Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(376,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.376");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.bt (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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(54\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 376.2 | ||
Character | \(\chi\) | \(=\) | 585.376 |
Dual form | 585.2.bt.b.571.2 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36351 | − | 1.36457i | −1.67126 | − | 0.964900i | −0.966937 | − | 0.255017i | \(-0.917919\pi\) |
−0.704320 | − | 0.709883i | \(-0.748748\pi\) | |||||||
\(3\) | 1.68089 | + | 0.417855i | 0.970463 | + | 0.241248i | ||||
\(4\) | 2.72413 | + | 4.71833i | 1.36206 | + | 2.35917i | ||||
\(5\) | −0.866025 | + | 0.500000i | −0.387298 | + | 0.223607i | ||||
\(6\) | −3.40262 | − | 3.28131i | −1.38911 | − | 1.33959i | ||||
\(7\) | 3.99906 | + | 2.30886i | 1.51150 | + | 0.872667i | 0.999910 | + | 0.0134398i | \(0.00427816\pi\) |
0.511594 | + | 0.859227i | \(0.329055\pi\) | |||||||
\(8\) | − | 9.41082i | − | 3.32723i | ||||||
\(9\) | 2.65080 | + | 1.40474i | 0.883598 | + | 0.468246i | ||||
\(10\) | 2.72915 | 0.863033 | ||||||||
\(11\) | 3.27016 | + | 1.88803i | 0.985992 | + | 0.569263i | 0.904074 | − | 0.427377i | \(-0.140562\pi\) |
0.0819179 | + | 0.996639i | \(0.473895\pi\) | |||||||
\(12\) | 2.60739 | + | 9.06929i | 0.752689 | + | 2.61808i | ||||
\(13\) | −3.58605 | − | 0.374474i | −0.994592 | − | 0.103860i | ||||
\(14\) | −6.30123 | − | 10.9140i | −1.68407 | − | 2.91690i | ||||
\(15\) | −1.66462 | + | 0.478573i | −0.429804 | + | 0.123567i | ||||
\(16\) | −7.39350 | + | 12.8059i | −1.84838 | + | 3.20148i | ||||
\(17\) | 0.475463 | 0.115317 | 0.0576584 | − | 0.998336i | \(-0.481637\pi\) | ||||
0.0576584 | + | 0.998336i | \(0.481637\pi\) | |||||||
\(18\) | −4.34832 | − | 6.93732i | −1.02491 | − | 1.63514i | ||||
\(19\) | 0.112571i | 0.0258256i | 0.999917 | + | 0.0129128i | \(0.00411039\pi\) | ||||
−0.999917 | + | 0.0129128i | \(0.995890\pi\) | |||||||
\(20\) | −4.71833 | − | 2.72413i | −1.05505 | − | 0.609134i | ||||
\(21\) | 5.75722 | + | 5.55197i | 1.25633 | + | 1.21154i | ||||
\(22\) | −5.15272 | − | 8.92477i | −1.09856 | − | 1.90277i | ||||
\(23\) | −1.58104 | − | 2.73845i | −0.329670 | − | 0.571006i | 0.652776 | − | 0.757551i | \(-0.273604\pi\) |
−0.982446 | + | 0.186545i | \(0.940271\pi\) | |||||||
\(24\) | 3.93235 | − | 15.8186i | 0.802688 | − | 3.22895i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 7.96468 | + | 5.77851i | 1.56200 | + | 1.13326i | ||||
\(27\) | 3.86872 | + | 3.46886i | 0.744536 | + | 0.667582i | ||||
\(28\) | 25.1585i | 4.75452i | ||||||||
\(29\) | −3.16117 | + | 5.47531i | −0.587014 | + | 1.01674i | 0.407607 | + | 0.913158i | \(0.366363\pi\) |
−0.994621 | + | 0.103581i | \(0.966970\pi\) | |||||||
\(30\) | 4.58741 | + | 1.14039i | 0.837542 | + | 0.208205i | ||||
\(31\) | −1.42093 | + | 0.820373i | −0.255206 | + | 0.147343i | −0.622146 | − | 0.782901i | \(-0.713739\pi\) |
0.366940 | + | 0.930245i | \(0.380406\pi\) | |||||||
\(32\) | 18.6493 | − | 10.7672i | 3.29676 | − | 1.90338i | ||||
\(33\) | 4.70787 | + | 4.54003i | 0.819535 | + | 0.790317i | ||||
\(34\) | −1.12376 | − | 0.648805i | −0.192724 | − | 0.111269i | ||||
\(35\) | −4.61772 | −0.780537 | ||||||||
\(36\) | 0.593096 | + | 16.3340i | 0.0988493 | + | 2.72234i | ||||
\(37\) | − | 5.54346i | − | 0.911339i | −0.890149 | − | 0.455669i | \(-0.849400\pi\) | ||
0.890149 | − | 0.455669i | \(-0.150600\pi\) | |||||||
\(38\) | 0.153612 | − | 0.266064i | 0.0249192 | − | 0.0431612i | ||||
\(39\) | −5.87129 | − | 2.12790i | −0.940159 | − | 0.340736i | ||||
\(40\) | 4.70541 | + | 8.15001i | 0.743990 | + | 1.28863i | ||||
\(41\) | −10.4728 | + | 6.04647i | −1.63558 | + | 0.944301i | −0.653246 | + | 0.757146i | \(0.726593\pi\) |
−0.982330 | + | 0.187155i | \(0.940073\pi\) | |||||||
\(42\) | −6.03120 | − | 20.9783i | −0.930634 | − | 3.23703i | ||||
\(43\) | 1.34138 | − | 2.32333i | 0.204558 | − | 0.354305i | −0.745434 | − | 0.666580i | \(-0.767758\pi\) |
0.949992 | + | 0.312275i | \(0.101091\pi\) | |||||||
\(44\) | 20.5730i | 3.10149i | ||||||||
\(45\) | −2.99802 | + | 0.108860i | −0.446919 | + | 0.0162278i | ||||
\(46\) | 8.62981i | 1.27240i | ||||||||
\(47\) | 5.28707 | + | 3.05249i | 0.771198 | + | 0.445252i | 0.833302 | − | 0.552818i | \(-0.186448\pi\) |
−0.0621036 | + | 0.998070i | \(0.519781\pi\) | |||||||
\(48\) | −17.7787 | + | 18.4360i | −2.56613 | + | 2.66100i | ||||
\(49\) | 7.16167 | + | 12.4044i | 1.02310 | + | 1.77205i | ||||
\(50\) | −2.36351 | + | 1.36457i | −0.334251 | + | 0.192980i | ||||
\(51\) | 0.799202 | + | 0.198674i | 0.111911 | + | 0.0278200i | ||||
\(52\) | −8.00198 | − | 17.9403i | −1.10967 | − | 2.48787i | ||||
\(53\) | −2.21477 | −0.304222 | −0.152111 | − | 0.988363i | \(-0.548607\pi\) | ||||
−0.152111 | + | 0.988363i | \(0.548607\pi\) | |||||||
\(54\) | −4.41026 | − | 13.4779i | −0.600161 | − | 1.83410i | ||||
\(55\) | −3.77606 | −0.509164 | ||||||||
\(56\) | 21.7283 | − | 37.6344i | 2.90356 | − | 5.02911i | ||||
\(57\) | −0.0470384 | + | 0.189220i | −0.00623039 | + | 0.0250628i | ||||
\(58\) | 14.9429 | − | 8.62731i | 1.96210 | − | 1.13282i | ||||
\(59\) | 7.78385 | − | 4.49401i | 1.01337 | − | 0.585070i | 0.101194 | − | 0.994867i | \(-0.467734\pi\) |
0.912177 | + | 0.409796i | \(0.134400\pi\) | |||||||
\(60\) | −6.79271 | − | 6.55054i | −0.876936 | − | 0.845672i | ||||
\(61\) | 0.717381 | − | 1.24254i | 0.0918513 | − | 0.159091i | −0.816439 | − | 0.577432i | \(-0.804055\pi\) |
0.908290 | + | 0.418341i | \(0.137388\pi\) | |||||||
\(62\) | 4.47784 | 0.568686 | ||||||||
\(63\) | 7.35736 | + | 11.7379i | 0.926940 | + | 1.47884i | ||||
\(64\) | −29.1964 | −3.64955 | ||||||||
\(65\) | 3.29285 | − | 1.46872i | 0.408428 | − | 0.182173i | ||||
\(66\) | −4.93191 | − | 17.1547i | −0.607076 | − | 2.11159i | ||||
\(67\) | 10.8645 | − | 6.27264i | 1.32731 | − | 0.766325i | 0.342431 | − | 0.939543i | \(-0.388750\pi\) |
0.984884 | + | 0.173217i | \(0.0554164\pi\) | |||||||
\(68\) | 1.29522 | + | 2.24339i | 0.157069 | + | 0.272051i | ||||
\(69\) | −1.51329 | − | 5.26368i | −0.182179 | − | 0.633673i | ||||
\(70\) | 10.9140 | + | 6.30123i | 1.30448 | + | 0.753140i | ||||
\(71\) | − | 9.75529i | − | 1.15774i | −0.815420 | − | 0.578870i | \(-0.803494\pi\) | ||
0.815420 | − | 0.578870i | \(-0.196506\pi\) | |||||||
\(72\) | 13.2197 | − | 24.9461i | 1.55796 | − | 2.93993i | ||||
\(73\) | 1.60702i | 0.188087i | 0.995568 | + | 0.0940435i | \(0.0299793\pi\) | ||||
−0.995568 | + | 0.0940435i | \(0.970021\pi\) | |||||||
\(74\) | −7.56446 | + | 13.1020i | −0.879351 | + | 1.52308i | ||||
\(75\) | 1.20232 | − | 1.24677i | 0.138832 | − | 0.143964i | ||||
\(76\) | −0.531149 | + | 0.306659i | −0.0609269 | + | 0.0351762i | ||||
\(77\) | 8.71840 | + | 15.1007i | 0.993553 | + | 1.72088i | ||||
\(78\) | 10.9732 | + | 13.0411i | 1.24247 | + | 1.47662i | ||||
\(79\) | 2.25865 | − | 3.91210i | 0.254118 | − | 0.440146i | −0.710537 | − | 0.703660i | \(-0.751548\pi\) |
0.964656 | + | 0.263514i | \(0.0848814\pi\) | |||||||
\(80\) | − | 14.7870i | − | 1.65324i | ||||||
\(81\) | 5.05343 | + | 7.44734i | 0.561492 | + | 0.827482i | ||||
\(82\) | 33.0035 | 3.64462 | ||||||||
\(83\) | −1.12664 | − | 0.650468i | −0.123665 | − | 0.0713981i | 0.436891 | − | 0.899514i | \(-0.356079\pi\) |
−0.560557 | + | 0.828116i | \(0.689413\pi\) | |||||||
\(84\) | −10.5126 | + | 42.2888i | −1.14702 | + | 4.61408i | ||||
\(85\) | −0.411763 | + | 0.237732i | −0.0446620 | + | 0.0257856i | ||||
\(86\) | −6.34072 | + | 3.66082i | −0.683738 | + | 0.394756i | ||||
\(87\) | −7.60147 | + | 7.88249i | −0.814963 | + | 0.845091i | ||||
\(88\) | 17.7679 | − | 30.7749i | 1.89406 | − | 3.28062i | ||||
\(89\) | − | 7.82871i | − | 0.829842i | −0.909857 | − | 0.414921i | \(-0.863809\pi\) | ||
0.909857 | − | 0.414921i | \(-0.136191\pi\) | |||||||
\(90\) | 7.23442 | + | 3.83374i | 0.762575 | + | 0.404111i | ||||
\(91\) | −13.4762 | − | 9.77724i | −1.41269 | − | 1.02493i | ||||
\(92\) | 8.61393 | − | 14.9198i | 0.898065 | − | 1.55549i | ||||
\(93\) | −2.73122 | + | 0.785217i | −0.283215 | + | 0.0814232i | ||||
\(94\) | −8.33071 | − | 14.4292i | −0.859247 | − | 1.48826i | ||||
\(95\) | −0.0562856 | − | 0.0974896i | −0.00577479 | − | 0.0100022i | ||||
\(96\) | 35.8465 | − | 10.3058i | 3.65857 | − | 1.05183i | ||||
\(97\) | −4.83079 | − | 2.78906i | −0.490492 | − | 0.283186i | 0.234286 | − | 0.972168i | \(-0.424725\pi\) |
−0.724779 | + | 0.688982i | \(0.758058\pi\) | |||||||
\(98\) | − | 39.0905i | − | 3.94874i | ||||||
\(99\) | 6.01635 | + | 9.59850i | 0.604666 | + | 0.964686i | ||||
\(100\) | 5.44826 | 0.544826 | ||||||||
\(101\) | −4.18649 | + | 7.25121i | −0.416571 | + | 0.721523i | −0.995592 | − | 0.0937903i | \(-0.970102\pi\) |
0.579021 | + | 0.815313i | \(0.303435\pi\) | |||||||
\(102\) | −1.61782 | − | 1.56014i | −0.160188 | − | 0.154477i | ||||
\(103\) | −6.26887 | − | 10.8580i | −0.617690 | − | 1.06987i | −0.989906 | − | 0.141724i | \(-0.954735\pi\) |
0.372217 | − | 0.928146i | \(-0.378598\pi\) | |||||||
\(104\) | −3.52411 | + | 33.7477i | −0.345567 | + | 3.30923i | ||||
\(105\) | −7.76189 | − | 1.92954i | −0.757483 | − | 0.188303i | ||||
\(106\) | 5.23464 | + | 3.02222i | 0.508433 | + | 0.293544i | ||||
\(107\) | 17.4030 | 1.68241 | 0.841206 | − | 0.540715i | \(-0.181846\pi\) | ||||
0.841206 | + | 0.540715i | \(0.181846\pi\) | |||||||
\(108\) | −5.82831 | + | 27.7035i | −0.560830 | + | 2.66577i | ||||
\(109\) | 14.5696i | 1.39551i | 0.716335 | + | 0.697757i | \(0.245818\pi\) | ||||
−0.716335 | + | 0.697757i | \(0.754182\pi\) | |||||||
\(110\) | 8.92477 | + | 5.15272i | 0.850943 | + | 0.491292i | ||||
\(111\) | 2.31636 | − | 9.31795i | 0.219859 | − | 0.884421i | ||||
\(112\) | −59.1342 | + | 34.1411i | −5.58765 | + | 3.22603i | ||||
\(113\) | −0.225447 | − | 0.390485i | −0.0212082 | − | 0.0367338i | 0.855226 | − | 0.518254i | \(-0.173418\pi\) |
