Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(97,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.y (of order \(9\), degree \(6\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 193.7 | ||
Character | \(\chi\) | \(=\) | 864.193 |
Dual form | 864.2.y.c.385.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.661519 | + | 1.60075i | 0.381928 | + | 0.924192i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.197119 | − | 1.11792i | 0.0881542 | − | 0.499947i | −0.908477 | − | 0.417935i | \(-0.862754\pi\) |
0.996631 | − | 0.0820126i | \(-0.0261348\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.270013 | − | 0.226568i | 0.102055 | − | 0.0856346i | −0.590332 | − | 0.807160i | \(-0.701003\pi\) |
0.692388 | + | 0.721526i | \(0.256559\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.12478 | + | 2.11785i | −0.708261 | + | 0.705950i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.174455 | + | 0.989381i | 0.0526000 | + | 0.298310i | 0.999747 | − | 0.0224902i | \(-0.00715946\pi\) |
−0.947147 | + | 0.320800i | \(0.896048\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.97001 | + | 2.17291i | −1.65578 | + | 0.602656i | −0.989692 | − | 0.143213i | \(-0.954257\pi\) |
−0.666092 | + | 0.745869i | \(0.732034\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.91990 | − | 0.423986i | 0.495716 | − | 0.109473i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.41720 | + | 5.91877i | −0.828794 | + | 1.43551i | 0.0701913 | + | 0.997534i | \(0.477639\pi\) |
−0.898985 | + | 0.437979i | \(0.855694\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.81718 | + | 3.14745i | 0.416890 | + | 0.722075i | 0.995625 | − | 0.0934409i | \(-0.0297866\pi\) |
−0.578735 | + | 0.815516i | \(0.696453\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.541297 | + | 0.282344i | 0.118121 | + | 0.0616125i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.200373 | − | 0.168133i | −0.0417806 | − | 0.0350581i | 0.621658 | − | 0.783289i | \(-0.286459\pi\) |
−0.663439 | + | 0.748231i | \(0.730904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.48758 | + | 1.26938i | 0.697517 | + | 0.253875i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.79573 | − | 2.00024i | −0.922939 | − | 0.384947i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.52890 | + | 0.920444i | 0.469605 | + | 0.170922i | 0.565973 | − | 0.824424i | \(-0.308500\pi\) |
−0.0963685 | + | 0.995346i | \(0.530723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.72245 | + | 4.80171i | 1.02778 | + | 0.862412i | 0.990585 | − | 0.136896i | \(-0.0437125\pi\) |
0.0371975 | + | 0.999308i | \(0.488157\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.46834 | + | 0.933752i | −0.255606 | + | 0.162545i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.200059 | − | 0.346513i | −0.0338162 | − | 0.0585714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.563717 | + | 0.976387i | −0.0926746 | + | 0.160517i | −0.908636 | − | 0.417590i | \(-0.862875\pi\) |
0.815961 | + | 0.578107i | \(0.196208\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.42756 | − | 8.11906i | −1.18936 | − | 1.30009i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.79162 | − | 0.652095i | 0.279804 | − | 0.101840i | −0.198307 | − | 0.980140i | \(-0.563544\pi\) |
0.478110 | + | 0.878300i | \(0.341322\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.06676 | + | 6.04992i | 0.162680 | + | 0.922605i | 0.951424 | + | 0.307883i | \(0.0996205\pi\) |
−0.788744 | + | 0.614722i | \(0.789268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.94874 | + | 2.79280i | 0.290502 | + | 0.416326i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.56245 | − | 7.18475i | 1.24896 | − | 1.04800i | 0.252193 | − | 0.967677i | \(-0.418848\pi\) |
0.996769 | − | 0.0803259i | \(-0.0255961\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.19396 | + | 6.77130i | −0.170566 | + | 0.967329i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.7350 | − | 1.55470i | −1.64323 | − | 0.217701i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.69660 | −1.19457 | −0.597285 | − | 0.802029i | \(-0.703754\pi\) | ||||
−0.597285 | + | 0.802029i | \(0.703754\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.14043 | 0.153776 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.83617 | + | 4.99095i | −0.508114 | + | 0.661067i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.32731 | − | 7.52756i | 0.172801 | − | 0.980004i | −0.767850 | − | 0.640630i | \(-0.778673\pi\) |
0.940651 | − | 0.339375i | \(-0.110215\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.448757 | + | 0.376552i | −0.0574574 | + | 0.0482125i | −0.671064 | − | 0.741399i | \(-0.734162\pi\) |
0.613607 | + | 0.789612i | \(0.289718\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0938827 | + | 1.05326i | −0.0118281 | + | 0.132698i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.25233 | + | 7.10230i | 0.155332 | + | 0.880931i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0913 | + | 3.67293i | −1.23285 | + | 0.448720i | −0.874572 | − | 0.484896i | \(-0.838858\pi\) |
−0.358276 | + | 0.933616i | \(0.616635\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.136587 | − | 0.431969i | 0.0164432 | − | 0.0520029i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.00739 | − | 8.67305i | 0.594268 | − | 1.02930i | −0.399382 | − | 0.916785i | \(-0.630775\pi\) |
0.993650 | − | 0.112517i | \(-0.0358914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.49979 | − | 4.32977i | −0.292579 | − | 0.506761i | 0.681840 | − | 0.731501i | \(-0.261180\pi\) |
−0.974419 | + | 0.224740i | \(0.927847\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.275152 | + | 6.42246i | 0.0317719 | + | 0.741601i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.271267 | + | 0.227620i | 0.0309137 | + | 0.0259397i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.961498 | + | 0.349957i | 0.108177 | + | 0.0393732i | 0.395542 | − | 0.918448i | \(-0.370557\pi\) |
−0.287365 | + | 0.957821i | \(0.592779\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.0294179 | − | 8.99995i | 0.00326866 | − | 0.999995i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.77701 | − | 2.83060i | −0.853637 | − | 0.310699i | −0.122115 | − | 0.992516i | \(-0.538968\pi\) |
−0.731522 | + | 0.681817i | \(0.761190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.94309 | + | 4.98685i | 0.644619 | + | 0.540900i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.199517 | + | 4.65702i | 0.0213905 | + | 0.499285i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.70362 | − | 6.41486i | −0.392583 | − | 0.679973i | 0.600207 | − | 0.799845i | \(-0.295085\pi\) |
−0.992789 | + | 0.119872i | \(0.961752\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.11967 | + | 1.93933i | −0.117373 | + | 0.203297i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.90081 | + | 12.3366i | −0.404495 | + | 1.27925i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.87679 | − | 1.41104i | 0.397750 | − | 0.144769i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.66356 | − | 9.43453i | −0.168909 | − | 0.957931i | −0.944942 | − | 0.327238i | \(-0.893882\pi\) |
0.776033 | − | 0.630693i | \(-0.217229\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.46604 | − | 1.73275i | −0.247846 | − | 0.174148i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.904353 | − | 0.758842i | 0.0899865 | − | 0.0755076i | −0.596685 | − | 0.802476i | \(-0.703516\pi\) |
0.686671 | + | 0.726968i | \(0.259071\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.55362 | − | 8.81102i | 0.153083 | − | 0.868176i | −0.807435 | − | 0.589957i | \(-0.799145\pi\) |
0.960518 | − | 0.278219i | \(-0.0897441\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.422336 | − | 0.549469i | 0.0412158 | − | 0.0536227i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.43537 | 0.718804 | 0.359402 | − | 0.933183i | \(-0.382981\pi\) | ||||
0.359402 | + | 0.933183i | \(0.382981\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.1862 | −1.16723 | −0.583613 | − | 0.812032i | \(-0.698361\pi\) | ||||
