Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.2 | ||
Root | \(1.25760 - 2.17823i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.277 |
Dual form | 483.2.i.h.415.2 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25760 | − | 2.17823i | −0.889259 | − | 1.54024i | −0.840753 | − | 0.541419i | \(-0.817887\pi\) |
−0.0485058 | − | 0.998823i | \(-0.515446\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −2.16313 | + | 3.74664i | −1.08156 | + | 1.87332i | ||||
\(5\) | −2.15868 | − | 3.73894i | −0.965390 | − | 1.67210i | −0.708564 | − | 0.705647i | \(-0.750657\pi\) |
−0.256826 | − | 0.966458i | \(-0.582677\pi\) | |||||||
\(6\) | −2.51520 | −1.02683 | ||||||||
\(7\) | 1.42694 | − | 2.22797i | 0.539332 | − | 0.842093i | ||||
\(8\) | 5.85100 | 2.06864 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −5.42951 | + | 9.40419i | −1.71696 | + | 2.97387i | ||||
\(11\) | −0.864575 | + | 1.49749i | −0.260679 | + | 0.451510i | −0.966423 | − | 0.256958i | \(-0.917280\pi\) |
0.705743 | + | 0.708468i | \(0.250613\pi\) | |||||||
\(12\) | 2.16313 | + | 3.74664i | 0.624441 | + | 1.08156i | ||||
\(13\) | −2.88941 | −0.801378 | −0.400689 | − | 0.916214i | \(-0.631229\pi\) | ||||
−0.400689 | + | 0.916214i | \(0.631229\pi\) | |||||||
\(14\) | −6.64755 | − | 0.306300i | −1.77663 | − | 0.0818622i | ||||
\(15\) | −4.31735 | −1.11474 | ||||||||
\(16\) | −3.03197 | − | 5.25153i | −0.757993 | − | 1.31288i | ||||
\(17\) | 2.46562 | − | 4.27058i | 0.598001 | − | 1.03577i | −0.395115 | − | 0.918632i | \(-0.629295\pi\) |
0.993116 | − | 0.117136i | \(-0.0373715\pi\) | |||||||
\(18\) | −1.25760 | + | 2.17823i | −0.296420 | + | 0.513414i | ||||
\(19\) | −1.22078 | − | 2.11445i | −0.280066 | − | 0.485089i | 0.691335 | − | 0.722535i | \(-0.257023\pi\) |
−0.971401 | + | 0.237446i | \(0.923690\pi\) | |||||||
\(20\) | 18.6780 | 4.17652 | ||||||||
\(21\) | −1.21601 | − | 2.34975i | −0.265355 | − | 0.512757i | ||||
\(22\) | 4.34917 | 0.927245 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | ||||
\(24\) | 2.92550 | − | 5.06711i | 0.597165 | − | 1.03432i | ||||
\(25\) | −6.81978 | + | 11.8122i | −1.36396 | + | 2.36244i | ||||
\(26\) | 3.63373 | + | 6.29380i | 0.712633 | + | 1.23432i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 5.26076 | + | 10.1656i | 0.994191 | + | 1.92112i | ||||
\(29\) | 8.05817 | 1.49636 | 0.748182 | − | 0.663493i | \(-0.230927\pi\) | ||||
0.748182 | + | 0.663493i | \(0.230927\pi\) | |||||||
\(30\) | 5.42951 | + | 9.40419i | 0.991289 | + | 1.71696i | ||||
\(31\) | −0.457930 | + | 0.793157i | −0.0822466 | + | 0.142455i | −0.904215 | − | 0.427078i | \(-0.859543\pi\) |
0.821968 | + | 0.569534i | \(0.192876\pi\) | |||||||
\(32\) | −1.77504 | + | 3.07445i | −0.313785 | + | 0.543491i | ||||
\(33\) | 0.864575 | + | 1.49749i | 0.150503 | + | 0.260679i | ||||
\(34\) | −12.4031 | −2.12711 | ||||||||
\(35\) | −11.4105 | − | 0.525765i | −1.92873 | − | 0.0888705i | ||||
\(36\) | 4.32625 | 0.721042 | ||||||||
\(37\) | 4.57790 | + | 7.92916i | 0.752603 | + | 1.30355i | 0.946557 | + | 0.322536i | \(0.104535\pi\) |
−0.193955 | + | 0.981011i | \(0.562131\pi\) | |||||||
\(38\) | −3.07051 | + | 5.31828i | −0.498103 | + | 0.862739i | ||||
\(39\) | −1.44471 | + | 2.50230i | −0.231338 | + | 0.400689i | ||||
\(40\) | −12.6304 | − | 21.8765i | −1.99704 | − | 3.45898i | ||||
\(41\) | −6.60783 | −1.03197 | −0.515985 | − | 0.856598i | \(-0.672574\pi\) | ||||
−0.515985 | + | 0.856598i | \(0.672574\pi\) | |||||||
\(42\) | −3.58904 | + | 5.60380i | −0.553801 | + | 0.864685i | ||||
\(43\) | 10.7440 | 1.63845 | 0.819223 | − | 0.573475i | \(-0.194405\pi\) | ||||
0.819223 | + | 0.573475i | \(0.194405\pi\) | |||||||
\(44\) | −3.74037 | − | 6.47851i | −0.563882 | − | 0.976672i | ||||
\(45\) | −2.15868 | + | 3.73894i | −0.321797 | + | 0.557368i | ||||
\(46\) | −1.25760 | + | 2.17823i | −0.185423 | + | 0.321163i | ||||
\(47\) | 0.199824 | + | 0.346106i | 0.0291474 | + | 0.0504847i | 0.880231 | − | 0.474545i | \(-0.157387\pi\) |
−0.851084 | + | 0.525030i | \(0.824054\pi\) | |||||||
\(48\) | −6.06395 | −0.875255 | ||||||||
\(49\) | −2.92770 | − | 6.35835i | −0.418243 | − | 0.908335i | ||||
\(50\) | 34.3063 | 4.85164 | ||||||||
\(51\) | −2.46562 | − | 4.27058i | −0.345256 | − | 0.598001i | ||||
\(52\) | 6.25016 | − | 10.8256i | 0.866741 | − | 1.50124i | ||||
\(53\) | −3.27256 | + | 5.66824i | −0.449521 | + | 0.778593i | −0.998355 | − | 0.0573383i | \(-0.981739\pi\) |
0.548834 | + | 0.835931i | \(0.315072\pi\) | |||||||
\(54\) | 1.25760 | + | 2.17823i | 0.171138 | + | 0.296420i | ||||
\(55\) | 7.46536 | 1.00663 | ||||||||
\(56\) | 8.34901 | − | 13.0358i | 1.11568 | − | 1.74199i | ||||
\(57\) | −2.44156 | −0.323393 | ||||||||
\(58\) | −10.1340 | − | 17.5526i | −1.33066 | − | 2.30476i | ||||
\(59\) | 0.917541 | − | 1.58923i | 0.119454 | − | 0.206900i | −0.800098 | − | 0.599870i | \(-0.795219\pi\) |
0.919551 | + | 0.392970i | \(0.128552\pi\) | |||||||
\(60\) | 9.33898 | − | 16.1756i | 1.20566 | − | 2.08826i | ||||
\(61\) | 0.650629 | + | 1.12692i | 0.0833045 | + | 0.144288i | 0.904667 | − | 0.426118i | \(-0.140119\pi\) |
−0.821363 | + | 0.570406i | \(0.806786\pi\) | |||||||
\(62\) | 2.30357 | 0.292554 | ||||||||
\(63\) | −2.64295 | − | 0.121779i | −0.332980 | − | 0.0153428i | ||||
\(64\) | −3.19874 | −0.399843 | ||||||||
\(65\) | 6.23731 | + | 10.8033i | 0.773642 | + | 1.33999i | ||||
\(66\) | 2.17458 | − | 3.76649i | 0.267673 | − | 0.463623i | ||||
\(67\) | 5.10699 | − | 8.84556i | 0.623918 | − | 1.08066i | −0.364831 | − | 0.931074i | \(-0.618873\pi\) |
0.988749 | − | 0.149583i | \(-0.0477933\pi\) | |||||||
\(68\) | 10.6669 | + | 18.4756i | 1.29355 | + | 2.24050i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 13.2047 | + | 25.5160i | 1.57826 | + | 3.04974i | ||||
\(71\) | −9.00190 | −1.06833 | −0.534164 | − | 0.845381i | \(-0.679374\pi\) | ||||
−0.534164 | + | 0.845381i | \(0.679374\pi\) | |||||||
\(72\) | −2.92550 | − | 5.06711i | −0.344773 | − | 0.597165i | ||||
\(73\) | 1.30858 | − | 2.26652i | 0.153158 | − | 0.265277i | −0.779229 | − | 0.626739i | \(-0.784389\pi\) |
0.932387 | + | 0.361463i | \(0.117722\pi\) | |||||||
\(74\) | 11.5144 | − | 19.9435i | 1.33852 | − | 2.31838i | ||||
\(75\) | 6.81978 | + | 11.8122i | 0.787480 | + | 1.36396i | ||||
\(76\) | 10.5628 | 1.21164 | ||||||||
\(77\) | 2.10266 | + | 4.06307i | 0.239621 | + | 0.463030i | ||||
\(78\) | 7.26746 | 0.822877 | ||||||||
\(79\) | −5.09351 | − | 8.82221i | −0.573064 | − | 0.992577i | −0.996249 | − | 0.0865331i | \(-0.972421\pi\) |
0.423185 | − | 0.906043i | \(-0.360912\pi\) | |||||||
\(80\) | −13.0901 | + | 22.6727i | −1.46352 | + | 2.53489i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 8.31002 | + | 14.3934i | 0.917688 | + | 1.58948i | ||||
\(83\) | −10.8838 | −1.19465 | −0.597327 | − | 0.801998i | \(-0.703771\pi\) | ||||
−0.597327 | + | 0.801998i | \(0.703771\pi\) | |||||||
\(84\) | 11.4341 | + | 0.526849i | 1.24756 | + | 0.0574839i | ||||
\(85\) | −21.2899 | −2.30922 | ||||||||
\(86\) | −13.5117 | − | 23.4029i | −1.45700 | − | 2.52360i | ||||
\(87\) | 4.02908 | − | 6.97858i | 0.431963 | − | 0.748182i | ||||
\(88\) | −5.05863 | + | 8.76180i | −0.539251 | + | 0.934011i | ||||
\(89\) | −7.49312 | − | 12.9785i | −0.794269 | − | 1.37571i | −0.923302 | − | 0.384074i | \(-0.874521\pi\) |
0.129033 | − | 0.991640i | \(-0.458813\pi\) | |||||||
\(90\) | 10.8590 | 1.14464 | ||||||||
\(91\) | −4.12301 | + | 6.43752i | −0.432209 | + | 0.674835i | ||||
\(92\) | 4.32625 | 0.451043 | ||||||||
\(93\) | 0.457930 | + | 0.793157i | 0.0474851 | + | 0.0822466i | ||||
\(94\) | 0.502599 | − | 0.870527i | 0.0518391 | − | 0.0897880i | ||||
\(95\) | −5.27054 | + | 9.12884i | −0.540746 | + | 0.936600i | ||||
\(96\) | 1.77504 | + | 3.07445i | 0.181164 | + | 0.313785i | ||||
\(97\) | −3.07116 | −0.311829 | −0.155914 | − | 0.987771i | \(-0.549832\pi\) | ||||
−0.155914 | + | 0.987771i | \(0.549832\pi\) | |||||||
\(98\) | −10.1681 | + | 14.3735i | −1.02713 | + | 1.45194i | ||||
\(99\) | 1.72915 | 0.173786 | ||||||||
\(100\) | −29.5041 | − | 51.1025i | −2.95041 | − | 5.11025i | ||||
\(101\) | −0.544049 | + | 0.942320i | −0.0541349 | + | 0.0937644i | −0.891823 | − | 0.452385i | \(-0.850573\pi\) |
0.837688 | + | 0.546149i | \(0.183907\pi\) | |||||||
\(102\) | −6.20154 | + | 10.7414i | −0.614044 | + | 1.06356i | ||||
\(103\) | 1.61555 | + | 2.79821i | 0.159185 | + | 0.275716i | 0.934575 | − | 0.355766i | \(-0.115780\pi\) |
−0.775390 | + | 0.631482i | \(0.782447\pi\) | |||||||
\(104\) | −16.9059 | −1.65776 | ||||||||
\(105\) | −6.16060 | + | 9.61894i | −0.601213 | + | 0.938712i | ||||
\(106\) | 16.4623 | 1.59896 | ||||||||
\(107\) | 0.468449 | + | 0.811378i | 0.0452867 | + | 0.0784389i | 0.887780 | − | 0.460268i | \(-0.152247\pi\) |
−0.842494 | + | 0.538706i | \(0.818913\pi\) | |||||||
\(108\) | 2.16313 | − | 3.74664i | 0.208147 | − | 0.360521i | ||||
\(109\) | 7.48909 | − | 12.9715i | 0.717324 | − | 1.24244i | −0.244732 | − | 0.969591i | \(-0.578700\pi\) |
0.962056 | − | 0.272852i | \(-0.0879668\pi\) | |||||||
\(110\) | −9.38845 | − | 16.2613i | −0.895153 | − | 1.55045i | ||||
\(111\) | 9.15581 | 0.869031 | ||||||||
\(112\) | −16.0267 | − | 0.738464i | −1.51438 | − | 0.0697783i | ||||
\(113\) | −14.1424 | −1.33040 | −0.665201 | − | 0.746665i | \(-0.731654\pi\) | ||||
−0.665201 | + | 0.746665i | \(0.731654\pi\) | |||||||
\(114\) | 3.07051 | + | 5.31828i | 0.287580 | + | 0.498103i | ||||
\(115\) | −2.15868 | + | 3.73894i | −0.201298 | + | 0.348658i | ||||
\(116\) | −17.4308 | + | 30.1911i | −1.61841 | + | 2.80317i | ||||
