Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(263,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.263");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.100088711424.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 13x^{6} + 130x^{4} - 507x^{2} + 1521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 263.1 | ||
Root | \(2.49541 + 1.44073i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.263 |
Dual form | 637.2.g.i.373.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.15139 | + | 1.99426i | −0.814154 | + | 1.41016i | 0.0957796 | + | 0.995403i | \(0.469466\pi\) |
−0.909934 | + | 0.414754i | \(0.863868\pi\) | |||||||
\(3\) | −2.16731 | −1.25130 | −0.625648 | − | 0.780106i | \(-0.715165\pi\) | ||||
−0.625648 | + | 0.780106i | \(0.715165\pi\) | |||||||
\(4\) | −1.65139 | − | 2.86029i | −0.825694 | − | 1.43014i | ||||
\(5\) | 1.08365 | + | 1.87694i | 0.484625 | + | 0.839395i | 0.999844 | − | 0.0176637i | \(-0.00562281\pi\) |
−0.515219 | + | 0.857058i | \(0.672289\pi\) | |||||||
\(6\) | 2.49541 | − | 4.32218i | 1.01875 | − | 1.76452i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 1.69722 | 0.565741 | ||||||||
\(10\) | −4.99082 | −1.57824 | ||||||||
\(11\) | 4.90833 | 1.47992 | 0.739958 | − | 0.672653i | \(-0.234845\pi\) | ||||
0.739958 | + | 0.672653i | \(0.234845\pi\) | |||||||
\(12\) | 3.57907 | + | 6.19912i | 1.03319 | + | 1.78953i | ||||
\(13\) | 1.41176 | + | 3.31767i | 0.391551 | + | 0.920156i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.34861 | − | 4.06792i | −0.606409 | − | 1.05033i | ||||
\(16\) | −0.151388 | + | 0.262211i | −0.0378470 | + | 0.0655528i | ||||
\(17\) | 3.57907 | + | 6.19912i | 0.868051 | + | 1.50351i | 0.863985 | + | 0.503517i | \(0.167961\pi\) |
0.00406561 | + | 0.999992i | \(0.498706\pi\) | |||||||
\(18\) | −1.95416 | + | 3.38471i | −0.460601 | + | 0.797784i | ||||
\(19\) | −2.16731 | −0.497215 | −0.248607 | − | 0.968604i | \(-0.579973\pi\) | ||||
−0.248607 | + | 0.968604i | \(0.579973\pi\) | |||||||
\(20\) | 3.57907 | − | 6.19912i | 0.800304 | − | 1.38617i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.65139 | + | 9.78849i | −1.20488 | + | 2.08691i | ||||
\(23\) | 0.302776 | − | 0.524423i | 0.0631331 | − | 0.109350i | −0.832731 | − | 0.553677i | \(-0.813224\pi\) |
0.895864 | + | 0.444328i | \(0.146557\pi\) | |||||||
\(24\) | −6.50192 | −1.32720 | ||||||||
\(25\) | 0.151388 | − | 0.262211i | 0.0302776 | − | 0.0524423i | ||||
\(26\) | −8.24179 | − | 1.00451i | −1.61635 | − | 0.197001i | ||||
\(27\) | 2.82352 | 0.543386 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.15139 | + | 1.99426i | 0.213807 | + | 0.370325i | 0.952903 | − | 0.303275i | \(-0.0980802\pi\) |
−0.739096 | + | 0.673601i | \(0.764747\pi\) | |||||||
\(30\) | 10.8167 | 1.97484 | ||||||||
\(31\) | −3.57907 | + | 6.19912i | −0.642819 | + | 1.11340i | 0.341981 | + | 0.939707i | \(0.388902\pi\) |
−0.984801 | + | 0.173689i | \(0.944431\pi\) | |||||||
\(32\) | 2.65139 | + | 4.59234i | 0.468704 | + | 0.811818i | ||||
\(33\) | −10.6379 | −1.85181 | ||||||||
\(34\) | −16.4836 | −2.82691 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.80278 | − | 4.85455i | −0.467129 | − | 0.809092i | ||||
\(37\) | −4.30278 | + | 7.45263i | −0.707372 | + | 1.22520i | 0.258457 | + | 0.966023i | \(0.416786\pi\) |
−0.965829 | + | 0.259181i | \(0.916547\pi\) | |||||||
\(38\) | 2.49541 | − | 4.32218i | 0.404809 | − | 0.701150i | ||||
\(39\) | −3.05971 | − | 7.19041i | −0.489946 | − | 1.15139i | ||||
\(40\) | 3.25096 | + | 5.63083i | 0.514022 | + | 0.890313i | ||||
\(41\) | −4.99082 | − | 8.64436i | −0.779436 | − | 1.35002i | −0.932267 | − | 0.361770i | \(-0.882173\pi\) |
0.152832 | − | 0.988252i | \(-0.451161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.25694 | − | 10.8373i | 0.954174 | − | 1.65268i | 0.217928 | − | 0.975965i | \(-0.430070\pi\) |
0.736247 | − | 0.676713i | \(-0.236596\pi\) | |||||||
\(44\) | −8.10555 | − | 14.0392i | −1.22196 | − | 2.11649i | ||||
\(45\) | 1.83920 | + | 3.18559i | 0.274172 | + | 0.474880i | ||||
\(46\) | 0.697224 | + | 1.20763i | 0.102800 | + | 0.178055i | ||||
\(47\) | −0.755550 | − | 1.30865i | −0.110208 | − | 0.190886i | 0.805646 | − | 0.592397i | \(-0.201818\pi\) |
−0.915854 | + | 0.401511i | \(0.868485\pi\) | |||||||
\(48\) | 0.328104 | − | 0.568293i | 0.0473577 | − | 0.0820260i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.348612 | + | 0.603814i | 0.0493012 | + | 0.0853922i | ||||
\(51\) | −7.75694 | − | 13.4354i | −1.08619 | − | 1.88133i | ||||
\(52\) | 7.15813 | − | 9.51680i | 0.992654 | − | 1.31974i | ||||
\(53\) | −1.19722 | + | 2.07365i | −0.164451 | + | 0.284838i | −0.936460 | − | 0.350773i | \(-0.885919\pi\) |
0.772009 | + | 0.635612i | \(0.219252\pi\) | |||||||
\(54\) | −3.25096 | + | 5.63083i | −0.442400 | + | 0.766259i | ||||
\(55\) | 5.31893 | + | 9.21265i | 0.717204 | + | 1.24223i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.69722 | 0.622163 | ||||||||
\(58\) | −5.30278 | −0.696289 | ||||||||
\(59\) | −1.41176 | − | 2.44524i | −0.183795 | − | 0.318343i | 0.759375 | − | 0.650654i | \(-0.225505\pi\) |
−0.943170 | + | 0.332311i | \(0.892172\pi\) | |||||||
\(60\) | −7.75694 | + | 13.4354i | −1.00142 | + | 1.73450i | ||||
\(61\) | −4.33462 | −0.554991 | −0.277495 | − | 0.960727i | \(-0.589504\pi\) | ||||
−0.277495 | + | 0.960727i | \(0.589504\pi\) | |||||||
\(62\) | −8.24179 | − | 14.2752i | −1.04671 | − | 1.81295i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.8167 | −1.60208 | ||||||||
\(65\) | −4.69722 | + | 6.24500i | −0.582619 | + | 0.774597i | ||||
\(66\) | 12.2483 | − | 21.2147i | 1.50766 | − | 2.61135i | ||||
\(67\) | 1.00000 | 0.122169 | 0.0610847 | − | 0.998133i | \(-0.480544\pi\) | ||||
0.0610847 | + | 0.998133i | \(0.480544\pi\) | |||||||
\(68\) | 11.8209 | − | 20.4743i | 1.43349 | − | 2.48288i | ||||
\(69\) | −0.656208 | + | 1.13659i | −0.0789982 | + | 0.136829i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | + | 3.46410i | −0.237356 | + | 0.411113i | −0.959955 | − | 0.280155i | \(-0.909614\pi\) |
0.722599 | + | 0.691268i | \(0.242948\pi\) | |||||||
\(72\) | 5.09167 | 0.600059 | ||||||||
\(73\) | −2.16731 | + | 3.75389i | −0.253664 | + | 0.439359i | −0.964532 | − | 0.263967i | \(-0.914969\pi\) |
0.710868 | + | 0.703326i | \(0.248302\pi\) | |||||||
\(74\) | −9.90833 | − | 17.1617i | −1.15182 | − | 1.99501i | ||||
\(75\) | −0.328104 | + | 0.568293i | −0.0378862 | + | 0.0656208i | ||||
\(76\) | 3.57907 | + | 6.19912i | 0.410547 | + | 0.711088i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 17.8625 | + | 2.17708i | 2.02253 | + | 0.246506i | ||||
\(79\) | 3.30278 | + | 5.72058i | 0.371591 | + | 0.643615i | 0.989811 | − | 0.142391i | \(-0.0454789\pi\) |
−0.618219 | + | 0.786006i | \(0.712146\pi\) | |||||||
\(80\) | −0.656208 | −0.0733663 | ||||||||
\(81\) | −11.2111 | −1.24568 | ||||||||
\(82\) | 22.9855 | 2.53832 | ||||||||
\(83\) | −2.82352 | −0.309921 | −0.154961 | − | 0.987921i | \(-0.549525\pi\) | ||||
−0.154961 | + | 0.987921i | \(0.549525\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.75694 | + | 13.4354i | −0.841358 | + | 1.45728i | ||||
\(86\) | 14.4083 | + | 24.9560i | 1.55369 | + | 2.69107i | ||||
\(87\) | −2.49541 | − | 4.32218i | −0.267536 | − | 0.463386i | ||||
\(88\) | 14.7250 | 1.56969 | ||||||||
\(89\) | 3.25096 | − | 5.63083i | 0.344601 | − | 0.596867i | −0.640680 | − | 0.767808i | \(-0.721347\pi\) |
0.985281 | + | 0.170941i | \(0.0546808\pi\) | |||||||
\(90\) | −8.47055 | −0.892874 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | 7.75694 | − | 13.4354i | 0.804357 | − | 1.39319i | ||||
\(94\) | 3.47972 | 0.358906 | ||||||||
\(95\) | −2.34861 | − | 4.06792i | −0.240963 | − | 0.417359i | ||||
\(96\) | −5.74637 | − | 9.95301i | −0.586487 | − | 1.01583i | ||||
\(97\) | −6.83003 | + | 11.8300i | −0.693484 | + | 1.20115i | 0.277205 | + | 0.960811i | \(0.410592\pi\) |
−0.970689 | + | 0.240339i | \(0.922741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.33053 | 0.837250 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 6.50192 | 0.646966 | 0.323483 | − | 0.946234i | \(-0.395146\pi\) | ||||
0.323483 | + | 0.946234i | \(0.395146\pi\) | |||||||
\(102\) | 35.7250 | 3.53730 | ||||||||
\(103\) | 5.74637 | + | 9.95301i | 0.566207 | + | 0.980699i | 0.996936 | + | 0.0782182i | \(0.0249231\pi\) |
−0.430729 | + | 0.902481i | \(0.641744\pi\) | |||||||
\(104\) | 4.23527 | + | 9.95301i | 0.415303 | + | 0.975973i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.75694 | − | 4.77516i | −0.267778 | − | 0.463804i | ||||
\(107\) | −2.84861 | + | 4.93394i | −0.275386 | + | 0.476982i | −0.970232 | − | 0.242176i | \(-0.922139\pi\) |
0.694847 | + | 0.719158i | \(0.255472\pi\) | |||||||
\(108\) | −4.66272 | − | 8.07607i | −0.448670 | − | 0.777120i | ||||
\(109\) | −4.10555 | + | 7.11102i | −0.393240 | + | 0.681113i | −0.992875 | − | 0.119162i | \(-0.961979\pi\) |
0.599634 | + | 0.800274i | \(0.295313\pi\) | |||||||
\(110\) | −24.4966 | −2.33566 | ||||||||
\(111\) | 9.32544 | − | 16.1521i | 0.885132 | − | 1.53309i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.40833 | + | 5.90340i | −0.320628 | + | 0.555345i | −0.980618 | − | 0.195930i | \(-0.937227\pi\) |
