Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (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: | \(5.08647060876\) |
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: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 491.6 | ||
Root | \(1.32725 - 0.488273i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.491 |
Dual form | 637.2.q.g.589.6 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.24179 | − | 1.29430i | 1.58519 | − | 0.915209i | 0.591104 | − | 0.806596i | \(-0.298692\pi\) |
0.994084 | − | 0.108613i | \(-0.0346409\pi\) | |||||||
\(3\) | −0.259233 | − | 0.449005i | −0.149668 | − | 0.259233i | 0.781437 | − | 0.623985i | \(-0.214487\pi\) |
−0.931105 | + | 0.364752i | \(0.881154\pi\) | |||||||
\(4\) | 2.35043 | − | 4.07106i | 1.17521 | − | 2.03553i | ||||
\(5\) | 1.61205i | 0.720932i | 0.932772 | + | 0.360466i | \(0.117382\pi\) | ||||
−0.932772 | + | 0.360466i | \(0.882618\pi\) | |||||||
\(6\) | −1.16229 | − | 0.671051i | −0.474504 | − | 0.273955i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 6.99143i | − | 2.47184i | ||||||
\(9\) | 1.36560 | − | 2.36528i | 0.455199 | − | 0.788428i | ||||
\(10\) | 2.08648 | + | 3.61389i | 0.659803 | + | 1.14281i | ||||
\(11\) | −2.34256 | + | 1.35248i | −0.706309 | + | 0.407788i | −0.809693 | − | 0.586854i | \(-0.800366\pi\) |
0.103384 | + | 0.994642i | \(0.467033\pi\) | |||||||
\(12\) | −2.43723 | −0.703568 | ||||||||
\(13\) | 2.36840 | − | 2.71858i | 0.656876 | − | 0.753998i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 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 | −0.611783 | − | 0.791026i | \(-0.709547\pi\) |
0.990940 | + | 0.134307i | \(0.0428808\pi\) | |||||||
\(18\) | − | 7.06997i | − | 1.66641i | ||||||
\(19\) | −3.18828 | − | 1.84075i | −0.731441 | − | 0.422297i | 0.0875083 | − | 0.996164i | \(-0.472110\pi\) |
−0.818949 | + | 0.573866i | \(0.805443\pi\) | |||||||
\(20\) | 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 | 0.950787 | − | 0.309846i | \(-0.100278\pi\) |
−0.743728 | + | 0.668482i | \(0.766944\pi\) | |||||||
\(24\) | −3.13918 | + | 1.81241i | −0.640783 | + | 0.369956i | ||||
\(25\) | 2.40128 | 0.480257 | ||||||||
\(26\) | 1.79081 | − | 9.15992i | 0.351206 | − | 1.79641i | ||||
\(27\) | −2.97143 | −0.571852 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.68636 | + | 4.65290i | 0.498844 | + | 0.864023i | 0.999999 | − | 0.00133469i | \(-0.000424845\pi\) |
−0.501155 | + | 0.865357i | \(0.667092\pi\) | |||||||
\(30\) | 1.08177 | − | 1.87368i | 0.197503 | − | 0.342086i | ||||
\(31\) | 10.4780i | 1.88191i | 0.338529 | + | 0.940956i | \(0.390071\pi\) | ||||
−0.338529 | + | 0.940956i | \(0.609929\pi\) | |||||||
\(32\) | −7.38583 | − | 4.26421i | −1.30564 | − | 0.753813i | ||||
\(33\) | 1.21454 | + | 0.701214i | 0.211424 | + | 0.122066i | ||||
\(34\) | − | 8.09354i | − | 1.38803i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.41947 | − | 11.1188i | −1.06991 | − | 1.85314i | ||||
\(37\) | −5.15585 | + | 2.97673i | −0.847616 | + | 0.489371i | −0.859846 | − | 0.510554i | \(-0.829440\pi\) |
0.0122297 | + | 0.999925i | \(0.496107\pi\) | |||||||
\(38\) | −9.52994 | −1.54596 | ||||||||
\(39\) | −1.83462 | − | 0.358678i | −0.293775 | − | 0.0574344i | ||||
\(40\) | 11.2706 | 1.78203 | ||||||||
\(41\) | −6.66970 | + | 3.85075i | −1.04163 | + | 0.601386i | −0.920295 | − | 0.391225i | \(-0.872051\pi\) |
−0.121337 | + | 0.992611i | \(0.538718\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.67800 | + | 2.90638i | −0.255892 | + | 0.443219i | −0.965138 | − | 0.261743i | \(-0.915703\pi\) |
0.709245 | + | 0.704962i | \(0.249036\pi\) | |||||||
\(44\) | 12.7156i | 1.91695i | ||||||||
\(45\) | 3.81296 | + | 2.20141i | 0.568403 | + | 0.328168i | ||||
\(46\) | 4.45229 | + | 2.57053i | 0.656454 | + | 0.379004i | ||||
\(47\) | − | 1.05508i | − | 0.153900i | −0.997035 | − | 0.0769500i | \(-0.975482\pi\) | ||
0.997035 | − | 0.0769500i | \(-0.0245182\pi\) | |||||||
\(48\) | −2.25437 | + | 3.90469i | −0.325390 | + | 0.563593i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.38318 | − | 3.10798i | 0.761297 | − | 0.439535i | ||||
\(51\) | −1.62104 | −0.226991 | ||||||||
\(52\) | −5.50074 | − | 16.0317i | −0.762816 | − | 2.22320i | ||||
\(53\) | 7.26568 | 0.998017 | 0.499009 | − | 0.866597i | \(-0.333698\pi\) | ||||
0.499009 | + | 0.866597i | \(0.333698\pi\) | |||||||
\(54\) | −6.66133 | + | 3.84592i | −0.906492 | + | 0.523363i | ||||
\(55\) | −2.18027 | − | 3.77633i | −0.293987 | − | 0.509201i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.90873i | 0.252818i | ||||||||
\(58\) | 12.0445 | + | 6.95390i | 1.58152 | + | 0.913092i | ||||
\(59\) | 9.89352 | + | 5.71203i | 1.28803 | + | 0.743643i | 0.978302 | − | 0.207183i | \(-0.0664297\pi\) |
0.309725 | + | 0.950826i | \(0.399763\pi\) | |||||||
\(60\) | − | 3.92895i | − | 0.507225i | ||||||
\(61\) | 1.46254 | − | 2.53319i | 0.187259 | − | 0.324341i | −0.757077 | − | 0.653326i | \(-0.773373\pi\) |
0.944335 | + | 0.328985i | \(0.106706\pi\) | |||||||
\(62\) | 13.5617 | + | 23.4896i | 1.72234 | + | 2.98318i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.68406 | −0.585507 | ||||||||
\(65\) | 4.38250 | + | 3.81799i | 0.543582 | + | 0.473563i | ||||
\(66\) | 3.63033 | 0.446862 | ||||||||
\(67\) | −11.7622 | + | 6.79091i | −1.43698 | + | 0.829642i | −0.997639 | − | 0.0686778i | \(-0.978122\pi\) |
−0.439343 | + | 0.898320i | \(0.644789\pi\) | |||||||
\(68\) | −7.34886 | − | 12.7286i | −0.891180 | − | 1.54357i | ||||
\(69\) | 0.514846 | − | 0.891740i | 0.0619802 | − | 0.107353i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.17009 | + | 0.675554i | 0.138865 | + | 0.0801736i | 0.567823 | − | 0.823151i | \(-0.307786\pi\) |
−0.428958 | + | 0.903324i | \(0.641119\pi\) | |||||||
\(72\) | −16.5367 | − | 9.54747i | −1.94887 | − | 1.12518i | ||||
\(73\) | − | 9.10335i | − | 1.06547i | −0.846283 | − | 0.532733i | \(-0.821165\pi\) | ||
0.846283 | − | 0.532733i | \(-0.178835\pi\) | |||||||
\(74\) | −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 | 0 | ||||||||
\(78\) | −4.57708 | + | 1.57047i | −0.518252 | + | 0.177821i | ||||
\(79\) | −6.20578 | −0.698205 | −0.349102 | − | 0.937085i | \(-0.613513\pi\) | ||||
−0.349102 | + | 0.937085i | \(0.613513\pi\) | |||||||
\(80\) | 12.1407 | − | 7.00946i | 1.35738 | − | 0.783682i | ||||
\(81\) | −3.32650 | − | 5.76166i | −0.369611 | − | 0.640185i | ||||
\(82\) | −9.96806 | + | 17.2652i | −1.10079 | + | 1.90662i | ||||
\(83\) | − | 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 | ||||
\(86\) | 8.68734i | 0.936780i | ||||||||
\(87\) | 1.39278 | − | 2.41237i | 0.149322 | − | 0.258633i | ||||
\(88\) | 9.45576 | + | 16.3779i | 1.00799 | + | 1.74589i | ||||
\(89\) | −1.52410 | + | 0.879938i | −0.161554 | + | 0.0932732i | −0.578597 | − | 0.815613i | \(-0.696400\pi\) |
0.417043 | + | 0.908887i | \(0.363066\pi\) | |||||||
\(90\) | 11.3972 | 1.20137 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.33607 | 0.973353 | ||||||||
\(93\) | 4.70469 | − | 2.71625i | 0.487853 | − | 0.281662i | ||||
\(94\) | −1.36560 | − | 2.36528i | −0.140851 | − | 0.243960i | ||||
\(95\) | 2.96739 | − | 5.13967i | 0.304448 | − | 0.527319i | ||||
\(96\) | 4.42170i | 0.451288i | ||||||||
\(97\) | −13.4078 | − | 7.74102i | −1.36136 | − | 0.785981i | −0.371555 | − | 0.928411i | \(-0.621175\pi\) |
−0.989805 | + | 0.142430i | \(0.954509\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.38776i | 0.742498i | ||||||||
\(100\) | 5.64404 | − | 9.77576i | 0.564404 | − | 0.977576i | ||||
\(101\) | −0.639651 | − | 1.10791i | −0.0636477 | − | 0.110241i | 0.832446 | − | 0.554107i | \(-0.186940\pi\) |
−0.896093 | + | 0.443866i | \(0.853607\pi\) | |||||||
\(102\) | −3.63404 | + | 2.09811i | −0.359823 | + | 0.207744i | ||||
\(103\) | 11.4673 | 1.12991 | 0.564956 | − | 0.825121i | \(-0.308893\pi\) | ||||
0.564956 | + | 0.825121i | \(0.308893\pi\) | |||||||
\(104\) | −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 | 0.963033 | − | 0.269385i | \(-0.0868205\pi\) |
−0.714811 | + | 0.699318i | \(0.753487\pi\) | |||||||
\(108\) | −6.98412 | + | 12.0969i | −0.672048 | + | 1.16402i | ||||
\(109\) | 1.72783i | 0.165496i | 0.996570 | + | 0.0827481i | \(0.0263697\pi\) | ||||
−0.996570 | + | 0.0827481i | \(0.973630\pi\) | |||||||
\(110\) | −9.77542 | − | 5.64384i | −0.932050 | − | 0.538119i | ||||
