Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [435,2,Mod(349,435)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(435, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("435.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.c (of order \(2\), degree \(1\), 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: | \(3.47349248793\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 435.349 |
Dual form | 435.2.c.a.349.1 |
$q$-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 \(\left(\mathbb{Z}/435\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(146\) | \(262\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | −2.00000 | − | 1.00000i | −0.894427 | − | 0.447214i | ||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.00000 | − | 4.00000i | 0.632456 | − | 1.26491i | ||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | − | 2.00000i | − | 0.577350i | ||||||
\(13\) | 4.00000i | 1.10940i | 0.832050 | + | 0.554700i | \(0.187167\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | 1.00000 | − | 2.00000i | 0.258199 | − | 0.516398i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | − | 8.00000i | − | 1.94029i | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||
0.242536 | − | 0.970143i | \(-0.422021\pi\) | |||||||
\(18\) | − | 2.00000i | − | 0.471405i | ||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 4.00000 | + | 2.00000i | 0.894427 | + | 0.447214i | ||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | − | 6.00000i | − | 1.27920i | ||||||
\(23\) | − | 1.00000i | − | 0.208514i | −0.994550 | − | 0.104257i | \(-0.966753\pi\) | ||
0.994550 | − | 0.104257i | \(-0.0332465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | −8.00000 | −1.56893 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 4.00000i | − | 0.755929i | ||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 4.00000 | + | 2.00000i | 0.730297 | + | 0.365148i | ||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | − | 8.00000i | − | 1.41421i | ||||||
\(33\) | − | 3.00000i | − | 0.522233i | ||||||
\(34\) | 16.0000 | 2.74398 | ||||||||
\(35\) | 2.00000 | − | 4.00000i | 0.338062 | − | 0.676123i | ||||
\(36\) | 2.00000 | 0.333333 | ||||||||
\(37\) | 7.00000i | 1.15079i | 0.817875 | + | 0.575396i | \(0.195152\pi\) | ||||
−0.817875 | + | 0.575396i | \(0.804848\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.00000 | 1.09322 | 0.546608 | − | 0.837389i | \(-0.315919\pi\) | ||||
0.546608 | + | 0.837389i | \(0.315919\pi\) | |||||||
\(42\) | − | 4.00000i | − | 0.617213i | ||||||
\(43\) | 9.00000i | 1.37249i | 0.727372 | + | 0.686244i | \(0.240742\pi\) | ||||
−0.727372 | + | 0.686244i | \(0.759258\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 2.00000 | + | 1.00000i | 0.298142 | + | 0.149071i | ||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | 12.0000i | 1.75038i | 0.483779 | + | 0.875190i | \(0.339264\pi\) | ||||
−0.483779 | + | 0.875190i | \(0.660736\pi\) | |||||||
\(48\) | − | 4.00000i | − | 0.577350i | ||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | −8.00000 | + | 6.00000i | −1.13137 | + | 0.848528i | ||||
\(51\) | 8.00000 | 1.12022 | ||||||||
\(52\) | − | 8.00000i | − | 1.10940i | ||||||
\(53\) | 9.00000i | 1.23625i | 0.786082 | + | 0.618123i | \(0.212106\pi\) | ||||
−0.786082 | + | 0.618123i | \(0.787894\pi\) | |||||||
\(54\) | 2.00000 | 0.272166 | ||||||||
\(55\) | 6.00000 | + | 3.00000i | 0.809040 | + | 0.404520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | −10.0000 | −1.30189 | −0.650945 | − | 0.759125i | \(-0.725627\pi\) | ||||
−0.650945 | + | 0.759125i | \(0.725627\pi\) | |||||||
\(60\) | −2.00000 | + | 4.00000i | −0.258199 | + | 0.516398i | ||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | − | 16.0000i | − | 2.03200i | ||||||
\(63\) | − | 2.00000i | − | 0.251976i | ||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 4.00000 | − | 8.00000i | 0.496139 | − | 0.992278i | ||||
\(66\) | 6.00000 | 0.738549 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 16.0000i | 1.94029i | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 8.00000 | + | 4.00000i | 0.956183 | + | 0.478091i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.00000i | − | 0.117041i | −0.998286 | − | 0.0585206i | \(-0.981362\pi\) | ||
0.998286 | − | 0.0585206i | \(-0.0186383\pi\) | |||||||
\(74\) | −14.0000 | −1.62747 | ||||||||
\(75\) | −4.00000 | + | 3.00000i | −0.461880 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.00000i | − | 0.683763i | ||||||
\(78\) | − | 8.00000i | − | 0.905822i | ||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 8.00000 | + | 4.00000i | 0.894427 | + | 0.447214i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.0000i | 1.54604i | ||||||||
\(83\) | 9.00000i | 0.987878i | 0.869496 | + | 0.493939i | \(0.164443\pi\) | ||||
−0.869496 | + | 0.493939i | \(0.835557\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | −8.00000 | + | 16.0000i | −0.867722 | + | 1.73544i | ||||
\(86\) | −18.0000 | −1.94099 | ||||||||
\(87\) | − | 1.00000i | − | 0.107211i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | −2.00000 | + | 4.00000i | −0.210819 | + | 0.421637i | ||||
\(91\) | −8.00000 | −0.838628 | ||||||||
\(92\) | 2.00000i | 0.208514i | ||||||||
\(93\) | − | 8.00000i | − | 0.829561i | ||||||
\(94\) | −24.0000 | −2.47541 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.00000 | 0.816497 | ||||||||
\(97\) | − | 13.0000i | − | 1.31995i | −0.751288 | − | 0.659975i | \(-0.770567\pi\) | ||
0.751288 | − | 0.659975i | \(-0.229433\pi\) | |||||||
\(98\) | 6.00000i | 0.606092i | ||||||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | −6.00000 | − | 8.00000i | −0.600000 | − | 0.800000i | ||||
\(101\) | 17.0000 | 1.69156 | 0.845782 | − | 0.533529i | \(-0.179135\pi\) | ||||
0.845782 | + | 0.533529i | \(0.179135\pi\) | |||||||
\(102\) | 16.0000i | 1.58424i | ||||||||
\(103\) | 4.00000i | 0.394132i | 0.980390 | + | 0.197066i | \(0.0631413\pi\) | ||||
−0.980390 | + | 0.197066i | \(0.936859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00000 | + | 2.00000i | 0.390360 | + | 0.195180i | ||||
\(106\) | −18.0000 | −1.74831 | ||||||||
\(107\) | 12.0000i | 1.16008i | 0.814587 | + | 0.580042i | \(0.196964\pi\) | ||||
−0.814587 | + | 0.580042i | \(0.803036\pi\) | |||||||
\(108\) | 2.00000i | 0.192450i | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | −6.00000 | + | 12.0000i | −0.572078 | + | 1.14416i | ||||
\(111\) | −7.00000 | −0.664411 | ||||||||
\(112\) | − | 8.00000i | − | 0.755929i | ||||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | + | 2.00000i | −0.0932505 | + | 0.186501i | ||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | − | 4.00000i | − | 0.369800i | ||||||
\(118\) | − | 20.0000i | − | 1.84115i | ||||||
\(119\) | 16.0000 | 1.46672 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 4.00000i | 0.362143i | ||||||||
\(123\) | 7.00000i | 0.631169i | ||||||||
\(124\) | 16.0000 | 1.43684 | ||||||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | − | 3.00000i | − | 0.266207i | −0.991102 | − | 0.133103i | \(-0.957506\pi\) | ||