0.659989 | + | 0.751275i | \(0.270561\pi\) | |||||||
\(114\) | −5.40833 | + | 9.36750i | −0.506536 | + | 0.877346i | ||||
\(115\) | 1.31242 | 0.122383 | ||||||||
\(116\) | 3.80278 | − | 6.58660i | 0.353079 | − | 0.611551i | ||||
\(117\) | 2.39607 | + | 5.63083i | 0.221517 | + | 0.520571i | ||||
\(118\) | 6.50192 | 0.598551 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −7.04584 | − | 12.2037i | −0.643194 | − | 1.11404i | ||||
\(121\) | 13.0917 | 1.19015 | ||||||||
\(122\) | 4.99082 | − | 8.64436i | 0.451848 | − | 0.782624i | ||||
\(123\) | 10.8167 | + | 18.7350i | 0.975305 | + | 1.68928i | ||||
\(124\) | 23.6417 | 2.12309 | ||||||||
\(125\) | 11.4927 | 1.02794 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.95416 | − | 6.84881i | −0.350875 | − | 0.607734i | 0.635528 | − | 0.772078i | \(-0.280783\pi\) |
−0.986403 | + | 0.164344i | \(0.947449\pi\) | |||||||
\(128\) | 9.45416 | − | 16.3751i | 0.835638 | − | 1.44737i | ||||
\(129\) | −13.5607 | + | 23.4878i | −1.19395 | + | 2.06799i | ||||
\(130\) | −7.04584 | − | 16.5579i | −0.617961 | − | 1.45222i | ||||
\(131\) | −5.31893 | − | 9.21265i | −0.464717 | − | 0.804913i | 0.534472 | − | 0.845186i | \(-0.320511\pi\) |
−0.999189 | + | 0.0402730i | \(0.987177\pi\) | |||||||
\(132\) | 17.5672 | + | 30.4273i | 1.52903 | + | 2.64836i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.15139 | + | 1.99426i | −0.0994648 | + | 0.172278i | ||||
\(135\) | 3.05971 | + | 5.29958i | 0.263338 | + | 0.456115i | ||||
\(136\) | 10.7372 | + | 18.5974i | 0.920707 | + | 1.59471i | ||||
\(137\) | −3.15139 | − | 5.45836i | −0.269241 | − | 0.466339i | 0.699425 | − | 0.714706i | \(-0.253440\pi\) |
−0.968666 | + | 0.248367i | \(0.920106\pi\) | |||||||
\(138\) | −1.51110 | − | 2.61730i | −0.128633 | − | 0.222800i | ||||
\(139\) | −5.31893 | + | 9.21265i | −0.451146 | + | 0.781407i | −0.998457 | − | 0.0555216i | \(-0.982318\pi\) |
0.547312 | + | 0.836929i | \(0.315651\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.63751 | + | 2.83625i | 0.137903 | + | 0.238855i | ||||
\(142\) | −4.60555 | − | 7.97705i | −0.386489 | − | 0.669419i | ||||
\(143\) | 6.92937 | + | 16.2842i | 0.579463 | + | 1.36175i | ||||
\(144\) | −0.256939 | + | 0.445032i | −0.0214116 | + | 0.0370860i | ||||
\(145\) | −2.49541 | + | 4.32218i | −0.207233 | + | 0.358938i | ||||
\(146\) | −4.99082 | − | 8.64436i | −0.413044 | − | 0.715412i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 28.4222 | 2.33629 | ||||||||
\(149\) | −17.5139 | −1.43479 | −0.717396 | − | 0.696665i | \(-0.754666\pi\) | ||||
−0.717396 | + | 0.696665i | \(0.754666\pi\) | |||||||
\(150\) | −0.755550 | − | 1.30865i | −0.0616904 | − | 0.106851i | ||||
\(151\) | −4.10555 | + | 7.11102i | −0.334105 | + | 0.578687i | −0.983313 | − | 0.181924i | \(-0.941767\pi\) |
0.649207 | + | 0.760611i | \(0.275101\pi\) | |||||||
\(152\) | −6.50192 | −0.527376 | ||||||||
\(153\) | 6.07448 | + | 10.5213i | 0.491092 | + | 0.850597i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.5139 | −1.24610 | ||||||||
\(156\) | −15.5139 | + | 20.6258i | −1.24210 | + | 1.65139i | ||||
\(157\) | −0.328104 | + | 0.568293i | −0.0261856 | + | 0.0453547i | −0.878821 | − | 0.477151i | \(-0.841669\pi\) |
0.852636 | + | 0.522506i | \(0.175003\pi\) | |||||||
\(158\) | −15.2111 | −1.21013 | ||||||||
\(159\) | 2.59475 | − | 4.49425i | 0.205777 | − | 0.356417i | ||||
\(160\) | −5.74637 | + | 9.95301i | −0.454291 | + | 0.786855i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.9083 | − | 22.3579i | 1.01417 | − | 1.75660i | ||||
\(163\) | −2.78890 | −0.218443 | −0.109222 | − | 0.994017i | \(-0.534836\pi\) | ||||
−0.109222 | + | 0.994017i | \(0.534836\pi\) | |||||||
\(164\) | −16.4836 | + | 28.5504i | −1.28715 | + | 2.22941i | ||||
\(165\) | −11.5278 | − | 19.9667i | −0.897435 | − | 1.55440i | ||||
\(166\) | 3.25096 | − | 5.63083i | 0.252324 | − | 0.437037i | ||||
\(167\) | 5.74637 | + | 9.95301i | 0.444668 | + | 0.770187i | 0.998029 | − | 0.0627542i | \(-0.0199884\pi\) |
−0.553361 | + | 0.832941i | \(0.686655\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.01388 | + | 9.36750i | −0.693375 | + | 0.720577i | ||||
\(170\) | −17.8625 | − | 30.9387i | −1.36999 | − | 2.37289i | ||||
\(171\) | −3.67841 | −0.281295 | ||||||||
\(172\) | −41.3305 | −3.15142 | ||||||||
\(173\) | −10.1803 | −0.773996 | −0.386998 | − | 0.922080i | \(-0.626488\pi\) | ||||
−0.386998 | + | 0.922080i | \(0.626488\pi\) | |||||||
\(174\) | 11.4927 | 0.871263 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.743061 | + | 1.28702i | −0.0560103 | + | 0.0970127i | ||||
\(177\) | 3.05971 | + | 5.29958i | 0.229982 | + | 0.398341i | ||||
\(178\) | 7.48624 | + | 12.9665i | 0.561117 | + | 0.971883i | ||||
\(179\) | 21.6056 | 1.61487 | 0.807437 | − | 0.589953i | \(-0.200854\pi\) | ||||
0.807437 | + | 0.589953i | \(0.200854\pi\) | |||||||
\(180\) | 6.07448 | − | 10.5213i | 0.452765 | − | 0.784212i | ||||
\(181\) | 24.2979 | 1.80605 | 0.903025 | − | 0.429588i | \(-0.141341\pi\) | ||||
0.903025 | + | 0.429588i | \(0.141341\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.39445 | 0.694458 | ||||||||
\(184\) | 0.908327 | − | 1.57327i | 0.0669627 | − | 0.115983i | ||||
\(185\) | −18.6509 | −1.37124 | ||||||||
\(186\) | 17.8625 | + | 30.9387i | 1.30974 | + | 2.26854i | ||||
\(187\) | 17.5672 | + | 30.4273i | 1.28464 | + | 2.22507i | ||||
\(188\) | −2.49541 | + | 4.32218i | −0.181997 | + | 0.315227i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.8167 | 0.784723 | ||||||||
\(191\) | 15.6972 | 1.13581 | 0.567906 | − | 0.823094i | \(-0.307754\pi\) | ||||
0.567906 | + | 0.823094i | \(0.307754\pi\) | |||||||
\(192\) | 27.7776 | 2.00468 | ||||||||
\(193\) | 19.8167 | 1.42643 | 0.713217 | − | 0.700943i | \(-0.247237\pi\) | ||||
0.713217 | + | 0.700943i | \(0.247237\pi\) | |||||||
\(194\) | −15.7280 | − | 27.2417i | −1.12921 | − | 1.95584i | ||||
\(195\) | 10.1803 | − | 13.5348i | 0.729029 | − | 0.969250i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.545837 | + | 0.945417i | 0.0388892 | + | 0.0673581i | 0.884815 | − | 0.465943i | \(-0.154285\pi\) |
−0.845926 | + | 0.533301i | \(0.820951\pi\) | |||||||
\(198\) | −9.59167 | + | 16.6133i | −0.681651 | + | 1.18065i | ||||
\(199\) | −3.57907 | − | 6.19912i | −0.253713 | − | 0.439444i | 0.710832 | − | 0.703362i | \(-0.248319\pi\) |
−0.964545 | + | 0.263918i | \(0.914985\pi\) | |||||||
\(200\) | 0.454163 | − | 0.786634i | 0.0321142 | − | 0.0556234i | ||||
\(201\) | −2.16731 | −0.152870 | ||||||||
\(202\) | −7.48624 | + | 12.9665i | −0.526730 | + | 0.912323i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −25.6194 | + | 44.3742i | −1.79372 | + | 3.10681i | ||||
\(205\) | 10.8167 | − | 18.7350i | 0.755468 | − | 1.30851i | ||||
\(206\) | −26.4652 | −1.84392 | ||||||||
\(207\) | 0.513878 | − | 0.890063i | 0.0357170 | − | 0.0618637i | ||||
\(208\) | −1.08365 | − | 0.132076i | −0.0751379 | − | 0.00915781i | ||||
\(209\) | −10.6379 | −0.735836 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.50000 | − | 12.9904i | −0.516321 | − | 0.894295i | −0.999820 | − | 0.0189499i | \(-0.993968\pi\) |
0.483499 | − | 0.875345i | \(-0.339366\pi\) | |||||||
\(212\) | 7.90833 | 0.543146 | ||||||||
\(213\) | 4.33462 | − | 7.50778i | 0.297003 | − | 0.514424i | ||||
\(214\) | −6.55971 | − | 11.3618i | −0.448413 | − | 0.776674i | ||||
\(215\) | 27.1214 | 1.84967 | ||||||||
\(216\) | 8.47055 | 0.576348 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.45416 | − | 16.3751i | −0.640317 | − | 1.10906i | ||||
\(219\) | 4.69722 | − | 8.13583i | 0.317409 | − | 0.549769i | ||||
\(220\) | 17.5672 | − | 30.4273i | 1.18438 | − | 2.05141i | ||||
\(221\) | −15.5139 | + | 20.6258i | −1.04358 | + | 1.38744i | ||||
\(222\) | 21.4744 | + | 37.1947i | 1.44127 | + | 2.49635i | ||||
\(223\) | −8.99734 | − | 15.5838i | −0.602506 | − | 1.04357i | −0.992440 | − | 0.122729i | \(-0.960836\pi\) |
0.389934 | − | 0.920843i | \(-0.372498\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.256939 | − | 0.445032i | 0.0171293 | − | 0.0296688i | ||||
\(226\) | −7.84861 | − | 13.5942i | −0.522082 | − | 0.904272i | ||||
\(227\) | −9.22610 | − | 15.9801i | −0.612358 | − | 1.06063i | −0.990842 | − | 0.135027i | \(-0.956888\pi\) |
0.378484 | − | 0.925608i | \(-0.376445\pi\) | |||||||
\(228\) | −7.75694 | − | 13.4354i | −0.513716 | − | 0.889782i | ||||
\(229\) | −7.81434 | − | 13.5348i | −0.516386 | − | 0.894407i | −0.999819 | − | 0.0190256i | \(-0.993944\pi\) |
0.483433 | − | 0.875381i | \(-0.339390\pi\) | |||||||
\(230\) | −1.51110 | + | 2.61730i | −0.0996390 | + | 0.172580i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.45416 | + | 5.98279i | 0.226777 | + | 0.392789i | ||||
\(233\) | 6.54584 | + | 11.3377i | 0.428832 | + | 0.742759i | 0.996770 | − | 0.0803127i | \(-0.0255919\pi\) |
−0.567938 | + | 0.823072i | \(0.692259\pi\) | |||||||
\(234\) | −13.9882 | − | 1.70488i | −0.914435 | − | 0.111451i | ||||
\(235\) | 1.63751 | − | 2.83625i | 0.106819 | − | 0.185017i | ||||
\(236\) | −4.66272 | + | 8.07607i | −0.303517 | + | 0.525707i | ||||
\(237\) | −7.15813 | − | 12.3982i | −0.464971 | − | 0.805353i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.39445 | 0.284253 | 0.142127 | − | 0.989848i | \(-0.454606\pi\) | ||||
