | − | 19.0211i | −0.322172 | − | 0.991545i | ||||
\(369\) | 3.70820 | + | 11.4127i | 0.193041 | + | 0.594120i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.85410 | − | 3.52671i | 0.252012 | − | 0.183098i | ||||
\(372\) | 1.85410 | − | 5.70634i | 0.0961307 | − | 0.295860i | ||||
\(373\) | 4.00000 | 0.207112 | 0.103556 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103556 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −27.0000 | −1.39427 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.3607 | − | 23.5114i | 1.66666 | − | 1.21090i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.96149 | − | 27.5806i | −0.460321 | − | 1.41672i | −0.864773 | − | 0.502163i | \(-0.832538\pi\) |
0.404452 | − | 0.914559i | \(-0.367462\pi\) | |||||||
\(380\) | 3.70820 | + | 11.4127i | 0.190227 | + | 0.585458i | ||||
\(381\) | −4.85410 | − | 3.52671i | −0.248683 | − | 0.180679i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.25329 | − | 16.1680i | 0.268431 | − | 0.826144i | −0.722453 | − | 0.691420i | \(-0.756985\pi\) |
0.990883 | − | 0.134724i | \(-0.0430147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.8328 | − | 45.6507i | 0.753994 | − | 2.32056i | ||||
\(388\) | −8.09017 | + | 5.87785i | −0.410716 | + | 0.298403i | ||||
\(389\) | −7.28115 | − | 5.29007i | −0.369169 | − | 0.268217i | 0.387697 | − | 0.921787i | \(-0.373271\pi\) |
−0.756866 | + | 0.653570i | \(0.773271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.09017 | + | 9.51057i | 0.156277 | + | 0.480970i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −43.6869 | + | 31.7404i | −2.20371 | + | 1.60109i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.00000 | 0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0000 | 0.903394 | 0.451697 | − | 0.892171i | \(-0.350819\pi\) | ||||
0.451697 | + | 0.892171i | \(0.350819\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.5623 | − | 10.5801i | 0.729027 | − | 0.529669i | ||||
\(400\) | 12.9443 | + | 9.40456i | 0.647214 | + | 0.470228i | ||||
\(401\) | −1.85410 | − | 5.70634i | −0.0925894 | − | 0.284961i | 0.894029 | − | 0.448010i | \(-0.147867\pi\) |
−0.986618 | + | 0.163049i | \(0.947867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.23607 | − | 2.35114i | −0.161200 | − | 0.117119i | ||||
\(404\) | 19.4164 | − | 14.1068i | 0.966002 | − | 0.701842i | ||||
\(405\) | −2.78115 | + | 8.55951i | −0.138197 | + | 0.425325i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.03444 | − | 24.7275i | 0.397278 | − | 1.22269i | −0.529896 | − | 0.848063i | \(-0.677769\pi\) |
0.927174 | − | 0.374632i | \(-0.122231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.28115 | − | 5.29007i | −0.359153 | − | 0.260940i | ||||
\(412\) | 7.41641 | + | 22.8254i | 0.365380 | + | 1.12452i | ||||
\(413\) | 0.927051 | + | 2.85317i | 0.0456172 | + | 0.140395i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.70820 | + | 7.05342i | −0.476557 | + | 0.346239i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.0000 | −1.46911 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.0000 | 0.781651 | 0.390826 | − | 0.920465i | \(-0.372190\pi\) | ||||
0.390826 | + | 0.920465i | \(0.372190\pi\) | |||||||
\(420\) | −1.85410 | + | 5.70634i | −0.0904709 | + | 0.278441i | ||||
\(421\) | −17.7984 | + | 12.9313i | −0.867440 | + | 0.630232i | −0.929899 | − | 0.367816i | \(-0.880106\pi\) |
0.0624590 | + | 0.998048i | \(0.480106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.8328 | + | 45.6507i | 0.721196 | + | 2.21961i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.47214 | − | 4.70228i | −0.313945 | − | 0.228094i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.618034 | − | 1.90211i | 0.0299088 | − | 0.0920497i | ||||
\(428\) | −20.0000 | −0.966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.18034 | − | 19.0211i | 0.297696 | − | 0.916216i | −0.684606 | − | 0.728913i | \(-0.740026\pi\) |
0.982302 | − | 0.187302i | \(-0.0599743\pi\) | |||||||
\(432\) | 29.1246 | − | 21.1603i | 1.40126 | − | 1.01807i | ||||
\(433\) | 20.2254 | + | 14.6946i | 0.971972 | + | 0.706179i | 0.955900 | − | 0.293692i | \(-0.0948840\pi\) |
0.0160718 | + | 0.999871i | \(0.494884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.27051 | − | 28.5317i | −0.444487 | − | 1.36799i | ||||
\(436\) | −6.47214 | − | 4.70228i | −0.309959 | − | 0.225198i | ||||
\(437\) | 24.2705 | − | 17.6336i | 1.16102 | − | 0.843527i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | 0.668184 | 0.334092 | − | 0.942541i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942541i | \(0.391570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.00000 | 0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.5517 | − | 22.9236i | 1.49906 | − | 1.08913i | 0.528313 | − | 0.849050i | \(-0.322825\pi\) |
0.970752 | − | 0.240084i | \(-0.0771751\pi\) | |||||||
\(444\) | 24.2705 | + | 17.6336i | 1.15183 | + | 0.836852i | ||||
\(445\) | 4.63525 | + | 14.2658i | 0.219732 | + | 0.676266i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 53.3951 | + | 38.7938i | 2.52550 | + | 1.83489i | ||||
