Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [55,2,Mod(32,55)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(55, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("55.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 55 = 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 55.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.439177211117\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Root | \(-1.58114 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 55.43 |
Dual form | 55.2.e.a.32.1 |
$q$-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 \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).
\(n\) | \(12\) | \(46\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58114 | − | 1.58114i | −1.11803 | − | 1.11803i | −0.992030 | − | 0.126004i | \(-0.959785\pi\) |
−0.126004 | − | 0.992030i | \(-0.540215\pi\) | |||||||
\(3\) | −1.00000 | − | 1.00000i | −0.577350 | − | 0.577350i | 0.356822 | − | 0.934172i | \(-0.383860\pi\) |
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 3.00000i | 1.50000i | ||||||||
\(5\) | −2.00000 | − | 1.00000i | −0.894427 | − | 0.447214i | ||||
\(6\) | 3.16228i | 1.29099i | ||||||||
\(7\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(8\) | 1.58114 | − | 1.58114i | 0.559017 | − | 0.559017i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 1.58114 | + | 4.74342i | 0.500000 | + | 1.50000i | ||||
\(11\) | 1.00000 | − | 3.16228i | 0.301511 | − | 0.953463i | ||||
\(12\) | 3.00000 | − | 3.00000i | 0.866025 | − | 0.866025i | ||||
\(13\) | 3.16228 | − | 3.16228i | 0.877058 | − | 0.877058i | −0.116171 | − | 0.993229i | \(-0.537062\pi\) |
0.993229 | + | 0.116171i | \(0.0370621\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | + | 3.00000i | 0.258199 | + | 0.774597i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.16228 | + | 3.16228i | 0.766965 | + | 0.766965i | 0.977571 | − | 0.210606i | \(-0.0675437\pi\) |
−0.210606 | + | 0.977571i | \(0.567544\pi\) | |||||||
\(18\) | −1.58114 | + | 1.58114i | −0.372678 | + | 0.372678i | ||||
\(19\) | −6.32456 | −1.45095 | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | 3.00000 | − | 6.00000i | 0.670820 | − | 1.34164i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.58114 | + | 3.41886i | −1.40310 | + | 0.728904i | ||||
\(23\) | −1.00000 | − | 1.00000i | −0.208514 | − | 0.208514i | 0.595121 | − | 0.803636i | \(-0.297104\pi\) |
−0.803636 | + | 0.595121i | \(0.797104\pi\) | |||||||
\(24\) | −3.16228 | −0.645497 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | −10.0000 | −1.96116 | ||||||||
\(27\) | −4.00000 | + | 4.00000i | −0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.32456 | 1.17444 | 0.587220 | − | 0.809427i | \(-0.300222\pi\) | ||||
0.587220 | + | 0.809427i | \(0.300222\pi\) | |||||||
\(30\) | 3.16228 | − | 6.32456i | 0.577350 | − | 1.15470i | ||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | −4.74342 | − | 4.74342i | −0.838525 | − | 0.838525i | ||||
\(33\) | −4.16228 | + | 2.16228i | −0.724560 | + | 0.376404i | ||||
\(34\) | − | 10.0000i | − | 1.71499i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 3.00000 | − | 3.00000i | 0.493197 | − | 0.493197i | −0.416115 | − | 0.909312i | \(-0.636609\pi\) |
0.909312 | + | 0.416115i | \(0.136609\pi\) | |||||||
\(38\) | 10.0000 | + | 10.0000i | 1.62221 | + | 1.62221i | ||||
\(39\) | −6.32456 | −1.01274 | ||||||||
\(40\) | −4.74342 | + | 1.58114i | −0.750000 | + | 0.250000i | ||||
\(41\) | 6.32456i | 0.987730i | 0.869539 | + | 0.493865i | \(0.164416\pi\) | ||||
−0.869539 | + | 0.493865i | \(0.835584\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 9.48683 | + | 3.00000i | 1.43019 | + | 0.452267i | ||||
\(45\) | −1.00000 | + | 2.00000i | −0.149071 | + | 0.298142i | ||||
\(46\) | 3.16228i | 0.466252i | ||||||||
\(47\) | 3.00000 | − | 3.00000i | 0.437595 | − | 0.437595i | −0.453607 | − | 0.891202i | \(-0.649863\pi\) |
0.891202 | + | 0.453607i | \(0.149863\pi\) | |||||||
\(48\) | −1.00000 | − | 1.00000i | −0.144338 | − | 0.144338i | ||||
\(49\) | − | 7.00000i | − | 1.00000i | ||||||
\(50\) | 1.58114 | − | 11.0680i | 0.223607 | − | 1.56525i | ||||
\(51\) | − | 6.32456i | − | 0.885615i | ||||||
\(52\) | 9.48683 | + | 9.48683i | 1.31559 | + | 1.31559i | ||||
\(53\) | −1.00000 | − | 1.00000i | −0.137361 | − | 0.137361i | 0.635083 | − | 0.772444i | \(-0.280966\pi\) |
−0.772444 | + | 0.635083i | \(0.780966\pi\) | |||||||
\(54\) | 12.6491 | 1.72133 | ||||||||
\(55\) | −5.16228 | + | 5.32456i | −0.696081 | + | 0.717963i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.32456 | + | 6.32456i | 0.837708 | + | 0.837708i | ||||
\(58\) | −10.0000 | − | 10.0000i | −1.31306 | − | 1.31306i | ||||
\(59\) | 6.00000i | 0.781133i | 0.920575 | + | 0.390567i | \(0.127721\pi\) | ||||
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | −9.00000 | + | 3.00000i | −1.16190 | + | 0.387298i | ||||
\(61\) | − | 6.32456i | − | 0.809776i | −0.914366 | − | 0.404888i | \(-0.867310\pi\) | ||
0.914366 | − | 0.404888i | \(-0.132690\pi\) | |||||||
\(62\) | −3.16228 | − | 3.16228i | −0.401610 | − | 0.401610i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000i | 1.62500i | ||||||||
\(65\) | −9.48683 | + | 3.16228i | −1.17670 | + | 0.392232i | ||||
\(66\) | 10.0000 | + | 3.16228i | 1.23091 | + | 0.389249i | ||||
\(67\) | 3.00000 | − | 3.00000i | 0.366508 | − | 0.366508i | −0.499694 | − | 0.866202i | \(-0.666554\pi\) |
0.866202 | + | 0.499694i | \(0.166554\pi\) | |||||||
\(68\) | −9.48683 | + | 9.48683i | −1.15045 | + | 1.15045i | ||||
\(69\) | 2.00000i | 0.240772i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −1.58114 | − | 1.58114i | −0.186339 | − | 0.186339i | ||||
\(73\) | −3.16228 | + | 3.16228i | −0.370117 | + | 0.370117i | −0.867520 | − | 0.497403i | \(-0.834287\pi\) |
0.497403 | + | 0.867520i | \(0.334287\pi\) | |||||||
\(74\) | −9.48683 | −1.10282 | ||||||||
\(75\) | 1.00000 | − | 7.00000i | 0.115470 | − | 0.808290i | ||||
\(76\) | − | 18.9737i | − | 2.17643i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.0000 | + | 10.0000i | 1.13228 | + | 1.13228i | ||||
\(79\) | 6.32456 | 0.711568 | 0.355784 | − | 0.934568i | \(-0.384214\pi\) | ||||
0.355784 | + | 0.934568i | \(0.384214\pi\) | |||||||
\(80\) | −2.00000 | − | 1.00000i | −0.223607 | − | 0.111803i | ||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 10.0000 | − | 10.0000i | 1.10432 | − | 1.10432i | ||||
\(83\) | 6.32456 | − | 6.32456i | 0.694210 | − | 0.694210i | −0.268945 | − | 0.963155i | \(-0.586675\pi\) |
0.963155 | + | 0.268945i | \(0.0866751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.16228 | − | 9.48683i | −0.342997 | − | 1.02899i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.32456 | − | 6.32456i | −0.678064 | − | 0.678064i | ||||
\(88\) | −3.41886 | − | 6.58114i | −0.364452 | − | 0.701552i | ||||
\(89\) | 6.00000i | 0.635999i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(90\) | 4.74342 | − | 1.58114i | 0.500000 | − | 0.166667i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.00000 | − | 3.00000i | 0.312772 | − | 0.312772i | ||||
\(93\) | −2.00000 | − | 2.00000i | −0.207390 | − | 0.207390i | ||||
\(94\) | −9.48683 | −0.978492 | ||||||||
\(95\) | 12.6491 | + | 6.32456i | 1.29777 | + | 0.648886i | ||||
\(96\) | 9.48683i | 0.968246i | ||||||||
\(97\) | −7.00000 | + | 7.00000i | −0.710742 | + | 0.710742i | −0.966691 | − | 0.255948i | \(-0.917612\pi\) |
0.255948 | + | 0.966691i | \(0.417612\pi\) | |||||||
\(98\) | −11.0680 | + | 11.0680i | −1.11803 | + | 1.11803i | ||||
\(99\) | −3.16228 | − | 1.00000i | −0.317821 | − | 0.100504i | ||||
\(100\) | −12.0000 | + | 9.00000i | −1.20000 | + | 0.900000i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | −10.0000 | + | 10.0000i | −0.990148 | + | 0.990148i | ||||
\(103\) | 9.00000 | + | 9.00000i | 0.886796 | + | 0.886796i | 0.994214 | − | 0.107418i | \(-0.0342582\pi\) |
−0.107418 | + | 0.994214i | \(0.534258\pi\) | |||||||
\(104\) | − | 10.0000i | − | 0.980581i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.16228i | 0.307148i | ||||||||
\(107\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | −12.0000 | − | 12.0000i | −1.15470 | − | 1.15470i | ||||
\(109\) | 12.6491 | 1.21157 | 0.605783 | − | 0.795630i | \(-0.292860\pi\) | ||||
0.605783 | + | 0.795630i | \(0.292860\pi\) | |||||||
\(110\) | 16.5811 | − | 0.256584i | 1.58095 | − | 0.0244643i | ||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.00000 | + | 9.00000i | 0.846649 | + | 0.846649i | 0.989713 | − | 0.143065i | \(-0.0456957\pi\) |
