Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(703,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.703");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.bk (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.1 | ||
Root | \(1.60599 + 0.430324i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.901 |
Dual form | 1386.2.bk.c.703.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.09005 | − | 0.629341i | −0.487486 | − | 0.281450i | 0.236045 | − | 0.971742i | \(-0.424149\pi\) |
−0.723531 | + | 0.690292i | \(0.757482\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.11465 | − | 1.59005i | 0.799262 | − | 0.600983i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.629341 | + | 1.09005i | 0.199015 | + | 0.344704i | ||||
\(11\) | −1.45007 | − | 2.98283i | −0.437213 | − | 0.899358i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.08338 | −1.13253 | −0.566263 | − | 0.824224i | \(-0.691612\pi\) | ||||
−0.566263 | + | 0.824224i | \(0.691612\pi\) | |||||||
\(14\) | −2.62636 | + | 0.319700i | −0.701926 | + | 0.0854435i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.60096 | + | 2.77294i | 0.388289 | + | 0.672537i | 0.992220 | − | 0.124501i | \(-0.0397329\pi\) |
−0.603930 | + | 0.797037i | \(0.706400\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.81407 | − | 6.60616i | 0.875007 | − | 1.51556i | 0.0182510 | − | 0.999833i | \(-0.494190\pi\) |
0.856756 | − | 0.515723i | \(-0.172476\pi\) | |||||||
\(20\) | − | 1.25868i | − | 0.281450i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.235617 | + | 3.30824i | −0.0502337 | + | 0.705320i | ||||
\(23\) | −4.12636 | + | 7.14707i | −0.860407 | + | 1.49027i | 0.0111305 | + | 0.999938i | \(0.496457\pi\) |
−0.871537 | + | 0.490330i | \(0.836876\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.70786 | − | 2.95810i | −0.341572 | − | 0.591620i | ||||
\(26\) | 3.53631 | + | 2.04169i | 0.693528 | + | 0.400409i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.43435 | + | 1.03631i | 0.460049 | + | 0.195845i | ||||
\(29\) | − | 3.54386i | − | 0.658079i | −0.944316 | − | 0.329039i | \(-0.893275\pi\) | ||
0.944316 | − | 0.329039i | \(-0.106725\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.95304 | + | 4.59169i | −1.42841 | + | 0.824692i | −0.996995 | − | 0.0774626i | \(-0.975318\pi\) |
−0.431413 | + | 0.902155i | \(0.641985\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3.20191i | − | 0.549124i | ||||||
\(35\) | −3.30576 | + | 0.402401i | −0.558775 | + | 0.0680182i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.154122 | − | 0.266948i | 0.0253376 | − | 0.0438860i | −0.853079 | − | 0.521782i | \(-0.825267\pi\) |
0.878416 | + | 0.477896i | \(0.158601\pi\) | |||||||
\(38\) | −6.60616 | + | 3.81407i | −1.07166 | + | 0.618723i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.629341 | + | 1.09005i | −0.0995076 | + | 0.172352i | ||||
\(41\) | 6.05276 | 0.945283 | 0.472641 | − | 0.881255i | \(-0.343301\pi\) | ||||
0.472641 | + | 0.881255i | \(0.343301\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.57607i | 1.15534i | 0.816270 | + | 0.577670i | \(0.196038\pi\) | ||||
−0.816270 | + | 0.577670i | \(0.803962\pi\) | |||||||
\(44\) | 1.85817 | − | 2.74722i | 0.280130 | − | 0.414158i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.14707 | − | 4.12636i | 1.05378 | − | 0.608399i | ||||
\(47\) | −4.07263 | − | 2.35133i | −0.594054 | − | 0.342977i | 0.172645 | − | 0.984984i | \(-0.444769\pi\) |
−0.766699 | + | 0.642007i | \(0.778102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.94348 | − | 6.72480i | 0.277640 | − | 0.960685i | ||||
\(50\) | 3.41572i | 0.483056i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.04169 | − | 3.53631i | −0.283132 | − | 0.490399i | ||||
\(53\) | −2.39830 | − | 4.15397i | −0.329431 | − | 0.570592i | 0.652968 | − | 0.757386i | \(-0.273524\pi\) |
−0.982399 | + | 0.186794i | \(0.940190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.296567 | + | 4.16403i | −0.0399891 | + | 0.561478i | ||||
\(56\) | −1.59005 | − | 2.11465i | −0.212479 | − | 0.282582i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.77193 | + | 3.06907i | −0.232666 | + | 0.402989i | ||||
\(59\) | −2.36710 | + | 1.36664i | −0.308170 | + | 0.177922i | −0.646107 | − | 0.763247i | \(-0.723604\pi\) |
0.337938 | + | 0.941169i | \(0.390271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.755050 | + | 1.30779i | −0.0966743 | + | 0.167445i | −0.910306 | − | 0.413936i | \(-0.864154\pi\) |
0.813632 | + | 0.581380i | \(0.197487\pi\) | |||||||
\(62\) | 9.18338 | 1.16629 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.45110 | + | 2.56984i | 0.552090 | + | 0.318750i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.69044 | − | 2.92792i | −0.206520 | − | 0.357703i | 0.744096 | − | 0.668073i | \(-0.232880\pi\) |
−0.950616 | + | 0.310370i | \(0.899547\pi\) | |||||||
\(68\) | −1.60096 | + | 2.77294i | −0.194145 | + | 0.336268i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.06407 | + | 1.30439i | 0.366227 | + | 0.155904i | ||||
\(71\) | −3.50810 | −0.416334 | −0.208167 | − | 0.978093i | \(-0.566750\pi\) | ||||
−0.208167 | + | 0.978093i | \(0.566750\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.483428 | + | 0.837321i | 0.0565809 | + | 0.0980011i | 0.892929 | − | 0.450198i | \(-0.148647\pi\) |
−0.836348 | + | 0.548200i | \(0.815313\pi\) | |||||||
\(74\) | −0.266948 | + | 0.154122i | −0.0310321 | + | 0.0179164i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.62813 | 0.875007 | ||||||||
\(77\) | −7.80925 | − | 4.00195i | −0.889946 | − | 0.456065i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.5212 | − | 7.80647i | −1.52125 | − | 0.878296i | −0.999685 | − | 0.0250865i | \(-0.992014\pi\) |
−0.521568 | − | 0.853210i | \(-0.674653\pi\) | |||||||
\(80\) | 1.09005 | − | 0.629341i | 0.121871 | − | 0.0703625i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.24185 | − | 3.02638i | −0.578865 | − | 0.334208i | ||||
\(83\) | 1.32998 | 0.145984 | 0.0729921 | − | 0.997333i | \(-0.476745\pi\) | ||||
0.0729921 | + | 0.997333i | \(0.476745\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 4.03019i | − | 0.437136i | ||||||
\(86\) | 3.78804 | − | 6.56107i | 0.408474 | − | 0.707498i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.98283 | + | 1.45007i | −0.317971 | + | 0.154578i | ||||
\(89\) | −9.22296 | − | 5.32488i | −0.977631 | − | 0.564436i | −0.0760772 | − | 0.997102i | \(-0.524240\pi\) |
−0.901554 | + | 0.432666i | \(0.857573\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.63492 | + | 6.49279i | −0.905186 | + | 0.680629i | ||||
\(92\) | −8.25273 | −0.860407 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.35133 | + | 4.07263i | 0.242521 | + | 0.420059i | ||||
\(95\) | −8.31505 | + | 4.80070i | −0.853106 | + | 0.492541i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.6748i | 1.08386i | 0.840424 | + | 0.541930i | \(0.182306\pi\) | ||||
−0.840424 | + | 0.541930i | \(0.817694\pi\) | |||||||
\(98\) | −5.04550 | + | 4.85211i | −0.509672 | + | 0.490137i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.70786 | − | 2.95810i | 0.170786 | − | 0.295810i | ||||
\(101\) | −5.03242 | − | 8.71642i | −0.500745 | − | 0.867316i | −1.00000 | 0.000860457i | \(-0.999726\pi\) | |
0.499255 | − | 0.866455i | \(-0.333607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.49868 | + | 1.44261i | 0.246202 | + | 0.142145i | 0.618024 | − | 0.786159i | \(-0.287933\pi\) |
−0.371822 | + | 0.928304i | \(0.621267\pi\) | |||||||
\(104\) | 4.08338i | 0.400409i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.79659i | 0.465886i | ||||||||
\(107\) | −14.1162 | − | 8.15002i | −1.36467 | − | 0.787892i | −0.374428 | − | 0.927256i | \(-0.622161\pi\) |
−0.990241 | + | 0.139364i | \(0.955494\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.96227 | + | 5.75172i | −0.954213 | + | 0.550915i | −0.894387 | − | 0.447294i | \(-0.852388\pi\) |
−0.0598257 | + | 0.998209i | \(0.519054\pi\) | |||||||
\(110\) | 2.33885 | − | 3.45787i | 0.223001 | − | 0.329695i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.319700 | + | 2.62636i | 0.0302088 | + | 0.248168i | ||||
\(113\) | −0.558958 | −0.0525824 | −0.0262912 | − | 0.999654i | \(-0.508370\pi\) | ||||
−0.0262912 | + | 0.999654i | \(0.508370\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.99589 | − | 5.19378i | 0.838872 | − | 0.484323i | ||||
\(116\) | 3.06907 | − | 1.77193i | 0.284956 | − | 0.164520i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.73329 | 0.251619 | ||||||||
\(119\) | 7.79458 | + | 3.31819i | 0.714528 | + | 0.304178i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.79458 | + | 8.65064i | −0.617689 | + | 0.786422i | ||||
