Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(49,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.q (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.7 | ||
Root | \(0.0996880 + 0.372041i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.49 |
Dual form | 570.2.q.c.349.7 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.78590 | − | 1.34557i | −0.798678 | − | 0.601759i | ||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | − | 2.32136i | − | 0.877391i | −0.898636 | − | 0.438696i | \(-0.855441\pi\) | ||
0.898636 | − | 0.438696i | \(-0.144559\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −0.873846 | − | 2.05825i | −0.276334 | − | 0.650876i | ||||
\(11\) | −2.85165 | −0.859804 | −0.429902 | − | 0.902875i | \(-0.641452\pi\) | ||||
−0.429902 | + | 0.902875i | \(0.641452\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −5.20277 | + | 3.00382i | −1.44299 | + | 0.833110i | −0.998048 | − | 0.0624492i | \(-0.980109\pi\) |
−0.444941 | + | 0.895560i | \(0.646776\pi\) | |||||||
\(14\) | 1.16068 | − | 2.01036i | 0.310205 | − | 0.537290i | ||||
\(15\) | 0.873846 | + | 2.05825i | 0.225626 | + | 0.531438i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.79487 | − | 2.19097i | −0.920391 | − | 0.531388i | −0.0366311 | − | 0.999329i | \(-0.511663\pi\) |
−0.883760 | + | 0.467941i | \(0.844996\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −2.63121 | + | 3.47516i | −0.603641 | + | 0.797256i | ||||
\(20\) | 0.272353 | − | 2.21942i | 0.0608999 | − | 0.496277i | ||||
\(21\) | −1.16068 | + | 2.01036i | −0.253281 | + | 0.438696i | ||||
\(22\) | −2.46960 | − | 1.42582i | −0.526520 | − | 0.303987i | ||||
\(23\) | 4.36172 | − | 2.51824i | 0.909481 | − | 0.525089i | 0.0292169 | − | 0.999573i | \(-0.490699\pi\) |
0.880264 | + | 0.474484i | \(0.157365\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 1.37886 | + | 4.80612i | 0.275772 | + | 0.961223i | ||||
\(26\) | −6.00764 | −1.17820 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.01036 | − | 1.16068i | 0.379922 | − | 0.219348i | ||||
\(29\) | −4.41039 | − | 7.63902i | −0.818989 | − | 1.41853i | −0.906428 | − | 0.422360i | \(-0.861202\pi\) |
0.0874397 | − | 0.996170i | \(-0.472131\pi\) | |||||||
\(30\) | −0.272353 | + | 2.21942i | −0.0497246 | + | 0.405209i | ||||
\(31\) | −0.685205 | −0.123066 | −0.0615332 | − | 0.998105i | \(-0.519599\pi\) | ||||
−0.0615332 | + | 0.998105i | \(0.519599\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 2.46960 | + | 1.42582i | 0.429902 | + | 0.248204i | ||||
\(34\) | −2.19097 | − | 3.79487i | −0.375748 | − | 0.650815i | ||||
\(35\) | −3.12356 | + | 4.14571i | −0.527978 | + | 0.700753i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | − | 7.79872i | − | 1.28210i | −0.767499 | − | 0.641050i | \(-0.778499\pi\) | ||
0.767499 | − | 0.641050i | \(-0.221501\pi\) | |||||||
\(38\) | −4.01627 | + | 1.69397i | −0.651526 | + | 0.274799i | ||||
\(39\) | 6.00764 | 0.961993 | ||||||||
\(40\) | 1.34557 | − | 1.78590i | 0.212754 | − | 0.282375i | ||||
\(41\) | 2.58128 | − | 4.47091i | 0.403128 | − | 0.698239i | −0.590973 | − | 0.806691i | \(-0.701256\pi\) |
0.994102 | + | 0.108452i | \(0.0345895\pi\) | |||||||
\(42\) | −2.01036 | + | 1.16068i | −0.310205 | + | 0.179097i | ||||
\(43\) | −2.24057 | − | 1.29360i | −0.341684 | − | 0.197271i | 0.319332 | − | 0.947643i | \(-0.396541\pi\) |
−0.661017 | + | 0.750371i | \(0.729875\pi\) | |||||||
\(44\) | −1.42582 | − | 2.46960i | −0.214951 | − | 0.372306i | ||||
\(45\) | 0.272353 | − | 2.21942i | 0.0405999 | − | 0.330852i | ||||
\(46\) | 5.03648 | 0.742588 | ||||||||
\(47\) | −6.83132 | + | 3.94406i | −0.996450 | + | 0.575301i | −0.907196 | − | 0.420708i | \(-0.861782\pi\) |
−0.0892540 | + | 0.996009i | \(0.528448\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | 1.61129 | 0.230184 | ||||||||
\(50\) | −1.20893 | + | 4.85165i | −0.170968 | + | 0.686127i | ||||
\(51\) | 2.19097 | + | 3.79487i | 0.306797 | + | 0.531388i | ||||
\(52\) | −5.20277 | − | 3.00382i | −0.721495 | − | 0.416555i | ||||
\(53\) | 4.86905 | − | 2.81115i | 0.668815 | − | 0.386141i | −0.126812 | − | 0.991927i | \(-0.540475\pi\) |
0.795628 | + | 0.605786i | \(0.207141\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 5.09275 | + | 3.83710i | 0.686706 | + | 0.517395i | ||||
\(56\) | 2.32136 | 0.310205 | ||||||||
\(57\) | 4.01627 | − | 1.69397i | 0.531968 | − | 0.224372i | ||||
\(58\) | − | 8.82078i | − | 1.15822i | ||||||
\(59\) | −0.724643 | + | 1.25512i | −0.0943405 | + | 0.163403i | −0.909333 | − | 0.416069i | \(-0.863408\pi\) |
0.814993 | + | 0.579471i | \(0.196741\pi\) | |||||||
\(60\) | −1.34557 | + | 1.78590i | −0.173713 | + | 0.230558i | ||||
\(61\) | 5.40264 | + | 9.35765i | 0.691737 | + | 1.19812i | 0.971268 | + | 0.237987i | \(0.0764876\pi\) |
−0.279531 | + | 0.960137i | \(0.590179\pi\) | |||||||
\(62\) | −0.593405 | − | 0.342602i | −0.0753625 | − | 0.0435105i | ||||
\(63\) | 2.01036 | − | 1.16068i | 0.253281 | − | 0.146232i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 13.3335 | + | 1.63620i | 1.65382 | + | 0.202945i | ||||
\(66\) | 1.42582 | + | 2.46960i | 0.175507 | + | 0.303987i | ||||
\(67\) | −5.89514 | + | 3.40356i | −0.720206 | + | 0.415811i | −0.814829 | − | 0.579702i | \(-0.803169\pi\) |
0.0946224 | + | 0.995513i | \(0.469836\pi\) | |||||||
\(68\) | − | 4.38194i | − | 0.531388i | ||||||
\(69\) | −5.03648 | −0.606321 | ||||||||
\(70\) | −4.77794 | + | 2.02851i | −0.571073 | + | 0.242453i | ||||
\(71\) | 1.15149 | − | 1.99443i | 0.136656 | − | 0.236696i | −0.789573 | − | 0.613657i | \(-0.789698\pi\) |
0.926229 | + | 0.376961i | \(0.123031\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 5.38195 | + | 3.10727i | 0.629909 | + | 0.363678i | 0.780717 | − | 0.624885i | \(-0.214854\pi\) |
−0.150808 | + | 0.988563i | \(0.548187\pi\) | |||||||
\(74\) | 3.89936 | − | 6.75389i | 0.453291 | − | 0.785123i | ||||
\(75\) | 1.20893 | − | 4.85165i | 0.139595 | − | 0.560220i | ||||
\(76\) | −4.32518 | − | 0.541114i | −0.496132 | − | 0.0620700i | ||||
\(77\) | 6.61970i | 0.754385i | ||||||||
\(78\) | 5.20277 | + | 3.00382i | 0.589098 | + | 0.340116i | ||||
\(79\) | 2.00683 | − | 3.47593i | 0.225786 | − | 0.391072i | −0.730769 | − | 0.682625i | \(-0.760838\pi\) |
0.956555 | + | 0.291552i | \(0.0941718\pi\) | |||||||
\(80\) | 2.05825 | − | 0.873846i | 0.230119 | − | 0.0976989i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.47091 | − | 2.58128i | 0.493729 | − | 0.285055i | ||||
\(83\) | 12.2192i | 1.34123i | 0.741806 | + | 0.670614i | \(0.233969\pi\) | ||||
−0.741806 | + | 0.670614i | \(0.766031\pi\) | |||||||
\(84\) | −2.32136 | −0.253281 | ||||||||
\(85\) | 3.82914 | + | 9.01912i | 0.415328 | + | 0.978261i | ||||
\(86\) | −1.29360 | − | 2.24057i | −0.139492 | − | 0.241607i | ||||
\(87\) | 8.82078i | 0.945687i | ||||||||
\(88\) | − | 2.85165i | − | 0.303987i | ||||||
\(89\) | −4.34444 | − | 7.52479i | −0.460510 | − | 0.797626i | 0.538477 | − | 0.842640i | \(-0.319000\pi\) |
−0.998986 | + | 0.0450142i | \(0.985667\pi\) | |||||||
\(90\) | 1.34557 | − | 1.78590i | 0.141836 | − | 0.188250i | ||||
\(91\) | 6.97295 | + | 12.0775i | 0.730964 | + | 1.26607i | ||||
\(92\) | 4.36172 | + | 2.51824i | 0.454740 | + | 0.262545i | ||||
\(93\) | 0.593405 | + | 0.342602i | 0.0615332 | + | 0.0355262i | ||||
\(94\) | −7.88813 | −0.813598 | ||||||||
\(95\) | 9.37516 | − | 2.66579i | 0.961871 | − | 0.273505i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −5.79684 | − | 3.34681i | −0.588580 | − | 0.339817i | 0.175956 | − | 0.984398i | \(-0.443698\pi\) |
−0.764536 | + | 0.644581i | \(0.777032\pi\) | |||||||
\(98\) | 1.39542 | + | 0.805646i | 0.140959 | + | 0.0813825i | ||||
\(99\) | −1.42582 | − | 2.46960i | −0.143301 | − | 0.248204i | ||||
\(100\) | −3.47279 | + | 3.59719i | −0.347279 | + | 0.359719i | ||||
\(101\) | −7.02206 | − | 12.1626i | −0.698721 | − | 1.21022i | −0.968910 | − | 0.247413i | \(-0.920419\pi\) |
0.270189 | − | 0.962807i | \(-0.412914\pi\) | |||||||
\(102\) | 4.38194i | 0.433876i | ||||||||
\(103\) | 14.0958i | 1.38890i | 0.719542 | + | 0.694449i | \(0.244352\pi\) | ||||
−0.719542 | + | 0.694449i | \(0.755648\pi\) | |||||||
\(104\) | −3.00382 | − | 5.20277i | −0.294549 | − | 0.510174i | ||||
\(105\) | 4.77794 | − | 2.02851i | 0.466279 | − | 0.197962i | ||||
\(106\) | 5.62229 | 0.546085 | ||||||||
\(107\) | − | 16.7729i | − | 1.62150i | −0.585395 | − | 0.810748i | \(-0.699060\pi\) | ||
0.585395 | − | 0.810748i | \(-0.300940\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 4.45191 | − | 7.71093i | 0.426416 | − | 0.738573i | −0.570136 | − | 0.821550i | \(-0.693109\pi\) |
0.996551 | + | 0.0829770i | \(0.0264428\pi\) | |||||||
\(110\) | 2.49190 | + | 5.86941i | 0.237593 | + | 0.559626i | ||||
\(111\) | −3.89936 | + | 6.75389i | −0.370111 | + | 0.641050i | ||||
\(112\) | 2.01036 | + | 1.16068i | 0.189961 | + | 0.109674i | ||||
\(113\) | 11.8870i | 1.11824i | 0.829087 | + | 0.559120i | \(0.188861\pi\) | ||||
−0.829087 | + | 0.559120i | \(0.811139\pi\) | |||||||
\(114\) | 4.32518 | + | 0.541114i | 0.405090 | + | 0.0506799i | ||||
\(115\) | −11.1781 | − | 1.37170i | −1.04236 | − | 0.127912i | ||||
\(116\) | 4.41039 | − | 7.63902i | 0.409494 | − | 0.709265i | ||||
\(117\) | −5.20277 | − | 3.00382i | −0.480997 | − | 0.277703i | ||||
\(118\) | −1.25512 | + | 0.724643i | −0.115543 | + | 0.0667088i | ||||
\(119\) | −5.08602 | + | 8.80925i | −0.466235 | + | 0.807543i | ||||
\(120\) | −2.05825 | + | 0.873846i | −0.187892 | + | 0.0797708i | ||||
\(121\) | −2.86810 | −0.260737 | ||||||||
\(122\) | 10.8053i | 0.978264i | ||||||||
\(123\) | −4.47091 | + | 2.58128i | −0.403128 | + | 0.232746i | ||||
\(124\) | −0.342602 | − | 0.593405i | −0.0307666 | − | 0.0532893i | ||||