−0.143065 | + | 0.989713i | \(0.545696\pi\) | |||||||
\(114\) | − | 20.0000i | − | 1.87317i | ||||||
\(115\) | 1.00000 | + | 3.00000i | 0.0932505 | + | 0.279751i | ||||
\(116\) | 18.9737i | 1.76166i | ||||||||
\(117\) | −3.16228 | − | 3.16228i | −0.292353 | − | 0.292353i | ||||
\(118\) | 9.48683 | − | 9.48683i | 0.873334 | − | 0.873334i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.32456 | + | 3.16228i | 0.577350 | + | 0.288675i | ||||
\(121\) | −9.00000 | − | 6.32456i | −0.818182 | − | 0.574960i | ||||
\(122\) | −10.0000 | + | 10.0000i | −0.905357 | + | 0.905357i | ||||
\(123\) | 6.32456 | − | 6.32456i | 0.570266 | − | 0.570266i | ||||
\(124\) | 6.00000i | 0.538816i | ||||||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.32456 | + | 6.32456i | 0.561214 | + | 0.561214i | 0.929652 | − | 0.368439i | \(-0.120108\pi\) |
−0.368439 | + | 0.929652i | \(0.620108\pi\) | |||||||
\(128\) | 11.0680 | − | 11.0680i | 0.978280 | − | 0.978280i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 20.0000 | + | 10.0000i | 1.75412 | + | 0.877058i | ||||
\(131\) | 12.6491i | 1.10516i | 0.833461 | + | 0.552579i | \(0.186356\pi\) | ||||
−0.833461 | + | 0.552579i | \(0.813644\pi\) | |||||||
\(132\) | −6.48683 | − | 12.4868i | −0.564606 | − | 1.08684i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.48683 | −0.819538 | ||||||||
\(135\) | 12.0000 | − | 4.00000i | 1.03280 | − | 0.344265i | ||||
\(136\) | 10.0000 | 0.857493 | ||||||||
\(137\) | 13.0000 | − | 13.0000i | 1.11066 | − | 1.11066i | 0.117604 | − | 0.993061i | \(-0.462479\pi\) |
0.993061 | − | 0.117604i | \(-0.0375215\pi\) | |||||||
\(138\) | 3.16228 | − | 3.16228i | 0.269191 | − | 0.269191i | ||||
\(139\) | −12.6491 | −1.07288 | −0.536442 | − | 0.843937i | \(-0.680232\pi\) | ||||
−0.536442 | + | 0.843937i | \(0.680232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 12.6491 | + | 12.6491i | 1.06149 | + | 1.06149i | ||||
\(143\) | −6.83772 | − | 13.1623i | −0.571799 | − | 1.10068i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −12.6491 | − | 6.32456i | −1.05045 | − | 0.525226i | ||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | −7.00000 | + | 7.00000i | −0.577350 | + | 0.577350i | ||||
\(148\) | 9.00000 | + | 9.00000i | 0.739795 | + | 0.739795i | ||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −12.6491 | + | 9.48683i | −1.03280 | + | 0.774597i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | −10.0000 | + | 10.0000i | −0.811107 | + | 0.811107i | ||||
\(153\) | 3.16228 | − | 3.16228i | 0.255655 | − | 0.255655i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | − | 2.00000i | −0.321288 | − | 0.160644i | ||||
\(156\) | − | 18.9737i | − | 1.51911i | ||||||
\(157\) | −7.00000 | + | 7.00000i | −0.558661 | + | 0.558661i | −0.928926 | − | 0.370265i | \(-0.879267\pi\) |
0.370265 | + | 0.928926i | \(0.379267\pi\) | |||||||
\(158\) | −10.0000 | − | 10.0000i | −0.795557 | − | 0.795557i | ||||
\(159\) | 2.00000i | 0.158610i | ||||||||
\(160\) | 4.74342 | + | 14.2302i | 0.375000 | + | 1.12500i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.90569 | − | 7.90569i | −0.621130 | − | 0.621130i | ||||
\(163\) | −1.00000 | − | 1.00000i | −0.0783260 | − | 0.0783260i | 0.666858 | − | 0.745184i | \(-0.267639\pi\) |
−0.745184 | + | 0.666858i | \(0.767639\pi\) | |||||||
\(164\) | −18.9737 | −1.48159 | ||||||||
\(165\) | 10.4868 | − | 0.162278i | 0.816399 | − | 0.0126333i | ||||
\(166\) | −20.0000 | −1.55230 | ||||||||
\(167\) | −12.6491 | − | 12.6491i | −0.978818 | − | 0.978818i | 0.0209627 | − | 0.999780i | \(-0.493327\pi\) |
−0.999780 | + | 0.0209627i | \(0.993327\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.00000i | − | 0.538462i | ||||||
\(170\) | −10.0000 | + | 20.0000i | −0.766965 | + | 1.53393i | ||||
\(171\) | 6.32456i | 0.483651i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.16228 | + | 3.16228i | −0.240424 | + | 0.240424i | −0.817025 | − | 0.576602i | \(-0.804378\pi\) |
0.576602 | + | 0.817025i | \(0.304378\pi\) | |||||||
\(174\) | 20.0000i | 1.51620i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | − | 3.16228i | 0.0753778 | − | 0.238366i | ||||
\(177\) | 6.00000 | − | 6.00000i | 0.450988 | − | 0.450988i | ||||
\(178\) | 9.48683 | − | 9.48683i | 0.711068 | − | 0.711068i | ||||
\(179\) | − | 4.00000i | − | 0.298974i | −0.988764 | − | 0.149487i | \(-0.952238\pi\) | ||
0.988764 | − | 0.149487i | \(-0.0477622\pi\) | |||||||
\(180\) | −6.00000 | − | 3.00000i | −0.447214 | − | 0.223607i | ||||
\(181\) | −8.00000 | −0.594635 | −0.297318 | − | 0.954779i | \(-0.596092\pi\) | ||||
−0.297318 | + | 0.954779i | \(0.596092\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.32456 | + | 6.32456i | −0.467525 | + | 0.467525i | ||||
\(184\) | −3.16228 | −0.233126 | ||||||||
\(185\) | −9.00000 | + | 3.00000i | −0.661693 | + | 0.220564i | ||||
\(186\) | 6.32456i | 0.463739i | ||||||||
\(187\) | 13.1623 | − | 6.83772i | 0.962521 | − | 0.500024i | ||||
\(188\) | 9.00000 | + | 9.00000i | 0.656392 | + | 0.656392i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.0000 | − | 30.0000i | −0.725476 | − | 2.17643i | ||||
\(191\) | 22.0000 | 1.59186 | 0.795932 | − | 0.605386i | \(-0.206981\pi\) | ||||
0.795932 | + | 0.605386i | \(0.206981\pi\) | |||||||
\(192\) | 13.0000 | − | 13.0000i | 0.938194 | − | 0.938194i | ||||
\(193\) | −15.8114 | + | 15.8114i | −1.13813 | + | 1.13813i | −0.149343 | + | 0.988785i | \(0.547716\pi\) |
−0.988785 | + | 0.149343i | \(0.952284\pi\) | |||||||
\(194\) | 22.1359 | 1.58927 | ||||||||
\(195\) | 12.6491 | + | 6.32456i | 0.905822 | + | 0.452911i | ||||
\(196\) | 21.0000 | 1.50000 | ||||||||
\(197\) | −3.16228 | − | 3.16228i | −0.225303 | − | 0.225303i | 0.585424 | − | 0.810727i | \(-0.300928\pi\) |
−0.810727 | + | 0.585424i | \(0.800928\pi\) | |||||||
\(198\) | 3.41886 | + | 6.58114i | 0.242968 | + | 0.467701i | ||||
\(199\) | 6.00000i | 0.425329i | 0.977125 | + | 0.212664i | \(0.0682141\pi\) | ||||
−0.977125 | + | 0.212664i | \(0.931786\pi\) | |||||||
\(200\) | 11.0680 | + | 1.58114i | 0.782624 | + | 0.111803i | ||||
\(201\) | −6.00000 | −0.423207 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 18.9737 | 1.32842 | ||||||||
\(205\) | 6.32456 | − | 12.6491i | 0.441726 | − | 0.883452i | ||||
\(206\) | − | 28.4605i | − | 1.98294i | ||||||
\(207\) | −1.00000 | + | 1.00000i | −0.0695048 | + | 0.0695048i | ||||
\(208\) | 3.16228 | − | 3.16228i | 0.219265 | − | 0.219265i | ||||
\(209\) | −6.32456 | + | 20.0000i | −0.437479 | + | 1.38343i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.2982i | 1.74160i | 0.491636 | + | 0.870801i | \(0.336399\pi\) | ||||
−0.491636 | + | 0.870801i | \(0.663601\pi\) | |||||||
\(212\) | 3.00000 | − | 3.00000i | 0.206041 | − | 0.206041i | ||||
\(213\) | 8.00000 | + | 8.00000i | 0.548151 | + | 0.548151i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 12.6491i | 0.860663i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −20.0000 | − | 20.0000i | −1.35457 | − | 1.35457i | ||||
\(219\) | 6.32456 | 0.427374 | ||||||||
\(220\) | −15.9737 | − | 15.4868i | −1.07694 | − | 1.04412i | ||||
\(221\) | 20.0000 | 1.34535 | ||||||||
\(222\) | 9.48683 | + | 9.48683i | 0.636715 | + | 0.636715i | ||||
\(223\) | −11.0000 | − | 11.0000i | −0.736614 | − | 0.736614i | 0.235307 | − | 0.971921i | \(-0.424391\pi\) |
−0.971921 | + | 0.235307i | \(0.924391\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | − | 3.00000i | 0.266667 | − | 0.200000i | ||||
\(226\) | − | 28.4605i | − | 1.89316i | ||||||
\(227\) | 6.32456 | + | 6.32456i | 0.419775 | + | 0.419775i | 0.885126 | − | 0.465351i | \(-0.154072\pi\) |
−0.465351 | + | 0.885126i | \(0.654072\pi\) | |||||||
\(228\) | −18.9737 | + | 18.9737i | −1.25656 | + | 1.25656i | ||||
\(229\) | − | 4.00000i | − | 0.264327i | −0.991228 | − | 0.132164i | \(-0.957808\pi\) | ||
0.991228 | − | 0.132164i | \(-0.0421925\pi\) | |||||||
\(230\) | 3.16228 | − | 6.32456i | 0.208514 | − | 0.417029i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.0000 | − | 10.0000i | 0.656532 | − | 0.656532i | ||||
\(233\) | −9.48683 | + | 9.48683i | −0.621503 | + | 0.621503i | −0.945916 | − | 0.324413i | \(-0.894833\pi\) |
0.324413 | + | 0.945916i | \(0.394833\pi\) | |||||||
\(234\) | 10.0000i | 0.653720i | ||||||||
\(235\) | −9.00000 | + | 3.00000i | −0.587095 | + | 0.195698i | ||||
\(236\) | −18.0000 | −1.17170 | ||||||||
\(237\) | −6.32456 | − | 6.32456i | −0.410824 | − | 0.410824i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.9737 | 1.22730 | 0.613652 | − | 0.789576i | \(-0.289700\pi\) | ||||
