Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4923,2,Mod(1,4923)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4923, 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("4923.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4923 = 3^{2} \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4923.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: | \(39.3103529151\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 547) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(2.59964\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4923.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59964 | 1.83822 | 0.919111 | − | 0.393999i | \(-0.128909\pi\) | ||||
0.919111 | + | 0.393999i | \(0.128909\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.75812 | 2.37906 | ||||||||
\(5\) | 3.02323 | 1.35203 | 0.676015 | − | 0.736888i | \(-0.263706\pi\) | ||||
0.676015 | + | 0.736888i | \(0.263706\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.561390 | −0.212185 | −0.106093 | − | 0.994356i | \(-0.533834\pi\) | ||||
−0.106093 | + | 0.994356i | \(0.533834\pi\) | |||||||
\(8\) | 7.17011 | 2.53502 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.85930 | 2.48533 | ||||||||
\(11\) | −4.23111 | −1.27573 | −0.637864 | − | 0.770149i | \(-0.720182\pi\) | ||||
−0.637864 | + | 0.770149i | \(0.720182\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.87964 | −1.35337 | −0.676684 | − | 0.736274i | \(-0.736584\pi\) | ||||
−0.676684 | + | 0.736274i | \(0.736584\pi\) | |||||||
\(14\) | −1.45941 | −0.390044 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.12345 | 2.28086 | ||||||||
\(17\) | 6.39965 | 1.55214 | 0.776071 | − | 0.630645i | \(-0.217210\pi\) | ||||
0.776071 | + | 0.630645i | \(0.217210\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.29628 | 1.44447 | 0.722233 | − | 0.691650i | \(-0.243116\pi\) | ||||
0.722233 | + | 0.691650i | \(0.243116\pi\) | |||||||
\(20\) | 14.3849 | 3.21656 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.9994 | −2.34507 | ||||||||
\(23\) | 9.21357 | 1.92116 | 0.960581 | − | 0.277999i | \(-0.0896713\pi\) | ||||
0.960581 | + | 0.277999i | \(0.0896713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.13991 | 0.827983 | ||||||||
\(26\) | −12.6853 | −2.48779 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.67116 | −0.504801 | ||||||||
\(29\) | −1.14750 | −0.213085 | −0.106542 | − | 0.994308i | \(-0.533978\pi\) | ||||
−0.106542 | + | 0.994308i | \(0.533978\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.52167 | −1.35093 | −0.675466 | − | 0.737391i | \(-0.736058\pi\) | ||||
−0.675466 | + | 0.737391i | \(0.736058\pi\) | |||||||
\(32\) | 9.37744 | 1.65771 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 16.6368 | 2.85318 | ||||||||
\(35\) | −1.69721 | −0.286881 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.74347 | 1.43742 | 0.718708 | − | 0.695312i | \(-0.244734\pi\) | ||||
0.718708 | + | 0.695312i | \(0.244734\pi\) | |||||||
\(38\) | 16.3680 | 2.65525 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 21.6769 | 3.42741 | ||||||||
\(41\) | −2.81890 | −0.440238 | −0.220119 | − | 0.975473i | \(-0.570645\pi\) | ||||
−0.220119 | + | 0.975473i | \(0.570645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.57023 | −0.239458 | −0.119729 | − | 0.992807i | \(-0.538203\pi\) | ||||
−0.119729 | + | 0.992807i | \(0.538203\pi\) | |||||||
\(44\) | −20.1321 | −3.03503 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 23.9520 | 3.53152 | ||||||||
\(47\) | 4.08126 | 0.595313 | 0.297657 | − | 0.954673i | \(-0.403795\pi\) | ||||
0.297657 | + | 0.954673i | \(0.403795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.68484 | −0.954977 | ||||||||
\(50\) | 10.7623 | 1.52202 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −23.2179 | −3.21974 | ||||||||
\(53\) | 4.00434 | 0.550039 | 0.275019 | − | 0.961439i | \(-0.411316\pi\) | ||||
0.275019 | + | 0.961439i | \(0.411316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.7916 | −1.72482 | ||||||||
\(56\) | −4.02522 | −0.537893 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.98307 | −0.391697 | ||||||||
\(59\) | 12.2872 | 1.59966 | 0.799828 | − | 0.600229i | \(-0.204924\pi\) | ||||
0.799828 | + | 0.600229i | \(0.204924\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.473603 | −0.0606386 | −0.0303193 | − | 0.999540i | \(-0.509652\pi\) | ||||
−0.0303193 | + | 0.999540i | \(0.509652\pi\) | |||||||
\(62\) | −19.5536 | −2.48331 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.13107 | 0.766383 | ||||||||
\(65\) | −14.7523 | −1.82979 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.80684 | 0.220740 | 0.110370 | − | 0.993891i | \(-0.464796\pi\) | ||||
0.110370 | + | 0.993891i | \(0.464796\pi\) | |||||||
\(68\) | 30.4503 | 3.69264 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.41213 | −0.527350 | ||||||||
\(71\) | 1.76871 | 0.209907 | 0.104954 | − | 0.994477i | \(-0.466531\pi\) | ||||
0.104954 | + | 0.994477i | \(0.466531\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.611682 | 0.0715919 | 0.0357960 | − | 0.999359i | \(-0.488603\pi\) | ||||
0.0357960 | + | 0.999359i | \(0.488603\pi\) | |||||||
\(74\) | 22.7298 | 2.64229 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 29.9584 | 3.43647 | ||||||||
\(77\) | 2.37530 | 0.270691 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.49642 | −0.280869 | −0.140434 | − | 0.990090i | \(-0.544850\pi\) | ||||
−0.140434 | + | 0.990090i | \(0.544850\pi\) | |||||||
\(80\) | 27.5823 | 3.08379 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.32811 | −0.809254 | ||||||||
\(83\) | −8.29336 | −0.910315 | −0.455158 | − | 0.890411i | \(-0.650417\pi\) | ||||
−0.455158 | + | 0.890411i | \(0.650417\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.3476 | 2.09854 | ||||||||
\(86\) | −4.08204 | −0.440178 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −30.3375 | −3.23399 | ||||||||
\(89\) | 14.8521 | 1.57432 | 0.787162 | − | 0.616746i | \(-0.211550\pi\) | ||||
0.787162 | + | 0.616746i | \(0.211550\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.73938 | 0.287165 | ||||||||
\(92\) | 43.8393 | 4.57056 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.6098 | 1.09432 | ||||||||
\(95\) | 19.0351 | 1.95296 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.36588 | −0.747891 | −0.373946 | − | 0.927451i | \(-0.621995\pi\) | ||||
−0.373946 | + | 0.927451i | \(0.621995\pi\) | |||||||
\(98\) | −17.3782 | −1.75546 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 19.6982 | 1.96982 | ||||||||
\(101\) | −5.05569 | −0.503060 | −0.251530 | − | 0.967849i | \(-0.580934\pi\) | ||||
−0.251530 | + | 0.967849i | \(0.580934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.90289 | 0.187497 | 0.0937486 | − | 0.995596i | \(-0.470115\pi\) | ||||
