Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.i (of order \(3\), 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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.8 | ||
Root | \(-0.526755 + 0.912367i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.277 |
Dual form | 483.2.i.h.415.8 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.526755 | + | 0.912367i | 0.372472 | + | 0.645141i | 0.989945 | − | 0.141451i | \(-0.0451769\pi\) |
−0.617473 | + | 0.786592i | \(0.711844\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.445058 | − | 0.770863i | 0.222529 | − | 0.385432i | ||||
\(5\) | −1.08806 | − | 1.88457i | −0.486594 | − | 0.842806i | 0.513287 | − | 0.858217i | \(-0.328428\pi\) |
−0.999881 | + | 0.0154108i | \(0.995094\pi\) | |||||||
\(6\) | 1.05351 | 0.430094 | ||||||||
\(7\) | 1.36439 | + | 2.26681i | 0.515692 | + | 0.856774i | ||||
\(8\) | 3.04477 | 1.07649 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.14628 | − | 1.98542i | 0.362486 | − | 0.627844i | ||||
\(11\) | 1.31121 | − | 2.27109i | 0.395346 | − | 0.684760i | −0.597799 | − | 0.801646i | \(-0.703958\pi\) |
0.993145 | + | 0.116886i | \(0.0372913\pi\) | |||||||
\(12\) | −0.445058 | − | 0.770863i | −0.128477 | − | 0.222529i | ||||
\(13\) | −3.30704 | −0.917208 | −0.458604 | − | 0.888641i | \(-0.651650\pi\) | ||||
−0.458604 | + | 0.888641i | \(0.651650\pi\) | |||||||
\(14\) | −1.34946 | + | 2.43888i | −0.360659 | + | 0.651818i | ||||
\(15\) | −2.17612 | −0.561871 | ||||||||
\(16\) | 0.713731 | + | 1.23622i | 0.178433 | + | 0.309054i | ||||
\(17\) | 1.48456 | − | 2.57133i | 0.360059 | − | 0.623640i | −0.627911 | − | 0.778285i | \(-0.716090\pi\) |
0.987970 | + | 0.154645i | \(0.0494233\pi\) | |||||||
\(18\) | 0.526755 | − | 0.912367i | 0.124157 | − | 0.215047i | ||||
\(19\) | −0.348884 | − | 0.604285i | −0.0800396 | − | 0.138633i | 0.823227 | − | 0.567712i | \(-0.192171\pi\) |
−0.903267 | + | 0.429080i | \(0.858838\pi\) | |||||||
\(20\) | −1.93700 | −0.433126 | ||||||||
\(21\) | 2.64531 | − | 0.0481928i | 0.577254 | − | 0.0105165i | ||||
\(22\) | 2.76276 | 0.589022 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | ||||
\(24\) | 1.52238 | − | 2.63685i | 0.310755 | − | 0.538244i | ||||
\(25\) | 0.132258 | − | 0.229078i | 0.0264516 | − | 0.0458156i | ||||
\(26\) | −1.74200 | − | 3.01723i | −0.341634 | − | 0.591728i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.35463 | − | 0.0428972i | 0.444984 | − | 0.00810681i | ||||
\(29\) | 7.31827 | 1.35897 | 0.679485 | − | 0.733690i | \(-0.262203\pi\) | ||||
0.679485 | + | 0.733690i | \(0.262203\pi\) | |||||||
\(30\) | −1.14628 | − | 1.98542i | −0.209281 | − | 0.362486i | ||||
\(31\) | −2.80105 | + | 4.85155i | −0.503083 | + | 0.871365i | 0.496911 | + | 0.867801i | \(0.334468\pi\) |
−0.999994 | + | 0.00356314i | \(0.998866\pi\) | |||||||
\(32\) | 2.29284 | − | 3.97132i | 0.405321 | − | 0.702037i | ||||
\(33\) | −1.31121 | − | 2.27109i | −0.228253 | − | 0.395346i | ||||
\(34\) | 3.12800 | 0.536448 | ||||||||
\(35\) | 2.78743 | − | 5.03772i | 0.471162 | − | 0.851530i | ||||
\(36\) | −0.890116 | −0.148353 | ||||||||
\(37\) | 2.26348 | + | 3.92045i | 0.372113 | + | 0.644519i | 0.989890 | − | 0.141834i | \(-0.0453000\pi\) |
−0.617777 | + | 0.786353i | \(0.711967\pi\) | |||||||
\(38\) | 0.367553 | − | 0.636621i | 0.0596250 | − | 0.103274i | ||||
\(39\) | −1.65352 | + | 2.86398i | −0.264775 | + | 0.458604i | ||||
\(40\) | −3.31288 | − | 5.73808i | −0.523813 | − | 0.907271i | ||||
\(41\) | 2.28774 | 0.357285 | 0.178643 | − | 0.983914i | \(-0.442829\pi\) | ||||
0.178643 | + | 0.983914i | \(0.442829\pi\) | |||||||
\(42\) | 1.43740 | + | 2.38811i | 0.221796 | + | 0.368493i | ||||
\(43\) | −7.79527 | −1.18877 | −0.594384 | − | 0.804182i | \(-0.702604\pi\) | ||||
−0.594384 | + | 0.804182i | \(0.702604\pi\) | |||||||
\(44\) | −1.16713 | − | 2.02153i | −0.175952 | − | 0.304758i | ||||
\(45\) | −1.08806 | + | 1.88457i | −0.162198 | + | 0.280935i | ||||
\(46\) | 0.526755 | − | 0.912367i | 0.0776658 | − | 0.134521i | ||||
\(47\) | 1.90697 | + | 3.30297i | 0.278160 | + | 0.481788i | 0.970928 | − | 0.239373i | \(-0.0769420\pi\) |
−0.692767 | + | 0.721161i | \(0.743609\pi\) | |||||||
\(48\) | 1.42746 | 0.206036 | ||||||||
\(49\) | −3.27687 | + | 6.18564i | −0.468124 | + | 0.883663i | ||||
\(50\) | 0.278671 | 0.0394100 | ||||||||
\(51\) | −1.48456 | − | 2.57133i | −0.207880 | − | 0.360059i | ||||
\(52\) | −1.47182 | + | 2.54927i | −0.204105 | + | 0.353521i | ||||
\(53\) | −1.56530 | + | 2.71117i | −0.215010 | + | 0.372408i | −0.953276 | − | 0.302102i | \(-0.902312\pi\) |
0.738266 | + | 0.674510i | \(0.235645\pi\) | |||||||
\(54\) | −0.526755 | − | 0.912367i | −0.0716823 | − | 0.124157i | ||||
\(55\) | −5.70671 | −0.769493 | ||||||||
\(56\) | 4.15426 | + | 6.90191i | 0.555136 | + | 0.922307i | ||||
\(57\) | −0.697769 | −0.0924217 | ||||||||
\(58\) | 3.85494 | + | 6.67695i | 0.506178 | + | 0.876727i | ||||
\(59\) | −6.08141 | + | 10.5333i | −0.791733 | + | 1.37132i | 0.133161 | + | 0.991094i | \(0.457487\pi\) |
−0.924893 | + | 0.380227i | \(0.875846\pi\) | |||||||
\(60\) | −0.968498 | + | 1.67749i | −0.125033 | + | 0.216563i | ||||
\(61\) | −0.742296 | − | 1.28569i | −0.0950412 | − | 0.164616i | 0.814585 | − | 0.580045i | \(-0.196965\pi\) |
−0.909626 | + | 0.415429i | \(0.863632\pi\) | |||||||
\(62\) | −5.90186 | −0.749537 | ||||||||
\(63\) | 1.28092 | − | 2.31500i | 0.161381 | − | 0.291663i | ||||
\(64\) | 7.68599 | 0.960749 | ||||||||
\(65\) | 3.59825 | + | 6.23236i | 0.446308 | + | 0.773029i | ||||
\(66\) | 1.38138 | − | 2.39262i | 0.170036 | − | 0.294511i | ||||
\(67\) | −5.63777 | + | 9.76490i | −0.688763 | + | 1.19297i | 0.283475 | + | 0.958980i | \(0.408513\pi\) |
−0.972238 | + | 0.233993i | \(0.924821\pi\) | |||||||
\(68\) | −1.32143 | − | 2.28879i | −0.160247 | − | 0.277556i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 6.06454 | − | 0.110485i | 0.724851 | − | 0.0132055i | ||||
\(71\) | 13.8643 | 1.64539 | 0.822693 | − | 0.568486i | \(-0.192471\pi\) | ||||
0.822693 | + | 0.568486i | \(0.192471\pi\) | |||||||
\(72\) | −1.52238 | − | 2.63685i | −0.179415 | − | 0.310755i | ||||
\(73\) | −0.352915 | + | 0.611266i | −0.0413055 | + | 0.0715433i | −0.885939 | − | 0.463802i | \(-0.846485\pi\) |
0.844634 | + | 0.535345i | \(0.179818\pi\) | |||||||
\(74\) | −2.38459 | + | 4.13024i | −0.277203 | + | 0.480131i | ||||
\(75\) | −0.132258 | − | 0.229078i | −0.0152719 | − | 0.0264516i | ||||
\(76\) | −0.621095 | −0.0712445 | ||||||||
\(77\) | 6.93715 | − | 0.126382i | 0.790561 | − | 0.0144026i | ||||
\(78\) | −3.48400 | −0.394485 | ||||||||
\(79\) | 4.30203 | + | 7.45134i | 0.484016 | + | 0.838341i | 0.999831 | − | 0.0183590i | \(-0.00584417\pi\) |
−0.515815 | + | 0.856700i | \(0.672511\pi\) | |||||||
\(80\) | 1.55316 | − | 2.69015i | 0.173649 | − | 0.300768i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.20508 | + | 2.08726i | 0.133079 | + | 0.230499i | ||||
\(83\) | −11.5918 | −1.27237 | −0.636185 | − | 0.771537i | \(-0.719489\pi\) | ||||
−0.636185 | + | 0.771537i | \(0.719489\pi\) | |||||||
\(84\) | 1.14017 | − | 2.06062i | 0.124402 | − | 0.224832i | ||||
\(85\) | −6.46115 | −0.700811 | ||||||||
\(86\) | −4.10620 | − | 7.11214i | −0.442783 | − | 0.766922i | ||||
\(87\) | 3.65914 | − | 6.33781i | 0.392301 | − | 0.679485i | ||||
\(88\) | 3.99234 | − | 6.91494i | 0.425585 | − | 0.737135i | ||||
\(89\) | 0.166888 | + | 0.289058i | 0.0176901 | + | 0.0306401i | 0.874735 | − | 0.484602i | \(-0.161035\pi\) |
−0.857045 | + | 0.515242i | \(0.827702\pi\) | |||||||
\(90\) | −2.29256 | −0.241657 | ||||||||
\(91\) | −4.51210 | − | 7.49644i | −0.472997 | − | 0.785840i | ||||
\(92\) | −0.890116 | −0.0928010 | ||||||||
\(93\) | 2.80105 | + | 4.85155i | 0.290455 | + | 0.503083i | ||||
\(94\) | −2.00901 | + | 3.47971i | −0.207214 | + | 0.358905i | ||||
\(95\) | −0.759213 | + | 1.31500i | −0.0778936 | + | 0.134916i | ||||
\(96\) | −2.29284 | − | 3.97132i | −0.234012 | − | 0.405321i | ||||
\(97\) | 0.124876 | 0.0126793 | 0.00633963 | − | 0.999980i | \(-0.497982\pi\) | ||||
0.00633963 | + | 0.999980i | \(0.497982\pi\) | |||||||
\(98\) | −7.36968 | + | 0.268614i | −0.744450 | + | 0.0271341i | ||||
\(99\) | −2.62243 | −0.263564 | ||||||||
\(100\) | −0.117725 | − | 0.203906i | −0.0117725 | − | 0.0203906i | ||||
\(101\) | 4.38986 | − | 7.60346i | 0.436807 | − | 0.756572i | −0.560634 | − | 0.828064i | \(-0.689443\pi\) |
0.997441 | + | 0.0714914i | \(0.0227758\pi\) | |||||||
\(102\) | 1.56400 | − | 2.70893i | 0.154859 | − | 0.268224i | ||||
\(103\) | 2.73241 | + | 4.73267i | 0.269232 | + | 0.466324i | 0.968664 | − | 0.248376i | \(-0.0798967\pi\) |
−0.699432 | + | 0.714700i | \(0.746563\pi\) | |||||||
\(104\) | −10.0692 | −0.987363 | ||||||||
\(105\) | −2.96908 | − | 4.93285i | −0.289752 | − | 0.481396i | ||||
\(106\) | −3.29811 | −0.320341 | ||||||||
\(107\) | −5.42133 | − | 9.39002i | −0.524100 | − | 0.907767i | −0.999606 | − | 0.0280551i | \(-0.991069\pi\) |
0.475507 | − | 0.879712i | \(-0.342265\pi\) | |||||||
\(108\) | −0.445058 | + | 0.770863i | −0.0428257 | + | 0.0741763i | ||||
\(109\) | 0.528680 | − | 0.915701i | 0.0506384 | − | 0.0877083i | −0.839595 | − | 0.543213i | \(-0.817208\pi\) |
0.890234 | + | 0.455504i | \(0.150541\pi\) | |||||||
\(110\) | −3.00604 | − | 5.20661i | −0.286615 | − | 0.496431i | ||||
\(111\) | 4.52695 | 0.429679 | ||||||||
\(112\) | −1.82846 | + | 3.30458i | −0.172774 | + | 0.312253i | ||||
\(113\) | −14.0938 | −1.32584 | −0.662918 | − | 0.748692i | \(-0.730682\pi\) | ||||
−0.662918 | + | 0.748692i | \(0.730682\pi\) | |||||||
\(114\) | −0.367553 | − | 0.636621i | −0.0344245 | − | 0.0596250i | ||||
