Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(518,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.518");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.k (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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 518.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.518 |
Dual form | 825.2.k.e.782.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 1.22474i | −0.866025 | − | 0.866025i | 0.126004 | − | 0.992030i | \(-0.459785\pi\) |
−0.992030 | + | 0.126004i | \(0.959785\pi\) | |||||||
\(3\) | −1.22474 | − | 1.22474i | −0.707107 | − | 0.707107i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.00000i | 1.22474i | ||||||||
\(7\) | −2.44949 | + | 2.44949i | −0.925820 | + | 0.925820i | −0.997433 | − | 0.0716124i | \(-0.977186\pi\) |
0.0716124 | + | 0.997433i | \(0.477186\pi\) | |||||||
\(8\) | −1.22474 | + | 1.22474i | −0.433013 | + | 0.433013i | ||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 1.22474 | − | 1.22474i | 0.353553 | − | 0.353553i | ||||
\(13\) | 2.44949 | + | 2.44949i | 0.679366 | + | 0.679366i | 0.959857 | − | 0.280491i | \(-0.0904971\pi\) |
−0.280491 | + | 0.959857i | \(0.590497\pi\) | |||||||
\(14\) | 6.00000 | 1.60357 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.00000 | 1.25000 | ||||||||
\(17\) | −4.89898 | − | 4.89898i | −1.18818 | − | 1.18818i | −0.977571 | − | 0.210606i | \(-0.932456\pi\) |
−0.210606 | − | 0.977571i | \(-0.567544\pi\) | |||||||
\(18\) | 3.67423 | − | 3.67423i | 0.866025 | − | 0.866025i | ||||
\(19\) | − | 2.00000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.00000 | 1.30931 | ||||||||
\(22\) | 1.22474 | − | 1.22474i | 0.261116 | − | 0.261116i | ||||
\(23\) | 4.89898 | − | 4.89898i | 1.02151 | − | 1.02151i | 0.0217443 | − | 0.999764i | \(-0.493078\pi\) |
0.999764 | − | 0.0217443i | \(-0.00692196\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 6.00000i | − | 1.17670i | ||||||
\(27\) | 3.67423 | − | 3.67423i | 0.707107 | − | 0.707107i | ||||
\(28\) | −2.44949 | − | 2.44949i | −0.462910 | − | 0.462910i | ||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −3.67423 | − | 3.67423i | −0.649519 | − | 0.649519i | ||||
\(33\) | 1.22474 | − | 1.22474i | 0.213201 | − | 0.213201i | ||||
\(34\) | 12.0000i | 2.05798i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | −2.44949 | + | 2.44949i | −0.397360 | + | 0.397360i | ||||
\(39\) | − | 6.00000i | − | 0.960769i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.00000i | − | 0.937043i | −0.883452 | − | 0.468521i | \(-0.844787\pi\) | ||
0.883452 | − | 0.468521i | \(-0.155213\pi\) | |||||||
\(42\) | −7.34847 | − | 7.34847i | −1.13389 | − | 1.13389i | ||||
\(43\) | 7.34847 | + | 7.34847i | 1.12063 | + | 1.12063i | 0.991647 | + | 0.128984i | \(0.0411717\pi\) |
0.128984 | + | 0.991647i | \(0.458828\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.0000 | −1.76930 | ||||||||
\(47\) | 4.89898 | + | 4.89898i | 0.714590 | + | 0.714590i | 0.967492 | − | 0.252902i | \(-0.0813851\pi\) |
−0.252902 | + | 0.967492i | \(0.581385\pi\) | |||||||
\(48\) | −6.12372 | − | 6.12372i | −0.883883 | − | 0.883883i | ||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.0000i | 1.68034i | ||||||||
\(52\) | −2.44949 | + | 2.44949i | −0.339683 | + | 0.339683i | ||||
\(53\) | 4.89898 | − | 4.89898i | 0.672927 | − | 0.672927i | −0.285463 | − | 0.958390i | \(-0.592147\pi\) |
0.958390 | + | 0.285463i | \(0.0921474\pi\) | |||||||
\(54\) | −9.00000 | −1.22474 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 6.00000i | − | 0.801784i | ||||||
\(57\) | −2.44949 | + | 2.44949i | −0.324443 | + | 0.324443i | ||||
\(58\) | 7.34847 | + | 7.34847i | 0.964901 | + | 0.964901i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | −4.89898 | − | 4.89898i | −0.622171 | − | 0.622171i | ||||
\(63\) | −7.34847 | − | 7.34847i | −0.925820 | − | 0.925820i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | −0.369274 | ||||||||
\(67\) | −2.44949 | + | 2.44949i | −0.299253 | + | 0.299253i | −0.840721 | − | 0.541468i | \(-0.817869\pi\) |
0.541468 | + | 0.840721i | \(0.317869\pi\) | |||||||
\(68\) | 4.89898 | − | 4.89898i | 0.594089 | − | 0.594089i | ||||
\(69\) | −12.0000 | −1.44463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | −3.67423 | − | 3.67423i | −0.433013 | − | 0.433013i | ||||
\(73\) | −2.44949 | − | 2.44949i | −0.286691 | − | 0.286691i | 0.549079 | − | 0.835770i | \(-0.314979\pi\) |
−0.835770 | + | 0.549079i | \(0.814979\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −2.44949 | − | 2.44949i | −0.279145 | − | 0.279145i | ||||
\(78\) | −7.34847 | + | 7.34847i | −0.832050 | + | 0.832050i | ||||
\(79\) | − | 10.0000i | − | 1.12509i | −0.826767 | − | 0.562544i | \(-0.809823\pi\) | ||
0.826767 | − | 0.562544i | \(-0.190177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −7.34847 | + | 7.34847i | −0.811503 | + | 0.811503i | ||||
\(83\) | 7.34847 | − | 7.34847i | 0.806599 | − | 0.806599i | −0.177518 | − | 0.984118i | \(-0.556807\pi\) |
0.984118 | + | 0.177518i | \(0.0568069\pi\) | |||||||
\(84\) | 6.00000i | 0.654654i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 18.0000i | − | 1.94099i | ||||||
\(87\) | 7.34847 | + | 7.34847i | 0.787839 | + | 0.787839i | ||||
\(88\) | −1.22474 | − | 1.22474i | −0.130558 | − | 0.130558i | ||||
\(89\) | 12.0000 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | −1.25794 | ||||||||
\(92\) | 4.89898 | + | 4.89898i | 0.510754 | + | 0.510754i | ||||
\(93\) | −4.89898 | − | 4.89898i | −0.508001 | − | 0.508001i | ||||
\(94\) | − | 12.0000i | − | 1.23771i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.00000i | 0.918559i | ||||||||
\(97\) | 9.79796 | − | 9.79796i | 0.994832 | − | 0.994832i | −0.00515471 | − | 0.999987i | \(-0.501641\pi\) |
0.999987 | + | 0.00515471i | \(0.00164080\pi\) | |||||||
\(98\) | −6.12372 | + | 6.12372i | −0.618590 | + | 0.618590i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 18.0000i | − | 1.79107i | −0.444994 | − | 0.895533i | \(-0.646794\pi\) | ||
0.444994 | − | 0.895533i | \(-0.353206\pi\) | |||||||
\(102\) | 14.6969 | − | 14.6969i | 1.45521 | − | 1.45521i | ||||
\(103\) | 2.44949 | + | 2.44949i | 0.241355 | + | 0.241355i | 0.817411 | − | 0.576055i | \(-0.195409\pi\) |
−0.576055 | + | 0.817411i | \(0.695409\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 2.44949 | + | 2.44949i | 0.236801 | + | 0.236801i | 0.815524 | − | 0.578723i | \(-0.196449\pi\) |
−0.578723 | + | 0.815524i | \(0.696449\pi\) | |||||||
\(108\) | 3.67423 | + | 3.67423i | 0.353553 | + | 0.353553i | ||||
\(109\) | − | 10.0000i | − | 0.957826i | −0.877862 | − | 0.478913i | \(-0.841031\pi\) | ||
0.877862 | − | 0.478913i | \(-0.158969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.2474 | + | 12.2474i | −1.15728 | + | 1.15728i | ||||
\(113\) | −4.89898 | + | 4.89898i | −0.460857 | + | 0.460857i | −0.898936 | − | 0.438079i | \(-0.855659\pi\) |
0.438079 | + | 0.898936i | \(0.355659\pi\) | |||||||
\(114\) | 6.00000 | 0.561951 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 6.00000i | − | 0.557086i | ||||||
\(117\) | −7.34847 | + | 7.34847i | −0.679366 | + | 0.679366i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 24.0000 | 2.20008 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −2.44949 | − | 2.44949i | −0.221766 | − | 0.221766i | ||||
\(123\) | −7.34847 | + | 7.34847i | −0.662589 | + | 0.662589i | ||||