\(117\) | 1.44471 | + | 2.50230i | 0.133563 | + | 0.231338i | ||||
\(118\) | −4.61560 | −0.424901 | ||||||||
\(119\) | −5.99644 | − | 11.5872i | −0.549693 | − | 1.06220i | ||||
\(120\) | −25.2608 | −2.30599 | ||||||||
\(121\) | 4.00502 | + | 6.93690i | 0.364093 | + | 0.630627i | ||||
\(122\) | 1.63646 | − | 2.83444i | 0.148158 | − | 0.256618i | ||||
\(123\) | −3.30392 | + | 5.72255i | −0.297904 | + | 0.515985i | ||||
\(124\) | −1.98112 | − | 3.43140i | −0.177910 | − | 0.308149i | ||||
\(125\) | 37.3000 | 3.33621 | ||||||||
\(126\) | 3.05851 | + | 5.91010i | 0.272474 | + | 0.526513i | ||||
\(127\) | −1.77968 | −0.157921 | −0.0789604 | − | 0.996878i | \(-0.525160\pi\) | ||||
−0.0789604 | + | 0.996878i | \(0.525160\pi\) | |||||||
\(128\) | 7.57281 | + | 13.1165i | 0.669349 | + | 1.15935i | ||||
\(129\) | 5.37200 | − | 9.30458i | 0.472979 | − | 0.819223i | ||||
\(130\) | 15.6881 | − | 27.1726i | 1.37594 | − | 2.38319i | ||||
\(131\) | −4.44632 | − | 7.70125i | −0.388477 | − | 0.672862i | 0.603768 | − | 0.797160i | \(-0.293665\pi\) |
−0.992245 | + | 0.124298i | \(0.960332\pi\) | |||||||
\(132\) | −7.48074 | −0.651115 | ||||||||
\(133\) | −6.45291 | − | 0.297332i | −0.559539 | − | 0.0257819i | ||||
\(134\) | −25.6902 | −2.21930 | ||||||||
\(135\) | 2.15868 | + | 3.73894i | 0.185789 | + | 0.321797i | ||||
\(136\) | 14.4263 | − | 24.9872i | 1.23705 | − | 2.14263i | ||||
\(137\) | −0.123702 | + | 0.214258i | −0.0105686 | + | 0.0183053i | −0.871261 | − | 0.490819i | \(-0.836697\pi\) |
0.860693 | + | 0.509125i | \(0.170031\pi\) | |||||||
\(138\) | 1.25760 | + | 2.17823i | 0.107054 | + | 0.185423i | ||||
\(139\) | −8.59949 | −0.729399 | −0.364699 | − | 0.931125i | \(-0.618828\pi\) | ||||
−0.364699 | + | 0.931125i | \(0.618828\pi\) | |||||||
\(140\) | 26.6523 | − | 41.6139i | 2.25253 | − | 3.51702i | ||||
\(141\) | 0.399649 | 0.0336565 | ||||||||
\(142\) | 11.3208 | + | 19.6082i | 0.950021 | + | 1.64548i | ||||
\(143\) | 2.49811 | − | 4.32686i | 0.208903 | − | 0.361830i | ||||
\(144\) | −3.03197 | + | 5.25153i | −0.252664 | + | 0.437628i | ||||
\(145\) | −17.3950 | − | 30.1290i | −1.44458 | − | 2.50208i | ||||
\(146\) | −6.58268 | −0.544787 | ||||||||
\(147\) | −6.97034 | − | 0.643713i | −0.574904 | − | 0.0530926i | ||||
\(148\) | −39.6103 | −3.25595 | ||||||||
\(149\) | −2.25334 | − | 3.90291i | −0.184601 | − | 0.319739i | 0.758841 | − | 0.651276i | \(-0.225766\pi\) |
−0.943442 | + | 0.331537i | \(0.892433\pi\) | |||||||
\(150\) | 17.1531 | − | 29.7101i | 1.40055 | − | 2.42582i | ||||
\(151\) | 2.26383 | − | 3.92107i | 0.184228 | − | 0.319092i | −0.759088 | − | 0.650988i | \(-0.774355\pi\) |
0.943316 | + | 0.331896i | \(0.107688\pi\) | |||||||
\(152\) | −7.14278 | − | 12.3717i | −0.579356 | − | 1.00347i | ||||
\(153\) | −4.93124 | −0.398667 | ||||||||
\(154\) | 6.20599 | − | 9.68981i | 0.500093 | − | 0.780827i | ||||
\(155\) | 3.95409 | 0.317600 | ||||||||
\(156\) | −6.25016 | − | 10.8256i | −0.500413 | − | 0.866741i | ||||
\(157\) | 1.63364 | − | 2.82954i | 0.130378 | − | 0.225822i | −0.793444 | − | 0.608643i | \(-0.791714\pi\) |
0.923822 | + | 0.382821i | \(0.125047\pi\) | |||||||
\(158\) | −12.8112 | + | 22.1897i | −1.01921 | + | 1.76532i | ||||
\(159\) | 3.27256 | + | 5.66824i | 0.259531 | + | 0.449521i | ||||
\(160\) | 15.3269 | 1.21170 | ||||||||
\(161\) | −2.64295 | − | 0.121779i | −0.208293 | − | 0.00959757i | ||||
\(162\) | 2.51520 | 0.197613 | ||||||||
\(163\) | −5.32102 | − | 9.21628i | −0.416774 | − | 0.721875i | 0.578838 | − | 0.815442i | \(-0.303506\pi\) |
−0.995613 | + | 0.0935677i | \(0.970173\pi\) | |||||||
\(164\) | 14.2936 | − | 24.7572i | 1.11614 | − | 1.93321i | ||||
\(165\) | 3.73268 | − | 6.46519i | 0.290589 | − | 0.503314i | ||||
\(166\) | 13.6875 | + | 23.7075i | 1.06236 | + | 1.84006i | ||||
\(167\) | 2.99812 | 0.232001 | 0.116001 | − | 0.993249i | \(-0.462993\pi\) | ||||
0.116001 | + | 0.993249i | \(0.462993\pi\) | |||||||
\(168\) | −7.11487 | − | 13.7484i | −0.548924 | − | 1.06071i | ||||
\(169\) | −4.65131 | −0.357793 | ||||||||
\(170\) | 26.7742 | + | 46.3744i | 2.05349 | + | 3.55675i | ||||
\(171\) | −1.22078 | + | 2.11445i | −0.0933554 | + | 0.161696i | ||||
\(172\) | −23.2406 | + | 40.2540i | −1.77208 | + | 3.06934i | ||||
\(173\) | 6.64982 | + | 11.5178i | 0.505576 | + | 0.875684i | 0.999979 | + | 0.00645084i | \(0.00205338\pi\) |
−0.494403 | + | 0.869233i | \(0.664613\pi\) | |||||||
\(174\) | −20.2679 | −1.53651 | ||||||||
\(175\) | 16.5858 | + | 32.0495i | 1.25377 | + | 2.42272i | ||||
\(176\) | 10.4855 | 0.790373 | ||||||||
\(177\) | −0.917541 | − | 1.58923i | −0.0689666 | − | 0.119454i | ||||
\(178\) | −18.8467 | + | 32.6435i | −1.41262 | + | 2.44673i | ||||
\(179\) | −9.81485 | + | 16.9998i | −0.733596 | + | 1.27063i | 0.221740 | + | 0.975106i | \(0.428826\pi\) |
−0.955336 | + | 0.295520i | \(0.904507\pi\) | |||||||
\(180\) | −9.33898 | − | 16.1756i | −0.696086 | − | 1.20566i | ||||
\(181\) | 19.2095 | 1.42783 | 0.713915 | − | 0.700232i | \(-0.246920\pi\) | ||||
0.713915 | + | 0.700232i | \(0.246920\pi\) | |||||||
\(182\) | 19.2075 | + | 0.885027i | 1.42375 | + | 0.0656026i | ||||
\(183\) | 1.30126 | 0.0961917 | ||||||||
\(184\) | −2.92550 | − | 5.06711i | −0.215671 | − | 0.373552i | ||||
\(185\) | 19.7644 | − | 34.2330i | 1.45311 | − | 2.51686i | ||||
\(186\) | 1.15179 | − | 1.99495i | 0.0844531 | − | 0.146277i | ||||
\(187\) | 4.26343 | + | 7.38448i | 0.311773 | + | 0.540007i | ||||
\(188\) | −1.72898 | −0.126099 | ||||||||
\(189\) | −1.42694 | + | 2.22797i | −0.103794 | + | 0.162061i | ||||
\(190\) | 26.5130 | 1.92345 | ||||||||
\(191\) | 3.57687 | + | 6.19533i | 0.258814 | + | 0.448278i | 0.965924 | − | 0.258825i | \(-0.0833351\pi\) |
−0.707111 | + | 0.707103i | \(0.750002\pi\) | |||||||
\(192\) | −1.59937 | + | 2.77019i | −0.115425 | + | 0.199921i | ||||
\(193\) | 10.9786 | − | 19.0156i | 0.790259 | − | 1.36877i | −0.135547 | − | 0.990771i | \(-0.543279\pi\) |
0.925806 | − | 0.377999i | \(-0.123388\pi\) | |||||||
\(194\) | 3.86229 | + | 6.68969i | 0.277296 | + | 0.480291i | ||||
\(195\) | 12.4746 | 0.893325 | ||||||||
\(196\) | 30.1554 | + | 2.78487i | 2.15396 | + | 0.198919i | ||||
\(197\) | 3.21028 | 0.228723 | 0.114361 | − | 0.993439i | \(-0.463518\pi\) | ||||
0.114361 | + | 0.993439i | \(0.463518\pi\) | |||||||
\(198\) | −2.17458 | − | 3.76649i | −0.154541 | − | 0.267673i | ||||
\(199\) | −6.35849 | + | 11.0132i | −0.450741 | + | 0.780707i | −0.998432 | − | 0.0559738i | \(-0.982174\pi\) |
0.547691 | + | 0.836681i | \(0.315507\pi\) | |||||||
\(200\) | −39.9025 | + | 69.1131i | −2.82153 | + | 4.88704i | ||||
\(201\) | −5.10699 | − | 8.84556i | −0.360219 | − | 0.623918i | ||||
\(202\) | 2.73679 | 0.192560 | ||||||||
\(203\) | 11.4985 | − | 17.9534i | 0.807037 | − | 1.26008i | ||||
\(204\) | 21.3338 | 1.49366 | ||||||||
\(205\) | 14.2642 | + | 24.7063i | 0.996253 | + | 1.72556i | ||||
\(206\) | 4.06343 | − | 7.03807i | 0.283113 | − | 0.490366i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | 8.76062 | + | 15.1738i | 0.607439 | + | 1.05212i | ||||
\(209\) | 4.22183 | 0.292030 | ||||||||
\(210\) | 28.6998 | + | 1.32241i | 1.98048 | + | 0.0912547i | ||||
\(211\) | −17.0500 | −1.17377 | −0.586884 | − | 0.809671i | \(-0.699646\pi\) | ||||
−0.586884 | + | 0.809671i | \(0.699646\pi\) | |||||||
\(212\) | −14.1579 | − | 24.5222i | −0.972370 | − | 1.68419i | ||||
\(213\) | −4.50095 | + | 7.79587i | −0.308400 | + | 0.534164i | ||||
\(214\) | 1.17825 | − | 2.04078i | 0.0805432 | − | 0.139505i | ||||
\(215\) | −23.1928 | − | 40.1712i | −1.58174 | − | 2.73965i | ||||
\(216\) | −5.85100 | −0.398110 | ||||||||
\(217\) | 1.11369 | + | 2.15204i | 0.0756024 | + | 0.146090i | ||||
\(218\) | −37.6732 | −2.55155 | ||||||||
\(219\) | −1.30858 | − | 2.26652i | −0.0884255 | − | 0.153158i | ||||
\(220\) | −16.1485 | + | 27.9700i | −1.08873 | + | 1.88574i | ||||
\(221\) | −7.12419 | + | 12.3395i | −0.479225 | + | 0.830042i | ||||
\(222\) | −11.5144 | − | 19.9435i | −0.772793 | − | 1.33852i | ||||
\(223\) | 23.3278 | 1.56215 | 0.781073 | − | 0.624440i | \(-0.214673\pi\) | ||||
0.781073 | + | 0.624440i | \(0.214673\pi\) | |||||||
\(224\) | 4.31692 | + | 8.34177i | 0.288436 | + | 0.557358i | ||||
\(225\) | 13.6396 | 0.909303 | ||||||||
\(226\) | 17.7855 | + | 30.8053i | 1.18307 | + | 2.04914i | ||||
\(227\) | 3.83797 | − | 6.64756i | 0.254735 | − | 0.441214i | −0.710088 | − | 0.704113i | \(-0.751345\pi\) |
0.964824 | + | 0.262898i | \(0.0846784\pi\) | |||||||
\(228\) | 5.28140 | − | 9.14765i | 0.349769 | − | 0.605818i | ||||
\(229\) | 11.4368 | + | 19.8091i | 0.755766 | + | 1.30903i | 0.944993 | + | 0.327092i | \(0.106069\pi\) |
−0.189227 | + | 0.981933i | \(0.560598\pi\) | |||||||
\(230\) | 10.8590 | 0.716023 | ||||||||
\(231\) | 4.57005 | + | 0.210575i | 0.300687 | + | 0.0138548i | ||||
\(232\) | 47.1483 | 3.09544 | ||||||||
\(233\) | −11.7779 | − | 20.4000i | −0.771599 | − | 1.33645i | −0.936686 | − | 0.350169i | \(-0.886124\pi\) |
0.165088 | − | 0.986279i | \(-0.447209\pi\) | |||||||
\(234\) | 3.63373 | − | 6.29380i | 0.237544 | − | 0.411439i | ||||
\(235\) | 0.862713 | − | 1.49426i | 0.0562772 | − | 0.0974749i | ||||
\(236\) | 3.96951 | + | 6.87540i | 0.258393 | + | 0.447550i | ||||
\(237\) | −10.1870 | −0.661718 | ||||||||
\(238\) | −17.6984 | + | 27.6337i | −1.14722 | + | 1.79123i | ||||
\(239\) | 13.1829 | 0.852732 | 0.426366 | − | 0.904551i | \(-0.359794\pi\) | ||||
0.426366 | + | 0.904551i | \(0.359794\pi\) | |||||||
\(240\) | 13.0901 | + | 22.6727i | 0.844963 | + | 1.46352i | ||||
