Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.a (trivial) |
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: | yes |
Analytic conductor: | \(60.7262307372\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 2x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2535) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80194 | −1.27416 | −0.637081 | − | 0.770797i | \(-0.719858\pi\) | ||||
−0.637081 | + | 0.770797i | \(0.719858\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.24698 | 0.623490 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.801938 | 0.303104 | 0.151552 | − | 0.988449i | \(-0.451573\pi\) | ||||
0.151552 | + | 0.988449i | \(0.451573\pi\) | |||||||
\(8\) | 1.35690 | 0.479735 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.80194 | −0.569823 | ||||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.44504 | −0.386204 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.93900 | −1.23475 | ||||||||
\(17\) | 0.396125 | 0.0960743 | 0.0480372 | − | 0.998846i | \(-0.484703\pi\) | ||||
0.0480372 | + | 0.998846i | \(0.484703\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.74094 | −0.628814 | −0.314407 | − | 0.949288i | \(-0.601806\pi\) | ||||
−0.314407 | + | 0.949288i | \(0.601806\pi\) | |||||||
\(20\) | 1.24698 | 0.278833 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.80194 | 0.384174 | ||||||||
\(23\) | −1.55496 | −0.324231 | −0.162116 | − | 0.986772i | \(-0.551832\pi\) | ||||
−0.162116 | + | 0.986772i | \(0.551832\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 7.34481 | 1.36390 | 0.681949 | − | 0.731400i | \(-0.261133\pi\) | ||||
0.681949 | + | 0.731400i | \(0.261133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.38404 | 0.428187 | 0.214093 | − | 0.976813i | \(-0.431320\pi\) | ||||
0.214093 | + | 0.976813i | \(0.431320\pi\) | |||||||
\(32\) | 6.18598 | 1.09354 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.713792 | −0.122414 | ||||||||
\(35\) | 0.801938 | 0.135552 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.96077 | −0.979945 | −0.489972 | − | 0.871738i | \(-0.662993\pi\) | ||||
−0.489972 | + | 0.871738i | \(0.662993\pi\) | |||||||
\(38\) | 4.93900 | 0.801212 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.35690 | 0.214544 | ||||||||
\(41\) | −8.80194 | −1.37463 | −0.687316 | − | 0.726359i | \(-0.741211\pi\) | ||||
−0.687316 | + | 0.726359i | \(0.741211\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.80194 | −1.03729 | −0.518643 | − | 0.854991i | \(-0.673563\pi\) | ||||
−0.518643 | + | 0.854991i | \(0.673563\pi\) | |||||||
\(44\) | −1.24698 | −0.187989 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.80194 | 0.413123 | ||||||||
\(47\) | 11.7899 | 1.71973 | 0.859864 | − | 0.510524i | \(-0.170548\pi\) | ||||
0.859864 | + | 0.510524i | \(0.170548\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.35690 | −0.908128 | ||||||||
\(50\) | −1.80194 | −0.254832 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.868313 | −0.119272 | −0.0596360 | − | 0.998220i | \(-0.518994\pi\) | ||||
−0.0596360 | + | 0.998220i | \(0.518994\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 1.08815 | 0.145410 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13.2349 | −1.73783 | ||||||||
\(59\) | 8.11960 | 1.05708 | 0.528541 | − | 0.848908i | \(-0.322739\pi\) | ||||
0.528541 | + | 0.848908i | \(0.322739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.11529 | −0.526909 | −0.263455 | − | 0.964672i | \(-0.584862\pi\) | ||||
−0.263455 | + | 0.964672i | \(0.584862\pi\) | |||||||
\(62\) | −4.29590 | −0.545579 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.26875 | −0.158594 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.93900 | 1.21424 | 0.607121 | − | 0.794609i | \(-0.292324\pi\) | ||||
0.607121 | + | 0.794609i | \(0.292324\pi\) | |||||||
\(68\) | 0.493959 | 0.0599014 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.44504 | −0.172716 | ||||||||
\(71\) | 6.07069 | 0.720458 | 0.360229 | − | 0.932864i | \(-0.382699\pi\) | ||||
0.360229 | + | 0.932864i | \(0.382699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.29052 | −0.502167 | −0.251084 | − | 0.967965i | \(-0.580787\pi\) | ||||
−0.251084 | + | 0.967965i | \(0.580787\pi\) | |||||||
\(74\) | 10.7409 | 1.24861 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.41789 | −0.392059 | ||||||||
\(77\) | −0.801938 | −0.0913893 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.1075 | −1.58722 | −0.793610 | − | 0.608427i | \(-0.791801\pi\) | ||||
−0.793610 | + | 0.608427i | \(0.791801\pi\) | |||||||
\(80\) | −4.93900 | −0.552197 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15.8605 | 1.75150 | ||||||||
\(83\) | −1.83877 | −0.201832 | −0.100916 | − | 0.994895i | \(-0.532177\pi\) | ||||
−0.100916 | + | 0.994895i | \(0.532177\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.396125 | 0.0429657 | ||||||||
\(86\) | 12.2567 | 1.32167 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.35690 | −0.144646 | ||||||||
\(89\) | 6.52111 | 0.691236 | 0.345618 | − | 0.938375i | \(-0.387669\pi\) | ||||
0.345618 | + | 0.938375i | \(0.387669\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.93900 | −0.202155 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.2446 | −2.19121 | ||||||||
\(95\) | −2.74094 | −0.281214 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1521 | −1.33540 | −0.667698 | − | 0.744432i | \(-0.732720\pi\) | ||||
−0.667698 | + | 0.744432i | \(0.732720\pi\) | |||||||
\(98\) | 11.4547 | 1.15710 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.24698 | 0.124698 | ||||||||
\(101\) | −17.8756 | −1.77869 | −0.889345 | − | 0.457237i | \(-0.848839\pi\) | ||||
−0.889345 | + | 0.457237i | \(0.848839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.39373 | 0.629993 | 0.314997 | − | 0.949093i | \(-0.397997\pi\) | ||||
0.314997 | + | 0.949093i | \(0.397997\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.56465 | 0.151972 | ||||||||
\(107\) | −15.6353 | −1.51152 | −0.755762 | − | 0.654846i | \(-0.772734\pi\) | ||||
−0.755762 | + | 0.654846i | \(0.772734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.42758 | 0.711433 | 0.355717 | − | 0.934594i | \(-0.384237\pi\) | ||||
0.355717 | + | 0.934594i | \(0.384237\pi\) | |||||||
\(110\) | 1.80194 | 0.171808 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.96077 | −0.374258 | ||||||||
