Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(211,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.i (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.3636603.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 4x^{3} + 12x^{2} - 16x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 811.2 | ||
Root | \(-1.55951 + 1.25217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.811 |
Dual form | 930.2.i.n.211.2 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −0.695350 | + | 1.20438i | −0.262817 | + | 0.455213i | −0.966990 | − | 0.254816i | \(-0.917985\pi\) |
0.704172 | + | 0.710029i | \(0.251318\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −2.61903 | − | 4.53629i | −0.789666 | − | 1.36774i | −0.926171 | − | 0.377103i | \(-0.876920\pi\) |
0.136505 | − | 0.990639i | \(-0.456413\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −0.390699 | − | 0.676711i | −0.108360 | − | 0.187686i | 0.806746 | − | 0.590899i | \(-0.201227\pi\) |
−0.915106 | + | 0.403213i | \(0.867893\pi\) | |||||||
\(14\) | 0.695350 | − | 1.20438i | 0.185840 | − | 0.321884i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.80465 | + | 3.12575i | −0.437692 | + | 0.758105i | −0.997511 | − | 0.0705101i | \(-0.977537\pi\) |
0.559819 | + | 0.828615i | \(0.310871\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −3.72833 | + | 6.45765i | −0.855337 | + | 1.48149i | 0.0209951 | + | 0.999780i | \(0.493317\pi\) |
−0.876332 | + | 0.481708i | \(0.840017\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 0.695350 | + | 1.20438i | 0.151738 | + | 0.262817i | ||||
\(22\) | 2.61903 | + | 4.53629i | 0.558378 | + | 0.967140i | ||||
\(23\) | 2.39070 | 0.498495 | 0.249248 | − | 0.968440i | \(-0.419817\pi\) | ||||
0.249248 | + | 0.968440i | \(0.419817\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0.390699 | + | 0.676711i | 0.0766224 | + | 0.132714i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.695350 | + | 1.20438i | −0.131409 | + | 0.227607i | ||||
\(29\) | −2.84735 | −0.528740 | −0.264370 | − | 0.964421i | \(-0.585164\pi\) | ||||
−0.264370 | + | 0.964421i | \(0.585164\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −5.54270 | − | 0.527670i | −0.995499 | − | 0.0947723i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.23805 | −0.911828 | ||||||||
\(34\) | 1.80465 | − | 3.12575i | 0.309495 | − | 0.536061i | ||||
\(35\) | 1.39070 | 0.235071 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 2.80465 | − | 4.85780i | 0.461082 | − | 0.798617i | −0.537933 | − | 0.842987i | \(-0.680795\pi\) |
0.999015 | + | 0.0443704i | \(0.0141282\pi\) | |||||||
\(38\) | 3.72833 | − | 6.45765i | 0.604815 | − | 1.04757i | ||||
\(39\) | −0.781399 | −0.125124 | ||||||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | −5.50973 | − | 9.54313i | −0.860475 | − | 1.49039i | −0.871471 | − | 0.490446i | \(-0.836834\pi\) |
0.0109968 | − | 0.999940i | \(-0.496500\pi\) | |||||||
\(42\) | −0.695350 | − | 1.20438i | −0.107295 | − | 0.185840i | ||||
\(43\) | −3.92368 | + | 6.79601i | −0.598355 | + | 1.03638i | 0.394709 | + | 0.918806i | \(0.370845\pi\) |
−0.993064 | + | 0.117575i | \(0.962488\pi\) | |||||||
\(44\) | −2.61903 | − | 4.53629i | −0.394833 | − | 0.683871i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | −2.39070 | −0.352489 | ||||||||
\(47\) | 1.17210 | 0.170968 | 0.0854840 | − | 0.996340i | \(-0.472756\pi\) | ||||
0.0854840 | + | 0.996340i | \(0.472756\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 2.53298 | + | 4.38725i | 0.361854 | + | 0.626749i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | 1.80465 | + | 3.12575i | 0.252702 | + | 0.437692i | ||||
\(52\) | −0.390699 | − | 0.676711i | −0.0541802 | − | 0.0938429i | ||||
\(53\) | 3.81438 | + | 6.60669i | 0.523945 | + | 0.907499i | 0.999611 | + | 0.0278735i | \(0.00887356\pi\) |
−0.475667 | + | 0.879626i | \(0.657793\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.61903 | + | 4.53629i | −0.353149 | + | 0.611673i | ||||
\(56\) | 0.695350 | − | 1.20438i | 0.0929200 | − | 0.160942i | ||||
\(57\) | 3.72833 | + | 6.45765i | 0.493829 | + | 0.855337i | ||||
\(58\) | 2.84735 | 0.373876 | ||||||||
\(59\) | −2.08605 | + | 3.61314i | −0.271580 | + | 0.470391i | −0.969267 | − | 0.246012i | \(-0.920880\pi\) |
0.697686 | + | 0.716403i | \(0.254213\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −9.45665 | −1.21080 | −0.605400 | − | 0.795921i | \(-0.706987\pi\) | ||||
−0.605400 | + | 0.795921i | \(0.706987\pi\) | |||||||
\(62\) | 5.54270 | + | 0.527670i | 0.703924 | + | 0.0670141i | ||||
\(63\) | 1.39070 | 0.175212 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.390699 | + | 0.676711i | −0.0484603 | + | 0.0839357i | ||||
\(66\) | 5.23805 | 0.644760 | ||||||||
\(67\) | −2.80465 | − | 4.85780i | −0.342643 | − | 0.593474i | 0.642280 | − | 0.766470i | \(-0.277989\pi\) |
−0.984923 | + | 0.172996i | \(0.944655\pi\) | |||||||
\(68\) | −1.80465 | + | 3.12575i | −0.218846 | + | 0.379052i | ||||
\(69\) | 1.19535 | − | 2.07041i | 0.143903 | − | 0.249248i | ||||
\(70\) | −1.39070 | −0.166220 | ||||||||
\(71\) | 1.60930 | + | 2.78739i | 0.190989 | + | 0.330802i | 0.945578 | − | 0.325395i | \(-0.105497\pi\) |
−0.754589 | + | 0.656197i | \(0.772164\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 1.00000 | + | 1.73205i | 0.117041 | + | 0.202721i | 0.918594 | − | 0.395203i | \(-0.129326\pi\) |
−0.801553 | + | 0.597924i | \(0.795992\pi\) | |||||||
\(74\) | −2.80465 | + | 4.85780i | −0.326034 | + | 0.564707i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | −3.72833 | + | 6.45765i | −0.427668 | + | 0.740744i | ||||
\(77\) | 7.28456 | 0.830152 | ||||||||
\(78\) | 0.781399 | 0.0884760 | ||||||||
\(79\) | −3.92368 | + | 6.79601i | −0.441448 | + | 0.764611i | −0.997797 | − | 0.0663381i | \(-0.978868\pi\) |
0.556349 | + | 0.830949i | \(0.312202\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 5.50973 | + | 9.54313i | 0.608447 | + | 1.05386i | ||||
\(83\) | −6.93340 | − | 12.0090i | −0.761040 | − | 1.31816i | −0.942315 | − | 0.334727i | \(-0.891356\pi\) |
0.181275 | − | 0.983432i | \(-0.441978\pi\) | |||||||
\(84\) | 0.695350 | + | 1.20438i | 0.0758689 | + | 0.131409i | ||||
\(85\) | 3.60930 | 0.391484 | ||||||||
\(86\) | 3.92368 | − | 6.79601i | 0.423101 | − | 0.732832i | ||||
\(87\) | −1.42368 | + | 2.46588i | −0.152634 | + | 0.264370i | ||||
\(88\) | 2.61903 | + | 4.53629i | 0.279189 | + | 0.483570i | ||||
\(89\) | −9.21860 | −0.977170 | −0.488585 | − | 0.872516i | \(-0.662487\pi\) | ||||
−0.488585 | + | 0.872516i | \(0.662487\pi\) | |||||||
\(90\) | 0.500000 | − | 0.866025i | 0.0527046 | − | 0.0912871i | ||||
\(91\) | 1.08669 | 0.113916 | ||||||||
\(92\) | 2.39070 | 0.249248 | ||||||||
\(93\) | −3.22833 | + | 4.53629i | −0.334762 | + | 0.470391i | ||||
\(94\) | −1.17210 | −0.120893 | ||||||||
\(95\) | 7.45665 | 0.765037 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 13.2846 | 1.34884 | 0.674421 | − | 0.738347i | \(-0.264393\pi\) | ||||
0.674421 | + | 0.738347i | \(0.264393\pi\) | |||||||
\(98\) | −2.53298 | − | 4.38725i | −0.255869 | − | 0.443179i | ||||
\(99\) | −2.61903 | + | 4.53629i | −0.263222 | + | 0.455914i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −14.6947 | −1.46218 | −0.731089 | − | 0.682282i | \(-0.760988\pi\) | ||||
−0.731089 | + | 0.682282i | \(0.760988\pi\) | |||||||
\(102\) | −1.80465 | − | 3.12575i | −0.178687 | − | 0.309495i | ||||
\(103\) | −3.08605 | − | 5.34519i | −0.304077 | − | 0.526678i | 0.672978 | − | 0.739662i | \(-0.265015\pi\) |
−0.977055 | + | 0.212985i | \(0.931681\pi\) | |||||||
\(104\) | 0.390699 | + | 0.676711i | 0.0383112 | + | 0.0663570i | ||||
\(105\) | 0.695350 | − | 1.20438i | 0.0678592 | − | 0.117536i | ||||
\(106\) | −3.81438 | − | 6.60669i | −0.370485 | − | 0.641699i | ||||
\(107\) | −0.695350 | + | 1.20438i | −0.0672220 | + | 0.116432i | −0.897677 | − | 0.440653i | \(-0.854747\pi\) |
0.830455 | + | 0.557085i | \(0.188080\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −7.45665 | −0.714218 | −0.357109 | − | 0.934063i | \(-0.616238\pi\) | ||||
−0.357109 | + | 0.934063i | \(0.616238\pi\) | |||||||
\(110\) | 2.61903 | − | 4.53629i | 0.249714 | − | 0.432518i | ||||
\(111\) | −2.80465 | − | 4.85780i | −0.266206 | − | 0.461082i | ||||
\(112\) | −0.695350 | + | 1.20438i | −0.0657044 | + | 0.113803i | ||||
\(113\) | −5.53298 | − | 9.58340i | −0.520499 | − | 0.901530i | −0.999716 | − | 0.0238339i | \(-0.992413\pi\) |
0.479217 | − | 0.877696i | \(-0.340921\pi\) | |||||||
\(114\) | −3.72833 | − | 6.45765i | −0.349190 | − | 0.604815i | ||||
\(115\) | −1.19535 | − | 2.07041i | −0.111467 | − | 0.193066i | ||||
\(116\) | −2.84735 | −0.264370 | ||||||||
\(117\) | −0.390699 | + | 0.676711i | −0.0361202 | + | 0.0625620i | ||||
\(118\) | 2.08605 | − | 3.61314i | 0.192036 | − | 0.332617i | ||||
\(119\) | −2.50973 | − | 4.34697i | −0.230066 | − | 0.398486i | ||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −8.21860 | + | 14.2350i | −0.747146 | + | 1.29409i | ||||
\(122\) | 9.45665 | 0.856165 | ||||||||
\(123\) | −11.0195 | −0.993591 | ||||||||
\(124\) | −5.54270 | − | 0.527670i | −0.497749 | − | 0.0473862i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.39070 | −0.123893 | ||||||||
\(127\) | −5.93340 | + | 10.2770i | −0.526504 | + | 0.911932i | 0.473019 | + | 0.881052i | \(0.343164\pi\) |
