Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(539,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.539");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.m (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: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 539.25 | ||
Character | \(\chi\) | \(=\) | 1080.539 |
Dual form | 1080.2.m.c.539.27 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.341092 | − | 1.37246i | 0.241188 | − | 0.970478i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.76731 | − | 0.936273i | −0.883656 | − | 0.468136i | ||||
\(5\) | −2.13531 | + | 0.663669i | −0.954939 | + | 0.296802i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.39866 | −1.66254 | −0.831269 | − | 0.555871i | \(-0.812385\pi\) | ||||
−0.831269 | + | 0.555871i | \(0.812385\pi\) | |||||||
\(8\) | −1.88782 | + | 2.10622i | −0.667444 | + | 0.744660i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.182525 | + | 3.15701i | 0.0577195 | + | 0.998333i | ||||
\(11\) | − | 0.633050i | − | 0.190872i | −0.995436 | − | 0.0954359i | \(-0.969576\pi\) | ||
0.995436 | − | 0.0954359i | \(-0.0304245\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.40649 | 0.944790 | 0.472395 | − | 0.881387i | \(-0.343390\pi\) | ||||
0.472395 | + | 0.881387i | \(0.343390\pi\) | |||||||
\(14\) | −1.50035 | + | 6.03700i | −0.400985 | + | 1.61346i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.24679 | + | 3.30937i | 0.561697 | + | 0.827343i | ||||
\(17\) | 5.48913 | 1.33131 | 0.665655 | − | 0.746260i | \(-0.268152\pi\) | ||||
0.665655 | + | 0.746260i | \(0.268152\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.323423 | 0.0741984 | 0.0370992 | − | 0.999312i | \(-0.488188\pi\) | ||||
0.0370992 | + | 0.999312i | \(0.488188\pi\) | |||||||
\(20\) | 4.39513 | + | 0.826320i | 0.982782 | + | 0.184771i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.868838 | − | 0.215928i | −0.185237 | − | 0.0460361i | ||||
\(23\) | 6.26839i | 1.30705i | 0.756905 | + | 0.653525i | \(0.226710\pi\) | ||||
−0.756905 | + | 0.653525i | \(0.773290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.11909 | − | 2.83428i | 0.823817 | − | 0.566856i | ||||
\(26\) | 1.16193 | − | 4.67528i | 0.227873 | − | 0.916899i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.77381 | + | 4.11835i | 1.46911 | + | 0.778294i | ||||
\(29\) | −3.77896 | −0.701736 | −0.350868 | − | 0.936425i | \(-0.614113\pi\) | ||||
−0.350868 | + | 0.936425i | \(0.614113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.86723i | − | 1.41300i | −0.707715 | − | 0.706498i | \(-0.750274\pi\) | ||
0.707715 | − | 0.706498i | \(-0.249726\pi\) | |||||||
\(32\) | 5.30835 | − | 1.95483i | 0.938393 | − | 0.345569i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.87230 | − | 7.53363i | 0.321097 | − | 1.29201i | ||||
\(35\) | 9.39250 | − | 2.91926i | 1.58762 | − | 0.493444i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.90433 | 0.970666 | 0.485333 | − | 0.874329i | \(-0.338698\pi\) | ||||
0.485333 | + | 0.874329i | \(0.338698\pi\) | |||||||
\(38\) | 0.110317 | − | 0.443887i | 0.0178958 | − | 0.0720079i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.63324 | − | 5.75031i | 0.416352 | − | 0.909204i | ||||
\(41\) | 0.877482i | 0.137040i | 0.997650 | + | 0.0685198i | \(0.0218276\pi\) | ||||
−0.997650 | + | 0.0685198i | \(0.978172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.31397i | − | 0.352878i | −0.984312 | − | 0.176439i | \(-0.943542\pi\) | ||
0.984312 | − | 0.176439i | \(-0.0564578\pi\) | |||||||
\(44\) | −0.592707 | + | 1.11880i | −0.0893540 | + | 0.168665i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.60314 | + | 2.13810i | 1.26846 | + | 0.315245i | ||||
\(47\) | 8.67090i | 1.26478i | 0.774650 | + | 0.632391i | \(0.217926\pi\) | ||||
−0.774650 | + | 0.632391i | \(0.782074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.3482 | 1.76403 | ||||||||
\(50\) | −2.48496 | − | 6.62005i | −0.351426 | − | 0.936216i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.02033 | − | 3.18940i | −0.834870 | − | 0.442291i | ||||
\(53\) | 7.09416i | 0.974457i | 0.873274 | + | 0.487229i | \(0.161992\pi\) | ||||
−0.873274 | + | 0.487229i | \(0.838008\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.420136 | + | 1.35176i | 0.0566511 | + | 0.182271i | ||||
\(56\) | 8.30386 | − | 9.26454i | 1.10965 | − | 1.23803i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.28897 | + | 5.18649i | −0.169251 | + | 0.681019i | ||||
\(59\) | 10.5321i | 1.37117i | 0.727993 | + | 0.685584i | \(0.240453\pi\) | ||||
−0.727993 | + | 0.685584i | \(0.759547\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 14.0673i | − | 1.80113i | −0.434717 | − | 0.900567i | \(-0.643152\pi\) | ||
0.434717 | − | 0.900567i | \(-0.356848\pi\) | |||||||
\(62\) | −10.7975 | − | 2.68345i | −1.37128 | − | 0.340798i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.872299 | − | 7.95230i | −0.109037 | − | 0.994038i | ||||
\(65\) | −7.27391 | + | 2.26078i | −0.902217 | + | 0.280416i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.99382i | 0.732262i | 0.930563 | + | 0.366131i | \(0.119318\pi\) | ||||
−0.930563 | + | 0.366131i | \(0.880682\pi\) | |||||||
\(68\) | −9.70101 | − | 5.13933i | −1.17642 | − | 0.623235i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.802867 | − | 13.8866i | −0.0959609 | − | 1.65977i | ||||
\(71\) | 10.7806 | 1.27942 | 0.639710 | − | 0.768617i | \(-0.279055\pi\) | ||||
0.639710 | + | 0.768617i | \(0.279055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.9654i | 1.63453i | 0.576264 | + | 0.817264i | \(0.304510\pi\) | ||||
−0.576264 | + | 0.817264i | \(0.695490\pi\) | |||||||
\(74\) | 2.01392 | − | 8.10348i | 0.234113 | − | 0.942010i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.571590 | − | 0.302812i | −0.0655659 | − | 0.0347350i | ||||
\(77\) | 2.78457i | 0.317331i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.33728i | 0.825508i | 0.910843 | + | 0.412754i | \(0.135433\pi\) | ||||
−0.910843 | + | 0.412754i | \(0.864567\pi\) | |||||||
\(80\) | −6.99391 | − | 5.57541i | −0.781943 | − | 0.623350i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.20431 | + | 0.299302i | 0.132994 | + | 0.0330524i | ||||
\(83\) | 1.90716 | 0.209338 | 0.104669 | − | 0.994507i | \(-0.466622\pi\) | ||||
0.104669 | + | 0.994507i | \(0.466622\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.7210 | + | 3.64297i | −1.27132 | + | 0.395135i | ||||
\(86\) | −3.17585 | − | 0.789278i | −0.342460 | − | 0.0851101i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.33334 | + | 1.19508i | 0.142135 | + | 0.127396i | ||||
\(89\) | 8.16899i | 0.865911i | 0.901415 | + | 0.432956i | \(0.142529\pi\) | ||||
−0.901415 | + | 0.432956i | \(0.857471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.9840 | −1.57075 | ||||||||
\(92\) | 5.86892 | − | 11.0782i | 0.611877 | − | 1.15498i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.9005 | + | 2.95758i | 1.22744 | + | 0.305051i | ||||
\(95\) | −0.690609 | + | 0.214646i | −0.0708549 | + | 0.0220222i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.27222i | 0.636847i | 0.947949 | + | 0.318424i | \(0.103153\pi\) | ||||
−0.947949 | + | 0.318424i | \(0.896847\pi\) | |||||||
\(98\) | 4.21188 | − | 16.9475i | 0.425464 | − | 1.71195i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.93337 | + | 1.15247i | −0.993337 | + | 0.115247i | ||||
\(101\) | −0.535487 | −0.0532830 | −0.0266415 | − | 0.999645i | \(-0.508481\pi\) | ||||
−0.0266415 | + | 0.999645i | \(0.508481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.5566 | 1.23724 | 0.618621 | − | 0.785689i | \(-0.287692\pi\) | ||||
0.618621 | + | 0.785689i | \(0.287692\pi\) | |||||||
\(104\) | −6.43083 | + | 7.17481i | −0.630595 | + | 0.703548i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.73647 | + | 2.41976i | 0.945690 | + | 0.235028i | ||||
\(107\) | −13.4267 | −1.29801 | −0.649003 | − | 0.760786i | \(-0.724814\pi\) | ||||
−0.649003 | + | 0.760786i | \(0.724814\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.43706i | − | 0.137646i | −0.997629 | − | 0.0688228i | \(-0.978076\pi\) | ||
0.997629 | − | 0.0688228i | \(-0.0219243\pi\) | |||||||
\(110\) | 1.99854 | − | 0.115548i | 0.190554 | − | 0.0110170i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.88286 | − | 14.5568i | −0.933842 | − | 1.37549i | ||||
\(113\) | 6.45479 | 0.607216 | 0.303608 | − | 0.952797i | \(-0.401809\pi\) | ||||