0.0937486 | + | 0.995596i | \(0.470115\pi\) | |||||||
\(104\) | −34.9875 | −3.43081 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.4098 | 1.01109 | ||||||||
\(107\) | −11.8307 | −1.14371 | −0.571856 | − | 0.820354i | \(-0.693776\pi\) | ||||
−0.571856 | + | 0.820354i | \(0.693776\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.76603 | 0.456503 | 0.228251 | − | 0.973602i | \(-0.426699\pi\) | ||||
0.228251 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(110\) | −33.2536 | −3.17060 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.12181 | −0.483965 | ||||||||
\(113\) | −12.6049 | −1.18577 | −0.592886 | − | 0.805287i | \(-0.702011\pi\) | ||||
−0.592886 | + | 0.805287i | \(0.702011\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.8547 | 2.59747 | ||||||||
\(116\) | −5.45992 | −0.506941 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 31.9423 | 2.94052 | ||||||||
\(119\) | −3.59270 | −0.329342 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.90230 | 0.627482 | ||||||||
\(122\) | −1.23120 | −0.111467 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −35.7890 | −3.21395 | ||||||||
\(125\) | −2.60024 | −0.232572 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.3142 | −1.80260 | −0.901298 | − | 0.433199i | \(-0.857385\pi\) | ||||
−0.901298 | + | 0.433199i | \(0.857385\pi\) | |||||||
\(128\) | −2.81634 | −0.248931 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −38.3505 | −3.36356 | ||||||||
\(131\) | −13.5167 | −1.18096 | −0.590478 | − | 0.807054i | \(-0.701061\pi\) | ||||
−0.590478 | + | 0.807054i | \(0.701061\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.53467 | −0.306494 | ||||||||
\(134\) | 4.69712 | 0.405770 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 45.8861 | 3.93470 | ||||||||
\(137\) | −8.32726 | −0.711446 | −0.355723 | − | 0.934591i | \(-0.615765\pi\) | ||||
−0.355723 | + | 0.934591i | \(0.615765\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.6457 | −1.41187 | −0.705936 | − | 0.708275i | \(-0.749474\pi\) | ||||
−0.705936 | + | 0.708275i | \(0.749474\pi\) | |||||||
\(140\) | −8.07552 | −0.682506 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.59801 | 0.385856 | ||||||||
\(143\) | 20.6463 | 1.72653 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.46914 | −0.288096 | ||||||||
\(146\) | 1.59015 | 0.131602 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 41.6024 | 3.41970 | ||||||||
\(149\) | −9.40634 | −0.770598 | −0.385299 | − | 0.922792i | \(-0.625902\pi\) | ||||
−0.385299 | + | 0.922792i | \(0.625902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.3010 | −1.65207 | −0.826035 | − | 0.563619i | \(-0.809409\pi\) | ||||
−0.826035 | + | 0.563619i | \(0.809409\pi\) | |||||||
\(152\) | 45.1450 | 3.66174 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.17492 | 0.497590 | ||||||||
\(155\) | −22.7397 | −1.82650 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.07853 | −0.485120 | −0.242560 | − | 0.970136i | \(-0.577987\pi\) | ||||
−0.242560 | + | 0.970136i | \(0.577987\pi\) | |||||||
\(158\) | −6.48978 | −0.516299 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 28.3502 | 2.24128 | ||||||||
\(161\) | −5.17240 | −0.407643 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.36070 | 0.576535 | 0.288267 | − | 0.957550i | \(-0.406921\pi\) | ||||
0.288267 | + | 0.957550i | \(0.406921\pi\) | |||||||
\(164\) | −13.4126 | −1.04735 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.5597 | −1.67336 | ||||||||
\(167\) | −7.50992 | −0.581135 | −0.290568 | − | 0.956854i | \(-0.593844\pi\) | ||||
−0.290568 | + | 0.956854i | \(0.593844\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8108 | 0.831604 | ||||||||
\(170\) | 50.2967 | 3.85758 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.47136 | −0.569686 | ||||||||
\(173\) | −5.25063 | −0.399198 | −0.199599 | − | 0.979878i | \(-0.563964\pi\) | ||||
−0.199599 | + | 0.979878i | \(0.563964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.32410 | −0.175686 | ||||||||
\(176\) | −38.6023 | −2.90976 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 38.6102 | 2.89396 | ||||||||
\(179\) | 9.57025 | 0.715314 | 0.357657 | − | 0.933853i | \(-0.383576\pi\) | ||||
0.357657 | + | 0.933853i | \(0.383576\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.66933 | −0.124081 | −0.0620403 | − | 0.998074i | \(-0.519761\pi\) | ||||
−0.0620403 | + | 0.998074i | \(0.519761\pi\) | |||||||
\(182\) | 7.12139 | 0.527872 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 66.0623 | 4.87018 | ||||||||
\(185\) | 26.4335 | 1.94343 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.0776 | −1.98011 | ||||||||
\(188\) | 19.4191 | 1.41629 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 49.4843 | 3.58997 | ||||||||
\(191\) | −26.7101 | −1.93268 | −0.966339 | − | 0.257272i | \(-0.917176\pi\) | ||||
−0.966339 | + | 0.257272i | \(0.917176\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.1594 | 1.23516 | 0.617582 | − | 0.786506i | \(-0.288112\pi\) | ||||
0.617582 | + | 0.786506i | \(0.288112\pi\) | |||||||
\(194\) | −19.1486 | −1.37479 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −31.8073 | −2.27195 | ||||||||
\(197\) | 5.98278 | 0.426255 | 0.213128 | − | 0.977024i | \(-0.431635\pi\) | ||||
0.213128 | + | 0.977024i | \(0.431635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0373 | 1.13685 | 0.568426 | − | 0.822734i | \(-0.307552\pi\) | ||||
0.568426 | + | 0.822734i | \(0.307552\pi\) | |||||||
\(200\) | 29.6836 | 2.09895 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.1430 | −0.924737 | ||||||||
\(203\) | 0.644192 | 0.0452134 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.52217 | −0.595214 | ||||||||
\(206\) | 4.94682 | 0.344661 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −44.5191 | −3.08684 | ||||||||
\(209\) | −26.6403 | −1.84274 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5087 | 0.792291 | 0.396146 | − | 0.918188i | \(-0.370348\pi\) | ||||
0.396146 | + | 0.918188i | \(0.370348\pi\) | |||||||
\(212\) | 19.0531 | 1.30857 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −30.7554 | −2.10240 | ||||||||
\(215\) | −4.74718 | −0.323755 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.22259 | 0.286648 | ||||||||
\(218\) | 12.3900 | 0.839154 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −60.8640 | −4.10345 | ||||||||
\(221\) | −31.2279 | −2.10062 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.40148 | 0.294745 | 0.147372 | − | 0.989081i | \(-0.452918\pi\) | ||||
0.147372 | + | 0.989081i | \(0.452918\pi\) | |||||||
\(224\) | −5.26440 | −0.351742 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −32.7682 | −2.17971 | ||||||||