0.613652 | + | 0.789576i | \(0.289700\pi\) | |||||||
\(240\) | 1.00000 | + | 3.00000i | 0.0645497 | + | 0.193649i | ||||
\(241\) | 6.32456i | 0.407400i | 0.979033 | + | 0.203700i | \(0.0652968\pi\) | ||||
−0.979033 | + | 0.203700i | \(0.934703\pi\) | |||||||
\(242\) | 4.23025 | + | 24.2302i | 0.271931 | + | 1.55758i | ||||
\(243\) | 7.00000 | + | 7.00000i | 0.449050 | + | 0.449050i | ||||
\(244\) | 18.9737 | 1.21466 | ||||||||
\(245\) | −7.00000 | + | 14.0000i | −0.447214 | + | 0.894427i | ||||
\(246\) | −20.0000 | −1.27515 | ||||||||
\(247\) | −20.0000 | + | 20.0000i | −1.27257 | + | 1.27257i | ||||
\(248\) | 3.16228 | − | 3.16228i | 0.200805 | − | 0.200805i | ||||
\(249\) | −12.6491 | −0.801605 | ||||||||
\(250\) | −14.2302 | + | 20.5548i | −0.900000 | + | 1.30000i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.16228 | + | 2.16228i | −0.261680 | + | 0.135941i | ||||
\(254\) | − | 20.0000i | − | 1.25491i | ||||||
\(255\) | −6.32456 | + | 12.6491i | −0.396059 | + | 0.792118i | ||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | −7.00000 | + | 7.00000i | −0.436648 | + | 0.436648i | −0.890882 | − | 0.454234i | \(-0.849913\pi\) |
0.454234 | + | 0.890882i | \(0.349913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.48683 | − | 28.4605i | −0.588348 | − | 1.76505i | ||||
\(261\) | − | 6.32456i | − | 0.391480i | ||||||
\(262\) | 20.0000 | − | 20.0000i | 1.23560 | − | 1.23560i | ||||
\(263\) | 18.9737 | − | 18.9737i | 1.16997 | − | 1.16997i | 0.187749 | − | 0.982217i | \(-0.439881\pi\) |
0.982217 | − | 0.187749i | \(-0.0601193\pi\) | |||||||
\(264\) | −3.16228 | + | 10.0000i | −0.194625 | + | 0.615457i | ||||
\(265\) | 1.00000 | + | 3.00000i | 0.0614295 | + | 0.184289i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00000 | − | 6.00000i | 0.367194 | − | 0.367194i | ||||
\(268\) | 9.00000 | + | 9.00000i | 0.549762 | + | 0.549762i | ||||
\(269\) | − | 24.0000i | − | 1.46331i | −0.681677 | − | 0.731653i | \(-0.738749\pi\) | ||
0.681677 | − | 0.731653i | \(-0.261251\pi\) | |||||||
\(270\) | −25.2982 | − | 12.6491i | −1.53960 | − | 0.769800i | ||||
\(271\) | − | 12.6491i | − | 0.768379i | −0.923254 | − | 0.384189i | \(-0.874481\pi\) | ||
0.923254 | − | 0.384189i | \(-0.125519\pi\) | |||||||
\(272\) | 3.16228 | + | 3.16228i | 0.191741 | + | 0.191741i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −41.1096 | −2.48352 | ||||||||
\(275\) | 15.6491 | − | 5.48683i | 0.943677 | − | 0.330868i | ||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | −9.48683 | − | 9.48683i | −0.570009 | − | 0.570009i | 0.362122 | − | 0.932131i | \(-0.382052\pi\) |
−0.932131 | + | 0.362122i | \(0.882052\pi\) | |||||||
\(278\) | 20.0000 | + | 20.0000i | 1.19952 | + | 1.19952i | ||||
\(279\) | − | 2.00000i | − | 0.119737i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.9737i | − | 1.13187i | −0.824448 | − | 0.565937i | \(-0.808515\pi\) | ||
0.824448 | − | 0.565937i | \(-0.191485\pi\) | |||||||
\(282\) | 9.48683 | + | 9.48683i | 0.564933 | + | 0.564933i | ||||
\(283\) | 6.32456 | − | 6.32456i | 0.375956 | − | 0.375956i | −0.493685 | − | 0.869641i | \(-0.664350\pi\) |
0.869641 | + | 0.493685i | \(0.164350\pi\) | |||||||
\(284\) | − | 24.0000i | − | 1.42414i | ||||||
\(285\) | −6.32456 | − | 18.9737i | −0.374634 | − | 1.12390i | ||||
\(286\) | −10.0000 | + | 31.6228i | −0.591312 | + | 1.86989i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.74342 | + | 4.74342i | −0.279508 | + | 0.279508i | ||||
\(289\) | 3.00000i | 0.176471i | ||||||||
\(290\) | 10.0000 | + | 30.0000i | 0.587220 | + | 1.76166i | ||||
\(291\) | 14.0000 | 0.820695 | ||||||||
\(292\) | −9.48683 | − | 9.48683i | −0.555175 | − | 0.555175i | ||||
\(293\) | −15.8114 | + | 15.8114i | −0.923711 | + | 0.923711i | −0.997289 | − | 0.0735783i | \(-0.976558\pi\) |
0.0735783 | + | 0.997289i | \(0.476558\pi\) | |||||||
\(294\) | 22.1359 | 1.29099 | ||||||||
\(295\) | 6.00000 | − | 12.0000i | 0.349334 | − | 0.698667i | ||||
\(296\) | − | 9.48683i | − | 0.551411i | ||||||
\(297\) | 8.64911 | + | 16.6491i | 0.501872 | + | 0.966079i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.32456 | −0.365758 | ||||||||
\(300\) | 21.0000 | + | 3.00000i | 1.21244 | + | 0.173205i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.32456 | −0.362738 | ||||||||
\(305\) | −6.32456 | + | 12.6491i | −0.362143 | + | 0.724286i | ||||
\(306\) | −10.0000 | −0.571662 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 18.0000i | − | 1.02398i | ||||||
\(310\) | 3.16228 | + | 9.48683i | 0.179605 | + | 0.538816i | ||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | −10.0000 | + | 10.0000i | −0.566139 | + | 0.566139i | ||||
\(313\) | 9.00000 | + | 9.00000i | 0.508710 | + | 0.508710i | 0.914130 | − | 0.405420i | \(-0.132875\pi\) |
−0.405420 | + | 0.914130i | \(0.632875\pi\) | |||||||
\(314\) | 22.1359 | 1.24920 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.9737i | 1.06735i | ||||||||
\(317\) | −17.0000 | + | 17.0000i | −0.954815 | + | 0.954815i | −0.999022 | − | 0.0442073i | \(-0.985924\pi\) |
0.0442073 | + | 0.999022i | \(0.485924\pi\) | |||||||
\(318\) | 3.16228 | − | 3.16228i | 0.177332 | − | 0.177332i | ||||
\(319\) | 6.32456 | − | 20.0000i | 0.354107 | − | 1.11979i | ||||
\(320\) | 13.0000 | − | 26.0000i | 0.726722 | − | 1.45344i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.0000 | − | 20.0000i | −1.11283 | − | 1.11283i | ||||
\(324\) | 15.0000i | 0.833333i | ||||||||
\(325\) | 22.1359 | + | 3.16228i | 1.22788 | + | 0.175412i | ||||
\(326\) | 3.16228i | 0.175142i | ||||||||
\(327\) | −12.6491 | − | 12.6491i | −0.699497 | − | 0.699497i | ||||
\(328\) | 10.0000 | + | 10.0000i | 0.552158 | + | 0.552158i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −16.8377 | − | 16.3246i | −0.926886 | − | 0.898637i | ||||
\(331\) | −18.0000 | −0.989369 | −0.494685 | − | 0.869072i | \(-0.664716\pi\) | ||||
−0.494685 | + | 0.869072i | \(0.664716\pi\) | |||||||
\(332\) | 18.9737 | + | 18.9737i | 1.04132 | + | 1.04132i | ||||
\(333\) | −3.00000 | − | 3.00000i | −0.164399 | − | 0.164399i | ||||
\(334\) | 40.0000i | 2.18870i | ||||||||
\(335\) | −9.00000 | + | 3.00000i | −0.491723 | + | 0.163908i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.48683 | + | 9.48683i | 0.516781 | + | 0.516781i | 0.916596 | − | 0.399815i | \(-0.130926\pi\) |
−0.399815 | + | 0.916596i | \(0.630926\pi\) | |||||||
\(338\) | −11.0680 | + | 11.0680i | −0.602018 | + | 0.602018i | ||||
\(339\) | − | 18.0000i | − | 0.977626i | ||||||
\(340\) | 28.4605 | − | 9.48683i | 1.54349 | − | 0.514496i | ||||
\(341\) | 2.00000 | − | 6.32456i | 0.108306 | − | 0.342494i | ||||
\(342\) | 10.0000 | − | 10.0000i | 0.540738 | − | 0.540738i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.00000 | − | 4.00000i | 0.107676 | − | 0.215353i | ||||
\(346\) | 10.0000 | 0.537603 | ||||||||
\(347\) | −18.9737 | − | 18.9737i | −1.01856 | − | 1.01856i | −0.999824 | − | 0.0187353i | \(-0.994036\pi\) |
−0.0187353 | − | 0.999824i | \(-0.505964\pi\) | |||||||
\(348\) | 18.9737 | − | 18.9737i | 1.01710 | − | 1.01710i | ||||
\(349\) | 31.6228 | 1.69273 | 0.846364 | − | 0.532605i | \(-0.178787\pi\) | ||||
0.846364 | + | 0.532605i | \(0.178787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.2982i | 1.35032i | ||||||||
\(352\) | −19.7434 | + | 10.2566i | −1.05233 | + | 0.546678i | ||||
\(353\) | −21.0000 | − | 21.0000i | −1.11772 | − | 1.11772i | −0.992076 | − | 0.125642i | \(-0.959901\pi\) |
−0.125642 | − | 0.992076i | \(-0.540099\pi\) | |||||||
\(354\) | −18.9737 | −1.00844 | ||||||||
\(355\) | 16.0000 | + | 8.00000i | 0.849192 | + | 0.424596i | ||||
\(356\) | −18.0000 | −0.953998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.32456 | + | 6.32456i | −0.334263 | + | 0.334263i | ||||
\(359\) | −18.9737 | −1.00139 | −0.500696 | − | 0.865623i | \(-0.666923\pi\) | ||||
−0.500696 | + | 0.865623i | \(0.666923\pi\) | |||||||
\(360\) | 1.58114 | + | 4.74342i | 0.0833333 | + | 0.250000i | ||||
\(361\) | 21.0000 | 1.10526 | ||||||||
\(362\) | 12.6491 | + | 12.6491i | 0.664822 | + | 0.664822i | ||||
\(363\) | 2.67544 | + | 15.3246i | 0.140424 | + | 0.804331i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.48683 | − | 3.16228i | 0.496564 | − | 0.165521i | ||||
\(366\) | 20.0000 | 1.04542 | ||||||||
\(367\) | 3.00000 | − | 3.00000i | 0.156599 | − | 0.156599i | −0.624459 | − | 0.781058i | \(-0.714680\pi\) |
0.781058 | + | 0.624459i | \(0.214680\pi\) | |||||||