0.303608 | + | 0.952797i | \(0.401809\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.16014 | − | 13.3849i | −0.387935 | − | 1.24815i | ||||
\(116\) | 6.67861 | + | 3.53814i | 0.620093 | + | 0.328508i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.4550 | + | 3.59243i | 1.33069 | + | 0.330710i | ||||
\(119\) | −24.1448 | −2.21335 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5992 | 0.963568 | ||||||||
\(122\) | −19.3069 | − | 4.79825i | −1.74796 | − | 0.434413i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.36587 | + | 13.9039i | −0.661475 | + | 1.24860i | ||||
\(125\) | −6.91450 | + | 8.78577i | −0.618451 | + | 0.785823i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.8023 | 0.958550 | 0.479275 | − | 0.877665i | \(-0.340900\pi\) | ||||
0.479275 | + | 0.877665i | \(0.340900\pi\) | |||||||
\(128\) | −11.2118 | − | 1.51527i | −0.990991 | − | 0.133932i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.621770 | + | 10.7543i | 0.0545329 | + | 0.943215i | ||||
\(131\) | − | 18.2846i | − | 1.59754i | −0.601639 | − | 0.798768i | \(-0.705485\pi\) | ||
0.601639 | − | 0.798768i | \(-0.294515\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.42263 | −0.123358 | ||||||||
\(134\) | 8.22630 | + | 2.04444i | 0.710644 | + | 0.176613i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.3625 | + | 11.5613i | −0.888575 | + | 0.991374i | ||||
\(137\) | 14.9351 | 1.27599 | 0.637997 | − | 0.770039i | \(-0.279763\pi\) | ||||
0.637997 | + | 0.770039i | \(0.279763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0327 | −1.35988 | −0.679939 | − | 0.733269i | \(-0.737994\pi\) | ||||
−0.679939 | + | 0.733269i | \(0.737994\pi\) | |||||||
\(140\) | −19.3327 | − | 3.63470i | −1.63391 | − | 0.307188i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.67717 | − | 14.7960i | 0.308581 | − | 1.24165i | ||||
\(143\) | − | 2.15648i | − | 0.180334i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.06925 | − | 2.50798i | 0.670115 | − | 0.208276i | ||||
\(146\) | 19.1670 | + | 4.76349i | 1.58627 | + | 0.394229i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.4348 | − | 5.52806i | −0.857735 | − | 0.454404i | ||||
\(149\) | 11.4476 | 0.937820 | 0.468910 | − | 0.883246i | \(-0.344647\pi\) | ||||
0.468910 | + | 0.883246i | \(0.344647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0407i | 0.979859i | 0.871762 | + | 0.489930i | \(0.162977\pi\) | ||||
−0.871762 | + | 0.489930i | \(0.837023\pi\) | |||||||
\(152\) | −0.610564 | + | 0.681200i | −0.0495233 | + | 0.0552526i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.82172 | + | 0.949795i | 0.307963 | + | 0.0765367i | ||||
\(155\) | 5.22124 | + | 16.7990i | 0.419380 | + | 1.34933i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.16913 | −0.332732 | −0.166366 | − | 0.986064i | \(-0.553203\pi\) | ||||
−0.166366 | + | 0.986064i | \(0.553203\pi\) | |||||||
\(158\) | 10.0701 | + | 2.50269i | 0.801138 | + | 0.199103i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.0376 | + | 7.69716i | −0.793543 | + | 0.608514i | ||||
\(161\) | − | 27.5725i | − | 2.17302i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.77553i | − | 0.139070i | −0.997580 | − | 0.0695350i | \(-0.977848\pi\) | ||
0.997580 | − | 0.0695350i | \(-0.0221516\pi\) | |||||||
\(164\) | 0.821563 | − | 1.55079i | 0.0641533 | − | 0.121096i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.650516 | − | 2.61750i | 0.0504898 | − | 0.203158i | ||||
\(167\) | 2.93164i | 0.226857i | 0.993546 | + | 0.113429i | \(0.0361833\pi\) | ||||
−0.993546 | + | 0.113429i | \(0.963817\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.39582 | −0.107371 | ||||||||
\(170\) | 1.00191 | + | 17.3292i | 0.0768426 | + | 1.32909i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.16651 | + | 4.08952i | −0.165195 | + | 0.311823i | ||||
\(173\) | − | 5.27138i | − | 0.400775i | −0.979717 | − | 0.200388i | \(-0.935780\pi\) | ||
0.979717 | − | 0.200388i | \(-0.0642202\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.1185 | + | 12.4670i | −1.36963 | + | 0.942419i | ||||
\(176\) | 2.09500 | − | 1.42233i | 0.157916 | − | 0.107212i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.2116 | + | 2.78638i | 0.840348 | + | 0.208848i | ||||
\(179\) | − | 11.6443i | − | 0.870340i | −0.900348 | − | 0.435170i | \(-0.856688\pi\) | ||
0.900348 | − | 0.435170i | \(-0.143312\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.6718i | 1.01622i | 0.861293 | + | 0.508109i | \(0.169655\pi\) | ||||
−0.861293 | + | 0.508109i | \(0.830345\pi\) | |||||||
\(182\) | −5.11092 | + | 20.5650i | −0.378847 | + | 1.52438i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.2026 | − | 11.8336i | −0.973308 | − | 0.872382i | ||||
\(185\) | −12.6076 | + | 3.91852i | −0.926927 | + | 0.288095i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.47489i | − | 0.254109i | ||||||
\(188\) | 8.11833 | − | 15.3242i | 0.592090 | − | 1.11763i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0590329 | + | 1.02105i | 0.00428270 | + | 0.0740747i | ||||
\(191\) | −6.04522 | −0.437417 | −0.218709 | − | 0.975790i | \(-0.570184\pi\) | ||||
−0.218709 | + | 0.975790i | \(0.570184\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 25.9530i | − | 1.86814i | −0.357088 | − | 0.934071i | \(-0.616230\pi\) | ||
0.357088 | − | 0.934071i | \(-0.383770\pi\) | |||||||
\(194\) | 8.60839 | + | 2.13940i | 0.618046 | + | 0.153600i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.8232 | − | 11.5613i | −1.55880 | − | 0.825807i | ||||
\(197\) | 10.4843i | 0.746973i | 0.927636 | + | 0.373487i | \(0.121838\pi\) | ||||
−0.927636 | + | 0.373487i | \(0.878162\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.19670i | − | 0.226608i | −0.993560 | − | 0.113304i | \(-0.963857\pi\) | ||
0.993560 | − | 0.113304i | \(-0.0361434\pi\) | |||||||
\(200\) | −1.80647 | + | 14.0263i | −0.127737 | + | 0.991808i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.182650 | + | 0.734937i | −0.0128512 | + | 0.0517100i | ||||
\(203\) | 16.6224 | 1.16666 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.582358 | − | 1.87370i | −0.0406736 | − | 0.130865i | ||||
\(206\) | 4.28297 | − | 17.2335i | 0.298409 | − | 1.20072i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.65366 | + | 11.2733i | 0.530686 | + | 0.781666i | ||||
\(209\) | − | 0.204743i | − | 0.0141624i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.2016 | −1.18421 | −0.592105 | − | 0.805861i | \(-0.701703\pi\) | ||||
−0.592105 | + | 0.805861i | \(0.701703\pi\) | |||||||
\(212\) | 6.64207 | − | 12.5376i | 0.456179 | − | 0.861085i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.57973 | + | 18.4276i | −0.313064 | + | 1.25969i | ||||
\(215\) | 1.53571 | + | 4.94105i | 0.104735 | + | 0.336977i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 34.6053i | 2.34916i | ||||||||
\(218\) | −1.97231 | − | 0.490170i | −0.133582 | − | 0.0331985i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.523102 | − | 2.78234i | 0.0352675 | − | 0.187585i | ||||
\(221\) | 18.6987 | 1.25781 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8087 | −0.790766 | −0.395383 | − | 0.918516i | \(-0.629388\pi\) | ||||
−0.395383 | + | 0.918516i | \(0.629388\pi\) | |||||||
\(224\) | −23.3497 | + | 8.59865i | −1.56011 | + | 0.574521i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.20168 | − | 8.85897i | 0.146453 | − | 0.589290i | ||||
\(227\) | −4.14942 | −0.275407 | −0.137703 | − | 0.990474i | \(-0.543972\pi\) | ||||
−0.137703 | + | 0.990474i | \(0.543972\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.7520i | − | 1.17308i | −0.809919 | − | 0.586542i | \(-0.800489\pi\) | ||
0.809919 | − | 0.586542i | \(-0.199511\pi\) | |||||||
\(230\) | −19.7893 | + | 1.14414i | −1.30487 | + | 0.0754423i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.13399 | − | 7.95931i | 0.468369 | − | 0.522555i | ||||
\(233\) | −7.55127 | −0.494700 | −0.247350 | − | 0.968926i | \(-0.579560\pi\) | ||||
−0.247350 | + | 0.968926i | \(0.579560\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.75461 | − | 18.5151i | −0.375389 | − | 1.20779i | ||||
\(236\) | 9.86096 | − | 18.6136i | 0.641894 | − | 1.21164i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.23561 | + | 33.1379i | −0.533835 | + | 2.14801i | ||||
\(239\) | −1.11479 | −0.0721100 | −0.0360550 | − | 0.999350i | \(-0.511479\pi\) | ||||
