Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(361,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.do (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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.2346760387617129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 667.6 | ||
Root | \(1.32725 - 0.488273i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.667 |
Dual form | 819.2.do.e.361.6 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.24179 | − | 1.29430i | 1.58519 | − | 0.915209i | 0.591104 | − | 0.806596i | \(-0.298692\pi\) |
0.994084 | − | 0.108613i | \(-0.0346409\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.35043 | − | 4.07106i | 1.17521 | − | 2.03553i | ||||
\(5\) | −1.39608 | − | 0.806027i | −0.624346 | − | 0.360466i | 0.154213 | − | 0.988038i | \(-0.450716\pi\) |
−0.778559 | + | 0.627571i | \(0.784049\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62954 | + | 0.292422i | 0.993873 | + | 0.110525i | ||||
\(8\) | − | 6.99143i | − | 2.47184i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.17296 | −1.31961 | ||||||||
\(11\) | − | 2.70496i | − | 0.815575i | −0.913077 | − | 0.407788i | \(-0.866300\pi\) | ||
0.913077 | − | 0.407788i | \(-0.133700\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.36840 | + | 2.71858i | 0.656876 | + | 0.753998i | ||||
\(14\) | 6.27337 | − | 2.74787i | 1.67663 | − | 0.734398i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.34816 | − | 7.53123i | −1.08704 | − | 1.88281i | ||||
\(17\) | −1.56330 | + | 2.70772i | −0.379157 | + | 0.656719i | −0.990940 | − | 0.134307i | \(-0.957119\pi\) |
0.611783 | + | 0.791026i | \(0.290453\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.68150i | − | 0.844595i | −0.906457 | − | 0.422297i | \(-0.861224\pi\) | ||
0.906457 | − | 0.422297i | \(-0.138776\pi\) | |||||||
\(20\) | −6.56276 | + | 3.78901i | −1.46748 | + | 0.847249i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.50103 | − | 6.06396i | −0.746421 | − | 1.29284i | ||||
\(23\) | −0.993019 | − | 1.71996i | −0.207059 | − | 0.358636i | 0.743728 | − | 0.668482i | \(-0.233056\pi\) |
−0.950787 | + | 0.309846i | \(0.899722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.20064 | − | 2.07957i | −0.240128 | − | 0.415914i | ||||
\(26\) | 8.82813 | + | 3.02907i | 1.73134 | + | 0.594050i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.37101 | − | 10.0177i | 1.39299 | − | 1.89317i | ||||
\(29\) | −2.68636 | + | 4.65290i | −0.498844 | + | 0.864023i | −0.999999 | − | 0.00133469i | \(-0.999575\pi\) |
0.501155 | + | 0.865357i | \(0.332908\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.07425 | + | 5.23902i | −1.62978 | + | 0.940956i | −0.645627 | + | 0.763653i | \(0.723404\pi\) |
−0.984156 | + | 0.177303i | \(0.943263\pi\) | |||||||
\(32\) | −7.38583 | − | 4.26421i | −1.30564 | − | 0.753813i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.09354i | 1.38803i | ||||||||
\(35\) | −3.43535 | − | 2.52773i | −0.580680 | − | 0.427264i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.15585 | − | 2.97673i | 0.847616 | − | 0.489371i | −0.0122297 | − | 0.999925i | \(-0.503893\pi\) |
0.859846 | + | 0.510554i | \(0.170560\pi\) | |||||||
\(38\) | −4.76497 | − | 8.25317i | −0.772981 | − | 1.33884i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.63528 | + | 9.76059i | −0.891016 | + | 1.54329i | ||||
\(41\) | 6.66970 | + | 3.85075i | 1.04163 | + | 0.601386i | 0.920295 | − | 0.391225i | \(-0.127949\pi\) |
0.121337 | + | 0.992611i | \(0.461282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.67800 | − | 2.90638i | −0.255892 | − | 0.443219i | 0.709245 | − | 0.704962i | \(-0.249036\pi\) |
−0.965138 | + | 0.261743i | \(0.915703\pi\) | |||||||
\(44\) | −11.0120 | − | 6.35780i | −1.66013 | − | 0.958475i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.45229 | − | 2.57053i | −0.656454 | − | 0.379004i | ||||
\(47\) | 0.913730 | + | 0.527542i | 0.133281 | + | 0.0769500i | 0.565158 | − | 0.824983i | \(-0.308815\pi\) |
−0.431877 | + | 0.901933i | \(0.642148\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.82898 | + | 1.53787i | 0.975568 | + | 0.219696i | ||||
\(50\) | −5.38318 | − | 3.10798i | −0.761297 | − | 0.439535i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.6343 | − | 3.25208i | 2.30676 | − | 0.450982i | ||||
\(53\) | 3.63284 | + | 6.29226i | 0.499009 | + | 0.864308i | 0.999999 | − | 0.00114437i | \(-0.000364265\pi\) |
−0.500991 | + | 0.865453i | \(0.667031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.18027 | + | 3.77633i | −0.293987 | + | 0.509201i | ||||
\(56\) | 2.04445 | − | 18.3843i | 0.273201 | − | 2.45670i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 13.9078i | 1.82618i | ||||||||
\(59\) | 9.89352 | + | 5.71203i | 1.28803 | + | 0.743643i | 0.978302 | − | 0.207183i | \(-0.0664297\pi\) |
0.309725 | + | 0.950826i | \(0.399763\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.92507 | −0.374517 | −0.187259 | − | 0.982311i | \(-0.559960\pi\) | ||||
−0.187259 | + | 0.982311i | \(0.559960\pi\) | |||||||
\(62\) | −13.5617 | + | 23.4896i | −1.72234 | + | 2.98318i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.68406 | −0.585507 | ||||||||
\(65\) | −1.11523 | − | 5.70435i | −0.138327 | − | 0.707537i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5818i | 1.65928i | 0.558296 | + | 0.829642i | \(0.311455\pi\) | ||||
−0.558296 | + | 0.829642i | \(0.688545\pi\) | |||||||
\(68\) | 7.34886 | + | 12.7286i | 0.891180 | + | 1.54357i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.9730 | − | 1.22027i | −1.31152 | − | 0.145850i | ||||
\(71\) | −1.17009 | + | 0.675554i | −0.138865 | + | 0.0801736i | −0.567823 | − | 0.823151i | \(-0.692214\pi\) |
0.428958 | + | 0.903324i | \(0.358881\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.88374 | − | 4.55168i | 0.922721 | − | 0.532733i | 0.0382192 | − | 0.999269i | \(-0.487831\pi\) |
0.884502 | + | 0.466536i | \(0.154498\pi\) | |||||||
\(74\) | 7.70557 | − | 13.3464i | 0.895754 | − | 1.55149i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.9876 | − | 8.65311i | −1.71920 | − | 0.992579i | ||||
\(77\) | 0.790989 | − | 7.11280i | 0.0901416 | − | 0.810578i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.10289 | − | 5.37436i | 0.349102 | − | 0.604663i | −0.636988 | − | 0.770874i | \(-0.719820\pi\) |
0.986090 | + | 0.166211i | \(0.0531532\pi\) | |||||||
\(80\) | 14.0189i | 1.56736i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 19.9361 | 2.20158 | ||||||||
\(83\) | − | 2.69672i | − | 0.296003i | −0.988987 | − | 0.148002i | \(-0.952716\pi\) | ||
0.988987 | − | 0.148002i | \(-0.0472841\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.36499 | − | 2.52013i | 0.473450 | − | 0.273346i | ||||
\(86\) | −7.52346 | − | 4.34367i | −0.811275 | − | 0.468390i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −18.9115 | −2.01597 | ||||||||
\(89\) | −1.52410 | + | 0.879938i | −0.161554 | + | 0.0932732i | −0.578597 | − | 0.815613i | \(-0.696400\pi\) |
0.417043 | + | 0.908887i | \(0.363066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.43284 | + | 7.84119i | 0.569516 | + | 0.821980i | ||||
\(92\) | −9.33607 | −0.973353 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.73119 | 0.281701 | ||||||||
\(95\) | −2.96739 | + | 5.13967i | −0.304448 | + | 0.527319i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.4078 | + | 7.74102i | −1.36136 | + | 0.785981i | −0.989805 | − | 0.142430i | \(-0.954509\pi\) |
−0.371555 | + | 0.928411i | \(0.621175\pi\) | |||||||
\(98\) | 17.2996 | − | 5.39116i | 1.74753 | − | 0.544589i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.2881 | −1.12881 | ||||||||
\(101\) | −1.27930 | −0.127295 | −0.0636477 | − | 0.997972i | \(-0.520273\pi\) | ||||
−0.0636477 | + | 0.997972i | \(0.520273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.73367 | + | 9.93101i | −0.564956 | + | 0.978532i | 0.432098 | + | 0.901827i | \(0.357773\pi\) |
−0.997054 | + | 0.0767054i | \(0.975560\pi\) | |||||||
\(104\) | 19.0068 | − | 16.5585i | 1.86377 | − | 1.62370i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.2881 | + | 9.40397i | 1.58204 | + | 0.913394i | ||||
\(107\) | −2.56763 | − | 4.44726i | −0.248222 | − | 0.429933i | 0.714811 | − | 0.699318i | \(-0.246513\pi\) |
−0.963033 | + | 0.269385i | \(0.913180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.49635 | + | 0.863916i | −0.143324 | + | 0.0827481i | −0.569947 | − | 0.821681i | \(-0.693036\pi\) |
0.426623 | + | 0.904429i | \(0.359703\pi\) | |||||||
\(110\) | 11.2877i | 1.07624i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.23136 | − | 21.0752i | −0.872282 | − | 1.99142i | ||||
\(113\) | −4.29556 | − | 7.44014i | −0.404093 | − | 0.699909i | 0.590123 | − | 0.807314i | \(-0.299079\pi\) |
