Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,2,Mod(49,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, base_ring=CyclotomicField(6))
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("688.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.i (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: | \(5.49370765906\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 2x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(-0.309017 - 0.535233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 688.337 |
Dual form | 688.2.i.e.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).
\(n\) | \(431\) | \(433\) | \(517\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.190983 | − | 0.330792i | −0.110264 | − | 0.190983i | 0.805613 | − | 0.592443i | \(-0.201836\pi\) |
−0.915877 | + | 0.401460i | \(0.868503\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.61803 | + | 2.80252i | 0.723607 | + | 1.25332i | 0.959545 | + | 0.281556i | \(0.0908504\pi\) |
−0.235938 | + | 0.971768i | \(0.575816\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.118034 | − | 0.204441i | 0.0446127 | − | 0.0772714i | −0.842857 | − | 0.538138i | \(-0.819128\pi\) |
0.887469 | + | 0.460866i | \(0.152461\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.42705 | − | 2.47172i | 0.475684 | − | 0.823908i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.38197 | 0.416678 | 0.208339 | − | 0.978057i | \(-0.433194\pi\) | ||||
0.208339 | + | 0.978057i | \(0.433194\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.80902 | + | 3.13331i | −0.501731 | + | 0.869024i | 0.498267 | + | 0.867024i | \(0.333970\pi\) |
−0.999998 | + | 0.00199999i | \(0.999363\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.618034 | − | 1.07047i | 0.159576 | − | 0.276393i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.54508 | − | 4.40822i | 0.617274 | − | 1.06915i | −0.372707 | − | 0.927949i | \(-0.621570\pi\) |
0.989981 | − | 0.141201i | \(-0.0450962\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.61803 | + | 2.80252i | 0.371202 | + | 0.642942i | 0.989751 | − | 0.142805i | \(-0.0456123\pi\) |
−0.618548 | + | 0.785747i | \(0.712279\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0901699 | −0.0196767 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.30902 | + | 5.73139i | 0.689978 | + | 1.19508i | 0.971845 | + | 0.235623i | \(0.0757130\pi\) |
−0.281867 | + | 0.959454i | \(0.590954\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.73607 | + | 4.73901i | −0.547214 | + | 0.947802i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.263932 | − | 0.457144i | −0.0459447 | − | 0.0795785i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.763932 | 0.129128 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.927051 | − | 1.60570i | −0.152406 | − | 0.263975i | 0.779705 | − | 0.626147i | \(-0.215369\pi\) |
−0.932112 | + | 0.362171i | \(0.882036\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.38197 | 0.221292 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.527864 | 0.0824385 | 0.0412193 | − | 0.999150i | \(-0.486876\pi\) | ||||
0.0412193 | + | 0.999150i | \(0.486876\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.50000 | + | 0.866025i | 0.991241 | + | 0.132068i | ||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.23607 | 1.37683 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.85410 | −1.14564 | −0.572819 | − | 0.819682i | \(-0.694150\pi\) | ||||
−0.572819 | + | 0.819682i | \(0.694150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47214 | + | 6.01392i | 0.496019 | + | 0.859131i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.94427 | −0.272253 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.80902 | + | 3.13331i | 0.248488 | + | 0.430393i | 0.963106 | − | 0.269121i | \(-0.0867331\pi\) |
−0.714619 | + | 0.699514i | \(0.753400\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.23607 | + | 3.87298i | 0.301511 | + | 0.522233i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.618034 | − | 1.07047i | 0.0818606 | − | 0.141787i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.09017 | 0.792873 | 0.396436 | − | 0.918062i | \(-0.370247\pi\) | ||||
0.396436 | + | 0.918062i | \(0.370247\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.92705 | − | 3.33775i | 0.246734 | − | 0.427355i | −0.715884 | − | 0.698219i | \(-0.753976\pi\) |
0.962618 | + | 0.270864i | \(0.0873094\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.336881 | − | 0.583495i | −0.0424430 | − | 0.0735135i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.7082 | −1.45222 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.42705 | + | 2.47172i | 0.174342 | + | 0.301969i | 0.939933 | − | 0.341358i | \(-0.110887\pi\) |
−0.765591 | + | 0.643327i | \(0.777553\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.26393 | − | 2.18919i | 0.152160 | − | 0.263548i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.89919 | − | 11.9497i | 0.818783 | − | 1.41817i | −0.0877966 | − | 0.996138i | \(-0.527983\pi\) |
0.906580 | − | 0.422035i | \(-0.138684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.42705 | − | 4.20378i | 0.284065 | − | 0.492015i | −0.688317 | − | 0.725410i | \(-0.741650\pi\) |
0.972382 | + | 0.233395i | \(0.0749836\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.09017 | 0.241352 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.163119 | − | 0.282530i | 0.0185891 | − | 0.0321973i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.80902 | + | 3.13331i | −0.203530 | + | 0.352525i | −0.949663 | − | 0.313272i | \(-0.898575\pi\) |
0.746133 | + | 0.665797i | \(0.231908\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.85410 | − | 6.67550i | −0.428234 | − | 0.741722i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.51722 | − | 11.2882i | −0.715358 | − | 1.23904i | −0.962821 | − | 0.270139i | \(-0.912930\pi\) |
0.247463 | − | 0.968897i | \(-0.420403\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.4721 | 1.78665 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.14590 | 0.122853 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.42705 | − | 4.20378i | −0.257267 | − | 0.445599i | 0.708242 | − | 0.705970i | \(-0.249489\pi\) |
−0.965509 | + | 0.260371i | \(0.916155\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.427051 | + | 0.739674i | 0.0447671 | + | 0.0775389i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.23607 | + | 9.06914i | −0.537209 | + | 0.930474i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.76393 | −0.483704 | −0.241852 | − | 0.970313i | \(-0.577755\pi\) | ||||
−0.241852 | + | 0.970313i | \(0.577755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.97214 | − | 3.41584i | 0.198207 | − | 0.343305i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.11803 | + | 7.13264i | −0.409760 | + | 0.709725i | −0.994863 | − | 0.101234i | \(-0.967721\pi\) |
0.585103 | + | 0.810959i | \(0.301054\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.20820 | − | 9.02087i | 0.513180 | − | 0.888853i | −0.486704 | − | 0.873567i | \(-0.661801\pi\) |
0.999883 | − | 0.0152859i | \(-0.00486585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.145898 | − | 0.252703i | −0.0142382 | − | 0.0246613i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.4721 | −1.59242 | −0.796211 | − | 0.605019i | \(-0.793165\pi\) | ||||
−0.796211 | + | 0.605019i | \(0.793165\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.57295 | + | 6.18853i | 0.342226 | + | 0.592754i | 0.984846 | − | 0.173432i | \(-0.0554857\pi\) |
