Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(703,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.703");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.bk (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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 462) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 703.1 | ||
Root | \(0.500000 + 2.40229i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.703 |
Dual form | 1386.2.bk.b.901.1 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −2.83045 | + | 1.63416i | −1.26581 | + | 0.730818i | −0.974193 | − | 0.225716i | \(-0.927528\pi\) |
−0.291621 | + | 0.956534i | \(0.594195\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.54243 | + | 0.732142i | 0.960950 | + | 0.276724i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.63416 | − | 2.83045i | 0.516767 | − | 0.895066i | ||||
\(11\) | 2.54485 | − | 2.12691i | 0.767302 | − | 0.641286i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.12518 | −1.42147 | −0.710734 | − | 0.703461i | \(-0.751637\pi\) | ||||
−0.710734 | + | 0.703461i | \(0.751637\pi\) | |||||||
\(14\) | −2.56788 | + | 0.637163i | −0.686296 | + | 0.170289i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.66290 | − | 4.61228i | 0.645848 | − | 1.11864i | −0.338257 | − | 0.941054i | \(-0.609837\pi\) |
0.984105 | − | 0.177587i | \(-0.0568292\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.13745 | − | 3.70217i | −0.490364 | − | 0.849336i | 0.509574 | − | 0.860427i | \(-0.329803\pi\) |
−0.999938 | + | 0.0110907i | \(0.996470\pi\) | |||||||
\(20\) | 3.26832i | 0.730818i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.14045 | + | 3.11438i | −0.243145 | + | 0.663988i | ||||
\(23\) | 2.68593 | + | 4.65217i | 0.560055 | + | 0.970044i | 0.997491 | + | 0.0707942i | \(0.0225533\pi\) |
−0.437436 | + | 0.899250i | \(0.644113\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.84095 | − | 4.92067i | 0.568190 | − | 0.984135i | ||||
\(26\) | 4.43853 | − | 2.56259i | 0.870468 | − | 0.502565i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.90527 | − | 1.83574i | 0.360062 | − | 0.346922i | ||||
\(29\) | − | 4.77874i | − | 0.887389i | −0.896178 | − | 0.443695i | \(-0.853667\pi\) | ||
0.896178 | − | 0.443695i | \(-0.146333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.59873 | + | 3.23243i | 1.00556 | + | 0.580561i | 0.909889 | − | 0.414852i | \(-0.136167\pi\) |
0.0956723 | + | 0.995413i | \(0.469500\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.32580i | 0.913367i | ||||||||
\(35\) | −8.39266 | + | 2.08245i | −1.41862 | + | 0.351999i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.06546 | − | 1.84544i | −0.175161 | − | 0.303388i | 0.765056 | − | 0.643964i | \(-0.222711\pi\) |
−0.940217 | + | 0.340576i | \(0.889378\pi\) | |||||||
\(38\) | 3.70217 | + | 2.13745i | 0.600571 | + | 0.346740i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.63416 | − | 2.83045i | −0.258383 | − | 0.447533i | ||||
\(41\) | −0.949652 | −0.148311 | −0.0741554 | − | 0.997247i | \(-0.523626\pi\) | ||||
−0.0741554 | + | 0.997247i | \(0.523626\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.20483i | − | 0.946228i | −0.881001 | − | 0.473114i | \(-0.843130\pi\) | ||
0.881001 | − | 0.473114i | \(-0.156870\pi\) | |||||||
\(44\) | −0.569529 | − | 3.26736i | −0.0858597 | − | 0.492573i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.65217 | − | 2.68593i | −0.685925 | − | 0.396019i | ||||
\(47\) | −10.4185 | + | 6.01513i | −1.51970 | + | 0.877397i | −0.519965 | + | 0.854188i | \(0.674055\pi\) |
−0.999731 | + | 0.0232091i | \(0.992612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.92794 | + | 3.72284i | 0.846848 | + | 0.531835i | ||||
\(50\) | 5.68190i | 0.803543i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.56259 | + | 4.43853i | −0.355367 | + | 0.615514i | ||||
\(53\) | 6.26996 | − | 10.8599i | 0.861246 | − | 1.49172i | −0.00948193 | − | 0.999955i | \(-0.503018\pi\) |
0.870727 | − | 0.491766i | \(-0.163648\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.72736 | + | 10.1788i | −0.502598 | + | 1.37251i | ||||
\(56\) | −0.732142 | + | 2.54243i | −0.0978366 | + | 0.339747i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.38937 | + | 4.13851i | 0.313740 | + | 0.543413i | ||||
\(59\) | 11.6778 | + | 6.74219i | 1.52032 | + | 0.877758i | 0.999713 | + | 0.0239621i | \(0.00762810\pi\) |
0.520608 | + | 0.853796i | \(0.325705\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.67030 | + | 4.62509i | 0.341897 | + | 0.592183i | 0.984785 | − | 0.173778i | \(-0.0555974\pi\) |
−0.642888 | + | 0.765960i | \(0.722264\pi\) | |||||||
\(62\) | −6.46485 | −0.821037 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 14.5065 | − | 8.37536i | 1.79931 | − | 1.03883i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.09675 | + | 5.36373i | −0.378328 | + | 0.655284i | −0.990819 | − | 0.135194i | \(-0.956834\pi\) |
0.612491 | + | 0.790478i | \(0.290168\pi\) | |||||||
\(68\) | −2.66290 | − | 4.61228i | −0.322924 | − | 0.559321i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.22703 | − | 5.99979i | 0.744272 | − | 0.717112i | ||||
\(71\) | 10.8061 | 1.28245 | 0.641226 | − | 0.767352i | \(-0.278426\pi\) | ||||
0.641226 | + | 0.767352i | \(0.278426\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.61476 | − | 11.4571i | 0.774199 | − | 1.34095i | −0.161045 | − | 0.986947i | \(-0.551486\pi\) |
0.935244 | − | 0.354005i | \(-0.115180\pi\) | |||||||
\(74\) | 1.84544 | + | 1.06546i | 0.214528 | + | 0.123858i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.27490 | −0.490364 | ||||||||
\(77\) | 8.02731 | − | 3.54433i | 0.914797 | − | 0.403913i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.93887 | − | 4.58351i | 0.893193 | − | 0.515685i | 0.0182072 | − | 0.999834i | \(-0.494204\pi\) |
0.874985 | + | 0.484149i | \(0.160871\pi\) | |||||||
\(80\) | 2.83045 | + | 1.63416i | 0.316454 | + | 0.182705i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.822423 | − | 0.474826i | 0.0908214 | − | 0.0524358i | ||||
\(83\) | −0.835847 | −0.0917462 | −0.0458731 | − | 0.998947i | \(-0.514607\pi\) | ||||
−0.0458731 | + | 0.998947i | \(0.514607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.4064i | 1.88799i | ||||||||
\(86\) | 3.10242 | + | 5.37354i | 0.334542 | + | 0.579444i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.12691 | + | 2.54485i | 0.226729 | + | 0.271282i | ||||
\(89\) | 5.39021 | − | 3.11204i | 0.571361 | − | 0.329875i | −0.186332 | − | 0.982487i | \(-0.559660\pi\) |
0.757693 | + | 0.652611i | \(0.226327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.0304 | − | 3.75236i | −1.36596 | − | 0.393354i | ||||
\(92\) | 5.37186 | 0.560055 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.01513 | − | 10.4185i | 0.620413 | − | 1.07459i | ||||
\(95\) | 12.0999 | + | 6.98586i | 1.24142 | + | 0.716734i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.624337i | 0.0633919i | 0.999498 | + | 0.0316959i | \(0.0100908\pi\) | ||||
−0.999498 | + | 0.0316959i | \(0.989909\pi\) | |||||||
\(98\) | −6.99517 | − | 0.260109i | −0.706618 | − | 0.0262750i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.84095 | − | 4.92067i | −0.284095 | − | 0.492067i | ||||
\(101\) | −6.58462 | + | 11.4049i | −0.655194 | + | 1.13483i | 0.326651 | + | 0.945145i | \(0.394080\pi\) |
−0.981845 | + | 0.189685i | \(0.939253\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.4421 | − | 6.60608i | 1.12742 | − | 0.650916i | 0.184135 | − | 0.982901i | \(-0.441052\pi\) |
0.943285 | + | 0.331985i | \(0.107718\pi\) | |||||||
\(104\) | − | 5.12518i | − | 0.502565i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.5399i | 1.21799i | ||||||||
\(107\) | 9.62104 | − | 5.55471i | 0.930101 | − | 0.536994i | 0.0432576 | − | 0.999064i | \(-0.486226\pi\) |
0.886844 | + | 0.462070i | \(0.152893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.17596 | + | 3.56569i | 0.591549 | + | 0.341531i | 0.765710 | − | 0.643186i | \(-0.222388\pi\) |
−0.174161 | + | 0.984717i | \(0.555721\pi\) | |||||||
\(110\) | −1.86140 | − | 10.6788i | −0.177478 | − | 1.01818i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.637163 | − | 2.56788i | −0.0602063 | − | 0.242642i | ||||
\(113\) | −2.41436 | −0.227124 | −0.113562 | − | 0.993531i | \(-0.536226\pi\) | ||||
−0.113562 | + | 0.993531i | \(0.536226\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.2048 | − | 8.77847i | −1.41785 | − | 0.818597i | ||||
\(116\) | −4.13851 | − | 2.38937i | −0.384251 | − | 0.221847i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.4844 | −1.24134 | ||||||||