−0.994215 | + | 0.107404i | \(0.965746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.20160i | 0.298551i | ||||||||
\(116\) | 12.6282 | + | 21.8726i | 1.17250 | + | 2.03082i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 29.5723 | 2.72235 | ||||||||
\(119\) | −4.90257 | + | 6.66292i | −0.449418 | + | 0.610789i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.68321 | 0.334837 | ||||||||
\(122\) | −6.55741 | + | 3.78592i | −0.593680 | + | 0.342761i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 49.2557i | 4.42330i | ||||||||
\(125\) | 11.9313i | 1.06716i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.56206 | + | 2.70556i | −0.138610 | + | 0.240080i | −0.926971 | − | 0.375133i | \(-0.877597\pi\) |
0.788361 | + | 0.615214i | \(0.210930\pi\) | |||||||
\(128\) | 4.27097 | − | 2.46585i | 0.377504 | − | 0.217952i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.88325 | − | 11.3445i | −0.866818 | − | 0.994981i | ||||
\(131\) | 5.10460 | − | 8.84142i | 0.445991 | − | 0.772479i | −0.552130 | − | 0.833758i | \(-0.686185\pi\) |
0.998121 | + | 0.0612793i | \(0.0195180\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.07655 | − | 9.68067i | 0.0933490 | − | 0.839420i | ||||
\(134\) | 17.5790 | + | 30.4476i | 1.51859 | + | 2.63028i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 18.9308 | + | 10.9297i | 1.62331 | + | 0.937216i | ||||
\(137\) | −8.65385 | − | 4.99630i | −0.739348 | − | 0.426863i | 0.0824839 | − | 0.996592i | \(-0.473715\pi\) |
−0.821832 | + | 0.569729i | \(0.807048\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.832100 | + | 1.44124i | 0.0705778 | + | 0.122244i | 0.899155 | − | 0.437631i | \(-0.144182\pi\) |
−0.828577 | + | 0.559875i | \(0.810849\pi\) | |||||||
\(140\) | −18.3651 | + | 8.04427i | −1.55213 | + | 0.679865i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.74874 | + | 3.02891i | −0.146751 | + | 0.254180i | ||||
\(143\) | 7.35364 | − | 6.40642i | 0.614942 | − | 0.535732i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.50073 | − | 4.33055i | 0.622902 | − | 0.359633i | ||||
\(146\) | 11.7825 | − | 20.4078i | 0.975124 | − | 1.68897i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 27.9863i | − | 2.30046i | ||||||
\(149\) | 19.7980i | 1.62192i | 0.585103 | + | 0.810959i | \(0.301054\pi\) | ||||
−0.585103 | + | 0.810959i | \(0.698946\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.52544 | − | 3.76746i | 0.531033 | − | 0.306592i | −0.210404 | − | 0.977614i | \(-0.567478\pi\) |
0.741437 | + | 0.671023i | \(0.234145\pi\) | |||||||
\(152\) | −25.7390 | −2.08771 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.43286 | − | 16.9692i | −0.598957 | − | 1.36742i | ||||
\(155\) | 16.8912 | 1.35673 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00223 | − | 12.1282i | −0.558839 | − | 0.967938i | −0.997594 | − | 0.0693309i | \(-0.977914\pi\) |
0.438755 | − | 0.898607i | \(-0.355420\pi\) | |||||||
\(158\) | − | 16.0643i | − | 1.27801i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.87414 | + | 11.9064i | 0.543448 | + | 0.941280i | ||||
\(161\) | −2.10823 | − | 4.81308i | −0.166152 | − | 0.379324i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.16995i | − | 0.561594i | −0.959767 | − | 0.280797i | \(-0.909401\pi\) | ||
0.959767 | − | 0.280797i | \(-0.0905987\pi\) | |||||||
\(164\) | 31.3533 | − | 18.1018i | 2.44828 | − | 1.41351i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.49036 | − | 6.04548i | −0.270904 | − | 0.469220i | ||||
\(167\) | −15.5716 | − | 8.99027i | −1.20497 | − | 0.695688i | −0.243312 | − | 0.969948i | \(-0.578234\pi\) |
−0.961656 | + | 0.274260i | \(0.911567\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.78135 | + | 12.8774i | −0.137027 | + | 0.990567i | ||||
\(170\) | 6.52361 | − | 11.2992i | 0.500338 | − | 0.866611i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.7761 | −1.20291 | ||||||||
\(173\) | −12.8116 | −0.974047 | −0.487023 | − | 0.873389i | \(-0.661917\pi\) | ||||
−0.487023 | + | 0.873389i | \(0.661917\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.54902 | − | 5.81942i | −0.192688 | − | 0.439906i | ||||
\(176\) | −20.3717 | + | 11.7616i | −1.53557 | + | 0.886562i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.27781 | + | 3.94528i | −0.170729 | + | 0.295711i | ||||
\(179\) | 1.84022 | 0.137545 | 0.0687723 | − | 0.997632i | \(-0.478092\pi\) | ||||
0.0687723 | + | 0.997632i | \(0.478092\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.29928 | −0.245234 | −0.122617 | − | 0.992454i | \(-0.539129\pi\) | ||||
−0.122617 | + | 0.992454i | \(0.539129\pi\) | |||||||
\(182\) | 22.3282 | + | 10.5466i | 1.65507 | + | 0.781767i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.0250 | + | 6.94262i | −0.886493 | + | 0.511817i | ||||
\(185\) | −9.59730 | −0.705607 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.32427 | + | 4.22867i | 0.535604 | + | 0.309231i | ||||
\(188\) | 4.29531 | − | 2.47990i | 0.313268 | − | 0.180865i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.3628i | 1.11453i | ||||||||
\(191\) | −4.89614 | −0.354272 | −0.177136 | − | 0.984186i | \(-0.556683\pi\) | ||||
−0.177136 | + | 0.984186i | \(0.556683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.01910i | 0.217320i | 0.994079 | + | 0.108660i | \(0.0346559\pi\) | ||||
−0.994079 | + | 0.108660i | \(0.965344\pi\) | |||||||
\(194\) | −20.0384 | + | 34.7075i | −1.43867 | + | 2.49186i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.3118 | − | 24.1865i | 1.59370 | − | 1.72761i | ||||
\(197\) | −4.02694 | − | 2.32496i | −0.286908 | − | 0.165646i | 0.349639 | − | 0.936885i | \(-0.386304\pi\) |
−0.636546 | + | 0.771238i | \(0.719638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.205360 | − | 0.355694i | 0.0145576 | − | 0.0252145i | −0.858655 | − | 0.512554i | \(-0.828699\pi\) |
0.873212 | + | 0.487340i | \(0.162033\pi\) | |||||||
\(200\) | −14.5392 | + | 8.39420i | −1.02808 | + | 0.593560i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.86793 | + | 1.65580i | −0.201787 | + | 0.116502i | ||||
\(203\) | −8.42450 | + | 11.4495i | −0.591284 | + | 0.803594i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.20762 | − | 10.7519i | −0.433559 | − | 0.750946i | ||||
\(206\) | 29.6844i | 2.06821i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.1761 | − | 29.6578i | 0.705583 | − | 2.05640i | ||||
\(209\) | −9.95831 | −0.688831 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.75800 | − | 6.50905i | 0.258711 | − | 0.448101i | −0.707186 | − | 0.707028i | \(-0.750035\pi\) |
0.965897 | + | 0.258927i | \(0.0833688\pi\) | |||||||
\(212\) | 34.1549 | 2.34577 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.5122 | − | 6.64656i | −0.786956 | − | 0.454349i | ||||
\(215\) | 5.41005i | 0.368962i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.3931 | + | 11.1227i | −1.72380 | + | 0.755059i | ||||
\(218\) | −2.23633 | + | 3.87344i | −0.151464 | + | 0.262343i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.2491 | + | 17.7520i | 0.690996 | + | 1.19684i | ||||
\(221\) | −11.0637 | + | 2.16300i | −0.744224 | + | 0.145499i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.5544 | − | 11.2897i | −1.30946 | − | 0.756016i | −0.327452 | − | 0.944868i | \(-0.606190\pi\) |
−0.982006 | + | 0.188852i | \(0.939523\pi\) | |||||||
\(224\) | −18.1744 | − | 13.3727i | −1.21433 | − | 0.893502i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.2595 | − | 11.1195i | −1.28113 | − | 0.739658i | ||||
\(227\) | −11.8401 | − | 6.83586i | −0.785853 | − | 0.453712i | 0.0526478 | − | 0.998613i | \(-0.483234\pi\) |
−0.838500 | + | 0.544901i | \(0.816567\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.86832 | − | 3.96543i | −0.453872 | − | 0.262043i | 0.255592 | − | 0.966785i | \(-0.417730\pi\) |
−0.709464 | + | 0.704742i | \(0.751063\pi\) | |||||||
\(230\) | 4.14383 | + | 7.17733i | 0.273236 | + | 0.473259i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 32.5305 | + | 18.7815i | 2.13573 | + | 1.23306i | ||||
\(233\) | 3.28585 | − | 5.69127i | 0.215263 | − | 0.372847i | −0.738091 | − | 0.674702i | \(-0.764272\pi\) |
0.953354 | + | 0.301854i | \(0.0976056\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.850427 | − | 1.47298i | −0.0554757 | − | 0.0960868i | ||||
\(236\) | 46.5080 | − | 26.8514i | 3.02741 | − | 1.74788i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.36673 | + | 21.2823i | −0.153412 | + | 1.37953i | ||||
\(239\) | − | 9.39284i | − | 0.607572i | −0.952740 | − | 0.303786i | \(-0.901749\pi\) | ||
0.952740 | − | 0.303786i | \(-0.0982508\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.73460 | + | 5.04292i | 0.562645 | + | 0.324843i | 0.754206 | − | 0.656637i | \(-0.228022\pi\) |
