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 | 230.12 | ||
Character | \(\chi\) | \(=\) | 429.230 |
Dual form | 429.2.p.b.263.12 |
$q$-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 | \(0.927744\pi\) | |||||||
\(3\) | 1.18696 | + | 1.26140i | 0.685290 | + | 0.728270i | ||||
\(4\) | −0.860909 | − | 1.49114i | −0.430455 | − | 0.745569i | ||||
\(5\) | 1.71348i | 0.766294i | 0.923687 | + | 0.383147i | \(0.125160\pi\) | ||||
−0.923687 | + | 0.383147i | \(0.874840\pi\) | |||||||
\(6\) | −3.25241 | + | 0.766347i | −1.32779 | + | 0.312860i | ||||
\(7\) | 3.58916 | − | 2.07221i | 1.35658 | − | 0.783220i | 0.367416 | − | 0.930057i | \(-0.380243\pi\) |
0.989161 | + | 0.146837i | \(0.0469092\pi\) | |||||||
\(8\) | −0.536667 | −0.189741 | ||||||||
\(9\) | −0.182262 | + | 2.99446i | −0.0607540 | + | 0.998153i | ||||
\(10\) | −2.86278 | − | 1.65283i | −0.905292 | − | 0.522670i | ||||
\(11\) | 2.70190 | + | 1.92347i | 0.814652 | + | 0.579949i | ||||
\(12\) | 0.859060 | − | 2.85587i | 0.247989 | − | 0.824419i | ||||
\(13\) | −3.28917 | + | 1.47695i | −0.912251 | + | 0.409631i | ||||
\(14\) | 7.99540i | 2.13686i | ||||||||
\(15\) | −2.16139 | + | 2.03383i | −0.558069 | + | 0.525134i | ||||
\(16\) | 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 | −0.817602 | − | 0.575784i | \(-0.804697\pi\) |
0.0898424 | + | 0.995956i | \(0.471364\pi\) | |||||||
\(20\) | 2.55504 | − | 1.47516i | 0.571325 | − | 0.329855i | ||||
\(21\) | 6.87407 | + | 2.06775i | 1.50004 | + | 0.451221i | ||||
\(22\) | −5.81987 | + | 2.65878i | −1.24080 | + | 0.566853i | ||||
\(23\) | −4.70378 | − | 2.71573i | −0.980805 | − | 0.566268i | −0.0782919 | − | 0.996930i | \(-0.524947\pi\) |
−0.902513 | + | 0.430662i | \(0.858280\pi\) | |||||||
\(24\) | −0.637002 | − | 0.676952i | −0.130027 | − | 0.138182i | ||||
\(25\) | 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 | \(-0.132786\pi\) | |||||||
\(30\) | −1.31312 | − | 5.57295i | −0.239743 | − | 1.01748i | ||||
\(31\) | −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 | ||||
\(33\) | 0.780766 | + | 5.69126i | 0.135914 | + | 0.990721i | ||||
\(34\) | −6.31909 | −1.08371 | ||||||||
\(35\) | 3.55069 | + | 6.14998i | 0.600176 | + | 1.03954i | ||||
\(36\) | 4.62206 | − | 2.30618i | 0.770344 | − | 0.384363i | ||||
\(37\) | 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 | ||||||
\(39\) | −5.76713 | − | 2.39589i | −0.923479 | − | 0.383649i | ||||
\(40\) | − | 0.919571i | − | 0.145397i | ||||||
\(41\) | −2.05502 | + | 3.55940i | −0.320941 | + | 0.555885i | −0.980682 | − | 0.195607i | \(-0.937332\pi\) |
0.659742 | + | 0.751492i | \(0.270666\pi\) | |||||||
\(42\) | −10.0854 | + | 9.49021i | −1.55621 | + | 1.46437i | ||||
\(43\) | 3.16703 | − | 1.82848i | 0.482967 | − | 0.278841i | −0.238685 | − | 0.971097i | \(-0.576716\pi\) |
0.721652 | + | 0.692256i | \(0.243383\pi\) | |||||||
\(44\) | 0.542079 | − | 5.68484i | 0.0817215 | − | 0.857022i | ||||
\(45\) | −5.13096 | − | 0.312303i | −0.764878 | − | 0.0465554i | ||||
\(46\) | 9.07453 | − | 5.23918i | 1.33797 | − | 0.772475i | ||||
\(47\) | − | 1.44769i | − | 0.211168i | −0.994410 | − | 0.105584i | \(-0.966329\pi\) | ||
0.994410 | − | 0.105584i | \(-0.0336711\pi\) | |||||||
\(48\) | 7.55104 | − | 1.77921i | 1.08990 | − | 0.256807i | ||||
\(49\) | 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 | \(-0.786129\pi\) | ||
0.782643 | − | 0.622471i | \(-0.213871\pi\) | |||||||
\(54\) | −1.70200 | − | 9.87888i | −0.231613 | − | 1.34435i | ||||
\(55\) | −3.29584 | + | 4.62966i | −0.444412 | + | 0.624263i | ||||
\(56\) | −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 | −0.958072 | − | 0.286529i | \(-0.907499\pi\) |
−0.230895 | + | 0.972979i | \(0.574165\pi\) | |||||||
\(60\) | 4.89349 | + | 1.47199i | 0.631747 | + | 0.190033i | ||||
\(61\) | 2.63306 | − | 1.52020i | 0.337129 | − | 0.194641i | −0.321873 | − | 0.946783i | \(-0.604312\pi\) |
0.659002 | + | 0.752142i | \(0.270979\pi\) | |||||||
\(62\) | 2.10249 | − | 3.64163i | 0.267017 | − | 0.462487i | ||||
\(63\) | 5.55096 | + | 11.1253i | 0.699356 | + | 1.40165i | ||||
\(64\) | −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 | ||||
\(69\) | −2.15757 | − | 9.15680i | −0.259740 | − | 1.10235i | ||||
\(70\) | −13.7000 | −1.63746 | ||||||||
\(71\) | −3.04416 | + | 1.75755i | −0.361275 | + | 0.208582i | −0.669640 | − | 0.742686i | \(-0.733552\pi\) |
0.308365 | + | 0.951268i | \(0.400218\pi\) | |||||||
\(72\) | 0.0978141 | − | 1.60703i | 0.0115275 | − | 0.189390i | ||||
\(73\) | 10.7920i | 1.26311i | 0.775333 | + | 0.631553i | \(0.217582\pi\) | ||||
−0.775333 | + | 0.631553i | \(0.782418\pi\) | |||||||
\(74\) | 4.37278 | + | 7.57388i | 0.508325 | + | 0.880445i | ||||
\(75\) | 2.44985 | + | 2.60349i | 0.282884 | + | 0.300625i | ||||
\(76\) | 5.46201 | + | 3.15349i | 0.626535 | + | 0.361730i | ||||
\(77\) | 13.6834 | + | 1.30478i | 1.55937 | + | 0.148694i | ||||
\(78\) | 9.56587 | − | 7.32428i | 1.08312 | − | 0.829311i | ||||
\(79\) | 5.74463i | 0.646322i | 0.946344 | + | 0.323161i | \(0.104745\pi\) | ||||
−0.946344 | + | 0.323161i | \(0.895255\pi\) | |||||||
\(80\) | 6.64645 | + | 3.83733i | 0.743096 | + | 0.429027i | ||||
\(81\) | −8.93356 | − | 1.09155i | −0.992618 | − | 0.121284i | ||||
\(82\) | −3.96455 | − | 6.86681i | −0.437812 | − | 0.758312i | ||||
\(83\) | −7.17926 | −0.788026 | −0.394013 | − | 0.919105i | \(-0.628914\pi\) | ||||
−0.394013 | + | 0.919105i | \(0.628914\pi\) | |||||||
\(84\) | −2.83464 | − | 12.0303i | −0.309285 | − | 1.31262i | ||||
\(85\) | −4.86058 | + | 2.80625i | −0.527203 | + | 0.304381i | ||||
\(86\) | 7.05503i | 0.760764i | ||||||||
\(87\) | 14.6714 | − | 3.45693i | 1.57294 | − | 0.370622i | ||||
\(88\) | −1.45002 | − | 1.03227i | −0.154573 | − | 0.110040i | ||||
\(89\) | 7.81452 | + | 4.51171i | 0.828337 | + | 0.478241i | 0.853283 | − | 0.521448i | \(-0.174608\pi\) |
−0.0249459 | + | 0.999689i | \(0.507941\pi\) | |||||||
\(90\) | 5.47110 | − | 8.27124i | 0.576705 | − | 0.871865i | ||||
\(91\) | −8.74483 | + | 12.1168i | −0.916707 | + | 1.27019i | ||||
\(92\) | 9.35198i | 0.975011i | ||||||||
\(93\) | −2.58715 | − | 2.74941i | −0.268275 | − | 0.285101i | ||||
\(94\) | 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 | \(0.0997034\pi\) | |||||||
\(102\) | −7.50049 | − | 7.97090i | −0.742659 | − | 0.789237i | ||||
\(103\) | 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 | \(-0.0542859\pi\) | |||||||
\(108\) | 8.39521 | + | 3.09294i | 0.807830 | + | 0.297618i | ||||
\(109\) | 8.34893i | 0.799683i | 0.916584 | + | 0.399841i | \(0.130935\pi\) | ||||
−0.916584 | + | 0.399841i | \(0.869065\pi\) | |||||||
\(110\) | −4.55577 | − | 9.97226i | −0.434376 | − | 0.950818i | ||||
\(111\) | 7.64254 | − | 1.80077i | 0.725398 | − | 0.170921i | ||||
\(112\) | − | 18.5627i | − | 1.75401i | ||||||
\(113\) | 6.72408 | − | 3.88215i | 0.632548 | − | 0.365202i | −0.149190 | − | 0.988809i | \(-0.547667\pi\) |
0.781738 | + | 0.623607i | \(0.214333\pi\) | |||||||
\(114\) | 8.91384 | − | 8.38778i | 0.834857 | − | 0.785587i | ||||
