Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,2,Mod(67,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.53363286007\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.35 | ||
Character | \(\chi\) | \(=\) | 693.67 |
Dual form | 693.2.k.c.331.35 |
$q$-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 \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(442\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.05826 | − | 1.83296i | 0.748304 | − | 1.29610i | −0.200332 | − | 0.979728i | \(-0.564202\pi\) |
0.948635 | − | 0.316372i | \(-0.102465\pi\) | |||||||
\(3\) | 0.638324 | − | 1.61014i | 0.368536 | − | 0.929613i | ||||
\(4\) | −1.23983 | − | 2.14745i | −0.619916 | − | 1.07373i | ||||
\(5\) | 2.56660 | 1.14782 | 0.573909 | − | 0.818919i | \(-0.305426\pi\) | ||||
0.573909 | + | 0.818919i | \(0.305426\pi\) | |||||||
\(6\) | −2.27581 | − | 2.87397i | −0.929095 | − | 1.17329i | ||||
\(7\) | 1.99855 | + | 1.73373i | 0.755379 | + | 0.655288i | ||||
\(8\) | −1.01522 | −0.358936 | ||||||||
\(9\) | −2.18509 | − | 2.05558i | −0.728362 | − | 0.685193i | ||||
\(10\) | 2.71613 | − | 4.70448i | 0.858917 | − | 1.48769i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −4.24911 | + | 0.625531i | −1.22661 | + | 0.180575i | ||||
\(13\) | −0.929012 | + | 1.60910i | −0.257662 | + | 0.446283i | −0.965615 | − | 0.259976i | \(-0.916285\pi\) |
0.707953 | + | 0.706259i | \(0.249619\pi\) | |||||||
\(14\) | 5.29284 | − | 1.82852i | 1.41457 | − | 0.488693i | ||||
\(15\) | 1.63832 | − | 4.13258i | 0.423013 | − | 1.06703i | ||||
\(16\) | 1.40529 | − | 2.43404i | 0.351324 | − | 0.608510i | ||||
\(17\) | −1.06686 | + | 1.84786i | −0.258752 | + | 0.448171i | −0.965908 | − | 0.258886i | \(-0.916644\pi\) |
0.707156 | + | 0.707058i | \(0.249978\pi\) | |||||||
\(18\) | −6.08019 | + | 1.82984i | −1.43311 | + | 0.431297i | ||||
\(19\) | −1.15601 | − | 2.00227i | −0.265207 | − | 0.459351i | 0.702411 | − | 0.711771i | \(-0.252107\pi\) |
−0.967618 | + | 0.252420i | \(0.918773\pi\) | |||||||
\(20\) | −3.18216 | − | 5.51166i | −0.711552 | − | 1.23244i | ||||
\(21\) | 4.06726 | − | 2.11125i | 0.887549 | − | 0.460713i | ||||
\(22\) | −1.05826 | + | 1.83296i | −0.225622 | + | 0.390789i | ||||
\(23\) | −1.77038 | −0.369149 | −0.184575 | − | 0.982818i | \(-0.559091\pi\) | ||||
−0.184575 | + | 0.982818i | \(0.559091\pi\) | |||||||
\(24\) | −0.648041 | + | 1.63465i | −0.132281 | + | 0.333671i | ||||
\(25\) | 1.58744 | 0.317487 | ||||||||
\(26\) | 1.96627 | + | 3.40569i | 0.385618 | + | 0.667910i | ||||
\(27\) | −4.70456 | + | 2.20616i | −0.905392 | + | 0.424576i | ||||
\(28\) | 1.24524 | − | 6.44132i | 0.235328 | − | 1.21729i | ||||
\(29\) | 2.80170 | + | 4.85268i | 0.520262 | + | 0.901120i | 0.999722 | + | 0.0235569i | \(0.00749909\pi\) |
−0.479460 | + | 0.877564i | \(0.659168\pi\) | |||||||
\(30\) | −5.84109 | − | 7.37633i | −1.06643 | − | 1.34673i | ||||
\(31\) | −0.889754 | − | 1.54110i | −0.159805 | − | 0.276790i | 0.774994 | − | 0.631969i | \(-0.217753\pi\) |
−0.934798 | + | 0.355180i | \(0.884420\pi\) | |||||||
\(32\) | −3.98956 | − | 6.91012i | −0.705261 | − | 1.22155i | ||||
\(33\) | −0.638324 | + | 1.61014i | −0.111118 | + | 0.280289i | ||||
\(34\) | 2.25803 | + | 3.91103i | 0.387250 | + | 0.670736i | ||||
\(35\) | 5.12947 | + | 4.44979i | 0.867038 | + | 0.752151i | ||||
\(36\) | −1.70512 | + | 7.24094i | −0.284186 | + | 1.20682i | ||||
\(37\) | −1.80917 | − | 3.13358i | −0.297426 | − | 0.515157i | 0.678120 | − | 0.734951i | \(-0.262795\pi\) |
−0.975546 | + | 0.219794i | \(0.929462\pi\) | |||||||
\(38\) | −4.89344 | −0.793820 | ||||||||
\(39\) | 1.99786 | + | 2.52296i | 0.319913 | + | 0.403997i | ||||
\(40\) | −2.60567 | −0.411993 | ||||||||
\(41\) | −4.82423 | + | 8.35581i | −0.753418 | + | 1.30496i | 0.192739 | + | 0.981250i | \(0.438263\pi\) |
−0.946157 | + | 0.323708i | \(0.895070\pi\) | |||||||
\(42\) | 0.434375 | − | 9.68939i | 0.0670256 | − | 1.49511i | ||||
\(43\) | 2.55974 | + | 4.43359i | 0.390356 | + | 0.676117i | 0.992496 | − | 0.122274i | \(-0.0390186\pi\) |
−0.602140 | + | 0.798390i | \(0.705685\pi\) | |||||||
\(44\) | 1.23983 | + | 2.14745i | 0.186912 | + | 0.323741i | ||||
\(45\) | −5.60824 | − | 5.27585i | −0.836027 | − | 0.786477i | ||||
\(46\) | −1.87352 | + | 3.24504i | −0.276236 | + | 0.478455i | ||||
\(47\) | 1.33353 | − | 2.30974i | 0.194515 | − | 0.336910i | −0.752226 | − | 0.658905i | \(-0.771020\pi\) |
0.946741 | + | 0.321995i | \(0.104353\pi\) | |||||||
\(48\) | −3.02211 | − | 3.81642i | −0.436204 | − | 0.550853i | ||||
\(49\) | 0.988373 | + | 6.92987i | 0.141196 | + | 0.989982i | ||||
\(50\) | 1.67992 | − | 2.90971i | 0.237577 | − | 0.411495i | ||||
\(51\) | 2.29430 | + | 2.89732i | 0.321266 | + | 0.405707i | ||||
\(52\) | 4.60728 | 0.638915 | ||||||||
\(53\) | −2.96849 | + | 5.14158i | −0.407754 | + | 0.706250i | −0.994638 | − | 0.103421i | \(-0.967021\pi\) |
0.586884 | + | 0.809671i | \(0.300355\pi\) | |||||||
\(54\) | −0.934834 | + | 10.9580i | −0.127215 | + | 1.49119i | ||||
\(55\) | −2.56660 | −0.346080 | ||||||||
\(56\) | −2.02897 | − | 1.76012i | −0.271133 | − | 0.235206i | ||||
\(57\) | −3.96183 | + | 0.583239i | −0.524757 | + | 0.0772519i | ||||
\(58\) | 11.8597 | 1.55726 | ||||||||
\(59\) | 3.89667 | + | 6.74923i | 0.507303 | + | 0.878675i | 0.999964 | + | 0.00845359i | \(0.00269089\pi\) |
−0.492661 | + | 0.870221i | \(0.663976\pi\) | |||||||
\(60\) | −10.9058 | + | 1.60549i | −1.40793 | + | 0.207268i | ||||
\(61\) | 1.70010 | − | 2.94466i | 0.217675 | − | 0.377025i | −0.736422 | − | 0.676523i | \(-0.763486\pi\) |
0.954097 | + | 0.299498i | \(0.0968193\pi\) | |||||||
\(62\) | −3.76637 | −0.478329 | ||||||||
\(63\) | −0.803180 | − | 7.89651i | −0.101191 | − | 0.994867i | ||||
\(64\) | −11.2668 | −1.40835 | ||||||||
\(65\) | −2.38440 | + | 4.12991i | −0.295749 | + | 0.512252i | ||||
\(66\) | 2.27581 | + | 2.87397i | 0.280133 | + | 0.353761i | ||||
\(67\) | −1.53909 | − | 2.66579i | −0.188030 | − | 0.325678i | 0.756563 | − | 0.653920i | \(-0.226877\pi\) |
−0.944593 | + | 0.328243i | \(0.893544\pi\) | |||||||
\(68\) | 5.29092 | 0.641618 | ||||||||
\(69\) | −1.13007 | + | 2.85055i | −0.136045 | + | 0.343166i | ||||
\(70\) | 13.5846 | − | 4.69308i | 1.62367 | − | 0.560931i | ||||
\(71\) | −13.1025 | −1.55498 | −0.777492 | − | 0.628893i | \(-0.783508\pi\) | ||||
−0.777492 | + | 0.628893i | \(0.783508\pi\) | |||||||
\(72\) | 2.21835 | + | 2.08687i | 0.261435 | + | 0.245940i | ||||
\(73\) | 5.55336 | − | 9.61870i | 0.649972 | − | 1.12578i | −0.333158 | − | 0.942871i | \(-0.608114\pi\) |
0.983129 | − | 0.182913i | \(-0.0585526\pi\) | |||||||
\(74\) | −7.65831 | −0.890260 | ||||||||
\(75\) | 1.01330 | − | 2.55599i | 0.117006 | − | 0.295140i | ||||
\(76\) | −2.86652 | + | 4.96495i | −0.328812 | + | 0.569519i | ||||
\(77\) | −1.99855 | − | 1.73373i | −0.227755 | − | 0.197577i | ||||
\(78\) | 6.73875 | − | 0.992041i | 0.763013 | − | 0.112327i | ||||
\(79\) | −2.43640 | + | 4.21997i | −0.274117 | + | 0.474784i | −0.969912 | − | 0.243456i | \(-0.921719\pi\) |
0.695795 | + | 0.718240i | \(0.255052\pi\) | |||||||
\(80\) | 3.60683 | − | 6.24721i | 0.403256 | − | 0.698459i | ||||
\(81\) | 0.549197 | + | 8.98323i | 0.0610219 | + | 0.998136i | ||||
\(82\) | 10.2106 | + | 17.6853i | 1.12757 | + | 1.95301i | ||||
\(83\) | 1.63826 | + | 2.83756i | 0.179823 | + | 0.311462i | 0.941820 | − | 0.336118i | \(-0.109114\pi\) |
−0.761997 | + | 0.647581i | \(0.775781\pi\) | |||||||
\(84\) | −9.57654 | − | 6.11665i | −1.04489 | − | 0.667381i | ||||
\(85\) | −2.73821 | + | 4.74271i | −0.297000 | + | 0.514419i | ||||
\(86\) | 10.8355 | 1.16842 | ||||||||
\(87\) | 9.60188 | − | 1.41354i | 1.02943 | − | 0.151547i | ||||
\(88\) | 1.01522 | 0.108223 | ||||||||
\(89\) | −6.01619 | − | 10.4203i | −0.637715 | − | 1.10455i | −0.985933 | − | 0.167141i | \(-0.946547\pi\) |
0.348218 | − | 0.937413i | \(-0.386787\pi\) | |||||||
\(90\) | −15.6054 | + | 4.69647i | −1.64495 | + | 0.495051i | ||||
\(91\) | −4.64641 | + | 1.60520i | −0.487076 | + | 0.168271i | ||||
\(92\) | 2.19497 | + | 3.80181i | 0.228842 | + | 0.396366i | ||||
\(93\) | −3.04933 | + | 0.448906i | −0.316201 | + | 0.0465494i | ||||
\(94\) | −2.82244 | − | 4.88861i | −0.291112 | − | 0.504221i | ||||
\(95\) | −2.96701 | − | 5.13902i | −0.304409 | − | 0.527252i | ||||
\(96\) | −13.6729 | + | 2.01285i | −1.39548 | + | 0.205435i | ||||
\(97\) | 7.02007 | + | 12.1591i | 0.712780 | + | 1.23457i | 0.963810 | + | 0.266592i | \(0.0858975\pi\) |
−0.251030 | + | 0.967979i | \(0.580769\pi\) | |||||||
\(98\) | 13.7481 | + | 5.52196i | 1.38877 | + | 0.557803i | ||||
\(99\) | 2.18509 | + | 2.05558i | 0.219609 | + | 0.206593i | ||||
\(100\) | −1.96816 | − | 3.40895i | −0.196816 | − | 0.340895i | ||||
\(101\) | 12.7900 | 1.27266 | 0.636328 | − | 0.771419i | \(-0.280453\pi\) | ||||
0.636328 | + | 0.771419i | \(0.280453\pi\) | |||||||
\(102\) | 7.73865 | − | 1.13924i | 0.766241 | − | 0.112802i | ||||
\(103\) | 14.8648 | 1.46467 | 0.732336 | − | 0.680943i | \(-0.238430\pi\) | ||||
0.732336 | + | 0.680943i | \(0.238430\pi\) | |||||||
\(104\) | 0.943155 | − | 1.63359i | 0.0924840 | − | 0.160187i | ||||
\(105\) | 10.4390 | − | 5.41874i | 1.01875 | − | 0.528815i | ||||
\(106\) | 6.28288 | + | 10.8823i | 0.610247 | + | 1.05698i | ||||
\(107\) | −6.72103 | − | 11.6412i | −0.649747 | − | 1.12539i | −0.983183 | − | 0.182622i | \(-0.941542\pi\) |
0.333437 | − | 0.942772i | \(-0.391792\pi\) | |||||||
\(108\) | 10.5705 | + | 7.36754i | 1.01715 | + | 0.708942i | ||||
\(109\) | 3.63203 | − | 6.29086i | 0.347885 | − | 0.602555i | −0.637988 | − | 0.770046i | \(-0.720233\pi\) |
0.985874 | + | 0.167491i | \(0.0535665\pi\) | |||||||
\(110\) | −2.71613 | + | 4.70448i | −0.258973 | + | 0.448555i | ||||
\(111\) | −6.20033 | + | 0.912779i | −0.588509 | + | 0.0866371i | ||||
\(112\) | 7.02851 | − | 2.42814i | 0.664132 | − | 0.229438i | ||||
\(113\) | 8.33506 | − | 14.4367i | 0.784096 | − | 1.35809i | −0.145441 | − | 0.989367i | \(-0.546460\pi\) |