−0.999523 | + | 0.0308800i | \(0.990169\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 3.92368 | + | 6.79601i | 0.345461 | + | 0.598355i | ||||
\(130\) | 0.390699 | − | 0.676711i | 0.0342666 | − | 0.0593515i | ||||
\(131\) | 6.31438 | − | 10.9368i | 0.551690 | − | 0.955554i | −0.446463 | − | 0.894802i | \(-0.647317\pi\) |
0.998153 | − | 0.0607525i | \(-0.0193500\pi\) | |||||||
\(132\) | −5.23805 | −0.455914 | ||||||||
\(133\) | −5.18498 | − | 8.98065i | −0.449595 | − | 0.778721i | ||||
\(134\) | 2.80465 | + | 4.85780i | 0.242285 | + | 0.419650i | ||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 1.80465 | − | 3.12575i | 0.154747 | − | 0.268031i | ||||
\(137\) | 6.82410 | + | 11.8197i | 0.583022 | + | 1.00982i | 0.995119 | + | 0.0986842i | \(0.0314634\pi\) |
−0.412096 | + | 0.911140i | \(0.635203\pi\) | |||||||
\(138\) | −1.19535 | + | 2.07041i | −0.101755 | + | 0.176245i | ||||
\(139\) | −0.238053 | −0.0201914 | −0.0100957 | − | 0.999949i | \(-0.503214\pi\) | ||||
−0.0100957 | + | 0.999949i | \(0.503214\pi\) | |||||||
\(140\) | 1.39070 | 0.117536 | ||||||||
\(141\) | 0.586049 | − | 1.01507i | 0.0493542 | − | 0.0854840i | ||||
\(142\) | −1.60930 | − | 2.78739i | −0.135050 | − | 0.233913i | ||||
\(143\) | −2.04650 | + | 3.54465i | −0.171137 | + | 0.296418i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 1.42368 | + | 2.46588i | 0.118230 | + | 0.204780i | ||||
\(146\) | −1.00000 | − | 1.73205i | −0.0827606 | − | 0.143346i | ||||
\(147\) | 5.06596 | 0.417833 | ||||||||
\(148\) | 2.80465 | − | 4.85780i | 0.230541 | − | 0.399308i | ||||
\(149\) | 10.8144 | − | 18.7310i | 0.885948 | − | 1.53451i | 0.0413253 | − | 0.999146i | \(-0.486842\pi\) |
0.844623 | − | 0.535362i | \(-0.179825\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | 0.456655 | 0.0371620 | 0.0185810 | − | 0.999827i | \(-0.494085\pi\) | ||||
0.0185810 | + | 0.999827i | \(0.494085\pi\) | |||||||
\(152\) | 3.72833 | − | 6.45765i | 0.302407 | − | 0.523785i | ||||
\(153\) | 3.60930 | 0.291795 | ||||||||
\(154\) | −7.28456 | −0.587006 | ||||||||
\(155\) | 2.31438 | + | 5.06396i | 0.185895 | + | 0.406747i | ||||
\(156\) | −0.781399 | −0.0625620 | ||||||||
\(157\) | 23.4956 | 1.87515 | 0.937575 | − | 0.347784i | \(-0.113066\pi\) | ||||
0.937575 | + | 0.347784i | \(0.113066\pi\) | |||||||
\(158\) | 3.92368 | − | 6.79601i | 0.312151 | − | 0.540661i | ||||
\(159\) | 7.62875 | 0.604999 | ||||||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −1.66237 | + | 2.87931i | −0.131013 | + | 0.226922i | ||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | 12.5226 | 0.980847 | 0.490423 | − | 0.871484i | \(-0.336842\pi\) | ||||
0.490423 | + | 0.871484i | \(0.336842\pi\) | |||||||
\(164\) | −5.50973 | − | 9.54313i | −0.430237 | − | 0.745193i | ||||
\(165\) | 2.61903 | + | 4.53629i | 0.203891 | + | 0.353149i | ||||
\(166\) | 6.93340 | + | 12.0090i | 0.538136 | + | 0.932080i | ||||
\(167\) | −9.35708 | + | 16.2069i | −0.724073 | + | 1.25413i | 0.235282 | + | 0.971927i | \(0.424399\pi\) |
−0.959355 | + | 0.282203i | \(0.908935\pi\) | |||||||
\(168\) | −0.695350 | − | 1.20438i | −0.0536474 | − | 0.0929200i | ||||
\(169\) | 6.19471 | − | 10.7295i | 0.476516 | − | 0.825350i | ||||
\(170\) | −3.60930 | −0.276821 | ||||||||
\(171\) | 7.45665 | 0.570225 | ||||||||
\(172\) | −3.92368 | + | 6.79601i | −0.299178 | + | 0.518191i | ||||
\(173\) | −3.42368 | − | 5.92998i | −0.260297 | − | 0.450848i | 0.706024 | − | 0.708188i | \(-0.250487\pi\) |
−0.966321 | + | 0.257340i | \(0.917154\pi\) | |||||||
\(174\) | 1.42368 | − | 2.46588i | 0.107929 | − | 0.186938i | ||||
\(175\) | −0.695350 | − | 1.20438i | −0.0525635 | − | 0.0910426i | ||||
\(176\) | −2.61903 | − | 4.53629i | −0.197417 | − | 0.341936i | ||||
\(177\) | 2.08605 | + | 3.61314i | 0.156797 | + | 0.271580i | ||||
\(178\) | 9.21860 | 0.690963 | ||||||||
\(179\) | −4.40043 | + | 7.62176i | −0.328903 | + | 0.569677i | −0.982295 | − | 0.187343i | \(-0.940012\pi\) |
0.653391 | + | 0.757020i | \(0.273346\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | −6.84735 | − | 11.8600i | −0.508960 | − | 0.881544i | −0.999946 | − | 0.0103770i | \(-0.996697\pi\) |
0.490986 | − | 0.871167i | \(-0.336636\pi\) | |||||||
\(182\) | −1.08669 | −0.0805509 | ||||||||
\(183\) | −4.72833 | + | 8.18970i | −0.349528 | + | 0.605400i | ||||
\(184\) | −2.39070 | −0.176245 | ||||||||
\(185\) | −5.60930 | −0.412404 | ||||||||
\(186\) | 3.22833 | − | 4.53629i | 0.236712 | − | 0.332617i | ||||
\(187\) | 18.9057 | 1.38252 | ||||||||
\(188\) | 1.17210 | 0.0854840 | ||||||||
\(189\) | 0.695350 | − | 1.20438i | 0.0505792 | − | 0.0876058i | ||||
\(190\) | −7.45665 | −0.540963 | ||||||||
\(191\) | 2.72833 | + | 4.72560i | 0.197415 | + | 0.341933i | 0.947689 | − | 0.319194i | \(-0.103412\pi\) |
−0.750275 | + | 0.661126i | \(0.770079\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −4.57632 | + | 7.92642i | −0.329411 | + | 0.570556i | −0.982395 | − | 0.186815i | \(-0.940183\pi\) |
0.652984 | + | 0.757372i | \(0.273517\pi\) | |||||||
\(194\) | −13.2846 | −0.953776 | ||||||||
\(195\) | 0.390699 | + | 0.676711i | 0.0279786 | + | 0.0484603i | ||||
\(196\) | 2.53298 | + | 4.38725i | 0.180927 | + | 0.313375i | ||||
\(197\) | −9.62875 | − | 16.6775i | −0.686020 | − | 1.18822i | −0.973115 | − | 0.230320i | \(-0.926023\pi\) |
0.287095 | − | 0.957902i | \(-0.407311\pi\) | |||||||
\(198\) | 2.61903 | − | 4.53629i | 0.186126 | − | 0.322380i | ||||
\(199\) | −8.93340 | − | 15.4731i | −0.633272 | − | 1.09686i | −0.986878 | − | 0.161465i | \(-0.948378\pi\) |
0.353606 | − | 0.935394i | \(-0.384955\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | −5.60930 | −0.395650 | ||||||||
\(202\) | 14.6947 | 1.03392 | ||||||||
\(203\) | 1.97991 | − | 3.42930i | 0.138962 | − | 0.240690i | ||||
\(204\) | 1.80465 | + | 3.12575i | 0.126351 | + | 0.218846i | ||||
\(205\) | −5.50973 | + | 9.54313i | −0.384816 | + | 0.666521i | ||||
\(206\) | 3.08605 | + | 5.34519i | 0.215015 | + | 0.372417i | ||||
\(207\) | −1.19535 | − | 2.07041i | −0.0830825 | − | 0.143903i | ||||
\(208\) | −0.390699 | − | 0.676711i | −0.0270901 | − | 0.0469215i | ||||
\(209\) | 39.0584 | 2.70172 | ||||||||
\(210\) | −0.695350 | + | 1.20438i | −0.0479837 | + | 0.0831102i | ||||
\(211\) | 7.72833 | − | 13.3859i | 0.532040 | − | 0.921520i | −0.467260 | − | 0.884120i | \(-0.654759\pi\) |
0.999300 | − | 0.0374005i | \(-0.0119077\pi\) | |||||||
\(212\) | 3.81438 | + | 6.60669i | 0.261972 | + | 0.453750i | ||||
\(213\) | 3.21860 | 0.220535 | ||||||||
\(214\) | 0.695350 | − | 1.20438i | 0.0475331 | − | 0.0823298i | ||||
\(215\) | 7.84735 | 0.535185 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 4.48963 | − | 6.30861i | 0.304776 | − | 0.428256i | ||||
\(218\) | 7.45665 | 0.505028 | ||||||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | −2.61903 | + | 4.53629i | −0.176575 | + | 0.305836i | ||||
\(221\) | 2.82030 | 0.189714 | ||||||||
\(222\) | 2.80465 | + | 4.85780i | 0.188236 | + | 0.326034i | ||||
\(223\) | −2.54270 | + | 4.40409i | −0.170272 | + | 0.294920i | −0.938515 | − | 0.345239i | \(-0.887798\pi\) |
0.768243 | + | 0.640158i | \(0.221131\pi\) | |||||||
\(224\) | 0.695350 | − | 1.20438i | 0.0464600 | − | 0.0804711i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 5.53298 | + | 9.58340i | 0.368048 | + | 0.637478i | ||||
\(227\) | −8.15200 | − | 14.1197i | −0.541068 | − | 0.937156i | −0.998843 | − | 0.0480887i | \(-0.984687\pi\) |
0.457776 | − | 0.889068i | \(-0.348646\pi\) | |||||||
\(228\) | 3.72833 | + | 6.45765i | 0.246915 | + | 0.427668i | ||||
\(229\) | 14.5757 | − | 25.2458i | 0.963188 | − | 1.66829i | 0.248782 | − | 0.968559i | \(-0.419970\pi\) |
0.714406 | − | 0.699731i | \(-0.246697\pi\) | |||||||
\(230\) | 1.19535 | + | 2.07041i | 0.0788190 | + | 0.136519i | ||||
\(231\) | 3.64228 | − | 6.30861i | 0.239644 | − | 0.415076i | ||||
\(232\) | 2.84735 | 0.186938 | ||||||||
\(233\) | 9.60930 | 0.629526 | 0.314763 | − | 0.949170i | \(-0.398075\pi\) | ||||
0.314763 | + | 0.949170i | \(0.398075\pi\) | |||||||
\(234\) | 0.390699 | − | 0.676711i | 0.0255408 | − | 0.0442380i | ||||
\(235\) | −0.586049 | − | 1.01507i | −0.0382296 | − | 0.0662156i | ||||
\(236\) | −2.08605 | + | 3.61314i | −0.135790 | + | 0.235196i | ||||
\(237\) | 3.92368 | + | 6.79601i | 0.254870 | + | 0.441448i | ||||
\(238\) | 2.50973 | + | 4.34697i | 0.162681 | + | 0.281772i | ||||
\(239\) | −1.84735 | − | 3.19971i | −0.119495 | − | 0.206972i | 0.800072 | − | 0.599903i | \(-0.204794\pi\) |
−0.919568 | + | 0.392931i | \(0.871461\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 12.8144 | − | 22.1952i | 0.825447 | − | 1.42972i | −0.0761310 | − | 0.997098i | \(-0.524257\pi\) |
0.901578 | − | 0.432618i | \(-0.142410\pi\) | |||||||
\(242\) | 8.21860 | − | 14.2350i | 0.528312 | − | 0.915063i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −9.45665 | −0.605400 | ||||||||
\(245\) | 2.53298 | − | 4.38725i | 0.161826 | − | 0.280291i | ||||
\(246\) | 11.0195 | 0.702575 | ||||||||
\(247\) | 5.82662 | 0.370739 | ||||||||
\(248\) | 5.54270 | + | 0.527670i | 0.351962 | + | 0.0335071i | ||||
\(249\) | −13.8668 | −0.878773 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −5.92368 | + | 10.2601i | −0.373899 | + | 0.647612i | −0.990162 | − | 0.139928i | \(-0.955313\pi\) |