−0.0360550 | + | 0.999350i | \(0.511479\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.4788 | 1.51240 | 0.756201 | − | 0.654339i | \(-0.227053\pi\) | ||||
0.756201 | + | 0.654339i | \(0.227053\pi\) | |||||||
\(242\) | 3.61532 | − | 14.5471i | 0.232401 | − | 0.935122i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.1708 | + | 24.8613i | −0.843176 | + | 1.59158i | ||||
\(245\) | −26.3673 | + | 8.19514i | −1.68454 | + | 0.523568i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.10174 | 0.0701019 | ||||||||
\(248\) | 16.5701 | + | 14.8519i | 1.05220 | + | 0.943096i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.69967 | + | 12.4867i | 0.613461 | + | 0.789725i | ||||
\(251\) | 19.8709i | 1.25424i | 0.778923 | + | 0.627119i | \(0.215766\pi\) | ||||
−0.778923 | + | 0.627119i | \(0.784234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.96820 | 0.249479 | ||||||||
\(254\) | 3.68458 | − | 14.8258i | 0.231191 | − | 0.930252i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.90390 | + | 14.8709i | −0.368994 | + | 0.929432i | ||||
\(257\) | 16.1801 | 1.00929 | 0.504643 | − | 0.863328i | \(-0.331624\pi\) | ||||
0.504643 | + | 0.863328i | \(0.331624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.9711 | −1.61377 | ||||||||
\(260\) | 14.9720 | + | 2.81485i | 0.928523 | + | 0.174570i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −25.0950 | − | 6.23674i | −1.55037 | − | 0.385307i | ||||
\(263\) | − | 12.5368i | − | 0.773051i | −0.922279 | − | 0.386525i | \(-0.873675\pi\) | ||
0.922279 | − | 0.386525i | \(-0.126325\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.70817 | − | 15.1482i | −0.289221 | − | 0.930548i | ||||
\(266\) | −0.485248 | + | 1.95251i | −0.0297524 | + | 0.119716i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.61185 | − | 10.5930i | 0.342798 | − | 0.647068i | ||||
\(269\) | 23.1238 | 1.40988 | 0.704941 | − | 0.709266i | \(-0.250973\pi\) | ||||
0.704941 | + | 0.709266i | \(0.250973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1608i | 0.617224i | 0.951188 | + | 0.308612i | \(0.0998645\pi\) | ||||
−0.951188 | + | 0.308612i | \(0.900136\pi\) | |||||||
\(272\) | 12.3329 | + | 18.1656i | 0.747793 | + | 1.10145i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.09425 | − | 20.4979i | 0.307755 | − | 1.23832i | ||||
\(275\) | −1.79424 | − | 2.60759i | −0.108197 | − | 0.157243i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.64642 | 0.339260 | 0.169630 | − | 0.985508i | \(-0.445743\pi\) | ||||
0.169630 | + | 0.985508i | \(0.445743\pi\) | |||||||
\(278\) | −5.46863 | + | 22.0043i | −0.327987 | + | 1.31973i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.5827 | + | 25.2937i | −0.692200 | + | 1.51159i | ||||
\(281\) | 29.4258i | 1.75540i | 0.479212 | + | 0.877699i | \(0.340923\pi\) | ||||
−0.479212 | + | 0.877699i | \(0.659077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.34373i | 0.139320i | 0.997571 | + | 0.0696602i | \(0.0221915\pi\) | ||||
−0.997571 | + | 0.0696602i | \(0.977809\pi\) | |||||||
\(284\) | −19.0527 | − | 10.0936i | −1.13057 | − | 0.598943i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.95969 | − | 0.735558i | −0.175010 | − | 0.0434944i | ||||
\(287\) | − | 3.85975i | − | 0.227834i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.1306 | 0.772387 | ||||||||
\(290\) | −0.689756 | − | 11.9302i | −0.0405039 | − | 0.700566i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.0754 | − | 24.6812i | 0.765182 | − | 1.44436i | ||||
\(293\) | 23.4485i | 1.36987i | 0.728603 | + | 0.684937i | \(0.240170\pi\) | ||||
−0.728603 | + | 0.684937i | \(0.759830\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.98986 | − | 22.4894i | −0.406965 | − | 1.30938i | ||||
\(296\) | −11.1463 | + | 12.4358i | −0.647865 | + | 0.722816i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.90467 | − | 15.7113i | 0.226191 | − | 0.910134i | ||||
\(299\) | 21.3532i | 1.23489i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.1784i | 0.586673i | ||||||||
\(302\) | 16.5254 | + | 4.10699i | 0.950932 | + | 0.236331i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.726663 | + | 1.07033i | 0.0416770 | + | 0.0613875i | ||||
\(305\) | 9.33604 | + | 30.0380i | 0.534580 | + | 1.71997i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.32995i | 0.0759041i | 0.999280 | + | 0.0379520i | \(0.0120834\pi\) | ||||
−0.999280 | + | 0.0379520i | \(0.987917\pi\) | |||||||
\(308\) | 2.60712 | − | 4.92121i | 0.148554 | − | 0.280412i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 24.8369 | − | 1.43597i | 1.41064 | − | 0.0815575i | ||||
\(311\) | 32.6861 | 1.85346 | 0.926729 | − | 0.375732i | \(-0.122609\pi\) | ||||
0.926729 | + | 0.375732i | \(0.122609\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.29685i | 0.468966i | 0.972120 | + | 0.234483i | \(0.0753397\pi\) | ||||
−0.972120 | + | 0.234483i | \(0.924660\pi\) | |||||||
\(314\) | −1.42206 | + | 5.72197i | −0.0802512 | + | 0.322910i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.86969 | − | 12.9673i | 0.386450 | − | 0.729465i | ||||
\(317\) | − | 29.8855i | − | 1.67854i | −0.543718 | − | 0.839268i | \(-0.682984\pi\) | ||
0.543718 | − | 0.839268i | \(-0.317016\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.39227i | 0.133941i | ||||||||
\(320\) | 7.14033 | + | 16.4017i | 0.399156 | + | 0.916883i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −37.8423 | − | 9.40477i | −2.10887 | − | 0.524107i | ||||
\(323\) | 1.77531 | 0.0987811 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0316 | − | 9.65494i | 0.778335 | − | 0.535560i | ||||
\(326\) | −2.43685 | − | 0.605618i | −0.134964 | − | 0.0335421i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.84817 | − | 1.65653i | −0.102048 | − | 0.0914663i | ||||
\(329\) | − | 38.1404i | − | 2.10275i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6308 | 0.639289 | 0.319645 | − | 0.947538i | \(-0.396437\pi\) | ||||
0.319645 | + | 0.947538i | \(0.396437\pi\) | |||||||
\(332\) | −3.37054 | − | 1.78562i | −0.184982 | − | 0.0979985i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.02357 | + | 0.999960i | 0.220160 | + | 0.0547154i | ||||
\(335\) | −3.97791 | − | 12.7987i | −0.217337 | − | 0.699265i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.39265i | − | 0.457177i | −0.973523 | − | 0.228588i | \(-0.926589\pi\) | ||
0.973523 | − | 0.228588i | \(-0.0734110\pi\) | |||||||
\(338\) | −0.476104 | + | 1.91571i | −0.0258966 | + | 0.104201i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 24.1255 | + | 4.53578i | 1.30839 | + | 0.245987i | ||||
\(341\) | −4.98035 | −0.269701 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −23.5250 | −1.27023 | ||||||||
\(344\) | 4.87373 | + | 4.36836i | 0.262774 | + | 0.235526i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.23477 | − | 1.79802i | −0.388944 | − | 0.0966624i | ||||
\(347\) | −14.3801 | −0.771965 | −0.385982 | − | 0.922506i | \(-0.626137\pi\) | ||||
−0.385982 | + | 0.922506i | \(0.626137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.6982i | 1.80382i | 0.431920 | + | 0.901912i | \(0.357836\pi\) | ||||
−0.431920 | + | 0.901912i | \(0.642164\pi\) | |||||||
\(350\) | 10.9305 | + | 29.1193i | 0.584259 | + | 1.55649i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.23751 | − | 3.36045i | −0.0659593 | − | 0.179113i | ||||
\(353\) | −26.3609 | −1.40305 | −0.701525 | − | 0.712645i | \(-0.747497\pi\) | ||||
−0.701525 | + | 0.712645i | \(0.747497\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.0199 | + | 7.15474i | −1.22177 | + | 0.379734i | ||||
\(356\) | 7.64840 | − | 14.4372i | 0.405365 | − | 0.765168i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.9814 | − | 3.97179i | −0.844646 | − | 0.209916i | ||||
\(359\) | −28.3508 | −1.49630 | −0.748149 | − | 0.663531i | \(-0.769057\pi\) | ||||
−0.748149 | + | 0.663531i | \(0.769057\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8954 | −0.994495 | ||||||||
\(362\) | 18.7641 | + | 4.66335i | 0.986218 | + | 0.245100i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 26.4814 | + | 14.0291i | 1.38800 | + | 0.735325i | ||||
\(365\) | −9.26841 | − | 29.8205i | −0.485131 | − | 1.56087i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2123 | 0.950675 | 0.475337 | − | 0.879804i | \(-0.342326\pi\) | ||||
0.475337 | + | 0.879804i | \(0.342326\pi\) | |||||||