\(448\) | 6.47214 | − | 4.70228i | 0.305780 | − | 0.222162i | ||||
\(449\) | 4.63525 | − | 14.2658i | 0.218751 | − | 0.673247i | −0.780115 | − | 0.625636i | \(-0.784839\pi\) |
0.998866 | − | 0.0476105i | \(-0.0151606\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 38.0000 | 1.78737 | ||||||||
\(453\) | 5.56231 | − | 17.1190i | 0.261340 | − | 0.804322i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.23607 | + | 2.35114i | 0.151709 | + | 0.110223i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.47214 | − | 7.60845i | −0.115642 | − | 0.355908i | 0.876439 | − | 0.481514i | \(-0.159913\pi\) |
−0.992080 | + | 0.125605i | \(0.959913\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.5623 | + | 10.5801i | −0.679710 | + | 0.493838i | ||||
\(460\) | −3.09017 | + | 9.51057i | −0.144080 | + | 0.443432i | ||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0000 | 0.604161 | 0.302081 | − | 0.953282i | \(-0.402319\pi\) | ||||
0.302081 | + | 0.953282i | \(0.402319\pi\) | |||||||
\(464\) | −12.3607 | + | 38.0423i | −0.573830 | + | 1.76607i | ||||
\(465\) | −2.42705 | + | 1.76336i | −0.112552 | + | 0.0817737i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.927051 | + | 2.85317i | 0.0428988 | + | 0.132029i | 0.970212 | − | 0.242257i | \(-0.0778878\pi\) |
−0.927313 | + | 0.374286i | \(0.877888\pi\) | |||||||
\(468\) | −14.8328 | − | 45.6507i | −0.685647 | − | 2.11020i | ||||
\(469\) | 2.42705 | + | 1.76336i | 0.112071 | + | 0.0814242i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.48936 | + | 19.9722i | −0.299014 | + | 0.920270i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.41641 | + | 22.8254i | −0.340288 | + | 1.04730i | ||||
\(476\) | −3.23607 | + | 2.35114i | −0.148325 | + | 0.107764i | ||||
\(477\) | 29.1246 | + | 21.1603i | 1.33352 | + | 0.968862i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.65248 | + | 26.6296i | 0.395342 | + | 1.21674i | 0.928695 | + | 0.370844i | \(0.120932\pi\) |
−0.533353 | + | 0.845893i | \(0.679068\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.1803 | − | 11.7557i | 0.737760 | − | 0.536014i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.0000 | 0.682524 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.00000 | 0.227038 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5172 | − | 7.64121i | 0.476581 | − | 0.346256i | −0.323420 | − | 0.946256i | \(-0.604833\pi\) |
0.800000 | + | 0.599999i | \(0.204833\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.70820 | − | 11.4127i | −0.167691 | − | 0.516099i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.2705 | − | 17.6336i | −1.09531 | − | 0.795791i | −0.115024 | − | 0.993363i | \(-0.536695\pi\) |
−0.980289 | + | 0.197571i | \(0.936695\pi\) | |||||||
\(492\) | −9.70820 | + | 7.05342i | −0.437680 | + | 0.317993i | ||||
\(493\) | 6.18034 | − | 19.0211i | 0.278349 | − | 0.856669i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 0.309017 | − | 0.951057i | 0.0138613 | − | 0.0426607i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.5967 | − | 25.8626i | −1.59353 | − | 1.15777i | −0.898674 | − | 0.438617i | \(-0.855468\pi\) |
−0.694855 | − | 0.719150i | \(-0.744532\pi\) | |||||||
\(500\) | −5.56231 | − | 17.1190i | −0.248754 | − | 0.765586i | ||||
\(501\) | −1.85410 | − | 5.70634i | −0.0828352 | − | 0.254940i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 1.23607 | − | 3.80423i | 0.0548416 | − | 0.168785i | ||||
\(509\) | 25.0795 | − | 18.2213i | 1.11163 | − | 0.807647i | 0.128711 | − | 0.991682i | \(-0.458916\pi\) |
0.982920 | + | 0.184035i | \(0.0589161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.09017 | − | 9.51057i | −0.136701 | − | 0.420723i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 43.6869 | + | 31.7404i | 1.92882 | + | 1.40137i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.70820 | − | 11.4127i | 0.163403 | − | 0.502903i | ||||
\(516\) | 48.0000 | 2.11308 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.8328 | − | 45.6507i | 0.651088 | − | 2.00384i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.66312 | − | 4.11450i | −0.248106 | − | 0.180259i | 0.456781 | − | 0.889579i | \(-0.349002\pi\) |
−0.704887 | + | 0.709320i | \(0.749002\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.88854 | − | 30.4338i | −0.432396 | − | 1.33078i | −0.895732 | − | 0.444595i | \(-0.853348\pi\) |
0.463336 | − | 0.886183i | \(-0.346652\pi\) | |||||||
\(524\) | −29.1246 | − | 21.1603i | −1.27231 | − | 0.924391i | ||||
\(525\) | −9.70820 | + | 7.05342i | −0.423701 | + | 0.307837i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.00000 | −0.0871214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | 0.0869565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.5623 | + | 10.5801i | −0.631950 | + | 0.459139i | ||||
\(532\) | 9.70820 | + | 7.05342i | 0.420904 | + | 0.305805i | ||||