\(368\) | −1.00000 | − | 1.00000i | −0.0521286 | − | 0.0521286i | ||||
\(369\) | 6.32456 | 0.329243 | ||||||||
\(370\) | 18.9737 | + | 9.48683i | 0.986394 | + | 0.493197i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.00000 | − | 6.00000i | 0.311086 | − | 0.311086i | ||||
\(373\) | −3.16228 | + | 3.16228i | −0.163737 | + | 0.163737i | −0.784220 | − | 0.620483i | \(-0.786937\pi\) |
0.620483 | + | 0.784220i | \(0.286937\pi\) | |||||||
\(374\) | −31.6228 | − | 10.0000i | −1.63517 | − | 0.517088i | ||||
\(375\) | −9.00000 | + | 13.0000i | −0.464758 | + | 0.671317i | ||||
\(376\) | − | 9.48683i | − | 0.489246i | ||||||
\(377\) | 20.0000 | − | 20.0000i | 1.03005 | − | 1.03005i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0000i | 1.33553i | 0.744372 | + | 0.667765i | \(0.232749\pi\) | ||||
−0.744372 | + | 0.667765i | \(0.767251\pi\) | |||||||
\(380\) | −18.9737 | + | 37.9473i | −0.973329 | + | 1.94666i | ||||
\(381\) | − | 12.6491i | − | 0.648034i | ||||||
\(382\) | −34.7851 | − | 34.7851i | −1.77976 | − | 1.77976i | ||||
\(383\) | 19.0000 | + | 19.0000i | 0.970855 | + | 0.970855i | 0.999587 | − | 0.0287325i | \(-0.00914709\pi\) |
−0.0287325 | + | 0.999587i | \(0.509147\pi\) | |||||||
\(384\) | −22.1359 | −1.12962 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 50.0000 | 2.54493 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −21.0000 | − | 21.0000i | −1.06611 | − | 1.06611i | ||||
\(389\) | 16.0000i | 0.811232i | 0.914044 | + | 0.405616i | \(0.132943\pi\) | ||||
−0.914044 | + | 0.405616i | \(0.867057\pi\) | |||||||
\(390\) | −10.0000 | − | 30.0000i | −0.506370 | − | 1.51911i | ||||
\(391\) | − | 6.32456i | − | 0.319847i | ||||||
\(392\) | −11.0680 | − | 11.0680i | −0.559017 | − | 0.559017i | ||||
\(393\) | 12.6491 | − | 12.6491i | 0.638063 | − | 0.638063i | ||||
\(394\) | 10.0000i | 0.503793i | ||||||||
\(395\) | −12.6491 | − | 6.32456i | −0.636446 | − | 0.318223i | ||||
\(396\) | 3.00000 | − | 9.48683i | 0.150756 | − | 0.476731i | ||||
\(397\) | 13.0000 | − | 13.0000i | 0.652451 | − | 0.652451i | −0.301131 | − | 0.953583i | \(-0.597364\pi\) |
0.953583 | + | 0.301131i | \(0.0973643\pi\) | |||||||
\(398\) | 9.48683 | − | 9.48683i | 0.475532 | − | 0.475532i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | 12.0000 | 0.599251 | 0.299626 | − | 0.954057i | \(-0.403138\pi\) | ||||
0.299626 | + | 0.954057i | \(0.403138\pi\) | |||||||
\(402\) | 9.48683 | + | 9.48683i | 0.473160 | + | 0.473160i | ||||
\(403\) | 6.32456 | − | 6.32456i | 0.315049 | − | 0.315049i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.0000 | − | 5.00000i | −0.496904 | − | 0.248452i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.48683 | − | 12.4868i | −0.321540 | − | 0.618949i | ||||
\(408\) | −10.0000 | − | 10.0000i | −0.495074 | − | 0.495074i | ||||
\(409\) | 12.6491 | 0.625458 | 0.312729 | − | 0.949842i | \(-0.398757\pi\) | ||||
0.312729 | + | 0.949842i | \(0.398757\pi\) | |||||||
\(410\) | −30.0000 | + | 10.0000i | −1.48159 | + | 0.493865i | ||||
\(411\) | −26.0000 | −1.28249 | ||||||||
\(412\) | −27.0000 | + | 27.0000i | −1.33019 | + | 1.33019i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.16228 | 0.155417 | ||||||||
\(415\) | −18.9737 | + | 6.32456i | −0.931381 | + | 0.310460i | ||||
\(416\) | −30.0000 | −1.47087 | ||||||||
\(417\) | 12.6491 | + | 12.6491i | 0.619430 | + | 0.619430i | ||||
\(418\) | 41.6228 | − | 21.6228i | 2.03584 | − | 1.05760i | ||||
\(419\) | 36.0000i | 1.75872i | 0.476162 | + | 0.879358i | \(0.342028\pi\) | ||||
−0.476162 | + | 0.879358i | \(0.657972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.0000 | −1.36464 | −0.682318 | − | 0.731055i | \(-0.739028\pi\) | ||||
−0.682318 | + | 0.731055i | \(0.739028\pi\) | |||||||
\(422\) | 40.0000 | − | 40.0000i | 1.94717 | − | 1.94717i | ||||
\(423\) | −3.00000 | − | 3.00000i | −0.145865 | − | 0.145865i | ||||
\(424\) | −3.16228 | −0.153574 | ||||||||
\(425\) | −3.16228 | + | 22.1359i | −0.153393 | + | 1.07375i | ||||
\(426\) | − | 25.2982i | − | 1.22570i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.32456 | + | 20.0000i | −0.305352 | + | 0.965609i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18.9737i | − | 0.913929i | −0.889485 | − | 0.456965i | \(-0.848937\pi\) | ||
0.889485 | − | 0.456965i | \(-0.151063\pi\) | |||||||
\(432\) | −4.00000 | + | 4.00000i | −0.192450 | + | 0.192450i | ||||
\(433\) | −1.00000 | − | 1.00000i | −0.0480569 | − | 0.0480569i | 0.682670 | − | 0.730727i | \(-0.260819\pi\) |
−0.730727 | + | 0.682670i | \(0.760819\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.32456 | + | 18.9737i | 0.303239 | + | 0.909718i | ||||
\(436\) | 37.9473i | 1.81735i | ||||||||
\(437\) | 6.32456 | + | 6.32456i | 0.302545 | + | 0.302545i | ||||
\(438\) | −10.0000 | − | 10.0000i | −0.477818 | − | 0.477818i | ||||
\(439\) | −12.6491 | −0.603709 | −0.301855 | − | 0.953354i | \(-0.597606\pi\) | ||||
−0.301855 | + | 0.953354i | \(0.597606\pi\) | |||||||
\(440\) | 0.256584 | + | 16.5811i | 0.0122321 | + | 0.790475i | ||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | −31.6228 | − | 31.6228i | −1.50414 | − | 1.50414i | ||||
\(443\) | −11.0000 | − | 11.0000i | −0.522626 | − | 0.522626i | 0.395738 | − | 0.918364i | \(-0.370489\pi\) |
−0.918364 | + | 0.395738i | \(0.870489\pi\) | |||||||
\(444\) | − | 18.0000i | − | 0.854242i | ||||||
\(445\) | 6.00000 | − | 12.0000i | 0.284427 | − | 0.568855i | ||||
\(446\) | 34.7851i | 1.64712i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000i | 0.283158i | 0.989927 | + | 0.141579i | \(0.0452178\pi\) | ||||
−0.989927 | + | 0.141579i | \(0.954782\pi\) | |||||||
\(450\) | −11.0680 | − | 1.58114i | −0.521749 | − | 0.0745356i | ||||
\(451\) | 20.0000 | + | 6.32456i | 0.941763 | + | 0.297812i | ||||
\(452\) | −27.0000 | + | 27.0000i | −1.26997 | + | 1.26997i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 20.0000i | − | 0.938647i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.0000 | 0.936586 | ||||||||
\(457\) | 15.8114 | + | 15.8114i | 0.739626 | + | 0.739626i | 0.972505 | − | 0.232880i | \(-0.0748149\pi\) |
−0.232880 | + | 0.972505i | \(0.574815\pi\) | |||||||
\(458\) | −6.32456 | + | 6.32456i | −0.295527 | + | 0.295527i | ||||
\(459\) | −25.2982 | −1.18082 | ||||||||
\(460\) | −9.00000 | + | 3.00000i | −0.419627 | + | 0.139876i | ||||
\(461\) | 25.2982i | 1.17826i | 0.808040 | + | 0.589128i | \(0.200529\pi\) | ||||
−0.808040 | + | 0.589128i | \(0.799471\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.00000 | + | 9.00000i | 0.418265 | + | 0.418265i | 0.884606 | − | 0.466340i | \(-0.154428\pi\) |
−0.466340 | + | 0.884606i | \(0.654428\pi\) | |||||||
\(464\) | 6.32456 | 0.293610 | ||||||||
\(465\) | 2.00000 | + | 6.00000i | 0.0927478 | + | 0.278243i | ||||
\(466\) | 30.0000 | 1.38972 | ||||||||
\(467\) | −7.00000 | + | 7.00000i | −0.323921 | + | 0.323921i | −0.850269 | − | 0.526348i | \(-0.823561\pi\) |
0.526348 | + | 0.850269i | \(0.323561\pi\) | |||||||
\(468\) | 9.48683 | − | 9.48683i | 0.438529 | − | 0.438529i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 18.9737 | + | 9.48683i | 0.875190 | + | 0.437595i | ||||
\(471\) | 14.0000 | 0.645086 | ||||||||
\(472\) | 9.48683 | + | 9.48683i | 0.436667 | + | 0.436667i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 20.0000i | 0.918630i | ||||||||
\(475\) | −18.9737 | − | 25.2982i | −0.870572 | − | 1.16076i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.00000 | + | 1.00000i | −0.0457869 | + | 0.0457869i | ||||
\(478\) | −30.0000 | − | 30.0000i | −1.37217 | − | 1.37217i | ||||
\(479\) | 6.32456 | 0.288976 | 0.144488 | − | 0.989507i | \(-0.453846\pi\) | ||||
0.144488 | + | 0.989507i | \(0.453846\pi\) | |||||||
\(480\) | 9.48683 | − | 18.9737i | 0.433013 | − | 0.866025i | ||||
\(481\) | − | 18.9737i | − | 0.865125i | ||||||
\(482\) | 10.0000 | − | 10.0000i | 0.455488 | − | 0.455488i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.9737 | − | 27.0000i | 0.862439 | − | 1.22727i | ||||
\(485\) | 21.0000 | − | 7.00000i | 0.953561 | − | 0.317854i | ||||
\(486\) | − | 22.1359i | − | 1.00411i | ||||||
\(487\) | 3.00000 | − | 3.00000i | 0.135943 | − | 0.135943i | −0.635861 | − | 0.771804i | \(-0.719355\pi\) |
0.771804 | + | 0.635861i | \(0.219355\pi\) | |||||||
\(488\) | −10.0000 | − | 10.0000i | −0.452679 | − | 0.452679i | ||||
\(489\) | 2.00000i | 0.0904431i | ||||||||
\(490\) | 33.2039 | − | 11.0680i | 1.50000 | − | 0.500000i | ||||
\(491\) | 6.32456i | 0.285423i | 0.989764 | + | 0.142712i | \(0.0455821\pi\) | ||||