0.991102 | − | 0.133103i | \(-0.0424943\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.00000 | −0.792406 | ||||||||
\(130\) | 16.0000 | + | 8.00000i | 1.40329 | + | 0.701646i | ||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 6.00000i | 0.522233i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 16.0000 | 1.38219 | ||||||||
\(135\) | −1.00000 | + | 2.00000i | −0.0860663 | + | 0.172133i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000i | 0.170872i | 0.996344 | + | 0.0854358i | \(0.0272282\pi\) | ||||
−0.996344 | + | 0.0854358i | \(0.972772\pi\) | |||||||
\(138\) | 2.00000i | 0.170251i | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | −4.00000 | + | 8.00000i | −0.338062 | + | 0.676123i | ||||
\(141\) | −12.0000 | −1.01058 | ||||||||
\(142\) | − | 16.0000i | − | 1.34269i | ||||||
\(143\) | − | 12.0000i | − | 1.00349i | ||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 2.00000 | + | 1.00000i | 0.166091 | + | 0.0830455i | ||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 3.00000i | 0.247436i | ||||||||
\(148\) | − | 14.0000i | − | 1.15079i | ||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −6.00000 | − | 8.00000i | −0.489898 | − | 0.653197i | ||||
\(151\) | −3.00000 | −0.244137 | −0.122068 | − | 0.992522i | \(-0.538953\pi\) | ||||
−0.122068 | + | 0.992522i | \(0.538953\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.00000i | 0.646762i | ||||||||
\(154\) | 12.0000 | 0.966988 | ||||||||
\(155\) | 16.0000 | + | 8.00000i | 1.28515 | + | 0.642575i | ||||
\(156\) | 8.00000 | 0.640513 | ||||||||
\(157\) | 2.00000i | 0.159617i | 0.996810 | + | 0.0798087i | \(0.0254309\pi\) | ||||
−0.996810 | + | 0.0798087i | \(0.974569\pi\) | |||||||
\(158\) | 20.0000i | 1.59111i | ||||||||
\(159\) | −9.00000 | −0.713746 | ||||||||
\(160\) | −8.00000 | + | 16.0000i | −0.632456 | + | 1.26491i | ||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | 2.00000i | 0.157135i | ||||||||
\(163\) | − | 1.00000i | − | 0.0783260i | −0.999233 | − | 0.0391630i | \(-0.987531\pi\) | ||
0.999233 | − | 0.0391630i | \(-0.0124692\pi\) | |||||||
\(164\) | −14.0000 | −1.09322 | ||||||||
\(165\) | −3.00000 | + | 6.00000i | −0.233550 | + | 0.467099i | ||||
\(166\) | −18.0000 | −1.39707 | ||||||||
\(167\) | − | 8.00000i | − | 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | −32.0000 | − | 16.0000i | −2.45429 | − | 1.22714i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 18.0000i | − | 1.37249i | ||||||
\(173\) | 9.00000i | 0.684257i | 0.939653 | + | 0.342129i | \(0.111148\pi\) | ||||
−0.939653 | + | 0.342129i | \(0.888852\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | −8.00000 | + | 6.00000i | −0.604743 | + | 0.453557i | ||||
\(176\) | 12.0000 | 0.904534 | ||||||||
\(177\) | − | 10.0000i | − | 0.751646i | ||||||
\(178\) | − | 20.0000i | − | 1.49906i | ||||||
\(179\) | −10.0000 | −0.747435 | −0.373718 | − | 0.927543i | \(-0.621917\pi\) | ||||
−0.373718 | + | 0.927543i | \(0.621917\pi\) | |||||||
\(180\) | −4.00000 | − | 2.00000i | −0.298142 | − | 0.149071i | ||||
\(181\) | 17.0000 | 1.26360 | 0.631800 | − | 0.775131i | \(-0.282316\pi\) | ||||
0.631800 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(182\) | − | 16.0000i | − | 1.18600i | ||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.00000 | − | 14.0000i | 0.514650 | − | 1.02930i | ||||
\(186\) | 16.0000 | 1.17318 | ||||||||
\(187\) | 24.0000i | 1.75505i | ||||||||
\(188\) | − | 24.0000i | − | 1.75038i | ||||||
\(189\) | 2.00000 | 0.145479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | −0.217072 | −0.108536 | − | 0.994092i | \(-0.534616\pi\) | ||||
−0.108536 | + | 0.994092i | \(0.534616\pi\) | |||||||
\(192\) | 8.00000i | 0.577350i | ||||||||
\(193\) | − | 6.00000i | − | 0.431889i | −0.976406 | − | 0.215945i | \(-0.930717\pi\) | ||
0.976406 | − | 0.215945i | \(-0.0692831\pi\) | |||||||
\(194\) | 26.0000 | 1.86669 | ||||||||
\(195\) | 8.00000 | + | 4.00000i | 0.572892 | + | 0.286446i | ||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | − | 13.0000i | − | 0.926212i | −0.886303 | − | 0.463106i | \(-0.846735\pi\) | ||
0.886303 | − | 0.463106i | \(-0.153265\pi\) | |||||||
\(198\) | 6.00000i | 0.426401i | ||||||||
\(199\) | 25.0000 | 1.77220 | 0.886102 | − | 0.463491i | \(-0.153403\pi\) | ||||
0.886102 | + | 0.463491i | \(0.153403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 34.0000i | 2.39223i | ||||||||
\(203\) | − | 2.00000i | − | 0.140372i | ||||||
\(204\) | −16.0000 | −1.12022 | ||||||||
\(205\) | −14.0000 | − | 7.00000i | −0.977802 | − | 0.488901i | ||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | − | 16.0000i | − | 1.10940i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.00000 | + | 8.00000i | −0.276026 | + | 0.552052i | ||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | − | 18.0000i | − | 1.23625i | ||||||
\(213\) | − | 8.00000i | − | 0.548151i | ||||||
\(214\) | −24.0000 | −1.64061 | ||||||||
\(215\) | 9.00000 | − | 18.0000i | 0.613795 | − | 1.22759i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.0000i | − | 1.08615i | ||||||
\(218\) | 10.0000i | 0.677285i | ||||||||
\(219\) | 1.00000 | 0.0675737 | ||||||||
\(220\) | −12.0000 | − | 6.00000i | −0.809040 | − | 0.404520i | ||||
\(221\) | 32.0000 | 2.15255 | ||||||||
\(222\) | − | 14.0000i | − | 0.939618i | ||||||
\(223\) | − | 6.00000i | − | 0.401790i | −0.979613 | − | 0.200895i | \(-0.935615\pi\) | ||
0.979613 | − | 0.200895i | \(-0.0643850\pi\) | |||||||
\(224\) | 16.0000 | 1.06904 | ||||||||
\(225\) | −3.00000 | − | 4.00000i | −0.200000 | − | 0.266667i | ||||
\(226\) | −28.0000 | −1.86253 | ||||||||
\(227\) | − | 3.00000i | − | 0.199117i | −0.995032 | − | 0.0995585i | \(-0.968257\pi\) | ||
0.995032 | − | 0.0995585i | \(-0.0317430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0000 | −1.32164 | −0.660819 | − | 0.750546i | \(-0.729791\pi\) | ||||
−0.660819 | + | 0.750546i | \(0.729791\pi\) | |||||||
\(230\) | −4.00000 | − | 2.00000i | −0.263752 | − | 0.131876i | ||||
\(231\) | 6.00000 | 0.394771 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.00000i | − | 0.0655122i | −0.999463 | − | 0.0327561i | \(-0.989572\pi\) | ||
0.999463 | − | 0.0327561i | \(-0.0104285\pi\) | |||||||
\(234\) | 8.00000 | 0.522976 | ||||||||
\(235\) | 12.0000 | − | 24.0000i | 0.782794 | − | 1.56559i | ||||
\(236\) | 20.0000 | 1.30189 | ||||||||
\(237\) | 10.0000i | 0.649570i | ||||||||
\(238\) | 32.0000i | 2.07425i | ||||||||
\(239\) | −30.0000 | −1.94054 | −0.970269 | − | 0.242028i | \(-0.922188\pi\) | ||||
−0.970269 | + | 0.242028i | \(0.922188\pi\) | |||||||
\(240\) | −4.00000 | + | 8.00000i | −0.258199 | + | 0.516398i | ||||
\(241\) | −3.00000 | −0.193247 | −0.0966235 | − | 0.995321i | \(-0.530804\pi\) | ||||
−0.0966235 | + | 0.995321i | \(0.530804\pi\) | |||||||
\(242\) | − | 4.00000i | − | 0.257130i | ||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | −6.00000 | − | 3.00000i | −0.383326 | − | 0.191663i | ||||
\(246\) | −14.0000 | −0.892607 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.00000 | −0.570352 | ||||||||
