Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 11x^{6} + 10x^{5} + 35x^{4} - 30x^{3} - 30x^{2} + 30x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.98451\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.98451 | 1.40326 | 0.701632 | − | 0.712540i | \(-0.252455\pi\) | ||||
0.701632 | + | 0.712540i | \(0.252455\pi\) | |||||||
\(3\) | 2.78639 | 1.60873 | 0.804363 | − | 0.594139i | \(-0.202507\pi\) | ||||
0.804363 | + | 0.594139i | \(0.202507\pi\) | |||||||
\(4\) | 1.93830 | 0.969150 | ||||||||
\(5\) | −0.0269243 | −0.0120409 | −0.00602046 | − | 0.999982i | \(-0.501916\pi\) | ||||
−0.00602046 | + | 0.999982i | \(0.501916\pi\) | |||||||
\(6\) | 5.52964 | 2.25747 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.122446 | −0.0432911 | ||||||||
\(9\) | 4.76399 | 1.58800 | ||||||||
\(10\) | −0.0534317 | −0.0168966 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 5.40087 | 1.55910 | ||||||||
\(13\) | −4.88112 | −1.35378 | −0.676889 | − | 0.736085i | \(-0.736672\pi\) | ||||
−0.676889 | + | 0.736085i | \(0.736672\pi\) | |||||||
\(14\) | 1.98451 | 0.530384 | ||||||||
\(15\) | −0.0750218 | −0.0193705 | ||||||||
\(16\) | −4.11959 | −1.02990 | ||||||||
\(17\) | 1.67878 | 0.407164 | 0.203582 | − | 0.979058i | \(-0.434742\pi\) | ||||
0.203582 | + | 0.979058i | \(0.434742\pi\) | |||||||
\(18\) | 9.45421 | 2.22838 | ||||||||
\(19\) | 1.37394 | 0.315204 | 0.157602 | − | 0.987503i | \(-0.449624\pi\) | ||||
0.157602 | + | 0.987503i | \(0.449624\pi\) | |||||||
\(20\) | −0.0521874 | −0.0116695 | ||||||||
\(21\) | 2.78639 | 0.608041 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.06246 | 1.68114 | 0.840570 | − | 0.541703i | \(-0.182220\pi\) | ||||
0.840570 | + | 0.541703i | \(0.182220\pi\) | |||||||
\(24\) | −0.341182 | −0.0696435 | ||||||||
\(25\) | −4.99928 | −0.999855 | ||||||||
\(26\) | −9.68665 | −1.89971 | ||||||||
\(27\) | 4.91517 | 0.945925 | ||||||||
\(28\) | 1.93830 | 0.366304 | ||||||||
\(29\) | −6.39316 | −1.18718 | −0.593590 | − | 0.804768i | \(-0.702290\pi\) | ||||
−0.593590 | + | 0.804768i | \(0.702290\pi\) | |||||||
\(30\) | −0.148882 | −0.0271820 | ||||||||
\(31\) | 4.01054 | 0.720315 | 0.360157 | − | 0.932892i | \(-0.382723\pi\) | ||||
0.360157 | + | 0.932892i | \(0.382723\pi\) | |||||||
\(32\) | −7.93050 | −1.40193 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.33156 | 0.571358 | ||||||||
\(35\) | −0.0269243 | −0.00455104 | ||||||||
\(36\) | 9.23404 | 1.53901 | ||||||||
\(37\) | 0.521038 | 0.0856581 | 0.0428290 | − | 0.999082i | \(-0.486363\pi\) | ||||
0.0428290 | + | 0.999082i | \(0.486363\pi\) | |||||||
\(38\) | 2.72661 | 0.442314 | ||||||||
\(39\) | −13.6007 | −2.17786 | ||||||||
\(40\) | 0.00329677 | 0.000521265 0 | ||||||||
\(41\) | −10.5987 | −1.65525 | −0.827623 | − | 0.561285i | \(-0.810307\pi\) | ||||
−0.827623 | + | 0.561285i | \(0.810307\pi\) | |||||||
\(42\) | 5.52964 | 0.853242 | ||||||||
\(43\) | 3.73968 | 0.570296 | 0.285148 | − | 0.958483i | \(-0.407957\pi\) | ||||
0.285148 | + | 0.958483i | \(0.407957\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.128267 | −0.0191209 | ||||||||
\(46\) | 16.0001 | 2.35908 | ||||||||
\(47\) | −8.95906 | −1.30681 | −0.653407 | − | 0.757007i | \(-0.726661\pi\) | ||||
−0.653407 | + | 0.757007i | \(0.726661\pi\) | |||||||
\(48\) | −11.4788 | −1.65682 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −9.92114 | −1.40306 | ||||||||
\(51\) | 4.67774 | 0.655015 | ||||||||
\(52\) | −9.46107 | −1.31201 | ||||||||
\(53\) | −3.96057 | −0.544027 | −0.272013 | − | 0.962293i | \(-0.587689\pi\) | ||||
−0.272013 | + | 0.962293i | \(0.587689\pi\) | |||||||
\(54\) | 9.75422 | 1.32738 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.122446 | −0.0163625 | ||||||||
\(57\) | 3.82834 | 0.507076 | ||||||||
\(58\) | −12.6873 | −1.66593 | ||||||||
\(59\) | 9.73022 | 1.26677 | 0.633383 | − | 0.773838i | \(-0.281666\pi\) | ||||
0.633383 | + | 0.773838i | \(0.281666\pi\) | |||||||
\(60\) | −0.145415 | −0.0187730 | ||||||||
\(61\) | 8.46723 | 1.08412 | 0.542059 | − | 0.840341i | \(-0.317645\pi\) | ||||
0.542059 | + | 0.840341i | \(0.317645\pi\) | |||||||
\(62\) | 7.95898 | 1.01079 | ||||||||
\(63\) | 4.76399 | 0.600206 | ||||||||
\(64\) | −7.49902 | −0.937377 | ||||||||
\(65\) | 0.131421 | 0.0163008 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.81285 | 0.343644 | 0.171822 | − | 0.985128i | \(-0.445035\pi\) | ||||
0.171822 | + | 0.985128i | \(0.445035\pi\) | |||||||
\(68\) | 3.25398 | 0.394603 | ||||||||
\(69\) | 22.4652 | 2.70449 | ||||||||
\(70\) | −0.0534317 | −0.00638631 | ||||||||
\(71\) | 2.04551 | 0.242757 | 0.121379 | − | 0.992606i | \(-0.461268\pi\) | ||||
0.121379 | + | 0.992606i | \(0.461268\pi\) | |||||||
\(72\) | −0.583330 | −0.0687461 | ||||||||
\(73\) | −10.4693 | −1.22534 | −0.612671 | − | 0.790338i | \(-0.709905\pi\) | ||||
−0.612671 | + | 0.790338i | \(0.709905\pi\) | |||||||
\(74\) | 1.03401 | 0.120201 | ||||||||
\(75\) | −13.9299 | −1.60849 | ||||||||
\(76\) | 2.66311 | 0.305479 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −26.9908 | −3.05611 | ||||||||
\(79\) | 5.85521 | 0.658763 | 0.329381 | − | 0.944197i | \(-0.393160\pi\) | ||||
0.329381 | + | 0.944197i | \(0.393160\pi\) | |||||||
\(80\) | 0.110917 | 0.0124009 | ||||||||
\(81\) | −0.596375 | −0.0662639 | ||||||||
\(82\) | −21.0334 | −2.32275 | ||||||||
\(83\) | 2.60548 | 0.285988 | 0.142994 | − | 0.989724i | \(-0.454327\pi\) | ||||
0.142994 | + | 0.989724i | \(0.454327\pi\) | |||||||
\(84\) | 5.40087 | 0.589283 | ||||||||
\(85\) | −0.0452000 | −0.00490263 | ||||||||
\(86\) | 7.42146 | 0.800276 | ||||||||
\(87\) | −17.8139 | −1.90985 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.21791 | 0.129099 | 0.0645493 | − | 0.997915i | \(-0.479439\pi\) | ||||
0.0645493 | + | 0.997915i | \(0.479439\pi\) | |||||||
\(90\) | −0.254548 | −0.0268317 | ||||||||
\(91\) | −4.88112 | −0.511680 | ||||||||
\(92\) | 15.6275 | 1.62928 | ||||||||
\(93\) | 11.1749 | 1.15879 | ||||||||
\(94\) | −17.7794 | −1.83380 | ||||||||
\(95\) | −0.0369924 | −0.00379534 | ||||||||
\(96\) | −22.0975 | −2.25532 | ||||||||
\(97\) | 3.39670 | 0.344883 | 0.172441 | − | 0.985020i | \(-0.444834\pi\) | ||||
0.172441 | + | 0.985020i | \(0.444834\pi\) | |||||||
\(98\) | 1.98451 | 0.200466 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.69009 | −0.969009 | ||||||||
\(101\) | −4.04836 | −0.402826 | −0.201413 | − | 0.979506i | \(-0.564553\pi\) | ||||
−0.201413 | + | 0.979506i | \(0.564553\pi\) | |||||||
\(102\) | 9.28304 | 0.919158 | ||||||||
\(103\) | −3.95297 | −0.389498 | −0.194749 | − | 0.980853i | \(-0.562389\pi\) | ||||
−0.194749 | + | 0.980853i | \(0.562389\pi\) | |||||||
\(104\) | 0.597672 | 0.0586066 | ||||||||
\(105\) | −0.0750218 | −0.00732138 | ||||||||
\(106\) | −7.85982 | −0.763413 | ||||||||
\(107\) | 10.3986 | 1.00527 | 0.502635 | − | 0.864498i | \(-0.332364\pi\) | ||||
0.502635 | + | 0.864498i | \(0.332364\pi\) | |||||||
\(108\) | 9.52707 | 0.916742 | ||||||||
\(109\) | −3.77697 | −0.361768 | −0.180884 | − | 0.983504i | \(-0.557896\pi\) | ||||
−0.180884 | + | 0.983504i | \(0.557896\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.45182 | 0.137800 | ||||||||
\(112\) | −4.11959 | −0.389265 | ||||||||
\(113\) | 6.34869 | 0.597234 | 0.298617 | − | 0.954373i | \(-0.403475\pi\) | ||||
0.298617 | + | 0.954373i | \(0.403475\pi\) | |||||||
\(114\) | 7.59740 | 0.711561 | ||||||||