\(115\) | −1.08806 | + | 1.88457i | −0.101462 | + | 0.175737i | ||||
\(116\) | 3.25706 | − | 5.64139i | 0.302410 | − | 0.523790i | ||||
\(117\) | 1.65352 | + | 2.86398i | 0.152868 | + | 0.264775i | ||||
\(118\) | −12.8137 | −1.17959 | ||||||||
\(119\) | 7.85425 | − | 0.143090i | 0.719998 | − | 0.0131171i | ||||
\(120\) | −6.62577 | −0.604847 | ||||||||
\(121\) | 2.06143 | + | 3.57050i | 0.187403 | + | 0.324591i | ||||
\(122\) | 0.782016 | − | 1.35449i | 0.0708004 | − | 0.122630i | ||||
\(123\) | 1.14387 | − | 1.98124i | 0.103139 | − | 0.178643i | ||||
\(124\) | 2.49326 | + | 4.31844i | 0.223901 | + | 0.387808i | ||||
\(125\) | −11.4562 | −1.02467 | ||||||||
\(126\) | 2.78686 | − | 0.0507716i | 0.248274 | − | 0.00452310i | ||||
\(127\) | 15.7177 | 1.39472 | 0.697360 | − | 0.716721i | \(-0.254358\pi\) | ||||
0.697360 | + | 0.716721i | \(0.254358\pi\) | |||||||
\(128\) | −0.537052 | − | 0.930201i | −0.0474691 | − | 0.0822190i | ||||
\(129\) | −3.89763 | + | 6.75090i | −0.343168 | + | 0.594384i | ||||
\(130\) | −3.79080 | + | 6.56585i | −0.332475 | + | 0.575863i | ||||
\(131\) | 5.00147 | + | 8.66280i | 0.436980 | + | 0.756872i | 0.997455 | − | 0.0712996i | \(-0.0227146\pi\) |
−0.560475 | + | 0.828172i | \(0.689381\pi\) | |||||||
\(132\) | −2.33427 | −0.203172 | ||||||||
\(133\) | 0.893786 | − | 1.61534i | 0.0775011 | − | 0.140068i | ||||
\(134\) | −11.8789 | −1.02618 | ||||||||
\(135\) | 1.08806 | + | 1.88457i | 0.0936452 | + | 0.162198i | ||||
\(136\) | 4.52014 | − | 7.82911i | 0.387599 | − | 0.671341i | ||||
\(137\) | −3.03387 | + | 5.25481i | −0.259201 | + | 0.448949i | −0.966028 | − | 0.258437i | \(-0.916792\pi\) |
0.706827 | + | 0.707386i | \(0.250126\pi\) | |||||||
\(138\) | −0.526755 | − | 0.912367i | −0.0448404 | − | 0.0776658i | ||||
\(139\) | 14.1199 | 1.19763 | 0.598815 | − | 0.800887i | \(-0.295638\pi\) | ||||
0.598815 | + | 0.800887i | \(0.295638\pi\) | |||||||
\(140\) | −2.64282 | − | 4.39080i | −0.223359 | − | 0.371091i | ||||
\(141\) | 3.81394 | 0.321192 | ||||||||
\(142\) | 7.30307 | + | 12.6493i | 0.612860 | + | 1.06150i | ||||
\(143\) | −4.33624 | + | 7.51059i | −0.362615 | + | 0.628067i | ||||
\(144\) | 0.713731 | − | 1.23622i | 0.0594776 | − | 0.103018i | ||||
\(145\) | −7.96271 | − | 13.7918i | −0.661267 | − | 1.14535i | ||||
\(146\) | −0.743598 | −0.0615406 | ||||||||
\(147\) | 3.71849 | + | 5.93067i | 0.306696 | + | 0.489153i | ||||
\(148\) | 4.02951 | 0.331224 | ||||||||
\(149\) | −0.507952 | − | 0.879799i | −0.0416131 | − | 0.0720759i | 0.844469 | − | 0.535605i | \(-0.179916\pi\) |
−0.886082 | + | 0.463529i | \(0.846583\pi\) | |||||||
\(150\) | 0.139335 | − | 0.241336i | 0.0113767 | − | 0.0197050i | ||||
\(151\) | −11.2693 | + | 19.5190i | −0.917080 | + | 1.58843i | −0.113254 | + | 0.993566i | \(0.536127\pi\) |
−0.803827 | + | 0.594864i | \(0.797206\pi\) | |||||||
\(152\) | −1.06227 | − | 1.83991i | −0.0861616 | − | 0.149236i | ||||
\(153\) | −2.96912 | −0.240039 | ||||||||
\(154\) | 3.76948 | + | 6.26265i | 0.303754 | + | 0.504659i | ||||
\(155\) | 12.1908 | 0.979189 | ||||||||
\(156\) | 1.47182 | + | 2.54927i | 0.117840 | + | 0.204105i | ||||
\(157\) | 5.68305 | − | 9.84334i | 0.453557 | − | 0.785584i | −0.545047 | − | 0.838406i | \(-0.683488\pi\) |
0.998604 | + | 0.0528218i | \(0.0168215\pi\) | |||||||
\(158\) | −4.53223 | + | 7.85006i | −0.360565 | + | 0.624517i | ||||
\(159\) | 1.56530 | + | 2.71117i | 0.124136 | + | 0.215010i | ||||
\(160\) | −9.97899 | −0.788909 | ||||||||
\(161\) | 1.28092 | − | 2.31500i | 0.100951 | − | 0.182448i | ||||
\(162\) | −1.05351 | −0.0827716 | ||||||||
\(163\) | −7.38352 | − | 12.7886i | −0.578322 | − | 1.00168i | −0.995672 | − | 0.0929373i | \(-0.970374\pi\) |
0.417350 | − | 0.908746i | \(-0.362959\pi\) | |||||||
\(164\) | 1.01818 | − | 1.76353i | 0.0795063 | − | 0.137709i | ||||
\(165\) | −2.85336 | + | 4.94216i | −0.222133 | + | 0.384746i | ||||
\(166\) | −6.10606 | − | 10.5760i | −0.473922 | − | 0.820858i | ||||
\(167\) | −8.85336 | −0.685093 | −0.342547 | − | 0.939501i | \(-0.611290\pi\) | ||||
−0.342547 | + | 0.939501i | \(0.611290\pi\) | |||||||
\(168\) | 8.05436 | − | 0.146736i | 0.621407 | − | 0.0113209i | ||||
\(169\) | −2.06349 | −0.158730 | ||||||||
\(170\) | −3.40345 | − | 5.89494i | −0.261032 | − | 0.452121i | ||||
\(171\) | −0.348884 | + | 0.604285i | −0.0266799 | + | 0.0462109i | ||||
\(172\) | −3.46935 | + | 6.00909i | −0.264535 | + | 0.458188i | ||||
\(173\) | −7.85202 | − | 13.6001i | −0.596978 | − | 1.03400i | −0.993265 | − | 0.115869i | \(-0.963035\pi\) |
0.396287 | − | 0.918127i | \(-0.370299\pi\) | |||||||
\(174\) | 7.70988 | 0.584484 | ||||||||
\(175\) | 0.699728 | − | 0.0127478i | 0.0528945 | − | 0.000963642i | ||||
\(176\) | 3.74342 | 0.282171 | ||||||||
\(177\) | 6.08141 | + | 10.5333i | 0.457107 | + | 0.791733i | ||||
\(178\) | −0.175818 | + | 0.304526i | −0.0131781 | + | 0.0228252i | ||||
\(179\) | 2.65376 | − | 4.59645i | 0.198351 | − | 0.343555i | −0.749643 | − | 0.661843i | \(-0.769775\pi\) |
0.947994 | + | 0.318288i | \(0.103108\pi\) | |||||||
\(180\) | 0.968498 | + | 1.67749i | 0.0721876 | + | 0.125033i | ||||
\(181\) | 1.93050 | 0.143493 | 0.0717463 | − | 0.997423i | \(-0.477143\pi\) | ||||
0.0717463 | + | 0.997423i | \(0.477143\pi\) | |||||||
\(182\) | 4.46273 | − | 8.06548i | 0.330799 | − | 0.597853i | ||||
\(183\) | −1.48459 | −0.109744 | ||||||||
\(184\) | −1.52238 | − | 2.63685i | −0.112232 | − | 0.194391i | ||||
\(185\) | 4.92559 | − | 8.53137i | 0.362136 | − | 0.627238i | ||||
\(186\) | −2.95093 | + | 5.11116i | −0.216373 | + | 0.374769i | ||||
\(187\) | −3.89316 | − | 6.74314i | −0.284696 | − | 0.493107i | ||||
\(188\) | 3.39485 | 0.247595 | ||||||||
\(189\) | −1.36439 | − | 2.26681i | −0.0992449 | − | 0.164886i | ||||
\(190\) | −1.59968 | −0.116053 | ||||||||
\(191\) | −5.22089 | − | 9.04284i | −0.377770 | − | 0.654317i | 0.612967 | − | 0.790108i | \(-0.289976\pi\) |
−0.990737 | + | 0.135791i | \(0.956642\pi\) | |||||||
\(192\) | 3.84300 | − | 6.65627i | 0.277344 | − | 0.480375i | ||||
\(193\) | −12.3081 | + | 21.3183i | −0.885959 | + | 1.53453i | −0.0413492 | + | 0.999145i | \(0.513166\pi\) |
−0.844610 | + | 0.535382i | \(0.820168\pi\) | |||||||
\(194\) | 0.0657792 | + | 0.113933i | 0.00472267 | + | 0.00817991i | ||||
\(195\) | 7.19650 | 0.515352 | ||||||||
\(196\) | 3.30989 | + | 5.27898i | 0.236420 | + | 0.377070i | ||||
\(197\) | 5.17797 | 0.368915 | 0.184458 | − | 0.982840i | \(-0.440947\pi\) | ||||
0.184458 | + | 0.982840i | \(0.440947\pi\) | |||||||
\(198\) | −1.38138 | − | 2.39262i | −0.0981703 | − | 0.170036i | ||||
\(199\) | 8.31855 | − | 14.4082i | 0.589687 | − | 1.02137i | −0.404587 | − | 0.914500i | \(-0.632585\pi\) |
0.994273 | − | 0.106867i | \(-0.0340821\pi\) | |||||||
\(200\) | 0.402695 | − | 0.697489i | 0.0284749 | − | 0.0493199i | ||||
\(201\) | 5.63777 | + | 9.76490i | 0.397658 | + | 0.688763i | ||||
\(202\) | 9.24952 | 0.650794 | ||||||||
\(203\) | 9.98500 | + | 16.5891i | 0.700809 | + | 1.16433i | ||||
\(204\) | −2.64286 | −0.185037 | ||||||||
\(205\) | −2.48919 | − | 4.31141i | −0.173853 | − | 0.301122i | ||||
\(206\) | −2.87862 | + | 4.98592i | −0.200563 | + | 0.347385i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | −2.36034 | − | 4.08822i | −0.163660 | − | 0.283467i | ||||
\(209\) | −1.82985 | −0.126573 | ||||||||
\(210\) | 2.93659 | − | 5.30729i | 0.202644 | − | 0.366238i | ||||
\(211\) | 28.5995 | 1.96887 | 0.984435 | − | 0.175751i | \(-0.0562354\pi\) | ||||
0.984435 | + | 0.175751i | \(0.0562354\pi\) | |||||||
\(212\) | 1.39330 | + | 2.41326i | 0.0956919 | + | 0.165743i | ||||
\(213\) | 6.93213 | − | 12.0068i | 0.474982 | − | 0.822693i | ||||
\(214\) | 5.71143 | − | 9.89248i | 0.390425 | − | 0.676236i | ||||
\(215\) | 8.48171 | + | 14.6907i | 0.578448 | + | 1.00190i | ||||
\(216\) | −3.04477 | −0.207170 | ||||||||
\(217\) | −14.8193 | + | 0.269981i | −1.00600 | + | 0.0183275i | ||||
\(218\) | 1.11394 | 0.0754456 | ||||||||
\(219\) | 0.352915 | + | 0.611266i | 0.0238478 | + | 0.0413055i | ||||
\(220\) | −2.53982 | + | 4.39909i | −0.171234 | + | 0.296587i | ||||
\(221\) | −4.90950 | + | 8.50350i | −0.330249 | + | 0.572008i | ||||
\(222\) | 2.38459 | + | 4.13024i | 0.160044 | + | 0.277203i | ||||
\(223\) | 16.5464 | 1.10803 | 0.554016 | − | 0.832506i | \(-0.313095\pi\) | ||||
0.554016 | + | 0.832506i | \(0.313095\pi\) | |||||||
\(224\) | 12.1306 | − | 0.220997i | 0.810508 | − | 0.0147660i | ||||
\(225\) | −0.264516 | −0.0176344 | ||||||||
\(226\) | −7.42400 | − | 12.8587i | −0.493837 | − | 0.855351i | ||||
\(227\) | 8.98250 | − | 15.5581i | 0.596189 | − | 1.03263i | −0.397189 | − | 0.917737i | \(-0.630014\pi\) |
0.993378 | − | 0.114893i | \(-0.0366526\pi\) | |||||||
\(228\) | −0.310548 | + | 0.537884i | −0.0205665 | + | 0.0356222i | ||||
\(229\) | −14.0030 | − | 24.2540i | −0.925348 | − | 1.60275i | −0.791001 | − | 0.611815i | \(-0.790440\pi\) |
−0.134346 | − | 0.990934i | \(-0.542893\pi\) | |||||||
\(230\) | −2.29256 | −0.151167 | ||||||||
\(231\) | 3.35912 | − | 6.07094i | 0.221014 | − | 0.399438i | ||||
\(232\) | 22.2824 | 1.46291 | ||||||||
\(233\) | −11.6231 | − | 20.1318i | −0.761454 | − | 1.31888i | −0.942101 | − | 0.335329i | \(-0.891153\pi\) |
0.180648 | − | 0.983548i | \(-0.442181\pi\) | |||||||
\(234\) | −1.74200 | + | 3.01723i | −0.113878 | + | 0.197243i | ||||
\(235\) | 4.14979 | − | 7.18765i | 0.270703 | − | 0.468871i | ||||
\(236\) | 5.41316 | + | 9.37587i | 0.352367 | + | 0.610317i | ||||
\(237\) | 8.60406 | 0.558894 | ||||||||
\(238\) | 4.26782 | + | 7.09058i | 0.276642 | + | 0.459614i | ||||
\(239\) | 6.43482 | 0.416234 | 0.208117 | − | 0.978104i | \(-0.433267\pi\) | ||||
0.208117 | + | 0.978104i | \(0.433267\pi\) | |||||||
