Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(30,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.30");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.u (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: | \(0.726638658394\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 88.1 | ||
Root | \(1.32725 + 0.488273i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.88 |
Dual form | 91.2.u.b.30.1 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 | −0.994084 | − | 0.108613i | \(-0.965359\pi\) |
−0.591104 | − | 0.806596i | \(-0.701308\pi\) | |||||||
\(3\) | 0.518466 | 0.299336 | 0.149668 | − | 0.988736i | \(-0.452179\pi\) | ||||
0.149668 | + | 0.988736i | \(0.452179\pi\) | |||||||
\(4\) | 2.35043 | + | 4.07106i | 1.17521 | + | 2.03553i | ||||
\(5\) | 1.39608 | − | 0.806027i | 0.624346 | − | 0.360466i | −0.154213 | − | 0.988038i | \(-0.549284\pi\) |
0.778559 | + | 0.627571i | \(0.215951\pi\) | |||||||
\(6\) | −1.16229 | − | 0.671051i | −0.474504 | − | 0.273955i | ||||
\(7\) | 2.62954 | − | 0.292422i | 0.993873 | − | 0.110525i | ||||
\(8\) | − | 6.99143i | − | 2.47184i | ||||||
\(9\) | −2.73119 | −0.910398 | ||||||||
\(10\) | −4.17296 | −1.31961 | ||||||||
\(11\) | − | 2.70496i | − | 0.815575i | −0.913077 | − | 0.407788i | \(-0.866300\pi\) | ||
0.913077 | − | 0.407788i | \(-0.133700\pi\) | |||||||
\(12\) | 1.21862 | + | 2.11070i | 0.351784 | + | 0.609308i | ||||
\(13\) | 2.36840 | − | 2.71858i | 0.656876 | − | 0.753998i | ||||
\(14\) | −6.27337 | − | 2.74787i | −1.67663 | − | 0.734398i | ||||
\(15\) | 0.723819 | − | 0.417897i | 0.186889 | − | 0.107901i | ||||
\(16\) | −4.34816 | + | 7.53123i | −1.08704 | + | 1.88281i | ||||
\(17\) | 1.56330 | + | 2.70772i | 0.379157 | + | 0.656719i | 0.990940 | − | 0.134307i | \(-0.0428808\pi\) |
−0.611783 | + | 0.791026i | \(0.709547\pi\) | |||||||
\(18\) | 6.12277 | + | 3.53498i | 1.44315 | + | 0.833204i | ||||
\(19\) | 3.68150i | 0.844595i | 0.906457 | + | 0.422297i | \(0.138776\pi\) | ||||
−0.906457 | + | 0.422297i | \(0.861224\pi\) | |||||||
\(20\) | 6.56276 | + | 3.78901i | 1.46748 | + | 0.847249i | ||||
\(21\) | 1.36333 | − | 0.151611i | 0.297502 | − | 0.0330842i | ||||
\(22\) | −3.50103 | + | 6.06396i | −0.746421 | + | 1.29284i | ||||
\(23\) | 0.993019 | − | 1.71996i | 0.207059 | − | 0.358636i | −0.743728 | − | 0.668482i | \(-0.766944\pi\) |
0.950787 | + | 0.309846i | \(0.100278\pi\) | |||||||
\(24\) | − | 3.62482i | − | 0.739913i | ||||||
\(25\) | −1.20064 | + | 2.07957i | −0.240128 | + | 0.415914i | ||||
\(26\) | −8.82813 | + | 3.02907i | −1.73134 | + | 0.594050i | ||||
\(27\) | −2.97143 | −0.571852 | ||||||||
\(28\) | 7.37101 | + | 10.0177i | 1.39299 | + | 1.89317i | ||||
\(29\) | 2.68636 | + | 4.65290i | 0.498844 | + | 0.864023i | 0.999999 | − | 0.00133469i | \(-0.000424845\pi\) |
−0.501155 | + | 0.865357i | \(0.667092\pi\) | |||||||
\(30\) | −2.16354 | −0.395006 | ||||||||
\(31\) | −9.07425 | − | 5.23902i | −1.62978 | − | 0.940956i | −0.984156 | − | 0.177303i | \(-0.943263\pi\) |
−0.645627 | − | 0.763653i | \(-0.723404\pi\) | |||||||
\(32\) | 7.38583 | − | 4.26421i | 1.30564 | − | 0.753813i | ||||
\(33\) | − | 1.40243i | − | 0.244131i | ||||||
\(34\) | − | 8.09354i | − | 1.38803i | ||||||
\(35\) | 3.43535 | − | 2.52773i | 0.580680 | − | 0.427264i | ||||
\(36\) | −6.41947 | − | 11.1188i | −1.06991 | − | 1.85314i | ||||
\(37\) | 5.15585 | + | 2.97673i | 0.847616 | + | 0.489371i | 0.859846 | − | 0.510554i | \(-0.170560\pi\) |
−0.0122297 | + | 0.999925i | \(0.503893\pi\) | |||||||
\(38\) | 4.76497 | − | 8.25317i | 0.772981 | − | 1.33884i | ||||
\(39\) | 1.22794 | − | 1.40949i | 0.196627 | − | 0.225699i | ||||
\(40\) | −5.63528 | − | 9.76059i | −0.891016 | − | 1.54329i | ||||
\(41\) | −6.66970 | + | 3.85075i | −1.04163 | + | 0.601386i | −0.920295 | − | 0.391225i | \(-0.872051\pi\) |
−0.121337 | + | 0.992611i | \(0.538718\pi\) | |||||||
\(42\) | −3.25253 | − | 1.42468i | −0.501876 | − | 0.219832i | ||||
\(43\) | −1.67800 | + | 2.90638i | −0.255892 | + | 0.443219i | −0.965138 | − | 0.261743i | \(-0.915703\pi\) |
0.709245 | + | 0.704962i | \(0.249036\pi\) | |||||||
\(44\) | 11.0120 | − | 6.35780i | 1.66013 | − | 0.958475i | ||||
\(45\) | −3.81296 | + | 2.20141i | −0.568403 | + | 0.328168i | ||||
\(46\) | −4.45229 | + | 2.57053i | −0.656454 | + | 0.379004i | ||||
\(47\) | −0.913730 | + | 0.527542i | −0.133281 | + | 0.0769500i | −0.565158 | − | 0.824983i | \(-0.691185\pi\) |
0.431877 | + | 0.901933i | \(0.357852\pi\) | |||||||
\(48\) | −2.25437 | + | 3.90469i | −0.325390 | + | 0.563593i | ||||
\(49\) | 6.82898 | − | 1.53787i | 0.975568 | − | 0.219696i | ||||
\(50\) | 5.38318 | − | 3.10798i | 0.761297 | − | 0.439535i | ||||
\(51\) | 0.810520 | + | 1.40386i | 0.113495 | + | 0.196580i | ||||
\(52\) | 16.6343 | + | 3.25208i | 2.30676 | + | 0.450982i | ||||
\(53\) | −3.63284 | + | 6.29226i | −0.499009 | + | 0.864308i | −0.999999 | − | 0.00114437i | \(-0.999636\pi\) |
0.500991 | + | 0.865453i | \(0.332969\pi\) | |||||||
\(54\) | 6.66133 | + | 3.84592i | 0.906492 | + | 0.523363i | ||||
\(55\) | −2.18027 | − | 3.77633i | −0.293987 | − | 0.509201i | ||||
\(56\) | −2.04445 | − | 18.3843i | −0.273201 | − | 2.45670i | ||||
\(57\) | 1.90873i | 0.252818i | ||||||||
\(58\) | − | 13.9078i | − | 1.82618i | ||||||
\(59\) | −9.89352 | + | 5.71203i | −1.28803 | + | 0.743643i | −0.978302 | − | 0.207183i | \(-0.933570\pi\) |
−0.309725 | + | 0.950826i | \(0.600237\pi\) | |||||||
\(60\) | 3.40257 | + | 1.96447i | 0.439270 | + | 0.253613i | ||||
\(61\) | −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 | ||||
\(63\) | −7.18179 | + | 0.798661i | −0.904820 | + | 0.100622i | ||||
\(64\) | −4.68406 | −0.585507 | ||||||||
\(65\) | 1.11523 | − | 5.70435i | 0.138327 | − | 0.707537i | ||||
\(66\) | −1.81516 | + | 3.14395i | −0.223431 | + | 0.386994i | ||||
\(67\) | − | 13.5818i | − | 1.65928i | −0.558296 | − | 0.829642i | \(-0.688545\pi\) | ||
0.558296 | − | 0.829642i | \(-0.311455\pi\) | |||||||
\(68\) | −7.34886 | + | 12.7286i | −0.891180 | + | 1.54357i | ||||
\(69\) | 0.514846 | − | 0.891740i | 0.0619802 | − | 0.107353i | ||||
\(70\) | −10.9730 | + | 1.22027i | −1.31152 | + | 0.145850i | ||||
\(71\) | 1.17009 | + | 0.675554i | 0.138865 | + | 0.0801736i | 0.567823 | − | 0.823151i | \(-0.307786\pi\) |
−0.428958 | + | 0.903324i | \(0.641119\pi\) | |||||||
\(72\) | 19.0949i | 2.25036i | ||||||||
\(73\) | 7.88374 | + | 4.55168i | 0.922721 | + | 0.532733i | 0.884502 | − | 0.466536i | \(-0.154498\pi\) |
0.0382192 | + | 0.999269i | \(0.487831\pi\) | |||||||
\(74\) | −7.70557 | − | 13.3464i | −0.895754 | − | 1.55149i | ||||
\(75\) | −0.622492 | + | 1.07819i | −0.0718791 | + | 0.124498i | ||||
\(76\) | −14.9876 | + | 8.65311i | −1.71920 | + | 0.992579i | ||||
\(77\) | −0.790989 | − | 7.11280i | −0.0901416 | − | 0.810578i | ||||
\(78\) | −4.57708 | + | 1.57047i | −0.518252 | + | 0.177821i | ||||
\(79\) | 3.10289 | + | 5.37436i | 0.349102 | + | 0.604663i | 0.986090 | − | 0.166211i | \(-0.0531532\pi\) |
−0.636988 | + | 0.770874i | \(0.719820\pi\) | |||||||
\(80\) | 14.0189i | 1.56736i | ||||||||
\(81\) | 6.65300 | 0.739222 | ||||||||
\(82\) | 19.9361 | 2.20158 | ||||||||
\(83\) | − | 2.69672i | − | 0.296003i | −0.988987 | − | 0.148002i | \(-0.952716\pi\) | ||
0.988987 | − | 0.148002i | \(-0.0472841\pi\) | |||||||
\(84\) | 3.82162 | + | 5.19384i | 0.416973 | + | 0.566694i | ||||
\(85\) | 4.36499 | + | 2.52013i | 0.473450 | + | 0.273346i | ||||
\(86\) | 7.52346 | − | 4.34367i | 0.811275 | − | 0.468390i | ||||
\(87\) | 1.39278 | + | 2.41237i | 0.149322 | + | 0.258633i | ||||
\(88\) | −18.9115 | −2.01597 | ||||||||
\(89\) | 1.52410 | + | 0.879938i | 0.161554 | + | 0.0932732i | 0.578597 | − | 0.815613i | \(-0.303600\pi\) |
−0.417043 | + | 0.908887i | \(0.636934\pi\) | |||||||
\(90\) | 11.3972 | 1.20137 | ||||||||
\(91\) | 5.43284 | − | 7.84119i | 0.569516 | − | 0.821980i | ||||
\(92\) | 9.33607 | 0.973353 | ||||||||
\(93\) | −4.70469 | − | 2.71625i | −0.487853 | − | 0.281662i | ||||
\(94\) | 2.73119 | 0.281701 | ||||||||
\(95\) | 2.96739 | + | 5.13967i | 0.304448 | + | 0.527319i | ||||
\(96\) | 3.82930 | − | 2.21085i | 0.390827 | − | 0.225644i | ||||
\(97\) | −13.4078 | − | 7.74102i | −1.36136 | − | 0.785981i | −0.371555 | − | 0.928411i | \(-0.621175\pi\) |
−0.989805 | + | 0.142430i | \(0.954509\pi\) | |||||||
\(98\) | −17.2996 | − | 5.39116i | −1.74753 | − | 0.544589i | ||||
\(99\) | 7.38776i | 0.742498i | ||||||||
\(100\) | −11.2881 | −1.12881 | ||||||||
\(101\) | 1.27930 | 0.127295 | 0.0636477 | − | 0.997972i | \(-0.479727\pi\) | ||||
0.0636477 | + | 0.997972i | \(0.479727\pi\) | |||||||
\(102\) | − | 4.19622i | − | 0.415488i | ||||||
\(103\) | −5.73367 | − | 9.93101i | −0.564956 | − | 0.978532i | −0.997054 | − | 0.0767054i | \(-0.975560\pi\) |
0.432098 | − | 0.901827i | \(-0.357773\pi\) | |||||||
\(104\) | −19.0068 | − | 16.5585i | −1.86377 | − | 1.62370i | ||||
\(105\) | 1.78111 | − | 1.31054i | 0.173819 | − | 0.127896i | ||||
\(106\) | 16.2881 | − | 9.40397i | 1.58204 | − | 0.913394i | ||||
\(107\) | 2.56763 | − | 4.44726i | 0.248222 | − | 0.429933i | −0.714811 | − | 0.699318i | \(-0.753487\pi\) |
0.963033 | + | 0.269385i | \(0.0868205\pi\) | |||||||
\(108\) | −6.98412 | − | 12.0969i | −0.672048 | − | 1.16402i | ||||
\(109\) | −1.49635 | − | 0.863916i | −0.143324 | − | 0.0827481i | 0.426623 | − | 0.904429i | \(-0.359703\pi\) |
−0.569947 | + | 0.821681i | \(0.693036\pi\) | |||||||
\(110\) | 11.2877i | 1.07624i | ||||||||
\(111\) | 2.67313 | + | 1.54333i | 0.253722 | + | 0.146487i | ||||
\(112\) | −9.23136 | + | 21.0752i | −0.872282 | + | 1.99142i | ||||
\(113\) | 4.29556 | − | 7.44014i | 0.404093 | − | 0.699909i | −0.590123 | − | 0.807314i | \(-0.700921\pi\) |
0.994215 | + | 0.107404i | \(0.0342540\pi\) | |||||||
\(114\) | 2.47048 | − | 4.27899i | 0.231381 | − | 0.400764i | ||||
