Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(323,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, 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("2070.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.j (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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.323 |
Dual form | 2070.2.j.c.737.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.12132 | − | 0.707107i | 0.948683 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | + | 1.00000i | 0.632456 | + | 0.316228i | ||||
\(11\) | − | 1.41421i | − | 0.426401i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | − | 4.00000i | −1.10940 | − | 1.10940i | −0.993229 | − | 0.116171i | \(-0.962938\pi\) |
−0.116171 | − | 0.993229i | \(-0.537062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.24264 | − | 4.24264i | −1.02899 | − | 1.02899i | −0.999567 | − | 0.0294245i | \(-0.990633\pi\) |
−0.0294245 | − | 0.999567i | \(-0.509367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 0.707107 | + | 2.12132i | 0.158114 | + | 0.474342i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.00000i | 0.213201 | − | 0.213201i | ||||
\(23\) | 0.707107 | − | 0.707107i | 0.147442 | − | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | − | 3.00000i | 0.800000 | − | 0.600000i | ||||
\(26\) | − | 5.65685i | − | 1.10940i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.65685 | 1.05045 | 0.525226 | − | 0.850963i | \(-0.323981\pi\) | ||||
0.525226 | + | 0.850963i | \(0.323981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.00000i | − | 1.02899i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | − | 3.00000i | 0.493197 | − | 0.493197i | −0.416115 | − | 0.909312i | \(-0.636609\pi\) |
0.909312 | + | 0.416115i | \(0.136609\pi\) | |||||||
\(38\) | 4.24264 | − | 4.24264i | 0.688247 | − | 0.688247i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | + | 2.00000i | −0.158114 | + | 0.316228i | ||||
\(41\) | − | 4.24264i | − | 0.662589i | −0.943527 | − | 0.331295i | \(-0.892515\pi\) | ||
0.943527 | − | 0.331295i | \(-0.107485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | + | 1.00000i | 0.152499 | + | 0.152499i | 0.779233 | − | 0.626734i | \(-0.215609\pi\) |
−0.626734 | + | 0.779233i | \(0.715609\pi\) | |||||||
\(44\) | 1.41421 | 0.213201 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −7.07107 | − | 7.07107i | −1.03142 | − | 1.03142i | −0.999490 | − | 0.0319312i | \(-0.989834\pi\) |
−0.0319312 | − | 0.999490i | \(-0.510166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 4.94975 | + | 0.707107i | 0.700000 | + | 0.100000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.00000 | − | 4.00000i | 0.554700 | − | 0.554700i | ||||
\(53\) | −4.24264 | + | 4.24264i | −0.582772 | + | 0.582772i | −0.935664 | − | 0.352892i | \(-0.885198\pi\) |
0.352892 | + | 0.935664i | \(0.385198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | − | 3.00000i | −0.134840 | − | 0.404520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | + | 4.00000i | 0.525226 | + | 0.525226i | ||||
\(59\) | 2.82843 | 0.368230 | 0.184115 | − | 0.982905i | \(-0.441058\pi\) | ||||
0.184115 | + | 0.982905i | \(0.441058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −11.3137 | − | 5.65685i | −1.40329 | − | 0.701646i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.00000 | + | 9.00000i | −1.09952 | + | 1.09952i | −0.105059 | + | 0.994466i | \(0.533503\pi\) |
−0.994466 | + | 0.105059i | \(0.966497\pi\) | |||||||
\(68\) | 4.24264 | − | 4.24264i | 0.514496 | − | 0.514496i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.24264i | 0.503509i | 0.967791 | + | 0.251754i | \(0.0810075\pi\) | ||||
−0.967791 | + | 0.251754i | \(0.918992\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.00000 | + | 9.00000i | 1.05337 | + | 1.05337i | 0.998493 | + | 0.0548772i | \(0.0174767\pi\) |
0.0548772 | + | 0.998493i | \(0.482523\pi\) | |||||||
\(74\) | 4.24264 | 0.493197 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | −2.12132 | + | 0.707107i | −0.237171 | + | 0.0790569i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | − | 3.00000i | 0.331295 | − | 0.331295i | ||||
\(83\) | −1.41421 | + | 1.41421i | −0.155230 | + | 0.155230i | −0.780449 | − | 0.625219i | \(-0.785010\pi\) |
0.625219 | + | 0.780449i | \(0.285010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | − | 6.00000i | −1.30158 | − | 0.650791i | ||||
\(86\) | 1.41421i | 0.152499i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | + | 1.00000i | 0.106600 | + | 0.106600i | ||||
\(89\) | 2.82843 | 0.299813 | 0.149906 | − | 0.988700i | \(-0.452103\pi\) | ||||
0.149906 | + | 0.988700i | \(0.452103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 10.0000i | − | 1.03142i | ||||||
\(95\) | −4.24264 | − | 12.7279i | −0.435286 | − | 1.30586i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | − | 8.00000i | 0.812277 | − | 0.812277i | −0.172698 | − | 0.984975i | \(-0.555248\pi\) |
0.984975 | + | 0.172698i | \(0.0552484\pi\) | |||||||
\(98\) | −4.94975 | + | 4.94975i | −0.500000 | + | 0.500000i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | − | 5.65685i | − | 0.562878i | −0.959579 | − | 0.281439i | \(-0.909188\pi\) | ||
0.959579 | − | 0.281439i | \(-0.0908117\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.0000 | + | 12.0000i | 1.18240 | + | 1.18240i | 0.979122 | + | 0.203273i | \(0.0651579\pi\) |
0.203273 | + | 0.979122i | \(0.434842\pi\) | |||||||
\(104\) | 5.65685 | 0.554700 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −8.48528 | − | 8.48528i | −0.820303 | − | 0.820303i | 0.165848 | − | 0.986151i | \(-0.446964\pi\) |
−0.986151 | + | 0.165848i | \(0.946964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000i | 0.766261i | 0.923694 | + | 0.383131i | \(0.125154\pi\) | ||||
−0.923694 | + | 0.383131i | \(0.874846\pi\) | |||||||
\(110\) | 1.41421 | − | 2.82843i | 0.134840 | − | 0.269680i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.41421 | − | 1.41421i | 0.133038 | − | 0.133038i | −0.637452 | − | 0.770490i | \(-0.720012\pi\) |
0.770490 | + | 0.637452i | \(0.220012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | − | 2.00000i | 0.0932505 | − | 0.186501i | ||||
\(116\) | 5.65685i | 0.525226i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00000 | + | 2.00000i | 0.184115 | + | 0.184115i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 1.41421 | + | 1.41421i | 0.128037 | + | 0.128037i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.36396 | − | 9.19239i | 0.569210 | − | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00000 | − | 9.00000i | 0.798621 | − | 0.798621i | −0.184257 | − | 0.982878i | \(-0.558988\pi\) |
0.982878 | + | 0.184257i | \(0.0589879\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.00000 | − | 12.0000i | −0.350823 | − | 1.05247i | ||||