\(227\) | −14.9252 | −0.990618 | −0.495309 | − | 0.868717i | \(-0.664945\pi\) | ||||
−0.495309 | + | 0.868717i | \(0.664945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.19125 | 0.276966 | 0.138483 | − | 0.990365i | \(-0.455777\pi\) | ||||
0.138483 | + | 0.990365i | \(0.455777\pi\) | |||||||
\(230\) | 72.4122 | 4.77472 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.22766 | −0.540173 | ||||||||
\(233\) | −1.32186 | −0.0865980 | −0.0432990 | − | 0.999062i | \(-0.513787\pi\) | ||||
−0.0432990 | + | 0.999062i | \(0.513787\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3386 | 0.804881 | ||||||||
\(236\) | 58.4639 | 3.80568 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.33971 | −0.605403 | ||||||||
\(239\) | 3.57501 | 0.231248 | 0.115624 | − | 0.993293i | \(-0.463113\pi\) | ||||
0.115624 | + | 0.993293i | \(0.463113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5198 | 0.935301 | 0.467650 | − | 0.883914i | \(-0.345101\pi\) | ||||
0.467650 | + | 0.883914i | \(0.345101\pi\) | |||||||
\(242\) | 17.9435 | 1.15345 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.25346 | −0.144263 | ||||||||
\(245\) | −20.2098 | −1.29116 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.7235 | −1.95489 | ||||||||
\(248\) | −53.9312 | −3.42464 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.75968 | −0.427520 | ||||||||
\(251\) | −5.30634 | −0.334933 | −0.167467 | − | 0.985878i | \(-0.553559\pi\) | ||||
−0.167467 | + | 0.985878i | \(0.553559\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.9836 | −2.45088 | ||||||||
\(254\) | −52.8097 | −3.31357 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −19.5836 | −1.22397 | ||||||||
\(257\) | 2.08054 | 0.129781 | 0.0648903 | − | 0.997892i | \(-0.479330\pi\) | ||||
0.0648903 | + | 0.997892i | \(0.479330\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.90849 | −0.304999 | ||||||||
\(260\) | −70.1930 | −4.35318 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −35.1384 | −2.17086 | ||||||||
\(263\) | −16.6250 | −1.02514 | −0.512570 | − | 0.858645i | \(-0.671306\pi\) | ||||
−0.512570 | + | 0.858645i | \(0.671306\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1060 | 0.743668 | ||||||||
\(266\) | −9.18885 | −0.563405 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.59714 | 0.525154 | ||||||||
\(269\) | 7.61200 | 0.464112 | 0.232056 | − | 0.972702i | \(-0.425455\pi\) | ||||
0.232056 | + | 0.972702i | \(0.425455\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.15827 | 0.252597 | 0.126298 | − | 0.991992i | \(-0.459690\pi\) | ||||
0.126298 | + | 0.991992i | \(0.459690\pi\) | |||||||
\(272\) | 58.3868 | 3.54022 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.6479 | −1.30779 | ||||||||
\(275\) | −17.5164 | −1.05628 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.42089 | 0.566047 | 0.283023 | − | 0.959113i | \(-0.408663\pi\) | ||||
0.283023 | + | 0.959113i | \(0.408663\pi\) | |||||||
\(278\) | −43.2729 | −2.59533 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.1692 | −0.727247 | ||||||||
\(281\) | 23.1796 | 1.38278 | 0.691391 | − | 0.722481i | \(-0.256998\pi\) | ||||
0.691391 | + | 0.722481i | \(0.256998\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.6282 | −1.46399 | −0.731997 | − | 0.681308i | \(-0.761412\pi\) | ||||
−0.731997 | + | 0.681308i | \(0.761412\pi\) | |||||||
\(284\) | 8.41573 | 0.499382 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 53.6729 | 3.17374 | ||||||||
\(287\) | 1.58250 | 0.0934120 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.9555 | 1.40915 | ||||||||
\(290\) | −9.01851 | −0.529585 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.91045 | 0.170321 | ||||||||
\(293\) | −23.3449 | −1.36382 | −0.681910 | − | 0.731436i | \(-0.738851\pi\) | ||||
−0.681910 | + | 0.731436i | \(0.738851\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 37.1470 | 2.16278 | ||||||||
\(296\) | 62.6916 | 3.64387 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.4531 | −1.41653 | ||||||||
\(299\) | −44.9589 | −2.60004 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.881513 | 0.0508096 | ||||||||
\(302\) | −52.7752 | −3.03687 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 57.4438 | 3.29463 | ||||||||
\(305\) | −1.43181 | −0.0819851 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.1646 | −0.751342 | −0.375671 | − | 0.926753i | \(-0.622588\pi\) | ||||
−0.375671 | + | 0.926753i | \(0.622588\pi\) | |||||||
\(308\) | 11.3020 | 0.643989 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −59.1151 | −3.35751 | ||||||||
\(311\) | 18.1219 | 1.02760 | 0.513800 | − | 0.857910i | \(-0.328237\pi\) | ||||
0.513800 | + | 0.857910i | \(0.328237\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.2295 | 0.804299 | 0.402150 | − | 0.915574i | \(-0.368263\pi\) | ||||
0.402150 | + | 0.915574i | \(0.368263\pi\) | |||||||
\(314\) | −15.8020 | −0.891758 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.8783 | −0.668204 | ||||||||
\(317\) | −0.706042 | −0.0396553 | −0.0198276 | − | 0.999803i | \(-0.506312\pi\) | ||||
−0.0198276 | + | 0.999803i | \(0.506312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.85518 | 0.271838 | ||||||||
\(320\) | 18.5356 | 1.03617 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.4464 | −0.749337 | ||||||||
\(323\) | 40.2940 | 2.24202 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.2013 | −1.12056 | ||||||||
\(326\) | 19.1352 | 1.05980 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −20.2118 | −1.11601 | ||||||||
\(329\) | −2.29118 | −0.126317 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.50165 | −0.0825381 | −0.0412691 | − | 0.999148i | \(-0.513140\pi\) | ||||
−0.0412691 | + | 0.999148i | \(0.513140\pi\) | |||||||
\(332\) | −39.4608 | −2.16569 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.5231 | −1.06825 | ||||||||
\(335\) | 5.46248 | 0.298447 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.5820 | −0.576437 | −0.288219 | − | 0.957565i | \(-0.593063\pi\) | ||||
−0.288219 | + | 0.957565i | \(0.593063\pi\) | |||||||
\(338\) | 28.1043 | 1.52867 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 92.0581 | 4.99255 | ||||||||
\(341\) | 31.8250 | 1.72342 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.68253 | 0.414818 | ||||||||
\(344\) | −11.2587 | −0.607031 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.6497 | −0.733815 | ||||||||
\(347\) | 21.9609 | 1.17892 | 0.589461 | − | 0.807797i | \(-0.299340\pi\) | ||||
0.589461 | + | 0.807797i | \(0.299340\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.7632 | −0.736727 | −0.368364 | − | 0.929682i | \(-0.620082\pi\) | ||||
−0.368364 | + | 0.929682i | \(0.620082\pi\) | |||||||
\(350\) | −6.04183 | −0.322949 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −39.6770 | −2.11479 | ||||||||