−0.876435 | + | 0.481521i | \(0.840085\pi\) | |||||||
\(114\) | 0.369381 | − | 0.383037i | 0.0345957 | − | 0.0358747i | ||||
\(115\) | 2.73845 | + | 1.58104i | 0.255362 | + | 0.147433i | ||||
\(116\) | −34.4457 | −3.19821 | ||||||||
\(117\) | −8.97985 | − | 6.03011i | −0.830188 | − | 0.557484i | ||||
\(118\) | −24.5297 | −2.25814 | ||||||||
\(119\) | 1.90141 | + | 1.09778i | 0.174302 | + | 0.100633i | ||||
\(120\) | 4.50376 | + | 15.6655i | 0.411136 | + | 1.43005i | ||||
\(121\) | 1.62932 | + | 2.82206i | 0.148120 | + | 0.256551i | ||||
\(122\) | −3.39108 | + | 1.95784i | −0.307014 | + | 0.177255i | ||||
\(123\) | −20.1302 | + | 5.78736i | −1.81508 | + | 0.521829i | ||||
\(124\) | −7.74158 | − | 4.46960i | −0.695215 | − | 0.401382i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −1.37190 | − | 37.7825i | −0.122219 | − | 3.36593i | ||||
\(127\) | −1.43741 | −0.127549 | −0.0637747 | − | 0.997964i | \(-0.520314\pi\) | ||||
−0.0637747 | + | 0.997964i | \(0.520314\pi\) | |||||||
\(128\) | 31.7075 | + | 18.3063i | 2.80258 | + | 1.61807i | ||||
\(129\) | 3.22552 | − | 3.34477i | 0.283992 | − | 0.294491i | ||||
\(130\) | −9.78687 | − | 1.02200i | −0.858366 | − | 0.0896349i | ||||
\(131\) | 6.21464 | + | 10.7641i | 0.542976 | + | 0.940461i | 0.998731 | + | 0.0503564i | \(0.0160357\pi\) |
−0.455756 | + | 0.890105i | \(0.650631\pi\) | |||||||
\(132\) | −8.59650 | + | 34.5809i | −0.748230 | + | 3.00988i | ||||
\(133\) | −0.259911 | + | 0.450180i | −0.0225372 | + | 0.0390355i | ||||
\(134\) | −34.2380 | −2.95771 | ||||||||
\(135\) | −5.08484 | − | 1.06976i | −0.437634 | − | 0.0920700i | ||||
\(136\) | − | 4.47450i | − | 0.383685i | ||||||
\(137\) | −2.55126 | − | 1.47297i | −0.217969 | − | 0.125844i | 0.387041 | − | 0.922063i | \(-0.373497\pi\) |
−0.605009 | + | 0.796218i | \(0.706831\pi\) | |||||||
\(138\) | −3.60601 | + | 14.5058i | −0.306964 | + | 1.23481i | ||||
\(139\) | 0.180328 | + | 0.312337i | 0.0152952 | + | 0.0264921i | 0.873572 | − | 0.486695i | \(-0.161798\pi\) |
−0.858276 | + | 0.513188i | \(0.828465\pi\) | |||||||
\(140\) | −12.5793 | − | 21.7879i | −1.06314 | − | 1.84142i | ||||
\(141\) | 7.61149 | + | 7.34013i | 0.641003 | + | 0.618151i | ||||
\(142\) | −13.3118 | + | 23.0568i | −1.11710 | + | 1.93488i | ||||
\(143\) | −11.0200 | − | 7.99517i | −0.921535 | − | 0.668589i | ||||
\(144\) | −37.5876 | + | 23.5600i | −3.13230 | + | 1.96333i | ||||
\(145\) | − | 6.32234i | − | 0.525042i | ||||||
\(146\) | 2.19289 | − | 3.79820i | 0.181485 | − | 0.314342i | ||||
\(147\) | 6.85477 | + | 23.8430i | 0.565372 | + | 1.96653i | ||||
\(148\) | 26.1559 | − | 15.1011i | 2.15000 | − | 1.24130i | ||||
\(149\) | 3.04895 | − | 1.76031i | 0.249780 | − | 0.144210i | −0.369884 | − | 0.929078i | \(-0.620602\pi\) |
0.619663 | + | 0.784868i | \(0.287269\pi\) | |||||||
\(150\) | −4.54300 | + | 1.30610i | −0.370935 | + | 0.106642i | ||||
\(151\) | 8.56013 | + | 4.94220i | 0.696614 | + | 0.402190i | 0.806085 | − | 0.591800i | \(-0.201582\pi\) |
−0.109471 | + | 0.993990i | \(0.534916\pi\) | |||||||
\(152\) | 1.05939 | 0.0859277 | ||||||||
\(153\) | 1.26036 | + | 0.667901i | 0.101894 | + | 0.0539966i | ||||
\(154\) | − | 47.5876i | − | 3.83472i | ||||||
\(155\) | 0.820373 | − | 1.42093i | 0.0658939 | − | 0.114132i | ||||
\(156\) | −5.95403 | − | 33.4994i | −0.476704 | − | 2.68210i | ||||
\(157\) | −6.57684 | − | 11.3914i | −0.524889 | − | 0.909134i | −0.999580 | − | 0.0289814i | \(-0.990774\pi\) |
0.474691 | − | 0.880152i | \(-0.342560\pi\) | |||||||
\(158\) | −10.6767 | + | 6.16420i | −0.849394 | + | 0.490398i | ||||
\(159\) | −3.72279 | − | 0.925453i | −0.295237 | − | 0.0733932i | ||||
\(160\) | −10.7672 | + | 18.6493i | −0.851219 | + | 1.47435i | ||||
\(161\) | − | 14.6016i | − | 1.15077i | ||||||
\(162\) | −1.78139 | − | 24.4977i | −0.139959 | − | 1.92472i | ||||
\(163\) | 10.6298i | 0.832590i | 0.909230 | + | 0.416295i | \(0.136672\pi\) | ||||
−0.909230 | + | 0.416295i | \(0.863328\pi\) | |||||||
\(164\) | −57.0585 | − | 32.9428i | −4.45552 | − | 2.57240i | ||||
\(165\) | −6.34715 | − | 1.57784i | −0.494125 | − | 0.122835i | ||||
\(166\) | 1.77522 | + | 3.07478i | 0.137784 | + | 0.238649i | ||||
\(167\) | −15.8516 | + | 9.15192i | −1.22663 | + | 0.708197i | −0.966324 | − | 0.257329i | \(-0.917158\pi\) |
−0.260309 | + | 0.965525i | \(0.583824\pi\) | |||||||
\(168\) | 52.2486 | − | 54.1802i | 4.03107 | − | 4.18009i | ||||
\(169\) | 12.7195 | + | 2.68577i | 0.978426 | + | 0.206597i | ||||
\(170\) | 1.29761 | 0.0995222 | ||||||||
\(171\) | −0.158133 | + | 0.298403i | −0.0120927 | + | 0.0228195i | ||||
\(172\) | 14.6163 | 1.11449 | ||||||||
\(173\) | 1.03253 | − | 1.78839i | 0.0785018 | − | 0.135969i | −0.824102 | − | 0.566442i | \(-0.808320\pi\) |
0.902604 | + | 0.430472i | \(0.141653\pi\) | |||||||
\(174\) | 28.7224 | − | 8.25759i | 2.17744 | − | 0.626007i | ||||
\(175\) | 3.99906 | − | 2.30886i | 0.302301 | − | 0.174533i | ||||
\(176\) | −48.3559 | + | 27.9183i | −3.64497 | + | 2.10442i | ||||
\(177\) | 14.9617 | − | 4.30143i | 1.12459 | − | 0.323315i | ||||
\(178\) | −10.6829 | + | 18.5033i | −0.800715 | + | 1.38688i | ||||
\(179\) | 12.1238 | 0.906172 | 0.453086 | − | 0.891467i | \(-0.350323\pi\) | ||||
0.453086 | + | 0.891467i | \(0.350323\pi\) | |||||||
\(180\) | −8.68064 | − | 13.8491i | −0.647017 | − | 1.03225i | ||||
\(181\) | −3.34386 | −0.248547 | −0.124274 | − | 0.992248i | \(-0.539660\pi\) | ||||
−0.124274 | + | 0.992248i | \(0.539660\pi\) | |||||||
\(182\) | 18.5095 | + | 41.4980i | 1.37202 | + | 3.07603i | ||||
\(183\) | 1.72504 | − | 1.78882i | 0.127519 | − | 0.132233i | ||||
\(184\) | −25.7710 | + | 14.8789i | −1.89987 | + | 1.09689i | ||||
\(185\) | 2.77173 | + | 4.80077i | 0.203782 | + | 0.352960i | ||||
\(186\) | 7.52677 | + | 1.87109i | 0.551889 | + | 0.137195i | ||||
\(187\) | 1.55484 | + | 0.897689i | 0.113701 | + | 0.0656455i | ||||
\(188\) | 33.2615i | 2.42585i | ||||||||
\(189\) | 7.46216 | + | 22.8045i | 0.542793 | + | 1.65879i | ||||
\(190\) | 0.307224i | 0.0222884i | ||||||||
\(191\) | 4.16937 | − | 7.22157i | 0.301685 | − | 0.522534i | −0.674833 | − | 0.737971i | \(-0.735784\pi\) |
0.976518 | + | 0.215437i | \(0.0691175\pi\) | |||||||
\(192\) | −49.0760 | − | 12.1999i | −3.54175 | − | 0.880448i | ||||
\(193\) | −8.66903 | + | 5.00507i | −0.624011 | + | 0.360273i | −0.778429 | − | 0.627733i | \(-0.783983\pi\) |
0.154418 | + | 0.988006i | \(0.450650\pi\) | |||||||
\(194\) | 7.61175 | + | 13.1839i | 0.546492 | + | 0.946552i | ||||
\(195\) | 6.14864 | − | 1.09283i | 0.440313 | − | 0.0782592i | ||||
\(196\) | −39.0186 | + | 67.5823i | −2.78705 | + | 4.82730i | ||||
\(197\) | − | 12.3180i | − | 0.877622i | −0.898579 | − | 0.438811i | \(-0.855400\pi\) | ||
0.898579 | − | 0.438811i | \(-0.144600\pi\) | |||||||
\(198\) | −1.12185 | − | 30.8959i | −0.0797262 | − | 2.19568i | ||||
\(199\) | −1.32463 | −0.0939008 | −0.0469504 | − | 0.998897i | \(-0.514950\pi\) | ||||
−0.0469504 | + | 0.998897i | \(0.514950\pi\) | |||||||
\(200\) | −8.15001 | − | 4.70541i | −0.576292 | − | 0.332723i | ||||
\(201\) | 20.8832 | − | 6.00384i | 1.47299 | − | 0.423478i | ||||
\(202\) | 19.7896 | − | 11.4256i | 1.39239 | − | 0.803899i | ||||
\(203\) | −25.2834 | + | 14.5974i | −1.77455 | + | 1.02454i | ||||
\(204\) | 1.23972 | + | 4.31212i | 0.0867976 | + | 0.301908i | ||||
\(205\) | 6.04647 | − | 10.4728i | 0.422304 | − | 0.731452i | ||||
\(206\) | 34.2173i | 2.38404i | ||||||||
\(207\) | −0.344224 | − | 9.48001i | −0.0239252 | − | 0.658906i | ||||
\(208\) | 31.3090 | − | 43.1540i | 2.17089 | − | 2.99219i | ||||
\(209\) | −0.212538 | + | 0.368127i | −0.0147016 | + | 0.0254638i | ||||
\(210\) | 15.7123 | + | 15.1522i | 1.08425 | + | 1.04560i | ||||
\(211\) | −3.88208 | − | 6.72396i | −0.267253 | − | 0.462896i | 0.700898 | − | 0.713261i | \(-0.252783\pi\) |
−0.968152 | + | 0.250365i | \(0.919449\pi\) | |||||||
\(212\) | −6.03333 | − | 10.4500i | −0.414370 | − | 0.717711i | ||||
\(213\) | 4.07629 | − | 16.3976i | 0.279303 | − | 1.12354i | ||||
\(214\) | −41.1322 | − | 23.7477i | −2.81174 | − | 1.62336i | ||||
\(215\) | 2.68275i | 0.182962i | ||||||||
\(216\) | 32.6448 | − | 36.4079i | 2.22120 | − | 2.47724i | ||||
\(217\) | −7.57651 | −0.514327 | ||||||||
\(218\) | 19.8813 | − | 34.4354i | 1.34653 | − | 2.33226i | ||||
\(219\) | −0.671499 | + | 2.70122i | −0.0453757 | + | 0.182532i | ||||
\(220\) | −10.2865 | − | 17.8167i | −0.693514 | − | 1.20120i | ||||
\(221\) | −1.70504 | − | 0.178049i | −0.114693 | − | 0.0119768i | ||||
\(222\) | −18.1898 | + | 18.8623i | −1.22082 | + | 1.26595i | ||||
\(223\) | −12.9585 | − | 7.48161i | −0.867767 | − | 0.501006i | −0.00116171 | − | 0.999999i | \(-0.500370\pi\) |
−0.866606 | + | 0.498994i | \(0.833703\pi\) | |||||||
\(224\) | 99.4395 | 6.64408 | ||||||||
\(225\) | 2.54194 | − | 1.59329i | 0.169462 | − | 0.106219i | ||||
\(226\) | 1.23056i | 0.0818554i | ||||||||
\(227\) | −3.81516 | − | 2.20268i | −0.253221 | − | 0.146197i | 0.368017 | − | 0.929819i | \(-0.380037\pi\) |
−0.621238 | + | 0.783622i | \(0.713370\pi\) | |||||||
\(228\) | −1.02094 | + | 0.293517i | −0.0676135 | + | 0.0194387i | ||||
\(229\) | 18.5963 | − | 10.7366i | 1.22888 | − | 0.709494i | 0.262084 | − | 0.965045i | \(-0.415590\pi\) |
0.966796 | + | 0.255551i | \(0.0822569\pi\) | |||||||
\(230\) | −4.31490 | − | 7.47363i | −0.284516 | − | 0.492797i | ||||
\(231\) | 8.34478 | + | 29.0257i | 0.549046 | + | 1.90975i | ||||
\(232\) | 51.5271 | + | 29.7492i | 3.38292 | + | 1.95313i | ||||
\(233\) | −24.1867 | −1.58453 | −0.792263 | − | 0.610180i | \(-0.791097\pi\) | ||||
−0.792263 | + | 0.610180i | \(0.791097\pi\) | |||||||
\(234\) | 12.9955 | + | 26.5059i | 0.849540 | + | 1.73275i | ||||
\(235\) | −6.10498 | −0.398245 | ||||||||
\(236\) | 42.4084 | + | 24.4845i | 2.76055 | + | 1.59381i | ||||
\(237\) | 5.43124 | − | 5.63203i | 0.352797 | − | 0.365840i | ||||
\(238\) | −2.99600 | − | 5.18923i | −0.194202 | − | 0.336367i | ||||