\(115\) | −0.217076 | −0.0202425 | ||||||||
\(116\) | −12.3919 | −1.15056 | ||||||||
\(117\) | −23.2536 | −2.14980 | ||||||||
\(118\) | 19.3098 | 1.77761 | ||||||||
\(119\) | 1.67878 | 0.153893 | ||||||||
\(120\) | 0.00918610 | 0.000838572 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 16.8033 | 1.52130 | ||||||||
\(123\) | −29.5323 | −2.66283 | ||||||||
\(124\) | 7.77363 | 0.698093 | ||||||||
\(125\) | 0.269224 | 0.0240801 | ||||||||
\(126\) | 9.45421 | 0.842248 | ||||||||
\(127\) | −5.03128 | −0.446454 | −0.223227 | − | 0.974766i | \(-0.571659\pi\) | ||||
−0.223227 | + | 0.974766i | \(0.571659\pi\) | |||||||
\(128\) | 0.979100 | 0.0865410 | ||||||||
\(129\) | 10.4202 | 0.917450 | ||||||||
\(130\) | 0.260807 | 0.0228743 | ||||||||
\(131\) | −3.76357 | −0.328825 | −0.164412 | − | 0.986392i | \(-0.552573\pi\) | ||||
−0.164412 | + | 0.986392i | \(0.552573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.37394 | 0.119136 | ||||||||
\(134\) | 5.58214 | 0.482223 | ||||||||
\(135\) | −0.132338 | −0.0113898 | ||||||||
\(136\) | −0.205559 | −0.0176266 | ||||||||
\(137\) | 19.1379 | 1.63506 | 0.817529 | − | 0.575887i | \(-0.195343\pi\) | ||||
0.817529 | + | 0.575887i | \(0.195343\pi\) | |||||||
\(138\) | 44.5825 | 3.79512 | ||||||||
\(139\) | 3.51108 | 0.297806 | 0.148903 | − | 0.988852i | \(-0.452426\pi\) | ||||
0.148903 | + | 0.988852i | \(0.452426\pi\) | |||||||
\(140\) | −0.0521874 | −0.00441064 | ||||||||
\(141\) | −24.9635 | −2.10230 | ||||||||
\(142\) | 4.05934 | 0.340652 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −19.6257 | −1.63548 | ||||||||
\(145\) | 0.172132 | 0.0142948 | ||||||||
\(146\) | −20.7766 | −1.71948 | ||||||||
\(147\) | 2.78639 | 0.229818 | ||||||||
\(148\) | 1.00993 | 0.0830155 | ||||||||
\(149\) | −3.12643 | −0.256127 | −0.128063 | − | 0.991766i | \(-0.540876\pi\) | ||||
−0.128063 | + | 0.991766i | \(0.540876\pi\) | |||||||
\(150\) | −27.6442 | −2.25714 | ||||||||
\(151\) | 19.7215 | 1.60491 | 0.802456 | − | 0.596712i | \(-0.203526\pi\) | ||||
0.802456 | + | 0.596712i | \(0.203526\pi\) | |||||||
\(152\) | −0.168233 | −0.0136455 | ||||||||
\(153\) | 7.99769 | 0.646575 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.107981 | −0.00867326 | ||||||||
\(156\) | −26.3623 | −2.11067 | ||||||||
\(157\) | −22.9546 | −1.83197 | −0.915987 | − | 0.401207i | \(-0.868591\pi\) | ||||
−0.915987 | + | 0.401207i | \(0.868591\pi\) | |||||||
\(158\) | 11.6198 | 0.924418 | ||||||||
\(159\) | −11.0357 | −0.875189 | ||||||||
\(160\) | 0.213524 | 0.0168805 | ||||||||
\(161\) | 8.06246 | 0.635411 | ||||||||
\(162\) | −1.18351 | −0.0929857 | ||||||||
\(163\) | 18.9891 | 1.48734 | 0.743670 | − | 0.668547i | \(-0.233083\pi\) | ||||
0.743670 | + | 0.668547i | \(0.233083\pi\) | |||||||
\(164\) | −20.5435 | −1.60418 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.17061 | 0.401317 | ||||||||
\(167\) | −3.02044 | −0.233728 | −0.116864 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116864 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(168\) | −0.341182 | −0.0263228 | ||||||||
\(169\) | 10.8253 | 0.832717 | ||||||||
\(170\) | −0.0897001 | −0.00687968 | ||||||||
\(171\) | 6.54544 | 0.500542 | ||||||||
\(172\) | 7.24863 | 0.552703 | ||||||||
\(173\) | 8.83629 | 0.671811 | 0.335905 | − | 0.941896i | \(-0.390958\pi\) | ||||
0.335905 | + | 0.941896i | \(0.390958\pi\) | |||||||
\(174\) | −35.3519 | −2.68002 | ||||||||
\(175\) | −4.99928 | −0.377910 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.1122 | 2.03788 | ||||||||
\(178\) | 2.41697 | 0.181159 | ||||||||
\(179\) | 8.46434 | 0.632654 | 0.316327 | − | 0.948650i | \(-0.397550\pi\) | ||||
0.316327 | + | 0.948650i | \(0.397550\pi\) | |||||||
\(180\) | −0.248620 | −0.0185311 | ||||||||
\(181\) | −24.2008 | −1.79883 | −0.899415 | − | 0.437095i | \(-0.856007\pi\) | ||||
−0.899415 | + | 0.437095i | \(0.856007\pi\) | |||||||
\(182\) | −9.68665 | −0.718022 | ||||||||
\(183\) | 23.5930 | 1.74405 | ||||||||
\(184\) | −0.987214 | −0.0727784 | ||||||||
\(185\) | −0.0140286 | −0.00103140 | ||||||||
\(186\) | 22.1769 | 1.62609 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −17.3653 | −1.26650 | ||||||||
\(189\) | 4.91517 | 0.357526 | ||||||||
\(190\) | −0.0734120 | −0.00532587 | ||||||||
\(191\) | −7.78718 | −0.563460 | −0.281730 | − | 0.959494i | \(-0.590908\pi\) | ||||
−0.281730 | + | 0.959494i | \(0.590908\pi\) | |||||||
\(192\) | −20.8952 | −1.50798 | ||||||||
\(193\) | 17.0637 | 1.22827 | 0.614134 | − | 0.789201i | \(-0.289505\pi\) | ||||
0.614134 | + | 0.789201i | \(0.289505\pi\) | |||||||
\(194\) | 6.74081 | 0.483962 | ||||||||
\(195\) | 0.366190 | 0.0262234 | ||||||||
\(196\) | 1.93830 | 0.138450 | ||||||||
\(197\) | −6.05536 | −0.431426 | −0.215713 | − | 0.976457i | \(-0.569208\pi\) | ||||
−0.215713 | + | 0.976457i | \(0.569208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.7181 | −0.972451 | −0.486226 | − | 0.873833i | \(-0.661627\pi\) | ||||
−0.486226 | + | 0.873833i | \(0.661627\pi\) | |||||||
\(200\) | 0.612140 | 0.0432848 | ||||||||
\(201\) | 7.83770 | 0.552829 | ||||||||
\(202\) | −8.03402 | −0.565272 | ||||||||
\(203\) | −6.39316 | −0.448712 | ||||||||
\(204\) | 9.06686 | 0.634807 | ||||||||
\(205\) | 0.285364 | 0.0199307 | ||||||||
\(206\) | −7.84472 | −0.546568 | ||||||||
\(207\) | 38.4095 | 2.66964 | ||||||||
\(208\) | 20.1082 | 1.39425 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.148882 | −0.0102738 | ||||||||
\(211\) | 18.0352 | 1.24160 | 0.620799 | − | 0.783970i | \(-0.286808\pi\) | ||||
0.620799 | + | 0.783970i | \(0.286808\pi\) | |||||||
\(212\) | −7.67678 | −0.527243 | ||||||||
\(213\) | 5.69959 | 0.390530 | ||||||||
\(214\) | 20.6362 | 1.41066 | ||||||||
\(215\) | −0.100688 | −0.00686690 | ||||||||
\(216\) | −0.601841 | −0.0409501 | ||||||||
\(217\) | 4.01054 | 0.272253 | ||||||||
\(218\) | −7.49546 | −0.507656 | ||||||||
\(219\) | −29.1717 | −1.97124 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.19432 | −0.551210 | ||||||||
\(222\) | 2.88115 | 0.193370 | ||||||||
\(223\) | −6.53314 | −0.437491 | −0.218746 | − | 0.975782i | \(-0.570197\pi\) | ||||
−0.218746 | + | 0.975782i | \(0.570197\pi\) | |||||||
\(224\) | −7.93050 | −0.529879 | ||||||||
\(225\) | −23.8165 | −1.58777 | ||||||||
\(226\) | 12.5991 | 0.838077 | ||||||||
\(227\) | 13.6077 | 0.903176 | 0.451588 | − | 0.892227i | \(-0.350858\pi\) | ||||
0.451588 | + | 0.892227i | \(0.350858\pi\) | |||||||
\(228\) | 7.42047 | 0.491433 | ||||||||
\(229\) | −19.4211 | −1.28338 | −0.641690 | − | 0.766964i | \(-0.721767\pi\) | ||||
−0.641690 | + | 0.766964i | \(0.721767\pi\) | |||||||
\(230\) | −0.430791 | −0.0284055 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.782815 | 0.0513943 | ||||||||
\(233\) | 4.36150 | 0.285731 | 0.142866 | − | 0.989742i | \(-0.454368\pi\) | ||||
0.142866 | + | 0.989742i | \(0.454368\pi\) | |||||||
\(234\) | −46.1471 | −3.01673 | ||||||||
\(235\) | 0.241217 | 0.0157353 | ||||||||
\(236\) | 18.8601 | 1.22769 | ||||||||
\(237\) | 16.3149 | 1.05977 | ||||||||
\(238\) | 3.33156 | 0.215953 | ||||||||
\(239\) | 10.5901 | 0.685018 | 0.342509 | − | 0.939515i | \(-0.388723\pi\) | ||||
0.342509 | + | 0.939515i | \(0.388723\pi\) | |||||||
\(240\) | 0.309059 | 0.0199497 | ||||||||
\(241\) | 18.6887 | 1.20384 | 0.601921 | − | 0.798555i | \(-0.294402\pi\) | ||||