\(353\) | 33.1723 | 1.76558 | 0.882791 | − | 0.469766i | \(-0.155662\pi\) | ||||
0.882791 | + | 0.469766i | \(0.155662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.34722 | 0.283801 | ||||||||
\(356\) | 70.6682 | 3.74541 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.8792 | 1.31491 | ||||||||
\(359\) | 18.0716 | 0.953782 | 0.476891 | − | 0.878962i | \(-0.341764\pi\) | ||||
0.476891 | + | 0.878962i | \(0.341764\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.6431 | 1.08648 | ||||||||
\(362\) | −4.33966 | −0.228087 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.0343 | 0.683182 | ||||||||
\(365\) | 1.84925 | 0.0967944 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.7727 | −1.71072 | −0.855361 | − | 0.518033i | \(-0.826665\pi\) | ||||
−0.855361 | + | 0.518033i | \(0.826665\pi\) | |||||||
\(368\) | 84.0595 | 4.38191 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 68.7175 | 3.57245 | ||||||||
\(371\) | −2.24800 | −0.116710 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.25311 | 0.168440 | 0.0842199 | − | 0.996447i | \(-0.473160\pi\) | ||||
0.0842199 | + | 0.996447i | \(0.473160\pi\) | |||||||
\(374\) | −70.3920 | −3.63988 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 29.2631 | 1.50913 | ||||||||
\(377\) | 5.59936 | 0.288382 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.1603 | −0.984198 | −0.492099 | − | 0.870539i | \(-0.663770\pi\) | ||||
−0.492099 | + | 0.870539i | \(0.663770\pi\) | |||||||
\(380\) | 90.5712 | 4.64620 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −69.4367 | −3.55269 | ||||||||
\(383\) | −22.6686 | −1.15831 | −0.579155 | − | 0.815217i | \(-0.696617\pi\) | ||||
−0.579155 | + | 0.815217i | \(0.696617\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.18108 | 0.365982 | ||||||||
\(386\) | 44.6084 | 2.27051 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −35.0477 | −1.77928 | ||||||||
\(389\) | 39.0808 | 1.98148 | 0.990738 | − | 0.135788i | \(-0.0433565\pi\) | ||||
0.990738 | + | 0.135788i | \(0.0433565\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 58.9636 | 2.98192 | ||||||||
\(392\) | −47.9310 | −2.42088 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.5531 | 0.783551 | ||||||||
\(395\) | −7.54724 | −0.379743 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.4671 | 0.876649 | 0.438324 | − | 0.898817i | \(-0.355572\pi\) | ||||
0.438324 | + | 0.898817i | \(0.355572\pi\) | |||||||
\(398\) | 41.6911 | 2.08979 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 37.7703 | 1.88851 | ||||||||
\(401\) | −7.16631 | −0.357868 | −0.178934 | − | 0.983861i | \(-0.557265\pi\) | ||||
−0.178934 | + | 0.983861i | \(0.557265\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.7030 | 1.82831 | ||||||||
\(404\) | −24.0556 | −1.19681 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.67467 | 0.0831123 | ||||||||
\(407\) | −36.9946 | −1.83375 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.3350 | −1.00550 | −0.502750 | − | 0.864432i | \(-0.667678\pi\) | ||||
−0.502750 | + | 0.864432i | \(0.667678\pi\) | |||||||
\(410\) | −22.1546 | −1.09414 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.05417 | 0.446067 | ||||||||
\(413\) | −6.89791 | −0.339424 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.0727 | −1.23077 | ||||||||
\(416\) | −45.7585 | −2.24350 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −69.2550 | −3.38737 | ||||||||
\(419\) | 28.3481 | 1.38490 | 0.692448 | − | 0.721468i | \(-0.256532\pi\) | ||||
0.692448 | + | 0.721468i | \(0.256532\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.21872 | −0.108134 | −0.0540670 | − | 0.998537i | \(-0.517218\pi\) | ||||
−0.0540670 | + | 0.998537i | \(0.517218\pi\) | |||||||
\(422\) | 29.9184 | 1.45641 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 28.7116 | 1.39436 | ||||||||
\(425\) | 26.4940 | 1.28515 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.265876 | 0.0128666 | ||||||||
\(428\) | −56.2916 | −2.72096 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.3409 | −0.595133 | ||||||||
\(431\) | 1.89601 | 0.0913274 | 0.0456637 | − | 0.998957i | \(-0.485460\pi\) | ||||
0.0456637 | + | 0.998957i | \(0.485460\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.8222 | −1.62539 | −0.812697 | − | 0.582687i | \(-0.802001\pi\) | ||||
−0.812697 | + | 0.582687i | \(0.802001\pi\) | |||||||
\(434\) | 10.9772 | 0.526923 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.6773 | 1.08605 | ||||||||
\(437\) | 58.0112 | 2.77505 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.31659 | 0.301474 | 0.150737 | − | 0.988574i | \(-0.451835\pi\) | ||||
0.150737 | + | 0.988574i | \(0.451835\pi\) | |||||||
\(440\) | −91.7173 | −4.37245 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −81.1814 | −3.86140 | ||||||||
\(443\) | −19.5315 | −0.927967 | −0.463984 | − | 0.885844i | \(-0.653580\pi\) | ||||
−0.463984 | + | 0.885844i | \(0.653580\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.9014 | 2.12853 | ||||||||
\(446\) | 11.4423 | 0.541807 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.44192 | −0.162615 | ||||||||
\(449\) | 15.3252 | 0.723242 | 0.361621 | − | 0.932325i | \(-0.382223\pi\) | ||||
0.361621 | + | 0.932325i | \(0.382223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.9271 | 0.561623 | ||||||||
\(452\) | −59.9757 | −2.82102 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −38.8000 | −1.82098 | ||||||||
\(455\) | 8.28176 | 0.388255 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.7763 | −0.691207 | −0.345603 | − | 0.938381i | \(-0.612326\pi\) | ||||
−0.345603 | + | 0.938381i | \(0.612326\pi\) | |||||||
\(458\) | 10.8957 | 0.509124 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 132.536 | 6.17953 | ||||||||
\(461\) | 28.1311 | 1.31020 | 0.655098 | − | 0.755544i | \(-0.272627\pi\) | ||||
0.655098 | + | 0.755544i | \(0.272627\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.7165 | 0.776880 | 0.388440 | − | 0.921474i | \(-0.373014\pi\) | ||||
0.388440 | + | 0.921474i | \(0.373014\pi\) | |||||||
\(464\) | −10.4691 | −0.486016 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.43636 | −0.159186 | ||||||||
\(467\) | 22.4105 | 1.03703 | 0.518517 | − | 0.855067i | \(-0.326484\pi\) | ||||
0.518517 | + | 0.855067i | \(0.326484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.01434 | −0.0468379 | ||||||||
\(470\) | 32.0759 | 1.47955 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 88.1005 | 4.05515 | ||||||||
\(473\) | 6.64383 | 0.305484 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.0660 | 1.19599 | ||||||||
\(476\) | −17.0945 | −0.783524 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.29372 | 0.425085 | ||||||||
