Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 251.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.251 |
Dual form | 605.2.g.a.511.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | − | 0.951057i | 0.218508 | − | 0.672499i | −0.780378 | − | 0.625308i | \(-0.784973\pi\) |
0.998886 | − | 0.0471903i | \(-0.0150267\pi\) | |||||||
\(3\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(4\) | 0.809017 | + | 0.587785i | 0.404508 | + | 0.293893i | ||||
\(5\) | 0.309017 | + | 0.951057i | 0.138197 | + | 0.425325i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(8\) | 2.42705 | − | 1.76336i | 0.858092 | − | 0.623440i | ||||
\(9\) | −0.927051 | + | 2.85317i | −0.309017 | + | 0.951057i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.618034 | − | 1.90211i | 0.171412 | − | 0.527551i | −0.828040 | − | 0.560670i | \(-0.810544\pi\) |
0.999451 | + | 0.0331183i | \(0.0105438\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | − | 0.951057i | −0.0772542 | − | 0.237764i | ||||
\(17\) | 1.85410 | + | 5.70634i | 0.449686 | + | 1.38399i | 0.877262 | + | 0.480011i | \(0.159367\pi\) |
−0.427576 | + | 0.903979i | \(0.640633\pi\) | |||||||
\(18\) | 2.42705 | + | 1.76336i | 0.572061 | + | 0.415627i | ||||
\(19\) | 3.23607 | − | 2.35114i | 0.742405 | − | 0.539389i | −0.151058 | − | 0.988525i | \(-0.548268\pi\) |
0.893463 | + | 0.449136i | \(0.148268\pi\) | |||||||
\(20\) | −0.309017 | + | 0.951057i | −0.0690983 | + | 0.212663i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.809017 | + | 0.587785i | −0.161803 | + | 0.117557i | ||||
\(26\) | −1.61803 | − | 1.17557i | −0.317323 | − | 0.230548i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.85410 | − | 3.52671i | −0.901384 | − | 0.654894i | 0.0374370 | − | 0.999299i | \(-0.488081\pi\) |
−0.938821 | + | 0.344405i | \(0.888081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.47214 | + | 7.60845i | −0.444009 | + | 1.36652i | 0.439558 | + | 0.898214i | \(0.355135\pi\) |
−0.883567 | + | 0.468304i | \(0.844865\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.42705 | + | 1.76336i | −0.404508 | + | 0.293893i | ||||
\(37\) | 1.61803 | + | 1.17557i | 0.266003 | + | 0.193263i | 0.712789 | − | 0.701378i | \(-0.247432\pi\) |
−0.446786 | + | 0.894641i | \(0.647432\pi\) | |||||||
\(38\) | −1.23607 | − | 3.80423i | −0.200517 | − | 0.617127i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.42705 | + | 1.76336i | 0.383750 | + | 0.278811i | ||||
\(41\) | −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 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.00000 | −0.447214 | ||||||||
\(46\) | 1.23607 | − | 3.80423i | 0.182248 | − | 0.560903i | ||||
\(47\) | 9.70820 | − | 7.05342i | 1.41609 | − | 1.02885i | 0.423685 | − | 0.905810i | \(-0.360736\pi\) |
0.992402 | − | 0.123038i | \(-0.0392637\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.16312 | − | 6.65740i | −0.309017 | − | 0.951057i | ||||
\(50\) | 0.309017 | + | 0.951057i | 0.0437016 | + | 0.134500i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.61803 | − | 1.17557i | 0.224381 | − | 0.163022i | ||||
\(53\) | −0.618034 | + | 1.90211i | −0.0848935 | + | 0.261275i | −0.984488 | − | 0.175450i | \(-0.943862\pi\) |
0.899595 | + | 0.436726i | \(0.143862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.85410 | + | 3.52671i | −0.637375 | + | 0.463080i | ||||
\(59\) | −3.23607 | − | 2.35114i | −0.421300 | − | 0.306092i | 0.356861 | − | 0.934158i | \(-0.383847\pi\) |
−0.778161 | + | 0.628065i | \(0.783847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.09017 | − | 9.51057i | −0.395656 | − | 1.21770i | −0.928450 | − | 0.371458i | \(-0.878858\pi\) |
0.532794 | − | 0.846245i | \(-0.321142\pi\) | |||||||
\(62\) | 6.47214 | + | 4.70228i | 0.821962 | + | 0.597190i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.16312 | − | 6.65740i | 0.270390 | − | 0.832174i | ||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.0000 | −1.95471 | −0.977356 | − | 0.211604i | \(-0.932131\pi\) | ||||
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | −1.85410 | + | 5.70634i | −0.224843 | + | 0.691995i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.47214 | + | 7.60845i | 0.293389 | + | 0.902957i | 0.983758 | + | 0.179500i | \(0.0574480\pi\) |
−0.690369 | + | 0.723457i | \(0.742552\pi\) | |||||||
\(72\) | 2.78115 | + | 8.55951i | 0.327762 | + | 1.00875i | ||||
\(73\) | −11.3262 | − | 8.22899i | −1.32564 | − | 0.963131i | −0.999844 | − | 0.0176895i | \(-0.994369\pi\) |
−0.325792 | − | 0.945441i | \(-0.605631\pi\) | |||||||
\(74\) | 1.61803 | − | 1.17557i | 0.188093 | − | 0.136657i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.47214 | − | 7.60845i | 0.278137 | − | 0.856018i | −0.710235 | − | 0.703964i | \(-0.751411\pi\) |
0.988372 | − | 0.152053i | \(-0.0485886\pi\) | |||||||
\(80\) | 0.809017 | − | 0.587785i | 0.0904508 | − | 0.0657164i | ||||
\(81\) | −7.28115 | − | 5.29007i | −0.809017 | − | 0.587785i | ||||
\(82\) | 0.618034 | + | 1.90211i | 0.0682504 | + | 0.210053i | ||||
\(83\) | −1.23607 | − | 3.80423i | −0.135676 | − | 0.417568i | 0.860018 | − | 0.510263i | \(-0.170452\pi\) |
−0.995695 | + | 0.0926948i | \(0.970452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.85410 | + | 3.52671i | −0.526501 | + | 0.382526i | ||||
\(86\) | 1.23607 | − | 3.80423i | 0.133289 | − | 0.410220i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | −0.927051 | + | 2.85317i | −0.0977198 | + | 0.300750i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.23607 | + | 2.35114i | 0.337383 | + | 0.245123i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.70820 | − | 11.4127i | −0.382472 | − | 1.17713i | ||||
\(95\) | 3.23607 | + | 2.35114i | 0.332014 | + | 0.241222i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.09017 | − | 9.51057i | 0.313759 | − | 0.965652i | −0.662503 | − | 0.749059i | \(-0.730506\pi\) |
0.976262 | − | 0.216592i | \(-0.0694942\pi\) | |||||||
\(98\) | −7.00000 | −0.707107 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −3.09017 | + | 9.51057i | −0.307483 | + | 0.946337i | 0.671255 | + | 0.741226i | \(0.265755\pi\) |
−0.978739 | + | 0.205110i | \(0.934245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.23607 | + | 2.35114i | 0.318859 | + | 0.231665i | 0.735689 | − | 0.677320i | \(-0.236859\pi\) |
−0.416829 | + | 0.908985i | \(0.636859\pi\) | |||||||
\(104\) | −1.85410 | − | 5.70634i | −0.181810 | − | 0.559553i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.61803 | + | 1.17557i | 0.157157 | + | 0.114182i | ||||
\(107\) | −9.70820 | + | 7.05342i | −0.938527 | + | 0.681880i | −0.948066 | − | 0.318074i | \(-0.896964\pi\) |
0.00953827 | + | 0.999955i | \(0.496964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.0000 | −1.72409 | −0.862044 | − | 0.506834i | \(-0.830816\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.85410 | − | 3.52671i | 0.456636 | − | 0.331765i | −0.335575 | − | 0.942014i | \(-0.608930\pi\) |
0.792210 | + | 0.610249i | \(0.208930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.23607 | + | 3.80423i | 0.115264 | + | 0.354746i | ||||
\(116\) | −1.85410 | − | 5.70634i | −0.172149 | − | 0.529820i | ||||
\(117\) | 4.85410 | + | 3.52671i | 0.448762 | + | 0.326045i | ||||
\(118\) | −3.23607 | + | 2.35114i | −0.297904 | + | 0.216440i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −10.0000 | −0.905357 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.47214 | + | 4.70228i | −0.581215 | + | 0.422277i | ||||