−0.642619 | + | 0.766186i | \(0.722152\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.354102 | + | 0.613323i | −0.0336099 | + | 0.0582140i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.3820 | −1.25887 | −0.629435 | − | 0.777053i | \(-0.716714\pi\) | ||||
−0.629435 | + | 0.777053i | \(0.716714\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.7082 | + | 18.5472i | −0.998545 | + | 1.72953i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.16312 | + | 8.94278i | 0.477331 | + | 0.826761i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.600813 | − | 1.04064i | −0.0550764 | − | 0.0953952i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.09017 | −0.826379 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.100813 | − | 0.174613i | −0.00909001 | − | 0.0157444i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.6525 | −1.47767 | −0.738834 | − | 0.673887i | \(-0.764623\pi\) | ||||
−0.738834 | + | 0.673887i | \(0.764623\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.954915 | − | 2.31555i | −0.0840756 | − | 0.203872i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.94427 | 0.694094 | 0.347047 | − | 0.937848i | \(-0.387184\pi\) | ||||
0.347047 | + | 0.937848i | \(0.387184\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.763932 | 0.0662413 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.61803 | − | 6.26662i | −0.311391 | − | 0.539345i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.70820 | −0.829428 | −0.414714 | − | 0.909952i | \(-0.636118\pi\) | ||||
−0.414714 | + | 0.909952i | \(0.636118\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.35410 | − | 16.2018i | −0.793405 | − | 1.37422i | −0.923847 | − | 0.382761i | \(-0.874973\pi\) |
0.130443 | − | 0.991456i | \(-0.458360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.50000 | + | 2.59808i | 0.126323 | + | 0.218797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.50000 | + | 4.33013i | −0.209061 | + | 0.362103i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.70820 | −0.806222 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.32624 | − | 2.29711i | 0.109386 | − | 0.189463i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.50000 | − | 7.79423i | −0.368654 | − | 0.638528i | 0.620701 | − | 0.784047i | \(-0.286848\pi\) |
−0.989355 | + | 0.145519i | \(0.953515\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.14590 | 0.174631 | 0.0873154 | − | 0.996181i | \(-0.472171\pi\) | ||||
0.0873154 | + | 0.996181i | \(0.472171\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.26393 | − | 12.5815i | −0.587254 | − | 1.01715i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.92705 | − | 10.2660i | 0.473030 | − | 0.819312i | −0.526493 | − | 0.850179i | \(-0.676493\pi\) |
0.999524 | + | 0.0308670i | \(0.00982682\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.690983 | − | 1.19682i | 0.0547985 | − | 0.0949138i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.56231 | 0.123127 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000 | − | 12.1244i | 0.548282 | − | 0.949653i | −0.450110 | − | 0.892973i | \(-0.648615\pi\) |
0.998392 | − | 0.0566798i | \(-0.0180514\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.854102 | − | 1.47935i | 0.0664917 | − | 0.115167i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.88197 | + | 8.45581i | 0.377778 | + | 0.654330i | 0.990739 | − | 0.135783i | \(-0.0433550\pi\) |
−0.612961 | + | 0.790113i | \(0.710022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0450850 | − | 0.0780895i | −0.00346807 | − | 0.00600688i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.23607 | 0.706300 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.23607 | −0.626177 | −0.313088 | − | 0.949724i | \(-0.601364\pi\) | ||||
−0.313088 | + | 0.949724i | \(0.601364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.645898 | + | 1.11873i | 0.0488253 | + | 0.0845679i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.16312 | − | 2.01458i | −0.0874254 | − | 0.151425i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.8262 | + | 18.7516i | −0.809191 | + | 1.40156i | 0.104234 | + | 0.994553i | \(0.466761\pi\) |
−0.913425 | + | 0.407007i | \(0.866572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.8090 | − | 18.7218i | 0.803428 | − | 1.39158i | −0.113919 | − | 0.993490i | \(-0.536341\pi\) |
0.917347 | − | 0.398088i | \(-0.130326\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.47214 | −0.108823 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.00000 | − | 5.19615i | 0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.51722 | − | 6.09201i | 0.257205 | − | 0.445492i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.263932 | + | 0.457144i | −0.0191982 | + | 0.0332523i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.7361 | − | 20.3275i | −0.849192 | − | 1.47084i | −0.881930 | − | 0.471380i | \(-0.843756\pi\) |
0.0327382 | − | 0.999464i | \(-0.489577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7082 | −0.770793 | −0.385397 | − | 0.922751i | \(-0.625935\pi\) | ||||
−0.385397 | + | 0.922751i | \(0.625935\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.23607 | + | 3.87298i | 0.160128 | + | 0.277350i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.47214 | + | 12.9421i | −0.532368 | + | 0.922088i | 0.466918 | + | 0.884301i | \(0.345364\pi\) |
−0.999286 | + | 0.0377873i | \(0.987969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.9443 | 1.13026 | 0.565130 | − | 0.825002i | \(-0.308826\pi\) | ||||
0.565130 | + | 0.825002i | \(0.308826\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.545085 | − | 0.944115i | 0.0384473 | − | 0.0665927i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.354102 | + | 0.613323i | 0.0248531 | + | 0.0430468i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.854102 | + | 1.47935i | 0.0596531 | + | 0.103322i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.8885 | 1.31284 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.23607 | + | 3.87298i | 0.154672 | + | 0.267900i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.76393 | 0.327963 | 0.163981 | − | 0.986463i | \(-0.447566\pi\) | ||||
0.163981 | + | 0.986463i | \(0.447566\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.27051 | −0.361129 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.09017 | + | 19.6176i | 0.551745 | + | 1.33791i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.85410 | −0.125289 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.20820 | + | 15.9491i | 0.619411 | + | 1.07285i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.23607 | −0.484563 | −0.242281 | − | 0.970206i | \(-0.577896\pi\) | ||||
−0.242281 | + | 0.970206i | \(0.577896\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.80902 | + | 13.5256i | 0.520601 | + | 0.901708i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.73607 | + | 6.47106i | 0.247972 | + | 0.429499i | 0.962963 | − | 0.269634i | \(-0.0869027\pi\) |
−0.714991 | + | 0.699133i | \(0.753569\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.85410 | − | 13.6037i | 0.519014 | − | 0.898958i | −0.480742 | − | 0.876862i | \(-0.659633\pi\) |
0.999756 | − | 0.0220961i | \(-0.00703396\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.124612 | −0.00819885 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.51722 | − | 9.55611i | 0.361445 | − | 0.626041i | −0.626754 | − | 0.779217i | \(-0.715617\pi\) |