\(113\) | 15.4765 | 1.45591 | 0.727953 | − | 0.685627i | \(-0.240472\pi\) | ||||
0.727953 | + | 0.685627i | \(0.240472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.55496 | −0.145001 | ||||||||
\(116\) | 9.15883 | 0.850376 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.6310 | −1.34689 | ||||||||
\(119\) | 0.317667 | 0.0291205 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 7.41550 | 0.671368 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.97285 | 0.266970 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.97823 | −0.885425 | −0.442712 | − | 0.896664i | \(-0.645984\pi\) | ||||
−0.442712 | + | 0.896664i | \(0.645984\pi\) | |||||||
\(128\) | −10.0858 | −0.891463 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.71917 | −0.412316 | −0.206158 | − | 0.978519i | \(-0.566096\pi\) | ||||
−0.206158 | + | 0.978519i | \(0.566096\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.19806 | −0.190596 | ||||||||
\(134\) | −17.9095 | −1.54714 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.537500 | 0.0460902 | ||||||||
\(137\) | 3.97046 | 0.339219 | 0.169610 | − | 0.985511i | \(-0.445749\pi\) | ||||
0.169610 | + | 0.985511i | \(0.445749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3351 | −1.30071 | −0.650354 | − | 0.759631i | \(-0.725380\pi\) | ||||
−0.650354 | + | 0.759631i | \(0.725380\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.9390 | −0.917981 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.34481 | 0.609954 | ||||||||
\(146\) | 7.73125 | 0.639843 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.43296 | −0.610986 | ||||||||
\(149\) | −15.1860 | −1.24408 | −0.622042 | − | 0.782984i | \(-0.713697\pi\) | ||||
−0.622042 | + | 0.782984i | \(0.713697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3448 | 1.41150 | 0.705750 | − | 0.708460i | \(-0.250610\pi\) | ||||
0.705750 | + | 0.708460i | \(0.250610\pi\) | |||||||
\(152\) | −3.71917 | −0.301664 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.44504 | 0.116445 | ||||||||
\(155\) | 2.38404 | 0.191491 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0489 | −1.60008 | −0.800039 | − | 0.599948i | \(-0.795188\pi\) | ||||
−0.800039 | + | 0.599948i | \(0.795188\pi\) | |||||||
\(158\) | 25.4209 | 2.02238 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.18598 | 0.489045 | ||||||||
\(161\) | −1.24698 | −0.0982758 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.68233 | −0.366749 | −0.183374 | − | 0.983043i | \(-0.558702\pi\) | ||||
−0.183374 | + | 0.983043i | \(0.558702\pi\) | |||||||
\(164\) | −10.9758 | −0.857069 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.31336 | 0.257166 | ||||||||
\(167\) | 10.5797 | 0.818683 | 0.409341 | − | 0.912381i | \(-0.365759\pi\) | ||||
0.409341 | + | 0.912381i | \(0.365759\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.713792 | −0.0547453 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.48188 | −0.646737 | ||||||||
\(173\) | 4.97823 | 0.378488 | 0.189244 | − | 0.981930i | \(-0.439396\pi\) | ||||
0.189244 | + | 0.981930i | \(0.439396\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.801938 | 0.0606208 | ||||||||
\(176\) | 4.93900 | 0.372291 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.7506 | −0.880747 | ||||||||
\(179\) | −13.5754 | −1.01467 | −0.507337 | − | 0.861748i | \(-0.669370\pi\) | ||||
−0.507337 | + | 0.861748i | \(0.669370\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.93661 | 0.738582 | 0.369291 | − | 0.929314i | \(-0.379601\pi\) | ||||
0.369291 | + | 0.929314i | \(0.379601\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.10992 | −0.155545 | ||||||||
\(185\) | −5.96077 | −0.438245 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.396125 | −0.0289675 | ||||||||
\(188\) | 14.7017 | 1.07223 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.93900 | 0.358313 | ||||||||
\(191\) | 18.8756 | 1.36579 | 0.682896 | − | 0.730516i | \(-0.260720\pi\) | ||||
0.682896 | + | 0.730516i | \(0.260720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3817 | 0.819269 | 0.409635 | − | 0.912250i | \(-0.365656\pi\) | ||||
0.409635 | + | 0.912250i | \(0.365656\pi\) | |||||||
\(194\) | 23.6993 | 1.70151 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.92692 | −0.566209 | ||||||||
\(197\) | −26.5840 | −1.89403 | −0.947017 | − | 0.321184i | \(-0.895919\pi\) | ||||
−0.947017 | + | 0.321184i | \(0.895919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.17523 | −0.579526 | −0.289763 | − | 0.957098i | \(-0.593577\pi\) | ||||
−0.289763 | + | 0.957098i | \(0.593577\pi\) | |||||||
\(200\) | 1.35690 | 0.0959470 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 32.2107 | 2.26634 | ||||||||
\(203\) | 5.89008 | 0.413403 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.80194 | −0.614754 | ||||||||
\(206\) | −11.5211 | −0.802714 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.74094 | 0.189595 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.6286 | 1.00708 | 0.503538 | − | 0.863973i | \(-0.332031\pi\) | ||||
0.503538 | + | 0.863973i | \(0.332031\pi\) | |||||||
\(212\) | −1.08277 | −0.0743649 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28.1739 | 1.92593 | ||||||||
\(215\) | −6.80194 | −0.463888 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.91185 | 0.129785 | ||||||||
\(218\) | −13.3840 | −0.906482 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.24698 | −0.0840713 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.2795 | −0.688366 | −0.344183 | − | 0.938902i | \(-0.611844\pi\) | ||||
−0.344183 | + | 0.938902i | \(0.611844\pi\) | |||||||
\(224\) | 4.96077 | 0.331455 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.8877 | −1.85506 | ||||||||
\(227\) | −5.43296 | −0.360598 | −0.180299 | − | 0.983612i | \(-0.557707\pi\) | ||||
−0.180299 | + | 0.983612i | \(0.557707\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.8998 | 1.31501 | 0.657507 | − | 0.753448i | \(-0.271611\pi\) | ||||
0.657507 | + | 0.753448i | \(0.271611\pi\) | |||||||
\(230\) | 2.80194 | 0.184754 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.96615 | 0.654310 | ||||||||
\(233\) | 11.4940 | 0.752994 | 0.376497 | − | 0.926418i | \(-0.377128\pi\) | ||||
0.376497 | + | 0.926418i | \(0.377128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.7899 | 0.769085 | ||||||||
\(236\) | 10.1250 | 0.659080 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.572417 | −0.0371043 | ||||||||