\(239\) | 5.83846 | − | 3.37084i | 0.377658 | − | 0.218041i | −0.299141 | − | 0.954209i | \(-0.596700\pi\) |
0.676799 | + | 0.736168i | \(0.263367\pi\) | |||||||
\(240\) | 6.17882 | − | 24.8554i | 0.398841 | − | 1.60441i | ||||
\(241\) | −7.59632 | − | 4.38574i | −0.489322 | − | 0.282510i | 0.234971 | − | 0.972002i | \(-0.424500\pi\) |
−0.724293 | + | 0.689492i | \(0.757834\pi\) | |||||||
\(242\) | − | 8.89329i | − | 0.571683i | ||||||
\(243\) | 5.38236 | + | 14.6298i | 0.345279 | + | 0.938500i | ||||
\(244\) | 7.81696 | 0.500430 | ||||||||
\(245\) | −12.4044 | − | 7.16167i | −0.792487 | − | 0.457542i | ||||
\(246\) | 55.4753 | + | 13.7907i | 3.53697 | + | 0.879260i | ||||
\(247\) | 0.0421550 | − | 0.403686i | 0.00268226 | − | 0.0256860i | ||||
\(248\) | 7.72038 | + | 13.3721i | 0.490245 | + | 0.849128i | ||||
\(249\) | −1.62196 | − | 1.56414i | −0.102788 | − | 0.0991233i | ||||
\(250\) | 1.36457 | − | 2.36351i | 0.0863033 | − | 0.149482i | ||||
\(251\) | −2.22703 | −0.140569 | −0.0702845 | − | 0.997527i | \(-0.522391\pi\) | ||||
−0.0702845 | + | 0.997527i | \(0.522391\pi\) | |||||||
\(252\) | −35.3411 | + | 66.6901i | −2.22628 | + | 4.20108i | ||||
\(253\) | − | 11.9402i | − | 0.750676i | ||||||
\(254\) | 3.39734 | + | 1.96145i | 0.213168 | + | 0.123072i | ||||
\(255\) | −0.791467 | + | 0.227544i | −0.0495636 | + | 0.0142494i | ||||
\(256\) | −20.7644 | − | 35.9649i | −1.29777 | − | 2.24781i | ||||
\(257\) | 9.65981 | + | 16.7313i | 0.602562 | + | 1.04367i | 0.992432 | + | 0.122798i | \(0.0391869\pi\) |
−0.389869 | + | 0.920870i | \(0.627480\pi\) | |||||||
\(258\) | −12.1878 | + | 3.50394i | −0.758777 | + | 0.218146i | ||||
\(259\) | 12.7991 | − | 22.1686i | 0.795295 | − | 1.37749i | ||||
\(260\) | 15.9001 | + | 11.5358i | 0.986080 | + | 0.715418i | ||||
\(261\) | −16.0710 | + | 10.0733i | −0.994768 | + | 0.623522i | ||||
\(262\) | − | 33.9214i | − | 2.09567i | ||||||
\(263\) | 5.67702 | − | 9.83289i | 0.350060 | − | 0.606322i | −0.636200 | − | 0.771524i | \(-0.719495\pi\) |
0.986260 | + | 0.165203i | \(0.0528279\pi\) | |||||||
\(264\) | 42.7254 | − | 44.3049i | 2.62956 | − | 2.72678i | ||||
\(265\) | 1.91805 | − | 1.10739i | 0.117825 | − | 0.0680262i | ||||
\(266\) | 1.22861 | − | 0.709337i | 0.0753308 | − | 0.0434922i | ||||
\(267\) | 3.27126 | − | 13.1592i | 0.200198 | − | 0.805331i | ||||
\(268\) | 59.1928 | + | 34.1750i | 3.61578 | + | 2.08757i | ||||
\(269\) | 9.62823 | 0.587044 | 0.293522 | − | 0.955952i | \(-0.405173\pi\) | ||||
0.293522 | + | 0.955952i | \(0.405173\pi\) | |||||||
\(270\) | 10.5583 | + | 9.46703i | 0.642559 | + | 0.576145i | ||||
\(271\) | − | 21.0694i | − | 1.27988i | −0.768426 | − | 0.639938i | \(-0.778960\pi\) | ||
0.768426 | − | 0.639938i | \(-0.221040\pi\) | |||||||
\(272\) | −3.51534 | + | 6.08875i | −0.213149 | + | 0.369184i | ||||
\(273\) | −18.5666 | − | 22.0656i | −1.12370 | − | 1.33547i | ||||
\(274\) | 4.01995 | + | 6.96276i | 0.242854 | + | 0.420636i | ||||
\(275\) | 3.27016 | − | 1.88803i | 0.197198 | − | 0.113853i | ||||
\(276\) | 20.7134 | − | 21.4791i | 1.24680 | − | 1.29289i | ||||
\(277\) | 10.6042 | − | 18.3670i | 0.637146 | − | 1.10357i | −0.348911 | − | 0.937156i | \(-0.613448\pi\) |
0.986056 | − | 0.166413i | \(-0.0532183\pi\) | |||||||
\(278\) | − | 0.984284i | − | 0.0590334i | ||||||
\(279\) | −4.91900 | + | 0.178611i | −0.294493 | + | 0.0106932i | ||||
\(280\) | 43.4565i | 2.59702i | ||||||||
\(281\) | −24.1490 | − | 13.9425i | −1.44061 | − | 0.831737i | −0.442721 | − | 0.896660i | \(-0.645987\pi\) |
−0.997890 | + | 0.0649224i | \(0.979320\pi\) | |||||||
\(282\) | −7.97371 | − | 27.7350i | −0.474827 | − | 1.65159i | ||||
\(283\) | 2.59505 | + | 4.49476i | 0.154260 | + | 0.267186i | 0.932789 | − | 0.360422i | \(-0.117367\pi\) |
−0.778529 | + | 0.627608i | \(0.784034\pi\) | |||||||
\(284\) | 46.0287 | − | 26.5747i | 2.73130 | − | 1.57692i | ||||
\(285\) | −0.0538736 | − | 0.187389i | −0.00319120 | − | 0.0110999i | ||||
\(286\) | 15.1358 | + | 33.9342i | 0.895000 | + | 2.00657i | ||||
\(287\) | −55.8418 | −3.29624 | ||||||||
\(288\) | 64.5604 | − | 2.34422i | 3.80426 | − | 0.138135i | ||||
\(289\) | −16.7739 | −0.986702 | ||||||||
\(290\) | −8.62731 | + | 14.9429i | −0.506613 | + | 0.877479i | ||||
\(291\) | −6.95461 | − | 6.70667i | −0.407687 | − | 0.393152i | ||||
\(292\) | −7.58243 | + | 4.37772i | −0.443728 | + | 0.256187i | ||||
\(293\) | 9.03451 | − | 5.21608i | 0.527802 | − | 0.304726i | −0.212319 | − | 0.977200i | \(-0.568102\pi\) |
0.740121 | + | 0.672474i | \(0.234768\pi\) | |||||||
\(294\) | 16.3342 | − | 65.7070i | 0.952628 | − | 3.83211i | ||||
\(295\) | −4.49401 | + | 7.78385i | −0.261651 | + | 0.453193i | ||||
\(296\) | −52.1685 | −3.03223 | ||||||||
\(297\) | 6.10205 | + | 18.6480i | 0.354077 | + | 1.08207i | ||||
\(298\) | −9.60831 | −0.556594 | ||||||||
\(299\) | 4.64423 | + | 10.4123i | 0.268583 | + | 0.602157i | ||||
\(300\) | 9.15793 | + | 2.27658i | 0.528734 | + | 0.131438i | ||||
\(301\) | 10.7285 | − | 6.19410i | 0.618380 | − | 0.357022i | ||||
\(302\) | −13.4880 | − | 23.3619i | −0.776147 | − | 1.34433i | ||||
\(303\) | −10.0670 | + | 10.4392i | −0.578333 | + | 0.599714i | ||||
\(304\) | −1.44158 | − | 0.832296i | −0.0826803 | − | 0.0477355i | ||||
\(305\) | 1.43476i | 0.0821543i | ||||||||
\(306\) | −2.06747 | − | 3.29844i | −0.118189 | − | 0.188559i | ||||
\(307\) | − | 7.43423i | − | 0.424294i | −0.977238 | − | 0.212147i | \(-0.931954\pi\) | ||
0.977238 | − | 0.212147i | \(-0.0680455\pi\) | |||||||
\(308\) | −47.5001 | + | 82.2725i | −2.70657 | + | 4.68791i | ||||
\(309\) | −6.00022 | − | 20.8706i | −0.341341 | − | 1.18729i | ||||
\(310\) | −3.87792 | + | 2.23892i | −0.220251 | + | 0.127162i | ||||
\(311\) | −13.2721 | − | 22.9880i | −0.752594 | − | 1.30353i | −0.946562 | − | 0.322523i | \(-0.895469\pi\) |
0.193968 | − | 0.981008i | \(-0.437864\pi\) | |||||||
\(312\) | −20.0253 | + | 55.2536i | −1.13371 | + | 3.12812i | ||||
\(313\) | 6.89074 | − | 11.9351i | 0.389488 | − | 0.674613i | −0.602893 | − | 0.797822i | \(-0.705985\pi\) |
0.992381 | + | 0.123209i | \(0.0393187\pi\) | |||||||
\(314\) | 35.8983i | 2.02586i | ||||||||
\(315\) | −12.2406 | − | 6.48668i | −0.689681 | − | 0.365483i | ||||
\(316\) | 24.6115 | 1.38450 | ||||||||
\(317\) | −1.99198 | − | 1.15007i | −0.111881 | − | 0.0645945i | 0.443015 | − | 0.896514i | \(-0.353909\pi\) |
−0.554896 | + | 0.831920i | \(0.687242\pi\) | |||||||
\(318\) | 7.53602 | + | 7.26735i | 0.422599 | + | 0.407533i | ||||
\(319\) | −20.6751 | + | 11.9368i | −1.15758 | + | 0.668331i | ||||
\(320\) | 25.2848 | − | 14.5982i | 1.41346 | − | 0.816064i | ||||
\(321\) | 29.2526 | + | 7.27192i | 1.63272 | + | 0.405879i | ||||
\(322\) | −19.9250 | + | 34.5111i | −1.11038 | + | 1.92323i | ||||
\(323\) | 0.0535235i | 0.00297813i | ||||||||
\(324\) | −21.3728 | + | 44.1313i | −1.18738 | + | 2.45174i | ||||
\(325\) | −2.11733 | + | 2.91838i | −0.117448 | + | 0.161882i | ||||
\(326\) | 14.5051 | − | 25.1237i | 0.803366 | − | 1.39147i | ||||
\(327\) | −6.08797 | + | 24.4899i | −0.336665 | + | 1.35429i | ||||
\(328\) | 56.9022 | + | 98.5576i | 3.14190 | + | 5.44193i | ||||
\(329\) | 14.0955 | + | 24.4142i | 0.777113 | + | 1.34600i | ||||
\(330\) | 12.8485 | + | 12.3904i | 0.707286 | + | 0.682070i | ||||
\(331\) | 22.8603 | + | 13.1984i | 1.25652 | + | 0.725451i | 0.972396 | − | 0.233337i | \(-0.0749644\pi\) |
0.284122 | + | 0.958788i | \(0.408298\pi\) | |||||||
\(332\) | − | 7.08783i | − | 0.388995i | ||||||
\(333\) | 7.78710 | − | 14.6946i | 0.426730 | − | 0.805257i | ||||
\(334\) | 49.9539 | 2.73336 | ||||||||
\(335\) | −6.27264 | + | 10.8645i | −0.342711 | + | 0.593593i | ||||
\(336\) | −113.664 | + | 32.6781i | −6.20089 | + | 1.78273i | ||||
\(337\) | −9.07033 | − | 15.7103i | −0.494092 | − | 0.855793i | 0.505885 | − | 0.862601i | \(-0.331166\pi\) |
−0.999977 | + | 0.00680836i | \(0.997833\pi\) | |||||||
\(338\) | −26.3979 | − | 23.7046i | −1.43585 | − | 1.28936i | ||||
\(339\) | −0.215786 | − | 0.750567i | −0.0117199 | − | 0.0407652i | ||||
\(340\) | −2.24339 | − | 1.29522i | −0.121665 | − | 0.0702433i | ||||
\(341\) | −6.19556 | −0.335508 | ||||||||
\(342\) | 0.780943 | − | 0.489496i | 0.0422286 | − | 0.0264689i | ||||
\(343\) | 33.8171i | 1.82595i | ||||||||
\(344\) | −21.8645 | − | 12.6234i | −1.17885 | − | 0.680611i | ||||
\(345\) | 3.94239 | + | 3.80184i | 0.212251 | + | 0.204684i | ||||
\(346\) | −4.88079 | + | 2.81793i | −0.262393 | + | 0.151493i | ||||
\(347\) | 2.39311 | + | 4.14498i | 0.128469 | + | 0.222514i | 0.923084 | − | 0.384600i | \(-0.125660\pi\) |
−0.794615 | + | 0.607114i | \(0.792327\pi\) | |||||||
\(348\) | −57.8996 | − | 14.3933i | −3.10374 | − | 0.771562i | ||||
\(349\) | −16.4569 | − | 9.50141i | −0.880919 | − | 0.508599i | −0.00995766 | − | 0.999950i | \(-0.503170\pi\) |
−0.870961 | + | 0.491352i | \(0.836503\pi\) | |||||||
\(350\) | −12.6025 | −0.673629 | ||||||||
\(351\) | −12.5744 | − | 13.8882i | −0.671174 | − | 0.741299i | ||||
\(352\) | 81.3149 | 4.33410 | ||||||||
\(353\) | 2.38986 | + | 1.37979i | 0.127200 | + | 0.0734387i | 0.562250 | − | 0.826968i | \(-0.309936\pi\) |
−0.435050 | + | 0.900406i | \(0.643269\pi\) | |||||||
\(354\) | −41.2317 | − | 10.2498i | −2.19144 | − | 0.544772i | ||||
\(355\) | 4.87765 | + | 8.44833i | 0.258879 | + | 0.448391i | ||||
\(356\) | 36.9385 | − | 21.3264i | 1.95773 | − | 1.13030i | ||||
\(357\) | 2.73735 | + | 2.63976i | 0.144876 | + | 0.139711i | ||||
\(358\) | −28.6546 | − | 16.5438i | −1.51445 | − | 0.874365i | ||||
\(359\) | − | 10.4831i | − | 0.553279i | −0.960974 | − | 0.276640i | \(-0.910779\pi\) | ||
0.960974 | − | 0.276640i | \(-0.0892208\pi\) | |||||||
\(360\) | 1.02446 | + | 28.2139i | 0.0539937 | + | 1.48700i | ||||
\(361\) | 18.9873 | 0.999333 | ||||||||
\(362\) | 7.90326 | + | 4.56295i | 0.415386 | + | 0.239823i | ||||
\(363\) | 1.55949 | + | 5.42439i | 0.0818522 | + | 0.284707i | ||||
\(364\) | 9.42122 | − | 90.2198i | 0.493806 | − | 4.72880i | ||||