0.142127 | + | 0.989848i | \(0.454606\pi\) | |||||||
\(240\) | 1.42221 | 0.0918029 | ||||||||
\(241\) | −4.66272 | − | 8.07607i | −0.300352 | − | 0.520225i | 0.675863 | − | 0.737027i | \(-0.263771\pi\) |
−0.976216 | + | 0.216802i | \(0.930438\pi\) | |||||||
\(242\) | −15.0736 | + | 26.1082i | −0.968967 | + | 1.67830i | ||||
\(243\) | 15.8274 | 1.01533 | ||||||||
\(244\) | 7.15813 | + | 12.3982i | 0.458252 | + | 0.793717i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −49.8167 | −3.17619 | ||||||||
\(247\) | −3.05971 | − | 7.19041i | −0.194685 | − | 0.457515i | ||||
\(248\) | −10.7372 | + | 18.5974i | −0.681813 | + | 1.18093i | ||||
\(249\) | 6.11943 | 0.387803 | ||||||||
\(250\) | −13.2326 | + | 22.9196i | −0.836904 | + | 1.44956i | ||||
\(251\) | 14.9725 | − | 25.9331i | 0.945054 | − | 1.63688i | 0.189411 | − | 0.981898i | \(-0.439342\pi\) |
0.755643 | − | 0.654984i | \(-0.227325\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.48612 | − | 2.57404i | 0.0934317 | − | 0.161828i | ||||
\(254\) | 18.2111 | 1.14267 | ||||||||
\(255\) | 16.8117 | − | 29.1187i | 1.05279 | − | 1.82348i | ||||
\(256\) | 8.95416 | + | 15.5091i | 0.559635 | + | 0.969317i | ||||
\(257\) | 3.15162 | − | 5.45877i | 0.196593 | − | 0.340508i | −0.750829 | − | 0.660497i | \(-0.770346\pi\) |
0.947421 | + | 0.319988i | \(0.103679\pi\) | |||||||
\(258\) | −31.2273 | − | 54.0872i | −1.94413 | − | 3.36732i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 25.6194 | + | 3.12250i | 1.58885 | + | 0.193649i | ||||
\(261\) | 1.95416 | + | 3.38471i | 0.120960 | + | 0.209508i | ||||
\(262\) | 24.4966 | 1.51340 | ||||||||
\(263\) | 15.4222 | 0.950974 | 0.475487 | − | 0.879723i | \(-0.342272\pi\) | ||||
0.475487 | + | 0.879723i | \(0.342272\pi\) | |||||||
\(264\) | −31.9136 | −1.96414 | ||||||||
\(265\) | −5.18951 | −0.318789 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.04584 | + | 12.2037i | −0.431198 | + | 0.746857i | ||||
\(268\) | −1.65139 | − | 2.86029i | −0.100875 | − | 0.174720i | ||||
\(269\) | −0.328104 | − | 0.568293i | −0.0200049 | − | 0.0346494i | 0.855850 | − | 0.517225i | \(-0.173035\pi\) |
−0.875855 | + | 0.482575i | \(0.839702\pi\) | |||||||
\(270\) | −14.0917 | −0.857592 | ||||||||
\(271\) | 7.25747 | − | 12.5703i | 0.440860 | − | 0.763592i | −0.556893 | − | 0.830584i | \(-0.688007\pi\) |
0.997754 | + | 0.0669918i | \(0.0213401\pi\) | |||||||
\(272\) | −2.16731 | −0.131412 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.5139 | 0.876815 | ||||||||
\(275\) | 0.743061 | − | 1.28702i | 0.0448083 | − | 0.0776102i | ||||
\(276\) | 4.33462 | 0.260913 | ||||||||
\(277\) | 0.105551 | + | 0.182820i | 0.00634196 | + | 0.0109846i | 0.869179 | − | 0.494498i | \(-0.164648\pi\) |
−0.862837 | + | 0.505482i | \(0.831315\pi\) | |||||||
\(278\) | −12.2483 | − | 21.2147i | −0.734604 | − | 1.27237i | ||||
\(279\) | −6.07448 | + | 10.5213i | −0.363670 | + | 0.629894i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.8167 | 1.42078 | 0.710391 | − | 0.703807i | \(-0.248518\pi\) | ||||
0.710391 | + | 0.703807i | \(0.248518\pi\) | |||||||
\(282\) | −7.54163 | −0.449098 | ||||||||
\(283\) | −18.6509 | −1.10868 | −0.554340 | − | 0.832290i | \(-0.687029\pi\) | ||||
−0.554340 | + | 0.832290i | \(0.687029\pi\) | |||||||
\(284\) | 13.2111 | 0.783935 | ||||||||
\(285\) | 5.09017 | + | 8.81643i | 0.301515 | + | 0.522240i | ||||
\(286\) | −40.4534 | − | 4.93046i | −2.39206 | − | 0.291544i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.50000 | + | 7.79423i | 0.265165 | + | 0.459279i | ||||
\(289\) | −17.1194 | + | 29.6517i | −1.00703 | + | 1.74422i | ||||
\(290\) | −5.74637 | − | 9.95301i | −0.337439 | − | 0.584461i | ||||
\(291\) | 14.8028 | − | 25.6392i | 0.867754 | − | 1.50299i | ||||
\(292\) | 14.3163 | 0.837796 | ||||||||
\(293\) | −14.3163 | + | 24.7965i | −0.836365 | + | 1.44863i | 0.0565490 | + | 0.998400i | \(0.481990\pi\) |
−0.892914 | + | 0.450227i | \(0.851343\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.05971 | − | 5.29958i | 0.178143 | − | 0.308554i | ||||
\(296\) | −12.9083 | + | 22.3579i | −0.750281 | + | 1.29953i | ||||
\(297\) | 13.8587 | 0.804166 | ||||||||
\(298\) | 20.1653 | − | 34.9273i | 1.16814 | − | 2.02328i | ||||
\(299\) | 2.16731 | + | 0.264152i | 0.125339 | + | 0.0152763i | ||||
\(300\) | 2.16731 | 0.125130 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.45416 | − | 16.3751i | −0.544026 | − | 0.942281i | ||||
\(303\) | −14.0917 | −0.809545 | ||||||||
\(304\) | 0.328104 | − | 0.568293i | 0.0188181 | − | 0.0325938i | ||||
\(305\) | −4.69722 | − | 8.13583i | −0.268962 | − | 0.465856i | ||||
\(306\) | −27.9763 | −1.59930 | ||||||||
\(307\) | −3.67841 | −0.209938 | −0.104969 | − | 0.994476i | \(-0.533474\pi\) | ||||
−0.104969 | + | 0.994476i | \(0.533474\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4542 | − | 21.5712i | −0.708493 | − | 1.22715i | ||||
\(310\) | 17.8625 | − | 30.9387i | 1.01452 | − | 1.75720i | ||||
\(311\) | 5.31893 | − | 9.21265i | 0.301609 | − | 0.522402i | −0.674892 | − | 0.737917i | \(-0.735810\pi\) |
0.976501 | + | 0.215515i | \(0.0691430\pi\) | |||||||
\(312\) | −9.17914 | − | 21.5712i | −0.519667 | − | 1.22123i | ||||
\(313\) | −2.82352 | − | 4.89047i | −0.159595 | − | 0.276426i | 0.775128 | − | 0.631804i | \(-0.217685\pi\) |
−0.934723 | + | 0.355378i | \(0.884352\pi\) | |||||||
\(314\) | −0.755550 | − | 1.30865i | −0.0426382 | − | 0.0738514i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.9083 | − | 18.8938i | 0.613641 | − | 1.06286i | ||||
\(317\) | 3.10555 | + | 5.37897i | 0.174425 | + | 0.302113i | 0.939962 | − | 0.341279i | \(-0.110860\pi\) |
−0.765537 | + | 0.643392i | \(0.777527\pi\) | |||||||
\(318\) | 5.97514 | + | 10.3492i | 0.335069 | + | 0.580357i | ||||
\(319\) | 5.65139 | + | 9.78849i | 0.316417 | + | 0.548050i | ||||
\(320\) | −13.8888 | − | 24.0561i | −0.776409 | − | 1.34478i | ||||
\(321\) | 6.17382 | − | 10.6934i | 0.344589 | − | 0.596846i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.75694 | − | 13.4354i | −0.431608 | − | 0.747566i | ||||
\(324\) | 18.5139 | + | 32.0670i | 1.02855 | + | 1.78150i | ||||
\(325\) | 1.08365 | + | 0.132076i | 0.0601103 | + | 0.00732625i | ||||
\(326\) | 3.21110 | − | 5.56179i | 0.177847 | − | 0.308039i | ||||
\(327\) | 8.89799 | − | 15.4118i | 0.492060 | − | 0.852273i | ||||
\(328\) | −14.9725 | − | 25.9331i | −0.826717 | − | 1.43192i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 53.0917 | 2.92260 | ||||||||
\(331\) | 4.30278 | 0.236502 | 0.118251 | − | 0.992984i | \(-0.462271\pi\) | ||||
0.118251 | + | 0.992984i | \(0.462271\pi\) | |||||||
\(332\) | 4.66272 | + | 8.07607i | 0.255900 | + | 0.443232i | ||||
\(333\) | −7.30278 | + | 12.6488i | −0.400190 | + | 0.693149i | ||||
\(334\) | −26.4652 | −1.44811 | ||||||||
\(335\) | 1.08365 | + | 1.87694i | 0.0592063 | + | 0.102548i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.1194 | 0.987028 | 0.493514 | − | 0.869738i | \(-0.335712\pi\) | ||||
0.493514 | + | 0.869738i | \(0.335712\pi\) | |||||||
\(338\) | −8.30278 | − | 28.7617i | −0.451611 | − | 1.56443i | ||||
\(339\) | 7.38689 | − | 12.7945i | 0.401201 | − | 0.694901i | ||||
\(340\) | 51.2389 | 2.77882 | ||||||||
\(341\) | −17.5672 | + | 30.4273i | −0.951319 | + | 1.64773i | ||||
\(342\) | 4.23527 | − | 7.33571i | 0.229017 | − | 0.396670i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 18.7708 | − | 32.5120i | 1.01205 | − | 1.75293i | ||||
\(345\) | −2.84441 | −0.153138 | ||||||||
\(346\) | 11.7215 | − | 20.3023i | 0.630152 | − | 1.09146i | ||||
\(347\) | −7.60555 | − | 13.1732i | −0.408287 | − | 0.707174i | 0.586411 | − | 0.810014i | \(-0.300541\pi\) |
−0.994698 | + | 0.102839i | \(0.967207\pi\) | |||||||
\(348\) | −8.24179 | + | 14.2752i | −0.441806 | + | 0.765231i | ||||
\(349\) | 5.09017 | + | 8.81643i | 0.272470 | + | 0.471932i | 0.969494 | − | 0.245116i | \(-0.0788260\pi\) |
−0.697023 | + | 0.717048i | \(0.745493\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.98612 | + | 9.36750i | 0.212763 | + | 0.500000i | ||||
\(352\) | 13.0139 | + | 22.5407i | 0.693642 | + | 1.20142i | ||||
\(353\) | 26.4652 | 1.40860 | 0.704301 | − | 0.709902i | \(-0.251261\pi\) | ||||
0.704301 | + | 0.709902i | \(0.251261\pi\) | |||||||
\(354\) | −14.0917 | −0.748964 | ||||||||
\(355\) | −8.66923 | −0.460115 | ||||||||
\(356\) | −21.4744 | −1.13814 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.8764 | + | 43.0871i | −1.31476 | + | 2.27723i | ||||
\(359\) | 6.04584 | + | 10.4717i | 0.319087 | + | 0.552675i | 0.980298 | − | 0.197525i | \(-0.0632904\pi\) |
−0.661211 | + | 0.750200i | \(0.729957\pi\) | |||||||
\(360\) | 5.51761 | + | 9.55678i | 0.290804 | + | 0.503687i | ||||
\(361\) | −14.3028 | −0.752778 | ||||||||
\(362\) | −27.9763 | + | 48.4564i | −1.47040 | + | 2.54681i | ||||
\(363\) | −28.3737 | −1.48923 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.39445 | −0.491728 | ||||||||
\(366\) | −10.8167 | + | 18.7350i | −0.565396 | + | 0.979294i | ||||
\(367\) | −25.6103 | −1.33685 | −0.668424 | − | 0.743780i | \(-0.733031\pi\) | ||||
−0.668424 | + | 0.743780i | \(0.733031\pi\) | |||||||
