Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [195,2,Mod(4,195)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(195, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("195.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 195.v (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.55708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 4.10 | ||
Character | \(\chi\) | \(=\) | 195.4 |
Dual form | 195.2.v.a.49.10 |
$q$-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 \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).
\(n\) | \(106\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.296043 | − | 0.512762i | 0.209334 | − | 0.362577i | −0.742171 | − | 0.670211i | \(-0.766204\pi\) |
0.951505 | + | 0.307633i | \(0.0995371\pi\) | |||||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.824717 | + | 1.42845i | 0.412359 | + | 0.714226i | ||||
\(5\) | −0.903471 | + | 2.04542i | −0.404045 | + | 0.914739i | ||||
\(6\) | −0.512762 | + | 0.296043i | −0.209334 | + | 0.120859i | ||||
\(7\) | 0.828705 | + | 1.43536i | 0.313221 | + | 0.542515i | 0.979058 | − | 0.203583i | \(-0.0652586\pi\) |
−0.665837 | + | 0.746097i | \(0.731925\pi\) | |||||||
\(8\) | 2.16078 | 0.763951 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0.781346 | + | 1.06880i | 0.247083 | + | 0.337983i | ||||
\(11\) | −1.22336 | − | 0.706307i | −0.368857 | − | 0.212960i | 0.304102 | − | 0.952639i | \(-0.401644\pi\) |
−0.672959 | + | 0.739680i | \(0.734977\pi\) | |||||||
\(12\) | − | 1.64943i | − | 0.476151i | ||||||
\(13\) | 0.0145731 | + | 3.60552i | 0.00404184 | + | 0.999992i | ||||
\(14\) | 0.981329 | 0.262271 | ||||||||
\(15\) | 1.80514 | − | 1.31965i | 0.466085 | − | 0.340732i | ||||
\(16\) | −1.00975 | + | 1.74894i | −0.252438 | + | 0.437235i | ||||
\(17\) | 2.83926 | − | 1.63925i | 0.688623 | − | 0.397577i | −0.114473 | − | 0.993426i | \(-0.536518\pi\) |
0.803096 | + | 0.595850i | \(0.203185\pi\) | |||||||
\(18\) | 0.592086 | 0.139556 | ||||||||
\(19\) | 7.29219 | − | 4.21015i | 1.67294 | − | 0.965875i | 0.706967 | − | 0.707247i | \(-0.250063\pi\) |
0.965977 | − | 0.258628i | \(-0.0832703\pi\) | |||||||
\(20\) | −3.66689 | + | 0.396326i | −0.819942 | + | 0.0886213i | ||||
\(21\) | − | 1.65741i | − | 0.361676i | ||||||
\(22\) | −0.724334 | + | 0.418195i | −0.154429 | + | 0.0891594i | ||||
\(23\) | −5.70016 | − | 3.29099i | −1.18857 | − | 0.686219i | −0.230585 | − | 0.973052i | \(-0.574064\pi\) |
−0.957980 | + | 0.286834i | \(0.907397\pi\) | |||||||
\(24\) | −1.87129 | − | 1.08039i | −0.381975 | − | 0.220534i | ||||
\(25\) | −3.36748 | − | 3.69596i | −0.673496 | − | 0.739191i | ||||
\(26\) | 1.85309 | + | 1.05992i | 0.363420 | + | 0.207867i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −1.36689 | + | 2.36753i | −0.258319 | + | 0.447421i | ||||
\(29\) | 0.252903 | − | 0.438041i | 0.0469629 | − | 0.0813422i | −0.841588 | − | 0.540119i | \(-0.818379\pi\) |
0.888551 | + | 0.458777i | \(0.151712\pi\) | |||||||
\(30\) | −0.142267 | − | 1.31628i | −0.0259742 | − | 0.240319i | ||||
\(31\) | 0.791382i | 0.142136i | 0.997471 | + | 0.0710682i | \(0.0226408\pi\) | ||||
−0.997471 | + | 0.0710682i | \(0.977359\pi\) | |||||||
\(32\) | 2.75864 | + | 4.77810i | 0.487663 | + | 0.844657i | ||||
\(33\) | 0.706307 | + | 1.22336i | 0.122952 | + | 0.212960i | ||||
\(34\) | − | 1.94115i | − | 0.332905i | ||||||
\(35\) | −3.68462 | + | 0.398243i | −0.622815 | + | 0.0673153i | ||||
\(36\) | −0.824717 | + | 1.42845i | −0.137453 | + | 0.238075i | ||||
\(37\) | −2.37878 | + | 4.12017i | −0.391069 | + | 0.677352i | −0.992591 | − | 0.121504i | \(-0.961228\pi\) |
0.601521 | + | 0.798857i | \(0.294561\pi\) | |||||||
\(38\) | − | 4.98554i | − | 0.808762i | ||||||
\(39\) | 1.79014 | − | 3.12976i | 0.286652 | − | 0.501163i | ||||
\(40\) | −1.95220 | + | 4.41970i | −0.308670 | + | 0.698816i | ||||
\(41\) | −7.67224 | − | 4.42957i | −1.19820 | − | 0.691782i | −0.238048 | − | 0.971253i | \(-0.576508\pi\) |
−0.960154 | + | 0.279471i | \(0.909841\pi\) | |||||||
\(42\) | −0.849856 | − | 0.490665i | −0.131136 | − | 0.0757112i | ||||
\(43\) | −1.93289 | + | 1.11596i | −0.294764 | + | 0.170182i | −0.640088 | − | 0.768301i | \(-0.721102\pi\) |
0.345325 | + | 0.938483i | \(0.387769\pi\) | |||||||
\(44\) | − | 2.33001i | − | 0.351263i | ||||||
\(45\) | −2.22312 | + | 0.240280i | −0.331403 | + | 0.0358189i | ||||
\(46\) | −3.37499 | + | 1.94855i | −0.497614 | + | 0.287298i | ||||
\(47\) | 3.43727 | 0.501377 | 0.250688 | − | 0.968068i | \(-0.419343\pi\) | ||||
0.250688 | + | 0.968068i | \(0.419343\pi\) | |||||||
\(48\) | 1.74894 | − | 1.00975i | 0.252438 | − | 0.145745i | ||||
\(49\) | 2.12650 | − | 3.68320i | 0.303785 | − | 0.526172i | ||||
\(50\) | −2.89206 | + | 0.632552i | −0.408999 | + | 0.0894563i | ||||
\(51\) | −3.27850 | −0.459082 | ||||||||
\(52\) | −5.13830 | + | 2.99435i | −0.712553 | + | 0.415242i | ||||
\(53\) | − | 0.422128i | − | 0.0579838i | −0.999580 | − | 0.0289919i | \(-0.990770\pi\) | ||
0.999580 | − | 0.0289919i | \(-0.00922970\pi\) | |||||||
\(54\) | −0.512762 | − | 0.296043i | −0.0697780 | − | 0.0402864i | ||||
\(55\) | 2.54996 | − | 1.86416i | 0.343837 | − | 0.251363i | ||||
\(56\) | 1.79065 | + | 3.10149i | 0.239285 | + | 0.414454i | ||||
\(57\) | −8.42030 | −1.11530 | ||||||||
\(58\) | −0.149740 | − | 0.259358i | −0.0196619 | − | 0.0340554i | ||||
\(59\) | 11.3443 | − | 6.54963i | 1.47690 | − | 0.852689i | 0.477241 | − | 0.878772i | \(-0.341637\pi\) |
0.999660 | + | 0.0260834i | \(0.00830355\pi\) | |||||||
\(60\) | 3.37378 | + | 1.49022i | 0.435554 | + | 0.192386i | ||||
\(61\) | −0.463750 | − | 0.803239i | −0.0593771 | − | 0.102844i | 0.834809 | − | 0.550540i | \(-0.185578\pi\) |
−0.894186 | + | 0.447696i | \(0.852245\pi\) | |||||||
\(62\) | 0.405790 | + | 0.234283i | 0.0515354 | + | 0.0297540i | ||||
\(63\) | −0.828705 | + | 1.43536i | −0.104407 | + | 0.180838i | ||||
\(64\) | −0.772299 | −0.0965374 | ||||||||
\(65\) | −7.38797 | − | 3.22768i | −0.916365 | − | 0.400344i | ||||
\(66\) | 0.836389 | 0.102952 | ||||||||
\(67\) | 6.21154 | − | 10.7587i | 0.758861 | − | 1.31439i | −0.184571 | − | 0.982819i | \(-0.559090\pi\) |
0.943432 | − | 0.331567i | \(-0.107577\pi\) | |||||||
\(68\) | 4.68318 | + | 2.70384i | 0.567919 | + | 0.327888i | ||||
\(69\) | 3.29099 | + | 5.70016i | 0.396188 | + | 0.686219i | ||||
\(70\) | −0.886603 | + | 2.00723i | −0.105969 | + | 0.239910i | ||||
\(71\) | 0.947838 | − | 0.547235i | 0.112488 | − | 0.0649448i | −0.442701 | − | 0.896670i | \(-0.645980\pi\) |
0.555188 | + | 0.831725i | \(0.312646\pi\) | |||||||
\(72\) | 1.08039 | + | 1.87129i | 0.127325 | + | 0.220534i | ||||
\(73\) | 11.2130 | 1.31239 | 0.656193 | − | 0.754593i | \(-0.272166\pi\) | ||||
0.656193 | + | 0.754593i | \(0.272166\pi\) | |||||||
\(74\) | 1.40844 | + | 2.43950i | 0.163728 | + | 0.283586i | ||||
\(75\) | 1.06834 | + | 4.88453i | 0.123362 | + | 0.564017i | ||||
\(76\) | 12.0280 | + | 6.94436i | 1.37971 | + | 0.796573i | ||||
\(77\) | − | 2.34128i | − | 0.266814i | ||||||
\(78\) | −1.07486 | − | 1.84446i | −0.121704 | − | 0.208844i | ||||
\(79\) | −9.25299 | −1.04104 | −0.520522 | − | 0.853849i | \(-0.674262\pi\) | ||||
−0.520522 | + | 0.853849i | \(0.674262\pi\) | |||||||
\(80\) | −2.66503 | − | 3.64548i | −0.297960 | − | 0.407577i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −4.54263 | + | 2.62269i | −0.501649 | + | 0.289627i | ||||
\(83\) | 4.02601 | 0.441912 | 0.220956 | − | 0.975284i | \(-0.429082\pi\) | ||||
0.220956 | + | 0.975284i | \(0.429082\pi\) | |||||||
\(84\) | 2.36753 | − | 1.36689i | 0.258319 | − | 0.149140i | ||||
\(85\) | 0.787759 | + | 7.28850i | 0.0854445 | + | 0.790549i | ||||
\(86\) | 1.32149i | 0.142499i | ||||||||
\(87\) | −0.438041 | + | 0.252903i | −0.0469629 | + | 0.0271141i | ||||
\(88\) | −2.64341 | − | 1.52617i | −0.281789 | − | 0.162691i | ||||
\(89\) | −0.517890 | − | 0.299004i | −0.0548962 | − | 0.0316943i | 0.472301 | − | 0.881437i | \(-0.343424\pi\) |
−0.527197 | + | 0.849743i | \(0.676757\pi\) | |||||||
\(90\) | −0.534933 | + | 1.21106i | −0.0563869 | + | 0.127657i | ||||
\(91\) | −5.16314 | + | 3.00883i | −0.541244 | + | 0.315411i | ||||
\(92\) | − | 10.8565i | − | 1.13187i | ||||||
\(93\) | 0.395691 | − | 0.685357i | 0.0410312 | − | 0.0710682i | ||||
\(94\) | 1.01758 | − | 1.76250i | 0.104955 | − | 0.181788i | ||||
\(95\) | 2.02323 | + | 18.7193i | 0.207579 | + | 1.92056i | ||||
\(96\) | − | 5.51728i | − | 0.563105i | ||||||
\(97\) | −1.57968 | − | 2.73609i | −0.160392 | − | 0.277808i | 0.774617 | − | 0.632431i | \(-0.217943\pi\) |
−0.935009 | + | 0.354623i | \(0.884609\pi\) | |||||||
\(98\) | −1.25907 | − | 2.18077i | −0.127185 | − | 0.220291i | ||||
\(99\) | − | 1.41261i | − | 0.141973i | ||||||
\(100\) | 2.50228 | − | 7.85840i | 0.250228 | − | 0.785840i | ||||
\(101\) | −4.47142 | + | 7.74473i | −0.444923 | + | 0.770629i | −0.998047 | − | 0.0624697i | \(-0.980102\pi\) |
0.553124 | + | 0.833099i | \(0.313436\pi\) | |||||||
\(102\) | −0.970577 | + | 1.68109i | −0.0961015 | + | 0.166453i | ||||
\(103\) | − | 15.0296i | − | 1.48091i | −0.672103 | − | 0.740457i | \(-0.734609\pi\) | ||
0.672103 | − | 0.740457i | \(-0.265391\pi\) | |||||||
\(104\) | 0.0314892 | + | 7.79074i | 0.00308777 | + | 0.763945i | ||||
\(105\) | 3.39010 | + | 1.49742i | 0.330840 | + | 0.146133i | ||||
\(106\) | −0.216451 | − | 0.124968i | −0.0210236 | − | 0.0121380i | ||||
\(107\) | 16.3559 | + | 9.44308i | 1.58118 | + | 0.912897i | 0.994687 | + | 0.102946i | \(0.0328270\pi\) |
0.586498 | + | 0.809951i | \(0.300506\pi\) | |||||||
\(108\) | 1.42845 | − | 0.824717i | 0.137453 | − | 0.0793584i | ||||
\(109\) | 6.71317i | 0.643005i | 0.946909 | + | 0.321502i | \(0.104188\pi\) | ||||
−0.946909 | + | 0.321502i | \(0.895812\pi\) | |||||||
\(110\) | −0.200968 | − | 1.85939i | −0.0191615 | − | 0.177286i | ||||
\(111\) | 4.12017 | − | 2.37878i | 0.391069 | − | 0.225784i | ||||
\(112\) | −3.34714 | −0.316275 | ||||||||
\(113\) | −16.9895 | + | 9.80892i | −1.59824 | + | 0.922745i | −0.606416 | + | 0.795148i | \(0.707393\pi\) |