\(131\) | − | 11.3137i | − | 0.988483i | −0.869325 | − | 0.494242i | \(-0.835446\pi\) | ||
0.869325 | − | 0.494242i | \(-0.164554\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −12.7279 | −1.09952 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | −12.7279 | − | 12.7279i | −1.08742 | − | 1.08742i | −0.995793 | − | 0.0916263i | \(-0.970793\pi\) |
−0.0916263 | − | 0.995793i | \(-0.529207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.00000i | − | 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.00000 | + | 3.00000i | −0.251754 | + | 0.251754i | ||||
\(143\) | −5.65685 | + | 5.65685i | −0.473050 | + | 0.473050i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0000 | − | 4.00000i | 0.996546 | − | 0.332182i | ||||
\(146\) | 12.7279i | 1.05337i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.00000 | + | 3.00000i | 0.246598 | + | 0.246598i | ||||
\(149\) | 1.41421 | 0.115857 | 0.0579284 | − | 0.998321i | \(-0.481550\pi\) | ||||
0.0579284 | + | 0.998321i | \(0.481550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | 4.24264 | + | 4.24264i | 0.344124 | + | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.00000 | − | 3.00000i | 0.239426 | − | 0.239426i | −0.577186 | − | 0.816612i | \(-0.695849\pi\) |
0.816612 | + | 0.577186i | \(0.195849\pi\) | |||||||
\(158\) | −2.82843 | + | 2.82843i | −0.225018 | + | 0.225018i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | − | 1.00000i | −0.158114 | − | 0.0790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0000 | + | 14.0000i | 1.09656 | + | 1.09656i | 0.994809 | + | 0.101755i | \(0.0324458\pi\) |
0.101755 | + | 0.994809i | \(0.467554\pi\) | |||||||
\(164\) | 4.24264 | 0.331295 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | 11.3137 | + | 11.3137i | 0.875481 | + | 0.875481i | 0.993063 | − | 0.117582i | \(-0.0375143\pi\) |
−0.117582 | + | 0.993063i | \(0.537514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000i | 1.46154i | ||||||||
\(170\) | −4.24264 | − | 12.7279i | −0.325396 | − | 0.976187i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00000 | + | 1.00000i | −0.0762493 | + | 0.0762493i | ||||
\(173\) | 1.41421 | − | 1.41421i | 0.107521 | − | 0.107521i | −0.651300 | − | 0.758820i | \(-0.725776\pi\) |
0.758820 | + | 0.651300i | \(0.225776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.41421i | 0.106600i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.00000 | + | 2.00000i | 0.149906 | + | 0.149906i | ||||
\(179\) | −2.82843 | −0.211407 | −0.105703 | − | 0.994398i | \(-0.533709\pi\) | ||||
−0.105703 | + | 0.994398i | \(0.533709\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000i | 0.0737210i | ||||||||
\(185\) | 4.24264 | − | 8.48528i | 0.311925 | − | 0.623850i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | + | 6.00000i | −0.438763 | + | 0.438763i | ||||
\(188\) | 7.07107 | − | 7.07107i | 0.515711 | − | 0.515711i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | − | 12.0000i | 0.435286 | − | 0.870572i | ||||
\(191\) | 22.6274i | 1.63726i | 0.574320 | + | 0.818631i | \(0.305267\pi\) | ||||
−0.574320 | + | 0.818631i | \(0.694733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.0000 | − | 15.0000i | −1.07972 | − | 1.07972i | −0.996534 | − | 0.0831899i | \(-0.973489\pi\) |
−0.0831899 | − | 0.996534i | \(-0.526511\pi\) | |||||||
\(194\) | 11.3137 | 0.812277 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | −12.7279 | − | 12.7279i | −0.906827 | − | 0.906827i | 0.0891879 | − | 0.996015i | \(-0.471573\pi\) |
−0.996015 | + | 0.0891879i | \(0.971573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000i | 1.41776i | 0.705328 | + | 0.708881i | \(0.250800\pi\) | ||||
−0.705328 | + | 0.708881i | \(0.749200\pi\) | |||||||
\(200\) | −0.707107 | + | 4.94975i | −0.0500000 | + | 0.350000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.00000 | − | 4.00000i | 0.281439 | − | 0.281439i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | − | 9.00000i | −0.209529 | − | 0.628587i | ||||
\(206\) | 16.9706i | 1.18240i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.00000 | + | 4.00000i | 0.277350 | + | 0.277350i | ||||
\(209\) | −8.48528 | −0.586939 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | −4.24264 | − | 4.24264i | −0.291386 | − | 0.291386i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 12.0000i | − | 0.820303i | ||||||
\(215\) | 2.82843 | + | 1.41421i | 0.192897 | + | 0.0964486i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.65685 | + | 5.65685i | −0.383131 | + | 0.383131i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.00000 | − | 1.00000i | 0.202260 | − | 0.0674200i | ||||
\(221\) | 33.9411i | 2.28313i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.00000 | + | 5.00000i | 0.334825 | + | 0.334825i | 0.854415 | − | 0.519591i | \(-0.173916\pi\) |
−0.519591 | + | 0.854415i | \(0.673916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.00000 | 0.133038 | ||||||||
\(227\) | 8.48528 | + | 8.48528i | 0.563188 | + | 0.563188i | 0.930212 | − | 0.367024i | \(-0.119623\pi\) |
−0.367024 | + | 0.930212i | \(0.619623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 26.0000i | − | 1.71813i | −0.511868 | − | 0.859064i | \(-0.671046\pi\) | ||
0.511868 | − | 0.859064i | \(-0.328954\pi\) | |||||||
\(230\) | 2.12132 | − | 0.707107i | 0.139876 | − | 0.0466252i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.00000 | + | 4.00000i | −0.262613 | + | 0.262613i | ||||
\(233\) | 7.07107 | − | 7.07107i | 0.463241 | − | 0.463241i | −0.436475 | − | 0.899716i | \(-0.643773\pi\) |
0.899716 | + | 0.436475i | \(0.143773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.0000 | − | 10.0000i | −1.30466 | − | 0.652328i | ||||
\(236\) | 2.82843i | 0.184115i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.07107 | 0.457389 | 0.228695 | − | 0.973498i | \(-0.426554\pi\) | ||||
0.228695 | + | 0.973498i | \(0.426554\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 6.36396 | + | 6.36396i | 0.409091 | + | 0.409091i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000i | 0.128037i | ||||||||
\(245\) | 4.94975 | + | 14.8492i | 0.316228 | + | 0.948683i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.0000 | + | 24.0000i | −1.52708 | + | 1.52708i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.0000 | − | 2.00000i | 0.695701 | − | 0.126491i | ||||
\(251\) | − | 1.41421i | − | 0.0892644i | −0.999003 | − | 0.0446322i | \(-0.985788\pi\) | ||
0.999003 | − | 0.0446322i | \(-0.0142116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00000 | − | 1.00000i | −0.0628695 | − | 0.0628695i | ||||
\(254\) | 12.7279 | 0.798621 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.48528 | − | 8.48528i | −0.529297 | − | 0.529297i | 0.391066 | − | 0.920363i | \(-0.372107\pi\) |