0.988199 | + | 0.153176i | \(0.0489501\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.7082 | − | 22.0113i | −0.828992 | − | 1.43586i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.38197 | 0.0897683 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.8541 | − | 18.7999i | −0.702093 | − | 1.21606i | −0.967730 | − | 0.251988i | \(-0.918916\pi\) |
0.265637 | − | 0.964073i | \(-0.414418\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.6353 | − | 25.3490i | 0.942740 | − | 1.63287i | 0.182525 | − | 0.983201i | \(-0.441573\pi\) |
0.760215 | − | 0.649672i | \(-0.225094\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.82624 | + | 8.35929i | −0.309603 | + | 0.536249i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.2361 | + | 19.4614i | −0.717846 | + | 1.24335i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.7082 | −0.744975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.48936 | + | 4.31169i | −0.157757 | + | 0.273242i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.40983 | + | 5.90600i | −0.215227 | + | 0.372783i | −0.953343 | − | 0.301890i | \(-0.902382\pi\) |
0.738116 | + | 0.674674i | \(0.235716\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.57295 | + | 7.92058i | 0.287499 | + | 0.497963i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.14590 | − | 5.44886i | −0.197004 | − | 0.341221i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.5623 | 1.46978 | 0.734888 | − | 0.678188i | \(-0.237235\pi\) | ||||
0.734888 | + | 0.678188i | \(0.237235\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.437694 | −0.0271970 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.28115 | + | 7.41517i | 0.264997 | + | 0.458988i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.25329 | − | 9.09896i | −0.323932 | − | 0.561066i | 0.657364 | − | 0.753573i | \(-0.271671\pi\) |
−0.981296 | + | 0.192507i | \(0.938338\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.85410 | + | 10.1396i | −0.359615 | + | 0.622871i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.927051 | + | 1.60570i | −0.0567346 | + | 0.0982672i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.56231 | −0.522053 | −0.261027 | − | 0.965332i | \(-0.584061\pi\) | ||||
−0.261027 | + | 0.965332i | \(0.584061\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.57295 | − | 6.18853i | 0.217041 | − | 0.375926i | −0.736861 | − | 0.676044i | \(-0.763693\pi\) |
0.953902 | + | 0.300118i | \(0.0970261\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.163119 | − | 0.282530i | 0.00987241 | − | 0.0170995i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.78115 | + | 6.54915i | −0.228012 | + | 0.394929i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.76393 | + | 3.05522i | 0.105984 | + | 0.183570i | 0.914140 | − | 0.405399i | \(-0.132867\pi\) |
−0.808156 | + | 0.588969i | \(0.799534\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.736068 | + | 1.27491i | 0.0439101 | + | 0.0760546i | 0.887145 | − | 0.461490i | \(-0.152685\pi\) |
−0.843235 | + | 0.537545i | \(0.819352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.61803 | − | 13.1948i | 0.452845 | − | 0.784351i | −0.545716 | − | 0.837970i | \(-0.683742\pi\) |
0.998561 | + | 0.0536192i | \(0.0170757\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0623059 | − | 0.107917i | 0.00367780 | − | 0.00637014i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.45492 | − | 7.71614i | −0.262054 | − | 0.453891i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.909830 | + | 1.57587i | 0.0533352 | + | 0.0923792i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.909830 | −0.0531528 | −0.0265764 | − | 0.999647i | \(-0.508461\pi\) | ||||
−0.0265764 | + | 0.999647i | \(0.508461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.85410 | + | 17.0678i | 0.573728 | + | 0.993726i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.09017 | −0.179310 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.9443 | −1.38473 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.944272 | − | 1.22665i | 0.0544269 | − | 0.0707027i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.14590 | 0.180727 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.4721 | 0.714152 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1074 | + | 24.4347i | 0.805151 | + | 1.39456i | 0.916189 | + | 0.400747i | \(0.131249\pi\) |
−0.111038 | + | 0.993816i | \(0.535417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.97871 | −0.226341 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.9164 | + | 20.6398i | 0.675717 | + | 1.17038i | 0.976259 | + | 0.216608i | \(0.0694994\pi\) |
−0.300541 | + | 0.953769i | \(0.597167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.5623 | + | 23.4906i | 0.766587 | + | 1.32777i | 0.939404 | + | 0.342813i | \(0.111380\pi\) |
−0.172817 | + | 0.984954i | \(0.555287\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.09017 | − | 1.88823i | 0.0614241 | − | 0.106390i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.3050 | −1.64593 | −0.822965 | − | 0.568092i | \(-0.807682\pi\) | ||||
−0.822965 | + | 0.568092i | \(0.807682\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.07295 | + | 3.59045i | −0.116063 | + | 0.201027i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.14590 | + | 5.44886i | 0.175587 | + | 0.304125i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.4721 | 0.916534 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.89919 | − | 17.1459i | −0.549108 | − | 0.951083i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.36475 | − | 2.36381i | 0.0754706 | − | 0.130719i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.927051 | + | 1.60570i | −0.0511100 | + | 0.0885251i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.73607 | − | 3.00696i | 0.0954229 | − | 0.165277i | −0.814362 | − | 0.580357i | \(-0.802913\pi\) |
0.909785 | + | 0.415080i | \(0.136246\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.29180 | −0.289989 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.61803 | + | 7.99867i | −0.252310 | + | 0.437014i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | + | 24.2487i | −0.762629 | + | 1.32091i | 0.178863 | + | 0.983874i | \(0.442758\pi\) |
−0.941491 | + | 0.337037i | \(0.890575\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.55573 | + | 4.42665i | 0.138808 | + | 0.240423i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.18034 | 0.440415 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.545085 | − | 0.944115i | −0.0292617 | − | 0.0506827i | 0.851024 | − | 0.525127i | \(-0.175982\pi\) |
−0.880285 | + | 0.474445i | \(0.842649\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.64590 | − | 6.31488i | −0.195160 | − | 0.338028i | 0.751793 | − | 0.659400i | \(-0.229189\pi\) |
−0.946953 | + | 0.321372i | \(0.895856\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.04508 | − | 7.00629i | 0.215911 | − | 0.373968i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.38197 | − | 11.0539i | 0.339678 | − | 0.588339i | −0.644694 | − | 0.764441i | \(-0.723015\pi\) |
0.984372 | + | 0.176101i | \(0.0563486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 44.6525 | 2.36991 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.229490 | + | 0.397489i | −0.0121459 | + | 0.0210373i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.3262 | + | 31.7420i | −0.967222 | + | 1.67528i | −0.263699 | + | 0.964605i | \(0.584942\pi\) |
−0.703523 | + | 0.710672i | \(0.748391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.26393 | − | 7.38535i | 0.224417 | − | 0.388702i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.73607 | + | 3.00696i | 0.0911199 | + | 0.157824i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.7082 | 0.822205 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.59017 | − | 2.75426i | −0.0830062 | − | 0.143771i | 0.821534 | − | 0.570160i | \(-0.193119\pi\) |