0.929537 | − | 0.368728i | \(-0.120207\pi\) | |||||||
\(114\) | −3.12360 | + | 7.87911i | −0.292552 | + | 0.737946i | ||||
\(115\) | −4.54385 | −0.423717 | ||||||||
\(116\) | 6.94727 | − | 12.0330i | 0.645038 | − | 1.11724i | ||||
\(117\) | 5.33759 | − | 1.60636i | 0.493461 | − | 0.148508i | ||||
\(118\) | 16.4948 | 1.51847 | ||||||||
\(119\) | −5.33585 | + | 1.84338i | −0.489137 | + | 0.168982i | ||||
\(120\) | −1.66326 | + | 4.19549i | −0.151834 | + | 0.382994i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.59830 | − | 6.23243i | −0.325774 | − | 0.564258i | ||||
\(123\) | 10.3746 | + | 13.1014i | 0.935444 | + | 1.18131i | ||||
\(124\) | −2.20629 | + | 3.82141i | −0.198131 | + | 0.343173i | ||||
\(125\) | −8.75869 | −0.783401 | ||||||||
\(126\) | −15.3240 | − | 6.88437i | −1.36517 | − | 0.613309i | ||||
\(127\) | −4.66388 | −0.413852 | −0.206926 | − | 0.978357i | \(-0.566346\pi\) | ||||
−0.206926 | + | 0.978357i | \(0.566346\pi\) | |||||||
\(128\) | −3.94410 | + | 6.83139i | −0.348613 | + | 0.603815i | ||||
\(129\) | 8.77264 | − | 1.29146i | 0.772387 | − | 0.113707i | ||||
\(130\) | 5.04664 | + | 8.74104i | 0.442620 | + | 0.766640i | ||||
\(131\) | 9.63639 | 0.841935 | 0.420968 | − | 0.907076i | \(-0.361691\pi\) | ||||
0.420968 | + | 0.907076i | \(0.361691\pi\) | |||||||
\(132\) | 4.24911 | − | 0.625531i | 0.369838 | − | 0.0544455i | ||||
\(133\) | 1.16105 | − | 6.00583i | 0.100676 | − | 0.520771i | ||||
\(134\) | −6.51504 | −0.562814 | ||||||||
\(135\) | −12.0747 | + | 5.66234i | −1.03923 | + | 0.487337i | ||||
\(136\) | 1.08310 | − | 1.87599i | 0.0928753 | − | 0.160865i | ||||
\(137\) | −19.0302 | −1.62586 | −0.812932 | − | 0.582359i | \(-0.802130\pi\) | ||||
−0.812932 | + | 0.582359i | \(0.802130\pi\) | |||||||
\(138\) | 4.02904 | + | 5.08801i | 0.342975 | + | 0.433120i | ||||
\(139\) | 7.51250 | − | 13.0120i | 0.637202 | − | 1.10367i | −0.348842 | − | 0.937182i | \(-0.613425\pi\) |
0.986044 | − | 0.166485i | \(-0.0532416\pi\) | |||||||
\(140\) | 3.19603 | − | 16.5323i | 0.270114 | − | 1.39723i | ||||
\(141\) | −2.86777 | − | 3.62152i | −0.241510 | − | 0.304987i | ||||
\(142\) | −13.8659 | + | 24.0164i | −1.16360 | + | 2.01541i | ||||
\(143\) | 0.929012 | − | 1.60910i | 0.0776879 | − | 0.134559i | ||||
\(144\) | −8.07405 | + | 2.42990i | −0.672838 | + | 0.202491i | ||||
\(145\) | 7.19084 | + | 12.4549i | 0.597166 | + | 1.03432i | ||||
\(146\) | −11.7538 | − | 20.3582i | −0.972752 | − | 1.68486i | ||||
\(147\) | 11.7889 | + | 2.83209i | 0.972336 | + | 0.233587i | ||||
\(148\) | −4.48614 | + | 7.77023i | −0.368759 | + | 0.638709i | ||||
\(149\) | −15.5615 | −1.27485 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(150\) | −3.61270 | − | 4.56224i | −0.294976 | − | 0.372506i | ||||
\(151\) | 0.573149 | 0.0466422 | 0.0233211 | − | 0.999728i | \(-0.492576\pi\) | ||||
0.0233211 | + | 0.999728i | \(0.492576\pi\) | |||||||
\(152\) | 1.17361 | + | 2.03275i | 0.0951921 | + | 0.164878i | ||||
\(153\) | 6.12960 | − | 1.84471i | 0.495549 | − | 0.149136i | ||||
\(154\) | −5.29284 | + | 1.82852i | −0.426509 | + | 0.147346i | ||||
\(155\) | −2.28364 | − | 3.95539i | −0.183427 | − | 0.317704i | ||||
\(156\) | 2.94094 | − | 7.41835i | 0.235463 | − | 0.593944i | ||||
\(157\) | −3.57344 | − | 6.18938i | −0.285192 | − | 0.493966i | 0.687464 | − | 0.726218i | \(-0.258724\pi\) |
−0.972656 | + | 0.232252i | \(0.925391\pi\) | |||||||
\(158\) | 5.15670 | + | 8.93167i | 0.410245 | + | 0.710565i | ||||
\(159\) | 6.38379 | + | 8.06167i | 0.506268 | + | 0.639332i | ||||
\(160\) | −10.2396 | − | 17.7355i | −0.809512 | − | 1.40212i | ||||
\(161\) | −3.53818 | − | 3.06936i | −0.278848 | − | 0.241899i | ||||
\(162\) | 17.0471 | + | 8.49994i | 1.33935 | + | 0.667819i | ||||
\(163\) | 2.32523 | + | 4.02742i | 0.182126 | + | 0.315452i | 0.942604 | − | 0.333912i | \(-0.108369\pi\) |
−0.760478 | + | 0.649363i | \(0.775035\pi\) | |||||||
\(164\) | 23.9249 | 1.86822 | ||||||||
\(165\) | −1.63832 | + | 4.13258i | −0.127543 | + | 0.321721i | ||||
\(166\) | 6.93485 | 0.538249 | ||||||||
\(167\) | 10.1331 | − | 17.5511i | 0.784124 | − | 1.35814i | −0.145397 | − | 0.989373i | \(-0.546446\pi\) |
0.929521 | − | 0.368769i | \(-0.120221\pi\) | |||||||
\(168\) | −4.12918 | + | 2.14339i | −0.318573 | + | 0.165367i | ||||
\(169\) | 4.77387 | + | 8.26859i | 0.367221 | + | 0.636045i | ||||
\(170\) | 5.79547 | + | 10.0381i | 0.444492 | + | 0.769884i | ||||
\(171\) | −1.58984 | + | 6.75139i | −0.121578 | + | 0.516292i | ||||
\(172\) | 6.34729 | − | 10.9938i | 0.483976 | − | 0.838272i | ||||
\(173\) | −7.83696 | + | 13.5740i | −0.595833 | + | 1.03201i | 0.397595 | + | 0.917561i | \(0.369845\pi\) |
−0.993429 | + | 0.114453i | \(0.963489\pi\) | |||||||
\(174\) | 7.57033 | − | 19.0958i | 0.573906 | − | 1.44765i | ||||
\(175\) | 3.17257 | + | 2.75218i | 0.239823 | + | 0.208046i | ||||
\(176\) | −1.40529 | + | 2.43404i | −0.105928 | + | 0.183473i | ||||
\(177\) | 13.3545 | − | 1.96598i | 1.00379 | − | 0.147772i | ||||
\(178\) | −25.4668 | −1.90882 | ||||||||
\(179\) | 10.6006 | − | 18.3608i | 0.792328 | − | 1.37235i | −0.132194 | − | 0.991224i | \(-0.542202\pi\) |
0.924522 | − | 0.381128i | \(-0.124464\pi\) | |||||||
\(180\) | −4.37636 | + | 18.5846i | −0.326194 | + | 1.38521i | ||||
\(181\) | 19.2753 | 1.43272 | 0.716359 | − | 0.697731i | \(-0.245807\pi\) | ||||
0.716359 | + | 0.697731i | \(0.245807\pi\) | |||||||
\(182\) | −1.97485 | + | 10.2154i | −0.146385 | + | 0.757217i | ||||
\(183\) | −3.65609 | − | 4.61704i | −0.270266 | − | 0.341301i | ||||
\(184\) | 1.79733 | 0.132501 | ||||||||
\(185\) | −4.64342 | − | 8.04265i | −0.341391 | − | 0.591307i | ||||
\(186\) | −2.40416 | + | 6.06437i | −0.176282 | + | 0.444661i | ||||
\(187\) | 1.06686 | − | 1.84786i | 0.0780166 | − | 0.135129i | ||||
\(188\) | −6.61340 | −0.482332 | ||||||||
\(189\) | −13.2272 | − | 3.74730i | −0.962134 | − | 0.272576i | ||||
\(190\) | −12.5595 | −0.911162 | ||||||||
\(191\) | −8.15778 | + | 14.1297i | −0.590276 | + | 1.02239i | 0.403919 | + | 0.914795i | \(0.367648\pi\) |
−0.994195 | + | 0.107593i | \(0.965686\pi\) | |||||||
\(192\) | −7.19187 | + | 18.1411i | −0.519029 | + | 1.30922i | ||||
\(193\) | 1.46546 | + | 2.53826i | 0.105486 | + | 0.182708i | 0.913937 | − | 0.405857i | \(-0.133027\pi\) |
−0.808450 | + | 0.588564i | \(0.799693\pi\) | |||||||
\(194\) | 29.7163 | 2.13350 | ||||||||
\(195\) | 5.12770 | + | 6.47543i | 0.367202 | + | 0.463715i | ||||
\(196\) | 13.6562 | − | 10.7144i | 0.975440 | − | 0.765312i | ||||
\(197\) | −21.1419 | −1.50630 | −0.753150 | − | 0.657849i | \(-0.771466\pi\) | ||||
−0.753150 | + | 0.657849i | \(0.771466\pi\) | |||||||
\(198\) | 6.08019 | − | 1.82984i | 0.432100 | − | 0.130041i | ||||
\(199\) | 3.21454 | − | 5.56775i | 0.227873 | − | 0.394687i | −0.729305 | − | 0.684189i | \(-0.760156\pi\) |
0.957177 | + | 0.289502i | \(0.0934897\pi\) | |||||||
\(200\) | −1.61160 | −0.113958 | ||||||||
\(201\) | −5.27472 | + | 0.776515i | −0.372050 | + | 0.0547712i | ||||
\(202\) | 13.5352 | − | 23.4436i | 0.952332 | − | 1.64949i | ||||
\(203\) | −2.81391 | + | 14.5557i | −0.197498 | + | 1.02161i | ||||
\(204\) | 3.37732 | − | 8.51910i | 0.236460 | − | 0.596457i | ||||
\(205\) | −12.3819 | + | 21.4460i | −0.864787 | + | 1.49785i | ||||
\(206\) | 15.7308 | − | 27.2466i | 1.09602 | − | 1.89836i | ||||
\(207\) | 3.86843 | + | 3.63915i | 0.268874 | + | 0.252939i | ||||
\(208\) | 2.61107 | + | 4.52251i | 0.181045 | + | 0.313579i | ||||
\(209\) | 1.15601 | + | 2.00227i | 0.0799628 | + | 0.138500i | ||||
\(210\) | 1.11487 | − | 24.8688i | 0.0769332 | − | 1.71611i | ||||
\(211\) | 1.23860 | − | 2.14531i | 0.0852685 | − | 0.147689i | −0.820237 | − | 0.572024i | \(-0.806159\pi\) |
0.905506 | + | 0.424334i | \(0.139492\pi\) | |||||||
\(212\) | 14.7217 | 1.01109 | ||||||||
\(213\) | −8.36366 | + | 21.0969i | −0.573068 | + | 1.44553i | ||||
\(214\) | −28.4504 | −1.94483 | ||||||||
\(215\) | 6.56982 | + | 11.3793i | 0.448058 | + | 0.776059i | ||||
\(216\) | 4.77618 | − | 2.23975i | 0.324978 | − | 0.152396i | ||||
\(217\) | 0.893633 | − | 4.62255i | 0.0606637 | − | 0.313799i | ||||
\(218\) | −7.68727 | − | 13.3147i | −0.520648 | − | 0.901788i | ||||
\(219\) | −11.9426 | − | 15.0815i | −0.807005 | − | 1.01911i | ||||
\(220\) | 3.18216 | + | 5.51166i | 0.214541 | + | 0.371596i | ||||
\(221\) | −1.98225 | − | 3.43336i | −0.133341 | − | 0.230953i | ||||
\(222\) | −4.88848 | + | 12.3309i | −0.328093 | + | 0.827598i | ||||
\(223\) | −11.8656 | − | 20.5519i | −0.794581 | − | 1.37626i | −0.923105 | − | 0.384549i | \(-0.874357\pi\) |
0.128523 | − | 0.991706i | \(-0.458976\pi\) | |||||||
\(224\) | 4.00695 | − | 20.7270i | 0.267726 | − | 1.38488i | ||||
\(225\) | −3.46869 | − | 3.26310i | −0.231246 | − | 0.217540i | ||||
\(226\) | −17.6413 | − | 30.5557i | −1.17348 | − | 2.03253i | ||||
\(227\) | 22.0629 | 1.46436 | 0.732182 | − | 0.681109i | \(-0.238502\pi\) | ||||
0.732182 | + | 0.681109i | \(0.238502\pi\) | |||||||
\(228\) | 6.16449 | + | 7.78473i | 0.408253 | + | 0.515556i | ||||
\(229\) | −14.0765 | −0.930199 | −0.465100 | − | 0.885258i | \(-0.653982\pi\) | ||||
−0.465100 | + | 0.885258i | \(0.653982\pi\) | |||||||
\(230\) | −4.80858 | + | 8.32871i | −0.317069 | + | 0.549179i | ||||
\(231\) | −4.06726 | + | 2.11125i | −0.267606 | + | 0.138910i | ||||
\(232\) | −2.84435 | − | 4.92656i | −0.186741 | − | 0.323444i | ||||
\(233\) | 11.9299 | + | 20.6633i | 0.781557 | + | 1.35370i | 0.931034 | + | 0.364931i | \(0.118908\pi\) |
−0.149477 | + | 0.988765i | \(0.547759\pi\) | |||||||
\(234\) | 2.70418 | − | 11.4836i | 0.176778 | − | 0.750703i | ||||
\(235\) | 3.42263 | − | 5.92817i | 0.223268 | − | 0.386711i | ||||
\(236\) | 9.66244 | − | 16.7358i | 0.628971 | − | 1.08941i | ||||
\(237\) | 5.23952 | + | 6.61665i | 0.340344 | + | 0.429798i | ||||
\(238\) | −2.26788 | + | 11.7312i | −0.147005 | + | 0.760420i | ||||
