Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,2,Mod(364,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.69570878012\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 364.11 | ||
Character | \(\chi\) | \(=\) | 1089.364 |
Dual form | 1089.2.e.p.727.11 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.332160 | + | 0.575318i | 0.234873 | + | 0.406812i | 0.959236 | − | 0.282607i | \(-0.0911993\pi\) |
−0.724363 | + | 0.689419i | \(0.757866\pi\) | |||||||
\(3\) | 1.61109 | − | 0.635904i | 0.930166 | − | 0.367139i | ||||
\(4\) | 0.779339 | − | 1.34985i | 0.389670 | − | 0.674927i | ||||
\(5\) | −0.558312 | + | 0.967024i | −0.249685 | + | 0.432466i | −0.963438 | − | 0.267930i | \(-0.913660\pi\) |
0.713754 | + | 0.700397i | \(0.246994\pi\) | |||||||
\(6\) | 0.900989 | + | 0.715670i | 0.367827 | + | 0.292171i | ||||
\(7\) | 1.95227 | + | 3.38143i | 0.737889 | + | 1.27806i | 0.953444 | + | 0.301570i | \(0.0975106\pi\) |
−0.215555 | + | 0.976492i | \(0.569156\pi\) | |||||||
\(8\) | 2.36410 | 0.835837 | ||||||||
\(9\) | 2.19125 | − | 2.04900i | 0.730417 | − | 0.683001i | ||||
\(10\) | −0.741796 | −0.234576 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.397211 | − | 2.67033i | 0.114665 | − | 0.770858i | ||||
\(13\) | −1.33900 | + | 2.31922i | −0.371372 | + | 0.643236i | −0.989777 | − | 0.142624i | \(-0.954446\pi\) |
0.618405 | + | 0.785860i | \(0.287779\pi\) | |||||||
\(14\) | −1.29693 | + | 2.24635i | −0.346620 | + | 0.600364i | ||||
\(15\) | −0.284558 | + | 1.91300i | −0.0734726 | + | 0.493934i | ||||
\(16\) | −0.773417 | − | 1.33960i | −0.193354 | − | 0.334900i | ||||
\(17\) | 5.54657 | 1.34524 | 0.672620 | − | 0.739988i | \(-0.265169\pi\) | ||||
0.672620 | + | 0.739988i | \(0.265169\pi\) | |||||||
\(18\) | 1.90668 | + | 0.580070i | 0.449408 | + | 0.136724i | ||||
\(19\) | −5.13234 | −1.17744 | −0.588720 | − | 0.808337i | \(-0.700368\pi\) | ||||
−0.588720 | + | 0.808337i | \(0.700368\pi\) | |||||||
\(20\) | 0.870228 | + | 1.50728i | 0.194589 | + | 0.337038i | ||||
\(21\) | 5.29556 | + | 4.20635i | 1.15559 | + | 0.917901i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.05719 | + | 1.83110i | −0.220439 | + | 0.381812i | −0.954941 | − | 0.296795i | \(-0.904082\pi\) |
0.734502 | + | 0.678606i | \(0.237416\pi\) | |||||||
\(24\) | 3.80879 | − | 1.50334i | 0.777467 | − | 0.306869i | ||||
\(25\) | 1.87658 | + | 3.25033i | 0.375315 | + | 0.650065i | ||||
\(26\) | −1.77905 | −0.348901 | ||||||||
\(27\) | 2.22734 | − | 4.69457i | 0.428652 | − | 0.903469i | ||||
\(28\) | 6.08592 | 1.15013 | ||||||||
\(29\) | −0.541520 | − | 0.937941i | −0.100558 | − | 0.174171i | 0.811357 | − | 0.584551i | \(-0.198729\pi\) |
−0.911915 | + | 0.410380i | \(0.865396\pi\) | |||||||
\(30\) | −1.19510 | + | 0.471711i | −0.218195 | + | 0.0861223i | ||||
\(31\) | 0.215081 | − | 0.372532i | 0.0386297 | − | 0.0669087i | −0.846064 | − | 0.533081i | \(-0.821034\pi\) |
0.884694 | + | 0.466172i | \(0.154367\pi\) | |||||||
\(32\) | 2.87790 | − | 4.98467i | 0.508746 | − | 0.881173i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.84235 | + | 3.19104i | 0.315960 | + | 0.547259i | ||||
\(35\) | −4.35990 | −0.736958 | ||||||||
\(36\) | −1.05813 | − | 4.55474i | −0.176355 | − | 0.759123i | ||||
\(37\) | −8.70580 | −1.43122 | −0.715612 | − | 0.698498i | \(-0.753852\pi\) | ||||
−0.715612 | + | 0.698498i | \(0.753852\pi\) | |||||||
\(38\) | −1.70476 | − | 2.95273i | −0.276549 | − | 0.478996i | ||||
\(39\) | −0.682457 | + | 4.58796i | −0.109281 | + | 0.734661i | ||||
\(40\) | −1.31991 | + | 2.28614i | −0.208695 | + | 0.361471i | ||||
\(41\) | 1.45954 | − | 2.52799i | 0.227942 | − | 0.394806i | −0.729256 | − | 0.684241i | \(-0.760134\pi\) |
0.957198 | + | 0.289434i | \(0.0934672\pi\) | |||||||
\(42\) | −0.661016 | + | 4.44382i | −0.101997 | + | 0.685696i | ||||
\(43\) | 1.11628 | + | 1.93346i | 0.170232 | + | 0.294850i | 0.938501 | − | 0.345277i | \(-0.112215\pi\) |
−0.768269 | + | 0.640127i | \(0.778882\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.758035 | + | 3.26298i | 0.113001 | + | 0.486416i | ||||
\(46\) | −1.40462 | −0.207101 | ||||||||
\(47\) | −6.41773 | − | 11.1158i | −0.936123 | − | 1.62141i | −0.772619 | − | 0.634870i | \(-0.781054\pi\) |
−0.163503 | − | 0.986543i | \(-0.552279\pi\) | |||||||
\(48\) | −2.09790 | − | 1.66640i | −0.302806 | − | 0.240524i | ||||
\(49\) | −4.12272 | + | 7.14077i | −0.588961 | + | 1.02011i | ||||
\(50\) | −1.24665 | + | 2.15926i | −0.176303 | + | 0.305365i | ||||
\(51\) | 8.93605 | − | 3.52709i | 1.25130 | − | 0.493891i | ||||
\(52\) | 2.08707 | + | 3.61492i | 0.289425 | + | 0.501299i | ||||
\(53\) | 5.64118 | 0.774876 | 0.387438 | − | 0.921896i | \(-0.373360\pi\) | ||||
0.387438 | + | 0.921896i | \(0.373360\pi\) | |||||||
\(54\) | 3.44070 | − | 0.277916i | 0.468221 | − | 0.0378196i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.61537 | + | 7.99405i | 0.616755 | + | 1.06825i | ||||
\(57\) | −8.26869 | + | 3.26368i | −1.09521 | + | 0.432285i | ||||
\(58\) | 0.359743 | − | 0.623093i | 0.0472366 | − | 0.0818162i | ||||
\(59\) | 1.18769 | − | 2.05713i | 0.154623 | − | 0.267816i | −0.778298 | − | 0.627895i | \(-0.783917\pi\) |
0.932922 | + | 0.360079i | \(0.117250\pi\) | |||||||
\(60\) | 2.36051 | + | 1.87499i | 0.304740 | + | 0.242060i | ||||
\(61\) | 2.04223 | + | 3.53724i | 0.261480 | + | 0.452897i | 0.966636 | − | 0.256156i | \(-0.0824560\pi\) |
−0.705155 | + | 0.709053i | \(0.749123\pi\) | |||||||
\(62\) | 0.285766 | 0.0362923 | ||||||||
\(63\) | 11.2065 | + | 3.40936i | 1.41188 | + | 0.429539i | ||||
\(64\) | 0.730027 | 0.0912533 | ||||||||
\(65\) | −1.49516 | − | 2.58969i | −0.185452 | − | 0.321212i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.87584 | − | 8.44521i | 0.595679 | − | 1.03175i | −0.397772 | − | 0.917484i | \(-0.630216\pi\) |
0.993451 | − | 0.114262i | \(-0.0364503\pi\) | |||||||
\(68\) | 4.32266 | − | 7.48706i | 0.524199 | − | 0.907940i | ||||
\(69\) | −0.538824 | + | 3.62235i | −0.0648668 | + | 0.436080i | ||||
\(70\) | −1.44819 | − | 2.50833i | −0.173091 | − | 0.299803i | ||||
\(71\) | 6.31707 | 0.749699 | 0.374849 | − | 0.927086i | \(-0.377694\pi\) | ||||
0.374849 | + | 0.927086i | \(0.377694\pi\) | |||||||
\(72\) | 5.18034 | − | 4.84406i | 0.610509 | − | 0.570877i | ||||
\(73\) | −11.6727 | −1.36618 | −0.683091 | − | 0.730333i | \(-0.739365\pi\) | ||||
−0.683091 | + | 0.730333i | \(0.739365\pi\) | |||||||
\(74\) | −2.89172 | − | 5.00861i | −0.336156 | − | 0.582239i | ||||
\(75\) | 5.09024 | + | 4.04326i | 0.587770 | + | 0.466875i | ||||
\(76\) | −3.99983 | + | 6.92792i | −0.458812 | + | 0.794686i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.86622 | + | 1.13131i | −0.324536 | + | 0.128095i | ||||
\(79\) | −2.25735 | − | 3.90985i | −0.253972 | − | 0.439893i | 0.710644 | − | 0.703552i | \(-0.248404\pi\) |
−0.964616 | + | 0.263659i | \(0.915071\pi\) | |||||||
\(80\) | 1.72723 | 0.193110 | ||||||||
\(81\) | 0.603167 | − | 8.97977i | 0.0670185 | − | 0.997752i | ||||
\(82\) | 1.93920 | 0.214149 | ||||||||
\(83\) | −0.241002 | − | 0.417427i | −0.0264534 | − | 0.0458186i | 0.852496 | − | 0.522734i | \(-0.175088\pi\) |
−0.878949 | + | 0.476916i | \(0.841755\pi\) | |||||||
\(84\) | 9.80500 | − | 3.87007i | 1.06981 | − | 0.422259i | ||||
\(85\) | −3.09671 | + | 5.36367i | −0.335886 | + | 0.581771i | ||||
\(86\) | −0.741570 | + | 1.28444i | −0.0799656 | + | 0.138504i | ||||
\(87\) | −1.46888 | − | 1.16676i | −0.157481 | − | 0.125089i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.0830 | 1.70480 | 0.852399 | − | 0.522891i | \(-0.175147\pi\) | ||||
0.852399 | + | 0.522891i | \(0.175147\pi\) | |||||||
\(90\) | −1.62546 | + | 1.51994i | −0.171339 | + | 0.160216i | ||||
\(91\) | −10.4564 | −1.09613 | ||||||||
\(92\) | 1.64782 | + | 2.85410i | 0.171797 | + | 0.297561i | ||||
\(93\) | 0.109622 | − | 0.736955i | 0.0113672 | − | 0.0764187i | ||||
\(94\) | 4.26343 | − | 7.38448i | 0.439739 | − | 0.761651i | ||||
\(95\) | 2.86545 | − | 4.96310i | 0.293989 | − | 0.509203i | ||||
\(96\) | 1.46680 | − | 9.86084i | 0.149704 | − | 1.00642i | ||||
\(97\) | −4.00783 | − | 6.94176i | −0.406933 | − | 0.704829i | 0.587611 | − | 0.809143i | \(-0.300068\pi\) |
−0.994544 | + | 0.104315i | \(0.966735\pi\) | |||||||
\(98\) | −5.47762 | −0.553323 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.84996 | 0.584996 | ||||||||
\(101\) | −0.880657 | − | 1.52534i | −0.0876287 | − | 0.151777i | 0.818880 | − | 0.573965i | \(-0.194596\pi\) |
−0.906508 | + | 0.422188i | \(0.861262\pi\) | |||||||
\(102\) | 4.99740 | + | 3.96951i | 0.494816 | + | 0.393040i | ||||
\(103\) | −1.34383 | + | 2.32759i | −0.132412 | + | 0.229344i | −0.924606 | − | 0.380925i | \(-0.875605\pi\) |
0.792194 | + | 0.610269i | \(0.208939\pi\) | |||||||
\(104\) | −3.16554 | + | 5.48287i | −0.310407 | + | 0.537640i | ||||
\(105\) | −7.02422 | + | 2.77248i | −0.685493 | + | 0.270566i | ||||
\(106\) | 1.87378 | + | 3.24548i | 0.181997 | + | 0.315229i | ||||
\(107\) | −10.2764 | −0.993456 | −0.496728 | − | 0.867906i | \(-0.665465\pi\) | ||||
−0.496728 | + | 0.867906i | \(0.665465\pi\) | |||||||
\(108\) | −4.60113 | − | 6.66525i | −0.442744 | − | 0.641364i | ||||
\(109\) | 2.36284 | 0.226319 | 0.113160 | − | 0.993577i | \(-0.463903\pi\) | ||||
0.113160 | + | 0.993577i | \(0.463903\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.0259 | + | 5.53605i | −1.33128 | + | 0.525459i | ||||
\(112\) | 3.01984 | − | 5.23052i | 0.285348 | − | 0.494237i | ||||
\(113\) | −0.766216 | + | 1.32713i | −0.0720796 | + | 0.124845i | −0.899813 | − | 0.436277i | \(-0.856297\pi\) |
0.827733 | + | 0.561122i | \(0.189630\pi\) | |||||||
\(114\) | −4.62418 | − | 3.67306i | −0.433094 | − | 0.344014i | ||||