\(240\) | −1.55316 | − | 2.69015i | −0.100256 | − | 0.173649i | ||||
\(241\) | −11.7589 | + | 20.3669i | −0.757455 | + | 1.31195i | 0.186690 | + | 0.982419i | \(0.440224\pi\) |
−0.944145 | + | 0.329531i | \(0.893109\pi\) | |||||||
\(242\) | −2.17174 | + | 3.76156i | −0.139605 | + | 0.241802i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −1.32146 | −0.0845977 | ||||||||
\(245\) | 15.2227 | − | 0.554845i | 0.972543 | − | 0.0354477i | ||||
\(246\) | 2.41016 | 0.153666 | ||||||||
\(247\) | 1.15377 | + | 1.99840i | 0.0734129 | + | 0.127155i | ||||
\(248\) | −8.52853 | + | 14.7718i | −0.541562 | + | 0.938013i | ||||
\(249\) | −5.79592 | + | 10.0388i | −0.367302 | + | 0.636185i | ||||
\(250\) | −6.03461 | − | 10.4523i | −0.381662 | − | 0.661059i | ||||
\(251\) | −3.12594 | −0.197307 | −0.0986537 | − | 0.995122i | \(-0.531454\pi\) | ||||
−0.0986537 | + | 0.995122i | \(0.531454\pi\) | |||||||
\(252\) | −1.21447 | − | 2.01773i | −0.0765043 | − | 0.127105i | ||||
\(253\) | −2.62243 | −0.164871 | ||||||||
\(254\) | 8.27937 | + | 14.3403i | 0.519494 | + | 0.899790i | ||||
\(255\) | −3.23058 | + | 5.59552i | −0.202307 | + | 0.350405i | ||||
\(256\) | 8.25178 | − | 14.2925i | 0.515736 | − | 0.893282i | ||||
\(257\) | 10.2668 | + | 17.7826i | 0.640426 | + | 1.10925i | 0.985338 | + | 0.170615i | \(0.0545756\pi\) |
−0.344912 | + | 0.938635i | \(0.612091\pi\) | |||||||
\(258\) | −8.21240 | −0.511282 | ||||||||
\(259\) | −5.79866 | + | 10.4799i | −0.360311 | + | 0.651190i | ||||
\(260\) | 6.40572 | 0.397266 | ||||||||
\(261\) | −3.65914 | − | 6.33781i | −0.226495 | − | 0.392301i | ||||
\(262\) | −5.26910 | + | 9.12634i | −0.325526 | + | 0.563827i | ||||
\(263\) | −9.72378 | + | 16.8421i | −0.599594 | + | 1.03853i | 0.393287 | + | 0.919416i | \(0.371338\pi\) |
−0.992881 | + | 0.119112i | \(0.961995\pi\) | |||||||
\(264\) | −3.99234 | − | 6.91494i | −0.245712 | − | 0.425585i | ||||
\(265\) | 6.81254 | 0.418491 | ||||||||
\(266\) | 1.94459 | − | 0.0354269i | 0.119230 | − | 0.00217216i | ||||
\(267\) | 0.333776 | 0.0204267 | ||||||||
\(268\) | 5.01827 | + | 8.69190i | 0.306540 | + | 0.530942i | ||||
\(269\) | −3.85970 | + | 6.68520i | −0.235330 | + | 0.407604i | −0.959369 | − | 0.282156i | \(-0.908950\pi\) |
0.724038 | + | 0.689760i | \(0.242284\pi\) | |||||||
\(270\) | −1.14628 | + | 1.98542i | −0.0697604 | + | 0.120829i | ||||
\(271\) | −15.4319 | − | 26.7288i | −0.937418 | − | 1.62366i | −0.770263 | − | 0.637726i | \(-0.779875\pi\) |
−0.167155 | − | 0.985931i | \(-0.553458\pi\) | |||||||
\(272\) | 4.23831 | 0.256985 | ||||||||
\(273\) | −8.74815 | + | 0.159376i | −0.529462 | + | 0.00964585i | ||||
\(274\) | −6.39242 | −0.386180 | ||||||||
\(275\) | −0.346838 | − | 0.600741i | −0.0209151 | − | 0.0362260i | ||||
\(276\) | −0.445058 | + | 0.770863i | −0.0267893 | + | 0.0464005i | ||||
\(277\) | −3.20072 | + | 5.54381i | −0.192313 | + | 0.333095i | −0.946016 | − | 0.324119i | \(-0.894932\pi\) |
0.753704 | + | 0.657214i | \(0.228265\pi\) | |||||||
\(278\) | 7.43771 | + | 12.8825i | 0.446084 | + | 0.772640i | ||||
\(279\) | 5.60209 | 0.335388 | ||||||||
\(280\) | 8.48708 | − | 15.3387i | 0.507200 | − | 0.916661i | ||||
\(281\) | −4.79227 | −0.285883 | −0.142941 | − | 0.989731i | \(-0.545656\pi\) | ||||
−0.142941 | + | 0.989731i | \(0.545656\pi\) | |||||||
\(282\) | 2.00901 | + | 3.47971i | 0.119635 | + | 0.207214i | ||||
\(283\) | 5.85073 | − | 10.1338i | 0.347790 | − | 0.602389i | −0.638067 | − | 0.769981i | \(-0.720266\pi\) |
0.985857 | + | 0.167592i | \(0.0535990\pi\) | |||||||
\(284\) | 6.17040 | − | 10.6874i | 0.366146 | − | 0.634183i | ||||
\(285\) | 0.759213 | + | 1.31500i | 0.0449719 | + | 0.0778936i | ||||
\(286\) | −9.13655 | −0.540255 | ||||||||
\(287\) | 3.12138 | + | 5.18588i | 0.184249 | + | 0.306113i | ||||
\(288\) | −4.58569 | −0.270214 | ||||||||
\(289\) | 4.09216 | + | 7.08783i | 0.240715 | + | 0.416931i | ||||
\(290\) | 8.38880 | − | 14.5298i | 0.492607 | − | 0.853221i | ||||
\(291\) | 0.0624381 | − | 0.108146i | 0.00366019 | − | 0.00633963i | ||||
\(292\) | 0.314135 | + | 0.544098i | 0.0183834 | + | 0.0318409i | ||||
\(293\) | 19.9031 | 1.16275 | 0.581376 | − | 0.813635i | \(-0.302515\pi\) | ||||
0.581376 | + | 0.813635i | \(0.302515\pi\) | |||||||
\(294\) | −3.45221 | + | 6.51664i | −0.201337 | + | 0.380058i | ||||
\(295\) | 26.4677 | 1.54101 | ||||||||
\(296\) | 6.89175 | + | 11.9369i | 0.400575 | + | 0.693816i | ||||
\(297\) | −1.31121 | + | 2.27109i | −0.0760844 | + | 0.131782i | ||||
\(298\) | 0.535133 | − | 0.926877i | 0.0309994 | − | 0.0536925i | ||||
\(299\) | 1.65352 | + | 2.86398i | 0.0956255 | + | 0.165628i | ||||
\(300\) | −0.235450 | −0.0135937 | ||||||||
\(301\) | −10.6358 | − | 17.6704i | −0.613038 | − | 1.01851i | ||||
\(302\) | −23.7446 | −1.36635 | ||||||||
\(303\) | −4.38986 | − | 7.60346i | −0.252191 | − | 0.436807i | ||||
\(304\) | 0.498019 | − | 0.862594i | 0.0285633 | − | 0.0494732i | ||||
\(305\) | −1.61532 | + | 2.79782i | −0.0924931 | + | 0.160203i | ||||
\(306\) | −1.56400 | − | 2.70893i | −0.0894079 | − | 0.154859i | ||||
\(307\) | 21.7588 | 1.24184 | 0.620920 | − | 0.783874i | \(-0.286759\pi\) | ||||
0.620920 | + | 0.783874i | \(0.286759\pi\) | |||||||
\(308\) | 2.99001 | − | 5.40384i | 0.170372 | − | 0.307912i | ||||
\(309\) | 5.46482 | 0.310883 | ||||||||
\(310\) | 6.42157 | + | 11.1225i | 0.364721 | + | 0.631715i | ||||
\(311\) | 4.07173 | − | 7.05244i | 0.230886 | − | 0.399907i | −0.727183 | − | 0.686444i | \(-0.759171\pi\) |
0.958069 | + | 0.286537i | \(0.0925041\pi\) | |||||||
\(312\) | −5.03458 | + | 8.72015i | −0.285027 | + | 0.493681i | ||||
\(313\) | −0.525219 | − | 0.909706i | −0.0296871 | − | 0.0514196i | 0.850800 | − | 0.525489i | \(-0.176118\pi\) |
−0.880487 | + | 0.474070i | \(0.842784\pi\) | |||||||
\(314\) | 11.9743 | 0.675749 | ||||||||
\(315\) | −5.75651 | + | 0.104873i | −0.324342 | + | 0.00590894i | ||||
\(316\) | 7.65861 | 0.430831 | ||||||||
\(317\) | −8.18399 | − | 14.1751i | −0.459658 | − | 0.796152i | 0.539284 | − | 0.842124i | \(-0.318695\pi\) |
−0.998943 | + | 0.0459720i | \(0.985361\pi\) | |||||||
\(318\) | −1.64906 | + | 2.85625i | −0.0924745 | + | 0.160171i | ||||
\(319\) | 9.59583 | − | 16.6205i | 0.537263 | − | 0.930567i | ||||
\(320\) | −8.36281 | − | 14.4848i | −0.467495 | − | 0.809725i | ||||
\(321\) | −10.8427 | −0.605178 | ||||||||
\(322\) | 2.78686 | − | 0.0507716i | 0.155306 | − | 0.00282939i | ||||
\(323\) | −2.07176 | −0.115276 | ||||||||
\(324\) | 0.445058 | + | 0.770863i | 0.0247254 | + | 0.0428257i | ||||
\(325\) | −0.437383 | + | 0.757570i | −0.0242616 | + | 0.0420224i | ||||
\(326\) | 7.77862 | − | 13.4730i | 0.430818 | − | 0.746198i | ||||
\(327\) | −0.528680 | − | 0.915701i | −0.0292361 | − | 0.0506384i | ||||
\(328\) | 6.96564 | 0.384613 | ||||||||
\(329\) | −4.88535 | + | 8.82929i | −0.269338 | + | 0.486775i | ||||
\(330\) | −6.01208 | −0.330954 | ||||||||
\(331\) | −14.6464 | − | 25.3684i | −0.805042 | − | 1.39437i | −0.916263 | − | 0.400577i | \(-0.868810\pi\) |
0.111221 | − | 0.993796i | \(-0.464524\pi\) | |||||||
\(332\) | −5.15904 | + | 8.93572i | −0.283139 | + | 0.490412i | ||||
\(333\) | 2.26348 | − | 3.92045i | 0.124038 | − | 0.214840i | ||||
\(334\) | −4.66355 | − | 8.07751i | −0.255178 | − | 0.441982i | ||||
\(335\) | 24.5369 | 1.34059 | ||||||||
\(336\) | 1.94762 | + | 3.23579i | 0.106251 | + | 0.176527i | ||||
\(337\) | −4.27417 | −0.232829 | −0.116414 | − | 0.993201i | \(-0.537140\pi\) | ||||
−0.116414 | + | 0.993201i | \(0.537140\pi\) | |||||||
\(338\) | −1.08695 | − | 1.88266i | −0.0591224 | − | 0.102403i | ||||
\(339\) | −7.04691 | + | 12.2056i | −0.382736 | + | 0.662918i | ||||
\(340\) | −2.87559 | + | 4.98066i | −0.155951 | + | 0.270114i | ||||
\(341\) | 7.34554 | + | 12.7229i | 0.397784 | + | 0.688981i | ||||
\(342\) | −0.735106 | −0.0397500 | ||||||||
\(343\) | −18.4926 | + | 1.01160i | −0.998507 | + | 0.0546214i | ||||
\(344\) | −23.7348 | −1.27969 | ||||||||
\(345\) | 1.08806 | + | 1.88457i | 0.0585791 | + | 0.101462i | ||||
\(346\) | 8.27218 | − | 14.3278i | 0.444715 | − | 0.770269i | ||||
\(347\) | −9.22195 | + | 15.9729i | −0.495060 | + | 0.857469i | −0.999984 | − | 0.00569469i | \(-0.998187\pi\) |
0.504924 | + | 0.863164i | \(0.331521\pi\) | |||||||
\(348\) | −3.25706 | − | 5.64139i | −0.174597 | − | 0.302410i | ||||
\(349\) | −19.9398 | −1.06736 | −0.533678 | − | 0.845688i | \(-0.679190\pi\) | ||||
−0.533678 | + | 0.845688i | \(0.679190\pi\) | |||||||
\(350\) | 0.380216 | + | 0.631694i | 0.0203234 | + | 0.0337655i | ||||
\(351\) | 3.30704 | 0.176517 | ||||||||
\(352\) | −6.01282 | − | 10.4145i | −0.320485 | − | 0.555095i | ||||
\(353\) | 11.0427 | − | 19.1266i | 0.587746 | − | 1.01801i | −0.406781 | − | 0.913526i | \(-0.633349\pi\) |
0.994527 | − | 0.104480i | \(-0.0333179\pi\) | |||||||
\(354\) | −6.40683 | + | 11.0970i | −0.340519 | + | 0.589797i | ||||
\(355\) | −15.0851 | − | 26.1282i | −0.800635 | − | 1.38674i | ||||
\(356\) | 0.297099 | 0.0157462 | ||||||||
\(357\) | 3.80321 | − | 6.87353i | 0.201287 | − | 0.363786i | ||||
\(358\) | 5.59153 | 0.295521 | ||||||||
\(359\) | 6.01948 | + | 10.4261i | 0.317696 | + | 0.550266i | 0.980007 | − | 0.198963i | \(-0.0637575\pi\) |
−0.662311 | + | 0.749229i | \(0.730424\pi\) | |||||||
\(360\) | −3.31288 | + | 5.73808i | −0.174604 | + | 0.302424i | ||||
\(361\) | 9.25656 | − | 16.0328i | 0.487187 | − | 0.843833i | ||||
\(362\) | 1.01690 | + | 1.76132i | 0.0534470 | + | 0.0925730i | ||||
\(363\) | 4.12286 | 0.216394 | ||||||||
\(364\) | −7.78687 | + | 0.141863i | −0.408143 | + | 0.00743563i | ||||
\(365\) | 1.53597 | 0.0803962 | ||||||||
\(366\) | −0.782016 | − | 1.35449i | −0.0408766 | − | 0.0708004i | ||||
