Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(178,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.178");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.v (of order \(12\), degree \(4\), not 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: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 313.1 | ||
Character | \(\chi\) | \(=\) | 735.313 |
Dual form | 735.2.v.a.472.1 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.681344 | − | 2.54281i | −0.481783 | − | 1.79804i | −0.594128 | − | 0.804370i | \(-0.702503\pi\) |
0.112345 | − | 0.993669i | \(-0.464164\pi\) | |||||||
\(3\) | −0.965926 | − | 0.258819i | −0.557678 | − | 0.149429i | ||||
\(4\) | −4.26961 | + | 2.46506i | −2.13481 | + | 1.23253i | ||||
\(5\) | −2.18437 | + | 0.478051i | −0.976879 | + | 0.213791i | ||||
\(6\) | 2.63251i | 1.07472i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.45433 | + | 5.45433i | 1.92840 | + | 1.92840i | ||||
\(9\) | 0.866025 | + | 0.500000i | 0.288675 | + | 0.166667i | ||||
\(10\) | 2.70390 | + | 5.22872i | 0.855049 | + | 1.65347i | ||||
\(11\) | 0.731395 | + | 1.26681i | 0.220524 | + | 0.381958i | 0.954967 | − | 0.296712i | \(-0.0958900\pi\) |
−0.734443 | + | 0.678670i | \(0.762557\pi\) | |||||||
\(12\) | 4.76213 | − | 1.27601i | 1.37471 | − | 0.368352i | ||||
\(13\) | −0.887844 | + | 0.887844i | −0.246244 | + | 0.246244i | −0.819427 | − | 0.573183i | \(-0.805708\pi\) |
0.573183 | + | 0.819427i | \(0.305708\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.23367 | + | 0.103594i | 0.576730 | + | 0.0267479i | ||||
\(16\) | 5.22294 | − | 9.04639i | 1.30573 | − | 2.26160i | ||||
\(17\) | 0.770902 | − | 2.87705i | 0.186971 | − | 0.697786i | −0.807229 | − | 0.590239i | \(-0.799034\pi\) |
0.994200 | − | 0.107547i | \(-0.0342997\pi\) | |||||||
\(18\) | 0.681344 | − | 2.54281i | 0.160594 | − | 0.599347i | ||||
\(19\) | −1.97993 | + | 3.42935i | −0.454228 | + | 0.786746i | −0.998643 | − | 0.0520695i | \(-0.983418\pi\) |
0.544415 | + | 0.838816i | \(0.316752\pi\) | |||||||
\(20\) | 8.14798 | − | 7.42570i | 1.82194 | − | 1.66044i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.72294 | − | 2.72294i | 0.580532 | − | 0.580532i | ||||
\(23\) | 5.64178 | − | 1.51171i | 1.17639 | − | 0.315214i | 0.382898 | − | 0.923790i | \(-0.374926\pi\) |
0.793495 | + | 0.608577i | \(0.208259\pi\) | |||||||
\(24\) | −3.85679 | − | 6.68016i | −0.787265 | − | 1.36358i | ||||
\(25\) | 4.54293 | − | 2.08848i | 0.908587 | − | 0.417696i | ||||
\(26\) | 2.86255 | + | 1.65269i | 0.561392 | + | 0.324120i | ||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.18572i | − | 0.962965i | −0.876456 | − | 0.481482i | \(-0.840099\pi\) | ||
0.876456 | − | 0.481482i | \(-0.159901\pi\) | |||||||
\(30\) | −1.25848 | − | 5.75038i | −0.229765 | − | 1.04987i | ||||
\(31\) | −5.28575 | + | 3.05173i | −0.949349 | + | 0.548107i | −0.892879 | − | 0.450297i | \(-0.851318\pi\) |
−0.0564703 | + | 0.998404i | \(0.517985\pi\) | |||||||
\(32\) | −11.6604 | − | 3.12439i | −2.06128 | − | 0.552319i | ||||
\(33\) | −0.378598 | − | 1.41295i | −0.0659054 | − | 0.245962i | ||||
\(34\) | −7.84104 | −1.34473 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.93012 | −0.821687 | ||||||||
\(37\) | 0.825607 | + | 3.08121i | 0.135729 | + | 0.506548i | 0.999994 | + | 0.00351049i | \(0.00111743\pi\) |
−0.864265 | + | 0.503037i | \(0.832216\pi\) | |||||||
\(38\) | 10.0692 | + | 2.69804i | 1.63344 | + | 0.437679i | ||||
\(39\) | 1.08738 | − | 0.627801i | 0.174121 | − | 0.100529i | ||||
\(40\) | −14.5217 | − | 9.30682i | −2.29609 | − | 1.47154i | ||||
\(41\) | 0.769968i | 0.120249i | 0.998191 | + | 0.0601244i | \(0.0191497\pi\) | ||||
−0.998191 | + | 0.0601244i | \(0.980850\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.18572 | − | 5.18572i | −0.790816 | − | 0.790816i | 0.190811 | − | 0.981627i | \(-0.438888\pi\) |
−0.981627 | + | 0.190811i | \(0.938888\pi\) | |||||||
\(44\) | −6.24554 | − | 3.60587i | −0.941551 | − | 0.543605i | ||||
\(45\) | −2.13074 | − | 0.678180i | −0.317633 | − | 0.101097i | ||||
\(46\) | −7.68800 | − | 13.3160i | −1.13353 | − | 1.96334i | ||||
\(47\) | 11.7074 | − | 3.13699i | 1.70770 | − | 0.457577i | 0.732841 | − | 0.680400i | \(-0.238194\pi\) |
0.974859 | + | 0.222823i | \(0.0715273\pi\) | |||||||
\(48\) | −7.38635 | + | 7.38635i | −1.06613 | + | 1.06613i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.40592 | − | 10.1289i | −1.18878 | − | 1.43244i | ||||
\(51\) | −1.48927 | + | 2.57949i | −0.208539 | + | 0.361201i | ||||
\(52\) | 1.60216 | − | 5.97934i | 0.222180 | − | 0.829185i | ||||
\(53\) | −0.199282 | + | 0.743732i | −0.0273735 | + | 0.102159i | −0.978261 | − | 0.207377i | \(-0.933507\pi\) |
0.950888 | + | 0.309537i | \(0.100174\pi\) | |||||||
\(54\) | −1.31626 | + | 2.27982i | −0.179120 | + | 0.310245i | ||||
\(55\) | −2.20324 | − | 2.41754i | −0.297084 | − | 0.325981i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.80005 | − | 2.80005i | 0.370876 | − | 0.370876i | ||||
\(58\) | −13.1863 | + | 3.53326i | −1.73145 | + | 0.463940i | ||||
\(59\) | −1.59816 | − | 2.76810i | −0.208063 | − | 0.360376i | 0.743041 | − | 0.669246i | \(-0.233383\pi\) |
−0.951104 | + | 0.308870i | \(0.900049\pi\) | |||||||
\(60\) | −9.79226 | + | 5.06382i | −1.26418 | + | 0.653736i | ||||
\(61\) | −1.23031 | − | 0.710320i | −0.157525 | − | 0.0909472i | 0.419165 | − | 0.907910i | \(-0.362323\pi\) |
−0.576690 | + | 0.816963i | \(0.695656\pi\) | |||||||
\(62\) | 11.3614 | + | 11.3614i | 1.44290 | + | 1.44290i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 10.8872i | 1.36090i | ||||||||
\(65\) | 1.51494 | − | 2.36381i | 0.187906 | − | 0.293195i | ||||
\(66\) | −3.33490 | + | 1.92541i | −0.410498 | + | 0.237001i | ||||
\(67\) | 8.10070 | + | 2.17058i | 0.989658 | + | 0.265178i | 0.717107 | − | 0.696963i | \(-0.245466\pi\) |
0.272551 | + | 0.962141i | \(0.412133\pi\) | |||||||
\(68\) | 3.80064 | + | 14.1842i | 0.460896 | + | 1.72009i | ||||
\(69\) | −5.84081 | −0.703150 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.62611 | 0.905053 | 0.452526 | − | 0.891751i | \(-0.350523\pi\) | ||||
0.452526 | + | 0.891751i | \(0.350523\pi\) | |||||||
\(72\) | 1.99642 | + | 7.45075i | 0.235281 | + | 0.878080i | ||||
\(73\) | 9.30780 | + | 2.49402i | 1.08940 | + | 0.291903i | 0.758439 | − | 0.651744i | \(-0.225962\pi\) |
0.330956 | + | 0.943646i | \(0.392629\pi\) | |||||||
\(74\) | 7.27241 | − | 4.19873i | 0.845401 | − | 0.488092i | ||||
\(75\) | −4.92868 | + | 0.841520i | −0.569114 | + | 0.0971703i | ||||
\(76\) | − | 19.5226i | − | 2.23940i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.33726 | − | 2.33726i | −0.264643 | − | 0.264643i | ||||
\(79\) | 3.91469 | + | 2.26015i | 0.440437 | + | 0.254286i | 0.703783 | − | 0.710415i | \(-0.251493\pi\) |
−0.263346 | + | 0.964701i | \(0.584826\pi\) | |||||||
\(80\) | −7.08418 | + | 22.2575i | −0.792035 | + | 2.48846i | ||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.95788 | − | 0.524613i | 0.216212 | − | 0.0579338i | ||||
\(83\) | 6.75794 | − | 6.75794i | 0.741781 | − | 0.741781i | −0.231140 | − | 0.972921i | \(-0.574246\pi\) |
0.972921 | + | 0.231140i | \(0.0742455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.308559 | + | 6.65306i | −0.0334679 | + | 0.721626i | ||||
\(86\) | −9.65306 | + | 16.7196i | −1.04092 | + | 1.80292i | ||||
\(87\) | −1.34216 | + | 5.00903i | −0.143895 | + | 0.537024i | ||||
\(88\) | −2.92035 | + | 10.8989i | −0.311310 | + | 1.16182i | ||||
\(89\) | 0.599954 | − | 1.03915i | 0.0635950 | − | 0.110150i | −0.832475 | − | 0.554063i | \(-0.813077\pi\) |
0.896070 | + | 0.443913i | \(0.146410\pi\) | |||||||
\(90\) | −0.272713 | + | 5.88016i | −0.0287465 | + | 0.619823i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −20.3618 | + | 20.3618i | −2.12286 | + | 2.12286i | ||||
\(93\) | 5.89549 | − | 1.57969i | 0.611334 | − | 0.163806i | ||||
\(94\) | −15.9535 | − | 27.6323i | −1.64548 | − | 2.85006i | ||||
\(95\) | 2.68550 | − | 8.43747i | 0.275527 | − | 0.865666i | ||||
\(96\) | 10.4544 | + | 6.03586i | 1.06700 | + | 0.616032i | ||||
\(97\) | 8.68829 | + | 8.68829i | 0.882162 | + | 0.882162i | 0.993754 | − | 0.111592i | \(-0.0355950\pi\) |
−0.111592 | + | 0.993754i | \(0.535595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.46279i | 0.147016i | ||||||||
\(100\) | −14.2483 | + | 20.1156i | −1.42483 | + | 2.01156i | ||||
\(101\) | 13.2866 | − | 7.67102i | 1.32207 | − | 0.763295i | 0.338008 | − | 0.941143i | \(-0.390247\pi\) |
0.984058 | + | 0.177848i | \(0.0569135\pi\) | |||||||
\(102\) | 7.57386 | + | 2.02941i | 0.749924 | + | 0.200941i | ||||
\(103\) | −3.04085 | − | 11.3486i | −0.299624 | − | 1.11821i | −0.937475 | − | 0.348052i | \(-0.886843\pi\) |
0.637851 | − | 0.770160i | \(-0.279823\pi\) | |||||||
\(104\) | −9.68519 | −0.949711 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.02695 | 0.196875 | ||||||||
\(107\) | 1.60693 | + | 5.99715i | 0.155348 | + | 0.579766i | 0.999075 | + | 0.0429945i | \(0.0136898\pi\) |
−0.843727 | + | 0.536772i | \(0.819644\pi\) | |||||||
\(108\) | 4.76213 | + | 1.27601i | 0.458237 | + | 0.122784i | ||||
\(109\) | −6.44831 | + | 3.72294i | −0.617636 | + | 0.356593i | −0.775948 | − | 0.630797i | \(-0.782728\pi\) |
0.158312 | + | 0.987389i | \(0.449395\pi\) | |||||||
\(110\) | −4.64619 | + | 7.24960i | −0.442997 | + | 0.691222i | ||||
\(111\) | − | 3.18990i | − | 0.302772i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.54445 | + | 2.54445i | 0.239362 | + | 0.239362i | 0.816586 | − | 0.577224i | \(-0.195864\pi\) |
−0.577224 | + | 0.816586i | \(0.695864\pi\) | |||||||
\(114\) | −9.02780 | − | 5.21220i | −0.845531 | − | 0.488168i | ||||
\(115\) | −11.6011 | + | 5.99920i | −1.08180 | + | 0.559428i | ||||
\(116\) | 12.7831 | + | 22.1410i | 1.18688 | + | 2.05574i | ||||
\(117\) | −1.21282 | + | 0.324974i | −0.112125 | + | 0.0300438i | ||||