0.616262 | + | 0.787541i | \(0.288646\pi\) | |||||||
\(252\) | 1.39070 | 0.0876058 | ||||||||
\(253\) | −6.26131 | − | 10.8449i | −0.393645 | − | 0.681813i | ||||
\(254\) | 5.93340 | − | 10.2770i | 0.372295 | − | 0.644834i | ||||
\(255\) | 1.80465 | − | 3.12575i | 0.113012 | − | 0.195742i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.28076 | + | 16.0747i | 0.578918 | + | 1.00271i | 0.995604 | + | 0.0936645i | \(0.0298581\pi\) |
−0.416686 | + | 0.909050i | \(0.636809\pi\) | |||||||
\(258\) | −3.92368 | − | 6.79601i | −0.244277 | − | 0.423101i | ||||
\(259\) | 3.90043 | + | 6.75573i | 0.242361 | + | 0.419781i | ||||
\(260\) | −0.390699 | + | 0.676711i | −0.0242301 | + | 0.0419678i | ||||
\(261\) | 1.42368 | + | 2.46588i | 0.0881234 | + | 0.152634i | ||||
\(262\) | −6.31438 | + | 10.9368i | −0.390103 | + | 0.675679i | ||||
\(263\) | −9.84735 | −0.607214 | −0.303607 | − | 0.952797i | \(-0.598191\pi\) | ||||
−0.303607 | + | 0.952797i | \(0.598191\pi\) | |||||||
\(264\) | 5.23805 | 0.322380 | ||||||||
\(265\) | 3.81438 | − | 6.60669i | 0.234315 | − | 0.405846i | ||||
\(266\) | 5.18498 | + | 8.98065i | 0.317912 | + | 0.550639i | ||||
\(267\) | −4.60930 | + | 7.98354i | −0.282085 | + | 0.488585i | ||||
\(268\) | −2.80465 | − | 4.85780i | −0.171321 | − | 0.296737i | ||||
\(269\) | −6.09577 | − | 10.5582i | −0.371666 | − | 0.643744i | 0.618156 | − | 0.786055i | \(-0.287880\pi\) |
−0.989822 | + | 0.142311i | \(0.954547\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | −16.6482 | −1.01131 | −0.505653 | − | 0.862737i | \(-0.668748\pi\) | ||||
−0.505653 | + | 0.862737i | \(0.668748\pi\) | |||||||
\(272\) | −1.80465 | + | 3.12575i | −0.109423 | + | 0.189526i | ||||
\(273\) | 0.543345 | − | 0.941101i | 0.0328847 | − | 0.0569581i | ||||
\(274\) | −6.82410 | − | 11.8197i | −0.412259 | − | 0.714054i | ||||
\(275\) | 5.23805 | 0.315867 | ||||||||
\(276\) | 1.19535 | − | 2.07041i | 0.0719516 | − | 0.124624i | ||||
\(277\) | 0.866806 | 0.0520813 | 0.0260407 | − | 0.999661i | \(-0.491710\pi\) | ||||
0.0260407 | + | 0.999661i | \(0.491710\pi\) | |||||||
\(278\) | 0.238053 | 0.0142775 | ||||||||
\(279\) | 2.31438 | + | 5.06396i | 0.138558 | + | 0.303171i | ||||
\(280\) | −1.39070 | −0.0831102 | ||||||||
\(281\) | 28.5150 | 1.70106 | 0.850531 | − | 0.525924i | \(-0.176280\pi\) | ||||
0.850531 | + | 0.525924i | \(0.176280\pi\) | |||||||
\(282\) | −0.586049 | + | 1.01507i | −0.0348987 | + | 0.0604463i | ||||
\(283\) | −5.50316 | −0.327129 | −0.163564 | − | 0.986533i | \(-0.552299\pi\) | ||||
−0.163564 | + | 0.986533i | \(0.552299\pi\) | |||||||
\(284\) | 1.60930 | + | 2.78739i | 0.0954944 | + | 0.165401i | ||||
\(285\) | 3.72833 | − | 6.45765i | 0.220847 | − | 0.382518i | ||||
\(286\) | 2.04650 | − | 3.54465i | 0.121012 | − | 0.209599i | ||||
\(287\) | 15.3247 | 0.904591 | ||||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | 1.98647 | + | 3.44067i | 0.116851 | + | 0.202393i | ||||
\(290\) | −1.42368 | − | 2.46588i | −0.0836012 | − | 0.144802i | ||||
\(291\) | 6.64228 | − | 11.5048i | 0.389377 | − | 0.674421i | ||||
\(292\) | 1.00000 | + | 1.73205i | 0.0585206 | + | 0.101361i | ||||
\(293\) | 0.595775 | − | 1.03191i | 0.0348055 | − | 0.0602850i | −0.848098 | − | 0.529840i | \(-0.822252\pi\) |
0.882903 | + | 0.469555i | \(0.155585\pi\) | |||||||
\(294\) | −5.06596 | −0.295453 | ||||||||
\(295\) | 4.17210 | 0.242909 | ||||||||
\(296\) | −2.80465 | + | 4.85780i | −0.163017 | + | 0.282354i | ||||
\(297\) | 2.61903 | + | 4.53629i | 0.151971 | + | 0.263222i | ||||
\(298\) | −10.8144 | + | 18.7310i | −0.626460 | + | 1.08506i | ||||
\(299\) | −0.934044 | − | 1.61781i | −0.0540172 | − | 0.0935605i | ||||
\(300\) | 0.500000 | + | 0.866025i | 0.0288675 | + | 0.0500000i | ||||
\(301\) | −5.45665 | − | 9.45120i | −0.314516 | − | 0.544758i | ||||
\(302\) | −0.456655 | −0.0262775 | ||||||||
\(303\) | −7.34735 | + | 12.7260i | −0.422094 | + | 0.731089i | ||||
\(304\) | −3.72833 | + | 6.45765i | −0.213834 | + | 0.370372i | ||||
\(305\) | 4.72833 | + | 8.18970i | 0.270743 | + | 0.468941i | ||||
\(306\) | −3.60930 | −0.206330 | ||||||||
\(307\) | 10.7478 | − | 18.6157i | 0.613408 | − | 1.06245i | −0.377253 | − | 0.926110i | \(-0.623131\pi\) |
0.990662 | − | 0.136344i | \(-0.0435353\pi\) | |||||||
\(308\) | 7.28456 | 0.415076 | ||||||||
\(309\) | −6.17210 | −0.351118 | ||||||||
\(310\) | −2.31438 | − | 5.06396i | −0.131448 | − | 0.287613i | ||||
\(311\) | −5.25751 | −0.298126 | −0.149063 | − | 0.988828i | \(-0.547626\pi\) | ||||
−0.149063 | + | 0.988828i | \(0.547626\pi\) | |||||||
\(312\) | 0.781399 | 0.0442380 | ||||||||
\(313\) | 10.4431 | − | 18.0880i | 0.590281 | − | 1.02240i | −0.403914 | − | 0.914797i | \(-0.632350\pi\) |
0.994194 | − | 0.107599i | \(-0.0343162\pi\) | |||||||
\(314\) | −23.4956 | −1.32593 | ||||||||
\(315\) | −0.695350 | − | 1.20438i | −0.0391785 | − | 0.0678592i | ||||
\(316\) | −3.92368 | + | 6.79601i | −0.220724 | + | 0.382305i | ||||
\(317\) | −3.20508 | + | 5.55135i | −0.180015 | + | 0.311795i | −0.941885 | − | 0.335934i | \(-0.890948\pi\) |
0.761870 | + | 0.647729i | \(0.224281\pi\) | |||||||
\(318\) | −7.62875 | −0.427799 | ||||||||
\(319\) | 7.45730 | + | 12.9164i | 0.417528 | + | 0.723180i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | 0.695350 | + | 1.20438i | 0.0388106 | + | 0.0672220i | ||||
\(322\) | 1.66237 | − | 2.87931i | 0.0926404 | − | 0.160458i | ||||
\(323\) | −13.4567 | − | 23.3076i | −0.748748 | − | 1.29687i | ||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 0.781399 | 0.0433442 | ||||||||
\(326\) | −12.5226 | −0.693563 | ||||||||
\(327\) | −3.72833 | + | 6.45765i | −0.206177 | + | 0.357109i | ||||
\(328\) | 5.50973 | + | 9.54313i | 0.304224 | + | 0.526931i | ||||
\(329\) | −0.815018 | + | 1.41165i | −0.0449334 | + | 0.0778269i | ||||
\(330\) | −2.61903 | − | 4.53629i | −0.144173 | − | 0.249714i | ||||
\(331\) | 17.3571 | + | 30.0633i | 0.954031 | + | 1.65243i | 0.736569 | + | 0.676362i | \(0.236445\pi\) |
0.217462 | + | 0.976069i | \(0.430222\pi\) | |||||||
\(332\) | −6.93340 | − | 12.0090i | −0.380520 | − | 0.659080i | ||||
\(333\) | −5.60930 | −0.307388 | ||||||||
\(334\) | 9.35708 | − | 16.2069i | 0.511997 | − | 0.886804i | ||||
\(335\) | −2.80465 | + | 4.85780i | −0.153234 | + | 0.265410i | ||||
\(336\) | 0.695350 | + | 1.20438i | 0.0379344 | + | 0.0657044i | ||||
\(337\) | −3.15265 | −0.171736 | −0.0858678 | − | 0.996307i | \(-0.527366\pi\) | ||||
−0.0858678 | + | 0.996307i | \(0.527366\pi\) | |||||||
\(338\) | −6.19471 | + | 10.7295i | −0.336948 | + | 0.583611i | ||||
\(339\) | −11.0660 | −0.601020 | ||||||||
\(340\) | 3.60930 | 0.195742 | ||||||||
\(341\) | 12.1228 | + | 26.5253i | 0.656488 | + | 1.43642i | ||||
\(342\) | −7.45665 | −0.403210 | ||||||||
\(343\) | −16.7801 | −0.906041 | ||||||||
\(344\) | 3.92368 | − | 6.79601i | 0.211550 | − | 0.366416i | ||||
\(345\) | −2.39070 | −0.128711 | ||||||||
\(346\) | 3.42368 | + | 5.92998i | 0.184058 | + | 0.318798i | ||||
\(347\) | −9.15200 | + | 15.8517i | −0.491305 | + | 0.850966i | −0.999950 | − | 0.0100108i | \(-0.996813\pi\) |
0.508645 | + | 0.860977i | \(0.330147\pi\) | |||||||
\(348\) | −1.42368 | + | 2.46588i | −0.0763171 | + | 0.132185i | ||||
\(349\) | 8.71416 | 0.466458 | 0.233229 | − | 0.972422i | \(-0.425071\pi\) | ||||
0.233229 | + | 0.972422i | \(0.425071\pi\) | |||||||
\(350\) | 0.695350 | + | 1.20438i | 0.0371680 | + | 0.0643769i | ||||
\(351\) | 0.390699 | + | 0.676711i | 0.0208540 | + | 0.0361202i | ||||
\(352\) | 2.61903 | + | 4.53629i | 0.139595 | + | 0.241785i | ||||
\(353\) | 5.36088 | − | 9.28532i | 0.285331 | − | 0.494208i | −0.687359 | − | 0.726318i | \(-0.741230\pi\) |
0.972689 | + | 0.232111i | \(0.0745632\pi\) | |||||||
\(354\) | −2.08605 | − | 3.61314i | −0.110872 | − | 0.192036i | ||||
\(355\) | 1.60930 | − | 2.78739i | 0.0854128 | − | 0.147939i | ||||
\(356\) | −9.21860 | −0.488585 | ||||||||
\(357\) | −5.01945 | −0.265658 | ||||||||
\(358\) | 4.40043 | − | 7.62176i | 0.232570 | − | 0.402823i | ||||
\(359\) | −9.11903 | − | 15.7946i | −0.481284 | − | 0.833608i | 0.518485 | − | 0.855086i | \(-0.326496\pi\) |
−0.999769 | + | 0.0214784i | \(0.993163\pi\) | |||||||
\(360\) | 0.500000 | − | 0.866025i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | −18.3009 | − | 31.6980i | −0.963203 | − | 1.66832i | ||||
\(362\) | 6.84735 | + | 11.8600i | 0.359889 | + | 0.623346i | ||||
\(363\) | 8.21860 | + | 14.2350i | 0.431365 | + | 0.747146i | ||||
\(364\) | 1.08669 | 0.0569581 | ||||||||
\(365\) | 1.00000 | − | 1.73205i | 0.0523424 | − | 0.0906597i | ||||
\(366\) | 4.72833 | − | 8.18970i | 0.247154 | − | 0.428083i | ||||
\(367\) | 12.0000 | + | 20.7846i | 0.626395 | + | 1.08495i | 0.988269 | + | 0.152721i | \(0.0488036\pi\) |
−0.361874 | + | 0.932227i | \(0.617863\pi\) | |||||||
\(368\) | 2.39070 | 0.124624 | ||||||||
\(369\) | −5.50973 | + | 9.54313i | −0.286825 | + | 0.496795i | ||||
\(370\) | 5.60930 | 0.291614 | ||||||||
\(371\) | −10.6093 | −0.550807 | ||||||||
\(372\) | −3.22833 | + | 4.53629i | −0.167381 | + | 0.235196i | ||||
\(373\) | −20.9598 | −1.08526 | −0.542629 | − | 0.839972i | \(-0.682571\pi\) | ||||
−0.542629 | + | 0.839972i | \(0.682571\pi\) | |||||||