−0.191562 | + | 0.981481i | \(0.561355\pi\) | |||||||
\(242\) | 8.25699 | − | 4.76718i | 0.530780 | − | 0.306446i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.87517 | + | 11.9081i | −0.440137 | + | 0.762340i | ||||
\(245\) | −8.29423 | − | 7.65133i | −0.529899 | − | 0.488826i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0085 | − | 8.71928i | 0.636823 | − | 0.554794i | ||||
\(248\) | 36.6282 | + | 63.4420i | 2.32590 | + | 4.02857i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.4426 | + | 26.7474i | 0.976678 | + | 1.69166i | ||||
\(251\) | 5.17427 | + | 8.96209i | 0.326597 | + | 0.565682i | 0.981834 | − | 0.189741i | \(-0.0607648\pi\) |
−0.655237 | + | 0.755423i | \(0.727431\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.65242 | + | 2.68607i | −0.292495 | + | 0.168872i | ||||
\(254\) | 8.08709i | 0.507429i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.0672 | − | 19.1689i | 0.691697 | − | 1.19805i | ||||
\(257\) | −3.99329 | − | 6.91658i | −0.249095 | − | 0.431445i | 0.714180 | − | 0.699962i | \(-0.246800\pi\) |
−0.963275 | + | 0.268517i | \(0.913466\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.4280 | − | 6.31975i | 0.896511 | − | 0.392690i | ||||
\(260\) | −25.8440 | − | 8.86749i | −1.60278 | − | 0.549939i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 26.4275i | − | 1.63270i | ||||||
\(263\) | −5.05934 | −0.311972 | −0.155986 | − | 0.987759i | \(-0.549856\pi\) | ||||
−0.155986 | + | 0.987759i | \(0.549856\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 11.7127i | − | 0.719503i | ||||||
\(266\) | −10.1163 | − | 23.0954i | −0.620269 | − | 1.41607i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 55.2924 | + | 31.9231i | 3.37752 | + | 1.95001i | ||||
\(269\) | 6.94512 | − | 12.0293i | 0.423451 | − | 0.733439i | −0.572823 | − | 0.819679i | \(-0.694152\pi\) |
0.996274 | + | 0.0862400i | \(0.0274852\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.21158 | + | 4.16361i | −0.438072 | + | 0.252921i | −0.702780 | − | 0.711408i | \(-0.748058\pi\) |
0.264707 | + | 0.964329i | \(0.414725\pi\) | |||||||
\(272\) | 27.1900 | 1.64863 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.8669 | −1.56267 | ||||||||
\(275\) | −5.62515 | + | 3.24768i | −0.339210 | + | 0.195843i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.6058 | + | 20.1018i | −0.697325 | + | 1.20780i | 0.272066 | + | 0.962279i | \(0.412293\pi\) |
−0.969391 | + | 0.245523i | \(0.921040\pi\) | |||||||
\(278\) | 3.73080 | + | 2.15398i | 0.223758 | + | 0.129187i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −17.6724 | + | 24.0180i | −1.05613 | + | 1.43535i | ||||
\(281\) | − | 27.1595i | − | 1.62020i | −0.586292 | − | 0.810100i | \(-0.699413\pi\) | ||
0.586292 | − | 0.810100i | \(-0.300587\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1513 | 0.960092 | 0.480046 | − | 0.877243i | \(-0.340620\pi\) | ||||
0.480046 | + | 0.877243i | \(0.340620\pi\) | |||||||
\(284\) | 6.35136i | 0.376884i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.19351 | − | 23.8797i | 0.484493 | − | 1.41204i | ||||
\(287\) | 16.4122 | + | 12.0761i | 0.968782 | + | 0.712828i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.61216 | + | 6.25645i | 0.212480 | + | 0.368027i | ||||
\(290\) | 11.2101 | − | 19.4164i | 0.658278 | − | 1.14017i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 42.7935i | − | 2.50430i | ||||||
\(293\) | 12.6831 | − | 7.32260i | 0.740956 | − | 0.427791i | −0.0814609 | − | 0.996677i | \(-0.525959\pi\) |
0.822417 | + | 0.568885i | \(0.192625\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.20810 | − | 15.9489i | −0.536116 | − | 0.928580i | ||||
\(296\) | −20.8116 | − | 36.0468i | −1.20965 | − | 2.09517i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.6246 | + | 44.3831i | 1.48439 | + | 2.57104i | ||||
\(299\) | 2.32398 | − | 6.77315i | 0.134399 | − | 0.391702i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.56248 | − | 8.13313i | −0.205338 | − | 0.468786i | ||||
\(302\) | 9.75246 | − | 16.8918i | 0.561191 | − | 0.972011i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −27.7263 | + | 16.0078i | −1.59021 | + | 0.918108i | ||||
\(305\) | 4.08363 | + | 2.35769i | 0.233828 | + | 0.135001i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.97844i | − | 0.512427i | −0.966620 | − | 0.256213i | \(-0.917525\pi\) | ||
0.966620 | − | 0.256213i | \(-0.0824750\pi\) | |||||||
\(308\) | −27.0975 | − | 19.9383i | −1.54402 | − | 1.13609i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 37.8665 | − | 21.8622i | 2.15067 | − | 1.24169i | ||||
\(311\) | −6.09080 | − | 10.5496i | −0.345378 | − | 0.598212i | 0.640045 | − | 0.768338i | \(-0.278916\pi\) |
−0.985422 | + | 0.170126i | \(0.945583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.56198 | + | 11.3657i | −0.370905 | + | 0.642427i | −0.989705 | − | 0.143122i | \(-0.954286\pi\) |
0.618800 | + | 0.785549i | \(0.287619\pi\) | |||||||
\(314\) | −31.3951 | − | 18.1260i | −1.77173 | − | 1.02291i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.5862 | − | 25.2641i | −0.820540 | − | 1.42122i | ||||
\(317\) | 14.4761 | + | 8.35775i | 0.813056 | + | 0.469418i | 0.848016 | − | 0.529971i | \(-0.177797\pi\) |
−0.0349599 | + | 0.999389i | \(0.511130\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.5859 | + | 7.26648i | 0.704675 | + | 0.406845i | ||||
\(320\) | 6.53932 | + | 3.77548i | 0.365559 | + | 0.211056i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.9558 | − | 8.06126i | −0.610543 | − | 0.449236i | ||||
\(323\) | 9.96849 | + | 5.75531i | 0.554661 | + | 0.320234i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.80988 | − | 8.18930i | 0.155864 | − | 0.454261i | ||||
\(326\) | −9.28007 | − | 16.0736i | −0.513976 | − | 0.890232i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 26.9223 | − | 46.6307i | 1.48653 | − | 2.57475i | ||||
\(329\) | 2.24843 | + | 1.65439i | 0.123960 | + | 0.0912094i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.96665i | 0.218027i | 0.994040 | + | 0.109013i | \(0.0347691\pi\) | ||||
−0.994040 | + | 0.109013i | \(0.965231\pi\) | |||||||
\(332\) | −10.9785 | − | 6.33843i | −0.602523 | − | 0.347867i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −46.5445 | −2.54680 | ||||||||
\(335\) | 10.9473 | − | 18.9613i | 0.598116 | − | 1.03597i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7032 | −0.746461 | −0.373230 | − | 0.927739i | \(-0.621750\pi\) | ||||
−0.373230 | + | 0.927739i | \(0.621750\pi\) | |||||||
\(338\) | 12.6738 | + | 31.1740i | 0.689362 | + | 1.69564i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 23.6935i | − | 1.28496i | ||||||
\(341\) | 14.1713 | + | 24.5455i | 0.767420 | + | 1.32921i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.5074 | + | 6.04084i | 0.945309 | + | 0.326175i | ||||
\(344\) | −20.3197 | + | 11.7316i | −1.09557 | + | 0.632526i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.7209 | + | 16.5820i | −1.54405 | + | 0.891456i | ||||
\(347\) | −13.1989 | + | 22.8612i | −0.708556 | + | 1.22725i | 0.256837 | + | 0.966455i | \(0.417320\pi\) |
−0.965393 | + | 0.260800i | \(0.916014\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.23507 | − | 2.44512i | −0.226698 | − | 0.130884i | 0.382350 | − | 0.924018i | \(-0.375115\pi\) |
−0.609048 | + | 0.793133i | \(0.708448\pi\) | |||||||
\(350\) | −13.2465 | − | 9.74673i | −0.708053 | − | 0.520984i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.5345 | + | 19.9784i | −0.614792 | + | 1.06485i | ||||
\(353\) | 13.5577i | 0.721605i | 0.932642 | + | 0.360802i | \(0.117497\pi\) | ||||
−0.932642 | + | 0.360802i | \(0.882503\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.17806 | 0.115599 | ||||||||
\(356\) | 8.27291i | 0.438464i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.12540 | − | 2.38180i | 0.218034 | − | 0.125882i | ||||
\(359\) | 7.43541 | + | 4.29284i | 0.392426 | + | 0.226567i | 0.683211 | − | 0.730221i | \(-0.260583\pi\) |
−0.290785 | + | 0.956789i | \(0.593916\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.44653 | 0.286659 | ||||||||
\(362\) | −7.39632 | + | 4.27026i | −0.388742 | + | 0.224440i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 44.6914 | − | 3.68725i | 2.34247 | − | 0.193264i | ||||
\(365\) | −14.6751 | −0.768130 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.66322 | −0.0868196 | −0.0434098 | − | 0.999057i | \(-0.513822\pi\) | ||||
−0.0434098 | + | 0.999057i | \(0.513822\pi\) | |||||||
\(368\) | −8.63560 | + | 14.9573i | −0.450162 | + | 0.779703i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −21.5152 | + | 12.4218i | −1.11852 | + | 0.645778i | ||||
\(371\) | 7.71270 | + | 17.6081i | 0.400424 | + | 0.914166i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.9635 | 0.723002 | 0.361501 | − | 0.932372i | \(-0.382264\pi\) | ||||
