Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.43828\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.43828 | 1.72413 | 0.862063 | − | 0.506801i | \(-0.169172\pi\) | ||||
0.862063 | + | 0.506801i | \(0.169172\pi\) | |||||||
\(3\) | −2.94523 | −1.70043 | −0.850213 | − | 0.526438i | \(-0.823527\pi\) | ||||
−0.850213 | + | 0.526438i | \(0.823527\pi\) | |||||||
\(4\) | 3.94523 | 1.97261 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −7.18129 | −2.93175 | ||||||||
\(7\) | −3.82025 | −1.44392 | −0.721959 | − | 0.691936i | \(-0.756758\pi\) | ||||
−0.721959 | + | 0.691936i | \(0.756758\pi\) | |||||||
\(8\) | 4.74301 | 1.67691 | ||||||||
\(9\) | 5.67435 | 1.89145 | ||||||||
\(10\) | 2.43828 | 0.771053 | ||||||||
\(11\) | −2.12498 | −0.640704 | −0.320352 | − | 0.947299i | \(-0.603801\pi\) | ||||
−0.320352 | + | 0.947299i | \(0.603801\pi\) | |||||||
\(12\) | −11.6196 | −3.35428 | ||||||||
\(13\) | 3.65438 | 1.01354 | 0.506772 | − | 0.862080i | \(-0.330839\pi\) | ||||
0.506772 | + | 0.862080i | \(0.330839\pi\) | |||||||
\(14\) | −9.31485 | −2.48950 | ||||||||
\(15\) | −2.94523 | −0.760454 | ||||||||
\(16\) | 3.67435 | 0.918588 | ||||||||
\(17\) | −3.04243 | −0.737898 | −0.368949 | − | 0.929450i | \(-0.620282\pi\) | ||||
−0.368949 | + | 0.929450i | \(0.620282\pi\) | |||||||
\(18\) | 13.8357 | 3.26110 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 3.94523 | 0.882179 | ||||||||
\(21\) | 11.2515 | 2.45528 | ||||||||
\(22\) | −5.18129 | −1.10466 | ||||||||
\(23\) | −4.81167 | −1.00330 | −0.501651 | − | 0.865070i | \(-0.667274\pi\) | ||||
−0.501651 | + | 0.865070i | \(0.667274\pi\) | |||||||
\(24\) | −13.9692 | −2.85146 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.91042 | 1.74748 | ||||||||
\(27\) | −7.87657 | −1.51585 | ||||||||
\(28\) | −15.0717 | −2.84829 | ||||||||
\(29\) | −6.03385 | −1.12046 | −0.560229 | − | 0.828338i | \(-0.689287\pi\) | ||||
−0.560229 | + | 0.828338i | \(0.689287\pi\) | |||||||
\(30\) | −7.18129 | −1.31112 | ||||||||
\(31\) | −3.57184 | −0.641521 | −0.320761 | − | 0.947160i | \(-0.603939\pi\) | ||||
−0.320761 | + | 0.947160i | \(0.603939\pi\) | |||||||
\(32\) | −0.526911 | −0.0931455 | ||||||||
\(33\) | 6.25853 | 1.08947 | ||||||||
\(34\) | −7.41831 | −1.27223 | ||||||||
\(35\) | −3.82025 | −0.645740 | ||||||||
\(36\) | 22.3866 | 3.73110 | ||||||||
\(37\) | −3.93134 | −0.646309 | −0.323154 | − | 0.946346i | \(-0.604743\pi\) | ||||
−0.323154 | + | 0.946346i | \(0.604743\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.7630 | −1.72346 | ||||||||
\(40\) | 4.74301 | 0.749936 | ||||||||
\(41\) | 7.60945 | 1.18840 | 0.594198 | − | 0.804318i | \(-0.297469\pi\) | ||||
0.594198 | + | 0.804318i | \(0.297469\pi\) | |||||||
\(42\) | 27.4343 | 4.23321 | ||||||||
\(43\) | −5.60415 | −0.854625 | −0.427312 | − | 0.904104i | \(-0.640540\pi\) | ||||
−0.427312 | + | 0.904104i | \(0.640540\pi\) | |||||||
\(44\) | −8.38351 | −1.26386 | ||||||||
\(45\) | 5.67435 | 0.845882 | ||||||||
\(46\) | −11.7322 | −1.72982 | ||||||||
\(47\) | −8.41831 | −1.22794 | −0.613969 | − | 0.789330i | \(-0.710428\pi\) | ||||
−0.613969 | + | 0.789330i | \(0.710428\pi\) | |||||||
\(48\) | −10.8218 | −1.56199 | ||||||||
\(49\) | 7.59430 | 1.08490 | ||||||||
\(50\) | 2.43828 | 0.344825 | ||||||||
\(51\) | 8.96065 | 1.25474 | ||||||||
\(52\) | 14.4174 | 1.99933 | ||||||||
\(53\) | −4.80028 | −0.659369 | −0.329685 | − | 0.944091i | \(-0.606942\pi\) | ||||
−0.329685 | + | 0.944091i | \(0.606942\pi\) | |||||||
\(54\) | −19.2053 | −2.61351 | ||||||||
\(55\) | −2.12498 | −0.286532 | ||||||||
\(56\) | −18.1195 | −2.42132 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.7122 | −1.93181 | ||||||||
\(59\) | 5.13510 | 0.668533 | 0.334266 | − | 0.942479i | \(-0.391511\pi\) | ||||
0.334266 | + | 0.942479i | \(0.391511\pi\) | |||||||
\(60\) | −11.6196 | −1.50008 | ||||||||
\(61\) | −13.5100 | −1.72978 | −0.864891 | − | 0.501960i | \(-0.832612\pi\) | ||||
−0.864891 | + | 0.501960i | \(0.832612\pi\) | |||||||
\(62\) | −8.70916 | −1.10606 | ||||||||
\(63\) | −21.6774 | −2.73110 | ||||||||
\(64\) | −8.63346 | −1.07918 | ||||||||
\(65\) | 3.65438 | 0.453270 | ||||||||
\(66\) | 15.2601 | 1.87839 | ||||||||
\(67\) | 5.38101 | 0.657395 | 0.328698 | − | 0.944435i | \(-0.393390\pi\) | ||||
0.328698 | + | 0.944435i | \(0.393390\pi\) | |||||||
\(68\) | −12.0031 | −1.45559 | ||||||||
\(69\) | 14.1714 | 1.70604 | ||||||||
\(70\) | −9.31485 | −1.11334 | ||||||||
\(71\) | 0.123434 | 0.0146489 | 0.00732443 | − | 0.999973i | \(-0.497669\pi\) | ||||
0.00732443 | + | 0.999973i | \(0.497669\pi\) | |||||||
\(72\) | 26.9135 | 3.17179 | ||||||||
\(73\) | −12.4860 | −1.46138 | −0.730689 | − | 0.682710i | \(-0.760801\pi\) | ||||
−0.730689 | + | 0.682710i | \(0.760801\pi\) | |||||||
\(74\) | −9.58572 | −1.11432 | ||||||||
\(75\) | −2.94523 | −0.340085 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.11794 | 0.925125 | ||||||||
\(78\) | −26.2432 | −2.97146 | ||||||||
\(79\) | 4.25699 | 0.478949 | 0.239474 | − | 0.970903i | \(-0.423025\pi\) | ||||
0.239474 | + | 0.970903i | \(0.423025\pi\) | |||||||
\(80\) | 3.67435 | 0.410805 | ||||||||
\(81\) | 6.17521 | 0.686134 | ||||||||
\(82\) | 18.5540 | 2.04895 | ||||||||
\(83\) | 4.39739 | 0.482677 | 0.241338 | − | 0.970441i | \(-0.422414\pi\) | ||||
0.241338 | + | 0.970441i | \(0.422414\pi\) | |||||||
\(84\) | 44.3897 | 4.84331 | ||||||||
\(85\) | −3.04243 | −0.329998 | ||||||||
\(86\) | −13.6645 | −1.47348 | ||||||||
\(87\) | 17.7711 | 1.90526 | ||||||||
\(88\) | −10.0788 | −1.07440 | ||||||||
\(89\) | 0.0772394 | 0.00818736 | 0.00409368 | − | 0.999992i | \(-0.498697\pi\) | ||||
0.00409368 | + | 0.999992i | \(0.498697\pi\) | |||||||
\(90\) | 13.8357 | 1.45841 | ||||||||
\(91\) | −13.9607 | −1.46347 | ||||||||
\(92\) | −18.9831 | −1.97913 | ||||||||
\(93\) | 10.5199 | 1.09086 | ||||||||
\(94\) | −20.5262 | −2.11712 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.55187 | 0.158387 | ||||||||
\(97\) | 18.0231 | 1.82996 | 0.914982 | − | 0.403495i | \(-0.132205\pi\) | ||||
0.914982 | + | 0.403495i | \(0.132205\pi\) | |||||||
\(98\) | 18.5171 | 1.87051 | ||||||||
\(99\) | −12.0579 | −1.21186 | ||||||||
\(100\) | 3.94523 | 0.394523 | ||||||||
\(101\) | 18.6498 | 1.85573 | 0.927864 | − | 0.372918i | \(-0.121643\pi\) | ||||
0.927864 | + | 0.372918i | \(0.121643\pi\) | |||||||
\(102\) | 21.8486 | 2.16333 | ||||||||
\(103\) | −0.377423 | −0.0371886 | −0.0185943 | − | 0.999827i | \(-0.505919\pi\) | ||||
−0.0185943 | + | 0.999827i | \(0.505919\pi\) | |||||||
\(104\) | 17.3328 | 1.69962 | ||||||||
\(105\) | 11.2515 | 1.09803 | ||||||||
\(106\) | −11.7044 | −1.13684 | ||||||||
\(107\) | −2.76144 | −0.266958 | −0.133479 | − | 0.991052i | \(-0.542615\pi\) | ||||
−0.133479 | + | 0.991052i | \(0.542615\pi\) | |||||||
\(108\) | −31.0748 | −2.99018 | ||||||||
\(109\) | 3.00308 | 0.287643 | 0.143822 | − | 0.989604i | \(-0.454061\pi\) | ||||
0.143822 | + | 0.989604i | \(0.454061\pi\) | |||||||
\(110\) | −5.18129 | −0.494017 | ||||||||
\(111\) | 11.5787 | 1.09900 | ||||||||
\(112\) | −14.0369 | −1.32637 | ||||||||
