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 | 178.8 | ||
Character | \(\chi\) | \(=\) | 735.178 |
Dual form | 735.2.v.a.607.8 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.54281 | + | 0.681344i | 1.79804 | + | 0.481783i | 0.993669 | − | 0.112345i | \(-0.0358361\pi\) |
0.804370 | + | 0.594128i | \(0.202503\pi\) | |||||||
\(3\) | 0.258819 | + | 0.965926i | 0.149429 | + | 0.557678i | ||||
\(4\) | 4.26961 | + | 2.46506i | 2.13481 | + | 1.23253i | ||||
\(5\) | 0.678180 | − | 2.13074i | 0.303291 | − | 0.952898i | ||||
\(6\) | 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 | ||||
\(10\) | 3.17625 | − | 4.95601i | 1.00442 | − | 1.56723i | ||||
\(11\) | 0.731395 | − | 1.26681i | 0.220524 | − | 0.381958i | −0.734443 | − | 0.678670i | \(-0.762557\pi\) |
0.954967 | + | 0.296712i | \(0.0958900\pi\) | |||||||
\(12\) | −1.27601 | + | 4.76213i | −0.368352 | + | 1.37471i | ||||
\(13\) | −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 | ||||
\(17\) | −2.87705 | + | 0.770902i | −0.697786 | + | 0.186971i | −0.590239 | − | 0.807229i | \(-0.700966\pi\) |
−0.107547 | + | 0.994200i | \(0.534300\pi\) | |||||||
\(18\) | −2.54281 | + | 0.681344i | −0.599347 | + | 0.160594i | ||||
\(19\) | −1.97993 | − | 3.42935i | −0.454228 | − | 0.786746i | 0.544415 | − | 0.838816i | \(-0.316752\pi\) |
−0.998643 | + | 0.0520695i | \(0.983418\pi\) | |||||||
\(20\) | 8.14798 | − | 7.42570i | 1.82194 | − | 1.66044i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.72294 | − | 2.72294i | 0.580532 | − | 0.580532i | ||||
\(23\) | −1.51171 | + | 5.64178i | −0.315214 | + | 1.17639i | 0.608577 | + | 0.793495i | \(0.291741\pi\) |
−0.923790 | + | 0.382898i | \(0.874926\pi\) | |||||||
\(24\) | −3.85679 | + | 6.68016i | −0.787265 | + | 1.36358i | ||||
\(25\) | −4.08014 | − | 2.89006i | −0.816029 | − | 0.578011i | ||||
\(26\) | −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 | \(-0.159901\pi\) | |||||||
\(30\) | 5.60921 | + | 1.78532i | 1.02410 | + | 0.325953i | ||||
\(31\) | 5.28575 | + | 3.05173i | 0.949349 | + | 0.548107i | 0.892879 | − | 0.450297i | \(-0.148682\pi\) |
0.0564703 | + | 0.998404i | \(0.482015\pi\) | |||||||
\(32\) | 3.12439 | + | 11.6604i | 0.552319 | + | 2.06128i | ||||
\(33\) | 1.41295 | + | 0.378598i | 0.245962 | + | 0.0659054i | ||||
\(34\) | −7.84104 | −1.34473 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.93012 | −0.821687 | ||||||||
\(37\) | −3.08121 | − | 0.825607i | −0.506548 | − | 0.135729i | −0.00351049 | − | 0.999994i | \(-0.501117\pi\) |
−0.503037 | + | 0.864265i | \(0.667784\pi\) | |||||||
\(38\) | −2.69804 | − | 10.0692i | −0.437679 | − | 1.63344i | ||||
\(39\) | −1.08738 | − | 0.627801i | −0.174121 | − | 0.100529i | ||||
\(40\) | 15.3208 | − | 7.92277i | 2.42243 | − | 1.25270i | ||||
\(41\) | 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 | ||||
\(45\) | 0.478051 | + | 2.18437i | 0.0712637 | + | 0.325626i | ||||
\(46\) | −7.68800 | + | 13.3160i | −1.13353 | + | 1.96334i | ||||
\(47\) | −3.13699 | + | 11.7074i | −0.457577 | + | 1.70770i | 0.222823 | + | 0.974859i | \(0.428473\pi\) |
−0.680400 | + | 0.732841i | \(0.738194\pi\) | |||||||
\(48\) | −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 | ||||
\(52\) | −5.97934 | + | 1.60216i | −0.829185 | + | 0.222180i | ||||
\(53\) | 0.743732 | − | 0.199282i | 0.102159 | − | 0.0273735i | −0.207377 | − | 0.978261i | \(-0.566493\pi\) |
0.309537 | + | 0.950888i | \(0.399826\pi\) | |||||||
\(54\) | −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 | ||||
\(58\) | 3.53326 | − | 13.1863i | 0.463940 | − | 1.73145i | ||||
\(59\) | −1.59816 | + | 2.76810i | −0.208063 | + | 0.360376i | −0.951104 | − | 0.308870i | \(-0.900049\pi\) |
0.743041 | + | 0.669246i | \(0.233383\pi\) | |||||||
\(60\) | 9.28153 | + | 5.94843i | 1.19824 | + | 0.767939i | ||||
\(61\) | 1.23031 | − | 0.710320i | 0.157525 | − | 0.0909472i | −0.419165 | − | 0.907910i | \(-0.637677\pi\) |
0.576690 | + | 0.816963i | \(0.304344\pi\) | |||||||
\(62\) | 11.3614 | + | 11.3614i | 1.44290 | + | 1.44290i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 10.8872i | 1.36090i | ||||||||
\(65\) | 1.28965 | + | 2.49389i | 0.159962 | + | 0.309329i | ||||
\(66\) | 3.33490 | + | 1.92541i | 0.410498 | + | 0.237001i | ||||
\(67\) | −2.17058 | − | 8.10070i | −0.265178 | − | 0.989658i | −0.962141 | − | 0.272551i | \(-0.912133\pi\) |
0.696963 | − | 0.717107i | \(-0.254534\pi\) | |||||||
\(68\) | −14.1842 | − | 3.80064i | −1.72009 | − | 0.460896i | ||||
\(69\) | −5.84081 | −0.703150 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.62611 | 0.905053 | 0.452526 | − | 0.891751i | \(-0.350523\pi\) | ||||
0.452526 | + | 0.891751i | \(0.350523\pi\) | |||||||
\(72\) | −7.45075 | − | 1.99642i | −0.878080 | − | 0.235281i | ||||
\(73\) | −2.49402 | − | 9.30780i | −0.291903 | − | 1.08940i | −0.943646 | − | 0.330956i | \(-0.892629\pi\) |
0.651744 | − | 0.758439i | \(-0.274038\pi\) | |||||||
\(74\) | −7.27241 | − | 4.19873i | −0.845401 | − | 0.488092i | ||||
\(75\) | 1.73556 | − | 4.68912i | 0.200405 | − | 0.541453i | ||||
\(76\) | − | 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 | \(-0.748507\pi\) |
0.263346 | + | 0.964701i | \(0.415174\pi\) | |||||||
\(80\) | 22.8176 | − | 4.99366i | 2.55109 | − | 0.558308i | ||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.524613 | + | 1.95788i | −0.0579338 | + | 0.216212i | ||||
\(83\) | 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 | ||||
\(87\) | 5.00903 | − | 1.34216i | 0.537024 | − | 0.143895i | ||||
\(88\) | 10.8989 | − | 2.92035i | 1.16182 | − | 0.311310i | ||||
\(89\) | 0.599954 | + | 1.03915i | 0.0635950 | + | 0.110150i | 0.896070 | − | 0.443913i | \(-0.146410\pi\) |
−0.832475 | + | 0.554063i | \(0.813077\pi\) | |||||||
\(90\) | −0.272713 | + | 5.88016i | −0.0287465 | + | 0.619823i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −20.3618 | + | 20.3618i | −2.12286 | + | 2.12286i | ||||
\(93\) | −1.57969 | + | 5.89549i | −0.163806 | + | 0.611334i | ||||
\(94\) | −15.9535 | + | 27.6323i | −1.64548 | + | 2.85006i | ||||
\(95\) | −8.64982 | + | 1.89302i | −0.887452 | + | 0.194220i | ||||
\(96\) | −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 | ||||||||
\(100\) | −10.2965 | − | 22.3972i | −1.02965 | − | 2.23972i | ||||
\(101\) | −13.2866 | − | 7.67102i | −1.32207 | − | 0.763295i | −0.338008 | − | 0.941143i | \(-0.609753\pi\) |
−0.984058 | + | 0.177848i | \(0.943086\pi\) | |||||||
\(102\) | −2.02941 | − | 7.57386i | −0.200941 | − | 0.749924i | ||||
\(103\) | 11.3486 | + | 3.04085i | 1.11821 | + | 0.299624i | 0.770160 | − | 0.637851i | \(-0.220177\pi\) |
0.348052 | + | 0.937475i | \(0.386843\pi\) | |||||||
\(104\) | −9.68519 | −0.949711 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.02695 | 0.196875 | ||||||||
\(107\) | −5.99715 | − | 1.60693i | −0.579766 | − | 0.155348i | −0.0429945 | − | 0.999075i | \(-0.513690\pi\) |
−0.536772 | + | 0.843727i | \(0.680356\pi\) | |||||||
\(108\) | −1.27601 | − | 4.76213i | −0.122784 | − | 0.458237i | ||||
\(109\) | 6.44831 | + | 3.72294i | 0.617636 | + | 0.356593i | 0.775948 | − | 0.630797i | \(-0.217272\pi\) |
−0.158312 | + | 0.987389i | \(0.550605\pi\) | |||||||
\(110\) | −3.95524 | − | 7.64852i | −0.377117 | − | 0.729258i | ||||
\(111\) | − | 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 | ||||