−0.920363 | + | 0.391066i | \(0.872107\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.65685 | − | 11.3137i | 0.350823 | − | 0.701646i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.00000 | − | 8.00000i | 0.494242 | − | 0.494242i | ||||
\(263\) | −19.7990 | + | 19.7990i | −1.22086 | + | 1.22086i | −0.253531 | + | 0.967327i | \(0.581592\pi\) |
−0.967327 | + | 0.253531i | \(0.918408\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | + | 12.0000i | −0.368577 | + | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.00000 | − | 9.00000i | −0.549762 | − | 0.549762i | ||||
\(269\) | −2.82843 | −0.172452 | −0.0862261 | − | 0.996276i | \(-0.527481\pi\) | ||||
−0.0862261 | + | 0.996276i | \(0.527481\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 4.24264 | + | 4.24264i | 0.257248 | + | 0.257248i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 18.0000i | − | 1.08742i | ||||||
\(275\) | −4.24264 | − | 5.65685i | −0.255841 | − | 0.341121i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0000 | − | 20.0000i | 1.20168 | − | 1.20168i | 0.228029 | − | 0.973654i | \(-0.426772\pi\) |
0.973654 | − | 0.228029i | \(-0.0732282\pi\) | |||||||
\(278\) | 2.82843 | − | 2.82843i | 0.169638 | − | 0.169638i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.7990i | − | 1.18111i | −0.806998 | − | 0.590554i | \(-0.798909\pi\) | ||
0.806998 | − | 0.590554i | \(-0.201091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0000 | + | 13.0000i | 0.772770 | + | 0.772770i | 0.978590 | − | 0.205820i | \(-0.0659862\pi\) |
−0.205820 | + | 0.978590i | \(0.565986\pi\) | |||||||
\(284\) | −4.24264 | −0.251754 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.00000 | −0.473050 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000i | 1.11765i | ||||||||
\(290\) | 11.3137 | + | 5.65685i | 0.664364 | + | 0.332182i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.00000 | + | 9.00000i | −0.526685 | + | 0.526685i | ||||
\(293\) | 11.3137 | − | 11.3137i | 0.660954 | − | 0.660954i | −0.294651 | − | 0.955605i | \(-0.595203\pi\) |
0.955605 | + | 0.294651i | \(0.0952034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | − | 2.00000i | 0.349334 | − | 0.116445i | ||||
\(296\) | 4.24264i | 0.246598i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | + | 1.00000i | 0.0579284 | + | 0.0579284i | ||||
\(299\) | −5.65685 | −0.327144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.41421 | − | 1.41421i | −0.0813788 | − | 0.0813788i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.00000i | 0.344124i | ||||||||
\(305\) | 4.24264 | − | 1.41421i | 0.242933 | − | 0.0809776i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.00000 | + | 8.00000i | −0.456584 | + | 0.456584i | −0.897532 | − | 0.440948i | \(-0.854642\pi\) |
0.440948 | + | 0.897532i | \(0.354642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.07107i | − | 0.400963i | −0.979697 | − | 0.200482i | \(-0.935749\pi\) | ||
0.979697 | − | 0.200482i | \(-0.0642507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | − | 10.0000i | −0.565233 | − | 0.565233i | 0.365556 | − | 0.930789i | \(-0.380879\pi\) |
−0.930789 | + | 0.365556i | \(0.880879\pi\) | |||||||
\(314\) | 4.24264 | 0.239426 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | −24.0416 | − | 24.0416i | −1.35031 | − | 1.35031i | −0.885309 | − | 0.465004i | \(-0.846053\pi\) |
−0.465004 | − | 0.885309i | \(-0.653947\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.00000i | − | 0.447914i | ||||||
\(320\) | −0.707107 | − | 2.12132i | −0.0395285 | − | 0.118585i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.4558 | + | 25.4558i | −1.41640 | + | 1.41640i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.0000 | − | 4.00000i | −1.55316 | − | 0.221880i | ||||
\(326\) | 19.7990i | 1.09656i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | + | 3.00000i | 0.165647 | + | 0.165647i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | −1.41421 | − | 1.41421i | −0.0776151 | − | 0.0776151i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.0000i | 0.875481i | ||||||||
\(335\) | −12.7279 | + | 25.4558i | −0.695401 | + | 1.39080i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0000 | + | 18.0000i | −0.980522 | + | 0.980522i | −0.999814 | − | 0.0192914i | \(-0.993859\pi\) |
0.0192914 | + | 0.999814i | \(0.493859\pi\) | |||||||
\(338\) | −13.4350 | + | 13.4350i | −0.730769 | + | 0.730769i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | − | 12.0000i | 0.325396 | − | 0.650791i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.41421 | −0.0762493 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | 0.107521 | ||||||||
\(347\) | 11.3137 | + | 11.3137i | 0.607352 | + | 0.607352i | 0.942253 | − | 0.334901i | \(-0.108703\pi\) |
−0.334901 | + | 0.942253i | \(0.608703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.0000i | − | 0.749403i | −0.927146 | − | 0.374701i | \(-0.877745\pi\) | ||
0.927146 | − | 0.374701i | \(-0.122255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | + | 1.00000i | −0.0533002 | + | 0.0533002i | ||||
\(353\) | 8.48528 | − | 8.48528i | 0.451626 | − | 0.451626i | −0.444268 | − | 0.895894i | \(-0.646536\pi\) |
0.895894 | + | 0.444268i | \(0.146536\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | + | 9.00000i | 0.159223 | + | 0.477670i | ||||
\(356\) | 2.82843i | 0.149906i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.00000 | − | 2.00000i | −0.105703 | − | 0.105703i | ||||
\(359\) | −28.2843 | −1.49279 | −0.746393 | − | 0.665505i | \(-0.768216\pi\) | ||||
−0.746393 | + | 0.665505i | \(0.768216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | −7.07107 | − | 7.07107i | −0.371647 | − | 0.371647i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.4558 | + | 12.7279i | 1.33242 | + | 0.666210i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | − | 4.00000i | 0.208798 | − | 0.208798i | −0.594958 | − | 0.803757i | \(-0.702831\pi\) |
0.803757 | + | 0.594958i | \(0.202831\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.00000 | − | 3.00000i | 0.467888 | − | 0.155963i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0000 | + | 13.0000i | 0.673114 | + | 0.673114i | 0.958433 | − | 0.285318i | \(-0.0920993\pi\) |
−0.285318 | + | 0.958433i | \(0.592099\pi\) | |||||||
\(374\) | −8.48528 | −0.438763 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.0000 | 0.515711 | ||||||||
\(377\) | −22.6274 | − | 22.6274i | −1.16537 | − | 1.16537i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 36.0000i | − | 1.84920i | −0.380945 | − | 0.924598i | \(-0.624401\pi\) | ||
0.380945 | − | 0.924598i | \(-0.375599\pi\) | |||||||
\(380\) | 12.7279 | − | 4.24264i | 0.652929 | − | 0.217643i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.0000 | + | 16.0000i | −0.818631 | + | 0.818631i | ||||
\(383\) | −5.65685 | + | 5.65685i | −0.289052 | + | 0.289052i | −0.836705 | − | 0.547653i | \(-0.815521\pi\) |