\(124\) | 4.00000i | 0.359211i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 18.0000i | 1.60357i | ||||||||
\(127\) | 2.44949 | − | 2.44949i | 0.217357 | − | 0.217357i | −0.590027 | − | 0.807384i | \(-0.700883\pi\) |
0.807384 | + | 0.590027i | \(0.200883\pi\) | |||||||
\(128\) | −8.57321 | + | 8.57321i | −0.757772 | + | 0.757772i | ||||
\(129\) | − | 18.0000i | − | 1.58481i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000i | 1.04844i | 0.851581 | + | 0.524222i | \(0.175644\pi\) | ||||
−0.851581 | + | 0.524222i | \(0.824356\pi\) | |||||||
\(132\) | 1.22474 | + | 1.22474i | 0.106600 | + | 0.106600i | ||||
\(133\) | 4.89898 | + | 4.89898i | 0.424795 | + | 0.424795i | ||||
\(134\) | 6.00000 | 0.518321 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0000 | 1.02899 | ||||||||
\(137\) | 9.79796 | + | 9.79796i | 0.837096 | + | 0.837096i | 0.988476 | − | 0.151380i | \(-0.0483716\pi\) |
−0.151380 | + | 0.988476i | \(0.548372\pi\) | |||||||
\(138\) | 14.6969 | + | 14.6969i | 1.25109 | + | 1.25109i | ||||
\(139\) | 22.0000i | 1.86602i | 0.359856 | + | 0.933008i | \(0.382826\pi\) | ||||
−0.359856 | + | 0.933008i | \(0.617174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 12.0000i | − | 1.01058i | ||||||
\(142\) | 14.6969 | − | 14.6969i | 1.23334 | − | 1.23334i | ||||
\(143\) | −2.44949 | + | 2.44949i | −0.204837 | + | 0.204837i | ||||
\(144\) | 15.0000i | 1.25000i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.00000i | 0.496564i | ||||||||
\(147\) | −6.12372 | + | 6.12372i | −0.505076 | + | 0.505076i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | 2.44949 | + | 2.44949i | 0.198680 | + | 0.198680i | ||||
\(153\) | 14.6969 | − | 14.6969i | 1.18818 | − | 1.18818i | ||||
\(154\) | 6.00000i | 0.483494i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.00000 | 0.480384 | ||||||||
\(157\) | 9.79796 | − | 9.79796i | 0.781962 | − | 0.781962i | −0.198199 | − | 0.980162i | \(-0.563509\pi\) |
0.980162 | + | 0.198199i | \(0.0635094\pi\) | |||||||
\(158\) | −12.2474 | + | 12.2474i | −0.974355 | + | 0.974355i | ||||
\(159\) | −12.0000 | −0.951662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.0000i | 1.89146i | ||||||||
\(162\) | 11.0227 | + | 11.0227i | 0.866025 | + | 0.866025i | ||||
\(163\) | −12.2474 | − | 12.2474i | −0.959294 | − | 0.959294i | 0.0399091 | − | 0.999203i | \(-0.487293\pi\) |
−0.999203 | + | 0.0399091i | \(0.987293\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.0000 | −1.39707 | ||||||||
\(167\) | 2.44949 | + | 2.44949i | 0.189547 | + | 0.189547i | 0.795500 | − | 0.605953i | \(-0.207208\pi\) |
−0.605953 | + | 0.795500i | \(0.707208\pi\) | |||||||
\(168\) | −7.34847 | + | 7.34847i | −0.566947 | + | 0.566947i | ||||
\(169\) | − | 1.00000i | − | 0.0769231i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | 0.458831 | ||||||||
\(172\) | −7.34847 | + | 7.34847i | −0.560316 | + | 0.560316i | ||||
\(173\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(174\) | − | 18.0000i | − | 1.36458i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.00000i | 0.376889i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.6969 | − | 14.6969i | −1.10158 | − | 1.10158i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 14.6969 | + | 14.6969i | 1.08941 | + | 1.08941i | ||||
\(183\) | −2.44949 | − | 2.44949i | −0.181071 | − | 0.181071i | ||||
\(184\) | 12.0000i | 0.884652i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.0000i | 0.879883i | ||||||||
\(187\) | 4.89898 | − | 4.89898i | 0.358249 | − | 0.358249i | ||||
\(188\) | −4.89898 | + | 4.89898i | −0.357295 | + | 0.357295i | ||||
\(189\) | 18.0000i | 1.30931i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 24.0000i | − | 1.73658i | −0.496058 | − | 0.868290i | \(-0.665220\pi\) | ||
0.496058 | − | 0.868290i | \(-0.334780\pi\) | |||||||
\(192\) | −1.22474 | + | 1.22474i | −0.0883883 | + | 0.0883883i | ||||
\(193\) | −7.34847 | − | 7.34847i | −0.528954 | − | 0.528954i | 0.391306 | − | 0.920261i | \(-0.372023\pi\) |
−0.920261 | + | 0.391306i | \(0.872023\pi\) | |||||||
\(194\) | −24.0000 | −1.72310 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.00000 | 0.357143 | ||||||||
\(197\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | 3.67423 | + | 3.67423i | 0.261116 | + | 0.261116i | ||||
\(199\) | − | 4.00000i | − | 0.283552i | −0.989899 | − | 0.141776i | \(-0.954719\pi\) | ||
0.989899 | − | 0.141776i | \(-0.0452813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | 0.423207 | ||||||||
\(202\) | −22.0454 | + | 22.0454i | −1.55111 | + | 1.55111i | ||||
\(203\) | 14.6969 | − | 14.6969i | 1.03152 | − | 1.03152i | ||||
\(204\) | −12.0000 | −0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 6.00000i | − | 0.418040i | ||||||
\(207\) | 14.6969 | + | 14.6969i | 1.02151 | + | 1.02151i | ||||
\(208\) | 12.2474 | + | 12.2474i | 0.849208 | + | 0.849208i | ||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0000 | 1.78991 | 0.894957 | − | 0.446153i | \(-0.147206\pi\) | ||||
0.894957 | + | 0.446153i | \(0.147206\pi\) | |||||||
\(212\) | 4.89898 | + | 4.89898i | 0.336463 | + | 0.336463i | ||||
\(213\) | 14.6969 | − | 14.6969i | 1.00702 | − | 1.00702i | ||||
\(214\) | − | 6.00000i | − | 0.410152i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.00000i | 0.612372i | ||||||||
\(217\) | −9.79796 | + | 9.79796i | −0.665129 | + | 0.665129i | ||||
\(218\) | −12.2474 | + | 12.2474i | −0.829502 | + | 0.829502i | ||||
\(219\) | 6.00000i | 0.405442i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 24.0000i | − | 1.61441i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.1464 | + | 17.1464i | 1.14821 | + | 1.14821i | 0.986905 | + | 0.161305i | \(0.0515703\pi\) |
0.161305 | + | 0.986905i | \(0.448430\pi\) | |||||||
\(224\) | 18.0000 | 1.20268 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.0000 | 0.798228 | ||||||||
\(227\) | 12.2474 | + | 12.2474i | 0.812892 | + | 0.812892i | 0.985066 | − | 0.172175i | \(-0.0550794\pi\) |
−0.172175 | + | 0.985066i | \(0.555079\pi\) | |||||||
\(228\) | −2.44949 | − | 2.44949i | −0.162221 | − | 0.162221i | ||||
\(229\) | 10.0000i | 0.660819i | 0.943838 | + | 0.330409i | \(0.107187\pi\) | ||||
−0.943838 | + | 0.330409i | \(0.892813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000i | 0.394771i | ||||||||
\(232\) | 7.34847 | − | 7.34847i | 0.482451 | − | 0.482451i | ||||
\(233\) | −4.89898 | + | 4.89898i | −0.320943 | + | 0.320943i | −0.849129 | − | 0.528186i | \(-0.822872\pi\) |
0.528186 | + | 0.849129i | \(0.322872\pi\) | |||||||
\(234\) | 18.0000 | 1.17670 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.2474 | + | 12.2474i | −0.795557 | + | 0.795557i | ||||
\(238\) | −29.3939 | − | 29.3939i | −1.90532 | − | 1.90532i | ||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 1.22474 | + | 1.22474i | 0.0787296 | + | 0.0787296i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.707107 | + | 0.707107i | ||||
\(244\) | 2.00000i | 0.128037i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.0000 | 1.14764 | ||||||||
\(247\) | 4.89898 | − | 4.89898i | 0.311715 | − | 0.311715i | ||||
\(248\) | −4.89898 | + | 4.89898i | −0.311086 | + | 0.311086i | ||||
\(249\) | −18.0000 | −1.14070 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.0000i | − | 0.757433i | −0.925513 | − | 0.378717i | \(-0.876365\pi\) | ||
0.925513 | − | 0.378717i | \(-0.123635\pi\) | |||||||
\(252\) | 7.34847 | − | 7.34847i | 0.462910 | − | 0.462910i | ||||
\(253\) | 4.89898 | + | 4.89898i | 0.307996 | + | 0.307996i | ||||
