Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6043,2,Mod(1,6043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6043, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6043 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6043.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: | \(48.2535979415\) |
Analytic rank: | \(1\) |
Dimension: | \(243\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70932 | −1.91578 | −0.957890 | − | 0.287134i | \(-0.907298\pi\) | ||||
−0.957890 | + | 0.287134i | \(0.907298\pi\) | |||||||
\(3\) | 3.28141 | 1.89452 | 0.947260 | − | 0.320466i | \(-0.103839\pi\) | ||||
0.947260 | + | 0.320466i | \(0.103839\pi\) | |||||||
\(4\) | 5.34043 | 2.67022 | ||||||||
\(5\) | −1.89583 | −0.847841 | −0.423920 | − | 0.905700i | \(-0.639346\pi\) | ||||
−0.423920 | + | 0.905700i | \(0.639346\pi\) | |||||||
\(6\) | −8.89039 | −3.62949 | ||||||||
\(7\) | 0.209771 | 0.0792860 | 0.0396430 | − | 0.999214i | \(-0.487378\pi\) | ||||
0.0396430 | + | 0.999214i | \(0.487378\pi\) | |||||||
\(8\) | −9.05031 | −3.19977 | ||||||||
\(9\) | 7.76762 | 2.58921 | ||||||||
\(10\) | 5.13641 | 1.62428 | ||||||||
\(11\) | −5.16465 | −1.55720 | −0.778601 | − | 0.627520i | \(-0.784070\pi\) | ||||
−0.778601 | + | 0.627520i | \(0.784070\pi\) | |||||||
\(12\) | 17.5241 | 5.05878 | ||||||||
\(13\) | 2.75290 | 0.763516 | 0.381758 | − | 0.924262i | \(-0.375319\pi\) | ||||
0.381758 | + | 0.924262i | \(0.375319\pi\) | |||||||
\(14\) | −0.568338 | −0.151895 | ||||||||
\(15\) | −6.22098 | −1.60625 | ||||||||
\(16\) | 13.8394 | 3.45984 | ||||||||
\(17\) | 2.29168 | 0.555814 | 0.277907 | − | 0.960608i | \(-0.410359\pi\) | ||||
0.277907 | + | 0.960608i | \(0.410359\pi\) | |||||||
\(18\) | −21.0450 | −4.96035 | ||||||||
\(19\) | −4.02607 | −0.923644 | −0.461822 | − | 0.886973i | \(-0.652804\pi\) | ||||
−0.461822 | + | 0.886973i | \(0.652804\pi\) | |||||||
\(20\) | −10.1245 | −2.26392 | ||||||||
\(21\) | 0.688344 | 0.150209 | ||||||||
\(22\) | 13.9927 | 2.98326 | ||||||||
\(23\) | 4.05305 | 0.845120 | 0.422560 | − | 0.906335i | \(-0.361132\pi\) | ||||
0.422560 | + | 0.906335i | \(0.361132\pi\) | |||||||
\(24\) | −29.6977 | −6.06203 | ||||||||
\(25\) | −1.40583 | −0.281166 | ||||||||
\(26\) | −7.45849 | −1.46273 | ||||||||
\(27\) | 15.6445 | 3.01079 | ||||||||
\(28\) | 1.12027 | 0.211711 | ||||||||
\(29\) | −3.59338 | −0.667273 | −0.333637 | − | 0.942702i | \(-0.608276\pi\) | ||||
−0.333637 | + | 0.942702i | \(0.608276\pi\) | |||||||
\(30\) | 16.8547 | 3.07723 | ||||||||
\(31\) | −3.60943 | −0.648272 | −0.324136 | − | 0.946011i | \(-0.605074\pi\) | ||||
−0.324136 | + | 0.946011i | \(0.605074\pi\) | |||||||
\(32\) | −19.3947 | −3.42852 | ||||||||
\(33\) | −16.9473 | −2.95015 | ||||||||
\(34\) | −6.20890 | −1.06482 | ||||||||