0.601921 | + | 0.798555i | \(0.294402\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.4072 | −1.05252 | ||||||||
\(244\) | 16.4120 | 1.05067 | ||||||||
\(245\) | −0.0269243 | −0.00172013 | ||||||||
\(246\) | −58.6072 | −3.73666 | ||||||||
\(247\) | −6.70637 | −0.426716 | ||||||||
\(248\) | −0.491074 | −0.0311832 | ||||||||
\(249\) | 7.25988 | 0.460076 | ||||||||
\(250\) | 0.534279 | 0.0337907 | ||||||||
\(251\) | 18.9832 | 1.19821 | 0.599103 | − | 0.800672i | \(-0.295524\pi\) | ||||
0.599103 | + | 0.800672i | \(0.295524\pi\) | |||||||
\(252\) | 9.23404 | 0.581690 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −9.98465 | −0.626493 | ||||||||
\(255\) | −0.125945 | −0.00788698 | ||||||||
\(256\) | 16.9411 | 1.05882 | ||||||||
\(257\) | −13.7090 | −0.855147 | −0.427573 | − | 0.903981i | \(-0.640631\pi\) | ||||
−0.427573 | + | 0.903981i | \(0.640631\pi\) | |||||||
\(258\) | 20.6791 | 1.28742 | ||||||||
\(259\) | 0.521038 | 0.0323757 | ||||||||
\(260\) | 0.254733 | 0.0157979 | ||||||||
\(261\) | −30.4569 | −1.88524 | ||||||||
\(262\) | −7.46887 | −0.461428 | ||||||||
\(263\) | 16.5767 | 1.02217 | 0.511083 | − | 0.859531i | \(-0.329244\pi\) | ||||
0.511083 | + | 0.859531i | \(0.329244\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.106636 | 0.00655059 | ||||||||
\(266\) | 2.72661 | 0.167179 | ||||||||
\(267\) | 3.39359 | 0.207684 | ||||||||
\(268\) | 5.45214 | 0.333043 | ||||||||
\(269\) | −8.54361 | −0.520913 | −0.260457 | − | 0.965486i | \(-0.583873\pi\) | ||||
−0.260457 | + | 0.965486i | \(0.583873\pi\) | |||||||
\(270\) | −0.262626 | −0.0159829 | ||||||||
\(271\) | −6.34553 | −0.385463 | −0.192732 | − | 0.981251i | \(-0.561735\pi\) | ||||
−0.192732 | + | 0.981251i | \(0.561735\pi\) | |||||||
\(272\) | −6.91589 | −0.419337 | ||||||||
\(273\) | −13.6007 | −0.823153 | ||||||||
\(274\) | 37.9794 | 2.29442 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 43.5443 | 2.62106 | ||||||||
\(277\) | −24.0044 | −1.44228 | −0.721142 | − | 0.692788i | \(-0.756382\pi\) | ||||
−0.721142 | + | 0.692788i | \(0.756382\pi\) | |||||||
\(278\) | 6.96780 | 0.417901 | ||||||||
\(279\) | 19.1062 | 1.14386 | ||||||||
\(280\) | 0.00329677 | 0.000197020 0 | ||||||||
\(281\) | −3.21144 | −0.191578 | −0.0957891 | − | 0.995402i | \(-0.530537\pi\) | ||||
−0.0957891 | + | 0.995402i | \(0.530537\pi\) | |||||||
\(282\) | −49.5404 | −2.95009 | ||||||||
\(283\) | −20.8034 | −1.23663 | −0.618317 | − | 0.785929i | \(-0.712185\pi\) | ||||
−0.618317 | + | 0.785929i | \(0.712185\pi\) | |||||||
\(284\) | 3.96481 | 0.235268 | ||||||||
\(285\) | −0.103075 | −0.00610567 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.5987 | −0.625624 | ||||||||
\(288\) | −37.7808 | −2.22626 | ||||||||
\(289\) | −14.1817 | −0.834218 | ||||||||
\(290\) | 0.341598 | 0.0200593 | ||||||||
\(291\) | 9.46455 | 0.554822 | ||||||||
\(292\) | −20.2927 | −1.18754 | ||||||||
\(293\) | 5.51744 | 0.322332 | 0.161166 | − | 0.986927i | \(-0.448474\pi\) | ||||
0.161166 | + | 0.986927i | \(0.448474\pi\) | |||||||
\(294\) | 5.52964 | 0.322495 | ||||||||
\(295\) | −0.261980 | −0.0152530 | ||||||||
\(296\) | −0.0637988 | −0.00370823 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.20444 | −0.359414 | ||||||||
\(299\) | −39.3538 | −2.27589 | ||||||||
\(300\) | −27.0004 | −1.55887 | ||||||||
\(301\) | 3.73968 | 0.215552 | ||||||||
\(302\) | 39.1376 | 2.25211 | ||||||||
\(303\) | −11.2803 | −0.648037 | ||||||||
\(304\) | −5.66008 | −0.324628 | ||||||||
\(305\) | −0.227974 | −0.0130538 | ||||||||
\(306\) | 15.8715 | 0.907315 | ||||||||
\(307\) | 8.60991 | 0.491394 | 0.245697 | − | 0.969347i | \(-0.420983\pi\) | ||||
0.245697 | + | 0.969347i | \(0.420983\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.0145 | −0.626594 | ||||||||
\(310\) | −0.214290 | −0.0121709 | ||||||||
\(311\) | 19.1258 | 1.08453 | 0.542263 | − | 0.840209i | \(-0.317568\pi\) | ||||
0.542263 | + | 0.840209i | \(0.317568\pi\) | |||||||
\(312\) | 1.66535 | 0.0942819 | ||||||||
\(313\) | −0.606755 | −0.0342958 | −0.0171479 | − | 0.999853i | \(-0.505459\pi\) | ||||
−0.0171479 | + | 0.999853i | \(0.505459\pi\) | |||||||
\(314\) | −45.5537 | −2.57074 | ||||||||
\(315\) | −0.128267 | −0.00722704 | ||||||||
\(316\) | 11.3492 | 0.638440 | ||||||||
\(317\) | −5.21283 | −0.292782 | −0.146391 | − | 0.989227i | \(-0.546766\pi\) | ||||
−0.146391 | + | 0.989227i | \(0.546766\pi\) | |||||||
\(318\) | −21.9005 | −1.22812 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.201906 | 0.0112869 | ||||||||
\(321\) | 28.9746 | 1.61720 | ||||||||
\(322\) | 16.0001 | 0.891650 | ||||||||
\(323\) | 2.30654 | 0.128339 | ||||||||
\(324\) | −1.15595 | −0.0642196 | ||||||||
\(325\) | 24.4021 | 1.35358 | ||||||||
\(326\) | 37.6841 | 2.08713 | ||||||||
\(327\) | −10.5241 | −0.581986 | ||||||||
\(328\) | 1.29777 | 0.0716574 | ||||||||
\(329\) | −8.95906 | −0.493929 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.669012 | 0.0367722 | 0.0183861 | − | 0.999831i | \(-0.494147\pi\) | ||||
0.0183861 | + | 0.999831i | \(0.494147\pi\) | |||||||
\(332\) | 5.05019 | 0.277165 | ||||||||
\(333\) | 2.48222 | 0.136025 | ||||||||
\(334\) | −5.99410 | −0.327983 | ||||||||
\(335\) | −0.0757340 | −0.00413779 | ||||||||
\(336\) | −11.4788 | −0.626220 | ||||||||
\(337\) | −6.60215 | −0.359642 | −0.179821 | − | 0.983699i | \(-0.557552\pi\) | ||||
−0.179821 | + | 0.983699i | \(0.557552\pi\) | |||||||
\(338\) | 21.4830 | 1.16852 | ||||||||
\(339\) | 17.6899 | 0.960785 | ||||||||
\(340\) | −0.0876111 | −0.00475138 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.9895 | 0.702393 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −0.457908 | −0.0246888 | ||||||||
\(345\) | −0.604860 | −0.0325646 | ||||||||
\(346\) | 17.5358 | 0.942728 | ||||||||
\(347\) | 12.2001 | 0.654937 | 0.327469 | − | 0.944862i | \(-0.393804\pi\) | ||||
0.327469 | + | 0.944862i | \(0.393804\pi\) | |||||||
\(348\) | −34.5286 | −1.85093 | ||||||||
\(349\) | −0.885800 | −0.0474158 | −0.0237079 | − | 0.999719i | \(-0.507547\pi\) | ||||
−0.0237079 | + | 0.999719i | \(0.507547\pi\) | |||||||
\(350\) | −9.92114 | −0.530307 | ||||||||
\(351\) | −23.9915 | −1.28057 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.36012 | 0.285291 | 0.142645 | − | 0.989774i | \(-0.454439\pi\) | ||||
0.142645 | + | 0.989774i | \(0.454439\pi\) | |||||||
\(354\) | 53.8046 | 2.85968 | ||||||||
\(355\) | −0.0550740 | −0.00292302 | ||||||||
\(356\) | 2.36068 | 0.125116 | ||||||||
\(357\) | 4.67774 | 0.247572 | ||||||||
\(358\) | 16.7976 | 0.887781 | ||||||||
\(359\) | 25.8450 | 1.36405 | 0.682023 | − | 0.731330i | \(-0.261100\pi\) | ||||
0.682023 | + | 0.731330i | \(0.261100\pi\) | |||||||
\(360\) | 0.0157058 | 0.000827767 0 | ||||||||
\(361\) | −17.1123 | −0.900647 | ||||||||
\(362\) | −48.0268 | −2.52423 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.46107 | −0.495895 | ||||||||
\(365\) | 0.281880 | 0.0147543 | ||||||||
\(366\) | 46.8207 | 2.44736 | ||||||||
\(367\) | −20.4504 | −1.06750 | −0.533752 | − | 0.845641i | \(-0.679218\pi\) | ||||
−0.533752 | + | 0.845641i | \(0.679218\pi\) | |||||||
\(368\) | −33.2141 | −1.73140 | ||||||||
\(369\) | −50.4923 | −2.62852 | ||||||||
\(370\) | −0.0278400 | −0.00144733 | ||||||||
\(371\) | −3.96057 | −0.205623 | ||||||||
\(372\) | 21.6604 | 1.12304 | ||||||||
\(373\) | 9.39109 | 0.486252 | 0.243126 | − | 0.969995i | \(-0.421827\pi\) | ||||