\(239\) | −22.0804 | −1.42826 | −0.714130 | − | 0.700013i | \(-0.753178\pi\) | ||||
−0.714130 | + | 0.700013i | \(0.753178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.3817 | 1.37731 | 0.688657 | − | 0.725088i | \(-0.258201\pi\) | ||||
0.688657 | + | 0.725088i | \(0.258201\pi\) | |||||||
\(242\) | 18.0194 | 1.15833 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.13169 | −0.328523 | ||||||||
\(245\) | −6.35690 | −0.406127 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.23490 | 0.205416 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.80194 | −0.113965 | ||||||||
\(251\) | −0.381059 | −0.0240522 | −0.0120261 | − | 0.999928i | \(-0.503828\pi\) | ||||
−0.0120261 | + | 0.999928i | \(0.503828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.55496 | 0.0977594 | ||||||||
\(254\) | 17.9801 | 1.12817 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.7114 | 1.29446 | ||||||||
\(257\) | 17.3207 | 1.08043 | 0.540216 | − | 0.841526i | \(-0.318342\pi\) | ||||
0.540216 | + | 0.841526i | \(0.318342\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.78017 | −0.297025 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.50365 | 0.525357 | ||||||||
\(263\) | −23.3545 | −1.44010 | −0.720050 | − | 0.693922i | \(-0.755881\pi\) | ||||
−0.720050 | + | 0.693922i | \(0.755881\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.868313 | −0.0533401 | ||||||||
\(266\) | 3.96077 | 0.242850 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.3937 | 0.757068 | ||||||||
\(269\) | 20.6310 | 1.25790 | 0.628948 | − | 0.777448i | \(-0.283486\pi\) | ||||
0.628948 | + | 0.777448i | \(0.283486\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.356896 | 0.0216799 | 0.0108399 | − | 0.999941i | \(-0.496549\pi\) | ||||
0.0108399 | + | 0.999941i | \(0.496549\pi\) | |||||||
\(272\) | −1.95646 | −0.118628 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.15452 | −0.432220 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.6025 | 0.997550 | 0.498775 | − | 0.866731i | \(-0.333783\pi\) | ||||
0.498775 | + | 0.866731i | \(0.333783\pi\) | |||||||
\(278\) | 27.6329 | 1.65731 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.08815 | 0.0650292 | ||||||||
\(281\) | 8.12737 | 0.484839 | 0.242419 | − | 0.970172i | \(-0.422059\pi\) | ||||
0.242419 | + | 0.970172i | \(0.422059\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.5851 | −0.866994 | −0.433497 | − | 0.901155i | \(-0.642720\pi\) | ||||
−0.433497 | + | 0.901155i | \(0.642720\pi\) | |||||||
\(284\) | 7.57002 | 0.449198 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.05861 | −0.416656 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8431 | −0.990770 | ||||||||
\(290\) | −13.2349 | −0.777180 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.35019 | −0.313096 | ||||||||
\(293\) | −25.4456 | −1.48655 | −0.743275 | − | 0.668986i | \(-0.766729\pi\) | ||||
−0.743275 | + | 0.668986i | \(0.766729\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.11960 | 0.472742 | ||||||||
\(296\) | −8.08815 | −0.470114 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.3642 | 1.58517 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.45473 | −0.314405 | ||||||||
\(302\) | −31.2543 | −1.79848 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 13.5375 | 0.776429 | ||||||||
\(305\) | −4.11529 | −0.235641 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.8955 | −0.850129 | −0.425064 | − | 0.905163i | \(-0.639749\pi\) | ||||
−0.425064 | + | 0.905163i | \(0.639749\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.29590 | −0.243991 | ||||||||
\(311\) | 6.21313 | 0.352314 | 0.176157 | − | 0.984362i | \(-0.443633\pi\) | ||||
0.176157 | + | 0.984362i | \(0.443633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.7694 | −0.608723 | −0.304362 | − | 0.952557i | \(-0.598443\pi\) | ||||
−0.304362 | + | 0.952557i | \(0.598443\pi\) | |||||||
\(314\) | 36.1269 | 2.03876 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.5918 | −0.989616 | ||||||||
\(317\) | −12.6504 | −0.710517 | −0.355259 | − | 0.934768i | \(-0.615607\pi\) | ||||
−0.355259 | + | 0.934768i | \(0.615607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.34481 | −0.411231 | ||||||||
\(320\) | −1.26875 | −0.0709253 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.24698 | 0.125219 | ||||||||
\(323\) | −1.08575 | −0.0604129 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.43727 | 0.467297 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.9433 | −0.659459 | ||||||||
\(329\) | 9.45473 | 0.521256 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.7972 | 1.96759 | 0.983795 | − | 0.179299i | \(-0.0573828\pi\) | ||||
0.983795 | + | 0.179299i | \(0.0573828\pi\) | |||||||
\(332\) | −2.29291 | −0.125840 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.0640 | −1.04313 | ||||||||
\(335\) | 9.93900 | 0.543026 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.51142 | −0.300226 | −0.150113 | − | 0.988669i | \(-0.547964\pi\) | ||||
−0.150113 | + | 0.988669i | \(0.547964\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.493959 | 0.0267887 | ||||||||
\(341\) | −2.38404 | −0.129103 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.7114 | −0.578361 | ||||||||
\(344\) | −9.22952 | −0.497622 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.97046 | −0.482255 | ||||||||
\(347\) | −18.6770 | −1.00263 | −0.501316 | − | 0.865264i | \(-0.667150\pi\) | ||||
−0.501316 | + | 0.865264i | \(0.667150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.7084 | 0.894381 | 0.447190 | − | 0.894439i | \(-0.352425\pi\) | ||||
0.447190 | + | 0.894439i | \(0.352425\pi\) | |||||||
\(350\) | −1.44504 | −0.0772407 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.18598 | −0.329714 | ||||||||
\(353\) | 16.9879 | 0.904176 | 0.452088 | − | 0.891973i | \(-0.350679\pi\) | ||||
0.452088 | + | 0.891973i | \(0.350679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.07069 | 0.322199 | ||||||||
\(356\) | 8.13169 | 0.430979 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.4620 | 1.29286 | ||||||||
\(359\) | −24.8213 | −1.31002 | −0.655009 | − | 0.755621i | \(-0.727335\pi\) | ||||
−0.655009 | + | 0.755621i | \(0.727335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.4873 | −0.604592 | ||||||||
\(362\) | −17.9051 | −0.941074 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.29052 | −0.224576 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.5459 | 0.654889 | 0.327444 | − | 0.944870i | \(-0.393813\pi\) | ||||