\(125\) | −0.809017 | − | 0.587785i | −0.0723607 | − | 0.0525731i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.94427 | + | 15.2169i | 0.438733 | + | 1.35028i | 0.889212 | + | 0.457495i | \(0.151253\pi\) |
−0.450479 | + | 0.892787i | \(0.648747\pi\) | |||||||
\(128\) | 2.42705 | + | 1.76336i | 0.214523 | + | 0.155860i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.618034 | − | 1.90211i | 0.0542052 | − | 0.166826i | ||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.94427 | + | 15.2169i | −0.427120 | + | 1.31454i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.5623 | + | 10.5801i | 1.24871 | + | 0.907239i | ||||
\(137\) | 5.56231 | + | 17.1190i | 0.475220 | + | 1.46258i | 0.845661 | + | 0.533720i | \(0.179207\pi\) |
−0.370441 | + | 0.928856i | \(0.620793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.70820 | − | 7.05342i | −0.823439 | − | 0.598264i | 0.0942564 | − | 0.995548i | \(-0.469953\pi\) |
−0.917696 | + | 0.397284i | \(0.869953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.00000 | 0.671345 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 1.85410 | − | 5.70634i | 0.153975 | − | 0.473886i | ||||
\(146\) | −11.3262 | + | 8.22899i | −0.937366 | + | 0.681036i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.618034 | + | 1.90211i | 0.0508021 | + | 0.156353i | ||||
\(149\) | −3.09017 | − | 9.51057i | −0.253157 | − | 0.779136i | −0.994187 | − | 0.107665i | \(-0.965663\pi\) |
0.741031 | − | 0.671471i | \(-0.234337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.47214 | + | 4.70228i | −0.526695 | + | 0.382666i | −0.819120 | − | 0.573622i | \(-0.805538\pi\) |
0.292425 | + | 0.956288i | \(0.405538\pi\) | |||||||
\(152\) | 3.70820 | − | 11.4127i | 0.300775 | − | 0.925690i | ||||
\(153\) | −18.0000 | −1.45521 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.61803 | − | 1.17557i | 0.129133 | − | 0.0938207i | −0.521344 | − | 0.853347i | \(-0.674569\pi\) |
0.650477 | + | 0.759526i | \(0.274569\pi\) | |||||||
\(158\) | −6.47214 | − | 4.70228i | −0.514895 | − | 0.374093i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.54508 | + | 4.75528i | 0.122150 | + | 0.375938i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.28115 | + | 5.29007i | −0.572061 | + | 0.415627i | ||||
\(163\) | 4.94427 | − | 15.2169i | 0.387265 | − | 1.19188i | −0.547558 | − | 0.836768i | \(-0.684443\pi\) |
0.934824 | − | 0.355112i | \(-0.115557\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | −2.47214 | + | 7.60845i | −0.191300 | + | 0.588760i | 0.808700 | + | 0.588221i | \(0.200171\pi\) |
−1.00000 | 0.000538710i | \(0.999829\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.28115 | + | 5.29007i | 0.560089 | + | 0.406928i | ||||
\(170\) | 1.85410 | + | 5.70634i | 0.142203 | + | 0.437656i | ||||
\(171\) | 3.70820 | + | 11.4127i | 0.283573 | + | 0.872749i | ||||
\(172\) | 3.23607 | + | 2.35114i | 0.246748 | + | 0.179273i | ||||
\(173\) | 4.85410 | − | 3.52671i | 0.369051 | − | 0.268131i | −0.387767 | − | 0.921758i | \(-0.626753\pi\) |
0.756817 | + | 0.653627i | \(0.226753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.09017 | − | 9.51057i | 0.231618 | − | 0.712847i | ||||
\(179\) | −3.23607 | + | 2.35114i | −0.241875 | + | 0.175733i | −0.702118 | − | 0.712060i | \(-0.747762\pi\) |
0.460243 | + | 0.887793i | \(0.347762\pi\) | |||||||
\(180\) | −2.42705 | − | 1.76336i | −0.180902 | − | 0.131433i | ||||
\(181\) | −3.09017 | − | 9.51057i | −0.229691 | − | 0.706915i | −0.997781 | − | 0.0665740i | \(-0.978793\pi\) |
0.768091 | − | 0.640341i | \(-0.221207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.70820 | − | 7.05342i | 0.715698 | − | 0.519985i | ||||
\(185\) | −0.618034 | + | 1.90211i | −0.0454388 | + | 0.139846i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.23607 | − | 2.35114i | 0.234769 | − | 0.170570i | ||||
\(191\) | −6.47214 | − | 4.70228i | −0.468307 | − | 0.340245i | 0.328474 | − | 0.944513i | \(-0.393466\pi\) |
−0.796781 | + | 0.604268i | \(0.793466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.03444 | − | 24.7275i | −0.578332 | − | 1.77992i | −0.624543 | − | 0.780991i | \(-0.714715\pi\) |
0.0462111 | − | 0.998932i | \(-0.485285\pi\) | |||||||
\(194\) | −8.09017 | − | 5.87785i | −0.580840 | − | 0.422005i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.16312 | − | 6.65740i | 0.154508 | − | 0.475528i | ||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −0.927051 | + | 2.85317i | −0.0655524 | + | 0.201750i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.09017 | + | 5.87785i | 0.569222 | + | 0.413564i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.61803 | − | 1.17557i | −0.113008 | − | 0.0821054i | ||||
\(206\) | 3.23607 | − | 2.35114i | 0.225468 | − | 0.163812i | ||||
\(207\) | −3.70820 | + | 11.4127i | −0.257738 | + | 0.793236i | ||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.23607 | − | 3.80423i | 0.0850944 | − | 0.261894i | −0.899451 | − | 0.437021i | \(-0.856034\pi\) |
0.984546 | + | 0.175127i | \(0.0560336\pi\) | |||||||
\(212\) | −1.61803 | + | 1.17557i | −0.111127 | + | 0.0807385i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.70820 | + | 11.4127i | 0.253488 | + | 0.780155i | ||||
\(215\) | 1.23607 | + | 3.80423i | 0.0842991 | + | 0.259446i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.56231 | + | 17.1190i | −0.376727 | + | 1.15945i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.23607 | − | 2.35114i | 0.216703 | − | 0.157444i | −0.474138 | − | 0.880450i | \(-0.657240\pi\) |
0.690841 | + | 0.723006i | \(0.257240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.927051 | − | 2.85317i | −0.0618034 | − | 0.190211i | ||||
\(226\) | −1.85410 | − | 5.70634i | −0.123333 | − | 0.379580i | ||||
\(227\) | 16.1803 | + | 11.7557i | 1.07393 | + | 0.780254i | 0.976614 | − | 0.215000i | \(-0.0689752\pi\) |
0.0973129 | + | 0.995254i | \(0.468975\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.09017 | + | 9.51057i | −0.204204 | + | 0.628476i | 0.795541 | + | 0.605900i | \(0.207187\pi\) |
−0.999745 | + | 0.0225760i | \(0.992813\pi\) | |||||||
\(230\) | 4.00000 | 0.263752 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.0000 | −1.18176 | ||||||||
\(233\) | 1.85410 | − | 5.70634i | 0.121466 | − | 0.373835i | −0.871774 | − | 0.489907i | \(-0.837031\pi\) |
0.993241 | + | 0.116073i | \(0.0370306\pi\) | |||||||
\(234\) | 4.85410 | − | 3.52671i | 0.317323 | − | 0.230548i | ||||
\(235\) | 9.70820 | + | 7.05342i | 0.633293 | + | 0.460115i | ||||
\(236\) | −1.23607 | − | 3.80423i | −0.0804612 | − | 0.247634i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.47214 | + | 4.70228i | −0.418648 | + | 0.304165i | −0.777093 | − | 0.629385i | \(-0.783307\pi\) |
0.358446 | + | 0.933551i | \(0.383307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.09017 | − | 9.51057i | 0.197828 | − | 0.608852i | ||||
\(245\) | 5.66312 | − | 4.11450i | 0.361803 | − | 0.262866i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.47214 | − | 7.60845i | −0.157298 | − | 0.484114i | ||||
\(248\) | 7.41641 | + | 22.8254i | 0.470942 | + | 1.44941i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.809017 | + | 0.587785i | −0.0511667 | + | 0.0371748i | ||||
\(251\) | 3.70820 | − | 11.4127i | 0.234060 | − | 0.720362i | −0.763185 | − | 0.646180i | \(-0.776365\pi\) |
0.997245 | − | 0.0741818i | \(-0.0236345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 16.0000 | 1.00393 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.7533 | − | 9.99235i | 0.859581 | − | 0.624522i | ||||