\(118\) | −5.94986 | + | 5.94986i | −0.547729 | + | 0.547729i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 11.6181 | + | 12.7482i | 1.06058 | + | 1.16375i | ||||
\(121\) | 4.43012 | − | 7.67320i | 0.402738 | − | 0.697564i | ||||
\(122\) | −0.967945 | + | 3.61242i | −0.0876337 | + | 0.327053i | ||||
\(123\) | 0.199282 | − | 0.743732i | 0.0179687 | − | 0.0670600i | ||||
\(124\) | 15.0454 | − | 26.0594i | 1.35112 | − | 2.34020i | ||||
\(125\) | −8.92504 | + | 6.73377i | −0.798280 | + | 0.602287i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.86025 | − | 7.86025i | 0.697484 | − | 0.697484i | −0.266383 | − | 0.963867i | \(-0.585829\pi\) |
0.963867 | + | 0.266383i | \(0.0858286\pi\) | |||||||
\(128\) | 4.36334 | − | 1.16915i | 0.385668 | − | 0.103339i | ||||
\(129\) | 3.66686 | + | 6.35119i | 0.322849 | + | 0.559191i | ||||
\(130\) | −7.04293 | − | 2.24165i | −0.617706 | − | 0.196605i | ||||
\(131\) | −5.35391 | − | 3.09108i | −0.467773 | − | 0.270069i | 0.247534 | − | 0.968879i | \(-0.420380\pi\) |
−0.715307 | + | 0.698810i | \(0.753713\pi\) | |||||||
\(132\) | 5.09947 | + | 5.09947i | 0.443851 | + | 0.443851i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 22.0775i | − | 1.90720i | ||||||
\(135\) | 1.88262 | + | 1.20655i | 0.162030 | + | 0.103843i | ||||
\(136\) | 19.8971 | − | 11.4876i | 1.70616 | − | 0.985054i | ||||
\(137\) | −12.3703 | − | 3.31460i | −1.05686 | − | 0.283185i | −0.311777 | − | 0.950155i | \(-0.600924\pi\) |
−0.745085 | + | 0.666970i | \(0.767591\pi\) | |||||||
\(138\) | 3.97960 | + | 14.8521i | 0.338766 | + | 1.26429i | ||||
\(139\) | 11.9913 | 1.01709 | 0.508544 | − | 0.861036i | \(-0.330184\pi\) | ||||
0.508544 | + | 0.861036i | \(0.330184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.1204 | −1.02072 | ||||||||
\(142\) | −5.19601 | − | 19.3918i | −0.436039 | − | 1.62732i | ||||
\(143\) | −1.77410 | − | 0.475368i | −0.148357 | − | 0.0397523i | ||||
\(144\) | 9.04639 | − | 5.22294i | 0.753866 | − | 0.435245i | ||||
\(145\) | 2.47904 | + | 11.3275i | 0.205873 | + | 0.940701i | ||||
\(146\) | − | 25.3673i | − | 2.09941i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.1204 | − | 11.1204i | −0.914091 | − | 0.914091i | ||||
\(149\) | −0.0838539 | − | 0.0484130i | −0.00686958 | − | 0.00396615i | 0.496561 | − | 0.868002i | \(-0.334596\pi\) |
−0.503431 | + | 0.864036i | \(0.667929\pi\) | |||||||
\(150\) | 5.49795 | + | 11.9593i | 0.448906 | + | 0.976475i | ||||
\(151\) | 6.72748 | + | 11.6523i | 0.547475 | + | 0.948254i | 0.998447 | + | 0.0557157i | \(0.0177440\pi\) |
−0.450972 | + | 0.892538i | \(0.648923\pi\) | |||||||
\(152\) | −29.5040 | + | 7.90558i | −2.39309 | + | 0.641227i | ||||
\(153\) | 2.10614 | − | 2.10614i | 0.170272 | − | 0.170272i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.0871 | − | 9.19296i | 0.810219 | − | 0.738397i | ||||
\(156\) | −3.09513 | + | 5.36093i | −0.247809 | + | 0.429218i | ||||
\(157\) | −0.603054 | + | 2.25063i | −0.0481290 | + | 0.179620i | −0.985806 | − | 0.167888i | \(-0.946305\pi\) |
0.937677 | + | 0.347508i | \(0.112972\pi\) | |||||||
\(158\) | 3.07988 | − | 11.4943i | 0.245022 | − | 0.914434i | ||||
\(159\) | 0.384984 | − | 0.666812i | 0.0305312 | − | 0.0528816i | ||||
\(160\) | 26.9642 | + | 1.25056i | 2.13171 | + | 0.0988653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.86147 | − | 1.86147i | 0.146251 | − | 0.146251i | ||||
\(163\) | 14.0354 | − | 3.76077i | 1.09934 | − | 0.294566i | 0.336842 | − | 0.941561i | \(-0.390641\pi\) |
0.762495 | + | 0.646995i | \(0.223974\pi\) | |||||||
\(164\) | −1.89802 | − | 3.28746i | −0.148210 | − | 0.256708i | ||||
\(165\) | 1.50246 | + | 2.90541i | 0.116966 | + | 0.226186i | ||||
\(166\) | −21.7887 | − | 12.5797i | −1.69113 | − | 0.976373i | ||||
\(167\) | −0.293008 | − | 0.293008i | −0.0226737 | − | 0.0226737i | 0.695679 | − | 0.718353i | \(-0.255104\pi\) |
−0.718353 | + | 0.695679i | \(0.755104\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4235i | 0.878728i | ||||||||
\(170\) | 17.1277 | − | 3.74842i | 1.31364 | − | 0.287490i | ||||
\(171\) | −3.42935 | + | 1.97993i | −0.262249 | + | 0.151409i | ||||
\(172\) | 34.9242 | + | 9.35790i | 2.66294 | + | 0.713533i | ||||
\(173\) | 1.26348 | + | 4.71537i | 0.0960606 | + | 0.358503i | 0.997178 | − | 0.0750719i | \(-0.0239186\pi\) |
−0.901118 | + | 0.433575i | \(0.857252\pi\) | |||||||
\(174\) | 13.6515 | 1.03492 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.2801 | 1.15178 | ||||||||
\(177\) | 0.827271 | + | 3.08742i | 0.0621815 | + | 0.232064i | ||||
\(178\) | −3.05114 | − | 0.817551i | −0.228693 | − | 0.0612781i | ||||
\(179\) | 1.72994 | − | 0.998779i | 0.129302 | − | 0.0746523i | −0.433954 | − | 0.900935i | \(-0.642882\pi\) |
0.563256 | + | 0.826283i | \(0.309549\pi\) | |||||||
\(180\) | 10.7692 | − | 2.35685i | 0.802689 | − | 0.175669i | ||||
\(181\) | − | 8.48528i | − | 0.630706i | −0.948974 | − | 0.315353i | \(-0.897877\pi\) | ||
0.948974 | − | 0.315353i | \(-0.102123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.00454 | + | 1.00454i | 0.0742581 | + | 0.0742581i | ||||
\(184\) | 39.0175 | + | 22.5268i | 2.87641 | + | 1.66070i | ||||
\(185\) | −3.27641 | − | 6.33581i | −0.240886 | − | 0.465818i | ||||
\(186\) | −8.03372 | − | 13.9148i | −0.589061 | − | 1.02028i | ||||
\(187\) | 4.20851 | − | 1.12767i | 0.307757 | − | 0.0824632i | ||||
\(188\) | −42.2532 | + | 42.2532i | −3.08163 | + | 3.08163i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −23.2847 | − | 1.07991i | −1.68925 | − | 0.0783447i | ||||
\(191\) | 3.91712 | − | 6.78465i | 0.283433 | − | 0.490920i | −0.688795 | − | 0.724956i | \(-0.741860\pi\) |
0.972228 | + | 0.234036i | \(0.0751934\pi\) | |||||||
\(192\) | 2.81781 | − | 10.5162i | 0.203358 | − | 0.758943i | ||||
\(193\) | 4.96393 | − | 18.5257i | 0.357312 | − | 1.33351i | −0.520239 | − | 0.854021i | \(-0.674157\pi\) |
0.877550 | − | 0.479485i | \(-0.159176\pi\) | |||||||
\(194\) | 16.1730 | − | 28.0124i | 1.16115 | − | 2.01117i | ||||
\(195\) | −2.07512 | + | 1.89117i | −0.148603 | + | 0.135430i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.4791 | + | 11.4791i | −0.817853 | + | 0.817853i | −0.985797 | − | 0.167943i | \(-0.946287\pi\) |
0.167943 | + | 0.985797i | \(0.446287\pi\) | |||||||
\(198\) | 3.71960 | − | 0.996663i | 0.264340 | − | 0.0708298i | ||||
\(199\) | 10.0734 | + | 17.4476i | 0.714084 | + | 1.23683i | 0.963312 | + | 0.268384i | \(0.0864897\pi\) |
−0.249228 | + | 0.968445i | \(0.580177\pi\) | |||||||
\(200\) | 36.1699 | + | 13.3874i | 2.55760 | + | 0.946632i | ||||
\(201\) | −7.26289 | − | 4.19323i | −0.512285 | − | 0.295768i | ||||
\(202\) | −28.5587 | − | 28.5587i | −2.00938 | − | 2.00938i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 14.6846i | − | 1.02812i | ||||||
\(205\) | −0.368084 | − | 1.68189i | −0.0257081 | − | 0.117469i | ||||
\(206\) | −26.7855 | + | 15.4646i | −1.86623 | + | 1.07747i | ||||
\(207\) | 5.64178 | + | 1.51171i | 0.392131 | + | 0.105071i | ||||
\(208\) | 3.39463 | + | 12.6689i | 0.235375 | + | 0.878433i | ||||
\(209\) | −5.79246 | −0.400673 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9662 | 0.823785 | 0.411892 | − | 0.911233i | \(-0.364868\pi\) | ||||
0.411892 | + | 0.911233i | \(0.364868\pi\) | |||||||
\(212\) | −0.982486 | − | 3.66669i | −0.0674774 | − | 0.251829i | ||||
\(213\) | −7.36626 | − | 1.97378i | −0.504728 | − | 0.135241i | ||||
\(214\) | 14.1548 | − | 8.17225i | 0.967599 | − | 0.558644i | ||||
\(215\) | 13.8066 | + | 8.84849i | 0.941601 | + | 0.603462i | ||||
\(216\) | − | 7.71359i | − | 0.524843i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 13.8602 | + | 13.8602i | 0.938734 | + | 0.938734i | ||||
\(219\) | −8.34514 | − | 4.81807i | −0.563912 | − | 0.325575i | ||||
\(220\) | 15.3664 | + | 4.89085i | 1.03600 | + | 0.329741i | ||||
\(221\) | 1.86993 | + | 3.23881i | 0.125785 | + | 0.217866i | ||||
\(222\) | −8.11132 | + | 2.17342i | −0.544396 | + | 0.145871i | ||||
\(223\) | 0.660910 | − | 0.660910i | 0.0442578 | − | 0.0442578i | −0.684632 | − | 0.728889i | \(-0.740037\pi\) |
0.728889 | + | 0.684632i | \(0.240037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.97854 | + | 0.462789i | 0.331902 | + | 0.0308526i | ||||
\(226\) | 4.73641 | − | 8.20370i | 0.315061 | − | 0.545702i | ||||
\(227\) | 6.35007 | − | 23.6988i | 0.421469 | − | 1.57294i | −0.350047 | − | 0.936732i | \(-0.613834\pi\) |
0.771516 | − | 0.636210i | \(-0.219499\pi\) | |||||||
\(228\) | −5.05283 | + | 18.8574i | −0.334632 | + | 1.24886i | ||||
\(229\) | −12.5391 | + | 21.7184i | −0.828607 | + | 1.43519i | 0.0705240 | + | 0.997510i | \(0.477533\pi\) |
−0.899131 | + | 0.437679i | \(0.855800\pi\) | |||||||
\(230\) | 23.1592 | + | 25.4118i | 1.52707 | + | 1.67560i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 28.2847 | − | 28.2847i | 1.85698 | − | 1.85698i | ||||
\(233\) | −3.06178 | + | 0.820401i | −0.200584 | + | 0.0537462i | −0.357712 | − | 0.933832i | \(-0.616443\pi\) |
0.157128 | + | 0.987578i | \(0.449776\pi\) | |||||||
\(234\) | 1.65269 | + | 2.86255i | 0.108040 | + | 0.187131i | ||||
\(235\) | −24.0736 | + | 12.4491i | −1.57039 | + | 0.812088i | ||||
\(236\) | 13.6471 | + | 7.87915i | 0.888350 | + | 0.512889i | ||||
\(237\) | −3.19633 | − | 3.19633i | −0.207624 | − | 0.207624i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3769i | 1.38276i | 0.722492 | + | 0.691380i | \(0.242997\pi\) | ||||
−0.722492 | + | 0.691380i | \(0.757003\pi\) | |||||||
\(240\) | 12.6035 | − | 19.6656i | 0.813549 | − | 1.26941i | ||||
\(241\) | −0.540512 | + | 0.312065i | −0.0348174 | + | 0.0201018i | −0.517308 | − | 0.855799i | \(-0.673066\pi\) |
0.482490 | + | 0.875901i | \(0.339732\pi\) | |||||||
\(242\) | −22.5299 | − | 6.03688i | −1.44828 | − | 0.388065i | ||||
\(243\) | −0.258819 | − | 0.965926i | −0.0166032 | − | 0.0619642i | ||||