\(241\) | 8.63351 | − | 14.9537i | 0.556134 | − | 0.963252i | −0.441681 | − | 0.897172i | \(-0.645618\pi\) |
0.997814 | − | 0.0660793i | \(-0.0210490\pi\) | |||||||
\(242\) | 10.0734 | − | 17.4477i | 0.647545 | − | 1.12158i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −5.62957 | −0.360396 | ||||||||
\(245\) | −17.4535 | + | 24.6721i | −1.11506 | + | 1.57624i | ||||
\(246\) | 16.6200 | 1.05966 | ||||||||
\(247\) | 3.52733 | + | 6.10952i | 0.224439 | + | 0.388740i | ||||
\(248\) | −2.67934 | + | 4.64076i | −0.170139 | + | 0.294689i | ||||
\(249\) | −5.44191 | + | 9.42566i | −0.344867 | + | 0.597327i | ||||
\(250\) | −46.9086 | − | 81.2480i | −2.96676 | − | 5.13858i | ||||
\(251\) | 4.74956 | 0.299790 | 0.149895 | − | 0.988702i | \(-0.452106\pi\) | ||||
0.149895 | + | 0.988702i | \(0.452106\pi\) | |||||||
\(252\) | 6.17329 | − | 9.63876i | 0.388881 | − | 0.607185i | ||||
\(253\) | 1.72915 | 0.108711 | ||||||||
\(254\) | 2.23812 | + | 3.87655i | 0.140432 | + | 0.243236i | ||||
\(255\) | −10.6450 | + | 18.4376i | −0.666613 | + | 1.15461i | ||||
\(256\) | 15.8484 | − | 27.4503i | 0.990527 | − | 1.71564i | ||||
\(257\) | −0.714418 | − | 1.23741i | −0.0445641 | − | 0.0771874i | 0.842883 | − | 0.538097i | \(-0.180857\pi\) |
−0.887447 | + | 0.460910i | \(0.847523\pi\) | |||||||
\(258\) | −27.0234 | −1.68240 | ||||||||
\(259\) | 24.1983 | + | 1.11499i | 1.50361 | + | 0.0692821i | ||||
\(260\) | −53.9683 | −3.34697 | ||||||||
\(261\) | −4.02908 | − | 6.97858i | −0.249394 | − | 0.431963i | ||||
\(262\) | −11.1834 | + | 19.3702i | −0.690913 | + | 1.19670i | ||||
\(263\) | −4.40873 | + | 7.63614i | −0.271854 | + | 0.470865i | −0.969337 | − | 0.245737i | \(-0.920970\pi\) |
0.697483 | + | 0.716602i | \(0.254303\pi\) | |||||||
\(264\) | 5.05863 | + | 8.76180i | 0.311337 | + | 0.539251i | ||||
\(265\) | 28.2576 | 1.73585 | ||||||||
\(266\) | 7.46754 | + | 14.4299i | 0.457864 | + | 0.884751i | ||||
\(267\) | −14.9862 | −0.917143 | ||||||||
\(268\) | 22.0941 | + | 38.2681i | 1.34961 | + | 2.33760i | ||||
\(269\) | 6.45927 | − | 11.1878i | 0.393829 | − | 0.682132i | −0.599122 | − | 0.800658i | \(-0.704484\pi\) |
0.992951 | + | 0.118526i | \(0.0378169\pi\) | |||||||
\(270\) | 5.42951 | − | 9.40419i | 0.330430 | − | 0.572321i | ||||
\(271\) | −6.67426 | − | 11.5602i | −0.405433 | − | 0.702230i | 0.588939 | − | 0.808177i | \(-0.299546\pi\) |
−0.994372 | + | 0.105947i | \(0.966212\pi\) | |||||||
\(272\) | −29.9028 | −1.81312 | ||||||||
\(273\) | 3.51355 | + | 6.78939i | 0.212650 | + | 0.410913i | ||||
\(274\) | 0.622271 | 0.0375927 | ||||||||
\(275\) | −11.7924 | − | 20.4251i | −0.711110 | − | 1.23168i | ||||
\(276\) | 2.16313 | − | 3.74664i | 0.130205 | − | 0.225521i | ||||
\(277\) | 7.74930 | − | 13.4222i | 0.465610 | − | 0.806461i | −0.533619 | − | 0.845725i | \(-0.679168\pi\) |
0.999229 | + | 0.0392646i | \(0.0125015\pi\) | |||||||
\(278\) | 10.8147 | + | 18.7317i | 0.648624 | + | 1.12345i | ||||
\(279\) | 0.915859 | 0.0548311 | ||||||||
\(280\) | −66.7630 | − | 3.07625i | −3.98985 | − | 0.183841i | ||||
\(281\) | 23.6088 | 1.40838 | 0.704192 | − | 0.710009i | \(-0.251309\pi\) | ||||
0.704192 | + | 0.710009i | \(0.251309\pi\) | |||||||
\(282\) | −0.502599 | − | 0.870527i | −0.0299293 | − | 0.0518391i | ||||
\(283\) | −11.8407 | + | 20.5087i | −0.703858 | + | 1.21912i | 0.263244 | + | 0.964729i | \(0.415207\pi\) |
−0.967102 | + | 0.254388i | \(0.918126\pi\) | |||||||
\(284\) | 19.4722 | − | 33.7269i | 1.15546 | − | 2.00132i | ||||
\(285\) | 5.27054 | + | 9.12884i | 0.312200 | + | 0.540746i | ||||
\(286\) | −12.5665 | −0.743074 | ||||||||
\(287\) | −9.42896 | + | 14.7220i | −0.556574 | + | 0.869015i | ||||
\(288\) | 3.55007 | 0.209190 | ||||||||
\(289\) | −3.65858 | − | 6.33684i | −0.215210 | − | 0.372755i | ||||
\(290\) | −43.7519 | + | 75.7806i | −2.56920 | + | 4.44999i | ||||
\(291\) | −1.53558 | + | 2.65970i | −0.0900172 | + | 0.155914i | ||||
\(292\) | 5.66124 | + | 9.80555i | 0.331299 | + | 0.573827i | ||||
\(293\) | 21.1268 | 1.23424 | 0.617121 | − | 0.786868i | \(-0.288299\pi\) | ||||
0.617121 | + | 0.786868i | \(0.288299\pi\) | |||||||
\(294\) | 7.36376 | + | 15.9925i | 0.429463 | + | 0.932704i | ||||
\(295\) | −7.92270 | −0.461277 | ||||||||
\(296\) | 26.7853 | + | 46.3935i | 1.55686 | + | 2.69657i | ||||
\(297\) | 0.864575 | − | 1.49749i | 0.0501678 | − | 0.0868931i | ||||
\(298\) | −5.66762 | + | 9.81661i | −0.328316 | + | 0.568661i | ||||
\(299\) | 1.44471 | + | 2.50230i | 0.0835495 | + | 0.144712i | ||||
\(300\) | −59.0081 | −3.40684 | ||||||||
\(301\) | 15.3310 | − | 23.9373i | 0.883666 | − | 1.37972i | ||||
\(302\) | −11.3880 | −0.655305 | ||||||||
\(303\) | 0.544049 | + | 0.942320i | 0.0312548 | + | 0.0541349i | ||||
\(304\) | −7.40274 | + | 12.8219i | −0.424577 | + | 0.735388i | ||||
\(305\) | 2.80899 | − | 4.86532i | 0.160843 | − | 0.278587i | ||||
\(306\) | 6.20154 | + | 10.7414i | 0.354518 | + | 0.614044i | ||||
\(307\) | −1.97923 | −0.112961 | −0.0564804 | − | 0.998404i | \(-0.517988\pi\) | ||||
−0.0564804 | + | 0.998404i | \(0.517988\pi\) | |||||||
\(308\) | −19.7712 | − | 0.911001i | −1.12657 | − | 0.0519091i | ||||
\(309\) | 3.23110 | 0.183811 | ||||||||
\(310\) | −4.97267 | − | 8.61292i | −0.282429 | − | 0.489181i | ||||
\(311\) | 1.94840 | − | 3.37472i | 0.110483 | − | 0.191363i | −0.805482 | − | 0.592620i | \(-0.798093\pi\) |
0.915965 | + | 0.401258i | \(0.131427\pi\) | |||||||
\(312\) | −8.45296 | + | 14.6410i | −0.478555 | + | 0.828881i | ||||
\(313\) | −8.82919 | − | 15.2926i | −0.499056 | − | 0.864390i | 0.500944 | − | 0.865480i | \(-0.332986\pi\) |
−0.999999 | + | 0.00109025i | \(0.999653\pi\) | |||||||
\(314\) | −8.21786 | −0.463761 | ||||||||
\(315\) | 5.24994 | + | 10.1447i | 0.295801 | + | 0.571589i | ||||
\(316\) | 44.0716 | 2.47922 | ||||||||
\(317\) | 6.16616 | + | 10.6801i | 0.346326 | + | 0.599855i | 0.985594 | − | 0.169130i | \(-0.0540957\pi\) |
−0.639268 | + | 0.768984i | \(0.720762\pi\) | |||||||
\(318\) | 8.23116 | − | 14.2568i | 0.461581 | − | 0.799481i | ||||
\(319\) | −6.96689 | + | 12.0670i | −0.390071 | + | 0.675623i | ||||
\(320\) | 6.90505 | + | 11.9599i | 0.386004 | + | 0.668579i | ||||
\(321\) | 0.936899 | 0.0522926 | ||||||||
\(322\) | 3.05851 | + | 5.91010i | 0.170444 | + | 0.329357i | ||||
\(323\) | −12.0399 | −0.669919 | ||||||||
\(324\) | −2.16313 | − | 3.74664i | −0.120174 | − | 0.208147i | ||||
\(325\) | 19.7051 | − | 34.1303i | 1.09304 | − | 1.89321i | ||||
\(326\) | −13.3835 | + | 23.1808i | −0.741241 | + | 1.28387i | ||||
\(327\) | −7.48909 | − | 12.9715i | −0.414147 | − | 0.717324i | ||||
\(328\) | −38.6624 | −2.13477 | ||||||||
\(329\) | 1.05625 | + | 0.0486690i | 0.0582330 | + | 0.00268321i | ||||
\(330\) | −18.7769 | −1.03363 | ||||||||
\(331\) | −2.90282 | − | 5.02784i | −0.159554 | − | 0.276355i | 0.775154 | − | 0.631772i | \(-0.217672\pi\) |
−0.934708 | + | 0.355417i | \(0.884339\pi\) | |||||||
\(332\) | 23.5431 | − | 40.7778i | 1.29209 | − | 2.23797i | ||||
\(333\) | 4.57790 | − | 7.92916i | 0.250868 | − | 0.434515i | ||||
\(334\) | −3.77044 | − | 6.53059i | −0.206309 | − | 0.357338i | ||||
\(335\) | −44.0973 | −2.40930 | ||||||||
\(336\) | −8.65287 | + | 13.5103i | −0.472053 | + | 0.737047i | ||||
\(337\) | −22.5441 | −1.22805 | −0.614027 | − | 0.789285i | \(-0.710452\pi\) | ||||
−0.614027 | + | 0.789285i | \(0.710452\pi\) | |||||||
\(338\) | 5.84949 | + | 10.1316i | 0.318170 | + | 0.551087i | ||||
\(339\) | −7.07118 | + | 12.2476i | −0.384054 | + | 0.665201i | ||||
\(340\) | 46.0528 | − | 79.7657i | 2.49756 | − | 4.32591i | ||||
\(341\) | −0.791829 | − | 1.37149i | −0.0428800 | − | 0.0742703i | ||||
\(342\) | 6.14102 | 0.332068 | ||||||||
\(343\) | −18.3438 | − | 2.55014i | −0.990475 | − | 0.137695i | ||||
\(344\) | 62.8631 | 3.38935 | ||||||||
\(345\) | 2.15868 | + | 3.73894i | 0.116219 | + | 0.201298i | ||||
\(346\) | 16.7256 | − | 28.9697i | 0.899176 | − | 1.55742i | ||||
\(347\) | 3.74865 | − | 6.49285i | 0.201238 | − | 0.348555i | −0.747690 | − | 0.664048i | \(-0.768837\pi\) |
0.948928 | + | 0.315494i | \(0.102170\pi\) | |||||||
\(348\) | 17.4308 | + | 30.1911i | 0.934391 | + | 1.61841i | ||||
\(349\) | −7.97347 | −0.426810 | −0.213405 | − | 0.976964i | \(-0.568455\pi\) | ||||
−0.213405 | + | 0.976964i | \(0.568455\pi\) | |||||||
\(350\) | 48.9529 | − | 76.4333i | 2.61664 | − | 4.08553i | ||||
\(351\) | 2.88941 | 0.154225 | ||||||||
\(352\) | −3.06930 | − | 5.31619i | −0.163594 | − | 0.283354i | ||||
\(353\) | 14.7645 | − | 25.5728i | 0.785833 | − | 1.36110i | −0.142668 | − | 0.989771i | \(-0.545568\pi\) |
0.928500 | − | 0.371331i | \(-0.121099\pi\) | |||||||
\(354\) | −2.30780 | + | 3.99723i | −0.122658 | + | 0.212450i | ||||
\(355\) | 19.4322 | + | 33.6575i | 1.03135 | + | 1.78636i | ||||
\(356\) | 64.8342 | 3.43621 | ||||||||
\(357\) | −13.0330 | − | 0.600524i | −0.689780 | − | 0.0317831i | ||||
\(358\) | 49.3727 | 2.60943 | ||||||||
\(359\) | 6.56032 | + | 11.3628i | 0.346241 | + | 0.599706i | 0.985578 | − | 0.169220i | \(-0.0541247\pi\) |
−0.639338 | + | 0.768926i | \(0.720791\pi\) | |||||||
\(360\) | −12.6304 | + | 21.8765i | −0.665681 | + | 1.15299i | ||||
\(361\) | 6.51939 | − | 11.2919i | 0.343126 | − | 0.594312i | ||||
\(362\) | −24.1579 | − | 41.8427i | −1.26971 | − | 2.19920i | ||||
\(363\) | 8.01004 | 0.420418 | ||||||||
\(364\) | −15.2005 | − | 29.3726i | −0.796723 | − | 1.53954i | ||||
\(365\) | −11.2992 | −0.591427 | ||||||||
\(366\) | −1.63646 | − | 2.83444i | −0.0855393 | − | 0.148158i | ||||
\(367\) | −2.63184 | + | 4.55848i | −0.137381 | + | 0.237951i | −0.926504 | − | 0.376284i | \(-0.877202\pi\) |