\(122\) | 1.30779 | − | 0.755050i | 0.118401 | − | 0.0683590i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.95304 | − | 4.59169i | −0.714204 | − | 0.412346i | ||||
\(125\) | 10.5927i | 0.947441i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.2829i | − | 1.00120i | −0.865679 | − | 0.500599i | \(-0.833113\pi\) | ||
0.865679 | − | 0.500599i | \(-0.166887\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.56984 | − | 4.45110i | −0.225390 | − | 0.390387i | ||||
\(131\) | 3.51694 | − | 6.09152i | 0.307276 | − | 0.532218i | −0.670489 | − | 0.741919i | \(-0.733916\pi\) |
0.977766 | + | 0.209701i | \(0.0672490\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.43871 | − | 20.0343i | −0.211463 | − | 1.73719i | ||||
\(134\) | 3.38087i | 0.292063i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.77294 | − | 1.60096i | 0.237778 | − | 0.137281i | ||||
\(137\) | 4.54487 | + | 7.87195i | 0.388294 | + | 0.672546i | 0.992220 | − | 0.124495i | \(-0.0397310\pi\) |
−0.603926 | + | 0.797041i | \(0.706398\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.86546 | 0.667140 | 0.333570 | − | 0.942725i | \(-0.391747\pi\) | ||||
0.333570 | + | 0.942725i | \(0.391747\pi\) | |||||||
\(140\) | −2.00137 | − | 2.66167i | −0.169147 | − | 0.224952i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.03810 | + | 1.75405i | 0.254952 | + | 0.147196i | ||||
\(143\) | 5.92120 | + | 12.1801i | 0.495156 | + | 1.01855i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.23030 | + | 3.86299i | −0.185216 | + | 0.320804i | ||||
\(146\) | − | 0.966855i | − | 0.0800175i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.308245 | 0.0253376 | ||||||||
\(149\) | −5.39617 | − | 3.11548i | −0.442072 | − | 0.255230i | 0.262404 | − | 0.964958i | \(-0.415485\pi\) |
−0.704476 | + | 0.709728i | \(0.748818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.1642 | + | 8.75506i | −1.23405 | + | 0.712476i | −0.967871 | − | 0.251448i | \(-0.919093\pi\) |
−0.266175 | + | 0.963925i | \(0.585760\pi\) | |||||||
\(152\) | −6.60616 | − | 3.81407i | −0.535830 | − | 0.309362i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.76203 | + | 7.37042i | 0.383735 | + | 0.593925i | ||||
\(155\) | 11.5590 | 0.928438 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.73252 | + | 3.88702i | −0.537314 | + | 0.310218i | −0.743989 | − | 0.668191i | \(-0.767069\pi\) |
0.206676 | + | 0.978409i | \(0.433735\pi\) | |||||||
\(158\) | 7.80647 | + | 13.5212i | 0.621049 | + | 1.07569i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.25868 | −0.0995076 | ||||||||
\(161\) | 2.63840 | + | 21.6747i | 0.207935 | + | 1.70820i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.10616 | − | 15.7723i | 0.713249 | − | 1.23538i | −0.250382 | − | 0.968147i | \(-0.580556\pi\) |
0.963631 | − | 0.267237i | \(-0.0861105\pi\) | |||||||
\(164\) | 3.02638 | + | 5.24185i | 0.236321 | + | 0.409319i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.15180 | − | 0.664990i | −0.0893967 | − | 0.0516132i | ||||
\(167\) | 14.3653 | 1.11162 | 0.555809 | − | 0.831310i | \(-0.312409\pi\) | ||||
0.555809 | + | 0.831310i | \(0.312409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.67402 | 0.282617 | ||||||||
\(170\) | −2.01510 | + | 3.49025i | −0.154551 | + | 0.267690i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.56107 | + | 3.78804i | −0.500277 | + | 0.288835i | ||||
\(173\) | 2.38160 | − | 4.12505i | 0.181069 | − | 0.313621i | −0.761176 | − | 0.648546i | \(-0.775377\pi\) |
0.942245 | + | 0.334924i | \(0.108711\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.31505 | − | 3.53976i | −0.628559 | − | 0.267580i | ||||
\(176\) | 3.30824 | + | 0.235617i | 0.249368 | + | 0.0177603i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.32488 | + | 9.22296i | 0.399116 | + | 0.691290i | ||||
\(179\) | −1.94526 | − | 3.36928i | −0.145395 | − | 0.251832i | 0.784125 | − | 0.620603i | \(-0.213112\pi\) |
−0.929520 | + | 0.368771i | \(0.879779\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0698i | 0.971474i | 0.874105 | + | 0.485737i | \(0.161449\pi\) | ||||
−0.874105 | + | 0.485737i | \(0.838551\pi\) | |||||||
\(182\) | 10.7245 | − | 1.30546i | 0.794949 | − | 0.0967670i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.14707 | + | 4.12636i | 0.526889 | + | 0.304200i | ||||
\(185\) | −0.336003 | + | 0.193991i | −0.0247034 | + | 0.0142625i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.94971 | − | 8.79635i | 0.435086 | − | 0.643253i | ||||
\(188\) | − | 4.70267i | − | 0.342977i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.60139 | 0.696558 | ||||||||
\(191\) | 3.00000 | − | 5.19615i | 0.217072 | − | 0.375980i | −0.736839 | − | 0.676068i | \(-0.763683\pi\) |
0.953912 | + | 0.300088i | \(0.0970159\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.12582 | − | 4.69144i | 0.584909 | − | 0.337698i | −0.178173 | − | 0.983999i | \(-0.557019\pi\) |
0.763082 | + | 0.646302i | \(0.223685\pi\) | |||||||
\(194\) | 5.33739 | − | 9.24463i | 0.383202 | − | 0.663726i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.79558 | − | 1.67930i | 0.485399 | − | 0.119950i | ||||
\(197\) | 17.3471i | 1.23593i | 0.786205 | + | 0.617966i | \(0.212043\pi\) | ||||
−0.786205 | + | 0.617966i | \(0.787957\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.53353 | − | 1.46273i | 0.179597 | − | 0.103690i | −0.407506 | − | 0.913202i | \(-0.633602\pi\) |
0.587103 | + | 0.809512i | \(0.300268\pi\) | |||||||
\(200\) | −2.95810 | + | 1.70786i | −0.209169 | + | 0.120764i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.0648i | 0.708160i | ||||||||
\(203\) | −5.63492 | − | 7.49402i | −0.395494 | − | 0.525977i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.59782 | − | 3.80925i | −0.460812 | − | 0.266050i | ||||
\(206\) | −1.44261 | − | 2.49868i | −0.100512 | − | 0.174091i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.04169 | − | 3.53631i | 0.141566 | − | 0.245199i | ||||
\(209\) | −25.2357 | − | 1.79732i | −1.74559 | − | 0.124323i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 0.252729i | − | 0.0173986i | −0.999962 | − | 0.00869931i | \(-0.997231\pi\) | ||
0.999962 | − | 0.00869931i | \(-0.00276911\pi\) | |||||||
\(212\) | 2.39830 | − | 4.15397i | 0.164716 | − | 0.285296i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.15002 | + | 14.1162i | 0.557124 | + | 0.964967i | ||||
\(215\) | 4.76793 | − | 8.25830i | 0.325170 | − | 0.563212i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.51686 | + | 22.3556i | −0.646047 | + | 1.51759i | ||||
\(218\) | 11.5034 | 0.779111 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.75444 | + | 1.82518i | −0.253124 | + | 0.123054i | ||||
\(221\) | −6.53732 | − | 11.3230i | −0.439748 | − | 0.761666i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.0370i | − | 1.27482i | −0.770527 | − | 0.637408i | \(-0.780007\pi\) | ||
0.770527 | − | 0.637408i | \(-0.219993\pi\) | |||||||
\(224\) | 1.03631 | − | 2.43435i | 0.0692416 | − | 0.162652i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.484072 | + | 0.279479i | 0.0322000 | + | 0.0185907i | ||||
\(227\) | −9.20350 | − | 15.9409i | −0.610858 | − | 1.05804i | −0.991096 | − | 0.133148i | \(-0.957491\pi\) |
0.380238 | − | 0.924888i | \(-0.375842\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.59674 | − | 2.65393i | −0.303761 | − | 0.175377i | 0.340370 | − | 0.940292i | \(-0.389448\pi\) |
−0.644131 | + | 0.764915i | \(0.722781\pi\) | |||||||
\(230\) | −10.3876 | −0.684936 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.54386 | −0.232666 | ||||||||
\(233\) | −18.4629 | − | 10.6596i | −1.20955 | − | 0.698332i | −0.246887 | − | 0.969044i | \(-0.579408\pi\) |
−0.962660 | + | 0.270712i | \(0.912741\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.95958 | + | 5.12614i | 0.193062 | + | 0.334393i | ||||
\(236\) | −2.36710 | − | 1.36664i | −0.154085 | − | 0.0889609i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.09121 | − | 6.77092i | −0.330014 | − | 0.438894i | ||||
\(239\) | 7.25163i | 0.469069i | 0.972108 | + | 0.234535i | \(0.0753566\pi\) | ||||
−0.972108 | + | 0.234535i | \(0.924643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.77705 | − | 3.07794i | −0.114470 | − | 0.198267i | 0.803098 | − | 0.595847i | \(-0.203184\pi\) |
−0.917568 | + | 0.397580i | \(0.869850\pi\) | |||||||
\(242\) | 10.2096 | − | 4.09439i | 0.656298 | − | 0.263197i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.51010 | −0.0966743 | ||||||||
\(245\) | −6.35068 | + | 6.10726i | −0.405730 | + | 0.390179i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.5743 | + | 26.9755i | −0.990968 | + | 1.71641i | ||||
