Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(459,637)]
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([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.k (of order \(6\), degree \(2\), not 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: | \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) |
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 | 569.6 | ||
Root | \(1.32725 + 0.488273i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.569 |
Dual form | 637.2.k.i.459.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.58860i | 1.83042i | 0.402981 | + | 0.915209i | \(0.367974\pi\) | ||||
−0.402981 | + | 0.915209i | \(0.632026\pi\) | |||||||
\(3\) | 0.259233 | − | 0.449005i | 0.149668 | − | 0.259233i | −0.781437 | − | 0.623985i | \(-0.785513\pi\) |
0.931105 | + | 0.364752i | \(0.118846\pi\) | |||||||
\(4\) | −4.70085 | −2.35043 | ||||||||
\(5\) | 1.39608 | + | 0.806027i | 0.624346 | + | 0.360466i | 0.778559 | − | 0.627571i | \(-0.215951\pi\) |
−0.154213 | + | 0.988038i | \(0.549284\pi\) | |||||||
\(6\) | 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 | \(-0.199634\pi\) |
−0.103384 | + | 0.994642i | \(0.532967\pi\) | |||||||
\(12\) | −1.21862 | + | 2.11070i | −0.351784 | + | 0.609308i | ||||
\(13\) | −2.36840 | + | 2.71858i | −0.656876 | + | 0.753998i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.723819 | − | 0.417897i | 0.186889 | − | 0.107901i | ||||
\(16\) | 8.69632 | 2.17408 | ||||||||
\(17\) | 3.12661 | 0.758314 | 0.379157 | − | 0.925332i | \(-0.376214\pi\) | ||||
0.379157 | + | 0.925332i | \(0.376214\pi\) | |||||||
\(18\) | −6.12277 | + | 3.53498i | −1.44315 | + | 0.833204i | ||||
\(19\) | −3.18828 | + | 1.84075i | −0.731441 | + | 0.422297i | −0.818949 | − | 0.573866i | \(-0.805443\pi\) |
0.0875083 | + | 0.996164i | \(0.472110\pi\) | |||||||
\(20\) | −6.56276 | − | 3.78901i | −1.46748 | − | 0.847249i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.50103 | + | 6.06396i | −0.746421 | + | 1.29284i | ||||
\(23\) | −1.98604 | −0.414117 | −0.207059 | − | 0.978329i | \(-0.566389\pi\) | ||||
−0.207059 | + | 0.978329i | \(0.566389\pi\) | |||||||
\(24\) | −3.13918 | − | 1.81241i | −0.640783 | − | 0.369956i | ||||
\(25\) | −1.20064 | − | 2.07957i | −0.240128 | − | 0.415914i | ||||
\(26\) | −7.03732 | − | 6.13084i | −1.38013 | − | 1.20236i | ||||
\(27\) | 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 | ||||
\(31\) | −9.07425 | + | 5.23902i | −1.62978 | + | 0.940956i | −0.645627 | + | 0.763653i | \(0.723404\pi\) |
−0.984156 | + | 0.177303i | \(0.943263\pi\) | |||||||
\(32\) | 8.52843i | 1.50763i | ||||||||
\(33\) | 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 | ||||
\(37\) | − | 5.95346i | − | 0.978743i | −0.872075 | − | 0.489371i | \(-0.837226\pi\) | ||
0.872075 | − | 0.489371i | \(-0.162774\pi\) | |||||||
\(38\) | −4.76497 | − | 8.25317i | −0.772981 | − | 1.33884i | ||||
\(39\) | 0.606687 | + | 1.76817i | 0.0971477 | + | 0.283134i | ||||
\(40\) | 5.63528 | − | 9.76059i | 0.891016 | − | 1.54329i | ||||
\(41\) | 6.66970 | − | 3.85075i | 1.04163 | − | 0.601386i | 0.121337 | − | 0.992611i | \(-0.461282\pi\) |
0.920295 | + | 0.391225i | \(0.127949\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.67800 | + | 2.90638i | −0.255892 | + | 0.443219i | −0.965138 | − | 0.261743i | \(-0.915703\pi\) |
0.709245 | + | 0.704962i | \(0.249036\pi\) | |||||||
\(44\) | −11.0120 | − | 6.35780i | −1.66013 | − | 0.958475i | ||||
\(45\) | 4.40283i | 0.656335i | ||||||||
\(46\) | − | 5.14106i | − | 0.758008i | ||||||
\(47\) | −0.913730 | − | 0.527542i | −0.133281 | − | 0.0769500i | 0.431877 | − | 0.901933i | \(-0.357852\pi\) |
−0.565158 | + | 0.824983i | \(0.691185\pi\) | |||||||
\(48\) | 2.25437 | − | 3.90469i | 0.325390 | − | 0.563593i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.38318 | − | 3.10798i | 0.761297 | − | 0.439535i | ||||
\(51\) | 0.810520 | − | 1.40386i | 0.113495 | − | 0.196580i | ||||
\(52\) | 11.1335 | − | 12.7796i | 1.54394 | − | 1.77222i | ||||
\(53\) | −3.63284 | − | 6.29226i | −0.499009 | − | 0.864308i | 0.500991 | − | 0.865453i | \(-0.332969\pi\) |
−0.999999 | + | 0.00114437i | \(0.999636\pi\) | |||||||
\(54\) | 7.69184i | 1.04673i | ||||||||
\(55\) | 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 | ||||
\(59\) | 11.4241i | 1.48729i | 0.668577 | + | 0.743643i | \(0.266904\pi\) | ||||
−0.668577 | + | 0.743643i | \(0.733096\pi\) | |||||||
\(60\) | −3.40257 | + | 1.96447i | −0.439270 | + | 0.253613i | ||||
\(61\) | −1.46254 | − | 2.53319i | −0.187259 | − | 0.324341i | 0.757077 | − | 0.653326i | \(-0.226627\pi\) |
−0.944335 | + | 0.328985i | \(0.893294\pi\) | |||||||
\(62\) | −13.5617 | − | 23.4896i | −1.72234 | − | 2.98318i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.68406 | −0.585507 | ||||||||
\(65\) | −5.49772 | + | 1.88636i | −0.681909 | + | 0.233974i | ||||
\(66\) | 1.81516 | + | 3.14395i | 0.223431 | + | 0.386994i | ||||
\(67\) | 11.7622 | + | 6.79091i | 1.43698 | + | 0.829642i | 0.997639 | − | 0.0686778i | \(-0.0218780\pi\) |
0.439343 | + | 0.898320i | \(0.355211\pi\) | |||||||
\(68\) | −14.6977 | −1.78236 | ||||||||
\(69\) | −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 | ||||
\(73\) | 7.88374 | − | 4.55168i | 0.922721 | − | 0.532733i | 0.0382192 | − | 0.999269i | \(-0.487831\pi\) |
0.884502 | + | 0.466536i | \(0.154498\pi\) | |||||||
\(74\) | 15.4111 | 1.79151 | ||||||||
\(75\) | −1.24498 | −0.143758 | ||||||||
\(76\) | 14.9876 | − | 8.65311i | 1.71920 | − | 0.992579i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.57708 | + | 1.57047i | −0.518252 | + | 0.177821i | ||||
\(79\) | 3.10289 | − | 5.37436i | 0.349102 | − | 0.604663i | −0.636988 | − | 0.770874i | \(-0.719820\pi\) |
0.986090 | + | 0.166211i | \(0.0531532\pi\) | |||||||
\(80\) | 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 | \(0.0472841\pi\) | ||||
−0.988987 | + | 0.148002i | \(0.952716\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.36499 | + | 2.52013i | 0.473450 | + | 0.273346i | ||||
\(86\) | −7.52346 | − | 4.34367i | −0.811275 | − | 0.468390i | ||||
\(87\) | 2.78557 | 0.298644 | ||||||||
\(88\) | 9.45576 | − | 16.3779i | 1.00799 | − | 1.74589i | ||||
\(89\) | 1.75988i | 0.186546i | 0.995641 | + | 0.0932732i | \(0.0297330\pi\) | ||||
−0.995641 | + | 0.0932732i | \(0.970267\pi\) | |||||||
\(90\) | −11.3972 | −1.20137 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.33607 | 0.973353 | ||||||||
\(93\) | 5.43251i | 0.563325i | ||||||||
\(94\) | 1.36560 | − | 2.36528i | 0.140851 | − | 0.243960i | ||||
\(95\) | −5.93478 | −0.608896 | ||||||||
\(96\) | 3.82930 | + | 2.21085i | 0.390827 | + | 0.225644i | ||||
\(97\) | 13.4078 | + | 7.74102i | 1.36136 | + | 0.785981i | 0.989805 | − | 0.142430i | \(-0.0454915\pi\) |
0.371555 | + | 0.928411i | \(0.378825\pi\) | |||||||
\(98\) | 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 | \(-0.813060\pi\) |
0.896093 | + | 0.443866i | \(0.146393\pi\) | |||||||
\(102\) | 3.63404 | + | 2.09811i | 0.359823 | + | 0.207744i | ||||
\(103\) | 5.73367 | − | 9.93101i | 0.564956 | − | 0.978532i | −0.432098 | − | 0.901827i | \(-0.642227\pi\) |
0.997054 | − | 0.0767054i | \(-0.0244401\pi\) | |||||||
\(104\) | 19.0068 | + | 16.5585i | 1.86377 | + | 1.62370i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.2881 | − | 9.40397i | 1.58204 | − | 0.913394i | ||||
\(107\) | −5.13525 | −0.496444 | −0.248222 | − | 0.968703i | \(-0.579846\pi\) | ||||
−0.248222 | + | 0.968703i | \(0.579846\pi\) | |||||||
\(108\) | −13.9682 | −1.34410 | ||||||||
\(109\) | 1.49635 | − | 0.863916i | 0.143324 | − | 0.0827481i | −0.426623 | − | 0.904429i | \(-0.640297\pi\) |
0.569947 | + | 0.821681i | \(0.306964\pi\) | |||||||