\(367\) | −10.8238 | + | 18.7474i | −0.565000 | + | 0.978608i | 0.432050 | + | 0.901850i | \(0.357790\pi\) |
−0.997050 | + | 0.0767584i | \(0.975543\pi\) | |||||||
\(368\) | 0.713731 | − | 1.23622i | 0.0372058 | − | 0.0644423i | ||||
\(369\) | −1.14387 | − | 1.98124i | −0.0595475 | − | 0.103139i | ||||
\(370\) | 10.3783 | 0.539543 | ||||||||
\(371\) | −8.28140 | + | 0.150872i | −0.429949 | + | 0.00783289i | ||||
\(372\) | 4.98651 | 0.258539 | ||||||||
\(373\) | −10.9713 | − | 19.0029i | −0.568074 | − | 0.983933i | −0.996756 | − | 0.0804778i | \(-0.974355\pi\) |
0.428682 | − | 0.903455i | \(-0.358978\pi\) | |||||||
\(374\) | 4.10148 | − | 7.10397i | 0.212082 | − | 0.367338i | ||||
\(375\) | −5.72810 | + | 9.92136i | −0.295798 | + | 0.512337i | ||||
\(376\) | 5.80628 | + | 10.0568i | 0.299436 | + | 0.518639i | ||||
\(377\) | −24.2018 | −1.24646 | ||||||||
\(378\) | 1.34946 | − | 2.43888i | 0.0694089 | − | 0.125442i | ||||
\(379\) | 11.8759 | 0.610026 | 0.305013 | − | 0.952348i | \(-0.401339\pi\) | ||||
0.305013 | + | 0.952348i | \(0.401339\pi\) | |||||||
\(380\) | 0.675788 | + | 1.17050i | 0.0346672 | + | 0.0600453i | ||||
\(381\) | 7.85884 | − | 13.6119i | 0.402621 | − | 0.697360i | ||||
\(382\) | 5.50026 | − | 9.52673i | 0.281418 | − | 0.487430i | ||||
\(383\) | 2.23345 | + | 3.86846i | 0.114124 | + | 0.197669i | 0.917429 | − | 0.397899i | \(-0.130260\pi\) |
−0.803305 | + | 0.595568i | \(0.796927\pi\) | |||||||
\(384\) | −1.07410 | −0.0548126 | ||||||||
\(385\) | −7.78620 | − | 12.9360i | −0.396821 | − | 0.659282i | ||||
\(386\) | −25.9335 | −1.31998 | ||||||||
\(387\) | 3.89763 | + | 6.75090i | 0.198128 | + | 0.343168i | ||||
\(388\) | 0.0555772 | − | 0.0962625i | 0.00282150 | − | 0.00488699i | ||||
\(389\) | 1.35712 | − | 2.35061i | 0.0688089 | − | 0.119181i | −0.829568 | − | 0.558405i | \(-0.811413\pi\) |
0.898377 | + | 0.439225i | \(0.144747\pi\) | |||||||
\(390\) | 3.79080 | + | 6.56585i | 0.191954 | + | 0.332475i | ||||
\(391\) | −2.96912 | −0.150155 | ||||||||
\(392\) | −9.97730 | + | 18.8338i | −0.503930 | + | 0.951252i | ||||
\(393\) | 10.0029 | 0.504581 | ||||||||
\(394\) | 2.72752 | + | 4.72421i | 0.137411 | + | 0.238002i | ||||
\(395\) | 9.36172 | − | 16.2150i | 0.471039 | − | 0.815864i | ||||
\(396\) | −1.16713 | + | 2.02153i | −0.0586507 | + | 0.101586i | ||||
\(397\) | 3.69088 | + | 6.39280i | 0.185240 | + | 0.320845i | 0.943657 | − | 0.330924i | \(-0.107360\pi\) |
−0.758417 | + | 0.651769i | \(0.774027\pi\) | |||||||
\(398\) | 17.5274 | 0.878567 | ||||||||
\(399\) | −0.952030 | − | 1.58171i | −0.0476611 | − | 0.0791845i | ||||
\(400\) | 0.377587 | 0.0188793 | ||||||||
\(401\) | −1.35095 | − | 2.33992i | −0.0674634 | − | 0.116850i | 0.830321 | − | 0.557286i | \(-0.188157\pi\) |
−0.897784 | + | 0.440436i | \(0.854824\pi\) | |||||||
\(402\) | −5.93945 | + | 10.2874i | −0.296233 | + | 0.513090i | ||||
\(403\) | 9.26317 | − | 16.0443i | 0.461431 | − | 0.799222i | ||||
\(404\) | −3.90748 | − | 6.76796i | −0.194405 | − | 0.336719i | ||||
\(405\) | 2.17612 | 0.108132 | ||||||||
\(406\) | −9.87574 | + | 17.8484i | −0.490125 | + | 0.885801i | ||||
\(407\) | 11.8716 | 0.588454 | ||||||||
\(408\) | −4.52014 | − | 7.82911i | −0.223780 | − | 0.387599i | ||||
\(409\) | −12.4048 | + | 21.4857i | −0.613376 | + | 1.06240i | 0.377292 | + | 0.926094i | \(0.376855\pi\) |
−0.990667 | + | 0.136303i | \(0.956478\pi\) | |||||||
\(410\) | 2.62239 | − | 4.54212i | 0.129511 | − | 0.224319i | ||||
\(411\) | 3.03387 | + | 5.25481i | 0.149650 | + | 0.259201i | ||||
\(412\) | 4.86432 | 0.239648 | ||||||||
\(413\) | −32.1745 | + | 0.586161i | −1.58320 | + | 0.0288431i | ||||
\(414\) | −1.05351 | −0.0517772 | ||||||||
\(415\) | 12.6126 | + | 21.8457i | 0.619128 | + | 1.07236i | ||||
\(416\) | −7.58253 | + | 13.1333i | −0.371764 | + | 0.643914i | ||||
\(417\) | 7.05993 | − | 12.2282i | 0.345726 | − | 0.598815i | ||||
\(418\) | −0.963882 | − | 1.66949i | −0.0471450 | − | 0.0816576i | ||||
\(419\) | −20.0785 | −0.980899 | −0.490450 | − | 0.871470i | \(-0.663167\pi\) | ||||
−0.490450 | + | 0.871470i | \(0.663167\pi\) | |||||||
\(420\) | −5.12396 | + | 0.0933493i | −0.250024 | + | 0.00455498i | ||||
\(421\) | −26.5979 | −1.29630 | −0.648151 | − | 0.761512i | \(-0.724458\pi\) | ||||
−0.648151 | + | 0.761512i | \(0.724458\pi\) | |||||||
\(422\) | 15.0649 | + | 26.0932i | 0.733349 | + | 1.27020i | ||||
\(423\) | 1.90697 | − | 3.30297i | 0.0927201 | − | 0.160596i | ||||
\(424\) | −4.76596 | + | 8.25489i | −0.231456 | + | 0.400893i | ||||
\(425\) | −0.392691 | − | 0.680160i | −0.0190483 | − | 0.0329926i | ||||
\(426\) | 14.6061 | 0.707670 | ||||||||
\(427\) | 1.90164 | − | 3.43683i | 0.0920269 | − | 0.166320i | ||||
\(428\) | −9.65122 | −0.466509 | ||||||||
\(429\) | 4.33624 | + | 7.51059i | 0.209356 | + | 0.362615i | ||||
\(430\) | −8.93557 | + | 15.4769i | −0.430911 | + | 0.746360i | ||||
\(431\) | 12.0110 | − | 20.8036i | 0.578548 | − | 1.00207i | −0.417098 | − | 0.908861i | \(-0.636953\pi\) |
0.995646 | − | 0.0932128i | \(-0.0297137\pi\) | |||||||
\(432\) | −0.713731 | − | 1.23622i | −0.0343394 | − | 0.0594776i | ||||
\(433\) | −14.0909 | −0.677165 | −0.338582 | − | 0.940937i | \(-0.609947\pi\) | ||||
−0.338582 | + | 0.940937i | \(0.609947\pi\) | |||||||
\(434\) | −8.05245 | − | 13.3784i | −0.386530 | − | 0.642184i | ||||
\(435\) | −15.9254 | −0.763565 | ||||||||
\(436\) | −0.470587 | − | 0.815080i | −0.0225370 | − | 0.0390353i | ||||
\(437\) | −0.348884 | + | 0.604285i | −0.0166894 | + | 0.0289069i | ||||
\(438\) | −0.371799 | + | 0.643975i | −0.0177653 | + | 0.0307703i | ||||
\(439\) | −1.44976 | − | 2.51106i | −0.0691933 | − | 0.119846i | 0.829353 | − | 0.558725i | \(-0.188709\pi\) |
−0.898546 | + | 0.438878i | \(0.855376\pi\) | |||||||
\(440\) | −17.3756 | −0.828350 | ||||||||
\(441\) | 6.99535 | − | 0.254970i | 0.333112 | − | 0.0121414i | ||||
\(442\) | −10.3444 | −0.492034 | ||||||||
\(443\) | −6.99794 | − | 12.1208i | −0.332482 | − | 0.575876i | 0.650516 | − | 0.759493i | \(-0.274553\pi\) |
−0.982998 | + | 0.183617i | \(0.941220\pi\) | |||||||
\(444\) | 2.01476 | − | 3.48966i | 0.0956161 | − | 0.165612i | ||||
\(445\) | 0.363167 | − | 0.629024i | 0.0172158 | − | 0.0298186i | ||||
\(446\) | 8.71593 | + | 15.0964i | 0.412711 | + | 0.714837i | ||||
\(447\) | −1.01590 | −0.0480506 | ||||||||
\(448\) | 10.4867 | + | 17.4227i | 0.495451 | + | 0.823145i | ||||
\(449\) | 12.6648 | 0.597690 | 0.298845 | − | 0.954302i | \(-0.403399\pi\) | ||||
0.298845 | + | 0.954302i | \(0.403399\pi\) | |||||||
\(450\) | −0.139335 | − | 0.241336i | −0.00656833 | − | 0.0113767i | ||||
\(451\) | 2.99972 | − | 5.19567i | 0.141251 | − | 0.244654i | ||||
\(452\) | −6.27257 | + | 10.8644i | −0.295037 | + | 0.511019i | ||||
\(453\) | 11.2693 | + | 19.5190i | 0.529477 | + | 0.917080i | ||||
\(454\) | 18.9263 | 0.888256 | ||||||||
\(455\) | −9.21815 | + | 16.6599i | −0.432153 | + | 0.781030i | ||||
\(456\) | −2.12454 | −0.0994908 | ||||||||
\(457\) | 1.77836 | + | 3.08021i | 0.0831881 | + | 0.144086i | 0.904618 | − | 0.426224i | \(-0.140156\pi\) |
−0.821430 | + | 0.570310i | \(0.806823\pi\) | |||||||
\(458\) | 14.7524 | − | 25.5518i | 0.689332 | − | 1.19396i | ||||
\(459\) | −1.48456 | + | 2.57133i | −0.0692934 | + | 0.120020i | ||||
\(460\) | 0.968498 | + | 1.67749i | 0.0451565 | + | 0.0782133i | ||||
\(461\) | 16.1441 | 0.751904 | 0.375952 | − | 0.926639i | \(-0.377316\pi\) | ||||
0.375952 | + | 0.926639i | \(0.377316\pi\) | |||||||
\(462\) | 7.30835 | − | 0.133145i | 0.340015 | − | 0.00619447i | ||||
\(463\) | 9.78687 | 0.454834 | 0.227417 | − | 0.973797i | \(-0.426972\pi\) | ||||
0.227417 | + | 0.973797i | \(0.426972\pi\) | |||||||
\(464\) | 5.22328 | + | 9.04698i | 0.242485 | + | 0.419996i | ||||
\(465\) | 6.09540 | − | 10.5575i | 0.282667 | − | 0.489594i | ||||
\(466\) | 12.2450 | − | 21.2090i | 0.567241 | − | 0.982490i | ||||
\(467\) | 15.0788 | + | 26.1172i | 0.697763 | + | 1.20856i | 0.969240 | + | 0.246116i | \(0.0791544\pi\) |
−0.271478 | + | 0.962445i | \(0.587512\pi\) | |||||||
\(468\) | 2.94365 | 0.136070 | ||||||||
\(469\) | −29.8273 | + | 0.543400i | −1.37730 | + | 0.0250919i | ||||
\(470\) | 8.74370 | 0.403317 | ||||||||
\(471\) | −5.68305 | − | 9.84334i | −0.261861 | − | 0.453557i | ||||
\(472\) | −18.5165 | + | 32.0715i | −0.852290 | + | 1.47621i | ||||
\(473\) | −10.2213 | + | 17.7038i | −0.469975 | + | 0.814020i | ||||
\(474\) | 4.53223 | + | 7.85006i | 0.208172 | + | 0.360565i | ||||
\(475\) | −0.184571 | −0.00846871 | ||||||||
\(476\) | 3.38529 | − | 6.11824i | 0.155165 | − | 0.280429i | ||||
\(477\) | 3.13059 | 0.143340 | ||||||||
\(478\) | 3.38957 | + | 5.87091i | 0.155035 | + | 0.268529i | ||||
\(479\) | −1.46083 | + | 2.53024i | −0.0667471 | + | 0.115609i | −0.897468 | − | 0.441080i | \(-0.854595\pi\) |
0.830721 | + | 0.556690i | \(0.187929\pi\) | |||||||
\(480\) | −4.98950 | + | 8.64206i | −0.227738 | + | 0.394454i | ||||
\(481\) | −7.48540 | − | 12.9651i | −0.341305 | − | 0.591158i | ||||
\(482\) | −24.7762 | −1.12852 | ||||||||
\(483\) | −1.36439 | − | 2.26681i | −0.0620820 | − | 0.103143i | ||||
\(484\) | 3.66983 | 0.166810 | ||||||||
\(485\) | −0.135873 | − | 0.235338i | −0.00616966 | − | 0.0106862i | ||||
\(486\) | −0.526755 | + | 0.912367i | −0.0238941 | + | 0.0413858i | ||||
\(487\) | −16.1191 | + | 27.9191i | −0.730427 | + | 1.26514i | 0.226274 | + | 0.974064i | \(0.427346\pi\) |
−0.956701 | + | 0.291073i | \(0.905988\pi\) | |||||||
\(488\) | −2.26012 | − | 3.91464i | −0.102311 | − | 0.177207i | ||||
\(489\) | −14.7670 | −0.667789 | ||||||||
\(490\) | 8.52486 | + | 13.5964i | 0.385114 | + | 0.614224i | ||||
\(491\) | −12.1670 | −0.549091 | −0.274546 | − | 0.961574i | \(-0.588527\pi\) | ||||