\(533\) | 2.47214 | + | 7.60845i | 0.107080 | + | 0.329559i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.09017 | + | 5.87785i | 0.349769 | + | 0.254122i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.927051 | + | 2.85317i | −0.0400052 | + | 0.123123i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −18.0000 | −0.774597 | ||||||||
\(541\) | −9.88854 | + | 30.4338i | −0.425142 | + | 1.30845i | 0.477717 | + | 0.878514i | \(0.341464\pi\) |
−0.902859 | + | 0.429938i | \(0.858536\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.1353 | + | 8.81678i | 0.520774 | + | 0.378364i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.23607 | + | 3.80423i | 0.0529473 | + | 0.162955i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.4164 | + | 14.1068i | −0.830186 | + | 0.603165i | −0.919612 | − | 0.392828i | \(-0.871497\pi\) |
0.0894262 | + | 0.995993i | \(0.471497\pi\) | |||||||
\(548\) | 1.85410 | − | 5.70634i | 0.0792033 | − | 0.243763i | ||||
\(549\) | 12.0000 | 0.512148 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −60.0000 | −2.55609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.85410 | − | 3.52671i | 0.206417 | − | 0.149971i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.63525 | − | 14.2658i | −0.196756 | − | 0.605552i | ||||
\(556\) | −6.18034 | − | 19.0211i | −0.262105 | − | 0.806676i | ||||
\(557\) | 11.3262 | + | 8.22899i | 0.479908 | + | 0.348674i | 0.801290 | − | 0.598276i | \(-0.204147\pi\) |
−0.321382 | + | 0.946950i | \(0.604147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.88854 | − | 30.4338i | 0.418241 | − | 1.28721i | ||||
\(560\) | −4.00000 | −0.169031 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.18034 | + | 19.0211i | −0.260470 | + | 0.801645i | 0.732232 | + | 0.681055i | \(0.238479\pi\) |
−0.992702 | + | 0.120590i | \(0.961521\pi\) | |||||||
\(564\) | −38.8328 | + | 28.2137i | −1.63516 | + | 1.18801i | ||||
\(565\) | −15.3713 | − | 11.1679i | −0.646676 | − | 0.469838i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.78115 | + | 8.55951i | 0.116797 | + | 0.359466i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.5623 | + | 10.5801i | −0.610484 | + | 0.443542i | −0.849585 | − | 0.527452i | \(-0.823147\pi\) |
0.239101 | + | 0.970995i | \(0.423147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.0000 | −0.626634 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.1803 | + | 11.7557i | −0.674767 | + | 0.490247i | ||||
\(576\) | 38.8328 | + | 28.2137i | 1.61803 | + | 1.17557i | ||||
\(577\) | −7.72542 | − | 23.7764i | −0.321614 | − | 0.989825i | −0.972946 | − | 0.231032i | \(-0.925790\pi\) |
0.651332 | − | 0.758793i | \(-0.274210\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.9787 | − | 24.6870i | −1.41211 | − | 1.02596i | ||||
\(580\) | 16.1803 | − | 11.7557i | 0.671852 | − | 0.488129i | ||||
\(581\) | −3.70820 | + | 11.4127i | −0.153842 | + | 0.473478i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.41641 | + | 22.8254i | −0.306631 | + | 0.943712i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.1246 | − | 21.1603i | −1.20210 | − | 0.873378i | −0.207612 | − | 0.978211i | \(-0.566569\pi\) |
−0.994490 | + | 0.104834i | \(0.966569\pi\) | |||||||
\(588\) | 1.85410 | + | 5.70634i | 0.0764619 | + | 0.235325i | ||||
\(589\) | 1.85410 | + | 5.70634i | 0.0763969 | + | 0.235126i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43.6869 | + | 31.7404i | −1.79704 | + | 1.30563i | ||||
\(592\) | −6.18034 | + | 19.0211i | −0.254010 | + | 0.781764i | ||||
\(593\) | −30.0000 | −1.23195 | −0.615976 | − | 0.787765i | \(-0.711238\pi\) | ||||
−0.615976 | + | 0.787765i | \(0.711238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.00000 | 0.0819920 | ||||||||
\(596\) | −13.5967 | + | 41.8465i | −0.556944 | + | 1.71410i | ||||
\(597\) | −19.4164 | + | 14.1068i | −0.794661 | + | 0.577355i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.8328 | − | 45.6507i | −0.606052 | − | 1.86524i | −0.489388 | − | 0.872066i | \(-0.662780\pi\) |
−0.116664 | − | 0.993171i | \(-0.537220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.47214 | + | 4.70228i | 0.264004 | + | 0.191810i | 0.711910 | − | 0.702270i | \(-0.247830\pi\) |
−0.447906 | + | 0.894080i | \(0.647830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.56231 | + | 17.1190i | −0.226515 | + | 0.697140i | ||||
\(604\) | 12.0000 | 0.488273 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.09017 | − | 9.51057i | 0.125426 | − | 0.386022i | −0.868552 | − | 0.495597i | \(-0.834949\pi\) |
0.993978 | + | 0.109576i | \(0.0349491\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.2705 | − | 17.6336i | −0.983491 | − | 0.714548i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.88854 | + | 30.4338i | 0.400048 | + | 1.23122i | ||||
\(612\) | −19.4164 | − | 14.1068i | −0.784862 | − | 0.570235i | ||||
\(613\) | 12.9443 | − | 9.40456i | 0.522814 | − | 0.379847i | −0.294849 | − | 0.955544i | \(-0.595269\pi\) |
0.817663 | + | 0.575697i | \(0.195269\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.00000 | 0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7533 | + | 9.99235i | −0.552791 | + | 0.401626i | −0.828814 | − | 0.559525i | \(-0.810984\pi\) |