\(115\) | −1.18048 | − | 2.04465i | −0.110080 | − | 0.190665i | ||||
\(116\) | −1.68811 | −0.156737 | ||||||||
\(117\) | 1.81800 | + | 7.82561i | 0.168074 | + | 0.723478i | ||||
\(118\) | 1.57801 | 0.145267 | ||||||||
\(119\) | 10.8284 | + | 18.7553i | 0.992638 | + | 1.71930i | ||||
\(120\) | −0.672725 | + | 4.52253i | −0.0614111 | + | 0.412849i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.35669 | + | 2.34986i | −0.122829 | + | 0.212746i | ||||
\(123\) | 0.743892 | − | 5.00096i | 0.0670745 | − | 0.450922i | ||||
\(124\) | −0.335242 | − | 0.580657i | −0.0301057 | − | 0.0521445i | ||||
\(125\) | −9.77397 | −0.874211 | ||||||||
\(126\) | 1.76088 | + | 7.57975i | 0.156872 | + | 0.675258i | ||||
\(127\) | −7.65133 | −0.678946 | −0.339473 | − | 0.940616i | \(-0.610249\pi\) | ||||
−0.339473 | + | 0.940616i | \(0.610249\pi\) | |||||||
\(128\) | −5.51331 | − | 9.54934i | −0.487313 | − | 0.844050i | ||||
\(129\) | 3.02793 | + | 2.40514i | 0.266595 | + | 0.211761i | ||||
\(130\) | 0.993266 | − | 1.72039i | 0.0871152 | − | 0.150888i | ||||
\(131\) | 2.67956 | − | 4.64113i | 0.234114 | − | 0.405498i | −0.724901 | − | 0.688853i | \(-0.758114\pi\) |
0.959015 | + | 0.283356i | \(0.0914477\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.0197 | − | 17.3547i | −0.868820 | − | 1.50484i | ||||
\(134\) | 6.47825 | 0.559635 | ||||||||
\(135\) | 3.29621 | + | 4.77493i | 0.283692 | + | 0.410960i | ||||
\(136\) | 13.1127 | 1.12440 | ||||||||
\(137\) | −8.36560 | − | 14.4896i | −0.714721 | − | 1.23793i | −0.963067 | − | 0.269262i | \(-0.913220\pi\) |
0.248346 | − | 0.968672i | \(-0.420113\pi\) | |||||||
\(138\) | −2.26298 | + | 0.893207i | −0.192638 | + | 0.0760348i | ||||
\(139\) | −6.87006 | + | 11.8993i | −0.582711 | + | 1.00928i | 0.412446 | + | 0.910982i | \(0.364675\pi\) |
−0.995157 | + | 0.0983023i | \(0.968659\pi\) | |||||||
\(140\) | −3.39784 | + | 5.88524i | −0.287170 | + | 0.497393i | ||||
\(141\) | −17.4082 | − | 13.8276i | −1.46603 | − | 1.16449i | ||||
\(142\) | 2.09828 | + | 3.63433i | 0.176084 | + | 0.304986i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.43959 | − | 1.35066i | −0.369966 | − | 0.112555i | ||||
\(145\) | 1.20935 | 0.100431 | ||||||||
\(146\) | −3.87720 | − | 6.71550i | −0.320879 | − | 0.555779i | ||||
\(147\) | −2.10125 | + | 14.1261i | −0.173309 | + | 1.16510i | ||||
\(148\) | −6.78477 | + | 11.7516i | −0.557704 | + | 0.965973i | ||||
\(149\) | −2.77983 | + | 4.81480i | −0.227732 | + | 0.394444i | −0.957136 | − | 0.289640i | \(-0.906464\pi\) |
0.729403 | + | 0.684084i | \(0.239798\pi\) | |||||||
\(150\) | −0.635387 | + | 4.27152i | −0.0518791 | + | 0.348768i | ||||
\(151\) | 0.0819538 | + | 0.141948i | 0.00666930 | + | 0.0115516i | 0.869341 | − | 0.494213i | \(-0.164544\pi\) |
−0.862671 | + | 0.505765i | \(0.831210\pi\) | |||||||
\(152\) | −12.1334 | −0.984147 | ||||||||
\(153\) | 12.1539 | − | 11.3649i | 0.982587 | − | 0.918801i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.240165 | + | 0.415978i | 0.0192905 | + | 0.0334121i | ||||
\(156\) | 5.66121 | + | 4.49679i | 0.453260 | + | 0.360032i | ||||
\(157\) | −11.9265 | + | 20.6573i | −0.951839 | + | 1.64863i | −0.210397 | + | 0.977616i | \(0.567476\pi\) |
−0.741442 | + | 0.671018i | \(0.765858\pi\) | |||||||
\(158\) | 1.49961 | − | 2.59739i | 0.119302 | − | 0.206638i | ||||
\(159\) | 9.08848 | − | 3.58725i | 0.720763 | − | 0.284488i | ||||
\(160\) | 3.21353 | + | 5.56600i | 0.254052 | + | 0.440031i | ||||
\(161\) | −8.25568 | −0.650638 | ||||||||
\(162\) | 5.36657 | − | 2.63571i | 0.421638 | − | 0.207081i | ||||
\(163\) | −4.19602 | −0.328658 | −0.164329 | − | 0.986406i | \(-0.552546\pi\) | ||||
−0.164329 | + | 0.986406i | \(0.552546\pi\) | |||||||
\(164\) | −2.27495 | − | 3.94033i | −0.177644 | − | 0.307688i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.160102 | − | 0.277306i | 0.0124264 | − | 0.0215231i | ||||
\(167\) | −7.92020 | + | 13.7182i | −0.612883 | + | 1.06155i | 0.377869 | + | 0.925859i | \(0.376657\pi\) |
−0.990752 | + | 0.135686i | \(0.956676\pi\) | |||||||
\(168\) | 12.5193 | + | 9.94425i | 0.965881 | + | 0.767215i | ||||
\(169\) | 2.91415 | + | 5.04745i | 0.224165 | + | 0.388265i | ||||
\(170\) | −4.11442 | −0.315562 | ||||||||
\(171\) | −11.2462 | + | 10.5162i | −0.860022 | + | 0.804193i | ||||
\(172\) | 3.47985 | 0.265336 | ||||||||
\(173\) | 1.30144 | + | 2.25417i | 0.0989470 | + | 0.171381i | 0.911249 | − | 0.411856i | \(-0.135119\pi\) |
−0.812302 | + | 0.583237i | \(0.801786\pi\) | |||||||
\(174\) | 0.183352 | − | 1.23262i | 0.0138999 | − | 0.0934450i | ||||
\(175\) | −7.32717 | + | 12.6910i | −0.553882 | + | 0.959352i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.605335 | − | 4.06949i | 0.0454997 | − | 0.305881i | ||||
\(178\) | 5.34215 | + | 9.25287i | 0.400411 | + | 0.693532i | ||||
\(179\) | 7.58802 | 0.567155 | 0.283578 | − | 0.958949i | \(-0.408479\pi\) | ||||
0.283578 | + | 0.958949i | \(0.408479\pi\) | |||||||
\(180\) | 4.99531 | + | 1.51973i | 0.372328 | + | 0.113274i | ||||
\(181\) | −2.40019 | −0.178405 | −0.0892023 | − | 0.996014i | \(-0.528432\pi\) | ||||
−0.0892023 | + | 0.996014i | \(0.528432\pi\) | |||||||
\(182\) | −3.47319 | − | 6.01575i | −0.257450 | − | 0.445917i | ||||
\(183\) | 5.53957 | + | 4.40017i | 0.409497 | + | 0.325270i | ||||
\(184\) | −2.49930 | + | 4.32892i | −0.184251 | + | 0.319132i | ||||
\(185\) | 4.86055 | − | 8.41872i | 0.357355 | − | 0.618956i | ||||
\(186\) | 0.460396 | − | 0.181720i | 0.0337579 | − | 0.0133243i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −20.0064 | −1.45911 | ||||||||
\(189\) | 20.2227 | − | 1.63345i | 1.47099 | − | 0.118816i | ||||
\(190\) | 3.80715 | 0.276200 | ||||||||
\(191\) | 8.25912 | + | 14.3052i | 0.597609 | + | 1.03509i | 0.993173 | + | 0.116650i | \(0.0372157\pi\) |
−0.395564 | + | 0.918438i | \(0.629451\pi\) | |||||||
\(192\) | 1.17614 | − | 0.464227i | 0.0848807 | − | 0.0335027i | ||||
\(193\) | 4.06748 | − | 7.04508i | 0.292784 | − | 0.507116i | −0.681683 | − | 0.731647i | \(-0.738752\pi\) |
0.974467 | + | 0.224531i | \(0.0720851\pi\) | |||||||
\(194\) | 2.66248 | − | 4.61155i | 0.191155 | − | 0.331090i | ||||
\(195\) | −4.05564 | − | 3.22146i | −0.290431 | − | 0.230694i | ||||
\(196\) | 6.42600 | + | 11.1302i | 0.459000 | + | 0.795011i | ||||
\(197\) | −22.9072 | −1.63207 | −0.816035 | − | 0.578003i | \(-0.803832\pi\) | ||||
−0.816035 | + | 0.578003i | \(0.803832\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.27177 | 0.657259 | 0.328629 | − | 0.944459i | \(-0.393413\pi\) | ||||
0.328629 | + | 0.944459i | \(0.393413\pi\) | |||||||
\(200\) | 4.43642 | + | 7.68410i | 0.313702 | + | 0.543348i | ||||
\(201\) | 2.48510 | − | 16.7066i | 0.175286 | − | 1.17839i | ||||
\(202\) | 0.585039 | − | 1.01332i | 0.0411632 | − | 0.0712967i | ||||
\(203\) | 2.11439 | − | 3.66223i | 0.148401 | − | 0.257038i | ||||
\(204\) | 2.20316 | − | 14.8112i | 0.154252 | − | 1.03699i | ||||
\(205\) | 1.62975 | + | 2.82282i | 0.113827 | + | 0.197154i | ||||
\(206\) | −1.78547 | −0.124400 | ||||||||
\(207\) | 1.43537 | + | 6.17860i | 0.0997654 | + | 0.429442i | ||||
\(208\) | 4.14243 | 0.287226 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.92822 | − | 3.12025i | −0.271073 | − | 0.215318i | ||||
\(211\) | −2.10529 | + | 3.64647i | −0.144934 | + | 0.251033i | −0.929348 | − | 0.369204i | \(-0.879630\pi\) |
0.784414 | + | 0.620237i | \(0.212964\pi\) | |||||||
\(212\) | 4.39640 | − | 7.61478i | 0.301946 | − | 0.522985i | ||||
\(213\) | 10.1774 | − | 4.01705i | 0.697344 | − | 0.275244i | ||||
\(214\) | −3.41341 | − | 5.91219i | −0.233336 | − | 0.404149i | ||||
\(215\) | −2.49294 | −0.170017 | ||||||||
\(216\) | 5.26567 | − | 11.0984i | 0.358283 | − | 0.755153i | ||||
\(217\) | 1.67959 | 0.114018 | ||||||||
\(218\) | 0.784842 | + | 1.35939i | 0.0531562 | + | 0.0920693i | ||||
\(219\) | −18.8058 | + | 7.42270i | −1.27078 | + | 0.501580i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.42687 | + | 12.8637i | −0.499585 | + | 0.865307i | ||||
\(222\) | −7.84383 | − | 6.23048i | −0.526443 | − | 0.418162i | ||||
\(223\) | 3.42953 | + | 5.94012i | 0.229658 | + | 0.397780i | 0.957707 | − | 0.287746i | \(-0.0929058\pi\) |
−0.728049 | + | 0.685526i | \(0.759572\pi\) | |||||||
\(224\) | 22.4738 | 1.50159 | ||||||||
\(225\) | 10.7720 | + | 3.27717i | 0.718132 | + | 0.218478i | ||||
\(226\) | −1.01803 | −0.0677181 | ||||||||
\(227\) | −14.0650 | − | 24.3612i | −0.933524 | − | 1.61691i | −0.777245 | − | 0.629198i | \(-0.783383\pi\) |
−0.156279 | − | 0.987713i | \(-0.549950\pi\) | |||||||
\(228\) | −2.03862 | + | 13.7050i | −0.135011 | + | 0.907638i | ||||
\(229\) | 7.01735 | − | 12.1544i | 0.463719 | − | 0.803186i | −0.535423 | − | 0.844584i | \(-0.679848\pi\) |
0.999143 | + | 0.0413982i | \(0.0131812\pi\) | |||||||
\(230\) | 0.784218 | − | 1.35831i | 0.0517098 | − | 0.0895640i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.28021 | − | 2.21739i | −0.0840499 | − | 0.145579i | ||||
\(233\) | −14.5096 | −0.950557 | −0.475278 | − | 0.879835i | \(-0.657653\pi\) | ||||
−0.475278 | + | 0.879835i | \(0.657653\pi\) | |||||||
\(234\) | −3.89835 | + | 3.64529i | −0.254843 | + | 0.238300i | ||||
\(235\) | 14.3324 | 0.934942 | ||||||||
\(236\) | −1.85122 | − | 3.20641i | −0.120504 | − | 0.208719i | ||||
\(237\) | −6.12310 | − | 4.86368i | −0.397738 | − | 0.315930i | ||||
\(238\) | −7.19353 | + | 12.4596i | −0.466287 | + | 0.807633i | ||||
\(239\) | 12.5741 | − | 21.7789i | 0.813349 | − | 1.40876i | −0.0971591 | − | 0.995269i | \(-0.530976\pi\) |
0.910508 | − | 0.413492i | \(-0.135691\pi\) | |||||||
\(240\) | 2.78273 | − | 1.09835i | 0.179625 | − | 0.0708984i | ||||
\(241\) | −8.87110 | − | 15.3652i | −0.571438 | − | 0.989759i | −0.996419 | − | 0.0845570i | \(-0.973053\pi\) |