\(113\) | −3.61708 | −0.340266 | −0.170133 | − | 0.985421i | \(-0.554420\pi\) | ||||
−0.170133 | + | 0.985421i | \(0.554420\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.81167 | −0.448690 | ||||||||
\(116\) | −23.8049 | −2.21023 | ||||||||
\(117\) | 20.7362 | 1.91707 | ||||||||
\(118\) | 12.5208 | 1.15264 | ||||||||
\(119\) | 11.6229 | 1.06547 | ||||||||
\(120\) | −13.9692 | −1.27521 | ||||||||
\(121\) | −6.48448 | −0.589498 | ||||||||
\(122\) | −32.9413 | −2.98236 | ||||||||
\(123\) | −22.4116 | −2.02078 | ||||||||
\(124\) | −14.0917 | −1.26547 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −52.8557 | −4.70876 | ||||||||
\(127\) | −13.6188 | −1.20847 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
−0.604236 | + | 0.796805i | \(0.706522\pi\) | |||||||
\(128\) | −19.9970 | −1.76750 | ||||||||
\(129\) | 16.5055 | 1.45323 | ||||||||
\(130\) | 8.91042 | 0.781495 | ||||||||
\(131\) | 5.67059 | 0.495442 | 0.247721 | − | 0.968831i | \(-0.420318\pi\) | ||||
0.247721 | + | 0.968831i | \(0.420318\pi\) | |||||||
\(132\) | 24.6913 | 2.14910 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.1204 | 1.13343 | ||||||||
\(135\) | −7.87657 | −0.677907 | ||||||||
\(136\) | −14.4303 | −1.23739 | ||||||||
\(137\) | −8.10501 | −0.692457 | −0.346229 | − | 0.938150i | \(-0.612538\pi\) | ||||
−0.346229 | + | 0.938150i | \(0.612538\pi\) | |||||||
\(138\) | 34.5540 | 2.94143 | ||||||||
\(139\) | −17.5325 | −1.48709 | −0.743543 | − | 0.668688i | \(-0.766856\pi\) | ||||
−0.743543 | + | 0.668688i | \(0.766856\pi\) | |||||||
\(140\) | −15.0717 | −1.27379 | ||||||||
\(141\) | 24.7938 | 2.08802 | ||||||||
\(142\) | 0.300966 | 0.0252565 | ||||||||
\(143\) | −7.76547 | −0.649382 | ||||||||
\(144\) | 20.8496 | 1.73746 | ||||||||
\(145\) | −6.03385 | −0.501084 | ||||||||
\(146\) | −30.4445 | −2.51960 | ||||||||
\(147\) | −22.3669 | −1.84479 | ||||||||
\(148\) | −15.5100 | −1.27492 | ||||||||
\(149\) | 19.1952 | 1.57253 | 0.786265 | − | 0.617889i | \(-0.212012\pi\) | ||||
0.786265 | + | 0.617889i | \(0.212012\pi\) | |||||||
\(150\) | −7.18129 | −0.586350 | ||||||||
\(151\) | 11.1473 | 0.907152 | 0.453576 | − | 0.891218i | \(-0.350148\pi\) | ||||
0.453576 | + | 0.891218i | \(0.350148\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.2638 | −1.39570 | ||||||||
\(154\) | 19.7938 | 1.59503 | ||||||||
\(155\) | −3.57184 | −0.286897 | ||||||||
\(156\) | −42.4624 | −3.39971 | ||||||||
\(157\) | 11.1452 | 0.889486 | 0.444743 | − | 0.895658i | \(-0.353295\pi\) | ||||
0.444743 | + | 0.895658i | \(0.353295\pi\) | |||||||
\(158\) | 10.3797 | 0.825768 | ||||||||
\(159\) | 14.1379 | 1.12121 | ||||||||
\(160\) | −0.526911 | −0.0416560 | ||||||||
\(161\) | 18.3818 | 1.44869 | ||||||||
\(162\) | 15.0569 | 1.18298 | ||||||||
\(163\) | −6.68669 | −0.523742 | −0.261871 | − | 0.965103i | \(-0.584340\pi\) | ||||
−0.261871 | + | 0.965103i | \(0.584340\pi\) | |||||||
\(164\) | 30.0210 | 2.34425 | ||||||||
\(165\) | 6.25853 | 0.487226 | ||||||||
\(166\) | 10.7221 | 0.832195 | ||||||||
\(167\) | 18.6569 | 1.44371 | 0.721856 | − | 0.692043i | \(-0.243289\pi\) | ||||
0.721856 | + | 0.692043i | \(0.243289\pi\) | |||||||
\(168\) | 53.3659 | 4.11727 | ||||||||
\(169\) | 0.354510 | 0.0272700 | ||||||||
\(170\) | −7.41831 | −0.568959 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −22.1096 | −1.68584 | ||||||||
\(173\) | −14.7385 | −1.12054 | −0.560272 | − | 0.828308i | \(-0.689304\pi\) | ||||
−0.560272 | + | 0.828308i | \(0.689304\pi\) | |||||||
\(174\) | 43.3309 | 3.28490 | ||||||||
\(175\) | −3.82025 | −0.288784 | ||||||||
\(176\) | −7.80791 | −0.588543 | ||||||||
\(177\) | −15.1240 | −1.13679 | ||||||||
\(178\) | 0.188331 | 0.0141160 | ||||||||
\(179\) | −12.1961 | −0.911582 | −0.455791 | − | 0.890087i | \(-0.650643\pi\) | ||||
−0.455791 | + | 0.890087i | \(0.650643\pi\) | |||||||
\(180\) | 22.3866 | 1.66860 | ||||||||
\(181\) | −13.1841 | −0.979966 | −0.489983 | − | 0.871732i | \(-0.662997\pi\) | ||||
−0.489983 | + | 0.871732i | \(0.662997\pi\) | |||||||
\(182\) | −34.0400 | −2.52321 | ||||||||
\(183\) | 39.7901 | 2.94137 | ||||||||
\(184\) | −22.8218 | −1.68244 | ||||||||
\(185\) | −3.93134 | −0.289038 | ||||||||
\(186\) | 25.6504 | 1.88078 | ||||||||
\(187\) | 6.46510 | 0.472775 | ||||||||
\(188\) | −33.2121 | −2.42224 | ||||||||
\(189\) | 30.0904 | 2.18876 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.61708 | 0.334080 | 0.167040 | − | 0.985950i | \(-0.446579\pi\) | ||||
0.167040 | + | 0.985950i | \(0.446579\pi\) | |||||||
\(192\) | 25.4275 | 1.83507 | ||||||||
\(193\) | −5.22468 | −0.376081 | −0.188040 | − | 0.982161i | \(-0.560214\pi\) | ||||
−0.188040 | + | 0.982161i | \(0.560214\pi\) | |||||||
\(194\) | 43.9453 | 3.15509 | ||||||||
\(195\) | −10.7630 | −0.770753 | ||||||||
\(196\) | 29.9612 | 2.14009 | ||||||||
\(197\) | 21.1783 | 1.50889 | 0.754445 | − | 0.656363i | \(-0.227906\pi\) | ||||
0.754445 | + | 0.656363i | \(0.227906\pi\) | |||||||
\(198\) | −29.4005 | −2.08940 | ||||||||
\(199\) | 15.3752 | 1.08992 | 0.544960 | − | 0.838462i | \(-0.316545\pi\) | ||||
0.544960 | + | 0.838462i | \(0.316545\pi\) | |||||||
\(200\) | 4.74301 | 0.335381 | ||||||||
\(201\) | −15.8483 | −1.11785 | ||||||||
\(202\) | 45.4736 | 3.19951 | ||||||||
\(203\) | 23.0508 | 1.61785 | ||||||||
\(204\) | 35.3518 | 2.47512 | ||||||||
\(205\) | 7.60945 | 0.531467 | ||||||||
\(206\) | −0.920265 | −0.0641179 | ||||||||
\(207\) | −27.3031 | −1.89770 | ||||||||
\(208\) | 13.4275 | 0.931029 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 27.4343 | 1.89315 | ||||||||
\(211\) | 20.8659 | 1.43647 | 0.718235 | − | 0.695800i | \(-0.244950\pi\) | ||||
0.718235 | + | 0.695800i | \(0.244950\pi\) | |||||||
\(212\) | −18.9382 | −1.30068 | ||||||||
\(213\) | −0.363540 | −0.0249093 | ||||||||
\(214\) | −6.73316 | −0.460270 | ||||||||
\(215\) | −5.60415 | −0.382200 | ||||||||
\(216\) | −37.3586 | −2.54193 | ||||||||
\(217\) | 13.6453 | 0.926305 | ||||||||
\(218\) | 7.32237 | 0.495934 | ||||||||
\(219\) | 36.7741 | 2.48497 | ||||||||
\(220\) | −8.38351 | −0.565216 | ||||||||
\(221\) | −11.1182 | −0.747892 | ||||||||
\(222\) | 28.2321 | 1.89482 | ||||||||
\(223\) | 13.6759 | 0.915806 | 0.457903 | − | 0.889002i | \(-0.348601\pi\) | ||||
0.457903 | + | 0.889002i | \(0.348601\pi\) | |||||||
\(224\) | 2.01293 | 0.134495 | ||||||||
\(225\) | 5.67435 | 0.378290 | ||||||||
\(226\) | −8.81947 | −0.586662 | ||||||||
\(227\) | 3.71196 | 0.246372 | 0.123186 | − | 0.992384i | \(-0.460689\pi\) | ||||
0.123186 | + | 0.992384i | \(0.460689\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3086 | 0.747293 | 0.373646 | − | 0.927571i | \(-0.378107\pi\) | ||||
0.373646 | + | 0.927571i | \(0.378107\pi\) | |||||||
\(230\) | −11.7322 | −0.773599 | ||||||||
\(231\) | −23.9092 | −1.57311 | ||||||||
\(232\) | −28.6186 | −1.87890 | ||||||||
\(233\) | −10.6753 | −0.699362 | −0.349681 | − | 0.936869i | \(-0.613710\pi\) | ||||
−0.349681 | + | 0.936869i | \(0.613710\pi\) | |||||||
\(234\) | 50.5608 | 3.30527 | ||||||||
\(235\) | −8.41831 | −0.549150 | ||||||||
\(236\) | 20.2591 | 1.31876 | ||||||||