\(111\) | 2.67313 | + | 1.54333i | 0.253722 | + | 0.146487i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 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 | ||||
\(115\) | −2.77267 | + | 1.60080i | −0.258552 | + | 0.149275i | ||||
\(116\) | 25.2563 | 2.34499 | ||||||||
\(117\) | −3.19593 | − | 9.31442i | −0.295464 | − | 0.861119i | ||||
\(118\) | 29.5723 | 2.72235 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.92170 | − | 5.06053i | −0.266714 | − | 0.461961i | ||||
\(121\) | −1.84160 | + | 3.18975i | −0.167419 | + | 0.289977i | ||||
\(122\) | − | 7.57184i | − | 0.685522i | ||||||
\(123\) | 3.45801 | + | 1.99648i | 0.311798 | + | 0.180017i | ||||
\(124\) | 42.6567 | + | 24.6279i | 3.83069 | + | 2.21165i | ||||
\(125\) | 11.9313i | 1.06716i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −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 | ||||
\(129\) | 1.73997 | 0.153196 | ||||||||
\(130\) | 14.7663 | + | 2.88688i | 1.29509 | + | 0.253196i | ||||
\(131\) | 10.2092 | 0.891982 | 0.445991 | − | 0.895038i | \(-0.352851\pi\) | ||||
0.445991 | + | 0.895038i | \(0.352851\pi\) | |||||||
\(132\) | 5.70937 | − | 3.29630i | 0.496936 | − | 0.286906i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −17.5790 | + | 30.4476i | −1.51859 | + | 2.63028i | ||||
\(135\) | − | 4.79010i | − | 0.412266i | ||||||
\(136\) | −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 | \(0.807048\pi\) | |||||||
\(138\) | − | 2.66546i | − | 0.226899i | ||||||
\(139\) | 0.832100 | − | 1.44124i | 0.0705778 | − | 0.122244i | −0.828577 | − | 0.559875i | \(-0.810849\pi\) |
0.899155 | + | 0.437631i | \(0.144182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.473738 | + | 0.273513i | −0.0398959 | + | 0.0230339i | ||||
\(142\) | 3.49748 | 0.293502 | ||||||||
\(143\) | −1.87130 | + | 9.57165i | −0.156486 | + | 0.800422i | ||||
\(144\) | −23.7513 | −1.97928 | ||||||||
\(145\) | −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 | ||||||||
\(149\) | −17.1456 | − | 9.89902i | −1.40462 | − | 0.810959i | −0.409760 | − | 0.912193i | \(-0.634387\pi\) |
−0.994863 | + | 0.101234i | \(0.967721\pi\) | |||||||
\(150\) | −2.79100 | − | 1.61138i | −0.227884 | − | 0.131569i | ||||
\(151\) | − | 7.53493i | − | 0.613184i | −0.951841 | − | 0.306592i | \(-0.900811\pi\) | ||
0.951841 | − | 0.306592i | \(-0.0991886\pi\) | |||||||
\(152\) | −12.8695 | + | 22.2906i | −1.04385 | + | 1.80801i | ||||
\(153\) | −4.26968 | − | 7.39531i | −0.345183 | − | 0.597875i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.8912 | −1.35673 | ||||||||
\(156\) | −5.77234 | + | 6.62581i | −0.462157 | + | 0.530489i | ||||
\(157\) | 14.0045 | 1.11768 | 0.558839 | − | 0.829276i | \(-0.311247\pi\) | ||||
0.558839 | + | 0.829276i | \(0.311247\pi\) | |||||||
\(158\) | −13.9121 | + | 8.03214i | −1.10679 | + | 0.639003i | ||||
\(159\) | −1.88350 | − | 3.26232i | −0.149371 | − | 0.258719i | ||||
\(160\) | 6.87414 | − | 11.9064i | 0.543448 | − | 0.941280i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −14.9146 | − | 8.61097i | −1.17181 | − | 0.676542i | ||||
\(163\) | −6.20936 | − | 3.58498i | −0.486355 | − | 0.280797i | 0.236706 | − | 0.971581i | \(-0.423932\pi\) |
−0.723061 | + | 0.690784i | \(0.757265\pi\) | |||||||
\(164\) | 36.2036i | 2.82703i | ||||||||
\(165\) | −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 | \(0.0884328\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.78135 | − | 12.8774i | −0.137027 | − | 0.990567i | ||||
\(170\) | 13.0472 | 1.00068 | ||||||||
\(171\) | −8.70780 | + | 5.02745i | −0.665902 | + | 0.384459i | ||||
\(172\) | 7.88803 | + | 13.6625i | 0.601456 | + | 1.04175i | ||||
\(173\) | −6.40579 | + | 11.0952i | −0.487023 | + | 0.843549i | −0.999889 | − | 0.0149198i | \(-0.995251\pi\) |
0.512865 | + | 0.858469i | \(0.328584\pi\) | |||||||
\(174\) | − | 7.21072i | − | 0.546643i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 20.3717 | + | 11.7616i | 1.53557 | + | 0.886562i | ||||
\(177\) | − | 5.92298i | − | 0.445199i | ||||||
\(178\) | −2.27781 | + | 3.94528i | −0.170729 | + | 0.295711i | ||||
\(179\) | 0.920110 | + | 1.59368i | 0.0687723 | + | 0.119117i | 0.898361 | − | 0.439258i | \(-0.144758\pi\) |
−0.829589 | + | 0.558375i | \(0.811425\pi\) | |||||||
\(180\) | 17.9242 | − | 10.3485i | 1.33599 | − | 0.771334i | ||||
\(181\) | −3.29928 | −0.245234 | −0.122617 | − | 0.992454i | \(-0.539129\pi\) | ||||
−0.122617 | + | 0.992454i | \(0.539129\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.51655 | −0.112107 | ||||||||
\(184\) | 12.0250 | − | 6.94262i | 0.886493 | − | 0.511817i | ||||
\(185\) | −4.79865 | − | 8.31150i | −0.352804 | − | 0.611074i | ||||
\(186\) | 7.03129 | − | 12.1786i | 0.515560 | − | 0.892975i | ||||
\(187\) | 8.45734i | 0.618462i | ||||||||
\(188\) | −4.29531 | − | 2.47990i | −0.313268 | − | 0.180865i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 15.3628i | − | 1.11453i | ||||||
\(191\) | −2.44807 | + | 4.24018i | −0.177136 | + | 0.306809i | −0.940898 | − | 0.338689i | \(-0.890017\pi\) |
0.763762 | + | 0.645498i | \(0.223350\pi\) | |||||||
\(192\) | 1.21426 | + | 2.10316i | 0.0876318 | + | 0.151783i | ||||
\(193\) | −2.61462 | + | 1.50955i | −0.188204 | + | 0.108660i | −0.591142 | − | 0.806568i | \(-0.701323\pi\) |
0.402937 | + | 0.915228i | \(0.367989\pi\) | |||||||
\(194\) | −40.0768 | −2.87735 | ||||||||
\(195\) | 0.578207 | − | 2.95751i | 0.0414063 | − | 0.211792i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 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 | −0.858655 | − | 0.512554i | \(-0.828699\pi\) |
0.873212 | + | 0.487340i | \(0.162033\pi\) | |||||||
\(200\) | − | 16.7884i | − | 1.18712i | ||||||
\(201\) | 6.09830 | + | 3.52085i | 0.430141 | + | 0.248342i | ||||
\(202\) | −2.86793 | − | 1.65580i | −0.201787 | − | 0.116502i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.81013 | + | 6.59934i | −0.266763 | + | 0.462047i | ||||
\(205\) | −6.20762 | − | 10.7519i | −0.433559 | − | 0.750946i | ||||
\(206\) | 25.7074 | − | 14.8422i | 1.79112 | − | 1.03410i | ||||
\(207\) | 5.42425 | 0.377012 | ||||||||
\(208\) | −30.7724 | − | 6.01616i | −2.13368 | − | 0.417146i | ||||
\(209\) | 9.95831 | 0.688831 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.75800 | + | 6.50905i | 0.258711 | + | 0.448101i | 0.965897 | − | 0.258927i | \(-0.0833688\pi\) |
−0.707186 | + | 0.707028i | \(0.750035\pi\) | |||||||
\(212\) | 17.0774 | − | 29.5790i | 1.17288 | − | 2.03149i | ||||
\(213\) | − | 0.700504i | − | 0.0479977i | ||||||
\(214\) | 11.5122 | + | 6.64656i | 0.786956 | + | 0.454349i | ||||
\(215\) | −4.68524 | − | 2.70502i | −0.319531 | − | 0.184481i | ||||
\(216\) | 20.7745i | 1.41353i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.23633 | + | 3.87344i | 0.151464 | + | 0.262343i | ||||
\(219\) | −4.08745 | + | 2.35989i | −0.276204 | + | 0.159467i | ||||
\(220\) | −20.4982 | −1.38199 | ||||||||
\(221\) | −3.65863 | − | 10.6629i | −0.246106 | − | 0.717267i | ||||
\(222\) | 7.99014 | 0.536263 | ||||||||
\(223\) | −19.5544 | + | 11.2897i | −1.30946 | + | 0.756016i | −0.982006 | − | 0.188852i | \(-0.939523\pi\) |
−0.327452 | + | 0.944868i | \(0.606190\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.27918 | − | 5.67971i | 0.218612 | − | 0.378648i | ||||
\(226\) | − | 22.2390i | − | 1.47932i | ||||||
\(227\) | −11.8401 | − | 6.83586i | −0.785853 | − | 0.453712i | 0.0526478 | − | 0.998613i | \(-0.483234\pi\) |
−0.838500 | + | 0.544901i | \(0.816567\pi\) | |||||||
\(228\) | 7.77057 | + | 4.48634i | 0.514618 | + | 0.297115i | ||||
\(229\) | − | 7.93086i | − | 0.524086i | −0.965056 | − | 0.262043i | \(-0.915604\pi\) | ||
0.965056 | − | 0.262043i | \(-0.0843962\pi\) | |||||||
\(230\) | −4.14383 | + | 7.17733i | −0.273236 | + | 0.473259i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 32.5305 | − | 18.7815i | 2.13573 | − | 1.23306i | ||||
\(233\) | 6.57171 | 0.430527 | 0.215263 | − | 0.976556i | \(-0.430939\pi\) | ||||
0.215263 | + | 0.976556i | \(0.430939\pi\) | |||||||
\(234\) | −19.2203 | − | 16.7445i | −1.25647 | − | 1.09462i | ||||
\(235\) | 1.70085 | 0.110951 | ||||||||
\(236\) | 46.5080 | − | 26.8514i | 3.02741 | − | 1.74788i | ||||
\(237\) | 1.60874 | + | 2.78642i | 0.104499 | + | 0.180998i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.39284i | − | 0.607572i | −0.952740 | − | 0.303786i | \(-0.901749\pi\) | ||
0.952740 | − | 0.303786i | \(-0.0982508\pi\) | |||||||
\(240\) | −6.29456 | − | 3.63417i | −0.406312 | − | 0.234584i | ||||