\(115\) | 10.9960 | + | 7.04722i | 1.02538 | + | 0.657156i | ||||
\(116\) | 12.7831 | − | 22.1410i | 1.18688 | − | 2.05574i | ||||
\(117\) | 0.324974 | − | 1.21282i | 0.0300438 | − | 0.112125i | ||||
\(118\) | −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 | ||||
\(122\) | 3.61242 | − | 0.967945i | 0.327053 | − | 0.0876337i | ||||
\(123\) | −0.743732 | + | 0.199282i | −0.0670600 | + | 0.0179687i | ||||
\(124\) | 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 | \(0.0858286\pi\) | |||||||
\(128\) | −1.16915 | + | 4.36334i | −0.103339 | + | 0.385668i | ||||
\(129\) | 3.66686 | − | 6.35119i | 0.322849 | − | 0.559191i | ||||
\(130\) | 1.58014 | + | 7.22018i | 0.138588 | + | 0.633252i | ||||
\(131\) | 5.35391 | − | 3.09108i | 0.467773 | − | 0.270069i | −0.247534 | − | 0.968879i | \(-0.579620\pi\) |
0.715307 | + | 0.698810i | \(0.246287\pi\) | |||||||
\(132\) | 5.09947 | + | 5.09947i | 0.443851 | + | 0.443851i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 22.0775i | − | 1.90720i | ||||||
\(135\) | −1.98621 | + | 1.02712i | −0.170946 | + | 0.0884003i | ||||
\(136\) | −19.8971 | − | 11.4876i | −1.70616 | − | 0.985054i | ||||
\(137\) | 3.31460 | + | 12.3703i | 0.283185 | + | 1.05686i | 0.950155 | + | 0.311777i | \(0.100924\pi\) |
−0.666970 | + | 0.745085i | \(0.732409\pi\) | |||||||
\(138\) | −14.8521 | − | 3.97960i | −1.26429 | − | 0.338766i | ||||
\(139\) | 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 | ||||||||
\(142\) | 19.3918 | + | 5.19601i | 1.62732 | + | 0.436039i | ||||
\(143\) | 0.475368 | + | 1.77410i | 0.0397523 | + | 0.148357i | ||||
\(144\) | −9.04639 | − | 5.22294i | −0.753866 | − | 0.435245i | ||||
\(145\) | −11.0495 | − | 3.51685i | −0.917607 | − | 0.292059i | ||||
\(146\) | − | 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 | \(-0.665404\pi\) |
0.503431 | + | 0.864036i | \(0.332071\pi\) | |||||||
\(150\) | 7.60811 | − | 10.7410i | 0.621199 | − | 0.877002i | ||||
\(151\) | 6.72748 | − | 11.6523i | 0.547475 | − | 0.948254i | −0.450972 | − | 0.892538i | \(-0.648923\pi\) |
0.998447 | − | 0.0557157i | \(-0.0177440\pi\) | |||||||
\(152\) | 7.90558 | − | 29.5040i | 0.641227 | − | 2.39309i | ||||
\(153\) | 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 | ||||
\(157\) | 2.25063 | − | 0.603054i | 0.179620 | − | 0.0481290i | −0.167888 | − | 0.985806i | \(-0.553695\pi\) |
0.347508 | + | 0.937677i | \(0.387028\pi\) | |||||||
\(158\) | −11.4943 | + | 3.07988i | −0.914434 | + | 0.245022i | ||||
\(159\) | 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 | ||||
\(163\) | −3.76077 | + | 14.0354i | −0.294566 | + | 1.09934i | 0.646995 | + | 0.762495i | \(0.276026\pi\) |
−0.941561 | + | 0.336842i | \(0.890641\pi\) | |||||||
\(164\) | −1.89802 | + | 3.28746i | −0.148210 | + | 0.256708i | ||||
\(165\) | 1.76493 | − | 2.75387i | 0.137399 | − | 0.214388i | ||||
\(166\) | 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 | ||||||||
\(170\) | −5.31763 | + | 16.7072i | −0.407844 | + | 1.28139i | ||||
\(171\) | 3.42935 | + | 1.97993i | 0.262249 | + | 0.151409i | ||||
\(172\) | −9.35790 | − | 34.9242i | −0.713533 | − | 2.66294i | ||||
\(173\) | −4.71537 | − | 1.26348i | −0.358503 | − | 0.0960606i | 0.0750719 | − | 0.997178i | \(-0.476081\pi\) |
−0.433575 | + | 0.901118i | \(0.642748\pi\) | |||||||
\(174\) | 13.6515 | 1.03492 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.2801 | 1.15178 | ||||||||
\(177\) | −3.08742 | − | 0.827271i | −0.232064 | − | 0.0621815i | ||||
\(178\) | 0.817551 | + | 3.05114i | 0.0612781 | + | 0.228693i | ||||
\(179\) | −1.72994 | − | 0.998779i | −0.129302 | − | 0.0746523i | 0.433954 | − | 0.900935i | \(-0.357118\pi\) |
−0.563256 | + | 0.826283i | \(0.690451\pi\) | |||||||
\(180\) | −3.34351 | + | 10.5048i | −0.249211 | + | 0.782984i | ||||
\(181\) | − | 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 | ||||
\(185\) | −3.84877 | + | 6.00536i | −0.282967 | + | 0.441523i | ||||
\(186\) | −8.03372 | + | 13.9148i | −0.589061 | + | 1.02028i | ||||
\(187\) | −1.12767 | + | 4.20851i | −0.0824632 | + | 0.307757i | ||||
\(188\) | −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 | 0.972228 | − | 0.234036i | \(-0.0751934\pi\) |
−0.688795 | + | 0.724956i | \(0.741860\pi\) | |||||||
\(192\) | −10.5162 | + | 2.81781i | −0.758943 | + | 0.203358i | ||||
\(193\) | −18.5257 | + | 4.96393i | −1.33351 | + | 0.357312i | −0.854021 | − | 0.520239i | \(-0.825843\pi\) |
−0.479485 | + | 0.877550i | \(0.659176\pi\) | |||||||
\(194\) | 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 | \(0.446287\pi\) | |||||||
\(198\) | −0.996663 | + | 3.71960i | −0.0708298 | + | 0.264340i | ||||
\(199\) | 10.0734 | − | 17.4476i | 0.714084 | − | 1.23683i | −0.249228 | − | 0.968445i | \(-0.580177\pi\) |
0.963312 | − | 0.268384i | \(-0.0864897\pi\) | |||||||
\(200\) | −6.49114 | − | 38.0178i | −0.458993 | − | 2.68826i | ||||
\(201\) | 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 | ||||||
\(205\) | 1.64060 | + | 0.522176i | 0.114585 | + | 0.0364704i | ||||
\(206\) | 26.7855 | + | 15.4646i | 1.86623 | + | 1.07747i | ||||
\(207\) | −1.51171 | − | 5.64178i | −0.105071 | − | 0.392131i | ||||
\(208\) | −12.6689 | − | 3.39463i | −0.878433 | − | 0.235375i | ||||
\(209\) | −5.79246 | −0.400673 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9662 | 0.823785 | 0.411892 | − | 0.911233i | \(-0.364868\pi\) | ||||
0.411892 | + | 0.911233i | \(0.364868\pi\) | |||||||
\(212\) | 3.66669 | + | 0.982486i | 0.251829 | + | 0.0674774i | ||||
\(213\) | 1.97378 | + | 7.36626i | 0.135241 | + | 0.504728i | ||||
\(214\) | −14.1548 | − | 8.17225i | −0.967599 | − | 0.558644i | ||||
\(215\) | −14.5663 | + | 7.53260i | −0.993414 | + | 0.513719i | ||||
\(216\) | − | 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 | ||||
\(220\) | −3.44758 | − | 15.7531i | −0.232436 | − | 1.06207i | ||||
\(221\) | 1.86993 | − | 3.23881i | 0.125785 | − | 0.217866i | ||||
\(222\) | 2.17342 | − | 8.11132i | 0.145871 | − | 0.544396i | ||||
\(223\) | 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 | ||||
\(227\) | −23.6988 | + | 6.35007i | −1.57294 | + | 0.421469i | −0.936732 | − | 0.350047i | \(-0.886166\pi\) |
−0.636210 | + | 0.771516i | \(0.719499\pi\) | |||||||
\(228\) | 18.8574 | − | 5.05283i | 1.24886 | − | 0.334632i | ||||
\(229\) | −12.5391 | − | 21.7184i | −0.828607 | − | 1.43519i | −0.899131 | − | 0.437679i | \(-0.855800\pi\) |
0.0705240 | − | 0.997510i | \(-0.477533\pi\) | |||||||
\(230\) | 23.1592 | + | 25.4118i | 1.52707 | + | 1.67560i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 28.2847 | − | 28.2847i | 1.85698 | − | 1.85698i | ||||
\(233\) | 0.820401 | − | 3.06178i | 0.0537462 | − | 0.200584i | −0.933832 | − | 0.357712i | \(-0.883557\pi\) |
0.987578 | + | 0.157128i | \(0.0502236\pi\) | |||||||
\(234\) | 1.65269 | − | 2.86255i | 0.108040 | − | 0.187131i | ||||
\(235\) | 22.8180 | + | 14.6238i | 1.48848 | + | 0.953954i | ||||
\(236\) | −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 | \(0.757003\pi\) | |||||||
\(240\) | 10.7291 | + | 20.7477i | 0.692563 | + | 1.33926i | ||||
\(241\) | 0.540512 | + | 0.312065i | 0.0348174 | + | 0.0201018i | 0.517308 | − | 0.855799i | \(-0.326934\pi\) |
−0.482490 | + | 0.875901i | \(0.660268\pi\) | |||||||
\(242\) | 6.03688 | + | 22.5299i | 0.388065 | + | 1.44828i | ||||