0.424981 | − | 0.905202i | \(-0.360281\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.73851 | − | 14.8508i | −0.303976 | − | 0.952680i | ||||
\(244\) | 6.36635 | 0.407564 | ||||||||
\(245\) | −4.60353 | − | 7.97355i | −0.294109 | − | 0.509411i | ||||
\(246\) | 3.12424 | − | 1.23315i | 0.199194 | − | 0.0786226i | ||||
\(247\) | 6.87222 | − | 11.9030i | 0.437269 | − | 0.757371i | ||||
\(248\) | 0.508474 | − | 0.880703i | 0.0322881 | − | 0.0559247i | ||||
\(249\) | −0.653721 | − | 0.519261i | −0.0414279 | − | 0.0329068i | ||||
\(250\) | −3.24653 | − | 5.62315i | −0.205328 | − | 0.355639i | ||||
\(251\) | −21.8775 | −1.38090 | −0.690448 | − | 0.723382i | \(-0.742586\pi\) | ||||
−0.690448 | + | 0.723382i | \(0.742586\pi\) | |||||||
\(252\) | 13.3358 | − | 12.4701i | 0.840076 | − | 0.785541i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.54147 | − | 4.40195i | −0.159466 | − | 0.276203i | ||||
\(255\) | −1.57832 | + | 10.6106i | −0.0988383 | + | 0.664461i | ||||
\(256\) | 4.39263 | − | 7.60827i | 0.274540 | − | 0.475517i | ||||
\(257\) | −2.58186 | + | 4.47191i | −0.161052 | + | 0.278950i | −0.935246 | − | 0.353998i | \(-0.884822\pi\) |
0.774194 | + | 0.632948i | \(0.218155\pi\) | |||||||
\(258\) | −0.377961 | + | 2.54092i | −0.0235308 | + | 0.158191i | ||||
\(259\) | −16.9961 | − | 29.4381i | −1.05608 | − | 1.82919i | ||||
\(260\) | −4.66095 | −0.289060 | ||||||||
\(261\) | −3.10845 | − | 0.945687i | −0.192408 | − | 0.0585366i | ||||
\(262\) | 3.56017 | 0.219948 | ||||||||
\(263\) | 13.9491 | + | 24.1605i | 0.860135 | + | 1.48980i | 0.871798 | + | 0.489866i | \(0.162954\pi\) |
−0.0116625 | + | 0.999932i | \(0.503712\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.14954 | + | 5.45516i | −0.193475 | + | 0.335108i | ||||
\(266\) | 6.65631 | − | 11.5291i | 0.408124 | − | 0.706892i | ||||
\(267\) | 25.9113 | − | 10.2273i | 1.58575 | − | 0.625899i | ||||
\(268\) | −7.59987 | − | 13.1634i | −0.464236 | − | 0.804080i | ||||
\(269\) | 3.01959 | 0.184108 | 0.0920538 | − | 0.995754i | \(-0.470657\pi\) | ||||
0.0920538 | + | 0.995754i | \(0.470657\pi\) | |||||||
\(270\) | −1.65223 | + | 3.48241i | −0.100552 | + | 0.211933i | ||||
\(271\) | −25.3748 | −1.54141 | −0.770705 | − | 0.637192i | \(-0.780096\pi\) | ||||
−0.770705 | + | 0.637192i | \(0.780096\pi\) | |||||||
\(272\) | −4.28981 | − | 7.43017i | −0.260108 | − | 0.450520i | ||||
\(273\) | −16.8462 | + | 6.64926i | −1.01958 | + | 0.402431i | ||||
\(274\) | 5.55744 | − | 9.62577i | 0.335737 | − | 0.581514i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.46973 | + | 3.55038i | 0.269046 | + | 0.213708i | ||||
\(277\) | 5.28219 | + | 9.14903i | 0.317376 | + | 0.549712i | 0.979940 | − | 0.199294i | \(-0.0638649\pi\) |
−0.662564 | + | 0.749006i | \(0.730532\pi\) | |||||||
\(278\) | −9.12784 | −0.547451 | ||||||||
\(279\) | −0.292022 | − | 1.25701i | −0.0174829 | − | 0.0752554i | ||||
\(280\) | −10.3073 | −0.615976 | ||||||||
\(281\) | 11.2853 | + | 19.5466i | 0.673222 | + | 1.16605i | 0.976985 | + | 0.213307i | \(0.0684235\pi\) |
−0.303763 | + | 0.952748i | \(0.598243\pi\) | |||||||
\(282\) | 2.17297 | − | 14.6082i | 0.129398 | − | 0.869908i | ||||
\(283\) | 2.93862 | − | 5.08983i | 0.174683 | − | 0.302559i | −0.765369 | − | 0.643592i | \(-0.777443\pi\) |
0.940051 | + | 0.341033i | \(0.110777\pi\) | |||||||
\(284\) | 4.92314 | − | 8.52713i | 0.292135 | − | 0.505992i | ||||
\(285\) | 1.46045 | − | 9.81817i | 0.0865095 | − | 0.581578i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.3977 | 0.672782 | ||||||||
\(288\) | −3.90740 | − | 16.8195i | −0.230246 | − | 0.991098i | ||||
\(289\) | 13.7644 | 0.809672 | ||||||||
\(290\) | 0.401698 | + | 0.695761i | 0.0235885 | + | 0.0408565i | ||||
\(291\) | −10.8713 | − | 8.63524i | −0.637286 | − | 0.506207i | ||||
\(292\) | −9.09697 | + | 15.7564i | −0.532360 | + | 0.922074i | ||||
\(293\) | −3.54705 | + | 6.14368i | −0.207221 | + | 0.358918i | −0.950838 | − | 0.309688i | \(-0.899775\pi\) |
0.743617 | + | 0.668606i | \(0.233109\pi\) | |||||||
\(294\) | −8.82496 | + | 3.48324i | −0.514682 | + | 0.203147i | ||||
\(295\) | 1.32620 | + | 2.29704i | 0.0772142 | + | 0.133739i | ||||
\(296\) | −20.5814 | −1.19627 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.69339 | −0.213953 | ||||||||
\(299\) | −2.83116 | − | 4.90371i | −0.163730 | − | 0.283589i | ||||
\(300\) | 9.42483 | − | 3.72001i | 0.544143 | − | 0.214775i | ||||
\(301\) | −4.35858 | + | 7.54928i | −0.251224 | + | 0.435133i | ||||
\(302\) | −0.0544436 | + | 0.0942990i | −0.00313287 | + | 0.00542630i | ||||
\(303\) | −2.38879 | − | 1.89746i | −0.137233 | − | 0.109006i | ||||
\(304\) | 3.96944 | + | 6.87527i | 0.227663 | + | 0.394324i | ||||
\(305\) | −4.56080 | −0.261150 | ||||||||
\(306\) | 10.5755 | + | 3.21740i | 0.604562 | + | 0.183926i | ||||
\(307\) | −18.5370 | −1.05796 | −0.528981 | − | 0.848633i | \(-0.677426\pi\) | ||||
−0.528981 | + | 0.848633i | \(0.677426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.684919 | + | 4.60451i | −0.0389637 | + | 0.261941i | ||||
\(310\) | −0.159546 | + | 0.276342i | −0.00906162 | + | 0.0156952i | ||||
\(311\) | −3.43812 | + | 5.95500i | −0.194958 | + | 0.337677i | −0.946887 | − | 0.321567i | \(-0.895790\pi\) |
0.751929 | + | 0.659244i | \(0.229124\pi\) | |||||||
\(312\) | −1.61340 | + | 10.8464i | −0.0913408 | + | 0.614057i | ||||
\(313\) | 12.6629 | + | 21.9328i | 0.715749 | + | 1.23971i | 0.962670 | + | 0.270679i | \(0.0872480\pi\) |
−0.246920 | + | 0.969036i | \(0.579419\pi\) | |||||||
\(314\) | −15.8460 | −0.894244 | ||||||||
\(315\) | −9.55364 | + | 8.93346i | −0.538287 | + | 0.503343i | ||||
\(316\) | −7.03698 | −0.395861 | ||||||||
\(317\) | −5.48963 | − | 9.50832i | −0.308328 | − | 0.534041i | 0.669668 | − | 0.742660i | \(-0.266436\pi\) |
−0.977997 | + | 0.208620i | \(0.933103\pi\) | |||||||
\(318\) | 5.08265 | + | 4.03723i | 0.285021 | + | 0.226397i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.407582 | + | 0.705953i | −0.0227845 | + | 0.0394640i | ||||
\(321\) | −16.5562 | + | 6.53480i | −0.924079 | + | 0.364737i | ||||
\(322\) | −2.74221 | − | 4.74964i | −0.152817 | − | 0.264687i | ||||
\(323\) | −28.4669 | −1.58394 | ||||||||
\(324\) | −11.6513 | − | 7.81247i | −0.647295 | − | 0.434026i | ||||
\(325\) | −10.0510 | −0.557527 | ||||||||
\(326\) | −1.39375 | − | 2.41405i | −0.0771928 | − | 0.133702i | ||||
\(327\) | 3.80676 | − | 1.50254i | 0.210514 | − | 0.0830907i | ||||
\(328\) | 3.45050 | − | 5.97644i | 0.190522 | − | 0.329994i | ||||
\(329\) | 25.0583 | − | 43.4023i | 1.38151 | − | 2.39284i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.85513 | + | 3.21317i | 0.101967 | + | 0.176612i | 0.912495 | − | 0.409088i | \(-0.134153\pi\) |
−0.810528 | + | 0.585700i | \(0.800820\pi\) | |||||||
\(332\) | −0.751289 | −0.0412323 | ||||||||
\(333\) | −19.0766 | + | 17.8382i | −1.04539 | + | 0.977528i | ||||
\(334\) | −10.5231 | −0.575798 | ||||||||
\(335\) | 5.44448 | + | 9.43012i | 0.297464 | + | 0.515222i | ||||
\(336\) | 1.53914 | − | 10.3472i | 0.0839670 | − | 0.564485i | ||||
\(337\) | 16.0976 | − | 27.8818i | 0.876891 | − | 1.51882i | 0.0221561 | − | 0.999755i | \(-0.492947\pi\) |
0.854735 | − | 0.519065i | \(-0.173720\pi\) | |||||||
\(338\) | −1.93593 | + | 3.35312i | −0.105301 | + | 0.182386i | ||||
\(339\) | −0.390522 | + | 2.62536i | −0.0212102 | + | 0.142590i | ||||
\(340\) | 4.82678 | + | 8.36023i | 0.261769 | + | 0.453397i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −9.78571 | − | 2.97712i | −0.529151 | − | 0.160984i | ||||
\(343\) | −4.86291 | −0.262572 | ||||||||
\(344\) | 2.63901 | + | 4.57090i | 0.142286 | + | 0.246446i | ||||
\(345\) | −3.20207 | − | 2.54346i | −0.172394 | − | 0.136935i | ||||
\(346\) | −0.864576 | + | 1.49749i | −0.0464799 | + | 0.0805055i | ||||
\(347\) | 10.7612 | − | 18.6390i | 0.577694 | − | 1.00060i | −0.418049 | − | 0.908424i | \(-0.637286\pi\) |
0.995743 | − | 0.0921708i | \(-0.0293806\pi\) | |||||||
\(348\) | −2.71971 | + | 1.07348i | −0.145792 | + | 0.0575444i | ||||
\(349\) | 8.40998 | + | 14.5665i | 0.450176 | + | 0.779727i | 0.998397 | − | 0.0566062i | \(-0.0180280\pi\) |
−0.548221 | + | 0.836334i | \(0.684695\pi\) | |||||||
\(350\) | −9.73518 | −0.520367 | ||||||||
\(351\) | 7.90531 | + | 11.4517i | 0.421954 | + | 0.611248i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.56543 | − | 2.71140i | −0.0833193 | − | 0.144313i | 0.821355 | − | 0.570418i | \(-0.193219\pi\) |
−0.904674 | + | 0.426105i | \(0.859885\pi\) | |||||||
\(354\) | 2.54232 | − | 1.00346i | 0.135123 | − | 0.0533334i | ||||
\(355\) | −3.52690 | + | 6.10876i | −0.187188 | + | 0.324219i | ||||
\(356\) | 12.5341 | − | 21.7098i | 0.664308 | − | 1.15062i | ||||
\(357\) | 29.3722 | + | 23.3308i | 1.55454 | + | 1.23480i | ||||
\(358\) | 2.52044 | + | 4.36553i | 0.133209 | + | 0.230725i | ||||
\(359\) | 8.48869 | 0.448016 | 0.224008 | − | 0.974587i | \(-0.428086\pi\) | ||||
0.224008 | + | 0.974587i | \(0.428086\pi\) | |||||||
\(360\) | 1.79207 | + | 7.71401i | 0.0944505 | + | 0.406564i | ||||
\(361\) | 7.34092 | 0.386364 | ||||||||
\(362\) | −0.797247 | − | 1.38087i | −0.0419024 | − | 0.0725770i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.14907 | + | 14.1146i | −0.427127 | + | 0.739806i | ||||
\(365\) | 6.51699 | − | 11.2878i | 0.341115 | − | 0.590828i | ||||
\(366\) | −0.691474 | + | 4.64858i | −0.0361439 | + | 0.242985i | ||||
\(367\) | 5.50548 | + | 9.53578i | 0.287384 | + | 0.497763i | 0.973184 | − | 0.230026i | \(-0.0738811\pi\) |
−0.685801 | + | 0.727789i | \(0.740548\pi\) | |||||||
\(368\) | 3.27059 | 0.170491 | ||||||||
\(369\) | −1.98165 | − | 8.53007i | −0.103161 | − | 0.444058i | ||||
\(370\) | 6.45792 | 0.335731 | ||||||||
