Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(131,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.131");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.e (of order \(2\), degree \(1\), 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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 131.11 | ||
Character | \(\chi\) | \(=\) | 572.131 |
Dual form | 572.2.e.b.131.12 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25608 | − | 0.649821i | −0.888182 | − | 0.459493i | ||||
\(3\) | − | 1.96816i | − | 1.13632i | −0.822919 | − | 0.568159i | \(-0.807656\pi\) | ||
0.822919 | − | 0.568159i | \(-0.192344\pi\) | |||||||
\(4\) | 1.15547 | + | 1.63245i | 0.577733 | + | 0.816226i | ||||
\(5\) | −3.24710 | −1.45215 | −0.726073 | − | 0.687617i | \(-0.758657\pi\) | ||||
−0.726073 | + | 0.687617i | \(0.758657\pi\) | |||||||
\(6\) | −1.27895 | + | 2.47217i | −0.522130 | + | 1.00926i | ||||
\(7\) | 4.43351 | 1.67571 | 0.837855 | − | 0.545893i | \(-0.183809\pi\) | ||||
0.837855 | + | 0.545893i | \(0.183809\pi\) | |||||||
\(8\) | −0.390556 | − | 2.80133i | −0.138083 | − | 0.990421i | ||||
\(9\) | −0.873660 | −0.291220 | ||||||||
\(10\) | 4.07861 | + | 2.11003i | 1.28977 | + | 0.667251i | ||||
\(11\) | 2.97258 | − | 1.47098i | 0.896266 | − | 0.443518i | ||||
\(12\) | 3.21293 | − | 2.27414i | 0.927492 | − | 0.656489i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | −5.56884 | − | 2.88099i | −1.48833 | − | 0.769976i | ||||
\(15\) | 6.39082i | 1.65010i | ||||||||
\(16\) | −1.32979 | + | 3.77249i | −0.332449 | + | 0.943121i | ||||
\(17\) | 2.63117i | 0.638153i | 0.947729 | + | 0.319076i | \(0.103373\pi\) | ||||
−0.947729 | + | 0.319076i | \(0.896627\pi\) | |||||||
\(18\) | 1.09739 | + | 0.567722i | 0.258656 | + | 0.133813i | ||||
\(19\) | 4.71143 | 1.08088 | 0.540439 | − | 0.841383i | \(-0.318258\pi\) | ||||
0.540439 | + | 0.841383i | \(0.318258\pi\) | |||||||
\(20\) | −3.75191 | − | 5.30073i | −0.838954 | − | 1.18528i | ||||
\(21\) | − | 8.72587i | − | 1.90414i | ||||||
\(22\) | −4.68966 | − | 0.0839736i | −0.999840 | − | 0.0179032i | ||||
\(23\) | 0.0430153i | 0.00896931i | 0.999990 | + | 0.00448466i | \(0.00142752\pi\) | ||||
−0.999990 | + | 0.00448466i | \(0.998572\pi\) | |||||||
\(24\) | −5.51348 | + | 0.768678i | −1.12543 | + | 0.156906i | ||||
\(25\) | 5.54365 | 1.10873 | ||||||||
\(26\) | −0.649821 | + | 1.25608i | −0.127440 | + | 0.246337i | ||||
\(27\) | − | 4.18498i | − | 0.805400i | ||||||
\(28\) | 5.12277 | + | 7.23749i | 0.968113 | + | 1.36776i | ||||
\(29\) | − | 4.26688i | − | 0.792339i | −0.918177 | − | 0.396169i | \(-0.870339\pi\) | ||
0.918177 | − | 0.396169i | \(-0.129661\pi\) | |||||||
\(30\) | 4.15288 | − | 8.02737i | 0.758209 | − | 1.46559i | ||||
\(31\) | − | 6.80753i | − | 1.22267i | −0.791372 | − | 0.611335i | \(-0.790633\pi\) | ||
0.791372 | − | 0.611335i | \(-0.209367\pi\) | |||||||
\(32\) | 4.12176 | − | 3.87441i | 0.728632 | − | 0.684905i | ||||
\(33\) | −2.89513 | − | 5.85051i | −0.503977 | − | 1.01844i | ||||
\(34\) | 1.70979 | − | 3.30496i | 0.293226 | − | 0.566796i | ||||
\(35\) | −14.3961 | −2.43338 | ||||||||
\(36\) | −1.00948 | − | 1.42621i | −0.168247 | − | 0.237701i | ||||
\(37\) | −1.79924 | −0.295793 | −0.147897 | − | 0.989003i | \(-0.547250\pi\) | ||||
−0.147897 | + | 0.989003i | \(0.547250\pi\) | |||||||
\(38\) | −5.91793 | − | 3.06159i | −0.960015 | − | 0.496655i | ||||
\(39\) | −1.96816 | −0.315158 | ||||||||
\(40\) | 1.26818 | + | 9.09621i | 0.200516 | + | 1.43824i | ||||
\(41\) | − | 1.50014i | − | 0.234283i | −0.993115 | − | 0.117142i | \(-0.962627\pi\) | ||
0.993115 | − | 0.117142i | \(-0.0373731\pi\) | |||||||
\(42\) | −5.67025 | + | 10.9604i | −0.874938 | + | 1.69122i | ||||
\(43\) | −7.61693 | −1.16157 | −0.580786 | − | 0.814057i | \(-0.697255\pi\) | ||||
−0.580786 | + | 0.814057i | \(0.697255\pi\) | |||||||
\(44\) | 5.83602 | + | 3.15292i | 0.879813 | + | 0.475320i | ||||
\(45\) | 2.83686 | 0.422894 | ||||||||
\(46\) | 0.0279522 | − | 0.0540306i | 0.00412133 | − | 0.00796638i | ||||
\(47\) | 11.8706i | 1.73150i | 0.500477 | + | 0.865750i | \(0.333158\pi\) | ||||
−0.500477 | + | 0.865750i | \(0.666842\pi\) | |||||||
\(48\) | 7.42486 | + | 2.61725i | 1.07169 | + | 0.377767i | ||||
\(49\) | 12.6560 | 1.80800 | ||||||||
\(50\) | −6.96326 | − | 3.60238i | −0.984754 | − | 0.509453i | ||||
\(51\) | 5.17857 | 0.725145 | ||||||||
\(52\) | 1.63245 | − | 1.15547i | 0.226380 | − | 0.160234i | ||||
\(53\) | −10.4429 | −1.43444 | −0.717220 | − | 0.696846i | \(-0.754586\pi\) | ||||
−0.717220 | + | 0.696846i | \(0.754586\pi\) | |||||||
\(54\) | −2.71949 | + | 5.25667i | −0.370075 | + | 0.715342i | ||||
\(55\) | −9.65225 | + | 4.77642i | −1.30151 | + | 0.644053i | ||||
\(56\) | −1.73154 | − | 12.4197i | −0.231386 | − | 1.65966i | ||||
\(57\) | − | 9.27286i | − | 1.22822i | ||||||
\(58\) | −2.77270 | + | 5.35953i | −0.364074 | + | 0.703741i | ||||
\(59\) | − | 9.82553i | − | 1.27918i | −0.768718 | − | 0.639588i | \(-0.779105\pi\) | ||
0.768718 | − | 0.639588i | \(-0.220895\pi\) | |||||||
\(60\) | −10.4327 | + | 7.38437i | −1.34686 | + | 0.953318i | ||||
\(61\) | − | 2.20258i | − | 0.282012i | −0.990009 | − | 0.141006i | \(-0.954966\pi\) | ||
0.990009 | − | 0.141006i | \(-0.0450337\pi\) | |||||||
\(62\) | −4.42368 | + | 8.55080i | −0.561807 | + | 1.08595i | ||||
\(63\) | −3.87338 | −0.488000 | ||||||||
\(64\) | −7.69493 | + | 2.18816i | −0.961866 | + | 0.273520i | ||||
\(65\) | 3.24710i | 0.402753i | ||||||||
\(66\) | −0.165274 | + | 9.23002i | −0.0203438 | + | 1.13614i | ||||
\(67\) | 3.35101i | 0.409391i | 0.978826 | + | 0.204695i | \(0.0656203\pi\) | ||||
−0.978826 | + | 0.204695i | \(0.934380\pi\) | |||||||
\(68\) | −4.29526 | + | 3.04023i | −0.520877 | + | 0.368682i | ||||
\(69\) | 0.0846611 | 0.0101920 | ||||||||
\(70\) | 18.0826 | + | 9.35485i | 2.16128 | + | 1.11812i | ||||
\(71\) | − | 14.6471i | − | 1.73829i | −0.494561 | − | 0.869143i | \(-0.664671\pi\) | ||
0.494561 | − | 0.869143i | \(-0.335329\pi\) | |||||||
\(72\) | 0.341213 | + | 2.44741i | 0.0402124 | + | 0.288430i | ||||
\(73\) | 7.04910i | 0.825035i | 0.910950 | + | 0.412517i | \(0.135350\pi\) | ||||
−0.910950 | + | 0.412517i | \(0.864650\pi\) | |||||||
\(74\) | 2.25999 | + | 1.16918i | 0.262718 | + | 0.135915i | ||||
\(75\) | − | 10.9108i | − | 1.25987i | ||||||
\(76\) | 5.44390 | + | 7.69119i | 0.624459 | + | 0.882240i | ||||
\(77\) | 13.1790 | − | 6.52161i | 1.50188 | − | 0.743207i | ||||
\(78\) | 2.47217 | + | 1.27895i | 0.279918 | + | 0.144813i | ||||
\(79\) | −1.99652 | −0.224626 | −0.112313 | − | 0.993673i | \(-0.535826\pi\) | ||||
−0.112313 | + | 0.993673i | \(0.535826\pi\) | |||||||
\(80\) | 4.31797 | − | 12.2496i | 0.482764 | − | 1.36955i | ||||
\(81\) | −10.8577 | −1.20641 | ||||||||
\(82\) | −0.974824 | + | 1.88430i | −0.107651 | + | 0.208086i | ||||
\(83\) | 12.3355 | 1.35400 | 0.677000 | − | 0.735983i | \(-0.263280\pi\) | ||||
0.677000 | + | 0.735983i | \(0.263280\pi\) | |||||||
\(84\) | 14.2446 | − | 10.0824i | 1.55421 | − | 1.10009i | ||||
\(85\) | − | 8.54368i | − | 0.926692i | ||||||
\(86\) | 9.56747 | + | 4.94964i | 1.03169 | + | 0.533733i | ||||
\(87\) | −8.39790 | −0.900349 | ||||||||
\(88\) | −5.28167 | − | 7.75268i | −0.563028 | − | 0.826438i | ||||
\(89\) | 9.79840 | 1.03863 | 0.519314 | − | 0.854584i | \(-0.326188\pi\) | ||||
0.519314 | + | 0.854584i | \(0.326188\pi\) | |||||||
\(90\) | −3.56332 | − | 1.84345i | −0.375607 | − | 0.194317i | ||||
\(91\) | − | 4.43351i | − | 0.464758i | ||||||
\(92\) | −0.0702204 | + | 0.0497028i | −0.00732098 | + | 0.00518187i | ||||
\(93\) | −13.3983 | −1.38934 | ||||||||
\(94\) | 7.71374 | − | 14.9104i | 0.795611 | − | 1.53789i | ||||
\(95\) | −15.2985 | −1.56959 | ||||||||
\(96\) | −7.62547 | − | 8.11230i | −0.778271 | − | 0.827958i | ||||
\(97\) | 10.6850 | 1.08490 | 0.542448 | − | 0.840089i | \(-0.317497\pi\) | ||||
0.542448 | + | 0.840089i | \(0.317497\pi\) | |||||||
\(98\) | −15.8970 | − | 8.22415i | −1.60584 | − | 0.830764i | ||||
\(99\) | −2.59702 | + | 1.28514i | −0.261010 | + | 0.129161i | ||||
\(100\) | 6.40551 | + | 9.04974i | 0.640551 | + | 0.904974i | ||||
\(101\) | 14.1836i | 1.41132i | 0.708549 | + | 0.705661i | \(0.249350\pi\) | ||||
−0.708549 | + | 0.705661i | \(0.750650\pi\) | |||||||
\(102\) | −6.50469 | − | 3.36514i | −0.644060 | − | 0.333199i | ||||
\(103\) | 2.61974i | 0.258131i | 0.991636 | + | 0.129066i | \(0.0411978\pi\) | ||||
−0.991636 | + | 0.129066i | \(0.958802\pi\) | |||||||
\(104\) | −2.80133 | + | 0.390556i | −0.274693 | + | 0.0382972i | ||||
\(105\) | 28.3338i | 2.76509i | ||||||||
\(106\) | 13.1171 | + | 6.78600i | 1.27404 | + | 0.659115i | ||||
\(107\) | 12.0361 | 1.16358 | 0.581788 | − | 0.813340i | \(-0.302353\pi\) | ||||
0.581788 | + | 0.813340i | \(0.302353\pi\) | |||||||
\(108\) | 6.83178 | − | 4.83561i | 0.657388 | − | 0.465306i | ||||
\(109\) | − | 16.6400i | − | 1.59383i | −0.604094 | − | 0.796913i | \(-0.706465\pi\) | ||
0.604094 | − | 0.796913i | \(-0.293535\pi\) | |||||||
\(110\) | 15.2278 | + | 0.272670i | 1.45191 | + | 0.0259981i | ||||
\(111\) | 3.54120i | 0.336116i | ||||||||
\(112\) | −5.89566 | + | 16.7254i | −0.557087 | + | 1.58040i | ||||
