Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(230,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.230");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.p (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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 230.11 | ||
Character | \(\chi\) | \(=\) | 429.230 |
Dual form | 429.2.p.b.263.11 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.964601 | + | 1.67074i | −0.682076 | + | 1.18139i | 0.292270 | + | 0.956336i | \(0.405589\pi\) |
−0.974346 | + | 0.225054i | \(0.927744\pi\) | |||||||
\(3\) | −1.68588 | − | 0.397235i | −0.973345 | − | 0.229344i | ||||
\(4\) | −0.860909 | − | 1.49114i | −0.430455 | − | 0.745569i | ||||
\(5\) | − | 1.71348i | − | 0.766294i | −0.923687 | − | 0.383147i | \(-0.874840\pi\) | ||
0.923687 | − | 0.383147i | \(-0.125160\pi\) | |||||||
\(6\) | 2.28988 | − | 2.43350i | 0.934840 | − | 0.993470i | ||||
\(7\) | −3.58916 | + | 2.07221i | −1.35658 | + | 0.783220i | −0.989161 | − | 0.146837i | \(-0.953091\pi\) |
−0.367416 | + | 0.930057i | \(0.619757\pi\) | |||||||
\(8\) | −0.536667 | −0.189741 | ||||||||
\(9\) | 2.68441 | + | 1.33939i | 0.894803 | + | 0.446462i | ||||
\(10\) | 2.86278 | + | 1.65283i | 0.905292 | + | 0.522670i | ||||
\(11\) | −3.01673 | − | 1.37817i | −0.909577 | − | 0.415535i | ||||
\(12\) | 0.859060 | + | 2.85587i | 0.247989 | + | 0.824419i | ||||
\(13\) | 3.28917 | − | 1.47695i | 0.912251 | − | 0.409631i | ||||
\(14\) | − | 7.99540i | − | 2.13686i | ||||||
\(15\) | −0.680657 | + | 2.88874i | −0.175745 | + | 0.745868i | ||||
\(16\) | 2.23949 | − | 3.87891i | 0.559872 | − | 0.969727i | ||||
\(17\) | 1.63775 | + | 2.83666i | 0.397212 | + | 0.687991i | 0.993381 | − | 0.114868i | \(-0.0366444\pi\) |
−0.596169 | + | 0.802859i | \(0.703311\pi\) | |||||||
\(18\) | −4.82714 | + | 3.19297i | −1.13777 | + | 0.752590i | ||||
\(19\) | 3.17223 | − | 1.83149i | 0.727760 | − | 0.420172i | −0.0898424 | − | 0.995956i | \(-0.528636\pi\) |
0.817602 | + | 0.575784i | \(0.195303\pi\) | |||||||
\(20\) | −2.55504 | + | 1.47516i | −0.571325 | + | 0.329855i | ||||
\(21\) | 6.87407 | − | 2.06775i | 1.50004 | − | 0.451221i | ||||
\(22\) | 5.21250 | − | 3.71077i | 1.11131 | − | 0.791139i | ||||
\(23\) | 4.70378 | + | 2.71573i | 0.980805 | + | 0.566268i | 0.902513 | − | 0.430662i | \(-0.141720\pi\) |
0.0782919 | + | 0.996930i | \(0.475053\pi\) | |||||||
\(24\) | 0.904759 | + | 0.213183i | 0.184683 | + | 0.0435159i | ||||
\(25\) | 2.06397 | 0.412794 | ||||||||
\(26\) | −0.705145 | + | 6.92000i | −0.138290 | + | 1.35712i | ||||
\(27\) | −3.99355 | − | 3.32439i | −0.768559 | − | 0.639779i | ||||
\(28\) | 6.17989 | + | 3.56796i | 1.16789 | + | 0.674281i | ||||
\(29\) | 4.35124 | − | 7.53656i | 0.808005 | − | 1.39950i | −0.106239 | − | 0.994341i | \(-0.533881\pi\) |
0.914244 | − | 0.405164i | \(-0.132786\pi\) | |||||||
\(30\) | −4.16976 | − | 3.92368i | −0.761290 | − | 0.716362i | ||||
\(31\) | −2.17965 | −0.391477 | −0.195739 | − | 0.980656i | \(-0.562710\pi\) | ||||
−0.195739 | + | 0.980656i | \(0.562710\pi\) | |||||||
\(32\) | 3.78376 | + | 6.55366i | 0.668880 | + | 1.15853i | ||||
\(33\) | 4.53839 | + | 3.52179i | 0.790032 | + | 0.613065i | ||||
\(34\) | −6.31909 | −1.08371 | ||||||||
\(35\) | 3.55069 | + | 6.14998i | 0.600176 | + | 1.03954i | ||||
\(36\) | −0.313822 | − | 5.15591i | −0.0523037 | − | 0.859319i | ||||
\(37\) | 2.26663 | − | 3.92591i | 0.372631 | − | 0.645416i | −0.617338 | − | 0.786698i | \(-0.711789\pi\) |
0.989969 | + | 0.141282i | \(0.0451224\pi\) | |||||||
\(38\) | 7.06662i | 1.14636i | ||||||||
\(39\) | −6.13185 | + | 1.18339i | −0.981882 | + | 0.189493i | ||||
\(40\) | 0.919571i | 0.145397i | ||||||||
\(41\) | −2.05502 | + | 3.55940i | −0.320941 | + | 0.555885i | −0.980682 | − | 0.195607i | \(-0.937332\pi\) |
0.659742 | + | 0.751492i | \(0.270666\pi\) | |||||||
\(42\) | −3.17606 | + | 13.4793i | −0.490076 | + | 2.07990i | ||||
\(43\) | −3.16703 | + | 1.82848i | −0.482967 | + | 0.278841i | −0.721652 | − | 0.692256i | \(-0.756617\pi\) |
0.238685 | + | 0.971097i | \(0.423284\pi\) | |||||||
\(44\) | 0.542079 | + | 5.68484i | 0.0817215 | + | 0.857022i | ||||
\(45\) | 2.29502 | − | 4.59969i | 0.342121 | − | 0.685682i | ||||
\(46\) | −9.07453 | + | 5.23918i | −1.33797 | + | 0.772475i | ||||
\(47\) | 1.44769i | 0.211168i | 0.994410 | + | 0.105584i | \(0.0336711\pi\) | ||||
−0.994410 | + | 0.105584i | \(0.966329\pi\) | |||||||
\(48\) | −5.31636 | + | 5.64978i | −0.767350 | + | 0.815476i | ||||
\(49\) | 5.08807 | − | 8.81279i | 0.726867 | − | 1.25897i | ||||
\(50\) | −1.99091 | + | 3.44835i | −0.281557 | + | 0.487671i | ||||
\(51\) | −1.63423 | − | 5.43285i | −0.228838 | − | 0.760751i | ||||
\(52\) | −5.03401 | − | 3.63309i | −0.698091 | − | 0.503819i | ||||
\(53\) | 9.06332i | 1.24494i | 0.782643 | + | 0.622471i | \(0.213871\pi\) | ||||
−0.782643 | + | 0.622471i | \(0.786129\pi\) | |||||||
\(54\) | 9.40636 | − | 3.46546i | 1.28004 | − | 0.471590i | ||||
\(55\) | −2.36148 | + | 5.16911i | −0.318422 | + | 0.697003i | ||||
\(56\) | 1.92619 | − | 1.11208i | 0.257398 | − | 0.148609i | ||||
\(57\) | −6.07554 | + | 1.82755i | −0.804725 | + | 0.242065i | ||||
\(58\) | 8.39441 | + | 14.5396i | 1.10224 | + | 1.90914i | ||||
\(59\) | 9.13262 | − | 5.27272i | 1.18897 | − | 0.686450i | 0.230895 | − | 0.972979i | \(-0.425835\pi\) |
0.958072 | + | 0.286529i | \(0.0925013\pi\) | |||||||
\(60\) | 4.89349 | − | 1.47199i | 0.631747 | − | 0.190033i | ||||
\(61\) | −2.63306 | + | 1.52020i | −0.337129 | + | 0.194641i | −0.659002 | − | 0.752142i | \(-0.729021\pi\) |
0.321873 | + | 0.946783i | \(0.395688\pi\) | |||||||
\(62\) | 2.10249 | − | 3.64163i | 0.267017 | − | 0.462487i | ||||
\(63\) | −12.4103 | + | 0.755369i | −1.56355 | + | 0.0951675i | ||||
\(64\) | −5.64131 | −0.705164 | ||||||||
\(65\) | −2.53073 | − | 5.63594i | −0.313898 | − | 0.699052i | ||||
\(66\) | −10.2617 | + | 4.18534i | −1.26313 | + | 0.515179i | ||||
\(67\) | 7.83852 | − | 13.5767i | 0.957628 | − | 1.65866i | 0.229392 | − | 0.973334i | \(-0.426326\pi\) |
0.728236 | − | 0.685326i | \(-0.240340\pi\) | |||||||
\(68\) | 2.81990 | − | 4.88422i | 0.341964 | − | 0.592298i | ||||
\(69\) | −6.85124 | − | 6.44690i | −0.824792 | − | 0.776116i | ||||
\(70\) | −13.7000 | −1.63746 | ||||||||
\(71\) | 3.04416 | − | 1.75755i | 0.361275 | − | 0.208582i | −0.308365 | − | 0.951268i | \(-0.599782\pi\) |
0.669640 | + | 0.742686i | \(0.266448\pi\) | |||||||
\(72\) | −1.44063 | − | 0.718805i | −0.169780 | − | 0.0847119i | ||||
\(73\) | − | 10.7920i | − | 1.26311i | −0.775333 | − | 0.631553i | \(-0.782418\pi\) | ||
0.775333 | − | 0.631553i | \(-0.217582\pi\) | |||||||
\(74\) | 4.37278 | + | 7.57388i | 0.508325 | + | 0.880445i | ||||
\(75\) | −3.47961 | − | 0.819882i | −0.401791 | − | 0.0946718i | ||||
\(76\) | −5.46201 | − | 3.15349i | −0.626535 | − | 0.361730i | ||||
\(77\) | 13.6834 | − | 1.30478i | 1.55937 | − | 0.148694i | ||||
\(78\) | 3.93766 | − | 11.3862i | 0.445852 | − | 1.28923i | ||||
\(79\) | − | 5.74463i | − | 0.646322i | −0.946344 | − | 0.323161i | \(-0.895255\pi\) | ||
0.946344 | − | 0.323161i | \(-0.104745\pi\) | |||||||
\(80\) | −6.64645 | − | 3.83733i | −0.743096 | − | 0.429027i | ||||
\(81\) | 5.41209 | + | 7.19091i | 0.601344 | + | 0.798991i | ||||
\(82\) | −3.96455 | − | 6.86681i | −0.437812 | − | 0.758312i | ||||
\(83\) | −7.17926 | −0.788026 | −0.394013 | − | 0.919105i | \(-0.628914\pi\) | ||||
−0.394013 | + | 0.919105i | \(0.628914\pi\) | |||||||
\(84\) | −9.00126 | − | 8.47004i | −0.982118 | − | 0.924157i | ||||
\(85\) | 4.86058 | − | 2.80625i | 0.527203 | − | 0.304381i | ||||
\(86\) | − | 7.05503i | − | 0.760764i | ||||||
\(87\) | −10.3295 | + | 10.9773i | −1.10744 | + | 1.17689i | ||||
\(88\) | 1.61898 | + | 0.739621i | 0.172584 | + | 0.0788439i | ||||
\(89\) | −7.81452 | − | 4.51171i | −0.828337 | − | 0.478241i | 0.0249459 | − | 0.999689i | \(-0.492059\pi\) |
−0.853283 | + | 0.521448i | \(0.825392\pi\) | |||||||
\(90\) | 5.47110 | + | 8.27124i | 0.576705 | + | 0.871865i | ||||
\(91\) | −8.74483 | + | 12.1168i | −0.916707 | + | 1.27019i | ||||
\(92\) | − | 9.35198i | − | 0.975011i | ||||||
\(93\) | 3.67464 | + | 0.865835i | 0.381042 | + | 0.0897829i | ||||
\(94\) | −2.41871 | − | 1.39644i | −0.249471 | − | 0.144032i | ||||
\(95\) | −3.13823 | − | 5.43557i | −0.321975 | − | 0.557678i | ||||
\(96\) | −3.77563 | − | 12.5518i | −0.385349 | − | 1.28106i | ||||
\(97\) | 6.32360 | + | 10.9528i | 0.642065 | + | 1.11209i | 0.984971 | + | 0.172719i | \(0.0552552\pi\) |
−0.342907 | + | 0.939369i | \(0.611411\pi\) | |||||||
\(98\) | 9.81591 | + | 17.0017i | 0.991557 | + | 1.71743i | ||||
\(99\) | −6.25222 | − | 7.74014i | −0.628372 | − | 0.777913i | ||||
\(100\) | −1.77689 | − | 3.07767i | −0.177689 | − | 0.307767i | ||||
\(101\) | 2.09865 | − | 3.63496i | 0.208823 | − | 0.361692i | −0.742521 | − | 0.669823i | \(-0.766370\pi\) |
0.951344 | + | 0.308131i | \(0.0997034\pi\) | |||||||
\(102\) | 10.6532 | + | 2.51017i | 1.05483 | + | 0.248543i | ||||
\(103\) | 14.5087 | 1.42958 | 0.714792 | − | 0.699337i | \(-0.246521\pi\) | ||||
0.714792 | + | 0.699337i | \(0.246521\pi\) | |||||||
\(104\) | −1.76519 | + | 0.792629i | −0.173091 | + | 0.0777237i | ||||
\(105\) | −3.54306 | − | 11.7786i | −0.345768 | − | 1.14947i | ||||
\(106\) | −15.1424 | − | 8.74248i | −1.47076 | − | 0.849145i | ||||
\(107\) | 6.61739 | − | 11.4617i | 0.639727 | − | 1.10804i | −0.345766 | − | 0.938321i | \(-0.612381\pi\) |
0.985493 | − | 0.169719i | \(-0.0542859\pi\) | |||||||
\(108\) | −1.51904 | + | 8.81693i | −0.146170 | + | 0.848410i | ||||
\(109\) | − | 8.34893i | − | 0.799683i | −0.916584 | − | 0.399841i | \(-0.869065\pi\) | ||
0.916584 | − | 0.399841i | \(-0.130935\pi\) | |||||||
\(110\) | −6.35835 | − | 8.93155i | −0.606245 | − | 0.851589i | ||||
\(111\) | −5.38078 | + | 5.71825i | −0.510721 | + | 0.542752i | ||||
\(112\) | 18.5627i | 1.75401i | ||||||||
\(113\) | −6.72408 | + | 3.88215i | −0.632548 | + | 0.365202i | −0.781738 | − | 0.623607i | \(-0.785667\pi\) |
0.149190 | + | 0.988809i | \(0.452333\pi\) | |||||||