0.789124 | + | 0.614234i | \(0.210535\pi\) | |||||||
\(368\) | −3.03197 | + | 5.25153i | −0.158053 | + | 0.273755i | ||||
\(369\) | 3.30392 | + | 5.72255i | 0.171995 | + | 0.297904i | ||||
\(370\) | −99.4232 | −5.16876 | ||||||||
\(371\) | 7.95893 | + | 15.3794i | 0.413207 | + | 0.798459i | ||||
\(372\) | −3.96224 | −0.205432 | ||||||||
\(373\) | 6.32477 | + | 10.9548i | 0.327484 | + | 0.567219i | 0.982012 | − | 0.188819i | \(-0.0604659\pi\) |
−0.654528 | + | 0.756038i | \(0.727133\pi\) | |||||||
\(374\) | 10.7234 | − | 18.5735i | 0.554494 | − | 0.960411i | ||||
\(375\) | 18.6500 | − | 32.3028i | 0.963082 | − | 1.66811i | ||||
\(376\) | 1.16917 | + | 2.02506i | 0.0602954 | + | 0.104435i | ||||
\(377\) | −23.2834 | −1.19915 | ||||||||
\(378\) | 6.64755 | + | 0.306300i | 0.341913 | + | 0.0157544i | ||||
\(379\) | 12.7987 | 0.657426 | 0.328713 | − | 0.944430i | \(-0.393385\pi\) | ||||
0.328713 | + | 0.944430i | \(0.393385\pi\) | |||||||
\(380\) | −22.8017 | − | 39.4937i | −1.16970 | − | 2.02598i | ||||
\(381\) | −0.889838 | + | 1.54125i | −0.0455878 | + | 0.0789604i | ||||
\(382\) | 8.99657 | − | 15.5825i | 0.460305 | − | 0.797271i | ||||
\(383\) | 8.31345 | + | 14.3993i | 0.424797 | + | 0.735771i | 0.996401 | − | 0.0847589i | \(-0.0270120\pi\) |
−0.571604 | + | 0.820530i | \(0.693679\pi\) | |||||||
\(384\) | 15.1456 | 0.772897 | ||||||||
\(385\) | 10.6526 | − | 16.6326i | 0.542907 | − | 0.847675i | ||||
\(386\) | −55.2270 | −2.81098 | ||||||||
\(387\) | −5.37200 | − | 9.30458i | −0.273074 | − | 0.472979i | ||||
\(388\) | 6.64330 | − | 11.5065i | 0.337262 | − | 0.584155i | ||||
\(389\) | 14.9352 | − | 25.8684i | 0.757242 | − | 1.31158i | −0.187010 | − | 0.982358i | \(-0.559880\pi\) |
0.944252 | − | 0.329224i | \(-0.106787\pi\) | |||||||
\(390\) | −15.6881 | − | 27.1726i | −0.794398 | − | 1.37594i | ||||
\(391\) | −4.93124 | −0.249384 | ||||||||
\(392\) | −17.1299 | − | 37.2027i | −0.865193 | − | 1.87902i | ||||
\(393\) | −8.89264 | −0.448574 | ||||||||
\(394\) | −4.03725 | − | 6.99272i | −0.203394 | − | 0.352288i | ||||
\(395\) | −21.9905 | + | 38.0886i | −1.10646 | + | 1.91645i | ||||
\(396\) | −3.74037 | + | 6.47851i | −0.187961 | + | 0.325557i | ||||
\(397\) | 2.99218 | + | 5.18262i | 0.150173 | + | 0.260108i | 0.931291 | − | 0.364276i | \(-0.118683\pi\) |
−0.781118 | + | 0.624384i | \(0.785350\pi\) | |||||||
\(398\) | 31.9858 | 1.60330 | ||||||||
\(399\) | −3.48395 | + | 5.43972i | −0.174416 | + | 0.272327i | ||||
\(400\) | 82.7095 | 4.13548 | ||||||||
\(401\) | 7.93175 | + | 13.7382i | 0.396092 | + | 0.686052i | 0.993240 | − | 0.116079i | \(-0.0370326\pi\) |
−0.597147 | + | 0.802131i | \(0.703699\pi\) | |||||||
\(402\) | −12.8451 | + | 22.2484i | −0.640656 | + | 1.10965i | ||||
\(403\) | 1.32315 | − | 2.29176i | 0.0659106 | − | 0.114161i | ||||
\(404\) | −2.35369 | − | 4.07671i | −0.117101 | − | 0.202824i | ||||
\(405\) | 4.31735 | 0.214531 | ||||||||
\(406\) | −53.5671 | − | 2.46822i | −2.65849 | − | 0.122496i | ||||
\(407\) | −15.8318 | −0.784752 | ||||||||
\(408\) | −14.4263 | − | 24.9872i | −0.714210 | − | 1.23705i | ||||
\(409\) | −12.4692 | + | 21.5973i | −0.616563 | + | 1.06792i | 0.373546 | + | 0.927612i | \(0.378142\pi\) |
−0.990108 | + | 0.140306i | \(0.955191\pi\) | |||||||
\(410\) | 35.8773 | − | 62.1413i | 1.77185 | − | 3.06894i | ||||
\(411\) | 0.123702 | + | 0.214258i | 0.00610176 | + | 0.0105686i | ||||
\(412\) | −13.9785 | −0.688673 | ||||||||
\(413\) | −2.23148 | − | 4.31198i | −0.109804 | − | 0.212179i | ||||
\(414\) | 2.51520 | 0.123616 | ||||||||
\(415\) | 23.4947 | + | 40.6939i | 1.15331 | + | 1.99759i | ||||
\(416\) | 5.12881 | − | 8.88335i | 0.251460 | − | 0.435542i | ||||
\(417\) | −4.29974 | + | 7.44737i | −0.210559 | + | 0.364699i | ||||
\(418\) | −5.30938 | − | 9.19611i | −0.259690 | − | 0.449796i | ||||
\(419\) | −13.2262 | −0.646140 | −0.323070 | − | 0.946375i | \(-0.604715\pi\) | ||||
−0.323070 | + | 0.946375i | \(0.604715\pi\) | |||||||
\(420\) | −22.7126 | − | 43.8885i | −1.10826 | − | 2.14154i | ||||
\(421\) | −5.82168 | −0.283731 | −0.141866 | − | 0.989886i | \(-0.545310\pi\) | ||||
−0.141866 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(422\) | 21.4421 | + | 37.1388i | 1.04378 | + | 1.80789i | ||||
\(423\) | 0.199824 | − | 0.346106i | 0.00971579 | − | 0.0168282i | ||||
\(424\) | −19.1477 | + | 33.1649i | −0.929897 | + | 1.61063i | ||||
\(425\) | 33.6300 | + | 58.2488i | 1.63129 | + | 2.82548i | ||||
\(426\) | 22.6416 | 1.09699 | ||||||||
\(427\) | 3.43915 | + | 0.158466i | 0.166432 | + | 0.00766873i | ||||
\(428\) | −4.05326 | −0.195922 | ||||||||
\(429\) | −2.49811 | − | 4.32686i | −0.120610 | − | 0.208903i | ||||
\(430\) | −58.3347 | + | 101.039i | −2.81315 | + | 4.87252i | ||||
\(431\) | −3.10956 | + | 5.38592i | −0.149782 | + | 0.259431i | −0.931147 | − | 0.364644i | \(-0.881191\pi\) |
0.781365 | + | 0.624075i | \(0.214524\pi\) | |||||||
\(432\) | 3.03197 | + | 5.25153i | 0.145876 | + | 0.252664i | ||||
\(433\) | −2.16316 | −0.103955 | −0.0519774 | − | 0.998648i | \(-0.516552\pi\) | ||||
−0.0519774 | + | 0.998648i | \(0.516552\pi\) | |||||||
\(434\) | 3.28705 | − | 5.13229i | 0.157784 | − | 0.246358i | ||||
\(435\) | −34.7900 | −1.66805 | ||||||||
\(436\) | 32.3997 | + | 56.1179i | 1.55166 | + | 2.68756i | ||||
\(437\) | −1.22078 | + | 2.11445i | −0.0583978 | + | 0.101148i | ||||
\(438\) | −3.29134 | + | 5.70077i | −0.157266 | + | 0.272393i | ||||
\(439\) | −5.76278 | − | 9.98142i | −0.275042 | − | 0.476387i | 0.695103 | − | 0.718910i | \(-0.255359\pi\) |
−0.970146 | + | 0.242522i | \(0.922025\pi\) | |||||||
\(440\) | 43.6798 | 2.08235 | ||||||||
\(441\) | −4.04264 | + | 5.71463i | −0.192507 | + | 0.272125i | ||||
\(442\) | 35.8376 | 1.70462 | ||||||||
\(443\) | −4.56520 | − | 7.90716i | −0.216899 | − | 0.375681i | 0.736959 | − | 0.675937i | \(-0.236261\pi\) |
−0.953858 | + | 0.300257i | \(0.902928\pi\) | |||||||
\(444\) | −19.8052 | + | 34.3035i | −0.939911 | + | 1.62797i | ||||
\(445\) | −32.3504 | + | 56.0326i | −1.53356 | + | 2.65620i | ||||
\(446\) | −29.3371 | − | 50.8134i | −1.38915 | − | 2.40608i | ||||
\(447\) | −4.50669 | −0.213159 | ||||||||
\(448\) | −4.56441 | + | 7.12670i | −0.215648 | + | 0.336705i | ||||
\(449\) | −20.6827 | −0.976079 | −0.488039 | − | 0.872822i | \(-0.662288\pi\) | ||||
−0.488039 | + | 0.872822i | \(0.662288\pi\) | |||||||
\(450\) | −17.1531 | − | 29.7101i | −0.808606 | − | 1.40055i | ||||
\(451\) | 5.71297 | − | 9.89515i | 0.269013 | − | 0.465944i | ||||
\(452\) | 30.5917 | − | 52.9864i | 1.43891 | − | 2.49227i | ||||
\(453\) | −2.26383 | − | 3.92107i | −0.106364 | − | 0.184228i | ||||
\(454\) | −19.3066 | −0.906102 | ||||||||
\(455\) | 32.9697 | + | 1.51915i | 1.54565 | + | 0.0712189i | ||||
\(456\) | −14.2856 | −0.668983 | ||||||||
\(457\) | −12.2979 | − | 21.3006i | −0.575271 | − | 0.996398i | −0.996012 | − | 0.0892174i | \(-0.971563\pi\) |
0.420742 | − | 0.907181i | \(-0.361770\pi\) | |||||||
\(458\) | 28.7659 | − | 49.8240i | 1.34414 | − | 2.32812i | ||||
\(459\) | −2.46562 | + | 4.27058i | −0.115085 | + | 0.199334i | ||||
\(460\) | −9.33898 | − | 16.1756i | −0.435432 | − | 0.754191i | ||||
\(461\) | −3.35047 | −0.156047 | −0.0780235 | − | 0.996952i | \(-0.524861\pi\) | ||||
−0.0780235 | + | 0.996952i | \(0.524861\pi\) | |||||||
\(462\) | −5.28863 | − | 10.2195i | −0.246049 | − | 0.475452i | ||||
\(463\) | −30.2309 | −1.40495 | −0.702476 | − | 0.711708i | \(-0.747922\pi\) | ||||
−0.702476 | + | 0.711708i | \(0.747922\pi\) | |||||||
\(464\) | −24.4322 | − | 42.3177i | −1.13423 | − | 1.96455i | ||||
\(465\) | 1.97704 | − | 3.42434i | 0.0916832 | − | 0.158800i | ||||
\(466\) | −29.6239 | + | 51.3101i | −1.37230 | + | 2.37690i | ||||
\(467\) | 15.0708 | + | 26.1034i | 0.697394 | + | 1.20792i | 0.969367 | + | 0.245617i | \(0.0789904\pi\) |
−0.271973 | + | 0.962305i | \(0.587676\pi\) | |||||||
\(468\) | −12.5003 | −0.577827 | ||||||||
\(469\) | −12.4203 | − | 24.0003i | −0.573516 | − | 1.10823i | ||||
\(470\) | −4.33980 | −0.200180 | ||||||||
\(471\) | −1.63364 | − | 2.82954i | −0.0752740 | − | 0.130378i | ||||
\(472\) | 5.36853 | − | 9.29856i | 0.247106 | − | 0.428001i | ||||
\(473\) | −9.28900 | + | 16.0890i | −0.427109 | + | 0.739774i | ||||
\(474\) | 12.8112 | + | 22.1897i | 0.588438 | + | 1.01921i | ||||
\(475\) | 33.3018 | 1.52799 | ||||||||
\(476\) | 56.3841 | + | 2.59802i | 2.58436 | + | 0.119080i | ||||
\(477\) | 6.54512 | 0.299681 | ||||||||
\(478\) | −16.5789 | − | 28.7154i | −0.758300 | − | 1.31341i | ||||
\(479\) | −14.5172 | + | 25.1445i | −0.663308 | + | 1.14888i | 0.316433 | + | 0.948615i | \(0.397515\pi\) |
−0.979741 | + | 0.200268i | \(0.935819\pi\) | |||||||
\(480\) | 7.66346 | − | 13.2735i | 0.349787 | − | 0.605849i | ||||
\(481\) | −13.2274 | − | 22.9106i | −0.603120 | − | 1.04463i | ||||
\(482\) | −43.4301 | −1.97819 | ||||||||
\(483\) | −1.42694 | + | 2.22797i | −0.0649279 | + | 0.101376i | ||||
\(484\) | −34.6534 | −1.57516 | ||||||||
\(485\) | 6.62963 | + | 11.4829i | 0.301036 | + | 0.521410i | ||||
\(486\) | 1.25760 | − | 2.17823i | 0.0570460 | − | 0.0988065i | ||||
\(487\) | 8.65283 | − | 14.9871i | 0.392097 | − | 0.679132i | −0.600629 | − | 0.799528i | \(-0.705083\pi\) |
0.992726 | + | 0.120396i | \(0.0384163\pi\) | |||||||
\(488\) | 3.80683 | + | 6.59362i | 0.172327 | + | 0.298479i | ||||
\(489\) | −10.6420 | −0.481250 | ||||||||
\(490\) | 75.6911 | + | 6.99010i | 3.41938 | + | 0.315781i | ||||
\(491\) | 14.2287 | 0.642133 | 0.321067 | − | 0.947057i | \(-0.395959\pi\) | ||||