\(254\) | −6.00000 | −0.376473 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −9.79796 | − | 9.79796i | −0.611180 | − | 0.611180i | 0.332074 | − | 0.943253i | \(-0.392252\pi\) |
−0.943253 | + | 0.332074i | \(0.892252\pi\) | |||||||
\(258\) | −22.0454 | + | 22.0454i | −1.37249 | + | 1.37249i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 18.0000i | − | 1.11417i | ||||||
\(262\) | 14.6969 | − | 14.6969i | 0.907980 | − | 0.907980i | ||||
\(263\) | −17.1464 | + | 17.1464i | −1.05729 | + | 1.05729i | −0.0590383 | + | 0.998256i | \(0.518803\pi\) |
−0.998256 | + | 0.0590383i | \(0.981197\pi\) | |||||||
\(264\) | 3.00000i | 0.184637i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 12.0000i | − | 0.735767i | ||||||
\(267\) | −14.6969 | − | 14.6969i | −0.899438 | − | 0.899438i | ||||
\(268\) | −2.44949 | − | 2.44949i | −0.149626 | − | 0.149626i | ||||
\(269\) | −24.0000 | −1.46331 | −0.731653 | − | 0.681677i | \(-0.761251\pi\) | ||||
−0.731653 | + | 0.681677i | \(0.761251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000 | 0.121491 | 0.0607457 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607457 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(272\) | −24.4949 | − | 24.4949i | −1.48522 | − | 1.48522i | ||||
\(273\) | 14.6969 | + | 14.6969i | 0.889499 | + | 0.889499i | ||||
\(274\) | − | 24.0000i | − | 1.44989i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 12.0000i | − | 0.722315i | ||||||
\(277\) | 12.2474 | − | 12.2474i | 0.735878 | − | 0.735878i | −0.235900 | − | 0.971777i | \(-0.575804\pi\) |
0.971777 | + | 0.235900i | \(0.0758036\pi\) | |||||||
\(278\) | 26.9444 | − | 26.9444i | 1.61602 | − | 1.61602i | ||||
\(279\) | 12.0000i | 0.718421i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000i | 1.78965i | 0.446417 | + | 0.894825i | \(0.352700\pi\) | ||||
−0.446417 | + | 0.894825i | \(0.647300\pi\) | |||||||
\(282\) | −14.6969 | + | 14.6969i | −0.875190 | + | 0.875190i | ||||
\(283\) | −12.2474 | − | 12.2474i | −0.728035 | − | 0.728035i | 0.242193 | − | 0.970228i | \(-0.422133\pi\) |
−0.970228 | + | 0.242193i | \(0.922133\pi\) | |||||||
\(284\) | −12.0000 | −0.712069 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | 0.354787 | ||||||||
\(287\) | 14.6969 | + | 14.6969i | 0.867533 | + | 0.867533i | ||||
\(288\) | 11.0227 | − | 11.0227i | 0.649519 | − | 0.649519i | ||||
\(289\) | 31.0000i | 1.82353i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.0000 | −1.40690 | ||||||||
\(292\) | 2.44949 | − | 2.44949i | 0.143346 | − | 0.143346i | ||||
\(293\) | 9.79796 | − | 9.79796i | 0.572403 | − | 0.572403i | −0.360396 | − | 0.932799i | \(-0.617359\pi\) |
0.932799 | + | 0.360396i | \(0.117359\pi\) | |||||||
\(294\) | 15.0000 | 0.874818 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.67423 | + | 3.67423i | 0.213201 | + | 0.213201i | ||||
\(298\) | −7.34847 | − | 7.34847i | −0.425685 | − | 0.425685i | ||||
\(299\) | 24.0000 | 1.38796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.0000 | −2.07501 | ||||||||
\(302\) | −12.2474 | − | 12.2474i | −0.704761 | − | 0.704761i | ||||
\(303\) | −22.0454 | + | 22.0454i | −1.26648 | + | 1.26648i | ||||
\(304\) | − | 10.0000i | − | 0.573539i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −36.0000 | −2.05798 | ||||||||
\(307\) | 17.1464 | − | 17.1464i | 0.978598 | − | 0.978598i | −0.0211774 | − | 0.999776i | \(-0.506741\pi\) |
0.999776 | + | 0.0211774i | \(0.00674148\pi\) | |||||||
\(308\) | 2.44949 | − | 2.44949i | 0.139573 | − | 0.139573i | ||||
\(309\) | − | 6.00000i | − | 0.341328i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 24.0000i | − | 1.36092i | −0.732787 | − | 0.680458i | \(-0.761781\pi\) | ||
0.732787 | − | 0.680458i | \(-0.238219\pi\) | |||||||
\(312\) | 7.34847 | + | 7.34847i | 0.416025 | + | 0.416025i | ||||
\(313\) | 4.89898 | + | 4.89898i | 0.276907 | + | 0.276907i | 0.831873 | − | 0.554966i | \(-0.187269\pi\) |
−0.554966 | + | 0.831873i | \(0.687269\pi\) | |||||||
\(314\) | −24.0000 | −1.35440 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | −4.89898 | − | 4.89898i | −0.275154 | − | 0.275154i | 0.556017 | − | 0.831171i | \(-0.312329\pi\) |
−0.831171 | + | 0.556017i | \(0.812329\pi\) | |||||||
\(318\) | 14.6969 | + | 14.6969i | 0.824163 | + | 0.824163i | ||||
\(319\) | − | 6.00000i | − | 0.335936i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 6.00000i | − | 0.334887i | ||||||
\(322\) | 29.3939 | − | 29.3939i | 1.63806 | − | 1.63806i | ||||
\(323\) | −9.79796 | + | 9.79796i | −0.545173 | + | 0.545173i | ||||
\(324\) | − | 9.00000i | − | 0.500000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 30.0000i | 1.66155i | ||||||||
\(327\) | −12.2474 | + | 12.2474i | −0.677285 | + | 0.677285i | ||||
\(328\) | 7.34847 | + | 7.34847i | 0.405751 | + | 0.405751i | ||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.0000 | −1.53902 | −0.769510 | − | 0.638635i | \(-0.779499\pi\) | ||||
−0.769510 | + | 0.638635i | \(0.779499\pi\) | |||||||
\(332\) | 7.34847 | + | 7.34847i | 0.403300 | + | 0.403300i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 6.00000i | − | 0.328305i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 30.0000 | 1.63663 | ||||||||
\(337\) | −22.0454 | + | 22.0454i | −1.20089 | + | 1.20089i | −0.226994 | + | 0.973896i | \(0.572890\pi\) |
−0.973896 | + | 0.226994i | \(0.927110\pi\) | |||||||
\(338\) | −1.22474 | + | 1.22474i | −0.0666173 | + | 0.0666173i | ||||
\(339\) | 12.0000 | 0.651751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.00000i | 0.216612i | ||||||||
\(342\) | −7.34847 | − | 7.34847i | −0.397360 | − | 0.397360i | ||||
\(343\) | −4.89898 | − | 4.89898i | −0.264520 | − | 0.264520i | ||||
\(344\) | −18.0000 | −0.970495 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.2474 | + | 12.2474i | 0.657477 | + | 0.657477i | 0.954783 | − | 0.297305i | \(-0.0960878\pi\) |
−0.297305 | + | 0.954783i | \(0.596088\pi\) | |||||||
\(348\) | −7.34847 | + | 7.34847i | −0.393919 | + | 0.393919i | ||||
\(349\) | − | 2.00000i | − | 0.107058i | −0.998566 | − | 0.0535288i | \(-0.982953\pi\) | ||
0.998566 | − | 0.0535288i | \(-0.0170469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | 0.960769 | ||||||||
\(352\) | 3.67423 | − | 3.67423i | 0.195837 | − | 0.195837i | ||||
\(353\) | 24.4949 | − | 24.4949i | 1.30373 | − | 1.30373i | 0.377875 | − | 0.925856i | \(-0.376655\pi\) |
0.925856 | − | 0.377875i | \(-0.123345\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.0000i | 0.635999i | ||||||||
\(357\) | −29.3939 | − | 29.3939i | −1.55569 | − | 1.55569i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | −12.2474 | − | 12.2474i | −0.643712 | − | 0.643712i | ||||
\(363\) | 1.22474 | + | 1.22474i | 0.0642824 | + | 0.0642824i | ||||
\(364\) | − | 12.0000i | − | 0.628971i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.00000i | 0.313625i | ||||||||
\(367\) | −2.44949 | + | 2.44949i | −0.127862 | + | 0.127862i | −0.768142 | − | 0.640280i | \(-0.778818\pi\) |
0.640280 | + | 0.768142i | \(0.278818\pi\) | |||||||
\(368\) | 24.4949 | − | 24.4949i | 1.27688 | − | 1.27688i | ||||
\(369\) | 18.0000 | 0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.0000i | 1.24602i | ||||||||
\(372\) | 4.89898 | − | 4.89898i | 0.254000 | − | 0.254000i | ||||
\(373\) | −17.1464 | − | 17.1464i | −0.887808 | − | 0.887808i | 0.106504 | − | 0.994312i | \(-0.466034\pi\) |
−0.994312 | + | 0.106504i | \(0.966034\pi\) | |||||||