−0.991826 | + | 0.127598i | \(0.959273\pi\) | |||||||
\(114\) | −2.49277 | + | 4.31761i | −0.233469 | + | 0.404381i | ||||
\(115\) | 11.8814 | − | 8.68590i | 1.10794 | − | 0.809964i | ||||
\(116\) | 0.834294 | 0.0774623 | ||||||||
\(117\) | −3.11519 | + | 1.81538i | −0.287999 | + | 0.167832i | ||||
\(118\) | − | 7.75589i | − | 0.713987i | ||||||
\(119\) | 4.70582 | + | 2.71691i | 0.431382 | + | 0.249059i | ||||
\(120\) | 3.90051 | − | 2.85147i | 0.356066 | − | 0.260302i | ||||
\(121\) | −4.50226 | − | 7.79814i | −0.409296 | − | 0.708922i | ||||
\(122\) | −0.549160 | −0.0497186 | ||||||||
\(123\) | 4.42957 | + | 7.67224i | 0.399401 | + | 0.691782i | ||||
\(124\) | −1.13045 | + | 0.652666i | −0.101518 | + | 0.0586112i | ||||
\(125\) | 10.6022 | − | 3.54871i | 0.948290 | − | 0.317407i | ||||
\(126\) | 0.490665 | + | 0.849856i | 0.0437119 | + | 0.0757112i | ||||
\(127\) | −14.2398 | − | 8.22136i | −1.26358 | − | 0.729527i | −0.289813 | − | 0.957083i | \(-0.593593\pi\) |
−0.973765 | + | 0.227556i | \(0.926927\pi\) | |||||||
\(128\) | −5.74591 | + | 9.95221i | −0.507872 | + | 0.879659i | ||||
\(129\) | 2.23191 | 0.196509 | ||||||||
\(130\) | −3.84219 | + | 2.83274i | −0.336982 | + | 0.248447i | ||||
\(131\) | 6.11561 | 0.534323 | 0.267162 | − | 0.963652i | \(-0.413914\pi\) | ||||
0.267162 | + | 0.963652i | \(0.413914\pi\) | |||||||
\(132\) | −1.16501 | + | 2.01785i | −0.101401 | + | 0.175631i | ||||
\(133\) | 12.0861 | + | 6.97794i | 1.04800 | + | 0.605064i | ||||
\(134\) | −3.67777 | − | 6.37008i | −0.317711 | − | 0.550291i | ||||
\(135\) | 2.04542 | + | 0.903471i | 0.176042 | + | 0.0777584i | ||||
\(136\) | 6.13502 | − | 3.54206i | 0.526074 | − | 0.303729i | ||||
\(137\) | 6.47453 | + | 11.2142i | 0.553156 | + | 0.958095i | 0.998044 | + | 0.0625088i | \(0.0199101\pi\) |
−0.444888 | + | 0.895586i | \(0.646757\pi\) | |||||||
\(138\) | 3.89710 | 0.331743 | ||||||||
\(139\) | 5.62458 | + | 9.74205i | 0.477070 | + | 0.826310i | 0.999655 | − | 0.0262776i | \(-0.00836540\pi\) |
−0.522584 | + | 0.852588i | \(0.675032\pi\) | |||||||
\(140\) | −3.60764 | − | 4.93487i | −0.304901 | − | 0.417072i | ||||
\(141\) | −2.97676 | − | 1.71863i | −0.250688 | − | 0.144735i | ||||
\(142\) | − | 0.648020i | − | 0.0543806i | ||||||
\(143\) | 2.52878 | − | 4.42114i | 0.211467 | − | 0.369715i | ||||
\(144\) | −2.01950 | −0.168292 | ||||||||
\(145\) | 0.667487 | + | 0.913050i | 0.0554318 | + | 0.0758247i | ||||
\(146\) | 3.31954 | − | 5.74961i | 0.274727 | − | 0.475841i | ||||
\(147\) | −3.68320 | + | 2.12650i | −0.303785 | + | 0.175391i | ||||
\(148\) | −7.84729 | −0.645043 | ||||||||
\(149\) | −17.0840 | + | 9.86345i | −1.39958 | + | 0.808045i | −0.994348 | − | 0.106171i | \(-0.966141\pi\) |
−0.405228 | + | 0.914216i | \(0.632808\pi\) | |||||||
\(150\) | 2.82088 | + | 0.898226i | 0.230324 | + | 0.0733398i | ||||
\(151\) | − | 3.42805i | − | 0.278971i | −0.990224 | − | 0.139485i | \(-0.955455\pi\) | ||
0.990224 | − | 0.139485i | \(-0.0445448\pi\) | |||||||
\(152\) | 15.7568 | − | 9.09720i | 1.27805 | − | 0.737881i | ||||
\(153\) | 2.83926 | + | 1.63925i | 0.229541 | + | 0.132526i | ||||
\(154\) | −1.20052 | − | 0.693120i | −0.0967405 | − | 0.0558532i | ||||
\(155\) | −1.61871 | − | 0.714991i | −0.130018 | − | 0.0574295i | ||||
\(156\) | 5.94707 | − | 0.0240373i | 0.476147 | − | 0.00192453i | ||||
\(157\) | − | 3.96627i | − | 0.316543i | −0.987396 | − | 0.158271i | \(-0.949408\pi\) | ||
0.987396 | − | 0.158271i | \(-0.0505921\pi\) | |||||||
\(158\) | −2.73928 | + | 4.74458i | −0.217926 | + | 0.377459i | ||||
\(159\) | −0.211064 | + | 0.365574i | −0.0167385 | + | 0.0289919i | ||||
\(160\) | −12.2656 | + | 1.32569i | −0.969679 | + | 0.104805i | ||||
\(161\) | − | 10.9090i | − | 0.859752i | ||||||
\(162\) | 0.296043 | + | 0.512762i | 0.0232593 | + | 0.0402864i | ||||
\(163\) | 0.997316 | + | 1.72740i | 0.0781158 | + | 0.135301i | 0.902437 | − | 0.430822i | \(-0.141776\pi\) |
−0.824321 | + | 0.566122i | \(0.808443\pi\) | |||||||
\(164\) | − | 14.6126i | − | 1.14105i | ||||||
\(165\) | −3.14041 | + | 0.339423i | −0.244481 | + | 0.0264241i | ||||
\(166\) | 1.19187 | − | 2.06439i | 0.0925073 | − | 0.160227i | ||||
\(167\) | −5.74274 | + | 9.94672i | −0.444387 | + | 0.769701i | −0.998009 | − | 0.0630672i | \(-0.979912\pi\) |
0.553622 | + | 0.832768i | \(0.313245\pi\) | |||||||
\(168\) | − | 3.58130i | − | 0.276303i | ||||||
\(169\) | −12.9996 | + | 0.105087i | −0.999967 | + | 0.00808362i | ||||
\(170\) | 3.97047 | + | 1.75378i | 0.304522 | + | 0.134509i | ||||
\(171\) | 7.29219 | + | 4.21015i | 0.557648 | + | 0.321958i | ||||
\(172\) | −3.18818 | − | 1.84070i | −0.243097 | − | 0.140352i | ||||
\(173\) | −10.9729 | + | 6.33521i | −0.834254 | + | 0.481657i | −0.855307 | − | 0.518122i | \(-0.826631\pi\) |
0.0210530 | + | 0.999778i | \(0.493298\pi\) | |||||||
\(174\) | 0.299481i | 0.0227036i | ||||||||
\(175\) | 2.51438 | − | 7.89640i | 0.190069 | − | 0.596911i | ||||
\(176\) | 2.47058 | − | 1.42639i | 0.186227 | − | 0.107518i | ||||
\(177\) | −13.0993 | −0.984601 | ||||||||
\(178\) | −0.306635 | + | 0.177036i | −0.0229833 | + | 0.0132694i | ||||
\(179\) | −4.28745 | + | 7.42609i | −0.320459 | + | 0.555052i | −0.980583 | − | 0.196105i | \(-0.937171\pi\) |
0.660124 | + | 0.751157i | \(0.270504\pi\) | |||||||
\(180\) | −2.17667 | − | 2.97746i | −0.162240 | − | 0.221927i | ||||
\(181\) | −22.9517 | −1.70599 | −0.852994 | − | 0.521921i | \(-0.825215\pi\) | ||||
−0.852994 | + | 0.521921i | \(0.825215\pi\) | |||||||
\(182\) | 0.0143010 | + | 3.53820i | 0.00106006 | + | 0.262269i | ||||
\(183\) | 0.927500i | 0.0685628i | ||||||||
\(184\) | −12.3168 | − | 7.11110i | −0.908005 | − | 0.524237i | ||||
\(185\) | −6.27832 | − | 8.58807i | −0.461591 | − | 0.631407i | ||||
\(186\) | −0.234283 | − | 0.405790i | −0.0171785 | − | 0.0297540i | ||||
\(187\) | −4.63126 | −0.338671 | ||||||||
\(188\) | 2.83477 | + | 4.90997i | 0.206747 | + | 0.358096i | ||||
\(189\) | 1.43536 | − | 0.828705i | 0.104407 | − | 0.0602794i | ||||
\(190\) | 10.1975 | + | 4.50430i | 0.739806 | + | 0.326776i | ||||
\(191\) | −2.14865 | − | 3.72158i | −0.155471 | − | 0.269284i | 0.777759 | − | 0.628562i | \(-0.216356\pi\) |
−0.933230 | + | 0.359278i | \(0.883023\pi\) | |||||||
\(192\) | 0.668830 | + | 0.386149i | 0.0482687 | + | 0.0278679i | ||||
\(193\) | 3.16587 | − | 5.48344i | 0.227884 | − | 0.394707i | −0.729297 | − | 0.684198i | \(-0.760153\pi\) |
0.957181 | + | 0.289491i | \(0.0934859\pi\) | |||||||
\(194\) | −1.87062 | −0.134302 | ||||||||
\(195\) | 4.78433 | + | 6.48924i | 0.342613 | + | 0.464704i | ||||
\(196\) | 7.01503 | 0.501074 | ||||||||
\(197\) | 11.1207 | − | 19.2617i | 0.792320 | − | 1.37234i | −0.132207 | − | 0.991222i | \(-0.542207\pi\) |
0.924527 | − | 0.381116i | \(-0.124460\pi\) | |||||||
\(198\) | −0.724334 | − | 0.418195i | −0.0514762 | − | 0.0297198i | ||||
\(199\) | −2.19713 | − | 3.80554i | −0.155750 | − | 0.269768i | 0.777582 | − | 0.628782i | \(-0.216446\pi\) |
−0.933332 | + | 0.359014i | \(0.883113\pi\) | |||||||
\(200\) | −7.27638 | − | 7.98614i | −0.514518 | − | 0.564706i | ||||
\(201\) | −10.7587 | + | 6.21154i | −0.758861 | + | 0.438129i | ||||
\(202\) | 2.64747 | + | 4.58555i | 0.186275 | + | 0.322638i | ||||
\(203\) | 0.838328 | 0.0588391 | ||||||||
\(204\) | −2.70384 | − | 4.68318i | −0.189306 | − | 0.327888i | ||||
\(205\) | 15.9920 | − | 11.6910i | 1.11693 | − | 0.816532i | ||||
\(206\) | −7.70662 | − | 4.44942i | −0.536946 | − | 0.310006i | ||||
\(207\) | − | 6.58198i | − | 0.457479i | ||||||
\(208\) | −6.32055 | − | 3.61519i | −0.438251 | − | 0.250668i | ||||
\(209\) | −11.8946 | −0.822769 | ||||||||
\(210\) | 1.77144 | − | 1.29501i | 0.122241 | − | 0.0893642i | ||||
\(211\) | 3.35237 | − | 5.80648i | 0.230787 | − | 0.399734i | −0.727253 | − | 0.686369i | \(-0.759203\pi\) |
0.958040 | + | 0.286635i | \(0.0925367\pi\) | |||||||
\(212\) | 0.602990 | − | 0.348136i | 0.0414135 | − | 0.0239101i | ||||
\(213\) | −1.09447 | −0.0749918 | ||||||||
\(214\) | 9.68410 | − | 5.59112i | 0.661991 | − | 0.382201i | ||||
\(215\) | −0.536285 | − | 4.96181i | −0.0365743 | − | 0.338393i | ||||
\(216\) | − | 2.16078i | − | 0.147022i | ||||||
\(217\) | −1.13592 | + | 0.655822i | −0.0771111 | + | 0.0445201i | ||||
\(218\) | 3.44225 | + | 1.98739i | 0.233139 | + | 0.134603i | ||||
\(219\) | −9.71077 | − | 5.60652i | −0.656193 | − | 0.378853i | ||||
\(220\) | 4.76586 | + | 2.10510i | 0.321314 | + | 0.141926i | ||||
\(221\) | 5.95173 | + | 10.2131i | 0.400357 | + | 0.687010i | ||||
\(222\) | − | 2.81689i | − | 0.189057i | ||||||
\(223\) | −6.78573 | + | 11.7532i | −0.454406 | + | 0.787055i | −0.998654 | − | 0.0518698i | \(-0.983482\pi\) |
0.544248 | + | 0.838925i | \(0.316815\pi\) | |||||||
\(224\) | −4.57219 | + | 7.91927i | −0.305493 | + | 0.529129i | ||||
\(225\) | 1.51705 | − | 4.76430i | 0.101137 | − | 0.317620i | ||||
\(226\) | 11.6154i | 0.772648i | ||||||||
\(227\) | 0.148503 | + | 0.257216i | 0.00985652 | + | 0.0170720i | 0.870912 | − | 0.491440i | \(-0.163529\pi\) |
−0.861055 | + | 0.508512i | \(0.830196\pi\) | |||||||
\(228\) | −6.94436 | − | 12.0280i | −0.459902 | − | 0.796573i | ||||
\(229\) | 14.3158i | 0.946014i | 0.881059 | + | 0.473007i | \(0.156832\pi\) | ||||
−0.881059 | + | 0.473007i | \(0.843168\pi\) | |||||||
\(230\) | −0.936396 | − | 8.66372i | −0.0617441 | − | 0.571269i | ||||
\(231\) | −1.17064 | + | 2.02761i | −0.0770225 | + | 0.133407i | ||||
\(232\) | 0.546468 | − | 0.946510i | 0.0358774 | − | 0.0621414i | ||||
\(233\) | − | 12.9800i | − | 0.850345i | −0.905112 | − | 0.425173i | \(-0.860213\pi\) | ||
0.905112 | − | 0.425173i | \(-0.139787\pi\) | |||||||
\(234\) | 0.00862852 | + | 2.13478i | 0.000564064 | + | 0.139555i | ||||
\(235\) | −3.10547 | + | 7.03065i | −0.202579 | + | 0.458629i | ||||
\(236\) | 18.7117 | + | 10.8032i | 1.21803 | + | 0.703227i | ||||
\(237\) | 8.01333 | + | 4.62650i | 0.520522 | + | 0.300523i | ||||
\(238\) | 2.78625 | − | 1.60864i | 0.180606 | − | 0.104273i | ||||