\(248\) | 4.59169 | + | 7.95304i | 0.291573 | + | 0.505019i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.29636 | − | 9.17356i | 0.334971 | − | 0.580187i | ||||
\(251\) | 0.735728i | 0.0464387i | 0.999730 | + | 0.0232194i | \(0.00739162\pi\) | ||||
−0.999730 | + | 0.0232194i | \(0.992608\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.3021 | + | 1.94448i | 1.71647 | + | 0.122249i | ||||
\(254\) | −5.64146 | + | 9.77130i | −0.353977 | + | 0.613106i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 14.0352 | + | 8.10325i | 0.875494 | + | 0.505467i | 0.869170 | − | 0.494513i | \(-0.164654\pi\) |
0.00632378 | + | 0.999980i | \(0.497987\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0985460 | − | 0.809564i | −0.00612335 | − | 0.0503038i | ||||
\(260\) | 5.13968i | 0.318750i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.09152 | + | 3.51694i | −0.376335 | + | 0.217277i | ||||
\(263\) | 21.0462 | − | 12.1510i | 1.29776 | − | 0.749264i | 0.317746 | − | 0.948176i | \(-0.397074\pi\) |
0.980017 | + | 0.198911i | \(0.0637406\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.03738i | 0.370874i | ||||||||
\(266\) | −7.90514 | + | 18.5695i | −0.484695 | + | 1.13857i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.69044 | − | 2.92792i | 0.103260 | − | 0.178851i | ||||
\(269\) | 23.4246 | − | 13.5242i | 1.42822 | − | 0.824586i | 0.431244 | − | 0.902236i | \(-0.358075\pi\) |
0.996981 | + | 0.0776498i | \(0.0247416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.22166 | + | 9.04417i | −0.317193 | + | 0.549394i | −0.979901 | − | 0.199483i | \(-0.936074\pi\) |
0.662708 | + | 0.748878i | \(0.269407\pi\) | |||||||
\(272\) | −3.20191 | −0.194145 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 9.08974i | − | 0.549131i | ||||||
\(275\) | −6.34700 | + | 9.38372i | −0.382738 | + | 0.565859i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.6675 | − | 10.2003i | 1.06153 | − | 0.612877i | 0.135678 | − | 0.990753i | \(-0.456679\pi\) |
0.925856 | + | 0.377876i | \(0.123345\pi\) | |||||||
\(278\) | −6.81169 | − | 3.93273i | −0.408538 | − | 0.235869i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.402401 | + | 3.30576i | 0.0240481 | + | 0.197557i | ||||
\(281\) | 9.99535i | 0.596272i | 0.954523 | + | 0.298136i | \(0.0963650\pi\) | ||||
−0.954523 | + | 0.298136i | \(0.903635\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.74448 | − | 3.02153i | −0.103699 | − | 0.179611i | 0.809507 | − | 0.587110i | \(-0.199734\pi\) |
−0.913206 | + | 0.407499i | \(0.866401\pi\) | |||||||
\(284\) | −1.75405 | − | 3.03810i | −0.104084 | − | 0.180278i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.962115 | − | 13.5088i | 0.0568911 | − | 0.798794i | ||||
\(287\) | 12.7995 | − | 9.62420i | 0.755529 | − | 0.568099i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.37387 | − | 5.84372i | 0.198463 | − | 0.343748i | ||||
\(290\) | 3.86299 | − | 2.23030i | 0.226843 | − | 0.130968i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.483428 | + | 0.837321i | −0.0282905 | + | 0.0490005i | ||||
\(293\) | 17.3549 | 1.01388 | 0.506942 | − | 0.861980i | \(-0.330776\pi\) | ||||
0.506942 | + | 0.861980i | \(0.330776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.44034 | 0.200304 | ||||||||
\(296\) | −0.266948 | − | 0.154122i | −0.0155160 | − | 0.00895819i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.11548 | + | 5.39617i | 0.180475 | + | 0.312592i | ||||
\(299\) | 16.8495 | − | 29.1842i | 0.974433 | − | 1.68777i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0463 | + | 16.0207i | 0.694339 | + | 0.923419i | ||||
\(302\) | 17.5101 | 1.00759 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.81407 | + | 6.60616i | 0.218752 | + | 0.378889i | ||||
\(305\) | 1.64609 | − | 0.950368i | 0.0942546 | − | 0.0544179i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.6829 | 1.29458 | 0.647290 | − | 0.762244i | \(-0.275902\pi\) | ||||
0.647290 | + | 0.762244i | \(0.275902\pi\) | |||||||
\(308\) | −0.438830 | − | 8.76398i | −0.0250047 | − | 0.499374i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.0104 | − | 5.77948i | −0.568550 | − | 0.328252i | ||||
\(311\) | −5.75141 | + | 3.32058i | −0.326133 | + | 0.188293i | −0.654123 | − | 0.756388i | \(-0.726962\pi\) |
0.327990 | + | 0.944681i | \(0.393629\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.435583 | − | 0.251484i | −0.0246206 | − | 0.0142147i | 0.487639 | − | 0.873045i | \(-0.337858\pi\) |
−0.512260 | + | 0.858831i | \(0.671191\pi\) | |||||||
\(314\) | 7.77404 | 0.438715 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 15.6129i | − | 0.878296i | ||||||
\(317\) | −5.27437 | + | 9.13547i | −0.296238 | + | 0.513099i | −0.975272 | − | 0.221008i | \(-0.929065\pi\) |
0.679034 | + | 0.734107i | \(0.262399\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.5707 | + | 5.13886i | −0.591848 | + | 0.287721i | ||||
\(320\) | 1.09005 | + | 0.629341i | 0.0609357 | + | 0.0351812i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.55242 | − | 20.0900i | 0.476608 | − | 1.11957i | ||||
\(323\) | 24.4246 | 1.35902 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.97385 | + | 12.0791i | 0.386839 | + | 0.670025i | ||||
\(326\) | −15.7723 | + | 9.10616i | −0.873548 | + | 0.504343i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.05276i | − | 0.334208i | ||||||
\(329\) | −12.3509 | + | 1.50344i | −0.680928 | + | 0.0828875i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.89029 | − | 5.00613i | 0.158865 | − | 0.275162i | −0.775595 | − | 0.631231i | \(-0.782550\pi\) |
0.934460 | + | 0.356069i | \(0.115883\pi\) | |||||||
\(332\) | 0.664990 | + | 1.15180i | 0.0364960 | + | 0.0632130i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.4407 | − | 7.18264i | −0.680724 | − | 0.393016i | ||||
\(335\) | 4.25544i | 0.232500i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.1226i | − | 0.605885i | −0.953009 | − | 0.302943i | \(-0.902031\pi\) | ||
0.953009 | − | 0.302943i | \(-0.0979690\pi\) | |||||||
\(338\) | −3.18180 | − | 1.83701i | −0.173067 | − | 0.0999202i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.49025 | − | 2.01510i | 0.189285 | − | 0.109284i | ||||
\(341\) | 25.2287 | + | 17.0643i | 1.36621 | + | 0.924084i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.58300 | − | 17.3108i | −0.355449 | − | 0.934696i | ||||
\(344\) | 7.57607 | 0.408474 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.12505 | + | 2.38160i | −0.221764 | + | 0.128035i | ||||
\(347\) | 12.7058 | − | 7.33569i | 0.682083 | − | 0.393801i | −0.118557 | − | 0.992947i | \(-0.537827\pi\) |
0.800639 | + | 0.599147i | \(0.204493\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.6769 | 1.32093 | 0.660463 | − | 0.750859i | \(-0.270360\pi\) | ||||
0.660463 | + | 0.750859i | \(0.270360\pi\) | |||||||
\(350\) | 5.43117 | + | 7.22304i | 0.290308 | + | 0.386088i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.74722 | − | 1.85817i | −0.146427 | − | 0.0990409i | ||||
\(353\) | 16.6664 | − | 9.62237i | 0.887065 | − | 0.512147i | 0.0140834 | − | 0.999901i | \(-0.495517\pi\) |
0.872981 | + | 0.487754i | \(0.162184\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.82400 | + | 2.20779i | 0.202957 | + | 0.117177i | ||||
\(356\) | − | 10.6498i | − | 0.564436i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.89051i | 0.205620i | ||||||||
\(359\) | −2.85275 | − | 1.64703i | −0.150562 | − | 0.0869271i | 0.422826 | − | 0.906211i | \(-0.361038\pi\) |
−0.573388 | + | 0.819284i | \(0.694371\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.5942 | − | 33.9381i | −1.03127 | − | 1.78622i | ||||
\(362\) | 6.53492 | − | 11.3188i | 0.343468 | − | 0.594904i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.94038 | − | 4.23167i | −0.521017 | − | 0.221800i | ||||
\(365\) | − | 1.21696i | − | 0.0636988i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.7957 | − | 15.4705i | 1.39873 | − | 0.807555i | 0.404467 | − | 0.914553i | \(-0.367457\pi\) |
0.994259 | + | 0.106998i | \(0.0341238\pi\) | |||||||
\(368\) | −4.12636 | − | 7.14707i | −0.215102 | − | 0.372567i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.387982 | 0.0201702 | ||||||||
\(371\) | −11.6766 | − | 4.97077i | −0.606218 | − | 0.258070i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.832767 | + | 0.480798i | 0.0431191 | + | 0.0248948i | 0.521405 | − | 0.853310i | \(-0.325408\pi\) |
−0.478286 | + | 0.878204i | \(0.658742\pi\) | |||||||
\(374\) | −9.55077 | + | 4.64301i | −0.493859 | + | 0.240084i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.35133 | + | 4.07263i | −0.121261 | + | 0.210030i | ||||