\(119\) | 10.1471 | − | 9.77678i | 0.930181 | − | 0.896236i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.95254 | − | 10.8253i | 0.177504 | − | 0.984120i | ||||
\(122\) | −4.62509 | − | 2.67030i | −0.418736 | − | 0.241758i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.59873 | − | 3.23243i | 0.502781 | − | 0.290281i | ||||
\(125\) | 2.22868i | 0.199339i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.8100i | 1.22544i | 0.790301 | + | 0.612719i | \(0.209924\pi\) | ||||
−0.790301 | + | 0.612719i | \(0.790076\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.37536 | + | 14.5065i | −0.734567 | + | 1.27231i | ||||
\(131\) | −5.89332 | − | 10.2075i | −0.514902 | − | 0.891836i | −0.999850 | − | 0.0172935i | \(-0.994495\pi\) |
0.484949 | − | 0.874543i | \(-0.338838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.72381 | − | 10.9774i | −0.236184 | − | 0.951864i | ||||
\(134\) | − | 6.19350i | − | 0.535037i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.61228 | + | 2.66290i | 0.395499 | + | 0.228342i | ||||
\(137\) | 2.43055 | − | 4.20984i | 0.207656 | − | 0.359671i | −0.743320 | − | 0.668936i | \(-0.766750\pi\) |
0.950976 | + | 0.309265i | \(0.100083\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.7827 | 1.42349 | 0.711744 | − | 0.702439i | \(-0.247906\pi\) | ||||
0.711744 | + | 0.702439i | \(0.247906\pi\) | |||||||
\(140\) | −2.39287 | + | 8.30948i | −0.202235 | + | 0.702279i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.35838 | + | 5.40306i | −0.785338 | + | 0.453415i | ||||
\(143\) | −13.0428 | + | 10.9008i | −1.09069 | + | 0.911568i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.80922 | + | 13.5260i | 0.648520 | + | 1.12327i | ||||
\(146\) | 13.2295i | 1.09488i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.13093 | −0.175161 | ||||||||
\(149\) | 6.25672 | − | 3.61232i | 0.512571 | − | 0.295933i | −0.221319 | − | 0.975201i | \(-0.571036\pi\) |
0.733890 | + | 0.679269i | \(0.237703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.22644 | − | 2.44014i | −0.343943 | − | 0.198576i | 0.318071 | − | 0.948067i | \(-0.396965\pi\) |
−0.662014 | + | 0.749491i | \(0.730298\pi\) | |||||||
\(152\) | 3.70217 | − | 2.13745i | 0.300286 | − | 0.173370i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.17969 | + | 7.08313i | −0.417392 | + | 0.570775i | ||||
\(155\) | −21.1292 | −1.69714 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.85996 | − | 1.65120i | −0.228249 | − | 0.131780i | 0.381515 | − | 0.924363i | \(-0.375403\pi\) |
−0.609764 | + | 0.792583i | \(0.708736\pi\) | |||||||
\(158\) | −4.58351 | + | 7.93887i | −0.364644 | + | 0.631583i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.26832 | −0.258383 | ||||||||
\(161\) | 3.42275 | + | 13.7943i | 0.269751 | + | 1.08714i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.42268 | + | 4.19621i | 0.189759 | + | 0.328672i | 0.945170 | − | 0.326579i | \(-0.105896\pi\) |
−0.755411 | + | 0.655252i | \(0.772563\pi\) | |||||||
\(164\) | −0.474826 | + | 0.822423i | −0.0370777 | + | 0.0642205i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.723865 | − | 0.417924i | 0.0561828 | − | 0.0324372i | ||||
\(167\) | −2.13922 | −0.165538 | −0.0827688 | − | 0.996569i | \(-0.526376\pi\) | ||||
−0.0827688 | + | 0.996569i | \(0.526376\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.2674 | 1.02057 | ||||||||
\(170\) | −8.70320 | − | 15.0744i | −0.667505 | − | 1.15615i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.37354 | − | 3.10242i | −0.409729 | − | 0.236557i | ||||
\(173\) | −8.87458 | − | 15.3712i | −0.674722 | − | 1.16865i | −0.976550 | − | 0.215290i | \(-0.930930\pi\) |
0.301828 | − | 0.953362i | \(-0.402403\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.8256 | − | 10.4305i | 0.818336 | − | 0.788472i | ||||
\(176\) | −3.11438 | − | 1.14045i | −0.234755 | − | 0.0859649i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.11204 | + | 5.39021i | −0.233257 | + | 0.404013i | ||||
\(179\) | 1.44235 | − | 2.49822i | 0.107806 | − | 0.186726i | −0.807075 | − | 0.590449i | \(-0.798951\pi\) |
0.914881 | + | 0.403723i | \(0.132284\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9351i | 0.812803i | 0.913695 | + | 0.406401i | \(0.133217\pi\) | ||||
−0.913695 | + | 0.406401i | \(0.866783\pi\) | |||||||
\(182\) | 13.1609 | − | 3.26558i | 0.975547 | − | 0.242061i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.65217 | + | 2.68593i | −0.342962 | + | 0.198009i | ||||
\(185\) | 6.03148 | + | 3.48228i | 0.443443 | + | 0.256022i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.03320 | − | 17.4013i | −0.221809 | − | 1.27251i | ||||
\(188\) | 12.0303i | 0.877397i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.9717 | −1.01362 | ||||||||
\(191\) | 6.43848 | + | 11.1518i | 0.465872 | + | 0.806914i | 0.999240 | − | 0.0389690i | \(-0.0124074\pi\) |
−0.533368 | + | 0.845883i | \(0.679074\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.23494 | − | 3.02239i | −0.376819 | − | 0.217557i | 0.299614 | − | 0.954060i | \(-0.403142\pi\) |
−0.676433 | + | 0.736504i | \(0.736475\pi\) | |||||||
\(194\) | −0.312169 | − | 0.540692i | −0.0224124 | − | 0.0388194i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.18805 | − | 3.27232i | 0.442003 | − | 0.233737i | ||||
\(197\) | 6.18237i | 0.440476i | 0.975446 | + | 0.220238i | \(0.0706833\pi\) | ||||
−0.975446 | + | 0.220238i | \(0.929317\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.36231 | − | 1.94123i | −0.238348 | − | 0.137610i | 0.376069 | − | 0.926591i | \(-0.377275\pi\) |
−0.614417 | + | 0.788981i | \(0.710609\pi\) | |||||||
\(200\) | 4.92067 | + | 2.84095i | 0.347944 | + | 0.200886i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 13.1692i | − | 0.926585i | ||||||
\(203\) | 3.49871 | − | 12.1496i | 0.245562 | − | 0.852736i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.68794 | − | 1.55188i | 0.187734 | − | 0.108388i | ||||
\(206\) | −6.60608 | + | 11.4421i | −0.460267 | + | 0.797206i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.56259 | + | 4.43853i | 0.177684 | + | 0.307757i | ||||
\(209\) | −13.3137 | − | 4.87532i | −0.920925 | − | 0.337233i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.04700i | − | 0.622821i | −0.950276 | − | 0.311410i | \(-0.899199\pi\) | ||
0.950276 | − | 0.311410i | \(-0.100801\pi\) | |||||||
\(212\) | −6.26996 | − | 10.8599i | −0.430623 | − | 0.745860i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.55471 | + | 9.62104i | −0.379712 | + | 0.657681i | ||||
\(215\) | 10.1397 | + | 17.5624i | 0.691521 | + | 1.19775i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.8678 | + | 12.3173i | 0.805639 | + | 0.836152i | ||||
\(218\) | −7.13138 | −0.482998 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.95141 | + | 8.31739i | 0.468664 | + | 0.560758i | ||||
\(221\) | −13.6478 | + | 23.6387i | −0.918052 | + | 1.59011i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.42935i | − | 0.363576i | −0.983338 | − | 0.181788i | \(-0.941812\pi\) | ||
0.983338 | − | 0.181788i | \(-0.0581885\pi\) | |||||||
\(224\) | 1.83574 | + | 1.90527i | 0.122656 | + | 0.127301i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.09090 | − | 1.20718i | 0.139084 | − | 0.0803004i | ||||
\(227\) | −5.92818 | + | 10.2679i | −0.393467 | + | 0.681505i | −0.992904 | − | 0.118917i | \(-0.962058\pi\) |
0.599437 | + | 0.800422i | \(0.295391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.56595 | + | 3.21350i | −0.367808 | + | 0.212354i | −0.672501 | − | 0.740097i | \(-0.734780\pi\) |
0.304692 | + | 0.952451i | \(0.401446\pi\) | |||||||
\(230\) | 17.5569 | 1.15767 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.77874 | 0.313740 | ||||||||
\(233\) | −1.73972 | + | 1.00443i | −0.113973 | + | 0.0658023i | −0.555903 | − | 0.831247i | \(-0.687627\pi\) |
0.441930 | + | 0.897050i | \(0.354294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.6594 | − | 34.0510i | 1.28243 | − | 2.22124i | ||||
\(236\) | 11.6778 | − | 6.74219i | 0.760161 | − | 0.438879i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.89924 | + | 13.5405i | −0.252750 | + | 0.877699i | ||||
\(239\) | 4.65869i | 0.301346i | 0.988584 | + | 0.150673i | \(0.0481440\pi\) | ||||
−0.988584 | + | 0.150673i | \(0.951856\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.98498 | + | 5.17014i | −0.192279 | + | 0.333038i | −0.946005 | − | 0.324151i | \(-0.894921\pi\) |
0.753726 | + | 0.657189i | \(0.228255\pi\) | |||||||