\(368\) | −20.7444 | + | 14.0837i | −1.08138 | + | 0.734165i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.07769 | + | 18.6400i | 0.0560264 | + | 0.969048i | ||||
\(371\) | − | 31.2048i | − | 1.62007i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.21739 | 0.373702 | 0.186851 | − | 0.982388i | \(-0.440172\pi\) | ||||
0.186851 | + | 0.982388i | \(0.440172\pi\) | |||||||
\(374\) | −4.76917 | − | 1.18526i | −0.246608 | − | 0.0612883i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.2628 | − | 16.3691i | −0.941832 | − | 0.844170i | ||||
\(377\) | −12.8730 | −0.662993 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.54353 | 0.336118 | 0.168059 | − | 0.985777i | \(-0.446250\pi\) | ||||
0.168059 | + | 0.985777i | \(0.446250\pi\) | |||||||
\(380\) | 1.42149 | + | 0.267251i | 0.0729208 | + | 0.0137097i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.06198 | + | 8.29685i | −0.105500 | + | 0.424504i | ||||
\(383\) | 15.3236i | 0.782999i | 0.920178 | + | 0.391500i | \(0.128044\pi\) | ||||
−0.920178 | + | 0.391500i | \(0.871956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.84803 | − | 5.94592i | −0.0941846 | − | 0.303032i | ||||
\(386\) | −35.6196 | − | 8.85238i | −1.81299 | − | 0.450574i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.87251 | − | 11.0850i | 0.298131 | − | 0.562754i | ||||
\(389\) | −0.599067 | −0.0303739 | −0.0151869 | − | 0.999885i | \(-0.504834\pi\) | ||||
−0.0151869 | + | 0.999885i | \(0.504834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.4080i | 1.74009i | ||||||||
\(392\) | −23.3112 | + | 26.0080i | −1.17739 | + | 1.31360i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.3893 | + | 3.57610i | 0.724921 | + | 0.180161i | ||||
\(395\) | −4.86953 | − | 15.6674i | −0.245012 | − | 0.788310i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.8269 | 0.643763 | 0.321881 | − | 0.946780i | \(-0.395685\pi\) | ||||
0.321881 | + | 0.946780i | \(0.395685\pi\) | |||||||
\(398\) | −4.38736 | − | 1.09037i | −0.219918 | − | 0.0546553i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.6344 | + | 7.26357i | 0.931719 | + | 0.363179i | ||||
\(401\) | − | 5.19431i | − | 0.259391i | −0.991554 | − | 0.129696i | \(-0.958600\pi\) | ||
0.991554 | − | 0.129696i | \(-0.0414000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 26.7996i | − | 1.33499i | ||||||
\(404\) | 0.946373 | + | 0.501362i | 0.0470838 | + | 0.0249437i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.66976 | − | 22.8136i | 0.281385 | − | 1.13222i | ||||
\(407\) | − | 3.73774i | − | 0.185273i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.10266 | 0.400651 | 0.200325 | − | 0.979729i | \(-0.435800\pi\) | ||||
0.200325 | + | 0.979729i | \(0.435800\pi\) | |||||||
\(410\) | −2.77022 | + | 0.160163i | −0.136811 | + | 0.00790987i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −22.1915 | − | 11.7564i | −1.09330 | − | 0.579198i | ||||
\(413\) | − | 46.3273i | − | 2.27962i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.07237 | + | 1.26572i | −0.199905 | + | 0.0621318i | ||||
\(416\) | 18.0829 | − | 6.65912i | 0.886585 | − | 0.326490i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.281002 | − | 0.0698362i | −0.0137443 | − | 0.00341580i | ||||
\(419\) | − | 3.51505i | − | 0.171721i | −0.996307 | − | 0.0858607i | \(-0.972636\pi\) | ||
0.996307 | − | 0.0858607i | \(-0.0273640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.14007i | 0.250512i | 0.992124 | + | 0.125256i | \(0.0399751\pi\) | ||||
−0.992124 | + | 0.125256i | \(0.960025\pi\) | |||||||
\(422\) | −5.86734 | + | 23.6086i | −0.285618 | + | 1.14925i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.9418 | − | 13.3925i | −0.725640 | − | 0.650396i | ||||
\(425\) | 22.6102 | − | 15.5577i | 1.09676 | − | 0.754661i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 61.8773i | 2.99445i | ||||||||
\(428\) | 23.7291 | + | 12.5710i | 1.14699 | + | 0.607644i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.30523 | − | 0.422359i | 0.352290 | − | 0.0203679i | ||||
\(431\) | 33.9083 | 1.63330 | 0.816652 | − | 0.577130i | \(-0.195828\pi\) | ||||
0.816652 | + | 0.577130i | \(0.195828\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.97168i | 0.335038i | 0.985869 | + | 0.167519i | \(0.0535755\pi\) | ||||
−0.985869 | + | 0.167519i | \(0.946425\pi\) | |||||||
\(434\) | 47.4945 | + | 11.8036i | 2.27981 | + | 0.566590i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.34548 | + | 2.53974i | −0.0644369 | + | 0.121631i | ||||
\(437\) | 2.02734i | 0.0969810i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.99992i | − | 0.0954509i | −0.998860 | − | 0.0477255i | \(-0.984803\pi\) | ||
0.998860 | − | 0.0477255i | \(-0.0151973\pi\) | |||||||
\(440\) | −3.64023 | − | 1.66697i | −0.173541 | − | 0.0794698i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.37797 | − | 25.6633i | 0.303369 | − | 1.22068i | ||||
\(443\) | −30.0436 | −1.42741 | −0.713707 | − | 0.700445i | \(-0.752985\pi\) | ||||
−0.713707 | + | 0.700445i | \(0.752985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.42151 | − | 17.4433i | −0.257004 | − | 0.826893i | ||||
\(446\) | −4.02784 | + | 16.2070i | −0.190724 | + | 0.767422i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.83695 | + | 34.9795i | 0.181279 | + | 1.65263i | ||||
\(449\) | 10.1557i | 0.479275i | 0.970862 | + | 0.239638i | \(0.0770286\pi\) | ||||
−0.970862 | + | 0.239638i | \(0.922971\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.555490 | 0.0261570 | ||||||||
\(452\) | −11.4076 | − | 6.04344i | −0.536570 | − | 0.284260i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.41534 | + | 5.69493i | −0.0664250 | + | 0.267276i | ||||
\(455\) | 31.9955 | − | 9.94442i | 1.49997 | − | 0.466202i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.9896i | 1.77708i | 0.458800 | + | 0.888540i | \(0.348280\pi\) | ||||
−0.458800 | + | 0.888540i | \(0.651720\pi\) | |||||||
\(458\) | −24.3640 | − | 6.05506i | −1.13845 | − | 0.282934i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.17970 | + | 27.5504i | −0.241505 | + | 1.28454i | ||||
\(461\) | −20.5143 | −0.955445 | −0.477722 | − | 0.878511i | \(-0.658538\pi\) | ||||
−0.477722 | + | 0.878511i | \(0.658538\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.0629776 | −0.00292682 | −0.00146341 | − | 0.999999i | \(-0.500466\pi\) | ||||
−0.00146341 | + | 0.999999i | \(0.500466\pi\) | |||||||
\(464\) | −8.49052 | − | 12.5060i | −0.394163 | − | 0.580576i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.57568 | + | 10.3638i | −0.119316 | + | 0.480095i | ||||
\(467\) | 21.9620 | 1.01628 | 0.508140 | − | 0.861274i | \(-0.330333\pi\) | ||||
0.508140 | + | 0.861274i | \(0.330333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 26.3648i | − | 1.21741i | ||||||
\(470\) | −27.3741 | + | 1.58266i | −1.26267 | + | 0.0730026i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.1830 | − | 19.8828i | −1.02105 | − | 0.915178i | ||||
\(473\) | −1.46486 | −0.0673544 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.33221 | − | 0.916671i | 0.0611259 | − | 0.0420598i | ||||
\(476\) | 42.6715 | + | 22.6062i | 1.95584 | + | 1.03615i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.380247 | + | 1.53001i | −0.0173921 | + | 0.0699812i | ||||
\(479\) | −7.64777 | −0.349436 | −0.174718 | − | 0.984619i | \(-0.555901\pi\) | ||||
−0.174718 | + | 0.984619i | \(0.555901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.1130 | 0.917076 | ||||||||
\(482\) | 8.00843 | − | 32.2238i | 0.364774 | − | 1.46775i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.7322 | − | 9.92379i | −0.851463 | − | 0.451081i | ||||
\(485\) | −4.16268 | − | 13.3931i | −0.189017 | − | 0.608150i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.23404 | 0.101234 | 0.0506171 | − | 0.998718i | \(-0.483881\pi\) | ||||
0.0506171 | + | 0.998718i | \(0.483881\pi\) | |||||||
\(488\) | 29.6288 | + | 26.5565i | 1.34123 | + | 1.20216i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.25386 | + | 38.9834i | 0.101819 | + | 1.76109i | ||||
\(491\) | − | 22.4276i | − | 1.01214i | −0.862491 | − | 0.506072i | \(-0.831097\pi\) | ||
0.862491 | − | 0.506072i | \(-0.168903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.7432 | −0.934228 | ||||||||
\(494\) | 0.375794 | − | 1.51210i | 0.0169078 | − | 0.0680324i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.0356 | − | 17.6760i | 1.16903 | − | 0.793675i | ||||