0.276022 | + | 0.961151i | \(0.410984\pi\) | |||||||
\(620\) | −1.61803 | − | 1.17557i | −0.0649818 | − | 0.0472120i | ||||
\(621\) | 13.9058 | + | 42.7975i | 0.558019 | + | 1.71741i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.1353 | + | 8.81678i | 0.486189 | + | 0.353237i | ||||
\(624\) | 38.8328 | − | 28.2137i | 1.55456 | − | 1.12945i | ||||
\(625\) | 3.39919 | − | 10.4616i | 0.135967 | − | 0.418465i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0000 | −0.558661 | ||||||||
\(629\) | 3.09017 | − | 9.51057i | 0.123213 | − | 0.379211i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.8435 | − | 15.8702i | −0.869574 | − | 0.631783i | 0.0608983 | − | 0.998144i | \(-0.480603\pi\) |
−0.930473 | + | 0.366361i | \(0.880603\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.85410 | − | 5.70634i | −0.0736939 | − | 0.226807i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.61803 | + | 1.17557i | −0.0642097 | + | 0.0466511i | ||||
\(636\) | −11.1246 | + | 34.2380i | −0.441120 | + | 1.35763i | ||||
\(637\) | 4.00000 | 0.158486 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.1353 | + | 8.81678i | −0.479314 | + | 0.348242i | −0.801060 | − | 0.598584i | \(-0.795730\pi\) |
0.321746 | + | 0.946826i | \(0.395730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.96149 | − | 27.5806i | −0.353407 | − | 1.08767i | −0.956928 | − | 0.290327i | \(-0.906236\pi\) |
0.603521 | − | 0.797347i | \(-0.293764\pi\) | |||||||
\(644\) | 3.09017 | + | 9.51057i | 0.121770 | + | 0.374769i | ||||
\(645\) | −19.4164 | − | 14.1068i | −0.764520 | − | 0.555457i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.48936 | + | 19.9722i | −0.255123 | + | 0.785188i | 0.738682 | + | 0.674054i | \(0.235448\pi\) |
−0.993805 | + | 0.111134i | \(0.964552\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.927051 | + | 2.85317i | −0.0363340 | + | 0.111825i | ||||
\(652\) | 6.47214 | − | 4.70228i | 0.253468 | − | 0.184156i | ||||
\(653\) | 13.7533 | + | 9.99235i | 0.538208 | + | 0.391031i | 0.823419 | − | 0.567434i | \(-0.192064\pi\) |
−0.285211 | + | 0.958465i | \(0.592064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.56231 | + | 17.1190i | 0.217337 | + | 0.668895i | ||||
\(656\) | −6.47214 | − | 4.70228i | −0.252694 | − | 0.183593i | ||||
\(657\) | 48.5410 | − | 35.2671i | 1.89377 | − | 1.37590i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.00000 | 0.0779089 | 0.0389545 | − | 0.999241i | \(-0.487597\pi\) | ||||
0.0389545 | + | 0.999241i | \(0.487597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.0000 | 1.36134 | 0.680671 | − | 0.732589i | \(-0.261688\pi\) | ||||
0.680671 | + | 0.732589i | \(0.261688\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.4164 | + | 14.1068i | −0.754071 | + | 0.547865i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.85410 | − | 5.70634i | −0.0718990 | − | 0.221282i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −40.4508 | − | 29.3893i | −1.56626 | − | 1.13796i | ||||
\(668\) | 3.23607 | − | 2.35114i | 0.125207 | − | 0.0909684i | ||||
\(669\) | −0.927051 | + | 2.85317i | −0.0358419 | + | 0.110310i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.23607 | + | 3.80423i | −0.0476469 | + | 0.146642i | −0.972049 | − | 0.234776i | \(-0.924564\pi\) |
0.924403 | + | 0.381418i | \(0.124564\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −29.1246 | − | 21.1603i | −1.12101 | − | 0.814459i | ||||
\(676\) | −1.85410 | − | 5.70634i | −0.0713116 | − | 0.219475i | ||||
\(677\) | −11.7426 | − | 36.1401i | −0.451307 | − | 1.38898i | −0.875417 | − | 0.483368i | \(-0.839413\pi\) |
0.424111 | − | 0.905610i | \(-0.360587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.04508 | − | 2.93893i | 0.155236 | − | 0.112786i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | −22.2492 | + | 68.4761i | −0.850720 | + | 2.61825i | ||||
\(685\) | −2.42705 | + | 1.76336i | −0.0927329 | + | 0.0673744i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.48936 | + | 19.9722i | 0.247584 | + | 0.761986i | ||||
\(688\) | 9.88854 | + | 30.4338i | 0.376997 | + | 1.16028i | ||||
\(689\) | 19.4164 | + | 14.1068i | 0.739706 | + | 0.537428i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.63525 | − | 14.2658i | 0.176333 | − | 0.542698i | −0.823358 | − | 0.567522i | \(-0.807902\pi\) |
0.999692 | + | 0.0248233i | \(0.00790230\pi\) | |||||||
\(692\) | 32.0000 | 1.21646 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.09017 | + | 9.51057i | −0.117217 | + | 0.360756i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.23607 | + | 2.35114i | 0.122575 | + | 0.0890558i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.56231 | + | 17.1190i | 0.210386 | + | 0.647501i | ||||
\(700\) | −6.47214 | − | 4.70228i | −0.244624 | − | 0.177730i | ||||
\(701\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.0000 | −1.13147 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.0000 | 0.903892 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.70820 | + | 7.05342i | −0.365115 | + | 0.265271i | ||||