\(368\) | 0.0916731 | + | 0.158782i | 0.00477879 | + | 0.00827711i | ||||
\(369\) | −8.47055 | − | 14.6714i | −0.440959 | − | 0.763764i | ||||
\(370\) | 21.4744 | − | 37.1947i | 1.11640 | − | 1.93366i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −51.2389 | −2.65661 | ||||||||
\(373\) | −12.6972 | −0.657437 | −0.328719 | − | 0.944428i | \(-0.606617\pi\) | ||||
−0.328719 | + | 0.944428i | \(0.606617\pi\) | |||||||
\(374\) | −80.9068 | −4.18359 | ||||||||
\(375\) | −24.9083 | −1.28626 | ||||||||
\(376\) | −2.26665 | − | 3.92595i | −0.116894 | − | 0.202466i | ||||
\(377\) | −4.99082 | + | 6.63534i | −0.257041 | + | 0.341737i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.05971 | + | 10.4957i | 0.311267 | + | 0.539130i | 0.978637 | − | 0.205596i | \(-0.0659134\pi\) |
−0.667370 | + | 0.744726i | \(0.732580\pi\) | |||||||
\(380\) | −7.75694 | + | 13.4354i | −0.397923 | + | 0.689222i | ||||
\(381\) | 8.56989 | + | 14.8435i | 0.439049 | + | 0.760455i | ||||
\(382\) | −18.0736 | + | 31.3044i | −0.924725 | + | 1.60167i | ||||
\(383\) | 22.3293 | 1.14097 | 0.570487 | − | 0.821307i | \(-0.306755\pi\) | ||||
0.570487 | + | 0.821307i | \(0.306755\pi\) | |||||||
\(384\) | −20.4901 | + | 35.4899i | −1.04563 | + | 1.81108i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.8167 | + | 39.5196i | −1.16134 | + | 2.01149i | ||||
\(387\) | 10.6194 | − | 18.3934i | 0.539816 | − | 0.934989i | ||||
\(388\) | 45.1161 | 2.29042 | ||||||||
\(389\) | −14.5139 | + | 25.1388i | −0.735883 | + | 1.27459i | 0.218452 | + | 0.975848i | \(0.429899\pi\) |
−0.954335 | + | 0.298739i | \(0.903434\pi\) | |||||||
\(390\) | 15.2705 | + | 35.8861i | 0.773252 | + | 1.81716i | ||||
\(391\) | 4.33462 | 0.219211 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.5278 | + | 19.9667i | 0.581498 | + | 1.00718i | ||||
\(394\) | −2.51388 | −0.126647 | ||||||||
\(395\) | −7.15813 | + | 12.3982i | −0.360165 | + | 0.623824i | ||||
\(396\) | −13.7569 | − | 23.8277i | −0.691312 | − | 1.19739i | ||||
\(397\) | −4.33462 | −0.217548 | −0.108774 | − | 0.994066i | \(-0.534693\pi\) | ||||
−0.108774 | + | 0.994066i | \(0.534693\pi\) | |||||||
\(398\) | 16.4836 | 0.826247 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0458365 | + | 0.0793912i | 0.00229183 | + | 0.00396956i | ||||
\(401\) | 5.05971 | − | 8.76368i | 0.252670 | − | 0.437637i | −0.711590 | − | 0.702595i | \(-0.752025\pi\) |
0.964260 | + | 0.264958i | \(0.0853579\pi\) | |||||||
\(402\) | 2.49541 | − | 4.32218i | 0.124460 | − | 0.215571i | ||||
\(403\) | −25.6194 | − | 3.12250i | −1.27619 | − | 0.155543i | ||||
\(404\) | −10.7372 | − | 18.5974i | −0.534196 | − | 0.925254i | ||||
\(405\) | −12.1490 | − | 21.0426i | −0.603687 | − | 1.04562i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1194 | + | 36.5799i | −1.04685 | + | 1.81320i | ||||
\(408\) | −23.2708 | − | 40.3062i | −1.15208 | − | 1.99546i | ||||
\(409\) | 1.73986 | + | 3.01353i | 0.0860306 | + | 0.149009i | 0.905830 | − | 0.423642i | \(-0.139248\pi\) |
−0.819799 | + | 0.572651i | \(0.805915\pi\) | |||||||
\(410\) | 24.9083 | + | 43.1425i | 1.23013 | + | 2.13066i | ||||
\(411\) | 6.83003 | + | 11.8300i | 0.336900 | + | 0.583529i | ||||
\(412\) | 18.9790 | − | 32.8726i | 0.935027 | − | 1.61952i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.18335 | + | 2.04962i | 0.0581583 | + | 0.100733i | ||||
\(415\) | −3.05971 | − | 5.29958i | −0.150195 | − | 0.260146i | ||||
\(416\) | −11.4927 | + | 15.2797i | −0.563478 | + | 0.749149i | ||||
\(417\) | 11.5278 | − | 19.9667i | 0.564517 | − | 0.977772i | ||||
\(418\) | 12.2483 | − | 21.2147i | 0.599084 | − | 1.03764i | ||||
\(419\) | −8.56989 | − | 14.8435i | −0.418667 | − | 0.725152i | 0.577139 | − | 0.816646i | \(-0.304169\pi\) |
−0.995806 | + | 0.0914942i | \(0.970836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.02776 | 0.245038 | 0.122519 | − | 0.992466i | \(-0.460903\pi\) | ||||
0.122519 | + | 0.992466i | \(0.460903\pi\) | |||||||
\(422\) | 34.5416 | 1.68146 | ||||||||
\(423\) | −1.28234 | − | 2.22107i | −0.0623494 | − | 0.107992i | ||||
\(424\) | −3.59167 | + | 6.22096i | −0.174427 | + | 0.302117i | ||||
\(425\) | 2.16731 | 0.105130 | ||||||||
\(426\) | 9.98165 | + | 17.2887i | 0.483612 | + | 0.837641i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.8167 | 0.909537 | ||||||||
\(429\) | −15.0181 | − | 35.2929i | −0.725080 | − | 1.70396i | ||||
\(430\) | −31.2273 | + | 54.0872i | −1.50591 | + | 2.60832i | ||||
\(431\) | −20.9361 | −1.00846 | −0.504228 | − | 0.863571i | \(-0.668223\pi\) | ||||
−0.504228 | + | 0.863571i | \(0.668223\pi\) | |||||||
\(432\) | −0.427446 | + | 0.740358i | −0.0205655 | + | 0.0356205i | ||||
\(433\) | 8.56989 | − | 14.8435i | 0.411843 | − | 0.713332i | −0.583249 | − | 0.812294i | \(-0.698219\pi\) |
0.995091 | + | 0.0989613i | \(0.0315520\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.40833 | − | 9.36750i | 0.259309 | − | 0.449137i | ||||
\(436\) | 27.1194 | 1.29879 | ||||||||
\(437\) | −0.656208 | + | 1.13659i | −0.0313907 | + | 0.0543703i | ||||
\(438\) | 10.8167 | + | 18.7350i | 0.516840 | + | 0.895193i | ||||
\(439\) | −1.83920 | + | 3.18559i | −0.0877804 | + | 0.152040i | −0.906573 | − | 0.422050i | \(-0.861311\pi\) |
0.818792 | + | 0.574090i | \(0.194644\pi\) | |||||||
\(440\) | 15.9568 | + | 27.6380i | 0.760710 | + | 1.31759i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23.2708 | − | 54.6871i | −1.10688 | − | 2.60120i | ||||
\(443\) | 10.1194 | + | 17.5274i | 0.480789 | + | 0.832750i | 0.999757 | − | 0.0220431i | \(-0.00701711\pi\) |
−0.518968 | + | 0.854793i | \(0.673684\pi\) | |||||||
\(444\) | −61.5997 | −2.92339 | ||||||||
\(445\) | 14.0917 | 0.668009 | ||||||||
\(446\) | 41.4377 | 1.96213 | ||||||||
\(447\) | 37.9580 | 1.79535 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.2111 | − | 17.6861i | 0.481892 | − | 0.834661i | −0.517892 | − | 0.855446i | \(-0.673283\pi\) |
0.999784 | + | 0.0207849i | \(0.00661652\pi\) | |||||||
\(450\) | 0.591673 | + | 1.02481i | 0.0278917 | + | 0.0483099i | ||||
\(451\) | −24.4966 | − | 42.4294i | −1.15350 | − | 1.99792i | ||||
\(452\) | 22.5139 | 1.05896 | ||||||||
\(453\) | 8.89799 | − | 15.4118i | 0.418064 | − | 0.724109i | ||||
\(454\) | 42.4913 | 1.99421 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.0917 | 0.659903 | ||||||||
\(457\) | −10.3028 | + | 17.8449i | −0.481944 | + | 0.834751i | −0.999785 | − | 0.0207258i | \(-0.993402\pi\) |
0.517842 | + | 0.855476i | \(0.326736\pi\) | |||||||
\(458\) | 35.9893 | 1.68167 | ||||||||
\(459\) | 10.1056 | + | 17.5033i | 0.471687 | + | 0.816985i | ||||
\(460\) | −2.16731 | − | 3.75389i | −0.101051 | − | 0.175026i | ||||
\(461\) | −12.5764 | + | 21.7830i | −0.585741 | + | 1.01453i | 0.409041 | + | 0.912516i | \(0.365863\pi\) |
−0.994783 | + | 0.102018i | \(0.967470\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.7889 | −0.640824 | −0.320412 | − | 0.947278i | \(-0.603821\pi\) | ||||
−0.320412 | + | 0.947278i | \(0.603821\pi\) | |||||||
\(464\) | −0.697224 | −0.0323678 | ||||||||
\(465\) | 33.6234 | 1.55925 | ||||||||
\(466\) | −30.1472 | −1.39654 | ||||||||
\(467\) | 6.40258 | + | 11.0896i | 0.296276 | + | 0.513165i | 0.975281 | − | 0.220968i | \(-0.0709218\pi\) |
−0.679005 | + | 0.734134i | \(0.737588\pi\) | |||||||
\(468\) | 12.1490 | − | 16.1521i | 0.561586 | − | 0.746633i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.77082 | + | 6.53125i | 0.173935 | + | 0.301264i | ||||
\(471\) | 0.711103 | − | 1.23167i | 0.0327659 | − | 0.0567522i | ||||
\(472\) | −4.23527 | − | 7.33571i | −0.194944 | − | 0.337653i | ||||
\(473\) | 30.7111 | − | 53.1932i | 1.41210 | − | 2.44583i | ||||
\(474\) | 32.9671 | 1.51423 | ||||||||
\(475\) | −0.328104 | + | 0.568293i | −0.0150544 | + | 0.0260751i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.03196 | + | 3.51946i | −0.0930370 | + | 0.161145i | ||||
\(478\) | −5.05971 | + | 8.76368i | −0.231426 | + | 0.400842i | ||||
\(479\) | 16.4836 | 0.753154 | 0.376577 | − | 0.926385i | \(-0.377101\pi\) | ||||
0.376577 | + | 0.926385i | \(0.377101\pi\) | |||||||
\(480\) | 12.4542 | − | 21.5712i | 0.568452 | − | 0.984588i | ||||
\(481\) | −30.7998 | − | 3.75389i | −1.40435 | − | 0.171163i | ||||
\(482\) | 21.4744 | 0.978132 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.6194 | − | 37.4460i | −0.982701 | − | 1.70209i | ||||
\(485\) | −29.6056 | −1.34432 | ||||||||
\(486\) | −18.2234 | + | 31.5639i | −0.826632 | + | 1.43177i | ||||
\(487\) | 15.6514 | + | 27.1090i | 0.709232 | + | 1.22843i | 0.965142 | + | 0.261725i | \(0.0842915\pi\) |
−0.255910 | + | 0.966701i | \(0.582375\pi\) | |||||||
\(488\) | −13.0038 | −0.588657 | ||||||||
\(489\) | 6.04440 | 0.273337 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.86249 | − | 17.0823i | −0.445088 | − | 0.770915i | 0.552970 | − | 0.833201i | \(-0.313494\pi\) |
−0.998058 | + | 0.0622859i | \(0.980161\pi\) | |||||||
\(492\) | 35.7250 | − | 61.8775i | 1.61061 | − | 2.78965i | ||||
\(493\) | −8.24179 | + | 14.2752i | −0.371191 | + | 0.642922i | ||||
\(494\) | 17.8625 | + | 2.17708i | 0.803671 | + | 0.0979516i | ||||
\(495\) | 9.02741 | + | 15.6359i | 0.405752 | + | 0.702783i | ||||