\(257\) | −14.5623 | − | 10.5801i | −0.908372 | − | 0.659971i | 0.0322308 | − | 0.999480i | \(-0.489739\pi\) |
−0.940603 | + | 0.339510i | \(0.889739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.61803 | + | 1.17557i | 0.100346 | + | 0.0729058i | ||||
\(261\) | 14.5623 | − | 10.5801i | 0.901384 | − | 0.654894i | ||||
\(262\) | −3.70820 | + | 11.4127i | −0.229094 | + | 0.705078i | ||||
\(263\) | 24.0000 | 1.47990 | 0.739952 | − | 0.672660i | \(-0.234848\pi\) | ||||
0.739952 | + | 0.672660i | \(0.234848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.00000 | −0.122859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.9443 | − | 9.40456i | −0.790697 | − | 0.574475i | ||||
\(269\) | −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 | ||||||||
\(271\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(272\) | 4.85410 | − | 3.52671i | 0.294323 | − | 0.213838i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.09017 | − | 9.51057i | 0.185670 | − | 0.571434i | −0.814289 | − | 0.580460i | \(-0.802873\pi\) |
0.999959 | + | 0.00902525i | \(0.00287287\pi\) | |||||||
\(278\) | −9.70820 | + | 7.05342i | −0.582259 | + | 0.423036i | ||||
\(279\) | −19.4164 | − | 14.1068i | −1.16243 | − | 0.844555i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.56231 | + | 17.1190i | 0.331819 | + | 1.02123i | 0.968268 | + | 0.249916i | \(0.0804029\pi\) |
−0.636448 | + | 0.771319i | \(0.719597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.23607 | + | 2.35114i | −0.192364 | + | 0.139761i | −0.679799 | − | 0.733399i | \(-0.737933\pi\) |
0.487434 | + | 0.873160i | \(0.337933\pi\) | |||||||
\(284\) | −2.47214 | + | 7.60845i | −0.146694 | + | 0.451479i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.63525 | + | 14.2658i | −0.273135 | + | 0.840623i | ||||
\(289\) | −15.3713 | + | 11.1679i | −0.904195 | + | 0.656936i | ||||
\(290\) | −4.85410 | − | 3.52671i | −0.285043 | − | 0.207096i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.32624 | − | 13.3148i | −0.253174 | − | 0.779189i | ||||
\(293\) | −8.09017 | − | 5.87785i | −0.472633 | − | 0.343388i | 0.325834 | − | 0.945427i | \(-0.394355\pi\) |
−0.798466 | + | 0.602039i | \(0.794355\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.23607 | − | 3.80423i | 0.0719667 | − | 0.221491i | ||||
\(296\) | 6.00000 | 0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.0000 | −0.579284 | ||||||||
\(299\) | 2.47214 | − | 7.60845i | 0.142967 | − | 0.440008i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.47214 | + | 7.60845i | 0.142255 | + | 0.437817i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.23607 | − | 2.35114i | −0.185601 | − | 0.134847i | ||||
\(305\) | 8.09017 | − | 5.87785i | 0.463242 | − | 0.336565i | ||||
\(306\) | −5.56231 | + | 17.1190i | −0.317976 | + | 0.978629i | ||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.47214 | + | 7.60845i | −0.140408 | + | 0.432131i | ||||
\(311\) | 19.4164 | − | 14.1068i | 1.10100 | − | 0.799926i | 0.119780 | − | 0.992800i | \(-0.461781\pi\) |
0.981223 | + | 0.192875i | \(0.0617811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.79837 | − | 20.9232i | −0.384267 | − | 1.18265i | −0.937011 | − | 0.349300i | \(-0.886419\pi\) |
0.552744 | − | 0.833351i | \(-0.313581\pi\) | |||||||
\(314\) | −0.618034 | − | 1.90211i | −0.0348777 | − | 0.107342i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.47214 | − | 4.70228i | 0.364086 | − | 0.264524i | ||||
\(317\) | −5.56231 | + | 17.1190i | −0.312410 | + | 0.961500i | 0.664397 | + | 0.747380i | \(0.268688\pi\) |
−0.976807 | + | 0.214120i | \(0.931312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 7.00000 | 0.391312 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.4164 | + | 14.1068i | 1.08036 | + | 0.784926i | ||||
\(324\) | −2.78115 | − | 8.55951i | −0.154508 | − | 0.475528i | ||||
\(325\) | 0.618034 | + | 1.90211i | 0.0342824 | + | 0.105510i | ||||
\(326\) | −12.9443 | − | 9.40456i | −0.716917 | − | 0.520871i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.85410 | + | 5.70634i | −0.102376 | + | 0.315080i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 1.23607 | − | 3.80423i | 0.0678380 | − | 0.208784i | ||||
\(333\) | −4.85410 | + | 3.52671i | −0.266003 | + | 0.193263i | ||||
\(334\) | 6.47214 | + | 4.70228i | 0.354140 | + | 0.257297i | ||||
\(335\) | −4.94427 | − | 15.2169i | −0.270134 | − | 0.831388i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.85410 | − | 3.52671i | −0.264420 | − | 0.192112i | 0.447673 | − | 0.894197i | \(-0.352253\pi\) |
−0.712093 | + | 0.702085i | \(0.752253\pi\) | |||||||
\(338\) | 7.28115 | − | 5.29007i | 0.396043 | − | 0.287742i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.00000 | −0.325396 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.0000 | 0.648886 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.70820 | − | 7.05342i | 0.523431 | − | 0.380295i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.85410 | − | 5.70634i | −0.0996771 | − | 0.306775i | ||||
\(347\) | −1.23607 | − | 3.80423i | −0.0663556 | − | 0.204222i | 0.912381 | − | 0.409342i | \(-0.134242\pi\) |
−0.978737 | + | 0.205120i | \(0.934242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.09017 | − | 5.87785i | 0.433057 | − | 0.314634i | −0.349813 | − | 0.936819i | \(-0.613755\pi\) |
0.782870 | + | 0.622185i | \(0.213755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.47214 | + | 4.70228i | −0.343505 | + | 0.249571i | ||||
\(356\) | 8.09017 | + | 5.87785i | 0.428778 | + | 0.311526i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.23607 | + | 3.80423i | 0.0653282 | + | 0.201060i | ||||
\(359\) | 25.8885 | + | 18.8091i | 1.36635 | + | 0.992708i | 0.998013 | + | 0.0630137i | \(0.0200712\pi\) |
0.368332 | + | 0.929694i | \(0.379929\pi\) | |||||||
\(360\) | −7.28115 | + | 5.29007i | −0.383750 | + | 0.278811i | ||||
\(361\) | −0.927051 | + | 2.85317i | −0.0487922 | + | 0.150167i | ||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.32624 | − | 13.3148i | 0.226446 | − | 0.696928i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.23607 | − | 2.35114i | −0.168921 | − | 0.122729i | 0.500113 | − | 0.865960i | \(-0.333292\pi\) |
−0.669034 | + | 0.743232i | \(0.733292\pi\) | |||||||
\(368\) | −1.23607 | − | 3.80423i | −0.0644345 | − | 0.198309i | ||||
\(369\) | −1.85410 | − | 5.70634i | −0.0965207 | − | 0.297060i | ||||
\(370\) | 1.61803 | + | 1.17557i | 0.0841176 | + | 0.0611150i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.0000 | 0.932005 | 0.466002 | − | 0.884783i | \(-0.345694\pi\) | ||||
0.466002 | + | 0.884783i | \(0.345694\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.1246 | − | 34.2380i | 0.573708 | − | 1.76569i | ||||
\(377\) | −9.70820 | + | 7.05342i | −0.499998 | + | 0.363270i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.18034 | + | 19.0211i | 0.317463 | + | 0.977050i | 0.974729 | + | 0.223391i | \(0.0717128\pi\) |
−0.657266 | + | 0.753659i | \(0.728287\pi\) | |||||||
\(380\) | 1.23607 | + | 3.80423i | 0.0634089 | + | 0.195153i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.47214 | + | 4.70228i | −0.331143 | + | 0.240590i | ||||
\(383\) | −3.70820 | + | 11.4127i | −0.189480 | + | 0.583161i | −0.999997 | − | 0.00255538i | \(-0.999187\pi\) |
0.810516 | + | 0.585716i | \(0.199187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.0000 | −1.32337 | ||||||||