\(374\) | −12.0000 | −0.620505 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.0000 | −0.618853 | ||||||||
\(377\) | −14.6969 | − | 14.6969i | −0.756931 | − | 0.756931i | ||||
\(378\) | 22.0454 | − | 22.0454i | 1.13389 | − | 1.13389i | ||||
\(379\) | − | 20.0000i | − | 1.02733i | −0.857991 | − | 0.513665i | \(-0.828287\pi\) | ||
0.857991 | − | 0.513665i | \(-0.171713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.00000 | −0.307389 | ||||||||
\(382\) | −29.3939 | + | 29.3939i | −1.50392 | + | 1.50392i | ||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | 21.0000 | 1.07165 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.0000i | 0.916176i | ||||||||
\(387\) | −22.0454 | + | 22.0454i | −1.12063 | + | 1.12063i | ||||
\(388\) | 9.79796 | + | 9.79796i | 0.497416 | + | 0.497416i | ||||
\(389\) | 12.0000 | 0.608424 | 0.304212 | − | 0.952604i | \(-0.401607\pi\) | ||||
0.304212 | + | 0.952604i | \(0.401607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −48.0000 | −2.42746 | ||||||||
\(392\) | 6.12372 | + | 6.12372i | 0.309295 | + | 0.309295i | ||||
\(393\) | 14.6969 | − | 14.6969i | 0.741362 | − | 0.741362i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | − | 3.00000i | − | 0.150756i | ||||||
\(397\) | −4.89898 | + | 4.89898i | −0.245873 | + | 0.245873i | −0.819274 | − | 0.573402i | \(-0.805623\pi\) |
0.573402 | + | 0.819274i | \(0.305623\pi\) | |||||||
\(398\) | −4.89898 | + | 4.89898i | −0.245564 | + | 0.245564i | ||||
\(399\) | − | 12.0000i | − | 0.600751i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.0000i | 1.19850i | 0.800561 | + | 0.599251i | \(0.204535\pi\) | ||||
−0.800561 | + | 0.599251i | \(0.795465\pi\) | |||||||
\(402\) | −7.34847 | − | 7.34847i | −0.366508 | − | 0.366508i | ||||
\(403\) | 9.79796 | + | 9.79796i | 0.488071 | + | 0.488071i | ||||
\(404\) | 18.0000 | 0.895533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −36.0000 | −1.78665 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −14.6969 | − | 14.6969i | −0.727607 | − | 0.727607i | ||||
\(409\) | 10.0000i | 0.494468i | 0.968956 | + | 0.247234i | \(0.0795217\pi\) | ||||
−0.968956 | + | 0.247234i | \(0.920478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 24.0000i | − | 1.18383i | ||||||
\(412\) | −2.44949 | + | 2.44949i | −0.120678 | + | 0.120678i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 36.0000i | − | 1.76930i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 18.0000i | − | 0.882523i | ||||||
\(417\) | 26.9444 | − | 26.9444i | 1.31947 | − | 1.31947i | ||||
\(418\) | −2.44949 | − | 2.44949i | −0.119808 | − | 0.119808i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | −31.8434 | − | 31.8434i | −1.55011 | − | 1.55011i | ||||
\(423\) | −14.6969 | + | 14.6969i | −0.714590 | + | 0.714590i | ||||
\(424\) | 12.0000i | 0.582772i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −36.0000 | −1.74421 | ||||||||
\(427\) | −4.89898 | + | 4.89898i | −0.237078 | + | 0.237078i | ||||
\(428\) | −2.44949 | + | 2.44949i | −0.118401 | + | 0.118401i | ||||
\(429\) | 6.00000 | 0.289683 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.0000i | 1.15604i | 0.816023 | + | 0.578020i | \(0.196174\pi\) | ||||
−0.816023 | + | 0.578020i | \(0.803826\pi\) | |||||||
\(432\) | 18.3712 | − | 18.3712i | 0.883883 | − | 0.883883i | ||||
\(433\) | −19.5959 | − | 19.5959i | −0.941720 | − | 0.941720i | 0.0566731 | − | 0.998393i | \(-0.481951\pi\) |
−0.998393 | + | 0.0566731i | \(0.981951\pi\) | |||||||
\(434\) | 24.0000 | 1.15204 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.0000 | 0.478913 | ||||||||
\(437\) | −9.79796 | − | 9.79796i | −0.468700 | − | 0.468700i | ||||
\(438\) | 7.34847 | − | 7.34847i | 0.351123 | − | 0.351123i | ||||
\(439\) | 26.0000i | 1.24091i | 0.784241 | + | 0.620456i | \(0.213053\pi\) | ||||
−0.784241 | + | 0.620456i | \(0.786947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.0000 | 0.714286 | ||||||||
\(442\) | −29.3939 | + | 29.3939i | −1.39812 | + | 1.39812i | ||||
\(443\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 42.0000i | − | 1.98876i | ||||||
\(447\) | −7.34847 | − | 7.34847i | −0.347571 | − | 0.347571i | ||||
\(448\) | 2.44949 | + | 2.44949i | 0.115728 | + | 0.115728i | ||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000 | 0.282529 | ||||||||
\(452\) | −4.89898 | − | 4.89898i | −0.230429 | − | 0.230429i | ||||
\(453\) | −12.2474 | − | 12.2474i | −0.575435 | − | 0.575435i | ||||
\(454\) | − | 30.0000i | − | 1.40797i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 6.00000i | − | 0.280976i | ||||||
\(457\) | 22.0454 | − | 22.0454i | 1.03124 | − | 1.03124i | 0.0317447 | − | 0.999496i | \(-0.489894\pi\) |
0.999496 | − | 0.0317447i | \(-0.0101063\pi\) | |||||||
\(458\) | 12.2474 | − | 12.2474i | 0.572286 | − | 0.572286i | ||||
\(459\) | −36.0000 | −1.68034 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.00000i | 0.279448i | 0.990190 | + | 0.139724i | \(0.0446215\pi\) | ||||
−0.990190 | + | 0.139724i | \(0.955378\pi\) | |||||||
\(462\) | 7.34847 | − | 7.34847i | 0.341882 | − | 0.341882i | ||||
\(463\) | 2.44949 | + | 2.44949i | 0.113837 | + | 0.113837i | 0.761731 | − | 0.647893i | \(-0.224350\pi\) |
−0.647893 | + | 0.761731i | \(0.724350\pi\) | |||||||
\(464\) | −30.0000 | −1.39272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0000 | 0.555889 | ||||||||
\(467\) | 24.4949 | + | 24.4949i | 1.13349 | + | 1.13349i | 0.989593 | + | 0.143896i | \(0.0459630\pi\) |
0.143896 | + | 0.989593i | \(0.454037\pi\) | |||||||
\(468\) | −7.34847 | − | 7.34847i | −0.339683 | − | 0.339683i | ||||
\(469\) | − | 12.0000i | − | 0.554109i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.0000 | −1.10586 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.34847 | + | 7.34847i | −0.337883 | + | 0.337883i | ||||
\(474\) | 30.0000 | 1.37795 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 24.0000i | 1.10004i | ||||||||
\(477\) | 14.6969 | + | 14.6969i | 0.672927 | + | 0.672927i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0000 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 12.2474 | + | 12.2474i | 0.557856 | + | 0.557856i | ||||
\(483\) | 29.3939 | − | 29.3939i | 1.33747 | − | 1.33747i | ||||
\(484\) | − | 1.00000i | − | 0.0454545i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 27.0000i | − | 1.22474i | ||||||
\(487\) | 17.1464 | − | 17.1464i | 0.776979 | − | 0.776979i | −0.202337 | − | 0.979316i | \(-0.564854\pi\) |
0.979316 | + | 0.202337i | \(0.0648537\pi\) | |||||||
\(488\) | −2.44949 | + | 2.44949i | −0.110883 | + | 0.110883i | ||||
\(489\) | 30.0000i | 1.35665i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.0000i | − | 0.541552i | −0.962642 | − | 0.270776i | \(-0.912720\pi\) | ||
0.962642 | − | 0.270776i | \(-0.0872803\pi\) | |||||||
\(492\) | −7.34847 | − | 7.34847i | −0.331295 | − | 0.331295i | ||||
\(493\) | 29.3939 | + | 29.3939i | 1.32383 | + | 1.32383i | ||||
\(494\) | −12.0000 | −0.539906 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | 0.898027 | ||||||||
\(497\) | −29.3939 | − | 29.3939i | −1.31850 | − | 1.31850i | ||||
\(498\) | 22.0454 | + | 22.0454i | 0.987878 | + | 0.987878i | ||||
\(499\) | − | 16.0000i | − | 0.716258i | −0.933672 | − | 0.358129i | \(-0.883415\pi\) | ||
0.933672 | − | 0.358129i | \(-0.116585\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 6.00000i | − | 0.268060i | ||||||
\(502\) | −14.6969 | + | 14.6969i | −0.655956 | + | 0.655956i | ||||