0.327444 | + | 0.944870i | \(0.393813\pi\) | |||||||
\(368\) | 7.67994 | 0.400345 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.7409 | 0.558395 | ||||||||
\(371\) | −0.696333 | −0.0361518 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.19136 | −0.217020 | −0.108510 | − | 0.994095i | \(-0.534608\pi\) | ||||
−0.108510 | + | 0.994095i | \(0.534608\pi\) | |||||||
\(374\) | 0.713792 | 0.0369093 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.9976 | 0.825014 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.24027 | 0.217808 | 0.108904 | − | 0.994052i | \(-0.465266\pi\) | ||||
0.108904 | + | 0.994052i | \(0.465266\pi\) | |||||||
\(380\) | −3.41789 | −0.175334 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −34.0127 | −1.74024 | ||||||||
\(383\) | −26.6437 | −1.36143 | −0.680715 | − | 0.732549i | \(-0.738331\pi\) | ||||
−0.680715 | + | 0.732549i | \(0.738331\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.801938 | −0.0408705 | ||||||||
\(386\) | −20.5090 | −1.04388 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.4004 | −0.832606 | ||||||||
\(389\) | 2.76377 | 0.140129 | 0.0700645 | − | 0.997542i | \(-0.477680\pi\) | ||||
0.0700645 | + | 0.997542i | \(0.477680\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.615957 | −0.0311503 | ||||||||
\(392\) | −8.62565 | −0.435661 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 47.9028 | 2.41331 | ||||||||
\(395\) | −14.1075 | −0.709827 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.72156 | −0.387534 | −0.193767 | − | 0.981048i | \(-0.562071\pi\) | ||||
−0.193767 | + | 0.981048i | \(0.562071\pi\) | |||||||
\(398\) | 14.7313 | 0.738411 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.93900 | −0.246950 | ||||||||
\(401\) | 21.8659 | 1.09193 | 0.545966 | − | 0.837807i | \(-0.316163\pi\) | ||||
0.545966 | + | 0.837807i | \(0.316163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −22.2905 | −1.10899 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.6136 | −0.526742 | ||||||||
\(407\) | 5.96077 | 0.295464 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.50173 | 0.123703 | 0.0618513 | − | 0.998085i | \(-0.480300\pi\) | ||||
0.0618513 | + | 0.998085i | \(0.480300\pi\) | |||||||
\(410\) | 15.8605 | 0.783296 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.97285 | 0.392794 | ||||||||
\(413\) | 6.51142 | 0.320406 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.83877 | −0.0902618 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.93900 | −0.241574 | ||||||||
\(419\) | −3.97392 | −0.194139 | −0.0970693 | − | 0.995278i | \(-0.530947\pi\) | ||||
−0.0970693 | + | 0.995278i | \(0.530947\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.1105 | −1.22381 | −0.611906 | − | 0.790931i | \(-0.709597\pi\) | ||||
−0.611906 | + | 0.790931i | \(0.709597\pi\) | |||||||
\(422\) | −26.3599 | −1.28318 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.17821 | −0.0572190 | ||||||||
\(425\) | 0.396125 | 0.0192149 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.30021 | −0.159708 | ||||||||
\(428\) | −19.4969 | −0.942420 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.2567 | 0.591069 | ||||||||
\(431\) | −7.01746 | −0.338019 | −0.169010 | − | 0.985614i | \(-0.554057\pi\) | ||||
−0.169010 | + | 0.985614i | \(0.554057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.8334 | −0.953132 | −0.476566 | − | 0.879139i | \(-0.658119\pi\) | ||||
−0.476566 | + | 0.879139i | \(0.658119\pi\) | |||||||
\(434\) | −3.44504 | −0.165367 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.26205 | 0.443572 | ||||||||
\(437\) | 4.26205 | 0.203881 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.2392 | −0.822783 | −0.411391 | − | 0.911459i | \(-0.634957\pi\) | ||||
−0.411391 | + | 0.911459i | \(0.634957\pi\) | |||||||
\(440\) | −1.35690 | −0.0646875 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.04115 | 0.0969779 | 0.0484889 | − | 0.998824i | \(-0.484559\pi\) | ||||
0.0484889 | + | 0.998824i | \(0.484559\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.52111 | 0.309130 | ||||||||
\(446\) | 18.5230 | 0.877091 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.01746 | −0.0480704 | ||||||||
\(449\) | 14.3502 | 0.677227 | 0.338614 | − | 0.940925i | \(-0.390042\pi\) | ||||
0.338614 | + | 0.940925i | \(0.390042\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.80194 | 0.414467 | ||||||||
\(452\) | 19.2989 | 0.907743 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.78986 | 0.459461 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.8122 | 1.16067 | 0.580333 | − | 0.814379i | \(-0.302922\pi\) | ||||
0.580333 | + | 0.814379i | \(0.302922\pi\) | |||||||
\(458\) | −35.8582 | −1.67554 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.93900 | −0.0904064 | ||||||||
\(461\) | 19.1739 | 0.893018 | 0.446509 | − | 0.894779i | \(-0.352667\pi\) | ||||
0.446509 | + | 0.894779i | \(0.352667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.8538 | −0.736790 | −0.368395 | − | 0.929669i | \(-0.620093\pi\) | ||||
−0.368395 | + | 0.929669i | \(0.620093\pi\) | |||||||
\(464\) | −36.2760 | −1.68407 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.7114 | −0.959437 | ||||||||
\(467\) | −20.2741 | −0.938175 | −0.469087 | − | 0.883152i | \(-0.655417\pi\) | ||||
−0.469087 | + | 0.883152i | \(0.655417\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.97046 | 0.368042 | ||||||||
\(470\) | −21.2446 | −0.979940 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.0175 | 0.507120 | ||||||||
\(473\) | 6.80194 | 0.312753 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.74094 | −0.125763 | ||||||||
\(476\) | 0.396125 | 0.0181563 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 39.7875 | 1.81984 | ||||||||
\(479\) | 14.4316 | 0.659398 | 0.329699 | − | 0.944086i | \(-0.393053\pi\) | ||||
0.329699 | + | 0.944086i | \(0.393053\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −38.5284 | −1.75492 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.4698 | −0.566809 | ||||||||
\(485\) | −13.1521 | −0.597207 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.0901 | −1.59008 | −0.795041 | − | 0.606555i | \(-0.792551\pi\) | ||||
−0.795041 | + | 0.606555i | \(0.792551\pi\) | |||||||