\(35\) | −0.397690 | −0.0672219 | ||||||||
\(36\) | 41.4825 | 6.91374 | ||||||||
\(37\) | 10.2030 | 1.67737 | 0.838685 | − | 0.544616i | \(-0.183325\pi\) | ||||
0.838685 | + | 0.544616i | \(0.183325\pi\) | |||||||
\(38\) | 10.9079 | 1.76950 | ||||||||
\(39\) | 9.03337 | 1.44650 | ||||||||
\(40\) | 17.1578 | 2.71289 | ||||||||
\(41\) | −11.0771 | −1.72996 | −0.864978 | − | 0.501809i | \(-0.832668\pi\) | ||||
−0.864978 | + | 0.501809i | \(0.832668\pi\) | |||||||
\(42\) | −1.86495 | −0.287768 | ||||||||
\(43\) | −5.57925 | −0.850827 | −0.425414 | − | 0.904999i | \(-0.639871\pi\) | ||||
−0.425414 | + | 0.904999i | \(0.639871\pi\) | |||||||
\(44\) | −27.5815 | −4.15806 | ||||||||
\(45\) | −14.7261 | −2.19523 | ||||||||
\(46\) | −10.9810 | −1.61907 | ||||||||
\(47\) | 4.13052 | 0.602499 | 0.301249 | − | 0.953545i | \(-0.402596\pi\) | ||||
0.301249 | + | 0.953545i | \(0.402596\pi\) | |||||||
\(48\) | 45.4125 | 6.55473 | ||||||||
\(49\) | −6.95600 | −0.993714 | ||||||||
\(50\) | 3.80885 | 0.538653 | ||||||||
\(51\) | 7.51993 | 1.05300 | ||||||||
\(52\) | 14.7017 | 2.03875 | ||||||||
\(53\) | −9.80144 | −1.34633 | −0.673166 | − | 0.739491i | \(-0.735066\pi\) | ||||
−0.673166 | + | 0.739491i | \(0.735066\pi\) | |||||||
\(54\) | −42.3860 | −5.76801 | ||||||||
\(55\) | 9.79130 | 1.32026 | ||||||||
\(56\) | −1.89849 | −0.253697 | ||||||||
\(57\) | −13.2112 | −1.74986 | ||||||||
\(58\) | 9.73562 | 1.27835 | ||||||||
\(59\) | −10.6133 | −1.38173 | −0.690866 | − | 0.722983i | \(-0.742771\pi\) | ||||
−0.690866 | + | 0.722983i | \(0.742771\pi\) | |||||||
\(60\) | −33.2227 | −4.28904 | ||||||||
\(61\) | 2.91134 | 0.372758 | 0.186379 | − | 0.982478i | \(-0.440325\pi\) | ||||
0.186379 | + | 0.982478i | \(0.440325\pi\) | |||||||
\(62\) | 9.77910 | 1.24195 | ||||||||
\(63\) | 1.62942 | 0.205288 | ||||||||
\(64\) | 24.8677 | 3.10846 | ||||||||
\(65\) | −5.21902 | −0.647340 | ||||||||
\(66\) | 45.9158 | 5.65184 | ||||||||
\(67\) | 5.60914 | 0.685265 | 0.342633 | − | 0.939469i | \(-0.388681\pi\) | ||||
0.342633 | + | 0.939469i | \(0.388681\pi\) | |||||||
\(68\) | 12.2386 | 1.48414 | ||||||||
\(69\) | 13.2997 | 1.60110 | ||||||||
\(70\) | 1.07747 | 0.128782 | ||||||||
\(71\) | −9.53179 | −1.13122 | −0.565608 | − | 0.824674i | \(-0.691358\pi\) | ||||
−0.565608 | + | 0.824674i | \(0.691358\pi\) | |||||||
\(72\) | −70.2994 | −8.28486 | ||||||||
\(73\) | −5.74436 | −0.672327 | −0.336163 | − | 0.941804i | \(-0.609129\pi\) | ||||
−0.336163 | + | 0.941804i | \(0.609129\pi\) | |||||||
\(74\) | −27.6433 | −3.21347 | ||||||||
\(75\) | −4.61310 | −0.532675 | ||||||||
\(76\) | −21.5010 | −2.46633 | ||||||||
\(77\) | −1.08340 | −0.123464 | ||||||||
\(78\) | −24.4743 | −2.77117 | ||||||||