\(497\) | −47.4201 | −2.12708 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.1585 | 0.902420 | 0.451210 | − | 0.892418i | \(-0.350993\pi\) | ||||
0.451210 | + | 0.892418i | \(0.350993\pi\) | |||||||
\(500\) | 20.4460 | − | 9.05334i | 0.914371 | − | 0.404878i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.2721 | + | 6.77780i | 1.21721 | + | 0.302508i | ||||
\(503\) | − | 17.3479i | − | 0.773506i | −0.922183 | − | 0.386753i | \(-0.873597\pi\) | ||
0.922183 | − | 0.386753i | \(-0.126403\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.14343 | − | 0.355386i | 0.0508820 | − | 0.0158145i | ||||
\(506\) | 1.35352 | − | 5.44621i | 0.0601714 | − | 0.242114i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.0911 | − | 10.1139i | −0.847029 | − | 0.448732i | ||||
\(509\) | 28.4216 | 1.25976 | 0.629882 | − | 0.776691i | \(-0.283103\pi\) | ||||
0.629882 | + | 0.776691i | \(0.283103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 61.4291i | − | 2.71746i | ||||||
\(512\) | 18.3960 | + | 13.1752i | 0.812997 | + | 0.582269i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.51890 | − | 22.2066i | 0.243428 | − | 0.979490i | ||||
\(515\) | −26.8123 | + | 8.33345i | −1.18149 | + | 0.367216i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.48911 | 0.241411 | ||||||||
\(518\) | −8.85855 | + | 35.6445i | −0.389222 | + | 1.56613i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.97010 | − | 19.5884i | 0.393365 | − | 0.859007i | ||||
\(521\) | − | 32.7743i | − | 1.43587i | −0.696111 | − | 0.717934i | \(-0.745088\pi\) | ||
0.696111 | − | 0.717934i | \(-0.254912\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 43.3032i | − | 1.89351i | −0.321948 | − | 0.946757i | \(-0.604338\pi\) | ||
0.321948 | − | 0.946757i | \(-0.395662\pi\) | |||||||
\(524\) | −17.1194 | + | 32.3147i | −0.747865 | + | 1.41167i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.2063 | − | 4.27619i | −0.750229 | − | 0.186451i | ||||
\(527\) | − | 43.1843i | − | 1.88114i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2927 | −0.708378 | ||||||||
\(530\) | −22.3963 | + | 1.29486i | −0.972833 | + | 0.0562452i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.51423 | + | 1.33197i | 0.109006 | + | 0.0577482i | ||||
\(533\) | 2.98913i | 0.129474i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.6701 | − | 8.91088i | 1.23952 | − | 0.385251i | ||||
\(536\) | −12.6243 | − | 11.3152i | −0.545286 | − | 0.488744i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.88734 | − | 31.7366i | 0.340047 | − | 1.36826i | ||||
\(539\) | − | 7.81704i | − | 0.336704i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 8.86985i | − | 0.381345i | −0.981654 | − | 0.190672i | \(-0.938933\pi\) | ||
0.981654 | − | 0.190672i | \(-0.0610668\pi\) | |||||||
\(542\) | 13.9453 | + | 3.46576i | 0.599003 | + | 0.148867i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 29.1383 | − | 10.7303i | 1.24929 | − | 0.460059i | ||||
\(545\) | 0.953734 | + | 3.06857i | 0.0408535 | + | 0.131443i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.1126i | 0.817197i | 0.912714 | + | 0.408598i | \(0.133982\pi\) | ||||
−0.912714 | + | 0.408598i | \(0.866018\pi\) | |||||||
\(548\) | −26.3950 | − | 13.9834i | −1.12754 | − | 0.597339i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.19082 | + | 1.57310i | −0.178697 | + | 0.0670772i | ||||
\(551\) | −1.22220 | −0.0520676 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 32.2742i | − | 1.37244i | ||||||
\(554\) | 1.92595 | − | 7.74950i | 0.0818257 | − | 0.329245i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 28.3348 | + | 15.0110i | 1.20166 | + | 0.636608i | ||||
\(557\) | − | 18.4103i | − | 0.780070i | −0.920800 | − | 0.390035i | \(-0.872463\pi\) | ||
0.920800 | − | 0.390035i | \(-0.127537\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.88253i | − | 0.333396i | ||||||
\(560\) | 30.7639 | + | 24.5243i | 1.30001 | + | 1.03634i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 40.3859 | + | 10.0369i | 1.70358 | + | 0.423382i | ||||
\(563\) | 1.23305 | 0.0519669 | 0.0259835 | − | 0.999662i | \(-0.491728\pi\) | ||||
0.0259835 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.7830 | + | 4.28385i | −0.579854 | + | 0.180223i | ||||
\(566\) | 3.21668 | + | 0.799428i | 0.135207 | + | 0.0336025i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.3518 | + | 22.7062i | −0.853941 | + | 0.952733i | ||||
\(569\) | 13.3647i | 0.560279i | 0.959959 | + | 0.280140i | \(0.0903808\pi\) | ||||
−0.959959 | + | 0.280140i | \(0.909619\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.7664 | 0.869045 | 0.434522 | − | 0.900661i | \(-0.356917\pi\) | ||||
0.434522 | + | 0.900661i | \(0.356917\pi\) | |||||||
\(572\) | −2.01905 | + | 3.81117i | −0.0844208 | + | 0.159353i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.29736 | − | 1.31653i | −0.221108 | − | 0.0549509i | ||||
\(575\) | 17.7664 | + | 25.8200i | 0.740908 | + | 1.07677i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.90816i | 0.370852i | 0.982658 | + | 0.185426i | \(0.0593664\pi\) | ||||
−0.982658 | + | 0.185426i | \(0.940634\pi\) | |||||||
\(578\) | 4.47874 | − | 18.0212i | 0.186291 | − | 0.749585i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −16.6090 | − | 3.12263i | −0.689653 | − | 0.129660i | ||||
\(581\) | −8.38894 | −0.348032 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.49096 | 0.185996 | ||||||||
\(584\) | −29.4142 | − | 26.3641i | −1.21717 | − | 1.09096i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 32.1821 | + | 7.99808i | 1.32943 | + | 0.330398i | ||||
\(587\) | 33.0278 | 1.36320 | 0.681601 | − | 0.731724i | \(-0.261284\pi\) | ||||
0.681601 | + | 0.731724i | \(0.261284\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.54445i | − | 0.104842i | ||||||
\(590\) | −33.2500 | + | 1.92238i | −1.36888 | + | 0.0791432i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.2658 | + | 19.5396i | 0.545220 | + | 0.803074i | ||||
\(593\) | −0.685529 | −0.0281513 | −0.0140757 | − | 0.999901i | \(-0.504481\pi\) | ||||
−0.0140757 | + | 0.999901i | \(0.504481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 51.5567 | − | 16.0242i | 2.11362 | − | 0.656928i | ||||
\(596\) | −20.2314 | − | 10.7180i | −0.828710 | − | 0.439028i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 29.3065 | + | 7.28341i | 1.19843 | + | 0.297841i | ||||
\(599\) | −23.7808 | −0.971656 | −0.485828 | − | 0.874055i | \(-0.661482\pi\) | ||||
−0.485828 | + | 0.874055i | \(0.661482\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.43712 | 0.0994123 | 0.0497062 | − | 0.998764i | \(-0.484172\pi\) | ||||
0.0497062 | + | 0.998764i | \(0.484172\pi\) | |||||||
\(602\) | 13.9695 | + | 3.47177i | 0.569353 | + | 0.141499i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.2734 | − | 21.2797i | 0.458708 | − | 0.865859i | ||||
\(605\) | −22.6327 | + | 7.03440i | −0.920149 | + | 0.285989i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.3537 | 1.15084 | 0.575420 | − | 0.817858i | \(-0.304839\pi\) | ||||
0.575420 | + | 0.817858i | \(0.304839\pi\) | |||||||
\(608\) | 1.71685 | − | 0.632238i | 0.0696273 | − | 0.0256407i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 44.4106 | − | 2.56764i | 1.79813 | − | 0.103961i | ||||
\(611\) | 29.5373i | 1.19495i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.2558 | −1.58553 | −0.792763 | − | 0.609530i | \(-0.791358\pi\) | ||||
−0.792763 | + | 0.609530i | \(0.791358\pi\) | |||||||
\(614\) | 1.82530 | + | 0.453634i | 0.0736633 | + | 0.0183072i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.86491 | − | 5.25676i | −0.236304 | − | 0.211801i | ||||
\(617\) | −40.7603 | −1.64095 | −0.820473 | − | 0.571685i | \(-0.806290\pi\) | ||||
−0.820473 | + | 0.571685i | \(0.806290\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.3834 | 0.457538 | 0.228769 | − | 0.973481i | \(-0.426530\pi\) | ||||
0.228769 | + | 0.973481i | \(0.426530\pi\) | |||||||
\(620\) | 6.50085 | − | 34.5775i | 0.261080 | − | 1.38867i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.1490 | − | 44.8604i | 0.447032 | − | 1.79874i | ||||
\(623\) | − | 35.9326i | − | 1.43961i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.93374 | − | 23.3493i | 0.357350 | − | 0.933971i | ||||
\(626\) | 11.3871 | + | 2.82999i | 0.455121 | + | 0.113109i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.36815 | + | 3.90344i | 0.294021 | + | 0.155764i | ||||