\(377\) | 14.4709i | 0.745292i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.41216 | −0.0725379 | −0.0362689 | − | 0.999342i | \(-0.511547\pi\) | ||||
−0.0362689 | + | 0.999342i | \(0.511547\pi\) | |||||||
\(380\) | −8.31505 | − | 4.80070i | −0.426553 | − | 0.246271i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.19615 | + | 3.00000i | −0.265858 | + | 0.153493i | ||||
\(383\) | −3.27426 | − | 1.89039i | −0.167307 | − | 0.0965946i | 0.414009 | − | 0.910273i | \(-0.364128\pi\) |
−0.581315 | + | 0.813678i | \(0.697462\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.99388 | + | 9.27702i | 0.305477 | + | 0.472800i | ||||
\(386\) | −9.38289 | −0.477576 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.24463 | + | 5.33739i | −0.469325 | + | 0.270965i | ||||
\(389\) | −1.68943 | − | 2.92618i | −0.0856574 | − | 0.148363i | 0.820014 | − | 0.572344i | \(-0.193966\pi\) |
−0.905671 | + | 0.423981i | \(0.860632\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.4245 | −1.33635 | ||||||||
\(392\) | −6.72480 | − | 1.94348i | −0.339654 | − | 0.0981604i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.67356 | − | 15.0230i | 0.436968 | − | 0.756850i | ||||
\(395\) | 9.82586 | + | 17.0189i | 0.494393 | + | 0.856313i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.98525 | − | 5.76499i | −0.501145 | − | 0.289336i | 0.228041 | − | 0.973652i | \(-0.426768\pi\) |
−0.729186 | + | 0.684315i | \(0.760101\pi\) | |||||||
\(398\) | −2.92547 | −0.146640 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.41572 | 0.170786 | ||||||||
\(401\) | 13.0261 | − | 22.5619i | 0.650494 | − | 1.12669i | −0.332509 | − | 0.943100i | \(-0.607895\pi\) |
0.983003 | − | 0.183588i | \(-0.0587714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.4753 | − | 18.7496i | 1.61771 | − | 0.933986i | ||||
\(404\) | 5.03242 | − | 8.71642i | 0.250372 | − | 0.433658i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.13297 | + | 9.30747i | 0.0562285 | + | 0.461922i | ||||
\(407\) | −1.01975 | − | 0.0726278i | −0.0505471 | − | 0.00360003i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.5109 | + | 30.3297i | 0.865856 | + | 1.49971i | 0.866194 | + | 0.499707i | \(0.166559\pi\) |
−0.000338063 | 1.00000i | \(0.500108\pi\) | ||||||||
\(410\) | 3.80925 | + | 6.59782i | 0.188126 | + | 0.325843i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.88523i | 0.142145i | ||||||||
\(413\) | −2.83254 | + | 6.65377i | −0.139380 | + | 0.327411i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.44974 | − | 0.837011i | −0.0711652 | − | 0.0410872i | ||||
\(416\) | −3.53631 | + | 2.04169i | −0.173382 | + | 0.100102i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.9561 | + | 14.1744i | 1.02500 | + | 0.693292i | ||||
\(419\) | − | 12.1242i | − | 0.592307i | −0.955140 | − | 0.296154i | \(-0.904296\pi\) | ||
0.955140 | − | 0.296154i | \(-0.0957040\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6940 | 0.911089 | 0.455545 | − | 0.890213i | \(-0.349445\pi\) | ||||
0.455545 | + | 0.890213i | \(0.349445\pi\) | |||||||
\(422\) | −0.126365 | + | 0.218870i | −0.00615134 | + | 0.0106544i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.15397 | + | 2.39830i | −0.201735 | + | 0.116472i | ||||
\(425\) | 5.46842 | − | 9.47158i | 0.265257 | − | 0.459439i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.482779 | + | 3.96607i | 0.0233633 | + | 0.191932i | ||||
\(428\) | − | 16.3000i | − | 0.787892i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.25830 | + | 4.76793i | −0.398251 | + | 0.229930i | ||||
\(431\) | −29.3945 | + | 16.9709i | −1.41588 | + | 0.817461i | −0.995934 | − | 0.0900869i | \(-0.971286\pi\) |
−0.419949 | + | 0.907548i | \(0.637952\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.0949i | 1.30210i | 0.759037 | + | 0.651048i | \(0.225670\pi\) | ||||
−0.759037 | + | 0.651048i | \(0.774330\pi\) | |||||||
\(434\) | 19.4196 | − | 14.6020i | 0.932172 | − | 0.700920i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.96227 | − | 5.75172i | −0.477106 | − | 0.275458i | ||||
\(437\) | 31.4765 | + | 54.5188i | 1.50572 | + | 2.60799i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2269 | − | 17.7135i | 0.488104 | − | 0.845421i | −0.511802 | − | 0.859103i | \(-0.671022\pi\) |
0.999906 | + | 0.0136821i | \(0.00435529\pi\) | |||||||
\(440\) | 4.16403 | + | 0.296567i | 0.198512 | + | 0.0141383i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.0746i | 0.621897i | ||||||||
\(443\) | −1.79868 | + | 3.11541i | −0.0854579 | + | 0.148017i | −0.905586 | − | 0.424162i | \(-0.860569\pi\) |
0.820128 | + | 0.572180i | \(0.193902\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.70233 | + | 11.6088i | 0.317721 | + | 0.550309i | ||||
\(446\) | −9.51852 | + | 16.4866i | −0.450715 | + | 0.780662i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.11465 | + | 1.59005i | −0.0999078 | + | 0.0751228i | ||||
\(449\) | −37.0664 | −1.74927 | −0.874637 | − | 0.484779i | \(-0.838900\pi\) | ||||
−0.874637 | + | 0.484779i | \(0.838900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.77694 | − | 18.0544i | −0.413290 | − | 0.850148i | ||||
\(452\) | −0.279479 | − | 0.484072i | −0.0131456 | − | 0.0227688i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.4070i | 0.863883i | ||||||||
\(455\) | 13.4987 | − | 1.64316i | 0.632828 | − | 0.0770324i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.7194 | + | 9.07561i | 0.735323 | + | 0.424539i | 0.820366 | − | 0.571838i | \(-0.193769\pi\) |
−0.0850431 | + | 0.996377i | \(0.527103\pi\) | |||||||
\(458\) | 2.65393 | + | 4.59674i | 0.124010 | + | 0.214792i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.99589 | + | 5.19378i | 0.419436 | + | 0.242161i | ||||
\(461\) | 22.4278 | 1.04457 | 0.522284 | − | 0.852772i | \(-0.325080\pi\) | ||||
0.522284 | + | 0.852772i | \(0.325080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.6274 | −0.726267 | −0.363134 | − | 0.931737i | \(-0.618293\pi\) | ||||
−0.363134 | + | 0.931737i | \(0.618293\pi\) | |||||||
\(464\) | 3.06907 | + | 1.77193i | 0.142478 | + | 0.0822598i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.6596 | + | 18.4629i | 0.493796 | + | 0.855279i | ||||
\(467\) | 5.27860 | + | 3.04760i | 0.244264 | + | 0.141026i | 0.617135 | − | 0.786857i | \(-0.288293\pi\) |
−0.372871 | + | 0.927883i | \(0.621626\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.23022 | − | 3.50365i | −0.380036 | − | 0.161783i | ||||
\(470\) | − | 5.91916i | − | 0.273031i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.36664 | + | 2.36710i | 0.0629048 | + | 0.108954i | ||||
\(473\) | 22.5982 | − | 10.9858i | 1.03906 | − | 0.505130i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.0556 | −1.19551 | ||||||||
\(476\) | 1.02365 | + | 8.40939i | 0.0469190 | + | 0.385444i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.62582 | − | 6.28010i | 0.165841 | − | 0.287245i | ||||
\(479\) | 15.3138 | + | 26.5242i | 0.699704 | + | 1.21192i | 0.968569 | + | 0.248745i | \(0.0800182\pi\) |
−0.268865 | + | 0.963178i | \(0.586648\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.629341 | + | 1.09005i | −0.0286955 | + | 0.0497020i | ||||
\(482\) | 3.55410i | 0.161885i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8890 | − | 1.55896i | −0.494953 | − | 0.0708617i | ||||
\(485\) | 6.71808 | − | 11.6361i | 0.305052 | − | 0.528366i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.58726 | + | 2.74922i | 0.0719258 | + | 0.124579i | 0.899745 | − | 0.436415i | \(-0.143752\pi\) |
−0.827819 | + | 0.560995i | \(0.810419\pi\) | |||||||
\(488\) | 1.30779 | + | 0.755050i | 0.0592007 | + | 0.0341795i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.55348 | − | 2.11370i | 0.386407 | − | 0.0954874i | ||||
\(491\) | − | 32.6507i | − | 1.47351i | −0.676162 | − | 0.736753i | \(-0.736358\pi\) | ||
0.676162 | − | 0.736753i | \(-0.263642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.82691 | − | 5.67357i | 0.442582 | − | 0.255525i | ||||
\(494\) | 26.9755 | − | 15.5743i | 1.21368 | − | 0.700721i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 9.18338i | − | 0.412346i | ||||||
\(497\) | −7.41839 | + | 5.57805i | −0.332760 | + | 0.250210i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.2274 | + | 24.6426i | −0.636906 | + | 1.10315i | 0.349202 | + | 0.937048i | \(0.386453\pi\) |
−0.986108 | + | 0.166106i | \(0.946881\pi\) | |||||||
\(500\) | −9.17356 | + | 5.29636i | −0.410254 | + | 0.236860i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.367864 | − | 0.637159i | 0.0164186 | − | 0.0284378i | ||||
\(503\) | −22.5058 | −1.00348 | −0.501741 | − | 0.865018i | \(-0.667307\pi\) | ||||