\(365\) | −0.803508 | − | 1.39172i | −0.0420575 | − | 0.0728458i | ||||
\(366\) | −6.51813 | + | 1.87394i | −0.340708 | + | 0.0979525i | ||||
\(367\) | −9.68919 | + | 16.7822i | −0.505771 | + | 0.876022i | 0.494206 | + | 0.869345i | \(0.335459\pi\) |
−0.999978 | + | 0.00667714i | \(0.997875\pi\) | |||||||
\(368\) | 46.7578 | 2.43742 | ||||||||
\(369\) | −36.2549 | + | 1.31643i | −1.88736 | + | 0.0685309i | ||||
\(370\) | − | 15.1289i | − | 0.786515i | ||||||
\(371\) | −8.85701 | − | 5.11360i | −0.459833 | − | 0.265485i | ||||
\(372\) | −11.1451 | − | 10.7478i | −0.577847 | − | 0.557246i | ||||
\(373\) | −14.8231 | − | 25.6744i | −0.767511 | − | 1.32937i | −0.938909 | − | 0.344167i | \(-0.888162\pi\) |
0.171397 | − | 0.985202i | \(-0.445172\pi\) | |||||||
\(374\) | −2.44993 | − | 4.24340i | −0.126683 | − | 0.219421i | ||||
\(375\) | −0.417855 | + | 1.68089i | −0.0215779 | + | 0.0868009i | ||||
\(376\) | 28.7264 | − | 49.7556i | 1.48145 | − | 2.56595i | ||||
\(377\) | 13.3865 | − | 18.4510i | 0.689439 | − | 0.950273i | ||||
\(378\) | 13.4816 | − | 64.0815i | 0.693417 | − | 3.29600i | ||||
\(379\) | − | 22.8221i | − | 1.17229i | −0.810205 | − | 0.586147i | \(-0.800644\pi\) | ||
0.810205 | − | 0.586147i | \(-0.199356\pi\) | |||||||
\(380\) | 0.306659 | − | 0.531149i | 0.0157313 | − | 0.0272473i | ||||
\(381\) | −2.41613 | − | 0.600628i | −0.123782 | − | 0.0307711i | ||||
\(382\) | −19.7087 | + | 11.3788i | −1.00839 | + | 0.582192i | ||||
\(383\) | −2.22332 | + | 1.28363i | −0.113606 | + | 0.0655907i | −0.555726 | − | 0.831365i | \(-0.687560\pi\) |
0.442120 | + | 0.896956i | \(0.354226\pi\) | |||||||
\(384\) | 45.6475 | + | 44.0201i | 2.32944 | + | 2.24639i | ||||
\(385\) | −15.1007 | − | 8.71840i | −0.769603 | − | 0.444331i | ||||
\(386\) | 27.3192 | 1.39051 | ||||||||
\(387\) | 6.81939 | − | 4.27440i | 0.346649 | − | 0.217280i | ||||
\(388\) | − | 30.3910i | − | 1.54287i | ||||||
\(389\) | −4.18812 | + | 7.25404i | −0.212346 | + | 0.367795i | −0.952448 | − | 0.304700i | \(-0.901444\pi\) |
0.740102 | + | 0.672495i | \(0.234777\pi\) | |||||||
\(390\) | −16.0236 | − | 5.80735i | −0.811388 | − | 0.294067i | ||||
\(391\) | −0.751728 | − | 1.30203i | −0.0380165 | − | 0.0658465i | ||||
\(392\) | 116.735 | − | 67.3972i | 5.89602 | − | 3.40407i | ||||
\(393\) | 5.94832 | + | 20.6901i | 0.300053 | + | 1.04368i | ||||
\(394\) | −16.8088 | + | 29.1138i | −0.846817 | + | 1.46673i | ||||
\(395\) | 4.51731i | 0.227290i | ||||||||
\(396\) | −28.8996 | + | 54.5347i | −1.45226 | + | 2.74047i | ||||
\(397\) | 37.9166i | 1.90298i | 0.307679 | + | 0.951490i | \(0.400448\pi\) | ||||
−0.307679 | + | 0.951490i | \(0.599552\pi\) | |||||||
\(398\) | 3.13079 | + | 1.80756i | 0.156932 | + | 0.0906049i | ||||
\(399\) | −0.624993 | + | 0.648098i | −0.0312888 | + | 0.0324455i | ||||
\(400\) | 7.39350 | + | 12.8059i | 0.369675 | + | 0.640296i | ||||
\(401\) | 19.2557 | − | 11.1173i | 0.961585 | − | 0.555172i | 0.0649247 | − | 0.997890i | \(-0.479319\pi\) |
0.896661 | + | 0.442719i | \(0.145986\pi\) | |||||||
\(402\) | −57.5503 | − | 14.3065i | −2.87035 | − | 0.713543i | ||||
\(403\) | 5.40273 | − | 2.40980i | 0.269129 | − | 0.120041i | ||||
\(404\) | −45.6182 | −2.26959 | ||||||||
\(405\) | −8.10007 | − | 3.92287i | −0.402496 | − | 0.194929i | ||||
\(406\) | 79.6770 | 3.95430 | ||||||||
\(407\) | 10.4662 | − | 18.1280i | 0.518791 | − | 0.898572i | ||||
\(408\) | 1.86969 | − | 7.52114i | 0.0925634 | − | 0.372352i | ||||
\(409\) | 18.0842 | − | 10.4409i | 0.894204 | − | 0.516269i | 0.0188889 | − | 0.999822i | \(-0.493987\pi\) |
0.875315 | + | 0.483553i | \(0.160654\pi\) | |||||||
\(410\) | −28.5818 | + | 16.5017i | −1.41156 | + | 0.814962i | ||||
\(411\) | −3.67290 | − | 3.54196i | −0.181171 | − | 0.174712i | ||||
\(412\) | 34.1544 | − | 59.1572i | 1.68267 | − | 2.91446i | ||||
\(413\) | 41.5042 | 2.04229 | ||||||||
\(414\) | −12.1226 | + | 22.8759i | −0.595794 | + | 1.12429i | ||||
\(415\) | 1.30094 | 0.0638604 | ||||||||
\(416\) | −70.9093 | + | 31.6279i | −3.47661 | + | 1.55069i | ||||
\(417\) | 0.172600 | + | 0.600356i | 0.00845227 | + | 0.0293996i | ||||
\(418\) | 1.00467 | − | 0.580048i | 0.0491401 | − | 0.0283711i | ||||
\(419\) | −5.01978 | − | 8.69451i | −0.245232 | − | 0.424754i | 0.716965 | − | 0.697109i | \(-0.245531\pi\) |
−0.962197 | + | 0.272355i | \(0.912197\pi\) | |||||||
\(420\) | −12.0402 | − | 41.8795i | −0.587502 | − | 2.04351i | ||||
\(421\) | −4.67787 | − | 2.70077i | −0.227986 | − | 0.131628i | 0.381657 | − | 0.924304i | \(-0.375354\pi\) |
−0.609642 | + | 0.792677i | \(0.708687\pi\) | |||||||
\(422\) | 21.1896i | 1.03149i | ||||||||
\(423\) | 9.72699 | + | 15.5185i | 0.472942 | + | 0.754534i | ||||
\(424\) | 20.8428i | 1.01222i | ||||||||
\(425\) | 0.237732 | − | 0.411763i | 0.0115317 | − | 0.0199734i | ||||
\(426\) | −32.0101 | + | 33.1935i | −1.55090 | + | 1.60823i | ||||
\(427\) | 5.73771 | − | 3.31267i | 0.277667 | − | 0.160311i | ||||
\(428\) | 47.4080 | + | 82.1131i | 2.29155 | + | 3.96909i | ||||
\(429\) | −15.1825 | − | 18.0438i | −0.733020 | − | 0.871160i | ||||
\(430\) | 3.66082 | − | 6.34072i | 0.176540 | − | 0.305777i | ||||
\(431\) | − | 29.5975i | − | 1.42566i | −0.701335 | − | 0.712831i | \(-0.747412\pi\) | ||
0.701335 | − | 0.712831i | \(-0.252588\pi\) | |||||||
\(432\) | −73.0254 | + | 23.8956i | −3.51343 | + | 1.14968i | ||||
\(433\) | −20.5685 | −0.988458 | −0.494229 | − | 0.869332i | \(-0.664550\pi\) | ||||
−0.494229 | + | 0.869332i | \(0.664550\pi\) | |||||||
\(434\) | 17.9072 | + | 10.3387i | 0.859572 | + | 0.496274i | ||||
\(435\) | 2.64182 | − | 10.6272i | 0.126665 | − | 0.509534i | ||||
\(436\) | −68.7441 | + | 39.6894i | −3.29225 | + | 1.90078i | ||||
\(437\) | 0.308271 | − | 0.177980i | 0.0147466 | − | 0.00851394i | ||||
\(438\) | 5.27311 | − | 5.46806i | 0.251959 | − | 0.261274i | ||||
\(439\) | −17.9052 | + | 31.0128i | −0.854571 | + | 1.48016i | 0.0224719 | + | 0.999747i | \(0.492846\pi\) |
−0.877043 | + | 0.480412i | \(0.840487\pi\) | |||||||
\(440\) | 35.5358i | 1.69410i | ||||||||
\(441\) | 1.55923 | + | 42.9417i | 0.0742493 | + | 2.04484i | ||||
\(442\) | 3.78691 | + | 2.74747i | 0.180125 | + | 0.130684i | ||||
\(443\) | 16.4749 | − | 28.5353i | 0.782745 | − | 1.35575i | −0.147592 | − | 0.989048i | \(-0.547152\pi\) |
0.930337 | − | 0.366706i | \(-0.119515\pi\) | |||||||
\(444\) | 50.2752 | − | 14.4540i | 2.38596 | − | 0.685955i | ||||
\(445\) | 3.91436 | + | 6.77986i | 0.185558 | + | 0.321396i | ||||
\(446\) | 20.4184 | + | 35.3658i | 0.966841 | + | 1.67462i | ||||
\(447\) | 5.86051 | − | 1.68488i | 0.277193 | − | 0.0796919i | ||||
\(448\) | −116.758 | − | 67.4104i | −5.51631 | − | 3.18484i | ||||
\(449\) | − | 6.88768i | − | 0.325050i | −0.986704 | − | 0.162525i | \(-0.948036\pi\) | ||
0.986704 | − | 0.162525i | \(-0.0519638\pi\) | |||||||
\(450\) | −8.18206 | + | 0.297094i | −0.385706 | + | 0.0140052i | ||||
\(451\) | −45.6637 | −2.15022 | ||||||||
\(452\) | 1.22829 | − | 2.12746i | 0.0577740 | − | 0.100068i | ||||
\(453\) | 12.3235 | + | 11.8842i | 0.579010 | + | 0.558368i | ||||
\(454\) | 6.01146 | + | 10.4121i | 0.282132 | + | 0.488666i | ||||
\(455\) | 16.5594 | + | 1.72922i | 0.776316 | + | 0.0810669i | ||||
\(456\) | 1.78072 | + | 0.442670i | 0.0833897 | + | 0.0207299i | ||||
\(457\) | −26.2730 | − | 15.1687i | −1.22900 | − | 0.709562i | −0.262177 | − | 0.965020i | \(-0.584441\pi\) |
−0.966820 | + | 0.255458i | \(0.917774\pi\) | |||||||
\(458\) | −58.6035 | −2.73836 | ||||||||
\(459\) | 1.83944 | + | 1.64931i | 0.0858575 | + | 0.0769834i | ||||
\(460\) | 17.2279i | 0.803253i | ||||||||
\(461\) | 17.8514 | + | 10.3065i | 0.831421 | + | 0.480021i | 0.854339 | − | 0.519716i | \(-0.173962\pi\) |
−0.0229182 | + | 0.999737i | \(0.507296\pi\) | |||||||
\(462\) | 19.8847 | − | 79.9896i | 0.925120 | − | 3.72145i | ||||
\(463\) | −33.8281 | + | 19.5306i | −1.57212 | + | 0.907666i | −0.576215 | + | 0.817298i | \(0.695471\pi\) |
−0.995908 | + | 0.0903681i | \(0.971196\pi\) | |||||||
\(464\) | −46.7442 | − | 80.9634i | −2.17005 | − | 3.75863i | ||||
\(465\) | 1.97270 | − | 2.04563i | 0.0914817 | − | 0.0948638i | ||||
\(466\) | 57.1657 | + | 33.0046i | 2.64815 | + | 1.52891i | ||||
\(467\) | −11.6991 | −0.541368 | −0.270684 | − | 0.962668i | \(-0.587250\pi\) | ||||
−0.270684 | + | 0.962668i | \(0.587250\pi\) | |||||||
\(468\) | 3.98979 | − | 58.7967i | 0.184428 | − | 2.71788i | ||||
\(469\) | 57.9306 | 2.67499 | ||||||||
\(470\) | 14.4292 | + | 8.33071i | 0.665570 | + | 0.384267i | ||||
\(471\) | −6.29499 | − | 21.8959i | −0.290058 | − | 1.00891i | ||||
\(472\) | −42.2923 | − | 73.2524i | −1.94666 | − | 3.37172i | ||||
\(473\) | 8.77304 | − | 5.06512i | 0.403385 | − | 0.232894i | ||||
\(474\) | −20.5221 | + | 5.90005i | −0.942613 | + | 0.270998i | ||||
\(475\) | 0.0974896 | + | 0.0562856i | 0.00447313 | + | 0.00258256i | ||||
\(476\) | 11.9620i | 0.548275i | ||||||||
\(477\) | −5.87091 | − | 3.11117i | −0.268810 | − | 0.142451i | ||||
\(478\) | −18.3990 | −0.841552 | ||||||||
\(479\) | 4.62394 | + | 2.66964i | 0.211273 | + | 0.121979i | 0.601903 | − | 0.798569i | \(-0.294409\pi\) |
−0.390630 | + | 0.920548i | \(0.627743\pi\) | |||||||
\(480\) | −25.8911 | + | 26.8483i | −1.18176 | + | 1.22545i | ||||
\(481\) | −2.07588 | + | 19.8791i | −0.0946520 | + | 0.906410i | ||||
\(482\) | 11.9693 | + | 20.7315i | 0.545188 | + | 0.944293i | ||||
\(483\) | 6.10136 | − | 24.5438i | 0.277621 | − | 1.11678i | ||||
\(484\) | −8.87693 | + | 15.3753i | −0.403497 | + | 0.698877i | ||||
\(485\) | 5.57811 | 0.253289 | ||||||||
\(486\) | 7.24213 | − | 41.9223i | 0.328510 | − | 1.90163i | ||||
\(487\) | 24.5506i | 1.11249i | 0.831017 | + | 0.556247i | \(0.187759\pi\) | ||||
−0.831017 | + | 0.556247i | \(0.812241\pi\) | |||||||
\(488\) | −11.6933 | − | 6.75114i | −0.529332 | − | 0.305610i | ||||
\(489\) | −4.44171 | + | 17.8675i | −0.200861 | + | 0.807998i | ||||
\(490\) | 19.5453 | + | 33.8534i | 0.882965 | + | 1.52934i | ||||