\(503\) | −17.1464 | + | 17.1464i | −0.764521 | + | 0.764521i | −0.977136 | − | 0.212615i | \(-0.931802\pi\) |
0.212615 | + | 0.977136i | \(0.431802\pi\) | |||||||
\(504\) | 18.0000 | 0.801784 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 12.0000i | − | 0.533465i | ||||||
\(507\) | −1.22474 | + | 1.22474i | −0.0543928 | + | 0.0543928i | ||||
\(508\) | 2.44949 | + | 2.44949i | 0.108679 | + | 0.108679i | ||||
\(509\) | −24.0000 | −1.06378 | −0.531891 | − | 0.846813i | \(-0.678518\pi\) | ||||
−0.531891 | + | 0.846813i | \(0.678518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | −6.12372 | − | 6.12372i | −0.270633 | − | 0.270633i | ||||
\(513\) | −7.34847 | − | 7.34847i | −0.324443 | − | 0.324443i | ||||
\(514\) | 24.0000i | 1.05859i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 18.0000 | 0.792406 | ||||||||
\(517\) | −4.89898 | + | 4.89898i | −0.215457 | + | 0.215457i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0000i | 1.05146i | 0.850652 | + | 0.525730i | \(0.176208\pi\) | ||||
−0.850652 | + | 0.525730i | \(0.823792\pi\) | |||||||
\(522\) | −22.0454 | + | 22.0454i | −0.964901 | + | 0.964901i | ||||
\(523\) | −7.34847 | − | 7.34847i | −0.321326 | − | 0.321326i | 0.527950 | − | 0.849276i | \(-0.322961\pi\) |
−0.849276 | + | 0.527950i | \(0.822961\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.0000 | 1.83129 | ||||||||
\(527\) | −19.5959 | − | 19.5959i | −0.853612 | − | 0.853612i | ||||
\(528\) | 6.12372 | − | 6.12372i | 0.266501 | − | 0.266501i | ||||
\(529\) | − | 25.0000i | − | 1.08696i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.89898 | + | 4.89898i | −0.212398 | + | 0.212398i | ||||
\(533\) | 14.6969 | − | 14.6969i | 0.636595 | − | 0.636595i | ||||
\(534\) | 36.0000i | 1.55787i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 6.00000i | − | 0.259161i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 29.3939 | + | 29.3939i | 1.26726 | + | 1.26726i | ||||
\(539\) | 5.00000 | 0.215365 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | −2.44949 | − | 2.44949i | −0.105215 | − | 0.105215i | ||||
\(543\) | −12.2474 | − | 12.2474i | −0.525588 | − | 0.525588i | ||||
\(544\) | 36.0000i | 1.54349i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 36.0000i | − | 1.54066i | ||||||
\(547\) | 12.2474 | − | 12.2474i | 0.523663 | − | 0.523663i | −0.395013 | − | 0.918676i | \(-0.629260\pi\) |
0.918676 | + | 0.395013i | \(0.129260\pi\) | |||||||
\(548\) | −9.79796 | + | 9.79796i | −0.418548 | + | 0.418548i | ||||
\(549\) | 6.00000i | 0.256074i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000i | 0.511217i | ||||||||
\(552\) | 14.6969 | − | 14.6969i | 0.625543 | − | 0.625543i | ||||
\(553\) | 24.4949 | + | 24.4949i | 1.04163 | + | 1.04163i | ||||
\(554\) | −30.0000 | −1.27458 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.0000 | −0.933008 | ||||||||
\(557\) | −19.5959 | − | 19.5959i | −0.830306 | − | 0.830306i | 0.157253 | − | 0.987558i | \(-0.449736\pi\) |
−0.987558 | + | 0.157253i | \(0.949736\pi\) | |||||||
\(558\) | 14.6969 | − | 14.6969i | 0.622171 | − | 0.622171i | ||||
\(559\) | 36.0000i | 1.52264i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0000 | −0.506640 | ||||||||
\(562\) | 36.7423 | − | 36.7423i | 1.54988 | − | 1.54988i | ||||
\(563\) | 7.34847 | − | 7.34847i | 0.309701 | − | 0.309701i | −0.535092 | − | 0.844794i | \(-0.679723\pi\) |
0.844794 | + | 0.535092i | \(0.179723\pi\) | |||||||
\(564\) | 12.0000 | 0.505291 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 30.0000i | 1.26099i | ||||||||
\(567\) | 22.0454 | − | 22.0454i | 0.925820 | − | 0.925820i | ||||
\(568\) | −14.6969 | − | 14.6969i | −0.616670 | − | 0.616670i | ||||
\(569\) | −18.0000 | −0.754599 | −0.377300 | − | 0.926091i | \(-0.623147\pi\) | ||||
−0.377300 | + | 0.926091i | \(0.623147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0000 | 0.585882 | 0.292941 | − | 0.956131i | \(-0.405366\pi\) | ||||
0.292941 | + | 0.956131i | \(0.405366\pi\) | |||||||
\(572\) | −2.44949 | − | 2.44949i | −0.102418 | − | 0.102418i | ||||
\(573\) | −29.3939 | + | 29.3939i | −1.22795 | + | 1.22795i | ||||
\(574\) | − | 36.0000i | − | 1.50261i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.00000 | 0.125000 | ||||||||
\(577\) | −14.6969 | + | 14.6969i | −0.611842 | + | 0.611842i | −0.943426 | − | 0.331584i | \(-0.892417\pi\) |
0.331584 | + | 0.943426i | \(0.392417\pi\) | |||||||
\(578\) | 37.9671 | − | 37.9671i | 1.57922 | − | 1.57922i | ||||
\(579\) | 18.0000i | 0.748054i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.0000i | 1.49353i | ||||||||
\(582\) | 29.3939 | + | 29.3939i | 1.21842 | + | 1.21842i | ||||
\(583\) | 4.89898 | + | 4.89898i | 0.202895 | + | 0.202895i | ||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.0000 | −0.991431 | ||||||||
\(587\) | 4.89898 | + | 4.89898i | 0.202203 | + | 0.202203i | 0.800943 | − | 0.598741i | \(-0.204332\pi\) |
−0.598741 | + | 0.800943i | \(0.704332\pi\) | |||||||
\(588\) | −6.12372 | − | 6.12372i | −0.252538 | − | 0.252538i | ||||
\(589\) | − | 8.00000i | − | 0.329634i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.6969 | + | 14.6969i | −0.603531 | + | 0.603531i | −0.941248 | − | 0.337717i | \(-0.890345\pi\) |
0.337717 | + | 0.941248i | \(0.390345\pi\) | |||||||
\(594\) | − | 9.00000i | − | 0.369274i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000i | 0.245770i | ||||||||
\(597\) | −4.89898 | + | 4.89898i | −0.200502 | + | 0.200502i | ||||
\(598\) | −29.3939 | − | 29.3939i | −1.20201 | − | 1.20201i | ||||
\(599\) | −12.0000 | −0.490307 | −0.245153 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245153 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 44.0908 | + | 44.0908i | 1.79701 | + | 1.79701i | ||||
\(603\) | −7.34847 | − | 7.34847i | −0.299253 | − | 0.299253i | ||||
\(604\) | 10.0000i | 0.406894i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 54.0000 | 2.19360 | ||||||||
\(607\) | −12.2474 | + | 12.2474i | −0.497109 | + | 0.497109i | −0.910537 | − | 0.413428i | \(-0.864331\pi\) |
0.413428 | + | 0.910537i | \(0.364331\pi\) | |||||||
\(608\) | −7.34847 | + | 7.34847i | −0.298020 | + | 0.298020i | ||||
\(609\) | −36.0000 | −1.45879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000i | 0.970936i | ||||||||
\(612\) | 14.6969 | + | 14.6969i | 0.594089 | + | 0.594089i | ||||
\(613\) | 2.44949 | + | 2.44949i | 0.0989340 | + | 0.0989340i | 0.754841 | − | 0.655907i | \(-0.227714\pi\) |
−0.655907 | + | 0.754841i | \(0.727714\pi\) | |||||||
\(614\) | −42.0000 | −1.69498 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.00000 | 0.241747 | ||||||||
\(617\) | −14.6969 | − | 14.6969i | −0.591676 | − | 0.591676i | 0.346408 | − | 0.938084i | \(-0.387401\pi\) |
−0.938084 | + | 0.346408i | \(0.887401\pi\) | |||||||
\(618\) | −7.34847 | + | 7.34847i | −0.295599 | + | 0.295599i | ||||
\(619\) | − | 4.00000i | − | 0.160774i | −0.996764 | − | 0.0803868i | \(-0.974384\pi\) | ||
0.996764 | − | 0.0803868i | \(-0.0256155\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 36.0000i | − | 1.44463i | ||||||
\(622\) | −29.3939 | + | 29.3939i | −1.17859 | + | 1.17859i | ||||
\(623\) | −29.3939 | + | 29.3939i | −1.17764 | + | 1.17764i | ||||
\(624\) | − | 30.0000i | − | 1.20096i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 12.0000i | − | 0.479616i | ||||||
\(627\) | −2.44949 | − | 2.44949i | −0.0978232 | − | 0.0978232i | ||||