\(110\) | −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 | \(0.0342540\pi\) | |||||||
\(114\) | −4.94095 | −0.462762 | ||||||||
\(115\) | −2.77267 | − | 1.60080i | −0.258552 | − | 0.149275i | ||||
\(116\) | −12.6282 | − | 21.8726i | −1.17250 | − | 2.03082i | ||||
\(117\) | −9.66449 | − | 1.88945i | −0.893482 | − | 0.174680i | ||||
\(118\) | −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 | ||||
\(122\) | 6.55741 | − | 3.78592i | 0.593680 | − | 0.342761i | ||||
\(123\) | − | 3.99297i | − | 0.360034i | ||||||
\(124\) | 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 | \(0.877597\pi\) | |||||||
\(128\) | 4.93170i | 0.435904i | ||||||||
\(129\) | 0.869985 | + | 1.50686i | 0.0765979 | + | 0.132671i | ||||
\(130\) | −4.88303 | − | 14.2314i | −0.428270 | − | 1.24818i | ||||
\(131\) | 5.10460 | − | 8.84142i | 0.445991 | − | 0.772479i | −0.552130 | − | 0.833758i | \(-0.686185\pi\) |
0.998121 | + | 0.0612793i | \(0.0195180\pi\) | |||||||
\(132\) | −5.70937 | + | 3.29630i | −0.496936 | + | 0.286906i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −17.5790 | + | 30.4476i | −1.51859 | + | 2.63028i | ||||
\(135\) | 4.14835 | + | 2.39505i | 0.357033 | + | 0.206133i | ||||
\(136\) | − | 21.8595i | − | 1.87443i | ||||||
\(137\) | 9.99261i | 0.853726i | 0.904316 | + | 0.426863i | \(0.140381\pi\) | ||||
−0.904316 | + | 0.426863i | \(0.859619\pi\) | |||||||
\(138\) | −2.30836 | − | 1.33273i | −0.196501 | − | 0.113450i | ||||
\(139\) | −0.832100 | + | 1.44124i | −0.0705778 | + | 0.122244i | −0.899155 | − | 0.437631i | \(-0.855818\pi\) |
0.828577 | + | 0.559875i | \(0.189151\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.473738 | + | 0.273513i | −0.0398959 | + | 0.0230339i | ||||
\(142\) | −1.74874 | + | 3.02891i | −0.146751 | + | 0.254180i | ||||
\(143\) | −9.22495 | + | 3.16523i | −0.771429 | + | 0.264690i | ||||
\(144\) | 11.8757 | + | 20.5692i | 0.989638 | + | 1.71410i | ||||
\(145\) | 8.66110i | 0.719265i | ||||||||
\(146\) | 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 | \(-0.365613\pi\) |
0.994863 | + | 0.101234i | \(0.0322792\pi\) | |||||||
\(150\) | − | 3.22276i | − | 0.263138i | ||||||
\(151\) | −6.52544 | + | 3.76746i | −0.531033 | + | 0.306592i | −0.741437 | − | 0.671023i | \(-0.765855\pi\) |
0.210404 | + | 0.977614i | \(0.432522\pi\) | |||||||
\(152\) | 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 | ||||||||
\(156\) | −2.85195 | − | 8.31190i | −0.228339 | − | 0.665485i | ||||
\(157\) | 7.00223 | + | 12.1282i | 0.558839 | + | 0.967938i | 0.997594 | + | 0.0693309i | \(0.0220864\pi\) |
−0.438755 | + | 0.898607i | \(0.644580\pi\) | |||||||
\(158\) | 13.9121 | + | 8.03214i | 1.10679 | + | 0.639003i | ||||
\(159\) | −3.76700 | −0.298743 | ||||||||
\(160\) | −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 | \(-0.576068\pi\) |
0.723061 | + | 0.690784i | \(0.242735\pi\) | |||||||
\(164\) | −31.3533 | + | 18.1018i | −2.44828 | + | 1.41351i | ||||
\(165\) | 2.26079 | 0.176002 | ||||||||
\(166\) | −6.98072 | −0.541809 | ||||||||
\(167\) | −15.5716 | + | 8.99027i | −1.20497 | + | 0.695688i | −0.961656 | − | 0.274260i | \(-0.911567\pi\) |
−0.243312 | + | 0.969948i | \(0.578234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.78135 | − | 12.8774i | −0.137027 | − | 0.990567i | ||||
\(170\) | −6.52361 | + | 11.2992i | −0.500338 | + | 0.866611i | ||||
\(171\) | −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 | \(-0.00474930\pi\) |
−0.512865 | + | 0.858469i | \(0.671416\pi\) | |||||||
\(174\) | 7.21072i | 0.546643i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 20.3717 | + | 11.7616i | 1.53557 | + | 0.886562i | ||||
\(177\) | 5.12945 | + | 2.96149i | 0.385553 | + | 0.222599i | ||||
\(178\) | −4.55561 | −0.341458 | ||||||||
\(179\) | 0.920110 | − | 1.59368i | 0.0687723 | − | 0.119117i | −0.829589 | − | 0.558375i | \(-0.811425\pi\) |
0.898361 | + | 0.439258i | \(0.144758\pi\) | |||||||
\(180\) | − | 20.6971i | − | 1.54267i | ||||||
\(181\) | 3.29928 | 0.245234 | 0.122617 | − | 0.992454i | \(-0.460871\pi\) | ||||
0.122617 | + | 0.992454i | \(0.460871\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.51655 | −0.112107 | ||||||||
\(184\) | 13.8852i | 1.02363i | ||||||||
\(185\) | 4.79865 | − | 8.31150i | 0.352804 | − | 0.611074i | ||||
\(186\) | −14.0626 | −1.03112 | ||||||||
\(187\) | 7.32427 | + | 4.22867i | 0.535604 | + | 0.309231i | ||||
\(188\) | 4.29531 | + | 2.47990i | 0.313268 | + | 0.180865i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 15.3628i | − | 1.11453i | ||||||
\(191\) | −2.44807 | − | 4.24018i | −0.177136 | − | 0.306809i | 0.763762 | − | 0.645498i | \(-0.223350\pi\) |
−0.940898 | + | 0.338689i | \(0.890017\pi\) | |||||||
\(192\) | −1.21426 | + | 2.10316i | −0.0876318 | + | 0.151783i | ||||
\(193\) | 2.61462 | + | 1.50955i | 0.188204 | + | 0.108660i | 0.591142 | − | 0.806568i | \(-0.298677\pi\) |
−0.402937 | + | 0.915228i | \(0.632011\pi\) | |||||||
\(194\) | −20.0384 | + | 34.7075i | −1.43867 | + | 2.49186i | ||||
\(195\) | −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 | \(0.280362\pi\) | |||||||
\(198\) | −19.1240 | −1.35908 | ||||||||
\(199\) | 0.410721 | 0.0291152 | 0.0145576 | − | 0.999894i | \(-0.495366\pi\) | ||||
0.0145576 | + | 0.999894i | \(0.495366\pi\) | |||||||
\(200\) | −14.5392 | + | 8.39420i | −1.02808 | + | 0.593560i | ||||
\(201\) | 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 | ||||
\(205\) | 12.4152 | 0.867118 | ||||||||
\(206\) | 25.7074 | + | 14.8422i | 1.79112 | + | 1.03410i | ||||
\(207\) | −2.71213 | − | 4.69754i | −0.188506 | − | 0.326502i | ||||
\(208\) | −20.5964 | + | 23.6416i | −1.42810 | + | 1.63925i | ||||
\(209\) | −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 | ||||
\(213\) | 0.606654 | − | 0.350252i | 0.0415672 | − | 0.0239989i | ||||
\(214\) | − | 13.2931i | − | 0.908699i | ||||||
\(215\) | −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 | ||||
\(219\) | − | 4.71978i | − | 0.318933i | ||||||
\(220\) | −10.2491 | − | 17.7520i | −0.690996 | − | 1.19684i | ||||
\(221\) | −7.40506 | + | 8.49993i | −0.498118 | + | 0.571767i | ||||
\(222\) | 3.99507 | − | 6.91967i | 0.268132 | − | 0.464418i | ||||
\(223\) | 19.5544 | − | 11.2897i | 1.30946 | − | 0.756016i | 0.327452 | − | 0.944868i | \(-0.393810\pi\) |
0.982006 | + | 0.188852i | \(0.0604766\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.27918 | − | 5.67971i | 0.218612 | − | 0.378648i | ||||
\(226\) | 19.2595 | + | 11.1195i | 1.28113 | + | 0.739658i | ||||
\(227\) | − | 13.6717i | − | 0.907424i | −0.891148 | − | 0.453712i | \(-0.850099\pi\) | ||
0.891148 | − | 0.453712i | \(-0.149901\pi\) | |||||||
\(228\) | − | 8.97268i | − | 0.594230i | ||||||
\(229\) | −6.86832 | − | 3.96543i | −0.453872 | − | 0.262043i | 0.255592 | − | 0.966785i | \(-0.417730\pi\) |
−0.709464 | + | 0.704742i | \(0.751063\pi\) | |||||||
\(230\) | 4.14383 | − | 7.17733i | 0.273236 | − | 0.473259i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 32.5305 | − | 18.7815i | 2.13573 | − | 1.23306i | ||||
\(233\) | −3.28585 | + | 5.69127i | −0.215263 | + | 0.372847i | −0.953354 | − | 0.301854i | \(-0.902394\pi\) |
0.738091 | + | 0.674702i | \(0.235728\pi\) | |||||||
\(234\) | 4.89104 | − | 25.0175i | 0.319738 | − | 1.63545i | ||||
\(235\) | −0.850427 | − | 1.47298i | −0.0554757 | − | 0.0960868i | ||||
\(236\) | − | 53.7028i | − | 3.49576i | ||||||
\(237\) | −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 | ||||
\(241\) | − | 10.0858i | − | 0.649686i | −0.945768 | − | 0.324843i | \(-0.894689\pi\) | ||
0.945768 | − | 0.324843i | \(-0.105311\pi\) | |||||||
\(242\) | 8.25699 | − | 4.76718i | 0.530780 | − | 0.306446i | ||||