\(250\) | 22.0000 | − | 4.00000i | 1.39140 | − | 0.252982i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 4.00000i | 0.251976i | ||||||||
\(253\) | 3.00000i | 0.188608i | ||||||||
\(254\) | 6.00000 | 0.376473 | ||||||||
\(255\) | −16.0000 | − | 8.00000i | −1.00196 | − | 0.500979i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | − | 23.0000i | − | 1.43470i | −0.696713 | − | 0.717350i | \(-0.745355\pi\) | ||
0.696713 | − | 0.717350i | \(-0.254645\pi\) | |||||||
\(258\) | − | 18.0000i | − | 1.12063i | ||||||
\(259\) | −14.0000 | −0.869918 | ||||||||
\(260\) | −8.00000 | + | 16.0000i | −0.496139 | + | 0.992278i | ||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 24.0000i | 1.48272i | ||||||||
\(263\) | 4.00000i | 0.246651i | 0.992366 | + | 0.123325i | \(0.0393559\pi\) | ||||
−0.992366 | + | 0.123325i | \(0.960644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | − | 18.0000i | 0.552866 | − | 1.10573i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.0000i | − | 0.611990i | ||||||
\(268\) | 16.0000i | 0.977356i | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | −4.00000 | − | 2.00000i | −0.243432 | − | 0.121716i | ||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | 32.0000i | 1.94029i | ||||||||
\(273\) | − | 8.00000i | − | 0.484182i | ||||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | −9.00000 | − | 12.0000i | −0.542720 | − | 0.723627i | ||||
\(276\) | −2.00000 | −0.120386 | ||||||||
\(277\) | − | 28.0000i | − | 1.68236i | −0.540758 | − | 0.841178i | \(-0.681862\pi\) | ||
0.540758 | − | 0.841178i | \(-0.318138\pi\) | |||||||
\(278\) | − | 10.0000i | − | 0.599760i | ||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | − | 24.0000i | − | 1.42918i | ||||||
\(283\) | 14.0000i | 0.832214i | 0.909316 | + | 0.416107i | \(0.136606\pi\) | ||||
−0.909316 | + | 0.416107i | \(0.863394\pi\) | |||||||
\(284\) | 16.0000 | 0.949425 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.0000 | 1.41915 | ||||||||
\(287\) | 14.0000i | 0.826394i | ||||||||
\(288\) | 8.00000i | 0.471405i | ||||||||
\(289\) | −47.0000 | −2.76471 | ||||||||
\(290\) | −2.00000 | + | 4.00000i | −0.117444 | + | 0.234888i | ||||
\(291\) | 13.0000 | 0.762073 | ||||||||
\(292\) | 2.00000i | 0.117041i | ||||||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | −6.00000 | −0.349927 | ||||||||
\(295\) | 20.0000 | + | 10.0000i | 1.16445 | + | 0.582223i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.00000i | 0.174078i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.00000 | 0.231326 | ||||||||
\(300\) | 8.00000 | − | 6.00000i | 0.461880 | − | 0.346410i | ||||
\(301\) | −18.0000 | −1.03750 | ||||||||
\(302\) | − | 6.00000i | − | 0.345261i | ||||||
\(303\) | 17.0000i | 0.976624i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | − | 2.00000i | −0.229039 | − | 0.114520i | ||||
\(306\) | −16.0000 | −0.914659 | ||||||||
\(307\) | 17.0000i | 0.970241i | 0.874447 | + | 0.485121i | \(0.161224\pi\) | ||||
−0.874447 | + | 0.485121i | \(0.838776\pi\) | |||||||
\(308\) | 12.0000i | 0.683763i | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | −16.0000 | + | 32.0000i | −0.908739 | + | 1.81748i | ||||
\(311\) | 17.0000 | 0.963982 | 0.481991 | − | 0.876176i | \(-0.339914\pi\) | ||||
0.481991 | + | 0.876176i | \(0.339914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.00000i | 0.226093i | 0.993590 | + | 0.113047i | \(0.0360610\pi\) | ||||
−0.993590 | + | 0.113047i | \(0.963939\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | −2.00000 | + | 4.00000i | −0.112687 | + | 0.225374i | ||||
\(316\) | −20.0000 | −1.12509 | ||||||||
\(317\) | 12.0000i | 0.673987i | 0.941507 | + | 0.336994i | \(0.109410\pi\) | ||||
−0.941507 | + | 0.336994i | \(0.890590\pi\) | |||||||
\(318\) | − | 18.0000i | − | 1.00939i | ||||||
\(319\) | 3.00000 | 0.167968 | ||||||||
\(320\) | −16.0000 | − | 8.00000i | −0.894427 | − | 0.447214i | ||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | 4.00000i | 0.222911i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | −16.0000 | + | 12.0000i | −0.887520 | + | 0.665640i | ||||
\(326\) | 2.00000 | 0.110770 | ||||||||
\(327\) | 5.00000i | 0.276501i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | −12.0000 | − | 6.00000i | −0.660578 | − | 0.330289i | ||||
\(331\) | 32.0000 | 1.75888 | 0.879440 | − | 0.476011i | \(-0.157918\pi\) | ||||
0.879440 | + | 0.476011i | \(0.157918\pi\) | |||||||
\(332\) | − | 18.0000i | − | 0.987878i | ||||||
\(333\) | − | 7.00000i | − | 0.383598i | ||||||
\(334\) | 16.0000 | 0.875481 | ||||||||
\(335\) | −8.00000 | + | 16.0000i | −0.437087 | + | 0.874173i | ||||
\(336\) | 8.00000 | 0.436436 | ||||||||
\(337\) | 22.0000i | 1.19842i | 0.800593 | + | 0.599208i | \(0.204518\pi\) | ||||
−0.800593 | + | 0.599208i | \(0.795482\pi\) | |||||||
\(338\) | − | 6.00000i | − | 0.326357i | ||||||
\(339\) | −14.0000 | −0.760376 | ||||||||
\(340\) | 16.0000 | − | 32.0000i | 0.867722 | − | 1.73544i | ||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.00000 | − | 1.00000i | −0.107676 | − | 0.0538382i | ||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | − | 3.00000i | − | 0.161048i | −0.996753 | − | 0.0805242i | \(-0.974341\pi\) | ||
0.996753 | − | 0.0805242i | \(-0.0256594\pi\) | |||||||
\(348\) | 2.00000i | 0.107211i | ||||||||
\(349\) | 5.00000 | 0.267644 | 0.133822 | − | 0.991005i | \(-0.457275\pi\) | ||||
0.133822 | + | 0.991005i | \(0.457275\pi\) | |||||||
\(350\) | −12.0000 | − | 16.0000i | −0.641427 | − | 0.855236i | ||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 24.0000i | 1.27920i | ||||||||
\(353\) | − | 26.0000i | − | 1.38384i | −0.721974 | − | 0.691920i | \(-0.756765\pi\) | ||
0.721974 | − | 0.691920i | \(-0.243235\pi\) | |||||||
\(354\) | 20.0000 | 1.06299 | ||||||||
\(355\) | 16.0000 | + | 8.00000i | 0.849192 | + | 0.424596i | ||||
\(356\) | 20.0000 | 1.06000 | ||||||||
\(357\) | 16.0000i | 0.846810i | ||||||||
\(358\) | − | 20.0000i | − | 1.05703i | ||||||
\(359\) | 15.0000 | 0.791670 | 0.395835 | − | 0.918322i | \(-0.370455\pi\) | ||||
0.395835 | + | 0.918322i | \(0.370455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 34.0000i | 1.78700i | ||||||||
\(363\) | − | 2.00000i | − | 0.104973i | ||||||
\(364\) | 16.0000 | 0.838628 | ||||||||
\(365\) | −1.00000 | + | 2.00000i | −0.0523424 | + | 0.104685i | ||||
\(366\) | −4.00000 | −0.209083 | ||||||||
\(367\) | − | 3.00000i | − | 0.156599i | −0.996930 | − | 0.0782994i | \(-0.975051\pi\) | ||
0.996930 | − | 0.0782994i | \(-0.0249490\pi\) | |||||||
\(368\) | 4.00000i | 0.208514i | ||||||||
\(369\) | −7.00000 | −0.364405 | ||||||||
\(370\) | 28.0000 | + | 14.0000i | 1.45565 | + | 0.727825i | ||||
\(371\) | −18.0000 | −0.934513 | ||||||||
\(372\) | 16.0000i | 0.829561i | ||||||||
\(373\) | 4.00000i | 0.207112i | 0.994624 | + | 0.103556i | \(0.0330221\pi\) | ||||
−0.994624 | + | 0.103556i | \(0.966978\pi\) | |||||||
\(374\) | −48.0000 | −2.48202 | ||||||||
\(375\) | 11.0000 | − | 2.00000i | 0.568038 | − | 0.103280i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.00000i | − | 0.206010i | ||||||