\(114\) | 2.80711 | − | 11.9135i | 0.262910 | − | 1.11580i | ||||
\(115\) | 4.65336 | − | 8.05985i | 0.433928 | − | 0.751585i | ||||
\(116\) | −14.9841 | −1.39124 | ||||||||
\(117\) | 10.8077 | + | 0.440738i | 0.999170 | + | 0.0407463i | ||||
\(118\) | 20.3443i | 1.87284i | ||||||||
\(119\) | −11.7563 | − | 6.78750i | −1.07770 | − | 0.622209i | ||||
\(120\) | 0.365286 | − | 1.55029i | 0.0333459 | − | 0.141522i | ||||
\(121\) | 7.20127 | + | 8.31515i | 0.654661 | + | 0.755922i | ||||
\(122\) | − | 5.86553i | − | 0.531041i | ||||||
\(123\) | 4.87845 | − | 5.18441i | 0.439875 | − | 0.467463i | ||||
\(124\) | 1.87648 | + | 3.25016i | 0.168513 | + | 0.291873i | ||||
\(125\) | − | 12.1040i | − | 1.08262i | ||||||
\(126\) | 10.7089 | − | 21.4629i | 0.954027 | − | 1.91207i | ||||
\(127\) | −3.14794 | − | 1.81747i | −0.279335 | − | 0.161274i | 0.353787 | − | 0.935326i | \(-0.384894\pi\) |
−0.633122 | + | 0.774052i | \(0.718227\pi\) | |||||||
\(128\) | −2.12590 | + | 3.68217i | −0.187905 | + | 0.325461i | ||||
\(129\) | 6.06558 | − | 1.82456i | 0.534045 | − | 0.160643i | ||||
\(130\) | 11.8573 | + | 1.20825i | 1.03996 | + | 0.105971i | ||||
\(131\) | 8.69314 | 0.759523 | 0.379761 | − | 0.925084i | \(-0.376006\pi\) | ||||
0.379761 | + | 0.925084i | \(0.376006\pi\) | |||||||
\(132\) | 1.34434 | − | 9.79931i | 0.117010 | − | 0.852921i | ||||
\(133\) | −7.59044 | + | 13.1470i | −0.658174 | + | 1.13999i | ||||
\(134\) | 15.1221 | + | 26.1922i | 1.30635 | + | 2.26266i | ||||
\(135\) | −5.69629 | + | 6.84288i | −0.490259 | + | 0.588942i | ||||
\(136\) | −0.878925 | − | 1.52234i | −0.0753672 | − | 0.130540i | ||||
\(137\) | −1.15732 | + | 0.668179i | −0.0988766 | + | 0.0570864i | −0.548623 | − | 0.836070i | \(-0.684848\pi\) |
0.449746 | + | 0.893156i | \(0.351514\pi\) | |||||||
\(138\) | 17.3798 | − | 5.22793i | 1.47947 | − | 0.445031i | ||||
\(139\) | −7.96240 | + | 4.59710i | −0.675362 | + | 0.389921i | −0.798105 | − | 0.602518i | \(-0.794164\pi\) |
0.122743 | + | 0.992438i | \(0.460831\pi\) | |||||||
\(140\) | 6.11365 | − | 10.5892i | 0.516698 | − | 0.894947i | ||||
\(141\) | 0.575074 | − | 2.44064i | 0.0484300 | − | 0.205539i | ||||
\(142\) | 6.78132i | 0.569076i | ||||||||
\(143\) | −11.9580 | − | 0.0775035i | −0.999979 | − | 0.00648117i | ||||
\(144\) | 11.2071 | − | 7.41303i | 0.933921 | − | 0.617753i | ||||
\(145\) | −12.9138 | − | 7.45578i | −1.07243 | − | 0.619169i | ||||
\(146\) | 18.0306 | + | 10.4100i | 1.49222 | + | 0.861534i | ||||
\(147\) | −12.0786 | + | 12.8362i | −0.996230 | + | 1.05871i | ||||
\(148\) | −7.80544 | −0.641603 | ||||||||
\(149\) | 4.00350 | + | 6.93427i | 0.327980 | + | 0.568077i | 0.982111 | − | 0.188304i | \(-0.0602990\pi\) |
−0.654131 | + | 0.756381i | \(0.726966\pi\) | |||||||
\(150\) | 4.72625 | − | 5.02266i | 0.385896 | − | 0.410099i | ||||
\(151\) | 14.4474i | 1.17571i | 0.808966 | + | 0.587855i | \(0.200028\pi\) | ||||
−0.808966 | + | 0.587855i | \(0.799972\pi\) | |||||||
\(152\) | −1.70243 | + | 0.982900i | −0.138086 | + | 0.0797237i | ||||
\(153\) | 0.596998 | + | 9.80833i | 0.0482645 | + | 0.792957i | ||||
\(154\) | −11.0191 | + | 24.1199i | −0.887941 | + | 1.94364i | ||||
\(155\) | 3.73480i | 0.299986i | ||||||||
\(156\) | 7.04356 | + | 8.12465i | 0.563936 | + | 0.650493i | ||||
\(157\) | −22.1309 | −1.76624 | −0.883120 | − | 0.469148i | \(-0.844561\pi\) | ||||
−0.883120 | + | 0.469148i | \(0.844561\pi\) | |||||||
\(158\) | 9.59778 | + | 5.54128i | 0.763558 | + | 0.440840i | ||||
\(159\) | 3.60027 | − | 15.2797i | 0.285520 | − | 1.21176i | ||||
\(160\) | 11.2296 | − | 6.48341i | 0.887778 | − | 0.512559i | ||||
\(161\) | −22.5102 | −1.77405 | ||||||||
\(162\) | −17.2346 | + | 2.10582i | −1.35408 | + | 0.165449i | ||||
\(163\) | −0.868763 | − | 1.50474i | −0.0680467 | − | 0.117860i | 0.829995 | − | 0.557771i | \(-0.188343\pi\) |
−0.898041 | + | 0.439911i | \(0.855010\pi\) | |||||||
\(164\) | 7.07675 | 0.552602 | ||||||||
\(165\) | 6.03454 | − | 7.77646i | 0.469788 | − | 0.605397i | ||||
\(166\) | 6.92512 | − | 11.9947i | 0.537493 | − | 0.930966i | ||||
\(167\) | 3.44254 | − | 5.96265i | 0.266392 | − | 0.461404i | −0.701536 | − | 0.712634i | \(-0.747502\pi\) |
0.967927 | + | 0.251231i | \(0.0808352\pi\) | |||||||
\(168\) | −3.68909 | + | 1.10970i | −0.284619 | + | 0.0856149i | ||||
\(169\) | 8.63726 | − | 9.71585i | 0.664405 | − | 0.747373i | ||||
\(170\) | 10.8277i | 0.830444i | ||||||||
\(171\) | 10.9686 | − | 0.667622i | 0.838792 | − | 0.0510543i | ||||
\(172\) | 5.45305 | + | 3.14832i | 0.415791 | + | 0.240057i | ||||
\(173\) | −6.66271 | − | 11.5402i | −0.506556 | − | 0.877382i | −0.999971 | − | 0.00758740i | \(-0.997585\pi\) |
0.493415 | − | 0.869794i | \(-0.335749\pi\) | |||||||
\(174\) | −8.37638 | − | 27.8466i | −0.635012 | − | 2.11104i | ||||
\(175\) | −7.40793 | + | 4.27697i | −0.559987 | + | 0.323308i | ||||
\(176\) | −12.1017 | + | 8.61520i | −0.912203 | + | 0.649395i | ||||
\(177\) | −17.4911 | + | 5.26140i | −1.31471 | + | 0.395471i | ||||
\(178\) | 15.0758 | − | 8.70400i | 1.12998 | − | 0.652393i | ||||
\(179\) | 18.5553 | + | 10.7129i | 1.38689 | + | 0.800721i | 0.992963 | − | 0.118421i | \(-0.0377832\pi\) |
0.393926 | + | 0.919142i | \(0.371117\pi\) | |||||||
\(180\) | −8.83458 | + | 0.537730i | −0.658491 | + | 0.0400800i | ||||
\(181\) | −9.13729 | −0.679169 | −0.339585 | − | 0.940575i | \(-0.610287\pi\) | ||||
−0.339585 | + | 0.940575i | \(0.610287\pi\) | |||||||
\(182\) | −11.8088 | − | 26.2982i | −0.875325 | − | 1.94935i | ||||
\(183\) | 5.04291 | − | 1.51693i | 0.372782 | − | 0.112135i | ||||
\(184\) | −2.52436 | − | 1.45744i | −0.186098 | − | 0.107444i | ||||
\(185\) | −6.72699 | − | 3.88383i | −0.494578 | − | 0.285545i | ||||
\(186\) | −4.99114 | + | 5.30417i | −0.365968 | + | 0.388921i | ||||
\(187\) | −1.03122 | − | 10.8145i | −0.0754104 | − | 0.790837i | ||||
\(188\) | 2.15871 | − | 1.24633i | 0.157440 | − | 0.0908981i | ||||
\(189\) | 21.2223 | + | 3.65633i | 1.54370 | + | 0.265959i | ||||
\(190\) | 12.1085 | 0.878446 | ||||||||
\(191\) | 12.0014 | − | 6.92899i | 0.868388 | − | 0.501364i | 0.00157552 | − | 0.999999i | \(-0.499498\pi\) |
0.866812 | + | 0.498635i | \(0.166165\pi\) | |||||||
\(192\) | 9.51059 | + | 2.24093i | 0.686368 | + | 0.161725i | ||||
\(193\) | 18.2513 | + | 10.5374i | 1.31376 | + | 0.758498i | 0.982716 | − | 0.185119i | \(-0.0592670\pi\) |
0.331040 | + | 0.943617i | \(0.392600\pi\) | |||||||
\(194\) | −24.3990 | −1.75175 | ||||||||
\(195\) | 2.02771 | + | 10.5068i | 0.145208 | + | 0.752410i | ||||
\(196\) | −17.5215 | −1.25153 | ||||||||
\(197\) | −1.67614 | + | 2.90316i | −0.119420 | + | 0.206841i | −0.919538 | − | 0.393001i | \(-0.871437\pi\) |
0.800118 | + | 0.599843i | \(0.204770\pi\) | |||||||
\(198\) | 18.9626 | − | 2.97967i | 1.34762 | − | 0.211756i | ||||
\(199\) | −1.88043 | − | 3.25700i | −0.133300 | − | 0.230882i | 0.791647 | − | 0.610979i | \(-0.209224\pi\) |
−0.924947 | + | 0.380097i | \(0.875891\pi\) | |||||||
\(200\) | −1.10767 | −0.0783238 | ||||||||
\(201\) | −18.6080 | + | 19.7750i | −1.31251 | + | 1.39482i | ||||
\(202\) | 4.04871 | + | 7.01257i | 0.284866 | + | 0.493403i | ||||
\(203\) | 36.0666i | 2.53138i | ||||||||
\(204\) | −6.69421 | + | 7.11406i | −0.468689 | + | 0.498084i | ||||
\(205\) | 6.09898 | + | 3.52125i | 0.425971 | + | 0.245935i | ||||
\(206\) | −13.9951 | + | 24.2402i | −0.975085 | + | 1.68890i | ||||
\(207\) | 8.98945 | + | 13.5903i | 0.624810 | + | 0.944590i | ||||
\(208\) | 1.63712 | − | 16.0660i | 0.113514 | − | 1.11398i | ||||
\(209\) | −12.0939 | + | 1.15321i | −0.836550 | + | 0.0797694i | ||||
\(210\) | 23.0966 | + | 5.44213i | 1.59382 | + | 0.375542i | ||||
\(211\) | −8.31881 | − | 4.80287i | −0.572690 | − | 0.330643i | 0.185533 | − | 0.982638i | \(-0.440599\pi\) |
−0.758223 | + | 0.651995i | \(0.773932\pi\) | |||||||
\(212\) | 13.5147 | − | 7.80270i | 0.928191 | − | 0.535891i | ||||
\(213\) | −5.83026 | + | 1.75377i | −0.399483 | + | 0.120166i | ||||
\(214\) | 12.7663 | + | 22.1118i | 0.872685 | + | 1.51153i | ||||
\(215\) | 3.13308 | + | 5.42665i | 0.213674 | + | 0.370095i | ||||
\(216\) | 2.14321 | + | 1.78409i | 0.145827 | + | 0.121392i | ||||
\(217\) | 7.82313 | − | 4.51669i | 0.531069 | − | 0.306613i | ||||
\(218\) | 13.9489 | + | 8.05339i | 0.944737 | + | 0.545444i | ||||
\(219\) | −4.28696 | + | 18.1940i | −0.289686 | + | 1.22944i | ||||
\(220\) | 9.74089 | − | 0.928845i | 0.656731 | − | 0.0626227i | ||||
\(221\) | 9.57642 | + | 6.91139i | 0.644180 | + | 0.464911i | ||||
\(222\) | −4.36339 | − | 14.5057i | −0.292851 | − | 0.973559i | ||||
\(223\) | −4.12973 | + | 7.15290i | −0.276547 | + | 0.478993i | −0.970524 | − | 0.241003i | \(-0.922523\pi\) |
0.693977 | + | 0.719997i | \(0.255857\pi\) | |||||||
\(224\) | −27.1611 | − | 15.6814i | −1.81477 | − | 1.04776i | ||||
\(225\) | 5.54054 | + | 2.76445i | 0.369369 | + | 0.184297i | ||||
\(226\) | − | 14.9789i | − | 0.996382i | ||||||
\(227\) | −2.53984 | − | 4.39914i | −0.168575 | − | 0.291981i | 0.769344 | − | 0.638835i | \(-0.220583\pi\) |
−0.937919 | + | 0.346854i | \(0.887250\pi\) | |||||||
\(228\) | 7.95563 | + | 7.48612i | 0.526874 | + | 0.495780i | ||||
\(229\) | 18.5371 | 1.22497 | 0.612483 | − | 0.790484i | \(-0.290171\pi\) | ||||
0.612483 | + | 0.790484i | \(0.290171\pi\) | |||||||
\(230\) | 8.97726 | + | 15.5491i | 0.591943 | + | 1.02528i | ||||
\(231\) | −23.5869 | − | 3.23581i | −1.55190 | − | 0.212901i | ||||
\(232\) | −2.33517 | + | 4.04463i | −0.153311 | + | 0.265543i | ||||
\(233\) | 25.4210 | 1.66538 | 0.832692 | − | 0.553736i | \(-0.186798\pi\) | ||||
0.832692 | + | 0.553736i | \(0.186798\pi\) | |||||||
\(234\) | −11.1614 | + | 17.6316i | −0.729647 | + | 1.15262i | ||||
\(235\) | 2.48060 | 0.161816 | ||||||||
\(236\) | −15.7247 | − | 9.07867i | −1.02359 | − | 0.590971i | ||||
\(237\) | −2.28197 | + | 9.68478i | −0.148230 | + | 0.629094i | ||||
\(238\) | 22.6802 | − | 13.0944i | 1.47014 | − | 0.848787i | ||||
\(239\) | 10.3761 | 0.671177 | 0.335589 | − | 0.942009i | \(-0.391065\pi\) | ||||
0.335589 | + | 0.942009i | \(0.391065\pi\) | |||||||