\(241\) | −8.73460 | − | 5.04292i | −0.562645 | − | 0.324843i | 0.191562 | − | 0.981481i | \(-0.438645\pi\) |
−0.754206 | + | 0.656637i | \(0.771978\pi\) | |||||||
\(242\) | 9.53435i | 0.612891i | ||||||||
\(243\) | −6.18182 | + | 10.7072i | −0.396564 | + | 0.686869i | ||||
\(244\) | −6.87517 | − | 11.9081i | −0.440137 | − | 0.762340i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.3362 | 0.659012 | ||||||||
\(247\) | −12.5553 | + | 4.30794i | −0.798878 | + | 0.274108i | ||||
\(248\) | 73.2565 | 4.65179 | ||||||||
\(249\) | −1.21084 | + | 0.699078i | −0.0767337 | + | 0.0443022i | ||||
\(250\) | 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 | \(0.272569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.65242 | − | 2.68607i | −0.292495 | − | 0.168872i | ||||
\(254\) | −7.00363 | − | 4.04355i | −0.439447 | − | 0.253715i | ||||
\(255\) | − | 2.61320i | − | 0.163645i | ||||||
\(256\) | 11.0672 | − | 19.1689i | 0.691697 | − | 1.19805i | ||||
\(257\) | 3.99329 | + | 6.91658i | 0.249095 | + | 0.431445i | 0.963275 | − | 0.268517i | \(-0.0865336\pi\) |
−0.714180 | + | 0.699962i | \(0.753200\pi\) | |||||||
\(258\) | 3.90065 | − | 2.25204i | 0.242844 | − | 0.140206i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 25.8440 | − | 8.86749i | 1.60278 | − | 0.549939i | ||||
\(261\) | 14.6739 | 0.908292 | ||||||||
\(262\) | 22.8869 | − | 13.2138i | 1.41396 | − | 0.816349i | ||||
\(263\) | −2.52967 | − | 4.38152i | −0.155986 | − | 0.270176i | 0.777431 | − | 0.628968i | \(-0.216522\pi\) |
−0.933418 | + | 0.358792i | \(0.883189\pi\) | |||||||
\(264\) | 4.90249 | − | 8.49136i | 0.301727 | − | 0.522607i | ||||
\(265\) | 11.7127i | 0.719503i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.790192 | + | 0.456218i | 0.0483590 | + | 0.0279201i | ||||
\(268\) | 63.8461i | 3.90002i | ||||||||
\(269\) | −6.94512 | + | 12.0293i | −0.423451 | + | 0.733439i | −0.996274 | − | 0.0862400i | \(-0.972515\pi\) |
0.572823 | + | 0.819679i | \(0.305848\pi\) | |||||||
\(270\) | −6.19983 | − | 10.7384i | −0.377310 | − | 0.653519i | ||||
\(271\) | 7.21158 | − | 4.16361i | 0.438072 | − | 0.252921i | −0.264707 | − | 0.964329i | \(-0.585275\pi\) |
0.702780 | + | 0.711408i | \(0.251942\pi\) | |||||||
\(272\) | −27.1900 | −1.64863 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.8669 | −1.56267 | ||||||||
\(275\) | −5.62515 | + | 3.24768i | −0.339210 | + | 0.195843i | ||||
\(276\) | −2.42022 | − | 4.19194i | −0.145680 | − | 0.252325i | ||||
\(277\) | −11.6058 | + | 20.1018i | −0.697325 | + | 1.20780i | 0.272066 | + | 0.962279i | \(0.412293\pi\) |
−0.969391 | + | 0.245523i | \(0.921040\pi\) | |||||||
\(278\) | − | 4.30795i | − | 0.258374i | ||||||
\(279\) | 24.7835 | + | 14.3088i | 1.48375 | + | 0.856644i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.1595i | − | 1.62020i | −0.586292 | − | 0.810100i | \(-0.699413\pi\) | ||
0.586292 | − | 0.810100i | \(-0.300587\pi\) | |||||||
\(282\) | −0.708015 | + | 1.22632i | −0.0421617 | + | 0.0730262i | ||||
\(283\) | −8.07563 | − | 13.9874i | −0.480046 | − | 0.831464i | 0.519692 | − | 0.854354i | \(-0.326047\pi\) |
−0.999738 | + | 0.0228894i | \(0.992713\pi\) | |||||||
\(284\) | 5.50044 | − | 3.17568i | 0.326391 | − | 0.188442i | ||||
\(285\) | −3.07698 | −0.182265 | ||||||||
\(286\) | 8.19351 | + | 23.8797i | 0.484493 | + | 1.41204i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −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 | ||||
\(291\) | 8.02691i | 0.470546i | ||||||||
\(292\) | −37.0603 | − | 21.3968i | −2.16879 | − | 1.25215i | ||||
\(293\) | −12.6831 | − | 7.32260i | −0.740956 | − | 0.427791i | 0.0814609 | − | 0.996677i | \(-0.474041\pi\) |
−0.822417 | + | 0.568885i | \(0.807375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.20810 | + | 15.9489i | −0.536116 | + | 0.928580i | ||||
\(296\) | 20.8116 | + | 36.0468i | 1.20965 | + | 2.09517i | ||||
\(297\) | 6.96075 | − | 4.01879i | 0.403904 | − | 0.233194i | ||||
\(298\) | −51.2492 | −2.96879 | ||||||||
\(299\) | 7.02771 | + | 1.37395i | 0.406423 | + | 0.0794577i | ||||
\(300\) | −5.85248 | −0.337893 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.75246 | − | 16.8918i | −0.561191 | − | 0.972011i | ||||
\(303\) | −0.331637 | + | 0.574412i | −0.0190521 | + | 0.0329991i | ||||
\(304\) | 32.0155i | 1.83622i | ||||||||
\(305\) | 4.08363 | + | 2.35769i | 0.233828 | + | 0.135001i | ||||
\(306\) | −19.1435 | − | 11.0525i | −1.09436 | − | 0.631830i | ||||
\(307\) | 8.97844i | 0.512427i | 0.966620 | + | 0.256213i | \(0.0824750\pi\) | ||||
−0.966620 | + | 0.256213i | \(0.917525\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.97271 | − | 5.14889i | −0.169112 | − | 0.292910i | ||||
\(310\) | −37.8665 | + | 21.8622i | −2.15067 | + | 1.24169i | ||||
\(311\) | −12.1816 | −0.690755 | −0.345378 | − | 0.938464i | \(-0.612249\pi\) | ||||
−0.345378 | + | 0.938464i | \(0.612249\pi\) | |||||||
\(312\) | −2.50767 | + | 12.8266i | −0.141969 | + | 0.726165i | ||||
\(313\) | 13.1240 | 0.741810 | 0.370905 | − | 0.928671i | \(-0.379047\pi\) | ||||
0.370905 | + | 0.928671i | \(0.379047\pi\) | |||||||
\(314\) | 31.3951 | − | 18.1260i | 1.77173 | − | 1.02291i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.5862 | + | 25.2641i | −0.820540 | + | 1.42122i | ||||
\(317\) | − | 16.7155i | − | 0.938836i | −0.882976 | − | 0.469418i | \(-0.844464\pi\) | ||
0.882976 | − | 0.469418i | \(-0.155536\pi\) | |||||||
\(318\) | −8.44485 | − | 4.87563i | −0.473564 | − | 0.273412i | ||||
\(319\) | −12.5859 | − | 7.26648i | −0.704675 | − | 0.406845i | ||||
\(320\) | − | 7.55095i | − | 0.422111i | ||||||
\(321\) | 1.33123 | − | 2.30575i | 0.0743018 | − | 0.128695i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.96849 | + | 5.75531i | −0.554661 | + | 0.320234i | ||||
\(324\) | −31.2748 | −1.73749 | ||||||||
\(325\) | 5.68720 | − | 6.52808i | 0.315469 | − | 0.362113i | ||||
\(326\) | −18.5601 | −1.02795 | ||||||||
\(327\) | 0.775804 | − | 0.447911i | 0.0429021 | − | 0.0247695i | ||||
\(328\) | 26.9223 | + | 46.6307i | 1.48653 | + | 2.57475i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.85228i | 0.322157i | ||||||||
\(331\) | 3.43522 | + | 1.98332i | 0.188817 | + | 0.109013i | 0.591428 | − | 0.806357i | \(-0.298564\pi\) |
−0.402612 | + | 0.915371i | \(0.631898\pi\) | |||||||
\(332\) | −10.9785 | − | 6.33843i | −0.602523 | − | 0.347867i | ||||
\(333\) | 16.2600i | 0.891045i | ||||||||
\(334\) | 23.2722 | − | 40.3087i | 1.27340 | − | 2.20559i | ||||
\(335\) | −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 | \(0.621750\pi\) | |||||||
\(338\) | −20.6606 | − | 26.5628i | −1.12379 | − | 1.44483i | ||||
\(339\) | −4.45421 | −0.241919 | ||||||||
\(340\) | 20.5192 | − | 11.8468i | 1.11281 | − | 0.642481i | ||||
\(341\) | −14.1713 | − | 24.5455i | −0.767420 | − | 1.32921i | ||||
\(342\) | −13.0141 | + | 22.5410i | −0.703720 | + | 1.21888i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 20.3197 | + | 11.7316i | 1.09557 | + | 0.632526i | ||||
\(345\) | 1.43753 | + | 0.829960i | 0.0773942 | + | 0.0446835i | ||||
\(346\) | 33.1641i | 1.78291i | ||||||||
\(347\) | 13.1989 | − | 22.8612i | 0.708556 | − | 1.22725i | −0.256837 | − | 0.966455i | \(-0.582680\pi\) |
0.965393 | − | 0.260800i | \(-0.0839863\pi\) | |||||||
\(348\) | −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 | \(0.375115\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.03753 | + | 8.07806i | −0.375636 | + | 0.431175i | ||||
\(352\) | 23.0690 | 1.22958 | ||||||||
\(353\) | 11.7413 | − | 6.77886i | 0.624928 | − | 0.360802i | −0.153857 | − | 0.988093i | \(-0.549170\pi\) |
0.778785 | + | 0.627291i | \(0.215836\pi\) | |||||||
\(354\) | −7.66612 | − | 13.2781i | −0.407450 | − | 0.705724i | ||||
\(355\) | −1.08903 | + | 1.88626i | −0.0577997 | + | 0.100112i | ||||
\(356\) | 8.27291i | 0.438464i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.12540 | + | 2.38180i | 0.218034 | + | 0.125882i | ||||
\(359\) | − | 8.58568i | − | 0.453135i | −0.973996 | − | 0.226567i | \(-0.927250\pi\) | ||
0.973996 | − | 0.226567i | \(-0.0727503\pi\) | |||||||
\(360\) | 15.3910 | − | 26.6581i | 0.811179 | − | 1.40500i | ||||
\(361\) | −2.72326 | − | 4.71683i | −0.143330 | − | 0.248254i | ||||
\(362\) | −7.39632 | + | 4.27026i | −0.388742 | + | 0.224440i | ||||
\(363\) | 1.90962 | 0.100229 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6751 | 0.768130 | ||||||||