\(378\) | 4.00000i | 0.205738i | ||||||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.00000 | 0.153695 | ||||||||
\(382\) | − | 6.00000i | − | 0.306987i | ||||||
\(383\) | 39.0000i | 1.99281i | 0.0847358 | + | 0.996403i | \(0.472995\pi\) | ||||
−0.0847358 | + | 0.996403i | \(0.527005\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | + | 12.0000i | −0.305788 | + | 0.611577i | ||||
\(386\) | 12.0000 | 0.610784 | ||||||||
\(387\) | − | 9.00000i | − | 0.457496i | ||||||
\(388\) | 26.0000i | 1.31995i | ||||||||
\(389\) | 25.0000 | 1.26755 | 0.633775 | − | 0.773517i | \(-0.281504\pi\) | ||||
0.633775 | + | 0.773517i | \(0.281504\pi\) | |||||||
\(390\) | −8.00000 | + | 16.0000i | −0.405096 | + | 0.810191i | ||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000i | 0.605320i | ||||||||
\(394\) | 26.0000 | 1.30986 | ||||||||
\(395\) | −20.0000 | − | 10.0000i | −1.00631 | − | 0.503155i | ||||
\(396\) | −6.00000 | −0.301511 | ||||||||
\(397\) | − | 8.00000i | − | 0.401508i | −0.979642 | − | 0.200754i | \(-0.935661\pi\) | ||
0.979642 | − | 0.200754i | \(-0.0643393\pi\) | |||||||
\(398\) | 50.0000i | 2.50627i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0000 | − | 16.0000i | −0.600000 | − | 0.800000i | ||||
\(401\) | −28.0000 | −1.39825 | −0.699127 | − | 0.714998i | \(-0.746428\pi\) | ||||
−0.699127 | + | 0.714998i | \(0.746428\pi\) | |||||||
\(402\) | 16.0000i | 0.798007i | ||||||||
\(403\) | − | 32.0000i | − | 1.59403i | ||||||
\(404\) | −34.0000 | −1.69156 | ||||||||
\(405\) | −2.00000 | − | 1.00000i | −0.0993808 | − | 0.0496904i | ||||
\(406\) | 4.00000 | 0.198517 | ||||||||
\(407\) | − | 21.0000i | − | 1.04093i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 14.0000 | − | 28.0000i | 0.691411 | − | 1.38282i | ||||
\(411\) | −2.00000 | −0.0986527 | ||||||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | − | 20.0000i | − | 0.984136i | ||||||
\(414\) | −2.00000 | −0.0982946 | ||||||||
\(415\) | 9.00000 | − | 18.0000i | 0.441793 | − | 0.883585i | ||||
\(416\) | 32.0000 | 1.56893 | ||||||||
\(417\) | − | 5.00000i | − | 0.244851i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | −8.00000 | − | 4.00000i | −0.390360 | − | 0.195180i | ||||
\(421\) | −28.0000 | −1.36464 | −0.682318 | − | 0.731055i | \(-0.739028\pi\) | ||||
−0.682318 | + | 0.731055i | \(0.739028\pi\) | |||||||
\(422\) | 24.0000i | 1.16830i | ||||||||
\(423\) | − | 12.0000i | − | 0.583460i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.0000 | − | 24.0000i | 1.55223 | − | 1.16417i | ||||
\(426\) | 16.0000 | 0.775203 | ||||||||
\(427\) | 4.00000i | 0.193574i | ||||||||
\(428\) | − | 24.0000i | − | 1.16008i | ||||||
\(429\) | 12.0000 | 0.579365 | ||||||||
\(430\) | 36.0000 | + | 18.0000i | 1.73607 | + | 0.868037i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 4.00000i | 0.192450i | ||||||||
\(433\) | 19.0000i | 0.913082i | 0.889702 | + | 0.456541i | \(0.150912\pi\) | ||||
−0.889702 | + | 0.456541i | \(0.849088\pi\) | |||||||
\(434\) | 32.0000 | 1.53605 | ||||||||
\(435\) | −1.00000 | + | 2.00000i | −0.0479463 | + | 0.0958927i | ||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2.00000i | 0.0955637i | ||||||||
\(439\) | −20.0000 | −0.954548 | −0.477274 | − | 0.878755i | \(-0.658375\pi\) | ||||
−0.477274 | + | 0.878755i | \(0.658375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 64.0000i | 3.04417i | ||||||||
\(443\) | − | 6.00000i | − | 0.285069i | −0.989790 | − | 0.142534i | \(-0.954475\pi\) | ||
0.989790 | − | 0.142534i | \(-0.0455251\pi\) | |||||||
\(444\) | 14.0000 | 0.664411 | ||||||||
\(445\) | 20.0000 | + | 10.0000i | 0.948091 | + | 0.474045i | ||||
\(446\) | 12.0000 | 0.568216 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.0000i | 0.755929i | ||||||||
\(449\) | −5.00000 | −0.235965 | −0.117982 | − | 0.993016i | \(-0.537643\pi\) | ||||
−0.117982 | + | 0.993016i | \(0.537643\pi\) | |||||||
\(450\) | 8.00000 | − | 6.00000i | 0.377124 | − | 0.282843i | ||||
\(451\) | −21.0000 | −0.988851 | ||||||||
\(452\) | − | 28.0000i | − | 1.31701i | ||||||
\(453\) | − | 3.00000i | − | 0.140952i | ||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | 16.0000 | + | 8.00000i | 0.750092 | + | 0.375046i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 28.0000i | − | 1.30978i | −0.755722 | − | 0.654892i | \(-0.772714\pi\) | ||
0.755722 | − | 0.654892i | \(-0.227286\pi\) | |||||||
\(458\) | − | 40.0000i | − | 1.86908i | ||||||
\(459\) | −8.00000 | −0.373408 | ||||||||
\(460\) | 2.00000 | − | 4.00000i | 0.0932505 | − | 0.186501i | ||||
\(461\) | −13.0000 | −0.605470 | −0.302735 | − | 0.953075i | \(-0.597900\pi\) | ||||
−0.302735 | + | 0.953075i | \(0.597900\pi\) | |||||||
\(462\) | 12.0000i | 0.558291i | ||||||||
\(463\) | − | 6.00000i | − | 0.278844i | −0.990233 | − | 0.139422i | \(-0.955476\pi\) | ||
0.990233 | − | 0.139422i | \(-0.0445244\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | −8.00000 | + | 16.0000i | −0.370991 | + | 0.741982i | ||||
\(466\) | 2.00000 | 0.0926482 | ||||||||
\(467\) | 42.0000i | 1.94353i | 0.235954 | + | 0.971764i | \(0.424178\pi\) | ||||
−0.235954 | + | 0.971764i | \(0.575822\pi\) | |||||||
\(468\) | 8.00000i | 0.369800i | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 48.0000 | + | 24.0000i | 2.21407 | + | 1.10704i | ||||
\(471\) | −2.00000 | −0.0921551 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 27.0000i | − | 1.24146i | ||||||
\(474\) | −20.0000 | −0.918630 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −32.0000 | −1.46672 | ||||||||
\(477\) | − | 9.00000i | − | 0.412082i | ||||||
\(478\) | − | 60.0000i | − | 2.74434i | ||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | −16.0000 | − | 8.00000i | −0.730297 | − | 0.365148i | ||||
\(481\) | −28.0000 | −1.27669 | ||||||||
\(482\) | − | 6.00000i | − | 0.273293i | ||||||
\(483\) | 2.00000i | 0.0910032i | ||||||||
\(484\) | 4.00000 | 0.181818 | ||||||||
\(485\) | −13.0000 | + | 26.0000i | −0.590300 | + | 1.18060i | ||||
\(486\) | −2.00000 | −0.0907218 | ||||||||
\(487\) | 22.0000i | 0.996915i | 0.866914 | + | 0.498458i | \(0.166100\pi\) | ||||
−0.866914 | + | 0.498458i | \(0.833900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.00000 | 0.0452216 | ||||||||
\(490\) | 6.00000 | − | 12.0000i | 0.271052 | − | 0.542105i | ||||
\(491\) | −28.0000 | −1.26362 | −0.631811 | − | 0.775122i | \(-0.717688\pi\) | ||||
−0.631811 | + | 0.775122i | \(0.717688\pi\) | |||||||
\(492\) | − | 14.0000i | − | 0.631169i | ||||||
\(493\) | 8.00000i | 0.360302i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.00000 | − | 3.00000i | −0.269680 | − | 0.134840i | ||||
\(496\) | 32.0000 | 1.43684 | ||||||||
\(497\) | − | 16.0000i | − | 0.717698i | ||||||
\(498\) | − | 18.0000i | − | 0.806599i | ||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 4.00000 | + | 22.0000i | 0.178885 | + | 0.983870i | ||||
\(501\) | 8.00000 | 0.357414 | ||||||||
\(502\) | 24.0000i | 1.07117i | ||||||||
\(503\) | 4.00000i | 0.178351i | 0.996016 | + | 0.0891756i | \(0.0284232\pi\) | ||||