−0.501741 | + | 0.865018i | \(0.667307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.6684i | 0.563739i | ||||||||
\(506\) | −22.6720 | − | 15.3350i | −1.00789 | − | 0.681724i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.77130 | − | 5.64146i | 0.433531 | − | 0.250299i | ||||
\(509\) | 11.6437 | + | 6.72249i | 0.516098 | + | 0.297969i | 0.735337 | − | 0.677702i | \(-0.237024\pi\) |
−0.219239 | + | 0.975671i | \(0.570357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.35366 | + | 1.00197i | 0.104120 | + | 0.0443244i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.10325 | − | 14.0352i | −0.357419 | − | 0.619068i | ||||
\(515\) | −1.81579 | − | 3.14505i | −0.0800134 | − | 0.138587i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.10803 | + | 15.5576i | −0.0487310 | + | 0.684221i | ||||
\(518\) | −0.319439 | + | 0.750376i | −0.0140353 | + | 0.0329696i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.56984 | − | 4.45110i | 0.112695 | − | 0.195193i | ||||
\(521\) | −34.2339 | + | 19.7649i | −1.49981 | + | 0.865918i | −1.00000 | 0.000215610i | \(-0.999931\pi\) | |
−0.499813 | + | 0.866133i | \(0.666598\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.8061 | − | 25.6449i | 0.647425 | − | 1.12137i | −0.336310 | − | 0.941751i | \(-0.609179\pi\) |
0.983736 | − | 0.179622i | \(-0.0574875\pi\) | |||||||
\(524\) | 7.03388 | 0.307276 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.3021 | −1.05962 | ||||||||
\(527\) | −25.4650 | − | 14.7022i | −1.10927 | − | 0.640438i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5538 | − | 39.0643i | −0.980599 | − | 1.69845i | ||||
\(530\) | 3.01869 | − | 5.22853i | 0.131124 | − | 0.227113i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.1308 | − | 12.1291i | 0.699360 | − | 0.525864i | ||||
\(533\) | −24.7158 | −1.07056 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.2583 | + | 17.7679i | 0.443504 | + | 0.768172i | ||||
\(536\) | −2.92792 | + | 1.69044i | −0.126467 | + | 0.0730157i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.0484 | −1.16614 | ||||||||
\(539\) | −22.8771 | + | 3.95437i | −0.985388 | + | 0.170327i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.1111 | − | 8.72442i | −0.649679 | − | 0.375092i | 0.138654 | − | 0.990341i | \(-0.455722\pi\) |
−0.788333 | + | 0.615249i | \(0.789056\pi\) | |||||||
\(542\) | 9.04417 | − | 5.22166i | 0.388480 | − | 0.224289i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.77294 | + | 1.60096i | 0.118889 | + | 0.0686405i | ||||
\(545\) | 14.4792 | 0.620220 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.16878i | 0.0499734i | 0.999688 | + | 0.0249867i | \(0.00795434\pi\) | ||||
−0.999688 | + | 0.0249867i | \(0.992046\pi\) | |||||||
\(548\) | −4.54487 | + | 7.87195i | −0.194147 | + | 0.336273i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.1885 | − | 4.95304i | 0.434440 | − | 0.211198i | ||||
\(551\) | −23.4113 | − | 13.5165i | −0.997355 | − | 0.575823i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.0053 | + | 4.99146i | −1.74372 | + | 0.212258i | ||||
\(554\) | −20.4006 | −0.866739 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.93273 | + | 6.81169i | 0.166785 | + | 0.288880i | ||||
\(557\) | 4.20151 | − | 2.42574i | 0.178024 | − | 0.102782i | −0.408340 | − | 0.912830i | \(-0.633892\pi\) |
0.586364 | + | 0.810048i | \(0.300559\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 30.9360i | − | 1.30845i | ||||||
\(560\) | 1.30439 | − | 3.06407i | 0.0551205 | − | 0.129481i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.99767 | − | 8.65622i | 0.210814 | − | 0.365141i | ||||
\(563\) | −13.0572 | − | 22.6158i | −0.550297 | − | 0.953143i | −0.998253 | − | 0.0590869i | \(-0.981181\pi\) |
0.447956 | − | 0.894056i | \(-0.352152\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.609293 | + | 0.351776i | 0.0256332 | + | 0.0147993i | ||||
\(566\) | 3.48896i | 0.146652i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.50810i | 0.147196i | ||||||||
\(569\) | −6.47913 | − | 3.74073i | −0.271619 | − | 0.156820i | 0.358004 | − | 0.933720i | \(-0.383457\pi\) |
−0.629623 | + | 0.776901i | \(0.716791\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.5249 | − | 16.4688i | 1.19373 | − | 0.689199i | 0.234578 | − | 0.972097i | \(-0.424629\pi\) |
0.959150 | + | 0.282898i | \(0.0912958\pi\) | |||||||
\(572\) | −7.58763 | + | 11.2179i | −0.317255 | + | 0.469045i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.8968 | + | 1.93507i | −0.663518 | + | 0.0807682i | ||||
\(575\) | 28.1890 | 1.17556 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.34703 | − | 0.777711i | 0.0560778 | − | 0.0323765i | −0.471699 | − | 0.881760i | \(-0.656359\pi\) |
0.527777 | + | 0.849383i | \(0.323026\pi\) | |||||||
\(578\) | −5.84372 | + | 3.37387i | −0.243067 | + | 0.140335i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.46060 | −0.185216 | ||||||||
\(581\) | 2.81244 | − | 2.11473i | 0.116680 | − | 0.0877340i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.91290 | + | 13.1773i | −0.369134 | + | 0.545747i | ||||
\(584\) | 0.837321 | − | 0.483428i | 0.0346486 | − | 0.0200044i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.0298 | − | 8.67744i | −0.620874 | − | 0.358462i | ||||
\(587\) | 42.8124i | 1.76706i | 0.468376 | + | 0.883529i | \(0.344839\pi\) | ||||
−0.468376 | + | 0.883529i | \(0.655161\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 70.0520i | 2.88644i | ||||||||
\(590\) | −2.97942 | − | 1.72017i | −0.122661 | − | 0.0708183i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.154122 | + | 0.266948i | 0.00633439 | + | 0.0109715i | ||||
\(593\) | −16.7711 | + | 29.0484i | −0.688707 | + | 1.19288i | 0.283549 | + | 0.958958i | \(0.408488\pi\) |
−0.972256 | + | 0.233918i | \(0.924845\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.40821 | − | 8.52244i | −0.262711 | − | 0.349386i | ||||
\(596\) | − | 6.23096i | − | 0.255230i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −29.1842 | + | 16.8495i | −1.19343 | + | 0.689029i | ||||
\(599\) | 7.00856 | + | 12.1392i | 0.286362 | + | 0.495993i | 0.972939 | − | 0.231064i | \(-0.0742207\pi\) |
−0.686577 | + | 0.727057i | \(0.740887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.1513 | −1.47464 | −0.737322 | − | 0.675542i | \(-0.763910\pi\) | ||||
−0.737322 | + | 0.675542i | \(0.763910\pi\) | |||||||
\(602\) | −2.42207 | − | 19.8975i | −0.0987163 | − | 0.810963i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.1642 | − | 8.75506i | −0.617023 | − | 0.356238i | ||||
\(605\) | 12.8506 | − | 5.15353i | 0.522453 | − | 0.209521i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.8196 | − | 25.6684i | 0.601511 | − | 1.04185i | −0.391082 | − | 0.920356i | \(-0.627899\pi\) |
0.992593 | − | 0.121491i | \(-0.0387676\pi\) | |||||||
\(608\) | − | 7.62813i | − | 0.309362i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.90074 | −0.0769586 | ||||||||
\(611\) | 16.6301 | + | 9.60139i | 0.672782 | + | 0.388431i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.9964 | + | 16.7411i | −1.17115 | + | 0.676166i | −0.953951 | − | 0.299961i | \(-0.903026\pi\) |
−0.217202 | + | 0.976127i | \(0.569693\pi\) | |||||||
\(614\) | −19.6439 | − | 11.3414i | −0.792765 | − | 0.457703i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00195 | + | 7.80925i | −0.161243 | + | 0.314644i | ||||
\(617\) | −8.79395 | −0.354031 | −0.177016 | − | 0.984208i | \(-0.556644\pi\) | ||||
−0.177016 | + | 0.984208i | \(0.556644\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.2445 | − | 13.9976i | 0.974469 | − | 0.562610i | 0.0738736 | − | 0.997268i | \(-0.476464\pi\) |
0.900596 | + | 0.434657i | \(0.143131\pi\) | |||||||
\(620\) | 5.77948 | + | 10.0104i | 0.232109 | + | 0.402025i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.64116 | 0.266286 | ||||||||
\(623\) | −27.9701 | + | 3.40473i | −1.12060 | + | 0.136408i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.87286 | + | 3.24390i | −0.0749146 | + | 0.129756i | ||||
\(626\) | 0.251484 | + | 0.435583i | 0.0100513 | + | 0.0174094i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.73252 | − | 3.88702i | −0.268657 | − | 0.155109i | ||||
\(629\) | 0.986974 | 0.0393532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.154087 | −0.00613412 | −0.00306706 | − | 0.999995i | \(-0.500976\pi\) | ||||
−0.00306706 | + | 0.999995i | \(0.500976\pi\) | |||||||
\(632\) | −7.80647 | + | 13.5212i | −0.310525 | + | 0.537844i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.13547 | − | 5.27437i | 0.362816 | − | 0.209472i | ||||
\(635\) | −7.10081 | + | 12.2990i | −0.281787 | + | 0.488069i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.93596 | + | 27.4599i | −0.314434 | + | 1.08800i | ||||