\(79\) | −10.9468 | −1.23161 | −0.615804 | − | 0.787899i | \(-0.711169\pi\) | ||||
−0.615804 | + | 0.787899i | \(0.711169\pi\) | |||||||
\(80\) | −26.2371 | −2.93339 | ||||||||
\(81\) | 28.0331 | 3.11479 | ||||||||
\(82\) | 30.0115 | 3.31422 | ||||||||
\(83\) | −8.59208 | −0.943104 | −0.471552 | − | 0.881838i | \(-0.656306\pi\) | ||||
−0.471552 | + | 0.881838i | \(0.656306\pi\) | |||||||
\(84\) | 3.67606 | 0.401091 | ||||||||
\(85\) | −4.34463 | −0.471241 | ||||||||
\(86\) | 15.1160 | 1.63000 | ||||||||
\(87\) | −11.7913 | −1.26416 | ||||||||
\(88\) | 46.7417 | 4.98268 | ||||||||
\(89\) | 11.4656 | 1.21536 | 0.607678 | − | 0.794184i | \(-0.292101\pi\) | ||||
0.607678 | + | 0.794184i | \(0.292101\pi\) | |||||||
\(90\) | 39.8977 | 4.20559 | ||||||||
\(91\) | 0.577478 | 0.0605362 | ||||||||
\(92\) | 21.6451 | 2.25665 | ||||||||
\(93\) | −11.8440 | −1.22816 | ||||||||
\(94\) | −11.1909 | −1.15426 | ||||||||
\(95\) | 7.63275 | 0.783103 | ||||||||
\(96\) | −63.6418 | −6.49541 | ||||||||
\(97\) | −5.66729 | −0.575426 | −0.287713 | − | 0.957717i | \(-0.592895\pi\) | ||||
−0.287713 | + | 0.957717i | \(0.592895\pi\) | |||||||
\(98\) | 18.8460 | 1.90374 | ||||||||
\(99\) | −40.1171 | −4.03192 | ||||||||
\(100\) | −7.50775 | −0.750775 | ||||||||
\(101\) | −0.295468 | −0.0294002 | −0.0147001 | − | 0.999892i | \(-0.504679\pi\) | ||||
−0.0147001 | + | 0.999892i | \(0.504679\pi\) | |||||||
\(102\) | −20.3739 | −2.01732 | ||||||||
\(103\) | −2.69414 | −0.265461 | −0.132731 | − | 0.991152i | \(-0.542374\pi\) | ||||
−0.132731 | + | 0.991152i | \(0.542374\pi\) | |||||||
\(104\) | −24.9146 | −2.44308 | ||||||||
\(105\) | −1.30498 | −0.127353 | ||||||||
\(106\) | 26.5553 | 2.57928 | ||||||||
\(107\) | 0.320073 | 0.0309427 | 0.0154713 | − | 0.999880i | \(-0.495075\pi\) | ||||
0.0154713 | + | 0.999880i | \(0.495075\pi\) | |||||||
\(108\) | 83.5484 | 8.03945 | ||||||||
\(109\) | −4.01260 | −0.384338 | −0.192169 | − | 0.981362i | \(-0.561552\pi\) | ||||
−0.192169 | + | 0.981362i | \(0.561552\pi\) | |||||||
\(110\) | −26.5278 | −2.52933 | ||||||||
\(111\) | 33.4803 | 3.17781 | ||||||||
\(112\) | 2.90310 | 0.274317 | ||||||||
\(113\) | 9.46731 | 0.890610 | 0.445305 | − | 0.895379i | \(-0.353095\pi\) | ||||
0.445305 | + | 0.895379i | \(0.353095\pi\) | |||||||
\(114\) | 35.7933 | 3.35235 | ||||||||
\(115\) | −7.68390 | −0.716527 | ||||||||
\(116\) | −19.1902 | −1.78176 | ||||||||
\(117\) | 21.3835 | 1.97690 | ||||||||
\(118\) | 28.7548 | 2.64710 | ||||||||
\(119\) | 0.480728 | 0.0440683 | ||||||||
\(120\) | 56.3018 | 5.13963 | ||||||||
\(121\) | 15.6736 | 1.42488 | ||||||||
\(122\) | −7.88775 | −0.714123 | ||||||||
\(123\) | −36.3485 | −3.27744 | ||||||||
\(124\) | −19.2759 | −1.73103 | ||||||||
\(125\) | 12.1444 | 1.08622 | ||||||||
\(126\) | −4.41463 | −0.393287 | ||||||||
