Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(87,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.87");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.m (of order \(8\), degree \(4\), 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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(116\) |
Relative dimension: | \(29\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 87.5 | ||
Character | \(\chi\) | \(=\) | 731.87 |
Dual form | 731.2.m.b.689.5 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.60811 | − | 1.60811i | −1.13711 | − | 1.13711i | −0.988966 | − | 0.148142i | \(-0.952671\pi\) |
−0.148142 | − | 0.988966i | \(-0.547329\pi\) | |||||||
\(3\) | −0.921811 | + | 0.381827i | −0.532208 | + | 0.220448i | −0.632570 | − | 0.774503i | \(-0.718000\pi\) |
0.100362 | + | 0.994951i | \(0.468000\pi\) | |||||||
\(4\) | 3.17206i | 1.58603i | ||||||||
\(5\) | 0.244536 | + | 0.590361i | 0.109360 | + | 0.264017i | 0.969080 | − | 0.246748i | \(-0.0793620\pi\) |
−0.859720 | + | 0.510766i | \(0.829362\pi\) | |||||||
\(6\) | 2.09640 | + | 0.868356i | 0.855851 | + | 0.354505i | ||||
\(7\) | −1.44759 | + | 3.49480i | −0.547139 | + | 1.32091i | 0.372459 | + | 0.928049i | \(0.378515\pi\) |
−0.919598 | + | 0.392861i | \(0.871485\pi\) | |||||||
\(8\) | 1.88481 | − | 1.88481i | 0.666381 | − | 0.666381i | ||||
\(9\) | −1.41738 | + | 1.41738i | −0.472459 | + | 0.472459i | ||||
\(10\) | 0.556127 | − | 1.34261i | 0.175863 | − | 0.424570i | ||||
\(11\) | −2.51124 | − | 1.04019i | −0.757169 | − | 0.313630i | −0.0295059 | − | 0.999565i | \(-0.509393\pi\) |
−0.727663 | + | 0.685935i | \(0.759393\pi\) | |||||||
\(12\) | −1.21118 | − | 2.92404i | −0.349637 | − | 0.844098i | ||||
\(13\) | 2.56367i | 0.711035i | 0.934670 | + | 0.355518i | \(0.115695\pi\) | ||||
−0.934670 | + | 0.355518i | \(0.884305\pi\) | |||||||
\(14\) | 7.94793 | − | 3.29214i | 2.12417 | − | 0.879862i | ||||
\(15\) | −0.450831 | − | 0.450831i | −0.116404 | − | 0.116404i | ||||
\(16\) | 0.282148 | 0.0705370 | ||||||||
\(17\) | −3.76350 | + | 1.68406i | −0.912783 | + | 0.408444i | ||||
\(18\) | 4.55861 | 1.07447 | ||||||||
\(19\) | −0.728044 | − | 0.728044i | −0.167025 | − | 0.167025i | 0.618646 | − | 0.785670i | \(-0.287682\pi\) |
−0.785670 | + | 0.618646i | \(0.787682\pi\) | |||||||
\(20\) | −1.87266 | + | 0.775682i | −0.418740 | + | 0.173448i | ||||
\(21\) | − | 3.77427i | − | 0.823614i | ||||||
\(22\) | 2.36562 | + | 5.71111i | 0.504352 | + | 1.21761i | ||||
\(23\) | −3.10552 | − | 1.28635i | −0.647546 | − | 0.268222i | 0.0346412 | − | 0.999400i | \(-0.488971\pi\) |
−0.682187 | + | 0.731177i | \(0.738971\pi\) | |||||||
\(24\) | −1.01777 | + | 2.45711i | −0.207751 | + | 0.501555i | ||||
\(25\) | 3.24681 | − | 3.24681i | 0.649361 | − | 0.649361i | ||||
\(26\) | 4.12268 | − | 4.12268i | 0.808524 | − | 0.808524i | ||||
\(27\) | 1.91084 | − | 4.61318i | 0.367741 | − | 0.887806i | ||||
\(28\) | −11.0857 | − | 4.59186i | −2.09500 | − | 0.867779i | ||||
\(29\) | −3.02073 | − | 7.29268i | −0.560935 | − | 1.35422i | −0.909019 | − | 0.416754i | \(-0.863168\pi\) |
0.348084 | − | 0.937463i | \(-0.386832\pi\) | |||||||
\(30\) | 1.44998i | 0.264728i | ||||||||
\(31\) | 6.15759 | − | 2.55056i | 1.10594 | − | 0.458094i | 0.246400 | − | 0.969168i | \(-0.420752\pi\) |
0.859536 | + | 0.511075i | \(0.170752\pi\) | |||||||
\(32\) | −4.22334 | − | 4.22334i | −0.746589 | − | 0.746589i | ||||
\(33\) | 2.71206 | 0.472110 | ||||||||
\(34\) | 8.76030 | + | 3.34399i | 1.50238 | + | 0.573489i | ||||
\(35\) | −2.41718 | −0.408578 | ||||||||
\(36\) | −4.49601 | − | 4.49601i | −0.749334 | − | 0.749334i | ||||
\(37\) | 5.47045 | − | 2.26594i | 0.899337 | − | 0.372517i | 0.115372 | − | 0.993322i | \(-0.463194\pi\) |
0.783965 | + | 0.620805i | \(0.213194\pi\) | |||||||
\(38\) | 2.34155i | 0.379850i | ||||||||
\(39\) | −0.978879 | − | 2.36322i | −0.156746 | − | 0.378418i | ||||
\(40\) | 1.57362 | + | 0.651815i | 0.248811 | + | 0.103061i | ||||
\(41\) | 0.304574 | − | 0.735308i | 0.0475665 | − | 0.114836i | −0.898310 | − | 0.439362i | \(-0.855205\pi\) |
0.945877 | + | 0.324526i | \(0.105205\pi\) | |||||||
\(42\) | −6.06946 | + | 6.06946i | −0.936538 | + | 0.936538i | ||||
\(43\) | 0.707107 | − | 0.707107i | 0.107833 | − | 0.107833i | ||||
\(44\) | 3.29955 | − | 7.96582i | 0.497426 | − | 1.20089i | ||||
\(45\) | −1.18336 | − | 0.490165i | −0.176405 | − | 0.0730695i | ||||
\(46\) | 2.92544 | + | 7.06263i | 0.431332 | + | 1.04133i | ||||
\(47\) | − | 7.44664i | − | 1.08620i | −0.839667 | − | 0.543102i | \(-0.817250\pi\) | ||
0.839667 | − | 0.543102i | \(-0.182750\pi\) | |||||||
\(48\) | −0.260087 | + | 0.107732i | −0.0375403 | + | 0.0155497i | ||||
\(49\) | −5.16835 | − | 5.16835i | −0.738336 | − | 0.738336i | ||||
\(50\) | −10.4425 | −1.47679 | ||||||||
\(51\) | 2.82622 | − | 2.98939i | 0.395750 | − | 0.418598i | ||||
\(52\) | −8.13213 | −1.12772 | ||||||||
\(53\) | 6.28294 | + | 6.28294i | 0.863028 | + | 0.863028i | 0.991689 | − | 0.128660i | \(-0.0410677\pi\) |
−0.128660 | + | 0.991689i | \(0.541068\pi\) | |||||||
\(54\) | −10.4914 | + | 4.34567i | −1.42769 | + | 0.591370i | ||||
\(55\) | − | 1.73690i | − | 0.234204i | ||||||
\(56\) | 3.85859 | + | 9.31547i | 0.515626 | + | 1.24483i | ||||
\(57\) | 0.949105 | + | 0.393132i | 0.125712 | + | 0.0520716i | ||||
\(58\) | −6.86979 | + | 16.5851i | −0.902048 | + | 2.17774i | ||||
\(59\) | −4.97677 | + | 4.97677i | −0.647920 | + | 0.647920i | −0.952490 | − | 0.304570i | \(-0.901487\pi\) |
0.304570 | + | 0.952490i | \(0.401487\pi\) | |||||||
\(60\) | 1.43006 | − | 1.43006i | 0.184620 | − | 0.184620i | ||||
\(61\) | −1.82194 | + | 4.39855i | −0.233276 | + | 0.563177i | −0.996559 | − | 0.0828868i | \(-0.973586\pi\) |
0.763283 | + | 0.646064i | \(0.223586\pi\) | |||||||
\(62\) | −14.0037 | − | 5.80052i | −1.77847 | − | 0.736667i | ||||
\(63\) | −2.90166 | − | 7.00523i | −0.365575 | − | 0.882576i | ||||
\(64\) | 13.0189i | 1.62737i | ||||||||
\(65\) | −1.51349 | + | 0.626909i | −0.187726 | + | 0.0777585i | ||||
\(66\) | −4.36131 | − | 4.36131i | −0.536840 | − | 0.536840i | ||||
\(67\) | −8.56149 | −1.04595 | −0.522976 | − | 0.852347i | \(-0.675178\pi\) | ||||
−0.522976 | + | 0.852347i | \(0.675178\pi\) | |||||||
\(68\) | −5.34193 | − | 11.9381i | −0.647805 | − | 1.44770i | ||||
\(69\) | 3.35387 | 0.403758 | ||||||||
\(70\) | 3.88710 | + | 3.88710i | 0.464598 | + | 0.464598i | ||||
\(71\) | 5.75355 | − | 2.38320i | 0.682821 | − | 0.282834i | −0.0141845 | − | 0.999899i | \(-0.504515\pi\) |
0.697006 | + | 0.717066i | \(0.254515\pi\) | |||||||
\(72\) | 5.34297i | 0.629675i | ||||||||
\(73\) | 0.737399 | + | 1.78024i | 0.0863060 | + | 0.208361i | 0.961140 | − | 0.276062i | \(-0.0890295\pi\) |
−0.874834 | + | 0.484423i | \(0.839030\pi\) | |||||||
\(74\) | −12.4410 | − | 5.15323i | −1.44624 | − | 0.599051i | ||||
\(75\) | −1.75322 | + | 4.23266i | −0.202445 | + | 0.488745i | ||||
\(76\) | 2.30940 | − | 2.30940i | 0.264906 | − | 0.264906i | ||||
\(77\) | 7.27052 | − | 7.27052i | 0.828553 | − | 0.828553i | ||||
\(78\) | −2.22618 | + | 5.37448i | −0.252066 | + | 0.608540i | ||||
\(79\) | −11.0682 | − | 4.58460i | −1.24527 | − | 0.515807i | −0.339912 | − | 0.940457i | \(-0.610397\pi\) |
−0.905358 | + | 0.424650i | \(0.860397\pi\) | |||||||
\(80\) | 0.0689952 | + | 0.166569i | 0.00771389 | + | 0.0186230i | ||||
\(81\) | − | 1.03133i | − | 0.114593i | ||||||
\(82\) | −1.67225 | + | 0.692668i | −0.184669 | + | 0.0764924i | ||||
\(83\) | 3.45906 | + | 3.45906i | 0.379681 | + | 0.379681i | 0.870987 | − | 0.491306i | \(-0.163480\pi\) |
−0.491306 | + | 0.870987i | \(0.663480\pi\) | |||||||
\(84\) | 11.9722 | 1.30628 | ||||||||
\(85\) | −1.91451 | − | 1.81001i | −0.207658 | − | 0.196323i | ||||
\(86\) | −2.27422 | −0.245235 | ||||||||
\(87\) | 5.56908 | + | 5.56908i | 0.597068 | + | 0.597068i | ||||
\(88\) | −6.69378 | + | 2.77265i | −0.713559 | + | 0.295566i | ||||
\(89\) | − | 0.0263658i | − | 0.00279477i | −0.999999 | − | 0.00139739i | \(-0.999555\pi\) | ||
0.999999 | − | 0.00139739i | \(-0.000444802\pi\) | |||||||
\(90\) | 1.11474 | + | 2.69122i | 0.117504 | + | 0.283680i | ||||
\(91\) | −8.95953 | − | 3.71116i | −0.939214 | − | 0.389035i | ||||
\(92\) | 4.08038 | − | 9.85091i | 0.425409 | − | 1.02703i | ||||
\(93\) | −4.70226 | + | 4.70226i | −0.487602 | + | 0.487602i | ||||
\(94\) | −11.9750 | + | 11.9750i | −1.23513 | + | 1.23513i | ||||
\(95\) | 0.251776 | − | 0.607841i | 0.0258317 | − | 0.0623632i | ||||
\(96\) | 5.50571 | + | 2.28054i | 0.561924 | + | 0.232757i | ||||
\(97\) | 2.91669 | + | 7.04152i | 0.296145 | + | 0.714958i | 0.999989 | + | 0.00460334i | \(0.00146529\pi\) |
−0.703844 | + | 0.710354i | \(0.748535\pi\) | |||||||
\(98\) | 16.6226i | 1.67914i | ||||||||
\(99\) | 5.03372 | − | 2.08504i | 0.505908 | − | 0.209554i | ||||
\(100\) | 10.2991 | + | 10.2991i | 1.02991 | + | 1.02991i | ||||
\(101\) | 1.68427 | 0.167591 | 0.0837955 | − | 0.996483i | \(-0.473296\pi\) | ||||
0.0837955 | + | 0.996483i | \(0.473296\pi\) | |||||||
\(102\) | −9.35216 | + | 0.262392i | −0.926002 | + | 0.0259807i | ||||
\(103\) | −9.88441 | −0.973940 | −0.486970 | − | 0.873419i | \(-0.661898\pi\) | ||||
−0.486970 | + | 0.873419i | \(0.661898\pi\) | |||||||
\(104\) | 4.83204 | + | 4.83204i | 0.473820 | + | 0.473820i | ||||
\(105\) | 2.22818 | − | 0.922944i | 0.217448 | − | 0.0900701i | ||||
\(106\) | − | 20.2074i | − | 1.96271i | ||||||
\(107\) | 3.49227 | + | 8.43108i | 0.337610 | + | 0.815063i | 0.997944 | + | 0.0640911i | \(0.0204148\pi\) |
−0.660334 | + | 0.750972i | \(0.729585\pi\) | |||||||
\(108\) | 14.6333 | + | 6.06130i | 1.40809 | + | 0.583249i | ||||
\(109\) | 1.35759 | − | 3.27750i | 0.130033 | − | 0.313928i | −0.845432 | − | 0.534084i | \(-0.820657\pi\) |
0.975465 | + | 0.220156i | \(0.0706567\pi\) | |||||||
\(110\) | −2.79314 | + | 2.79314i | −0.266315 | + | 0.266315i | ||||
\(111\) | −4.17753 | + | 4.17753i | −0.396513 | + | 0.396513i | ||||