\(638\) | 11.7240 | + | 0.834995i | 0.464156 | + | 0.0330578i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.629341 | − | 1.09005i | −0.0248769 | − | 0.0430880i | ||||
\(641\) | −9.92017 | − | 17.1822i | −0.391823 | − | 0.678658i | 0.600867 | − | 0.799349i | \(-0.294822\pi\) |
−0.992690 | + | 0.120691i | \(0.961489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.2948i | 0.997529i | 0.866737 | + | 0.498765i | \(0.166213\pi\) | ||||
−0.866737 | + | 0.498765i | \(0.833787\pi\) | |||||||
\(644\) | −17.4516 | + | 13.1223i | −0.687690 | + | 0.517089i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.1523 | − | 12.2123i | −0.832228 | − | 0.480487i | ||||
\(647\) | −0.813596 | + | 0.469730i | −0.0319857 | + | 0.0184670i | −0.515908 | − | 0.856644i | \(-0.672545\pi\) |
0.483922 | + | 0.875111i | \(0.339212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.50893 | + | 5.07892i | 0.294751 | + | 0.199365i | ||||
\(650\) | − | 13.9477i | − | 0.547073i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.2123 | 0.713249 | ||||||||
\(653\) | −5.50375 | + | 9.53278i | −0.215379 | + | 0.373047i | −0.953390 | − | 0.301742i | \(-0.902432\pi\) |
0.738011 | + | 0.674789i | \(0.235765\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.66729 | + | 4.42671i | −0.299586 | + | 0.172966i | ||||
\(656\) | −3.02638 | + | 5.24185i | −0.118160 | + | 0.204660i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.4479 | + | 4.87344i | 0.446287 | + | 0.189986i | ||||
\(659\) | 29.9068i | 1.16500i | 0.812830 | + | 0.582501i | \(0.197926\pi\) | ||||
−0.812830 | + | 0.582501i | \(0.802074\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.32896 | − | 1.34463i | 0.0905861 | − | 0.0522999i | −0.454023 | − | 0.890990i | \(-0.650011\pi\) |
0.544609 | + | 0.838690i | \(0.316678\pi\) | |||||||
\(662\) | −5.00613 | + | 2.89029i | −0.194569 | + | 0.112334i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.32998i | − | 0.0516132i | ||||||
\(665\) | −9.95006 | + | 23.3731i | −0.385847 | + | 0.906371i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.3282 | + | 14.6233i | 0.980713 | + | 0.566215i | ||||
\(668\) | 7.18264 | + | 12.4407i | 0.277905 | + | 0.481345i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.12772 | − | 3.68532i | 0.0822011 | − | 0.142376i | ||||
\(671\) | 4.99578 | + | 0.355806i | 0.192860 | + | 0.0137357i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.56361i | 0.137367i | 0.997638 | + | 0.0686836i | \(0.0218799\pi\) | ||||
−0.997638 | + | 0.0686836i | \(0.978120\pi\) | |||||||
\(674\) | −5.56129 | + | 9.63243i | −0.214213 | + | 0.371027i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.83701 | + | 3.18180i | 0.0706543 | + | 0.122377i | ||||
\(677\) | 15.5901 | − | 27.0029i | 0.599178 | − | 1.03781i | −0.393765 | − | 0.919211i | \(-0.628828\pi\) |
0.992943 | − | 0.118595i | \(-0.0378390\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.9734 | + | 22.5734i | 0.651381 | + | 0.866288i | ||||
\(680\) | −4.03019 | −0.154551 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.3166 | − | 27.3925i | −0.509918 | − | 1.04891i | ||||
\(683\) | −7.79993 | − | 13.5099i | −0.298456 | − | 0.516941i | 0.677327 | − | 0.735682i | \(-0.263138\pi\) |
−0.975783 | + | 0.218741i | \(0.929805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 11.4411i | − | 0.437142i | ||||||
\(686\) | −2.95436 | + | 18.2831i | −0.112798 | + | 0.698052i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.56107 | − | 3.78804i | −0.250138 | − | 0.144417i | ||||
\(689\) | 9.79316 | + | 16.9623i | 0.373090 | + | 0.646210i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.8902 | − | 18.4118i | −1.21316 | − | 0.700419i | −0.249714 | − | 0.968320i | \(-0.580337\pi\) |
−0.963447 | + | 0.267901i | \(0.913670\pi\) | |||||||
\(692\) | 4.76319 | 0.181069 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.6714 | −0.556918 | ||||||||
\(695\) | −8.57375 | − | 4.95006i | −0.325221 | − | 0.187766i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.69021 | + | 16.7839i | 0.367043 | + | 0.635737i | ||||
\(698\) | −21.3708 | − | 12.3385i | −0.808899 | − | 0.467018i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.09201 | − | 8.97092i | −0.0412739 | − | 0.339069i | ||||
\(701\) | − | 15.6940i | − | 0.592754i | −0.955071 | − | 0.296377i | \(-0.904222\pi\) | ||
0.955071 | − | 0.296377i | \(-0.0957784\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.17567 | − | 2.03631i | −0.0443411 | − | 0.0768010i | ||||
\(704\) | 1.45007 | + | 2.98283i | 0.0546516 | + | 0.112420i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.2447 | −0.724285 | ||||||||
\(707\) | −24.5014 | − | 10.4303i | −0.921468 | − | 0.392273i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.1733 | − | 21.0847i | 0.457176 | − | 0.791852i | −0.541634 | − | 0.840614i | \(-0.682194\pi\) |
0.998810 | + | 0.0487621i | \(0.0155276\pi\) | |||||||
\(710\) | −2.20779 | − | 3.82400i | −0.0828569 | − | 0.143512i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.32488 | + | 9.22296i | −0.199558 | + | 0.345645i | ||||
\(713\) | − | 75.7880i | − | 2.83828i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.21100 | − | 17.0033i | 0.0452887 | − | 0.635888i | ||||
\(716\) | 1.94526 | − | 3.36928i | 0.0726976 | − | 0.125916i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.64703 | + | 2.85275i | 0.0614668 | + | 0.106464i | ||||
\(719\) | −36.9070 | − | 21.3083i | −1.37640 | − | 0.794665i | −0.384676 | − | 0.923051i | \(-0.625687\pi\) |
−0.991724 | + | 0.128386i | \(0.959020\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.57766 | − | 0.922408i | 0.282207 | − | 0.0343523i | ||||
\(722\) | 39.1884i | 1.45844i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.3188 | + | 6.53492i | −0.420661 | + | 0.242868i | ||||
\(725\) | −10.4831 | + | 6.05242i | −0.389332 | + | 0.224781i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.2698i | − | 0.863031i | −0.902106 | − | 0.431515i | \(-0.857979\pi\) | ||
0.902106 | − | 0.431515i | \(-0.142021\pi\) | |||||||
\(728\) | 6.49279 | + | 8.63492i | 0.240639 | + | 0.320031i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.608482 | + | 1.05392i | −0.0225209 | + | 0.0390074i | ||||
\(731\) | −21.0080 | + | 12.1290i | −0.777008 | + | 0.448606i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.8378 | + | 32.6281i | −0.695791 | + | 1.20515i | 0.274122 | + | 0.961695i | \(0.411613\pi\) |
−0.969913 | + | 0.243450i | \(0.921721\pi\) | |||||||
\(734\) | −30.9410 | −1.14205 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.25273i | 0.304200i | ||||||||
\(737\) | −6.28225 | + | 9.28799i | −0.231410 | + | 0.342127i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.479784 | − | 0.277003i | 0.0176491 | − | 0.0101897i | −0.491149 | − | 0.871075i | \(-0.663423\pi\) |
0.508799 | + | 0.860886i | \(0.330090\pi\) | |||||||
\(740\) | −0.336003 | − | 0.193991i | −0.0123517 | − | 0.00713126i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.62682 | + | 10.1431i | 0.279990 | + | 0.372365i | ||||
\(743\) | − | 20.1974i | − | 0.740972i | −0.928838 | − | 0.370486i | \(-0.879191\pi\) | ||
0.928838 | − | 0.370486i | \(-0.120809\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.92140 | + | 6.79207i | 0.143669 | + | 0.248842i | ||||
\(746\) | −0.480798 | − | 0.832767i | −0.0176033 | − | 0.0304898i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.5927 | + | 0.754426i | 0.387308 | + | 0.0275845i | ||||
\(749\) | −42.8098 | + | 5.21112i | −1.56424 | + | 0.190410i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.70031 | + | 6.40913i | −0.135026 | + | 0.233872i | −0.925607 | − | 0.378485i | \(-0.876445\pi\) |
0.790581 | + | 0.612357i | \(0.209779\pi\) | |||||||
\(752\) | 4.07263 | − | 2.35133i | 0.148513 | − | 0.0857443i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.23547 | − | 12.5322i | 0.263500 | − | 0.456396i | ||||
\(755\) | 22.0397 | 0.802106 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.1994 | −1.06127 | −0.530636 | − | 0.847600i | \(-0.678047\pi\) | ||||
−0.530636 | + | 0.847600i | \(0.678047\pi\) | |||||||
\(758\) | 1.22297 | + | 0.706081i | 0.0444202 | + | 0.0256460i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.80070 | + | 8.31505i | 0.174140 | + | 0.301619i | ||||
\(761\) | 25.4831 | − | 44.1380i | 0.923761 | − | 1.60000i | 0.130220 | − | 0.991485i | \(-0.458432\pi\) |
0.793541 | − | 0.608517i | \(-0.208235\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.9212 | + | 28.0034i | −0.431576 | + | 1.01379i | ||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.89039 | + | 3.27426i | 0.0683027 | + | 0.118304i | ||||