−0.274546 | + | 0.961574i | \(0.588527\pi\) | |||||||
\(492\) | −1.01818 | − | 1.76353i | −0.0459030 | − | 0.0795063i | ||||
\(493\) | 10.8644 | − | 18.8177i | 0.489309 | − | 0.847508i | ||||
\(494\) | −1.21551 | + | 2.10533i | −0.0546885 | + | 0.0947233i | ||||
\(495\) | 2.85336 | + | 4.94216i | 0.128249 | + | 0.222133i | ||||
\(496\) | −7.99677 | −0.359066 | ||||||||
\(497\) | 18.9163 | + | 31.4277i | 0.848512 | + | 1.40972i | ||||
\(498\) | −12.2121 | −0.547238 | ||||||||
\(499\) | −15.9148 | − | 27.5652i | −0.712444 | − | 1.23399i | −0.963937 | − | 0.266131i | \(-0.914255\pi\) |
0.251492 | − | 0.967859i | \(-0.419079\pi\) | |||||||
\(500\) | −5.09867 | + | 8.83116i | −0.228020 | + | 0.394942i | ||||
\(501\) | −4.42668 | + | 7.66723i | −0.197769 | + | 0.342547i | ||||
\(502\) | −1.64660 | − | 2.85200i | −0.0734915 | − | 0.127291i | ||||
\(503\) | 0.217299 | 0.00968890 | 0.00484445 | − | 0.999988i | \(-0.498458\pi\) | ||||
0.00484445 | + | 0.999988i | \(0.498458\pi\) | |||||||
\(504\) | 3.90010 | − | 7.04865i | 0.173724 | − | 0.313972i | ||||
\(505\) | −19.1057 | −0.850192 | ||||||||
\(506\) | −1.38138 | − | 2.39262i | −0.0614098 | − | 0.106365i | ||||
\(507\) | −1.03174 | + | 1.78703i | −0.0458213 | + | 0.0793649i | ||||
\(508\) | 6.99528 | − | 12.1162i | 0.310366 | − | 0.537569i | ||||
\(509\) | −7.57985 | − | 13.1287i | −0.335971 | − | 0.581919i | 0.647700 | − | 0.761896i | \(-0.275731\pi\) |
−0.983671 | + | 0.179977i | \(0.942398\pi\) | |||||||
\(510\) | −6.80689 | −0.301414 | ||||||||
\(511\) | −1.86714 | + | 0.0340159i | −0.0825973 | + | 0.00150477i | ||||
\(512\) | 15.2385 | 0.673452 | ||||||||
\(513\) | 0.348884 | + | 0.604285i | 0.0154036 | + | 0.0266799i | ||||
\(514\) | −10.8162 | + | 18.7342i | −0.477082 | + | 0.826330i | ||||
\(515\) | 5.94604 | − | 10.2988i | 0.262014 | − | 0.453821i | ||||
\(516\) | 3.46935 | + | 6.00909i | 0.152729 | + | 0.264535i | ||||
\(517\) | 10.0018 | 0.439878 | ||||||||
\(518\) | −12.6160 | + | 0.229841i | −0.554315 | + | 0.0100986i | ||||
\(519\) | −15.7040 | −0.689330 | ||||||||
\(520\) | 10.9558 | + | 18.9761i | 0.480445 | + | 0.832156i | ||||
\(521\) | 13.2885 | − | 23.0163i | 0.582179 | − | 1.00836i | −0.413041 | − | 0.910712i | \(-0.635534\pi\) |
0.995221 | − | 0.0976518i | \(-0.0311331\pi\) | |||||||
\(522\) | 3.85494 | − | 6.67695i | 0.168726 | − | 0.292242i | ||||
\(523\) | 18.2681 | + | 31.6412i | 0.798807 | + | 1.38357i | 0.920394 | + | 0.390993i | \(0.127868\pi\) |
−0.121587 | + | 0.992581i | \(0.538798\pi\) | |||||||
\(524\) | 8.90377 | 0.388963 | ||||||||
\(525\) | 0.338824 | − | 0.612356i | 0.0147875 | − | 0.0267254i | ||||
\(526\) | −20.4882 | −0.893328 | ||||||||
\(527\) | 8.31664 | + | 14.4048i | 0.362279 | + | 0.627485i | ||||
\(528\) | 1.87171 | − | 3.24189i | 0.0814557 | − | 0.141085i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | 3.58854 | + | 6.21553i | 0.155876 | + | 0.269985i | ||||
\(531\) | 12.1628 | 0.527822 | ||||||||
\(532\) | −0.847417 | − | 1.40791i | −0.0367402 | − | 0.0610404i | ||||
\(533\) | −7.56565 | −0.327705 | ||||||||
\(534\) | 0.175818 | + | 0.304526i | 0.00760839 | + | 0.0131781i | ||||
\(535\) | −11.7974 | + | 20.4338i | −0.510048 | + | 0.883429i | ||||
\(536\) | −17.1657 | + | 29.7319i | −0.741445 | + | 1.28422i | ||||
\(537\) | −2.65376 | − | 4.59645i | −0.114518 | − | 0.198351i | ||||
\(538\) | −8.13247 | −0.350616 | ||||||||
\(539\) | 9.75147 | + | 15.5528i | 0.420026 | + | 0.669905i | ||||
\(540\) | 1.93700 | 0.0833550 | ||||||||
\(541\) | −4.97320 | − | 8.61383i | −0.213814 | − | 0.370337i | 0.739091 | − | 0.673606i | \(-0.235255\pi\) |
−0.952905 | + | 0.303268i | \(0.901922\pi\) | |||||||
\(542\) | 16.2576 | − | 28.1590i | 0.698325 | − | 1.20953i | ||||
\(543\) | 0.965248 | − | 1.67186i | 0.0414228 | − | 0.0717463i | ||||
\(544\) | −6.80773 | − | 11.7913i | −0.291879 | − | 0.505549i | ||||
\(545\) | −2.30094 | −0.0985614 | ||||||||
\(546\) | −4.75354 | − | 7.89757i | −0.203433 | − | 0.337985i | ||||
\(547\) | −35.8124 | −1.53123 | −0.765614 | − | 0.643300i | \(-0.777565\pi\) | ||||
−0.765614 | + | 0.643300i | \(0.777565\pi\) | |||||||
\(548\) | 2.70049 | + | 4.67739i | 0.115359 | + | 0.199808i | ||||
\(549\) | −0.742296 | + | 1.28569i | −0.0316804 | + | 0.0548721i | ||||
\(550\) | 0.365397 | − | 0.632886i | 0.0155806 | − | 0.0269864i | ||||
\(551\) | −2.55323 | − | 4.42233i | −0.108771 | − | 0.188397i | ||||
\(552\) | −3.04477 | −0.129594 | ||||||||
\(553\) | −11.0211 | + | 19.9184i | −0.468666 | + | 0.847018i | ||||
\(554\) | −6.74398 | −0.286524 | ||||||||
\(555\) | −4.92559 | − | 8.53137i | −0.209079 | − | 0.362136i | ||||
\(556\) | 6.28415 | − | 10.8845i | 0.266507 | − | 0.461604i | ||||
\(557\) | 6.75130 | − | 11.6936i | 0.286062 | − | 0.495474i | −0.686804 | − | 0.726842i | \(-0.740987\pi\) |
0.972866 | + | 0.231369i | \(0.0743204\pi\) | |||||||
\(558\) | 2.95093 | + | 5.11116i | 0.124923 | + | 0.216373i | ||||
\(559\) | 25.7793 | 1.09035 | ||||||||
\(560\) | 8.21719 | − | 0.149702i | 0.347240 | − | 0.00632608i | ||||
\(561\) | −7.78631 | −0.328738 | ||||||||
\(562\) | −2.52435 | − | 4.37231i | −0.106483 | − | 0.184435i | ||||
\(563\) | −18.7091 | + | 32.4051i | −0.788495 | + | 1.36571i | 0.138394 | + | 0.990377i | \(0.455806\pi\) |
−0.926889 | + | 0.375336i | \(0.877527\pi\) | |||||||
\(564\) | 1.69743 | − | 2.94003i | 0.0714745 | − | 0.123797i | ||||
\(565\) | 15.3349 | + | 26.5608i | 0.645144 | + | 1.11742i | ||||
\(566\) | 12.3276 | 0.518168 | ||||||||
\(567\) | −2.64531 | + | 0.0481928i | −0.111093 | + | 0.00202391i | ||||
\(568\) | 42.2135 | 1.77124 | ||||||||
\(569\) | −21.4927 | − | 37.2264i | −0.901019 | − | 1.56061i | −0.826174 | − | 0.563416i | \(-0.809487\pi\) |
−0.0748455 | − | 0.997195i | \(-0.523846\pi\) | |||||||
\(570\) | −0.799839 | + | 1.38536i | −0.0335016 | + | 0.0580264i | ||||
\(571\) | 10.3749 | − | 17.9698i | 0.434175 | − | 0.752012i | −0.563053 | − | 0.826421i | \(-0.690373\pi\) |
0.997228 | + | 0.0744082i | \(0.0237068\pi\) | |||||||
\(572\) | 3.85976 | + | 6.68529i | 0.161385 | + | 0.279526i | ||||
\(573\) | −10.4418 | −0.436211 | ||||||||
\(574\) | −3.08722 | + | 5.57953i | −0.128858 | + | 0.232885i | ||||
\(575\) | −0.264516 | −0.0110311 | ||||||||
\(576\) | −3.84300 | − | 6.65627i | −0.160125 | − | 0.277344i | ||||
\(577\) | 19.1817 | − | 33.2237i | 0.798544 | − | 1.38312i | −0.122020 | − | 0.992528i | \(-0.538937\pi\) |
0.920564 | − | 0.390592i | \(-0.127730\pi\) | |||||||
\(578\) | −4.31113 | + | 7.46710i | −0.179319 | + | 0.310590i | ||||
\(579\) | 12.3081 | + | 21.3183i | 0.511509 | + | 0.885959i | ||||
\(580\) | −14.1755 | −0.588604 | ||||||||
\(581\) | −15.8158 | − | 26.2765i | −0.656151 | − | 1.09013i | ||||
\(582\) | 0.131558 | 0.00545327 | ||||||||
\(583\) | 4.10488 | + | 7.10986i | 0.170007 | + | 0.294460i | ||||
\(584\) | −1.07454 | + | 1.86116i | −0.0444649 | + | 0.0770155i | ||||
\(585\) | 3.59825 | − | 6.23236i | 0.148769 | − | 0.257676i | ||||
\(586\) | 10.4841 | + | 18.1589i | 0.433093 | + | 0.750139i | ||||
\(587\) | −21.7316 | −0.896958 | −0.448479 | − | 0.893793i | \(-0.648034\pi\) | ||||
−0.448479 | + | 0.893793i | \(0.648034\pi\) | |||||||
\(588\) | 6.22668 | − | 0.226953i | 0.256784 | − | 0.00935938i | ||||
\(589\) | 3.90896 | 0.161066 | ||||||||
\(590\) | 13.9420 | + | 24.1483i | 0.573984 | + | 0.994169i | ||||
\(591\) | 2.58899 | − | 4.48426i | 0.106497 | − | 0.184458i | ||||
\(592\) | −3.23102 | + | 5.59630i | −0.132794 | + | 0.230006i | ||||
\(593\) | 0.434004 | + | 0.751716i | 0.0178224 | + | 0.0308693i | 0.874799 | − | 0.484486i | \(-0.160993\pi\) |
−0.856977 | + | 0.515355i | \(0.827660\pi\) | |||||||
\(594\) | −2.76276 | −0.113357 | ||||||||
\(595\) | −8.81555 | − | 14.6462i | −0.361402 | − | 0.600436i | ||||
\(596\) | −0.904273 | −0.0370404 | ||||||||
\(597\) | −8.31855 | − | 14.4082i | −0.340456 | − | 0.589687i | ||||
\(598\) | −1.74200 | + | 3.01723i | −0.0712357 | + | 0.123384i | ||||
\(599\) | 6.53259 | − | 11.3148i | 0.266914 | − | 0.462309i | −0.701149 | − | 0.713015i | \(-0.747329\pi\) |
0.968063 | + | 0.250706i | \(0.0806626\pi\) | |||||||
\(600\) | −0.402695 | − | 0.697489i | −0.0164400 | − | 0.0284749i | ||||
\(601\) | −14.4244 | −0.588385 | −0.294192 | − | 0.955746i | \(-0.595051\pi\) | ||||
−0.294192 | + | 0.955746i | \(0.595051\pi\) | |||||||
\(602\) | 10.5194 | − | 19.0117i | 0.428740 | − | 0.774860i | ||||
\(603\) | 11.2755 | 0.459176 | ||||||||
\(604\) | 10.0310 | + | 17.3741i | 0.408154 | + | 0.706943i | ||||
\(605\) | 4.48592 | − | 7.76983i | 0.182378 | − | 0.315889i | ||||
\(606\) | 4.62476 | − | 8.01032i | 0.187868 | − | 0.325397i | ||||
\(607\) | −14.4916 | − | 25.1002i | −0.588195 | − | 1.01878i | −0.994469 | − | 0.105032i | \(-0.966505\pi\) |
0.406274 | − | 0.913751i | \(-0.366828\pi\) | |||||||
\(608\) | −3.19975 | −0.129767 | ||||||||
\(609\) | 19.3591 | − | 0.352688i | 0.784471 | − | 0.0142917i | ||||
\(610\) | −3.40352 | −0.137804 | ||||||||
\(611\) | −6.30643 | − | 10.9231i | −0.255131 | − | 0.441900i | ||||
\(612\) | −1.32143 | + | 2.28879i | −0.0534157 | + | 0.0925187i | ||||
\(613\) | 2.97847 | − | 5.15886i | 0.120299 | − | 0.208364i | −0.799586 | − | 0.600551i | \(-0.794948\pi\) |
0.919886 | + | 0.392187i | \(0.128281\pi\) | |||||||
\(614\) | 11.4616 | + | 19.8520i | 0.462551 | + | 0.801161i | ||||
\(615\) | −4.97839 | −0.200748 | ||||||||
\(616\) | 21.1220 | − | 0.384805i | 0.851029 | − | 0.0155042i | ||||
\(617\) | −40.0363 | −1.61180 | −0.805901 | − | 0.592050i | \(-0.798319\pi\) | ||||
−0.805901 | + | 0.592050i | \(0.798319\pi\) | |||||||
\(618\) | 2.87862 | + | 4.98592i | 0.115795 | + | 0.200563i | ||||