0.547653 | + | 0.836705i | \(0.315521\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 21.2132i | − | 1.07972i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.00000 | + | 8.00000i | 0.406138 | + | 0.406138i | ||||
\(389\) | 24.0416 | 1.21896 | 0.609480 | − | 0.792802i | \(-0.291378\pi\) | ||||
0.609480 | + | 0.792802i | \(0.291378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.00000 | −0.303433 | ||||||||
\(392\) | −4.94975 | − | 4.94975i | −0.250000 | − | 0.250000i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 18.0000i | − | 0.906827i | ||||||
\(395\) | 2.82843 | + | 8.48528i | 0.142314 | + | 0.426941i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0000 | + | 16.0000i | −0.803017 | + | 0.803017i | −0.983566 | − | 0.180549i | \(-0.942213\pi\) |
0.180549 | + | 0.983566i | \(0.442213\pi\) | |||||||
\(398\) | −14.1421 | + | 14.1421i | −0.708881 | + | 0.708881i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | + | 3.00000i | −0.200000 | + | 0.150000i | ||||
\(401\) | 22.6274i | 1.12996i | 0.825105 | + | 0.564980i | \(0.191116\pi\) | ||||
−0.825105 | + | 0.564980i | \(0.808884\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.65685 | 0.281439 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.24264 | − | 4.24264i | −0.210300 | − | 0.210300i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0000i | 1.28562i | 0.766027 | + | 0.642809i | \(0.222231\pi\) | ||||
−0.766027 | + | 0.642809i | \(0.777769\pi\) | |||||||
\(410\) | 4.24264 | − | 8.48528i | 0.209529 | − | 0.419058i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.0000 | + | 12.0000i | −0.591198 | + | 0.591198i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.00000 | + | 4.00000i | −0.0981761 | + | 0.196352i | ||||
\(416\) | 5.65685i | 0.277350i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.00000 | − | 6.00000i | −0.293470 | − | 0.293470i | ||||
\(419\) | 15.5563 | 0.759977 | 0.379989 | − | 0.924991i | \(-0.375928\pi\) | ||||
0.379989 | + | 0.924991i | \(0.375928\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.0000 | −1.94948 | −0.974740 | − | 0.223341i | \(-0.928304\pi\) | ||||
−0.974740 | + | 0.223341i | \(0.928304\pi\) | |||||||
\(422\) | 11.3137 | + | 11.3137i | 0.550743 | + | 0.550743i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 6.00000i | − | 0.291386i | ||||||
\(425\) | −29.6985 | − | 4.24264i | −1.44059 | − | 0.205798i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.48528 | − | 8.48528i | 0.410152 | − | 0.410152i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.00000 | + | 3.00000i | 0.0482243 | + | 0.144673i | ||||
\(431\) | 33.9411i | 1.63489i | 0.576009 | + | 0.817443i | \(0.304609\pi\) | ||||
−0.576009 | + | 0.817443i | \(0.695391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.00000 | + | 4.00000i | 0.192228 | + | 0.192228i | 0.796658 | − | 0.604430i | \(-0.206599\pi\) |
−0.604430 | + | 0.796658i | \(0.706599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | −0.383131 | ||||||||
\(437\) | −4.24264 | − | 4.24264i | −0.202953 | − | 0.202953i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.0000i | 0.477274i | 0.971109 | + | 0.238637i | \(0.0767006\pi\) | ||||
−0.971109 | + | 0.238637i | \(0.923299\pi\) | |||||||
\(440\) | 2.82843 | + | 1.41421i | 0.134840 | + | 0.0674200i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0000 | + | 24.0000i | −1.14156 | + | 1.14156i | ||||
\(443\) | −2.82843 | + | 2.82843i | −0.134383 | + | 0.134383i | −0.771099 | − | 0.636716i | \(-0.780292\pi\) |
0.636716 | + | 0.771099i | \(0.280292\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 2.00000i | 0.284427 | − | 0.0948091i | ||||
\(446\) | 7.07107i | 0.334825i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.8701 | 1.26808 | 0.634038 | − | 0.773302i | \(-0.281396\pi\) | ||||
0.634038 | + | 0.773302i | \(0.281396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 1.41421 | + | 1.41421i | 0.0665190 | + | 0.0665190i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0000i | 0.563188i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.0000 | + | 20.0000i | −0.935561 | + | 0.935561i | −0.998046 | − | 0.0624853i | \(-0.980097\pi\) |
0.0624853 | + | 0.998046i | \(0.480097\pi\) | |||||||
\(458\) | 18.3848 | − | 18.3848i | 0.859064 | − | 0.859064i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.00000 | + | 1.00000i | 0.0932505 | + | 0.0466252i | ||||
\(461\) | 11.3137i | 0.526932i | 0.964669 | + | 0.263466i | \(0.0848657\pi\) | ||||
−0.964669 | + | 0.263466i | \(0.915134\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.00000 | − | 5.00000i | −0.232370 | − | 0.232370i | 0.581311 | − | 0.813681i | \(-0.302540\pi\) |
−0.813681 | + | 0.581311i | \(0.802540\pi\) | |||||||
\(464\) | −5.65685 | −0.262613 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.0000 | 0.463241 | ||||||||
\(467\) | −18.3848 | − | 18.3848i | −0.850746 | − | 0.850746i | 0.139479 | − | 0.990225i | \(-0.455457\pi\) |
−0.990225 | + | 0.139479i | \(0.955457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.07107 | − | 21.2132i | −0.326164 | − | 0.978492i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.00000 | + | 2.00000i | −0.0920575 | + | 0.0920575i | ||||
\(473\) | 1.41421 | − | 1.41421i | 0.0650256 | − | 0.0650256i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.0000 | − | 24.0000i | −0.825897 | − | 1.10120i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.00000 | + | 5.00000i | 0.228695 | + | 0.228695i | ||||
\(479\) | 28.2843 | 1.29234 | 0.646171 | − | 0.763193i | \(-0.276369\pi\) | ||||
0.646171 | + | 0.763193i | \(0.276369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | 7.07107 | + | 7.07107i | 0.322078 | + | 0.322078i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.00000i | 0.409091i | ||||||||
\(485\) | 11.3137 | − | 22.6274i | 0.513729 | − | 1.02746i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.00000 | − | 3.00000i | 0.135943 | − | 0.135943i | −0.635861 | − | 0.771804i | \(-0.719355\pi\) |
0.771804 | + | 0.635861i | \(0.219355\pi\) | |||||||
\(488\) | −1.41421 | + | 1.41421i | −0.0640184 | + | 0.0640184i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.00000 | + | 14.0000i | −0.316228 | + | 0.632456i | ||||
\(491\) | 5.65685i | 0.255290i | 0.991820 | + | 0.127645i | \(0.0407419\pi\) | ||||
−0.991820 | + | 0.127645i | \(0.959258\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.0000 | − | 24.0000i | −1.08091 | − | 1.08091i | ||||
\(494\) | −33.9411 | −1.52708 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.0000i | 1.61158i | 0.592200 | + | 0.805791i | \(0.298259\pi\) | ||||
−0.592200 | + | 0.805791i | \(0.701741\pi\) | |||||||
\(500\) | 9.19239 | + | 6.36396i | 0.411096 | + | 0.284605i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.00000 | − | 1.00000i | 0.0446322 | − | 0.0446322i | ||||
\(503\) | 25.4558 | − | 25.4558i | 1.13502 | − | 1.13502i | 0.145690 | − | 0.989330i | \(-0.453460\pi\) |