−0.583613 | + | 0.812032i | \(0.698361\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.93586 | − | 0.256470i | −0.183744 | − | 0.0243431i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.233045 | + | 1.32166i | −0.0219230 | + | 0.124332i | −0.993805 | − | 0.111136i | \(-0.964551\pi\) |
0.971882 | + | 0.235468i | \(0.0756622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.227455 | + | 0.190858i | −0.0212103 | + | 0.0177976i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.08310 | − | 17.2606i | 0.747283 | − | 1.59574i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.418314 | + | 2.37238i | 0.0383468 | + | 0.217475i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.38818 | − | 3.41702i | 0.853471 | − | 0.310638i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.22903 | + | 2.43655i | 0.200985 | + | 0.219697i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.94443 | − | 8.56400i | 0.442243 | − | 0.765987i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.94881 | + | 8.57158i | 0.439136 | + | 0.760605i | 0.997623 | − | 0.0689078i | \(-0.0219514\pi\) |
−0.558487 | + | 0.829513i | \(0.688618\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.97871 | + | 5.70976i | −0.790532 | + | 0.502717i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.99616 | + | 7.54867i | 0.785998 | + | 0.659530i | 0.944751 | − | 0.327788i | \(-0.106303\pi\) |
−0.158754 | + | 0.987318i | \(0.550748\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.20377 | + | 0.438138i | 0.104381 | + | 0.0379914i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.18143 | + | 4.96694i | −0.273814 | + | 0.427486i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.84492 | + | 2.85532i | 0.670237 | + | 0.243946i | 0.654650 | − | 0.755932i | \(-0.272816\pi\) |
0.0155870 | + | 0.999879i | \(0.495038\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.5541 | + | 12.2123i | 1.23446 | + | 1.03584i | 0.997936 | + | 0.0642116i | \(0.0204533\pi\) |
0.236526 | + | 0.971625i | \(0.423991\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.1652 | + | 8.95347i | 1.44557 | + | 0.754018i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.19133 | − | 5.52754i | −0.266872 | − | 0.462237i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.52747 | − | 2.64566i | 0.126850 | − | 0.219710i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.6290 | + | 2.56811i | −0.959142 | + | 0.211814i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.08932 | − | 2.94427i | 0.662703 | − | 0.241204i | 0.0112999 | − | 0.999936i | \(-0.496403\pi\) |
0.651403 | + | 0.758732i | \(0.274181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.46966 | + | 19.6774i | 0.282357 | + | 1.60133i | 0.714575 | + | 0.699559i | \(0.246620\pi\) |
−0.432218 | + | 0.901769i | \(0.642269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.27425 | − | 19.8132i | −0.426398 | − | 1.60181i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.49591 | − | 5.45072i | 0.521764 | − | 0.437812i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.97900 | + | 11.2234i | −0.157941 | + | 0.895729i | 0.798106 | + | 0.602517i | \(0.205835\pi\) |
−0.956047 | + | 0.293212i | \(0.905276\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.75297 | − | 13.9211i | −0.456240 | − | 1.10401i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0921967 | −0.00726612 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.60010 | 0.438633 | 0.219317 | − | 0.975654i | \(-0.429617\pi\) | ||||
0.219317 | + | 0.975654i | \(0.429617\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.754418 | + | 1.82555i | 0.0587314 | + | 0.142118i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.66909 | − | 15.1372i | 0.206541 | − | 1.17135i | −0.688457 | − | 0.725278i | \(-0.741711\pi\) |
0.894997 | − | 0.446072i | \(-0.147177\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.9610 | − | 17.5883i | 1.61238 | − | 1.35295i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.5270 | − | 2.83914i | −0.805016 | − | 0.217114i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.450506 | − | 2.55495i | −0.0342514 | − | 0.194249i | 0.962881 | − | 0.269926i | \(-0.0869993\pi\) |
−0.997132 | + | 0.0756771i | \(0.975888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.22929 | − | 0.447426i | 0.0929258 | − | 0.0338222i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.9278 | − | 2.85493i | 0.971710 | − | 0.214590i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.80474 | + | 3.12590i | −0.134893 | + | 0.233641i | −0.925556 | − | 0.378610i | \(-0.876402\pi\) |
0.790664 | + | 0.612250i | \(0.209736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.28962 | − | 9.16189i | −0.393174 | − | 0.680998i | 0.599692 | − | 0.800231i | \(-0.295290\pi\) |
−0.992866 | + | 0.119233i | \(0.961956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.899626 | − | 0.469250i | −0.0665022 | − | 0.0346880i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.980400 | + | 0.822653i | 0.0720804 | + | 0.0604826i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.45207 | − | 2.34836i | −0.471822 | − | 0.171729i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.74810 | + | 0.546466i | −0.127156 | + | 0.0397496i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.5529 | + | 6.75272i | 1.34244 | + | 0.488610i | 0.910581 | − | 0.413330i | \(-0.135634\pi\) |
0.431863 | + | 0.901939i | \(0.357857\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.305206 | − | 0.256098i | −0.0219692 | − | 0.0184343i | 0.631737 | − | 0.775183i | \(-0.282342\pi\) |
−0.653706 | + | 0.756749i | \(0.726787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.5405 | + | 6.70296i | −0.754824 | + | 0.480009i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.80979 | − | 6.59874i | −0.271436 | − | 0.470141i | 0.697794 | − | 0.716299i | \(-0.254165\pi\) |
−0.969230 | + | 0.246158i | \(0.920832\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.53510 | + | 16.5153i | −0.675925 | + | 1.17074i | 0.300272 | + | 0.953853i | \(0.402922\pi\) |
−0.976198 | + | 0.216883i | \(0.930411\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.5550 | − | 13.7239i | −0.885563 | − | 0.968009i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.891380 | − | 0.324436i | 0.0625626 | − | 0.0227709i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.375826 | − | 2.13142i | −0.0262489 | − | 0.148865i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.781828 | − | 0.0671137i | 0.0543408 | − | 0.00466473i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.79701 | + | 2.34697i | −0.193473 | + | 0.162343i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.95089 | + | 22.4066i | −0.271990 | + | 1.54253i | 0.476372 | + | 0.879244i | \(0.341951\pi\) |
−0.748363 | + | 0.663290i | \(0.769160\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.1958 | + | 2.27817i | 1.17824 | + | 0.156098i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.97359 | 0.475595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.63305 | 0.178743 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.27721 | − | 6.86577i | 0.356601 | − | 0.463945i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.53982 | − | 42.7604i | 0.507183 | − | 2.87638i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8621 | − | 14.9881i | 1.19613 | − | 1.00368i | 0.196403 | − | 0.980523i | \(-0.437074\pi\) |
0.999732 | − | 0.0231532i | \(-0.00737055\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.0987 | + | 4.68903i | −0.673247 | + | 0.312602i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.94722 | − | 28.0571i | −0.328358 | − | 1.86221i | −0.484940 | − | 0.874547i | \(-0.661159\pi\) |
0.156582 | − | 0.987665i | \(-0.449952\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.0057 | + | 4.73367i | −0.859438 | + | 0.312810i | −0.733882 | − | 0.679277i | \(-0.762294\pi\) |
−0.125556 | + | 0.992087i | \(0.540071\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.184914 | + | 0.584805i | −0.0121664 | + | 0.0384774i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.0225 | + | 24.2877i | −0.918644 | + | 1.59114i | −0.117167 | + | 0.993112i | \(0.537381\pi\) |