\(488\) | −5.58402 | −0.252777 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.4547 | 0.517472 | ||||||||
\(491\) | −2.75973 | −0.124545 | −0.0622723 | − | 0.998059i | \(-0.519835\pi\) | ||||
−0.0622723 | + | 0.998059i | \(0.519835\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.90946 | 0.131036 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.7748 | −0.528704 | ||||||||
\(497\) | 4.86831 | 0.218374 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3840 | 0.778217 | 0.389108 | − | 0.921192i | \(-0.372783\pi\) | ||||
0.389108 | + | 0.921192i | \(0.372783\pi\) | |||||||
\(500\) | 1.24698 | 0.0557666 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.686645 | 0.0306465 | ||||||||
\(503\) | −12.9987 | −0.579582 | −0.289791 | − | 0.957090i | \(-0.593586\pi\) | ||||
−0.289791 | + | 0.957090i | \(0.593586\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.8756 | −0.795454 | ||||||||
\(506\) | −2.80194 | −0.124561 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.4426 | −0.552053 | ||||||||
\(509\) | −0.839838 | −0.0372252 | −0.0186126 | − | 0.999827i | \(-0.505925\pi\) | ||||
−0.0186126 | + | 0.999827i | \(0.505925\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.44073 | −0.152209 | ||||||||
\(512\) | −17.1491 | −0.757892 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −31.2107 | −1.37665 | ||||||||
\(515\) | 6.39373 | 0.281741 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.7899 | −0.518517 | ||||||||
\(518\) | 8.61356 | 0.378458 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.2416 | 1.14967 | 0.574833 | − | 0.818271i | \(-0.305067\pi\) | ||||
0.574833 | + | 0.818271i | \(0.305067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.2349 | −1.27835 | −0.639176 | − | 0.769060i | \(-0.720725\pi\) | ||||
−0.639176 | + | 0.769060i | \(0.720725\pi\) | |||||||
\(524\) | −5.88471 | −0.257075 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.0834 | 1.83492 | ||||||||
\(527\) | 0.944378 | 0.0411377 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5821 | −0.894874 | ||||||||
\(530\) | 1.56465 | 0.0679639 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.74094 | −0.118835 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.6353 | −0.675974 | ||||||||
\(536\) | 13.4862 | 0.582515 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −37.1758 | −1.60276 | ||||||||
\(539\) | 6.35690 | 0.273811 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.4746 | 0.794284 | 0.397142 | − | 0.917757i | \(-0.370002\pi\) | ||||
0.397142 | + | 0.917757i | \(0.370002\pi\) | |||||||
\(542\) | −0.643104 | −0.0276237 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.45042 | 0.105061 | ||||||||
\(545\) | 7.42758 | 0.318163 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.450419 | −0.0192585 | −0.00962926 | − | 0.999954i | \(-0.503065\pi\) | ||||
−0.00962926 | + | 0.999954i | \(0.503065\pi\) | |||||||
\(548\) | 4.95108 | 0.211500 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.80194 | 0.0768349 | ||||||||
\(551\) | −20.1317 | −0.857639 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.3134 | −0.481093 | ||||||||
\(554\) | −29.9168 | −1.27104 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.1226 | −0.810978 | ||||||||
\(557\) | 30.4058 | 1.28834 | 0.644168 | − | 0.764884i | \(-0.277204\pi\) | ||||
0.644168 | + | 0.764884i | \(0.277204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.96077 | −0.167373 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.6450 | −0.617763 | ||||||||
\(563\) | 45.0471 | 1.89851 | 0.949255 | − | 0.314508i | \(-0.101840\pi\) | ||||
0.949255 | + | 0.314508i | \(0.101840\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.4765 | 0.651101 | ||||||||
\(566\) | 26.2814 | 1.10469 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.23729 | 0.345629 | ||||||||
\(569\) | −16.4892 | −0.691262 | −0.345631 | − | 0.938370i | \(-0.612335\pi\) | ||||
−0.345631 | + | 0.938370i | \(0.612335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.9124 | 1.79583 | 0.897915 | − | 0.440169i | \(-0.145081\pi\) | ||||
0.897915 | + | 0.440169i | \(0.145081\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.7192 | 0.530888 | ||||||||
\(575\) | −1.55496 | −0.0648462 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.8377 | −1.53357 | −0.766787 | − | 0.641902i | \(-0.778146\pi\) | ||||
−0.766787 | + | 0.641902i | \(0.778146\pi\) | |||||||
\(578\) | 30.3502 | 1.26240 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.15883 | 0.380300 | ||||||||
\(581\) | −1.47458 | −0.0611760 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.868313 | 0.0359619 | ||||||||
\(584\) | −5.82179 | −0.240907 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 45.8514 | 1.89411 | ||||||||
\(587\) | −25.1860 | −1.03954 | −0.519768 | − | 0.854307i | \(-0.673982\pi\) | ||||
−0.519768 | + | 0.854307i | \(0.673982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.53452 | −0.269250 | ||||||||
\(590\) | −14.6310 | −0.602350 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 29.4403 | 1.20999 | ||||||||
\(593\) | −19.1263 | −0.785423 | −0.392712 | − | 0.919662i | \(-0.628463\pi\) | ||||
−0.392712 | + | 0.919662i | \(0.628463\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.317667 | 0.0130231 | ||||||||
\(596\) | −18.9366 | −0.775674 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.1825 | −1.72353 | −0.861766 | − | 0.507307i | \(-0.830641\pi\) | ||||
−0.861766 | + | 0.507307i | \(0.830641\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.2277 | 1.72250 | 0.861252 | − | 0.508178i | \(-0.169681\pi\) | ||||
0.861252 | + | 0.508178i | \(0.169681\pi\) | |||||||
\(602\) | 9.82908 | 0.400604 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.6286 | 0.880056 | ||||||||
\(605\) | −10.0000 | −0.406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.0284750 | −0.00115577 | −0.000577883 | − | 1.00000i | \(-0.500184\pi\) | ||||
−0.000577883 | 1.00000i | \(0.500184\pi\) | ||||||||
\(608\) | −16.9554 | −0.687632 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.41550 | 0.300245 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.2064 | 0.896909 | 0.448454 | − | 0.893806i | \(-0.351975\pi\) | ||||
0.448454 | + | 0.893806i | \(0.351975\pi\) | |||||||
\(614\) | 26.8407 | 1.08320 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.08815 | −0.0438427 | ||||||||
\(617\) | −12.3653 | −0.497806 | −0.248903 | − | 0.968528i | \(-0.580070\pi\) | ||||