\(708\) | −14.5623 | − | 10.5801i | −0.547285 | − | 0.397626i | ||||
\(709\) | 12.0517 | + | 37.0912i | 0.452610 | + | 1.39299i | 0.873919 | + | 0.486072i | \(0.161571\pi\) |
−0.421309 | + | 0.906917i | \(0.638429\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.1246 | + | 21.1603i | 1.09226 | + | 0.793572i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.54508 | + | 4.75528i | −0.0578639 | + | 0.178087i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.00000 | −0.0747435 | ||||||||
\(717\) | 3.70820 | − | 11.4127i | 0.138485 | − | 0.426214i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.89919 | + | 6.46564i | 0.331884 | + | 0.241128i | 0.741229 | − | 0.671252i | \(-0.234243\pi\) |
−0.409346 | + | 0.912379i | \(0.634243\pi\) | |||||||
\(720\) | −7.41641 | − | 22.8254i | −0.276393 | − | 0.850651i | ||||
\(721\) | −3.70820 | − | 11.4127i | −0.138101 | − | 0.425030i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.1246 | − | 21.1603i | 1.08316 | − | 0.786959i | ||||
\(724\) | −3.09017 | + | 9.51057i | −0.114845 | + | 0.353457i | ||||
\(725\) | 40.0000 | 1.48556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.0000 | −0.704671 | −0.352335 | − | 0.935874i | \(-0.614612\pi\) | ||||
−0.352335 | + | 0.935874i | \(0.614612\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.8435 | − | 15.8702i | 0.809017 | − | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.94427 | − | 15.2169i | −0.182871 | − | 0.562818i | ||||
\(732\) | 3.70820 | + | 11.4127i | 0.137059 | + | 0.421825i | ||||
\(733\) | −3.23607 | − | 2.35114i | −0.119527 | − | 0.0868414i | 0.526416 | − | 0.850227i | \(-0.323536\pi\) |
−0.645943 | + | 0.763386i | \(0.723536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.927051 | − | 2.85317i | 0.0341948 | − | 0.105241i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.56231 | − | 17.1190i | 0.204613 | − | 0.629733i | −0.795116 | − | 0.606457i | \(-0.792590\pi\) |
0.999729 | − | 0.0232763i | \(-0.00740975\pi\) | |||||||
\(740\) | 8.09017 | − | 5.87785i | 0.297401 | − | 0.216074i | ||||
\(741\) | 58.2492 | + | 42.3205i | 2.13984 | + | 1.55468i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.41641 | + | 22.8254i | 0.272082 | + | 0.837381i | 0.989977 | + | 0.141230i | \(0.0451057\pi\) |
−0.717895 | + | 0.696151i | \(0.754894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.7984 | − | 12.9313i | 0.652082 | − | 0.473765i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −72.0000 | −2.63434 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.0000 | 0.365392 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.6074 | − | 13.5191i | 0.678993 | − | 0.493318i | −0.194030 | − | 0.980996i | \(-0.562156\pi\) |
0.873024 | + | 0.487678i | \(0.162156\pi\) | |||||||
\(752\) | −25.8885 | − | 18.8091i | −0.944058 | − | 0.685898i | ||||
\(753\) | 19.4681 | + | 59.9166i | 0.709456 | + | 2.18348i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.85410 | − | 3.52671i | −0.176659 | − | 0.128350i | ||||
\(756\) | −14.5623 | + | 10.5801i | −0.529626 | + | 0.384796i | ||||
\(757\) | 11.7426 | − | 36.1401i | 0.426794 | − | 1.31354i | −0.474473 | − | 0.880270i | \(-0.657361\pi\) |
0.901266 | − | 0.433266i | \(-0.142639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.8328 | − | 45.6507i | 0.537689 | − | 1.65484i | −0.200077 | − | 0.979780i | \(-0.564119\pi\) |
0.737766 | − | 0.675057i | \(-0.235881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.23607 | + | 2.35114i | 0.117154 | + | 0.0851170i | ||||
\(764\) | −3.09017 | − | 9.51057i | −0.111798 | − | 0.344080i | ||||
\(765\) | 3.70820 | + | 11.4127i | 0.134070 | + | 0.412626i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.70820 | + | 7.05342i | −0.350543 | + | 0.254684i | ||||
\(768\) | −14.8328 | + | 45.6507i | −0.535233 | + | 1.64728i | ||||
\(769\) | −40.0000 | −1.44244 | −0.721218 | − | 0.692708i | \(-0.756418\pi\) | ||||
−0.721218 | + | 0.692708i | \(0.756418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | 8.65248 | − | 26.6296i | 0.311409 | − | 0.958420i | ||||
\(773\) | 4.85410 | − | 3.52671i | 0.174590 | − | 0.126847i | −0.497059 | − | 0.867717i | \(-0.665587\pi\) |
0.671648 | + | 0.740870i | \(0.265587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.23607 | − | 3.80423i | −0.0444009 | − | 0.136652i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.1353 | − | 8.81678i | −0.435350 | − | 0.316300i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.70820 | − | 11.4127i | 0.132860 | − | 0.408902i | ||||
\(780\) | −24.0000 | −0.859338 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.8115 | − | 85.5951i | 0.993903 | − | 3.05892i | ||||
\(784\) | −3.23607 | + | 2.35114i | −0.115574 | + | 0.0839693i | ||||
\(785\) | 5.66312 | + | 4.11450i | 0.202125 | + | 0.146853i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.79837 | + | 20.9232i | 0.242336 | + | 0.745833i | 0.996063 | + | 0.0886458i | \(0.0282539\pi\) |
−0.753727 | + | 0.657187i | \(0.771746\pi\) | |||||||