0.321067 | + | 0.947057i | \(0.395959\pi\) | |||||||
\(492\) | −14.2936 | − | 24.7572i | −0.644404 | − | 1.11614i | ||||
\(493\) | 19.8684 | − | 34.4131i | 0.894827 | − | 1.54989i | ||||
\(494\) | 8.87197 | − | 15.3667i | 0.399169 | − | 0.691380i | ||||
\(495\) | −3.73268 | − | 6.46519i | −0.167771 | − | 0.290589i | ||||
\(496\) | 5.55372 | 0.249369 | ||||||||
\(497\) | −12.8451 | + | 20.0560i | −0.576184 | + | 0.899633i | ||||
\(498\) | 27.3750 | 1.22670 | ||||||||
\(499\) | −5.55858 | − | 9.62774i | −0.248836 | − | 0.430997i | 0.714367 | − | 0.699771i | \(-0.246715\pi\) |
−0.963203 | + | 0.268774i | \(0.913381\pi\) | |||||||
\(500\) | −80.6846 | + | 139.750i | −3.60832 | + | 6.24980i | ||||
\(501\) | 1.49906 | − | 2.59644i | 0.0669730 | − | 0.116001i | ||||
\(502\) | −5.97306 | − | 10.3456i | −0.266591 | − | 0.461749i | ||||
\(503\) | 25.5401 | 1.13878 | 0.569389 | − | 0.822068i | \(-0.307180\pi\) | ||||
0.569389 | + | 0.822068i | \(0.307180\pi\) | |||||||
\(504\) | −15.4639 | − | 0.712531i | −0.688816 | − | 0.0317387i | ||||
\(505\) | 4.69770 | 0.209045 | ||||||||
\(506\) | −2.17458 | − | 3.76649i | −0.0966720 | − | 0.167441i | ||||
\(507\) | −2.32565 | + | 4.02815i | −0.103286 | + | 0.178896i | ||||
\(508\) | 3.84966 | − | 6.66781i | 0.170801 | − | 0.295836i | ||||
\(509\) | −15.1797 | − | 26.2920i | −0.672829 | − | 1.16537i | −0.977098 | − | 0.212788i | \(-0.931746\pi\) |
0.304269 | − | 0.952586i | \(-0.401588\pi\) | |||||||
\(510\) | 53.5485 | 2.37117 | ||||||||
\(511\) | −3.18249 | − | 6.14966i | −0.140785 | − | 0.272045i | ||||
\(512\) | −49.4328 | −2.18464 | ||||||||
\(513\) | 1.22078 | + | 2.11445i | 0.0538988 | + | 0.0933554i | ||||
\(514\) | −1.79691 | + | 3.11233i | −0.0792581 | + | 0.137279i | ||||
\(515\) | 6.97489 | − | 12.0809i | 0.307351 | − | 0.532347i | ||||
\(516\) | 23.2406 | + | 40.2540i | 1.02311 | + | 1.77208i | ||||
\(517\) | −0.691053 | −0.0303925 | ||||||||
\(518\) | −28.0031 | − | 54.1117i | −1.23039 | − | 2.37753i | ||||
\(519\) | 13.2996 | 0.583789 | ||||||||
\(520\) | 36.4944 | + | 63.2102i | 1.60039 | + | 2.77195i | ||||
\(521\) | 12.3504 | − | 21.3914i | 0.541079 | − | 0.937176i | −0.457763 | − | 0.889074i | \(-0.651349\pi\) |
0.998842 | − | 0.0481022i | \(-0.0153173\pi\) | |||||||
\(522\) | −10.1340 | + | 17.5526i | −0.443552 | + | 0.768254i | ||||
\(523\) | 14.2677 | + | 24.7123i | 0.623881 | + | 1.08059i | 0.988756 | + | 0.149537i | \(0.0477783\pi\) |
−0.364875 | + | 0.931056i | \(0.618888\pi\) | |||||||
\(524\) | 38.4718 | 1.68065 | ||||||||
\(525\) | 36.0486 | + | 1.66102i | 1.57329 | + | 0.0724927i | ||||
\(526\) | 22.1777 | 0.966994 | ||||||||
\(527\) | 2.25816 | + | 3.91125i | 0.0983671 | + | 0.170377i | ||||
\(528\) | 5.24274 | − | 9.08069i | 0.228161 | − | 0.395186i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −35.5368 | − | 61.5516i | −1.54362 | − | 2.67363i | ||||
\(531\) | −1.83508 | −0.0796357 | ||||||||
\(532\) | 15.0725 | − | 23.5336i | 0.653474 | − | 1.02031i | ||||
\(533\) | 19.0927 | 0.826998 | ||||||||
\(534\) | 18.8467 | + | 32.6435i | 0.815577 | + | 1.41262i | ||||
\(535\) | 2.02246 | − | 3.50301i | 0.0874387 | − | 0.151448i | ||||
\(536\) | 29.8810 | − | 51.7553i | 1.29066 | − | 2.23549i | ||||
\(537\) | 9.81485 | + | 16.9998i | 0.423542 | + | 0.733596i | ||||
\(538\) | −32.4928 | −1.40086 | ||||||||
\(539\) | 12.0528 | + | 1.11308i | 0.519149 | + | 0.0479436i | ||||
\(540\) | −18.6780 | −0.803771 | ||||||||
\(541\) | 3.87196 | + | 6.70643i | 0.166469 | + | 0.288332i | 0.937176 | − | 0.348857i | \(-0.113430\pi\) |
−0.770707 | + | 0.637189i | \(0.780097\pi\) | |||||||
\(542\) | −16.7871 | + | 29.0762i | −0.721069 | + | 1.24893i | ||||
\(543\) | 9.60475 | − | 16.6359i | 0.412179 | − | 0.713915i | ||||
\(544\) | 8.75313 | + | 15.1609i | 0.375287 | + | 0.650017i | ||||
\(545\) | −64.6661 | −2.76999 | ||||||||
\(546\) | 10.3702 | − | 16.1917i | 0.443804 | − | 0.692940i | ||||
\(547\) | 36.8996 | 1.57771 | 0.788856 | − | 0.614578i | \(-0.210674\pi\) | ||||
0.788856 | + | 0.614578i | \(0.210674\pi\) | |||||||
\(548\) | −0.535165 | − | 0.926933i | −0.0228611 | − | 0.0395966i | ||||
\(549\) | 0.650629 | − | 1.12692i | 0.0277682 | − | 0.0480959i | ||||
\(550\) | −29.6603 | + | 51.3732i | −1.26472 | + | 2.19056i | ||||
\(551\) | −9.83725 | − | 17.0386i | −0.419081 | − | 0.725870i | ||||
\(552\) | −5.85100 | −0.249035 | ||||||||
\(553\) | −26.9237 | − | 1.24057i | −1.14491 | − | 0.0527544i | ||||
\(554\) | −38.9821 | −1.65619 | ||||||||
\(555\) | −19.7644 | − | 34.2330i | −0.838954 | − | 1.45311i | ||||
\(556\) | 18.6018 | − | 32.2192i | 0.788891 | − | 1.36640i | ||||
\(557\) | −14.1322 | + | 24.4778i | −0.598802 | + | 1.03716i | 0.394196 | + | 0.919026i | \(0.371023\pi\) |
−0.992998 | + | 0.118130i | \(0.962310\pi\) | |||||||
\(558\) | −1.15179 | − | 1.99495i | −0.0487590 | − | 0.0844531i | ||||
\(559\) | −31.0438 | −1.31301 | ||||||||
\(560\) | 31.8354 | + | 61.5169i | 1.34529 | + | 2.59956i | ||||
\(561\) | 8.52686 | 0.360004 | ||||||||
\(562\) | −29.6905 | − | 51.4255i | −1.25242 | − | 2.16925i | ||||
\(563\) | 4.81106 | − | 8.33300i | 0.202762 | − | 0.351194i | −0.746655 | − | 0.665211i | \(-0.768342\pi\) |
0.949417 | + | 0.314017i | \(0.101675\pi\) | |||||||
\(564\) | −0.864490 | + | 1.49734i | −0.0364016 | + | 0.0630494i | ||||
\(565\) | 30.5288 | + | 52.8774i | 1.28436 | + | 2.22457i | ||||
\(566\) | 59.5637 | 2.50365 | ||||||||
\(567\) | 1.21601 | + | 2.34975i | 0.0510676 | + | 0.0986802i | ||||
\(568\) | −52.6701 | −2.20999 | ||||||||
\(569\) | 7.85731 | + | 13.6093i | 0.329396 | + | 0.570530i | 0.982392 | − | 0.186831i | \(-0.0598217\pi\) |
−0.652996 | + | 0.757361i | \(0.726488\pi\) | |||||||
\(570\) | 13.2565 | − | 22.9609i | 0.555253 | − | 0.961726i | ||||
\(571\) | −5.67209 | + | 9.82434i | −0.237369 | + | 0.411136i | −0.959959 | − | 0.280142i | \(-0.909619\pi\) |
0.722589 | + | 0.691278i | \(0.242952\pi\) | |||||||
\(572\) | 10.8075 | + | 18.7191i | 0.451883 | + | 0.782684i | ||||
\(573\) | 7.15375 | 0.298852 | ||||||||
\(574\) | 43.9259 | + | 2.02398i | 1.83343 | + | 0.0844793i | ||||
\(575\) | 13.6396 | 0.568809 | ||||||||
\(576\) | 1.59937 | + | 2.77019i | 0.0666405 | + | 0.115425i | ||||
\(577\) | 3.97526 | − | 6.88535i | 0.165492 | − | 0.286641i | −0.771338 | − | 0.636426i | \(-0.780412\pi\) |
0.936830 | + | 0.349785i | \(0.113745\pi\) | |||||||
\(578\) | −9.20207 | + | 15.9384i | −0.382755 | + | 0.662952i | ||||
\(579\) | −10.9786 | − | 19.0156i | −0.456257 | − | 0.790259i | ||||
\(580\) | 150.510 | 6.24959 | ||||||||
\(581\) | −15.5305 | + | 24.2488i | −0.644315 | + | 1.00601i | ||||
\(582\) | 7.72458 | 0.320194 | ||||||||
\(583\) | −5.65875 | − | 9.80125i | −0.234362 | − | 0.405926i | ||||
\(584\) | 7.65649 | − | 13.2614i | 0.316828 | − | 0.548762i | ||||
\(585\) | 6.23731 | − | 10.8033i | 0.257881 | − | 0.446663i | ||||
\(586\) | −26.5691 | − | 46.0191i | −1.09756 | − | 1.90103i | ||||
\(587\) | 21.2897 | 0.878718 | 0.439359 | − | 0.898311i | \(-0.355206\pi\) | ||||
0.439359 | + | 0.898311i | \(0.355206\pi\) | |||||||
\(588\) | 17.4895 | − | 24.7229i | 0.721254 | − | 1.01956i | ||||
\(589\) | 2.23613 | 0.0921379 | ||||||||
\(590\) | 9.96360 | + | 17.2575i | 0.410195 | + | 0.710478i | ||||
\(591\) | 1.60514 | − | 2.78018i | 0.0660266 | − | 0.114361i | ||||
\(592\) | 27.7602 | − | 48.0820i | 1.14094 | − | 1.97616i | ||||
\(593\) | 4.83858 | + | 8.38066i | 0.198696 | + | 0.344152i | 0.948106 | − | 0.317954i | \(-0.102996\pi\) |
−0.749410 | + | 0.662107i | \(0.769663\pi\) | |||||||
\(594\) | −4.34917 | −0.178448 | ||||||||
\(595\) | −30.3794 | + | 47.4333i | −1.24543 | + | 1.94458i | ||||
\(596\) | 19.4971 | 0.798631 | ||||||||
\(597\) | 6.35849 | + | 11.0132i | 0.260236 | + | 0.450741i | ||||
\(598\) | 3.63373 | − | 6.29380i | 0.148594 | − | 0.257373i | ||||
\(599\) | −12.9896 | + | 22.4986i | −0.530740 | + | 0.919268i | 0.468617 | + | 0.883402i | \(0.344753\pi\) |
−0.999357 | + | 0.0358668i | \(0.988581\pi\) | |||||||
\(600\) | 39.9025 | + | 69.1131i | 1.62901 | + | 2.82153i | ||||
\(601\) | 31.2857 | 1.27617 | 0.638084 | − | 0.769967i | \(-0.279727\pi\) | ||||
0.638084 | + | 0.769967i | \(0.279727\pi\) | |||||||
\(602\) | −71.4213 | − | 3.29089i | −2.91092 | − | 0.134127i | ||||
\(603\) | −10.2140 | −0.415945 | ||||||||
\(604\) | 9.79389 | + | 16.9635i | 0.398508 | + | 0.690236i | ||||
\(605\) | 17.2911 | − | 29.9490i | 0.702983 | − | 1.21760i | ||||
\(606\) | 1.36839 | − | 2.37013i | 0.0555872 | − | 0.0962798i | ||||
\(607\) | −14.4582 | − | 25.0423i | −0.586838 | − | 1.01643i | −0.994644 | − | 0.103365i | \(-0.967039\pi\) |
0.407805 | − | 0.913069i | \(-0.366294\pi\) | |||||||
\(608\) | 8.66771 | 0.351522 | ||||||||
\(609\) | −9.79881 | − | 18.9347i | −0.397068 | − | 0.767272i | ||||
\(610\) | −14.1304 | −0.572123 | ||||||||
\(611\) | −0.577375 | − | 1.00004i | −0.0233581 | − | 0.0404574i | ||||
\(612\) | 10.6669 | − | 18.4756i | 0.431184 | − | 0.746832i | ||||
\(613\) | 23.9924 | − | 41.5560i | 0.969043 | − | 1.67843i | 0.270707 | − | 0.962662i | \(-0.412742\pi\) |
0.698336 | − | 0.715770i | \(-0.253924\pi\) | |||||||
\(614\) | 2.48909 | + | 4.31123i | 0.100451 | + | 0.173987i | ||||
\(615\) | 28.5283 | 1.15037 | ||||||||
\(616\) | 12.3027 | + | 23.7730i | 0.495689 | + | 0.957842i | ||||
\(617\) | 41.9964 | 1.69071 | 0.845355 | − | 0.534205i | \(-0.179389\pi\) | ||||
0.845355 | + | 0.534205i | \(0.179389\pi\) | |||||||
\(618\) | −4.06343 | − | 7.03807i | −0.163455 | − | 0.283113i | ||||