0.989330 | − | 0.145690i | \(-0.0465401\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.00000 | − | 12.0000i | −0.177998 | − | 0.533993i | ||||
\(506\) | − | 1.41421i | − | 0.0628695i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.00000 | + | 9.00000i | 0.399310 | + | 0.399310i | ||||
\(509\) | 39.5980 | 1.75515 | 0.877575 | − | 0.479440i | \(-0.159160\pi\) | ||||
0.877575 | + | 0.479440i | \(0.159160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 12.0000i | − | 0.529297i | ||||||
\(515\) | 33.9411 | + | 16.9706i | 1.49562 | + | 0.747812i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0000 | + | 10.0000i | −0.439799 | + | 0.439799i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.0000 | − | 4.00000i | 0.526235 | − | 0.175412i | ||||
\(521\) | 14.1421i | 0.619578i | 0.950805 | + | 0.309789i | \(0.100258\pi\) | ||||
−0.950805 | + | 0.309789i | \(0.899742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0000 | − | 13.0000i | −0.568450 | − | 0.568450i | 0.363244 | − | 0.931694i | \(-0.381669\pi\) |
−0.931694 | + | 0.363244i | \(0.881669\pi\) | |||||||
\(524\) | 11.3137 | 0.494242 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.0000 | −1.22086 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | −12.7279 | + | 4.24264i | −0.552866 | + | 0.184289i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.9706 | + | 16.9706i | −0.735077 | + | 0.735077i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.0000 | − | 12.0000i | −1.03761 | − | 0.518805i | ||||
\(536\) | − | 12.7279i | − | 0.549762i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.00000 | − | 2.00000i | −0.0862261 | − | 0.0862261i | ||||
\(539\) | 9.89949 | 0.426401 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0000 | −0.601907 | −0.300954 | − | 0.953639i | \(-0.597305\pi\) | ||||
−0.300954 | + | 0.953639i | \(0.597305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.00000i | 0.257248i | ||||||||
\(545\) | 5.65685 | + | 16.9706i | 0.242313 | + | 0.726939i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | − | 8.00000i | 0.342055 | − | 0.342055i | −0.515084 | − | 0.857140i | \(-0.672239\pi\) |
0.857140 | + | 0.515084i | \(0.172239\pi\) | |||||||
\(548\) | 12.7279 | − | 12.7279i | 0.543710 | − | 0.543710i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000 | − | 7.00000i | 0.0426401 | − | 0.298481i | ||||
\(551\) | − | 33.9411i | − | 1.44594i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 28.2843 | 1.20168 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | 5.65685 | + | 5.65685i | 0.239689 | + | 0.239689i | 0.816721 | − | 0.577033i | \(-0.195789\pi\) |
−0.577033 | + | 0.816721i | \(0.695789\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.00000i | − | 0.338364i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.0000 | − | 14.0000i | 0.590554 | − | 0.590554i | ||||
\(563\) | −29.6985 | + | 29.6985i | −1.25164 | + | 1.25164i | −0.296658 | + | 0.954984i | \(0.595872\pi\) |
−0.954984 | + | 0.296658i | \(0.904128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | − | 4.00000i | 0.0841406 | − | 0.168281i | ||||
\(566\) | 18.3848i | 0.772770i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.00000 | − | 3.00000i | −0.125877 | − | 0.125877i | ||||
\(569\) | 33.9411 | 1.42289 | 0.711443 | − | 0.702744i | \(-0.248042\pi\) | ||||
0.711443 | + | 0.702744i | \(0.248042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.0000 | 1.50655 | 0.753277 | − | 0.657704i | \(-0.228472\pi\) | ||||
0.753277 | + | 0.657704i | \(0.228472\pi\) | |||||||
\(572\) | −5.65685 | − | 5.65685i | −0.236525 | − | 0.236525i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.707107 | − | 4.94975i | 0.0294884 | − | 0.206419i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.00000 | + | 3.00000i | −0.124892 | + | 0.124892i | −0.766790 | − | 0.641898i | \(-0.778147\pi\) |
0.641898 | + | 0.766790i | \(0.278147\pi\) | |||||||
\(578\) | −13.4350 | + | 13.4350i | −0.558824 | + | 0.558824i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.00000 | + | 12.0000i | 0.166091 | + | 0.498273i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | + | 6.00000i | 0.248495 | + | 0.248495i | ||||
\(584\) | −12.7279 | −0.526685 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.0000 | 0.660954 | ||||||||
\(587\) | −28.2843 | − | 28.2843i | −1.16742 | − | 1.16742i | −0.982813 | − | 0.184604i | \(-0.940900\pi\) |
−0.184604 | − | 0.982813i | \(-0.559100\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 5.65685 | + | 2.82843i | 0.232889 | + | 0.116445i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.00000 | + | 3.00000i | −0.123299 | + | 0.123299i | ||||
\(593\) | −8.48528 | + | 8.48528i | −0.348449 | + | 0.348449i | −0.859532 | − | 0.511083i | \(-0.829245\pi\) |
0.511083 | + | 0.859532i | \(0.329245\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.41421i | 0.0579284i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.00000 | − | 4.00000i | −0.163572 | − | 0.163572i | ||||
\(599\) | 24.0416 | 0.982314 | 0.491157 | − | 0.871071i | \(-0.336574\pi\) | ||||
0.491157 | + | 0.871071i | \(0.336574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 2.00000i | − | 0.0813788i | ||||||
\(605\) | 19.0919 | − | 6.36396i | 0.776195 | − | 0.258732i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.0000 | − | 27.0000i | 1.09590 | − | 1.09590i | 0.101011 | − | 0.994885i | \(-0.467792\pi\) |
0.994885 | − | 0.101011i | \(-0.0322077\pi\) | |||||||
\(608\) | −4.24264 | + | 4.24264i | −0.172062 | + | 0.172062i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.00000 | + | 2.00000i | 0.161955 | + | 0.0809776i | ||||
\(611\) | 56.5685i | 2.28852i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0000 | + | 17.0000i | 0.686624 | + | 0.686624i | 0.961484 | − | 0.274861i | \(-0.0886317\pi\) |
−0.274861 | + | 0.961484i | \(0.588632\pi\) | |||||||
\(614\) | −11.3137 | −0.456584 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.89949 | + | 9.89949i | 0.398539 | + | 0.398539i | 0.877717 | − | 0.479179i | \(-0.159065\pi\) |
−0.479179 | + | 0.877717i | \(0.659065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0000i | 0.401934i | 0.979598 | + | 0.200967i | \(0.0644084\pi\) | ||||
−0.979598 | + | 0.200967i | \(0.935592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.00000 | − | 5.00000i | 0.200482 | − | 0.200482i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | − | 14.1421i | − | 0.565233i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.00000 | + | 3.00000i | 0.119713 | + | 0.119713i | ||||
\(629\) | −25.4558 | −1.01499 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | −2.82843 | − | 2.82843i | −0.112509 | − | 0.112509i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 34.0000i | − | 1.35031i | ||||||