\(788\) | −29.1246 | − | 21.1603i | −1.03752 | − | 0.753803i | ||||
\(789\) | −43.6869 | + | 31.7404i | −1.55530 | + | 1.12999i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.0000 | −0.675562 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000 | 0.284088 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.5623 | − | 10.5801i | 0.516472 | − | 0.375239i | ||||
\(796\) | −12.9443 | − | 9.40456i | −0.458798 | − | 0.333336i | ||||
\(797\) | 7.10739 | + | 21.8743i | 0.251757 | + | 0.774827i | 0.994451 | + | 0.105197i | \(0.0335474\pi\) |
−0.742695 | + | 0.669630i | \(0.766453\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9443 | + | 9.40456i | 0.457935 | + | 0.332710i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.8115 | + | 85.5951i | −0.982672 | + | 3.02435i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −18.0000 | −0.634811 | ||||||||
\(805\) | 1.54508 | − | 4.75528i | 0.0544571 | − | 0.167602i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −43.6869 | − | 31.7404i | −1.53785 | − | 1.11732i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.27051 | − | 28.5317i | −0.325934 | − | 1.00312i | −0.971017 | − | 0.239009i | \(-0.923177\pi\) |
0.645084 | − | 0.764112i | \(-0.276823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.7984 | + | 12.9313i | −0.624985 | + | 0.454078i | −0.854659 | − | 0.519189i | \(-0.826234\pi\) |
0.229674 | + | 0.973268i | \(0.426234\pi\) | |||||||
\(812\) | 6.18034 | − | 19.0211i | 0.216887 | − | 0.667511i | ||||
\(813\) | 48.0000 | 1.68343 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | −0.140114 | ||||||||
\(816\) | 7.41641 | − | 22.8254i | 0.259626 | − | 0.799047i | ||||
\(817\) | −38.8328 | + | 28.2137i | −1.35859 | + | 0.987072i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.41641 | + | 22.8254i | 0.259150 | + | 0.797582i | ||||
\(820\) | 1.23607 | + | 3.80423i | 0.0431654 | + | 0.132849i | ||||
\(821\) | 14.5623 | + | 10.5801i | 0.508228 | + | 0.369249i | 0.812151 | − | 0.583447i | \(-0.198297\pi\) |
−0.303923 | + | 0.952697i | \(0.598297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.72542 | + | 23.7764i | −0.269291 | + | 0.828794i | 0.721382 | + | 0.692537i | \(0.243507\pi\) |
−0.990674 | + | 0.136257i | \(0.956493\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.18034 | + | 19.0211i | −0.214911 | + | 0.661430i | 0.784248 | + | 0.620447i | \(0.213049\pi\) |
−0.999160 | + | 0.0409825i | \(0.986951\pi\) | |||||||
\(828\) | −48.5410 | + | 35.2671i | −1.68692 | + | 1.22562i | ||||
\(829\) | 23.4615 | + | 17.0458i | 0.814851 | + | 0.592024i | 0.915233 | − | 0.402925i | \(-0.132006\pi\) |
−0.100382 | + | 0.994949i | \(0.532006\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.2492 | + | 68.4761i | 0.771817 | + | 2.37541i | ||||
\(832\) | 25.8885 | + | 18.8091i | 0.897524 | + | 0.652089i | ||||
\(833\) | 1.61803 | − | 1.17557i | 0.0560616 | − | 0.0407311i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.00000 | −0.0692129 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.00000 | −0.311086 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.4058 | + | 26.4503i | −1.25687 | + | 0.913167i | −0.998599 | − | 0.0529065i | \(-0.983151\pi\) |
−0.258267 | + | 0.966074i | \(0.583151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.9402 | + | 67.5250i | 0.756559 | + | 2.32845i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.70820 | + | 7.05342i | 0.334368 | + | 0.242933i | ||||
\(844\) | 3.23607 | − | 2.35114i | 0.111390 | − | 0.0809296i | ||||
\(845\) | −0.927051 | + | 2.85317i | −0.0318915 | + | 0.0981520i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24.0000 | −0.824163 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.2254 | − | 14.6946i | −0.693319 | − | 0.503725i | ||||
\(852\) | 1.85410 | + | 5.70634i | 0.0635205 | + | 0.195496i | ||||
\(853\) | 10.5066 | + | 32.3359i | 0.359738 | + | 1.10716i | 0.953211 | + | 0.302307i | \(0.0977566\pi\) |
−0.593472 | + | 0.804854i | \(0.702243\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.1246 | − | 21.1603i | 0.996041 | − | 0.723666i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.0000 | 0.956462 | 0.478231 | − | 0.878234i | \(-0.341278\pi\) | ||||
0.478231 | + | 0.878234i | \(0.341278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.0000 | 1.87658 | 0.938288 | − | 0.345855i | \(-0.112411\pi\) | ||||
0.938288 | + | 0.345855i | \(0.112411\pi\) | |||||||
\(860\) | 4.94427 | − | 15.2169i | 0.168598 | − | 0.518892i | ||||
\(861\) | 4.85410 | − | 3.52671i | 0.165427 | − | 0.120190i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.0689 | + | 49.4549i | 0.546991 | + | 1.68347i | 0.716208 | + | 0.697887i | \(0.245876\pi\) |
−0.169217 | + | 0.985579i | \(0.554124\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.9443 | − | 9.40456i | −0.440118 | − | 0.319765i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.0517 | − | 37.0912i | 0.409296 | − | 1.25968i | ||||
