Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1999,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, 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("3330.1999");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.d (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: | \(26.5901838731\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1999.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1999 |
Dual form | 3330.2.d.c.1999.1 |
$q$-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 \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) | ||
0.981981 | − | 0.188982i | \(-0.0605189\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | − | 1.00000i | −0.632456 | − | 0.316228i | ||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.00000i | − | 0.727607i | −0.931476 | − | 0.363803i | \(-0.881478\pi\) | ||
0.931476 | − | 0.363803i | \(-0.118522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 1.00000 | − | 2.00000i | 0.223607 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000i | 0.639602i | ||||||||
\(23\) | 8.00000i | 1.66812i | 0.551677 | + | 0.834058i | \(0.313988\pi\) | ||||
−0.551677 | + | 0.834058i | \(0.686012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00000 | −1.25724 | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 2.00000 | + | 1.00000i | 0.338062 | + | 0.169031i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00000 | + | 1.00000i | 0.316228 | + | 0.158114i | ||||
\(41\) | −11.0000 | −1.71791 | −0.858956 | − | 0.512050i | \(-0.828886\pi\) | ||||
−0.858956 | + | 0.512050i | \(0.828886\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0000i | 1.67748i | 0.544529 | + | 0.838742i | \(0.316708\pi\) | ||||
−0.544529 | + | 0.838742i | \(0.683292\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.00000 | −1.17954 | ||||||||
\(47\) | 4.00000i | 0.583460i | 0.956501 | + | 0.291730i | \(0.0942309\pi\) | ||||
−0.956501 | + | 0.291730i | \(0.905769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.00000 | 0.857143 | ||||||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.00000i | 0.554700i | ||||||||
\(53\) | − | 11.0000i | − | 1.51097i | −0.655168 | − | 0.755483i | \(-0.727402\pi\) | ||
0.655168 | − | 0.755483i | \(-0.272598\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | + | 6.00000i | −0.404520 | + | 0.809040i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 3.00000i | − | 0.393919i | ||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.0000 | −1.92055 | −0.960277 | − | 0.279050i | \(-0.909981\pi\) | ||||
−0.960277 | + | 0.279050i | \(0.909981\pi\) | |||||||
\(62\) | − | 7.00000i | − | 0.889001i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 8.00000 | + | 4.00000i | 0.992278 | + | 0.496139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785709\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(68\) | 3.00000i | 0.363803i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | + | 2.00000i | −0.119523 | + | 0.239046i | ||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000i | 0.234082i | 0.993127 | + | 0.117041i | \(0.0373409\pi\) | ||||
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.00000i | − | 0.341882i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −1.00000 | + | 2.00000i | −0.111803 | + | 0.223607i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 11.0000i | − | 1.21475i | ||||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | + | 3.00000i | 0.650791 | + | 0.325396i | ||||
\(86\) | −11.0000 | −1.18616 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 3.00000i | − | 0.319801i | ||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | − | 8.00000i | − | 0.834058i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.00000 | −0.412568 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00000i | 0.101535i | 0.998711 | + | 0.0507673i | \(0.0161667\pi\) | ||||
−0.998711 | + | 0.0507673i | \(0.983833\pi\) | |||||||
\(98\) | 6.00000i | 0.606092i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | −14.0000 | −1.39305 | −0.696526 | − | 0.717532i | \(-0.745272\pi\) | ||||
−0.696526 | + | 0.717532i | \(0.745272\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | −4.00000 | −0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.0000 | 1.06841 | ||||||||
\(107\) | − | 10.0000i | − | 0.966736i | −0.875417 | − | 0.483368i | \(-0.839413\pi\) | ||
0.875417 | − | 0.483368i | \(-0.160587\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0000 | 1.05361 | 0.526804 | − | 0.849987i | \(-0.323390\pi\) | ||||
0.526804 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(110\) | −6.00000 | − | 3.00000i | −0.572078 | − | 0.286039i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | 1.00000i | 0.0940721i | 0.998893 | + | 0.0470360i | \(0.0149776\pi\) | ||||
−0.998893 | + | 0.0470360i | \(0.985022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.0000 | − | 8.00000i | −1.49201 | − | 0.746004i | ||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 12.0000i | − | 1.10469i | ||||||
\(119\) | −3.00000 | −0.275010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | − | 15.0000i | − | 1.35804i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.00000 | 0.628619 | ||||||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.0000i | − | 1.41977i | −0.704317 | − | 0.709885i | \(-0.748747\pi\) | ||
0.704317 | − | 0.709885i | \(-0.251253\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.00000 | + | 8.00000i | −0.350823 | + | 0.701646i | ||||
\(131\) | 10.0000 | 0.873704 | 0.436852 | − | 0.899533i | \(-0.356093\pi\) | ||||
0.436852 | + | 0.899533i | \(0.356093\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | 6.00000i | 0.512615i | 0.966595 | + | 0.256307i | \(0.0825059\pi\) | ||||
−0.966595 | + | 0.256307i | \(0.917494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.00000 | −0.0848189 | −0.0424094 | − | 0.999100i | \(-0.513503\pi\) | ||||
−0.0424094 | + | 0.999100i | \(0.513503\pi\) | |||||||
\(140\) | −2.00000 | − | 1.00000i | −0.169031 | − | 0.0845154i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 6.00000i | − | 0.503509i | ||||||