\(115\) | 4.65336 | − | 8.05985i | 0.433928 | − | 0.751585i | ||||
\(116\) | −14.9841 | −1.39124 | ||||||||
\(117\) | −3.82316 | − | 10.1185i | −0.353452 | − | 0.935453i | ||||
\(118\) | − | 20.3443i | − | 1.87284i | ||||||
\(119\) | 11.7563 | + | 6.78750i | 1.07770 | + | 0.622209i | ||||
\(120\) | 1.15995 | − | 1.09149i | 0.105888 | − | 0.0996392i | ||||
\(121\) | 3.60049 | + | 10.3941i | 0.327317 | + | 0.944914i | ||||
\(122\) | 5.86553i | 0.531041i | ||||||||
\(123\) | −6.92906 | + | 1.63266i | −0.624772 | + | 0.147212i | ||||
\(124\) | 1.87648 | + | 3.25016i | 0.168513 | + | 0.291873i | ||||
\(125\) | 12.1040i | 1.08262i | ||||||||
\(126\) | −23.9419 | − | 1.45726i | −2.13291 | − | 0.129823i | ||||
\(127\) | 3.14794 | + | 1.81747i | 0.279335 | + | 0.161274i | 0.633122 | − | 0.774052i | \(-0.281773\pi\) |
−0.353787 | + | 0.935326i | \(0.615106\pi\) | |||||||
\(128\) | −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 | \(0.376006\pi\) | |||||||
\(132\) | 7.81429 | − | 6.06389i | 0.680146 | − | 0.527794i | ||||
\(133\) | −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 | −0.449746 | − | 0.893156i | \(-0.648486\pi\) |
0.548623 | + | 0.836070i | \(0.315152\pi\) | |||||||
\(138\) | 17.3798 | + | 5.22793i | 1.47947 | + | 0.445031i | ||||
\(139\) | 7.96240 | − | 4.59710i | 0.675362 | − | 0.389921i | −0.122743 | − | 0.992438i | \(-0.539169\pi\) |
0.798105 | + | 0.602518i | \(0.205836\pi\) | |||||||
\(140\) | 6.11365 | − | 10.5892i | 0.516698 | − | 0.894947i | ||||
\(141\) | 1.82612 | − | 1.71835i | 0.153787 | − | 0.144711i | ||||
\(142\) | − | 6.78132i | − | 0.569076i | ||||||
\(143\) | −11.7279 | − | 2.33608i | −0.980733 | − | 0.195352i | ||||
\(144\) | 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 | ||||
\(147\) | 17.1558 | − | 4.04232i | 1.41499 | − | 0.333405i | ||||
\(148\) | −7.80544 | −0.641603 | ||||||||
\(149\) | 4.00350 | + | 6.93427i | 0.327980 | + | 0.568077i | 0.982111 | − | 0.188304i | \(-0.0602990\pi\) |
−0.654131 | + | 0.756381i | \(0.726966\pi\) | |||||||
\(150\) | −6.71288 | + | 1.58172i | −0.548104 | + | 0.129147i | ||||
\(151\) | − | 14.4474i | − | 1.17571i | −0.808966 | − | 0.587855i | \(-0.799972\pi\) | ||
0.808966 | − | 0.587855i | \(-0.200028\pi\) | |||||||
\(152\) | 1.70243 | − | 0.982900i | 0.138086 | − | 0.0797237i | ||||
\(153\) | −8.79276 | + | 4.38715i | −0.710853 | + | 0.354680i | ||||
\(154\) | −15.3790 | + | 21.6028i | −1.23927 | + | 1.74080i | ||||
\(155\) | − | 3.73480i | − | 0.299986i | ||||||
\(156\) | 1.39237 | + | 10.6622i | 0.111479 | + | 0.853661i | ||||
\(157\) | −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 | ||||
\(159\) | 11.4325 | − | 10.7578i | 0.906654 | − | 0.853147i | ||||
\(160\) | −11.2296 | + | 6.48341i | −0.887778 | + | 0.512559i | ||||
\(161\) | −22.5102 | −1.77405 | ||||||||
\(162\) | 10.4410 | − | 13.8727i | 0.820324 | − | 1.08994i | ||||
\(163\) | −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 | ||||||||
\(165\) | −9.75188 | + | 1.33783i | −0.759183 | + | 0.104150i | ||||
\(166\) | 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 | ||||||
\(171\) | −4.90614 | − | 9.83292i | −0.375182 | − | 0.751942i | ||||
\(172\) | −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 | ||||
\(176\) | 13.5118 | − | 6.17281i | 1.01849 | − | 0.465293i | ||||
\(177\) | −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 | −0.393926 | − | 0.919142i | \(-0.628883\pi\) |
−0.992963 | + | 0.118421i | \(0.962217\pi\) | |||||||
\(180\) | 3.95160 | + | 7.91984i | 0.294535 | + | 0.590310i | ||||
\(181\) | −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 | ||||
\(186\) | 7.08912 | − | 1.67037i | 0.519800 | − | 0.122477i | ||||
\(187\) | −1.03122 | + | 10.8145i | −0.0754104 | + | 0.790837i | ||||
\(188\) | −2.15871 | + | 1.24633i | −0.157440 | + | 0.0908981i | ||||
\(189\) | −7.44468 | + | 20.2072i | −0.541521 | + | 1.46986i | ||||
\(190\) | 12.1085 | 0.878446 | ||||||||
\(191\) | −12.0014 | + | 6.92899i | −0.868388 | + | 0.501364i | −0.866812 | − | 0.498635i | \(-0.833835\pi\) |
−0.00157552 | + | 0.999999i | \(0.500502\pi\) | |||||||
\(192\) | −6.69600 | − | 7.11595i | −0.483242 | − | 0.513549i | ||||
\(193\) | −18.2513 | − | 10.5374i | −1.31376 | − | 0.758498i | −0.331040 | − | 0.943617i | \(-0.607400\pi\) |
−0.982716 | + | 0.185119i | \(0.940733\pi\) | |||||||
\(194\) | −24.3990 | −1.75175 | ||||||||
\(195\) | 4.10531 | − | 9.88188i | 0.293988 | − | 0.707656i | ||||
\(196\) | −17.5215 | −1.25153 | ||||||||
\(197\) | −1.67614 | + | 2.90316i | −0.119420 | + | 0.206841i | −0.919538 | − | 0.393001i | \(-0.871437\pi\) |
0.800118 | + | 0.599843i | \(0.204770\pi\) | |||||||
\(198\) | −6.90085 | − | 17.9120i | −0.490422 | − | 1.27295i | ||||
\(199\) | −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 | ||||||||
\(201\) | 26.4297 | − | 6.22748i | 1.86421 | − | 0.439253i | ||||
\(202\) | 4.04871 | + | 7.01257i | 0.284866 | + | 0.493403i | ||||
\(203\) | − | 36.0666i | − | 2.53138i | ||||||
\(204\) | 9.50806 | − | 2.24033i | 0.665697 | − | 0.156855i | ||||
\(205\) | −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 | ||||
\(210\) | −16.2613 | − | 17.2812i | −1.12214 | − | 1.19252i | ||||
\(211\) | 8.31881 | + | 4.80287i | 0.572690 | + | 0.330643i | 0.758223 | − | 0.651995i | \(-0.226068\pi\) |
−0.185533 | + | 0.982638i | \(0.559401\pi\) | |||||||
\(212\) | −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 | ||||
\(219\) | −13.6130 | + | 12.8096i | −0.919882 | + | 0.865595i | ||||
\(220\) | 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 | ||||
\(225\) | −0.376183 | + | 6.18047i | −0.0250789 | + | 0.412031i | ||||
\(226\) | 14.9789i | 0.996382i | ||||||||
\(227\) | −2.53984 | − | 4.39914i | −0.168575 | − | 0.291981i | 0.769344 | − | 0.638835i | \(-0.220583\pi\) |
−0.937919 | + | 0.346854i | \(0.887250\pi\) | |||||||
\(228\) | 2.50536 | + | 10.6328i | 0.165921 | + | 0.704177i | ||||
\(229\) | 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 | ||||
\(231\) | 14.5957 | + | 18.8090i | 0.960330 | + | 1.23754i | ||||
\(232\) | −2.33517 | + | 4.04463i | −0.153311 | + | 0.265543i | ||||
\(233\) | 25.4210 | 1.66538 | 0.832692 | − | 0.553736i | \(-0.186798\pi\) | ||||
0.832692 | + | 0.553736i | \(0.186798\pi\) | |||||||
\(234\) | 20.5931 | + | 3.37278i | 1.34622 | + | 0.220486i | ||||
\(235\) | 2.48060 | 0.161816 | ||||||||
\(236\) | 15.7247 | + | 9.07867i | 1.02359 | + | 0.590971i | ||||
\(237\) | −7.24628 | + | 6.81864i | −0.470697 | + | 0.442918i | ||||
\(238\) | −22.6802 | + | 13.0944i | −1.47014 | + | 0.848787i | ||||
\(239\) | 10.3761 | 0.671177 | 0.335589 | − | 0.942009i | \(-0.391065\pi\) | ||||
0.335589 | + | 0.942009i | \(0.391065\pi\) | |||||||
\(240\) | 3.04865 | + | 12.9386i | 0.196789 | + | 0.835182i | ||||
\(241\) | −11.8170 | + | 6.82255i | −0.761200 | + | 0.439479i | −0.829726 | − | 0.558170i | \(-0.811504\pi\) |
0.0685265 | + | 0.997649i | \(0.478170\pi\) | |||||||
\(242\) | −20.8388 | − | 4.01064i | −1.33957 | − | 0.257814i | ||||