\(240\) | 9.68082 | + | 9.10950i | 0.624894 | + | 0.588016i | ||||
\(241\) | 11.8170 | − | 6.82255i | 0.761200 | − | 0.439479i | −0.0685265 | − | 0.997649i | \(-0.521830\pi\) |
0.829726 | + | 0.558170i | \(0.188496\pi\) | |||||||
\(242\) | −20.8388 | + | 4.01064i | −1.33957 | + | 0.257814i | ||||
\(243\) | −6.26767 | − | 14.2729i | −0.402071 | − | 0.915608i | ||||
\(244\) | 4.53365 | + | 2.61750i | 0.290237 | + | 0.167569i | ||||
\(245\) | −15.1006 | − | 8.71833i | −0.964741 | − | 0.556994i | ||||
\(246\) | 3.95604 | + | 13.1515i | 0.252228 | + | 0.838509i | ||||
\(247\) | 7.72899 | − | 10.7093i | 0.491784 | − | 0.681416i | ||||
\(248\) | 1.16975 | 0.0742791 | ||||||||
\(249\) | 12.1034 | + | 2.85186i | 0.767021 | + | 0.180729i | ||||
\(250\) | 20.2226 | + | 11.6755i | 1.27899 | + | 0.738426i | ||||
\(251\) | −2.21624 | + | 1.27955i | −0.139888 | + | 0.0807643i | −0.568311 | − | 0.822814i | \(-0.692403\pi\) |
0.428423 | + | 0.903578i | \(0.359069\pi\) | |||||||
\(252\) | 11.8105 | + | 17.8551i | 0.743990 | + | 1.12477i | ||||
\(253\) | −10.4473 | − | 14.6752i | −0.656814 | − | 0.922623i | ||||
\(254\) | 6.07302 | − | 3.50626i | 0.381055 | − | 0.220002i | ||||
\(255\) | −9.30911 | + | 2.80023i | −0.582959 | + | 0.175357i | ||||
\(256\) | −9.74261 | − | 16.8747i | −0.608913 | − | 1.05467i | ||||
\(257\) | −4.10951 | − | 2.37263i | −0.256344 | − | 0.148000i | 0.366321 | − | 0.930488i | \(-0.380617\pi\) |
−0.622666 | + | 0.782488i | \(0.713950\pi\) | |||||||
\(258\) | −2.80251 | + | 11.8940i | −0.174477 | + | 0.740486i | ||||
\(259\) | 18.7877i | 1.16741i | ||||||||
\(260\) | −6.22524 | + | 8.62570i | −0.386073 | + | 0.534943i | ||||
\(261\) | 21.7749 | − | 14.4032i | 1.34783 | − | 0.891537i | ||||
\(262\) | −8.38541 | + | 14.5239i | −0.518052 | + | 0.897293i | ||||
\(263\) | 0.0220398 | − | 0.0381740i | 0.00135903 | − | 0.00235391i | −0.865345 | − | 0.501176i | \(-0.832901\pi\) |
0.866704 | + | 0.498823i | \(0.166234\pi\) | |||||||
\(264\) | −2.43561 | − | 1.89003i | −0.149901 | − | 0.116323i | ||||
\(265\) | 15.5299 | 0.953992 | ||||||||
\(266\) | −14.6435 | − | 25.3633i | −0.897850 | − | 1.55512i | ||||
\(267\) | 11.3822 | + | 10.7104i | 0.696576 | + | 0.655467i | ||||
\(268\) | −26.9930 | −1.64886 | ||||||||
\(269\) | 2.63966 | − | 1.52401i | 0.160943 | − | 0.0929204i | −0.417365 | − | 0.908739i | \(-0.637046\pi\) |
0.578308 | + | 0.815818i | \(0.303713\pi\) | |||||||
\(270\) | −5.93802 | − | 16.1177i | −0.361376 | − | 0.980890i | ||||
\(271\) | 4.19786 | + | 2.42363i | 0.255002 | + | 0.147225i | 0.622052 | − | 0.782976i | \(-0.286299\pi\) |
−0.367051 | + | 0.930201i | \(0.619632\pi\) | |||||||
\(272\) | 14.6709 | 0.889552 | ||||||||
\(273\) | 19.5560 | − | 16.9538i | 1.18358 | − | 1.02609i | ||||
\(274\) | − | 2.57811i | − | 0.155749i | ||||||
\(275\) | −6.22643 | − | 2.84451i | −0.375468 | − | 0.171530i | ||||
\(276\) | −3.71494 | + | 15.7663i | −0.223613 | + | 0.949022i | ||||
\(277\) | −16.6384 | + | 9.60616i | −0.999702 | + | 0.577178i | −0.908160 | − | 0.418623i | \(-0.862513\pi\) |
−0.0915416 | + | 0.995801i | \(0.529179\pi\) | |||||||
\(278\) | − | 17.7374i | − | 1.06382i | ||||||
\(279\) | −5.85107 | − | 2.91939i | −0.350295 | − | 0.174780i | ||||
\(280\) | −1.90554 | − | 3.30049i | −0.113878 | − | 0.197242i | ||||
\(281\) | −6.47979 | −0.386552 | −0.193276 | − | 0.981144i | \(-0.561911\pi\) | ||||
−0.193276 | + | 0.981144i | \(0.561911\pi\) | |||||||
\(282\) | 3.52295 | + | 3.31504i | 0.209789 | + | 0.197408i | ||||
\(283\) | 13.6552 | + | 7.88385i | 0.811719 | + | 0.468646i | 0.847552 | − | 0.530712i | \(-0.178075\pi\) |
−0.0358337 | + | 0.999358i | \(0.511409\pi\) | |||||||
\(284\) | −5.24149 | − | 3.02618i | −0.311025 | − | 0.179571i | ||||
\(285\) | 3.13149 | + | 10.4104i | 0.185493 | + | 0.616656i | ||||
\(286\) | 11.6642 | − | 19.9039i | 0.689718 | − | 1.17694i | ||||
\(287\) | − | 17.0337i | − | 1.00547i | ||||||
\(288\) | 1.37927 | + | 22.6606i | 0.0812743 | + | 1.33529i | ||||
\(289\) | 3.13557 | − | 5.43097i | 0.184445 | − | 0.319469i | ||||
\(290\) | 24.9133 | − | 14.3837i | 1.46296 | − | 0.844640i | ||||
\(291\) | −6.31002 | − | 20.9771i | −0.369900 | − | 1.22970i | ||||
\(292\) | −16.0924 | + | 9.29092i | −0.941734 | + | 0.543710i | ||||
\(293\) | −15.9337 | − | 27.5979i | −0.930854 | − | 1.61229i | −0.781866 | − | 0.623447i | \(-0.785732\pi\) |
−0.148988 | − | 0.988839i | \(-0.547602\pi\) | |||||||
\(294\) | −9.79482 | − | 32.5620i | −0.571246 | − | 1.89906i | ||||
\(295\) | −9.03473 | − | 15.6486i | −0.526022 | − | 0.911098i | ||||
\(296\) | −1.21642 | + | 2.10691i | −0.0707032 | + | 0.122462i | ||||
\(297\) | 7.46585 | + | 15.5326i | 0.433213 | + | 0.901292i | ||||
\(298\) | −15.4471 | −0.894828 | ||||||||
\(299\) | 19.4825 | + | 1.98526i | 1.12670 | + | 0.114810i | ||||
\(300\) | 1.77307 | + | 5.89443i | 0.102368 | + | 0.340315i | ||||
\(301\) | 7.57799 | − | 13.1255i | 0.436788 | − | 0.756539i | ||||
\(302\) | −24.1378 | − | 13.9359i | −1.38897 | − | 0.801924i | ||||
\(303\) | −4.98201 | + | 5.29447i | −0.286209 | + | 0.304159i | ||||
\(304\) | − | 16.4064i | − | 0.940971i | ||||||
\(305\) | 2.60484 | + | 4.51171i | 0.149152 | + | 0.258340i | ||||
\(306\) | −16.9630 | − | 8.46370i | −0.969711 | − | 0.483837i | ||||
\(307\) | 28.7316i | 1.63980i | 0.572506 | + | 0.819900i | \(0.305971\pi\) | ||||
−0.572506 | + | 0.819900i | \(0.694029\pi\) | |||||||
\(308\) | −13.7258 | − | 19.2805i | −0.782098 | − | 1.09861i | ||||
\(309\) | −24.4600 | − | 5.76337i | −1.39148 | − | 0.327866i | ||||
\(310\) | −6.23987 | − | 3.60259i | −0.354401 | − | 0.204613i | ||||
\(311\) | − | 19.2304i | − | 1.09046i | −0.838288 | − | 0.545228i | \(-0.816443\pi\) | ||
0.838288 | − | 0.545228i | \(-0.183557\pi\) | |||||||
\(312\) | 3.29076 | − | 0.635084i | 0.186303 | − | 0.0359546i | ||||
\(313\) | −17.3332 | −0.979733 | −0.489866 | − | 0.871798i | \(-0.662954\pi\) | ||||
−0.489866 | + | 0.871798i | \(0.662954\pi\) | |||||||
\(314\) | 21.3475 | − | 36.9749i | 1.20471 | − | 2.08662i | ||||
\(315\) | 1.29431 | + | 21.2648i | 0.0729263 | + | 1.19814i | ||||
\(316\) | −8.56605 | + | 4.94561i | −0.481878 | + | 0.278212i | ||||
\(317\) | 33.6635i | 1.89073i | 0.326012 | + | 0.945366i | \(0.394295\pi\) | ||||
−0.326012 | + | 0.945366i | \(0.605705\pi\) | |||||||
\(318\) | 22.0555 | + | 20.7539i | 1.23681 | + | 1.16382i | ||||
\(319\) | −23.5132 | + | 16.7390i | −1.31649 | + | 0.937203i | ||||
\(320\) | 9.66630i | 0.540362i | ||||||||
\(321\) | −15.7091 | + | 16.6944i | −0.876798 | + | 0.931788i | ||||
\(322\) | 21.7133 | − | 37.6086i | 1.21004 | − | 2.09584i | ||||
\(323\) | 10.3906 | + | 5.99903i | 0.578150 | + | 0.333795i | ||||
\(324\) | 6.06333 | − | 14.2609i | 0.336852 | − | 0.792273i | ||||
\(325\) | 6.78874 | − | 3.04837i | 0.376572 | − | 0.169093i | ||||
\(326\) | 3.35204 | 0.185652 | ||||||||
\(327\) | −3.31649 | + | 14.0753i | −0.183402 | + | 0.778368i | ||||
\(328\) | 1.10286 | − | 1.91022i | 0.0608954 | − | 0.105474i | ||||
\(329\) | −2.99991 | − | 5.19600i | −0.165391 | − | 0.286465i | ||||
\(330\) | 7.17151 | + | 17.5833i | 0.394779 | + | 0.967929i | ||||
\(331\) | 11.1119 | + | 19.2463i | 0.610764 | + | 1.05787i | 0.991112 | + | 0.133030i | \(0.0424707\pi\) |
−0.380348 | + | 0.924843i | \(0.624196\pi\) | |||||||
\(332\) | 6.18069 | + | 10.7053i | 0.339210 | + | 0.587528i | ||||
\(333\) | 11.3429 | − | 7.50286i | 0.621585 | − | 0.411154i | ||||
\(334\) | 6.64135 | + | 11.5032i | 0.363399 | + | 0.629425i | ||||
\(335\) | −23.2635 | − | 13.4312i | −1.27102 | − | 0.733824i | ||||
\(336\) | 7.37377 | − | 31.2946i | 0.402272 | − | 1.70726i | ||||
\(337\) | − | 31.7148i | − | 1.72762i | −0.503821 | − | 0.863808i | \(-0.668073\pi\) | ||
0.503821 | − | 0.863808i | \(-0.331927\pi\) | |||||||
\(338\) | 7.90113 | + | 23.8025i | 0.429765 | + | 1.29469i | ||||
\(339\) | 12.8781 | − | 3.87381i | 0.699445 | − | 0.210397i | ||||
\(340\) | −8.36903 | − | 4.83186i | −0.453874 | − | 0.262045i | ||||
\(341\) | 6.57541 | + | 3.00394i | 0.356079 | + | 0.162672i | ||||
\(342\) | −9.46493 | + | 18.9697i | −0.511805 | + | 1.02576i | ||||
\(343\) | 13.1632i | 0.710747i | ||||||||
\(344\) | 1.69964 | − | 0.981288i | 0.0916385 | − | 0.0529075i | ||||
\(345\) | −11.0467 | + | 11.7395i | −0.594733 | + | 0.632033i | ||||
\(346\) | 25.7074 | 1.38204 | ||||||||
\(347\) | −1.34141 | − | 2.32338i | −0.0720105 | − | 0.124726i | 0.827772 | − | 0.561065i | \(-0.189608\pi\) |
−0.899782 | + | 0.436339i | \(0.856275\pi\) | |||||||
\(348\) | 25.2614 | + | 5.95221i | 1.35415 | + | 0.319072i | ||||
\(349\) | 1.10768 | + | 0.639520i | 0.0592928 | + | 0.0342327i | 0.529353 | − | 0.848401i | \(-0.322435\pi\) |
−0.470061 | + | 0.882634i | \(0.655768\pi\) | |||||||
\(350\) | − | 16.5023i | − | 0.882083i | ||||||
\(351\) | −18.0454 | − | 5.03622i | −0.963192 | − | 0.268814i | ||||
\(352\) | −2.38248 | − | 24.9853i | −0.126986 | − | 1.33172i | ||||
\(353\) | 10.2087 | + | 5.89397i | 0.543352 | + | 0.313704i | 0.746436 | − | 0.665457i | \(-0.231763\pi\) |
−0.203084 | + | 0.979161i | \(0.565097\pi\) | |||||||
\(354\) | 8.08147 | − | 34.2981i | 0.429526 | − | 1.82292i | ||||
\(355\) | −3.01153 | − | 5.21612i | −0.159835 | − | 0.276843i | ||||
\(356\) | 15.5367i | 0.823444i | ||||||||
\(357\) | 17.1235 | + | 16.1129i | 0.906272 | + | 0.852787i | ||||
\(358\) | −35.7970 | + | 20.6674i | −1.89193 | + | 1.09231i | ||||
\(359\) | 18.0155 | 0.950822 | 0.475411 | − | 0.879764i | \(-0.342299\pi\) | ||||
0.475411 | + | 0.879764i | \(0.342299\pi\) | |||||||
\(360\) | −1.23166 | + | 2.46850i | −0.0649142 | + | 0.130102i | ||||
\(361\) | −2.79130 | + | 4.83468i | −0.146911 | + | 0.254457i | ||||
\(362\) | 8.81384 | − | 15.2660i | 0.463245 | − | 0.802364i | ||||
\(363\) | −8.83744 | − | 16.8790i | −0.463845 | − | 0.885916i | ||||
\(364\) | 25.5964 | + | 2.60826i | 1.34162 | + | 0.136710i | ||||
\(365\) | −18.4919 | −0.967911 | ||||||||
\(366\) | −2.33000 | + | 9.88861i | −0.121791 | + | 0.516886i | ||||
\(367\) | −2.71701 | + | 4.70601i | −0.141827 | + | 0.245651i | −0.928185 | − | 0.372120i | \(-0.878631\pi\) |