\(143\) | − | 12.0000i | − | 1.00349i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.00000 | − | 6.00000i | 0.249136 | − | 0.498273i | ||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | −4.00000 | −0.327693 | −0.163846 | − | 0.986486i | \(-0.552390\pi\) | ||||
−0.163846 | + | 0.986486i | \(0.552390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0000 | −1.13930 | −0.569652 | − | 0.821886i | \(-0.692922\pi\) | ||||
−0.569652 | + | 0.821886i | \(0.692922\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.00000 | 0.241747 | ||||||||
\(155\) | 7.00000 | − | 14.0000i | 0.562254 | − | 1.12451i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000i | 0.399043i | 0.979893 | + | 0.199522i | \(0.0639388\pi\) | ||||
−0.979893 | + | 0.199522i | \(0.936061\pi\) | |||||||
\(158\) | 8.00000i | 0.636446i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | − | 1.00000i | −0.158114 | − | 0.0790569i | ||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.00000i | 0.234978i | 0.993074 | + | 0.117489i | \(0.0374845\pi\) | ||||
−0.993074 | + | 0.117489i | \(0.962515\pi\) | |||||||
\(164\) | 11.0000 | 0.858956 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | − | 14.0000i | − | 1.08335i | −0.840587 | − | 0.541676i | \(-0.817790\pi\) | ||
0.840587 | − | 0.541676i | \(-0.182210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | −3.00000 | + | 6.00000i | −0.230089 | + | 0.460179i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 11.0000i | − | 0.838742i | ||||||
\(173\) | 13.0000i | 0.988372i | 0.869356 | + | 0.494186i | \(0.164534\pi\) | ||||
−0.869356 | + | 0.494186i | \(0.835466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00000 | + | 3.00000i | −0.302372 | + | 0.226779i | ||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | − | 4.00000i | − | 0.296500i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000 | 0.589768 | ||||||||
\(185\) | −2.00000 | − | 1.00000i | −0.147043 | − | 0.0735215i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.00000i | − | 0.658145i | ||||||
\(188\) | − | 4.00000i | − | 0.291730i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.0000 | 1.23008 | 0.615038 | − | 0.788497i | \(-0.289140\pi\) | ||||
0.615038 | + | 0.788497i | \(0.289140\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 14.0000i | − | 1.00774i | −0.863779 | − | 0.503871i | \(-0.831909\pi\) | ||
0.863779 | − | 0.503871i | \(-0.168091\pi\) | |||||||
\(194\) | −1.00000 | −0.0717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | −4.00000 | + | 3.00000i | −0.282843 | + | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 14.0000i | − | 0.985037i | ||||||
\(203\) | 3.00000i | 0.210559i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0000 | − | 22.0000i | 0.768273 | − | 1.53655i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.00000i | − | 0.277350i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00000 | −0.0688428 | −0.0344214 | − | 0.999407i | \(-0.510959\pi\) | ||||
−0.0344214 | + | 0.999407i | \(0.510959\pi\) | |||||||
\(212\) | 11.0000i | 0.755483i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.0000 | 0.683586 | ||||||||
\(215\) | −22.0000 | − | 11.0000i | −1.50039 | − | 0.750194i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.00000i | 0.475191i | ||||||||
\(218\) | 11.0000i | 0.745014i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.00000 | − | 6.00000i | 0.202260 | − | 0.404520i | ||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.0000i | 0.736614i | 0.929704 | + | 0.368307i | \(0.120063\pi\) | ||||
−0.929704 | + | 0.368307i | \(0.879937\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.00000 | −0.0665190 | ||||||||
\(227\) | 17.0000i | 1.12833i | 0.825662 | + | 0.564165i | \(0.190802\pi\) | ||||
−0.825662 | + | 0.564165i | \(0.809198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0000 | −1.32164 | −0.660819 | − | 0.750546i | \(-0.729791\pi\) | ||||
−0.660819 | + | 0.750546i | \(0.729791\pi\) | |||||||
\(230\) | 8.00000 | − | 16.0000i | 0.527504 | − | 1.05501i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000i | 0.196960i | ||||||||
\(233\) | − | 6.00000i | − | 0.393073i | −0.980497 | − | 0.196537i | \(-0.937031\pi\) | ||
0.980497 | − | 0.196537i | \(-0.0629694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | − | 4.00000i | −0.521862 | − | 0.260931i | ||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 3.00000i | − | 0.194461i | ||||||
\(239\) | −17.0000 | −1.09964 | −0.549819 | − | 0.835284i | \(-0.685303\pi\) | ||||
−0.549819 | + | 0.835284i | \(0.685303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0000 | −0.901819 | −0.450910 | − | 0.892570i | \(-0.648900\pi\) | ||||
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | − | 2.00000i | − | 0.128565i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.0000 | 0.960277 | ||||||||
\(245\) | −6.00000 | + | 12.0000i | −0.383326 | + | 0.766652i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7.00000i | 0.444500i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.00000 | + | 11.0000i | 0.126491 | + | 0.695701i | ||||
\(251\) | −20.0000 | −1.26239 | −0.631194 | − | 0.775625i | \(-0.717435\pi\) | ||||
−0.631194 | + | 0.775625i | \(0.717435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.0000i | 1.50887i | ||||||||
\(254\) | 16.0000 | 1.00393 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.00000i | 0.374270i | 0.982334 | + | 0.187135i | \(0.0599201\pi\) | ||||
−0.982334 | + | 0.187135i | \(0.940080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00000 | 0.0621370 | ||||||||
\(260\) | −8.00000 | − | 4.00000i | −0.496139 | − | 0.248069i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.0000i | 0.617802i | ||||||||
\(263\) | − | 31.0000i | − | 1.91154i | −0.294112 | − | 0.955771i | \(-0.595024\pi\) | ||
0.294112 | − | 0.955771i | \(-0.404976\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.0000 | + | 11.0000i | 1.35145 | + | 0.675725i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 4.00000i | − | 0.244339i | ||||||