−0.904540 | + | 0.426389i | \(0.859785\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.753289 | − | 1.30473i | 0.0392147 | − | 0.0679218i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.854102 | 0.0443428 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.00000 | + | 5.19615i | −0.155334 | + | 0.269047i | −0.933181 | − | 0.359408i | \(-0.882979\pi\) |
0.777847 | + | 0.628454i | \(0.216312\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.291796 | + | 0.505406i | 0.0150683 | + | 0.0260990i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.42705 | − | 9.39993i | −0.279507 | − | 0.484121i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3607 | −0.891758 | −0.445879 | − | 0.895093i | \(-0.647109\pi\) | ||||
−0.445879 | + | 0.895093i | \(0.647109\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.18034 | + | 5.50851i | 0.162934 | + | 0.282210i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.12461 | 0.108563 | 0.0542813 | − | 0.998526i | \(-0.482713\pi\) | ||||
0.0542813 | + | 0.998526i | \(0.482713\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.05573 | 0.0538049 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.4164 | − | 14.8303i | 0.580329 | − | 0.753869i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.0689 | 1.16964 | 0.584819 | − | 0.811164i | \(-0.301165\pi\) | ||||
0.584819 | + | 0.811164i | \(0.301165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.6869 | 1.70362 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.51722 | − | 2.62790i | −0.0765337 | − | 0.132560i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.7082 | −0.589104 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.79180 | − | 4.83553i | −0.140116 | − | 0.242688i | 0.787424 | − | 0.616412i | \(-0.211414\pi\) |
−0.927540 | + | 0.373723i | \(0.878081\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.145898 | − | 0.252703i | −0.00730404 | − | 0.0126510i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.708204 | + | 1.22665i | −0.0353660 | + | 0.0612557i | −0.883167 | − | 0.469059i | \(-0.844593\pi\) |
0.847801 | + | 0.530315i | \(0.177926\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.4721 | − | 21.6024i | 0.619745 | − | 1.07343i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.28115 | − | 2.21902i | −0.0635044 | − | 0.109993i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.0902 | 0.993395 | 0.496697 | − | 0.867924i | \(-0.334546\pi\) | ||||
0.496697 | + | 0.867924i | \(0.334546\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.85410 | + | 3.21140i | 0.0914561 | + | 0.158407i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.718847 | − | 1.24508i | 0.0353722 | − | 0.0612664i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.0902 | − | 36.5292i | 1.03528 | − | 1.79315i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.57295 | + | 6.18853i | −0.174968 | + | 0.303054i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.76393 | 0.281587 | 0.140793 | − | 0.990039i | \(-0.455035\pi\) | ||||
0.140793 | + | 0.990039i | \(0.455035\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.8262 | + | 20.4836i | −0.576376 | + | 0.998312i | 0.419515 | + | 0.907748i | \(0.362200\pi\) |
−0.995891 | + | 0.0905634i | \(0.971133\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.2082 | + | 19.4132i | −0.544962 | + | 0.943901i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.9271 | + | 24.1224i | 0.675561 | + | 1.17011i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.454915 | − | 0.787936i | −0.0220149 | − | 0.0381309i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.90983 | 0.0922075 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.201626 | 0.00971199 | 0.00485599 | − | 0.999988i | \(-0.498454\pi\) | ||||
0.00485599 | + | 0.999988i | \(0.498454\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.6459 | + | 18.4392i | 0.511609 | + | 0.886133i | 0.999909 | + | 0.0134574i | \(0.00428377\pi\) |
−0.488300 | + | 0.872676i | \(0.662383\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.85410 | + | 3.21140i | 0.0888974 | + | 0.153975i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.7082 | + | 18.5472i | −0.512243 | + | 0.887231i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.92705 | − | 6.80185i | 0.187428 | − | 0.324635i | −0.756964 | − | 0.653457i | \(-0.773318\pi\) |
0.944392 | + | 0.328822i | \(0.106652\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.8197 | 0.943793 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.23607 | + | 5.60503i | −0.153750 | + | 0.266303i | −0.932603 | − | 0.360903i | \(-0.882468\pi\) |
0.778853 | + | 0.627206i | \(0.215802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.85410 | − | 13.6037i | 0.372320 | − | 0.644877i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.71885 | + | 2.97713i | −0.0812987 | + | 0.140813i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.4164 | − | 18.0417i | −0.491581 | − | 0.851443i | 0.508372 | − | 0.861137i | \(-0.330247\pi\) |
−0.999953 | + | 0.00969466i | \(0.996914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.729490 | 0.0343504 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.409830 | − | 0.709846i | −0.0192555 | − | 0.0333515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.38197 | + | 2.39364i | −0.0647876 | + | 0.112215i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.29180 | −0.107206 | −0.0536028 | − | 0.998562i | \(-0.517070\pi\) | ||||
−0.0536028 | + | 0.998562i | \(0.517070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.69098 | + | 9.85707i | −0.265632 | + | 0.460089i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.79837 | − | 15.2392i | −0.409781 | − | 0.709762i | 0.585084 | − | 0.810973i | \(-0.301062\pi\) |
−0.994865 | + | 0.101211i | \(0.967728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.9164 | + | 20.6398i | 0.553802 | + | 0.959214i | 0.997996 | + | 0.0632829i | \(0.0201571\pi\) |
−0.444193 | + | 0.895931i | \(0.646510\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.4721 | − | 28.5306i | −0.762240 | − | 1.32024i | −0.941694 | − | 0.336471i | \(-0.890766\pi\) |
0.179454 | − | 0.983766i | \(-0.442567\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.673762 | 0.0311114 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.52786 | −0.208633 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.98278 | + | 1.19682i | 0.413029 | + | 0.0550297i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.7082 | −0.812508 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.3262 | 0.472806 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0902 | − | 31.3331i | −0.826561 | − | 1.43165i | −0.900720 | − | 0.434399i | \(-0.856961\pi\) |
0.0741595 | − | 0.997246i | \(-0.476373\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.70820 | 0.305868 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.298374 | − | 0.516799i | −0.0135765 | − | 0.0235152i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.70820 | − | 13.3510i | −0.350012 | − | 0.606238i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.16312 | + | 12.4069i | −0.324592 | + | 0.562210i | −0.981430 | − | 0.191822i | \(-0.938560\pi\) |
0.656838 | + | 0.754032i | \(0.271894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.34752 | −0.241823 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.82624 | + | 8.35929i | −0.217805 | + | 0.377249i | −0.954137 | − | 0.299371i | \(-0.903223\pi\) |