\(112\) | −0.408435 | + | 0.986050i | −0.0385935 | + | 0.0931730i | ||||
\(113\) | 7.42308 | + | 3.07474i | 0.698304 | + | 0.289247i | 0.703455 | − | 0.710740i | \(-0.251640\pi\) |
−0.00515084 | + | 0.999987i | \(0.501640\pi\) | |||||||
\(114\) | −0.894067 | − | 2.15847i | −0.0837371 | − | 0.202159i | ||||
\(115\) | − | 2.14794i | − | 0.200296i | ||||||
\(116\) | 23.1328 | − | 9.58194i | 2.14783 | − | 0.889660i | ||||
\(117\) | −3.63369 | − | 3.63369i | −0.335935 | − | 0.335935i | ||||
\(118\) | 16.0064 | 1.47351 | ||||||||
\(119\) | −0.437421 | − | 15.5905i | −0.0400983 | − | 1.42918i | ||||
\(120\) | −1.69946 | −0.155139 | ||||||||
\(121\) | −2.55382 | − | 2.55382i | −0.232166 | − | 0.232166i | ||||
\(122\) | 10.0033 | − | 4.14349i | 0.905653 | − | 0.375134i | ||||
\(123\) | 0.794109i | 0.0716024i | ||||||||
\(124\) | 8.09053 | + | 19.5323i | 0.726551 | + | 1.75405i | ||||
\(125\) | 5.66255 | + | 2.34551i | 0.506474 | + | 0.209788i | ||||
\(126\) | −6.59901 | + | 15.9314i | −0.587886 | + | 1.41928i | ||||
\(127\) | −13.1824 | + | 13.1824i | −1.16975 | + | 1.16975i | −0.187485 | + | 0.982267i | \(0.560034\pi\) |
−0.982267 | + | 0.187485i | \(0.939966\pi\) | |||||||
\(128\) | 12.4893 | − | 12.4893i | 1.10390 | − | 1.10390i | ||||
\(129\) | −0.381827 | + | 0.921811i | −0.0336179 | + | 0.0811609i | ||||
\(130\) | 3.44201 | + | 1.42573i | 0.301884 | + | 0.125045i | ||||
\(131\) | −8.20703 | − | 19.8135i | −0.717052 | − | 1.73112i | −0.681578 | − | 0.731746i | \(-0.738706\pi\) |
−0.0354744 | − | 0.999371i | \(-0.511294\pi\) | |||||||
\(132\) | 8.60284i | 0.748781i | ||||||||
\(133\) | 3.59828 | − | 1.49046i | 0.312010 | − | 0.129239i | ||||
\(134\) | 13.7678 | + | 13.7678i | 1.18936 | + | 1.18936i | ||||
\(135\) | 3.19071 | 0.274612 | ||||||||
\(136\) | −3.91936 | + | 10.2676i | −0.336082 | + | 0.880440i | ||||
\(137\) | −11.0348 | −0.942764 | −0.471382 | − | 0.881929i | \(-0.656245\pi\) | ||||
−0.471382 | + | 0.881929i | \(0.656245\pi\) | |||||||
\(138\) | −5.39340 | − | 5.39340i | −0.459117 | − | 0.459117i | ||||
\(139\) | 17.7840 | − | 7.36636i | 1.50842 | − | 0.624806i | 0.533185 | − | 0.845998i | \(-0.320995\pi\) |
0.975230 | + | 0.221192i | \(0.0709949\pi\) | |||||||
\(140\) | − | 7.66745i | − | 0.648018i | ||||||
\(141\) | 2.84332 | + | 6.86439i | 0.239451 | + | 0.578086i | ||||
\(142\) | −13.0848 | − | 5.41991i | −1.09805 | − | 0.454829i | ||||
\(143\) | 2.66671 | − | 6.43801i | 0.223002 | − | 0.538374i | ||||
\(144\) | −0.399910 | + | 0.399910i | −0.0333258 | + | 0.0333258i | ||||
\(145\) | 3.56664 | − | 3.56664i | 0.296193 | − | 0.296193i | ||||
\(146\) | 1.67701 | − | 4.04865i | 0.138790 | − | 0.335069i | ||||
\(147\) | 6.73765 | + | 2.79083i | 0.555712 | + | 0.230184i | ||||
\(148\) | 7.18769 | + | 17.3526i | 0.590824 | + | 1.42638i | ||||
\(149\) | − | 21.7288i | − | 1.78009i | −0.455869 | − | 0.890047i | \(-0.650672\pi\) | ||
0.455869 | − | 0.890047i | \(-0.349328\pi\) | |||||||
\(150\) | 9.62598 | − | 3.98721i | 0.785958 | − | 0.325554i | ||||
\(151\) | −9.72489 | − | 9.72489i | −0.791400 | − | 0.791400i | 0.190321 | − | 0.981722i | \(-0.439047\pi\) |
−0.981722 | + | 0.190321i | \(0.939047\pi\) | |||||||
\(152\) | −2.74445 | −0.222604 | ||||||||
\(153\) | 2.94736 | − | 7.72124i | 0.238280 | − | 0.624226i | ||||
\(154\) | −23.3837 | −1.88431 | ||||||||
\(155\) | 3.01150 | + | 3.01150i | 0.241889 | + | 0.241889i | ||||
\(156\) | 7.49629 | − | 3.10506i | 0.600183 | − | 0.248604i | ||||
\(157\) | 21.0078i | 1.67661i | 0.545205 | + | 0.838303i | \(0.316452\pi\) | ||||
−0.545205 | + | 0.838303i | \(0.683548\pi\) | |||||||
\(158\) | 10.4264 | + | 25.1715i | 0.829477 | + | 2.00254i | ||||
\(159\) | −8.19068 | − | 3.39269i | −0.649563 | − | 0.269058i | ||||
\(160\) | 1.46054 | − | 3.52605i | 0.115466 | − | 0.278759i | ||||
\(161\) | 8.99107 | − | 8.99107i | 0.708595 | − | 0.708595i | ||||
\(162\) | −1.65850 | + | 1.65850i | −0.130304 | + | 0.130304i | ||||
\(163\) | 6.45944 | − | 15.5945i | 0.505942 | − | 1.22145i | −0.440258 | − | 0.897871i | \(-0.645113\pi\) |
0.946200 | − | 0.323582i | \(-0.104887\pi\) | |||||||
\(164\) | 2.33244 | + | 0.966129i | 0.182133 | + | 0.0754420i | ||||
\(165\) | 0.663196 | + | 1.60110i | 0.0516297 | + | 0.124645i | ||||
\(166\) | − | 11.1251i | − | 0.863477i | ||||||
\(167\) | −1.37713 | + | 0.570426i | −0.106565 | + | 0.0441409i | −0.435329 | − | 0.900271i | \(-0.643368\pi\) |
0.328764 | + | 0.944412i | \(0.393368\pi\) | |||||||
\(168\) | −7.11378 | − | 7.11378i | −0.548840 | − | 0.548840i | ||||
\(169\) | 6.42757 | 0.494429 | ||||||||
\(170\) | 0.168045 | + | 5.98946i | 0.0128885 | + | 0.459371i | ||||
\(171\) | 2.06382 | 0.157825 | ||||||||
\(172\) | 2.24299 | + | 2.24299i | 0.171026 | + | 0.171026i | ||||
\(173\) | 3.92812 | − | 1.62708i | 0.298650 | − | 0.123705i | −0.228327 | − | 0.973585i | \(-0.573326\pi\) |
0.526977 | + | 0.849880i | \(0.323326\pi\) | |||||||
\(174\) | − | 17.9114i | − | 1.35786i | ||||||
\(175\) | 6.64688 | + | 16.0470i | 0.502457 | + | 1.21304i | ||||
\(176\) | −0.708542 | − | 0.293488i | −0.0534084 | − | 0.0221225i | ||||
\(177\) | 2.68738 | − | 6.48790i | 0.201996 | − | 0.487660i | ||||
\(178\) | −0.0423992 | + | 0.0423992i | −0.00317796 | + | 0.00317796i | ||||
\(179\) | −7.95969 | + | 7.95969i | −0.594935 | + | 0.594935i | −0.938960 | − | 0.344026i | \(-0.888209\pi\) |
0.344026 | + | 0.938960i | \(0.388209\pi\) | |||||||
\(180\) | 1.55483 | − | 3.75370i | 0.115890 | − | 0.279784i | ||||
\(181\) | 1.21431 | + | 0.502982i | 0.0902586 | + | 0.0373863i | 0.427356 | − | 0.904083i | \(-0.359445\pi\) |
−0.337097 | + | 0.941470i | \(0.609445\pi\) | |||||||
\(182\) | 8.43998 | + | 20.3759i | 0.625613 | + | 1.51036i | ||||
\(183\) | − | 4.75030i | − | 0.351152i | ||||||
\(184\) | −8.27784 | + | 3.42879i | −0.610250 | + | 0.252774i | ||||
\(185\) | 2.67544 | + | 2.67544i | 0.196702 | + | 0.196702i | ||||
\(186\) | 15.1236 | 1.10891 | ||||||||
\(187\) | 11.2028 | − | 0.314316i | 0.819231 | − | 0.0229850i | ||||
\(188\) | 23.6212 | 1.72275 | ||||||||
\(189\) | 13.3560 | + | 13.3560i | 0.971507 | + | 0.971507i | ||||
\(190\) | −1.38236 | + | 0.572593i | −0.100287 | + | 0.0415403i | ||||
\(191\) | − | 18.6821i | − | 1.35179i | −0.737000 | − | 0.675893i | \(-0.763758\pi\) | ||
0.737000 | − | 0.675893i | \(-0.236242\pi\) | |||||||
\(192\) | −4.97098 | − | 12.0010i | −0.358749 | − | 0.866098i | ||||
\(193\) | −1.51912 | − | 0.629239i | −0.109348 | − | 0.0452936i | 0.327339 | − | 0.944907i | \(-0.393848\pi\) |
−0.436687 | + | 0.899614i | \(0.643848\pi\) | |||||||
\(194\) | 6.63319 | − | 16.0139i | 0.476235 | − | 1.14973i | ||||
\(195\) | 1.15578 | − | 1.15578i | 0.0827674 | − | 0.0827674i | ||||
\(196\) | 16.3943 | − | 16.3943i | 1.17102 | − | 1.17102i | ||||
\(197\) | −2.56550 | + | 6.19366i | −0.182784 | + | 0.441280i | −0.988538 | − | 0.150970i | \(-0.951760\pi\) |
0.805754 | + | 0.592250i | \(0.201760\pi\) | |||||||
\(198\) | −11.4478 | − | 4.74182i | −0.813558 | − | 0.336987i | ||||
\(199\) | −5.78492 | − | 13.9660i | −0.410082 | − | 0.990026i | −0.985115 | − | 0.171896i | \(-0.945011\pi\) |
0.575033 | − | 0.818130i | \(-0.304989\pi\) | |||||||
\(200\) | − | 12.2392i | − | 0.865443i | ||||||
\(201\) | 7.89207 | − | 3.26900i | 0.556664 | − | 0.230578i | ||||
\(202\) | −2.70850 | − | 2.70850i | −0.190569 | − | 0.190569i | ||||
\(203\) | 29.8592 | 2.09571 | ||||||||
\(204\) | 9.48252 | + | 8.96494i | 0.663909 | + | 0.627672i | ||||
\(205\) | 0.508576 | 0.0355205 | ||||||||
\(206\) | 15.8953 | + | 15.8953i | 1.10748 | + | 1.10748i | ||||
\(207\) | 6.22494 | − | 2.57845i | 0.432663 | − | 0.179215i | ||||
\(208\) | 0.723335i | 0.0501543i | ||||||||
\(209\) | 1.07099 | + | 2.58560i | 0.0740820 | + | 0.178850i | ||||
\(210\) | −5.06737 | − | 2.09897i | −0.349682 | − | 0.144843i | ||||
\(211\) | 2.43340 | − | 5.87474i | 0.167522 | − | 0.404433i | −0.817717 | − | 0.575621i | \(-0.804760\pi\) |
0.985238 | + | 0.171187i | \(0.0547604\pi\) | |||||||
\(212\) | −19.9299 | + | 19.9299i | −1.36879 | + | 1.36879i | ||||
\(213\) | −4.39372 | + | 4.39372i | −0.301053 | + | 0.301053i | ||||
\(214\) | 7.94217 | − | 19.1741i | 0.542916 | − | 1.31071i | ||||
\(215\) | 0.590361 | + | 0.244536i | 0.0402623 | + | 0.0166772i | ||||
\(216\) | −5.09339 | − | 12.2965i | −0.346561 | − | 0.836673i | ||||
\(217\) | 25.2117i | 1.71148i | ||||||||
\(218\) | −7.45375 | + | 3.08744i | −0.504831 | + | 0.209108i | ||||
\(219\) | −1.35948 | − | 1.35948i | −0.0918655 | − | 0.0918655i | ||||
\(220\) | 5.50957 | 0.371455 | ||||||||
\(221\) | −4.31737 | − | 9.64839i | −0.290418 | − | 0.649021i | ||||
\(222\) | 13.4359 | 0.901757 | ||||||||
\(223\) | −7.32182 | − | 7.32182i | −0.490305 | − | 0.490305i | 0.418097 | − | 0.908402i | \(-0.362697\pi\) |
−0.908402 | + | 0.418097i | \(0.862697\pi\) | |||||||
\(224\) | 20.8734 | − | 8.64606i | 1.39466 | − | 0.577689i | ||||
\(225\) | 9.20389i | 0.613593i | ||||||||
\(226\) | −6.99262 | − | 16.8817i | −0.465142 | − | 1.12295i | ||||
\(227\) | −21.7596 | − | 9.01311i | −1.44423 | − | 0.598221i | −0.483413 | − | 0.875393i | \(-0.660603\pi\) |
−0.960820 | + | 0.277171i | \(0.910603\pi\) | |||||||
\(228\) | −1.24704 | + | 3.01062i | −0.0825872 | + | 0.199383i | ||||
\(229\) | −12.6749 | + | 12.6749i | −0.837583 | + | 0.837583i | −0.988540 | − | 0.150957i | \(-0.951764\pi\) |
0.150957 | + | 0.988540i | \(0.451764\pi\) | |||||||
\(230\) | −3.45413 | + | 3.45413i | −0.227758 | + | 0.227758i | ||||
\(231\) | −3.92597 | + | 9.47812i | −0.258310 | + | 0.623615i | ||||
\(232\) | −19.4388 | − | 8.05182i | −1.27622 | − | 0.528628i | ||||
\(233\) | 6.57072 | + | 15.8631i | 0.430462 | + | 1.03923i | 0.979139 | + | 0.203193i | \(0.0651320\pi\) |
−0.548676 | + | 0.836035i | \(0.684868\pi\) | |||||||
\(234\) | 11.6868i | 0.763989i | ||||||||
\(235\) | 4.39621 | − | 1.82097i | 0.286777 | − | 0.118787i | ||||