\(243\) | −9.22688 | − | 12.5644i | −0.591904 | − | 0.806008i | ||||
\(244\) | −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 | ||||||||
\(249\) | −8.52148 | − | 9.05592i | −0.540027 | − | 0.573896i | ||||
\(250\) | −20.2226 | − | 11.6755i | −1.27899 | − | 0.738426i | ||||
\(251\) | 2.21624 | − | 1.27955i | 0.139888 | − | 0.0807643i | −0.428423 | − | 0.903578i | \(-0.640931\pi\) |
0.568311 | + | 0.822814i | \(0.307597\pi\) | |||||||
\(252\) | 11.8105 | − | 17.8551i | 0.743990 | − | 1.12477i | ||||
\(253\) | −7.48548 | − | 16.3852i | −0.470608 | − | 1.03013i | ||||
\(254\) | −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 | 0.622666 | − | 0.782488i | \(-0.286050\pi\) |
−0.366321 | + | 0.930488i | \(0.619383\pi\) | |||||||
\(258\) | −8.89922 | + | 8.37402i | −0.554041 | + | 0.521344i | ||||
\(259\) | − | 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 | \(0.166234\pi\) | |||||||
\(264\) | −0.419012 | − | 3.05431i | −0.0257884 | − | 0.187980i | ||||
\(265\) | 15.5299 | 0.953992 | ||||||||
\(266\) | −14.6435 | − | 25.3633i | −0.897850 | − | 1.55512i | ||||
\(267\) | 3.58442 | + | 15.2124i | 0.219363 | + | 0.930987i | ||||
\(268\) | −26.9930 | −1.64886 | ||||||||
\(269\) | −2.63966 | + | 1.52401i | −0.160943 | + | 0.0929204i | −0.578308 | − | 0.815818i | \(-0.696287\pi\) |
0.417365 | + | 0.908739i | \(0.362954\pi\) | |||||||
\(270\) | 16.9273 | − | 2.91636i | 1.03016 | − | 0.177484i | ||||
\(271\) | −4.19786 | − | 2.42363i | −0.255002 | − | 0.147225i | 0.367051 | − | 0.930201i | \(-0.380368\pi\) |
−0.622052 | + | 0.782976i | \(0.713701\pi\) | |||||||
\(272\) | 14.6709 | 0.889552 | ||||||||
\(273\) | −25.6639 | + | 3.35144i | −1.55325 | + | 0.202838i | ||||
\(274\) | 2.57811i | 0.155749i | ||||||||
\(275\) | 5.57663 | + | 3.96999i | 0.336284 | + | 0.239400i | ||||
\(276\) | −11.7966 | + | 11.1004i | −0.710071 | + | 0.668166i | ||||
\(277\) | 16.6384 | − | 9.60616i | 0.999702 | − | 0.577178i | 0.0915416 | − | 0.995801i | \(-0.470821\pi\) |
0.908160 | + | 0.418623i | \(0.137487\pi\) | |||||||
\(278\) | 17.7374i | 1.06382i | ||||||||
\(279\) | 0.397268 | − | 6.52688i | 0.0237838 | − | 0.390754i | ||||
\(280\) | −1.90554 | − | 3.30049i | −0.113878 | − | 0.197242i | ||||
\(281\) | −6.47979 | −0.386552 | −0.193276 | − | 0.981144i | \(-0.561911\pi\) | ||||
−0.193276 | + | 0.981144i | \(0.561911\pi\) | |||||||
\(282\) | 1.10943 | + | 4.70849i | 0.0660659 | + | 0.280386i | ||||
\(283\) | −13.6552 | − | 7.88385i | −0.811719 | − | 0.468646i | 0.0358337 | − | 0.999358i | \(-0.488591\pi\) |
−0.847552 | + | 0.530712i | \(0.821925\pi\) | |||||||
\(284\) | 5.24149 | + | 3.02618i | 0.311025 | + | 0.179571i | ||||
\(285\) | 3.13149 | − | 10.4104i | 0.185493 | − | 0.616656i | ||||
\(286\) | 15.2157 | − | 17.3408i | 0.899722 | − | 1.02538i | ||||
\(287\) | 17.0337i | 1.00547i | ||||||||
\(288\) | −20.3143 | + | 10.1358i | −1.19703 | + | 0.597259i | ||||
\(289\) | 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 | ||||
\(297\) | −17.1845 | + | 1.30067i | −0.997148 | + | 0.0754726i | ||||
\(298\) | −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 | ||||
\(303\) | 7.07615 | − | 1.66731i | 0.406514 | − | 0.0957846i | ||||
\(304\) | 16.4064i | 0.940971i | ||||||||
\(305\) | 2.60484 | + | 4.51171i | 0.149152 | + | 0.258340i | ||||
\(306\) | 1.15173 | − | 18.9222i | 0.0658400 | − | 1.08171i | ||||
\(307\) | − | 28.7316i | − | 1.63980i | −0.572506 | − | 0.819900i | \(-0.694029\pi\) | ||
0.572506 | − | 0.819900i | \(-0.305971\pi\) | |||||||
\(308\) | −9.83454 | − | 21.5271i | −0.560375 | − | 1.22662i | ||||
\(309\) | 17.2212 | + | 18.3013i | 0.979680 | + | 1.04112i | ||||
\(310\) | 6.23987 | + | 3.60259i | 0.354401 | + | 0.204613i | ||||
\(311\) | 19.2304i | 1.09046i | 0.838288 | + | 0.545228i | \(0.183557\pi\) | ||||
−0.838288 | + | 0.545228i | \(0.816443\pi\) | |||||||
\(312\) | 3.09503 | + | 1.28579i | 0.175221 | + | 0.0727937i | ||||
\(313\) | −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 | ||||
\(315\) | −19.0630 | + | 9.51149i | −1.07408 | + | 0.535912i | ||||
\(316\) | 8.56605 | − | 4.94561i | 0.481878 | − | 0.278212i | ||||
\(317\) | − | 33.6635i | − | 1.89073i | −0.326012 | − | 0.945366i | \(-0.605705\pi\) | ||
0.326012 | − | 0.945366i | \(-0.394295\pi\) | |||||||
\(318\) | 6.94565 | + | 29.4776i | 0.389493 | + | 1.65302i | ||||
\(319\) | 26.2530 | − | 11.9935i | 1.46988 | − | 0.671508i | ||||
\(320\) | − | 9.66630i | − | 0.540362i | ||||||
\(321\) | 22.3123 | − | 5.25732i | 1.24535 | − | 0.293435i | ||||
\(322\) | 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 | ||||||||
\(327\) | −10.5313 | + | 9.90983i | −0.582385 | + | 0.548015i | ||||
\(328\) | 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 | ||||
\(336\) | 23.4150 | − | 22.0332i | 1.27739 | − | 1.20201i | ||||
\(337\) | 31.7148i | 1.72762i | 0.503821 | + | 0.863808i | \(0.331927\pi\) | ||||
−0.503821 | + | 0.863808i | \(0.668073\pi\) | |||||||
\(338\) | 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 | ||||
\(341\) | −5.88919 | − | 4.19250i | −0.318918 | − | 0.227037i | ||||
\(342\) | 21.1607 | + | 1.28798i | 1.14424 | + | 0.0696458i | ||||
\(343\) | − | 13.1632i | − | 0.710747i | ||||||
\(344\) | −1.69964 | + | 0.981288i | −0.0916385 | + | 0.0529075i | ||||
\(345\) | 15.6900 | − | 3.69696i | 0.844723 | − | 0.199037i | ||||
\(346\) | 25.7074 | 1.38204 | ||||||||
\(347\) | −1.34141 | − | 2.32338i | −0.0720105 | − | 0.124726i | 0.827772 | − | 0.561065i | \(-0.189608\pi\) |
−0.899782 | + | 0.436339i | \(0.856275\pi\) | |||||||
\(348\) | −17.7855 | − | 18.9009i | −0.953402 | − | 1.01320i | ||||
\(349\) | −1.10768 | − | 0.639520i | −0.0592928 | − | 0.0342327i | 0.470061 | − | 0.882634i | \(-0.344232\pi\) |
−0.529353 | + | 0.848401i | \(0.677565\pi\) | |||||||
\(350\) | 16.5023i | 0.882083i | ||||||||
\(351\) | 8.22551 | − | 16.8327i | 0.439045 | − | 0.898465i | ||||
\(352\) | −2.38248 | + | 24.9853i | −0.126986 | + | 1.33172i | ||||
\(353\) | −10.2087 | − | 5.89397i | −0.543352 | − | 0.313704i | 0.203084 | − | 0.979161i | \(-0.434903\pi\) |
−0.746436 | + | 0.665457i | \(0.768237\pi\) | |||||||
\(354\) | 25.6623 | − | 24.1478i | 1.36394 | − | 1.28344i | ||||
\(355\) | −3.01153 | − | 5.21612i | −0.159835 | − | 0.276843i | ||||
\(356\) | − | 15.5367i | − | 0.823444i | ||||||
\(357\) | 5.39247 | + | 22.8859i | 0.285400 | + | 1.21125i | ||||
\(358\) | 35.7970 | − | 20.6674i | 1.89193 | − | 1.09231i | ||||
\(359\) | 18.0155 | 0.950822 | 0.475411 | − | 0.879764i | \(-0.342299\pi\) | ||||
0.475411 | + | 0.879764i | \(0.342299\pi\) | |||||||
\(360\) | 2.75362 | + | 0.167603i | 0.145128 | + | 0.00883345i | ||||
\(361\) | −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 | ||||||||
\(366\) | −7.39879 | + | 6.96214i | −0.386741 | + | 0.363917i | ||||
\(367\) | −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 | −0.972674 | − | 0.232175i | \(-0.925416\pi\) |
−0.285268 | + | 0.958448i | \(0.592083\pi\) | |||||||
\(374\) | −17.0735 | − | 12.1546i | −0.882851 | − | 0.628500i | ||||