\(496\) | −1.08365 | − | 1.87694i | −0.0486575 | − | 0.0842773i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.04584 | + | 12.2037i | −0.315731 | + | 0.546863i | ||||
\(499\) | 4.16527 | + | 7.21445i | 0.186463 | + | 0.322963i | 0.944069 | − | 0.329749i | \(-0.106964\pi\) |
−0.757606 | + | 0.652713i | \(0.773631\pi\) | |||||||
\(500\) | −18.9790 | − | 32.8726i | −0.848766 | − | 1.47011i | ||||
\(501\) | −12.4542 | − | 21.5712i | −0.556411 | − | 0.963732i | ||||
\(502\) | 34.4782 | + | 59.7181i | 1.53884 | + | 2.66535i | ||||
\(503\) | −9.75289 | + | 16.8925i | −0.434860 | + | 0.753199i | −0.997284 | − | 0.0736495i | \(-0.976535\pi\) |
0.562424 | + | 0.826849i | \(0.309869\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.04584 | + | 12.2037i | 0.313536 | + | 0.543060i | ||||
\(506\) | 3.42221 | + | 5.92743i | 0.152136 | + | 0.263507i | ||||
\(507\) | 19.5359 | − | 20.3023i | 0.867618 | − | 0.901655i | ||||
\(508\) | −13.0597 | + | 22.6201i | −0.579431 | + | 1.00360i | ||||
\(509\) | 10.7372 | − | 18.5974i | 0.475918 | − | 0.824314i | −0.523701 | − | 0.851902i | \(-0.675449\pi\) |
0.999619 | + | 0.0275878i | \(0.00878258\pi\) | |||||||
\(510\) | 38.7135 | + | 67.0538i | 1.71426 | + | 2.96919i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.42221 | −0.151242 | ||||||||
\(513\) | −6.11943 | −0.270179 | ||||||||
\(514\) | 7.25747 | + | 12.5703i | 0.320113 | + | 0.554453i | ||||
\(515\) | −12.4542 | + | 21.5712i | −0.548796 | + | 0.950543i | ||||
\(516\) | 89.5760 | 3.94336 | ||||||||
\(517\) | −3.70849 | − | 6.42329i | −0.163099 | − | 0.282496i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.0639 | 0.968498 | ||||||||
\(520\) | −14.0917 | + | 18.7350i | −0.617961 | + | 0.821584i | ||||
\(521\) | −10.8365 | + | 18.7694i | −0.474757 | + | 0.822304i | −0.999582 | − | 0.0289063i | \(-0.990798\pi\) |
0.524825 | + | 0.851210i | \(0.324131\pi\) | |||||||
\(522\) | −9.00000 | −0.393919 | ||||||||
\(523\) | 12.1490 | − | 21.0426i | 0.531237 | − | 0.920129i | −0.468099 | − | 0.883676i | \(-0.655061\pi\) |
0.999335 | − | 0.0364529i | \(-0.0116059\pi\) | |||||||
\(524\) | −17.5672 | + | 30.4273i | −0.767428 | + | 1.32922i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.7569 | + | 30.7559i | −0.774239 | + | 1.34102i | ||||
\(527\) | −51.2389 | −2.23200 | ||||||||
\(528\) | 1.61044 | − | 2.78937i | 0.0700855 | − | 0.121392i | ||||
\(529\) | 11.3167 | + | 19.6010i | 0.492028 | + | 0.852218i | ||||
\(530\) | 5.97514 | − | 10.3492i | 0.259543 | − | 0.449542i | ||||
\(531\) | −2.39607 | − | 4.15012i | −0.103981 | − | 0.180100i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.6333 | − | 28.7617i | 0.937043 | − | 1.24581i | ||||
\(534\) | −16.2250 | − | 28.1025i | −0.702124 | − | 1.21611i | ||||
\(535\) | −12.3476 | −0.533835 | ||||||||
\(536\) | 3.00000 | 0.129580 | ||||||||
\(537\) | −46.8259 | −2.02069 | ||||||||
\(538\) | 1.51110 | 0.0651481 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.1056 | − | 17.5033i | 0.434874 | − | 0.753223i | ||||
\(541\) | −13.9680 | − | 24.1934i | −0.600533 | − | 1.04015i | −0.992740 | − | 0.120277i | \(-0.961622\pi\) |
0.392207 | − | 0.919877i | \(-0.371712\pi\) | |||||||
\(542\) | 16.7123 | + | 28.9466i | 0.717856 | + | 1.24336i | ||||
\(543\) | −52.6611 | −2.25990 | ||||||||
\(544\) | −18.9790 | + | 32.8726i | −0.813717 | + | 1.40940i | ||||
\(545\) | −17.7960 | −0.762296 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.0000 | 1.23995 | 0.619975 | − | 0.784621i | \(-0.287143\pi\) | ||||
0.619975 | + | 0.784621i | \(0.287143\pi\) | |||||||
\(548\) | −10.4083 | + | 18.0278i | −0.444622 | + | 0.770107i | ||||
\(549\) | −7.35682 | −0.313981 | ||||||||
\(550\) | 1.71110 | + | 2.96372i | 0.0729617 | + | 0.126373i | ||||
\(551\) | −2.49541 | − | 4.32218i | −0.106308 | − | 0.184131i | ||||
\(552\) | −1.96862 | + | 3.40976i | −0.0837902 | + | 0.145129i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.486122 | −0.0206533 | ||||||||
\(555\) | 40.4222 | 1.71583 | ||||||||
\(556\) | 35.1345 | 1.49003 | ||||||||
\(557\) | 6.09167 | 0.258112 | 0.129056 | − | 0.991637i | \(-0.458805\pi\) | ||||
0.129056 | + | 0.991637i | \(0.458805\pi\) | |||||||
\(558\) | −13.9882 | − | 24.2282i | −0.592166 | − | 1.02566i | ||||
\(559\) | 44.7880 | + | 5.45877i | 1.89433 | + | 0.230881i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38.0736 | − | 65.9454i | −1.60747 | − | 2.78422i | ||||
\(562\) | −27.4222 | + | 47.4967i | −1.15674 | + | 2.00353i | ||||
\(563\) | 0.656208 | + | 1.13659i | 0.0276559 | + | 0.0479014i | 0.879522 | − | 0.475858i | \(-0.157862\pi\) |
−0.851866 | + | 0.523759i | \(0.824529\pi\) | |||||||
\(564\) | 5.40833 | − | 9.36750i | 0.227732 | − | 0.394443i | ||||
\(565\) | −14.7738 | −0.621538 | ||||||||
\(566\) | 21.4744 | − | 37.1947i | 0.902636 | − | 1.56341i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00000 | + | 10.3923i | −0.251754 | + | 0.436051i | ||||
\(569\) | 17.3028 | − | 29.9693i | 0.725370 | − | 1.25638i | −0.233451 | − | 0.972368i | \(-0.575002\pi\) |
0.958822 | − | 0.284009i | \(-0.0916647\pi\) | |||||||
\(570\) | −23.4430 | −0.981920 | ||||||||
\(571\) | 5.36249 | − | 9.28811i | 0.224413 | − | 0.388695i | −0.731730 | − | 0.681595i | \(-0.761287\pi\) |
0.956143 | + | 0.292899i | \(0.0946201\pi\) | |||||||
\(572\) | 35.1345 | − | 46.7115i | 1.46905 | − | 1.95311i | ||||
\(573\) | −34.0207 | −1.42124 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.0916731 | − | 0.158782i | −0.00382303 | − | 0.00662169i | ||||
\(576\) | −21.7527 | −0.906364 | ||||||||
\(577\) | 16.5829 | − | 28.7225i | 0.690356 | − | 1.19573i | −0.281366 | − | 0.959601i | \(-0.590787\pi\) |
0.971721 | − | 0.236131i | \(-0.0758793\pi\) | |||||||
\(578\) | −39.4222 | − | 68.2813i | −1.63975 | − | 2.84013i | ||||
\(579\) | −42.9488 | −1.78489 | ||||||||
\(580\) | 16.4836 | 0.684443 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 34.0875 | + | 59.0412i | 1.41297 | + | 2.44734i | ||||
\(583\) | −5.87637 | + | 10.1782i | −0.243374 | + | 0.421537i | ||||
\(584\) | −6.50192 | + | 11.2617i | −0.269052 | + | 0.466011i | ||||
\(585\) | −7.97224 | + | 10.5992i | −0.329612 | + | 0.438221i | ||||
\(586\) | −32.9671 | − | 57.1008i | −1.36186 | − | 2.35881i | ||||
\(587\) | 0.984312 | + | 1.70488i | 0.0406269 | + | 0.0703679i | 0.885624 | − | 0.464403i | \(-0.153731\pi\) |
−0.844997 | + | 0.534771i | \(0.820398\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.75694 | − | 13.4354i | 0.319619 | − | 0.553597i | ||||
\(590\) | 7.04584 | + | 12.2037i | 0.290072 | + | 0.502420i | ||||
\(591\) | −1.18300 | − | 2.04901i | −0.0486620 | − | 0.0842850i | ||||
\(592\) | −1.30278 | − | 2.25647i | −0.0535437 | − | 0.0927405i | ||||
\(593\) | 3.15162 | + | 5.45877i | 0.129422 | + | 0.224165i | 0.923453 | − | 0.383712i | \(-0.125355\pi\) |
−0.794031 | + | 0.607877i | \(0.792021\pi\) | |||||||
\(594\) | −15.9568 | + | 27.6380i | −0.654715 | + | 1.13400i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 28.9222 | + | 50.0947i | 1.18470 | + | 2.05196i | ||||
\(597\) | 7.75694 | + | 13.4354i | 0.317470 | + | 0.549875i | ||||
\(598\) | −3.02220 | + | 4.01804i | −0.123587 | + | 0.164310i | ||||
\(599\) | 5.25694 | − | 9.10529i | 0.214793 | − | 0.372032i | −0.738416 | − | 0.674346i | \(-0.764426\pi\) |
0.953208 | + | 0.302314i | \(0.0977591\pi\) | |||||||
\(600\) | −0.984312 | + | 1.70488i | −0.0401844 | + | 0.0696014i | ||||
\(601\) | 4.56338 | + | 7.90400i | 0.186144 | + | 0.322411i | 0.943961 | − | 0.330056i | \(-0.107068\pi\) |
−0.757817 | + | 0.652467i | \(0.773734\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.69722 | 0.0691163 | ||||||||
\(604\) | 27.1194 | 1.10347 | ||||||||
\(605\) | 14.1868 | + | 24.5723i | 0.576777 | + | 0.999008i | ||||
\(606\) | 16.2250 | − | 28.1025i | 0.659095 | − | 1.14159i | ||||
\(607\) | −38.8129 | −1.57537 | −0.787683 | − | 0.616081i | \(-0.788719\pi\) | ||||
−0.787683 | + | 0.616081i | \(0.788719\pi\) | |||||||
\(608\) | −5.74637 | − | 9.95301i | −0.233046 | − | 0.403648i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21.6333 | 0.875907 | ||||||||
\(611\) | 3.27502 | − | 4.35416i | 0.132493 | − | 0.176151i | ||||
\(612\) | 20.0626 | − | 34.7495i | 0.810984 | − | 1.40467i | ||||
\(613\) | 31.9083 | 1.28877 | 0.644383 | − | 0.764703i | \(-0.277114\pi\) | ||||
0.644383 | + | 0.764703i | \(0.277114\pi\) | |||||||
\(614\) | 4.23527 | − | 7.33571i | 0.170922 | − | 0.296045i | ||||
\(615\) | −23.4430 | + | 40.6045i | −0.945314 | + | 1.63733i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.92221 | + | 13.7217i | −0.318936 | + | 0.552413i | −0.980266 | − | 0.197681i | \(-0.936659\pi\) |
0.661330 | + | 0.750095i | \(0.269992\pi\) | |||||||
\(618\) | 57.3583 | 2.30729 | ||||||||
\(619\) | −14.9725 | + | 25.9331i | −0.601794 | + | 1.04234i | 0.390755 | + | 0.920495i | \(0.372214\pi\) |
−0.992549 | + | 0.121844i | \(0.961119\pi\) | |||||||
\(620\) | 25.6194 | + | 44.3742i | 1.02890 | + | 1.78211i | ||||
\(621\) | 0.854892 | − | 1.48072i | 0.0343056 | − | 0.0594191i | ||||
\(622\) | 12.2483 | + | 21.2147i | 0.491112 | + | 0.850631i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.34861 | + | 0.286249i | 0.0940197 | + | 0.0114591i | ||||
\(625\) | 11.6972 | + | 20.2602i | 0.467889 | + | 0.810407i | ||||