0.361501 | + | 0.932372i | \(0.382264\pi\) | |||||||
\(374\) | 21.8927 | 1.13204 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.68828 | − | 6.38828i | 0.190208 | − | 0.329450i | ||||
\(377\) | −19.0117 | + | 3.71687i | −0.979150 | + | 0.191429i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3454 | − | 15.7879i | −1.40464 | − | 0.810969i | −0.409775 | − | 0.912187i | \(-0.634393\pi\) |
−0.994864 | + | 0.101218i | \(0.967726\pi\) | |||||||
\(380\) | 13.9493 | + | 24.1608i | 0.715582 | + | 1.23943i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.9761 | + | 6.33707i | −0.561588 | + | 0.324233i | ||||
\(383\) | − | 31.9082i | − | 1.63043i | −0.579156 | − | 0.815217i | \(-0.696618\pi\) | ||
0.579156 | − | 0.815217i | \(-0.303382\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.83739 | + | 9.29247i | −0.348466 | + | 0.473588i | ||||
\(386\) | 3.90762 | + | 6.76820i | 0.198893 | + | 0.344492i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 72.7788i | 3.69478i | ||||||||
\(389\) | 12.7075 | + | 22.0100i | 0.644296 | + | 1.11595i | 0.984464 | + | 0.175589i | \(0.0561829\pi\) |
−0.340168 | + | 0.940365i | \(0.610484\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.20956 | 0.314031 | ||||||||
\(392\) | 10.7519 | − | 47.7443i | 0.543054 | − | 2.41145i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.0368 | −0.606403 | ||||||||
\(395\) | −8.66376 | + | 5.00203i | −0.435921 | + | 0.251679i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.15897i | 0.208733i | 0.994539 | + | 0.104366i | \(0.0332815\pi\) | ||||
−0.994539 | + | 0.104366i | \(0.966719\pi\) | |||||||
\(398\) | − | 1.06319i | − | 0.0532930i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.4412 | + | 18.0846i | −0.522058 | + | 0.904231i | ||||
\(401\) | 16.9753 | − | 9.80067i | 0.847704 | − | 0.489422i | −0.0121716 | − | 0.999926i | \(-0.503874\pi\) |
0.859875 | + | 0.510504i | \(0.170541\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −35.7342 | − | 12.2610i | −1.78005 | − | 0.610762i | ||||
\(404\) | −3.00691 | + | 5.20811i | −0.149599 | + | 0.259113i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.06695 | + | 36.5711i | −0.201839 | + | 1.81500i | ||||
\(407\) | −8.05193 | − | 13.9463i | −0.399119 | − | 0.691295i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.2712 | − | 8.81685i | −0.755114 | − | 0.435965i | 0.0724249 | − | 0.997374i | \(-0.476926\pi\) |
−0.827539 | + | 0.561409i | \(0.810260\pi\) | |||||||
\(410\) | −27.8324 | − | 16.0690i | −1.37454 | − | 0.793594i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 26.9532 | + | 46.6842i | 1.32789 | + | 2.29997i | ||||
\(413\) | 24.3451 | + | 17.9131i | 1.19794 | + | 0.881446i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.17363 | + | 3.76483i | −0.106699 | + | 0.184808i | ||||
\(416\) | −5.90001 | − | 30.1783i | −0.289272 | − | 1.47962i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.3245 | + | 12.8890i | −1.09193 | + | 0.630424i | ||||
\(419\) | 14.9455 | − | 25.8864i | 0.730137 | − | 1.26463i | −0.226688 | − | 0.973968i | \(-0.572790\pi\) |
0.956824 | − | 0.290666i | \(-0.0938770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.8528i | 0.626407i | 0.949686 | + | 0.313203i | \(0.101402\pi\) | ||||
−0.949686 | + | 0.313203i | \(0.898598\pi\) | |||||||
\(422\) | − | 19.4559i | − | 0.947100i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 43.9919 | − | 25.3987i | 2.13644 | − | 1.23347i | ||||
\(425\) | 7.50787 | 0.364185 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.69160 | − | 0.855355i | −0.372223 | − | 0.0413936i | ||||
\(428\) | −24.1401 | −1.16685 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.00223 | + | 12.1282i | 0.337677 | + | 0.584874i | ||||
\(431\) | − | 8.97060i | − | 0.432098i | −0.976382 | − | 0.216049i | \(-0.930683\pi\) | ||
0.976382 | − | 0.216049i | \(-0.0693172\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.72531 | − | 2.98833i | −0.0829132 | − | 0.143610i | 0.821587 | − | 0.570083i | \(-0.193089\pi\) |
−0.904500 | + | 0.426473i | \(0.859756\pi\) | |||||||
\(434\) | −42.5300 | + | 57.8012i | −2.04151 | + | 2.77454i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.12228i | 0.388987i | ||||||||
\(437\) | −6.33204 | + | 3.65580i | −0.302902 | + | 0.174881i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.2572 | − | 33.3544i | −0.919096 | − | 1.59192i | −0.800792 | − | 0.598943i | \(-0.795588\pi\) |
−0.118304 | − | 0.992977i | \(-0.537746\pi\) | |||||||
\(440\) | 26.4020 | + | 15.2432i | 1.25867 | + | 0.726691i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.0029 | + | 19.1687i | −1.04657 | + | 0.911764i | ||||
\(443\) | −7.51997 | + | 13.0250i | −0.357284 | + | 0.618835i | −0.987506 | − | 0.157580i | \(-0.949631\pi\) |
0.630222 | + | 0.776415i | \(0.282964\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.83701 | 0.134487 | ||||||||
\(446\) | −58.4492 | −2.76765 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.3169 | − | 1.36972i | −0.581920 | − | 0.0647133i | ||||
\(449\) | −33.7087 | + | 19.4617i | −1.59081 | + | 0.918456i | −0.597646 | + | 0.801760i | \(0.703897\pi\) |
−0.993168 | + | 0.116696i | \(0.962770\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.4161 | − | 18.0412i | 0.490476 | − | 0.849529i | ||||
\(452\) | −40.3856 | −1.89958 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −35.3906 | −1.66097 | ||||||||
\(455\) | −1.26446 | − | 15.3259i | −0.0592788 | − | 0.718491i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.0721 | + | 6.96982i | −0.564708 | + | 0.326034i | −0.755033 | − | 0.655687i | \(-0.772379\pi\) |
0.190325 | + | 0.981721i | \(0.439046\pi\) | |||||||
\(458\) | −20.5298 | −0.959295 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.0339 | + | 7.52512i | 0.607709 | + | 0.350861i | ||||
\(461\) | −32.4443 | + | 18.7317i | −1.51108 | + | 0.872424i | −0.511167 | + | 0.859481i | \(0.670787\pi\) |
−0.999916 | + | 0.0129430i | \(0.995880\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.75275i | − | 0.313827i | −0.987612 | − | 0.156913i | \(-0.949846\pi\) | ||
0.987612 | − | 0.156913i | \(-0.0501544\pi\) | |||||||
\(464\) | 46.7228 | 2.16905 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 17.0115i | − | 0.788044i | ||||||
\(467\) | −2.52516 | + | 4.37371i | −0.116851 | + | 0.202391i | −0.918518 | − | 0.395379i | \(-0.870613\pi\) |
0.801667 | + | 0.597770i | \(0.203947\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.97162 | + | 35.7140i | −0.183393 | + | 1.64912i | ||||
\(470\) | −3.81296 | − | 2.20141i | −0.175879 | − | 0.101544i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 39.9353 | − | 69.1699i | 1.83817 | − | 3.18380i | ||||
\(473\) | −7.86163 | + | 4.53892i | −0.361478 | + | 0.208700i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.65595 | + | 4.42017i | −0.351279 | + | 0.202811i | ||||
\(476\) | 15.6020 | + | 35.6194i | 0.715117 | + | 1.63261i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.1572 | − | 21.0568i | −0.556055 | − | 0.963116i | ||||
\(479\) | − | 9.45319i | − | 0.431927i | −0.976401 | − | 0.215964i | \(-0.930711\pi\) | ||
0.976401 | − | 0.215964i | \(-0.0692892\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.3036 | + | 6.96649i | 0.925764 | + | 0.317645i | ||||
\(482\) | 26.1082 | 1.18920 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.65711 | − | 14.9946i | 0.393505 | − | 0.681571i | ||||
\(485\) | 24.9579 | 1.13328 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.6407 | + | 19.9998i | 1.56972 | + | 0.906277i | 0.996201 | + | 0.0870831i | \(0.0277546\pi\) |
0.573517 | + | 0.819194i | \(0.305579\pi\) | |||||||
\(488\) | 20.4504i | 0.925748i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −28.4971 | − | 6.41748i | −1.28737 | − | 0.289912i | ||||
\(491\) | 3.38049 | − | 5.85517i | 0.152559 | − | 0.264240i | −0.779608 | − | 0.626267i | \(-0.784582\pi\) |
0.932168 | + | 0.362027i | \(0.117915\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.39918 | − | 14.5478i | −0.378280 | − | 0.655200i | ||||
\(494\) | 11.1515 | − | 32.5008i | 0.501732 | − | 1.46228i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 78.9125 | + | 45.5602i | 3.54328 | + | 2.04571i | ||||
\(497\) | −3.27436 | + | 1.43424i | −0.146875 | + | 0.0643343i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.83591 | + | 5.67877i | 0.440316 | + | 0.254217i | 0.703732 | − | 0.710466i | \(-0.251516\pi\) |
−0.263416 | + | 0.964682i | \(0.584849\pi\) | |||||||
\(500\) | 48.5729 | + | 28.0436i | 2.17225 | + | 1.25415i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23.1993 | + | 13.3941i | 1.03543 | + | 0.597808i | ||||