\(619\) | −5.25875 | + | 9.10842i | −0.211367 | + | 0.366098i | −0.952143 | − | 0.305654i | \(-0.901125\pi\) |
0.740776 | + | 0.671752i | \(0.234458\pi\) | |||||||
\(620\) | 5.42561 | − | 9.39744i | 0.217898 | − | 0.377410i | ||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | 8.57921 | 0.343995 | ||||||||
\(623\) | −0.427540 | + | 0.772692i | −0.0171290 | + | 0.0309573i | ||||
\(624\) | −4.72067 | −0.188978 | ||||||||
\(625\) | 11.8037 | + | 20.4447i | 0.472149 | + | 0.817786i | ||||
\(626\) | 0.553324 | − | 0.958385i | 0.0221153 | − | 0.0383048i | ||||
\(627\) | −0.914925 | + | 1.58470i | −0.0365386 | + | 0.0632867i | ||||
\(628\) | −5.05858 | − | 8.76171i | −0.201859 | − | 0.349630i | ||||
\(629\) | 13.4411 | 0.535930 | ||||||||
\(630\) | −3.12795 | − | 5.19680i | −0.124621 | − | 0.207046i | ||||
\(631\) | 44.9392 | 1.78900 | 0.894501 | − | 0.447065i | \(-0.147531\pi\) | ||||
0.894501 | + | 0.447065i | \(0.147531\pi\) | |||||||
\(632\) | 13.0987 | + | 22.6876i | 0.521038 | + | 0.902464i | ||||
\(633\) | 14.2997 | − | 24.7679i | 0.568364 | − | 0.984435i | ||||
\(634\) | 8.62191 | − | 14.9336i | 0.342420 | − | 0.593089i | ||||
\(635\) | −17.1018 | − | 29.6211i | −0.678663 | − | 1.17548i | ||||
\(636\) | 2.78659 | 0.110496 | ||||||||
\(637\) | 10.8367 | − | 20.4562i | 0.429367 | − | 0.810503i | ||||
\(638\) | 20.2186 | 0.800462 | ||||||||
\(639\) | −6.93213 | − | 12.0068i | −0.274231 | − | 0.474982i | ||||
\(640\) | −1.16869 | + | 2.02423i | −0.0461964 | + | 0.0800146i | ||||
\(641\) | 16.0204 | − | 27.7482i | 0.632769 | − | 1.09599i | −0.354214 | − | 0.935164i | \(-0.615252\pi\) |
0.986983 | − | 0.160824i | \(-0.0514151\pi\) | |||||||
\(642\) | −5.71143 | − | 9.89248i | −0.225412 | − | 0.390425i | ||||
\(643\) | 38.5772 | 1.52134 | 0.760669 | − | 0.649140i | \(-0.224871\pi\) | ||||
0.760669 | + | 0.649140i | \(0.224871\pi\) | |||||||
\(644\) | −1.21447 | − | 2.01773i | −0.0478567 | − | 0.0795095i | ||||
\(645\) | 16.9634 | 0.667934 | ||||||||
\(646\) | −1.09131 | − | 1.89020i | −0.0429370 | − | 0.0743691i | ||||
\(647\) | −15.4667 | + | 26.7891i | −0.608058 | + | 1.05319i | 0.383502 | + | 0.923540i | \(0.374718\pi\) |
−0.991560 | + | 0.129648i | \(0.958615\pi\) | |||||||
\(648\) | −1.52238 | + | 2.63685i | −0.0598049 | + | 0.103585i | ||||
\(649\) | 15.9481 | + | 27.6229i | 0.626017 | + | 1.08429i | ||||
\(650\) | −0.921575 | −0.0361472 | ||||||||
\(651\) | −7.17583 | + | 12.9689i | −0.281243 | + | 0.508290i | ||||
\(652\) | −13.1444 | −0.514774 | ||||||||
\(653\) | −21.2788 | − | 36.8560i | −0.832704 | − | 1.44229i | −0.895886 | − | 0.444284i | \(-0.853458\pi\) |
0.0631822 | − | 0.998002i | \(-0.479875\pi\) | |||||||
\(654\) | 0.556970 | − | 0.964701i | 0.0217793 | − | 0.0377228i | ||||
\(655\) | 10.8838 | − | 18.8513i | 0.425264 | − | 0.736579i | ||||
\(656\) | 1.63283 | + | 2.82815i | 0.0637513 | + | 0.110421i | ||||
\(657\) | 0.705829 | 0.0275370 | ||||||||
\(658\) | −10.6289 | + | 0.193640i | −0.414359 | + | 0.00754888i | ||||
\(659\) | 32.5053 | 1.26623 | 0.633113 | − | 0.774059i | \(-0.281777\pi\) | ||||
0.633113 | + | 0.774059i | \(0.281777\pi\) | |||||||
\(660\) | 2.53982 | + | 4.39909i | 0.0988623 | + | 0.171234i | ||||
\(661\) | −16.7914 | + | 29.0835i | −0.653109 | + | 1.13122i | 0.329255 | + | 0.944241i | \(0.393202\pi\) |
−0.982364 | + | 0.186977i | \(0.940131\pi\) | |||||||
\(662\) | 15.4302 | − | 26.7259i | 0.599711 | − | 1.03873i | ||||
\(663\) | 4.90950 | + | 8.50350i | 0.190669 | + | 0.330249i | ||||
\(664\) | −35.2945 | −1.36969 | ||||||||
\(665\) | −4.01671 | + | 0.0731772i | −0.155761 | + | 0.00283769i | ||||
\(666\) | 4.76919 | 0.184802 | ||||||||
\(667\) | −3.65914 | − | 6.33781i | −0.141682 | − | 0.245401i | ||||
\(668\) | −3.94026 | + | 6.82473i | −0.152453 | + | 0.264057i | ||||
\(669\) | 8.27322 | − | 14.3296i | 0.319861 | − | 0.554016i | ||||
\(670\) | 12.9249 | + | 22.3866i | 0.499334 | + | 0.864871i | ||||
\(671\) | −3.89324 | −0.150297 | ||||||||
\(672\) | 5.87390 | − | 10.6159i | 0.226591 | − | 0.409517i | ||||
\(673\) | −1.23960 | −0.0477832 | −0.0238916 | − | 0.999715i | \(-0.507606\pi\) | ||||
−0.0238916 | + | 0.999715i | \(0.507606\pi\) | |||||||
\(674\) | −2.25144 | − | 3.89961i | −0.0867222 | − | 0.150207i | ||||
\(675\) | −0.132258 | + | 0.229078i | −0.00509062 | + | 0.00881721i | ||||
\(676\) | −0.918371 | + | 1.59067i | −0.0353220 | + | 0.0611795i | ||||
\(677\) | −2.84916 | − | 4.93490i | −0.109502 | − | 0.189663i | 0.806066 | − | 0.591825i | \(-0.201592\pi\) |
−0.915569 | + | 0.402162i | \(0.868259\pi\) | |||||||
\(678\) | −14.8480 | −0.570234 | ||||||||
\(679\) | 0.170380 | + | 0.283071i | 0.00653859 | + | 0.0108633i | ||||
\(680\) | −19.6727 | −0.754414 | ||||||||
\(681\) | −8.98250 | − | 15.5581i | −0.344210 | − | 0.596189i | ||||
\(682\) | −7.73861 | + | 13.4037i | −0.296327 | + | 0.513253i | ||||
\(683\) | −13.6259 | + | 23.6007i | −0.521380 | + | 0.903056i | 0.478311 | + | 0.878190i | \(0.341249\pi\) |
−0.999691 | + | 0.0248657i | \(0.992084\pi\) | |||||||
\(684\) | 0.310548 | + | 0.537884i | 0.0118741 | + | 0.0205665i | ||||
\(685\) | 13.2041 | 0.504503 | ||||||||
\(686\) | −10.6640 | − | 16.3392i | −0.407155 | − | 0.623833i | ||||
\(687\) | −28.0061 | −1.06850 | ||||||||
\(688\) | −5.56372 | − | 9.63665i | −0.212115 | − | 0.367394i | ||||
\(689\) | 5.17650 | − | 8.96596i | 0.197209 | − | 0.341576i | ||||
\(690\) | −1.14628 | + | 1.98542i | −0.0436382 | + | 0.0755835i | ||||
\(691\) | 22.5757 | + | 39.1023i | 0.858820 | + | 1.48752i | 0.873055 | + | 0.487622i | \(0.162136\pi\) |
−0.0142345 | + | 0.999899i | \(0.504531\pi\) | |||||||
\(692\) | −13.9784 | −0.531379 | ||||||||
\(693\) | −3.57802 | − | 5.94455i | −0.135918 | − | 0.225815i | ||||
\(694\) | −19.4308 | −0.737584 | ||||||||
\(695\) | −15.3632 | − | 26.6099i | −0.582760 | − | 1.00937i | ||||
\(696\) | 11.1412 | − | 19.2972i | 0.422307 | − | 0.731457i | ||||
\(697\) | 3.39629 | − | 5.88255i | 0.128644 | − | 0.222817i | ||||
\(698\) | −10.5034 | − | 18.1925i | −0.397560 | − | 0.688594i | ||||
\(699\) | −23.2462 | −0.879251 | ||||||||
\(700\) | 0.301593 | − | 0.545068i | 0.0113991 | − | 0.0206016i | ||||
\(701\) | −0.456514 | −0.0172423 | −0.00862116 | − | 0.999963i | \(-0.502744\pi\) | ||||
−0.00862116 | + | 0.999963i | \(0.502744\pi\) | |||||||
\(702\) | 1.74200 | + | 3.01723i | 0.0657476 | + | 0.113878i | ||||
\(703\) | 1.57938 | − | 2.73557i | 0.0595675 | − | 0.103174i | ||||
\(704\) | 10.0780 | − | 17.4556i | 0.379828 | − | 0.657882i | ||||
\(705\) | −4.14979 | − | 7.18765i | −0.156290 | − | 0.270703i | ||||
\(706\) | 23.2673 | 0.875676 | ||||||||
\(707\) | 23.2251 | − | 0.423119i | 0.873470 | − | 0.0159130i | ||||
\(708\) | 10.8263 | 0.406878 | ||||||||
\(709\) | 4.95123 | + | 8.57579i | 0.185948 | + | 0.322071i | 0.943895 | − | 0.330245i | \(-0.107131\pi\) |
−0.757948 | + | 0.652315i | \(0.773798\pi\) | |||||||
\(710\) | 15.8923 | − | 27.5263i | 0.596429 | − | 1.03304i | ||||
\(711\) | 4.30203 | − | 7.45134i | 0.161339 | − | 0.279447i | ||||
\(712\) | 0.508135 | + | 0.880115i | 0.0190431 | + | 0.0329837i | ||||
\(713\) | 5.60209 | 0.209800 | ||||||||
\(714\) | 8.27454 | − | 0.150747i | 0.309667 | − | 0.00564157i | ||||
\(715\) | 18.8723 | 0.705785 | ||||||||
\(716\) | −2.36215 | − | 4.09137i | −0.0882779 | − | 0.152902i | ||||
\(717\) | 3.21741 | − | 5.57271i | 0.120156 | − | 0.208117i | ||||
\(718\) | −6.34159 | + | 10.9840i | −0.236666 | + | 0.409918i | ||||
\(719\) | 13.6043 | + | 23.5633i | 0.507355 | + | 0.878764i | 0.999964 | + | 0.00851331i | \(0.00270990\pi\) |
−0.492609 | + | 0.870251i | \(0.663957\pi\) | |||||||
\(720\) | −3.10632 | −0.115766 | ||||||||
\(721\) | −6.99999 | + | 12.6511i | −0.260693 | + | 0.471151i | ||||
\(722\) | 19.5038 | 0.725855 | ||||||||
\(723\) | 11.7589 | + | 20.3669i | 0.437317 | + | 0.757455i | ||||
\(724\) | 0.859183 | − | 1.48815i | 0.0319313 | − | 0.0553066i | ||||
\(725\) | 0.967902 | − | 1.67645i | 0.0359470 | − | 0.0622620i | ||||
\(726\) | 2.17174 | + | 3.76156i | 0.0806008 | + | 0.139605i | ||||
\(727\) | −29.0386 | −1.07698 | −0.538491 | − | 0.842631i | \(-0.681006\pi\) | ||||
−0.538491 | + | 0.842631i | \(0.681006\pi\) | |||||||
\(728\) | −13.7383 | − | 22.8249i | −0.509175 | − | 0.845947i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.809078 | + | 1.40136i | 0.0299453 | + | 0.0518668i | ||||
\(731\) | −11.5725 | + | 20.0442i | −0.428026 | + | 0.741363i | ||||
\(732\) | −0.660729 | + | 1.14442i | −0.0244213 | + | 0.0422989i | ||||
\(733\) | 10.3993 | + | 18.0121i | 0.384108 | + | 0.665294i | 0.991645 | − | 0.128997i | \(-0.0411758\pi\) |
−0.607537 | + | 0.794291i | \(0.707843\pi\) | |||||||
\(734\) | −22.8060 | −0.841786 | ||||||||
\(735\) | 7.13084 | − | 13.4607i | 0.263025 | − | 0.496504i | ||||
\(736\) | −4.58569 | −0.169031 | ||||||||
\(737\) | 14.7847 | + | 25.6078i | 0.544600 | + | 0.943275i | ||||
\(738\) | 1.20508 | − | 2.08726i | 0.0443596 | − | 0.0768330i | ||||
\(739\) | −8.42350 | + | 14.5899i | −0.309864 | + | 0.536699i | −0.978332 | − | 0.207041i | \(-0.933617\pi\) |
0.668469 | + | 0.743740i | \(0.266950\pi\) | |||||||
\(740\) | −4.38434 | − | 7.59391i | −0.161172 | − | 0.279158i | ||||
\(741\) | 2.30755 | 0.0847699 | ||||||||
\(742\) | −4.49992 | − | 7.47620i | −0.165197 | − | 0.274460i | ||||
\(743\) | −38.5982 | −1.41603 | −0.708016 | − | 0.706197i | \(-0.750409\pi\) | ||||
−0.708016 | + | 0.706197i | \(0.750409\pi\) | |||||||
\(744\) | 8.52853 | + | 14.7718i | 0.312671 | + | 0.541562i | ||||
\(745\) | −1.10536 | + | 1.91454i | −0.0404974 | + | 0.0701435i | ||||
\(746\) | 11.5584 | − | 20.0198i | 0.423183 | − | 0.732975i | ||||