\(125\) | 4.00448 | − | 10.4386i | 0.358172 | − | 0.933656i | ||||
\(126\) | 2.32136 | 0.206803 | ||||||||
\(127\) | 7.72660 | − | 4.46095i | 0.685625 | − | 0.395846i | −0.116346 | − | 0.993209i | \(-0.537118\pi\) |
0.801971 | + | 0.597363i | \(0.203785\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 1.29360 | + | 2.24057i | 0.113895 | + | 0.197271i | ||||
\(130\) | 10.7290 | + | 8.08373i | 0.940999 | + | 0.708990i | ||||
\(131\) | 0.0274319 | − | 0.0475134i | 0.00239673 | − | 0.00415127i | −0.864825 | − | 0.502074i | \(-0.832570\pi\) |
0.867221 | + | 0.497923i | \(0.165904\pi\) | |||||||
\(132\) | 2.85165i | 0.248204i | ||||||||
\(133\) | 8.06710 | + | 6.10798i | 0.699506 | + | 0.529629i | ||||
\(134\) | −6.80712 | −0.588046 | ||||||||
\(135\) | −1.34557 | + | 1.78590i | −0.115809 | + | 0.153706i | ||||
\(136\) | 2.19097 | − | 3.79487i | 0.187874 | − | 0.325407i | ||||
\(137\) | 15.5732 | − | 8.99119i | 1.33051 | − | 0.768169i | 0.345131 | − | 0.938555i | \(-0.387835\pi\) |
0.985377 | + | 0.170386i | \(0.0545013\pi\) | |||||||
\(138\) | −4.36172 | − | 2.51824i | −0.371294 | − | 0.214367i | ||||
\(139\) | −10.3327 | − | 17.8967i | −0.876405 | − | 1.51798i | −0.855258 | − | 0.518202i | \(-0.826601\pi\) |
−0.0211474 | − | 0.999776i | \(-0.506732\pi\) | |||||||
\(140\) | −5.15207 | − | 0.632228i | −0.435429 | − | 0.0534330i | ||||
\(141\) | 7.88813 | 0.664300 | ||||||||
\(142\) | 1.99443 | − | 1.15149i | 0.167369 | − | 0.0966306i | ||||
\(143\) | 14.8365 | − | 8.56584i | 1.24069 | − | 0.716312i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −2.40236 | + | 19.5770i | −0.199505 | + | 1.62578i | ||||
\(146\) | 3.10727 | + | 5.38195i | 0.257159 | + | 0.445413i | ||||
\(147\) | −1.39542 | − | 0.805646i | −0.115092 | − | 0.0664485i | ||||
\(148\) | 6.75389 | − | 3.89936i | 0.555166 | − | 0.320525i | ||||
\(149\) | −1.92651 | + | 3.33682i | −0.157826 | + | 0.273363i | −0.934084 | − | 0.357052i | \(-0.883782\pi\) |
0.776258 | + | 0.630415i | \(0.217115\pi\) | |||||||
\(150\) | 3.47279 | − | 3.59719i | 0.283552 | − | 0.293709i | ||||
\(151\) | 7.77324 | 0.632577 | 0.316289 | − | 0.948663i | \(-0.397563\pi\) | ||||
0.316289 | + | 0.948663i | \(0.397563\pi\) | |||||||
\(152\) | −3.47516 | − | 2.63121i | −0.281873 | − | 0.213419i | ||||
\(153\) | − | 4.38194i | − | 0.354259i | ||||||
\(154\) | −3.30985 | + | 5.73283i | −0.266715 | + | 0.461964i | ||||
\(155\) | 1.22371 | + | 0.921994i | 0.0982904 | + | 0.0740563i | ||||
\(156\) | 3.00382 | + | 5.20277i | 0.240498 | + | 0.416555i | ||||
\(157\) | 16.6929 | + | 9.63765i | 1.33224 | + | 0.769169i | 0.985642 | − | 0.168846i | \(-0.0540040\pi\) |
0.346596 | + | 0.938014i | \(0.387337\pi\) | |||||||
\(158\) | 3.47593 | − | 2.00683i | 0.276530 | − | 0.159655i | ||||
\(159\) | −5.62229 | −0.445877 | ||||||||
\(160\) | 2.21942 | + | 0.272353i | 0.175461 | + | 0.0215314i | ||||
\(161\) | −5.84574 | − | 10.1251i | −0.460709 | − | 0.797971i | ||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | 15.9168i | 1.24670i | 0.781944 | + | 0.623348i | \(0.214228\pi\) | ||||
−0.781944 | + | 0.623348i | \(0.785772\pi\) | |||||||
\(164\) | 5.16256 | 0.403128 | ||||||||
\(165\) | −2.49190 | − | 5.86941i | −0.193994 | − | 0.456933i | ||||
\(166\) | −6.10958 | + | 10.5821i | −0.474196 | + | 0.821331i | ||||
\(167\) | −16.4675 | + | 9.50754i | −1.27430 | + | 0.735716i | −0.975794 | − | 0.218693i | \(-0.929821\pi\) |
−0.298503 | + | 0.954409i | \(0.596487\pi\) | |||||||
\(168\) | −2.01036 | − | 1.16068i | −0.155102 | − | 0.0895484i | ||||
\(169\) | 11.5459 | − | 19.9981i | 0.888146 | − | 1.53831i | ||||
\(170\) | −1.19343 | + | 9.72536i | −0.0915321 | + | 0.745901i | ||||
\(171\) | −4.32518 | − | 0.541114i | −0.330755 | − | 0.0413800i | ||||
\(172\) | − | 2.58719i | − | 0.197271i | ||||||
\(173\) | −12.3792 | − | 7.14712i | −0.941172 | − | 0.543386i | −0.0508444 | − | 0.998707i | \(-0.516191\pi\) |
−0.890327 | + | 0.455321i | \(0.849525\pi\) | |||||||
\(174\) | −4.41039 | + | 7.63902i | −0.334351 | + | 0.579112i | ||||
\(175\) | 11.1567 | − | 3.20083i | 0.843369 | − | 0.241960i | ||||
\(176\) | 1.42582 | − | 2.46960i | 0.107476 | − | 0.186153i | ||||
\(177\) | 1.25512 | − | 0.724643i | 0.0943405 | − | 0.0544675i | ||||
\(178\) | − | 8.68888i | − | 0.651259i | ||||||
\(179\) | −6.66682 | −0.498301 | −0.249151 | − | 0.968465i | \(-0.580151\pi\) | ||||
−0.249151 | + | 0.968465i | \(0.580151\pi\) | |||||||
\(180\) | 2.05825 | − | 0.873846i | 0.153413 | − | 0.0651326i | ||||
\(181\) | −3.06793 | − | 5.31382i | −0.228038 | − | 0.394973i | 0.729189 | − | 0.684313i | \(-0.239898\pi\) |
−0.957226 | + | 0.289340i | \(0.906564\pi\) | |||||||
\(182\) | 13.9459i | 1.03374i | ||||||||
\(183\) | − | 10.8053i | − | 0.798749i | ||||||
\(184\) | 2.51824 | + | 4.36172i | 0.185647 | + | 0.321550i | ||||
\(185\) | −10.4937 | + | 13.9277i | −0.771516 | + | 1.02399i | ||||
\(186\) | 0.342602 | + | 0.593405i | 0.0251208 | + | 0.0435105i | ||||
\(187\) | 10.8216 | + | 6.24787i | 0.791356 | + | 0.456890i | ||||
\(188\) | −6.83132 | − | 3.94406i | −0.498225 | − | 0.287650i | ||||
\(189\) | −2.32136 | −0.168854 | ||||||||
\(190\) | 9.45202 | + | 2.37893i | 0.685722 | + | 0.172586i | ||||
\(191\) | −18.8448 | −1.36356 | −0.681780 | − | 0.731557i | \(-0.738794\pi\) | ||||
−0.681780 | + | 0.731557i | \(0.738794\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | −14.3105 | − | 8.26218i | −1.03009 | − | 0.594725i | −0.113082 | − | 0.993586i | \(-0.536072\pi\) |
−0.917012 | + | 0.398861i | \(0.869406\pi\) | |||||||
\(194\) | −3.34681 | − | 5.79684i | −0.240287 | − | 0.416189i | ||||
\(195\) | −10.7290 | − | 8.08373i | −0.768322 | − | 0.578888i | ||||
\(196\) | 0.805646 | + | 1.39542i | 0.0575461 | + | 0.0996728i | ||||
\(197\) | − | 6.90254i | − | 0.491786i | −0.969297 | − | 0.245893i | \(-0.920919\pi\) | ||
0.969297 | − | 0.245893i | \(-0.0790811\pi\) | |||||||
\(198\) | − | 2.85165i | − | 0.202658i | ||||||
\(199\) | 3.26514 | + | 5.65540i | 0.231460 | + | 0.400900i | 0.958238 | − | 0.285972i | \(-0.0923164\pi\) |
−0.726778 | + | 0.686872i | \(0.758983\pi\) | |||||||
\(200\) | −4.80612 | + | 1.37886i | −0.339844 | + | 0.0975001i | ||||
\(201\) | 6.80712 | 0.480137 | ||||||||
\(202\) | − | 14.0441i | − | 0.988141i | ||||||
\(203\) | −17.7329 | + | 10.2381i | −1.24461 | + | 0.718573i | ||||
\(204\) | −2.19097 | + | 3.79487i | −0.153398 | + | 0.265694i | ||||
\(205\) | −10.6258 | + | 4.51128i | −0.742141 | + | 0.315082i | ||||
\(206\) | −7.04788 | + | 12.2073i | −0.491049 | + | 0.850522i | ||||
\(207\) | 4.36172 | + | 2.51824i | 0.303160 | + | 0.175030i | ||||
\(208\) | − | 6.00764i | − | 0.416555i | ||||||
\(209\) | 7.50328 | − | 9.90993i | 0.519013 | − | 0.685484i | ||||
\(210\) | 5.15207 | + | 0.632228i | 0.355527 | + | 0.0436279i | ||||
\(211\) | −11.1943 | + | 19.3891i | −0.770648 | + | 1.33480i | 0.166560 | + | 0.986031i | \(0.446734\pi\) |
−0.937208 | + | 0.348771i | \(0.886599\pi\) | |||||||
\(212\) | 4.86905 | + | 2.81115i | 0.334408 | + | 0.193070i | ||||
\(213\) | −1.99443 | + | 1.15149i | −0.136656 | + | 0.0788986i | ||||
\(214\) | 8.38645 | − | 14.5258i | 0.573286 | − | 0.992960i | ||||
\(215\) | 2.26081 | + | 5.32509i | 0.154186 | + | 0.363168i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.59061i | 0.107977i | ||||||||
\(218\) | 7.71093 | − | 4.45191i | 0.522250 | − | 0.301521i | ||||
\(219\) | −3.10727 | − | 5.38195i | −0.209970 | − | 0.363678i | ||||
\(220\) | −0.776654 | + | 6.32900i | −0.0523620 | + | 0.426701i | ||||
\(221\) | 26.3251 | 1.77082 | ||||||||
\(222\) | −6.75389 | + | 3.89936i | −0.453291 | + | 0.261708i | ||||
\(223\) | 1.62511 | + | 0.938256i | 0.108825 | + | 0.0628302i | 0.553425 | − | 0.832899i | \(-0.313321\pi\) |
−0.444600 | + | 0.895729i | \(0.646654\pi\) | |||||||
\(224\) | 1.16068 | + | 2.01036i | 0.0775512 | + | 0.134323i | ||||
\(225\) | −3.47279 | + | 3.59719i | −0.231519 | + | 0.239812i | ||||
\(226\) | −5.94352 | + | 10.2945i | −0.395357 | + | 0.684779i | ||||
\(227\) | 20.3703i | 1.35203i | 0.736890 | + | 0.676013i | \(0.236294\pi\) | ||||
−0.736890 | + | 0.676013i | \(0.763706\pi\) | |||||||
\(228\) | 3.47516 | + | 2.63121i | 0.230148 | + | 0.174256i | ||||
\(229\) | −10.7813 | −0.712449 | −0.356224 | − | 0.934400i | \(-0.615936\pi\) | ||||
−0.356224 | + | 0.934400i | \(0.615936\pi\) | |||||||
\(230\) | −8.99463 | − | 6.77695i | −0.593089 | − | 0.446859i | ||||
\(231\) | 3.30985 | − | 5.73283i | 0.217772 | − | 0.377192i | ||||
\(232\) | 7.63902 | − | 4.41039i | 0.501526 | − | 0.289556i | ||||
\(233\) | −11.7576 | − | 6.78823i | −0.770263 | − | 0.444711i | 0.0627056 | − | 0.998032i | \(-0.480027\pi\) |
−0.832968 | + | 0.553321i | \(0.813360\pi\) | |||||||
\(234\) | −3.00382 | − | 5.20277i | −0.196366 | − | 0.340116i | ||||
\(235\) | 17.5071 | + | 2.14835i | 1.14203 | + | 0.140143i | ||||
\(236\) | −1.44929 | −0.0943405 | ||||||||
\(237\) | −3.47593 | + | 2.00683i | −0.225786 | + | 0.130357i | ||||
\(238\) | −8.80925 | + | 5.08602i | −0.571019 | + | 0.329678i | ||||
\(239\) | 2.08081 | 0.134596 | 0.0672981 | − | 0.997733i | \(-0.478562\pi\) | ||||
0.0672981 | + | 0.997733i | \(0.478562\pi\) | |||||||
\(240\) | −2.21942 | − | 0.272353i | −0.143263 | − | 0.0175803i | ||||
\(241\) | −8.51317 | − | 14.7453i | −0.548382 | − | 0.949825i | −0.998386 | − | 0.0567985i | \(-0.981911\pi\) |
0.450004 | − | 0.893027i | \(-0.351423\pi\) | |||||||
\(242\) | −2.48385 | − | 1.43405i | −0.159668 | − | 0.0921843i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −5.40264 | + | 9.35765i | −0.345869 | + | 0.599062i | ||||
\(245\) | −2.87760 | − | 2.16811i | −0.183843 | − | 0.138516i | ||||
\(246\) | −5.16256 | −0.329153 | ||||||||
\(247\) | 3.25082 | − | 25.9842i | 0.206845 | − | 1.65333i | ||||