\(767\) | 9.66576 | − | 5.58053i | 0.349010 | − | 0.201501i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.9963 | 1.18988 | 0.594938 | − | 0.803771i | \(-0.297176\pi\) | ||||
0.594938 | + | 0.803771i | \(0.297176\pi\) | |||||||
\(770\) | −0.552347 | − | 11.0311i | −0.0199052 | − | 0.397532i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.12582 | + | 4.69144i | 0.292455 | + | 0.168849i | ||||
\(773\) | 28.1797 | − | 16.2696i | 1.01355 | − | 0.585175i | 0.101323 | − | 0.994854i | \(-0.467692\pi\) |
0.912230 | + | 0.409678i | \(0.134359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.1654 | + | 15.6839i | 0.975808 | + | 0.563383i | ||||
\(776\) | 10.6748 | 0.383202 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.37886i | 0.121138i | ||||||||
\(779\) | 23.0856 | − | 39.9855i | 0.827129 | − | 1.43263i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.08699 | + | 10.4641i | 0.182027 | + | 0.374434i | ||||
\(782\) | 22.8843 | + | 13.2123i | 0.818341 | + | 0.472470i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.85211 | + | 5.04550i | 0.173290 | + | 0.180196i | ||||
\(785\) | 9.78505 | 0.349243 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.0577 | − | 17.4205i | −0.358519 | − | 0.620973i | 0.629195 | − | 0.777248i | \(-0.283385\pi\) |
−0.987714 | + | 0.156275i | \(0.950051\pi\) | |||||||
\(788\) | −15.0230 | + | 8.67356i | −0.535174 | + | 0.308983i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 19.6517i | − | 0.699177i | ||||||
\(791\) | −1.18200 | + | 0.888772i | −0.0420271 | + | 0.0316011i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.08316 | − | 5.34019i | 0.109486 | − | 0.189636i | ||||
\(794\) | 5.76499 | + | 9.98525i | 0.204592 | + | 0.354363i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.53353 | + | 1.46273i | 0.0897985 | + | 0.0518452i | ||||
\(797\) | 31.1568i | 1.10363i | 0.833966 | + | 0.551816i | \(0.186065\pi\) | ||||
−0.833966 | + | 0.551816i | \(0.813935\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.0575i | − | 0.532697i | ||||||
\(800\) | −2.95810 | − | 1.70786i | −0.104585 | − | 0.0603819i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.5619 | + | 13.0261i | −0.796689 | + | 0.459969i | ||||
\(803\) | 1.79658 | − | 2.65616i | 0.0634001 | − | 0.0937339i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.7648 | − | 25.2870i | 0.379409 | − | 0.891248i | ||||
\(806\) | −37.4993 | −1.32086 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.71642 | + | 5.03242i | −0.306642 | + | 0.177040i | ||||
\(809\) | −12.6960 | + | 7.33001i | −0.446366 | + | 0.257709i | −0.706294 | − | 0.707918i | \(-0.749634\pi\) |
0.259928 | + | 0.965628i | \(0.416301\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.7501 | 1.60650 | 0.803251 | − | 0.595640i | \(-0.203102\pi\) | ||||
0.803251 | + | 0.595640i | \(0.203102\pi\) | |||||||
\(812\) | 3.67255 | − | 8.62700i | 0.128881 | − | 0.302748i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.846815 | + | 0.572772i | 0.0296809 | + | 0.0200757i | ||||
\(815\) | −19.8523 | + | 11.4618i | −0.695397 | + | 0.401488i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.0487 | + | 28.8956i | 1.75098 | + | 1.01093i | ||||
\(818\) | − | 35.0217i | − | 1.22451i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 7.61851i | − | 0.266050i | ||||||
\(821\) | 6.11121 | + | 3.52831i | 0.213283 | + | 0.123139i | 0.602836 | − | 0.797865i | \(-0.294037\pi\) |
−0.389553 | + | 0.921004i | \(0.627371\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.2038 | + | 24.6016i | 0.495112 | + | 0.857559i | 0.999984 | − | 0.00563530i | \(-0.00179378\pi\) |
−0.504872 | + | 0.863194i | \(0.668460\pi\) | |||||||
\(824\) | 1.44261 | − | 2.49868i | 0.0502559 | − | 0.0870457i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.77994 | − | 4.34606i | 0.201110 | − | 0.151219i | ||||
\(827\) | 0.161893i | 0.00562957i | 0.999996 | + | 0.00281478i | \(0.000895975\pi\) | ||||
−0.999996 | + | 0.00281478i | \(0.999104\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.0966 | + | 12.1801i | −0.732715 | + | 0.423033i | −0.819415 | − | 0.573201i | \(-0.805701\pi\) |
0.0866997 | + | 0.996234i | \(0.472368\pi\) | |||||||
\(830\) | 0.837011 | + | 1.44974i | 0.0290531 | + | 0.0503214i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.08338 | 0.141566 | ||||||||
\(833\) | 21.7589 | − | 5.37697i | 0.753900 | − | 0.186301i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.6589 | − | 9.04066i | −0.541898 | − | 0.312865i | ||||
\(836\) | −11.0613 | − | 22.7534i | −0.382564 | − | 0.786944i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.06211 | + | 10.4999i | −0.209412 | + | 0.362713i | ||||
\(839\) | 3.31341i | 0.114392i | 0.998363 | + | 0.0571958i | \(0.0182159\pi\) | ||||
−0.998363 | + | 0.0571958i | \(0.981784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.4410 | 0.566932 | ||||||||
\(842\) | −16.1895 | − | 9.34699i | −0.557926 | − | 0.322119i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.218870 | − | 0.126365i | 0.00753382 | − | 0.00434965i | ||||
\(845\) | −4.00487 | − | 2.31221i | −0.137772 | − | 0.0795425i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.613188 | + | 29.0968i | −0.0210694 | + | 0.999778i | ||||
\(848\) | 4.79659 | 0.164716 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.47158 | + | 5.46842i | −0.324873 | + | 0.187565i | ||||
\(851\) | 1.27193 | + | 2.20305i | 0.0436012 | + | 0.0755196i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.0905 | 0.585169 | 0.292584 | − | 0.956240i | \(-0.405485\pi\) | ||||
0.292584 | + | 0.956240i | \(0.405485\pi\) | |||||||
\(854\) | 1.56494 | − | 3.67611i | 0.0535511 | − | 0.125794i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.15002 | + | 14.1162i | −0.278562 | + | 0.482483i | ||||
\(857\) | 11.2484 | + | 19.4827i | 0.384237 | + | 0.665517i | 0.991663 | − | 0.128859i | \(-0.0411314\pi\) |
−0.607426 | + | 0.794376i | \(0.707798\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.3698 | − | 19.2661i | −1.13856 | − | 0.657350i | −0.192489 | − | 0.981299i | \(-0.561656\pi\) |
−0.946074 | + | 0.323950i | \(0.894989\pi\) | |||||||
\(860\) | 9.53587 | 0.325170 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.9418 | 1.15606 | ||||||||
\(863\) | −12.8730 | + | 22.2967i | −0.438202 | + | 0.758989i | −0.997551 | − | 0.0699437i | \(-0.977718\pi\) |
0.559348 | + | 0.828933i | \(0.311051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.19212 | + | 2.99767i | −0.176537 | + | 0.101924i | ||||
\(866\) | 13.5474 | − | 23.4648i | 0.460360 | − | 0.797368i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −24.1189 | + | 2.93593i | −0.818649 | + | 0.0996519i | ||||
\(869\) | −3.67867 | + | 51.6514i | −0.124790 | + | 1.75215i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.90270 | + | 11.9558i | 0.233889 | + | 0.405108i | ||||
\(872\) | 5.75172 | + | 9.96227i | 0.194778 | + | 0.337365i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 62.9529i | − | 2.12941i | ||||||
\(875\) | 16.8430 | + | 22.3999i | 0.569396 | + | 0.757254i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.7676 | − | 8.52609i | −0.498667 | − | 0.287906i | 0.229496 | − | 0.973310i | \(-0.426292\pi\) |
−0.728163 | + | 0.685404i | \(0.759626\pi\) | |||||||
\(878\) | −17.7135 | + | 10.2269i | −0.597803 | + | 0.345142i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.45787 | − | 2.33885i | −0.116565 | − | 0.0788426i | ||||
\(881\) | 38.3968i | 1.29362i | 0.762651 | + | 0.646811i | \(0.223898\pi\) | ||||
−0.762651 | + | 0.646811i | \(0.776102\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.3727 | −1.19038 | −0.595192 | − | 0.803583i | \(-0.702924\pi\) | ||||
−0.595192 | + | 0.803583i | \(0.702924\pi\) | |||||||
\(884\) | 6.53732 | − | 11.3230i | 0.219874 | − | 0.380833i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.11541 | − | 1.79868i | 0.104664 | − | 0.0604279i | ||||
\(887\) | −1.05289 | + | 1.82365i | −0.0353525 | + | 0.0612322i | −0.883160 | − | 0.469071i | \(-0.844589\pi\) |
0.847808 | + | 0.530304i | \(0.177922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.9404 | − | 23.8594i | −0.601702 | − | 0.800219i | ||||
\(890\) | − | 13.4047i | − | 0.449325i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.4866 | − | 9.51852i | 0.552011 | − | 0.318704i | ||||
\(893\) | −31.0665 | + | 17.9363i | −1.03960 | + | 0.600215i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.89692i | 0.163686i | ||||||||
\(896\) | 2.62636 | − | 0.319700i | 0.0877407 | − | 0.0106804i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32.1005 | + | 18.5332i | 1.07121 | + | 0.618461i | ||||