\(387\) | −3.70820 | + | 11.4127i | −0.188499 | + | 0.580139i | ||||
\(388\) | 8.09017 | − | 5.87785i | 0.410716 | − | 0.298403i | ||||
\(389\) | −4.85410 | − | 3.52671i | −0.246113 | − | 0.178811i | 0.457890 | − | 0.889009i | \(-0.348606\pi\) |
−0.704002 | + | 0.710198i | \(0.748606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.41641 | + | 22.8254i | 0.375064 | + | 1.15433i | ||||
\(392\) | −16.9894 | − | 12.3435i | −0.858092 | − | 0.623440i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.618034 | − | 1.90211i | 0.0311361 | − | 0.0958271i | ||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.0000 | 1.50566 | 0.752828 | − | 0.658217i | \(-0.228689\pi\) | ||||
0.752828 | + | 0.658217i | \(0.228689\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.809017 | + | 0.587785i | 0.0404508 | + | 0.0293893i | ||||
\(401\) | 0.618034 | + | 1.90211i | 0.0308631 | + | 0.0949870i | 0.965301 | − | 0.261138i | \(-0.0840977\pi\) |
−0.934438 | + | 0.356125i | \(0.884098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.9443 | + | 9.40456i | 0.644800 | + | 0.468475i | ||||
\(404\) | −8.09017 | + | 5.87785i | −0.402501 | + | 0.292434i | ||||
\(405\) | 2.78115 | − | 8.55951i | 0.138197 | − | 0.425325i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.85410 | + | 5.70634i | −0.0916794 | + | 0.282160i | −0.986374 | − | 0.164518i | \(-0.947393\pi\) |
0.894695 | + | 0.446678i | \(0.147393\pi\) | |||||||
\(410\) | −1.61803 | + | 1.17557i | −0.0799090 | + | 0.0580573i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.23607 | + | 3.80423i | 0.0608967 | + | 0.187421i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.70820 | + | 7.05342i | 0.477132 | + | 0.346657i | ||||
\(415\) | 3.23607 | − | 2.35114i | 0.158852 | − | 0.115413i | ||||
\(416\) | 3.09017 | − | 9.51057i | 0.151508 | − | 0.466294i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.85410 | + | 3.52671i | −0.236574 | + | 0.171881i | −0.699756 | − | 0.714382i | \(-0.746708\pi\) |
0.463181 | + | 0.886264i | \(0.346708\pi\) | |||||||
\(422\) | −3.23607 | − | 2.35114i | −0.157529 | − | 0.114452i | ||||
\(423\) | 11.1246 | + | 34.2380i | 0.540897 | + | 1.66471i | ||||
\(424\) | 1.85410 | + | 5.70634i | 0.0900432 | + | 0.277124i | ||||
\(425\) | −4.85410 | − | 3.52671i | −0.235459 | − | 0.171071i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | −7.41641 | + | 22.8254i | −0.357236 | + | 1.09946i | 0.597466 | + | 0.801894i | \(0.296174\pi\) |
−0.954702 | + | 0.297564i | \(0.903826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.7984 | + | 12.9313i | 0.855335 | + | 0.621437i | 0.926612 | − | 0.376019i | \(-0.122707\pi\) |
−0.0712766 | + | 0.997457i | \(0.522707\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.5623 | − | 10.5801i | −0.697408 | − | 0.506697i | ||||
\(437\) | 12.9443 | − | 9.40456i | 0.619208 | − | 0.449881i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 1.00000 | ||||||||
\(442\) | 3.70820 | − | 11.4127i | 0.176381 | − | 0.542846i | ||||
\(443\) | −6.47214 | + | 4.70228i | −0.307500 | + | 0.223412i | −0.730823 | − | 0.682567i | \(-0.760864\pi\) |
0.423323 | + | 0.905979i | \(0.360864\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.09017 | + | 9.51057i | 0.146488 | + | 0.450844i | ||||
\(446\) | −1.23607 | − | 3.80423i | −0.0585295 | − | 0.180135i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.618034 | − | 1.90211i | 0.0291668 | − | 0.0897663i | −0.935413 | − | 0.353556i | \(-0.884972\pi\) |
0.964580 | + | 0.263790i | \(0.0849724\pi\) | |||||||
\(450\) | −3.00000 | −0.141421 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.1803 | − | 11.7557i | 0.759381 | − | 0.551723i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.03444 | − | 24.7275i | −0.375835 | − | 1.15670i | −0.942913 | − | 0.333038i | \(-0.891926\pi\) |
0.567078 | − | 0.823664i | \(-0.308074\pi\) | |||||||
\(458\) | 8.09017 | + | 5.87785i | 0.378029 | + | 0.274654i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.23607 | + | 3.80423i | −0.0576320 | + | 0.177373i | ||||
\(461\) | −34.0000 | −1.58354 | −0.791769 | − | 0.610821i | \(-0.790840\pi\) | ||||
−0.791769 | + | 0.610821i | \(0.790840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.0000 | −1.67306 | −0.836531 | − | 0.547920i | \(-0.815420\pi\) | ||||
−0.836531 | + | 0.547920i | \(0.815420\pi\) | |||||||
\(464\) | −1.85410 | + | 5.70634i | −0.0860745 | + | 0.264910i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.85410 | − | 3.52671i | −0.224862 | − | 0.163372i | ||||
\(467\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(468\) | 1.85410 | + | 5.70634i | 0.0857059 | + | 0.263776i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.70820 | − | 7.05342i | 0.447806 | − | 0.325350i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.0000 | −0.552345 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.23607 | + | 3.80423i | −0.0567147 | + | 0.174550i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.85410 | − | 3.52671i | −0.222254 | − | 0.161477i | ||||
\(478\) | 2.47214 | + | 7.60845i | 0.113073 | + | 0.348003i | ||||
\(479\) | 7.41641 | + | 22.8254i | 0.338864 | + | 1.04292i | 0.964787 | + | 0.263032i | \(0.0847225\pi\) |
−0.625923 | + | 0.779885i | \(0.715277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.23607 | − | 2.35114i | 0.147552 | − | 0.107203i | ||||
\(482\) | 3.09017 | − | 9.51057i | 0.140753 | − | 0.433194i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0000 | 0.454077 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.6525 | + | 16.4580i | −1.02648 | + | 0.745783i | −0.967601 | − | 0.252482i | \(-0.918753\pi\) |
−0.0588802 | + | 0.998265i | \(0.518753\pi\) | |||||||
\(488\) | −24.2705 | − | 17.6336i | −1.09867 | − | 0.798234i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.16312 | − | 6.65740i | −0.0977198 | − | 0.300750i | ||||
\(491\) | 22.6525 | + | 16.4580i | 1.02229 | + | 0.742739i | 0.966751 | − | 0.255718i | \(-0.0823118\pi\) |
0.0555405 | + | 0.998456i | \(0.482312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.1246 | − | 34.2380i | 0.501027 | − | 1.54200i | ||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.1246 | + | 21.1603i | 1.30380 | + | 0.947264i | 0.999985 | − | 0.00546838i | \(-0.00174065\pi\) |
0.303812 | + | 0.952732i | \(0.401741\pi\) | |||||||
\(500\) | −0.309017 | − | 0.951057i | −0.0138197 | − | 0.0425325i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.70820 | − | 7.05342i | −0.433298 | − | 0.314810i | ||||
\(503\) | 12.9443 | − | 9.40456i | 0.577157 | − | 0.419329i | −0.260541 | − | 0.965463i | \(-0.583901\pi\) |
0.837698 | + | 0.546134i | \(0.183901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0000 | −0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.94427 | + | 15.2169i | −0.219367 | + | 0.675141i | ||||
\(509\) | −11.3262 | + | 8.22899i | −0.502027 | + | 0.364744i | −0.809791 | − | 0.586719i | \(-0.800419\pi\) |
0.307764 | + | 0.951463i | \(0.400419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.39919 | − | 10.4616i | −0.150224 | − | 0.462343i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.5623 | + | 10.5801i | −0.642316 | + | 0.466670i | ||||
\(515\) | −1.23607 | + | 3.80423i | −0.0544677 | + | 0.167634i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.85410 | − | 3.52671i | 0.212866 | − | 0.154657i | ||||
\(521\) | 4.85410 | + | 3.52671i | 0.212662 | + | 0.154508i | 0.689017 | − | 0.724745i | \(-0.258042\pi\) |