\(491\) | 20.2214 | + | 35.0245i | 0.912580 | + | 1.58063i | 0.810407 | + | 0.585868i | \(0.199246\pi\) |
0.102173 | + | 0.994767i | \(0.467420\pi\) | |||||||
\(492\) | −82.1439 | − | 79.2154i | −3.70333 | − | 3.57130i | ||||
\(493\) | −1.50302 | + | 2.60331i | −0.0676926 | + | 0.117247i | ||||
\(494\) | −0.650494 | + | 0.896595i | −0.0292671 | + | 0.0403397i | ||||
\(495\) | −10.0096 | − | 5.30437i | −0.449896 | − | 0.238414i | ||||
\(496\) | − | 24.2617i | − | 1.08938i | ||||||
\(497\) | 22.5236 | − | 39.0120i | 1.01032 | − | 1.74993i | ||||
\(498\) | 1.69915 | + | 5.91016i | 0.0761407 | + | 0.264840i | ||||
\(499\) | 6.71322 | − | 3.87588i | 0.300525 | − | 0.173508i | −0.342154 | − | 0.939644i | \(-0.611156\pi\) |
0.642679 | + | 0.766136i | \(0.277823\pi\) | |||||||
\(500\) | −4.71833 | + | 2.72413i | −0.211010 | + | 0.121827i | ||||
\(501\) | −30.4690 | + | 8.75972i | −1.36125 | + | 0.391356i | ||||
\(502\) | 5.26362 | + | 3.03895i | 0.234927 | + | 0.135635i | ||||
\(503\) | 35.2135 | 1.57009 | 0.785046 | − | 0.619437i | \(-0.212639\pi\) | ||||
0.785046 | + | 0.619437i | \(0.212639\pi\) | |||||||
\(504\) | 110.464 | − | 69.2387i | 4.92044 | − | 3.08414i | ||||
\(505\) | − | 8.37298i | − | 0.372593i | ||||||
\(506\) | −16.2933 | + | 28.2209i | −0.724327 | + | 1.25457i | ||||
\(507\) | 20.2579 | + | 9.82940i | 0.899685 | + | 0.436539i | ||||
\(508\) | −3.91569 | − | 6.78217i | −0.173731 | − | 0.300910i | ||||
\(509\) | −25.7902 | + | 14.8900i | −1.14313 | + | 0.659986i | −0.947203 | − | 0.320633i | \(-0.896104\pi\) |
−0.195925 | + | 0.980619i | \(0.562771\pi\) | |||||||
\(510\) | 2.18114 | + | 0.542212i | 0.0965826 | + | 0.0240096i | ||||
\(511\) | −3.71038 | + | 6.42656i | −0.164137 | + | 0.284294i | ||||
\(512\) | 40.1127i | 1.77275i | ||||||||
\(513\) | −0.390494 | + | 0.435507i | −0.0172407 | + | 0.0192281i | ||||
\(514\) | − | 52.7261i | − | 2.32565i | ||||||
\(515\) | 10.8580 | + | 6.26887i | 0.478460 | + | 0.276239i | ||||
\(516\) | 24.5685 | + | 6.10750i | 1.08157 | + | 0.268868i | ||||
\(517\) | 11.5264 | + | 19.9643i | 0.506930 | + | 0.878029i | ||||
\(518\) | −60.5015 | + | 34.9306i | −2.65828 | + | 1.53476i | ||||
\(519\) | 2.48286 | − | 2.57465i | 0.108985 | − | 0.113015i | ||||
\(520\) | −13.8219 | − | 30.9884i | −0.606129 | − | 1.35893i | ||||
\(521\) | 37.3604 | 1.63679 | 0.818394 | − | 0.574658i | \(-0.194865\pi\) | ||||
0.818394 | + | 0.574658i | \(0.194865\pi\) | |||||||
\(522\) | 51.7297 | − | 1.87833i | 2.26415 | − | 0.0822124i | ||||
\(523\) | −15.6389 | −0.683843 | −0.341922 | − | 0.939728i | \(-0.611078\pi\) | ||||
−0.341922 | + | 0.939728i | \(0.611078\pi\) | |||||||
\(524\) | −33.8590 | + | 58.6455i | −1.47914 | + | 2.56194i | ||||
\(525\) | 7.68676 | − | 2.20992i | 0.335478 | − | 0.0964487i | ||||
\(526\) | −26.8354 | + | 15.4934i | −1.17008 | + | 0.675546i | ||||
\(527\) | −0.675599 | + | 0.390057i | −0.0294295 | + | 0.0169912i | ||||
\(528\) | −92.9469 | + | 26.7219i | −4.04500 | + | 1.16292i | ||||
\(529\) | 6.50060 | − | 11.2594i | 0.282635 | − | 0.489538i | ||||
\(530\) | −6.04444 | −0.262554 | ||||||||
\(531\) | 26.9463 | − | 0.978433i | 1.16937 | − | 0.0424604i | ||||
\(532\) | −2.83213 | −0.122788 | ||||||||
\(533\) | 39.8203 | − | 17.7612i | 1.72481 | − | 0.769322i | ||||
\(534\) | −25.6884 | + | 26.6381i | −1.11165 | + | 1.15274i | ||||
\(535\) | −15.0714 | + | 8.70150i | −0.651595 | + | 0.376199i | ||||
\(536\) | −59.0307 | − | 102.244i | −2.54974 | − | 4.41628i | ||||
\(537\) | 20.3787 | + | 5.06597i | 0.879406 | + | 0.218613i | ||||
\(538\) | −22.7565 | − | 13.1384i | −0.981100 | − | 0.566439i | ||||
\(539\) | 54.0858i | 2.32964i | ||||||||
\(540\) | −8.80430 | − | 26.9061i | −0.378877 | − | 1.15786i | ||||
\(541\) | 0.563222i | 0.0242148i | 0.999927 | + | 0.0121074i | \(0.00385400\pi\) | ||||
−0.999927 | + | 0.0121074i | \(0.996146\pi\) | |||||||
\(542\) | −28.7508 | + | 49.7979i | −1.23495 | + | 2.13900i | ||||
\(543\) | −5.62067 | − | 1.39725i | −0.241206 | − | 0.0599617i | ||||
\(544\) | 8.86704 | − | 5.11939i | 0.380171 | − | 0.219492i | ||||
\(545\) | −7.28479 | − | 12.6176i | −0.312046 | − | 0.540480i | ||||
\(546\) | 13.7723 | + | 77.4879i | 0.589402 | + | 3.31618i | ||||
\(547\) | −10.7895 | + | 18.6880i | −0.461326 | + | 0.799040i | −0.999027 | − | 0.0440956i | \(-0.985959\pi\) |
0.537702 | + | 0.843135i | \(0.319293\pi\) | |||||||
\(548\) | − | 16.0502i | − | 0.685632i | ||||||
\(549\) | 3.64707 | − | 2.28599i | 0.155653 | − | 0.0975637i | ||||
\(550\) | −10.3054 | −0.439425 | ||||||||
\(551\) | −0.616362 | − | 0.355857i | −0.0262579 | − | 0.0151600i | ||||
\(552\) | −49.5355 | + | 14.2413i | −2.10837 | + | 0.606150i | ||||
\(553\) | 18.0650 | − | 10.4298i | 0.768202 | − | 0.443521i | ||||
\(554\) | −50.1264 | + | 28.9405i | −2.12967 | + | 1.22956i | ||||
\(555\) | 2.65295 | + | 9.22776i | 0.112611 | + | 0.391697i | ||||
\(556\) | −0.982474 | + | 1.70169i | −0.0416662 | + | 0.0721679i | ||||
\(557\) | 4.64485i | 0.196809i | 0.995147 | + | 0.0984043i | \(0.0313738\pi\) | ||||
−0.995147 | + | 0.0984043i | \(0.968626\pi\) | |||||||
\(558\) | 11.8698 | + | 6.29019i | 0.502490 | + | 0.266285i | ||||
\(559\) | −5.68027 | + | 7.82928i | −0.240250 | + | 0.331143i | ||||
\(560\) | 34.1411 | − | 59.1342i | 1.44273 | − | 2.49888i | ||||
\(561\) | 2.23842 | + | 2.15862i | 0.0945061 | + | 0.0911368i | ||||
\(562\) | 38.0511 | + | 65.9064i | 1.60509 | + | 2.78009i | ||||
\(563\) | −6.32849 | − | 10.9613i | −0.266714 | − | 0.461963i | 0.701297 | − | 0.712869i | \(-0.252605\pi\) |
−0.968011 | + | 0.250907i | \(0.919271\pi\) | |||||||
\(564\) | −13.8985 | + | 55.9090i | −0.585232 | + | 2.35419i | ||||
\(565\) | 0.390485 | + | 0.225447i | 0.0164278 | + | 0.00948462i | ||||
\(566\) | − | 14.1646i | − | 0.595381i | ||||||
\(567\) | 3.01412 | + | 41.4500i | 0.126581 | + | 1.74074i | ||||
\(568\) | −91.8053 | −3.85206 | ||||||||
\(569\) | −12.8814 | + | 22.3113i | −0.540017 | + | 0.935337i | 0.458885 | + | 0.888496i | \(0.348249\pi\) |
−0.998902 | + | 0.0468414i | \(0.985084\pi\) | |||||||
\(570\) | −0.128375 | + | 0.516410i | −0.00537703 | + | 0.0216300i | ||||
\(571\) | −4.30979 | − | 7.46477i | −0.180359 | − | 0.312391i | 0.761644 | − | 0.647996i | \(-0.224393\pi\) |
−0.942003 | + | 0.335605i | \(0.891059\pi\) | |||||||
\(572\) | 7.70404 | − | 73.7757i | 0.322122 | − | 3.08472i | ||||
\(573\) | 10.0258 | − | 10.3965i | 0.418835 | − | 0.434319i | ||||
\(574\) | 131.983 | + | 76.2004i | 5.50886 | + | 3.18054i | ||||
\(575\) | −3.16209 | −0.131868 | ||||||||
\(576\) | −77.3937 | − | 41.0133i | −3.22474 | − | 1.70889i | ||||
\(577\) | 9.19409i | 0.382755i | 0.981517 | + | 0.191377i | \(0.0612955\pi\) | ||||
−0.981517 | + | 0.191377i | \(0.938705\pi\) | |||||||
\(578\) | 39.6454 | + | 22.8893i | 1.64903 | + | 0.952069i | ||||
\(579\) | −16.6631 | + | 4.79058i | −0.692495 | + | 0.199090i | ||||
\(580\) | 29.8309 | − | 17.2229i | 1.23866 | − | 0.715141i | ||||
\(581\) | −3.00368 | − | 5.20252i | −0.124614 | − | 0.215837i | ||||
\(582\) | 7.28556 | + | 25.3414i | 0.301996 | + | 1.05043i | ||||
\(583\) | −7.24267 | − | 4.18156i | −0.299961 | − | 0.173182i | ||||
\(584\) | 15.1233 | 0.625808 | ||||||||
\(585\) | 10.7918 | + | 0.732305i | 0.446188 | + | 0.0302771i | ||||
\(586\) | −28.4709 | −1.17612 | ||||||||
\(587\) | 23.2824 | + | 13.4421i | 0.960966 | + | 0.554814i | 0.896470 | − | 0.443104i | \(-0.146123\pi\) |
0.0644959 | + | 0.997918i | \(0.479456\pi\) | |||||||
\(588\) | −93.8257 | + | 97.2944i | −3.86931 | + | 4.01235i | ||||
\(589\) | −0.0923504 | − | 0.159956i | −0.00380523 | − | 0.00659086i | ||||
\(590\) | 21.2433 | − | 12.2648i | 0.874573 | − | 0.504935i | ||||
\(591\) | 5.14714 | − | 20.7052i | 0.211725 | − | 0.851700i | ||||
\(592\) | 70.9891 | + | 40.9856i | 2.91763 | + | 1.68450i | ||||
\(593\) | − | 8.64729i | − | 0.355102i | −0.984112 | − | 0.177551i | \(-0.943183\pi\) | ||
0.984112 | − | 0.177551i | \(-0.0568174\pi\) | |||||||
\(594\) | 11.0243 | − | 52.4015i | 0.452333 | − | 2.15006i | ||||
\(595\) | −2.19556 | −0.0900090 | ||||||||
\(596\) | 16.6115 | + | 9.59063i | 0.680432 | + | 0.392848i | ||||
\(597\) | −2.22657 | − | 0.553504i | −0.0911273 | − | 0.0226534i | ||||
\(598\) | 3.23164 | − | 30.9469i | 0.132152 | − | 1.26551i | ||||
\(599\) | −13.1393 | − | 22.7580i | −0.536859 | − | 0.929867i | −0.999071 | − | 0.0430977i | \(-0.986277\pi\) |
0.462212 | − | 0.886770i | \(-0.347056\pi\) | |||||||
\(600\) | −11.7331 | − | 11.3148i | −0.479002 | − | 0.461925i | ||||
\(601\) | 22.3720 | − | 38.7494i | 0.912571 | − | 1.58062i | 0.102153 | − | 0.994769i | \(-0.467427\pi\) |
0.810418 | − | 0.585851i | \(-0.199240\pi\) | |||||||
\(602\) | −33.8093 | −1.37796 | ||||||||
\(603\) | 37.6111 | − | 1.36568i | 1.53164 | − | 0.0556147i | ||||
\(604\) | 53.8527i | 2.19124i | ||||||||
\(605\) | −2.82206 | − | 1.62932i | −0.114733 | − | 0.0662411i | ||||
\(606\) | 38.0385 | − | 10.9359i | 1.54521 | − | 0.444242i | ||||
\(607\) | 20.7581 | + | 35.9541i | 0.842545 | + | 1.45933i | 0.887736 | + | 0.460353i | \(0.152277\pi\) |
−0.0451906 | + | 0.998978i | \(0.514390\pi\) | |||||||
\(608\) | 1.21207 | + | 2.09937i | 0.0491561 | + | 0.0851408i | ||||
\(609\) | −48.5983 | + | 13.9718i | −1.96930 | + | 0.566168i | ||||
\(610\) | 1.95784 | − | 3.39108i | 0.0792707 | − | 0.137301i | ||||
\(611\) | −17.8166 | − | 12.9263i | −0.720784 | − | 0.522941i | ||||
\(612\) | 0.281995 | + | 7.76622i | 0.0113990 | + | 0.313931i | ||||
\(613\) | 30.1598i | 1.21814i | 0.793116 | + | 0.609070i | \(0.208457\pi\) | ||||
−0.793116 | + | 0.609070i | \(0.791543\pi\) | |||||||
\(614\) | −10.1446 | + | 17.5709i | −0.409401 | + | 0.709104i | ||||
\(615\) | 14.5396 | − | 15.0771i | 0.586292 | − | 0.607967i | ||||
\(616\) | 142.110 | − | 82.0472i | 5.72577 | − | 3.30578i | ||||
\(617\) | 5.17977 | − | 2.99054i | 0.208530 | − | 0.120395i | −0.392098 | − | 0.919923i | \(-0.628251\pi\) |
0.600628 | + | 0.799529i | \(0.294917\pi\) | |||||||