0.736332 | + | 0.676621i | \(0.236556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.63525 | + | 13.2246i | 0.343875 | + | 0.595608i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.7639 | 0.573696 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.62868 | − | 2.82095i | −0.0730562 | − | 0.126537i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.57295 | − | 6.18853i | 0.159947 | − | 0.277037i | −0.774902 | − | 0.632081i | \(-0.782201\pi\) |
0.934849 | + | 0.355044i | \(0.115534\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.86475 | − | 3.22983i | 0.0833107 | − | 0.144298i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.26393 | + | 3.92125i | −0.100944 | + | 0.174840i | −0.912074 | − | 0.410026i | \(-0.865520\pi\) |
0.811130 | + | 0.584866i | \(0.198853\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.6525 | −1.18602 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.0172209 | + | 0.0298275i | −0.000764808 | + | 0.00132469i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.64590 | + | 4.58283i | −0.117277 | + | 0.203130i | −0.918688 | − | 0.394984i | \(-0.870750\pi\) |
0.801410 | + | 0.598115i | \(0.204083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.572949 | − | 0.992377i | −0.0253458 | − | 0.0439002i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.61803 | − | 6.26662i | −0.159740 | − | 0.276678i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.7082 | 1.48536 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.8541 | −0.477363 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.57295 | + | 2.72443i | 0.0690448 | + | 0.119589i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.51722 | − | 6.09201i | −0.154092 | − | 0.266896i | 0.778636 | − | 0.627476i | \(-0.215912\pi\) |
−0.932728 | + | 0.360580i | \(0.882579\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.91641 | + | 15.4437i | −0.389887 | + | 0.675305i | −0.992434 | − | 0.122779i | \(-0.960819\pi\) |
0.602547 | + | 0.798084i | \(0.294153\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.246711 | − | 0.427316i | 0.0107674 | − | 0.0186496i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.3992 | + | 18.0119i | −0.452139 | + | 0.783127i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.69098 | − | 15.0532i | 0.377157 | − | 0.653254i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.954915 | + | 1.65396i | −0.0413620 | + | 0.0716410i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.6525 | − | 46.1634i | −1.15229 | − | 1.99582i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.27051 | 0.356899 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.79837 | + | 8.31103i | 0.206681 | + | 0.357981i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0279 | − | 17.3688i | 0.431132 | − | 0.746742i | −0.565839 | − | 0.824515i | \(-0.691448\pi\) |
0.996971 | + | 0.0777737i | \(0.0247812\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.25735 | −0.354357 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.5623 | + | 20.0265i | −0.495275 | + | 0.857841i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.5000 | + | 18.1865i | 0.448948 | + | 0.777600i | 0.998318 | − | 0.0579790i | \(-0.0184657\pi\) |
−0.549370 | + | 0.835579i | \(0.685132\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.50000 | − | 9.52628i | −0.234734 | − | 0.406572i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.70820 | −0.413583 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.427051 | + | 0.739674i | 0.0181601 | + | 0.0314541i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.29180 | −0.0972813 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.4377 | −0.781230 | −0.390615 | − | 0.920554i | \(-0.627738\pi\) | ||||
−0.390615 | + | 0.920554i | \(0.627738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.4721 | + | 18.7999i | −0.612106 | + | 0.795149i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.68692 | −0.113442 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.3262 | −0.603779 | −0.301889 | − | 0.953343i | \(-0.597617\pi\) | ||||
−0.301889 | + | 0.953343i | \(0.597617\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.6525 | − | 37.5032i | −0.910927 | − | 1.57777i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.81966 | −0.0764185 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.02786 | + | 6.97647i | 0.168857 | + | 0.292469i | 0.938018 | − | 0.346586i | \(-0.112659\pi\) |
−0.769161 | + | 0.639055i | \(0.779326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.4098 | − | 18.0304i | −0.435638 | − | 0.754547i | 0.561710 | − | 0.827334i | \(-0.310144\pi\) |
−0.997347 | + | 0.0727876i | \(0.976810\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.48278 | + | 7.76440i | −0.187271 | + | 0.324363i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −36.2148 | −1.51026 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6074 | + | 20.1046i | −0.483222 | + | 0.836965i | −0.999814 | − | 0.0192664i | \(-0.993867\pi\) |
0.516592 | + | 0.856231i | \(0.327200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.04508 | + | 3.54219i | 0.0849908 | + | 0.147208i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.07701 | −0.127656 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.50000 | + | 4.33013i | 0.103539 | + | 0.179336i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.7082 | + | 28.9395i | −0.690799 | + | 1.19650i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.3713 | + | 23.1598i | −0.551894 | + | 0.955908i | 0.446244 | + | 0.894911i | \(0.352761\pi\) |
−0.998138 | + | 0.0609966i | \(0.980572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.70820 | 0.234804 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.7639 | − | 18.6437i | 0.442022 | − | 0.765604i | −0.555818 | − | 0.831304i | \(-0.687595\pi\) |
0.997839 | + | 0.0657001i | \(0.0209281\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.94427 | − | 3.36758i | 0.0797074 | − | 0.138057i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.04508 | − | 5.27424i | −0.124627 | − | 0.215860i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.8820 | + | 27.5084i | 0.648920 | + | 1.12396i | 0.983381 | + | 0.181552i | \(0.0581122\pi\) |
−0.334462 | + | 0.942409i | \(0.608555\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.58359 | 0.105387 | 0.0526935 | − | 0.998611i | \(-0.483219\pi\) | ||||
0.0526935 | + | 0.998611i | \(0.483219\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.14590 | 0.331727 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.7082 | − | 25.4754i | −0.597974 | − | 1.03572i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.57295 | − | 14.8488i | −0.347965 | − | 0.602694i | 0.637923 | − | 0.770100i | \(-0.279794\pi\) |
−0.985888 | + | 0.167407i | \(0.946461\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.135255 | − | 0.234268i | 0.00548081 | − | 0.00949303i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.2082 | − | 24.6093i | 0.574802 | − | 0.995587i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.7984 | 1.20354 | 0.601772 | − | 0.798668i | \(-0.294461\pi\) | ||||
0.601772 | + | 0.798668i | \(0.294461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.326238 | − | 0.565061i | 0.0131552 | − | 0.0227854i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.85410 | − | 3.21140i | 0.0746433 | − | 0.129286i | −0.826288 | − | 0.563248i | \(-0.809552\pi\) |