−0.476355 | + | 0.879253i | \(0.658042\pi\) | |||||||
\(522\) | −5.56231 | − | 17.1190i | −0.243456 | − | 0.749279i | ||||
\(523\) | −6.18034 | − | 19.0211i | −0.270247 | − | 0.831736i | −0.990438 | − | 0.137960i | \(-0.955946\pi\) |
0.720190 | − | 0.693776i | \(-0.244054\pi\) | |||||||
\(524\) | −9.70820 | − | 7.05342i | −0.424105 | − | 0.308130i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.41641 | − | 22.8254i | 0.323371 | − | 0.995233i | ||||
\(527\) | −48.0000 | −2.09091 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −0.618034 | + | 1.90211i | −0.0268457 | + | 0.0826225i | ||||
\(531\) | 9.70820 | − | 7.05342i | 0.421300 | − | 0.306092i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.23607 | + | 3.80423i | 0.0535400 | + | 0.164779i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.70820 | − | 7.05342i | −0.419722 | − | 0.304946i | ||||
\(536\) | −38.8328 | + | 28.2137i | −1.67732 | + | 1.21865i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.0000 | −0.776035 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.5066 | + | 32.3359i | −0.451713 | + | 1.39023i | 0.423238 | + | 0.906019i | \(0.360893\pi\) |
−0.874951 | + | 0.484211i | \(0.839107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.27051 | + | 28.5317i | 0.397470 | + | 1.22329i | ||||
\(545\) | −5.56231 | − | 17.1190i | −0.238263 | − | 0.733298i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.70820 | + | 7.05342i | −0.415093 | + | 0.301583i | −0.775660 | − | 0.631151i | \(-0.782583\pi\) |
0.360568 | + | 0.932733i | \(0.382583\pi\) | |||||||
\(548\) | −5.56231 | + | 17.1190i | −0.237610 | + | 0.731288i | ||||
\(549\) | 30.0000 | 1.28037 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.0000 | −1.02243 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.09017 | − | 5.87785i | −0.343718 | − | 0.249726i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.70820 | − | 11.4127i | −0.157263 | − | 0.484005i | ||||
\(557\) | −8.09017 | − | 5.87785i | −0.342792 | − | 0.249053i | 0.403047 | − | 0.915179i | \(-0.367951\pi\) |
−0.745839 | + | 0.666127i | \(0.767951\pi\) | |||||||
\(558\) | −19.4164 | + | 14.1068i | −0.821962 | + | 0.597190i | ||||
\(559\) | 2.47214 | − | 7.60845i | 0.104560 | − | 0.321803i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000 | 0.759284 | ||||||||
\(563\) | 11.1246 | − | 34.2380i | 0.468846 | − | 1.44296i | −0.385233 | − | 0.922819i | \(-0.625879\pi\) |
0.854080 | − | 0.520142i | \(-0.174121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.85410 | + | 3.52671i | 0.204214 | + | 0.148370i | ||||
\(566\) | 1.23607 | + | 3.80423i | 0.0519558 | + | 0.159904i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.4164 | + | 14.1068i | 0.814694 | + | 0.591910i | ||||
\(569\) | −21.0344 | + | 15.2824i | −0.881810 | + | 0.640672i | −0.933730 | − | 0.357979i | \(-0.883466\pi\) |
0.0519200 | + | 0.998651i | \(0.483466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.0000 | 1.50655 | 0.753277 | − | 0.657704i | \(-0.228472\pi\) | ||||
0.753277 | + | 0.657704i | \(0.228472\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.23607 | + | 2.35114i | −0.134953 | + | 0.0980494i | ||||
\(576\) | 16.9894 | + | 12.3435i | 0.707890 | + | 0.514312i | ||||
\(577\) | −6.79837 | − | 20.9232i | −0.283020 | − | 0.871046i | −0.986985 | − | 0.160811i | \(-0.948589\pi\) |
0.703965 | − | 0.710235i | \(-0.251411\pi\) | |||||||
\(578\) | 5.87132 | + | 18.0701i | 0.244215 | + | 0.751616i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.85410 | − | 3.52671i | 0.201556 | − | 0.146439i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −42.0000 | −1.73797 | ||||||||
\(585\) | −1.85410 | + | 5.70634i | −0.0766577 | + | 0.235928i | ||||
\(586\) | −8.09017 | + | 5.87785i | −0.334202 | + | 0.242812i | ||||
\(587\) | 19.4164 | + | 14.1068i | 0.801401 | + | 0.582252i | 0.911325 | − | 0.411688i | \(-0.135061\pi\) |
−0.109924 | + | 0.993940i | \(0.535061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.88854 | + | 30.4338i | 0.407450 | + | 1.25400i | ||||
\(590\) | −3.23607 | − | 2.35114i | −0.133227 | − | 0.0967949i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.618034 | − | 1.90211i | 0.0254010 | − | 0.0781764i | ||||
\(593\) | 22.0000 | 0.903432 | 0.451716 | − | 0.892162i | \(-0.350812\pi\) | ||||
0.451716 | + | 0.892162i | \(0.350812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.09017 | − | 9.51057i | 0.126578 | − | 0.389568i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.47214 | − | 4.70228i | −0.264665 | − | 0.192291i | ||||
\(599\) | 7.41641 | + | 22.8254i | 0.303026 | + | 0.932619i | 0.980406 | + | 0.196986i | \(0.0631152\pi\) |
−0.677380 | + | 0.735633i | \(0.736885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.61803 | − | 1.17557i | −0.0660010 | − | 0.0479525i | 0.554296 | − | 0.832320i | \(-0.312988\pi\) |
−0.620297 | + | 0.784367i | \(0.712988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.8328 | − | 45.6507i | 0.604039 | − | 1.85904i | ||||
\(604\) | −8.00000 | −0.325515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.88854 | + | 30.4338i | −0.401364 | + | 1.23527i | 0.522530 | + | 0.852621i | \(0.324988\pi\) |
−0.923894 | + | 0.382649i | \(0.875012\pi\) | |||||||
\(608\) | 16.1803 | − | 11.7557i | 0.656199 | − | 0.476757i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.09017 | − | 9.51057i | −0.125117 | − | 0.385072i | ||||
\(611\) | −7.41641 | − | 22.8254i | −0.300036 | − | 0.923415i | ||||
\(612\) | −14.5623 | − | 10.5801i | −0.588646 | − | 0.427677i | ||||
\(613\) | −27.5066 | + | 19.9847i | −1.11098 | + | 0.807174i | −0.982818 | − | 0.184579i | \(-0.940908\pi\) |
−0.128162 | + | 0.991753i | \(0.540908\pi\) | |||||||
\(614\) | 6.18034 | − | 19.0211i | 0.249418 | − | 0.767630i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000 | 0.0805170 | 0.0402585 | − | 0.999189i | \(-0.487182\pi\) | ||||
0.0402585 | + | 0.999189i | \(0.487182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.1803 | − | 11.7557i | 0.650343 | − | 0.472502i | −0.213045 | − | 0.977042i | \(-0.568338\pi\) |
0.863388 | + | 0.504541i | \(0.168338\pi\) | |||||||
\(620\) | −6.47214 | − | 4.70228i | −0.259927 | − | 0.188848i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.41641 | − | 22.8254i | −0.297371 | − | 0.915213i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.309017 | − | 0.951057i | 0.0123607 | − | 0.0380423i | ||||
\(626\) | −22.0000 | −0.879297 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.00000 | 0.0798087 | ||||||||
\(629\) | −3.70820 | + | 11.4127i | −0.147856 | + | 0.455053i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.3607 | − | 23.5114i | −1.28826 | − | 0.935974i | −0.288490 | − | 0.957483i | \(-0.593153\pi\) |
−0.999769 | + | 0.0215086i | \(0.993153\pi\) | |||||||
\(632\) | −7.41641 | − | 22.8254i | −0.295009 | − | 0.907944i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.5623 | + | 10.5801i | 0.578343 | + | 0.420191i | ||||
\(635\) | −12.9443 | + | 9.40456i | −0.513678 | + | 0.373209i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.0000 | −0.554700 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.0000 | −0.949425 | ||||||||
\(640\) | −0.927051 | + | 2.85317i | −0.0366449 | + | 0.112781i | ||||
\(641\) | −27.5066 | + | 19.9847i | −1.08644 | + | 0.789348i | −0.978795 | − | 0.204841i | \(-0.934332\pi\) |