\(629\) | 32.4096 | 1.29226 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.7246i | 0.825035i | 0.910950 | + | 0.412517i | \(0.135350\pi\) | ||||
−0.910950 | + | 0.412517i | \(0.864650\pi\) | |||||||
\(632\) | −15.4539 | − | 13.8514i | −0.614723 | − | 0.550980i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −41.0167 | − | 10.1937i | −1.62898 | − | 0.404843i | ||||
\(635\) | −23.0663 | + | 7.16916i | −0.915357 | + | 0.284500i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42.0641 | 1.66664 | ||||||||
\(638\) | 3.28331 | + | 0.815985i | 0.129987 | + | 0.0323051i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.9462 | − | 4.20535i | 0.986087 | − | 0.166231i | ||||
\(641\) | − | 1.64857i | − | 0.0651148i | −0.999470 | − | 0.0325574i | \(-0.989635\pi\) | ||
0.999470 | − | 0.0325574i | \(-0.0103652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.4116i | 1.27819i | 0.769128 | + | 0.639095i | \(0.220691\pi\) | ||||
−0.769128 | + | 0.639095i | \(0.779309\pi\) | |||||||
\(644\) | −25.8154 | + | 48.7293i | −1.01727 | + | 1.92020i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.605545 | − | 2.43655i | 0.0238249 | − | 0.0958649i | ||||
\(647\) | 3.92161i | 0.154174i | 0.997024 | + | 0.0770871i | \(0.0245620\pi\) | ||||
−0.997024 | + | 0.0770871i | \(0.975438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.66737 | 0.261717 | ||||||||
\(650\) | −8.46498 | − | 22.5511i | −0.332024 | − | 0.884528i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.66238 | + | 3.13791i | −0.0651038 | + | 0.122890i | ||||
\(653\) | − | 16.8499i | − | 0.659387i | −0.944088 | − | 0.329693i | \(-0.893055\pi\) | ||
0.944088 | − | 0.329693i | \(-0.106945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.1350 | + | 39.0433i | 0.474152 | + | 1.52555i | ||||
\(656\) | −2.90392 | + | 1.97152i | −0.113379 | + | 0.0769747i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −52.3463 | − | 13.0094i | −2.04067 | − | 0.507158i | ||||
\(659\) | 31.2375i | 1.21684i | 0.793615 | + | 0.608420i | \(0.208196\pi\) | ||||
−0.793615 | + | 0.608420i | \(0.791804\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 37.8548i | − | 1.47238i | −0.676774 | − | 0.736191i | \(-0.736623\pi\) | ||
0.676774 | − | 0.736191i | \(-0.263377\pi\) | |||||||
\(662\) | 3.96719 | − | 15.9629i | 0.154189 | − | 0.620416i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.60036 | + | 4.01689i | −0.139721 | + | 0.155885i | ||||
\(665\) | 3.03775 | − | 0.944155i | 0.117799 | − | 0.0366128i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 23.6880i | − | 0.917203i | ||||||
\(668\) | 2.74482 | − | 5.18113i | 0.106200 | − | 0.200464i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.9225 | + | 1.09402i | −0.731041 | + | 0.0422658i | ||||
\(671\) | −8.90531 | −0.343786 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.36802i | 0.245469i | 0.992440 | + | 0.122735i | \(0.0391664\pi\) | ||||
−0.992440 | + | 0.122735i | \(0.960834\pi\) | |||||||
\(674\) | −11.5186 | − | 2.86267i | −0.443680 | − | 0.110266i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.46685 | + | 1.30687i | 0.0948790 | + | 0.0502642i | ||||
\(677\) | 16.6484i | 0.639851i | 0.947443 | + | 0.319926i | \(0.103658\pi\) | ||||
−0.947443 | + | 0.319926i | \(0.896342\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 27.5894i | − | 1.05878i | ||||||
\(680\) | 14.4542 | − | 31.5642i | 0.554293 | − | 1.21043i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.69876 | + | 6.83535i | −0.0650488 | + | 0.261739i | ||||
\(683\) | −29.5071 | −1.12906 | −0.564529 | − | 0.825413i | \(-0.690942\pi\) | ||||
−0.564529 | + | 0.825413i | \(0.690942\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.8911 | + | 9.91199i | −1.21850 | + | 0.378718i | ||||
\(686\) | −8.02420 | + | 32.2872i | −0.306365 | + | 1.23273i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.65781 | − | 5.19901i | 0.291951 | − | 0.198210i | ||||
\(689\) | 24.1662i | 0.920658i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.8365 | 1.21112 | 0.605559 | − | 0.795800i | \(-0.292949\pi\) | ||||
0.605559 | + | 0.795800i | \(0.292949\pi\) | |||||||
\(692\) | −4.93545 | + | 9.31617i | −0.187618 | + | 0.354148i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.90494 | + | 19.7362i | −0.186189 | + | 0.749175i | ||||
\(695\) | 34.2348 | − | 10.6404i | 1.29860 | − | 0.403614i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.81662i | 0.182442i | ||||||||
\(698\) | 46.2496 | + | 11.4942i | 1.75057 | + | 0.435061i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 43.6935 | − | 5.06931i | 1.65146 | − | 0.191602i | ||||
\(701\) | 4.54314 | 0.171592 | 0.0857960 | − | 0.996313i | \(-0.472657\pi\) | ||||
0.0857960 | + | 0.996313i | \(0.472657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.90960 | 0.0720218 | ||||||||
\(704\) | −5.03420 | + | 0.552209i | −0.189734 | + | 0.0208122i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.99150 | + | 36.1794i | −0.338400 | + | 1.36163i | ||||
\(707\) | 2.35543 | 0.0885849 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 7.01898i | − | 0.263603i | −0.991276 | − | 0.131802i | \(-0.957924\pi\) | ||
0.991276 | − | 0.131802i | \(-0.0420762\pi\) | |||||||
\(710\) | 1.96773 | + | 34.0344i | 0.0738475 | + | 1.27729i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.2057 | − | 15.4216i | −0.644810 | − | 0.577947i | ||||
\(713\) | 49.3149 | 1.84686 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.43119 | + | 4.60475i | 0.0535234 | + | 0.172208i | ||||
\(716\) | −10.9023 | + | 20.5792i | −0.407438 | + | 0.769081i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.67023 | + | 38.9104i | −0.360890 | + | 1.45213i | ||||
\(719\) | −32.6924 | −1.21922 | −0.609610 | − | 0.792702i | \(-0.708674\pi\) | ||||
−0.609610 | + | 0.792702i | \(0.708674\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −55.2324 | −2.05696 | ||||||||
\(722\) | −6.44507 | + | 25.9332i | −0.239861 | + | 0.965135i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.8006 | − | 24.1624i | 0.475729 | − | 0.897988i | ||||
\(725\) | −15.5659 | + | 10.7106i | −0.578102 | + | 0.397783i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.4300 | 0.572268 | 0.286134 | − | 0.958190i | \(-0.407630\pi\) | ||||
0.286134 | + | 0.958190i | \(0.407630\pi\) | |||||||
\(728\) | 28.2870 | − | 31.5596i | 1.04839 | − | 1.16967i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −44.0889 | + | 2.54904i | −1.63180 | + | 0.0943442i | ||||
\(731\) | − | 12.7017i | − | 0.469790i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.2010 | −1.85421 | −0.927107 | − | 0.374796i | \(-0.877713\pi\) | ||||
−0.927107 | + | 0.374796i | \(0.877713\pi\) | |||||||
\(734\) | 6.21207 | − | 24.9957i | 0.229292 | − | 0.922609i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.2537 | + | 33.2748i | 0.451676 | + | 1.22653i | ||||
\(737\) | 3.79439 | 0.139768 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.6261 | 1.34731 | 0.673657 | − | 0.739044i | \(-0.264723\pi\) | ||||
0.673657 | + | 0.739044i | \(0.264723\pi\) | |||||||
\(740\) | 25.9503 | + | 4.87887i | 0.953953 | + | 0.179351i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −42.8274 | − | 10.6437i | −1.57225 | − | 0.390743i | ||||
\(743\) | 35.5474i | 1.30411i | 0.758172 | + | 0.652055i | \(0.226093\pi\) | ||||
−0.758172 | + | 0.652055i | \(0.773907\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.4441 | + | 7.59739i | −0.895561 | + | 0.278347i | ||||
\(746\) | 2.46179 | − | 9.90561i | 0.0901327 | − | 0.362670i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.25345 | + | 6.14122i | −0.118958 | + | 0.224545i | ||||
\(749\) | 59.0594 | 2.15798 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 41.1833i | − | 1.50280i | −0.659848 | − | 0.751399i | \(-0.729379\pi\) | ||
0.659848 | − | 0.751399i | \(-0.270621\pi\) | |||||||
\(752\) | −28.6952 | + | 19.4817i | −1.04641 | + | 0.710423i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.39088 | + | 17.6677i | −0.159906 | + | 0.643420i | ||||
\(755\) | −7.99105 | − | 25.7106i | −0.290824 | − | 0.935706i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.89555 | 0.214278 | 0.107139 | − | 0.994244i | \(-0.465831\pi\) | ||||
0.107139 | + | 0.994244i | \(0.465831\pi\) | |||||||
\(758\) | 2.23194 | − | 8.98075i | 0.0810679 | − | 0.326196i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.851651 | − | 1.85978i | 0.0308926 | − | 0.0674614i | ||||