\(239\) | 2.99808 | − | 5.19283i | 0.193930 | − | 0.335896i | −0.752619 | − | 0.658456i | \(-0.771210\pi\) |
0.946549 | + | 0.322560i | \(0.104543\pi\) | |||||||
\(240\) | −7.75654 | − | 9.79523i | −0.500683 | − | 0.632280i | ||||
\(241\) | −15.3912 | −0.991432 | −0.495716 | − | 0.868485i | \(-0.665094\pi\) | ||||
−0.495716 | + | 0.868485i | \(0.665094\pi\) | |||||||
\(242\) | 1.05826 | − | 1.83296i | 0.0680276 | − | 0.117827i | ||||
\(243\) | 14.8148 | + | 4.84993i | 0.950370 | + | 0.311123i | ||||
\(244\) | −8.43135 | −0.539762 | ||||||||
\(245\) | 2.53676 | + | 17.7862i | 0.162067 | + | 1.13632i | ||||
\(246\) | 34.9933 | − | 5.15153i | 2.23109 | − | 0.328449i | ||||
\(247\) | 4.29579 | 0.273334 | ||||||||
\(248\) | 0.903299 | + | 1.56456i | 0.0573596 | + | 0.0993497i | ||||
\(249\) | 5.61460 | − | 0.826551i | 0.355811 | − | 0.0523805i | ||||
\(250\) | −9.26898 | + | 16.0543i | −0.586221 | + | 1.01537i | ||||
\(251\) | 9.85982 | 0.622346 | 0.311173 | − | 0.950353i | \(-0.399278\pi\) | ||||
0.311173 | + | 0.950353i | \(0.399278\pi\) | |||||||
\(252\) | −15.9616 | + | 11.5151i | −1.00549 | + | 0.725386i | ||||
\(253\) | 1.77038 | 0.111303 | ||||||||
\(254\) | −4.93560 | + | 8.54871i | −0.309687 | + | 0.536394i | ||||
\(255\) | 5.88856 | + | 7.43627i | 0.368756 | + | 0.465677i | ||||
\(256\) | −2.91903 | − | 5.05590i | −0.182439 | − | 0.315994i | ||||
\(257\) | −18.3119 | −1.14226 | −0.571132 | − | 0.820858i | \(-0.693496\pi\) | ||||
−0.571132 | + | 0.820858i | \(0.693496\pi\) | |||||||
\(258\) | 6.91654 | − | 17.4466i | 0.430605 | − | 1.08618i | ||||
\(259\) | 1.81706 | − | 9.39922i | 0.112907 | − | 0.584039i | ||||
\(260\) | 11.8250 | 0.733358 | ||||||||
\(261\) | 3.85312 | − | 16.3626i | 0.238502 | − | 1.01282i | ||||
\(262\) | 10.1978 | − | 17.6631i | 0.630023 | − | 1.09123i | ||||
\(263\) | −0.386445 | −0.0238292 | −0.0119146 | − | 0.999929i | \(-0.503793\pi\) | ||||
−0.0119146 | + | 0.999929i | \(0.503793\pi\) | |||||||
\(264\) | 0.648041 | − | 1.63465i | 0.0398842 | − | 0.100606i | ||||
\(265\) | −7.61893 | + | 13.1964i | −0.468027 | + | 0.810647i | ||||
\(266\) | −9.77976 | − | 8.48389i | −0.599635 | − | 0.520181i | ||||
\(267\) | −20.6185 | + | 3.03534i | −1.26183 | + | 0.185760i | ||||
\(268\) | −3.81643 | + | 6.61026i | −0.233126 | + | 0.403786i | ||||
\(269\) | −12.5045 | + | 21.6584i | −0.762413 | + | 1.32054i | 0.179190 | + | 0.983815i | \(0.442652\pi\) |
−0.941603 | + | 0.336724i | \(0.890681\pi\) | |||||||
\(270\) | −2.39935 | + | 28.1247i | −0.146020 | + | 1.71162i | ||||
\(271\) | 2.91056 | + | 5.04124i | 0.176804 | + | 0.306233i | 0.940784 | − | 0.339006i | \(-0.110091\pi\) |
−0.763980 | + | 0.645240i | \(0.776758\pi\) | |||||||
\(272\) | 2.99851 | + | 5.19357i | 0.181811 | + | 0.314906i | ||||
\(273\) | −0.381324 | + | 8.50599i | −0.0230788 | + | 0.514806i | ||||
\(274\) | −20.1390 | + | 34.8817i | −1.21664 | + | 2.10728i | ||||
\(275\) | −1.58744 | −0.0957260 | ||||||||
\(276\) | 7.52253 | − | 1.10743i | 0.452803 | − | 0.0666592i | ||||
\(277\) | −13.4360 | −0.807293 | −0.403646 | − | 0.914915i | \(-0.632257\pi\) | ||||
−0.403646 | + | 0.914915i | \(0.632257\pi\) | |||||||
\(278\) | −15.9004 | − | 27.5403i | −0.953641 | − | 1.65175i | ||||
\(279\) | −1.22366 | + | 5.19639i | −0.0732587 | + | 0.311100i | ||||
\(280\) | −5.20756 | − | 4.51753i | −0.311211 | − | 0.269974i | ||||
\(281\) | 8.10418 | + | 14.0368i | 0.483455 | + | 0.837368i | 0.999819 | − | 0.0190006i | \(-0.00604846\pi\) |
−0.516365 | + | 0.856369i | \(0.672715\pi\) | |||||||
\(282\) | −9.67296 | + | 1.42400i | −0.576016 | + | 0.0847980i | ||||
\(283\) | 10.1814 | + | 17.6348i | 0.605224 | + | 1.04828i | 0.992016 | + | 0.126112i | \(0.0402497\pi\) |
−0.386792 | + | 0.922167i | \(0.626417\pi\) | |||||||
\(284\) | 16.2449 | + | 28.1371i | 0.963960 | + | 1.66963i | ||||
\(285\) | −10.1684 | + | 1.49694i | −0.602326 | + | 0.0886712i | ||||
\(286\) | −1.96627 | − | 3.40569i | −0.116268 | − | 0.201383i | ||||
\(287\) | −24.1281 | + | 8.33557i | −1.42424 | + | 0.492033i | ||||
\(288\) | −5.48676 | + | 23.3001i | −0.323311 | + | 1.37297i | ||||
\(289\) | 6.22362 | + | 10.7796i | 0.366095 | + | 0.634095i | ||||
\(290\) | 30.4391 | 1.78745 | ||||||||
\(291\) | 24.0589 | − | 3.54182i | 1.41036 | − | 0.207625i | ||||
\(292\) | −27.5410 | −1.61171 | ||||||||
\(293\) | −4.41771 | + | 7.65170i | −0.258085 | + | 0.447017i | −0.965729 | − | 0.259553i | \(-0.916425\pi\) |
0.707644 | + | 0.706569i | \(0.249758\pi\) | |||||||
\(294\) | 17.6669 | − | 18.6116i | 1.03035 | − | 1.08545i | ||||
\(295\) | 10.0012 | + | 17.3226i | 0.582292 | + | 1.00856i | ||||
\(296\) | 1.83672 | + | 3.18128i | 0.106757 | + | 0.184908i | ||||
\(297\) | 4.70456 | − | 2.20616i | 0.272986 | − | 0.128015i | ||||
\(298\) | −16.4681 | + | 28.5236i | −0.953973 | + | 1.65233i | ||||
\(299\) | 1.64470 | − | 2.84871i | 0.0951156 | − | 0.164745i | ||||
\(300\) | −6.74520 | + | 0.992991i | −0.389434 | + | 0.0573303i | ||||
\(301\) | −2.57090 | + | 13.2986i | −0.148184 | + | 0.766520i | ||||
\(302\) | 0.606541 | − | 1.05056i | 0.0349025 | − | 0.0604529i | ||||
\(303\) | 8.16418 | − | 20.5937i | 0.469020 | − | 1.18308i | ||||
\(304\) | −6.49813 | −0.372693 | ||||||||
\(305\) | 4.36347 | − | 7.55776i | 0.249852 | − | 0.432756i | ||||
\(306\) | 3.10543 | − | 13.1875i | 0.177526 | − | 0.753879i | ||||
\(307\) | 28.2303 | 1.61119 | 0.805593 | − | 0.592469i | \(-0.201847\pi\) | ||||
0.805593 | + | 0.592469i | \(0.201847\pi\) | |||||||
\(308\) | −1.24524 | + | 6.44132i | −0.0709540 | + | 0.367028i | ||||
\(309\) | 9.48856 | − | 23.9344i | 0.539785 | − | 1.36158i | ||||
\(310\) | −9.66676 | −0.549035 | ||||||||
\(311\) | −1.72190 | − | 2.98242i | −0.0976400 | − | 0.169117i | 0.813067 | − | 0.582170i | \(-0.197796\pi\) |
−0.910707 | + | 0.413052i | \(0.864463\pi\) | |||||||
\(312\) | −2.02827 | − | 2.56137i | −0.114828 | − | 0.145009i | ||||
\(313\) | 3.63277 | − | 6.29213i | 0.205336 | − | 0.355652i | −0.744904 | − | 0.667172i | \(-0.767505\pi\) |
0.950240 | + | 0.311520i | \(0.100838\pi\) | |||||||
\(314\) | −15.1265 | −0.853639 | ||||||||
\(315\) | −2.06144 | − | 20.2672i | −0.116149 | − | 1.14193i | ||||
\(316\) | 12.0829 | 0.679718 | ||||||||
\(317\) | −12.6092 | + | 21.8398i | −0.708203 | + | 1.22664i | 0.257320 | + | 0.966326i | \(0.417161\pi\) |
−0.965523 | + | 0.260318i | \(0.916173\pi\) | |||||||
\(318\) | 21.5325 | − | 3.16989i | 1.20748 | − | 0.177759i | ||||
\(319\) | −2.80170 | − | 4.85268i | −0.156865 | − | 0.271698i | ||||
\(320\) | −28.9174 | −1.61653 | ||||||||
\(321\) | −23.0341 | + | 3.39095i | −1.28564 | + | 0.189264i | ||||
\(322\) | −9.37033 | + | 3.23718i | −0.522188 | + | 0.180401i | ||||
\(323\) | 4.93320 | 0.274491 | ||||||||
\(324\) | 18.6102 | − | 12.3171i | 1.03390 | − | 0.684282i | ||||
\(325\) | −1.47475 | + | 2.55434i | −0.0818043 | + | 0.141689i | ||||
\(326\) | 9.84281 | 0.545143 | ||||||||
\(327\) | −7.81074 | − | 9.86368i | −0.431935 | − | 0.545462i | ||||
\(328\) | 4.89767 | − | 8.48301i | 0.270429 | − | 0.468396i | ||||
\(329\) | 6.66957 | − | 2.30414i | 0.367705 | − | 0.127031i | ||||
\(330\) | 5.84109 | + | 7.37633i | 0.321541 | + | 0.406054i | ||||
\(331\) | 3.71091 | − | 6.42748i | 0.203970 | − | 0.353286i | −0.745834 | − | 0.666132i | \(-0.767949\pi\) |
0.949804 | + | 0.312845i | \(0.101282\pi\) | |||||||
\(332\) | 4.06235 | − | 7.03620i | 0.222950 | − | 0.386161i | ||||
\(333\) | −2.48812 | + | 10.5660i | −0.136348 | + | 0.579015i | ||||
\(334\) | −21.4470 | − | 37.1472i | −1.17353 | − | 2.03261i | ||||
\(335\) | −3.95023 | − | 6.84201i | −0.215824 | − | 0.373819i | ||||
\(336\) | 0.576819 | − | 12.8668i | 0.0314681 | − | 0.701942i | ||||
\(337\) | −4.26866 | + | 7.39353i | −0.232529 | + | 0.402751i | −0.958552 | − | 0.284919i | \(-0.908033\pi\) |
0.726023 | + | 0.687670i | \(0.241367\pi\) | |||||||
\(338\) | 20.2080 | 1.09917 | ||||||||
\(339\) | −17.9247 | − | 22.6359i | −0.973535 | − | 1.22941i | ||||
\(340\) | 13.5797 | 0.736461 | ||||||||
\(341\) | 0.889754 | + | 1.54110i | 0.0481829 | + | 0.0834552i | ||||
\(342\) | 10.6926 | + | 10.0588i | 0.578188 | + | 0.543920i | ||||
\(343\) | −10.0392 | + | 15.5632i | −0.542066 | + | 0.840336i | ||||
\(344\) | −2.59870 | − | 4.50109i | −0.140113 | − | 0.242682i | ||||
\(345\) | −2.90045 | + | 7.31623i | −0.156155 | + | 0.393893i | ||||
\(346\) | 16.5871 | + | 28.7297i | 0.891728 | + | 1.54452i | ||||
\(347\) | −17.2358 | − | 29.8532i | −0.925265 | − | 1.60261i | −0.791135 | − | 0.611642i | \(-0.790509\pi\) |
−0.134130 | − | 0.990964i | \(-0.542824\pi\) | |||||||
\(348\) | −14.9402 | − | 18.8670i | −0.800880 | − | 1.01138i | ||||
\(349\) | −12.0505 | − | 20.8721i | −0.645050 | − | 1.11726i | −0.984290 | − | 0.176560i | \(-0.943503\pi\) |
0.339240 | − | 0.940700i | \(-0.389830\pi\) | |||||||
\(350\) | 8.40205 | − | 2.90266i | 0.449109 | − | 0.155154i | ||||
\(351\) | 0.820660 | − | 9.61964i | 0.0438036 | − | 0.513458i | ||||
\(352\) | 3.98956 | + | 6.91012i | 0.212644 | + | 0.368311i | ||||
\(353\) | 9.08111 | 0.483339 | 0.241669 | − | 0.970359i | \(-0.422305\pi\) | ||||
0.241669 | + | 0.970359i | \(0.422305\pi\) | |||||||
\(354\) | 10.5290 | − | 26.5589i | 0.559610 | − | 1.41159i | ||||
\(355\) | −33.6290 | −1.78484 | ||||||||
\(356\) | −14.9181 | + | 25.8390i | −0.790660 | + | 1.36946i | ||||
\(357\) | −0.437905 | + | 9.76813i | −0.0231764 | + | 0.516984i | ||||
\(358\) | −22.4365 | − | 38.8611i | −1.18580 | − | 2.05387i | ||||
\(359\) | −3.73295 | − | 6.46566i | −0.197018 | − | 0.341244i | 0.750542 | − | 0.660822i | \(-0.229792\pi\) |
−0.947560 | + | 0.319578i | \(0.896459\pi\) | |||||||
\(360\) | 5.69362 | + | 5.35617i | 0.300080 | + | 0.282295i | ||||
\(361\) | 6.82729 | − | 11.8252i | 0.359331 | − | 0.622379i | ||||
\(362\) | 20.3983 | − | 35.3308i | 1.07211 | − | 1.85695i | ||||
\(363\) | 0.638324 | − | 1.61014i | 0.0335033 | − | 0.0845103i | ||||
\(364\) | 9.20786 | + | 7.98777i | 0.482623 | + | 0.418673i | ||||