\(248\) | − | 0.685205i | − | 0.0435105i | ||||||
\(249\) | 6.10958 | − | 10.5821i | 0.387179 | − | 0.670614i | ||||
\(250\) | 8.68728 | − | 7.03784i | 0.549432 | − | 0.445112i | ||||
\(251\) | 9.62571 | + | 16.6722i | 0.607569 | + | 1.05234i | 0.991640 | + | 0.129037i | \(0.0411886\pi\) |
−0.384070 | + | 0.923304i | \(0.625478\pi\) | |||||||
\(252\) | 2.01036 | + | 1.16068i | 0.126641 | + | 0.0731159i | ||||
\(253\) | −12.4381 | + | 7.18113i | −0.781976 | + | 0.451474i | ||||
\(254\) | 8.92191 | 0.559810 | ||||||||
\(255\) | 1.19343 | − | 9.72536i | 0.0747356 | − | 0.609026i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 15.3212 | − | 8.84568i | 0.955708 | − | 0.551779i | 0.0608589 | − | 0.998146i | \(-0.480616\pi\) |
0.894850 | + | 0.446368i | \(0.147283\pi\) | |||||||
\(258\) | 2.58719i | 0.161072i | ||||||||
\(259\) | −18.1036 | −1.12490 | ||||||||
\(260\) | 5.24975 | + | 12.3652i | 0.325576 | + | 0.766859i | ||||
\(261\) | 4.41039 | − | 7.63902i | 0.272996 | − | 0.472843i | ||||
\(262\) | 0.0475134 | − | 0.0274319i | 0.00293539 | − | 0.00169475i | ||||
\(263\) | −9.98291 | − | 5.76364i | −0.615573 | − | 0.355401i | 0.159570 | − | 0.987187i | \(-0.448989\pi\) |
−0.775143 | + | 0.631785i | \(0.782322\pi\) | |||||||
\(264\) | −1.42582 | + | 2.46960i | −0.0877534 | + | 0.151993i | ||||
\(265\) | −12.4782 | − | 1.53125i | −0.766532 | − | 0.0940637i | ||||
\(266\) | 3.93232 | + | 9.32321i | 0.241106 | + | 0.571643i | ||||
\(267\) | 8.68888i | 0.531751i | ||||||||
\(268\) | −5.89514 | − | 3.40356i | −0.360103 | − | 0.207906i | ||||
\(269\) | 10.2776 | − | 17.8013i | 0.626635 | − | 1.08536i | −0.361587 | − | 0.932338i | \(-0.617765\pi\) |
0.988222 | − | 0.153025i | \(-0.0489016\pi\) | |||||||
\(270\) | −2.05825 | + | 0.873846i | −0.125261 | + | 0.0531805i | ||||
\(271\) | 12.9912 | − | 22.5014i | 0.789159 | − | 1.36686i | −0.137324 | − | 0.990526i | \(-0.543850\pi\) |
0.926483 | − | 0.376337i | \(-0.122816\pi\) | |||||||
\(272\) | 3.79487 | − | 2.19097i | 0.230098 | − | 0.132847i | ||||
\(273\) | − | 13.9459i | − | 0.844044i | ||||||
\(274\) | 17.9824 | 1.08636 | ||||||||
\(275\) | −3.93202 | − | 13.7053i | −0.237110 | − | 0.826464i | ||||
\(276\) | −2.51824 | − | 4.36172i | −0.151580 | − | 0.262545i | ||||
\(277\) | 4.14296i | 0.248926i | 0.992224 | + | 0.124463i | \(0.0397208\pi\) | ||||
−0.992224 | + | 0.124463i | \(0.960279\pi\) | |||||||
\(278\) | − | 20.6653i | − | 1.23942i | ||||||
\(279\) | −0.342602 | − | 0.593405i | −0.0205111 | − | 0.0355262i | ||||
\(280\) | −4.14571 | − | 3.12356i | −0.247754 | − | 0.186668i | ||||
\(281\) | −4.29844 | − | 7.44511i | −0.256423 | − | 0.444138i | 0.708858 | − | 0.705351i | \(-0.249211\pi\) |
−0.965281 | + | 0.261213i | \(0.915877\pi\) | |||||||
\(282\) | 6.83132 | + | 3.94406i | 0.406799 | + | 0.234866i | ||||
\(283\) | 12.4490 | + | 7.18742i | 0.740015 | + | 0.427248i | 0.822075 | − | 0.569379i | \(-0.192816\pi\) |
−0.0820596 | + | 0.996627i | \(0.526150\pi\) | |||||||
\(284\) | 2.30297 | 0.136656 | ||||||||
\(285\) | −9.45202 | − | 2.37893i | −0.559889 | − | 0.140916i | ||||
\(286\) | 17.1317 | 1.01302 | ||||||||
\(287\) | −10.3786 | − | 5.99208i | −0.612628 | − | 0.353701i | ||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | 1.10069 | + | 1.90644i | 0.0647462 | + | 0.112144i | ||||
\(290\) | −11.8690 | + | 15.7530i | −0.696972 | + | 0.925048i | ||||
\(291\) | 3.34681 | + | 5.79684i | 0.196193 | + | 0.339817i | ||||
\(292\) | 6.21454i | 0.363678i | ||||||||
\(293\) | − | 8.47490i | − | 0.495109i | −0.968874 | − | 0.247554i | \(-0.920373\pi\) | ||
0.968874 | − | 0.247554i | \(-0.0796269\pi\) | |||||||
\(294\) | −0.805646 | − | 1.39542i | −0.0469862 | − | 0.0813825i | ||||
\(295\) | 2.98299 | − | 1.26645i | 0.173677 | − | 0.0737357i | ||||
\(296\) | 7.79872 | 0.453291 | ||||||||
\(297\) | 2.85165i | 0.165469i | ||||||||
\(298\) | −3.33682 | + | 1.92651i | −0.193297 | + | 0.111600i | ||||
\(299\) | −15.1287 | + | 26.2037i | −0.874914 | + | 1.51540i | ||||
\(300\) | 4.80612 | − | 1.37886i | 0.277481 | − | 0.0796085i | ||||
\(301\) | −3.00290 | + | 5.20118i | −0.173084 | + | 0.299791i | ||||
\(302\) | 6.73182 | + | 3.88662i | 0.387373 | + | 0.223650i | ||||
\(303\) | 14.0441i | 0.806814i | ||||||||
\(304\) | −1.69397 | − | 4.01627i | −0.0971560 | − | 0.230349i | ||||
\(305\) | 2.94285 | − | 23.9814i | 0.168507 | − | 1.37317i | ||||
\(306\) | 2.19097 | − | 3.79487i | 0.125249 | − | 0.216938i | ||||
\(307\) | −18.6780 | − | 10.7838i | −1.06601 | − | 0.615462i | −0.138922 | − | 0.990303i | \(-0.544364\pi\) |
−0.927089 | + | 0.374841i | \(0.877697\pi\) | |||||||
\(308\) | −5.73283 | + | 3.30985i | −0.326658 | + | 0.188596i | ||||
\(309\) | 7.04788 | − | 12.2073i | 0.400940 | − | 0.694449i | ||||
\(310\) | 0.598763 | + | 1.41032i | 0.0340074 | + | 0.0801009i | ||||
\(311\) | 6.25433 | 0.354650 | 0.177325 | − | 0.984152i | \(-0.443256\pi\) | ||||
0.177325 | + | 0.984152i | \(0.443256\pi\) | |||||||
\(312\) | 6.00764i | 0.340116i | ||||||||
\(313\) | −15.3732 | + | 8.87575i | −0.868947 | + | 0.501687i | −0.866998 | − | 0.498311i | \(-0.833954\pi\) |
−0.00194901 | + | 0.999998i | \(0.500620\pi\) | |||||||
\(314\) | 9.63765 | + | 16.6929i | 0.543884 | + | 0.942035i | ||||
\(315\) | −5.15207 | − | 0.632228i | −0.290286 | − | 0.0356220i | ||||
\(316\) | 4.01365 | 0.225786 | ||||||||
\(317\) | −0.640437 | + | 0.369757i | −0.0359705 | + | 0.0207676i | −0.517877 | − | 0.855455i | \(-0.673278\pi\) |
0.481907 | + | 0.876222i | \(0.339944\pi\) | |||||||
\(318\) | −4.86905 | − | 2.81115i | −0.273043 | − | 0.157641i | ||||
\(319\) | 12.5769 | + | 21.7838i | 0.704170 | + | 1.21966i | ||||
\(320\) | 1.78590 | + | 1.34557i | 0.0998347 | + | 0.0752199i | ||||
\(321\) | −8.38645 | + | 14.5258i | −0.468086 | + | 0.810748i | ||||
\(322\) | − | 11.6915i | − | 0.651540i | ||||||
\(323\) | 17.5991 | − | 7.42288i | 0.979238 | − | 0.413020i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −21.6106 | − | 20.8633i | −1.19874 | − | 1.15729i | ||||
\(326\) | −7.95838 | + | 13.7843i | −0.440774 | + | 0.763442i | ||||
\(327\) | −7.71093 | + | 4.45191i | −0.426416 | + | 0.246191i | ||||
\(328\) | 4.47091 | + | 2.58128i | 0.246865 | + | 0.142527i | ||||
\(329\) | 9.15559 | + | 15.8579i | 0.504764 | + | 0.874277i | ||||
\(330\) | 0.776654 | − | 6.32900i | 0.0427534 | − | 0.348400i | ||||
\(331\) | −4.54461 | −0.249794 | −0.124897 | − | 0.992170i | \(-0.539860\pi\) | ||||
−0.124897 | + | 0.992170i | \(0.539860\pi\) | |||||||
\(332\) | −10.5821 | + | 6.10958i | −0.580769 | + | 0.335307i | ||||
\(333\) | 6.75389 | − | 3.89936i | 0.370111 | − | 0.213683i | ||||
\(334\) | −19.0151 | −1.04046 | ||||||||
\(335\) | 15.1079 | + | 1.85394i | 0.825431 | + | 0.101291i | ||||
\(336\) | −1.16068 | − | 2.01036i | −0.0633203 | − | 0.109674i | ||||
\(337\) | −17.9486 | − | 10.3626i | −0.977722 | − | 0.564488i | −0.0761405 | − | 0.997097i | \(-0.524260\pi\) |
−0.901582 | + | 0.432609i | \(0.857593\pi\) | |||||||
\(338\) | 19.9981 | − | 11.5459i | 1.08775 | − | 0.628014i | ||||
\(339\) | 5.94352 | − | 10.2945i | 0.322808 | − | 0.559120i | ||||
\(340\) | −5.89622 | + | 7.82569i | −0.319767 | + | 0.424408i | ||||
\(341\) | 1.95396 | 0.105813 | ||||||||
\(342\) | −3.47516 | − | 2.63121i | −0.187915 | − | 0.142279i | ||||
\(343\) | − | 19.9899i | − | 1.07935i | ||||||
\(344\) | 1.29360 | − | 2.24057i | 0.0697460 | − | 0.120804i | ||||
\(345\) | 8.99463 | + | 6.77695i | 0.484255 | + | 0.364859i | ||||
\(346\) | −7.14712 | − | 12.3792i | −0.384232 | − | 0.665509i | ||||
\(347\) | −10.7406 | − | 6.20108i | −0.576585 | − | 0.332891i | 0.183190 | − | 0.983077i | \(-0.441358\pi\) |
−0.759775 | + | 0.650186i | \(0.774691\pi\) | |||||||
\(348\) | −7.63902 | + | 4.41039i | −0.409494 | + | 0.236422i | ||||
\(349\) | 14.4163 | 0.771684 | 0.385842 | − | 0.922565i | \(-0.373911\pi\) | ||||
0.385842 | + | 0.922565i | \(0.373911\pi\) | |||||||
\(350\) | 11.2624 | + | 2.80636i | 0.602002 | + | 0.150006i | ||||
\(351\) | 3.00382 | + | 5.20277i | 0.160332 | + | 0.277703i | ||||
\(352\) | 2.46960 | − | 1.42582i | 0.131630 | − | 0.0759967i | ||||
\(353\) | 35.6707i | 1.89856i | 0.314430 | + | 0.949281i | \(0.398187\pi\) | ||||
−0.314430 | + | 0.949281i | \(0.601813\pi\) | |||||||
\(354\) | 1.44929 | 0.0770287 | ||||||||
\(355\) | −4.74009 | + | 2.01244i | −0.251578 | + | 0.106809i | ||||
\(356\) | 4.34444 | − | 7.52479i | 0.230255 | − | 0.398813i | ||||
\(357\) | 8.80925 | − | 5.08602i | 0.466235 | − | 0.269181i | ||||
\(358\) | −5.77363 | − | 3.33341i | −0.305146 | − | 0.176176i | ||||
\(359\) | 1.15286 | − | 1.99682i | 0.0608457 | − | 0.105388i | −0.833998 | − | 0.551768i | \(-0.813954\pi\) |
0.894844 | + | 0.446380i | \(0.147287\pi\) | |||||||
\(360\) | 2.21942 | + | 0.272353i | 0.116974 | + | 0.0143542i | ||||
\(361\) | −5.15348 | − | 18.2877i | −0.271236 | − | 0.962513i | ||||
\(362\) | − | 6.13587i | − | 0.322494i | ||||||
\(363\) | 2.48385 | + | 1.43405i | 0.130368 | + | 0.0752682i | ||||
\(364\) | −6.97295 | + | 12.0775i | −0.365482 | + | 0.633033i | ||||
\(365\) | −5.43054 | − | 12.7911i | −0.284248 | − | 0.669515i | ||||
\(366\) | 5.40264 | − | 9.35765i | 0.282400 | − | 0.489132i | ||||
\(367\) | 9.47038 | − | 5.46773i | 0.494350 | − | 0.285413i | −0.232027 | − | 0.972709i | \(-0.574536\pi\) |
0.726377 | + | 0.687296i | \(0.241203\pi\) | |||||||
\(368\) | 5.03648i | 0.262545i | ||||||||
\(369\) | 5.16256 | 0.268752 | ||||||||
\(370\) | −16.0517 | + | 6.81487i | −0.834489 | + | 0.354288i | ||||
\(371\) | −6.52568 | − | 11.3028i | −0.338796 | − | 0.586813i | ||||
\(372\) | 0.685205i | 0.0355262i | ||||||||
\(373\) | 23.3847i | 1.21082i | 0.795915 | + | 0.605408i | \(0.206990\pi\) | ||||
−0.795915 | + | 0.605408i | \(0.793010\pi\) | |||||||