\(503\) | −6.96423 | − | 12.0624i | −0.310520 | − | 0.537836i | 0.667955 | − | 0.744202i | \(-0.267170\pi\) |
−0.978475 | + | 0.206365i | \(0.933836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.78601 | + | 1.03115i | 0.0794763 | + | 0.0458857i | ||||
\(506\) | −6.95317 | + | 12.0432i | −0.309106 | + | 0.535388i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.34301 | + | 12.7185i | 0.325793 | + | 0.564290i | ||||
\(509\) | −17.1602 | + | 9.90746i | −0.760614 | + | 0.439141i | −0.829516 | − | 0.558483i | \(-0.811384\pi\) |
0.0689022 | + | 0.997623i | \(0.478050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.0616 | − | 9.66345i | 0.975949 | − | 0.427486i | ||||
\(512\) | − | 47.4335i | − | 2.09628i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.9043 | − | 10.3370i | −0.789724 | − | 0.455947i | ||||
\(515\) | 16.0093 | − | 9.24299i | 0.705455 | − | 0.407295i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.42698 | − | 2.47160i | 0.0627585 | − | 0.108701i | ||||
\(518\) | 24.1649 | − | 32.8417i | 1.06174 | − | 1.44298i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −39.8816 | + | 7.79704i | −1.74892 | + | 0.341923i | ||||
\(521\) | −15.5476 | − | 26.9292i | −0.681151 | − | 1.17979i | −0.974630 | − | 0.223823i | \(-0.928146\pi\) |
0.293479 | − | 0.955966i | \(-0.405187\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.3601 | − | 19.6763i | −0.496742 | − | 0.860383i | 0.503251 | − | 0.864140i | \(-0.332137\pi\) |
−0.999993 | + | 0.00375758i | \(0.998804\pi\) | |||||||
\(524\) | −23.9960 | − | 41.5622i | −1.04827 | − | 1.81565i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.3420 | + | 6.54831i | −0.494535 | + | 0.285520i | ||||
\(527\) | − | 32.7607i | − | 1.42708i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.52783 | − | 16.5027i | 0.414253 | − | 0.717508i | ||||
\(530\) | −15.1597 | − | 26.2574i | −0.658495 | − | 1.14055i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −36.8802 | − | 27.1364i | −1.59896 | − | 1.17651i | ||||
\(533\) | 5.32794 | + | 27.2522i | 0.230779 | + | 1.18043i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.27830i | 0.357902i | ||||||||
\(536\) | 94.9564 | 4.10149 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 35.9563i | − | 1.55018i | ||||||
\(539\) | 4.15988 | − | 18.4721i | 0.179179 | − | 0.795649i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.81754 | − | 1.04936i | −0.0781423 | − | 0.0451155i | 0.460420 | − | 0.887701i | \(-0.347699\pi\) |
−0.538562 | + | 0.842586i | \(0.681032\pi\) | |||||||
\(542\) | −10.7779 | + | 18.6679i | −0.462951 | + | 0.801855i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 23.0926 | − | 13.3325i | 0.990087 | − | 0.571627i | ||||
\(545\) | 2.78536 | 0.119312 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.3770 | 1.08504 | 0.542521 | − | 0.840042i | \(-0.317470\pi\) | ||||
0.542521 | + | 0.840042i | \(0.317470\pi\) | |||||||
\(548\) | −40.6805 | + | 23.4869i | −1.73778 | + | 1.00331i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.40696 | + | 14.5613i | −0.358474 | + | 0.620895i | ||||
\(551\) | 17.1297 | + | 9.88983i | 0.729749 | + | 0.421321i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.73076 | − | 13.2248i | 0.413794 | − | 0.562374i | ||||
\(554\) | 60.0855i | 2.55279i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.82316 | 0.331776 | ||||||||
\(557\) | 44.2503i | 1.87495i | 0.348058 | + | 0.937473i | \(0.386841\pi\) | ||||
−0.348058 | + | 0.937473i | \(0.613159\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.92705 | − | 11.4452i | 0.166097 | − | 0.484082i | ||||
\(560\) | −4.09944 | + | 36.8634i | −0.173233 | + | 1.55776i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35.1526 | − | 60.8860i | −1.48282 | − | 2.56832i | ||||
\(563\) | 19.4453 | − | 33.6803i | 0.819523 | − | 1.41946i | −0.0865108 | − | 0.996251i | \(-0.527572\pi\) |
0.906034 | − | 0.423205i | \(-0.139095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.8494i | 0.582647i | ||||||||
\(566\) | 36.2078 | − | 20.9046i | 1.52193 | − | 0.878685i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.72309 | + | 8.18063i | 0.198177 | + | 0.343252i | ||||
\(569\) | −23.0789 | − | 39.9739i | −0.967520 | − | 1.67579i | −0.702687 | − | 0.711499i | \(-0.748017\pi\) |
−0.264832 | − | 0.964294i | \(-0.585317\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5684 | + | 18.3050i | 0.442274 | + | 0.766041i | 0.997858 | − | 0.0654194i | \(-0.0208385\pi\) |
−0.555584 | + | 0.831461i | \(0.687505\pi\) | |||||||
\(572\) | −8.79673 | − | 44.9949i | −0.367810 | − | 1.88133i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 52.4229 | + | 5.82976i | 2.18809 | + | 0.243329i | ||||
\(575\) | −2.38452 | + | 4.13011i | −0.0994413 | + | 0.172237i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.9368 | + | 12.6652i | −0.913239 | + | 0.527259i | −0.881472 | − | 0.472237i | \(-0.843447\pi\) |
−0.0317671 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(578\) | 16.1955 | + | 9.35045i | 0.673642 | + | 0.388927i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 40.7146i | − | 1.69058i | ||||||
\(581\) | 0.788579 | − | 7.09113i | 0.0327158 | − | 0.294190i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.0203 | − | 9.82667i | 0.704908 | − | 0.406979i | ||||
\(584\) | −31.8227 | − | 55.1186i | −1.31683 | − | 2.28082i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.9553 | − | 32.8315i | 0.783036 | − | 1.35626i | ||||
\(587\) | −3.08554 | − | 1.78144i | −0.127354 | − | 0.0735278i | 0.434970 | − | 0.900445i | \(-0.356759\pi\) |
−0.562324 | + | 0.826917i | \(0.690092\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.2875 | + | 33.4069i | 0.794727 | + | 1.37651i | ||||
\(590\) | −41.2853 | − | 23.8361i | −1.69969 | − | 0.981316i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −44.8369 | − | 25.8866i | −1.84278 | − | 1.06393i | ||||
\(593\) | 21.9568 | + | 12.6768i | 0.901659 | + | 0.520573i | 0.877738 | − | 0.479141i | \(-0.159052\pi\) |
0.0239212 | + | 0.999714i | \(0.492385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.2149 | − | 5.35037i | 0.500761 | − | 0.219344i | ||||
\(596\) | 80.5990 | + | 46.5338i | 3.30146 | + | 1.90610i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.55661 | − | 18.1919i | −0.145441 | − | 0.743924i | ||||
\(599\) | 5.46078 | + | 9.45835i | 0.223122 | + | 0.386458i | 0.955754 | − | 0.294166i | \(-0.0950420\pi\) |
−0.732633 | + | 0.680624i | \(0.761709\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1282 | + | 21.0067i | −0.494720 | + | 0.856880i | −0.999981 | − | 0.00608649i | \(-0.998063\pi\) |
0.505262 | + | 0.862966i | \(0.331396\pi\) | |||||||
\(602\) | −18.5131 | − | 13.6219i | −0.754536 | − | 0.555187i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 35.4206i | − | 1.44124i | ||||||
\(605\) | −5.14205 | − | 2.96876i | −0.209054 | − | 0.120697i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.85447 | −0.399981 | −0.199990 | − | 0.979798i | \(-0.564091\pi\) | ||||
−0.199990 | + | 0.979798i | \(0.564091\pi\) | |||||||
\(608\) | −15.6987 | + | 27.1910i | −0.636667 | + | 1.10274i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.2062 | 0.494215 | ||||||||
\(611\) | 0.729914 | + | 3.73348i | 0.0295291 | + | 0.151040i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.67688i | − | 0.148508i | −0.997239 | − | 0.0742540i | \(-0.976342\pi\) | ||
0.997239 | − | 0.0742540i | \(-0.0236575\pi\) | |||||||
\(614\) | −11.6208 | − | 20.1278i | −0.468977 | − | 0.812293i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −49.7286 | − | 5.53015i | −2.00362 | − | 0.222816i | ||||
\(617\) | −16.2352 | + | 9.37341i | −0.653605 | + | 0.377359i | −0.789836 | − | 0.613318i | \(-0.789834\pi\) |
0.136231 | + | 0.990677i | \(0.456501\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7650 | + | 7.94725i | −0.553264 | + | 0.319427i | −0.750437 | − | 0.660942i | \(-0.770157\pi\) |
0.197174 | + | 0.980369i | \(0.436824\pi\) | |||||||
\(620\) | 39.7014 | − | 68.7649i | 1.59445 | − | 2.76167i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −27.3086 | − | 15.7667i | −1.09498 | − | 0.632185i | ||||
\(623\) | −4.26499 | + | 1.86815i | −0.170873 | + | 0.0748460i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.61371 | − | 6.25913i | 0.144549 | − | 0.250365i | ||||
\(626\) | 33.9727i | 1.35782i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −65.8330 | −2.62702 | ||||||||
\(629\) | 18.6141i | 0.742194i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.0998 | + | 9.87255i | −0.680731 | + | 0.393020i | −0.800130 | − | 0.599826i | \(-0.795236\pi\) |
0.119400 | + | 0.992846i | \(0.461903\pi\) | |||||||