\(371\) | 11.0131 | + | 19.0753i | 0.571773 | + | 0.990339i | ||||
\(372\) | −0.909350 | − | 0.722311i | −0.0471476 | − | 0.0374501i | ||||
\(373\) | −5.50342 | + | 9.53220i | −0.284956 | + | 0.493558i | −0.972599 | − | 0.232491i | \(-0.925312\pi\) |
0.687642 | + | 0.726050i | \(0.258646\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.7468 | + | 6.21531i | −0.813161 | + | 0.320957i | ||||
\(376\) | −15.1722 | − | 26.2790i | −0.782446 | − | 1.35524i | ||||
\(377\) | 2.90039 | 0.149378 | ||||||||
\(378\) | 7.65694 | + | 11.0919i | 0.393831 | + | 0.570508i | ||||
\(379\) | 25.3868 | 1.30403 | 0.652017 | − | 0.758204i | \(-0.273923\pi\) | ||||
0.652017 | + | 0.758204i | \(0.273923\pi\) | |||||||
\(380\) | −4.46631 | − | 7.73587i | −0.229117 | − | 0.396842i | ||||
\(381\) | −12.3270 | + | 4.86551i | −0.631532 | + | 0.249268i | ||||
\(382\) | −5.48670 | + | 9.50324i | −0.280724 | + | 0.486228i | ||||
\(383\) | 6.05737 | − | 10.4917i | 0.309517 | − | 0.536099i | −0.668740 | − | 0.743497i | \(-0.733166\pi\) |
0.978257 | + | 0.207397i | \(0.0664993\pi\) | |||||||
\(384\) | −14.9549 | − | 11.8789i | −0.763166 | − | 0.606195i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.40422 | 0.275068 | ||||||||
\(387\) | 6.40773 | + | 1.94943i | 0.325723 | + | 0.0990950i | ||||
\(388\) | −12.4938 | −0.634278 | ||||||||
\(389\) | −7.17554 | − | 12.4284i | −0.363814 | − | 0.630145i | 0.624771 | − | 0.780808i | \(-0.285192\pi\) |
−0.988585 | + | 0.150663i | \(0.951859\pi\) | |||||||
\(390\) | 0.506244 | − | 3.40333i | 0.0256347 | − | 0.172334i | ||||
\(391\) | −5.86377 | + | 10.1563i | −0.296544 | + | 0.513629i | ||||
\(392\) | −9.74654 | + | 16.8815i | −0.492275 | + | 0.852645i | ||||
\(393\) | 1.36571 | − | 9.18125i | 0.0688908 | − | 0.463133i | ||||
\(394\) | −7.60886 | − | 13.1789i | −0.383329 | − | 0.663945i | ||||
\(395\) | 5.04123 | 0.253652 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.03882 | −0.252891 | −0.126446 | − | 0.991974i | \(-0.540357\pi\) | ||||
−0.126446 | + | 0.991974i | \(0.540357\pi\) | |||||||
\(398\) | 3.07971 | + | 5.33422i | 0.154372 | + | 0.267380i | ||||
\(399\) | −27.1786 | − | 21.5884i | −1.36063 | − | 1.08077i | ||||
\(400\) | 2.90275 | − | 5.02772i | 0.145138 | − | 0.251386i | ||||
\(401\) | 9.10009 | − | 15.7618i | 0.454437 | − | 0.787108i | −0.544219 | − | 0.838943i | \(-0.683174\pi\) |
0.998656 | + | 0.0518357i | \(0.0165072\pi\) | |||||||
\(402\) | 10.4371 | − | 4.11954i | 0.520554 | − | 0.205464i | ||||
\(403\) | 0.575989 | + | 0.997641i | 0.0286920 | + | 0.0496961i | ||||
\(404\) | −2.74532 | −0.136585 | ||||||||
\(405\) | 8.34689 | + | 5.59678i | 0.414761 | + | 0.278106i | ||||
\(406\) | 2.80926 | 0.139421 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 21.1257 | − | 8.33840i | 1.04588 | − | 0.412812i | ||||
\(409\) | −8.21523 | + | 14.2292i | −0.406217 | + | 0.703588i | −0.994462 | − | 0.105094i | \(-0.966486\pi\) |
0.588245 | + | 0.808682i | \(0.299819\pi\) | |||||||
\(410\) | −1.08268 | + | 1.87526i | −0.0534697 | + | 0.0926123i | ||||
\(411\) | −22.6918 | − | 18.0245i | −1.11930 | − | 0.889081i | ||||
\(412\) | 2.09460 | + | 3.62796i | 0.103194 | + | 0.178737i | ||||
\(413\) | 9.27473 | 0.456380 | ||||||||
\(414\) | −3.07789 | + | 2.87808i | −0.151270 | + | 0.141450i | ||||
\(415\) | 0.538216 | 0.0264200 | ||||||||
\(416\) | 7.70703 | + | 13.3490i | 0.377868 | + | 0.654487i | ||||
\(417\) | −3.50150 | + | 23.5396i | −0.171469 | + | 1.15274i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.70324 | − | 15.0745i | 0.425181 | − | 0.736435i | −0.571256 | − | 0.820772i | \(-0.693544\pi\) |
0.996437 | + | 0.0843365i | \(0.0268771\pi\) | |||||||
\(420\) | −1.73180 | + | 11.6424i | −0.0845032 | + | 0.568090i | ||||
\(421\) | −2.27432 | − | 3.93924i | −0.110844 | − | 0.191987i | 0.805267 | − | 0.592912i | \(-0.202022\pi\) |
−0.916111 | + | 0.400925i | \(0.868689\pi\) | |||||||
\(422\) | −2.79717 | −0.136164 | ||||||||
\(423\) | −36.8393 | − | 11.2076i | −1.79119 | − | 0.544934i | ||||
\(424\) | 13.3363 | 0.647670 | ||||||||
\(425\) | 10.4086 | + | 18.0282i | 0.504889 | + | 0.874494i | ||||
\(426\) | 5.69161 | + | 4.52094i | 0.275760 | + | 0.219040i | ||||
\(427\) | −7.97396 | + | 13.8113i | −0.385887 | + | 0.668376i | ||||
\(428\) | −8.00879 | + | 13.8716i | −0.387120 | + | 0.670511i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.828055 | − | 1.43423i | −0.0399323 | − | 0.0691648i | ||||
\(431\) | 12.4848 | 0.601372 | 0.300686 | − | 0.953723i | \(-0.402784\pi\) | ||||
0.300686 | + | 0.953723i | \(0.402784\pi\) | |||||||
\(432\) | −8.01150 | + | 0.647113i | −0.385453 | + | 0.0311342i | ||||
\(433\) | 28.6862 | 1.37857 | 0.689284 | − | 0.724491i | \(-0.257925\pi\) | ||||
0.689284 | + | 0.724491i | \(0.257925\pi\) | |||||||
\(434\) | 0.557892 | + | 0.966298i | 0.0267797 | + | 0.0463838i | ||||
\(435\) | 1.94837 | − | 0.769030i | 0.0934174 | − | 0.0368722i | ||||
\(436\) | 1.84146 | − | 3.18949i | 0.0881897 | − | 0.152749i | ||||
\(437\) | 5.42585 | − | 9.39785i | 0.259554 | − | 0.449560i | ||||
\(438\) | −10.5169 | − | 8.35378i | −0.502519 | − | 0.399159i | ||||
\(439\) | 2.05404 | + | 3.55769i | 0.0980338 | + | 0.169799i | 0.910871 | − | 0.412692i | \(-0.135411\pi\) |
−0.812837 | + | 0.582491i | \(0.802078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.59753 | + | 24.0947i | 0.266549 | + | 1.14737i | ||||
\(442\) | −9.86764 | −0.469356 | ||||||||
\(443\) | 10.6149 | + | 18.3855i | 0.504327 | + | 0.873520i | 0.999987 | + | 0.00500337i | \(0.00159263\pi\) |
−0.495661 | + | 0.868516i | \(0.665074\pi\) | |||||||
\(444\) | −3.45803 | + | 23.2473i | −0.164111 | + | 1.10327i | ||||
\(445\) | −8.97935 | + | 15.5527i | −0.425662 | + | 0.737268i | ||||
\(446\) | −2.27831 | + | 3.94614i | −0.107881 | + | 0.186855i | ||||
\(447\) | −1.41681 | + | 9.52481i | −0.0670129 | + | 0.450508i | ||||
\(448\) | 1.42521 | + | 2.46854i | 0.0673348 | + | 0.116627i | ||||
\(449\) | 25.8949 | 1.22205 | 0.611027 | − | 0.791610i | \(-0.290757\pi\) | ||||
0.611027 | + | 0.791610i | \(0.290757\pi\) | |||||||
\(450\) | 1.69261 | + | 7.28586i | 0.0797903 | + | 0.343459i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.19428 | + | 2.06856i | 0.0561744 | + | 0.0972970i | ||||
\(453\) | 0.222301 | + | 0.176577i | 0.0104446 | + | 0.00829631i | ||||
\(454\) | 9.34364 | − | 16.1837i | 0.438519 | − | 0.759537i | ||||
\(455\) | 5.83792 | − | 10.1116i | 0.273686 | − | 0.474038i | ||||
\(456\) | −19.5480 | + | 7.71567i | −0.915420 | + | 0.361319i | ||||
\(457\) | 5.15193 | + | 8.92340i | 0.240997 | + | 0.417419i | 0.960999 | − | 0.276553i | \(-0.0891923\pi\) |
−0.720002 | + | 0.693972i | \(0.755859\pi\) | |||||||
\(458\) | 9.32354 | 0.435660 | ||||||||
\(459\) | 12.3541 | − | 26.0387i | 0.576641 | − | 1.21538i | ||||
\(460\) | −3.67998 | −0.171580 | ||||||||
\(461\) | 12.7266 | + | 22.0432i | 0.592738 | + | 1.02665i | 0.993862 | + | 0.110628i | \(0.0352863\pi\) |
−0.401124 | + | 0.916024i | \(0.631380\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.9277 | − | 34.5158i | 0.926119 | − | 1.60409i | 0.136368 | − | 0.990658i | \(-0.456457\pi\) |
0.789751 | − | 0.613427i | \(-0.210210\pi\) | |||||||
\(464\) | −0.837642 | + | 1.45084i | −0.0388866 | + | 0.0673535i | ||||
\(465\) | 0.651450 | + | 0.517457i | 0.0302103 | + | 0.0239965i | ||||
\(466\) | −4.81952 | − | 8.34765i | −0.223260 | − | 0.386697i | ||||
\(467\) | −17.3769 | −0.804108 | −0.402054 | − | 0.915616i | \(-0.631704\pi\) | ||||
−0.402054 | + | 0.915616i | \(0.631704\pi\) | |||||||
\(468\) | 11.9803 | + | 3.64477i | 0.553789 | + | 0.168480i | ||||
\(469\) | 38.0759 | 1.75818 | ||||||||
\(470\) | 4.76065 | + | 8.24568i | 0.219592 | + | 0.380345i | ||||
\(471\) | −6.07866 | + | 40.8650i | −0.280090 | + | 1.88296i | ||||
\(472\) | 2.80781 | − | 4.86327i | 0.129240 | − | 0.223850i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.764314 | − | 5.13826i | 0.0351061 | − | 0.236008i | ||||
\(475\) | −9.63123 | − | 16.6818i | −0.441911 | − | 0.765412i | ||||
\(476\) | 33.7560 | 1.54720 | ||||||||
\(477\) | 12.3613 | − | 11.5588i | 0.565983 | − | 0.529241i | ||||
\(478\) | 16.7064 | 0.764134 | ||||||||
\(479\) | 10.9480 | + | 18.9625i | 0.500226 | + | 0.866417i | 1.00000 | 0.000261184i | \(8.31374e-5\pi\) | |
−0.499774 | + | 0.866156i | \(0.666584\pi\) | |||||||
\(480\) | 8.71674 | + | 6.92385i | 0.397863 | + | 0.316029i | ||||
\(481\) | 11.6571 | − | 20.1907i | 0.531517 | − | 0.920615i | ||||
\(482\) | 5.89325 | − | 10.2074i | 0.268430 | − | 0.464935i | ||||
\(483\) | −13.3007 | + | 5.24982i | −0.605202 | + | 0.238875i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.95046 | 0.406420 | ||||||||
\(486\) | 6.97000 | − | 7.65900i | 0.316166 | − | 0.347419i | ||||
\(487\) | 3.27116 | 0.148230 | 0.0741152 | − | 0.997250i | \(-0.476387\pi\) | ||||
0.0741152 | + | 0.997250i | \(0.476387\pi\) | |||||||
\(488\) | 4.82803 | + | 8.36240i | 0.218555 | + | 0.378548i | ||||
\(489\) | −6.76019 | + | 2.66827i | −0.305706 | + | 0.120663i | ||||
\(490\) | 3.05822 | − | 5.29699i | 0.138156 | − | 0.239294i | ||||
\(491\) | 3.61195 | − | 6.25608i | 0.163005 | − | 0.282333i | −0.772940 | − | 0.634479i | \(-0.781215\pi\) |
0.935945 | + | 0.352146i | \(0.114548\pi\) | |||||||
\(492\) | −6.17083 | − | 4.90159i | −0.278203 | − | 0.220981i | ||||
\(493\) | −3.00358 | − | 5.20235i | −0.135274 | − | 0.234302i | ||||
\(494\) | 9.13071 | 0.410810 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.665390 | −0.0298769 | ||||||||
\(497\) | 12.3326 | + | 21.3608i | 0.553194 | + | 0.958161i | ||||
\(498\) | 0.0816004 | − | 0.548575i | 0.00365660 | − | 0.0245822i | ||||
\(499\) | −7.41726 | + | 12.8471i | −0.332042 | + | 0.575114i | −0.982912 | − | 0.184076i | \(-0.941071\pi\) |