\(236\) | −15.7866 | − | 15.7866i | −1.02762 | − | 1.02762i | ||||
\(237\) | 11.9533 | 0.776450 | ||||||||
\(238\) | −24.3679 | + | 25.7748i | −1.57954 | + | 1.67073i | ||||
\(239\) | −25.8798 | −1.67402 | −0.837012 | − | 0.547185i | \(-0.815700\pi\) | ||||
−0.837012 | + | 0.547185i | \(0.815700\pi\) | |||||||
\(240\) | −0.127201 | − | 0.127201i | −0.00821079 | − | 0.00821079i | ||||
\(241\) | 5.64562 | − | 2.33849i | 0.363666 | − | 0.150636i | −0.193365 | − | 0.981127i | \(-0.561940\pi\) |
0.557032 | + | 0.830491i | \(0.311940\pi\) | |||||||
\(242\) | 8.21368i | 0.527996i | ||||||||
\(243\) | 6.12631 | + | 14.7902i | 0.393003 | + | 0.948794i | ||||
\(244\) | −13.9525 | − | 5.77931i | −0.893216 | − | 0.369982i | ||||
\(245\) | 1.78735 | − | 4.31504i | 0.114189 | − | 0.275678i | ||||
\(246\) | 1.27702 | − | 1.27702i | 0.0814197 | − | 0.0814197i | ||||
\(247\) | 1.86647 | − | 1.86647i | 0.118760 | − | 0.118760i | ||||
\(248\) | 6.79857 | − | 16.4132i | 0.431710 | − | 1.04224i | ||||
\(249\) | −4.50936 | − | 1.86784i | −0.285769 | − | 0.118369i | ||||
\(250\) | −5.33419 | − | 12.8779i | −0.337364 | − | 0.814468i | ||||
\(251\) | 11.4766i | 0.724394i | 0.932102 | + | 0.362197i | \(0.117973\pi\) | ||||
−0.932102 | + | 0.362197i | \(0.882027\pi\) | |||||||
\(252\) | 22.2210 | − | 9.20425i | 1.39979 | − | 0.579813i | ||||
\(253\) | 6.46068 | + | 6.46068i | 0.406179 | + | 0.406179i | ||||
\(254\) | 42.3977 | 2.66027 | ||||||||
\(255\) | 2.45593 | + | 0.937478i | 0.153796 | + | 0.0587072i | ||||
\(256\) | −14.1304 | −0.883151 | ||||||||
\(257\) | −21.8515 | − | 21.8515i | −1.36306 | − | 1.36306i | −0.869994 | − | 0.493062i | \(-0.835878\pi\) |
−0.493062 | − | 0.869994i | \(-0.664122\pi\) | |||||||
\(258\) | 2.09640 | − | 0.868356i | 0.130516 | − | 0.0540615i | ||||
\(259\) | 22.3983i | 1.39176i | ||||||||
\(260\) | −1.98860 | − | 4.80089i | −0.123327 | − | 0.297739i | ||||
\(261\) | 14.6180 | + | 6.05497i | 0.904831 | + | 0.374793i | ||||
\(262\) | −18.6646 | + | 45.0603i | −1.15310 | + | 2.78383i | ||||
\(263\) | 16.8536 | − | 16.8536i | 1.03924 | − | 1.03924i | 0.0400425 | − | 0.999198i | \(-0.487251\pi\) |
0.999198 | − | 0.0400425i | \(-0.0127493\pi\) | |||||||
\(264\) | 5.11172 | − | 5.11172i | 0.314605 | − | 0.314605i | ||||
\(265\) | −2.17280 | + | 5.24561i | −0.133474 | + | 0.322235i | ||||
\(266\) | −8.18326 | − | 3.38962i | −0.501748 | − | 0.207831i | ||||
\(267\) | 0.0100672 | + | 0.0243043i | 0.000616101 | + | 0.00148740i | ||||
\(268\) | − | 27.1576i | − | 1.65891i | ||||||
\(269\) | 12.9790 | − | 5.37607i | 0.791343 | − | 0.327785i | 0.0498597 | − | 0.998756i | \(-0.484123\pi\) |
0.741483 | + | 0.670971i | \(0.234123\pi\) | |||||||
\(270\) | −5.13102 | − | 5.13102i | −0.312264 | − | 0.312264i | ||||
\(271\) | −12.8469 | −0.780393 | −0.390197 | − | 0.920732i | \(-0.627593\pi\) | ||||
−0.390197 | + | 0.920732i | \(0.627593\pi\) | |||||||
\(272\) | −1.06186 | + | 0.475153i | −0.0643850 | + | 0.0288104i | ||||
\(273\) | 9.67601 | 0.585619 | ||||||||
\(274\) | 17.7452 | + | 17.7452i | 1.07202 | + | 1.07202i | ||||
\(275\) | −11.5308 | + | 4.77622i | −0.695335 | + | 0.288017i | ||||
\(276\) | 10.6387i | 0.640373i | ||||||||
\(277\) | −11.5754 | − | 27.9456i | −0.695501 | − | 1.67909i | −0.733393 | − | 0.679805i | \(-0.762064\pi\) |
0.0378920 | − | 0.999282i | \(-0.487936\pi\) | |||||||
\(278\) | −40.4446 | − | 16.7527i | −2.42570 | − | 1.00476i | ||||
\(279\) | −5.11253 | + | 12.3427i | −0.306079 | + | 0.738940i | ||||
\(280\) | −4.55592 | + | 4.55592i | −0.272269 | + | 0.272269i | ||||
\(281\) | −14.2480 | + | 14.2480i | −0.849963 | + | 0.849963i | −0.990128 | − | 0.140165i | \(-0.955237\pi\) |
0.140165 | + | 0.990128i | \(0.455237\pi\) | |||||||
\(282\) | 6.46634 | − | 15.6111i | 0.385065 | − | 0.929629i | ||||
\(283\) | −10.9050 | − | 4.51699i | −0.648233 | − | 0.268507i | 0.0342443 | − | 0.999413i | \(-0.489098\pi\) |
−0.682478 | + | 0.730906i | \(0.739098\pi\) | |||||||
\(284\) | 7.55966 | + | 18.2506i | 0.448583 | + | 1.08298i | ||||
\(285\) | 0.656449i | 0.0388847i | ||||||||
\(286\) | −14.6414 | + | 6.06468i | −0.865766 | + | 0.358612i | ||||
\(287\) | 2.12885 | + | 2.12885i | 0.125662 | + | 0.125662i | ||||
\(288\) | 11.9721 | 0.705465 | ||||||||
\(289\) | 11.3279 | − | 12.6759i | 0.666347 | − | 0.745642i | ||||
\(290\) | −11.4711 | −0.673608 | ||||||||
\(291\) | −5.37728 | − | 5.37728i | −0.315221 | − | 0.315221i | ||||
\(292\) | −5.64703 | + | 2.33908i | −0.330467 | + | 0.136884i | ||||
\(293\) | 16.8522i | 0.984518i | 0.870449 | + | 0.492259i | \(0.163829\pi\) | ||||
−0.870449 | + | 0.492259i | \(0.836171\pi\) | |||||||
\(294\) | −6.34695 | − | 15.3229i | −0.370161 | − | 0.893649i | ||||
\(295\) | −4.15509 | − | 1.72109i | −0.241918 | − | 0.100206i | ||||
\(296\) | 6.03990 | − | 14.5816i | 0.351062 | − | 0.847539i | ||||
\(297\) | −9.59718 | + | 9.59718i | −0.556885 | + | 0.556885i | ||||
\(298\) | −34.9424 | + | 34.9424i | −2.02416 | + | 2.02416i | ||||
\(299\) | 3.29778 | − | 7.96155i | 0.190716 | − | 0.460428i | ||||
\(300\) | −13.4262 | − | 5.56133i | −0.775165 | − | 0.321084i | ||||
\(301\) | 1.44759 | + | 3.49480i | 0.0834379 | + | 0.201437i | ||||
\(302\) | 31.2775i | 1.79982i | ||||||||
\(303\) | −1.55258 | + | 0.643098i | −0.0891932 | + | 0.0369450i | ||||
\(304\) | −0.205416 | − | 0.205416i | −0.0117814 | − | 0.0117814i | ||||
\(305\) | −3.04226 | −0.174199 | ||||||||
\(306\) | −17.1563 | + | 7.67695i | −0.980762 | + | 0.438862i | ||||
\(307\) | −8.60388 | −0.491049 | −0.245525 | − | 0.969390i | \(-0.578960\pi\) | ||||
−0.245525 | + | 0.969390i | \(0.578960\pi\) | |||||||
\(308\) | 23.0625 | + | 23.0625i | 1.31411 | + | 1.31411i | ||||
\(309\) | 9.11156 | − | 3.77413i | 0.518338 | − | 0.214703i | ||||
\(310\) | − | 9.68567i | − | 0.550109i | ||||||
\(311\) | 9.76657 | + | 23.5786i | 0.553811 | + | 1.33702i | 0.914596 | + | 0.404370i | \(0.132509\pi\) |
−0.360784 | + | 0.932649i | \(0.617491\pi\) | |||||||
\(312\) | −6.29922 | − | 2.60922i | −0.356623 | − | 0.147718i | ||||
\(313\) | −4.33786 | + | 10.4725i | −0.245191 | + | 0.591942i | −0.997784 | − | 0.0665436i | \(-0.978803\pi\) |
0.752593 | + | 0.658486i | \(0.228803\pi\) | |||||||
\(314\) | 33.7829 | − | 33.7829i | 1.90648 | − | 1.90648i | ||||
\(315\) | 3.42606 | − | 3.42606i | 0.193036 | − | 0.193036i | ||||
\(316\) | 14.5426 | − | 35.1090i | 0.818087 | − | 1.97504i | ||||
\(317\) | 1.84590 | + | 0.764596i | 0.103676 | + | 0.0429440i | 0.433919 | − | 0.900952i | \(-0.357131\pi\) |
−0.330243 | + | 0.943896i | \(0.607131\pi\) | |||||||
\(318\) | 7.71571 | + | 18.6274i | 0.432676 | + | 1.04457i | ||||
\(319\) | 21.4558i | 1.20130i | ||||||||
\(320\) | −7.68587 | + | 3.18359i | −0.429653 | + | 0.177968i | ||||
\(321\) | −6.43842 | − | 6.43842i | −0.359358 | − | 0.359358i | ||||
\(322\) | −28.9173 | −1.61150 | ||||||||
\(323\) | 3.96606 | + | 1.51393i | 0.220678 | + | 0.0842371i | ||||
\(324\) | 3.27146 | 0.181748 | ||||||||
\(325\) | 8.32375 | + | 8.32375i | 0.461719 | + | 0.461719i | ||||
\(326\) | −35.4652 | + | 14.6902i | −1.96424 | + | 0.813613i | ||||
\(327\) | 3.53960i | 0.195740i | ||||||||
\(328\) | −0.811850 | − | 1.95998i | −0.0448269 | − | 0.108222i | ||||
\(329\) | 26.0245 | + | 10.7797i | 1.43478 | + | 0.594304i | ||||
\(330\) | 1.50825 | − | 3.64124i | 0.0830265 | − | 0.200444i | ||||
\(331\) | −9.54746 | + | 9.54746i | −0.524776 | + | 0.524776i | −0.919010 | − | 0.394234i | \(-0.871010\pi\) |
0.394234 | + | 0.919010i | \(0.371010\pi\) | |||||||
\(332\) | −10.9723 | + | 10.9723i | −0.602186 | + | 0.602186i | ||||
\(333\) | −4.54201 | + | 10.9654i | −0.248900 | + | 0.600899i | ||||
\(334\) | 3.13189 | + | 1.29727i | 0.171369 | + | 0.0709835i | ||||
\(335\) | −2.09359 | − | 5.05437i | −0.114385 | − | 0.276150i | ||||
\(336\) | − | 1.06490i | − | 0.0580952i | ||||||
\(337\) | 12.2510 | − | 5.07453i | 0.667354 | − | 0.276427i | −0.0231752 | − | 0.999731i | \(-0.507378\pi\) |
0.690530 | + | 0.723304i | \(0.257378\pi\) | |||||||
\(338\) | −10.3363 | − | 10.3363i | −0.562219 | − | 0.562219i | ||||
\(339\) | −8.01669 | −0.435407 | ||||||||
\(340\) | 5.74147 | − | 6.07295i | 0.311375 | − | 0.329352i | ||||
\(341\) | −18.1163 | −0.981052 | ||||||||
\(342\) | −3.31886 | − | 3.31886i | −0.179464 | − | 0.179464i | ||||
\(343\) | 1.08041 | − | 0.447522i | 0.0583369 | − | 0.0241639i | ||||
\(344\) | − | 2.66552i | − | 0.143715i | ||||||
\(345\) | 0.820139 | + | 1.97999i | 0.0441548 | + | 0.106599i | ||||
\(346\) | −8.93341 | − | 3.70034i | −0.480263 | − | 0.198931i | ||||
\(347\) | −6.73450 | + | 16.2585i | −0.361527 | + | 0.872803i | 0.633550 | + | 0.773701i | \(0.281597\pi\) |
−0.995077 | + | 0.0991019i | \(0.968403\pi\) | |||||||
\(348\) | −17.6655 | + | 17.6655i | −0.946968 | + | 0.946968i | ||||
\(349\) | −9.30407 | + | 9.30407i | −0.498035 | + | 0.498035i | −0.910826 | − | 0.412791i | \(-0.864554\pi\) |
0.412791 | + | 0.910826i | \(0.364554\pi\) | |||||||
\(350\) | 15.1164 | − | 36.4943i | 0.808008 | − | 1.95070i | ||||
\(351\) | 11.8267 | + | 4.89877i | 0.631262 | + | 0.261477i | ||||
\(352\) | 6.21276 | + | 14.9989i | 0.331141 | + | 0.799446i | ||||
\(353\) | − | 4.00210i | − | 0.213010i | −0.994312 | − | 0.106505i | \(-0.966034\pi\) | ||
0.994312 | − | 0.106505i | \(-0.0339661\pi\) | |||||||
\(354\) | −14.7549 | + | 6.11168i | −0.784214 | + | 0.324832i | ||||
\(355\) | 2.81390 | + | 2.81390i | 0.149346 | + | 0.149346i | ||||
\(356\) | 0.0836340 | 0.00443259 | ||||||||
\(357\) | 6.35609 | + | 14.2045i | 0.336400 | + | 0.751781i | ||||
\(358\) | 25.6002 | 1.35301 | ||||||||
\(359\) | −6.63651 | − | 6.63651i | −0.350262 | − | 0.350262i | 0.509945 | − | 0.860207i | \(-0.329666\pi\) |
−0.860207 | + | 0.509945i | \(0.829666\pi\) | |||||||
\(360\) | −3.15428 | + | 1.30655i | −0.166245 | + | 0.0688610i | ||||
\(361\) | − | 17.9399i | − | 0.944206i | ||||||