\(269\) | −16.0000 | −0.975537 | −0.487769 | − | 0.872973i | \(-0.662189\pi\) | ||||
−0.487769 | + | 0.872973i | \(0.662189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.0000 | 1.33640 | 0.668202 | − | 0.743980i | \(-0.267064\pi\) | ||||
0.668202 | + | 0.743980i | \(0.267064\pi\) | |||||||
\(272\) | − | 3.00000i | − | 0.181902i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −9.00000 | − | 12.0000i | −0.542720 | − | 0.723627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | − | 1.00000i | − | 0.0599760i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | − | 2.00000i | 0.0597614 | − | 0.119523i | ||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8.00000i | − | 0.475551i | −0.971320 | − | 0.237775i | \(-0.923582\pi\) | ||
0.971320 | − | 0.237775i | \(-0.0764182\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.0000 | 0.709575 | ||||||||
\(287\) | 11.0000i | 0.649309i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 6.00000 | + | 3.00000i | 0.352332 | + | 0.176166i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 2.00000i | − | 0.117041i | ||||||
\(293\) | 15.0000i | 0.876309i | 0.898900 | + | 0.438155i | \(0.144368\pi\) | ||||
−0.898900 | + | 0.438155i | \(0.855632\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | − | 24.0000i | 0.698667 | − | 1.39733i | ||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 4.00000i | − | 0.231714i | ||||||
\(299\) | 32.0000 | 1.85061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0000 | 0.634029 | ||||||||
\(302\) | − | 14.0000i | − | 0.805609i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.0000 | − | 30.0000i | 0.858898 | − | 1.71780i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000i | 0.456584i | 0.973593 | + | 0.228292i | \(0.0733141\pi\) | ||||
−0.973593 | + | 0.228292i | \(0.926686\pi\) | |||||||
\(308\) | 3.00000i | 0.170941i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.0000 | + | 7.00000i | 0.795147 | + | 0.397573i | ||||
\(311\) | −3.00000 | −0.170114 | −0.0850572 | − | 0.996376i | \(-0.527107\pi\) | ||||
−0.0850572 | + | 0.996376i | \(0.527107\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 14.0000i | − | 0.791327i | −0.918396 | − | 0.395663i | \(-0.870515\pi\) | ||
0.918396 | − | 0.395663i | \(-0.129485\pi\) | |||||||
\(314\) | −5.00000 | −0.282166 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | − | 21.0000i | − | 1.17948i | −0.807594 | − | 0.589739i | \(-0.799231\pi\) | ||
0.807594 | − | 0.589739i | \(-0.200769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | −0.503903 | ||||||||
\(320\) | 1.00000 | − | 2.00000i | 0.0559017 | − | 0.111803i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.00000i | 0.445823i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0000 | + | 12.0000i | −0.887520 | + | 0.665640i | ||||
\(326\) | −3.00000 | −0.166155 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.0000i | 0.607373i | ||||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | 0.109930 | 0.0549650 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549650 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(332\) | 12.0000i | 0.658586i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.0000 | 0.766046 | ||||||||
\(335\) | −8.00000 | − | 4.00000i | −0.437087 | − | 0.218543i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.0000i | 1.52526i | 0.646837 | + | 0.762629i | \(0.276092\pi\) | ||||
−0.646837 | + | 0.762629i | \(0.723908\pi\) | |||||||
\(338\) | − | 3.00000i | − | 0.163178i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.00000 | − | 3.00000i | −0.325396 | − | 0.162698i | ||||
\(341\) | −21.0000 | −1.13721 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 13.0000i | − | 0.701934i | ||||||
\(344\) | 11.0000 | 0.593080 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.0000 | −0.698884 | ||||||||
\(347\) | 12.0000i | 0.644194i | 0.946707 | + | 0.322097i | \(0.104388\pi\) | ||||
−0.946707 | + | 0.322097i | \(0.895612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | −3.00000 | − | 4.00000i | −0.160357 | − | 0.213809i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00000i | 0.159901i | ||||||||
\(353\) | 3.00000i | 0.159674i | 0.996808 | + | 0.0798369i | \(0.0254400\pi\) | ||||
−0.996808 | + | 0.0798369i | \(0.974560\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | − | 12.0000i | 0.318447 | − | 0.636894i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.0000i | 0.528516i | ||||||||
\(359\) | −14.0000 | −0.738892 | −0.369446 | − | 0.929252i | \(-0.620452\pi\) | ||||
−0.369446 | + | 0.929252i | \(0.620452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | − | 16.0000i | − | 0.840941i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | −4.00000 | − | 2.00000i | −0.209370 | − | 0.104685i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.0000i | − | 0.678594i | −0.940679 | − | 0.339297i | \(-0.889811\pi\) | ||
0.940679 | − | 0.339297i | \(-0.110189\pi\) | |||||||
\(368\) | 8.00000i | 0.417029i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.00000 | − | 2.00000i | 0.0519875 | − | 0.103975i | ||||
\(371\) | −11.0000 | −0.571092 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 38.0000i | 1.96757i | 0.179364 | + | 0.983783i | \(0.442596\pi\) | ||||
−0.179364 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(374\) | 9.00000 | 0.465379 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00000 | 0.206284 | ||||||||
\(377\) | 12.0000i | 0.618031i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.0000i | 0.869796i | ||||||||
\(383\) | 16.0000i | 0.817562i | 0.912633 | + | 0.408781i | \(0.134046\pi\) | ||||
−0.912633 | + | 0.408781i | \(0.865954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 3.00000i | 0.305788 | + | 0.152894i | ||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1.00000i | − | 0.0507673i | ||||||
\(389\) | 23.0000 | 1.16615 | 0.583073 | − | 0.812420i | \(-0.301850\pi\) | ||||
0.583073 | + | 0.812420i | \(0.301850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | − | 6.00000i | − | 0.303046i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.00000 | −0.100759 | ||||||||