0.650870 | + | 0.759189i | \(0.274404\pi\) | |||||||
\(500\) | −7.61724 | + | 13.1934i | −0.340653 | + | 0.590029i | ||||
\(501\) | −4.03674 | + | 27.1378i | −0.180348 | + | 1.21243i | ||||
\(502\) | −7.26683 | − | 12.5865i | −0.324335 | − | 0.561764i | ||||
\(503\) | −32.9813 | −1.47057 | −0.735283 | − | 0.677760i | \(-0.762951\pi\) | ||||
−0.735283 | + | 0.677760i | \(0.762951\pi\) | |||||||
\(504\) | 26.4933 | + | 8.06007i | 1.18010 | + | 0.359024i | ||||
\(505\) | 1.96673 | 0.0875181 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.90466 | + | 6.27880i | 0.351058 | + | 0.278851i | ||||
\(508\) | −5.96298 | + | 10.3282i | −0.264565 | + | 0.458239i | ||||
\(509\) | −19.3347 | + | 33.4887i | −0.856995 | + | 1.48436i | 0.0177866 | + | 0.999842i | \(0.494338\pi\) |
−0.874782 | + | 0.484517i | \(0.838995\pi\) | |||||||
\(510\) | −6.62872 | + | 2.61638i | −0.293525 | + | 0.115855i | ||||
\(511\) | −22.7882 | − | 39.4704i | −1.00809 | − | 1.74607i | ||||
\(512\) | −16.2170 | −0.716698 | ||||||||
\(513\) | −11.4315 | + | 24.0941i | −0.504712 | + | 1.06378i | ||||
\(514\) | −3.43036 | −0.151307 | ||||||||
\(515\) | −1.50055 | − | 2.59904i | −0.0661223 | − | 0.114527i | ||||
\(516\) | 5.60638 | − | 2.21285i | 0.246807 | − | 0.0974155i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.2908 | − | 19.5563i | 0.496091 | − | 0.859255i | ||||
\(519\) | 3.53018 | + | 2.80408i | 0.154958 | + | 0.123086i | ||||
\(520\) | −3.53471 | − | 6.12230i | −0.155007 | − | 0.268481i | ||||
\(521\) | −17.4844 | −0.766005 | −0.383002 | − | 0.923747i | \(-0.625110\pi\) | ||||
−0.383002 | + | 0.923747i | \(0.625110\pi\) | |||||||
\(522\) | −0.488433 | − | 2.10247i | −0.0213781 | − | 0.0920226i | ||||
\(523\) | 14.4881 | 0.633522 | 0.316761 | − | 0.948505i | \(-0.397405\pi\) | ||||
0.316761 | + | 0.948505i | \(0.397405\pi\) | |||||||
\(524\) | −4.17657 | − | 7.23404i | −0.182454 | − | 0.316020i | ||||
\(525\) | −3.73448 | + | 25.1058i | −0.162986 | + | 1.09571i | ||||
\(526\) | −9.26664 | + | 16.0503i | −0.404045 | + | 0.699826i | ||||
\(527\) | 1.19296 | − | 2.06627i | 0.0519663 | − | 0.0900082i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.26470 | + | 16.0469i | 0.402813 | + | 0.697693i | ||||
\(530\) | −4.18461 | −0.181768 | ||||||||
\(531\) | −1.61255 | − | 6.94126i | −0.0699788 | − | 0.301225i | ||||
\(532\) | −31.2350 | −1.35421 | ||||||||
\(533\) | 3.90865 | + | 6.76998i | 0.169302 | + | 0.293240i | ||||
\(534\) | 14.4906 | + | 11.5102i | 0.627071 | + | 0.498093i | ||||
\(535\) | 5.73743 | − | 9.93751i | 0.248051 | − | 0.429636i | ||||
\(536\) | 11.5270 | − | 19.9653i | 0.497890 | − | 0.862371i | ||||
\(537\) | 12.2250 | − | 4.82525i | 0.527548 | − | 0.208225i | ||||
\(538\) | 1.00299 | + | 1.73722i | 0.0432418 | + | 0.0748971i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.01432 | − | 0.728114i | 0.387915 | − | 0.0313330i | ||||
\(541\) | 33.0983 | 1.42301 | 0.711503 | − | 0.702683i | \(-0.248015\pi\) | ||||
0.711503 | + | 0.702683i | \(0.248015\pi\) | |||||||
\(542\) | −8.42851 | − | 14.5986i | −0.362035 | − | 0.627064i | ||||
\(543\) | −3.86693 | + | 1.52629i | −0.165946 | + | 0.0654994i | ||||
\(544\) | 15.9625 | − | 27.6478i | 0.684385 | − | 1.18539i | ||||
\(545\) | −1.31920 | + | 2.28493i | −0.0565084 | + | 0.0978754i | ||||
\(546\) | −9.42108 | − | 7.48332i | −0.403185 | − | 0.320257i | ||||
\(547\) | −4.60707 | − | 7.97968i | −0.196984 | − | 0.341186i | 0.750565 | − | 0.660796i | \(-0.229781\pi\) |
−0.947549 | + | 0.319610i | \(0.896448\pi\) | |||||||
\(548\) | −26.0786 | −1.11402 | ||||||||
\(549\) | 11.7229 | + | 3.56645i | 0.500319 | + | 0.152213i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.77927 | + | 4.81383i | 0.118401 | + | 0.205076i | ||||
\(552\) | −1.27384 | + | 8.56362i | −0.0542180 | + | 0.364492i | ||||
\(553\) | 8.81393 | − | 15.2662i | 0.374807 | − | 0.649184i | ||||
\(554\) | −3.50907 | + | 6.07788i | −0.149086 | + | 0.258225i | ||||
\(555\) | 2.47730 | − | 16.6542i | 0.105156 | − | 0.706931i | ||||
\(556\) | 10.7082 | + | 18.5472i | 0.454129 | + | 0.786575i | ||||
\(557\) | 37.0518 | 1.56994 | 0.784968 | − | 0.619536i | \(-0.212679\pi\) | ||||
0.784968 | + | 0.619536i | \(0.212679\pi\) | |||||||
\(558\) | 0.626185 | − | 0.585535i | 0.0265085 | − | 0.0247877i | ||||
\(559\) | −5.97883 | −0.252877 | ||||||||
\(560\) | 3.37202 | + | 5.84052i | 0.142494 | + | 0.246807i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.49703 | + | 12.9852i | −0.316243 | + | 0.547749i | ||||
\(563\) | 13.4970 | − | 23.3775i | 0.568832 | − | 0.985246i | −0.427850 | − | 0.903850i | \(-0.640729\pi\) |
0.996682 | − | 0.0813962i | \(-0.0259379\pi\) | |||||||
\(564\) | −32.2322 | + | 12.7221i | −1.35722 | + | 0.535698i | ||||
\(565\) | −0.855575 | − | 1.48190i | −0.0359943 | − | 0.0623440i | ||||
\(566\) | 3.90436 | 0.164113 | ||||||||
\(567\) | 31.5420 | − | 15.4914i | 1.32464 | − | 0.650576i | ||||
\(568\) | 14.9342 | 0.626625 | ||||||||
\(569\) | 13.7379 | + | 23.7947i | 0.575921 | + | 0.997524i | 0.995941 | + | 0.0900095i | \(0.0286898\pi\) |
−0.420020 | + | 0.907515i | \(0.637977\pi\) | |||||||
\(570\) | 6.13368 | − | 2.42098i | 0.256911 | − | 0.101404i | ||||
\(571\) | 19.5052 | − | 33.7840i | 0.816266 | − | 1.41381i | −0.0921492 | − | 0.995745i | \(-0.529374\pi\) |
0.908415 | − | 0.418069i | \(-0.137293\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.4030 | + | 17.7950i | 0.935897 | + | 0.743398i | ||||
\(574\) | 3.78585 | + | 6.55728i | 0.158018 | + | 0.273696i | ||||
\(575\) | −7.93558 | −0.330937 | ||||||||
\(576\) | 1.59967 | − | 1.49583i | 0.0666530 | − | 0.0623261i | ||||
\(577\) | −29.1659 | −1.21419 | −0.607096 | − | 0.794629i | \(-0.707666\pi\) | ||||
−0.607096 | + | 0.794629i | \(0.707666\pi\) | |||||||
\(578\) | 4.57199 | + | 7.91893i | 0.190170 | + | 0.329384i | ||||
\(579\) | 2.07310 | − | 13.9368i | 0.0861550 | − | 0.579195i | ||||
\(580\) | 0.942493 | − | 1.63245i | 0.0391349 | − | 0.0677836i | ||||
\(581\) | 0.941002 | − | 1.62986i | 0.0390393 | − | 0.0676181i | ||||
\(582\) | 1.35700 | − | 9.12273i | 0.0562496 | − | 0.378149i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −27.5954 | −1.14191 | ||||||||
\(585\) | −8.58257 | − | 2.61108i | −0.354846 | − | 0.107955i | ||||
\(586\) | −4.71276 | −0.194682 | ||||||||
\(587\) | 2.54397 | + | 4.40628i | 0.105001 | + | 0.181867i | 0.913739 | − | 0.406303i | \(-0.133182\pi\) |
−0.808738 | + | 0.588169i | \(0.799849\pi\) | |||||||
\(588\) | 17.4306 | + | 13.8454i | 0.718826 | + | 0.570975i | ||||
\(589\) | −1.10387 | + | 1.91196i | −0.0454842 | + | 0.0787809i | ||||
\(590\) | −0.881020 | + | 1.52597i | −0.0362710 | + | 0.0628232i | ||||
\(591\) | −36.9057 | + | 14.5668i | −1.51810 | + | 0.599197i | ||||
\(592\) | 6.73321 | + | 11.6623i | 0.276733 | + | 0.479316i | ||||
\(593\) | 3.46422 | 0.142258 | 0.0711292 | − | 0.997467i | \(-0.477340\pi\) | ||||
0.0711292 | + | 0.997467i | \(0.477340\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.1825 | −0.991386 | ||||||||
\(596\) | 4.33286 | + | 7.50473i | 0.177481 | + | 0.307406i | ||||
\(597\) | 14.9377 | − | 5.89596i | 0.611360 | − | 0.241306i | ||||
\(598\) | 1.88080 | − | 3.25763i | 0.0769114 | − | 0.133215i | ||||
\(599\) | −12.4374 | + | 21.5422i | −0.508179 | + | 0.880192i | 0.491776 | + | 0.870722i | \(0.336348\pi\) |
−0.999955 | + | 0.00947029i | \(0.996985\pi\) | |||||||
\(600\) | 12.0338 | + | 9.55868i | 0.491280 | + | 0.390231i | ||||
\(601\) | −5.53406 | − | 9.58527i | −0.225739 | − | 0.390991i | 0.730802 | − | 0.682590i | \(-0.239146\pi\) |
−0.956541 | + | 0.291598i | \(0.905813\pi\) | |||||||
\(602\) | −5.79098 | −0.236023 | ||||||||
\(603\) | −6.62007 | − | 28.4962i | −0.269590 | − | 1.16045i | ||||
\(604\) | 0.255479 | 0.0103953 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.298180 | − | 2.00458i | 0.0121127 | − | 0.0814304i | ||||
\(607\) | 13.9805 | − | 24.2149i | 0.567451 | − | 0.982854i | −0.429366 | − | 0.903131i | \(-0.641263\pi\) |
0.996817 | − | 0.0797235i | \(-0.0254037\pi\) | |||||||
\(608\) | −14.7704 | + | 25.5830i | −0.599017 | + | 1.03753i | ||||
\(609\) | 1.07765 | − | 7.24475i | 0.0436687 | − | 0.293572i | ||||
\(610\) | −1.51492 | − | 2.62391i | −0.0613371 | − | 0.106239i | ||||
\(611\) | 34.3734 | 1.39060 | ||||||||
\(612\) | −5.86899 | − | 25.2632i | −0.237240 | − | 1.02120i | ||||
\(613\) | 10.9923 | 0.443974 | 0.221987 | − | 0.975050i | \(-0.428746\pi\) | ||||
0.221987 | + | 0.975050i | \(0.428746\pi\) | |||||||
\(614\) | −6.15726 | − | 10.6647i | −0.248487 | − | 0.430391i | ||||
\(615\) | 4.42073 | + | 3.51146i | 0.178261 | + | 0.141596i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.31311 | + | 16.1308i | −0.374932 | + | 0.649401i | −0.990317 | − | 0.138826i | \(-0.955667\pi\) |
0.615385 | + | 0.788227i | \(0.289001\pi\) | |||||||
\(618\) | −2.87656 | + | 1.13539i | −0.115712 | + | 0.0456720i | ||||
\(619\) | −1.34424 | − | 2.32829i | −0.0540296 | − | 0.0935820i | 0.837746 | − | 0.546061i | \(-0.183873\pi\) |
−0.891775 | + | 0.452479i | \(0.850540\pi\) | |||||||
\(620\) | 0.748679 | 0.0300677 | ||||||||
\(621\) | 6.24152 | + | 9.04154i | 0.250463 | + | 0.362825i | ||||
\(622\) | −4.56803 | −0.183161 | ||||||||
\(623\) | 31.3985 | + | 54.3837i | 1.25795 | + | 2.17884i | ||||
\(624\) | 6.67385 | − | 2.63419i | 0.267168 | − | 0.105452i | ||||
\(625\) | −3.92596 | + | 6.79996i | −0.157038 | + | 0.271998i | ||||
\(626\) | −8.41222 | + | 14.5704i | −0.336220 | + | 0.582350i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.5896 | + | 32.1981i | 0.741805 | + | 1.28484i | ||||
\(629\) | −48.2873 | −1.92534 | ||||||||
\(630\) | −8.31292 | − | 2.52905i | −0.331195 | − | 0.100760i | ||||
\(631\) | −39.2289 | −1.56168 | −0.780839 | − | 0.624732i | \(-0.785208\pi\) | ||||