0.786358 | + | 0.617771i | \(0.211964\pi\) | |||||||
\(368\) | 21.0681 | − | 12.1637i | 1.09825 | − | 0.634075i | ||||
\(369\) | −10.2839 | + | 6.80242i | −0.535360 | + | 0.354120i | ||||
\(370\) | 12.9777 | − | 7.49269i | 0.674680 | − | 0.389526i | ||||
\(371\) | −18.7811 | − | 32.5297i | −0.975064 | − | 1.68886i | ||||
\(372\) | −1.87245 | − | 6.22480i | −0.0970821 | − | 0.322741i | ||||
\(373\) | 24.2949 | − | 14.0267i | 1.25794 | − | 0.726273i | 0.285268 | − | 0.958448i | \(-0.407917\pi\) |
0.972674 | + | 0.232175i | \(0.0745841\pi\) | |||||||
\(374\) | 19.0630 | + | 8.70880i | 0.985722 | + | 0.450321i | ||||
\(375\) | −4.80814 | + | 20.4059i | −0.248291 | + | 1.05376i | ||||
\(376\) | − | 0.776929i | − | 0.0400671i | ||||||
\(377\) | 3.18085 | − | 31.2156i | 0.163822 | − | 1.60768i | ||||
\(378\) | −26.5798 | + | 31.9300i | −1.36712 | + | 1.64230i | ||||
\(379\) | −12.6903 | + | 21.9802i | −0.651856 | + | 1.12905i | 0.330817 | + | 0.943695i | \(0.392676\pi\) |
−0.982672 | + | 0.185352i | \(0.940658\pi\) | |||||||
\(380\) | −5.40346 | + | 9.35906i | −0.277192 | + | 0.480110i | ||||
\(381\) | 4.58510 | + | 4.31451i | 0.234902 | + | 0.221039i | ||||
\(382\) | 26.7348i | 1.36787i | ||||||||
\(383\) | −16.7318 | + | 9.66011i | −0.854955 | + | 0.493609i | −0.862320 | − | 0.506364i | \(-0.830989\pi\) |
0.00736430 | + | 0.999973i | \(0.497656\pi\) | |||||||
\(384\) | 5.04672 | − | 5.36323i | 0.257539 | − | 0.273691i | ||||
\(385\) | −2.23573 | − | 23.4463i | −0.113943 | − | 1.19493i | ||||
\(386\) | −35.2104 | + | 20.3287i | −1.79216 | + | 1.03471i | ||||
\(387\) | −10.9506 | + | 0.666527i | −0.556652 | + | 0.0338815i | ||||
\(388\) | 10.8881 | − | 18.8587i | 0.552759 | − | 0.957407i | ||||
\(389\) | − | 2.53818i | − | 0.128691i | −0.997928 | − | 0.0643455i | \(-0.979504\pi\) | ||
0.997928 | − | 0.0643455i | \(-0.0204960\pi\) | |||||||
\(390\) | −19.5101 | − | 6.74712i | −0.987932 | − | 0.341654i | ||||
\(391\) | 17.7907i | 0.899714i | ||||||||
\(392\) | −2.73060 | + | 4.72954i | −0.137916 | + | 0.238878i | ||||
\(393\) | −14.6556 | − | 3.45322i | −0.739278 | − | 0.174192i | ||||
\(394\) | −3.23361 | − | 5.60077i | −0.162907 | − | 0.282163i | ||||
\(395\) | −9.84334 | −0.495272 | ||||||||
\(396\) | −6.15903 | + | 15.9865i | −0.309503 | + | 0.803351i | ||||
\(397\) | −1.96766 | − | 3.40809i | −0.0987542 | − | 0.171047i | 0.812415 | − | 0.583080i | \(-0.198152\pi\) |
−0.911169 | + | 0.412032i | \(0.864819\pi\) | |||||||
\(398\) | 7.25545 | 0.363683 | ||||||||
\(399\) | 18.0191 | − | 19.1492i | 0.902081 | − | 0.958657i | ||||
\(400\) | 4.62224 | − | 8.00595i | 0.231112 | − | 0.400297i | ||||
\(401\) | 13.8961 | + | 8.02294i | 0.693940 | + | 0.400646i | 0.805086 | − | 0.593158i | \(-0.202119\pi\) |
−0.111147 | + | 0.993804i | \(0.535452\pi\) | |||||||
\(402\) | −15.0896 | − | 50.1641i | −0.752601 | − | 2.50196i | ||||
\(403\) | −7.16924 | + | 3.21923i | −0.357125 | + | 0.160361i | ||||
\(404\) | −7.22698 | −0.359556 | ||||||||
\(405\) | 12.3215 | − | 9.27354i | 0.612261 | − | 0.460806i | ||||
\(406\) | −60.2579 | − | 34.7899i | −2.99055 | − | 1.72659i | ||||
\(407\) | −12.2484 | + | 8.71960i | −0.607130 | + | 0.432214i | ||||
\(408\) | 0.877037 | + | 2.91563i | 0.0434198 | + | 0.144345i | ||||
\(409\) | 6.57086 | − | 3.79369i | 0.324908 | − | 0.187586i | −0.328670 | − | 0.944445i | \(-0.606600\pi\) |
0.653578 | + | 0.756859i | \(0.273267\pi\) | |||||||
\(410\) | −11.7662 | + | 6.79320i | −0.581090 | + | 0.335492i | ||||
\(411\) | 2.21653 | − | 0.666744i | 0.109333 | − | 0.0328881i | ||||
\(412\) | −12.4907 | − | 21.6345i | −0.615371 | − | 1.06585i | ||||
\(413\) | −21.8523 | + | 37.8493i | −1.07528 | + | 1.86244i | ||||
\(414\) | −31.3770 | + | 1.90981i | −1.54210 | + | 0.0938620i | ||||
\(415\) | 12.3016i | 0.603859i | ||||||||
\(416\) | 22.1248 | + | 15.9677i | 1.08476 | + | 0.782880i | ||||
\(417\) | 15.2498 | − | 4.58722i | 0.746787 | − | 0.224637i | ||||
\(418\) | 9.73903 | − | 21.3181i | 0.476352 | − | 1.04270i | ||||
\(419\) | 1.76546 | + | 1.01929i | 0.0862484 | + | 0.0497955i | 0.542504 | − | 0.840053i | \(-0.317476\pi\) |
−0.456256 | + | 0.889849i | \(0.650810\pi\) | |||||||
\(420\) | −14.5133 | + | 15.4235i | −0.708176 | + | 0.752591i | ||||
\(421\) | −17.8359 | −0.869267 | −0.434633 | − | 0.900607i | \(-0.643122\pi\) | ||||
−0.434633 | + | 0.900607i | \(0.643122\pi\) | |||||||
\(422\) | 16.0487 | − | 9.26570i | 0.781237 | − | 0.451047i | ||||
\(423\) | −1.93902 | + | 3.88620i | −0.0942783 | + | 0.188953i | ||||
\(424\) | − | 4.86399i | − | 0.236216i | ||||||
\(425\) | 3.38026 | + | 5.85478i | 0.163967 | + | 0.283999i | ||||
\(426\) | 2.69378 | − | 11.4325i | 0.130514 | − | 0.553907i | ||||
\(427\) | 6.30032 | − | 10.9125i | 0.304894 | − | 0.528092i | ||||
\(428\) | −22.7879 | −1.10149 | ||||||||
\(429\) | 20.1290 | + | 4.88081i | 0.971839 | + | 0.235648i | ||||
\(430\) | −12.0887 | −0.582968 | ||||||||
\(431\) | −16.4501 | + | 28.4924i | −0.792373 | + | 1.37243i | 0.132121 | + | 0.991234i | \(0.457821\pi\) |
−0.924494 | + | 0.381197i | \(0.875512\pi\) | |||||||
\(432\) | −21.8385 | + | 8.04567i | −1.05071 | + | 0.387098i | ||||
\(433\) | 1.81721 | + | 3.14751i | 0.0873297 | + | 0.151259i | 0.906382 | − | 0.422460i | \(-0.138833\pi\) |
−0.819052 | + | 0.573719i | \(0.805500\pi\) | |||||||
\(434\) | 17.4272i | 0.836532i | ||||||||
\(435\) | 18.8094 | + | 17.6994i | 0.901844 | + | 0.848621i | ||||
\(436\) | −12.4494 | + | 7.18768i | −0.596219 | + | 0.344227i | ||||
\(437\) | 19.8953 | 0.951720 | ||||||||
\(438\) | −26.2623 | − | 24.7124i | −1.25486 | − | 1.18080i | ||||
\(439\) | −3.84060 | − | 2.21737i | −0.183302 | − | 0.105829i | 0.405541 | − | 0.914077i | \(-0.367083\pi\) |
−0.588843 | + | 0.808247i | \(0.700416\pi\) | |||||||
\(440\) | 1.26733 | − | 2.77410i | 0.0604176 | − | 0.132250i | ||||
\(441\) | 25.4622 | − | 16.8422i | 1.21248 | − | 0.802012i | ||||
\(442\) | −20.7845 | + | 9.33295i | −0.988620 | + | 0.443923i | ||||
\(443\) | − | 18.2152i | − | 0.865432i | −0.901530 | − | 0.432716i | \(-0.857555\pi\) | ||
0.901530 | − | 0.432716i | \(-0.142445\pi\) | |||||||
\(444\) | 13.1591 | + | 3.10060i | 0.624502 | + | 0.147148i | ||||
\(445\) | −7.73075 | + | 13.3901i | −0.366473 | + | 0.634749i | ||||
\(446\) | −7.96708 | − | 13.7994i | −0.377252 | − | 0.653420i | ||||
\(447\) | −3.99490 | − | 13.2807i | −0.188952 | − | 0.628156i | ||||
\(448\) | 20.2476 | − | 11.6899i | 0.956609 | − | 0.552298i | ||||
\(449\) | 4.80448 | − | 2.77387i | 0.226737 | − | 0.130907i | −0.382329 | − | 0.924026i | \(-0.624878\pi\) |
0.609066 | + | 0.793120i | \(0.291544\pi\) | |||||||
\(450\) | −9.96308 | + | 6.59019i | −0.469664 | + | 0.310665i | ||||
\(451\) | 11.1049 | − | 7.90557i | 0.522910 | − | 0.372259i | ||||
\(452\) | 11.5777 | + | 6.68436i | 0.544567 | + | 0.314406i | ||||
\(453\) | 5.73901 | − | 24.3566i | 0.269642 | − | 1.14437i | ||||
\(454\) | 9.79974 | 0.459925 | ||||||||
\(455\) | 20.7620 | + | 14.9841i | 0.973338 | + | 0.702467i | ||||
\(456\) | 3.26055 | − | 0.980788i | 0.152689 | − | 0.0459296i | ||||
\(457\) | −22.4480 | − | 12.9603i | −1.05007 | − | 0.606259i | −0.127403 | − | 0.991851i | \(-0.540664\pi\) |
−0.922670 | + | 0.385592i | \(0.873997\pi\) | |||||||
\(458\) | −17.8809 | + | 30.9706i | −0.835519 | + | 1.44716i | ||||
\(459\) | 2.88975 | − | 16.7729i | 0.134882 | − | 0.782890i | ||||
\(460\) | −16.0245 | −0.747145 | ||||||||
\(461\) | 8.83315 | + | 15.2995i | 0.411401 | + | 0.712567i | 0.995043 | − | 0.0994436i | \(-0.0317063\pi\) |
−0.583642 | + | 0.812011i | \(0.698373\pi\) | |||||||
\(462\) | 28.1581 | − | 36.2863i | 1.31004 | − | 1.68819i | ||||
\(463\) | −30.0204 | −1.39517 | −0.697583 | − | 0.716504i | \(-0.745741\pi\) | ||||
−0.697583 | + | 0.716504i | \(0.745741\pi\) | |||||||
\(464\) | −19.4891 | − | 33.7561i | −0.904758 | − | 1.56709i | ||||
\(465\) | 1.48359 | − | 6.29644i | 0.0688001 | − | 0.291990i | ||||
\(466\) | −24.5211 | + | 42.4718i | −1.13592 | + | 1.96747i | ||||
\(467\) | 18.9378i | 0.876335i | 0.898893 | + | 0.438167i | \(0.144372\pi\) | ||||
−0.898893 | + | 0.438167i | \(0.855628\pi\) | |||||||
\(468\) | −8.64722 | − | 16.4952i | −0.399718 | − | 0.762490i | ||||
\(469\) | 64.9721i | 3.00013i | ||||||||
\(470\) | −2.39279 | + | 4.14443i | −0.110371 | + | 0.191168i | ||||
\(471\) | 37.3101 | + | 8.79118i | 1.71916 | + | 0.405076i | ||||
\(472\) | −4.90118 | + | 2.82970i | −0.225595 | + | 0.130247i | ||||
\(473\) | 12.0740 | − | 1.15132i | 0.555164 | − | 0.0529378i | ||||
\(474\) | −13.9795 | − | 13.1545i | −0.642102 | − | 0.604207i | ||||
\(475\) | 6.54739 | − | 3.78014i | 0.300415 | − | 0.173445i | ||||
\(476\) | 23.3737i | 1.07133i | ||||||||
\(477\) | −12.1393 | + | 24.3296i | −0.555819 | + | 1.11398i | ||||
\(478\) | −10.0088 | + | 17.3358i | −0.457794 | + | 0.792922i | ||||
\(479\) | 19.8678 | − | 34.4121i | 0.907785 | − | 1.57233i | 0.0906509 | − | 0.995883i | \(-0.471105\pi\) |
0.817134 | − | 0.576447i | \(-0.195561\pi\) | |||||||
\(480\) | −21.5072 | + | 6.46948i | −0.981667 | + | 0.295290i | ||||
\(481\) | 1.65695 | − | 16.2607i | 0.0755506 | − | 0.741423i | ||||
\(482\) | 26.3241i | 1.19903i | ||||||||
\(483\) | 37.9495 | + | 8.94184i | 1.72676 | + | 0.406868i | ||||
\(484\) | 6.19939 | − | 17.8967i | 0.281791 | − | 0.813486i | ||||
\(485\) | 18.7675 | − | 10.8354i | 0.852186 | − | 0.492010i | ||||
\(486\) | 29.8921 | + | 3.29603i | 1.35593 | + | 0.149511i | ||||
\(487\) | −12.8327 | − | 22.2269i | −0.581505 | − | 1.00720i | −0.995301 | − | 0.0968261i | \(-0.969131\pi\) |
0.413797 | − | 0.910369i | \(-0.364202\pi\) | |||||||
\(488\) | 1.41308 | − | 0.815840i | 0.0639670 | − | 0.0369314i | ||||
\(489\) | 0.866896 | + | 2.88192i | 0.0392024 | + | 0.130325i | ||||
\(490\) | 29.1321 | − | 16.8194i | 1.31605 | − | 0.759824i | ||||
\(491\) | 15.8918 | − | 27.5254i | 0.717186 | − | 1.24220i | −0.244925 | − | 0.969542i | \(-0.578763\pi\) |
0.962110 | − | 0.272660i | \(-0.0879034\pi\) | |||||||
\(492\) | −11.9306 | − | 2.81114i | −0.537872 | − | 0.126736i | ||||