\(243\) | 0.965926 | + | 0.258819i | 0.0619642 | + | 0.0166032i | ||||
\(244\) | 7.00393 | 0.448381 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.02695 | −0.129234 | ||||||||
\(247\) | 4.80260 | + | 1.28685i | 0.305582 | + | 0.0818805i | ||||
\(248\) | 12.1851 | + | 45.4754i | 0.773754 | + | 2.88769i | ||||
\(249\) | 8.27676 | + | 4.77859i | 0.524518 | + | 0.302831i | ||||
\(250\) | −27.2827 | + | 11.0417i | −1.72551 | + | 0.698337i | ||||
\(251\) | 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 | ||||
\(255\) | −6.50622 | + | 1.42389i | −0.407435 | + | 0.0891677i | ||||
\(256\) | 4.94133 | − | 8.55863i | 0.308833 | − | 0.534914i | ||||
\(257\) | −7.79833 | + | 29.1038i | −0.486446 | + | 1.81544i | 0.0870116 | + | 0.996207i | \(0.472268\pi\) |
−0.573458 | + | 0.819235i | \(0.694398\pi\) | |||||||
\(258\) | 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 | ||||
\(262\) | 15.7201 | − | 4.21218i | 0.971190 | − | 0.260230i | ||||
\(263\) | 22.3275 | − | 5.98263i | 1.37677 | − | 0.368905i | 0.506824 | − | 0.862049i | \(-0.330819\pi\) |
0.869947 | + | 0.493145i | \(0.164153\pi\) | |||||||
\(264\) | 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 | ||||
\(268\) | 10.7012 | − | 39.9374i | 0.653680 | − | 2.43957i | ||||
\(269\) | −8.29515 | + | 14.3676i | −0.505764 | + | 0.876009i | 0.494213 | + | 0.869341i | \(0.335456\pi\) |
−0.999978 | + | 0.00666889i | \(0.997877\pi\) | |||||||
\(270\) | −5.75038 | + | 1.25848i | −0.349957 | + | 0.0765884i | ||||
\(271\) | 6.73796 | − | 3.89016i | 0.409302 | − | 0.236311i | −0.281188 | − | 0.959653i | \(-0.590728\pi\) |
0.690490 | + | 0.723342i | \(0.257395\pi\) | |||||||
\(272\) | −22.0005 | − | 22.0005i | −1.33398 | − | 1.33398i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 33.7136i | 2.03671i | ||||||||
\(275\) | −6.64536 | + | 3.05501i | −0.400730 | + | 0.184224i | ||||
\(276\) | −24.9380 | − | 14.3979i | −1.50109 | − | 0.866654i | ||||
\(277\) | 7.80024 | + | 29.1109i | 0.468671 | + | 1.74910i | 0.644422 | + | 0.764670i | \(0.277098\pi\) |
−0.175751 | + | 0.984435i | \(0.556235\pi\) | |||||||
\(278\) | 30.4916 | + | 8.17019i | 1.82876 | + | 0.490016i | ||||
\(279\) | −6.10346 | −0.365405 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.1519 | −1.26182 | −0.630908 | − | 0.775858i | \(-0.717317\pi\) | ||||
−0.630908 | + | 0.775858i | \(0.717317\pi\) | |||||||
\(282\) | −30.8199 | − | 8.25816i | −1.83530 | − | 0.491766i | ||||
\(283\) | −0.971693 | − | 3.62641i | −0.0577611 | − | 0.215567i | 0.931013 | − | 0.364986i | \(-0.118926\pi\) |
−0.988774 | + | 0.149419i | \(0.952260\pi\) | |||||||
\(284\) | 32.5605 | + | 18.7988i | 1.93211 | + | 1.11551i | ||||
\(285\) | −4.06725 | − | 7.86513i | −0.240923 | − | 0.465890i | ||||
\(286\) | 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 | ||||
\(290\) | −25.7005 | − | 16.4712i | −1.50919 | − | 0.967221i | ||||
\(291\) | −6.14355 | + | 10.6409i | −0.360141 | + | 0.623783i | ||||
\(292\) | 12.2958 | − | 45.8886i | 0.719558 | − | 2.68543i | ||||
\(293\) | 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 | ||||
\(297\) | −1.41295 | + | 0.378598i | −0.0819875 | + | 0.0219685i | ||||
\(298\) | 0.246211 | − | 0.0659719i | 0.0142626 | − | 0.00382165i | ||||
\(299\) | −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 | ||||
\(303\) | 3.97081 | − | 14.8193i | 0.228117 | − | 0.851345i | ||||
\(304\) | 20.6821 | − | 35.8225i | 1.18620 | − | 2.05456i | ||||
\(305\) | −0.679139 | − | 3.10320i | −0.0388874 | − | 0.177689i | ||||
\(306\) | 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 | ||||||||
\(310\) | 31.9133 | − | 16.5032i | 1.81255 | − | 0.937316i | ||||
\(311\) | −26.9029 | − | 15.5324i | −1.52553 | − | 0.880763i | −0.999542 | − | 0.0302685i | \(-0.990364\pi\) |
−0.525984 | − | 0.850494i | \(-0.676303\pi\) | |||||||
\(312\) | −2.50671 | − | 9.35518i | −0.141915 | − | 0.529633i | ||||
\(313\) | 7.81948 | + | 2.09522i | 0.441983 | + | 0.118429i | 0.472946 | − | 0.881091i | \(-0.343191\pi\) |
−0.0309625 | + | 0.999521i | \(0.509857\pi\) | |||||||
\(314\) | 6.13381 | 0.346151 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.2856 | −1.25366 | ||||||||
\(317\) | −1.02804 | − | 0.275463i | −0.0577406 | − | 0.0154715i | 0.229833 | − | 0.973230i | \(-0.426182\pi\) |
−0.287574 | + | 0.957759i | \(0.592849\pi\) | |||||||
\(318\) | 0.524613 | + | 1.95788i | 0.0294188 | + | 0.109793i | ||||
\(319\) | −6.56934 | − | 3.79281i | −0.367813 | − | 0.212357i | ||||
\(320\) | 23.1978 | + | 7.38348i | 1.29680 | + | 0.412749i | ||||
\(321\) | − | 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 | ||||
\(325\) | 6.18845 | − | 1.05661i | 0.343274 | − | 0.0586104i | ||||
\(326\) | −19.1259 | + | 33.1270i | −1.05928 | + | 1.83473i | ||||
\(327\) | −1.92713 | + | 7.19216i | −0.106571 | + | 0.397727i | ||||
\(328\) | −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 | 0.562801 | − | 0.826592i | \(-0.309724\pi\) |
−0.997251 | + | 0.0741038i | \(0.976390\pi\) | |||||||
\(332\) | 45.5125 | − | 12.1950i | 2.49783 | − | 0.669290i | ||||
\(333\) | 3.08121 | − | 0.825607i | 0.168849 | − | 0.0452430i | ||||
\(334\) | −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 | \(0.969185\pi\) | |||||||
\(338\) | −7.78331 | + | 29.0477i | −0.423357 | + | 1.57999i | ||||
\(339\) | −1.79920 | + | 3.11630i | −0.0977190 | + | 0.169254i | ||||
\(340\) | −17.7176 | + | 27.6454i | −0.960873 | + | 1.49928i | ||||
\(341\) | 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 | ||||||
\(345\) | −3.96112 | + | 12.4453i | −0.213259 | + | 0.670030i | ||||
\(346\) | −11.1294 | − | 6.42558i | −0.598322 | − | 0.345441i | ||||
\(347\) | −7.35151 | − | 27.4362i | −0.394650 | − | 1.47285i | −0.822376 | − | 0.568945i | \(-0.807352\pi\) |
0.427726 | − | 0.903908i | \(-0.359315\pi\) | |||||||
\(348\) | 24.6951 | + | 6.61704i | 1.32380 | + | 0.354710i | ||||
\(349\) | −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 | ||||||||
\(352\) | 17.0567 | + | 4.57032i | 0.909124 | + | 0.243599i | ||||
\(353\) | 4.57130 | + | 17.0603i | 0.243306 | + | 0.908029i | 0.974227 | + | 0.225568i | \(0.0724238\pi\) |
−0.730922 | + | 0.682461i | \(0.760910\pi\) | |||||||
\(354\) | −7.28706 | − | 4.20719i | −0.387303 | − | 0.223610i | ||||
\(355\) | 5.17187 | − | 16.2493i | 0.274495 | − | 0.862423i | ||||
\(356\) | 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 | \(-0.576973\pi\) |
0.721093 | + | 0.692838i | \(0.243640\pi\) | |||||||
\(360\) | −9.30682 | + | 14.5217i | −0.490512 | + | 0.765362i | ||||
\(361\) | 1.65972 | − | 2.87471i | 0.0873535 | − | 0.151301i | ||||
\(362\) | 5.78140 | − | 21.5765i | 0.303864 | − | 1.13403i | ||||
\(363\) | −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 | ||||
\(367\) | 15.2871 | − | 4.09618i | 0.797982 | − | 0.213819i | 0.163284 | − | 0.986579i | \(-0.447791\pi\) |
0.634698 | + | 0.772760i | \(0.281125\pi\) | |||||||
\(368\) | −58.9334 | + | 15.7911i | −3.07211 | + | 0.823170i | ||||
\(369\) | −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 | ||||
\(373\) | 6.32295 | − | 23.5976i | 0.327390 | − | 1.22184i | −0.584497 | − | 0.811396i | \(-0.698708\pi\) |
0.911887 | − | 0.410440i | \(-0.134625\pi\) | |||||||
\(374\) | −5.73489 | + | 9.93312i | −0.296544 | + | 0.513630i | ||||
\(375\) | −8.81429 | − | 6.87810i | −0.455168 | − | 0.355184i | ||||