−0.989764 | + | 0.142712i | \(0.954418\pi\) | |||||||
\(492\) | 18.9737 | + | 18.9737i | 0.855399 | + | 0.855399i | ||||
\(493\) | 20.0000 | + | 20.0000i | 0.900755 | + | 0.900755i | ||||
\(494\) | 63.2456 | 2.84555 | ||||||||
\(495\) | 5.32456 | + | 5.16228i | 0.239321 | + | 0.232027i | ||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 20.0000 | + | 20.0000i | 0.896221 | + | 0.896221i | ||||
\(499\) | − | 34.0000i | − | 1.52205i | −0.648723 | − | 0.761025i | \(-0.724697\pi\) | ||
0.648723 | − | 0.761025i | \(-0.275303\pi\) | |||||||
\(500\) | 33.0000 | − | 6.00000i | 1.47580 | − | 0.268328i | ||||
\(501\) | 25.2982i | 1.13024i | ||||||||
\(502\) | −18.9737 | − | 18.9737i | −0.846836 | − | 0.846836i | ||||
\(503\) | −6.32456 | + | 6.32456i | −0.281998 | + | 0.281998i | −0.833905 | − | 0.551907i | \(-0.813900\pi\) |
0.551907 | + | 0.833905i | \(0.313900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.0000 | + | 3.16228i | 0.444554 | + | 0.140580i | ||||
\(507\) | −7.00000 | + | 7.00000i | −0.310881 | + | 0.310881i | ||||
\(508\) | −18.9737 | + | 18.9737i | −0.841820 | + | 0.841820i | ||||
\(509\) | − | 4.00000i | − | 0.177297i | −0.996063 | − | 0.0886484i | \(-0.971745\pi\) | ||
0.996063 | − | 0.0886484i | \(-0.0282548\pi\) | |||||||
\(510\) | 30.0000 | − | 10.0000i | 1.32842 | − | 0.442807i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.90569 | − | 7.90569i | −0.349386 | − | 0.349386i | ||||
\(513\) | 25.2982 | − | 25.2982i | 1.11694 | − | 1.11694i | ||||
\(514\) | 22.1359 | 0.976375 | ||||||||
\(515\) | −9.00000 | − | 27.0000i | −0.396587 | − | 1.18976i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.48683 | − | 12.4868i | −0.285291 | − | 0.549170i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.32456 | 0.277617 | ||||||||
\(520\) | −10.0000 | + | 20.0000i | −0.438529 | + | 0.877058i | ||||
\(521\) | −28.0000 | −1.22670 | −0.613351 | − | 0.789810i | \(-0.710179\pi\) | ||||
−0.613351 | + | 0.789810i | \(0.710179\pi\) | |||||||
\(522\) | −10.0000 | + | 10.0000i | −0.437688 | + | 0.437688i | ||||
\(523\) | −18.9737 | + | 18.9737i | −0.829660 | + | 0.829660i | −0.987470 | − | 0.157809i | \(-0.949557\pi\) |
0.157809 | + | 0.987470i | \(0.449557\pi\) | |||||||
\(524\) | −37.9473 | −1.65774 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −60.0000 | −2.61612 | ||||||||
\(527\) | 6.32456 | + | 6.32456i | 0.275502 | + | 0.275502i | ||||
\(528\) | −4.16228 | + | 2.16228i | −0.181140 | + | 0.0941011i | ||||
\(529\) | − | 21.0000i | − | 0.913043i | ||||||
\(530\) | 3.16228 | − | 6.32456i | 0.137361 | − | 0.274721i | ||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.0000 | + | 20.0000i | 0.866296 | + | 0.866296i | ||||
\(534\) | −18.9737 | −0.821071 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 9.48683i | − | 0.409769i | ||||||
\(537\) | −4.00000 | + | 4.00000i | −0.172613 | + | 0.172613i | ||||
\(538\) | −37.9473 | + | 37.9473i | −1.63603 | + | 1.63603i | ||||
\(539\) | −22.1359 | − | 7.00000i | −0.953463 | − | 0.301511i | ||||
\(540\) | 12.0000 | + | 36.0000i | 0.516398 | + | 1.54919i | ||||
\(541\) | 37.9473i | 1.63148i | 0.578416 | + | 0.815742i | \(0.303671\pi\) | ||||
−0.578416 | + | 0.815742i | \(0.696329\pi\) | |||||||
\(542\) | −20.0000 | + | 20.0000i | −0.859074 | + | 0.859074i | ||||
\(543\) | 8.00000 | + | 8.00000i | 0.343313 | + | 0.343313i | ||||
\(544\) | − | 30.0000i | − | 1.28624i | ||||||
\(545\) | −25.2982 | − | 12.6491i | −1.08366 | − | 0.541828i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.6491 | + | 12.6491i | 0.540837 | + | 0.540837i | 0.923774 | − | 0.382937i | \(-0.125088\pi\) |
−0.382937 | + | 0.923774i | \(0.625088\pi\) | |||||||
\(548\) | 39.0000 | + | 39.0000i | 1.66600 | + | 1.66600i | ||||
\(549\) | −6.32456 | −0.269925 | ||||||||
\(550\) | −33.4189 | − | 16.0680i | −1.42499 | − | 0.685141i | ||||
\(551\) | −40.0000 | −1.70406 | ||||||||
\(552\) | 3.16228 | + | 3.16228i | 0.134595 | + | 0.134595i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 30.0000i | 1.27458i | ||||||||
\(555\) | 12.0000 | + | 6.00000i | 0.509372 | + | 0.254686i | ||||
\(556\) | − | 37.9473i | − | 1.60933i | ||||||
\(557\) | 15.8114 | + | 15.8114i | 0.669950 | + | 0.669950i | 0.957704 | − | 0.287754i | \(-0.0929086\pi\) |
−0.287754 | + | 0.957704i | \(0.592909\pi\) | |||||||
\(558\) | −3.16228 | + | 3.16228i | −0.133870 | + | 0.133870i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.0000 | − | 6.32456i | −0.844401 | − | 0.267023i | ||||
\(562\) | −30.0000 | + | 30.0000i | −1.26547 | + | 1.26547i | ||||
\(563\) | 18.9737 | − | 18.9737i | 0.799645 | − | 0.799645i | −0.183395 | − | 0.983039i | \(-0.558709\pi\) |
0.983039 | + | 0.183395i | \(0.0587086\pi\) | |||||||
\(564\) | − | 18.0000i | − | 0.757937i | ||||||
\(565\) | −9.00000 | − | 27.0000i | −0.378633 | − | 1.13590i | ||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.6491 | + | 12.6491i | −0.530745 | + | 0.530745i | ||||
\(569\) | −37.9473 | −1.59083 | −0.795417 | − | 0.606062i | \(-0.792748\pi\) | ||||
−0.795417 | + | 0.606062i | \(0.792748\pi\) | |||||||
\(570\) | −20.0000 | + | 40.0000i | −0.837708 | + | 1.67542i | ||||
\(571\) | − | 44.2719i | − | 1.85272i | −0.376638 | − | 0.926360i | \(-0.622920\pi\) | ||
0.376638 | − | 0.926360i | \(-0.377080\pi\) | |||||||
\(572\) | 39.4868 | − | 20.5132i | 1.65103 | − | 0.857699i | ||||
\(573\) | −22.0000 | − | 22.0000i | −0.919063 | − | 0.919063i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | − | 7.00000i | 0.0417029 | − | 0.291920i | ||||
\(576\) | 13.0000 | 0.541667 | ||||||||
\(577\) | 23.0000 | − | 23.0000i | 0.957503 | − | 0.957503i | −0.0416305 | − | 0.999133i | \(-0.513255\pi\) |
0.999133 | + | 0.0416305i | \(0.0132552\pi\) | |||||||
\(578\) | 4.74342 | − | 4.74342i | 0.197300 | − | 0.197300i | ||||
\(579\) | 31.6228 | 1.31420 | ||||||||
\(580\) | 18.9737 | − | 37.9473i | 0.787839 | − | 1.57568i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −22.1359 | − | 22.1359i | −0.917564 | − | 0.917564i | ||||
\(583\) | −4.16228 | + | 2.16228i | −0.172384 | + | 0.0895524i | ||||
\(584\) | 10.0000i | 0.413803i | ||||||||
\(585\) | 3.16228 | + | 9.48683i | 0.130744 | + | 0.392232i | ||||
\(586\) | 50.0000 | 2.06548 | ||||||||
\(587\) | −7.00000 | + | 7.00000i | −0.288921 | + | 0.288921i | −0.836653 | − | 0.547733i | \(-0.815491\pi\) |
0.547733 | + | 0.836653i | \(0.315491\pi\) | |||||||
\(588\) | −21.0000 | − | 21.0000i | −0.866025 | − | 0.866025i | ||||
\(589\) | −12.6491 | −0.521198 | ||||||||
\(590\) | −28.4605 | + | 9.48683i | −1.17170 | + | 0.390567i | ||||
\(591\) | 6.32456i | 0.260157i | ||||||||
\(592\) | 3.00000 | − | 3.00000i | 0.123299 | − | 0.123299i | ||||
\(593\) | 15.8114 | − | 15.8114i | 0.649296 | − | 0.649296i | −0.303527 | − | 0.952823i | \(-0.598164\pi\) |
0.952823 | + | 0.303527i | \(0.0981642\pi\) | |||||||
\(594\) | 12.6491 | − | 40.0000i | 0.518999 | − | 1.64122i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.00000 | − | 6.00000i | 0.245564 | − | 0.245564i | ||||
\(598\) | 10.0000 | + | 10.0000i | 0.408930 | + | 0.408930i | ||||
\(599\) | 16.0000i | 0.653742i | 0.945069 | + | 0.326871i | \(0.105994\pi\) | ||||
−0.945069 | + | 0.326871i | \(0.894006\pi\) | |||||||
\(600\) | −9.48683 | − | 12.6491i | −0.387298 | − | 0.516398i | ||||
\(601\) | − | 31.6228i | − | 1.28992i | −0.764216 | − | 0.644960i | \(-0.776874\pi\) | ||
0.764216 | − | 0.644960i | \(-0.223126\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.00000 | − | 3.00000i | −0.122169 | − | 0.122169i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.6754 | + | 21.6491i | 0.474674 | + | 0.880162i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.6228 | + | 31.6228i | 1.28353 | + | 1.28353i | 0.938646 | + | 0.344883i | \(0.112082\pi\) |
0.344883 | + | 0.938646i | \(0.387918\pi\) | |||||||
\(608\) | 30.0000 | + | 30.0000i | 1.21666 | + | 1.21666i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30.0000 | − | 10.0000i | 1.21466 | − | 0.404888i | ||||
\(611\) | − | 18.9737i | − | 0.767592i | ||||||
\(612\) | 9.48683 | + | 9.48683i | 0.383482 | + | 0.383482i | ||||
\(613\) | −28.4605 | + | 28.4605i | −1.14951 | + | 1.14951i | −0.162859 | + | 0.986649i | \(0.552072\pi\) |
−0.986649 | + | 0.162859i | \(0.947928\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.9737 | + | 6.32456i | −0.765092 | + | 0.255031i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.0000 | + | 17.0000i | −0.684394 | + | 0.684394i | −0.960987 | − | 0.276593i | \(-0.910795\pi\) |