\(899\) | 16.2723 | + | 28.1845i | 0.542712 | + | 0.940005i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.67914 | − | 13.3007i | 0.255829 | − | 0.443109i | ||||
\(902\) | −1.42613 | + | 20.0240i | −0.0474851 | + | 0.666727i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.558958i | 0.0185907i | ||||||||
\(905\) | 8.22539 | − | 14.2468i | 0.273421 | − | 0.473579i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.2204 | − | 43.6831i | −0.837431 | − | 1.45047i | −0.892035 | − | 0.451965i | \(-0.850723\pi\) |
0.0546043 | − | 0.998508i | \(-0.482610\pi\) | |||||||
\(908\) | 9.20350 | − | 15.9409i | 0.305429 | − | 0.529018i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.5118 | − | 5.32632i | −0.414761 | − | 0.176566i | ||||
\(911\) | 1.24825 | 0.0413565 | 0.0206782 | − | 0.999786i | \(-0.493417\pi\) | ||||
0.0206782 | + | 0.999786i | \(0.493417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.92857 | − | 3.96711i | −0.0638262 | − | 0.131292i | ||||
\(914\) | −9.07561 | − | 15.7194i | −0.300195 | − | 0.519952i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 5.30786i | − | 0.175377i | ||||||
\(917\) | −2.24873 | − | 18.4735i | −0.0742597 | − | 0.610050i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.0660 | − | 8.12103i | −0.463996 | − | 0.267888i | 0.249727 | − | 0.968316i | \(-0.419659\pi\) |
−0.713723 | + | 0.700428i | \(0.752992\pi\) | |||||||
\(920\) | −5.19378 | − | 8.99589i | −0.171234 | − | 0.296586i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.4231 | − | 11.2139i | −0.639665 | − | 0.369311i | ||||
\(923\) | 14.3249 | 0.471510 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05288 | −0.0346184 | ||||||||
\(926\) | 13.5337 | + | 7.81370i | 0.444746 | + | 0.256774i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.77193 | − | 3.06907i | −0.0581665 | − | 0.100747i | ||||
\(929\) | 20.7072 | + | 11.9553i | 0.679382 | + | 0.392242i | 0.799622 | − | 0.600503i | \(-0.205033\pi\) |
−0.120240 | + | 0.992745i | \(0.538366\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.0125 | − | 38.4877i | −1.21304 | − | 1.26138i | ||||
\(932\) | − | 21.3192i | − | 0.698332i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.04760 | − | 5.27860i | −0.0997206 | − | 0.172721i | ||||
\(935\) | −12.0214 | + | 5.84407i | −0.393142 | + | 0.191122i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.2482 | 0.922827 | 0.461414 | − | 0.887185i | \(-0.347342\pi\) | ||||
0.461414 | + | 0.887185i | \(0.347342\pi\) | |||||||
\(938\) | 5.37576 | + | 7.14936i | 0.175525 | + | 0.233435i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.95958 | + | 5.12614i | −0.0965309 | + | 0.167196i | ||||
\(941\) | −29.3512 | − | 50.8377i | −0.956821 | − | 1.65726i | −0.730144 | − | 0.683293i | \(-0.760547\pi\) |
−0.226677 | − | 0.973970i | \(-0.572786\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.9759 | + | 43.2595i | −0.813327 | + | 1.40872i | ||||
\(944\) | − | 2.73329i | − | 0.0889609i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.0635 | − | 1.78505i | −0.814885 | − | 0.0580371i | ||||
\(947\) | −22.1672 | + | 38.3948i | −0.720338 | + | 1.24766i | 0.240526 | + | 0.970643i | \(0.422680\pi\) |
−0.960864 | + | 0.277020i | \(0.910653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.97402 | − | 3.41910i | −0.0640794 | − | 0.110989i | ||||
\(950\) | 22.5648 | + | 13.0278i | 0.732098 | + | 0.422677i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.31819 | − | 7.79458i | 0.107543 | − | 0.252624i | ||||
\(953\) | − | 13.9238i | − | 0.451037i | −0.974239 | − | 0.225518i | \(-0.927592\pi\) | ||
0.974239 | − | 0.225518i | \(-0.0724075\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.54031 | + | 3.77605i | −0.211639 | + | 0.122190i | ||||
\(956\) | −6.28010 | + | 3.62582i | −0.203113 | + | 0.117267i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 30.6275i | − | 0.989531i | ||||||
\(959\) | 22.1276 | + | 9.41982i | 0.714537 | + | 0.304182i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.6672 | − | 46.1890i | 0.860233 | − | 1.48997i | ||||
\(962\) | 1.09005 | − | 0.629341i | 0.0351447 | − | 0.0202908i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.77705 | − | 3.07794i | 0.0572349 | − | 0.0991337i | ||||
\(965\) | −11.8101 | −0.380180 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 29.3085i | − | 0.942499i | −0.882000 | − | 0.471250i | \(-0.843803\pi\) | ||
0.882000 | − | 0.471250i | \(-0.156197\pi\) | |||||||
\(968\) | 8.65064 | + | 6.79458i | 0.278042 | + | 0.218386i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.6361 | + | 6.71808i | −0.373611 | + | 0.215705i | ||||
\(971\) | 0.0286574 | + | 0.0165453i | 0.000919659 | + | 0.000530965i | 0.500460 | − | 0.865760i | \(-0.333164\pi\) |
−0.499540 | + | 0.866291i | \(0.666498\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.6327 | − | 12.5065i | 0.533219 | − | 0.400939i | ||||
\(974\) | − | 3.17453i | − | 0.101718i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.755050 | − | 1.30779i | −0.0241686 | − | 0.0418612i | ||||
\(977\) | 21.0948 | + | 36.5373i | 0.674883 | + | 1.16893i | 0.976503 | + | 0.215503i | \(0.0691392\pi\) |
−0.301620 | + | 0.953428i | \(0.597527\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.50926 | + | 35.2320i | −0.0801964 | + | 1.12602i | ||||
\(980\) | −8.46438 | − | 2.44622i | −0.270385 | − | 0.0781416i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.3254 | + | 28.2763i | −0.520963 | + | 0.902335i | ||||
\(983\) | 44.0056 | − | 25.4067i | 1.40356 | − | 0.810347i | 0.408806 | − | 0.912621i | \(-0.365945\pi\) |
0.994756 | + | 0.102274i | \(0.0326120\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.9173 | − | 18.9092i | 0.347853 | − | 0.602499i | ||||
\(986\) | −11.3471 | −0.361367 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.1486 | −0.990968 | ||||||||
\(989\) | −54.1467 | − | 31.2616i | −1.72177 | − | 0.994062i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.2614 | − | 40.2899i | −0.738923 | − | 1.27985i | −0.952981 | − | 0.303030i | \(-0.902002\pi\) |
0.214058 | − | 0.976821i | \(-0.431332\pi\) | |||||||
\(992\) | −4.59169 | + | 7.95304i | −0.145786 | + | 0.252509i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.21354 | − | 1.12154i | 0.292236 | − | 0.0355731i | ||||
\(995\) | −3.68223 | −0.116735 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.26888 | + | 3.92981i | 0.0718560 | + | 0.124458i | 0.899715 | − | 0.436478i | \(-0.143774\pi\) |
−0.827859 | + | 0.560937i | \(0.810441\pi\) | |||||||
\(998\) | 24.6426 | − | 14.2274i | 0.780048 | − | 0.450361i | ||||
\(999\) | 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 | 1386.2.bk.c.901.1 | 16 | ||
3.2 | odd | 2 | 154.2.i.a.131.6 | yes | 16 | ||
7.3 | odd | 6 | inner | 1386.2.bk.c.703.5 | 16 | ||
11.10 | odd | 2 | inner | 1386.2.bk.c.901.5 | 16 | ||
12.11 | even | 2 | 1232.2.bn.b.593.5 | 16 | |||
21.2 | odd | 6 | 1078.2.c.b.1077.4 | 16 | |||
21.5 | even | 6 | 1078.2.c.b.1077.5 | 16 | |||
21.11 | odd | 6 | 1078.2.i.c.1011.3 | 16 | |||
21.17 | even | 6 | 154.2.i.a.87.2 | ✓ | 16 | ||
21.20 | even | 2 | 1078.2.i.c.901.7 | 16 | |||
33.32 | even | 2 | 154.2.i.a.131.2 | yes | 16 | ||
77.10 | even | 6 | inner | 1386.2.bk.c.703.1 | 16 | ||
84.59 | odd | 6 | 1232.2.bn.b.241.6 | 16 | |||
132.131 | odd | 2 | 1232.2.bn.b.593.6 | 16 | |||
231.32 | even | 6 | 1078.2.i.c.1011.7 | 16 | |||
231.65 | even | 6 | 1078.2.c.b.1077.12 | 16 | |||
231.131 | odd | 6 | 1078.2.c.b.1077.13 | 16 | |||
231.164 | odd | 6 | 154.2.i.a.87.6 | yes | 16 | ||
231.230 | odd | 2 | 1078.2.i.c.901.3 | 16 | |||
924.395 | even | 6 | 1232.2.bn.b.241.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.2 | ✓ | 16 | 21.17 | even | 6 | ||
154.2.i.a.87.6 | yes | 16 | 231.164 | odd | 6 | ||
154.2.i.a.131.2 | yes | 16 | 33.32 | even | 2 | ||
154.2.i.a.131.6 | yes | 16 | 3.2 | odd | 2 | ||
1078.2.c.b.1077.4 | 16 | 21.2 | odd | 6 | |||
1078.2.c.b.1077.5 | 16 | 21.5 | even | 6 | |||
1078.2.c.b.1077.12 | 16 | 231.65 | even | 6 | |||
1078.2.c.b.1077.13 | 16 | 231.131 | odd | 6 | |||
1078.2.i.c.901.3 | 16 | 231.230 | odd | 2 | |||
1078.2.i.c.901.7 | 16 | 21.20 | even | 2 | |||
1078.2.i.c.1011.3 | 16 | 21.11 | odd | 6 | |||
1078.2.i.c.1011.7 | 16 | 231.32 | even | 6 | |||
1232.2.bn.b.241.5 | 16 | 924.395 | even | 6 | |||
1232.2.bn.b.241.6 | 16 | 84.59 | odd | 6 | |||
1232.2.bn.b.593.5 | 16 | 12.11 | even | 2 | |||
1232.2.bn.b.593.6 | 16 | 132.131 | odd | 2 | |||
1386.2.bk.c.703.1 | 16 | 77.10 | even | 6 | inner | ||
1386.2.bk.c.703.5 | 16 | 7.3 | odd | 6 | inner | ||
1386.2.bk.c.901.1 | 16 | 1.1 | even | 1 | trivial | ||
1386.2.bk.c.901.5 | 16 | 11.10 | odd | 2 | inner |