\(619\) | 4.71191 | − | 8.16126i | 0.189388 | − | 0.328029i | −0.755659 | − | 0.654966i | \(-0.772683\pi\) |
0.945046 | + | 0.326937i | \(0.106016\pi\) | |||||||
\(620\) | −8.55319 | + | 14.8146i | −0.343504 | + | 0.594967i | ||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | −9.80123 | −0.392994 | ||||||||
\(623\) | −39.6078 | − | 1.82502i | −1.58685 | − | 0.0731177i | ||||
\(624\) | 17.5212 | 0.701411 | ||||||||
\(625\) | −46.4198 | − | 80.4015i | −1.85679 | − | 3.21606i | ||||
\(626\) | −22.2072 | + | 38.4640i | −0.887579 | + | 1.53733i | ||||
\(627\) | 2.11091 | − | 3.65621i | 0.0843017 | − | 0.146015i | ||||
\(628\) | 7.06752 | + | 12.2413i | 0.282025 | + | 0.488481i | ||||
\(629\) | 45.1495 | 1.80023 | ||||||||
\(630\) | 15.4952 | − | 24.1936i | 0.617342 | − | 0.963895i | ||||
\(631\) | 6.84273 | 0.272405 | 0.136202 | − | 0.990681i | \(-0.456510\pi\) | ||||
0.136202 | + | 0.990681i | \(0.456510\pi\) | |||||||
\(632\) | −29.8021 | − | 51.6187i | −1.18546 | − | 2.05328i | ||||
\(633\) | −8.52498 | + | 14.7657i | −0.338838 | + | 0.586884i | ||||
\(634\) | 15.5092 | − | 26.8626i | 0.615947 | − | 1.06685i | ||||
\(635\) | 3.84175 | + | 6.65410i | 0.152455 | + | 0.264060i | ||||
\(636\) | −28.3159 | −1.12280 | ||||||||
\(637\) | 8.45932 | + | 18.3719i | 0.335170 | + | 0.727920i | ||||
\(638\) | 35.0463 | 1.38750 | ||||||||
\(639\) | 4.50095 | + | 7.79587i | 0.178055 | + | 0.308400i | ||||
\(640\) | 32.6945 | − | 56.6286i | 1.29236 | − | 2.23844i | ||||
\(641\) | −3.51011 | + | 6.07968i | −0.138641 | + | 0.240133i | −0.926982 | − | 0.375105i | \(-0.877607\pi\) |
0.788342 | + | 0.615238i | \(0.210940\pi\) | |||||||
\(642\) | −1.17825 | − | 2.04078i | −0.0465017 | − | 0.0805432i | ||||
\(643\) | −47.1743 | −1.86037 | −0.930185 | − | 0.367090i | \(-0.880354\pi\) | ||||
−0.930185 | + | 0.367090i | \(0.880354\pi\) | |||||||
\(644\) | 6.17329 | − | 9.63876i | 0.243262 | − | 0.379820i | ||||
\(645\) | −46.3857 | −1.82643 | ||||||||
\(646\) | 15.1414 | + | 26.2257i | 0.595732 | + | 1.03184i | ||||
\(647\) | −11.9835 | + | 20.7560i | −0.471119 | + | 0.816003i | −0.999454 | − | 0.0330335i | \(-0.989483\pi\) |
0.528335 | + | 0.849036i | \(0.322817\pi\) | |||||||
\(648\) | −2.92550 | + | 5.06711i | −0.114924 | + | 0.199055i | ||||
\(649\) | 1.58657 | + | 2.74801i | 0.0622782 | + | 0.107869i | ||||
\(650\) | −99.1249 | −3.88800 | ||||||||
\(651\) | 2.42057 | + | 0.111533i | 0.0948695 | + | 0.00437132i | ||||
\(652\) | 46.0401 | 1.80307 | ||||||||
\(653\) | 9.16565 | + | 15.8754i | 0.358679 | + | 0.621251i | 0.987740 | − | 0.156105i | \(-0.0498938\pi\) |
−0.629061 | + | 0.777356i | \(0.716560\pi\) | |||||||
\(654\) | −18.8366 | + | 32.6259i | −0.736569 | + | 1.27577i | ||||
\(655\) | −19.1963 | + | 33.2490i | −0.750063 | + | 1.29915i | ||||
\(656\) | 20.0348 | + | 34.7012i | 0.782226 | + | 1.35486i | ||||
\(657\) | −2.61716 | −0.102105 | ||||||||
\(658\) | −1.22233 | − | 2.36196i | −0.0476514 | − | 0.0920789i | ||||
\(659\) | 16.4341 | 0.640183 | 0.320092 | − | 0.947387i | \(-0.396286\pi\) | ||||
0.320092 | + | 0.947387i | \(0.396286\pi\) | |||||||
\(660\) | 16.1485 | + | 27.9700i | 0.628580 | + | 1.08873i | ||||
\(661\) | 15.0175 | − | 26.0111i | 0.584113 | − | 1.01171i | −0.410872 | − | 0.911693i | \(-0.634776\pi\) |
0.994985 | − | 0.100021i | \(-0.0318910\pi\) | |||||||
\(662\) | −7.30119 | + | 12.6460i | −0.283769 | + | 0.491502i | ||||
\(663\) | 7.12419 | + | 12.3395i | 0.276681 | + | 0.479225i | ||||
\(664\) | −63.6812 | −2.47131 | ||||||||
\(665\) | 12.8181 | + | 24.7689i | 0.497063 | + | 0.960497i | ||||
\(666\) | −23.0287 | −0.892345 | ||||||||
\(667\) | −4.02908 | − | 6.97858i | −0.156007 | − | 0.270212i | ||||
\(668\) | −6.48530 | + | 11.2329i | −0.250924 | + | 0.434613i | ||||
\(669\) | 11.6639 | − | 20.2025i | 0.450953 | − | 0.781073i | ||||
\(670\) | 55.4569 | + | 96.0542i | 2.14249 | + | 3.71090i | ||||
\(671\) | −2.25007 | −0.0868630 | ||||||||
\(672\) | 9.38265 | + | 0.432326i | 0.361944 | + | 0.0166773i | ||||
\(673\) | 17.0642 | 0.657776 | 0.328888 | − | 0.944369i | \(-0.393326\pi\) | ||||
0.328888 | + | 0.944369i | \(0.393326\pi\) | |||||||
\(674\) | 28.3515 | + | 49.1062i | 1.09206 | + | 1.89150i | ||||
\(675\) | 6.81978 | − | 11.8122i | 0.262493 | − | 0.454652i | ||||
\(676\) | 10.0614 | − | 17.4268i | 0.386975 | − | 0.670261i | ||||
\(677\) | 18.8278 | + | 32.6106i | 0.723610 | + | 1.25333i | 0.959544 | + | 0.281560i | \(0.0908518\pi\) |
−0.235934 | + | 0.971769i | \(0.575815\pi\) | |||||||
\(678\) | 35.5709 | 1.36609 | ||||||||
\(679\) | −4.38235 | + | 6.84244i | −0.168179 | + | 0.262589i | ||||
\(680\) | −124.567 | −4.77694 | ||||||||
\(681\) | −3.83797 | − | 6.64756i | −0.147071 | − | 0.254735i | ||||
\(682\) | −1.99161 | + | 3.44957i | −0.0762628 | + | 0.132091i | ||||
\(683\) | 20.3875 | − | 35.3121i | 0.780104 | − | 1.35118i | −0.151776 | − | 0.988415i | \(-0.548499\pi\) |
0.931880 | − | 0.362766i | \(-0.118167\pi\) | |||||||
\(684\) | −5.28140 | − | 9.14765i | −0.201939 | − | 0.349769i | ||||
\(685\) | 1.06813 | 0.0408111 | ||||||||
\(686\) | 17.5145 | + | 43.1642i | 0.668705 | + | 1.64802i | ||||
\(687\) | 22.8736 | 0.872683 | ||||||||
\(688\) | −32.5755 | − | 56.4225i | −1.24193 | − | 2.15109i | ||||
\(689\) | 9.45578 | − | 16.3779i | 0.360236 | − | 0.623948i | ||||
\(690\) | 5.42951 | − | 9.40419i | 0.206698 | − | 0.358012i | ||||
\(691\) | −1.99453 | − | 3.45463i | −0.0758756 | − | 0.131420i | 0.825591 | − | 0.564269i | \(-0.190842\pi\) |
−0.901467 | + | 0.432848i | \(0.857509\pi\) | |||||||
\(692\) | −57.5376 | −2.18725 | ||||||||
\(693\) | 2.46739 | − | 3.85250i | 0.0937284 | − | 0.146344i | ||||
\(694\) | −18.8572 | −0.715811 | ||||||||
\(695\) | 18.5635 | + | 32.1529i | 0.704154 | + | 1.21963i | ||||
\(696\) | 23.5742 | − | 40.8316i | 0.893576 | − | 1.54772i | ||||
\(697\) | −16.2924 | + | 28.2193i | −0.617119 | + | 1.06888i | ||||
\(698\) | 10.0275 | + | 17.3681i | 0.379545 | + | 0.657391i | ||||
\(699\) | −23.5559 | −0.890965 | ||||||||
\(700\) | −155.955 | − | 7.18598i | −5.89456 | − | 0.271604i | ||||
\(701\) | 3.27653 | 0.123753 | 0.0618763 | − | 0.998084i | \(-0.480292\pi\) | ||||
0.0618763 | + | 0.998084i | \(0.480292\pi\) | |||||||
\(702\) | −3.63373 | − | 6.29380i | −0.137146 | − | 0.237544i | ||||
\(703\) | 11.1772 | − | 19.3595i | 0.421557 | − | 0.730158i | ||||
\(704\) | 2.76555 | − | 4.79008i | 0.104231 | − | 0.180533i | ||||
\(705\) | −0.862713 | − | 1.49426i | −0.0324916 | − | 0.0562772i | ||||
\(706\) | −74.2712 | −2.79523 | ||||||||
\(707\) | 1.32314 | + | 2.55676i | 0.0497617 | + | 0.0961567i | ||||
\(708\) | 7.93902 | 0.298367 | ||||||||
\(709\) | 3.58140 | + | 6.20316i | 0.134502 | + | 0.232965i | 0.925407 | − | 0.378974i | \(-0.123723\pi\) |
−0.790905 | + | 0.611939i | \(0.790390\pi\) | |||||||
\(710\) | 48.8759 | − | 84.6556i | 1.83428 | − | 3.17707i | ||||
\(711\) | −5.09351 | + | 8.82221i | −0.191021 | + | 0.330859i | ||||
\(712\) | −43.8422 | − | 75.9369i | −1.64306 | − | 2.84586i | ||||
\(713\) | 0.915859 | 0.0342992 | ||||||||
\(714\) | 15.0823 | + | 29.1441i | 0.564440 | + | 1.09069i | ||||
\(715\) | −21.5705 | −0.806690 | ||||||||
\(716\) | −42.4615 | − | 73.5455i | −1.58686 | − | 2.74852i | ||||
\(717\) | 6.59146 | − | 11.4167i | 0.246163 | − | 0.426366i | ||||
\(718\) | 16.5006 | − | 28.5798i | 0.615795 | − | 1.06659i | ||||
\(719\) | −24.6871 | − | 42.7593i | −0.920673 | − | 1.59465i | −0.798377 | − | 0.602158i | \(-0.794308\pi\) |
−0.122296 | − | 0.992494i | \(-0.539026\pi\) | |||||||
\(720\) | 26.1802 | 0.975679 | ||||||||
\(721\) | 8.53962 | + | 0.393481i | 0.318032 | + | 0.0146540i | ||||
\(722\) | −32.7952 | −1.22051 | ||||||||
\(723\) | −8.63351 | − | 14.9537i | −0.321084 | − | 0.556134i | ||||
\(724\) | −41.5526 | + | 71.9711i | −1.54429 | + | 2.67479i | ||||
\(725\) | −54.9549 | + | 95.1847i | −2.04097 | + | 3.53507i | ||||
\(726\) | −10.0734 | − | 17.4477i | −0.373860 | − | 0.647545i | ||||
\(727\) | −15.4034 | −0.571281 | −0.285640 | − | 0.958337i | \(-0.592206\pi\) | ||||
−0.285640 | + | 0.958337i | \(0.592206\pi\) | |||||||
\(728\) | −24.1237 | + | 37.6659i | −0.894084 | + | 1.39599i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.2099 | + | 24.6122i | 0.525932 | + | 0.910940i | ||||
\(731\) | 26.4907 | − | 45.8832i | 0.979792 | − | 1.69705i | ||||
\(732\) | −2.81478 | + | 4.87535i | −0.104037 | + | 0.180198i | ||||
\(733\) | −6.10551 | − | 10.5751i | −0.225512 | − | 0.390599i | 0.730961 | − | 0.682420i | \(-0.239072\pi\) |
−0.956473 | + | 0.291821i | \(0.905739\pi\) | |||||||
\(734\) | 13.2392 | 0.488669 | ||||||||
\(735\) | 12.6399 | + | 27.4512i | 0.466230 | + | 1.01255i | ||||
\(736\) | 3.55007 | 0.130857 | ||||||||
\(737\) | 8.83075 | + | 15.2953i | 0.325285 | + | 0.563410i | ||||
\(738\) | 8.31002 | − | 14.3934i | 0.305896 | − | 0.529828i | ||||
\(739\) | −16.2402 | + | 28.1288i | −0.597404 | + | 1.03473i | 0.395798 | + | 0.918337i | \(0.370468\pi\) |
−0.993203 | + | 0.116397i | \(0.962865\pi\) | |||||||
\(740\) | 85.5059 | + | 148.101i | 3.14326 | + | 5.44429i | ||||
\(741\) | 7.05467 | 0.259160 | ||||||||
\(742\) | 23.4907 | − | 36.6776i | 0.862371 | − | 1.34648i | ||||
\(743\) | −40.1671 | −1.47359 | −0.736795 | − | 0.676117i | \(-0.763662\pi\) | ||||
−0.736795 | + | 0.676117i | \(0.763662\pi\) | |||||||
\(744\) | 2.67934 | + | 4.64076i | 0.0982295 | + | 0.170139i | ||||
\(745\) | −9.72849 | + | 16.8502i | −0.356424 | + | 0.617345i | ||||
\(746\) | 15.9081 | − | 27.5536i | 0.582436 | − | 1.00881i | ||||
\(747\) | 5.44191 | + | 9.42566i | 0.199109 | + | 0.344867i | ||||