\(374\) | 6.24787 | + | 10.8216i | 0.323070 | + | 0.559573i | ||||
\(375\) | −8.68728 | + | 7.03784i | −0.448609 | + | 0.363433i | ||||
\(376\) | −3.94406 | − | 6.83132i | −0.203400 | − | 0.352298i | ||||
\(377\) | 45.8925 | + | 26.4960i | 2.36358 | + | 1.36462i | ||||
\(378\) | −2.01036 | − | 1.16068i | −0.103402 | − | 0.0596989i | ||||
\(379\) | −23.2493 | −1.19424 | −0.597118 | − | 0.802154i | \(-0.703687\pi\) | ||||
−0.597118 | + | 0.802154i | \(0.703687\pi\) | |||||||
\(380\) | 6.99622 | + | 6.78623i | 0.358899 | + | 0.348126i | ||||
\(381\) | −8.92191 | −0.457083 | ||||||||
\(382\) | −16.3200 | − | 9.42238i | −0.835006 | − | 0.482091i | ||||
\(383\) | −17.9351 | − | 10.3548i | −0.916441 | − | 0.529107i | −0.0339428 | − | 0.999424i | \(-0.510806\pi\) |
−0.882498 | + | 0.470317i | \(0.844140\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 8.90730 | − | 11.8221i | 0.453958 | − | 0.602510i | ||||
\(386\) | −8.26218 | − | 14.3105i | −0.420534 | − | 0.728386i | ||||
\(387\) | − | 2.58719i | − | 0.131514i | ||||||
\(388\) | − | 6.69361i | − | 0.339817i | ||||||
\(389\) | 18.1887 | + | 31.5037i | 0.922203 | + | 1.59730i | 0.795999 | + | 0.605297i | \(0.206946\pi\) |
0.126203 | + | 0.992004i | \(0.459721\pi\) | |||||||
\(390\) | −5.24975 | − | 12.3652i | −0.265832 | − | 0.626138i | ||||
\(391\) | −22.0695 | −1.11610 | ||||||||
\(392\) | 1.61129i | 0.0813825i | ||||||||
\(393\) | −0.0475134 | + | 0.0274319i | −0.00239673 | + | 0.00138376i | ||||
\(394\) | 3.45127 | − | 5.97778i | 0.173873 | − | 0.301156i | ||||
\(395\) | −8.26110 | + | 3.50731i | −0.415661 | + | 0.176472i | ||||
\(396\) | 1.42582 | − | 2.46960i | 0.0716504 | − | 0.124102i | ||||
\(397\) | −28.6128 | − | 16.5196i | −1.43604 | − | 0.829096i | −0.438464 | − | 0.898749i | \(-0.644477\pi\) |
−0.997571 | + | 0.0696530i | \(0.977811\pi\) | |||||||
\(398\) | 6.53029i | 0.327334i | ||||||||
\(399\) | −3.93232 | − | 9.32321i | −0.196862 | − | 0.466745i | ||||
\(400\) | −4.85165 | − | 1.20893i | −0.242582 | − | 0.0604465i | ||||
\(401\) | −10.5982 | + | 18.3566i | −0.529249 | + | 0.916685i | 0.470170 | + | 0.882576i | \(0.344193\pi\) |
−0.999418 | + | 0.0341092i | \(0.989141\pi\) | |||||||
\(402\) | 5.89514 | + | 3.40356i | 0.294023 | + | 0.169754i | ||||
\(403\) | 3.56496 | − | 2.05823i | 0.177583 | − | 0.102528i | ||||
\(404\) | 7.02206 | − | 12.1626i | 0.349361 | − | 0.605110i | ||||
\(405\) | 2.05825 | − | 0.873846i | 0.102275 | − | 0.0434217i | ||||
\(406\) | −20.4762 | −1.01622 | ||||||||
\(407\) | 22.2392i | 1.10236i | ||||||||
\(408\) | −3.79487 | + | 2.19097i | −0.187874 | + | 0.108469i | ||||
\(409\) | −5.26086 | − | 9.11207i | −0.260133 | − | 0.450563i | 0.706144 | − | 0.708068i | \(-0.250433\pi\) |
−0.966277 | + | 0.257505i | \(0.917100\pi\) | |||||||
\(410\) | −11.4579 | − | 1.40604i | −0.565865 | − | 0.0694392i | ||||
\(411\) | −17.9824 | −0.887005 | ||||||||
\(412\) | −12.2073 | + | 7.04788i | −0.601410 | + | 0.347224i | ||||
\(413\) | 2.91358 | + | 1.68216i | 0.143368 | + | 0.0827735i | ||||
\(414\) | 2.51824 | + | 4.36172i | 0.123765 | + | 0.214367i | ||||
\(415\) | 16.4418 | − | 21.8222i | 0.807096 | − | 1.07121i | ||||
\(416\) | 3.00382 | − | 5.20277i | 0.147275 | − | 0.255087i | ||||
\(417\) | 20.6653i | 1.01199i | ||||||||
\(418\) | 11.4530 | − | 4.83061i | 0.560185 | − | 0.236273i | ||||
\(419\) | −26.3874 | −1.28911 | −0.644555 | − | 0.764558i | \(-0.722957\pi\) | ||||
−0.644555 | + | 0.764558i | \(0.722957\pi\) | |||||||
\(420\) | 4.14571 | + | 3.12356i | 0.202290 | + | 0.152414i | ||||
\(421\) | −4.24202 | + | 7.34740i | −0.206743 | + | 0.358090i | −0.950687 | − | 0.310152i | \(-0.899620\pi\) |
0.743943 | + | 0.668243i | \(0.232953\pi\) | |||||||
\(422\) | −19.3891 | + | 11.1943i | −0.943847 | + | 0.544931i | ||||
\(423\) | −6.83132 | − | 3.94406i | −0.332150 | − | 0.191767i | ||||
\(424\) | 2.81115 | + | 4.86905i | 0.136521 | + | 0.236462i | ||||
\(425\) | 5.29745 | − | 21.2596i | 0.256964 | − | 1.03124i | ||||
\(426\) | −2.30297 | −0.111579 | ||||||||
\(427\) | 21.7225 | − | 12.5415i | 1.05122 | − | 0.606924i | ||||
\(428\) | 14.5258 | − | 8.38645i | 0.702129 | − | 0.405374i | ||||
\(429\) | −17.1317 | −0.827126 | ||||||||
\(430\) | −0.704628 | + | 5.74206i | −0.0339802 | + | 0.276907i | ||||
\(431\) | 9.83833 | + | 17.0405i | 0.473896 | + | 0.820811i | 0.999553 | − | 0.0298849i | \(-0.00951409\pi\) |
−0.525658 | + | 0.850696i | \(0.676181\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 12.0899 | − | 6.98010i | 0.581003 | − | 0.335442i | −0.180529 | − | 0.983570i | \(-0.557781\pi\) |
0.761532 | + | 0.648127i | \(0.224448\pi\) | |||||||
\(434\) | −0.795303 | + | 1.37751i | −0.0381758 | + | 0.0661224i | ||||
\(435\) | 11.8690 | − | 15.7530i | 0.569075 | − | 0.755299i | ||||
\(436\) | 8.90382 | 0.426416 | ||||||||
\(437\) | −2.72531 | + | 21.7837i | −0.130369 | + | 1.04205i | ||||
\(438\) | − | 6.21454i | − | 0.296942i | ||||||
\(439\) | 10.2610 | − | 17.7725i | 0.489729 | − | 0.848236i | −0.510201 | − | 0.860055i | \(-0.670429\pi\) |
0.999930 | + | 0.0118193i | \(0.00376230\pi\) | |||||||
\(440\) | −3.83710 | + | 5.09275i | −0.182927 | + | 0.242787i | ||||
\(441\) | 0.805646 | + | 1.39542i | 0.0383641 | + | 0.0664485i | ||||
\(442\) | 22.7982 | + | 13.1626i | 1.08440 | + | 0.626079i | ||||
\(443\) | 20.4256 | − | 11.7927i | 0.970450 | − | 0.560290i | 0.0710768 | − | 0.997471i | \(-0.477356\pi\) |
0.899374 | + | 0.437181i | \(0.144023\pi\) | |||||||
\(444\) | −7.79872 | −0.370111 | ||||||||
\(445\) | −2.36644 | + | 19.2843i | −0.112180 | + | 0.914162i | ||||
\(446\) | 0.938256 | + | 1.62511i | 0.0444277 | + | 0.0769510i | ||||
\(447\) | 3.33682 | − | 1.92651i | 0.157826 | − | 0.0911209i | ||||
\(448\) | 2.32136i | 0.109674i | ||||||||
\(449\) | −28.2500 | −1.33320 | −0.666601 | − | 0.745415i | \(-0.732251\pi\) | ||||
−0.666601 | + | 0.745415i | \(0.732251\pi\) | |||||||
\(450\) | −4.80612 | + | 1.37886i | −0.226562 | + | 0.0650001i | ||||
\(451\) | −7.36090 | + | 12.7495i | −0.346611 | + | 0.600349i | ||||
\(452\) | −10.2945 | + | 5.94352i | −0.484212 | + | 0.279560i | ||||
\(453\) | −6.73182 | − | 3.88662i | −0.316289 | − | 0.182609i | ||||
\(454\) | −10.1852 | + | 17.6412i | −0.478013 | + | 0.827943i | ||||
\(455\) | 3.79820 | − | 30.9518i | 0.178063 | − | 1.45104i | ||||
\(456\) | 1.69397 | + | 4.01627i | 0.0793275 | + | 0.188079i | ||||
\(457\) | − | 31.6784i | − | 1.48185i | −0.671587 | − | 0.740926i | \(-0.734387\pi\) | ||
0.671587 | − | 0.740926i | \(-0.265613\pi\) | |||||||
\(458\) | −9.33688 | − | 5.39065i | −0.436284 | − | 0.251889i | ||||
\(459\) | −2.19097 | + | 3.79487i | −0.102266 | + | 0.177129i | ||||
\(460\) | −4.40110 | − | 10.3663i | −0.205203 | − | 0.483333i | ||||
\(461\) | 0.595751 | − | 1.03187i | 0.0277469 | − | 0.0480590i | −0.851819 | − | 0.523837i | \(-0.824500\pi\) |
0.879565 | + | 0.475778i | \(0.157833\pi\) | |||||||
\(462\) | 5.73283 | − | 3.30985i | 0.266715 | − | 0.153988i | ||||
\(463\) | 19.8469i | 0.922366i | 0.887305 | + | 0.461183i | \(0.152575\pi\) | ||||
−0.887305 | + | 0.461183i | \(0.847425\pi\) | |||||||
\(464\) | 8.82078 | 0.409494 | ||||||||
\(465\) | −0.598763 | − | 1.41032i | −0.0277670 | − | 0.0654021i | ||||
\(466\) | −6.78823 | − | 11.7576i | −0.314458 | − | 0.544658i | ||||
\(467\) | 14.2451i | 0.659184i | 0.944123 | + | 0.329592i | \(0.106911\pi\) | ||||
−0.944123 | + | 0.329592i | \(0.893089\pi\) | |||||||
\(468\) | − | 6.00764i | − | 0.277703i | ||||||
\(469\) | 7.90089 | + | 13.6847i | 0.364829 | + | 0.631903i | ||||
\(470\) | 14.0874 | + | 10.6141i | 0.649803 | + | 0.489590i | ||||
\(471\) | −9.63765 | − | 16.6929i | −0.444080 | − | 0.769169i | ||||
\(472\) | −1.25512 | − | 0.724643i | −0.0577715 | − | 0.0333544i | ||||
\(473\) | 6.38933 | + | 3.68888i | 0.293782 | + | 0.169615i | ||||
\(474\) | −4.01365 | −0.184353 | ||||||||
\(475\) | −20.3301 | − | 7.85413i | −0.932809 | − | 0.360372i | ||||
\(476\) | −10.1720 | −0.466235 | ||||||||
\(477\) | 4.86905 | + | 2.81115i | 0.222938 | + | 0.128714i | ||||
\(478\) | 1.80203 | + | 1.04040i | 0.0824231 | + | 0.0475870i | ||||
\(479\) | 14.3482 | + | 24.8519i | 0.655588 | + | 1.13551i | 0.981746 | + | 0.190196i | \(0.0609123\pi\) |
−0.326159 | + | 0.945315i | \(0.605754\pi\) | |||||||
\(480\) | −1.78590 | − | 1.34557i | −0.0815147 | − | 0.0614168i | ||||
\(481\) | 23.4260 | + | 40.5749i | 1.06813 | + | 1.85006i | ||||
\(482\) | − | 17.0263i | − | 0.775529i | ||||||
\(483\) | 11.6915i | 0.531980i | ||||||||
\(484\) | −1.43405 | − | 2.48385i | −0.0651842 | − | 0.112902i | ||||
\(485\) | 5.84918 | + | 13.7771i | 0.265598 | + | 0.625587i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 19.6433i | 0.890122i | 0.895500 | + | 0.445061i | \(0.146818\pi\) | ||||
−0.895500 | + | 0.445061i | \(0.853182\pi\) | |||||||
\(488\) | −9.35765 | + | 5.40264i | −0.423601 | + | 0.244566i | ||||
\(489\) | 7.95838 | − | 13.7843i | 0.359890 | − | 0.623348i | ||||
\(490\) | −1.40802 | − | 3.31644i | −0.0636079 | − | 0.149822i | ||||
\(491\) | 4.99544 | − | 8.65235i | 0.225441 | − | 0.390475i | −0.731011 | − | 0.682366i | \(-0.760951\pi\) |
0.956452 | + | 0.291891i | \(0.0942844\pi\) | |||||||
\(492\) | −4.47091 | − | 2.58128i | −0.201564 | − | 0.116373i | ||||
\(493\) | 38.6521i | 1.74080i | ||||||||
\(494\) | 15.8074 | − | 20.8775i | 0.711207 | − | 0.939324i | ||||
\(495\) | −0.776654 | + | 6.32900i | −0.0349080 | + | 0.284468i | ||||
\(496\) | 0.342602 | − | 0.593405i | 0.0153833 | − | 0.0266446i | ||||
\(497\) | −4.62980 | − | 2.67301i | −0.207675 | − | 0.119901i | ||||
\(498\) | 10.5821 | − | 6.10958i | 0.474196 | − | 0.273777i | ||||
\(499\) | −7.18085 | + | 12.4376i | −0.321459 | + | 0.556784i | −0.980789 | − | 0.195070i | \(-0.937507\pi\) |