\(493\) | 28.5049 | 1.28380 | ||||||||
\(494\) | 10.4370 | + | 23.2433i | 0.469584 | + | 1.04577i | ||||
\(495\) | −13.2626 | + | 10.7131i | −0.596110 | + | 0.481517i | ||||
\(496\) | −4.88131 | + | 8.45467i | −0.219177 | + | 0.379626i | ||||
\(497\) | −7.28399 | + | 12.6162i | −0.326732 | + | 0.565916i | ||||
\(498\) | −16.4396 | + | 17.4707i | −0.736678 | + | 0.782881i | ||||
\(499\) | −6.35324 | −0.284410 | −0.142205 | − | 0.989837i | \(-0.545419\pi\) | ||||
−0.142205 | + | 0.989837i | \(0.545419\pi\) | |||||||
\(500\) | −18.0488 | + | 10.4205i | −0.807165 | + | 0.466017i | ||||
\(501\) | −8.17230 | + | 8.68484i | −0.365111 | + | 0.388010i | ||||
\(502\) | − | 4.93701i | − | 0.220350i | ||||||
\(503\) | −15.1946 | − | 26.3178i | −0.677492 | − | 1.17345i | −0.975734 | − | 0.218960i | \(-0.929733\pi\) |
0.298242 | − | 0.954490i | \(-0.403600\pi\) | |||||||
\(504\) | 6.66018 | − | 0.405382i | 0.296668 | − | 0.0180571i | ||||
\(505\) | −6.22845 | − | 3.59600i | −0.277162 | − | 0.160020i | ||||
\(506\) | 34.5959 | − | 3.29890i | 1.53797 | − | 0.146654i | ||||
\(507\) | −18.4209 | + | 12.9488i | −0.818101 | + | 0.575075i | ||||
\(508\) | 6.25869i | 0.277685i | ||||||||
\(509\) | −7.90008 | − | 4.56111i | −0.350165 | − | 0.202168i | 0.314593 | − | 0.949227i | \(-0.398132\pi\) |
−0.664758 | + | 0.747059i | \(0.731465\pi\) | |||||||
\(510\) | 4.30113 | − | 18.2542i | 0.190457 | − | 0.808309i | ||||
\(511\) | 22.3632 | + | 38.7342i | 0.989290 | + | 1.71350i | ||||
\(512\) | 29.0873 | 1.28549 | ||||||||
\(513\) | −18.7570 | − | 3.23160i | −0.828143 | − | 0.142678i | ||||
\(514\) | 7.92808 | − | 4.57728i | 0.349693 | − | 0.201895i | ||||
\(515\) | − | 24.8604i | − | 1.09548i | ||||||
\(516\) | −7.94258 | − | 7.47384i | −0.349653 | − | 0.329018i | ||||
\(517\) | 1.99517 | − | 4.36729i | 0.0877475 | − | 0.192073i | ||||
\(518\) | −31.3893 | − | 18.1226i | −1.37916 | − | 0.796261i | ||||
\(519\) | 6.64840 | + | 22.1020i | 0.291832 | + | 0.970171i | ||||
\(520\) | 1.35816 | + | 3.02463i | 0.0595592 | + | 0.132639i | ||||
\(521\) | − | 1.86793i | − | 0.0818355i | −0.999163 | − | 0.0409178i | \(-0.986972\pi\) | ||
0.999163 | − | 0.0409178i | \(-0.0130282\pi\) | |||||||
\(522\) | 3.05997 | + | 50.2734i | 0.133931 | + | 2.20041i | ||||
\(523\) | 10.4710 | + | 6.04544i | 0.457865 | + | 0.264349i | 0.711146 | − | 0.703044i | \(-0.248176\pi\) |
−0.253281 | + | 0.967393i | \(0.581510\pi\) | |||||||
\(524\) | −7.48400 | − | 12.9627i | −0.326940 | − | 0.566277i | ||||
\(525\) | 14.1879 | − | 4.26778i | 0.619209 | − | 0.186261i | ||||
\(526\) | 0.0425191 | + | 0.0736453i | 0.00185392 | + | 0.00321109i | ||||
\(527\) | −3.56972 | − | 6.18293i | −0.155499 | − | 0.269333i | ||||
\(528\) | 23.8244 | − | 9.71699i | 1.03682 | − | 0.422878i | ||||
\(529\) | 3.25033 | + | 5.62974i | 0.141319 | + | 0.244771i | ||||
\(530\) | −14.9801 | + | 25.9463i | −0.650695 | + | 1.12704i | ||||
\(531\) | 31.5779 | − | 1.92204i | 1.37036 | − | 0.0834092i | ||||
\(532\) | 26.1387 | 1.13326 | ||||||||
\(533\) | −1.50227 | + | 14.7426i | −0.0650704 | + | 0.638574i | ||||
\(534\) | −28.8735 | + | 8.68531i | −1.24948 | + | 0.375850i | ||||
\(535\) | −19.6394 | − | 11.3388i | −0.849084 | − | 0.490219i | ||||
\(536\) | −4.20668 | + | 7.28618i | −0.181701 | + | 0.314715i | ||||
\(537\) | −27.0266 | − | 25.4316i | −1.16628 | − | 1.09745i | ||||
\(538\) | 5.88024i | 0.253515i | ||||||||
\(539\) | −27.4949 | + | 19.5735i | −1.18429 | + | 0.843092i | ||||
\(540\) | 15.1077 | + | 2.60286i | 0.650131 | + | 0.112009i | ||||
\(541\) | − | 19.4924i | − | 0.838045i | −0.907976 | − | 0.419023i | \(-0.862373\pi\) | ||
0.907976 | − | 0.419023i | \(-0.137627\pi\) | |||||||
\(542\) | −8.09851 | + | 4.67568i | −0.347861 | + | 0.200838i | ||||
\(543\) | 15.4044 | + | 3.62965i | 0.661066 | + | 0.155763i | ||||
\(544\) | −12.3937 | + | 21.4665i | −0.531374 | + | 0.920368i | ||||
\(545\) | −14.3058 | −0.612792 | ||||||||
\(546\) | 9.46164 | + | 49.0266i | 0.404921 | + | 2.09815i | ||||
\(547\) | 9.55999i | 0.408756i | 0.978892 | + | 0.204378i | \(0.0655171\pi\) | ||||
−0.978892 | + | 0.204378i | \(0.934483\pi\) | |||||||
\(548\) | 1.99270 | + | 1.15048i | 0.0851238 | + | 0.0491462i | ||||
\(549\) | −9.10434 | + | 0.554149i | −0.388564 | + | 0.0236505i | ||||
\(550\) | 10.7584 | − | 7.65892i | 0.458742 | − | 0.326577i | ||||
\(551\) | − | 31.8770i | − | 1.35800i | ||||||
\(552\) | 3.67683 | + | 3.45984i | 0.156496 | + | 0.147261i | ||||
\(553\) | 11.9041 | + | 20.6184i | 0.506212 | + | 0.876785i | ||||
\(554\) | − | 37.0644i | − | 1.57472i | ||||||
\(555\) | 9.79813 | + | 9.21989i | 0.415907 | + | 0.391362i | ||||
\(556\) | 13.7098 | + | 7.91537i | 0.581426 | + | 0.335686i | ||||
\(557\) | 1.16163 | − | 2.01200i | 0.0492199 | − | 0.0852513i | −0.840366 | − | 0.542020i | \(-0.817660\pi\) |
0.889586 | + | 0.456768i | \(0.150993\pi\) | |||||||
\(558\) | 10.5215 | − | 6.95956i | 0.445410 | − | 0.294622i | ||||
\(559\) | −7.71632 | + | 10.6917i | −0.326365 | + | 0.452212i | ||||
\(560\) | 31.8069 | 1.34409 | ||||||||
\(561\) | −2.55739 | + | 18.6417i | −0.107973 | + | 0.787052i | ||||
\(562\) | 6.25041 | − | 10.8260i | 0.263658 | − | 0.456669i | ||||
\(563\) | −4.14745 | − | 7.18359i | −0.174794 | − | 0.302752i | 0.765296 | − | 0.643679i | \(-0.222593\pi\) |
−0.940090 | + | 0.340926i | \(0.889259\pi\) | |||||||
\(564\) | −4.13442 | + | 1.24365i | −0.174090 | + | 0.0523673i | ||||
\(565\) | 6.65201 | + | 11.5216i | 0.279852 | + | 0.484718i | ||||
\(566\) | −26.3437 | + | 15.2095i | −1.10731 | + | 0.639304i | ||||
\(567\) | −34.3259 | − | 14.5944i | −1.44155 | − | 0.612908i | ||||
\(568\) | −1.63370 | + | 0.943218i | −0.0685486 | + | 0.0395765i | ||||
\(569\) | −19.3951 | + | 33.5933i | −0.813086 | + | 1.40831i | 0.0976083 | + | 0.995225i | \(0.468881\pi\) |
−0.910694 | + | 0.413081i | \(0.864453\pi\) | |||||||
\(570\) | −20.4136 | − | 4.80994i | −0.855032 | − | 0.201466i | ||||
\(571\) | 3.30522i | 0.138319i | 0.997606 | + | 0.0691596i | \(0.0220318\pi\) | ||||
−0.997606 | + | 0.0691596i | \(0.977968\pi\) | |||||||
\(572\) | 10.1792 | + | 17.8978i | 0.425614 | + | 0.748344i | ||||
\(573\) | −22.9853 | + | 6.91410i | −0.960226 | + | 0.288841i | ||||
\(574\) | 28.4589 | + | 16.4307i | 1.18785 | + | 0.685805i | ||||
\(575\) | 9.70845 | + | 5.60518i | 0.404870 | + | 0.233752i | ||||
\(576\) | −15.1436 | − | 7.55589i | −0.630982 | − | 0.314829i | ||||
\(577\) | −3.78483 | −0.157565 | −0.0787824 | − | 0.996892i | \(-0.525103\pi\) | ||||
−0.0787824 | + | 0.996892i | \(0.525103\pi\) | |||||||
\(578\) | 6.04915 | + | 10.4774i | 0.251611 | + | 0.435804i | ||||
\(579\) | −26.5837 | − | 25.0149i | −1.10478 | − | 1.03958i | ||||
\(580\) | 25.6750i | 1.06610i | ||||||||
\(581\) | 25.7675 | − | 14.8769i | 1.06902 | − | 0.617198i | ||||
\(582\) | 41.1339 | + | 9.69215i | 1.70505 | + | 0.401753i | ||||
\(583\) | 12.4908 | − | 27.3415i | 0.517317 | − | 1.13237i | ||||
\(584\) | 5.79171i | 0.239663i | ||||||||
\(585\) | 0.755198 | − | 18.5188i | 0.0312236 | − | 0.765657i | ||||
\(586\) | 61.4784 | 2.53965 | ||||||||
\(587\) | −4.57662 | − | 2.64231i | −0.188897 | − | 0.109060i | 0.402569 | − | 0.915390i | \(-0.368117\pi\) |
−0.591466 | + | 0.806330i | \(0.701451\pi\) | |||||||
\(588\) | 29.5392 | + | 6.96015i | 1.21817 | + | 0.287032i | ||||
\(589\) | −6.91436 | + | 3.99201i | −0.284901 | + | 0.164488i | ||||
\(590\) | 34.8596 | 1.43515 | ||||||||
\(591\) | 3.97901 | − | 4.22856i | 0.163675 | − | 0.173940i | ||||
\(592\) | −10.1522 | − | 17.5841i | −0.417252 | − | 0.722701i | ||||
\(593\) | −16.7919 | −0.689559 | −0.344779 | − | 0.938684i | \(-0.612046\pi\) | ||||
−0.344779 | + | 0.938684i | \(0.612046\pi\) | |||||||
\(594\) | −33.1524 | − | 2.50926i | −1.36026 | − | 0.102956i | ||||
\(595\) | −11.6303 | + | 20.1442i | −0.476795 | + | 0.825832i | ||||
\(596\) | 6.89330 | − | 11.9396i | 0.282361 | − | 0.489063i | ||||
\(597\) | 1.87639 | + | 6.23789i | 0.0767955 | + | 0.255300i | ||||
\(598\) | −22.1097 | + | 30.6352i | −0.904132 | + | 1.25276i | ||||
\(599\) | − | 25.7279i | − | 1.05121i | −0.850727 | − | 0.525607i | \(-0.823838\pi\) | ||
0.850727 | − | 0.525607i | \(-0.176162\pi\) | |||||||
\(600\) | 1.86739 | + | 0.440004i | 0.0762361 | + | 0.0179631i | ||||
\(601\) | 32.7717 | + | 18.9207i | 1.33678 | + | 0.771793i | 0.986329 | − | 0.164787i | \(-0.0526935\pi\) |
0.350455 | + | 0.936579i | \(0.386027\pi\) | |||||||
\(602\) | 14.6195 | + | 25.3217i | 0.595845 | + | 1.03203i | ||||
\(603\) | 39.2263 | − | 25.9467i | 1.59742 | − | 1.05663i | ||||
\(604\) | 21.5430 | − | 12.4379i | 0.876574 | − | 0.506090i | ||||
\(605\) | 14.2479 | − | 12.3393i | 0.579259 | − | 0.501663i | ||||
\(606\) | −4.04001 | − | 13.4307i | −0.164114 | − | 0.545584i | ||||
\(607\) | 15.9973 | − | 9.23603i | 0.649309 | − | 0.374879i | −0.138882 | − | 0.990309i | \(-0.544351\pi\) |
0.788192 | + | 0.615430i | \(0.211018\pi\) | |||||||
\(608\) | 24.0059 | + | 13.8598i | 0.973568 | + | 0.562090i | ||||
\(609\) | 14.3269 | − | 60.8041i | 0.580557 | − | 2.46391i | ||||
\(610\) | −10.0505 | −0.406933 | ||||||||
\(611\) | 2.13816 | + | 4.76170i | 0.0865008 | + | 0.192638i | ||||
\(612\) | 14.1116 | − | 9.33429i | 0.570428 | − | 0.377316i | ||||
\(613\) | 5.19968 | + | 3.00204i | 0.210013 | + | 0.121251i | 0.601318 | − | 0.799010i | \(-0.294643\pi\) |
−0.391304 | + | 0.920261i | \(0.627976\pi\) | |||||||
\(614\) | −48.0030 | − | 27.7145i | −1.93724 | − | 1.11847i | ||||
\(615\) | −8.88341 | − | 8.35915i | −0.358214 | − | 0.337073i | ||||
\(616\) | −7.34343 | + | 0.700234i | −0.295875 | + | 0.0282132i | ||||
\(617\) | 7.05118 | − | 4.07100i | 0.283870 | − | 0.163892i | −0.351304 | − | 0.936261i | \(-0.614262\pi\) |
0.635174 | + | 0.772369i | \(0.280928\pi\) | |||||||
\(618\) | 33.2232 | − | 35.3068i | 1.33643 | − | 1.42025i | ||||
\(619\) | −35.5739 | −1.42984 | −0.714918 | − | 0.699208i | \(-0.753536\pi\) | ||||
−0.714918 | + | 0.699208i | \(0.753536\pi\) | |||||||
\(620\) | 5.56911 | − | 3.21532i | 0.223661 | − | 0.129131i | ||||
\(621\) | −9.75662 | − | 26.4826i | −0.391520 | − | 1.06271i | ||||