\(375\) | −15.2680 | + | 14.3669i | −0.788436 | + | 0.741906i | ||||
\(376\) | 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 | ||||
\(381\) | 1.44392 | + | 6.12807i | 0.0739745 | + | 0.313951i | ||||
\(382\) | − | 26.7348i | − | 1.36787i | ||||||
\(383\) | 16.7318 | − | 9.66011i | 0.854955 | − | 0.493609i | −0.00736430 | − | 0.999973i | \(-0.502344\pi\) |
0.862320 | + | 0.506364i | \(0.169011\pi\) | |||||||
\(384\) | −7.16806 | + | 1.68897i | −0.365793 | + | 0.0861899i | ||||
\(385\) | −2.23573 | + | 23.4463i | −0.113943 | + | 1.19493i | ||||
\(386\) | 35.2104 | − | 20.3287i | 1.79216 | − | 1.03471i | ||||
\(387\) | 4.89809 | + | 9.81680i | 0.248984 | + | 0.499016i | ||||
\(388\) | 10.8881 | − | 18.8587i | 0.552759 | − | 0.957407i | ||||
\(389\) | 2.53818i | 0.128691i | 0.997928 | + | 0.0643455i | \(0.0204960\pi\) | ||||
−0.997928 | + | 0.0643455i | \(0.979504\pi\) | |||||||
\(390\) | 12.5500 | + | 16.3910i | 0.635496 | + | 0.829989i | ||||
\(391\) | − | 17.7907i | − | 0.899714i | ||||||
\(392\) | −2.73060 | + | 4.72954i | −0.137916 | + | 0.238878i | ||||
\(393\) | 10.3184 | + | 10.9655i | 0.520494 | + | 0.553138i | ||||
\(394\) | −3.23361 | − | 5.60077i | −0.162907 | − | 0.282163i | ||||
\(395\) | −9.84334 | −0.495272 | ||||||||
\(396\) | 16.9242 | + | 2.65937i | 0.850474 | + | 0.133638i | ||||
\(397\) | −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 | ||||||||
\(399\) | −25.5932 | + | 6.03038i | −1.28126 | + | 0.301897i | ||||
\(400\) | 4.62224 | − | 8.00595i | 0.231112 | − | 0.400297i | ||||
\(401\) | −13.8961 | − | 8.02294i | −0.693940 | − | 0.400646i | 0.111147 | − | 0.993804i | \(-0.464548\pi\) |
−0.805086 | + | 0.593158i | \(0.797881\pi\) | |||||||
\(402\) | −15.0896 | + | 50.1641i | −0.752601 | + | 2.50196i | ||||
\(403\) | 7.16924 | − | 3.21923i | 0.357125 | − | 0.160361i | ||||
\(404\) | −7.22698 | −0.359556 | ||||||||
\(405\) | 1.87036 | − | 15.3075i | 0.0929389 | − | 0.760637i | ||||
\(406\) | 60.2579 | + | 34.7899i | 2.99055 | + | 1.72659i | ||||
\(407\) | 13.6756 | − | 6.24761i | 0.677874 | − | 0.309683i | ||||
\(408\) | 0.877037 | − | 2.91563i | 0.0434198 | − | 0.144345i | ||||
\(409\) | −6.57086 | + | 3.79369i | −0.324908 | + | 0.187586i | −0.653578 | − | 0.756859i | \(-0.726733\pi\) |
0.328670 | + | 0.944445i | \(0.393400\pi\) | |||||||
\(410\) | 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 | ||||
\(414\) | 14.0346 | + | 28.1282i | 0.689762 | + | 1.38243i | ||||
\(415\) | − | 12.3016i | − | 0.603859i | ||||||
\(416\) | −22.1248 | − | 15.9677i | −1.08476 | − | 0.782880i | ||||
\(417\) | 15.2498 | + | 4.58722i | 0.746787 | + | 0.224637i | ||||
\(418\) | 13.5925 | − | 19.0933i | 0.664829 | − | 0.933883i | ||||
\(419\) | −1.76546 | − | 1.01929i | −0.0862484 | − | 0.0497955i | 0.456256 | − | 0.889849i | \(-0.349190\pi\) |
−0.542504 | + | 0.840053i | \(0.682524\pi\) | |||||||
\(420\) | 20.6138 | − | 4.85712i | 1.00585 | − | 0.237003i | ||||
\(421\) | −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 | ||||
\(423\) | 4.33505 | + | 0.263859i | 0.210777 | + | 0.0128293i | ||||
\(424\) | 4.86399i | 0.236216i | ||||||||
\(425\) | 3.38026 | + | 5.85478i | 0.163967 | + | 0.283999i | ||||
\(426\) | 8.55396 | − | 8.04914i | 0.414441 | − | 0.389982i | ||||
\(427\) | 6.30032 | − | 10.9125i | 0.304894 | − | 0.528092i | ||||
\(428\) | −22.7879 | −1.10149 | ||||||||
\(429\) | −10.9738 | − | 17.5664i | −0.529818 | − | 0.848112i | ||||
\(430\) | −12.0887 | −0.582968 | ||||||||
\(431\) | −16.4501 | + | 28.4924i | −0.792373 | + | 1.37243i | 0.132121 | + | 0.991234i | \(0.457821\pi\) |
−0.924494 | + | 0.381197i | \(0.875512\pi\) | |||||||
\(432\) | 3.95150 | + | 22.9355i | 0.190117 | + | 1.10349i | ||||
\(433\) | 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 | ||||||
\(435\) | 5.92340 | + | 25.1392i | 0.284005 | + | 1.20533i | ||||
\(436\) | 12.4494 | − | 7.18768i | 0.596219 | − | 0.344227i | ||||
\(437\) | 19.8953 | 0.951720 | ||||||||
\(438\) | −8.27041 | − | 35.1000i | −0.395175 | − | 1.67714i | ||||
\(439\) | 3.84060 | + | 2.21737i | 0.183302 | + | 0.105829i | 0.588843 | − | 0.808247i | \(-0.299584\pi\) |
−0.405541 | + | 0.914077i | \(0.632917\pi\) | |||||||
\(440\) | 1.76877 | − | 2.48459i | 0.0843229 | − | 0.118448i | ||||
\(441\) | 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 | \(0.142445\pi\) | ||||
−0.901530 | + | 0.432716i | \(0.857555\pi\) | |||||||
\(444\) | −9.26473 | − | 9.84579i | −0.439685 | − | 0.467260i | ||||
\(445\) | −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 | −0.609066 | − | 0.793120i | \(-0.708456\pi\) |
0.382329 | + | 0.924026i | \(0.375122\pi\) | |||||||
\(450\) | −9.96308 | − | 6.59019i | −0.469664 | − | 0.310665i | ||||
\(451\) | −12.3989 | + | 5.66436i | −0.583840 | + | 0.266724i | ||||
\(452\) | −11.5777 | − | 6.68436i | −0.544567 | − | 0.314406i | ||||
\(453\) | 18.2239 | − | 17.1484i | 0.856235 | − | 0.805703i | ||||
\(454\) | 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 | 0.922670 | − | 0.385592i | \(-0.126003\pi\) |
0.127403 | + | 0.991851i | \(0.459336\pi\) | |||||||
\(458\) | −17.8809 | + | 30.9706i | −0.835519 | + | 1.44716i | ||||
\(459\) | −15.9706 | − | 5.88383i | −0.745443 | − | 0.274634i | ||||
\(460\) | −16.0245 | −0.747145 | ||||||||
\(461\) | 8.83315 | + | 15.2995i | 0.411401 | + | 0.712567i | 0.995043 | − | 0.0994436i | \(-0.0317063\pi\) |
−0.583642 | + | 0.812011i | \(0.698373\pi\) | |||||||
\(462\) | −45.5039 | + | 6.24254i | −2.11703 | + | 0.290429i | ||||
\(463\) | −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 | ||||
\(465\) | 4.71108 | − | 4.43305i | 0.218471 | − | 0.205578i | ||||
\(466\) | −24.5211 | + | 42.4718i | −1.13592 | + | 1.96747i | ||||
\(467\) | − | 18.9378i | − | 0.876335i | −0.898893 | − | 0.438167i | \(-0.855628\pi\) | ||
0.898893 | − | 0.438167i | \(-0.144372\pi\) | |||||||
\(468\) | −11.7966 | + | 14.4120i | −0.545300 | + | 0.666193i | ||||
\(469\) | − | 64.9721i | − | 3.00013i | ||||||
\(470\) | −2.39279 | + | 4.14443i | −0.110371 | + | 0.191168i | ||||
\(471\) | −26.2685 | − | 27.9159i | −1.21039 | − | 1.28630i | ||||
\(472\) | 4.90118 | − | 2.82970i | 0.225595 | − | 0.130247i | ||||
\(473\) | 12.0740 | + | 1.15132i | 0.555164 | + | 0.0529378i | ||||
\(474\) | −4.40238 | − | 18.6839i | −0.202208 | − | 0.858180i | ||||
\(475\) | −6.54739 | + | 3.78014i | −0.300415 | + | 0.173445i | ||||
\(476\) | − | 23.3737i | − | 1.07133i | ||||||
\(477\) | 27.1397 | + | 1.65190i | 1.24264 | + | 0.0756353i | ||||
\(478\) | −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 | ||||||
\(483\) | −26.7186 | − | 28.3943i | −1.21574 | − | 1.29199i | ||||
\(484\) | 12.3993 | − | 14.3172i | 0.563604 | − | 0.650781i | ||||
\(485\) | −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 | \(-0.0879034\pi\) | |||||||
\(492\) | 8.39981 | + | 8.92662i | 0.378693 | + | 0.402443i | ||||
\(493\) | 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 | ||||
\(498\) | 23.3499 | − | 5.50181i | 1.04633 | − | 0.246542i | ||||