\(244\) | 7.00393 | 0.448381 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.02695 | −0.129234 | ||||||||
\(247\) | −1.28685 | − | 4.80260i | −0.0818805 | − | 0.305582i | ||||
\(248\) | −45.4754 | − | 12.1851i | −2.88769 | − | 0.773754i | ||||
\(249\) | −8.27676 | + | 4.77859i | −0.524518 | + | 0.302831i | ||||
\(250\) | 23.2037 | + | 18.1067i | 1.46753 | + | 1.14517i | ||||
\(251\) | 16.3443i | 1.03164i | 0.856696 | + | 0.515822i | \(0.172513\pi\) | ||||
−0.856696 | + | 0.515822i | \(0.827487\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.04143 | + | 6.04143i | 0.379821 | + | 0.379821i | ||||
\(254\) | −25.3427 | − | 14.6316i | −1.59014 | − | 0.918068i | ||||
\(255\) | 2.01998 | − | 6.34650i | 0.126496 | − | 0.397433i | ||||
\(256\) | 4.94133 | + | 8.55863i | 0.308833 | + | 0.534914i | ||||
\(257\) | 29.1038 | − | 7.79833i | 1.81544 | − | 0.486446i | 0.819235 | − | 0.573458i | \(-0.194398\pi\) |
0.996207 | + | 0.0870116i | \(0.0277317\pi\) | |||||||
\(258\) | 13.6515 | − | 13.6515i | 0.849904 | − | 0.849904i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.641275 | + | 13.8270i | −0.0397702 | + | 0.857514i | ||||
\(261\) | 2.59286 | − | 4.49097i | 0.160494 | − | 0.277984i | ||||
\(262\) | −4.21218 | + | 15.7201i | −0.260230 | + | 0.971190i | ||||
\(263\) | −5.98263 | + | 22.3275i | −0.368905 | + | 1.37677i | 0.493145 | + | 0.869947i | \(0.335847\pi\) |
−0.862049 | + | 0.506824i | \(0.830819\pi\) | |||||||
\(264\) | 5.64168 | − | 9.77167i | 0.347221 | − | 0.601405i | ||||
\(265\) | 0.0797641 | − | 1.71985i | 0.00489987 | − | 0.105650i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.848464 | + | 0.848464i | −0.0519251 | + | 0.0519251i | ||||
\(268\) | −39.9374 | + | 10.7012i | −2.43957 | + | 0.653680i | ||||
\(269\) | −8.29515 | − | 14.3676i | −0.505764 | − | 0.876009i | −0.999978 | − | 0.00666889i | \(-0.997877\pi\) |
0.494213 | − | 0.869341i | \(-0.335456\pi\) | |||||||
\(270\) | 1.78532 | − | 5.60921i | 0.108651 | − | 0.341366i | ||||
\(271\) | −6.73796 | − | 3.89016i | −0.409302 | − | 0.236311i | 0.281188 | − | 0.959653i | \(-0.409272\pi\) |
−0.690490 | + | 0.723342i | \(0.742605\pi\) | |||||||
\(272\) | −22.0005 | − | 22.0005i | −1.33398 | − | 1.33398i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 33.7136i | 2.03671i | ||||||||
\(275\) | 5.96839 | + | 4.22754i | 0.359908 | + | 0.254930i | ||||
\(276\) | 24.9380 | − | 14.3979i | 1.50109 | − | 0.866654i | ||||
\(277\) | −29.1109 | − | 7.80024i | −1.74910 | − | 0.468671i | −0.764670 | − | 0.644422i | \(-0.777098\pi\) |
−0.984435 | + | 0.175751i | \(0.943765\pi\) | |||||||
\(278\) | −8.17019 | − | 30.4916i | −0.490016 | − | 1.82876i | ||||
\(279\) | −6.10346 | −0.365405 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.1519 | −1.26182 | −0.630908 | − | 0.775858i | \(-0.717317\pi\) | ||||
−0.630908 | + | 0.775858i | \(0.717317\pi\) | |||||||
\(282\) | 8.25816 | + | 30.8199i | 0.491766 | + | 1.83530i | ||||
\(283\) | 3.62641 | + | 0.971693i | 0.215567 | + | 0.0577611i | 0.364986 | − | 0.931013i | \(-0.381074\pi\) |
−0.149419 | + | 0.988774i | \(0.547740\pi\) | |||||||
\(284\) | −32.5605 | + | 18.7988i | −1.93211 | + | 1.11551i | ||||
\(285\) | −4.77778 | + | 7.45491i | −0.283011 | + | 0.441591i | ||||
\(286\) | 4.83508i | 0.285905i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −8.53599 | − | 8.53599i | −0.502988 | − | 0.502988i | ||||
\(289\) | 7.03933 | + | 4.06416i | 0.414078 | + | 0.239068i | ||||
\(290\) | 27.1147 | − | 14.0217i | 1.59223 | − | 0.823382i | ||||
\(291\) | −6.14355 | − | 10.6409i | −0.360141 | − | 0.623783i | ||||
\(292\) | −45.8886 | + | 12.2958i | −2.68543 | + | 0.719558i | ||||
\(293\) | 1.56714 | − | 1.56714i | 0.0915536 | − | 0.0915536i | −0.659847 | − | 0.751400i | \(-0.729379\pi\) |
0.751400 | + | 0.659847i | \(0.229379\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.81428 | + | 5.28255i | 0.280298 | + | 0.307562i | ||||
\(296\) | −12.3028 | + | 21.3091i | −0.715085 | + | 1.23856i | ||||
\(297\) | 0.378598 | − | 1.41295i | 0.0219685 | − | 0.0819875i | ||||
\(298\) | −0.0659719 | + | 0.246211i | −0.00382165 | + | 0.0142626i | ||||
\(299\) | −3.66686 | + | 6.35119i | −0.212060 | + | 0.367299i | ||||
\(300\) | 18.9691 | − | 15.7425i | 1.09518 | − | 0.908891i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 25.0460 | − | 25.0460i | 1.44123 | − | 1.44123i | ||||
\(303\) | −14.8193 | + | 3.97081i | −0.851345 | + | 0.228117i | ||||
\(304\) | 20.6821 | + | 35.8225i | 1.18620 | + | 2.05456i | ||||
\(305\) | 3.02702 | + | 0.963450i | 0.173327 | + | 0.0551670i | ||||
\(306\) | −6.79054 | − | 3.92052i | −0.388189 | − | 0.224121i | ||||
\(307\) | 17.3551 | + | 17.3551i | 0.990510 | + | 0.990510i | 0.999955 | − | 0.00944588i | \(-0.00300676\pi\) |
−0.00944588 | + | 0.999955i | \(0.503007\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.7489i | 0.668374i | ||||||||
\(310\) | −30.2488 | − | 19.3861i | −1.71802 | − | 1.10106i | ||||
\(311\) | 26.9029 | − | 15.5324i | 1.52553 | − | 0.880763i | 0.525984 | − | 0.850494i | \(-0.323697\pi\) |
0.999542 | − | 0.0302685i | \(-0.00963624\pi\) | |||||||
\(312\) | 9.35518 | + | 2.50671i | 0.529633 | + | 0.141915i | ||||
\(313\) | −2.09522 | − | 7.81948i | −0.118429 | − | 0.441983i | 0.881091 | − | 0.472946i | \(-0.156809\pi\) |
−0.999521 | + | 0.0309625i | \(0.990143\pi\) | |||||||
\(314\) | 6.13381 | 0.346151 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.2856 | −1.25366 | ||||||||
\(317\) | 0.275463 | + | 1.02804i | 0.0154715 | + | 0.0577406i | 0.973230 | − | 0.229833i | \(-0.0738180\pi\) |
−0.957759 | + | 0.287574i | \(0.907151\pi\) | |||||||
\(318\) | −1.95788 | − | 0.524613i | −0.109793 | − | 0.0294188i | ||||
\(319\) | 6.56934 | − | 3.79281i | 0.367813 | − | 0.212357i | ||||
\(320\) | −5.20464 | − | 23.7817i | −0.290948 | − | 1.32943i | ||||
\(321\) | − | 6.20871i | − | 0.346536i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.34005 | + | 8.34005i | 0.464053 | + | 0.464053i | ||||
\(324\) | −4.26961 | − | 2.46506i | −0.237201 | − | 0.136948i | ||||
\(325\) | −2.17917 | + | 5.88766i | −0.120879 | + | 0.326589i | ||||
\(326\) | −19.1259 | − | 33.1270i | −1.05928 | − | 1.83473i | ||||
\(327\) | 7.19216 | − | 1.92713i | 0.397727 | − | 0.106571i | ||||
\(328\) | −4.19966 | + | 4.19966i | −0.231887 | + | 0.231887i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.36421 | − | 5.80005i | 0.350338 | − | 0.319282i | ||||
\(331\) | −7.90412 | + | 13.6903i | −0.434449 | + | 0.752489i | −0.997251 | − | 0.0741038i | \(-0.976390\pi\) |
0.562801 | + | 0.826592i | \(0.309724\pi\) | |||||||
\(332\) | −12.1950 | + | 45.5125i | −0.669290 | + | 2.49783i | ||||
\(333\) | −0.825607 | + | 3.08121i | −0.0452430 | + | 0.168849i | ||||
\(334\) | −0.545426 | + | 0.944705i | −0.0298444 | + | 0.0516920i | ||||
\(335\) | −18.7326 | − | 0.868788i | −1.02347 | − | 0.0474670i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.0460 | + | 20.0460i | −1.09197 | + | 1.09197i | −0.0966558 | + | 0.995318i | \(0.530815\pi\) |
−0.995318 | + | 0.0966558i | \(0.969185\pi\) | |||||||
\(338\) | 29.0477 | − | 7.78331i | 1.57999 | − | 0.423357i | ||||
\(339\) | −1.79920 | − | 3.11630i | −0.0977190 | − | 0.169254i | ||||
\(340\) | −15.0828 | − | 29.1666i | −0.817978 | − | 1.58178i | ||||
\(341\) | −7.73194 | − | 4.46404i | −0.418708 | − | 0.241741i | ||||
\(342\) | 7.37117 | + | 7.37117i | 0.398587 | + | 0.398587i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 56.5693i | − | 3.05001i | ||||||
\(345\) | 12.7585 | − | 2.79220i | 0.686893 | − | 0.150327i | ||||
\(346\) | 11.1294 | − | 6.42558i | 0.598322 | − | 0.345441i | ||||
\(347\) | 27.4362 | + | 7.35151i | 1.47285 | + | 0.394650i | 0.903908 | − | 0.427726i | \(-0.140685\pi\) |
0.568945 | + | 0.822376i | \(0.307352\pi\) | |||||||
\(348\) | −6.61704 | − | 24.6951i | −0.354710 | − | 1.32380i | ||||
\(349\) | −14.7663 | −0.790420 | −0.395210 | − | 0.918591i | \(-0.629328\pi\) | ||||
−0.395210 | + | 0.918591i | \(0.629328\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.25560 | 0.0670190 | ||||||||
\(352\) | −4.57032 | − | 17.0567i | −0.243599 | − | 0.909124i | ||||
\(353\) | −17.0603 | − | 4.57130i | −0.908029 | − | 0.243306i | −0.225568 | − | 0.974227i | \(-0.572424\pi\) |
−0.682461 | + | 0.730922i | \(0.739090\pi\) | |||||||
\(354\) | 7.28706 | − | 4.20719i | 0.387303 | − | 0.223610i | ||||
\(355\) | −16.6582 | + | 3.64567i | −0.884127 | + | 0.193492i | ||||
\(356\) | 5.91570i | 0.313531i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.71839 | − | 3.71839i | −0.196523 | − | 0.196523i | ||||
\(359\) | −9.12549 | − | 5.26861i | −0.481625 | − | 0.278066i | 0.239468 | − | 0.970904i | \(-0.423027\pi\) |
−0.721093 | + | 0.692838i | \(0.756360\pi\) | |||||||
\(360\) | −7.92277 | − | 15.3208i | −0.417567 | − | 0.807477i | ||||
\(361\) | 1.65972 | + | 2.87471i | 0.0873535 | + | 0.151301i | ||||
\(362\) | −21.5765 | + | 5.78140i | −1.13403 | + | 0.303864i | ||||
\(363\) | −6.26514 | + | 6.26514i | −0.328835 | + | 0.328835i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.5239 | − | 0.998247i | −1.12661 | − | 0.0522507i | ||||
\(366\) | 1.86993 | − | 3.23881i | 0.0977427 | − | 0.169295i | ||||
\(367\) | −4.09618 | + | 15.2871i | −0.213819 | + | 0.797982i | 0.772760 | + | 0.634698i | \(0.218875\pi\) |
−0.986579 | + | 0.163284i | \(0.947791\pi\) | |||||||
\(368\) | 15.7911 | − | 58.9334i | 0.823170 | − | 3.07211i | ||||
\(369\) | −0.384984 | + | 0.666812i | −0.0200415 | + | 0.0347128i | ||||
\(370\) | −13.8784 | + | 12.6482i | −0.721505 | + | 0.657546i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −21.2774 | + | 21.2774i | −1.10318 | + | 1.10318i | ||||
\(373\) | −23.5976 | + | 6.32295i | −1.22184 | + | 0.327390i | −0.811396 | − | 0.584497i | \(-0.801292\pi\) |