\(365\) | 14.2533 | − | 24.6874i | 0.746049 | − | 1.29220i | ||||
\(366\) | −12.3320 | + | 1.81544i | −0.644601 | + | 0.0948947i | ||||
\(367\) | −24.3051 | −1.26872 | −0.634358 | − | 0.773039i | \(-0.718735\pi\) | ||||
−0.634358 | + | 0.773039i | \(0.718735\pi\) | |||||||
\(368\) | −2.48790 | + | 4.30917i | −0.129691 | + | 0.224631i | ||||
\(369\) | 27.7174 | − | 8.34158i | 1.44291 | − | 0.434245i | ||||
\(370\) | −19.6558 | −1.02186 | ||||||||
\(371\) | −14.8468 | + | 5.12913i | −0.770806 | + | 0.266291i | ||||
\(372\) | 4.74467 | + | 5.99173i | 0.246000 | + | 0.310657i | ||||
\(373\) | 25.5290 | 1.32184 | 0.660920 | − | 0.750456i | \(-0.270166\pi\) | ||||
0.660920 | + | 0.750456i | \(0.270166\pi\) | |||||||
\(374\) | −2.25803 | − | 3.91103i | −0.116760 | − | 0.202235i | ||||
\(375\) | −5.59088 | + | 14.1027i | −0.288712 | + | 0.728260i | ||||
\(376\) | −1.35383 | + | 2.34490i | −0.0698184 | + | 0.120929i | ||||
\(377\) | −10.4112 | −0.536206 | ||||||||
\(378\) | −20.8664 | + | 20.2793i | −1.07325 | + | 1.04305i | ||||
\(379\) | −24.3496 | −1.25075 | −0.625376 | − | 0.780323i | \(-0.715055\pi\) | ||||
−0.625376 | + | 0.780323i | \(0.715055\pi\) | |||||||
\(380\) | −7.35720 | + | 12.7430i | −0.377416 | + | 0.653704i | ||||
\(381\) | −2.97706 | + | 7.50948i | −0.152520 | + | 0.384722i | ||||
\(382\) | 17.2661 | + | 29.9058i | 0.883411 | + | 1.53011i | ||||
\(383\) | 10.4407 | 0.533492 | 0.266746 | − | 0.963767i | \(-0.414051\pi\) | ||||
0.266746 | + | 0.963767i | \(0.414051\pi\) | |||||||
\(384\) | 8.48186 | + | 10.7112i | 0.432838 | + | 0.546603i | ||||
\(385\) | −5.12947 | − | 4.44979i | −0.261422 | − | 0.226782i | ||||
\(386\) | 6.20337 | 0.315743 | ||||||||
\(387\) | 3.52036 | − | 14.9495i | 0.178950 | − | 0.759927i | ||||
\(388\) | 17.4074 | − | 30.1505i | 0.883728 | − | 1.53066i | ||||
\(389\) | −7.66041 | −0.388398 | −0.194199 | − | 0.980962i | \(-0.562211\pi\) | ||||
−0.194199 | + | 0.980962i | \(0.562211\pi\) | |||||||
\(390\) | 17.2957 | − | 2.54617i | 0.875800 | − | 0.128930i | ||||
\(391\) | 1.88875 | − | 3.27141i | 0.0955181 | − | 0.165442i | ||||
\(392\) | −1.00342 | − | 7.03537i | −0.0506803 | − | 0.355340i | ||||
\(393\) | 6.15114 | − | 15.5159i | 0.310284 | − | 0.782674i | ||||
\(394\) | −22.3737 | + | 38.7523i | −1.12717 | + | 1.95231i | ||||
\(395\) | −6.25327 | + | 10.8310i | −0.314636 | + | 0.544966i | ||||
\(396\) | 1.70512 | − | 7.24094i | 0.0856854 | − | 0.363871i | ||||
\(397\) | 0.725935 | + | 1.25736i | 0.0364337 | + | 0.0631049i | 0.883667 | − | 0.468116i | \(-0.155067\pi\) |
−0.847234 | + | 0.531221i | \(0.821734\pi\) | |||||||
\(398\) | −6.80364 | − | 11.7843i | −0.341036 | − | 0.590691i | ||||
\(399\) | −8.92908 | − | 5.70311i | −0.447013 | − | 0.285513i | ||||
\(400\) | 2.23082 | − | 3.86389i | 0.111541 | − | 0.193194i | ||||
\(401\) | −4.28115 | −0.213790 | −0.106895 | − | 0.994270i | \(-0.534091\pi\) | ||||
−0.106895 | + | 0.994270i | \(0.534091\pi\) | |||||||
\(402\) | −4.15871 | + | 10.4901i | −0.207418 | + | 0.523200i | ||||
\(403\) | 3.30637 | 0.164702 | ||||||||
\(404\) | −15.8575 | − | 27.4660i | −0.788940 | − | 1.36648i | ||||
\(405\) | 1.40957 | + | 23.0564i | 0.0700420 | + | 1.14568i | ||||
\(406\) | 23.7022 | + | 20.5615i | 1.17632 | + | 1.02045i | ||||
\(407\) | 1.80917 | + | 3.13358i | 0.0896774 | + | 0.155326i | ||||
\(408\) | −2.32923 | − | 2.94143i | −0.115314 | − | 0.145623i | ||||
\(409\) | 2.57805 | + | 4.46532i | 0.127476 | + | 0.220796i | 0.922698 | − | 0.385523i | \(-0.125979\pi\) |
−0.795222 | + | 0.606319i | \(0.792646\pi\) | |||||||
\(410\) | 26.2065 | + | 45.3910i | 1.29425 | + | 2.24170i | ||||
\(411\) | −12.1475 | + | 30.6413i | −0.599190 | + | 1.51142i | ||||
\(412\) | −18.4299 | − | 31.9215i | −0.907975 | − | 1.57266i | ||||
\(413\) | −3.91366 | + | 20.2444i | −0.192578 | + | 0.996162i | ||||
\(414\) | 10.7642 | − | 3.23951i | 0.529033 | − | 0.159213i | ||||
\(415\) | 4.20477 | + | 7.28288i | 0.206404 | + | 0.357502i | ||||
\(416\) | 14.8254 | 0.726875 | ||||||||
\(417\) | −16.1558 | − | 20.4021i | −0.791151 | − | 0.999093i | ||||
\(418\) | 4.89344 | 0.239346 | ||||||||
\(419\) | −14.2813 | + | 24.7360i | −0.697689 | + | 1.20843i | 0.271577 | + | 0.962417i | \(0.412455\pi\) |
−0.969266 | + | 0.246016i | \(0.920879\pi\) | |||||||
\(420\) | −24.5792 | − | 15.6990i | −1.19934 | − | 0.766033i | ||||
\(421\) | 6.01232 | + | 10.4136i | 0.293022 | + | 0.507530i | 0.974523 | − | 0.224288i | \(-0.0720056\pi\) |
−0.681500 | + | 0.731818i | \(0.738672\pi\) | |||||||
\(422\) | −2.62152 | − | 4.54060i | −0.127613 | − | 0.221033i | ||||
\(423\) | −7.66171 | + | 2.30580i | −0.372525 | + | 0.112112i | ||||
\(424\) | 3.01368 | − | 5.21985i | 0.146357 | − | 0.253499i | ||||
\(425\) | −1.69357 | + | 2.93336i | −0.0821504 | + | 0.142289i | ||||
\(426\) | 29.8188 | + | 37.6563i | 1.44473 | + | 1.82445i | ||||
\(427\) | 8.50296 | − | 2.93752i | 0.411487 | − | 0.142157i | ||||
\(428\) | −16.6659 | + | 28.8662i | −0.805577 | + | 1.39530i | ||||
\(429\) | −1.99786 | − | 2.52296i | −0.0964574 | − | 0.121810i | ||||
\(430\) | 27.8103 | 1.34113 | ||||||||
\(431\) | 8.25079 | − | 14.2908i | 0.397427 | − | 0.688363i | −0.595981 | − | 0.802999i | \(-0.703237\pi\) |
0.993408 | + | 0.114635i | \(0.0365700\pi\) | |||||||
\(432\) | −1.24139 | + | 14.5514i | −0.0597265 | + | 0.700104i | ||||
\(433\) | −31.9072 | −1.53336 | −0.766682 | − | 0.642027i | \(-0.778094\pi\) | ||||
−0.766682 | + | 0.642027i | \(0.778094\pi\) | |||||||
\(434\) | −7.52726 | − | 6.52986i | −0.361320 | − | 0.313443i | ||||
\(435\) | 24.6442 | − | 3.62798i | 1.18160 | − | 0.173948i | ||||
\(436\) | −18.0124 | −0.862640 | ||||||||
\(437\) | 2.04657 | + | 3.54477i | 0.0979009 | + | 0.169569i | ||||
\(438\) | −40.2822 | + | 5.93013i | −1.92476 | + | 0.283352i | ||||
\(439\) | 17.8736 | − | 30.9579i | 0.853058 | − | 1.47754i | −0.0253769 | − | 0.999678i | \(-0.508079\pi\) |
0.878435 | − | 0.477862i | \(-0.158588\pi\) | |||||||
\(440\) | 2.60567 | 0.124221 | ||||||||
\(441\) | 12.0852 | − | 17.1740i | 0.575486 | − | 0.817811i | ||||
\(442\) | −8.39097 | −0.399118 | ||||||||
\(443\) | −19.8900 | + | 34.4505i | −0.945002 | + | 1.63679i | −0.189254 | + | 0.981928i | \(0.560607\pi\) |
−0.755748 | + | 0.654863i | \(0.772726\pi\) | |||||||
\(444\) | 9.64753 | + | 12.1832i | 0.457851 | + | 0.578191i | ||||
\(445\) | −15.4412 | − | 26.7449i | −0.731981 | − | 1.26783i | ||||
\(446\) | −50.2277 | −2.37835 | ||||||||
\(447\) | −9.93328 | + | 25.0562i | −0.469828 | + | 1.18512i | ||||
\(448\) | −22.5172 | − | 19.5336i | −1.06384 | − | 0.922875i | ||||
\(449\) | −29.0017 | −1.36868 | −0.684338 | − | 0.729165i | \(-0.739909\pi\) | ||||
−0.684338 | + | 0.729165i | \(0.739909\pi\) | |||||||
\(450\) | −9.65191 | + | 2.90476i | −0.454996 | + | 0.136931i | ||||
\(451\) | 4.82423 | − | 8.35581i | 0.227164 | − | 0.393460i | ||||
\(452\) | −41.3363 | −1.94430 | ||||||||
\(453\) | 0.365855 | − | 0.922849i | 0.0171893 | − | 0.0433592i | ||||
\(454\) | 23.3483 | − | 40.4404i | 1.09579 | − | 1.89796i | ||||
\(455\) | −11.9255 | + | 4.11990i | −0.559075 | + | 0.193144i | ||||
\(456\) | 4.02214 | − | 0.592118i | 0.188354 | − | 0.0277285i | ||||
\(457\) | 18.9562 | − | 32.8330i | 0.886732 | − | 1.53586i | 0.0430155 | − | 0.999074i | \(-0.486304\pi\) |
0.843716 | − | 0.536790i | \(-0.180363\pi\) | |||||||
\(458\) | −14.8966 | + | 25.8016i | −0.696072 | + | 1.20563i | ||||
\(459\) | 0.942431 | − | 11.0470i | 0.0439889 | − | 0.515631i | ||||
\(460\) | 5.63362 | + | 9.75772i | 0.262669 | + | 0.454956i | ||||
\(461\) | 3.70303 | + | 6.41384i | 0.172467 | + | 0.298722i | 0.939282 | − | 0.343147i | \(-0.111493\pi\) |
−0.766815 | + | 0.641869i | \(0.778159\pi\) | |||||||
\(462\) | −0.434375 | + | 9.68939i | −0.0202090 | + | 0.450791i | ||||
\(463\) | 20.9557 | − | 36.2963i | 0.973892 | − | 1.68683i | 0.290350 | − | 0.956921i | \(-0.406228\pi\) |
0.683542 | − | 0.729911i | \(-0.260438\pi\) | |||||||
\(464\) | 15.7488 | 0.731121 | ||||||||
\(465\) | −7.82642 | + | 1.15216i | −0.362941 | + | 0.0534302i | ||||
\(466\) | 50.5000 | 2.33937 | ||||||||
\(467\) | −20.9977 | − | 36.3691i | −0.971657 | − | 1.68296i | −0.690553 | − | 0.723282i | \(-0.742633\pi\) |
−0.281104 | − | 0.959677i | \(-0.590701\pi\) | |||||||
\(468\) | −10.0673 | − | 9.47062i | −0.465361 | − | 0.437780i | ||||
\(469\) | 1.54580 | − | 7.99606i | 0.0713785 | − | 0.369224i | ||||
\(470\) | −7.24407 | − | 12.5471i | −0.334144 | − | 0.578755i | ||||
\(471\) | −12.2468 | + | 1.80290i | −0.564301 | + | 0.0830733i | ||||
\(472\) | −3.95599 | − | 6.85198i | −0.182089 | − | 0.315388i | ||||
\(473\) | −2.55974 | − | 4.43359i | −0.117697 | − | 0.203857i | ||||
\(474\) | 17.6729 | − | 2.60170i | 0.811741 | − | 0.119500i | ||||
\(475\) | −1.83509 | − | 3.17847i | −0.0841998 | − | 0.145838i | ||||
\(476\) | 10.5741 | + | 9.17301i | 0.484665 | + | 0.420444i | ||||
\(477\) | 17.0553 | − | 5.13282i | 0.780910 | − | 0.235016i | ||||
\(478\) | −6.34550 | − | 10.9907i | −0.290236 | − | 0.502704i | ||||
\(479\) | 17.2609 | 0.788670 | 0.394335 | − | 0.918967i | \(-0.370975\pi\) | ||||
0.394335 | + | 0.918967i | \(0.370975\pi\) | |||||||
\(480\) | −35.0928 | + | 5.16617i | −1.60176 | + | 0.235802i | ||||
\(481\) | 6.72297 | 0.306541 | ||||||||
\(482\) | −16.2879 | + | 28.2114i | −0.741892 | + | 1.28500i | ||||
\(483\) | −7.20059 | + | 3.73772i | −0.327638 | + | 0.170072i | ||||
\(484\) | −1.23983 | − | 2.14745i | −0.0563560 | − | 0.0976115i | ||||
\(485\) | 18.0177 | + | 31.2076i | 0.818142 | + | 1.41706i | ||||
\(486\) | 24.5677 | − | 22.0225i | 1.11441 | − | 0.998960i | ||||
\(487\) | 8.83490 | − | 15.3025i | 0.400347 | − | 0.693422i | −0.593420 | − | 0.804893i | \(-0.702223\pi\) |
0.993768 | + | 0.111471i | \(0.0355561\pi\) | |||||||
\(488\) | −1.72598 | + | 2.98949i | −0.0781315 | + | 0.135328i | ||||
\(489\) | 7.96895 | − | 1.17314i | 0.360368 | − | 0.0530514i | ||||
\(490\) | 35.2860 | + | 14.1727i | 1.59406 | + | 0.640256i | ||||