\(113\) | −19.1558 | −1.80203 | −0.901015 | − | 0.433788i | \(-0.857177\pi\) | ||||
−0.901015 | + | 0.433788i | \(0.857177\pi\) | |||||||
\(114\) | −6.02570 | + | 11.6474i | −0.564358 | + | 1.09088i | ||||
\(115\) | − | 0.139675i | − | 0.0130248i | ||||||
\(116\) | 6.96547 | − | 4.93023i | 0.646727 | − | 0.457761i | ||||
\(117\) | 0.873660i | 0.0807699i | ||||||||
\(118\) | −6.38483 | + | 12.3416i | −0.587772 | + | 1.13614i | ||||
\(119\) | 11.6653i | 1.06936i | ||||||||
\(120\) | 17.9028 | − | 2.49597i | 1.63429 | − | 0.227850i | ||||
\(121\) | 6.67243 | − | 8.74521i | 0.606584 | − | 0.795019i | ||||
\(122\) | −1.43128 | + | 2.76662i | −0.129582 | + | 0.250478i | ||||
\(123\) | −2.95253 | −0.266220 | ||||||||
\(124\) | 11.1130 | − | 7.86588i | 0.997974 | − | 0.706377i | ||||
\(125\) | −1.76529 | −0.157893 | ||||||||
\(126\) | 4.86527 | + | 2.51700i | 0.433433 | + | 0.224232i | ||||
\(127\) | 0.128545 | 0.0114065 | 0.00570327 | − | 0.999984i | \(-0.498185\pi\) | ||||
0.00570327 | + | 0.999984i | \(0.498185\pi\) | |||||||
\(128\) | 11.0873 | + | 2.25183i | 0.979992 | + | 0.199035i | ||||
\(129\) | 14.9914i | 1.31992i | ||||||||
\(130\) | 2.11003 | − | 4.07861i | 0.185062 | − | 0.357718i | ||||
\(131\) | 13.9983 | 1.22304 | 0.611520 | − | 0.791229i | \(-0.290558\pi\) | ||||
0.611520 | + | 0.791229i | \(0.290558\pi\) | |||||||
\(132\) | 6.20545 | − | 11.4862i | 0.540115 | − | 0.999748i | ||||
\(133\) | 20.8882 | 1.81124 | ||||||||
\(134\) | 2.17755 | − | 4.20913i | 0.188112 | − | 0.363613i | ||||
\(135\) | 13.5890i | 1.16956i | ||||||||
\(136\) | 7.37079 | − | 1.02762i | 0.632040 | − | 0.0881178i | ||||
\(137\) | 1.61613 | 0.138075 | 0.0690377 | − | 0.997614i | \(-0.478007\pi\) | ||||
0.0690377 | + | 0.997614i | \(0.478007\pi\) | |||||||
\(138\) | −0.106341 | − | 0.0550145i | −0.00905235 | − | 0.00468315i | ||||
\(139\) | 7.22209 | 0.612569 | 0.306285 | − | 0.951940i | \(-0.400914\pi\) | ||||
0.306285 | + | 0.951940i | \(0.400914\pi\) | |||||||
\(140\) | −16.6342 | − | 23.5009i | −1.40584 | − | 1.98618i | ||||
\(141\) | 23.3632 | 1.96754 | ||||||||
\(142\) | −9.51796 | + | 18.3979i | −0.798729 | + | 1.54391i | ||||
\(143\) | −1.47098 | − | 2.97258i | −0.123010 | − | 0.248579i | ||||
\(144\) | 1.16179 | − | 3.29587i | 0.0968156 | − | 0.274656i | ||||
\(145\) | 13.8550i | 1.15059i | ||||||||
\(146\) | 4.58065 | − | 8.85422i | 0.379097 | − | 0.732781i | ||||
\(147\) | − | 24.9091i | − | 2.05447i | ||||||
\(148\) | −2.07896 | − | 2.93717i | −0.170890 | − | 0.241434i | ||||
\(149\) | 5.41263i | 0.443420i | 0.975113 | + | 0.221710i | \(0.0711638\pi\) | ||||
−0.975113 | + | 0.221710i | \(0.928836\pi\) | |||||||
\(150\) | −7.09006 | + | 13.7048i | −0.578901 | + | 1.11899i | ||||
\(151\) | −4.89798 | −0.398592 | −0.199296 | − | 0.979939i | \(-0.563866\pi\) | ||||
−0.199296 | + | 0.979939i | \(0.563866\pi\) | |||||||
\(152\) | −1.84008 | − | 13.1983i | −0.149250 | − | 1.07052i | ||||
\(153\) | − | 2.29875i | − | 0.185843i | ||||||
\(154\) | −20.7917 | − | 0.372298i | −1.67544 | − | 0.0300006i | ||||
\(155\) | 22.1047i | 1.77550i | ||||||||
\(156\) | −2.27414 | − | 3.21293i | −0.182077 | − | 0.257240i | ||||
\(157\) | −19.0917 | −1.52369 | −0.761843 | − | 0.647761i | \(-0.775705\pi\) | ||||
−0.761843 | + | 0.647761i | \(0.775705\pi\) | |||||||
\(158\) | 2.50779 | + | 1.29738i | 0.199509 | + | 0.103214i | ||||
\(159\) | 20.5533i | 1.62998i | ||||||||
\(160\) | −13.3838 | + | 12.5806i | −1.05808 | + | 0.994583i | ||||
\(161\) | 0.190709i | 0.0150300i | ||||||||
\(162\) | 13.6381 | + | 7.05555i | 1.07151 | + | 0.554337i | ||||
\(163\) | 3.00305i | 0.235217i | 0.993060 | + | 0.117608i | \(0.0375228\pi\) | ||||
−0.993060 | + | 0.117608i | \(0.962477\pi\) | |||||||
\(164\) | 2.44891 | − | 1.73337i | 0.191228 | − | 0.135353i | ||||
\(165\) | 9.40077 | + | 18.9972i | 0.731849 | + | 1.47893i | ||||
\(166\) | −15.4944 | − | 8.01588i | −1.20260 | − | 0.622153i | ||||
\(167\) | 8.68938 | 0.672405 | 0.336202 | − | 0.941790i | \(-0.390857\pi\) | ||||
0.336202 | + | 0.941790i | \(0.390857\pi\) | |||||||
\(168\) | −24.4441 | + | 3.40794i | −1.88590 | + | 0.262928i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | −5.55186 | + | 10.7315i | −0.425808 | + | 0.823071i | ||||
\(171\) | −4.11619 | −0.314773 | ||||||||
\(172\) | −8.80111 | − | 12.4343i | −0.671078 | − | 0.948104i | ||||
\(173\) | 3.41141i | 0.259365i | 0.991556 | + | 0.129682i | \(0.0413958\pi\) | ||||
−0.991556 | + | 0.129682i | \(0.958604\pi\) | |||||||
\(174\) | 10.5484 | + | 5.45713i | 0.799674 | + | 0.413704i | ||||
\(175\) | 24.5779 | 1.85791 | ||||||||
\(176\) | 1.59634 | + | 13.1701i | 0.120329 | + | 0.992734i | ||||
\(177\) | −19.3382 | −1.45355 | ||||||||
\(178\) | −12.3076 | − | 6.36720i | −0.922490 | − | 0.477242i | ||||
\(179\) | 20.2599i | 1.51429i | 0.653245 | + | 0.757146i | \(0.273407\pi\) | ||||
−0.653245 | + | 0.757146i | \(0.726593\pi\) | |||||||
\(180\) | 3.27790 | + | 4.63103i | 0.244320 | + | 0.345177i | ||||
\(181\) | −0.387206 | −0.0287808 | −0.0143904 | − | 0.999896i | \(-0.504581\pi\) | ||||
−0.0143904 | + | 0.999896i | \(0.504581\pi\) | |||||||
\(182\) | −2.88099 | + | 5.56884i | −0.213553 | + | 0.412790i | ||||
\(183\) | −4.33504 | −0.320455 | ||||||||
\(184\) | 0.120500 | − | 0.0167999i | 0.00888339 | − | 0.00123851i | ||||
\(185\) | 5.84231 | 0.429536 | ||||||||
\(186\) | 16.8293 | + | 8.70651i | 1.23399 | + | 0.638392i | ||||
\(187\) | 3.87040 | + | 7.82136i | 0.283032 | + | 0.571955i | ||||
\(188\) | −19.3781 | + | 13.7160i | −1.41329 | + | 1.00035i | ||||
\(189\) | − | 18.5542i | − | 1.34962i | ||||||
\(190\) | 19.2161 | + | 9.94128i | 1.39408 | + | 0.721216i | ||||
\(191\) | 9.65674i | 0.698737i | 0.936985 | + | 0.349369i | \(0.113604\pi\) | ||||
−0.936985 | + | 0.349369i | \(0.886396\pi\) | |||||||
\(192\) | 4.30665 | + | 15.1449i | 0.310805 | + | 1.09299i | ||||
\(193\) | − | 15.6944i | − | 1.12971i | −0.825191 | − | 0.564854i | \(-0.808932\pi\) | ||
0.825191 | − | 0.564854i | \(-0.191068\pi\) | |||||||
\(194\) | −13.4212 | − | 6.94333i | −0.963585 | − | 0.498502i | ||||
\(195\) | 6.39082 | 0.457656 | ||||||||
\(196\) | 14.6236 | + | 20.6603i | 1.04454 | + | 1.47574i | ||||
\(197\) | 2.74588i | 0.195636i | 0.995204 | + | 0.0978178i | \(0.0311862\pi\) | ||||
−0.995204 | + | 0.0978178i | \(0.968814\pi\) | |||||||
\(198\) | 4.09717 | + | 0.0733643i | 0.291173 | + | 0.00521377i | ||||
\(199\) | 21.4785i | 1.52257i | 0.648417 | + | 0.761285i | \(0.275431\pi\) | ||||
−0.648417 | + | 0.761285i | \(0.724569\pi\) | |||||||
\(200\) | −2.16511 | − | 15.5296i | −0.153096 | − | 1.09811i | ||||
\(201\) | 6.59532 | 0.465198 | ||||||||
\(202\) | 9.21681 | − | 17.8157i | 0.648492 | − | 1.25351i | ||||
\(203\) | − | 18.9172i | − | 1.32773i | ||||||
\(204\) | 5.98367 | + | 8.45376i | 0.418940 | + | 0.591882i | ||||
\(205\) | 4.87112i | 0.340213i | ||||||||
\(206\) | 1.70236 | − | 3.29060i | 0.118609 | − | 0.229267i | ||||
\(207\) | − | 0.0375807i | − | 0.00261204i | ||||||
\(208\) | 3.77249 | + | 1.32979i | 0.261575 | + | 0.0922046i | ||||
\(209\) | 14.0051 | − | 6.93043i | 0.968753 | − | 0.479388i | ||||
\(210\) | 18.4119 | − | 35.5894i | 1.27054 | − | 2.45590i | ||||
\(211\) | −16.8319 | −1.15876 | −0.579378 | − | 0.815059i | \(-0.696705\pi\) | ||||
−0.579378 | + | 0.815059i | \(0.696705\pi\) | |||||||
\(212\) | −12.0664 | − | 17.0475i | −0.828724 | − | 1.17083i | ||||
\(213\) | −28.8278 | −1.97525 | ||||||||
\(214\) | −15.1183 | − | 7.82132i | −1.03347 | − | 0.534655i | ||||
\(215\) | 24.7329 | 1.68677 | ||||||||
\(216\) | −11.7235 | + | 1.63447i | −0.797685 | + | 0.111212i | ||||
\(217\) | − | 30.1813i | − | 2.04884i | ||||||
\(218\) | −10.8130 | + | 20.9012i | −0.732352 | + | 1.41561i | ||||
\(219\) | 13.8738 | 0.937502 | ||||||||
\(220\) | −18.9501 | − | 10.2378i | −1.27762 | − | 0.690235i | ||||
\(221\) | 2.63117 | 0.176992 | ||||||||
\(222\) | 2.30114 | − | 4.44802i | 0.154443 | − | 0.298532i | ||||
\(223\) | 8.72379i | 0.584188i | 0.956390 | + | 0.292094i | \(0.0943520\pi\) | ||||
−0.956390 | + | 0.292094i | \(0.905648\pi\) | |||||||
\(224\) | 18.2739 | − | 17.1772i | 1.22098 | − | 1.14770i | ||||
\(225\) | −4.84327 | −0.322884 | ||||||||
\(226\) | 24.0612 | + | 12.4479i | 1.60053 | + | 0.828019i | ||||
\(227\) | −11.1722 | −0.741522 | −0.370761 | − | 0.928728i | \(-0.620903\pi\) | ||||
−0.370761 | + | 0.928728i | \(0.620903\pi\) | |||||||
\(228\) | 15.1375 | − | 10.7145i | 1.00251 | − | 0.709584i | ||||
\(229\) | −14.1298 | −0.933724 | −0.466862 | − | 0.884330i | \(-0.654616\pi\) | ||||
−0.466862 | + | 0.884330i | \(0.654616\pi\) | |||||||
\(230\) | −0.0907637 | + | 0.175443i | −0.00598478 | + | 0.0115684i | ||||
\(231\) | −12.8356 | − | 25.9383i | −0.844520 | − | 1.70662i | ||||
\(232\) | −11.9529 | + | 1.66646i | −0.784749 | + | 0.109408i | ||||
\(233\) | 5.12682i | 0.335869i | 0.985798 | + | 0.167935i | \(0.0537098\pi\) | ||||
−0.985798 | + | 0.167935i | \(0.946290\pi\) | |||||||
\(234\) | 0.567722 | − | 1.09739i | 0.0371131 | − | 0.0717383i | ||||
\(235\) | − | 38.5449i | − | 2.51439i | ||||||
\(236\) | 16.0397 | − | 11.3531i | 1.04410 | − | 0.739022i | ||||
\(237\) | 3.92948i | 0.255247i | ||||||||