−0.410440 | + | 0.911887i | \(0.634625\pi\) | |||||||
\(374\) | −5.73489 | − | 9.93312i | −0.296544 | − | 0.513630i | ||||
\(375\) | 10.3638 | − | 4.19435i | 0.535182 | − | 0.216595i | ||||
\(376\) | 80.9662 | + | 46.7459i | 4.17551 | + | 2.41073i | ||||
\(377\) | 4.60412 | + | 4.60412i | 0.237124 | + | 0.237124i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.6237i | − | 0.905267i | −0.891697 | − | 0.452634i | \(-0.850485\pi\) | ||
0.891697 | − | 0.452634i | \(-0.149515\pi\) | |||||||
\(380\) | 9.33283 | + | 42.6447i | 0.478764 | + | 2.18762i | ||||
\(381\) | −9.62680 | + | 5.55803i | −0.493196 | + | 0.284747i | ||||
\(382\) | −19.9210 | − | 5.33782i | −1.01925 | − | 0.273106i | ||||
\(383\) | −5.90211 | − | 22.0270i | −0.301584 | − | 1.12553i | −0.935846 | − | 0.352408i | \(-0.885363\pi\) |
0.634263 | − | 0.773118i | \(-0.281304\pi\) | |||||||
\(384\) | −4.51726 | −0.230520 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −50.4894 | −2.56984 | ||||||||
\(387\) | −1.89811 | − | 7.08383i | −0.0964862 | − | 0.360091i | ||||
\(388\) | −58.5128 | − | 15.6785i | −2.97054 | − | 0.795953i | ||||
\(389\) | −13.3377 | + | 7.70053i | −0.676249 | + | 0.390432i | −0.798440 | − | 0.602074i | \(-0.794341\pi\) |
0.122191 | + | 0.992507i | \(0.461008\pi\) | |||||||
\(390\) | 6.22277 | + | 3.98811i | 0.315102 | + | 0.201946i | ||||
\(391\) | − | 17.3971i | − | 0.879807i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.37145 | + | 4.37145i | 0.220510 | + | 0.220510i | ||||
\(394\) | 37.0105 | + | 21.3680i | 1.86456 | + | 1.07650i | ||||
\(395\) | −9.63159 | − | 3.06557i | −0.484618 | − | 0.154246i | ||||
\(396\) | −3.60587 | − | 6.24554i | −0.181202 | − | 0.313850i | ||||
\(397\) | 22.0997 | − | 5.92159i | 1.10915 | − | 0.297196i | 0.342665 | − | 0.939458i | \(-0.388670\pi\) |
0.766486 | + | 0.642261i | \(0.222004\pi\) | |||||||
\(398\) | 37.5026 | − | 37.5026i | 1.87983 | − | 1.87983i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.83424 | − | 52.0051i | 0.241712 | − | 2.60026i | ||||
\(401\) | 0.488797 | − | 0.846622i | 0.0244094 | − | 0.0422783i | −0.853563 | − | 0.520990i | \(-0.825563\pi\) |
0.877972 | + | 0.478712i | \(0.158896\pi\) | |||||||
\(402\) | −5.71407 | + | 21.3252i | −0.284992 | + | 1.06360i | ||||
\(403\) | 1.98346 | − | 7.40238i | 0.0988033 | − | 0.368739i | ||||
\(404\) | −37.8191 | + | 65.5046i | −1.88157 | + | 3.25897i | ||||
\(405\) | −1.50619 | − | 1.65269i | −0.0748431 | − | 0.0821230i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.29947 | + | 3.29947i | −0.163549 | + | 0.163549i | ||||
\(408\) | −22.1923 | + | 5.94642i | −1.09868 | + | 0.294392i | ||||
\(409\) | 12.1586 | + | 21.0593i | 0.601203 | + | 1.04131i | 0.992639 | + | 0.121108i | \(0.0386449\pi\) |
−0.391437 | + | 0.920205i | \(0.628022\pi\) | |||||||
\(410\) | −4.02595 | + | 2.08192i | −0.198827 | + | 0.102819i | ||||
\(411\) | 11.0909 | + | 6.40331i | 0.547072 | + | 0.315852i | ||||
\(412\) | 40.9583 | + | 40.9583i | 2.01787 | + | 2.01787i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 15.3760i | − | 0.755689i | ||||||
\(415\) | −11.5312 | + | 17.9925i | −0.566044 | + | 0.883216i | ||||
\(416\) | 13.1266 | − | 7.57863i | 0.643583 | − | 0.371573i | ||||
\(417\) | −11.5827 | − | 3.10357i | −0.567207 | − | 0.151983i | ||||
\(418\) | 3.94666 | + | 14.7291i | 0.193037 | + | 0.720425i | ||||
\(419\) | −15.9893 | −0.781127 | −0.390563 | − | 0.920576i | \(-0.627720\pi\) | ||||
−0.390563 | + | 0.920576i | \(0.627720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7000 | 0.716433 | 0.358216 | − | 0.933639i | \(-0.383385\pi\) | ||||
0.358216 | + | 0.933639i | \(0.383385\pi\) | |||||||
\(422\) | −8.15308 | − | 30.4277i | −0.396886 | − | 1.48120i | ||||
\(423\) | 11.7074 | + | 3.13699i | 0.569233 | + | 0.152526i | ||||
\(424\) | −5.14351 | + | 2.96961i | −0.249791 | + | 0.144217i | ||||
\(425\) | −2.50650 | − | 14.6802i | −0.121583 | − | 0.712096i | ||||
\(426\) | 20.0758i | 0.972677i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −21.6443 | − | 21.6443i | −1.04622 | − | 1.04622i | ||||
\(429\) | 1.59061 | + | 0.918340i | 0.0767955 | + | 0.0443379i | ||||
\(430\) | 13.0930 | − | 41.1364i | 0.631401 | − | 1.98377i | ||||
\(431\) | −11.1361 | − | 19.2883i | −0.536407 | − | 0.929084i | −0.999094 | − | 0.0425619i | \(-0.986448\pi\) |
0.462687 | − | 0.886522i | \(-0.346885\pi\) | |||||||
\(432\) | −10.0899 | + | 2.70359i | −0.485452 | + | 0.130077i | ||||
\(433\) | 28.0171 | − | 28.0171i | 1.34642 | − | 1.34642i | 0.456896 | − | 0.889520i | \(-0.348961\pi\) |
0.889520 | − | 0.456896i | \(-0.151039\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.537211 | − | 11.5832i | 0.0257573 | − | 0.555371i | ||||
\(436\) | 18.3545 | − | 31.7910i | 0.879023 | − | 1.52251i | ||||
\(437\) | −5.98618 | + | 22.3407i | −0.286358 | + | 1.06870i | ||||
\(438\) | −6.56553 | + | 24.5029i | −0.313713 | + | 1.17079i | ||||
\(439\) | −1.17828 | + | 2.04084i | −0.0562363 | + | 0.0974042i | −0.892773 | − | 0.450507i | \(-0.851243\pi\) |
0.836537 | + | 0.547911i | \(0.184577\pi\) | |||||||
\(440\) | 1.16889 | − | 25.2033i | 0.0557246 | − | 1.20152i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.96162 | − | 6.96162i | 0.331130 | − | 0.331130i | ||||
\(443\) | 7.47553 | − | 2.00306i | 0.355173 | − | 0.0951684i | −0.0768206 | − | 0.997045i | \(-0.524477\pi\) |
0.431994 | + | 0.901877i | \(0.357810\pi\) | |||||||
\(444\) | 7.86331 | + | 13.6196i | 0.373176 | + | 0.646360i | ||||
\(445\) | −0.813754 | + | 2.55670i | −0.0385756 | + | 0.121199i | ||||
\(446\) | −2.13088 | − | 1.23026i | −0.100900 | − | 0.0582546i | ||||
\(447\) | 0.0684664 | + | 0.0684664i | 0.00323835 | + | 0.00323835i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.20020i | 0.0566410i | 0.999599 | + | 0.0283205i | \(0.00901591\pi\) | ||||
−0.999599 | + | 0.0283205i | \(0.990984\pi\) | |||||||
\(450\) | −2.21531 | − | 12.9748i | −0.104431 | − | 0.611638i | ||||
\(451\) | −0.975405 | + | 0.563150i | −0.0459300 | + | 0.0265177i | ||||
\(452\) | −17.1360 | − | 4.59159i | −0.806011 | − | 0.215970i | ||||
\(453\) | −3.48240 | − | 12.9965i | −0.163617 | − | 0.610629i | ||||
\(454\) | −64.5881 | −3.03127 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 30.5448 | 1.43039 | ||||||||
\(457\) | −7.71489 | − | 28.7924i | −0.360887 | − | 1.34685i | −0.872912 | − | 0.487879i | \(-0.837771\pi\) |
0.512024 | − | 0.858971i | \(-0.328896\pi\) | |||||||
\(458\) | 63.7692 | + | 17.0869i | 2.97974 | + | 0.798418i | ||||
\(459\) | −2.57949 | + | 1.48927i | −0.120400 | + | 0.0695131i | ||||
\(460\) | 34.7436 | − | 54.2116i | 1.61993 | − | 2.52763i | ||||
\(461\) | − | 21.9670i | − | 1.02311i | −0.859252 | − | 0.511553i | \(-0.829071\pi\) | ||
0.859252 | − | 0.511553i | \(-0.170929\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.6776 | − | 21.6776i | −1.00744 | − | 1.00744i | −0.999972 | − | 0.00746987i | \(-0.997622\pi\) |
−0.00746987 | − | 0.999972i | \(-0.502378\pi\) | |||||||
\(464\) | −46.9121 | − | 27.0847i | −2.17784 | − | 1.25738i | ||||
\(465\) | −12.1227 | + | 6.26898i | −0.562179 | + | 0.290717i | ||||
\(466\) | 4.17225 | + | 7.22655i | 0.193276 | + | 0.334763i | ||||
\(467\) | 9.71653 | − | 2.60354i | 0.449627 | − | 0.120477i | −0.0268978 | − | 0.999638i | \(-0.508563\pi\) |
0.476525 | + | 0.879161i | \(0.341896\pi\) | |||||||
\(468\) | 4.37718 | − | 4.37718i | 0.202335 | − | 0.202335i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 48.0581 | + | 52.7326i | 2.21676 | + | 2.43237i | ||||
\(471\) | 1.16501 | − | 2.01786i | 0.0536809 | − | 0.0929780i | ||||
\(472\) | 6.38123 | − | 23.8151i | 0.293720 | − | 1.09618i | ||||
\(473\) | 2.77653 | − | 10.3622i | 0.127665 | − | 0.476452i | ||||
\(474\) | −5.94986 | + | 10.3055i | −0.273286 | + | 0.473346i | ||||
\(475\) | −1.83259 | + | 19.7144i | −0.0840848 | + | 0.904557i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.544449 | + | 0.544449i | −0.0249286 | + | 0.0249286i | ||||
\(478\) | 54.3575 | − | 14.5651i | 2.48626 | − | 0.666190i | ||||
\(479\) | 15.8875 | + | 27.5179i | 0.725917 | + | 1.25733i | 0.958595 | + | 0.284771i | \(0.0919177\pi\) |
−0.232678 | + | 0.972554i | \(0.574749\pi\) | |||||||
\(480\) | −25.7217 | − | 8.18679i | −1.17403 | − | 0.373674i | ||||
\(481\) | −3.46864 | − | 2.00262i | −0.158157 | − | 0.0913117i | ||||
\(482\) | 1.16180 | + | 1.16180i | 0.0529184 | + | 0.0529184i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 43.6821i | 1.98555i | ||||||||
\(485\) | −23.1319 | − | 14.8250i | −1.05036 | − | 0.673168i | ||||
\(486\) | −2.27982 | + | 1.31626i | −0.103415 | + | 0.0597066i | ||||
\(487\) | 6.57642 | + | 1.76215i | 0.298006 | + | 0.0798505i | 0.404724 | − | 0.914439i | \(-0.367368\pi\) |
−0.106718 | + | 0.994289i | \(0.534034\pi\) | |||||||
\(488\) | −2.83620 | − | 10.5848i | −0.128389 | − | 0.479153i | ||||
\(489\) | −14.5305 | −0.657092 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.3401 | 1.27897 | 0.639484 | − | 0.768804i | \(-0.279148\pi\) | ||||
0.639484 | + | 0.768804i | \(0.279148\pi\) | |||||||
\(492\) | 0.982486 | + | 3.66669i | 0.0442939 | + | 0.165307i | ||||
\(493\) | −14.9196 | − | 3.99769i | −0.671943 | − | 0.180047i | ||||
\(494\) | −11.3353 | + | 6.54445i | −0.510000 | + | 0.294449i | ||||
\(495\) | −0.699288 | − | 3.19527i | −0.0314307 | − | 0.143617i | ||||
\(496\) | 63.7559i | 2.86273i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 17.7904 | + | 17.7904i | 0.797206 | + | 0.797206i | ||||
\(499\) | 2.93753 | + | 1.69599i | 0.131502 | + | 0.0759227i | 0.564308 | − | 0.825564i | \(-0.309143\pi\) |
−0.432806 | + | 0.901487i | \(0.642476\pi\) | |||||||
\(500\) | 21.5073 | − | 50.7514i | 0.961836 | − | 2.26967i | ||||
\(501\) | 0.207188 | + | 0.358861i | 0.00925649 | + | 0.0160327i | ||||
\(502\) | 41.5605 | − | 11.1361i | 1.85494 | − | 0.497029i | ||||