\(635\) | 12.7279 | − | 25.4558i | 0.505092 | − | 1.01018i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.0000 | − | 28.0000i | 1.10940 | − | 1.10940i | ||||
\(638\) | 5.65685 | − | 5.65685i | 0.223957 | − | 0.223957i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | − | 2.00000i | 0.0395285 | − | 0.0790569i | ||||
\(641\) | − | 8.48528i | − | 0.335148i | −0.985859 | − | 0.167574i | \(-0.946407\pi\) | ||
0.985859 | − | 0.167574i | \(-0.0535934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.00000 | − | 9.00000i | −0.354925 | − | 0.354925i | 0.507013 | − | 0.861938i | \(-0.330750\pi\) |
−0.861938 | + | 0.507013i | \(0.830750\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36.0000 | −1.41640 | ||||||||
\(647\) | −1.41421 | − | 1.41421i | −0.0555985 | − | 0.0555985i | 0.678761 | − | 0.734359i | \(-0.262517\pi\) |
−0.734359 | + | 0.678761i | \(0.762517\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.00000i | − | 0.157014i | ||||||
\(650\) | −16.9706 | − | 22.6274i | −0.665640 | − | 0.887520i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.0000 | + | 14.0000i | −0.548282 | + | 0.548282i | ||||
\(653\) | 21.2132 | − | 21.2132i | 0.830137 | − | 0.830137i | −0.157398 | − | 0.987535i | \(-0.550311\pi\) |
0.987535 | + | 0.157398i | \(0.0503107\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | − | 24.0000i | −0.312586 | − | 0.937758i | ||||
\(656\) | 4.24264i | 0.165647i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.3848 | −0.716169 | −0.358085 | − | 0.933689i | \(-0.616570\pi\) | ||||
−0.358085 | + | 0.933689i | \(0.616570\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0000 | 0.933492 | 0.466746 | − | 0.884391i | \(-0.345426\pi\) | ||||
0.466746 | + | 0.884391i | \(0.345426\pi\) | |||||||
\(662\) | 5.65685 | + | 5.65685i | 0.219860 | + | 0.219860i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 2.00000i | − | 0.0776151i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00000 | − | 4.00000i | 0.154881 | − | 0.154881i | ||||
\(668\) | −11.3137 | + | 11.3137i | −0.437741 | + | 0.437741i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −27.0000 | + | 9.00000i | −1.04310 | + | 0.347700i | ||||
\(671\) | − | 2.82843i | − | 0.109190i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.0000 | + | 15.0000i | 0.578208 | + | 0.578208i | 0.934409 | − | 0.356202i | \(-0.115928\pi\) |
−0.356202 | + | 0.934409i | \(0.615928\pi\) | |||||||
\(674\) | −25.4558 | −0.980522 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.0000 | −0.730769 | ||||||||
\(677\) | −2.82843 | − | 2.82843i | −0.108705 | − | 0.108705i | 0.650662 | − | 0.759367i | \(-0.274491\pi\) |
−0.759367 | + | 0.650662i | \(0.774491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.7279 | − | 4.24264i | 0.488094 | − | 0.162698i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9411 | + | 33.9411i | −1.29872 | + | 1.29872i | −0.369484 | + | 0.929237i | \(0.620466\pi\) |
−0.929237 | + | 0.369484i | \(0.879534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.0000 | − | 18.0000i | −1.37549 | − | 0.687745i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | − | 1.00000i | −0.0381246 | − | 0.0381246i | ||||
\(689\) | 33.9411 | 1.29305 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0000 | 1.67384 | 0.836919 | − | 0.547326i | \(-0.184354\pi\) | ||||
0.836919 | + | 0.547326i | \(0.184354\pi\) | |||||||
\(692\) | 1.41421 | + | 1.41421i | 0.0537603 | + | 0.0537603i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0000i | 0.607352i | ||||||||
\(695\) | −2.82843 | − | 8.48528i | −0.107288 | − | 0.321865i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | + | 18.0000i | −0.681799 | + | 0.681799i | ||||
\(698\) | 9.89949 | − | 9.89949i | 0.374701 | − | 0.374701i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7.07107i | − | 0.267071i | −0.991044 | − | 0.133535i | \(-0.957367\pi\) | ||
0.991044 | − | 0.133535i | \(-0.0426329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0000 | − | 18.0000i | −0.678883 | − | 0.678883i | ||||
\(704\) | −1.41421 | −0.0533002 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0000 | 0.451626 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.00000i | 0.225335i | 0.993633 | + | 0.112667i | \(0.0359394\pi\) | ||||
−0.993633 | + | 0.112667i | \(0.964061\pi\) | |||||||
\(710\) | −4.24264 | + | 8.48528i | −0.159223 | + | 0.318447i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.00000 | + | 2.00000i | −0.0749532 | + | 0.0749532i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | + | 16.0000i | −0.299183 | + | 0.598366i | ||||
\(716\) | − | 2.82843i | − | 0.105703i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.0000 | − | 20.0000i | −0.746393 | − | 0.746393i | ||||
\(719\) | −26.8701 | −1.00208 | −0.501042 | − | 0.865423i | \(-0.667050\pi\) | ||||
−0.501042 | + | 0.865423i | \(0.667050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.0208 | − | 12.0208i | −0.447368 | − | 0.447368i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 10.0000i | − | 0.371647i | ||||||
\(725\) | 22.6274 | − | 16.9706i | 0.840361 | − | 0.630271i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.0000 | + | 18.0000i | −0.667583 | + | 0.667583i | −0.957156 | − | 0.289573i | \(-0.906487\pi\) |
0.289573 | + | 0.957156i | \(0.406487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.00000 | + | 27.0000i | 0.333105 | + | 0.999315i | ||||
\(731\) | − | 8.48528i | − | 0.313839i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.0000 | − | 35.0000i | −1.29275 | − | 1.29275i | −0.933076 | − | 0.359678i | \(-0.882887\pi\) |
−0.359678 | − | 0.933076i | \(-0.617113\pi\) | |||||||
\(734\) | 5.65685 | 0.208798 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 12.7279 | + | 12.7279i | 0.468839 | + | 0.468839i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 16.0000i | − | 0.588570i | −0.955718 | − | 0.294285i | \(-0.904919\pi\) | ||
0.955718 | − | 0.294285i | \(-0.0950814\pi\) | |||||||
\(740\) | 8.48528 | + | 4.24264i | 0.311925 | + | 0.155963i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.2843 | − | 28.2843i | 1.03765 | − | 1.03765i | 0.0383863 | − | 0.999263i | \(-0.487778\pi\) |
0.999263 | − | 0.0383863i | \(-0.0122217\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.00000 | − | 1.00000i | 0.109911 | − | 0.0366372i | ||||
\(746\) | 18.3848i | 0.673114i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.00000 | − | 6.00000i | −0.219382 | − | 0.219382i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.0000 | 1.75154 | 0.875772 | − | 0.482724i | \(-0.160353\pi\) | ||||
0.875772 | + | 0.482724i | \(0.160353\pi\) | |||||||
\(752\) | 7.07107 | + | 7.07107i | 0.257855 | + | 0.257855i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 32.0000i | − | 1.16537i | ||||||
\(755\) | −4.24264 | + | 1.41421i | −0.154406 | + | 0.0514685i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | + | 15.0000i | −0.545184 | + | 0.545184i | −0.925044 | − | 0.379860i | \(-0.875972\pi\) |