\(632\) | −37.5745 | − | 21.6936i | −1.49463 | − | 0.862927i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 43.2698 | 1.71846 | ||||||||
\(635\) | 4.36151 | − | 2.51812i | 0.173081 | − | 0.0999286i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.9929 | + | 22.2074i | 0.475177 | + | 0.879890i | ||||
\(638\) | 37.6200 | 1.48939 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.95016 | −0.314258 | ||||||||
\(641\) | 14.8893 | − | 25.7890i | 0.588092 | − | 1.01860i | −0.406390 | − | 0.913699i | \(-0.633213\pi\) |
0.994482 | − | 0.104905i | \(-0.0334539\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.0220 | − | 5.78623i | 0.395231 | − | 0.228187i | −0.289193 | − | 0.957271i | \(-0.593387\pi\) |
0.684424 | + | 0.729084i | \(0.260054\pi\) | |||||||
\(644\) | −24.5496 | − | 2.73007i | −0.967389 | − | 0.107580i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 29.7964 | 1.17232 | ||||||||
\(647\) | 25.5065 | 1.00276 | 0.501382 | − | 0.865226i | \(-0.332825\pi\) | ||||
0.501382 | + | 0.865226i | \(0.332825\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4508 | − | 26.7616i | 0.606497 | − | 1.05048i | ||||
\(650\) | −4.30024 | − | 21.9956i | −0.168669 | − | 0.862737i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29.1893 | − | 16.8524i | −1.14314 | − | 0.659993i | ||||
\(653\) | −22.4146 | − | 38.8233i | −0.877152 | − | 1.51927i | −0.854452 | − | 0.519530i | \(-0.826107\pi\) |
−0.0227004 | − | 0.999742i | \(-0.507226\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.2529 | + | 8.22889i | −0.556905 | + | 0.321529i | ||||
\(656\) | − | 66.9747i | − | 2.61492i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.18179 | + | 0.798661i | 0.279975 | + | 0.0311350i | ||||
\(659\) | 20.5867 | + | 35.6572i | 0.801944 | + | 1.38901i | 0.918335 | + | 0.395805i | \(0.129534\pi\) |
−0.116390 | + | 0.993204i | \(0.537132\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 21.8938i | − | 0.851569i | −0.904825 | − | 0.425785i | \(-0.859998\pi\) | ||
0.904825 | − | 0.425785i | \(-0.140002\pi\) | |||||||
\(662\) | 5.13404 | + | 8.89241i | 0.199540 | + | 0.345613i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.8539 | −0.731673 | ||||||||
\(665\) | −9.30583 | + | 12.6473i | −0.360865 | + | 0.490439i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.6704 | 0.413160 | ||||||||
\(668\) | −73.1999 | + | 42.2620i | −2.83219 | + | 1.63516i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 56.6764i | − | 2.18960i | ||||||
\(671\) | 7.91219i | 0.305447i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.8344 | − | 30.8901i | 0.687466 | − | 1.19073i | −0.285189 | − | 0.958471i | \(-0.592056\pi\) |
0.972655 | − | 0.232254i | \(-0.0746102\pi\) | |||||||
\(674\) | −30.7197 | + | 17.7361i | −1.18328 | + | 0.683167i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 48.2376 | + | 37.5193i | 1.85529 | + | 1.44305i | ||||
\(677\) | 1.27766 | − | 2.21297i | 0.0491044 | − | 0.0850514i | −0.840428 | − | 0.541923i | \(-0.817697\pi\) |
0.889533 | + | 0.456871i | \(0.151030\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.5201 | + | 16.4346i | −1.43989 | + | 0.630701i | ||||
\(680\) | −17.6193 | − | 30.5175i | −0.675670 | − | 1.17029i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 63.5384 | + | 36.6839i | 2.43301 | + | 1.40470i | ||||
\(683\) | 30.9517 | + | 17.8700i | 1.18433 | + | 0.683775i | 0.957013 | − | 0.290045i | \(-0.0936704\pi\) |
0.227320 | + | 0.973820i | \(0.427004\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.05431 | + | 13.9505i | 0.307739 | + | 0.533020i | ||||
\(686\) | 47.0666 | − | 9.11748i | 1.79701 | − | 0.348107i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.5924 | + | 25.2748i | −0.556330 | + | 0.963592i | ||||
\(689\) | −8.50199 | + | 24.7788i | −0.323900 | + | 0.943995i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.5419 | − | 13.0146i | 0.857536 | − | 0.495099i | −0.00565028 | − | 0.999984i | \(-0.501799\pi\) |
0.863186 | + | 0.504885i | \(0.168465\pi\) | |||||||
\(692\) | −30.1127 | + | 52.1567i | −1.14471 | + | 1.98270i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 68.3335i | 2.59391i | ||||||||
\(695\) | − | 2.68278i | − | 0.101764i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.8535 | + | 12.0398i | −0.789884 | + | 0.456040i | ||||
\(698\) | −12.6589 | −0.479146 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −29.6825 | − | 3.30088i | −1.12189 | − | 0.124762i | ||||
\(701\) | 1.12731 | 0.0425779 | 0.0212890 | − | 0.999773i | \(-0.493223\pi\) | ||||
0.0212890 | + | 0.999773i | \(0.493223\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.9588 | − | 18.9813i | −0.413321 | − | 0.715892i | ||||
\(704\) | 12.6702i | 0.477525i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.5478 | + | 30.3936i | 0.660419 | + | 1.14388i | ||||
\(707\) | −3.36398 | − | 0.374096i | −0.126515 | − | 0.0140693i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.05031i | 0.227224i | 0.993525 | + | 0.113612i | \(0.0362421\pi\) | ||||
−0.993525 | + | 0.113612i | \(0.963758\pi\) | |||||||
\(710\) | 4.88276 | − | 2.81906i | 0.183247 | − | 0.105798i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.15202 | + | 10.6556i | 0.230557 | + | 0.399336i | ||||
\(713\) | 18.0218 | + | 10.4049i | 0.674922 | + | 0.389666i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.4300 | + | 3.01664i | −0.577050 | + | 0.112816i | ||||
\(716\) | 4.32530 | − | 7.49164i | 0.161644 | − | 0.279976i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.2249 | 0.829425 | ||||||||
\(719\) | 47.1177 | 1.75719 | 0.878597 | − | 0.477563i | \(-0.158480\pi\) | ||||
0.878597 | + | 0.477563i | \(0.158480\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.9810 | + | 24.4374i | −0.669647 | + | 0.910095i | ||||
\(722\) | 12.2100 | − | 7.04944i | 0.454409 | − | 0.262353i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.75473 | + | 13.4316i | −0.288202 | + | 0.499181i | ||||
\(725\) | 12.9014 | 0.479146 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.9215 | 0.664671 | 0.332335 | − | 0.943161i | \(-0.392163\pi\) | ||||
0.332335 | + | 0.943161i | \(0.392163\pi\) | |||||||
\(728\) | 54.8211 | − | 37.9833i | 2.03181 | − | 1.40775i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32.8985 | + | 18.9940i | −1.21763 | + | 0.702999i | ||||
\(731\) | 10.4929 | 0.388093 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.2037 | + | 22.6343i | 1.44802 | + | 0.836016i | 0.998364 | − | 0.0571848i | \(-0.0182124\pi\) |
0.449658 | + | 0.893201i | \(0.351546\pi\) | |||||||
\(734\) | −3.72861 | + | 2.15271i | −0.137625 | + | 0.0794581i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.9378i | 0.624335i | ||||||||
\(737\) | 36.7382 | 1.35327 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.2613i | 0.708539i | 0.935143 | + | 0.354270i | \(0.115270\pi\) | ||||
−0.935143 | + | 0.354270i | \(0.884730\pi\) | |||||||
\(740\) | −22.5577 | + | 39.0712i | −0.829239 | + | 1.43628i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 40.0804 | + | 29.4911i | 1.47140 | + | 1.08265i | ||||
\(743\) | −30.2115 | − | 17.4426i | −1.10835 | − | 0.639908i | −0.169951 | − | 0.985453i | \(-0.554361\pi\) |
−0.938402 | + | 0.345545i | \(0.887694\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.9577 | − | 27.6396i | 0.584647 | − | 1.01264i | ||||
\(746\) | 31.3032 | − | 18.0729i | 1.14609 | − | 0.661697i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 34.4303 | − | 19.8784i | 1.25890 | − | 0.726825i | ||||
\(749\) | −5.45120 | − | 12.4451i | −0.199183 | − | 0.454733i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.4834 | − | 21.6219i | −0.455526 | − | 0.788993i | 0.543193 | − | 0.839608i | \(-0.317215\pi\) |
−0.998718 | + | 0.0506146i | \(0.983882\pi\) | |||||||
\(752\) | − | 9.17535i | − | 0.334591i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −37.8095 | + | 32.9393i | −1.37694 | + | 1.19958i | ||||
\(755\) | −12.1467 | −0.442064 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.30243 | − | 9.18408i | 0.192720 | − | 0.333801i | −0.753431 | − | 0.657527i | \(-0.771602\pi\) |
0.946151 | + | 0.323726i | \(0.104936\pi\) | |||||||
\(758\) | −81.7370 | −2.96882 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 35.9337 | + | 20.7463i | 1.30345 | + | 0.752548i | ||||
\(761\) | 32.6388i | 1.18316i | 0.806248 | + | 0.591578i | \(0.201495\pi\) | ||||
−0.806248 | + | 0.591578i | \(0.798505\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.18733 | + | 1.83414i | −0.151592 | + | 0.0664002i | ||||
\(764\) | −11.5080 | + | 19.9325i | −0.416345 | + | 0.721131i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41.2988 | − | 71.5316i | −1.49219 | − | 2.58454i | ||||