\(238\) | 7.58037 | − | 14.6526i | 0.491363 | − | 0.949785i | ||||
\(239\) | −10.5322 | −0.681274 | −0.340637 | − | 0.940195i | \(-0.610643\pi\) | ||||
−0.340637 | + | 0.940195i | \(0.610643\pi\) | |||||||
\(240\) | −24.1093 | − | 8.49847i | −1.55625 | − | 0.548574i | ||||
\(241\) | 18.8992i | 1.21740i | 0.793399 | + | 0.608702i | \(0.208310\pi\) | ||||
−0.793399 | + | 0.608702i | \(0.791690\pi\) | |||||||
\(242\) | −14.0639 | + | 6.64879i | −0.904062 | + | 0.427400i | ||||
\(243\) | 8.81476i | 0.565467i | ||||||||
\(244\) | 3.59561 | − | 2.54501i | 0.230185 | − | 0.162928i | ||||
\(245\) | −41.0954 | −2.62549 | ||||||||
\(246\) | 3.70860 | + | 1.91861i | 0.236452 | + | 0.122326i | ||||
\(247\) | − | 4.71143i | − | 0.299781i | ||||||
\(248\) | −19.0702 | + | 2.65873i | −1.21096 | + | 0.168829i | ||||
\(249\) | − | 24.2783i | − | 1.53858i | ||||||
\(250\) | 2.21735 | + | 1.14712i | 0.140237 | + | 0.0725505i | ||||
\(251\) | − | 26.8996i | − | 1.69789i | −0.528484 | − | 0.848943i | \(-0.677239\pi\) | ||
0.528484 | − | 0.848943i | \(-0.322761\pi\) | |||||||
\(252\) | −4.47556 | − | 6.32310i | −0.281934 | − | 0.398318i | ||||
\(253\) | 0.0632747 | + | 0.127866i | 0.00397805 | + | 0.00803889i | ||||
\(254\) | −0.161463 | − | 0.0835313i | −0.0101311 | − | 0.00524122i | ||||
\(255\) | −16.8153 | −1.05302 | ||||||||
\(256\) | −12.4633 | − | 10.0333i | −0.778956 | − | 0.627079i | ||||
\(257\) | −1.07645 | −0.0671468 | −0.0335734 | − | 0.999436i | \(-0.510689\pi\) | ||||
−0.0335734 | + | 0.999436i | \(0.510689\pi\) | |||||||
\(258\) | 9.74169 | − | 18.8303i | 0.606491 | − | 1.17232i | ||||
\(259\) | −7.97696 | −0.495664 | ||||||||
\(260\) | −5.30073 | + | 3.75191i | −0.328737 | + | 0.232684i | ||||
\(261\) | 3.72780i | 0.230745i | ||||||||
\(262\) | −17.5830 | − | 9.09640i | −1.08628 | − | 0.561977i | ||||
\(263\) | 14.9965 | 0.924723 | 0.462362 | − | 0.886691i | \(-0.347002\pi\) | ||||
0.462362 | + | 0.886691i | \(0.347002\pi\) | |||||||
\(264\) | −15.2585 | + | 10.3952i | −0.939097 | + | 0.639779i | ||||
\(265\) | 33.9091 | 2.08302 | ||||||||
\(266\) | −26.2372 | − | 13.5736i | −1.60871 | − | 0.832250i | ||||
\(267\) | − | 19.2848i | − | 1.18021i | ||||||
\(268\) | −5.47035 | + | 3.87197i | −0.334155 | + | 0.236519i | ||||
\(269\) | 2.55255 | 0.155632 | 0.0778160 | − | 0.996968i | \(-0.475205\pi\) | ||||
0.0778160 | + | 0.996968i | \(0.475205\pi\) | |||||||
\(270\) | 8.83044 | − | 17.0689i | 0.537404 | − | 1.03878i | ||||
\(271\) | −1.38884 | −0.0843660 | −0.0421830 | − | 0.999110i | \(-0.513431\pi\) | ||||
−0.0421830 | + | 0.999110i | \(0.513431\pi\) | |||||||
\(272\) | −9.92606 | − | 3.49892i | −0.601856 | − | 0.212153i | ||||
\(273\) | −8.72587 | −0.528114 | ||||||||
\(274\) | −2.02999 | − | 1.05019i | −0.122636 | − | 0.0634446i | ||||
\(275\) | 16.4789 | − | 8.15461i | 0.993717 | − | 0.491741i | ||||
\(276\) | 0.0978231 | + | 0.138205i | 0.00588826 | + | 0.00831897i | ||||
\(277\) | 3.21600i | 0.193230i | 0.995322 | + | 0.0966152i | \(0.0308016\pi\) | ||||
−0.995322 | + | 0.0966152i | \(0.969198\pi\) | |||||||
\(278\) | −9.07151 | − | 4.69306i | −0.544073 | − | 0.281471i | ||||
\(279\) | 5.94747i | 0.356066i | ||||||||
\(280\) | 5.62247 | + | 40.3281i | 0.336007 | + | 2.41007i | ||||
\(281\) | 19.1473i | 1.14223i | 0.820870 | + | 0.571115i | \(0.193489\pi\) | ||||
−0.820870 | + | 0.571115i | \(0.806511\pi\) | |||||||
\(282\) | −29.3460 | − | 15.1819i | −1.74753 | − | 0.904068i | ||||
\(283\) | 18.9770 | 1.12807 | 0.564033 | − | 0.825752i | \(-0.309249\pi\) | ||||
0.564033 | + | 0.825752i | \(0.309249\pi\) | |||||||
\(284\) | 23.9106 | − | 16.9242i | 1.41883 | − | 1.00427i | ||||
\(285\) | 30.1099i | 1.78356i | ||||||||
\(286\) | −0.0839736 | + | 4.68966i | −0.00496546 | + | 0.277306i | ||||
\(287\) | − | 6.65091i | − | 0.392591i | ||||||
\(288\) | −3.60102 | + | 3.38492i | −0.212192 | + | 0.199458i | ||||
\(289\) | 10.0769 | 0.592761 | ||||||||
\(290\) | 9.00324 | − | 17.4029i | 0.528689 | − | 1.02194i | ||||
\(291\) | − | 21.0298i | − | 1.23279i | ||||||
\(292\) | −11.5073 | + | 8.14500i | −0.673414 | + | 0.476650i | ||||
\(293\) | 25.4147i | 1.48474i | 0.669989 | + | 0.742371i | \(0.266299\pi\) | ||||
−0.669989 | + | 0.742371i | \(0.733701\pi\) | |||||||
\(294\) | −16.1864 | + | 31.2878i | −0.944013 | + | 1.82474i | ||||
\(295\) | 31.9045i | 1.85755i | ||||||||
\(296\) | 0.702705 | + | 5.04027i | 0.0408439 | + | 0.292960i | ||||
\(297\) | −6.15603 | − | 12.4402i | −0.357209 | − | 0.721852i | ||||
\(298\) | 3.51724 | − | 6.79869i | 0.203748 | − | 0.393837i | ||||
\(299\) | 0.0430153 | 0.00248764 | ||||||||
\(300\) | 17.8114 | − | 12.6071i | 1.02834 | − | 0.727869i | ||||
\(301\) | −33.7698 | −1.94646 | ||||||||
\(302\) | 6.15225 | + | 3.18281i | 0.354022 | + | 0.183150i | ||||
\(303\) | 27.9157 | 1.60371 | ||||||||
\(304\) | −6.26524 | + | 17.7738i | −0.359336 | + | 1.01940i | ||||
\(305\) | 7.15201i | 0.409523i | ||||||||
\(306\) | −1.49377 | + | 2.88741i | −0.0853934 | + | 0.165062i | ||||
\(307\) | −7.51797 | −0.429073 | −0.214537 | − | 0.976716i | \(-0.568824\pi\) | ||||
−0.214537 | + | 0.976716i | \(0.568824\pi\) | |||||||
\(308\) | 25.8741 | + | 13.9785i | 1.47431 | + | 0.796499i | ||||
\(309\) | 5.15608 | 0.293319 | ||||||||
\(310\) | 14.3641 | − | 27.7653i | 0.815827 | − | 1.57696i | ||||
\(311\) | − | 15.5561i | − | 0.882106i | −0.897481 | − | 0.441053i | \(-0.854605\pi\) | ||
0.897481 | − | 0.441053i | \(-0.145395\pi\) | |||||||
\(312\) | 0.768678 | + | 5.51348i | 0.0435178 | + | 0.312139i | ||||
\(313\) | 14.5247 | 0.820982 | 0.410491 | − | 0.911865i | \(-0.365357\pi\) | ||||
0.410491 | + | 0.911865i | \(0.365357\pi\) | |||||||
\(314\) | 23.9807 | + | 12.4062i | 1.35331 | + | 0.700123i | ||||
\(315\) | 12.5772 | 0.708648 | ||||||||
\(316\) | −2.30692 | − | 3.25923i | −0.129774 | − | 0.183346i | ||||
\(317\) | −18.6400 | −1.04693 | −0.523464 | − | 0.852048i | \(-0.675361\pi\) | ||||
−0.523464 | + | 0.852048i | \(0.675361\pi\) | |||||||
\(318\) | 13.3559 | − | 25.8165i | 0.748964 | − | 1.44772i | ||||
\(319\) | −6.27649 | − | 12.6836i | −0.351416 | − | 0.710146i | ||||
\(320\) | 24.9862 | − | 7.10516i | 1.39677 | − | 0.397191i | ||||
\(321\) | − | 23.6890i | − | 1.32219i | ||||||
\(322\) | 0.123927 | − | 0.239545i | 0.00690616 | − | 0.0133493i | ||||
\(323\) | 12.3966i | 0.689765i | ||||||||
\(324\) | −12.5457 | − | 17.7247i | −0.696984 | − | 0.984703i | ||||
\(325\) | − | 5.54365i | − | 0.307507i | ||||||
\(326\) | 1.95144 | − | 3.77206i | 0.108080 | − | 0.208915i | ||||
\(327\) | −32.7503 | −1.81110 | ||||||||
\(328\) | −4.20240 | + | 0.585891i | −0.232039 | + | 0.0323504i | ||||
\(329\) | 52.6283i | 2.90149i | ||||||||
\(330\) | 0.536660 | − | 29.9708i | 0.0295421 | − | 1.64984i | ||||
\(331\) | 3.68073i | 0.202311i | 0.994871 | + | 0.101156i | \(0.0322540\pi\) | ||||
−0.994871 | + | 0.101156i | \(0.967746\pi\) | |||||||
\(332\) | 14.2533 | + | 20.1372i | 0.782251 | + | 1.10517i | ||||
\(333\) | 1.57192 | 0.0861409 | ||||||||
\(334\) | −10.9145 | − | 5.64654i | −0.597217 | − | 0.308965i | ||||
\(335\) | − | 10.8810i | − | 0.594495i | ||||||
\(336\) | 32.9182 | + | 11.6036i | 1.79584 | + | 0.633029i | ||||
\(337\) | 1.56649i | 0.0853321i | 0.999089 | + | 0.0426660i | \(0.0135851\pi\) | ||||
−0.999089 | + | 0.0426660i | \(0.986415\pi\) | |||||||
\(338\) | 1.25608 | + | 0.649821i | 0.0683217 | + | 0.0353456i | ||||
\(339\) | 37.7018i | 2.04768i | ||||||||
\(340\) | 13.9471 | − | 9.87193i | 0.756390 | − | 0.535381i | ||||
\(341\) | −10.0138 | − | 20.2359i | −0.542275 | − | 1.09584i | ||||
\(342\) | 5.17026 | + | 2.67478i | 0.279576 | + | 0.144636i | ||||
\(343\) | 25.0761 | 1.35398 | ||||||||
\(344\) | 2.97484 | + | 21.3376i | 0.160393 | + | 1.15044i | ||||
\(345\) | −0.274903 | −0.0148003 | ||||||||
\(346\) | 2.21681 | − | 4.28500i | 0.119176 | − | 0.230363i | ||||
\(347\) | 2.65428 | 0.142489 | 0.0712446 | − | 0.997459i | \(-0.477303\pi\) | ||||
0.0712446 | + | 0.997459i | \(0.477303\pi\) | |||||||
\(348\) | −9.70349 | − | 13.7092i | −0.520162 | − | 0.734888i | ||||
\(349\) | 24.6358i | 1.31873i | 0.751825 | + | 0.659363i | \(0.229174\pi\) | ||||
−0.751825 | + | 0.659363i | \(0.770826\pi\) | |||||||
\(350\) | −30.8717 | − | 15.9712i | −1.65016 | − | 0.853696i | ||||
\(351\) | −4.18498 | −0.223378 | ||||||||
\(352\) | 6.55308 | − | 17.5800i | 0.349280 | − | 0.937018i | ||||
\(353\) | −13.5304 | −0.720152 | −0.360076 | − | 0.932923i | \(-0.617249\pi\) | ||||
−0.360076 | + | 0.932923i | \(0.617249\pi\) | |||||||
\(354\) | 24.2903 | + | 12.5664i | 1.29102 | + | 0.667896i | ||||
\(355\) | 47.5604i | 2.52425i | ||||||||
\(356\) | 11.3217 | + | 15.9954i | 0.600050 | + | 0.847755i | ||||
\(357\) | 22.9593 | 1.21513 | ||||||||
\(358\) | 13.1653 | − | 25.4480i | 0.695806 | − | 1.34497i | ||||
\(359\) | 14.1427 | 0.746426 | 0.373213 | − | 0.927746i | \(-0.378256\pi\) | ||||
0.373213 | + | 0.927746i | \(0.378256\pi\) | |||||||
\(360\) | −1.10795 | − | 7.94699i | −0.0583943 | − | 0.418843i | ||||
\(361\) | 3.19761 | 0.168296 | ||||||||
\(362\) | 0.486361 | + | 0.251614i | 0.0255626 | + | 0.0132246i | ||||
\(363\) | −17.2120 | − | 13.1324i | −0.903395 | − | 0.689273i | ||||