\(243\) | 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 | ||||||||
\(247\) | 2.54689 | − | 13.0272i | 0.162054 | − | 0.828902i | ||||
\(248\) | 36.6282 | + | 63.4420i | 2.32590 | + | 4.02857i | ||||
\(249\) | 1.21084 | + | 0.699078i | 0.0767337 | + | 0.0443022i | ||||
\(250\) | 30.8853 | 1.95336 | ||||||||
\(251\) | 5.17427 | − | 8.96209i | 0.326597 | − | 0.565682i | −0.655237 | − | 0.755423i | \(-0.727431\pi\) |
0.981834 | + | 0.189741i | \(0.0607648\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.65242 | − | 2.68607i | −0.292495 | − | 0.168872i | ||||
\(254\) | 7.00363 | − | 4.04355i | 0.439447 | − | 0.253715i | ||||
\(255\) | 2.26310 | − | 1.30660i | 0.141721 | − | 0.0818225i | ||||
\(256\) | −22.1343 | −1.38339 | ||||||||
\(257\) | 7.98658 | 0.498189 | 0.249095 | − | 0.968479i | \(-0.419867\pi\) | ||||
0.249095 | + | 0.968479i | \(0.419867\pi\) | |||||||
\(258\) | −3.90065 | + | 2.25204i | −0.242844 | + | 0.140206i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 25.8440 | − | 8.86749i | 1.60278 | − | 0.549939i | ||||
\(261\) | −7.33696 | + | 12.7080i | −0.454146 | + | 0.786604i | ||||
\(262\) | 22.8869 | + | 13.2138i | 1.41396 | + | 0.816349i | ||||
\(263\) | −2.52967 | + | 4.38152i | −0.155986 | + | 0.270176i | −0.933418 | − | 0.358792i | \(-0.883189\pi\) |
0.777431 | + | 0.628968i | \(0.216522\pi\) | |||||||
\(264\) | −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 | ||||
\(268\) | −55.2924 | − | 31.9231i | −3.37752 | − | 1.95001i | ||||
\(269\) | −13.8902 | −0.846902 | −0.423451 | − | 0.905919i | \(-0.639181\pi\) | ||||
−0.423451 | + | 0.905919i | \(0.639181\pi\) | |||||||
\(270\) | −6.19983 | + | 10.7384i | −0.377310 | + | 0.653519i | ||||
\(271\) | − | 8.32721i | − | 0.505842i | −0.967487 | − | 0.252921i | \(-0.918609\pi\) | ||
0.967487 | − | 0.252921i | \(-0.0813913\pi\) | |||||||
\(272\) | 27.1900 | 1.64863 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.8669 | −1.56267 | ||||||||
\(275\) | − | 6.49537i | − | 0.391685i | ||||||
\(276\) | 2.42022 | − | 4.19194i | 0.145680 | − | 0.252325i | ||||
\(277\) | 23.2116 | 1.39465 | 0.697325 | − | 0.716755i | \(-0.254374\pi\) | ||||
0.697325 | + | 0.716755i | \(0.254374\pi\) | |||||||
\(278\) | −3.73080 | − | 2.15398i | −0.223758 | − | 0.129187i | ||||
\(279\) | −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 | \(-0.673953\pi\) |
0.999738 | + | 0.0228894i | \(0.00728654\pi\) | |||||||
\(284\) | −5.50044 | − | 3.17568i | −0.326391 | − | 0.188442i | ||||
\(285\) | −1.53849 | + | 2.66474i | −0.0911323 | + | 0.157846i | ||||
\(286\) | −8.19351 | − | 23.8797i | −0.484493 | − | 1.41204i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −20.1721 | + | 11.6464i | −1.18865 | + | 0.686270i | ||||
\(289\) | −7.22433 | −0.424960 | ||||||||
\(290\) | −22.4201 | −1.31656 | ||||||||
\(291\) | 6.95151 | − | 4.01345i | 0.407504 | − | 0.235273i | ||||
\(292\) | −37.0603 | + | 21.3968i | −2.16879 | + | 1.25215i | ||||
\(293\) | 12.6831 | + | 7.32260i | 0.740956 | + | 0.427791i | 0.822417 | − | 0.568885i | \(-0.192625\pi\) |
−0.0814609 | + | 0.996677i | \(0.525959\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.20810 | + | 15.9489i | −0.536116 | + | 0.928580i | ||||
\(296\) | −41.6232 | −2.41930 | ||||||||
\(297\) | 6.96075 | + | 4.01879i | 0.403904 | + | 0.233194i | ||||
\(298\) | 25.6246 | + | 44.3831i | 1.48439 | + | 2.57104i | ||||
\(299\) | 4.70373 | − | 5.39920i | 0.272024 | − | 0.312244i | ||||
\(300\) | 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 | ||||
\(304\) | −27.7263 | + | 16.0078i | −1.59021 | + | 0.918108i | ||||
\(305\) | − | 4.71537i | − | 0.270001i | ||||||
\(306\) | −19.1435 | + | 11.0525i | −1.09436 | + | 0.631830i | ||||
\(307\) | − | 8.97844i | − | 0.512427i | −0.966620 | − | 0.256213i | \(-0.917525\pi\) | ||
0.966620 | − | 0.256213i | \(-0.0824750\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.97271 | − | 5.14889i | −0.169112 | − | 0.292910i | ||||
\(310\) | − | 43.7245i | − | 2.48338i | ||||||
\(311\) | −6.09080 | − | 10.5496i | −0.345378 | − | 0.598212i | 0.640045 | − | 0.768338i | \(-0.278916\pi\) |
−0.985422 | + | 0.170126i | \(0.945583\pi\) | |||||||
\(312\) | 12.3620 | − | 4.24161i | 0.699862 | − | 0.240134i | ||||
\(313\) | 6.56198 | − | 11.3657i | 0.370905 | − | 0.642427i | −0.618800 | − | 0.785549i | \(-0.712381\pi\) |
0.989705 | + | 0.143122i | \(0.0457141\pi\) | |||||||
\(314\) | −31.3951 | + | 18.1260i | −1.77173 | + | 1.02291i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.5862 | + | 25.2641i | −0.820540 | + | 1.42122i | ||||
\(317\) | 14.4761 | + | 8.35775i | 0.813056 | + | 0.469418i | 0.848016 | − | 0.529971i | \(-0.177797\pi\) |
−0.0349599 | + | 0.999389i | \(0.511130\pi\) | |||||||
\(318\) | − | 9.75127i | − | 0.546824i | ||||||
\(319\) | 14.5330i | 0.813689i | ||||||||
\(320\) | −6.53932 | − | 3.77548i | −0.365559 | − | 0.211056i | ||||
\(321\) | −1.33123 | + | 2.30575i | −0.0743018 | + | 0.128695i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.96849 | + | 5.75531i | −0.554661 | + | 0.320234i | ||||
\(324\) | 15.6374 | − | 27.0847i | 0.868743 | − | 1.50471i | ||||
\(325\) | 8.49708 | + | 1.66122i | 0.471333 | + | 0.0921480i | ||||
\(326\) | 9.28007 | + | 16.0736i | 0.513976 | + | 0.890232i | ||||
\(327\) | − | 0.895821i | − | 0.0495390i | ||||||
\(328\) | −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 | \(-0.701436\pi\) |
0.402612 | + | 0.915371i | \(0.368102\pi\) | |||||||
\(332\) | − | 12.6769i | − | 0.695733i | ||||||
\(333\) | 14.0816 | − | 8.13002i | 0.771668 | − | 0.445523i | ||||
\(334\) | −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 | \(0.621750\pi\) | |||||||
\(338\) | 33.3344 | − | 4.61121i | 1.81315 | − | 0.250817i | ||||
\(339\) | −2.22710 | − | 3.85746i | −0.120960 | − | 0.209508i | ||||
\(340\) | −20.5192 | − | 11.8468i | −1.11281 | − | 0.642481i | ||||
\(341\) | −28.3426 | −1.53484 | ||||||||
\(342\) | 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 | ||||
\(346\) | −28.7209 | + | 16.5820i | −1.54405 | + | 0.891456i | ||||
\(347\) | −26.3979 | −1.41711 | −0.708556 | − | 0.705655i | \(-0.750653\pi\) | ||||
−0.708556 | + | 0.705655i | \(0.750653\pi\) | |||||||
\(348\) | −13.0945 | −0.701941 | ||||||||
\(349\) | 4.23507 | − | 2.44512i | 0.226698 | − | 0.130884i | −0.382350 | − | 0.924018i | \(-0.624885\pi\) |
0.609048 | + | 0.793133i | \(0.291552\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.03753 | + | 8.07806i | −0.375636 | + | 0.431175i | ||||
\(352\) | −11.5345 | + | 19.9784i | −0.614792 | + | 1.06485i | ||||
\(353\) | 11.7413 | + | 6.77886i | 0.624928 | + | 0.360802i | 0.778785 | − | 0.627291i | \(-0.215836\pi\) |
−0.153857 | + | 0.988093i | \(0.549170\pi\) | |||||||
\(354\) | −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 | ||||
\(359\) | 7.43541 | + | 4.29284i | 0.392426 | + | 0.226567i | 0.683211 | − | 0.730221i | \(-0.260583\pi\) |
−0.290785 | + | 0.956789i | \(0.593916\pi\) | |||||||
\(360\) | 30.7821 | 1.62236 | ||||||||
\(361\) | −2.72326 | + | 4.71683i | −0.143330 | + | 0.248254i | ||||
\(362\) | 8.54053i | 0.448880i | ||||||||
\(363\) | −1.90962 | −0.100229 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6751 | 0.768130 | ||||||||
\(366\) | − | 3.92574i | − | 0.205202i | ||||||
\(367\) | −0.831612 | + | 1.44039i | −0.0434098 | + | 0.0751880i | −0.886914 | − | 0.461935i | \(-0.847155\pi\) |
0.843504 | + | 0.537123i | \(0.180489\pi\) | |||||||
\(368\) | −17.2712 | −0.900324 | ||||||||
\(369\) | 18.2162 | + | 10.5171i | 0.948299 | + | 0.547501i | ||||
\(370\) | 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 | 0.626707 | − | 0.779255i | \(-0.284402\pi\) |
−0.988208 | + | 0.153117i | \(0.951069\pi\) | |||||||