0.659330 | + | 0.751854i | \(0.270840\pi\) | |||||||
\(500\) | 11.0423 | − | 1.75131i | 0.493828 | − | 0.0783210i | ||||
\(501\) | 19.0151 | 0.849531 | ||||||||
\(502\) | 19.2514i | 0.859233i | ||||||||
\(503\) | 7.26003 | − | 4.19158i | 0.323709 | − | 0.186893i | −0.329336 | − | 0.944213i | \(-0.606825\pi\) |
0.653044 | + | 0.757320i | \(0.273491\pi\) | |||||||
\(504\) | 1.16068 | + | 2.01036i | 0.0517008 | + | 0.0895484i | ||||
\(505\) | −3.82495 | + | 31.1698i | −0.170208 | + | 1.38704i | ||||
\(506\) | −14.3623 | −0.638480 | ||||||||
\(507\) | −19.9981 | + | 11.5459i | −0.888146 | + | 0.512771i | ||||
\(508\) | 7.72660 | + | 4.46095i | 0.342812 | + | 0.197923i | ||||
\(509\) | 5.67635 | + | 9.83173i | 0.251600 | + | 0.435784i | 0.963966 | − | 0.266024i | \(-0.0857100\pi\) |
−0.712367 | + | 0.701808i | \(0.752377\pi\) | |||||||
\(510\) | 5.89622 | − | 7.82569i | 0.261089 | − | 0.346527i | ||||
\(511\) | 7.21308 | − | 12.4934i | 0.319088 | − | 0.552677i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 3.47516 | + | 2.63121i | 0.153432 | + | 0.116171i | ||||
\(514\) | 17.6914 | 0.780333 | ||||||||
\(515\) | 18.9669 | − | 25.1736i | 0.835781 | − | 1.10928i | ||||
\(516\) | −1.29360 | + | 2.24057i | −0.0569474 | + | 0.0986357i | ||||
\(517\) | 19.4805 | − | 11.2471i | 0.856752 | − | 0.494646i | ||||
\(518\) | −15.6782 | − | 9.05181i | −0.688860 | − | 0.397714i | ||||
\(519\) | 7.14712 | + | 12.3792i | 0.313724 | + | 0.543386i | ||||
\(520\) | −1.63620 | + | 13.3335i | −0.0717520 | + | 0.584712i | ||||
\(521\) | −29.3742 | −1.28691 | −0.643453 | − | 0.765485i | \(-0.722499\pi\) | ||||
−0.643453 | + | 0.765485i | \(0.722499\pi\) | |||||||
\(522\) | 7.63902 | − | 4.41039i | 0.334351 | − | 0.193037i | ||||
\(523\) | 35.2243 | − | 20.3368i | 1.54025 | − | 0.889265i | 0.541429 | − | 0.840746i | \(-0.317883\pi\) |
0.998822 | − | 0.0485186i | \(-0.0154500\pi\) | |||||||
\(524\) | 0.0548638 | 0.00239673 | ||||||||
\(525\) | −11.2624 | − | 2.80636i | −0.491532 | − | 0.122480i | ||||
\(526\) | −5.76364 | − | 9.98291i | −0.251307 | − | 0.435276i | ||||
\(527\) | 2.60026 | + | 1.50126i | 0.113269 | + | 0.0653960i | ||||
\(528\) | −2.46960 | + | 1.42582i | −0.107476 | + | 0.0620510i | ||||
\(529\) | 1.18305 | − | 2.04911i | 0.0514371 | − | 0.0890917i | ||||
\(530\) | −10.0408 | − | 7.56521i | −0.436146 | − | 0.328612i | ||||
\(531\) | −1.44929 | −0.0628937 | ||||||||
\(532\) | −1.25612 | + | 10.0403i | −0.0544597 | + | 0.435302i | ||||
\(533\) | 31.0148i | 1.34340i | ||||||||
\(534\) | −4.34444 | + | 7.52479i | −0.188002 | + | 0.325630i | ||||
\(535\) | −22.5692 | + | 29.9547i | −0.975750 | + | 1.29505i | ||||
\(536\) | −3.40356 | − | 5.89514i | −0.147011 | − | 0.254631i | ||||
\(537\) | 5.77363 | + | 3.33341i | 0.249151 | + | 0.143847i | ||||
\(538\) | 17.8013 | − | 10.2776i | 0.767468 | − | 0.443098i | ||||
\(539\) | −4.59484 | −0.197914 | ||||||||
\(540\) | −2.21942 | − | 0.272353i | −0.0955086 | − | 0.0117202i | ||||
\(541\) | −12.6792 | − | 21.9610i | −0.545122 | − | 0.944179i | −0.998599 | − | 0.0529108i | \(-0.983150\pi\) |
0.453478 | − | 0.891268i | \(-0.350183\pi\) | |||||||
\(542\) | 22.5014 | − | 12.9912i | 0.966518 | − | 0.558019i | ||||
\(543\) | 6.13587i | 0.263315i | ||||||||
\(544\) | 4.38194 | 0.187874 | ||||||||
\(545\) | −18.3263 | + | 7.78056i | −0.785012 | + | 0.333283i | ||||
\(546\) | 6.97295 | − | 12.0775i | 0.298415 | − | 0.516870i | ||||
\(547\) | 27.8110 | − | 16.0567i | 1.18911 | − | 0.686535i | 0.231009 | − | 0.972952i | \(-0.425797\pi\) |
0.958105 | + | 0.286417i | \(0.0924641\pi\) | |||||||
\(548\) | 15.5732 | + | 8.99119i | 0.665254 | + | 0.384085i | ||||
\(549\) | −5.40264 | + | 9.35765i | −0.230579 | + | 0.399375i | ||||
\(550\) | 3.44744 | − | 13.8352i | 0.146999 | − | 0.589935i | ||||
\(551\) | 38.1515 | + | 4.77304i | 1.62531 | + | 0.203338i | ||||
\(552\) | − | 5.03648i | − | 0.214367i | ||||||
\(553\) | −8.06887 | − | 4.65857i | −0.343123 | − | 0.198102i | ||||
\(554\) | −2.07148 | + | 3.58791i | −0.0880087 | + | 0.152435i | ||||
\(555\) | 16.0517 | − | 6.81487i | 0.681357 | − | 0.289275i | ||||
\(556\) | 10.3327 | − | 17.8967i | 0.438203 | − | 0.758989i | ||||
\(557\) | −6.90306 | + | 3.98549i | −0.292492 | + | 0.168870i | −0.639065 | − | 0.769153i | \(-0.720679\pi\) |
0.346573 | + | 0.938023i | \(0.387345\pi\) | |||||||
\(558\) | − | 0.685205i | − | 0.0290070i | ||||||
\(559\) | 15.5429 | 0.657396 | ||||||||
\(560\) | −2.02851 | − | 4.77794i | −0.0857202 | − | 0.201905i | ||||
\(561\) | −6.24787 | − | 10.8216i | −0.263785 | − | 0.456890i | ||||
\(562\) | − | 8.59688i | − | 0.362637i | ||||||
\(563\) | − | 13.8459i | − | 0.583537i | −0.956489 | − | 0.291768i | \(-0.905756\pi\) | ||
0.956489 | − | 0.291768i | \(-0.0942436\pi\) | |||||||
\(564\) | 3.94406 | + | 6.83132i | 0.166075 | + | 0.287650i | ||||
\(565\) | 15.9949 | − | 21.2290i | 0.672911 | − | 0.893113i | ||||
\(566\) | 7.18742 | + | 12.4490i | 0.302110 | + | 0.523270i | ||||
\(567\) | 2.01036 | + | 1.16068i | 0.0844270 | + | 0.0487440i | ||||
\(568\) | 1.99443 | + | 1.15149i | 0.0836846 | + | 0.0483153i | ||||
\(569\) | 28.6171 | 1.19969 | 0.599845 | − | 0.800117i | \(-0.295229\pi\) | ||||
0.599845 | + | 0.800117i | \(0.295229\pi\) | |||||||
\(570\) | −6.99622 | − | 6.78623i | −0.293040 | − | 0.284244i | ||||
\(571\) | 18.2331 | 0.763033 | 0.381517 | − | 0.924362i | \(-0.375402\pi\) | ||||
0.381517 | + | 0.924362i | \(0.375402\pi\) | |||||||
\(572\) | 14.8365 | + | 8.56584i | 0.620344 | + | 0.358156i | ||||
\(573\) | 16.3200 | + | 9.42238i | 0.681780 | + | 0.393626i | ||||
\(574\) | −5.99208 | − | 10.3786i | −0.250105 | − | 0.433194i | ||||
\(575\) | 18.1171 | + | 17.4906i | 0.755537 | + | 0.729409i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 37.3878i | − | 1.55647i | −0.627970 | − | 0.778237i | \(-0.716114\pi\) | ||
0.627970 | − | 0.778237i | \(-0.283886\pi\) | |||||||
\(578\) | 2.20137i | 0.0915650i | ||||||||
\(579\) | 8.26218 | + | 14.3105i | 0.343365 | + | 0.594725i | ||||
\(580\) | −18.1554 | + | 7.70800i | −0.753860 | + | 0.320057i | ||||
\(581\) | 28.3651 | 1.17678 | ||||||||
\(582\) | 6.69361i | 0.277459i | ||||||||
\(583\) | −13.8848 | + | 8.01640i | −0.575050 | + | 0.332005i | ||||
\(584\) | −3.10727 | + | 5.38195i | −0.128580 | + | 0.222707i | ||||
\(585\) | 5.24975 | + | 12.3652i | 0.217051 | + | 0.511240i | ||||
\(586\) | 4.23745 | − | 7.33948i | 0.175047 | − | 0.303191i | ||||
\(587\) | 1.52408 | + | 0.879926i | 0.0629053 | + | 0.0363184i | 0.531123 | − | 0.847295i | \(-0.321770\pi\) |
−0.468217 | + | 0.883613i | \(0.655104\pi\) | |||||||
\(588\) | − | 1.61129i | − | 0.0664485i | ||||||
\(589\) | 1.80292 | − | 2.38120i | 0.0742879 | − | 0.0981155i | ||||
\(590\) | 3.21657 | + | 0.394717i | 0.132424 | + | 0.0162502i | ||||
\(591\) | −3.45127 | + | 5.97778i | −0.141966 | + | 0.245893i | ||||
\(592\) | 6.75389 | + | 3.89936i | 0.277583 | + | 0.160263i | ||||
\(593\) | 9.65263 | − | 5.57295i | 0.396386 | − | 0.228854i | −0.288537 | − | 0.957469i | \(-0.593169\pi\) |
0.684923 | + | 0.728615i | \(0.259836\pi\) | |||||||
\(594\) | −1.42582 | + | 2.46960i | −0.0585023 | + | 0.101329i | ||||
\(595\) | 20.9366 | − | 8.88880i | 0.858318 | − | 0.364405i | ||||
\(596\) | −3.85302 | −0.157826 | ||||||||
\(597\) | − | 6.53029i | − | 0.267267i | ||||||
\(598\) | −26.2037 | + | 15.1287i | −1.07155 | + | 0.618658i | ||||
\(599\) | 19.0286 | + | 32.9586i | 0.777489 | + | 1.34665i | 0.933385 | + | 0.358877i | \(0.116840\pi\) |
−0.155896 | + | 0.987774i | \(0.549826\pi\) | |||||||
\(600\) | 4.85165 | + | 1.20893i | 0.198068 | + | 0.0493543i | ||||
\(601\) | 34.4084 | 1.40355 | 0.701775 | − | 0.712399i | \(-0.252391\pi\) | ||||
0.701775 | + | 0.712399i | \(0.252391\pi\) | |||||||
\(602\) | −5.20118 | + | 3.00290i | −0.211984 | + | 0.122389i | ||||
\(603\) | −5.89514 | − | 3.40356i | −0.240069 | − | 0.138604i | ||||
\(604\) | 3.88662 | + | 6.73182i | 0.158144 | + | 0.273914i | ||||
\(605\) | 5.12214 | + | 3.85925i | 0.208245 | + | 0.156901i | ||||
\(606\) | −7.02206 | + | 12.1626i | −0.285252 | + | 0.494071i | ||||
\(607\) | − | 16.1885i | − | 0.657071i | −0.944492 | − | 0.328536i | \(-0.893445\pi\) | ||
0.944492 | − | 0.328536i | \(-0.106555\pi\) | |||||||
\(608\) | 0.541114 | − | 4.32518i | 0.0219451 | − | 0.175409i | ||||
\(609\) | 20.4762 | 0.829737 | ||||||||
\(610\) | 14.5393 | − | 19.2971i | 0.588679 | − | 0.781318i | ||||
\(611\) | 23.6945 | − | 41.0401i | 0.958578 | − | 1.66031i | ||||
\(612\) | 3.79487 | − | 2.19097i | 0.153398 | − | 0.0885647i | ||||
\(613\) | 16.7637 | + | 9.67851i | 0.677078 | + | 0.390911i | 0.798753 | − | 0.601659i | \(-0.205493\pi\) |
−0.121675 | + | 0.992570i | \(0.538827\pi\) | |||||||
\(614\) | −10.7838 | − | 18.6780i | −0.435197 | − | 0.753784i | ||||
\(615\) | 11.4579 | + | 1.40604i | 0.462027 | + | 0.0566969i | ||||
\(616\) | −6.61970 | −0.266715 | ||||||||
\(617\) | 7.58517 | − | 4.37930i | 0.305367 | − | 0.176304i | −0.339484 | − | 0.940612i | \(-0.610253\pi\) |
0.644852 | + | 0.764308i | \(0.276919\pi\) | |||||||
\(618\) | 12.2073 | − | 7.04788i | 0.491049 | − | 0.283507i | ||||
\(619\) | 36.5640 | 1.46963 | 0.734815 | − | 0.678268i | \(-0.237269\pi\) | ||||
0.734815 | + | 0.678268i | \(0.237269\pi\) | |||||||
\(620\) | −0.186617 | + | 1.52076i | −0.00749473 | + | 0.0610750i | ||||
\(621\) | −2.51824 | − | 4.36172i | −0.101053 | − | 0.175030i | ||||
\(622\) | 5.41641 | + | 3.12716i | 0.217178 | + | 0.125388i | ||||
\(623\) | −17.4677 | + | 10.0850i | −0.699830 | + | 0.404047i | ||||
\(624\) | −3.00382 | + | 5.20277i | −0.120249 | + | 0.208278i | ||||
\(625\) | −21.1975 | + | 13.2539i | −0.847900 | + | 0.530157i | ||||
\(626\) | −17.7515 | −0.709492 | ||||||||