\(115\) | − | 3.20160i | − | 0.298551i | ||||||
\(116\) | −12.6282 | + | 21.8726i | −1.17250 | + | 2.03082i | ||||
\(117\) | −6.46856 | + | 7.42497i | −0.598019 | + | 0.686438i | ||||
\(118\) | 29.5723 | 2.72235 | ||||||||
\(119\) | 4.90257 | + | 6.66292i | 0.449418 | + | 0.610789i | ||||
\(120\) | −2.92170 | − | 5.06053i | −0.266714 | − | 0.461961i | ||||
\(121\) | 3.68321 | 0.334837 | ||||||||
\(122\) | 6.55741 | + | 3.78592i | 0.593680 | + | 0.342761i | ||||
\(123\) | −3.45801 | + | 1.99648i | −0.311798 | + | 0.180017i | ||||
\(124\) | − | 49.2557i | − | 4.42330i | ||||||
\(125\) | 11.9313i | 1.06716i | ||||||||
\(126\) | 17.1338 | + | 7.50495i | 1.52640 | + | 0.668595i | ||||
\(127\) | −1.56206 | − | 2.70556i | −0.138610 | − | 0.240080i | 0.788361 | − | 0.615214i | \(-0.210930\pi\) |
−0.926971 | + | 0.375133i | \(0.877597\pi\) | |||||||
\(128\) | −4.27097 | − | 2.46585i | −0.377504 | − | 0.217952i | ||||
\(129\) | −0.869985 | + | 1.50686i | −0.0765979 | + | 0.132671i | ||||
\(130\) | −9.88325 | + | 11.3445i | −0.866818 | + | 0.994981i | ||||
\(131\) | −5.10460 | − | 8.84142i | −0.445991 | − | 0.772479i | 0.552130 | − | 0.833758i | \(-0.313815\pi\) |
−0.998121 | + | 0.0612793i | \(0.980482\pi\) | |||||||
\(132\) | 5.70937 | − | 3.29630i | 0.496936 | − | 0.286906i | ||||
\(133\) | 1.07655 | + | 9.68067i | 0.0933490 | + | 0.839420i | ||||
\(134\) | −17.5790 | + | 30.4476i | −1.51859 | + | 2.63028i | ||||
\(135\) | −4.14835 | + | 2.39505i | −0.357033 | + | 0.206133i | ||||
\(136\) | 18.9308 | − | 10.9297i | 1.62331 | − | 0.937216i | ||||
\(137\) | 8.65385 | − | 4.99630i | 0.739348 | − | 0.426863i | −0.0824839 | − | 0.996592i | \(-0.526285\pi\) |
0.821832 | + | 0.569729i | \(0.192952\pi\) | |||||||
\(138\) | −2.30836 | + | 1.33273i | −0.196501 | + | 0.113450i | ||||
\(139\) | 0.832100 | − | 1.44124i | 0.0705778 | − | 0.122244i | −0.828577 | − | 0.559875i | \(-0.810849\pi\) |
0.899155 | + | 0.437631i | \(0.144182\pi\) | |||||||
\(140\) | 18.3651 | + | 8.04427i | 1.55213 | + | 0.679865i | ||||
\(141\) | −0.473738 | + | 0.273513i | −0.0398959 | + | 0.0230339i | ||||
\(142\) | −1.74874 | − | 3.02891i | −0.146751 | − | 0.254180i | ||||
\(143\) | −7.35364 | − | 6.40642i | −0.614942 | − | 0.535732i | ||||
\(144\) | 11.8757 | − | 20.5692i | 0.989638 | − | 1.71410i | ||||
\(145\) | 7.50073 | + | 4.33055i | 0.622902 | + | 0.359633i | ||||
\(146\) | −11.7825 | − | 20.4078i | −0.975124 | − | 1.68897i | ||||
\(147\) | 3.54059 | − | 0.797334i | 0.292023 | − | 0.0657630i | ||||
\(148\) | 27.9863i | 2.30046i | ||||||||
\(149\) | 19.7980i | 1.62192i | 0.585103 | + | 0.810959i | \(0.301054\pi\) | ||||
−0.585103 | + | 0.810959i | \(0.698946\pi\) | |||||||
\(150\) | 2.79100 | − | 1.61138i | 0.227884 | − | 0.131569i | ||||
\(151\) | 6.52544 | + | 3.76746i | 0.531033 | + | 0.306592i | 0.741437 | − | 0.671023i | \(-0.234145\pi\) |
−0.210404 | + | 0.977614i | \(0.567478\pi\) | |||||||
\(152\) | 25.7390 | 2.08771 | ||||||||
\(153\) | −4.26968 | − | 7.39531i | −0.345183 | − | 0.597875i | ||||
\(154\) | −7.43286 | + | 16.9692i | −0.598957 | + | 1.36742i | ||||
\(155\) | −16.8912 | −1.35673 | ||||||||
\(156\) | 8.62429 | + | 1.68609i | 0.690496 | + | 0.134995i | ||||
\(157\) | −7.00223 | + | 12.1282i | −0.558839 | + | 0.967938i | 0.438755 | + | 0.898607i | \(0.355420\pi\) |
−0.997594 | + | 0.0693309i | \(0.977914\pi\) | |||||||
\(158\) | − | 16.0643i | − | 1.27801i | ||||||
\(159\) | −1.88350 | + | 3.26232i | −0.149371 | + | 0.258719i | ||||
\(160\) | 6.87414 | − | 11.9064i | 0.543448 | − | 0.941280i | ||||
\(161\) | 2.10823 | − | 4.81308i | 0.166152 | − | 0.379324i | ||||
\(162\) | −14.9146 | − | 8.61097i | −1.17181 | − | 0.676542i | ||||
\(163\) | 7.16995i | 0.561594i | 0.959767 | + | 0.280797i | \(0.0905987\pi\) | ||||
−0.959767 | + | 0.280797i | \(0.909401\pi\) | |||||||
\(164\) | −31.3533 | − | 18.1018i | −2.44828 | − | 1.41351i | ||||
\(165\) | −1.13039 | − | 1.95790i | −0.0880011 | − | 0.152422i | ||||
\(166\) | −3.49036 | + | 6.04548i | −0.270904 | + | 0.469220i | ||||
\(167\) | 15.5716 | − | 8.99027i | 1.20497 | − | 0.695688i | 0.243312 | − | 0.969948i | \(-0.421766\pi\) |
0.961656 | + | 0.274260i | \(0.0884328\pi\) | |||||||
\(168\) | −1.05998 | − | 9.53161i | −0.0817790 | − | 0.735380i | ||||
\(169\) | −1.78135 | − | 12.8774i | −0.137027 | − | 0.990567i | ||||
\(170\) | −6.52361 | − | 11.2992i | −0.500338 | − | 0.866611i | ||||
\(171\) | − | 10.0549i | − | 0.768917i | ||||||
\(172\) | −15.7761 | −1.20291 | ||||||||
\(173\) | 12.8116 | 0.974047 | 0.487023 | − | 0.873389i | \(-0.338083\pi\) | ||||
0.487023 | + | 0.873389i | \(0.338083\pi\) | |||||||
\(174\) | − | 7.21072i | − | 0.546643i | ||||||
\(175\) | −2.54902 | + | 5.81942i | −0.192688 | + | 0.439906i | ||||
\(176\) | 20.3717 | + | 11.7616i | 1.53557 | + | 0.886562i | ||||
\(177\) | −5.12945 | + | 2.96149i | −0.385553 | + | 0.222599i | ||||
\(178\) | −2.27781 | − | 3.94528i | −0.170729 | − | 0.295711i | ||||
\(179\) | −1.84022 | −0.137545 | −0.0687723 | − | 0.997632i | \(-0.521908\pi\) | ||||
−0.0687723 | + | 0.997632i | \(0.521908\pi\) | |||||||
\(180\) | −17.9242 | − | 10.3485i | −1.33599 | − | 0.771334i | ||||
\(181\) | −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 | ||||
\(183\) | −1.51655 | −0.112107 | ||||||||
\(184\) | −12.0250 | − | 6.94262i | −0.886493 | − | 0.511817i | ||||
\(185\) | 9.59730 | 0.705607 | ||||||||
\(186\) | 7.03129 | + | 12.1786i | 0.515560 | + | 0.892975i | ||||
\(187\) | 7.32427 | − | 4.22867i | 0.535604 | − | 0.309231i | ||||
\(188\) | −4.29531 | − | 2.47990i | −0.313268 | − | 0.180865i | ||||
\(189\) | −7.81349 | + | 0.868911i | −0.568348 | + | 0.0632040i | ||||
\(190\) | − | 15.3628i | − | 1.11453i | ||||||
\(191\) | 4.89614 | 0.354272 | 0.177136 | − | 0.984186i | \(-0.443317\pi\) | ||||
0.177136 | + | 0.984186i | \(0.443317\pi\) | |||||||
\(192\) | −2.42852 | −0.175264 | ||||||||
\(193\) | − | 3.01910i | − | 0.217320i | −0.994079 | − | 0.108660i | \(-0.965344\pi\) | ||
0.994079 | − | 0.108660i | \(-0.0346559\pi\) | |||||||
\(194\) | 20.0384 | + | 34.7075i | 1.43867 | + | 2.49186i | ||||
\(195\) | 0.578207 | − | 2.95751i | 0.0414063 | − | 0.211792i | ||||
\(196\) | 22.3118 | + | 24.1865i | 1.59370 | + | 1.72761i | ||||
\(197\) | 4.02694 | − | 2.32496i | 0.286908 | − | 0.165646i | −0.349639 | − | 0.936885i | \(-0.613696\pi\) |
0.636546 | + | 0.771238i | \(0.280362\pi\) | |||||||
\(198\) | 9.56198 | − | 16.5618i | 0.679540 | − | 1.17700i | ||||
\(199\) | 0.205360 | + | 0.355694i | 0.0145576 | + | 0.0252145i | 0.873212 | − | 0.487340i | \(-0.162033\pi\) |
−0.858655 | + | 0.512554i | \(0.828699\pi\) | |||||||
\(200\) | 14.5392 | + | 8.39420i | 1.02808 | + | 0.593560i | ||||
\(201\) | − | 7.04171i | − | 0.496684i | ||||||
\(202\) | −2.86793 | − | 1.65580i | −0.201787 | − | 0.116502i | ||||
\(203\) | 8.42450 | + | 11.4495i | 0.591284 | + | 0.803594i | ||||
\(204\) | −3.81013 | + | 6.59934i | −0.266763 | + | 0.462047i | ||||
\(205\) | −6.20762 | + | 10.7519i | −0.433559 | + | 0.750946i | ||||
\(206\) | 29.6844i | 2.06821i | ||||||||
\(207\) | −2.71213 | + | 4.69754i | −0.188506 | + | 0.326502i | ||||
\(208\) | 10.1761 | + | 29.6578i | 0.705583 | + | 2.05640i | ||||
\(209\) | 9.95831 | 0.688831 | ||||||||
\(210\) | −5.68912 | + | 0.632666i | −0.392586 | + | 0.0436581i | ||||
\(211\) | 3.75800 | + | 6.50905i | 0.258711 | + | 0.448101i | 0.965897 | − | 0.258927i | \(-0.0833688\pi\) |
−0.707186 | + | 0.707028i | \(0.750035\pi\) | |||||||
\(212\) | −34.1549 | −2.34577 | ||||||||
\(213\) | 0.606654 | + | 0.350252i | 0.0415672 | + | 0.0239989i | ||||
\(214\) | −11.5122 | + | 6.64656i | −0.786956 | + | 0.454349i | ||||
\(215\) | 5.41005i | 0.368962i | ||||||||
\(216\) | 20.7745i | 1.41353i | ||||||||
\(217\) | −25.3931 | − | 11.1227i | −1.72380 | − | 0.755059i | ||||
\(218\) | 2.23633 | + | 3.87344i | 0.151464 | + | 0.262343i | ||||
\(219\) | 4.08745 | + | 2.35989i | 0.276204 | + | 0.159467i | ||||
\(220\) | 10.2491 | − | 17.7520i | 0.690996 | − | 1.19684i | ||||
\(221\) | 11.0637 | + | 2.16300i | 0.744224 | + | 0.145499i | ||||
\(222\) | −3.99507 | − | 6.91967i | −0.268132 | − | 0.464418i | ||||
\(223\) | −19.5544 | + | 11.2897i | −1.30946 | + | 0.756016i | −0.982006 | − | 0.188852i | \(-0.939523\pi\) |
−0.327452 | + | 0.944868i | \(0.606190\pi\) | |||||||
\(224\) | 18.1744 | − | 13.3727i | 1.21433 | − | 0.893502i | ||||
\(225\) | 3.27918 | − | 5.67971i | 0.218612 | − | 0.378648i | ||||
\(226\) | −19.2595 | + | 11.1195i | −1.28113 | + | 0.739658i | ||||
\(227\) | 11.8401 | − | 6.83586i | 0.785853 | − | 0.453712i | −0.0526478 | − | 0.998613i | \(-0.516766\pi\) |
0.838500 | + | 0.544901i | \(0.183433\pi\) | |||||||
\(228\) | −7.77057 | + | 4.48634i | −0.514618 | + | 0.297115i | ||||
\(229\) | −6.86832 | + | 3.96543i | −0.453872 | + | 0.262043i | −0.709464 | − | 0.704742i | \(-0.751063\pi\) |
0.255592 | + | 0.966785i | \(0.417730\pi\) | |||||||
\(230\) | −4.14383 | + | 7.17733i | −0.273236 | + | 0.473259i | ||||
\(231\) | −0.410101 | − | 3.68774i | −0.0269827 | − | 0.242636i | ||||
\(232\) | 32.5305 | − | 18.7815i | 2.13573 | − | 1.23306i | ||||
\(233\) | −3.28585 | − | 5.69127i | −0.215263 | − | 0.372847i | 0.738091 | − | 0.674702i | \(-0.235728\pi\) |
−0.953354 | + | 0.301854i | \(0.902394\pi\) | |||||||
\(234\) | 24.1113 | − | 8.27298i | 1.57621 | − | 0.540822i | ||||
\(235\) | −0.850427 | + | 1.47298i | −0.0554757 | + | 0.0960868i | ||||
\(236\) | −46.5080 | − | 26.8514i | −3.02741 | − | 1.74788i | ||||
\(237\) | 1.60874 | + | 2.78642i | 0.104499 | + | 0.180998i | ||||
\(238\) | −2.36673 | − | 21.2823i | −0.153412 | − | 1.37953i | ||||
\(239\) | − | 9.39284i | − | 0.607572i | −0.952740 | − | 0.303786i | \(-0.901749\pi\) | ||
0.952740 | − | 0.303786i | \(-0.0982508\pi\) | |||||||
\(240\) | 7.26833i | 0.469169i | ||||||||