0.243126 | + | 0.969995i | \(0.421827\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.750163 | 0.0387383 | ||||||||
\(376\) | 1.09700 | 0.0565734 | ||||||||
\(377\) | 31.2058 | 1.60718 | ||||||||
\(378\) | 9.75422 | 0.501703 | ||||||||
\(379\) | −5.63593 | −0.289498 | −0.144749 | − | 0.989468i | \(-0.546238\pi\) | ||||
−0.144749 | + | 0.989468i | \(0.546238\pi\) | |||||||
\(380\) | −0.0717024 | −0.00367826 | ||||||||
\(381\) | −14.0191 | −0.718222 | ||||||||
\(382\) | −15.4538 | −0.790684 | ||||||||
\(383\) | −1.25944 | −0.0643544 | −0.0321772 | − | 0.999482i | \(-0.510244\pi\) | ||||
−0.0321772 | + | 0.999482i | \(0.510244\pi\) | |||||||
\(384\) | 2.72816 | 0.139221 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 33.8631 | 1.72359 | ||||||||
\(387\) | 17.8158 | 0.905629 | ||||||||
\(388\) | 6.58383 | 0.334243 | ||||||||
\(389\) | −5.88409 | −0.298335 | −0.149168 | − | 0.988812i | \(-0.547659\pi\) | ||||
−0.149168 | + | 0.988812i | \(0.547659\pi\) | |||||||
\(390\) | 0.726710 | 0.0367984 | ||||||||
\(391\) | 13.5351 | 0.684499 | ||||||||
\(392\) | −0.122446 | −0.00618444 | ||||||||
\(393\) | −10.4868 | −0.528989 | ||||||||
\(394\) | −12.0169 | −0.605405 | ||||||||
\(395\) | −0.157648 | −0.00793212 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.86018 | 0.243925 | 0.121963 | − | 0.992535i | \(-0.461081\pi\) | ||||
0.121963 | + | 0.992535i | \(0.461081\pi\) | |||||||
\(398\) | −27.2238 | −1.36461 | ||||||||
\(399\) | 3.82834 | 0.191657 | ||||||||
\(400\) | 20.5950 | 1.02975 | ||||||||
\(401\) | −25.5322 | −1.27502 | −0.637508 | − | 0.770444i | \(-0.720035\pi\) | ||||
−0.637508 | + | 0.770444i | \(0.720035\pi\) | |||||||
\(402\) | 15.5540 | 0.775765 | ||||||||
\(403\) | −19.5759 | −0.975147 | ||||||||
\(404\) | −7.84692 | −0.390399 | ||||||||
\(405\) | 0.0160570 | 0.000797878 0 | ||||||||
\(406\) | −12.6873 | −0.629661 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.572769 | −0.0283563 | ||||||||
\(409\) | 21.0267 | 1.03970 | 0.519851 | − | 0.854257i | \(-0.325988\pi\) | ||||
0.519851 | + | 0.854257i | \(0.325988\pi\) | |||||||
\(410\) | 0.566309 | 0.0279680 | ||||||||
\(411\) | 53.3256 | 2.63036 | ||||||||
\(412\) | −7.66204 | −0.377481 | ||||||||
\(413\) | 9.73022 | 0.478793 | ||||||||
\(414\) | 76.2242 | 3.74622 | ||||||||
\(415\) | −0.0701507 | −0.00344356 | ||||||||
\(416\) | 38.7097 | 1.89790 | ||||||||
\(417\) | 9.78326 | 0.479088 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.3141 | −1.52980 | −0.764898 | − | 0.644151i | \(-0.777211\pi\) | ||||
−0.764898 | + | 0.644151i | \(0.777211\pi\) | |||||||
\(420\) | −0.145415 | −0.00709551 | ||||||||
\(421\) | 12.7886 | 0.623280 | 0.311640 | − | 0.950200i | \(-0.399122\pi\) | ||||
0.311640 | + | 0.950200i | \(0.399122\pi\) | |||||||
\(422\) | 35.7912 | 1.74229 | ||||||||
\(423\) | −42.6809 | −2.07522 | ||||||||
\(424\) | 0.484955 | 0.0235515 | ||||||||
\(425\) | −8.39268 | −0.407105 | ||||||||
\(426\) | 11.3109 | 0.548016 | ||||||||
\(427\) | 8.46723 | 0.409758 | ||||||||
\(428\) | 20.1556 | 0.974258 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.199818 | −0.00963607 | ||||||||
\(431\) | 21.0679 | 1.01480 | 0.507402 | − | 0.861709i | \(-0.330606\pi\) | ||||
0.507402 | + | 0.861709i | \(0.330606\pi\) | |||||||
\(432\) | −20.2485 | −0.974206 | ||||||||
\(433\) | 38.0030 | 1.82631 | 0.913155 | − | 0.407613i | \(-0.133639\pi\) | ||||
0.913155 | + | 0.407613i | \(0.133639\pi\) | |||||||
\(434\) | 7.95898 | 0.382043 | ||||||||
\(435\) | 0.479626 | 0.0229963 | ||||||||
\(436\) | −7.32090 | −0.350608 | ||||||||
\(437\) | 11.0773 | 0.529901 | ||||||||
\(438\) | −57.8916 | −2.76617 | ||||||||
\(439\) | −37.7677 | −1.80256 | −0.901278 | − | 0.433241i | \(-0.857370\pi\) | ||||
−0.901278 | + | 0.433241i | \(0.857370\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.76399 | 0.226857 | ||||||||
\(442\) | −16.2618 | −0.773493 | ||||||||
\(443\) | −1.02792 | −0.0488381 | −0.0244190 | − | 0.999702i | \(-0.507774\pi\) | ||||
−0.0244190 | + | 0.999702i | \(0.507774\pi\) | |||||||
\(444\) | 2.81405 | 0.133549 | ||||||||
\(445\) | −0.0327915 | −0.00155447 | ||||||||
\(446\) | −12.9651 | −0.613916 | ||||||||
\(447\) | −8.71146 | −0.412038 | ||||||||
\(448\) | −7.49902 | −0.354295 | ||||||||
\(449\) | 20.1333 | 0.950149 | 0.475074 | − | 0.879946i | \(-0.342421\pi\) | ||||
0.475074 | + | 0.879946i | \(0.342421\pi\) | |||||||
\(450\) | −47.2642 | −2.22806 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.3057 | 0.578809 | ||||||||
\(453\) | 54.9518 | 2.58186 | ||||||||
\(454\) | 27.0047 | 1.26739 | ||||||||
\(455\) | 0.131421 | 0.00616111 | ||||||||
\(456\) | −0.468764 | −0.0219519 | ||||||||
\(457\) | −24.1456 | −1.12948 | −0.564742 | − | 0.825268i | \(-0.691024\pi\) | ||||
−0.564742 | + | 0.825268i | \(0.691024\pi\) | |||||||
\(458\) | −38.5414 | −1.80092 | ||||||||
\(459\) | 8.25148 | 0.385146 | ||||||||
\(460\) | −0.420759 | −0.0196180 | ||||||||
\(461\) | 11.5885 | 0.539731 | 0.269865 | − | 0.962898i | \(-0.413021\pi\) | ||||
0.269865 | + | 0.962898i | \(0.413021\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.6077 | 1.00419 | 0.502097 | − | 0.864811i | \(-0.332562\pi\) | ||||
0.502097 | + | 0.864811i | \(0.332562\pi\) | |||||||
\(464\) | 26.3372 | 1.22268 | ||||||||
\(465\) | −0.300878 | −0.0139529 | ||||||||
\(466\) | 8.65547 | 0.400957 | ||||||||
\(467\) | 15.9149 | 0.736456 | 0.368228 | − | 0.929736i | \(-0.379965\pi\) | ||||
0.368228 | + | 0.929736i | \(0.379965\pi\) | |||||||
\(468\) | −45.0724 | −2.08347 | ||||||||
\(469\) | 2.81285 | 0.129885 | ||||||||
\(470\) | 0.478698 | 0.0220807 | ||||||||
\(471\) | −63.9605 | −2.94714 | ||||||||
\(472\) | −1.19142 | −0.0548397 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 32.3772 | 1.48713 | ||||||||
\(475\) | −6.86871 | −0.315158 | ||||||||
\(476\) | 3.25398 | 0.149146 | ||||||||
\(477\) | −18.8681 | −0.863913 | ||||||||
\(478\) | 21.0162 | 0.961261 | ||||||||
\(479\) | 5.28372 | 0.241419 | 0.120710 | − | 0.992688i | \(-0.461483\pi\) | ||||
0.120710 | + | 0.992688i | \(0.461483\pi\) | |||||||
\(480\) | 0.594961 | 0.0271561 | ||||||||
\(481\) | −2.54325 | −0.115962 | ||||||||
\(482\) | 37.0879 | 1.68931 | ||||||||
\(483\) | 22.4652 | 1.02220 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0914540 | −0.00415271 | ||||||||
\(486\) | −32.5604 | −1.47697 | ||||||||
\(487\) | −27.0656 | −1.22646 | −0.613229 | − | 0.789905i | \(-0.710130\pi\) | ||||
−0.613229 | + | 0.789905i | \(0.710130\pi\) | |||||||
\(488\) | −1.03678 | −0.0469326 | ||||||||
\(489\) | 52.9111 | 2.39272 | ||||||||
\(490\) | −0.0534317 | −0.00241380 | ||||||||
\(491\) | 18.8000 | 0.848431 | 0.424215 | − | 0.905561i | \(-0.360550\pi\) | ||||
0.424215 | + | 0.905561i | \(0.360550\pi\) | |||||||
\(492\) | −57.2424 | −2.58069 | ||||||||
\(493\) | −10.7327 | −0.483377 | ||||||||
\(494\) | −13.3089 | −0.598795 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.5218 | −0.741851 | ||||||||
\(497\) | 2.04551 | 0.0917536 | ||||||||
\(498\) | 14.4073 | 0.645608 | ||||||||
\(499\) | −39.7667 | −1.78020 | −0.890100 | − | 0.455765i | \(-0.849366\pi\) | ||||
−0.890100 | + | 0.455765i | \(0.849366\pi\) | |||||||
\(500\) | 0.521836 | 0.0233372 | ||||||||
\(501\) | −8.41612 | −0.376005 | ||||||||
\(502\) | 37.6724 | 1.68140 | ||||||||
\(503\) | 40.5624 | 1.80859 | 0.904294 | − | 0.426910i | \(-0.140398\pi\) | ||||
0.904294 | + | 0.426910i | \(0.140398\pi\) | |||||||