\(767\) | 7.90323 | + | 40.4247i | 0.285369 | + | 1.45965i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.1851 | − | 26.0876i | −1.62942 | − | 0.940744i | −0.984267 | − | 0.176686i | \(-0.943462\pi\) |
−0.645148 | − | 0.764057i | \(-0.723204\pi\) | |||||||
\(770\) | −3.30077 | + | 29.6814i | −0.118951 | + | 1.06964i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.2909 | + | 7.09618i | 0.442360 | + | 0.255397i | ||||
\(773\) | 30.9221 | + | 17.8529i | 1.11219 | + | 0.642123i | 0.939396 | − | 0.342835i | \(-0.111387\pi\) |
0.172794 | + | 0.984958i | \(0.444721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.7898 | + | 12.5804i | 0.782714 | + | 0.451900i | ||||
\(776\) | 54.1208 | + | 93.7400i | 1.94282 | + | 3.36507i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 56.9752 | + | 32.8947i | 2.04266 | + | 1.17933i | ||||
\(779\) | 14.1766 | − | 24.5545i | 0.507928 | − | 0.879757i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.82735 | + | 3.16506i | 0.0653876 | + | 0.113255i | ||||
\(782\) | 13.9206 | − | 8.03703i | 0.497798 | − | 0.287404i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.1114 | − | 58.1175i | −0.646836 | − | 2.07563i | ||||
\(785\) | 22.5760i | 0.805770i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.28813 | + | 3.05310i | 0.188501 | + | 0.108831i | 0.591281 | − | 0.806466i | \(-0.298622\pi\) |
−0.402779 | + | 0.915297i | \(0.631956\pi\) | |||||||
\(788\) | −18.9301 | + | 10.9293i | −0.674356 | + | 0.389339i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.9482 | + | 22.4270i | −0.460678 | + | 0.797918i | ||||
\(791\) | −9.11971 | − | 20.8203i | −0.324259 | − | 0.740283i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.92774 | − | 7.95204i | −0.246011 | − | 0.282385i | ||||
\(794\) | 5.38296 | + | 9.32356i | 0.191034 | + | 0.330881i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.965369 | − | 1.67207i | −0.0342166 | − | 0.0592649i | ||||
\(797\) | 23.1149 | + | 40.0363i | 0.818773 | + | 1.41816i | 0.906586 | + | 0.422020i | \(0.138679\pi\) |
−0.0878129 | + | 0.996137i | \(0.527988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.85688 | + | 1.64942i | −0.101069 | + | 0.0583522i | ||||
\(800\) | 20.4792i | 0.724048i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.3700 | − | 43.9422i | 0.895847 | − | 1.55165i | ||||
\(803\) | −12.3121 | − | 21.3252i | −0.434484 | − | 0.752549i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.936218 | + | 8.41874i | −0.0329974 | + | 0.296722i | ||||
\(806\) | −95.9780 | + | 18.7642i | −3.38068 | + | 0.660939i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.94415i | 0.314654i | ||||||||
\(809\) | −39.2879 | −1.38129 | −0.690644 | − | 0.723195i | \(-0.742673\pi\) | ||||
−0.690644 | + | 0.723195i | \(0.742673\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.90664i | 0.242525i | 0.992620 | + | 0.121262i | \(0.0386943\pi\) | ||||
−0.992620 | + | 0.121262i | \(0.961306\pi\) | |||||||
\(812\) | 26.8102 | + | 61.2077i | 0.940855 | + | 2.14797i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −36.1015 | − | 20.8432i | −1.26536 | − | 0.730555i | ||||
\(815\) | −5.77917 | + | 10.0098i | −0.202436 | + | 0.350629i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.6998 | + | 6.17756i | −0.374340 | + | 0.216125i | ||||
\(818\) | −45.6466 | −1.59600 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −58.3622 | −2.03810 | ||||||||
\(821\) | 1.65453 | − | 0.955244i | 0.0577435 | − | 0.0333382i | −0.470850 | − | 0.882213i | \(-0.656053\pi\) |
0.528594 | + | 0.848875i | \(0.322719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.789844 | − | 1.36805i | 0.0275322 | − | 0.0476872i | −0.851931 | − | 0.523654i | \(-0.824568\pi\) |
0.879463 | + | 0.475967i | \(0.157902\pi\) | |||||||
\(824\) | 69.4320 | + | 40.0866i | 2.41878 | + | 1.39648i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 77.7617 | + | 8.64760i | 2.70567 | + | 0.300888i | ||||
\(827\) | − | 32.5050i | − | 1.13031i | −0.824985 | − | 0.565155i | \(-0.808816\pi\) | ||
0.824985 | − | 0.565155i | \(-0.191184\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.0538 | 1.21747 | 0.608735 | − | 0.793373i | \(-0.291677\pi\) | ||||
0.608735 | + | 0.793373i | \(0.291677\pi\) | |||||||
\(830\) | 11.2533i | 0.390608i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.0937 | − | 12.7340i | −0.384606 | − | 0.441472i | ||||
\(833\) | −14.8399 | + | 16.0868i | −0.514172 | + | 0.557375i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.4928 | + | 25.1023i | 0.501544 | + | 0.868700i | ||||
\(836\) | −23.4063 | + | 40.5409i | −0.809523 | + | 1.40214i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 77.3760i | − | 2.67291i | ||||||
\(839\) | −4.63746 | + | 2.67744i | −0.160103 | + | 0.0924354i | −0.577911 | − | 0.816100i | \(-0.696132\pi\) |
0.417808 | + | 0.908535i | \(0.362798\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.0669890 | + | 0.116028i | 0.00230997 | + | 0.00400098i | ||||
\(842\) | 16.6354 | + | 28.8133i | 0.573293 | + | 0.992973i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.6658 | − | 30.5981i | −0.608082 | − | 1.05323i | ||||
\(845\) | 12.8664 | − | 16.5420i | 0.442618 | − | 0.569063i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.68515 | + | 1.07705i | 0.332786 | + | 0.0370079i | ||||
\(848\) | 31.5923 | − | 54.7195i | 1.08488 | − | 1.87907i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.8311 | − | 9.71744i | 0.577302 | − | 0.333305i | ||||
\(851\) | −10.2397 | − | 5.91190i | −0.351013 | − | 0.202657i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.6270i | 1.69920i | 0.527431 | + | 0.849598i | \(0.323155\pi\) | ||||
−0.527431 | + | 0.849598i | \(0.676845\pi\) | |||||||
\(854\) | −18.3501 | + | 8.03771i | −0.627926 | + | 0.275045i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.0927 | + | 17.9514i | −1.06273 | + | 0.613566i | ||||
\(857\) | −2.94196 | − | 5.09563i | −0.100496 | − | 0.174063i | 0.811393 | − | 0.584500i | \(-0.198709\pi\) |
−0.911889 | + | 0.410437i | \(0.865376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.6931 | + | 37.5735i | −0.740159 | + | 1.28199i | 0.212264 | + | 0.977212i | \(0.431916\pi\) |
−0.952423 | + | 0.304780i | \(0.901417\pi\) | |||||||
\(860\) | 22.0246 | + | 12.7159i | 0.751033 | + | 0.433609i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.6106 | − | 20.1102i | −0.395460 | − | 0.684957i | ||||
\(863\) | 26.9570 | + | 15.5636i | 0.917626 | + | 0.529792i | 0.882877 | − | 0.469604i | \(-0.155603\pi\) |
0.0347490 | + | 0.999396i | \(0.488937\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.8860 | + | 10.3265i | 0.608142 | + | 0.351111i | ||||
\(866\) | −7.73558 | − | 4.46614i | −0.262866 | − | 0.151766i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.4035 | + | 129.520i | −0.488885 | + | 4.39620i | ||||
\(869\) | −14.5374 | − | 8.39318i | −0.493148 | − | 0.284719i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.9233 | + | 32.1672i | −1.25110 | + | 1.08994i | ||||
\(872\) | 6.04001 | + | 10.4616i | 0.204540 | + | 0.354274i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.46341 | + | 16.3911i | −0.320105 | + | 0.554438i | ||||
\(875\) | −3.48896 | + | 31.3738i | −0.117949 | + | 1.06063i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 29.9106i | − | 1.01001i | −0.863117 | − | 0.505004i | \(-0.831491\pi\) | ||
0.863117 | − | 0.505004i | \(-0.168509\pi\) | |||||||
\(878\) | −86.3413 | − | 49.8492i | −2.91388 | − | 1.68233i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 37.9206 | 1.27830 | ||||||||
\(881\) | −7.28477 | + | 12.6176i | −0.245430 | + | 0.425097i | −0.962252 | − | 0.272159i | \(-0.912262\pi\) |
0.716822 | + | 0.697256i | \(0.245596\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.9296 | 1.64661 | 0.823307 | − | 0.567597i | \(-0.192127\pi\) | ||||
0.823307 | + | 0.567597i | \(0.192127\pi\) | |||||||
\(884\) | −17.1987 | + | 50.1249i | −0.578454 | + | 1.68588i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38.9324i | 1.30796i | ||||||||
\(887\) | 27.2951 | + | 47.2765i | 0.916480 | + | 1.58739i | 0.804719 | + | 0.593655i | \(0.202316\pi\) |
0.111761 | + | 0.993735i | \(0.464351\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.89866 | + | 6.65761i | −0.164296 | + | 0.223289i | ||||
\(890\) | 6.36000 | − | 3.67195i | 0.213188 | − | 0.123084i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −91.9222 | + | 53.0713i | −3.07778 | + | 1.77696i | ||||
\(893\) | 1.94215 | − | 3.36390i | 0.0649916 | − | 0.112569i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.56909 | − | 1.48327i | −0.0858753 | − | 0.0495801i | ||||
\(896\) | 11.9518 | − | 5.23512i | 0.399281 | − | 0.174893i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −50.3787 | + | 87.2584i | −1.68116 | + | 2.91185i | ||||