\(241\) | 8.73460 | − | 5.04292i | 0.562645 | − | 0.324843i | −0.191562 | − | 0.981481i | \(-0.561355\pi\) |
0.754206 | + | 0.656637i | \(0.228022\pi\) | |||||||
\(242\) | −8.25699 | − | 4.76718i | −0.530780 | − | 0.306446i | ||||
\(243\) | 12.3636 | 0.793128 | ||||||||
\(244\) | −6.87517 | − | 11.9081i | −0.440137 | − | 0.762340i | ||||
\(245\) | 8.29423 | − | 7.65133i | 0.529899 | − | 0.488826i | ||||
\(246\) | 10.3362 | 0.659012 | ||||||||
\(247\) | 10.0085 | + | 8.71928i | 0.636823 | + | 0.554794i | ||||
\(248\) | −36.6282 | + | 63.4420i | −2.32590 | + | 4.02857i | ||||
\(249\) | − | 1.39816i | − | 0.0886045i | ||||||
\(250\) | 15.4426 | − | 26.7474i | 0.976678 | − | 1.69166i | ||||
\(251\) | −5.17427 | + | 8.96209i | −0.326597 | + | 0.565682i | −0.981834 | − | 0.189741i | \(-0.939235\pi\) |
0.655237 | + | 0.755423i | \(0.272569\pi\) | |||||||
\(252\) | −20.1317 | − | 27.3603i | −1.26818 | − | 1.72354i | ||||
\(253\) | −4.65242 | − | 2.68607i | −0.292495 | − | 0.168872i | ||||
\(254\) | 8.08709i | 0.507429i | ||||||||
\(255\) | 2.26310 | + | 1.30660i | 0.141721 | + | 0.0818225i | ||||
\(256\) | 11.0672 | + | 19.1689i | 0.691697 | + | 1.19805i | ||||
\(257\) | 3.99329 | − | 6.91658i | 0.249095 | − | 0.431445i | −0.714180 | − | 0.699962i | \(-0.753200\pi\) |
0.963275 | + | 0.268517i | \(0.0865336\pi\) | |||||||
\(258\) | 3.90065 | − | 2.25204i | 0.242844 | − | 0.140206i | ||||
\(259\) | 14.4280 | + | 6.31975i | 0.896511 | + | 0.392690i | ||||
\(260\) | 25.8440 | − | 8.86749i | 1.60278 | − | 0.549939i | ||||
\(261\) | −7.33696 | − | 12.7080i | −0.454146 | − | 0.786604i | ||||
\(262\) | 26.4275i | 1.63270i | ||||||||
\(263\) | 5.05934 | 0.311972 | 0.155986 | − | 0.987759i | \(-0.450144\pi\) | ||||
0.155986 | + | 0.987759i | \(0.450144\pi\) | |||||||
\(264\) | −9.80498 | −0.603455 | ||||||||
\(265\) | 11.7127i | 0.719503i | ||||||||
\(266\) | 10.1163 | − | 23.0954i | 0.620269 | − | 1.41607i | ||||
\(267\) | 0.790192 | + | 0.456218i | 0.0483590 | + | 0.0279201i | ||||
\(268\) | 55.2924 | − | 31.9231i | 3.37752 | − | 1.95001i | ||||
\(269\) | −6.94512 | − | 12.0293i | −0.423451 | − | 0.733439i | 0.572823 | − | 0.819679i | \(-0.305848\pi\) |
−0.996274 | + | 0.0862400i | \(0.972515\pi\) | |||||||
\(270\) | 12.3997 | 0.754619 | ||||||||
\(271\) | −7.21158 | − | 4.16361i | −0.438072 | − | 0.252921i | 0.264707 | − | 0.964329i | \(-0.414725\pi\) |
−0.702780 | + | 0.711408i | \(0.748058\pi\) | |||||||
\(272\) | −27.1900 | −1.64863 | ||||||||
\(273\) | 2.81674 | − | 4.06539i | 0.170477 | − | 0.246049i | ||||
\(274\) | −25.8669 | −1.56267 | ||||||||
\(275\) | 5.62515 | + | 3.24768i | 0.339210 | + | 0.195843i | ||||
\(276\) | 4.84043 | 0.291360 | ||||||||
\(277\) | −11.6058 | − | 20.1018i | −0.697325 | − | 1.20780i | −0.969391 | − | 0.245523i | \(-0.921040\pi\) |
0.272066 | − | 0.962279i | \(-0.412293\pi\) | |||||||
\(278\) | −3.73080 | + | 2.15398i | −0.223758 | + | 0.129187i | ||||
\(279\) | 24.7835 | + | 14.3088i | 1.48375 | + | 0.856644i | ||||
\(280\) | −17.6724 | − | 24.0180i | −1.05613 | − | 1.43535i | ||||
\(281\) | − | 27.1595i | − | 1.62020i | −0.586292 | − | 0.810100i | \(-0.699413\pi\) | ||
0.586292 | − | 0.810100i | \(-0.300587\pi\) | |||||||
\(282\) | 1.41603 | 0.0843234 | ||||||||
\(283\) | 16.1513 | 0.960092 | 0.480046 | − | 0.877243i | \(-0.340620\pi\) | ||||
0.480046 | + | 0.877243i | \(0.340620\pi\) | |||||||
\(284\) | 6.35136i | 0.376884i | ||||||||
\(285\) | 1.53849 | + | 2.66474i | 0.0911323 | + | 0.157846i | ||||
\(286\) | 8.19351 | + | 23.8797i | 0.484493 | + | 1.41204i | ||||
\(287\) | −16.4122 | + | 12.0761i | −0.968782 | + | 0.712828i | ||||
\(288\) | −20.1721 | + | 11.6464i | −1.18865 | + | 0.686270i | ||||
\(289\) | 3.61216 | − | 6.25645i | 0.212480 | − | 0.368027i | ||||
\(290\) | −11.2101 | − | 19.4164i | −0.658278 | − | 1.14017i | ||||
\(291\) | −6.95151 | − | 4.01345i | −0.407504 | − | 0.235273i | ||||
\(292\) | 42.7935i | 2.50430i | ||||||||
\(293\) | −12.6831 | − | 7.32260i | −0.740956 | − | 0.427791i | 0.0814609 | − | 0.996677i | \(-0.474041\pi\) |
−0.822417 | + | 0.568885i | \(0.807375\pi\) | |||||||
\(294\) | −8.96927 | − | 2.79513i | −0.523098 | − | 0.163015i | ||||
\(295\) | −9.20810 | + | 15.9489i | −0.536116 | + | 0.928580i | ||||
\(296\) | 20.8116 | − | 36.0468i | 1.20965 | − | 2.09517i | ||||
\(297\) | 8.03758i | 0.466388i | ||||||||
\(298\) | 25.6246 | − | 44.3831i | 1.48439 | − | 2.57104i | ||||
\(299\) | −2.32398 | − | 6.77315i | −0.134399 | − | 0.391702i | ||||
\(300\) | −5.85248 | −0.337893 | ||||||||
\(301\) | −3.56248 | + | 8.13313i | −0.205338 | + | 0.468786i | ||||
\(302\) | −9.75246 | − | 16.8918i | −0.561191 | − | 0.972011i | ||||
\(303\) | 0.663274 | 0.0381041 | ||||||||
\(304\) | −27.7263 | − | 16.0078i | −1.59021 | − | 0.918108i | ||||
\(305\) | −4.08363 | + | 2.35769i | −0.233828 | + | 0.135001i | ||||
\(306\) | 22.1050i | 1.26366i | ||||||||
\(307\) | 8.97844i | 0.512427i | 0.966620 | + | 0.256213i | \(0.0824750\pi\) | ||||
−0.966620 | + | 0.256213i | \(0.917525\pi\) | |||||||
\(308\) | 27.0975 | − | 19.9383i | 1.54402 | − | 1.13609i | ||||
\(309\) | −2.97271 | − | 5.14889i | −0.169112 | − | 0.292910i | ||||
\(310\) | 37.8665 | + | 21.8622i | 2.15067 | + | 1.24169i | ||||
\(311\) | 6.09080 | − | 10.5496i | 0.345378 | − | 0.598212i | −0.640045 | − | 0.768338i | \(-0.721084\pi\) |
0.985422 | + | 0.170126i | \(0.0544175\pi\) | |||||||
\(312\) | −9.85436 | − | 8.58502i | −0.557893 | − | 0.486031i | ||||
\(313\) | −6.56198 | − | 11.3657i | −0.370905 | − | 0.642427i | 0.618800 | − | 0.785549i | \(-0.287619\pi\) |
−0.989705 | + | 0.143122i | \(0.954286\pi\) | |||||||
\(314\) | 31.3951 | − | 18.1260i | 1.77173 | − | 1.02291i | ||||
\(315\) | −9.38260 | + | 6.90371i | −0.528650 | + | 0.388980i | ||||
\(316\) | −14.5862 | + | 25.2641i | −0.820540 | + | 1.42122i | ||||
\(317\) | −14.4761 | + | 8.35775i | −0.813056 | + | 0.469418i | −0.848016 | − | 0.529971i | \(-0.822203\pi\) |
0.0349599 | + | 0.999389i | \(0.488870\pi\) | |||||||
\(318\) | 8.44485 | − | 4.87563i | 0.473564 | − | 0.273412i | ||||
\(319\) | 12.5859 | − | 7.26648i | 0.704675 | − | 0.406845i | ||||
\(320\) | −6.53932 | + | 3.77548i | −0.365559 | + | 0.211056i | ||||
\(321\) | 1.33123 | − | 2.30575i | 0.0743018 | − | 0.128695i | ||||
\(322\) | −10.9558 | + | 8.06126i | −0.610543 | + | 0.449236i | ||||
\(323\) | −9.96849 | + | 5.75531i | −0.554661 | + | 0.320234i | ||||
\(324\) | 15.6374 | + | 27.0847i | 0.868743 | + | 1.50471i | ||||
\(325\) | 2.80988 | + | 8.18930i | 0.155864 | + | 0.454261i | ||||
\(326\) | 9.28007 | − | 16.0736i | 0.513976 | − | 0.890232i | ||||
\(327\) | −0.775804 | − | 0.447911i | −0.0429021 | − | 0.0247695i | ||||
\(328\) | 26.9223 | + | 46.6307i | 1.48653 | + | 2.57475i | ||||
\(329\) | −2.24843 | + | 1.65439i | −0.123960 | + | 0.0912094i | ||||
\(330\) | 5.85228i | 0.322157i | ||||||||
\(331\) | − | 3.96665i | − | 0.218027i | −0.994040 | − | 0.109013i | \(-0.965231\pi\) | ||
0.994040 | − | 0.109013i | \(-0.0347691\pi\) | |||||||
\(332\) | 10.9785 | − | 6.33843i | 0.602523 | − | 0.347867i | ||||
\(333\) | −14.0816 | − | 8.13002i | −0.771668 | − | 0.445523i | ||||
\(334\) | −46.5445 | −2.54680 | ||||||||
\(335\) | −10.9473 | − | 18.9613i | −0.598116 | − | 1.03597i | ||||
\(336\) | −4.78615 | + | 10.9268i | −0.261106 | + | 0.596104i | ||||
\(337\) | −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 | ||||
\(339\) | 2.22710 | − | 3.85746i | 0.120960 | − | 0.209508i | ||||
\(340\) | 23.6935i | 1.28496i | ||||||||
\(341\) | −14.1713 | + | 24.5455i | −0.767420 | + | 1.32921i | ||||
\(342\) | −13.0141 | + | 22.5410i | −0.703720 | + | 1.21888i | ||||
\(343\) | 17.5074 | − | 6.04084i | 0.945309 | − | 0.326175i | ||||
\(344\) | 20.3197 | + | 11.7316i | 1.09557 | + | 0.632526i | ||||
\(345\) | − | 1.65992i | − | 0.0893671i | ||||||
\(346\) | −28.7209 | − | 16.5820i | −1.54405 | − | 0.891456i | ||||
\(347\) | 13.1989 | + | 22.8612i | 0.708556 | + | 1.22725i | 0.965393 | + | 0.260800i | \(0.0839863\pi\) |
−0.256837 | + | 0.966455i | \(0.582680\pi\) | |||||||
\(348\) | −6.54727 | + | 11.3402i | −0.350971 | + | 0.607899i | ||||
\(349\) | −4.23507 | + | 2.44512i | −0.226698 | + | 0.130884i | −0.609048 | − | 0.793133i | \(-0.708448\pi\) |
0.382350 | + | 0.924018i | \(0.375115\pi\) | |||||||
\(350\) | 13.2465 | − | 9.74673i | 0.708053 | − | 0.520984i | ||||
\(351\) | −7.03753 | + | 8.07806i | −0.375636 | + | 0.431175i | ||||
\(352\) | −11.5345 | − | 19.9784i | −0.614792 | − | 1.06485i | ||||
\(353\) | 13.5577i | 0.721605i | 0.932642 | + | 0.360802i | \(0.117497\pi\) | ||||
−0.932642 | + | 0.360802i | \(0.882503\pi\) | |||||||
\(354\) | 15.3322 | 0.814899 | ||||||||
\(355\) | 2.17806 | 0.115599 | ||||||||
\(356\) | 8.27291i | 0.438464i | ||||||||
\(357\) | 2.54181 | + | 3.45450i | 0.134527 | + | 0.182831i | ||||
\(358\) | 4.12540 | + | 2.38180i | 0.218034 | + | 0.125882i | ||||
\(359\) | −7.43541 | + | 4.29284i | −0.392426 | + | 0.226567i | −0.683211 | − | 0.730221i | \(-0.739417\pi\) |
0.290785 | + | 0.956789i | \(0.406084\pi\) | |||||||
\(360\) | 15.3910 | + | 26.6581i | 0.811179 | + | 1.40500i | ||||
\(361\) | 5.44653 | 0.286659 | ||||||||
\(362\) | 7.39632 | + | 4.27026i | 0.388742 | + | 0.224440i | ||||
\(363\) | 1.90962 | 0.100229 | ||||||||
\(364\) | 44.6914 | + | 3.68725i | 2.34247 | + | 0.193264i | ||||
\(365\) | 14.6751 | 0.768130 | ||||||||
\(366\) | 3.39979 | + | 1.96287i | 0.177710 | + | 0.102601i | ||||
\(367\) | −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 | ||||
\(369\) | 18.2162 | − | 10.5171i | 0.948299 | − | 0.547501i | ||||
\(370\) | −21.5152 | − | 12.4218i | −1.11852 | − | 0.645778i | ||||
\(371\) | −7.71270 | + | 17.6081i | −0.400424 | + | 0.914166i | ||||
\(372\) | − | 25.5374i | − | 1.32405i | ||||||
\(373\) | 13.9635 | 0.723002 | 0.361501 | − | 0.932372i | \(-0.382264\pi\) | ||||