−0.107649 | + | 0.994189i | \(0.534332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.94427 | − | 15.2169i | −0.194983 | − | 0.600096i | −0.999977 | − | 0.00681282i | \(-0.997831\pi\) |
0.804994 | − | 0.593283i | \(-0.202169\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.4164 | − | 14.1068i | 0.763928 | − | 0.555026i | ||||
\(647\) | 6.18034 | − | 19.0211i | 0.242974 | − | 0.747798i | −0.752989 | − | 0.658033i | \(-0.771389\pi\) |
0.995963 | − | 0.0897645i | \(-0.0286114\pi\) | |||||||
\(648\) | −27.0000 | −1.06066 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.9443 | − | 9.40456i | 0.506937 | − | 0.368311i | ||||
\(653\) | 8.09017 | + | 5.87785i | 0.316593 | + | 0.230018i | 0.734720 | − | 0.678370i | \(-0.237313\pi\) |
−0.418127 | + | 0.908388i | \(0.637313\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.70820 | − | 11.4127i | −0.144892 | − | 0.445930i | ||||
\(656\) | 1.61803 | + | 1.17557i | 0.0631736 | + | 0.0458983i | ||||
\(657\) | 33.9787 | − | 24.6870i | 1.32564 | − | 0.963131i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0000 | −0.388955 | −0.194477 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194477 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(662\) | 1.23607 | − | 3.80423i | 0.0480411 | − | 0.147855i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.70820 | − | 7.05342i | −0.376751 | − | 0.273726i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.85410 | + | 5.70634i | 0.0718450 | + | 0.221116i | ||||
\(667\) | −19.4164 | − | 14.1068i | −0.751806 | − | 0.546219i | ||||
\(668\) | −6.47214 | + | 4.70228i | −0.250414 | + | 0.181937i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.0000 | −0.618134 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.03444 | + | 24.7275i | −0.309705 | + | 0.953174i | 0.668174 | + | 0.744005i | \(0.267076\pi\) |
−0.977879 | + | 0.209169i | \(0.932924\pi\) | |||||||
\(674\) | −4.85410 | + | 3.52671i | −0.186973 | + | 0.135844i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.78115 | + | 8.55951i | 0.106967 | + | 0.329212i | ||||
\(677\) | −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 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.56231 | + | 17.1190i | −0.213305 | + | 0.656484i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.0000 | −0.612223 | −0.306111 | − | 0.951996i | \(-0.599028\pi\) | ||||
−0.306111 | + | 0.951996i | \(0.599028\pi\) | |||||||
\(684\) | −3.70820 | + | 11.4127i | −0.141787 | + | 0.436375i | ||||
\(685\) | −14.5623 | + | 10.5801i | −0.556397 | + | 0.404246i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.23607 | − | 3.80423i | −0.0471246 | − | 0.145035i | ||||
\(689\) | 3.23607 | + | 2.35114i | 0.123284 | + | 0.0895713i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.65248 | + | 26.6296i | −0.329156 | + | 1.01304i | 0.640374 | + | 0.768063i | \(0.278779\pi\) |
−0.969530 | + | 0.244974i | \(0.921221\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | 3.70820 | − | 11.4127i | 0.140660 | − | 0.432908i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.70820 | − | 7.05342i | −0.367724 | − | 0.267167i | ||||
\(698\) | −3.09017 | − | 9.51057i | −0.116965 | − | 0.359980i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.7984 | + | 12.9313i | −0.672235 | + | 0.488408i | −0.870773 | − | 0.491686i | \(-0.836381\pi\) |
0.198537 | + | 0.980093i | \(0.436381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.00000 | 0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.56231 | − | 17.1190i | 0.209340 | − | 0.644283i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.09017 | − | 9.51057i | −0.116054 | − | 0.357177i | 0.876112 | − | 0.482108i | \(-0.160129\pi\) |
−0.992165 | + | 0.124932i | \(0.960129\pi\) | |||||||
\(710\) | 2.47214 | + | 7.60845i | 0.0927776 | + | 0.285540i | ||||
\(711\) | 19.4164 | + | 14.1068i | 0.728172 | + | 0.529048i | ||||
\(712\) | 24.2705 | − | 17.6336i | 0.909576 | − | 0.660846i | ||||
\(713\) | −9.88854 | + | 30.4338i | −0.370329 | + | 1.13976i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.00000 | −0.149487 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25.8885 | − | 18.8091i | 0.966152 | − | 0.701950i | ||||
\(719\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(720\) | 0.927051 | + | 2.85317i | 0.0345492 | + | 0.106331i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.42705 | + | 1.76336i | 0.0903255 | + | 0.0656253i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.09017 | − | 9.51057i | 0.114845 | − | 0.353457i | ||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 52.0000 | 1.92857 | 0.964287 | − | 0.264861i | \(-0.0853260\pi\) | ||||
0.964287 | + | 0.264861i | \(0.0853260\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.8435 | − | 15.8702i | 0.809017 | − | 0.587785i | ||||
\(730\) | −11.3262 | − | 8.22899i | −0.419203 | − | 0.304569i | ||||
\(731\) | 7.41641 | + | 22.8254i | 0.274306 | + | 0.844226i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.9787 | − | 24.6870i | −1.25503 | − | 0.911834i | −0.256530 | − | 0.966536i | \(-0.582579\pi\) |
−0.998503 | + | 0.0547019i | \(0.982579\pi\) | |||||||
\(734\) | −3.23607 | + | 2.35114i | −0.119445 | + | 0.0867822i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.0000 | 0.737210 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.00000 | −0.220863 | ||||||||
\(739\) | 1.23607 | − | 3.80423i | 0.0454695 | − | 0.139941i | −0.925744 | − | 0.378150i | \(-0.876560\pi\) |
0.971214 | + | 0.238209i | \(0.0765604\pi\) | |||||||
\(740\) | −1.61803 | + | 1.17557i | −0.0594801 | + | 0.0432148i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.3607 | + | 38.0423i | 0.453469 | + | 1.39564i | 0.872923 | + | 0.487858i | \(0.162222\pi\) |
−0.419453 | + | 0.907777i | \(0.637778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.09017 | − | 5.87785i | 0.296401 | − | 0.215348i | ||||
\(746\) | 5.56231 | − | 17.1190i | 0.203650 | − | 0.626772i | ||||
\(747\) | 12.0000 | 0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.9443 | + | 9.40456i | −0.472343 | + | 0.343177i | −0.798354 | − | 0.602189i | \(-0.794295\pi\) |
0.326011 | + | 0.945366i | \(0.394295\pi\) | |||||||
\(752\) | −9.70820 | − | 7.05342i | −0.354022 | − | 0.257212i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.70820 | + | 11.4127i | 0.135045 | + | 0.415625i | ||||
\(755\) | −6.47214 | − | 4.70228i | −0.235545 | − | 0.171134i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.85410 | − | 5.70634i | 0.0673885 | − | 0.207400i | −0.911692 | − | 0.410875i | \(-0.865223\pi\) |
0.979080 | + | 0.203474i | \(0.0652233\pi\) | |||||||
\(758\) | 20.0000 | 0.726433 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | 0.435286 | ||||||||
\(761\) | 3.09017 | − | 9.51057i | 0.112019 | − | 0.344758i | −0.879295 | − | 0.476278i | \(-0.841986\pi\) |
0.991314 | + | 0.131520i | \(0.0419857\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.47214 | − | 7.60845i | −0.0894387 | − | 0.275264i | ||||
\(765\) | −5.56231 | − | 17.1190i | −0.201106 | − | 0.618939i | ||||
\(766\) | 9.70820 | + | 7.05342i | 0.350772 | + | 0.254851i | ||||
\(767\) | −6.47214 | + | 4.70228i | −0.233695 | + | 0.169790i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.03444 | − | 24.7275i | 0.289166 | − | 0.889961i | ||||
\(773\) | −11.3262 | + | 8.22899i | −0.407376 | + | 0.295976i | −0.772539 | − | 0.634968i | \(-0.781013\pi\) |
0.365162 | + | 0.930944i | \(0.381013\pi\) | |||||||
\(774\) | 9.70820 | + | 7.05342i | 0.348954 | + | 0.253530i | ||||