\(374\) | −10.9463 | + | 18.9596i | −0.566022 | + | 0.980378i | ||||
\(375\) | −5.35719 | − | 3.09298i | −0.276644 | − | 0.159721i | ||||
\(376\) | −3.68828 | + | 6.38828i | −0.190208 | + | 0.329450i | ||||
\(377\) | −19.0117 | − | 3.71687i | −0.979150 | − | 0.191429i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3454 | + | 15.7879i | −1.40464 | + | 0.810969i | −0.994864 | − | 0.101218i | \(-0.967726\pi\) |
−0.409775 | + | 0.912187i | \(0.634393\pi\) | |||||||
\(380\) | 27.8985 | 1.43116 | ||||||||
\(381\) | −1.61975 | −0.0829822 | ||||||||
\(382\) | 10.9761 | − | 6.33707i | 0.561588 | − | 0.324233i | ||||
\(383\) | 27.6333 | − | 15.9541i | 1.41200 | − | 0.815217i | 0.416420 | − | 0.909172i | \(-0.363284\pi\) |
0.995576 | + | 0.0939554i | \(0.0299511\pi\) | |||||||
\(384\) | 2.21435 | + | 1.27846i | 0.113001 | + | 0.0652410i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.90762 | + | 6.76820i | −0.198893 | + | 0.344492i | ||||
\(387\) | −9.16588 | −0.465928 | ||||||||
\(388\) | −63.0283 | − | 36.3894i | −3.19978 | − | 1.84739i | ||||
\(389\) | −12.7075 | − | 22.0100i | −0.644296 | − | 1.11595i | −0.984464 | − | 0.175589i | \(-0.943817\pi\) |
0.340168 | − | 0.940365i | \(-0.389516\pi\) | |||||||
\(390\) | −7.65581 | − | 1.49675i | −0.387667 | − | 0.0757908i | ||||
\(391\) | −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 | ||||
\(395\) | 8.66376 | − | 5.00203i | 0.435921 | − | 0.251679i | ||||
\(396\) | − | 34.7288i | − | 1.74519i | ||||||
\(397\) | 3.60178 | − | 2.07949i | 0.180768 | − | 0.104366i | −0.406885 | − | 0.913479i | \(-0.633385\pi\) |
0.587653 | + | 0.809113i | \(0.300052\pi\) | |||||||
\(398\) | 1.06319i | 0.0532930i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.4412 | − | 18.0846i | −0.522058 | − | 0.904231i | ||||
\(401\) | 19.6013i | 0.978844i | 0.872047 | + | 0.489422i | \(0.162792\pi\) | ||||
−0.872047 | + | 0.489422i | \(0.837208\pi\) | |||||||
\(402\) | 9.11409 | + | 15.7861i | 0.454569 | + | 0.787337i | ||||
\(403\) | 7.24877 | − | 37.0772i | 0.361087 | − | 1.84695i | ||||
\(404\) | −3.00691 | + | 5.20811i | −0.149599 | + | 0.259113i | ||||
\(405\) | −9.28811 | + | 5.36249i | −0.461530 | + | 0.266464i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.05193 | − | 13.9463i | 0.399119 | − | 0.691295i | ||||
\(408\) | −9.81500 | − | 5.66669i | −0.485915 | − | 0.280543i | ||||
\(409\) | 17.6337i | 0.871930i | 0.899964 | + | 0.435965i | \(0.143593\pi\) | ||||
−0.899964 | + | 0.435965i | \(0.856407\pi\) | |||||||
\(410\) | 32.1381i | 1.58719i | ||||||||
\(411\) | 4.48673 | + | 2.59041i | 0.221314 | + | 0.127776i | ||||
\(412\) | −26.9532 | + | 46.6842i | −1.32789 | + | 2.29997i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.1601 | − | 7.02061i | 0.597634 | − | 0.345044i | ||||
\(415\) | −2.17363 | + | 3.76483i | −0.106699 | + | 0.184808i | ||||
\(416\) | −23.1852 | − | 20.1987i | −1.13675 | − | 0.990324i | ||||
\(417\) | 0.431416 | + | 0.747234i | 0.0211265 | + | 0.0365922i | ||||
\(418\) | − | 25.7781i | − | 1.26085i | ||||||
\(419\) | 14.9455 | + | 25.8864i | 0.730137 | + | 1.26463i | 0.956824 | + | 0.290666i | \(0.0938770\pi\) |
−0.226688 | + | 0.973968i | \(0.572790\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | − | 2.88164i | − | 0.140110i | ||||||
\(424\) | −43.9919 | + | 25.3987i | −2.13644 | + | 1.23347i | ||||
\(425\) | −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 | ||||||||
\(429\) | −0.970207 | + | 4.96257i | −0.0468421 | + | 0.239595i | ||||
\(430\) | −7.00223 | − | 12.1282i | −0.337677 | − | 0.584874i | ||||
\(431\) | 7.76876 | + | 4.48530i | 0.374208 | + | 0.216049i | 0.675295 | − | 0.737547i | \(-0.264016\pi\) |
−0.301087 | + | 0.953597i | \(0.597350\pi\) | |||||||
\(432\) | 25.8405 | 1.24325 | ||||||||
\(433\) | 1.72531 | − | 2.98833i | 0.0829132 | − | 0.143610i | −0.821587 | − | 0.570083i | \(-0.806911\pi\) |
0.904500 | + | 0.426473i | \(0.140244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.88887 | + | 2.24524i | 0.186457 | + | 0.107651i | ||||
\(436\) | −7.03410 | + | 4.06114i | −0.336872 | + | 0.194493i | ||||
\(437\) | 6.33204 | − | 3.65580i | 0.302902 | − | 0.174881i | ||||
\(438\) | 12.2176 | 0.583780 | ||||||||
\(439\) | −38.5144 | −1.83819 | −0.919096 | − | 0.394034i | \(-0.871079\pi\) | ||||
−0.919096 | + | 0.394034i | \(0.871079\pi\) | |||||||
\(440\) | 26.4020 | − | 15.2432i | 1.25867 | − | 0.726691i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.0029 | − | 19.1687i | −1.04657 | − | 0.911764i | ||||
\(443\) | 7.51997 | − | 13.0250i | 0.357284 | − | 0.618835i | −0.630222 | − | 0.776415i | \(-0.717036\pi\) |
0.987506 | + | 0.157580i | \(0.0503693\pi\) | |||||||
\(444\) | 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 | \(0.296103\pi\) | |||||||
\(450\) | 14.7025 | + | 8.48850i | 0.693083 | + | 0.400152i | ||||
\(451\) | 20.8322 | 0.980952 | ||||||||
\(452\) | −20.1928 | + | 34.9750i | −0.949790 | + | 1.64509i | ||||
\(453\) | 3.90660i | 0.183548i | ||||||||
\(454\) | 35.3906 | 1.66097 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.3448 | 0.624927 | ||||||||
\(457\) | 13.9396i | 0.652069i | 0.945358 | + | 0.326034i | \(0.105713\pi\) | ||||
−0.945358 | + | 0.326034i | \(0.894287\pi\) | |||||||
\(458\) | 10.2649 | − | 17.7793i | 0.479648 | − | 0.830774i | ||||
\(459\) | 9.29049 | 0.433643 | ||||||||
\(460\) | 13.0339 | + | 7.52512i | 0.607709 | + | 0.350861i | ||||
\(461\) | −32.4443 | − | 18.7317i | −1.51108 | − | 0.872424i | −0.999916 | − | 0.0129430i | \(-0.995880\pi\) |
−0.511167 | − | 0.859481i | \(-0.670787\pi\) | |||||||
\(462\) | 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 | ||||
\(467\) | −2.52516 | + | 4.37371i | −0.116851 | + | 0.202391i | −0.918518 | − | 0.395379i | \(-0.870613\pi\) |
0.801667 | + | 0.597770i | \(0.203947\pi\) | |||||||
\(468\) | 45.4314 | + | 8.88205i | 2.10006 | + | 0.410573i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.81296 | − | 2.20141i | 0.175879 | − | 0.101544i | ||||
\(471\) | 7.26084 | 0.334562 | ||||||||
\(472\) | 79.8705 | 3.67634 | ||||||||
\(473\) | −7.86163 | + | 4.53892i | −0.361478 | + | 0.208700i | ||||
\(474\) | 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 | ||||
\(478\) | 24.3143 | 1.11211 | ||||||||
\(479\) | −8.18670 | − | 4.72659i | −0.374060 | − | 0.215964i | 0.301171 | − | 0.953570i | \(-0.402623\pi\) |
−0.675231 | + | 0.737607i | \(0.735956\pi\) | |||||||
\(480\) | 3.56401 | + | 6.17304i | 0.162674 | + | 0.281759i | ||||
\(481\) | 16.1850 | + | 14.1002i | 0.737971 | + | 0.642913i | ||||
\(482\) | 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 | ||||
\(486\) | −27.7167 | + | 16.0023i | −1.25726 | + | 0.725877i | ||||
\(487\) | 39.9996i | 1.81255i | 0.422684 | + | 0.906277i | \(0.361088\pi\) | ||||
−0.422684 | + | 0.906277i | \(0.638912\pi\) | |||||||
\(488\) | −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 | \(0.882085\pi\) | |||||||
\(492\) | 18.7704i | 0.846233i | ||||||||
\(493\) | 8.39918 | + | 14.5478i | 0.378280 | + | 0.655200i | ||||
\(494\) | 33.7223 | + | 6.59287i | 1.51724 | + | 0.296627i | ||||
\(495\) | −5.95473 | + | 10.3139i | −0.267645 | + | 0.463575i | ||||
\(496\) | −78.9125 | + | 45.5602i | −3.54328 | + | 2.04571i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.80963 | + | 3.13438i | −0.0810916 | + | 0.140455i | ||||
\(499\) | −9.83591 | − | 5.67877i | −0.440316 | − | 0.254217i | 0.263416 | − | 0.964682i | \(-0.415151\pi\) |
−0.703732 | + | 0.710466i | \(0.748484\pi\) | |||||||
\(500\) | 56.0871i | 2.50829i | ||||||||
\(501\) | 9.32230i | 0.416490i | ||||||||
\(502\) | 23.1993 | + | 13.3941i | 1.03543 | + | 0.597808i | ||||
\(503\) | −6.96423 | + | 12.0624i | −0.310520 | + | 0.537836i | −0.978475 | − | 0.206365i | \(-0.933836\pi\) |