\(504\) | −0.583330 | −0.0259836 | ||||||||
\(505\) | 0.108999 | 0.00485040 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.1636 | 1.33961 | ||||||||
\(508\) | −9.75213 | −0.432681 | ||||||||
\(509\) | −15.4809 | −0.686179 | −0.343090 | − | 0.939303i | \(-0.611473\pi\) | ||||
−0.343090 | + | 0.939303i | \(0.611473\pi\) | |||||||
\(510\) | −0.249940 | −0.0110675 | ||||||||
\(511\) | −10.4693 | −0.463136 | ||||||||
\(512\) | 31.6616 | 1.39926 | ||||||||
\(513\) | 6.75315 | 0.298159 | ||||||||
\(514\) | −27.2058 | −1.20000 | ||||||||
\(515\) | 0.106431 | 0.00468991 | ||||||||
\(516\) | 20.1975 | 0.889147 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.03401 | 0.0454317 | ||||||||
\(519\) | 24.6214 | 1.08076 | ||||||||
\(520\) | −0.0160919 | −0.000705677 0 | ||||||||
\(521\) | 37.4738 | 1.64176 | 0.820878 | − | 0.571103i | \(-0.193484\pi\) | ||||
0.820878 | + | 0.571103i | \(0.193484\pi\) | |||||||
\(522\) | −60.4423 | −2.64549 | ||||||||
\(523\) | −20.8115 | −0.910024 | −0.455012 | − | 0.890485i | \(-0.650365\pi\) | ||||
−0.455012 | + | 0.890485i | \(0.650365\pi\) | |||||||
\(524\) | −7.29493 | −0.318681 | ||||||||
\(525\) | −13.9299 | −0.607953 | ||||||||
\(526\) | 32.8968 | 1.43437 | ||||||||
\(527\) | 6.73281 | 0.293286 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 42.0033 | 1.82623 | ||||||||
\(530\) | 0.211620 | 0.00919220 | ||||||||
\(531\) | 46.3547 | 2.01162 | ||||||||
\(532\) | 2.66311 | 0.115460 | ||||||||
\(533\) | 51.7337 | 2.24084 | ||||||||
\(534\) | 6.73463 | 0.291436 | ||||||||
\(535\) | −0.279975 | −0.0121044 | ||||||||
\(536\) | −0.344421 | −0.0148767 | ||||||||
\(537\) | 23.5850 | 1.01777 | ||||||||
\(538\) | −16.9549 | −0.730979 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.256510 | −0.0110384 | ||||||||
\(541\) | −17.4259 | −0.749196 | −0.374598 | − | 0.927187i | \(-0.622219\pi\) | ||||
−0.374598 | + | 0.927187i | \(0.622219\pi\) | |||||||
\(542\) | −12.5928 | −0.540907 | ||||||||
\(543\) | −67.4329 | −2.89382 | ||||||||
\(544\) | −13.3136 | −0.570814 | ||||||||
\(545\) | 0.101692 | 0.00435602 | ||||||||
\(546\) | −26.9908 | −1.15510 | ||||||||
\(547\) | −15.7960 | −0.675386 | −0.337693 | − | 0.941256i | \(-0.609647\pi\) | ||||
−0.337693 | + | 0.941256i | \(0.609647\pi\) | |||||||
\(548\) | 37.0949 | 1.58462 | ||||||||
\(549\) | 40.3378 | 1.72157 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.78382 | −0.374203 | ||||||||
\(552\) | −2.75077 | −0.117080 | ||||||||
\(553\) | 5.85521 | 0.248989 | ||||||||
\(554\) | −47.6371 | −2.02390 | ||||||||
\(555\) | −0.0390892 | −0.00165924 | ||||||||
\(556\) | 6.80553 | 0.288619 | ||||||||
\(557\) | −16.8351 | −0.713325 | −0.356663 | − | 0.934233i | \(-0.616085\pi\) | ||||
−0.356663 | + | 0.934233i | \(0.616085\pi\) | |||||||
\(558\) | 37.9165 | 1.60513 | ||||||||
\(559\) | −18.2538 | −0.772055 | ||||||||
\(560\) | 0.110917 | 0.00468711 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.37315 | −0.268835 | ||||||||
\(563\) | −37.4304 | −1.57750 | −0.788751 | − | 0.614713i | \(-0.789272\pi\) | ||||
−0.788751 | + | 0.614713i | \(0.789272\pi\) | |||||||
\(564\) | −48.3867 | −2.03745 | ||||||||
\(565\) | −0.170934 | −0.00719125 | ||||||||
\(566\) | −41.2846 | −1.73532 | ||||||||
\(567\) | −0.596375 | −0.0250454 | ||||||||
\(568\) | −0.250464 | −0.0105092 | ||||||||
\(569\) | −2.76910 | −0.116087 | −0.0580433 | − | 0.998314i | \(-0.518486\pi\) | ||||
−0.0580433 | + | 0.998314i | \(0.518486\pi\) | |||||||
\(570\) | −0.204555 | −0.00856786 | ||||||||
\(571\) | −8.85289 | −0.370482 | −0.185241 | − | 0.982693i | \(-0.559307\pi\) | ||||
−0.185241 | + | 0.982693i | \(0.559307\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.6981 | −0.906453 | ||||||||
\(574\) | −21.0334 | −0.877916 | ||||||||
\(575\) | −40.3065 | −1.68090 | ||||||||
\(576\) | −35.7252 | −1.48855 | ||||||||
\(577\) | 37.1682 | 1.54733 | 0.773667 | − | 0.633593i | \(-0.218420\pi\) | ||||
0.773667 | + | 0.633593i | \(0.218420\pi\) | |||||||
\(578\) | −28.1438 | −1.17063 | ||||||||
\(579\) | 47.5461 | 1.97595 | ||||||||
\(580\) | 0.333643 | 0.0138538 | ||||||||
\(581\) | 2.60548 | 0.108093 | ||||||||
\(582\) | 18.7825 | 0.778562 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.28193 | 0.0530464 | ||||||||
\(585\) | 0.626088 | 0.0258855 | ||||||||
\(586\) | 10.9494 | 0.452317 | ||||||||
\(587\) | −35.3189 | −1.45777 | −0.728884 | − | 0.684638i | \(-0.759960\pi\) | ||||
−0.728884 | + | 0.684638i | \(0.759960\pi\) | |||||||
\(588\) | 5.40087 | 0.222728 | ||||||||
\(589\) | 5.51025 | 0.227046 | ||||||||
\(590\) | −0.519902 | −0.0214040 | ||||||||
\(591\) | −16.8726 | −0.694046 | ||||||||
\(592\) | −2.14646 | −0.0882191 | ||||||||
\(593\) | −8.09224 | −0.332308 | −0.166154 | − | 0.986100i | \(-0.553135\pi\) | ||||
−0.166154 | + | 0.986100i | \(0.553135\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0452000 | −0.00185302 | ||||||||
\(596\) | −6.05995 | −0.248225 | ||||||||
\(597\) | −38.2241 | −1.56441 | ||||||||
\(598\) | −78.0983 | −3.19368 | ||||||||
\(599\) | 3.83616 | 0.156741 | 0.0783706 | − | 0.996924i | \(-0.475028\pi\) | ||||
0.0783706 | + | 0.996924i | \(0.475028\pi\) | |||||||
\(600\) | 1.70566 | 0.0696334 | ||||||||
\(601\) | −14.3366 | −0.584804 | −0.292402 | − | 0.956296i | \(-0.594455\pi\) | ||||
−0.292402 | + | 0.956296i | \(0.594455\pi\) | |||||||
\(602\) | 7.42146 | 0.302476 | ||||||||
\(603\) | 13.4004 | 0.545705 | ||||||||
\(604\) | 38.2261 | 1.55540 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −22.3859 | −0.909367 | ||||||||
\(607\) | 13.7786 | 0.559255 | 0.279627 | − | 0.960109i | \(-0.409789\pi\) | ||||
0.279627 | + | 0.960109i | \(0.409789\pi\) | |||||||
\(608\) | −10.8960 | −0.441893 | ||||||||
\(609\) | −17.8139 | −0.721854 | ||||||||
\(610\) | −0.452419 | −0.0183179 | ||||||||
\(611\) | 43.7303 | 1.76914 | ||||||||
\(612\) | 15.5019 | 0.626628 | ||||||||
\(613\) | −9.54435 | −0.385493 | −0.192746 | − | 0.981249i | \(-0.561739\pi\) | ||||
−0.192746 | + | 0.981249i | \(0.561739\pi\) | |||||||
\(614\) | 17.0865 | 0.689555 | ||||||||
\(615\) | 0.795137 | 0.0320630 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.5153 | −1.26876 | −0.634379 | − | 0.773023i | \(-0.718744\pi\) | ||||
−0.634379 | + | 0.773023i | \(0.718744\pi\) | |||||||
\(618\) | −21.8585 | −0.879277 | ||||||||
\(619\) | 20.5297 | 0.825159 | 0.412579 | − | 0.910922i | \(-0.364628\pi\) | ||||
0.412579 | + | 0.910922i | \(0.364628\pi\) | |||||||
\(620\) | −0.209300 | −0.00840568 | ||||||||
\(621\) | 39.6284 | 1.59023 | ||||||||
\(622\) | 37.9555 | 1.52188 | ||||||||
\(623\) | 1.21791 | 0.0487947 | ||||||||
\(624\) | 56.0294 | 2.24297 | ||||||||
\(625\) | 24.9891 | 0.999565 | ||||||||
\(626\) | −1.20411 | −0.0481261 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −44.4928 | −1.77546 | ||||||||
\(629\) | 0.874707 | 0.0348769 | ||||||||
\(630\) | −0.254548 | −0.0101414 | ||||||||
\(631\) | 35.9658 | 1.43178 | 0.715889 | − | 0.698214i | \(-0.246022\pi\) | ||||
0.715889 | + | 0.698214i | \(0.246022\pi\) | |||||||
\(632\) | −0.716946 | −0.0285186 | ||||||||
\(633\) | 50.2533 | 1.99739 | ||||||||
\(634\) | −10.3449 | −0.410850 | ||||||||
\(635\) | 0.135464 | 0.00537572 | ||||||||
\(636\) | −21.3905 | −0.848190 | ||||||||
\(637\) | −4.88112 | −0.193397 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.74478 | 0.385498 | ||||||||