\(242\) | 3.72171 | + | 10.3513i | 0.239241 | + | 0.665405i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.34060 | 0.341897 | ||||||||
\(245\) | −22.8624 | − | 0.850118i | −1.46063 | − | 0.0543121i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.9548 | + | 18.9743i | 0.697037 | + | 1.20730i | ||||
\(248\) | −3.23243 | + | 5.59873i | −0.205259 | + | 0.355520i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.11434 | − | 1.93010i | −0.0704771 | − | 0.122070i | ||||
\(251\) | 1.45699i | 0.0919645i | 0.998942 | + | 0.0459822i | \(0.0146418\pi\) | ||||
−0.998942 | + | 0.0459822i | \(0.985358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.7300 | + | 6.12635i | 1.05181 | + | 0.385161i | ||||
\(254\) | −6.90499 | − | 11.9598i | −0.433258 | − | 0.750424i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −22.8407 | + | 13.1871i | −1.42477 | + | 0.822589i | −0.996701 | − | 0.0811588i | \(-0.974138\pi\) |
−0.428065 | + | 0.903748i | \(0.640805\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.35775 | − | 5.47198i | −0.0843665 | − | 0.340012i | ||||
\(260\) | − | 16.7507i | − | 1.03883i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.2075 | + | 5.89332i | 0.630623 | + | 0.364091i | ||||
\(263\) | 27.1221 | + | 15.6589i | 1.67242 | + | 0.965571i | 0.966279 | + | 0.257497i | \(0.0828977\pi\) |
0.706138 | + | 0.708074i | \(0.250436\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 40.9845i | 2.51766i | ||||||||
\(266\) | 7.84761 | + | 8.14484i | 0.481168 | + | 0.499392i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.09675 | + | 5.36373i | 0.189164 | + | 0.327642i | ||||
\(269\) | −2.64139 | − | 1.52501i | −0.161049 | − | 0.0929815i | 0.417310 | − | 0.908764i | \(-0.362973\pi\) |
−0.578358 | + | 0.815783i | \(0.696306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.2246 | − | 19.4416i | −0.681847 | − | 1.18099i | −0.974417 | − | 0.224750i | \(-0.927844\pi\) |
0.292569 | − | 0.956244i | \(-0.405490\pi\) | |||||||
\(272\) | −5.32580 | −0.322924 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.86111i | 0.293670i | ||||||||
\(275\) | −3.23601 | − | 18.5648i | −0.195139 | − | 1.11950i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.7724 | − | 10.2609i | −1.06784 | − | 0.616518i | −0.140250 | − | 0.990116i | \(-0.544791\pi\) |
−0.927591 | + | 0.373598i | \(0.878124\pi\) | |||||||
\(278\) | −14.5342 | + | 8.39134i | −0.871705 | + | 0.503279i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.08245 | − | 8.39266i | −0.124450 | − | 0.501557i | ||||
\(281\) | − | 13.8822i | − | 0.828141i | −0.910245 | − | 0.414071i | \(-0.864107\pi\) | ||
0.910245 | − | 0.414071i | \(-0.135893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.8931 | − | 25.7956i | 0.885304 | − | 1.53339i | 0.0399386 | − | 0.999202i | \(-0.487284\pi\) |
0.845365 | − | 0.534189i | \(-0.179383\pi\) | |||||||
\(284\) | 5.40306 | − | 9.35838i | 0.320613 | − | 0.555318i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.84502 | − | 15.9618i | 0.345624 | − | 0.943838i | ||||
\(287\) | −2.41443 | − | 0.695280i | −0.142519 | − | 0.0410411i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.68205 | − | 9.84161i | −0.334238 | − | 0.578918i | ||||
\(290\) | −13.5260 | − | 7.80922i | −0.794272 | − | 0.458573i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.61476 | − | 11.4571i | −0.387099 | − | 0.670476i | ||||
\(293\) | −10.3943 | −0.607243 | −0.303621 | − | 0.952793i | \(-0.598196\pi\) | ||||
−0.303621 | + | 0.952793i | \(0.598196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −44.0712 | −2.56593 | ||||||||
\(296\) | 1.84544 | − | 1.06546i | 0.107264 | − | 0.0619289i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.61232 | + | 6.25672i | −0.209256 | + | 0.362442i | ||||
\(299\) | −13.7659 | − | 23.8432i | −0.796100 | − | 1.37889i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.54282 | − | 15.7754i | 0.261844 | − | 0.909277i | ||||
\(302\) | 4.88028 | 0.280828 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.13745 | + | 3.70217i | −0.122591 | + | 0.212334i | ||||
\(305\) | −15.1163 | − | 8.72739i | −0.865556 | − | 0.499729i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.37847 | −0.0786736 | −0.0393368 | − | 0.999226i | \(-0.512525\pi\) | ||||
−0.0393368 | + | 0.999226i | \(0.512525\pi\) | |||||||
\(308\) | 0.944181 | − | 8.72402i | 0.0537997 | − | 0.497097i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.2984 | − | 10.5646i | 1.03928 | − | 0.600029i | ||||
\(311\) | −9.11149 | − | 5.26052i | −0.516665 | − | 0.298297i | 0.218904 | − | 0.975746i | \(-0.429752\pi\) |
−0.735569 | + | 0.677450i | \(0.763085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.96323 | − | 1.13347i | 0.110968 | − | 0.0640676i | −0.443489 | − | 0.896280i | \(-0.646259\pi\) |
0.554457 | + | 0.832212i | \(0.312926\pi\) | |||||||
\(314\) | 3.30239 | 0.186365 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 9.16702i | − | 0.515685i | ||||||
\(317\) | −2.47085 | − | 4.27963i | −0.138777 | − | 0.240368i | 0.788257 | − | 0.615346i | \(-0.210984\pi\) |
−0.927034 | + | 0.374978i | \(0.877650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.1639 | − | 12.1612i | −0.569071 | − | 0.680895i | ||||
\(320\) | 2.83045 | − | 1.63416i | 0.158227 | − | 0.0913523i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.86134 | − | 10.2348i | −0.549551 | − | 0.570365i | ||||
\(323\) | −22.7672 | −1.26680 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.5604 | + | 25.2193i | −0.807665 | + | 1.39892i | ||||
\(326\) | −4.19621 | − | 2.42268i | −0.232406 | − | 0.134180i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 0.949652i | − | 0.0524358i | ||||||
\(329\) | −30.8923 | + | 7.66524i | −1.70315 | + | 0.422598i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.47446 | − | 11.2141i | −0.355869 | − | 0.616383i | 0.631398 | − | 0.775459i | \(-0.282482\pi\) |
−0.987266 | + | 0.159077i | \(0.949148\pi\) | |||||||
\(332\) | −0.417924 | + | 0.723865i | −0.0229365 | + | 0.0397272i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.85262 | − | 1.06961i | 0.101371 | − | 0.0585264i | ||||
\(335\) | − | 20.2423i | − | 1.10596i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.22142i | 0.447849i | 0.974606 | + | 0.223925i | \(0.0718869\pi\) | ||||
−0.974606 | + | 0.223925i | \(0.928113\pi\) | |||||||
\(338\) | −11.4899 | + | 6.63372i | −0.624970 | + | 0.360827i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.0744 | + | 8.70320i | 0.817523 | + | 0.471997i | ||||
\(341\) | 21.1230 | − | 3.68192i | 1.14387 | − | 0.199387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.3457 | + | 13.8052i | 0.666607 | + | 0.745409i | ||||
\(344\) | 6.20483 | 0.334542 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.3712 | + | 8.87458i | 0.826362 | + | 0.477100i | ||||
\(347\) | −27.1635 | − | 15.6829i | −1.45821 | − | 0.841901i | −0.459291 | − | 0.888286i | \(-0.651897\pi\) |
−0.998924 | + | 0.0463849i | \(0.985230\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.15342 | 0.168799 | 0.0843993 | − | 0.996432i | \(-0.473103\pi\) | ||||
0.0843993 | + | 0.996432i | \(0.473103\pi\) | |||||||
\(350\) | −4.15996 | + | 14.4459i | −0.222359 | + | 0.772164i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.26736 | − | 0.569529i | 0.174151 | − | 0.0303560i | ||||
\(353\) | 7.06177 | + | 4.07712i | 0.375860 | + | 0.217003i | 0.676016 | − | 0.736887i | \(-0.263705\pi\) |
−0.300155 | + | 0.953890i | \(0.597039\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.5862 | + | 17.6589i | −1.62335 | + | 0.937239i | ||||
\(356\) | − | 6.22408i | − | 0.329875i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.88470i | 0.152461i | ||||||||
\(359\) | 8.26228 | − | 4.77023i | 0.436067 | − | 0.251763i | −0.265861 | − | 0.964011i | \(-0.585656\pi\) |
0.701928 | + | 0.712248i | \(0.252323\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.362625 | − | 0.628085i | 0.0190855 | − | 0.0330571i | ||||
\(362\) | −5.46757 | − | 9.47011i | −0.287369 | − | 0.497738i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.76485 | + | 9.40850i | −0.511817 | + | 0.493139i | ||||
\(365\) | 43.2383i | 2.26319i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.86022 | − | 3.38340i | −0.305901 | − | 0.176612i | 0.339190 | − | 0.940718i | \(-0.389847\pi\) |
−0.645091 | + | 0.764106i | \(0.723180\pi\) | |||||||
\(368\) | 2.68593 | − | 4.65217i | 0.140014 | − | 0.242511i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.96456 | −0.362070 | ||||||||