0.900931 | + | 0.433962i | \(0.142885\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.63525 | − | 2.83234i | 0.0657264 | − | 0.113842i | −0.831290 | − | 0.555840i | \(-0.812397\pi\) |
0.897016 | + | 0.441998i | \(0.145730\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.39919 | − | 12.8158i | −0.296919 | − | 0.514279i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.14590 | −0.0459094 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.2082 | + | 19.4132i | 0.448328 | + | 0.776527i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.854102 | − | 1.47935i | 0.0341095 | − | 0.0590795i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.43769 | −0.376306 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.95492 | + | 13.7783i | −0.316680 | + | 0.548506i | −0.979793 | − | 0.200013i | \(-0.935902\pi\) |
0.663113 | + | 0.748519i | \(0.269235\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.909830 | − | 1.57587i | −0.0361625 | − | 0.0626353i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.9443 | − | 46.6688i | −1.06925 | − | 1.85200i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.1246 | −0.995473 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.6910 | − | 34.1058i | −0.778963 | − | 1.34920i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.1803 | 1.31054 | 0.655272 | − | 0.755393i | \(-0.272554\pi\) | ||||
0.655272 | + | 0.755393i | \(0.272554\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.5623 | −1.16582 | −0.582912 | − | 0.812535i | \(-0.698087\pi\) | ||||
−0.582912 | + | 0.812535i | \(0.698087\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.94427 | − | 6.42280i | 0.194681 | − | 0.252897i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.3262 | 1.46745 | 0.733723 | − | 0.679449i | \(-0.237781\pi\) | ||||
0.733723 | + | 0.679449i | \(0.237781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.41641 | 0.330373 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.88854 | 0.113037 | 0.0565187 | − | 0.998402i | \(-0.482000\pi\) | ||||
0.0565187 | + | 0.998402i | \(0.482000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.8541 | + | 22.2640i | 0.502251 | + | 0.869925i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.92705 | − | 11.9980i | −0.270250 | − | 0.468087i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.68034 | − | 13.3027i | 0.299184 | − | 0.518201i | −0.676766 | − | 0.736198i | \(-0.736619\pi\) |
0.975949 | + | 0.217997i | \(0.0699524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.3951 | 1.18223 | 0.591117 | − | 0.806586i | \(-0.298687\pi\) | ||||
0.591117 | + | 0.806586i | \(0.298687\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.51722 | − | 6.09201i | 0.136598 | − | 0.236594i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.23607 | + | 2.14093i | 0.0479327 | + | 0.0830218i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.8541 | −0.768754 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.38197 | + | 2.39364i | 0.0534299 | + | 0.0925433i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.66312 | − | 4.61266i | 0.102809 | − | 0.178070i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.9164 | − | 34.4962i | 0.767721 | − | 1.32973i | −0.171075 | − | 0.985258i | \(-0.554724\pi\) |
0.938796 | − | 0.344474i | \(-0.111943\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.11803 | − | 10.5967i | 0.235483 | − | 0.407869i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.2361 | −1.39267 | −0.696333 | − | 0.717719i | \(-0.745186\pi\) | ||||
−0.696333 | + | 0.717719i | \(0.745186\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.562306 | + | 0.973942i | −0.0215793 | + | 0.0373765i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.42705 | − | 2.47172i | 0.0546847 | − | 0.0947167i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.5623 | + | 25.2227i | 0.557211 | + | 0.965118i | 0.997728 | + | 0.0673736i | \(0.0214619\pi\) |
−0.440517 | + | 0.897744i | \(0.645205\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.7082 | − | 27.2074i | −0.600180 | − | 1.03954i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.00000 | −0.228914 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.0902 | −0.498696 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.6353 | + | 42.6695i | 0.937169 | + | 1.62322i | 0.770719 | + | 0.637175i | \(0.219897\pi\) |
0.166450 | + | 0.986050i | \(0.446770\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.465558 | − | 0.806370i | −0.0176851 | − | 0.0306315i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.2705 | − | 52.4301i | 1.14823 | − | 1.98879i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.34346 | − | 2.32694i | 0.0508871 | − | 0.0881391i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.21478 | −0.159418 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.7533 | + | 20.3573i | −0.443916 | + | 0.768884i | −0.997976 | − | 0.0635921i | \(-0.979744\pi\) |
0.554060 | + | 0.832476i | \(0.313078\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.00000 | − | 5.19615i | 0.113147 | − | 0.195977i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.85410 | + | 8.40755i | −0.182816 | + | 0.316647i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.972136 | + | 1.68379i | 0.0365609 | + | 0.0633254i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.88854 | −0.258705 | −0.129352 | − | 0.991599i | \(-0.541290\pi\) | ||||
−0.129352 | + | 0.991599i | \(0.541290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.16312 | + | 8.94278i | 0.193632 | + | 0.335381i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.1803 | −0.605110 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.14590 | + | 7.18091i | −0.154831 | + | 0.268176i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.89919 | + | 11.9497i | 0.257296 | + | 0.445650i | 0.965517 | − | 0.260341i | \(-0.0838350\pi\) |
−0.708220 | + | 0.705991i | \(0.750502\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.22949 | − | 2.12954i | −0.0457886 | − | 0.0793082i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.1803 | −0.415801 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.20820 | − | 14.2170i | −0.304845 | − | 0.528007i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.9787 | −1.07476 | −0.537381 | − | 0.843340i | \(-0.680586\pi\) | ||||
−0.537381 | + | 0.843340i | \(0.680586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.3607 | − | 26.4493i | 0.753067 | − | 0.978263i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.5410 | −1.57129 | −0.785644 | − | 0.618679i | \(-0.787668\pi\) | ||||
−0.785644 | + | 0.618679i | \(0.787668\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.58359 | 0.316611 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.97214 | + | 3.41584i | 0.0726446 | + | 0.125824i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.5410 | 0.645257 | 0.322628 | − | 0.946526i | \(-0.395434\pi\) | ||||
0.322628 | + | 0.946526i | \(0.395434\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.23607 | + | 3.87298i | 0.0821440 | + | 0.142278i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.68034 | − | 9.83864i | −0.208391 | − | 0.360945i | 0.742817 | − | 0.669495i | \(-0.233489\pi\) |
−0.951208 | + | 0.308550i | \(0.900156\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.5623 | − | 25.2227i | 0.533522 | − | 0.924087i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −37.2016 | −1.36114 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.94427 | + | 3.36758i | −0.0710421 | + | 0.123049i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.48936 | + | 7.77579i | 0.163819 | + | 0.283743i | 0.936235 | − | 0.351374i | \(-0.114285\pi\) |