\(395\) | −8.00000 | + | 16.0000i | −0.402524 | + | 0.805047i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 14.0000i | − | 0.702640i | −0.936255 | − | 0.351320i | \(-0.885733\pi\) | ||
0.936255 | − | 0.351320i | \(-0.114267\pi\) | |||||||
\(398\) | − | 16.0000i | − | 0.802008i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.0000i | 1.39478i | ||||||||
\(404\) | 14.0000 | 0.696526 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00000 | −0.148888 | ||||||||
\(407\) | 3.00000i | 0.148704i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.00000 | 0.197787 | 0.0988936 | − | 0.995098i | \(-0.468470\pi\) | ||||
0.0988936 | + | 0.995098i | \(0.468470\pi\) | |||||||
\(410\) | 22.0000 | + | 11.0000i | 1.08650 | + | 0.543251i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0000i | 0.590481i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.0000 | + | 12.0000i | 1.17811 | + | 0.589057i | ||||
\(416\) | 4.00000 | 0.196116 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.0000 | −1.46211 | −0.731055 | − | 0.682318i | \(-0.760972\pi\) | ||||
−0.731055 | + | 0.682318i | \(0.760972\pi\) | |||||||
\(422\) | − | 1.00000i | − | 0.0486792i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.0000 | −0.534207 | ||||||||
\(425\) | −12.0000 | + | 9.00000i | −0.582086 | + | 0.436564i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.0000i | 0.725901i | ||||||||
\(428\) | 10.0000i | 0.483368i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.0000 | − | 22.0000i | 0.530467 | − | 1.06093i | ||||
\(431\) | −23.0000 | −1.10787 | −0.553936 | − | 0.832560i | \(-0.686875\pi\) | ||||
−0.553936 | + | 0.832560i | \(0.686875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 16.0000i | − | 0.768911i | −0.923144 | − | 0.384455i | \(-0.874389\pi\) | ||
0.923144 | − | 0.384455i | \(-0.125611\pi\) | |||||||
\(434\) | −7.00000 | −0.336011 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.0000 | −0.526804 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.00000 | −0.334092 | −0.167046 | − | 0.985949i | \(-0.553423\pi\) | ||||
−0.167046 | + | 0.985949i | \(0.553423\pi\) | |||||||
\(440\) | 6.00000 | + | 3.00000i | 0.286039 | + | 0.143019i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 12.0000i | − | 0.570782i | ||||||
\(443\) | − | 34.0000i | − | 1.61539i | −0.589601 | − | 0.807694i | \(-0.700715\pi\) | ||
0.589601 | − | 0.807694i | \(-0.299285\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.0000 | −0.520865 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | 36.0000 | 1.69895 | 0.849473 | − | 0.527633i | \(-0.176920\pi\) | ||||
0.849473 | + | 0.527633i | \(0.176920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.0000 | −1.55391 | ||||||||
\(452\) | − | 1.00000i | − | 0.0470360i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.0000 | −0.797850 | ||||||||
\(455\) | 4.00000 | − | 8.00000i | 0.187523 | − | 0.375046i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.0000i | 1.73079i | 0.501093 | + | 0.865393i | \(0.332931\pi\) | ||||
−0.501093 | + | 0.865393i | \(0.667069\pi\) | |||||||
\(458\) | − | 20.0000i | − | 0.934539i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.0000 | + | 8.00000i | 0.746004 | + | 0.373002i | ||||
\(461\) | −3.00000 | −0.139724 | −0.0698620 | − | 0.997557i | \(-0.522256\pi\) | ||||
−0.0698620 | + | 0.997557i | \(0.522256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.00000i | − | 0.185896i | −0.995671 | − | 0.0929479i | \(-0.970371\pi\) | ||
0.995671 | − | 0.0929479i | \(-0.0296290\pi\) | |||||||
\(464\) | −3.00000 | −0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | 3.00000i | 0.138823i | 0.997588 | + | 0.0694117i | \(0.0221122\pi\) | ||||
−0.997588 | + | 0.0694117i | \(0.977888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 4.00000 | − | 8.00000i | 0.184506 | − | 0.369012i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.0000i | 0.552345i | ||||||||
\(473\) | 33.0000i | 1.51734i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.00000 | 0.137505 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 17.0000i | − | 0.777562i | ||||||
\(479\) | −36.0000 | −1.64488 | −0.822441 | − | 0.568850i | \(-0.807388\pi\) | ||||
−0.822441 | + | 0.568850i | \(0.807388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | − | 14.0000i | − | 0.637683i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | −2.00000 | − | 1.00000i | −0.0908153 | − | 0.0454077i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 36.0000i | − | 1.63132i | −0.578535 | − | 0.815658i | \(-0.696375\pi\) | ||
0.578535 | − | 0.815658i | \(-0.303625\pi\) | |||||||
\(488\) | 15.0000i | 0.679018i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.0000 | − | 6.00000i | −0.542105 | − | 0.271052i | ||||
\(491\) | 36.0000 | 1.62466 | 0.812329 | − | 0.583200i | \(-0.198200\pi\) | ||||
0.812329 | + | 0.583200i | \(0.198200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000i | 0.405340i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.00000 | −0.314309 | ||||||||
\(497\) | 6.00000i | 0.269137i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0000 | 0.805791 | 0.402895 | − | 0.915246i | \(-0.368004\pi\) | ||||
0.402895 | + | 0.915246i | \(0.368004\pi\) | |||||||
\(500\) | −11.0000 | + | 2.00000i | −0.491935 | + | 0.0894427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 20.0000i | − | 0.892644i | ||||||
\(503\) | 26.0000i | 1.15928i | 0.814872 | + | 0.579641i | \(0.196807\pi\) | ||||
−0.814872 | + | 0.579641i | \(0.803193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0000 | − | 28.0000i | 0.622992 | − | 1.24598i | ||||
\(506\) | −24.0000 | −1.06693 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.0000i | 0.709885i | ||||||||
\(509\) | 30.0000 | 1.32973 | 0.664863 | − | 0.746965i | \(-0.268490\pi\) | ||||
0.664863 | + | 0.746965i | \(0.268490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.0000i | 0.527759i | ||||||||
\(518\) | 1.00000i | 0.0439375i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.00000 | − | 8.00000i | 0.175412 | − | 0.350823i | ||||