\(627\) | −11.4530 | + | 4.83061i | −0.457389 | + | 0.192916i | ||||
\(628\) | 19.2753i | 0.769169i | ||||||||
\(629\) | −17.0867 | + | 29.5951i | −0.681293 | + | 1.18003i | ||||
\(630\) | −4.14571 | − | 3.12356i | −0.165169 | − | 0.124446i | ||||
\(631\) | 12.0437 | + | 20.8604i | 0.479453 | + | 0.830437i | 0.999722 | − | 0.0235650i | \(-0.00750166\pi\) |
−0.520269 | + | 0.854002i | \(0.674168\pi\) | |||||||
\(632\) | 3.47593 | + | 2.00683i | 0.138265 | + | 0.0798273i | ||||
\(633\) | 19.3891 | − | 11.1943i | 0.770648 | − | 0.444934i | ||||
\(634\) | −0.739513 | −0.0293698 | ||||||||
\(635\) | −19.8015 | − | 2.42991i | −0.785797 | − | 0.0964279i | ||||
\(636\) | −2.81115 | − | 4.86905i | −0.111469 | − | 0.193070i | ||||
\(637\) | −8.38318 | + | 4.84003i | −0.332154 | + | 0.191769i | ||||
\(638\) | 25.1538i | 0.995847i | ||||||||
\(639\) | 2.30297 | 0.0911042 | ||||||||
\(640\) | 0.873846 | + | 2.05825i | 0.0345418 | + | 0.0813595i | ||||
\(641\) | −12.7503 | + | 22.0841i | −0.503605 | + | 0.872270i | 0.496386 | + | 0.868102i | \(0.334660\pi\) |
−0.999991 | + | 0.00416788i | \(0.998673\pi\) | |||||||
\(642\) | −14.5258 | + | 8.38645i | −0.573286 | + | 0.330987i | ||||
\(643\) | −8.09885 | − | 4.67587i | −0.319387 | − | 0.184398i | 0.331732 | − | 0.943374i | \(-0.392367\pi\) |
−0.651119 | + | 0.758975i | \(0.725700\pi\) | |||||||
\(644\) | 5.84574 | − | 10.1251i | 0.230354 | − | 0.398985i | ||||
\(645\) | 0.704628 | − | 5.74206i | 0.0277447 | − | 0.226094i | ||||
\(646\) | 18.9527 | + | 2.37113i | 0.745683 | + | 0.0932907i | ||||
\(647\) | − | 2.93501i | − | 0.115387i | −0.998334 | − | 0.0576935i | \(-0.981625\pi\) | ||
0.998334 | − | 0.0576935i | \(-0.0183746\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 2.06643 | − | 3.57916i | 0.0811144 | − | 0.140494i | ||||
\(650\) | −8.28370 | − | 28.8734i | −0.324914 | − | 1.13251i | ||||
\(651\) | 0.795303 | − | 1.37751i | 0.0311704 | − | 0.0539887i | ||||
\(652\) | −13.7843 | + | 7.95838i | −0.539835 | + | 0.311674i | ||||
\(653\) | − | 13.5336i | − | 0.529613i | −0.964302 | − | 0.264806i | \(-0.914692\pi\) | ||
0.964302 | − | 0.264806i | \(-0.0853080\pi\) | |||||||
\(654\) | −8.90382 | −0.348167 | ||||||||
\(655\) | −0.112923 | + | 0.0479425i | −0.00441228 | + | 0.00187327i | ||||
\(656\) | 2.58128 | + | 4.47091i | 0.100782 | + | 0.174560i | ||||
\(657\) | 6.21454i | 0.242452i | ||||||||
\(658\) | 18.3112i | 0.713844i | ||||||||
\(659\) | −11.2236 | − | 19.4399i | −0.437210 | − | 0.757270i | 0.560263 | − | 0.828315i | \(-0.310700\pi\) |
−0.997473 | + | 0.0710447i | \(0.977367\pi\) | |||||||
\(660\) | 3.83710 | − | 5.09275i | 0.149359 | − | 0.198235i | ||||
\(661\) | −4.81389 | − | 8.33791i | −0.187239 | − | 0.324307i | 0.757090 | − | 0.653311i | \(-0.226620\pi\) |
−0.944329 | + | 0.329004i | \(0.893287\pi\) | |||||||
\(662\) | −3.93574 | − | 2.27230i | −0.152967 | − | 0.0883156i | ||||
\(663\) | −22.7982 | − | 13.1626i | −0.885410 | − | 0.511191i | ||||
\(664\) | −12.2192 | −0.474196 | ||||||||
\(665\) | −6.18826 | − | 21.7631i | −0.239971 | − | 0.843937i | ||||
\(666\) | 7.79872 | 0.302194 | ||||||||
\(667\) | −38.4737 | − | 22.2128i | −1.48971 | − | 0.860084i | ||||
\(668\) | −16.4675 | − | 9.50754i | −0.637148 | − | 0.367858i | ||||
\(669\) | −0.938256 | − | 1.62511i | −0.0362751 | − | 0.0628302i | ||||
\(670\) | 12.1568 | + | 9.15949i | 0.469659 | + | 0.353862i | ||||
\(671\) | −15.4064 | − | 26.6847i | −0.594758 | − | 1.03015i | ||||
\(672\) | − | 2.32136i | − | 0.0895484i | ||||||
\(673\) | 3.35484i | 0.129320i | 0.997907 | + | 0.0646598i | \(0.0205962\pi\) | ||||
−0.997907 | + | 0.0646598i | \(0.979404\pi\) | |||||||
\(674\) | −10.3626 | − | 17.9486i | −0.399153 | − | 0.691354i | ||||
\(675\) | 4.80612 | − | 1.37886i | 0.184987 | − | 0.0530724i | ||||
\(676\) | 23.0918 | 0.888146 | ||||||||
\(677\) | − | 18.6287i | − | 0.715958i | −0.933730 | − | 0.357979i | \(-0.883466\pi\) | ||
0.933730 | − | 0.357979i | \(-0.116534\pi\) | |||||||
\(678\) | 10.2945 | − | 5.94352i | 0.395357 | − | 0.228260i | ||||
\(679\) | −7.76914 | + | 13.4565i | −0.298152 | + | 0.516415i | ||||
\(680\) | −9.01912 | + | 3.82914i | −0.345868 | + | 0.146841i | ||||
\(681\) | 10.1852 | − | 17.6412i | 0.390296 | − | 0.676013i | ||||
\(682\) | 1.69218 | + | 0.976981i | 0.0647970 | + | 0.0374105i | ||||
\(683\) | 22.3842i | 0.856506i | 0.903659 | + | 0.428253i | \(0.140871\pi\) | ||||
−0.903659 | + | 0.428253i | \(0.859129\pi\) | |||||||
\(684\) | −1.69397 | − | 4.01627i | −0.0647707 | − | 0.153566i | ||||
\(685\) | −39.9104 | − | 4.89755i | −1.52490 | − | 0.187126i | ||||
\(686\) | 9.99495 | − | 17.3118i | 0.381609 | − | 0.660966i | ||||
\(687\) | 9.33688 | + | 5.39065i | 0.356224 | + | 0.205666i | ||||
\(688\) | 2.24057 | − | 1.29360i | 0.0854211 | − | 0.0493179i | ||||
\(689\) | −16.8884 | + | 29.2515i | −0.643396 | + | 1.11439i | ||||
\(690\) | 4.40110 | + | 10.3663i | 0.167547 | + | 0.394639i | ||||
\(691\) | −43.1700 | −1.64226 | −0.821132 | − | 0.570738i | \(-0.806657\pi\) | ||||
−0.821132 | + | 0.570738i | \(0.806657\pi\) | |||||||
\(692\) | − | 14.2942i | − | 0.543386i | ||||||
\(693\) | −5.73283 | + | 3.30985i | −0.217772 | + | 0.125731i | ||||
\(694\) | −6.20108 | − | 10.7406i | −0.235390 | − | 0.407707i | ||||
\(695\) | −5.62826 | + | 45.8651i | −0.213492 | + | 1.73976i | ||||
\(696\) | −8.82078 | −0.334351 | ||||||||
\(697\) | −19.5912 | + | 11.3110i | −0.742071 | + | 0.428435i | ||||
\(698\) | 12.4848 | + | 7.20813i | 0.472558 | + | 0.272832i | ||||
\(699\) | 6.78823 | + | 11.7576i | 0.256754 | + | 0.444711i | ||||
\(700\) | 8.35036 | + | 8.06159i | 0.315614 | + | 0.304699i | ||||
\(701\) | −14.1571 | + | 24.5208i | −0.534705 | + | 0.926137i | 0.464472 | + | 0.885588i | \(0.346244\pi\) |
−0.999178 | + | 0.0405493i | \(0.987089\pi\) | |||||||
\(702\) | 6.00764i | 0.226744i | ||||||||
\(703\) | 27.1018 | + | 20.5200i | 1.02216 | + | 0.773928i | ||||
\(704\) | 2.85165 | 0.107476 | ||||||||
\(705\) | −14.0874 | − | 10.6141i | −0.530562 | − | 0.399749i | ||||
\(706\) | −17.8354 | + | 30.8918i | −0.671243 | + | 1.16263i | ||||
\(707\) | −28.2337 | + | 16.3007i | −1.06184 | + | 0.613052i | ||||
\(708\) | 1.25512 | + | 0.724643i | 0.0471702 | + | 0.0272338i | ||||
\(709\) | 8.52409 | + | 14.7642i | 0.320129 | + | 0.554480i | 0.980514 | − | 0.196447i | \(-0.0629404\pi\) |
−0.660385 | + | 0.750927i | \(0.729607\pi\) | |||||||
\(710\) | −5.11126 | − | 0.627221i | −0.191822 | − | 0.0235392i | ||||
\(711\) | 4.01365 | 0.150524 | ||||||||
\(712\) | 7.52479 | − | 4.34444i | 0.282003 | − | 0.162815i | ||||
\(713\) | −2.98867 | + | 1.72551i | −0.111927 | + | 0.0646208i | ||||
\(714\) | 10.1720 | 0.380679 | ||||||||
\(715\) | −38.0224 | − | 4.66586i | −1.42196 | − | 0.174493i | ||||
\(716\) | −3.33341 | − | 5.77363i | −0.124575 | − | 0.215771i | ||||
\(717\) | −1.80203 | − | 1.04040i | −0.0672981 | − | 0.0388546i | ||||
\(718\) | 1.99682 | − | 1.15286i | 0.0745205 | − | 0.0430244i | ||||
\(719\) | −1.65729 | + | 2.87050i | −0.0618063 | + | 0.107052i | −0.895273 | − | 0.445518i | \(-0.853019\pi\) |
0.833467 | + | 0.552570i | \(0.186353\pi\) | |||||||
\(720\) | 1.78590 | + | 1.34557i | 0.0665565 | + | 0.0501466i | ||||
\(721\) | 32.7213 | 1.21861 | ||||||||
\(722\) | 4.68083 | − | 18.4144i | 0.174202 | − | 0.685313i | ||||
\(723\) | 17.0263i | 0.633217i | ||||||||
\(724\) | 3.06793 | − | 5.31382i | 0.114019 | − | 0.197486i | ||||
\(725\) | 30.6327 | − | 31.7300i | 1.13767 | − | 1.17842i | ||||
\(726\) | 1.43405 | + | 2.48385i | 0.0532226 | + | 0.0921843i | ||||
\(727\) | −29.7663 | − | 17.1856i | −1.10397 | − | 0.637379i | −0.166711 | − | 0.986006i | \(-0.553315\pi\) |
−0.937261 | + | 0.348627i | \(0.886648\pi\) | |||||||
\(728\) | −12.0775 | + | 6.97295i | −0.447622 | + | 0.258435i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 1.69255 | − | 13.7927i | 0.0626439 | − | 0.510489i | ||||
\(731\) | 5.66845 | + | 9.81805i | 0.209655 | + | 0.363134i | ||||
\(732\) | 9.35765 | − | 5.40264i | 0.345869 | − | 0.199687i | ||||
\(733\) | − | 39.0068i | − | 1.44075i | −0.693585 | − | 0.720375i | \(-0.743970\pi\) | ||
0.693585 | − | 0.720375i | \(-0.256030\pi\) | |||||||
\(734\) | 10.9355 | 0.403635 | ||||||||
\(735\) | 1.40802 | + | 3.31644i | 0.0519356 | + | 0.122329i | ||||
\(736\) | −2.51824 | + | 4.36172i | −0.0928235 | + | 0.160775i | ||||
\(737\) | 16.8109 | − | 9.70576i | 0.619236 | − | 0.357516i | ||||
\(738\) | 4.47091 | + | 2.58128i | 0.164576 | + | 0.0950182i | ||||
\(739\) | −4.19339 | + | 7.26316i | −0.154256 | + | 0.267180i | −0.932788 | − | 0.360426i | \(-0.882631\pi\) |
0.778532 | + | 0.627605i | \(0.215965\pi\) | |||||||
\(740\) | −17.3086 | − | 2.12400i | −0.636278 | − | 0.0780798i | ||||
\(741\) | −15.8074 | + | 20.8775i | −0.580698 | + | 0.766955i | ||||
\(742\) | − | 13.0514i | − | 0.479131i | ||||||
\(743\) | −1.64985 | − | 0.952540i | −0.0605270 | − | 0.0349453i | 0.469431 | − | 0.882969i | \(-0.344459\pi\) |
−0.529958 | + | 0.848024i | \(0.677792\pi\) | |||||||
\(744\) | −0.342602 | + | 0.593405i | −0.0125604 | + | 0.0217553i | ||||
\(745\) | 7.93049 | − | 3.36695i | 0.290551 | − | 0.123355i | ||||
\(746\) | −11.6924 | + | 20.2518i | −0.428088 | + | 0.741470i | ||||
\(747\) | −10.5821 | + | 6.10958i | −0.387179 | + | 0.223538i | ||||
\(748\) | 12.4957i | 0.456890i | ||||||||
\(749\) | −38.9359 | −1.42269 | ||||||||
\(750\) | −11.0423 | + | 1.75131i | −0.403209 | + | 0.0639488i | ||||
\(751\) | −5.63534 | − | 9.76069i | −0.205636 | − | 0.356173i | 0.744699 | − | 0.667401i | \(-0.232593\pi\) |
−0.950335 | + | 0.311228i | \(0.899260\pi\) | |||||||
\(752\) | − | 7.88813i | − | 0.287650i | ||||||
\(753\) | − | 19.2514i | − | 0.701561i | ||||||
\(754\) | 26.4960 | + | 45.8925i | 0.964929 | + | 1.67131i | ||||