\(239\) | 13.6665i | 0.884015i | 0.897011 | + | 0.442007i | \(0.145734\pi\) | ||||
−0.897011 | + | 0.442007i | \(0.854266\pi\) | |||||||
\(240\) | 0.485246 | + | 4.48959i | 0.0313225 | + | 0.289802i | ||||
\(241\) | 10.5045 | − | 6.06478i | 0.676655 | − | 0.390667i | −0.121939 | − | 0.992538i | \(-0.538911\pi\) |
0.798594 | + | 0.601871i | \(0.205578\pi\) | |||||||
\(242\) | −5.33145 | −0.342719 | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 0.764925 | − | 1.32489i | 0.0489693 | − | 0.0848173i | ||||
\(245\) | 5.61246 | + | 7.67724i | 0.358567 | + | 0.490481i | ||||
\(246\) | 5.24537 | 0.334433 | ||||||||
\(247\) | 15.2861 | + | 26.2308i | 0.972628 | + | 1.66903i | ||||
\(248\) | 1.71000i | 0.108585i | ||||||||
\(249\) | −3.48663 | − | 2.01301i | −0.220956 | − | 0.127569i | ||||
\(250\) | 1.31906 | − | 6.48697i | 0.0834249 | − | 0.410272i | ||||
\(251\) | −6.88951 | − | 11.9330i | −0.434862 | − | 0.753203i | 0.562422 | − | 0.826850i | \(-0.309870\pi\) |
−0.997284 | + | 0.0736468i | \(0.976536\pi\) | |||||||
\(252\) | −2.73379 | −0.172212 | ||||||||
\(253\) | 4.64890 | + | 8.05213i | 0.292274 | + | 0.506233i | ||||
\(254\) | −8.43119 | + | 4.86775i | −0.529020 | + | 0.305430i | ||||
\(255\) | 2.96203 | − | 6.70591i | 0.185490 | − | 0.419940i | ||||
\(256\) | 2.62977 | + | 4.55490i | 0.164361 | + | 0.284681i | ||||
\(257\) | 4.84978 | + | 2.80002i | 0.302521 | + | 0.174661i | 0.643575 | − | 0.765383i | \(-0.277450\pi\) |
−0.341054 | + | 0.940044i | \(0.610784\pi\) | |||||||
\(258\) | 0.660743 | − | 1.14444i | 0.0411360 | − | 0.0712497i | ||||
\(259\) | −7.88523 | −0.489965 | ||||||||
\(260\) | −1.48240 | − | 13.2153i | −0.0919346 | − | 0.819577i | ||||
\(261\) | 0.505806 | 0.0313086 | ||||||||
\(262\) | 1.81048 | − | 3.13585i | 0.111852 | − | 0.193733i | ||||
\(263\) | −7.77693 | − | 4.49001i | −0.479546 | − | 0.276866i | 0.240681 | − | 0.970604i | \(-0.422629\pi\) |
−0.720227 | + | 0.693738i | \(0.755962\pi\) | |||||||
\(264\) | 1.52617 | + | 2.64341i | 0.0939295 | + | 0.162691i | ||||
\(265\) | 0.863429 | + | 0.381381i | 0.0530401 | + | 0.0234280i | ||||
\(266\) | 7.15604 | − | 4.13154i | 0.438765 | − | 0.253321i | ||||
\(267\) | 0.299004 | + | 0.517890i | 0.0182987 | + | 0.0316943i | ||||
\(268\) | 20.4911 | 1.25169 | ||||||||
\(269\) | 2.03862 | + | 3.53099i | 0.124297 | + | 0.215288i | 0.921458 | − | 0.388478i | \(-0.126999\pi\) |
−0.797161 | + | 0.603767i | \(0.793666\pi\) | |||||||
\(270\) | 1.06880 | − | 0.781346i | 0.0650449 | − | 0.0475512i | ||||
\(271\) | 17.1435 | + | 9.89780i | 1.04139 | + | 0.601249i | 0.920228 | − | 0.391384i | \(-0.128003\pi\) |
0.121166 | + | 0.992632i | \(0.461337\pi\) | |||||||
\(272\) | 6.62093i | 0.401453i | ||||||||
\(273\) | 5.97583 | − | 0.0241536i | 0.361673 | − | 0.00146184i | ||||
\(274\) | 7.66696 | 0.463178 | ||||||||
\(275\) | 1.50916 | + | 6.89996i | 0.0910057 | + | 0.416083i | ||||
\(276\) | −5.42827 | + | 9.40204i | −0.326743 | + | 0.565936i | ||||
\(277\) | 12.5813 | − | 7.26380i | 0.755935 | − | 0.436439i | −0.0718991 | − | 0.997412i | \(-0.522906\pi\) |
0.827834 | + | 0.560972i | \(0.189573\pi\) | |||||||
\(278\) | 6.66047 | 0.399468 | ||||||||
\(279\) | −0.685357 | + | 0.395691i | −0.0410312 | + | 0.0236894i | ||||
\(280\) | −7.96165 | + | 0.860515i | −0.475800 | + | 0.0514256i | ||||
\(281\) | 11.7874i | 0.703176i | 0.936155 | + | 0.351588i | \(0.114358\pi\) | ||||
−0.936155 | + | 0.351588i | \(0.885642\pi\) | |||||||
\(282\) | −1.76250 | + | 1.01758i | −0.104955 | + | 0.0605959i | ||||
\(283\) | −20.0067 | − | 11.5509i | −1.18928 | − | 0.686630i | −0.231135 | − | 0.972922i | \(-0.574244\pi\) |
−0.958142 | + | 0.286292i | \(0.907577\pi\) | |||||||
\(284\) | 1.56340 | + | 0.902628i | 0.0927705 | + | 0.0535611i | ||||
\(285\) | 7.60750 | − | 17.2230i | 0.450629 | − | 1.02020i | ||||
\(286\) | −1.51837 | − | 2.60551i | −0.0897828 | − | 0.154067i | ||||
\(287\) | − | 14.6832i | − | 0.866723i | ||||||
\(288\) | −2.75864 | + | 4.77810i | −0.162554 | + | 0.281552i | ||||
\(289\) | −3.12572 | + | 5.41390i | −0.183866 | + | 0.318465i | ||||
\(290\) | 0.665782 | − | 0.0719593i | 0.0390961 | − | 0.00422560i | ||||
\(291\) | 3.15936i | 0.185205i | ||||||||
\(292\) | 9.24758 | + | 16.0173i | 0.541174 | + | 0.937340i | ||||
\(293\) | −4.79244 | − | 8.30075i | −0.279977 | − | 0.484935i | 0.691401 | − | 0.722471i | \(-0.256994\pi\) |
−0.971379 | + | 0.237536i | \(0.923660\pi\) | |||||||
\(294\) | 2.51814i | 0.146861i | ||||||||
\(295\) | 3.14749 | + | 29.1212i | 0.183254 | + | 1.69550i | ||||
\(296\) | −5.14002 | + | 8.90278i | −0.298758 | + | 0.517464i | ||||
\(297\) | −0.706307 | + | 1.22336i | −0.0409841 | + | 0.0709865i | ||||
\(298\) | 11.6800i | 0.676606i | ||||||||
\(299\) | 11.7827 | − | 20.6000i | 0.681409 | − | 1.19133i | ||||
\(300\) | −6.09624 | + | 5.55443i | −0.351966 | + | 0.320685i | ||||
\(301\) | −3.20360 | − | 1.84960i | −0.184652 | − | 0.106609i | ||||
\(302\) | −1.75777 | − | 1.01485i | −0.101148 | − | 0.0583980i | ||||
\(303\) | 7.74473 | − | 4.47142i | 0.444923 | − | 0.256876i | ||||
\(304\) | 17.0048i | 0.975292i | ||||||||
\(305\) | 2.06194 | − | 0.222860i | 0.118067 | − | 0.0127609i | ||||
\(306\) | 1.68109 | − | 0.970577i | 0.0961015 | − | 0.0554842i | ||||
\(307\) | −25.2144 | −1.43906 | −0.719530 | − | 0.694461i | \(-0.755643\pi\) | ||||
−0.719530 | + | 0.694461i | \(0.755643\pi\) | |||||||
\(308\) | 3.34441 | − | 1.93089i | 0.190565 | − | 0.110023i | ||||
\(309\) | −7.51482 | + | 13.0161i | −0.427503 | + | 0.740457i | ||||
\(310\) | −0.845827 | + | 0.618343i | −0.0480398 | + | 0.0351195i | ||||
\(311\) | 1.70269 | 0.0965509 | 0.0482755 | − | 0.998834i | \(-0.484627\pi\) | ||||
0.0482755 | + | 0.998834i | \(0.484627\pi\) | |||||||
\(312\) | 3.86810 | − | 6.76272i | 0.218988 | − | 0.382864i | ||||
\(313\) | 25.1073i | 1.41915i | 0.704632 | + | 0.709573i | \(0.251112\pi\) | ||||
−0.704632 | + | 0.709573i | \(0.748888\pi\) | |||||||
\(314\) | −2.03375 | − | 1.17419i | −0.114771 | − | 0.0662632i | ||||
\(315\) | −2.18720 | − | 2.99185i | −0.123235 | − | 0.168572i | ||||
\(316\) | −7.63110 | − | 13.2175i | −0.429283 | − | 0.743540i | ||||
\(317\) | 1.89871 | 0.106642 | 0.0533210 | − | 0.998577i | \(-0.483019\pi\) | ||||
0.0533210 | + | 0.998577i | \(0.483019\pi\) | |||||||
\(318\) | 0.124968 | + | 0.216451i | 0.00700787 | + | 0.0121380i | ||||
\(319\) | −0.618783 | + | 0.357255i | −0.0346452 | + | 0.0200024i | ||||
\(320\) | 0.697750 | − | 1.57967i | 0.0390054 | − | 0.0883065i | ||||
\(321\) | −9.44308 | − | 16.3559i | −0.527061 | − | 0.912897i | ||||
\(322\) | −5.59373 | − | 3.22954i | −0.311727 | − | 0.179975i | ||||
\(323\) | 13.8030 | − | 23.9075i | 0.768018 | − | 1.33025i | ||||
\(324\) | −1.64943 | −0.0916352 | ||||||||
\(325\) | 13.2768 | − | 12.1954i | 0.736463 | − | 0.676478i | ||||
\(326\) | 1.18099 | 0.0654092 | ||||||||
\(327\) | 3.35658 | − | 5.81377i | 0.185620 | − | 0.321502i | ||||
\(328\) | −16.5780 | − | 9.57132i | −0.915368 | − | 0.528488i | ||||
\(329\) | 2.84848 | + | 4.93371i | 0.157042 | + | 0.272004i | ||||
\(330\) | −0.755654 | + | 1.71077i | −0.0415974 | + | 0.0941746i | ||||
\(331\) | −17.5641 | + | 10.1406i | −0.965410 | + | 0.557380i | −0.897834 | − | 0.440334i | \(-0.854860\pi\) |
−0.0675763 | + | 0.997714i | \(0.521527\pi\) | |||||||
\(332\) | 3.32032 | + | 5.75097i | 0.182226 | + | 0.315625i | ||||
\(333\) | −4.75757 | −0.260713 | ||||||||
\(334\) | 3.40020 | + | 5.88932i | 0.186051 | + | 0.322249i | ||||
\(335\) | 16.3941 | + | 22.4254i | 0.895706 | + | 1.22523i | ||||
\(336\) | 2.89871 | + | 1.67357i | 0.158137 | + | 0.0913007i | ||||
\(337\) | 16.8233i | 0.916421i | 0.888844 | + | 0.458211i | \(0.151509\pi\) | ||||
−0.888844 | + | 0.458211i | \(0.848491\pi\) | |||||||
\(338\) | −3.79455 | + | 6.69679i | −0.206396 | + | 0.364258i | ||||
\(339\) | 19.6178 | 1.06549 | ||||||||
\(340\) | −9.76160 | + | 7.13623i | −0.529397 | + | 0.387016i | ||||
\(341\) | 0.558959 | − | 0.968145i | 0.0302693 | − | 0.0524280i | ||||
\(342\) | 4.31761 | − | 2.49277i | 0.233469 | − | 0.134794i | ||||
\(343\) | 18.6508 | 1.00705 | ||||||||
\(344\) | −4.17656 | + | 2.41134i | −0.225185 | + | 0.130011i | ||||
\(345\) | −14.6325 | + | 1.58152i | −0.787789 | + | 0.0851461i | ||||
\(346\) | 7.50197i | 0.403309i | ||||||||
\(347\) | −7.06423 | + | 4.07853i | −0.379228 | + | 0.218947i | −0.677482 | − | 0.735539i | \(-0.736929\pi\) |
0.298255 | + | 0.954486i | \(0.403596\pi\) | |||||||
\(348\) | −0.722520 | − | 0.417147i | −0.0387311 | − | 0.0223614i | ||||
\(349\) | 12.7740 | + | 7.37508i | 0.683777 | + | 0.394779i | 0.801277 | − | 0.598294i | \(-0.204155\pi\) |
−0.117500 | + | 0.993073i | \(0.537488\pi\) | |||||||
\(350\) | −3.30460 | − | 3.62695i | −0.176639 | − | 0.193869i | ||||
\(351\) | 3.60552 | − | 0.0145731i | 0.192449 | − | 0.000777853i | ||||
\(352\) | − | 7.79378i | − | 0.415410i | ||||||
\(353\) | 7.81315 | − | 13.5328i | 0.415852 | − | 0.720277i | −0.579666 | − | 0.814854i | \(-0.696817\pi\) |
0.995517 | + | 0.0945779i | \(0.0301502\pi\) | |||||||
\(354\) | −3.87794 | + | 6.71680i | −0.206110 | + | 0.356994i | ||||
\(355\) | 0.262979 | + | 2.43314i | 0.0139575 | + | 0.129138i | ||||
\(356\) | − | 0.986374i | − | 0.0522777i | ||||||
\(357\) | −2.71691 | − | 4.70582i | −0.143794 | − | 0.249059i | ||||
\(358\) | 2.53854 | + | 4.39688i | 0.134166 | + | 0.232382i | ||||
\(359\) | − | 23.5802i | − | 1.24452i | −0.782812 | − | 0.622258i | \(-0.786215\pi\) | ||
0.782812 | − | 0.622258i | \(-0.213785\pi\) | |||||||
\(360\) | −4.80367 | + | 0.519193i | −0.253176 | + | 0.0273639i | ||||
\(361\) | 25.9507 | − | 44.9480i | 1.36583 | − | 2.36568i | ||||
\(362\) | −6.79469 | + | 11.7688i | −0.357121 | + | 0.618552i | ||||
\(363\) | 9.00452i | 0.472615i | ||||||||
\(364\) | −8.55610 | − | 4.89386i | −0.448461 | − | 0.256508i | ||||
\(365\) | −10.1307 | + | 22.9354i | −0.530263 | + | 1.20049i | ||||
\(366\) | 0.475586 | + | 0.274580i | 0.0248593 | + | 0.0143525i | ||||
\(367\) | −12.4839 | − | 7.20758i | −0.651654 | − | 0.376233i | 0.137435 | − | 0.990511i | \(-0.456114\pi\) |