\(366\) | −3.39979 | + | 1.96287i | −0.177710 | + | 0.102601i | ||||
\(367\) | 0.831612 | + | 1.44039i | 0.0434098 | + | 0.0751880i | 0.886914 | − | 0.461935i | \(-0.152845\pi\) |
−0.843504 | + | 0.537123i | \(0.819511\pi\) | |||||||
\(368\) | 8.63560 | − | 14.9573i | 0.450162 | − | 0.779703i | ||||
\(369\) | 21.0343i | 1.09500i | ||||||||
\(370\) | −21.5152 | − | 12.4218i | −1.11852 | − | 0.645778i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 25.5374i | − | 1.32405i | ||||||
\(373\) | −6.98174 | + | 12.0927i | −0.361501 | + | 0.626138i | −0.988208 | − | 0.153117i | \(-0.951069\pi\) |
0.626707 | + | 0.779255i | \(0.284402\pi\) | |||||||
\(374\) | 10.9463 | + | 18.9596i | 0.566022 | + | 0.980378i | ||||
\(375\) | 5.35719 | − | 3.09298i | 0.276644 | − | 0.159721i | ||||
\(376\) | −7.37655 | −0.380417 | ||||||||
\(377\) | 19.0117 | + | 3.71687i | 0.979150 | + | 0.191429i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −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 | ||||
\(382\) | 12.6741i | 0.648466i | ||||||||
\(383\) | 27.6333 | + | 15.9541i | 1.41200 | + | 0.815217i | 0.995576 | − | 0.0939554i | \(-0.0299511\pi\) |
0.416420 | + | 0.909172i | \(0.363284\pi\) | |||||||
\(384\) | −2.21435 | − | 1.27846i | −0.113001 | − | 0.0652410i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.90762 | + | 6.76820i | −0.198893 | + | 0.344492i | ||||
\(387\) | 4.58294 | + | 7.93788i | 0.232964 | + | 0.403505i | ||||
\(388\) | −63.0283 | + | 36.3894i | −3.19978 | + | 1.84739i | ||||
\(389\) | 25.4150 | 1.28859 | 0.644296 | − | 0.764776i | \(-0.277150\pi\) | ||||
0.644296 | + | 0.764776i | \(0.277150\pi\) | |||||||
\(390\) | −2.53168 | − | 7.37850i | −0.128197 | − | 0.373625i | ||||
\(391\) | 6.20956 | 0.314031 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.64656 | − | 4.58398i | −0.133501 | − | 0.231231i | ||||
\(394\) | 6.01838 | − | 10.4241i | 0.303202 | − | 0.525161i | ||||
\(395\) | − | 10.0041i | − | 0.503358i | ||||||
\(396\) | 30.0760 | + | 17.3644i | 1.51138 | + | 0.872593i | ||||
\(397\) | 3.60178 | + | 2.07949i | 0.180768 | + | 0.104366i | 0.587653 | − | 0.809113i | \(-0.300052\pi\) |
−0.406885 | + | 0.913479i | \(0.633385\pi\) | |||||||
\(398\) | − | 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 | \(0.170541\pi\) | |||||||
\(402\) | 18.2282 | 0.909139 | ||||||||
\(403\) | 28.4854 | + | 24.8162i | 1.41896 | + | 1.23618i | ||||
\(404\) | −6.01381 | −0.299198 | ||||||||
\(405\) | 9.28811 | − | 5.36249i | 0.461530 | − | 0.266464i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.05193 | − | 13.9463i | 0.399119 | − | 0.691295i | ||||
\(408\) | 11.3334i | 0.561086i | ||||||||
\(409\) | 15.2712 | + | 8.81685i | 0.755114 | + | 0.435965i | 0.827539 | − | 0.561409i | \(-0.189740\pi\) |
−0.0724249 | + | 0.997374i | \(0.523074\pi\) | |||||||
\(410\) | −27.8324 | − | 16.0690i | −1.37454 | − | 0.793594i | ||||
\(411\) | 5.18083i | 0.255551i | ||||||||
\(412\) | 26.9532 | − | 46.6842i | 1.32789 | − | 2.29997i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.1601 | − | 7.02061i | 0.597634 | − | 0.345044i | ||||
\(415\) | 4.34725 | 0.213398 | ||||||||
\(416\) | −29.0852 | + | 9.97961i | −1.42602 | + | 0.489291i | ||||
\(417\) | −0.862831 | −0.0422530 | ||||||||
\(418\) | 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 | \(-0.427210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.8528i | − | 0.626407i | −0.949686 | − | 0.313203i | \(-0.898598\pi\) | ||
0.949686 | − | 0.313203i | \(-0.101402\pi\) | |||||||
\(422\) | 16.8493 | + | 9.72796i | 0.820212 | + | 0.473550i | ||||
\(423\) | −2.49557 | − | 1.44082i | −0.121339 | − | 0.0700551i | ||||
\(424\) | − | 50.7975i | − | 2.46694i | ||||||
\(425\) | 3.75393 | − | 6.50200i | 0.182093 | − | 0.315394i | ||||
\(426\) | −0.906662 | − | 1.57038i | −0.0439279 | − | 0.0760854i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.1401 | 1.16685 | ||||||||
\(429\) | 4.78282 | − | 1.64106i | 0.230917 | − | 0.0792313i | ||||
\(430\) | −14.0045 | −0.675355 | ||||||||
\(431\) | −7.76876 | + | 4.48530i | −0.374208 | + | 0.216049i | −0.675295 | − | 0.737547i | \(-0.735984\pi\) |
0.301087 | + | 0.953597i | \(0.402650\pi\) | |||||||
\(432\) | 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 | \(0.193089\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.88887 | + | 2.24524i | 0.186457 | + | 0.107651i | ||||
\(436\) | 7.03410 | + | 4.06114i | 0.336872 | + | 0.194493i | ||||
\(437\) | − | 7.31161i | − | 0.349762i | ||||||
\(438\) | −6.10881 | + | 10.5808i | −0.291890 | + | 0.505569i | ||||
\(439\) | −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 | ||||
\(443\) | −15.0399 | −0.714569 | −0.357284 | − | 0.933996i | \(-0.616297\pi\) | ||||
−0.357284 | + | 0.933996i | \(0.616297\pi\) | |||||||
\(444\) | 12.5660 | − | 7.25498i | 0.596356 | − | 0.344306i | ||||
\(445\) | −1.41851 | − | 2.45693i | −0.0672437 | − | 0.116469i | ||||
\(446\) | −29.2246 | + | 50.6185i | −1.38382 | + | 2.39685i | ||||
\(447\) | 10.2646i | 0.485499i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.7087 | + | 19.4617i | 1.59081 | + | 0.918456i | 0.993168 | + | 0.116696i | \(0.0372304\pi\) |
0.597646 | + | 0.801760i | \(0.296103\pi\) | |||||||
\(450\) | − | 16.9770i | − | 0.800303i | ||||||
\(451\) | 10.4161 | − | 18.0412i | 0.490476 | − | 0.849529i | ||||
\(452\) | −20.1928 | − | 34.9750i | −0.949790 | − | 1.64509i | ||||
\(453\) | −3.38322 | + | 1.95330i | −0.158957 | + | 0.0917741i | ||||
\(454\) | −35.3906 | −1.66097 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.3448 | 0.624927 | ||||||||
\(457\) | 12.0721 | − | 6.96982i | 0.564708 | − | 0.326034i | −0.190325 | − | 0.981721i | \(-0.560954\pi\) |
0.755033 | + | 0.655687i | \(0.227621\pi\) | |||||||
\(458\) | −10.2649 | − | 17.7793i | −0.479648 | − | 0.830774i | ||||
\(459\) | −4.64524 | + | 8.04580i | −0.216821 | + | 0.375546i | ||||
\(460\) | 15.0502i | 0.701721i | ||||||||
\(461\) | 32.4443 | + | 18.7317i | 1.51108 | + | 0.872424i | 0.999916 | + | 0.0129430i | \(0.00412001\pi\) |
0.511167 | + | 0.859481i | \(0.329213\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.75275i | 0.313827i | 0.987612 | + | 0.156913i | \(0.0501544\pi\) | ||||
−0.987612 | + | 0.156913i | \(0.949846\pi\) | |||||||
\(464\) | 23.3614 | − | 40.4631i | 1.08453 | − | 1.87845i | ||||
\(465\) | 4.37875 | + | 7.58421i | 0.203059 | + | 0.351709i | ||||
\(466\) | 14.7324 | − | 8.50576i | 0.682466 | − | 0.394022i | ||||
\(467\) | −5.05032 | −0.233701 | −0.116851 | − | 0.993150i | \(-0.537280\pi\) | ||||
−0.116851 | + | 0.993150i | \(0.537280\pi\) | |||||||
\(468\) | −45.4314 | − | 8.88205i | −2.10006 | − | 0.410573i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 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 | ||||
\(473\) | − | 9.07783i | − | 0.417399i | ||||||
\(474\) | 7.21294 | + | 4.16439i | 0.331301 | + | 0.191277i | ||||
\(475\) | −7.65595 | − | 4.42017i | −0.351279 | − | 0.202811i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.92198 | − | 17.1854i | 0.454296 | − | 0.786864i | ||||
\(478\) | −12.1572 | − | 21.0568i | −0.556055 | − | 0.963116i | ||||
\(479\) | −8.18670 | + | 4.72659i | −0.374060 | + | 0.215964i | −0.675231 | − | 0.737607i | \(-0.735956\pi\) |
0.301171 | + | 0.953570i | \(0.402623\pi\) | |||||||
\(480\) | −7.12801 | −0.325348 | ||||||||
\(481\) | −4.11864 | + | 21.0667i | −0.187794 | + | 0.960558i | ||||
\(482\) | −26.1082 | −1.18920 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.65711 | + | 14.9946i | 0.393505 | + | 0.681571i | ||||
\(485\) | 12.4789 | − | 21.6142i | 0.566639 | − | 0.981448i | ||||
\(486\) | 32.0045i | 1.45175i | ||||||||
\(487\) | −34.6407 | − | 19.9998i | −1.56972 | − | 0.906277i | −0.996201 | − | 0.0870831i | \(-0.972245\pi\) |
−0.573517 | − | 0.819194i | \(-0.694421\pi\) | |||||||
\(488\) | −17.7106 | − | 10.2252i | −0.801721 | − | 0.462874i | ||||
\(489\) | 3.71737i | 0.168105i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −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 | ||||
\(493\) | 16.7984 | 0.756560 | ||||||||
\(494\) | −22.5707 | + | 25.9079i | −1.01551 | + | 1.16565i | ||||
\(495\) | −11.9095 | −0.535291 | ||||||||
\(496\) | 78.9125 | − | 45.5602i | 3.54328 | − | 2.04571i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.80963 | + | 3.13438i | −0.0810916 | + | 0.140455i | ||||
\(499\) | 11.3575i | 0.508433i | 0.967147 | + | 0.254217i | \(0.0818176\pi\) | ||||