\(640\) | −0.0263616 | −0.00104203 | ||||||||
\(641\) | 13.6205 | 0.537976 | 0.268988 | − | 0.963144i | \(-0.413311\pi\) | ||||
0.268988 | + | 0.963144i | \(0.413311\pi\) | |||||||
\(642\) | 57.5005 | 2.26937 | ||||||||
\(643\) | 21.9891 | 0.867166 | 0.433583 | − | 0.901114i | \(-0.357249\pi\) | ||||
0.433583 | + | 0.901114i | \(0.357249\pi\) | |||||||
\(644\) | 15.6275 | 0.615809 | ||||||||
\(645\) | −0.280558 | −0.0110470 | ||||||||
\(646\) | 4.57737 | 0.180094 | ||||||||
\(647\) | −14.8203 | −0.582644 | −0.291322 | − | 0.956625i | \(-0.594095\pi\) | ||||
−0.291322 | + | 0.956625i | \(0.594095\pi\) | |||||||
\(648\) | 0.0730235 | 0.00286863 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 48.4262 | 1.89943 | ||||||||
\(651\) | 11.1749 | 0.437981 | ||||||||
\(652\) | 36.8065 | 1.44145 | ||||||||
\(653\) | 43.3776 | 1.69750 | 0.848748 | − | 0.528798i | \(-0.177357\pi\) | ||||
0.848748 | + | 0.528798i | \(0.177357\pi\) | |||||||
\(654\) | −20.8853 | −0.816679 | ||||||||
\(655\) | 0.101332 | 0.00395936 | ||||||||
\(656\) | 43.6625 | 1.70473 | ||||||||
\(657\) | −49.8758 | −1.94584 | ||||||||
\(658\) | −17.7794 | −0.693113 | ||||||||
\(659\) | 42.2093 | 1.64424 | 0.822121 | − | 0.569313i | \(-0.192791\pi\) | ||||
0.822121 | + | 0.569313i | \(0.192791\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.2794 | 0.633197 | 0.316599 | − | 0.948560i | \(-0.397459\pi\) | ||||
0.316599 | + | 0.948560i | \(0.397459\pi\) | |||||||
\(662\) | 1.32766 | 0.0516012 | ||||||||
\(663\) | −22.8326 | −0.886745 | ||||||||
\(664\) | −0.319029 | −0.0123807 | ||||||||
\(665\) | −0.0369924 | −0.00143451 | ||||||||
\(666\) | 4.92600 | 0.190879 | ||||||||
\(667\) | −51.5446 | −1.99582 | ||||||||
\(668\) | −5.85451 | −0.226518 | ||||||||
\(669\) | −18.2039 | −0.703803 | ||||||||
\(670\) | −0.150295 | −0.00580642 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −22.0975 | −0.852430 | ||||||||
\(673\) | −5.31047 | −0.204704 | −0.102352 | − | 0.994748i | \(-0.532637\pi\) | ||||
−0.102352 | + | 0.994748i | \(0.532637\pi\) | |||||||
\(674\) | −13.1021 | −0.504673 | ||||||||
\(675\) | −24.5723 | −0.945787 | ||||||||
\(676\) | 20.9827 | 0.807027 | ||||||||
\(677\) | −33.7947 | −1.29884 | −0.649419 | − | 0.760431i | \(-0.724988\pi\) | ||||
−0.649419 | + | 0.760431i | \(0.724988\pi\) | |||||||
\(678\) | 35.1059 | 1.34824 | ||||||||
\(679\) | 3.39670 | 0.130354 | ||||||||
\(680\) | 0.00553455 | 0.000212240 0 | ||||||||
\(681\) | 37.9164 | 1.45296 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.8834 | −0.607761 | −0.303880 | − | 0.952710i | \(-0.598282\pi\) | ||||
−0.303880 | + | 0.952710i | \(0.598282\pi\) | |||||||
\(684\) | 12.6870 | 0.485100 | ||||||||
\(685\) | −0.515274 | −0.0196876 | ||||||||
\(686\) | 1.98451 | 0.0757691 | ||||||||
\(687\) | −54.1148 | −2.06461 | ||||||||
\(688\) | −15.4060 | −0.587347 | ||||||||
\(689\) | 19.3320 | 0.736492 | ||||||||
\(690\) | −1.20035 | −0.0456967 | ||||||||
\(691\) | 25.5375 | 0.971490 | 0.485745 | − | 0.874100i | \(-0.338548\pi\) | ||||
0.485745 | + | 0.874100i | \(0.338548\pi\) | |||||||
\(692\) | 17.1274 | 0.651085 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.2113 | 0.919050 | ||||||||
\(695\) | −0.0945336 | −0.00358586 | ||||||||
\(696\) | 2.18123 | 0.0826794 | ||||||||
\(697\) | −17.7929 | −0.673956 | ||||||||
\(698\) | −1.75788 | −0.0665369 | ||||||||
\(699\) | 12.1529 | 0.459663 | ||||||||
\(700\) | −9.69009 | −0.366251 | ||||||||
\(701\) | −3.29535 | −0.124464 | −0.0622319 | − | 0.998062i | \(-0.519822\pi\) | ||||
−0.0622319 | + | 0.998062i | \(0.519822\pi\) | |||||||
\(702\) | −47.6115 | −1.79698 | ||||||||
\(703\) | 0.715875 | 0.0269997 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.672125 | 0.0253137 | ||||||||
\(706\) | 10.6372 | 0.400338 | ||||||||
\(707\) | −4.04836 | −0.152254 | ||||||||
\(708\) | 52.5516 | 1.97501 | ||||||||
\(709\) | −44.9026 | −1.68635 | −0.843176 | − | 0.537638i | \(-0.819317\pi\) | ||||
−0.843176 | + | 0.537638i | \(0.819317\pi\) | |||||||
\(710\) | −0.109295 | −0.00410177 | ||||||||
\(711\) | 27.8942 | 1.04611 | ||||||||
\(712\) | −0.149128 | −0.00558882 | ||||||||
\(713\) | 32.3348 | 1.21095 | ||||||||
\(714\) | 9.28304 | 0.347409 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.4064 | 0.613137 | ||||||||
\(717\) | 29.5082 | 1.10201 | ||||||||
\(718\) | 51.2898 | 1.91412 | ||||||||
\(719\) | 3.19264 | 0.119065 | 0.0595327 | − | 0.998226i | \(-0.481039\pi\) | ||||
0.0595327 | + | 0.998226i | \(0.481039\pi\) | |||||||
\(720\) | 0.528409 | 0.0196926 | ||||||||
\(721\) | −3.95297 | −0.147216 | ||||||||
\(722\) | −33.9596 | −1.26385 | ||||||||
\(723\) | 52.0740 | 1.93665 | ||||||||
\(724\) | −46.9084 | −1.74334 | ||||||||
\(725\) | 31.9612 | 1.18701 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.1654 | 0.747891 | 0.373946 | − | 0.927451i | \(-0.378005\pi\) | ||||
0.373946 | + | 0.927451i | \(0.378005\pi\) | |||||||
\(728\) | 0.597672 | 0.0221512 | ||||||||
\(729\) | −43.9279 | −1.62696 | ||||||||
\(730\) | 0.559395 | 0.0207041 | ||||||||
\(731\) | 6.27810 | 0.232204 | ||||||||
\(732\) | 45.7303 | 1.69024 | ||||||||
\(733\) | −19.7094 | −0.727985 | −0.363992 | − | 0.931402i | \(-0.618587\pi\) | ||||
−0.363992 | + | 0.931402i | \(0.618587\pi\) | |||||||
\(734\) | −40.5842 | −1.49799 | ||||||||
\(735\) | −0.0750218 | −0.00276722 | ||||||||
\(736\) | −63.9394 | −2.35684 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −100.203 | −3.68851 | ||||||||
\(739\) | −34.5575 | −1.27122 | −0.635610 | − | 0.772010i | \(-0.719251\pi\) | ||||
−0.635610 | + | 0.772010i | \(0.719251\pi\) | |||||||
\(740\) | −0.0271916 | −0.000999584 0 | ||||||||
\(741\) | −18.6866 | −0.686469 | ||||||||
\(742\) | −7.85982 | −0.288543 | ||||||||
\(743\) | −25.8381 | −0.947910 | −0.473955 | − | 0.880549i | \(-0.657174\pi\) | ||||
−0.473955 | + | 0.880549i | \(0.657174\pi\) | |||||||
\(744\) | −1.36832 | −0.0501652 | ||||||||
\(745\) | 0.0841770 | 0.00308401 | ||||||||
\(746\) | 18.6368 | 0.682340 | ||||||||
\(747\) | 12.4125 | 0.454148 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.3986 | 0.379957 | ||||||||
\(750\) | 1.48871 | 0.0543600 | ||||||||
\(751\) | −35.7199 | −1.30344 | −0.651719 | − | 0.758460i | \(-0.725952\pi\) | ||||
−0.651719 | + | 0.758460i | \(0.725952\pi\) | |||||||
\(752\) | 36.9077 | 1.34589 | ||||||||
\(753\) | 52.8946 | 1.92758 | ||||||||
\(754\) | 61.9283 | 2.25530 | ||||||||
\(755\) | −0.530988 | −0.0193246 | ||||||||
\(756\) | 9.52707 | 0.346496 | ||||||||
\(757\) | −14.8197 | −0.538629 | −0.269315 | − | 0.963052i | \(-0.586797\pi\) | ||||
−0.269315 | + | 0.963052i | \(0.586797\pi\) | |||||||
\(758\) | −11.1846 | −0.406242 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.00452957 | 0.000164305 0 | ||||||||
\(761\) | −21.7759 | −0.789377 | −0.394689 | − | 0.918815i | \(-0.629148\pi\) | ||||
−0.394689 | + | 0.918815i | \(0.629148\pi\) | |||||||
\(762\) | −27.8212 | −1.00785 | ||||||||
\(763\) | −3.77697 | −0.136736 | ||||||||
\(764\) | −15.0939 | −0.546077 | ||||||||
\(765\) | −0.215332 | −0.00778536 | ||||||||
\(766\) | −2.49938 | −0.0903062 | ||||||||
\(767\) | −47.4943 | −1.71492 | ||||||||
\(768\) | 47.2045 | 1.70335 | ||||||||
\(769\) | −35.6991 | −1.28734 | −0.643672 | − | 0.765302i | \(-0.722590\pi\) | ||||
−0.643672 | + | 0.765302i | \(0.722590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.1988 | −1.37570 | ||||||||