\(376\) | −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 | \(-0.149515\pi\) | |||||||
\(380\) | −41.5978 | − | 13.2399i | −2.13392 | − | 0.679191i | ||||
\(381\) | 9.62680 | + | 5.55803i | 0.493196 | + | 0.284747i | ||||
\(382\) | 5.33782 | + | 19.9210i | 0.273106 | + | 1.01925i | ||||
\(383\) | 22.0270 | + | 5.90211i | 1.12553 | + | 0.301584i | 0.773118 | − | 0.634263i | \(-0.218696\pi\) |
0.352408 | + | 0.935846i | \(0.385363\pi\) | |||||||
\(384\) | −4.51726 | −0.230520 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −50.4894 | −2.56984 | ||||||||
\(387\) | 7.08383 | + | 1.89811i | 0.360091 | + | 0.0964862i | ||||
\(388\) | 15.6785 | + | 58.5128i | 0.795953 | + | 2.97054i | ||||
\(389\) | 13.3377 | + | 7.70053i | 0.676249 | + | 0.390432i | 0.798440 | − | 0.602074i | \(-0.205659\pi\) |
−0.122191 | + | 0.992507i | \(0.538992\pi\) | |||||||
\(390\) | −6.56519 | + | 3.39502i | −0.332441 | + | 0.171914i | ||||
\(391\) | − | 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 | ||||
\(395\) | 2.16093 | + | 9.87398i | 0.108728 | + | 0.496814i | ||||
\(396\) | −3.60587 | + | 6.24554i | −0.181202 | + | 0.313850i | ||||
\(397\) | −5.92159 | + | 22.0997i | −0.297196 | + | 1.10915i | 0.642261 | + | 0.766486i | \(0.277996\pi\) |
−0.939458 | + | 0.342665i | \(0.888670\pi\) | |||||||
\(398\) | 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 | 0.877972 | − | 0.478712i | \(-0.158896\pi\) |
−0.853563 | + | 0.520990i | \(0.825563\pi\) | |||||||
\(402\) | 21.3252 | − | 5.71407i | 1.06360 | − | 0.284992i | ||||
\(403\) | −7.40238 | + | 1.98346i | −0.368739 | + | 0.0988033i | ||||
\(404\) | −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 | ||||
\(408\) | 5.94642 | − | 22.1923i | 0.294392 | − | 1.09868i | ||||
\(409\) | 12.1586 | − | 21.0593i | 0.601203 | − | 1.04131i | −0.391437 | − | 0.920205i | \(-0.628022\pi\) |
0.992639 | − | 0.121108i | \(-0.0386449\pi\) | |||||||
\(410\) | 3.81597 | + | 2.44561i | 0.188457 | + | 0.120780i | ||||
\(411\) | −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 | ||||||
\(415\) | −9.81635 | − | 18.9825i | −0.481866 | − | 0.931817i | ||||
\(416\) | −13.1266 | − | 7.57863i | −0.643583 | − | 0.371573i | ||||
\(417\) | 3.10357 | + | 11.5827i | 0.151983 | + | 0.567207i | ||||
\(418\) | −14.7291 | − | 3.94666i | −0.720425 | − | 0.193037i | ||||
\(419\) | −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 | \(0.383385\pi\) | |||||||
\(422\) | 30.4277 | + | 8.15308i | 1.48120 | + | 0.396886i | ||||
\(423\) | −3.13699 | − | 11.7074i | −0.152526 | − | 0.569233i | ||||
\(424\) | 5.14351 | + | 2.96961i | 0.249791 | + | 0.144217i | ||||
\(425\) | 13.9667 | + | 5.16943i | 0.677485 | + | 0.250754i | ||||
\(426\) | 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 | ||||
\(430\) | −42.1717 | + | 9.22932i | −2.03370 | + | 0.445077i | ||||
\(431\) | −11.1361 | + | 19.2883i | −0.536407 | + | 0.929084i | 0.462687 | + | 0.886522i | \(0.346885\pi\) |
−0.999094 | + | 0.0425619i | \(0.986448\pi\) | |||||||
\(432\) | 2.70359 | − | 10.0899i | 0.130077 | − | 0.485452i | ||||
\(433\) | 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 | ||||
\(437\) | 22.3407 | − | 5.98618i | 1.06870 | − | 0.286358i | ||||
\(438\) | 24.5029 | − | 6.56553i | 1.17079 | − | 0.313713i | ||||
\(439\) | −1.17828 | − | 2.04084i | −0.0562363 | − | 0.0974042i | 0.836537 | − | 0.547911i | \(-0.184577\pi\) |
−0.892773 | + | 0.450507i | \(0.851243\pi\) | |||||||
\(440\) | 1.16889 | − | 25.2033i | 0.0557246 | − | 1.20152i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.96162 | − | 6.96162i | 0.331130 | − | 0.331130i | ||||
\(443\) | −2.00306 | + | 7.47553i | −0.0951684 | + | 0.355173i | −0.997045 | − | 0.0768206i | \(-0.975523\pi\) |
0.901877 | + | 0.431994i | \(0.142190\pi\) | |||||||
\(444\) | 7.86331 | − | 13.6196i | 0.373176 | − | 0.646360i | ||||
\(445\) | 2.62104 | − | 0.573618i | 0.124249 | − | 0.0271921i | ||||
\(446\) | 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 | \(0.990984\pi\) | |||||||
\(450\) | 12.3442 | + | 4.56888i | 0.581909 | + | 0.215379i | ||||
\(451\) | 0.975405 | + | 0.563150i | 0.0459300 | + | 0.0265177i | ||||
\(452\) | 4.59159 | + | 17.1360i | 0.215970 | + | 0.806011i | ||||
\(453\) | 12.9965 | + | 3.48240i | 0.610629 | + | 0.163617i | ||||
\(454\) | −64.5881 | −3.03127 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 30.5448 | 1.43039 | ||||||||
\(457\) | 28.7924 | + | 7.71489i | 1.34685 | + | 0.360887i | 0.858971 | − | 0.512024i | \(-0.171104\pi\) |
0.487879 | + | 0.872912i | \(0.337771\pi\) | |||||||
\(458\) | −17.0869 | − | 63.7692i | −0.798418 | − | 2.97974i | ||||
\(459\) | 2.57949 | + | 1.48927i | 0.120400 | + | 0.0695131i | ||||
\(460\) | 29.5768 | + | 57.1947i | 1.37902 | + | 2.66672i | ||||
\(461\) | − | 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 | ||||
\(465\) | 11.4905 | + | 7.36412i | 0.532858 | + | 0.341503i | ||||
\(466\) | 4.17225 | − | 7.22655i | 0.193276 | − | 0.334763i | ||||
\(467\) | −2.60354 | + | 9.71653i | −0.120477 | + | 0.449627i | −0.999638 | − | 0.0268978i | \(-0.991437\pi\) |
0.879161 | + | 0.476525i | \(0.158104\pi\) | |||||||
\(468\) | 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 | ||||
\(472\) | −23.8151 | + | 6.38123i | −1.09618 | + | 0.293720i | ||||
\(473\) | −10.3622 | + | 2.77653i | −0.476452 | + | 0.127665i | ||||
\(474\) | −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 | ||||
\(478\) | −14.5651 | + | 54.3575i | −0.666190 | + | 2.48626i | ||||
\(479\) | 15.8875 | − | 27.5179i | 0.725917 | − | 1.25733i | −0.232678 | − | 0.972554i | \(-0.574749\pi\) |
0.958595 | − | 0.284771i | \(-0.0919177\pi\) | |||||||
\(480\) | 5.77090 | + | 26.3691i | 0.263404 | + | 1.20358i | ||||
\(481\) | 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 | ||||||||
\(485\) | 24.4047 | − | 12.6203i | 1.10816 | − | 0.573058i | ||||
\(486\) | 2.27982 | + | 1.31626i | 0.103415 | + | 0.0597066i | ||||
\(487\) | −1.76215 | − | 6.57642i | −0.0798505 | − | 0.298006i | 0.914439 | − | 0.404724i | \(-0.132632\pi\) |
−0.994289 | + | 0.106718i | \(0.965966\pi\) | |||||||
\(488\) | 10.5848 | + | 2.83620i | 0.479153 | + | 0.128389i | ||||
\(489\) | −14.5305 | −0.657092 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.3401 | 1.27897 | 0.639484 | − | 0.768804i | \(-0.279148\pi\) | ||||
0.639484 | + | 0.768804i | \(0.279148\pi\) | |||||||
\(492\) | −3.66669 | − | 0.982486i | −0.165307 | − | 0.0442939i | ||||
\(493\) | 3.99769 | + | 14.9196i | 0.180047 | + | 0.671943i | ||||
\(494\) | 11.3353 | + | 6.54445i | 0.510000 | + | 0.294449i | ||||
\(495\) | 3.11683 | + | 0.992034i | 0.140091 | + | 0.0445886i | ||||
\(496\) | 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 | \(-0.690857\pi\) |
0.432806 | + | 0.901487i | \(0.357524\pi\) | |||||||
\(500\) | −54.7056 | + | 6.74980i | −2.44651 | + | 0.301860i | ||||
\(501\) | 0.207188 | − | 0.358861i | 0.00925649 | − | 0.0160327i | ||||
\(502\) | −11.1361 | + | 41.5605i | −0.497029 | + | 1.85494i | ||||
\(503\) | 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 | ||||
\(507\) | −11.0342 | + | 2.95661i | −0.490047 | + | 0.131308i | ||||
\(508\) | 52.9362 | − | 14.1842i | 2.34866 | − | 0.629323i | ||||
\(509\) | −19.4726 | − | 33.7275i | −0.863108 | − | 1.49495i | −0.868914 | − | 0.494963i | \(-0.835182\pi\) |