0.361501 | + | 0.932372i | \(0.382264\pi\) | |||||||
\(374\) | −21.8927 | −1.13204 | ||||||||
\(375\) | 6.18595i | 0.319441i | ||||||||
\(376\) | 3.68828 | + | 6.38828i | 0.190208 | + | 0.329450i | ||||
\(377\) | 19.0117 | + | 3.71687i | 0.979150 | + | 0.191429i | ||||
\(378\) | 18.6409 | + | 8.16509i | 0.958783 | + | 0.419967i | ||||
\(379\) | −27.3454 | + | 15.7879i | −1.40464 | + | 0.810969i | −0.994864 | − | 0.101218i | \(-0.967726\pi\) |
−0.409775 | + | 0.912187i | \(0.634393\pi\) | |||||||
\(380\) | −13.9493 | + | 24.1608i | −0.715582 | + | 1.23943i | ||||
\(381\) | −0.809874 | − | 1.40274i | −0.0414911 | − | 0.0718647i | ||||
\(382\) | −10.9761 | − | 6.33707i | −0.561588 | − | 0.324233i | ||||
\(383\) | − | 31.9082i | − | 1.63043i | −0.579156 | − | 0.815217i | \(-0.696618\pi\) | ||
0.579156 | − | 0.815217i | \(-0.303382\pi\) | |||||||
\(384\) | −2.21435 | − | 1.27846i | −0.113001 | − | 0.0652410i | ||||
\(385\) | −6.83739 | − | 9.29247i | −0.348466 | − | 0.473588i | ||||
\(386\) | −3.90762 | + | 6.76820i | −0.198893 | + | 0.344492i | ||||
\(387\) | 4.58294 | − | 7.93788i | 0.232964 | − | 0.403505i | ||||
\(388\) | − | 72.7788i | − | 3.69478i | ||||||
\(389\) | −12.7075 | + | 22.0100i | −0.644296 | + | 1.11595i | 0.340168 | + | 0.940365i | \(0.389516\pi\) |
−0.984464 | + | 0.175589i | \(0.943817\pi\) | |||||||
\(390\) | −5.12413 | + | 5.88175i | −0.259470 | + | 0.297834i | ||||
\(391\) | 6.20956 | 0.314031 | ||||||||
\(392\) | −10.7519 | − | 47.7443i | −0.543054 | − | 2.41145i | ||||
\(393\) | −2.64656 | − | 4.58398i | −0.133501 | − | 0.231231i | ||||
\(394\) | −12.0368 | −0.606403 | ||||||||
\(395\) | 8.66376 | + | 5.00203i | 0.435921 | + | 0.251679i | ||||
\(396\) | −30.0760 | + | 17.3644i | −1.51138 | + | 0.872593i | ||||
\(397\) | − | 4.15897i | − | 0.208733i | −0.994539 | − | 0.104366i | \(-0.966719\pi\) | ||
0.994539 | − | 0.104366i | \(-0.0332815\pi\) | |||||||
\(398\) | − | 1.06319i | − | 0.0532930i | ||||||
\(399\) | 0.558156 | + | 5.01910i | 0.0279427 | + | 0.251269i | ||||
\(400\) | −10.4412 | − | 18.0846i | −0.522058 | − | 0.904231i | ||||
\(401\) | −16.9753 | − | 9.80067i | −0.847704 | − | 0.489422i | 0.0121716 | − | 0.999926i | \(-0.496126\pi\) |
−0.859875 | + | 0.510504i | \(0.829459\pi\) | |||||||
\(402\) | −9.11409 | + | 15.7861i | −0.454569 | + | 0.787337i | ||||
\(403\) | −35.7342 | + | 12.2610i | −1.78005 | + | 0.610762i | ||||
\(404\) | 3.00691 | + | 5.20811i | 0.149599 | + | 0.259113i | ||||
\(405\) | 9.28811 | − | 5.36249i | 0.461530 | − | 0.266464i | ||||
\(406\) | −4.06695 | − | 36.5711i | −0.201839 | − | 1.81500i | ||||
\(407\) | 8.05193 | − | 13.9463i | 0.399119 | − | 0.691295i | ||||
\(408\) | 9.81500 | − | 5.66669i | 0.485915 | − | 0.280543i | ||||
\(409\) | −15.2712 | + | 8.81685i | −0.755114 | + | 0.435965i | −0.827539 | − | 0.561409i | \(-0.810260\pi\) |
0.0724249 | + | 0.997374i | \(0.476926\pi\) | |||||||
\(410\) | 27.8324 | − | 16.0690i | 1.37454 | − | 0.793594i | ||||
\(411\) | 4.48673 | − | 2.59041i | 0.221314 | − | 0.127776i | ||||
\(412\) | 26.9532 | − | 46.6842i | 1.32789 | − | 2.29997i | ||||
\(413\) | −24.3451 | + | 17.9131i | −1.19794 | + | 0.881446i | ||||
\(414\) | 12.1601 | − | 7.02061i | 0.597634 | − | 0.345044i | ||||
\(415\) | −2.17363 | − | 3.76483i | −0.106699 | − | 0.184808i | ||||
\(416\) | 5.90001 | − | 30.1783i | 0.289272 | − | 1.47962i | ||||
\(417\) | 0.431416 | − | 0.747234i | 0.0211265 | − | 0.0365922i | ||||
\(418\) | −22.3245 | − | 12.8890i | −1.09193 | − | 0.630424i | ||||
\(419\) | −14.9455 | − | 25.8864i | −0.730137 | − | 1.26463i | −0.956824 | − | 0.290666i | \(-0.906123\pi\) |
0.226688 | − | 0.973968i | \(-0.427210\pi\) | |||||||
\(420\) | 9.52165 | + | 4.17068i | 0.464609 | + | 0.203508i | ||||
\(421\) | − | 12.8528i | − | 0.626407i | −0.949686 | − | 0.313203i | \(-0.898598\pi\) | ||
0.949686 | − | 0.313203i | \(-0.101402\pi\) | |||||||
\(422\) | − | 19.4559i | − | 0.947100i | ||||||
\(423\) | 2.49557 | − | 1.44082i | 0.121339 | − | 0.0700551i | ||||
\(424\) | 43.9919 | + | 25.3987i | 2.13644 | + | 1.23347i | ||||
\(425\) | −7.50787 | −0.364185 | ||||||||
\(426\) | −0.906662 | − | 1.57038i | −0.0439279 | − | 0.0760854i | ||||
\(427\) | −7.69160 | + | 0.855355i | −0.372223 | + | 0.0413936i | ||||
\(428\) | 24.1401 | 1.16685 | ||||||||
\(429\) | −3.81261 | − | 3.32151i | −0.184075 | − | 0.160364i | ||||
\(430\) | 7.00223 | − | 12.1282i | 0.337677 | − | 0.584874i | ||||
\(431\) | − | 8.97060i | − | 0.432098i | −0.976382 | − | 0.216049i | \(-0.930683\pi\) | ||
0.976382 | − | 0.216049i | \(-0.0693172\pi\) | |||||||
\(432\) | 12.9202 | − | 22.3785i | 0.621625 | − | 1.07669i | ||||
\(433\) | −1.72531 | + | 2.98833i | −0.0829132 | + | 0.143610i | −0.904500 | − | 0.426473i | \(-0.859756\pi\) |
0.821587 | + | 0.570083i | \(0.193089\pi\) | |||||||
\(434\) | 42.5300 | + | 57.8012i | 2.04151 | + | 2.77454i | ||||
\(435\) | 3.88887 | + | 2.24524i | 0.186457 | + | 0.107651i | ||||
\(436\) | − | 8.12228i | − | 0.388987i | ||||||
\(437\) | 6.33204 | + | 3.65580i | 0.302902 | + | 0.174881i | ||||
\(438\) | −6.10881 | − | 10.5808i | −0.291890 | − | 0.505569i | ||||
\(439\) | −19.2572 | + | 33.3544i | −0.919096 | + | 1.59192i | −0.118304 | + | 0.992977i | \(0.537746\pi\) |
−0.800792 | + | 0.598943i | \(0.795588\pi\) | |||||||
\(440\) | −26.4020 | + | 15.2432i | −1.25867 | + | 0.726691i | ||||
\(441\) | −18.6513 | + | 4.20023i | −0.888155 | + | 0.200011i | ||||
\(442\) | −22.0029 | − | 19.1687i | −1.04657 | − | 0.911764i | ||||
\(443\) | 7.51997 | + | 13.0250i | 0.357284 | + | 0.618835i | 0.987506 | − | 0.157580i | \(-0.0503693\pi\) |
−0.630222 | + | 0.776415i | \(0.717036\pi\) | |||||||
\(444\) | 14.5100i | 0.688612i | ||||||||
\(445\) | 2.83701 | 0.134487 | ||||||||
\(446\) | 58.4492 | 2.76765 | ||||||||
\(447\) | 10.2646i | 0.485499i | ||||||||
\(448\) | −12.3169 | + | 1.36972i | −0.581920 | + | 0.0647133i | ||||
\(449\) | 33.7087 | + | 19.4617i | 1.59081 | + | 0.918456i | 0.993168 | + | 0.116696i | \(0.0372304\pi\) |
0.597646 | + | 0.801760i | \(0.296103\pi\) | |||||||
\(450\) | −14.7025 | + | 8.48850i | −0.693083 | + | 0.400152i | ||||
\(451\) | 10.4161 | + | 18.0412i | 0.490476 | + | 0.849529i | ||||
\(452\) | 40.3856 | 1.89958 | ||||||||
\(453\) | 3.38322 | + | 1.95330i | 0.158957 | + | 0.0917741i | ||||
\(454\) | −35.3906 | −1.66097 | ||||||||
\(455\) | 1.26446 | − | 15.3259i | 0.0592788 | − | 0.718491i | ||||
\(456\) | 13.3448 | 0.624927 | ||||||||
\(457\) | −12.0721 | − | 6.96982i | −0.564708 | − | 0.326034i | 0.190325 | − | 0.981721i | \(-0.439046\pi\) |
−0.755033 | + | 0.655687i | \(0.772379\pi\) | |||||||
\(458\) | 20.5298 | 0.959295 | ||||||||
\(459\) | −4.64524 | − | 8.04580i | −0.216821 | − | 0.375546i | ||||
\(460\) | 13.0339 | − | 7.52512i | 0.607709 | − | 0.350861i | ||||
\(461\) | 32.4443 | + | 18.7317i | 1.51108 | + | 0.872424i | 0.999916 | + | 0.0129430i | \(0.00412001\pi\) |
0.511167 | + | 0.859481i | \(0.329213\pi\) | |||||||
\(462\) | −3.85368 | + | 8.79795i | −0.179290 | + | 0.409318i | ||||
\(463\) | 6.75275i | 0.313827i | 0.987612 | + | 0.156913i | \(0.0501544\pi\) | ||||
−0.987612 | + | 0.156913i | \(0.949846\pi\) | |||||||
\(464\) | −46.7228 | −2.16905 | ||||||||
\(465\) | −8.75749 | −0.406119 | ||||||||
\(466\) | 17.0115i | 0.788044i | ||||||||
\(467\) | 2.52516 | + | 4.37371i | 0.116851 | + | 0.202391i | 0.918518 | − | 0.395379i | \(-0.129387\pi\) |
−0.801667 | + | 0.597770i | \(0.796053\pi\) | |||||||
\(468\) | −45.4314 | − | 8.88205i | −2.10006 | − | 0.410573i | ||||
\(469\) | −3.97162 | − | 35.7140i | −0.183393 | − | 1.64912i | ||||
\(470\) | 3.81296 | − | 2.20141i | 0.175879 | − | 0.101544i | ||||
\(471\) | −3.63042 | + | 6.28807i | −0.167281 | + | 0.289739i | ||||
\(472\) | 39.9353 | + | 69.1699i | 1.83817 | + | 3.18380i | ||||
\(473\) | 7.86163 | + | 4.53892i | 0.361478 | + | 0.208700i | ||||
\(474\) | − | 8.32878i | − | 0.382554i | ||||||
\(475\) | −7.65595 | − | 4.42017i | −0.351279 | − | 0.202811i | ||||
\(476\) | −15.6020 | + | 35.6194i | −0.715117 | + | 1.63261i | ||||
\(477\) | 9.92198 | − | 17.1854i | 0.454296 | − | 0.786864i | ||||
\(478\) | −12.1572 | + | 21.0568i | −0.556055 | + | 0.963116i | ||||
\(479\) | − | 9.45319i | − | 0.431927i | −0.976401 | − | 0.215964i | \(-0.930711\pi\) | ||
0.976401 | − | 0.215964i | \(-0.0692892\pi\) | |||||||
\(480\) | 3.56401 | − | 6.17304i | 0.162674 | − | 0.281759i | ||||
\(481\) | 20.3036 | − | 6.96649i | 0.925764 | − | 0.317645i | ||||
\(482\) | −26.1082 | −1.18920 | ||||||||
\(483\) | 1.09305 | − | 2.49542i | 0.0497353 | − | 0.113546i | ||||
\(484\) | 8.65711 | + | 14.9946i | 0.393505 | + | 0.681571i | ||||
\(485\) | −24.9579 | −1.13328 | ||||||||
\(486\) | −27.7167 | − | 16.0023i | −1.25726 | − | 0.725877i | ||||
\(487\) | 34.6407 | − | 19.9998i | 1.56972 | − | 0.906277i | 0.573517 | − | 0.819194i | \(-0.305579\pi\) |
0.996201 | − | 0.0870831i | \(-0.0277546\pi\) | |||||||
\(488\) | 20.4504i | 0.925748i | ||||||||
\(489\) | 3.71737i | 0.168105i | ||||||||
\(490\) | −28.4971 | + | 6.41748i | −1.28737 | + | 0.289912i | ||||
\(491\) | −3.38049 | − | 5.85517i | −0.152559 | − | 0.264240i | 0.779608 | − | 0.626267i | \(-0.215418\pi\) |
−0.932168 | + | 0.362027i | \(0.882085\pi\) | |||||||
\(492\) | −16.2556 | − | 9.38518i | −0.732859 | − | 0.423116i | ||||
\(493\) | −8.39918 | + | 14.5478i | −0.378280 | + | 0.655200i | ||||
\(494\) | −11.1515 | − | 32.5008i | −0.501732 | − | 1.46228i | ||||
\(495\) | 5.95473 | + | 10.3139i | 0.267645 | + | 0.463575i | ||||
\(496\) | 78.9125 | − | 45.5602i | 3.54328 | − | 2.04571i | ||||
\(497\) | 3.27436 | + | 1.43424i | 0.146875 | + | 0.0643343i | ||||
\(498\) | −1.80963 | + | 3.13438i | −0.0810916 | + | 0.140455i | ||||
\(499\) | 9.83591 | − | 5.67877i | 0.440316 | − | 0.254217i | −0.263416 | − | 0.964682i | \(-0.584849\pi\) |