0.379860 | + | 0.925044i | \(0.375972\pi\) | |||||||
\(758\) | 25.4558 | − | 25.4558i | 0.924598 | − | 0.924598i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | + | 6.00000i | 0.435286 | + | 0.217643i | ||||
\(761\) | 1.41421i | 0.0512652i | 0.999671 | + | 0.0256326i | \(0.00816000\pi\) | ||||
−0.999671 | + | 0.0256326i | \(0.991840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −22.6274 | −0.818631 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.00000 | −0.289052 | ||||||||
\(767\) | −11.3137 | − | 11.3137i | −0.408514 | − | 0.408514i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 26.0000i | − | 0.937584i | −0.883309 | − | 0.468792i | \(-0.844689\pi\) | ||
0.883309 | − | 0.468792i | \(-0.155311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15.0000 | − | 15.0000i | 0.539862 | − | 0.539862i | ||||
\(773\) | 4.24264 | − | 4.24264i | 0.152597 | − | 0.152597i | −0.626680 | − | 0.779277i | \(-0.715587\pi\) |
0.779277 | + | 0.626680i | \(0.215587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.3137i | 0.406138i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.0000 | + | 17.0000i | 0.609480 | + | 0.609480i | ||||
\(779\) | −25.4558 | −0.912050 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | −4.24264 | − | 4.24264i | −0.151717 | − | 0.151717i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 7.00000i | − | 0.250000i | ||||||
\(785\) | 4.24264 | − | 8.48528i | 0.151426 | − | 0.302853i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.0000 | + | 19.0000i | −0.677277 | + | 0.677277i | −0.959383 | − | 0.282106i | \(-0.908967\pi\) |
0.282106 | + | 0.959383i | \(0.408967\pi\) | |||||||
\(788\) | 12.7279 | − | 12.7279i | 0.453413 | − | 0.453413i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.00000 | + | 8.00000i | −0.142314 | + | 0.284627i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | − | 8.00000i | −0.284088 | − | 0.284088i | ||||
\(794\) | −22.6274 | −0.803017 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | −1.41421 | − | 1.41421i | −0.0500940 | − | 0.0500940i | 0.681616 | − | 0.731710i | \(-0.261277\pi\) |
−0.731710 | + | 0.681616i | \(0.761277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.0000i | 2.12265i | ||||||||
\(800\) | −4.94975 | − | 0.707107i | −0.175000 | − | 0.0250000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.0000 | + | 16.0000i | −0.564980 | + | 0.564980i | ||||
\(803\) | 12.7279 | − | 12.7279i | 0.449159 | − | 0.449159i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.00000 | + | 4.00000i | 0.140720 | + | 0.140720i | ||||
\(809\) | −4.24264 | −0.149163 | −0.0745817 | − | 0.997215i | \(-0.523762\pi\) | ||||
−0.0745817 | + | 0.997215i | \(0.523762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 6.00000i | − | 0.210300i | ||||||
\(815\) | 39.5980 | + | 19.7990i | 1.38706 | + | 0.693528i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.00000 | − | 6.00000i | 0.209913 | − | 0.209913i | ||||
\(818\) | −18.3848 | + | 18.3848i | −0.642809 | + | 0.642809i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.00000 | − | 3.00000i | 0.314294 | − | 0.104765i | ||||
\(821\) | 48.0833i | 1.67812i | 0.544041 | + | 0.839059i | \(0.316894\pi\) | ||||
−0.544041 | + | 0.839059i | \(0.683106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.0000 | + | 39.0000i | 1.35945 | + | 1.35945i | 0.874588 | + | 0.484866i | \(0.161132\pi\) |
0.484866 | + | 0.874588i | \(0.338868\pi\) | |||||||
\(824\) | −16.9706 | −0.591198 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.82843 | + | 2.82843i | 0.0983540 | + | 0.0983540i | 0.754572 | − | 0.656218i | \(-0.227845\pi\) |
−0.656218 | + | 0.754572i | \(0.727845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.0000i | 1.59765i | 0.601566 | + | 0.798823i | \(0.294544\pi\) | ||||
−0.601566 | + | 0.798823i | \(0.705456\pi\) | |||||||
\(830\) | −4.24264 | + | 1.41421i | −0.147264 | + | 0.0490881i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | + | 4.00000i | −0.138675 | + | 0.138675i | ||||
\(833\) | 29.6985 | − | 29.6985i | 1.02899 | − | 1.02899i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.0000 | + | 16.0000i | 1.10741 | + | 0.553703i | ||||
\(836\) | − | 8.48528i | − | 0.293470i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.0000 | + | 11.0000i | 0.379989 | + | 0.379989i | ||||
\(839\) | −36.7696 | −1.26943 | −0.634713 | − | 0.772748i | \(-0.718882\pi\) | ||||
−0.634713 | + | 0.772748i | \(0.718882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | −28.2843 | − | 28.2843i | −0.974740 | − | 0.974740i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.0000i | 0.550743i | ||||||||
\(845\) | 13.4350 | + | 40.3051i | 0.462179 | + | 1.38654i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.24264 | − | 4.24264i | 0.145693 | − | 0.145693i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.0000 | − | 24.0000i | −0.617395 | − | 0.823193i | ||||
\(851\) | − | 4.24264i | − | 0.145436i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.0000 | + | 20.0000i | 0.684787 | + | 0.684787i | 0.961075 | − | 0.276288i | \(-0.0891043\pi\) |
−0.276288 | + | 0.961075i | \(0.589104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | 19.7990 | + | 19.7990i | 0.676321 | + | 0.676321i | 0.959166 | − | 0.282845i | \(-0.0912782\pi\) |
−0.282845 | + | 0.959166i | \(0.591278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0000i | 1.36478i | 0.730987 | + | 0.682391i | \(0.239060\pi\) | ||||
−0.730987 | + | 0.682391i | \(0.760940\pi\) | |||||||
\(860\) | −1.41421 | + | 2.82843i | −0.0482243 | + | 0.0964486i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.0000 | + | 24.0000i | −0.817443 | + | 0.817443i | ||||
\(863\) | −35.3553 | + | 35.3553i | −1.20351 | + | 1.20351i | −0.230418 | + | 0.973092i | \(0.574009\pi\) |
−0.973092 | + | 0.230418i | \(0.925991\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | − | 4.00000i | 0.0680020 | − | 0.136004i | ||||
\(866\) | 5.65685i | 0.192228i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.65685 | 0.191896 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 72.0000 | 2.43963 | ||||||||
\(872\) | −5.65685 | − | 5.65685i | −0.191565 | − | 0.191565i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 6.00000i | − | 0.202953i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.0000 | − | 32.0000i | 1.08056 | − | 1.08056i | 0.0841064 | − | 0.996457i | \(-0.473196\pi\) |
0.996457 | − | 0.0841064i | \(-0.0268036\pi\) | |||||||
\(878\) | −7.07107 | + | 7.07107i | −0.238637 | + | 0.238637i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.00000 | + | 3.00000i | 0.0337100 | + | 0.101130i | ||||
\(881\) | − | 36.7696i | − | 1.23880i | −0.785076 | − | 0.619399i | \(-0.787376\pi\) | ||