−0.801477 | + | 0.598026i | \(0.795952\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.34412 | − | 10.9883i | −0.413845 | − | 0.716801i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.0758573 | + | 1.77062i | 0.00492746 | + | 0.115014i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.59901 | − | 7.21542i | −0.556224 | − | 0.466727i | 0.320818 | − | 0.947141i | \(-0.396042\pi\) |
−0.877042 | + | 0.480414i | \(0.840487\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.1216 | + | 5.50382i | 0.974070 | + | 0.354533i | 0.779532 | − | 0.626362i | \(-0.215457\pi\) |
0.194538 | + | 0.980895i | \(0.437679\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.4261 | − | 5.90655i | 0.925435 | − | 0.378905i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.33439 | + | 2.66950i | 0.468577 | + | 0.170548i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.6877 | − | 14.8418i | −1.12544 | − | 0.944359i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.613566 | − | 14.3215i | −0.0388832 | − | 0.907589i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.38678 | + | 4.13402i | 0.150652 | + | 0.260937i | 0.931467 | − | 0.363825i | \(-0.118529\pi\) |
−0.780815 | + | 0.624762i | \(0.785196\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.131391 | − | 0.227576i | 0.00826050 | − | 0.0143076i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.05121 | + | 12.8123i | −0.253697 | + | 0.802337i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.7312 | − | 8.27347i | 1.41793 | − | 0.516085i | 0.484484 | − | 0.874800i | \(-0.339007\pi\) |
0.933447 | + | 0.358715i | \(0.116785\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0690069 | + | 0.391358i | 0.00428788 | + | 0.0243178i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.32273 | + | 3.40009i | −0.453266 | + | 0.210460i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.1834 | + | 20.2923i | −1.49121 | + | 1.25128i | −0.598116 | + | 0.801409i | \(0.704084\pi\) |
−0.893096 | + | 0.449866i | \(0.851472\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.71426 | + | 9.72207i | −0.105306 | + | 0.597222i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.81855 | − | 10.1721i | 0.478487 | − | 0.622523i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.7911 | −1.32863 | −0.664314 | − | 0.747454i | \(-0.731276\pi\) | ||||
−0.664314 | + | 0.747454i | \(0.731276\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.92553 | −0.359950 | −0.179975 | − | 0.983671i | \(-0.557602\pi\) | ||||
−0.179975 | + | 0.983671i | \(0.557602\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.84506 | − | 0.509408i | −0.232714 | − | 0.0308308i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.647472 | + | 3.67200i | −0.0390440 | + | 0.221430i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0419 | − | 11.7826i | 0.843696 | − | 0.707945i | −0.114696 | − | 0.993401i | \(-0.536589\pi\) |
0.958392 | + | 0.285456i | \(0.0921449\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.3283 | + | 1.91671i | −1.33676 | + | 0.114750i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.13446 | + | 29.1190i | 0.306296 | + | 1.73709i | 0.617339 | + | 0.786697i | \(0.288211\pi\) |
−0.311043 | + | 0.950396i | \(0.600678\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.5780 | − | 8.21771i | 1.34212 | − | 0.488492i | 0.431641 | − | 0.902046i | \(-0.357935\pi\) |
0.910480 | + | 0.413554i | \(0.135713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.82328 | + | 5.27233i | 0.285706 | + | 0.312306i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.336016 | − | 0.581997i | 0.0198344 | − | 0.0343542i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8546 | − | 25.7289i | −0.873798 | − | 1.51346i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0018 | − | 8.90406i | 0.820801 | − | 0.521966i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.6795 | − | 9.80023i | −0.682321 | − | 0.572536i | 0.234362 | − | 0.972149i | \(-0.424700\pi\) |
−0.916684 | + | 0.399614i | \(0.869144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.15354 | − | 2.96764i | −0.474717 | − | 0.172783i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.14237 | − | 5.09376i | 0.0662868 | − | 0.295570i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.56156 | + | 0.568363i | 0.0903076 | + | 0.0328693i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.65876 | + | 1.39186i | 0.0956093 | + | 0.0802257i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.81296 | + | 0.945652i | 0.104152 | + | 0.0543263i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.332495 | + | 0.575898i | 0.0190386 | + | 0.0329758i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.4109 | − | 23.2284i | 0.765401 | − | 1.32571i | −0.174633 | − | 0.984634i | \(-0.555874\pi\) |
0.940034 | − | 0.341080i | \(-0.110793\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.1320 | − | 3.34171i | 0.860828 | − | 0.190103i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.5687 | + | 8.57831i | −1.33646 | + | 0.486431i | −0.908696 | − | 0.417459i | \(-0.862921\pi\) |
−0.427763 | + | 0.903891i | \(0.640698\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.87988 | + | 16.3326i | 0.162780 | + | 0.923174i | 0.951323 | + | 0.308194i | \(0.0997247\pi\) |
−0.788543 | + | 0.614980i | \(0.789164\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.15895 | + | 0.312569i | 0.0652992 | + | 0.0176113i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.64434 | − | 5.57526i | 0.373183 | − | 0.313138i | −0.436836 | − | 0.899541i | \(-0.643901\pi\) |
0.810019 | + | 0.586403i | \(0.199457\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.469492 | + | 2.66262i | −0.0262865 | + | 0.149078i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.91864 | + | 11.9021i | 0.274532 | + | 0.664313i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.8387 | −1.38206 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.5792 | −1.30794 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.06141 | − | 19.5070i | −0.445797 | − | 1.07874i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.684140 | − | 3.87995i | 0.0377179 | − | 0.213909i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.43549 | − | 2.04362i | 0.133866 | − | 0.112327i | −0.573396 | − | 0.819278i | \(-0.694374\pi\) |
0.707262 | + | 0.706951i | \(0.249930\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.870064 | − | 3.26848i | −0.0476792 | − | 0.179112i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.11685 | + | 12.0052i | 0.115656 | + | 0.655916i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.1370 | + | 4.05355i | −0.606674 | + | 0.220811i | −0.627047 | − | 0.778981i | \(-0.715737\pi\) |
0.0203735 | + | 0.999792i | \(0.493514\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.26982 | + | 0.501260i | −0.123279 | + | 0.0272247i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.75241 | + | 6.49937i | −0.203204 | + | 0.351960i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.44544 | + | 4.23563i | 0.132042 | + | 0.228703i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.455981 | − | 0.237842i | −0.0245492 | − | 0.0128050i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.0597 | + | 12.6366i | 0.808449 | + | 0.678369i | 0.950237 | − | 0.311528i | \(-0.100841\pi\) |
−0.141788 | + | 0.989897i | \(0.545285\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.8103 | + | 4.29860i | 0.632192 | + | 0.230099i | 0.638185 | − | 0.769883i | \(-0.279686\pi\) |
−0.00599329 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.9769 | + | 1.52081i | 1.76018 | + | 0.0811748i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.8715 | + | 9.05249i | 1.32378 | + | 0.481815i | 0.904667 | − | 0.426120i | \(-0.140120\pi\) |
0.419110 | + | 0.907935i | \(0.362342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.70869 | − | 7.30746i | −0.462209 | − | 0.387840i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.52085 | + | 2.23899i | −0.186343 | + | 0.118500i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.48467 | − | 6.03563i | −0.183914 | − | 0.318549i | 0.759296 | − | 0.650745i | \(-0.225543\pi\) |