\(748\) | −36.8893 | −1.34881 | ||||||||
\(749\) | 2.47617 | + | 0.114095i | 0.0904774 | + | 0.00416894i | ||||
\(750\) | −93.8171 | −3.42572 | ||||||||
\(751\) | −22.1518 | − | 38.3680i | −0.808330 | − | 1.40007i | −0.914020 | − | 0.405670i | \(-0.867038\pi\) |
0.105689 | − | 0.994399i | \(-0.466295\pi\) | |||||||
\(752\) | 1.21172 | − | 2.09877i | 0.0441870 | − | 0.0765342i | ||||
\(753\) | 2.37478 | − | 4.11324i | 0.0865418 | − | 0.149895i | ||||
\(754\) | 29.2812 | + | 50.7165i | 1.06636 | + | 1.84699i | ||||
\(755\) | −19.5475 | −0.711406 | ||||||||
\(756\) | −5.26076 | − | 10.1656i | −0.191332 | − | 0.369719i | ||||
\(757\) | 41.4696 | 1.50724 | 0.753620 | − | 0.657311i | \(-0.228306\pi\) | ||||
0.753620 | + | 0.657311i | \(0.228306\pi\) | |||||||
\(758\) | −16.0957 | − | 27.8786i | −0.584622 | − | 1.01259i | ||||
\(759\) | 0.864575 | − | 1.49749i | 0.0313821 | − | 0.0543554i | ||||
\(760\) | −30.8379 | + | 53.4128i | −1.11861 | + | 1.93749i | ||||
\(761\) | 1.58650 | + | 2.74790i | 0.0575107 | + | 0.0996114i | 0.893347 | − | 0.449367i | \(-0.148350\pi\) |
−0.835837 | + | 0.548978i | \(0.815017\pi\) | |||||||
\(762\) | 4.47625 | 0.162157 | ||||||||
\(763\) | −18.2136 | − | 35.1950i | −0.659377 | − | 1.27414i | ||||
\(764\) | −30.9489 | −1.11969 | ||||||||
\(765\) | 10.6450 | + | 18.4376i | 0.384869 | + | 0.666613i | ||||
\(766\) | 20.9100 | − | 36.2172i | 0.755510 | − | 1.30858i | ||||
\(767\) | −2.65115 | + | 4.59193i | −0.0957275 | + | 0.165805i | ||||
\(768\) | −15.8484 | − | 27.4503i | −0.571881 | − | 0.990527i | ||||
\(769\) | −13.6487 | −0.492184 | −0.246092 | − | 0.969246i | \(-0.579147\pi\) | ||||
−0.246092 | + | 0.969246i | \(0.579147\pi\) | |||||||
\(770\) | −49.6263 | − | 2.28664i | −1.78841 | − | 0.0824048i | ||||
\(771\) | −1.42884 | −0.0514582 | ||||||||
\(772\) | 47.4963 | + | 82.2661i | 1.70943 | + | 2.96082i | ||||
\(773\) | 14.2374 | − | 24.6599i | 0.512083 | − | 0.886954i | −0.487819 | − | 0.872945i | \(-0.662207\pi\) |
0.999902 | − | 0.0140088i | \(-0.00445929\pi\) | |||||||
\(774\) | −13.5117 | + | 23.4029i | −0.485667 | + | 0.841201i | ||||
\(775\) | −6.24595 | − | 10.8183i | −0.224361 | − | 0.388605i | ||||
\(776\) | −17.9693 | −0.645061 | ||||||||
\(777\) | 13.0648 | − | 20.3989i | 0.468696 | − | 0.731805i | ||||
\(778\) | −75.1299 | −2.69354 | ||||||||
\(779\) | 8.06671 | + | 13.9719i | 0.289020 | + | 0.500597i | ||||
\(780\) | −26.9841 | + | 46.7379i | −0.966187 | + | 1.67349i | ||||
\(781\) | 7.78282 | − | 13.4802i | 0.278491 | − | 0.482361i | ||||
\(782\) | 6.20154 | + | 10.7414i | 0.221767 | + | 0.384111i | ||||
\(783\) | −8.05817 | −0.287975 | ||||||||
\(784\) | −24.5144 | + | 34.6532i | −0.875513 | + | 1.23762i | ||||
\(785\) | −14.1060 | −0.503464 | ||||||||
\(786\) | 11.1834 | + | 19.3702i | 0.398899 | + | 0.690913i | ||||
\(787\) | −24.0339 | + | 41.6280i | −0.856717 | + | 1.48388i | 0.0183253 | + | 0.999832i | \(0.494167\pi\) |
−0.875043 | + | 0.484046i | \(0.839167\pi\) | |||||||
\(788\) | −6.94423 | + | 12.0278i | −0.247378 | + | 0.428471i | ||||
\(789\) | 4.40873 | + | 7.63614i | 0.156955 | + | 0.271854i | ||||
\(790\) | 110.621 | 3.93572 | ||||||||
\(791\) | −20.1803 | + | 31.5088i | −0.717528 | + | 1.12032i | ||||
\(792\) | 10.1173 | 0.359501 | ||||||||
\(793\) | −1.87993 | − | 3.25614i | −0.0667584 | − | 0.115629i | ||||
\(794\) | 7.52595 | − | 13.0353i | 0.267086 | − | 0.462607i | ||||
\(795\) | 14.1288 | − | 24.4718i | 0.501097 | − | 0.867926i | ||||
\(796\) | −27.5084 | − | 47.6460i | −0.975010 | − | 1.68877i | ||||
\(797\) | −28.0705 | −0.994308 | −0.497154 | − | 0.867662i | \(-0.665622\pi\) | ||||
−0.497154 | + | 0.867662i | \(0.665622\pi\) | |||||||
\(798\) | 16.2304 | + | 0.747850i | 0.574550 | + | 0.0264736i | ||||
\(799\) | 1.97077 | 0.0697207 | ||||||||
\(800\) | −24.2107 | − | 41.9341i | −0.855977 | − | 1.48260i | ||||
\(801\) | −7.49312 | + | 12.9785i | −0.264756 | + | 0.458571i | ||||
\(802\) | 19.9500 | − | 34.5543i | 0.704458 | − | 1.22016i | ||||
\(803\) | 2.26273 | + | 3.91916i | 0.0798500 | + | 0.138304i | ||||
\(804\) | 44.1882 | 1.55840 | ||||||||
\(805\) | 5.24994 | + | 10.1447i | 0.185036 | + | 0.357554i | ||||
\(806\) | −6.65597 | −0.234446 | ||||||||
\(807\) | −6.45927 | − | 11.1878i | −0.227377 | − | 0.393829i | ||||
\(808\) | −3.18323 | + | 5.51351i | −0.111986 | + | 0.193965i | ||||
\(809\) | −21.3800 | + | 37.0312i | −0.751681 | + | 1.30195i | 0.195327 | + | 0.980738i | \(0.437423\pi\) |
−0.947008 | + | 0.321211i | \(0.895910\pi\) | |||||||
\(810\) | −5.42951 | − | 9.40419i | −0.190774 | − | 0.330430i | ||||
\(811\) | 50.7214 | 1.78107 | 0.890534 | − | 0.454916i | \(-0.150331\pi\) | ||||
0.890534 | + | 0.454916i | \(0.150331\pi\) | |||||||
\(812\) | 42.3921 | + | 81.9162i | 1.48767 | + | 2.87469i | ||||
\(813\) | −13.3485 | −0.468153 | ||||||||
\(814\) | 19.9101 | + | 34.4852i | 0.697847 | + | 1.20871i | ||||
\(815\) | −22.9727 | + | 39.7899i | −0.804700 | + | 1.39378i | ||||
\(816\) | −14.9514 | + | 25.8966i | −0.523404 | + | 0.906562i | ||||
\(817\) | −13.1161 | − | 22.7177i | −0.458873 | − | 0.794792i | ||||
\(818\) | 62.7252 | 2.19314 | ||||||||
\(819\) | 7.63656 | + | 0.351871i | 0.266843 | + | 0.0122954i | ||||
\(820\) | −123.421 | −4.31004 | ||||||||
\(821\) | −21.1418 | − | 36.6188i | −0.737856 | − | 1.27800i | −0.953459 | − | 0.301522i | \(-0.902505\pi\) |
0.215604 | − | 0.976481i | \(-0.430828\pi\) | |||||||
\(822\) | 0.311135 | − | 0.538902i | 0.0108521 | − | 0.0187964i | ||||
\(823\) | 8.24278 | − | 14.2769i | 0.287325 | − | 0.497662i | −0.685845 | − | 0.727747i | \(-0.740567\pi\) |
0.973170 | + | 0.230086i | \(0.0739006\pi\) | |||||||
\(824\) | 9.45256 | + | 16.3723i | 0.329296 | + | 0.570357i | ||||
\(825\) | −23.5848 | −0.821119 | ||||||||
\(826\) | −6.58618 | + | 10.2834i | −0.229162 | + | 0.357806i | ||||
\(827\) | 21.3447 | 0.742229 | 0.371115 | − | 0.928587i | \(-0.378976\pi\) | ||||
0.371115 | + | 0.928587i | \(0.378976\pi\) | |||||||
\(828\) | −2.16313 | − | 3.74664i | −0.0751738 | − | 0.130205i | ||||
\(829\) | −4.41319 | + | 7.64387i | −0.153276 | + | 0.265483i | −0.932430 | − | 0.361350i | \(-0.882316\pi\) |
0.779154 | + | 0.626833i | \(0.215649\pi\) | |||||||
\(830\) | 59.0938 | − | 102.354i | 2.05118 | − | 3.55274i | ||||
\(831\) | −7.74930 | − | 13.4222i | −0.268820 | − | 0.465610i | ||||
\(832\) | 9.24248 | 0.320425 | ||||||||
\(833\) | −34.3724 | − | 3.17431i | −1.19093 | − | 0.109983i | ||||
\(834\) | 21.6295 | 0.748967 | ||||||||
\(835\) | −6.47196 | − | 11.2098i | −0.223972 | − | 0.387930i | ||||
\(836\) | −9.13234 | + | 15.8177i | −0.315849 | + | 0.547066i | ||||
\(837\) | 0.457930 | − | 0.793157i | 0.0158284 | − | 0.0274155i | ||||
\(838\) | 16.6332 | + | 28.8096i | 0.574586 | + | 0.995212i | ||||
\(839\) | −32.7270 | −1.12986 | −0.564932 | − | 0.825138i | \(-0.691097\pi\) | ||||
−0.564932 | + | 0.825138i | \(0.691097\pi\) | |||||||
\(840\) | −36.0456 | + | 56.2804i | −1.24369 | + | 1.94186i | ||||
\(841\) | 35.9341 | 1.23911 | ||||||||
\(842\) | 7.32135 | + | 12.6810i | 0.252310 | + | 0.437014i | ||||
\(843\) | 11.8044 | − | 20.4458i | 0.406566 | − | 0.704192i | ||||
\(844\) | 36.8812 | − | 63.8802i | 1.26950 | − | 2.19885i | ||||
\(845\) | 10.0407 | + | 17.3910i | 0.345410 | + | 0.598267i | ||||
\(846\) | −1.00520 | −0.0345594 | ||||||||
\(847\) | 21.1701 | + | 0.975458i | 0.727413 | + | 0.0335171i | ||||
\(848\) | 39.6893 | 1.36294 | ||||||||
\(849\) | 11.8407 | + | 20.5087i | 0.406373 | + | 0.703858i | ||||
\(850\) | 84.5862 | − | 146.508i | 2.90128 | − | 5.02517i | ||||
\(851\) | 4.57790 | − | 7.92916i | 0.156929 | − | 0.271808i | ||||
\(852\) | −19.4722 | − | 33.7269i | −0.667108 | − | 1.15546i | ||||
\(853\) | 8.42097 | 0.288329 | 0.144164 | − | 0.989554i | \(-0.453951\pi\) | ||||
0.144164 | + | 0.989554i | \(0.453951\pi\) | |||||||
\(854\) | −3.97991 | − | 7.69056i | −0.136190 | − | 0.263165i | ||||
\(855\) | 10.5411 | 0.360497 | ||||||||
\(856\) | 2.74090 | + | 4.74737i | 0.0936819 | + | 0.162262i | ||||
\(857\) | 2.80361 | − | 4.85600i | 0.0957697 | − | 0.165878i | −0.814160 | − | 0.580641i | \(-0.802802\pi\) |
0.909930 | + | 0.414763i | \(0.136135\pi\) | |||||||
\(858\) | −6.28326 | + | 10.8829i | −0.214507 | + | 0.371537i | ||||
\(859\) | −3.10337 | − | 5.37519i | −0.105886 | − | 0.183399i | 0.808214 | − | 0.588889i | \(-0.200434\pi\) |
−0.914100 | + | 0.405490i | \(0.867101\pi\) | |||||||
\(860\) | 200.676 | 6.84300 | ||||||||
\(861\) | 8.03518 | + | 15.5267i | 0.273838 | + | 0.529150i | ||||
\(862\) | 15.6424 | 0.532781 | ||||||||
\(863\) | 3.65496 | + | 6.33058i | 0.124416 | + | 0.215495i | 0.921505 | − | 0.388367i | \(-0.126961\pi\) |
−0.797088 | + | 0.603863i | \(0.793628\pi\) | |||||||
\(864\) | 1.77504 | − | 3.07445i | 0.0603879 | − | 0.104595i | ||||
\(865\) | 28.7096 | − | 49.7265i | 0.976156 | − | 1.69075i | ||||
\(866\) | 2.72039 | + | 4.71186i | 0.0924428 | + | 0.160116i | ||||
\(867\) | −7.31715 | −0.248504 | ||||||||
\(868\) | −10.4720 | − | 0.482519i | −0.355442 | − | 0.0163778i | ||||
\(869\) | 17.6149 | 0.597544 | ||||||||
\(870\) | 43.7519 | + | 75.7806i | 1.48333 | + | 2.56920i | ||||
\(871\) | −14.7562 | + | 25.5585i | −0.499994 | + | 0.866015i | ||||
\(872\) | 43.8186 | − | 75.8961i | 1.48389 | − | 2.57017i | ||||
\(873\) | 1.53558 | + | 2.65970i | 0.0519714 | + | 0.0900172i | ||||
\(874\) | 6.14102 | 0.207723 | ||||||||
\(875\) | 53.2248 | − | 83.1033i | 1.79933 | − | 2.80940i | ||||
\(876\) | 11.3225 | 0.382551 | ||||||||
\(877\) | 16.3936 | + | 28.3946i | 0.553573 | + | 0.958816i | 0.998013 | + | 0.0630076i | \(0.0200692\pi\) |