\(503\) | 8.32921 | − | 8.32921i | 0.371381 | − | 0.371381i | −0.496599 | − | 0.867980i | \(-0.665418\pi\) |
0.867980 | + | 0.496599i | \(0.165418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.3557 | + | 23.1080i | −1.12831 | + | 1.02829i | ||||
\(506\) | 11.2459 | − | 19.4785i | 0.499942 | − | 0.865925i | ||||
\(507\) | 2.95661 | − | 11.0342i | 0.131308 | − | 0.490047i | ||||
\(508\) | −14.1842 | + | 52.9362i | −0.629323 | + | 2.34866i | ||||
\(509\) | −19.4726 | + | 33.7275i | −0.863108 | + | 1.49495i | 0.00580659 | + | 0.999983i | \(0.498152\pi\) |
−0.868914 | + | 0.494963i | \(0.835182\pi\) | |||||||
\(510\) | −17.5143 | − | 0.812285i | −0.775545 | − | 0.0359686i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.7846 | − | 24.7846i | 1.09534 | − | 1.09534i | ||||
\(513\) | 3.82494 | − | 1.02489i | 0.168875 | − | 0.0452500i | ||||
\(514\) | −39.6594 | − | 68.6920i | −1.74930 | − | 3.02988i | ||||
\(515\) | 12.0676 | + | 23.3359i | 0.531760 | + | 1.02830i | ||||
\(516\) | −31.3121 | − | 18.0781i | −1.37844 | − | 0.795843i | ||||
\(517\) | 12.5367 | + | 12.5367i | 0.551364 | + | 0.551364i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.88171i | − | 0.214283i | ||||||
\(520\) | 21.1560 | − | 4.63002i | 0.927753 | − | 0.203040i | ||||
\(521\) | −6.12042 | + | 3.53363i | −0.268141 | + | 0.154811i | −0.628042 | − | 0.778179i | \(-0.716144\pi\) |
0.359902 | + | 0.932990i | \(0.382810\pi\) | |||||||
\(522\) | −13.1863 | − | 3.53326i | −0.577150 | − | 0.154647i | ||||
\(523\) | −5.33985 | − | 19.9286i | −0.233495 | − | 0.871416i | −0.978821 | − | 0.204716i | \(-0.934373\pi\) |
0.745326 | − | 0.666700i | \(-0.232294\pi\) | |||||||
\(524\) | 30.4788 | 1.33147 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 60.8508 | 2.65322 | ||||||||
\(527\) | 4.70517 | + | 17.5599i | 0.204960 | + | 0.764923i | ||||
\(528\) | −14.7595 | − | 3.95478i | −0.642323 | − | 0.172110i | ||||
\(529\) | 9.62588 | − | 5.55750i | 0.418516 | − | 0.241631i | ||||
\(530\) | −4.42761 | + | 0.968986i | −0.192323 | + | 0.0420901i | ||||
\(531\) | − | 3.19633i | − | 0.138709i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.683611 | − | 0.683611i | −0.0296105 | − | 0.0296105i | ||||
\(534\) | 2.73558 | + | 1.57939i | 0.118380 | + | 0.0683468i | ||||
\(535\) | −6.37708 | − | 12.3318i | −0.275705 | − | 0.533150i | ||||
\(536\) | 32.3449 | + | 56.0229i | 1.39708 | + | 2.41982i | ||||
\(537\) | −1.92949 | + | 0.517006i | −0.0832638 | + | 0.0223105i | ||||
\(538\) | −30.8823 | + | 30.8823i | −1.33143 | + | 1.33143i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −11.0123 | − | 0.510732i | −0.473892 | − | 0.0219784i | ||||
\(541\) | −9.30063 | + | 16.1092i | −0.399865 | + | 0.692587i | −0.993709 | − | 0.111993i | \(-0.964276\pi\) |
0.593844 | + | 0.804581i | \(0.297610\pi\) | |||||||
\(542\) | −5.30108 | + | 19.7839i | −0.227701 | + | 0.849792i | ||||
\(543\) | −2.19615 | + | 8.19615i | −0.0942459 | + | 0.351731i | ||||
\(544\) | −17.9780 | + | 31.1388i | −0.770801 | + | 1.33507i | ||||
\(545\) | 12.3057 | − | 11.2149i | 0.527120 | − | 0.480393i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.22715 | + | 7.22715i | −0.309011 | + | 0.309011i | −0.844526 | − | 0.535515i | \(-0.820118\pi\) |
0.535515 | + | 0.844526i | \(0.320118\pi\) | |||||||
\(548\) | 60.9869 | − | 16.3414i | 2.60523 | − | 0.698069i | ||||
\(549\) | −0.710320 | − | 1.23031i | −0.0303157 | − | 0.0525084i | ||||
\(550\) | 6.68332 | − | 18.0569i | 0.284978 | − | 0.769949i | ||||
\(551\) | 17.7837 | + | 10.2674i | 0.757609 | + | 0.437406i | ||||
\(552\) | −31.8577 | − | 31.8577i | −1.35595 | − | 1.35595i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 79.3382i | 3.37076i | ||||||||
\(555\) | 1.52494 | + | 6.96792i | 0.0647300 | + | 0.295772i | ||||
\(556\) | −51.1981 | + | 29.5593i | −2.17128 | + | 1.25359i | ||||
\(557\) | 0.763508 | + | 0.204581i | 0.0323509 | + | 0.00866839i | 0.274958 | − | 0.961456i | \(-0.411336\pi\) |
−0.242607 | + | 0.970125i | \(0.578003\pi\) | |||||||
\(558\) | 4.15856 | + | 15.5200i | 0.176046 | + | 0.657012i | ||||
\(559\) | 9.20823 | 0.389467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.35697 | −0.183951 | ||||||||
\(562\) | 14.4117 | + | 53.7853i | 0.607922 | + | 2.26879i | ||||
\(563\) | 0.959599 | + | 0.257124i | 0.0404423 | + | 0.0108365i | 0.278983 | − | 0.960296i | \(-0.410003\pi\) |
−0.238541 | + | 0.971132i | \(0.576669\pi\) | |||||||
\(564\) | 51.7494 | − | 29.8775i | 2.17904 | − | 1.25807i | ||||
\(565\) | −6.77439 | − | 4.34164i | −0.285001 | − | 0.182654i | ||||
\(566\) | − | 9.88333i | − | 0.415427i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 41.5953 | + | 41.5953i | 1.74530 | + | 1.74530i | ||||
\(569\) | 8.41819 | + | 4.86025i | 0.352909 | + | 0.203752i | 0.665966 | − | 0.745982i | \(-0.268020\pi\) |
−0.313057 | + | 0.949734i | \(0.601353\pi\) | |||||||
\(570\) | 22.2117 | + | 7.06962i | 0.930348 | + | 0.296114i | ||||
\(571\) | 0.493342 | + | 0.854493i | 0.0206457 | + | 0.0357594i | 0.876164 | − | 0.482014i | \(-0.160094\pi\) |
−0.855518 | + | 0.517773i | \(0.826761\pi\) | |||||||
\(572\) | 8.74652 | − | 2.34362i | 0.365710 | − | 0.0979918i | ||||
\(573\) | −5.53964 | + | 5.53964i | −0.231422 | + | 0.231422i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.4731 | − | 18.6504i | 0.937192 | − | 0.777774i | ||||
\(576\) | −5.44360 | + | 9.42859i | −0.226817 | + | 0.392858i | ||||
\(577\) | 3.78872 | − | 14.1397i | 0.157726 | − | 0.588643i | −0.841130 | − | 0.540833i | \(-0.818109\pi\) |
0.998856 | − | 0.0478100i | \(-0.0152242\pi\) | |||||||
\(578\) | 5.53819 | − | 20.6688i | 0.230358 | − | 0.859708i | ||||
\(579\) | −9.58958 | + | 16.6096i | −0.398529 | + | 0.690273i | ||||
\(580\) | −38.5076 | − | 42.2532i | −1.59894 | − | 1.75447i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −22.8720 | + | 22.8720i | −0.948076 | + | 0.948076i | ||||
\(583\) | −1.08792 | + | 0.291508i | −0.0450572 | + | 0.0120730i | ||||
\(584\) | 37.1646 | + | 64.3710i | 1.53788 | + | 2.66369i | ||||
\(585\) | 2.49389 | − | 1.28965i | 0.103110 | − | 0.0533205i | ||||
\(586\) | −5.05272 | − | 2.91719i | −0.208726 | − | 0.120508i | ||||
\(587\) | 21.1413 | + | 21.1413i | 0.872594 | + | 0.872594i | 0.992755 | − | 0.120160i | \(-0.0383409\pi\) |
−0.120160 | + | 0.992755i | \(0.538341\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 24.1689i | − | 0.995862i | ||||||
\(590\) | 10.1524 | − | 15.8410i | 0.417966 | − | 0.652165i | ||||
\(591\) | 14.0590 | − | 8.11696i | 0.578310 | − | 0.333887i | ||||
\(592\) | 32.1859 | + | 8.62419i | 1.32283 | + | 0.354452i | ||||
\(593\) | −2.59079 | − | 9.66895i | −0.106391 | − | 0.397056i | 0.892108 | − | 0.451821i | \(-0.149226\pi\) |
−0.998499 | + | 0.0547654i | \(0.982559\pi\) | |||||||
\(594\) | −3.85081 | −0.158001 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.477365 | 0.0195536 | ||||||||
\(597\) | −5.21437 | − | 19.4603i | −0.213410 | − | 0.796457i | ||||
\(598\) | 18.6483 | + | 4.99679i | 0.762585 | + | 0.204334i | ||||
\(599\) | 6.18210 | − | 3.56924i | 0.252594 | − | 0.145835i | −0.368358 | − | 0.929684i | \(-0.620080\pi\) |
0.620951 | + | 0.783849i | \(0.286746\pi\) | |||||||
\(600\) | −31.4726 | − | 22.2927i | −1.28486 | − | 0.910096i | ||||
\(601\) | 35.0829i | 1.43106i | 0.698580 | + | 0.715532i | \(0.253815\pi\) | ||||
−0.698580 | + | 0.715532i | \(0.746185\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.93012 | + | 5.93012i | 0.241493 | + | 0.241493i | ||||
\(604\) | −57.4475 | − | 33.1673i | −2.33750 | − | 1.34956i | ||||
\(605\) | −6.00884 | + | 18.8789i | −0.244294 | + | 0.767537i | ||||
\(606\) | 20.1941 | + | 34.9771i | 0.820328 | + | 1.42085i | ||||
\(607\) | −7.32715 | + | 1.96330i | −0.297400 | + | 0.0796880i | −0.404434 | − | 0.914567i | \(-0.632531\pi\) |
0.107034 | + | 0.994255i | \(0.465865\pi\) | |||||||
\(608\) | 33.8014 | − | 33.8014i | 1.37083 | − | 1.37083i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.387427 | − | 8.35359i | 0.0156865 | − | 0.338227i | ||||
\(611\) | −7.60919 | + | 13.1795i | −0.307835 | + | 0.533186i | ||||
\(612\) | −3.80064 | + | 14.1842i | −0.153632 | + | 0.573362i | ||||
\(613\) | −3.83917 | + | 14.3280i | −0.155062 | + | 0.578701i | 0.844038 | + | 0.536284i | \(0.180172\pi\) |
−0.999100 | + | 0.0424169i | \(0.986494\pi\) | |||||||
\(614\) | 32.3060 | − | 55.9557i | 1.30376 | − | 2.25819i | ||||
\(615\) | −0.0797641 | + | 1.71985i | −0.00321640 | + | 0.0693511i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.7986 | − | 19.7986i | 0.797060 | − | 0.797060i | −0.185571 | − | 0.982631i | \(-0.559414\pi\) |
0.982631 | + | 0.185571i | \(0.0594135\pi\) | |||||||
\(618\) | 29.8754 | − | 8.00508i | 1.20176 | − | 0.322011i | ||||
\(619\) | −6.03375 | − | 10.4508i | −0.242517 | − | 0.420052i | 0.718914 | − | 0.695099i | \(-0.244640\pi\) |
−0.961431 | + | 0.275048i | \(0.911306\pi\) | |||||||
\(620\) | −20.4070 | + | 64.1158i | −0.819564 | + | 2.57495i | ||||
\(621\) | −5.05829 | − | 2.92040i | −0.202982 | − | 0.117192i | ||||
\(622\) | −57.8262 | − | 57.8262i | −2.31862 | − | 2.31862i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 13.1158i | − | 0.525054i | ||||||
\(625\) | 16.2765 | − | 18.9757i | 0.651060 | − | 0.759026i | ||||
\(626\) | −18.4559 | + | 10.6555i | −0.737647 | + | 0.425880i | ||||
\(627\) | 5.59508 | + | 1.49920i | 0.223446 | + | 0.0598722i | ||||
\(628\) | −2.97313 | − | 11.0959i | −0.118641 | − | 0.442774i | ||||
\(629\) | 9.50124 | 0.378839 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.4435 | 1.21194 | 0.605969 | − | 0.795488i | \(-0.292786\pi\) | ||||
0.605969 | + | 0.795488i | \(0.292786\pi\) | |||||||
\(632\) | 9.02442 | + | 33.6796i | 0.358972 | + | 1.33970i | ||||
\(633\) | −11.5584 | − | 3.09707i | −0.459406 | − | 0.123098i | ||||
\(634\) | 2.42643 | − | 1.40090i | 0.0963660 | − | 0.0556369i | ||||