\(237\) | −12.5378 | −0.814417 | ||||||||
\(238\) | 28.3398 | 1.83700 | ||||||||
\(239\) | −17.2813 | −1.11783 | −0.558916 | − | 0.829224i | \(-0.688783\pi\) | ||||
−0.558916 | + | 0.829224i | \(0.688783\pi\) | |||||||
\(240\) | −10.8218 | −0.698544 | ||||||||
\(241\) | 17.4986 | 1.12719 | 0.563593 | − | 0.826052i | \(-0.309419\pi\) | ||||
0.563593 | + | 0.826052i | \(0.309419\pi\) | |||||||
\(242\) | −15.8110 | −1.01637 | ||||||||
\(243\) | 5.44232 | 0.349125 | ||||||||
\(244\) | −53.3001 | −3.41219 | ||||||||
\(245\) | 7.59430 | 0.485182 | ||||||||
\(246\) | −54.6457 | −3.48408 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −16.9413 | −1.07577 | ||||||||
\(249\) | −12.9513 | −0.820756 | ||||||||
\(250\) | 2.43828 | 0.154211 | ||||||||
\(251\) | 17.9012 | 1.12991 | 0.564956 | − | 0.825121i | \(-0.308893\pi\) | ||||
0.564956 | + | 0.825121i | \(0.308893\pi\) | |||||||
\(252\) | −85.5224 | −5.38740 | ||||||||
\(253\) | 10.2247 | 0.642820 | ||||||||
\(254\) | −33.2065 | −2.08356 | ||||||||
\(255\) | 8.96065 | 0.561138 | ||||||||
\(256\) | −31.4914 | −1.96821 | ||||||||
\(257\) | −26.7208 | −1.66680 | −0.833400 | − | 0.552671i | \(-0.813609\pi\) | ||||
−0.833400 | + | 0.552671i | \(0.813609\pi\) | |||||||
\(258\) | 40.2450 | 2.50555 | ||||||||
\(259\) | 15.0187 | 0.933217 | ||||||||
\(260\) | 14.4174 | 0.894127 | ||||||||
\(261\) | −34.2382 | −2.11929 | ||||||||
\(262\) | 13.8265 | 0.854204 | ||||||||
\(263\) | −19.7817 | −1.21979 | −0.609895 | − | 0.792482i | \(-0.708789\pi\) | ||||
−0.609895 | + | 0.792482i | \(0.708789\pi\) | |||||||
\(264\) | 29.6843 | 1.82694 | ||||||||
\(265\) | −4.80028 | −0.294879 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.227487 | −0.0139220 | ||||||||
\(268\) | 21.2293 | 1.29679 | ||||||||
\(269\) | 7.04833 | 0.429744 | 0.214872 | − | 0.976642i | \(-0.431067\pi\) | ||||
0.214872 | + | 0.976642i | \(0.431067\pi\) | |||||||
\(270\) | −19.2053 | −1.16880 | ||||||||
\(271\) | 26.1672 | 1.58955 | 0.794773 | − | 0.606907i | \(-0.207590\pi\) | ||||
0.794773 | + | 0.606907i | \(0.207590\pi\) | |||||||
\(272\) | −11.1790 | −0.677825 | ||||||||
\(273\) | 41.1173 | 2.48853 | ||||||||
\(274\) | −19.7623 | −1.19388 | ||||||||
\(275\) | −2.12498 | −0.128141 | ||||||||
\(276\) | 55.9096 | 3.36536 | ||||||||
\(277\) | 2.86953 | 0.172413 | 0.0862066 | − | 0.996277i | \(-0.472525\pi\) | ||||
0.0862066 | + | 0.996277i | \(0.472525\pi\) | |||||||
\(278\) | −42.7492 | −2.56393 | ||||||||
\(279\) | −20.2679 | −1.21341 | ||||||||
\(280\) | −18.1195 | −1.08285 | ||||||||
\(281\) | −22.4401 | −1.33866 | −0.669332 | − | 0.742963i | \(-0.733420\pi\) | ||||
−0.669332 | + | 0.742963i | \(0.733420\pi\) | |||||||
\(282\) | 60.4544 | 3.60001 | ||||||||
\(283\) | −4.68139 | −0.278280 | −0.139140 | − | 0.990273i | \(-0.544434\pi\) | ||||
−0.139140 | + | 0.990273i | \(0.544434\pi\) | |||||||
\(284\) | 0.486973 | 0.0288965 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.9344 | −1.11962 | ||||||||
\(287\) | −29.0700 | −1.71595 | ||||||||
\(288\) | −2.98988 | −0.176180 | ||||||||
\(289\) | −7.74360 | −0.455506 | ||||||||
\(290\) | −14.7122 | −0.863933 | ||||||||
\(291\) | −53.0820 | −3.11172 | ||||||||
\(292\) | −49.2602 | −2.88273 | ||||||||
\(293\) | 3.26229 | 0.190585 | 0.0952926 | − | 0.995449i | \(-0.469621\pi\) | ||||
0.0952926 | + | 0.995449i | \(0.469621\pi\) | |||||||
\(294\) | −54.5369 | −3.18066 | ||||||||
\(295\) | 5.13510 | 0.298977 | ||||||||
\(296\) | −18.6464 | −1.08380 | ||||||||
\(297\) | 16.7375 | 0.971209 | ||||||||
\(298\) | 46.8033 | 2.71124 | ||||||||
\(299\) | −17.5837 | −1.01689 | ||||||||
\(300\) | −11.6196 | −0.670857 | ||||||||
\(301\) | 21.4093 | 1.23401 | ||||||||
\(302\) | 27.1802 | 1.56404 | ||||||||
\(303\) | −54.9280 | −3.15553 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.5100 | −0.773582 | ||||||||
\(306\) | −42.0941 | −2.40636 | ||||||||
\(307\) | −1.71746 | −0.0980207 | −0.0490103 | − | 0.998798i | \(-0.515607\pi\) | ||||
−0.0490103 | + | 0.998798i | \(0.515607\pi\) | |||||||
\(308\) | 32.0271 | 1.82491 | ||||||||
\(309\) | 1.11160 | 0.0632365 | ||||||||
\(310\) | −8.70916 | −0.494647 | ||||||||
\(311\) | −0.892946 | −0.0506343 | −0.0253172 | − | 0.999679i | \(-0.508060\pi\) | ||||
−0.0253172 | + | 0.999679i | \(0.508060\pi\) | |||||||
\(312\) | −51.0489 | −2.89008 | ||||||||
\(313\) | 11.5358 | 0.652040 | 0.326020 | − | 0.945363i | \(-0.394292\pi\) | ||||
0.326020 | + | 0.945363i | \(0.394292\pi\) | |||||||
\(314\) | 27.1752 | 1.53359 | ||||||||
\(315\) | −21.6774 | −1.22139 | ||||||||
\(316\) | 16.7948 | 0.944780 | ||||||||
\(317\) | 18.8246 | 1.05729 | 0.528647 | − | 0.848842i | \(-0.322699\pi\) | ||||
0.528647 | + | 0.848842i | \(0.322699\pi\) | |||||||
\(318\) | 34.4722 | 1.93311 | ||||||||
\(319\) | 12.8218 | 0.717883 | ||||||||
\(320\) | −8.63346 | −0.482625 | ||||||||
\(321\) | 8.13305 | 0.453943 | ||||||||
\(322\) | 44.8200 | 2.49772 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 24.3626 | 1.35348 | ||||||||
\(325\) | 3.65438 | 0.202709 | ||||||||
\(326\) | −16.3041 | −0.902998 | ||||||||
\(327\) | −8.84476 | −0.489116 | ||||||||
\(328\) | 36.0917 | 1.99283 | ||||||||
\(329\) | 32.1601 | 1.77304 | ||||||||
\(330\) | 15.2601 | 0.840039 | ||||||||
\(331\) | −15.5779 | −0.856240 | −0.428120 | − | 0.903722i | \(-0.640824\pi\) | ||||
−0.428120 | + | 0.903722i | \(0.640824\pi\) | |||||||
\(332\) | 17.3487 | 0.952134 | ||||||||
\(333\) | −22.3078 | −1.22246 | ||||||||
\(334\) | 45.4908 | 2.48914 | ||||||||
\(335\) | 5.38101 | 0.293996 | ||||||||
\(336\) | 41.3419 | 2.25539 | ||||||||
\(337\) | −6.43425 | −0.350496 | −0.175248 | − | 0.984524i | \(-0.556073\pi\) | ||||
−0.175248 | + | 0.984524i | \(0.556073\pi\) | |||||||
\(338\) | 0.864396 | 0.0470170 | ||||||||
\(339\) | 10.6531 | 0.578598 | ||||||||
\(340\) | −12.0031 | −0.650959 | ||||||||
\(341\) | 7.59007 | 0.411026 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.27039 | −0.122590 | ||||||||
\(344\) | −26.5805 | −1.43313 | ||||||||
\(345\) | 14.1714 | 0.762965 | ||||||||
\(346\) | −35.9366 | −1.93196 | ||||||||
\(347\) | −19.3367 | −1.03805 | −0.519023 | − | 0.854760i | \(-0.673704\pi\) | ||||
−0.519023 | + | 0.854760i | \(0.673704\pi\) | |||||||
\(348\) | 70.1108 | 3.75833 | ||||||||
\(349\) | 7.78870 | 0.416920 | 0.208460 | − | 0.978031i | \(-0.433155\pi\) | ||||
0.208460 | + | 0.978031i | \(0.433155\pi\) | |||||||
\(350\) | −9.31485 | −0.497900 | ||||||||
\(351\) | −28.7840 | −1.53638 | ||||||||
\(352\) | 1.11967 | 0.0596788 | ||||||||
\(353\) | −24.7007 | −1.31468 | −0.657342 | − | 0.753593i | \(-0.728319\pi\) | ||||
−0.657342 | + | 0.753593i | \(0.728319\pi\) | |||||||
\(354\) | −36.8767 | −1.95997 | ||||||||
\(355\) | 0.123434 | 0.00655117 | ||||||||
\(356\) | 0.304727 | 0.0161505 | ||||||||
\(357\) | −34.2319 | −1.81175 | ||||||||
\(358\) | −29.7376 | −1.57168 | ||||||||
\(359\) | 24.8224 | 1.31008 | 0.655038 | − | 0.755596i | \(-0.272653\pi\) | ||||
0.655038 | + | 0.755596i | \(0.272653\pi\) | |||||||
\(360\) | 26.9135 | 1.41847 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −32.1466 | −1.68959 | ||||||||