0.667955 | + | 0.744202i | \(0.267170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.78601 | − | 1.03115i | 0.0794763 | − | 0.0458857i | ||||
\(506\) | 6.95317 | − | 12.0432i | 0.309106 | − | 0.535388i | ||||
\(507\) | −6.24379 | − | 2.53840i | −0.277296 | − | 0.112734i | ||||
\(508\) | 7.34301 | + | 12.7185i | 0.325793 | + | 0.564290i | ||||
\(509\) | 19.8149i | 0.878281i | 0.898418 | + | 0.439141i | \(0.144717\pi\) | ||||
−0.898418 | + | 0.439141i | \(0.855283\pi\) | |||||||
\(510\) | 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 | ||||
\(514\) | 20.6741i | 0.911894i | ||||||||
\(515\) | 16.0093 | − | 9.24299i | 0.705455 | − | 0.407295i | ||||
\(516\) | −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 | ||||||||
\(520\) | 13.1883 | + | 38.4370i | 0.578347 | + | 1.68557i | ||||
\(521\) | −15.5476 | − | 26.9292i | −0.681151 | − | 1.17979i | −0.974630 | − | 0.223823i | \(-0.928146\pi\) |
0.293479 | − | 0.955966i | \(-0.405187\pi\) | |||||||
\(522\) | −32.8959 | − | 18.9924i | −1.43981 | − | 0.831277i | ||||
\(523\) | −22.7202 | −0.993485 | −0.496742 | − | 0.867898i | \(-0.665471\pi\) | ||||
−0.496742 | + | 0.867898i | \(0.665471\pi\) | |||||||
\(524\) | −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 | ||||
\(528\) | 10.5620 | − | 6.09798i | 0.459652 | − | 0.265380i | ||||
\(529\) | −19.0557 | −0.828507 | ||||||||
\(530\) | 30.3194 | 1.31699 | ||||||||
\(531\) | −27.0211 | + | 15.6007i | −1.17262 | + | 0.677011i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.32794 | + | 27.2522i | −0.230779 | + | 1.18043i | ||||
\(534\) | −1.18097 | + | 2.04549i | −0.0511054 | + | 0.0885171i | ||||
\(535\) | −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 | ||||
\(541\) | 1.81754 | + | 1.04936i | 0.0781423 | + | 0.0451155i | 0.538562 | − | 0.842586i | \(-0.318968\pi\) |
−0.460420 | + | 0.887701i | \(0.652301\pi\) | |||||||
\(542\) | 21.5558 | 0.925902 | ||||||||
\(543\) | 0.855283 | − | 1.48139i | 0.0367037 | − | 0.0635727i | ||||
\(544\) | 26.6650i | 1.14325i | ||||||||
\(545\) | 2.78536 | 0.119312 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.3770 | 1.08504 | 0.542521 | − | 0.840042i | \(-0.317470\pi\) | ||||
0.542521 | + | 0.840042i | \(0.317470\pi\) | |||||||
\(548\) | − | 46.9738i | − | 2.00662i | ||||||
\(549\) | 3.99447 | − | 6.91862i | 0.170480 | − | 0.295280i | ||||
\(550\) | 16.8139 | 0.716948 | ||||||||
\(551\) | −17.1297 | − | 9.88983i | −0.729749 | − | 0.421321i | ||||
\(552\) | 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 | −0.985904 | − | 0.167309i | \(-0.946492\pi\) |
−0.637846 | − | 0.770164i | \(-0.720174\pi\) | |||||||
\(558\) | 37.0397 | − | 64.1547i | 1.56802 | − | 2.71588i | ||||
\(559\) | −3.92705 | − | 11.4452i | −0.166097 | − | 0.484082i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.79738 | − | 2.19242i | 0.160326 | − | 0.0925641i | ||||
\(562\) | 70.3051 | 2.96564 | ||||||||
\(563\) | −38.8907 | −1.63905 | −0.819523 | − | 0.573046i | \(-0.805762\pi\) | ||||
−0.819523 | + | 0.573046i | \(0.805762\pi\) | |||||||
\(564\) | 2.22697 | − | 1.28574i | 0.0937725 | − | 0.0541396i | ||||
\(565\) | 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 | ||||
\(569\) | −46.1579 | −1.93504 | −0.967520 | − | 0.252796i | \(-0.918650\pi\) | ||||
−0.967520 | + | 0.252796i | \(0.918650\pi\) | |||||||
\(570\) | −6.89796 | − | 3.98254i | −0.288924 | − | 0.166810i | ||||
\(571\) | 10.5684 | + | 18.3050i | 0.442274 | + | 0.766041i | 0.997858 | − | 0.0654194i | \(-0.0208385\pi\) |
−0.555584 | + | 0.831461i | \(0.687505\pi\) | |||||||
\(572\) | 43.3651 | − | 14.8793i | 1.81319 | − | 0.622134i | ||||
\(573\) | −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 | ||||
\(577\) | −21.9368 | + | 12.6652i | −0.913239 | + | 0.527259i | −0.881472 | − | 0.472237i | \(-0.843447\pi\) |
−0.0317671 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(578\) | − | 18.7009i | − | 0.777855i | ||||||
\(579\) | 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 | ||||
\(583\) | − | 19.6533i | − | 0.813958i | ||||||
\(584\) | −31.8227 | − | 55.1186i | −1.31683 | − | 2.28082i | ||||
\(585\) | −11.9694 | − | 10.4277i | −0.494876 | − | 0.431131i | ||||
\(586\) | −18.9553 | + | 32.8315i | −0.783036 | + | 1.35626i | ||||
\(587\) | −3.08554 | + | 1.78144i | −0.127354 | + | 0.0735278i | −0.562324 | − | 0.826917i | \(-0.690092\pi\) |
0.434970 | + | 0.900445i | \(0.356759\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.2875 | − | 33.4069i | 0.794727 | − | 1.37651i | ||||
\(590\) | −41.2853 | − | 23.8361i | −1.69969 | − | 0.981316i | ||||
\(591\) | − | 2.41082i | − | 0.0991679i | ||||||
\(592\) | − | 51.7732i | − | 2.12786i | ||||||
\(593\) | −21.9568 | − | 12.6768i | −0.901659 | − | 0.520573i | −0.0239212 | − | 0.999714i | \(-0.507615\pi\) |
−0.877738 | + | 0.479141i | \(0.840948\pi\) | |||||||
\(594\) | −10.4030 | + | 18.0186i | −0.426842 | + | 0.739312i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −80.5990 | + | 46.5338i | −3.30146 | + | 1.90610i | ||||
\(597\) | 0.106472 | − | 0.184415i | 0.00435762 | − | 0.00754762i | ||||
\(598\) | 13.9764 | + | 12.1761i | 0.571537 | + | 0.497917i | ||||
\(599\) | −5.46078 | − | 9.45835i | −0.223122 | − | 0.386458i | 0.732633 | − | 0.680624i | \(-0.238291\pi\) |
−0.955754 | + | 0.294166i | \(0.904958\pi\) | |||||||
\(600\) | 8.70421i | 0.355348i | ||||||||
\(601\) | 12.1282 | + | 21.0067i | 0.494720 | + | 0.856880i | 0.999981 | − | 0.00608649i | \(-0.00193740\pi\) |
−0.505262 | + | 0.862966i | \(0.668604\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.0946i | 1.51061i | ||||||||
\(604\) | 30.6751 | − | 17.7103i | 1.24815 | − | 0.720621i | ||||
\(605\) | − | 5.93753i | − | 0.241395i | ||||||
\(606\) | 1.48692 | − | 0.858476i | 0.0604022 | − | 0.0348732i | ||||
\(607\) | −4.92724 | − | 8.53422i | −0.199990 | − | 0.346393i | 0.748535 | − | 0.663096i | \(-0.230758\pi\) |
−0.948525 | + | 0.316702i | \(0.897424\pi\) | |||||||
\(608\) | −15.6987 | − | 27.1910i | −0.636667 | − | 1.10274i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.2062 | 0.494215 | ||||||||
\(611\) | 3.59825 | − | 1.23462i | 0.145569 | − | 0.0499472i | ||||
\(612\) | −20.0712 | − | 34.7643i | −0.811328 | − | 1.40526i | ||||
\(613\) | −3.18428 | − | 1.83844i | −0.128612 | − | 0.0742540i | 0.434314 | − | 0.900762i | \(-0.356991\pi\) |
−0.562926 | + | 0.826508i | \(0.690324\pi\) | |||||||
\(614\) | 23.2416 | 0.937955 | ||||||||
\(615\) | 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 | ||||
\(619\) | −13.7650 | + | 7.94725i | −0.553264 | + | 0.319427i | −0.750437 | − | 0.660942i | \(-0.770157\pi\) |
0.197174 | + | 0.980369i | \(0.436824\pi\) | |||||||
\(620\) | 79.4029 | 3.18890 | ||||||||
\(621\) | −5.90137 | −0.236814 | ||||||||
\(622\) | 27.3086 | − | 15.7667i | 1.09498 | − | 0.632185i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.27594 | + | 15.3765i | 0.211207 | + | 0.615555i | ||||
\(625\) | 3.61371 | − | 6.25913i | 0.144549 | − | 0.250365i | ||||
\(626\) | 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 | \(0.795236\pi\) | |||||||
\(632\) | −37.5745 | − | 21.6936i | −1.49463 | − | 0.862927i | ||||
\(633\) | 3.89679 | 0.154883 | ||||||||
\(634\) | −21.6349 | + | 37.4727i | −0.859231 | + | 1.48823i | ||||
\(635\) | − | 5.03624i | − | 0.199857i | ||||||
\(636\) | 17.7081 | 0.702173 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −37.6200 | −1.48939 | ||||||||
\(639\) | 3.69014i | 0.145980i | ||||||||
\(640\) | −3.97508 | + | 6.88504i | −0.157129 | + | 0.272155i | ||||
\(641\) | 29.7786 | 1.17618 | 0.588092 | − | 0.808794i | \(-0.299879\pi\) | ||||
0.588092 | + | 0.808794i | \(0.299879\pi\) | |||||||