0.00580659 | − | 0.999983i | \(-0.498152\pi\) | |||||||
\(510\) | −17.5143 | − | 0.812285i | −0.775545 | − | 0.0359686i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.7846 | − | 24.7846i | 1.09534 | − | 1.09534i | ||||
\(513\) | −1.02489 | + | 3.82494i | −0.0452500 | + | 0.168875i | ||||
\(514\) | −39.6594 | + | 68.6920i | −1.74930 | + | 3.02988i | ||||
\(515\) | 14.1757 | − | 22.1187i | 0.624655 | − | 0.974668i | ||||
\(516\) | 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 | ||||||
\(520\) | −6.56830 | + | 20.6367i | −0.288039 | + | 0.904978i | ||||
\(521\) | 6.12042 | + | 3.53363i | 0.268141 | + | 0.154811i | 0.628042 | − | 0.778179i | \(-0.283856\pi\) |
−0.359902 | + | 0.932990i | \(0.617190\pi\) | |||||||
\(522\) | 3.53326 | + | 13.1863i | 0.154647 | + | 0.577150i | ||||
\(523\) | 19.9286 | + | 5.33985i | 0.871416 | + | 0.233495i | 0.666700 | − | 0.745326i | \(-0.267706\pi\) |
0.204716 | + | 0.978821i | \(0.434373\pi\) | |||||||
\(524\) | 30.4788 | 1.33147 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 60.8508 | 2.65322 | ||||||||
\(527\) | −17.5599 | − | 4.70517i | −0.764923 | − | 0.204960i | ||||
\(528\) | 3.95478 | + | 14.7595i | 0.172110 | + | 0.642323i | ||||
\(529\) | −9.62588 | − | 5.55750i | −0.418516 | − | 0.241631i | ||||
\(530\) | 1.37464 | − | 4.31891i | 0.0597104 | − | 0.187602i | ||||
\(531\) | − | 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 | ||||
\(535\) | −7.49111 | + | 11.6886i | −0.323869 | + | 0.505343i | ||||
\(536\) | 32.3449 | − | 56.0229i | 1.39708 | − | 2.41982i | ||||
\(537\) | 0.517006 | − | 1.92949i | 0.0223105 | − | 0.0832638i | ||||
\(538\) | −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 | 0.593844 | − | 0.804581i | \(-0.297610\pi\) |
−0.993709 | + | 0.111993i | \(0.964276\pi\) | |||||||
\(542\) | 19.7839 | − | 5.30108i | 0.849792 | − | 0.227701i | ||||
\(543\) | 8.19615 | − | 2.19615i | 0.351731 | − | 0.0942459i | ||||
\(544\) | −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 | \(0.320118\pi\) | |||||||
\(548\) | −16.3414 | + | 60.9869i | −0.698069 | + | 2.60523i | ||||
\(549\) | −0.710320 | + | 1.23031i | −0.0303157 | + | 0.0525084i | ||||
\(550\) | −18.9794 | + | 3.24053i | −0.809284 | + | 0.138177i | ||||
\(551\) | −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 | ||||||||
\(555\) | −6.79687 | − | 2.16333i | −0.288511 | − | 0.0918281i | ||||
\(556\) | 51.1981 | + | 29.5593i | 2.17128 | + | 1.25359i | ||||
\(557\) | −0.204581 | − | 0.763508i | −0.00866839 | − | 0.0323509i | 0.961456 | − | 0.274958i | \(-0.0886640\pi\) |
−0.970125 | + | 0.242607i | \(0.921997\pi\) | |||||||
\(558\) | −15.5200 | − | 4.15856i | −0.657012 | − | 0.176046i | ||||
\(559\) | 9.20823 | 0.389467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.35697 | −0.183951 | ||||||||
\(562\) | −53.7853 | − | 14.4117i | −2.26879 | − | 0.607922i | ||||
\(563\) | −0.257124 | − | 0.959599i | −0.0108365 | − | 0.0404423i | 0.960296 | − | 0.278983i | \(-0.0899975\pi\) |
−0.971132 | + | 0.238541i | \(0.923331\pi\) | |||||||
\(564\) | −51.7494 | − | 29.8775i | −2.17904 | − | 1.25807i | ||||
\(565\) | 7.14717 | − | 3.69598i | 0.300684 | − | 0.155491i | ||||
\(566\) | − | 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 | \(-0.731980\pi\) |
0.313057 | + | 0.949734i | \(0.398647\pi\) | |||||||
\(570\) | −4.98340 | − | 22.7707i | −0.208732 | − | 0.953762i | ||||
\(571\) | 0.493342 | − | 0.854493i | 0.0206457 | − | 0.0357594i | −0.855518 | − | 0.517773i | \(-0.826761\pi\) |
0.876164 | + | 0.482014i | \(0.160094\pi\) | |||||||
\(572\) | −2.34362 | + | 8.74652i | −0.0979918 | + | 0.365710i | ||||
\(573\) | −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 | ||||
\(577\) | −14.1397 | + | 3.78872i | −0.588643 | + | 0.157726i | −0.540833 | − | 0.841130i | \(-0.681891\pi\) |
−0.0478100 | + | 0.998856i | \(0.515224\pi\) | |||||||
\(578\) | −20.6688 | + | 5.53819i | −0.859708 | + | 0.230358i | ||||
\(579\) | −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 | ||||
\(583\) | 0.291508 | − | 1.08792i | 0.0120730 | − | 0.0450572i | ||||
\(584\) | 37.1646 | − | 64.3710i | 1.53788 | − | 2.66369i | ||||
\(585\) | −2.36381 | − | 1.51494i | −0.0977317 | − | 0.0626352i | ||||
\(586\) | 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 | ||||||
\(590\) | 8.64256 | + | 16.7127i | 0.355809 | + | 0.688052i | ||||
\(591\) | −14.0590 | − | 8.11696i | −0.578310 | − | 0.333887i | ||||
\(592\) | −8.62419 | − | 32.1859i | −0.354452 | − | 1.32283i | ||||
\(593\) | 9.66895 | + | 2.59079i | 0.397056 | + | 0.106391i | 0.451821 | − | 0.892108i | \(-0.350774\pi\) |
−0.0547654 | + | 0.998499i | \(0.517441\pi\) | |||||||
\(594\) | −3.85081 | −0.158001 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.477365 | 0.0195536 | ||||||||
\(597\) | 19.4603 | + | 5.21437i | 0.796457 | + | 0.213410i | ||||
\(598\) | −4.99679 | − | 18.6483i | −0.204334 | − | 0.762585i | ||||
\(599\) | −6.18210 | − | 3.56924i | −0.252594 | − | 0.145835i | 0.368358 | − | 0.929684i | \(-0.379920\pi\) |
−0.620951 | + | 0.783849i | \(0.713254\pi\) | |||||||
\(600\) | 35.0423 | − | 16.1097i | 1.43060 | − | 0.657675i | ||||
\(601\) | 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 | ||||
\(605\) | 19.3540 | − | 4.23565i | 0.786854 | − | 0.172204i | ||||
\(606\) | 20.1941 | − | 34.9771i | 0.820328 | − | 1.42085i | ||||
\(607\) | 1.96330 | − | 7.32715i | 0.0796880 | − | 0.297400i | −0.914567 | − | 0.404434i | \(-0.867469\pi\) |
0.994255 | + | 0.107034i | \(0.0341353\pi\) | |||||||
\(608\) | 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 | ||||
\(612\) | 14.1842 | − | 3.80064i | 0.573362 | − | 0.153632i | ||||
\(613\) | 14.3280 | − | 3.83917i | 0.578701 | − | 0.155062i | 0.0424169 | − | 0.999100i | \(-0.486494\pi\) |
0.536284 | + | 0.844038i | \(0.319828\pi\) | |||||||
\(614\) | 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 | \(0.0594135\pi\) | |||||||
\(618\) | −8.00508 | + | 29.8754i | −0.322011 | + | 1.20176i | ||||
\(619\) | −6.03375 | + | 10.4508i | −0.242517 | + | 0.420052i | −0.961431 | − | 0.275048i | \(-0.911306\pi\) |
0.718914 | + | 0.695099i | \(0.244640\pi\) | |||||||
\(620\) | 65.7294 | − | 14.3850i | 2.63976 | − | 0.577714i | ||||
\(621\) | 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 | ||||||
\(625\) | 8.29516 | + | 23.5837i | 0.331806 | + | 0.943348i | ||||
\(626\) | 18.4559 | + | 10.6555i | 0.737647 | + | 0.425880i | ||||
\(627\) | −1.49920 | − | 5.59508i | −0.0598722 | − | 0.223446i | ||||
\(628\) | 11.0959 | + | 2.97313i | 0.442774 | + | 0.118641i | ||||
\(629\) | 9.50124 | 0.378839 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.4435 | 1.21194 | 0.605969 | − | 0.795488i | \(-0.292786\pi\) | ||||
0.605969 | + | 0.795488i | \(0.292786\pi\) | |||||||
\(632\) | −33.6796 | − | 9.02442i | −1.33970 | − | 0.358972i | ||||
\(633\) | 3.09707 | + | 11.5584i | 0.123098 | + | 0.459406i | ||||
\(634\) | −2.42643 | − | 1.40090i | −0.0963660 | − | 0.0556369i | ||||
\(635\) | −11.4175 | − | 22.0788i | −0.453090 | − | 0.876172i | ||||
\(636\) | 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 | ||||
\(640\) | 8.50426 | + | 5.45029i | 0.336160 | + | 0.215442i | ||||
\(641\) | −18.2964 | + | 31.6904i | −0.722666 | + | 1.25169i | 0.237262 | + | 0.971446i | \(0.423750\pi\) |
−0.959928 | + | 0.280248i | \(0.909583\pi\) | |||||||