\(362\) | −1.14389 | − | 2.76159i | −0.0601215 | − | 0.145146i | ||||
\(363\) | 3.32926 | + | 1.37903i | 0.174741 | + | 0.0723800i | ||||
\(364\) | 11.7720 | − | 28.4202i | 0.617022 | − | 1.48962i | ||||
\(365\) | −0.870663 | + | 0.870663i | −0.0455726 | + | 0.0455726i | ||||
\(366\) | −7.63902 | + | 7.63902i | −0.399298 | + | 0.399298i | ||||
\(367\) | 13.2786 | − | 32.0574i | 0.693138 | − | 1.67338i | −0.0452223 | − | 0.998977i | \(-0.514400\pi\) |
0.738360 | − | 0.674406i | \(-0.235600\pi\) | |||||||
\(368\) | −0.876216 | − | 0.362941i | −0.0456759 | − | 0.0189196i | ||||
\(369\) | 0.610511 | + | 1.47390i | 0.0317820 | + | 0.0767284i | ||||
\(370\) | − | 8.60482i | − | 0.447343i | ||||||
\(371\) | −31.0528 | + | 12.8625i | −1.61218 | + | 0.667786i | ||||
\(372\) | −14.9159 | − | 14.9159i | −0.773352 | − | 0.773352i | ||||
\(373\) | −1.29148 | −0.0668701 | −0.0334351 | − | 0.999441i | \(-0.510645\pi\) | ||||
−0.0334351 | + | 0.999441i | \(0.510645\pi\) | |||||||
\(374\) | −18.5209 | − | 17.5100i | −0.957691 | − | 0.905418i | ||||
\(375\) | −6.11538 | −0.315797 | ||||||||
\(376\) | −14.0355 | − | 14.0355i | −0.723825 | − | 0.723825i | ||||
\(377\) | 18.6961 | − | 7.74416i | 0.962896 | − | 0.398845i | ||||
\(378\) | − | 42.9560i | − | 2.20942i | ||||||
\(379\) | −0.192321 | − | 0.464305i | −0.00987888 | − | 0.0238497i | 0.918863 | − | 0.394576i | \(-0.129109\pi\) |
−0.928742 | + | 0.370727i | \(0.879109\pi\) | |||||||
\(380\) | 1.92811 | + | 0.798649i | 0.0989099 | + | 0.0409698i | ||||
\(381\) | 7.11831 | − | 17.1851i | 0.364682 | − | 0.880420i | ||||
\(382\) | −30.0429 | + | 30.0429i | −1.53713 | + | 1.53713i | ||||
\(383\) | −6.15263 | + | 6.15263i | −0.314385 | + | 0.314385i | −0.846606 | − | 0.532221i | \(-0.821358\pi\) |
0.532221 | + | 0.846606i | \(0.321358\pi\) | |||||||
\(384\) | −6.74400 | + | 16.2815i | −0.344153 | + | 0.830860i | ||||
\(385\) | 6.07013 | + | 2.51433i | 0.309363 | + | 0.128142i | ||||
\(386\) | 1.43103 | + | 3.45480i | 0.0728373 | + | 0.175845i | ||||
\(387\) | 2.00447i | 0.101893i | ||||||||
\(388\) | −22.3361 | + | 9.25193i | −1.13394 | + | 0.469695i | ||||
\(389\) | −20.8363 | − | 20.8363i | −1.05644 | − | 1.05644i | −0.998309 | − | 0.0581362i | \(-0.981484\pi\) |
−0.0581362 | − | 0.998309i | \(-0.518516\pi\) | |||||||
\(390\) | −3.71726 | −0.188231 | ||||||||
\(391\) | 13.8539 | − | 0.388697i | 0.700623 | − | 0.0196573i | ||||
\(392\) | −19.4827 | −0.984025 | ||||||||
\(393\) | 15.1307 | + | 15.1307i | 0.763241 | + | 0.763241i | ||||
\(394\) | 14.0857 | − | 5.83450i | 0.709629 | − | 0.293938i | ||||
\(395\) | − | 7.65533i | − | 0.385181i | ||||||
\(396\) | 6.61386 | + | 15.9673i | 0.332359 | + | 0.802386i | ||||
\(397\) | −22.3405 | − | 9.25372i | −1.12124 | − | 0.464431i | −0.256443 | − | 0.966559i | \(-0.582551\pi\) |
−0.864793 | + | 0.502128i | \(0.832551\pi\) | |||||||
\(398\) | −13.1562 | + | 31.7618i | −0.659459 | + | 1.59207i | ||||
\(399\) | −2.74783 | + | 2.74783i | −0.137564 | + | 0.137564i | ||||
\(400\) | 0.916079 | − | 0.916079i | 0.0458040 | − | 0.0458040i | ||||
\(401\) | 7.10666 | − | 17.1570i | 0.354890 | − | 0.856780i | −0.641112 | − | 0.767447i | \(-0.721527\pi\) |
0.996002 | − | 0.0893324i | \(-0.0284734\pi\) | |||||||
\(402\) | −17.9483 | − | 7.43442i | −0.895179 | − | 0.370795i | ||||
\(403\) | 6.53880 | + | 15.7861i | 0.325721 | + | 0.786360i | ||||
\(404\) | 5.34260i | 0.265804i | ||||||||
\(405\) | 0.608860 | − | 0.252198i | 0.0302545 | − | 0.0125318i | ||||
\(406\) | −48.0171 | − | 48.0171i | −2.38305 | − | 2.38305i | ||||
\(407\) | −16.0946 | −0.797782 | ||||||||
\(408\) | −0.307540 | − | 10.9613i | −0.0152255 | − | 0.542666i | ||||
\(409\) | 5.79719 | 0.286652 | 0.143326 | − | 0.989675i | \(-0.454220\pi\) | ||||
0.143326 | + | 0.989675i | \(0.454220\pi\) | |||||||
\(410\) | −0.817849 | − | 0.817849i | −0.0403907 | − | 0.0403907i | ||||
\(411\) | 10.1720 | − | 4.21337i | 0.501746 | − | 0.207830i | ||||
\(412\) | − | 31.3540i | − | 1.54470i | ||||||
\(413\) | −10.1885 | − | 24.5971i | −0.501342 | − | 1.21035i | ||||
\(414\) | −14.1569 | − | 5.86396i | −0.695771 | − | 0.288198i | ||||
\(415\) | −1.19623 | + | 2.88796i | −0.0587206 | + | 0.141764i | ||||
\(416\) | 10.8273 | − | 10.8273i | 0.530851 | − | 0.530851i | ||||
\(417\) | −13.5808 | + | 13.5808i | −0.665053 | + | 0.665053i | ||||
\(418\) | 2.43566 | − | 5.88021i | 0.119132 | − | 0.287611i | ||||
\(419\) | 24.3903 | + | 10.1028i | 1.19154 | + | 0.493553i | 0.888257 | − | 0.459347i | \(-0.151917\pi\) |
0.303285 | + | 0.952900i | \(0.401917\pi\) | |||||||
\(420\) | 2.92763 | + | 7.06794i | 0.142854 | + | 0.344880i | ||||
\(421\) | − | 8.05999i | − | 0.392820i | −0.980522 | − | 0.196410i | \(-0.937072\pi\) | ||
0.980522 | − | 0.196410i | \(-0.0629283\pi\) | |||||||
\(422\) | −13.3604 | + | 5.53407i | −0.650375 | + | 0.269394i | ||||
\(423\) | 10.5547 | + | 10.5547i | 0.513187 | + | 0.513187i | ||||
\(424\) | 23.6843 | 1.15021 | ||||||||
\(425\) | −6.75155 | + | 17.6872i | −0.327499 | + | 0.857954i | ||||
\(426\) | 14.1312 | 0.684659 | ||||||||
\(427\) | −12.7346 | − | 12.7346i | −0.616272 | − | 0.616272i | ||||
\(428\) | −26.7439 | + | 11.0777i | −1.29272 | + | 0.535460i | ||||
\(429\) | 6.95285i | 0.335687i | ||||||||
\(430\) | −0.556127 | − | 1.34261i | −0.0268188 | − | 0.0647463i | ||||
\(431\) | 12.9800 | + | 5.37650i | 0.625225 | + | 0.258977i | 0.672723 | − | 0.739895i | \(-0.265125\pi\) |
−0.0474977 | + | 0.998871i | \(0.515125\pi\) | |||||||
\(432\) | 0.539140 | − | 1.30160i | 0.0259394 | − | 0.0626232i | ||||
\(433\) | 19.5323 | − | 19.5323i | 0.938662 | − | 0.938662i | −0.0595629 | − | 0.998225i | \(-0.518971\pi\) |
0.998225 | + | 0.0595629i | \(0.0189707\pi\) | |||||||
\(434\) | 40.5433 | − | 40.5433i | 1.94614 | − | 1.94614i | ||||
\(435\) | −1.92593 | + | 4.64960i | −0.0923412 | + | 0.222931i | ||||
\(436\) | 10.3964 | + | 4.30634i | 0.497899 | + | 0.206236i | ||||
\(437\) | 1.32444 | + | 3.19747i | 0.0633564 | + | 0.152956i | ||||
\(438\) | 4.37241i | 0.208922i | ||||||||
\(439\) | −29.5258 | + | 12.2300i | −1.40919 | + | 0.583705i | −0.952119 | − | 0.305727i | \(-0.901101\pi\) |
−0.457069 | + | 0.889431i | \(0.651101\pi\) | |||||||
\(440\) | −3.27373 | − | 3.27373i | −0.156069 | − | 0.156069i | ||||
\(441\) | 14.6510 | 0.697666 | ||||||||
\(442\) | −8.57289 | + | 22.4585i | −0.407771 | + | 1.06824i | ||||
\(443\) | −12.6819 | −0.602534 | −0.301267 | − | 0.953540i | \(-0.597410\pi\) | ||||
−0.301267 | + | 0.953540i | \(0.597410\pi\) | |||||||
\(444\) | −13.2514 | − | 13.2514i | −0.628882 | − | 0.628882i | ||||
\(445\) | 0.0155653 | − | 0.00644738i | 0.000737868 | − | 0.000305635i | ||||
\(446\) | 23.5486i | 1.11506i | ||||||||
\(447\) | 8.29664 | + | 20.0298i | 0.392417 | + | 0.947379i | ||||
\(448\) | −45.4986 | − | 18.8461i | −2.14961 | − | 0.890396i | ||||
\(449\) | 3.27292 | − | 7.90153i | 0.154459 | − | 0.372896i | −0.827641 | − | 0.561258i | \(-0.810318\pi\) |
0.982100 | + | 0.188362i | \(0.0603177\pi\) | |||||||
\(450\) | 14.8009 | − | 14.8009i | 0.697722 | − | 0.697722i | ||||
\(451\) | −1.52972 | + | 1.52972i | −0.0720318 | + | 0.0720318i | ||||
\(452\) | −9.75326 | + | 23.5465i | −0.458755 | + | 1.10753i | ||||
\(453\) | 12.6777 | + | 5.25129i | 0.595652 | + | 0.246727i | ||||
\(454\) | 20.4978 | + | 49.4860i | 0.962008 | + | 2.32249i | ||||
\(455\) | − | 6.19687i | − | 0.290514i | ||||||
\(456\) | 2.52986 | − | 1.04790i | 0.118472 | − | 0.0490725i | ||||
\(457\) | 23.8166 | + | 23.8166i | 1.11409 | + | 1.11409i | 0.992591 | + | 0.121503i | \(0.0387714\pi\) |
0.121503 | + | 0.992591i | \(0.461229\pi\) | |||||||
\(458\) | 40.7655 | 1.90485 | ||||||||
\(459\) | 0.577400 | + | 20.5797i | 0.0269507 | + | 0.960577i | ||||
\(460\) | 6.81339 | 0.317676 | ||||||||
\(461\) | 2.21754 | + | 2.21754i | 0.103281 | + | 0.103281i | 0.756859 | − | 0.653578i | \(-0.226733\pi\) |
−0.653578 | + | 0.756859i | \(0.726733\pi\) | |||||||
\(462\) | 21.5553 | − | 8.92850i | 1.00284 | − | 0.415391i | ||||
\(463\) | − | 29.1181i | − | 1.35323i | −0.736336 | − | 0.676617i | \(-0.763445\pi\) | ||
0.736336 | − | 0.676617i | \(-0.236555\pi\) | |||||||
\(464\) | −0.852292 | − | 2.05761i | −0.0395667 | − | 0.0955224i | ||||
\(465\) | −3.92590 | − | 1.62616i | −0.182059 | − | 0.0754115i | ||||
\(466\) | 14.9432 | − | 36.0762i | 0.692233 | − | 1.67120i | ||||
\(467\) | 18.2843 | − | 18.2843i | 0.846095 | − | 0.846095i | −0.143548 | − | 0.989643i | \(-0.545851\pi\) |
0.989643 | + | 0.143548i | \(0.0458512\pi\) | |||||||
\(468\) | 11.5263 | − | 11.5263i | 0.532803 | − | 0.532803i | ||||
\(469\) | 12.3936 | − | 29.9207i | 0.572281 | − | 1.38161i | ||||
\(470\) | −9.99792 | − | 4.14128i | −0.461170 | − | 0.191023i | ||||
\(471\) | −8.02134 | − | 19.3652i | −0.369604 | − | 0.892302i | ||||
\(472\) | 18.7605i | 0.863523i | ||||||||
\(473\) | −2.51124 | + | 1.04019i | −0.115467 | + | 0.0478281i | ||||
\(474\) | −19.2223 | − | 19.2223i | −0.882908 | − | 0.882908i | ||||
\(475\) | −4.72763 | −0.216919 | ||||||||
\(476\) | 49.4541 | − | 1.38753i | 2.26672 | − | 0.0635971i | ||||
\(477\) | −17.8106 | −0.815491 | ||||||||
\(478\) | 41.6176 | + | 41.6176i | 1.90355 | + | 1.90355i | ||||
\(479\) | 10.0704 | − | 4.17129i | 0.460128 | − | 0.190591i | −0.140564 | − | 0.990072i | \(-0.544892\pi\) |
0.600692 | + | 0.799480i | \(0.294892\pi\) | |||||||
\(480\) | 3.80803i | 0.173812i | ||||||||
\(481\) | 5.80912 | + | 14.0245i | 0.264873 | + | 0.639460i | ||||
\(482\) | −12.8394 | − | 5.31824i | −0.584817 | − | 0.242239i | ||||
\(483\) | −4.85503 | + | 11.7211i | −0.220912 | + | 0.533328i | ||||
\(484\) | 8.10089 | − | 8.10089i | 0.368222 | − | 0.368222i | ||||
\(485\) | −3.44380 | + | 3.44380i | −0.156375 | + | 0.156375i | ||||
\(486\) | 13.9326 | − | 33.6362i | 0.631994 | − | 1.52577i | ||||
\(487\) | −8.04076 | − | 3.33059i | −0.364362 | − | 0.150924i | 0.192989 | − | 0.981201i | \(-0.438182\pi\) |