\(642\) | −5.96867 | − | 3.44601i | −0.235565 | − | 0.136003i | ||||
\(643\) | −10.0220 | − | 5.78623i | −0.395231 | − | 0.228187i | 0.289193 | − | 0.957271i | \(-0.406613\pi\) |
−0.684424 | + | 0.729084i | \(0.739946\pi\) | |||||||
\(644\) | 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 | 0.498616 | + | 0.866823i | \(0.333842\pi\) |
−0.999999 | + | 0.00159698i | \(0.999492\pi\) | |||||||
\(648\) | 40.2823 | + | 23.2570i | 1.58244 | + | 0.913620i | ||||
\(649\) | −15.4508 | + | 26.7616i | −0.606497 | + | 1.05048i | ||||
\(650\) | −4.30024 | + | 21.9956i | −0.168669 | + | 0.862737i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29.1893 | + | 16.8524i | −1.14314 | + | 0.659993i | ||||
\(653\) | −44.8293 | −1.75430 | −0.877152 | − | 0.480212i | \(-0.840560\pi\) | ||||
−0.877152 | + | 0.480212i | \(0.840560\pi\) | |||||||
\(654\) | 2.31892 | 0.0906771 | ||||||||
\(655\) | 14.2529 | − | 8.22889i | 0.556905 | − | 0.321529i | ||||
\(656\) | 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 | \(0.870466\pi\) | |||||||
\(660\) | −10.6276 | −0.413680 | ||||||||
\(661\) | 18.9606 | + | 10.9469i | 0.737481 | + | 0.425785i | 0.821153 | − | 0.570709i | \(-0.193331\pi\) |
−0.0836719 | + | 0.996493i | \(0.526665\pi\) | |||||||
\(662\) | −5.13404 | − | 8.89241i | −0.199540 | − | 0.345613i | ||||
\(663\) | 1.89687 | + | 5.52837i | 0.0736684 | + | 0.214704i | ||||
\(664\) | 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 | ||||
\(668\) | 73.1999 | − | 42.2620i | 2.83219 | − | 1.63516i | ||||
\(669\) | − | 11.7067i | − | 0.452606i | ||||||
\(670\) | −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 | \(0.592056\pi\) | |||||||
\(674\) | − | 35.4721i | − | 1.36633i | ||||||
\(675\) | −3.56762 | − | 6.17930i | −0.137318 | − | 0.237841i | ||||
\(676\) | 8.37388 | + | 60.5347i | 0.322072 | + | 2.32826i | ||||
\(677\) | 1.27766 | − | 2.21297i | 0.0491044 | − | 0.0850514i | −0.840428 | − | 0.541923i | \(-0.817697\pi\) |
0.889533 | + | 0.456871i | \(0.151030\pi\) | |||||||
\(678\) | 9.98541 | − | 5.76508i | 0.383488 | − | 0.221407i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 17.6193 | − | 30.5175i | 0.675670 | − | 1.17029i | ||||
\(681\) | −6.13867 | − | 3.54416i | −0.235234 | − | 0.135813i | ||||
\(682\) | − | 73.3678i | − | 2.80940i | ||||||
\(683\) | − | 35.7399i | − | 1.36755i | −0.729693 | − | 0.683775i | \(-0.760337\pi\) | ||
0.729693 | − | 0.683775i | \(-0.239663\pi\) | |||||||
\(684\) | 40.9341 | + | 23.6333i | 1.56515 | + | 0.903642i | ||||
\(685\) | −8.05431 | + | 13.9505i | −0.307739 | + | 0.533020i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.56099 | + | 2.05594i | −0.135860 | + | 0.0784390i | ||||
\(688\) | −14.5924 | + | 25.2748i | −0.556330 | + | 0.963592i | ||||
\(689\) | 25.7100 | + | 5.02643i | 0.979474 | + | 0.191492i | ||||
\(690\) | −2.14843 | − | 3.72120i | −0.0817895 | − | 0.141664i | ||||
\(691\) | 26.0292i | 0.990197i | 0.868837 | + | 0.495099i | \(0.164868\pi\) | ||||
−0.868837 | + | 0.495099i | \(0.835132\pi\) | |||||||
\(692\) | −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 | ||||
\(696\) | − | 19.4751i | − | 0.738202i | ||||||
\(697\) | 20.8535 | − | 12.0398i | 0.789884 | − | 0.456040i | ||||
\(698\) | 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 | \(0.506777\pi\) | |||||||
\(702\) | −20.9109 | − | 18.2174i | −0.789230 | − | 0.687570i | ||||
\(703\) | 10.9588 | + | 18.9813i | 0.413321 | + | 0.715892i | ||||
\(704\) | −10.9727 | − | 6.33509i | −0.413549 | − | 0.238763i | ||||
\(705\) | −0.881834 | −0.0332118 | ||||||||
\(706\) | −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 | \(-0.702909\pi\) |
0.398372 | + | 0.917224i | \(0.369575\pi\) | |||||||
\(710\) | −4.88276 | + | 2.81906i | −0.183247 | + | 0.105798i | ||||
\(711\) | 16.9492 | 0.635644 | ||||||||
\(712\) | 12.3040 | 0.461114 | ||||||||
\(713\) | 18.0218 | − | 10.4049i | 0.674922 | − | 0.389666i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.4300 | − | 3.01664i | −0.577050 | − | 0.112816i | ||||
\(716\) | −4.32530 | + | 7.49164i | −0.161644 | + | 0.279976i | ||||
\(717\) | −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 | −0.852880 | − | 0.522106i | \(-0.825146\pi\) |
−0.0257170 | − | 0.999669i | \(-0.508187\pi\) | |||||||
\(720\) | 38.2884i | 1.42692i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.2100 | − | 7.04944i | −0.454409 | − | 0.262353i | ||||
\(723\) | −4.52859 | − | 2.61458i | −0.168420 | − | 0.0972374i | ||||
\(724\) | −15.5095 | −0.576404 | ||||||||
\(725\) | 6.45070 | − | 11.1729i | 0.239573 | − | 0.414953i | ||||
\(726\) | − | 4.94324i | − | 0.183461i | ||||||
\(727\) | −17.9215 | −0.664671 | −0.332335 | − | 0.943161i | \(-0.607837\pi\) | ||||
−0.332335 | + | 0.943161i | \(0.607837\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.5489 | −0.501810 | ||||||||
\(730\) | 37.9880i | 1.40600i | ||||||||
\(731\) | −5.24644 | + | 9.08711i | −0.194047 | + | 0.336099i | ||||
\(732\) | 7.12908 | 0.263498 | ||||||||
\(733\) | 39.2037 | + | 22.6343i | 1.44802 | + | 0.836016i | 0.998364 | − | 0.0571848i | \(-0.0182124\pi\) |
0.449658 | + | 0.893201i | \(0.351546\pi\) | |||||||
\(734\) | −3.72861 | − | 2.15271i | −0.137625 | − | 0.0794581i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 16.9378i | − | 0.624335i | ||||||
\(737\) | 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 | \(-0.218063\pi\) |
−0.160765 | + | 0.986993i | \(0.551396\pi\) | |||||||
\(740\) | −22.5577 | + | 39.0712i | −0.829239 | + | 1.43628i | ||||
\(741\) | −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 | \(0.112306\pi\) | |||||||
\(744\) | 37.9810 | 1.39245 | ||||||||
\(745\) | 31.9155 | 1.16929 | ||||||||
\(746\) | 31.3032 | − | 18.0729i | 1.14609 | − | 0.661697i | ||||
\(747\) | −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 | ||||
\(751\) | 24.9668 | 0.911051 | 0.455526 | − | 0.890223i | \(-0.349451\pi\) | ||||
0.455526 | + | 0.890223i | \(0.349451\pi\) | |||||||
\(752\) | −7.94609 | − | 4.58767i | −0.289764 | − | 0.167295i | ||||
\(753\) | −2.68268 | − | 4.64654i | −0.0977623 | − | 0.169329i | ||||
\(754\) | 9.62150 | − | 49.2136i | 0.350394 | − | 1.79225i | ||||
\(755\) | −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 | ||||
\(759\) | −2.41212 | + | 1.39264i | −0.0875543 | + | 0.0505495i | ||||
\(760\) | 41.4926i | 1.50510i | ||||||||
\(761\) | −28.2660 | + | 16.3194i | −1.02464 | + | 0.591578i | −0.915446 | − | 0.402442i | \(-0.868162\pi\) |
−0.109198 | + | 0.994020i | \(0.534828\pi\) | |||||||
\(762\) | − | 4.19288i | − | 0.151892i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.5080 | + | 19.9325i | 0.416345 | + | 0.721131i | ||||
\(765\) | 13.7659i | 0.497708i | ||||||||
\(766\) | 41.2988 | + | 71.5316i | 1.49219 | + | 2.58454i | ||||
\(767\) | −31.0572 | − | 27.0568i | −1.12141 | − | 0.976963i | ||||
\(768\) | −5.73794 | + | 9.93841i | −0.207050 | + | 0.358621i | ||||
\(769\) | 45.1851 | − | 26.0876i | 1.62942 | − | 0.940744i | 0.645148 | − | 0.764057i | \(-0.276796\pi\) |
0.984267 | − | 0.176686i | \(-0.0565378\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.07039 | − | 3.58601i | 0.0745631 | − | 0.129147i | ||||
\(772\) | −12.2909 | − | 7.09618i | −0.442360 | − | 0.255397i | ||||
\(773\) | 35.7057i | 1.28425i | 0.766602 | + | 0.642123i | \(0.221946\pi\) | ||||
−0.766602 | + | 0.642123i | \(0.778054\pi\) | |||||||
\(774\) | − | 23.7268i | − | 0.852842i | ||||||
\(775\) | 21.7898 | + | 12.5804i | 0.782714 | + | 0.451900i | ||||
\(776\) | 54.1208 | − | 93.7400i | 1.94282 | − | 3.36507i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 56.9752 | − | 32.8947i | 2.04266 | − | 1.17933i | ||||