\(364\) | 7.23749 | − | 5.12277i | 0.379348 | − | 0.268506i | ||||
\(365\) | − | 22.8891i | − | 1.19807i | ||||||
\(366\) | 5.44515 | + | 2.81700i | 0.284623 | + | 0.147247i | ||||
\(367\) | 2.81256i | 0.146814i | 0.997302 | + | 0.0734072i | \(0.0233873\pi\) | ||||
−0.997302 | + | 0.0734072i | \(0.976613\pi\) | |||||||
\(368\) | −0.162275 | − | 0.0572015i | −0.00845915 | − | 0.00298184i | ||||
\(369\) | 1.31062i | 0.0682279i | ||||||||
\(370\) | −7.33841 | − | 3.79646i | −0.381506 | − | 0.197368i | ||||
\(371\) | −46.2987 | −2.40371 | ||||||||
\(372\) | −15.4813 | − | 21.8721i | −0.802669 | − | 1.13402i | ||||
\(373\) | 37.0235i | 1.91700i | 0.285090 | + | 0.958501i | \(0.407977\pi\) | ||||
−0.285090 | + | 0.958501i | \(0.592023\pi\) | |||||||
\(374\) | 0.220949 | − | 12.3393i | 0.0114250 | − | 0.638051i | ||||
\(375\) | 3.47439i | 0.179416i | ||||||||
\(376\) | 33.2534 | − | 4.63612i | 1.71491 | − | 0.239090i | ||||
\(377\) | −4.26688 | −0.219755 | ||||||||
\(378\) | −12.0569 | + | 23.3055i | −0.620139 | + | 1.19870i | ||||
\(379\) | 9.88028i | 0.507516i | 0.967268 | + | 0.253758i | \(0.0816667\pi\) | ||||
−0.967268 | + | 0.253758i | \(0.918333\pi\) | |||||||
\(380\) | −17.6769 | − | 24.9740i | −0.906806 | − | 1.28114i | ||||
\(381\) | − | 0.252998i | − | 0.0129615i | ||||||
\(382\) | 6.27515 | − | 12.1296i | 0.321064 | − | 0.620606i | ||||
\(383\) | 8.45161i | 0.431857i | 0.976409 | + | 0.215929i | \(0.0692779\pi\) | ||||
−0.976409 | + | 0.215929i | \(0.930722\pi\) | |||||||
\(384\) | 4.43196 | − | 21.8217i | 0.226168 | − | 1.11358i | ||||
\(385\) | −42.7934 | + | 21.1763i | −2.18095 | + | 1.07925i | ||||
\(386\) | −10.1985 | + | 19.7134i | −0.519092 | + | 1.00339i | ||||
\(387\) | 6.65461 | 0.338273 | ||||||||
\(388\) | 12.3462 | + | 17.4427i | 0.626781 | + | 0.885521i | ||||
\(389\) | 21.0938 | 1.06950 | 0.534749 | − | 0.845011i | \(-0.320406\pi\) | ||||
0.534749 | + | 0.845011i | \(0.320406\pi\) | |||||||
\(390\) | −8.02737 | − | 4.15288i | −0.406481 | − | 0.210289i | ||||
\(391\) | −0.113181 | −0.00572379 | ||||||||
\(392\) | −4.94289 | − | 35.4537i | −0.249654 | − | 1.79068i | ||||
\(393\) | − | 27.5510i | − | 1.38976i | ||||||
\(394\) | 1.78433 | − | 3.44904i | 0.0898931 | − | 0.173760i | ||||
\(395\) | 6.48291 | 0.326191 | ||||||||
\(396\) | −5.09869 | − | 2.75458i | −0.256219 | − | 0.138423i | ||||
\(397\) | −2.44016 | −0.122468 | −0.0612342 | − | 0.998123i | \(-0.519504\pi\) | ||||
−0.0612342 | + | 0.998123i | \(0.519504\pi\) | |||||||
\(398\) | 13.9572 | − | 26.9787i | 0.699610 | − | 1.35232i | ||||
\(399\) | − | 41.1114i | − | 2.05814i | ||||||
\(400\) | −7.37192 | + | 20.9134i | −0.368596 | + | 1.04567i | ||||
\(401\) | −6.63786 | −0.331479 | −0.165739 | − | 0.986170i | \(-0.553001\pi\) | ||||
−0.165739 | + | 0.986170i | \(0.553001\pi\) | |||||||
\(402\) | −8.28424 | − | 4.28577i | −0.413180 | − | 0.213755i | ||||
\(403\) | −6.80753 | −0.339107 | ||||||||
\(404\) | −23.1541 | + | 16.3887i | −1.15196 | + | 0.815368i | ||||
\(405\) | 35.2560 | 1.75189 | ||||||||
\(406\) | −12.2928 | + | 23.7615i | −0.610082 | + | 1.17927i | ||||
\(407\) | −5.34838 | + | 2.64665i | −0.265110 | + | 0.131190i | ||||
\(408\) | −2.02252 | − | 14.5069i | −0.100130 | − | 0.718199i | ||||
\(409\) | 3.66960i | 0.181450i | 0.995876 | + | 0.0907251i | \(0.0289185\pi\) | ||||
−0.995876 | + | 0.0907251i | \(0.971082\pi\) | |||||||
\(410\) | 3.16535 | − | 6.11850i | 0.156326 | − | 0.302171i | ||||
\(411\) | − | 3.18080i | − | 0.156898i | ||||||
\(412\) | −4.27660 | + | 3.02703i | −0.210693 | + | 0.149131i | ||||
\(413\) | − | 43.5616i | − | 2.14353i | ||||||
\(414\) | −0.0244207 | + | 0.0472044i | −0.00120021 | + | 0.00231997i | ||||
\(415\) | −40.0547 | −1.96621 | ||||||||
\(416\) | −3.87441 | − | 4.12176i | −0.189959 | − | 0.202086i | ||||
\(417\) | − | 14.2142i | − | 0.696074i | ||||||
\(418\) | −22.0950 | − | 0.395636i | −1.08070 | − | 0.0193512i | ||||
\(419\) | 27.2616i | 1.33182i | 0.746033 | + | 0.665909i | \(0.231956\pi\) | ||||
−0.746033 | + | 0.665909i | \(0.768044\pi\) | |||||||
\(420\) | −46.2535 | + | 32.7387i | −2.25694 | + | 1.59749i | ||||
\(421\) | 15.5302 | 0.756894 | 0.378447 | − | 0.925623i | \(-0.376458\pi\) | ||||
0.378447 | + | 0.925623i | \(0.376458\pi\) | |||||||
\(422\) | 21.1422 | + | 10.9377i | 1.02919 | + | 0.532440i | ||||
\(423\) | − | 10.3708i | − | 0.504247i | ||||||
\(424\) | 4.07854 | + | 29.2540i | 0.198071 | + | 1.42070i | ||||
\(425\) | 14.5863i | 0.707540i | ||||||||
\(426\) | 36.2099 | + | 18.7329i | 1.75438 | + | 0.907611i | ||||
\(427\) | − | 9.76518i | − | 0.472570i | ||||||
\(428\) | 13.9073 | + | 19.6484i | 0.672237 | + | 0.949741i | ||||
\(429\) | −5.85051 | + | 2.89513i | −0.282465 | + | 0.139778i | ||||
\(430\) | −31.0665 | − | 16.0720i | −1.49816 | − | 0.775059i | ||||
\(431\) | −9.83196 | −0.473589 | −0.236794 | − | 0.971560i | \(-0.576097\pi\) | ||||
−0.236794 | + | 0.971560i | \(0.576097\pi\) | |||||||
\(432\) | 15.7878 | + | 5.56516i | 0.759590 | + | 0.267754i | ||||
\(433\) | −0.171638 | −0.00824838 | −0.00412419 | − | 0.999991i | \(-0.501313\pi\) | ||||
−0.00412419 | + | 0.999991i | \(0.501313\pi\) | |||||||
\(434\) | −19.6124 | + | 37.9101i | −0.941426 | + | 1.81974i | ||||
\(435\) | 27.2688 | 1.30744 | ||||||||
\(436\) | 27.1641 | − | 19.2270i | 1.30092 | − | 0.920807i | ||||
\(437\) | 0.202664i | 0.00969473i | ||||||||
\(438\) | −17.4265 | − | 9.01546i | −0.832672 | − | 0.430775i | ||||
\(439\) | −14.2897 | −0.682009 | −0.341005 | − | 0.940062i | \(-0.610767\pi\) | ||||
−0.341005 | + | 0.940062i | \(0.610767\pi\) | |||||||
\(440\) | 17.1501 | + | 25.1737i | 0.817599 | + | 1.20011i | ||||
\(441\) | −11.0571 | −0.526527 | ||||||||
\(442\) | −3.30496 | − | 1.70979i | −0.157201 | − | 0.0813264i | ||||
\(443\) | − | 23.0592i | − | 1.09558i | −0.836617 | − | 0.547788i | \(-0.815470\pi\) | ||
0.836617 | − | 0.547788i | \(-0.184530\pi\) | |||||||
\(444\) | −5.78083 | + | 4.09174i | −0.274346 | + | 0.194185i | ||||
\(445\) | −31.8164 | −1.50824 | ||||||||
\(446\) | 5.66890 | − | 10.9578i | 0.268430 | − | 0.518865i | ||||
\(447\) | 10.6529 | 0.503866 | ||||||||
\(448\) | −34.1156 | + | 9.70122i | −1.61181 | + | 0.458339i | ||||
\(449\) | −10.1080 | −0.477024 | −0.238512 | − | 0.971139i | \(-0.576660\pi\) | ||||
−0.238512 | + | 0.971139i | \(0.576660\pi\) | |||||||
\(450\) | 6.08352 | + | 3.14725i | 0.286780 | + | 0.148363i | ||||
\(451\) | −2.20668 | − | 4.45929i | −0.103909 | − | 0.209980i | ||||
\(452\) | −22.1339 | − | 31.2710i | −1.04109 | − | 1.47086i | ||||
\(453\) | 9.64002i | 0.452928i | ||||||||
\(454\) | 14.0331 | + | 7.25990i | 0.658607 | + | 0.340724i | ||||
\(455\) | 14.3961i | 0.674897i | ||||||||
\(456\) | −25.9764 | + | 3.62158i | −1.21646 | + | 0.169596i | ||||
\(457\) | − | 23.7906i | − | 1.11288i | −0.830888 | − | 0.556440i | \(-0.812167\pi\) | ||
0.830888 | − | 0.556440i | \(-0.187833\pi\) | |||||||
\(458\) | 17.7481 | + | 9.18184i | 0.829317 | + | 0.429039i | ||||
\(459\) | 11.0114 | 0.513968 | ||||||||
\(460\) | 0.228013 | − | 0.161390i | 0.0106311 | − | 0.00752484i | ||||
\(461\) | − | 16.8140i | − | 0.783104i | −0.920156 | − | 0.391552i | \(-0.871938\pi\) | ||
0.920156 | − | 0.391552i | \(-0.128062\pi\) | |||||||
\(462\) | −0.732742 | + | 40.9214i | −0.0340903 | + | 1.90384i | ||||
\(463\) | 19.1240i | 0.888769i | 0.895836 | + | 0.444385i | \(0.146578\pi\) | ||||
−0.895836 | + | 0.444385i | \(0.853422\pi\) | |||||||
\(464\) | 16.0967 | + | 5.67407i | 0.747272 | + | 0.263412i | ||||
\(465\) | 43.5057 | 2.01753 | ||||||||
\(466\) | 3.33152 | − | 6.43969i | 0.154329 | − | 0.298313i | ||||
\(467\) | − | 6.90045i | − | 0.319315i | −0.987172 | − | 0.159657i | \(-0.948961\pi\) | ||
0.987172 | − | 0.159657i | \(-0.0510390\pi\) | |||||||
\(468\) | −1.42621 | + | 1.00948i | −0.0659264 | + | 0.0466634i | ||||
\(469\) | 14.8567i | 0.686020i | ||||||||
\(470\) | −25.0473 | + | 48.4154i | −1.15534 | + | 2.23324i | ||||
\(471\) | 37.5756i | 1.73139i | ||||||||
\(472\) | −27.5246 | + | 3.83742i | −1.26692 | + | 0.176632i | ||||
\(473\) | −22.6419 | + | 11.2044i | −1.04108 | + | 0.515177i | ||||
\(474\) | 2.55346 | − | 4.93574i | 0.117284 | − | 0.226706i | ||||
\(475\) | 26.1186 | 1.19840 | ||||||||
\(476\) | −19.0431 | + | 13.4789i | −0.872838 | + | 0.617804i | ||||
\(477\) | 9.12353 | 0.417738 | ||||||||
\(478\) | 13.2293 | + | 6.84407i | 0.605095 | + | 0.313040i | ||||
\(479\) | −16.3169 | −0.745537 | −0.372769 | − | 0.927924i | \(-0.621591\pi\) | ||||
−0.372769 | + | 0.927924i | \(0.621591\pi\) | |||||||
\(480\) | 24.7606 | + | 26.3414i | 1.13016 | + | 1.20232i | ||||
\(481\) | 1.79924i | 0.0820383i | ||||||||
\(482\) | 12.2811 | − | 23.7389i | 0.559388 | − | 1.08128i | ||||
\(483\) | 0.375346 | 0.0170788 | ||||||||
\(484\) | 21.9859 | + | 0.787616i | 0.999359 | + | 0.0358007i | ||||
\(485\) | −34.6952 | −1.57543 | ||||||||
\(486\) | 5.72801 | − | 11.0720i | 0.259828 | − | 0.502237i | ||||
\(487\) | − | 38.1232i | − | 1.72753i | −0.503899 | − | 0.863763i | \(-0.668102\pi\) | ||
0.503899 | − | 0.863763i | \(-0.331898\pi\) | |||||||
\(488\) | −6.17017 | + | 0.860233i | −0.279311 | + | 0.0389409i | ||||
\(489\) | 5.91048 | 0.267281 | ||||||||