0.276593 | + | 0.960987i | \(0.410795\pi\) | |||||||
\(618\) | −28.4605 | + | 28.4605i | −1.14485 | + | 1.14485i | ||||
\(619\) | 36.0000i | 1.44696i | 0.690344 | + | 0.723481i | \(0.257459\pi\) | ||||
−0.690344 | + | 0.723481i | \(0.742541\pi\) | |||||||
\(620\) | 6.00000 | − | 12.0000i | 0.240966 | − | 0.481932i | ||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | 12.6491 | + | 12.6491i | 0.507183 | + | 0.507183i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.32456 | −0.253185 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | − | 28.4605i | − | 1.13751i | ||||||
\(627\) | 26.3246 | − | 13.6754i | 1.05130 | − | 0.546145i | ||||
\(628\) | −21.0000 | − | 21.0000i | −0.837991 | − | 0.837991i | ||||
\(629\) | 18.9737 | 0.756530 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 10.0000 | − | 10.0000i | 0.397779 | − | 0.397779i | ||||
\(633\) | 25.2982 | − | 25.2982i | 1.00551 | − | 1.00551i | ||||
\(634\) | 53.7587 | 2.13503 | ||||||||
\(635\) | −6.32456 | − | 18.9737i | −0.250982 | − | 0.752947i | ||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | −22.1359 | − | 22.1359i | −0.877058 | − | 0.877058i | ||||
\(638\) | −41.6228 | + | 21.6228i | −1.64786 | + | 0.856054i | ||||
\(639\) | 8.00000i | 0.316475i | ||||||||
\(640\) | −33.2039 | + | 11.0680i | −1.31250 | + | 0.437500i | ||||
\(641\) | −8.00000 | −0.315981 | −0.157991 | − | 0.987441i | \(-0.550502\pi\) | ||||
−0.157991 | + | 0.987441i | \(0.550502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.0000 | − | 11.0000i | −0.433798 | − | 0.433798i | 0.456120 | − | 0.889918i | \(-0.349239\pi\) |
−0.889918 | + | 0.456120i | \(0.849239\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 63.2456i | 2.48836i | ||||||||
\(647\) | 13.0000 | − | 13.0000i | 0.511083 | − | 0.511083i | −0.403775 | − | 0.914858i | \(-0.632302\pi\) |
0.914858 | + | 0.403775i | \(0.132302\pi\) | |||||||
\(648\) | 7.90569 | − | 7.90569i | 0.310565 | − | 0.310565i | ||||
\(649\) | 18.9737 | + | 6.00000i | 0.744782 | + | 0.235521i | ||||
\(650\) | −30.0000 | − | 40.0000i | −1.17670 | − | 1.56893i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.00000 | − | 3.00000i | 0.117489 | − | 0.117489i | ||||
\(653\) | −1.00000 | − | 1.00000i | −0.0391330 | − | 0.0391330i | 0.687270 | − | 0.726403i | \(-0.258809\pi\) |
−0.726403 | + | 0.687270i | \(0.758809\pi\) | |||||||
\(654\) | 40.0000i | 1.56412i | ||||||||
\(655\) | 12.6491 | − | 25.2982i | 0.494242 | − | 0.988483i | ||||
\(656\) | 6.32456i | 0.246932i | ||||||||
\(657\) | 3.16228 | + | 3.16228i | 0.123372 | + | 0.123372i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.6491 | 0.492739 | 0.246370 | − | 0.969176i | \(-0.420762\pi\) | ||||
0.246370 | + | 0.969176i | \(0.420762\pi\) | |||||||
\(660\) | 0.486833 | + | 31.4605i | 0.0189499 | + | 1.22460i | ||||
\(661\) | 42.0000 | 1.63361 | 0.816805 | − | 0.576913i | \(-0.195743\pi\) | ||||
0.816805 | + | 0.576913i | \(0.195743\pi\) | |||||||
\(662\) | 28.4605 | + | 28.4605i | 1.10615 | + | 1.10615i | ||||
\(663\) | −20.0000 | − | 20.0000i | −0.776736 | − | 0.776736i | ||||
\(664\) | − | 20.0000i | − | 0.776151i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.48683i | 0.367607i | ||||||||
\(667\) | −6.32456 | − | 6.32456i | −0.244888 | − | 0.244888i | ||||
\(668\) | 37.9473 | − | 37.9473i | 1.46823 | − | 1.46823i | ||||
\(669\) | 22.0000i | 0.850569i | ||||||||
\(670\) | 18.9737 | + | 9.48683i | 0.733017 | + | 0.366508i | ||||
\(671\) | −20.0000 | − | 6.32456i | −0.772091 | − | 0.244157i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.4605 | − | 28.4605i | 1.09707 | − | 1.09707i | 0.102320 | − | 0.994752i | \(-0.467373\pi\) |
0.994752 | − | 0.102320i | \(-0.0326266\pi\) | |||||||
\(674\) | − | 30.0000i | − | 1.15556i | ||||||
\(675\) | −28.0000 | − | 4.00000i | −1.07772 | − | 0.153960i | ||||
\(676\) | 21.0000 | 0.807692 | ||||||||
\(677\) | −9.48683 | − | 9.48683i | −0.364609 | − | 0.364609i | 0.500898 | − | 0.865506i | \(-0.333003\pi\) |
−0.865506 | + | 0.500898i | \(0.833003\pi\) | |||||||
\(678\) | −28.4605 | + | 28.4605i | −1.09302 | + | 1.09302i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −20.0000 | − | 10.0000i | −0.766965 | − | 0.383482i | ||||
\(681\) | − | 12.6491i | − | 0.484715i | ||||||
\(682\) | −13.1623 | + | 6.83772i | −0.504010 | + | 0.261830i | ||||
\(683\) | 29.0000 | + | 29.0000i | 1.10965 | + | 1.10965i | 0.993196 | + | 0.116459i | \(0.0371542\pi\) |
0.116459 | + | 0.993196i | \(0.462846\pi\) | |||||||
\(684\) | −18.9737 | −0.725476 | ||||||||
\(685\) | −39.0000 | + | 13.0000i | −1.49011 | + | 0.496704i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.00000 | + | 4.00000i | −0.152610 | + | 0.152610i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.32456 | −0.240946 | ||||||||
\(690\) | −9.48683 | + | 3.16228i | −0.361158 | + | 0.120386i | ||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | −9.48683 | − | 9.48683i | −0.360635 | − | 0.360635i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 60.0000i | 2.27757i | ||||||||
\(695\) | 25.2982 | + | 12.6491i | 0.959616 | + | 0.479808i | ||||
\(696\) | −20.0000 | −0.758098 | ||||||||
\(697\) | −20.0000 | + | 20.0000i | −0.757554 | + | 0.757554i | ||||
\(698\) | −50.0000 | − | 50.0000i | −1.89253 | − | 1.89253i | ||||
\(699\) | 18.9737 | 0.717650 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.6228i | 1.19438i | 0.802101 | + | 0.597188i | \(0.203715\pi\) | ||||
−0.802101 | + | 0.597188i | \(0.796285\pi\) | |||||||
\(702\) | 40.0000 | − | 40.0000i | 1.50970 | − | 1.50970i | ||||
\(703\) | −18.9737 | + | 18.9737i | −0.715605 | + | 0.715605i | ||||
\(704\) | 41.1096 | + | 13.0000i | 1.54938 | + | 0.489956i | ||||
\(705\) | 12.0000 | + | 6.00000i | 0.451946 | + | 0.225973i | ||||
\(706\) | 66.4078i | 2.49929i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.0000 | + | 18.0000i | 0.676481 | + | 0.676481i | ||||
\(709\) | 6.00000i | 0.225335i | 0.993633 | + | 0.112667i | \(0.0359394\pi\) | ||||
−0.993633 | + | 0.112667i | \(0.964061\pi\) | |||||||
\(710\) | −12.6491 | − | 37.9473i | −0.474713 | − | 1.42414i | ||||
\(711\) | − | 6.32456i | − | 0.237189i | ||||||
\(712\) | 9.48683 | + | 9.48683i | 0.355534 | + | 0.355534i | ||||
\(713\) | −2.00000 | − | 2.00000i | −0.0749006 | − | 0.0749006i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.513167 | + | 33.1623i | 0.0191914 | + | 1.24020i | ||||
\(716\) | 12.0000 | 0.448461 | ||||||||
\(717\) | −18.9737 | − | 18.9737i | −0.708585 | − | 0.708585i | ||||
\(718\) | 30.0000 | + | 30.0000i | 1.11959 | + | 1.11959i | ||||
\(719\) | − | 24.0000i | − | 0.895049i | −0.894272 | − | 0.447524i | \(-0.852306\pi\) | ||
0.894272 | − | 0.447524i | \(-0.147694\pi\) | |||||||
\(720\) | −1.00000 | + | 2.00000i | −0.0372678 | + | 0.0745356i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −33.2039 | − | 33.2039i | −1.23572 | − | 1.23572i | ||||
\(723\) | 6.32456 | − | 6.32456i | 0.235213 | − | 0.235213i | ||||
\(724\) | − | 24.0000i | − | 0.891953i | ||||||
\(725\) | 18.9737 | + | 25.2982i | 0.704664 | + | 0.939552i | ||||
\(726\) | 20.0000 | − | 28.4605i | 0.742270 | − | 1.05627i | ||||
\(727\) | 23.0000 | − | 23.0000i | 0.853023 | − | 0.853023i | −0.137482 | − | 0.990504i | \(-0.543901\pi\) |
0.990504 | + | 0.137482i | \(0.0439008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | −20.0000 | − | 10.0000i | −0.740233 | − | 0.370117i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −18.9737 | − | 18.9737i | −0.701287 | − | 0.701287i | ||||
\(733\) | −9.48683 | + | 9.48683i | −0.350404 | + | 0.350404i | −0.860260 | − | 0.509856i | \(-0.829699\pi\) |
0.509856 | + | 0.860260i | \(0.329699\pi\) | |||||||
\(734\) | −9.48683 | −0.350165 | ||||||||
\(735\) | 21.0000 | − | 7.00000i | 0.774597 | − | 0.258199i | ||||
\(736\) | 9.48683i | 0.349689i | ||||||||
\(737\) | −6.48683 | − | 12.4868i | −0.238946 | − | 0.459958i | ||||
\(738\) | −10.0000 | − | 10.0000i | −0.368105 | − | 0.368105i | ||||
\(739\) | −12.6491 | −0.465305 | −0.232653 | − | 0.972560i | \(-0.574740\pi\) | ||||
−0.232653 | + | 0.972560i | \(0.574740\pi\) | |||||||
\(740\) | −9.00000 | − | 27.0000i | −0.330847 | − | 0.992540i | ||||
\(741\) | 40.0000 | 1.46944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | −6.32456 | −0.231869 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.0000 | 0.366126 | ||||||||
\(747\) | −6.32456 | − | 6.32456i | −0.231403 | − | 0.231403i | ||||