\(479\) | 15.0630 | 0.688247 | 0.344123 | − | 0.938924i | \(-0.388176\pi\) | ||||
0.344123 | + | 0.938924i | \(0.388176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.6649 | −1.94535 | ||||||||
\(482\) | 37.7462 | 1.71929 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 32.8420 | 1.49282 | ||||||||
\(485\) | −22.2687 | −1.01117 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.0354 | 1.76886 | 0.884432 | − | 0.466669i | \(-0.154546\pi\) | ||||
0.884432 | + | 0.466669i | \(0.154546\pi\) | |||||||
\(488\) | −3.39578 | −0.153720 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −52.5382 | −2.37343 | ||||||||
\(491\) | −21.8721 | −0.987075 | −0.493537 | − | 0.869725i | \(-0.664296\pi\) | ||||
−0.493537 | + | 0.869725i | \(0.664296\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.34356 | −0.330737 | ||||||||
\(494\) | −79.8701 | −3.59353 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −68.6236 | −3.08129 | ||||||||
\(497\) | −0.992936 | −0.0445393 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.4160 | 0.913947 | 0.456973 | − | 0.889480i | \(-0.348933\pi\) | ||||
0.456973 | + | 0.889480i | \(0.348933\pi\) | |||||||
\(500\) | −12.3722 | −0.553304 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.7946 | −0.615681 | ||||||||
\(503\) | 17.2592 | 0.769551 | 0.384776 | − | 0.923010i | \(-0.374279\pi\) | ||||
0.384776 | + | 0.923010i | \(0.374279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.2845 | −0.680152 | ||||||||
\(506\) | −101.343 | −4.50526 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −96.6575 | −4.28848 | ||||||||
\(509\) | 29.7166 | 1.31717 | 0.658584 | − | 0.752508i | \(-0.271156\pi\) | ||||
0.658584 | + | 0.752508i | \(0.271156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.343392 | −0.0151908 | ||||||||
\(512\) | −45.2776 | −2.00100 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.40865 | 0.238566 | ||||||||
\(515\) | 5.75287 | 0.253502 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.2683 | −0.759458 | ||||||||
\(518\) | −12.7603 | −0.560655 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −105.775 | −4.63855 | ||||||||
\(521\) | −32.4429 | −1.42135 | −0.710675 | − | 0.703520i | \(-0.751610\pi\) | ||||
−0.710675 | + | 0.703520i | \(0.751610\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.45155 | 0.238380 | 0.119190 | − | 0.992871i | \(-0.461970\pi\) | ||||
0.119190 | + | 0.992871i | \(0.461970\pi\) | |||||||
\(524\) | −64.3138 | −2.80956 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −43.2189 | −1.88443 | ||||||||
\(527\) | −48.1361 | −2.09684 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 61.8899 | 2.69087 | ||||||||
\(530\) | 31.4713 | 1.36703 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −16.8184 | −0.729168 | ||||||||
\(533\) | 13.7552 | 0.595803 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.7668 | −1.54633 | ||||||||
\(536\) | 12.9552 | 0.559580 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.7884 | 0.853140 | ||||||||
\(539\) | 28.2843 | 1.21829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.1191 | 1.33792 | 0.668958 | − | 0.743301i | \(-0.266741\pi\) | ||||
0.668958 | + | 0.743301i | \(0.266741\pi\) | |||||||
\(542\) | 10.8100 | 0.464329 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 60.0123 | 2.57301 | ||||||||
\(545\) | 14.4088 | 0.617205 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | −0.0427569 | ||||||||
\(548\) | −39.6221 | −1.69257 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −45.5364 | −1.94168 | ||||||||
\(551\) | −7.22495 | −0.307793 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.40146 | 0.0595963 | ||||||||
\(554\) | 24.4909 | 1.04052 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −79.2023 | −3.35893 | ||||||||
\(557\) | −41.0931 | −1.74117 | −0.870585 | − | 0.492017i | \(-0.836260\pi\) | ||||
−0.870585 | + | 0.492017i | \(0.836260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.66217 | 0.324075 | ||||||||
\(560\) | −15.4844 | −0.654335 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 60.2587 | 2.54186 | ||||||||
\(563\) | −6.83856 | −0.288211 | −0.144105 | − | 0.989562i | \(-0.546030\pi\) | ||||
−0.144105 | + | 0.989562i | \(0.546030\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.1076 | −1.60320 | ||||||||
\(566\) | −64.0244 | −2.69115 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.6818 | 0.532118 | ||||||||
\(569\) | 27.4209 | 1.14955 | 0.574773 | − | 0.818313i | \(-0.305091\pi\) | ||||
0.574773 | + | 0.818313i | \(0.305091\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.1032 | −1.42718 | −0.713588 | − | 0.700566i | \(-0.752931\pi\) | ||||
−0.713588 | + | 0.700566i | \(0.752931\pi\) | |||||||
\(572\) | 98.2374 | 4.10751 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.11392 | 0.171712 | ||||||||
\(575\) | 38.1434 | 1.59069 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.6417 | −1.40052 | −0.700260 | − | 0.713888i | \(-0.746933\pi\) | ||||
−0.700260 | + | 0.713888i | \(0.746933\pi\) | |||||||
\(578\) | 62.2756 | 2.59032 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −16.5066 | −0.685398 | ||||||||
\(581\) | 4.65581 | 0.193155 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.9428 | −0.701700 | ||||||||
\(584\) | 4.38582 | 0.181487 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −60.6882 | −2.50701 | ||||||||
\(587\) | 13.2895 | 0.548516 | 0.274258 | − | 0.961656i | \(-0.411568\pi\) | ||||
0.274258 | + | 0.961656i | \(0.411568\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −47.3586 | −1.95138 | ||||||||
\(590\) | 96.5688 | 3.97567 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 79.7705 | 3.27855 | ||||||||
\(593\) | 44.2951 | 1.81898 | 0.909491 | − | 0.415724i | \(-0.136472\pi\) | ||||
0.909491 | + | 0.415724i | \(0.136472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.8615 | −0.445280 | ||||||||
\(596\) | −44.7565 | −1.83330 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −116.877 | −4.77945 | ||||||||
\(599\) | −5.59011 | −0.228406 | −0.114203 | − | 0.993457i | \(-0.536431\pi\) | ||||
−0.114203 | + | 0.993457i | \(0.536431\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.4727 | 1.03905 | 0.519526 | − | 0.854454i | \(-0.326108\pi\) | ||||
0.519526 | + | 0.854454i | \(0.326108\pi\) | |||||||
\(602\) | 2.29161 | 0.0933992 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −96.5944 | −3.93037 | ||||||||
\(605\) | 20.8672 | 0.848374 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.4291 | −1.11331 | −0.556657 | − | 0.830742i | \(-0.687916\pi\) | ||||
−0.556657 | + | 0.830742i | \(0.687916\pi\) | |||||||
\(608\) | 59.0430 | 2.39451 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.72218 | −0.150707 | ||||||||