−0.557350 | + | 0.830277i | \(0.688182\pi\) | |||||||
\(488\) | 4.85642 | + | 11.7244i | 0.219840 | + | 0.530741i | ||||
\(489\) | 16.8415i | 0.761601i | ||||||||
\(490\) | −9.81333 | + | 4.06481i | −0.443321 | + | 0.183630i | ||||
\(491\) | −1.03090 | − | 1.03090i | −0.0465239 | − | 0.0465239i | 0.683462 | − | 0.729986i | \(-0.260473\pi\) |
−0.729986 | + | 0.683462i | \(0.760473\pi\) | |||||||
\(492\) | −2.51896 | −0.113564 | ||||||||
\(493\) | 23.6498 | + | 22.3590i | 1.06513 | + | 1.00700i | ||||
\(494\) | −6.00298 | −0.270087 | ||||||||
\(495\) | 2.46185 | + | 2.46185i | 0.110652 | + | 0.110652i | ||||
\(496\) | 1.73735 | − | 0.719634i | 0.0780094 | − | 0.0323125i | ||||
\(497\) | 23.5574i | 1.05669i | ||||||||
\(498\) | 4.24787 | + | 10.2553i | 0.190351 | + | 0.459549i | ||||
\(499\) | −17.2153 | − | 7.13082i | −0.770663 | − | 0.319219i | −0.0375222 | − | 0.999296i | \(-0.511946\pi\) |
−0.733141 | + | 0.680077i | \(0.761946\pi\) | |||||||
\(500\) | −7.44009 | + | 17.9620i | −0.332731 | + | 0.803283i | ||||
\(501\) | 1.05165 | − | 1.05165i | 0.0469842 | − | 0.0469842i | ||||
\(502\) | 18.4556 | − | 18.4556i | 0.823714 | − | 0.823714i | ||||
\(503\) | −0.199984 | + | 0.482804i | −0.00891684 | + | 0.0215272i | −0.928275 | − | 0.371894i | \(-0.878709\pi\) |
0.919358 | + | 0.393421i | \(0.128709\pi\) | |||||||
\(504\) | −18.6726 | − | 7.73445i | −0.831744 | − | 0.344520i | ||||
\(505\) | 0.411863 | + | 0.994326i | 0.0183277 | + | 0.0442469i | ||||
\(506\) | − | 20.7790i | − | 0.923739i | ||||||
\(507\) | −5.92501 | + | 2.45422i | −0.263139 | + | 0.108996i | ||||
\(508\) | −41.8155 | − | 41.8155i | −1.85526 | − | 1.85526i | ||||
\(509\) | 9.12190 | 0.404321 | 0.202160 | − | 0.979352i | \(-0.435204\pi\) | ||||
0.202160 | + | 0.979352i | \(0.435204\pi\) | |||||||
\(510\) | −2.44184 | − | 5.45699i | −0.108127 | − | 0.241639i | ||||
\(511\) | −7.28903 | −0.322448 | ||||||||
\(512\) | −2.25520 | − | 2.25520i | −0.0996666 | − | 0.0996666i | ||||
\(513\) | −4.74977 | + | 1.96742i | −0.209707 | + | 0.0868637i | ||||
\(514\) | 70.2793i | 3.09989i | ||||||||
\(515\) | −2.41709 | − | 5.83537i | −0.106510 | − | 0.257137i | ||||
\(516\) | −2.92404 | − | 1.21118i | −0.128724 | − | 0.0533191i | ||||
\(517\) | −7.74593 | + | 18.7003i | −0.340666 | + | 0.822440i | ||||
\(518\) | 36.0190 | − | 36.0190i | 1.58258 | − | 1.58258i | ||||
\(519\) | −2.99972 | + | 2.99972i | −0.131673 | + | 0.131673i | ||||
\(520\) | −1.67104 | + | 4.03425i | −0.0732800 | + | 0.176914i | ||||
\(521\) | −7.65588 | − | 3.17117i | −0.335410 | − | 0.138931i | 0.208621 | − | 0.977997i | \(-0.433103\pi\) |
−0.544031 | + | 0.839065i | \(0.683103\pi\) | |||||||
\(522\) | −13.7703 | − | 33.2445i | −0.602710 | − | 1.45507i | ||||
\(523\) | 2.41846i | 0.105752i | 0.998601 | + | 0.0528760i | \(0.0168388\pi\) | ||||
−0.998601 | + | 0.0528760i | \(0.983161\pi\) | |||||||
\(524\) | 62.8498 | − | 26.0332i | 2.74560 | − | 1.13727i | ||||
\(525\) | −12.2543 | − | 12.2543i | −0.534823 | − | 0.534823i | ||||
\(526\) | −54.2052 | −2.36346 | ||||||||
\(527\) | −18.8788 | + | 19.9688i | −0.822375 | + | 0.869853i | ||||
\(528\) | 0.765203 | 0.0333012 | ||||||||
\(529\) | −8.27388 | − | 8.27388i | −0.359734 | − | 0.359734i | ||||
\(530\) | 11.9296 | − | 4.94142i | 0.518191 | − | 0.214642i | ||||
\(531\) | − | 14.1079i | − | 0.612231i | ||||||
\(532\) | 4.72782 | + | 11.4140i | 0.204977 | + | 0.494858i | ||||
\(533\) | 1.88509 | + | 0.780830i | 0.0816523 | + | 0.0338215i | ||||
\(534\) | 0.0228949 | − | 0.0552732i | 0.000990760 | − | 0.00239191i | ||||
\(535\) | −4.12340 | + | 4.12340i | −0.178270 | + | 0.178270i | ||||
\(536\) | −16.1368 | + | 16.1368i | −0.697002 | + | 0.697002i | ||||
\(537\) | 4.29810 | − | 10.3765i | 0.185477 | − | 0.447781i | ||||
\(538\) | −29.5170 | − | 12.2264i | −1.27257 | − | 0.527116i | ||||
\(539\) | 7.60291 | + | 18.3551i | 0.327481 | + | 0.790608i | ||||
\(540\) | 10.1211i | 0.435544i | ||||||||
\(541\) | 24.6940 | − | 10.2286i | 1.06168 | − | 0.439762i | 0.217632 | − | 0.976031i | \(-0.430167\pi\) |
0.844047 | + | 0.536269i | \(0.180167\pi\) | |||||||
\(542\) | 20.6593 | + | 20.6593i | 0.887391 | + | 0.887391i | ||||
\(543\) | −1.31141 | −0.0562781 | ||||||||
\(544\) | 23.0069 | + | 8.78221i | 0.986413 | + | 0.376534i | ||||
\(545\) | 2.26689 | 0.0971027 | ||||||||
\(546\) | −15.5601 | − | 15.5601i | −0.665912 | − | 0.665912i | ||||
\(547\) | −14.8693 | + | 6.15907i | −0.635766 | + | 0.263343i | −0.677201 | − | 0.735798i | \(-0.736807\pi\) |
0.0414349 | + | 0.999141i | \(0.486807\pi\) | |||||||
\(548\) | − | 35.0030i | − | 1.49525i | ||||||
\(549\) | −3.65203 | − | 8.81678i | −0.155865 | − | 0.376291i | ||||
\(550\) | 26.2236 | + | 10.8622i | 1.11818 | + | 0.463164i | ||||
\(551\) | −3.11017 | + | 7.50861i | −0.132498 | + | 0.319878i | ||||
\(552\) | 6.32140 | − | 6.32140i | 0.269057 | − | 0.269057i | ||||
\(553\) | 32.0445 | − | 32.0445i | 1.36267 | − | 1.36267i | ||||
\(554\) | −26.3251 | + | 63.5543i | −1.11844 | + | 2.70016i | ||||
\(555\) | −3.48780 | − | 1.44470i | −0.148049 | − | 0.0613239i | ||||
\(556\) | 23.3665 | + | 56.4118i | 0.990962 | + | 2.39239i | ||||
\(557\) | 11.2120i | 0.475069i | 0.971379 | + | 0.237535i | \(0.0763394\pi\) | ||||
−0.971379 | + | 0.237535i | \(0.923661\pi\) | |||||||
\(558\) | 28.0700 | − | 11.6270i | 1.18830 | − | 0.492210i | ||||
\(559\) | 1.81279 | + | 1.81279i | 0.0766729 | + | 0.0766729i | ||||
\(560\) | −0.682002 | −0.0288199 | ||||||||
\(561\) | −10.2069 | + | 4.56727i | −0.430934 | + | 0.192830i | ||||
\(562\) | 45.8247 | 1.93300 | ||||||||
\(563\) | −9.55205 | − | 9.55205i | −0.402571 | − | 0.402571i | 0.476567 | − | 0.879138i | \(-0.341881\pi\) |
−0.879138 | + | 0.476567i | \(0.841881\pi\) | |||||||
\(564\) | −21.7743 | + | 9.01920i | −0.916863 | + | 0.379777i | ||||
\(565\) | 5.13418i | 0.215996i | ||||||||
\(566\) | 10.2726 | + | 24.8003i | 0.431790 | + | 1.04243i | ||||
\(567\) | 3.60431 | + | 1.49295i | 0.151367 | + | 0.0626981i | ||||
\(568\) | 6.35247 | − | 15.3362i | 0.266544 | − | 0.643494i | ||||
\(569\) | −5.68110 | + | 5.68110i | −0.238164 | + | 0.238164i | −0.816089 | − | 0.577926i | \(-0.803862\pi\) |
0.577926 | + | 0.816089i | \(0.303862\pi\) | |||||||
\(570\) | 1.05564 | − | 1.05564i | 0.0442161 | − | 0.0442161i | ||||
\(571\) | −1.52567 | + | 3.68330i | −0.0638475 | + | 0.154142i | −0.952583 | − | 0.304279i | \(-0.901585\pi\) |
0.888736 | + | 0.458420i | \(0.151585\pi\) | |||||||
\(572\) | 20.4218 | + | 8.45898i | 0.853877 | + | 0.353688i | ||||
\(573\) | 7.13331 | + | 17.2213i | 0.297998 | + | 0.719431i | ||||
\(574\) | − | 6.84688i | − | 0.285783i | ||||||
\(575\) | −14.2596 | + | 5.90650i | −0.594664 | + | 0.246318i | ||||
\(576\) | −18.4527 | − | 18.4527i | −0.768864 | − | 0.768864i | ||||
\(577\) | −7.59744 | −0.316286 | −0.158143 | − | 0.987416i | \(-0.550551\pi\) | ||||
−0.158143 | + | 0.987416i | \(0.550551\pi\) | |||||||
\(578\) | −38.6009 | + | 2.16774i | −1.60558 | + | 0.0901662i | ||||
\(579\) | 1.64060 | 0.0681809 | ||||||||
\(580\) | 11.3136 | + | 11.3136i | 0.469772 | + | 0.469772i | ||||
\(581\) | −17.0960 | + | 7.08140i | −0.709263 | + | 0.293786i | ||||
\(582\) | 17.2945i | 0.716882i | ||||||||
\(583\) | −9.24254 | − | 22.3135i | −0.382787 | − | 0.924129i | ||||
\(584\) | 4.74527 | + | 1.96555i | 0.196361 | + | 0.0813352i | ||||
\(585\) | 1.25662 | − | 3.03376i | 0.0519550 | − | 0.125430i | ||||
\(586\) | 27.1003 | − | 27.1003i | 1.11950 | − | 1.11950i | ||||
\(587\) | −23.2523 | + | 23.2523i | −0.959725 | + | 0.959725i | −0.999220 | − | 0.0394943i | \(-0.987425\pi\) |
0.0394943 | + | 0.999220i | \(0.487425\pi\) | |||||||
\(588\) | −8.85268 | + | 21.3722i | −0.365078 | + | 0.881377i | ||||
\(589\) | −6.33991 | − | 2.62608i | −0.261231 | − | 0.108206i | ||||
\(590\) | 3.91414 | + | 9.44957i | 0.161143 | + | 0.389032i | ||||
\(591\) | − | 6.68896i | − | 0.275147i | ||||||
\(592\) | 1.54348 | − | 0.639329i | 0.0634365 | − | 0.0262763i | ||||
\(593\) | −21.0995 | − | 21.0995i | −0.866454 | − | 0.866454i | 0.125624 | − | 0.992078i | \(-0.459907\pi\) |
−0.992078 | + | 0.125624i | \(0.959907\pi\) | |||||||
\(594\) | 30.8667 | 1.26648 | ||||||||
\(595\) | 9.09707 | − | 4.07067i | 0.372943 | − | 0.166881i | ||||
\(596\) | 68.9251 | 2.82328 | ||||||||
\(597\) | 10.6652 | + | 10.6652i | 0.436498 | + | 0.436498i | ||||
\(598\) | −18.1063 | + | 7.49987i | −0.740421 | + | 0.306692i | ||||
\(599\) | 44.9954i | 1.83846i | 0.393719 | + | 0.919231i | \(0.371188\pi\) | ||||
−0.393719 | + | 0.919231i | \(0.628812\pi\) | |||||||
\(600\) | 4.67326 | + | 11.2822i | 0.190785 | + | 0.460596i | ||||
\(601\) | 20.5131 | + | 8.49680i | 0.836747 | + | 0.346592i | 0.759570 | − | 0.650426i | \(-0.225409\pi\) |
0.0771768 | + | 0.997017i | \(0.475409\pi\) | |||||||
\(602\) | 3.29214 | − | 7.94793i | 0.134178 | − | 0.323933i | ||||
\(603\) | 12.1349 | − | 12.1349i | 0.494169 | − | 0.494169i | ||||
\(604\) | 30.8480 | − | 30.8480i | 1.25519 | − | 1.25519i | ||||
\(605\) | 0.883178 | − | 2.13218i | 0.0359063 | − | 0.0866854i | ||||
\(606\) | 3.53090 | + | 1.46255i | 0.143433 | + | 0.0594118i | ||||
\(607\) | −6.64544 | − | 16.0435i | −0.269730 | − | 0.651186i | 0.729740 | − | 0.683724i | \(-0.239641\pi\) |
−0.999470 | + | 0.0325384i | \(0.989641\pi\) | |||||||
\(608\) | 6.14956i | 0.249397i | ||||||||
\(609\) | −27.5246 | + | 11.4011i | −1.11535 | + | 0.461994i | ||||
\(610\) | 4.89231 | + | 4.89231i | 0.198084 | + | 0.198084i | ||||
\(611\) | 19.0908 | 0.772330 | ||||||||
\(612\) | 24.4923 | + | 9.34920i | 0.990041 | + | 0.377919i | ||||
\(613\) | −31.6201 | −1.27712 | −0.638561 | − | 0.769571i | \(-0.720470\pi\) | ||||
−0.638561 | + | 0.769571i | \(0.720470\pi\) | |||||||
\(614\) | 13.8360 | + | 13.8360i | 0.558376 | + | 0.558376i | ||||
\(615\) | −0.468811 | + | 0.194188i | −0.0189043 | + | 0.00783041i | ||||
\(616\) | − | 27.4071i | − | 1.10426i | ||||||