\(371\) | 23.8919 | − | 23.0201i | 1.24041 | − | 1.19514i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.412900 | + | 0.238388i | −0.0213791 | + | 0.0123433i | −0.510651 | − | 0.859788i | \(-0.670596\pi\) |
0.489272 | + | 0.872131i | \(0.337262\pi\) | |||||||
\(374\) | 11.3275 | + | 13.5534i | 0.585730 | + | 0.700828i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.01513 | − | 10.4185i | −0.310207 | − | 0.537294i | ||||
\(377\) | 24.4919i | 1.26140i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.2564 | −0.783669 | −0.391835 | − | 0.920036i | \(-0.628160\pi\) | ||||
−0.391835 | + | 0.920036i | \(0.628160\pi\) | |||||||
\(380\) | 12.0999 | − | 6.98586i | 0.620710 | − | 0.358367i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.1518 | − | 6.43848i | −0.570574 | − | 0.329421i | ||||
\(383\) | −10.5825 | + | 6.10983i | −0.540743 | + | 0.312198i | −0.745380 | − | 0.666640i | \(-0.767732\pi\) |
0.204637 | + | 0.978838i | \(0.434399\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.9289 | + | 23.1499i | −0.862776 | + | 1.17983i | ||||
\(386\) | 6.04479 | 0.307672 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.540692 | + | 0.312169i | 0.0274495 | + | 0.0158480i | ||||
\(389\) | 14.0160 | − | 24.2765i | 0.710641 | − | 1.23087i | −0.253975 | − | 0.967211i | \(-0.581738\pi\) |
0.964617 | − | 0.263656i | \(-0.0849285\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.6094 | 1.44684 | ||||||||
\(392\) | −3.72284 | + | 5.92794i | −0.188032 | + | 0.299406i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.09118 | − | 5.35409i | −0.155732 | − | 0.269735i | ||||
\(395\) | −14.9804 | + | 25.9468i | −0.753744 | + | 1.30552i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.1090 | + | 15.0741i | −1.31038 | + | 0.756546i | −0.982158 | − | 0.188057i | \(-0.939781\pi\) |
−0.328217 | + | 0.944602i | \(0.606448\pi\) | |||||||
\(398\) | 3.88246 | 0.194610 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.68190 | −0.284095 | ||||||||
\(401\) | −1.60532 | − | 2.78050i | −0.0801661 | − | 0.138852i | 0.823155 | − | 0.567817i | \(-0.192212\pi\) |
−0.903321 | + | 0.428965i | \(0.858878\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.6945 | − | 16.5668i | −1.42937 | − | 0.825249i | ||||
\(404\) | 6.58462 | + | 11.4049i | 0.327597 | + | 0.567415i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.04484 | + | 12.2712i | 0.151113 | + | 0.609011i | ||||
\(407\) | −6.63653 | − | 2.43023i | −0.328960 | − | 0.120462i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.1522 | + | 29.7084i | −0.848120 | + | 1.46899i | 0.0347647 | + | 0.999396i | \(0.488932\pi\) |
−0.882884 | + | 0.469591i | \(0.844402\pi\) | |||||||
\(410\) | −1.55188 | + | 2.68794i | −0.0766420 | + | 0.132748i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 13.2122i | − | 0.650916i | ||||||
\(413\) | 24.7538 | + | 25.6914i | 1.21806 | + | 1.26419i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.36582 | − | 1.36591i | 0.116134 | − | 0.0670498i | ||||
\(416\) | −4.43853 | − | 2.56259i | −0.217617 | − | 0.125641i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.9676 | − | 2.43468i | 0.683179 | − | 0.119084i | ||||
\(419\) | − | 12.7969i | − | 0.625168i | −0.949890 | − | 0.312584i | \(-0.898805\pi\) | ||
0.949890 | − | 0.312584i | \(-0.101195\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0356 | 1.70753 | 0.853766 | − | 0.520657i | \(-0.174313\pi\) | ||||
0.853766 | + | 0.520657i | \(0.174313\pi\) | |||||||
\(422\) | 4.52350 | + | 7.83493i | 0.220200 | + | 0.381398i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.8599 | + | 6.26996i | 0.527403 | + | 0.304496i | ||||
\(425\) | −15.1303 | − | 26.2065i | −0.733929 | − | 1.27120i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.40283 | + | 13.7140i | 0.164675 | + | 0.663668i | ||||
\(428\) | − | 11.1094i | − | 0.536994i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.5624 | − | 10.1397i | −0.846936 | − | 0.488979i | ||||
\(431\) | −22.4488 | − | 12.9608i | −1.08132 | − | 0.624302i | −0.150070 | − | 0.988675i | \(-0.547950\pi\) |
−0.931253 | + | 0.364374i | \(0.881283\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.5108i | − | 1.41820i | −0.705110 | − | 0.709098i | \(-0.749102\pi\) | ||
0.705110 | − | 0.709098i | \(-0.250898\pi\) | |||||||
\(434\) | −16.4365 | − | 4.73319i | −0.788975 | − | 0.227200i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.17596 | − | 3.56569i | 0.295775 | − | 0.170766i | ||||
\(437\) | 11.4821 | − | 19.8875i | 0.549262 | − | 0.951350i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.71039 | − | 9.89069i | −0.272542 | − | 0.472057i | 0.696970 | − | 0.717100i | \(-0.254531\pi\) |
−0.969512 | + | 0.245043i | \(0.921198\pi\) | |||||||
\(440\) | −10.1788 | − | 3.72736i | −0.485255 | − | 0.177695i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 27.2956i | − | 1.29832i | ||||||
\(443\) | 12.7606 | + | 22.1020i | 0.606273 | + | 1.05010i | 0.991849 | + | 0.127420i | \(0.0406696\pi\) |
−0.385575 | + | 0.922676i | \(0.625997\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.1711 | + | 17.6169i | −0.482158 | + | 0.835122i | ||||
\(446\) | 2.71468 | + | 4.70196i | 0.128544 | + | 0.222644i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.54243 | − | 0.732142i | −0.120119 | − | 0.0345904i | ||||
\(449\) | −25.9959 | −1.22682 | −0.613412 | − | 0.789763i | \(-0.710203\pi\) | ||||
−0.613412 | + | 0.789763i | \(0.710203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.41672 | + | 2.01982i | −0.113799 | + | 0.0951097i | ||||
\(452\) | −1.20718 | + | 2.09090i | −0.0567809 | + | 0.0983474i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 11.8564i | − | 0.556446i | ||||||
\(455\) | 43.0139 | − | 10.6729i | 2.01652 | − | 0.500355i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.95633 | + | 4.01624i | −0.325403 | + | 0.187872i | −0.653798 | − | 0.756669i | \(-0.726826\pi\) |
0.328395 | + | 0.944540i | \(0.393492\pi\) | |||||||
\(458\) | 3.21350 | − | 5.56595i | 0.150157 | − | 0.260080i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.2048 | + | 8.77847i | −0.708926 | + | 0.409298i | ||||
\(461\) | 33.5115 | 1.56078 | 0.780392 | − | 0.625290i | \(-0.215019\pi\) | ||||
0.780392 | + | 0.625290i | \(0.215019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7419 | −0.731587 | −0.365793 | − | 0.930696i | \(-0.619202\pi\) | ||||
−0.365793 | + | 0.930696i | \(0.619202\pi\) | |||||||
\(464\) | −4.13851 | + | 2.38937i | −0.192125 | + | 0.110924i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.00443 | − | 1.73972i | 0.0465293 | − | 0.0805911i | ||||
\(467\) | −8.86193 | + | 5.11644i | −0.410081 | + | 0.236760i | −0.690825 | − | 0.723022i | \(-0.742752\pi\) |
0.280743 | + | 0.959783i | \(0.409419\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.8003 | + | 11.3697i | −0.544887 | + | 0.525002i | ||||
\(470\) | 39.3187i | 1.81364i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.74219 | + | 11.6778i | −0.310334 | + | 0.537515i | ||||
\(473\) | −13.1971 | − | 15.7904i | −0.606803 | − | 0.726042i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.2896 | −1.11448 | ||||||||
\(476\) | −3.39340 | − | 13.6760i | −0.155536 | − | 0.626839i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.32934 | − | 4.03454i | −0.106542 | − | 0.184536i | ||||
\(479\) | 2.59813 | − | 4.50009i | 0.118712 | − | 0.205614i | −0.800546 | − | 0.599272i | \(-0.795457\pi\) |
0.919257 | + | 0.393657i | \(0.128790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.46070 | + | 9.45820i | 0.248986 | + | 0.431257i | ||||
\(482\) | − | 5.96996i | − | 0.271924i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.39873 | − | 7.10361i | −0.381761 | − | 0.322891i | ||||
\(485\) | −1.02027 | − | 1.76715i | −0.0463279 | − | 0.0802423i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.7741 | − | 27.3216i | 0.714794 | − | 1.23806i | −0.248245 | − | 0.968697i | \(-0.579854\pi\) |
0.963039 | − | 0.269362i | \(-0.0868128\pi\) | |||||||
\(488\) | −4.62509 | + | 2.67030i | −0.209368 | + | 0.120879i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 20.2245 | − | 10.6950i | 0.913650 | − | 0.483150i | ||||
\(491\) | − | 7.14182i | − | 0.322306i | −0.986929 | − | 0.161153i | \(-0.948479\pi\) | ||
0.986929 | − | 0.161153i | \(-0.0515212\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.0409 | − | 12.7253i | −0.992670 | − | 0.573118i | ||||
\(494\) | −18.9743 | − | 10.9548i | −0.853693 | − | 0.492880i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 6.46485i | − | 0.290281i | ||||||