−0.789090 | + | 0.614278i | \(0.789447\pi\) | |||||||
\(368\) | 11.5115 | − | 6.64615i | 0.600077 | − | 0.346455i | ||||
\(369\) | − | 8.85914i | − | 0.461188i | ||||||
\(370\) | −6.26228 | + | 0.676843i | −0.325561 | + | 0.0351874i | ||||
\(371\) | 0.605906 | − | 0.349820i | 0.0314571 | − | 0.0181617i | ||||
\(372\) | 1.30533 | 0.0676783 | ||||||||
\(373\) | 9.00480 | − | 5.19893i | 0.466251 | − | 0.269190i | −0.248418 | − | 0.968653i | \(-0.579911\pi\) |
0.714669 | + | 0.699463i | \(0.246577\pi\) | |||||||
\(374\) | −1.37105 | + | 2.37473i | −0.0708954 | + | 0.122794i | ||||
\(375\) | −10.9561 | − | 2.22782i | −0.565772 | − | 0.115044i | ||||
\(376\) | 7.42717 | 0.383027 | ||||||||
\(377\) | 1.58305 | + | 0.905464i | 0.0815313 | + | 0.0466338i | ||||
\(378\) | − | 0.981329i | − | 0.0504741i | ||||||
\(379\) | −3.38172 | − | 1.95244i | −0.173708 | − | 0.100290i | 0.410625 | − | 0.911804i | \(-0.365310\pi\) |
−0.584333 | + | 0.811514i | \(0.698644\pi\) | |||||||
\(380\) | −25.0711 | + | 18.3282i | −1.28612 | + | 0.940219i | ||||
\(381\) | 8.22136 | + | 14.2398i | 0.421193 | + | 0.729527i | ||||
\(382\) | −2.54437 | −0.130182 | ||||||||
\(383\) | −16.2604 | − | 28.1639i | −0.830869 | − | 1.43911i | −0.897350 | − | 0.441320i | \(-0.854510\pi\) |
0.0664805 | − | 0.997788i | \(-0.478823\pi\) | |||||||
\(384\) | 9.95221 | − | 5.74591i | 0.507872 | − | 0.293220i | ||||
\(385\) | 4.78890 | + | 2.11528i | 0.244065 | + | 0.107805i | ||||
\(386\) | −1.87447 | − | 3.24667i | −0.0954078 | − | 0.165251i | ||||
\(387\) | −1.93289 | − | 1.11596i | −0.0982545 | − | 0.0567273i | ||||
\(388\) | 2.60558 | − | 4.51300i | 0.132278 | − | 0.229113i | ||||
\(389\) | 36.5188 | 1.85158 | 0.925789 | − | 0.378042i | \(-0.123402\pi\) | ||||
0.925789 | + | 0.378042i | \(0.123402\pi\) | |||||||
\(390\) | 4.74380 | − | 0.532128i | 0.240212 | − | 0.0269453i | ||||
\(391\) | −21.5790 | −1.09130 | ||||||||
\(392\) | 4.59489 | − | 7.95858i | 0.232077 | − | 0.401969i | ||||
\(393\) | −5.29627 | − | 3.05780i | −0.267162 | − | 0.154246i | ||||
\(394\) | −6.58443 | − | 11.4046i | −0.331719 | − | 0.574554i | ||||
\(395\) | 8.35982 | − | 18.9263i | 0.420628 | − | 0.952283i | ||||
\(396\) | 2.01785 | − | 1.16501i | 0.101401 | − | 0.0585438i | ||||
\(397\) | 5.15633 | + | 8.93103i | 0.258789 | + | 0.448235i | 0.965918 | − | 0.258849i | \(-0.0833433\pi\) |
−0.707129 | + | 0.707085i | \(0.750010\pi\) | |||||||
\(398\) | −2.60178 | −0.130415 | ||||||||
\(399\) | −6.97794 | − | 12.0861i | −0.349334 | − | 0.605064i | ||||
\(400\) | 9.86431 | − | 2.15752i | 0.493216 | − | 0.107876i | ||||
\(401\) | −18.0710 | − | 10.4333i | −0.902421 | − | 0.521013i | −0.0244360 | − | 0.999701i | \(-0.507779\pi\) |
−0.877985 | + | 0.478689i | \(0.841112\pi\) | |||||||
\(402\) | 7.35554i | 0.366861i | ||||||||
\(403\) | −2.85335 | + | 0.0115329i | −0.142135 | + | 0.000574493i | ||||
\(404\) | −14.7506 | −0.733871 | ||||||||
\(405\) | −1.31965 | − | 1.80514i | −0.0655739 | − | 0.0896981i | ||||
\(406\) | 0.248181 | − | 0.429862i | 0.0123170 | − | 0.0213337i | ||||
\(407\) | 5.82021 | − | 3.36030i | 0.288497 | − | 0.166564i | ||||
\(408\) | −7.08412 | −0.350716 | ||||||||
\(409\) | 3.35024 | − | 1.93426i | 0.165659 | − | 0.0956432i | −0.414878 | − | 0.909877i | \(-0.636176\pi\) |
0.580537 | + | 0.814234i | \(0.302843\pi\) | |||||||
\(410\) | −1.26036 | − | 11.6611i | −0.0622447 | − | 0.575900i | ||||
\(411\) | − | 12.9491i | − | 0.638730i | ||||||
\(412\) | 21.4691 | − | 12.3952i | 1.05771 | − | 0.610668i | ||||
\(413\) | 18.8021 | + | 10.8554i | 0.925192 | + | 0.534160i | ||||
\(414\) | −3.37499 | − | 1.94855i | −0.165871 | − | 0.0957659i | ||||
\(415\) | −3.63739 | + | 8.23489i | −0.178552 | + | 0.404235i | ||||
\(416\) | −17.1873 | + | 10.0160i | −0.842679 | + | 0.491073i | ||||
\(417\) | − | 11.2492i | − | 0.550873i | ||||||
\(418\) | −3.52132 | + | 6.09911i | −0.172234 | + | 0.298317i | ||||
\(419\) | 10.8008 | − | 18.7076i | 0.527656 | − | 0.913926i | −0.471825 | − | 0.881692i | \(-0.656405\pi\) |
0.999480 | − | 0.0322339i | \(-0.0102621\pi\) | |||||||
\(420\) | 0.656875 | + | 6.07754i | 0.0320522 | + | 0.296554i | ||||
\(421\) | − | 11.8818i | − | 0.579085i | −0.957165 | − | 0.289542i | \(-0.906497\pi\) | ||
0.957165 | − | 0.289542i | \(-0.0935031\pi\) | |||||||
\(422\) | −1.98489 | − | 3.43793i | −0.0966230 | − | 0.167356i | ||||
\(423\) | 1.71863 | + | 2.97676i | 0.0835628 | + | 0.144735i | ||||
\(424\) | − | 0.912126i | − | 0.0442968i | ||||||
\(425\) | −15.6198 | − | 4.97366i | −0.757670 | − | 0.241258i | ||||
\(426\) | −0.324010 | + | 0.561202i | −0.0156983 | + | 0.0271903i | ||||
\(427\) | 0.768624 | − | 1.33130i | 0.0371963 | − | 0.0644259i | ||||
\(428\) | 31.1515i | 1.50576i | ||||||||
\(429\) | −4.40056 | + | 2.56443i | −0.212461 | + | 0.123812i | ||||
\(430\) | −2.70299 | − | 1.19392i | −0.130350 | − | 0.0575761i | ||||
\(431\) | −9.43023 | − | 5.44454i | −0.454238 | − | 0.262254i | 0.255380 | − | 0.966841i | \(-0.417799\pi\) |
−0.709618 | + | 0.704586i | \(0.751133\pi\) | |||||||
\(432\) | 1.74894 | + | 1.00975i | 0.0841459 | + | 0.0485816i | ||||
\(433\) | −27.7614 | + | 16.0280i | −1.33413 | + | 0.770258i | −0.985929 | − | 0.167163i | \(-0.946539\pi\) |
−0.348197 | + | 0.937421i | \(0.613206\pi\) | |||||||
\(434\) | 0.776606i | 0.0372783i | ||||||||
\(435\) | −0.121535 | − | 1.12447i | −0.00582717 | − | 0.0539141i | ||||
\(436\) | −9.58944 | + | 5.53646i | −0.459251 | + | 0.265149i | ||||
\(437\) | −55.4222 | −2.65120 | ||||||||
\(438\) | −5.74961 | + | 3.31954i | −0.274727 | + | 0.158614i | ||||
\(439\) | 12.5421 | − | 21.7235i | 0.598600 | − | 1.03681i | −0.394427 | − | 0.918927i | \(-0.629057\pi\) |
0.993028 | − | 0.117879i | \(-0.0376096\pi\) | |||||||
\(440\) | 5.50991 | − | 4.02803i | 0.262675 | − | 0.192029i | ||||
\(441\) | 4.25299 | 0.202524 | ||||||||
\(442\) | 6.99888 | − | 0.0282886i | 0.332903 | − | 0.00134555i | ||||
\(443\) | 32.0707i | 1.52373i | 0.647738 | + | 0.761863i | \(0.275715\pi\) | ||||
−0.647738 | + | 0.761863i | \(0.724285\pi\) | |||||||
\(444\) | 6.79595 | + | 3.92365i | 0.322522 | + | 0.186208i | ||||
\(445\) | 1.07949 | − | 0.789160i | 0.0511726 | − | 0.0374098i | ||||
\(446\) | 4.01774 | + | 6.95893i | 0.190245 | + | 0.329515i | ||||
\(447\) | 19.7269 | 0.933050 | ||||||||
\(448\) | −0.640008 | − | 1.10853i | −0.0302375 | − | 0.0523729i | ||||
\(449\) | −20.8143 | + | 12.0171i | −0.982286 | + | 0.567123i | −0.902960 | − | 0.429725i | \(-0.858610\pi\) |
−0.0793266 | + | 0.996849i | \(0.525277\pi\) | |||||||
\(450\) | −1.99384 | − | 2.18832i | −0.0939904 | − | 0.103159i | ||||
\(451\) | 6.25727 | + | 10.8379i | 0.294643 | + | 0.510337i | ||||
\(452\) | −28.0231 | − | 16.1792i | −1.31810 | − | 0.761004i | ||||
\(453\) | −1.71402 | + | 2.96878i | −0.0805319 | + | 0.139485i | ||||
\(454\) | 0.175854 | 0.00825322 | ||||||||
\(455\) | −1.48957 | − | 13.2792i | −0.0698321 | − | 0.622537i | ||||
\(456\) | −18.1944 | −0.852031 | ||||||||
\(457\) | −2.15807 | + | 3.73789i | −0.100950 | + | 0.174851i | −0.912077 | − | 0.410020i | \(-0.865522\pi\) |
0.811126 | + | 0.584871i | \(0.198855\pi\) | |||||||
\(458\) | 7.34059 | + | 4.23809i | 0.343003 | + | 0.198033i | ||||
\(459\) | −1.63925 | − | 2.83926i | −0.0765137 | − | 0.132526i | ||||
\(460\) | 22.2062 | + | 9.80857i | 1.03537 | + | 0.457327i | ||||
\(461\) | −0.533988 | + | 0.308298i | −0.0248703 | + | 0.0143589i | −0.512384 | − | 0.858757i | \(-0.671237\pi\) |
0.487513 | + | 0.873116i | \(0.337904\pi\) | |||||||
\(462\) | 0.693120 | + | 1.20052i | 0.0322468 | + | 0.0558532i | ||||
\(463\) | −13.3637 | −0.621062 | −0.310531 | − | 0.950563i | \(-0.600507\pi\) | ||||
−0.310531 | + | 0.950563i | \(0.600507\pi\) | |||||||
\(464\) | 0.510738 | + | 0.884624i | 0.0237104 | + | 0.0410676i | ||||
\(465\) | 1.04435 | + | 1.42855i | 0.0484304 | + | 0.0662476i | ||||
\(466\) | −6.65562 | − | 3.84263i | −0.308316 | − | 0.178006i | ||||
\(467\) | 26.1210i | 1.20873i | 0.796706 | + | 0.604367i | \(0.206574\pi\) | ||||
−0.796706 | + | 0.604367i | \(0.793426\pi\) | |||||||
\(468\) | −5.16233 | − | 2.95272i | −0.238629 | − | 0.136489i | ||||
\(469\) | 20.5901 | 0.950765 | ||||||||
\(470\) | 2.68569 | + | 3.67374i | 0.123882 | + | 0.169457i | ||||
\(471\) | −1.98314 | + | 3.43489i | −0.0913781 | + | 0.158271i | ||||
\(472\) | 24.5125 | − | 14.1523i | 1.12828 | − | 0.651412i | ||||
\(473\) | 3.15283 | 0.144967 | ||||||||
\(474\) | 4.74458 | − | 2.73928i | 0.217926 | − | 0.125820i | ||||
\(475\) | −40.1168 | − | 12.7740i | −1.84069 | − | 0.586113i | ||||
\(476\) | 8.96272i | 0.410806i | ||||||||
\(477\) | 0.365574 | − | 0.211064i | 0.0167385 | − | 0.00966397i | ||||
\(478\) | 7.00768 | + | 4.04588i | 0.320524 | + | 0.185054i | ||||
\(479\) | −7.51515 | − | 4.33887i | −0.343376 | − | 0.198248i | 0.318388 | − | 0.947960i | \(-0.396859\pi\) |
−0.661764 | + | 0.749712i | \(0.730192\pi\) | |||||||
\(480\) | 11.2851 | + | 4.98470i | 0.515094 | + | 0.227519i | ||||
\(481\) | −14.8900 | − | 8.51671i | −0.678927 | − | 0.388329i | ||||
\(482\) | − | 7.18175i | − | 0.327120i | ||||||
\(483\) | −5.45452 | + | 9.44750i | −0.248189 | + | 0.429876i | ||||
\(484\) | 7.42618 | − | 12.8625i | 0.337554 | − | 0.584660i | ||||
\(485\) | 7.02365 | − | 0.759133i | 0.318927 | − | 0.0344704i | ||||
\(486\) | − | 0.592086i | − | 0.0268576i | ||||||
\(487\) | −14.2580 | − | 24.6955i | −0.646090 | − | 1.11906i | −0.984049 | − | 0.177899i | \(-0.943070\pi\) |
0.337959 | − | 0.941161i | \(-0.390263\pi\) | |||||||
\(488\) | −1.00206 | − | 1.73562i | −0.0453612 | − | 0.0785679i | ||||
\(489\) | − | 1.99463i | − | 0.0902004i | ||||||
\(490\) | 5.59813 | − | 0.605059i | 0.252898 | − | 0.0273338i | ||||
\(491\) | −16.2907 | + | 28.2163i | −0.735189 | + | 1.27338i | 0.219452 | + | 0.975623i | \(0.429573\pi\) |
−0.954641 | + | 0.297761i | \(0.903760\pi\) | |||||||
\(492\) | −7.30628 | + | 12.6548i | −0.329393 | + | 0.570525i | ||||
\(493\) | − | 1.65829i | − | 0.0746854i | ||||||