−0.943210 | + | 0.332197i | \(0.892210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.89570 | − | 5.01550i | 0.152405 | − | 0.263973i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.6802 | + | 12.7677i | 0.613054 | + | 0.670129i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.33308 | + | 1.94108i | −0.279146 | + | 0.101601i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.91583 | + | 16.5365i | 0.152205 | + | 0.863197i | 0.961297 | + | 0.275515i | \(0.0888483\pi\) |
−0.809092 | + | 0.587682i | \(0.800041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.42576 | + | 5.17994i | −0.126280 | + | 0.269657i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.34820 | + | 1.97037i | −0.121912 | + | 0.102297i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.03231 | + | 17.1971i | −0.157007 | + | 0.890431i | 0.799921 | + | 0.600105i | \(0.204875\pi\) |
−0.956928 | + | 0.290326i | \(0.906236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.9796 | + | 2.24953i | 0.876825 | + | 0.116165i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.0976 | −0.880572 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5959 | 0.749743 | 0.374871 | − | 0.927077i | \(-0.377687\pi\) | ||||
0.374871 | + | 0.927077i | \(0.377687\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.4472 | + | 13.5921i | −0.535227 | + | 0.696342i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.16033 | + | 17.9231i | −0.161485 | + | 0.915829i | 0.791129 | + | 0.611649i | \(0.209494\pi\) |
−0.952615 | + | 0.304180i | \(0.901618\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.307932 | − | 0.258386i | 0.0156937 | − | 0.0131685i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.0795 | − | 10.5955i | −0.766533 | − | 0.538601i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.49255 | + | 31.1498i | 0.278483 | + | 1.57936i | 0.727675 | + | 0.685922i | \(0.240601\pi\) |
−0.449191 | + | 0.893436i | \(0.648288\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.67985 | − | 0.611416i | 0.0849538 | − | 0.0309206i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.13239 | + | 19.3942i | −0.309338 | + | 0.978306i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.580752 | − | 1.00589i | 0.0292208 | − | 0.0506119i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.80621 | − | 10.0566i | −0.291405 | − | 0.504729i | 0.682737 | − | 0.730664i | \(-0.260789\pi\) |
−0.974142 | + | 0.225936i | \(0.927456\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0949717 | + | 2.21678i | 0.00475453 | + | 0.110978i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.8708 | − | 18.3517i | −1.09217 | − | 0.916442i | −0.0952991 | − | 0.995449i | \(-0.530381\pi\) |
−0.996874 | + | 0.0790065i | \(0.974825\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −44.5968 | − | 16.2319i | −2.22152 | − | 0.808569i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.0554 | − | 1.80695i | −0.499656 | − | 0.0897879i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.06436 | − | 0.387396i | −0.0527585 | − | 0.0192025i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.2607 | + | 19.5181i | 1.15017 | + | 0.965106i | 0.999724 | − | 0.0235126i | \(-0.00748497\pi\) |
0.150445 | + | 0.988618i | \(0.451929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.618924 | + | 14.4466i | 0.0305293 | + | 0.712597i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.34711 | − | 2.33327i | −0.0662870 | − | 0.114812i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.69737 | + | 8.13608i | −0.230585 | + | 0.399384i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.92105 | + | 31.3761i | −0.485836 | + | 1.53650i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.7518 | − | 9.00893i | 1.20921 | − | 0.440115i | 0.342778 | − | 0.939417i | \(-0.388632\pi\) |
0.866428 | + | 0.499301i | \(0.166410\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.58090 | + | 14.6370i | 0.125785 | + | 0.713364i | 0.980838 | + | 0.194823i | \(0.0624134\pi\) |
−0.855053 | + | 0.518541i | \(0.826476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.97714 | + | 33.4000i | −0.144753 | + | 1.62396i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.4309 | + | 16.3045i | −0.942539 | + | 0.790884i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0358557 | + | 0.203348i | −0.00173518 | + | 0.00984069i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.73708 | − | 8.76509i | 0.325269 | − | 0.423183i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.4640 | 0.648537 | 0.324269 | − | 0.945965i | \(-0.394882\pi\) | ||||
0.324269 | + | 0.945965i | \(0.394882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.7619 | −0.757469 | −0.378734 | − | 0.925505i | \(-0.623641\pi\) | ||||
−0.378734 | + | 0.925505i | \(0.623641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.24549 | + | 0.694943i | 0.251502 | + | 0.0333200i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.165076 | − | 0.936190i | 0.00789664 | − | 0.0447841i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.3515 | − | 13.7205i | 0.780412 | − | 0.654844i | −0.162940 | − | 0.986636i | \(-0.552098\pi\) |
0.943352 | + | 0.331792i | \(0.107653\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.8037 | − | 16.9162i | −0.562081 | − | 0.805533i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.06776 | + | 11.7268i | 0.0982421 | + | 0.557158i | 0.993706 | + | 0.112023i | \(0.0357332\pi\) |
−0.895464 | + | 0.445135i | \(0.853156\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.90132 | + | 2.87585i | −0.374559 | + | 0.136328i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0643 | + | 11.0013i | 0.476024 | + | 0.520342i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.25423 | − | 14.2967i | 0.389541 | − | 0.674705i | −0.602847 | − | 0.797857i | \(-0.705967\pi\) |
0.992388 | + | 0.123152i | \(0.0393002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.957726 | + | 1.65883i | 0.0450976 | + | 0.0781113i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −29.2034 | + | 18.5711i | −1.37209 | + | 0.872545i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.94730 | + | 1.63398i | 0.0912907 | + | 0.0766020i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.23844 | + | 2.27061i | 0.291822 | + | 0.106214i | 0.483783 | − | 0.875188i | \(-0.339262\pi\) |
−0.191961 | + | 0.981403i | \(0.561485\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.2270 | − | 21.5496i | 1.31752 | − | 1.00585i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.95197 | + | 3.62222i | 0.463510 | + | 0.168704i | 0.563210 | − | 0.826314i | \(-0.309566\pi\) |
−0.0997004 | + | 0.995017i | \(0.531788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.2070 | − | 15.2775i | −0.846150 | − | 0.710004i | 0.112788 | − | 0.993619i | \(-0.464022\pi\) |
−0.958938 | + | 0.283615i | \(0.908466\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.0224 | + | 6.79256i | 0.603899 | + | 0.314997i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.0232 | + | 19.0928i | 0.510095 | + | 0.883510i | 0.999932 | + | 0.0116961i | \(0.00372307\pi\) |
−0.489837 | + | 0.871814i | \(0.662944\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.89261 | + | 3.27810i | −0.0873928 | + | 0.151369i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.2751 | + | 4.25665i | −0.888148 | + | 0.196136i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.79958 | + | 2.11087i | −0.266665 | + | 0.0970581i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.34227 | + | 13.2837i | 0.107471 | + | 0.609497i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.4784 | − | 18.4181i | 0.846068 | − | 0.843307i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.69074 | − | 4.77510i | 0.260016 | − | 0.218180i | −0.503455 | − | 0.864022i | \(-0.667938\pi\) |
0.763471 | + | 0.645842i | \(0.223493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.24380 | − | 7.05395i | 0.0567125 | − | 0.321633i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0609899 | − | 0.147584i | −0.00277514 | − | 0.00671529i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.8749 | −0.493805 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.1968 | −1.59492 | −0.797460 | − | 0.603372i | \(-0.793823\pi\) | ||||