\(611\) | −19.9151 | −0.805678 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.8113 | 0.679000 | 0.339500 | − | 0.940606i | \(-0.389742\pi\) | ||||
0.339500 | + | 0.940606i | \(0.389742\pi\) | |||||||
\(614\) | −34.2231 | −1.38113 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.0312 | 0.686205 | ||||||||
\(617\) | −12.2317 | −0.492429 | −0.246215 | − | 0.969215i | \(-0.579187\pi\) | ||||
−0.246215 | + | 0.969215i | \(0.579187\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.1538 | −0.689471 | −0.344736 | − | 0.938700i | \(-0.612031\pi\) | ||||
−0.344736 | + | 0.938700i | \(0.612031\pi\) | |||||||
\(620\) | −108.198 | −4.34535 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 47.1105 | 1.88896 | ||||||||
\(623\) | −8.33784 | −0.334048 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.5607 | −1.14243 | ||||||||
\(626\) | 36.9916 | 1.47848 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.9224 | −1.15413 | ||||||||
\(629\) | 55.9551 | 2.23108 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.57839 | −0.261882 | −0.130941 | − | 0.991390i | \(-0.541800\pi\) | ||||
−0.130941 | + | 0.991390i | \(0.541800\pi\) | |||||||
\(632\) | −17.8996 | −0.712007 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.83545 | −0.0728952 | ||||||||
\(635\) | −61.4146 | −2.43716 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.6196 | 1.29244 | ||||||||
\(638\) | 12.6217 | 0.499698 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.51443 | −0.336562 | ||||||||
\(641\) | −2.33872 | −0.0923737 | −0.0461868 | − | 0.998933i | \(-0.514707\pi\) | ||||
−0.0461868 | + | 0.998933i | \(0.514707\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.3754 | −0.685218 | −0.342609 | − | 0.939478i | \(-0.611311\pi\) | ||||
−0.342609 | + | 0.939478i | \(0.611311\pi\) | |||||||
\(644\) | −24.6109 | −0.969805 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 104.750 | 4.12132 | ||||||||
\(647\) | −38.9519 | −1.53136 | −0.765679 | − | 0.643223i | \(-0.777597\pi\) | ||||
−0.765679 | + | 0.643223i | \(0.777597\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51.9885 | −2.04073 | ||||||||
\(650\) | −52.5160 | −2.05985 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 35.0231 | 1.37161 | ||||||||
\(653\) | 7.75059 | 0.303304 | 0.151652 | − | 0.988434i | \(-0.451541\pi\) | ||||
0.151652 | + | 0.988434i | \(0.451541\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.8639 | −1.59669 | ||||||||
\(656\) | −25.7180 | −1.00412 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.95624 | −0.232198 | ||||||||
\(659\) | 22.3674 | 0.871309 | 0.435655 | − | 0.900114i | \(-0.356517\pi\) | ||||
0.435655 | + | 0.900114i | \(0.356517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.2526 | 1.17669 | 0.588345 | − | 0.808610i | \(-0.299780\pi\) | ||||
0.588345 | + | 0.808610i | \(0.299780\pi\) | |||||||
\(662\) | −3.90375 | −0.151723 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −59.4643 | −2.30766 | ||||||||
\(665\) | −10.6861 | −0.414389 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.5725 | −0.409370 | ||||||||
\(668\) | −35.7331 | −1.38255 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.2005 | 0.548612 | ||||||||
\(671\) | 2.00386 | 0.0773583 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.7416 | 0.452604 | 0.226302 | − | 0.974057i | \(-0.427336\pi\) | ||||
0.226302 | + | 0.974057i | \(0.427336\pi\) | |||||||
\(674\) | −27.5093 | −1.05962 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 51.4393 | 1.97843 | ||||||||
\(677\) | 30.4285 | 1.16946 | 0.584732 | − | 0.811227i | \(-0.301200\pi\) | ||||
0.584732 | + | 0.811227i | \(0.301200\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.13513 | 0.158692 | ||||||||
\(680\) | 138.724 | 5.31984 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 82.7336 | 3.16803 | ||||||||
\(683\) | 11.6989 | 0.447647 | 0.223823 | − | 0.974630i | \(-0.428146\pi\) | ||||
0.223823 | + | 0.974630i | \(0.428146\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.1752 | −0.961895 | ||||||||
\(686\) | 19.9718 | 0.762527 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.3259 | −0.546171 | ||||||||
\(689\) | −19.5397 | −0.744404 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.2076 | 1.03502 | 0.517512 | − | 0.855676i | \(-0.326858\pi\) | ||||
0.517512 | + | 0.855676i | \(0.326858\pi\) | |||||||
\(692\) | −24.9831 | −0.949716 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 57.0903 | 2.16712 | ||||||||
\(695\) | −50.3239 | −1.90889 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0399 | −0.683311 | ||||||||
\(698\) | −35.7794 | −1.35427 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.0584 | −0.417967 | ||||||||
\(701\) | 21.2354 | 0.802049 | 0.401024 | − | 0.916067i | \(-0.368654\pi\) | ||||
0.401024 | + | 0.916067i | \(0.368654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 55.0513 | 2.07630 | ||||||||
\(704\) | −25.9412 | −0.977697 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 86.2359 | 3.24553 | ||||||||
\(707\) | 2.83821 | 0.106742 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.8807 | 0.633967 | 0.316983 | − | 0.948431i | \(-0.397330\pi\) | ||||
0.316983 | + | 0.948431i | \(0.397330\pi\) | |||||||
\(710\) | 13.9008 | 0.521689 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 106.491 | 3.99094 | ||||||||
\(713\) | −69.3015 | −2.59536 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 62.4184 | 2.33432 | ||||||||
\(716\) | 45.5364 | 1.70177 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 46.9796 | 1.75326 | ||||||||
\(719\) | 20.3235 | 0.757941 | 0.378970 | − | 0.925409i | \(-0.376278\pi\) | ||||
0.378970 | + | 0.925409i | \(0.376278\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.06826 | −0.0397842 | ||||||||
\(722\) | 53.6646 | 1.99719 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.94288 | −0.295195 | ||||||||
\(725\) | −4.75053 | −0.176430 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.13646 | −0.338853 | −0.169426 | − | 0.985543i | \(-0.554191\pi\) | ||||
−0.169426 | + | 0.985543i | \(0.554191\pi\) | |||||||
\(728\) | 19.6416 | 0.727967 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.80739 | 0.177929 | ||||||||
\(731\) | −10.0489 | −0.371674 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.55001 | −0.241930 | −0.120965 | − | 0.992657i | \(-0.538599\pi\) | ||||
−0.120965 | + | 0.992657i | \(0.538599\pi\) | |||||||
\(734\) | −85.1972 | −3.14469 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 86.3997 | 3.18474 | ||||||||
\(737\) | −7.64493 | −0.281605 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.2949 | −1.37192 | −0.685958 | − | 0.727641i | \(-0.740617\pi\) | ||||
−0.685958 | + | 0.727641i | \(0.740617\pi\) | |||||||
\(740\) | 125.774 | 4.62353 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.84398 | −0.214539 | ||||||||