\(868\) | −2.00000 | −0.0678844 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.70820 | + | 11.4127i | −0.125648 | + | 0.386704i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.2705 | + | 17.6336i | 0.821432 | + | 0.596806i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.78115 | + | 8.55951i | 0.0940201 | + | 0.289364i | ||||
\(876\) | 48.5410 | + | 35.2671i | 1.64005 | + | 1.19157i | ||||
\(877\) | −30.7426 | + | 22.3358i | −1.03811 | + | 0.754228i | −0.969915 | − | 0.243445i | \(-0.921723\pi\) |
−0.0681906 | + | 0.997672i | \(0.521723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.0000 | −0.607125 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.0000 | 0.909653 | 0.454827 | − | 0.890580i | \(-0.349701\pi\) | ||||
0.454827 | + | 0.890580i | \(0.349701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.5967 | − | 25.8626i | 1.19793 | − | 0.870344i | 0.203847 | − | 0.979003i | \(-0.434656\pi\) |
0.994079 | + | 0.108659i | \(0.0346555\pi\) | |||||||
\(884\) | −12.9443 | − | 9.40456i | −0.435363 | − | 0.316310i | ||||
\(885\) | 2.78115 | + | 8.55951i | 0.0934874 | + | 0.287725i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.61803 | − | 1.17557i | −0.0543283 | − | 0.0394718i | 0.560290 | − | 0.828297i | \(-0.310690\pi\) |
−0.614618 | + | 0.788825i | \(0.710690\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.618034 | + | 1.90211i | −0.0207282 | + | 0.0637948i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.00000 | −0.0669650 | ||||||||
\(893\) | 14.8328 | − | 45.6507i | 0.496361 | − | 1.52764i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.809017 | + | 0.587785i | 0.0270425 | + | 0.0196475i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.5410 | + | 57.0634i | 0.619067 | + | 1.90529i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.09017 | − | 5.87785i | 0.269822 | − | 0.196037i | ||||
\(900\) | 14.8328 | − | 45.6507i | 0.494427 | − | 1.52169i | ||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.0000 | −0.798670 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.04508 | − | 2.93893i | 0.134463 | − | 0.0976932i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.3607 | − | 38.0423i | −0.410430 | − | 1.26317i | −0.916275 | − | 0.400549i | \(-0.868820\pi\) |
0.505846 | − | 0.862624i | \(-0.331180\pi\) | |||||||
\(908\) | 2.47214 | + | 7.60845i | 0.0820407 | + | 0.252495i | ||||
\(909\) | −58.2492 | − | 42.3205i | −1.93200 | − | 1.40368i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(912\) | −72.0000 | −2.38416 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.85410 | − | 5.70634i | 0.0612947 | − | 0.188646i | ||||
\(916\) | −11.3262 | + | 8.22899i | −0.374229 | + | 0.271894i | ||||
\(917\) | 14.5623 | + | 10.5801i | 0.480890 | + | 0.349387i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.8328 | − | 45.6507i | −0.489289 | − | 1.50588i | −0.825671 | − | 0.564152i | \(-0.809203\pi\) |
0.336381 | − | 0.941726i | \(-0.390797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 67.9574 | − | 49.3740i | 2.23927 | − | 1.62693i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.00000 | 0.131662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0000 | 0.657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 58.2492 | − | 42.3205i | 1.91316 | − | 1.38999i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.27051 | − | 28.5317i | −0.304156 | − | 0.936095i | −0.979991 | − | 0.199042i | \(-0.936217\pi\) |
0.675835 | − | 0.737053i | \(-0.263783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.85410 | − | 3.52671i | −0.159087 | − | 0.115583i | ||||
\(932\) | −9.70820 | + | 7.05342i | −0.318003 | + | 0.231043i | ||||
\(933\) | −7.41641 | + | 22.8254i | −0.242802 | + | 0.747269i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.1246 | + | 34.2380i | −0.363425 | + | 1.11851i | 0.587536 | + | 0.809198i | \(0.300098\pi\) |
−0.950961 | + | 0.309310i | \(0.899902\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −55.8222 | − | 40.5572i | −1.82169 | − | 1.32353i | ||||
\(940\) | 4.94427 | + | 15.2169i | 0.161264 | + | 0.496321i | ||||
\(941\) | −17.9230 | − | 55.1613i | −0.584273 | − | 1.79821i | −0.602172 | − | 0.798366i | \(-0.705698\pi\) |
0.0178992 | − | 0.999840i | \(-0.494302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.09017 | − | 5.87785i | 0.263452 | − | 0.191409i | ||||
\(944\) | 3.70820 | − | 11.4127i | 0.120692 | − | 0.371451i | ||||
\(945\) | 9.00000 | 0.292770 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.00000 | 0.162478 | 0.0812391 | − | 0.996695i | \(-0.474112\pi\) | ||||
0.0812391 | + | 0.996695i | \(0.474112\pi\) | |||||||
\(948\) | −11.1246 | + | 34.2380i | −0.361311 | + | 1.11200i | ||||
\(949\) | 32.3607 | − | 23.5114i | 1.05047 | − | 0.763213i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.34346 | − | 25.6785i | −0.270555 | − | 0.832683i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.5967 | + | 25.8626i | 1.15309 | + | 0.837770i | 0.988889 | − | 0.148656i | \(-0.0474948\pi\) |
0.164203 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.54508 | + | 4.75528i | −0.0499978 | + | 0.153877i | ||||