−0.967147 | + | 0.254217i | \(0.918182\pi\) | |||||||
\(500\) | 48.5729 | + | 28.0436i | 2.17225 | + | 1.25415i | ||||
\(501\) | −8.07335 | − | 4.66115i | −0.360691 | − | 0.208245i | ||||
\(502\) | 26.7882i | 1.19562i | ||||||||
\(503\) | 6.96423 | − | 12.0624i | 0.310520 | − | 0.537836i | −0.667955 | − | 0.744202i | \(-0.732830\pi\) |
0.978475 | + | 0.206365i | \(0.0661635\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.78601 | − | 1.03115i | 0.0794763 | − | 0.0458857i | ||||
\(506\) | −13.9063 | −0.618212 | ||||||||
\(507\) | −5.32022 | + | 4.13807i | −0.236279 | + | 0.183778i | ||||
\(508\) | −14.6860 | −0.651587 | ||||||||
\(509\) | −17.1602 | + | 9.90746i | −0.760614 | + | 0.439141i | −0.829516 | − | 0.558483i | \(-0.811384\pi\) |
0.0689022 | + | 0.997623i | \(0.478050\pi\) | |||||||
\(510\) | −3.38227 | − | 5.85826i | −0.149769 | − | 0.259408i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 47.4335i | − | 2.09628i | ||||||
\(513\) | 9.47373 | + | 5.46966i | 0.418276 | + | 0.241491i | ||||
\(514\) | 17.9043 | + | 10.3370i | 0.789724 | + | 0.455947i | ||||
\(515\) | 18.4860i | 0.814590i | ||||||||
\(516\) | 4.08967 | − | 7.08352i | 0.180038 | − | 0.311835i | ||||
\(517\) | 1.42698 | + | 2.47160i | 0.0627585 | + | 0.108701i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.64237 | 0.291568 | ||||||||
\(520\) | 26.6932 | − | 30.6399i | 1.17057 | − | 1.34365i | ||||
\(521\) | −31.0951 | −1.36230 | −0.681151 | − | 0.732143i | \(-0.738520\pi\) | ||||
−0.681151 | + | 0.732143i | \(0.738520\pi\) | |||||||
\(522\) | 32.8959 | − | 18.9924i | 1.43981 | − | 0.831277i | ||||
\(523\) | −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 | ||||
\(527\) | 28.3716 | + | 16.3804i | 1.23589 | + | 0.713540i | ||||
\(528\) | − | 12.1960i | − | 0.530761i | ||||||
\(529\) | 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 | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.32794 | + | 27.2522i | −0.230779 | + | 1.18043i | ||||
\(534\) | 2.36193 | 0.102211 | ||||||||
\(535\) | −7.16922 | + | 4.13915i | −0.309952 | + | 0.178951i | ||||
\(536\) | 47.4782 | + | 82.2346i | 2.05074 | + | 3.55199i | ||||
\(537\) | 0.477046 | − | 0.826267i | 0.0205860 | − | 0.0356561i | ||||
\(538\) | 35.9563i | 1.55018i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −19.5008 | − | 11.2588i | −0.839180 | − | 0.484501i | ||||
\(541\) | − | 2.09872i | − | 0.0902310i | −0.998982 | − | 0.0451155i | \(-0.985634\pi\) | ||
0.998982 | − | 0.0451155i | \(-0.0143656\pi\) | |||||||
\(542\) | 10.7779 | − | 18.6679i | 0.462951 | − | 0.801855i | ||||
\(543\) | 0.855283 | + | 1.48139i | 0.0367037 | + | 0.0635727i | ||||
\(544\) | −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 | ||||
\(549\) | −3.99447 | − | 6.91862i | −0.170480 | − | 0.295280i | ||||
\(550\) | −8.40696 | + | 14.5613i | −0.358474 | + | 0.620895i | ||||
\(551\) | − | 19.7797i | − | 0.842642i | ||||||
\(552\) | −6.23454 | − | 3.59951i | −0.265360 | − | 0.153205i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 60.0855i | 2.55279i | ||||||||
\(555\) | −2.48794 | + | 4.30923i | −0.105607 | + | 0.182917i | ||||
\(556\) | −3.91158 | − | 6.77506i | −0.165888 | − | 0.287327i | ||||
\(557\) | 38.3219 | − | 22.1252i | 1.62375 | − | 0.937473i | 0.637846 | − | 0.770164i | \(-0.279826\pi\) |
0.985904 | − | 0.167309i | \(-0.0535078\pi\) | |||||||
\(558\) | 74.0794 | 3.13603 | ||||||||
\(559\) | 3.92705 | + | 11.4452i | 0.166097 | + | 0.484082i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 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 | 0.0865108 | + | 0.996251i | \(0.472428\pi\) |
−0.906034 | + | 0.423205i | \(0.860905\pi\) | |||||||
\(564\) | 2.57149i | 0.108279i | ||||||||
\(565\) | 11.9939 | + | 6.92468i | 0.504587 | + | 0.291324i | ||||
\(566\) | −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 | \(0.251983\pi\) |
0.264832 | + | 0.964294i | \(0.414683\pi\) | |||||||
\(570\) | −6.89796 | + | 3.98254i | −0.288924 | + | 0.166810i | ||||
\(571\) | −21.1368 | −0.884548 | −0.442274 | − | 0.896880i | \(-0.645828\pi\) | ||||
−0.442274 | + | 0.896880i | \(0.645828\pi\) | |||||||
\(572\) | 34.5684 | + | 30.1157i | 1.44538 | + | 1.25920i | ||||
\(573\) | 2.53848 | 0.106047 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.38452 | + | 4.13011i | 0.0994413 | + | 0.172237i | ||||
\(576\) | −6.39653 | + | 11.0791i | −0.266522 | + | 0.461630i | ||||
\(577\) | 25.3304i | 1.05452i | 0.849705 | + | 0.527259i | \(0.176780\pi\) | ||||
−0.849705 | + | 0.527259i | \(0.823220\pi\) | |||||||
\(578\) | 16.1955 | + | 9.35045i | 0.673642 | + | 0.388927i | ||||
\(579\) | 1.35559 | + | 0.782650i | 0.0563364 | + | 0.0325258i | ||||
\(580\) | 40.7146i | 1.69058i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.3892 | + | 17.9947i | 0.430647 | + | 0.745903i | ||||
\(583\) | −17.0203 | + | 9.82667i | −0.704908 | + | 0.406979i | ||||
\(584\) | −63.6455 | −2.63367 | ||||||||
\(585\) | 15.0153 | − | 5.15201i | 0.620808 | − | 0.213009i | ||||
\(586\) | −37.9106 | −1.56607 | ||||||||
\(587\) | 3.08554 | − | 1.78144i | 0.127354 | − | 0.0735278i | −0.434970 | − | 0.900445i | \(-0.643241\pi\) |
0.562324 | + | 0.826917i | \(0.309908\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.2875 | − | 33.4069i | 0.794727 | − | 1.37651i | ||||
\(590\) | 47.6722i | 1.96263i | ||||||||
\(591\) | −2.08783 | − | 1.20541i | −0.0858819 | − | 0.0495839i | ||||
\(592\) | 44.8369 | + | 25.8866i | 1.84278 | + | 1.06393i | ||||
\(593\) | − | 25.3536i | − | 1.04115i | −0.853817 | − | 0.520573i | \(-0.825718\pi\) | ||
0.853817 | − | 0.520573i | \(-0.174282\pi\) | |||||||
\(594\) | 10.4030 | − | 18.0186i | 0.426842 | − | 0.739312i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −80.5990 | + | 46.5338i | −3.30146 | + | 1.90610i | ||||
\(597\) | −0.212945 | −0.00871524 | ||||||||
\(598\) | 17.5330 | − | 6.01585i | 0.716977 | − | 0.246007i | ||||
\(599\) | 10.9216 | 0.446243 | 0.223122 | − | 0.974791i | \(-0.428375\pi\) | ||||
0.223122 | + | 0.974791i | \(0.428375\pi\) | |||||||
\(600\) | −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 | \(0.998063\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.0946i | 1.51061i | ||||||||
\(604\) | −30.6751 | − | 17.7103i | −1.24815 | − | 0.720621i | ||||
\(605\) | −5.14205 | − | 2.96876i | −0.209054 | − | 0.120697i | ||||
\(606\) | 1.71695i | 0.0697464i | ||||||||
\(607\) | 4.92724 | − | 8.53422i | 0.199990 | − | 0.346393i | −0.748535 | − | 0.663096i | \(-0.769242\pi\) |
0.948525 | + | 0.316702i | \(0.102576\pi\) | |||||||
\(608\) | 15.6987 | + | 27.1910i | 0.636667 | + | 1.10274i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.2062 | 0.494215 | ||||||||
\(611\) | −2.86833 | − | 2.49886i | −0.116040 | − | 0.101093i | ||||
\(612\) | −40.1423 | −1.62266 | ||||||||
\(613\) | 3.18428 | − | 1.83844i | 0.128612 | − | 0.0742540i | −0.434314 | − | 0.900762i | \(-0.643009\pi\) |
0.562926 | + | 0.826508i | \(0.309676\pi\) | |||||||
\(614\) | 11.6208 | + | 20.1278i | 0.468977 | + | 0.812293i | ||||
\(615\) | −3.21844 | + | 5.57450i | −0.129780 | + | 0.224785i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.2352 | + | 9.37341i | 0.653605 | + | 0.377359i | 0.789836 | − | 0.613318i | \(-0.210166\pi\) |
−0.136231 | + | 0.990677i | \(0.543499\pi\) | |||||||
\(618\) | −13.3284 | − | 7.69517i | −0.536148 | − | 0.309545i | ||||
\(619\) | 15.8945i | 0.638854i | 0.947611 | + | 0.319427i | \(0.103490\pi\) | ||||
−0.947611 | + | 0.319427i | \(0.896510\pi\) | |||||||
\(620\) | −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 | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.27594 | + | 15.3765i | 0.211207 | + | 0.615555i | ||||
\(625\) | −7.22743 | −0.289097 | ||||||||
\(626\) | 29.4212 | − | 16.9864i | 1.17591 | − | 0.678911i | ||||
\(627\) | −2.58152 | − | 4.47133i | −0.103096 | − | 0.178568i | ||||
\(628\) | 32.9165 | − | 57.0130i | 1.31351 | − | 2.27507i | ||||
\(629\) | 18.6141i | 0.742194i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.0998 | − | 9.87255i | −0.680731 | − | 0.393020i | 0.119400 | − | 0.992846i | \(-0.461903\pi\) |
−0.800130 | + | 0.599826i | \(0.795236\pi\) | |||||||
\(632\) | 43.3873i | 1.72585i | ||||||||
\(633\) | 1.94839 | − | 3.37472i | 0.0774417 | − | 0.134133i | ||||
\(634\) | −21.6349 | − | 37.4727i | −0.859231 | − | 1.48823i | ||||
\(635\) | 4.36151 | − | 2.51812i | 0.173081 | − | 0.0999286i | ||||