\(618\) | −14.2979 | + | 57.5157i | −0.575145 | + | 2.31362i | ||||
\(619\) | 10.1403 | + | 5.85448i | 0.407571 | + | 0.235311i | 0.689746 | − | 0.724052i | \(-0.257722\pi\) |
−0.282174 | + | 0.959363i | \(0.591056\pi\) | |||||||
\(620\) | 8.93921 | 0.359007 | ||||||||
\(621\) | 3.38266 | − | 16.0787i | 0.135742 | − | 0.645216i | ||||
\(622\) | 72.4433i | 2.90471i | ||||||||
\(623\) | 18.0754 | − | 31.3075i | 0.724176 | − | 1.25431i | ||||
\(624\) | 70.6591 | − | 59.4547i | 2.82863 | − | 2.38009i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −32.5727 | + | 18.8059i | −1.30187 | + | 0.751634i | ||||
\(627\) | −0.511077 | + | 0.529971i | −0.0204104 | + | 0.0211650i | ||||
\(628\) | 35.8323 | − | 62.0634i | 1.42986 | − | 2.47660i | ||||
\(629\) | − | 2.63571i | − | 0.105093i | ||||||
\(630\) | 20.0793 | + | 32.0346i | 0.799980 | + | 1.27629i | ||||
\(631\) | 46.3399i | 1.84476i | 0.386280 | + | 0.922382i | \(0.373760\pi\) | ||||
−0.386280 | + | 0.922382i | \(0.626240\pi\) | |||||||
\(632\) | −36.8161 | − | 21.2558i | −1.46446 | − | 0.845509i | ||||
\(633\) | −3.71572 | − | 12.9244i | −0.147687 | − | 0.513698i | ||||
\(634\) | 3.13872 | + | 5.43643i | 0.124655 | + | 0.215908i | ||||
\(635\) | 1.24483 | − | 0.718705i | 0.0493997 | − | 0.0285209i | ||||
\(636\) | −5.77478 | − | 20.0864i | −0.228985 | − | 0.796478i | ||||
\(637\) | −21.0370 | − | 47.1646i | −0.833517 | − | 1.86873i | ||||
\(638\) | 65.1544 | 2.57949 | ||||||||
\(639\) | 13.7036 | − | 25.8593i | 0.542107 | − | 1.02298i | ||||
\(640\) | −36.6127 | −1.44724 | ||||||||
\(641\) | 5.31211 | − | 9.20085i | 0.209816 | − | 0.363412i | −0.741841 | − | 0.670576i | \(-0.766047\pi\) |
0.951656 | + | 0.307165i | \(0.0993802\pi\) | |||||||
\(642\) | −59.2157 | − | 57.1046i | −2.33706 | − | 2.25374i | ||||
\(643\) | −28.5448 | + | 16.4803i | −1.12570 | + | 0.649921i | −0.942849 | − | 0.333220i | \(-0.891865\pi\) |
−0.182847 | + | 0.983141i | \(0.558531\pi\) | |||||||
\(644\) | 68.8953 | − | 39.7767i | 2.71486 | − | 1.56742i | ||||
\(645\) | −1.12100 | + | 4.50942i | −0.0441394 | + | 0.177558i | ||||
\(646\) | 0.0730368 | − | 0.126503i | 0.00287360 | − | 0.00497721i | ||||
\(647\) | 0.532069 | 0.0209178 | 0.0104589 | − | 0.999945i | \(-0.496671\pi\) | ||||
0.0104589 | + | 0.999945i | \(0.496671\pi\) | |||||||
\(648\) | 70.0855 | − | 47.5569i | 2.75322 | − | 1.86821i | ||||
\(649\) | 33.9393 | 1.33223 | ||||||||
\(650\) | 8.98668 | − | 4.00836i | 0.352487 | − | 0.157221i | ||||
\(651\) | −12.7353 | − | 3.16588i | −0.499135 | − | 0.124081i | ||||
\(652\) | −50.1549 | + | 28.9569i | −1.96422 | + | 1.13404i | ||||
\(653\) | −16.3267 | − | 28.2786i | −0.638912 | − | 1.10663i | −0.985672 | − | 0.168674i | \(-0.946052\pi\) |
0.346760 | − | 0.937954i | \(-0.387282\pi\) | |||||||
\(654\) | 47.8073 | − | 49.5747i | 1.86941 | − | 1.93852i | ||||
\(655\) | −10.7641 | − | 6.21464i | −0.420587 | − | 0.242826i | ||||
\(656\) | − | 178.819i | − | 6.98169i | ||||||
\(657\) | −2.25743 | + | 4.25987i | −0.0880709 | + | 0.166193i | ||||
\(658\) | − | 76.9377i | − | 2.99935i | ||||||
\(659\) | −1.52693 | + | 2.64472i | −0.0594808 | + | 0.103024i | −0.894232 | − | 0.447603i | \(-0.852278\pi\) |
0.834752 | + | 0.550627i | \(0.185611\pi\) | |||||||
\(660\) | −9.84567 | − | 34.2462i | −0.383242 | − | 1.33303i | ||||
\(661\) | −14.5034 | + | 8.37353i | −0.564116 | + | 0.325692i | −0.754796 | − | 0.655960i | \(-0.772264\pi\) |
0.190680 | + | 0.981652i | \(0.438931\pi\) | |||||||
\(662\) | −36.0205 | − | 62.3893i | −1.39998 | − | 2.42483i | ||||
\(663\) | −2.79158 | − | 1.01174i | −0.108416 | − | 0.0392926i | ||||
\(664\) | −6.12143 | + | 10.6026i | −0.237558 | + | 0.411462i | ||||
\(665\) | − | 0.519823i | − | 0.0201579i | ||||||
\(666\) | −38.4567 | + | 24.1047i | −1.49017 | + | 0.934039i | ||||
\(667\) | 19.9918 | 0.774085 | ||||||||
\(668\) | −86.3635 | − | 49.8620i | −3.34151 | − | 1.92922i | ||||
\(669\) | −18.6557 | − | 17.9906i | −0.721270 | − | 0.695555i | ||||
\(670\) | 29.6510 | − | 17.1190i | 1.14552 | − | 0.661364i | ||||
\(671\) | 4.69191 | − | 2.70888i | 0.181129 | − | 0.104575i | ||||
\(672\) | 167.147 | + | 41.5513i | 6.44784 | + | 1.60287i | ||||
\(673\) | −4.75179 | + | 8.23034i | −0.183168 | + | 0.317256i | −0.942958 | − | 0.332913i | \(-0.891969\pi\) |
0.759790 | + | 0.650169i | \(0.225302\pi\) | |||||||
\(674\) | 49.5086i | 1.90700i | ||||||||
\(675\) | 4.93848 | − | 1.61598i | 0.190082 | − | 0.0621993i | ||||
\(676\) | 21.9773 | + | 67.3314i | 0.845282 | + | 2.58967i | ||||
\(677\) | 0.888100 | − | 1.53823i | 0.0341325 | − | 0.0591192i | −0.848455 | − | 0.529268i | \(-0.822467\pi\) |
0.882587 | + | 0.470149i | \(0.155800\pi\) | |||||||
\(678\) | −0.514193 | + | 2.06843i | −0.0197475 | + | 0.0794376i | ||||
\(679\) | −12.8791 | − | 22.3072i | −0.494254 | − | 0.856073i | ||||
\(680\) | 2.23725 | + | 3.87503i | 0.0857945 | + | 0.148601i | ||||
\(681\) | −5.49247 | − | 5.29666i | −0.210472 | − | 0.202968i | ||||
\(682\) | 14.6433 | + | 8.45430i | 0.560720 | + | 0.323732i | ||||
\(683\) | 45.0955i | 1.72553i | 0.505605 | + | 0.862765i | \(0.331269\pi\) | ||||
−0.505605 | + | 0.862765i | \(0.668731\pi\) | |||||||
\(684\) | −1.83874 | + | 0.0667656i | −0.0703060 | + | 0.00255285i | ||||
\(685\) | 2.94594 | 0.112558 | ||||||||
\(686\) | 46.1460 | − | 79.9273i | 1.76186 | − | 3.05164i | ||||
\(687\) | 35.7447 | − | 10.2765i | 1.36375 | − | 0.392073i | ||||
\(688\) | 19.8349 | + | 34.3551i | 0.756200 | + | 1.30978i | ||||
\(689\) | 7.94229 | + | 0.829374i | 0.302577 | + | 0.0315966i | ||||
\(690\) | −4.13000 | − | 14.3654i | −0.157226 | − | 0.546880i | ||||
\(691\) | 4.61829 | + | 2.66637i | 0.175688 | + | 0.101434i | 0.585265 | − | 0.810842i | \(-0.300990\pi\) |
−0.409577 | + | 0.912275i | \(0.634324\pi\) | |||||||
\(692\) | 11.2510 | 0.427698 | ||||||||
\(693\) | 1.89816 | + | 52.2759i | 0.0721053 | + | 1.98580i | ||||
\(694\) | − | 13.0623i | − | 0.495838i | ||||||
\(695\) | −0.312337 | − | 0.180328i | −0.0118476 | − | 0.00684023i | ||||
\(696\) | 74.1806 | + | 71.5360i | 2.81181 | + | 2.71156i | ||||
\(697\) | −4.97943 | + | 2.87488i | −0.188609 | + | 0.108894i | ||||
\(698\) | 25.9308 | + | 44.9134i | 0.981494 | + | 1.70000i | ||||
\(699\) | −40.6553 | − | 10.1065i | −1.53772 | − | 0.382265i | ||||
\(700\) | 21.7879 | + | 12.5793i | 0.823506 | + | 0.475452i | ||||
\(701\) | −18.7366 | −0.707673 | −0.353837 | − | 0.935307i | \(-0.615123\pi\) | ||||
−0.353837 | + | 0.935307i | \(0.615123\pi\) | |||||||
\(702\) | 10.7683 | + | 49.9838i | 0.406424 | + | 1.88652i | ||||
\(703\) | 0.624034 | 0.0235359 | ||||||||
\(704\) | −95.4770 | − | 55.1237i | −3.59843 | − | 2.07755i | ||||
\(705\) | −10.2618 | − | 2.55099i | −0.386482 | − | 0.0960760i | ||||
\(706\) | −3.76565 | − | 6.52230i | −0.141722 | − | 0.245470i | ||||
\(707\) | −33.4841 | + | 19.3320i | −1.25930 | + | 0.727056i | ||||
\(708\) | 61.0530 | + | 58.8764i | 2.29451 | + | 2.21271i | ||||
\(709\) | −33.3321 | − | 19.2443i | −1.25181 | − | 0.722736i | −0.280345 | − | 0.959899i | \(-0.590449\pi\) |
−0.971470 | + | 0.237164i | \(0.923782\pi\) | |||||||
\(710\) | − | 26.6237i | − | 0.999168i | ||||||
\(711\) | 11.4827 | − | 7.19737i | 0.430635 | − | 0.269922i | ||||
\(712\) | −73.6746 | −2.76107 | ||||||||
\(713\) | 4.49310 | + | 2.59409i | 0.168268 | + | 0.0971494i | ||||
\(714\) | −2.86761 | − | 9.97442i | −0.107318 | − | 0.373283i | ||||
\(715\) | 13.5411 | + | 1.41404i | 0.506410 | + | 0.0528820i | ||||
\(716\) | 33.0267 | + | 57.2039i | 1.23426 | + | 2.13781i | ||||
\(717\) | 11.2223 | − | 3.22638i | 0.419106 | − | 0.120491i | ||||
\(718\) | −14.3050 | + | 24.7770i | −0.533859 | + | 0.924671i | ||||
\(719\) | −30.4253 | −1.13467 | −0.567336 | − | 0.823486i | \(-0.692026\pi\) | ||||
−0.567336 | + | 0.823486i | \(0.692026\pi\) | |||||||
\(720\) | 20.7719 | − | 39.1973i | 0.774121 | − | 1.46080i | ||||
\(721\) | − | 57.8957i | − | 2.15615i | ||||||
\(722\) | −44.8768 | − | 25.9096i | −1.67014 | − | 0.964257i | ||||
\(723\) | −10.9360 | − | 10.5461i | −0.406714 | − | 0.392214i | ||||
\(724\) | −9.10911 | − | 15.7774i | −0.338538 | − | 0.586364i | ||||
\(725\) | 3.16117 | + | 5.47531i | 0.117403 | + | 0.203348i | ||||
\(726\) | 3.71610 | − | 14.9487i | 0.137918 | − | 0.554797i | ||||
\(727\) | 26.2966 | − | 45.5470i | 0.975286 | − | 1.68925i | 0.296298 | − | 0.955095i | \(-0.404248\pi\) |
0.678988 | − | 0.734150i | \(-0.262419\pi\) | |||||||
\(728\) | −92.0118 | + | 126.822i | −3.41018 | + | 4.70035i | ||||
\(729\) | 2.93405 | + | 26.8401i | 0.108669 | + | 0.994078i | ||||
\(730\) | 4.38579i | 0.162325i | ||||||||
\(731\) | 0.637775 | − | 1.10466i | 0.0235890 | − | 0.0408573i | ||||
\(732\) | 13.1395 | + | 3.26635i | 0.485649 | + | 0.120728i | ||||
\(733\) | −8.95840 | + | 5.17214i | −0.330886 | + | 0.191037i | −0.656234 | − | 0.754557i | \(-0.727852\pi\) |
0.325348 | + | 0.945594i | \(0.394518\pi\) | |||||||
\(734\) | 45.8010 | − | 26.4432i | 1.69055 | − | 0.976038i | ||||
\(735\) | −17.8579 | − | 17.2212i | −0.658698 | − | 0.635214i | ||||
\(736\) | −58.9706 | − | 34.0467i | −2.17369 | − | 1.25498i | ||||
\(737\) | 47.3718 | 1.74496 | ||||||||
\(738\) | 87.4854 | + | 46.3612i | 3.22038 | + | 1.70658i | ||||
\(739\) | − | 12.1858i | − | 0.448261i | −0.974559 | − | 0.224130i | \(-0.928046\pi\) | ||
0.974559 | − | 0.224130i | \(-0.0719541\pi\) | |||||||
\(740\) | −15.1011 | + | 26.1559i | −0.555127 | + | 0.961509i | ||||
\(741\) | 0.239540 | − | 0.660939i | 0.00879973 | − | 0.0242802i | ||||
\(742\) | 13.9558 | + | 24.1721i | 0.512333 | + | 0.887386i | ||||
\(743\) | −35.8410 | + | 20.6928i | −1.31488 | + | 0.759146i | −0.982900 | − | 0.184140i | \(-0.941050\pi\) |
−0.331980 | + | 0.943286i | \(0.607717\pi\) | |||||||
\(744\) | 7.38953 | + | 25.7030i | 0.270913 | + | 0.942319i | ||||
\(745\) | −1.76031 | + | 3.04895i | −0.0644928 | + | 0.111705i | ||||
\(746\) | 80.9089i | 2.96229i | ||||||||
\(747\) | −2.07276 | − | 3.30689i | −0.0758385 | − | 0.120993i | ||||