\(363\) | 19.0982 | 1.00240 | ||||||||
\(364\) | −55.0779 | −2.88687 | ||||||||
\(365\) | −12.4860 | −0.653548 | ||||||||
\(366\) | 97.0195 | 5.07129 | ||||||||
\(367\) | −7.01716 | −0.366293 | −0.183146 | − | 0.983086i | \(-0.558628\pi\) | ||||
−0.183146 | + | 0.983086i | \(0.558628\pi\) | |||||||
\(368\) | −17.6798 | −0.921621 | ||||||||
\(369\) | 43.1787 | 2.24779 | ||||||||
\(370\) | −9.58572 | −0.498338 | ||||||||
\(371\) | 18.3383 | 0.952075 | ||||||||
\(372\) | 41.5033 | 2.15184 | ||||||||
\(373\) | −36.2105 | −1.87491 | −0.937455 | − | 0.348107i | \(-0.886825\pi\) | ||||
−0.937455 | + | 0.348107i | \(0.886825\pi\) | |||||||
\(374\) | 15.7637 | 0.815124 | ||||||||
\(375\) | −2.94523 | −0.152091 | ||||||||
\(376\) | −39.9281 | −2.05914 | ||||||||
\(377\) | −22.0500 | −1.13563 | ||||||||
\(378\) | 73.3690 | 3.77370 | ||||||||
\(379\) | −28.2455 | −1.45087 | −0.725437 | − | 0.688288i | \(-0.758362\pi\) | ||||
−0.725437 | + | 0.688288i | \(0.758362\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 40.1104 | 2.05492 | ||||||||
\(382\) | 11.2578 | 0.575997 | ||||||||
\(383\) | 26.4312 | 1.35057 | 0.675287 | − | 0.737555i | \(-0.264020\pi\) | ||||
0.675287 | + | 0.737555i | \(0.264020\pi\) | |||||||
\(384\) | 58.8957 | 3.00551 | ||||||||
\(385\) | 8.11794 | 0.413728 | ||||||||
\(386\) | −12.7392 | −0.648411 | ||||||||
\(387\) | −31.7999 | −1.61648 | ||||||||
\(388\) | 71.1050 | 3.60981 | ||||||||
\(389\) | −5.61736 | −0.284811 | −0.142406 | − | 0.989808i | \(-0.545484\pi\) | ||||
−0.142406 | + | 0.989808i | \(0.545484\pi\) | |||||||
\(390\) | −26.2432 | −1.32888 | ||||||||
\(391\) | 14.6392 | 0.740335 | ||||||||
\(392\) | 36.0199 | 1.81928 | ||||||||
\(393\) | −16.7012 | −0.842462 | ||||||||
\(394\) | 51.6387 | 2.60152 | ||||||||
\(395\) | 4.25699 | 0.214192 | ||||||||
\(396\) | −47.5710 | −2.39053 | ||||||||
\(397\) | −29.0391 | −1.45743 | −0.728715 | − | 0.684818i | \(-0.759882\pi\) | ||||
−0.728715 | + | 0.684818i | \(0.759882\pi\) | |||||||
\(398\) | 37.4891 | 1.87916 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.67435 | 0.183718 | ||||||||
\(401\) | 25.4613 | 1.27148 | 0.635739 | − | 0.771904i | \(-0.280695\pi\) | ||||
0.635739 | + | 0.771904i | \(0.280695\pi\) | |||||||
\(402\) | −38.6426 | −1.92732 | ||||||||
\(403\) | −13.0529 | −0.650210 | ||||||||
\(404\) | 73.5778 | 3.66063 | ||||||||
\(405\) | 6.17521 | 0.306849 | ||||||||
\(406\) | 56.2044 | 2.78938 | ||||||||
\(407\) | 8.35401 | 0.414093 | ||||||||
\(408\) | 42.5005 | 2.10409 | ||||||||
\(409\) | −19.8024 | −0.979166 | −0.489583 | − | 0.871957i | \(-0.662851\pi\) | ||||
−0.489583 | + | 0.871957i | \(0.662851\pi\) | |||||||
\(410\) | 18.5540 | 0.916317 | ||||||||
\(411\) | 23.8711 | 1.17747 | ||||||||
\(412\) | −1.48902 | −0.0733588 | ||||||||
\(413\) | −19.6174 | −0.965307 | ||||||||
\(414\) | −66.5727 | −3.27187 | ||||||||
\(415\) | 4.39739 | 0.215859 | ||||||||
\(416\) | −1.92553 | −0.0944070 | ||||||||
\(417\) | 51.6371 | 2.52868 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.172123 | 0.00840877 | 0.00420439 | − | 0.999991i | \(-0.498662\pi\) | ||||
0.00420439 | + | 0.999991i | \(0.498662\pi\) | |||||||
\(420\) | 44.3897 | 2.16599 | ||||||||
\(421\) | 17.4056 | 0.848297 | 0.424149 | − | 0.905593i | \(-0.360573\pi\) | ||||
0.424149 | + | 0.905593i | \(0.360573\pi\) | |||||||
\(422\) | 50.8771 | 2.47666 | ||||||||
\(423\) | −47.7685 | −2.32258 | ||||||||
\(424\) | −22.7678 | −1.10570 | ||||||||
\(425\) | −3.04243 | −0.147580 | ||||||||
\(426\) | −0.886412 | −0.0429468 | ||||||||
\(427\) | 51.6117 | 2.49766 | ||||||||
\(428\) | −10.8945 | −0.526605 | ||||||||
\(429\) | 22.8711 | 1.10423 | ||||||||
\(430\) | −13.6645 | −0.658961 | ||||||||
\(431\) | −5.06518 | −0.243981 | −0.121990 | − | 0.992531i | \(-0.538928\pi\) | ||||
−0.121990 | + | 0.992531i | \(0.538928\pi\) | |||||||
\(432\) | −28.9413 | −1.39244 | ||||||||
\(433\) | 12.5169 | 0.601524 | 0.300762 | − | 0.953699i | \(-0.402759\pi\) | ||||
0.300762 | + | 0.953699i | \(0.402759\pi\) | |||||||
\(434\) | 33.2712 | 1.59707 | ||||||||
\(435\) | 17.7711 | 0.852057 | ||||||||
\(436\) | 11.8478 | 0.567409 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 89.6658 | 4.28440 | ||||||||
\(439\) | −14.7581 | −0.704367 | −0.352183 | − | 0.935931i | \(-0.614561\pi\) | ||||
−0.352183 | + | 0.935931i | \(0.614561\pi\) | |||||||
\(440\) | −10.0788 | −0.480487 | ||||||||
\(441\) | 43.0928 | 2.05204 | ||||||||
\(442\) | −27.1094 | −1.28946 | ||||||||
\(443\) | 5.35950 | 0.254638 | 0.127319 | − | 0.991862i | \(-0.459363\pi\) | ||||
0.127319 | + | 0.991862i | \(0.459363\pi\) | |||||||
\(444\) | 45.6805 | 2.16790 | ||||||||
\(445\) | 0.0772394 | 0.00366150 | ||||||||
\(446\) | 33.3457 | 1.57896 | ||||||||
\(447\) | −56.5341 | −2.67397 | ||||||||
\(448\) | 32.9820 | 1.55825 | ||||||||
\(449\) | −7.16065 | −0.337932 | −0.168966 | − | 0.985622i | \(-0.554043\pi\) | ||||
−0.168966 | + | 0.985622i | \(0.554043\pi\) | |||||||
\(450\) | 13.8357 | 0.652220 | ||||||||
\(451\) | −16.1699 | −0.761411 | ||||||||
\(452\) | −14.2702 | −0.671214 | ||||||||
\(453\) | −32.8312 | −1.54255 | ||||||||
\(454\) | 9.05082 | 0.424776 | ||||||||
\(455\) | −13.9607 | −0.654485 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.3884 | 1.51507 | 0.757534 | − | 0.652796i | \(-0.226404\pi\) | ||||
0.757534 | + | 0.652796i | \(0.226404\pi\) | |||||||
\(458\) | 27.5736 | 1.28843 | ||||||||
\(459\) | 23.9639 | 1.11854 | ||||||||
\(460\) | −18.9831 | −0.885092 | ||||||||
\(461\) | −25.2124 | −1.17426 | −0.587130 | − | 0.809493i | \(-0.699742\pi\) | ||||
−0.587130 | + | 0.809493i | \(0.699742\pi\) | |||||||
\(462\) | −58.2973 | −2.71224 | ||||||||
\(463\) | −40.8494 | −1.89843 | −0.949216 | − | 0.314627i | \(-0.898121\pi\) | ||||
−0.949216 | + | 0.314627i | \(0.898121\pi\) | |||||||
\(464\) | −22.1705 | −1.02924 | ||||||||
\(465\) | 10.5199 | 0.487847 | ||||||||
\(466\) | −26.0294 | −1.20579 | ||||||||
\(467\) | 14.6209 | 0.676577 | 0.338288 | − | 0.941042i | \(-0.390152\pi\) | ||||
0.338288 | + | 0.941042i | \(0.390152\pi\) | |||||||
\(468\) | 81.8092 | 3.78163 | ||||||||
\(469\) | −20.5568 | −0.949225 | ||||||||
\(470\) | −20.5262 | −0.946805 | ||||||||
\(471\) | −32.8252 | −1.51250 | ||||||||
\(472\) | 24.3558 | 1.12107 | ||||||||
\(473\) | 11.9087 | 0.547562 | ||||||||
\(474\) | −30.5707 | −1.40416 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 45.8548 | 2.10175 | ||||||||
\(477\) | −27.2385 | −1.24716 | ||||||||
\(478\) | −42.1366 | −1.92729 | ||||||||
\(479\) | 1.06944 | 0.0488640 | 0.0244320 | − | 0.999701i | \(-0.492222\pi\) | ||||
0.0244320 | + | 0.999701i | \(0.492222\pi\) | |||||||
\(480\) | 1.55187 | 0.0708329 | ||||||||
\(481\) | −14.3666 | −0.655062 | ||||||||
\(482\) | 42.6666 | 1.94341 | ||||||||
\(483\) | −54.1385 | −2.46339 | ||||||||
\(484\) | −25.5827 | −1.16285 | ||||||||
\(485\) | 18.0231 | 0.818385 | ||||||||
\(486\) | 13.2699 | 0.601936 | ||||||||
\(487\) | −6.25304 | −0.283352 | −0.141676 | − | 0.989913i | \(-0.545249\pi\) | ||||
−0.141676 | + | 0.989913i | \(0.545249\pi\) | |||||||