0.785076 | − | 0.619399i | \(-0.212624\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.0000 | − | 30.0000i | −1.00958 | − | 1.00958i | −0.999954 | − | 0.00962672i | \(-0.996936\pi\) |
−0.00962672 | − | 0.999954i | \(-0.503064\pi\) | |||||||
\(884\) | −33.9411 | −1.14156 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.00000 | −0.134383 | ||||||||
\(887\) | −24.0416 | − | 24.0416i | −0.807239 | − | 0.807239i | 0.176976 | − | 0.984215i | \(-0.443368\pi\) |
−0.984215 | + | 0.176976i | \(0.943368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.65685 | + | 2.82843i | 0.189618 | + | 0.0948091i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.00000 | + | 5.00000i | −0.167412 | + | 0.167412i | ||||
\(893\) | −42.4264 | + | 42.4264i | −1.41975 | + | 1.41975i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.00000 | + | 2.00000i | −0.200558 | + | 0.0668526i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.0000 | + | 19.0000i | 0.634038 | + | 0.634038i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | −4.24264 | − | 4.24264i | −0.141264 | − | 0.141264i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.00000i | 0.0665190i | ||||||||
\(905\) | −21.2132 | + | 7.07107i | −0.705151 | + | 0.235050i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.00000 | − | 3.00000i | 0.0996134 | − | 0.0996134i | −0.655544 | − | 0.755157i | \(-0.727561\pi\) |
0.755157 | + | 0.655544i | \(0.227561\pi\) | |||||||
\(908\) | −8.48528 | + | 8.48528i | −0.281594 | + | 0.281594i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.82843i | − | 0.0937100i | −0.998902 | − | 0.0468550i | \(-0.985080\pi\) | ||
0.998902 | − | 0.0468550i | \(-0.0149199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.00000 | + | 2.00000i | 0.0661903 | + | 0.0661903i | ||||
\(914\) | −28.2843 | −0.935561 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 48.0000i | − | 1.58337i | −0.610927 | − | 0.791687i | \(-0.709203\pi\) | ||
0.610927 | − | 0.791687i | \(-0.290797\pi\) | |||||||
\(920\) | 0.707107 | + | 2.12132i | 0.0233126 | + | 0.0699379i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.00000 | + | 8.00000i | −0.263466 | + | 0.263466i | ||||
\(923\) | 16.9706 | − | 16.9706i | 0.558593 | − | 0.558593i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | − | 21.0000i | 0.0986394 | − | 0.690476i | ||||
\(926\) | − | 7.07107i | − | 0.232370i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.00000 | − | 4.00000i | −0.131306 | − | 0.131306i | ||||
\(929\) | 4.24264 | 0.139197 | 0.0695983 | − | 0.997575i | \(-0.477828\pi\) | ||||
0.0695983 | + | 0.997575i | \(0.477828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.0000 | 1.37649 | ||||||||
\(932\) | 7.07107 | + | 7.07107i | 0.231621 | + | 0.231621i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 26.0000i | − | 0.850746i | ||||||
\(935\) | −8.48528 | + | 16.9706i | −0.277498 | + | 0.554997i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.00000 | − | 4.00000i | 0.130674 | − | 0.130674i | −0.638745 | − | 0.769419i | \(-0.720546\pi\) |
0.769419 | + | 0.638745i | \(0.220546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.0000 | − | 20.0000i | 0.326164 | − | 0.652328i | ||||
\(941\) | − | 49.4975i | − | 1.61357i | −0.590844 | − | 0.806786i | \(-0.701205\pi\) | ||
0.590844 | − | 0.806786i | \(-0.298795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.00000 | − | 3.00000i | −0.0976934 | − | 0.0976934i | ||||
\(944\) | −2.82843 | −0.0920575 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | 0.0650256 | ||||||||
\(947\) | 33.9411 | + | 33.9411i | 1.10294 | + | 1.10294i | 0.994054 | + | 0.108884i | \(0.0347277\pi\) |
0.108884 | + | 0.994054i | \(0.465272\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 72.0000i | − | 2.33722i | ||||||
\(950\) | 4.24264 | − | 29.6985i | 0.137649 | − | 0.963546i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.3848 | + | 18.3848i | −0.595541 | + | 0.595541i | −0.939123 | − | 0.343582i | \(-0.888360\pi\) |
0.343582 | + | 0.939123i | \(0.388360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.0000 | + | 48.0000i | 0.517748 | + | 1.55324i | ||||
\(956\) | 7.07107i | 0.228695i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.0000 | + | 20.0000i | 0.646171 | + | 0.646171i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −16.9706 | − | 16.9706i | −0.547153 | − | 0.547153i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.0000i | 0.322078i | ||||||||
\(965\) | −42.4264 | − | 21.2132i | −1.36575 | − | 0.682877i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.0000 | − | 33.0000i | 1.06121 | − | 1.06121i | 0.0632081 | − | 0.998000i | \(-0.479867\pi\) |
0.998000 | − | 0.0632081i | \(-0.0201332\pi\) | |||||||
\(968\) | −6.36396 | + | 6.36396i | −0.204545 | + | 0.204545i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.0000 | − | 8.00000i | 0.770594 | − | 0.256865i | ||||
\(971\) | − | 7.07107i | − | 0.226921i | −0.993542 | − | 0.113461i | \(-0.963806\pi\) | ||
0.993542 | − | 0.113461i | \(-0.0361936\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.24264 | 0.135943 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | −1.41421 | − | 1.41421i | −0.0452447 | − | 0.0452447i | 0.684122 | − | 0.729367i | \(-0.260185\pi\) |
−0.729367 | + | 0.684122i | \(0.760185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.00000i | − | 0.127841i | ||||||
\(980\) | −14.8492 | + | 4.94975i | −0.474342 | + | 0.158114i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.00000 | + | 4.00000i | −0.127645 | + | 0.127645i | ||||
\(983\) | 2.82843 | − | 2.82843i | 0.0902128 | − | 0.0902128i | −0.660560 | − | 0.750773i | \(-0.729681\pi\) |
0.750773 | + | 0.660560i | \(0.229681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | − | 18.0000i | −1.14706 | − | 0.573528i | ||||
\(986\) | − | 33.9411i | − | 1.08091i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.0000 | − | 24.0000i | −0.763542 | − | 0.763542i | ||||
\(989\) | 1.41421 | 0.0449694 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.0000 | 1.20711 | 0.603555 | − | 0.797321i | \(-0.293750\pi\) | ||||
0.603555 | + | 0.797321i | \(0.293750\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.1421 | + | 42.4264i | 0.448336 | + | 1.34501i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(998\) | −25.4558 | + | 25.4558i | −0.805791 | + | 0.805791i | ||||
\(999\) | 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 | 2070.2.j.c.323.2 | yes | 4 | |
3.2 | odd | 2 | inner | 2070.2.j.c.323.1 | ✓ | 4 | |
5.2 | odd | 4 | inner | 2070.2.j.c.737.1 | yes | 4 | |
15.2 | even | 4 | inner | 2070.2.j.c.737.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.c.323.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
2070.2.j.c.323.2 | yes | 4 | 1.1 | even | 1 | trivial | |
2070.2.j.c.737.1 | yes | 4 | 5.2 | odd | 4 | inner | |
2070.2.j.c.737.2 | yes | 4 | 15.2 | even | 4 | inner |