\(635\) | −13.4121 | + | 20.9273i | −0.532242 | + | 0.830474i | ||||
\(636\) | 3.79604i | 0.150523i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.1204 | − | 14.1204i | −0.559032 | − | 0.559032i | ||||
\(639\) | 6.60440 | + | 3.81305i | 0.261266 | + | 0.150842i | ||||
\(640\) | −8.97222 | + | 4.63976i | −0.354658 | + | 0.183403i | ||||
\(641\) | −18.2964 | − | 31.6904i | −0.722666 | − | 1.25169i | −0.959928 | − | 0.280248i | \(-0.909583\pi\) |
0.237262 | − | 0.971446i | \(-0.423750\pi\) | |||||||
\(642\) | −15.7876 | + | 4.23027i | −0.623086 | + | 0.166955i | ||||
\(643\) | 12.1140 | − | 12.1140i | 0.477731 | − | 0.477731i | −0.426675 | − | 0.904405i | \(-0.640315\pi\) |
0.904405 | + | 0.426675i | \(0.140315\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.0460 | − | 12.1204i | −0.434935 | − | 0.477240i | ||||
\(646\) | 15.5247 | − | 26.8896i | 0.610813 | − | 1.05796i | ||||
\(647\) | 6.99030 | − | 26.0881i | 0.274817 | − | 1.02563i | −0.681147 | − | 0.732147i | \(-0.738519\pi\) |
0.955964 | − | 0.293484i | \(-0.0948148\pi\) | |||||||
\(648\) | −1.99642 | + | 7.45075i | −0.0784269 | + | 0.292693i | ||||
\(649\) | 2.33778 | − | 4.04915i | 0.0917658 | − | 0.158943i | ||||
\(650\) | 16.4560 | + | 1.52970i | 0.645457 | + | 0.0599997i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −50.6552 | + | 50.6552i | −1.98381 | + | 1.98381i | ||||
\(653\) | −27.8271 | + | 7.45625i | −1.08896 | + | 0.291786i | −0.758261 | − | 0.651951i | \(-0.773951\pi\) |
−0.330698 | + | 0.943737i | \(0.607284\pi\) | |||||||
\(654\) | −9.80067 | − | 16.9753i | −0.383237 | − | 0.663785i | ||||
\(655\) | 13.1726 | + | 4.19262i | 0.514696 | + | 0.163819i | ||||
\(656\) | 6.96543 | + | 4.02149i | 0.271954 | + | 0.157013i | ||||
\(657\) | 6.81378 | + | 6.81378i | 0.265831 | + | 0.265831i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 31.4882i | − | 1.22661i | −0.789847 | − | 0.613304i | \(-0.789840\pi\) | ||
0.789847 | − | 0.613304i | \(-0.210160\pi\) | |||||||
\(660\) | −13.5769 | − | 8.70131i | −0.528481 | − | 0.338698i | ||||
\(661\) | 41.7321 | − | 24.0940i | 1.62319 | − | 0.937149i | 0.637129 | − | 0.770757i | \(-0.280122\pi\) |
0.986060 | − | 0.166392i | \(-0.0532116\pi\) | |||||||
\(662\) | 40.1974 | + | 10.7709i | 1.56231 | + | 0.418621i | ||||
\(663\) | −0.967945 | − | 3.61242i | −0.0375919 | − | 0.140295i | ||||
\(664\) | 73.7201 | 2.86089 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.39746 | 0.325395 | ||||||||
\(667\) | −7.83932 | − | 29.2567i | −0.303540 | − | 1.13283i | ||||
\(668\) | 1.97332 | + | 0.528748i | 0.0763499 | + | 0.0204579i | ||||
\(669\) | −0.809446 | + | 0.467334i | −0.0312950 | + | 0.0180682i | ||||
\(670\) | 10.5542 | + | 48.2253i | 0.407743 | + | 1.86311i | ||||
\(671\) | − | 2.07810i | − | 0.0802241i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.6900 | − | 30.6900i | −1.18301 | − | 1.18301i | −0.978960 | − | 0.204055i | \(-0.934588\pi\) |
−0.204055 | − | 0.978960i | \(-0.565412\pi\) | |||||||
\(674\) | 64.6314 | + | 37.3149i | 2.48951 | + | 1.43732i | ||||
\(675\) | −4.68912 | − | 1.73556i | −0.180484 | − | 0.0668018i | ||||
\(676\) | −28.1595 | − | 48.7738i | −1.08306 | − | 1.87591i | ||||
\(677\) | −2.10450 | + | 0.563899i | −0.0808825 | + | 0.0216724i | −0.299033 | − | 0.954243i | \(-0.596664\pi\) |
0.218151 | + | 0.975915i | \(0.429998\pi\) | |||||||
\(678\) | −6.69830 | + | 6.69830i | −0.257246 | + | 0.257246i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −37.9710 | + | 34.6050i | −1.45612 | + | 1.32704i | ||||
\(681\) | −12.2674 | + | 21.2477i | −0.470087 | + | 0.814215i | ||||
\(682\) | −6.08310 | + | 22.7024i | −0.232934 | + | 0.869321i | ||||
\(683\) | 5.20319 | − | 19.4186i | 0.199094 | − | 0.743030i | −0.792074 | − | 0.610424i | \(-0.790999\pi\) |
0.991169 | − | 0.132606i | \(-0.0423345\pi\) | |||||||
\(684\) | 9.76132 | − | 16.9071i | 0.373234 | − | 0.646459i | ||||
\(685\) | 28.6057 | + | 1.32669i | 1.09297 | + | 0.0506903i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.7330 | − | 17.7330i | 0.676555 | − | 0.676555i | ||||
\(688\) | −73.9968 | + | 19.8274i | −2.82110 | + | 0.755912i | ||||
\(689\) | −0.483386 | − | 0.837249i | −0.0184155 | − | 0.0318967i | ||||
\(690\) | −15.7930 | − | 30.5399i | −0.601228 | − | 1.16264i | ||||
\(691\) | 8.91028 | + | 5.14435i | 0.338963 | + | 0.195700i | 0.659813 | − | 0.751429i | \(-0.270635\pi\) |
−0.320850 | + | 0.947130i | \(0.603969\pi\) | |||||||
\(692\) | −17.0182 | − | 17.0182i | −0.646937 | − | 0.646937i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 74.7741i | − | 2.83838i | ||||||
\(695\) | −26.1934 | + | 5.73245i | −0.993572 | + | 0.217444i | ||||
\(696\) | −34.6415 | + | 20.0003i | −1.31308 | + | 0.758108i | ||||
\(697\) | 2.21523 | + | 0.593570i | 0.0839079 | + | 0.0224831i | ||||
\(698\) | 10.0609 | + | 37.5478i | 0.380811 | + | 1.42121i | ||||
\(699\) | 3.16979 | 0.119892 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.3183 | −1.67388 | −0.836939 | − | 0.547297i | \(-0.815657\pi\) | ||||
−0.836939 | + | 0.547297i | \(0.815657\pi\) | |||||||
\(702\) | −0.855497 | − | 3.19276i | −0.0322887 | − | 0.120503i | ||||
\(703\) | −12.2012 | − | 3.26930i | −0.460176 | − | 0.123304i | ||||
\(704\) | −13.7920 | + | 7.96284i | −0.519807 | + | 0.300111i | ||||
\(705\) | 26.4754 | − | 5.79417i | 0.997122 | − | 0.218221i | ||||
\(706\) | 46.4958i | 1.74989i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.1428 | − | 11.1428i | −0.418772 | − | 0.418772i | ||||
\(709\) | −0.708388 | − | 0.408988i | −0.0266041 | − | 0.0153599i | 0.486639 | − | 0.873603i | \(-0.338223\pi\) |
−0.513243 | + | 0.858243i | \(0.671556\pi\) | |||||||
\(710\) | 20.6203 | + | 39.8748i | 0.773864 | + | 1.49647i | ||||
\(711\) | 2.26015 | + | 3.91469i | 0.0847621 | + | 0.146812i | ||||
\(712\) | 8.94022 | − | 2.39553i | 0.335049 | − | 0.0897761i | ||||
\(713\) | −25.2077 | + | 25.2077i | −0.944037 | + | 0.944037i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.10253 | + | 0.190269i | 0.153426 | + | 0.00711567i | ||||
\(716\) | −4.92411 | + | 8.52880i | −0.184022 | + | 0.318736i | ||||
\(717\) | 5.53276 | − | 20.6485i | 0.206625 | − | 0.771134i | ||||
\(718\) | −7.17947 | + | 26.7941i | −0.267935 | + | 0.999949i | ||||
\(719\) | 0.00381028 | − | 0.00659960i | 0.000142099 | − | 0.000246124i | −0.865954 | − | 0.500123i | \(-0.833288\pi\) |
0.866096 | + | 0.499877i | \(0.166621\pi\) | |||||||
\(720\) | −17.2638 | + | 15.7335i | −0.643385 | + | 0.586351i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.17902 | − | 6.17902i | 0.229959 | − | 0.229959i | ||||
\(723\) | 0.602863 | − | 0.161537i | 0.0224207 | − | 0.00600761i | ||||
\(724\) | 20.9167 | + | 36.2289i | 0.777365 | + | 1.34644i | ||||
\(725\) | −10.8303 | − | 23.5584i | −0.402227 | − | 0.874937i | ||||
\(726\) | 20.1998 | + | 11.6624i | 0.749685 | + | 0.432831i | ||||
\(727\) | −28.5738 | − | 28.5738i | −1.05974 | − | 1.05974i | −0.998098 | − | 0.0616465i | \(-0.980365\pi\) |
−0.0616465 | − | 0.998098i | \(-0.519635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 12.1269 | + | 55.4115i | 0.448835 | + | 2.05087i | ||||
\(731\) | −18.9173 | + | 10.9219i | −0.699680 | + | 0.403960i | ||||
\(732\) | −6.76528 | − | 1.81275i | −0.250052 | − | 0.0670012i | ||||
\(733\) | 8.84033 | + | 32.9926i | 0.326525 | + | 1.21861i | 0.912770 | + | 0.408475i | \(0.133939\pi\) |
−0.586244 | + | 0.810134i | \(0.699394\pi\) | |||||||
\(734\) | 41.6632 | 1.53782 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −70.5085 | −2.59898 | ||||||||
\(737\) | 3.17510 | + | 11.8496i | 0.116956 | + | 0.436486i | ||||
\(738\) | 1.95788 | + | 0.524613i | 0.0720707 | + | 0.0193113i | ||||
\(739\) | 32.8676 | − | 18.9761i | 1.20905 | − | 0.698047i | 0.246500 | − | 0.969143i | \(-0.420719\pi\) |
0.962552 | + | 0.271096i | \(0.0873860\pi\) | |||||||
\(740\) | 29.6072 | + | 18.9749i | 1.08838 | + | 0.697532i | ||||
\(741\) | 4.97202i | 0.182652i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.8022 | − | 18.8022i | −0.689784 | − | 0.689784i | 0.272400 | − | 0.962184i | \(-0.412183\pi\) |
−0.962184 | + | 0.272400i | \(0.912183\pi\) | |||||||
\(744\) | 40.7721 | + | 23.5398i | 1.49478 | + | 0.863010i | ||||
\(745\) | 0.206312 | + | 0.0656655i | 0.00755867 | + | 0.00240580i | ||||
\(746\) | 32.1562 | + | 55.6961i | 1.17732 | + | 2.03918i | ||||
\(747\) | 9.23152 | − | 2.47358i | 0.337764 | − | 0.0905035i | ||||
\(748\) | −15.1889 | + | 15.1889i | −0.555363 | + | 0.555363i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −17.7267 | − | 23.4953i | −0.647289 | − | 0.857927i | ||||
\(751\) | −0.0529576 | + | 0.0917252i | −0.00193245 | + | 0.00334710i | −0.866990 | − | 0.498326i | \(-0.833948\pi\) |
0.865058 | + | 0.501673i | \(0.167282\pi\) | |||||||
\(752\) | 32.7686 | − | 122.294i | 1.19495 | − | 4.45960i | ||||
\(753\) | 4.23022 | − | 15.7874i | 0.154158 | − | 0.575325i | ||||
\(754\) | 8.57041 | − | 14.8444i | 0.312116 | − | 0.540601i | ||||
\(755\) | −20.2657 | − | 22.2369i | −0.737545 | − | 0.809284i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.14514 | − | 3.14514i | 0.114312 | − | 0.114312i | −0.647637 | − | 0.761949i | \(-0.724243\pi\) |
0.761949 | + | 0.647637i | \(0.224243\pi\) | |||||||
\(758\) | −44.8137 | + | 12.0078i | −1.62771 | + | 0.436143i | ||||
\(759\) | −4.27193 | − | 7.39921i | −0.155061 | − | 0.268574i | ||||
\(760\) | 60.6684 | − | 31.3731i | 2.20067 | − | 1.13802i | ||||
\(761\) | −30.4082 | − | 17.5562i | −1.10230 | − | 0.636410i | −0.165472 | − | 0.986214i | \(-0.552915\pi\) |
−0.936823 | + | 0.349804i | \(0.886248\pi\) | |||||||
\(762\) | 20.6922 | + | 20.6922i | 0.749599 | + | 0.749599i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 38.6238i | 1.39736i | ||||||||
\(765\) | −3.59375 | + | 5.60744i | −0.129932 | + | 0.202737i | ||||