−0.996016 | + | 0.0891756i | \(0.971577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.0000 | − | 17.0000i | −1.51298 | − | 0.756490i | ||||
\(506\) | −6.00000 | −0.266733 | ||||||||
\(507\) | − | 3.00000i | − | 0.133235i | ||||||
\(508\) | 6.00000i | 0.266207i | ||||||||
\(509\) | 40.0000 | 1.77297 | 0.886484 | − | 0.462758i | \(-0.153140\pi\) | ||||
0.886484 | + | 0.462758i | \(0.153140\pi\) | |||||||
\(510\) | 16.0000 | − | 32.0000i | 0.708492 | − | 1.41698i | ||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | 32.0000i | 1.41421i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 46.0000 | 2.02897 | ||||||||
\(515\) | 4.00000 | − | 8.00000i | 0.176261 | − | 0.352522i | ||||
\(516\) | 18.0000 | 0.792406 | ||||||||
\(517\) | − | 36.0000i | − | 1.58328i | ||||||
\(518\) | − | 28.0000i | − | 1.23025i | ||||||
\(519\) | −9.00000 | −0.395056 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 2.00000i | 0.0875376i | ||||||||
\(523\) | 4.00000i | 0.174908i | 0.996169 | + | 0.0874539i | \(0.0278730\pi\) | ||||
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(524\) | −24.0000 | −1.04844 | ||||||||
\(525\) | −6.00000 | − | 8.00000i | −0.261861 | − | 0.349149i | ||||
\(526\) | −8.00000 | −0.348817 | ||||||||
\(527\) | 64.0000i | 2.78788i | ||||||||
\(528\) | 12.0000i | 0.522233i | ||||||||
\(529\) | 22.0000 | 0.956522 | ||||||||
\(530\) | 36.0000 | + | 18.0000i | 1.56374 | + | 0.781870i | ||||
\(531\) | 10.0000 | 0.433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.0000i | 1.21281i | ||||||||
\(534\) | 20.0000 | 0.865485 | ||||||||
\(535\) | 12.0000 | − | 24.0000i | 0.518805 | − | 1.03761i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 10.0000i | − | 0.431532i | ||||||
\(538\) | 20.0000i | 0.862261i | ||||||||
\(539\) | −9.00000 | −0.387657 | ||||||||
\(540\) | 2.00000 | − | 4.00000i | 0.0860663 | − | 0.172133i | ||||
\(541\) | −8.00000 | −0.343947 | −0.171973 | − | 0.985102i | \(-0.555014\pi\) | ||||
−0.171973 | + | 0.985102i | \(0.555014\pi\) | |||||||
\(542\) | 24.0000i | 1.03089i | ||||||||
\(543\) | 17.0000i | 0.729540i | ||||||||
\(544\) | −64.0000 | −2.74398 | ||||||||
\(545\) | −10.0000 | − | 5.00000i | −0.428353 | − | 0.214176i | ||||
\(546\) | 16.0000 | 0.684737 | ||||||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | − | 4.00000i | − | 0.170872i | ||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 24.0000 | − | 18.0000i | 1.02336 | − | 0.767523i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.0000i | 0.850487i | ||||||||
\(554\) | 56.0000 | 2.37921 | ||||||||
\(555\) | 14.0000 | + | 7.00000i | 0.594267 | + | 0.297133i | ||||
\(556\) | 10.0000 | 0.424094 | ||||||||
\(557\) | 47.0000i | 1.99145i | 0.0923462 | + | 0.995727i | \(0.470563\pi\) | ||||
−0.0923462 | + | 0.995727i | \(0.529437\pi\) | |||||||
\(558\) | 16.0000i | 0.677334i | ||||||||
\(559\) | −36.0000 | −1.52264 | ||||||||
\(560\) | −8.00000 | + | 16.0000i | −0.338062 | + | 0.676123i | ||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | − | 36.0000i | − | 1.51857i | ||||||
\(563\) | − | 46.0000i | − | 1.93867i | −0.245745 | − | 0.969334i | \(-0.579033\pi\) | ||
0.245745 | − | 0.969334i | \(-0.420967\pi\) | |||||||
\(564\) | 24.0000 | 1.01058 | ||||||||
\(565\) | 14.0000 | − | 28.0000i | 0.588984 | − | 1.17797i | ||||
\(566\) | −28.0000 | −1.17693 | ||||||||
\(567\) | 2.00000i | 0.0839921i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.0000 | −0.962520 | −0.481260 | − | 0.876578i | \(-0.659821\pi\) | ||||
−0.481260 | + | 0.876578i | \(0.659821\pi\) | |||||||
\(572\) | 24.0000i | 1.00349i | ||||||||
\(573\) | − | 3.00000i | − | 0.125327i | ||||||
\(574\) | −28.0000 | −1.16870 | ||||||||
\(575\) | 4.00000 | − | 3.00000i | 0.166812 | − | 0.125109i | ||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | − | 18.0000i | − | 0.749350i | −0.927156 | − | 0.374675i | \(-0.877754\pi\) | ||
0.927156 | − | 0.374675i | \(-0.122246\pi\) | |||||||
\(578\) | − | 94.0000i | − | 3.90988i | ||||||
\(579\) | 6.00000 | 0.249351 | ||||||||
\(580\) | −4.00000 | − | 2.00000i | −0.166091 | − | 0.0830455i | ||||
\(581\) | −18.0000 | −0.746766 | ||||||||
\(582\) | 26.0000i | 1.07773i | ||||||||
\(583\) | − | 27.0000i | − | 1.11823i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.00000 | + | 8.00000i | −0.165380 | + | 0.330759i | ||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | − | 6.00000i | − | 0.247436i | ||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −20.0000 | + | 40.0000i | −0.823387 | + | 1.64677i | ||||
\(591\) | 13.0000 | 0.534749 | ||||||||
\(592\) | − | 28.0000i | − | 1.15079i | ||||||
\(593\) | − | 6.00000i | − | 0.246390i | −0.992382 | − | 0.123195i | \(-0.960686\pi\) | ||
0.992382 | − | 0.123195i | \(-0.0393141\pi\) | |||||||
\(594\) | −6.00000 | −0.246183 | ||||||||
\(595\) | −32.0000 | − | 16.0000i | −1.31187 | − | 0.655936i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.0000i | 1.02318i | ||||||||
\(598\) | 8.00000i | 0.327144i | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | − | 36.0000i | − | 1.46725i | ||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | 6.00000 | 0.244137 | ||||||||
\(605\) | 4.00000 | + | 2.00000i | 0.162623 | + | 0.0813116i | ||||
\(606\) | −34.0000 | −1.38116 | ||||||||
\(607\) | − | 8.00000i | − | 0.324710i | −0.986732 | − | 0.162355i | \(-0.948091\pi\) | ||
0.986732 | − | 0.162355i | \(-0.0519090\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | 4.00000 | − | 8.00000i | 0.161955 | − | 0.323911i | ||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | − | 16.0000i | − | 0.646762i | ||||||
\(613\) | 34.0000i | 1.37325i | 0.727013 | + | 0.686624i | \(0.240908\pi\) | ||||
−0.727013 | + | 0.686624i | \(0.759092\pi\) | |||||||
\(614\) | −34.0000 | −1.37213 | ||||||||
\(615\) | 7.00000 | − | 14.0000i | 0.282267 | − | 0.564534i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18.0000i | − | 0.724653i | −0.932051 | − | 0.362326i | \(-0.881983\pi\) | ||
0.932051 | − | 0.362326i | \(-0.118017\pi\) | |||||||
\(618\) | − | 8.00000i | − | 0.321807i | ||||||
\(619\) | 30.0000 | 1.20580 | 0.602901 | − | 0.797816i | \(-0.294011\pi\) | ||||
0.602901 | + | 0.797816i | \(0.294011\pi\) | |||||||
\(620\) | −32.0000 | − | 16.0000i | −1.28515 | − | 0.642575i | ||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 34.0000i | 1.36328i | ||||||||
\(623\) | − | 20.0000i | − | 0.801283i | ||||||
\(624\) | 16.0000 | 0.640513 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | −8.00000 | −0.319744 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 4.00000i | − | 0.159617i | ||||||
\(629\) | 56.0000 | 2.23287 | ||||||||
\(630\) | −8.00000 | − | 4.00000i | −0.318728 | − | 0.159364i | ||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0000i | 0.476957i | ||||||||
\(634\) | −24.0000 | −0.953162 | ||||||||
\(635\) | −3.00000 | + | 6.00000i | −0.119051 | + | 0.238103i | ||||
\(636\) | 18.0000 | 0.713746 | ||||||||
\(637\) | 12.0000i | 0.475457i | ||||||||
\(638\) | 6.00000i | 0.237542i | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.0000 | −1.69840 | −0.849199 | − | 0.528073i | \(-0.822915\pi\) | ||||