\(374\) | −18.9057 | −0.977591 | ||||||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | −1.17210 | −0.0604463 | ||||||||
\(377\) | 1.11246 | + | 1.92684i | 0.0572946 | + | 0.0992371i | ||||
\(378\) | −0.695350 | + | 1.20438i | −0.0357649 | + | 0.0619467i | ||||
\(379\) | −7.67526 | + | 13.2939i | −0.394251 | + | 0.682864i | −0.993005 | − | 0.118070i | \(-0.962329\pi\) |
0.598754 | + | 0.800933i | \(0.295663\pi\) | |||||||
\(380\) | 7.45665 | 0.382518 | ||||||||
\(381\) | 5.93340 | + | 10.2770i | 0.303977 | + | 0.526504i | ||||
\(382\) | −2.72833 | − | 4.72560i | −0.139593 | − | 0.241783i | ||||
\(383\) | 3.58605 | + | 6.21122i | 0.183239 | + | 0.317378i | 0.942982 | − | 0.332845i | \(-0.108009\pi\) |
−0.759743 | + | 0.650223i | \(0.774675\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −3.64228 | − | 6.30861i | −0.185628 | − | 0.321517i | ||||
\(386\) | 4.57632 | − | 7.92642i | 0.232929 | − | 0.403444i | ||||
\(387\) | 7.84735 | 0.398903 | ||||||||
\(388\) | 13.2846 | 0.674421 | ||||||||
\(389\) | −8.48647 | + | 14.6990i | −0.430281 | + | 0.745269i | −0.996897 | − | 0.0787129i | \(-0.974919\pi\) |
0.566616 | + | 0.823982i | \(0.308252\pi\) | |||||||
\(390\) | −0.390699 | − | 0.676711i | −0.0197838 | − | 0.0342666i | ||||
\(391\) | −4.31438 | + | 7.47272i | −0.218187 | + | 0.377912i | ||||
\(392\) | −2.53298 | − | 4.38725i | −0.127935 | − | 0.221589i | ||||
\(393\) | −6.31438 | − | 10.9368i | −0.318518 | − | 0.551690i | ||||
\(394\) | 9.62875 | + | 16.6775i | 0.485090 | + | 0.840200i | ||||
\(395\) | 7.84735 | 0.394843 | ||||||||
\(396\) | −2.61903 | + | 4.53629i | −0.131611 | + | 0.227957i | ||||
\(397\) | 13.3144 | − | 23.0612i | 0.668229 | − | 1.15741i | −0.310169 | − | 0.950681i | \(-0.600386\pi\) |
0.978399 | − | 0.206726i | \(-0.0662809\pi\) | |||||||
\(398\) | 8.93340 | + | 15.4731i | 0.447791 | + | 0.775597i | ||||
\(399\) | −10.3700 | −0.519148 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 18.1319 | 0.905464 | 0.452732 | − | 0.891647i | \(-0.350449\pi\) | ||||
0.452732 | + | 0.891647i | \(0.350449\pi\) | |||||||
\(402\) | 5.60930 | 0.279766 | ||||||||
\(403\) | 1.80845 | + | 3.95697i | 0.0900853 | + | 0.197111i | ||||
\(404\) | −14.6947 | −0.731089 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −1.97991 | + | 3.42930i | −0.0982611 | + | 0.170193i | ||||
\(407\) | −29.3818 | −1.45640 | ||||||||
\(408\) | −1.80465 | − | 3.12575i | −0.0893435 | − | 0.154747i | ||||
\(409\) | −6.51945 | + | 11.2920i | −0.322366 | + | 0.558355i | −0.980976 | − | 0.194130i | \(-0.937812\pi\) |
0.658610 | + | 0.752485i | \(0.271145\pi\) | |||||||
\(410\) | 5.50973 | − | 9.54313i | 0.272106 | − | 0.471301i | ||||
\(411\) | 13.6482 | 0.673216 | ||||||||
\(412\) | −3.08605 | − | 5.34519i | −0.152039 | − | 0.263339i | ||||
\(413\) | −2.90107 | − | 5.02479i | −0.142752 | − | 0.247254i | ||||
\(414\) | 1.19535 | + | 2.07041i | 0.0587482 | + | 0.101755i | ||||
\(415\) | −6.93340 | + | 12.0090i | −0.340347 | + | 0.589499i | ||||
\(416\) | 0.390699 | + | 0.676711i | 0.0191556 | + | 0.0331785i | ||||
\(417\) | −0.119027 | + | 0.206160i | −0.00582876 | + | 0.0100957i | ||||
\(418\) | −39.0584 | −1.91041 | ||||||||
\(419\) | −2.76195 | −0.134930 | −0.0674650 | − | 0.997722i | \(-0.521491\pi\) | ||||
−0.0674650 | + | 0.997722i | \(0.521491\pi\) | |||||||
\(420\) | 0.695350 | − | 1.20438i | 0.0339296 | − | 0.0587678i | ||||
\(421\) | −6.96638 | − | 12.0661i | −0.339521 | − | 0.588067i | 0.644822 | − | 0.764333i | \(-0.276932\pi\) |
−0.984343 | + | 0.176266i | \(0.943598\pi\) | |||||||
\(422\) | −7.72833 | + | 13.3859i | −0.376209 | + | 0.651613i | ||||
\(423\) | −0.586049 | − | 1.01507i | −0.0284947 | − | 0.0493542i | ||||
\(424\) | −3.81438 | − | 6.60669i | −0.185242 | − | 0.320849i | ||||
\(425\) | −1.80465 | − | 3.12575i | −0.0875384 | − | 0.151621i | ||||
\(426\) | −3.21860 | −0.155942 | ||||||||
\(427\) | 6.57568 | − | 11.3894i | 0.318220 | − | 0.551172i | ||||
\(428\) | −0.695350 | + | 1.20438i | −0.0336110 | + | 0.0582159i | ||||
\(429\) | 2.04650 | + | 3.54465i | 0.0988061 | + | 0.171137i | ||||
\(430\) | −7.84735 | −0.378433 | ||||||||
\(431\) | −7.68182 | + | 13.3053i | −0.370020 | + | 0.640894i | −0.989568 | − | 0.144065i | \(-0.953983\pi\) |
0.619548 | + | 0.784959i | \(0.287316\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −3.25751 | −0.156546 | −0.0782729 | − | 0.996932i | \(-0.524941\pi\) | ||||
−0.0782729 | + | 0.996932i | \(0.524941\pi\) | |||||||
\(434\) | −4.48963 | + | 6.30861i | −0.215509 | + | 0.302823i | ||||
\(435\) | 2.84735 | 0.136520 | ||||||||
\(436\) | −7.45665 | −0.357109 | ||||||||
\(437\) | −8.91331 | + | 15.4383i | −0.426381 | + | 0.738514i | ||||
\(438\) | −2.00000 | −0.0955637 | ||||||||
\(439\) | −11.7911 | − | 20.4228i | −0.562760 | − | 0.974728i | −0.997254 | − | 0.0740539i | \(-0.976406\pi\) |
0.434495 | − | 0.900674i | \(-0.356927\pi\) | |||||||
\(440\) | 2.61903 | − | 4.53629i | 0.124857 | − | 0.216259i | ||||
\(441\) | 2.53298 | − | 4.38725i | 0.120618 | − | 0.208916i | ||||
\(442\) | −2.82030 | −0.134148 | ||||||||
\(443\) | 11.0660 | + | 19.1668i | 0.525759 | + | 0.910642i | 0.999550 | + | 0.0300044i | \(0.00955212\pi\) |
−0.473790 | + | 0.880638i | \(0.657115\pi\) | |||||||
\(444\) | −2.80465 | − | 4.85780i | −0.133103 | − | 0.230541i | ||||
\(445\) | 4.60930 | + | 7.98354i | 0.218502 | + | 0.378456i | ||||
\(446\) | 2.54270 | − | 4.40409i | 0.120401 | − | 0.208540i | ||||
\(447\) | −10.8144 | − | 18.7310i | −0.511502 | − | 0.885948i | ||||
\(448\) | −0.695350 | + | 1.20438i | −0.0328522 | + | 0.0569016i | ||||
\(449\) | −24.9133 | −1.17573 | −0.587866 | − | 0.808958i | \(-0.700032\pi\) | ||||
−0.587866 | + | 0.808958i | \(0.700032\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −28.8602 | + | 49.9874i | −1.35898 | + | 2.35381i | ||||
\(452\) | −5.53298 | − | 9.58340i | −0.260249 | − | 0.450765i | ||||
\(453\) | 0.228327 | − | 0.395475i | 0.0107278 | − | 0.0185810i | ||||
\(454\) | 8.15200 | + | 14.1197i | 0.382593 | + | 0.662670i | ||||
\(455\) | −0.543345 | − | 0.941101i | −0.0254724 | − | 0.0441195i | ||||
\(456\) | −3.72833 | − | 6.45765i | −0.174595 | − | 0.302407i | ||||
\(457\) | 28.8203 | 1.34816 | 0.674078 | − | 0.738660i | \(-0.264541\pi\) | ||||
0.674078 | + | 0.738660i | \(0.264541\pi\) | |||||||
\(458\) | −14.5757 | + | 25.2458i | −0.681077 | + | 1.17966i | ||||
\(459\) | 1.80465 | − | 3.12575i | 0.0842339 | − | 0.145897i | ||||
\(460\) | −1.19535 | − | 2.07041i | −0.0557335 | − | 0.0965332i | ||||
\(461\) | −17.1708 | −0.799725 | −0.399862 | − | 0.916575i | \(-0.630942\pi\) | ||||
−0.399862 | + | 0.916575i | \(0.630942\pi\) | |||||||
\(462\) | −3.64228 | + | 6.30861i | −0.169454 | + | 0.293503i | ||||
\(463\) | −22.7412 | −1.05687 | −0.528437 | − | 0.848973i | \(-0.677222\pi\) | ||||
−0.528437 | + | 0.848973i | \(0.677222\pi\) | |||||||
\(464\) | −2.84735 | −0.132185 | ||||||||
\(465\) | 5.54270 | + | 0.527670i | 0.257037 | + | 0.0244701i | ||||
\(466\) | −9.60930 | −0.445142 | ||||||||
\(467\) | −7.56151 | −0.349905 | −0.174953 | − | 0.984577i | \(-0.555977\pi\) | ||||
−0.174953 | + | 0.984577i | \(0.555977\pi\) | |||||||
\(468\) | −0.390699 | + | 0.676711i | −0.0180601 | + | 0.0312810i | ||||
\(469\) | 7.80085 | 0.360210 | ||||||||
\(470\) | 0.586049 | + | 1.01507i | 0.0270324 | + | 0.0468215i | ||||
\(471\) | 11.7478 | − | 20.3478i | 0.541309 | − | 0.937575i | ||||
\(472\) | 2.08605 | − | 3.61314i | 0.0960182 | − | 0.166308i | ||||
\(473\) | 41.1049 | 1.89000 | ||||||||
\(474\) | −3.92368 | − | 6.79601i | −0.180220 | − | 0.312151i | ||||
\(475\) | −3.72833 | − | 6.45765i | −0.171067 | − | 0.296297i | ||||
\(476\) | −2.50973 | − | 4.34697i | −0.115033 | − | 0.199243i | ||||
\(477\) | 3.81438 | − | 6.60669i | 0.174648 | − | 0.302500i | ||||
\(478\) | 1.84735 | + | 3.19971i | 0.0844960 | + | 0.146351i | ||||
\(479\) | −9.57568 | + | 16.5856i | −0.437524 | + | 0.757814i | −0.997498 | − | 0.0706964i | \(-0.977478\pi\) |
0.559974 | + | 0.828510i | \(0.310811\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −4.38310 | −0.199852 | ||||||||
\(482\) | −12.8144 | + | 22.1952i | −0.583679 | + | 1.01096i | ||||
\(483\) | 1.66237 | + | 2.87931i | 0.0756405 | + | 0.131013i | ||||
\(484\) | −8.21860 | + | 14.2350i | −0.373573 | + | 0.647047i | ||||
\(485\) | −6.64228 | − | 11.5048i | −0.301610 | − | 0.522404i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −2.15200 | − | 3.72738i | −0.0975166 | − | 0.168904i | 0.813140 | − | 0.582069i | \(-0.197757\pi\) |
−0.910656 | + | 0.413165i | \(0.864423\pi\) | |||||||
\(488\) | 9.45665 | 0.428083 | ||||||||
\(489\) | 6.26131 | − | 10.8449i | 0.283146 | − | 0.490423i | ||||
\(490\) | −2.53298 | + | 4.38725i | −0.114428 | + | 0.198196i | ||||
\(491\) | −13.2943 | − | 23.0264i | −0.599963 | − | 1.03917i | −0.992826 | − | 0.119569i | \(-0.961849\pi\) |
0.392863 | − | 0.919597i | \(-0.371485\pi\) | |||||||
\(492\) | −11.0195 | −0.496795 | ||||||||
\(493\) | 5.13848 | − | 8.90011i | 0.231425 | − | 0.400841i | ||||
\(494\) | −5.82662 | −0.262152 | ||||||||
\(495\) | 5.23805 | 0.235433 | ||||||||
\(496\) | −5.54270 | − | 0.527670i | −0.248875 | − | 0.0236931i | ||||
\(497\) | −4.47611 | −0.200781 | ||||||||
\(498\) | 13.8668 | 0.621386 | ||||||||