\(622\) | 32.1290 | + | 18.5497i | 1.28825 | + | 0.743774i | ||||
\(623\) | 37.3968 | 1.49827 | ||||||||
\(624\) | −9.14197 | + | 26.4351i | −0.365972 | + | 1.05825i | ||||
\(625\) | −10.4202 | −0.416807 | ||||||||
\(626\) | 16.7197 | − | 28.9593i | 0.668252 | − | 1.15745i | ||||
\(627\) | 20.8469 | + | 2.85993i | 0.832546 | + | 0.114214i | ||||
\(628\) | 19.0527 | + | 33.0003i | 0.760286 | + | 1.31685i | ||||
\(629\) | 14.8486 | 0.592054 | ||||||||
\(630\) | −36.7764 | − | 18.3496i | −1.46521 | − | 0.731065i | ||||
\(631\) | −4.31785 | − | 7.47874i | −0.171891 | − | 0.297724i | 0.767190 | − | 0.641420i | \(-0.221654\pi\) |
−0.939081 | + | 0.343696i | \(0.888321\pi\) | |||||||
\(632\) | 3.08296i | 0.122633i | ||||||||
\(633\) | 12.1167 | + | 11.4016i | 0.481595 | + | 0.453173i | ||||
\(634\) | −56.2429 | − | 32.4719i | −2.23369 | − | 1.28962i | ||||
\(635\) | −3.11420 | + | 5.39395i | −0.123583 | + | 0.214052i | ||||
\(636\) | −25.8837 | + | 7.78593i | −1.02635 | + | 0.308732i | ||||
\(637\) | 3.71949 | − | 36.5016i | 0.147372 | − | 1.44624i | ||||
\(638\) | −5.28562 | − | 55.4308i | −0.209260 | − | 2.19453i | ||||
\(639\) | 10.5258 | − | 0.640668i | 0.416394 | − | 0.0253444i | ||||
\(640\) | 6.30935 | + | 3.64271i | 0.249399 | + | 0.143991i | ||||
\(641\) | 1.65745 | − | 0.956932i | 0.0654655 | − | 0.0377965i | −0.466910 | − | 0.884305i | \(-0.654633\pi\) |
0.532375 | + | 0.846508i | \(0.321299\pi\) | |||||||
\(642\) | −12.7388 | − | 42.3492i | −0.502762 | − | 1.67139i | ||||
\(643\) | −9.79884 | − | 16.9721i | −0.386429 | − | 0.669314i | 0.605538 | − | 0.795817i | \(-0.292958\pi\) |
−0.991966 | + | 0.126503i | \(0.959625\pi\) | |||||||
\(644\) | 19.3792 | + | 33.5658i | 0.763648 | + | 1.32268i | ||||
\(645\) | −3.12635 | − | 10.3933i | −0.123100 | − | 0.409235i | ||||
\(646\) | −20.0456 | + | 11.5733i | −0.788684 | + | 0.455347i | ||||
\(647\) | 14.0810 | + | 8.12968i | 0.553582 | + | 0.319611i | 0.750566 | − | 0.660796i | \(-0.229781\pi\) |
−0.196983 | + | 0.980407i | \(0.563115\pi\) | |||||||
\(648\) | −2.90449 | − | 3.85913i | −0.114099 | − | 0.151601i | ||||
\(649\) | −34.8174 | + | 3.32002i | −1.36670 | + | 0.130322i | ||||
\(650\) | −1.45540 | + | 14.2827i | −0.0570854 | + | 0.560213i | ||||
\(651\) | −14.9831 | + | 4.50698i | −0.587233 | + | 0.176643i | ||||
\(652\) | −1.49585 | + | 2.59089i | −0.0585821 | + | 0.101467i | ||||
\(653\) | −33.4686 | − | 19.3231i | −1.30973 | − | 0.756171i | −0.327677 | − | 0.944790i | \(-0.606266\pi\) |
−0.982050 | + | 0.188619i | \(0.939599\pi\) | |||||||
\(654\) | −20.3171 | − | 19.1181i | −0.794461 | − | 0.747576i | ||||
\(655\) | − | 14.8956i | − | 0.582018i | ||||||
\(656\) | 9.20440 | + | 15.9425i | 0.359371 | + | 0.622449i | ||||
\(657\) | 14.4546 | − | 28.9701i | 0.563929 | − | 1.13023i | ||||
\(658\) | 11.5749 | 0.451236 | ||||||||
\(659\) | 11.0405 | + | 19.1227i | 0.430077 | + | 0.744915i | 0.996879 | − | 0.0789387i | \(-0.0251531\pi\) |
−0.566803 | + | 0.823854i | \(0.691820\pi\) | |||||||
\(660\) | −16.7910 | − | 2.30350i | −0.653588 | − | 0.0896637i | ||||
\(661\) | 2.38985 | − | 4.13934i | 0.0929545 | − | 0.161002i | −0.815799 | − | 0.578336i | \(-0.803702\pi\) |
0.908753 | + | 0.417334i | \(0.137036\pi\) | |||||||
\(662\) | −42.8741 | −1.66635 | ||||||||
\(663\) | −13.3993 | − | 15.4559i | −0.520385 | − | 0.600257i | ||||
\(664\) | 3.85287 | 0.149521 | ||||||||
\(665\) | 22.5272 | + | 13.0061i | 0.873568 | + | 0.504355i | ||||
\(666\) | 1.59398 | + | 26.1882i | 0.0617656 | + | 1.01477i | ||||
\(667\) | 40.9345 | − | 23.6335i | 1.58499 | − | 0.915094i | ||||
\(668\) | −11.8549 | −0.458678 | ||||||||
\(669\) | 9.80362 | − | 10.4185i | 0.379030 | − | 0.402802i | ||||
\(670\) | 44.8800 | − | 25.9115i | 1.73387 | − | 1.00105i | ||||
\(671\) | 10.0383 | − | 0.957206i | 0.387525 | − | 0.0369525i | ||||
\(672\) | 39.5612 | + | 37.2264i | 1.52611 | + | 1.43604i | ||||
\(673\) | 30.5284 | + | 17.6256i | 1.17678 | + | 0.679416i | 0.955268 | − | 0.295741i | \(-0.0955665\pi\) |
0.221515 | + | 0.975157i | \(0.428900\pi\) | |||||||
\(674\) | 52.9871 | + | 30.5921i | 2.04099 | + | 1.17837i | ||||
\(675\) | −8.24256 | − | 6.86144i | −0.317256 | − | 0.264097i | ||||
\(676\) | −21.9236 | − | 4.51489i | −0.843215 | − | 0.173649i | ||||
\(677\) | 1.93182 | 0.0742457 | 0.0371229 | − | 0.999311i | \(-0.488181\pi\) | ||||
0.0371229 | + | 0.999311i | \(0.488181\pi\) | |||||||
\(678\) | −5.95015 | + | 25.2527i | −0.228514 | + | 0.969824i | ||||
\(679\) | −45.3929 | − | 26.2076i | −1.74202 | − | 1.00576i | ||||
\(680\) | −2.60851 | + | 1.50603i | −0.100032 | + | 0.0577534i | ||||
\(681\) | 2.53439 | + | 8.42535i | 0.0971180 | + | 0.322860i | ||||
\(682\) | −11.3614 | + | 8.08819i | −0.435052 | + | 0.309713i | ||||
\(683\) | −5.46171 | + | 3.15332i | −0.208987 | + | 0.120658i | −0.600840 | − | 0.799369i | \(-0.705167\pi\) |
0.391854 | + | 0.920028i | \(0.371834\pi\) | |||||||
\(684\) | −10.4385 | − | 15.7810i | −0.399127 | − | 0.603401i | ||||
\(685\) | 1.14492 | + | 1.98305i | 0.0437450 | + | 0.0757685i | ||||
\(686\) | −21.9923 | − | 12.6972i | −0.839669 | − | 0.484783i | ||||
\(687\) | −31.2514 | − | 7.36359i | −1.19231 | − | 0.280939i | ||||
\(688\) | 16.3795i | 0.624462i | ||||||||
\(689\) | 13.3860 | + | 29.8108i | 0.509967 | + | 1.13570i | ||||
\(690\) | −8.95797 | − | 29.7800i | −0.341024 | − | 1.13371i | ||||
\(691\) | 18.8097 | − | 32.5793i | 0.715555 | − | 1.23938i | −0.247191 | − | 0.968967i | \(-0.579507\pi\) |
0.962745 | − | 0.270410i | \(-0.0871592\pi\) | |||||||
\(692\) | −11.4720 | + | 19.8701i | −0.436099 | + | 0.755346i | ||||
\(693\) | 38.4794 | + | 14.8248i | 1.46171 | + | 0.563146i | ||||
\(694\) | 5.17569 | 0.196466 | ||||||||
\(695\) | 7.87705 | + | 13.6435i | 0.298794 | + | 0.517526i | ||||
\(696\) | 5.54349 | − | 5.89116i | 0.210125 | − | 0.223304i | ||||
\(697\) | −13.4624 | −0.509926 | ||||||||
\(698\) | −2.13694 | + | 1.23376i | −0.0808844 | + | 0.0466986i | ||||
\(699\) | −42.8568 | − | 10.0981i | −1.62099 | − | 0.381946i | ||||
\(700\) | 12.7551 | + | 7.36417i | 0.482098 | + | 0.278339i | ||||
\(701\) | −35.6093 | −1.34494 | −0.672472 | − | 0.740123i | \(-0.734767\pi\) | ||||
−0.672472 | + | 0.740123i | \(0.734767\pi\) | |||||||
\(702\) | 25.8208 | − | 25.2912i | 0.974544 | − | 0.954554i | ||||
\(703\) | − | 16.6052i | − | 0.626277i | ||||||
\(704\) | 17.0183 | + | 7.77470i | 0.641401 | + | 0.293020i | ||||
\(705\) | −4.18200 | − | 0.985381i | −0.157503 | − | 0.0371116i | ||||
\(706\) | −19.6946 | + | 11.3707i | −0.741214 | + | 0.427940i | ||||
\(707\) | 17.3953i | 0.654218i | ||||||||
\(708\) | 22.9037 | + | 21.5520i | 0.860773 | + | 0.809974i | ||||
\(709\) | 25.8235 | + | 44.7276i | 0.969822 | + | 1.67978i | 0.696059 | + | 0.717985i | \(0.254935\pi\) |
0.273763 | + | 0.961797i | \(0.411731\pi\) | |||||||
\(710\) | 11.6197 | 0.436079 | ||||||||
\(711\) | 7.69428 | − | 15.4209i | 0.288558 | − | 0.578330i | ||||
\(712\) | 4.19380 | + | 2.42129i | 0.157169 | + | 0.0907416i | ||||
\(713\) | −10.2526 | − | 5.91934i | −0.383963 | − | 0.221681i | ||||
\(714\) | −43.4378 | + | 13.0663i | −1.62562 | + | 0.488995i | ||||
\(715\) | −0.132801 | + | 20.4899i | −0.00496648 | + | 0.766278i | ||||
\(716\) | − | 36.8914i | − | 1.37870i | ||||||
\(717\) | −17.4930 | − | 4.12177i | −0.653287 | − | 0.153930i | ||||
\(718\) | −17.3778 | + | 30.0992i | −0.648533 | + | 1.12329i | ||||
\(719\) | −10.9779 | + | 6.33810i | −0.409407 | + | 0.236371i | −0.690535 | − | 0.723299i | \(-0.742625\pi\) |
0.281128 | + | 0.959670i | \(0.409291\pi\) | |||||||
\(720\) | −12.7021 | − | 19.2031i | −0.473380 | − | 0.715658i | ||||
\(721\) | −52.0741 | + | 30.0650i | −1.93934 | + | 1.11968i | ||||
\(722\) | −5.38499 | − | 9.32707i | −0.200408 | − | 0.347118i | ||||
\(723\) | −22.6322 | + | 6.80789i | −0.841702 | + | 0.253188i | ||||
\(724\) | 7.86638 | + | 13.6250i | 0.292352 | + | 0.506368i | ||||
\(725\) | 8.98082 | − | 15.5552i | 0.333539 | − | 0.577707i | ||||
\(726\) | 36.7249 | + | 1.51643i | 1.36299 | + | 0.0562799i | ||||
\(727\) | 10.3708 | 0.384630 | 0.192315 | − | 0.981333i | \(-0.438400\pi\) | ||||
0.192315 | + | 0.981333i | \(0.438400\pi\) | |||||||
\(728\) | 4.69307 | − | 6.50271i | 0.173937 | − | 0.241006i | ||||
\(729\) | 4.89686 | + | 26.5522i | 0.181365 | + | 0.983416i | ||||
\(730\) | 17.8373 | − | 30.8951i | 0.660188 | − | 1.14348i | ||||
\(731\) | −10.3736 | − | 5.98919i | −0.383681 | − | 0.221518i | ||||
\(732\) | −6.60344 | − | 6.21374i | −0.244070 | − | 0.229666i | ||||
\(733\) | − | 1.45846i | − | 0.0538696i | −0.999637 | − | 0.0269348i | \(-0.991425\pi\) | ||
0.999637 | − | 0.0269348i | \(-0.00857465\pi\) | |||||||
\(734\) | −5.24167 | − | 9.07883i | −0.193473 | − | 0.335106i | ||||
\(735\) | 21.9946 | + | 20.6966i | 0.811283 | + | 0.763405i | ||||
\(736\) | 41.1026i | 1.51506i | ||||||||
\(737\) | −42.3578 | + | 30.1544i | −1.56027 | + | 1.11075i | ||||
\(738\) | −1.44518 | − | 23.7434i | −0.0531976 | − | 0.874006i | ||||
\(739\) | 20.8762 | + | 12.0529i | 0.767945 | + | 0.443373i | 0.832141 | − | 0.554564i | \(-0.187115\pi\) |
−0.0641961 | + | 0.997937i | \(0.520448\pi\) | |||||||
\(740\) | 13.3745i | 0.491657i | ||||||||
\(741\) | −17.2843 | + | 14.9844i | −0.634954 | + | 0.550465i | ||||
\(742\) | 72.4649 | 2.66027 | ||||||||
\(743\) | 4.88608 | − | 8.46294i | 0.179253 | − | 0.310475i | −0.762372 | − | 0.647139i | \(-0.775965\pi\) |
0.941625 | + | 0.336664i | \(0.109299\pi\) | |||||||
\(744\) | −1.97206 | − | 0.464665i | −0.0722992 | − | 0.0170355i | ||||
\(745\) | 11.8818 | − | 6.85994i | 0.435314 | − | 0.251329i | ||||
\(746\) | 54.1205i | 1.98149i | ||||||||
\(747\) | −19.2721 | − | 9.61579i | −0.705128 | − | 0.351824i | ||||
\(748\) | −15.2382 | + | 10.8480i | −0.557163 | + | 0.396643i | ||||
\(749\) | 54.8503i | 2.00419i | ||||||||
\(750\) | −29.4550 | − | 27.7167i | −1.07555 | − | 1.01207i | ||||
\(751\) | −25.8225 | + | 44.7258i | −0.942275 | + | 1.63207i | −0.181157 | + | 0.983454i | \(0.557984\pi\) |
−0.761118 | + | 0.648614i | \(0.775349\pi\) | |||||||