\(494\) | 17.9755 | − | 0.0726547i | 0.808755 | − | 0.00326889i | ||||
\(495\) | 2.88939 | + | 1.27626i | 0.129868 | + | 0.0573635i | ||||
\(496\) | −1.38408 | − | 0.799098i | −0.0621470 | − | 0.0358806i | ||||
\(497\) | 1.57096 | + | 0.906992i | 0.0704670 | + | 0.0406842i | ||||
\(498\) | −2.06439 | + | 1.19187i | −0.0925073 | + | 0.0534091i | ||||
\(499\) | − | 28.2348i | − | 1.26396i | −0.774983 | − | 0.631982i | \(-0.782242\pi\) | ||
0.774983 | − | 0.631982i | \(-0.217758\pi\) | |||||||
\(500\) | 13.8130 | + | 12.2180i | 0.617735 | + | 0.546408i | ||||
\(501\) | 9.94672 | − | 5.74274i | 0.444387 | − | 0.256567i | ||||
\(502\) | −8.15837 | −0.364126 | ||||||||
\(503\) | −4.34699 | + | 2.50973i | −0.193823 | + | 0.111903i | −0.593771 | − | 0.804634i | \(-0.702361\pi\) |
0.399948 | + | 0.916538i | \(0.369028\pi\) | |||||||
\(504\) | −1.79065 | + | 3.10149i | −0.0797618 | + | 0.138151i | ||||
\(505\) | −11.8014 | − | 16.1431i | −0.525156 | − | 0.718357i | ||||
\(506\) | 5.50510 | 0.244731 | ||||||||
\(507\) | 11.3105 | + | 6.40878i | 0.502317 | + | 0.284624i | ||||
\(508\) | − | 27.1212i | − | 1.20331i | ||||||
\(509\) | 19.8608 | + | 11.4666i | 0.880313 | + | 0.508249i | 0.870762 | − | 0.491705i | \(-0.163626\pi\) |
0.00955142 | + | 0.999954i | \(0.496960\pi\) | |||||||
\(510\) | −2.56164 | − | 3.50405i | −0.113431 | − | 0.155162i | ||||
\(511\) | 9.29229 | + | 16.0947i | 0.411067 | + | 0.711989i | ||||
\(512\) | −19.8695 | −0.878118 | ||||||||
\(513\) | −4.21015 | − | 7.29219i | −0.185883 | − | 0.321958i | ||||
\(514\) | 2.87149 | − | 1.65786i | 0.126656 | − | 0.0731249i | ||||
\(515\) | 30.7419 | + | 13.5789i | 1.35465 | + | 0.598356i | ||||
\(516\) | 1.84070 | + | 3.18818i | 0.0810322 | + | 0.140352i | ||||
\(517\) | −4.20501 | − | 2.42777i | −0.184936 | − | 0.106773i | ||||
\(518\) | −2.33437 | + | 4.04325i | −0.102566 | + | 0.177650i | ||||
\(519\) | 12.6704 | 0.556169 | ||||||||
\(520\) | −15.9638 | − | 6.97430i | −0.700058 | − | 0.305843i | ||||
\(521\) | 42.3619 | 1.85591 | 0.927955 | − | 0.372692i | \(-0.121565\pi\) | ||||
0.927955 | + | 0.372692i | \(0.121565\pi\) | |||||||
\(522\) | 0.149740 | − | 0.259358i | 0.00655396 | − | 0.0113518i | ||||
\(523\) | 1.31741 | + | 0.760610i | 0.0576065 | + | 0.0332591i | 0.528527 | − | 0.848917i | \(-0.322745\pi\) |
−0.470920 | + | 0.882176i | \(0.656078\pi\) | |||||||
\(524\) | 5.04365 | + | 8.73585i | 0.220333 | + | 0.381627i | ||||
\(525\) | −6.12571 | + | 5.58129i | −0.267348 | + | 0.243587i | ||||
\(526\) | −4.60461 | + | 2.65847i | −0.200771 | + | 0.115915i | ||||
\(527\) | 1.29727 | + | 2.24694i | 0.0565101 | + | 0.0978784i | ||||
\(528\) | −2.85278 | −0.124151 | ||||||||
\(529\) | 10.1612 | + | 17.5997i | 0.441792 | + | 0.765206i | ||||
\(530\) | 0.451170 | − | 0.329828i | 0.0195976 | − | 0.0143268i | ||||
\(531\) | 11.3443 | + | 6.54963i | 0.492300 | + | 0.284230i | ||||
\(532\) | 23.0193i | 0.998014i | ||||||||
\(533\) | 15.8591 | − | 27.7270i | 0.686934 | − | 1.20099i | ||||
\(534\) | 0.354072 | 0.0153222 | ||||||||
\(535\) | −34.0922 | + | 24.9231i | −1.47393 | + | 1.07752i | ||||
\(536\) | 13.4218 | − | 23.2472i | 0.579732 | − | 1.00413i | ||||
\(537\) | 7.42609 | − | 4.28745i | 0.320459 | − | 0.185017i | ||||
\(538\) | 2.41408 | 0.104078 | ||||||||
\(539\) | −5.20294 | + | 3.00392i | −0.224107 | + | 0.129388i | ||||
\(540\) | 0.396326 | + | 3.66689i | 0.0170552 | + | 0.157798i | ||||
\(541\) | 38.8503i | 1.67030i | 0.550019 | + | 0.835152i | \(0.314620\pi\) | ||||
−0.550019 | + | 0.835152i | \(0.685380\pi\) | |||||||
\(542\) | 10.1504 | − | 5.86035i | 0.435998 | − | 0.251724i | ||||
\(543\) | 19.8768 | + | 11.4759i | 0.852994 | + | 0.492476i | ||||
\(544\) | 15.6650 | + | 9.04420i | 0.671632 | + | 0.387767i | ||||
\(545\) | −13.7312 | − | 6.06516i | −0.588182 | − | 0.259803i | ||||
\(546\) | 1.75672 | − | 3.07132i | 0.0751805 | − | 0.131441i | ||||
\(547\) | − | 25.8936i | − | 1.10713i | −0.832806 | − | 0.553565i | \(-0.813267\pi\) | ||
0.832806 | − | 0.553565i | \(-0.186733\pi\) | |||||||
\(548\) | −10.6793 | + | 18.4971i | −0.456198 | + | 0.790157i | ||||
\(549\) | 0.463750 | − | 0.803239i | 0.0197924 | − | 0.0342814i | ||||
\(550\) | 3.98481 | + | 1.26885i | 0.169913 | + | 0.0541038i | ||||
\(551\) | − | 4.25904i | − | 0.181441i | ||||||
\(552\) | 7.11110 | + | 12.3168i | 0.302668 | + | 0.524237i | ||||
\(553\) | −7.66800 | − | 13.2814i | −0.326077 | − | 0.564781i | ||||
\(554\) | − | 8.60159i | − | 0.365447i | ||||||
\(555\) | 1.14315 | + | 10.5766i | 0.0485240 | + | 0.448953i | ||||
\(556\) | −9.27737 | + | 16.0689i | −0.393448 | + | 0.681472i | ||||
\(557\) | 0.649455 | − | 1.12489i | 0.0275183 | − | 0.0476631i | −0.851938 | − | 0.523642i | \(-0.824573\pi\) |
0.879457 | + | 0.475979i | \(0.157906\pi\) | |||||||
\(558\) | 0.468566i | 0.0198360i | ||||||||
\(559\) | −4.05178 | − | 6.95283i | −0.171372 | − | 0.294073i | ||||
\(560\) | 3.02405 | − | 6.84630i | 0.127789 | − | 0.289309i | ||||
\(561\) | 4.01079 | + | 2.31563i | 0.169336 | + | 0.0977659i | ||||
\(562\) | 6.04411 | + | 3.48957i | 0.254955 | + | 0.147199i | ||||
\(563\) | 19.1708 | − | 11.0683i | 0.807955 | − | 0.466473i | −0.0382903 | − | 0.999267i | \(-0.512191\pi\) |
0.846245 | + | 0.532794i | \(0.178858\pi\) | |||||||
\(564\) | − | 5.66955i | − | 0.238731i | ||||||
\(565\) | −4.71378 | − | 43.6128i | −0.198310 | − | 1.83481i | ||||
\(566\) | −11.8457 | + | 6.83913i | −0.497913 | + | 0.287470i | ||||
\(567\) | −1.65741 | −0.0696047 | ||||||||
\(568\) | 2.04807 | − | 1.18245i | 0.0859351 | − | 0.0496146i | ||||
\(569\) | 18.6123 | − | 32.2374i | 0.780267 | − | 1.35146i | −0.151519 | − | 0.988454i | \(-0.548416\pi\) |
0.931786 | − | 0.363008i | \(-0.118250\pi\) | |||||||
\(570\) | −6.57917 | − | 8.99960i | −0.275571 | − | 0.376952i | ||||
\(571\) | −2.36985 | −0.0991752 | −0.0495876 | − | 0.998770i | \(-0.515791\pi\) | ||||
−0.0495876 | + | 0.998770i | \(0.515791\pi\) | |||||||
\(572\) | 8.40092 | − | 0.0339555i | 0.351260 | − | 0.00141975i | ||||
\(573\) | 4.29731i | 0.179523i | ||||||||
\(574\) | −7.52899 | − | 4.34686i | −0.314254 | − | 0.181435i | ||||
\(575\) | 7.03182 | + | 32.1499i | 0.293247 | + | 1.34074i | ||||
\(576\) | −0.386149 | − | 0.668830i | −0.0160896 | − | 0.0278679i | ||||
\(577\) | 18.2135 | 0.758238 | 0.379119 | − | 0.925348i | \(-0.376227\pi\) | ||||
0.379119 | + | 0.925348i | \(0.376227\pi\) | |||||||
\(578\) | 1.85069 | + | 3.20550i | 0.0769787 | + | 0.133331i | ||||
\(579\) | −5.48344 | + | 3.16587i | −0.227884 | + | 0.131569i | ||||
\(580\) | −0.753761 | + | 1.70648i | −0.0312982 | + | 0.0708578i | ||||
\(581\) | 3.33638 | + | 5.77877i | 0.138416 | + | 0.239744i | ||||
\(582\) | 1.62000 | + | 0.935308i | 0.0671512 | + | 0.0387698i | ||||
\(583\) | −0.298152 | + | 0.516415i | −0.0123482 | + | 0.0213877i | ||||
\(584\) | 24.2289 | 1.00260 | ||||||||
\(585\) | −0.898733 | − | 8.01201i | −0.0371581 | − | 0.331256i | ||||
\(586\) | −5.67508 | −0.234435 | ||||||||
\(587\) | −13.0547 | + | 22.6115i | −0.538827 | + | 0.933275i | 0.460141 | + | 0.887846i | \(0.347799\pi\) |
−0.998968 | + | 0.0454293i | \(0.985534\pi\) | |||||||
\(588\) | −6.07520 | − | 3.50752i | −0.250537 | − | 0.144648i | ||||
\(589\) | 3.33184 | + | 5.77091i | 0.137286 | + | 0.237786i | ||||
\(590\) | 15.8640 | + | 7.00722i | 0.653112 | + | 0.288483i | ||||
\(591\) | −19.2617 | + | 11.1207i | −0.792320 | + | 0.457446i | ||||
\(592\) | −4.80395 | − | 8.32069i | −0.197441 | − | 0.341978i | ||||
\(593\) | −24.8984 | −1.02245 | −0.511226 | − | 0.859446i | \(-0.670809\pi\) | ||||
−0.511226 | + | 0.859446i | \(0.670809\pi\) | |||||||
\(594\) | 0.418195 | + | 0.724334i | 0.0171587 | + | 0.0297198i | ||||
\(595\) | −9.80880 | + | 7.17073i | −0.402121 | + | 0.293971i | ||||
\(596\) | −28.1789 | − | 16.2691i | −1.15425 | − | 0.666409i | ||||
\(597\) | 4.39426i | 0.179845i | ||||||||
\(598\) | −7.07472 | − | 12.1402i | −0.289307 | − | 0.496449i | ||||
\(599\) | −6.57002 | −0.268444 | −0.134222 | − | 0.990951i | \(-0.542853\pi\) | ||||
−0.134222 | + | 0.990951i | \(0.542853\pi\) | |||||||
\(600\) | 2.30846 | + | 10.5544i | 0.0942423 | + | 0.430881i | ||||
\(601\) | −12.8209 | + | 22.2064i | −0.522975 | + | 0.905819i | 0.476668 | + | 0.879084i | \(0.341845\pi\) |
−0.999643 | + | 0.0267356i | \(0.991489\pi\) | |||||||
\(602\) | −1.89681 | + | 1.09512i | −0.0773080 | + | 0.0446338i | ||||
\(603\) | 12.4231 | 0.505907 | ||||||||
\(604\) | 4.89680 | − | 2.82717i | 0.199248 | − | 0.115036i | ||||
\(605\) | 20.0181 | − | 2.16361i | 0.813853 | − | 0.0879632i | ||||
\(606\) | − | 5.29493i | − | 0.215092i | ||||||
\(607\) | 34.4882 | − | 19.9118i | 1.39983 | − | 0.808195i | 0.405460 | − | 0.914113i | \(-0.367111\pi\) |
0.994375 | + | 0.105918i | \(0.0337781\pi\) | |||||||
\(608\) | 40.2330 | + | 23.2286i | 1.63167 | + | 0.942043i | ||||
\(609\) | −0.726013 | − | 0.419164i | −0.0294195 | − | 0.0169854i | ||||
\(610\) | 0.496150 | − | 1.12326i | 0.0200885 | − | 0.0454796i | ||||
\(611\) | 0.0500916 | + | 12.3931i | 0.00202649 | + | 0.501373i | ||||
\(612\) | 5.40767i | 0.218592i | ||||||||
\(613\) | 17.7378 | − | 30.7228i | 0.716423 | − | 1.24088i | −0.245985 | − | 0.969274i | \(-0.579111\pi\) |
0.962408 | − | 0.271608i | \(-0.0875553\pi\) | |||||||
\(614\) | −7.46454 | + | 12.9290i | −0.301244 | + | 0.521771i | ||||
\(615\) | −19.6949 | + | 2.12868i | −0.794176 | + | 0.0858365i | ||||
\(616\) | − | 5.05899i | − | 0.203833i | ||||||
\(617\) | 5.58683 | + | 9.67668i | 0.224917 | + | 0.389568i | 0.956295 | − | 0.292405i | \(-0.0944554\pi\) |
−0.731377 | + | 0.681973i | \(0.761122\pi\) | |||||||
\(618\) | 4.44942 | + | 7.70662i | 0.178982 | + | 0.310006i | ||||
\(619\) | 35.2047i | 1.41500i | 0.706715 | + | 0.707498i | \(0.250176\pi\) | ||||
−0.706715 | + | 0.707498i | \(0.749824\pi\) | |||||||
\(620\) | −0.313646 | − | 2.90191i | −0.0125963 | − | 0.116544i | ||||
\(621\) | −3.29099 | + | 5.70016i | −0.132063 | + | 0.228740i | ||||
\(622\) | 0.504071 | − | 0.873076i | 0.0202114 | − | 0.0350072i | ||||