0.703732 | + | 0.710466i | \(0.251516\pi\) | |||||||
\(500\) | −48.5729 | + | 28.0436i | −2.17225 | + | 1.25415i | ||||
\(501\) | 8.07335 | − | 4.66115i | 0.360691 | − | 0.208245i | ||||
\(502\) | 23.1993 | − | 13.3941i | 1.03543 | − | 0.597808i | ||||
\(503\) | 6.96423 | − | 12.0624i | 0.310520 | − | 0.537836i | −0.667955 | − | 0.744202i | \(-0.732830\pi\) |
0.978475 | + | 0.206365i | \(0.0661635\pi\) | |||||||
\(504\) | 5.58378 | + | 50.2110i | 0.248721 | + | 2.23657i | ||||
\(505\) | 1.78601 | − | 1.03115i | 0.0794763 | − | 0.0458857i | ||||
\(506\) | 6.95317 | + | 12.0432i | 0.309106 | + | 0.535388i | ||||
\(507\) | −0.923570 | − | 6.67648i | −0.0410172 | − | 0.296513i | ||||
\(508\) | 7.34301 | − | 12.7185i | 0.325793 | − | 0.564290i | ||||
\(509\) | 17.1602 | + | 9.90746i | 0.760614 | + | 0.439141i | 0.829516 | − | 0.558483i | \(-0.188616\pi\) |
−0.0689022 | + | 0.997623i | \(0.521950\pi\) | |||||||
\(510\) | −3.38227 | − | 5.85826i | −0.149769 | − | 0.259408i | ||||
\(511\) | 22.0616 | + | 9.66345i | 0.975949 | + | 0.427486i | ||||
\(512\) | − | 47.4335i | − | 2.09628i | ||||||
\(513\) | − | 10.9393i | − | 0.482983i | ||||||
\(514\) | −17.9043 | + | 10.3370i | −0.789724 | + | 0.455947i | ||||
\(515\) | −16.0093 | − | 9.24299i | −0.705455 | − | 0.407295i | ||||
\(516\) | −8.17934 | −0.360076 | ||||||||
\(517\) | 1.42698 | + | 2.47160i | 0.0627585 | + | 0.108701i | ||||
\(518\) | −24.1649 | − | 32.8417i | −1.06174 | − | 1.44298i | ||||
\(519\) | 6.64237 | 0.291568 | ||||||||
\(520\) | −39.8816 | − | 7.79704i | −1.74892 | − | 0.341923i | ||||
\(521\) | 15.5476 | − | 26.9292i | 0.681151 | − | 1.17979i | −0.293479 | − | 0.955966i | \(-0.594813\pi\) |
0.974630 | − | 0.223823i | \(-0.0718537\pi\) | |||||||
\(522\) | 37.9849i | 1.66255i | ||||||||
\(523\) | −11.3601 | + | 19.6763i | −0.496742 | + | 0.860383i | −0.999993 | − | 0.00375758i | \(-0.998804\pi\) |
0.503251 | + | 0.864140i | \(0.332137\pi\) | |||||||
\(524\) | 23.9960 | − | 41.5622i | 1.04827 | − | 1.81565i | ||||
\(525\) | −1.32158 | + | 3.01717i | −0.0576786 | + | 0.131680i | ||||
\(526\) | −11.3420 | − | 6.54831i | −0.494535 | − | 0.285520i | ||||
\(527\) | − | 32.7607i | − | 1.42708i | ||||||
\(528\) | 10.5620 | + | 6.09798i | 0.459652 | + | 0.265380i | ||||
\(529\) | 9.52783 | + | 16.5027i | 0.414253 | + | 0.717508i | ||||
\(530\) | 15.1597 | − | 26.2574i | 0.658495 | − | 1.14055i | ||||
\(531\) | 27.0211 | − | 15.6007i | 1.17262 | − | 0.677011i | ||||
\(532\) | −36.8802 | + | 27.1364i | −1.59896 | + | 1.17651i | ||||
\(533\) | −5.32794 | + | 27.2522i | −0.230779 | + | 1.18043i | ||||
\(534\) | −1.18097 | − | 2.04549i | −0.0511054 | − | 0.0885171i | ||||
\(535\) | − | 8.27830i | − | 0.357902i | ||||||
\(536\) | −94.9564 | −4.10149 | ||||||||
\(537\) | −0.954091 | −0.0411721 | ||||||||
\(538\) | 35.9563i | 1.55018i | ||||||||
\(539\) | −4.15988 | − | 18.4721i | −0.179179 | − | 0.795649i | ||||
\(540\) | −19.5008 | − | 11.2588i | −0.839180 | − | 0.484501i | ||||
\(541\) | −1.81754 | + | 1.04936i | −0.0781423 | + | 0.0451155i | −0.538562 | − | 0.842586i | \(-0.681032\pi\) |
0.460420 | + | 0.887701i | \(0.347699\pi\) | |||||||
\(542\) | 10.7779 | + | 18.6679i | 0.462951 | + | 0.801855i | ||||
\(543\) | −1.71057 | −0.0734074 | ||||||||
\(544\) | 23.0926 | + | 13.3325i | 0.990087 | + | 0.571627i | ||||
\(545\) | −2.78536 | −0.119312 | ||||||||
\(546\) | −11.5764 | + | 5.46806i | −0.495424 | + | 0.234011i | ||||
\(547\) | 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 | ||||
\(549\) | 7.98894 | 0.340959 | ||||||||
\(550\) | −8.40696 | − | 14.5613i | −0.358474 | − | 0.620895i | ||||
\(551\) | −17.1297 | + | 9.88983i | −0.729749 | + | 0.421321i | ||||
\(552\) | −6.23454 | − | 3.59951i | −0.265360 | − | 0.153205i | ||||
\(553\) | 9.73076 | + | 13.2248i | 0.413794 | + | 0.562374i | ||||
\(554\) | 60.0855i | 2.55279i | ||||||||
\(555\) | 4.97587 | 0.211214 | ||||||||
\(556\) | 7.82316 | 0.331776 | ||||||||
\(557\) | 44.2503i | 1.87495i | 0.348058 | + | 0.937473i | \(0.386841\pi\) | ||||
−0.348058 | + | 0.937473i | \(0.613159\pi\) | |||||||
\(558\) | −37.0397 | − | 64.1547i | −1.56802 | − | 2.71588i | ||||
\(559\) | 3.92705 | + | 11.4452i | 0.166097 | + | 0.484082i | ||||
\(560\) | 4.09944 | + | 36.8634i | 0.173233 | + | 1.55776i | ||||
\(561\) | 3.79738 | − | 2.19242i | 0.160326 | − | 0.0925641i | ||||
\(562\) | −35.1526 | + | 60.8860i | −1.48282 | + | 2.56832i | ||||
\(563\) | −19.4453 | − | 33.6803i | −0.819523 | − | 1.41946i | −0.906034 | − | 0.423205i | \(-0.860905\pi\) |
0.0865108 | − | 0.996251i | \(-0.472428\pi\) | |||||||
\(564\) | −2.22697 | − | 1.28574i | −0.0937725 | − | 0.0541396i | ||||
\(565\) | − | 13.8494i | − | 0.582647i | ||||||
\(566\) | −36.2078 | − | 20.9046i | −1.52193 | − | 0.878685i | ||||
\(567\) | 17.4943 | − | 1.94548i | 0.734693 | − | 0.0817026i | ||||
\(568\) | 4.72309 | − | 8.18063i | 0.198177 | − | 0.343252i | ||||
\(569\) | 23.0789 | − | 39.9739i | 0.967520 | − | 1.67579i | 0.264832 | − | 0.964294i | \(-0.414683\pi\) |
0.702687 | − | 0.711499i | \(-0.251983\pi\) | |||||||
\(570\) | − | 7.96508i | − | 0.333620i | ||||||
\(571\) | 10.5684 | − | 18.3050i | 0.442274 | − | 0.766041i | −0.555584 | − | 0.831461i | \(-0.687505\pi\) |
0.997858 | + | 0.0654194i | \(0.0208385\pi\) | |||||||
\(572\) | 8.79673 | − | 44.9949i | 0.367810 | − | 1.88133i | ||||
\(573\) | 2.53848 | 0.106047 | ||||||||
\(574\) | 52.4229 | − | 5.82976i | 2.18809 | − | 0.243329i | ||||
\(575\) | 2.38452 | + | 4.13011i | 0.0994413 | + | 0.172237i | ||||
\(576\) | 12.7931 | 0.533045 | ||||||||
\(577\) | −21.9368 | − | 12.6652i | −0.913239 | − | 0.527259i | −0.0317671 | − | 0.999495i | \(-0.510113\pi\) |
−0.881472 | + | 0.472237i | \(0.843447\pi\) | |||||||
\(578\) | −16.1955 | + | 9.35045i | −0.673642 | + | 0.388927i | ||||
\(579\) | − | 1.56530i | − | 0.0650517i | ||||||
\(580\) | 40.7146i | 1.69058i | ||||||||
\(581\) | −0.788579 | − | 7.09113i | −0.0327158 | − | 0.294190i | ||||
\(582\) | 10.3892 | + | 17.9947i | 0.430647 | + | 0.745903i | ||||
\(583\) | 17.0203 | + | 9.82667i | 0.704908 | + | 0.406979i | ||||
\(584\) | 31.8227 | − | 55.1186i | 1.31683 | − | 2.28082i | ||||
\(585\) | −3.04590 | + | 15.5797i | −0.125933 | + | 0.644140i | ||||
\(586\) | 18.9553 | + | 32.8315i | 0.783036 | + | 1.35626i | ||||
\(587\) | 3.08554 | − | 1.78144i | 0.127354 | − | 0.0735278i | −0.434970 | − | 0.900445i | \(-0.643241\pi\) |
0.562324 | + | 0.826917i | \(0.309908\pi\) | |||||||
\(588\) | 11.5679 | + | 12.5399i | 0.477052 | + | 0.517136i | ||||
\(589\) | 19.2875 | − | 33.4069i | 0.794727 | − | 1.37651i | ||||
\(590\) | 41.2853 | − | 23.8361i | 1.69969 | − | 0.981316i | ||||
\(591\) | 2.08783 | − | 1.20541i | 0.0858819 | − | 0.0495839i | ||||
\(592\) | −44.8369 | + | 25.8866i | −1.84278 | + | 1.06393i | ||||
\(593\) | −21.9568 | + | 12.6768i | −0.901659 | + | 0.520573i | −0.877738 | − | 0.479141i | \(-0.840948\pi\) |
−0.0239212 | + | 0.999714i | \(0.507615\pi\) | |||||||
\(594\) | 10.4030 | − | 18.0186i | 0.426842 | − | 0.739312i | ||||
\(595\) | 12.2149 | + | 5.35037i | 0.500761 | + | 0.219344i | ||||
\(596\) | −80.5990 | + | 46.5338i | −3.30146 | + | 1.90610i | ||||
\(597\) | 0.106472 | + | 0.184415i | 0.00435762 | + | 0.00754762i | ||||
\(598\) | −3.55661 | + | 18.1919i | −0.145441 | + | 0.743924i | ||||
\(599\) | −5.46078 | + | 9.45835i | −0.223122 | + | 0.386458i | −0.955754 | − | 0.294166i | \(-0.904958\pi\) |
0.732633 | + | 0.680624i | \(0.238291\pi\) | |||||||
\(600\) | 7.53807 | + | 4.35211i | 0.307740 | + | 0.177674i | ||||
\(601\) | −12.1282 | − | 21.0067i | −0.494720 | − | 0.856880i | 0.505262 | − | 0.862966i | \(-0.331396\pi\) |
−0.999981 | + | 0.00608649i | \(0.998063\pi\) | |||||||
\(602\) | 18.5131 | − | 13.6219i | 0.754536 | − | 0.555187i | ||||
\(603\) | 37.0946i | 1.51061i | ||||||||
\(604\) | 35.4206i | 1.44124i | ||||||||
\(605\) | 5.14205 | − | 2.96876i | 0.209054 | − | 0.120697i | ||||
\(606\) | −1.48692 | − | 0.858476i | −0.0604022 | − | 0.0348732i | ||||
\(607\) | −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 | ||||
\(609\) | 4.36781 | + | 5.93615i | 0.176993 | + | 0.240545i | ||||
\(610\) | 12.2062 | 0.494215 | ||||||||
\(611\) | −0.729914 | + | 3.73348i | −0.0295291 | + | 0.151040i | ||||
\(612\) | 20.0712 | − | 34.7643i | 0.811328 | − | 1.40526i | ||||
\(613\) | 3.67688i | 0.148508i | 0.997239 | + | 0.0742540i | \(0.0236575\pi\) | ||||
−0.997239 | + | 0.0742540i | \(0.976342\pi\) | |||||||
\(614\) | 11.6208 | − | 20.1278i | 0.468977 | − | 0.812293i | ||||
\(615\) | −3.21844 | + | 5.57450i | −0.129780 | + | 0.224785i | ||||
\(616\) | −49.7286 | + | 5.53015i | −2.00362 | + | 0.222816i | ||||
\(617\) | 16.2352 | + | 9.37341i | 0.653605 | + | 0.377359i | 0.789836 | − | 0.613318i | \(-0.210166\pi\) |
−0.136231 | + | 0.990677i | \(0.543499\pi\) | |||||||
\(618\) | 15.3903i | 0.619090i | ||||||||
\(619\) | −13.7650 | − | 7.94725i | −0.553264 | − | 0.319427i | 0.197174 | − | 0.980369i | \(-0.436824\pi\) |
−0.750437 | + | 0.660942i | \(0.770157\pi\) | |||||||
\(620\) | −39.7014 | − | 68.7649i | −1.59445 | − | 2.76167i | ||||
\(621\) | −2.95068 | + | 5.11073i | −0.118407 | + | 0.205087i | ||||
\(622\) | −27.3086 | + | 15.7667i | −1.09498 | + | 0.632185i | ||||
\(623\) | 4.26499 | + | 1.86815i | 0.170873 | + | 0.0748460i | ||||
\(624\) | 5.27594 | + | 15.3765i | 0.211207 | + | 0.615555i | ||||
\(625\) | 3.61371 | + | 6.25913i | 0.144549 | + | 0.250365i | ||||
\(626\) | 33.9727i | 1.35782i | ||||||||
\(627\) | 5.16304 | 0.206192 | ||||||||
\(628\) | −65.8330 | −2.62702 | ||||||||
\(629\) | 18.6141i | 0.742194i | ||||||||
\(630\) | 29.9693 | − | 3.33278i | 1.19401 | − | 0.132781i | ||||
\(631\) | −17.0998 | − | 9.87255i | −0.680731 | − | 0.393020i | 0.119400 | − | 0.992846i | \(-0.461903\pi\) |
−0.800130 | + | 0.599826i | \(0.795236\pi\) | |||||||