\(743\) | 45.7404 | 1.67805 | 0.839026 | − | 0.544092i | \(-0.183126\pi\) | ||||
0.839026 | + | 0.544092i | \(0.183126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.4375 | −1.04187 | ||||||||
\(746\) | 8.45692 | 0.309630 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −128.838 | −4.71080 | ||||||||
\(749\) | 6.64161 | 0.242679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.4995 | −1.40487 | −0.702434 | − | 0.711749i | \(-0.747903\pi\) | ||||
−0.702434 | + | 0.711749i | \(0.747903\pi\) | |||||||
\(752\) | 37.2352 | 1.35783 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.5563 | 0.530109 | ||||||||
\(755\) | −61.3745 | −2.23365 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.5989 | 0.748681 | 0.374340 | − | 0.927291i | \(-0.377869\pi\) | ||||
0.374340 | + | 0.927291i | \(0.377869\pi\) | |||||||
\(758\) | −49.8098 | −1.80917 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 136.484 | 4.95078 | ||||||||
\(761\) | −18.6360 | −0.675555 | −0.337778 | − | 0.941226i | \(-0.609675\pi\) | ||||
−0.337778 | + | 0.941226i | \(0.609675\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.67560 | −0.0968632 | ||||||||
\(764\) | −127.090 | −4.59795 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −58.9301 | −2.12923 | ||||||||
\(767\) | −59.9571 | −2.16492 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.6001 | 1.17559 | 0.587795 | − | 0.809010i | \(-0.299996\pi\) | ||||
0.587795 | + | 0.809010i | \(0.299996\pi\) | |||||||
\(770\) | 18.6682 | 0.672756 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 81.6467 | 2.93853 | ||||||||
\(773\) | 50.6910 | 1.82323 | 0.911614 | − | 0.411047i | \(-0.134837\pi\) | ||||
0.911614 | + | 0.411047i | \(0.134837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.1391 | −1.11855 | ||||||||
\(776\) | −52.8141 | −1.89592 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 101.596 | 3.64239 | ||||||||
\(779\) | −17.7486 | −0.635908 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.48361 | −0.267785 | ||||||||
\(782\) | 153.284 | 5.48143 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −60.9888 | −2.17817 | ||||||||
\(785\) | −18.3768 | −0.655896 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.5394 | 0.625213 | 0.312607 | − | 0.949883i | \(-0.398798\pi\) | ||||
0.312607 | + | 0.949883i | \(0.398798\pi\) | |||||||
\(788\) | 28.4668 | 1.01409 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19.6201 | −0.698052 | ||||||||
\(791\) | 7.07627 | 0.251603 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.31101 | 0.0820663 | ||||||||
\(794\) | 45.4081 | 1.61147 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 76.3072 | 2.70464 | ||||||||
\(797\) | 11.2655 | 0.399044 | 0.199522 | − | 0.979893i | \(-0.436061\pi\) | ||||
0.199522 | + | 0.979893i | \(0.436061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.1186 | 0.924011 | ||||||||
\(800\) | 38.8218 | 1.37256 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.6298 | −0.657841 | ||||||||
\(803\) | −2.58809 | −0.0913318 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.6374 | −0.551145 | ||||||||
\(806\) | 95.4146 | 3.36084 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −36.2499 | −1.27527 | ||||||||
\(809\) | 1.43789 | 0.0505534 | 0.0252767 | − | 0.999680i | \(-0.491953\pi\) | ||||
0.0252767 | + | 0.999680i | \(0.491953\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.2119 | −1.37692 | −0.688458 | − | 0.725276i | \(-0.741712\pi\) | ||||
−0.688458 | + | 0.725276i | \(0.741712\pi\) | |||||||
\(812\) | 3.06514 | 0.107565 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −96.1725 | −3.37084 | ||||||||
\(815\) | 22.2531 | 0.779492 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.88663 | −0.345889 | ||||||||
\(818\) | −52.8636 | −1.84833 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −40.5495 | −1.41605 | ||||||||
\(821\) | −9.41950 | −0.328743 | −0.164371 | − | 0.986399i | \(-0.552560\pi\) | ||||
−0.164371 | + | 0.986399i | \(0.552560\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.7149 | −1.00094 | −0.500470 | − | 0.865754i | \(-0.666839\pi\) | ||||
−0.500470 | + | 0.865754i | \(0.666839\pi\) | |||||||
\(824\) | 13.6439 | 0.475308 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.9321 | −0.623936 | ||||||||
\(827\) | −32.2145 | −1.12021 | −0.560104 | − | 0.828422i | \(-0.689239\pi\) | ||||
−0.560104 | + | 0.828422i | \(0.689239\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.3853 | −1.43737 | −0.718685 | − | 0.695335i | \(-0.755256\pi\) | ||||
−0.718685 | + | 0.695335i | \(0.755256\pi\) | |||||||
\(830\) | −65.1800 | −2.26243 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −29.9174 | −1.03720 | ||||||||
\(833\) | −42.7806 | −1.48226 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.7042 | −0.785711 | ||||||||
\(836\) | −126.757 | −4.38400 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 73.6948 | 2.54575 | ||||||||
\(839\) | −31.6092 | −1.09127 | −0.545635 | − | 0.838023i | \(-0.683711\pi\) | ||||
−0.545635 | + | 0.838023i | \(0.683711\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6833 | −0.954595 | ||||||||
\(842\) | −5.76788 | −0.198774 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 54.7597 | 1.88491 | ||||||||
\(845\) | 32.6837 | 1.12435 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.87488 | −0.133142 | ||||||||
\(848\) | 36.5334 | 1.25456 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 68.8748 | 2.36238 | ||||||||
\(851\) | 80.5585 | 2.76151 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.9128 | 0.921477 | 0.460739 | − | 0.887536i | \(-0.347585\pi\) | ||||
0.460739 | + | 0.887536i | \(0.347585\pi\) | |||||||
\(854\) | 0.691180 | 0.0236517 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −84.8270 | −2.89933 | ||||||||
\(857\) | −25.4512 | −0.869398 | −0.434699 | − | 0.900576i | \(-0.643145\pi\) | ||||
−0.434699 | + | 0.900576i | \(0.643145\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.5688 | 1.14535 | 0.572676 | − | 0.819781i | \(-0.305905\pi\) | ||||
0.572676 | + | 0.819781i | \(0.305905\pi\) | |||||||
\(860\) | −22.5876 | −0.770231 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.92893 | 0.167880 | ||||||||
\(863\) | −21.3439 | −0.726554 | −0.363277 | − | 0.931681i | \(-0.618342\pi\) | ||||
−0.363277 | + | 0.931681i | \(0.618342\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.8739 | −0.539728 | ||||||||
\(866\) | −87.9256 | −2.98783 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.0916 | 0.681953 | ||||||||
\(869\) | 10.5626 | 0.358312 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.81671 | −0.298743 | ||||||||
\(872\) | 34.1729 | 1.15724 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 150.808 | 5.10116 | ||||||||