\(642\) | 4.23027 | − | 15.7876i | 0.166955 | − | 0.623086i | ||||
\(643\) | 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 | ||||
\(647\) | −26.0881 | + | 6.99030i | −1.02563 | + | 0.274817i | −0.732147 | − | 0.681147i | \(-0.761481\pi\) |
−0.293484 | + | 0.955964i | \(0.594815\pi\) | |||||||
\(648\) | 7.45075 | − | 1.99642i | 0.292693 | − | 0.0784269i | ||||
\(649\) | 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 | ||||
\(653\) | 7.45625 | − | 27.8271i | 0.291786 | − | 1.08896i | −0.651951 | − | 0.758261i | \(-0.726049\pi\) |
0.943737 | − | 0.330698i | \(-0.107284\pi\) | |||||||
\(654\) | −9.80067 | + | 16.9753i | −0.383237 | + | 0.663785i | ||||
\(655\) | −2.95539 | − | 13.5041i | −0.115477 | − | 0.527650i | ||||
\(656\) | −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 | \(-0.210160\pi\) | |||||||
\(660\) | 14.3240 | − | 7.40730i | 0.557561 | − | 0.288329i | ||||
\(661\) | −41.7321 | − | 24.0940i | −1.62319 | − | 0.937149i | −0.986060 | − | 0.166392i | \(-0.946788\pi\) |
−0.637129 | − | 0.770757i | \(-0.719878\pi\) | |||||||
\(662\) | −10.7709 | − | 40.1974i | −0.418621 | − | 1.56231i | ||||
\(663\) | 3.61242 | + | 0.967945i | 0.140295 | + | 0.0375919i | ||||
\(664\) | 73.7201 | 2.86089 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.39746 | 0.325395 | ||||||||
\(667\) | 29.2567 | + | 7.83932i | 1.13283 | + | 0.303540i | ||||
\(668\) | −0.528748 | − | 1.97332i | −0.0204579 | − | 0.0763499i | ||||
\(669\) | 0.809446 | + | 0.467334i | 0.0312950 | + | 0.0180682i | ||||
\(670\) | −47.0414 | − | 14.9725i | −1.81737 | − | 0.578438i | ||||
\(671\) | − | 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 | ||||
\(675\) | 0.841520 | + | 4.92868i | 0.0323901 | + | 0.189705i | ||||
\(676\) | −28.1595 | + | 48.7738i | −1.08306 | + | 1.87591i | ||||
\(677\) | 0.563899 | − | 2.10450i | 0.0216724 | − | 0.0808825i | −0.954243 | − | 0.299033i | \(-0.903336\pi\) |
0.975915 | + | 0.218151i | \(0.0700025\pi\) | |||||||
\(678\) | −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 | ||||
\(682\) | 22.7024 | − | 6.08310i | 0.869321 | − | 0.232934i | ||||
\(683\) | −19.4186 | + | 5.20319i | −0.743030 | + | 0.199094i | −0.610424 | − | 0.792074i | \(-0.709001\pi\) |
−0.132606 | + | 0.991169i | \(0.542334\pi\) | |||||||
\(684\) | 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 | ||||
\(688\) | 19.8274 | − | 73.9968i | 0.755912 | − | 2.82110i | ||||
\(689\) | −0.483386 | + | 0.837249i | −0.0184155 | + | 0.0318967i | ||||
\(690\) | −18.5519 | + | 28.9471i | −0.706258 | + | 1.10200i | ||||
\(691\) | −8.91028 | + | 5.14435i | −0.338963 | + | 0.195700i | −0.659813 | − | 0.751429i | \(-0.729365\pi\) |
0.320850 | + | 0.947130i | \(0.396031\pi\) | |||||||
\(692\) | −17.0182 | − | 17.0182i | −0.646937 | − | 0.646937i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 74.7741i | − | 2.83838i | ||||||
\(695\) | 8.13225 | − | 25.5504i | 0.308474 | − | 0.969180i | ||||
\(696\) | 34.6415 | + | 20.0003i | 1.31308 | + | 0.758108i | ||||
\(697\) | −0.593570 | − | 2.21523i | −0.0224831 | − | 0.0839079i | ||||
\(698\) | −37.5478 | − | 10.0609i | −1.42121 | − | 0.380811i | ||||
\(699\) | 3.16979 | 0.119892 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.3183 | −1.67388 | −0.836939 | − | 0.547297i | \(-0.815657\pi\) | ||||
−0.836939 | + | 0.547297i | \(0.815657\pi\) | |||||||
\(702\) | 3.19276 | + | 0.855497i | 0.120503 | + | 0.0322887i | ||||
\(703\) | 3.26930 | + | 12.2012i | 0.123304 | + | 0.460176i | ||||
\(704\) | 13.7920 | + | 7.96284i | 0.519807 | + | 0.300111i | ||||
\(705\) | −8.21981 | + | 25.8255i | −0.309576 | + | 0.972643i | ||||
\(706\) | 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 | \(-0.661777\pi\) |
0.513243 | + | 0.858243i | \(0.328444\pi\) | |||||||
\(710\) | 24.2225 | − | 37.7951i | 0.909053 | − | 1.41842i | ||||
\(711\) | 2.26015 | − | 3.91469i | 0.0847621 | − | 0.146812i | ||||
\(712\) | −2.39553 | + | 8.94022i | −0.0897761 | + | 0.335049i | ||||
\(713\) | −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 | ||||
\(717\) | −20.6485 | + | 5.53276i | −0.771134 | + | 0.206625i | ||||
\(718\) | 26.7941 | − | 7.17947i | 0.999949 | − | 0.267935i | ||||
\(719\) | 0.00381028 | + | 0.00659960i | 0.000142099 | + | 0.000246124i | 0.866096 | − | 0.499877i | \(-0.166621\pi\) |
−0.865954 | + | 0.500123i | \(0.833288\pi\) | |||||||
\(720\) | −17.2638 | + | 15.7335i | −0.643385 | + | 0.586351i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.17902 | − | 6.17902i | 0.229959 | − | 0.229959i | ||||
\(723\) | −0.161537 | + | 0.602863i | −0.00600761 | + | 0.0224207i | ||||
\(724\) | 20.9167 | − | 36.2289i | 0.777365 | − | 1.34644i | ||||
\(725\) | −14.9870 | + | 21.1585i | −0.556604 | + | 0.785807i | ||||
\(726\) | −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 | ||||||||
\(730\) | −54.0512 | − | 17.2036i | −2.00052 | − | 0.636732i | ||||
\(731\) | 18.9173 | + | 10.9219i | 0.699680 | + | 0.403960i | ||||
\(732\) | 1.81275 | + | 6.76528i | 0.0670012 | + | 0.250052i | ||||
\(733\) | −32.9926 | − | 8.84033i | −1.21861 | − | 0.326525i | −0.408475 | − | 0.912770i | \(-0.633939\pi\) |
−0.810134 | + | 0.586244i | \(0.800606\pi\) | |||||||
\(734\) | 41.6632 | 1.53782 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −70.5085 | −2.59898 | ||||||||
\(737\) | −11.8496 | − | 3.17510i | −0.436486 | − | 0.116956i | ||||
\(738\) | −0.524613 | − | 1.95788i | −0.0193113 | − | 0.0720707i | ||||
\(739\) | −32.8676 | − | 18.9761i | −1.20905 | − | 0.698047i | −0.246500 | − | 0.969143i | \(-0.579281\pi\) |
−0.962552 | + | 0.271096i | \(0.912614\pi\) | |||||||
\(740\) | −31.2363 | + | 16.1531i | −1.14827 | + | 0.593799i | ||||
\(741\) | 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 | ||||
\(745\) | −0.0462878 | − | 0.211504i | −0.00169586 | − | 0.00774890i | ||||
\(746\) | 32.1562 | − | 55.6961i | 1.17732 | − | 2.03918i | ||||
\(747\) | −2.47358 | + | 9.23152i | −0.0905035 | + | 0.337764i | ||||
\(748\) | −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 | 0.865058 | − | 0.501673i | \(-0.167282\pi\) |
−0.866990 | + | 0.498326i | \(0.833948\pi\) | |||||||
\(752\) | −122.294 | + | 32.7686i | −4.45960 | + | 1.19495i | ||||
\(753\) | −15.7874 | + | 4.23022i | −0.575325 | + | 0.154158i | ||||
\(754\) | 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 | \(0.224243\pi\) | |||||||
\(758\) | 12.0078 | − | 44.8137i | 0.436143 | − | 1.62771i | ||||
\(759\) | −4.27193 | + | 7.39921i | −0.155061 | + | 0.268574i | ||||
\(760\) | −57.5041 | − | 36.8538i | −2.08589 | − | 1.33683i | ||||
\(761\) | 30.4082 | − | 17.5562i | 1.10230 | − | 0.636410i | 0.165472 | − | 0.986214i | \(-0.447085\pi\) |
0.936823 | + | 0.349804i | \(0.113752\pi\) | |||||||
\(762\) | 20.6922 | + | 20.6922i | 0.749599 | + | 0.749599i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 38.6238i | 1.39736i | ||||||||
\(765\) | −3.05931 | − | 5.91600i | −0.110610 | − | 0.213893i | ||||
\(766\) | 51.9891 | + | 30.0159i | 1.87844 | + | 1.08452i | ||||
\(767\) | −1.03872 | − | 3.87656i | −0.0375061 | − | 0.139975i | ||||
\(768\) | 9.54591 | + | 2.55782i | 0.344458 | + | 0.0922973i | ||||
\(769\) | −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 | ||||||||
\(772\) | −91.3338 | − | 24.4728i | −3.28717 | − | 0.880796i | ||||