\(636\) | −17.7081 | −0.702173 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −37.6200 | −1.48939 | ||||||||
\(639\) | 3.19575 | − | 1.84507i | 0.126422 | − | 0.0729898i | ||||
\(640\) | 3.97508 | + | 6.88504i | 0.157129 | + | 0.272155i | ||||
\(641\) | −14.8893 | + | 25.7890i | −0.588092 | + | 1.01860i | 0.406390 | + | 0.913699i | \(0.366787\pi\) |
−0.994482 | + | 0.104905i | \(0.966546\pi\) | |||||||
\(642\) | − | 6.89203i | − | 0.272007i | ||||||
\(643\) | 10.0220 | + | 5.78623i | 0.395231 | + | 0.228187i | 0.684424 | − | 0.729084i | \(-0.260054\pi\) |
−0.289193 | + | 0.957271i | \(0.593387\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.80493i | 0.110444i | ||||||||
\(646\) | −14.8982 | + | 25.8044i | −0.586162 | + | 1.01526i | ||||
\(647\) | 12.7533 | + | 22.0893i | 0.501382 | + | 0.868420i | 0.999999 | + | 0.00159698i | \(0.000508335\pi\) |
−0.498616 | + | 0.866823i | \(0.666158\pi\) | |||||||
\(648\) | −40.2823 | + | 23.2570i | −1.58244 | + | 0.913620i | ||||
\(649\) | −30.9016 | −1.21299 | ||||||||
\(650\) | 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 | \(0.173893\pi\) |
0.0227004 | + | 0.999742i | \(0.492774\pi\) | |||||||
\(654\) | 1.15946 | − | 2.00825i | 0.0453386 | − | 0.0785287i | ||||
\(655\) | 16.4578i | 0.643058i | ||||||||
\(656\) | 58.0018 | + | 33.4874i | 2.26459 | + | 1.30746i | ||||
\(657\) | −21.5320 | − | 12.4315i | −0.840043 | − | 0.484999i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −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 | ||||
\(661\) | 18.9606 | − | 10.9469i | 0.737481 | − | 0.425785i | −0.0836719 | − | 0.996493i | \(-0.526665\pi\) |
0.821153 | + | 0.570709i | \(0.193331\pi\) | |||||||
\(662\) | 10.2681 | 0.399080 | ||||||||
\(663\) | −3.83927 | + | 4.40692i | −0.149105 | + | 0.171151i | ||||
\(664\) | −18.8539 | −0.731673 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 21.0454 | + | 36.4517i | 0.815492 | + | 1.41247i | ||||
\(667\) | −5.33520 | + | 9.24084i | −0.206580 | + | 0.357807i | ||||
\(668\) | − | 84.5239i | − | 3.27033i | ||||||
\(669\) | 10.1383 | + | 5.85334i | 0.391968 | + | 0.226303i | ||||
\(670\) | −49.0832 | − | 28.3382i | −1.89625 | − | 1.09480i | ||||
\(671\) | 7.91219i | 0.305447i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 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 | ||||
\(675\) | −7.13524 | −0.274635 | ||||||||
\(676\) | −56.6115 | − | 23.0153i | −2.17736 | − | 0.885205i | ||||
\(677\) | 2.55532 | 0.0982089 | 0.0491044 | − | 0.998794i | \(-0.484363\pi\) | ||||
0.0491044 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(678\) | −9.98541 | + | 5.76508i | −0.383488 | + | 0.221407i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 17.6193 | − | 30.5175i | 0.675670 | − | 1.17029i | ||||
\(681\) | 7.08832i | 0.271625i | ||||||||
\(682\) | −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 | \(0.427004\pi\) | |||||||
\(684\) | 47.2666i | 1.80728i | ||||||||
\(685\) | 8.05431 | − | 13.9505i | 0.307739 | − | 0.533020i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.56099 | + | 2.05594i | −0.135860 | + | 0.0784390i | ||||
\(688\) | 29.1848 | 1.11266 | ||||||||
\(689\) | 17.2080 | − | 19.7523i | 0.655574 | − | 0.752503i | ||||
\(690\) | 4.29687 | 0.163579 | ||||||||
\(691\) | −22.5419 | + | 13.0146i | −0.857536 | + | 0.495099i | −0.863186 | − | 0.504885i | \(-0.831535\pi\) |
0.00565028 | + | 0.999984i | \(0.498201\pi\) | |||||||
\(692\) | 30.1127 | + | 52.1567i | 1.14471 | + | 1.98270i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 68.3335i | − | 2.59391i | ||||||
\(695\) | 2.32336 | + | 1.34139i | 0.0881299 | + | 0.0508818i | ||||
\(696\) | −16.8659 | − | 9.73755i | −0.639301 | − | 0.369101i | ||||
\(697\) | 24.0796i | 0.912079i | ||||||||
\(698\) | −6.32944 | + | 10.9629i | −0.239573 | + | 0.414952i | ||||
\(699\) | −1.70360 | − | 2.95073i | −0.0644362 | − | 0.111607i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.12731 | −0.0425779 | −0.0212890 | − | 0.999773i | \(-0.506777\pi\) | ||||
−0.0212890 | + | 0.999773i | \(0.506777\pi\) | |||||||
\(702\) | −5.32126 | + | 27.2180i | −0.200838 | + | 1.02728i | ||||
\(703\) | 21.9177 | 0.826641 | ||||||||
\(704\) | 10.9727 | − | 6.33509i | 0.413549 | − | 0.238763i | ||||
\(705\) | −0.440917 | − | 0.763691i | −0.0166059 | − | 0.0287623i | ||||
\(706\) | 17.5478 | − | 30.3936i | 0.660419 | − | 1.14388i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −24.1128 | − | 13.9215i | −0.906215 | − | 0.523203i | ||||
\(709\) | 5.23972 | + | 3.02515i | 0.196782 | + | 0.113612i | 0.595153 | − | 0.803612i | \(-0.297091\pi\) |
−0.398372 | + | 0.917224i | \(0.630425\pi\) | |||||||
\(710\) | 5.63813i | 0.211595i | ||||||||
\(711\) | −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 | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.4300 | − | 3.01664i | −0.577050 | − | 0.112816i | ||||
\(716\) | 8.65061 | 0.323288 | ||||||||
\(717\) | −4.21743 | + | 2.43493i | −0.157503 | + | 0.0909342i | ||||
\(718\) | −11.1124 | − | 19.2473i | −0.414713 | − | 0.718304i | ||||
\(719\) | 23.5589 | − | 40.8052i | 0.878597 | − | 1.52178i | 0.0257170 | − | 0.999669i | \(-0.491813\pi\) |
0.852880 | − | 0.522106i | \(-0.174854\pi\) | |||||||
\(720\) | − | 38.2884i | − | 1.42692i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.2100 | − | 7.04944i | −0.454409 | − | 0.262353i | ||||
\(723\) | 5.22916i | 0.194475i | ||||||||
\(724\) | −7.75473 | + | 13.4316i | −0.288202 | + | 0.499181i | ||||
\(725\) | 6.45070 | + | 11.1729i | 0.239573 | + | 0.414953i | ||||
\(726\) | 4.28097 | − | 2.47162i | 0.158882 | − | 0.0917303i | ||||
\(727\) | 17.9215 | 0.664671 | 0.332335 | − | 0.943161i | \(-0.392163\pi\) | ||||
0.332335 | + | 0.943161i | \(0.392163\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.5489 | −0.501810 | ||||||||
\(730\) | 32.8985 | − | 18.9940i | 1.21763 | − | 0.702999i | ||||
\(731\) | 5.24644 | + | 9.08711i | 0.194047 | + | 0.336099i | ||||
\(732\) | −3.56454 | + | 6.17396i | −0.131749 | + | 0.228196i | ||||
\(733\) | 45.2685i | 1.67203i | 0.548705 | + | 0.836016i | \(0.315121\pi\) | ||||
−0.548705 | + | 0.836016i | \(0.684879\pi\) | |||||||
\(734\) | 3.72861 | + | 2.15271i | 0.137625 | + | 0.0794581i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 16.9378i | − | 0.624335i | ||||||
\(737\) | 18.3691 | − | 31.8163i | 0.676635 | − | 1.17197i | ||||
\(738\) | 27.2247 | + | 47.1546i | 1.00215 | + | 1.73578i | ||||
\(739\) | −16.6808 | + | 9.63066i | −0.613613 | + | 0.354270i | −0.774378 | − | 0.632723i | \(-0.781937\pi\) |
0.160765 | + | 0.986993i | \(0.448604\pi\) | |||||||
\(740\) | −45.1155 | −1.65848 | ||||||||
\(741\) | 5.18905 | + | 4.52065i | 0.190624 | + | 0.166070i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 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 | ||||
\(746\) | 36.1459i | 1.32339i | ||||||||
\(747\) | −6.37850 | − | 3.68263i | −0.233377 | − | 0.134740i | ||||
\(748\) | 34.4303 | + | 19.8784i | 1.25890 | + | 0.726825i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.00648 | − | 13.8676i | 0.292355 | − | 0.506374i | ||||
\(751\) | −12.4834 | − | 21.6219i | −0.455526 | − | 0.788993i | 0.543193 | − | 0.839608i | \(-0.317215\pi\) |
−0.998718 | + | 0.0506146i | \(0.983882\pi\) | |||||||
\(752\) | −7.94609 | + | 4.58767i | −0.289764 | + | 0.167295i | ||||
\(753\) | 5.36536 | 0.195525 | ||||||||
\(754\) | 47.4310 | − | 16.2743i | 1.72733 | − | 0.592676i | ||||
\(755\) | 12.1467 | 0.442064 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.30243 | + | 9.18408i | 0.192720 | + | 0.333801i | 0.946151 | − | 0.323726i | \(-0.104936\pi\) |
−0.753431 | + | 0.657527i | \(0.771602\pi\) | |||||||
\(758\) | −40.8685 | + | 70.7863i | −1.48441 | + | 2.57108i | ||||
\(759\) | 2.78527i | 0.101099i | ||||||||
\(760\) | −35.9337 | − | 20.7463i | −1.30345 | − | 0.752548i | ||||
\(761\) | −28.2660 | − | 16.3194i | −1.02464 | − | 0.591578i | −0.109198 | − | 0.994020i | \(-0.534828\pi\) |
−0.915446 | + | 0.402442i | \(0.868162\pi\) | |||||||
\(762\) | 4.19288i | 0.151892i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.5080 | + | 19.9325i | 0.416345 | + | 0.721131i | ||||
\(765\) | 11.9216 | − | 6.88296i | 0.431028 | − | 0.248854i | ||||
\(766\) | 82.5976 | 2.98437 | ||||||||
\(767\) | 38.9604 | − | 13.3680i | 1.40678 | − | 0.482689i | ||||
\(768\) | −11.4759 | −0.414100 | ||||||||