\(752\) | 5.61546 | + | 3.24209i | 0.204775 | + | 0.118227i | ||||
\(753\) | 4.24461 | − | 1.27680i | 0.154682 | − | 0.0465291i | ||||
\(754\) | 49.0848 | + | 35.4249i | 1.78756 | + | 1.29010i | ||||
\(755\) | 24.7554 | 0.900940 | ||||||||
\(756\) | −12.8184 | − | 34.7932i | −0.466201 | − | 1.26542i | ||||
\(757\) | 7.89389 | − | 13.6726i | 0.286908 | − | 0.496940i | −0.686162 | − | 0.727449i | \(-0.740706\pi\) |
0.973070 | + | 0.230509i | \(0.0740392\pi\) | |||||||
\(758\) | −24.4821 | − | 42.4042i | −0.889230 | − | 1.54019i | ||||
\(759\) | 11.7833 | + | 28.8907i | 0.427708 | + | 1.04867i | ||||
\(760\) | 1.68418 | + | 2.91709i | 0.0610918 | + | 0.105814i | ||||
\(761\) | 5.22100 | + | 9.04303i | 0.189261 | + | 0.327810i | 0.945004 | − | 0.327059i | \(-0.106057\pi\) |
−0.755743 | + | 0.654868i | \(0.772724\pi\) | |||||||
\(762\) | −11.6312 | + | 3.49873i | −0.421354 | + | 0.126745i | ||||
\(763\) | 17.3007 | + | 29.9657i | 0.626328 | + | 1.08483i | ||||
\(764\) | −20.6642 | − | 11.9305i | −0.747603 | − | 0.431629i | ||||
\(765\) | 16.8064 | − | 1.02295i | 0.607638 | − | 0.0369847i | ||||
\(766\) | − | 37.2726i | − | 1.34671i | ||||||
\(767\) | 22.2512 | − | 30.8313i | 0.803445 | − | 1.11325i | ||||
\(768\) | 9.72168 | + | 32.3189i | 0.350801 | + | 1.16621i | ||||
\(769\) | −24.7415 | − | 14.2845i | −0.892201 | − | 0.515113i | −0.0175394 | − | 0.999846i | \(-0.505583\pi\) |
−0.874662 | + | 0.484734i | \(0.838917\pi\) | |||||||
\(770\) | 41.3292 | + | 18.8810i | 1.48940 | + | 0.680423i | ||||
\(771\) | 5.98567 | + | 5.63242i | 0.215569 | + | 0.202847i | ||||
\(772\) | − | 36.2869i | − | 1.30600i | ||||||
\(773\) | 18.5994 | − | 10.7384i | 0.668975 | − | 0.386233i | −0.126713 | − | 0.991939i | \(-0.540443\pi\) |
0.795688 | + | 0.605706i | \(0.207109\pi\) | |||||||
\(774\) | 9.44941 | − | 18.9386i | 0.339652 | − | 0.680733i | ||||
\(775\) | −4.49874 | −0.161599 | ||||||||
\(776\) | −3.39367 | − | 5.87801i | −0.121826 | − | 0.211008i | ||||
\(777\) | 7.46312 | − | 31.6738i | 0.267738 | − | 1.13629i | ||||
\(778\) | 4.24064 | + | 2.44833i | 0.152034 | + | 0.0877771i | ||||
\(779\) | 15.0550i | 0.539401i | ||||||||
\(780\) | 13.9215 | − | 12.0690i | 0.498469 | − | 0.432141i | ||||
\(781\) | −11.6056 | + | 1.10665i | −0.415281 | + | 0.0395992i | ||||
\(782\) | −29.7236 | − | 17.1609i | −1.06291 | − | 0.613673i | ||||
\(783\) | −42.4314 | + | 15.6324i | −1.51637 | + | 0.558657i | ||||
\(784\) | −22.7893 | − | 39.4723i | −0.813905 | − | 1.40973i | ||||
\(785\) | 37.9210i | 1.35346i | ||||||||
\(786\) | 19.9062 | − | 21.1547i | 0.710032 | − | 0.754563i | ||||
\(787\) | 15.9266 | − | 9.19525i | 0.567723 | − | 0.327775i | −0.188516 | − | 0.982070i | \(-0.560368\pi\) |
0.756240 | + | 0.654295i | \(0.227034\pi\) | |||||||
\(788\) | 5.77201 | 0.205619 | ||||||||
\(789\) | −0.0523205 | + | 0.0556019i | −0.00186266 | + | 0.00197948i | ||||
\(790\) | 9.49490 | − | 16.4456i | 0.337813 | − | 0.585110i | ||||
\(791\) | 16.0892 | − | 27.8674i | 0.572067 | − | 0.990849i | ||||
\(792\) | 3.35536 | + | 4.15388i | 0.119228 | + | 0.147602i | ||||
\(793\) | −6.41533 | + | 8.88907i | −0.227815 | + | 0.315660i | ||||
\(794\) | 7.59204 | 0.269431 | ||||||||
\(795\) | −26.1815 | − | 6.16901i | −0.928563 | − | 0.218792i | ||||
\(796\) | −3.23776 | + | 5.60796i | −0.114759 | + | 0.198769i | ||||
\(797\) | 17.2948 | − | 9.98516i | 0.612614 | − | 0.353693i | −0.161374 | − | 0.986893i | \(-0.551593\pi\) |
0.773988 | + | 0.633201i | \(0.218259\pi\) | |||||||
\(798\) | 14.6120 | + | 48.5764i | 0.517260 | + | 1.71959i | ||||
\(799\) | −4.10661 | + | 2.37095i | −0.145281 | + | 0.0838783i | ||||
\(800\) | 7.80956 | + | 13.5266i | 0.276110 | + | 0.478236i | ||||
\(801\) | −14.9344 | − | 22.5779i | −0.527682 | − | 0.797752i | ||||
\(802\) | −26.8084 | + | 15.4779i | −0.946639 | + | 0.546542i | ||||
\(803\) | −14.8732 | + | 32.5565i | −0.524865 | + | 1.14889i | ||||
\(804\) | 45.5071 | + | 10.7226i | 1.60491 | + | 0.378157i | ||||
\(805\) | 38.5708i | 1.35944i | ||||||||
\(806\) | 1.53697 | − | 15.0832i | 0.0541375 | − | 0.531283i | ||||
\(807\) | −5.05555 | + | 1.52073i | −0.177964 | + | 0.0535324i | ||||
\(808\) | −1.12627 | + | 1.95077i | −0.0396222 | + | 0.0686277i | ||||
\(809\) | −24.3042 | + | 42.0960i | −0.854489 | + | 1.48002i | 0.0226301 | + | 0.999744i | \(0.492796\pi\) |
−0.877119 | + | 0.480274i | \(0.840537\pi\) | |||||||
\(810\) | 3.60830 | + | 29.5313i | 0.126783 | + | 1.03762i | ||||
\(811\) | 19.0035i | 0.667303i | 0.942697 | + | 0.333651i | \(0.108281\pi\) | ||||
−0.942697 | + | 0.333651i | \(0.891719\pi\) | |||||||
\(812\) | 53.7804 | − | 31.0501i | 1.88732 | − | 1.08964i | ||||
\(813\) | −6.11434 | − | 5.75350i | −0.214439 | − | 0.201784i | ||||
\(814\) | −2.75336 | − | 28.8748i | −0.0965052 | − | 1.01206i | ||||
\(815\) | −2.57835 | + | 1.48861i | −0.0903157 | + | 0.0521438i | ||||
\(816\) | −24.7334 | − | 5.82779i | −0.865841 | − | 0.204013i | ||||
\(817\) | −6.69769 | + | 11.6007i | −0.234323 | + | 0.405859i | ||||
\(818\) | 14.6376i | 0.511791i | ||||||||
\(819\) | −39.7038 | + | 20.8138i | −1.38736 | + | 0.727294i | ||||
\(820\) | − | 12.1259i | − | 0.423455i | ||||||
\(821\) | 3.60701 | − | 6.24752i | 0.125885 | − | 0.218040i | −0.796193 | − | 0.605042i | \(-0.793156\pi\) |
0.922079 | + | 0.387002i | \(0.126489\pi\) | |||||||
\(822\) | −1.02411 | + | 4.34639i | −0.0357201 | + | 0.151598i | ||||
\(823\) | −2.69247 | − | 4.66349i | −0.0938535 | − | 0.162559i | 0.815276 | − | 0.579073i | \(-0.196585\pi\) |
−0.909130 | + | 0.416514i | \(0.863252\pi\) | |||||||
\(824\) | −7.78634 | −0.271250 | ||||||||
\(825\) | 9.36710 | + | 7.26887i | 0.326121 | + | 0.253070i | ||||
\(826\) | −42.1575 | − | 73.0190i | −1.46685 | − | 2.54066i | ||||
\(827\) | −37.3026 | −1.29714 | −0.648569 | − | 0.761156i | \(-0.724632\pi\) | ||||
−0.648569 | + | 0.761156i | \(0.724632\pi\) | |||||||
\(828\) | 12.5259 | − | 25.1045i | 0.435305 | − | 0.872442i | ||||
\(829\) | 5.16945 | − | 8.95376i | 0.179543 | − | 0.310977i | −0.762181 | − | 0.647364i | \(-0.775872\pi\) |
0.941724 | + | 0.336387i | \(0.109205\pi\) | |||||||
\(830\) | −20.5527 | − | 11.8661i | −0.713393 | − | 0.411878i | ||||
\(831\) | 31.8662 | − | 9.58552i | 1.10543 | − | 0.332518i | ||||
\(832\) | −18.5552 | + | 8.33191i | −0.643286 | + | 0.288857i | ||||
\(833\) | 33.3319 | 1.15488 | ||||||||
\(834\) | −7.04594 | + | 29.9033i | −0.243981 | + | 1.03547i | ||||
\(835\) | −10.2169 | − | 5.89874i | −0.353571 | − | 0.204134i | ||||
\(836\) | 12.1313 | + | 17.0408i | 0.419570 | + | 0.589369i | ||||
\(837\) | 8.70454 | + | 7.24601i | 0.300873 | + | 0.250459i | ||||
\(838\) | −3.40593 | + | 1.96641i | −0.117656 | + | 0.0679286i | ||||
\(839\) | −18.7996 | + | 10.8540i | −0.649036 | + | 0.374721i | −0.788087 | − | 0.615564i | \(-0.788928\pi\) |
0.139051 | + | 0.990285i | \(0.455595\pi\) | |||||||
\(840\) | 1.90145 | + | 6.32120i | 0.0656062 | + | 0.218102i | ||||
\(841\) | −23.3665 | − | 40.4720i | −0.805743 | − | 1.39559i | ||||
\(842\) | 17.2045 | − | 29.7991i | 0.592906 | − | 1.02694i | ||||
\(843\) | 10.9242 | + | 2.57400i | 0.376249 | + | 0.0886534i | ||||
\(844\) | 16.5393i | 0.569307i | ||||||||
\(845\) | −16.6480 | − | 14.7998i | −0.572707 | − | 0.509129i | ||||
\(846\) | −4.62243 | − | 6.98822i | −0.158923 | − | 0.240260i | ||||
\(847\) | −43.0772 | − | 14.9219i | −1.48015 | − | 0.512723i | ||||
\(848\) | 35.1558 | + | 20.2972i | 1.20725 | + | 0.697009i | ||||
\(849\) | −19.8894 | − | 18.7156i | −0.682602 | − | 0.642317i | ||||
\(850\) | −13.0424 | −0.447351 | ||||||||
\(851\) | 21.3234 | − | 12.3111i | 0.730957 | − | 0.422018i | ||||
\(852\) | 7.63444 | + | 7.18389i | 0.261552 | + | 0.246116i | ||||
\(853\) | − | 3.69558i | − | 0.126534i | −0.997997 | − | 0.0632671i | \(-0.979848\pi\) | ||
0.997997 | − | 0.0632671i | \(-0.0201520\pi\) | |||||||
\(854\) | 12.1546 | + | 21.0524i | 0.415922 | + | 0.720397i | ||||
\(855\) | −1.14396 | − | 18.7946i | −0.0391226 | − | 0.642761i | ||||
\(856\) | −3.55134 | + | 6.15109i | −0.121382 | + | 0.210240i | ||||
\(857\) | −10.5639 | −0.360857 | −0.180429 | − | 0.983588i | \(-0.557748\pi\) | ||||
−0.180429 | + | 0.983588i | \(0.557748\pi\) | |||||||
\(858\) | −27.5710 | + | 28.9223i | −0.941259 | + | 0.987391i | ||||
\(859\) | −48.7450 | −1.66316 | −0.831579 | − | 0.555406i | \(-0.812563\pi\) | ||||
−0.831579 | + | 0.555406i | \(0.812563\pi\) | |||||||
\(860\) | 5.39460 | − | 9.34372i | 0.183954 | − | 0.318618i | ||||
\(861\) | −6.76639 | + | 28.7169i | −0.230598 | + | 0.978668i | ||||
\(862\) | −31.7355 | − | 54.9676i | −1.08092 | − | 1.87220i | ||||
\(863\) | 6.66363i | 0.226833i | 0.993548 | + | 0.113416i | \(0.0361794\pi\) | ||||
−0.993548 | + | 0.113416i | \(0.963821\pi\) | |||||||
\(864\) | 6.67631 | − | 38.7511i | 0.227133 | − | 1.31834i | ||||
\(865\) | −19.7739 | + | 11.4165i | −0.672332 | + | 0.388171i | ||||
\(866\) | −7.01154 | −0.238262 | ||||||||
\(867\) | −7.44358 | + | 7.91042i | −0.252797 | + | 0.268652i | ||||
\(868\) | −13.4700 | − | 7.77691i | −0.457202 | − | 0.263966i | ||||
\(869\) | −7.91710 | + | 17.3300i | −0.268569 | + | 0.587880i | ||||
\(870\) | −47.7146 | + | 14.3528i | −1.61768 | + | 0.486606i | ||||
\(871\) | 5.73014 | − | 56.2332i | 0.194158 | − | 1.90539i | ||||
\(872\) | 4.48060i | 0.151732i | ||||||||
\(873\) | 2.30511 | + | 37.8715i | 0.0780160 | + | 1.28176i | ||||
\(874\) | −19.1910 | + | 33.2398i | −0.649145 | + | 1.12435i | ||||
\(875\) | 25.0820 | + | 43.4433i | 0.847926 | + | 1.46865i | ||||
\(876\) | 30.8205 | − | 9.27096i | 1.04133 | − | 0.313237i | ||||
\(877\) | −14.0157 | + | 8.09196i | −0.473276 | + | 0.273246i | −0.717610 | − | 0.696445i | \(-0.754764\pi\) |
0.244334 | + | 0.969691i | \(0.421431\pi\) | |||||||
\(878\) | 7.40929 | − | 4.27775i | 0.250051 | − | 0.144367i | ||||
\(879\) | 15.8994 | + | 52.8562i | 0.536274 | + | 1.78280i | ||||
\(880\) | 14.7620 | + | 20.7361i | 0.497627 | + | 0.699015i | ||||
\(881\) | −38.1631 | − | 22.0335i | −1.28575 | − | 0.742326i | −0.307854 | − | 0.951434i | \(-0.599611\pi\) |