\(628\) | 9.79796 | + | 9.79796i | 0.390981 | + | 0.390981i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 12.2474 | + | 12.2474i | 0.487177 | + | 0.487177i | ||||
\(633\) | −31.8434 | − | 31.8434i | −1.26566 | − | 1.26566i | ||||
\(634\) | 12.0000i | 0.476581i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 12.0000i | − | 0.475831i | ||||||
\(637\) | 12.2474 | − | 12.2474i | 0.485262 | − | 0.485262i | ||||
\(638\) | −7.34847 | + | 7.34847i | −0.290929 | + | 0.290929i | ||||
\(639\) | −36.0000 | −1.42414 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0000i | 0.473972i | 0.971513 | + | 0.236986i | \(0.0761595\pi\) | ||||
−0.971513 | + | 0.236986i | \(0.923841\pi\) | |||||||
\(642\) | −7.34847 | + | 7.34847i | −0.290021 | + | 0.290021i | ||||
\(643\) | −12.2474 | − | 12.2474i | −0.482992 | − | 0.482992i | 0.423094 | − | 0.906086i | \(-0.360944\pi\) |
−0.906086 | + | 0.423094i | \(0.860944\pi\) | |||||||
\(644\) | −24.0000 | −0.945732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0000 | 0.944267 | ||||||||
\(647\) | −19.5959 | − | 19.5959i | −0.770395 | − | 0.770395i | 0.207780 | − | 0.978175i | \(-0.433376\pi\) |
−0.978175 | + | 0.207780i | \(0.933376\pi\) | |||||||
\(648\) | 11.0227 | − | 11.0227i | 0.433013 | − | 0.433013i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.0000 | 0.940634 | ||||||||
\(652\) | 12.2474 | − | 12.2474i | 0.479647 | − | 0.479647i | ||||
\(653\) | −29.3939 | + | 29.3939i | −1.15027 | + | 1.15027i | −0.163773 | + | 0.986498i | \(0.552367\pi\) |
−0.986498 | + | 0.163773i | \(0.947633\pi\) | |||||||
\(654\) | 30.0000 | 1.17309 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 30.0000i | − | 1.17130i | ||||||
\(657\) | 7.34847 | − | 7.34847i | 0.286691 | − | 0.286691i | ||||
\(658\) | 29.3939 | + | 29.3939i | 1.14589 | + | 1.14589i | ||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.0000 | 1.32245 | 0.661223 | − | 0.750189i | \(-0.270038\pi\) | ||||
0.661223 | + | 0.750189i | \(0.270038\pi\) | |||||||
\(662\) | 34.2929 | + | 34.2929i | 1.33283 | + | 1.33283i | ||||
\(663\) | −29.3939 | + | 29.3939i | −1.14156 | + | 1.14156i | ||||
\(664\) | 18.0000i | 0.698535i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.3939 | + | 29.3939i | −1.13814 | + | 1.13814i | ||||
\(668\) | −2.44949 | + | 2.44949i | −0.0947736 | + | 0.0947736i | ||||
\(669\) | − | 42.0000i | − | 1.62381i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.00000i | 0.0772091i | ||||||||
\(672\) | −22.0454 | − | 22.0454i | −0.850420 | − | 0.850420i | ||||
\(673\) | −2.44949 | − | 2.44949i | −0.0944209 | − | 0.0944209i | 0.658319 | − | 0.752739i | \(-0.271268\pi\) |
−0.752739 | + | 0.658319i | \(0.771268\pi\) | |||||||
\(674\) | 54.0000 | 2.08000 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(678\) | −14.6969 | − | 14.6969i | −0.564433 | − | 0.564433i | ||||
\(679\) | 48.0000i | 1.84207i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 30.0000i | − | 1.14960i | ||||||
\(682\) | 4.89898 | − | 4.89898i | 0.187592 | − | 0.187592i | ||||
\(683\) | −14.6969 | + | 14.6969i | −0.562363 | + | 0.562363i | −0.929978 | − | 0.367615i | \(-0.880174\pi\) |
0.367615 | + | 0.929978i | \(0.380174\pi\) | |||||||
\(684\) | 6.00000i | 0.229416i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.0000i | 0.458162i | ||||||||
\(687\) | 12.2474 | − | 12.2474i | 0.467269 | − | 0.467269i | ||||
\(688\) | 36.7423 | + | 36.7423i | 1.40079 | + | 1.40079i | ||||
\(689\) | 24.0000 | 0.914327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.34847 | − | 7.34847i | 0.279145 | − | 0.279145i | ||||
\(694\) | − | 30.0000i | − | 1.13878i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.0000 | −0.682288 | ||||||||
\(697\) | −29.3939 | + | 29.3939i | −1.11337 | + | 1.11337i | ||||
\(698\) | −2.44949 | + | 2.44949i | −0.0927146 | + | 0.0927146i | ||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 18.0000i | − | 0.679851i | −0.940452 | − | 0.339925i | \(-0.889598\pi\) | ||
0.940452 | − | 0.339925i | \(-0.110402\pi\) | |||||||
\(702\) | −22.0454 | − | 22.0454i | −0.832050 | − | 0.832050i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −60.0000 | −2.25813 | ||||||||
\(707\) | 44.0908 | + | 44.0908i | 1.65821 | + | 1.65821i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.0000i | 1.72757i | 0.503864 | + | 0.863783i | \(0.331911\pi\) | ||||
−0.503864 | + | 0.863783i | \(0.668089\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.0000 | 1.12509 | ||||||||
\(712\) | −14.6969 | + | 14.6969i | −0.550791 | + | 0.550791i | ||||
\(713\) | 19.5959 | − | 19.5959i | 0.733873 | − | 0.733873i | ||||
\(714\) | 72.0000i | 2.69453i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29.3939 | − | 29.3939i | −1.09697 | − | 1.09697i | ||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0000 | −0.446903 | ||||||||
\(722\) | −18.3712 | − | 18.3712i | −0.683704 | − | 0.683704i | ||||
\(723\) | 12.2474 | + | 12.2474i | 0.455488 | + | 0.455488i | ||||
\(724\) | 10.0000i | 0.371647i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 3.00000i | − | 0.111340i | ||||||
\(727\) | −22.0454 | + | 22.0454i | −0.817619 | + | 0.817619i | −0.985763 | − | 0.168144i | \(-0.946223\pi\) |
0.168144 | + | 0.985763i | \(0.446223\pi\) | |||||||
\(728\) | 14.6969 | − | 14.6969i | 0.544705 | − | 0.544705i | ||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 72.0000i | − | 2.66302i | ||||||
\(732\) | 2.44949 | − | 2.44949i | 0.0905357 | − | 0.0905357i | ||||
\(733\) | 22.0454 | + | 22.0454i | 0.814266 | + | 0.814266i | 0.985270 | − | 0.171005i | \(-0.0547013\pi\) |
−0.171005 | + | 0.985270i | \(0.554701\pi\) | |||||||
\(734\) | 6.00000 | 0.221464 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −36.0000 | −1.32698 | ||||||||
\(737\) | −2.44949 | − | 2.44949i | −0.0902281 | − | 0.0902281i | ||||
\(738\) | −22.0454 | − | 22.0454i | −0.811503 | − | 0.811503i | ||||
\(739\) | − | 38.0000i | − | 1.39785i | −0.715194 | − | 0.698926i | \(-0.753662\pi\) | ||
0.715194 | − | 0.698926i | \(-0.246338\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.0000 | −0.440831 | ||||||||
\(742\) | 29.3939 | − | 29.3939i | 1.07908 | − | 1.07908i | ||||
\(743\) | 12.2474 | − | 12.2474i | 0.449315 | − | 0.449315i | −0.445812 | − | 0.895127i | \(-0.647085\pi\) |
0.895127 | + | 0.445812i | \(0.147085\pi\) | |||||||
\(744\) | 12.0000 | 0.439941 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 42.0000i | 1.53773i | ||||||||
\(747\) | 22.0454 | + | 22.0454i | 0.806599 | + | 0.806599i | ||||
\(748\) | 4.89898 | + | 4.89898i | 0.179124 | + | 0.179124i | ||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | 0.145962 | 0.0729810 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729810 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(752\) | 24.4949 | + | 24.4949i | 0.893237 | + | 0.893237i | ||||
\(753\) | −14.6969 | + | 14.6969i | −0.535586 | + | 0.535586i | ||||
\(754\) | 36.0000i | 1.31104i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.0000 | −0.654654 | ||||||||
\(757\) | −9.79796 | + | 9.79796i | −0.356113 | + | 0.356113i | −0.862378 | − | 0.506265i | \(-0.831026\pi\) |
0.506265 | + | 0.862378i | \(0.331026\pi\) | |||||||
\(758\) | −24.4949 | + | 24.4949i | −0.889695 | + | 0.889695i | ||||
\(759\) | − | 12.0000i | − | 0.435572i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0000i | 1.52250i | 0.648459 | + | 0.761249i | \(0.275414\pi\) | ||||
−0.648459 | + | 0.761249i | \(0.724586\pi\) | |||||||
\(762\) | 7.34847 | + | 7.34847i | 0.266207 | + | 0.266207i | ||||