−0.797460 | + | 0.603372i | \(0.793823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.70457 | + | 8.96434i | 0.167527 | + | 0.405381i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.89179 | − | 10.7289i | 0.0853751 | − | 0.484186i | −0.911900 | − | 0.410413i | \(-0.865385\pi\) |
0.997275 | − | 0.0737736i | \(-0.0235042\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.0897 | + | 11.8226i | −0.634567 | + | 0.532465i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.42317 | + | 2.41527i | −0.108914 | + | 0.108558i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.612975 | − | 3.47635i | −0.0274957 | − | 0.155936i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.12558 | + | 2.22953i | −0.274219 | + | 0.0998074i | −0.475469 | − | 0.879732i | \(-0.657722\pi\) |
0.201251 | + | 0.979540i | \(0.435499\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.9964 | − | 5.74099i | 1.16144 | − | 0.256489i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.05531 | + | 1.82784i | −0.0470537 | + | 0.0814995i | −0.888593 | − | 0.458696i | \(-0.848317\pi\) |
0.841539 | + | 0.540196i | \(0.181650\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.670057 | − | 1.16057i | −0.0298171 | − | 0.0516448i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 42.0206 | + | 21.9182i | 1.86620 | + | 0.973421i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.2708 | + | 22.0438i | 1.16443 | + | 0.977076i | 0.999957 | − | 0.00930502i | \(-0.00296192\pi\) |
0.164477 | + | 0.986381i | \(0.447406\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.65596 | − | 0.602722i | −0.0732556 | − | 0.0266628i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.41904 | − | 18.7291i | −0.106803 | − | 0.826912i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.54374 | − | 3.47364i | −0.420547 | − | 0.153067i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.60221 | + | 7.21811i | 0.378325 | + | 0.317452i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.79181 | − | 2.41129i | 0.166442 | − | 0.105844i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.72026 | + | 8.17573i | 0.206798 | + | 0.358185i | 0.950704 | − | 0.310099i | \(-0.100362\pi\) |
−0.743906 | + | 0.668284i | \(0.767029\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.9783 | − | 22.4791i | 0.567502 | − | 0.982942i | −0.429311 | − | 0.903157i | \(-0.641243\pi\) |
0.996812 | − | 0.0797847i | \(-0.0254233\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.52942 | + | 1.67181i | 0.0667493 | + | 0.0729636i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −47.9750 | + | 17.4615i | −2.08982 | + | 0.760634i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.98203 | − | 22.5832i | −0.173132 | − | 0.981878i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.1220 | + | 18.8055i | 0.569446 | + | 0.816088i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.27904 | + | 7.78604i | −0.401920 | + | 0.337251i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.46565 | − | 8.31212i | 0.0633656 | − | 0.359364i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.19765 | − | 0.821088i | −0.267448 | − | 0.0354326i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.90769 | −0.297535 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.8373 | −1.36879 | −0.684396 | − | 0.729110i | \(-0.739934\pi\) | ||||
−0.684396 | + | 0.729110i | \(0.739934\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.1667 | − | 14.5281i | 0.479208 | − | 0.623461i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.40213 | + | 13.6231i | −0.102896 | + | 0.583551i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.2687 | − | 26.2376i | 1.33695 | − | 1.12184i | 0.354558 | − | 0.935034i | \(-0.384631\pi\) |
0.982397 | − | 0.186804i | \(-0.0598130\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.156031 | − | 1.75049i | 0.00665926 | − | 0.0747092i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.69842 | + | 9.63221i | 0.0723550 | + | 0.410346i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.338906 | − | 0.123352i | 0.0144118 | − | 0.00524545i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.668306 | + | 2.11357i | −0.0283680 | + | 0.0897162i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.989874 | + | 1.71451i | −0.0419423 | + | 0.0726462i | −0.886234 | − | 0.463237i | \(-0.846688\pi\) |
0.844292 | + | 0.535883i | \(0.180021\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.5145 | − | 33.8001i | −0.825376 | − | 1.42959i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.509035 | − | 11.8816i | −0.0214915 | − | 0.501642i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.7427 | − | 15.7270i | −0.789912 | − | 0.662815i | 0.155812 | − | 0.987787i | \(-0.450201\pi\) |
−0.945724 | + | 0.324972i | \(0.894645\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.43157 | + | 0.521050i | 0.0602267 | + | 0.0219207i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.03116 | − | 2.43677i | −0.0853006 | − | 0.102335i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.8514 | − | 5.76944i | −0.664526 | − | 0.241868i | −0.0123366 | − | 0.999924i | \(-0.503927\pi\) |
−0.652189 | + | 0.758056i | \(0.726149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.5783 | − | 10.5544i | −0.526384 | − | 0.441689i | 0.340467 | − | 0.940257i | \(-0.389415\pi\) |
−0.866851 | + | 0.498568i | \(0.833859\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.46373 | + | 34.1656i | 0.0611483 | + | 1.42729i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.485392 | − | 0.840724i | −0.0202423 | − | 0.0350606i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.17077 | + | 15.8842i | −0.381784 | + | 0.661270i | −0.991317 | − | 0.131491i | \(-0.958024\pi\) |
0.609533 | + | 0.792761i | \(0.291357\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.208049 | − | 0.657971i | 0.00864621 | − | 0.0273443i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.74122 | + | 0.997722i | −0.113725 | + | 0.0413925i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.51716 | − | 8.60425i | −0.0628344 | − | 0.356352i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.7025 | − | 12.4386i | −0.731909 | − | 0.514273i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.7449 | + | 13.2116i | −0.649863 | + | 0.545300i | −0.907029 | − | 0.421067i | \(-0.861656\pi\) |
0.257166 | + | 0.966367i | \(0.417211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.71441 | + | 26.7367i | −0.194254 | + | 1.10167i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.04267 | − | 10.4637i | 0.330831 | − | 0.430419i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.4370 | −0.921375 | −0.460688 | − | 0.887562i | \(-0.652397\pi\) | ||||
−0.460688 | + | 0.887562i | \(0.652397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.73457 | 0.112107 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.7444 | − | 4.33811i | −1.34014 | − | 0.177547i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.17302 | + | 29.3377i | −0.211364 | + | 1.19871i | 0.675742 | + | 0.737139i | \(0.263824\pi\) |
−0.887106 | + | 0.461566i | \(0.847288\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0367 | − | 11.7782i | 0.572569 | − | 0.480442i | −0.309928 | − | 0.950760i | \(-0.600305\pi\) |
0.882497 | + | 0.470318i | \(0.155861\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.6631 | − | 29.1760i | 0.556405 | − | 1.18814i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.96935 | − | 11.1688i | −0.0800656 | − | 0.454074i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.6293 | − | 7.14448i | 0.796729 | − | 0.289985i | 0.0885984 | − | 0.996067i | \(-0.471761\pi\) |
0.708130 | + | 0.706082i | \(0.249539\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.10900 | + | 1.21225i | 0.0449391 | + | 0.0491230i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.5061 | + | 61.4984i | −1.43642 | + | 2.48796i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.3880 | + | 23.1887i | 0.540737 | + | 0.936584i | 0.998862 | + | 0.0476964i | \(0.0151880\pi\) |
−0.458125 | + | 0.888888i | \(0.651479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.16324 | − | 2.01158i | 0.127554 | − | 0.0811146i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.19155 | + | 6.03443i | 0.289521 | + | 0.242937i | 0.775967 | − | 0.630774i | \(-0.217262\pi\) |