\(488\) | −64.0782 | −2.90068 | ||||||||
\(489\) | 19.6938 | 0.890585 | ||||||||
\(490\) | 18.5171 | 0.836516 | ||||||||
\(491\) | −0.813681 | −0.0367209 | −0.0183605 | − | 0.999831i | \(-0.505845\pi\) | ||||
−0.0183605 | + | 0.999831i | \(0.505845\pi\) | |||||||
\(492\) | −88.4186 | −3.98622 | ||||||||
\(493\) | 18.3576 | 0.826784 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.0579 | −0.541960 | ||||||||
\(496\) | −13.1242 | −0.589294 | ||||||||
\(497\) | −0.471547 | −0.0211518 | ||||||||
\(498\) | −31.5790 | −1.41509 | ||||||||
\(499\) | 1.57636 | 0.0705676 | 0.0352838 | − | 0.999377i | \(-0.488766\pi\) | ||||
0.0352838 | + | 0.999377i | \(0.488766\pi\) | |||||||
\(500\) | 3.94523 | 0.176436 | ||||||||
\(501\) | −54.9487 | −2.45493 | ||||||||
\(502\) | 43.6481 | 1.94811 | ||||||||
\(503\) | 3.00182 | 0.133845 | 0.0669223 | − | 0.997758i | \(-0.478682\pi\) | ||||
0.0669223 | + | 0.997758i | \(0.478682\pi\) | |||||||
\(504\) | −102.816 | −4.57980 | ||||||||
\(505\) | 18.6498 | 0.829907 | ||||||||
\(506\) | 24.9307 | 1.10830 | ||||||||
\(507\) | −1.04411 | −0.0463707 | ||||||||
\(508\) | −53.7292 | −2.38385 | ||||||||
\(509\) | −32.7217 | −1.45036 | −0.725182 | − | 0.688557i | \(-0.758245\pi\) | ||||
−0.725182 | + | 0.688557i | \(0.758245\pi\) | |||||||
\(510\) | 21.8486 | 0.967473 | ||||||||
\(511\) | 47.6997 | 2.11011 | ||||||||
\(512\) | −36.7910 | −1.62595 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −65.1529 | −2.87377 | ||||||||
\(515\) | −0.377423 | −0.0166313 | ||||||||
\(516\) | 65.1179 | 2.86665 | ||||||||
\(517\) | 17.8887 | 0.786745 | ||||||||
\(518\) | 36.6199 | 1.60898 | ||||||||
\(519\) | 43.4081 | 1.90540 | ||||||||
\(520\) | 17.3328 | 0.760092 | ||||||||
\(521\) | −16.4073 | −0.718819 | −0.359409 | − | 0.933180i | \(-0.617022\pi\) | ||||
−0.359409 | + | 0.933180i | \(0.617022\pi\) | |||||||
\(522\) | −83.4824 | −3.65393 | ||||||||
\(523\) | −20.4437 | −0.893940 | −0.446970 | − | 0.894549i | \(-0.647497\pi\) | ||||
−0.446970 | + | 0.894549i | \(0.647497\pi\) | |||||||
\(524\) | 22.3718 | 0.977315 | ||||||||
\(525\) | 11.2515 | 0.491055 | ||||||||
\(526\) | −48.2333 | −2.10307 | ||||||||
\(527\) | 10.8671 | 0.473378 | ||||||||
\(528\) | 22.9960 | 1.00077 | ||||||||
\(529\) | 0.152154 | 0.00661541 | ||||||||
\(530\) | −11.7044 | −0.508409 | ||||||||
\(531\) | 29.1384 | 1.26450 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.8079 | 1.20449 | ||||||||
\(534\) | −0.554678 | −0.0240033 | ||||||||
\(535\) | −2.76144 | −0.119387 | ||||||||
\(536\) | 25.5222 | 1.10239 | ||||||||
\(537\) | 35.9203 | 1.55008 | ||||||||
\(538\) | 17.1858 | 0.740933 | ||||||||
\(539\) | −16.1377 | −0.695101 | ||||||||
\(540\) | −31.0748 | −1.33725 | ||||||||
\(541\) | −28.8016 | −1.23828 | −0.619139 | − | 0.785281i | \(-0.712518\pi\) | ||||
−0.619139 | + | 0.785281i | \(0.712518\pi\) | |||||||
\(542\) | 63.8031 | 2.74058 | ||||||||
\(543\) | 38.8301 | 1.66636 | ||||||||
\(544\) | 1.60309 | 0.0687320 | ||||||||
\(545\) | 3.00308 | 0.128638 | ||||||||
\(546\) | 100.256 | 4.29054 | ||||||||
\(547\) | 26.9553 | 1.15253 | 0.576264 | − | 0.817264i | \(-0.304510\pi\) | ||||
0.576264 | + | 0.817264i | \(0.304510\pi\) | |||||||
\(548\) | −31.9761 | −1.36595 | ||||||||
\(549\) | −76.6606 | −3.27180 | ||||||||
\(550\) | −5.18129 | −0.220931 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 67.2153 | 2.86087 | ||||||||
\(553\) | −16.2628 | −0.691563 | ||||||||
\(554\) | 6.99672 | 0.297262 | ||||||||
\(555\) | 11.5787 | 0.491488 | ||||||||
\(556\) | −69.1696 | −2.93345 | ||||||||
\(557\) | 7.95439 | 0.337039 | 0.168519 | − | 0.985698i | \(-0.446101\pi\) | ||||
0.168519 | + | 0.985698i | \(0.446101\pi\) | |||||||
\(558\) | −49.4188 | −2.09207 | ||||||||
\(559\) | −20.4797 | −0.866199 | ||||||||
\(560\) | −14.0369 | −0.593169 | ||||||||
\(561\) | −19.0412 | −0.803919 | ||||||||
\(562\) | −54.7153 | −2.30803 | ||||||||
\(563\) | −34.0931 | −1.43685 | −0.718426 | − | 0.695603i | \(-0.755137\pi\) | ||||
−0.718426 | + | 0.695603i | \(0.755137\pi\) | |||||||
\(564\) | 97.8172 | 4.11885 | ||||||||
\(565\) | −3.61708 | −0.152172 | ||||||||
\(566\) | −11.4146 | −0.479789 | ||||||||
\(567\) | −23.5908 | −0.990722 | ||||||||
\(568\) | 0.585446 | 0.0245648 | ||||||||
\(569\) | 25.7236 | 1.07839 | 0.539195 | − | 0.842181i | \(-0.318729\pi\) | ||||
0.539195 | + | 0.842181i | \(0.318729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.6325 | −1.32378 | −0.661890 | − | 0.749601i | \(-0.730245\pi\) | ||||
−0.661890 | + | 0.749601i | \(0.730245\pi\) | |||||||
\(572\) | −30.6365 | −1.28098 | ||||||||
\(573\) | −13.5983 | −0.568079 | ||||||||
\(574\) | −70.8809 | −2.95851 | ||||||||
\(575\) | −4.81167 | −0.200660 | ||||||||
\(576\) | −48.9893 | −2.04122 | ||||||||
\(577\) | 26.8689 | 1.11856 | 0.559282 | − | 0.828977i | \(-0.311077\pi\) | ||||
0.559282 | + | 0.828977i | \(0.311077\pi\) | |||||||
\(578\) | −18.8811 | −0.785350 | ||||||||
\(579\) | 15.3879 | 0.639498 | ||||||||
\(580\) | −23.8049 | −0.988445 | ||||||||
\(581\) | −16.7991 | −0.696946 | ||||||||
\(582\) | −129.429 | −5.36500 | ||||||||
\(583\) | 10.2005 | 0.422461 | ||||||||
\(584\) | −59.2213 | −2.45060 | ||||||||
\(585\) | 20.7362 | 0.857338 | ||||||||
\(586\) | 7.95439 | 0.328593 | ||||||||
\(587\) | 42.5145 | 1.75476 | 0.877380 | − | 0.479796i | \(-0.159289\pi\) | ||||
0.877380 | + | 0.479796i | \(0.159289\pi\) | |||||||
\(588\) | −88.2426 | −3.63906 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 12.5208 | 0.515474 | ||||||||
\(591\) | −62.3748 | −2.56576 | ||||||||
\(592\) | −14.4451 | −0.593691 | ||||||||
\(593\) | −23.2139 | −0.953280 | −0.476640 | − | 0.879099i | \(-0.658145\pi\) | ||||
−0.476640 | + | 0.879099i | \(0.658145\pi\) | |||||||
\(594\) | 40.8108 | 1.67449 | ||||||||
\(595\) | 11.6229 | 0.476491 | ||||||||
\(596\) | 75.7293 | 3.10199 | ||||||||
\(597\) | −45.2834 | −1.85333 | ||||||||
\(598\) | −42.8740 | −1.75325 | ||||||||
\(599\) | −0.313115 | −0.0127935 | −0.00639676 | − | 0.999980i | \(-0.502036\pi\) | ||||
−0.00639676 | + | 0.999980i | \(0.502036\pi\) | |||||||
\(600\) | −13.9692 | −0.570292 | ||||||||
\(601\) | −20.9580 | −0.854893 | −0.427447 | − | 0.904041i | \(-0.640587\pi\) | ||||
−0.427447 | + | 0.904041i | \(0.640587\pi\) | |||||||
\(602\) | 52.2018 | 2.12759 | ||||||||
\(603\) | 30.5338 | 1.24343 | ||||||||
\(604\) | 43.9785 | 1.78946 | ||||||||
\(605\) | −6.48448 | −0.263631 | ||||||||
\(606\) | −133.930 | −5.44053 | ||||||||
\(607\) | −10.1085 | −0.410290 | −0.205145 | − | 0.978732i | \(-0.565767\pi\) | ||||
−0.205145 | + | 0.978732i | \(0.565767\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −67.8899 | −2.75104 | ||||||||
\(610\) | −32.9413 | −1.33375 | ||||||||
\(611\) | −30.7637 | −1.24457 | ||||||||
\(612\) | −68.1097 | −2.75317 | ||||||||
\(613\) | −36.3560 | −1.46840 | −0.734202 | − | 0.678931i | \(-0.762444\pi\) | ||||
−0.734202 | + | 0.678931i | \(0.762444\pi\) | |||||||
\(614\) | −4.18766 | −0.169000 | ||||||||
\(615\) | −22.4116 | −0.903721 | ||||||||
\(616\) | 38.5035 | 1.55135 | ||||||||