\(521\) | 7.00000 | 0.306676 | 0.153338 | − | 0.988174i | \(-0.450998\pi\) | ||||
0.153338 | + | 0.988174i | \(0.450998\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000i | 0.174908i | 0.996169 | + | 0.0874539i | \(0.0278730\pi\) | ||||
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(524\) | −10.0000 | −0.436852 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 31.0000 | 1.35166 | ||||||||
\(527\) | 21.0000i | 0.914774i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.0000 | −1.78261 | ||||||||
\(530\) | −11.0000 | + | 22.0000i | −0.477809 | + | 0.955619i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.0000i | 1.90585i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.0000 | + | 10.0000i | 0.864675 | + | 0.432338i | ||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 16.0000i | − | 0.689809i | ||||||
\(539\) | 18.0000 | 0.775315 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.0000 | 1.11783 | 0.558914 | − | 0.829226i | \(-0.311218\pi\) | ||||
0.558914 | + | 0.829226i | \(0.311218\pi\) | |||||||
\(542\) | 22.0000i | 0.944981i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.00000 | 0.128624 | ||||||||
\(545\) | −11.0000 | + | 22.0000i | −0.471188 | + | 0.942376i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 35.0000i | − | 1.49649i | −0.663421 | − | 0.748246i | \(-0.730896\pi\) | ||
0.663421 | − | 0.748246i | \(-0.269104\pi\) | |||||||
\(548\) | − | 6.00000i | − | 0.256307i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.0000 | − | 9.00000i | 0.511682 | − | 0.383761i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.00000i | − | 0.340195i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.00000 | 0.0424094 | ||||||||
\(557\) | − | 6.00000i | − | 0.254228i | −0.991888 | − | 0.127114i | \(-0.959429\pi\) | ||
0.991888 | − | 0.127114i | \(-0.0405714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.0000 | 1.86100 | ||||||||
\(560\) | 2.00000 | + | 1.00000i | 0.0845154 | + | 0.0422577i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 6.00000i | − | 0.253095i | ||||||
\(563\) | 19.0000i | 0.800755i | 0.916350 | + | 0.400377i | \(0.131121\pi\) | ||||
−0.916350 | + | 0.400377i | \(0.868879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | − | 1.00000i | −0.0841406 | − | 0.0420703i | ||||
\(566\) | 8.00000 | 0.336265 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | 14.0000 | 0.586911 | 0.293455 | − | 0.955973i | \(-0.405195\pi\) | ||||
0.293455 | + | 0.955973i | \(0.405195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | 12.0000i | 0.501745i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.0000 | −0.459131 | ||||||||
\(575\) | 32.0000 | − | 24.0000i | 1.33449 | − | 1.00087i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | 8.00000i | 0.332756i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.00000 | + | 6.00000i | −0.124568 | + | 0.249136i | ||||
\(581\) | −12.0000 | −0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 33.0000i | − | 1.36672i | ||||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.0000 | −0.619644 | ||||||||
\(587\) | 15.0000i | 0.619116i | 0.950881 | + | 0.309558i | \(0.100181\pi\) | ||||
−0.950881 | + | 0.309558i | \(0.899819\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 24.0000 | + | 12.0000i | 0.988064 | + | 0.494032i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | 36.0000i | 1.47834i | 0.673517 | + | 0.739171i | \(0.264783\pi\) | ||||
−0.673517 | + | 0.739171i | \(0.735217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.00000 | − | 6.00000i | 0.122988 | − | 0.245976i | ||||
\(596\) | 4.00000 | 0.163846 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.0000i | 1.30858i | ||||||||
\(599\) | −32.0000 | −1.30748 | −0.653742 | − | 0.756717i | \(-0.726802\pi\) | ||||
−0.653742 | + | 0.756717i | \(0.726802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.0000 | −1.91717 | −0.958585 | − | 0.284807i | \(-0.908071\pi\) | ||||
−0.958585 | + | 0.284807i | \(0.908071\pi\) | |||||||
\(602\) | 11.0000i | 0.448327i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.0000 | 0.569652 | ||||||||
\(605\) | 2.00000 | − | 4.00000i | 0.0813116 | − | 0.162623i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.0000i | 1.70473i | 0.522949 | + | 0.852364i | \(0.324832\pi\) | ||||
−0.522949 | + | 0.852364i | \(0.675168\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 30.0000 | + | 15.0000i | 1.21466 | + | 0.607332i | ||||
\(611\) | 16.0000 | 0.647291 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 15.0000i | − | 0.605844i | −0.953015 | − | 0.302922i | \(-0.902038\pi\) | ||
0.953015 | − | 0.302922i | \(-0.0979622\pi\) | |||||||
\(614\) | −8.00000 | −0.322854 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.00000 | −0.120873 | ||||||||
\(617\) | − | 42.0000i | − | 1.69086i | −0.534089 | − | 0.845428i | \(-0.679345\pi\) | ||
0.534089 | − | 0.845428i | \(-0.320655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.0000 | 1.40677 | 0.703384 | − | 0.710810i | \(-0.251671\pi\) | ||||
0.703384 | + | 0.710810i | \(0.251671\pi\) | |||||||
\(620\) | −7.00000 | + | 14.0000i | −0.281127 | + | 0.562254i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 3.00000i | − | 0.120289i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 14.0000 | 0.559553 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 5.00000i | − | 0.199522i | ||||||
\(629\) | 3.00000 | 0.119618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.0000 | 1.47295 | 0.736473 | − | 0.676467i | \(-0.236490\pi\) | ||||
0.736473 | + | 0.676467i | \(0.236490\pi\) | |||||||
\(632\) | − | 8.00000i | − | 0.318223i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.0000 | 0.834017 | ||||||||
\(635\) | 32.0000 | + | 16.0000i | 1.26988 | + | 0.634941i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 24.0000i | − | 0.950915i | ||||||
\(638\) | − | 9.00000i | − | 0.356313i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.00000 | + | 1.00000i | 0.0790569 | + | 0.0395285i | ||||
\(641\) | 25.0000 | 0.987441 | 0.493720 | − | 0.869621i | \(-0.335637\pi\) | ||||