\(623\) | − | 0.991143i | − | 0.0397093i | ||||||
\(624\) | 3.66616 | + | 6.29112i | 0.146764 | + | 0.251846i | ||||
\(625\) | −2.32018 | + | 24.8921i | −0.0928071 | + | 0.995684i | ||||
\(626\) | 12.8740 | + | 7.43283i | 0.514550 | + | 0.297076i | ||||
\(627\) | 10.3011 | + | 5.94732i | 0.411385 | + | 0.237513i | ||||
\(628\) | 5.66563 | − | 3.27105i | 0.226083 | − | 0.130529i | ||||
\(629\) | 15.5977i | 0.621920i | ||||||||
\(630\) | −2.18161 | + | 0.235794i | −0.0869175 | + | 0.00939426i | ||||
\(631\) | 4.83806 | − | 2.79326i | 0.192600 | − | 0.111198i | −0.400599 | − | 0.916253i | \(-0.631198\pi\) |
0.593199 | + | 0.805056i | \(0.297865\pi\) | |||||||
\(632\) | −19.9937 | −0.795306 | ||||||||
\(633\) | −5.80648 | + | 3.35237i | −0.230787 | + | 0.133245i | ||||
\(634\) | 0.562099 | − | 0.973584i | 0.0223238 | − | 0.0386659i | ||||
\(635\) | 29.6814 | − | 21.6986i | 1.17787 | − | 0.861083i | ||||
\(636\) | −0.696273 | −0.0276090 | ||||||||
\(637\) | 13.3109 | + | 7.61346i | 0.527395 | + | 0.301656i | ||||
\(638\) | 0.423051i | 0.0167487i | ||||||||
\(639\) | 0.947838 | + | 0.547235i | 0.0374959 | + | 0.0216483i | ||||
\(640\) | −15.1652 | − | 20.7443i | −0.599456 | − | 0.819992i | ||||
\(641\) | −10.8579 | − | 18.8064i | −0.428861 | − | 0.742809i | 0.567911 | − | 0.823090i | \(-0.307752\pi\) |
−0.996772 | + | 0.0802807i | \(0.974418\pi\) | |||||||
\(642\) | −11.1822 | −0.441328 | ||||||||
\(643\) | −8.01232 | − | 13.8777i | −0.315975 | − | 0.547285i | 0.663669 | − | 0.748026i | \(-0.268998\pi\) |
−0.979644 | + | 0.200741i | \(0.935665\pi\) | |||||||
\(644\) | 15.5830 | − | 8.99686i | 0.614057 | − | 0.354526i | ||||
\(645\) | −2.01647 | + | 4.56520i | −0.0793985 | + | 0.179755i | ||||
\(646\) | −8.17255 | − | 14.1553i | −0.321545 | − | 0.556932i | ||||
\(647\) | −9.58441 | − | 5.53356i | −0.376802 | − | 0.217547i | 0.299624 | − | 0.954057i | \(-0.403139\pi\) |
−0.676426 | + | 0.736511i | \(0.736472\pi\) | |||||||
\(648\) | −1.08039 | + | 1.87129i | −0.0424417 | + | 0.0735112i | ||||
\(649\) | −18.5042 | −0.726353 | ||||||||
\(650\) | −2.32283 | − | 10.4182i | −0.0911087 | − | 0.408635i | ||||
\(651\) | 1.31164 | 0.0514074 | ||||||||
\(652\) | −1.64501 | + | 2.84924i | −0.0644234 | + | 0.111585i | ||||
\(653\) | −24.6070 | − | 14.2069i | −0.962946 | − | 0.555957i | −0.0658676 | − | 0.997828i | \(-0.520981\pi\) |
−0.897079 | + | 0.441871i | \(0.854315\pi\) | |||||||
\(654\) | −1.98739 | − | 3.44225i | −0.0777130 | − | 0.134603i | ||||
\(655\) | −5.52528 | + | 12.5090i | −0.215890 | + | 0.488766i | ||||
\(656\) | 15.4941 | − | 8.94552i | 0.604943 | − | 0.349264i | ||||
\(657\) | 5.60652 | + | 9.71077i | 0.218731 | + | 0.378853i | ||||
\(658\) | 3.37309 | 0.131497 | ||||||||
\(659\) | −13.1876 | − | 22.8416i | −0.513717 | − | 0.889783i | −0.999873 | − | 0.0159116i | \(-0.994935\pi\) |
0.486157 | − | 0.873872i | \(-0.338398\pi\) | |||||||
\(660\) | −3.07480 | − | 4.20600i | −0.119686 | − | 0.163718i | ||||
\(661\) | 25.3928 | + | 14.6606i | 0.987667 | + | 0.570230i | 0.904576 | − | 0.426312i | \(-0.140188\pi\) |
0.0830907 | + | 0.996542i | \(0.473521\pi\) | |||||||
\(662\) | 12.0083i | 0.466714i | ||||||||
\(663\) | −0.0477778 | − | 11.8207i | −0.00185554 | − | 0.459078i | ||||
\(664\) | 8.69933 | 0.337599 | ||||||||
\(665\) | −25.1923 | + | 18.4169i | −0.976916 | + | 0.714176i | ||||
\(666\) | −1.40844 | + | 2.43950i | −0.0545761 | + | 0.0945286i | ||||
\(667\) | −2.88318 | + | 1.66460i | −0.111637 | + | 0.0644537i | ||||
\(668\) | −18.9446 | −0.732987 | ||||||||
\(669\) | 11.7532 | − | 6.78573i | 0.454406 | − | 0.262352i | ||||
\(670\) | 16.3522 | − | 1.76739i | 0.631742 | − | 0.0682803i | ||||
\(671\) | 1.31020i | 0.0505797i | ||||||||
\(672\) | 7.91927 | − | 4.57219i | 0.305493 | − | 0.176376i | ||||
\(673\) | 35.3958 | + | 20.4358i | 1.36441 | + | 0.787741i | 0.990207 | − | 0.139607i | \(-0.0445839\pi\) |
0.374200 | + | 0.927348i | \(0.377917\pi\) | |||||||
\(674\) | 8.62632 | + | 4.98041i | 0.332274 | + | 0.191838i | ||||
\(675\) | −3.69596 | + | 3.36748i | −0.142257 | + | 0.129614i | ||||
\(676\) | −10.8711 | − | 18.4826i | −0.418119 | − | 0.710869i | ||||
\(677\) | − | 33.8996i | − | 1.30287i | −0.758705 | − | 0.651435i | \(-0.774167\pi\) | ||
0.758705 | − | 0.651435i | \(-0.225833\pi\) | |||||||
\(678\) | 5.80772 | − | 10.0593i | 0.223044 | − | 0.386324i | ||||
\(679\) | 2.61818 | − | 4.53482i | 0.100477 | − | 0.174030i | ||||
\(680\) | 1.70217 | + | 15.7488i | 0.0652754 | + | 0.603941i | ||||
\(681\) | − | 0.297007i | − | 0.0113813i | ||||||
\(682\) | −0.330952 | − | 0.573225i | −0.0126728 | − | 0.0219499i | ||||
\(683\) | 5.28626 | + | 9.15608i | 0.202273 | + | 0.350347i | 0.949261 | − | 0.314491i | \(-0.101834\pi\) |
−0.746987 | + | 0.664838i | \(0.768500\pi\) | |||||||
\(684\) | 13.8887i | 0.531049i | ||||||||
\(685\) | −28.7873 | + | 3.11140i | −1.09991 | + | 0.118881i | ||||
\(686\) | 5.52145 | − | 9.56342i | 0.210810 | − | 0.365133i | ||||
\(687\) | 7.15790 | − | 12.3978i | 0.273091 | − | 0.473007i | ||||
\(688\) | − | 4.50735i | − | 0.171841i | ||||||
\(689\) | 1.52199 | − | 0.00615171i | 0.0579833 | − | 0.000234361i | ||||
\(690\) | −3.52092 | + | 7.97120i | −0.134039 | + | 0.303458i | ||||
\(691\) | 8.65326 | + | 4.99596i | 0.329186 | + | 0.190055i | 0.655479 | − | 0.755213i | \(-0.272467\pi\) |
−0.326294 | + | 0.945268i | \(0.605800\pi\) | |||||||
\(692\) | −18.0991 | − | 10.4495i | −0.688024 | − | 0.397231i | ||||
\(693\) | 2.02761 | − | 1.17064i | 0.0770225 | − | 0.0444689i | ||||
\(694\) | 4.82968i | 0.183332i | ||||||||
\(695\) | −25.0082 | + | 2.70295i | −0.948616 | + | 0.102529i | ||||
\(696\) | −0.946510 | + | 0.546468i | −0.0358774 | + | 0.0207138i | ||||
\(697\) | −29.0447 | −1.10015 | ||||||||
\(698\) | 7.56331 | − | 4.36668i | 0.286276 | − | 0.165281i | ||||
\(699\) | −6.48998 | + | 11.2410i | −0.245473 | + | 0.425173i | ||||
\(700\) | 13.3533 | − | 2.92063i | 0.504706 | − | 0.110389i | ||||
\(701\) | 30.4957 | 1.15181 | 0.575903 | − | 0.817518i | \(-0.304651\pi\) | ||||
0.575903 | + | 0.817518i | \(0.304651\pi\) | |||||||
\(702\) | 1.05992 | − | 1.85309i | 0.0400040 | − | 0.0699403i | ||||
\(703\) | 40.0601i | 1.51090i | ||||||||
\(704\) | 0.944799 | + | 0.545480i | 0.0356085 | + | 0.0205586i | ||||
\(705\) | 6.20474 | − | 4.53599i | 0.233684 | − | 0.170835i | ||||
\(706\) | −4.62606 | − | 8.01256i | −0.174104 | − | 0.301557i | ||||
\(707\) | −14.8220 | −0.557437 | ||||||||
\(708\) | −10.8032 | − | 18.7117i | −0.406008 | − | 0.703227i | ||||
\(709\) | −9.17071 | + | 5.29471i | −0.344413 | + | 0.198847i | −0.662222 | − | 0.749308i | \(-0.730386\pi\) |
0.317809 | + | 0.948155i | \(0.397053\pi\) | |||||||
\(710\) | 1.32547 | + | 0.585468i | 0.0497441 | + | 0.0219722i | ||||
\(711\) | −4.62650 | − | 8.01333i | −0.173507 | − | 0.300523i | ||||
\(712\) | −1.11905 | − | 0.646081i | −0.0419380 | − | 0.0242129i | ||||
\(713\) | 2.60443 | − | 4.51100i | 0.0975366 | − | 0.168938i | ||||
\(714\) | −3.21729 | −0.120404 | ||||||||
\(715\) | 6.75841 | + | 9.16679i | 0.252750 | + | 0.342818i | ||||
\(716\) | −14.1437 | −0.528576 | ||||||||
\(717\) | 6.83327 | − | 11.8356i | 0.255193 | − | 0.442007i | ||||
\(718\) | −12.0910 | − | 6.98076i | −0.451233 | − | 0.260520i | ||||
\(719\) | −3.68101 | − | 6.37570i | −0.137279 | − | 0.237774i | 0.789187 | − | 0.614153i | \(-0.210502\pi\) |
−0.926466 | + | 0.376379i | \(0.877169\pi\) | |||||||
\(720\) | 1.82456 | − | 4.13073i | 0.0679974 | − | 0.153943i | ||||
\(721\) | 21.5729 | − | 12.4551i | 0.803418 | − | 0.463854i | ||||
\(722\) | −15.3651 | − | 26.6131i | −0.571828 | − | 0.990436i | ||||
\(723\) | −12.1296 | −0.451103 | ||||||||
\(724\) | −18.9287 | − | 32.7854i | −0.703478 | − | 1.21846i | ||||
\(725\) | −2.47063 | + | 0.540375i | −0.0917567 | + | 0.0200690i | ||||
\(726\) | 4.61717 | + | 2.66573i | 0.171359 | + | 0.0989344i | ||||
\(727\) | 30.8420i | 1.14387i | 0.820300 | + | 0.571934i | \(0.193807\pi\) | ||||
−0.820300 | + | 0.571934i | \(0.806193\pi\) | |||||||
\(728\) | −11.1564 | + | 6.50142i | −0.413484 | + | 0.240959i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 8.76126 | + | 11.9845i | 0.324269 | + | 0.443565i | ||||
\(731\) | −3.65867 | + | 6.33700i | −0.135321 | + | 0.234382i | ||||
\(732\) | −1.32489 | + | 0.764925i | −0.0489693 | + | 0.0282724i | ||||
\(733\) | −30.7552 | −1.13597 | −0.567985 | − | 0.823039i | \(-0.692277\pi\) | ||||
−0.567985 | + | 0.823039i | \(0.692277\pi\) | |||||||
\(734\) | −7.39154 | + | 4.26751i | −0.272827 | + | 0.157517i | ||||
\(735\) | −1.02191 | − | 9.45492i | −0.0376937 | − | 0.348750i | ||||
\(736\) | − | 36.3146i | − | 1.33857i | ||||||
\(737\) | −15.1979 | + | 8.77452i | −0.559822 | + | 0.323213i | ||||
\(738\) | −4.54263 | − | 2.62269i | −0.167216 | − | 0.0965424i | ||||
\(739\) | −31.3327 | − | 18.0899i | −1.15259 | − | 0.665449i | −0.203074 | − | 0.979163i | \(-0.565093\pi\) |
−0.949517 | + | 0.313715i | \(0.898426\pi\) | |||||||
\(740\) | 7.08980 | − | 16.0510i | 0.260626 | − | 0.590046i | ||||
\(741\) | −0.122710 | − | 30.3596i | −0.00450785 | − | 1.11529i | ||||
\(742\) | − | 0.414247i | − | 0.0152075i | ||||||
\(743\) | −7.22170 | + | 12.5084i | −0.264938 | + | 0.458887i | −0.967547 | − | 0.252689i | \(-0.918685\pi\) |
0.702609 | + | 0.711576i | \(0.252018\pi\) | |||||||
\(744\) | 0.855001 | − | 1.48091i | 0.0313459 | − | 0.0542926i | ||||
\(745\) | −4.73998 | − | 43.8553i | −0.173660 | − | 1.60673i | ||||
\(746\) | − | 6.15642i | − | 0.225403i | ||||||
\(747\) | 2.01301 | + | 3.48663i | 0.0736521 | + | 0.127569i | ||||
\(748\) | −3.81948 | − | 6.61553i | −0.139654 | − | 0.241888i | ||||
\(749\) | 31.3021i | 1.14375i | ||||||||
\(750\) | −4.38583 | + | 4.95835i | −0.160148 | + | 0.181053i | ||||
\(751\) | −0.691642 | + | 1.19796i | −0.0252384 | + | 0.0437142i | −0.878369 | − | 0.477984i | \(-0.841368\pi\) |
0.853130 | + | 0.521698i | \(0.174701\pi\) | |||||||
\(752\) | −3.47078 | + | 6.01157i | −0.126566 | + | 0.219219i | ||||
\(753\) | 13.7790i | 0.502136i | ||||||||