\(779\) | −14.1766 | + | 24.5545i | −0.507928 | + | 0.879757i | ||||
\(780\) | 2.71807 | − | 13.9028i | 0.0973225 | − | 0.497801i | ||||
\(781\) | 1.82735 | + | 3.16506i | 0.0653876 | + | 0.113255i | ||||
\(782\) | − | 16.0741i | − | 0.574808i | ||||||
\(783\) | 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 | ||||
\(787\) | − | 6.10621i | − | 0.217663i | −0.994060 | − | 0.108831i | \(-0.965289\pi\) | ||
0.994060 | − | 0.108831i | \(-0.0347109\pi\) | |||||||
\(788\) | −18.9301 | + | 10.9293i | −0.674356 | + | 0.389339i | ||||
\(789\) | 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 | ||||||||
\(793\) | 10.3505 | + | 2.02358i | 0.367559 | + | 0.0718595i | ||||
\(794\) | 5.38296 | + | 9.32356i | 0.191034 | + | 0.330881i | ||||
\(795\) | −5.25904 | − | 3.03631i | −0.186519 | − | 0.107687i | ||||
\(796\) | −1.93074 | −0.0684332 | ||||||||
\(797\) | 23.1149 | − | 40.0363i | 0.818773 | − | 1.41816i | −0.0878129 | − | 0.996137i | \(-0.527988\pi\) |
0.906586 | − | 0.422020i | \(-0.138679\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.85688 | − | 1.64942i | −0.101069 | − | 0.0583522i | ||||
\(800\) | 17.7355 | − | 10.2396i | 0.627044 | − | 0.362024i | ||||
\(801\) | −4.16260 | + | 2.40328i | −0.147078 | + | 0.0849157i | ||||
\(802\) | −50.7400 | −1.79169 | ||||||||
\(803\) | 24.6242 | 0.868968 | ||||||||
\(804\) | −28.6672 | + | 16.5510i | −1.01101 | + | 0.583710i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 95.9780 | + | 18.7642i | 3.38068 | + | 0.660939i | ||||
\(807\) | −3.60080 | + | 6.23678i | −0.126754 | + | 0.219545i | ||||
\(808\) | −7.74586 | − | 4.47208i | −0.272498 | − | 0.157327i | ||||
\(809\) | −19.6439 | + | 34.0243i | −0.690644 | + | 1.19623i | 0.280983 | + | 0.959713i | \(0.409339\pi\) |
−0.971627 | + | 0.236518i | \(0.923994\pi\) | |||||||
\(810\) | −13.8814 | − | 24.0432i | −0.487741 | − | 0.844792i | ||||
\(811\) | 6.90664i | 0.242525i | 0.992620 | + | 0.121262i | \(0.0386943\pi\) | ||||
−0.992620 | + | 0.121262i | \(0.961306\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.73896 | − | 2.15869i | −0.131131 | − | 0.0757085i | ||||
\(814\) | 36.1015 | + | 20.8432i | 1.26536 | + | 0.730555i | ||||
\(815\) | 11.5583 | 0.404871 | ||||||||
\(816\) | 7.04853 | − | 12.2084i | 0.246748 | − | 0.427380i | ||||
\(817\) | − | 12.3551i | − | 0.432251i | ||||||
\(818\) | −45.6466 | −1.59600 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −58.3622 | −2.03810 | ||||||||
\(821\) | 1.91049i | 0.0666765i | 0.999444 | + | 0.0333382i | \(0.0106139\pi\) | ||||
−0.999444 | + | 0.0333382i | \(0.989386\pi\) | |||||||
\(822\) | −6.70554 | + | 11.6143i | −0.233883 | + | 0.405097i | ||||
\(823\) | −1.57969 | −0.0550645 | −0.0275322 | − | 0.999621i | \(-0.508765\pi\) | ||||
−0.0275322 | + | 0.999621i | \(0.508765\pi\) | |||||||
\(824\) | −69.4320 | − | 40.0866i | −2.41878 | − | 1.39648i | ||||
\(825\) | −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 | −0.382714 | − | 0.923867i | \(-0.625011\pi\) |
0.991449 | − | 0.130493i | \(-0.0416561\pi\) | |||||||
\(830\) | −9.74564 | − | 5.62665i | −0.338276 | − | 0.195304i | ||||
\(831\) | 6.01721 | − | 10.4221i | 0.208735 | − | 0.361539i | ||||
\(832\) | 11.0937 | − | 12.7340i | 0.384606 | − | 0.441472i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.93429 | + | 1.11676i | −0.0669790 | + | 0.0386703i | ||||
\(835\) | −28.9856 | −1.00309 | ||||||||
\(836\) | 46.8126 | 1.61905 | ||||||||
\(837\) | −26.9635 | + | 15.5674i | −0.931994 | + | 0.538087i | ||||
\(838\) | −67.0096 | + | 38.6880i | −2.31481 | + | 1.33645i | ||||
\(839\) | −4.63746 | − | 2.67744i | −0.160103 | − | 0.0924354i | 0.417808 | − | 0.908535i | \(-0.362798\pi\) |
−0.577911 | + | 0.816100i | \(0.696132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.0669890 | − | 0.116028i | 0.00230997 | − | 0.00400098i | ||||
\(842\) | 33.2708 | 1.14659 | ||||||||
\(843\) | −12.1947 | − | 7.04064i | −0.420009 | − | 0.242492i | ||||
\(844\) | −17.6658 | − | 30.5981i | −0.608082 | − | 1.05323i | ||||
\(845\) | 7.89260 | − | 19.4137i | 0.271514 | − | 0.667850i | ||||
\(846\) | 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 | ||||
\(850\) | 16.8311 | − | 9.71744i | 0.577302 | − | 0.333305i | ||||
\(851\) | 11.8238i | 0.405314i | ||||||||
\(852\) | −2.85179 | + | 1.64648i | −0.0977008 | + | 0.0564076i | ||||
\(853\) | 49.6270i | 1.69920i | 0.527431 | + | 0.849598i | \(0.323155\pi\) | ||||
−0.527431 | + | 0.849598i | \(0.676845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.10452 | − | 14.0374i | −0.277169 | − | 0.480070i | ||||
\(856\) | 35.9028i | 1.22713i | ||||||||
\(857\) | −2.94196 | − | 5.09563i | −0.100496 | − | 0.174063i | 0.811393 | − | 0.584500i | \(-0.198709\pi\) |
−0.911889 | + | 0.410437i | \(0.865376\pi\) | |||||||
\(858\) | −12.8461 | − | 2.51148i | −0.438559 | − | 0.0857405i | ||||
\(859\) | 21.6931 | − | 37.5735i | 0.740159 | − | 1.28199i | −0.212264 | − | 0.977212i | \(-0.568084\pi\) |
0.952423 | − | 0.304780i | \(-0.0985830\pi\) | |||||||
\(860\) | 22.0246 | − | 12.7159i | 0.751033 | − | 0.433609i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.6106 | + | 20.1102i | −0.395460 | + | 0.684957i | ||||
\(863\) | 26.9570 | + | 15.5636i | 0.917626 | + | 0.529792i | 0.882877 | − | 0.469604i | \(-0.155603\pi\) |
0.0347490 | + | 0.999396i | \(0.488937\pi\) | |||||||
\(864\) | 25.3416i | 0.862139i | ||||||||
\(865\) | 20.6530i | 0.702222i | ||||||||
\(866\) | 7.73558 | + | 4.46614i | 0.262866 | + | 0.151766i | ||||
\(867\) | −1.87278 | + | 3.24376i | −0.0636031 | + | 0.110164i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.5374 | − | 8.39318i | 0.493148 | − | 0.284719i | ||||
\(870\) | −5.81203 | + | 10.0667i | −0.197046 | + | 0.341294i | ||||
\(871\) | −46.3192 | + | 15.8929i | −1.56947 | + | 0.538510i | ||||
\(872\) | −6.04001 | − | 10.4616i | −0.204540 | − | 0.354274i | ||||
\(873\) | 42.2844i | 1.43111i | ||||||||
\(874\) | 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 | \(-0.498158\pi\) |
0.868905 | + | 0.494979i | \(0.164824\pi\) | |||||||
\(878\) | − | 99.6984i | − | 3.36466i | ||||||
\(879\) | 6.57576 | − | 3.79652i | 0.221795 | − | 0.128053i | ||||
\(880\) | 18.9603 | + | 32.8402i | 0.639152 | + | 1.10704i | ||||
\(881\) | −7.28477 | − | 12.6176i | −0.245430 | − | 0.425097i | 0.716822 | − | 0.697256i | \(-0.245596\pi\) |
−0.962252 | + | 0.272159i | \(0.912262\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.9296 | 1.64661 | 0.823307 | − | 0.567597i | \(-0.192127\pi\) | ||||
0.823307 | + | 0.567597i | \(0.192127\pi\) | |||||||
\(884\) | 34.8101 | − | 39.9569i | 1.17079 | − | 1.34390i | ||||
\(885\) | 4.77408 | + | 8.26896i | 0.160479 | + | 0.277958i | ||||
\(886\) | 33.7164 | + | 19.4662i | 1.13273 | + | 0.653980i | ||||
\(887\) | −54.5902 | −1.83296 | −0.916480 | − | 0.400080i | \(-0.868982\pi\) | ||||
−0.916480 | + | 0.400080i | \(0.868982\pi\) | |||||||
\(888\) | −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 | ||||
\(892\) | −91.9222 | + | 53.0713i | −3.07778 | + | 1.77696i | ||||
\(893\) | 3.88430 | 0.129983 | ||||||||
\(894\) | 26.5710 | 0.888666 | ||||||||
\(895\) | 2.56909 | − | 1.48327i | 0.0858753 | − | 0.0495801i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.20490 | − | 3.51165i | −0.0402306 | − | 0.117251i | ||||
\(898\) | −50.3787 | + | 87.2584i | −1.68116 | + | 2.91185i | ||||
\(899\) | −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 | ||||
\(905\) | 4.60606 | + | 2.65931i | 0.153111 | + | 0.0883985i | ||||
\(906\) | −10.1126 | −0.335970 | ||||||||
\(907\) | 11.3628 | − | 19.6809i | 0.377295 | − | 0.653494i | −0.613373 | − | 0.789793i | \(-0.710188\pi\) |
0.990668 | + | 0.136300i | \(0.0435211\pi\) | |||||||