−0.780839 | + | 0.624732i | \(0.785208\pi\) | |||||||
\(632\) | −5.33662 | − | 9.24329i | −0.212279 | − | 0.367678i | ||||
\(633\) | −1.07302 | + | 7.21356i | −0.0426485 | + | 0.286713i | ||||
\(634\) | 3.64688 | − | 6.31657i | 0.144836 | − | 0.250863i | ||||
\(635\) | 4.27183 | − | 7.39902i | 0.169522 | − | 0.293621i | ||||
\(636\) | 2.24074 | − | 15.0638i | 0.0888510 | − | 0.597319i | ||||
\(637\) | −11.0407 | − | 19.1230i | −0.437447 | − | 0.757681i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.8423 | − | 12.9437i | 0.547593 | − | 0.512045i | ||||
\(640\) | 12.3126 | 0.486698 | ||||||||
\(641\) | −12.8745 | − | 22.2993i | −0.508511 | − | 0.880768i | −0.999951 | − | 0.00985628i | \(-0.996863\pi\) |
0.491440 | − | 0.870911i | \(-0.336471\pi\) | |||||||
\(642\) | −9.25891 | − | 7.35450i | −0.365420 | − | 0.290259i | ||||
\(643\) | 6.66603 | − | 11.5459i | 0.262883 | − | 0.455326i | −0.704124 | − | 0.710077i | \(-0.748660\pi\) |
0.967007 | + | 0.254751i | \(0.0819935\pi\) | |||||||
\(644\) | −6.43397 | + | 11.1440i | −0.253534 | + | 0.439134i | ||||
\(645\) | −4.01636 | + | 1.58527i | −0.158144 | + | 0.0624199i | ||||
\(646\) | −9.45557 | − | 16.3775i | −0.372024 | − | 0.644365i | ||||
\(647\) | 23.8506 | 0.937663 | 0.468832 | − | 0.883288i | \(-0.344675\pi\) | ||||
0.468832 | + | 0.883288i | \(0.344675\pi\) | |||||||
\(648\) | 1.42595 | − | 21.2291i | 0.0560165 | − | 0.833957i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.33853 | − | 5.78250i | −0.130948 | − | 0.226808i | ||||
\(651\) | 2.70597 | − | 1.06806i | 0.106056 | − | 0.0418605i | ||||
\(652\) | −3.27013 | + | 5.66402i | −0.128068 | + | 0.221820i | ||||
\(653\) | −6.36247 | + | 11.0201i | −0.248983 | + | 0.431251i | −0.963244 | − | 0.268629i | \(-0.913430\pi\) |
0.714261 | + | 0.699879i | \(0.246763\pi\) | |||||||
\(654\) | 2.12889 | + | 1.69102i | 0.0832464 | + | 0.0661239i | ||||
\(655\) | 2.99206 | + | 5.18240i | 0.116909 | + | 0.202493i | ||||
\(656\) | −4.51533 | −0.176294 | ||||||||
\(657\) | −25.5778 | + | 23.9173i | −0.997883 | + | 0.933105i | ||||
\(658\) | 33.2935 | 1.29792 | ||||||||
\(659\) | 13.6263 | + | 23.6015i | 0.530806 | + | 0.919383i | 0.999354 | + | 0.0359452i | \(0.0114442\pi\) |
−0.468547 | + | 0.883438i | \(0.655223\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8220 | + | 37.7968i | −0.848777 | + | 1.47012i | 0.0335234 | + | 0.999438i | \(0.489327\pi\) |
−0.882300 | + | 0.470687i | \(0.844006\pi\) | |||||||
\(662\) | −1.23240 | + | 2.13458i | −0.0478985 | + | 0.0829627i | ||||
\(663\) | −3.78530 | + | 25.4474i | −0.147009 | + | 0.988296i | ||||
\(664\) | −0.569753 | − | 0.986841i | −0.0221107 | − | 0.0382969i | ||||
\(665\) | 22.3765 | 0.867724 | ||||||||
\(666\) | −16.5991 | − | 5.04997i | −0.643203 | − | 0.195682i | ||||
\(667\) | 2.28996 | 0.0886675 | ||||||||
\(668\) | 12.3450 | + | 21.3822i | 0.477644 | + | 0.827304i | ||||
\(669\) | 9.30265 | + | 7.38924i | 0.359661 | + | 0.285685i | ||||
\(670\) | −3.61688 | + | 6.26462i | −0.139732 | + | 0.242023i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 36.2074 | − | 14.2912i | 1.39673 | − | 0.551294i | ||||
\(673\) | 13.3433 | + | 23.1113i | 0.514348 | + | 0.890877i | 0.999861 | + | 0.0166477i | \(0.00529938\pi\) |
−0.485513 | + | 0.874229i | \(0.661367\pi\) | |||||||
\(674\) | 21.3879 | 0.823831 | ||||||||
\(675\) | 19.4386 | − | 1.57012i | 0.748194 | − | 0.0604339i | ||||
\(676\) | 9.08443 | 0.349401 | ||||||||
\(677\) | −13.5415 | − | 23.4546i | −0.520443 | − | 0.901434i | −0.999717 | − | 0.0237689i | \(-0.992433\pi\) |
0.479274 | − | 0.877665i | \(-0.340900\pi\) | |||||||
\(678\) | −1.64014 | + | 0.647367i | −0.0629891 | + | 0.0248620i | ||||
\(679\) | 15.6487 | − | 27.1044i | 0.600543 | − | 1.04017i | ||||
\(680\) | −7.32095 | + | 12.6803i | −0.280746 | + | 0.486266i | ||||
\(681\) | −38.1514 | − | 30.3043i | −1.46196 | − | 1.16126i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.7343 | −0.640322 | −0.320161 | − | 0.947363i | \(-0.603737\pi\) | ||||
−0.320161 | + | 0.947363i | \(0.603737\pi\) | |||||||
\(684\) | 5.43068 | + | 23.3765i | 0.207647 | + | 0.893822i | ||||
\(685\) | 18.6824 | 0.713820 | ||||||||
\(686\) | −1.61526 | − | 2.79772i | −0.0616711 | − | 0.106817i | ||||
\(687\) | 3.57657 | − | 24.0443i | 0.136455 | − | 0.917346i | ||||
\(688\) | 1.72671 | − | 2.99074i | 0.0658301 | − | 0.114021i | ||||
\(689\) | −7.55356 | + | 13.0831i | −0.287768 | + | 0.498428i | ||||
\(690\) | 0.399697 | − | 2.68705i | 0.0152162 | − | 0.102294i | ||||
\(691\) | 18.7598 | + | 32.4929i | 0.713656 | + | 1.23609i | 0.963476 | + | 0.267796i | \(0.0862953\pi\) |
−0.249820 | + | 0.968292i | \(0.580371\pi\) | |||||||
\(692\) | 4.05707 | 0.154226 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2978 | 0.542738 | ||||||||
\(695\) | −7.67127 | − | 13.2870i | −0.290988 | − | 0.504005i | ||||
\(696\) | −3.47259 | − | 2.75833i | −0.131628 | − | 0.104554i | ||||
\(697\) | 8.09543 | − | 14.0217i | 0.306636 | − | 0.531109i | ||||
\(698\) | −5.58692 | + | 9.67683i | −0.211468 | + | 0.366273i | ||||
\(699\) | −23.3764 | + | 9.22673i | −0.884175 | + | 0.348987i | ||||
\(700\) | 11.4207 | + | 19.7812i | 0.431662 | + | 0.747660i | ||||
\(701\) | 10.2007 | 0.385275 | 0.192637 | − | 0.981270i | \(-0.438296\pi\) | ||||
0.192637 | + | 0.981270i | \(0.438296\pi\) | |||||||
\(702\) | −3.96256 | + | 8.35188i | −0.149557 | + | 0.315221i | ||||
\(703\) | 44.6811 | 1.68518 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.0908 | − | 9.11402i | 0.869651 | − | 0.343254i | ||||
\(706\) | 1.03995 | − | 1.80124i | 0.0391388 | − | 0.0677905i | ||||
\(707\) | 3.43856 | − | 5.95577i | 0.129321 | − | 0.223990i | ||||
\(708\) | −5.02146 | − | 3.98862i | −0.188718 | − | 0.149902i | ||||
\(709\) | 7.24884 | + | 12.5554i | 0.272236 | + | 0.471526i | 0.969434 | − | 0.245352i | \(-0.0789036\pi\) |
−0.697198 | + | 0.716878i | \(0.745570\pi\) | |||||||
\(710\) | −4.68598 | −0.175862 | ||||||||
\(711\) | −12.9577 | − | 3.94214i | −0.485953 | − | 0.147842i | ||||
\(712\) | 38.0220 | 1.42493 | ||||||||
\(713\) | 0.454763 | + | 0.787673i | 0.0170310 | + | 0.0294986i | ||||
\(714\) | −3.66637 | + | 24.6479i | −0.137210 | + | 0.922426i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.91364 | − | 10.2427i | 0.221003 | − | 0.382789i | ||||
\(717\) | 6.40870 | − | 43.0838i | 0.239337 | − | 1.60899i | ||||
\(718\) | 2.81961 | + | 4.88370i | 0.105227 | + | 0.182258i | ||||
\(719\) | 19.2266 | 0.717032 | 0.358516 | − | 0.933524i | \(-0.383283\pi\) | ||||
0.358516 | + | 0.933524i | \(0.383283\pi\) | |||||||
\(720\) | 3.78480 | − | 3.53910i | 0.141051 | − | 0.131895i | ||||
\(721\) | −10.4941 | −0.390821 | ||||||||
\(722\) | 2.43836 | + | 4.22337i | 0.0907464 | + | 0.157177i | ||||
\(723\) | −24.0630 | − | 19.1136i | −0.894912 | − | 0.710843i | ||||
\(724\) | −1.87056 | + | 3.23991i | −0.0695188 | + | 0.120410i | ||||
\(725\) | 2.03241 | − | 3.52023i | 0.0754818 | − | 0.130738i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.363414 | − | 0.629451i | −0.0134783 | − | 0.0233450i | 0.859208 | − | 0.511627i | \(-0.170957\pi\) |
−0.872686 | + | 0.488282i | \(0.837624\pi\) | |||||||
\(728\) | −24.7200 | −0.916183 | ||||||||
\(729\) | −17.0779 | − | 20.9128i | −0.632514 | − | 0.774549i | ||||
\(730\) | 8.65874 | 0.320474 | ||||||||
\(731\) | 6.19154 | + | 10.7241i | 0.229003 | + | 0.396644i | ||||
\(732\) | 10.2568 | − | 4.04839i | 0.379102 | − | 0.149633i | ||||
\(733\) | 0.937944 | − | 1.62457i | 0.0346438 | − | 0.0600048i | −0.848184 | − | 0.529702i | \(-0.822304\pi\) |
0.882827 | + | 0.469697i | \(0.155637\pi\) | |||||||
\(734\) | −3.65740 | + | 6.33481i | −0.134997 | + | 0.233822i | ||||
\(735\) | −12.4871 | − | 9.91874i | −0.460595 | − | 0.365858i | ||||
\(736\) | 6.08497 | + | 10.5395i | 0.224295 | + | 0.388490i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 4.24928 | − | 3.97343i | 0.156418 | − | 0.146264i | ||||
\(739\) | −52.5826 | −1.93428 | −0.967140 | − | 0.254243i | \(-0.918174\pi\) | ||||
−0.967140 | + | 0.254243i | \(0.918174\pi\) | |||||||
\(740\) | −7.57603 | − | 13.1221i | −0.278500 | − | 0.482377i | ||||
\(741\) | 3.50260 | − | 23.5470i | 0.128671 | − | 0.865020i | ||||
\(742\) | −7.31624 | + | 12.6721i | −0.268588 | + | 0.465208i | ||||
\(743\) | 16.6664 | − | 28.8671i | 0.611431 | − | 1.05903i | −0.379568 | − | 0.925164i | \(-0.623928\pi\) |
0.990999 | − | 0.133866i | \(-0.0427392\pi\) | |||||||
\(744\) | 0.259157 | − | 1.74224i | 0.00950116 | − | 0.0638735i | ||||
\(745\) | −3.10402 | − | 5.37632i | −0.113723 | − | 0.196973i | ||||
\(746\) | −7.31206 | −0.267714 | ||||||||
\(747\) | −1.38341 | − | 0.420875i | −0.0506162 | − | 0.0153990i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.0623 | − | 34.7489i | −0.733060 | − | 1.26970i | ||||
\(750\) | −8.80624 | − | 6.99494i | −0.321559 | − | 0.255419i | ||||
\(751\) | 11.6820 | − | 20.2339i | 0.426284 | − | 0.738345i | −0.570256 | − | 0.821467i | \(-0.693156\pi\) |
0.996539 | + | 0.0831223i | \(0.0264892\pi\) | |||||||
\(752\) | −9.92717 | + | 17.1944i | −0.362007 | + | 0.627014i | ||||
\(753\) | −35.2467 | + | 13.9120i | −1.28446 | + | 0.506981i | ||||
\(754\) | 0.963394 | + | 1.66865i | 0.0350847 | + | 0.0607685i | ||||
\(755\) | −0.183023 | −0.00666089 | ||||||||
\(756\) | 13.5554 | − | 28.5708i | 0.493007 | − | 1.03911i | ||||
\(757\) | −33.8030 | −1.22859 | −0.614296 | − | 0.789076i | \(-0.710560\pi\) | ||||
−0.614296 | + | 0.789076i | \(0.710560\pi\) | |||||||
\(758\) | 8.43250 | + | 14.6055i | 0.306282 | + | 0.530496i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.77421 | − | 11.7333i | 0.245726 | − | 0.425611i | ||||
\(761\) | −10.0560 | + | 17.4174i | −0.364528 | + | 0.631381i | −0.988700 | − | 0.149906i | \(-0.952103\pi\) |