\(748\) | 9.78168i | 0.357654i | ||||||||
\(749\) | 69.5957 | + | 40.1811i | 2.54297 | + | 1.46819i | ||||
\(750\) | 3.28131 | − | 3.40262i | 0.119816 | − | 0.124246i | ||||
\(751\) | −10.8042 | − | 18.7134i | −0.394250 | − | 0.682862i | 0.598755 | − | 0.800932i | \(-0.295662\pi\) |
−0.993005 | + | 0.118071i | \(0.962329\pi\) | |||||||
\(752\) | −78.1799 | + | 45.1372i | −2.85093 | + | 1.64598i | ||||
\(753\) | −3.74340 | − | 0.930575i | −0.136417 | − | 0.0339121i | ||||
\(754\) | −56.8168 | + | 25.3422i | −2.06915 | + | 0.922909i | ||||
\(755\) | −9.88439 | −0.359730 | ||||||||
\(756\) | −87.2714 | + | 97.3314i | −3.17403 | + | 3.53991i | ||||
\(757\) | −21.1040 | −0.767036 | −0.383518 | − | 0.923533i | \(-0.625288\pi\) | ||||
−0.383518 | + | 0.923533i | \(0.625288\pi\) | |||||||
\(758\) | −31.1425 | + | 53.9404i | −1.13115 | + | 1.95920i | ||||
\(759\) | 4.98928 | − | 20.0702i | 0.181099 | − | 0.728503i | ||||
\(760\) | −0.917457 | + | 0.529694i | −0.0332796 | + | 0.0192140i | ||||
\(761\) | 1.79140 | − | 1.03427i | 0.0649382 | − | 0.0374921i | −0.467179 | − | 0.884163i | \(-0.654730\pi\) |
0.532118 | + | 0.846670i | \(0.321396\pi\) | |||||||
\(762\) | 4.89095 | + | 4.71658i | 0.177180 | + | 0.170864i | ||||
\(763\) | −33.6391 | + | 58.2647i | −1.21782 | + | 2.10932i | ||||
\(764\) | 45.4316 | 1.64366 | ||||||||
\(765\) | −1.42545 | + | 0.0517588i | −0.0515373 | + | 0.00187134i | ||||
\(766\) | 7.00646 | 0.253154 | ||||||||
\(767\) | −29.5962 | + | 13.2009i | −1.06866 | + | 0.476657i | ||||
\(768\) | −19.8745 | − | 69.1296i | −0.717160 | − | 2.49450i | ||||
\(769\) | −0.922793 | + | 0.532774i | −0.0332767 | + | 0.0192123i | −0.516546 | − | 0.856259i | \(-0.672783\pi\) |
0.483269 | + | 0.875472i | \(0.339449\pi\) | |||||||
\(770\) | 23.7938 | + | 41.2121i | 0.857469 | + | 1.48518i | ||||
\(771\) | 9.24585 | + | 32.1599i | 0.332981 | + | 1.15821i | ||||
\(772\) | −47.2311 | − | 27.2689i | −1.69989 | − | 0.981430i | ||||
\(773\) | − | 43.1846i | − | 1.55324i | −0.629969 | − | 0.776620i | \(-0.716932\pi\) | ||
0.629969 | − | 0.776620i | \(-0.283068\pi\) | |||||||
\(774\) | −21.9504 | + | 0.797031i | −0.788992 | + | 0.0286487i | ||||
\(775\) | 1.64075i | 0.0589373i | ||||||||
\(776\) | −26.2473 | + | 45.4617i | −0.942223 | + | 1.63198i | ||||
\(777\) | 30.7771 | − | 31.9149i | 1.10412 | − | 1.14494i | ||||
\(778\) | 19.7974 | − | 11.4300i | 0.709770 | − | 0.409786i | ||||
\(779\) | −0.680659 | − | 1.17894i | −0.0243872 | − | 0.0422398i | ||||
\(780\) | 21.9060 | + | 26.0343i | 0.784361 | + | 0.932177i | ||||
\(781\) | 18.4183 | − | 31.9014i | 0.659058 | − | 1.14152i | ||||
\(782\) | 4.10316i | 0.146729i | ||||||||
\(783\) | −31.2227 | + | 10.2168i | −1.11581 | + | 0.365119i | ||||
\(784\) | −211.799 | −7.56426 | ||||||||
\(785\) | 11.3914 | + | 6.57684i | 0.406577 | + | 0.234737i | ||||
\(786\) | 14.1742 | − | 57.0181i | 0.505577 | − | 2.03377i | ||||
\(787\) | 36.8085 | − | 21.2514i | 1.31208 | − | 0.757530i | 0.329640 | − | 0.944107i | \(-0.393073\pi\) |
0.982440 | + | 0.186577i | \(0.0597392\pi\) | |||||||
\(788\) | 58.1204 | − | 33.5559i | 2.07046 | − | 1.19538i | ||||
\(789\) | 13.6512 | − | 14.1558i | 0.485995 | − | 0.503962i | ||||
\(790\) | 6.16420 | − | 10.6767i | 0.219313 | − | 0.379860i | ||||
\(791\) | − | 2.08210i | − | 0.0740310i | ||||||
\(792\) | 90.3297 | − | 56.6188i | 3.20973 | − | 2.01186i | ||||
\(793\) | −3.03787 | + | 4.18718i | −0.107878 | + | 0.148691i | ||||
\(794\) | 51.7401 | − | 89.6164i | 1.83619 | − | 3.18037i | ||||
\(795\) | 3.68676 | − | 1.05993i | 0.130756 | − | 0.0375919i | ||||
\(796\) | −3.60847 | − | 6.25006i | −0.127899 | − | 0.221527i | ||||
\(797\) | 24.7683 | + | 42.8999i | 0.877337 | + | 1.51959i | 0.854252 | + | 0.519859i | \(0.174016\pi\) |
0.0230851 | + | 0.999734i | \(0.492651\pi\) | |||||||
\(798\) | 2.36156 | − | 0.678939i | 0.0835982 | − | 0.0240342i | ||||
\(799\) | 2.51381 | + | 1.45135i | 0.0889321 | + | 0.0513450i | ||||
\(800\) | − | 21.5343i | − | 0.761354i | ||||||
\(801\) | 10.9973 | − | 20.7523i | 0.388570 | − | 0.733247i | ||||
\(802\) | −60.6816 | −2.14274 | ||||||||
\(803\) | −3.03409 | + | 5.25521i | −0.107071 | + | 0.185452i | ||||
\(804\) | 85.2166 | + | 82.1785i | 3.00536 | + | 2.89821i | ||||
\(805\) | 7.30082 | + | 12.6454i | 0.257320 | + | 0.445691i | ||||
\(806\) | −16.0578 | − | 1.67683i | −0.565611 | − | 0.0590640i | ||||
\(807\) | 16.1840 | + | 4.02320i | 0.569704 | + | 0.141623i | ||||
\(808\) | 68.2398 | + | 39.3983i | 2.40067 | + | 1.38603i | ||||
\(809\) | 15.3582 | 0.539965 | 0.269983 | − | 0.962865i | \(-0.412982\pi\) | ||||
0.269983 | + | 0.962865i | \(0.412982\pi\) | |||||||
\(810\) | 13.7916 | + | 20.3249i | 0.484586 | + | 0.714144i | ||||
\(811\) | 15.5024i | 0.544364i | 0.962246 | + | 0.272182i | \(0.0877453\pi\) | ||||
−0.962246 | + | 0.272182i | \(0.912255\pi\) | |||||||
\(812\) | −137.751 | − | 79.5304i | −4.83410 | − | 2.79097i | ||||
\(813\) | 8.80396 | − | 35.4154i | 0.308768 | − | 1.24207i | ||||
\(814\) | −49.4741 | + | 28.5639i | −1.73407 | + | 1.00116i | ||||
\(815\) | −5.31490 | − | 9.20567i | −0.186173 | − | 0.322461i | ||||
\(816\) | −8.45312 | + | 8.76562i | −0.295918 | + | 0.306858i | ||||
\(817\) | 0.261541 | + | 0.151001i | 0.00915015 | + | 0.00528284i | ||||
\(818\) | −56.9895 | −1.99259 | ||||||||
\(819\) | −21.9883 | − | 44.8480i | −0.768334 | − | 1.56712i | ||||
\(820\) | 65.8855 | 2.30082 | ||||||||
\(821\) | 18.7990 | + | 10.8536i | 0.656088 | + | 0.378793i | 0.790785 | − | 0.612094i | \(-0.209673\pi\) |
−0.134697 | + | 0.990887i | \(0.543006\pi\) | |||||||
\(822\) | 3.84768 | + | 13.3834i | 0.134203 | + | 0.466800i | ||||
\(823\) | 21.4761 | + | 37.1977i | 0.748611 | + | 1.29663i | 0.948489 | + | 0.316811i | \(0.102612\pi\) |
−0.199878 | + | 0.979821i | \(0.564055\pi\) | |||||||
\(824\) | −102.183 | + | 58.9951i | −3.55970 | + | 2.05519i | ||||
\(825\) | 6.28571 | − | 1.80712i | 0.218840 | − | 0.0629159i | ||||
\(826\) | −98.0956 | − | 56.6355i | −3.41318 | − | 1.97060i | ||||
\(827\) | − | 6.95047i | − | 0.241692i | −0.992671 | − | 0.120846i | \(-0.961439\pi\) | ||
0.992671 | − | 0.120846i | \(-0.0385607\pi\) | |||||||
\(828\) | 43.7921 | − | 27.4489i | 1.52188 | − | 0.953917i | ||||
\(829\) | 17.6505 | 0.613027 | 0.306514 | − | 0.951866i | \(-0.400838\pi\) | ||||
0.306514 | + | 0.951866i | \(0.400838\pi\) | |||||||
\(830\) | −3.07478 | − | 1.77522i | −0.106727 | − | 0.0616189i | ||||
\(831\) | 25.4993 | − | 26.4420i | 0.884561 | − | 0.917262i | ||||
\(832\) | 104.700 | + | 10.9333i | 3.62981 | + | 0.379044i | ||||
\(833\) | 3.40511 | + | 5.89782i | 0.117980 | + | 0.204347i | ||||
\(834\) | 0.411288 | − | 1.65448i | 0.0142417 | − | 0.0572898i | ||||
\(835\) | 9.15192 | − | 15.8516i | 0.316715 | − | 0.548567i | ||||
\(836\) | −2.31592 | −0.0800979 | ||||||||
\(837\) | −8.34293 | − | 1.75520i | −0.288374 | − | 0.0606686i | ||||
\(838\) | 27.3994i | 0.946498i | ||||||||
\(839\) | 16.8431 | + | 9.72436i | 0.581488 | + | 0.335722i | 0.761724 | − | 0.647901i | \(-0.224353\pi\) |
−0.180237 | + | 0.983623i | \(0.557686\pi\) | |||||||
\(840\) | −18.1585 | + | 73.0457i | −0.626528 | + | 2.52032i | ||||
\(841\) | −5.48598 | − | 9.50200i | −0.189172 | − | 0.327655i | ||||
\(842\) | 7.37081 | + | 12.7666i | 0.254015 | + | 0.439967i | ||||
\(843\) | −34.7660 | − | 33.5265i | −1.19740 | − | 1.15472i | ||||
\(844\) | 21.1506 | − | 36.6339i | 0.728033 | − | 1.26099i | ||||
\(845\) | −12.3583 | + | 4.03383i | −0.425139 | + | 0.138768i | ||||
\(846\) | −1.81376 | − | 49.9513i | −0.0623582 | − | 1.71736i | ||||
\(847\) | 15.0474i | 0.517036i | ||||||||
\(848\) | 16.3749 | − | 28.3622i | 0.562317 | − | 0.973962i | ||||
\(849\) | 2.48384 | + | 8.63956i | 0.0852453 | + | 0.296509i | ||||
\(850\) | −1.12376 | + | 0.648805i | −0.0385448 | + | 0.0222538i | ||||
\(851\) | −15.1805 | + | 8.76445i | −0.520380 | + | 0.300441i | ||||
\(852\) | 88.4736 | − | 25.4359i | 3.03106 | − | 0.871418i | ||||
\(853\) | −40.8634 | − | 23.5925i | −1.39913 | − | 0.807791i | −0.404833 | − | 0.914391i | \(-0.632670\pi\) |
−0.994302 | + | 0.106600i | \(0.966004\pi\) | |||||||
\(854\) | −18.0815 | −0.618737 | ||||||||
\(855\) | −0.0122545 | − | 0.337491i | −0.000419094 | − | 0.0115420i | ||||
\(856\) | − | 163.776i | − | 5.59776i | ||||||
\(857\) | −12.2627 | + | 21.2396i | −0.418885 | + | 0.725531i | −0.995828 | − | 0.0912542i | \(-0.970912\pi\) |
0.576942 | + | 0.816785i | \(0.304246\pi\) | |||||||
\(858\) | 11.2621 | + | 63.3644i | 0.384482 | + | 2.16322i | ||||
\(859\) | 25.0585 | + | 43.4026i | 0.854984 | + | 1.48088i | 0.876660 | + | 0.481111i | \(0.159767\pi\) |
−0.0216754 | + | 0.999765i | \(0.506900\pi\) | |||||||
\(860\) | −12.6581 | + | 7.30817i | −0.431638 | + | 0.249206i | ||||
\(861\) | −93.8641 | − | 23.3338i | −3.19888 | − | 0.795213i | ||||
\(862\) | −40.3880 | + | 69.9542i | −1.37562 | + | 2.38265i | ||||
\(863\) | − | 8.13933i | − | 0.277066i | −0.990358 | − | 0.138533i | \(-0.955761\pi\) | ||
0.990358 | − | 0.138533i | \(-0.0442387\pi\) | |||||||
\(864\) | 109.499 | + | 23.0365i | 3.72522 | + | 0.783718i | ||||
\(865\) | 2.06506i | 0.0702141i | ||||||||
\(866\) | 48.6139 | + | 28.0672i | 1.65197 | + | 0.953764i | ||||
\(867\) | −28.1952 | − | 7.00907i | −0.957558 | − | 0.238040i | ||||
\(868\) | −20.6394 | − | 35.7485i | −0.700546 | − | 1.21338i | ||||
\(869\) | 14.7723 | − | 8.52881i | 0.501117 | − | 0.289320i | ||||
\(870\) | −20.7455 | + | 21.5125i | −0.703340 | + | 0.729342i | ||||
\(871\) | −41.3097 | + | 18.4255i | −1.39973 | + | 0.624326i | ||||
\(872\) | 137.112 | 4.64319 | ||||||||
\(873\) | −8.88754 | − | 14.1792i | −0.300798 | − | 0.479893i | ||||
\(874\) | −0.971469 | −0.0328604 | ||||||||
\(875\) | −2.30886 | + | 3.99906i | −0.0780537 | + | 0.135193i | ||||
\(876\) | −14.5745 | + | 4.19012i | −0.492427 | + | 0.141571i | ||||
\(877\) | 6.28510 | − | 3.62870i | 0.212233 | − | 0.122533i | −0.390116 | − | 0.920766i | \(-0.627565\pi\) |