−0.486446 | + | 0.873711i | \(0.661707\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.1099 | − | 16.7826i | −1.85331 | − | 0.674551i | −0.983428 | − | 0.181298i | \(-0.941970\pi\) |
−0.869886 | − | 0.493254i | \(-0.835807\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.624627 | + | 1.20711i | 0.0250654 | + | 0.0484397i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.45343 | − | 0.892974i | −0.0982945 | − | 0.0357763i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.61632 | + | 4.71266i | 0.224653 | + | 0.188506i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.60719 | − | 2.92474i | −0.223930 | − | 0.116803i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.85268 | − | 6.67303i | −0.153616 | − | 0.266071i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.91387 | − | 8.51108i | 0.195618 | − | 0.338821i | −0.751485 | − | 0.659750i | \(-0.770662\pi\) |
0.947103 | + | 0.320930i | \(0.103995\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −38.4809 | + | 8.49802i | −1.52948 | + | 0.337766i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.5578 | − | 3.84273i | 0.418974 | − | 0.152494i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.58544 | − | 43.0191i | −0.300546 | − | 1.70448i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.72861 | + | 29.0333i | 0.305739 | + | 1.14854i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5954 | − | 13.0861i | 0.615982 | − | 0.516870i | −0.280556 | − | 0.959838i | \(-0.590519\pi\) |
0.896538 | + | 0.442968i | \(0.146074\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.22411 | − | 6.94226i | 0.0482741 | − | 0.273776i | −0.951111 | − | 0.308851i | \(-0.900056\pi\) |
0.999385 | + | 0.0350744i | \(0.0111668\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.61316 | + | 11.1629i | 0.181643 | + | 0.439541i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.2433 | −1.26762 | −0.633808 | − | 0.773491i | \(-0.718509\pi\) | ||||
−0.633808 | + | 0.773491i | \(0.718509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.67917 | 0.301434 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.74181 | + | 4.21485i | 0.0682671 | + | 0.165193i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.63666 | − | 26.2958i | 0.181447 | − | 1.02903i | −0.748990 | − | 0.662581i | \(-0.769461\pi\) |
0.930436 | − | 0.366453i | \(-0.119428\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.2121 | − | 8.56896i | 0.399019 | − | 0.334817i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.4813 | + | 3.90564i | 0.564970 | + | 0.152373i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.373461 | + | 2.11800i | 0.0145480 | + | 0.0825057i | 0.991217 | − | 0.132243i | \(-0.0422179\pi\) |
−0.976669 | + | 0.214749i | \(0.931107\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.7031 | − | 10.4471i | 1.11642 | − | 0.406344i | 0.283077 | − | 0.959097i | \(-0.408645\pi\) |
0.833345 | + | 0.552753i | \(0.186423\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 73.4364 | − | 16.2175i | 2.85203 | − | 0.629836i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.727088 | − | 1.25935i | 0.0281953 | − | 0.0488357i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.351966 | − | 0.609622i | −0.0136282 | − | 0.0236047i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 35.8083 | + | 18.6778i | 1.38443 | + | 0.722126i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.450841 | − | 0.378300i | −0.0174045 | − | 0.0146041i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.282579 | + | 0.102850i | 0.0108926 | + | 0.00396459i | 0.347461 | − | 0.937695i | \(-0.387044\pi\) |
−0.336568 | + | 0.941659i | \(0.609266\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.1864 | − | 13.0636i | −0.546036 | − | 0.502818i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.0992 | − | 5.49567i | −0.580311 | − | 0.211216i | 0.0351518 | − | 0.999382i | \(-0.488809\pi\) |
−0.615463 | + | 0.788166i | \(0.711031\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.58675 | − | 2.17054i | −0.0992702 | − | 0.0832976i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41.6396 | − | 26.4795i | 1.59563 | − | 1.01470i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.62750 | − | 4.55097i | −0.100539 | − | 0.174138i | 0.811368 | − | 0.584536i | \(-0.198723\pi\) |
−0.911907 | + | 0.410398i | \(0.865390\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.73839 | − | 8.20713i | 0.181044 | − | 0.313578i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.1809 | − | 17.6874i | −0.617340 | − | 0.674815i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 51.9188 | − | 18.8969i | 1.97795 | − | 0.719915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.725322 | − | 4.11351i | −0.0275926 | − | 0.156485i | 0.967898 | − | 0.251342i | \(-0.0808718\pi\) |
−0.995491 | + | 0.0948567i | \(0.969761\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.05845 | + | 0.0908595i | −0.0402072 | + | 0.00345147i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.5212 | − | 13.8630i | 0.626687 | − | 0.525853i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.26272 | + | 12.8325i | −0.0857066 | + | 0.486066i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −48.1546 | − | 6.37971i | −1.82137 | − | 0.241303i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.8425 | 1.35375 | 0.676877 | − | 0.736096i | \(-0.263333\pi\) | ||||
0.676877 | + | 0.736096i | \(0.263333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.09751 | −0.154540 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.3928 | − | 17.4243i | 0.504402 | − | 0.656239i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0722579 | − | 0.409795i | 0.00271754 | − | 0.0154119i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.9098 | − | 24.2582i | 1.08573 | − | 0.911035i | 0.0893450 | − | 0.996001i | \(-0.471523\pi\) |
0.996384 | + | 0.0849661i | \(0.0270782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.78413 | + | 1.29273i | −0.104413 | + | 0.0484811i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.339299 | − | 1.92426i | −0.0127069 | − | 0.0720642i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.80840 | + | 2.47806i | −0.254620 | + | 0.0926740i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.86166 | − | 18.5380i | 0.218908 | − | 0.692314i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.2562 | − | 38.5488i | 0.830015 | − | 1.43763i | −0.0680099 | − | 0.997685i | \(-0.521665\pi\) |
0.898025 | − | 0.439944i | \(-0.145002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.57680 | − | 2.73109i | −0.0587230 | − | 0.101711i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.19302 | + | 27.8468i | 0.0443689 | + | 1.03563i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.65136 | + | 6.42025i | 0.284164 | + | 0.238442i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.2017 | − | 4.44107i | −0.452537 | − | 0.164710i | 0.105688 | − | 0.994399i | \(-0.466295\pi\) |
−0.558226 | + | 0.829689i | \(0.688518\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.9980 | + | 19.1853i | 0.703631 | + | 0.710565i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.4535 | − | 14.3599i | −1.45924 | − | 0.531120i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.8200 | − | 32.5738i | −1.43385 | − | 1.20314i | −0.943393 | − | 0.331677i | \(-0.892386\pi\) |
−0.490456 | − | 0.871466i | \(-0.663170\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.578646 | + | 13.5064i | 0.0213437 | + | 0.498192i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.39440 | − | 9.34338i | −0.198705 | − | 0.344168i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.4350 | + | 26.7342i | −0.567786 | + | 0.983435i | 0.428998 | + | 0.903305i | \(0.358867\pi\) |
−0.996784 | + | 0.0801296i | \(0.974467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0571 | − | 38.1317i | 0.442930 | − | 1.40080i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.8293 | − | 7.58126i | 0.764155 | − | 0.278130i | 0.0696052 | − | 0.997575i | \(-0.477826\pi\) |