\(626\) | 13.0038 | 0.519738 | ||||||||
\(627\) | 23.0555 | 0.920748 | ||||||||
\(628\) | 2.16731 | 0.0864850 | ||||||||
\(629\) | −61.5997 | −2.45614 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.4542 | + | 19.8392i | −0.455983 | + | 0.789786i | −0.998744 | − | 0.0501013i | \(-0.984046\pi\) |
0.542761 | + | 0.839887i | \(0.317379\pi\) | |||||||
\(632\) | 9.90833 | + | 17.1617i | 0.394132 | + | 0.682657i | ||||
\(633\) | 16.2548 | + | 28.1542i | 0.646071 | + | 1.11903i | ||||
\(634\) | −14.3028 | −0.568036 | ||||||||
\(635\) | 8.56989 | − | 14.8435i | 0.340086 | − | 0.589046i | ||||
\(636\) | −17.1398 | −0.679637 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −26.0278 | −1.03045 | ||||||||
\(639\) | −3.39445 | + | 5.87936i | −0.134282 | + | 0.232584i | ||||
\(640\) | 40.9802 | 1.61988 | ||||||||
\(641\) | 7.25694 | + | 12.5694i | 0.286632 | + | 0.496461i | 0.973004 | − | 0.230790i | \(-0.0741310\pi\) |
−0.686372 | + | 0.727251i | \(0.740798\pi\) | |||||||
\(642\) | 14.2169 | + | 24.6244i | 0.561097 | + | 0.971849i | ||||
\(643\) | 8.56989 | − | 14.8435i | 0.337963 | − | 0.585370i | −0.646086 | − | 0.763265i | \(-0.723595\pi\) |
0.984050 | + | 0.177895i | \(0.0569286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −58.7805 | −2.31448 | ||||||||
\(646\) | 35.7250 | 1.40558 | ||||||||
\(647\) | 32.9671 | 1.29607 | 0.648036 | − | 0.761610i | \(-0.275591\pi\) | ||||
0.648036 | + | 0.761610i | \(0.275591\pi\) | |||||||
\(648\) | −33.6333 | −1.32124 | ||||||||
\(649\) | −6.92937 | − | 12.0020i | −0.272002 | − | 0.471121i | ||||
\(650\) | −1.51110 | + | 2.00902i | −0.0592702 | + | 0.0788002i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.60555 | + | 7.97705i | 0.180367 | + | 0.312405i | ||||
\(653\) | 23.3764 | − | 40.4891i | 0.914788 | − | 1.58446i | 0.107577 | − | 0.994197i | \(-0.465691\pi\) |
0.807211 | − | 0.590262i | \(-0.200976\pi\) | |||||||
\(654\) | 20.4901 | + | 35.4899i | 0.801226 | + | 1.38776i | ||||
\(655\) | 11.5278 | − | 19.9667i | 0.450427 | − | 0.780162i | ||||
\(656\) | 3.02220 | 0.117997 | ||||||||
\(657\) | −3.67841 | + | 6.37119i | −0.143508 | + | 0.248564i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.81665 | − | 17.0029i | 0.382403 | − | 0.662341i | −0.609003 | − | 0.793168i | \(-0.708430\pi\) |
0.991405 | + | 0.130828i | \(0.0417634\pi\) | |||||||
\(660\) | −38.0736 | + | 65.9454i | −1.48201 | + | 2.56692i | ||||
\(661\) | 22.9855 | 0.894032 | 0.447016 | − | 0.894526i | \(-0.352487\pi\) | ||||
0.447016 | + | 0.894526i | \(0.352487\pi\) | |||||||
\(662\) | −4.95416 | + | 8.58086i | −0.192549 | + | 0.333505i | ||||
\(663\) | 33.6234 | − | 44.7025i | 1.30582 | − | 1.73610i | ||||
\(664\) | −8.47055 | −0.328721 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.8167 | − | 29.1273i | −0.651632 | − | 1.12866i | ||||
\(667\) | 1.39445 | 0.0539933 | ||||||||
\(668\) | 18.9790 | − | 32.8726i | 0.734319 | − | 1.27188i | ||||
\(669\) | 19.5000 | + | 33.7750i | 0.753914 | + | 1.30582i | ||||
\(670\) | −4.99082 | −0.192812 | ||||||||
\(671\) | −21.2757 | −0.821340 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.10555 | + | 1.91487i | 0.0426159 | + | 0.0738129i | 0.886547 | − | 0.462639i | \(-0.153098\pi\) |
−0.843931 | + | 0.536452i | \(0.819764\pi\) | |||||||
\(674\) | −20.8625 | + | 36.1349i | −0.803593 | + | 1.39186i | ||||
\(675\) | 0.427446 | − | 0.740358i | 0.0164524 | − | 0.0284964i | ||||
\(676\) | 41.6791 | + | 10.3129i | 1.60304 | + | 0.396651i | ||||
\(677\) | −13.2326 | − | 22.9196i | −0.508571 | − | 0.880870i | −0.999951 | − | 0.00992485i | \(-0.996841\pi\) |
0.491380 | − | 0.870945i | \(-0.336493\pi\) | |||||||
\(678\) | 17.0104 | + | 29.4628i | 0.653279 | + | 1.13151i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −23.2708 | + | 40.3062i | −0.892395 | + | 1.54567i | ||||
\(681\) | 19.9958 | + | 34.6337i | 0.766241 | + | 1.32717i | ||||
\(682\) | −40.4534 | − | 70.0673i | −1.54904 | − | 2.68302i | ||||
\(683\) | 1.80278 | + | 3.12250i | 0.0689813 | + | 0.119479i | 0.898453 | − | 0.439069i | \(-0.144692\pi\) |
−0.829472 | + | 0.558549i | \(0.811358\pi\) | |||||||
\(684\) | 6.07448 | + | 10.5213i | 0.232263 | + | 0.402292i | ||||
\(685\) | 6.83003 | − | 11.8300i | 0.260962 | − | 0.451999i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9361 | + | 29.3342i | 0.646152 | + | 1.11917i | ||||
\(688\) | 1.89445 | + | 3.28128i | 0.0722252 | + | 0.125098i | ||||
\(689\) | −8.56989 | − | 1.04450i | −0.326487 | − | 0.0397923i | ||||
\(690\) | 3.27502 | − | 5.67250i | 0.124678 | − | 0.215948i | ||||
\(691\) | −18.8796 | + | 32.7005i | −0.718215 | + | 1.24399i | 0.243491 | + | 0.969903i | \(0.421707\pi\) |
−0.961706 | + | 0.274082i | \(0.911626\pi\) | |||||||
\(692\) | 16.8117 | + | 29.1187i | 0.639084 | + | 1.10693i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.0278 | 1.32964 | ||||||||
\(695\) | −23.0555 | −0.874545 | ||||||||
\(696\) | −7.48624 | − | 12.9665i | −0.283765 | − | 0.491495i | ||||
\(697\) | 35.7250 | − | 61.8775i | 1.35318 | − | 2.34378i | ||||
\(698\) | −23.4430 | −0.887331 | ||||||||
\(699\) | −14.1868 | − | 24.5723i | −0.536596 | − | 0.929411i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.02776 | 0.340974 | 0.170487 | − | 0.985360i | \(-0.445466\pi\) | ||||
0.170487 | + | 0.985360i | \(0.445466\pi\) | |||||||
\(702\) | −23.2708 | − | 2.83625i | −0.878300 | − | 0.107047i | ||||
\(703\) | 9.32544 | − | 16.1521i | 0.351716 | − | 0.609189i | ||||
\(704\) | −62.9083 | −2.37095 | ||||||||
\(705\) | −3.54899 | + | 6.14703i | −0.133663 | + | 0.231510i | ||||
\(706\) | −30.4717 | + | 52.7786i | −1.14682 | + | 1.98635i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.1056 | − | 17.5033i | 0.379790 | − | 0.657815i | ||||
\(709\) | 32.7250 | 1.22901 | 0.614506 | − | 0.788912i | \(-0.289355\pi\) | ||||
0.614506 | + | 0.788912i | \(0.289355\pi\) | |||||||
\(710\) | 9.98165 | − | 17.2887i | 0.374605 | − | 0.648834i | ||||
\(711\) | 5.60555 | + | 9.70910i | 0.210225 | + | 0.364120i | ||||
\(712\) | 9.75289 | − | 16.8925i | 0.365505 | − | 0.633073i | ||||
\(713\) | 2.16731 | + | 3.75389i | 0.0811663 | + | 0.140584i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.0555 | + | 30.6525i | −0.862227 | + | 1.14634i | ||||
\(716\) | −35.6791 | − | 61.7981i | −1.33339 | − | 2.30950i | ||||
\(717\) | −9.52412 | −0.355685 | ||||||||
\(718\) | −27.8444 | −1.03914 | ||||||||
\(719\) | 22.7868 | 0.849805 | 0.424902 | − | 0.905239i | \(-0.360308\pi\) | ||||
0.424902 | + | 0.905239i | \(0.360308\pi\) | |||||||
\(720\) | −1.11373 | −0.0415064 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.4680 | − | 28.5235i | 0.612877 | − | 1.06153i | ||||
\(723\) | 10.1056 | + | 17.5033i | 0.375829 | + | 0.650956i | ||||
\(724\) | −40.1253 | − | 69.4990i | −1.49124 | − | 2.58291i | ||||
\(725\) | 0.697224 | 0.0258943 | ||||||||
\(726\) | 32.6691 | − | 56.5846i | 1.21246 | − | 2.10005i | ||||
\(727\) | −37.1031 | −1.37608 | −0.688038 | − | 0.725674i | \(-0.741528\pi\) | ||||
−0.688038 | + | 0.725674i | \(0.741528\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.669468 | −0.0247951 | ||||||||
\(730\) | 10.8167 | − | 18.7350i | 0.400342 | − | 0.693413i | ||||
\(731\) | 89.5760 | 3.31309 | ||||||||
\(732\) | −15.5139 | − | 26.8708i | −0.573409 | − | 0.993174i | ||||
\(733\) | −3.35030 | − | 5.80290i | −0.123746 | − | 0.214335i | 0.797496 | − | 0.603324i | \(-0.206158\pi\) |
−0.921242 | + | 0.388990i | \(0.872824\pi\) | |||||||
\(734\) | 29.4874 | − | 51.0737i | 1.08840 | − | 1.88517i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.21110 | 0.118363 | ||||||||
\(737\) | 4.90833 | 0.180801 | ||||||||
\(738\) | 39.0115 | 1.43603 | ||||||||
\(739\) | −33.2111 | −1.22169 | −0.610845 | − | 0.791750i | \(-0.709170\pi\) | ||||
−0.610845 | + | 0.791750i | \(0.709170\pi\) | |||||||
\(740\) | 30.7998 | + | 53.3469i | 1.13222 | + | 1.96107i | ||||
\(741\) | 6.63134 | + | 15.5838i | 0.243609 | + | 0.572487i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.6514 | + | 35.7693i | 0.757626 | + | 1.31225i | 0.944058 | + | 0.329779i | \(0.106974\pi\) |
−0.186432 | + | 0.982468i | \(0.559692\pi\) | |||||||
\(744\) | 23.2708 | − | 40.3062i | 0.853150 | − | 1.47770i | ||||
\(745\) | −18.9790 | − | 32.8726i | −0.695336 | − | 1.20436i | ||||
\(746\) | 14.6194 | − | 25.3216i | 0.535255 | − | 0.927089i | ||||
\(747\) | −4.79214 | −0.175335 | ||||||||
\(748\) | 58.0206 | − | 100.495i | 2.12144 | − | 3.67445i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 28.6791 | − | 49.6737i | 1.04721 | − | 1.81383i | ||||
\(751\) | 5.80278 | − | 10.0507i | 0.211746 | − | 0.366755i | −0.740515 | − | 0.672040i | \(-0.765418\pi\) |
0.952261 | + | 0.305285i | \(0.0987516\pi\) | |||||||
\(752\) | 0.457524 | 0.0166842 | ||||||||
\(753\) | −32.4500 | + | 56.2050i | −1.18254 | + | 2.04822i | ||||
\(754\) | −7.48624 | − | 17.5929i | −0.272633 | − | 0.640694i | ||||
\(755\) | −17.7960 | −0.647662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.11943 | − | 5.40301i | −0.113378 | − | 0.196376i | 0.803752 | − | 0.594964i | \(-0.202834\pi\) |
−0.917130 | + | 0.398588i | \(0.869500\pi\) | |||||||
\(758\) | −27.9083 | −1.01368 | ||||||||