\(617\) | 35.3399 | 1.42273 | 0.711365 | − | 0.702822i | \(-0.248077\pi\) | ||||
0.711365 | + | 0.702822i | \(0.248077\pi\) | |||||||
\(618\) | 2.71039 | 0.109028 | ||||||||
\(619\) | −32.5878 | −1.30982 | −0.654908 | − | 0.755709i | \(-0.727292\pi\) | ||||
−0.654908 | + | 0.755709i | \(0.727292\pi\) | |||||||
\(620\) | −14.0917 | −0.565937 | ||||||||
\(621\) | 37.8994 | 1.52085 | ||||||||
\(622\) | −2.17726 | −0.0873000 | ||||||||
\(623\) | −0.295074 | −0.0118219 | ||||||||
\(624\) | −39.5470 | −1.58315 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 28.1275 | 1.12420 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 43.9704 | 1.75461 | ||||||||
\(629\) | 11.9608 | 0.476910 | ||||||||
\(630\) | −52.8557 | −2.10582 | ||||||||
\(631\) | 1.66950 | 0.0664616 | 0.0332308 | − | 0.999448i | \(-0.489420\pi\) | ||||
0.0332308 | + | 0.999448i | \(0.489420\pi\) | |||||||
\(632\) | 20.1909 | 0.803153 | ||||||||
\(633\) | −61.4549 | −2.44261 | ||||||||
\(634\) | 45.8997 | 1.82291 | ||||||||
\(635\) | −13.6188 | −0.540445 | ||||||||
\(636\) | 55.7772 | 2.21171 | ||||||||
\(637\) | 27.7525 | 1.09959 | ||||||||
\(638\) | 31.2632 | 1.23772 | ||||||||
\(639\) | 0.700405 | 0.0277076 | ||||||||
\(640\) | −19.9970 | −0.790451 | ||||||||
\(641\) | 21.3997 | 0.845238 | 0.422619 | − | 0.906307i | \(-0.361111\pi\) | ||||
0.422619 | + | 0.906307i | \(0.361111\pi\) | |||||||
\(642\) | 19.8307 | 0.782655 | ||||||||
\(643\) | −8.43473 | −0.332633 | −0.166317 | − | 0.986072i | \(-0.553187\pi\) | ||||
−0.166317 | + | 0.986072i | \(0.553187\pi\) | |||||||
\(644\) | 72.5202 | 2.85770 | ||||||||
\(645\) | 16.5055 | 0.649903 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.2025 | −1.14807 | −0.574034 | − | 0.818831i | \(-0.694622\pi\) | ||||
−0.574034 | + | 0.818831i | \(0.694622\pi\) | |||||||
\(648\) | 29.2891 | 1.15058 | ||||||||
\(649\) | −10.9120 | −0.428332 | ||||||||
\(650\) | 8.91042 | 0.349495 | ||||||||
\(651\) | −40.1885 | −1.57511 | ||||||||
\(652\) | −26.3805 | −1.03314 | ||||||||
\(653\) | −7.61427 | −0.297970 | −0.148985 | − | 0.988839i | \(-0.547601\pi\) | ||||
−0.148985 | + | 0.988839i | \(0.547601\pi\) | |||||||
\(654\) | −21.5660 | −0.843299 | ||||||||
\(655\) | 5.67059 | 0.221568 | ||||||||
\(656\) | 27.9598 | 1.09165 | ||||||||
\(657\) | −70.8501 | −2.76412 | ||||||||
\(658\) | 78.4153 | 3.05695 | ||||||||
\(659\) | −18.2941 | −0.712637 | −0.356318 | − | 0.934365i | \(-0.615968\pi\) | ||||
−0.356318 | + | 0.934365i | \(0.615968\pi\) | |||||||
\(660\) | 24.6913 | 0.961108 | ||||||||
\(661\) | −20.3586 | −0.791859 | −0.395930 | − | 0.918281i | \(-0.629578\pi\) | ||||
−0.395930 | + | 0.918281i | \(0.629578\pi\) | |||||||
\(662\) | −37.9834 | −1.47627 | ||||||||
\(663\) | 32.7456 | 1.27174 | ||||||||
\(664\) | 20.8569 | 0.809404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −54.3928 | −2.10768 | ||||||||
\(667\) | 29.0329 | 1.12416 | ||||||||
\(668\) | 73.6056 | 2.84789 | ||||||||
\(669\) | −40.2786 | −1.55726 | ||||||||
\(670\) | 13.1204 | 0.506887 | ||||||||
\(671\) | 28.7085 | 1.10828 | ||||||||
\(672\) | −5.92853 | −0.228698 | ||||||||
\(673\) | 29.6829 | 1.14419 | 0.572096 | − | 0.820186i | \(-0.306130\pi\) | ||||
0.572096 | + | 0.820186i | \(0.306130\pi\) | |||||||
\(674\) | −15.6885 | −0.604299 | ||||||||
\(675\) | −7.87657 | −0.303169 | ||||||||
\(676\) | 1.39862 | 0.0537932 | ||||||||
\(677\) | 9.17128 | 0.352481 | 0.176240 | − | 0.984347i | \(-0.443606\pi\) | ||||
0.176240 | + | 0.984347i | \(0.443606\pi\) | |||||||
\(678\) | 25.9753 | 0.997576 | ||||||||
\(679\) | −68.8526 | −2.64232 | ||||||||
\(680\) | −14.4303 | −0.553376 | ||||||||
\(681\) | −10.9326 | −0.418937 | ||||||||
\(682\) | 18.5067 | 0.708660 | ||||||||
\(683\) | −15.6556 | −0.599043 | −0.299522 | − | 0.954089i | \(-0.596827\pi\) | ||||
−0.299522 | + | 0.954089i | \(0.596827\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.10501 | −0.309676 | ||||||||
\(686\) | −5.53586 | −0.211360 | ||||||||
\(687\) | −33.3064 | −1.27072 | ||||||||
\(688\) | −20.5916 | −0.785048 | ||||||||
\(689\) | −17.5421 | −0.668299 | ||||||||
\(690\) | 34.5540 | 1.31545 | ||||||||
\(691\) | −13.7912 | −0.524643 | −0.262321 | − | 0.964981i | \(-0.584488\pi\) | ||||
−0.262321 | + | 0.964981i | \(0.584488\pi\) | |||||||
\(692\) | −58.1466 | −2.21040 | ||||||||
\(693\) | 46.0640 | 1.74983 | ||||||||
\(694\) | −47.1483 | −1.78972 | ||||||||
\(695\) | −17.5325 | −0.665045 | ||||||||
\(696\) | 84.2883 | 3.19494 | ||||||||
\(697\) | −23.1513 | −0.876916 | ||||||||
\(698\) | 18.9911 | 0.718822 | ||||||||
\(699\) | 31.4412 | 1.18921 | ||||||||
\(700\) | −15.0717 | −0.569658 | ||||||||
\(701\) | −13.7313 | −0.518622 | −0.259311 | − | 0.965794i | \(-0.583496\pi\) | ||||
−0.259311 | + | 0.965794i | \(0.583496\pi\) | |||||||
\(702\) | −70.1835 | −2.64891 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 18.3459 | 0.691437 | ||||||||
\(705\) | 24.7938 | 0.933790 | ||||||||
\(706\) | −60.2272 | −2.26668 | ||||||||
\(707\) | −71.2470 | −2.67952 | ||||||||
\(708\) | −59.6677 | −2.24245 | ||||||||
\(709\) | −12.3146 | −0.462483 | −0.231242 | − | 0.972896i | \(-0.574279\pi\) | ||||
−0.231242 | + | 0.972896i | \(0.574279\pi\) | |||||||
\(710\) | 0.300966 | 0.0112950 | ||||||||
\(711\) | 24.1557 | 0.905908 | ||||||||
\(712\) | 0.366347 | 0.0137294 | ||||||||
\(713\) | 17.1865 | 0.643640 | ||||||||
\(714\) | −83.4671 | −3.12368 | ||||||||
\(715\) | −7.76547 | −0.290412 | ||||||||
\(716\) | −48.1165 | −1.79820 | ||||||||
\(717\) | 50.8972 | 1.90079 | ||||||||
\(718\) | 60.5240 | 2.25874 | ||||||||
\(719\) | −6.92307 | −0.258187 | −0.129094 | − | 0.991632i | \(-0.541207\pi\) | ||||
−0.129094 | + | 0.991632i | \(0.541207\pi\) | |||||||
\(720\) | 20.8496 | 0.777017 | ||||||||
\(721\) | 1.44185 | 0.0536973 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −51.5374 | −1.91670 | ||||||||
\(724\) | −52.0142 | −1.93309 | ||||||||
\(725\) | −6.03385 | −0.224092 | ||||||||
\(726\) | 46.5669 | 1.72826 | ||||||||
\(727\) | 34.2263 | 1.26938 | 0.634692 | − | 0.772765i | \(-0.281127\pi\) | ||||
0.634692 | + | 0.772765i | \(0.281127\pi\) | |||||||
\(728\) | −66.2155 | −2.45411 | ||||||||
\(729\) | −34.5545 | −1.27980 | ||||||||
\(730\) | −30.4445 | −1.12680 | ||||||||
\(731\) | 17.0503 | 0.630626 | ||||||||
\(732\) | 156.981 | 5.80218 | ||||||||
\(733\) | 37.5214 | 1.38589 | 0.692943 | − | 0.720993i | \(-0.256314\pi\) | ||||
0.692943 | + | 0.720993i | \(0.256314\pi\) | |||||||
\(734\) | −17.1098 | −0.631535 | ||||||||
\(735\) | −22.3669 | −0.825017 | ||||||||
\(736\) | 2.53532 | 0.0934531 | ||||||||
\(737\) | −11.4345 | −0.421196 | ||||||||
\(738\) | 105.282 | 3.87548 | ||||||||
\(739\) | −38.6683 | −1.42244 | −0.711218 | − | 0.702972i | \(-0.751856\pi\) | ||||
−0.711218 | + | 0.702972i | \(0.751856\pi\) | |||||||
\(740\) | −15.5100 | −0.570160 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 44.7139 | 1.64150 | ||||||||
\(743\) | 34.5415 | 1.26720 | 0.633602 | − | 0.773659i | \(-0.281576\pi\) | ||||
0.633602 | + | 0.773659i | \(0.281576\pi\) | |||||||
\(744\) | 49.8959 | 1.82927 | ||||||||
\(745\) | 19.1952 | 0.703257 | ||||||||