\(499\) | −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 | ||||
\(501\) | 11.6074 | − | 2.73500i | 0.518582 | − | 0.122191i | ||||
\(502\) | 4.93701i | 0.220350i | ||||||||
\(503\) | −15.1946 | − | 26.3178i | −0.677492 | − | 1.17345i | −0.975734 | − | 0.218960i | \(-0.929733\pi\) |
0.298242 | − | 0.954490i | \(-0.403600\pi\) | |||||||
\(504\) | −2.97902 | − | 5.97058i | −0.132696 | − | 0.265951i | ||||
\(505\) | 6.22845 | + | 3.59600i | 0.277162 | + | 0.160020i | ||||
\(506\) | 34.5959 | + | 3.29890i | 1.53797 | + | 0.146654i | ||||
\(507\) | 22.5076 | − | 0.637263i | 0.999599 | − | 0.0283019i | ||||
\(508\) | − | 6.25869i | − | 0.277685i | ||||||
\(509\) | 7.90008 | + | 4.56111i | 0.350165 | + | 0.202168i | 0.664758 | − | 0.747059i | \(-0.268535\pi\) |
−0.314593 | + | 0.949227i | \(0.601868\pi\) | |||||||
\(510\) | 13.6580 | − | 12.8520i | 0.604787 | − | 0.569095i | ||||
\(511\) | 22.3632 | + | 38.7342i | 0.989290 | + | 1.71350i | ||||
\(512\) | 29.0873 | 1.28549 | ||||||||
\(513\) | 6.57987 | − | 17.8599i | 0.290509 | − | 0.788532i | ||||
\(514\) | −7.92808 | + | 4.57728i | −0.349693 | + | 0.201895i | ||||
\(515\) | 24.8604i | 1.09548i | ||||||||
\(516\) | −2.50125 | − | 10.6154i | −0.110111 | − | 0.467317i | ||||
\(517\) | 2.78460 | − | 3.91151i | 0.122466 | − | 0.172028i | ||||
\(518\) | 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 | \(0.0130282\pi\) | ||||
−0.999163 | + | 0.0409178i | \(0.986972\pi\) | |||||||
\(522\) | −45.0681 | + | 22.4867i | −1.97258 | + | 0.984217i | ||||
\(523\) | −10.4710 | − | 6.04544i | −0.457865 | − | 0.264349i | 0.253281 | − | 0.967393i | \(-0.418490\pi\) |
−0.711146 | + | 0.703044i | \(0.751824\pi\) | |||||||
\(524\) | −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 | ||||
\(531\) | −14.1244 | − | 28.3083i | −0.612948 | − | 1.22847i | ||||
\(532\) | 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 | ||||
\(537\) | −8.51110 | − | 36.1215i | −0.367281 | − | 1.55876i | ||||
\(538\) | − | 5.88024i | − | 0.253515i | ||||||
\(539\) | 30.6986 | − | 14.0245i | 1.32228 | − | 0.604077i | ||||
\(540\) | −5.29970 | + | 14.3851i | −0.228063 | + | 0.619035i | ||||
\(541\) | 19.4924i | 0.838045i | 0.907976 | + | 0.419023i | \(0.137627\pi\) | ||||
−0.907976 | + | 0.419023i | \(0.862373\pi\) | |||||||
\(542\) | 8.09851 | − | 4.67568i | 0.347861 | − | 0.200838i | ||||
\(543\) | −10.8456 | − | 11.5258i | −0.465428 | − | 0.494619i | ||||
\(544\) | −12.3937 | + | 21.4665i | −0.531374 | + | 0.920368i | ||||
\(545\) | −14.3058 | −0.612792 | ||||||||
\(546\) | 19.1561 | − | 46.1105i | 0.819804 | − | 1.97335i | ||||
\(547\) | − | 9.55999i | − | 0.408756i | −0.978892 | − | 0.204378i | \(-0.934483\pi\) | ||
0.978892 | − | 0.204378i | \(-0.0655171\pi\) | |||||||
\(548\) | −1.99270 | − | 1.15048i | −0.0851238 | − | 0.0491462i | ||||
\(549\) | 4.07226 | + | 8.16166i | 0.173800 | + | 0.348331i | ||||
\(550\) | −12.0120 | + | 5.48763i | −0.512195 | + | 0.233993i | ||||
\(551\) | 31.8770i | 1.35800i | ||||||||
\(552\) | 1.15789 | + | 4.91415i | 0.0492833 | + | 0.209160i | ||||
\(553\) | 11.9041 | + | 20.6184i | 0.506212 | + | 0.876785i | ||||
\(554\) | 37.0644i | 1.57472i | ||||||||
\(555\) | 3.08559 | + | 13.0954i | 0.130976 | + | 0.555868i | ||||
\(556\) | −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 | ||||||||
\(561\) | −14.8655 | + | 11.5356i | −0.627621 | + | 0.487034i | ||||
\(562\) | 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 | \(0.864453\pi\) | |||||||
\(570\) | 14.3723 | + | 15.2737i | 0.601991 | + | 0.639746i | ||||
\(571\) | − | 3.30522i | − | 0.138319i | −0.997606 | − | 0.0691596i | \(-0.977968\pi\) | ||
0.997606 | − | 0.0691596i | \(-0.0220318\pi\) | |||||||
\(572\) | 6.61321 | + | 19.4990i | 0.276512 | + | 0.815295i | ||||
\(573\) | −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 | ||||
\(576\) | 1.02820 | − | 16.8927i | 0.0428415 | − | 0.703861i | ||||
\(577\) | −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 | ||||
\(579\) | −8.37165 | − | 35.5296i | −0.347914 | − | 1.47656i | ||||
\(580\) | − | 25.6750i | − | 1.06610i | ||||||
\(581\) | −25.7675 | + | 14.8769i | −1.06902 | + | 0.617198i | ||||
\(582\) | −28.9606 | − | 30.7769i | −1.20046 | − | 1.27574i | ||||
\(583\) | 17.4331 | − | 24.4881i | 0.722004 | − | 1.01420i | ||||
\(584\) | − | 5.79171i | − | 0.239663i | ||||||
\(585\) | 17.3378 | − | 6.55093i | 0.716832 | − | 0.270848i | ||||
\(586\) | 61.4784 | 2.53965 | ||||||||
\(587\) | 4.57662 | + | 2.64231i | 0.188897 | + | 0.109060i | 0.591466 | − | 0.806330i | \(-0.298549\pi\) |
−0.402569 | + | 0.915390i | \(0.631883\pi\) | |||||||
\(588\) | −20.7972 | − | 22.1016i | −0.857664 | − | 0.911454i | ||||
\(589\) | 6.91436 | − | 3.99201i | 0.284901 | − | 0.164488i | ||||
\(590\) | 34.8596 | 1.43515 | ||||||||
\(591\) | −5.65155 | + | 1.33164i | −0.232474 | + | 0.0547764i | ||||
\(592\) | −10.1522 | − | 17.5841i | −0.417252 | − | 0.722701i | ||||
\(593\) | −16.7919 | −0.689559 | −0.344779 | − | 0.938684i | \(-0.612046\pi\) | ||||
−0.344779 | + | 0.938684i | \(0.612046\pi\) | |||||||
\(594\) | 14.4031 | − | 29.9655i | 0.590968 | − | 1.22950i | ||||
\(595\) | −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 | \(0.176162\pi\) | ||||
−0.850727 | + | 0.525607i | \(0.823838\pi\) | |||||||
\(600\) | −1.31475 | − | 1.39721i | −0.0536745 | − | 0.0570408i | ||||
\(601\) | −32.7717 | − | 18.9207i | −1.33678 | − | 0.771793i | −0.350455 | − | 0.936579i | \(-0.613973\pi\) |
−0.986329 | + | 0.164787i | \(0.947306\pi\) | |||||||
\(602\) | 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 | ||||
\(605\) | −17.8101 | + | 6.16939i | −0.724082 | + | 0.250821i | ||||
\(606\) | −4.04001 | + | 13.4307i | −0.164114 | + | 0.545584i | ||||
\(607\) | −15.9973 | + | 9.23603i | −0.649309 | + | 0.374879i | −0.788192 | − | 0.615430i | \(-0.788982\pi\) |
0.138882 | + | 0.990309i | \(0.455649\pi\) | |||||||
\(608\) | −24.0059 | − | 13.8598i | −0.973568 | − | 0.562090i | ||||
\(609\) | 45.4945 | − | 42.8096i | 1.84353 | − | 1.73473i | ||||
\(610\) | −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 | 0.391304 | − | 0.920261i | \(-0.372024\pi\) |
−0.601318 | + | 0.799010i | \(0.705357\pi\) | |||||||
\(614\) | 48.0030 | + | 27.7145i | 1.93724 | + | 1.11847i | ||||
\(615\) | −2.79753 | − | 11.8728i | −0.112807 | − | 0.478759i | ||||
\(616\) | −7.34343 | − | 0.700234i | −0.295875 | − | 0.0282132i | ||||
\(617\) | −7.05118 | + | 4.07100i | −0.283870 | + | 0.163892i | −0.635174 | − | 0.772369i | \(-0.719072\pi\) |
0.351304 | + | 0.936261i | \(0.385738\pi\) | |||||||
\(618\) | −47.1882 | + | 11.1187i | −1.89819 | + | 0.447260i | ||||
\(619\) | −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 | ||||
\(621\) | 27.8129 | − | 4.79180i | 1.11609 | − | 0.192288i | ||||
\(622\) | −32.1290 | − | 18.5497i | −1.28825 | − | 0.743774i | ||||
\(623\) | 37.3968 | 1.49827 | ||||||||
\(624\) | −22.2088 | + | 17.0046i | −0.889065 | + | 0.680728i | ||||
\(625\) | −10.4202 | −0.416807 | ||||||||