\(773\) | 0.919332 | + | 3.43099i | 0.0330661 | + | 0.123404i | 0.980486 | − | 0.196588i | \(-0.0629862\pi\) |
−0.947420 | + | 0.319993i | \(0.896320\pi\) | |||||||
\(774\) | 16.7196 | + | 9.65306i | 0.600973 | + | 0.346972i | ||||
\(775\) | −12.7470 | − | 27.7276i | −0.457884 | − | 0.996005i | ||||
\(776\) | 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 | ||||
\(780\) | −13.5218 | + | 2.95927i | −0.484159 | + | 0.105959i | ||||
\(781\) | 5.57770 | − | 9.66085i | 0.199586 | − | 0.345693i | ||||
\(782\) | 11.8534 | − | 44.2374i | 0.423876 | − | 1.58193i | ||||
\(783\) | −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 | ||||
\(787\) | 17.3959 | − | 4.66123i | 0.620098 | − | 0.166155i | 0.0649257 | − | 0.997890i | \(-0.479319\pi\) |
0.555172 | + | 0.831735i | \(0.312652\pi\) | |||||||
\(788\) | −77.3081 | + | 20.7146i | −2.75399 | + | 0.737929i | ||||
\(789\) | 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 | ||||
\(793\) | −0.461671 | + | 1.72298i | −0.0163944 | + | 0.0611847i | ||||
\(794\) | −30.1150 | + | 52.1607i | −1.06874 | + | 1.85111i | ||||
\(795\) | 1.68189 | − | 0.368084i | 0.0596506 | − | 0.0130546i | ||||
\(796\) | 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 | ||||||
\(800\) | 20.9512 | − | 56.6057i | 0.740736 | − | 2.00131i | ||||
\(801\) | −1.03915 | − | 0.599954i | −0.0367166 | − | 0.0211983i | ||||
\(802\) | 0.666079 | + | 2.48584i | 0.0235201 | + | 0.0877781i | ||||
\(803\) | −13.6153 | − | 3.64822i | −0.480475 | − | 0.128743i | ||||
\(804\) | 41.3463 | 1.45817 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.1743 | −0.710609 | ||||||||
\(807\) | −16.0250 | − | 4.29389i | −0.564107 | − | 0.151152i | ||||
\(808\) | −30.6292 | − | 114.310i | −1.07753 | − | 4.02140i | ||||
\(809\) | −24.0937 | − | 13.9105i | −0.847090 | − | 0.489067i | 0.0125781 | − | 0.999921i | \(-0.495996\pi\) |
−0.859668 | + | 0.510853i | \(0.829329\pi\) | |||||||
\(810\) | −2.70390 | − | 5.22872i | −0.0950054 | − | 0.183719i | ||||
\(811\) | − | 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 | ||||
\(815\) | 27.3554 | + | 17.5318i | 0.958217 | + | 0.614111i | ||||
\(816\) | 15.5567 | − | 26.9450i | 0.544594 | − | 0.943264i | ||||
\(817\) | −7.51626 | + | 28.0510i | −0.262961 | + | 0.981382i | ||||
\(818\) | 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 | 0.998754 | − | 0.0499094i | \(-0.0158933\pi\) |
−0.542600 | + | 0.839991i | \(0.682560\pi\) | |||||||
\(822\) | −32.5648 | + | 8.72572i | −1.13583 | + | 0.304345i | ||||
\(823\) | −18.7550 | + | 5.02538i | −0.653757 | + | 0.175174i | −0.570427 | − | 0.821348i | \(-0.693222\pi\) |
−0.0833299 | + | 0.996522i | \(0.526556\pi\) | |||||||
\(824\) | 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 | \(0.123432\pi\) | |||||||
\(828\) | 7.45292 | − | 27.8147i | 0.259007 | − | 0.966627i | ||||
\(829\) | 23.6498 | − | 40.9627i | 0.821392 | − | 1.42269i | −0.0832545 | − | 0.996528i | \(-0.526531\pi\) |
0.904646 | − | 0.426164i | \(-0.140135\pi\) | |||||||
\(830\) | −12.0275 | − | 54.9574i | −0.417480 | − | 1.90760i | ||||
\(831\) | −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 | ||||||||
\(835\) | −0.823038 | + | 0.425614i | −0.0284824 | + | 0.0147290i | ||||
\(836\) | −24.7315 | − | 14.2788i | −0.855358 | − | 0.493841i | ||||
\(837\) | −1.57969 | − | 5.89549i | −0.0546021 | − | 0.203778i | ||||
\(838\) | −40.6577 | − | 10.8942i | −1.40450 | − | 0.376334i | ||||
\(839\) | −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 | ||||||||
\(842\) | 37.3793 | + | 10.0157i | 1.28817 | + | 0.345165i | ||||
\(843\) | −5.47451 | − | 20.4312i | −0.188552 | − | 0.703686i | ||||
\(844\) | 51.0909 | + | 29.4973i | 1.75862 | + | 1.01534i | ||||
\(845\) | 24.3405 | + | 7.74716i | 0.837338 | + | 0.266511i | ||||
\(846\) | − | 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 | ||||
\(850\) | 31.9926 | + | 22.6610i | 1.09734 | + | 0.777267i | ||||
\(851\) | 9.31580 | − | 16.1354i | 0.319341 | − | 0.553116i | ||||
\(852\) | −9.73099 | + | 36.3166i | −0.333378 | + | 1.24418i | ||||
\(853\) | −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 | ||||
\(857\) | 12.1915 | − | 3.26670i | 0.416454 | − | 0.111588i | −0.0445069 | − | 0.999009i | \(-0.514172\pi\) |
0.460960 | + | 0.887421i | \(0.347505\pi\) | |||||||
\(858\) | −4.67033 | + | 1.25141i | −0.159443 | + | 0.0427225i | ||||
\(859\) | 10.1851 | + | 17.6410i | 0.347510 | + | 0.601905i | 0.985806 | − | 0.167886i | \(-0.0536940\pi\) |
−0.638297 | + | 0.769791i | \(0.720361\pi\) | |||||||
\(860\) | −80.7608 | − | 3.74556i | −2.75392 | − | 0.127723i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41.4589 | + | 41.4589i | −1.41210 | + | 1.41210i | ||||
\(863\) | −5.45430 | + | 20.3557i | −0.185666 | + | 0.692917i | 0.808820 | + | 0.588056i | \(0.200106\pi\) |
−0.994487 | + | 0.104861i | \(0.966560\pi\) | |||||||
\(864\) | 6.03586 | − | 10.4544i | 0.205344 | − | 0.355666i | ||||
\(865\) | −5.89002 | + | 9.19038i | −0.200267 | + | 0.312482i | ||||
\(866\) | 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 | ||||||||
\(870\) | 9.25816 | − | 29.0878i | 0.313881 | − | 0.986170i | ||||
\(871\) | 9.11929 | + | 5.26503i | 0.308995 | + | 0.178399i | ||||
\(872\) | 14.8651 | + | 55.4773i | 0.503396 | + | 1.87870i | ||||
\(873\) | −11.8684 | − | 3.18013i | −0.401685 | − | 0.107631i | ||||
\(874\) | 60.8869 | 2.05953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 47.5074 | 1.60512 | ||||||||
\(877\) | −32.0516 | − | 8.58820i | −1.08231 | − | 0.290003i | −0.326765 | − | 0.945105i | \(-0.605959\pi\) |
−0.755540 | + | 0.655103i | \(0.772625\pi\) | |||||||
\(878\) | −1.60563 | − | 5.99230i | −0.0541874 | − | 0.202230i | ||||
\(879\) | 1.91935 | + | 1.10814i | 0.0647381 | + | 0.0373766i | ||||
\(880\) | 10.3627 | − | 32.5580i | 0.349325 | − | 1.09753i | ||||
\(881\) | − | 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 | ||||
\(885\) | −3.85653 | + | 6.01746i | −0.129636 | + | 0.202275i | ||||
\(886\) | −10.1868 | + | 17.6441i | −0.342233 | + | 0.592765i | ||||
\(887\) | 7.04416 | − | 26.2892i | 0.236520 | − | 0.882704i | −0.740938 | − | 0.671574i | \(-0.765619\pi\) |
0.977458 | − | 0.211131i | \(-0.0677146\pi\) | |||||||
\(888\) | 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 | ||||
\(892\) | 4.45101 | − | 1.19265i | 0.149031 | − | 0.0399327i | ||||
\(893\) | 46.3598 | − | 12.4221i | 1.55137 | − | 0.415689i | ||||
\(894\) | 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 | ||||
\(898\) | −0.817751 | + | 3.05189i | −0.0272887 | + | 0.101843i | ||||
\(899\) | 15.8254 | − | 27.4104i | 0.527808 | − | 0.914190i | ||||
\(900\) | 20.1156 | + | 14.2483i | 0.670521 | + | 0.474944i | ||||
\(901\) | −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 | ||||||||
\(905\) | −18.0800 | − | 5.75455i | −0.600998 | − | 0.191288i | ||||
\(906\) | 30.6749 | + | 17.7102i | 1.01911 | + | 0.588381i | ||||
\(907\) | −5.44798 | − | 20.3321i | −0.180897 | − | 0.675117i | −0.995472 | − | 0.0950584i | \(-0.969696\pi\) |
0.814575 | − | 0.580059i | \(-0.196970\pi\) | |||||||
\(908\) | −116.838 | − | 31.3066i | −3.87740 | − | 1.03895i | ||||
\(909\) | 15.3420 | 0.508863 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.7484 | −0.786819 | −0.393410 | − | 0.919363i | \(-0.628705\pi\) | ||||
−0.393410 | + | 0.919363i | \(0.628705\pi\) | |||||||