\(754\) | 0.932939 | − | 0.543672i | 0.0339756 | − | 0.0197994i | ||||
\(755\) | 7.01179 | + | 3.09714i | 0.255185 | + | 0.112717i | ||||
\(756\) | 2.36753 | + | 1.36689i | 0.0861062 | + | 0.0497134i | ||||
\(757\) | 44.1964 | + | 25.5168i | 1.60635 | + | 0.927424i | 0.990179 | + | 0.139808i | \(0.0446485\pi\) |
0.616167 | + | 0.787616i | \(0.288685\pi\) | |||||||
\(758\) | −2.00227 | + | 1.15601i | −0.0727258 | + | 0.0419883i | ||||
\(759\) | − | 9.29780i | − | 0.337489i | ||||||
\(760\) | 4.37176 | + | 40.4484i | 0.158580 | + | 1.46722i | ||||
\(761\) | −2.32993 | + | 1.34518i | −0.0844598 | + | 0.0487629i | −0.541635 | − | 0.840614i | \(-0.682195\pi\) |
0.457175 | + | 0.889377i | \(0.348861\pi\) | |||||||
\(762\) | 9.73550 | 0.352680 | ||||||||
\(763\) | −9.63580 | + | 5.56323i | −0.348840 | + | 0.201403i | ||||
\(764\) | 3.54406 | − | 6.13849i | 0.128220 | − | 0.222083i | ||||
\(765\) | −5.91815 | + | 4.32647i | −0.213971 | + | 0.156424i | ||||
\(766\) | −19.2552 | −0.695717 | ||||||||
\(767\) | 23.7802 | + | 40.8066i | 0.858651 | + | 1.47344i | ||||
\(768\) | − | 5.25955i | − | 0.189788i | ||||||
\(769\) | 8.85248 | + | 5.11098i | 0.319228 | + | 0.184307i | 0.651049 | − | 0.759036i | \(-0.274329\pi\) |
−0.331820 | + | 0.943343i | \(0.607663\pi\) | |||||||
\(770\) | 2.50235 | − | 1.82935i | 0.0901786 | − | 0.0659252i | ||||
\(771\) | −2.80002 | − | 4.84978i | −0.100840 | − | 0.174661i | ||||
\(772\) | 10.4438 | 0.375880 | ||||||||
\(773\) | 9.46421 | + | 16.3925i | 0.340404 | + | 0.589597i | 0.984508 | − | 0.175341i | \(-0.0561028\pi\) |
−0.644104 | + | 0.764938i | \(0.722770\pi\) | |||||||
\(774\) | −1.14444 | + | 0.660743i | −0.0411360 | + | 0.0237499i | ||||
\(775\) | 2.92491 | − | 2.66496i | 0.105066 | − | 0.0957283i | ||||
\(776\) | −3.41334 | − | 5.91208i | −0.122532 | − | 0.212231i | ||||
\(777\) | 6.82881 | + | 3.94262i | 0.244982 | + | 0.141441i | ||||
\(778\) | 10.8111 | − | 18.7254i | 0.387598 | − | 0.671340i | ||||
\(779\) | −74.5966 | −2.67270 | ||||||||
\(780\) | −5.32384 | + | 12.1860i | −0.190624 | + | 0.436328i | ||||
\(781\) | −1.54606 | −0.0553225 | ||||||||
\(782\) | −6.38832 | + | 11.0649i | −0.228446 | + | 0.395680i | ||||
\(783\) | −0.438041 | − | 0.252903i | −0.0156543 | − | 0.00903802i | ||||
\(784\) | 4.29446 | + | 7.43823i | 0.153374 | + | 0.265651i | ||||
\(785\) | 8.11269 | + | 3.58341i | 0.289554 | + | 0.127898i | ||||
\(786\) | −3.13585 | + | 1.81048i | −0.111852 | + | 0.0645778i | ||||
\(787\) | 10.9136 | + | 18.9030i | 0.389029 | + | 0.673818i | 0.992319 | − | 0.123703i | \(-0.0394772\pi\) |
−0.603290 | + | 0.797522i | \(0.706144\pi\) | |||||||
\(788\) | 36.6858 | 1.30688 | ||||||||
\(789\) | 4.49001 | + | 7.77693i | 0.159849 | + | 0.276866i | ||||
\(790\) | −7.22979 | − | 9.88958i | −0.257224 | − | 0.351855i | ||||
\(791\) | −28.1586 | − | 16.2574i | −1.00121 | − | 0.578046i | ||||
\(792\) | − | 3.05235i | − | 0.108460i | ||||||
\(793\) | 2.88934 | − | 1.68377i | 0.102603 | − | 0.0597923i | ||||
\(794\) | 6.10598 | 0.216693 | ||||||||
\(795\) | −0.557061 | − | 0.762000i | −0.0197569 | − | 0.0270254i | ||||
\(796\) | 3.62402 | − | 6.27699i | 0.128450 | − | 0.222482i | ||||
\(797\) | 33.5184 | − | 19.3519i | 1.18728 | − | 0.685478i | 0.229594 | − | 0.973286i | \(-0.426260\pi\) |
0.957688 | + | 0.287809i | \(0.0929267\pi\) | |||||||
\(798\) | −8.26308 | −0.292510 | ||||||||
\(799\) | 9.75931 | − | 5.63454i | 0.345260 | − | 0.199336i | ||||
\(800\) | 8.37000 | − | 26.2860i | 0.295924 | − | 0.929349i | ||||
\(801\) | − | 0.598008i | − | 0.0211296i | ||||||
\(802\) | −10.6996 | + | 6.17740i | −0.377815 | + | 0.218131i | ||||
\(803\) | −13.7176 | − | 7.91985i | −0.484083 | − | 0.279485i | ||||
\(804\) | −17.7458 | − | 10.2455i | −0.625846 | − | 0.361332i | ||||
\(805\) | 22.3135 | + | 9.85600i | 0.786449 | + | 0.347378i | ||||
\(806\) | −0.838799 | + | 1.46650i | −0.0295454 | + | 0.0516553i | ||||
\(807\) | − | 4.07724i | − | 0.143526i | ||||||
\(808\) | −9.66175 | + | 16.7347i | −0.339899 | + | 0.588723i | ||||
\(809\) | −21.3022 | + | 36.8965i | −0.748946 | + | 1.29721i | 0.199383 | + | 0.979922i | \(0.436106\pi\) |
−0.948328 | + | 0.317291i | \(0.897227\pi\) | |||||||
\(810\) | −1.31628 | + | 0.142267i | −0.0462493 | + | 0.00499874i | ||||
\(811\) | 9.60428i | 0.337252i | 0.985680 | + | 0.168626i | \(0.0539330\pi\) | ||||
−0.985680 | + | 0.168626i | \(0.946067\pi\) | |||||||
\(812\) | 0.691383 | + | 1.19751i | 0.0242628 | + | 0.0420244i | ||||
\(813\) | −9.89780 | − | 17.1435i | −0.347131 | − | 0.601249i | ||||
\(814\) | − | 3.97918i | − | 0.139470i | ||||||
\(815\) | −4.43431 | + | 0.479271i | −0.155327 | + | 0.0167881i | ||||
\(816\) | 3.31047 | − | 5.73390i | 0.115890 | − | 0.200727i | ||||
\(817\) | −9.39669 | + | 16.2755i | −0.328749 | + | 0.569409i | ||||
\(818\) | − | 2.29050i | − | 0.0800855i | ||||||
\(819\) | −5.18729 | − | 2.96700i | −0.181259 | − | 0.103675i | ||||
\(820\) | 29.8888 | + | 13.2020i | 1.04376 | + | 0.461035i | ||||
\(821\) | −29.9683 | − | 17.3022i | −1.04590 | − | 0.603851i | −0.124402 | − | 0.992232i | \(-0.539701\pi\) |
−0.921499 | + | 0.388381i | \(0.873035\pi\) | |||||||
\(822\) | −6.63978 | − | 3.83348i | −0.231589 | − | 0.133708i | ||||
\(823\) | −24.0422 | + | 13.8808i | −0.838057 | + | 0.483853i | −0.856603 | − | 0.515975i | \(-0.827430\pi\) |
0.0185460 | + | 0.999828i | \(0.494096\pi\) | |||||||
\(824\) | − | 32.4757i | − | 1.13135i | ||||||
\(825\) | 2.14301 | − | 6.73012i | 0.0746100 | − | 0.234313i | ||||
\(826\) | 11.1325 | − | 6.42734i | 0.387349 | − | 0.223636i | ||||
\(827\) | −27.8932 | −0.969943 | −0.484971 | − | 0.874530i | \(-0.661170\pi\) | ||||
−0.484971 | + | 0.874530i | \(0.661170\pi\) | |||||||
\(828\) | 9.40204 | − | 5.42827i | 0.326743 | − | 0.188645i | ||||
\(829\) | −7.47706 | + | 12.9507i | −0.259689 | + | 0.449795i | −0.966159 | − | 0.257949i | \(-0.916953\pi\) |
0.706469 | + | 0.707744i | \(0.250287\pi\) | |||||||
\(830\) | 3.14571 | + | 4.30299i | 0.109189 | + | 0.149359i | ||||
\(831\) | −14.5276 | −0.503957 | ||||||||
\(832\) | −0.0112548 | − | 2.78454i | −0.000390189 | − | 0.0965366i | ||||
\(833\) | − | 13.9434i | − | 0.483112i | ||||||
\(834\) | −5.76813 | − | 3.33023i | −0.199734 | − | 0.115317i | ||||
\(835\) | −15.1568 | − | 20.7329i | −0.524523 | − | 0.717492i | ||||
\(836\) | −9.80971 | − | 16.9909i | −0.339276 | − | 0.587643i | ||||
\(837\) | 0.791382 | 0.0273542 | ||||||||
\(838\) | −6.39503 | − | 11.0765i | −0.220913 | − | 0.382632i | ||||
\(839\) | 20.9723 | − | 12.1084i | 0.724044 | − | 0.418027i | −0.0921951 | − | 0.995741i | \(-0.529388\pi\) |
0.816239 | + | 0.577714i | \(0.196055\pi\) | |||||||
\(840\) | 7.32525 | + | 3.23560i | 0.252745 | + | 0.111639i | ||||
\(841\) | 14.3721 | + | 24.8932i | 0.495589 | + | 0.858385i | ||||
\(842\) | −6.09254 | − | 3.51753i | −0.209963 | − | 0.121222i | ||||
\(843\) | 5.89369 | − | 10.2082i | 0.202989 | − | 0.351588i | ||||
\(844\) | 11.0590 | 0.380667 | ||||||||
\(845\) | 11.5298 | − | 26.6845i | 0.396637 | − | 0.917975i | ||||
\(846\) | 2.03516 | 0.0699702 | ||||||||
\(847\) | 7.46209 | − | 12.9247i | 0.256400 | − | 0.444099i | ||||
\(848\) | 0.738277 | + | 0.426244i | 0.0253525 | + | 0.0146373i | ||||
\(849\) | 11.5509 | + | 20.0067i | 0.396426 | + | 0.686630i | ||||
\(850\) | −7.17442 | + | 6.53680i | −0.246081 | + | 0.224210i | ||||
\(851\) | 27.1189 | − | 15.6571i | 0.929623 | − | 0.536718i | ||||
\(852\) | −0.902628 | − | 1.56340i | −0.0309235 | − | 0.0535611i | ||||
\(853\) | 25.6140 | 0.877008 | 0.438504 | − | 0.898729i | \(-0.355508\pi\) | ||||
0.438504 | + | 0.898729i | \(0.355508\pi\) | |||||||
\(854\) | −0.455091 | − | 0.788242i | −0.0155729 | − | 0.0269731i | ||||
\(855\) | −15.1998 | + | 11.1118i | −0.519822 | + | 0.380017i | ||||
\(856\) | 35.3415 | + | 20.4044i | 1.20795 | + | 0.697409i | ||||
\(857\) | − | 38.9380i | − | 1.33010i | −0.746800 | − | 0.665049i | \(-0.768411\pi\) | ||
0.746800 | − | 0.665049i | \(-0.231589\pi\) | |||||||
\(858\) | 0.0121888 | + | 3.01562i | 0.000416118 | + | 0.102952i | ||||
\(859\) | −32.9648 | −1.12474 | −0.562372 | − | 0.826885i | \(-0.690111\pi\) | ||||
−0.562372 | + | 0.826885i | \(0.690111\pi\) | |||||||
\(860\) | 6.64543 | − | 4.85815i | 0.226607 | − | 0.165662i | ||||
\(861\) | −7.34161 | + | 12.7160i | −0.250201 | + | 0.433361i | ||||
\(862\) | −5.58351 | + | 3.22364i | −0.190175 | + | 0.109798i | ||||
\(863\) | 12.9022 | 0.439197 | 0.219598 | − | 0.975590i | \(-0.429525\pi\) | ||||
0.219598 | + | 0.975590i | \(0.429525\pi\) | |||||||
\(864\) | 4.77810 | − | 2.75864i | 0.162554 | − | 0.0938508i | ||||
\(865\) | −3.04445 | − | 28.1679i | −0.103514 | − | 0.957736i | ||||
\(866\) | 18.9799i | 0.644965i | ||||||||
\(867\) | 5.41390 | − | 3.12572i | 0.183866 | − | 0.106155i | ||||
\(868\) | −1.87362 | − | 1.08174i | −0.0635948 | − | 0.0367165i | ||||
\(869\) | 11.3197 | + | 6.53546i | 0.383996 | + | 0.221700i | ||||
\(870\) | −0.612564 | − | 0.270572i | −0.0207679 | − | 0.00917326i | ||||
\(871\) | 38.8813 | + | 22.2391i | 1.31744 | + | 0.753542i | ||||
\(872\) | 14.5057i | 0.491224i | ||||||||
\(873\) | 1.57968 | − | 2.73609i | 0.0534641 | − | 0.0926026i | ||||
\(874\) | −16.4074 | + | 28.4184i | −0.554987 | + | 0.961266i | ||||
\(875\) | 13.8798 | + | 12.2771i | 0.469222 | + | 0.415042i | ||||
\(876\) | − | 18.4952i | − | 0.624894i | ||||||
\(877\) | 5.73911 | + | 9.94043i | 0.193796 | + | 0.335664i | 0.946505 | − | 0.322689i | \(-0.104587\pi\) |
−0.752709 | + | 0.658353i | \(0.771253\pi\) | |||||||
\(878\) | −7.42599 | − | 12.8622i | −0.250615 | − | 0.434078i | ||||
\(879\) | 9.58488i | 0.323290i | ||||||||
\(880\) | 0.685466 | + | 6.34206i | 0.0231070 | + | 0.213791i | ||||
\(881\) | 0.584497 | − | 1.01238i | 0.0196922 | − | 0.0341079i | −0.856011 | − | 0.516957i | \(-0.827065\pi\) |
0.875704 | + | 0.482849i | \(0.160398\pi\) | |||||||
\(882\) | 1.25907 | − | 2.18077i | 0.0423951 | − | 0.0734304i | ||||
\(883\) | − | 1.40478i | − | 0.0472746i | −0.999721 | − | 0.0236373i | \(-0.992475\pi\) | ||