\(617\) | −6.13476 | − | 14.8106i | −0.246976 | − | 0.596253i | 0.750968 | − | 0.660338i | \(-0.229587\pi\) |
−0.997944 | + | 0.0640854i | \(0.979587\pi\) | |||||||
\(618\) | −20.7217 | − | 8.58319i | −0.833547 | − | 0.345267i | ||||
\(619\) | −8.95319 | + | 21.6149i | −0.359859 | + | 0.868777i | 0.635460 | + | 0.772134i | \(0.280811\pi\) |
−0.995319 | + | 0.0966432i | \(0.969189\pi\) | |||||||
\(620\) | −9.55266 | + | 9.55266i | −0.383644 | + | 0.383644i | ||||
\(621\) | −11.8683 | + | 11.8683i | −0.476259 | + | 0.476259i | ||||
\(622\) | 22.2113 | − | 53.6228i | 0.890592 | − | 2.15008i | ||||
\(623\) | 0.0921432 | + | 0.0381670i | 0.00369164 | + | 0.00152913i | ||||
\(624\) | −0.276189 | − | 0.666778i | −0.0110564 | − | 0.0266925i | ||||
\(625\) | − | 19.0419i | − | 0.761675i | ||||||
\(626\) | 23.8168 | − | 9.86524i | 0.951911 | − | 0.394294i | ||||
\(627\) | −1.97450 | − | 1.97450i | −0.0788540 | − | 0.0788540i | ||||
\(628\) | −66.6381 | −2.65915 | ||||||||
\(629\) | −16.7721 | + | 17.7404i | −0.668747 | + | 0.707356i | ||||
\(630\) | −11.0190 | −0.439007 | ||||||||
\(631\) | 16.8505 | + | 16.8505i | 0.670808 | + | 0.670808i | 0.957902 | − | 0.287094i | \(-0.0926892\pi\) |
−0.287094 | + | 0.957902i | \(0.592689\pi\) | |||||||
\(632\) | −29.5025 | + | 12.2203i | −1.17355 | + | 0.486099i | ||||
\(633\) | 6.34453i | 0.252172i | ||||||||
\(634\) | −1.73886 | − | 4.19797i | −0.0690588 | − | 0.166723i | ||||
\(635\) | −11.0060 | − | 4.55882i | −0.436759 | − | 0.180911i | ||||
\(636\) | 10.7618 | − | 25.9813i | 0.426734 | − | 1.03023i | ||||
\(637\) | 13.2500 | − | 13.2500i | 0.524983 | − | 0.524983i | ||||
\(638\) | 34.5034 | − | 34.5034i | 1.36600 | − | 1.36600i | ||||
\(639\) | −4.77706 | + | 11.5328i | −0.188978 | + | 0.456232i | ||||
\(640\) | 10.4272 | + | 4.31910i | 0.412173 | + | 0.170728i | ||||
\(641\) | −7.82656 | − | 18.8950i | −0.309131 | − | 0.746307i | −0.999734 | − | 0.0230734i | \(-0.992655\pi\) |
0.690603 | − | 0.723234i | \(-0.257345\pi\) | |||||||
\(642\) | 20.7074i | 0.817257i | ||||||||
\(643\) | 36.8114 | − | 15.2478i | 1.45170 | − | 0.601314i | 0.489098 | − | 0.872229i | \(-0.337326\pi\) |
0.962603 | + | 0.270915i | \(0.0873262\pi\) | |||||||
\(644\) | 28.5202 | + | 28.5202i | 1.12385 | + | 1.12385i | ||||
\(645\) | −0.637571 | −0.0251043 | ||||||||
\(646\) | −3.94331 | − | 8.81244i | −0.155147 | − | 0.346721i | ||||
\(647\) | 14.7545 | 0.580061 | 0.290031 | − | 0.957017i | \(-0.406335\pi\) | ||||
0.290031 | + | 0.957017i | \(0.406335\pi\) | |||||||
\(648\) | −1.94387 | − | 1.94387i | −0.0763624 | − | 0.0763624i | ||||
\(649\) | 17.6747 | − | 7.32109i | 0.693791 | − | 0.287378i | ||||
\(650\) | − | 26.7711i | − | 1.05005i | ||||||
\(651\) | −9.62650 | − | 23.2404i | −0.377292 | − | 0.910864i | ||||
\(652\) | 49.4666 | + | 20.4897i | 1.93726 | + | 0.802440i | ||||
\(653\) | −7.28654 | + | 17.5913i | −0.285144 | + | 0.688399i | −0.999940 | − | 0.0109339i | \(-0.996520\pi\) |
0.714796 | + | 0.699333i | \(0.246520\pi\) | |||||||
\(654\) | 5.69208 | − | 5.69208i | 0.222578 | − | 0.222578i | ||||
\(655\) | 9.69023 | − | 9.69023i | 0.378628 | − | 0.378628i | ||||
\(656\) | 0.0859350 | − | 0.207465i | 0.00335520 | − | 0.00810017i | ||||
\(657\) | −3.56844 | − | 1.47810i | −0.139218 | − | 0.0576661i | ||||
\(658\) | −24.5154 | − | 59.1854i | −0.955709 | − | 2.30729i | ||||
\(659\) | − | 19.7181i | − | 0.768108i | −0.923311 | − | 0.384054i | \(-0.874528\pi\) | ||
0.923311 | − | 0.384054i | \(-0.125472\pi\) | |||||||
\(660\) | −5.07878 | + | 2.10370i | −0.197691 | + | 0.0818864i | ||||
\(661\) | 21.3612 | + | 21.3612i | 0.830853 | + | 0.830853i | 0.987634 | − | 0.156780i | \(-0.0501115\pi\) |
−0.156780 | + | 0.987634i | \(0.550111\pi\) | |||||||
\(662\) | 30.7068 | 1.19345 | ||||||||
\(663\) | 7.66381 | + | 7.24551i | 0.297638 | + | 0.281392i | ||||
\(664\) | 13.0393 | 0.506024 | ||||||||
\(665\) | 1.75981 | + | 1.75981i | 0.0682426 | + | 0.0682426i | ||||
\(666\) | 24.9376 | − | 10.3295i | 0.966314 | − | 0.400260i | ||||
\(667\) | 26.5333i | 1.02737i | ||||||||
\(668\) | −1.80943 | − | 4.36834i | −0.0700088 | − | 0.169016i | ||||
\(669\) | 9.54500 | + | 3.95367i | 0.369031 | + | 0.152858i | ||||
\(670\) | −4.76127 | + | 11.4947i | −0.183944 | + | 0.444080i | ||||
\(671\) | 9.15067 | − | 9.15067i | 0.353258 | − | 0.353258i | ||||
\(672\) | −15.9401 | + | 15.9401i | −0.614901 | + | 0.614901i | ||||
\(673\) | 14.5841 | − | 35.2091i | 0.562176 | − | 1.35721i | −0.345847 | − | 0.938291i | \(-0.612408\pi\) |
0.908022 | − | 0.418922i | \(-0.137592\pi\) | |||||||
\(674\) | −27.8614 | − | 11.5406i | −1.07318 | − | 0.444526i | ||||
\(675\) | −8.77396 | − | 21.1822i | −0.337710 | − | 0.815304i | ||||
\(676\) | 20.3887i | 0.784179i | ||||||||
\(677\) | −0.635991 | + | 0.263436i | −0.0244431 | + | 0.0101247i | −0.394872 | − | 0.918736i | \(-0.629211\pi\) |
0.370428 | + | 0.928861i | \(0.379211\pi\) | |||||||
\(678\) | 12.8918 | + | 12.8918i | 0.495105 | + | 0.495105i | ||||
\(679\) | −28.8309 | −1.10643 | ||||||||
\(680\) | −7.02002 | + | 0.196959i | −0.269205 | + | 0.00755305i | ||||
\(681\) | 23.4996 | 0.900508 | ||||||||
\(682\) | 29.1331 | + | 29.1331i | 1.11556 | + | 1.11556i | ||||
\(683\) | −35.9530 | + | 14.8922i | −1.37570 | + | 0.569835i | −0.943329 | − | 0.331860i | \(-0.892324\pi\) |
−0.432374 | + | 0.901694i | \(0.642324\pi\) | |||||||
\(684\) | 6.54658i | 0.250315i | ||||||||
\(685\) | −2.69839 | − | 6.51450i | −0.103100 | − | 0.248906i | ||||
\(686\) | −2.45710 | − | 1.01776i | −0.0938124 | − | 0.0388584i | ||||
\(687\) | 6.84427 | − | 16.5235i | 0.261125 | − | 0.630412i | ||||
\(688\) | 0.199509 | − | 0.199509i | 0.00760620 | − | 0.00760620i | ||||
\(689\) | −16.1074 | + | 16.1074i | −0.613644 | + | 0.613644i | ||||
\(690\) | 1.86517 | − | 4.50293i | 0.0710060 | − | 0.171424i | ||||
\(691\) | 1.98209 | + | 0.821007i | 0.0754021 | + | 0.0312326i | 0.420066 | − | 0.907494i | \(-0.362007\pi\) |
−0.344664 | + | 0.938726i | \(0.612007\pi\) | |||||||
\(692\) | 5.16121 | + | 12.4603i | 0.196200 | + | 0.473668i | ||||
\(693\) | 20.6101i | 0.782914i | ||||||||
\(694\) | 36.9754 | − | 15.3157i | 1.40357 | − | 0.581377i | ||||
\(695\) | 8.69762 | + | 8.69762i | 0.329919 | + | 0.329919i | ||||
\(696\) | 20.9933 | 0.795749 | ||||||||
\(697\) | 0.0920335 | + | 3.28025i | 0.00348602 | + | 0.124248i | ||||
\(698\) | 29.9240 | 1.13264 | ||||||||
\(699\) | −12.1139 | − | 12.1139i | −0.458191 | − | 0.458191i | ||||
\(700\) | −50.9020 | + | 21.0843i | −1.92392 | + | 0.796912i | ||||
\(701\) | 19.8333i | 0.749095i | 0.927208 | + | 0.374548i | \(0.122202\pi\) | ||||
−0.927208 | + | 0.374548i | \(0.877798\pi\) | |||||||
\(702\) | −11.1409 | − | 26.8964i | −0.420485 | − | 1.01514i | ||||
\(703\) | −5.63243 | − | 2.33303i | −0.212431 | − | 0.0879918i | ||||
\(704\) | 13.5422 | − | 32.6937i | 0.510391 | − | 1.23219i | ||||
\(705\) | −3.35718 | + | 3.35718i | −0.126439 | + | 0.126439i | ||||
\(706\) | −6.43584 | + | 6.43584i | −0.242216 | + | 0.242216i | ||||
\(707\) | −2.43814 | + | 5.88618i | −0.0916955 | + | 0.221373i | ||||
\(708\) | 20.5800 | + | 8.52452i | 0.773444 | + | 0.320371i | ||||
\(709\) | 5.25475 | + | 12.6861i | 0.197346 | + | 0.476436i | 0.991313 | − | 0.131526i | \(-0.0419875\pi\) |
−0.793967 | + | 0.607961i | \(0.791988\pi\) | |||||||
\(710\) | − | 9.05013i | − | 0.339645i | ||||||
\(711\) | 22.1859 | − | 9.18970i | 0.832036 | − | 0.344641i | ||||
\(712\) | −0.0496945 | − | 0.0496945i | −0.00186238 | − | 0.00186238i | ||||
\(713\) | −22.4034 | −0.839016 | ||||||||
\(714\) | 12.6211 | − | 33.0638i | 0.472333 | − | 1.23738i | ||||
\(715\) | 4.45286 | 0.166527 | ||||||||
\(716\) | −25.2486 | − | 25.2486i | −0.943585 | − | 0.943585i | ||||
\(717\) | 23.8563 | − | 9.88159i | 0.890928 | − | 0.369035i | ||||
\(718\) | 21.3445i | 0.796571i | ||||||||
\(719\) | −20.0609 | − | 48.4313i | −0.748145 | − | 1.80618i | −0.568959 | − | 0.822366i | \(-0.692654\pi\) |
−0.179186 | − | 0.983815i | \(-0.557346\pi\) | |||||||
\(720\) | −0.333883 | − | 0.138299i | −0.0124431 | − | 0.00515410i | ||||
\(721\) | 14.3086 | − | 34.5440i | 0.532880 | − | 1.28649i | ||||
\(722\) | −28.8494 | + | 28.8494i | −1.07366 | + | 1.07366i | ||||
\(723\) | −4.31129 | + | 4.31129i | −0.160339 | + | 0.160339i | ||||
\(724\) | −1.59549 | + | 3.85185i | −0.0592959 | + | 0.143153i | ||||
\(725\) | −33.4856 | − | 13.8702i | −1.24363 | − | 0.515127i | ||||
\(726\) | −3.13620 | − | 7.57146i | −0.116395 | − | 0.281003i | ||||
\(727\) | − | 24.8956i | − | 0.923325i | −0.887056 | − | 0.461663i | \(-0.847253\pi\) | ||
0.887056 | − | 0.461663i | \(-0.152747\pi\) | |||||||
\(728\) | −23.8818 | + | 9.89217i | −0.885119 | + | 0.366628i | ||||
\(729\) | −9.10681 | − | 9.10681i | −0.337289 | − | 0.337289i | ||||
\(730\) | 2.80025 | 0.103642 | ||||||||
\(731\) | −1.47039 | + | 3.85201i | −0.0543843 | + | 0.142472i | ||||
\(732\) | 15.0682 | 0.556938 | ||||||||
\(733\) | 24.5184 | + | 24.5184i | 0.905606 | + | 0.905606i | 0.995914 | − | 0.0903077i | \(-0.0287851\pi\) |
−0.0903077 | + | 0.995914i | \(0.528785\pi\) | |||||||
\(734\) | −72.9055 | + | 30.1984i | −2.69099 | + | 1.11465i | ||||
\(735\) | 4.66010i | 0.171890i | ||||||||
\(736\) | 7.68299 | + | 18.5484i | 0.283199 | + | 0.683702i | ||||
\(737\) | 21.5000 | + | 8.90558i | 0.791962 | + | 0.328041i | ||||
\(738\) | 1.38844 | − | 3.35198i | 0.0511090 | − | 0.123388i | ||||
\(739\) | 8.63027 | − | 8.63027i | 0.317470 | − | 0.317470i | −0.530325 | − | 0.847795i | \(-0.677930\pi\) |
0.847795 | + | 0.530325i | \(0.177930\pi\) | |||||||
\(740\) | −8.48666 | + | 8.48666i | −0.311976 | + | 0.311976i | ||||
\(741\) | −1.00786 | + | 2.43320i | −0.0370248 | + | 0.0893857i | ||||
\(742\) | 70.6207 | + | 29.2521i | 2.59257 | + | 1.07388i | ||||
\(743\) | −4.20321 | − | 10.1475i | −0.154201 | − | 0.372274i | 0.827834 | − | 0.560973i | \(-0.189573\pi\) |