−0.849199 | + | 0.528073i | \(0.822915\pi\) | |||||||
\(642\) | − | 24.0000i | − | 0.947204i | ||||||
\(643\) | − | 16.0000i | − | 0.630978i | −0.948929 | − | 0.315489i | \(-0.897831\pi\) | ||
0.948929 | − | 0.315489i | \(-0.102169\pi\) | |||||||
\(644\) | −4.00000 | −0.157622 | ||||||||
\(645\) | 18.0000 | + | 9.00000i | 0.708749 | + | 0.354375i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 33.0000i | − | 1.29736i | −0.761060 | − | 0.648682i | \(-0.775321\pi\) | ||
0.761060 | − | 0.648682i | \(-0.224679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.0000 | 1.17760 | ||||||||
\(650\) | −24.0000 | − | 32.0000i | −0.941357 | − | 1.25514i | ||||
\(651\) | 16.0000 | 0.627089 | ||||||||
\(652\) | 2.00000i | 0.0783260i | ||||||||
\(653\) | − | 36.0000i | − | 1.40879i | −0.709809 | − | 0.704394i | \(-0.751219\pi\) | ||
0.709809 | − | 0.704394i | \(-0.248781\pi\) | |||||||
\(654\) | −10.0000 | −0.391031 | ||||||||
\(655\) | −24.0000 | − | 12.0000i | −0.937758 | − | 0.468879i | ||||
\(656\) | −28.0000 | −1.09322 | ||||||||
\(657\) | 1.00000i | 0.0390137i | ||||||||
\(658\) | − | 48.0000i | − | 1.87123i | ||||||
\(659\) | −25.0000 | −0.973862 | −0.486931 | − | 0.873441i | \(-0.661884\pi\) | ||||
−0.486931 | + | 0.873441i | \(0.661884\pi\) | |||||||
\(660\) | 6.00000 | − | 12.0000i | 0.233550 | − | 0.467099i | ||||
\(661\) | −13.0000 | −0.505641 | −0.252821 | − | 0.967513i | \(-0.581358\pi\) | ||||
−0.252821 | + | 0.967513i | \(0.581358\pi\) | |||||||
\(662\) | 64.0000i | 2.48743i | ||||||||
\(663\) | 32.0000i | 1.24278i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14.0000 | 0.542489 | ||||||||
\(667\) | 1.00000i | 0.0387202i | ||||||||
\(668\) | 16.0000i | 0.619059i | ||||||||
\(669\) | 6.00000 | 0.231973 | ||||||||
\(670\) | −32.0000 | − | 16.0000i | −1.23627 | − | 0.618134i | ||||
\(671\) | −6.00000 | −0.231627 | ||||||||
\(672\) | 16.0000i | 0.617213i | ||||||||
\(673\) | − | 6.00000i | − | 0.231283i | −0.993291 | − | 0.115642i | \(-0.963108\pi\) | ||
0.993291 | − | 0.115642i | \(-0.0368924\pi\) | |||||||
\(674\) | −44.0000 | −1.69482 | ||||||||
\(675\) | 4.00000 | − | 3.00000i | 0.153960 | − | 0.115470i | ||||
\(676\) | 6.00000 | 0.230769 | ||||||||
\(677\) | 22.0000i | 0.845529i | 0.906240 | + | 0.422764i | \(0.138940\pi\) | ||||
−0.906240 | + | 0.422764i | \(0.861060\pi\) | |||||||
\(678\) | − | 28.0000i | − | 1.07533i | ||||||
\(679\) | 26.0000 | 0.997788 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.00000 | 0.114960 | ||||||||
\(682\) | 48.0000i | 1.83801i | ||||||||
\(683\) | 39.0000i | 1.49229i | 0.665782 | + | 0.746147i | \(0.268098\pi\) | ||||
−0.665782 | + | 0.746147i | \(0.731902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | − | 4.00000i | 0.0764161 | − | 0.152832i | ||||
\(686\) | −40.0000 | −1.52721 | ||||||||
\(687\) | − | 20.0000i | − | 0.763048i | ||||||
\(688\) | − | 36.0000i | − | 1.37249i | ||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 2.00000 | − | 4.00000i | 0.0761387 | − | 0.152277i | ||||
\(691\) | −8.00000 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | − | 18.0000i | − | 0.684257i | ||||||
\(693\) | 6.00000i | 0.227921i | ||||||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | 10.0000 | + | 5.00000i | 0.379322 | + | 0.189661i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 56.0000i | − | 2.12115i | ||||||
\(698\) | 10.0000i | 0.378506i | ||||||||
\(699\) | 1.00000 | 0.0378235 | ||||||||
\(700\) | 16.0000 | − | 12.0000i | 0.604743 | − | 0.453557i | ||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | 8.00000i | 0.301941i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −24.0000 | −0.904534 | ||||||||
\(705\) | 24.0000 | + | 12.0000i | 0.903892 | + | 0.451946i | ||||
\(706\) | 52.0000 | 1.95705 | ||||||||
\(707\) | 34.0000i | 1.27870i | ||||||||
\(708\) | 20.0000i | 0.751646i | ||||||||
\(709\) | 45.0000 | 1.69001 | 0.845005 | − | 0.534758i | \(-0.179597\pi\) | ||||
0.845005 | + | 0.534758i | \(0.179597\pi\) | |||||||
\(710\) | −16.0000 | + | 32.0000i | −0.600469 | + | 1.20094i | ||||
\(711\) | −10.0000 | −0.375029 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.00000i | 0.299602i | ||||||||
\(714\) | −32.0000 | −1.19757 | ||||||||
\(715\) | −12.0000 | + | 24.0000i | −0.448775 | + | 0.897549i | ||||
\(716\) | 20.0000 | 0.747435 | ||||||||
\(717\) | − | 30.0000i | − | 1.12037i | ||||||
\(718\) | 30.0000i | 1.11959i | ||||||||
\(719\) | −30.0000 | −1.11881 | −0.559406 | − | 0.828894i | \(-0.688971\pi\) | ||||
−0.559406 | + | 0.828894i | \(0.688971\pi\) | |||||||
\(720\) | −8.00000 | − | 4.00000i | −0.298142 | − | 0.149071i | ||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | − | 38.0000i | − | 1.41421i | ||||||
\(723\) | − | 3.00000i | − | 0.111571i | ||||||
\(724\) | −34.0000 | −1.26360 | ||||||||
\(725\) | −3.00000 | − | 4.00000i | −0.111417 | − | 0.148556i | ||||
\(726\) | 4.00000 | 0.148454 | ||||||||
\(727\) | − | 8.00000i | − | 0.296704i | −0.988935 | − | 0.148352i | \(-0.952603\pi\) | ||
0.988935 | − | 0.148352i | \(-0.0473968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −4.00000 | − | 2.00000i | −0.148047 | − | 0.0740233i | ||||
\(731\) | 72.0000 | 2.66302 | ||||||||
\(732\) | − | 4.00000i | − | 0.147844i | ||||||
\(733\) | 34.0000i | 1.25582i | 0.778287 | + | 0.627909i | \(0.216089\pi\) | ||||
−0.778287 | + | 0.627909i | \(0.783911\pi\) | |||||||
\(734\) | 6.00000 | 0.221464 | ||||||||
\(735\) | 3.00000 | − | 6.00000i | 0.110657 | − | 0.221313i | ||||
\(736\) | −8.00000 | −0.294884 | ||||||||
\(737\) | 24.0000i | 0.884051i | ||||||||
\(738\) | − | 14.0000i | − | 0.515347i | ||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | −14.0000 | + | 28.0000i | −0.514650 | + | 1.02930i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 36.0000i | − | 1.32160i | ||||||
\(743\) | 44.0000i | 1.61420i | 0.590412 | + | 0.807102i | \(0.298965\pi\) | ||||
−0.590412 | + | 0.807102i | \(0.701035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.00000 | −0.292901 | ||||||||
\(747\) | − | 9.00000i | − | 0.329293i | ||||||
\(748\) | − | 48.0000i | − | 1.75505i | ||||||
\(749\) | −24.0000 | −0.876941 | ||||||||
\(750\) | 4.00000 | + | 22.0000i | 0.146059 | + | 0.803326i | ||||
\(751\) | 22.0000 | 0.802791 | 0.401396 | − | 0.915905i | \(-0.368525\pi\) | ||||
0.401396 | + | 0.915905i | \(0.368525\pi\) | |||||||
\(752\) | − | 48.0000i | − | 1.75038i | ||||||
\(753\) | 12.0000i | 0.437304i | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 6.00000 | + | 3.00000i | 0.218362 | + | 0.109181i | ||||
\(756\) | −4.00000 | −0.145479 | ||||||||
\(757\) | − | 3.00000i | − | 0.109037i | −0.998513 | − | 0.0545184i | \(-0.982638\pi\) | ||
0.998513 | − | 0.0545184i | \(-0.0173624\pi\) | |||||||
\(758\) | 20.0000i | 0.726433i | ||||||||
\(759\) | −3.00000 | −0.108893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0000 | 1.52250 | 0.761249 | − | 0.648459i | \(-0.224586\pi\) | ||||
0.761249 | + | 0.648459i | \(0.224586\pi\) | |||||||
\(762\) | 6.00000i | 0.217357i | ||||||||