\(626\) | 16.7197 | − | 28.9593i | 0.668252 | − | 1.15745i | ||||
\(627\) | −12.9002 | − | 16.6240i | −0.515186 | − | 0.663899i | ||||
\(628\) | 19.0527 | + | 33.0003i | 0.760286 | + | 1.31685i | ||||
\(629\) | 14.8486 | 0.592054 | ||||||||
\(630\) | 2.49699 | − | 41.0241i | 0.0994825 | − | 1.63444i | ||||
\(631\) | −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 | ||||||
\(633\) | 3.81574 | + | 16.1941i | 0.151662 | + | 0.643660i | ||||
\(634\) | 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 | ||||
\(639\) | −4.70806 | − | 9.43594i | −0.186248 | − | 0.373280i | ||||
\(640\) | −6.30935 | − | 3.64271i | −0.249399 | − | 0.143991i | ||||
\(641\) | −1.65745 | + | 0.956932i | −0.0654655 | + | 0.0377965i | −0.532375 | − | 0.846508i | \(-0.678701\pi\) |
0.466910 | + | 0.884305i | \(0.345367\pi\) | |||||||
\(642\) | −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 | 0.196983 | − | 0.980407i | \(-0.436885\pi\) |
−0.750566 | + | 0.660796i | \(0.770219\pi\) | |||||||
\(648\) | 4.79435 | + | 0.585801i | 0.188340 | + | 0.0230124i | ||||
\(649\) | −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 | 0.982050 | − | 0.188619i | \(-0.0604011\pi\) |
0.327677 | + | 0.944790i | \(0.393734\pi\) | |||||||
\(654\) | −6.39818 | − | 27.1542i | −0.250189 | − | 1.06181i | ||||
\(655\) | 14.8956i | 0.582018i | ||||||||
\(656\) | 9.20440 | + | 15.9425i | 0.359371 | + | 0.622449i | ||||
\(657\) | −32.3162 | − | 1.96697i | −1.26077 | − | 0.0767388i | ||||
\(658\) | 11.5749 | 0.451236 | ||||||||
\(659\) | 11.0405 | + | 19.1227i | 0.430077 | + | 0.744915i | 0.996879 | − | 0.0789387i | \(-0.0251531\pi\) |
−0.566803 | + | 0.823854i | \(0.691820\pi\) | |||||||
\(660\) | 10.3904 | + | 13.3897i | 0.404445 | + | 0.521192i | ||||
\(661\) | 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 | ||||||||
\(663\) | −2.64878 | − | 20.2832i | −0.102870 | − | 0.787736i | ||||
\(664\) | 3.85287 | 0.149521 | ||||||||
\(665\) | −22.5272 | − | 13.0061i | −0.873568 | − | 0.504355i | ||||
\(666\) | −23.4766 | + | 11.7137i | −0.909702 | + | 0.453896i | ||||
\(667\) | −40.9345 | + | 23.6335i | −1.58499 | + | 0.915094i | ||||
\(668\) | −11.8549 | −0.458678 | ||||||||
\(669\) | −13.9245 | + | 3.28095i | −0.538351 | + | 0.126849i | ||||
\(670\) | −44.8800 | + | 25.9115i | −1.73387 | + | 1.00105i | ||||
\(671\) | 10.0383 | + | 0.957206i | 0.387525 | + | 0.0369525i | ||||
\(672\) | 12.4585 | + | 52.8742i | 0.480595 | + | 2.03967i | ||||
\(673\) | −30.5284 | − | 17.6256i | −1.17678 | − | 0.679416i | −0.221515 | − | 0.975157i | \(-0.571100\pi\) |
−0.955268 | + | 0.295741i | \(0.904433\pi\) | |||||||
\(674\) | −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 | \(0.488181\pi\) | |||||||
\(678\) | −18.8944 | + | 17.7793i | −0.725635 | + | 0.682811i | ||||
\(679\) | 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 | ||||
\(682\) | 12.6853 | − | 5.79520i | 0.485745 | − | 0.221910i | ||||
\(683\) | 5.46171 | − | 3.15332i | 0.208987 | − | 0.120658i | −0.391854 | − | 0.920028i | \(-0.628166\pi\) |
0.600840 | + | 0.799369i | \(0.294833\pi\) | |||||||
\(684\) | −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 | ||||
\(687\) | 22.0028 | + | 23.3827i | 0.839457 | + | 0.892106i | ||||
\(688\) | − | 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 | ||||
\(693\) | −6.40108 | + | 40.7365i | −0.243157 | + | 1.54745i | ||||
\(694\) | 5.17569 | 0.196466 | ||||||||
\(695\) | 7.87705 | + | 13.6435i | 0.298794 | + | 0.517526i | ||||
\(696\) | −7.87364 | + | 1.85522i | −0.298450 | + | 0.0703220i | ||||
\(697\) | −13.4624 | −0.509926 | ||||||||
\(698\) | 2.13694 | − | 1.23376i | 0.0808844 | − | 0.0466986i | ||||
\(699\) | 30.1736 | + | 32.0660i | 1.14127 | + | 1.21285i | ||||
\(700\) | −12.7551 | − | 7.36417i | −0.482098 | − | 0.278339i | ||||
\(701\) | −35.6093 | −1.34494 | −0.672472 | − | 0.740123i | \(-0.734767\pi\) | ||||
−0.672472 | + | 0.740123i | \(0.734767\pi\) | |||||||
\(702\) | 20.1888 | + | 29.9795i | 0.761975 | + | 1.13150i | ||||
\(703\) | 16.6052i | 0.626277i | ||||||||
\(704\) | −15.2422 | − | 10.8509i | −0.574463 | − | 0.408959i | ||||
\(705\) | 2.94436 | + | 3.12903i | 0.110891 | + | 0.117846i | ||||
\(706\) | 19.6946 | − | 11.3707i | 0.741214 | − | 0.427940i | ||||
\(707\) | − | 17.3953i | − | 0.654218i | ||||||
\(708\) | 7.21274 | + | 30.6112i | 0.271071 | + | 1.15044i | ||||
\(709\) | 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 | ||||||||
\(711\) | −17.2021 | − | 1.04703i | −0.645128 | − | 0.0392666i | ||||
\(712\) | −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 | ||||
\(715\) | 4.00283 | − | 20.0955i | 0.149697 | − | 0.751530i | ||||
\(716\) | 36.8914i | 1.37870i | ||||||||
\(717\) | 12.3161 | + | 13.0885i | 0.459951 | + | 0.488798i | ||||
\(718\) | −17.3778 | + | 30.0992i | −0.648533 | + | 1.12329i | ||||
\(719\) | 10.9779 | − | 6.33810i | 0.409407 | − | 0.236371i | −0.281128 | − | 0.959670i | \(-0.590709\pi\) |
0.690535 | + | 0.723299i | \(0.257375\pi\) | |||||||
\(720\) | −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 | ||||
\(726\) | −19.6757 | − | 31.0465i | −0.730235 | − | 1.15224i | ||||
\(727\) | 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 | ||||
\(732\) | −2.07953 | − | 8.82562i | −0.0768617 | − | 0.326204i | ||||
\(733\) | 1.45846i | 0.0538696i | 0.999637 | + | 0.0269348i | \(0.00857465\pi\) | ||||
−0.999637 | + | 0.0269348i | \(0.991425\pi\) | |||||||
\(734\) | −5.24167 | − | 9.07883i | −0.193473 | − | 0.335106i | ||||
\(735\) | 6.92646 | + | 29.3962i | 0.255486 | + | 1.08429i | ||||
\(736\) | − | 41.1026i | − | 1.51506i | ||||||
\(737\) | 47.2934 | − | 21.6057i | 1.74207 | − | 0.795856i | ||||
\(738\) | 21.2850 | − | 10.6201i | 0.783510 | − | 0.390932i | ||||
\(739\) | −20.8762 | − | 12.0529i | −0.767945 | − | 0.443373i | 0.0641961 | − | 0.997937i | \(-0.479552\pi\) |
−0.832141 | + | 0.554564i | \(0.812885\pi\) | |||||||
\(740\) | − | 13.3745i | − | 0.491657i | ||||||
\(741\) | 22.6827 | − | 2.96212i | 0.833269 | − | 0.108816i | ||||
\(742\) | 72.4649 | 2.66027 | ||||||||
\(743\) | 4.88608 | − | 8.46294i | 0.179253 | − | 0.310475i | −0.762372 | − | 0.647139i | \(-0.775965\pi\) |
0.941625 | + | 0.336664i | \(0.109299\pi\) | |||||||
\(744\) | 1.38844 | + | 1.47552i | 0.0509027 | + | 0.0540952i | ||||
\(745\) | −11.8818 | + | 6.85994i | −0.435314 | + | 0.251329i | ||||
\(746\) | − | 54.1205i | − | 1.98149i | ||||||
\(747\) | 1.30851 | − | 21.4980i | 0.0478758 | − | 0.786570i | ||||
\(748\) | 17.0138 | − | 7.77264i | 0.622085 | − | 0.284196i | ||||
\(749\) | − | 54.8503i | − | 2.00419i | ||||||
\(750\) | −9.27587 | − | 39.3672i | −0.338707 | − | 1.43749i | ||||
\(751\) | −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 | ||||||||
\(756\) | 36.5410 | − | 6.29554i | 1.32898 | − | 0.228967i | ||||
\(757\) | 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 | ||||
\(765\) | −7.51731 | − | 15.0663i | −0.271789 | − | 0.544722i | ||||
\(766\) | 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 | 0.874662 | − | 0.484734i | \(-0.161083\pi\) |