\(912\) | 39.9548 | + | 10.7059i | 1.32304 | + | 0.354507i | ||||
\(913\) | −3.61832 | − | 13.5038i | −0.119749 | − | 0.446910i | ||||
\(914\) | 67.9570 | + | 39.2350i | 2.24782 | + | 1.29778i | ||||
\(915\) | 2.82169 | − | 1.45917i | 0.0932822 | − | 0.0482385i | ||||
\(916\) | − | 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 | \(-0.465809\pi\) |
0.914638 | + | 0.404273i | \(0.132475\pi\) | |||||||
\(920\) | 21.5379 | + | 98.4136i | 0.710084 | + | 3.24460i | ||||
\(921\) | −12.2719 | + | 21.2556i | −0.404374 | + | 0.700396i | ||||
\(922\) | 14.9671 | − | 55.8580i | 0.492915 | − | 1.83958i | ||||
\(923\) | −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 | ||||
\(927\) | −11.3486 | + | 3.04085i | −0.372737 | + | 0.0998746i | ||||
\(928\) | 60.4675 | − | 16.2022i | 1.98494 | − | 0.531864i | ||||
\(929\) | −2.79468 | − | 4.84053i | −0.0916905 | − | 0.158813i | 0.816532 | − | 0.577300i | \(-0.195894\pi\) |
−0.908223 | + | 0.418487i | \(0.862560\pi\) | |||||||
\(930\) | 24.2006 | + | 26.5545i | 0.793569 | + | 0.870758i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11.0503 | − | 11.0503i | 0.361963 | − | 0.361963i | ||||
\(933\) | 8.04017 | − | 30.0063i | 0.263223 | − | 0.982363i | ||||
\(934\) | −13.2406 | + | 22.9334i | −0.433246 | + | 0.750404i | ||||
\(935\) | 8.20250 | + | 5.25690i | 0.268250 | + | 0.171919i | ||||
\(936\) | 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 | ||||||||
\(940\) | 61.3755 | + | 118.686i | 2.00185 | + | 3.87111i | ||||
\(941\) | 14.8214 | + | 8.55714i | 0.483164 | + | 0.278955i | 0.721734 | − | 0.692170i | \(-0.243345\pi\) |
−0.238570 | + | 0.971125i | \(0.576679\pi\) | |||||||
\(942\) | 1.58755 | + | 5.92481i | 0.0517251 | + | 0.193041i | ||||
\(943\) | −4.34399 | − | 1.16397i | −0.141460 | − | 0.0379040i | ||||
\(944\) | −33.3884 | −1.08670 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.2408 | −0.918187 | ||||||||
\(947\) | −9.31836 | − | 2.49685i | −0.302806 | − | 0.0811366i | 0.104217 | − | 0.994555i | \(-0.466766\pi\) |
−0.407023 | + | 0.913418i | \(0.633433\pi\) | |||||||
\(948\) | −5.76794 | − | 21.5262i | −0.187334 | − | 0.699140i | ||||
\(949\) | 10.4782 | + | 6.04957i | 0.340136 | + | 0.196378i | ||||
\(950\) | −18.0922 | + | 48.8813i | −0.586988 | + | 1.58592i | ||||
\(951\) | − | 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 | ||||
\(955\) | 17.1129 | − | 3.74517i | 0.553759 | − | 0.121191i | ||||
\(956\) | −52.6955 | + | 91.2712i | −1.70429 | + | 2.95192i | ||||
\(957\) | 1.96330 | − | 7.32715i | 0.0634646 | − | 0.236853i | ||||
\(958\) | 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 | ||||
\(962\) | 10.1846 | − | 2.72895i | 0.328364 | − | 0.0879849i | ||||
\(963\) | 5.99715 | − | 1.60693i | 0.193255 | − | 0.0517826i | ||||
\(964\) | 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 | \(0.0604012\pi\) | |||||||
\(968\) | −17.6888 | + | 66.0155i | −0.568540 | + | 2.12182i | ||||
\(969\) | −5.89731 | + | 10.2144i | −0.189449 | + | 0.328135i | ||||
\(970\) | 70.6555 | − | 15.4630i | 2.26861 | − | 0.496488i | ||||
\(971\) | −18.3615 | + | 10.6010i | −0.589247 | + | 0.340202i | −0.764800 | − | 0.644268i | \(-0.777162\pi\) |
0.175552 | + | 0.984470i | \(0.443829\pi\) | |||||||
\(972\) | 3.48612 | + | 3.48612i | 0.111817 | + | 0.111817i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 17.9232i | − | 0.574297i | ||||||
\(975\) | 2.62230 | + | 5.70411i | 0.0839808 | + | 0.182678i | ||||
\(976\) | 12.8517 | + | 7.41991i | 0.411372 | + | 0.237506i | ||||
\(977\) | 3.00015 | + | 11.1967i | 0.0959834 | + | 0.358215i | 0.997167 | − | 0.0752233i | \(-0.0239670\pi\) |
−0.901183 | + | 0.433438i | \(0.857300\pi\) | |||||||
\(978\) | −36.9484 | − | 9.90028i | −1.18148 | − | 0.316576i | ||||
\(979\) | 1.75521 | 0.0560969 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.44587 | −0.237728 | ||||||||
\(982\) | 72.0634 | + | 19.3093i | 2.29964 | + | 0.616186i | ||||
\(983\) | 0.640231 | + | 2.38938i | 0.0204202 | + | 0.0762093i | 0.975384 | − | 0.220513i | \(-0.0707731\pi\) |
−0.954964 | + | 0.296722i | \(0.904106\pi\) | |||||||
\(984\) | −5.14351 | − | 2.96961i | −0.163969 | − | 0.0946676i | ||||
\(985\) | 16.6742 | + | 32.2440i | 0.531283 | + | 1.02738i | ||||
\(986\) | 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 | ||||
\(990\) | 7.24960 | + | 4.64619i | 0.230407 | + | 0.147666i | ||||
\(991\) | 18.5627 | − | 32.1515i | 0.589662 | − | 1.02133i | −0.404614 | − | 0.914488i | \(-0.632594\pi\) |
0.994276 | − | 0.106838i | \(-0.0340725\pi\) | |||||||
\(992\) | −19.0696 | + | 71.1687i | −0.605460 | + | 2.25961i | ||||
\(993\) | 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 | ||||
\(997\) | −55.3975 | + | 14.8437i | −1.75446 | + | 0.470106i | −0.985569 | − | 0.169277i | \(-0.945857\pi\) |
−0.768889 | + | 0.639382i | \(0.779190\pi\) | |||||||
\(998\) | −8.62515 | + | 2.31110i | −0.273024 | + | 0.0731566i | ||||
\(999\) | 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.178.8 | 32 | ||
5.2 | odd | 4 | inner | 735.2.v.a.472.2 | 32 | ||
7.2 | even | 3 | inner | 735.2.v.a.313.1 | 32 | ||
7.3 | odd | 6 | 105.2.m.a.13.1 | ✓ | 16 | ||
7.4 | even | 3 | 105.2.m.a.13.2 | yes | 16 | ||
7.5 | odd | 6 | inner | 735.2.v.a.313.2 | 32 | ||
7.6 | odd | 2 | inner | 735.2.v.a.178.7 | 32 | ||
21.11 | odd | 6 | 315.2.p.e.118.7 | 16 | |||
21.17 | even | 6 | 315.2.p.e.118.8 | 16 | |||
28.3 | even | 6 | 1680.2.cz.d.433.6 | 16 | |||
28.11 | odd | 6 | 1680.2.cz.d.433.3 | 16 | |||
35.2 | odd | 12 | inner | 735.2.v.a.607.7 | 32 | ||
35.3 | even | 12 | 525.2.m.b.307.7 | 16 | |||
35.4 | even | 6 | 525.2.m.b.118.7 | 16 | |||
35.12 | even | 12 | inner | 735.2.v.a.607.8 | 32 | ||
35.17 | even | 12 | 105.2.m.a.97.2 | yes | 16 | ||
35.18 | odd | 12 | 525.2.m.b.307.8 | 16 | |||
35.24 | odd | 6 | 525.2.m.b.118.8 | 16 | |||
35.27 | even | 4 | inner | 735.2.v.a.472.1 | 32 | ||
35.32 | odd | 12 | 105.2.m.a.97.1 | yes | 16 | ||
105.17 | odd | 12 | 315.2.p.e.307.7 | 16 | |||
105.32 | even | 12 | 315.2.p.e.307.8 | 16 | |||
140.67 | even | 12 | 1680.2.cz.d.97.6 | 16 | |||
140.87 | odd | 12 | 1680.2.cz.d.97.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.1 | ✓ | 16 | 7.3 | odd | 6 | ||
105.2.m.a.13.2 | yes | 16 | 7.4 | even | 3 | ||
105.2.m.a.97.1 | yes | 16 | 35.32 | odd | 12 | ||
105.2.m.a.97.2 | yes | 16 | 35.17 | even | 12 | ||
315.2.p.e.118.7 | 16 | 21.11 | odd | 6 | |||
315.2.p.e.118.8 | 16 | 21.17 | even | 6 | |||
315.2.p.e.307.7 | 16 | 105.17 | odd | 12 | |||
315.2.p.e.307.8 | 16 | 105.32 | even | 12 | |||
525.2.m.b.118.7 | 16 | 35.4 | even | 6 | |||
525.2.m.b.118.8 | 16 | 35.24 | odd | 6 | |||
525.2.m.b.307.7 | 16 | 35.3 | even | 12 | |||
525.2.m.b.307.8 | 16 | 35.18 | odd | 12 | |||
735.2.v.a.178.7 | 32 | 7.6 | odd | 2 | inner | ||
735.2.v.a.178.8 | 32 | 1.1 | even | 1 | trivial | ||
735.2.v.a.313.1 | 32 | 7.2 | even | 3 | inner | ||
735.2.v.a.313.2 | 32 | 7.5 | odd | 6 | inner | ||
735.2.v.a.472.1 | 32 | 35.27 | even | 4 | inner | ||
735.2.v.a.472.2 | 32 | 5.2 | odd | 4 | inner | ||
735.2.v.a.607.7 | 32 | 35.2 | odd | 12 | inner | ||
735.2.v.a.607.8 | 32 | 35.12 | even | 12 | inner | ||
1680.2.cz.d.97.3 | 16 | 140.87 | odd | 12 | |||
1680.2.cz.d.97.6 | 16 | 140.67 | even | 12 | |||
1680.2.cz.d.433.3 | 16 | 28.11 | odd | 6 | |||
1680.2.cz.d.433.6 | 16 | 28.3 | even | 6 |