0.624172 | + | 0.781287i | \(0.285436\pi\) | |||||||
\(762\) | −6.89376 | − | 5.47583i | −0.249735 | − | 0.198368i | ||||
\(763\) | 4.61291 | + | 7.98979i | 0.166998 | + | 0.289250i | ||||
\(764\) | 25.7466 | 0.931480 | ||||||||
\(765\) | 4.20449 | + | 18.0983i | 0.152014 | + | 0.654346i | ||||
\(766\) | 8.04807 | 0.290788 | ||||||||
\(767\) | 3.18063 | + | 5.50901i | 0.114846 | + | 0.198919i | ||||
\(768\) | 2.23882 | − | 15.0509i | 0.0807865 | − | 0.543104i | ||||
\(769\) | −0.313500 | + | 0.542997i | −0.0113051 | + | 0.0195810i | −0.871623 | − | 0.490178i | \(-0.836932\pi\) |
0.860318 | + | 0.509759i | \(0.170265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.31591 | + | 8.84649i | −0.0473914 | + | 0.318598i | ||||
\(772\) | −6.33989 | − | 10.9810i | −0.228178 | − | 0.395215i | ||||
\(773\) | 28.7378 | 1.03363 | 0.516813 | − | 0.856098i | \(-0.327118\pi\) | ||||
0.516813 | + | 0.856098i | \(0.327118\pi\) | |||||||
\(774\) | 1.00685 | + | 4.33401i | 0.0361905 | + | 0.155783i | ||||
\(775\) | 1.61447 | 0.0579933 | ||||||||
\(776\) | −9.47491 | − | 16.4110i | −0.340130 | − | 0.589122i | ||||
\(777\) | −46.1021 | − | 36.6196i | −1.65390 | − | 1.31372i | ||||
\(778\) | 4.76686 | − | 8.25644i | 0.170900 | − | 0.296008i | ||||
\(779\) | −7.49085 | + | 12.9745i | −0.268387 | + | 0.464861i | ||||
\(780\) | −7.50923 | + | 2.96392i | −0.268874 | + | 0.106125i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −7.79085 | −0.278600 | ||||||||
\(783\) | −5.60938 | + | 0.453087i | −0.200463 | + | 0.0161920i | ||||
\(784\) | 12.7543 | 0.455512 | ||||||||
\(785\) | −13.3174 | − | 23.0664i | −0.475319 | − | 0.823277i | ||||
\(786\) | 5.73578 | − | 2.26393i | 0.204588 | − | 0.0807517i | ||||
\(787\) | 7.05147 | − | 12.2135i | 0.251358 | − | 0.435364i | −0.712542 | − | 0.701629i | \(-0.752456\pi\) |
0.963900 | + | 0.266265i | \(0.0857896\pi\) | |||||||
\(788\) | −17.8525 | + | 30.9214i | −0.635968 | + | 1.10153i | ||||
\(789\) | 37.8370 | + | 30.0545i | 1.34703 | + | 1.06997i | ||||
\(790\) | 1.67450 | + | 2.90031i | 0.0595759 | + | 0.103188i | ||||
\(791\) | −5.98345 | −0.212747 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9382 | −0.388426 | ||||||||
\(794\) | −1.67370 | − | 2.89893i | −0.0593973 | − | 0.102879i | ||||
\(795\) | −1.60524 | + | 10.7916i | −0.0569322 | + | 0.382738i | ||||
\(796\) | 7.22586 | − | 12.5156i | 0.256114 | − | 0.443602i | ||||
\(797\) | −13.0773 | + | 22.6506i | −0.463223 | + | 0.802326i | −0.999119 | − | 0.0419576i | \(-0.986641\pi\) |
0.535896 | + | 0.844284i | \(0.319974\pi\) | |||||||
\(798\) | 3.39256 | − | 22.8072i | 0.120095 | − | 0.807365i | ||||
\(799\) | −35.5964 | − | 61.6548i | −1.25931 | − | 2.18119i | ||||
\(800\) | 21.6024 | 0.763760 | ||||||||
\(801\) | 35.2420 | − | 32.9542i | 1.24521 | − | 1.16438i | ||||
\(802\) | 12.0908 | 0.426939 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −20.6148 | − | 16.3746i | −0.727026 | − | 0.577489i | ||||
\(805\) | 4.60924 | − | 7.98344i | 0.162454 | − | 0.281379i | ||||
\(806\) | −0.382641 | + | 0.662754i | −0.0134780 | + | 0.0233445i | ||||
\(807\) | 4.86484 | − | 1.92017i | 0.171251 | − | 0.0675932i | ||||
\(808\) | −2.08196 | − | 3.60607i | −0.0732433 | − | 0.126861i | ||||
\(809\) | 15.8533 | 0.557374 | 0.278687 | − | 0.960382i | \(-0.410101\pi\) | ||||
0.278687 | + | 0.960382i | \(0.410101\pi\) | |||||||
\(810\) | −0.447427 | + | 6.66115i | −0.0157210 | + | 0.234049i | ||||
\(811\) | −36.3264 | −1.27559 | −0.637796 | − | 0.770206i | \(-0.720154\pi\) | ||||
−0.637796 | + | 0.770206i | \(0.720154\pi\) | |||||||
\(812\) | −3.29565 | − | 5.70824i | −0.115655 | − | 0.200320i | ||||
\(813\) | −40.8812 | + | 16.1360i | −1.43377 | + | 0.565913i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.34269 | − | 4.05766i | 0.0820608 | − | 0.142134i | ||||
\(816\) | −11.6362 | − | 9.24280i | −0.407347 | − | 0.323563i | ||||
\(817\) | −5.72915 | − | 9.92318i | −0.200438 | − | 0.347168i | ||||
\(818\) | −10.9151 | −0.381637 | ||||||||
\(819\) | −22.9126 | + | 21.4252i | −0.800630 | + | 0.748656i | ||||
\(820\) | 5.08053 | 0.177420 | ||||||||
\(821\) | 8.17837 | + | 14.1653i | 0.285427 | + | 0.494374i | 0.972713 | − | 0.232013i | \(-0.0745313\pi\) |
−0.687286 | + | 0.726387i | \(0.741198\pi\) | |||||||
\(822\) | 2.83249 | − | 19.0420i | 0.0987946 | − | 0.664167i | ||||
\(823\) | 13.0873 | − | 22.6678i | 0.456193 | − | 0.790150i | −0.542563 | − | 0.840015i | \(-0.682546\pi\) |
0.998756 | + | 0.0498656i | \(0.0158793\pi\) | |||||||
\(824\) | −3.17696 | + | 5.50265i | −0.110675 | + | 0.191694i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.08070 | + | 5.33592i | 0.107191 | + | 0.185661i | ||||
\(827\) | 5.53930 | 0.192620 | 0.0963101 | − | 0.995351i | \(-0.469296\pi\) | ||||
0.0963101 | + | 0.995351i | \(0.469296\pi\) | |||||||
\(828\) | 9.45885 | + | 2.87767i | 0.328718 | + | 0.100006i | ||||
\(829\) | 18.5033 | 0.642647 | 0.321324 | − | 0.946969i | \(-0.395872\pi\) | ||||
0.321324 | + | 0.946969i | \(0.395872\pi\) | |||||||
\(830\) | 0.178774 | + | 0.309646i | 0.00620534 | + | 0.0107480i | ||||
\(831\) | 14.3280 | + | 11.3810i | 0.497033 | + | 0.394802i | ||||
\(832\) | −0.977507 | + | 1.69309i | −0.0338890 | + | 0.0586974i | ||||
\(833\) | −22.8670 | + | 39.6068i | −0.792294 | + | 1.37229i | ||||
\(834\) | −14.7058 | + | 5.80443i | −0.509221 | + | 0.200991i | ||||
\(835\) | −8.84388 | − | 15.3180i | −0.306055 | − | 0.530103i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.26981 | − | 1.83947i | −0.0438912 | − | 0.0635813i | ||||
\(838\) | 11.5635 | 0.399454 | ||||||||
\(839\) | 8.98265 | + | 15.5584i | 0.310115 | + | 0.537136i | 0.978387 | − | 0.206782i | \(-0.0662990\pi\) |
−0.668272 | + | 0.743917i | \(0.732966\pi\) | |||||||
\(840\) | −16.6060 | + | 6.55443i | −0.572960 | + | 0.226149i | ||||
\(841\) | 13.9135 | − | 24.0989i | 0.479776 | − | 0.830997i | ||||
\(842\) | 1.51088 | − | 2.61692i | 0.0520683 | − | 0.0901850i | ||||
\(843\) | 30.6114 | + | 24.3151i | 1.05431 | + | 0.837458i | ||||
\(844\) | 3.28147 | + | 5.68367i | 0.112953 | + | 0.195640i | ||||
\(845\) | −6.50801 | −0.223882 | ||||||||
\(846\) | −5.78858 | − | 24.9170i | −0.199015 | − | 0.856666i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.36299 | − | 7.55692i | −0.149826 | − | 0.259506i | ||||
\(849\) | 1.49774 | − | 10.0689i | 0.0514024 | − | 0.345563i | ||||
\(850\) | −6.91462 | + | 11.9765i | −0.237169 | + | 0.410790i | ||||
\(851\) | 9.20367 | − | 15.9412i | 0.315498 | − | 0.546458i | ||||
\(852\) | 2.50921 | − | 16.8687i | 0.0859640 | − | 0.577911i | ||||
\(853\) | −13.9565 | − | 24.1734i | −0.477863 | − | 0.827683i | 0.521815 | − | 0.853059i | \(-0.325255\pi\) |
−0.999678 | + | 0.0253757i | \(0.991922\pi\) | |||||||
\(854\) | −10.5945 | −0.362537 | ||||||||
\(855\) | −3.89049 | − | 16.7467i | −0.133052 | − | 0.572725i | ||||
\(856\) | −24.2944 | −0.830367 | ||||||||
\(857\) | 4.24983 | + | 7.36093i | 0.145172 | + | 0.251445i | 0.929437 | − | 0.368981i | \(-0.120293\pi\) |
−0.784265 | + | 0.620426i | \(0.786960\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.9259 | + | 24.1203i | −0.475145 | + | 0.822974i | −0.999595 | − | 0.0284667i | \(-0.990938\pi\) |
0.524450 | + | 0.851441i | \(0.324271\pi\) | |||||||
\(860\) | −1.94284 | + | 3.36510i | −0.0662504 | + | 0.114749i | ||||
\(861\) | 18.3627 | − | 7.24782i | 0.625799 | − | 0.247005i | ||||
\(862\) | 4.14695 | + | 7.18273i | 0.141246 | + | 0.244645i | ||||
\(863\) | 13.5940 | 0.462745 | 0.231372 | − | 0.972865i | \(-0.425678\pi\) | ||||
0.231372 | + | 0.972865i | \(0.425678\pi\) | |||||||
\(864\) | −16.9908 | − | 24.6131i | −0.578038 | − | 0.837353i | ||||
\(865\) | −2.90645 | −0.0988221 | ||||||||
\(866\) | 9.52840 | + | 16.5037i | 0.323788 | + | 0.560818i | ||||
\(867\) | 22.1758 | − | 8.75286i | 0.753129 | − | 0.297263i | ||||
\(868\) | 1.30897 | − | 2.26720i | 0.0444293 | − | 0.0769538i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.08961 | + | 0.865495i | 0.0369412 | + | 0.0293430i | ||||
\(871\) | 13.0575 | + | 22.6163i | 0.442438 | + | 0.766324i | ||||
\(872\) | 5.58600 | 0.189166 | ||||||||
\(873\) | −23.0058 | − | 6.99909i | −0.778630 | − | 0.236883i | ||||
\(874\) | 7.20901 | 0.243848 | ||||||||
\(875\) | −19.0814 | − | 33.0500i | −0.645071 | − | 1.11730i | ||||
\(876\) | −4.63651 | + | 31.1699i | −0.156653 | + | 1.05313i | ||||
\(877\) | −18.0890 | + | 31.3310i | −0.610822 | + | 1.05797i | 0.380281 | + | 0.924871i | \(0.375827\pi\) |
−0.991102 | + | 0.133103i | \(0.957506\pi\) | |||||||
\(878\) | −1.36454 | + | 2.36345i | −0.0460509 | + | 0.0797625i | ||||
\(879\) | −1.80785 | + | 12.1536i | −0.0609772 | + | 0.409932i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.6423 | 0.897601 | 0.448800 | − | 0.893632i | \(-0.351851\pi\) | ||||
0.448800 | + | 0.893632i | \(0.351851\pi\) | |||||||
\(882\) | −12.0028 | + | 11.2237i | −0.404157 | + | 0.377920i | ||||
\(883\) | −20.4764 | −0.689087 | −0.344544 | − | 0.938770i | \(-0.611966\pi\) | ||||
−0.344544 | + | 0.938770i | \(0.611966\pi\) | |||||||
\(884\) | 11.5761 | + | 20.0504i | 0.389346 | + | 0.674367i | ||||
\(885\) | 3.59733 | + | 2.85741i | 0.120923 | + | 0.0960510i | ||||
\(886\) | −7.05166 | + | 12.2138i | −0.236905 | + | 0.410332i | ||||
\(887\) | 16.0006 | − | 27.7138i | 0.537247 | − | 0.930539i | −0.461804 | − | 0.886982i | \(-0.652798\pi\) |
0.999051 | − | 0.0435570i | \(-0.0138690\pi\) | |||||||
\(888\) | −33.1586 | + | 13.0878i | −1.11273 | + | 0.439198i | ||||
\(889\) | −14.9375 | − | 25.8725i | −0.500987 | − | 0.867734i | ||||
\(890\) | −11.9303 | −0.399906 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.6911 | 0.357963 | ||||||||