\(490\) | 51.6190 | + | 26.7046i | 2.33191 | + | 1.20639i | ||||
\(491\) | 23.0861 | 1.04186 | 0.520931 | − | 0.853599i | \(-0.325585\pi\) | ||||
0.520931 | + | 0.853599i | \(0.325585\pi\) | |||||||
\(492\) | −3.41154 | − | 4.81985i | −0.153804 | − | 0.217296i | ||||
\(493\) | 11.2269 | 0.505633 | ||||||||
\(494\) | −3.06159 | + | 5.91793i | −0.137747 | + | 0.266260i | ||||
\(495\) | 8.43278 | − | 4.17297i | 0.379025 | − | 0.187561i | ||||
\(496\) | 25.6813 | + | 9.05262i | 1.15313 | + | 0.406475i | ||||
\(497\) | − | 64.9379i | − | 2.91286i | ||||||
\(498\) | −15.7765 | + | 30.4955i | −0.706964 | + | 1.36653i | ||||
\(499\) | − | 20.7554i | − | 0.929138i | −0.885537 | − | 0.464569i | \(-0.846209\pi\) | ||
0.885537 | − | 0.464569i | \(-0.153791\pi\) | |||||||
\(500\) | −2.03974 | − | 2.88176i | −0.0912199 | − | 0.128876i | ||||
\(501\) | − | 17.1021i | − | 0.764066i | ||||||
\(502\) | −17.4799 | + | 33.7880i | −0.780166 | + | 1.50803i | ||||
\(503\) | 35.2656 | 1.57241 | 0.786207 | − | 0.617963i | \(-0.212042\pi\) | ||||
0.786207 | + | 0.617963i | \(0.212042\pi\) | |||||||
\(504\) | 1.51277 | + | 10.8506i | 0.0673843 | + | 0.483325i | ||||
\(505\) | − | 46.0556i | − | 2.04945i | ||||||
\(506\) | 0.00361215 | − | 0.201727i | 0.000160580 | − | 0.00896788i | ||||
\(507\) | 1.96816i | 0.0874091i | ||||||||
\(508\) | 0.148530 | + | 0.209844i | 0.00658994 | + | 0.00931031i | ||||
\(509\) | 31.3323 | 1.38878 | 0.694389 | − | 0.719600i | \(-0.255675\pi\) | ||||
0.694389 | + | 0.719600i | \(0.255675\pi\) | |||||||
\(510\) | 21.1214 | + | 10.9269i | 0.935270 | + | 0.483853i | ||||
\(511\) | 31.2523i | 1.38252i | ||||||||
\(512\) | 9.13506 | + | 20.7015i | 0.403716 | + | 0.914884i | ||||
\(513\) | − | 19.7173i | − | 0.870539i | ||||||
\(514\) | 1.35210 | + | 0.699497i | 0.0596386 | + | 0.0308535i | ||||
\(515\) | − | 8.50657i | − | 0.374844i | ||||||
\(516\) | −24.4727 | + | 17.3220i | −1.07735 | + | 0.762559i | ||||
\(517\) | 17.4614 | + | 35.2862i | 0.767951 | + | 1.55188i | ||||
\(518\) | 10.0197 | + | 5.18359i | 0.440240 | + | 0.227754i | ||||
\(519\) | 6.71421 | 0.294721 | ||||||||
\(520\) | 9.09621 | − | 1.26818i | 0.398895 | − | 0.0556132i | ||||
\(521\) | −14.0072 | −0.613668 | −0.306834 | − | 0.951763i | \(-0.599270\pi\) | ||||
−0.306834 | + | 0.951763i | \(0.599270\pi\) | |||||||
\(522\) | 2.42240 | − | 4.68241i | 0.106026 | − | 0.204943i | ||||
\(523\) | 4.74895 | 0.207657 | 0.103829 | − | 0.994595i | \(-0.466891\pi\) | ||||
0.103829 | + | 0.994595i | \(0.466891\pi\) | |||||||
\(524\) | 16.1746 | + | 22.8516i | 0.706591 | + | 0.998276i | ||||
\(525\) | − | 48.3732i | − | 2.11118i | ||||||
\(526\) | −18.8368 | − | 9.74503i | −0.821322 | − | 0.424903i | ||||
\(527\) | 17.9118 | 0.780250 | ||||||||
\(528\) | 25.9209 | − | 3.14185i | 1.12806 | − | 0.136732i | ||||
\(529\) | 22.9981 | 0.999920 | ||||||||
\(530\) | −42.5925 | − | 22.0348i | −1.85010 | − | 0.957131i | ||||
\(531\) | 8.58417i | 0.372521i | ||||||||
\(532\) | 24.1356 | + | 34.0990i | 1.04641 | + | 1.47838i | ||||
\(533\) | −1.50014 | −0.0649784 | ||||||||
\(534\) | −12.5317 | + | 24.2233i | −0.542299 | + | 1.04824i | ||||
\(535\) | −39.0825 | −1.68968 | ||||||||
\(536\) | 9.38728 | − | 1.30876i | 0.405469 | − | 0.0565297i | ||||
\(537\) | 39.8747 | 1.72072 | ||||||||
\(538\) | −3.20621 | − | 1.65870i | −0.138229 | − | 0.0715117i | ||||
\(539\) | 37.6210 | − | 18.6168i | 1.62045 | − | 0.801881i | ||||
\(540\) | −22.1835 | + | 15.7017i | −0.954624 | + | 0.675693i | ||||
\(541\) | 14.6610i | 0.630325i | 0.949038 | + | 0.315163i | \(0.102059\pi\) | ||||
−0.949038 | + | 0.315163i | \(0.897941\pi\) | |||||||
\(542\) | 1.74449 | + | 0.902497i | 0.0749323 | + | 0.0387656i | ||||
\(543\) | 0.762084i | 0.0327042i | ||||||||
\(544\) | 10.1942 | + | 10.8451i | 0.437074 | + | 0.464979i | ||||
\(545\) | 54.0319i | 2.31447i | ||||||||
\(546\) | 10.9604 | + | 5.67025i | 0.469061 | + | 0.242664i | ||||
\(547\) | −36.7535 | −1.57147 | −0.785733 | − | 0.618566i | \(-0.787714\pi\) | ||||
−0.785733 | + | 0.618566i | \(0.787714\pi\) | |||||||
\(548\) | 1.86738 | + | 2.63825i | 0.0797707 | + | 0.112701i | ||||
\(549\) | 1.92431i | 0.0821275i | ||||||||
\(550\) | −25.9979 | − | 0.465520i | −1.10855 | − | 0.0198499i | ||||
\(551\) | − | 20.1031i | − | 0.856421i | ||||||
\(552\) | −0.0330649 | − | 0.237164i | −0.00140734 | − | 0.0100944i | ||||
\(553\) | −8.85161 | −0.376409 | ||||||||
\(554\) | 2.08982 | − | 4.03954i | 0.0887880 | − | 0.171624i | ||||
\(555\) | − | 11.4986i | − | 0.488089i | ||||||
\(556\) | 8.34488 | + | 11.7897i | 0.353902 | + | 0.499995i | ||||
\(557\) | − | 5.32657i | − | 0.225694i | −0.993612 | − | 0.112847i | \(-0.964003\pi\) | ||
0.993612 | − | 0.112847i | \(-0.0359970\pi\) | |||||||
\(558\) | 3.86479 | − | 7.47049i | 0.163609 | − | 0.316251i | ||||
\(559\) | 7.61693i | 0.322162i | ||||||||
\(560\) | 19.1438 | − | 54.3089i | 0.808973 | − | 2.29497i | ||||
\(561\) | 15.3937 | − | 7.61758i | 0.649923 | − | 0.321615i | ||||
\(562\) | 12.4423 | − | 24.0505i | 0.524847 | − | 1.01451i | ||||
\(563\) | −28.2126 | −1.18902 | −0.594510 | − | 0.804088i | \(-0.702654\pi\) | ||||
−0.594510 | + | 0.804088i | \(0.702654\pi\) | |||||||
\(564\) | 26.9954 | + | 38.1393i | 1.13671 | + | 1.60595i | ||||
\(565\) | 62.2009 | 2.61681 | ||||||||
\(566\) | −23.8366 | − | 12.3317i | −1.00193 | − | 0.518338i | ||||
\(567\) | −48.1377 | −2.02159 | ||||||||
\(568\) | −41.0313 | + | 5.72050i | −1.72163 | + | 0.240027i | ||||
\(569\) | 44.4460i | 1.86327i | 0.363391 | + | 0.931637i | \(0.381619\pi\) | ||||
−0.363391 | + | 0.931637i | \(0.618381\pi\) | |||||||
\(570\) | 19.5660 | − | 37.8204i | 0.819531 | − | 1.58412i | ||||
\(571\) | −16.4445 | −0.688180 | −0.344090 | − | 0.938937i | \(-0.611813\pi\) | ||||
−0.344090 | + | 0.938937i | \(0.611813\pi\) | |||||||
\(572\) | 3.15292 | − | 5.83602i | 0.131830 | − | 0.244016i | ||||
\(573\) | 19.0060 | 0.793988 | ||||||||
\(574\) | −4.32190 | + | 8.35406i | −0.180392 | + | 0.348692i | ||||
\(575\) | 0.238462i | 0.00994455i | ||||||||
\(576\) | 6.72275 | − | 1.91170i | 0.280115 | − | 0.0796543i | ||||
\(577\) | 37.3254 | 1.55388 | 0.776938 | − | 0.629577i | \(-0.216772\pi\) | ||||
0.776938 | + | 0.629577i | \(0.216772\pi\) | |||||||
\(578\) | −12.6574 | − | 6.54820i | −0.526479 | − | 0.272369i | ||||
\(579\) | −30.8891 | −1.28371 | ||||||||
\(580\) | −22.6176 | + | 16.0090i | −0.939143 | + | 0.664736i | ||||
\(581\) | 54.6897 | 2.26891 | ||||||||
\(582\) | −13.6656 | + | 26.4151i | −0.566457 | + | 1.09494i | ||||
\(583\) | −31.0423 | + | 15.3613i | −1.28564 | + | 0.636200i | ||||
\(584\) | 19.7469 | − | 2.75307i | 0.817131 | − | 0.113923i | ||||
\(585\) | − | 2.83686i | − | 0.117290i | ||||||
\(586\) | 16.5150 | − | 31.9229i | 0.682228 | − | 1.31872i | ||||
\(587\) | 44.5232i | 1.83767i | 0.394641 | + | 0.918835i | \(0.370869\pi\) | ||||
−0.394641 | + | 0.918835i | \(0.629131\pi\) | |||||||
\(588\) | 40.6629 | − | 28.7816i | 1.67691 | − | 1.18693i | ||||
\(589\) | − | 32.0732i | − | 1.32156i | ||||||
\(590\) | 20.7322 | − | 40.0745i | 0.853531 | − | 1.64984i | ||||
\(591\) | 5.40433 | 0.222304 | ||||||||
\(592\) | 2.39262 | − | 6.78761i | 0.0983361 | − | 0.278969i | ||||
\(593\) | − | 24.9092i | − | 1.02290i | −0.859313 | − | 0.511449i | \(-0.829109\pi\) | ||
0.859313 | − | 0.511449i | \(-0.170891\pi\) | |||||||
\(594\) | −0.351428 | + | 19.6262i | −0.0144193 | + | 0.805271i | ||||
\(595\) | − | 37.8785i | − | 1.55287i | ||||||
\(596\) | −8.83586 | + | 6.25411i | −0.361931 | + | 0.256178i | ||||
\(597\) | 42.2731 | 1.73012 | ||||||||
\(598\) | −0.0540306 | − | 0.0279522i | −0.00220948 | − | 0.00114305i | ||||
\(599\) | 3.19345i | 0.130481i | 0.997870 | + | 0.0652404i | \(0.0207814\pi\) | ||||
−0.997870 | + | 0.0652404i | \(0.979219\pi\) | |||||||
\(600\) | −30.5648 | + | 4.26128i | −1.24780 | + | 0.173966i | ||||
\(601\) | − | 19.2008i | − | 0.783217i | −0.920132 | − | 0.391608i | \(-0.871919\pi\) | ||
0.920132 | − | 0.391608i | \(-0.128081\pi\) | |||||||
\(602\) | 42.4175 | + | 21.9443i | 1.72881 | + | 0.894382i | ||||
\(603\) | − | 2.92764i | − | 0.119223i | ||||||
\(604\) | −5.65945 | − | 7.99572i | −0.230280 | − | 0.325341i | ||||
\(605\) | −21.6660 | + | 28.3966i | −0.880850 | + | 1.15448i | ||||
\(606\) | −35.0643 | − | 18.1402i | −1.42439 | − | 0.736894i | ||||
\(607\) | 32.1463 | 1.30478 | 0.652390 | − | 0.757884i | \(-0.273766\pi\) | ||||
0.652390 | + | 0.757884i | \(0.273766\pi\) | |||||||
\(608\) | 19.4194 | − | 18.2540i | 0.787562 | − | 0.740299i | ||||
\(609\) | −37.2322 | −1.50872 | ||||||||
\(610\) | 4.64752 | − | 8.98349i | 0.188173 | − | 0.363731i | ||||
\(611\) | 11.8706 | 0.480232 | ||||||||
\(612\) | 3.75259 | − | 2.65613i | 0.151690 | − | 0.107368i | ||||
\(613\) | 2.71563i | 0.109683i | 0.998495 | + | 0.0548416i | \(0.0174654\pi\) | ||||
−0.998495 | + | 0.0548416i | \(0.982535\pi\) | |||||||
\(614\) | 9.44317 | + | 4.88533i | 0.381095 | + | 0.197156i | ||||
\(615\) | 9.58714 | 0.386591 | ||||||||
\(616\) | −23.4163 | − | 34.3716i | −0.943471 | − | 1.38487i | ||||
\(617\) | 23.5303 | 0.947295 | 0.473647 | − | 0.880715i | \(-0.342937\pi\) | ||||
0.473647 | + | 0.880715i | \(0.342937\pi\) | |||||||