\(775\) | −2.47214 | − | 7.60845i | −0.0888017 | − | 0.273304i | ||||
\(776\) | −9.27051 | − | 28.5317i | −0.332792 | − | 1.02423i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.85410 | + | 3.52671i | −0.174028 | + | 0.126439i | ||||
\(779\) | −2.47214 | + | 7.60845i | −0.0885735 | + | 0.272601i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 24.0000 | 0.858238 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.66312 | + | 4.11450i | −0.202254 | + | 0.146946i | ||||
\(785\) | 1.61803 | + | 1.17557i | 0.0577501 | + | 0.0419579i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0689 | + | 49.4549i | 0.572794 | + | 1.76288i | 0.643571 | + | 0.765386i | \(0.277452\pi\) |
−0.0707776 | + | 0.997492i | \(0.522548\pi\) | |||||||
\(788\) | 1.61803 | + | 1.17557i | 0.0576401 | + | 0.0418780i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.47214 | − | 7.60845i | 0.0879547 | − | 0.270697i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | −0.710221 | ||||||||
\(794\) | 9.27051 | − | 28.5317i | 0.328998 | − | 1.01255i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.618034 | − | 1.90211i | −0.0218919 | − | 0.0673763i | 0.939514 | − | 0.342511i | \(-0.111277\pi\) |
−0.961406 | + | 0.275135i | \(0.911277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 58.2492 | + | 42.3205i | 2.06071 | + | 1.49719i | ||||
\(800\) | −4.04508 | + | 2.93893i | −0.143015 | + | 0.103907i | ||||
\(801\) | −9.27051 | + | 28.5317i | −0.327557 | + | 1.00812i | ||||
\(802\) | 2.00000 | 0.0706225 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.9443 | − | 9.40456i | 0.455943 | − | 0.331262i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.27051 | + | 28.5317i | 0.326135 | + | 1.00374i | ||||
\(809\) | 5.56231 | + | 17.1190i | 0.195560 | + | 0.601873i | 0.999970 | + | 0.00779717i | \(0.00248194\pi\) |
−0.804409 | + | 0.594075i | \(0.797518\pi\) | |||||||
\(810\) | −7.28115 | − | 5.29007i | −0.255834 | − | 0.185874i | ||||
\(811\) | 9.70820 | − | 7.05342i | 0.340901 | − | 0.247679i | −0.404141 | − | 0.914697i | \(-0.632429\pi\) |
0.745042 | + | 0.667018i | \(0.232429\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.0000 | 0.560456 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.9443 | − | 9.40456i | 0.452863 | − | 0.329024i | ||||
\(818\) | 4.85410 | + | 3.52671i | 0.169720 | + | 0.123309i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.618034 | − | 1.90211i | −0.0215827 | − | 0.0664247i | ||||
\(821\) | 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 | ||||||||
\(823\) | −11.1246 | + | 34.2380i | −0.387780 | + | 1.19346i | 0.546664 | + | 0.837352i | \(0.315897\pi\) |
−0.934444 | + | 0.356111i | \(0.884103\pi\) | |||||||
\(824\) | 12.0000 | 0.418040 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.70820 | − | 11.4127i | 0.128947 | − | 0.396858i | −0.865653 | − | 0.500645i | \(-0.833096\pi\) |
0.994600 | + | 0.103787i | \(0.0330962\pi\) | |||||||
\(828\) | −9.70820 | + | 7.05342i | −0.337383 | + | 0.245123i | ||||
\(829\) | 1.61803 | + | 1.17557i | 0.0561966 | + | 0.0408293i | 0.615529 | − | 0.788114i | \(-0.288942\pi\) |
−0.559332 | + | 0.828944i | \(0.688942\pi\) | |||||||
\(830\) | −1.23607 | − | 3.80423i | −0.0429045 | − | 0.132047i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.3262 | − | 8.22899i | −0.392667 | − | 0.285289i | ||||
\(833\) | 33.9787 | − | 24.6870i | 1.17729 | − | 0.855353i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.65248 | + | 26.6296i | −0.298895 | + | 0.919904i | ||||
\(839\) | 25.8885 | − | 18.8091i | 0.893772 | − | 0.649363i | −0.0430869 | − | 0.999071i | \(-0.513719\pi\) |
0.936859 | + | 0.349708i | \(0.113719\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.16312 | + | 6.65740i | 0.0745903 | + | 0.229565i | ||||
\(842\) | 1.85410 | + | 5.70634i | 0.0638966 | + | 0.196653i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.23607 | − | 2.35114i | 0.111390 | − | 0.0809296i | ||||
\(845\) | −2.78115 | + | 8.55951i | −0.0956746 | + | 0.294456i | ||||
\(846\) | 36.0000 | 1.23771 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.00000 | 0.0686803 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.85410 | + | 3.52671i | −0.166494 | + | 0.120965i | ||||
\(851\) | 6.47214 | + | 4.70228i | 0.221862 | + | 0.161192i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.618034 | + | 1.90211i | 0.0211611 | + | 0.0651271i | 0.961079 | − | 0.276272i | \(-0.0890991\pi\) |
−0.939918 | + | 0.341399i | \(0.889099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.70820 | + | 7.05342i | −0.332014 | + | 0.241222i | ||||
\(856\) | −11.1246 | + | 34.2380i | −0.380231 | + | 1.17023i | ||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.0000 | 0.955348 | 0.477674 | − | 0.878537i | \(-0.341480\pi\) | ||||
0.477674 | + | 0.878537i | \(0.341480\pi\) | |||||||
\(860\) | −1.23607 | + | 3.80423i | −0.0421496 | + | 0.129723i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.4164 | + | 14.1068i | 0.661325 | + | 0.480481i | ||||
\(863\) | 1.23607 | + | 3.80423i | 0.0420762 | + | 0.129497i | 0.969888 | − | 0.243551i | \(-0.0783124\pi\) |
−0.927812 | + | 0.373049i | \(0.878312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.85410 | + | 3.52671i | 0.165044 | + | 0.119912i | ||||
\(866\) | 17.7984 | − | 12.9313i | 0.604813 | − | 0.439423i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.88854 | + | 30.4338i | −0.335061 | + | 1.03121i | ||||
\(872\) | −43.6869 | + | 31.7404i | −1.47943 | + | 1.07487i | ||||
\(873\) | 24.2705 | + | 17.6336i | 0.821432 | + | 0.596806i | ||||
\(874\) | −4.94427 | − | 15.2169i | −0.167242 | − | 0.514719i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.7984 | − | 12.9313i | 0.601008 | − | 0.436658i | −0.245228 | − | 0.969465i | \(-0.578863\pi\) |
0.846237 | + | 0.532807i | \(0.178863\pi\) | |||||||
\(878\) | −2.47214 | + | 7.60845i | −0.0834305 | + | 0.256773i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 6.48936 | − | 19.9722i | 0.218508 | − | 0.672499i | ||||
\(883\) | 12.9443 | − | 9.40456i | 0.435609 | − | 0.316489i | −0.348279 | − | 0.937391i | \(-0.613234\pi\) |
0.783888 | + | 0.620902i | \(0.213234\pi\) | |||||||
\(884\) | 9.70820 | + | 7.05342i | 0.326522 | + | 0.237232i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.47214 | + | 7.60845i | 0.0830530 | + | 0.255611i | ||||
\(887\) | −45.3050 | − | 32.9160i | −1.52119 | − | 1.10521i | −0.960893 | − | 0.276919i | \(-0.910687\pi\) |
−0.560298 | − | 0.828291i | \(-0.689313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.0000 | 0.335201 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.00000 | 0.133930 | ||||||||
\(893\) | 14.8328 | − | 45.6507i | 0.496361 | − | 1.52764i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.23607 | − | 2.35114i | −0.108170 | − | 0.0785900i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.61803 | − | 1.17557i | −0.0539945 | − | 0.0392293i | ||||
\(899\) | 38.8328 | − | 28.2137i | 1.29515 | − | 0.940979i | ||||
\(900\) | 0.927051 | − | 2.85317i | 0.0309017 | − | 0.0951057i | ||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.56231 | − | 17.1190i | 0.185000 | − | 0.569370i | ||||
\(905\) | 8.09017 | − | 5.87785i | 0.268926 | − | 0.195386i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.3607 | − | 38.0423i | −0.410430 | − | 1.26317i | −0.916275 | − | 0.400549i | \(-0.868820\pi\) |
0.505846 | − | 0.862624i | \(-0.331180\pi\) | |||||||
\(908\) | 6.18034 | + | 19.0211i | 0.205102 | + | 0.631238i | ||||