0.493720 | + | 0.869621i | \(0.335637\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.00000i | 0.276053i | 0.990429 | + | 0.138027i | \(0.0440759\pi\) | ||||
−0.990429 | + | 0.138027i | \(0.955924\pi\) | |||||||
\(644\) | −8.00000 | −0.315244 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.00000i | 0.0786281i | 0.999227 | + | 0.0393141i | \(0.0125173\pi\) | ||||
−0.999227 | + | 0.0393141i | \(0.987483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.0000 | −1.41312 | ||||||||
\(650\) | −12.0000 | − | 16.0000i | −0.470679 | − | 0.627572i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 3.00000i | − | 0.117489i | ||||||
\(653\) | − | 38.0000i | − | 1.48705i | −0.668705 | − | 0.743527i | \(-0.733151\pi\) | ||
0.668705 | − | 0.743527i | \(-0.266849\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.0000 | + | 20.0000i | −0.390732 | + | 0.781465i | ||||
\(656\) | −11.0000 | −0.429478 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.00000i | 0.155936i | ||||||||
\(659\) | 48.0000 | 1.86981 | 0.934907 | − | 0.354892i | \(-0.115482\pi\) | ||||
0.934907 | + | 0.354892i | \(0.115482\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.0000 | −0.972387 | −0.486194 | − | 0.873851i | \(-0.661615\pi\) | ||||
−0.486194 | + | 0.873851i | \(0.661615\pi\) | |||||||
\(662\) | 2.00000i | 0.0777322i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 24.0000i | − | 0.929284i | ||||||
\(668\) | 14.0000i | 0.541676i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.00000 | − | 8.00000i | 0.154533 | − | 0.309067i | ||||
\(671\) | −45.0000 | −1.73721 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | −28.0000 | −1.07852 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | − | 42.0000i | − | 1.61419i | −0.590421 | − | 0.807096i | \(-0.701038\pi\) | ||
0.590421 | − | 0.807096i | \(-0.298962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.00000 | 0.0383765 | ||||||||
\(680\) | 3.00000 | − | 6.00000i | 0.115045 | − | 0.230089i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 21.0000i | − | 0.804132i | ||||||
\(683\) | − | 13.0000i | − | 0.497431i | −0.968577 | − | 0.248716i | \(-0.919992\pi\) | ||
0.968577 | − | 0.248716i | \(-0.0800084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | − | 6.00000i | −0.458496 | − | 0.229248i | ||||
\(686\) | 13.0000 | 0.496342 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.0000i | 0.419371i | ||||||||
\(689\) | −44.0000 | −1.67627 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.0000 | −1.55971 | −0.779857 | − | 0.625958i | \(-0.784708\pi\) | ||||
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | − | 13.0000i | − | 0.494186i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 1.00000 | − | 2.00000i | 0.0379322 | − | 0.0758643i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.0000i | 1.24996i | ||||||||
\(698\) | 6.00000i | 0.227103i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.00000 | − | 3.00000i | 0.151186 | − | 0.113389i | ||||
\(701\) | 22.0000 | 0.830929 | 0.415464 | − | 0.909610i | \(-0.363619\pi\) | ||||
0.415464 | + | 0.909610i | \(0.363619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −3.00000 | −0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.00000 | −0.112906 | ||||||||
\(707\) | 14.0000i | 0.526524i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.0000 | −1.08912 | −0.544559 | − | 0.838723i | \(-0.683303\pi\) | ||||
−0.544559 | + | 0.838723i | \(0.683303\pi\) | |||||||
\(710\) | 12.0000 | + | 6.00000i | 0.450352 | + | 0.225176i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 56.0000i | − | 2.09722i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | + | 12.0000i | 0.897549 | + | 0.448775i | ||||
\(716\) | −10.0000 | −0.373718 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 14.0000i | − | 0.522475i | ||||||
\(719\) | 20.0000 | 0.745874 | 0.372937 | − | 0.927857i | \(-0.378351\pi\) | ||||
0.372937 | + | 0.927857i | \(0.378351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 19.0000i | − | 0.707107i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.0000 | 0.594635 | ||||||||
\(725\) | 9.00000 | + | 12.0000i | 0.334252 | + | 0.445669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0000i | 0.519231i | 0.965712 | + | 0.259616i | \(0.0835959\pi\) | ||||
−0.965712 | + | 0.259616i | \(0.916404\pi\) | |||||||
\(728\) | 4.00000i | 0.148250i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.00000 | − | 4.00000i | 0.0740233 | − | 0.148047i | ||||
\(731\) | 33.0000 | 1.22055 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00000i | 0.0369358i | 0.999829 | + | 0.0184679i | \(0.00587886\pi\) | ||||
−0.999829 | + | 0.0184679i | \(0.994121\pi\) | |||||||
\(734\) | 13.0000 | 0.479839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.00000 | −0.294884 | ||||||||
\(737\) | 12.0000i | 0.442026i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.0000 | 0.551784 | 0.275892 | − | 0.961189i | \(-0.411027\pi\) | ||||
0.275892 | + | 0.961189i | \(0.411027\pi\) | |||||||
\(740\) | 2.00000 | + | 1.00000i | 0.0735215 | + | 0.0367607i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 11.0000i | − | 0.403823i | ||||||
\(743\) | 13.0000i | 0.476924i | 0.971152 | + | 0.238462i | \(0.0766432\pi\) | ||||
−0.971152 | + | 0.238462i | \(0.923357\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.00000 | − | 8.00000i | 0.146549 | − | 0.293097i | ||||
\(746\) | −38.0000 | −1.39128 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.00000i | 0.329073i | ||||||||
\(749\) | −10.0000 | −0.365392 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | 4.00000i | 0.145865i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.0000 | −0.437014 | ||||||||
\(755\) | 14.0000 | − | 28.0000i | 0.509512 | − | 1.01902i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.0000i | 1.01768i | 0.860862 | + | 0.508839i | \(0.169925\pi\) | ||||
−0.860862 | + | 0.508839i | \(0.830075\pi\) | |||||||
\(758\) | − | 12.0000i | − | 0.435860i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.00000 | −0.253750 | −0.126875 | − | 0.991919i | \(-0.540495\pi\) | ||||