\(763\) | 10.0000i | 0.362024i | ||||||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | 8.00000 | − | 16.0000i | 0.289241 | − | 0.578481i | ||||
\(766\) | −78.0000 | −2.81825 | ||||||||
\(767\) | − | 40.0000i | − | 1.44432i | ||||||
\(768\) | 16.0000i | 0.577350i | ||||||||
\(769\) | 40.0000 | 1.44244 | 0.721218 | − | 0.692708i | \(-0.243582\pi\) | ||||
0.721218 | + | 0.692708i | \(0.243582\pi\) | |||||||
\(770\) | −24.0000 | − | 12.0000i | −0.864900 | − | 0.432450i | ||||
\(771\) | 23.0000 | 0.828325 | ||||||||
\(772\) | 12.0000i | 0.431889i | ||||||||
\(773\) | 24.0000i | 0.863220i | 0.902060 | + | 0.431610i | \(0.142054\pi\) | ||||
−0.902060 | + | 0.431610i | \(0.857946\pi\) | |||||||
\(774\) | 18.0000 | 0.646997 | ||||||||
\(775\) | −24.0000 | − | 32.0000i | −0.862105 | − | 1.14947i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 14.0000i | − | 0.502247i | ||||||
\(778\) | 50.0000i | 1.79259i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −16.0000 | − | 8.00000i | −0.572892 | − | 0.286446i | ||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | − | 16.0000i | − | 0.572159i | ||||||
\(783\) | 1.00000i | 0.0357371i | ||||||||
\(784\) | −12.0000 | −0.428571 | ||||||||
\(785\) | 2.00000 | − | 4.00000i | 0.0713831 | − | 0.142766i | ||||
\(786\) | −24.0000 | −0.856052 | ||||||||
\(787\) | − | 38.0000i | − | 1.35455i | −0.735728 | − | 0.677277i | \(-0.763160\pi\) | ||
0.735728 | − | 0.677277i | \(-0.236840\pi\) | |||||||
\(788\) | 26.0000i | 0.926212i | ||||||||
\(789\) | −4.00000 | −0.142404 | ||||||||
\(790\) | 20.0000 | − | 40.0000i | 0.711568 | − | 1.42314i | ||||
\(791\) | −28.0000 | −0.995565 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000i | 0.284088i | ||||||||
\(794\) | 16.0000 | 0.567819 | ||||||||
\(795\) | 18.0000 | + | 9.00000i | 0.638394 | + | 0.319197i | ||||
\(796\) | −50.0000 | −1.77220 | ||||||||
\(797\) | − | 8.00000i | − | 0.283375i | −0.989911 | − | 0.141687i | \(-0.954747\pi\) | ||
0.989911 | − | 0.141687i | \(-0.0452527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 96.0000 | 3.39624 | ||||||||
\(800\) | 32.0000 | − | 24.0000i | 1.13137 | − | 0.848528i | ||||
\(801\) | 10.0000 | 0.353333 | ||||||||
\(802\) | − | 56.0000i | − | 1.97743i | ||||||
\(803\) | 3.00000i | 0.105868i | ||||||||
\(804\) | −16.0000 | −0.564276 | ||||||||
\(805\) | −4.00000 | − | 2.00000i | −0.140981 | − | 0.0704907i | ||||
\(806\) | 64.0000 | 2.25430 | ||||||||
\(807\) | 10.0000i | 0.352017i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.0000 | 1.58212 | 0.791058 | − | 0.611741i | \(-0.209531\pi\) | ||||
0.791058 | + | 0.611741i | \(0.209531\pi\) | |||||||
\(810\) | 2.00000 | − | 4.00000i | 0.0702728 | − | 0.140546i | ||||
\(811\) | −13.0000 | −0.456492 | −0.228246 | − | 0.973604i | \(-0.573299\pi\) | ||||
−0.228246 | + | 0.973604i | \(0.573299\pi\) | |||||||
\(812\) | 4.00000i | 0.140372i | ||||||||
\(813\) | 12.0000i | 0.420858i | ||||||||
\(814\) | 42.0000 | 1.47210 | ||||||||
\(815\) | −1.00000 | + | 2.00000i | −0.0350285 | + | 0.0700569i | ||||
\(816\) | −32.0000 | −1.12022 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 20.0000i | 0.699284i | ||||||||
\(819\) | 8.00000 | 0.279543 | ||||||||
\(820\) | 28.0000 | + | 14.0000i | 0.977802 | + | 0.488901i | ||||
\(821\) | −48.0000 | −1.67521 | −0.837606 | − | 0.546275i | \(-0.816045\pi\) | ||||
−0.837606 | + | 0.546275i | \(0.816045\pi\) | |||||||
\(822\) | − | 4.00000i | − | 0.139516i | ||||||
\(823\) | − | 16.0000i | − | 0.557725i | −0.960331 | − | 0.278862i | \(-0.910043\pi\) | ||
0.960331 | − | 0.278862i | \(-0.0899574\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.0000 | − | 9.00000i | 0.417786 | − | 0.313340i | ||||
\(826\) | 40.0000 | 1.39178 | ||||||||
\(827\) | 22.0000i | 0.765015i | 0.923952 | + | 0.382507i | \(0.124939\pi\) | ||||
−0.923952 | + | 0.382507i | \(0.875061\pi\) | |||||||
\(828\) | − | 2.00000i | − | 0.0695048i | ||||||
\(829\) | −50.0000 | −1.73657 | −0.868286 | − | 0.496064i | \(-0.834778\pi\) | ||||
−0.868286 | + | 0.496064i | \(0.834778\pi\) | |||||||
\(830\) | 36.0000 | + | 18.0000i | 1.24958 | + | 0.624789i | ||||
\(831\) | 28.0000 | 0.971309 | ||||||||
\(832\) | 32.0000i | 1.10940i | ||||||||
\(833\) | − | 24.0000i | − | 0.831551i | ||||||
\(834\) | 10.0000 | 0.346272 | ||||||||
\(835\) | −8.00000 | + | 16.0000i | −0.276851 | + | 0.553703i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000i | 0.276520i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | − | 56.0000i | − | 1.92989i | ||||||
\(843\) | − | 18.0000i | − | 0.619953i | ||||||
\(844\) | −24.0000 | −0.826114 | ||||||||
\(845\) | 6.00000 | + | 3.00000i | 0.206406 | + | 0.103203i | ||||
\(846\) | 24.0000 | 0.825137 | ||||||||
\(847\) | − | 4.00000i | − | 0.137442i | ||||||
\(848\) | − | 36.0000i | − | 1.23625i | ||||||
\(849\) | −14.0000 | −0.480479 | ||||||||
\(850\) | 48.0000 | + | 64.0000i | 1.64639 | + | 2.19518i | ||||
\(851\) | 7.00000 | 0.239957 | ||||||||
\(852\) | 16.0000i | 0.548151i | ||||||||
\(853\) | 19.0000i | 0.650548i | 0.945620 | + | 0.325274i | \(0.105456\pi\) | ||||
−0.945620 | + | 0.325274i | \(0.894544\pi\) | |||||||
\(854\) | −8.00000 | −0.273754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.00000i | 0.239115i | 0.992827 | + | 0.119558i | \(0.0381477\pi\) | ||||
−0.992827 | + | 0.119558i | \(0.961852\pi\) | |||||||
\(858\) | 24.0000i | 0.819346i | ||||||||
\(859\) | 30.0000 | 1.02359 | 0.511793 | − | 0.859109i | \(-0.328981\pi\) | ||||
0.511793 | + | 0.859109i | \(0.328981\pi\) | |||||||
\(860\) | −18.0000 | + | 36.0000i | −0.613795 | + | 1.22759i | ||||
\(861\) | −14.0000 | −0.477119 | ||||||||
\(862\) | 24.0000i | 0.817443i | ||||||||
\(863\) | 44.0000i | 1.49778i | 0.662696 | + | 0.748889i | \(0.269412\pi\) | ||||
−0.662696 | + | 0.748889i | \(0.730588\pi\) | |||||||
\(864\) | −8.00000 | −0.272166 | ||||||||
\(865\) | 9.00000 | − | 18.0000i | 0.306009 | − | 0.612018i | ||||
\(866\) | −38.0000 | −1.29129 | ||||||||
\(867\) | − | 47.0000i | − | 1.59620i | ||||||
\(868\) | 32.0000i | 1.08615i | ||||||||
\(869\) | −30.0000 | −1.01768 | ||||||||
\(870\) | −4.00000 | − | 2.00000i | −0.135613 | − | 0.0678064i | ||||
\(871\) | 32.0000 | 1.08428 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.0000i | 0.439983i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.0000 | − | 4.00000i | 0.743736 | − | 0.135225i | ||||
\(876\) | −2.00000 | −0.0675737 | ||||||||
\(877\) | 52.0000i | 1.75592i | 0.478738 | + | 0.877958i | \(0.341094\pi\) | ||||
−0.478738 | + | 0.877958i | \(0.658906\pi\) | |||||||
\(878\) | − | 40.0000i | − | 1.34993i | ||||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | −24.0000 | − | 12.0000i | −0.809040 | − | 0.404520i | ||||
\(881\) | 57.0000 | 1.92038 | 0.960189 | − | 0.279350i | \(-0.0901189\pi\) | ||||
0.960189 | + | 0.279350i | \(0.0901189\pi\) | |||||||
\(882\) | − | 6.00000i | − | 0.202031i | ||||||
\(883\) | 4.00000i | 0.134611i | 0.997732 | + | 0.0673054i | \(0.0214402\pi\) | ||||
−0.997732 | + | 0.0673054i | \(0.978560\pi\) | |||||||
\(884\) | −64.0000 | −2.15255 | ||||||||