0.694549 | + | 0.719445i | \(0.255604\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.69689 | − | 9.62355i | −0.0621693 | − | 0.352580i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.5192 | − | 10.4561i | 0.823936 | − | 0.382570i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.00765 | − | 1.68462i | 0.0733578 | − | 0.0615545i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.16179 | − | 40.6165i | 0.261337 | − | 1.48212i | −0.517929 | − | 0.855424i | \(-0.673297\pi\) |
0.779266 | − | 0.626693i | \(-0.215592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.03863 | + | 6.55537i | −0.183618 | + | 0.238891i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.6817 | 0.825470 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.1131 | 1.93043 | 0.965215 | − | 0.261458i | \(-0.0842032\pi\) | ||||
0.965215 | + | 0.261458i | \(0.0842032\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.451210 | + | 0.0597781i | 0.0163779 | + | 0.00216981i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.32415 | − | 7.50962i | 0.0480003 | − | 0.272223i | −0.951356 | − | 0.308093i | \(-0.900309\pi\) |
0.999356 | + | 0.0358700i | \(0.0114202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.29043 | + | 2.76100i | −0.119122 | + | 0.0999550i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −23.1892 | + | 1.99061i | −0.838407 | + | 0.0719706i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.43262 | + | 47.8237i | 0.304484 | + | 1.72682i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.6268 | + | 11.5112i | −1.14049 | + | 0.415104i | −0.842090 | − | 0.539337i | \(-0.818675\pi\) |
−0.298400 | + | 0.954441i | \(0.596453\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.2808 | + | 30.9138i | 1.01851 | + | 1.11333i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.0399 | + | 45.1024i | −0.936590 | + | 1.62222i | −0.164815 | + | 0.986324i | \(0.552703\pi\) |
−0.771774 | + | 0.635896i | \(0.780631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.8624 | + | 24.0103i | 0.497950 | + | 0.862476i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.580816 | + | 0.369353i | −0.0208366 | + | 0.0132505i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.30813 | + | 4.45405i | 0.190184 | + | 0.159583i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.45451 | + | 3.44116i | 0.338309 | + | 0.123134i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.2868 | − | 9.47262i | −0.367620 | − | 0.338524i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.1568 | + | 4.42470i | 0.433894 | + | 0.157924i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.0547 | + | 26.0580i | 1.10698 | + | 0.928868i | 0.997875 | − | 0.0651623i | \(-0.0207565\pi\) |
0.109107 | + | 0.994030i | \(0.465201\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −48.4806 | − | 25.2878i | −1.72595 | − | 0.900269i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.236522 | + | 0.409667i | 0.00840974 | + | 0.0145661i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.86087 | − | 3.22313i | 0.0660815 | − | 0.114457i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.6966 | + | 3.68723i | −0.592167 | + | 0.130773i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.47037 | + | 3.44693i | −0.335458 | + | 0.122097i | −0.504257 | − | 0.863554i | \(-0.668233\pi\) |
0.168799 | + | 0.985651i | \(0.446011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2652 | + | 75.2309i | 0.469290 | + | 2.66148i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.4551 | + | 5.78648i | 0.758079 | + | 0.204455i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.84769 | − | 3.22860i | 0.135782 | − | 0.113935i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0181737 | + | 0.103068i | −0.000640539 | + | 0.00363267i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.4152 | − | 34.8821i | −0.507440 | − | 1.22791i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.5243 | −0.686439 | −0.343219 | − | 0.939255i | \(-0.611517\pi\) | ||||
−0.343219 | + | 0.939255i | \(0.611517\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.4755 | 0.402960 | 0.201480 | − | 0.979493i | \(-0.435425\pi\) | ||||
0.201480 | + | 0.979493i | \(0.435425\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.91985 | − | 9.48528i | −0.137475 | − | 0.332663i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.10388 | − | 6.26044i | 0.0386674 | − | 0.219294i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.1033 | + | 14.3514i | −0.598370 | + | 0.502092i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.72815 | − | 6.49195i | −0.0603863 | − | 0.226847i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.476815 | + | 2.70415i | 0.0166410 | + | 0.0943755i | 0.991997 | − | 0.126261i | \(-0.0402977\pi\) |
−0.975356 | + | 0.220636i | \(0.929187\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.7815 | + | 13.0234i | −1.24726 | + | 0.453967i | −0.879477 | − | 0.475942i | \(-0.842107\pi\) |
−0.367788 | + | 0.929910i | \(0.619885\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.30625 | + | 1.39266i | −0.219556 | + | 0.0484861i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.94797 | + | 3.37399i | −0.0677377 | + | 0.117325i | −0.897905 | − | 0.440189i | \(-0.854911\pi\) |
0.830167 | + | 0.557514i | \(0.188245\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.6323 | − | 23.6118i | −0.473469 | − | 0.820073i | 0.526069 | − | 0.850442i | \(-0.323665\pi\) |
−0.999539 | + | 0.0303686i | \(0.990332\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.1499 | + | 14.6831i | 0.976509 | + | 0.509353i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35.9978 | − | 30.2057i | −1.24725 | − | 1.04657i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.3960 | − | 5.96764i | −0.567406 | − | 0.206519i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.8388 | − | 34.4740i | −0.616597 | − | 1.19160i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.85271 | + | 2.85815i | 0.271106 | + | 0.0986745i | 0.473996 | − | 0.880527i | \(-0.342811\pi\) |
−0.202890 | + | 0.979202i | \(0.565033\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.6672 | − | 13.9854i | −0.574730 | − | 0.482256i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −43.2156 | + | 27.4817i | −1.48842 | + | 0.946522i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.5305 | − | 26.8996i | −0.534265 | − | 0.925374i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.76075 | − | 3.04970i | 0.0604999 | − | 0.104789i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.0902 | + | 30.7054i | 0.964054 | + | 1.05381i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.277116 | − | 0.100862i | 0.00949941 | − | 0.00345750i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.42088 | + | 19.4008i | 0.117129 | + | 0.664270i | 0.985674 | + | 0.168661i | \(0.0539442\pi\) |
−0.868545 | + | 0.495610i | \(0.834945\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.24898 | + | 11.2086i | −0.179511 | + | 0.383326i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.9664 | − | 25.1448i | 1.02363 | − | 0.858930i | 0.0335529 | − | 0.999437i | \(-0.489318\pi\) |
0.990080 | + | 0.140507i | \(0.0448733\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.50602 | + | 8.54104i | −0.0513846 | + | 0.291417i | −0.999661 | − | 0.0260287i | \(-0.991714\pi\) |
0.948277 | + | 0.317445i | \(0.102825\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.15391 | + | 0.152875i | 0.0393252 | + | 0.00520996i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.8525 | 0.641747 | 0.320874 | − | 0.947122i | \(-0.396024\pi\) | ||||
0.320874 | + | 0.947122i | \(0.396024\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.94502 | −0.100134 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.3588 | − | 40.7986i | 1.06500 | − | 1.38559i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.178503 | + | 1.01234i | −0.00605529 | + | 0.0343413i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.2642 | − | 43.8549i | 1.77091 | − | 1.48597i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.5156 | + | 16.5232i | 0.795884 | + | 0.559224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.605267 | − | 3.43264i | −0.0204618 | − | 0.116044i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.2429 | − | 4.45604i | 0.413413 | − | 0.150470i | −0.126936 | − | 0.991911i | \(-0.540514\pi\) |