\(632\) | 37.5745 | − | 21.6936i | 1.49463 | − | 0.862927i | ||||
\(633\) | 1.94839 | + | 3.37472i | 0.0774417 | + | 0.134133i | ||||
\(634\) | 43.2698 | 1.71846 | ||||||||
\(635\) | −4.36151 | − | 2.51812i | −0.173081 | − | 0.0999286i | ||||
\(636\) | −17.7081 | −0.702173 | ||||||||
\(637\) | 11.9929 | − | 22.2074i | 0.475177 | − | 0.879890i | ||||
\(638\) | −37.6200 | −1.48939 | ||||||||
\(639\) | −3.19575 | − | 1.84507i | −0.126422 | − | 0.0729898i | ||||
\(640\) | −7.95016 | −0.314258 | ||||||||
\(641\) | −14.8893 | − | 25.7890i | −0.588092 | − | 1.01860i | −0.994482 | − | 0.104905i | \(-0.966546\pi\) |
0.406390 | − | 0.913699i | \(-0.366787\pi\) | |||||||
\(642\) | −5.96867 | + | 3.44601i | −0.235565 | + | 0.136003i | ||||
\(643\) | 10.0220 | + | 5.78623i | 0.395231 | + | 0.228187i | 0.684424 | − | 0.729084i | \(-0.260054\pi\) |
−0.289193 | + | 0.957271i | \(0.593387\pi\) | |||||||
\(644\) | 24.5496 | − | 2.73007i | 0.967389 | − | 0.107580i | ||||
\(645\) | 2.80493i | 0.110444i | ||||||||
\(646\) | 29.7964 | 1.17232 | ||||||||
\(647\) | −25.5065 | −1.00276 | −0.501382 | − | 0.865226i | \(-0.667175\pi\) | ||||
−0.501382 | + | 0.865226i | \(0.667175\pi\) | |||||||
\(648\) | − | 46.5140i | − | 1.82724i | ||||||
\(649\) | 15.4508 | + | 26.7616i | 0.606497 | + | 1.05048i | ||||
\(650\) | 4.30024 | − | 21.9956i | 0.168669 | − | 0.862737i | ||||
\(651\) | −13.1655 | − | 5.76675i | −0.515995 | − | 0.226017i | ||||
\(652\) | −29.1893 | + | 16.8524i | −1.14314 | + | 0.659993i | ||||
\(653\) | 22.4146 | − | 38.8233i | 0.877152 | − | 1.51927i | 0.0227004 | − | 0.999742i | \(-0.492774\pi\) |
0.854452 | − | 0.519530i | \(-0.173893\pi\) | |||||||
\(654\) | 1.15946 | + | 2.00825i | 0.0453386 | + | 0.0785287i | ||||
\(655\) | −14.2529 | − | 8.22889i | −0.556905 | − | 0.321529i | ||||
\(656\) | − | 66.9747i | − | 2.61492i | ||||||
\(657\) | −21.5320 | − | 12.4315i | −0.840043 | − | 0.484999i | ||||
\(658\) | 7.18179 | − | 0.798661i | 0.279975 | − | 0.0311350i | ||||
\(659\) | −20.5867 | + | 35.6572i | −0.801944 | + | 1.38901i | 0.116390 | + | 0.993204i | \(0.462868\pi\) |
−0.918335 | + | 0.395805i | \(0.870466\pi\) | |||||||
\(660\) | 5.31382 | − | 9.20380i | 0.206840 | − | 0.358258i | ||||
\(661\) | 21.8938i | 0.851569i | 0.904825 | + | 0.425785i | \(0.140002\pi\) | ||||
−0.904825 | + | 0.425785i | \(0.859998\pi\) | |||||||
\(662\) | −5.13404 | + | 8.89241i | −0.199540 | + | 0.345613i | ||||
\(663\) | 5.73614 | + | 1.12144i | 0.222773 | + | 0.0435533i | ||||
\(664\) | −18.8539 | −0.731673 | ||||||||
\(665\) | 9.30583 | + | 12.6473i | 0.360865 | + | 0.490439i | ||||
\(666\) | 21.0454 | + | 36.4517i | 0.815492 | + | 1.41247i | ||||
\(667\) | 10.6704 | 0.413160 | ||||||||
\(668\) | 73.1999 | + | 42.2620i | 2.83219 | + | 1.63516i | ||||
\(669\) | −10.1383 | + | 5.85334i | −0.391968 | + | 0.226303i | ||||
\(670\) | 56.6764i | 2.18960i | ||||||||
\(671\) | 7.91219i | 0.305447i | ||||||||
\(672\) | 9.42281 | − | 6.93329i | 0.363493 | − | 0.267458i | ||||
\(673\) | 17.8344 | + | 30.8901i | 0.687466 | + | 1.19073i | 0.972655 | + | 0.232254i | \(0.0746102\pi\) |
−0.285189 | + | 0.958471i | \(0.592056\pi\) | |||||||
\(674\) | 30.7197 | + | 17.7361i | 1.18328 | + | 0.683167i | ||||
\(675\) | 3.56762 | − | 6.17930i | 0.137318 | − | 0.237841i | ||||
\(676\) | 48.2376 | − | 37.5193i | 1.85529 | − | 1.44305i | ||||
\(677\) | −1.27766 | − | 2.21297i | −0.0491044 | − | 0.0850514i | 0.840428 | − | 0.541923i | \(-0.182303\pi\) |
−0.889533 | + | 0.456871i | \(0.848970\pi\) | |||||||
\(678\) | −9.98541 | + | 5.76508i | −0.383488 | + | 0.221407i | ||||
\(679\) | −37.5201 | − | 16.4346i | −1.43989 | − | 0.630701i | ||||
\(680\) | 17.6193 | − | 30.5175i | 0.675670 | − | 1.17029i | ||||
\(681\) | 6.13867 | − | 3.54416i | 0.235234 | − | 0.135813i | ||||
\(682\) | 63.5384 | − | 36.6839i | 2.43301 | − | 1.40470i | ||||
\(683\) | −30.9517 | + | 17.8700i | −1.18433 | + | 0.683775i | −0.957013 | − | 0.290045i | \(-0.906330\pi\) |
−0.227320 | + | 0.973820i | \(0.572996\pi\) | |||||||
\(684\) | 40.9341 | − | 23.6333i | 1.56515 | − | 0.903642i | ||||
\(685\) | 8.05431 | − | 13.9505i | 0.307739 | − | 0.533020i | ||||
\(686\) | −47.0666 | − | 9.11748i | −1.79701 | − | 0.348107i | ||||
\(687\) | −3.56099 | + | 2.05594i | −0.135860 | + | 0.0784390i | ||||
\(688\) | −14.5924 | − | 25.2748i | −0.556330 | − | 0.963592i | ||||
\(689\) | 8.50199 | + | 24.7788i | 0.323900 | + | 0.943995i | ||||
\(690\) | −2.14843 | + | 3.72120i | −0.0817895 | + | 0.141664i | ||||
\(691\) | 22.5419 | + | 13.0146i | 0.857536 | + | 0.495099i | 0.863186 | − | 0.504885i | \(-0.168465\pi\) |
−0.00565028 | + | 0.999984i | \(0.501799\pi\) | |||||||
\(692\) | 30.1127 | + | 52.1567i | 1.14471 | + | 1.98270i | ||||
\(693\) | 2.16034 | + | 19.4264i | 0.0820647 | + | 0.737949i | ||||
\(694\) | − | 68.3335i | − | 2.59391i | ||||||
\(695\) | − | 2.68278i | − | 0.101764i | ||||||
\(696\) | 16.8659 | − | 9.73755i | 0.639301 | − | 0.369101i | ||||
\(697\) | −20.8535 | − | 12.0398i | −0.789884 | − | 0.456040i | ||||
\(698\) | 12.6589 | 0.479146 | ||||||||
\(699\) | −1.70360 | − | 2.95073i | −0.0644362 | − | 0.111607i | ||||
\(700\) | −29.6825 | + | 3.30088i | −1.12189 | + | 0.124762i | ||||
\(701\) | −1.12731 | −0.0425779 | −0.0212890 | − | 0.999773i | \(-0.506777\pi\) | ||||
−0.0212890 | + | 0.999773i | \(0.506777\pi\) | |||||||
\(702\) | 26.2321 | − | 9.00067i | 0.990068 | − | 0.339709i | ||||
\(703\) | −10.9588 | + | 18.9813i | −0.413321 | + | 0.715892i | ||||
\(704\) | 12.6702i | 0.477525i | ||||||||
\(705\) | −0.440917 | + | 0.763691i | −0.0166059 | + | 0.0287623i | ||||
\(706\) | 17.5478 | − | 30.3936i | 0.660419 | − | 1.14388i | ||||
\(707\) | 3.36398 | − | 0.374096i | 0.126515 | − | 0.0140693i | ||||
\(708\) | −24.1128 | − | 13.9215i | −0.906215 | − | 0.523203i | ||||
\(709\) | − | 6.05031i | − | 0.227224i | −0.993525 | − | 0.113612i | \(-0.963758\pi\) | ||
0.993525 | − | 0.113612i | \(-0.0362421\pi\) | |||||||
\(710\) | −4.88276 | − | 2.81906i | −0.183247 | − | 0.105798i | ||||
\(711\) | −8.47459 | − | 14.6784i | −0.317822 | − | 0.550484i | ||||
\(712\) | 6.15202 | − | 10.6556i | 0.230557 | − | 0.399336i | ||||
\(713\) | −18.0218 | + | 10.4049i | −0.674922 | + | 0.389666i | ||||
\(714\) | −1.22707 | − | 11.0341i | −0.0459219 | − | 0.412942i | ||||
\(715\) | −15.4300 | − | 3.01664i | −0.577050 | − | 0.112816i | ||||
\(716\) | −4.32530 | − | 7.49164i | −0.161644 | − | 0.279976i | ||||
\(717\) | − | 4.86986i | − | 0.181868i | ||||||
\(718\) | 22.2249 | 0.829425 | ||||||||
\(719\) | −47.1177 | −1.75719 | −0.878597 | − | 0.477563i | \(-0.841520\pi\) | ||||
−0.878597 | + | 0.477563i | \(0.841520\pi\) | |||||||
\(720\) | − | 38.2884i | − | 1.42692i | ||||||
\(721\) | −17.9810 | − | 24.4374i | −0.669647 | − | 0.910095i | ||||
\(722\) | −12.2100 | − | 7.04944i | −0.454409 | − | 0.262353i | ||||
\(723\) | 4.52859 | − | 2.61458i | 0.168420 | − | 0.0972374i | ||||
\(724\) | −7.75473 | − | 13.4316i | −0.288202 | − | 0.499181i | ||||
\(725\) | −12.9014 | −0.479146 | ||||||||
\(726\) | −4.28097 | − | 2.47162i | −0.158882 | − | 0.0917303i | ||||
\(727\) | 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 | ||||
\(729\) | −13.5489 | −0.501810 | ||||||||
\(730\) | −32.8985 | − | 18.9940i | −1.21763 | − | 0.702999i | ||||
\(731\) | −10.4929 | −0.388093 | ||||||||
\(732\) | −3.56454 | − | 6.17396i | −0.131749 | − | 0.228196i | ||||
\(733\) | 39.2037 | − | 22.6343i | 1.44802 | − | 0.836016i | 0.449658 | − | 0.893201i | \(-0.351546\pi\) |
0.998364 | + | 0.0571848i | \(0.0182124\pi\) | |||||||
\(734\) | 3.72861 | + | 2.15271i | 0.137625 | + | 0.0794581i | ||||
\(735\) | 4.30028 | − | 3.96695i | 0.158618 | − | 0.146323i | ||||
\(736\) | − | 16.9378i | − | 0.624335i | ||||||
\(737\) | −36.7382 | −1.35327 | ||||||||
\(738\) | −54.4494 | −2.00431 | ||||||||
\(739\) | − | 19.2613i | − | 0.708539i | −0.935143 | − | 0.354270i | \(-0.884730\pi\) | ||
0.935143 | − | 0.354270i | \(-0.115270\pi\) | |||||||
\(740\) | 22.5577 | + | 39.0712i | 0.829239 | + | 1.43628i | ||||
\(741\) | 5.18905 | + | 4.52065i | 0.190624 | + | 0.166070i | ||||
\(742\) | 40.0804 | − | 29.4911i | 1.47140 | − | 1.08265i | ||||
\(743\) | 30.2115 | − | 17.4426i | 1.10835 | − | 0.639908i | 0.169951 | − | 0.985453i | \(-0.445639\pi\) |
0.938402 | + | 0.345545i | \(0.112306\pi\) | |||||||
\(744\) | −18.9905 | + | 32.8925i | −0.696225 | + | 1.20590i | ||||
\(745\) | 15.9577 | + | 27.6396i | 0.584647 | + | 1.01264i | ||||
\(746\) | −31.3032 | − | 18.0729i | −1.14609 | − | 0.661697i | ||||
\(747\) | 7.36525i | 0.269480i | ||||||||
\(748\) | 34.4303 | + | 19.8784i | 1.25890 | + | 0.726825i | ||||
\(749\) | 5.45120 | − | 12.4451i | 0.199183 | − | 0.454733i | ||||
\(750\) | 8.00648 | − | 13.8676i | 0.292355 | − | 0.506374i | ||||
\(751\) | −12.4834 | + | 21.6219i | −0.455526 | + | 0.788993i | −0.998718 | − | 0.0506146i | \(-0.983882\pi\) |
0.543193 | + | 0.839608i | \(0.317215\pi\) | |||||||
\(752\) | − | 9.17535i | − | 0.334591i | ||||||
\(753\) | −2.68268 | + | 4.64654i | −0.0977623 | + | 0.169329i | ||||
\(754\) | −37.8095 | − | 32.9393i | −1.37694 | − | 1.19958i | ||||
\(755\) | 12.1467 | 0.442064 | ||||||||
\(756\) | −21.9024 | − | 29.7669i | −0.796584 | − | 1.08261i | ||||
\(757\) | 5.30243 | + | 9.18408i | 0.192720 | + | 0.333801i | 0.946151 | − | 0.323726i | \(-0.104936\pi\) |
−0.753431 | + | 0.657527i | \(0.771602\pi\) | |||||||
\(758\) | 81.7370 | 2.96882 | ||||||||
\(759\) | −2.41212 | − | 1.39264i | −0.0875543 | − | 0.0505495i | ||||
\(760\) | 35.9337 | − | 20.7463i | 1.30345 | − | 0.752548i | ||||
\(761\) | 32.6388i | 1.18316i | 0.806248 | + | 0.591578i | \(0.201495\pi\) | ||||
−0.806248 | + | 0.591578i | \(0.798505\pi\) | |||||||
\(762\) | 4.19288i | 0.151892i | ||||||||
\(763\) | −4.18733 | − | 1.83414i | −0.151592 | − | 0.0664002i | ||||