−0.248903 | + | 0.968528i | \(0.580070\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.2586 | 0.934842 | 0.467421 | − | 0.884035i | \(-0.345183\pi\) | ||||
0.467421 | + | 0.884035i | \(0.345183\pi\) | |||||||
\(620\) | 2.97285 | 0.119393 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.1957 | −0.448905 | ||||||||
\(623\) | 5.22952 | 0.209516 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.4058 | 0.775612 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −25.0006 | −0.997632 | ||||||||
\(629\) | −2.36121 | −0.0941475 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.3817 | −1.80661 | −0.903307 | − | 0.428994i | \(-0.858868\pi\) | ||||
−0.903307 | + | 0.428994i | \(0.858868\pi\) | |||||||
\(632\) | −19.1424 | −0.761445 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.7952 | 0.905314 | ||||||||
\(635\) | −9.97823 | −0.395974 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.2349 | 0.523975 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.0858 | −0.398674 | ||||||||
\(641\) | 0.511418 | 0.0201998 | 0.0100999 | − | 0.999949i | \(-0.496785\pi\) | ||||
0.0100999 | + | 0.999949i | \(0.496785\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.6668 | −0.815019 | −0.407509 | − | 0.913201i | \(-0.633603\pi\) | ||||
−0.407509 | + | 0.913201i | \(0.633603\pi\) | |||||||
\(644\) | −1.55496 | −0.0612739 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.95646 | 0.0769759 | ||||||||
\(647\) | −28.3491 | −1.11452 | −0.557260 | − | 0.830338i | \(-0.688147\pi\) | ||||
−0.557260 | + | 0.830338i | \(0.688147\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.11960 | −0.318722 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.83877 | −0.228664 | ||||||||
\(653\) | 38.4959 | 1.50646 | 0.753230 | − | 0.657757i | \(-0.228495\pi\) | ||||
0.753230 | + | 0.657757i | \(0.228495\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.71917 | −0.184393 | ||||||||
\(656\) | 43.4728 | 1.69733 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17.0368 | −0.664165 | ||||||||
\(659\) | −36.4432 | −1.41963 | −0.709814 | − | 0.704390i | \(-0.751221\pi\) | ||||
−0.709814 | + | 0.704390i | \(0.751221\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.4198 | −0.949821 | −0.474910 | − | 0.880034i | \(-0.657520\pi\) | ||||
−0.474910 | + | 0.880034i | \(0.657520\pi\) | |||||||
\(662\) | −64.5042 | −2.50703 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.49502 | −0.0968257 | ||||||||
\(665\) | −2.19806 | −0.0852372 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.4209 | −0.442218 | ||||||||
\(668\) | 13.1927 | 0.510440 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17.9095 | −0.691903 | ||||||||
\(671\) | 4.11529 | 0.158869 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.9366 | −0.884141 | −0.442071 | − | 0.896980i | \(-0.645756\pi\) | ||||
−0.442071 | + | 0.896980i | \(0.645756\pi\) | |||||||
\(674\) | 9.93123 | 0.382537 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.9530 | −0.497824 | −0.248912 | − | 0.968526i | \(-0.580073\pi\) | ||||
−0.248912 | + | 0.968526i | \(0.580073\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.5472 | −0.404764 | ||||||||
\(680\) | 0.537500 | 0.0206122 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.29590 | 0.164498 | ||||||||
\(683\) | −38.6316 | −1.47820 | −0.739099 | − | 0.673597i | \(-0.764748\pi\) | ||||
−0.739099 | + | 0.673597i | \(0.764748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.97046 | 0.151703 | ||||||||
\(686\) | 19.3013 | 0.736926 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 33.5948 | 1.28079 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.1347 | −1.33659 | −0.668293 | − | 0.743898i | \(-0.732975\pi\) | ||||
−0.668293 | + | 0.743898i | \(0.732975\pi\) | |||||||
\(692\) | 6.20775 | 0.235983 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.6547 | 1.27752 | ||||||||
\(695\) | −15.3351 | −0.581694 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.48666 | −0.132067 | ||||||||
\(698\) | −30.1075 | −1.13959 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −19.6286 | −0.741363 | −0.370682 | − | 0.928760i | \(-0.620876\pi\) | ||||
−0.370682 | + | 0.928760i | \(0.620876\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3381 | 0.616203 | ||||||||
\(704\) | 1.26875 | 0.0478178 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.6112 | −1.15207 | ||||||||
\(707\) | −14.3351 | −0.539128 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.88769 | −0.146005 | −0.0730026 | − | 0.997332i | \(-0.523258\pi\) | ||||
−0.0730026 | + | 0.997332i | \(0.523258\pi\) | |||||||
\(710\) | −10.9390 | −0.410533 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.84846 | 0.331610 | ||||||||
\(713\) | −3.70709 | −0.138831 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.9282 | −0.632638 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 44.7265 | 1.66918 | ||||||||
\(719\) | −7.42998 | −0.277091 | −0.138546 | − | 0.990356i | \(-0.544243\pi\) | ||||
−0.138546 | + | 0.990356i | \(0.544243\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.12737 | 0.190953 | ||||||||
\(722\) | 20.6993 | 0.770349 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.3907 | 0.460499 | ||||||||
\(725\) | 7.34481 | 0.272780 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.0127 | −1.74360 | −0.871802 | − | 0.489859i | \(-0.837048\pi\) | ||||
−0.871802 | + | 0.489859i | \(0.837048\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.73125 | 0.286146 | ||||||||
\(731\) | −2.69441 | −0.0996565 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.8683 | −0.918532 | −0.459266 | − | 0.888299i | \(-0.651888\pi\) | ||||
−0.459266 | + | 0.888299i | \(0.651888\pi\) | |||||||
\(734\) | −22.6069 | −0.834434 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.61894 | −0.354559 | ||||||||
\(737\) | −9.93900 | −0.366108 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.8437 | −1.35532 | −0.677658 | − | 0.735377i | \(-0.737005\pi\) | ||||
−0.677658 | + | 0.735377i | \(0.737005\pi\) | |||||||
\(740\) | −7.43296 | −0.273241 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.25475 | 0.0460633 | ||||||||
\(743\) | 20.9028 | 0.766848 | 0.383424 | − | 0.923572i | \(-0.374745\pi\) | ||||
0.383424 | + | 0.923572i | \(0.374745\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.1860 | −0.556371 | ||||||||