\(618\) | −6.47644 | − | 3.35053i | −0.260521 | − | 0.134778i | ||||
\(619\) | 25.6100i | 1.02935i | 0.857385 | + | 0.514676i | \(0.172088\pi\) | ||||
−0.857385 | + | 0.514676i | \(0.827912\pi\) | |||||||
\(620\) | −36.0849 | + | 25.5413i | −1.44920 | + | 1.02576i | ||||
\(621\) | 0.180018 | 0.00722389 | ||||||||
\(622\) | −10.1087 | + | 19.5397i | −0.405321 | + | 0.783470i | ||||
\(623\) | 43.4413 | 1.74044 | ||||||||
\(624\) | 2.61725 | − | 7.42486i | 0.104774 | − | 0.297232i | ||||
\(625\) | −21.9862 | −0.879447 | ||||||||
\(626\) | −18.2441 | − | 9.43842i | −0.729181 | − | 0.377235i | ||||
\(627\) | −13.6402 | − | 27.5643i | −0.544737 | − | 1.10081i | ||||
\(628\) | −22.0599 | − | 31.1663i | −0.880284 | − | 1.24367i | ||||
\(629\) | − | 4.73411i | − | 0.188761i | ||||||
\(630\) | −15.7980 | − | 8.17295i | −0.629408 | − | 0.325618i | ||||
\(631\) | 2.88055i | 0.114673i | 0.998355 | + | 0.0573365i | \(0.0182608\pi\) | ||||
−0.998355 | + | 0.0573365i | \(0.981739\pi\) | |||||||
\(632\) | 0.779755 | + | 5.59293i | 0.0310170 | + | 0.222475i | ||||
\(633\) | 33.1279i | 1.31672i | ||||||||
\(634\) | 23.4133 | + | 12.1127i | 0.929862 | + | 0.481056i | ||||
\(635\) | −0.417399 | −0.0165640 | ||||||||
\(636\) | −33.5522 | + | 23.7486i | −1.33043 | + | 0.941695i | ||||
\(637\) | − | 12.6560i | − | 0.501450i | ||||||
\(638\) | −0.358305 | + | 20.0102i | −0.0141854 | + | 0.792212i | ||||
\(639\) | 12.7965i | 0.506223i | ||||||||
\(640\) | −36.0017 | − | 7.31191i | −1.42309 | − | 0.289029i | ||||
\(641\) | −4.02107 | −0.158823 | −0.0794113 | − | 0.996842i | \(-0.525304\pi\) | ||||
−0.0794113 | + | 0.996842i | \(0.525304\pi\) | |||||||
\(642\) | −15.3936 | + | 29.7553i | −0.607538 | + | 1.17435i | ||||
\(643\) | − | 14.7579i | − | 0.581993i | −0.956724 | − | 0.290997i | \(-0.906013\pi\) | ||
0.956724 | − | 0.290997i | \(-0.0939868\pi\) | |||||||
\(644\) | −0.311323 | + | 0.220358i | −0.0122678 | + | 0.00868331i | ||||
\(645\) | − | 48.6784i | − | 1.91671i | ||||||
\(646\) | 8.05556 | − | 15.5711i | 0.316942 | − | 0.612636i | ||||
\(647\) | 37.3430i | 1.46810i | 0.679093 | + | 0.734052i | \(0.262373\pi\) | ||||
−0.679093 | + | 0.734052i | \(0.737627\pi\) | |||||||
\(648\) | 4.24054 | + | 30.4160i | 0.166584 | + | 1.19485i | ||||
\(649\) | −14.4532 | − | 29.2072i | −0.567337 | − | 1.14648i | ||||
\(650\) | −3.60238 | + | 6.96326i | −0.141297 | + | 0.273122i | ||||
\(651\) | −59.4016 | −2.32813 | ||||||||
\(652\) | −4.90233 | + | 3.46992i | −0.191990 | + | 0.135893i | ||||
\(653\) | −22.7622 | −0.890753 | −0.445377 | − | 0.895343i | \(-0.646930\pi\) | ||||
−0.445377 | + | 0.895343i | \(0.646930\pi\) | |||||||
\(654\) | 41.1369 | + | 21.2818i | 1.60858 | + | 0.832185i | ||||
\(655\) | −45.4540 | −1.77603 | ||||||||
\(656\) | 5.65927 | + | 1.99488i | 0.220957 | + | 0.0778871i | ||||
\(657\) | − | 6.15851i | − | 0.240266i | ||||||
\(658\) | 34.1989 | − | 66.1053i | 1.33321 | − | 2.57705i | ||||
\(659\) | 10.7424 | 0.418464 | 0.209232 | − | 0.977866i | \(-0.432904\pi\) | ||||
0.209232 | + | 0.977866i | \(0.432904\pi\) | |||||||
\(660\) | −20.1497 | + | 37.2969i | −0.784327 | + | 1.45178i | ||||
\(661\) | −2.43331 | −0.0946446 | −0.0473223 | − | 0.998880i | \(-0.515069\pi\) | ||||
−0.0473223 | + | 0.998880i | \(0.515069\pi\) | |||||||
\(662\) | 2.39181 | − | 4.62329i | 0.0929605 | − | 0.179689i | ||||
\(663\) | − | 5.17857i | − | 0.201119i | ||||||
\(664\) | −4.81772 | − | 34.5559i | −0.186964 | − | 1.34103i | ||||
\(665\) | −67.8261 | −2.63018 | ||||||||
\(666\) | −1.97446 | − | 1.02147i | −0.0765088 | − | 0.0395811i | ||||
\(667\) | 0.183541 | 0.00710674 | ||||||||
\(668\) | 10.0403 | + | 14.1850i | 0.388471 | + | 0.548834i | ||||
\(669\) | 17.1698 | 0.663824 | ||||||||
\(670\) | −7.07073 | + | 13.6675i | −0.273166 | + | 0.528020i | ||||
\(671\) | −3.23996 | − | 6.54735i | −0.125077 | − | 0.252758i | ||||
\(672\) | −33.8076 | − | 35.9660i | −1.30416 | − | 1.38742i | ||||
\(673\) | 7.53854i | 0.290589i | 0.989388 | + | 0.145295i | \(0.0464130\pi\) | ||||
−0.989388 | + | 0.145295i | \(0.953587\pi\) | |||||||
\(674\) | 1.01794 | − | 1.96763i | 0.0392095 | − | 0.0757904i | ||||
\(675\) | − | 23.2001i | − | 0.892972i | ||||||
\(676\) | −1.15547 | − | 1.63245i | −0.0444410 | − | 0.0627866i | ||||
\(677\) | 31.5739i | 1.21349i | 0.794898 | + | 0.606743i | \(0.207524\pi\) | ||||
−0.794898 | + | 0.606743i | \(0.792476\pi\) | |||||||
\(678\) | 24.4994 | − | 47.3564i | 0.940894 | − | 1.81871i | ||||
\(679\) | 47.3720 | 1.81797 | ||||||||
\(680\) | −23.9337 | + | 3.33679i | −0.917815 | + | 0.127960i | ||||
\(681\) | 21.9886i | 0.842606i | ||||||||
\(682\) | −0.571653 | + | 31.9250i | −0.0218897 | + | 1.22247i | ||||
\(683\) | 19.3540i | 0.740560i | 0.928920 | + | 0.370280i | \(0.120738\pi\) | ||||
−0.928920 | + | 0.370280i | \(0.879262\pi\) | |||||||
\(684\) | −4.75612 | − | 6.71948i | −0.181855 | − | 0.256926i | ||||
\(685\) | −5.24773 | −0.200506 | ||||||||
\(686\) | −31.4975 | − | 16.2949i | −1.20258 | − | 0.622144i | ||||
\(687\) | 27.8097i | 1.06101i | ||||||||
\(688\) | 10.1290 | − | 28.7348i | 0.386163 | − | 1.09550i | ||||
\(689\) | 10.4429i | 0.397842i | ||||||||
\(690\) | 0.345300 | + | 0.178638i | 0.0131453 | + | 0.00680062i | ||||
\(691\) | − | 6.00107i | − | 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114146i | \(-0.0364131\pi\) | |||||||
\(692\) | −5.56896 | + | 3.94177i | −0.211700 | + | 0.149844i | ||||
\(693\) | −11.5139 | + | 5.69767i | −0.437378 | + | 0.216437i | ||||
\(694\) | −3.33399 | − | 1.72481i | −0.126556 | − | 0.0654728i | ||||
\(695\) | −23.4508 | −0.889541 | ||||||||
\(696\) | 3.27985 | + | 23.5253i | 0.124323 | + | 0.891725i | ||||
\(697\) | 3.94714 | 0.149508 | ||||||||
\(698\) | 16.0089 | − | 30.9445i | 0.605944 | − | 1.17127i | ||||
\(699\) | 10.0904 | 0.381655 | ||||||||
\(700\) | 28.3989 | + | 40.1221i | 1.07338 | + | 1.51647i | ||||
\(701\) | − | 21.4823i | − | 0.811375i | −0.914012 | − | 0.405688i | \(-0.867032\pi\) | ||
0.914012 | − | 0.405688i | \(-0.132968\pi\) | |||||||
\(702\) | 5.25667 | + | 2.71949i | 0.198400 | + | 0.102640i | ||||
\(703\) | −8.47701 | −0.319716 | ||||||||
\(704\) | −19.6550 | + | 17.8236i | −0.740777 | + | 0.671751i | ||||
\(705\) | −75.8626 | −2.85715 | ||||||||
\(706\) | 16.9953 | + | 8.79236i | 0.639626 | + | 0.330905i | ||||
\(707\) | 62.8832i | 2.36497i | ||||||||
\(708\) | −22.3447 | − | 31.5687i | −0.839765 | − | 1.18643i | ||||
\(709\) | 31.2876 | 1.17503 | 0.587515 | − | 0.809213i | \(-0.300106\pi\) | ||||
0.587515 | + | 0.809213i | \(0.300106\pi\) | |||||||
\(710\) | 30.9058 | − | 59.7397i | 1.15987 | − | 2.24199i | ||||
\(711\) | 1.74428 | 0.0654157 | ||||||||
\(712\) | −3.82683 | − | 27.4486i | −0.143416 | − | 1.02868i | ||||
\(713\) | 0.292828 | 0.0109665 | ||||||||
\(714\) | −28.8386 | − | 14.9194i | −1.07926 | − | 0.558344i | ||||
\(715\) | 4.77642 | + | 9.65225i | 0.178628 | + | 0.360974i | ||||
\(716\) | −33.0732 | + | 23.4096i | −1.23600 | + | 0.874857i | ||||
\(717\) | 20.7292i | 0.774145i | ||||||||
\(718\) | −17.7644 | − | 9.19025i | −0.662962 | − | 0.342977i | ||||
\(719\) | − | 37.4361i | − | 1.39613i | −0.716034 | − | 0.698065i | \(-0.754044\pi\) | ||
0.716034 | − | 0.698065i | \(-0.245956\pi\) | |||||||
\(720\) | −3.77244 | + | 10.7020i | −0.140590 | + | 0.398840i | ||||
\(721\) | 11.6147i | 0.432553i | ||||||||
\(722\) | −4.01645 | − | 2.07788i | −0.149477 | − | 0.0773305i | ||||
\(723\) | 37.1967 | 1.38336 | ||||||||
\(724\) | −0.447404 | − | 0.632095i | −0.0166276 | − | 0.0234916i | ||||
\(725\) | − | 23.6541i | − | 0.878490i | ||||||
\(726\) | 13.0859 | + | 27.6800i | 0.485663 | + | 1.02730i | ||||
\(727\) | − | 8.13794i | − | 0.301820i | −0.988548 | − | 0.150910i | \(-0.951780\pi\) | ||
0.988548 | − | 0.150910i | \(-0.0482203\pi\) | |||||||
\(728\) | −12.4197 | + | 1.73154i | −0.460306 | + | 0.0641750i | ||||
\(729\) | −15.2242 | −0.563860 | ||||||||
\(730\) | −14.8738 | + | 28.7505i | −0.550505 | + | 1.06411i | ||||
\(731\) | − | 20.0415i | − | 0.741260i | ||||||
\(732\) | −5.00900 | − | 7.07674i | −0.185138 | − | 0.261564i | ||||
\(733\) | 23.1590i | 0.855396i | 0.903922 | + | 0.427698i | \(0.140675\pi\) | ||||
−0.903922 | + | 0.427698i | \(0.859325\pi\) | |||||||
\(734\) | 1.82766 | − | 3.53280i | 0.0674602 | − | 0.130398i | ||||
\(735\) | 80.8823i | 2.98339i | ||||||||
\(736\) | 0.166659 | + | 0.177299i | 0.00614313 | + | 0.00653533i | ||||
\(737\) | 4.92927 | + | 9.96112i | 0.181572 | + | 0.366923i | ||||
\(738\) | 0.851665 | − | 1.64624i | 0.0313502 | − | 0.0605988i | ||||
\(739\) | 16.9726 | 0.624346 | 0.312173 | − | 0.950025i | \(-0.398943\pi\) | ||||
0.312173 | + | 0.950025i | \(0.398943\pi\) | |||||||
\(740\) | 6.75060 | + | 9.53729i | 0.248157 | + | 0.350598i | ||||
\(741\) | −9.27286 | −0.340647 | ||||||||
\(742\) | 58.1548 | + | 30.0858i | 2.13493 | + | 1.10449i | ||||
\(743\) | 31.8960 | 1.17015 | 0.585075 | − | 0.810979i | \(-0.301065\pi\) | ||||
0.585075 | + | 0.810979i | \(0.301065\pi\) | |||||||
\(744\) | 5.23280 | + | 37.5332i | 0.191844 | + | 1.37603i | ||||
\(745\) | − | 17.5753i | − | 0.643911i | ||||||
\(746\) | 24.0586 | − | 46.5044i | 0.880848 | − | 1.70265i | ||||
\(747\) | −10.7771 | −0.394312 | ||||||||