\(908\) | 64.2688i | 2.13283i | ||||||||
\(909\) | 3.49402 | 0.115889 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2359 | −1.39934 | −0.699669 | − | 0.714467i | \(-0.746669\pi\) | ||||
−0.699669 | + | 0.714467i | \(0.746669\pi\) | |||||||
\(912\) | 16.5990i | 0.549646i | ||||||||
\(913\) | −3.64725 | + | 6.31722i | −0.120706 | + | 0.209070i | ||||
\(914\) | −36.0842 | −1.19356 | ||||||||
\(915\) | −2.11722 | − | 1.22238i | −0.0699933 | − | 0.0404106i | ||||
\(916\) | 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 | −0.999974 | − | 0.00723365i | \(-0.997697\pi\) |
0.493722 | − | 0.869620i | \(-0.335636\pi\) | |||||||
\(920\) | −11.1919 | + | 19.3849i | −0.368985 | + | 0.639101i | ||||
\(921\) | −4.03136 | − | 2.32751i | −0.132838 | − | 0.0766940i | ||||
\(922\) | 48.4890 | − | 83.9854i | 1.59690 | − | 2.76591i | ||||
\(923\) | −4.60780 | + | 1.58101i | −0.151668 | + | 0.0520396i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.3806 | + | 7.14797i | −0.407073 | + | 0.235024i | ||||
\(926\) | −17.4802 | −0.574434 | ||||||||
\(927\) | 31.3195 | 1.02867 | ||||||||
\(928\) | −39.6819 | + | 22.9104i | −1.30262 | + | 0.752070i | ||||
\(929\) | 32.4110 | − | 18.7125i | 1.06337 | − | 0.613936i | 0.137007 | − | 0.990570i | \(-0.456252\pi\) |
0.926362 | + | 0.376634i | \(0.122918\pi\) | |||||||
\(930\) | −19.6325 | − | 11.3348i | −0.643775 | − | 0.371684i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15.4463 | − | 26.7538i | 0.505961 | − | 0.876350i | ||||
\(933\) | −6.31574 | −0.206768 | ||||||||
\(934\) | −11.3218 | − | 6.53663i | −0.370460 | − | 0.213885i | ||||
\(935\) | 6.81684 | + | 11.8071i | 0.222935 | + | 0.386134i | ||||
\(936\) | −13.2100 | + | 67.5686i | −0.431782 | + | 2.20855i | ||||
\(937\) | −44.3386 | −1.44848 | −0.724239 | − | 0.689549i | \(-0.757809\pi\) | ||||
−0.724239 | + | 0.689549i | \(0.757809\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.40216 | − | 5.89272i | −0.111025 | − | 0.192302i | ||||
\(940\) | 3.99773 | + | 6.92427i | 0.130392 | + | 0.225845i | ||||
\(941\) | 23.8202 | − | 13.7526i | 0.776518 | − | 0.448323i | −0.0586770 | − | 0.998277i | \(-0.518688\pi\) |
0.835195 | + | 0.549954i | \(0.185355\pi\) | |||||||
\(942\) | 18.7954i | 0.612388i | ||||||||
\(943\) | −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 | ||||
\(947\) | − | 5.08330i | − | 0.165185i | −0.996583 | − | 0.0825925i | \(-0.973680\pi\) | ||
0.996583 | − | 0.0825925i | \(-0.0263200\pi\) | |||||||
\(948\) | 7.56246 | + | 13.0986i | 0.245617 | + | 0.425422i | ||||
\(949\) | −6.29775 | + | 32.2128i | −0.204434 | + | 1.04567i | ||||
\(950\) | −11.4420 | + | 19.8182i | −0.371229 | + | 0.642987i | ||||
\(951\) | 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 | \(0.115853\pi\) | |||||||
\(954\) | 44.4861 | + | 25.6840i | 1.44029 | + | 0.831552i | ||||
\(955\) | − | 7.89284i | − | 0.255406i | ||||||
\(956\) | 44.1543i | 1.42805i | ||||||||
\(957\) | 6.52536 | + | 3.76742i | 0.210935 | + | 0.121783i | ||||
\(958\) | 12.2353 | − | 21.1921i | 0.395303 | − | 0.684685i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.39041 | + | 1.95746i | −0.109425 | + | 0.0631766i | ||||
\(961\) | 39.3947 | − | 68.2336i | 1.27080 | − | 2.20108i | ||||
\(962\) | −36.4997 | + | 41.8964i | −1.17680 | + | 1.35079i | ||||
\(963\) | −7.01268 | − | 12.1463i | −0.225981 | − | 0.391410i | ||||
\(964\) | 47.4121i | 1.52704i | ||||||||
\(965\) | 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 | ||||
\(969\) | 5.96786i | 0.191715i | ||||||||
\(970\) | −55.9504 | + | 32.3030i | −1.79646 | + | 1.03719i | ||||
\(971\) | 12.4620 | + | 21.5848i | 0.399925 | + | 0.692691i | 0.993716 | − | 0.111929i | \(-0.0357028\pi\) |
−0.593791 | + | 0.804619i | \(0.702369\pi\) | |||||||
\(972\) | −29.0598 | − | 50.3331i | −0.932094 | − | 1.61443i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −103.543 | −3.31773 | ||||||||
\(975\) | 2.94862 | − | 3.38459i | 0.0944314 | − | 0.108394i | ||||
\(976\) | −12.7187 | − | 22.0294i | −0.407115 | − | 0.705144i | ||||
\(977\) | 24.5197 | + | 14.1565i | 0.784456 | + | 0.452906i | 0.838007 | − | 0.545659i | \(-0.183721\pi\) |
−0.0535514 | + | 0.998565i | \(0.517054\pi\) | |||||||
\(978\) | 9.62280 | 0.307703 | ||||||||
\(979\) | −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 | ||||
\(983\) | 32.7805 | − | 18.9258i | 1.04554 | − | 0.603641i | 0.124140 | − | 0.992265i | \(-0.460383\pi\) |
0.921396 | + | 0.388624i | \(0.127049\pi\) | |||||||
\(984\) | −27.9166 | −0.889947 | ||||||||
\(985\) | 7.49591 | 0.238839 | ||||||||
\(986\) | −37.6585 | + | 21.7421i | −1.19929 | + | 0.692410i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.9725 | + | 61.2391i | −0.380897 | + | 1.94827i | ||||
\(989\) | 3.33257 | − | 5.77218i | 0.105970 | − | 0.183545i | ||||
\(990\) | −26.6986 | − | 15.4144i | −0.848536 | − | 0.489903i | ||||
\(991\) | −29.2079 | + | 50.5896i | −0.927820 | + | 1.60703i | −0.140858 | + | 0.990030i | \(0.544986\pi\) |
−0.786962 | + | 0.617001i | \(0.788347\pi\) | |||||||
\(992\) | −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 | ||||
\(996\) | −5.69197 | − | 3.28626i | −0.180357 | − | 0.104129i | ||||
\(997\) | −28.0588 | −0.888632 | −0.444316 | − | 0.895870i | \(-0.646553\pi\) | ||||
−0.444316 | + | 0.895870i | \(0.646553\pi\) | |||||||
\(998\) | 14.7001 | − | 25.4613i | 0.465322 | − | 0.805962i | ||||
\(999\) | − | 17.6903i | − | 0.559696i |
(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.k.i.569.6 | 12 | ||
7.2 | even | 3 | 637.2.q.i.491.6 | 12 | |||
7.3 | odd | 6 | 91.2.u.b.88.1 | yes | 12 | ||
7.4 | even | 3 | 637.2.u.g.361.1 | 12 | |||
7.5 | odd | 6 | 637.2.q.g.491.6 | 12 | |||
7.6 | odd | 2 | 91.2.k.b.23.6 | yes | 12 | ||
13.4 | even | 6 | 637.2.u.g.30.1 | 12 | |||
21.17 | even | 6 | 819.2.do.e.361.6 | 12 | |||
21.20 | even | 2 | 819.2.bm.f.478.1 | 12 | |||
91.2 | odd | 12 | 8281.2.a.co.1.12 | 12 | |||
91.4 | even | 6 | inner | 637.2.k.i.459.1 | 12 | ||
91.17 | odd | 6 | 91.2.k.b.4.1 | ✓ | 12 | ||
91.24 | even | 12 | 1183.2.e.j.508.12 | 24 | |||
91.30 | even | 6 | 637.2.q.i.589.6 | 12 | |||
91.37 | odd | 12 | 8281.2.a.co.1.1 | 12 | |||
91.41 | even | 12 | 1183.2.e.j.170.1 | 24 | |||
91.54 | even | 12 | 8281.2.a.cp.1.12 | 12 | |||
91.69 | odd | 6 | 91.2.u.b.30.1 | yes | 12 | ||
91.76 | even | 12 | 1183.2.e.j.170.12 | 24 | |||
91.80 | even | 12 | 1183.2.e.j.508.1 | 24 | |||
91.82 | odd | 6 | 637.2.q.g.589.6 | 12 | |||
91.89 | even | 12 | 8281.2.a.cp.1.1 | 12 | |||
273.17 | even | 6 | 819.2.bm.f.550.6 | 12 | |||
273.251 | even | 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 | 91.17 | odd | 6 | ||
91.2.k.b.23.6 | yes | 12 | 7.6 | odd | 2 | ||
91.2.u.b.30.1 | yes | 12 | 91.69 | odd | 6 | ||
91.2.u.b.88.1 | yes | 12 | 7.3 | odd | 6 | ||
637.2.k.i.459.1 | 12 | 91.4 | even | 6 | inner | ||
637.2.k.i.569.6 | 12 | 1.1 | even | 1 | trivial | ||
637.2.q.g.491.6 | 12 | 7.5 | odd | 6 | |||
637.2.q.g.589.6 | 12 | 91.82 | odd | 6 | |||
637.2.q.i.491.6 | 12 | 7.2 | even | 3 | |||
637.2.q.i.589.6 | 12 | 91.30 | even | 6 | |||
637.2.u.g.30.1 | 12 | 13.4 | even | 6 | |||
637.2.u.g.361.1 | 12 | 7.4 | even | 3 | |||
819.2.bm.f.478.1 | 12 | 21.20 | even | 2 | |||
819.2.bm.f.550.6 | 12 | 273.17 | even | 6 | |||
819.2.do.e.361.6 | 12 | 21.17 | even | 6 | |||
819.2.do.e.667.6 | 12 | 273.251 | even | 6 | |||
1183.2.e.j.170.1 | 24 | 91.41 | even | 12 | |||
1183.2.e.j.170.12 | 24 | 91.76 | even | 12 | |||
1183.2.e.j.508.1 | 24 | 91.80 | even | 12 | |||
1183.2.e.j.508.12 | 24 | 91.24 | even | 12 | |||
8281.2.a.co.1.1 | 12 | 91.37 | odd | 12 | |||
8281.2.a.co.1.12 | 12 | 91.2 | odd | 12 | |||
8281.2.a.cp.1.1 | 12 | 91.89 | even | 12 | |||
8281.2.a.cp.1.12 | 12 | 91.54 | even | 12 |