\(875\) | 1.45975 | 0.0493485 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.2943 | −1.09050 | −0.545251 | − | 0.838273i | \(-0.683566\pi\) | ||||
−0.545251 | + | 0.838273i | \(0.683566\pi\) | |||||||
\(878\) | 16.4208 | 0.554176 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −116.704 | −3.93408 | ||||||||
\(881\) | −16.3456 | −0.550698 | −0.275349 | − | 0.961344i | \(-0.588793\pi\) | ||||
−0.275349 | + | 0.961344i | \(0.588793\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.21171 | 0.242693 | 0.121347 | − | 0.992610i | \(-0.461279\pi\) | ||||
0.121347 | + | 0.992610i | \(0.461279\pi\) | |||||||
\(884\) | −148.586 | −4.99750 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −50.7747 | −1.70581 | ||||||||
\(887\) | −35.6173 | −1.19591 | −0.597956 | − | 0.801529i | \(-0.704020\pi\) | ||||
−0.597956 | + | 0.801529i | \(0.704020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.4042 | 0.382485 | ||||||||
\(890\) | 116.727 | 3.91271 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.9428 | 0.701216 | ||||||||
\(893\) | 25.6968 | 0.859910 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.9330 | 0.967125 | ||||||||
\(896\) | 1.58106 | 0.0528196 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.8401 | 1.32948 | ||||||||
\(899\) | 8.63109 | 0.287863 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.6264 | 0.853738 | ||||||||
\(902\) | 31.0060 | 1.03239 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −90.3786 | −3.00595 | ||||||||
\(905\) | −5.04677 | −0.167760 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.0472 | −1.62859 | −0.814293 | − | 0.580454i | \(-0.802875\pi\) | ||||
−0.814293 | + | 0.580454i | \(0.802875\pi\) | |||||||
\(908\) | −71.0157 | −2.35674 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 21.5296 | 0.713699 | ||||||||
\(911\) | 45.6848 | 1.51361 | 0.756803 | − | 0.653643i | \(-0.226760\pi\) | ||||
0.756803 | + | 0.653643i | \(0.226760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.0901 | 1.16131 | ||||||||
\(914\) | −38.4131 | −1.27059 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.9425 | 0.658917 | ||||||||
\(917\) | 7.58811 | 0.250581 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.9459 | −0.427045 | −0.213522 | − | 0.976938i | \(-0.568494\pi\) | ||||
−0.213522 | + | 0.976938i | \(0.568494\pi\) | |||||||
\(920\) | 199.721 | 6.58462 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 73.1307 | 2.40843 | ||||||||
\(923\) | −8.63067 | −0.284082 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.1972 | 1.19016 | ||||||||
\(926\) | 43.4568 | 1.42808 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10.7606 | −0.353233 | ||||||||
\(929\) | 4.49235 | 0.147389 | 0.0736946 | − | 0.997281i | \(-0.476521\pi\) | ||||
0.0736946 | + | 0.997281i | \(0.476521\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.0896 | −1.37943 | ||||||||
\(932\) | −6.28957 | −0.206022 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 58.2592 | 1.90630 | ||||||||
\(935\) | −81.8618 | −2.67717 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.90994 | −0.0623951 | −0.0311975 | − | 0.999513i | \(-0.509932\pi\) | ||||
−0.0311975 | + | 0.999513i | \(0.509932\pi\) | |||||||
\(938\) | −2.63692 | −0.0860984 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 58.7085 | 1.91486 | ||||||||
\(941\) | 1.34900 | 0.0439761 | 0.0219881 | − | 0.999758i | \(-0.493000\pi\) | ||||
0.0219881 | + | 0.999758i | \(0.493000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.9721 | −0.845768 | ||||||||
\(944\) | 112.102 | 3.64860 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.2716 | 0.561547 | ||||||||
\(947\) | 23.5579 | 0.765530 | 0.382765 | − | 0.923846i | \(-0.374972\pi\) | ||||
0.382765 | + | 0.923846i | \(0.374972\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.98478 | −0.0968902 | ||||||||
\(950\) | 67.7623 | 2.19850 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.7600 | −0.834887 | ||||||||
\(953\) | −44.6075 | −1.44498 | −0.722489 | − | 0.691383i | \(-0.757002\pi\) | ||||
−0.722489 | + | 0.691383i | \(0.757002\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −80.7509 | −2.61304 | ||||||||
\(956\) | 17.0103 | 0.550152 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39.1584 | 1.26515 | ||||||||
\(959\) | 4.67484 | 0.150958 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.5756 | 0.825019 | ||||||||
\(962\) | −110.913 | −3.57599 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 69.0868 | 2.22514 | ||||||||
\(965\) | 51.8769 | 1.66998 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.74032 | −0.281070 | −0.140535 | − | 0.990076i | \(-0.544882\pi\) | ||||
−0.140535 | + | 0.990076i | \(0.544882\pi\) | |||||||
\(968\) | 49.4902 | 1.59068 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −57.8906 | −1.85876 | ||||||||
\(971\) | −36.7867 | −1.18054 | −0.590271 | − | 0.807205i | \(-0.700979\pi\) | ||||
−0.590271 | + | 0.807205i | \(0.700979\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.34474 | 0.299579 | ||||||||
\(974\) | 101.478 | 3.25156 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.32089 | −0.138308 | ||||||||
\(977\) | 17.6031 | 0.563172 | 0.281586 | − | 0.959536i | \(-0.409140\pi\) | ||||
0.281586 | + | 0.959536i | \(0.409140\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −62.8411 | −2.00841 | ||||||||
\(980\) | −96.1606 | −3.07174 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −56.8596 | −1.81446 | ||||||||
\(983\) | 50.6464 | 1.61537 | 0.807684 | − | 0.589615i | \(-0.200721\pi\) | ||||
0.807684 | + | 0.589615i | \(0.200721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0873 | 0.576309 | ||||||||
\(986\) | −19.0906 | −0.607969 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −146.186 | −4.65080 | ||||||||
\(989\) | −14.4675 | −0.460039 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.79288 | 0.152251 | 0.0761254 | − | 0.997098i | \(-0.475745\pi\) | ||||
0.0761254 | + | 0.997098i | \(0.475745\pi\) | |||||||
\(992\) | −70.5341 | −2.23946 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.58127 | −0.0818730 | ||||||||
\(995\) | 48.4844 | 1.53706 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.0839 | 0.382700 | 0.191350 | − | 0.981522i | \(-0.438714\pi\) | ||||
0.191350 | + | 0.981522i | \(0.438714\pi\) | |||||||
\(998\) | 53.0743 | 1.68004 | ||||||||
\(999\) | 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 | 4923.2.a.l.1.17 | 18 | ||
3.2 | odd | 2 | 547.2.a.b.1.2 | ✓ | 18 | ||
12.11 | even | 2 | 8752.2.a.s.1.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.2.a.b.1.2 | ✓ | 18 | 3.2 | odd | 2 | ||
4923.2.a.l.1.17 | 18 | 1.1 | even | 1 | trivial | ||
8752.2.a.s.1.3 | 18 | 12.11 | even | 2 |