\(772\) | 33.0745 | 1.19038 | ||||||||
\(773\) | 42.6229 | 1.53304 | 0.766520 | − | 0.642220i | \(-0.221987\pi\) | ||||
0.766520 | + | 0.642220i | \(0.221987\pi\) | |||||||
\(774\) | 35.3557 | 1.27084 | ||||||||
\(775\) | −20.0498 | −0.720210 | ||||||||
\(776\) | −0.415912 | −0.0149304 | ||||||||
\(777\) | 1.45182 | 0.0520836 | ||||||||
\(778\) | −11.6771 | −0.418643 | ||||||||
\(779\) | −14.5620 | −0.521739 | ||||||||
\(780\) | 0.709786 | 0.0254144 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 26.8606 | 0.960533 | ||||||||
\(783\) | −31.4235 | −1.12298 | ||||||||
\(784\) | −4.11959 | −0.147128 | ||||||||
\(785\) | 0.618037 | 0.0220587 | ||||||||
\(786\) | −20.8112 | −0.742311 | ||||||||
\(787\) | −47.0867 | −1.67846 | −0.839230 | − | 0.543777i | \(-0.816994\pi\) | ||||
−0.839230 | + | 0.543777i | \(0.816994\pi\) | |||||||
\(788\) | −11.7371 | −0.418117 | ||||||||
\(789\) | 46.1893 | 1.64438 | ||||||||
\(790\) | −0.312854 | −0.0111309 | ||||||||
\(791\) | 6.34869 | 0.225733 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.3295 | −1.46765 | ||||||||
\(794\) | 9.64509 | 0.342291 | ||||||||
\(795\) | 0.297129 | 0.0105381 | ||||||||
\(796\) | −26.5898 | −0.942451 | ||||||||
\(797\) | −7.48263 | −0.265048 | −0.132524 | − | 0.991180i | \(-0.542308\pi\) | ||||
−0.132524 | + | 0.991180i | \(0.542308\pi\) | |||||||
\(798\) | 7.59740 | 0.268945 | ||||||||
\(799\) | −15.0403 | −0.532087 | ||||||||
\(800\) | 39.6468 | 1.40173 | ||||||||
\(801\) | 5.80213 | 0.205008 | ||||||||
\(802\) | −50.6690 | −1.78918 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 15.1918 | 0.535774 | ||||||||
\(805\) | −0.217076 | −0.00765094 | ||||||||
\(806\) | −38.8487 | −1.36839 | ||||||||
\(807\) | −23.8059 | −0.838006 | ||||||||
\(808\) | 0.495704 | 0.0174388 | ||||||||
\(809\) | 34.7490 | 1.22171 | 0.610855 | − | 0.791743i | \(-0.290826\pi\) | ||||
0.610855 | + | 0.791743i | \(0.290826\pi\) | |||||||
\(810\) | 0.0318653 | 0.00111963 | ||||||||
\(811\) | 12.8133 | 0.449935 | 0.224968 | − | 0.974366i | \(-0.427772\pi\) | ||||
0.224968 | + | 0.974366i | \(0.427772\pi\) | |||||||
\(812\) | −12.3919 | −0.434869 | ||||||||
\(813\) | −17.6811 | −0.620105 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.511268 | −0.0179089 | ||||||||
\(816\) | −19.2704 | −0.674599 | ||||||||
\(817\) | 5.13810 | 0.179759 | ||||||||
\(818\) | 41.7277 | 1.45898 | ||||||||
\(819\) | −23.2536 | −0.812546 | ||||||||
\(820\) | 0.553121 | 0.0193158 | ||||||||
\(821\) | −54.3225 | −1.89587 | −0.947934 | − | 0.318466i | \(-0.896832\pi\) | ||||
−0.947934 | + | 0.318466i | \(0.896832\pi\) | |||||||
\(822\) | 105.825 | 3.69109 | ||||||||
\(823\) | −19.7697 | −0.689129 | −0.344565 | − | 0.938763i | \(-0.611973\pi\) | ||||
−0.344565 | + | 0.938763i | \(0.611973\pi\) | |||||||
\(824\) | 0.484024 | 0.0168618 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.3098 | 0.671873 | ||||||||
\(827\) | 12.3098 | 0.428055 | 0.214028 | − | 0.976828i | \(-0.431342\pi\) | ||||
0.214028 | + | 0.976828i | \(0.431342\pi\) | |||||||
\(828\) | 74.4491 | 2.58728 | ||||||||
\(829\) | −25.7259 | −0.893496 | −0.446748 | − | 0.894660i | \(-0.647418\pi\) | ||||
−0.446748 | + | 0.894660i | \(0.647418\pi\) | |||||||
\(830\) | −0.139215 | −0.00483223 | ||||||||
\(831\) | −66.8857 | −2.32024 | ||||||||
\(832\) | 36.6036 | 1.26900 | ||||||||
\(833\) | 1.67878 | 0.0581662 | ||||||||
\(834\) | 19.4150 | 0.672288 | ||||||||
\(835\) | 0.0813232 | 0.00281431 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.7125 | 0.681363 | ||||||||
\(838\) | −62.1434 | −2.14671 | ||||||||
\(839\) | −46.6136 | −1.60928 | −0.804640 | − | 0.593762i | \(-0.797642\pi\) | ||||
−0.804640 | + | 0.593762i | \(0.797642\pi\) | |||||||
\(840\) | 0.00918610 | 0.000316950 0 | ||||||||
\(841\) | 11.8725 | 0.409397 | ||||||||
\(842\) | 25.3793 | 0.874627 | ||||||||
\(843\) | −8.94833 | −0.308197 | ||||||||
\(844\) | 34.9577 | 1.20329 | ||||||||
\(845\) | −0.291465 | −0.0100267 | ||||||||
\(846\) | −84.7009 | −2.91208 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16.3160 | 0.560292 | ||||||||
\(849\) | −57.9664 | −1.98940 | ||||||||
\(850\) | −16.6554 | −0.571275 | ||||||||
\(851\) | 4.20085 | 0.144003 | ||||||||
\(852\) | 11.0475 | 0.378482 | ||||||||
\(853\) | −9.80881 | −0.335847 | −0.167924 | − | 0.985800i | \(-0.553706\pi\) | ||||
−0.167924 | + | 0.985800i | \(0.553706\pi\) | |||||||
\(854\) | 16.8033 | 0.574998 | ||||||||
\(855\) | −0.176232 | −0.00602699 | ||||||||
\(856\) | −1.27326 | −0.0435193 | ||||||||
\(857\) | −32.9168 | −1.12442 | −0.562208 | − | 0.826996i | \(-0.690048\pi\) | ||||
−0.562208 | + | 0.826996i | \(0.690048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.4747 | −0.971543 | −0.485772 | − | 0.874086i | \(-0.661461\pi\) | ||||
−0.485772 | + | 0.874086i | \(0.661461\pi\) | |||||||
\(860\) | −0.195164 | −0.00665505 | ||||||||
\(861\) | −29.5323 | −1.00646 | ||||||||
\(862\) | 41.8095 | 1.42404 | ||||||||
\(863\) | 29.2770 | 0.996600 | 0.498300 | − | 0.867005i | \(-0.333958\pi\) | ||||
0.498300 | + | 0.867005i | \(0.333958\pi\) | |||||||
\(864\) | −38.9798 | −1.32612 | ||||||||
\(865\) | −0.237911 | −0.00808922 | ||||||||
\(866\) | 75.4176 | 2.56279 | ||||||||
\(867\) | −39.5158 | −1.34203 | ||||||||
\(868\) | 7.77363 | 0.263854 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.951826 | 0.0322699 | ||||||||
\(871\) | −13.7298 | −0.465218 | ||||||||
\(872\) | 0.462474 | 0.0156613 | ||||||||
\(873\) | 16.1819 | 0.547673 | ||||||||
\(874\) | 21.9832 | 0.743591 | ||||||||
\(875\) | 0.269224 | 0.00910143 | ||||||||
\(876\) | −56.5435 | −1.91043 | ||||||||
\(877\) | −22.6025 | −0.763233 | −0.381616 | − | 0.924321i | \(-0.624632\pi\) | ||||
−0.381616 | + | 0.924321i | \(0.624632\pi\) | |||||||
\(878\) | −74.9506 | −2.52946 | ||||||||
\(879\) | 15.3738 | 0.518544 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.1102 | −1.18289 | −0.591447 | − | 0.806344i | \(-0.701443\pi\) | ||||
−0.591447 | + | 0.806344i | \(0.701443\pi\) | |||||||
\(882\) | 9.45421 | 0.318340 | ||||||||
\(883\) | 15.2032 | 0.511628 | 0.255814 | − | 0.966726i | \(-0.417657\pi\) | ||||
0.255814 | + | 0.966726i | \(0.417657\pi\) | |||||||
\(884\) | −15.8830 | −0.534205 | ||||||||
\(885\) | −0.729978 | −0.0245380 | ||||||||
\(886\) | −2.03993 | −0.0685327 | ||||||||
\(887\) | −38.5316 | −1.29377 | −0.646883 | − | 0.762589i | \(-0.723928\pi\) | ||||
−0.646883 | + | 0.762589i | \(0.723928\pi\) | |||||||
\(888\) | −0.177769 | −0.00596553 | ||||||||
\(889\) | −5.03128 | −0.168744 | ||||||||
\(890\) | −0.0650753 | −0.00218133 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.6632 | −0.423995 | ||||||||
\(893\) | −12.3092 | −0.411912 | ||||||||
\(894\) | −17.2880 | −0.578198 | ||||||||
\(895\) | −0.227897 | −0.00761774 | ||||||||
\(896\) | 0.979100 | 0.0327094 | ||||||||
\(897\) | −109.655 | −3.66128 | ||||||||
\(898\) | 39.9548 | 1.33331 | ||||||||
\(899\) | −25.6400 | −0.855143 | ||||||||
\(900\) | −46.1635 | −1.53878 | ||||||||
\(901\) | −6.64893 | −0.221508 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.4202 | 0.346764 | ||||||||
\(904\) | −0.777369 | −0.0258549 | ||||||||
\(905\) | 0.651590 | 0.0216596 | ||||||||
\(906\) | 109.053 | 3.62303 | ||||||||
\(907\) | −56.4214 | −1.87344 | −0.936721 | − | 0.350076i | \(-0.886156\pi\) | ||||
−0.936721 | + | 0.350076i | \(0.886156\pi\) | |||||||