−0.977893 | + | 0.209107i | \(0.932944\pi\) | |||||||
\(882\) | 3.57814 | + | 58.7867i | 0.120482 | + | 1.97945i | ||||
\(883\) | 57.2309 | 1.92597 | 0.962986 | − | 0.269552i | \(-0.0868756\pi\) | ||||
0.962986 | + | 0.269552i | \(0.0868756\pi\) | |||||||
\(884\) | 2.06141 | − | 20.2299i | 0.0693328 | − | 0.680404i | ||||
\(885\) | 9.01532 | + | 29.9707i | 0.303047 | + | 1.00745i | ||||
\(886\) | 30.4329 | + | 17.5704i | 1.02241 | + | 0.590290i | ||||
\(887\) | −0.507853 | + | 0.879627i | −0.0170520 | + | 0.0295350i | −0.874426 | − | 0.485160i | \(-0.838761\pi\) |
0.857373 | + | 0.514695i | \(0.172095\pi\) | |||||||
\(888\) | 2.88769 | − | 3.06880i | 0.0969045 | − | 0.102982i | ||||
\(889\) | 15.0646 | 0.505252 | ||||||||
\(890\) | −14.9142 | − | 25.8321i | −0.499924 | − | 0.865894i | ||||
\(891\) | −6.41647 | − | 29.1518i | −0.214960 | − | 0.976623i | ||||
\(892\) | 14.2213 | 0.476164 | ||||||||
\(893\) | 2.65143 | + | 4.59241i | 0.0887267 | + | 0.153679i | ||||
\(894\) | 26.0420 | + | 6.13614i | 0.870976 | + | 0.205223i | ||||
\(895\) | 18.3564 | − | 31.7943i | 0.613588 | − | 1.06276i | ||||
\(896\) | − | 17.6212i | − | 0.588684i | ||||||
\(897\) | −32.0566 | − | 11.0860i | −1.07034 | − | 0.370152i | ||||
\(898\) | 10.7027i | 0.357153i | ||||||||
\(899\) | −9.48418 | + | 16.4271i | −0.316315 | + | 0.547874i | ||||
\(900\) | −0.647720 | − | 10.6417i | −0.0215907 | − | 0.354722i | ||||
\(901\) | −25.7096 | + | 14.8434i | −0.856510 | + | 0.494506i | ||||
\(902\) | 2.49632 | + | 26.1791i | 0.0831182 | + | 0.871669i | ||||
\(903\) | −17.9895 | + | 19.1178i | −0.598653 | + | 0.636199i | ||||
\(904\) | 3.60860 | − | 2.08342i | 0.120020 | − | 0.0692936i | ||||
\(905\) | 15.6566i | 0.520443i | ||||||||
\(906\) | 35.1576 | + | 33.0828i | 1.16803 | + | 1.09910i | ||||
\(907\) | 9.74671 | − | 16.8818i | 0.323634 | − | 0.560551i | −0.657601 | − | 0.753367i | \(-0.728429\pi\) |
0.981235 | + | 0.192816i | \(0.0617620\pi\) | |||||||
\(908\) | −4.37315 | + | 7.57452i | −0.145128 | + | 0.251369i | ||||
\(909\) | 10.5022 | − | 6.94682i | 0.348337 | − | 0.230412i | ||||
\(910\) | −45.0616 | + | 20.2342i | −1.49378 | + | 0.670756i | ||||
\(911\) | 22.8242i | 0.756198i | 0.925765 | + | 0.378099i | \(0.123422\pi\) | ||||
−0.925765 | + | 0.378099i | \(0.876578\pi\) | |||||||
\(912\) | −6.51720 | + | 27.6593i | −0.215806 | + | 0.915890i | ||||
\(913\) | 21.6579 | + | 9.89427i | 0.716770 | + | 0.327452i | ||||
\(914\) | 43.3067 | − | 25.0031i | 1.43246 | − | 0.827030i | ||||
\(915\) | −2.59924 | − | 8.64095i | −0.0859282 | − | 0.285661i | ||||
\(916\) | −15.9588 | − | 27.6414i | −0.527292 | − | 0.913297i | ||||
\(917\) | −31.2011 | + | 18.0140i | −1.03035 | + | 0.594873i | ||||
\(918\) | 25.2356 | + | 21.0071i | 0.832898 | + | 0.693338i | ||||
\(919\) | 20.4576 | − | 11.8112i | 0.674833 | − | 0.389615i | −0.123073 | − | 0.992398i | \(-0.539275\pi\) |
0.797905 | + | 0.602783i | \(0.205941\pi\) | |||||||
\(920\) | −2.49730 | + | 4.32546i | −0.0823337 | + | 0.142606i | ||||
\(921\) | 11.4132 | − | 48.4382i | 0.376078 | − | 1.59609i | ||||
\(922\) | −34.0819 | −1.12243 | ||||||||
\(923\) | 7.41695 | − | 10.2769i | 0.244132 | − | 0.338269i | ||||
\(924\) | 15.4811 | + | 37.9571i | 0.509292 | + | 1.24870i | ||||
\(925\) | 4.67825 | − | 8.10296i | 0.153820 | − | 0.266424i | ||||
\(926\) | 28.9577 | − | 50.1562i | 0.951609 | − | 1.64823i | ||||
\(927\) | 38.9472 | + | 19.4327i | 1.27920 | + | 0.638255i | ||||
\(928\) | 65.8561 | 2.16183 | ||||||||
\(929\) | 37.4887 | − | 21.6441i | 1.22997 | − | 0.710121i | 0.262943 | − | 0.964811i | \(-0.415307\pi\) |
0.967023 | + | 0.254690i | \(0.0819736\pi\) | |||||||
\(930\) | 9.08862 | + | 8.55225i | 0.298028 | + | 0.280439i | ||||
\(931\) | − | 37.2749i | − | 1.22164i | ||||||
\(932\) | −21.8852 | − | 37.9062i | −0.716873 | − | 1.24166i | ||||
\(933\) | −7.63900 | + | 32.4202i | −0.250090 | + | 1.06139i | ||||
\(934\) | −31.6400 | − | 18.2674i | −1.03529 | − | 0.597727i | ||||
\(935\) | −18.5305 | + | 1.76698i | −0.606013 | + | 0.0577865i | ||||
\(936\) | −5.80012 | − | 0.236530i | −0.189583 | − | 0.00773122i | ||||
\(937\) | − | 55.6524i | − | 1.81808i | −0.416704 | − | 0.909042i | \(-0.636815\pi\) | ||
0.416704 | − | 0.909042i | \(-0.363185\pi\) | |||||||
\(938\) | −108.551 | − | 62.6722i | −3.54433 | − | 2.04632i | ||||
\(939\) | 29.2218 | + | 6.88538i | 0.953618 | + | 0.224696i | ||||
\(940\) | −2.13557 | − | 3.69892i | −0.0696546 | − | 0.120645i | ||||
\(941\) | −9.25699 | −0.301769 | −0.150885 | − | 0.988551i | \(-0.548212\pi\) | ||||
−0.150885 | + | 0.988551i | \(0.548212\pi\) | |||||||
\(942\) | −50.6772 | + | 53.8555i | −1.65115 | + | 1.75471i | ||||
\(943\) | −19.3327 | + | 11.1618i | −0.629560 | + | 0.363477i | ||||
\(944\) | − | 47.2328i | − | 1.53730i | ||||||
\(945\) | 6.26507 | − | 36.3641i | 0.203803 | − | 1.18293i | ||||
\(946\) | −9.72306 | + | 21.2831i | −0.316124 | + | 0.691973i | ||||
\(947\) | 31.4410 | + | 18.1525i | 1.02170 | + | 0.589876i | 0.914595 | − | 0.404372i | \(-0.132510\pi\) |
0.107101 | + | 0.994248i | \(0.465843\pi\) | |||||||
\(948\) | 16.4059 | − | 4.93498i | 0.532840 | − | 0.160281i | ||||
\(949\) | −15.9392 | − | 35.4967i | −0.517408 | − | 1.15227i | ||||
\(950\) | 14.5853i | 0.473209i | ||||||||
\(951\) | 13.3723 | − | 56.7528i | 0.433628 | − | 1.84033i | ||||
\(952\) | 6.30922 | + | 3.64263i | 0.204483 | + | 0.118058i | ||||
\(953\) | −11.3686 | − | 19.6910i | −0.368265 | − | 0.637854i | 0.621029 | − | 0.783788i | \(-0.286715\pi\) |
−0.989294 | + | 0.145933i | \(0.953382\pi\) | |||||||
\(954\) | −28.9389 | − | 43.7499i | −0.936931 | − | 1.41646i | ||||
\(955\) | −11.8727 | − | 20.5641i | −0.384192 | − | 0.665440i | ||||
\(956\) | −8.93292 | − | 15.4723i | −0.288911 | − | 0.500409i | ||||
\(957\) | 46.2898 | − | 18.8797i | 1.49634 | − | 0.610295i | ||||
\(958\) | 38.3291 | + | 66.3879i | 1.23836 | + | 2.14490i | ||||
\(959\) | 2.76921 | − | 4.79641i | 0.0894224 | − | 0.154884i | ||||
\(960\) | 3.83980 | − | 16.2963i | 0.123929 | − | 0.525959i | ||||
\(961\) | −26.2491 | −0.846746 | ||||||||
\(962\) | 25.5690 | + | 18.4534i | 0.824378 | + | 0.594961i | ||||
\(963\) | 33.1153 | − | 21.9045i | 1.06713 | − | 0.705863i | ||||
\(964\) | −20.3467 | − | 11.7472i | −0.655324 | − | 0.378352i | ||||
\(965\) | 18.0557 | − | 31.2733i | 0.581232 | − | 1.00672i | ||||
\(966\) | −51.5456 | + | 54.7784i | −1.65845 | + | 1.76247i | ||||
\(967\) | − | 16.0880i | − | 0.517356i | −0.965964 | − | 0.258678i | \(-0.916713\pi\) | ||
0.965964 | − | 0.258678i | \(-0.0832869\pi\) | |||||||
\(968\) | −3.86469 | − | 4.46247i | −0.124216 | − | 0.143429i | ||||
\(969\) | −15.1344 | − | 14.2412i | −0.486185 | − | 0.457493i | ||||
\(970\) | 41.8073i | 1.34235i | ||||||||
\(971\) | −11.2948 | + | 6.52107i | −0.362468 | + | 0.209271i | −0.670163 | − | 0.742214i | \(-0.733776\pi\) |
0.307695 | + | 0.951485i | \(0.400442\pi\) | |||||||
\(972\) | −15.8870 | + | 21.6337i | −0.509576 | + | 0.693900i | ||||
\(973\) | 19.0522 | − | 32.9995i | 0.610787 | − | 1.05791i | ||||
\(974\) | 49.5137 | 1.58652 | ||||||||
\(975\) | −12.6560 | + | 2.44247i | −0.405315 | + | 0.0782217i | ||||
\(976\) | 13.6179i | 0.435897i | ||||||||
\(977\) | −21.6654 | − | 12.5085i | −0.693138 | − | 0.400183i | 0.111649 | − | 0.993748i | \(-0.464387\pi\) |
−0.804786 | + | 0.593564i | \(0.797720\pi\) | |||||||
\(978\) | −5.65114 | − | 1.33155i | −0.180704 | − | 0.0425782i | ||||
\(979\) | 17.3563 | + | 24.3804i | 0.554711 | + | 0.779200i | ||||
\(980\) | 30.0228i | 0.959042i | ||||||||
\(981\) | 11.1824 | − | 22.4119i | 0.357028 | − | 0.715558i | ||||
\(982\) | 30.6584 | + | 53.1020i | 0.978350 | + | 1.69455i | ||||
\(983\) | 13.4470i | 0.428891i | 0.976736 | + | 0.214446i | \(0.0687945\pi\) | ||||
−0.976736 | + | 0.214446i | \(0.931206\pi\) | |||||||
\(984\) | −2.61810 | + | 2.78230i | −0.0834621 | + | 0.0886966i | ||||
\(985\) | 4.97451 | + | 2.87204i | 0.158501 | + | 0.0915107i | ||||
\(986\) | −27.4959 | + | 47.6242i | −0.875646 | + | 1.51666i | ||||
\(987\) | 2.99347 | + | 9.95153i | 0.0952832 | + | 0.316761i | ||||
\(988\) | −22.6230 | − | 2.30527i | −0.719733 | − | 0.0733405i | ||||
\(989\) | −19.8627 | −0.631596 | ||||||||
\(990\) | −5.10562 | − | 32.4922i | −0.162267 | − | 1.03267i | ||||
\(991\) | 25.1960 | − | 43.6407i | 0.800376 | − | 1.38629i | −0.118992 | − | 0.992895i | \(-0.537966\pi\) |
0.919369 | − | 0.393397i | \(-0.128700\pi\) | |||||||
\(992\) | −8.24727 | − | 14.2847i | −0.261851 | − | 0.453540i | ||||
\(993\) | −11.0880 | − | 36.8611i | −0.351867 | − | 1.16975i | ||||
\(994\) | −14.0523 | − | 24.3393i | −0.445712 | − | 0.771995i | ||||
\(995\) | −5.58082 | + | 3.22209i | −0.176924 | + | 0.102147i | ||||
\(996\) | −6.16741 | − | 20.5030i | −0.195422 | − | 0.649663i | ||||
\(997\) | −39.8364 | + | 22.9996i | −1.26163 | + | 0.728403i | −0.973390 | − | 0.229155i | \(-0.926404\pi\) |
−0.288241 | + | 0.957558i | \(0.593071\pi\) | |||||||
\(998\) | 6.12834 | − | 10.6146i | 0.193989 | − | 0.335999i | ||||
\(999\) | −22.1031 | + | 8.14317i | −0.699313 | + | 0.257638i |
(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 | 429.2.p.b.230.11 | ✓ | 96 | |
3.2 | odd | 2 | inner | 429.2.p.b.230.38 | yes | 96 | |
11.10 | odd | 2 | inner | 429.2.p.b.230.37 | yes | 96 | |
13.3 | even | 3 | inner | 429.2.p.b.263.12 | yes | 96 | |
33.32 | even | 2 | inner | 429.2.p.b.230.12 | yes | 96 | |
39.29 | odd | 6 | inner | 429.2.p.b.263.37 | yes | 96 | |
143.120 | odd | 6 | inner | 429.2.p.b.263.38 | yes | 96 | |
429.263 | even | 6 | inner | 429.2.p.b.263.11 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.p.b.230.11 | ✓ | 96 | 1.1 | even | 1 | trivial | |
429.2.p.b.230.12 | yes | 96 | 33.32 | even | 2 | inner | |
429.2.p.b.230.37 | yes | 96 | 11.10 | odd | 2 | inner | |
429.2.p.b.230.38 | yes | 96 | 3.2 | odd | 2 | inner | |
429.2.p.b.263.11 | yes | 96 | 429.263 | even | 6 | inner | |
429.2.p.b.263.12 | yes | 96 | 13.3 | even | 3 | inner | |
429.2.p.b.263.37 | yes | 96 | 39.29 | odd | 6 | inner | |
429.2.p.b.263.38 | yes | 96 | 143.120 | odd | 6 | inner |