\(491\) | 2.15787 | − | 3.73755i | 0.0973835 | − | 0.168673i | −0.813217 | − | 0.581960i | \(-0.802286\pi\) |
0.910601 | + | 0.413287i | \(0.135619\pi\) | |||||||
\(492\) | 15.2719 | − | 38.5225i | 0.688509 | − | 1.73673i | ||||
\(493\) | −11.9561 | −0.538475 | ||||||||
\(494\) | 4.54606 | − | 7.87401i | 0.204537 | − | 0.354268i | ||||
\(495\) | 5.60824 | + | 5.27585i | 0.252072 | + | 0.237132i | ||||
\(496\) | −5.00146 | −0.224572 | ||||||||
\(497\) | −26.1860 | − | 22.7162i | −1.17460 | − | 1.01896i | ||||
\(498\) | 4.42668 | − | 11.1661i | 0.198364 | − | 0.500363i | ||||
\(499\) | −15.4549 | −0.691857 | −0.345929 | − | 0.938261i | \(-0.612436\pi\) | ||||
−0.345929 | + | 0.938261i | \(0.612436\pi\) | |||||||
\(500\) | 10.8593 | + | 18.8089i | 0.485643 | + | 0.841158i | ||||
\(501\) | −21.7914 | − | 27.5190i | −0.973569 | − | 1.22946i | ||||
\(502\) | 10.4343 | − | 18.0727i | 0.465704 | − | 0.806623i | ||||
\(503\) | 10.2318 | 0.456215 | 0.228107 | − | 0.973636i | \(-0.426746\pi\) | ||||
0.228107 | + | 0.973636i | \(0.426746\pi\) | |||||||
\(504\) | 0.815407 | + | 8.01673i | 0.0363211 | + | 0.357093i | ||||
\(505\) | 32.8269 | 1.46078 | ||||||||
\(506\) | 1.87352 | − | 3.24504i | 0.0832882 | − | 0.144259i | ||||
\(507\) | 16.3608 | − | 2.40855i | 0.726611 | − | 0.106968i | ||||
\(508\) | 5.78243 | + | 10.0155i | 0.256554 | + | 0.444364i | ||||
\(509\) | 13.3448 | 0.591500 | 0.295750 | − | 0.955265i | \(-0.404430\pi\) | ||||
0.295750 | + | 0.955265i | \(0.404430\pi\) | |||||||
\(510\) | 19.8620 | − | 2.92398i | 0.879506 | − | 0.129476i | ||||
\(511\) | 27.7749 | − | 9.59540i | 1.22869 | − | 0.424476i | ||||
\(512\) | −28.1328 | −1.24330 | ||||||||
\(513\) | 9.85583 | + | 6.86943i | 0.435146 | + | 0.303293i | ||||
\(514\) | −19.3788 | + | 33.5650i | −0.854761 | + | 1.48049i | ||||
\(515\) | 38.1520 | 1.68118 | ||||||||
\(516\) | −13.6500 | − | 17.2376i | −0.600906 | − | 0.758845i | ||||
\(517\) | −1.33353 | + | 2.30974i | −0.0586484 | + | 0.101582i | ||||
\(518\) | −15.3055 | − | 13.2774i | −0.672484 | − | 0.583377i | ||||
\(519\) | 16.8535 | + | 21.2832i | 0.739787 | + | 0.934229i | ||||
\(520\) | 2.42070 | − | 4.19278i | 0.106155 | − | 0.183866i | ||||
\(521\) | −5.22825 | + | 9.05559i | −0.229054 | + | 0.396733i | −0.957528 | − | 0.288341i | \(-0.906896\pi\) |
0.728474 | + | 0.685073i | \(0.240230\pi\) | |||||||
\(522\) | −25.9145 | − | 24.3786i | −1.13425 | − | 1.06702i | ||||
\(523\) | −8.33846 | − | 14.4426i | −0.364615 | − | 0.631533i | 0.624099 | − | 0.781345i | \(-0.285466\pi\) |
−0.988714 | + | 0.149813i | \(0.952133\pi\) | |||||||
\(524\) | −11.9475 | − | 20.6937i | −0.521930 | − | 0.904008i | ||||
\(525\) | 6.45652 | − | 3.35148i | 0.281786 | − | 0.146271i | ||||
\(526\) | −0.408960 | + | 0.708340i | −0.0178315 | + | 0.0308851i | ||||
\(527\) | 3.79697 | 0.165399 | ||||||||
\(528\) | 3.02211 | + | 3.81642i | 0.131520 | + | 0.166089i | ||||
\(529\) | −19.8658 | −0.863729 | ||||||||
\(530\) | 16.1256 | + | 27.9304i | 0.700453 | + | 1.21322i | ||||
\(531\) | 5.35901 | − | 22.7576i | 0.232561 | − | 0.987594i | ||||
\(532\) | −14.3367 | + | 4.95292i | −0.621576 | + | 0.214736i | ||||
\(533\) | −8.96353 | − | 15.5253i | −0.388254 | − | 0.672475i | ||||
\(534\) | −16.2561 | + | 41.0050i | −0.703469 | + | 1.77446i | ||||
\(535\) | −17.2502 | − | 29.8782i | −0.745791 | − | 1.29175i | ||||
\(536\) | 1.56252 | + | 2.70637i | 0.0674907 | + | 0.116897i | ||||
\(537\) | −22.7968 | − | 28.7886i | −0.983755 | − | 1.24232i | ||||
\(538\) | 26.4661 | + | 45.8406i | 1.14103 | + | 1.97633i | ||||
\(539\) | −0.988373 | − | 6.92987i | −0.0425722 | − | 0.298491i | ||||
\(540\) | 27.1302 | + | 18.9095i | 1.16750 | + | 0.813737i | ||||
\(541\) | −0.849669 | − | 1.47167i | −0.0365301 | − | 0.0632720i | 0.847182 | − | 0.531302i | \(-0.178297\pi\) |
−0.883712 | + | 0.468030i | \(0.844964\pi\) | |||||||
\(542\) | 12.3205 | 0.529212 | ||||||||
\(543\) | 12.3039 | − | 31.0358i | 0.528009 | − | 1.33187i | ||||
\(544\) | 17.0252 | 0.729950 | ||||||||
\(545\) | 9.32197 | − | 16.1461i | 0.399309 | − | 0.691624i | ||||
\(546\) | 15.1876 | + | 9.70051i | 0.649970 | + | 0.415144i | ||||
\(547\) | 13.5504 | + | 23.4700i | 0.579373 | + | 1.00350i | 0.995551 | + | 0.0942211i | \(0.0300360\pi\) |
−0.416178 | + | 0.909283i | \(0.636631\pi\) | |||||||
\(548\) | 23.5943 | + | 40.8666i | 1.00790 | + | 1.74573i | ||||
\(549\) | −9.76783 | + | 2.93964i | −0.416881 | + | 0.125461i | ||||
\(550\) | −1.67992 | + | 2.90971i | −0.0716321 | + | 0.124071i | ||||
\(551\) | 6.47757 | − | 11.2195i | 0.275954 | − | 0.477966i | ||||
\(552\) | 1.14728 | − | 2.89395i | 0.0488314 | − | 0.123175i | ||||
\(553\) | −12.1855 | + | 4.20975i | −0.518182 | + | 0.179017i | ||||
\(554\) | −14.2188 | + | 24.6277i | −0.604100 | + | 1.04633i | ||||
\(555\) | −15.9138 | + | 2.34274i | −0.675502 | + | 0.0994437i | ||||
\(556\) | −37.2570 | −1.58005 | ||||||||
\(557\) | −4.30101 | + | 7.44957i | −0.182240 | + | 0.315648i | −0.942643 | − | 0.333803i | \(-0.891668\pi\) |
0.760403 | + | 0.649451i | \(0.225001\pi\) | |||||||
\(558\) | 8.22984 | + | 7.74206i | 0.348397 | + | 0.327748i | ||||
\(559\) | −9.51210 | −0.402319 | ||||||||
\(560\) | 18.0394 | − | 6.23208i | 0.762303 | − | 0.263353i | ||||
\(561\) | −2.29430 | − | 2.89732i | −0.0968655 | − | 0.122325i | ||||
\(562\) | 34.3053 | 1.44708 | ||||||||
\(563\) | 7.90771 | + | 13.6966i | 0.333270 | + | 0.577241i | 0.983151 | − | 0.182795i | \(-0.0585145\pi\) |
−0.649881 | + | 0.760036i | \(0.725181\pi\) | |||||||
\(564\) | −4.22149 | + | 10.6485i | −0.177757 | + | 0.448382i | ||||
\(565\) | 21.3928 | − | 37.0534i | 0.900000 | − | 1.55885i | ||||
\(566\) | 43.0985 | 1.81156 | ||||||||
\(567\) | −14.4769 | + | 18.9056i | −0.607972 | + | 0.793959i | ||||
\(568\) | 13.3020 | 0.558139 | ||||||||
\(569\) | −3.17014 | + | 5.49085i | −0.132899 | + | 0.230188i | −0.924793 | − | 0.380471i | \(-0.875762\pi\) |
0.791894 | + | 0.610659i | \(0.209095\pi\) | |||||||
\(570\) | −8.01702 | + | 20.2225i | −0.335796 | + | 0.847028i | ||||
\(571\) | 0.0809891 | + | 0.140277i | 0.00338929 | + | 0.00587042i | 0.867715 | − | 0.497062i | \(-0.165588\pi\) |
−0.864326 | + | 0.502932i | \(0.832254\pi\) | |||||||
\(572\) | −4.60728 | −0.192640 | ||||||||
\(573\) | 17.5434 | + | 22.1545i | 0.732887 | + | 0.925516i | ||||
\(574\) | −10.2551 | + | 53.0472i | −0.428039 | + | 2.21415i | ||||
\(575\) | −2.81036 | −0.117200 | ||||||||
\(576\) | 24.6189 | + | 23.1598i | 1.02579 | + | 0.964992i | ||||
\(577\) | 20.5912 | − | 35.6650i | 0.857224 | − | 1.48476i | −0.0173425 | − | 0.999850i | \(-0.505521\pi\) |
0.874566 | − | 0.484906i | \(-0.161146\pi\) | |||||||
\(578\) | 26.3448 | 1.09580 | ||||||||
\(579\) | 5.02238 | − | 0.739367i | 0.208723 | − | 0.0307271i | ||||
\(580\) | 17.8309 | − | 30.8840i | 0.740387 | − | 1.28239i | ||||
\(581\) | −1.64541 | + | 8.51130i | −0.0682630 | + | 0.353108i | ||||
\(582\) | 18.9686 | − | 47.8473i | 0.786273 | − | 1.98333i | ||||
\(583\) | 2.96849 | − | 5.14158i | 0.122942 | − | 0.212942i | ||||
\(584\) | −5.63790 | + | 9.76513i | −0.233298 | + | 0.404084i | ||||
\(585\) | 13.6995 | − | 4.12287i | 0.566403 | − | 0.170460i | ||||
\(586\) | 9.35018 | + | 16.1950i | 0.386252 | + | 0.669009i | ||||
\(587\) | 11.3628 | + | 19.6809i | 0.468992 | + | 0.812318i | 0.999372 | − | 0.0354423i | \(-0.0112840\pi\) |
−0.530380 | + | 0.847760i | \(0.677951\pi\) | |||||||
\(588\) | −8.53455 | − | 28.8275i | −0.351959 | − | 1.18883i | ||||
\(589\) | −2.05713 | + | 3.56305i | −0.0847624 | + | 0.146813i | ||||
\(590\) | 42.3355 | 1.74292 | ||||||||
\(591\) | −13.4954 | + | 34.0414i | −0.555126 | + | 1.40028i | ||||
\(592\) | −10.1697 | −0.417971 | ||||||||
\(593\) | 21.1695 | + | 36.6666i | 0.869327 | + | 1.50572i | 0.862685 | + | 0.505741i | \(0.168781\pi\) |
0.00664168 | + | 0.999978i | \(0.497886\pi\) | |||||||
\(594\) | 0.934834 | − | 10.9580i | 0.0383567 | − | 0.449611i | ||||
\(595\) | −13.6950 | + | 4.73122i | −0.561440 | + | 0.193961i | ||||
\(596\) | 19.2937 | + | 33.4176i | 0.790299 | + | 1.36884i | ||||
\(597\) | −6.91292 | − | 8.72988i | −0.282927 | − | 0.357290i | ||||
\(598\) | −3.48105 | − | 6.02936i | −0.142351 | − | 0.246559i | ||||
\(599\) | −12.9555 | − | 22.4395i | −0.529346 | − | 0.916854i | −0.999414 | − | 0.0342239i | \(-0.989104\pi\) |
0.470068 | − | 0.882630i | \(-0.344229\pi\) | |||||||
\(600\) | −1.02872 | + | 2.59490i | −0.0419975 | + | 0.105936i | ||||
\(601\) | −0.0851273 | − | 0.147445i | −0.00347242 | − | 0.00601440i | 0.864284 | − | 0.503004i | \(-0.167772\pi\) |
−0.867756 | + | 0.496990i | \(0.834439\pi\) | |||||||
\(602\) | 21.6552 | + | 18.7858i | 0.882600 | + | 0.765651i | ||||
\(603\) | −2.11668 | + | 8.98869i | −0.0861980 | + | 0.366048i | ||||
\(604\) | −0.710609 | − | 1.23081i | −0.0289143 | − | 0.0500810i | ||||
\(605\) | 2.56660 | 0.104347 | ||||||||
\(606\) | −29.1076 | − | 36.7581i | −1.18242 | − | 1.49320i | ||||
\(607\) | 5.81274 | 0.235932 | 0.117966 | − | 0.993018i | \(-0.462363\pi\) | ||||
0.117966 | + | 0.993018i | \(0.462363\pi\) | |||||||
\(608\) | −9.22393 | + | 15.9763i | −0.374080 | + | 0.647925i | ||||
\(609\) | 21.6405 | + | 13.8220i | 0.876916 | + | 0.560097i | ||||
\(610\) | −9.23539 | − | 15.9962i | −0.373930 | − | 0.647666i | ||||
\(611\) | 2.47773 | + | 4.29155i | 0.100238 | + | 0.173617i | ||||
\(612\) | −11.5611 | − | 10.8759i | −0.467330 | − | 0.439632i | ||||
\(613\) | −14.8034 | + | 25.6402i | −0.597904 | + | 1.03560i | 0.395226 | + | 0.918584i | \(0.370666\pi\) |
−0.993130 | + | 0.117016i | \(0.962667\pi\) | |||||||
\(614\) | 29.8750 | − | 51.7450i | 1.20566 | − | 2.08826i | ||||
\(615\) | 26.6274 | + | 33.6260i | 1.07372 | + | 1.35593i | ||||
\(616\) | 2.02897 | + | 1.76012i | 0.0817496 | + | 0.0709173i | ||||
\(617\) | 13.6833 | − | 23.7002i | 0.550869 | − | 0.954132i | −0.447344 | − | 0.894362i | \(-0.647630\pi\) |
0.998212 | − | 0.0597703i | \(-0.0190368\pi\) | |||||||