\(764\) | 11.5080 | + | 19.9325i | 0.416345 | + | 0.721131i | ||||
\(765\) | −11.9216 | − | 6.88296i | −0.431028 | − | 0.248854i | ||||
\(766\) | −41.2988 | + | 71.5316i | −1.49219 | + | 2.58454i | ||||
\(767\) | −7.90323 | + | 40.4247i | −0.285369 | + | 1.45965i | ||||
\(768\) | 5.73794 | + | 9.93841i | 0.207050 | + | 0.358621i | ||||
\(769\) | −45.1851 | + | 26.0876i | −1.62942 | + | 0.940744i | −0.645148 | + | 0.764057i | \(0.723204\pi\) |
−0.984267 | + | 0.176686i | \(0.943462\pi\) | |||||||
\(770\) | 3.30077 | + | 29.6814i | 0.118951 | + | 1.06964i | ||||
\(771\) | 2.07039 | − | 3.58601i | 0.0745631 | − | 0.129147i | ||||
\(772\) | 12.2909 | − | 7.09618i | 0.442360 | − | 0.255397i | ||||
\(773\) | −30.9221 | + | 17.8529i | −1.11219 | + | 0.642123i | −0.939396 | − | 0.342835i | \(-0.888613\pi\) |
−0.172794 | + | 0.984958i | \(0.555279\pi\) | |||||||
\(774\) | −20.5480 | + | 11.8634i | −0.738583 | + | 0.426421i | ||||
\(775\) | 21.7898 | − | 12.5804i | 0.782714 | − | 0.451900i | ||||
\(776\) | −54.1208 | + | 93.7400i | −1.94282 | + | 3.36507i | ||||
\(777\) | 7.48041 | + | 3.27658i | 0.268358 | + | 0.117546i | ||||
\(778\) | 56.9752 | − | 32.8947i | 2.04266 | − | 1.17933i | ||||
\(779\) | −14.1766 | − | 24.5545i | −0.507928 | − | 0.879757i | ||||
\(780\) | 13.3992 | − | 4.59749i | 0.479769 | − | 0.164617i | ||||
\(781\) | 1.82735 | − | 3.16506i | 0.0653876 | − | 0.113255i | ||||
\(782\) | −13.9206 | − | 8.03703i | −0.497798 | − | 0.287404i | ||||
\(783\) | −7.98231 | − | 13.8258i | −0.285265 | − | 0.494093i | ||||
\(784\) | −18.1114 | + | 58.1175i | −0.646836 | + | 2.07563i | ||||
\(785\) | 22.5760i | 0.805770i | ||||||||
\(786\) | 13.7018i | 0.488726i | ||||||||
\(787\) | 5.28813 | − | 3.05310i | 0.188501 | − | 0.108831i | −0.402779 | − | 0.915297i | \(-0.631956\pi\) |
0.591281 | + | 0.806466i | \(0.298622\pi\) | |||||||
\(788\) | 18.9301 | + | 10.9293i | 0.674356 | + | 0.389339i | ||||
\(789\) | 2.62310 | 0.0933847 | ||||||||
\(790\) | −12.9482 | − | 22.4270i | −0.460678 | − | 0.797918i | ||||
\(791\) | 9.11971 | − | 20.8203i | 0.324259 | − | 0.740283i | ||||
\(792\) | 51.6510 | 1.83534 | ||||||||
\(793\) | −6.92774 | + | 7.95204i | −0.246011 | + | 0.282385i | ||||
\(794\) | −5.38296 | + | 9.32356i | −0.191034 | + | 0.330881i | ||||
\(795\) | 6.07261i | 0.215373i | ||||||||
\(796\) | −0.965369 | + | 1.67207i | −0.0342166 | + | 0.0592649i | ||||
\(797\) | −23.1149 | + | 40.0363i | −0.818773 | + | 1.41816i | 0.0878129 | + | 0.996137i | \(0.472012\pi\) |
−0.906586 | + | 0.422020i | \(0.861321\pi\) | |||||||
\(798\) | 5.24495 | − | 11.9742i | 0.185669 | − | 0.423882i | ||||
\(799\) | −2.85688 | − | 1.64942i | −0.101069 | − | 0.0583522i | ||||
\(800\) | 20.4792i | 0.724048i | ||||||||
\(801\) | −4.16260 | − | 2.40328i | −0.147078 | − | 0.0849157i | ||||
\(802\) | 25.3700 | + | 43.9422i | 0.895847 | + | 1.55165i | ||||
\(803\) | 12.3121 | − | 21.3252i | 0.434484 | − | 0.752549i | ||||
\(804\) | 28.6672 | − | 16.5510i | 1.01101 | − | 0.583710i | ||||
\(805\) | −0.936218 | − | 8.41874i | −0.0329974 | − | 0.296722i | ||||
\(806\) | 95.9780 | + | 18.7642i | 3.38068 | + | 0.660939i | ||||
\(807\) | −3.60080 | − | 6.23678i | −0.126754 | − | 0.219545i | ||||
\(808\) | − | 8.94415i | − | 0.314654i | ||||||
\(809\) | 39.2879 | 1.38129 | 0.690644 | − | 0.723195i | \(-0.257327\pi\) | ||||
0.690644 | + | 0.723195i | \(0.257327\pi\) | |||||||
\(810\) | −27.7627 | −0.975482 | ||||||||
\(811\) | − | 6.90664i | − | 0.242525i | −0.992620 | − | 0.121262i | \(-0.961306\pi\) | ||
0.992620 | − | 0.121262i | \(-0.0386943\pi\) | |||||||
\(812\) | −26.8102 | + | 61.2077i | −0.940855 | + | 2.14797i | ||||
\(813\) | −3.73896 | − | 2.15869i | −0.131131 | − | 0.0757085i | ||||
\(814\) | −36.1015 | + | 20.8432i | −1.26536 | + | 0.730555i | ||||
\(815\) | 5.77917 | + | 10.0098i | 0.202436 | + | 0.350629i | ||||
\(816\) | −14.0971 | −0.493496 | ||||||||
\(817\) | −10.6998 | − | 6.17756i | −0.374340 | − | 0.216125i | ||||
\(818\) | 45.6466 | 1.59600 | ||||||||
\(819\) | −14.8381 | + | 21.4158i | −0.518486 | + | 0.748329i | ||||
\(820\) | −58.3622 | −2.03810 | ||||||||
\(821\) | −1.65453 | − | 0.955244i | −0.0577435 | − | 0.0333382i | 0.470850 | − | 0.882213i | \(-0.343947\pi\) |
−0.528594 | + | 0.848875i | \(0.677281\pi\) | |||||||
\(822\) | −13.4111 | −0.467765 | ||||||||
\(823\) | 0.789844 | + | 1.36805i | 0.0275322 | + | 0.0476872i | 0.879463 | − | 0.475967i | \(-0.157902\pi\) |
−0.851931 | + | 0.523654i | \(0.824568\pi\) | |||||||
\(824\) | −69.4320 | + | 40.0866i | −2.41878 | + | 1.39648i | ||||
\(825\) | 2.91645 | + | 1.68381i | 0.101538 | + | 0.0586228i | ||||
\(826\) | 77.7617 | − | 8.64760i | 2.70567 | − | 0.300888i | ||||
\(827\) | − | 32.5050i | − | 1.13031i | −0.824985 | − | 0.565155i | \(-0.808816\pi\) | ||
0.824985 | − | 0.565155i | \(-0.191184\pi\) | |||||||
\(828\) | −25.4986 | −0.886138 | ||||||||
\(829\) | 35.0538 | 1.21747 | 0.608735 | − | 0.793373i | \(-0.291677\pi\) | ||||
0.608735 | + | 0.793373i | \(0.291677\pi\) | |||||||
\(830\) | 11.2533i | 0.390608i | ||||||||
\(831\) | −6.01721 | − | 10.4221i | −0.208735 | − | 0.361539i | ||||
\(832\) | −11.0937 | + | 12.7340i | −0.384606 | + | 0.441472i | ||||
\(833\) | 14.8399 | + | 16.0868i | 0.514172 | + | 0.557375i | ||||
\(834\) | −1.93429 | + | 1.11676i | −0.0669790 | + | 0.0386703i | ||||
\(835\) | 14.4928 | − | 25.1023i | 0.501544 | − | 0.868700i | ||||
\(836\) | 23.4063 | + | 40.5409i | 0.809523 | + | 1.40214i | ||||
\(837\) | 26.9635 | + | 15.5674i | 0.931994 | + | 0.538087i | ||||
\(838\) | 77.3760i | 2.67291i | ||||||||
\(839\) | 4.63746 | + | 2.67744i | 0.160103 | + | 0.0924354i | 0.577911 | − | 0.816100i | \(-0.303868\pi\) |
−0.417808 | + | 0.908535i | \(0.637202\pi\) | |||||||
\(840\) | −9.16254 | − | 12.4525i | −0.316138 | − | 0.429653i | ||||
\(841\) | 0.0669890 | − | 0.116028i | 0.00230997 | − | 0.00400098i | ||||
\(842\) | −16.6354 | + | 28.8133i | −0.573293 | + | 0.992973i | ||||
\(843\) | − | 14.0813i | − | 0.484985i | ||||||
\(844\) | −17.6658 | + | 30.5981i | −0.608082 | + | 1.05323i | ||||
\(845\) | −12.8664 | − | 16.5420i | −0.442618 | − | 0.569063i | ||||
\(846\) | −7.45942 | −0.256460 | ||||||||
\(847\) | 9.68515 | − | 1.07705i | 0.332786 | − | 0.0370079i | ||||
\(848\) | −31.5923 | − | 54.7195i | −1.08488 | − | 1.87907i | ||||
\(849\) | 8.37387 | 0.287391 | ||||||||
\(850\) | 16.8311 | + | 9.71744i | 0.577302 | + | 0.333305i | ||||
\(851\) | 10.2397 | − | 5.91190i | 0.351013 | − | 0.202657i | ||||
\(852\) | 3.29297i | 0.112815i | ||||||||
\(853\) | − | 49.6270i | − | 1.69920i | −0.527431 | − | 0.849598i | \(-0.676845\pi\) | ||
0.527431 | − | 0.849598i | \(-0.323155\pi\) | |||||||
\(854\) | 18.3501 | + | 8.03771i | 0.627926 | + | 0.275045i | ||||
\(855\) | −8.10452 | − | 14.0374i | −0.277169 | − | 0.480070i | ||||
\(856\) | −31.0927 | − | 17.9514i | −1.06273 | − | 0.613566i | ||||
\(857\) | 2.94196 | − | 5.09563i | 0.100496 | − | 0.174063i | −0.811393 | − | 0.584500i | \(-0.801291\pi\) |
0.911889 | + | 0.410437i | \(0.134624\pi\) | |||||||
\(858\) | 4.24806 | + | 12.3808i | 0.145026 | + | 0.422674i | ||||
\(859\) | −21.6931 | − | 37.5735i | −0.740159 | − | 1.28199i | −0.952423 | − | 0.304780i | \(-0.901417\pi\) |
0.212264 | − | 0.977212i | \(-0.431916\pi\) | |||||||
\(860\) | −22.0246 | + | 12.7159i | −0.751033 | + | 0.433609i | ||||
\(861\) | −8.50917 | + | 6.26103i | −0.289992 | + | 0.213376i | ||||
\(862\) | −11.6106 | + | 20.1102i | −0.395460 | + | 0.684957i | ||||
\(863\) | −26.9570 | + | 15.5636i | −0.917626 | + | 0.529792i | −0.882877 | − | 0.469604i | \(-0.844397\pi\) |
−0.0347490 | + | 0.999396i | \(0.511063\pi\) | |||||||
\(864\) | −21.9465 | + | 12.6708i | −0.746634 | + | 0.431069i | ||||
\(865\) | 17.8860 | − | 10.3265i | 0.608142 | − | 0.351111i | ||||
\(866\) | 7.73558 | − | 4.46614i | 0.262866 | − | 0.151766i | ||||
\(867\) | 1.87278 | − | 3.24376i | 0.0636031 | − | 0.110164i | ||||
\(868\) | −14.4035 | − | 129.520i | −0.488885 | − | 4.39620i | ||||
\(869\) | 14.5374 | − | 8.39318i | 0.493148 | − | 0.284719i | ||||
\(870\) | −5.81203 | − | 10.0667i | −0.197046 | − | 0.341294i | ||||
\(871\) | −36.9233 | − | 32.1672i | −1.25110 | − | 1.08994i | ||||
\(872\) | −6.04001 | + | 10.4616i | −0.204540 | + | 0.354274i | ||||
\(873\) | 36.6194 | + | 21.1422i | 1.23938 | + | 0.715556i | ||||
\(874\) | −9.46341 | − | 16.3911i | −0.320105 | − | 0.554438i | ||||
\(875\) | 3.48896 | + | 31.3738i | 0.117949 | + | 1.06063i | ||||
\(876\) | 22.1870i | 0.749629i | ||||||||
\(877\) | 29.9106i | 1.01001i | 0.863117 | + | 0.505004i | \(0.168509\pi\) | ||||
−0.863117 | + | 0.505004i | \(0.831491\pi\) | |||||||
\(878\) | 86.3413 | − | 49.8492i | 2.91388 | − | 1.68233i | ||||
\(879\) | −6.57576 | − | 3.79652i | −0.221795 | − | 0.128053i | ||||
\(880\) | 37.9206 | 1.27830 | ||||||||
\(881\) | 7.28477 | + | 12.6176i | 0.245430 | + | 0.425097i | 0.962252 | − | 0.272159i | \(-0.0877375\pi\) |
−0.716822 | + | 0.697256i | \(0.754404\pi\) | |||||||
\(882\) | 47.2486 | + | 14.7243i | 1.59094 | + | 0.495793i | ||||
\(883\) | 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 | ||||
\(885\) | −4.77408 | + | 8.26896i | −0.160479 | + | 0.277958i | ||||
\(886\) | − | 38.9324i | − | 1.30796i | ||||||
\(887\) | −27.2951 | + | 47.2765i | −0.916480 | + | 1.58739i | −0.111761 | + | 0.993735i | \(0.535649\pi\) |
−0.804719 | + | 0.593655i | \(0.797684\pi\) | |||||||
\(888\) | 10.7901 | − | 18.6890i | 0.362092 | − | 0.627162i | ||||
\(889\) | −4.89866 | − | 6.65761i | −0.164296 | − | 0.223289i | ||||
\(890\) | −6.36000 | − | 3.67195i | −0.213188 | − | 0.123084i | ||||
\(891\) | − | 17.9961i | − | 0.602891i | ||||||
\(892\) | −91.9222 | − | 53.0713i | −3.07778 | − | 1.77696i | ||||
\(893\) | −1.94215 | − | 3.36390i | −0.0649916 | − | 0.112569i | ||||
\(894\) | 13.2855 | − | 23.0111i | 0.444333 | − | 0.769607i | ||||