\(761\) | 41.5797i | 1.50726i | 0.657297 | + | 0.753632i | \(0.271700\pi\) | ||||
−0.657297 | + | 0.753632i | \(0.728300\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.32115i | 0.228841i | ||||||||
\(764\) | 10.6838 | + | 5.65998i | 0.386526 | + | 0.204771i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.0311 | + | 5.22676i | 0.759884 | + | 0.188850i | ||||
\(767\) | 35.8777i | 1.29547i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.0235 | −0.938432 | −0.469216 | − | 0.883083i | \(-0.655463\pi\) | ||||
−0.469216 | + | 0.883083i | \(0.655463\pi\) | |||||||
\(770\) | −8.79091 | + | 0.508255i | −0.316802 | + | 0.0183162i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24.2991 | + | 45.8671i | −0.874545 | + | 1.65079i | ||||
\(773\) | 10.4488i | 0.375819i | 0.982186 | + | 0.187909i | \(0.0601711\pi\) | ||||
−0.982186 | + | 0.187909i | \(0.939829\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.2979 | − | 32.4058i | −0.800965 | − | 1.16405i | ||||
\(776\) | −13.2107 | − | 11.8408i | −0.474235 | − | 0.425060i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.204337 | + | 0.822197i | −0.00732583 | + | 0.0294772i | ||||
\(779\) | 0.283798i | 0.0101681i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.82465i | − | 0.244205i | ||||||
\(782\) | 47.2238 | + | 11.7363i | 1.68872 | + | 0.419689i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.7438 | + | 40.8649i | 0.990851 | + | 1.45946i | ||||
\(785\) | 8.90237 | − | 2.76692i | 0.317739 | − | 0.0987556i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.5171i | 1.26605i | 0.774132 | + | 0.633024i | \(0.218187\pi\) | ||||
−0.774132 | + | 0.633024i | \(0.781813\pi\) | |||||||
\(788\) | 9.81613 | − | 18.5290i | 0.349685 | − | 0.660067i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −23.1638 | + | 1.33924i | −0.824132 | + | 0.0476479i | ||||
\(791\) | −28.3924 | −1.00952 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 47.9202i | − | 1.70169i | ||||||
\(794\) | 4.37515 | − | 17.6044i | 0.155268 | − | 0.624758i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.99298 | + | 5.64957i | −0.106083 | + | 0.200244i | ||||
\(797\) | 20.0999i | 0.711977i | 0.934490 | + | 0.355988i | \(0.115856\pi\) | ||||
−0.934490 | + | 0.355988i | \(0.884144\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.5957i | 1.68382i | ||||||||
\(800\) | 16.3250 | − | 23.0975i | 0.577177 | − | 0.816619i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.12899 | − | 1.77174i | −0.251734 | − | 0.0625622i | ||||
\(803\) | 8.84080 | 0.311985 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.2990 | + | 58.8758i | 0.644956 | + | 2.07510i | ||||
\(806\) | −36.7815 | − | 9.14115i | −1.29557 | − | 0.321983i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.01090 | − | 1.12785i | 0.0355634 | − | 0.0396777i | ||||
\(809\) | − | 32.5036i | − | 1.14276i | −0.820684 | − | 0.571382i | \(-0.806407\pi\) | ||
0.820684 | − | 0.571382i | \(-0.193593\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.5091 | −1.24689 | −0.623447 | − | 0.781866i | \(-0.714268\pi\) | ||||
−0.623447 | + | 0.781866i | \(0.714268\pi\) | |||||||
\(812\) | −29.3769 | − | 15.5631i | −1.03093 | − | 0.546157i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.12991 | − | 1.27491i | −0.179803 | − | 0.0446856i | ||||
\(815\) | 1.17836 | + | 3.79130i | 0.0412763 | + | 0.132803i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.748393i | − | 0.0261830i | ||||||
\(818\) | 2.76375 | − | 11.1206i | 0.0966324 | − | 0.388823i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.725081 | + | 3.85665i | −0.0253209 | + | 0.134680i | ||||
\(821\) | −12.6596 | −0.441821 | −0.220911 | − | 0.975294i | \(-0.570903\pi\) | ||||
−0.220911 | + | 0.975294i | \(0.570903\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.2106 | −0.948500 | −0.474250 | − | 0.880390i | \(-0.657281\pi\) | ||||
−0.474250 | + | 0.880390i | \(0.657281\pi\) | |||||||
\(824\) | −23.7046 | + | 26.4470i | −0.825790 | + | 0.921325i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −63.5826 | − | 15.8019i | −2.21232 | − | 0.549818i | ||||
\(827\) | 37.0039 | 1.28675 | 0.643376 | − | 0.765551i | \(-0.277533\pi\) | ||||
0.643376 | + | 0.765551i | \(0.277533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.1179i | 1.15023i | 0.818072 | + | 0.575116i | \(0.195043\pi\) | ||||
−0.818072 | + | 0.575116i | \(0.804957\pi\) | |||||||
\(830\) | 0.348104 | + | 6.02090i | 0.0120829 | + | 0.208989i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.97148 | − | 27.0894i | −0.103018 | − | 0.939157i | ||||
\(833\) | 67.7810 | 2.34847 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.94564 | − | 6.25996i | −0.0673317 | − | 0.216635i | ||||
\(836\) | −0.191695 | + | 0.361845i | −0.00662992 | + | 0.0125147i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.82427 | − | 1.19895i | −0.166652 | − | 0.0414172i | ||||
\(839\) | −29.0655 | −1.00345 | −0.501726 | − | 0.865026i | \(-0.667302\pi\) | ||||
−0.501726 | + | 0.865026i | \(0.667302\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7194 | −0.507567 | ||||||||
\(842\) | 7.05455 | + | 1.75324i | 0.243116 | + | 0.0604205i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30.4007 | + | 16.1054i | 1.04643 | + | 0.554372i | ||||
\(845\) | 2.98051 | − | 0.926364i | 0.102533 | − | 0.0318679i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.6225 | −1.60197 | ||||||||
\(848\) | −23.4772 | + | 15.9391i | −0.806211 | + | 0.547350i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.6402 | − | 36.3383i | −0.467857 | − | 1.24639i | ||||
\(851\) | 37.0106i | 1.26871i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.9301 | 1.50414 | 0.752069 | − | 0.659084i | \(-0.229056\pi\) | ||||
0.752069 | + | 0.659084i | \(0.229056\pi\) | |||||||
\(854\) | 84.9244 | + | 21.1059i | 2.90605 | + | 0.722228i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.3471 | − | 28.2795i | 0.866346 | − | 0.966574i | ||||
\(857\) | 8.72872 | 0.298167 | 0.149084 | − | 0.988825i | \(-0.452368\pi\) | ||||
0.149084 | + | 0.988825i | \(0.452368\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.59497 | 0.259137 | 0.129569 | − | 0.991570i | \(-0.458641\pi\) | ||||
0.129569 | + | 0.991570i | \(0.458641\pi\) | |||||||
\(860\) | 1.91208 | − | 10.1702i | 0.0652015 | − | 0.346802i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.5658 | − | 46.5379i | 0.393934 | − | 1.58509i | ||||
\(863\) | 11.9244i | 0.405910i | 0.979188 | + | 0.202955i | \(0.0650546\pi\) | ||||
−0.979188 | + | 0.202955i | \(0.934945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.49845 | + | 11.2560i | 0.118951 | + | 0.382716i | ||||
\(866\) | 9.56838 | + | 2.37798i | 0.325147 | + | 0.0808072i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.4000 | − | 61.1584i | 1.09973 | − | 2.07585i | ||||
\(869\) | 4.64486 | 0.157566 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.4179i | 0.691834i | ||||||||
\(872\) | 3.02676 | + | 2.71291i | 0.102499 | + | 0.0918707i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.78245 | + | 0.691510i | 0.0941179 | + | 0.0233907i | ||||
\(875\) | 30.4145 | − | 38.6456i | 1.02820 | − | 1.30646i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.3668 | 0.755272 | 0.377636 | − | 0.925954i | \(-0.376737\pi\) | ||||
0.377636 | + | 0.925954i | \(0.376737\pi\) | |||||||
\(878\) | −2.74482 | − | 0.682156i | −0.0926331 | − | 0.0230217i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.52951 | + | 4.42750i | −0.118980 | + | 0.149251i | ||||
\(881\) | 18.7665i | 0.632259i | 0.948716 | + | 0.316130i | \(0.102383\pi\) | ||||
−0.948716 | + | 0.316130i | \(0.897617\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 22.0307i | − | 0.741393i | −0.928754 | − | 0.370697i | \(-0.879119\pi\) | ||
0.928754 | − | 0.370697i | \(-0.120881\pi\) | |||||||
\(884\) | −33.0464 | − | 17.5071i | −1.11147 | − | 0.588826i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.2476 | + | 41.2337i | −0.344276 | + | 1.38527i | ||||
\(887\) | − | 39.7930i | − | 1.33612i | −0.744108 | − | 0.668059i | \(-0.767125\pi\) | ||
0.744108 | − | 0.668059i | \(-0.232875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47.5157 | −1.59363 | ||||||||
\(890\) | −25.7896 | + | 1.49105i | −0.864468 | + | 0.0499800i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.8696 | + | 11.0561i | 0.698766 | + | 0.370186i | ||||