0.999721 | − | 0.0236373i | \(-0.00752468\pi\) | |||||||
\(884\) | −9.68049 | + | 16.9247i | −0.325590 | + | 0.569240i | ||||
\(885\) | 11.8348 | − | 26.7935i | 0.397823 | − | 0.900653i | ||||
\(886\) | 16.4446 | + | 9.49431i | 0.552468 | + | 0.318968i | ||||
\(887\) | −15.0410 | − | 8.68394i | −0.505028 | − | 0.291578i | 0.225759 | − | 0.974183i | \(-0.427514\pi\) |
−0.730788 | + | 0.682605i | \(0.760847\pi\) | |||||||
\(888\) | 8.90278 | − | 5.14002i | 0.298758 | − | 0.172488i | ||||
\(889\) | − | 27.2523i | − | 0.914013i | ||||||
\(890\) | −0.0850765 | − | 0.787145i | −0.00285177 | − | 0.0263851i | ||||
\(891\) | 1.22336 | − | 0.706307i | 0.0409841 | − | 0.0236622i | ||||
\(892\) | −22.3852 | −0.749513 | ||||||||
\(893\) | 25.0652 | − | 14.4714i | 0.838775 | − | 0.484267i | ||||
\(894\) | 5.84001 | − | 10.1152i | 0.195319 | − | 0.338303i | ||||
\(895\) | −11.3159 | − | 15.4789i | −0.378248 | − | 0.517402i | ||||
\(896\) | −19.0467 | −0.636304 | ||||||||
\(897\) | −20.5041 | + | 11.9488i | −0.684612 | + | 0.398959i | ||||
\(898\) | 14.2303i | 0.474873i | ||||||||
\(899\) | 0.346658 | + | 0.200143i | 0.0115617 | + | 0.00667514i | ||||
\(900\) | 8.05671 | − | 1.76216i | 0.268557 | − | 0.0587388i | ||||
\(901\) | −0.691974 | − | 1.19853i | −0.0230530 | − | 0.0399290i | ||||
\(902\) | 7.40969 | 0.246716 | ||||||||
\(903\) | 1.84960 | + | 3.20360i | 0.0615508 | + | 0.106609i | ||||
\(904\) | −36.7107 | + | 21.1949i | −1.22098 | + | 0.704932i | ||||
\(905\) | 20.7362 | − | 46.9459i | 0.689295 | − | 1.56053i | ||||
\(906\) | 1.01485 | + | 1.75777i | 0.0337161 | + | 0.0583980i | ||||
\(907\) | −7.93327 | − | 4.58028i | −0.263420 | − | 0.152086i | 0.362474 | − | 0.931994i | \(-0.381932\pi\) |
−0.625894 | + | 0.779908i | \(0.715266\pi\) | |||||||
\(908\) | −0.244947 | + | 0.424260i | −0.00812884 | + | 0.0140796i | ||||
\(909\) | −8.94284 | −0.296615 | ||||||||
\(910\) | −7.25003 | − | 3.16741i | −0.240336 | − | 0.104999i | ||||
\(911\) | 46.2229 | 1.53143 | 0.765717 | − | 0.643177i | \(-0.222384\pi\) | ||||
0.765717 | + | 0.643177i | \(0.222384\pi\) | |||||||
\(912\) | 8.50240 | − | 14.7266i | 0.281543 | − | 0.487646i | ||||
\(913\) | −4.92526 | − | 2.84360i | −0.163002 | − | 0.0941095i | ||||
\(914\) | 1.27777 | + | 2.21316i | 0.0422647 | + | 0.0732047i | ||||
\(915\) | −1.89713 | − | 0.837970i | −0.0627171 | − | 0.0277024i | ||||
\(916\) | −20.4494 | + | 11.8065i | −0.675668 | + | 0.390097i | ||||
\(917\) | 5.06803 | + | 8.77809i | 0.167361 | + | 0.289878i | ||||
\(918\) | −1.94115 | −0.0640676 | ||||||||
\(919\) | −6.81590 | − | 11.8055i | −0.224836 | − | 0.389427i | 0.731434 | − | 0.681912i | \(-0.238851\pi\) |
−0.956270 | + | 0.292485i | \(0.905518\pi\) | |||||||
\(920\) | 25.6730 | − | 18.7683i | 0.846415 | − | 0.618773i | ||||
\(921\) | 21.8363 | + | 12.6072i | 0.719530 | + | 0.415421i | ||||
\(922\) | 0.365078i | 0.0120232i | ||||||||
\(923\) | 1.98688 | + | 3.40948i | 0.0653989 | + | 0.112224i | ||||
\(924\) | −3.86179 | −0.127043 | ||||||||
\(925\) | 23.2385 | − | 5.08272i | 0.764076 | − | 0.167119i | ||||
\(926\) | −3.95622 | + | 6.85238i | −0.130010 | + | 0.225183i | ||||
\(927\) | 13.0161 | − | 7.51482i | 0.427503 | − | 0.246819i | ||||
\(928\) | 2.79067 | 0.0916083 | ||||||||
\(929\) | −37.6193 | + | 21.7195i | −1.23425 | + | 0.712594i | −0.967913 | − | 0.251286i | \(-0.919147\pi\) |
−0.266336 | + | 0.963880i | \(0.585813\pi\) | |||||||
\(930\) | 1.04168 | − | 0.112587i | 0.0341580 | − | 0.00369188i | ||||
\(931\) | − | 35.8115i | − | 1.17367i | ||||||
\(932\) | 18.5412 | − | 10.7048i | 0.607338 | − | 0.350647i | ||||
\(933\) | −1.47458 | − | 0.851347i | −0.0482755 | − | 0.0278719i | ||||
\(934\) | 13.3938 | + | 7.73293i | 0.438260 | + | 0.253029i | ||||
\(935\) | 4.18421 | − | 9.47286i | 0.136838 | − | 0.309796i | ||||
\(936\) | −6.73123 | + | 3.92264i | −0.220017 | + | 0.128215i | ||||
\(937\) | − | 30.4186i | − | 0.993731i | −0.867828 | − | 0.496865i | \(-0.834484\pi\) | ||
0.867828 | − | 0.496865i | \(-0.165516\pi\) | |||||||
\(938\) | 6.09557 | − | 10.5578i | 0.199027 | − | 0.344726i | ||||
\(939\) | 12.5536 | − | 21.7435i | 0.409672 | − | 0.709573i | ||||
\(940\) | −12.6041 | + | 1.36228i | −0.411100 | + | 0.0444327i | ||||
\(941\) | 55.9477i | 1.82384i | 0.410363 | + | 0.911922i | \(0.365402\pi\) | ||||
−0.410363 | + | 0.911922i | \(0.634598\pi\) | |||||||
\(942\) | 1.17419 | + | 2.03375i | 0.0382571 | + | 0.0662632i | ||||
\(943\) | 29.1553 | + | 50.4985i | 0.949428 | + | 1.64446i | ||||
\(944\) | 26.4540i | 0.861003i | ||||||||
\(945\) | 0.398243 | + | 3.68462i | 0.0129548 | + | 0.119861i | ||||
\(946\) | 0.933375 | − | 1.61665i | 0.0303466 | − | 0.0525619i | ||||
\(947\) | −12.1131 | + | 20.9804i | −0.393622 | + | 0.681773i | −0.992924 | − | 0.118750i | \(-0.962111\pi\) |
0.599303 | + | 0.800523i | \(0.295445\pi\) | |||||||
\(948\) | 15.2622i | 0.495693i | ||||||||
\(949\) | 0.163408 | + | 40.4288i | 0.00530446 | + | 1.31238i | ||||
\(950\) | −18.4263 | + | 16.7887i | −0.597829 | + | 0.544698i | ||||
\(951\) | −1.64433 | − | 0.949353i | −0.0533210 | − | 0.0307849i | ||||
\(952\) | 10.1682 | + | 5.87064i | 0.329555 | + | 0.190269i | ||||
\(953\) | −33.2441 | + | 19.1935i | −1.07688 | + | 0.621739i | −0.930054 | − | 0.367423i | \(-0.880240\pi\) |
−0.146830 | + | 0.989162i | \(0.546907\pi\) | |||||||
\(954\) | − | 0.249936i | − | 0.00809199i | ||||||
\(955\) | 9.55343 | − | 1.03256i | 0.309142 | − | 0.0334128i | ||||
\(956\) | −19.5220 | + | 11.2710i | −0.631386 | + | 0.364531i | ||||
\(957\) | 0.714509 | 0.0230968 | ||||||||
\(958\) | −4.44961 | + | 2.56899i | −0.143760 | + | 0.0830002i | ||||
\(959\) | −10.7309 | + | 18.5865i | −0.346520 | + | 0.600191i | ||||
\(960\) | −1.39411 | + | 1.01916i | −0.0449946 | + | 0.0328934i | ||||
\(961\) | 30.3737 | 0.979797 | ||||||||
\(962\) | −8.77513 | + | 5.11373i | −0.282922 | + | 0.164873i | ||||
\(963\) | 18.8862i | 0.608598i | ||||||||
\(964\) | 17.3265 | + | 10.0035i | 0.558049 | + | 0.322190i | ||||
\(965\) | 8.35567 | + | 11.4297i | 0.268978 | + | 0.367934i | ||||
\(966\) | 3.22954 | + | 5.59373i | 0.103909 | + | 0.179975i | ||||
\(967\) | −2.66874 | −0.0858209 | −0.0429104 | − | 0.999079i | \(-0.513663\pi\) | ||||
−0.0429104 | + | 0.999079i | \(0.513663\pi\) | |||||||
\(968\) | −9.72839 | − | 16.8501i | −0.312682 | − | 0.541582i | ||||
\(969\) | −23.9075 | + | 13.8030i | −0.768018 | + | 0.443416i | ||||
\(970\) | 1.69005 | − | 3.82619i | 0.0542642 | − | 0.122852i | ||||
\(971\) | 20.4823 | + | 35.4763i | 0.657307 | + | 1.13849i | 0.981310 | + | 0.192433i | \(0.0616380\pi\) |
−0.324003 | + | 0.946056i | \(0.605029\pi\) | |||||||
\(972\) | 1.42845 | + | 0.824717i | 0.0458176 | + | 0.0264528i | ||||
\(973\) | −9.32222 | + | 16.1466i | −0.298857 | + | 0.517635i | ||||
\(974\) | −16.8839 | −0.540994 | ||||||||
\(975\) | −17.5957 | + | 3.92312i | −0.563514 | + | 0.125640i | ||||
\(976\) | 1.87309 | 0.0599561 | ||||||||
\(977\) | 21.7302 | − | 37.6377i | 0.695209 | − | 1.20414i | −0.274901 | − | 0.961473i | \(-0.588645\pi\) |
0.970110 | − | 0.242665i | \(-0.0780217\pi\) | |||||||
\(978\) | −1.02277 | − | 0.590497i | −0.0327046 | − | 0.0188820i | ||||
\(979\) | 0.422377 | + | 0.731578i | 0.0134992 | + | 0.0233813i | ||||
\(980\) | −6.33788 | + | 14.3487i | −0.202456 | + | 0.458352i | ||||
\(981\) | −5.81377 | + | 3.35658i | −0.185620 | + | 0.107167i | ||||
\(982\) | 9.64549 | + | 16.7065i | 0.307800 | + | 0.533125i | ||||
\(983\) | 22.1143 | 0.705337 | 0.352669 | − | 0.935748i | \(-0.385274\pi\) | ||||
0.352669 | + | 0.935748i | \(0.385274\pi\) | |||||||
\(984\) | 9.57132 | + | 16.5780i | 0.305123 | + | 0.528488i | ||||
\(985\) | 29.3509 | + | 40.1490i | 0.935199 | + | 1.27925i | ||||
\(986\) | −0.850305 | − | 0.490924i | −0.0270792 | − | 0.0156342i | ||||
\(987\) | − | 5.69696i | − | 0.181336i | ||||||
\(988\) | −24.8628 | + | 43.4684i | −0.790990 | + | 1.38291i | ||||
\(989\) | 14.6904 | 0.467128 | ||||||||
\(990\) | 1.50980 | − | 1.10374i | 0.0479846 | − | 0.0350792i | ||||
\(991\) | −21.4294 | + | 37.1168i | −0.680727 | + | 1.17905i | 0.294033 | + | 0.955795i | \(0.405003\pi\) |
−0.974759 | + | 0.223258i | \(0.928331\pi\) | |||||||
\(992\) | −3.78130 | + | 2.18314i | −0.120057 | + | 0.0693147i | ||||
\(993\) | 20.2813 | 0.643607 | ||||||||
\(994\) | 0.930141 | − | 0.537017i | 0.0295023 | − | 0.0170332i | ||||
\(995\) | 9.76897 | − | 1.05585i | 0.309697 | − | 0.0334728i | ||||
\(996\) | − | 6.64065i | − | 0.210417i | ||||||
\(997\) | −22.6378 | + | 13.0699i | −0.716946 | + | 0.413929i | −0.813627 | − | 0.581387i | \(-0.802510\pi\) |
0.0966819 | + | 0.995315i | \(0.469177\pi\) | |||||||
\(998\) | −14.4777 | − | 8.35872i | −0.458285 | − | 0.264591i | ||||
\(999\) | 4.12017 | + | 2.37878i | 0.130356 | + | 0.0752614i |
(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 | 195.2.v.a.4.10 | yes | 32 | |
3.2 | odd | 2 | 585.2.bf.c.199.7 | 32 | |||
5.2 | odd | 4 | 975.2.bc.m.901.5 | 16 | |||
5.3 | odd | 4 | 975.2.bc.n.901.4 | 16 | |||
5.4 | even | 2 | inner | 195.2.v.a.4.7 | ✓ | 32 | |
13.10 | even | 6 | inner | 195.2.v.a.49.7 | yes | 32 | |
15.14 | odd | 2 | 585.2.bf.c.199.10 | 32 | |||
39.23 | odd | 6 | 585.2.bf.c.244.10 | 32 | |||
65.23 | odd | 12 | 975.2.bc.n.751.4 | 16 | |||
65.49 | even | 6 | inner | 195.2.v.a.49.10 | yes | 32 | |
65.62 | odd | 12 | 975.2.bc.m.751.5 | 16 | |||
195.179 | odd | 6 | 585.2.bf.c.244.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.v.a.4.7 | ✓ | 32 | 5.4 | even | 2 | inner | |
195.2.v.a.4.10 | yes | 32 | 1.1 | even | 1 | trivial | |
195.2.v.a.49.7 | yes | 32 | 13.10 | even | 6 | inner | |
195.2.v.a.49.10 | yes | 32 | 65.49 | even | 6 | inner | |
585.2.bf.c.199.7 | 32 | 3.2 | odd | 2 | |||
585.2.bf.c.199.10 | 32 | 15.14 | odd | 2 | |||
585.2.bf.c.244.7 | 32 | 195.179 | odd | 6 | |||
585.2.bf.c.244.10 | 32 | 39.23 | odd | 6 | |||
975.2.bc.m.751.5 | 16 | 65.62 | odd | 12 | |||
975.2.bc.m.901.5 | 16 | 5.2 | odd | 4 | |||
975.2.bc.n.751.4 | 16 | 65.23 | odd | 12 | |||
975.2.bc.n.901.4 | 16 | 5.3 | odd | 4 |