\(909\) | −24.2705 | − | 17.6336i | −0.805002 | − | 0.584868i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.47214 | − | 7.60845i | 0.0819055 | − | 0.252079i | −0.901715 | − | 0.432331i | \(-0.857691\pi\) |
0.983621 | + | 0.180252i | \(0.0576912\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −26.0000 | −0.860004 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.09017 | + | 5.87785i | −0.267307 | + | 0.194210i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.41641 | + | 22.8254i | 0.244645 | + | 0.752939i | 0.995695 | + | 0.0926936i | \(0.0295477\pi\) |
−0.751050 | + | 0.660245i | \(0.770452\pi\) | |||||||
\(920\) | 9.70820 | + | 7.05342i | 0.320070 | + | 0.232544i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.5066 | + | 32.3359i | −0.346016 | + | 1.06493i | ||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | −11.1246 | + | 34.2380i | −0.365577 | + | 1.12513i | ||||
\(927\) | −9.70820 | + | 7.05342i | −0.318859 | + | 0.231665i | ||||
\(928\) | −24.2705 | − | 17.6336i | −0.796719 | − | 0.578850i | ||||
\(929\) | −4.32624 | − | 13.3148i | −0.141939 | − | 0.436844i | 0.854665 | − | 0.519179i | \(-0.173762\pi\) |
−0.996605 | + | 0.0823350i | \(0.973762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.6525 | − | 16.4580i | −0.742405 | − | 0.539389i | ||||
\(932\) | 4.85410 | − | 3.52671i | 0.159001 | − | 0.115521i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 18.0000 | 0.588348 | ||||||||
\(937\) | 1.85410 | − | 5.70634i | 0.0605709 | − | 0.186418i | −0.916193 | − | 0.400738i | \(-0.868754\pi\) |
0.976763 | + | 0.214320i | \(0.0687537\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.70820 | + | 11.4127i | 0.120948 | + | 0.372241i | ||||
\(941\) | −0.618034 | − | 1.90211i | −0.0201473 | − | 0.0620071i | 0.940477 | − | 0.339856i | \(-0.110378\pi\) |
−0.960625 | + | 0.277849i | \(0.910378\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.47214 | + | 4.70228i | −0.210762 | + | 0.153127i | ||||
\(944\) | −1.23607 | + | 3.80423i | −0.0402306 | + | 0.123817i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.6525 | + | 16.4580i | −0.735330 | + | 0.534249i | ||||
\(950\) | 3.23607 | + | 2.35114i | 0.104992 | + | 0.0762811i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.9787 | + | 24.6870i | 1.10068 | + | 0.799690i | 0.981171 | − | 0.193143i | \(-0.0618683\pi\) |
0.119508 | + | 0.992833i | \(0.461868\pi\) | |||||||
\(954\) | −4.85410 | + | 3.52671i | −0.157157 | + | 0.114182i | ||||
\(955\) | 2.47214 | − | 7.60845i | 0.0799964 | − | 0.246204i | ||||
\(956\) | −8.00000 | −0.258738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.0000 | 0.775405 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.6976 | − | 19.3969i | −0.861212 | − | 0.625707i | ||||
\(962\) | −1.23607 | − | 3.80423i | −0.0398524 | − | 0.122653i | ||||
\(963\) | −11.1246 | − | 34.2380i | −0.358486 | − | 1.10331i | ||||
\(964\) | 8.09017 | + | 5.87785i | 0.260567 | + | 0.189313i | ||||
\(965\) | 21.0344 | − | 15.2824i | 0.677123 | − | 0.491958i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.09017 | − | 9.51057i | 0.0992194 | − | 0.305366i | ||||
\(971\) | −29.1246 | + | 21.1603i | −0.934653 | + | 0.679065i | −0.947128 | − | 0.320857i | \(-0.896029\pi\) |
0.0124744 | + | 0.999922i | \(0.496029\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.65248 | + | 26.6296i | 0.277243 | + | 0.853267i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.09017 | + | 5.87785i | −0.258960 | + | 0.188145i | ||||
\(977\) | 3.09017 | − | 9.51057i | 0.0988633 | − | 0.304270i | −0.889378 | − | 0.457173i | \(-0.848862\pi\) |
0.988241 | + | 0.152903i | \(0.0488621\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 7.00000 | 0.223607 | ||||||||
\(981\) | 16.6869 | − | 51.3571i | 0.532772 | − | 1.63970i | ||||
\(982\) | 22.6525 | − | 16.4580i | 0.722870 | − | 0.525195i | ||||
\(983\) | 3.23607 | + | 2.35114i | 0.103215 | + | 0.0749898i | 0.638195 | − | 0.769874i | \(-0.279681\pi\) |
−0.534981 | + | 0.844864i | \(0.679681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.618034 | + | 1.90211i | 0.0196922 | + | 0.0606064i | ||||
\(986\) | −29.1246 | − | 21.1603i | −0.927517 | − | 0.673880i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.47214 | − | 7.60845i | 0.0786491 | − | 0.242057i | ||||
\(989\) | 16.0000 | 0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | −12.3607 | + | 38.0423i | −0.392452 | + | 1.20784i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.2148 | + | 27.0381i | 1.17860 | + | 0.856306i | 0.992013 | − | 0.126132i | \(-0.0402562\pi\) |
0.186590 | + | 0.982438i | \(0.440256\pi\) | |||||||
\(998\) | 29.1246 | − | 21.1603i | 0.921923 | − | 0.669817i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 605.2.g.a.251.1 | 4 | ||
11.2 | odd | 10 | 605.2.g.c.366.1 | 4 | |||
11.3 | even | 5 | inner | 605.2.g.a.81.1 | 4 | ||
11.4 | even | 5 | 55.2.a.a.1.1 | ✓ | 1 | ||
11.5 | even | 5 | inner | 605.2.g.a.511.1 | 4 | ||
11.6 | odd | 10 | 605.2.g.c.511.1 | 4 | |||
11.7 | odd | 10 | 605.2.a.b.1.1 | 1 | |||
11.8 | odd | 10 | 605.2.g.c.81.1 | 4 | |||
11.9 | even | 5 | inner | 605.2.g.a.366.1 | 4 | ||
11.10 | odd | 2 | 605.2.g.c.251.1 | 4 | |||
33.26 | odd | 10 | 495.2.a.a.1.1 | 1 | |||
33.29 | even | 10 | 5445.2.a.i.1.1 | 1 | |||
44.7 | even | 10 | 9680.2.a.r.1.1 | 1 | |||
44.15 | odd | 10 | 880.2.a.h.1.1 | 1 | |||
55.4 | even | 10 | 275.2.a.a.1.1 | 1 | |||
55.29 | odd | 10 | 3025.2.a.f.1.1 | 1 | |||
55.37 | odd | 20 | 275.2.b.b.199.2 | 2 | |||
55.48 | odd | 20 | 275.2.b.b.199.1 | 2 | |||
77.48 | odd | 10 | 2695.2.a.c.1.1 | 1 | |||
88.37 | even | 10 | 3520.2.a.p.1.1 | 1 | |||
88.59 | odd | 10 | 3520.2.a.n.1.1 | 1 | |||
132.59 | even | 10 | 7920.2.a.i.1.1 | 1 | |||
143.103 | even | 10 | 9295.2.a.b.1.1 | 1 | |||
165.59 | odd | 10 | 2475.2.a.i.1.1 | 1 | |||
165.92 | even | 20 | 2475.2.c.f.199.1 | 2 | |||
165.158 | even | 20 | 2475.2.c.f.199.2 | 2 | |||
220.59 | odd | 10 | 4400.2.a.p.1.1 | 1 | |||
220.103 | even | 20 | 4400.2.b.n.4049.2 | 2 | |||
220.147 | even | 20 | 4400.2.b.n.4049.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.a.1.1 | ✓ | 1 | 11.4 | even | 5 | ||
275.2.a.a.1.1 | 1 | 55.4 | even | 10 | |||
275.2.b.b.199.1 | 2 | 55.48 | odd | 20 | |||
275.2.b.b.199.2 | 2 | 55.37 | odd | 20 | |||
495.2.a.a.1.1 | 1 | 33.26 | odd | 10 | |||
605.2.a.b.1.1 | 1 | 11.7 | odd | 10 | |||
605.2.g.a.81.1 | 4 | 11.3 | even | 5 | inner | ||
605.2.g.a.251.1 | 4 | 1.1 | even | 1 | trivial | ||
605.2.g.a.366.1 | 4 | 11.9 | even | 5 | inner | ||
605.2.g.a.511.1 | 4 | 11.5 | even | 5 | inner | ||
605.2.g.c.81.1 | 4 | 11.8 | odd | 10 | |||
605.2.g.c.251.1 | 4 | 11.10 | odd | 2 | |||
605.2.g.c.366.1 | 4 | 11.2 | odd | 10 | |||
605.2.g.c.511.1 | 4 | 11.6 | odd | 10 | |||
880.2.a.h.1.1 | 1 | 44.15 | odd | 10 | |||
2475.2.a.i.1.1 | 1 | 165.59 | odd | 10 | |||
2475.2.c.f.199.1 | 2 | 165.92 | even | 20 | |||
2475.2.c.f.199.2 | 2 | 165.158 | even | 20 | |||
2695.2.a.c.1.1 | 1 | 77.48 | odd | 10 | |||
3025.2.a.f.1.1 | 1 | 55.29 | odd | 10 | |||
3520.2.a.n.1.1 | 1 | 88.59 | odd | 10 | |||
3520.2.a.p.1.1 | 1 | 88.37 | even | 10 | |||
4400.2.a.p.1.1 | 1 | 220.59 | odd | 10 | |||
4400.2.b.n.4049.1 | 2 | 220.147 | even | 20 | |||
4400.2.b.n.4049.2 | 2 | 220.103 | even | 20 | |||
5445.2.a.i.1.1 | 1 | 33.29 | even | 10 | |||
7920.2.a.i.1.1 | 1 | 132.59 | even | 10 | |||
9295.2.a.b.1.1 | 1 | 143.103 | even | 10 | |||
9680.2.a.r.1.1 | 1 | 44.7 | even | 10 |