−0.126875 | + | 0.991919i | \(0.540495\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 11.0000i | − | 0.398227i | ||||||
\(764\) | −17.0000 | −0.615038 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | 48.0000i | 1.73318i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.0000 | 1.58668 | 0.793340 | − | 0.608778i | \(-0.208340\pi\) | ||||
0.793340 | + | 0.608778i | \(0.208340\pi\) | |||||||
\(770\) | −3.00000 | + | 6.00000i | −0.108112 | + | 0.216225i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.0000i | 0.503871i | ||||||||
\(773\) | 51.0000i | 1.83434i | 0.398493 | + | 0.917171i | \(0.369533\pi\) | ||||
−0.398493 | + | 0.917171i | \(0.630467\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.0000 | + | 28.0000i | 0.754342 | + | 1.00579i | ||||
\(776\) | 1.00000 | 0.0358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.0000i | 0.824590i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | 24.0000i | 0.858238i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.00000 | 0.214286 | ||||||||
\(785\) | −10.0000 | − | 5.00000i | −0.356915 | − | 0.178458i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 22.0000i | − | 0.784215i | −0.919919 | − | 0.392108i | \(-0.871746\pi\) | ||
0.919919 | − | 0.392108i | \(-0.128254\pi\) | |||||||
\(788\) | − | 2.00000i | − | 0.0712470i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.0000 | − | 8.00000i | −0.569254 | − | 0.284627i | ||||
\(791\) | 1.00000 | 0.0355559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 60.0000i | 2.13066i | ||||||||
\(794\) | 14.0000 | 0.496841 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.0000 | 0.567105 | ||||||||
\(797\) | 12.0000i | 0.425062i | 0.977154 | + | 0.212531i | \(0.0681706\pi\) | ||||
−0.977154 | + | 0.212531i | \(0.931829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 4.00000 | − | 3.00000i | 0.141421 | − | 0.106066i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 10.0000i | − | 0.353112i | ||||||
\(803\) | 6.00000i | 0.211735i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | + | 16.0000i | −0.281963 | + | 0.563926i | ||||
\(806\) | −28.0000 | −0.986258 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.0000i | 0.492518i | ||||||||
\(809\) | −12.0000 | −0.421898 | −0.210949 | − | 0.977497i | \(-0.567655\pi\) | ||||
−0.210949 | + | 0.977497i | \(0.567655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | − | 3.00000i | − | 0.105279i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.00000 | −0.105150 | ||||||||
\(815\) | −6.00000 | − | 3.00000i | −0.210171 | − | 0.105085i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 4.00000i | 0.139857i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.0000 | + | 22.0000i | −0.384137 | + | 0.768273i | ||||
\(821\) | 14.0000 | 0.488603 | 0.244302 | − | 0.969699i | \(-0.421441\pi\) | ||||
0.244302 | + | 0.969699i | \(0.421441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.0000i | 1.39431i | 0.716919 | + | 0.697156i | \(0.245552\pi\) | ||||
−0.716919 | + | 0.697156i | \(0.754448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.0000 | −0.417533 | ||||||||
\(827\) | − | 3.00000i | − | 0.104320i | −0.998639 | − | 0.0521601i | \(-0.983389\pi\) | ||
0.998639 | − | 0.0521601i | \(-0.0166106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.0000 | 0.798823 | 0.399412 | − | 0.916772i | \(-0.369214\pi\) | ||||
0.399412 | + | 0.916772i | \(0.369214\pi\) | |||||||
\(830\) | −12.0000 | + | 24.0000i | −0.416526 | + | 0.833052i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.00000i | 0.138675i | ||||||||
\(833\) | − | 18.0000i | − | 0.623663i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.0000 | + | 14.0000i | 0.968980 | + | 0.484490i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.0000i | 0.690889i | ||||||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | − | 30.0000i | − | 1.03387i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.00000 | 0.0344214 | ||||||||
\(845\) | 3.00000 | − | 6.00000i | 0.103203 | − | 0.206406i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000i | 0.0687208i | ||||||||
\(848\) | − | 11.0000i | − | 0.377742i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.00000 | − | 12.0000i | −0.308697 | − | 0.411597i | ||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 30.0000i | − | 1.02718i | −0.858036 | − | 0.513590i | \(-0.828315\pi\) | ||
0.858036 | − | 0.513590i | \(-0.171685\pi\) | |||||||
\(854\) | −15.0000 | −0.513289 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.0000 | −0.341793 | ||||||||
\(857\) | − | 17.0000i | − | 0.580709i | −0.956919 | − | 0.290354i | \(-0.906227\pi\) | ||
0.956919 | − | 0.290354i | \(-0.0937732\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | 0.682391 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(860\) | 22.0000 | + | 11.0000i | 0.750194 | + | 0.375097i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 23.0000i | − | 0.783383i | ||||||
\(863\) | 39.0000i | 1.32758i | 0.747921 | + | 0.663788i | \(0.231052\pi\) | ||||
−0.747921 | + | 0.663788i | \(0.768948\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.0000 | − | 13.0000i | −0.884027 | − | 0.442013i | ||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 7.00000i | − | 0.237595i | ||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.0000 | 0.542139 | ||||||||
\(872\) | − | 11.0000i | − | 0.372507i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.00000 | − | 11.0000i | −0.0676123 | − | 0.371868i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.00000i | 0.0337676i | 0.999857 | + | 0.0168838i | \(0.00537454\pi\) | ||||
−0.999857 | + | 0.0168838i | \(0.994625\pi\) | |||||||
\(878\) | − | 7.00000i | − | 0.236239i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.00000 | + | 6.00000i | −0.101130 | + | 0.202260i | ||||
\(881\) | −39.0000 | −1.31394 | −0.656972 | − | 0.753915i | \(-0.728163\pi\) | ||||
−0.656972 | + | 0.753915i | \(0.728163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0000i | 0.975928i | 0.872864 | + | 0.487964i | \(0.162260\pi\) | ||||