0.602349 | + | 0.798233i | \(0.294232\pi\) | |||||||
\(878\) | 84.6386 | − | 48.8661i | 2.85641 | − | 1.64915i | ||||
\(879\) | 17.3656 | − | 4.99255i | 0.585727 | − | 0.168394i | ||||
\(880\) | 27.9183 | − | 48.3559i | 0.941126 | − | 1.63008i | ||||
\(881\) | −12.0209 | −0.404993 | −0.202496 | − | 0.979283i | \(-0.564905\pi\) | ||||
−0.202496 | + | 0.979283i | \(0.564905\pi\) | |||||||
\(882\) | 54.9119 | − | 103.621i | 1.84898 | − | 3.48910i | ||||
\(883\) | −25.4194 | −0.855430 | −0.427715 | − | 0.903914i | \(-0.640681\pi\) | ||||
−0.427715 | + | 0.903914i | \(0.640681\pi\) | |||||||
\(884\) | −3.80465 | − | 8.52995i | −0.127964 | − | 0.286893i | ||||
\(885\) | −10.8065 | + | 11.2060i | −0.363255 | + | 0.376685i | ||||
\(886\) | −77.8772 | + | 44.9624i | −2.61634 | + | 1.51054i | ||||
\(887\) | −27.1443 | − | 47.0153i | −0.911417 | − | 1.57862i | −0.812064 | − | 0.583568i | \(-0.801656\pi\) |
−0.0993528 | − | 0.995052i | \(-0.531677\pi\) | |||||||
\(888\) | −87.6895 | − | 21.7988i | −2.94267 | − | 0.731521i | ||||
\(889\) | −5.74829 | − | 3.31878i | −0.192791 | − | 0.111308i | ||||
\(890\) | − | 21.3657i | − | 0.716181i | ||||||
\(891\) | 2.46474 | + | 33.8950i | 0.0825719 | + | 1.13553i | ||||
\(892\) | − | 81.5235i | − | 2.72961i | ||||||
\(893\) | −0.343623 | + | 0.595172i | −0.0114989 | + | 0.0199167i | ||||
\(894\) | −16.1505 | − | 4.01488i | −0.540154 | − | 0.134278i | ||||
\(895\) | −10.4995 | + | 6.06188i | −0.350959 | + | 0.202626i | ||||
\(896\) | 84.5336 | + | 146.416i | 2.82407 | + | 4.89143i | ||||
\(897\) | 3.45563 | + | 19.4425i | 0.115380 | + | 0.649167i | ||||
\(898\) | −9.39876 | + | 16.2791i | −0.313641 | + | 0.543241i | ||||
\(899\) | − | 10.3734i | − | 0.345971i | ||||||
\(900\) | 14.4422 | + | 7.65337i | 0.481407 | + | 0.255112i | ||||
\(901\) | −1.05304 | −0.0350819 | ||||||||
\(902\) | 107.927 | + | 62.3115i | 3.59357 | + | 2.07475i | ||||
\(903\) | 20.6217 | − | 5.92866i | 0.686247 | − | 0.197294i | ||||
\(904\) | −3.67478 | + | 2.12164i | −0.122222 | + | 0.0705646i | ||||
\(905\) | 2.89587 | − | 1.67193i | 0.0962620 | − | 0.0555769i | ||||
\(906\) | −12.9100 | − | 44.9048i | −0.428906 | − | 1.49186i | ||||
\(907\) | 6.53507 | − | 11.3191i | 0.216993 | − | 0.375844i | −0.736894 | − | 0.676008i | \(-0.763708\pi\) |
0.953887 | + | 0.300165i | \(0.0970417\pi\) | |||||||
\(908\) | − | 24.0016i | − | 0.796521i | ||||||
\(909\) | −21.2836 | + | 13.3406i | −0.705931 | + | 0.442478i | ||||
\(910\) | −36.7787 | − | 26.6835i | −1.21920 | − | 0.884551i | ||||
\(911\) | −29.0511 | + | 50.3180i | −0.962506 | + | 1.66711i | −0.246334 | + | 0.969185i | \(0.579226\pi\) |
−0.716172 | + | 0.697924i | \(0.754107\pi\) | |||||||
\(912\) | −2.07536 | − | 2.00137i | −0.0687221 | − | 0.0662720i | ||||
\(913\) | −2.45621 | − | 4.25427i | −0.0812885 | − | 0.140796i | ||||
\(914\) | 41.3977 | + | 71.7029i | 1.36931 | + | 2.37172i | ||||
\(915\) | −0.599522 | + | 2.41168i | −0.0198196 | + | 0.0797277i | ||||
\(916\) | 101.318 | + | 58.4957i | 3.34763 | + | 1.93275i | ||||
\(917\) | 57.3949i | 1.89535i | ||||||||
\(918\) | −2.09692 | − | 6.40822i | −0.0692086 | − | 0.211503i | ||||
\(919\) | 52.4703 | 1.73084 | 0.865418 | − | 0.501051i | \(-0.167053\pi\) | ||||
0.865418 | + | 0.501051i | \(0.167053\pi\) | |||||||
\(920\) | 14.8789 | − | 25.7710i | 0.490543 | − | 0.849646i | ||||
\(921\) | 3.10643 | − | 12.4961i | 0.102360 | − | 0.411762i | ||||
\(922\) | −28.1279 | − | 48.7190i | −0.926345 | − | 1.60448i | ||||
\(923\) | −3.65310 | + | 34.9830i | −0.120243 | + | 1.15148i | ||||
\(924\) | −114.220 | + | 118.443i | −3.75758 | + | 3.89649i | ||||
\(925\) | −4.80077 | − | 2.77173i | −0.157848 | − | 0.0911339i | ||||
\(926\) | 106.604 | 3.50323 | ||||||||
\(927\) | −1.36485 | − | 37.5884i | −0.0448277 | − | 1.23457i | ||||
\(928\) | 136.147i | 4.46926i | ||||||||
\(929\) | −16.8605 | − | 9.73442i | −0.553176 | − | 0.319376i | 0.197226 | − | 0.980358i | \(-0.436807\pi\) |
−0.750402 | + | 0.660982i | \(0.770140\pi\) | |||||||
\(930\) | −7.45392 | + | 2.14298i | −0.244424 | + | 0.0702709i | ||||
\(931\) | −1.39638 | + | 0.806198i | −0.0457644 | + | 0.0264221i | ||||
\(932\) | −65.8878 | − | 114.121i | −2.15823 | − | 3.73816i | ||||
\(933\) | −12.7034 | − | 44.1862i | −0.415890 | − | 1.44659i | ||||
\(934\) | 27.6509 | + | 15.9642i | 0.904764 | + | 0.522366i | ||||
\(935\) | −1.79538 | −0.0587151 | ||||||||
\(936\) | −56.7483 | + | 84.5077i | −1.85488 | + | 2.76222i | ||||
\(937\) | −46.2692 | −1.51155 | −0.755775 | − | 0.654831i | \(-0.772740\pi\) | ||||
−0.755775 | + | 0.654831i | \(0.772740\pi\) | |||||||
\(938\) | −136.920 | − | 79.0507i | −4.47059 | − | 2.58110i | ||||
\(939\) | 16.5697 | − | 17.1823i | 0.540733 | − | 0.560724i | ||||
\(940\) | −16.6308 | − | 28.8053i | −0.542436 | − | 0.939526i | ||||
\(941\) | −32.8208 | + | 18.9491i | −1.06993 | + | 0.617723i | −0.928162 | − | 0.372177i | \(-0.878612\pi\) |
−0.141766 | + | 0.989900i | \(0.545278\pi\) | |||||||
\(942\) | −15.0003 | + | 60.3412i | −0.488736 | + | 1.96602i | ||||
\(943\) | 33.1159 | + | 19.1195i | 1.07840 | + | 0.622616i | ||||
\(944\) | 132.906i | 4.32572i | ||||||||
\(945\) | −17.8647 | − | 16.0182i | −0.581138 | − | 0.521073i | ||||
\(946\) | −27.6469 | −0.898880 | ||||||||
\(947\) | −13.3754 | − | 7.72231i | −0.434643 | − | 0.250941i | 0.266679 | − | 0.963785i | \(-0.414073\pi\) |
−0.701323 | + | 0.712844i | \(0.747407\pi\) | |||||||
\(948\) | 41.3692 | + | 10.2840i | 1.34361 | + | 0.334009i | ||||
\(949\) | 0.601786 | − | 5.76284i | 0.0195348 | − | 0.187070i | ||||
\(950\) | −0.153612 | − | 0.266064i | −0.00498383 | − | 0.00863225i | ||||
\(951\) | −2.86775 | − | 2.76551i | −0.0929931 | − | 0.0896778i | ||||
\(952\) | 10.3310 | − | 17.8938i | 0.334829 | − | 0.579941i | ||||
\(953\) | 13.1318 | 0.425381 | 0.212690 | − | 0.977120i | \(-0.431777\pi\) | ||||
0.212690 | + | 0.977120i | \(0.431777\pi\) | |||||||
\(954\) | 9.63054 | + | 15.3646i | 0.311800 | + | 0.497447i | ||||
\(955\) | 8.33875i | 0.269835i | ||||||||
\(956\) | 31.8094 | + | 18.3652i | 1.02879 | + | 0.593973i | ||||
\(957\) | −39.7404 | + | 11.4252i | −1.28463 | + | 0.369325i | ||||
\(958\) | −7.28584 | − | 12.6194i | −0.235395 | − | 0.407716i | ||||
\(959\) | −6.80176 | − | 11.7810i | −0.219640 | − | 0.380428i | ||||
\(960\) | 48.6010 | − | 13.9726i | 1.56859 | − | 0.450964i | ||||
\(961\) | −14.1540 | + | 24.5154i | −0.456580 | + | 0.790820i | ||||
\(962\) | 32.0329 | − | 44.1519i | 1.03278 | − | 1.42351i | ||||
\(963\) | 46.1318 | + | 24.4466i | 1.48658 | + | 0.787782i | ||||
\(964\) | − | 47.7892i | − | 1.53919i | ||||||
\(965\) | 5.00507 | − | 8.66903i | 0.161119 | − | 0.279066i | ||||
\(966\) | −47.9124 | + | 49.6837i | −1.54156 | + | 1.59855i | ||||
\(967\) | 5.62128 | − | 3.24545i | 0.180768 | − | 0.104367i | −0.406885 | − | 0.913479i | \(-0.633385\pi\) |
0.587653 | + | 0.809113i | \(0.300052\pi\) | |||||||
\(968\) | 26.5579 | − | 15.3332i | 0.853602 | − | 0.492827i | ||||
\(969\) | −0.0223650 | + | 0.0899672i | −0.000718469 | + | 0.00289016i | ||||
\(970\) | −13.1839 | − | 7.61175i | −0.423311 | − | 0.244399i | ||||
\(971\) | 13.5504 | 0.434853 | 0.217427 | − | 0.976077i | \(-0.430234\pi\) | ||||
0.217427 | + | 0.976077i | \(0.430234\pi\) | |||||||
\(972\) | −54.3658 | + | 65.2492i | −1.74379 | + | 2.09287i | ||||
\(973\) | 1.66541i | 0.0533905i | ||||||||
\(974\) | 33.5011 | − | 58.0257i | 1.07345 | − | 1.85926i | ||||
\(975\) | −4.77846 | + | 4.02074i | −0.153033 | + | 0.128767i | ||||
\(976\) | 10.6079 | + | 18.3735i | 0.339551 | + | 0.588120i | ||||
\(977\) | 40.1497 | − | 23.1805i | 1.28450 | − | 0.741609i | 0.306835 | − | 0.951763i | \(-0.400730\pi\) |
0.977668 | + | 0.210154i | \(0.0673965\pi\) | |||||||
\(978\) | 34.8796 | − | 36.1691i | 1.11533 | − | 1.15656i | ||||
\(979\) | 14.7808 | − | 25.6012i | 0.472398 | − | 0.818217i | ||||
\(980\) | − | 78.0373i | − | 2.49281i | ||||||
\(981\) | −20.4664 | + | 38.6210i | −0.653443 | + | 1.23307i | ||||
\(982\) | − | 110.375i | − | 3.52219i | ||||||
\(983\) | −14.8310 | − | 8.56269i | −0.473036 | − | 0.273107i | 0.244474 | − | 0.969656i | \(-0.421385\pi\) |
−0.717510 | + | 0.696549i | \(0.754718\pi\) | |||||||
\(984\) | 54.4638 | + | 189.442i | 1.73624 | + | 6.03917i | ||||
\(985\) | 6.15900 | + | 10.6677i | 0.196242 | + | 0.339901i | ||||
\(986\) | 7.10481 | − | 4.10197i | 0.226263 | − | 0.130633i | ||||
\(987\) | 13.4915 | + | 46.9275i | 0.429439 | + | 1.49372i | ||||
\(988\) | 2.01956 | − | 0.900793i | 0.0642508 | − | 0.0286580i | ||||
\(989\) | −8.48310 | −0.269747 | ||||||||
\(990\) | 16.4195 | + | 26.1957i | 0.521847 | + | 0.832556i | ||||
\(991\) | −43.9561 | −1.39631 | −0.698155 | − | 0.715946i | \(-0.745995\pi\) | ||||
−0.698155 | + | 0.715946i | \(0.745995\pi\) | |||||||
\(992\) | −17.6662 | + | 30.5987i | −0.560902 | + | 0.971511i | ||||
\(993\) | 32.9108 | + | 31.7374i | 1.04439 | + | 1.00716i | ||||
\(994\) | −106.470 | + | 61.4703i | −3.37701 | + | 1.94972i | ||||
\(995\) | 1.14717 | − | 0.662317i | 0.0363676 | − | 0.0209969i | ||||
\(996\) | 2.96168 | − | 11.9139i | 0.0938446 | − | 0.377506i | ||||
\(997\) | −6.77470 | + | 11.7341i | −0.214557 | + | 0.371623i | −0.953135 | − | 0.302544i | \(-0.902164\pi\) |
0.738579 | + | 0.674167i | \(0.235497\pi\) | |||||||
\(998\) | −21.1557 | −0.669673 | ||||||||
\(999\) | 19.2295 | − | 21.4461i | 0.608393 | − | 0.678525i |
(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 | 585.2.bt.b.376.2 | ✓ | 108 | |
9.4 | even | 3 | inner | 585.2.bt.b.571.53 | yes | 108 | |
13.12 | even | 2 | inner | 585.2.bt.b.376.53 | yes | 108 | |
117.103 | even | 6 | inner | 585.2.bt.b.571.2 | yes | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.bt.b.376.2 | ✓ | 108 | 1.1 | even | 1 | trivial | |
585.2.bt.b.376.53 | yes | 108 | 13.12 | even | 2 | inner | |
585.2.bt.b.571.2 | yes | 108 | 117.103 | even | 6 | inner | |
585.2.bt.b.571.53 | yes | 108 | 9.4 | even | 3 | inner |