0.0175394 | + | 0.999846i | \(0.494417\pi\) | |||||||
\(770\) | −37.0160 | − | 26.3516i | −1.33396 | − | 0.949646i | ||||
\(771\) | 1.88498 | + | 7.99995i | 0.0678860 | + | 0.288111i | ||||
\(772\) | 36.2869i | 1.30600i | ||||||||
\(773\) | −18.5994 | + | 10.7384i | −0.668975 | + | 0.386233i | −0.795688 | − | 0.605706i | \(-0.792891\pi\) |
0.126713 | + | 0.991939i | \(0.459557\pi\) | |||||||
\(774\) | −21.1260 | − | 1.28586i | −0.759358 | − | 0.0462194i | ||||
\(775\) | −4.49874 | −0.161599 | ||||||||
\(776\) | −3.39367 | − | 5.87801i | −0.121826 | − | 0.211008i | ||||
\(777\) | 23.6988 | − | 22.3002i | 0.850188 | − | 0.800014i | ||||
\(778\) | −4.24064 | − | 2.44833i | −0.152034 | − | 0.0877771i | ||||
\(779\) | − | 15.0550i | − | 0.539401i | ||||||
\(780\) | −18.2696 | + | 2.38581i | −0.654155 | + | 0.0854258i | ||||
\(781\) | −11.6056 | − | 1.10665i | −0.415281 | − | 0.0395992i | ||||
\(782\) | 29.7236 | + | 17.1609i | 1.06291 | + | 0.613673i | ||||
\(783\) | 7.67760 | + | 44.5628i | 0.274375 | + | 1.59255i | ||||
\(784\) | −22.7893 | − | 39.4723i | −0.813905 | − | 1.40973i | ||||
\(785\) | − | 37.9210i | − | 1.35346i | ||||||
\(786\) | −28.2736 | + | 6.66196i | −1.00849 | + | 0.237624i | ||||
\(787\) | −15.9266 | + | 9.19525i | −0.567723 | + | 0.327775i | −0.756240 | − | 0.654295i | \(-0.772966\pi\) |
0.188516 | + | 0.982070i | \(0.439632\pi\) | |||||||
\(788\) | 5.77201 | 0.205619 | ||||||||
\(789\) | 0.0743129 | − | 0.0175099i | 0.00264561 | − | 0.000623371i | ||||
\(790\) | 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 | ||||||||
\(795\) | 18.4333 | + | 19.5894i | 0.653761 | + | 0.694763i | ||||
\(796\) | −3.23776 | + | 5.60796i | −0.114759 | + | 0.198769i | ||||
\(797\) | −17.2948 | + | 9.98516i | −0.612614 | + | 0.353693i | −0.773988 | − | 0.633201i | \(-0.781741\pi\) |
0.161374 | + | 0.986893i | \(0.448407\pi\) | |||||||
\(798\) | 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 | ||||
\(803\) | −20.7581 | + | 29.1588i | −0.732538 | + | 1.02899i | ||||
\(804\) | −32.0396 | − | 34.0490i | −1.12995 | − | 1.20082i | ||||
\(805\) | − | 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 | \(0.840537\pi\) | |||||||
\(810\) | 23.7707 | + | 17.8905i | 0.835217 | + | 0.628609i | ||||
\(811\) | − | 19.0035i | − | 0.667303i | −0.942697 | − | 0.333651i | \(-0.891719\pi\) | ||
0.942697 | − | 0.333651i | \(-0.108281\pi\) | |||||||
\(812\) | −53.7804 | + | 31.0501i | −1.88732 | + | 1.08964i | ||||
\(813\) | −1.92551 | − | 8.17193i | −0.0675304 | − | 0.286602i | ||||
\(814\) | −2.75336 | + | 28.8748i | −0.0965052 | + | 1.01206i | ||||
\(815\) | 2.57835 | − | 1.48861i | 0.0903157 | − | 0.0521438i | ||||
\(816\) | 17.4137 | + | 18.5058i | 0.609601 | + | 0.647834i | ||||
\(817\) | −6.69769 | + | 11.6007i | −0.234323 | + | 0.405859i | ||||
\(818\) | − | 14.6376i | − | 0.511791i | ||||||
\(819\) | −34.6895 | − | 28.3945i | −1.21215 | − | 0.992183i | ||||
\(820\) | 12.1259i | 0.423455i | ||||||||
\(821\) | 3.60701 | − | 6.24752i | 0.125885 | − | 0.218040i | −0.796193 | − | 0.605042i | \(-0.793156\pi\) |
0.922079 | + | 0.387002i | \(0.126489\pi\) | |||||||
\(822\) | −3.25202 | + | 3.06010i | −0.113427 | + | 0.106733i | ||||
\(823\) | −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 | ||||||||
\(825\) | 1.61148 | + | 11.7466i | 0.0561044 | + | 0.408964i | ||||
\(826\) | −42.1575 | − | 73.0190i | −1.46685 | − | 2.54066i | ||||
\(827\) | −37.3026 | −1.29714 | −0.648569 | − | 0.761156i | \(-0.724632\pi\) | ||||
−0.648569 | + | 0.761156i | \(0.724632\pi\) | |||||||
\(828\) | −28.0041 | − | 1.70451i | −0.973210 | − | 0.0592358i | ||||
\(829\) | 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 | ||||||||
\(834\) | −22.3740 | + | 21.0536i | −0.774749 | + | 0.729027i | ||||
\(835\) | 10.2169 | + | 5.89874i | 0.353571 | + | 0.204134i | ||||
\(836\) | 8.69212 | + | 19.0264i | 0.300623 | + | 0.658043i | ||||
\(837\) | 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 | −0.139051 | − | 0.990285i | \(-0.544405\pi\) |
0.788087 | + | 0.615564i | \(0.211072\pi\) | |||||||
\(840\) | 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 | ||||
\(843\) | −7.69124 | − | 8.17361i | −0.264900 | − | 0.281514i | ||||
\(844\) | − | 16.5393i | − | 0.569307i | ||||||
\(845\) | 16.6480 | + | 14.7998i | 0.572707 | + | 0.509129i | ||||
\(846\) | −4.62243 | + | 6.98822i | −0.158923 | + | 0.240260i | ||||
\(847\) | 34.4614 | + | 29.8450i | 1.18411 | + | 1.02549i | ||||
\(848\) | −35.1558 | − | 20.2972i | −1.20725 | − | 0.697009i | ||||
\(849\) | −6.26349 | − | 26.5825i | −0.214962 | − | 0.912309i | ||||
\(850\) | −13.0424 | −0.447351 | ||||||||
\(851\) | −21.3234 | + | 12.3111i | −0.730957 | + | 0.422018i | ||||
\(852\) | 2.40421 | + | 10.2036i | 0.0823668 | + | 0.349568i | ||||
\(853\) | 3.69558i | 0.126534i | 0.997997 | + | 0.0632671i | \(0.0201520\pi\) | ||||
−0.997997 | + | 0.0632671i | \(0.979848\pi\) | |||||||
\(854\) | 12.1546 | + | 21.0524i | 0.415922 | + | 0.720397i | ||||
\(855\) | 16.8486 | − | 8.40659i | 0.576209 | − | 0.287499i | ||||
\(856\) | −3.55134 | + | 6.15109i | −0.121382 | + | 0.210240i | ||||
\(857\) | −10.5639 | −0.360857 | −0.180429 | − | 0.983588i | \(-0.557748\pi\) | ||||
−0.180429 | + | 0.983588i | \(0.557748\pi\) | |||||||
\(858\) | 39.9341 | − | 1.38974i | 1.36333 | − | 0.0474450i | ||||
\(859\) | −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 | ||||
\(861\) | −21.4863 | + | 20.2183i | −0.732252 | + | 0.689038i | ||||
\(862\) | −31.7355 | − | 54.9676i | −1.08092 | − | 1.87220i | ||||
\(863\) | − | 6.66363i | − | 0.226833i | −0.993548 | − | 0.113416i | \(-0.963821\pi\) | ||
0.993548 | − | 0.113416i | \(-0.0361794\pi\) | |||||||
\(864\) | −36.8975 | − | 13.5937i | −1.25528 | − | 0.462466i | ||||
\(865\) | 19.7739 | − | 11.4165i | 0.672332 | − | 0.388171i | ||||
\(866\) | −7.01154 | −0.238262 | ||||||||
\(867\) | 10.5724 | − | 2.49112i | 0.359058 | − | 0.0846028i | ||||
\(868\) | 13.4700 | + | 7.77691i | 0.457202 | + | 0.263966i | ||||
\(869\) | −11.0497 | + | 15.5214i | −0.374834 | + | 0.526528i | ||||
\(870\) | −47.7146 | − | 14.3528i | −1.61768 | − | 0.486606i | ||||
\(871\) | −5.73014 | + | 56.2332i | −0.194158 | + | 1.90539i | ||||
\(872\) | − | 4.48060i | − | 0.151732i | ||||||
\(873\) | −33.9503 | + | 16.9395i | −1.14904 | + | 0.573315i | ||||
\(874\) | −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 | −0.244334 | − | 0.969691i | \(-0.578569\pi\) |
0.717610 | + | 0.696445i | \(0.245236\pi\) | |||||||
\(878\) | −7.40929 | + | 4.27775i | −0.250051 | + | 0.144367i | ||||
\(879\) | 15.8994 | − | 52.8562i | 0.536274 | − | 1.78280i | ||||
\(880\) | 10.5770 | + | 23.1523i | 0.356551 | + | 0.780465i | ||||
\(881\) | 38.1631 | + | 22.0335i | 1.28575 | + | 0.742326i | 0.977893 | − | 0.209107i | \(-0.0670558\pi\) |
0.307854 | + | 0.951434i | \(0.400389\pi\) | |||||||
\(882\) | −52.6998 | + | 26.2946i | −1.77450 | + | 0.885384i | ||||