−0.772416 | + | 0.635117i | \(0.780952\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.60488 | 0.0949270 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.47214 | + | 6.01392i | 0.126364 | + | 0.218869i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.98936 | + | 13.8380i | −0.290378 | + | 0.502950i | −0.973899 | − | 0.226981i | \(-0.927114\pi\) |
0.683521 | + | 0.729931i | \(0.260448\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.74671 | − | 3.02539i | 0.0634016 | − | 0.109815i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.04508 | − | 8.73834i | 0.182884 | − | 0.316765i | −0.759977 | − | 0.649950i | \(-0.774790\pi\) |
0.942862 | + | 0.333185i | \(0.108123\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.68692 | 0.0610705 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 23.5066 | − | 40.7146i | 0.849882 | − | 1.47204i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.0172 | + | 19.0824i | −0.397809 | + | 0.689025i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.94427 | + | 13.7599i | 0.286478 | + | 0.496194i | 0.972966 | − | 0.230946i | \(-0.0741822\pi\) |
−0.686489 | + | 0.727140i | \(0.740849\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.50000 | − | 7.79423i | −0.162064 | − | 0.280702i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.5967 | −1.20839 | −0.604196 | − | 0.796836i | \(-0.706505\pi\) | ||||
−0.604196 | + | 0.796836i | \(0.706505\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0835921 | + | 0.144786i | 0.00299885 | + | 0.00519416i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.854102 | + | 1.47935i | 0.0306014 | + | 0.0530031i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.53444 | − | 16.5141i | 0.341169 | − | 0.590922i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.35410 | − | 5.80948i | 0.119866 | − | 0.207614i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.3607 | 1.36915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.7254 | + | 39.3616i | −0.810074 | + | 1.40309i | 0.102738 | + | 0.994708i | \(0.467240\pi\) |
−0.912812 | + | 0.408381i | \(0.866094\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.00658 | + | 3.47549i | −0.0714361 | + | 0.123731i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.57953 | + | 2.73582i | −0.0561615 | + | 0.0972746i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.97214 | + | 12.0761i | 0.247588 | + | 0.428835i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.47214 | 0.158610 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.88197 | + | 3.25966i | 0.0666627 | + | 0.115463i | 0.897430 | − | 0.441156i | \(-0.145432\pi\) |
−0.830768 | + | 0.556619i | \(0.812098\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.9894 | + | 34.6226i | −0.707173 | + | 1.22486i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.8541 | −0.489511 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.35410 | − | 5.80948i | 0.118364 | − | 0.205012i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.52786 | + | 4.37839i | 0.0890955 | + | 0.154318i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.63525 | + | 2.83234i | 0.0575637 | + | 0.0997033i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.7426 | −1.32696 | −0.663480 | − | 0.748194i | \(-0.730921\pi\) | ||||
−0.663480 | + | 0.748194i | \(0.730921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.1976 | − | 22.8588i | −0.463429 | − | 0.802683i | 0.535700 | − | 0.844408i | \(-0.320048\pi\) |
−0.999129 | + | 0.0417257i | \(0.986714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.72949 | −0.0957274 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 45.3050 | 1.58696 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.09017 | + | 19.6176i | 0.283039 | + | 0.686334i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.43769 | 0.0851799 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.3262 | −0.534889 | −0.267445 | − | 0.963573i | \(-0.586179\pi\) | ||||
−0.267445 | + | 0.963573i | \(0.586179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.0066 | − | 20.7960i | −0.418523 | − | 0.724903i | 0.577268 | − | 0.816555i | \(-0.304119\pi\) |
−0.995791 | + | 0.0916516i | \(0.970785\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.88854 | 0.100566 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.59017 | − | 11.4145i | −0.229163 | − | 0.396921i | 0.728398 | − | 0.685155i | \(-0.240265\pi\) |
−0.957560 | + | 0.288233i | \(0.906932\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.5795 | + | 35.6448i | 0.714757 | + | 1.23799i | 0.963053 | + | 0.269311i | \(0.0867958\pi\) |
−0.248297 | + | 0.968684i | \(0.579871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.673762 | − | 1.16699i | 0.0233725 | − | 0.0404824i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.3475 | 1.22472 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.7984 | + | 27.3636i | −0.546725 | + | 0.946956i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.88854 | 0.341390 | 0.170695 | − | 0.985324i | \(-0.445399\pi\) | ||||
0.170695 | + | 0.985324i | \(0.445399\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.281153 | − | 0.486971i | 0.00968342 | − | 0.0167722i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.145898 | − | 0.252703i | 0.00501904 | − | 0.00869324i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.07295 | + | 1.85840i | −0.0368670 | + | 0.0638555i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.81966 | −0.199730 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.13525 | − | 10.6266i | 0.210314 | − | 0.364274i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.8713 | + | 46.5425i | −0.920057 | + | 1.59358i | −0.120732 | + | 0.992685i | \(0.538524\pi\) |
−0.799325 | + | 0.600900i | \(0.794809\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.9443 | + | 25.8842i | 0.511083 | + | 0.885222i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.90983 | + | 11.9682i | 0.236035 | + | 0.408825i | 0.959573 | − | 0.281460i | \(-0.0908186\pi\) |
−0.723538 | + | 0.690285i | \(0.757485\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.5836 | 0.770542 | 0.385271 | − | 0.922803i | \(-0.374108\pi\) | ||||
0.385271 | + | 0.922803i | \(0.374108\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0475975 | −0.00162212 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.2533 | − | 24.6874i | −0.485188 | − | 0.840370i | 0.514668 | − | 0.857390i | \(-0.327915\pi\) |
−0.999855 | + | 0.0170203i | \(0.994582\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.3262 | − | 23.0817i | −0.453106 | − | 0.784802i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.70163 | + | 2.94730i | −0.0577903 | + | 0.100096i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.50000 | + | 4.33013i | −0.0848067 | + | 0.146889i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.3262 | −0.349891 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.79837 | + | 11.7751i | −0.230090 | + | 0.398528i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.180340 | + | 0.312358i | −0.00609660 | + | 0.0105596i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.8262 | + | 20.4836i | −0.399344 | + | 0.691684i | −0.993645 | − | 0.112559i | \(-0.964095\pi\) |
0.594301 | + | 0.804242i | \(0.297429\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.173762 | + | 0.300965i | 0.00586085 | + | 0.0101513i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.2361 | 1.28821 | 0.644103 | − | 0.764939i | \(-0.277231\pi\) | ||||