\(746\) | 7.55257 | 0.276519 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.493959 | −0.0180609 | ||||||||
\(749\) | −12.5386 | −0.458149 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.72481 | 0.135920 | 0.0679601 | − | 0.997688i | \(-0.478351\pi\) | ||||
0.0679601 | + | 0.997688i | \(0.478351\pi\) | |||||||
\(752\) | −58.2301 | −2.12343 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.3448 | 0.631242 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.4446 | −1.43364 | −0.716819 | − | 0.697260i | \(-0.754402\pi\) | ||||
−0.716819 | + | 0.697260i | \(0.754402\pi\) | |||||||
\(758\) | −7.64071 | −0.277523 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.71917 | −0.134908 | ||||||||
\(761\) | −28.1396 | −1.02006 | −0.510029 | − | 0.860157i | \(-0.670365\pi\) | ||||
−0.510029 | + | 0.860157i | \(0.670365\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.95646 | 0.215638 | ||||||||
\(764\) | 23.5375 | 0.851557 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 48.0103 | 1.73468 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.9909 | 1.69454 | 0.847268 | − | 0.531166i | \(-0.178246\pi\) | ||||
0.847268 | + | 0.531166i | \(0.178246\pi\) | |||||||
\(770\) | 1.44504 | 0.0520757 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.1927 | 0.510806 | ||||||||
\(773\) | 15.9594 | 0.574021 | 0.287011 | − | 0.957927i | \(-0.407338\pi\) | ||||
0.287011 | + | 0.957927i | \(0.407338\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.38404 | 0.0856374 | ||||||||
\(776\) | −17.8461 | −0.640637 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.98015 | −0.178547 | ||||||||
\(779\) | 24.1256 | 0.864388 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.07069 | −0.217226 | ||||||||
\(782\) | 1.10992 | 0.0396905 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 31.3967 | 1.12131 | ||||||||
\(785\) | −20.0489 | −0.715577 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.0465 | −1.53444 | −0.767221 | − | 0.641382i | \(-0.778361\pi\) | ||||
−0.767221 | + | 0.641382i | \(0.778361\pi\) | |||||||
\(788\) | −33.1497 | −1.18091 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 25.4209 | 0.904434 | ||||||||
\(791\) | 12.4112 | 0.441291 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.9138 | 0.493781 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.1943 | −0.361329 | ||||||||
\(797\) | 44.7646 | 1.58564 | 0.792822 | − | 0.609453i | \(-0.208611\pi\) | ||||
0.792822 | + | 0.609453i | \(0.208611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.67025 | 0.165222 | ||||||||
\(800\) | 6.18598 | 0.218707 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −39.4010 | −1.39130 | ||||||||
\(803\) | 4.29052 | 0.151409 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.24698 | −0.0439503 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −24.2553 | −0.853300 | ||||||||
\(809\) | 37.5918 | 1.32166 | 0.660829 | − | 0.750537i | \(-0.270205\pi\) | ||||
0.660829 | + | 0.750537i | \(0.270205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.5797 | −0.582192 | −0.291096 | − | 0.956694i | \(-0.594020\pi\) | ||||
−0.291096 | + | 0.956694i | \(0.594020\pi\) | |||||||
\(812\) | 7.34481 | 0.257752 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.7409 | −0.376470 | ||||||||
\(815\) | −4.68233 | −0.164015 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.6437 | 0.652260 | ||||||||
\(818\) | −4.50796 | −0.157617 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.9758 | −0.383293 | ||||||||
\(821\) | 3.49263 | 0.121894 | 0.0609468 | − | 0.998141i | \(-0.480588\pi\) | ||||
0.0609468 | + | 0.998141i | \(0.480588\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.9318 | −1.25250 | −0.626252 | − | 0.779620i | \(-0.715412\pi\) | ||||
−0.626252 | + | 0.779620i | \(0.715412\pi\) | |||||||
\(824\) | 8.67563 | 0.302230 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.7332 | −0.408249 | ||||||||
\(827\) | −23.2319 | −0.807853 | −0.403926 | − | 0.914791i | \(-0.632355\pi\) | ||||
−0.403926 | + | 0.914791i | \(0.632355\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.9028 | −1.10803 | −0.554014 | − | 0.832507i | \(-0.686905\pi\) | ||||
−0.554014 | + | 0.832507i | \(0.686905\pi\) | |||||||
\(830\) | 3.31336 | 0.115008 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.51812 | −0.0872478 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5797 | 0.366126 | ||||||||
\(836\) | 3.41789 | 0.118210 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.16075 | 0.247364 | ||||||||
\(839\) | −34.3978 | −1.18754 | −0.593772 | − | 0.804634i | \(-0.702362\pi\) | ||||
−0.593772 | + | 0.804634i | \(0.702362\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.9463 | 0.860217 | ||||||||
\(842\) | 45.2476 | 1.55933 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.2416 | 0.627902 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.01938 | −0.275549 | ||||||||
\(848\) | 4.28860 | 0.147271 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.713792 | −0.0244829 | ||||||||
\(851\) | 9.26875 | 0.317729 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.5991 | −1.69824 | −0.849120 | − | 0.528200i | \(-0.822867\pi\) | ||||
−0.849120 | + | 0.528200i | \(0.822867\pi\) | |||||||
\(854\) | 5.94677 | 0.203494 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.2155 | −0.725132 | ||||||||
\(857\) | −30.5042 | −1.04200 | −0.521002 | − | 0.853555i | \(-0.674442\pi\) | ||||
−0.521002 | + | 0.853555i | \(0.674442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.8595 | 0.950553 | 0.475277 | − | 0.879836i | \(-0.342348\pi\) | ||||
0.475277 | + | 0.879836i | \(0.342348\pi\) | |||||||
\(860\) | −8.48188 | −0.289230 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.6450 | 0.430691 | ||||||||
\(863\) | −18.4413 | −0.627750 | −0.313875 | − | 0.949464i | \(-0.601627\pi\) | ||||
−0.313875 | + | 0.949464i | \(0.601627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.97823 | 0.169265 | ||||||||
\(866\) | 35.7385 | 1.21445 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.38404 | 0.0809197 | ||||||||
\(869\) | 14.1075 | 0.478565 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.0785 | 0.341300 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.67994 | −0.259778 | ||||||||
\(875\) | 0.801938 | 0.0271104 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.5163 | −1.23307 | −0.616534 | − | 0.787328i | \(-0.711464\pi\) | ||||