\(769\) | −45.1851 | + | 26.0876i | −1.62942 | + | 0.940744i | −0.645148 | + | 0.764057i | \(0.723204\pi\) |
−0.984267 | + | 0.176686i | \(0.943462\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.07039 | − | 3.58601i | 0.0745631 | − | 0.129147i | ||||
\(772\) | 14.1924i | 0.510794i | ||||||||
\(773\) | 30.9221 | + | 17.8529i | 1.11219 | + | 0.642123i | 0.939396 | − | 0.342835i | \(-0.111387\pi\) |
0.172794 | + | 0.984958i | \(0.444721\pi\) | |||||||
\(774\) | 20.5480 | + | 11.8634i | 0.738583 | + | 0.426421i | ||||
\(775\) | 25.1607i | 0.903800i | ||||||||
\(776\) | −54.1208 | + | 93.7400i | −1.94282 | + | 3.36507i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 56.9752 | − | 32.8947i | 2.04266 | − | 1.17933i | ||||
\(779\) | 28.3531 | 1.01586 | ||||||||
\(780\) | −10.6812 | − | 9.30533i | −0.382447 | − | 0.333184i | ||||
\(781\) | −3.65469 | −0.130775 | ||||||||
\(782\) | 13.9206 | − | 8.03703i | 0.497798 | − | 0.287404i | ||||
\(783\) | −7.98231 | − | 13.8258i | −0.285265 | − | 0.494093i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.5760i | 0.805770i | ||||||||
\(786\) | −11.8661 | − | 6.85089i | −0.423249 | − | 0.244363i | ||||
\(787\) | −5.28813 | − | 3.05310i | −0.188501 | − | 0.108831i | 0.402779 | − | 0.915297i | \(-0.368044\pi\) |
−0.591281 | + | 0.806466i | \(0.701378\pi\) | |||||||
\(788\) | − | 21.8586i | − | 0.778679i | ||||||
\(789\) | −1.31155 | + | 2.27167i | −0.0466923 | + | 0.0808735i | ||||
\(790\) | −12.9482 | − | 22.4270i | −0.460678 | − | 0.797918i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 51.6510 | 1.83534 | ||||||||
\(793\) | −3.42280 | − | 9.97562i | −0.121547 | − | 0.354245i | ||||
\(794\) | 10.7659 | 0.382068 | ||||||||
\(795\) | 5.25904 | − | 3.03631i | 0.186519 | − | 0.107687i | ||||
\(796\) | −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 | \(0.861321\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.85688 | − | 1.64942i | −0.101069 | − | 0.0583522i | ||||
\(800\) | −17.7355 | − | 10.2396i | −0.627044 | − | 0.362024i | ||||
\(801\) | 4.80656i | 0.169831i | ||||||||
\(802\) | 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 | 0 | ||||||||
\(806\) | 95.9780 | + | 18.7642i | 3.38068 | + | 0.660939i | ||||
\(807\) | 7.20161 | 0.253509 | ||||||||
\(808\) | −7.74586 | + | 4.47208i | −0.272498 | + | 0.157327i | ||||
\(809\) | −19.6439 | − | 34.0243i | −0.690644 | − | 1.19623i | −0.971627 | − | 0.236518i | \(-0.923994\pi\) |
0.280983 | − | 0.959713i | \(-0.409339\pi\) | |||||||
\(810\) | 13.8814 | − | 24.0432i | 0.487741 | − | 0.844792i | ||||
\(811\) | − | 6.90664i | − | 0.242525i | −0.992620 | − | 0.121262i | \(-0.961306\pi\) | ||
0.992620 | − | 0.121262i | \(-0.0386943\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.73896 | − | 2.15869i | −0.131131 | − | 0.0757085i | ||||
\(814\) | − | 41.6864i | − | 1.46111i | ||||||
\(815\) | 5.77917 | − | 10.0098i | 0.202436 | − | 0.350629i | ||||
\(816\) | 7.04853 | + | 12.2084i | 0.246748 | + | 0.427380i | ||||
\(817\) | 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 | \(0.322719\pi\) | |||||||
\(822\) | 6.70554 | + | 11.6143i | 0.233883 | + | 0.405097i | ||||
\(823\) | 0.789844 | − | 1.36805i | 0.0275322 | − | 0.0476872i | −0.851931 | − | 0.523654i | \(-0.824568\pi\) |
0.879463 | + | 0.475967i | \(0.157902\pi\) | |||||||
\(824\) | − | 80.1732i | − | 2.79296i | ||||||
\(825\) | 2.91645 | + | 1.68381i | 0.101538 | + | 0.0586228i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32.5050i | − | 1.13031i | −0.824985 | − | 0.565155i | \(-0.808816\pi\) | ||
0.824985 | − | 0.565155i | \(-0.191184\pi\) | |||||||
\(828\) | 12.7493 | − | 22.0824i | 0.443069 | − | 0.767418i | ||||
\(829\) | −17.5269 | − | 30.3575i | −0.608735 | − | 1.05436i | −0.991449 | − | 0.130493i | \(-0.958344\pi\) |
0.382714 | − | 0.923867i | \(-0.374989\pi\) | |||||||
\(830\) | 9.74564 | − | 5.62665i | 0.338276 | − | 0.195304i | ||||
\(831\) | 12.0344 | 0.417469 | ||||||||
\(832\) | −11.0937 | + | 12.7340i | −0.384606 | + | 0.441472i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −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 | ||||
\(837\) | − | 31.1347i | − | 1.07617i | ||||||
\(838\) | −67.0096 | − | 38.6880i | −2.31481 | − | 1.33645i | ||||
\(839\) | 4.63746 | + | 2.67744i | 0.160103 | + | 0.0924354i | 0.577911 | − | 0.816100i | \(-0.303868\pi\) |
−0.417808 | + | 0.908535i | \(0.637202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.0669890 | − | 0.116028i | 0.00230997 | − | 0.00400098i | ||||
\(842\) | −16.6354 | − | 28.8133i | −0.573293 | − | 0.992973i | ||||
\(843\) | −12.1947 | + | 7.04064i | −0.420009 | + | 0.242492i | ||||
\(844\) | 35.3316 | 1.21616 | ||||||||
\(845\) | 20.7590 | − | 2.87164i | 0.714132 | − | 0.0987873i | ||||
\(846\) | −7.45942 | −0.256460 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −31.5923 | − | 54.7195i | −1.08488 | − | 1.87907i | ||||
\(849\) | −4.18694 | + | 7.25199i | −0.143695 | + | 0.248888i | ||||
\(850\) | − | 19.4349i | − | 0.666611i | ||||||
\(851\) | −10.2397 | − | 5.91190i | −0.351013 | − | 0.202657i | ||||
\(852\) | −2.85179 | − | 1.64648i | −0.0977008 | − | 0.0564076i | ||||
\(853\) | − | 49.6270i | − | 1.69920i | −0.527431 | − | 0.849598i | \(-0.676845\pi\) | ||
0.527431 | − | 0.849598i | \(-0.323155\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.10452 | − | 14.0374i | −0.277169 | − | 0.480070i | ||||
\(856\) | 31.0927 | − | 17.9514i | 1.06273 | − | 0.613566i | ||||
\(857\) | −5.88392 | −0.200991 | −0.100496 | − | 0.994938i | \(-0.532043\pi\) | ||||
−0.100496 | + | 0.994938i | \(0.532043\pi\) | |||||||
\(858\) | 8.59807 | − | 9.86933i | 0.293533 | − | 0.336933i | ||||
\(859\) | 43.3862 | 1.48032 | 0.740159 | − | 0.672432i | \(-0.234750\pi\) | ||||
0.740159 | + | 0.672432i | \(0.234750\pi\) | |||||||
\(860\) | −22.0246 | + | 12.7159i | −0.751033 | + | 0.433609i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.6106 | + | 20.1102i | −0.395460 | + | 0.684957i | ||||
\(863\) | − | 31.1272i | − | 1.05958i | −0.848128 | − | 0.529792i | \(-0.822270\pi\) | ||
0.848128 | − | 0.529792i | \(-0.177730\pi\) | |||||||
\(864\) | 21.9465 | + | 12.6708i | 0.746634 | + | 0.431069i | ||||
\(865\) | −17.8860 | − | 10.3265i | −0.608142 | − | 0.351111i | ||||
\(866\) | 8.93228i | 0.303531i | ||||||||
\(867\) | 1.87278 | − | 3.24376i | 0.0636031 | − | 0.110164i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.5374 | − | 8.39318i | 0.493148 | − | 0.284719i | ||||
\(870\) | 11.6241 | 0.394093 | ||||||||
\(871\) | −9.39598 | + | 48.0601i | −0.318371 | + | 1.62845i | ||||
\(872\) | 12.0800 | 0.409081 | ||||||||
\(873\) | −36.6194 | + | 21.1422i | −1.23938 | + | 0.715556i | ||||
\(874\) | −9.46341 | − | 16.3911i | −0.320105 | − | 0.554438i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 22.1870i | 0.749629i | ||||||||
\(877\) | −25.9033 | − | 14.9553i | −0.874693 | − | 0.505004i | −0.00578807 | − | 0.999983i | \(-0.501842\pi\) |
−0.868905 | + | 0.494979i | \(0.835176\pi\) | |||||||
\(878\) | −86.3413 | − | 49.8492i | −2.91388 | − | 1.68233i | ||||
\(879\) | 7.59304i | 0.256107i | ||||||||
\(880\) | −18.9603 | + | 32.8402i | −0.639152 | + | 1.10704i | ||||
\(881\) | 7.28477 | + | 12.6176i | 0.245430 | + | 0.425097i | 0.962252 | − | 0.272159i | \(-0.0877375\pi\) |
−0.716822 | + | 0.697256i | \(0.754404\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.9296 | 1.64661 | 0.823307 | − | 0.567597i | \(-0.192127\pi\) | ||||
0.823307 | + | 0.567597i | \(0.192127\pi\) | |||||||
\(884\) | −52.0088 | − | 10.1680i | −1.74924 | − | 0.341986i | ||||
\(885\) | 9.54817 | 0.320958 | ||||||||
\(886\) | −33.7164 | + | 19.4662i | −1.13273 | + | 0.653980i | ||||
\(887\) | −27.2951 | − | 47.2765i | −0.916480 | − | 1.58739i | −0.804719 | − | 0.593655i | \(-0.797684\pi\) |
−0.111761 | − | 0.993735i | \(-0.535649\pi\) | |||||||
\(888\) | 10.7901 | − | 18.6890i | 0.362092 | − | 0.627162i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.36000 | − | 3.67195i | −0.213188 | − | 0.123084i | ||||
\(891\) | 15.5851 | + | 8.99803i | 0.522119 | + | 0.301445i | ||||
\(892\) | 106.143i | 3.55392i | ||||||||
\(893\) | −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 | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.20490 | − | 3.51165i | −0.0402306 | − | 0.117251i | ||||
\(898\) | 100.757 | 3.36232 | ||||||||
\(899\) | −48.7533 | + | 28.1477i | −1.62601 | + | 0.938780i | ||||