\(766\) | −51.9891 | + | 30.0159i | −1.87844 | + | 1.08452i | ||||
\(767\) | 3.87656 | + | 1.03872i | 0.139975 | + | 0.0375061i | ||||
\(768\) | −2.55782 | − | 9.54591i | −0.0922973 | − | 0.344458i | ||||
\(769\) | −8.16835 | −0.294558 | −0.147279 | − | 0.989095i | \(-0.547052\pi\) | ||||
−0.147279 | + | 0.989095i | \(0.547052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.1304 | −1.08512 | ||||||||
\(772\) | 24.4728 | + | 91.3338i | 0.880796 | + | 3.28717i | ||||
\(773\) | −3.43099 | − | 0.919332i | −0.123404 | − | 0.0330661i | 0.196588 | − | 0.980486i | \(-0.437014\pi\) |
−0.319993 | + | 0.947420i | \(0.603680\pi\) | |||||||
\(774\) | −16.7196 | + | 9.65306i | −0.600973 | + | 0.346972i | ||||
\(775\) | −17.6393 | + | 24.9030i | −0.633624 | + | 0.894542i | ||||
\(776\) | 94.7776i | 3.40232i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.6686 | + | 28.6686i | 1.02782 | + | 1.02782i | ||||
\(779\) | −2.64049 | − | 1.52449i | −0.0946052 | − | 0.0546204i | ||||
\(780\) | 4.19812 | − | 13.1899i | 0.150317 | − | 0.472274i | ||||
\(781\) | 5.57770 | + | 9.66085i | 0.199586 | + | 0.345693i | ||||
\(782\) | −44.2374 | + | 11.8534i | −1.58193 | + | 0.423876i | ||||
\(783\) | −3.66686 | + | 3.66686i | −0.131043 | + | 0.131043i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.241377 | − | 5.20449i | 0.00861510 | − | 0.185756i | ||||
\(786\) | 8.13731 | − | 14.0942i | 0.290248 | − | 0.502725i | ||||
\(787\) | −4.66123 | + | 17.3959i | −0.166155 | + | 0.620098i | 0.831735 | + | 0.555172i | \(0.187348\pi\) |
−0.997890 | + | 0.0649257i | \(0.979319\pi\) | |||||||
\(788\) | 20.7146 | − | 77.3081i | 0.737929 | − | 2.75399i | ||||
\(789\) | 11.5576 | − | 20.0183i | 0.411460 | − | 0.712669i | ||||
\(790\) | −1.23274 | + | 26.5800i | −0.0438590 | + | 0.945675i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.97854 | + | 7.97854i | −0.283505 | + | 0.283505i | ||||
\(793\) | 1.72298 | − | 0.461671i | 0.0611847 | − | 0.0163944i | ||||
\(794\) | −30.1150 | − | 52.1607i | −1.06874 | − | 1.85111i | ||||
\(795\) | −0.522176 | + | 1.64060i | −0.0185197 | + | 0.0581862i | ||||
\(796\) | −86.0189 | − | 49.6630i | −3.04886 | − | 1.76026i | ||||
\(797\) | −23.3462 | − | 23.3462i | −0.826967 | − | 0.826967i | 0.160129 | − | 0.987096i | \(-0.448809\pi\) |
−0.987096 | + | 0.160129i | \(0.948809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 36.1010i | − | 1.27716i | ||||||
\(800\) | −59.4976 | + | 10.1586i | −2.10356 | + | 0.359160i | ||||
\(801\) | 1.03915 | − | 0.599954i | 0.0367166 | − | 0.0211983i | ||||
\(802\) | −2.48584 | − | 0.666079i | −0.0877781 | − | 0.0235201i | ||||
\(803\) | 3.64822 | + | 13.6153i | 0.128743 | + | 0.480475i | ||||
\(804\) | 41.3463 | 1.45817 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.1743 | −0.710609 | ||||||||
\(807\) | 4.29389 | + | 16.0250i | 0.151152 | + | 0.564107i | ||||
\(808\) | 114.310 | + | 30.6292i | 4.02140 | + | 1.07753i | ||||
\(809\) | 24.0937 | − | 13.9105i | 0.847090 | − | 0.489067i | −0.0125781 | − | 0.999921i | \(-0.504004\pi\) |
0.859668 | + | 0.510853i | \(0.170671\pi\) | |||||||
\(810\) | −3.17625 | + | 4.95601i | −0.111602 | + | 0.174136i | ||||
\(811\) | − | 5.12216i | − | 0.179863i | −0.995948 | − | 0.0899317i | \(-0.971335\pi\) | ||
0.995948 | − | 0.0899317i | \(-0.0286649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.50152 | + | 5.50152i | 0.192947 | + | 0.192947i | ||||
\(814\) | 10.6380 | + | 6.14186i | 0.372862 | + | 0.215272i | ||||
\(815\) | −28.8606 | + | 14.9246i | −1.01094 | + | 0.522784i | ||||
\(816\) | 15.5567 | + | 26.9450i | 0.544594 | + | 0.943264i | ||||
\(817\) | 28.0510 | − | 7.51626i | 0.981382 | − | 0.262961i | ||||
\(818\) | 45.2656 | − | 45.2656i | 1.58267 | − | 1.58267i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.71755 | + | 6.27368i | 0.199665 | + | 0.219086i | ||||
\(821\) | 13.0702 | − | 22.6383i | 0.456154 | − | 0.790082i | −0.542600 | − | 0.839991i | \(-0.682560\pi\) |
0.998754 | + | 0.0499094i | \(0.0158933\pi\) | |||||||
\(822\) | 8.72572 | − | 32.5648i | 0.304345 | − | 1.13583i | ||||
\(823\) | 5.02538 | − | 18.7550i | 0.175174 | − | 0.653757i | −0.821348 | − | 0.570427i | \(-0.806778\pi\) |
0.996522 | − | 0.0833299i | \(-0.0265555\pi\) | |||||||
\(824\) | 45.3133 | − | 78.4849i | 1.57856 | − | 2.73415i | ||||
\(825\) | −4.67086 | − | 5.62823i | −0.162618 | − | 0.195950i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.7484 | − | 15.7484i | 0.547624 | − | 0.547624i | −0.378129 | − | 0.925753i | \(-0.623432\pi\) |
0.925753 | + | 0.378129i | \(0.123432\pi\) | |||||||
\(828\) | −27.8147 | + | 7.45292i | −0.966627 | + | 0.259007i | ||||
\(829\) | 23.6498 | + | 40.9627i | 0.821392 | + | 1.42269i | 0.904646 | + | 0.426164i | \(0.140135\pi\) |
−0.0832545 | + | 0.996528i | \(0.526531\pi\) | |||||||
\(830\) | 53.6082 | + | 17.0626i | 1.86077 | + | 0.592251i | ||||
\(831\) | 26.1001 | + | 15.0689i | 0.905403 | + | 0.522735i | ||||
\(832\) | −9.66613 | − | 9.66613i | −0.335113 | − | 0.335113i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 31.5672i | 1.09308i | ||||||||
\(835\) | 0.780111 | + | 0.499965i | 0.0269969 | + | 0.0173020i | ||||
\(836\) | 24.7315 | − | 14.2788i | 0.855358 | − | 0.493841i | ||||
\(837\) | 5.89549 | + | 1.57969i | 0.203778 | + | 0.0546021i | ||||
\(838\) | 10.8942 | + | 40.6577i | 0.376334 | + | 1.40450i | ||||
\(839\) | −10.8244 | −0.373699 | −0.186850 | − | 0.982389i | \(-0.559828\pi\) | ||||
−0.186850 | + | 0.982389i | \(0.559828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.10826 | 0.0726986 | ||||||||
\(842\) | −10.0157 | − | 37.3793i | −0.345165 | − | 1.28817i | ||||
\(843\) | 20.4312 | + | 5.47451i | 0.703686 | + | 0.188552i | ||||
\(844\) | −51.0909 | + | 29.4973i | −1.75862 | + | 1.01534i | ||||
\(845\) | −5.46100 | − | 24.9531i | −0.187864 | − | 0.858411i | ||||
\(846\) | − | 31.9071i | − | 1.09699i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.68725 | + | 5.68725i | 0.195301 | + | 0.195301i | ||||
\(849\) | −3.25135 | − | 1.87717i | −0.111586 | − | 0.0644242i | ||||
\(850\) | −35.6213 | + | 16.3759i | −1.22180 | + | 0.561687i | ||||
\(851\) | 9.31580 | + | 16.1354i | 0.319341 | + | 0.553116i | ||||
\(852\) | 36.3166 | − | 9.73099i | 1.24418 | − | 0.333378i | ||||
\(853\) | −33.5751 | + | 33.5751i | −1.14959 | + | 1.14959i | −0.162958 | + | 0.986633i | \(0.552103\pi\) |
−0.986633 | + | 0.162958i | \(0.947897\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.54445 | − | 5.96431i | 0.223815 | − | 0.203975i | ||||
\(856\) | −23.9457 | + | 41.4752i | −0.818447 | + | 1.41759i | ||||
\(857\) | −3.26670 | + | 12.1915i | −0.111588 | + | 0.416454i | −0.999009 | − | 0.0445069i | \(-0.985828\pi\) |
0.887421 | + | 0.460960i | \(0.152495\pi\) | |||||||
\(858\) | 1.25141 | − | 4.67033i | 0.0427225 | − | 0.159443i | ||||
\(859\) | 10.1851 | − | 17.6410i | 0.347510 | − | 0.601905i | −0.638297 | − | 0.769791i | \(-0.720361\pi\) |
0.985806 | + | 0.167886i | \(0.0536940\pi\) | |||||||
\(860\) | −80.7608 | − | 3.74556i | −2.75392 | − | 0.127723i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41.4589 | + | 41.4589i | −1.41210 | + | 1.41210i | ||||
\(863\) | 20.3557 | − | 5.45430i | 0.692917 | − | 0.185666i | 0.104861 | − | 0.994487i | \(-0.466560\pi\) |
0.588056 | + | 0.808820i | \(0.299894\pi\) | |||||||
\(864\) | 6.03586 | + | 10.4544i | 0.205344 | + | 0.355666i | ||||
\(865\) | −5.01409 | − | 9.69610i | −0.170484 | − | 0.329677i | ||||
\(866\) | −90.3315 | − | 52.1529i | −3.06959 | − | 1.77223i | ||||
\(867\) | −5.74759 | − | 5.74759i | −0.195198 | − | 0.195198i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.61223i | 0.224305i | ||||||||
\(870\) | −29.8199 | + | 6.52611i | −1.01099 | + | 0.221256i | ||||
\(871\) | −9.11929 | + | 5.26503i | −0.308995 | + | 0.178399i | ||||
\(872\) | −55.4773 | − | 14.8651i | −1.87870 | − | 0.503396i | ||||
\(873\) | 3.18013 | + | 11.8684i | 0.107631 | + | 0.401685i | ||||
\(874\) | 60.8869 | 2.05953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 47.5074 | 1.60512 | ||||||||
\(877\) | 8.58820 | + | 32.0516i | 0.290003 | + | 1.08231i | 0.945105 | + | 0.326765i | \(0.105959\pi\) |
−0.655103 | + | 0.755540i | \(0.727375\pi\) | |||||||
\(878\) | 5.99230 | + | 1.60563i | 0.202230 | + | 0.0541874i | ||||
\(879\) | −1.91935 | + | 1.10814i | −0.0647381 | + | 0.0373766i | ||||
\(880\) | −33.3774 | + | 7.30468i | −1.12515 | + | 0.246241i | ||||
\(881\) | − | 34.9639i | − | 1.17796i | −0.808147 | − | 0.588981i | \(-0.799529\pi\) | ||
0.808147 | − | 0.588981i | \(-0.200471\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.3814 | + | 19.3814i | 0.652235 | + | 0.652235i | 0.953531 | − | 0.301295i | \(-0.0974190\pi\) |
−0.301295 | + | 0.953531i | \(0.597419\pi\) | |||||||
\(884\) | −15.9677 | − | 9.21897i | −0.537053 | − | 0.310068i | ||||
\(885\) | −3.28301 | − | 6.34858i | −0.110357 | − | 0.213405i | ||||
\(886\) | −10.1868 | − | 17.6441i | −0.342233 | − | 0.592765i | ||||
\(887\) | −26.2892 | + | 7.04416i | −0.882704 | + | 0.236520i | −0.671574 | − | 0.740938i | \(-0.734381\pi\) |
−0.211131 | + | 0.977458i | \(0.567715\pi\) | |||||||
\(888\) | 17.3988 | − | 17.3988i | 0.583865 | − | 0.583865i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.05565 | + | 0.327230i | 0.236506 | + | 0.0109688i | ||||
\(891\) | −0.731395 | + | 1.26681i | −0.0245026 | + | 0.0424398i | ||||
\(892\) | −1.19265 | + | 4.45101i | −0.0399327 | + | 0.149031i | ||||
\(893\) | −12.4221 | + | 46.3598i | −0.415689 | + | 1.55137i | ||||
\(894\) | 0.127448 | − | 0.220746i | 0.00426250 | − | 0.00738286i | ||||
\(895\) | −3.30135 | + | 3.00870i | −0.110352 | + | 0.100570i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.18572 | − | 5.18572i | 0.173146 | − | 0.173146i | ||||
\(898\) | 3.05189 | − | 0.817751i | 0.101843 | − | 0.0272887i | ||||