−0.616534 | + | 0.787328i | \(0.711464\pi\) | |||||||
\(878\) | 31.0640 | 1.04836 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.93900 | 0.166494 | ||||||||
\(881\) | −12.0562 | −0.406184 | −0.203092 | − | 0.979160i | \(-0.565099\pi\) | ||||
−0.203092 | + | 0.979160i | \(0.565099\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.3414 | −1.82873 | −0.914366 | − | 0.404888i | \(-0.867310\pi\) | ||||
−0.914366 | + | 0.404888i | \(0.867310\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.67802 | −0.123566 | ||||||||
\(887\) | 5.92500 | 0.198942 | 0.0994710 | − | 0.995040i | \(-0.468285\pi\) | ||||
0.0994710 | + | 0.995040i | \(0.468285\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00192 | −0.268376 | ||||||||
\(890\) | −11.7506 | −0.393882 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.8183 | −0.429189 | ||||||||
\(893\) | −32.3153 | −1.08139 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.5754 | −0.453776 | ||||||||
\(896\) | −8.08815 | −0.270206 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.8582 | −0.862898 | ||||||||
\(899\) | 17.5104 | 0.584003 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.343960 | −0.0114590 | ||||||||
\(902\) | −15.8605 | −0.528098 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.0000 | 0.698450 | ||||||||
\(905\) | 9.93661 | 0.330304 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.5784 | 0.915725 | 0.457863 | − | 0.889023i | \(-0.348615\pi\) | ||||
0.457863 | + | 0.889023i | \(0.348615\pi\) | |||||||
\(908\) | −6.77479 | −0.224829 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.5670 | 0.648285 | 0.324142 | − | 0.946008i | \(-0.394924\pi\) | ||||
0.324142 | + | 0.946008i | \(0.394924\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.83877 | 0.0608545 | ||||||||
\(914\) | −44.7101 | −1.47888 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.8146 | 0.819898 | ||||||||
\(917\) | −3.78448 | −0.124975 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.3739 | −0.606098 | −0.303049 | − | 0.952975i | \(-0.598005\pi\) | ||||
−0.303049 | + | 0.952975i | \(0.598005\pi\) | |||||||
\(920\) | −2.10992 | −0.0695619 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.5502 | −1.13785 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.96077 | −0.195989 | ||||||||
\(926\) | 28.5676 | 0.938791 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 45.4349 | 1.49147 | ||||||||
\(929\) | 8.94305 | 0.293412 | 0.146706 | − | 0.989180i | \(-0.453133\pi\) | ||||
0.146706 | + | 0.989180i | \(0.453133\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.4239 | 0.571044 | ||||||||
\(932\) | 14.3327 | 0.469484 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 36.5327 | 1.19539 | ||||||||
\(935\) | −0.396125 | −0.0129547 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.7047 | −1.16642 | −0.583211 | − | 0.812321i | \(-0.698204\pi\) | ||||
−0.583211 | + | 0.812321i | \(0.698204\pi\) | |||||||
\(938\) | −14.3623 | −0.468945 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.7017 | 0.479517 | ||||||||
\(941\) | 1.55257 | 0.0506122 | 0.0253061 | − | 0.999680i | \(-0.491944\pi\) | ||||
0.0253061 | + | 0.999680i | \(0.491944\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.6866 | 0.445698 | ||||||||
\(944\) | −40.1027 | −1.30523 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.2567 | −0.398499 | ||||||||
\(947\) | −5.96940 | −0.193979 | −0.0969896 | − | 0.995285i | \(-0.530921\pi\) | ||||
−0.0969896 | + | 0.995285i | \(0.530921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.93900 | 0.160242 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.431041 | 0.0139701 | ||||||||
\(953\) | 2.24459 | 0.0727093 | 0.0363546 | − | 0.999339i | \(-0.488425\pi\) | ||||
0.0363546 | + | 0.999339i | \(0.488425\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.8756 | 0.610800 | ||||||||
\(956\) | −27.5338 | −0.890506 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.0049 | −0.840180 | ||||||||
\(959\) | 3.18406 | 0.102819 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.3163 | −0.816656 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.6625 | 0.858741 | ||||||||
\(965\) | 11.3817 | 0.366388 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.1624 | 1.83822 | 0.919110 | − | 0.394002i | \(-0.128910\pi\) | ||||
0.919110 | + | 0.394002i | \(0.128910\pi\) | |||||||
\(968\) | −13.5690 | −0.436123 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23.6993 | 0.760939 | ||||||||
\(971\) | 13.8474 | 0.444384 | 0.222192 | − | 0.975003i | \(-0.428679\pi\) | ||||
0.222192 | + | 0.975003i | \(0.428679\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.2978 | −0.394250 | ||||||||
\(974\) | 63.2301 | 2.02602 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.3254 | 0.650601 | ||||||||
\(977\) | 40.7493 | 1.30369 | 0.651843 | − | 0.758354i | \(-0.273996\pi\) | ||||
0.651843 | + | 0.758354i | \(0.273996\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.52111 | −0.208415 | ||||||||
\(980\) | −7.92692 | −0.253216 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.97285 | 0.158690 | ||||||||
\(983\) | 21.4644 | 0.684609 | 0.342304 | − | 0.939589i | \(-0.388793\pi\) | ||||
0.342304 | + | 0.939589i | \(0.388793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.5840 | −0.847037 | ||||||||
\(986\) | −5.24267 | −0.166961 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.5767 | 0.336320 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.1584 | 1.40274 | 0.701368 | − | 0.712799i | \(-0.252573\pi\) | ||||
0.701368 | + | 0.712799i | \(0.252573\pi\) | |||||||
\(992\) | 14.7476 | 0.468238 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.77240 | −0.278244 | ||||||||
\(995\) | −8.17523 | −0.259172 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −56.7426 | −1.79706 | −0.898528 | − | 0.438916i | \(-0.855362\pi\) | ||||
−0.898528 | + | 0.438916i | \(0.855362\pi\) | |||||||
\(998\) | −31.3250 | −0.991574 | ||||||||
\(999\) | 0 | 0 |
(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 | 7605.2.a.bq.1.1 | 3 | ||
3.2 | odd | 2 | 2535.2.a.bd.1.3 | yes | 3 | ||
13.12 | even | 2 | 7605.2.a.bz.1.3 | 3 | |||
39.38 | odd | 2 | 2535.2.a.v.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2535.2.a.v.1.1 | ✓ | 3 | 39.38 | odd | 2 | ||
2535.2.a.bd.1.3 | yes | 3 | 3.2 | odd | 2 | ||
7605.2.a.bq.1.1 | 3 | 1.1 | even | 1 | trivial | ||
7605.2.a.bz.1.3 | 3 | 13.12 | even | 2 |