\(900\) | −15.4150 | − | 26.6995i | −0.513832 | − | 0.889983i | ||||
\(901\) | 11.3585 | − | 19.6734i | 0.378405 | − | 0.655417i | ||||
\(902\) | − | 53.9263i | − | 1.79555i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −52.0172 | − | 30.0321i | −1.73007 | − | 0.998854i | ||||
\(905\) | − | 5.31862i | − | 0.176797i | ||||||
\(906\) | −5.05632 | + | 8.75780i | −0.167985 | + | 0.290958i | ||||
\(907\) | 11.3628 | + | 19.6809i | 0.377295 | + | 0.653494i | 0.990668 | − | 0.136300i | \(-0.0435211\pi\) |
−0.613373 | + | 0.789793i | \(0.710188\pi\) | |||||||
\(908\) | −55.6584 | + | 32.1344i | −1.84709 | + | 1.06642i | ||||
\(909\) | −3.49402 | −0.115889 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||
\(913\) | 3.64725 | + | 6.31722i | 0.120706 | + | 0.209070i | ||||
\(914\) | 18.0421 | − | 31.2498i | 0.596779 | − | 1.03365i | ||||
\(915\) | − | 2.44476i | − | 0.0808213i | ||||||
\(916\) | −32.2870 | − | 18.6409i | −1.06679 | − | 0.615912i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 24.0494i | 0.793747i | ||||||||
\(919\) | −15.3470 | + | 26.5818i | −0.506251 | + | 0.876853i | 0.493722 | + | 0.869620i | \(0.335636\pi\) |
−0.999974 | + | 0.00723365i | \(0.997697\pi\) | |||||||
\(920\) | 11.1919 | + | 19.3849i | 0.368985 | + | 0.639101i | ||||
\(921\) | 4.03136 | − | 2.32751i | 0.132838 | − | 0.0766940i | ||||
\(922\) | 96.9780 | 3.19380 | ||||||||
\(923\) | 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 | ||||
\(927\) | 15.6598 | − | 27.1235i | 0.514334 | − | 0.890853i | ||||
\(928\) | − | 45.8208i | − | 1.50414i | ||||||
\(929\) | 32.4110 | + | 18.7125i | 1.06337 | + | 0.613936i | 0.926362 | − | 0.376634i | \(-0.122918\pi\) |
0.137007 | + | 0.990570i | \(0.456252\pi\) | |||||||
\(930\) | 19.6325 | + | 11.3348i | 0.643775 | + | 0.371684i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.4463 | − | 26.7538i | 0.505961 | − | 0.876350i | ||||
\(933\) | 3.15787 | + | 5.46960i | 0.103384 | + | 0.179067i | ||||
\(934\) | −11.3218 | + | 6.53663i | −0.370460 | + | 0.213885i | ||||
\(935\) | −13.6337 | −0.445869 | ||||||||
\(936\) | −65.1211 | + | 22.3441i | −2.12855 | + | 0.730340i | ||||
\(937\) | 44.3386 | 1.44848 | 0.724239 | − | 0.689549i | \(-0.242191\pi\) | ||||
0.724239 | + | 0.689549i | \(0.242191\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.40216 | − | 5.89272i | −0.111025 | − | 0.192302i | ||||
\(940\) | 3.99773 | − | 6.92427i | 0.130392 | − | 0.225845i | ||||
\(941\) | − | 27.5052i | − | 0.896646i | −0.893872 | − | 0.448323i | \(-0.852022\pi\) | ||
0.893872 | − | 0.448323i | \(-0.147978\pi\) | |||||||
\(942\) | −16.2773 | − | 9.39771i | −0.530343 | − | 0.306194i | ||||
\(943\) | −13.2463 | − | 7.64774i | −0.431358 | − | 0.249045i | ||||
\(944\) | − | 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 | \(0.359653\pi\) | |||||||
\(948\) | 15.1249 | 0.491235 | ||||||||
\(949\) | −24.7482 | − | 21.5604i | −0.803360 | − | 0.699880i | ||||
\(950\) | −22.8841 | −0.742458 | ||||||||
\(951\) | −7.50534 | + | 4.33321i | −0.243377 | + | 0.140514i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.90718 | − | 8.49949i | 0.158959 | − | 0.275326i | −0.775534 | − | 0.631305i | \(-0.782519\pi\) |
0.934494 | + | 0.355980i | \(0.115853\pi\) | |||||||
\(954\) | − | 51.3681i | − | 1.66310i | ||||||
\(955\) | −6.83540 | − | 3.94642i | −0.221188 | − | 0.127703i | ||||
\(956\) | −38.2388 | − | 22.0772i | −1.23673 | − | 0.714027i | ||||
\(957\) | 7.53484i | 0.243567i | ||||||||
\(958\) | −12.2353 | + | 21.1921i | −0.395303 | + | 0.684685i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.39041 | + | 1.95746i | −0.109425 | + | 0.0631766i | ||||
\(961\) | −78.7893 | −2.54159 | ||||||||
\(962\) | 18.0335 | + | 52.5579i | 0.581422 | + | 1.69453i | ||||
\(963\) | 14.0254 | 0.451961 | ||||||||
\(964\) | −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 | \(-0.986196\pi\) | ||
0.999060 | − | 0.0433518i | \(-0.0138036\pi\) | |||||||
\(968\) | 22.3009 | + | 12.8754i | 0.716779 | + | 0.413832i | ||||
\(969\) | 5.16832 | + | 2.98393i | 0.166030 | + | 0.0958577i | ||||
\(970\) | − | 64.6060i | − | 2.07437i | ||||||
\(971\) | −12.4620 | + | 21.5848i | −0.399925 | + | 0.692691i | −0.993716 | − | 0.111929i | \(-0.964297\pi\) |
0.593791 | + | 0.804619i | \(0.297631\pi\) | |||||||
\(972\) | 29.0598 | + | 50.3331i | 0.932094 | + | 1.61443i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −103.543 | −3.31773 | ||||||||
\(975\) | −4.40545 | − | 0.861286i | −0.141087 | − | 0.0275832i | ||||
\(976\) | −25.4373 | −0.814230 | ||||||||
\(977\) | −24.5197 | + | 14.1565i | −0.784456 | + | 0.452906i | −0.838007 | − | 0.545659i | \(-0.816279\pi\) |
0.0535514 | + | 0.998565i | \(0.482946\pi\) | |||||||
\(978\) | 4.81140 | + | 8.33359i | 0.153852 | + | 0.266479i | ||||
\(979\) | 2.38019 | − | 4.12262i | 0.0760713 | − | 0.131759i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.08681 | + | 2.35952i | 0.130482 | + | 0.0753337i | ||||
\(982\) | −15.1567 | − | 8.75073i | −0.483670 | − | 0.279247i | ||||
\(983\) | − | 37.8517i | − | 1.20728i | −0.797256 | − | 0.603641i | \(-0.793716\pi\) | ||
0.797256 | − | 0.603641i | \(-0.206284\pi\) | |||||||
\(984\) | 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 | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.9725 | + | 61.2391i | −0.380897 | + | 1.94827i | ||||
\(989\) | −6.66514 | −0.211939 | ||||||||
\(990\) | −26.6986 | + | 15.4144i | −0.848536 | + | 0.489903i | ||||
\(991\) | −29.2079 | − | 50.5896i | −0.927820 | − | 1.60703i | −0.786962 | − | 0.617001i | \(-0.788347\pi\) |
−0.140858 | − | 0.990030i | \(-0.544986\pi\) | |||||||
\(992\) | 44.6806 | − | 77.3891i | 1.41861 | − | 2.45711i | ||||
\(993\) | − | 2.05657i | − | 0.0652633i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.573399 | + | 0.331052i | 0.0181780 | + | 0.0104950i | ||||
\(996\) | 6.57252i | 0.208258i | ||||||||
\(997\) | −14.0294 | + | 24.2997i | −0.444316 | + | 0.769578i | −0.998004 | − | 0.0631462i | \(-0.979887\pi\) |
0.553688 | + | 0.832724i | \(0.313220\pi\) | |||||||
\(998\) | 14.7001 | + | 25.4613i | 0.465322 | + | 0.805962i | ||||
\(999\) | 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 | 637.2.q.g.491.6 | 12 | ||
7.2 | even | 3 | 91.2.u.b.88.1 | yes | 12 | ||
7.3 | odd | 6 | 637.2.k.i.569.6 | 12 | |||
7.4 | even | 3 | 91.2.k.b.23.6 | yes | 12 | ||
7.5 | odd | 6 | 637.2.u.g.361.1 | 12 | |||
7.6 | odd | 2 | 637.2.q.i.491.6 | 12 | |||
13.2 | odd | 12 | 8281.2.a.cp.1.12 | 12 | |||
13.4 | even | 6 | inner | 637.2.q.g.589.6 | 12 | ||
13.11 | odd | 12 | 8281.2.a.cp.1.1 | 12 | |||
21.2 | odd | 6 | 819.2.do.e.361.6 | 12 | |||
21.11 | odd | 6 | 819.2.bm.f.478.1 | 12 | |||
91.2 | odd | 12 | 1183.2.e.j.508.1 | 24 | |||
91.4 | even | 6 | 91.2.u.b.30.1 | yes | 12 | ||
91.11 | odd | 12 | 1183.2.e.j.170.12 | 24 | |||
91.17 | odd | 6 | 637.2.u.g.30.1 | 12 | |||
91.30 | even | 6 | 91.2.k.b.4.1 | ✓ | 12 | ||
91.37 | odd | 12 | 1183.2.e.j.508.12 | 24 | |||
91.41 | even | 12 | 8281.2.a.co.1.12 | 12 | |||
91.67 | odd | 12 | 1183.2.e.j.170.1 | 24 | |||
91.69 | odd | 6 | 637.2.q.i.589.6 | 12 | |||
91.76 | even | 12 | 8281.2.a.co.1.1 | 12 | |||
91.82 | odd | 6 | 637.2.k.i.459.1 | 12 | |||
273.95 | odd | 6 | 819.2.do.e.667.6 | 12 | |||
273.212 | odd | 6 | 819.2.bm.f.550.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.1 | ✓ | 12 | 91.30 | even | 6 | ||
91.2.k.b.23.6 | yes | 12 | 7.4 | even | 3 | ||
91.2.u.b.30.1 | yes | 12 | 91.4 | even | 6 | ||
91.2.u.b.88.1 | yes | 12 | 7.2 | even | 3 | ||
637.2.k.i.459.1 | 12 | 91.82 | odd | 6 | |||
637.2.k.i.569.6 | 12 | 7.3 | odd | 6 | |||
637.2.q.g.491.6 | 12 | 1.1 | even | 1 | trivial | ||
637.2.q.g.589.6 | 12 | 13.4 | even | 6 | inner | ||
637.2.q.i.491.6 | 12 | 7.6 | odd | 2 | |||
637.2.q.i.589.6 | 12 | 91.69 | odd | 6 | |||
637.2.u.g.30.1 | 12 | 91.17 | odd | 6 | |||
637.2.u.g.361.1 | 12 | 7.5 | odd | 6 | |||
819.2.bm.f.478.1 | 12 | 21.11 | odd | 6 | |||
819.2.bm.f.550.6 | 12 | 273.212 | odd | 6 | |||
819.2.do.e.361.6 | 12 | 21.2 | odd | 6 | |||
819.2.do.e.667.6 | 12 | 273.95 | odd | 6 | |||
1183.2.e.j.170.1 | 24 | 91.67 | odd | 12 | |||
1183.2.e.j.170.12 | 24 | 91.11 | odd | 12 | |||
1183.2.e.j.508.1 | 24 | 91.2 | odd | 12 | |||
1183.2.e.j.508.12 | 24 | 91.37 | odd | 12 | |||
8281.2.a.co.1.1 | 12 | 91.76 | even | 12 | |||
8281.2.a.co.1.12 | 12 | 91.41 | even | 12 | |||
8281.2.a.cp.1.1 | 12 | 13.11 | odd | 12 | |||
8281.2.a.cp.1.12 | 12 | 13.2 | odd | 12 |