\(746\) | −88.2915 | −3.23258 | ||||||||
\(747\) | 24.9523 | 0.912959 | ||||||||
\(748\) | 25.5063 | 0.932601 | ||||||||
\(749\) | 10.5494 | 0.385466 | ||||||||
\(750\) | −7.18129 | −0.262224 | ||||||||
\(751\) | 33.3178 | 1.21578 | 0.607892 | − | 0.794020i | \(-0.292015\pi\) | ||||
0.607892 | + | 0.794020i | \(0.292015\pi\) | |||||||
\(752\) | −30.9318 | −1.12797 | ||||||||
\(753\) | −52.7230 | −1.92133 | ||||||||
\(754\) | −53.7642 | −1.95798 | ||||||||
\(755\) | 11.1473 | 0.405691 | ||||||||
\(756\) | 118.714 | 4.31757 | ||||||||
\(757\) | 27.2310 | 0.989728 | 0.494864 | − | 0.868970i | \(-0.335218\pi\) | ||||
0.494864 | + | 0.868970i | \(0.335218\pi\) | |||||||
\(758\) | −68.8706 | −2.50149 | ||||||||
\(759\) | −30.1140 | −1.09307 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.1113 | 0.729033 | 0.364516 | − | 0.931197i | \(-0.381234\pi\) | ||||
0.364516 | + | 0.931197i | \(0.381234\pi\) | |||||||
\(762\) | 97.8006 | 3.54294 | ||||||||
\(763\) | −11.4725 | −0.415334 | ||||||||
\(764\) | 18.2154 | 0.659011 | ||||||||
\(765\) | −17.2638 | −0.624175 | ||||||||
\(766\) | 64.4469 | 2.32856 | ||||||||
\(767\) | 18.7656 | 0.677587 | ||||||||
\(768\) | 92.7493 | 3.34680 | ||||||||
\(769\) | −3.25931 | −0.117534 | −0.0587669 | − | 0.998272i | \(-0.518717\pi\) | ||||
−0.0587669 | + | 0.998272i | \(0.518717\pi\) | |||||||
\(770\) | 19.7938 | 0.713320 | ||||||||
\(771\) | 78.6988 | 2.83427 | ||||||||
\(772\) | −20.6125 | −0.741861 | ||||||||
\(773\) | −49.6874 | −1.78713 | −0.893565 | − | 0.448933i | \(-0.851804\pi\) | ||||
−0.893565 | + | 0.448933i | \(0.851804\pi\) | |||||||
\(774\) | −77.5372 | −2.78702 | ||||||||
\(775\) | −3.57184 | −0.128304 | ||||||||
\(776\) | 85.4835 | 3.06868 | ||||||||
\(777\) | −44.2335 | −1.58687 | ||||||||
\(778\) | −13.6967 | −0.491051 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −42.4624 | −1.52040 | ||||||||
\(781\) | −0.262293 | −0.00938559 | ||||||||
\(782\) | 35.6945 | 1.27643 | ||||||||
\(783\) | 47.5260 | 1.69844 | ||||||||
\(784\) | 27.9041 | 0.996576 | ||||||||
\(785\) | 11.1452 | 0.397790 | ||||||||
\(786\) | −40.7222 | −1.45251 | ||||||||
\(787\) | −27.1159 | −0.966578 | −0.483289 | − | 0.875461i | \(-0.660558\pi\) | ||||
−0.483289 | + | 0.875461i | \(0.660558\pi\) | |||||||
\(788\) | 83.5531 | 2.97646 | ||||||||
\(789\) | 58.2615 | 2.07416 | ||||||||
\(790\) | 10.3797 | 0.369295 | ||||||||
\(791\) | 13.8181 | 0.491317 | ||||||||
\(792\) | −57.1905 | −2.03218 | ||||||||
\(793\) | −49.3708 | −1.75321 | ||||||||
\(794\) | −70.8055 | −2.51279 | ||||||||
\(795\) | 14.1379 | 0.501420 | ||||||||
\(796\) | 60.6586 | 2.14999 | ||||||||
\(797\) | −27.3573 | −0.969044 | −0.484522 | − | 0.874779i | \(-0.661006\pi\) | ||||
−0.484522 | + | 0.874779i | \(0.661006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.6122 | 0.906093 | ||||||||
\(800\) | −0.526911 | −0.0186291 | ||||||||
\(801\) | 0.438283 | 0.0154860 | ||||||||
\(802\) | 62.0820 | 2.19219 | ||||||||
\(803\) | 26.5325 | 0.936311 | ||||||||
\(804\) | −62.5251 | −2.20509 | ||||||||
\(805\) | 18.3818 | 0.647872 | ||||||||
\(806\) | −31.8266 | −1.12104 | ||||||||
\(807\) | −20.7589 | −0.730748 | ||||||||
\(808\) | 88.4564 | 3.11188 | ||||||||
\(809\) | −12.3922 | −0.435686 | −0.217843 | − | 0.975984i | \(-0.569902\pi\) | ||||
−0.217843 | + | 0.975984i | \(0.569902\pi\) | |||||||
\(810\) | 15.0569 | 0.529046 | ||||||||
\(811\) | 14.5389 | 0.510528 | 0.255264 | − | 0.966871i | \(-0.417838\pi\) | ||||
0.255264 | + | 0.966871i | \(0.417838\pi\) | |||||||
\(812\) | 90.9407 | 3.19139 | ||||||||
\(813\) | −77.0683 | −2.70290 | ||||||||
\(814\) | 20.3694 | 0.713948 | ||||||||
\(815\) | −6.68669 | −0.234225 | ||||||||
\(816\) | 32.9246 | 1.15259 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −48.2839 | −1.68821 | ||||||||
\(819\) | −79.2176 | −2.76809 | ||||||||
\(820\) | 30.0210 | 1.04838 | ||||||||
\(821\) | 6.47357 | 0.225929 | 0.112965 | − | 0.993599i | \(-0.463965\pi\) | ||||
0.112965 | + | 0.993599i | \(0.463965\pi\) | |||||||
\(822\) | 58.2044 | 2.03011 | ||||||||
\(823\) | 0.210155 | 0.00732553 | 0.00366276 | − | 0.999993i | \(-0.498834\pi\) | ||||
0.00366276 | + | 0.999993i | \(0.498834\pi\) | |||||||
\(824\) | −1.79012 | −0.0623619 | ||||||||
\(825\) | 6.25853 | 0.217894 | ||||||||
\(826\) | −47.8327 | −1.66431 | ||||||||
\(827\) | 23.1396 | 0.804643 | 0.402322 | − | 0.915498i | \(-0.368203\pi\) | ||||
0.402322 | + | 0.915498i | \(0.368203\pi\) | |||||||
\(828\) | −107.717 | −3.74342 | ||||||||
\(829\) | 24.6843 | 0.857321 | 0.428660 | − | 0.903466i | \(-0.358986\pi\) | ||||
0.428660 | + | 0.903466i | \(0.358986\pi\) | |||||||
\(830\) | 10.7221 | 0.372169 | ||||||||
\(831\) | −8.45141 | −0.293176 | ||||||||
\(832\) | −31.5500 | −1.09380 | ||||||||
\(833\) | −23.1052 | −0.800547 | ||||||||
\(834\) | 125.906 | 4.35977 | ||||||||
\(835\) | 18.6569 | 0.645648 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 28.1338 | 0.972448 | ||||||||
\(838\) | 0.419685 | 0.0144978 | ||||||||
\(839\) | 31.2238 | 1.07797 | 0.538983 | − | 0.842317i | \(-0.318809\pi\) | ||||
0.538983 | + | 0.842317i | \(0.318809\pi\) | |||||||
\(840\) | 53.3659 | 1.84130 | ||||||||
\(841\) | 7.40738 | 0.255427 | ||||||||
\(842\) | 42.4398 | 1.46257 | ||||||||
\(843\) | 66.0912 | 2.27630 | ||||||||
\(844\) | 82.3208 | 2.83360 | ||||||||
\(845\) | 0.354510 | 0.0121955 | ||||||||
\(846\) | −116.473 | −4.00443 | ||||||||
\(847\) | 24.7723 | 0.851187 | ||||||||
\(848\) | −17.6379 | −0.605689 | ||||||||
\(849\) | 13.7877 | 0.473194 | ||||||||
\(850\) | −7.41831 | −0.254446 | ||||||||
\(851\) | 18.9163 | 0.648443 | ||||||||
\(852\) | −1.43425 | −0.0491364 | ||||||||
\(853\) | 27.1366 | 0.929140 | 0.464570 | − | 0.885536i | \(-0.346209\pi\) | ||||
0.464570 | + | 0.885536i | \(0.346209\pi\) | |||||||
\(854\) | 125.844 | 4.30629 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.0975 | −0.447664 | ||||||||
\(857\) | −47.6457 | −1.62755 | −0.813773 | − | 0.581183i | \(-0.802590\pi\) | ||||
−0.813773 | + | 0.581183i | \(0.802590\pi\) | |||||||
\(858\) | 55.7661 | 1.90382 | ||||||||
\(859\) | −19.6361 | −0.669974 | −0.334987 | − | 0.942223i | \(-0.608732\pi\) | ||||
−0.334987 | + | 0.942223i | \(0.608732\pi\) | |||||||
\(860\) | −22.1096 | −0.753932 | ||||||||
\(861\) | 85.6177 | 2.91784 | ||||||||
\(862\) | −12.3503 | −0.420654 | ||||||||
\(863\) | 49.3684 | 1.68052 | 0.840260 | − | 0.542183i | \(-0.182402\pi\) | ||||
0.840260 | + | 0.542183i | \(0.182402\pi\) | |||||||
\(864\) | 4.15025 | 0.141194 | ||||||||
\(865\) | −14.7385 | −0.501123 | ||||||||
\(866\) | 30.5197 | 1.03710 | ||||||||
\(867\) | 22.8066 | 0.774554 | ||||||||
\(868\) | 53.8339 | 1.82724 | ||||||||
\(869\) | −9.04600 | −0.306865 | ||||||||
\(870\) | 43.3309 | 1.46905 | ||||||||
\(871\) | 19.6643 | 0.666299 | ||||||||
\(872\) | 14.2437 | 0.482351 | ||||||||
\(873\) | 102.269 | 3.46129 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.82025 | −0.129148 | ||||||||
\(876\) | 145.082 | 4.90188 | ||||||||
\(877\) | −41.1968 | −1.39112 | −0.695559 | − | 0.718469i | \(-0.744843\pi\) | ||||