\(747\) | 5.79592 | + | 10.0388i | 0.212062 | + | 0.367302i | ||||
\(748\) | −6.93072 | −0.253412 | ||||||||
\(749\) | 13.8886 | − | 25.1008i | 0.507477 | − | 0.917163i | ||||
\(750\) | −12.0692 | −0.440706 | ||||||||
\(751\) | −12.0016 | − | 20.7874i | −0.437945 | − | 0.758542i | 0.559586 | − | 0.828772i | \(-0.310960\pi\) |
−0.997531 | + | 0.0702297i | \(0.977627\pi\) | |||||||
\(752\) | −2.72213 | + | 4.71486i | −0.0992658 | + | 0.171933i | ||||
\(753\) | −1.56297 | + | 2.70714i | −0.0569577 | + | 0.0986537i | ||||
\(754\) | −12.7484 | − | 22.0809i | −0.464271 | − | 0.804140i | ||||
\(755\) | 49.0465 | 1.78498 | ||||||||
\(756\) | −2.35463 | + | 0.0428972i | −0.0856372 | + | 0.00156016i | ||||
\(757\) | −6.54398 | −0.237845 | −0.118923 | − | 0.992904i | \(-0.537944\pi\) | ||||
−0.118923 | + | 0.992904i | \(0.537944\pi\) | |||||||
\(758\) | 6.25571 | + | 10.8352i | 0.227218 | + | 0.393553i | ||||
\(759\) | −1.31121 | + | 2.27109i | −0.0475941 | + | 0.0824354i | ||||
\(760\) | −2.31163 | + | 4.00385i | −0.0838515 | + | 0.145235i | ||||
\(761\) | −8.00453 | − | 13.8642i | −0.290164 | − | 0.502579i | 0.683684 | − | 0.729778i | \(-0.260376\pi\) |
−0.973848 | + | 0.227199i | \(0.927043\pi\) | |||||||
\(762\) | 16.5587 | 0.599860 | ||||||||
\(763\) | 2.79705 | − | 0.0509572i | 0.101260 | − | 0.00184477i | ||||
\(764\) | −9.29439 | −0.336259 | ||||||||
\(765\) | 3.23058 | + | 5.59552i | 0.116802 | + | 0.202307i | ||||
\(766\) | −2.35297 | + | 4.07546i | −0.0850162 | + | 0.147252i | ||||
\(767\) | 20.1115 | − | 34.8341i | 0.726183 | − | 1.25779i | ||||
\(768\) | −8.25178 | − | 14.2925i | −0.297761 | − | 0.515736i | ||||
\(769\) | 35.3103 | 1.27332 | 0.636661 | − | 0.771144i | \(-0.280315\pi\) | ||||
0.636661 | + | 0.771144i | \(0.280315\pi\) | |||||||
\(770\) | 7.70099 | − | 13.9180i | 0.277525 | − | 0.501570i | ||||
\(771\) | 20.5336 | 0.739500 | ||||||||
\(772\) | 10.9557 | + | 18.9758i | 0.394303 | + | 0.682953i | ||||
\(773\) | 27.1450 | − | 47.0166i | 0.976339 | − | 1.69107i | 0.300895 | − | 0.953657i | \(-0.402714\pi\) |
0.675444 | − | 0.737412i | \(-0.263952\pi\) | |||||||
\(774\) | −4.10620 | + | 7.11214i | −0.147594 | + | 0.255641i | ||||
\(775\) | 0.740922 | + | 1.28332i | 0.0266147 | + | 0.0460980i | ||||
\(776\) | 0.380219 | 0.0136491 | ||||||||
\(777\) | 6.17654 | + | 10.2617i | 0.221582 | + | 0.368138i | ||||
\(778\) | 2.85949 | 0.102518 | ||||||||
\(779\) | −0.798157 | − | 1.38245i | −0.0285969 | − | 0.0495313i | ||||
\(780\) | 3.20286 | − | 5.54752i | 0.114681 | − | 0.198633i | ||||
\(781\) | 18.1790 | − | 31.4870i | 0.650497 | − | 1.12669i | ||||
\(782\) | −1.56400 | − | 2.70893i | −0.0559285 | − | 0.0968710i | ||||
\(783\) | −7.31827 | −0.261534 | ||||||||
\(784\) | −9.98560 | + | 0.363960i | −0.356629 | + | 0.0129986i | ||||
\(785\) | −24.7340 | −0.882793 | ||||||||
\(786\) | 5.26910 | + | 9.12634i | 0.187942 | + | 0.325526i | ||||
\(787\) | −25.9797 | + | 44.9982i | −0.926077 | + | 1.60401i | −0.136257 | + | 0.990674i | \(0.543507\pi\) |
−0.789820 | + | 0.613339i | \(0.789826\pi\) | |||||||
\(788\) | 2.30450 | − | 3.99151i | 0.0820944 | − | 0.142192i | ||||
\(789\) | 9.72378 | + | 16.8421i | 0.346176 | + | 0.599594i | ||||
\(790\) | 19.7253 | 0.701796 | ||||||||
\(791\) | −19.2295 | − | 31.9480i | −0.683723 | − | 1.13594i | ||||
\(792\) | −7.98469 | −0.283723 | ||||||||
\(793\) | 2.45480 | + | 4.25184i | 0.0871725 | + | 0.150987i | ||||
\(794\) | −3.88838 | + | 6.73488i | −0.137994 | + | 0.239012i | ||||
\(795\) | 3.40627 | − | 5.89983i | 0.120808 | − | 0.209245i | ||||
\(796\) | −7.40448 | − | 12.8249i | −0.262445 | − | 0.454568i | ||||
\(797\) | 24.3737 | 0.863361 | 0.431680 | − | 0.902027i | \(-0.357921\pi\) | ||||
0.431680 | + | 0.902027i | \(0.357921\pi\) | |||||||
\(798\) | 0.941613 | − | 1.70177i | 0.0333327 | − | 0.0602422i | ||||
\(799\) | 11.3241 | 0.400616 | ||||||||
\(800\) | −0.606495 | − | 1.05048i | −0.0214428 | − | 0.0371401i | ||||
\(801\) | 0.166888 | − | 0.289058i | 0.00589669 | − | 0.0102134i | ||||
\(802\) | 1.42324 | − | 2.46513i | 0.0502565 | − | 0.0870468i | ||||
\(803\) | 0.925494 | + | 1.60300i | 0.0326600 | + | 0.0565687i | ||||
\(804\) | 10.0365 | 0.353961 | ||||||||
\(805\) | −5.75651 | + | 0.104873i | −0.202890 | + | 0.00369629i | ||||
\(806\) | 19.5177 | 0.687481 | ||||||||
\(807\) | 3.85970 | + | 6.68520i | 0.135868 | + | 0.235330i | ||||
\(808\) | 13.3661 | − | 23.1508i | 0.470218 | − | 0.814441i | ||||
\(809\) | −4.71611 | + | 8.16855i | −0.165810 | + | 0.287191i | −0.936943 | − | 0.349483i | \(-0.886357\pi\) |
0.771133 | + | 0.636674i | \(0.219690\pi\) | |||||||
\(810\) | 1.14628 | + | 1.98542i | 0.0402762 | + | 0.0697604i | ||||
\(811\) | 26.7248 | 0.938436 | 0.469218 | − | 0.883082i | \(-0.344536\pi\) | ||||
0.469218 | + | 0.883082i | \(0.344536\pi\) | |||||||
\(812\) | 17.2319 | − | 0.313934i | 0.604720 | − | 0.0110169i | ||||
\(813\) | −30.8637 | −1.08244 | ||||||||
\(814\) | 6.25343 | + | 10.8313i | 0.219183 | + | 0.379635i | ||||
\(815\) | −16.0674 | + | 27.8296i | −0.562817 | + | 0.974827i | ||||
\(816\) | 2.11915 | − | 3.67048i | 0.0741852 | − | 0.128493i | ||||
\(817\) | 2.71965 | + | 4.71057i | 0.0951484 | + | 0.164802i | ||||
\(818\) | −26.1371 | −0.913861 | ||||||||
\(819\) | −4.23605 | + | 7.65581i | −0.148020 | + | 0.267516i | ||||
\(820\) | −4.43134 | −0.154749 | ||||||||
\(821\) | 22.0582 | + | 38.2060i | 0.769837 | + | 1.33340i | 0.937651 | + | 0.347578i | \(0.112996\pi\) |
−0.167814 | + | 0.985819i | \(0.553671\pi\) | |||||||
\(822\) | −3.19621 | + | 5.53600i | −0.111481 | + | 0.193090i | ||||
\(823\) | −0.738602 | + | 1.27930i | −0.0257461 | + | 0.0445935i | −0.878611 | − | 0.477538i | \(-0.841529\pi\) |
0.852865 | + | 0.522131i | \(0.174863\pi\) | |||||||
\(824\) | 8.31955 | + | 14.4099i | 0.289825 | + | 0.501992i | ||||
\(825\) | −0.693675 | −0.0241507 | ||||||||
\(826\) | −17.4829 | − | 29.0462i | −0.608307 | − | 1.01064i | ||||
\(827\) | −39.6798 | −1.37980 | −0.689900 | − | 0.723904i | \(-0.742346\pi\) | ||||
−0.689900 | + | 0.723904i | \(0.742346\pi\) | |||||||
\(828\) | 0.445058 | + | 0.770863i | 0.0154668 | + | 0.0267893i | ||||
\(829\) | 1.55399 | − | 2.69159i | 0.0539724 | − | 0.0934829i | −0.837777 | − | 0.546013i | \(-0.816145\pi\) |
0.891749 | + | 0.452530i | \(0.149478\pi\) | |||||||
\(830\) | −13.2875 | + | 23.0146i | −0.461216 | + | 0.798850i | ||||
\(831\) | 3.20072 | + | 5.54381i | 0.111032 | + | 0.192313i | ||||
\(832\) | −25.4179 | −0.881207 | ||||||||
\(833\) | 11.0406 | + | 17.6089i | 0.382536 | + | 0.610111i | ||||
\(834\) | 14.8754 | 0.515093 | ||||||||
\(835\) | 9.63297 | + | 16.6848i | 0.333363 | + | 0.577401i | ||||
\(836\) | −0.814389 | + | 1.41056i | −0.0281662 | + | 0.0487853i | ||||
\(837\) | 2.80105 | − | 4.85155i | 0.0968183 | − | 0.167694i | ||||
\(838\) | −10.5765 | − | 18.3190i | −0.365358 | − | 0.632818i | ||||
\(839\) | 52.8937 | 1.82609 | 0.913046 | − | 0.407856i | \(-0.133724\pi\) | ||||
0.913046 | + | 0.407856i | \(0.133724\pi\) | |||||||
\(840\) | −9.04015 | − | 15.0194i | −0.311915 | − | 0.518217i | ||||
\(841\) | 24.5571 | 0.846798 | ||||||||
\(842\) | −14.0106 | − | 24.2670i | −0.482837 | − | 0.836297i | ||||
\(843\) | −2.39614 | + | 4.15023i | −0.0825273 | + | 0.142941i | ||||
\(844\) | 12.7284 | − | 22.0463i | 0.438131 | − | 0.758864i | ||||
\(845\) | 2.24519 | + | 3.88879i | 0.0772370 | + | 0.133778i | ||||
\(846\) | 4.01803 | 0.138143 | ||||||||
\(847\) | −5.28106 | + | 9.54445i | −0.181459 | + | 0.327951i | ||||
\(848\) | −4.46880 | −0.153459 | ||||||||
\(849\) | −5.85073 | − | 10.1338i | −0.200796 | − | 0.347790i | ||||
\(850\) | 0.413704 | − | 0.716556i | 0.0141899 | − | 0.0245777i | ||||
\(851\) | 2.26348 | − | 3.92045i | 0.0775909 | − | 0.134391i | ||||
\(852\) | −6.17040 | − | 10.6874i | −0.211394 | − | 0.366146i | ||||
\(853\) | 14.0250 | 0.480205 | 0.240103 | − | 0.970748i | \(-0.422819\pi\) | ||||
0.240103 | + | 0.970748i | \(0.422819\pi\) | |||||||
\(854\) | 4.13735 | − | 0.0753751i | 0.141577 | − | 0.00257928i | ||||
\(855\) | 1.51843 | 0.0519291 | ||||||||
\(856\) | −16.5067 | − | 28.5904i | −0.564187 | − | 0.977200i | ||||
\(857\) | −11.0928 | + | 19.2133i | −0.378923 | + | 0.656313i | −0.990906 | − | 0.134558i | \(-0.957039\pi\) |
0.611983 | + | 0.790871i | \(0.290372\pi\) | |||||||
\(858\) | −4.56827 | + | 7.91248i | −0.155958 | + | 0.270128i | ||||
\(859\) | −3.25991 | − | 5.64634i | −0.111227 | − | 0.192651i | 0.805038 | − | 0.593223i | \(-0.202145\pi\) |
−0.916265 | + | 0.400572i | \(0.868811\pi\) | |||||||
\(860\) | 15.0994 | 0.514886 | ||||||||
\(861\) | 6.05179 | − | 0.110253i | 0.206244 | − | 0.00375740i | ||||
\(862\) | 25.3073 | 0.861972 | ||||||||
\(863\) | 7.92773 | + | 13.7312i | 0.269863 | + | 0.467417i | 0.968826 | − | 0.247741i | \(-0.0796882\pi\) |
−0.698963 | + | 0.715158i | \(0.746355\pi\) | |||||||
\(864\) | −2.29284 | + | 3.97132i | −0.0780041 | + | 0.135107i | ||||
\(865\) | −17.0869 | + | 29.5954i | −0.580972 | + | 1.00627i | ||||
\(866\) | −7.42245 | − | 12.8561i | −0.252225 | − | 0.436867i | ||||
\(867\) | 8.18432 | 0.277954 | ||||||||
\(868\) | −6.38732 | + | 11.5438i | −0.216800 | + | 0.391822i | ||||
\(869\) | 22.5636 | 0.765416 | ||||||||
\(870\) | −8.38880 | − | 14.5298i | −0.284407 | − | 0.492607i | ||||
\(871\) | 18.6443 | − | 32.2929i | 0.631739 | − | 1.09420i | ||||
\(872\) | 1.60971 | − | 2.78810i | 0.0545116 | − | 0.0944169i | ||||
\(873\) | −0.0624381 | − | 0.108146i | −0.00211321 | − | 0.00366019i | ||||
\(874\) | −0.735106 | −0.0248653 | ||||||||
\(875\) | −15.6308 | − | 25.9690i | −0.528416 | − | 0.877914i | ||||
\(876\) | 0.628270 | 0.0212273 | ||||||||
\(877\) | 17.1200 | + | 29.6527i | 0.578102 | + | 1.00130i | 0.995697 | + | 0.0926686i | \(0.0295397\pi\) |