−0.444440 | + | 0.895808i | \(0.646597\pi\) | |||||||
\(878\) | −14.4946 | + | 25.1053i | −0.489168 | + | 0.847263i | ||||
\(879\) | 10.5634 | − | 18.2964i | 0.356295 | − | 0.617121i | ||||
\(880\) | −22.6348 | − | 39.2046i | −0.763018 | − | 1.32159i | ||||
\(881\) | 17.0828 | 0.575533 | 0.287767 | − | 0.957701i | \(-0.407087\pi\) | ||||
0.287767 | + | 0.957701i | \(0.407087\pi\) | |||||||
\(882\) | 17.5318 | + | 1.61907i | 0.590327 | + | 0.0545169i | ||||
\(883\) | 26.9824 | 0.908030 | 0.454015 | − | 0.890994i | \(-0.349991\pi\) | ||||
0.454015 | + | 0.890994i | \(0.349991\pi\) | |||||||
\(884\) | −30.8210 | − | 53.3836i | −1.03662 | − | 1.79549i | ||||
\(885\) | −3.96135 | + | 6.86126i | −0.133159 | + | 0.230639i | ||||
\(886\) | −11.4824 | + | 19.8881i | −0.385759 | + | 0.668155i | ||||
\(887\) | −3.40233 | − | 5.89301i | −0.114239 | − | 0.197868i | 0.803236 | − | 0.595661i | \(-0.203110\pi\) |
−0.917475 | + | 0.397793i | \(0.869776\pi\) | |||||||
\(888\) | 53.5706 | 1.79771 | ||||||||
\(889\) | −2.53949 | + | 3.96507i | −0.0851717 | + | 0.132984i | ||||
\(890\) | 162.736 | 5.45492 | ||||||||
\(891\) | −0.864575 | − | 1.49749i | −0.0289644 | − | 0.0501678i | ||||
\(892\) | −50.4610 | + | 87.4010i | −1.68956 | + | 2.92640i | ||||
\(893\) | 0.487883 | − | 0.845039i | 0.0163264 | − | 0.0282781i | ||||
\(894\) | 5.66762 | + | 9.81661i | 0.189554 | + | 0.328316i | ||||
\(895\) | 84.7484 | 2.83283 | ||||||||
\(896\) | 40.0291 | + | 1.84443i | 1.33728 | + | 0.0616180i | ||||
\(897\) | 2.88941 | 0.0964746 | ||||||||
\(898\) | 26.0107 | + | 45.0518i | 0.867987 | + | 1.50340i | ||||
\(899\) | −3.69007 | + | 6.39140i | −0.123071 | + | 0.213165i | ||||
\(900\) | −29.5041 | + | 51.1025i | −0.983469 | + | 1.70342i | ||||
\(901\) | 16.1378 | + | 27.9515i | 0.537628 | + | 0.931199i | ||||
\(902\) | −28.7386 | −0.956889 | ||||||||
\(903\) | −13.0648 | − | 25.2457i | −0.434770 | − | 0.840125i | ||||
\(904\) | −82.7469 | −2.75212 | ||||||||
\(905\) | −41.4671 | − | 71.8231i | −1.37841 | − | 2.38748i | ||||
\(906\) | −5.69399 | + | 9.86228i | −0.189170 | + | 0.327652i | ||||
\(907\) | 2.71457 | − | 4.70177i | 0.0901357 | − | 0.156120i | −0.817432 | − | 0.576025i | \(-0.804603\pi\) |
0.907568 | + | 0.419905i | \(0.137937\pi\) | |||||||
\(908\) | 16.6040 | + | 28.7590i | 0.551024 | + | 0.954402i | ||||
\(909\) | 1.08810 | 0.0360899 | ||||||||
\(910\) | −38.1537 | − | 73.7262i | −1.26478 | − | 2.44400i | ||||
\(911\) | −15.8106 | −0.523829 | −0.261914 | − | 0.965091i | \(-0.584354\pi\) | ||||
−0.261914 | + | 0.965091i | \(0.584354\pi\) | |||||||
\(912\) | 7.40274 | + | 12.8219i | 0.245129 | + | 0.424577i | ||||
\(913\) | 9.40988 | − | 16.2984i | 0.311422 | − | 0.539398i | ||||
\(914\) | −30.9317 | + | 53.5752i | −1.02313 | + | 1.77211i | ||||
\(915\) | −2.80899 | − | 4.86532i | −0.0928625 | − | 0.160843i | ||||
\(916\) | −98.9571 | −3.26963 | ||||||||
\(917\) | −23.5028 | − | 1.08294i | −0.776130 | − | 0.0357619i | ||||
\(918\) | 12.4031 | 0.409363 | ||||||||
\(919\) | −18.6790 | − | 32.3530i | −0.616165 | − | 1.06723i | −0.990179 | − | 0.139805i | \(-0.955352\pi\) |
0.374014 | − | 0.927423i | \(-0.377981\pi\) | |||||||
\(920\) | −12.6304 | + | 21.8765i | −0.416412 | + | 0.721247i | ||||
\(921\) | −0.989617 | + | 1.71407i | −0.0326090 | + | 0.0564804i | ||||
\(922\) | 4.21356 | + | 7.29810i | 0.138766 | + | 0.240350i | ||||
\(923\) | 26.0102 | 0.856135 | ||||||||
\(924\) | −10.6746 | + | 16.6669i | −0.351167 | + | 0.548300i | ||||
\(925\) | −124.881 | −4.10607 | ||||||||
\(926\) | 38.0185 | + | 65.8500i | 1.24937 | + | 2.16396i | ||||
\(927\) | 1.61555 | − | 2.79821i | 0.0530616 | − | 0.0919053i | ||||
\(928\) | −14.3035 | + | 24.7744i | −0.469536 | + | 0.813261i | ||||
\(929\) | −16.3535 | − | 28.3250i | −0.536539 | − | 0.929314i | −0.999087 | − | 0.0427192i | \(-0.986398\pi\) |
0.462548 | − | 0.886594i | \(-0.346935\pi\) | |||||||
\(930\) | −9.94534 | −0.326121 | ||||||||
\(931\) | −9.87035 | + | 13.9526i | −0.323488 | + | 0.457279i | ||||
\(932\) | 101.909 | 3.33813 | ||||||||
\(933\) | −1.94840 | − | 3.37472i | −0.0637876 | − | 0.110483i | ||||
\(934\) | 37.9062 | − | 65.6554i | 1.24033 | − | 2.14831i | ||||
\(935\) | 18.4067 | − | 31.8814i | 0.601965 | − | 1.04263i | ||||
\(936\) | 8.45296 | + | 14.6410i | 0.276294 | + | 0.478555i | ||||
\(937\) | 49.2657 | 1.60944 | 0.804721 | − | 0.593654i | \(-0.202315\pi\) | ||||
0.804721 | + | 0.593654i | \(0.202315\pi\) | |||||||
\(938\) | −36.6583 | + | 57.2370i | −1.19694 | + | 1.86886i | ||||
\(939\) | −17.6584 | −0.576260 | ||||||||
\(940\) | 3.73231 | + | 6.46455i | 0.121735 | + | 0.210851i | ||||
\(941\) | 5.43419 | − | 9.41229i | 0.177149 | − | 0.306832i | −0.763754 | − | 0.645508i | \(-0.776646\pi\) |
0.940903 | + | 0.338676i | \(0.109979\pi\) | |||||||
\(942\) | −4.10893 | + | 7.11688i | −0.133876 | + | 0.231880i | ||||
\(943\) | 3.30392 | + | 5.72255i | 0.107590 | + | 0.186352i | ||||
\(944\) | −11.1278 | −0.362180 | ||||||||
\(945\) | 11.4105 | + | 0.525765i | 0.371185 | + | 0.0171031i | ||||
\(946\) | 46.7275 | 1.51924 | ||||||||
\(947\) | −15.7953 | − | 27.3583i | −0.513279 | − | 0.889026i | −0.999881 | − | 0.0154021i | \(-0.995097\pi\) |
0.486602 | − | 0.873624i | \(-0.338236\pi\) | |||||||
\(948\) | 22.0358 | − | 38.1671i | 0.715689 | − | 1.23961i | ||||
\(949\) | −3.78102 | + | 6.54892i | −0.122737 | + | 0.212587i | ||||
\(950\) | −41.8804 | − | 72.5390i | −1.35878 | − | 2.35347i | ||||
\(951\) | 12.3323 | 0.399903 | ||||||||
\(952\) | −35.0851 | − | 67.7966i | −1.13712 | − | 2.19730i | ||||
\(953\) | −7.60480 | −0.246344 | −0.123172 | − | 0.992385i | \(-0.539307\pi\) | ||||
−0.123172 | + | 0.992385i | \(0.539307\pi\) | |||||||
\(954\) | −8.23116 | − | 14.2568i | −0.266494 | − | 0.461581i | ||||
\(955\) | 15.4426 | − | 26.7474i | 0.499712 | − | 0.865527i | ||||
\(956\) | −28.5163 | + | 49.3917i | −0.922283 | + | 1.59744i | ||||
\(957\) | 6.96689 | + | 12.0670i | 0.225208 | + | 0.390071i | ||||
\(958\) | 73.0274 | 2.35941 | ||||||||
\(959\) | 0.300845 | + | 0.581337i | 0.00971480 | + | 0.0187723i | ||||
\(960\) | 13.8101 | 0.445719 | ||||||||
\(961\) | 15.0806 | + | 26.1204i | 0.486471 | + | 0.842592i | ||||
\(962\) | −33.2697 | + | 57.6248i | −1.07266 | + | 1.85790i | ||||
\(963\) | 0.468449 | − | 0.811378i | 0.0150956 | − | 0.0261463i | ||||
\(964\) | 37.3508 | + | 64.6934i | 1.20299 | + | 2.08363i | ||||
\(965\) | −94.7973 | −3.05163 | ||||||||
\(966\) | 6.64755 | + | 0.306300i | 0.213881 | + | 0.00985505i | ||||
\(967\) | 10.3379 | 0.332446 | 0.166223 | − | 0.986088i | \(-0.446843\pi\) | ||||
0.166223 | + | 0.986088i | \(0.446843\pi\) | |||||||
\(968\) | 23.4333 | + | 40.5878i | 0.753176 | + | 1.30454i | ||||
\(969\) | −6.01996 | + | 10.4269i | −0.193389 | + | 0.334960i | ||||
\(970\) | 16.6749 | − | 28.8817i | 0.535398 | − | 0.927337i | ||||
\(971\) | −9.87947 | − | 17.1117i | −0.317047 | − | 0.549142i | 0.662823 | − | 0.748776i | \(-0.269358\pi\) |
−0.979871 | + | 0.199634i | \(0.936025\pi\) | |||||||
\(972\) | −4.32625 | −0.138765 | ||||||||
\(973\) | −12.2709 | + | 19.1594i | −0.393388 | + | 0.614222i | ||||
\(974\) | −43.5273 | −1.39470 | ||||||||
\(975\) | −19.7051 | − | 34.1303i | −0.631069 | − | 1.09304i | ||||
\(976\) | 3.94538 | − | 6.83359i | 0.126288 | − | 0.218738i | ||||
\(977\) | 9.80885 | − | 16.9894i | 0.313813 | − | 0.543540i | −0.665371 | − | 0.746512i | \(-0.731727\pi\) |
0.979184 | + | 0.202972i | \(0.0650601\pi\) | |||||||
\(978\) | 13.3835 | + | 23.1808i | 0.427956 | + | 0.741241i | ||||
\(979\) | 25.9135 | 0.828198 | ||||||||
\(980\) | −54.6834 | − | 118.761i | −1.74680 | − | 3.79368i | ||||
\(981\) | −14.9782 | −0.478216 | ||||||||
\(982\) | −17.8941 | − | 30.9934i | −0.571023 | − | 0.989040i | ||||
\(983\) | 7.55281 | − | 13.0818i | 0.240897 | − | 0.417246i | −0.720073 | − | 0.693898i | \(-0.755892\pi\) |
0.960970 | + | 0.276652i | \(0.0892250\pi\) | |||||||
\(984\) | −19.3312 | + | 33.4826i | −0.616256 | + | 1.06739i | ||||
\(985\) | −6.92995 | − | 12.0030i | −0.220807 | − | 0.382448i | ||||
\(986\) | −99.9461 | −3.18293 | ||||||||
\(987\) | 0.570274 | − | 0.890405i | 0.0181520 | − | 0.0283419i | ||||
\(988\) | −30.5203 | −0.970979 | ||||||||
\(989\) | −5.37200 | − | 9.30458i | −0.170820 | − | 0.295869i | ||||
\(990\) | −9.38845 | + | 16.2613i | −0.298384 | + | 0.516817i | ||||
\(991\) | −20.6412 | + | 35.7517i | −0.655690 | + | 1.13569i | 0.326030 | + | 0.945360i | \(0.394289\pi\) |
−0.981720 | + | 0.190330i | \(0.939044\pi\) | |||||||
\(992\) | −1.62568 | − | 2.81576i | −0.0516155 | − | 0.0894006i | ||||
\(993\) | −5.80565 | −0.184237 | ||||||||
\(994\) | 59.8406 | + | 2.75728i | 1.89803 | + | 0.0874557i | ||||
\(995\) | 54.9037 | 1.74056 | ||||||||
\(996\) | −23.5431 | − | 40.7778i | −0.745991 | − | 1.29209i | ||||
\(997\) | −9.26904 | + | 16.0545i | −0.293554 | + | 0.508450i | −0.974647 | − | 0.223746i | \(-0.928171\pi\) |
0.681094 | + | 0.732196i | \(0.261505\pi\) | |||||||
\(998\) | −13.9810 | + | 24.2157i | −0.442559 | + | 0.766535i | ||||
\(999\) | −4.57790 | − | 7.92916i | −0.144838 | − | 0.250868i |
(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 | 483.2.i.h.277.2 | ✓ | 20 | |
7.2 | even | 3 | inner | 483.2.i.h.415.2 | yes | 20 | |
7.3 | odd | 6 | 3381.2.a.bj.1.9 | 10 | |||
7.4 | even | 3 | 3381.2.a.bi.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
483.2.i.h.415.2 | yes | 20 | 7.2 | even | 3 | inner | |
3381.2.a.bi.1.9 | 10 | 7.4 | even | 3 | |||
3381.2.a.bj.1.9 | 10 | 7.3 | odd | 6 |