\(883\) | 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 | \(0.172095\pi\) | |||||||
\(888\) | −4.10150 | + | 0.966414i | −0.137637 | + | 0.0324307i | ||||
\(889\) | 15.0646 | 0.505252 | ||||||||
\(890\) | −14.9142 | − | 25.8321i | −0.499924 | − | 0.865894i | ||||
\(891\) | −22.0380 | − | 20.1327i | −0.738300 | − | 0.674472i | ||||
\(892\) | 14.2213 | 0.476164 | ||||||||
\(893\) | 2.65143 | + | 4.59241i | 0.0887267 | + | 0.153679i | ||||
\(894\) | −18.3351 | − | 19.4850i | −0.613217 | − | 0.651676i | ||||
\(895\) | 18.3564 | − | 31.7943i | 0.613588 | − | 1.06276i | ||||
\(896\) | 17.6212i | 0.588684i | ||||||||
\(897\) | 20.6207 | + | 26.9316i | 0.688505 | + | 0.899221i | ||||
\(898\) | − | 10.7027i | − | 0.357153i | ||||||
\(899\) | −9.48418 | + | 16.4271i | −0.316315 | + | 0.547874i | ||||
\(900\) | 9.53980 | − | 4.75988i | 0.317993 | − | 0.158663i | ||||
\(901\) | 25.7096 | − | 14.8434i | 0.856510 | − | 0.494506i | ||||
\(902\) | 2.49632 | − | 26.1791i | 0.0831182 | − | 0.871669i | ||||
\(903\) | 25.5512 | − | 6.02049i | 0.850291 | − | 0.200349i | ||||
\(904\) | −3.60860 | + | 2.08342i | −0.120020 | + | 0.0692936i | ||||
\(905\) | − | 15.6566i | − | 0.520443i | ||||||
\(906\) | 11.0717 | + | 46.9888i | 0.367833 | + | 1.56110i | ||||
\(907\) | 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 | \(-0.876578\pi\) | ||
0.925765 | − | 0.378099i | \(-0.123422\pi\) | |||||||
\(912\) | −20.6950 | + | 19.4737i | −0.685281 | + | 0.644838i | ||||
\(913\) | −19.3976 | − | 13.8091i | −0.641967 | − | 0.457015i | ||||
\(914\) | −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 | −0.797905 | − | 0.602783i | \(-0.794059\pi\) |
0.123073 | + | 0.992398i | \(0.460725\pi\) | |||||||
\(920\) | −2.49730 | + | 4.32546i | −0.0823337 | + | 0.142606i | ||||
\(921\) | 36.2421 | − | 34.1032i | 1.19422 | − | 1.12374i | ||||
\(922\) | −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 | ||||
\(927\) | −2.64438 | + | 43.4457i | −0.0868530 | + | 1.42694i | ||||
\(928\) | 65.8561 | 2.16183 | ||||||||
\(929\) | −37.4887 | + | 21.6441i | −1.22997 | + | 0.710121i | −0.967023 | − | 0.254690i | \(-0.918026\pi\) |
−0.262943 | + | 0.964811i | \(0.584693\pi\) | |||||||
\(930\) | 2.86215 | + | 12.1471i | 0.0938537 | + | 0.398319i | ||||
\(931\) | 37.2749i | 1.22164i | ||||||||
\(932\) | −21.8852 | − | 37.9062i | −0.716873 | − | 1.24166i | ||||
\(933\) | −24.2572 | + | 22.8257i | −0.794146 | + | 0.747279i | ||||
\(934\) | 31.6400 | + | 18.2674i | 1.03529 | + | 0.597727i | ||||
\(935\) | −18.5305 | − | 1.76698i | −0.606013 | − | 0.0577865i | ||||
\(936\) | 2.05177 | + | 5.43025i | 0.0670641 | + | 0.177493i | ||||
\(937\) | 55.6524i | 1.81808i | 0.416704 | + | 0.909042i | \(0.363185\pi\) | ||||
−0.416704 | + | 0.909042i | \(0.636815\pi\) | |||||||
\(938\) | 108.551 | + | 62.6722i | 3.54433 | + | 2.04632i | ||||
\(939\) | −20.5738 | − | 21.8642i | −0.671401 | − | 0.713510i | ||||
\(940\) | −2.13557 | − | 3.69892i | −0.0696546 | − | 0.120645i | ||||
\(941\) | −9.25699 | −0.301769 | −0.150885 | − | 0.988551i | \(-0.548212\pi\) | ||||
−0.150885 | + | 0.988551i | \(0.548212\pi\) | |||||||
\(942\) | 71.9788 | − | 16.9600i | 2.34520 | − | 0.552585i | ||||
\(943\) | 19.3327 | − | 11.1618i | 0.629560 | − | 0.363477i | ||||
\(944\) | 47.2328i | 1.53730i | ||||||||
\(945\) | −34.6248 | − | 12.7564i | −1.12634 | − | 0.414964i | ||||
\(946\) | −13.5702 | + | 19.0620i | −0.441204 | + | 0.619758i | ||||
\(947\) | −31.4410 | − | 18.1525i | −1.02170 | − | 0.589876i | −0.107101 | − | 0.994248i | \(-0.534157\pi\) |
−0.914595 | + | 0.404372i | \(0.867490\pi\) | |||||||
\(948\) | 16.4059 | + | 4.93498i | 0.532840 | + | 0.160281i | ||||
\(949\) | −15.9392 | − | 35.4967i | −0.517408 | − | 1.15227i | ||||
\(950\) | − | 14.5853i | − | 0.473209i | ||||||
\(951\) | 42.4632 | − | 39.9572i | 1.37696 | − | 1.29570i | ||||
\(952\) | −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 | ||||
\(960\) | 12.1931 | − | 11.4735i | 0.393530 | − | 0.370305i | ||||
\(961\) | −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 | ||||
\(966\) | 73.2123 | − | 17.2506i | 2.35557 | − | 0.555029i | ||||
\(967\) | 16.0880i | 0.517356i | 0.965964 | + | 0.258678i | \(0.0832869\pi\) | ||||
−0.965964 | + | 0.258678i | \(0.916713\pi\) | |||||||
\(968\) | −1.93227 | − | 5.57815i | −0.0621054 | − | 0.179289i | ||||
\(969\) | −4.76605 | − | 20.2273i | −0.153108 | − | 0.649795i | ||||
\(970\) | − | 41.8073i | − | 1.34235i | ||||||
\(971\) | 11.2948 | − | 6.52107i | 0.362468 | − | 0.209271i | −0.307695 | − | 0.951485i | \(-0.599558\pi\) |
0.670163 | + | 0.742214i | \(0.266224\pi\) | |||||||
\(972\) | −10.7918 | + | 24.5754i | −0.346147 | + | 0.788256i | ||||
\(973\) | 19.0522 | − | 32.9995i | 0.610787 | − | 1.05791i | ||||
\(974\) | 49.5137 | 1.58652 | ||||||||
\(975\) | −11.9032 | − | 4.94504i | −0.381207 | − | 0.158368i | ||||
\(976\) | − | 13.6179i | − | 0.435897i | ||||||
\(977\) | 21.6654 | + | 12.5085i | 0.693138 | + | 0.400183i | 0.804786 | − | 0.593564i | \(-0.202280\pi\) |
−0.111649 | + | 0.993748i | \(0.535613\pi\) | |||||||
\(978\) | 3.97873 | + | 4.22826i | 0.127226 | + | 0.135205i | ||||
\(979\) | 12.4358 | + | 27.2212i | 0.397451 | + | 0.869993i | ||||
\(980\) | − | 30.0228i | − | 0.959042i | ||||||
\(981\) | −25.0005 | − | 1.52169i | −0.798206 | − | 0.0485840i | ||||
\(982\) | 30.6584 | + | 53.1020i | 0.978350 | + | 1.69455i | ||||
\(983\) | − | 13.4470i | − | 0.428891i | −0.976736 | − | 0.214446i | \(-0.931206\pi\) | ||
0.976736 | − | 0.214446i | \(-0.0687945\pi\) | |||||||
\(984\) | 3.71860 | − | 0.876193i | 0.118545 | − | 0.0279320i | ||||
\(985\) | −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 | ||||||||
\(990\) | 30.6919 | − | 11.8245i | 0.975452 | − | 0.375807i | ||||
\(991\) | 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 | 0.288241 | − | 0.957558i | \(-0.406929\pi\) |
0.973390 | + | 0.229155i | \(0.0735961\pi\) | |||||||
\(998\) | 6.12834 | − | 10.6146i | 0.193989 | − | 0.335999i | ||||
\(999\) | 3.99938 | + | 23.2135i | 0.126535 | + | 0.734442i |
(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.230.12 | yes | 96 | |
3.2 | odd | 2 | inner | 429.2.p.b.230.37 | yes | 96 | |
11.10 | odd | 2 | inner | 429.2.p.b.230.38 | yes | 96 | |
13.3 | even | 3 | inner | 429.2.p.b.263.11 | yes | 96 | |
33.32 | even | 2 | inner | 429.2.p.b.230.11 | ✓ | 96 | |
39.29 | odd | 6 | inner | 429.2.p.b.263.38 | yes | 96 | |
143.120 | odd | 6 | inner | 429.2.p.b.263.37 | yes | 96 | |
429.263 | even | 6 | inner | 429.2.p.b.263.12 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.p.b.230.11 | ✓ | 96 | 33.32 | even | 2 | inner | |
429.2.p.b.230.12 | yes | 96 | 1.1 | even | 1 | trivial | |
429.2.p.b.230.37 | yes | 96 | 3.2 | odd | 2 | inner | |
429.2.p.b.230.38 | yes | 96 | 11.10 | odd | 2 | inner | |
429.2.p.b.263.11 | yes | 96 | 13.3 | even | 3 | inner | |
429.2.p.b.263.12 | yes | 96 | 429.263 | even | 6 | inner | |
429.2.p.b.263.37 | yes | 96 | 143.120 | odd | 6 | inner | |
429.2.p.b.263.38 | yes | 96 | 39.29 | odd | 6 | inner |