\(899\) | 15.8254 | + | 27.4104i | 0.527808 | + | 0.914190i | ||||
\(900\) | −22.3972 | + | 10.2965i | −0.746574 | + | 0.343216i | ||||
\(901\) | 1.98612 | + | 1.14669i | 0.0661673 | + | 0.0382017i | ||||
\(902\) | 2.09657 | + | 2.09657i | 0.0698082 | + | 0.0698082i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.7565i | 0.923169i | ||||||||
\(905\) | 4.05640 | + | 18.5350i | 0.134839 | + | 0.616124i | ||||
\(906\) | −30.6749 | + | 17.7102i | −1.01911 | + | 0.588381i | ||||
\(907\) | 20.3321 | + | 5.44798i | 0.675117 | + | 0.180897i | 0.580059 | − | 0.814575i | \(-0.303030\pi\) |
0.0950584 | + | 0.995472i | \(0.469696\pi\) | |||||||
\(908\) | 31.3066 | + | 116.838i | 1.03895 | + | 3.87740i | ||||
\(909\) | 15.3420 | 0.508863 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.7484 | −0.786819 | −0.393410 | − | 0.919363i | \(-0.628705\pi\) | ||||
−0.393410 | + | 0.919363i | \(0.628705\pi\) | |||||||
\(912\) | −10.7059 | − | 39.9548i | −0.354507 | − | 1.32304i | ||||
\(913\) | 13.5038 | + | 3.61832i | 0.446910 | + | 0.119749i | ||||
\(914\) | −67.9570 | + | 39.2350i | −2.24782 | + | 1.29778i | ||||
\(915\) | −2.67452 | − | 1.71407i | −0.0884169 | − | 0.0566655i | ||||
\(916\) | − | 123.639i | − | 4.08514i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.54445 | + | 5.54445i | 0.182994 | + | 0.182994i | ||||
\(919\) | −30.9773 | − | 17.8848i | −1.02185 | − | 0.589964i | −0.107209 | − | 0.994237i | \(-0.534191\pi\) |
−0.914638 | + | 0.404273i | \(0.867525\pi\) | |||||||
\(920\) | −95.9976 | − | 30.5544i | −3.16495 | − | 1.00735i | ||||
\(921\) | −12.2719 | − | 21.2556i | −0.404374 | − | 0.700396i | ||||
\(922\) | −55.8580 | + | 14.9671i | −1.83958 | + | 0.492915i | ||||
\(923\) | −6.77080 | + | 6.77080i | −0.222863 | + | 0.222863i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.1857 | + | 12.2735i | 0.334905 | + | 0.403549i | ||||
\(926\) | −40.3521 | + | 69.8919i | −1.32605 | + | 2.29679i | ||||
\(927\) | 3.04085 | − | 11.3486i | 0.0998746 | − | 0.372737i | ||||
\(928\) | −16.2022 | + | 60.4675i | −0.531864 | + | 1.98494i | ||||
\(929\) | −2.79468 | + | 4.84053i | −0.0916905 | + | 0.158813i | −0.908223 | − | 0.418487i | \(-0.862560\pi\) |
0.816532 | + | 0.577300i | \(0.195894\pi\) | |||||||
\(930\) | 24.2006 | + | 26.5545i | 0.793569 | + | 0.870758i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11.0503 | − | 11.0503i | 0.361963 | − | 0.361963i | ||||
\(933\) | −30.0063 | + | 8.04017i | −0.982363 | + | 0.263223i | ||||
\(934\) | −13.2406 | − | 22.9334i | −0.433246 | − | 0.750404i | ||||
\(935\) | −8.65386 | + | 4.47513i | −0.283011 | + | 0.146352i | ||||
\(936\) | −8.38762 | − | 4.84260i | −0.274158 | − | 0.158285i | ||||
\(937\) | 20.4143 | + | 20.4143i | 0.666906 | + | 0.666906i | 0.956999 | − | 0.290092i | \(-0.0936861\pi\) |
−0.290092 | + | 0.956999i | \(0.593686\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.09533i | 0.264181i | ||||||||
\(940\) | 72.0974 | − | 112.496i | 2.35156 | − | 3.66921i | ||||
\(941\) | −14.8214 | + | 8.55714i | −0.483164 | + | 0.278955i | −0.721734 | − | 0.692170i | \(-0.756655\pi\) |
0.238570 | + | 0.971125i | \(0.423321\pi\) | |||||||
\(942\) | −5.92481 | − | 1.58755i | −0.193041 | − | 0.0517251i | ||||
\(943\) | 1.16397 | + | 4.34399i | 0.0379040 | + | 0.141460i | ||||
\(944\) | −33.3884 | −1.08670 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.2408 | −0.918187 | ||||||||
\(947\) | 2.49685 | + | 9.31836i | 0.0811366 | + | 0.302806i | 0.994555 | − | 0.104217i | \(-0.0332336\pi\) |
−0.913418 | + | 0.407023i | \(0.866567\pi\) | |||||||
\(948\) | 21.5262 | + | 5.76794i | 0.699140 | + | 0.187334i | ||||
\(949\) | −10.4782 | + | 6.04957i | −0.340136 | + | 0.196378i | ||||
\(950\) | 51.3785 | − | 8.77234i | 1.66694 | − | 0.284612i | ||||
\(951\) | − | 1.06431i | − | 0.0345125i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.7169 | + | 30.7169i | 0.995017 | + | 0.995017i | 0.999988 | − | 0.00497101i | \(-0.00158233\pi\) |
−0.00497101 | + | 0.999988i | \(0.501582\pi\) | |||||||
\(954\) | 1.75539 | + | 1.01347i | 0.0568328 | + | 0.0328125i | ||||
\(955\) | −5.31302 | + | 16.6928i | −0.171925 | + | 0.540165i | ||||
\(956\) | −52.6955 | − | 91.2712i | −1.70429 | − | 2.95192i | ||||
\(957\) | −7.32715 | + | 1.96330i | −0.236853 | + | 0.0634646i | ||||
\(958\) | 59.1480 | − | 59.1480i | 1.91099 | − | 1.91099i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.12785 | + | 24.3184i | −0.0364012 | + | 0.784872i | ||||
\(961\) | 3.12611 | − | 5.41458i | 0.100842 | − | 0.174664i | ||||
\(962\) | −2.72895 | + | 10.1846i | −0.0879849 | + | 0.328364i | ||||
\(963\) | −1.60693 | + | 5.99715i | −0.0517826 | + | 0.193255i | ||||
\(964\) | 1.53852 | − | 2.66479i | 0.0495523 | − | 0.0858271i | ||||
\(965\) | −1.98685 | + | 42.8399i | −0.0639589 | + | 1.37906i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.6730 | − | 24.6730i | 0.793431 | − | 0.793431i | −0.188619 | − | 0.982050i | \(-0.560401\pi\) |
0.982050 | + | 0.188619i | \(0.0604012\pi\) | |||||||
\(968\) | 66.0155 | − | 17.6888i | 2.12182 | − | 0.568540i | ||||
\(969\) | −5.89731 | − | 10.2144i | −0.189449 | − | 0.328135i | ||||
\(970\) | −21.9364 | + | 68.9209i | −0.704334 | + | 2.21292i | ||||
\(971\) | 18.3615 | + | 10.6010i | 0.589247 | + | 0.340202i | 0.764800 | − | 0.644268i | \(-0.222838\pi\) |
−0.175552 | + | 0.984470i | \(0.556171\pi\) | |||||||
\(972\) | 3.48612 | + | 3.48612i | 0.111817 | + | 0.111817i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 17.9232i | − | 0.574297i | ||||||
\(975\) | 3.62876 | − | 5.12303i | 0.116213 | − | 0.164068i | ||||
\(976\) | −12.8517 | + | 7.41991i | −0.411372 | + | 0.237506i | ||||
\(977\) | −11.1967 | − | 3.00015i | −0.358215 | − | 0.0959834i | 0.0752233 | − | 0.997167i | \(-0.476033\pi\) |
−0.433438 | + | 0.901183i | \(0.642700\pi\) | |||||||
\(978\) | 9.90028 | + | 36.9484i | 0.316576 | + | 1.18148i | ||||
\(979\) | 1.75521 | 0.0560969 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.44587 | −0.237728 | ||||||||
\(982\) | −19.3093 | − | 72.0634i | −0.616186 | − | 2.29964i | ||||
\(983\) | −2.38938 | − | 0.640231i | −0.0762093 | − | 0.0204202i | 0.220513 | − | 0.975384i | \(-0.429227\pi\) |
−0.296722 | + | 0.954964i | \(0.595894\pi\) | |||||||
\(984\) | 5.14351 | − | 2.96961i | 0.163969 | − | 0.0946676i | ||||
\(985\) | 19.5870 | − | 30.5622i | 0.624094 | − | 0.973794i | ||||
\(986\) | 40.6615i | 1.29492i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.3331 | + | 17.3331i | 0.551438 | + | 0.551438i | ||||
\(989\) | −37.0961 | − | 21.4174i | −1.17959 | − | 0.681034i | ||||
\(990\) | −7.64852 | + | 3.95524i | −0.243086 | + | 0.125706i | ||||
\(991\) | 18.5627 | + | 32.1515i | 0.589662 | + | 1.02133i | 0.994276 | + | 0.106838i | \(0.0340725\pi\) |
−0.404614 | + | 0.914488i | \(0.632594\pi\) | |||||||
\(992\) | 71.1687 | − | 19.0696i | 2.25961 | − | 0.605460i | ||||
\(993\) | 11.1781 | − | 11.1781i | 0.354727 | − | 0.354727i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.3449 | − | 33.2964i | −0.961996 | − | 1.05557i | ||||
\(996\) | 23.5590 | − | 40.8054i | 0.746496 | − | 1.29297i | ||||
\(997\) | 14.8437 | − | 55.3975i | 0.470106 | − | 1.75446i | −0.169277 | − | 0.985569i | \(-0.554143\pi\) |
0.639382 | − | 0.768889i | \(-0.279190\pi\) | |||||||
\(998\) | 2.31110 | − | 8.62515i | 0.0731566 | − | 0.273024i | ||||
\(999\) | 1.59495 | − | 2.76254i | 0.0504620 | − | 0.0874028i |
(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 | 735.2.v.a.313.1 | 32 | ||
5.2 | odd | 4 | inner | 735.2.v.a.607.7 | 32 | ||
7.2 | even | 3 | 105.2.m.a.13.2 | yes | 16 | ||
7.3 | odd | 6 | inner | 735.2.v.a.178.7 | 32 | ||
7.4 | even | 3 | inner | 735.2.v.a.178.8 | 32 | ||
7.5 | odd | 6 | 105.2.m.a.13.1 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 735.2.v.a.313.2 | 32 | ||
21.2 | odd | 6 | 315.2.p.e.118.7 | 16 | |||
21.5 | even | 6 | 315.2.p.e.118.8 | 16 | |||
28.19 | even | 6 | 1680.2.cz.d.433.6 | 16 | |||
28.23 | odd | 6 | 1680.2.cz.d.433.3 | 16 | |||
35.2 | odd | 12 | 105.2.m.a.97.1 | yes | 16 | ||
35.9 | even | 6 | 525.2.m.b.118.7 | 16 | |||
35.12 | even | 12 | 105.2.m.a.97.2 | yes | 16 | ||
35.17 | even | 12 | inner | 735.2.v.a.472.1 | 32 | ||
35.19 | odd | 6 | 525.2.m.b.118.8 | 16 | |||
35.23 | odd | 12 | 525.2.m.b.307.8 | 16 | |||
35.27 | even | 4 | inner | 735.2.v.a.607.8 | 32 | ||
35.32 | odd | 12 | inner | 735.2.v.a.472.2 | 32 | ||
35.33 | even | 12 | 525.2.m.b.307.7 | 16 | |||
105.2 | even | 12 | 315.2.p.e.307.8 | 16 | |||
105.47 | odd | 12 | 315.2.p.e.307.7 | 16 | |||
140.47 | odd | 12 | 1680.2.cz.d.97.3 | 16 | |||
140.107 | even | 12 | 1680.2.cz.d.97.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.1 | ✓ | 16 | 7.5 | odd | 6 | ||
105.2.m.a.13.2 | yes | 16 | 7.2 | even | 3 | ||
105.2.m.a.97.1 | yes | 16 | 35.2 | odd | 12 | ||
105.2.m.a.97.2 | yes | 16 | 35.12 | even | 12 | ||
315.2.p.e.118.7 | 16 | 21.2 | odd | 6 | |||
315.2.p.e.118.8 | 16 | 21.5 | even | 6 | |||
315.2.p.e.307.7 | 16 | 105.47 | odd | 12 | |||
315.2.p.e.307.8 | 16 | 105.2 | even | 12 | |||
525.2.m.b.118.7 | 16 | 35.9 | even | 6 | |||
525.2.m.b.118.8 | 16 | 35.19 | odd | 6 | |||
525.2.m.b.307.7 | 16 | 35.33 | even | 12 | |||
525.2.m.b.307.8 | 16 | 35.23 | odd | 12 | |||
735.2.v.a.178.7 | 32 | 7.3 | odd | 6 | inner | ||
735.2.v.a.178.8 | 32 | 7.4 | even | 3 | inner | ||
735.2.v.a.313.1 | 32 | 1.1 | even | 1 | trivial | ||
735.2.v.a.313.2 | 32 | 7.6 | odd | 2 | inner | ||
735.2.v.a.472.1 | 32 | 35.17 | even | 12 | inner | ||
735.2.v.a.472.2 | 32 | 35.32 | odd | 12 | inner | ||
735.2.v.a.607.7 | 32 | 5.2 | odd | 4 | inner | ||
735.2.v.a.607.8 | 32 | 35.27 | even | 4 | inner | ||
1680.2.cz.d.97.3 | 16 | 140.47 | odd | 12 | |||
1680.2.cz.d.97.6 | 16 | 140.107 | even | 12 | |||
1680.2.cz.d.433.3 | 16 | 28.23 | odd | 6 | |||
1680.2.cz.d.433.6 | 16 | 28.19 | even | 6 |