\(497\) | 27.4739 | + | 7.91162i | 1.23237 | + | 0.354885i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3818 | + | 30.1061i | 0.778114 | + | 1.34773i | 0.933027 | + | 0.359805i | \(0.117157\pi\) |
−0.154913 | + | 0.987928i | \(0.549510\pi\) | |||||||
\(500\) | 1.93010 | + | 1.11434i | 0.0863165 | + | 0.0498349i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.728495 | − | 1.26179i | −0.0325143 | − | 0.0563165i | ||||
\(503\) | 3.06150 | 0.136506 | 0.0682529 | − | 0.997668i | \(-0.478258\pi\) | ||||
0.0682529 | + | 0.997668i | \(0.478258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 43.0413i | − | 1.91531i | ||||||
\(506\) | −17.5518 | + | 3.05943i | −0.780272 | + | 0.136008i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.9598 | + | 6.90499i | 0.530630 | + | 0.306360i | ||||
\(509\) | 24.6258 | − | 14.2177i | 1.09152 | − | 0.630188i | 0.157538 | − | 0.987513i | \(-0.449644\pi\) |
0.933980 | + | 0.357325i | \(0.116311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.2058 | − | 24.2860i | 1.11504 | − | 1.07435i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.1871 | − | 22.8407i | 0.581658 | − | 1.00746i | ||||
\(515\) | −21.5908 | + | 37.3963i | −0.951403 | + | 1.64788i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.7199 | + | 37.4668i | −0.603402 | + | 1.64779i | ||||
\(518\) | 3.91184 | + | 4.06000i | 0.171876 | + | 0.178386i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.37536 | + | 14.5065i | 0.367284 | + | 0.636154i | ||||
\(521\) | 3.15741 | + | 1.82293i | 0.138329 | + | 0.0798642i | 0.567567 | − | 0.823327i | \(-0.307885\pi\) |
−0.429238 | + | 0.903191i | \(0.641218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9730 | − | 20.7378i | −0.523542 | − | 0.906801i | −0.999625 | − | 0.0274006i | \(-0.991277\pi\) |
0.476083 | − | 0.879401i | \(-0.342056\pi\) | |||||||
\(524\) | −11.7866 | −0.514902 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −31.3179 | −1.36552 | ||||||||
\(527\) | 29.8177 | − | 17.2152i | 1.29888 | − | 0.749908i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.92843 | + | 5.07220i | −0.127323 | + | 0.220530i | ||||
\(530\) | −20.4922 | − | 35.4936i | −0.890126 | − | 1.54174i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.8686 | − | 3.12983i | −0.471215 | − | 0.135695i | ||||
\(533\) | 4.86714 | 0.210819 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.1546 | + | 31.4446i | −0.784890 | + | 1.35947i | ||||
\(536\) | −5.36373 | − | 3.09675i | −0.231678 | − | 0.133759i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.05002 | 0.131496 | ||||||||
\(539\) | 23.0039 | − | 3.13408i | 0.990846 | − | 0.134994i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.2883 | + | 21.5284i | −1.60315 | + | 0.925580i | −0.612299 | + | 0.790626i | \(0.709755\pi\) |
−0.990852 | + | 0.134954i | \(0.956911\pi\) | |||||||
\(542\) | 19.4416 | + | 11.2246i | 0.835089 | + | 0.482139i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.61228 | − | 2.66290i | 0.197750 | − | 0.114171i | ||||
\(545\) | −23.3076 | −0.998389 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.00013i | − | 0.342061i | −0.985266 | − | 0.171030i | \(-0.945290\pi\) | ||
0.985266 | − | 0.171030i | \(-0.0547097\pi\) | |||||||
\(548\) | −2.43055 | − | 4.20984i | −0.103828 | − | 0.179836i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.0849 | + | 14.4596i | 0.515301 | + | 0.616560i | ||||
\(551\) | −17.6917 | + | 10.2143i | −0.753692 | + | 0.435144i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.5398 | − | 5.84089i | 1.00102 | − | 0.248380i | ||||
\(554\) | 20.5218 | 0.871888 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.39134 | − | 14.5342i | 0.355872 | − | 0.616388i | ||||
\(557\) | 20.2134 | + | 11.6702i | 0.856471 | + | 0.494484i | 0.862829 | − | 0.505496i | \(-0.168691\pi\) |
−0.00635822 | + | 0.999980i | \(0.502024\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.8009i | 1.34503i | ||||||||
\(560\) | 5.99979 | + | 6.22703i | 0.253537 | + | 0.263140i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.94109 | + | 12.0223i | 0.292792 | + | 0.507131i | ||||
\(563\) | 13.2190 | − | 22.8960i | 0.557116 | − | 0.964953i | −0.440620 | − | 0.897694i | \(-0.645241\pi\) |
0.997736 | − | 0.0672592i | \(-0.0214254\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.83371 | − | 3.94545i | 0.287496 | − | 0.165986i | ||||
\(566\) | 29.7862i | 1.25201i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.8061i | 0.453415i | ||||||||
\(569\) | −21.6494 | + | 12.4993i | −0.907590 | + | 0.523997i | −0.879655 | − | 0.475612i | \(-0.842227\pi\) |
−0.0279352 | + | 0.999610i | \(0.508893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.6593 | + | 21.7426i | 1.57599 | + | 0.909899i | 0.995411 | + | 0.0956961i | \(0.0305077\pi\) |
0.580581 | + | 0.814203i | \(0.302826\pi\) | |||||||
\(572\) | 2.91894 | + | 16.7458i | 0.122047 | + | 0.700177i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.43860 | − | 0.605084i | 0.101785 | − | 0.0252557i | ||||
\(575\) | 30.5224 | 1.27287 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.0746 | + | 13.8995i | 1.00224 | + | 0.578643i | 0.908910 | − | 0.416992i | \(-0.136916\pi\) |
0.0933293 | + | 0.995635i | \(0.470249\pi\) | |||||||
\(578\) | 9.84161 | + | 5.68205i | 0.409357 | + | 0.236342i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15.6184 | 0.648520 | ||||||||
\(581\) | −2.12509 | − | 0.611959i | −0.0881634 | − | 0.0253883i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.14185 | − | 40.9724i | −0.295785 | − | 1.69690i | ||||
\(584\) | 11.4571 | + | 6.61476i | 0.474098 | + | 0.273721i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00174 | − | 5.19716i | 0.371859 | − | 0.214693i | ||||
\(587\) | 11.2683i | 0.465091i | 0.972585 | + | 0.232546i | \(0.0747055\pi\) | ||||
−0.972585 | + | 0.232546i | \(0.925294\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 27.6366i | − | 1.13875i | ||||||
\(590\) | 38.1668 | − | 22.0356i | 1.57130 | − | 0.907192i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.06546 | + | 1.84544i | −0.0437903 | + | 0.0758471i | ||||
\(593\) | 7.85106 | + | 13.5984i | 0.322405 | + | 0.558421i | 0.980984 | − | 0.194090i | \(-0.0621755\pi\) |
−0.658579 | + | 0.752512i | \(0.728842\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.7440 | + | 44.2546i | −0.522451 | + | 1.81426i | ||||
\(596\) | − | 7.22464i | − | 0.295933i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 23.8432 | + | 13.7659i | 0.975020 | + | 0.562928i | ||||
\(599\) | 4.79001 | − | 8.29654i | 0.195714 | − | 0.338987i | −0.751420 | − | 0.659824i | \(-0.770631\pi\) |
0.947134 | + | 0.320837i | \(0.103964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.7398 | 1.49865 | 0.749324 | − | 0.662204i | \(-0.230379\pi\) | ||||
0.749324 | + | 0.662204i | \(0.230379\pi\) | |||||||
\(602\) | 3.95349 | + | 15.9333i | 0.161132 | + | 0.649392i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.22644 | + | 2.44014i | −0.171972 | + | 0.0992878i | ||||
\(605\) | 12.1637 | + | 33.8313i | 0.494526 | + | 1.37544i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.2326 | + | 35.0438i | 0.821215 | + | 1.42239i | 0.904778 | + | 0.425883i | \(0.140037\pi\) |
−0.0835632 | + | 0.996502i | \(0.526630\pi\) | |||||||
\(608\) | − | 4.27490i | − | 0.173370i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.4548 | 0.706723 | ||||||||
\(611\) | 53.3967 | − | 30.8286i | 2.16020 | − | 1.24719i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.07028 | − | 5.23673i | −0.366345 | − | 0.211509i | 0.305515 | − | 0.952187i | \(-0.401171\pi\) |
−0.671860 | + | 0.740678i | \(0.734505\pi\) | |||||||
\(614\) | 1.19379 | − | 0.689237i | 0.0481776 | − | 0.0278153i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.54433 | + | 8.02731i | 0.142805 | + | 0.323430i | ||||
\(617\) | 14.4244 | 0.580706 | 0.290353 | − | 0.956920i | \(-0.406227\pi\) | ||||
0.290353 | + | 0.956920i | \(0.406227\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.7932 | + | 22.3973i | 1.55923 | + | 0.900223i | 0.997331 | + | 0.0730178i | \(0.0232630\pi\) |
0.561901 | + | 0.827205i | \(0.310070\pi\) | |||||||
\(620\) | −10.5646 | + | 18.2984i | −0.424285 | + | 0.734882i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.5210 | 0.421855 | ||||||||
\(623\) | 15.9827 | − | 3.96575i | 0.640333 | − | 0.158885i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.5627 | + | 18.2952i | 0.422510 | + | 0.731808i | ||||