\(899\) | − | 56.2955i | − | 1.87756i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.7169 | −0.756810 | ||||||||
\(902\) | − | 53.9263i | − | 1.79555i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −52.0172 | + | 30.0321i | −1.73007 | + | 0.998854i | ||||
\(905\) | 4.60606 | + | 2.65931i | 0.153111 | + | 0.0883985i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.7255 | −0.754589 | −0.377295 | − | 0.926093i | \(-0.623146\pi\) | ||||
−0.377295 | + | 0.926093i | \(0.623146\pi\) | |||||||
\(908\) | −55.6584 | + | 32.1344i | −1.84709 | + | 1.06642i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.6710 | − | 32.7210i | −0.751537 | − | 1.08469i | ||||
\(911\) | 42.2359 | 1.39934 | 0.699669 | − | 0.714467i | \(-0.253331\pi\) | ||||
0.699669 | + | 0.714467i | \(0.253331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.29450 | −0.241413 | ||||||||
\(914\) | −18.0421 | + | 31.2498i | −0.596779 | + | 1.03365i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −32.2870 | + | 18.6409i | −1.06679 | + | 0.615912i | ||||
\(917\) | 16.0082 | − | 21.7562i | 0.528637 | − | 0.718453i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.6940 | 1.01250 | 0.506251 | − | 0.862386i | \(-0.331031\pi\) | ||||
0.506251 | + | 0.862386i | \(0.331031\pi\) | |||||||
\(920\) | 22.3838 | 0.737971 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −48.4890 | + | 83.9854i | −1.59690 | + | 2.76591i | ||||
\(923\) | −4.60780 | − | 1.58101i | −0.151668 | − | 0.0520396i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.3806 | − | 7.14797i | −0.407073 | − | 0.235024i | ||||
\(926\) | −8.74009 | − | 15.1383i | −0.287217 | − | 0.497474i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 39.6819 | − | 22.9104i | 1.30262 | − | 0.752070i | ||||
\(929\) | − | 37.4250i | − | 1.22787i | −0.789355 | − | 0.613936i | \(-0.789585\pi\) | ||
0.789355 | − | 0.613936i | \(-0.210415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.66168 | − | 25.1409i | 0.185554 | − | 0.823960i | ||||
\(932\) | −15.4463 | − | 26.7538i | −0.505961 | − | 0.876350i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.0733i | 0.427770i | ||||||||
\(935\) | −6.81684 | − | 11.8071i | −0.222935 | − | 0.386134i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.3386 | 1.44848 | 0.724239 | − | 0.689549i | \(-0.242191\pi\) | ||||
0.724239 | + | 0.689549i | \(0.242191\pi\) | |||||||
\(938\) | 37.3210 | + | 85.2038i | 1.21857 | + | 2.78200i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.99546 | −0.260783 | ||||||||
\(941\) | −23.8202 | + | 13.7526i | −0.776518 | + | 0.448323i | −0.835195 | − | 0.549954i | \(-0.814645\pi\) |
0.0586770 | + | 0.998277i | \(0.481312\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 15.2955i | − | 0.498089i | ||||||
\(944\) | − | 99.3472i | − | 3.23348i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.7494 | + | 20.3506i | −0.382007 | + | 0.661656i | ||||
\(947\) | −4.40226 | + | 2.54165i | −0.143054 | + | 0.0825925i | −0.569819 | − | 0.821770i | \(-0.692987\pi\) |
0.426765 | + | 0.904363i | \(0.359653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.0459 | + | 10.6524i | 1.00779 | + | 0.345790i | ||||
\(950\) | −11.4420 | + | 19.8182i | −0.371229 | + | 0.642987i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 46.5834 | + | 34.2760i | 1.50978 | + | 1.11089i | ||||
\(953\) | −4.90718 | − | 8.49949i | −0.158959 | − | 0.275326i | 0.775534 | − | 0.631305i | \(-0.217481\pi\) |
−0.934494 | + | 0.355980i | \(0.884147\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.83540 | + | 3.94642i | 0.221188 | + | 0.127703i | ||||
\(956\) | −38.2388 | − | 22.0772i | −1.23673 | − | 0.714027i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.2353 | − | 21.1921i | −0.395303 | − | 0.684685i | ||||
\(959\) | −21.2946 | − | 15.6686i | −0.687640 | − | 0.505964i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39.3947 | − | 68.2336i | 1.27080 | − | 2.20108i | ||||
\(962\) | 54.5332 | − | 10.6615i | 1.75822 | − | 0.343741i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 41.0601 | − | 23.7060i | 1.32246 | − | 0.763520i | ||||
\(965\) | 2.43348 | − | 4.21490i | 0.0783364 | − | 0.135683i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.69619i | 0.0867036i | 0.999060 | + | 0.0433518i | \(0.0138036\pi\) | ||||
−0.999060 | + | 0.0433518i | \(0.986196\pi\) | |||||||
\(968\) | − | 25.7509i | − | 0.827665i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 55.9504 | − | 32.3030i | 1.79646 | − | 1.03719i | ||||
\(971\) | −24.9240 | −0.799850 | −0.399925 | − | 0.916548i | \(-0.630964\pi\) | ||||
−0.399925 | + | 0.916548i | \(0.630964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.76659 | + | 4.03313i | 0.0566344 | + | 0.129296i | ||||
\(974\) | 103.543 | 3.31773 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.7187 | + | 22.0294i | 0.407115 | + | 0.705144i | ||||
\(977\) | − | 28.3129i | − | 0.905811i | −0.891558 | − | 0.452906i | \(-0.850387\pi\) | ||
0.891558 | − | 0.452906i | \(-0.149613\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.38019 | + | 4.12262i | 0.0760713 | + | 0.131759i | ||||
\(980\) | −50.6440 | + | 15.7824i | −1.61776 | + | 0.504150i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 17.5015i | − | 0.558494i | ||||||
\(983\) | −32.7805 | + | 18.9258i | −1.04554 | + | 0.603641i | −0.921396 | − | 0.388624i | \(-0.872951\pi\) |
−0.124140 | + | 0.992265i | \(0.539617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.74795 | + | 6.49165i | 0.119420 | + | 0.206841i | ||||
\(986\) | −37.6585 | − | 21.7421i | −1.19929 | − | 0.692410i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.9725 | − | 61.2391i | −0.380897 | − | 1.94827i | ||||
\(989\) | −3.33257 | + | 5.77218i | −0.105970 | + | 0.183545i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.4158 | 1.85564 | 0.927820 | − | 0.373028i | \(-0.121681\pi\) | ||||
0.927820 | + | 0.373028i | \(0.121681\pi\) | |||||||
\(992\) | 89.3612 | 2.83722 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.48410 | + | 7.45327i | −0.173945 | + | 0.236403i | ||||
\(995\) | −0.573399 | + | 0.331052i | −0.0181780 | + | 0.0104950i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0294 | + | 24.2997i | −0.444316 | + | 0.769578i | −0.998004 | − | 0.0631462i | \(-0.979887\pi\) |
0.553688 | + | 0.832724i | \(0.313220\pi\) | |||||||
\(998\) | 29.4001 | 0.930645 | ||||||||
\(999\) | 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 | 819.2.do.e.667.6 | 12 | ||
3.2 | odd | 2 | 91.2.u.b.30.1 | yes | 12 | ||
7.4 | even | 3 | 819.2.bm.f.550.6 | 12 | |||
13.10 | even | 6 | 819.2.bm.f.478.1 | 12 | |||
21.2 | odd | 6 | 637.2.q.g.589.6 | 12 | |||
21.5 | even | 6 | 637.2.q.i.589.6 | 12 | |||
21.11 | odd | 6 | 91.2.k.b.4.1 | ✓ | 12 | ||
21.17 | even | 6 | 637.2.k.i.459.1 | 12 | |||
21.20 | even | 2 | 637.2.u.g.30.1 | 12 | |||
39.20 | even | 12 | 1183.2.e.j.170.1 | 24 | |||
39.23 | odd | 6 | 91.2.k.b.23.6 | yes | 12 | ||
39.32 | even | 12 | 1183.2.e.j.170.12 | 24 | |||
91.88 | even | 6 | inner | 819.2.do.e.361.6 | 12 | ||
273.23 | odd | 6 | 637.2.q.g.491.6 | 12 | |||
273.32 | even | 12 | 1183.2.e.j.508.12 | 24 | |||
273.62 | even | 6 | 637.2.k.i.569.6 | 12 | |||
273.101 | even | 6 | 637.2.u.g.361.1 | 12 | |||
273.110 | odd | 12 | 8281.2.a.co.1.1 | 12 | |||
273.137 | even | 12 | 1183.2.e.j.508.1 | 24 | |||
273.149 | even | 12 | 8281.2.a.cp.1.1 | 12 | |||
273.179 | odd | 6 | 91.2.u.b.88.1 | yes | 12 | ||
273.215 | odd | 12 | 8281.2.a.co.1.12 | 12 | |||
273.254 | even | 12 | 8281.2.a.cp.1.12 | 12 | |||
273.257 | even | 6 | 637.2.q.i.491.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.1 | ✓ | 12 | 21.11 | odd | 6 | ||
91.2.k.b.23.6 | yes | 12 | 39.23 | odd | 6 | ||
91.2.u.b.30.1 | yes | 12 | 3.2 | odd | 2 | ||
91.2.u.b.88.1 | yes | 12 | 273.179 | odd | 6 | ||
637.2.k.i.459.1 | 12 | 21.17 | even | 6 | |||
637.2.k.i.569.6 | 12 | 273.62 | even | 6 | |||
637.2.q.g.491.6 | 12 | 273.23 | odd | 6 | |||
637.2.q.g.589.6 | 12 | 21.2 | odd | 6 | |||
637.2.q.i.491.6 | 12 | 273.257 | even | 6 | |||
637.2.q.i.589.6 | 12 | 21.5 | even | 6 | |||
637.2.u.g.30.1 | 12 | 21.20 | even | 2 | |||
637.2.u.g.361.1 | 12 | 273.101 | even | 6 | |||
819.2.bm.f.478.1 | 12 | 13.10 | even | 6 | |||
819.2.bm.f.550.6 | 12 | 7.4 | even | 3 | |||
819.2.do.e.361.6 | 12 | 91.88 | even | 6 | inner | ||
819.2.do.e.667.6 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.e.j.170.1 | 24 | 39.20 | even | 12 | |||
1183.2.e.j.170.12 | 24 | 39.32 | even | 12 | |||
1183.2.e.j.508.1 | 24 | 273.137 | even | 12 | |||
1183.2.e.j.508.12 | 24 | 273.32 | even | 12 | |||
8281.2.a.co.1.1 | 12 | 273.110 | odd | 12 | |||
8281.2.a.co.1.12 | 12 | 273.215 | odd | 12 | |||
8281.2.a.cp.1.1 | 12 | 273.149 | even | 12 | |||
8281.2.a.cp.1.12 | 12 | 273.254 | even | 12 |