\(763\) | 24.4949 | + | 24.4949i | 0.886775 | + | 0.886775i | ||||
\(764\) | 24.0000 | 0.868290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −23.2702 | − | 23.2702i | −0.839689 | − | 0.839689i | ||||
\(769\) | − | 22.0000i | − | 0.793340i | −0.917961 | − | 0.396670i | \(-0.870166\pi\) | ||
0.917961 | − | 0.396670i | \(-0.129834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.0000i | 0.864339i | ||||||||
\(772\) | 7.34847 | − | 7.34847i | 0.264477 | − | 0.264477i | ||||
\(773\) | 19.5959 | − | 19.5959i | 0.704816 | − | 0.704816i | −0.260624 | − | 0.965440i | \(-0.583928\pi\) |
0.965440 | + | 0.260624i | \(0.0839283\pi\) | |||||||
\(774\) | 54.0000 | 1.94099 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.0000i | 0.861550i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.6969 | − | 14.6969i | −0.526911 | − | 0.526911i | ||||
\(779\) | −12.0000 | −0.429945 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | −0.429394 | ||||||||
\(782\) | 58.7878 | + | 58.7878i | 2.10225 | + | 2.10225i | ||||
\(783\) | −22.0454 | + | 22.0454i | −0.787839 | + | 0.787839i | ||||
\(784\) | − | 25.0000i | − | 0.892857i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −36.0000 | −1.28408 | ||||||||
\(787\) | 2.44949 | − | 2.44949i | 0.0873149 | − | 0.0873149i | −0.662100 | − | 0.749415i | \(-0.730335\pi\) |
0.749415 | + | 0.662100i | \(0.230335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 42.0000 | 1.49524 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 24.0000i | − | 0.853342i | ||||||
\(792\) | 3.67423 | − | 3.67423i | 0.130558 | − | 0.130558i | ||||
\(793\) | 4.89898 | + | 4.89898i | 0.173968 | + | 0.173968i | ||||
\(794\) | 12.0000 | 0.425864 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.00000 | 0.141776 | ||||||||
\(797\) | 14.6969 | + | 14.6969i | 0.520592 | + | 0.520592i | 0.917750 | − | 0.397158i | \(-0.130004\pi\) |
−0.397158 | + | 0.917750i | \(0.630004\pi\) | |||||||
\(798\) | −14.6969 | + | 14.6969i | −0.520266 | + | 0.520266i | ||||
\(799\) | − | 48.0000i | − | 1.69812i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.0000i | 1.27200i | ||||||||
\(802\) | 29.3939 | − | 29.3939i | 1.03793 | − | 1.03793i | ||||
\(803\) | 2.44949 | − | 2.44949i | 0.0864406 | − | 0.0864406i | ||||
\(804\) | 6.00000i | 0.211604i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 24.0000i | − | 0.845364i | ||||||
\(807\) | 29.3939 | + | 29.3939i | 1.03471 | + | 1.03471i | ||||
\(808\) | 22.0454 | + | 22.0454i | 0.775555 | + | 0.775555i | ||||
\(809\) | 42.0000 | 1.47664 | 0.738321 | − | 0.674450i | \(-0.235619\pi\) | ||||
0.738321 | + | 0.674450i | \(0.235619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | 14.6969 | + | 14.6969i | 0.515761 | + | 0.515761i | ||||
\(813\) | −2.44949 | − | 2.44949i | −0.0859074 | − | 0.0859074i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 60.0000i | 2.10042i | ||||||||
\(817\) | 14.6969 | − | 14.6969i | 0.514181 | − | 0.514181i | ||||
\(818\) | 12.2474 | − | 12.2474i | 0.428222 | − | 0.428222i | ||||
\(819\) | − | 36.0000i | − | 1.25794i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 18.0000i | − | 0.628204i | −0.949389 | − | 0.314102i | \(-0.898297\pi\) | ||
0.949389 | − | 0.314102i | \(-0.101703\pi\) | |||||||
\(822\) | −29.3939 | + | 29.3939i | −1.02523 | + | 1.02523i | ||||
\(823\) | −22.0454 | − | 22.0454i | −0.768455 | − | 0.768455i | 0.209380 | − | 0.977834i | \(-0.432856\pi\) |
−0.977834 | + | 0.209380i | \(0.932856\pi\) | |||||||
\(824\) | −6.00000 | −0.209020 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.34847 | + | 7.34847i | 0.255531 | + | 0.255531i | 0.823234 | − | 0.567702i | \(-0.192168\pi\) |
−0.567702 | + | 0.823234i | \(0.692168\pi\) | |||||||
\(828\) | −14.6969 | + | 14.6969i | −0.510754 | + | 0.510754i | ||||
\(829\) | − | 50.0000i | − | 1.73657i | −0.496064 | − | 0.868286i | \(-0.665222\pi\) | ||
0.496064 | − | 0.868286i | \(-0.334778\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.0000 | −1.04069 | ||||||||
\(832\) | 2.44949 | − | 2.44949i | 0.0849208 | − | 0.0849208i | ||||
\(833\) | −24.4949 | + | 24.4949i | −0.848698 | + | 0.848698i | ||||
\(834\) | −66.0000 | −2.28539 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.00000i | 0.0691714i | ||||||||
\(837\) | 14.6969 | − | 14.6969i | 0.508001 | − | 0.508001i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −12.2474 | − | 12.2474i | −0.422075 | − | 0.422075i | ||||
\(843\) | 36.7423 | − | 36.7423i | 1.26547 | − | 1.26547i | ||||
\(844\) | 26.0000i | 0.894957i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 36.0000 | 1.23771 | ||||||||
\(847\) | 2.44949 | − | 2.44949i | 0.0841655 | − | 0.0841655i | ||||
\(848\) | 24.4949 | − | 24.4949i | 0.841158 | − | 0.841158i | ||||
\(849\) | 30.0000i | 1.02960i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 14.6969 | + | 14.6969i | 0.503509 | + | 0.503509i | ||||
\(853\) | −2.44949 | − | 2.44949i | −0.0838689 | − | 0.0838689i | 0.663928 | − | 0.747797i | \(-0.268888\pi\) |
−0.747797 | + | 0.663928i | \(0.768888\pi\) | |||||||
\(854\) | 12.0000 | 0.410632 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | −0.205076 | ||||||||
\(857\) | −4.89898 | − | 4.89898i | −0.167346 | − | 0.167346i | 0.618466 | − | 0.785812i | \(-0.287755\pi\) |
−0.785812 | + | 0.618466i | \(0.787755\pi\) | |||||||
\(858\) | −7.34847 | − | 7.34847i | −0.250873 | − | 0.250873i | ||||
\(859\) | − | 4.00000i | − | 0.136478i | −0.997669 | − | 0.0682391i | \(-0.978262\pi\) | ||
0.997669 | − | 0.0682391i | \(-0.0217381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 36.0000i | − | 1.22688i | ||||||
\(862\) | 29.3939 | − | 29.3939i | 1.00116 | − | 1.00116i | ||||
\(863\) | −29.3939 | + | 29.3939i | −1.00058 | + | 1.00058i | −0.000579374 | 1.00000i | \(0.500184\pi\) | |
−1.00000 | 0.000579374i | \(0.999816\pi\) | ||||||||
\(864\) | −27.0000 | −0.918559 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 48.0000i | 1.63111i | ||||||||
\(867\) | 37.9671 | − | 37.9671i | 1.28943 | − | 1.28943i | ||||
\(868\) | −9.79796 | − | 9.79796i | −0.332564 | − | 0.332564i | ||||
\(869\) | 10.0000 | 0.339227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | −0.406604 | ||||||||
\(872\) | 12.2474 | + | 12.2474i | 0.414751 | + | 0.414751i | ||||
\(873\) | 29.3939 | + | 29.3939i | 0.994832 | + | 0.994832i | ||||
\(874\) | 24.0000i | 0.811812i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | −7.34847 | + | 7.34847i | −0.248140 | + | 0.248140i | −0.820207 | − | 0.572067i | \(-0.806142\pi\) |
0.572067 | + | 0.820207i | \(0.306142\pi\) | |||||||
\(878\) | 31.8434 | − | 31.8434i | 1.07466 | − | 1.07466i | ||||
\(879\) | −24.0000 | −0.809500 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.0000i | 1.21287i | 0.795133 | + | 0.606435i | \(0.207401\pi\) | ||||
−0.795133 | + | 0.606435i | \(0.792599\pi\) | |||||||
\(882\) | −18.3712 | − | 18.3712i | −0.618590 | − | 0.618590i | ||||
\(883\) | −2.44949 | − | 2.44949i | −0.0824319 | − | 0.0824319i | 0.664689 | − | 0.747121i | \(-0.268564\pi\) |
−0.747121 | + | 0.664689i | \(0.768564\pi\) | |||||||
\(884\) | 24.0000 | 0.807207 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.34847 | + | 7.34847i | 0.246737 | + | 0.246737i | 0.819630 | − | 0.572893i | \(-0.194179\pi\) |
−0.572893 | + | 0.819630i | \(0.694179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.0000i | 0.402467i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 9.00000i | − | 0.301511i | ||||||