−0.695559 | + | 0.718469i | \(0.744843\pi\) | |||||||
\(878\) | −35.9845 | −1.21442 | ||||||||
\(879\) | −9.60819 | −0.324076 | ||||||||
\(880\) | −7.80791 | −0.263205 | ||||||||
\(881\) | −10.4510 | −0.352103 | −0.176052 | − | 0.984381i | \(-0.556333\pi\) | ||||
−0.176052 | + | 0.984381i | \(0.556333\pi\) | |||||||
\(882\) | 105.072 | 3.53797 | ||||||||
\(883\) | −50.2957 | −1.69259 | −0.846293 | − | 0.532717i | \(-0.821171\pi\) | ||||
−0.846293 | + | 0.532717i | \(0.821171\pi\) | |||||||
\(884\) | −43.8639 | −1.47530 | ||||||||
\(885\) | −15.1240 | −0.508388 | ||||||||
\(886\) | 13.0680 | 0.439027 | ||||||||
\(887\) | 0.201711 | 0.00677278 | 0.00338639 | − | 0.999994i | \(-0.498922\pi\) | ||||
0.00338639 | + | 0.999994i | \(0.498922\pi\) | |||||||
\(888\) | 54.9178 | 1.84292 | ||||||||
\(889\) | 52.0272 | 1.74494 | ||||||||
\(890\) | 0.188331 | 0.00631288 | ||||||||
\(891\) | −13.1222 | −0.439609 | ||||||||
\(892\) | 53.9545 | 1.80653 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −137.846 | −4.61027 | ||||||||
\(895\) | −12.1961 | −0.407672 | ||||||||
\(896\) | 76.3935 | 2.55213 | ||||||||
\(897\) | 51.7879 | 1.72915 | ||||||||
\(898\) | −17.4597 | −0.582637 | ||||||||
\(899\) | 21.5520 | 0.718798 | ||||||||
\(900\) | 22.3866 | 0.746220 | ||||||||
\(901\) | 14.6045 | 0.486548 | ||||||||
\(902\) | −39.4268 | −1.31277 | ||||||||
\(903\) | −63.0551 | −2.09834 | ||||||||
\(904\) | −17.1558 | −0.570595 | ||||||||
\(905\) | −13.1841 | −0.438254 | ||||||||
\(906\) | −80.0518 | −2.65954 | ||||||||
\(907\) | −6.11841 | −0.203158 | −0.101579 | − | 0.994827i | \(-0.532390\pi\) | ||||
−0.101579 | + | 0.994827i | \(0.532390\pi\) | |||||||
\(908\) | 14.6445 | 0.485996 | ||||||||
\(909\) | 105.826 | 3.51002 | ||||||||
\(910\) | −34.0400 | −1.12842 | ||||||||
\(911\) | 0.960234 | 0.0318140 | 0.0159070 | − | 0.999873i | \(-0.494936\pi\) | ||||
0.0159070 | + | 0.999873i | \(0.494936\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.34435 | −0.309253 | ||||||||
\(914\) | 78.9722 | 2.61217 | ||||||||
\(915\) | 39.7901 | 1.31542 | ||||||||
\(916\) | 44.6149 | 1.47412 | ||||||||
\(917\) | −21.6631 | −0.715378 | ||||||||
\(918\) | 58.4308 | 1.92851 | ||||||||
\(919\) | −51.3264 | −1.69310 | −0.846551 | − | 0.532307i | \(-0.821325\pi\) | ||||
−0.846551 | + | 0.532307i | \(0.821325\pi\) | |||||||
\(920\) | −22.8218 | −0.752412 | ||||||||
\(921\) | 5.05831 | 0.166677 | ||||||||
\(922\) | −61.4750 | −2.02457 | ||||||||
\(923\) | 0.451073 | 0.0148473 | ||||||||
\(924\) | −94.3270 | −3.10313 | ||||||||
\(925\) | −3.93134 | −0.129262 | ||||||||
\(926\) | −99.6023 | −3.27314 | ||||||||
\(927\) | −2.14163 | −0.0703404 | ||||||||
\(928\) | 3.17930 | 0.104366 | ||||||||
\(929\) | −46.0177 | −1.50979 | −0.754896 | − | 0.655844i | \(-0.772313\pi\) | ||||
−0.754896 | + | 0.655844i | \(0.772313\pi\) | |||||||
\(930\) | 25.6504 | 0.841111 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −42.1165 | −1.37957 | ||||||||
\(933\) | 2.62993 | 0.0860999 | ||||||||
\(934\) | 35.6500 | 1.16650 | ||||||||
\(935\) | 6.46510 | 0.211431 | ||||||||
\(936\) | 98.3522 | 3.21474 | ||||||||
\(937\) | −3.79467 | −0.123966 | −0.0619832 | − | 0.998077i | \(-0.519743\pi\) | ||||
−0.0619832 | + | 0.998077i | \(0.519743\pi\) | |||||||
\(938\) | −50.1233 | −1.63658 | ||||||||
\(939\) | −33.9754 | −1.10875 | ||||||||
\(940\) | −33.2121 | −1.08326 | ||||||||
\(941\) | −23.1763 | −0.755526 | −0.377763 | − | 0.925902i | \(-0.623307\pi\) | ||||
−0.377763 | + | 0.925902i | \(0.623307\pi\) | |||||||
\(942\) | −80.0371 | −2.60775 | ||||||||
\(943\) | −36.6142 | −1.19232 | ||||||||
\(944\) | 18.8682 | 0.614106 | ||||||||
\(945\) | 30.0904 | 0.978842 | ||||||||
\(946\) | 29.0367 | 0.944066 | ||||||||
\(947\) | 18.3891 | 0.597565 | 0.298783 | − | 0.954321i | \(-0.403419\pi\) | ||||
0.298783 | + | 0.954321i | \(0.403419\pi\) | |||||||
\(948\) | −49.4644 | −1.60653 | ||||||||
\(949\) | −45.6287 | −1.48117 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −55.4427 | −1.79785 | ||||||||
\(952\) | 55.1273 | 1.78669 | ||||||||
\(953\) | −14.6072 | −0.473174 | −0.236587 | − | 0.971610i | \(-0.576029\pi\) | ||||
−0.236587 | + | 0.971610i | \(0.576029\pi\) | |||||||
\(954\) | −66.4151 | −2.15027 | ||||||||
\(955\) | 4.61708 | 0.149405 | ||||||||
\(956\) | −68.1785 | −2.20505 | ||||||||
\(957\) | −37.7631 | −1.22071 | ||||||||
\(958\) | 2.60760 | 0.0842477 | ||||||||
\(959\) | 30.9631 | 0.999852 | ||||||||
\(960\) | 25.4275 | 0.820669 | ||||||||
\(961\) | −18.2420 | −0.588450 | ||||||||
\(962\) | −35.0299 | −1.12941 | ||||||||
\(963\) | −15.6694 | −0.504938 | ||||||||
\(964\) | 69.0361 | 2.22350 | ||||||||
\(965\) | −5.22468 | −0.168188 | ||||||||
\(966\) | −132.005 | −4.24719 | ||||||||
\(967\) | 59.4737 | 1.91254 | 0.956272 | − | 0.292478i | \(-0.0944798\pi\) | ||||
0.956272 | + | 0.292478i | \(0.0944798\pi\) | |||||||
\(968\) | −30.7559 | −0.988533 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 43.9453 | 1.41100 | ||||||||
\(971\) | −22.3008 | −0.715667 | −0.357833 | − | 0.933785i | \(-0.616484\pi\) | ||||
−0.357833 | + | 0.933785i | \(0.616484\pi\) | |||||||
\(972\) | 21.4712 | 0.688689 | ||||||||
\(973\) | 66.9785 | 2.14723 | ||||||||
\(974\) | −15.2467 | −0.488535 | ||||||||
\(975\) | −10.7630 | −0.344691 | ||||||||
\(976\) | −49.6406 | −1.58896 | ||||||||
\(977\) | 15.2734 | 0.488638 | 0.244319 | − | 0.969695i | \(-0.421436\pi\) | ||||
0.244319 | + | 0.969695i | \(0.421436\pi\) | |||||||
\(978\) | 48.0191 | 1.53548 | ||||||||
\(979\) | −0.164132 | −0.00524567 | ||||||||
\(980\) | 29.9612 | 0.957077 | ||||||||
\(981\) | 17.0406 | 0.544063 | ||||||||
\(982\) | −1.98398 | −0.0633115 | ||||||||
\(983\) | 41.4127 | 1.32086 | 0.660431 | − | 0.750887i | \(-0.270374\pi\) | ||||
0.660431 | + | 0.750887i | \(0.270374\pi\) | |||||||
\(984\) | −106.298 | −3.38866 | ||||||||
\(985\) | 21.1783 | 0.674797 | ||||||||
\(986\) | 44.7610 | 1.42548 | ||||||||
\(987\) | −94.7186 | −3.01493 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.9653 | 0.857447 | ||||||||
\(990\) | −29.4005 | −0.934408 | ||||||||
\(991\) | 18.9609 | 0.602314 | 0.301157 | − | 0.953575i | \(-0.402627\pi\) | ||||
0.301157 | + | 0.953575i | \(0.402627\pi\) | |||||||
\(992\) | 1.88204 | 0.0597549 | ||||||||
\(993\) | 45.8805 | 1.45597 | ||||||||
\(994\) | −1.14976 | −0.0364683 | ||||||||
\(995\) | 15.3752 | 0.487427 | ||||||||
\(996\) | −51.0958 | −1.61903 | ||||||||
\(997\) | −22.5133 | −0.713002 | −0.356501 | − | 0.934295i | \(-0.616030\pi\) | ||||
−0.356501 | + | 0.934295i | \(0.616030\pi\) | |||||||
\(998\) | 3.84361 | 0.121668 | ||||||||
\(999\) | 30.9655 | 0.979704 |
(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 | 1805.2.a.n.1.4 | yes | 4 | |
5.4 | even | 2 | 9025.2.a.bh.1.1 | 4 | |||
19.18 | odd | 2 | 1805.2.a.j.1.1 | ✓ | 4 | ||
95.94 | odd | 2 | 9025.2.a.bo.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.j.1.1 | ✓ | 4 | 19.18 | odd | 2 | ||
1805.2.a.n.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
9025.2.a.bh.1.1 | 4 | 5.4 | even | 2 | |||
9025.2.a.bo.1.4 | 4 | 95.94 | odd | 2 |