\(618\) | −33.8294 | − | 42.7210i | −1.36082 | − | 1.71849i | ||||
\(619\) | 22.0770 | 0.887349 | 0.443674 | − | 0.896188i | \(-0.353675\pi\) | ||||
0.443674 | + | 0.896188i | \(0.353675\pi\) | |||||||
\(620\) | −5.66267 | + | 9.80803i | −0.227418 | + | 0.393900i | ||||
\(621\) | 8.32884 | − | 3.90574i | 0.334225 | − | 0.156732i | ||||
\(622\) | −7.28888 | −0.292257 | ||||||||
\(623\) | 6.04242 | − | 31.2560i | 0.242084 | − | 1.25224i | ||||
\(624\) | 8.94857 | − | 1.31736i | 0.358229 | − | 0.0527366i | ||||
\(625\) | −30.4172 | −1.21669 | ||||||||
\(626\) | −7.68883 | − | 13.3174i | −0.307307 | − | 0.532272i | ||||
\(627\) | 3.96183 | − | 0.583239i | 0.158220 | − | 0.0232923i | ||||
\(628\) | −8.86094 | + | 15.3476i | −0.353590 | + | 0.612436i | ||||
\(629\) | 7.72054 | 0.307838 | ||||||||
\(630\) | −39.3305 | − | 17.6694i | −1.56697 | − | 0.703967i | ||||
\(631\) | 40.1182 | 1.59708 | 0.798540 | − | 0.601941i | \(-0.205606\pi\) | ||||
0.798540 | + | 0.601941i | \(0.205606\pi\) | |||||||
\(632\) | 2.47349 | − | 4.28422i | 0.0983903 | − | 0.170417i | ||||
\(633\) | −2.66362 | − | 3.36371i | −0.105869 | − | 0.133696i | ||||
\(634\) | 26.6876 | + | 46.2244i | 1.05990 | + | 1.83580i | ||||
\(635\) | −11.9703 | −0.475027 | ||||||||
\(636\) | 9.39724 | − | 23.7040i | 0.372625 | − | 0.939926i | ||||
\(637\) | −12.0690 | − | 4.84755i | −0.478193 | − | 0.192067i | ||||
\(638\) | −11.8597 | −0.469530 | ||||||||
\(639\) | 28.6301 | + | 26.9333i | 1.13259 | + | 1.06546i | ||||
\(640\) | −10.1229 | + | 17.5334i | −0.400144 | + | 0.693070i | ||||
\(641\) | 22.2973 | 0.880692 | 0.440346 | − | 0.897828i | \(-0.354856\pi\) | ||||
0.440346 | + | 0.897828i | \(0.354856\pi\) | |||||||
\(642\) | −18.1606 | + | 45.8091i | −0.716741 | + | 1.80794i | ||||
\(643\) | 1.71771 | − | 2.97516i | 0.0677399 | − | 0.117329i | −0.830166 | − | 0.557516i | \(-0.811755\pi\) |
0.897906 | + | 0.440187i | \(0.145088\pi\) | |||||||
\(644\) | −2.20454 | + | 11.4036i | −0.0868711 | + | 0.449364i | ||||
\(645\) | 22.5158 | − | 3.31466i | 0.886561 | − | 0.130515i | ||||
\(646\) | 5.22062 | − | 9.04237i | 0.205402 | − | 0.355767i | ||||
\(647\) | −23.2216 | + | 40.2211i | −0.912937 | + | 1.58125i | −0.103043 | + | 0.994677i | \(0.532858\pi\) |
−0.809894 | + | 0.586577i | \(0.800475\pi\) | |||||||
\(648\) | −0.557557 | − | 9.11999i | −0.0219029 | − | 0.358267i | ||||
\(649\) | −3.89667 | − | 6.74923i | −0.152958 | − | 0.264930i | ||||
\(650\) | 3.12134 | + | 5.40631i | 0.122429 | + | 0.212053i | ||||
\(651\) | −6.87251 | − | 4.38955i | −0.269355 | − | 0.172040i | ||||
\(652\) | 5.76580 | − | 9.98665i | 0.225806 | − | 0.391108i | ||||
\(653\) | 0.929311 | 0.0363668 | 0.0181834 | − | 0.999835i | \(-0.494212\pi\) | ||||
0.0181834 | + | 0.999835i | \(0.494212\pi\) | |||||||
\(654\) | −26.3455 | + | 3.87845i | −1.03019 | + | 0.151659i | ||||
\(655\) | 24.7328 | 0.966389 | ||||||||
\(656\) | 13.5589 | + | 23.4847i | 0.529387 | + | 0.916925i | ||||
\(657\) | −31.9066 | + | 9.60232i | −1.24479 | + | 0.374622i | ||||
\(658\) | 2.83474 | − | 14.6635i | 0.110510 | − | 0.571641i | ||||
\(659\) | −4.28567 | − | 7.42301i | −0.166946 | − | 0.289159i | 0.770399 | − | 0.637563i | \(-0.220057\pi\) |
−0.937345 | + | 0.348403i | \(0.886724\pi\) | |||||||
\(660\) | 10.9058 | − | 1.60549i | 0.424506 | − | 0.0624935i | ||||
\(661\) | −19.5529 | − | 33.8666i | −0.760518 | − | 1.31726i | −0.942584 | − | 0.333970i | \(-0.891612\pi\) |
0.182065 | − | 0.983286i | \(-0.441722\pi\) | |||||||
\(662\) | −7.85422 | − | 13.6039i | −0.305263 | − | 0.528731i | ||||
\(663\) | −6.79351 | + | 1.00010i | −0.263838 | + | 0.0388408i | ||||
\(664\) | −1.66321 | − | 2.88076i | −0.0645449 | − | 0.111795i | ||||
\(665\) | 2.97995 | − | 15.4146i | 0.115557 | − | 0.597751i | ||||
\(666\) | 16.7341 | + | 15.7423i | 0.648432 | + | 0.610000i | ||||
\(667\) | −4.96006 | − | 8.59108i | −0.192054 | − | 0.332648i | ||||
\(668\) | −50.2535 | −1.94437 | ||||||||
\(669\) | −40.6655 | + | 5.98655i | −1.57222 | + | 0.231453i | ||||
\(670\) | −16.7215 | −0.646009 | ||||||||
\(671\) | −1.70010 | + | 2.94466i | −0.0656316 | + | 0.113677i | ||||
\(672\) | −30.8156 | − | 19.6823i | −1.18874 | − | 0.759261i | ||||
\(673\) | 25.1966 | + | 43.6418i | 0.971258 | + | 1.68227i | 0.691768 | + | 0.722120i | \(0.256832\pi\) |
0.279490 | + | 0.960149i | \(0.409835\pi\) | |||||||
\(674\) | 9.03471 | + | 15.6486i | 0.348004 | + | 0.602761i | ||||
\(675\) | −7.46819 | + | 3.50215i | −0.287451 | + | 0.134798i | ||||
\(676\) | 11.8376 | − | 20.5033i | 0.455293 | − | 0.788590i | ||||
\(677\) | −2.96406 | + | 5.13391i | −0.113918 | + | 0.197312i | −0.917347 | − | 0.398089i | \(-0.869674\pi\) |
0.803429 | + | 0.595401i | \(0.203007\pi\) | |||||||
\(678\) | −60.4597 | + | 8.90055i | −2.32194 | + | 0.341824i | ||||
\(679\) | −7.05067 | + | 36.4714i | −0.270580 | + | 1.39965i | ||||
\(680\) | 2.77989 | − | 4.81491i | 0.106604 | − | 0.184643i | ||||
\(681\) | 14.0833 | − | 35.5242i | 0.539671 | − | 1.36129i | ||||
\(682\) | 3.76637 | 0.144222 | ||||||||
\(683\) | 2.69080 | − | 4.66059i | 0.102960 | − | 0.178333i | −0.809943 | − | 0.586509i | \(-0.800502\pi\) |
0.912903 | + | 0.408176i | \(0.133835\pi\) | |||||||
\(684\) | 16.4694 | − | 4.95649i | 0.629724 | − | 0.189516i | ||||
\(685\) | −48.8430 | −1.86620 | ||||||||
\(686\) | 17.9027 | + | 34.8714i | 0.683529 | + | 1.33140i | ||||
\(687\) | −8.98535 | + | 22.6651i | −0.342812 | + | 0.864726i | ||||
\(688\) | 14.3887 | 0.548565 | ||||||||
\(689\) | −5.51553 | − | 9.55318i | −0.210125 | − | 0.363947i | ||||
\(690\) | 10.3409 | + | 13.0589i | 0.393673 | + | 0.497144i | ||||
\(691\) | −1.32759 | + | 2.29946i | −0.0505040 | + | 0.0874755i | −0.890172 | − | 0.455624i | \(-0.849416\pi\) |
0.839668 | + | 0.543100i | \(0.182749\pi\) | |||||||
\(692\) | 38.8661 | 1.47747 | ||||||||
\(693\) | 0.803180 | + | 7.89651i | 0.0305103 | + | 0.299964i | ||||
\(694\) | −72.9598 | −2.76952 | ||||||||
\(695\) | 19.2816 | − | 33.3967i | 0.731392 | − | 1.26681i | ||||
\(696\) | −9.74805 | + | 1.43505i | −0.369499 | + | 0.0543956i | ||||
\(697\) | −10.2936 | − | 17.8290i | −0.389896 | − | 0.675320i | ||||
\(698\) | −51.0104 | −1.93077 | ||||||||
\(699\) | 40.8859 | − | 6.01900i | 1.54645 | − | 0.227659i | ||||
\(700\) | 1.97674 | − | 10.2252i | 0.0747136 | − | 0.386476i | ||||
\(701\) | 4.47309 | 0.168946 | 0.0844731 | − | 0.996426i | \(-0.473079\pi\) | ||||
0.0844731 | + | 0.996426i | \(0.473079\pi\) | |||||||
\(702\) | −16.7640 | − | 11.6843i | −0.632715 | − | 0.440996i | ||||
\(703\) | −4.18284 | + | 7.24489i | −0.157759 | + | 0.273246i | ||||
\(704\) | 11.2668 | 0.424634 | ||||||||
\(705\) | −7.36042 | − | 9.29500i | −0.277210 | − | 0.350070i | ||||
\(706\) | 9.61019 | − | 16.6453i | 0.361684 | − | 0.626455i | ||||
\(707\) | 25.5615 | + | 22.1744i | 0.961338 | + | 0.833955i | ||||
\(708\) | −20.7792 | − | 26.2407i | −0.780931 | − | 0.986187i | ||||
\(709\) | −10.5936 | + | 18.3486i | −0.397851 | + | 0.689098i | −0.993461 | − | 0.114176i | \(-0.963577\pi\) |
0.595610 | + | 0.803274i | \(0.296910\pi\) | |||||||
\(710\) | −35.5882 | + | 61.6406i | −1.33560 | + | 2.31333i | ||||
\(711\) | 13.9982 | − | 4.21279i | 0.524975 | − | 0.157992i | ||||
\(712\) | 6.10778 | + | 10.5790i | 0.228899 | + | 0.396464i | ||||
\(713\) | 1.57520 | + | 2.72833i | 0.0589917 | + | 0.102177i | ||||
\(714\) | 17.4412 | + | 11.1399i | 0.652720 | + | 0.416900i | ||||
\(715\) | 2.38440 | − | 4.12991i | 0.0891716 | − | 0.154450i | ||||
\(716\) | −52.5720 | −1.96471 | ||||||||
\(717\) | −6.44742 | − | 8.14202i | −0.240783 | − | 0.304069i | ||||
\(718\) | −15.8017 | −0.589716 | ||||||||
\(719\) | 7.49753 | + | 12.9861i | 0.279611 | + | 0.484300i | 0.971288 | − | 0.237907i | \(-0.0764612\pi\) |
−0.691677 | + | 0.722207i | \(0.743128\pi\) | |||||||
\(720\) | −20.7229 | + | 6.23657i | −0.772295 | + | 0.232423i | ||||
\(721\) | 29.7080 | + | 25.7715i | 1.10638 | + | 0.959782i | ||||
\(722\) | −14.4501 | − | 25.0283i | −0.537777 | − | 0.931457i | ||||
\(723\) | −9.82455 | + | 24.7819i | −0.365379 | + | 0.921649i | ||||
\(724\) | −23.8981 | − | 41.3927i | −0.888166 | − | 1.53835i | ||||
\(725\) | 4.44752 | + | 7.70333i | 0.165177 | + | 0.286094i | ||||
\(726\) | −2.27581 | − | 2.87397i | −0.0844631 | − | 0.106663i | ||||
\(727\) | 12.7155 | + | 22.0240i | 0.471593 | + | 0.816824i | 0.999472 | − | 0.0324963i | \(-0.0103457\pi\) |
−0.527879 | + | 0.849320i | \(0.677012\pi\) | |||||||
\(728\) | 4.71714 | − | 1.62964i | 0.174829 | − | 0.0603983i | ||||
\(729\) | 17.2657 | − | 20.7580i | 0.639470 | − | 0.768816i | ||||
\(730\) | −30.1673 | − | 52.2513i | −1.11654 | − | 1.93391i | ||||
\(731\) | −10.9235 | −0.404021 | ||||||||
\(732\) | −5.38193 | + | 13.5756i | −0.198922 | + | 0.501770i | ||||
\(733\) | −25.3527 | −0.936422 | −0.468211 | − | 0.883617i | \(-0.655101\pi\) | ||||
−0.468211 | + | 0.883617i | \(0.655101\pi\) | |||||||
\(734\) | −25.7211 | + | 44.5503i | −0.949385 | + | 1.64438i | ||||
\(735\) | 30.2575 | + | 7.26883i | 1.11607 | + | 0.268115i | ||||
\(736\) | 7.06303 | + | 12.2335i | 0.260347 | + | 0.450934i | ||||
\(737\) | 1.53909 | + | 2.66579i | 0.0566932 | + | 0.0981955i | ||||
\(738\) | 14.0424 | − | 59.6324i | 0.516909 | − | 2.19510i | ||||
\(739\) | 10.2114 | − | 17.6866i | 0.375631 | − | 0.650612i | −0.614790 | − | 0.788691i | \(-0.710759\pi\) |
0.990421 | + | 0.138078i | \(0.0440926\pi\) | |||||||
\(740\) | −11.5141 | + | 19.9431i | −0.423268 | + | 0.733122i | ||||
\(741\) | 2.74210 | − | 6.91680i | 0.100734 | − | 0.254095i | ||||
\(742\) | −6.31027 | + | 32.6415i | −0.231657 | + | 1.19831i | ||||
\(743\) | −7.29649 | + | 12.6379i | −0.267682 | + | 0.463639i | −0.968263 | − | 0.249934i | \(-0.919591\pi\) |
0.700581 | + | 0.713573i | \(0.252924\pi\) | |||||||
\(744\) | 3.09575 | − | 0.455740i | 0.113496 | − | 0.0167082i | ||||
\(745\) | −39.9402 | −1.46329 | ||||||||
\(746\) | 27.0163 | − | 46.7937i | 0.989138 | − | 1.71324i | ||||