0.644103 | + | 0.764939i | \(0.277231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.5623 | − | 23.4906i | −0.456408 | − | 0.790522i | 0.542360 | − | 0.840146i | \(-0.317531\pi\) |
−0.998768 | + | 0.0496245i | \(0.984198\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.76393 | − | 6.51932i | 0.126523 | − | 0.219145i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.9574 | −1.37522 | −0.687608 | − | 0.726082i | \(-0.741339\pi\) | ||||
−0.687608 | + | 0.726082i | \(0.741339\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.96556 | + | 3.40445i | −0.0659227 | + | 0.114181i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.32624 | − | 9.22531i | −0.178436 | − | 0.309060i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.7082 | − | 22.0113i | −0.425264 | − | 0.736579i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −70.0689 | −2.34214 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.57295 | + | 7.92058i | 0.152686 | + | 0.264460i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.4164 | 0.613540 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.586105 | − | 0.0780895i | −0.0195043 | − | 0.00259865i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 69.9574 | 2.32546 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.29180 | 0.275325 | 0.137662 | − | 0.990479i | \(-0.456041\pi\) | ||||
0.137662 | + | 0.990479i | \(0.456041\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.7533 | + | 20.3573i | 0.389832 | + | 0.675209i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.97871 | −0.131821 | −0.0659103 | − | 0.997826i | \(-0.520995\pi\) | ||||
−0.0659103 | + | 0.997826i | \(0.520995\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.00658 | − | 15.5999i | −0.298074 | − | 0.516280i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.38197 | − | 4.12569i | −0.0787454 | − | 0.136391i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.937694 | − | 1.62413i | 0.0309654 | − | 0.0536336i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.3951 | 1.46446 | 0.732230 | − | 0.681057i | \(-0.238480\pi\) | ||||
0.732230 | + | 0.681057i | \(0.238480\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.38854 | − | 9.33323i | 0.177559 | − | 0.307540i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.9615 | + | 43.2346i | 0.821618 | + | 1.42308i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.1459 | 0.333595 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.8647 | − | 25.7465i | −0.488222 | − | 0.845626i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.3820 | + | 26.6423i | −0.504666 | + | 0.874107i | 0.495320 | + | 0.868711i | \(0.335051\pi\) |
−0.999985 | + | 0.00539616i | \(0.998282\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.2361 | + | 19.4614i | −0.368247 | + | 0.637823i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.55166 | − | 7.88371i | 0.149015 | − | 0.258101i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.7639 | 0.744460 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.8369 | − | 34.3585i | 0.648043 | − | 1.12244i | −0.335547 | − | 0.942023i | \(-0.608921\pi\) |
0.983590 | − | 0.180419i | \(-0.0577455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.18034 | − | 8.97261i | 0.169054 | − | 0.292810i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.8820 | + | 18.8481i | 0.354742 | + | 0.614431i | 0.987074 | − | 0.160267i | \(-0.0512354\pi\) |
−0.632332 | + | 0.774698i | \(0.717902\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.74671 | + | 3.02539i | 0.0568807 | + | 0.0985203i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.70820 | −0.0555679 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.3607 | 0.629138 | 0.314569 | − | 0.949235i | \(-0.398140\pi\) | ||||
0.314569 | + | 0.949235i | \(0.398140\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.78115 | + | 15.2094i | 0.285048 | + | 0.493718i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.59675 | + | 9.69385i | 0.181487 | + | 0.314345i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.55573 | − | 2.69460i | 0.0503950 | − | 0.0872867i | −0.839728 | − | 0.543008i | \(-0.817285\pi\) |
0.890122 | + | 0.455721i | \(0.150619\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.9787 | − | 65.7811i | 1.22896 | − | 2.12863i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.58359 | 0.0511903 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.14590 | + | 1.98475i | −0.0370030 | + | 0.0640910i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.5066 | + | 40.7146i | −0.757489 | + | 1.31201i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.3262 | − | 30.0099i | −0.557751 | − | 0.966054i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.1033 | 1.57906 | 0.789528 | − | 0.613714i | \(-0.210325\pi\) | ||||
0.789528 | + | 0.613714i | \(0.210325\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.14590 | − | 5.44886i | −0.101061 | − | 0.175042i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.6803 | − | 23.6950i | 0.439023 | − | 0.760410i | −0.558591 | − | 0.829443i | \(-0.688658\pi\) |
0.997614 | + | 0.0690328i | \(0.0219913\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.41641 | −0.141584 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.78115 | + | 6.54915i | −0.121094 | + | 0.209741i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.3820 | − | 31.8385i | −0.588091 | − | 1.01860i | −0.994482 | − | 0.104905i | \(-0.966546\pi\) |
0.406391 | − | 0.913699i | \(-0.366787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.35410 | − | 5.80948i | −0.107198 | − | 0.185672i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.3951 | 0.651166 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.763932 | − | 1.32317i | −0.0243656 | − | 0.0422025i | 0.853585 | − | 0.520953i | \(-0.174423\pi\) |
−0.877951 | + | 0.478750i | \(0.841090\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.3607 | −1.54090 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.708204 | 0.0225424 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.5451 | + | 40.1197i | 0.526103 | + | 1.27573i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.1803 | 1.05401 | 0.527004 | − | 0.849863i | \(-0.323315\pi\) | ||||
0.527004 | + | 0.849863i | \(0.323315\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.32624 | −0.0420869 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.7984 | + | 44.6841i | 0.817863 | + | 1.41658i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.4508 | 1.15441 | 0.577205 | − | 0.816599i | \(-0.304143\pi\) | ||||
0.577205 | + | 0.816599i | \(0.304143\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.07295 | + | 3.59045i | 0.0655852 | + | 0.113597i |
(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 | 688.2.i.e.337.2 | 4 | ||
4.3 | odd | 2 | 43.2.c.b.36.1 | yes | 4 | ||
12.11 | even | 2 | 387.2.h.d.208.2 | 4 | |||
43.6 | even | 3 | inner | 688.2.i.e.49.2 | 4 | ||
172.7 | even | 6 | 1849.2.a.h.1.2 | 2 | |||
172.79 | odd | 6 | 1849.2.a.e.1.1 | 2 | |||
172.135 | odd | 6 | 43.2.c.b.6.1 | ✓ | 4 | ||
516.479 | even | 6 | 387.2.h.d.307.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.c.b.6.1 | ✓ | 4 | 172.135 | odd | 6 | ||
43.2.c.b.36.1 | yes | 4 | 4.3 | odd | 2 | ||
387.2.h.d.208.2 | 4 | 12.11 | even | 2 | |||
387.2.h.d.307.2 | 4 | 516.479 | even | 6 | |||
688.2.i.e.49.2 | 4 | 43.6 | even | 3 | inner | ||
688.2.i.e.337.2 | 4 | 1.1 | even | 1 | trivial | ||
1849.2.a.e.1.1 | 2 | 172.79 | odd | 6 | |||
1849.2.a.h.1.2 | 2 | 172.7 | even | 6 |