\(626\) | −1.13347 | + | 1.96323i | −0.0453026 | + | 0.0784664i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.85996 | + | 1.65120i | −0.114125 | + | 0.0658900i | ||||
\(629\) | −11.3489 | −0.452510 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.1975 | 0.525383 | 0.262692 | − | 0.964880i | \(-0.415390\pi\) | ||||
0.262692 | + | 0.964880i | \(0.415390\pi\) | |||||||
\(632\) | 4.58351 | + | 7.93887i | 0.182322 | + | 0.315791i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.27963 | + | 2.47085i | 0.169966 | + | 0.0981298i | ||||
\(635\) | −22.5677 | − | 39.0884i | −0.895572 | − | 1.55118i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.3817 | − | 19.0802i | −1.20377 | − | 0.755986i | ||||
\(638\) | 14.8828 | + | 5.44993i | 0.589216 | + | 0.215765i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.63416 | + | 2.83045i | −0.0645958 | + | 0.111883i | ||||
\(641\) | 10.7925 | − | 18.6931i | 0.426278 | − | 0.738335i | −0.570261 | − | 0.821463i | \(-0.693158\pi\) |
0.996539 | + | 0.0831289i | \(0.0264913\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 28.9651i | − | 1.14227i | −0.820855 | − | 0.571137i | \(-0.806503\pi\) | ||
0.820855 | − | 0.571137i | \(-0.193497\pi\) | |||||||
\(644\) | 13.6576 | + | 3.93296i | 0.538185 | + | 0.154980i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.7170 | − | 11.3836i | 0.775755 | − | 0.447882i | ||||
\(647\) | −25.4299 | − | 14.6820i | −0.999753 | − | 0.577208i | −0.0915779 | − | 0.995798i | \(-0.529191\pi\) |
−0.908175 | + | 0.418590i | \(0.862524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.0583 | − | 7.67974i | 1.72944 | − | 0.301456i | ||||
\(650\) | − | 29.1208i | − | 1.14221i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.84536 | 0.189759 | ||||||||
\(653\) | −19.1225 | − | 33.1211i | −0.748320 | − | 1.29613i | −0.948628 | − | 0.316395i | \(-0.897528\pi\) |
0.200308 | − | 0.979733i | \(-0.435806\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.3615 | + | 19.2612i | 1.30354 | + | 0.752599i | ||||
\(656\) | 0.474826 | + | 0.822423i | 0.0185388 | + | 0.0321102i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.9209 | − | 22.0844i | 0.893549 | − | 0.860941i | ||||
\(659\) | 0.210272i | 0.00819105i | 0.999992 | + | 0.00409553i | \(0.00130365\pi\) | ||||
−0.999992 | + | 0.00409553i | \(0.998696\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.07735 | + | 4.66346i | 0.314172 | + | 0.181388i | 0.648792 | − | 0.760966i | \(-0.275274\pi\) |
−0.334620 | + | 0.942353i | \(0.608608\pi\) | |||||||
\(662\) | 11.2141 | + | 6.47446i | 0.435848 | + | 0.251637i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 0.835847i | − | 0.0324372i | ||||||
\(665\) | 25.6485 | + | 26.6199i | 0.994605 | + | 1.03228i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.2315 | − | 12.8354i | 0.860807 | − | 0.496987i | ||||
\(668\) | −1.06961 | + | 1.85262i | −0.0413844 | + | 0.0716799i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.1212 | + | 17.5304i | 0.391015 | + | 0.677257i | ||||
\(671\) | 16.6327 | + | 6.09070i | 0.642096 | + | 0.235129i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.7351i | 0.606545i | 0.952904 | + | 0.303273i | \(0.0980793\pi\) | ||||
−0.952904 | + | 0.303273i | \(0.901921\pi\) | |||||||
\(674\) | −4.11071 | − | 7.11996i | −0.158339 | − | 0.274251i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.63372 | − | 11.4899i | 0.255143 | − | 0.441921i | ||||
\(677\) | 6.53943 | + | 11.3266i | 0.251331 | + | 0.435318i | 0.963892 | − | 0.266292i | \(-0.0857985\pi\) |
−0.712562 | + | 0.701609i | \(0.752465\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.457103 | + | 1.58734i | −0.0175420 | + | 0.0609164i | ||||
\(680\) | −17.4064 | −0.667505 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.4521 | + | 13.7501i | −0.629983 | + | 0.526520i | ||||
\(683\) | −12.5854 | + | 21.7986i | −0.481568 | + | 0.834101i | −0.999776 | − | 0.0211540i | \(-0.993266\pi\) |
0.518208 | + | 0.855255i | \(0.326599\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.8876i | 0.607036i | ||||||||
\(686\) | −17.5943 | − | 5.78276i | −0.671754 | − | 0.220787i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.37354 | + | 3.10242i | −0.204864 | + | 0.118278i | ||||
\(689\) | −32.1347 | + | 55.6589i | −1.22423 | + | 2.12043i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.686294 | − | 0.396232i | 0.0261079 | − | 0.0150734i | −0.486889 | − | 0.873464i | \(-0.661868\pi\) |
0.512997 | + | 0.858390i | \(0.328535\pi\) | |||||||
\(692\) | −17.7492 | −0.674722 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.3657 | 1.19063 | ||||||||
\(695\) | −47.5025 | + | 27.4256i | −1.80187 | + | 1.04031i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.52883 | + | 4.38006i | −0.0957862 | + | 0.165907i | ||||
\(698\) | −2.73094 | + | 1.57671i | −0.103368 | + | 0.0596793i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.62030 | − | 14.5905i | −0.136835 | − | 0.551468i | ||||
\(701\) | 39.5754i | 1.49474i | 0.664406 | + | 0.747372i | \(0.268685\pi\) | ||||
−0.664406 | + | 0.747372i | \(0.731315\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.55475 | + | 7.88906i | −0.171786 | + | 0.297542i | ||||
\(704\) | −2.54485 | + | 2.12691i | −0.0959127 | + | 0.0801608i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.15423 | −0.306889 | ||||||||
\(707\) | −25.0910 | + | 24.1753i | −0.943643 | + | 0.909206i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.2211 | − | 31.5598i | −0.684307 | − | 1.18525i | −0.973654 | − | 0.228030i | \(-0.926771\pi\) |
0.289347 | − | 0.957224i | \(-0.406562\pi\) | |||||||
\(710\) | 17.6589 | − | 30.5862i | 0.662728 | − | 1.14788i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.11204 | + | 5.39021i | 0.116629 | + | 0.202007i | ||||
\(713\) | 34.7283i | 1.30058i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.1034 | − | 52.1681i | 0.714427 | − | 1.95098i | ||||
\(716\) | −1.44235 | − | 2.49822i | −0.0539031 | − | 0.0933629i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.77023 | + | 8.26228i | −0.178023 | + | 0.308346i | ||||
\(719\) | 12.2632 | − | 7.08018i | 0.457341 | − | 0.264046i | −0.253584 | − | 0.967313i | \(-0.581610\pi\) |
0.710926 | + | 0.703267i | \(0.248276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.9273 | − | 8.41830i | 1.26352 | − | 0.313514i | ||||
\(722\) | 0.725250i | 0.0269910i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.47011 | + | 5.46757i | 0.351954 | + | 0.203201i | ||||
\(725\) | −23.5146 | − | 13.5762i | −0.873311 | − | 0.504206i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.58699i | − | 0.318474i | −0.987240 | − | 0.159237i | \(-0.949097\pi\) | ||
0.987240 | − | 0.159237i | \(-0.0509033\pi\) | |||||||
\(728\) | 3.75236 | − | 13.0304i | 0.139072 | − | 0.482940i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −21.6191 | − | 37.4454i | −0.800160 | − | 1.38592i | ||||
\(731\) | −28.6184 | − | 16.5228i | −1.05849 | − | 0.611119i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.3598 | − | 36.9962i | −0.788942 | − | 1.36649i | −0.926616 | − | 0.376010i | \(-0.877296\pi\) |
0.137674 | − | 0.990478i | \(-0.456037\pi\) | |||||||
\(734\) | 6.76680 | 0.249767 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.37186i | 0.198009i | ||||||||
\(737\) | 3.52738 | + | 20.2364i | 0.129933 | + | 0.745417i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.7537 | − | 16.6009i | −1.05772 | − | 0.610675i | −0.132920 | − | 0.991127i | \(-0.542435\pi\) |
−0.924801 | + | 0.380452i | \(0.875769\pi\) | |||||||
\(740\) | 6.03148 | − | 3.48228i | 0.221722 | − | 0.128011i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.18100 | + | 31.8819i | −0.337045 | + | 1.17042i | ||||
\(743\) | 8.11448i | 0.297691i | 0.988860 | + | 0.148846i | \(0.0475557\pi\) | ||||
−0.988860 | + | 0.148846i | \(0.952444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.8062 | + | 20.4490i | −0.432546 | + | 0.749192i | ||||
\(746\) | 0.238388 | − | 0.412900i | 0.00872800 | − | 0.0151173i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.5866 | − | 6.07382i | −0.606465 | − | 0.222081i | ||||
\(749\) | 28.5277 | − | 7.07852i | 1.04238 | − | 0.258643i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0376756 | − | 0.0652561i | −0.00137480 | − | 0.00238123i | 0.865337 | − | 0.501190i | \(-0.167104\pi\) |
−0.866712 | + | 0.498809i | \(0.833771\pi\) | |||||||
\(752\) | 10.4185 | + | 6.01513i | 0.379924 | + | 0.219349i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.2459 | − | 21.2106i | −0.445971 | − | 0.772444i | ||||