\(755\) | −13.8822 | − | 10.4595i | −0.505225 | − | 0.380659i | ||||
\(756\) | −1.16068 | − | 2.01036i | −0.0422135 | − | 0.0731159i | ||||
\(757\) | 38.7692 | + | 22.3834i | 1.40909 | + | 0.813540i | 0.995301 | − | 0.0968318i | \(-0.0308709\pi\) |
0.413792 | + | 0.910372i | \(0.364204\pi\) | |||||||
\(758\) | −20.1345 | − | 11.6246i | −0.731317 | − | 0.422226i | ||||
\(759\) | 14.3623 | 0.521317 | ||||||||
\(760\) | 2.66579 | + | 9.37516i | 0.0966985 | + | 0.340073i | ||||
\(761\) | −33.7181 | −1.22228 | −0.611139 | − | 0.791523i | \(-0.709289\pi\) | ||||
−0.611139 | + | 0.791523i | \(0.709289\pi\) | |||||||
\(762\) | −7.72660 | − | 4.46095i | −0.279905 | − | 0.161603i | ||||
\(763\) | −17.8998 | − | 10.3345i | −0.648018 | − | 0.374133i | ||||
\(764\) | −9.42238 | − | 16.3200i | −0.340890 | − | 0.590439i | ||||
\(765\) | −5.89622 | + | 7.82569i | −0.213178 | + | 0.282938i | ||||
\(766\) | −10.3548 | − | 17.9351i | −0.374135 | − | 0.648021i | ||||
\(767\) | − | 8.70680i | − | 0.314384i | ||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 16.2178 | + | 28.0901i | 0.584830 | + | 1.01296i | 0.994897 | + | 0.100900i | \(0.0321723\pi\) |
−0.410066 | + | 0.912056i | \(0.634494\pi\) | |||||||
\(770\) | 13.6250 | − | 5.78460i | 0.491011 | − | 0.208462i | ||||
\(771\) | −17.6914 | −0.637139 | ||||||||
\(772\) | − | 16.5244i | − | 0.594725i | ||||||
\(773\) | 35.2122 | − | 20.3298i | 1.26649 | − | 0.731211i | 0.292172 | − | 0.956366i | \(-0.405622\pi\) |
0.974323 | + | 0.225155i | \(0.0722888\pi\) | |||||||
\(774\) | 1.29360 | − | 2.24057i | 0.0464973 | − | 0.0805358i | ||||
\(775\) | −0.944801 | − | 3.29317i | −0.0339383 | − | 0.118294i | ||||
\(776\) | 3.34681 | − | 5.79684i | 0.120143 | − | 0.208094i | ||||
\(777\) | 15.6782 | + | 9.05181i | 0.562452 | + | 0.324732i | ||||
\(778\) | 36.3774i | 1.30419i | ||||||||
\(779\) | 8.74524 | + | 20.7343i | 0.313331 | + | 0.742882i | ||||
\(780\) | 1.63620 | − | 13.3335i | 0.0585853 | − | 0.477415i | ||||
\(781\) | −3.28363 | + | 5.68742i | −0.117498 | + | 0.203512i | ||||
\(782\) | −19.1128 | − | 11.0348i | −0.683471 | − | 0.394602i | ||||
\(783\) | −7.63902 | + | 4.41039i | −0.272996 | + | 0.157614i | ||||
\(784\) | −0.805646 | + | 1.39542i | −0.0287731 | + | 0.0498364i | ||||
\(785\) | −16.8436 | − | 39.6734i | −0.601175 | − | 1.41600i | ||||
\(786\) | −0.0548638 | −0.00195693 | ||||||||
\(787\) | 33.0432i | 1.17786i | 0.808183 | + | 0.588931i | \(0.200451\pi\) | ||||
−0.808183 | + | 0.588931i | \(0.799549\pi\) | |||||||
\(788\) | 5.97778 | − | 3.45127i | 0.212949 | − | 0.122946i | ||||
\(789\) | 5.76364 | + | 9.98291i | 0.205191 | + | 0.355401i | ||||
\(790\) | −8.90798 | − | 1.09313i | −0.316932 | − | 0.0388918i | ||||
\(791\) | 27.5941 | 0.981133 | ||||||||
\(792\) | 2.46960 | − | 1.42582i | 0.0877534 | − | 0.0506645i | ||||
\(793\) | −56.2174 | − | 32.4571i | −1.99634 | − | 1.15259i | ||||
\(794\) | −16.5196 | − | 28.6128i | −0.586259 | − | 1.01543i | ||||
\(795\) | 10.0408 | + | 7.56521i | 0.356112 | + | 0.268310i | ||||
\(796\) | −3.26514 | + | 5.65540i | −0.115730 | + | 0.200450i | ||||
\(797\) | − | 25.1288i | − | 0.890109i | −0.895504 | − | 0.445054i | \(-0.853184\pi\) | ||
0.895504 | − | 0.445054i | \(-0.146816\pi\) | |||||||
\(798\) | 1.25612 | − | 10.0403i | 0.0444661 | − | 0.355423i | ||||
\(799\) | 34.5653 | 1.22283 | ||||||||
\(800\) | −3.59719 | − | 3.47279i | −0.127180 | − | 0.122782i | ||||
\(801\) | 4.34444 | − | 7.52479i | 0.153503 | − | 0.265875i | ||||
\(802\) | −18.3566 | + | 10.5982i | −0.648194 | + | 0.374235i | ||||
\(803\) | −15.3474 | − | 8.86083i | −0.541599 | − | 0.312692i | ||||
\(804\) | 3.40356 | + | 5.89514i | 0.120034 | + | 0.207906i | ||||
\(805\) | −3.18420 | + | 25.9483i | −0.112228 | + | 0.914557i | ||||
\(806\) | 4.11647 | 0.144996 | ||||||||
\(807\) | −17.8013 | + | 10.2776i | −0.626635 | + | 0.361788i | ||||
\(808\) | 12.1626 | − | 7.02206i | 0.427878 | − | 0.247035i | ||||
\(809\) | 22.9578 | 0.807152 | 0.403576 | − | 0.914946i | \(-0.367767\pi\) | ||||
0.403576 | + | 0.914946i | \(0.367767\pi\) | |||||||
\(810\) | 2.21942 | + | 0.272353i | 0.0779825 | + | 0.00956950i | ||||
\(811\) | −27.0425 | − | 46.8390i | −0.949590 | − | 1.64474i | −0.746289 | − | 0.665622i | \(-0.768166\pi\) |
−0.203301 | − | 0.979116i | \(-0.565167\pi\) | |||||||
\(812\) | −17.7329 | − | 10.2381i | −0.622303 | − | 0.359287i | ||||
\(813\) | −22.5014 | + | 12.9912i | −0.789159 | + | 0.455621i | ||||
\(814\) | −11.1196 | + | 19.2597i | −0.389742 | + | 0.675052i | ||||
\(815\) | 21.4172 | − | 28.4257i | 0.750211 | − | 0.995708i | ||||
\(816\) | −4.38194 | −0.153398 | ||||||||
\(817\) | 10.3909 | − | 4.38263i | 0.363531 | − | 0.153329i | ||||
\(818\) | − | 10.5217i | − | 0.367883i | ||||||
\(819\) | −6.97295 | + | 12.0775i | −0.243655 | + | 0.422022i | ||||
\(820\) | −9.21980 | − | 6.94661i | −0.321970 | − | 0.242586i | ||||
\(821\) | 5.40068 | + | 9.35426i | 0.188485 | + | 0.326466i | 0.944745 | − | 0.327805i | \(-0.106309\pi\) |
−0.756260 | + | 0.654271i | \(0.772976\pi\) | |||||||
\(822\) | −15.5732 | − | 8.99119i | −0.543178 | − | 0.313604i | ||||
\(823\) | 29.3326 | − | 16.9352i | 1.02247 | − | 0.590324i | 0.107652 | − | 0.994189i | \(-0.465667\pi\) |
0.914819 | + | 0.403865i | \(0.132333\pi\) | |||||||
\(824\) | −14.0958 | −0.491049 | ||||||||
\(825\) | −3.44744 | + | 13.8352i | −0.120025 | + | 0.481680i | ||||
\(826\) | 1.68216 | + | 2.91358i | 0.0585297 | + | 0.101376i | ||||
\(827\) | −14.8973 | + | 8.60097i | −0.518030 | + | 0.299085i | −0.736128 | − | 0.676842i | \(-0.763348\pi\) |
0.218098 | + | 0.975927i | \(0.430015\pi\) | |||||||
\(828\) | 5.03648i | 0.175030i | ||||||||
\(829\) | −15.3463 | −0.532998 | −0.266499 | − | 0.963835i | \(-0.585867\pi\) | ||||
−0.266499 | + | 0.963835i | \(0.585867\pi\) | |||||||
\(830\) | 25.1501 | − | 10.6777i | 0.872973 | − | 0.370627i | ||||
\(831\) | 2.07148 | − | 3.58791i | 0.0718588 | − | 0.124463i | ||||
\(832\) | 5.20277 | − | 3.00382i | 0.180374 | − | 0.104139i | ||||
\(833\) | −6.11464 | − | 3.53029i | −0.211860 | − | 0.122317i | ||||
\(834\) | −10.3327 | + | 17.8967i | −0.357791 | + | 0.619712i | ||||
\(835\) | 42.2024 | + | 5.17881i | 1.46048 | + | 0.179220i | ||||
\(836\) | 12.3339 | + | 1.54307i | 0.426577 | + | 0.0533680i | ||||
\(837\) | 0.685205i | 0.0236841i | ||||||||
\(838\) | −22.8522 | − | 13.1937i | −0.789415 | − | 0.455769i | ||||
\(839\) | 22.5501 | − | 39.0579i | 0.778516 | − | 1.34843i | −0.154281 | − | 0.988027i | \(-0.549306\pi\) |
0.932797 | − | 0.360402i | \(-0.117361\pi\) | |||||||
\(840\) | 2.02851 | + | 4.77794i | 0.0699902 | + | 0.164855i | ||||
\(841\) | −24.4030 | + | 42.2673i | −0.841484 | + | 1.45749i | ||||
\(842\) | −7.34740 | + | 4.24202i | −0.253208 | + | 0.146190i | ||||
\(843\) | 8.59688i | 0.296092i | ||||||||
\(844\) | −22.3886 | −0.770648 | ||||||||
\(845\) | −47.5287 | + | 20.1787i | −1.63504 | + | 0.694167i | ||||
\(846\) | −3.94406 | − | 6.83132i | −0.135600 | − | 0.234866i | ||||
\(847\) | 6.65790i | 0.228768i | ||||||||
\(848\) | 5.62229i | 0.193070i | ||||||||
\(849\) | −7.18742 | − | 12.4490i | −0.246672 | − | 0.427248i | ||||
\(850\) | 15.2175 | − | 15.7626i | 0.521957 | − | 0.540654i | ||||
\(851\) | −19.6390 | − | 34.0158i | −0.673217 | − | 1.16605i | ||||
\(852\) | −1.99443 | − | 1.15149i | −0.0683282 | − | 0.0394493i | ||||
\(853\) | −11.3790 | − | 6.56967i | −0.389609 | − | 0.224941i | 0.292381 | − | 0.956302i | \(-0.405552\pi\) |
−0.681991 | + | 0.731361i | \(0.738886\pi\) | |||||||
\(854\) | 25.0829 | 0.858320 | ||||||||
\(855\) | 6.99622 | + | 6.78623i | 0.239266 | + | 0.232084i | ||||
\(856\) | 16.7729 | 0.573286 | ||||||||
\(857\) | −19.8940 | − | 11.4858i | −0.679566 | − | 0.392348i | 0.120125 | − | 0.992759i | \(-0.461670\pi\) |
−0.799692 | + | 0.600411i | \(0.795004\pi\) | |||||||
\(858\) | −14.8365 | − | 8.56584i | −0.506509 | − | 0.292433i | ||||
\(859\) | −11.2488 | − | 19.4834i | −0.383803 | − | 0.664766i | 0.607800 | − | 0.794090i | \(-0.292052\pi\) |
−0.991602 | + | 0.129325i | \(0.958719\pi\) | |||||||
\(860\) | −3.48126 | + | 4.62046i | −0.118710 | + | 0.157556i | ||||
\(861\) | 5.99208 | + | 10.3786i | 0.204209 | + | 0.353701i | ||||
\(862\) | 19.6767i | 0.670190i | ||||||||
\(863\) | − | 24.1235i | − | 0.821175i | −0.911821 | − | 0.410587i | \(-0.865324\pi\) | ||
0.911821 | − | 0.410587i | \(-0.134676\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 12.4910 | + | 29.4211i | 0.424706 | + | 1.00035i | ||||
\(866\) | 13.9602 | 0.474387 | ||||||||
\(867\) | − | 2.20137i | − | 0.0747625i | ||||||
\(868\) | −1.37751 | + | 0.795303i | −0.0467556 | + | 0.0269943i | ||||
\(869\) | −5.72276 | + | 9.91212i | −0.194131 | + | 0.336246i | ||||
\(870\) | 18.1554 | − | 7.70800i | 0.615525 | − | 0.261326i | ||||
\(871\) | 20.4474 | − | 35.4159i | 0.692833 | − | 1.20002i | ||||
\(872\) | 7.71093 | + | 4.45191i | 0.261125 | + | 0.150761i | ||||
\(873\) | − | 6.69361i | − | 0.226544i | ||||||
\(874\) | −13.2520 | + | 17.5026i | −0.448256 | + | 0.592033i | ||||
\(875\) | −24.2317 | − | 9.29584i | −0.819181 | − | 0.314257i | ||||
\(876\) | 3.10727 | − | 5.38195i | 0.104985 | − | 0.181839i | ||||
\(877\) | −1.11105 | − | 0.641465i | −0.0375175 | − | 0.0216607i | 0.481124 | − | 0.876653i | \(-0.340229\pi\) |
−0.518641 | + | 0.854992i | \(0.673562\pi\) | |||||||
\(878\) | 17.7725 | − | 10.2610i | 0.599793 | − | 0.346291i | ||||
\(879\) | −4.23745 | + | 7.33948i | −0.142926 | + | 0.247554i | ||||
\(880\) | −5.86941 | + | 2.49190i | −0.197858 | + | 0.0840019i | ||||
\(881\) | −18.1444 | −0.611301 | −0.305650 | − | 0.952144i | \(-0.598874\pi\) | ||||
−0.305650 | + | 0.952144i | \(0.598874\pi\) | |||||||