\(748\) | 20.5132 | + | 39.4868i | 0.750036 | + | 1.44378i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 34.7851 | − | 6.32456i | 1.27017 | − | 0.230940i | ||||
\(751\) | −8.00000 | −0.291924 | −0.145962 | − | 0.989290i | \(-0.546628\pi\) | ||||
−0.145962 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(752\) | 3.00000 | − | 3.00000i | 0.109399 | − | 0.109399i | ||||
\(753\) | −12.0000 | − | 12.0000i | −0.437304 | − | 0.437304i | ||||
\(754\) | −63.2456 | −2.30327 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.0000 | + | 27.0000i | −0.981332 | + | 0.981332i | −0.999829 | − | 0.0184972i | \(-0.994112\pi\) |
0.0184972 | + | 0.999829i | \(0.494112\pi\) | |||||||
\(758\) | 41.1096 | − | 41.1096i | 1.49317 | − | 1.49317i | ||||
\(759\) | 6.32456 | + | 2.00000i | 0.229567 | + | 0.0725954i | ||||
\(760\) | 30.0000 | − | 10.0000i | 1.08821 | − | 0.362738i | ||||
\(761\) | − | 37.9473i | − | 1.37559i | −0.725905 | − | 0.687795i | \(-0.758579\pi\) | ||
0.725905 | − | 0.687795i | \(-0.241421\pi\) | |||||||
\(762\) | −20.0000 | + | 20.0000i | −0.724524 | + | 0.724524i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 66.0000i | 2.38780i | ||||||||
\(765\) | −9.48683 | + | 3.16228i | −0.342997 | + | 0.114332i | ||||
\(766\) | − | 60.0833i | − | 2.17090i | ||||||
\(767\) | 18.9737 | + | 18.9737i | 0.685099 | + | 0.685099i | ||||
\(768\) | 9.00000 | + | 9.00000i | 0.324760 | + | 0.324760i | ||||
\(769\) | −6.32456 | −0.228069 | −0.114035 | − | 0.993477i | \(-0.536377\pi\) | ||||
−0.114035 | + | 0.993477i | \(0.536377\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0000 | 0.504198 | ||||||||
\(772\) | −47.4342 | − | 47.4342i | −1.70719 | − | 1.70719i | ||||
\(773\) | −11.0000 | − | 11.0000i | −0.395643 | − | 0.395643i | 0.481050 | − | 0.876693i | \(-0.340255\pi\) |
−0.876693 | + | 0.481050i | \(0.840255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | + | 8.00000i | 0.215526 | + | 0.287368i | ||||
\(776\) | 22.1359i | 0.794634i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.2982 | − | 25.2982i | 0.906985 | − | 0.906985i | ||||
\(779\) | − | 40.0000i | − | 1.43315i | ||||||
\(780\) | −18.9737 | + | 37.9473i | −0.679366 | + | 1.35873i | ||||
\(781\) | −8.00000 | + | 25.2982i | −0.286263 | + | 0.905242i | ||||
\(782\) | −10.0000 | + | 10.0000i | −0.357599 | + | 0.357599i | ||||
\(783\) | −25.2982 | + | 25.2982i | −0.904085 | + | 0.904085i | ||||
\(784\) | − | 7.00000i | − | 0.250000i | ||||||
\(785\) | 21.0000 | − | 7.00000i | 0.749522 | − | 0.249841i | ||||
\(786\) | −40.0000 | −1.42675 | ||||||||
\(787\) | 25.2982 | + | 25.2982i | 0.901784 | + | 0.901784i | 0.995590 | − | 0.0938063i | \(-0.0299034\pi\) |
−0.0938063 | + | 0.995590i | \(0.529903\pi\) | |||||||
\(788\) | 9.48683 | − | 9.48683i | 0.337954 | − | 0.337954i | ||||
\(789\) | −37.9473 | −1.35096 | ||||||||
\(790\) | 10.0000 | + | 30.0000i | 0.355784 | + | 1.06735i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.58114 | + | 3.41886i | −0.233851 | + | 0.121484i | ||||
\(793\) | −20.0000 | − | 20.0000i | −0.710221 | − | 0.710221i | ||||
\(794\) | −41.1096 | −1.45893 | ||||||||
\(795\) | 2.00000 | − | 4.00000i | 0.0709327 | − | 0.141865i | ||||
\(796\) | −18.0000 | −0.637993 | ||||||||
\(797\) | 13.0000 | − | 13.0000i | 0.460484 | − | 0.460484i | −0.438330 | − | 0.898814i | \(-0.644430\pi\) |
0.898814 | + | 0.438330i | \(0.144430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.9737 | 0.671240 | ||||||||
\(800\) | 4.74342 | − | 33.2039i | 0.167705 | − | 1.17394i | ||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | −18.9737 | − | 18.9737i | −0.669983 | − | 0.669983i | ||||
\(803\) | 6.83772 | + | 13.1623i | 0.241298 | + | 0.464487i | ||||
\(804\) | − | 18.0000i | − | 0.634811i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | −24.0000 | + | 24.0000i | −0.844840 | + | 0.844840i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.9737 | −0.667079 | −0.333539 | − | 0.942736i | \(-0.608243\pi\) | ||||
−0.333539 | + | 0.942736i | \(0.608243\pi\) | |||||||
\(810\) | 7.90569 | + | 23.7171i | 0.277778 | + | 0.833333i | ||||
\(811\) | − | 6.32456i | − | 0.222085i | −0.993816 | − | 0.111043i | \(-0.964581\pi\) | ||
0.993816 | − | 0.111043i | \(-0.0354190\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.6491 | + | 12.6491i | −0.443624 | + | 0.443624i | ||||
\(814\) | −9.48683 | + | 30.0000i | −0.332513 | + | 1.05150i | ||||
\(815\) | 1.00000 | + | 3.00000i | 0.0350285 | + | 0.105085i | ||||
\(816\) | − | 6.32456i | − | 0.221404i | ||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −20.0000 | − | 20.0000i | −0.699284 | − | 0.699284i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 37.9473 | + | 18.9737i | 1.32518 | + | 0.662589i | ||||
\(821\) | 18.9737i | 0.662186i | 0.943598 | + | 0.331093i | \(0.107417\pi\) | ||||
−0.943598 | + | 0.331093i | \(0.892583\pi\) | |||||||
\(822\) | 41.1096 | + | 41.1096i | 1.43386 | + | 1.43386i | ||||
\(823\) | −11.0000 | − | 11.0000i | −0.383436 | − | 0.383436i | 0.488903 | − | 0.872338i | \(-0.337397\pi\) |
−0.872338 | + | 0.488903i | \(0.837397\pi\) | |||||||
\(824\) | 28.4605 | 0.991468 | ||||||||
\(825\) | −21.1359 | − | 10.1623i | −0.735859 | − | 0.353805i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.32456 | + | 6.32456i | 0.219926 | + | 0.219926i | 0.808467 | − | 0.588541i | \(-0.200297\pi\) |
−0.588541 | + | 0.808467i | \(0.700297\pi\) | |||||||
\(828\) | −3.00000 | − | 3.00000i | −0.104257 | − | 0.104257i | ||||
\(829\) | 6.00000i | 0.208389i | 0.994557 | + | 0.104194i | \(0.0332264\pi\) | ||||
−0.994557 | + | 0.104194i | \(0.966774\pi\) | |||||||
\(830\) | 40.0000 | + | 20.0000i | 1.38842 | + | 0.694210i | ||||
\(831\) | 18.9737i | 0.658189i | ||||||||
\(832\) | 41.1096 | + | 41.1096i | 1.42522 | + | 1.42522i | ||||
\(833\) | 22.1359 | − | 22.1359i | 0.766965 | − | 0.766965i | ||||
\(834\) | − | 40.0000i | − | 1.38509i | ||||||
\(835\) | 12.6491 | + | 37.9473i | 0.437741 | + | 1.31322i | ||||
\(836\) | −60.0000 | − | 18.9737i | −2.07514 | − | 0.656218i | ||||
\(837\) | −8.00000 | + | 8.00000i | −0.276520 | + | 0.276520i | ||||
\(838\) | 56.9210 | − | 56.9210i | 1.96630 | − | 1.96630i | ||||
\(839\) | 6.00000i | 0.207143i | 0.994622 | + | 0.103572i | \(0.0330271\pi\) | ||||
−0.994622 | + | 0.103572i | \(0.966973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0000 | 0.379310 | ||||||||
\(842\) | 44.2719 | + | 44.2719i | 1.52571 | + | 1.52571i | ||||
\(843\) | −18.9737 | + | 18.9737i | −0.653488 | + | 0.653488i | ||||
\(844\) | −75.8947 | −2.61240 | ||||||||
\(845\) | −7.00000 | + | 14.0000i | −0.240807 | + | 0.481615i | ||||
\(846\) | 9.48683i | 0.326164i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.00000 | − | 1.00000i | −0.0343401 | − | 0.0343401i | ||||
\(849\) | −12.6491 | −0.434116 | ||||||||
\(850\) | 40.0000 | − | 30.0000i | 1.37199 | − | 1.02899i | ||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | −24.0000 | + | 24.0000i | −0.822226 | + | 0.822226i | ||||
\(853\) | 9.48683 | − | 9.48683i | 0.324823 | − | 0.324823i | −0.525791 | − | 0.850614i | \(-0.676231\pi\) |
0.850614 | + | 0.525791i | \(0.176231\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.32456 | − | 12.6491i | 0.216295 | − | 0.432590i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.8114 | − | 15.8114i | −0.540107 | − | 0.540107i | 0.383453 | − | 0.923560i | \(-0.374735\pi\) |
−0.923560 | + | 0.383453i | \(0.874735\pi\) | |||||||
\(858\) | 41.6228 | − | 21.6228i | 1.42098 | − | 0.738189i | ||||
\(859\) | − | 44.0000i | − | 1.50126i | −0.660722 | − | 0.750630i | \(-0.729750\pi\) | ||
0.660722 | − | 0.750630i | \(-0.270250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.0000 | + | 30.0000i | −1.02180 | + | 1.02180i | ||||
\(863\) | −1.00000 | − | 1.00000i | −0.0340404 | − | 0.0340404i | 0.689882 | − | 0.723922i | \(-0.257663\pi\) |
−0.723922 | + | 0.689882i | \(0.757663\pi\) | |||||||
\(864\) | 37.9473 | 1.29099 | ||||||||
\(865\) | 9.48683 | − | 3.16228i | 0.322562 | − | 0.107521i | ||||
\(866\) | 3.16228i | 0.107459i | ||||||||
\(867\) | 3.00000 | − | 3.00000i | 0.101885 | − | 0.101885i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.32456 | − | 20.0000i | 0.214546 | − | 0.678454i | ||||
\(870\) | 20.0000 | − | 40.0000i | 0.678064 | − | 1.35613i | ||||
\(871\) | − | 18.9737i | − | 0.642898i | ||||||
\(872\) | 20.0000 | − | 20.0000i | 0.677285 | − | 0.677285i | ||||
\(873\) | 7.00000 | + | 7.00000i | 0.236914 | + | 0.236914i | ||||