\(499\) | 19.7943 | − | 34.2847i | 0.886114 | − | 1.53479i | 0.0416821 | − | 0.999131i | \(-0.486728\pi\) |
0.844432 | − | 0.535663i | \(-0.179938\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 9.35708 | + | 16.2069i | 0.418044 | + | 0.724073i | ||||
\(502\) | 5.92368 | − | 10.2601i | 0.264387 | − | 0.457931i | ||||
\(503\) | −15.5951 | + | 27.0116i | −0.695353 | + | 1.20439i | 0.274709 | + | 0.961527i | \(0.411418\pi\) |
−0.970062 | + | 0.242859i | \(0.921915\pi\) | |||||||
\(504\) | −1.39070 | −0.0619467 | ||||||||
\(505\) | 7.34735 | + | 12.7260i | 0.326953 | + | 0.566299i | ||||
\(506\) | 6.26131 | + | 10.8449i | 0.278349 | + | 0.482115i | ||||
\(507\) | −6.19471 | − | 10.7295i | −0.275117 | − | 0.476516i | ||||
\(508\) | −5.93340 | + | 10.2770i | −0.263252 | + | 0.455966i | ||||
\(509\) | 17.5389 | + | 30.3783i | 0.777398 | + | 1.34649i | 0.933437 | + | 0.358742i | \(0.116794\pi\) |
−0.156038 | + | 0.987751i | \(0.549872\pi\) | |||||||
\(510\) | −1.80465 | + | 3.12575i | −0.0799113 | + | 0.138410i | ||||
\(511\) | −2.78140 | −0.123042 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.72833 | − | 6.45765i | 0.164610 | − | 0.285112i | ||||
\(514\) | −9.28076 | − | 16.0747i | −0.409357 | − | 0.709027i | ||||
\(515\) | −3.08605 | + | 5.34519i | −0.135988 | + | 0.235537i | ||||
\(516\) | 3.92368 | + | 6.79601i | 0.172730 | + | 0.299178i | ||||
\(517\) | −3.06976 | − | 5.31697i | −0.135008 | − | 0.233840i | ||||
\(518\) | −3.90043 | − | 6.75573i | −0.171375 | − | 0.296830i | ||||
\(519\) | −6.84735 | −0.300565 | ||||||||
\(520\) | 0.390699 | − | 0.676711i | 0.0171333 | − | 0.0296757i | ||||
\(521\) | 0.980548 | − | 1.69836i | 0.0429586 | − | 0.0744065i | −0.843747 | − | 0.536742i | \(-0.819655\pi\) |
0.886705 | + | 0.462335i | \(0.152988\pi\) | |||||||
\(522\) | −1.42368 | − | 2.46588i | −0.0623127 | − | 0.107929i | ||||
\(523\) | −21.1049 | −0.922851 | −0.461426 | − | 0.887179i | \(-0.652662\pi\) | ||||
−0.461426 | + | 0.887179i | \(0.652662\pi\) | |||||||
\(524\) | 6.31438 | − | 10.9368i | 0.275845 | − | 0.477777i | ||||
\(525\) | −1.39070 | −0.0606951 | ||||||||
\(526\) | 9.84735 | 0.429365 | ||||||||
\(527\) | 11.6520 | − | 16.3728i | 0.507569 | − | 0.713211i | ||||
\(528\) | −5.23805 | −0.227957 | ||||||||
\(529\) | −17.2846 | −0.751502 | ||||||||
\(530\) | −3.81438 | + | 6.60669i | −0.165686 | + | 0.286976i | ||||
\(531\) | 4.17210 | 0.181054 | ||||||||
\(532\) | −5.18498 | − | 8.98065i | −0.224797 | − | 0.389361i | ||||
\(533\) | −4.30529 | + | 7.45698i | −0.186483 | + | 0.322998i | ||||
\(534\) | 4.60930 | − | 7.98354i | 0.199464 | − | 0.345482i | ||||
\(535\) | 1.39070 | 0.0601252 | ||||||||
\(536\) | 2.80465 | + | 4.85780i | 0.121142 | + | 0.209825i | ||||
\(537\) | 4.40043 | + | 7.62176i | 0.189892 | + | 0.328903i | ||||
\(538\) | 6.09577 | + | 10.5582i | 0.262808 | + | 0.455196i | ||||
\(539\) | 13.2679 | − | 22.9806i | 0.571488 | − | 0.989846i | ||||
\(540\) | 0.500000 | + | 0.866025i | 0.0215166 | + | 0.0372678i | ||||
\(541\) | −17.7478 | + | 30.7401i | −0.763037 | + | 1.32162i | 0.178242 | + | 0.983987i | \(0.442959\pi\) |
−0.941278 | + | 0.337631i | \(0.890374\pi\) | |||||||
\(542\) | 16.6482 | 0.715102 | ||||||||
\(543\) | −13.6947 | −0.587696 | ||||||||
\(544\) | 1.80465 | − | 3.12575i | 0.0773737 | − | 0.134015i | ||||
\(545\) | 3.72833 | + | 6.45765i | 0.159704 | + | 0.276615i | ||||
\(546\) | −0.543345 | + | 0.941101i | −0.0232530 | + | 0.0402754i | ||||
\(547\) | −17.9431 | − | 31.0784i | −0.767193 | − | 1.32882i | −0.939079 | − | 0.343700i | \(-0.888320\pi\) |
0.171887 | − | 0.985117i | \(-0.445014\pi\) | |||||||
\(548\) | 6.82410 | + | 11.8197i | 0.291511 | + | 0.504912i | ||||
\(549\) | 4.72833 | + | 8.18970i | 0.201800 | + | 0.349528i | ||||
\(550\) | −5.23805 | −0.223351 | ||||||||
\(551\) | 10.6159 | − | 18.3872i | 0.452251 | − | 0.783322i | ||||
\(552\) | −1.19535 | + | 2.07041i | −0.0508775 | + | 0.0881223i | ||||
\(553\) | −5.45665 | − | 9.45120i | −0.232041 | − | 0.401906i | ||||
\(554\) | −0.866806 | −0.0368271 | ||||||||
\(555\) | −2.80465 | + | 4.85780i | −0.119051 | + | 0.206202i | ||||
\(556\) | −0.238053 | −0.0100957 | ||||||||
\(557\) | −27.7607 | −1.17626 | −0.588129 | − | 0.808767i | \(-0.700135\pi\) | ||||
−0.588129 | + | 0.808767i | \(0.700135\pi\) | |||||||
\(558\) | −2.31438 | − | 5.06396i | −0.0979754 | − | 0.214374i | ||||
\(559\) | 6.13191 | 0.259352 | ||||||||
\(560\) | 1.39070 | 0.0587678 | ||||||||
\(561\) | 9.45285 | − | 16.3728i | 0.399100 | − | 0.691261i | ||||
\(562\) | −28.5150 | −1.20283 | ||||||||
\(563\) | −1.35115 | − | 2.34027i | −0.0569444 | − | 0.0986305i | 0.836148 | − | 0.548504i | \(-0.184802\pi\) |
−0.893092 | + | 0.449873i | \(0.851469\pi\) | |||||||
\(564\) | 0.586049 | − | 1.01507i | 0.0246771 | − | 0.0427420i | ||||
\(565\) | −5.53298 | + | 9.58340i | −0.232774 | + | 0.403177i | ||||
\(566\) | 5.50316 | 0.231315 | ||||||||
\(567\) | −0.695350 | − | 1.20438i | −0.0292019 | − | 0.0505792i | ||||
\(568\) | −1.60930 | − | 2.78739i | −0.0675248 | − | 0.116956i | ||||
\(569\) | 20.5615 | + | 35.6136i | 0.861984 | + | 1.49300i | 0.870011 | + | 0.493031i | \(0.164111\pi\) |
−0.00802797 | + | 0.999968i | \(0.502555\pi\) | |||||||
\(570\) | −3.72833 | + | 6.45765i | −0.156162 | + | 0.270481i | ||||
\(571\) | 2.84735 | + | 4.93176i | 0.119158 | + | 0.206388i | 0.919434 | − | 0.393244i | \(-0.128647\pi\) |
−0.800276 | + | 0.599632i | \(0.795314\pi\) | |||||||
\(572\) | −2.04650 | + | 3.54465i | −0.0855686 | + | 0.148209i | ||||
\(573\) | 5.45665 | 0.227955 | ||||||||
\(574\) | −15.3247 | −0.639642 | ||||||||
\(575\) | −1.19535 | + | 2.07041i | −0.0498495 | + | 0.0863419i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −17.6288 | + | 30.5339i | −0.733895 | + | 1.27114i | 0.221312 | + | 0.975203i | \(0.428966\pi\) |
−0.955207 | + | 0.295940i | \(0.904367\pi\) | |||||||
\(578\) | −1.98647 | − | 3.44067i | −0.0826264 | − | 0.143113i | ||||
\(579\) | 4.57632 | + | 7.92642i | 0.190185 | + | 0.329411i | ||||
\(580\) | 1.42368 | + | 2.46588i | 0.0591150 | + | 0.102390i | ||||
\(581\) | 19.2846 | 0.800058 | ||||||||
\(582\) | −6.64228 | + | 11.5048i | −0.275331 | + | 0.476888i | ||||
\(583\) | 19.9799 | − | 34.6062i | 0.827483 | − | 1.43324i | ||||
\(584\) | −1.00000 | − | 1.73205i | −0.0413803 | − | 0.0716728i | ||||
\(585\) | 0.781399 | 0.0323069 | ||||||||
\(586\) | −0.595775 | + | 1.03191i | −0.0246112 | + | 0.0426279i | ||||
\(587\) | −36.6093 | −1.51103 | −0.755514 | − | 0.655133i | \(-0.772613\pi\) | ||||
−0.755514 | + | 0.655133i | \(0.772613\pi\) | |||||||
\(588\) | 5.06596 | 0.208916 | ||||||||
\(589\) | 24.0725 | − | 33.8255i | 0.991891 | − | 1.39376i | ||||
\(590\) | −4.17210 | −0.171763 | ||||||||
\(591\) | −19.2575 | −0.792148 | ||||||||
\(592\) | 2.80465 | − | 4.85780i | 0.115270 | − | 0.199654i | ||||
\(593\) | 15.5497 | 0.638548 | 0.319274 | − | 0.947662i | \(-0.396561\pi\) | ||||
0.319274 | + | 0.947662i | \(0.396561\pi\) | |||||||
\(594\) | −2.61903 | − | 4.53629i | −0.107460 | − | 0.186126i | ||||
\(595\) | −2.50973 | + | 4.34697i | −0.102889 | + | 0.178209i | ||||
\(596\) | 10.8144 | − | 18.7310i | 0.442974 | − | 0.767254i | ||||
\(597\) | −17.8668 | −0.731240 | ||||||||
\(598\) | 0.934044 | + | 1.61781i | 0.0381959 | + | 0.0661573i | ||||
\(599\) | 8.62875 | + | 14.9454i | 0.352561 | + | 0.610654i | 0.986697 | − | 0.162567i | \(-0.0519775\pi\) |
−0.634136 | + | 0.773221i | \(0.718644\pi\) | |||||||
\(600\) | −0.500000 | − | 0.866025i | −0.0204124 | − | 0.0353553i | ||||
\(601\) | 3.85772 | − | 6.68177i | 0.157360 | − | 0.272555i | −0.776556 | − | 0.630048i | \(-0.783035\pi\) |
0.933916 | + | 0.357493i | \(0.116368\pi\) | |||||||
\(602\) | 5.45665 | + | 9.45120i | 0.222397 | + | 0.385202i | ||||
\(603\) | −2.80465 | + | 4.85780i | −0.114214 | + | 0.197825i | ||||
\(604\) | 0.456655 | 0.0185810 | ||||||||
\(605\) | 16.4372 | 0.668267 | ||||||||
\(606\) | 7.34735 | − | 12.7260i | 0.298466 | − | 0.516958i | ||||
\(607\) | −11.6947 | − | 20.2558i | −0.474674 | − | 0.822159i | 0.524906 | − | 0.851160i | \(-0.324101\pi\) |
−0.999579 | + | 0.0290016i | \(0.990767\pi\) | |||||||
\(608\) | 3.72833 | − | 6.45765i | 0.151204 | − | 0.261892i | ||||
\(609\) | −1.97991 | − | 3.42930i | −0.0802299 | − | 0.138962i | ||||
\(610\) | −4.72833 | − | 8.18970i | −0.191444 | − | 0.331591i | ||||
\(611\) | −0.457938 | − | 0.793171i | −0.0185262 | − | 0.0320883i | ||||
\(612\) | 3.60930 | 0.145897 | ||||||||
\(613\) | 13.6482 | − | 23.6394i | 0.551246 | − | 0.954786i | −0.446939 | − | 0.894564i | \(-0.647486\pi\) |
0.998185 | − | 0.0602214i | \(-0.0191807\pi\) | |||||||
\(614\) | −10.7478 | + | 18.6157i | −0.433745 | + | 0.751269i | ||||
\(615\) | 5.50973 | + | 9.54313i | 0.222174 | + | 0.384816i | ||||
\(616\) | −7.28456 | −0.293503 | ||||||||
\(617\) | −10.0233 | + | 17.3608i | −0.403521 | + | 0.698919i | −0.994148 | − | 0.108026i | \(-0.965547\pi\) |
0.590627 | + | 0.806945i | \(0.298880\pi\) | |||||||
\(618\) | 6.17210 | 0.248278 | ||||||||
\(619\) | −5.82919 | −0.234295 | −0.117147 | − | 0.993115i | \(-0.537375\pi\) | ||||
−0.117147 | + | 0.993115i | \(0.537375\pi\) | |||||||
\(620\) | 2.31438 | + | 5.06396i | 0.0929476 | + | 0.203373i | ||||
\(621\) | −2.39070 | −0.0959355 | ||||||||
\(622\) | 5.25751 | 0.210807 | ||||||||