\(893\) | 2.80437i | 0.0938447i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.72800 | + | 24.8643i | 0.258318 | + | 0.831121i | ||||
\(896\) | 49.3168 | + | 6.66515i | 1.64756 | + | 0.222667i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.9383 | + | 3.46401i | 0.465126 | + | 0.115596i | ||||
\(899\) | 29.7300i | 0.991550i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.9408i | 1.29731i | ||||||||
\(902\) | 0.189473 | − | 0.762390i | 0.00630877 | − | 0.0253848i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.1855 | + | 13.5952i | −0.405282 | + | 0.452169i | ||||
\(905\) | −9.07357 | − | 29.1936i | −0.301616 | − | 0.970427i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.7832i | 0.822914i | 0.911429 | + | 0.411457i | \(0.134980\pi\) | ||||
−0.911429 | + | 0.411457i | \(0.865020\pi\) | |||||||
\(908\) | 7.33333 | + | 3.88499i | 0.243365 | + | 0.128928i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.73496 | − | 47.3046i | −0.0906630 | − | 1.56813i | ||||
\(911\) | 26.0401 | 0.862747 | 0.431374 | − | 0.902173i | \(-0.358029\pi\) | ||||
0.431374 | + | 0.902173i | \(0.358029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.20733i | − | 0.0399566i | ||||||
\(914\) | 52.1394 | + | 12.9580i | 1.72462 | + | 0.428611i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.6207 | + | 31.3733i | −0.549163 | + | 1.03660i | ||||
\(917\) | 80.4279i | 2.65596i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 31.9640i | − | 1.05439i | −0.849743 | − | 0.527197i | \(-0.823243\pi\) | ||
0.849743 | − | 0.527197i | \(-0.176757\pi\) | |||||||
\(920\) | 36.0452 | + | 16.5062i | 1.18837 | + | 0.544192i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.99725 | + | 28.1551i | −0.230442 | + | 0.927239i | ||||
\(923\) | 36.7240 | 1.20878 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.3204 | − | 16.7345i | 0.799651 | − | 0.550227i | ||||
\(926\) | −0.0214812 | + | 0.0864345i | −0.000705915 | + | 0.00284041i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.0601 | + | 7.38724i | −0.658504 | + | 0.242498i | ||||
\(929\) | − | 55.1162i | − | 1.80830i | −0.427211 | − | 0.904152i | \(-0.640504\pi\) | ||
0.427211 | − | 0.904152i | \(-0.359496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.99370 | 0.130888 | ||||||||
\(932\) | 13.3454 | + | 7.07004i | 0.437145 | + | 0.231587i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.49106 | − | 30.1421i | 0.245115 | − | 0.986278i | ||||
\(935\) | 2.30618 | + | 7.41997i | 0.0754202 | + | 0.242659i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.0794i | 0.557960i | 0.960297 | + | 0.278980i | \(0.0899964\pi\) | ||||
−0.960297 | + | 0.278980i | \(0.910004\pi\) | |||||||
\(938\) | −36.1847 | − | 8.99282i | −1.18147 | − | 0.293626i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.16494 | + | 38.1098i | −0.233695 | + | 1.24300i | ||||
\(941\) | −46.5090 | −1.51615 | −0.758075 | − | 0.652168i | \(-0.773860\pi\) | ||||
−0.758075 | + | 0.652168i | \(0.773860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.50040 | −0.179118 | ||||||||
\(944\) | −34.8548 | + | 23.6635i | −1.13443 | + | 0.770181i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.499653 | + | 2.01047i | −0.0162451 | + | 0.0653660i | ||||
\(947\) | 2.59658 | 0.0843776 | 0.0421888 | − | 0.999110i | \(-0.486567\pi\) | ||||
0.0421888 | + | 0.999110i | \(0.486567\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.5730i | 1.54429i | ||||||||
\(950\) | −0.803692 | − | 2.14108i | −0.0260752 | − | 0.0694657i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 45.5810 | − | 50.8543i | 1.47729 | − | 1.64820i | ||||
\(953\) | −34.8096 | −1.12759 | −0.563797 | − | 0.825914i | \(-0.690660\pi\) | ||||
−0.563797 | + | 0.825914i | \(0.690660\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.9084 | − | 4.01203i | 0.417707 | − | 0.129826i | ||||
\(956\) | 1.97019 | + | 1.04375i | 0.0637204 | + | 0.0337573i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.60859 | + | 10.4963i | −0.0842798 | + | 0.339120i | ||||
\(959\) | −65.6946 | −2.12139 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8933 | −0.996559 | ||||||||
\(962\) | 6.86040 | − | 27.6044i | 0.221188 | − | 0.890002i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −41.4944 | − | 21.9826i | −1.33644 | − | 0.708011i | ||||
\(965\) | 17.2242 | + | 55.4178i | 0.554468 | + | 1.78396i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.55004 | 0.210635 | 0.105318 | − | 0.994439i | \(-0.466414\pi\) | ||||
0.105318 | + | 0.994439i | \(0.466414\pi\) | |||||||
\(968\) | −20.0094 | + | 22.3243i | −0.643128 | + | 0.717531i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.8014 | + | 1.14484i | −0.635785 | + | 0.0367585i | ||||
\(971\) | − | 27.4146i | − | 0.879778i | −0.898052 | − | 0.439889i | \(-0.855018\pi\) | ||
0.898052 | − | 0.439889i | \(-0.144982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.5225 | 2.26085 | ||||||||
\(974\) | 0.762014 | − | 3.06614i | 0.0244165 | − | 0.0982455i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 46.5540 | − | 31.6062i | 1.49016 | − | 1.01169i | ||||
\(977\) | −14.1922 | −0.454048 | −0.227024 | − | 0.973889i | \(-0.572900\pi\) | ||||
−0.227024 | + | 0.973889i | \(0.572900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.17138 | 0.165278 | ||||||||
\(980\) | 54.2721 | + | 10.2036i | 1.73366 | + | 0.325942i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.7811 | − | 7.64988i | −0.982264 | − | 0.244118i | ||||
\(983\) | 6.12231i | 0.195272i | 0.995222 | + | 0.0976358i | \(0.0311280\pi\) | ||||
−0.995222 | + | 0.0976358i | \(0.968872\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.95809 | − | 22.3871i | −0.221703 | − | 0.713314i | ||||
\(986\) | −7.07535 | + | 28.4693i | −0.225325 | + | 0.906648i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.94712 | − | 1.03153i | −0.0619460 | − | 0.0328173i | ||||
\(989\) | 14.5049 | 0.461229 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 36.8386i | − | 1.17022i | −0.810955 | − | 0.585109i | \(-0.801052\pi\) | ||
0.810955 | − | 0.585109i | \(-0.198948\pi\) | |||||||
\(992\) | −15.3791 | − | 41.7621i | −0.488288 | − | 1.32595i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.1746 | + | 65.0824i | −0.513028 | + | 2.06429i | ||||
\(995\) | 2.12155 | + | 6.82594i | 0.0672577 | + | 0.216397i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.2385 | −0.640960 | −0.320480 | − | 0.947255i | \(-0.603844\pi\) | ||||
−0.320480 | + | 0.947255i | \(0.603844\pi\) | |||||||
\(998\) | 6.87591 | − | 27.6668i | 0.217653 | − | 0.875779i | ||||
\(999\) | 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 | 1080.2.m.c.539.25 | yes | 48 | |
3.2 | odd | 2 | inner | 1080.2.m.c.539.24 | yes | 48 | |
4.3 | odd | 2 | 4320.2.m.c.2159.8 | 48 | |||
5.4 | even | 2 | inner | 1080.2.m.c.539.23 | yes | 48 | |
8.3 | odd | 2 | inner | 1080.2.m.c.539.28 | yes | 48 | |
8.5 | even | 2 | 4320.2.m.c.2159.41 | 48 | |||
12.11 | even | 2 | 4320.2.m.c.2159.42 | 48 | |||
15.14 | odd | 2 | inner | 1080.2.m.c.539.26 | yes | 48 | |
20.19 | odd | 2 | 4320.2.m.c.2159.5 | 48 | |||
24.5 | odd | 2 | 4320.2.m.c.2159.7 | 48 | |||
24.11 | even | 2 | inner | 1080.2.m.c.539.21 | ✓ | 48 | |
40.19 | odd | 2 | inner | 1080.2.m.c.539.22 | yes | 48 | |
40.29 | even | 2 | 4320.2.m.c.2159.44 | 48 | |||
60.59 | even | 2 | 4320.2.m.c.2159.43 | 48 | |||
120.29 | odd | 2 | 4320.2.m.c.2159.6 | 48 | |||
120.59 | even | 2 | inner | 1080.2.m.c.539.27 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.m.c.539.21 | ✓ | 48 | 24.11 | even | 2 | inner | |
1080.2.m.c.539.22 | yes | 48 | 40.19 | odd | 2 | inner | |
1080.2.m.c.539.23 | yes | 48 | 5.4 | even | 2 | inner | |
1080.2.m.c.539.24 | yes | 48 | 3.2 | odd | 2 | inner | |
1080.2.m.c.539.25 | yes | 48 | 1.1 | even | 1 | trivial | |
1080.2.m.c.539.26 | yes | 48 | 15.14 | odd | 2 | inner | |
1080.2.m.c.539.27 | yes | 48 | 120.59 | even | 2 | inner | |
1080.2.m.c.539.28 | yes | 48 | 8.3 | odd | 2 | inner | |
4320.2.m.c.2159.5 | 48 | 20.19 | odd | 2 | |||
4320.2.m.c.2159.6 | 48 | 120.29 | odd | 2 | |||
4320.2.m.c.2159.7 | 48 | 24.5 | odd | 2 | |||
4320.2.m.c.2159.8 | 48 | 4.3 | odd | 2 | |||
4320.2.m.c.2159.41 | 48 | 8.5 | even | 2 | |||
4320.2.m.c.2159.42 | 48 | 12.11 | even | 2 | |||
4320.2.m.c.2159.43 | 48 | 60.59 | even | 2 | |||
4320.2.m.c.2159.44 | 48 | 40.29 | even | 2 |