\(908\) | 26.3758 | 0.875312 | ||||||||
\(909\) | −19.2863 | −0.639687 | ||||||||
\(910\) | 0.260807 | 0.00864566 | ||||||||
\(911\) | −30.5904 | −1.01350 | −0.506752 | − | 0.862092i | \(-0.669154\pi\) | ||||
−0.506752 | + | 0.862092i | \(0.669154\pi\) | |||||||
\(912\) | −15.7712 | −0.522237 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −47.9173 | −1.58496 | ||||||||
\(915\) | −0.635226 | −0.0209999 | ||||||||
\(916\) | −37.6439 | −1.24379 | ||||||||
\(917\) | −3.76357 | −0.124284 | ||||||||
\(918\) | 16.3752 | 0.540462 | ||||||||
\(919\) | 32.8904 | 1.08495 | 0.542477 | − | 0.840071i | \(-0.317487\pi\) | ||||
0.542477 | + | 0.840071i | \(0.317487\pi\) | |||||||
\(920\) | 0.0265801 | 0.000876319 0 | ||||||||
\(921\) | 23.9906 | 0.790517 | ||||||||
\(922\) | 22.9976 | 0.757385 | ||||||||
\(923\) | −9.98437 | −0.328640 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.60481 | −0.0856457 | ||||||||
\(926\) | 42.8808 | 1.40915 | ||||||||
\(927\) | −18.8319 | −0.618521 | ||||||||
\(928\) | 50.7010 | 1.66434 | ||||||||
\(929\) | 21.8326 | 0.716305 | 0.358152 | − | 0.933663i | \(-0.383407\pi\) | ||||
0.358152 | + | 0.933663i | \(0.383407\pi\) | |||||||
\(930\) | −0.597097 | −0.0195796 | ||||||||
\(931\) | 1.37394 | 0.0450291 | ||||||||
\(932\) | 8.45390 | 0.276917 | ||||||||
\(933\) | 53.2921 | 1.74471 | ||||||||
\(934\) | 31.5835 | 1.03344 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.84730 | 0.0930670 | ||||||||
\(937\) | −34.9523 | −1.14184 | −0.570921 | − | 0.821005i | \(-0.693414\pi\) | ||||
−0.570921 | + | 0.821005i | \(0.693414\pi\) | |||||||
\(938\) | 5.58214 | 0.182263 | ||||||||
\(939\) | −1.69066 | −0.0551726 | ||||||||
\(940\) | 0.467550 | 0.0152498 | ||||||||
\(941\) | −20.4205 | −0.665689 | −0.332845 | − | 0.942982i | \(-0.608008\pi\) | ||||
−0.332845 | + | 0.942982i | \(0.608008\pi\) | |||||||
\(942\) | −126.931 | −4.13562 | ||||||||
\(943\) | −85.4520 | −2.78270 | ||||||||
\(944\) | −40.0845 | −1.30464 | ||||||||
\(945\) | −0.132338 | −0.00430494 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.3122 | −0.367597 | −0.183799 | − | 0.982964i | \(-0.558839\pi\) | ||||
−0.183799 | + | 0.982964i | \(0.558839\pi\) | |||||||
\(948\) | 31.6232 | 1.02707 | ||||||||
\(949\) | 51.1021 | 1.65884 | ||||||||
\(950\) | −13.6311 | −0.442250 | ||||||||
\(951\) | −14.5250 | −0.471005 | ||||||||
\(952\) | −0.205559 | −0.00666222 | ||||||||
\(953\) | −4.55919 | −0.147687 | −0.0738434 | − | 0.997270i | \(-0.523526\pi\) | ||||
−0.0738434 | + | 0.997270i | \(0.523526\pi\) | |||||||
\(954\) | −37.4441 | −1.21230 | ||||||||
\(955\) | 0.209665 | 0.00678459 | ||||||||
\(956\) | 20.5268 | 0.663885 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.4856 | 0.338775 | ||||||||
\(959\) | 19.1379 | 0.617994 | ||||||||
\(960\) | 0.562590 | 0.0181575 | ||||||||
\(961\) | −14.9156 | −0.481147 | ||||||||
\(962\) | −5.04711 | −0.162725 | ||||||||
\(963\) | 49.5388 | 1.59637 | ||||||||
\(964\) | 36.2242 | 1.16670 | ||||||||
\(965\) | −0.459428 | −0.0147895 | ||||||||
\(966\) | 44.5825 | 1.43442 | ||||||||
\(967\) | −38.9153 | −1.25143 | −0.625715 | − | 0.780052i | \(-0.715193\pi\) | ||||
−0.625715 | + | 0.780052i | \(0.715193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.42694 | 0.206463 | ||||||||
\(970\) | −0.181492 | −0.00582735 | ||||||||
\(971\) | 42.3409 | 1.35878 | 0.679392 | − | 0.733775i | \(-0.262243\pi\) | ||||
0.679392 | + | 0.733775i | \(0.262243\pi\) | |||||||
\(972\) | −31.8021 | −1.02005 | ||||||||
\(973\) | 3.51108 | 0.112560 | ||||||||
\(974\) | −53.7120 | −1.72104 | ||||||||
\(975\) | 67.9937 | 2.17754 | ||||||||
\(976\) | −34.8815 | −1.11653 | ||||||||
\(977\) | 35.6575 | 1.14078 | 0.570392 | − | 0.821372i | \(-0.306791\pi\) | ||||
0.570392 | + | 0.821372i | \(0.306791\pi\) | |||||||
\(978\) | 105.003 | 3.35762 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.0521874 | −0.00166707 | ||||||||
\(981\) | −17.9934 | −0.574487 | ||||||||
\(982\) | 37.3088 | 1.19057 | ||||||||
\(983\) | −29.5213 | −0.941583 | −0.470791 | − | 0.882245i | \(-0.656032\pi\) | ||||
−0.470791 | + | 0.882245i | \(0.656032\pi\) | |||||||
\(984\) | 3.61610 | 0.115277 | ||||||||
\(985\) | 0.163036 | 0.00519477 | ||||||||
\(986\) | −21.2992 | −0.678305 | ||||||||
\(987\) | −24.9635 | −0.794596 | ||||||||
\(988\) | −12.9989 | −0.413552 | ||||||||
\(989\) | 30.1511 | 0.958748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.7292 | −0.976145 | −0.488072 | − | 0.872803i | \(-0.662300\pi\) | ||||
−0.488072 | + | 0.872803i | \(0.662300\pi\) | |||||||
\(992\) | −31.8056 | −1.00983 | ||||||||
\(993\) | 1.86413 | 0.0591564 | ||||||||
\(994\) | 4.05934 | 0.128755 | ||||||||
\(995\) | 0.369351 | 0.0117092 | ||||||||
\(996\) | 14.0718 | 0.445883 | ||||||||
\(997\) | 49.9958 | 1.58338 | 0.791691 | − | 0.610922i | \(-0.209201\pi\) | ||||
0.791691 | + | 0.610922i | \(0.209201\pi\) | |||||||
\(998\) | −78.9175 | −2.49809 | ||||||||
\(999\) | 2.56099 | 0.0810261 |
(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 | 847.2.a.p.1.7 | 8 | ||
3.2 | odd | 2 | 7623.2.a.ct.1.2 | 8 | |||
7.6 | odd | 2 | 5929.2.a.bt.1.7 | 8 | |||
11.2 | odd | 10 | 847.2.f.x.323.4 | 16 | |||
11.3 | even | 5 | 847.2.f.w.372.4 | 16 | |||
11.4 | even | 5 | 847.2.f.w.148.4 | 16 | |||
11.5 | even | 5 | 77.2.f.b.36.1 | yes | 16 | ||
11.6 | odd | 10 | 847.2.f.x.729.4 | 16 | |||
11.7 | odd | 10 | 847.2.f.v.148.1 | 16 | |||
11.8 | odd | 10 | 847.2.f.v.372.1 | 16 | |||
11.9 | even | 5 | 77.2.f.b.15.1 | ✓ | 16 | ||
11.10 | odd | 2 | 847.2.a.o.1.2 | 8 | |||
33.5 | odd | 10 | 693.2.m.i.190.4 | 16 | |||
33.20 | odd | 10 | 693.2.m.i.631.4 | 16 | |||
33.32 | even | 2 | 7623.2.a.cw.1.7 | 8 | |||
77.5 | odd | 30 | 539.2.q.f.410.4 | 32 | |||
77.9 | even | 15 | 539.2.q.g.312.1 | 32 | |||
77.16 | even | 15 | 539.2.q.g.410.4 | 32 | |||
77.20 | odd | 10 | 539.2.f.e.246.1 | 16 | |||
77.27 | odd | 10 | 539.2.f.e.344.1 | 16 | |||
77.31 | odd | 30 | 539.2.q.f.422.4 | 32 | |||
77.38 | odd | 30 | 539.2.q.f.520.1 | 32 | |||
77.53 | even | 15 | 539.2.q.g.422.4 | 32 | |||
77.60 | even | 15 | 539.2.q.g.520.1 | 32 | |||
77.75 | odd | 30 | 539.2.q.f.312.1 | 32 | |||
77.76 | even | 2 | 5929.2.a.bs.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.1 | ✓ | 16 | 11.9 | even | 5 | ||
77.2.f.b.36.1 | yes | 16 | 11.5 | even | 5 | ||
539.2.f.e.246.1 | 16 | 77.20 | odd | 10 | |||
539.2.f.e.344.1 | 16 | 77.27 | odd | 10 | |||
539.2.q.f.312.1 | 32 | 77.75 | odd | 30 | |||
539.2.q.f.410.4 | 32 | 77.5 | odd | 30 | |||
539.2.q.f.422.4 | 32 | 77.31 | odd | 30 | |||
539.2.q.f.520.1 | 32 | 77.38 | odd | 30 | |||
539.2.q.g.312.1 | 32 | 77.9 | even | 15 | |||
539.2.q.g.410.4 | 32 | 77.16 | even | 15 | |||
539.2.q.g.422.4 | 32 | 77.53 | even | 15 | |||
539.2.q.g.520.1 | 32 | 77.60 | even | 15 | |||
693.2.m.i.190.4 | 16 | 33.5 | odd | 10 | |||
693.2.m.i.631.4 | 16 | 33.20 | odd | 10 | |||
847.2.a.o.1.2 | 8 | 11.10 | odd | 2 | |||
847.2.a.p.1.7 | 8 | 1.1 | even | 1 | trivial | ||
847.2.f.v.148.1 | 16 | 11.7 | odd | 10 | |||
847.2.f.v.372.1 | 16 | 11.8 | odd | 10 | |||
847.2.f.w.148.4 | 16 | 11.4 | even | 5 | |||
847.2.f.w.372.4 | 16 | 11.3 | even | 5 | |||
847.2.f.x.323.4 | 16 | 11.2 | odd | 10 | |||
847.2.f.x.729.4 | 16 | 11.6 | odd | 10 | |||
5929.2.a.bs.1.2 | 8 | 77.76 | even | 2 | |||
5929.2.a.bt.1.7 | 8 | 7.6 | odd | 2 | |||
7623.2.a.ct.1.2 | 8 | 3.2 | odd | 2 | |||
7623.2.a.cw.1.7 | 8 | 33.32 | even | 2 |