\(759\) | −3.22088 | + | 5.57873i | −0.116911 | + | 0.202495i | ||||
\(760\) | −7.04584 | − | 12.2037i | −0.255579 | − | 0.442676i | ||||
\(761\) | 42.2926 | 1.53311 | 0.766553 | − | 0.642182i | \(-0.221971\pi\) | ||||
0.766553 | + | 0.642182i | \(0.221971\pi\) | |||||||
\(762\) | −39.4691 | −1.42981 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −25.9222 | − | 44.8986i | −0.937832 | − | 1.62437i | ||||
\(765\) | −13.1653 | + | 22.8029i | −0.475991 | + | 0.824441i | ||||
\(766\) | −25.7097 | + | 44.5305i | −0.928928 | + | 1.60895i | ||||
\(767\) | 6.11943 | − | 8.13583i | 0.220960 | − | 0.293768i | ||||
\(768\) | −19.4064 | − | 33.6129i | −0.700269 | − | 1.21290i | ||||
\(769\) | 23.5424 | + | 40.7766i | 0.848959 | + | 1.47044i | 0.882138 | + | 0.470991i | \(0.156104\pi\) |
−0.0331785 | + | 0.999449i | \(0.510563\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.83053 | + | 11.8308i | −0.245996 | + | 0.426077i | ||||
\(772\) | −32.7250 | − | 56.6813i | −1.17780 | − | 2.04001i | ||||
\(773\) | 14.2169 | + | 24.6244i | 0.511347 | + | 0.885679i | 0.999914 | + | 0.0131525i | \(0.00418670\pi\) |
−0.488566 | + | 0.872527i | \(0.662480\pi\) | |||||||
\(774\) | 24.4542 | + | 42.3559i | 0.878987 | + | 1.52245i | ||||
\(775\) | 1.08365 | + | 1.87694i | 0.0389260 | + | 0.0674218i | ||||
\(776\) | −20.4901 | + | 35.4899i | −0.735551 | + | 1.27401i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.4222 | − | 57.8890i | −1.19824 | − | 2.07542i | ||||
\(779\) | 10.8167 | + | 18.7350i | 0.387547 | + | 0.671251i | ||||
\(780\) | −55.5252 | − | 6.76742i | −1.98812 | − | 0.242312i | ||||
\(781\) | −9.81665 | + | 17.0029i | −0.351267 | + | 0.608413i | ||||
\(782\) | −4.99082 | + | 8.64436i | −0.178472 | + | 0.309122i | ||||
\(783\) | 3.25096 | + | 5.63083i | 0.116180 | + | 0.201230i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.42221 | −0.0507607 | ||||||||
\(786\) | −53.0917 | −1.89372 | ||||||||
\(787\) | −15.6287 | − | 27.0697i | −0.557102 | − | 0.964930i | −0.997737 | − | 0.0672428i | \(-0.978580\pi\) |
0.440634 | − | 0.897687i | \(-0.354754\pi\) | |||||||
\(788\) | 1.80278 | − | 3.12250i | 0.0642212 | − | 0.111234i | ||||
\(789\) | −33.4247 | −1.18995 | ||||||||
\(790\) | −16.4836 | − | 28.5504i | −0.586459 | − | 1.01578i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 24.9916 | 0.888038 | ||||||||
\(793\) | −6.11943 | − | 14.3808i | −0.217307 | − | 0.510678i | ||||
\(794\) | 4.99082 | − | 8.64436i | 0.177118 | − | 0.306777i | ||||
\(795\) | 11.2473 | 0.398899 | ||||||||
\(796\) | −11.8209 | + | 20.4743i | −0.418979 | + | 0.725693i | ||||
\(797\) | 13.0038 | − | 22.5233i | 0.460620 | − | 0.797817i | −0.538372 | − | 0.842707i | \(-0.680960\pi\) |
0.998992 | + | 0.0448902i | \(0.0142938\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.40833 | − | 9.36750i | 0.191333 | − | 0.331398i | ||||
\(800\) | 1.60555 | 0.0567648 | ||||||||
\(801\) | 5.51761 | − | 9.55678i | 0.194955 | − | 0.337672i | ||||
\(802\) | 11.6514 | + | 20.1808i | 0.411425 | + | 0.712609i | ||||
\(803\) | −10.6379 | + | 18.4253i | −0.375402 | + | 0.650215i | ||||
\(804\) | 3.57907 | + | 6.19912i | 0.126224 | + | 0.218626i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 35.7250 | − | 47.4967i | 1.25836 | − | 1.67300i | ||||
\(807\) | 0.711103 | + | 1.23167i | 0.0250320 | + | 0.0433567i | ||||
\(808\) | 19.5058 | 0.686211 | ||||||||
\(809\) | 20.0278 | 0.704138 | 0.352069 | − | 0.935974i | \(-0.385478\pi\) | ||||
0.352069 | + | 0.935974i | \(0.385478\pi\) | |||||||
\(810\) | 55.9526 | 1.96598 | ||||||||
\(811\) | −0.854892 | −0.0300193 | −0.0150097 | − | 0.999887i | \(-0.504778\pi\) | ||||
−0.0150097 | + | 0.999887i | \(0.504778\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.7292 | + | 27.2437i | −0.551647 | + | 0.955480i | ||||
\(814\) | −48.6333 | − | 84.2354i | −1.70460 | − | 2.95245i | ||||
\(815\) | −3.02220 | − | 5.23460i | −0.105863 | − | 0.183360i | ||||
\(816\) | 4.69722 | 0.164436 | ||||||||
\(817\) | −13.5607 | + | 23.4878i | −0.474429 | + | 0.821736i | ||||
\(818\) | −8.01302 | −0.280169 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −71.4500 | −2.49514 | ||||||||
\(821\) | 27.9222 | − | 48.3627i | 0.974492 | − | 1.68787i | 0.292889 | − | 0.956146i | \(-0.405383\pi\) |
0.681602 | − | 0.731723i | \(-0.261283\pi\) | |||||||
\(822\) | −31.4560 | −1.09716 | ||||||||
\(823\) | −21.1333 | − | 36.6040i | −0.736661 | − | 1.27593i | −0.953991 | − | 0.299836i | \(-0.903068\pi\) |
0.217330 | − | 0.976098i | \(-0.430265\pi\) | |||||||
\(824\) | 17.2391 | + | 29.8590i | 0.600553 | + | 1.04019i | ||||
\(825\) | −1.61044 | + | 2.78937i | −0.0560684 | + | 0.0971133i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.7527 | −0.582550 | −0.291275 | − | 0.956639i | \(-0.594079\pi\) | ||||
−0.291275 | + | 0.956639i | \(0.594079\pi\) | |||||||
\(828\) | −3.39445 | −0.117965 | ||||||||
\(829\) | −50.7631 | −1.76308 | −0.881538 | − | 0.472113i | \(-0.843492\pi\) | ||||
−0.881538 | + | 0.472113i | \(0.843492\pi\) | |||||||
\(830\) | 14.0917 | 0.489129 | ||||||||
\(831\) | −0.228762 | − | 0.396228i | −0.00793567 | − | 0.0137450i | ||||
\(832\) | −18.0940 | − | 42.5214i | −0.627297 | − | 1.47417i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 26.5458 | + | 45.9787i | 0.919207 | + | 1.59211i | ||||
\(835\) | −12.4542 | + | 21.5712i | −0.430994 | + | 0.746504i | ||||
\(836\) | 17.5672 | + | 30.4273i | 0.607575 | + | 1.05235i | ||||
\(837\) | −10.1056 | + | 17.5033i | −0.349299 | + | 0.605004i | ||||
\(838\) | 39.4691 | 1.36344 | ||||||||
\(839\) | 6.73069 | − | 11.6579i | 0.232369 | − | 0.402475i | −0.726136 | − | 0.687551i | \(-0.758686\pi\) |
0.958505 | + | 0.285076i | \(0.0920189\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.8486 | − | 20.5224i | 0.408573 | − | 0.707669i | ||||
\(842\) | −5.78890 | + | 10.0267i | −0.199499 | + | 0.345542i | ||||
\(843\) | −51.6180 | −1.77782 | ||||||||
\(844\) | −24.7708 | + | 42.9043i | −0.852647 | + | 1.47683i | ||||
\(845\) | −27.3502 | − | 6.76742i | −0.940875 | − | 0.232806i | ||||
\(846\) | 5.90587 | 0.203048 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.362490 | − | 0.627852i | −0.0124480 | − | 0.0215605i | ||||
\(849\) | 40.4222 | 1.38729 | ||||||||
\(850\) | −2.49541 | + | 4.32218i | −0.0855919 | + | 0.148250i | ||||
\(851\) | 2.60555 | + | 4.51295i | 0.0893171 | + | 0.154702i | ||||
\(852\) | −28.6325 | −0.980934 | ||||||||
\(853\) | −12.8052 | −0.438440 | −0.219220 | − | 0.975675i | \(-0.570351\pi\) | ||||
−0.219220 | + | 0.975675i | \(0.570351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.98612 | − | 6.90417i | −0.136322 | − | 0.236117i | ||||
\(856\) | −8.54584 | + | 14.8018i | −0.292091 | + | 0.505916i | ||||
\(857\) | 1.64052 | − | 2.84146i | 0.0560391 | − | 0.0970626i | −0.836645 | − | 0.547746i | \(-0.815486\pi\) |
0.892684 | + | 0.450683i | \(0.148820\pi\) | |||||||
\(858\) | 87.6749 | + | 10.6858i | 2.99317 | + | 0.364808i | ||||
\(859\) | 1.51110 | + | 2.61730i | 0.0515581 | + | 0.0893012i | 0.890653 | − | 0.454684i | \(-0.150248\pi\) |
−0.839095 | + | 0.543986i | \(0.816915\pi\) | |||||||
\(860\) | −44.7880 | − | 77.5751i | −1.52726 | − | 2.64529i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.1056 | − | 41.7520i | 0.821038 | − | 1.42208i | ||||
\(863\) | −4.90833 | − | 8.50147i | −0.167081 | − | 0.289393i | 0.770311 | − | 0.637668i | \(-0.220101\pi\) |
−0.937392 | + | 0.348275i | \(0.886768\pi\) | |||||||
\(864\) | 7.48624 | + | 12.9665i | 0.254687 | + | 0.441131i | ||||
\(865\) | −11.0320 | − | 19.1079i | −0.375098 | − | 0.649689i | ||||
\(866\) | 19.7345 | + | 34.1812i | 0.670607 | + | 1.16153i | ||||
\(867\) | 37.1031 | − | 64.2644i | 1.26009 | − | 2.18253i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.2111 | + | 28.0785i | 0.549924 | + | 0.952496i | ||||
\(870\) | 12.4542 | + | 21.5712i | 0.422236 | + | 0.731334i | ||||
\(871\) | 1.41176 | + | 3.31767i | 0.0478356 | + | 0.112415i | ||||
\(872\) | −12.3167 | + | 21.3331i | −0.417095 | + | 0.722429i | ||||
\(873\) | −11.5921 | + | 20.0781i | −0.392333 | + | 0.679540i | ||||
\(874\) | −1.51110 | − | 2.61730i | −0.0511137 | − | 0.0885316i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −31.0278 | −1.04833 | ||||||||
\(877\) | −45.6056 | −1.53999 | −0.769995 | − | 0.638050i | \(-0.779741\pi\) | ||||
−0.769995 | + | 0.638050i | \(0.779741\pi\) | |||||||
\(878\) | −4.23527 | − | 7.33571i | −0.142934 | − | 0.247568i | ||||
\(879\) | 31.0278 | − | 53.7417i | 1.04654 | − | 1.81266i | ||||
\(880\) | −3.22088 | −0.108576 | ||||||||
\(881\) | 9.42478 | + | 16.3242i | 0.317529 | + | 0.549976i | 0.979972 | − | 0.199136i | \(-0.0638136\pi\) |
−0.662443 | + | 0.749112i | \(0.730480\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.3944 | −0.820939 | −0.410469 | − | 0.911874i | \(-0.634635\pi\) | ||||
−0.410469 | + | 0.911874i | \(0.634635\pi\) | |||||||
\(884\) | 84.6152 | + | 10.3129i | 2.84592 | + | 0.346861i | ||||
\(885\) | −6.63134 | + | 11.4858i | −0.222910 | + | 0.386092i | ||||
\(886\) | −46.6056 | −1.56574 | ||||||||
\(887\) | 17.3385 | − | 30.0311i | 0.582169 | − | 1.00835i | −0.413053 | − | 0.910707i | \(-0.635538\pi\) |