−0.982035 | + | 0.188699i | \(0.939573\pi\) | |||||||
\(744\) | 17.7257i | 0.649857i | ||||||||
\(745\) | 12.8278 | − | 5.31347i | 0.469976 | − | 0.194670i | ||||
\(746\) | 2.07684 | + | 2.07684i | 0.0760386 | + | 0.0760386i | ||||
\(747\) | −9.80558 | −0.358767 | ||||||||
\(748\) | 0.997028 | + | 35.5360i | 0.0364550 | + | 1.29933i | ||||
\(749\) | −34.5203 | −1.26134 | ||||||||
\(750\) | 9.83422 | + | 9.83422i | 0.359095 | + | 0.359095i | ||||
\(751\) | −5.00906 | + | 2.07482i | −0.182783 | + | 0.0757113i | −0.472198 | − | 0.881492i | \(-0.656539\pi\) |
0.289415 | + | 0.957204i | \(0.406539\pi\) | |||||||
\(752\) | − | 2.10105i | − | 0.0766175i | ||||||
\(753\) | −4.38205 | − | 10.5792i | −0.159691 | − | 0.385528i | ||||
\(754\) | −42.5189 | − | 17.6119i | −1.54845 | − | 0.641388i | ||||
\(755\) | 3.36311 | − | 8.11928i | 0.122396 | − | 0.295491i | ||||
\(756\) | −42.3661 | + | 42.3661i | −1.54084 | + | 1.54084i | ||||
\(757\) | −2.23033 | + | 2.23033i | −0.0810626 | + | 0.0810626i | −0.746476 | − | 0.665413i | \(-0.768256\pi\) |
0.665413 | + | 0.746476i | \(0.268256\pi\) | |||||||
\(758\) | −0.437380 | + | 1.05593i | −0.0158864 | + | 0.0383531i | ||||
\(759\) | −8.42238 | − | 3.48866i | −0.305713 | − | 0.126630i | ||||
\(760\) | −0.671114 | − | 1.62021i | −0.0243439 | − | 0.0587713i | ||||
\(761\) | − | 9.22097i | − | 0.334260i | −0.985935 | − | 0.167130i | \(-0.946550\pi\) | ||
0.985935 | − | 0.167130i | \(-0.0534500\pi\) | |||||||
\(762\) | −39.0827 | + | 16.1886i | −1.41582 | + | 0.586450i | ||||
\(763\) | 9.48898 | + | 9.48898i | 0.343524 | + | 0.343524i | ||||
\(764\) | 59.2607 | 2.14398 | ||||||||
\(765\) | 5.27906 | − | 0.148114i | 0.190865 | − | 0.00535506i | ||||
\(766\) | 19.7883 | 0.714979 | ||||||||
\(767\) | −12.7588 | − | 12.7588i | −0.460694 | − | 0.460694i | ||||
\(768\) | 13.0256 | − | 5.39537i | 0.470020 | − | 0.194688i | ||||
\(769\) | 20.5337i | 0.740464i | 0.928939 | + | 0.370232i | \(0.120722\pi\) | ||||
−0.928939 | + | 0.370232i | \(0.879278\pi\) | |||||||
\(770\) | −5.71813 | − | 13.8048i | −0.206067 | − | 0.497490i | ||||
\(771\) | 28.4864 | + | 11.7994i | 1.02591 | + | 0.424946i | ||||
\(772\) | 1.99598 | − | 4.81873i | 0.0718370 | − | 0.173430i | ||||
\(773\) | −5.41911 | + | 5.41911i | −0.194912 | + | 0.194912i | −0.797815 | − | 0.602903i | \(-0.794011\pi\) |
0.602903 | + | 0.797815i | \(0.294011\pi\) | |||||||
\(774\) | 3.22342 | − | 3.22342i | 0.115864 | − | 0.115864i | ||||
\(775\) | 11.7113 | − | 28.2737i | 0.420684 | − | 1.01562i | ||||
\(776\) | 18.7693 | + | 7.77451i | 0.673779 | + | 0.279089i | ||||
\(777\) | −8.55226 | − | 20.6470i | −0.306811 | − | 0.740706i | ||||
\(778\) | 67.0145i | 2.40258i | ||||||||
\(779\) | −0.757079 | + | 0.313593i | −0.0271252 | + | 0.0112356i | ||||
\(780\) | 3.66622 | + | 3.66622i | 0.131272 | + | 0.131272i | ||||
\(781\) | −16.9276 | −0.605716 | ||||||||
\(782\) | −22.9038 | − | 21.6536i | −0.819037 | − | 0.774332i | ||||
\(783\) | −39.4146 | −1.40856 | ||||||||
\(784\) | −1.45824 | − | 1.45824i | −0.0520799 | − | 0.0520799i | ||||
\(785\) | −12.4022 | + | 5.13715i | −0.442653 | + | 0.183353i | ||||
\(786\) | − | 48.6637i | − | 1.73578i | ||||||
\(787\) | 4.86879 | + | 11.7543i | 0.173554 | + | 0.418995i | 0.986590 | − | 0.163217i | \(-0.0521871\pi\) |
−0.813037 | + | 0.582213i | \(0.802187\pi\) | |||||||
\(788\) | −19.6467 | − | 8.13792i | −0.699884 | − | 0.289901i | ||||
\(789\) | −9.10070 | + | 21.9710i | −0.323994 | + | 0.782190i | ||||
\(790\) | −12.3106 | + | 12.3106i | −0.437993 | + | 0.437993i | ||||
\(791\) | −21.4912 | + | 21.4912i | −0.764139 | + | 0.764139i | ||||
\(792\) | 5.55771 | − | 13.4175i | 0.197485 | − | 0.476770i | ||||
\(793\) | −11.2765 | − | 4.67086i | −0.400439 | − | 0.165867i | ||||
\(794\) | 21.0450 | + | 50.8071i | 0.746858 | + | 1.80308i | ||||
\(795\) | − | 5.66509i | − | 0.200920i | ||||||
\(796\) | 44.3011 | − | 18.3501i | 1.57021 | − | 0.650403i | ||||
\(797\) | 29.4157 | + | 29.4157i | 1.04196 | + | 1.04196i | 0.999080 | + | 0.0428772i | \(0.0136524\pi\) |
0.0428772 | + | 0.999080i | \(0.486348\pi\) | |||||||
\(798\) | 8.83766 | 0.312850 | ||||||||
\(799\) | 12.5406 | + | 28.0255i | 0.443653 | + | 0.991469i | ||||
\(800\) | −27.4248 | −0.969611 | ||||||||
\(801\) | 0.0373703 | + | 0.0373703i | 0.00132041 | + | 0.00132041i | ||||
\(802\) | −39.0187 | + | 16.1621i | −1.37780 | + | 0.570703i | ||||
\(803\) | − | 5.23765i | − | 0.184833i | ||||||
\(804\) | 10.3695 | + | 25.0341i | 0.365703 | + | 0.882886i | ||||
\(805\) | 7.50661 | + | 3.10934i | 0.264573 | + | 0.109590i | ||||
\(806\) | 14.8706 | − | 35.9009i | 0.523796 | − | 1.26456i | ||||
\(807\) | −9.91145 | + | 9.91145i | −0.348899 | + | 0.348899i | ||||
\(808\) | 3.17452 | − | 3.17452i | 0.111679 | − | 0.111679i | ||||
\(809\) | −5.49174 | + | 13.2582i | −0.193079 | + | 0.466134i | −0.990538 | − | 0.137239i | \(-0.956177\pi\) |
0.797459 | + | 0.603373i | \(0.206177\pi\) | |||||||
\(810\) | −1.38468 | − | 0.573553i | −0.0486527 | − | 0.0201526i | ||||
\(811\) | −18.7407 | − | 45.2441i | −0.658076 | − | 1.58874i | −0.800772 | − | 0.598970i | \(-0.795577\pi\) |
0.142696 | − | 0.989767i | \(-0.454423\pi\) | |||||||
\(812\) | 94.7154i | 3.32386i | ||||||||
\(813\) | 11.8424 | − | 4.90528i | 0.415331 | − | 0.172036i | ||||
\(814\) | 25.8820 | + | 25.8820i | 0.907165 | + | 0.907165i | ||||
\(815\) | 10.7859 | 0.377815 | ||||||||
\(816\) | 0.797412 | − | 0.843449i | 0.0279150 | − | 0.0295266i | ||||
\(817\) | −1.02961 | −0.0360215 | ||||||||
\(818\) | −9.32254 | − | 9.32254i | −0.325955 | − | 0.325955i | ||||
\(819\) | 17.9591 | − | 7.43892i | 0.627543 | − | 0.259937i | ||||
\(820\) | 1.61324i | 0.0563366i | ||||||||
\(821\) | 12.1394 | + | 29.3070i | 0.423666 | + | 1.02282i | 0.981257 | + | 0.192705i | \(0.0617259\pi\) |
−0.557591 | + | 0.830116i | \(0.688274\pi\) | |||||||
\(822\) | −23.1333 | − | 9.58211i | −0.806865 | − | 0.334214i | ||||
\(823\) | 10.0406 | − | 24.2401i | 0.349992 | − | 0.844956i | −0.646628 | − | 0.762806i | \(-0.723821\pi\) |
0.996620 | − | 0.0821504i | \(-0.0261788\pi\) | |||||||
\(824\) | −18.6302 | + | 18.6302i | −0.649015 | + | 0.649015i | ||||
\(825\) | 8.80555 | − | 8.80555i | 0.306570 | − | 0.306570i | ||||
\(826\) | −23.1708 | + | 55.9392i | −0.806215 | + | 1.94637i | ||||
\(827\) | 21.8165 | + | 9.03671i | 0.758636 | + | 0.314237i | 0.728260 | − | 0.685301i | \(-0.240330\pi\) |
0.0303760 | + | 0.999539i | \(0.490330\pi\) | |||||||
\(828\) | 8.17901 | + | 19.7459i | 0.284240 | + | 0.686217i | ||||
\(829\) | 23.9642i | 0.832311i | 0.909294 | + | 0.416155i | \(0.136623\pi\) | ||||
−0.909294 | + | 0.416155i | \(0.863377\pi\) | |||||||
\(830\) | 6.56784 | − | 2.72049i | 0.227973 | − | 0.0944295i | ||||
\(831\) | 21.3407 | + | 21.3407i | 0.740302 | + | 0.740302i | ||||
\(832\) | −33.3763 | −1.15712 | ||||||||
\(833\) | 28.1549 | + | 10.7473i | 0.975509 | + | 0.372372i | ||||
\(834\) | 43.6789 | 1.51248 | ||||||||
\(835\) | −0.673514 | − | 0.673514i | −0.0233079 | − | 0.0233079i | ||||
\(836\) | −8.20168 | + | 3.39725i | −0.283661 | + | 0.117496i | ||||
\(837\) | − | 33.2798i | − | 1.15032i | ||||||
\(838\) | −22.9759 | − | 55.4687i | −0.793689 | − | 1.91613i | ||||
\(839\) | 31.1030 | + | 12.8833i | 1.07380 | + | 0.444781i | 0.848329 | − | 0.529470i | \(-0.177609\pi\) |
0.225467 | + | 0.974251i | \(0.427609\pi\) | |||||||
\(840\) | 2.46013 | − | 5.93927i | 0.0848825 | − | 0.204924i | ||||
\(841\) | −23.5523 | + | 23.5523i | −0.812149 | + | 0.812149i | ||||
\(842\) | −12.9614 | + | 12.9614i | −0.446679 | + | 0.446679i | ||||
\(843\) | 7.69368 | − | 18.5742i | 0.264984 | − | 0.639729i | ||||
\(844\) | 18.6350 | + | 7.71888i | 0.641444 | + | 0.265695i | ||||
\(845\) | 1.57177 | + | 3.79459i | 0.0540705 | + | 0.130538i | ||||
\(846\) | − | 33.9463i | − | 1.16710i | ||||||
\(847\) | 12.6220 | − | 5.22821i | 0.433697 | − | 0.179643i | ||||
\(848\) | 1.77272 | + | 1.77272i | 0.0608754 | + | 0.0608754i | ||||
\(849\) | 11.7770 | 0.404187 | ||||||||
\(850\) | 39.3003 | − | 17.5857i | 1.34799 | − | 0.603185i | ||||
\(851\) | −19.9034 | −0.682280 | ||||||||
\(852\) | −13.9371 | − | 13.9371i | −0.477479 | − | 0.477479i | ||||
\(853\) | −30.4294 | + | 12.6043i | −1.04188 | + | 0.431563i | −0.836988 | − | 0.547221i | \(-0.815686\pi\) |
−0.204896 | + | 0.978784i | \(0.565686\pi\) | |||||||
\(854\) | 40.9575i | 1.40154i | ||||||||
\(855\) | 0.504678 | + | 1.21840i | 0.0172596 | + | 0.0416684i | ||||
\(856\) | 22.4732 | + | 9.30872i | 0.768119 | + | 0.318165i | ||||
\(857\) | −0.711156 | + | 1.71688i | −0.0242926 | + | 0.0586476i | −0.935560 | − | 0.353167i | \(-0.885105\pi\) |
0.911268 | + | 0.411814i | \(0.135105\pi\) | |||||||
\(858\) | 11.1810 | − | 11.1810i | 0.381712 | − | 0.381712i | ||||
\(859\) | −31.0170 | + | 31.0170i | −1.05829 | + | 1.05829i | −0.0600938 | + | 0.998193i | \(0.519140\pi\) |
−0.998193 | + | 0.0600938i | \(0.980860\pi\) | |||||||
\(860\) | −0.775682 | + | 1.87266i | −0.0264505 | + | 0.0638572i | ||||
\(861\) | −2.77525 | − | 1.14955i | −0.0945803 | − | 0.0391765i | ||||
\(862\) | −12.2273 | − | 29.5194i | −0.416464 | − | 1.00543i | ||||
\(863\) | 11.1194i | 0.378509i | 0.981928 | + | 0.189255i | \(0.0606072\pi\) | ||||
−0.981928 | + | 0.189255i | \(0.939393\pi\) | |||||||
\(864\) | −27.5532 | + | 11.4129i | −0.937378 | + | 0.388275i | ||||
\(865\) | 1.92113 | + | 1.92113i | 0.0653204 | + | 0.0653204i | ||||
\(866\) | −62.8203 | −2.13472 | ||||||||
\(867\) | −5.60219 | + | 16.0101i | −0.190260 | + | 0.543731i | ||||
\(868\) | −79.9731 | −2.71446 | ||||||||
\(869\) | 23.0261 | + | 23.0261i | 0.781106 | + | 0.781106i | ||||
\(870\) | 10.5742 | − | 4.37998i | 0.358499 | − | 0.148495i | ||||
\(871\) | − | 21.9489i | − | 0.743709i | ||||||
\(872\) | −3.61867 | − | 8.73625i | −0.122544 | − | 0.295847i | ||||
\(873\) | −14.1145 | − | 5.84643i | −0.477705 | − | 0.197872i | ||||