\(893\) | 32.9380 | + | 57.0503i | 1.10223 | + | 1.90912i | ||||
\(894\) | −5.95041 | + | 2.34865i | −0.199011 | + | 0.0785504i | ||||
\(895\) | −4.23648 | + | 7.33780i | −0.141610 | + | 0.245275i | ||||
\(896\) | 21.5270 | − | 37.2858i | 0.719165 | − | 1.24563i | ||||
\(897\) | −7.67955 | − | 6.09999i | −0.256413 | − | 0.203673i | ||||
\(898\) | 8.60125 | + | 14.8978i | 0.287027 | + | 0.497146i | ||||
\(899\) | −0.465884 | −0.0155381 | ||||||||
\(900\) | 12.8187 | − | 11.9866i | 0.427291 | − | 0.399553i | ||||
\(901\) | 31.2892 | 1.04239 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.22146 | + | 14.9342i | −0.0739256 | + | 0.496980i | ||||
\(904\) | −1.81141 | + | 3.13746i | −0.0602467 | + | 0.104350i | ||||
\(905\) | 1.34005 | − | 2.32104i | 0.0445449 | − | 0.0771540i | ||||
\(906\) | −0.0277486 | + | 0.186546i | −0.000921885 | + | 0.00619756i | ||||
\(907\) | 24.5251 | + | 42.4788i | 0.814344 | + | 1.41048i | 0.909798 | + | 0.415051i | \(0.136236\pi\) |
−0.0954547 | + | 0.995434i | \(0.530431\pi\) | |||||||
\(908\) | −43.8455 | −1.45506 | ||||||||
\(909\) | −5.05518 | − | 1.53794i | −0.167670 | − | 0.0510103i | ||||
\(910\) | 7.75650 | 0.257125 | ||||||||
\(911\) | 11.6906 | + | 20.2488i | 0.387328 | + | 0.670872i | 0.992089 | − | 0.125535i | \(-0.0400647\pi\) |
−0.604761 | + | 0.796407i | \(0.706731\pi\) | |||||||
\(912\) | 10.7672 | + | 8.55253i | 0.356536 | + | 0.283203i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −3.42253 | + | 5.92800i | −0.113207 | + | 0.196081i | ||||
\(915\) | −7.34787 | + | 2.90023i | −0.242913 | + | 0.0958786i | ||||
\(916\) | −10.9378 | − | 18.9448i | −0.361395 | − | 0.625954i | ||||
\(917\) | 20.9249 | 0.691001 | ||||||||
\(918\) | 19.0841 | − | 1.54148i | 0.629869 | − | 0.0508765i | ||||
\(919\) | −7.59931 | −0.250678 | −0.125339 | − | 0.992114i | \(-0.540002\pi\) | ||||
−0.125339 | + | 0.992114i | \(0.540002\pi\) | |||||||
\(920\) | −2.79078 | − | 4.83377i | −0.0920093 | − | 0.159365i | ||||
\(921\) | −29.8649 | + | 11.7878i | −0.984081 | + | 0.388420i | ||||
\(922\) | −8.45456 | + | 14.6437i | −0.278436 | + | 0.482265i | ||||
\(923\) | −8.45857 | + | 14.6507i | −0.278417 | + | 0.482233i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.3371 | − | 28.2967i | −0.537160 | − | 0.930389i | ||||
\(926\) | 26.4768 | 0.870081 | ||||||||
\(927\) | 1.82456 | + | 7.85384i | 0.0599263 | + | 0.257954i | ||||
\(928\) | −6.23377 | −0.204633 | ||||||||
\(929\) | 7.43837 | + | 12.8836i | 0.244045 | + | 0.422699i | 0.961863 | − | 0.273533i | \(-0.0881922\pi\) |
−0.717818 | + | 0.696231i | \(0.754859\pi\) | |||||||
\(930\) | −0.0813170 | + | 0.546670i | −0.00266649 | + | 0.0179260i | ||||
\(931\) | 21.1592 | − | 36.6489i | 0.693466 | − | 1.20112i | ||||
\(932\) | −11.3079 | + | 19.5859i | −0.370403 | + | 0.641557i | ||||
\(933\) | −1.75233 | + | 11.7804i | −0.0573686 | + | 0.385672i | ||||
\(934\) | −5.77192 | − | 9.99727i | −0.188863 | − | 0.327121i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.29794 | + | 18.5006i | 0.140482 | + | 0.604710i | ||||
\(937\) | 17.8231 | 0.582257 | 0.291128 | − | 0.956684i | \(-0.405969\pi\) | ||||
0.291128 | + | 0.956684i | \(0.405969\pi\) | |||||||
\(938\) | 12.6473 | + | 21.9058i | 0.412949 | + | 0.715248i | ||||
\(939\) | 34.3483 | + | 27.2834i | 1.12091 | + | 0.890360i | ||||
\(940\) | 11.1698 | − | 19.3466i | 0.364318 | − | 0.631018i | ||||
\(941\) | −21.3296 | + | 36.9439i | −0.695324 | + | 1.20434i | 0.274748 | + | 0.961516i | \(0.411406\pi\) |
−0.970071 | + | 0.242820i | \(0.921928\pi\) | |||||||
\(942\) | −25.5295 | + | 10.0766i | −0.831795 | + | 0.328312i | ||||
\(943\) | 3.08601 | + | 5.34513i | 0.100494 | + | 0.174062i | ||||
\(944\) | −3.67430 | −0.119588 | ||||||||
\(945\) | −9.71100 | + | 20.4678i | −0.315899 | + | 0.665819i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.44670 | − | 5.96986i | −0.112003 | − | 0.193994i | 0.804575 | − | 0.593851i | \(-0.202393\pi\) |
−0.916578 | + | 0.399857i | \(0.869060\pi\) | |||||||
\(948\) | −11.3372 | + | 4.47484i | −0.368216 | + | 0.145336i | ||||
\(949\) | 15.6297 | − | 27.0715i | 0.507363 | − | 0.878778i | ||||
\(950\) | 6.39822 | − | 11.0820i | 0.207586 | − | 0.359549i | ||||
\(951\) | −14.8907 | − | 11.8279i | −0.482864 | − | 0.383547i | ||||
\(952\) | 25.5995 | + | 44.3396i | 0.829683 | + | 1.43705i | ||||
\(953\) | −23.6805 | −0.767085 | −0.383543 | − | 0.923523i | \(-0.625296\pi\) | ||||
−0.383543 | + | 0.923523i | \(0.625296\pi\) | |||||||
\(954\) | 10.7559 | + | 3.27228i | 0.348236 | + | 0.105944i | ||||
\(955\) | −18.4446 | −0.596855 | ||||||||
\(956\) | −19.5989 | − | 33.9463i | −0.633874 | − | 1.09790i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.27297 | + | 12.5972i | −0.234979 | + | 0.406996i | ||||
\(959\) | 32.6638 | − | 56.5754i | 1.05477 | − | 1.82692i | ||||
\(960\) | −0.207735 | + | 1.39654i | −0.00670462 | + | 0.0450732i | ||||
\(961\) | 15.4075 | + | 26.6865i | 0.497015 | + | 0.860856i | ||||
\(962\) | 15.4881 | 0.499356 | ||||||||
\(963\) | −22.5181 | + | 21.0564i | −0.725637 | + | 0.678532i | ||||
\(964\) | −27.6544 | −0.890688 | ||||||||
\(965\) | 4.54184 | + | 7.86670i | 0.146207 | + | 0.253238i | ||||
\(966\) | −7.43827 | − | 5.90834i | −0.239323 | − | 0.190098i | ||||
\(967\) | 15.5700 | − | 26.9680i | 0.500696 | − | 0.867231i | −0.499303 | − | 0.866427i | \(-0.666411\pi\) |
1.00000 | 0.000804082i | \(-0.000255947\pi\) | ||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −45.8628 | + | 18.1022i | −1.47333 | + | 0.581527i | ||||
\(970\) | 2.97299 | + | 5.14937i | 0.0954569 | + | 0.165336i | ||||
\(971\) | 13.3548 | 0.428577 | 0.214288 | − | 0.976770i | \(-0.431257\pi\) | ||||
0.214288 | + | 0.976770i | \(0.431257\pi\) | |||||||
\(972\) | −23.7393 | − | 5.17751i | −0.761440 | − | 0.166069i | ||||
\(973\) | −53.6488 | −1.71990 | ||||||||
\(974\) | 1.08655 | + | 1.88196i | 0.0348153 | + | 0.0603018i | ||||
\(975\) | −16.1930 | + | 6.39145i | −0.518592 | + | 0.204690i | ||||
\(976\) | 3.15899 | − | 5.47153i | 0.101117 | − | 0.175139i | ||||
\(977\) | 4.45796 | − | 7.72142i | 0.142623 | − | 0.247030i | −0.785861 | − | 0.618404i | \(-0.787780\pi\) |
0.928484 | + | 0.371373i | \(0.121113\pi\) | |||||||
\(978\) | −3.78057 | − | 3.00297i | −0.120889 | − | 0.0960244i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −14.3508 | −0.458421 | ||||||||
\(981\) | 5.17758 | − | 4.84147i | 0.165307 | − | 0.154576i | ||||
\(982\) | 4.79899 | 0.153142 | ||||||||
\(983\) | 8.42927 | + | 14.5999i | 0.268852 | + | 0.465665i | 0.968566 | − | 0.248758i | \(-0.0800224\pi\) |
−0.699714 | + | 0.714423i | \(0.746689\pi\) | |||||||
\(984\) | 1.75864 | − | 11.8228i | 0.0560633 | − | 0.376897i | ||||
\(985\) | 12.7894 | − | 22.1518i | 0.407503 | − | 0.705815i | ||||
\(986\) | 1.99534 | − | 3.45603i | 0.0635446 | − | 0.110062i | ||||
\(987\) | 12.7716 | − | 85.8599i | 0.406525 | − | 2.73295i | ||||
\(988\) | −10.7116 | − | 18.5530i | −0.340781 | − | 0.590249i | ||||
\(989\) | −4.72049 | −0.150103 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.5356 | −1.06529 | −0.532647 | − | 0.846338i | \(-0.678803\pi\) | ||||
−0.532647 | + | 0.846338i | \(0.678803\pi\) | |||||||
\(992\) | −1.23796 | − | 2.14422i | −0.0393054 | − | 0.0680790i | ||||
\(993\) | 5.03205 | + | 3.99704i | 0.159687 | + | 0.126842i | ||||
\(994\) | −8.19282 | + | 14.1904i | −0.259861 | + | 0.450092i | ||||
\(995\) | −5.17654 | + | 8.96603i | −0.164107 | + | 0.284242i | ||||
\(996\) | −1.21040 | + | 0.477748i | −0.0383529 | + | 0.0151380i | ||||
\(997\) | 1.62184 | + | 2.80910i | 0.0513641 | + | 0.0889652i | 0.890564 | − | 0.454857i | \(-0.150310\pi\) |
−0.839200 | + | 0.543823i | \(0.816976\pi\) | |||||||
\(998\) | −9.85487 | −0.311950 | ||||||||
\(999\) | −19.3908 | + | 40.8699i | −0.613498 | + | 1.29307i |
(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 | 1089.2.e.p.364.11 | 36 | ||
9.4 | even | 3 | 9801.2.a.cm.1.8 | 18 | |||
9.5 | odd | 6 | 9801.2.a.cp.1.11 | 18 | |||
9.7 | even | 3 | inner | 1089.2.e.p.727.11 | 36 | ||
11.5 | even | 5 | 99.2.m.b.58.4 | yes | 72 | ||
11.9 | even | 5 | 99.2.m.b.4.6 | ✓ | 72 | ||
11.10 | odd | 2 | 1089.2.e.o.364.8 | 36 | |||
33.5 | odd | 10 | 297.2.n.b.91.6 | 72 | |||
33.20 | odd | 10 | 297.2.n.b.37.4 | 72 | |||
99.5 | odd | 30 | 891.2.f.e.487.4 | 36 | |||
99.16 | even | 15 | 99.2.m.b.25.6 | yes | 72 | ||
99.20 | odd | 30 | 297.2.n.b.235.6 | 72 | |||
99.31 | even | 15 | 891.2.f.f.730.6 | 36 | |||
99.32 | even | 6 | 9801.2.a.cn.1.8 | 18 | |||
99.38 | odd | 30 | 297.2.n.b.289.4 | 72 | |||
99.43 | odd | 6 | 1089.2.e.o.727.8 | 36 | |||
99.49 | even | 15 | 891.2.f.f.487.6 | 36 | |||
99.76 | odd | 6 | 9801.2.a.co.1.11 | 18 | |||
99.86 | odd | 30 | 891.2.f.e.730.4 | 36 | |||
99.97 | even | 15 | 99.2.m.b.70.4 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.4.6 | ✓ | 72 | 11.9 | even | 5 | ||
99.2.m.b.25.6 | yes | 72 | 99.16 | even | 15 | ||
99.2.m.b.58.4 | yes | 72 | 11.5 | even | 5 | ||
99.2.m.b.70.4 | yes | 72 | 99.97 | even | 15 | ||
297.2.n.b.37.4 | 72 | 33.20 | odd | 10 | |||
297.2.n.b.91.6 | 72 | 33.5 | odd | 10 | |||
297.2.n.b.235.6 | 72 | 99.20 | odd | 30 | |||
297.2.n.b.289.4 | 72 | 99.38 | odd | 30 | |||
891.2.f.e.487.4 | 36 | 99.5 | odd | 30 | |||
891.2.f.e.730.4 | 36 | 99.86 | odd | 30 | |||
891.2.f.f.487.6 | 36 | 99.49 | even | 15 | |||
891.2.f.f.730.6 | 36 | 99.31 | even | 15 | |||
1089.2.e.o.364.8 | 36 | 11.10 | odd | 2 | |||
1089.2.e.o.727.8 | 36 | 99.43 | odd | 6 | |||
1089.2.e.p.364.11 | 36 | 1.1 | even | 1 | trivial | ||
1089.2.e.p.727.11 | 36 | 9.7 | even | 3 | inner | ||
9801.2.a.cm.1.8 | 18 | 9.4 | even | 3 | |||
9801.2.a.cn.1.8 | 18 | 99.32 | even | 6 | |||
9801.2.a.co.1.11 | 18 | 99.76 | odd | 6 | |||
9801.2.a.cp.1.11 | 18 | 9.5 | odd | 6 |