\(747\) | 2.25307 | − | 9.56789i | 0.0824357 | − | 0.350071i | ||||
\(748\) | −5.29092 | −0.193455 | ||||||||
\(749\) | 6.75033 | − | 34.9178i | 0.246652 | − | 1.27587i | ||||
\(750\) | 19.9331 | + | 25.1722i | 0.727853 | + | 0.919158i | ||||
\(751\) | 14.8029 | 0.540167 | 0.270083 | − | 0.962837i | \(-0.412949\pi\) | ||||
0.270083 | + | 0.962837i | \(0.412949\pi\) | |||||||
\(752\) | −3.74800 | − | 6.49172i | −0.136675 | − | 0.236729i | ||||
\(753\) | 6.29376 | − | 15.8757i | 0.229357 | − | 0.578541i | ||||
\(754\) | −11.0178 | + | 19.0834i | −0.401245 | + | 0.694977i | ||||
\(755\) | 1.47104 | 0.0535368 | ||||||||
\(756\) | 8.35231 | + | 33.0507i | 0.303771 | + | 1.20204i | ||||
\(757\) | 30.1009 | 1.09403 | 0.547017 | − | 0.837121i | \(-0.315763\pi\) | ||||
0.547017 | + | 0.837121i | \(0.315763\pi\) | |||||||
\(758\) | −25.7682 | + | 44.6318i | −0.935943 | + | 1.62110i | ||||
\(759\) | 1.13007 | − | 2.85055i | 0.0410191 | − | 0.103469i | ||||
\(760\) | 3.01218 | + | 5.21725i | 0.109263 | + | 0.189250i | ||||
\(761\) | 11.1545 | 0.404349 | 0.202175 | − | 0.979350i | \(-0.435199\pi\) | ||||
0.202175 | + | 0.979350i | \(0.435199\pi\) | |||||||
\(762\) | 10.6141 | + | 13.4038i | 0.384508 | + | 0.485570i | ||||
\(763\) | 18.1654 | − | 6.27562i | 0.657633 | − | 0.227193i | ||||
\(764\) | 40.4571 | 1.46369 | ||||||||
\(765\) | 15.7322 | − | 4.73463i | 0.568800 | − | 0.171181i | ||||
\(766\) | 11.0489 | − | 19.1373i | 0.399214 | − | 0.691459i | ||||
\(767\) | −14.4802 | −0.522850 | ||||||||
\(768\) | −10.0040 | + | 1.47273i | −0.360987 | + | 0.0531426i | ||||
\(769\) | −19.7817 | + | 34.2630i | −0.713348 | + | 1.23555i | 0.250246 | + | 0.968182i | \(0.419489\pi\) |
−0.963593 | + | 0.267372i | \(0.913845\pi\) | |||||||
\(770\) | −13.5846 | + | 4.69308i | −0.489555 | + | 0.169127i | ||||
\(771\) | −11.6889 | + | 29.4847i | −0.420966 | + | 1.06186i | ||||
\(772\) | 3.63386 | − | 6.29403i | 0.130785 | − | 0.226527i | ||||
\(773\) | −14.6510 | + | 25.3764i | −0.526961 | + | 0.912724i | 0.472545 | + | 0.881307i | \(0.343335\pi\) |
−0.999506 | + | 0.0314174i | \(0.989998\pi\) | |||||||
\(774\) | −23.6764 | − | 22.2732i | −0.851032 | − | 0.800593i | ||||
\(775\) | −1.41243 | − | 2.44640i | −0.0507359 | − | 0.0878772i | ||||
\(776\) | −7.12694 | − | 12.3442i | −0.255842 | − | 0.443132i | ||||
\(777\) | −13.9742 | − | 8.92546i | −0.501320 | − | 0.320199i | ||||
\(778\) | −8.10671 | + | 14.0412i | −0.290640 | + | 0.503403i | ||||
\(779\) | 22.3074 | 0.799246 | ||||||||
\(780\) | 7.54821 | − | 19.0399i | 0.270269 | − | 0.681740i | ||||
\(781\) | 13.1025 | 0.468845 | ||||||||
\(782\) | −3.99758 | − | 6.92400i | −0.142953 | − | 0.247602i | ||||
\(783\) | −23.8865 | − | 16.6487i | −0.853636 | − | 0.594976i | ||||
\(784\) | 18.2565 | + | 7.33277i | 0.652020 | + | 0.261885i | ||||
\(785\) | −9.17159 | − | 15.8857i | −0.327348 | − | 0.566984i | ||||
\(786\) | −21.9306 | − | 27.6947i | −0.782237 | − | 0.987837i | ||||
\(787\) | 14.0841 | + | 24.3943i | 0.502043 | + | 0.869563i | 0.999997 | + | 0.00236027i | \(0.000751298\pi\) |
−0.497955 | + | 0.867203i | \(0.665915\pi\) | |||||||
\(788\) | 26.2125 | + | 45.4013i | 0.933780 | + | 1.61735i | ||||
\(789\) | −0.246677 | + | 0.622230i | −0.00878195 | + | 0.0221520i | ||||
\(790\) | 13.2352 | + | 22.9240i | 0.470887 | + | 0.815600i | ||||
\(791\) | 41.6874 | − | 14.4018i | 1.48223 | − | 0.512068i | ||||
\(792\) | −2.21835 | − | 2.08687i | −0.0788256 | − | 0.0741538i | ||||
\(793\) | 3.15882 | + | 5.47125i | 0.112173 | + | 0.194290i | ||||
\(794\) | 3.07292 | 0.109054 | ||||||||
\(795\) | 16.3846 | + | 20.6911i | 0.581103 | + | 0.733838i | ||||
\(796\) | −15.9420 | −0.565048 | ||||||||
\(797\) | −6.18443 | + | 10.7117i | −0.219064 | + | 0.379430i | −0.954522 | − | 0.298140i | \(-0.903634\pi\) |
0.735458 | + | 0.677570i | \(0.236967\pi\) | |||||||
\(798\) | −19.9029 | + | 10.3313i | −0.704554 | + | 0.365724i | ||||
\(799\) | 2.84538 | + | 4.92833i | 0.100662 | + | 0.174352i | ||||
\(800\) | −6.33318 | − | 10.9694i | −0.223912 | − | 0.387826i | ||||
\(801\) | −8.27395 | + | 35.1361i | −0.292346 | + | 1.24147i | ||||
\(802\) | −4.53057 | + | 7.84718i | −0.159980 | + | 0.277094i | ||||
\(803\) | −5.55336 | + | 9.61870i | −0.195974 | + | 0.339437i | ||||
\(804\) | 8.20730 | + | 10.3645i | 0.289449 | + | 0.365527i | ||||
\(805\) | −9.08110 | − | 7.87781i | −0.320067 | − | 0.277656i | ||||
\(806\) | 3.49900 | − | 6.06045i | 0.123247 | − | 0.213470i | ||||
\(807\) | 26.8912 | + | 33.9591i | 0.946613 | + | 1.19542i | ||||
\(808\) | −12.9847 | −0.456801 | ||||||||
\(809\) | 26.4921 | − | 45.8856i | 0.931411 | − | 1.61325i | 0.150499 | − | 0.988610i | \(-0.451912\pi\) |
0.780912 | − | 0.624641i | \(-0.214755\pi\) | |||||||
\(810\) | 43.7531 | + | 21.8160i | 1.53733 | + | 0.766535i | ||||
\(811\) | −42.1161 | −1.47890 | −0.739449 | − | 0.673213i | \(-0.764914\pi\) | ||||
−0.739449 | + | 0.673213i | \(0.764914\pi\) | |||||||
\(812\) | 34.7465 | − | 12.0039i | 1.21936 | − | 0.421254i | ||||
\(813\) | 9.97496 | − | 1.46846i | 0.349837 | − | 0.0515011i | ||||
\(814\) | 7.65831 | 0.268424 | ||||||||
\(815\) | 5.96794 | + | 10.3368i | 0.209048 | + | 0.362081i | ||||
\(816\) | 10.2764 | − | 1.51283i | 0.359745 | − | 0.0529597i | ||||
\(817\) | 5.91816 | − | 10.2505i | 0.207050 | − | 0.358621i | ||||
\(818\) | 10.9130 | 0.381564 | ||||||||
\(819\) | 13.4524 | + | 6.04356i | 0.470065 | + | 0.211179i | ||||
\(820\) | 61.4058 | 2.14438 | ||||||||
\(821\) | 21.4164 | − | 37.0944i | 0.747439 | − | 1.29460i | −0.201608 | − | 0.979466i | \(-0.564617\pi\) |
0.949047 | − | 0.315136i | \(-0.102050\pi\) | |||||||
\(822\) | 43.3092 | + | 54.6923i | 1.51058 | + | 1.90761i | ||||
\(823\) | −5.13618 | − | 8.89613i | −0.179036 | − | 0.310100i | 0.762515 | − | 0.646971i | \(-0.223965\pi\) |
−0.941551 | + | 0.336872i | \(0.890631\pi\) | |||||||
\(824\) | −15.0911 | −0.525723 | ||||||||
\(825\) | −1.01330 | + | 2.55599i | −0.0352785 | + | 0.0889882i | ||||
\(826\) | 32.9656 | + | 28.5975i | 1.14702 | + | 0.995033i | ||||
\(827\) | −33.5144 | −1.16541 | −0.582705 | − | 0.812684i | \(-0.698006\pi\) | ||||
−0.582705 | + | 0.812684i | \(0.698006\pi\) | |||||||
\(828\) | 3.01870 | − | 12.8192i | 0.104907 | − | 0.445498i | ||||
\(829\) | 10.6212 | − | 18.3964i | 0.368889 | − | 0.638935i | −0.620503 | − | 0.784204i | \(-0.713072\pi\) |
0.989392 | + | 0.145269i | \(0.0464048\pi\) | |||||||
\(830\) | 17.7990 | 0.617812 | ||||||||
\(831\) | −8.57654 | + | 21.6339i | −0.297517 | + | 0.750470i | ||||
\(832\) | 10.4670 | − | 18.1294i | 0.362878 | − | 0.628523i | ||||
\(833\) | −13.8599 | − | 5.56684i | −0.480216 | − | 0.192879i | ||||
\(834\) | −54.4932 | + | 8.02219i | −1.88694 | + | 0.277786i | ||||
\(835\) | 26.0077 | − | 45.0466i | 0.900032 | − | 1.55890i | ||||
\(836\) | 2.86652 | − | 4.96495i | 0.0991405 | − | 0.171716i | ||||
\(837\) | 7.58581 | + | 5.28724i | 0.262204 | + | 0.182754i | ||||
\(838\) | 30.2268 | + | 52.3543i | 1.04417 | + | 1.80855i | ||||
\(839\) | −12.3794 | − | 21.4418i | −0.427386 | − | 0.740254i | 0.569254 | − | 0.822162i | \(-0.307232\pi\) |
−0.996640 | + | 0.0819078i | \(0.973899\pi\) | |||||||
\(840\) | −10.5980 | + | 5.50124i | −0.365664 | + | 0.189811i | ||||
\(841\) | −1.19901 | + | 2.07675i | −0.0413453 | + | 0.0716122i | ||||
\(842\) | 25.4504 | 0.877079 | ||||||||
\(843\) | 27.7743 | − | 4.08879i | 0.956599 | − | 0.140825i | ||||
\(844\) | −6.14261 | −0.211437 | ||||||||
\(845\) | 12.2526 | + | 21.2222i | 0.421503 | + | 0.730065i | ||||
\(846\) | −3.88165 | + | 16.4838i | −0.133454 | + | 0.566724i | ||||
\(847\) | 1.99855 | + | 1.73373i | 0.0686709 | + | 0.0595716i | ||||
\(848\) | 8.34321 | + | 14.4509i | 0.286507 | + | 0.496245i | ||||
\(849\) | 34.8935 | − | 5.13682i | 1.19754 | − | 0.176295i | ||||
\(850\) | 3.58449 | + | 6.20851i | 0.122947 | + | 0.212950i | ||||
\(851\) | 3.20292 | + | 5.54762i | 0.109795 | + | 0.190170i | ||||
\(852\) | 55.6741 | − | 8.19604i | 1.90736 | − | 0.280792i | ||||
\(853\) | −0.328688 | − | 0.569305i | −0.0112541 | − | 0.0194926i | 0.860344 | − | 0.509715i | \(-0.170249\pi\) |
−0.871598 | + | 0.490222i | \(0.836916\pi\) | |||||||
\(854\) | 3.61398 | − | 18.6943i | 0.123668 | − | 0.639705i | ||||
\(855\) | −4.08047 | + | 17.3281i | −0.139549 | + | 0.592609i | ||||
\(856\) | 6.82335 | + | 11.8184i | 0.233217 | + | 0.403944i | ||||
\(857\) | −39.0815 | −1.33500 | −0.667500 | − | 0.744610i | \(-0.732635\pi\) | ||||
−0.667500 | + | 0.744610i | \(0.732635\pi\) | |||||||
\(858\) | −6.73875 | + | 0.992041i | −0.230057 | + | 0.0338677i | ||||
\(859\) | 17.6371 | 0.601770 | 0.300885 | − | 0.953660i | \(-0.402718\pi\) | ||||
0.300885 | + | 0.953660i | \(0.402718\pi\) | |||||||
\(860\) | 16.2910 | − | 28.2168i | 0.555517 | − | 0.962184i | ||||
\(861\) | −1.98016 | + | 44.1704i | −0.0674836 | + | 1.50532i | ||||
\(862\) | −17.4630 | − | 30.2468i | −0.594792 | − | 1.03021i | ||||
\(863\) | 0.850995 | + | 1.47397i | 0.0289682 | + | 0.0501744i | 0.880146 | − | 0.474703i | \(-0.157445\pi\) |
−0.851178 | + | 0.524877i | \(0.824111\pi\) | |||||||
\(864\) | 34.0140 | + | 23.7074i | 1.15718 | + | 0.806543i | ||||
\(865\) | −20.1144 | + | 34.8391i | −0.683909 | + | 1.18456i | ||||
\(866\) | −33.7662 | + | 58.4848i | −1.14742 | + | 1.98739i | ||||
\(867\) | 21.3293 | − | 3.13999i | 0.724383 | − | 0.106640i | ||||
\(868\) | −11.0347 | + | 3.81215i | −0.374541 | + | 0.129393i | ||||
\(869\) | 2.43640 | − | 4.21997i | 0.0826493 | − | 0.143153i | ||||
\(870\) | 19.4300 | − | 49.0112i | 0.658739 | − | 1.66163i | ||||
\(871\) | 5.71934 | 0.193792 | ||||||||
\(872\) | −3.68732 | + | 6.38663i | −0.124869 | + | 0.216279i | ||||
\(873\) | 9.65456 | − | 40.9990i | 0.326757 | − | 1.38761i | ||||
\(874\) | 8.66323 | 0.293038 | ||||||||
\(875\) | −17.5046 | − | 15.1852i | −0.591765 | − | 0.513353i | ||||
\(876\) | −17.5800 | + | 44.3447i | −0.593975 | + | 1.49827i | ||||
\(877\) | −41.6362 | −1.40595 | −0.702977 | − | 0.711213i | \(-0.748146\pi\) | ||||