\(748\) | −8.29587 | + | 15.3556i | −0.303327 | + | 0.561455i | ||||
\(749\) | 53.3623 | 1.94982 | ||||||||
\(750\) | 2.25773 | − | 4.36410i | 0.0824405 | − | 0.159354i | ||||
\(751\) | − | 29.8967i | − | 1.09095i | −0.838129 | − | 0.545473i | \(-0.816350\pi\) | ||
0.838129 | − | 0.545473i | \(-0.183650\pi\) | |||||||
\(752\) | −44.7815 | − | 15.7854i | −1.63301 | − | 0.575635i | ||||
\(753\) | −52.9427 | −1.92934 | ||||||||
\(754\) | 5.35953 | + | 2.77270i | 0.195183 | + | 0.100976i | ||||
\(755\) | 15.9042 | 0.578814 | ||||||||
\(756\) | 30.2888 | − | 21.4387i | 1.10159 | − | 0.779719i | ||||
\(757\) | −27.9620 | −1.01630 | −0.508148 | − | 0.861270i | \(-0.669670\pi\) | ||||
−0.508148 | + | 0.861270i | \(0.669670\pi\) | |||||||
\(758\) | 6.42041 | − | 12.4104i | 0.233200 | − | 0.450766i | ||||
\(759\) | 0.251662 | − | 0.124535i | 0.00913474 | − | 0.00452033i | ||||
\(760\) | 5.97492 | + | 42.8562i | 0.216733 | + | 1.55456i | ||||
\(761\) | − | 16.1869i | − | 0.586775i | −0.955994 | − | 0.293387i | \(-0.905217\pi\) | ||
0.955994 | − | 0.293387i | \(-0.0947825\pi\) | |||||||
\(762\) | −0.164403 | + | 0.317785i | −0.00595570 | + | 0.0115121i | ||||
\(763\) | − | 73.7738i | − | 2.67079i | ||||||
\(764\) | −15.7642 | + | 11.1580i | −0.570327 | + | 0.403684i | ||||
\(765\) | 7.46426i | 0.269871i | ||||||||
\(766\) | 5.49203 | − | 10.6159i | 0.198435 | − | 0.383568i | ||||
\(767\) | −9.82553 | −0.354779 | ||||||||
\(768\) | −19.7471 | + | 24.5298i | −0.712561 | + | 0.885142i | ||||
\(769\) | − | 2.32712i | − | 0.0839181i | −0.999119 | − | 0.0419591i | \(-0.986640\pi\) | ||
0.999119 | − | 0.0419591i | \(-0.0133599\pi\) | |||||||
\(770\) | 67.5126 | + | 1.20889i | 2.43299 | + | 0.0435653i | ||||
\(771\) | 2.11862i | 0.0763002i | ||||||||
\(772\) | 25.6204 | − | 18.1344i | 0.922097 | − | 0.652670i | ||||
\(773\) | 24.0481 | 0.864949 | 0.432475 | − | 0.901646i | \(-0.357641\pi\) | ||||
0.432475 | + | 0.901646i | \(0.357641\pi\) | |||||||
\(774\) | −8.35871 | − | 4.32430i | −0.300448 | − | 0.155434i | ||||
\(775\) | − | 37.7386i | − | 1.35561i | ||||||
\(776\) | −4.17309 | − | 29.9322i | −0.149805 | − | 1.07450i | ||||
\(777\) | 15.6999i | 0.563232i | ||||||||
\(778\) | −26.4955 | − | 13.7072i | −0.949908 | − | 0.491426i | ||||
\(779\) | − | 7.06783i | − | 0.253231i | ||||||
\(780\) | 7.38437 | + | 10.4327i | 0.264403 | + | 0.373550i | ||||
\(781\) | −21.5455 | − | 43.5395i | −0.770960 | − | 1.55797i | ||||
\(782\) | 0.142164 | + | 0.0735471i | 0.00508377 | + | 0.00263004i | ||||
\(783\) | −17.8568 | −0.638150 | ||||||||
\(784\) | −16.8299 | + | 47.7447i | −0.601068 | + | 1.70517i | ||||
\(785\) | 61.9928 | 2.21262 | ||||||||
\(786\) | −17.9032 | + | 34.6062i | −0.638585 | + | 1.23436i | ||||
\(787\) | 43.5633 | 1.55287 | 0.776433 | − | 0.630200i | \(-0.217027\pi\) | ||||
0.776433 | + | 0.630200i | \(0.217027\pi\) | |||||||
\(788\) | −4.48251 | + | 3.17277i | −0.159683 | + | 0.113025i | ||||
\(789\) | − | 29.5155i | − | 1.05078i | ||||||
\(790\) | −8.14304 | − | 4.21273i | −0.289716 | − | 0.149882i | ||||
\(791\) | −84.9276 | −3.01968 | ||||||||
\(792\) | 4.61438 | + | 6.77320i | 0.163965 | + | 0.240675i | ||||
\(793\) | −2.20258 | −0.0782161 | ||||||||
\(794\) | 3.06504 | + | 1.58567i | 0.108774 | + | 0.0562733i | ||||
\(795\) | − | 66.7386i | − | 2.36697i | ||||||
\(796\) | −35.0626 | + | 24.8177i | −1.24276 | + | 0.879639i | ||||
\(797\) | −31.4745 | −1.11488 | −0.557442 | − | 0.830216i | \(-0.688217\pi\) | ||||
−0.557442 | + | 0.830216i | \(0.688217\pi\) | |||||||
\(798\) | −26.7150 | + | 51.6391i | −0.945701 | + | 1.82800i | ||||
\(799\) | −31.2335 | −1.10496 | ||||||||
\(800\) | 22.8496 | − | 21.4784i | 0.807856 | − | 0.759376i | ||||
\(801\) | −8.56046 | −0.302469 | ||||||||
\(802\) | 8.33767 | + | 4.31342i | 0.294413 | + | 0.152312i | ||||
\(803\) | 10.3691 | + | 20.9540i | 0.365917 | + | 0.739450i | ||||
\(804\) | 7.62067 | + | 10.7665i | 0.268760 | + | 0.379707i | ||||
\(805\) | − | 0.619251i | − | 0.0218257i | ||||||
\(806\) | 8.55080 | + | 4.42368i | 0.301189 | + | 0.155817i | ||||
\(807\) | − | 5.02384i | − | 0.176848i | ||||||
\(808\) | 39.7330 | − | 5.53950i | 1.39780 | − | 0.194879i | ||||
\(809\) | 42.0775i | 1.47937i | 0.672955 | + | 0.739683i | \(0.265025\pi\) | ||||
−0.672955 | + | 0.739683i | \(0.734975\pi\) | |||||||
\(810\) | −44.2843 | − | 22.9101i | −1.55599 | − | 0.804978i | ||||
\(811\) | −0.451090 | −0.0158399 | −0.00791996 | − | 0.999969i | \(-0.502521\pi\) | ||||
−0.00791996 | + | 0.999969i | \(0.502521\pi\) | |||||||
\(812\) | 30.8815 | − | 21.8582i | 1.08373 | − | 0.767074i | ||||
\(813\) | 2.73346i | 0.0958667i | ||||||||
\(814\) | 8.43784 | + | 0.151089i | 0.295746 | + | 0.00529566i | ||||
\(815\) | − | 9.75119i | − | 0.341569i | ||||||
\(816\) | −6.88643 | + | 19.5361i | −0.241073 | + | 0.683900i | ||||
\(817\) | −35.8867 | −1.25552 | ||||||||
\(818\) | 2.38458 | − | 4.60931i | 0.0833750 | − | 0.161161i | ||||
\(819\) | 3.87338i | 0.135347i | ||||||||
\(820\) | −7.95186 | + | 5.62841i | −0.277691 | + | 0.196553i | ||||
\(821\) | 2.42693i | 0.0847004i | 0.999103 | + | 0.0423502i | \(0.0134845\pi\) | ||||
−0.999103 | + | 0.0423502i | \(0.986515\pi\) | |||||||
\(822\) | −2.06695 | + | 3.99534i | −0.0720932 | + | 0.139354i | ||||
\(823\) | − | 10.9604i | − | 0.382056i | −0.981585 | − | 0.191028i | \(-0.938818\pi\) | ||
0.981585 | − | 0.191028i | \(-0.0611821\pi\) | |||||||
\(824\) | 7.33878 | − | 1.02316i | 0.255658 | − | 0.0356434i | ||||
\(825\) | −16.0496 | − | 32.4332i | −0.558775 | − | 1.12918i | ||||
\(826\) | −28.3072 | + | 54.7168i | −0.984935 | + | 1.90384i | ||||
\(827\) | −37.0988 | −1.29005 | −0.645026 | − | 0.764161i | \(-0.723153\pi\) | ||||
−0.645026 | + | 0.764161i | \(0.723153\pi\) | |||||||
\(828\) | 0.0613487 | − | 0.0434233i | 0.00213202 | − | 0.00150906i | ||||
\(829\) | −30.3272 | −1.05331 | −0.526653 | − | 0.850080i | \(-0.676553\pi\) | ||||
−0.526653 | + | 0.850080i | \(0.676553\pi\) | |||||||
\(830\) | 50.3118 | + | 26.0284i | 1.74635 | + | 0.903458i | ||||
\(831\) | 6.32960 | 0.219571 | ||||||||
\(832\) | 2.18816 | + | 7.69493i | 0.0758607 | + | 0.266774i | ||||
\(833\) | 33.3002i | 1.15378i | ||||||||
\(834\) | −9.23670 | + | 17.8542i | −0.319841 | + | 0.618240i | ||||
\(835\) | −28.2153 | −0.976430 | ||||||||
\(836\) | 27.4960 | + | 14.8548i | 0.950970 | + | 0.513763i | ||||
\(837\) | −28.4894 | −0.984738 | ||||||||
\(838\) | 17.7152 | − | 34.2428i | 0.611961 | − | 1.18290i | ||||
\(839\) | 24.2451i | 0.837035i | 0.908209 | + | 0.418517i | \(0.137450\pi\) | ||||
−0.908209 | + | 0.418517i | \(0.862550\pi\) | |||||||
\(840\) | 79.3723 | − | 11.0659i | 2.73860 | − | 0.381811i | ||||
\(841\) | 10.7938 | 0.372199 | ||||||||
\(842\) | −19.5071 | − | 10.0918i | −0.672260 | − | 0.347787i | ||||
\(843\) | 37.6849 | 1.29794 | ||||||||
\(844\) | −19.4487 | − | 27.4773i | −0.669452 | − | 0.945806i | ||||
\(845\) | 3.24710 | 0.111704 | ||||||||
\(846\) | −6.73918 | + | 13.0266i | −0.231698 | + | 0.447863i | ||||
\(847\) | 29.5823 | − | 38.7720i | 1.01646 | − | 1.33222i | ||||
\(848\) | 13.8869 | − | 39.3956i | 0.476878 | − | 1.35285i | ||||
\(849\) | − | 37.3498i | − | 1.28184i | ||||||
\(850\) | 9.47848 | − | 18.3215i | 0.325109 | − | 0.628424i | ||||
\(851\) | − | 0.0773949i | − | 0.00265306i | ||||||
\(852\) | −33.3095 | − | 47.0599i | −1.14117 | − | 1.61225i | ||||
\(853\) | − | 44.5598i | − | 1.52570i | −0.646577 | − | 0.762849i | \(-0.723800\pi\) | ||
0.646577 | − | 0.762849i | \(-0.276200\pi\) | |||||||
\(854\) | −6.34562 | + | 12.2658i | −0.217143 | + | 0.419728i | ||||
\(855\) | 13.3657 | 0.457096 | ||||||||
\(856\) | −4.70079 | − | 33.7172i | −0.160670 | − | 1.15243i | ||||
\(857\) | − | 27.6364i | − | 0.944041i | −0.881588 | − | 0.472020i | \(-0.843525\pi\) | ||
0.881588 | − | 0.472020i | \(-0.156475\pi\) | |||||||
\(858\) | 9.23002 | + | 0.165274i | 0.315108 | + | 0.00564235i | ||||
\(859\) | − | 10.5383i | − | 0.359562i | −0.983707 | − | 0.179781i | \(-0.942461\pi\) | ||
0.983707 | − | 0.179781i | \(-0.0575389\pi\) | |||||||
\(860\) | 28.5781 | + | 40.3753i | 0.974504 | + | 1.37679i | ||||
\(861\) | −13.0901 | −0.446108 | ||||||||
\(862\) | 12.3497 | + | 6.38901i | 0.420633 | + | 0.217610i | ||||
\(863\) | 32.2287i | 1.09708i | 0.836126 | + | 0.548538i | \(0.184815\pi\) | ||||
−0.836126 | + | 0.548538i | \(0.815185\pi\) | |||||||
\(864\) | −16.2143 | − | 17.2495i | −0.551623 | − | 0.586840i | ||||
\(865\) | − | 11.0772i | − | 0.376636i | ||||||
\(866\) | 0.215590 | + | 0.111534i | 0.00732606 | + | 0.00379007i | ||||
\(867\) | − | 19.8330i | − | 0.673565i | ||||||
\(868\) | 49.2695 | − | 34.8735i | 1.67231 | − | 1.18368i | ||||
\(869\) | −5.93482 | + | 2.93685i | −0.201325 | + | 0.0996257i | ||||
\(870\) | −34.2518 | − | 17.7198i | −1.16124 | − | 0.600759i | ||||
\(871\) | 3.35101 | 0.113544 | ||||||||
\(872\) | −46.6143 | + | 6.49887i | −1.57856 | + | 0.220080i | ||||
\(873\) | −9.33505 | −0.315943 | ||||||||
\(874\) | 0.131695 | − | 0.254562i | 0.00445465 | − | 0.00861068i | ||||
\(875\) | −7.82646 | −0.264582 | ||||||||
\(876\) | 16.0307 | + | 22.6482i | 0.541626 | + | 0.765213i | ||||