\(882\) | 1.61129i | 0.0542550i | ||||||||
\(883\) | 39.6706 | − | 22.9039i | 1.33502 | − | 0.770776i | 0.348958 | − | 0.937138i | \(-0.386535\pi\) |
0.986065 | + | 0.166362i | \(0.0532021\pi\) | |||||||
\(884\) | 13.1626 | + | 22.7982i | 0.442705 | + | 0.766787i | ||||
\(885\) | −3.21657 | − | 0.394717i | −0.108124 | − | 0.0132683i | ||||
\(886\) | 23.5855 | 0.792369 | ||||||||
\(887\) | −50.4856 | + | 29.1479i | −1.69514 | + | 0.978689i | −0.744896 | + | 0.667180i | \(0.767501\pi\) |
−0.950243 | + | 0.311509i | \(0.899166\pi\) | |||||||
\(888\) | −6.75389 | − | 3.89936i | −0.226646 | − | 0.130854i | ||||
\(889\) | −10.3555 | − | 17.9362i | −0.347312 | − | 0.601561i | ||||
\(890\) | −11.6915 | + | 15.5174i | −0.391901 | + | 0.520146i | ||||
\(891\) | 1.42582 | − | 2.46960i | 0.0477669 | − | 0.0827347i | ||||
\(892\) | 1.87651i | 0.0628302i | ||||||||
\(893\) | 4.26837 | − | 34.1176i | 0.142836 | − | 1.14170i | ||||
\(894\) | 3.85302 | 0.128864 | ||||||||
\(895\) | 11.9063 | + | 8.97070i | 0.397982 | + | 0.299857i | ||||
\(896\) | −1.16068 | + | 2.01036i | −0.0387756 | + | 0.0671613i | ||||
\(897\) | 26.2037 | − | 15.1287i | 0.874914 | − | 0.505132i | ||||
\(898\) | −24.4653 | − | 14.1250i | −0.816416 | − | 0.471358i | ||||
\(899\) | 3.02202 | + | 5.23429i | 0.100790 | + | 0.174573i | ||||
\(900\) | −4.85165 | − | 1.20893i | −0.161722 | − | 0.0402977i | ||||
\(901\) | −24.6365 | −0.820762 | ||||||||
\(902\) | −12.7495 | + | 7.36090i | −0.424511 | + | 0.245091i | ||||
\(903\) | 5.20118 | − | 3.00290i | 0.173084 | − | 0.0999303i | ||||
\(904\) | −11.8870 | −0.395357 | ||||||||
\(905\) | −1.67112 | + | 13.6181i | −0.0555499 | + | 0.452680i | ||||
\(906\) | −3.88662 | − | 6.73182i | −0.129124 | − | 0.223650i | ||||
\(907\) | −27.2008 | − | 15.7044i | −0.903187 | − | 0.521455i | −0.0249542 | − | 0.999689i | \(-0.507944\pi\) |
−0.878233 | + | 0.478233i | \(0.841277\pi\) | |||||||
\(908\) | −17.6412 | + | 10.1852i | −0.585444 | + | 0.338006i | ||||
\(909\) | 7.02206 | − | 12.1626i | 0.232907 | − | 0.403407i | ||||
\(910\) | 18.7652 | − | 24.9060i | 0.622062 | − | 0.825624i | ||||
\(911\) | 19.8665 | 0.658206 | 0.329103 | − | 0.944294i | \(-0.393254\pi\) | ||||
0.329103 | + | 0.944294i | \(0.393254\pi\) | |||||||
\(912\) | −0.541114 | + | 4.32518i | −0.0179181 | + | 0.143221i | ||||
\(913\) | − | 34.8448i | − | 1.15319i | ||||||
\(914\) | 15.8392 | − | 27.4343i | 0.523914 | − | 0.907445i | ||||
\(915\) | −14.5393 | + | 19.2971i | −0.480655 | + | 0.637943i | ||||
\(916\) | −5.39065 | − | 9.33688i | −0.178112 | − | 0.308499i | ||||
\(917\) | −0.110296 | − | 0.0636793i | −0.00364228 | − | 0.00210287i | ||||
\(918\) | −3.79487 | + | 2.19097i | −0.125249 | + | 0.0723127i | ||||
\(919\) | 40.8314 | 1.34690 | 0.673451 | − | 0.739231i | \(-0.264811\pi\) | ||||
0.673451 | + | 0.739231i | \(0.264811\pi\) | |||||||
\(920\) | 1.37170 | − | 11.1781i | 0.0452235 | − | 0.368530i | ||||
\(921\) | 10.7838 | + | 18.6780i | 0.355337 | + | 0.615462i | ||||
\(922\) | 1.03187 | − | 0.595751i | 0.0339828 | − | 0.0196200i | ||||
\(923\) | 13.8354i | 0.455399i | ||||||||
\(924\) | 6.61970 | 0.217772 | ||||||||
\(925\) | 37.4815 | − | 10.7533i | 1.23238 | − | 0.353568i | ||||
\(926\) | −9.92347 | + | 17.1880i | −0.326106 | + | 0.564831i | ||||
\(927\) | −12.2073 | + | 7.04788i | −0.400940 | + | 0.231483i | ||||
\(928\) | 7.63902 | + | 4.41039i | 0.250763 | + | 0.144778i | ||||
\(929\) | 10.3109 | − | 17.8591i | 0.338291 | − | 0.585937i | −0.645821 | − | 0.763489i | \(-0.723485\pi\) |
0.984111 | + | 0.177553i | \(0.0568180\pi\) | |||||||
\(930\) | 0.186617 | − | 1.52076i | 0.00611942 | − | 0.0498676i | ||||
\(931\) | −4.23964 | + | 5.59950i | −0.138949 | + | 0.183516i | ||||
\(932\) | − | 13.5765i | − | 0.444711i | ||||||
\(933\) | −5.41641 | − | 3.12716i | −0.177325 | − | 0.102379i | ||||
\(934\) | −7.12255 | + | 12.3366i | −0.233057 | + | 0.403666i | ||||
\(935\) | −10.9193 | − | 25.7194i | −0.357101 | − | 0.841113i | ||||
\(936\) | 3.00382 | − | 5.20277i | 0.0981830 | − | 0.170058i | ||||
\(937\) | −11.5342 | + | 6.65926i | −0.376805 | + | 0.217548i | −0.676427 | − | 0.736509i | \(-0.736473\pi\) |
0.299622 | + | 0.954058i | \(0.403139\pi\) | |||||||
\(938\) | 15.8018i | 0.515946i | ||||||||
\(939\) | 17.7515 | 0.579298 | ||||||||
\(940\) | 6.89300 | + | 16.2357i | 0.224825 | + | 0.529551i | ||||
\(941\) | 2.77725 | + | 4.81033i | 0.0905356 | + | 0.156812i | 0.907737 | − | 0.419540i | \(-0.137809\pi\) |
−0.817201 | + | 0.576353i | \(0.804475\pi\) | |||||||
\(942\) | − | 19.2753i | − | 0.628023i | ||||||
\(943\) | − | 26.0011i | − | 0.846713i | ||||||
\(944\) | −0.724643 | − | 1.25512i | −0.0235851 | − | 0.0408506i | ||||
\(945\) | 4.14571 | + | 3.12356i | 0.134860 | + | 0.101609i | ||||
\(946\) | 3.68888 | + | 6.38933i | 0.119936 | + | 0.207735i | ||||
\(947\) | 1.05045 | + | 0.606477i | 0.0341350 | + | 0.0197079i | 0.516970 | − | 0.856003i | \(-0.327060\pi\) |
−0.482835 | + | 0.875711i | \(0.660393\pi\) | |||||||
\(948\) | −3.47593 | − | 2.00683i | −0.112893 | − | 0.0651787i | ||||
\(949\) | −37.3347 | −1.21194 | ||||||||
\(950\) | −13.6793 | − | 16.9669i | −0.443815 | − | 0.550480i | ||||
\(951\) | 0.739513 | 0.0239804 | ||||||||
\(952\) | −8.80925 | − | 5.08602i | −0.285510 | − | 0.164839i | ||||
\(953\) | 5.12855 | + | 2.96097i | 0.166130 | + | 0.0959153i | 0.580760 | − | 0.814075i | \(-0.302756\pi\) |
−0.414630 | + | 0.909990i | \(0.636089\pi\) | |||||||
\(954\) | 2.81115 | + | 4.86905i | 0.0910142 | + | 0.157641i | ||||
\(955\) | 33.6548 | + | 25.3570i | 1.08904 | + | 0.820534i | ||||
\(956\) | 1.04040 | + | 1.80203i | 0.0336491 | + | 0.0582819i | ||||
\(957\) | − | 25.1538i | − | 0.813105i | ||||||
\(958\) | 28.6965i | 0.927141i | ||||||||
\(959\) | −20.8718 | − | 36.1510i | −0.673985 | − | 1.16738i | ||||
\(960\) | −0.873846 | − | 2.05825i | −0.0282032 | − | 0.0664297i | ||||
\(961\) | −30.5305 | −0.984855 | ||||||||
\(962\) | 46.8519i | 1.51057i | ||||||||
\(963\) | 14.5258 | − | 8.38645i | 0.468086 | − | 0.270249i | ||||
\(964\) | 8.51317 | − | 14.7453i | 0.274191 | − | 0.474913i | ||||
\(965\) | 14.4397 | + | 34.0113i | 0.464832 | + | 1.09486i | ||||
\(966\) | −5.84574 | + | 10.1251i | −0.188084 | + | 0.325770i | ||||
\(967\) | 38.8853 | + | 22.4505i | 1.25047 | + | 0.721958i | 0.971202 | − | 0.238256i | \(-0.0765758\pi\) |
0.279265 | + | 0.960214i | \(0.409909\pi\) | |||||||
\(968\) | − | 2.86810i | − | 0.0921843i | ||||||
\(969\) | −18.9527 | − | 2.37113i | −0.608848 | − | 0.0761715i | ||||
\(970\) | −1.82302 | + | 14.8559i | −0.0585337 | + | 0.476995i | ||||
\(971\) | −3.97050 | + | 6.87710i | −0.127419 | + | 0.220697i | −0.922676 | − | 0.385576i | \(-0.874003\pi\) |
0.795257 | + | 0.606273i | \(0.207336\pi\) | |||||||
\(972\) | 0.866025 | + | 0.500000i | 0.0277778 | + | 0.0160375i | ||||
\(973\) | −41.5447 | + | 23.9858i | −1.33186 | + | 0.768950i | ||||
\(974\) | −9.82164 | + | 17.0116i | −0.314706 | + | 0.545086i | ||||
\(975\) | 8.28370 | + | 28.8734i | 0.265291 | + | 0.924690i | ||||
\(976\) | −10.8053 | −0.345869 | ||||||||
\(977\) | 25.2607i | 0.808162i | 0.914723 | + | 0.404081i | \(0.132409\pi\) | ||||
−0.914723 | + | 0.404081i | \(0.867591\pi\) | |||||||
\(978\) | 13.7843 | − | 7.95838i | 0.440774 | − | 0.254481i | ||||
\(979\) | 12.3888 | + | 21.4581i | 0.395948 | + | 0.685802i | ||||
\(980\) | 0.438840 | − | 3.57613i | 0.0140182 | − | 0.114235i | ||||
\(981\) | 8.90382 | 0.284277 | ||||||||
\(982\) | 8.65235 | − | 4.99544i | 0.276108 | − | 0.159411i | ||||
\(983\) | −9.18945 | − | 5.30553i | −0.293098 | − | 0.169220i | 0.346240 | − | 0.938146i | \(-0.387458\pi\) |
−0.639338 | + | 0.768926i | \(0.720792\pi\) | |||||||
\(984\) | −2.58128 | − | 4.47091i | −0.0822882 | − | 0.142527i | ||||
\(985\) | −9.28788 | + | 12.3272i | −0.295937 | + | 0.392778i | ||||
\(986\) | −19.3260 | + | 33.4737i | −0.615467 | + | 1.06602i | ||||
\(987\) | − | 18.3112i | − | 0.582851i | ||||||
\(988\) | 24.1283 | − | 10.1768i | 0.767625 | − | 0.323767i | ||||
\(989\) | −13.0303 | −0.414340 | ||||||||
\(990\) | −3.83710 | + | 5.09275i | −0.121951 | + | 0.161858i | ||||
\(991\) | 10.6138 | − | 18.3837i | 0.337159 | − | 0.583976i | −0.646738 | − | 0.762712i | \(-0.723867\pi\) |
0.983897 | + | 0.178736i | \(0.0572007\pi\) | |||||||
\(992\) | 0.593405 | − | 0.342602i | 0.0188406 | − | 0.0108776i | ||||
\(993\) | 3.93574 | + | 2.27230i | 0.124897 | + | 0.0721093i | ||||
\(994\) | −2.67301 | − | 4.62980i | −0.0847829 | − | 0.146848i | ||||
\(995\) | 1.77854 | − | 14.4935i | 0.0563836 | − | 0.459473i | ||||
\(996\) | 12.2192 | 0.387179 | ||||||||
\(997\) | 34.4427 | − | 19.8855i | 1.09081 | − | 0.629780i | 0.157019 | − | 0.987596i | \(-0.449812\pi\) |
0.933792 | + | 0.357816i | \(0.116478\pi\) | |||||||
\(998\) | −12.4376 | + | 7.18085i | −0.393705 | + | 0.227306i | ||||
\(999\) | −7.79872 | −0.246740 |
(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 | 570.2.q.c.49.7 | yes | 20 | |
3.2 | odd | 2 | 1710.2.t.c.1189.4 | 20 | |||
5.4 | even | 2 | inner | 570.2.q.c.49.5 | ✓ | 20 | |
15.14 | odd | 2 | 1710.2.t.c.1189.6 | 20 | |||
19.7 | even | 3 | inner | 570.2.q.c.349.5 | yes | 20 | |
57.26 | odd | 6 | 1710.2.t.c.919.6 | 20 | |||
95.64 | even | 6 | inner | 570.2.q.c.349.7 | yes | 20 | |
285.254 | odd | 6 | 1710.2.t.c.919.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.c.49.5 | ✓ | 20 | 5.4 | even | 2 | inner | |
570.2.q.c.49.7 | yes | 20 | 1.1 | even | 1 | trivial | |
570.2.q.c.349.5 | yes | 20 | 19.7 | even | 3 | inner | |
570.2.q.c.349.7 | yes | 20 | 95.64 | even | 6 | inner | |
1710.2.t.c.919.4 | 20 | 285.254 | odd | 6 | |||
1710.2.t.c.919.6 | 20 | 57.26 | odd | 6 | |||
1710.2.t.c.1189.4 | 20 | 3.2 | odd | 2 | |||
1710.2.t.c.1189.6 | 20 | 15.14 | odd | 2 |