−0.702977 | + | 0.711213i | \(0.748146\pi\) | |||||||
\(878\) | −37.8298 | − | 65.5231i | −1.27669 | − | 2.21130i | ||||
\(879\) | 9.50035 | + | 11.9974i | 0.320439 | + | 0.404662i | ||||
\(880\) | −3.60683 | + | 6.24721i | −0.121586 | + | 0.210593i | ||||
\(881\) | 21.7833 | 0.733896 | 0.366948 | − | 0.930241i | \(-0.380403\pi\) | ||||
0.366948 | + | 0.930241i | \(0.380403\pi\) | |||||||
\(882\) | −18.6900 | − | 40.3264i | −0.629327 | − | 1.35786i | ||||
\(883\) | −31.8967 | −1.07341 | −0.536704 | − | 0.843770i | \(-0.680331\pi\) | ||||
−0.536704 | + | 0.843770i | \(0.680331\pi\) | |||||||
\(884\) | −4.91533 | + | 8.51360i | −0.165320 | + | 0.286343i | ||||
\(885\) | 34.2757 | − | 5.04588i | 1.15217 | − | 0.169616i | ||||
\(886\) | 42.0976 | + | 72.9152i | 1.41430 | + | 2.44963i | ||||
\(887\) | 6.23191 | 0.209247 | 0.104623 | − | 0.994512i | \(-0.466636\pi\) | ||||
0.104623 | + | 0.994512i | \(0.466636\pi\) | |||||||
\(888\) | 6.29472 | − | 0.926675i | 0.211237 | − | 0.0310972i | ||||
\(889\) | −9.32097 | − | 8.08589i | −0.312615 | − | 0.271192i | ||||
\(890\) | −65.3631 | −2.19098 | ||||||||
\(891\) | −0.549197 | − | 8.98323i | −0.0183988 | − | 0.300949i | ||||
\(892\) | −29.4228 | + | 50.9618i | −0.985148 | + | 1.70633i | ||||
\(893\) | −6.16628 | −0.206347 | ||||||||
\(894\) | 35.4150 | + | 44.7233i | 1.18445 | + | 1.49577i | ||||
\(895\) | 27.2076 | − | 47.1249i | 0.909449 | − | 1.57521i | ||||
\(896\) | −19.7262 | + | 6.81484i | −0.659007 | + | 0.227668i | ||||
\(897\) | −3.53696 | − | 4.46660i | −0.118096 | − | 0.149135i | ||||
\(898\) | −30.6914 | + | 53.1591i | −1.02419 | + | 1.77394i | ||||
\(899\) | 4.98564 | − | 8.63539i | 0.166280 | − | 0.288006i | ||||
\(900\) | −2.70677 | + | 11.4945i | −0.0902256 | + | 0.383151i | ||||
\(901\) | −6.33394 | − | 10.9707i | −0.211014 | − | 0.365487i | ||||
\(902\) | −10.2106 | − | 17.6853i | −0.339975 | − | 0.588854i | ||||
\(903\) | 19.7716 | + | 12.6283i | 0.657956 | + | 0.420244i | ||||
\(904\) | −8.46195 | + | 14.6565i | −0.281440 | + | 0.487469i | ||||
\(905\) | 49.4719 | 1.64450 | ||||||||
\(906\) | −1.30438 | − | 1.64721i | −0.0433350 | − | 0.0547250i | ||||
\(907\) | −33.9075 | −1.12588 | −0.562940 | − | 0.826498i | \(-0.690330\pi\) | ||||
−0.562940 | + | 0.826498i | \(0.690330\pi\) | |||||||
\(908\) | −27.3543 | − | 47.3790i | −0.907783 | − | 1.57233i | ||||
\(909\) | −27.9473 | − | 26.2909i | −0.926953 | − | 0.872014i | ||||
\(910\) | −5.06864 | + | 26.2189i | −0.168024 | + | 0.869147i | ||||
\(911\) | −7.39888 | − | 12.8152i | −0.245136 | − | 0.424588i | 0.717034 | − | 0.697038i | \(-0.245499\pi\) |
−0.962170 | + | 0.272450i | \(0.912166\pi\) | |||||||
\(912\) | −4.14791 | + | 10.4629i | −0.137351 | + | 0.346461i | ||||
\(913\) | −1.63826 | − | 2.83756i | −0.0542187 | − | 0.0939095i | ||||
\(914\) | −40.1211 | − | 69.4918i | −1.32709 | − | 2.29859i | ||||
\(915\) | −9.38372 | − | 11.8501i | −0.310216 | − | 0.391752i | ||||
\(916\) | 17.4525 | + | 30.2286i | 0.576646 | + | 0.998780i | ||||
\(917\) | 19.2588 | + | 16.7069i | 0.635981 | + | 0.551710i | ||||
\(918\) | −19.2514 | − | 13.4181i | −0.635392 | − | 0.442862i | ||||
\(919\) | 2.02331 | + | 3.50447i | 0.0667427 | + | 0.115602i | 0.897466 | − | 0.441084i | \(-0.145406\pi\) |
−0.830723 | + | 0.556686i | \(0.812073\pi\) | |||||||
\(920\) | 4.61303 | 0.152087 | ||||||||
\(921\) | 18.0201 | − | 45.4546i | 0.593781 | − | 1.49778i | ||||
\(922\) | 15.6751 | 0.516232 | ||||||||
\(923\) | 12.1724 | − | 21.0832i | 0.400660 | − | 0.693963i | ||||
\(924\) | 9.57654 | + | 6.11665i | 0.315045 | + | 0.201223i | ||||
\(925\) | −2.87195 | − | 4.97436i | −0.0944291 | − | 0.163556i | ||||
\(926\) | −44.3531 | − | 76.8219i | −1.45753 | − | 2.52452i | ||||
\(927\) | −32.4809 | − | 30.5558i | −1.06681 | − | 1.00358i | ||||
\(928\) | 22.3551 | − | 38.7201i | 0.733841 | − | 1.27105i | ||||
\(929\) | 17.5601 | − | 30.4149i | 0.576127 | − | 0.997881i | −0.419792 | − | 0.907621i | \(-0.637897\pi\) |
0.995918 | − | 0.0902600i | \(-0.0287698\pi\) | |||||||
\(930\) | −6.17052 | + | 15.5648i | −0.202339 | + | 0.510390i | ||||
\(931\) | 12.7329 | − | 9.98998i | 0.417303 | − | 0.327408i | ||||
\(932\) | 29.5823 | − | 51.2380i | 0.969000 | − | 1.67836i | ||||
\(933\) | −5.90123 | + | 0.868747i | −0.193198 | + | 0.0284415i | ||||
\(934\) | −88.8841 | −2.90838 | ||||||||
\(935\) | 2.73821 | − | 4.74271i | 0.0895489 | − | 0.155103i | ||||
\(936\) | −5.41885 | + | 1.63081i | −0.177121 | + | 0.0533047i | ||||
\(937\) | 6.91061 | 0.225760 | 0.112880 | − | 0.993609i | \(-0.463992\pi\) | ||||
0.112880 | + | 0.993609i | \(0.463992\pi\) | |||||||
\(938\) | −13.0206 | − | 11.2953i | −0.425138 | − | 0.368805i | ||||
\(939\) | −7.81232 | − | 9.86567i | −0.254945 | − | 0.321954i | ||||
\(940\) | −16.9740 | −0.553630 | ||||||||
\(941\) | 14.3510 | + | 24.8566i | 0.467829 | + | 0.810303i | 0.999324 | − | 0.0367578i | \(-0.0117030\pi\) |
−0.531495 | + | 0.847061i | \(0.678370\pi\) | |||||||
\(942\) | −9.65562 | + | 24.3558i | −0.314597 | + | 0.793555i | ||||
\(943\) | 8.54071 | − | 14.7929i | 0.278124 | − | 0.481724i | ||||
\(944\) | 21.9039 | 0.712910 | ||||||||
\(945\) | −33.9488 | − | 9.61783i | −1.10436 | − | 0.312868i | ||||
\(946\) | −10.8355 | −0.352292 | ||||||||
\(947\) | −14.5078 | + | 25.1283i | −0.471441 | + | 0.816560i | −0.999466 | − | 0.0326690i | \(-0.989599\pi\) |
0.528025 | + | 0.849229i | \(0.322933\pi\) | |||||||
\(948\) | 7.71282 | − | 19.4552i | 0.250501 | − | 0.631875i | ||||
\(949\) | 10.3183 | + | 17.8718i | 0.334945 | + | 0.580143i | ||||
\(950\) | −7.76802 | −0.252028 | ||||||||
\(951\) | 27.1163 | + | 34.2434i | 0.879306 | + | 1.11042i | ||||
\(952\) | 5.41708 | − | 1.87144i | 0.175569 | − | 0.0606538i | ||||
\(953\) | 43.0740 | 1.39530 | 0.697651 | − | 0.716437i | \(-0.254228\pi\) | ||||
0.697651 | + | 0.716437i | \(0.254228\pi\) | |||||||
\(954\) | 8.64072 | − | 36.6936i | 0.279754 | − | 1.18800i | ||||
\(955\) | −20.9378 | + | 36.2653i | −0.677530 | + | 1.17352i | ||||
\(956\) | −14.8685 | −0.480881 | ||||||||
\(957\) | −9.60188 | + | 1.41354i | −0.310385 | + | 0.0456931i | ||||
\(958\) | 18.2665 | − | 31.6386i | 0.590165 | − | 1.02220i | ||||
\(959\) | −38.0328 | − | 32.9933i | −1.22814 | − | 1.06541i | ||||
\(960\) | −18.4587 | + | 46.5610i | −0.595751 | + | 1.50275i | ||||
\(961\) | 13.9167 | − | 24.1044i | 0.448925 | − | 0.777561i | ||||
\(962\) | 7.11466 | − | 12.3230i | 0.229386 | − | 0.397308i | ||||
\(963\) | −9.24330 | + | 39.2525i | −0.297861 | + | 1.26490i | ||||
\(964\) | 19.0825 | + | 33.0518i | 0.614605 | + | 1.06453i | ||||
\(965\) | 3.76126 | + | 6.51469i | 0.121079 | + | 0.209715i | ||||
\(966\) | −0.769009 | + | 17.1539i | −0.0247424 | + | 0.551917i | ||||
\(967\) | 3.82707 | − | 6.62867i | 0.123070 | − | 0.213164i | −0.797907 | − | 0.602781i | \(-0.794059\pi\) |
0.920977 | + | 0.389617i | \(0.127393\pi\) | |||||||
\(968\) | −1.01522 | −0.0326305 | ||||||||
\(969\) | 3.14898 | − | 7.94313i | 0.101160 | − | 0.255170i | ||||
\(970\) | 76.2697 | 2.44887 | ||||||||
\(971\) | −16.0197 | − | 27.7469i | −0.514096 | − | 0.890441i | −0.999866 | − | 0.0163541i | \(-0.994794\pi\) |
0.485770 | − | 0.874087i | \(-0.338539\pi\) | |||||||
\(972\) | −7.95288 | − | 37.8272i | −0.255089 | − | 1.21331i | ||||
\(973\) | 37.5734 | − | 12.9805i | 1.20455 | − | 0.416136i | ||||
\(974\) | −18.6993 | − | 32.3881i | −0.599163 | − | 1.03778i | ||||
\(975\) | 3.17147 | + | 4.00504i | 0.101568 | + | 0.128264i | ||||
\(976\) | −4.77828 | − | 8.27622i | −0.152949 | − | 0.264915i | ||||
\(977\) | −21.5360 | − | 37.3014i | −0.688997 | − | 1.19338i | −0.972163 | − | 0.234307i | \(-0.924718\pi\) |
0.283165 | − | 0.959071i | \(-0.408615\pi\) | |||||||
\(978\) | 6.28290 | − | 15.8483i | 0.200905 | − | 0.506772i | ||||
\(979\) | 6.01619 | + | 10.4203i | 0.192278 | + | 0.333036i | ||||
\(980\) | 35.0499 | − | 27.4995i | 1.11963 | − | 0.878439i | ||||
\(981\) | −20.8677 | + | 6.28015i | −0.666253 | + | 0.200510i | ||||
\(982\) | −4.56719 | − | 7.91060i | −0.145745 | − | 0.252437i | ||||
\(983\) | 11.7905 | 0.376057 | 0.188029 | − | 0.982164i | \(-0.439790\pi\) | ||||
0.188029 | + | 0.982164i | \(0.439790\pi\) | |||||||
\(984\) | −10.5325 | − | 13.3008i | −0.335764 | − | 0.424015i | ||||
\(985\) | −54.2629 | −1.72896 | ||||||||
\(986\) | −12.6527 | + | 21.9150i | −0.402943 | + | 0.697917i | ||||
\(987\) | 0.547361 | − | 12.2097i | 0.0174227 | − | 0.388639i | ||||
\(988\) | −5.32606 | − | 9.22500i | −0.169444 | − | 0.293486i | ||||
\(989\) | −4.53170 | − | 7.84914i | −0.144100 | − | 0.249588i | ||||
\(990\) | 15.6054 | − | 4.69647i | 0.495973 | − | 0.149264i | ||||
\(991\) | −28.5783 | + | 49.4990i | −0.907819 | + | 1.57239i | −0.0907302 | + | 0.995876i | \(0.528920\pi\) |
−0.817088 | + | 0.576512i | \(0.804413\pi\) | |||||||
\(992\) | −7.09945 | + | 12.2966i | −0.225408 | + | 0.390418i | ||||
\(993\) | −7.98037 | − | 10.0779i | −0.253249 | − | 0.319812i | ||||
\(994\) | −69.3496 | + | 23.9583i | −2.19964 | + | 0.759910i | ||||
\(995\) | 8.25044 | − | 14.2902i | 0.261556 | − | 0.453029i | ||||
\(996\) | −8.73615 | − | 11.0323i | −0.276815 | − | 0.349572i | ||||
\(997\) | 3.01322 | 0.0954297 | 0.0477149 | − | 0.998861i | \(-0.484806\pi\) | ||||
0.0477149 | + | 0.998861i | \(0.484806\pi\) | |||||||
\(998\) | −16.3553 | + | 28.3283i | −0.517719 | + | 0.896716i | ||||
\(999\) | 15.4245 | + | 10.7508i | 0.488011 | + | 0.340139i |
(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 | 693.2.k.c.67.35 | ✓ | 80 | |
7.2 | even | 3 | 693.2.l.c.562.6 | yes | 80 | ||
9.7 | even | 3 | 693.2.l.c.529.6 | yes | 80 | ||
63.16 | even | 3 | inner | 693.2.k.c.331.35 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.2.k.c.67.35 | ✓ | 80 | 1.1 | even | 1 | trivial | |
693.2.k.c.331.35 | yes | 80 | 63.16 | even | 3 | inner | |
693.2.l.c.529.6 | yes | 80 | 9.7 | even | 3 | ||
693.2.l.c.562.6 | yes | 80 | 7.2 | even | 3 |