\(623\) | 6.41015 | − | 11.1027i | 0.256817 | − | 0.444821i | ||||
\(624\) | −0.781399 | −0.0312810 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −10.4431 | + | 18.0880i | −0.417391 | + | 0.722943i | ||||
\(627\) | 19.5292 | − | 33.8255i | 0.779920 | − | 1.35086i | ||||
\(628\) | 23.4956 | 0.937575 | ||||||||
\(629\) | 10.1228 | + | 17.5332i | 0.403624 | + | 0.699096i | ||||
\(630\) | 0.695350 | + | 1.20438i | 0.0277034 | + | 0.0479837i | ||||
\(631\) | 16.6850 | + | 28.8992i | 0.664219 | + | 1.15046i | 0.979497 | + | 0.201461i | \(0.0645689\pi\) |
−0.315278 | + | 0.948999i | \(0.602098\pi\) | |||||||
\(632\) | 3.92368 | − | 6.79601i | 0.156075 | − | 0.270331i | ||||
\(633\) | −7.72833 | − | 13.3859i | −0.307173 | − | 0.532040i | ||||
\(634\) | 3.20508 | − | 5.55135i | 0.127290 | − | 0.220472i | ||||
\(635\) | 11.8668 | 0.470920 | ||||||||
\(636\) | 7.62875 | 0.302500 | ||||||||
\(637\) | 1.97927 | − | 3.42819i | 0.0784213 | − | 0.135830i | ||||
\(638\) | −7.45730 | − | 12.9164i | −0.295237 | − | 0.511366i | ||||
\(639\) | 1.60930 | − | 2.78739i | 0.0636630 | − | 0.110267i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −7.66237 | − | 13.2716i | −0.302645 | − | 0.524197i | 0.674089 | − | 0.738650i | \(-0.264536\pi\) |
−0.976734 | + | 0.214453i | \(0.931203\pi\) | |||||||
\(642\) | −0.695350 | − | 1.20438i | −0.0274433 | − | 0.0475331i | ||||
\(643\) | 2.63635 | 0.103968 | 0.0519838 | − | 0.998648i | \(-0.483446\pi\) | ||||
0.0519838 | + | 0.998648i | \(0.483446\pi\) | |||||||
\(644\) | −1.66237 | + | 2.87931i | −0.0655066 | + | 0.113461i | ||||
\(645\) | 3.92368 | − | 6.79601i | 0.154495 | − | 0.267593i | ||||
\(646\) | 13.4567 | + | 23.3076i | 0.529445 | + | 0.917026i | ||||
\(647\) | −33.9717 | −1.33556 | −0.667782 | − | 0.744357i | \(-0.732756\pi\) | ||||
−0.667782 | + | 0.744357i | \(0.732756\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 21.8537 | 0.857832 | ||||||||
\(650\) | −0.781399 | −0.0306490 | ||||||||
\(651\) | −3.21860 | − | 7.04244i | −0.126147 | − | 0.276015i | ||||
\(652\) | 12.5226 | 0.490423 | ||||||||
\(653\) | −13.9340 | −0.545281 | −0.272641 | − | 0.962116i | \(-0.587897\pi\) | ||||
−0.272641 | + | 0.962116i | \(0.587897\pi\) | |||||||
\(654\) | 3.72833 | − | 6.45765i | 0.145789 | − | 0.252514i | ||||
\(655\) | −12.6288 | −0.493446 | ||||||||
\(656\) | −5.50973 | − | 9.54313i | −0.215119 | − | 0.372596i | ||||
\(657\) | 1.00000 | − | 1.73205i | 0.0390137 | − | 0.0675737i | ||||
\(658\) | 0.815018 | − | 1.41165i | 0.0317727 | − | 0.0550319i | ||||
\(659\) | −3.58225 | −0.139545 | −0.0697723 | − | 0.997563i | \(-0.522227\pi\) | ||||
−0.0697723 | + | 0.997563i | \(0.522227\pi\) | |||||||
\(660\) | 2.61903 | + | 4.53629i | 0.101945 | + | 0.176575i | ||||
\(661\) | −4.05307 | − | 7.02013i | −0.157646 | − | 0.273051i | 0.776373 | − | 0.630273i | \(-0.217057\pi\) |
−0.934019 | + | 0.357222i | \(0.883724\pi\) | |||||||
\(662\) | −17.3571 | − | 30.0633i | −0.674602 | − | 1.16845i | ||||
\(663\) | 1.41015 | − | 2.44245i | 0.0547657 | − | 0.0948570i | ||||
\(664\) | 6.93340 | + | 12.0090i | 0.269068 | + | 0.466040i | ||||
\(665\) | −5.18498 | + | 8.98065i | −0.201065 | + | 0.348255i | ||||
\(666\) | 5.60930 | 0.217356 | ||||||||
\(667\) | −6.80717 | −0.263575 | ||||||||
\(668\) | −9.35708 | + | 16.2069i | −0.362036 | + | 0.627065i | ||||
\(669\) | 2.54270 | + | 4.40409i | 0.0983066 | + | 0.170272i | ||||
\(670\) | 2.80465 | − | 4.85780i | 0.108353 | − | 0.187673i | ||||
\(671\) | 24.7672 | + | 42.8981i | 0.956128 | + | 1.65606i | ||||
\(672\) | −0.695350 | − | 1.20438i | −0.0268237 | − | 0.0464600i | ||||
\(673\) | −0.576323 | − | 0.998221i | −0.0222156 | − | 0.0384786i | 0.854704 | − | 0.519116i | \(-0.173739\pi\) |
−0.876919 | + | 0.480637i | \(0.840405\pi\) | |||||||
\(674\) | 3.15265 | 0.121435 | ||||||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 6.19471 | − | 10.7295i | 0.238258 | − | 0.412675i | ||||
\(677\) | 23.2905 | + | 40.3403i | 0.895126 | + | 1.55040i | 0.833649 | + | 0.552295i | \(0.186248\pi\) |
0.0614774 | + | 0.998108i | \(0.480419\pi\) | |||||||
\(678\) | 11.0660 | 0.424985 | ||||||||
\(679\) | −9.23741 | + | 15.9997i | −0.354499 | + | 0.614011i | ||||
\(680\) | −3.60930 | −0.138410 | ||||||||
\(681\) | −16.3040 | −0.624771 | ||||||||
\(682\) | −12.1228 | − | 26.5253i | −0.464207 | − | 1.01571i | ||||
\(683\) | 44.6482 | 1.70842 | 0.854208 | − | 0.519931i | \(-0.174042\pi\) | ||||
0.854208 | + | 0.519931i | \(0.174042\pi\) | |||||||
\(684\) | 7.45665 | 0.285112 | ||||||||
\(685\) | 6.82410 | − | 11.8197i | 0.260736 | − | 0.451607i | ||||
\(686\) | 16.7801 | 0.640668 | ||||||||
\(687\) | −14.5757 | − | 25.2458i | −0.556097 | − | 0.963188i | ||||
\(688\) | −3.92368 | + | 6.79601i | −0.149589 | + | 0.259095i | ||||
\(689\) | 2.98055 | − | 5.16246i | 0.113550 | − | 0.196674i | ||||
\(690\) | 2.39070 | 0.0910124 | ||||||||
\(691\) | 6.66237 | + | 11.5396i | 0.253449 | + | 0.438986i | 0.964473 | − | 0.264182i | \(-0.0851018\pi\) |
−0.711024 | + | 0.703167i | \(0.751768\pi\) | |||||||
\(692\) | −3.42368 | − | 5.92998i | −0.130149 | − | 0.225424i | ||||
\(693\) | −3.64228 | − | 6.30861i | −0.138359 | − | 0.239644i | ||||
\(694\) | 9.15200 | − | 15.8517i | 0.347405 | − | 0.601724i | ||||
\(695\) | 0.119027 | + | 0.206160i | 0.00451494 | + | 0.00782010i | ||||
\(696\) | 1.42368 | − | 2.46588i | 0.0539643 | − | 0.0934690i | ||||
\(697\) | 39.7725 | 1.50649 | ||||||||
\(698\) | −8.71416 | −0.329836 | ||||||||
\(699\) | 4.80465 | − | 8.32190i | 0.181729 | − | 0.314763i | ||||
\(700\) | −0.695350 | − | 1.20438i | −0.0262817 | − | 0.0455213i | ||||
\(701\) | −13.2814 | + | 23.0041i | −0.501631 | + | 0.868851i | 0.498367 | + | 0.866966i | \(0.333933\pi\) |
−0.999998 | + | 0.00188492i | \(0.999400\pi\) | |||||||
\(702\) | −0.390699 | − | 0.676711i | −0.0147460 | − | 0.0255408i | ||||
\(703\) | 20.9133 | + | 36.2229i | 0.788760 | + | 1.36617i | ||||
\(704\) | −2.61903 | − | 4.53629i | −0.0987083 | − | 0.170968i | ||||
\(705\) | −1.17210 | −0.0441438 | ||||||||
\(706\) | −5.36088 | + | 9.28532i | −0.201759 | + | 0.349457i | ||||
\(707\) | 10.2180 | − | 17.6980i | 0.384286 | − | 0.665603i | ||||
\(708\) | 2.08605 | + | 3.61314i | 0.0783985 | + | 0.135790i | ||||
\(709\) | 37.3222 | 1.40166 | 0.700832 | − | 0.713326i | \(-0.252812\pi\) | ||||
0.700832 | + | 0.713326i | \(0.252812\pi\) | |||||||
\(710\) | −1.60930 | + | 2.78739i | −0.0603960 | + | 0.104609i | ||||
\(711\) | 7.84735 | 0.294299 | ||||||||
\(712\) | 9.21860 | 0.345482 | ||||||||
\(713\) | −13.2509 | − | 1.26150i | −0.496252 | − | 0.0472435i | ||||
\(714\) | 5.01945 | 0.187848 | ||||||||
\(715\) | 4.09301 | 0.153070 | ||||||||
\(716\) | −4.40043 | + | 7.62176i | −0.164452 | + | 0.284839i | ||||
\(717\) | −3.69471 | −0.137981 | ||||||||
\(718\) | 9.11903 | + | 15.7946i | 0.340319 | + | 0.589450i | ||||
\(719\) | −19.9664 | + | 34.5828i | −0.744620 | + | 1.28972i | 0.205752 | + | 0.978604i | \(0.434036\pi\) |
−0.950372 | + | 0.311116i | \(0.899297\pi\) | |||||||
\(720\) | −0.500000 | + | 0.866025i | −0.0186339 | + | 0.0322749i | ||||
\(721\) | 8.58353 | 0.319667 | ||||||||
\(722\) | 18.3009 | + | 31.6980i | 0.681087 | + | 1.17968i | ||||
\(723\) | −12.8144 | − | 22.1952i | −0.476572 | − | 0.825447i | ||||
\(724\) | −6.84735 | − | 11.8600i | −0.254480 | − | 0.440772i | ||||
\(725\) | 1.42368 | − | 2.46588i | 0.0528740 | − | 0.0915805i | ||||
\(726\) | −8.21860 | − | 14.2350i | −0.305021 | − | 0.528312i | ||||
\(727\) | −17.8869 | + | 30.9810i | −0.663388 | + | 1.14902i | 0.316331 | + | 0.948649i | \(0.397549\pi\) |
−0.979720 | + | 0.200374i | \(0.935784\pi\) | |||||||
\(728\) | −1.08669 | −0.0402754 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.00000 | + | 1.73205i | −0.0370117 | + | 0.0641061i | ||||
\(731\) | −14.1617 | − | 24.5288i | −0.523791 | − | 0.907232i | ||||
\(732\) | −4.72833 | + | 8.18970i | −0.174764 | + | 0.302700i | ||||
\(733\) | 11.5059 | + | 19.9288i | 0.424981 | + | 0.736089i | 0.996419 | − | 0.0845567i | \(-0.0269474\pi\) |
−0.571438 | + | 0.820646i | \(0.693614\pi\) | |||||||
\(734\) | −12.0000 | − | 20.7846i | −0.442928 | − | 0.767174i | ||||
\(735\) | −2.53298 | − | 4.38725i | −0.0934303 | − | 0.161826i | ||||
\(736\) | −2.39070 | −0.0881223 | ||||||||
\(737\) | −14.6909 | + | 25.4454i | −0.541147 | + | 0.937293i | ||||
\(738\) | 5.50973 | − | 9.54313i | 0.202816 | − | 0.351287i | ||||
\(739\) | 14.9004 | + | 25.8083i | 0.548121 | + | 0.949373i | 0.998403 | + | 0.0564872i | \(0.0179900\pi\) |
−0.450282 | + | 0.892886i | \(0.648677\pi\) | |||||||
\(740\) | −5.60930 | −0.206202 | ||||||||
\(741\) | 2.91331 | − | 5.04600i | 0.107023 | − | 0.185369i | ||||
\(742\) | 10.6093 | 0.389480 | ||||||||
\(743\) | −13.3712 | −0.490543 | −0.245272 | − | 0.969454i | \(-0.578877\pi\) | ||||
−0.245272 | + | 0.969454i | \(0.578877\pi\) | |||||||
\(744\) | 3.22833 | − | 4.53629i | 0.118356 | − | 0.166308i | ||||
\(745\) | −21.6288 | −0.792416 | ||||||||
\(746\) | 20.9598 | 0.767393 | ||||||||
\(747\) | −6.93340 | + | 12.0090i | −0.253680 | + | 0.439387i | ||||
\(748\) | 18.9057 | 0.691261 | ||||||||
\(749\) | −0.967022 | − | 1.67493i | −0.0353342 | − | 0.0612007i | ||||
\(750\) | −0.500000 | + | 0.866025i | −0.0182574 | + | 0.0316228i | ||||