\(895\) | −2.56909 | + | 1.48327i | −0.0858753 | + | 0.0495801i | ||||
\(896\) | −11.9518 | − | 5.23512i | −0.399281 | − | 0.174893i | ||||
\(897\) | −1.20490 | − | 3.51165i | −0.0402306 | − | 0.117251i | ||||
\(898\) | −50.3787 | − | 87.2584i | −1.68116 | − | 2.91185i | ||||
\(899\) | − | 56.2955i | − | 1.87756i | ||||||
\(900\) | 30.8299 | 1.02766 | ||||||||
\(901\) | −22.7169 | −0.756810 | ||||||||
\(902\) | − | 53.9263i | − | 1.79555i | ||||||
\(903\) | −1.84702 | + | 4.21675i | −0.0614651 | + | 0.140325i | ||||
\(904\) | −52.0172 | − | 30.0321i | −1.73007 | − | 0.998854i | ||||
\(905\) | −4.60606 | + | 2.65931i | −0.153111 | + | 0.0883985i | ||||
\(906\) | −5.05632 | − | 8.75780i | −0.167985 | − | 0.290958i | ||||
\(907\) | −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 | ||||
\(909\) | −3.49402 | −0.115889 | ||||||||
\(910\) | −22.6710 | + | 32.7210i | −0.751537 | + | 1.08469i | ||||
\(911\) | −42.2359 | −1.39934 | −0.699669 | − | 0.714467i | \(-0.746669\pi\) | ||||
−0.699669 | + | 0.714467i | \(0.746669\pi\) | |||||||
\(912\) | −14.3751 | − | 8.29948i | −0.476008 | − | 0.274823i | ||||
\(913\) | −7.29450 | −0.241413 | ||||||||
\(914\) | 18.0421 | + | 31.2498i | 0.596779 | + | 1.03365i | ||||
\(915\) | −2.11722 | + | 1.22238i | −0.0699933 | + | 0.0404106i | ||||
\(916\) | −32.2870 | − | 18.6409i | −1.06679 | − | 0.615912i | ||||
\(917\) | −16.0082 | − | 21.7562i | −0.528637 | − | 0.718453i | ||||
\(918\) | 24.0494i | 0.793747i | ||||||||
\(919\) | 30.6940 | 1.01250 | 0.506251 | − | 0.862386i | \(-0.331031\pi\) | ||||
0.506251 | + | 0.862386i | \(0.331031\pi\) | |||||||
\(920\) | −22.3838 | −0.737971 | ||||||||
\(921\) | 4.65502i | 0.153388i | ||||||||
\(922\) | −48.4890 | − | 83.9854i | −1.59690 | − | 2.76591i | ||||
\(923\) | 4.60780 | − | 1.58101i | 0.151668 | − | 0.0520396i | ||||
\(924\) | 14.0491 | − | 10.3373i | 0.462182 | − | 0.340073i | ||||
\(925\) | −12.3806 | + | 7.14797i | −0.407073 | + | 0.235024i | ||||
\(926\) | 8.74009 | − | 15.1383i | 0.287217 | − | 0.497474i | ||||
\(927\) | 15.6598 | + | 27.1235i | 0.514334 | + | 0.890853i | ||||
\(928\) | 39.6819 | + | 22.9104i | 1.30262 | + | 0.752070i | ||||
\(929\) | − | 37.4250i | − | 1.22787i | −0.789355 | − | 0.613936i | \(-0.789585\pi\) | ||
0.789355 | − | 0.613936i | \(-0.210415\pi\) | |||||||
\(930\) | 19.6325 | + | 11.3348i | 0.643775 | + | 0.371684i | ||||
\(931\) | 5.66168 | + | 25.1409i | 0.185554 | + | 0.823960i | ||||
\(932\) | 15.4463 | − | 26.7538i | 0.505961 | − | 0.876350i | ||||
\(933\) | 3.15787 | − | 5.46960i | 0.103384 | − | 0.179067i | ||||
\(934\) | − | 13.0733i | − | 0.427770i | ||||||
\(935\) | 6.81684 | − | 11.8071i | 0.222935 | − | 0.386134i | ||||
\(936\) | 51.9111 | + | 45.2245i | 1.69677 | + | 1.47821i | ||||
\(937\) | 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 | ||||
\(939\) | −3.40216 | − | 5.89272i | −0.111025 | − | 0.192302i | ||||
\(940\) | −7.99546 | −0.260783 | ||||||||
\(941\) | 23.8202 | + | 13.7526i | 0.776518 | + | 0.448323i | 0.835195 | − | 0.549954i | \(-0.185355\pi\) |
−0.0586770 | + | 0.998277i | \(0.518688\pi\) | |||||||
\(942\) | 16.2773 | − | 9.39771i | 0.530343 | − | 0.306194i | ||||
\(943\) | 15.2955i | 0.498089i | ||||||||
\(944\) | − | 99.3472i | − | 3.23348i | ||||||
\(945\) | −10.2079 | + | 7.51095i | −0.332063 | + | 0.244331i | ||||
\(946\) | −11.7494 | − | 20.3506i | −0.382007 | − | 0.661656i | ||||
\(947\) | 4.40226 | + | 2.54165i | 0.143054 | + | 0.0825925i | 0.569819 | − | 0.821770i | \(-0.307013\pi\) |
−0.426765 | + | 0.904363i | \(0.640347\pi\) | |||||||
\(948\) | −7.56246 | + | 13.0986i | −0.245617 | + | 0.425422i | ||||
\(949\) | 31.0459 | − | 10.6524i | 1.00779 | − | 0.345790i | ||||
\(950\) | 11.4420 | + | 19.8182i | 0.371229 | + | 0.642987i | ||||
\(951\) | −7.50534 | + | 4.33321i | −0.243377 | + | 0.140514i | ||||
\(952\) | 46.5834 | − | 34.2760i | 1.50978 | − | 1.11089i | ||||
\(953\) | 4.90718 | − | 8.49949i | 0.158959 | − | 0.275326i | −0.775534 | − | 0.631305i | \(-0.782519\pi\) |
0.934494 | + | 0.355980i | \(0.115853\pi\) | |||||||
\(954\) | −44.4861 | + | 25.6840i | −1.44029 | + | 0.831552i | ||||
\(955\) | 6.83540 | − | 3.94642i | 0.221188 | − | 0.127703i | ||||
\(956\) | 38.2388 | − | 22.0772i | 1.23673 | − | 0.714027i | ||||
\(957\) | 6.52536 | − | 3.76742i | 0.210935 | − | 0.121783i | ||||
\(958\) | −12.2353 | + | 21.1921i | −0.395303 | + | 0.684685i | ||||
\(959\) | 21.2946 | − | 15.6686i | 0.687640 | − | 0.505964i | ||||
\(960\) | −3.39041 | + | 1.95746i | −0.109425 | + | 0.0631766i | ||||
\(961\) | 39.3947 | + | 68.2336i | 1.27080 | + | 2.20108i | ||||
\(962\) | −54.5332 | − | 10.6615i | −1.75822 | − | 0.343741i | ||||
\(963\) | −7.01268 | + | 12.1463i | −0.225981 | + | 0.391410i | ||||
\(964\) | 41.0601 | + | 23.7060i | 1.32246 | + | 0.763520i | ||||
\(965\) | −2.43348 | − | 4.21490i | −0.0783364 | − | 0.135683i | ||||
\(966\) | −5.68021 | + | 4.17949i | −0.182758 | + | 0.134473i | ||||
\(967\) | − | 2.69619i | − | 0.0867036i | −0.999060 | − | 0.0433518i | \(-0.986196\pi\) | ||
0.999060 | − | 0.0433518i | \(-0.0138036\pi\) | |||||||
\(968\) | − | 25.7509i | − | 0.827665i | ||||||
\(969\) | −5.16832 | + | 2.98393i | −0.166030 | + | 0.0958577i | ||||
\(970\) | 55.9504 | + | 32.3030i | 1.79646 | + | 1.03719i | ||||
\(971\) | 24.9240 | 0.799850 | 0.399925 | − | 0.916548i | \(-0.369036\pi\) | ||||
0.399925 | + | 0.916548i | \(0.369036\pi\) | |||||||
\(972\) | 29.0598 | + | 50.3331i | 0.932094 | + | 1.61443i | ||||
\(973\) | 1.76659 | − | 4.03313i | 0.0566344 | − | 0.129296i | ||||
\(974\) | −103.543 | −3.31773 | ||||||||
\(975\) | 1.45683 | + | 4.24587i | 0.0466558 | + | 0.135977i | ||||
\(976\) | 12.7187 | − | 22.0294i | 0.407115 | − | 0.705144i | ||||
\(977\) | − | 28.3129i | − | 0.905811i | −0.891558 | − | 0.452906i | \(-0.850387\pi\) | ||
0.891558 | − | 0.452906i | \(-0.149613\pi\) | |||||||
\(978\) | 4.81140 | − | 8.33359i | 0.153852 | − | 0.266479i | ||||
\(979\) | 2.38019 | − | 4.12262i | 0.0760713 | − | 0.131759i | ||||
\(980\) | 50.6440 | + | 15.7824i | 1.61776 | + | 0.504150i | ||||
\(981\) | 4.08681 | + | 2.35952i | 0.130482 | + | 0.0753337i | ||||
\(982\) | 17.5015i | 0.558494i | ||||||||
\(983\) | 32.7805 | + | 18.9258i | 1.04554 | + | 0.603641i | 0.921396 | − | 0.388624i | \(-0.127049\pi\) |
0.124140 | + | 0.992265i | \(0.460383\pi\) | |||||||
\(984\) | 13.9583 | + | 24.1764i | 0.444974 | + | 0.770717i | ||||
\(985\) | 3.74795 | − | 6.49165i | 0.119420 | − | 0.206841i | ||||
\(986\) | 37.6585 | − | 21.7421i | 1.19929 | − | 0.692410i | ||||
\(987\) | −1.16573 | + | 0.857744i | −0.0371057 | + | 0.0273023i | ||||
\(988\) | −11.9725 | + | 61.2391i | −0.380897 | + | 1.94827i | ||||
\(989\) | 3.33257 | + | 5.77218i | 0.105970 | + | 0.183545i | ||||
\(990\) | − | 30.8289i | − | 0.979805i | ||||||
\(991\) | 58.4158 | 1.85564 | 0.927820 | − | 0.373028i | \(-0.121681\pi\) | ||||
0.927820 | + | 0.373028i | \(0.121681\pi\) | |||||||
\(992\) | −89.3612 | −2.83722 | ||||||||
\(993\) | − | 2.05657i | − | 0.0652633i | ||||||
\(994\) | −5.48410 | − | 7.45327i | −0.173945 | − | 0.236403i | ||||
\(995\) | 0.573399 | + | 0.331052i | 0.0181780 | + | 0.0104950i | ||||
\(996\) | 5.69197 | − | 3.28626i | 0.180357 | − | 0.104129i | ||||
\(997\) | −14.0294 | − | 24.2997i | −0.444316 | − | 0.769578i | 0.553688 | − | 0.832724i | \(-0.313220\pi\) |
−0.998004 | + | 0.0631462i | \(0.979887\pi\) | |||||||
\(998\) | −29.4001 | −0.930645 | ||||||||
\(999\) | −15.3202 | − | 8.84514i | −0.484711 | − | 0.279848i |
(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 | 91.2.u.b.88.1 | yes | 12 | |
3.2 | odd | 2 | 819.2.do.e.361.6 | 12 | |||
7.2 | even | 3 | 91.2.k.b.23.6 | yes | 12 | ||
7.3 | odd | 6 | 637.2.q.i.491.6 | 12 | |||
7.4 | even | 3 | 637.2.q.g.491.6 | 12 | |||
7.5 | odd | 6 | 637.2.k.i.569.6 | 12 | |||
7.6 | odd | 2 | 637.2.u.g.361.1 | 12 | |||
13.2 | odd | 12 | 1183.2.e.j.508.1 | 24 | |||
13.4 | even | 6 | 91.2.k.b.4.1 | ✓ | 12 | ||
13.11 | odd | 12 | 1183.2.e.j.508.12 | 24 | |||
21.2 | odd | 6 | 819.2.bm.f.478.1 | 12 | |||
39.17 | odd | 6 | 819.2.bm.f.550.6 | 12 | |||
91.2 | odd | 12 | 1183.2.e.j.170.1 | 24 | |||
91.4 | even | 6 | 637.2.q.g.589.6 | 12 | |||
91.11 | odd | 12 | 8281.2.a.cp.1.1 | 12 | |||
91.17 | odd | 6 | 637.2.q.i.589.6 | 12 | |||
91.24 | even | 12 | 8281.2.a.co.1.1 | 12 | |||
91.30 | even | 6 | inner | 91.2.u.b.30.1 | yes | 12 | |
91.37 | odd | 12 | 1183.2.e.j.170.12 | 24 | |||
91.67 | odd | 12 | 8281.2.a.cp.1.12 | 12 | |||
91.69 | odd | 6 | 637.2.k.i.459.1 | 12 | |||
91.80 | even | 12 | 8281.2.a.co.1.12 | 12 | |||
91.82 | odd | 6 | 637.2.u.g.30.1 | 12 | |||
273.212 | odd | 6 | 819.2.do.e.667.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.1 | ✓ | 12 | 13.4 | even | 6 | ||
91.2.k.b.23.6 | yes | 12 | 7.2 | even | 3 | ||
91.2.u.b.30.1 | yes | 12 | 91.30 | even | 6 | inner | |
91.2.u.b.88.1 | yes | 12 | 1.1 | even | 1 | trivial | |
637.2.k.i.459.1 | 12 | 91.69 | odd | 6 | |||
637.2.k.i.569.6 | 12 | 7.5 | odd | 6 | |||
637.2.q.g.491.6 | 12 | 7.4 | even | 3 | |||
637.2.q.g.589.6 | 12 | 91.4 | even | 6 | |||
637.2.q.i.491.6 | 12 | 7.3 | odd | 6 | |||
637.2.q.i.589.6 | 12 | 91.17 | odd | 6 | |||
637.2.u.g.30.1 | 12 | 91.82 | odd | 6 | |||
637.2.u.g.361.1 | 12 | 7.6 | odd | 2 | |||
819.2.bm.f.478.1 | 12 | 21.2 | odd | 6 | |||
819.2.bm.f.550.6 | 12 | 39.17 | odd | 6 | |||
819.2.do.e.361.6 | 12 | 3.2 | odd | 2 | |||
819.2.do.e.667.6 | 12 | 273.212 | odd | 6 | |||
1183.2.e.j.170.1 | 24 | 91.2 | odd | 12 | |||
1183.2.e.j.170.12 | 24 | 91.37 | odd | 12 | |||
1183.2.e.j.508.1 | 24 | 13.2 | odd | 12 | |||
1183.2.e.j.508.12 | 24 | 13.11 | odd | 12 | |||
8281.2.a.co.1.1 | 12 | 91.24 | even | 12 | |||
8281.2.a.co.1.12 | 12 | 91.80 | even | 12 | |||
8281.2.a.cp.1.1 | 12 | 91.11 | odd | 12 | |||
8281.2.a.cp.1.12 | 12 | 91.67 | odd | 12 |