\(877\) | 55.7387i | 1.88216i | 0.338182 | + | 0.941081i | \(0.390188\pi\) | ||||
−0.338182 | + | 0.941081i | \(0.609812\pi\) | |||||||
\(878\) | 17.9490 | + | 9.28573i | 0.605748 | + | 0.313378i | ||||
\(879\) | 50.0202 | 1.68714 | ||||||||
\(880\) | −5.18347 | − | 42.7646i | −0.174735 | − | 1.44160i | ||||
\(881\) | 56.2426 | 1.89486 | 0.947431 | − | 0.319960i | \(-0.103670\pi\) | ||||
0.947431 | + | 0.319960i | \(0.103670\pi\) | |||||||
\(882\) | 13.8885 | + | 7.18510i | 0.467651 | + | 0.241935i | ||||
\(883\) | − | 21.5284i | − | 0.724488i | −0.932083 | − | 0.362244i | \(-0.882011\pi\) | ||
0.932083 | − | 0.362244i | \(-0.117989\pi\) | |||||||
\(884\) | 3.04023 | + | 4.29526i | 0.102254 | + | 0.144465i | ||||
\(885\) | 62.7932 | 2.11077 | ||||||||
\(886\) | −14.9843 | + | 28.9642i | −0.503409 | + | 0.973070i | ||||
\(887\) | 16.2054 | 0.544126 | 0.272063 | − | 0.962279i | \(-0.412294\pi\) | ||||
0.272063 | + | 0.962279i | \(0.412294\pi\) | |||||||
\(888\) | 9.92007 | − | 1.38304i | 0.332896 | − | 0.0464117i | ||||
\(889\) | 0.569907 | 0.0191141 | ||||||||
\(890\) | 39.9639 | + | 20.6749i | 1.33959 | + | 0.693025i | ||||
\(891\) | −32.2753 | + | 15.9715i | −1.08126 | + | 0.535064i | ||||
\(892\) | −14.2412 | + | 10.0800i | −0.476829 | + | 0.337505i | ||||
\(893\) | 55.9274i | 1.87154i | ||||||||
\(894\) | −13.3809 | − | 6.92249i | −0.447525 | − | 0.231523i | ||||
\(895\) | − | 65.7858i | − | 2.19898i | ||||||
\(896\) | 49.1559 | + | 9.98351i | 1.64218 | + | 0.333526i | ||||
\(897\) | − | 0.0846611i | − | 0.00282675i | ||||||
\(898\) | 12.6964 | + | 6.56836i | 0.423684 | + | 0.219189i | ||||
\(899\) | −29.0469 | −0.968768 | ||||||||
\(900\) | −5.59623 | − | 7.90639i | −0.186541 | − | 0.263546i | ||||
\(901\) | − | 27.4770i | − | 0.915392i | ||||||
\(902\) | −0.125972 | + | 7.03517i | −0.00419442 | + | 0.234246i | ||||
\(903\) | 66.4643i | 2.21179i | ||||||||
\(904\) | 7.48143 | + | 53.6619i | 0.248829 | + | 1.78477i | ||||
\(905\) | 1.25730 | 0.0417939 | ||||||||
\(906\) | 6.26428 | − | 12.1086i | 0.208117 | − | 0.402282i | ||||
\(907\) | 43.5176i | 1.44498i | 0.691383 | + | 0.722488i | \(0.257002\pi\) | ||||
−0.691383 | + | 0.722488i | \(0.742998\pi\) | |||||||
\(908\) | −12.9091 | − | 18.2380i | −0.428402 | − | 0.605250i | ||||
\(909\) | − | 12.3917i | − | 0.411005i | ||||||
\(910\) | 9.35485 | − | 18.0826i | 0.310110 | − | 0.599431i | ||||
\(911\) | 12.0795i | 0.400213i | 0.979774 | + | 0.200107i | \(0.0641288\pi\) | ||||
−0.979774 | + | 0.200107i | \(0.935871\pi\) | |||||||
\(912\) | 34.9817 | + | 12.3310i | 1.15836 | + | 0.408320i | ||||
\(913\) | 36.6683 | − | 18.1453i | 1.21354 | − | 0.600523i | ||||
\(914\) | −15.4596 | + | 29.8829i | −0.511360 | + | 0.988439i | ||||
\(915\) | 14.0763 | 0.465348 | ||||||||
\(916\) | −16.3265 | − | 23.0662i | −0.539443 | − | 0.762130i | ||||
\(917\) | 62.0617 | 2.04946 | ||||||||
\(918\) | −13.8312 | − | 7.15544i | −0.456497 | − | 0.236165i | ||||
\(919\) | −22.3771 | −0.738151 | −0.369075 | − | 0.929399i | \(-0.620326\pi\) | ||||
−0.369075 | + | 0.929399i | \(0.620326\pi\) | |||||||
\(920\) | −0.391276 | + | 0.0545510i | −0.0129000 | + | 0.00179849i | ||||
\(921\) | 14.7966i | 0.487564i | ||||||||
\(922\) | −10.9261 | + | 21.1197i | −0.359831 | + | 0.695539i | ||||
\(923\) | −14.6471 | −0.482114 | ||||||||
\(924\) | 27.5119 | − | 50.9243i | 0.905076 | − | 1.67529i | ||||
\(925\) | −9.97437 | −0.327955 | ||||||||
\(926\) | 12.4272 | − | 24.0213i | 0.408383 | − | 0.789388i | ||||
\(927\) | − | 2.28876i | − | 0.0751729i | ||||||
\(928\) | −16.5316 | − | 17.5871i | −0.542677 | − | 0.577323i | ||||
\(929\) | −26.1944 | −0.859409 | −0.429704 | − | 0.902970i | \(-0.641382\pi\) | ||||
−0.429704 | + | 0.902970i | \(0.641382\pi\) | |||||||
\(930\) | −54.6466 | − | 28.2709i | −1.79193 | − | 0.927039i | ||||
\(931\) | 59.6280 | 1.95423 | ||||||||
\(932\) | −8.36929 | + | 5.92387i | −0.274145 | + | 0.194043i | ||||
\(933\) | −30.6169 | −1.00235 | ||||||||
\(934\) | −4.48406 | + | 8.66751i | −0.146723 | + | 0.283610i | ||||
\(935\) | −12.5676 | − | 25.3967i | −0.411004 | − | 0.830562i | ||||
\(936\) | 2.44741 | − | 0.341213i | 0.0799961 | − | 0.0111529i | ||||
\(937\) | 42.0828i | 1.37478i | 0.726287 | + | 0.687392i | \(0.241244\pi\) | ||||
−0.726287 | + | 0.687392i | \(0.758756\pi\) | |||||||
\(938\) | 9.65420 | − | 18.6612i | 0.315221 | − | 0.609310i | ||||
\(939\) | − | 28.5869i | − | 0.932897i | ||||||
\(940\) | 62.9227 | − | 44.5373i | 2.05231 | − | 1.45265i | ||||
\(941\) | − | 7.83575i | − | 0.255438i | −0.991810 | − | 0.127719i | \(-0.959234\pi\) | ||
0.991810 | − | 0.127719i | \(-0.0407656\pi\) | |||||||
\(942\) | 24.4174 | − | 47.1979i | 0.795562 | − | 1.53779i | ||||
\(943\) | 0.0645292 | 0.00210136 | ||||||||
\(944\) | 37.0667 | + | 13.0659i | 1.20642 | + | 0.425260i | ||||
\(945\) | 60.2472i | 1.95984i | ||||||||
\(946\) | 35.7209 | + | 0.639621i | 1.16139 | + | 0.0207959i | ||||
\(947\) | 46.2314i | 1.50232i | 0.660120 | + | 0.751160i | \(0.270505\pi\) | ||||
−0.660120 | + | 0.751160i | \(0.729495\pi\) | |||||||
\(948\) | −6.41468 | + | 4.54038i | −0.208339 | + | 0.147465i | ||||
\(949\) | 7.04910 | 0.228823 | ||||||||
\(950\) | −32.8070 | − | 16.9724i | −1.06440 | − | 0.550657i | ||||
\(951\) | 36.6866i | 1.18964i | ||||||||
\(952\) | 32.6785 | − | 4.55597i | 1.05912 | − | 0.147660i | ||||
\(953\) | 38.0378i | 1.23217i | 0.787682 | + | 0.616083i | \(0.211281\pi\) | ||||
−0.787682 | + | 0.616083i | \(0.788719\pi\) | |||||||
\(954\) | −11.4599 | − | 5.92866i | −0.371027 | − | 0.191947i | ||||
\(955\) | − | 31.3564i | − | 1.01467i | ||||||
\(956\) | −12.1697 | − | 17.1934i | −0.393595 | − | 0.556073i | ||||
\(957\) | −24.9634 | + | 12.3532i | −0.806952 | + | 0.399321i | ||||
\(958\) | 20.4953 | + | 10.6030i | 0.662172 | + | 0.342569i | ||||
\(959\) | 7.16513 | 0.231374 | ||||||||
\(960\) | −13.9841 | − | 49.1769i | −0.451335 | − | 1.58718i | ||||
\(961\) | −15.3425 | −0.494920 | ||||||||
\(962\) | 1.16918 | − | 2.25999i | 0.0376960 | − | 0.0728649i | ||||
\(963\) | −10.5155 | −0.338857 | ||||||||
\(964\) | −30.8520 | + | 21.8374i | −0.993677 | + | 0.703335i | ||||
\(965\) | 50.9613i | 1.64050i | ||||||||
\(966\) | −0.471464 | − | 0.243908i | −0.0151691 | − | 0.00784760i | ||||
\(967\) | 23.8027 | 0.765443 | 0.382722 | − | 0.923864i | \(-0.374987\pi\) | ||||
0.382722 | + | 0.923864i | \(0.374987\pi\) | |||||||
\(968\) | −27.1042 | − | 15.2762i | −0.871162 | − | 0.490995i | ||||
\(969\) | 24.3985 | 0.783793 | ||||||||
\(970\) | 43.5799 | + | 22.5457i | 1.39927 | + | 0.723898i | ||||
\(971\) | − | 4.14136i | − | 0.132903i | −0.997790 | − | 0.0664513i | \(-0.978832\pi\) | ||
0.997790 | − | 0.0664513i | \(-0.0211677\pi\) | |||||||
\(972\) | −14.3897 | + | 10.1852i | −0.461549 | + | 0.326689i | ||||
\(973\) | 32.0192 | 1.02649 | ||||||||
\(974\) | −24.7732 | + | 47.8857i | −0.793785 | + | 1.53436i | ||||
\(975\) | −10.9108 | −0.349425 | ||||||||
\(976\) | 8.30922 | + | 2.92898i | 0.265972 | + | 0.0937545i | ||||
\(977\) | −45.5445 | −1.45710 | −0.728549 | − | 0.684994i | \(-0.759805\pi\) | ||||
−0.728549 | + | 0.684994i | \(0.759805\pi\) | |||||||
\(978\) | −7.42403 | − | 3.84075i | −0.237394 | − | 0.122814i | ||||
\(979\) | 29.1265 | − | 14.4133i | 0.930887 | − | 0.460650i | ||||
\(980\) | −47.4843 | − | 67.0862i | −1.51683 | − | 2.14299i | ||||
\(981\) | 14.5377i | 0.464154i | ||||||||
\(982\) | −28.9980 | − | 15.0018i | −0.925363 | − | 0.478728i | ||||
\(983\) | 16.6727i | 0.531778i | 0.964004 | + | 0.265889i | \(0.0856654\pi\) | ||||
−0.964004 | + | 0.265889i | \(0.914335\pi\) | |||||||
\(984\) | 1.15313 | + | 8.27101i | 0.0367604 | + | 0.263670i | ||||
\(985\) | − | 8.91613i | − | 0.284092i | ||||||
\(986\) | −14.1018 | − | 7.29546i | −0.449094 | − | 0.232335i | ||||
\(987\) | 103.581 | 3.29702 | ||||||||
\(988\) | 7.69119 | − | 5.44390i | 0.244689 | − | 0.173194i | ||||
\(989\) | − | 0.327645i | − | 0.0104185i | ||||||
\(990\) | −13.3039 | − | 0.238221i | −0.422826 | − | 0.00757117i | ||||
\(991\) | 18.8655i | 0.599283i | 0.954052 | + | 0.299641i | \(0.0968670\pi\) | ||||
−0.954052 | + | 0.299641i | \(0.903133\pi\) | |||||||
\(992\) | −26.3752 | − | 28.0591i | −0.837413 | − | 0.890876i | ||||
\(993\) | 7.24427 | 0.229890 | ||||||||
\(994\) | −42.1980 | + | 81.5671i | −1.33844 | + | 2.58715i | ||||
\(995\) | − | 69.7428i | − | 2.21100i | ||||||
\(996\) | 39.6332 | − | 28.0528i | 1.25582 | − | 0.888886i | ||||
\(997\) | − | 56.3280i | − | 1.78393i | −0.452109 | − | 0.891963i | \(-0.649328\pi\) | ||
0.452109 | − | 0.891963i | \(-0.350672\pi\) | |||||||
\(998\) | −13.4873 | + | 26.0704i | −0.426932 | + | 0.825243i | ||||
\(999\) | 7.52979i | 0.238232i |
(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 | 572.2.e.b.131.11 | ✓ | 64 | |
4.3 | odd | 2 | inner | 572.2.e.b.131.53 | yes | 64 | |
11.10 | odd | 2 | inner | 572.2.e.b.131.54 | yes | 64 | |
44.43 | even | 2 | inner | 572.2.e.b.131.12 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.e.b.131.11 | ✓ | 64 | 1.1 | even | 1 | trivial | |
572.2.e.b.131.12 | yes | 64 | 44.43 | even | 2 | inner | |
572.2.e.b.131.53 | yes | 64 | 4.3 | odd | 2 | inner | |
572.2.e.b.131.54 | yes | 64 | 11.10 | odd | 2 | inner |