\(751\) | −8.07568 | + | 13.9875i | −0.294686 | + | 0.510411i | −0.974912 | − | 0.222592i | \(-0.928548\pi\) |
0.680226 | + | 0.733002i | \(0.261882\pi\) | |||||||
\(752\) | 1.17210 | 0.0427420 | ||||||||
\(753\) | 5.92368 | + | 10.2601i | 0.215871 | + | 0.373899i | ||||
\(754\) | −1.11246 | − | 1.92684i | −0.0405134 | − | 0.0701712i | ||||
\(755\) | −0.228327 | − | 0.395475i | −0.00830968 | − | 0.0143928i | ||||
\(756\) | 0.695350 | − | 1.20438i | 0.0252896 | − | 0.0438029i | ||||
\(757\) | 6.98963 | + | 12.1064i | 0.254043 | + | 0.440015i | 0.964635 | − | 0.263589i | \(-0.0849063\pi\) |
−0.710592 | + | 0.703604i | \(0.751573\pi\) | |||||||
\(758\) | 7.67526 | − | 13.2939i | 0.278778 | − | 0.482857i | ||||
\(759\) | −12.5226 | −0.454542 | ||||||||
\(760\) | −7.45665 | −0.270481 | ||||||||
\(761\) | 8.74778 | − | 15.1516i | 0.317107 | − | 0.549245i | −0.662776 | − | 0.748817i | \(-0.730622\pi\) |
0.979883 | + | 0.199572i | \(0.0639553\pi\) | |||||||
\(762\) | −5.93340 | − | 10.2770i | −0.214945 | − | 0.372295i | ||||
\(763\) | 5.18498 | − | 8.98065i | 0.187709 | − | 0.325121i | ||||
\(764\) | 2.72833 | + | 4.72560i | 0.0987074 | + | 0.170966i | ||||
\(765\) | −1.80465 | − | 3.12575i | −0.0652473 | − | 0.113012i | ||||
\(766\) | −3.58605 | − | 6.21122i | −0.129569 | − | 0.224420i | ||||
\(767\) | 3.26007 | 0.117714 | ||||||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −2.57632 | + | 4.46232i | −0.0929046 | + | 0.160915i | −0.908732 | − | 0.417380i | \(-0.862948\pi\) |
0.815828 | + | 0.578295i | \(0.196282\pi\) | |||||||
\(770\) | 3.64228 | + | 6.30861i | 0.131259 | + | 0.227347i | ||||
\(771\) | 18.5615 | 0.668477 | ||||||||
\(772\) | −4.57632 | + | 7.92642i | −0.164705 | + | 0.285278i | ||||
\(773\) | −15.5628 | −0.559755 | −0.279877 | − | 0.960036i | \(-0.590294\pi\) | ||||
−0.279877 | + | 0.960036i | \(0.590294\pi\) | |||||||
\(774\) | −7.84735 | −0.282067 | ||||||||
\(775\) | 3.22833 | − | 4.53629i | 0.115965 | − | 0.162948i | ||||
\(776\) | −13.2846 | −0.476888 | ||||||||
\(777\) | 7.80085 | 0.279854 | ||||||||
\(778\) | 8.48647 | − | 14.6990i | 0.304255 | − | 0.526985i | ||||
\(779\) | 82.1682 | 2.94398 | ||||||||
\(780\) | 0.390699 | + | 0.676711i | 0.0139893 | + | 0.0242301i | ||||
\(781\) | 8.42960 | − | 14.6005i | 0.301635 | − | 0.522447i | ||||
\(782\) | 4.31438 | − | 7.47272i | 0.154282 | − | 0.267224i | ||||
\(783\) | 2.84735 | 0.101756 | ||||||||
\(784\) | 2.53298 | + | 4.38725i | 0.0904635 | + | 0.156687i | ||||
\(785\) | −11.7478 | − | 20.3478i | −0.419296 | − | 0.726242i | ||||
\(786\) | 6.31438 | + | 10.9368i | 0.225226 | + | 0.390103i | ||||
\(787\) | 4.12939 | − | 7.15232i | 0.147197 | − | 0.254953i | −0.782993 | − | 0.622030i | \(-0.786308\pi\) |
0.930190 | + | 0.367077i | \(0.119642\pi\) | |||||||
\(788\) | −9.62875 | − | 16.6775i | −0.343010 | − | 0.594111i | ||||
\(789\) | −4.92368 | + | 8.52806i | −0.175288 | + | 0.303607i | ||||
\(790\) | −7.84735 | −0.279196 | ||||||||
\(791\) | 15.3894 | 0.547185 | ||||||||
\(792\) | 2.61903 | − | 4.53629i | 0.0930631 | − | 0.161190i | ||||
\(793\) | 3.69471 | + | 6.39942i | 0.131203 | + | 0.227250i | ||||
\(794\) | −13.3144 | + | 23.0612i | −0.472510 | + | 0.818411i | ||||
\(795\) | −3.81438 | − | 6.60669i | −0.135282 | − | 0.234315i | ||||
\(796\) | −8.93340 | − | 15.4731i | −0.316636 | − | 0.548430i | ||||
\(797\) | 1.64228 | + | 2.84451i | 0.0581725 | + | 0.100758i | 0.893645 | − | 0.448774i | \(-0.148139\pi\) |
−0.835473 | + | 0.549532i | \(0.814806\pi\) | |||||||
\(798\) | 10.3700 | 0.367093 | ||||||||
\(799\) | −2.11523 | + | 3.66368i | −0.0748313 | + | 0.129612i | ||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 4.60930 | + | 7.98354i | 0.162862 | + | 0.282085i | ||||
\(802\) | −18.1319 | −0.640260 | ||||||||
\(803\) | 5.23805 | − | 9.07257i | 0.184847 | − | 0.320164i | ||||
\(804\) | −5.60930 | −0.197825 | ||||||||
\(805\) | 3.32474 | 0.117182 | ||||||||
\(806\) | −1.80845 | − | 3.95697i | −0.0636999 | − | 0.139378i | ||||
\(807\) | −12.1915 | −0.429163 | ||||||||
\(808\) | 14.6947 | 0.516958 | ||||||||
\(809\) | 20.6416 | − | 35.7524i | 0.725721 | − | 1.25699i | −0.232955 | − | 0.972487i | \(-0.574840\pi\) |
0.958676 | − | 0.284499i | \(-0.0918271\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −4.37125 | − | 7.57122i | −0.153495 | − | 0.265862i | 0.779015 | − | 0.627005i | \(-0.215720\pi\) |
−0.932510 | + | 0.361144i | \(0.882386\pi\) | |||||||
\(812\) | 1.97991 | − | 3.42930i | 0.0694811 | − | 0.120345i | ||||
\(813\) | −8.32410 | + | 14.4178i | −0.291939 | + | 0.505653i | ||||
\(814\) | 29.3818 | 1.02983 | ||||||||
\(815\) | −6.26131 | − | 10.8449i | −0.219324 | − | 0.379880i | ||||
\(816\) | 1.80465 | + | 3.12575i | 0.0631754 | + | 0.109423i | ||||
\(817\) | −29.2575 | − | 50.6755i | −1.02359 | − | 1.77291i | ||||
\(818\) | 6.51945 | − | 11.2920i | 0.227947 | − | 0.394816i | ||||
\(819\) | −0.543345 | − | 0.941101i | −0.0189860 | − | 0.0328847i | ||||
\(820\) | −5.50973 | + | 9.54313i | −0.192408 | + | 0.333260i | ||||
\(821\) | 7.03890 | 0.245659 | 0.122830 | − | 0.992428i | \(-0.460803\pi\) | ||||
0.122830 | + | 0.992428i | \(0.460803\pi\) | |||||||
\(822\) | −13.6482 | −0.476036 | ||||||||
\(823\) | 4.74185 | − | 8.21313i | 0.165291 | − | 0.286292i | −0.771468 | − | 0.636268i | \(-0.780477\pi\) |
0.936758 | + | 0.349977i | \(0.113810\pi\) | |||||||
\(824\) | 3.08605 | + | 5.34519i | 0.107508 | + | 0.186209i | ||||
\(825\) | 2.61903 | − | 4.53629i | 0.0911828 | − | 0.157933i | ||||
\(826\) | 2.90107 | + | 5.02479i | 0.100941 | + | 0.174835i | ||||
\(827\) | 6.78140 | + | 11.7457i | 0.235812 | + | 0.408439i | 0.959508 | − | 0.281680i | \(-0.0908916\pi\) |
−0.723696 | + | 0.690119i | \(0.757558\pi\) | |||||||
\(828\) | −1.19535 | − | 2.07041i | −0.0415413 | − | 0.0719516i | ||||
\(829\) | −23.8398 | −0.827989 | −0.413994 | − | 0.910279i | \(-0.635867\pi\) | ||||
−0.413994 | + | 0.910279i | \(0.635867\pi\) | |||||||
\(830\) | 6.93340 | − | 12.0090i | 0.240662 | − | 0.416839i | ||||
\(831\) | 0.433403 | − | 0.750676i | 0.0150346 | − | 0.0260407i | ||||
\(832\) | −0.390699 | − | 0.676711i | −0.0135451 | − | 0.0234607i | ||||
\(833\) | −18.2846 | −0.633522 | ||||||||
\(834\) | 0.119027 | − | 0.206160i | 0.00412156 | − | 0.00713875i | ||||
\(835\) | 18.7142 | 0.647630 | ||||||||
\(836\) | 39.0584 | 1.35086 | ||||||||
\(837\) | 5.54270 | + | 0.527670i | 0.191584 | + | 0.0182389i | ||||
\(838\) | 2.76195 | 0.0954099 | ||||||||
\(839\) | −11.8398 | −0.408754 | −0.204377 | − | 0.978892i | \(-0.565517\pi\) | ||||
−0.204377 | + | 0.978892i | \(0.565517\pi\) | |||||||
\(840\) | −0.695350 | + | 1.20438i | −0.0239918 | + | 0.0415551i | ||||
\(841\) | −20.8926 | −0.720434 | ||||||||
\(842\) | 6.96638 | + | 12.0661i | 0.240077 | + | 0.415826i | ||||
\(843\) | 14.2575 | − | 24.6947i | 0.491055 | − | 0.850531i | ||||
\(844\) | 7.72833 | − | 13.3859i | 0.266020 | − | 0.460760i | ||||
\(845\) | −12.3894 | −0.426209 | ||||||||
\(846\) | 0.586049 | + | 1.01507i | 0.0201488 | + | 0.0348987i | ||||
\(847\) | −11.4296 | − | 19.7967i | −0.392726 | − | 0.680221i | ||||
\(848\) | 3.81438 | + | 6.60669i | 0.130986 | + | 0.226875i | ||||
\(849\) | −2.75158 | + | 4.76588i | −0.0944340 | + | 0.163564i | ||||
\(850\) | 1.80465 | + | 3.12575i | 0.0618990 | + | 0.107212i | ||||
\(851\) | 6.70508 | − | 11.6135i | 0.229847 | − | 0.398107i | ||||
\(852\) | 3.21860 | 0.110267 | ||||||||
\(853\) | 25.0452 | 0.857532 | 0.428766 | − | 0.903416i | \(-0.358948\pi\) | ||||
0.428766 | + | 0.903416i | \(0.358948\pi\) | |||||||
\(854\) | −6.57568 | + | 11.3894i | −0.225015 | + | 0.389738i | ||||
\(855\) | −3.72833 | − | 6.45765i | −0.127506 | − | 0.220847i | ||||
\(856\) | 0.695350 | − | 1.20438i | 0.0237666 | − | 0.0411649i | ||||
\(857\) | −20.3533 | − | 35.2529i | −0.695255 | − | 1.20422i | −0.970095 | − | 0.242727i | \(-0.921958\pi\) |
0.274840 | − | 0.961490i | \(-0.411375\pi\) | |||||||
\(858\) | −2.04650 | − | 3.54465i | −0.0698665 | − | 0.121012i | ||||
\(859\) | 7.11903 | + | 12.3305i | 0.242898 | + | 0.420712i | 0.961539 | − | 0.274670i | \(-0.0885686\pi\) |
−0.718640 | + | 0.695382i | \(0.755235\pi\) | |||||||
\(860\) | 7.84735 | 0.267593 | ||||||||
\(861\) | 7.66237 | − | 13.2716i | 0.261133 | − | 0.452296i | ||||
\(862\) | 7.68182 | − | 13.3053i | 0.261644 | − | 0.453181i | ||||
\(863\) | −11.8175 | − | 20.4686i | −0.402274 | − | 0.696758i | 0.591726 | − | 0.806139i | \(-0.298447\pi\) |
−0.994000 | + | 0.109381i | \(0.965113\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −3.42368 | + | 5.92998i | −0.116409 | + | 0.201625i | ||||
\(866\) | 3.25751 | 0.110695 | ||||||||
\(867\) | 3.97295 | 0.134928 | ||||||||
\(868\) | 4.48963 | − | 6.30861i | 0.152388 | − | 0.214128i | ||||
\(869\) | 41.1049 | 1.39439 | ||||||||
\(870\) | −2.84735 | −0.0965343 | ||||||||
\(871\) | −2.19155 | + | 3.79588i | −0.0742578 | + | 0.128618i | ||||
\(872\) | 7.45665 | 0.252514 | ||||||||
\(873\) | −6.64228 | − | 11.5048i | −0.224807 | − | 0.389377i | ||||
\(874\) | 8.91331 | − | 15.4383i | 0.301497 | − | 0.522208i | ||||
\(875\) | −0.695350 | + | 1.20438i | −0.0235071 | + | 0.0407155i | ||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | 15.8706 | + | 27.4887i | 0.535912 | + | 0.928227i | 0.999119 | + | 0.0419768i | \(0.0133656\pi\) |