\(892\) | −17.1464 | + | 17.1464i | −0.574105 | + | 0.574105i | ||||
\(893\) | 9.79796 | − | 9.79796i | 0.327876 | − | 0.327876i | ||||
\(894\) | 18.0000i | 0.602010i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 42.0000i | − | 1.40312i | ||||||
\(897\) | −29.3939 | − | 29.3939i | −0.981433 | − | 0.981433i | ||||
\(898\) | −14.6969 | − | 14.6969i | −0.490443 | − | 0.490443i | ||||
\(899\) | −24.0000 | −0.800445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.0000 | −1.59911 | ||||||||
\(902\) | −7.34847 | − | 7.34847i | −0.244677 | − | 0.244677i | ||||
\(903\) | 44.0908 | + | 44.0908i | 1.46725 | + | 1.46725i | ||||
\(904\) | − | 12.0000i | − | 0.399114i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 30.0000i | 0.996683i | ||||||||
\(907\) | −7.34847 | + | 7.34847i | −0.244002 | + | 0.244002i | −0.818503 | − | 0.574502i | \(-0.805196\pi\) |
0.574502 | + | 0.818503i | \(0.305196\pi\) | |||||||
\(908\) | −12.2474 | + | 12.2474i | −0.406446 | + | 0.406446i | ||||
\(909\) | 54.0000 | 1.79107 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000i | 1.59031i | 0.606406 | + | 0.795155i | \(0.292611\pi\) | ||||
−0.606406 | + | 0.795155i | \(0.707389\pi\) | |||||||
\(912\) | −12.2474 | + | 12.2474i | −0.405554 | + | 0.405554i | ||||
\(913\) | 7.34847 | + | 7.34847i | 0.243199 | + | 0.243199i | ||||
\(914\) | −54.0000 | −1.78616 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | −29.3939 | − | 29.3939i | −0.970671 | − | 0.970671i | ||||
\(918\) | 44.0908 | + | 44.0908i | 1.45521 | + | 1.45521i | ||||
\(919\) | − | 26.0000i | − | 0.857661i | −0.903385 | − | 0.428830i | \(-0.858926\pi\) | ||
0.903385 | − | 0.428830i | \(-0.141074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42.0000 | −1.38395 | ||||||||
\(922\) | 7.34847 | − | 7.34847i | 0.242009 | − | 0.242009i | ||||
\(923\) | −29.3939 | + | 29.3939i | −0.967511 | + | 0.967511i | ||||
\(924\) | −6.00000 | −0.197386 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 6.00000i | − | 0.197172i | ||||||
\(927\) | −7.34847 | + | 7.34847i | −0.241355 | + | 0.241355i | ||||
\(928\) | 22.0454 | + | 22.0454i | 0.723676 | + | 0.723676i | ||||
\(929\) | 36.0000 | 1.18112 | 0.590561 | − | 0.806993i | \(-0.298907\pi\) | ||||
0.590561 | + | 0.806993i | \(0.298907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.0000 | −0.327737 | ||||||||
\(932\) | −4.89898 | − | 4.89898i | −0.160471 | − | 0.160471i | ||||
\(933\) | −29.3939 | + | 29.3939i | −0.962312 | + | 0.962312i | ||||
\(934\) | − | 60.0000i | − | 1.96326i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 18.0000i | − | 0.588348i | ||||||
\(937\) | 12.2474 | − | 12.2474i | 0.400107 | − | 0.400107i | −0.478164 | − | 0.878271i | \(-0.658698\pi\) |
0.878271 | + | 0.478164i | \(0.158698\pi\) | |||||||
\(938\) | −14.6969 | + | 14.6969i | −0.479872 | + | 0.479872i | ||||
\(939\) | − | 12.0000i | − | 0.391605i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 6.00000i | − | 0.195594i | −0.995206 | − | 0.0977972i | \(-0.968820\pi\) | ||
0.995206 | − | 0.0977972i | \(-0.0311797\pi\) | |||||||
\(942\) | 29.3939 | + | 29.3939i | 0.957704 | + | 0.957704i | ||||
\(943\) | −29.3939 | − | 29.3939i | −0.957196 | − | 0.957196i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.0000 | 0.585230 | ||||||||
\(947\) | 4.89898 | + | 4.89898i | 0.159195 | + | 0.159195i | 0.782210 | − | 0.623015i | \(-0.214092\pi\) |
−0.623015 | + | 0.782210i | \(0.714092\pi\) | |||||||
\(948\) | −12.2474 | − | 12.2474i | −0.397779 | − | 0.397779i | ||||
\(949\) | − | 12.0000i | − | 0.389536i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0000i | 0.389127i | ||||||||
\(952\) | −29.3939 | + | 29.3939i | −0.952661 | + | 0.952661i | ||||
\(953\) | −14.6969 | + | 14.6969i | −0.476081 | + | 0.476081i | −0.903876 | − | 0.427795i | \(-0.859290\pi\) |
0.427795 | + | 0.903876i | \(0.359290\pi\) | |||||||
\(954\) | − | 36.0000i | − | 1.16554i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.34847 | + | 7.34847i | −0.237542 | + | 0.237542i | ||||
\(958\) | −29.3939 | − | 29.3939i | −0.949673 | − | 0.949673i | ||||
\(959\) | −48.0000 | −1.55000 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.34847 | + | 7.34847i | −0.236801 | + | 0.236801i | ||||
\(964\) | − | 10.0000i | − | 0.322078i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −72.0000 | −2.31656 | ||||||||
\(967\) | −36.7423 | + | 36.7423i | −1.18155 | + | 1.18155i | −0.202213 | + | 0.979342i | \(0.564813\pi\) |
−0.979342 | + | 0.202213i | \(0.935187\pi\) | |||||||
\(968\) | 1.22474 | − | 1.22474i | 0.0393648 | − | 0.0393648i | ||||
\(969\) | 24.0000 | 0.770991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 12.0000i | − | 0.385098i | −0.981287 | − | 0.192549i | \(-0.938325\pi\) | ||
0.981287 | − | 0.192549i | \(-0.0616755\pi\) | |||||||
\(972\) | −11.0227 | + | 11.0227i | −0.353553 | + | 0.353553i | ||||
\(973\) | −53.8888 | − | 53.8888i | −1.72759 | − | 1.72759i | ||||
\(974\) | −42.0000 | −1.34577 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | −19.5959 | − | 19.5959i | −0.626929 | − | 0.626929i | 0.320365 | − | 0.947294i | \(-0.396194\pi\) |
−0.947294 | + | 0.320365i | \(0.896194\pi\) | |||||||
\(978\) | 36.7423 | − | 36.7423i | 1.17489 | − | 1.17489i | ||||
\(979\) | 12.0000i | 0.383522i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.0000 | 0.957826 | ||||||||
\(982\) | −14.6969 | + | 14.6969i | −0.468998 | + | 0.468998i | ||||
\(983\) | −9.79796 | + | 9.79796i | −0.312506 | + | 0.312506i | −0.845880 | − | 0.533373i | \(-0.820924\pi\) |
0.533373 | + | 0.845880i | \(0.320924\pi\) | |||||||
\(984\) | − | 18.0000i | − | 0.573819i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 72.0000i | − | 2.29295i | ||||||
\(987\) | 29.3939 | + | 29.3939i | 0.935617 | + | 0.935617i | ||||
\(988\) | 4.89898 | + | 4.89898i | 0.155857 | + | 0.155857i | ||||
\(989\) | 72.0000 | 2.28947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.0000 | −1.65183 | −0.825917 | − | 0.563791i | \(-0.809342\pi\) | ||||
−0.825917 | + | 0.563791i | \(0.809342\pi\) | |||||||
\(992\) | −14.6969 | − | 14.6969i | −0.466628 | − | 0.466628i | ||||
\(993\) | 34.2929 | + | 34.2929i | 1.08825 | + | 1.08825i | ||||
\(994\) | 72.0000i | 2.28370i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 18.0000i | − | 0.570352i | ||||||
\(997\) | 26.9444 | − | 26.9444i | 0.853337 | − | 0.853337i | −0.137205 | − | 0.990543i | \(-0.543812\pi\) |
0.990543 | + | 0.137205i | \(0.0438120\pi\) | |||||||
\(998\) | −19.5959 | + | 19.5959i | −0.620298 | + | 0.620298i | ||||
\(999\) | 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 | 825.2.k.e.518.1 | yes | 4 | |
3.2 | odd | 2 | 825.2.k.d.518.2 | yes | 4 | ||
5.2 | odd | 4 | 825.2.k.d.782.2 | yes | 4 | ||
5.3 | odd | 4 | 825.2.k.d.782.1 | yes | 4 | ||
5.4 | even | 2 | inner | 825.2.k.e.518.2 | yes | 4 | |
15.2 | even | 4 | inner | 825.2.k.e.782.1 | yes | 4 | |
15.8 | even | 4 | inner | 825.2.k.e.782.2 | yes | 4 | |
15.14 | odd | 2 | 825.2.k.d.518.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.k.d.518.1 | ✓ | 4 | 15.14 | odd | 2 | ||
825.2.k.d.518.2 | yes | 4 | 3.2 | odd | 2 | ||
825.2.k.d.782.1 | yes | 4 | 5.3 | odd | 4 | ||
825.2.k.d.782.2 | yes | 4 | 5.2 | odd | 4 | ||
825.2.k.e.518.1 | yes | 4 | 1.1 | even | 1 | trivial | |
825.2.k.e.518.2 | yes | 4 | 5.4 | even | 2 | inner | |
825.2.k.e.782.1 | yes | 4 | 15.2 | even | 4 | inner | |
825.2.k.e.782.2 | yes | 4 | 15.8 | even | 4 | inner |