−0.872864 | + | 0.487964i | \(0.837740\pi\) | |||||||
\(884\) | 12.0000 | 0.403604 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34.0000 | 1.14225 | ||||||||
\(887\) | 7.00000i | 0.235037i | 0.993071 | + | 0.117518i | \(0.0374939\pi\) | ||||
−0.993071 | + | 0.117518i | \(0.962506\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 11.0000i | − | 0.368307i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.0000 | + | 20.0000i | −0.334263 | + | 0.668526i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36.0000i | 1.20134i | ||||||||
\(899\) | 21.0000 | 0.700389 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.0000 | −1.09939 | ||||||||
\(902\) | − | 33.0000i | − | 1.09878i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.00000 | 0.0332595 | ||||||||
\(905\) | 16.0000 | − | 32.0000i | 0.531858 | − | 1.06372i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 28.0000i | − | 0.929725i | −0.885383 | − | 0.464862i | \(-0.846104\pi\) | ||
0.885383 | − | 0.464862i | \(-0.153896\pi\) | |||||||
\(908\) | − | 17.0000i | − | 0.564165i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.00000 | + | 4.00000i | 0.265197 | + | 0.132599i | ||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 36.0000i | − | 1.19143i | ||||||
\(914\) | −37.0000 | −1.22385 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.0000 | 0.660819 | ||||||||
\(917\) | − | 10.0000i | − | 0.330229i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | −8.00000 | + | 16.0000i | −0.263752 | + | 0.527504i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 3.00000i | − | 0.0987997i | ||||||
\(923\) | 24.0000i | 0.789970i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | − | 3.00000i | 0.131519 | − | 0.0986394i | ||||
\(926\) | 4.00000 | 0.131448 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 3.00000i | − | 0.0984798i | ||||||
\(929\) | −15.0000 | −0.492134 | −0.246067 | − | 0.969253i | \(-0.579138\pi\) | ||||
−0.246067 | + | 0.969253i | \(0.579138\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.00000i | 0.196537i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.00000 | −0.0981630 | ||||||||
\(935\) | 18.0000 | + | 9.00000i | 0.588663 | + | 0.294331i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28.0000i | − | 0.914720i | −0.889282 | − | 0.457360i | \(-0.848795\pi\) | ||
0.889282 | − | 0.457360i | \(-0.151205\pi\) | |||||||
\(938\) | 4.00000i | 0.130605i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.00000 | + | 4.00000i | 0.260931 | + | 0.130466i | ||||
\(941\) | −26.0000 | −0.847576 | −0.423788 | − | 0.905761i | \(-0.639300\pi\) | ||||
−0.423788 | + | 0.905761i | \(0.639300\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 88.0000i | − | 2.86567i | ||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.0000 | −1.07292 | ||||||||
\(947\) | 37.0000i | 1.20234i | 0.799122 | + | 0.601169i | \(0.205298\pi\) | ||||
−0.799122 | + | 0.601169i | \(0.794702\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00000 | 0.259691 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.00000i | 0.0972306i | ||||||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.0000 | + | 34.0000i | −0.550107 | + | 1.10021i | ||||
\(956\) | 17.0000 | 0.549819 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 36.0000i | − | 1.16311i | ||||||
\(959\) | 6.00000 | 0.193750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 4.00000i | 0.128965i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.0000 | 0.450910 | ||||||||
\(965\) | 28.0000 | + | 14.0000i | 0.901352 | + | 0.450676i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.0000i | 1.09337i | 0.837340 | + | 0.546683i | \(0.184110\pi\) | ||||
−0.837340 | + | 0.546683i | \(0.815890\pi\) | |||||||
\(968\) | 2.00000i | 0.0642824i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.00000 | − | 2.00000i | 0.0321081 | − | 0.0642161i | ||||
\(971\) | 1.00000 | 0.0320915 | 0.0160458 | − | 0.999871i | \(-0.494892\pi\) | ||||
0.0160458 | + | 0.999871i | \(0.494892\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.00000i | 0.0320585i | ||||||||
\(974\) | 36.0000 | 1.15351 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.0000 | −0.480138 | ||||||||
\(977\) | 33.0000i | 1.05576i | 0.849318 | + | 0.527882i | \(0.177014\pi\) | ||||
−0.849318 | + | 0.527882i | \(0.822986\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.00000 | − | 12.0000i | 0.191663 | − | 0.383326i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.0000i | 1.14881i | ||||||||
\(983\) | 11.0000i | 0.350846i | 0.984493 | + | 0.175423i | \(0.0561292\pi\) | ||||
−0.984493 | + | 0.175423i | \(0.943871\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.00000 | − | 2.00000i | −0.127451 | − | 0.0637253i | ||||
\(986\) | −9.00000 | −0.286618 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −88.0000 | −2.79824 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.0000 | −1.42947 | −0.714736 | − | 0.699394i | \(-0.753453\pi\) | ||||
−0.714736 | + | 0.699394i | \(0.753453\pi\) | |||||||
\(992\) | − | 7.00000i | − | 0.222250i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.00000 | −0.190308 | ||||||||
\(995\) | 16.0000 | − | 32.0000i | 0.507234 | − | 1.01447i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.0000i | 1.39349i | 0.717317 | + | 0.696747i | \(0.245370\pi\) | ||||
−0.717317 | + | 0.696747i | \(0.754630\pi\) | |||||||
\(998\) | 18.0000i | 0.569780i | ||||||||
\(999\) | 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 | 3330.2.d.c.1999.2 | 2 | ||
3.2 | odd | 2 | 370.2.b.b.149.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 3330.2.d.c.1999.1 | 2 | ||
15.2 | even | 4 | 1850.2.a.l.1.1 | 1 | |||
15.8 | even | 4 | 1850.2.a.d.1.1 | 1 | |||
15.14 | odd | 2 | 370.2.b.b.149.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.b.b.149.1 | ✓ | 2 | 3.2 | odd | 2 | ||
370.2.b.b.149.2 | yes | 2 | 15.14 | odd | 2 | ||
1850.2.a.d.1.1 | 1 | 15.8 | even | 4 | |||
1850.2.a.l.1.1 | 1 | 15.2 | even | 4 | |||
3330.2.d.c.1999.1 | 2 | 5.4 | even | 2 | inner | ||
3330.2.d.c.1999.2 | 2 | 1.1 | even | 1 | trivial |