\(874\) | 3.01206 | − | 7.27175i | 0.101884 | − | 0.245971i | ||||
\(875\) | −16.3941 | + | 16.3941i | −0.554223 | + | 0.554223i | ||||
\(876\) | 4.31237 | − | 4.31237i | 0.145701 | − | 0.145701i | ||||
\(877\) | −17.3611 | + | 41.9135i | −0.586243 | + | 1.41532i | 0.300825 | + | 0.953679i | \(0.402738\pi\) |
−0.887069 | + | 0.461638i | \(0.847262\pi\) | |||||||
\(878\) | 67.1480 | + | 27.8136i | 2.26614 | + | 0.938664i | ||||
\(879\) | −6.43463 | − | 15.5346i | −0.217035 | − | 0.523968i | ||||
\(880\) | − | 0.490064i | − | 0.0165200i | ||||||
\(881\) | 23.0013 | − | 9.52747i | 0.774935 | − | 0.320989i | 0.0400655 | − | 0.999197i | \(-0.487243\pi\) |
0.734870 | + | 0.678208i | \(0.237243\pi\) | |||||||
\(882\) | −23.5605 | − | 23.5605i | −0.793322 | − | 0.793322i | ||||
\(883\) | 1.59743 | 0.0537578 | 0.0268789 | − | 0.999639i | \(-0.491443\pi\) | ||||
0.0268789 | + | 0.999639i | \(0.491443\pi\) | |||||||
\(884\) | 30.6053 | − | 13.6950i | 1.02937 | − | 0.460612i | ||||
\(885\) | 4.48736 | 0.150841 | ||||||||
\(886\) | 20.3939 | + | 20.3939i | 0.685146 | + | 0.685146i | ||||
\(887\) | −45.2950 | + | 18.7618i | −1.52086 | + | 0.629959i | −0.977763 | − | 0.209713i | \(-0.932747\pi\) |
−0.543093 | + | 0.839672i | \(0.682747\pi\) | |||||||
\(888\) | 15.7477i | 0.528458i | ||||||||
\(889\) | −26.9872 | − | 65.1528i | −0.905121 | − | 2.18515i | ||||
\(890\) | −0.0353990 | − | 0.0146627i | −0.00118658 | − | 0.000491496i | ||||
\(891\) | −1.07279 | + | 2.58993i | −0.0359397 | + | 0.0867660i | ||||
\(892\) | 23.2253 | − | 23.2253i | 0.777639 | − | 0.777639i | ||||
\(893\) | −5.42148 | + | 5.42148i | −0.181423 | + | 0.181423i | ||||
\(894\) | 18.8683 | − | 45.5522i | 0.631052 | − | 1.52349i | ||||
\(895\) | −6.64551 | − | 2.75266i | −0.222135 | − | 0.0920113i | ||||
\(896\) | 25.5681 | + | 61.7268i | 0.854170 | + | 2.06215i | ||||
\(897\) | 8.59822i | 0.287086i | ||||||||
\(898\) | −17.9698 | + | 7.44333i | −0.599660 | + | 0.248387i | ||||
\(899\) | −37.2008 | − | 37.2008i | −1.24072 | − | 1.24072i | ||||
\(900\) | −29.1953 | −0.973177 | ||||||||
\(901\) | −34.2267 | − | 13.0650i | −1.14026 | − | 0.435259i | ||||
\(902\) | 4.91993 | 0.163816 | ||||||||
\(903\) | −2.66881 | − | 2.66881i | −0.0888126 | − | 0.0888126i | ||||
\(904\) | 19.7864 | − | 8.19579i | 0.658085 | − | 0.272588i | ||||
\(905\) | 0.839875i | 0.0279184i | ||||||||
\(906\) | −11.9426 | − | 28.8319i | −0.396765 | − | 0.957876i | ||||
\(907\) | −43.3406 | − | 17.9523i | −1.43910 | − | 0.596096i | −0.479522 | − | 0.877530i | \(-0.659190\pi\) |
−0.959580 | + | 0.281434i | \(0.909190\pi\) | |||||||
\(908\) | 28.5901 | − | 69.0227i | 0.948797 | − | 2.29060i | ||||
\(909\) | −2.38724 | + | 2.38724i | −0.0791799 | + | 0.0791799i | ||||
\(910\) | −9.96527 | + | 9.96527i | −0.330345 | + | 0.330345i | ||||
\(911\) | 3.07887 | − | 7.43305i | 0.102007 | − | 0.246268i | −0.864633 | − | 0.502403i | \(-0.832449\pi\) |
0.966641 | + | 0.256135i | \(0.0824493\pi\) | |||||||
\(912\) | 0.267788 | + | 0.110921i | 0.00886734 | + | 0.00367297i | ||||
\(913\) | −5.08846 | − | 12.2846i | −0.168403 | − | 0.406562i | ||||
\(914\) | − | 76.5996i | − | 2.53369i | ||||||
\(915\) | 2.80439 | − | 1.16162i | 0.0927103 | − | 0.0384019i | ||||
\(916\) | −40.2057 | − | 40.2057i | −1.32843 | − | 1.32843i | ||||
\(917\) | 81.1248 | 2.67898 | ||||||||
\(918\) | 32.1659 | − | 34.0230i | 1.06163 | − | 1.12293i | ||||
\(919\) | 1.37930 | 0.0454989 | 0.0227494 | − | 0.999741i | \(-0.492758\pi\) | ||||
0.0227494 | + | 0.999741i | \(0.492758\pi\) | |||||||
\(920\) | −4.04845 | − | 4.04845i | −0.133473 | − | 0.133473i | ||||
\(921\) | 7.93115 | − | 3.28519i | 0.261340 | − | 0.108251i | ||||
\(922\) | − | 7.13211i | − | 0.234883i | ||||||
\(923\) | 6.10975 | + | 14.7502i | 0.201105 | + | 0.485510i | ||||
\(924\) | −30.0652 | − | 12.4534i | −0.989072 | − | 0.409687i | ||||
\(925\) | 10.4044 | − | 25.1185i | 0.342096 | − | 0.825893i | ||||
\(926\) | −46.8252 | + | 46.8252i | −1.53877 | + | 1.53877i | ||||
\(927\) | 14.0099 | − | 14.0099i | 0.460147 | − | 0.460147i | ||||
\(928\) | −18.0419 | + | 43.5571i | −0.592255 | + | 1.42983i | ||||
\(929\) | −10.9036 | − | 4.51642i | −0.357736 | − | 0.148179i | 0.196575 | − | 0.980489i | \(-0.437018\pi\) |
−0.554311 | + | 0.832310i | \(0.687018\pi\) | |||||||
\(930\) | 3.69825 | + | 8.92835i | 0.121270 | + | 0.292772i | ||||
\(931\) | 7.52557i | 0.246640i | ||||||||
\(932\) | −50.3188 | + | 20.8427i | −1.64825 | + | 0.682727i | ||||
\(933\) | −18.0059 | − | 18.0059i | −0.589485 | − | 0.589485i | ||||
\(934\) | −58.8064 | −1.92420 | ||||||||
\(935\) | 2.92505 | + | 6.53684i | 0.0956592 | + | 0.213778i | ||||
\(936\) | −13.6976 | −0.447721 | ||||||||
\(937\) | 5.07802 | + | 5.07802i | 0.165892 | + | 0.165892i | 0.785171 | − | 0.619279i | \(-0.212575\pi\) |
−0.619279 | + | 0.785171i | \(0.712575\pi\) | |||||||
\(938\) | −68.0461 | + | 28.1856i | −2.22178 | + | 0.920293i | ||||
\(939\) | − | 11.3100i | − | 0.369088i | ||||||
\(940\) | 5.77622 | + | 13.9450i | 0.188400 | + | 0.454837i | ||||
\(941\) | −45.5441 | − | 18.8650i | −1.48469 | − | 0.614980i | −0.514539 | − | 0.857467i | \(-0.672037\pi\) |
−0.970155 | + | 0.242487i | \(0.922037\pi\) | |||||||
\(942\) | −18.2423 | + | 44.0407i | −0.594365 | + | 1.43492i | ||||
\(943\) | −1.89173 | + | 1.89173i | −0.0616030 | + | 0.0616030i | ||||
\(944\) | −1.40418 | + | 1.40418i | −0.0457023 | + | 0.0457023i | ||||
\(945\) | −4.61885 | + | 11.1509i | −0.150251 | + | 0.362738i | ||||
\(946\) | 5.71111 | + | 2.36562i | 0.185684 | + | 0.0769130i | ||||
\(947\) | 13.3751 | + | 32.2903i | 0.434632 | + | 1.04929i | 0.977775 | + | 0.209655i | \(0.0672340\pi\) |
−0.543143 | + | 0.839640i | \(0.682766\pi\) | |||||||
\(948\) | 37.9166i | 1.23147i | ||||||||
\(949\) | −4.56395 | + | 1.89045i | −0.148152 | + | 0.0613666i | ||||
\(950\) | 7.60257 | + | 7.60257i | 0.246660 | + | 0.246660i | ||||
\(951\) | −1.99351 | −0.0646440 | ||||||||
\(952\) | −30.2096 | − | 28.5607i | −0.979099 | − | 0.925657i | ||||
\(953\) | −19.0277 | −0.616367 | −0.308184 | − | 0.951327i | \(-0.599721\pi\) | ||||
−0.308184 | + | 0.951327i | \(0.599721\pi\) | |||||||
\(954\) | 28.6415 | + | 28.6415i | 0.927301 | + | 0.927301i | ||||
\(955\) | 11.0292 | − | 4.56843i | 0.356895 | − | 0.147831i | ||||
\(956\) | − | 82.0923i | − | 2.65505i | ||||||
\(957\) | −8.19241 | − | 19.7782i | −0.264823 | − | 0.639339i | ||||
\(958\) | −22.9023 | − | 9.48642i | −0.739938 | − | 0.306492i | ||||
\(959\) | 15.9739 | − | 38.5643i | 0.515823 | − | 1.24531i | ||||
\(960\) | 5.86934 | − | 5.86934i | 0.189432 | − | 0.189432i | ||||
\(961\) | 9.49028 | − | 9.49028i | 0.306138 | − | 0.306138i | ||||
\(962\) | 13.2112 | − | 31.8947i | 0.425946 | − | 1.02832i | ||||
\(963\) | −16.8999 | − | 7.00016i | −0.544591 | − | 0.225577i | ||||
\(964\) | 7.41784 | + | 17.9083i | 0.238913 | + | 0.576786i | ||||
\(965\) | − | 1.05070i | − | 0.0338232i | ||||||
\(966\) | 26.6563 | − | 11.0414i | 0.857652 | − | 0.355251i | ||||
\(967\) | 32.8397 | + | 32.8397i | 1.05605 | + | 1.05605i | 0.998333 | + | 0.0577200i | \(0.0183831\pi\) |
0.0577200 | + | 0.998333i | \(0.481617\pi\) | |||||||
\(968\) | −9.62694 | −0.309422 | ||||||||
\(969\) | −4.23401 | + | 0.118793i | −0.136016 | + | 0.00381618i | ||||
\(970\) | 11.0761 | 0.355631 | ||||||||
\(971\) | −13.4294 | − | 13.4294i | −0.430969 | − | 0.430969i | 0.457989 | − | 0.888958i | \(-0.348570\pi\) |
−0.888958 | + | 0.457989i | \(0.848570\pi\) | |||||||
\(972\) | −46.9155 | + | 19.4330i | −1.50482 | + | 0.623315i | ||||
\(973\) | 72.8148i | 2.33434i | ||||||||
\(974\) | 7.57449 | + | 18.2864i | 0.242702 | + | 0.585935i | ||||
\(975\) | −10.8512 | − | 4.49469i | −0.347515 | − | 0.143945i | ||||
\(976\) | −0.514057 | + | 1.24104i | −0.0164545 | + | 0.0397248i | ||||
\(977\) | 17.3442 | − | 17.3442i | 0.554890 | − | 0.554890i | −0.372958 | − | 0.927848i | \(-0.621657\pi\) |
0.927848 | + | 0.372958i | \(0.121657\pi\) | |||||||
\(978\) | 27.0831 | − | 27.0831i | 0.866022 | − | 0.866022i | ||||
\(979\) | −0.0274255 | + | 0.0662110i | −0.000876523 | + | 0.00211611i | ||||
\(980\) | 13.6876 | + | 5.66957i | 0.437233 | + | 0.181108i | ||||
\(981\) | 2.72124 | + | 6.56966i | 0.0868826 | + | 0.209753i | ||||
\(982\) | 3.31561i | 0.105805i | ||||||||
\(983\) | 19.4688 | − | 8.06426i | 0.620959 | − | 0.257210i | −0.0499470 | − | 0.998752i | \(-0.515905\pi\) |
0.670906 | + | 0.741542i | \(0.265905\pi\) | |||||||
\(984\) | 1.49674 | + | 1.49674i | 0.0477145 | + | 0.0477145i | ||||
\(985\) | −4.28385 | −0.136495 | ||||||||
\(986\) | −2.07585 | − | 73.9873i | −0.0661086 | − | 2.35624i | ||||
\(987\) | −28.1057 | −0.894613 | ||||||||
\(988\) | 5.92055 | + | 5.92055i | 0.188358 | + | 0.188358i | ||||
\(989\) | −3.10552 | + | 1.28635i | −0.0987499 | + | 0.0409035i | ||||
\(990\) | − | 7.91786i | − | 0.251646i | ||||||
\(991\) | 4.17804 | + | 10.0867i | 0.132720 | + | 0.320414i | 0.976243 | − | 0.216679i | \(-0.0695225\pi\) |
−0.843523 | + | 0.537093i | \(0.819522\pi\) | |||||||
\(992\) | −36.7775 | − | 15.2337i | −1.16769 | − | 0.483672i | ||||
\(993\) | 5.15548 | − | 12.4464i | 0.163604 | − | 0.394976i | ||||
\(994\) | 37.8830 | − | 37.8830i | 1.20158 | − | 1.20158i | ||||
\(995\) | 6.83038 | − | 6.83038i | 0.216538 | − | 0.216538i | ||||
\(996\) | 5.92489 | − | 14.3040i | 0.187737 | − | 0.453238i | ||||
\(997\) | 25.9821 | + | 10.7621i | 0.822861 | + | 0.340840i | 0.754073 | − | 0.656791i | \(-0.228087\pi\) |
0.0687883 | + | 0.997631i | \(0.478087\pi\) | |||||||
\(998\) | 16.2170 | + | 39.1513i | 0.513341 | + | 1.23931i | ||||
\(999\) | − | 29.5660i | − | 0.935427i |
(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 | 731.2.m.b.87.5 | ✓ | 116 | |
17.9 | even | 8 | inner | 731.2.m.b.689.5 | yes | 116 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.m.b.87.5 | ✓ | 116 | 1.1 | even | 1 | trivial | |
731.2.m.b.689.5 | yes | 116 | 17.9 | even | 8 | inner |