0.540349 | + | 0.841441i | \(0.318292\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.96151 | − | 25.1789i | 0.268535 | − | 0.849263i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.5155 | − | 28.6057i | 0.556421 | − | 0.963749i | −0.441371 | − | 0.897325i | \(-0.645508\pi\) |
0.997791 | − | 0.0664243i | \(-0.0211591\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.90985 | − | 17.1644i | −0.333493 | − | 0.577627i | 0.649701 | − | 0.760190i | \(-0.274894\pi\) |
−0.983194 | + | 0.182563i | \(0.941561\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.643272 | − | 15.0149i | −0.0216234 | − | 0.504721i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.6197 | − | 13.9456i | −0.558035 | − | 0.468247i | 0.319616 | − | 0.947547i | \(-0.396446\pi\) |
−0.877651 | + | 0.479300i | \(0.840891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.27829 | + | 1.19320i | 0.109950 | + | 0.0400186i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.90951 | − | 1.54098i | 0.298480 | − | 0.0516247i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.1732 | + | 13.8939i | 1.27742 | + | 0.464942i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.13875 | + | 2.63372i | 0.104917 | + | 0.0880356i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.123199 | + | 2.87565i | 0.00411351 | + | 0.0960152i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.0518 | + | 17.4102i | 0.335247 | + | 0.580664i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.7181 | − | 51.4732i | 0.990052 | − | 1.71482i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.13072 | + | 3.57600i | −0.0376281 | + | 0.119002i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.2849 | + | 4.10737i | −0.375123 | + | 0.136534i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.38024 | + | 24.8416i | 0.145443 | + | 0.824850i | 0.967010 | + | 0.254738i | \(0.0819892\pi\) |
−0.821567 | + | 0.570112i | \(0.806900\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.314441 | + | 3.52766i | −0.0104293 | + | 0.117005i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.5370 | + | 13.0371i | −0.514765 | + | 0.431939i | −0.862802 | − | 0.505541i | \(-0.831293\pi\) |
0.348037 | + | 0.937481i | \(0.386848\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.44381 | − | 8.18823i | 0.0477830 | − | 0.270991i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.701915 | + | 0.913208i | −0.0232046 | + | 0.0301897i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.13937 | 0.136694 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.9944 | 1.15436 | 0.577180 | − | 0.816617i | \(-0.304153\pi\) | ||||
0.577180 | + | 0.816617i | \(0.304153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.0543 | + | 6.10146i | 1.51754 | + | 0.201050i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.0484 | + | 62.6588i | −0.363664 | + | 2.06244i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.20541 | + | 2.68966i | −0.105393 | + | 0.0884355i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.3593 | + | 22.0119i | 0.504466 | + | 0.722964i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.78870 | − | 32.8293i | −0.189921 | − | 1.07710i | −0.919468 | − | 0.393165i | \(-0.871380\pi\) |
0.729547 | − | 0.683931i | \(-0.239731\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.4820 | + | 8.54675i | −0.769591 | + | 0.280108i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.3229 | − | 32.0528i | −0.959987 | − | 1.04936i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.89709 | + | 6.74996i | −0.127449 | + | 0.220747i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.96117 | + | 3.39685i | 0.0640687 | + | 0.110970i | 0.896281 | − | 0.443488i | \(-0.146259\pi\) |
−0.832212 | + | 0.554458i | \(0.812926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.2393 | + | 15.4143i | −0.791019 | + | 0.503027i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.4739 | + | 13.8232i | 0.537033 | + | 0.450625i | 0.870522 | − | 0.492130i | \(-0.163781\pi\) |
−0.333489 | + | 0.942754i | \(0.608226\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.468629 | − | 0.170567i | −0.0152607 | − | 0.00555443i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.266320 | + | 2.06195i | 0.00866339 | + | 0.0670752i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.7169 | − | 6.08445i | −0.543226 | − | 0.197718i | 0.0558084 | − | 0.998441i | \(-0.482226\pi\) |
−0.599034 | + | 0.800723i | \(0.704449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.3320 | + | 20.4170i | 0.789850 | + | 0.662763i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.3199 | + | 6.94776i | 0.431929 | + | 0.225297i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.9355 | + | 20.6729i | 0.386629 | + | 0.669661i | 0.991994 | − | 0.126287i | \(-0.0403061\pi\) |
−0.605365 | + | 0.795948i | \(0.706973\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.2061 | − | 19.4095i | 0.362621 | − | 0.628078i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.57276 | + | 1.00984i | −0.147816 | + | 0.0326434i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.76516 | − | 1.00643i | 0.0892915 | − | 0.0324995i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.30697 | + | 24.4261i | 0.138935 | + | 0.787938i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.7986 | + | 15.7470i | −0.509101 | + | 0.507440i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.346458 | + | 0.290712i | −0.0111529 | + | 0.00935836i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.32943 | − | 30.2247i | 0.171383 | − | 0.971960i | −0.770854 | − | 0.637012i | \(-0.780170\pi\) |
0.942237 | − | 0.334948i | \(-0.108719\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.4313 | − | 39.7605i | −0.527849 | − | 1.27729i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.3837 | −1.36016 | −0.680078 | − | 0.733140i | \(-0.738054\pi\) | ||||
−0.680078 | + | 0.733140i | \(0.738054\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.69672 | 0.214687 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.5981 | − | 37.7443i | −0.499538 | − | 1.20878i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.23952 | + | 24.0435i | −0.135634 | + | 0.769220i | 0.838782 | + | 0.544468i | \(0.183268\pi\) |
−0.974416 | + | 0.224752i | \(0.927843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.70062 | − | 4.78339i | 0.182193 | − | 0.152878i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.8930 | − | 25.8085i | 0.826701 | − | 0.824003i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.27232 | − | 18.5582i | −0.104371 | − | 0.591915i | −0.991470 | − | 0.130336i | \(-0.958394\pi\) |
0.887099 | − | 0.461579i | \(-0.152717\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.12782 | + | 2.95828i | −0.258974 | + | 0.0942588i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.66340 | − | 1.47153i | 0.212098 | − | 0.0468392i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.803439 | − | 1.39160i | 0.0255479 | − | 0.0442502i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.7816 | − | 18.6742i | −0.342488 | − | 0.593207i | 0.642406 | − | 0.766364i | \(-0.277936\pi\) |
−0.984894 | + | 0.173158i | \(0.944603\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.88244 | + | 2.54671i | 0.154939 | + | 0.0808173i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.5831 | + | 13.9149i | 0.525721 | + | 0.441132i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.91532 | + | 1.42506i | 0.123999 | + | 0.0451321i | 0.403275 | − | 0.915079i | \(-0.367872\pi\) |
−0.279275 | + | 0.960211i | \(0.590094\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.65645 | − | 3.55492i | 0.147324 | − | 0.112473i |
(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 | 864.2.y.c.193.7 | yes | 54 | |
4.3 | odd | 2 | 864.2.y.b.193.3 | ✓ | 54 | ||
27.7 | even | 9 | inner | 864.2.y.c.385.7 | yes | 54 | |
108.7 | odd | 18 | 864.2.y.b.385.3 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.y.b.193.3 | ✓ | 54 | 4.3 | odd | 2 | ||
864.2.y.b.385.3 | yes | 54 | 108.7 | odd | 18 | ||
864.2.y.c.193.7 | yes | 54 | 1.1 | even | 1 | trivial | |
864.2.y.c.385.7 | yes | 54 | 27.7 | even | 9 | inner |