\(956\) | 8.00000 | 0.258738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.927051 | + | 2.85317i | −0.0299360 | + | 0.0921337i | ||||
\(960\) | 19.4164 | − | 14.1068i | 0.626662 | − | 0.455296i | ||||
\(961\) | 24.2705 | + | 17.6336i | 0.782920 | + | 0.568824i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.5410 | + | 57.0634i | 0.597476 | + | 1.83884i | ||||
\(964\) | 19.4164 | + | 14.1068i | 0.625360 | + | 0.454351i | ||||
\(965\) | −11.3262 | + | 8.22899i | −0.364604 | + | 0.264901i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.0000 | 1.09337 | 0.546683 | − | 0.837340i | \(-0.315890\pi\) | ||||
0.546683 | + | 0.837340i | \(0.315890\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.0000 | 1.15649 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.4615 | + | 17.0458i | −0.752915 | + | 0.547025i | −0.896729 | − | 0.442580i | \(-0.854063\pi\) |
0.143814 | + | 0.989605i | \(0.454063\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.09017 | + | 9.51057i | 0.0990663 | + | 0.304895i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −38.8328 | − | 28.2137i | −1.24365 | − | 0.903561i | ||||
\(976\) | −6.47214 | + | 4.70228i | −0.207168 | + | 0.150516i | ||||
\(977\) | −9.57953 | + | 29.4828i | −0.306476 | + | 0.943237i | 0.672646 | + | 0.739964i | \(0.265158\pi\) |
−0.979122 | + | 0.203272i | \(0.934842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.00000 | 0.0638877 | ||||||||
\(981\) | −7.41641 | + | 22.8254i | −0.236788 | + | 0.728758i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.8435 | + | 15.8702i | 0.696698 | + | 0.506181i | 0.878855 | − | 0.477089i | \(-0.158308\pi\) |
−0.182157 | + | 0.983269i | \(0.558308\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.56231 | + | 17.1190i | 0.177230 | + | 0.545457i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.4164 | − | 14.1068i | 0.618031 | − | 0.449026i | ||||
\(988\) | −14.8328 | + | 45.6507i | −0.471895 | + | 1.45234i | ||||
\(989\) | −40.0000 | −1.27193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −41.2599 | + | 29.9770i | −1.30934 | + | 0.951293i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.47214 | + | 7.60845i | 0.0783720 | + | 0.241204i | ||||
\(996\) | −22.2492 | − | 68.4761i | −0.704994 | − | 2.16975i | ||||
\(997\) | −9.70820 | − | 7.05342i | −0.307462 | − | 0.223384i | 0.423345 | − | 0.905969i | \(-0.360856\pi\) |
−0.730807 | + | 0.682585i | \(0.760856\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.9058 | − | 42.7975i | 0.439959 | − | 1.35405i |
(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 | 847.2.f.h.372.1 | 4 | ||
11.2 | odd | 10 | 847.2.f.i.729.1 | 4 | |||
11.3 | even | 5 | inner | 847.2.f.h.323.1 | 4 | ||
11.4 | even | 5 | 847.2.a.b.1.1 | 1 | |||
11.5 | even | 5 | inner | 847.2.f.h.148.1 | 4 | ||
11.6 | odd | 10 | 847.2.f.i.148.1 | 4 | |||
11.7 | odd | 10 | 77.2.a.a.1.1 | ✓ | 1 | ||
11.8 | odd | 10 | 847.2.f.i.323.1 | 4 | |||
11.9 | even | 5 | inner | 847.2.f.h.729.1 | 4 | ||
11.10 | odd | 2 | 847.2.f.i.372.1 | 4 | |||
33.26 | odd | 10 | 7623.2.a.j.1.1 | 1 | |||
33.29 | even | 10 | 693.2.a.c.1.1 | 1 | |||
44.7 | even | 10 | 1232.2.a.l.1.1 | 1 | |||
55.7 | even | 20 | 1925.2.b.e.1849.2 | 2 | |||
55.18 | even | 20 | 1925.2.b.e.1849.1 | 2 | |||
55.29 | odd | 10 | 1925.2.a.h.1.1 | 1 | |||
77.18 | odd | 30 | 539.2.e.f.177.1 | 2 | |||
77.40 | even | 30 | 539.2.e.c.67.1 | 2 | |||
77.48 | odd | 10 | 5929.2.a.f.1.1 | 1 | |||
77.51 | odd | 30 | 539.2.e.f.67.1 | 2 | |||
77.62 | even | 10 | 539.2.a.c.1.1 | 1 | |||
77.73 | even | 30 | 539.2.e.c.177.1 | 2 | |||
88.29 | odd | 10 | 4928.2.a.bj.1.1 | 1 | |||
88.51 | even | 10 | 4928.2.a.a.1.1 | 1 | |||
231.62 | odd | 10 | 4851.2.a.j.1.1 | 1 | |||
308.139 | odd | 10 | 8624.2.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.a.1.1 | ✓ | 1 | 11.7 | odd | 10 | ||
539.2.a.c.1.1 | 1 | 77.62 | even | 10 | |||
539.2.e.c.67.1 | 2 | 77.40 | even | 30 | |||
539.2.e.c.177.1 | 2 | 77.73 | even | 30 | |||
539.2.e.f.67.1 | 2 | 77.51 | odd | 30 | |||
539.2.e.f.177.1 | 2 | 77.18 | odd | 30 | |||
693.2.a.c.1.1 | 1 | 33.29 | even | 10 | |||
847.2.a.b.1.1 | 1 | 11.4 | even | 5 | |||
847.2.f.h.148.1 | 4 | 11.5 | even | 5 | inner | ||
847.2.f.h.323.1 | 4 | 11.3 | even | 5 | inner | ||
847.2.f.h.372.1 | 4 | 1.1 | even | 1 | trivial | ||
847.2.f.h.729.1 | 4 | 11.9 | even | 5 | inner | ||
847.2.f.i.148.1 | 4 | 11.6 | odd | 10 | |||
847.2.f.i.323.1 | 4 | 11.8 | odd | 10 | |||
847.2.f.i.372.1 | 4 | 11.10 | odd | 2 | |||
847.2.f.i.729.1 | 4 | 11.2 | odd | 10 | |||
1232.2.a.l.1.1 | 1 | 44.7 | even | 10 | |||
1925.2.a.h.1.1 | 1 | 55.29 | odd | 10 | |||
1925.2.b.e.1849.1 | 2 | 55.18 | even | 20 | |||
1925.2.b.e.1849.2 | 2 | 55.7 | even | 20 | |||
4851.2.a.j.1.1 | 1 | 231.62 | odd | 10 | |||
4928.2.a.a.1.1 | 1 | 88.51 | even | 10 | |||
4928.2.a.bj.1.1 | 1 | 88.29 | odd | 10 | |||
5929.2.a.f.1.1 | 1 | 77.48 | odd | 10 | |||
7623.2.a.j.1.1 | 1 | 33.26 | odd | 10 | |||
8624.2.a.a.1.1 | 1 | 308.139 | odd | 10 |