\(885\) | −10.0000 | + | 20.0000i | −0.336146 | + | 0.672293i | ||||
\(886\) | 12.0000 | 0.403148 | ||||||||
\(887\) | 22.0000i | 0.738688i | 0.929293 | + | 0.369344i | \(0.120418\pi\) | ||||
−0.929293 | + | 0.369344i | \(0.879582\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.00000 | 0.201234 | ||||||||
\(890\) | −20.0000 | + | 40.0000i | −0.670402 | + | 1.34080i | ||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | 12.0000i | 0.401790i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0000 | + | 10.0000i | 0.668526 | + | 0.334263i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.00000i | 0.133556i | ||||||||
\(898\) | − | 10.0000i | − | 0.333704i | ||||||
\(899\) | 8.00000 | 0.266815 | ||||||||
\(900\) | 6.00000 | + | 8.00000i | 0.200000 | + | 0.266667i | ||||
\(901\) | 72.0000 | 2.39867 | ||||||||
\(902\) | − | 42.0000i | − | 1.39845i | ||||||
\(903\) | − | 18.0000i | − | 0.599002i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −34.0000 | − | 17.0000i | −1.13020 | − | 0.565099i | ||||
\(906\) | 6.00000 | 0.199337 | ||||||||
\(907\) | 37.0000i | 1.22856i | 0.789086 | + | 0.614282i | \(0.210554\pi\) | ||||
−0.789086 | + | 0.614282i | \(0.789446\pi\) | |||||||
\(908\) | 6.00000i | 0.199117i | ||||||||
\(909\) | −17.0000 | −0.563854 | ||||||||
\(910\) | −16.0000 | + | 32.0000i | −0.530395 | + | 1.06079i | ||||
\(911\) | 27.0000 | 0.894550 | 0.447275 | − | 0.894397i | \(-0.352395\pi\) | ||||
0.447275 | + | 0.894397i | \(0.352395\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 27.0000i | − | 0.893570i | ||||||
\(914\) | 56.0000 | 1.85232 | ||||||||
\(915\) | 2.00000 | − | 4.00000i | 0.0661180 | − | 0.132236i | ||||
\(916\) | 40.0000 | 1.32164 | ||||||||
\(917\) | 24.0000i | 0.792550i | ||||||||
\(918\) | − | 16.0000i | − | 0.528079i | ||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.0000 | −0.560169 | ||||||||
\(922\) | − | 26.0000i | − | 0.856264i | ||||||
\(923\) | − | 32.0000i | − | 1.05329i | ||||||
\(924\) | −12.0000 | −0.394771 | ||||||||
\(925\) | −28.0000 | + | 21.0000i | −0.920634 | + | 0.690476i | ||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | − | 4.00000i | − | 0.131377i | ||||||
\(928\) | 8.00000i | 0.262613i | ||||||||
\(929\) | −20.0000 | −0.656179 | −0.328089 | − | 0.944647i | \(-0.606405\pi\) | ||||
−0.328089 | + | 0.944647i | \(0.606405\pi\) | |||||||
\(930\) | −32.0000 | − | 16.0000i | −1.04932 | − | 0.524661i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.00000i | 0.0655122i | ||||||||
\(933\) | 17.0000i | 0.556555i | ||||||||
\(934\) | −84.0000 | −2.74856 | ||||||||
\(935\) | 24.0000 | − | 48.0000i | 0.784884 | − | 1.56977i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000i | 0.718709i | 0.933201 | + | 0.359354i | \(0.117003\pi\) | ||||
−0.933201 | + | 0.359354i | \(0.882997\pi\) | |||||||
\(938\) | 32.0000i | 1.04484i | ||||||||
\(939\) | −4.00000 | −0.130535 | ||||||||
\(940\) | −24.0000 | + | 48.0000i | −0.782794 | + | 1.56559i | ||||
\(941\) | 42.0000 | 1.36916 | 0.684580 | − | 0.728937i | \(-0.259985\pi\) | ||||
0.684580 | + | 0.728937i | \(0.259985\pi\) | |||||||
\(942\) | − | 4.00000i | − | 0.130327i | ||||||
\(943\) | − | 7.00000i | − | 0.227951i | ||||||
\(944\) | 40.0000 | 1.30189 | ||||||||
\(945\) | −4.00000 | − | 2.00000i | −0.130120 | − | 0.0650600i | ||||
\(946\) | 54.0000 | 1.75569 | ||||||||
\(947\) | 12.0000i | 0.389948i | 0.980808 | + | 0.194974i | \(0.0624622\pi\) | ||||
−0.980808 | + | 0.194974i | \(0.937538\pi\) | |||||||
\(948\) | − | 20.0000i | − | 0.649570i | ||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 18.0000 | 0.582772 | ||||||||
\(955\) | 6.00000 | + | 3.00000i | 0.194155 | + | 0.0970777i | ||||
\(956\) | 60.0000 | 1.94054 | ||||||||
\(957\) | 3.00000i | 0.0969762i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.00000 | −0.129167 | ||||||||
\(960\) | 8.00000 | − | 16.0000i | 0.258199 | − | 0.516398i | ||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | − | 56.0000i | − | 1.80551i | ||||||
\(963\) | − | 12.0000i | − | 0.386695i | ||||||
\(964\) | 6.00000 | 0.193247 | ||||||||
\(965\) | −6.00000 | + | 12.0000i | −0.193147 | + | 0.386294i | ||||
\(966\) | −4.00000 | −0.128698 | ||||||||
\(967\) | − | 3.00000i | − | 0.0964735i | −0.998836 | − | 0.0482367i | \(-0.984640\pi\) | ||
0.998836 | − | 0.0482367i | \(-0.0153602\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −52.0000 | − | 26.0000i | −1.66962 | − | 0.834810i | ||||
\(971\) | −3.00000 | −0.0962746 | −0.0481373 | − | 0.998841i | \(-0.515328\pi\) | ||||
−0.0481373 | + | 0.998841i | \(0.515328\pi\) | |||||||
\(972\) | − | 2.00000i | − | 0.0641500i | ||||||
\(973\) | − | 10.0000i | − | 0.320585i | ||||||
\(974\) | −44.0000 | −1.40985 | ||||||||
\(975\) | −12.0000 | − | 16.0000i | −0.384308 | − | 0.512410i | ||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | − | 13.0000i | − | 0.415907i | −0.978139 | − | 0.207953i | \(-0.933320\pi\) | ||
0.978139 | − | 0.207953i | \(-0.0666802\pi\) | |||||||
\(978\) | 2.00000i | 0.0639529i | ||||||||
\(979\) | 30.0000 | 0.958804 | ||||||||
\(980\) | 12.0000 | + | 6.00000i | 0.383326 | + | 0.191663i | ||||
\(981\) | −5.00000 | −0.159638 | ||||||||
\(982\) | − | 56.0000i | − | 1.78703i | ||||||
\(983\) | − | 36.0000i | − | 1.14822i | −0.818778 | − | 0.574111i | \(-0.805348\pi\) | ||
0.818778 | − | 0.574111i | \(-0.194652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.0000 | + | 26.0000i | −0.414214 | + | 0.828429i | ||||
\(986\) | −16.0000 | −0.509544 | ||||||||
\(987\) | − | 24.0000i | − | 0.763928i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.00000 | 0.286183 | ||||||||
\(990\) | 6.00000 | − | 12.0000i | 0.190693 | − | 0.381385i | ||||
\(991\) | −33.0000 | −1.04828 | −0.524140 | − | 0.851632i | \(-0.675613\pi\) | ||||
−0.524140 | + | 0.851632i | \(0.675613\pi\) | |||||||
\(992\) | 64.0000i | 2.03200i | ||||||||
\(993\) | 32.0000i | 1.01549i | ||||||||
\(994\) | 32.0000 | 1.01498 | ||||||||
\(995\) | −50.0000 | − | 25.0000i | −1.58511 | − | 0.792553i | ||||
\(996\) | 18.0000 | 0.570352 | ||||||||
\(997\) | 7.00000i | 0.221692i | 0.993838 | + | 0.110846i | \(0.0353561\pi\) | ||||
−0.993838 | + | 0.110846i | \(0.964644\pi\) | |||||||
\(998\) | − | 40.0000i | − | 1.26618i | ||||||
\(999\) | 7.00000 | 0.221470 |
(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 | 435.2.c.a.349.2 | yes | 2 | |
3.2 | odd | 2 | 1305.2.c.a.784.1 | 2 | |||
5.2 | odd | 4 | 2175.2.a.a.1.1 | 1 | |||
5.3 | odd | 4 | 2175.2.a.j.1.1 | 1 | |||
5.4 | even | 2 | inner | 435.2.c.a.349.1 | ✓ | 2 | |
15.2 | even | 4 | 6525.2.a.l.1.1 | 1 | |||
15.8 | even | 4 | 6525.2.a.b.1.1 | 1 | |||
15.14 | odd | 2 | 1305.2.c.a.784.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
435.2.c.a.349.1 | ✓ | 2 | 5.4 | even | 2 | inner | |
435.2.c.a.349.2 | yes | 2 | 1.1 | even | 1 | trivial | |
1305.2.c.a.784.1 | 2 | 3.2 | odd | 2 | |||
1305.2.c.a.784.2 | 2 | 15.14 | odd | 2 | |||
2175.2.a.a.1.1 | 1 | 5.2 | odd | 4 | |||
2175.2.a.j.1.1 | 1 | 5.3 | odd | 4 | |||
6525.2.a.b.1.1 | 1 | 15.8 | even | 4 | |||
6525.2.a.l.1.1 | 1 | 15.2 | even | 4 |