\(755\) | 15.9503 | 0.580491 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.134400 | −0.00488484 | −0.00244242 | − | 0.999997i | \(-0.500777\pi\) | ||||
−0.00244242 | + | 0.999997i | \(0.500777\pi\) | |||||||
\(758\) | 13.2124 | − | 7.62821i | 0.479898 | − | 0.277069i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.98586 | + | 12.0999i | −0.253404 | + | 0.438908i | ||||
\(761\) | 7.35142 | + | 12.7330i | 0.266489 | + | 0.461572i | 0.967953 | − | 0.251133i | \(-0.0808031\pi\) |
−0.701464 | + | 0.712705i | \(0.747470\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.0914 | + | 13.5872i | 0.473939 | + | 0.491890i | ||||
\(764\) | 12.8770 | 0.465872 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.10983 | − | 10.5825i | 0.220757 | − | 0.382363i | ||||
\(767\) | −59.8508 | − | 34.5549i | −2.16109 | − | 1.24770i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.17040 | −0.258571 | −0.129286 | − | 0.991607i | \(-0.541268\pi\) | ||||
−0.129286 | + | 0.991607i | \(0.541268\pi\) | |||||||
\(770\) | 3.08588 | − | 28.5129i | 0.111207 | − | 1.02753i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.23494 | + | 3.02239i | −0.188410 | + | 0.108778i | ||||
\(773\) | 32.2256 | + | 18.6055i | 1.15907 | + | 0.669192i | 0.951082 | − | 0.308939i | \(-0.0999739\pi\) |
0.207992 | + | 0.978131i | \(0.433307\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.8114 | − | 18.3663i | 1.14270 | − | 0.659739i | ||||
\(776\) | −0.624337 | −0.0224124 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.0321i | 1.00500i | ||||||||
\(779\) | 2.02983 | + | 3.51577i | 0.0727263 | + | 0.125966i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.5000 | − | 22.9836i | 0.984027 | − | 0.822419i | ||||
\(782\) | −24.7765 | + | 14.3047i | −0.886006 | + | 0.511536i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.260109 | − | 6.99517i | 0.00928960 | − | 0.249827i | ||||
\(785\) | 10.7933 | 0.385229 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.5599 | + | 37.3429i | −0.768529 | + | 1.33113i | 0.169831 | + | 0.985473i | \(0.445678\pi\) |
−0.938360 | + | 0.345658i | \(0.887656\pi\) | |||||||
\(788\) | 5.35409 | + | 3.09118i | 0.190732 | + | 0.110119i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 29.9607i | − | 1.06596i | ||||||
\(791\) | −6.13834 | − | 1.76765i | −0.218254 | − | 0.0628505i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.6858 | − | 23.7044i | −0.485995 | − | 0.841769i | ||||
\(794\) | 15.0741 | − | 26.1090i | 0.534959 | − | 0.926575i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.36231 | + | 1.94123i | −0.119174 | + | 0.0688050i | ||||
\(797\) | 30.1768i | 1.06892i | 0.845195 | + | 0.534458i | \(0.179484\pi\) | ||||
−0.845195 | + | 0.534458i | \(0.820516\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 64.0707i | 2.26666i | ||||||||
\(800\) | 4.92067 | − | 2.84095i | 0.173972 | − | 0.100443i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.78050 | + | 1.60532i | 0.0981830 | + | 0.0566860i | ||||
\(803\) | −7.53459 | − | 43.2256i | −0.265890 | − | 1.52540i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −32.2300 | − | 33.4507i | −1.13596 | − | 1.17898i | ||||
\(806\) | 33.1335 | 1.16708 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.4049 | − | 6.58462i | −0.401223 | − | 0.231646i | ||||
\(809\) | −40.0519 | − | 23.1240i | −1.40815 | − | 0.812996i | −0.412940 | − | 0.910758i | \(-0.635498\pi\) |
−0.995210 | + | 0.0977627i | \(0.968831\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.9534 | −0.806003 | −0.403001 | − | 0.915199i | \(-0.632033\pi\) | ||||
−0.403001 | + | 0.915199i | \(0.632033\pi\) | |||||||
\(812\) | −8.77253 | − | 9.10479i | −0.307855 | − | 0.319515i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.96251 | − | 1.21363i | 0.244036 | − | 0.0425376i | ||||
\(815\) | −13.7145 | − | 7.91809i | −0.480399 | − | 0.277359i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.9713 | + | 13.2625i | −0.803666 | + | 0.463997i | ||||
\(818\) | − | 34.3043i | − | 1.19942i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 3.10377i | − | 0.108388i | ||||||
\(821\) | −14.2638 | + | 8.23523i | −0.497812 | + | 0.287412i | −0.727809 | − | 0.685780i | \(-0.759461\pi\) |
0.229998 | + | 0.973191i | \(0.426128\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.10784 | + | 10.5791i | −0.212906 | + | 0.368764i | −0.952623 | − | 0.304155i | \(-0.901626\pi\) |
0.739717 | + | 0.672918i | \(0.234959\pi\) | |||||||
\(824\) | 6.60608 | + | 11.4421i | 0.230134 | + | 0.398603i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −34.2831 | − | 9.87247i | −1.19286 | − | 0.343507i | ||||
\(827\) | 4.55524i | 0.158401i | 0.996859 | + | 0.0792007i | \(0.0252368\pi\) | ||||
−0.996859 | + | 0.0792007i | \(0.974763\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.1952 | − | 18.5879i | −1.11819 | − | 0.645585i | −0.177249 | − | 0.984166i | \(-0.556720\pi\) |
−0.940937 | + | 0.338581i | \(0.890053\pi\) | |||||||
\(830\) | −1.36591 | + | 2.36582i | −0.0474113 | + | 0.0821188i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.12518 | 0.177684 | ||||||||
\(833\) | 32.9563 | − | 17.4277i | 1.14187 | − | 0.603835i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.05494 | − | 3.49582i | 0.209540 | − | 0.120978i | ||||
\(836\) | −10.8790 | + | 9.09231i | −0.376257 | + | 0.314464i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.39844 | + | 11.0824i | 0.221030 | + | 0.382836i | ||||
\(839\) | − | 39.5086i | − | 1.36399i | −0.731358 | − | 0.681994i | \(-0.761113\pi\) | ||
0.731358 | − | 0.681994i | \(-0.238887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.16366 | 0.212540 | ||||||||
\(842\) | −30.3417 | + | 17.5178i | −1.04565 | + | 0.603704i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.83493 | − | 4.52350i | −0.269689 | − | 0.155705i | ||||
\(845\) | −37.5528 | + | 21.6811i | −1.29185 | + | 0.745853i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.8899 | − | 26.0931i | 0.442901 | − | 0.896570i | ||||
\(848\) | −12.5399 | −0.430623 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.2065 | + | 15.1303i | 0.898876 | + | 0.518966i | ||||
\(851\) | 5.72353 | − | 9.91344i | 0.196200 | − | 0.339828i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.2280 | −1.17194 | −0.585972 | − | 0.810331i | \(-0.699287\pi\) | ||||
−0.585972 | + | 0.810331i | \(0.699287\pi\) | |||||||
\(854\) | −9.80396 | − | 10.1753i | −0.335484 | − | 0.348191i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.55471 | + | 9.62104i | 0.189856 | + | 0.328840i | ||||
\(857\) | −0.822073 | + | 1.42387i | −0.0280815 | + | 0.0486385i | −0.879725 | − | 0.475484i | \(-0.842273\pi\) |
0.851643 | + | 0.524122i | \(0.175606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0267 | + | 10.9850i | −0.649181 | + | 0.374805i | −0.788142 | − | 0.615493i | \(-0.788957\pi\) |
0.138961 | + | 0.990298i | \(0.455624\pi\) | |||||||
\(860\) | 20.2794 | 0.691521 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.9217 | 0.882896 | ||||||||
\(863\) | 4.76103 | + | 8.24634i | 0.162067 | + | 0.280709i | 0.935610 | − | 0.353036i | \(-0.114851\pi\) |
−0.773543 | + | 0.633744i | \(0.781517\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50.2380 | + | 29.0049i | 1.70814 | + | 0.986198i | ||||
\(866\) | 14.7554 | + | 25.5571i | 0.501408 | + | 0.868464i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.6010 | − | 4.11917i | 0.563474 | − | 0.139814i | ||||
\(869\) | 10.4546 | − | 28.5496i | 0.354646 | − | 0.968478i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.8714 | − | 27.4901i | 0.537782 | − | 0.931465i | ||||
\(872\) | −3.56569 | + | 6.17596i | −0.120750 | + | 0.209144i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22.9641i | 0.776774i | ||||||||
\(875\) | −1.63171 | + | 5.66628i | −0.0551619 | + | 0.191555i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.0244 | − | 17.3346i | 1.01385 | − | 0.585347i | 0.101534 | − | 0.994832i | \(-0.467625\pi\) |
0.912317 | + | 0.409485i | \(0.134292\pi\) | |||||||
\(878\) | 9.89069 | + | 5.71039i | 0.333795 | + | 0.192716i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.6788 | − | 1.86140i | 0.359981 | − | 0.0627479i | ||||
\(881\) | 9.30311i | 0.313430i | 0.987644 | + | 0.156715i | \(0.0500904\pi\) | ||||
−0.987644 | + | 0.156715i | \(0.949910\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.2050 | −1.35301 | −0.676503 | − | 0.736440i | \(-0.736505\pi\) | ||||
−0.676503 | + | 0.736440i | \(0.736505\pi\) | |||||||
\(884\) | 13.6478 | + | 23.6387i | 0.459026 | + | 0.795056i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.1020 | − | 12.7606i | −0.742530 | − | 0.428700i | ||||