−0.463206 | + | 0.886250i | \(0.653301\pi\) | |||||||
\(878\) | 11.7911 | + | 20.4228i | 0.397931 | + | 0.689237i | ||||
\(879\) | −0.595775 | − | 1.03191i | −0.0200950 | − | 0.0348055i | ||||
\(880\) | −2.61903 | + | 4.53629i | −0.0882874 | + | 0.152918i | ||||
\(881\) | −19.5562 | − | 33.8724i | −0.658866 | − | 1.14119i | −0.980910 | − | 0.194465i | \(-0.937703\pi\) |
0.322043 | − | 0.946725i | \(-0.395630\pi\) | |||||||
\(882\) | −2.53298 | + | 4.38725i | −0.0852898 | + | 0.147726i | ||||
\(883\) | −54.6545 | −1.83927 | −0.919636 | − | 0.392773i | \(-0.871516\pi\) | ||||
−0.919636 | + | 0.392773i | \(0.871516\pi\) | |||||||
\(884\) | 2.82030 | 0.0948570 | ||||||||
\(885\) | 2.08605 | − | 3.61314i | 0.0701218 | − | 0.121454i | ||||
\(886\) | −11.0660 | − | 19.1668i | −0.371768 | − | 0.643921i | ||||
\(887\) | 19.5059 | − | 33.7853i | 0.654945 | − | 1.13440i | −0.326963 | − | 0.945037i | \(-0.606025\pi\) |
0.981908 | − | 0.189361i | \(-0.0606415\pi\) | |||||||
\(888\) | 2.80465 | + | 4.85780i | 0.0941179 | + | 0.163017i | ||||
\(889\) | −8.25158 | − | 14.2922i | −0.276749 | − | 0.479343i | ||||
\(890\) | −4.60930 | − | 7.98354i | −0.154504 | − | 0.267609i | ||||
\(891\) | 5.23805 | 0.175481 | ||||||||
\(892\) | −2.54270 | + | 4.40409i | −0.0851360 | + | 0.147460i | ||||
\(893\) | −4.36996 | + | 7.56900i | −0.146235 | + | 0.253287i | ||||
\(894\) | 10.8144 | + | 18.7310i | 0.361687 | + | 0.626460i | ||||
\(895\) | 8.80085 | 0.294180 | ||||||||
\(896\) | 0.695350 | − | 1.20438i | 0.0232300 | − | 0.0402355i | ||||
\(897\) | −1.86809 | −0.0623737 | ||||||||
\(898\) | 24.9133 | 0.831368 | ||||||||
\(899\) | 15.7820 | + | 1.50246i | 0.526361 | + | 0.0501099i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −27.5345 | −0.917306 | ||||||||
\(902\) | 28.8602 | − | 49.9874i | 0.960941 | − | 1.66440i | ||||
\(903\) | −10.9133 | −0.363172 | ||||||||
\(904\) | 5.53298 | + | 9.58340i | 0.184024 | + | 0.318739i | ||||
\(905\) | −6.84735 | + | 11.8600i | −0.227614 | + | 0.394239i | ||||
\(906\) | −0.228327 | + | 0.395475i | −0.00758567 | + | 0.0131388i | ||||
\(907\) | 37.5628 | 1.24725 | 0.623626 | − | 0.781723i | \(-0.285659\pi\) | ||||
0.623626 | + | 0.781723i | \(0.285659\pi\) | |||||||
\(908\) | −8.15200 | − | 14.1197i | −0.270534 | − | 0.468578i | ||||
\(909\) | 7.34735 | + | 12.7260i | 0.243696 | + | 0.422094i | ||||
\(910\) | 0.543345 | + | 0.941101i | 0.0180117 | + | 0.0311972i | ||||
\(911\) | 7.42304 | − | 12.8571i | 0.245936 | − | 0.425974i | −0.716458 | − | 0.697630i | \(-0.754238\pi\) |
0.962394 | + | 0.271656i | \(0.0875713\pi\) | |||||||
\(912\) | 3.72833 | + | 6.45765i | 0.123457 | + | 0.213834i | ||||
\(913\) | −36.3175 | + | 62.9038i | −1.20193 | + | 2.08181i | ||||
\(914\) | −28.8203 | −0.953291 | ||||||||
\(915\) | 9.45665 | 0.312627 | ||||||||
\(916\) | 14.5757 | − | 25.2458i | 0.481594 | − | 0.834145i | ||||
\(917\) | 8.78140 | + | 15.2098i | 0.289987 | + | 0.502273i | ||||
\(918\) | −1.80465 | + | 3.12575i | −0.0595623 | + | 0.103165i | ||||
\(919\) | 18.3137 | + | 31.7203i | 0.604114 | + | 1.04636i | 0.992191 | + | 0.124730i | \(0.0398063\pi\) |
−0.388076 | + | 0.921627i | \(0.626860\pi\) | |||||||
\(920\) | 1.19535 | + | 2.07041i | 0.0394095 | + | 0.0682593i | ||||
\(921\) | −10.7478 | − | 18.6157i | −0.354151 | − | 0.613408i | ||||
\(922\) | 17.1708 | 0.565491 | ||||||||
\(923\) | 1.25751 | − | 2.17806i | 0.0413913 | − | 0.0716918i | ||||
\(924\) | 3.64228 | − | 6.30861i | 0.119822 | − | 0.207538i | ||||
\(925\) | 2.80465 | + | 4.85780i | 0.0922163 | + | 0.159723i | ||||
\(926\) | 22.7412 | 0.747323 | ||||||||
\(927\) | −3.08605 | + | 5.34519i | −0.101359 | + | 0.175559i | ||||
\(928\) | 2.84735 | 0.0934690 | ||||||||
\(929\) | −53.0195 | −1.73951 | −0.869756 | − | 0.493482i | \(-0.835724\pi\) | ||||
−0.869756 | + | 0.493482i | \(0.835724\pi\) | |||||||
\(930\) | −5.54270 | − | 0.527670i | −0.181752 | − | 0.0173030i | ||||
\(931\) | −37.7751 | −1.23803 | ||||||||
\(932\) | 9.60930 | 0.314763 | ||||||||
\(933\) | −2.62875 | + | 4.55313i | −0.0860615 | + | 0.149063i | ||||
\(934\) | 7.56151 | 0.247420 | ||||||||
\(935\) | −9.45285 | − | 16.3728i | −0.309141 | − | 0.535449i | ||||
\(936\) | 0.390699 | − | 0.676711i | 0.0127704 | − | 0.0221190i | ||||
\(937\) | 21.9133 | − | 37.9550i | 0.715877 | − | 1.23993i | −0.246744 | − | 0.969081i | \(-0.579361\pi\) |
0.962620 | − | 0.270854i | \(-0.0873060\pi\) | |||||||
\(938\) | −7.80085 | −0.254707 | ||||||||
\(939\) | −10.4431 | − | 18.0880i | −0.340799 | − | 0.590281i | ||||
\(940\) | −0.586049 | − | 1.01507i | −0.0191148 | − | 0.0331078i | ||||
\(941\) | −9.89070 | − | 17.1312i | −0.322428 | − | 0.558461i | 0.658561 | − | 0.752528i | \(-0.271166\pi\) |
−0.980988 | + | 0.194067i | \(0.937832\pi\) | |||||||
\(942\) | −11.7478 | + | 20.3478i | −0.382763 | + | 0.662966i | ||||
\(943\) | −13.1721 | − | 22.8147i | −0.428943 | − | 0.742950i | ||||
\(944\) | −2.08605 | + | 3.61314i | −0.0678951 | + | 0.117598i | ||||
\(945\) | −1.39070 | −0.0452395 | ||||||||
\(946\) | −41.1049 | −1.33643 | ||||||||
\(947\) | −14.8279 | + | 25.6827i | −0.481842 | + | 0.834575i | −0.999783 | − | 0.0208416i | \(-0.993365\pi\) |
0.517941 | + | 0.855417i | \(0.326699\pi\) | |||||||
\(948\) | 3.92368 | + | 6.79601i | 0.127435 | + | 0.220724i | ||||
\(949\) | 0.781399 | − | 1.35342i | 0.0253653 | − | 0.0439339i | ||||
\(950\) | 3.72833 | + | 6.45765i | 0.120963 | + | 0.209514i | ||||
\(951\) | 3.20508 | + | 5.55135i | 0.103932 | + | 0.180015i | ||||
\(952\) | 2.50973 | + | 4.34697i | 0.0813407 | + | 0.140886i | ||||
\(953\) | 41.4567 | 1.34291 | 0.671456 | − | 0.741044i | \(-0.265669\pi\) | ||||
0.671456 | + | 0.741044i | \(0.265669\pi\) | |||||||
\(954\) | −3.81438 | + | 6.60669i | −0.123495 | + | 0.213900i | ||||
\(955\) | 2.72833 | − | 4.72560i | 0.0882866 | − | 0.152917i | ||||
\(956\) | −1.84735 | − | 3.19971i | −0.0597477 | − | 0.103486i | ||||
\(957\) | 14.9146 | 0.482120 | ||||||||
\(958\) | 9.57568 | − | 16.5856i | 0.309376 | − | 0.535855i | ||||
\(959\) | −18.9805 | −0.612914 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 30.4431 | + | 5.84944i | 0.982036 | + | 0.188691i | ||||
\(962\) | 4.38310 | 0.141317 | ||||||||
\(963\) | 1.39070 | 0.0448147 | ||||||||
\(964\) | 12.8144 | − | 22.1952i | 0.412723 | − | 0.714858i | ||||
\(965\) | 9.15265 | 0.294634 | ||||||||
\(966\) | −1.66237 | − | 2.87931i | −0.0534859 | − | 0.0926404i | ||||
\(967\) | −2.87441 | + | 4.97862i | −0.0924347 | + | 0.160102i | −0.908535 | − | 0.417809i | \(-0.862798\pi\) |
0.816100 | + | 0.577910i | \(0.196132\pi\) | |||||||
\(968\) | 8.21860 | − | 14.2350i | 0.264156 | − | 0.457531i | ||||
\(969\) | −26.9133 | −0.864580 | ||||||||
\(970\) | 6.64228 | + | 11.5048i | 0.213271 | + | 0.369396i | ||||
\(971\) | 7.99027 | + | 13.8396i | 0.256420 | + | 0.444133i | 0.965280 | − | 0.261216i | \(-0.0841236\pi\) |
−0.708860 | + | 0.705349i | \(0.750790\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 0.165530 | − | 0.286707i | 0.00530666 | − | 0.00919140i | ||||
\(974\) | 2.15200 | + | 3.72738i | 0.0689547 | + | 0.119433i | ||||
\(975\) | 0.390699 | − | 0.676711i | 0.0125124 | − | 0.0216721i | ||||
\(976\) | −9.45665 | −0.302700 | ||||||||
\(977\) | −28.7814 | −0.920799 | −0.460399 | − | 0.887712i | \(-0.652294\pi\) | ||||
−0.460399 | + | 0.887712i | \(0.652294\pi\) | |||||||
\(978\) | −6.26131 | + | 10.8449i | −0.200214 | + | 0.346782i | ||||
\(979\) | 24.1438 | + | 41.8182i | 0.771638 | + | 1.33652i | ||||
\(980\) | 2.53298 | − | 4.38725i | 0.0809130 | − | 0.140145i | ||||
\(981\) | 3.72833 | + | 6.45765i | 0.119036 | + | 0.206177i | ||||
\(982\) | 13.2943 | + | 23.0264i | 0.424238 | + | 0.734801i | ||||
\(983\) | 12.8474 | + | 22.2523i | 0.409767 | + | 0.709737i | 0.994863 | − | 0.101227i | \(-0.0322767\pi\) |
−0.585096 | + | 0.810964i | \(0.698943\pi\) | |||||||
\(984\) | 11.0195 | 0.351287 | ||||||||
\(985\) | −9.62875 | + | 16.6775i | −0.306798 | + | 0.531389i | ||||
\(986\) | −5.13848 | + | 8.90011i | −0.163642 | + | 0.283437i | ||||
\(987\) | 0.815018 | + | 1.41165i | 0.0259423 | + | 0.0449334i | ||||
\(988\) | 5.82662 | 0.185369 | ||||||||
\(989\) | −9.38033 | + | 16.2472i | −0.298277 | + | 0.516631i | ||||
\(990\) | −5.23805 | −0.166476 | ||||||||
\(991\) | −2.03890 | −0.0647679 | −0.0323840 | − | 0.999476i | \(-0.510310\pi\) | ||||
−0.0323840 | + | 0.999476i | \(0.510310\pi\) | |||||||
\(992\) | 5.54270 | + | 0.527670i | 0.175981 | + | 0.0167535i | ||||
\(993\) | 34.7142 | 1.10162 | ||||||||
\(994\) | 4.47611 | 0.141973 | ||||||||
\(995\) | −8.93340 | + | 15.4731i | −0.283208 | + | 0.490530i | ||||
\(996\) | −13.8668 | −0.439387 | ||||||||
\(997\) | −22.8602 | − | 39.5951i | −0.723991 | − | 1.25399i | −0.959388 | − | 0.282090i | \(-0.908972\pi\) |
0.235397 | − | 0.971899i | \(-0.424361\pi\) | |||||||
\(998\) | −19.7943 | + | 34.2847i | −0.626577 | + | 1.08526i | ||||
\(999\) | −2.80465 | + | 4.85780i | −0.0887352 | + | 0.153694i |
(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 | 930.2.i.n.811.2 | yes | 6 | |
31.25 | even | 3 | inner | 930.2.i.n.211.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.i.n.211.2 | ✓ | 6 | 31.25 | even | 3 | inner | |
930.2.i.n.811.2 | yes | 6 | 1.1 | even | 1 | trivial |