\(874\) | − | 20.0000i | − | 0.676510i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18.9737i | 0.641061i | ||||||||
\(877\) | −41.1096 | − | 41.1096i | −1.38817 | − | 1.38817i | −0.829157 | − | 0.559016i | \(-0.811179\pi\) |
−0.559016 | − | 0.829157i | \(-0.688821\pi\) | |||||||
\(878\) | 20.0000 | + | 20.0000i | 0.674967 | + | 0.674967i | ||||
\(879\) | 31.6228 | 1.06661 | ||||||||
\(880\) | −5.16228 | + | 5.32456i | −0.174020 | + | 0.179491i | ||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 11.0680 | + | 11.0680i | 0.372678 | + | 0.372678i | ||||
\(883\) | 19.0000 | + | 19.0000i | 0.639401 | + | 0.639401i | 0.950408 | − | 0.311007i | \(-0.100666\pi\) |
−0.311007 | + | 0.950408i | \(0.600666\pi\) | |||||||
\(884\) | 60.0000i | 2.01802i | ||||||||
\(885\) | −18.0000 | + | 6.00000i | −0.605063 | + | 0.201688i | ||||
\(886\) | 34.7851i | 1.16863i | ||||||||
\(887\) | −6.32456 | − | 6.32456i | −0.212358 | − | 0.212358i | 0.592911 | − | 0.805268i | \(-0.297979\pi\) |
−0.805268 | + | 0.592911i | \(0.797979\pi\) | |||||||
\(888\) | −9.48683 | + | 9.48683i | −0.318357 | + | 0.318357i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −28.4605 | + | 9.48683i | −0.953998 | + | 0.317999i | ||||
\(891\) | 5.00000 | − | 15.8114i | 0.167506 | − | 0.529701i | ||||
\(892\) | 33.0000 | − | 33.0000i | 1.10492 | − | 1.10492i | ||||
\(893\) | −18.9737 | + | 18.9737i | −0.634930 | + | 0.634930i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00000 | + | 8.00000i | −0.133705 | + | 0.267411i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.32456 | + | 6.32456i | 0.211171 | + | 0.211171i | ||||
\(898\) | 9.48683 | − | 9.48683i | 0.316580 | − | 0.316580i | ||||
\(899\) | 12.6491 | 0.421871 | ||||||||
\(900\) | 9.00000 | + | 12.0000i | 0.300000 | + | 0.400000i | ||||
\(901\) | − | 6.32456i | − | 0.210701i | ||||||
\(902\) | −21.6228 | − | 41.6228i | −0.719960 | − | 1.38589i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28.4605 | 0.946582 | ||||||||
\(905\) | 16.0000 | + | 8.00000i | 0.531858 | + | 0.265929i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.0000 | + | 17.0000i | −0.564476 | + | 0.564476i | −0.930576 | − | 0.366100i | \(-0.880693\pi\) |
0.366100 | + | 0.930576i | \(0.380693\pi\) | |||||||
\(908\) | −18.9737 | + | 18.9737i | −0.629663 | + | 0.629663i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.0000 | 1.39152 | 0.695761 | − | 0.718273i | \(-0.255067\pi\) | ||||
0.695761 | + | 0.718273i | \(0.255067\pi\) | |||||||
\(912\) | 6.32456 | + | 6.32456i | 0.209427 | + | 0.209427i | ||||
\(913\) | −13.6754 | − | 26.3246i | −0.452591 | − | 0.871216i | ||||
\(914\) | − | 50.0000i | − | 1.65385i | ||||||
\(915\) | 18.9737 | − | 6.32456i | 0.627250 | − | 0.209083i | ||||
\(916\) | 12.0000 | 0.396491 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 40.0000 | + | 40.0000i | 1.32020 | + | 1.32020i | ||||
\(919\) | −37.9473 | −1.25177 | −0.625883 | − | 0.779917i | \(-0.715261\pi\) | ||||
−0.625883 | + | 0.779917i | \(0.715261\pi\) | |||||||
\(920\) | 6.32456 | + | 3.16228i | 0.208514 | + | 0.104257i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 40.0000 | − | 40.0000i | 1.31733 | − | 1.31733i | ||||
\(923\) | −25.2982 | + | 25.2982i | −0.832701 | + | 0.832701i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.0000 | + | 3.00000i | 0.690476 | + | 0.0986394i | ||||
\(926\) | − | 28.4605i | − | 0.935270i | ||||||
\(927\) | 9.00000 | − | 9.00000i | 0.295599 | − | 0.295599i | ||||
\(928\) | −30.0000 | − | 30.0000i | −0.984798 | − | 0.984798i | ||||
\(929\) | − | 4.00000i | − | 0.131236i | −0.997845 | − | 0.0656179i | \(-0.979098\pi\) | ||
0.997845 | − | 0.0656179i | \(-0.0209018\pi\) | |||||||
\(930\) | 6.32456 | − | 12.6491i | 0.207390 | − | 0.414781i | ||||
\(931\) | 44.2719i | 1.45095i | ||||||||
\(932\) | −28.4605 | − | 28.4605i | −0.932255 | − | 0.932255i | ||||
\(933\) | 8.00000 | + | 8.00000i | 0.261908 | + | 0.261908i | ||||
\(934\) | 22.1359 | 0.724310 | ||||||||
\(935\) | −33.1623 | + | 0.513167i | −1.08452 | + | 0.0167824i | ||||
\(936\) | −10.0000 | −0.326860 | ||||||||
\(937\) | 9.48683 | + | 9.48683i | 0.309921 | + | 0.309921i | 0.844879 | − | 0.534958i | \(-0.179672\pi\) |
−0.534958 | + | 0.844879i | \(0.679672\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 18.0000i | − | 0.587408i | ||||||
\(940\) | −9.00000 | − | 27.0000i | −0.293548 | − | 0.880643i | ||||
\(941\) | 37.9473i | 1.23705i | 0.785766 | + | 0.618524i | \(0.212269\pi\) | ||||
−0.785766 | + | 0.618524i | \(0.787731\pi\) | |||||||
\(942\) | −22.1359 | − | 22.1359i | −0.721228 | − | 0.721228i | ||||
\(943\) | 6.32456 | − | 6.32456i | 0.205956 | − | 0.205956i | ||||
\(944\) | 6.00000i | 0.195283i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.00000 | + | 7.00000i | −0.227469 | + | 0.227469i | −0.811635 | − | 0.584165i | \(-0.801422\pi\) |
0.584165 | + | 0.811635i | \(0.301422\pi\) | |||||||
\(948\) | 18.9737 | − | 18.9737i | 0.616236 | − | 0.616236i | ||||
\(949\) | 20.0000i | 0.649227i | ||||||||
\(950\) | −10.0000 | + | 70.0000i | −0.324443 | + | 2.27110i | ||||
\(951\) | 34.0000 | 1.10253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.48683 | − | 9.48683i | 0.307309 | − | 0.307309i | −0.536556 | − | 0.843865i | \(-0.680275\pi\) |
0.843865 | + | 0.536556i | \(0.180275\pi\) | |||||||
\(954\) | 3.16228 | 0.102383 | ||||||||
\(955\) | −44.0000 | − | 22.0000i | −1.42381 | − | 0.711903i | ||||
\(956\) | 56.9210i | 1.84096i | ||||||||
\(957\) | −26.3246 | + | 13.6754i | −0.850952 | + | 0.442064i | ||||
\(958\) | −10.0000 | − | 10.0000i | −0.323085 | − | 0.323085i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −39.0000 | + | 13.0000i | −1.25872 | + | 0.419573i | ||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −30.0000 | + | 30.0000i | −0.967239 | + | 0.967239i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.9737 | −0.611101 | ||||||||
\(965\) | 47.4342 | − | 15.8114i | 1.52696 | − | 0.508987i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.9737 | + | 18.9737i | 0.610152 | + | 0.610152i | 0.942986 | − | 0.332834i | \(-0.108005\pi\) |
−0.332834 | + | 0.942986i | \(0.608005\pi\) | |||||||
\(968\) | −24.2302 | + | 4.23025i | −0.778790 | + | 0.135965i | ||||
\(969\) | 40.0000i | 1.28499i | ||||||||
\(970\) | −44.2719 | − | 22.1359i | −1.42148 | − | 0.710742i | ||||
\(971\) | 42.0000 | 1.34784 | 0.673922 | − | 0.738802i | \(-0.264608\pi\) | ||||
0.673922 | + | 0.738802i | \(0.264608\pi\) | |||||||
\(972\) | −21.0000 | + | 21.0000i | −0.673575 | + | 0.673575i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.48683 | −0.303978 | ||||||||
\(975\) | −18.9737 | − | 25.2982i | −0.607644 | − | 0.810191i | ||||
\(976\) | − | 6.32456i | − | 0.202444i | ||||||
\(977\) | −17.0000 | + | 17.0000i | −0.543878 | + | 0.543878i | −0.924663 | − | 0.380785i | \(-0.875654\pi\) |
0.380785 | + | 0.924663i | \(0.375654\pi\) | |||||||
\(978\) | 3.16228 | − | 3.16228i | 0.101118 | − | 0.101118i | ||||
\(979\) | 18.9737 | + | 6.00000i | 0.606401 | + | 0.191761i | ||||
\(980\) | −42.0000 | − | 21.0000i | −1.34164 | − | 0.670820i | ||||
\(981\) | − | 12.6491i | − | 0.403855i | ||||||
\(982\) | 10.0000 | − | 10.0000i | 0.319113 | − | 0.319113i | ||||
\(983\) | 29.0000 | + | 29.0000i | 0.924956 | + | 0.924956i | 0.997374 | − | 0.0724180i | \(-0.0230716\pi\) |
−0.0724180 | + | 0.997374i | \(0.523072\pi\) | |||||||
\(984\) | − | 20.0000i | − | 0.637577i | ||||||
\(985\) | 3.16228 | + | 9.48683i | 0.100759 | + | 0.302276i | ||||
\(986\) | − | 63.2456i | − | 2.01415i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −60.0000 | − | 60.0000i | −1.90885 | − | 1.90885i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −0.256584 | − | 16.5811i | −0.00815476 | − | 0.526983i | ||||
\(991\) | −58.0000 | −1.84243 | −0.921215 | − | 0.389053i | \(-0.872802\pi\) | ||||
−0.921215 | + | 0.389053i | \(0.872802\pi\) | |||||||
\(992\) | −9.48683 | − | 9.48683i | −0.301207 | − | 0.301207i | ||||
\(993\) | 18.0000 | + | 18.0000i | 0.571213 | + | 0.571213i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.00000 | − | 12.0000i | 0.190213 | − | 0.380426i | ||||
\(996\) | − | 37.9473i | − | 1.20241i | ||||||
\(997\) | −34.7851 | − | 34.7851i | −1.10165 | − | 1.10165i | −0.994211 | − | 0.107442i | \(-0.965734\pi\) |
−0.107442 | − | 0.994211i | \(-0.534266\pi\) | |||||||
\(998\) | −53.7587 | + | 53.7587i | −1.70170 | + | 1.70170i | ||||
\(999\) | 24.0000i | 0.759326i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))