\(887\) | 7.54456 | + | 13.0676i | 0.253322 | + | 0.438766i | 0.964438 | − | 0.264308i | \(-0.0851436\pi\) |
−0.711117 | + | 0.703074i | \(0.751810\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.1109 | + | 35.1110i | −0.339108 | + | 1.17758i | ||||
\(890\) | − | 20.3423i | − | 0.681874i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.70196 | − | 2.71468i | −0.157433 | − | 0.0908940i | ||||
\(893\) | 44.5381 | + | 25.7141i | 1.49041 | + | 0.860488i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.42811i | 0.315147i | ||||||||
\(896\) | 2.56788 | − | 0.637163i | 0.0857869 | − | 0.0212861i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.5131 | − | 12.9980i | 0.751273 | − | 0.433747i | ||||
\(899\) | 15.4469 | − | 26.7549i | 0.515184 | − | 0.892324i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.3925 | − | 57.8376i | −1.11247 | − | 1.92685i | ||||
\(902\) | 1.08303 | − | 2.95758i | 0.0360611 | − | 0.0984766i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 2.41436i | − | 0.0803004i | ||||||
\(905\) | −17.8698 | − | 30.9513i | −0.594011 | − | 1.02886i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.26851 | − | 16.0535i | 0.307756 | − | 0.533049i | −0.670115 | − | 0.742257i | \(-0.733755\pi\) |
0.977871 | + | 0.209208i | \(0.0670887\pi\) | |||||||
\(908\) | 5.92818 | + | 10.2679i | 0.196734 | + | 0.340752i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −31.9146 | + | 30.7500i | −1.05796 | + | 1.01935i | ||||
\(911\) | 33.6539 | 1.11500 | 0.557502 | − | 0.830176i | \(-0.311760\pi\) | ||||
0.557502 | + | 0.830176i | \(0.311760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.12711 | + | 1.77777i | −0.0703970 | + | 0.0588356i | ||||
\(914\) | 4.01624 | − | 6.95633i | 0.132845 | − | 0.230095i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.42701i | 0.212354i | ||||||||
\(917\) | −7.51002 | − | 30.2667i | −0.248003 | − | 0.999495i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.9496 | + | 6.89909i | −0.394180 | + | 0.227580i | −0.683970 | − | 0.729510i | \(-0.739748\pi\) |
0.289790 | + | 0.957090i | \(0.406415\pi\) | |||||||
\(920\) | 8.77847 | − | 15.2048i | 0.289418 | − | 0.501286i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29.0218 | + | 16.7557i | −0.955781 | + | 0.551821i | ||||
\(923\) | −55.3833 | −1.82296 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.1077 | −0.398100 | ||||||||
\(926\) | 13.6329 | − | 7.87094i | 0.448004 | − | 0.258655i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.38937 | − | 4.13851i | 0.0784349 | − | 0.135853i | ||||
\(929\) | 27.2253 | − | 15.7186i | 0.893234 | − | 0.515709i | 0.0182352 | − | 0.999834i | \(-0.494195\pi\) |
0.874999 | + | 0.484125i | \(0.160862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.11194 | − | 29.9036i | 0.0364423 | − | 0.980051i | ||||
\(932\) | 2.00886i | 0.0658023i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.11644 | − | 8.86193i | 0.167415 | − | 0.289971i | ||||
\(935\) | 37.0218 | + | 44.2967i | 1.21074 | + | 1.44866i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.0822 | 0.427377 | 0.213689 | − | 0.976902i | \(-0.431452\pi\) | ||||
0.213689 | + | 0.976902i | \(0.431452\pi\) | |||||||
\(938\) | 4.53452 | − | 15.7466i | 0.148057 | − | 0.514143i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.6594 | − | 34.0510i | −0.641217 | − | 1.11062i | ||||
\(941\) | 19.1723 | − | 33.2075i | 0.625001 | − | 1.08253i | −0.363540 | − | 0.931579i | \(-0.618432\pi\) |
0.988541 | − | 0.150954i | \(-0.0482347\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.55070 | − | 4.41794i | −0.0830622 | − | 0.143868i | ||||
\(944\) | − | 13.4844i | − | 0.438879i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.3242 | + | 7.07632i | 0.628284 | + | 0.230071i | ||||
\(947\) | 20.4702 | + | 35.4555i | 0.665193 | + | 1.15215i | 0.979233 | + | 0.202738i | \(0.0649841\pi\) |
−0.314040 | + | 0.949410i | \(0.601683\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33.9018 | + | 58.7196i | −1.10050 | + | 1.90612i | ||||
\(950\) | 21.0354 | − | 12.1448i | 0.682478 | − | 0.394029i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.77678 | + | 10.1471i | 0.316867 | + | 0.328869i | ||||
\(953\) | 19.7503i | 0.639776i | 0.947455 | + | 0.319888i | \(0.103645\pi\) | ||||
−0.947455 | + | 0.319888i | \(0.896355\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.4475 | − | 21.0430i | −1.17941 | − | 0.680936i | ||||
\(956\) | 4.03454 | + | 2.32934i | 0.130486 | + | 0.0753364i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.19626i | 0.167883i | ||||||||
\(959\) | 9.26172 | − | 8.92373i | 0.299077 | − | 0.288162i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.39717 | + | 9.34818i | 0.174102 | + | 0.301554i | ||||
\(962\) | −9.45820 | − | 5.46070i | −0.304945 | − | 0.176060i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.98498 | + | 5.17014i | 0.0961397 | + | 0.166519i | ||||
\(965\) | 19.7563 | 0.635977 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.4927i | 1.17352i | 0.809759 | + | 0.586762i | \(0.199598\pi\) | ||||
−0.809759 | + | 0.586762i | \(0.800402\pi\) | |||||||
\(968\) | 10.8253 | + | 1.95254i | 0.347939 | + | 0.0627570i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.76715 | + | 1.02027i | 0.0567399 | + | 0.0327588i | ||||
\(971\) | 44.5292 | − | 25.7089i | 1.42901 | − | 0.825039i | 0.431967 | − | 0.901889i | \(-0.357820\pi\) |
0.997043 | + | 0.0768499i | \(0.0244862\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.6688 | + | 12.2873i | 1.36790 | + | 0.393913i | ||||
\(974\) | 31.5483i | 1.01087i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.67030 | − | 4.62509i | 0.0854742 | − | 0.148046i | ||||
\(977\) | 3.90814 | − | 6.76910i | 0.125033 | − | 0.216563i | −0.796713 | − | 0.604358i | \(-0.793430\pi\) |
0.921746 | + | 0.387795i | \(0.126763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.09827 | − | 19.3841i | 0.226862 | − | 0.619520i | ||||
\(980\) | −12.1674 | + | 19.3744i | −0.388675 | + | 0.618892i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.57091 | + | 6.18500i | 0.113952 | + | 0.197371i | ||||
\(983\) | −12.7959 | − | 7.38773i | −0.408126 | − | 0.235632i | 0.281858 | − | 0.959456i | \(-0.409049\pi\) |
−0.689984 | + | 0.723824i | \(0.742383\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.1030 | − | 17.4989i | −0.321908 | − | 0.557560i | ||||
\(986\) | 25.4506 | 0.810512 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.9096 | 0.697037 | ||||||||
\(989\) | 28.8659 | − | 16.6657i | 0.917883 | − | 0.529940i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.272746 | − | 0.472410i | 0.00866407 | − | 0.0150066i | −0.861661 | − | 0.507485i | \(-0.830575\pi\) |
0.870325 | + | 0.492478i | \(0.163909\pi\) | |||||||
\(992\) | 3.23243 | + | 5.59873i | 0.102630 | + | 0.177760i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −27.7489 | + | 6.88527i | −0.880141 | + | 0.218387i | ||||
\(995\) | 12.6891 | 0.402272 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.9612 | + | 32.8418i | −0.600508 | + | 1.04011i | 0.392236 | + | 0.919865i | \(0.371702\pi\) |
−0.992744 | + | 0.120246i | \(0.961632\pi\) | |||||||
\(998\) | −30.1061 | − | 17.3818i | −0.952991 | − | 0.550210i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.bk.b.703.1 | 16 | ||
3.2 | odd | 2 | 462.2.p.b.241.8 | yes | 16 | ||
7.5 | odd | 6 | 1386.2.bk.a.901.5 | 16 | |||
11.10 | odd | 2 | 1386.2.bk.a.703.5 | 16 | |||
21.5 | even | 6 | 462.2.p.a.439.4 | yes | 16 | ||
21.11 | odd | 6 | 3234.2.e.b.2155.16 | 16 | |||
21.17 | even | 6 | 3234.2.e.a.2155.9 | 16 | |||
33.32 | even | 2 | 462.2.p.a.241.4 | ✓ | 16 | ||
77.54 | even | 6 | inner | 1386.2.bk.b.901.1 | 16 | ||
231.32 | even | 6 | 3234.2.e.a.2155.8 | 16 | |||
231.131 | odd | 6 | 462.2.p.b.439.8 | yes | 16 | ||
231.164 | odd | 6 | 3234.2.e.b.2155.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.4 | ✓ | 16 | 33.32 | even | 2 | ||
462.2.p.a.439.4 | yes | 16 | 21.5 | even | 6 | ||
462.2.p.b.241.8 | yes | 16 | 3.2 | odd | 2 | ||
462.2.p.b.439.8 | yes | 16 | 231.131 | odd | 6 | ||
1386.2.bk.a.703.5 | 16 | 11.10 | odd | 2 | |||
1386.2.bk.a.901.5 | 16 | 7.5 | odd | 6 | |||
1386.2.bk.b.703.1 | 16 | 1.1 | even | 1 | trivial | ||
1386.2.bk.b.901.1 | 16 | 77.54 | even | 6 | inner | ||
3234.2.e.a.2155.8 | 16 | 231.32 | even | 6 | |||
3234.2.e.a.2155.9 | 16 | 21.17 | even | 6 | |||
3234.2.e.b.2155.1 | 16 | 231.164 | odd | 6 | |||
3234.2.e.b.2155.16 | 16 | 21.11 | odd | 6 |