−0.417595 | + | 0.908633i | \(0.637127\pi\) | |||||||
\(878\) | 1.52734 | − | 2.64543i | 0.0515451 | − | 0.0892788i | ||||
\(879\) | 9.95155 | − | 17.2366i | 0.335658 | − | 0.581376i | ||||
\(880\) | −4.07306 | − | 7.05474i | −0.137303 | − | 0.237815i | ||||
\(881\) | −41.1806 | −1.38741 | −0.693704 | − | 0.720260i | \(-0.744023\pi\) | ||||
−0.693704 | + | 0.720260i | \(0.744023\pi\) | |||||||
\(882\) | 3.91747 | + | 6.24802i | 0.131908 | + | 0.210382i | ||||
\(883\) | 43.6733 | 1.46972 | 0.734862 | − | 0.678216i | \(-0.237247\pi\) | ||||
0.734862 | + | 0.678216i | \(0.237247\pi\) | |||||||
\(884\) | 4.37003 | + | 7.56911i | 0.146980 | + | 0.254577i | ||||
\(885\) | 13.2339 | − | 22.9217i | 0.444851 | − | 0.770505i | ||||
\(886\) | 7.37241 | − | 12.7694i | 0.247681 | − | 0.428996i | ||||
\(887\) | 6.16986 | + | 10.6865i | 0.207164 | + | 0.358818i | 0.950820 | − | 0.309744i | \(-0.100243\pi\) |
−0.743656 | + | 0.668562i | \(0.766910\pi\) | |||||||
\(888\) | 13.7835 | 0.462544 | ||||||||
\(889\) | 21.4451 | + | 35.6290i | 0.719245 | + | 1.19496i | ||||
\(890\) | 0.765201 | 0.0256496 | ||||||||
\(891\) | 1.31121 | + | 2.27109i | 0.0439273 | + | 0.0760844i | ||||
\(892\) | 7.36413 | − | 12.7550i | 0.246569 | − | 0.427071i | ||||
\(893\) | 1.33062 | − | 2.30471i | 0.0445277 | − | 0.0771242i | ||||
\(894\) | −0.535133 | − | 0.926877i | −0.0178975 | − | 0.0309994i | ||||
\(895\) | −11.5498 | −0.386067 | ||||||||
\(896\) | 1.37584 | − | 2.48656i | 0.0459636 | − | 0.0830700i | ||||
\(897\) | 3.30704 | 0.110419 | ||||||||
\(898\) | 6.67126 | + | 11.5550i | 0.222623 | + | 0.385594i | ||||
\(899\) | −20.4988 | + | 35.5050i | −0.683674 | + | 1.18416i | ||||
\(900\) | −0.117725 | + | 0.203906i | −0.00392417 | + | 0.00679686i | ||||
\(901\) | 4.64756 | + | 8.04980i | 0.154833 | + | 0.268178i | ||||
\(902\) | 6.32047 | 0.210449 | ||||||||
\(903\) | −20.6209 | + | 0.375676i | −0.686221 | + | 0.0125017i | ||||
\(904\) | −42.9124 | −1.42725 | ||||||||
\(905\) | −2.10049 | − | 3.63816i | −0.0698227 | − | 0.120937i | ||||
\(906\) | −11.8723 | + | 20.5634i | −0.394431 | + | 0.683174i | ||||
\(907\) | 11.7736 | − | 20.3925i | 0.390936 | − | 0.677122i | −0.601637 | − | 0.798770i | \(-0.705485\pi\) |
0.992573 | + | 0.121648i | \(0.0388179\pi\) | |||||||
\(908\) | −7.99547 | − | 13.8486i | −0.265339 | − | 0.459580i | ||||
\(909\) | −8.77972 | −0.291205 | ||||||||
\(910\) | −20.0557 | + | 0.365378i | −0.664839 | + | 0.0121122i | ||||
\(911\) | 19.5967 | 0.649268 | 0.324634 | − | 0.945840i | \(-0.394759\pi\) | ||||
0.324634 | + | 0.945840i | \(0.394759\pi\) | |||||||
\(912\) | −0.498019 | − | 0.862594i | −0.0164911 | − | 0.0285633i | ||||
\(913\) | −15.1994 | + | 26.3261i | −0.503027 | + | 0.871268i | ||||
\(914\) | −1.87352 | + | 3.24503i | −0.0619705 | + | 0.107336i | ||||
\(915\) | 1.61532 | + | 2.79782i | 0.0534009 | + | 0.0924931i | ||||
\(916\) | −24.9287 | −0.823667 | ||||||||
\(917\) | −12.8130 | + | 23.1568i | −0.423121 | + | 0.764706i | ||||
\(918\) | −3.12800 | −0.103239 | ||||||||
\(919\) | 19.1264 | + | 33.1278i | 0.630920 | + | 1.09279i | 0.987364 | + | 0.158469i | \(0.0506559\pi\) |
−0.356444 | + | 0.934317i | \(0.616011\pi\) | |||||||
\(920\) | −3.31288 | + | 5.73808i | −0.109223 | + | 0.189179i | ||||
\(921\) | 10.8794 | − | 18.8437i | 0.358488 | − | 0.620920i | ||||
\(922\) | 8.50397 | + | 14.7293i | 0.280063 | + | 0.485084i | ||||
\(923\) | −45.8497 | −1.50916 | ||||||||
\(924\) | −3.18486 | − | 5.29134i | −0.104774 | − | 0.174072i | ||||
\(925\) | 1.19745 | 0.0393720 | ||||||||
\(926\) | 5.15528 | + | 8.92921i | 0.169413 | + | 0.293432i | ||||
\(927\) | 2.73241 | − | 4.73267i | 0.0897441 | − | 0.155441i | ||||
\(928\) | 16.7797 | − | 29.0632i | 0.550819 | − | 0.954047i | ||||
\(929\) | 16.3841 | + | 28.3781i | 0.537546 | + | 0.931057i | 0.999035 | + | 0.0439110i | \(0.0139818\pi\) |
−0.461490 | + | 0.887146i | \(0.652685\pi\) | |||||||
\(930\) | 12.8431 | 0.421143 | ||||||||
\(931\) | 4.88114 | − | 0.177910i | 0.159973 | − | 0.00583077i | ||||
\(932\) | −20.6918 | −0.677782 | ||||||||
\(933\) | −4.07173 | − | 7.05244i | −0.133302 | − | 0.230886i | ||||
\(934\) | −15.8857 | + | 27.5148i | −0.519794 | + | 0.900310i | ||||
\(935\) | −8.47196 | + | 14.6739i | −0.277063 | + | 0.479887i | ||||
\(936\) | 5.03458 | + | 8.72015i | 0.164560 | + | 0.285027i | ||||
\(937\) | −49.1394 | −1.60531 | −0.802657 | − | 0.596441i | \(-0.796581\pi\) | ||||
−0.802657 | + | 0.596441i | \(0.796581\pi\) | |||||||
\(938\) | −16.2075 | − | 26.9272i | −0.529193 | − | 0.879205i | ||||
\(939\) | −1.05044 | −0.0342797 | ||||||||
\(940\) | −3.69380 | − | 6.39784i | −0.120478 | − | 0.208675i | ||||
\(941\) | −29.8420 | + | 51.6879i | −0.972821 | + | 1.68498i | −0.285876 | + | 0.958266i | \(0.592285\pi\) |
−0.686945 | + | 0.726710i | \(0.741049\pi\) | |||||||
\(942\) | 5.98715 | − | 10.3701i | 0.195072 | − | 0.337875i | ||||
\(943\) | −1.14387 | − | 1.98124i | −0.0372495 | − | 0.0645181i | ||||
\(944\) | −17.3620 | −0.565084 | ||||||||
\(945\) | −2.78743 | + | 5.03772i | −0.0906751 | + | 0.163877i | ||||
\(946\) | −21.5364 | −0.700210 | ||||||||
\(947\) | 1.33035 | + | 2.30423i | 0.0432304 | + | 0.0748773i | 0.886831 | − | 0.462094i | \(-0.152902\pi\) |
−0.843601 | + | 0.536971i | \(0.819568\pi\) | |||||||
\(948\) | 3.82931 | − | 6.63255i | 0.124370 | − | 0.215415i | ||||
\(949\) | 1.16710 | − | 2.02148i | 0.0378858 | − | 0.0656200i | ||||
\(950\) | −0.0972238 | − | 0.168397i | −0.00315436 | − | 0.00546351i | ||||
\(951\) | −16.3680 | −0.530768 | ||||||||
\(952\) | 23.9144 | − | 0.435677i | 0.775069 | − | 0.0141204i | ||||
\(953\) | −23.2051 | −0.751686 | −0.375843 | − | 0.926683i | \(-0.622647\pi\) | ||||
−0.375843 | + | 0.926683i | \(0.622647\pi\) | |||||||
\(954\) | 1.64906 | + | 2.85625i | 0.0533902 | + | 0.0924745i | ||||
\(955\) | −11.3613 | + | 19.6783i | −0.367642 | + | 0.636774i | ||||
\(956\) | 2.86387 | − | 4.96036i | 0.0926240 | − | 0.160430i | ||||
\(957\) | −9.59583 | − | 16.6205i | −0.310189 | − | 0.537263i | ||||
\(958\) | −3.07800 | −0.0994458 | ||||||||
\(959\) | −16.0510 | + | 0.292421i | −0.518315 | + | 0.00944277i | ||||
\(960\) | −16.7256 | −0.539817 | ||||||||
\(961\) | −0.191710 | − | 0.332051i | −0.00618419 | − | 0.0107113i | ||||
\(962\) | 7.88595 | − | 13.6589i | 0.254253 | − | 0.440379i | ||||
\(963\) | −5.42133 | + | 9.39002i | −0.174700 | + | 0.302589i | ||||
\(964\) | 10.4667 | + | 18.1289i | 0.337111 | + | 0.583894i | ||||
\(965\) | 53.5679 | 1.72441 | ||||||||
\(966\) | 1.34946 | − | 2.43888i | 0.0434182 | − | 0.0784697i | ||||
\(967\) | −6.58436 | −0.211739 | −0.105869 | − | 0.994380i | \(-0.533763\pi\) | ||||
−0.105869 | + | 0.994380i | \(0.533763\pi\) | |||||||
\(968\) | 6.27658 | + | 10.8714i | 0.201737 | + | 0.349419i | ||||
\(969\) | −1.03588 | + | 1.79420i | −0.0332773 | + | 0.0576379i | ||||
\(970\) | 0.143143 | − | 0.247931i | 0.00459605 | − | 0.00796060i | ||||
\(971\) | −20.9110 | − | 36.2190i | −0.671067 | − | 1.16232i | −0.977602 | − | 0.210463i | \(-0.932503\pi\) |
0.306535 | − | 0.951859i | \(-0.400830\pi\) | |||||||
\(972\) | 0.890116 | 0.0285505 | ||||||||
\(973\) | 19.2650 | + | 32.0070i | 0.617608 | + | 1.02610i | ||||
\(974\) | −33.9633 | −1.08825 | ||||||||
\(975\) | 0.437383 | + | 0.757570i | 0.0140075 | + | 0.0242616i | ||||
\(976\) | 1.05960 | − | 1.83528i | 0.0339169 | − | 0.0587458i | ||||
\(977\) | 8.62798 | − | 14.9441i | 0.276033 | − | 0.478104i | −0.694362 | − | 0.719626i | \(-0.744313\pi\) |
0.970395 | + | 0.241522i | \(0.0776466\pi\) | |||||||
\(978\) | −7.77862 | − | 13.4730i | −0.248733 | − | 0.430818i | ||||
\(979\) | 0.875303 | 0.0279748 | ||||||||
\(980\) | 6.34728 | − | 11.9816i | 0.202756 | − | 0.382737i | ||||
\(981\) | −1.05736 | −0.0337589 | ||||||||
\(982\) | −6.40905 | − | 11.1008i | −0.204521 | − | 0.354241i | ||||
\(983\) | −30.5595 | + | 52.9306i | −0.974697 | + | 1.68822i | −0.293764 | + | 0.955878i | \(0.594908\pi\) |
−0.680932 | + | 0.732346i | \(0.738425\pi\) | |||||||
\(984\) | 3.48282 | − | 6.03242i | 0.111028 | − | 0.192306i | ||||
\(985\) | −5.63394 | − | 9.75827i | −0.179512 | − | 0.310924i | ||||
\(986\) | 22.8916 | 0.729016 | ||||||||
\(987\) | 5.20371 | + | 8.64549i | 0.165636 | + | 0.275189i | ||||
\(988\) | 2.05399 | 0.0653460 | ||||||||
\(989\) | 3.89763 | + | 6.75090i | 0.123938 | + | 0.214666i | ||||
\(990\) | −3.00604 | + | 5.20661i | −0.0955382 | + | 0.165477i | ||||
\(991\) | −13.8482 | + | 23.9857i | −0.439901 | + | 0.761931i | −0.997681 | − | 0.0680574i | \(-0.978320\pi\) |
0.557780 | + | 0.829989i | \(0.311653\pi\) | |||||||
\(992\) | 12.8447 | + | 22.2477i | 0.407820 | + | 0.706366i | ||||
\(993\) | −29.2929 | −0.929582 | ||||||||
\(994\) | −18.7093 | + | 33.8133i | −0.593423 | + | 1.07249i | ||||
\(995\) | −36.2043 | −1.14775 | ||||||||
\(996\) | 5.15904 | + | 8.93572i | 0.163471 | + | 0.283139i | ||||
\(997\) | −7.82041 | + | 13.5453i | −0.247675 | + | 0.428985i | −0.962880 | − | 0.269929i | \(-0.913000\pi\) |
0.715205 | + | 0.698914i | \(0.246333\pi\) | |||||||
\(998\) | 16.7664 | − | 29.0403i | 0.530731 | − | 0.919254i | ||||
\(999\) | −2.26348 | − | 3.92045i | −0.0716132 | − | 0.124038i |
(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 | 483.2.i.h.277.8 | ✓ | 20 | |
7.2 | even | 3 | inner | 483.2.i.h.415.8 | yes | 20 | |
7.3 | odd | 6 | 3381.2.a.bj.1.3 | 10 | |||
7.4 | even | 3 | 3381.2.a.bi.1.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.8 | ✓ | 20 | 1.1 | even | 1 | trivial | |
483.2.i.h.415.8 | yes | 20 | 7.2 | even | 3 | inner | |
3381.2.a.bi.1.3 | 10 | 7.4 | even | 3 | |||
3381.2.a.bj.1.3 | 10 | 7.3 | odd | 6 |