0.995222 | − | 0.0976388i | \(-0.0311290\pi\) | |||||||
\(888\) | 27.9763 | − | 48.4564i | 0.938824 | − | 1.62609i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −16.2250 | + | 28.1025i | −0.543863 | + | 0.941998i | ||||
\(891\) | −55.0278 | −1.84350 | ||||||||
\(892\) | −29.7162 | + | 51.4699i | −0.994971 | + | 1.72334i | ||||
\(893\) | 1.63751 | + | 2.83625i | 0.0547972 | + | 0.0949115i | ||||
\(894\) | −43.7043 | + | 75.6981i | −1.46169 | + | 2.53172i | ||||
\(895\) | 23.4129 | + | 40.5524i | 0.782608 | + | 1.35552i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.69722 | − | 0.572498i | −0.156836 | − | 0.0191152i | ||||
\(898\) | 23.5139 | + | 40.7272i | 0.784668 | + | 1.35909i | ||||
\(899\) | −16.4836 | −0.549758 | ||||||||
\(900\) | −1.69722 | −0.0565741 | ||||||||
\(901\) | −17.1398 | −0.571009 | ||||||||
\(902\) | 112.820 | 3.75651 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.2250 | + | 17.7102i | −0.340078 | + | 0.589032i | ||||
\(905\) | 26.3305 | + | 45.6058i | 0.875256 | + | 1.51599i | ||||
\(906\) | 20.4901 | + | 35.4899i | 0.680737 | + | 1.17907i | ||||
\(907\) | −38.8444 | −1.28981 | −0.644904 | − | 0.764264i | \(-0.723103\pi\) | ||||
−0.644904 | + | 0.764264i | \(0.723103\pi\) | |||||||
\(908\) | −30.4717 | + | 52.7786i | −1.01124 | + | 1.75152i | ||||
\(909\) | 11.0352 | 0.366015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.9361 | 1.19062 | 0.595308 | − | 0.803498i | \(-0.297030\pi\) | ||||
0.595308 | + | 0.803498i | \(0.297030\pi\) | |||||||
\(912\) | −0.711103 | + | 1.23167i | −0.0235470 | + | 0.0407845i | ||||
\(913\) | −13.8587 | −0.458657 | ||||||||
\(914\) | −23.7250 | − | 41.0929i | −0.784753 | − | 1.35923i | ||||
\(915\) | 10.1803 | + | 17.6329i | 0.336551 | + | 0.582924i | ||||
\(916\) | −25.8090 | + | 44.7025i | −0.852754 | + | 1.47701i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −46.5416 | −1.53610 | ||||||||
\(919\) | 53.4500 | 1.76315 | 0.881576 | − | 0.472043i | \(-0.156483\pi\) | ||||
0.881576 | + | 0.472043i | \(0.156483\pi\) | |||||||
\(920\) | 3.93725 | 0.129807 | ||||||||
\(921\) | 7.97224 | 0.262694 | ||||||||
\(922\) | −28.9606 | − | 50.1613i | −0.953768 | − | 1.65197i | ||||
\(923\) | −14.3163 | − | 1.74487i | −0.471226 | − | 0.0574330i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.30278 | + | 2.25647i | 0.0428350 | + | 0.0741924i | ||||
\(926\) | 15.8764 | − | 27.4987i | 0.521730 | − | 0.903663i | ||||
\(927\) | 9.75289 | + | 16.8925i | 0.320327 | + | 0.554822i | ||||
\(928\) | −6.10555 | + | 10.5751i | −0.200425 | + | 0.347145i | ||||
\(929\) | 17.1398 | 0.562338 | 0.281169 | − | 0.959658i | \(-0.409278\pi\) | ||||
0.281169 | + | 0.959658i | \(0.409278\pi\) | |||||||
\(930\) | −38.7135 | + | 67.0538i | −1.26947 | + | 2.19878i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.6194 | − | 37.4460i | 0.708168 | − | 1.22658i | ||||
\(933\) | −11.5278 | + | 19.9667i | −0.377402 | + | 0.653679i | ||||
\(934\) | −29.4874 | −0.964858 | ||||||||
\(935\) | −38.0736 | + | 65.9454i | −1.24514 | + | 2.15665i | ||||
\(936\) | 7.18821 | + | 16.8925i | 0.234954 | + | 0.552148i | ||||
\(937\) | 19.7646 | 0.645682 | 0.322841 | − | 0.946453i | \(-0.395362\pi\) | ||||
0.322841 | + | 0.946453i | \(0.395362\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.11943 | + | 10.5992i | 0.199700 | + | 0.345891i | ||||
\(940\) | −10.8167 | −0.352800 | ||||||||
\(941\) | −2.72417 | + | 4.71841i | −0.0888055 | + | 0.153816i | −0.907006 | − | 0.421117i | \(-0.861638\pi\) |
0.818201 | + | 0.574932i | \(0.194972\pi\) | |||||||
\(942\) | 1.63751 | + | 2.83625i | 0.0533529 | + | 0.0924100i | ||||
\(943\) | −6.04440 | −0.196833 | ||||||||
\(944\) | 0.854892 | 0.0278244 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 70.7208 | + | 122.492i | 2.29933 | + | 3.98256i | ||||
\(947\) | −13.9403 | + | 24.1453i | −0.452998 | + | 0.784616i | −0.998571 | − | 0.0534475i | \(-0.982979\pi\) |
0.545572 | + | 0.838064i | \(0.316312\pi\) | |||||||
\(948\) | −23.6417 | + | 40.9486i | −0.767847 | + | 1.32995i | ||||
\(949\) | −15.5139 | − | 1.89083i | −0.503602 | − | 0.0613790i | ||||
\(950\) | −0.755550 | − | 1.30865i | −0.0245133 | − | 0.0424582i | ||||
\(951\) | −6.73069 | − | 11.6579i | −0.218257 | − | 0.378033i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.1972 | + | 29.7865i | −0.557073 | + | 0.964878i | 0.440666 | + | 0.897671i | \(0.354742\pi\) |
−0.997739 | + | 0.0672073i | \(0.978591\pi\) | |||||||
\(954\) | −4.67914 | − | 8.10452i | −0.151493 | − | 0.262393i | ||||
\(955\) | 17.0104 | + | 29.4628i | 0.550442 | + | 0.953394i | ||||
\(956\) | −7.25694 | − | 12.5694i | −0.234706 | − | 0.406523i | ||||
\(957\) | −12.2483 | − | 21.2147i | −0.395931 | − | 0.685773i | ||||
\(958\) | −18.9790 | + | 32.8726i | −0.613183 | + | 1.06206i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 30.1013 | + | 52.1371i | 0.971517 | + | 1.68272i | ||||
\(961\) | −10.1194 | − | 17.5274i | −0.326433 | − | 0.565399i | ||||
\(962\) | 42.9488 | − | 57.1008i | 1.38472 | − | 1.84100i | ||||
\(963\) | −4.83473 | + | 8.37400i | −0.155797 | + | 0.269849i | ||||
\(964\) | −15.3999 | + | 26.6734i | −0.495998 | + | 0.859094i | ||||
\(965\) | 21.4744 | + | 37.1947i | 0.691285 | + | 1.19734i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.4500 | −1.36510 | −0.682549 | − | 0.730839i | \(-0.739129\pi\) | ||||
−0.682549 | + | 0.730839i | \(0.739129\pi\) | |||||||
\(968\) | 39.2750 | 1.26235 | ||||||||
\(969\) | 16.8117 | + | 29.1187i | 0.540069 | + | 0.935427i | ||||
\(970\) | 34.0875 | − | 59.0412i | 1.09448 | − | 1.89570i | ||||
\(971\) | 31.4560 | 1.00947 | 0.504736 | − | 0.863274i | \(-0.331590\pi\) | ||||
0.504736 | + | 0.863274i | \(0.331590\pi\) | |||||||
\(972\) | −26.1371 | − | 45.2708i | −0.838348 | − | 1.45206i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −72.0833 | −2.30970 | ||||||||
\(975\) | −2.34861 | − | 0.286249i | −0.0752158 | − | 0.00916731i | ||||
\(976\) | 0.656208 | − | 1.13659i | 0.0210047 | − | 0.0363812i | ||||
\(977\) | −3.97224 | −0.127083 | −0.0635417 | − | 0.997979i | \(-0.520240\pi\) | ||||
−0.0635417 | + | 0.997979i | \(0.520240\pi\) | |||||||
\(978\) | −6.95945 | + | 12.0541i | −0.222539 | + | 0.385448i | ||||
\(979\) | 15.9568 | − | 27.6380i | 0.509981 | − | 0.883313i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.96804 | + | 12.0690i | −0.222472 | + | 0.385334i | ||||
\(982\) | 45.4222 | 1.44948 | ||||||||
\(983\) | 14.6444 | − | 25.3648i | 0.467083 | − | 0.809011i | −0.532210 | − | 0.846612i | \(-0.678638\pi\) |
0.999293 | + | 0.0376012i | \(0.0119717\pi\) | |||||||
\(984\) | 32.4500 | + | 56.2050i | 1.03447 | + | 1.79175i | ||||
\(985\) | −1.18300 | + | 2.04901i | −0.0376934 | + | 0.0652869i | ||||
\(986\) | −18.9790 | − | 32.8726i | −0.604414 | − | 1.04688i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.5139 | + | 20.6258i | −0.493562 | + | 0.656195i | ||||
\(989\) | −3.78890 | − | 6.56256i | −0.120480 | − | 0.208677i | ||||
\(990\) | −41.5762 | −1.32138 | ||||||||
\(991\) | −6.66947 | −0.211863 | −0.105931 | − | 0.994373i | \(-0.533782\pi\) | ||||
−0.105931 | + | 0.994373i | \(0.533782\pi\) | |||||||
\(992\) | −37.9580 | −1.20517 | ||||||||
\(993\) | −9.32544 | −0.295934 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.75694 | − | 13.4354i | 0.245912 | − | 0.425931i | ||||
\(996\) | −10.1056 | − | 17.5033i | −0.320207 | − | 0.554614i | ||||
\(997\) | 26.3659 | + | 45.6670i | 0.835016 | + | 1.44629i | 0.894018 | + | 0.448032i | \(0.147875\pi\) |
−0.0590018 | + | 0.998258i | \(0.518792\pi\) | |||||||
\(998\) | −19.1833 | −0.607238 | ||||||||
\(999\) | −12.1490 | + | 21.0426i | −0.384376 | + | 0.665759i |
(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 | 637.2.g.i.263.1 | 8 | ||
7.2 | even | 3 | 637.2.h.j.471.4 | 8 | |||
7.3 | odd | 6 | 637.2.f.h.393.1 | yes | 8 | ||
7.4 | even | 3 | 637.2.f.h.393.2 | yes | 8 | ||
7.5 | odd | 6 | 637.2.h.j.471.3 | 8 | |||
7.6 | odd | 2 | inner | 637.2.g.i.263.2 | 8 | ||
13.9 | even | 3 | 637.2.h.j.165.4 | 8 | |||
91.3 | odd | 6 | 8281.2.a.bu.1.4 | 4 | |||
91.9 | even | 3 | inner | 637.2.g.i.373.1 | 8 | ||
91.10 | odd | 6 | 8281.2.a.bo.1.2 | 4 | |||
91.48 | odd | 6 | 637.2.h.j.165.3 | 8 | |||
91.61 | odd | 6 | inner | 637.2.g.i.373.2 | 8 | ||
91.74 | even | 3 | 637.2.f.h.295.2 | yes | 8 | ||
91.81 | even | 3 | 8281.2.a.bu.1.3 | 4 | |||
91.87 | odd | 6 | 637.2.f.h.295.1 | ✓ | 8 | ||
91.88 | even | 6 | 8281.2.a.bo.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.h.295.1 | ✓ | 8 | 91.87 | odd | 6 | ||
637.2.f.h.295.2 | yes | 8 | 91.74 | even | 3 | ||
637.2.f.h.393.1 | yes | 8 | 7.3 | odd | 6 | ||
637.2.f.h.393.2 | yes | 8 | 7.4 | even | 3 | ||
637.2.g.i.263.1 | 8 | 1.1 | even | 1 | trivial | ||
637.2.g.i.263.2 | 8 | 7.6 | odd | 2 | inner | ||
637.2.g.i.373.1 | 8 | 91.9 | even | 3 | inner | ||
637.2.g.i.373.2 | 8 | 91.61 | odd | 6 | inner | ||
637.2.h.j.165.3 | 8 | 91.48 | odd | 6 | |||
637.2.h.j.165.4 | 8 | 13.9 | even | 3 | |||
637.2.h.j.471.3 | 8 | 7.5 | odd | 6 | |||
637.2.h.j.471.4 | 8 | 7.2 | even | 3 | |||
8281.2.a.bo.1.1 | 4 | 91.88 | even | 6 | |||
8281.2.a.bo.1.2 | 4 | 91.10 | odd | 6 | |||
8281.2.a.bu.1.3 | 4 | 91.81 | even | 3 | |||
8281.2.a.bu.1.4 | 4 | 91.3 | odd | 6 |