\(127\) | 20.1483 | 1.78787 | 0.893935 | − | 0.448196i | \(-0.147933\pi\) | ||||
0.893935 | + | 0.448196i | \(0.147933\pi\) | |||||||
\(128\) | −28.5853 | −2.52661 | ||||||||
\(129\) | −18.3078 | −1.61191 | ||||||||
\(130\) | 14.1400 | 1.24016 | ||||||||
\(131\) | 0.686860 | 0.0600113 | 0.0300056 | − | 0.999550i | \(-0.490447\pi\) | ||||
0.0300056 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(132\) | −90.5060 | −7.87754 | ||||||||
\(133\) | −0.844554 | −0.0732321 | ||||||||
\(134\) | −15.1970 | −1.31282 | ||||||||
\(135\) | −29.6593 | −2.55267 | ||||||||
\(136\) | −20.7404 | −1.77848 | ||||||||
\(137\) | 16.3954 | 1.40075 | 0.700377 | − | 0.713773i | \(-0.253015\pi\) | ||||
0.700377 | + | 0.713773i | \(0.253015\pi\) | |||||||
\(138\) | −36.0332 | −3.06735 | ||||||||
\(139\) | 16.7569 | 1.42130 | 0.710651 | − | 0.703545i | \(-0.248401\pi\) | ||||
0.710651 | + | 0.703545i | \(0.248401\pi\) | |||||||
\(140\) | −2.12384 | −0.179497 | ||||||||
\(141\) | 13.5539 | 1.14145 | ||||||||
\(142\) | 25.8247 | 2.16716 | ||||||||
\(143\) | −14.2178 | −1.18895 | ||||||||
\(144\) | 107.499 | 8.95824 | ||||||||
\(145\) | 6.81243 | 0.565741 | ||||||||
\(146\) | 15.5633 | 1.28803 | ||||||||
\(147\) | −22.8254 | −1.88261 | ||||||||
\(148\) | 54.4887 | 4.47894 | ||||||||
\(149\) | −5.26544 | −0.431362 | −0.215681 | − | 0.976464i | \(-0.569197\pi\) | ||||
−0.215681 | + | 0.976464i | \(0.569197\pi\) | |||||||
\(150\) | 12.4984 | 1.02049 | ||||||||
\(151\) | −10.6145 | −0.863793 | −0.431897 | − | 0.901923i | \(-0.642156\pi\) | ||||
−0.431897 | + | 0.901923i | \(0.642156\pi\) | |||||||
\(152\) | 36.4372 | 2.95545 | ||||||||
\(153\) | 17.8009 | 1.43912 | ||||||||
\(154\) | 2.93527 | 0.236531 | ||||||||
\(155\) | 6.84285 | 0.549631 | ||||||||
\(156\) | 48.2421 | 3.86246 | ||||||||
\(157\) | 4.47300 | 0.356984 | 0.178492 | − | 0.983941i | \(-0.442878\pi\) | ||||
0.178492 | + | 0.983941i | \(0.442878\pi\) | |||||||
\(158\) | 29.6584 | 2.35949 | ||||||||
\(159\) | −32.1625 | −2.55065 | ||||||||
\(160\) | 36.7690 | 2.90684 | ||||||||
\(161\) | 0.850214 | 0.0670062 | ||||||||
\(162\) | −75.9507 | −5.96725 | ||||||||
\(163\) | 18.5835 | 1.45558 | 0.727788 | − | 0.685803i | \(-0.240549\pi\) | ||||
0.727788 | + | 0.685803i | \(0.240549\pi\) | |||||||
\(164\) | −59.1566 | −4.61936 | ||||||||
\(165\) | 32.1292 | 2.50126 | ||||||||
\(166\) | 23.2787 | 1.80678 | ||||||||
\(167\) | −1.18642 | −0.0918078 | −0.0459039 | − | 0.998946i | \(-0.514617\pi\) | ||||
−0.0459039 | + | 0.998946i | \(0.514617\pi\) | |||||||
\(168\) | −6.22973 | −0.480634 | ||||||||
\(169\) | −5.42156 | −0.417043 | ||||||||
\(170\) | 11.7710 | 0.902795 | ||||||||
\(171\) | −31.2730 | −2.39151 | ||||||||
\(172\) | −29.7956 | −2.27189 | ||||||||
\(173\) | −22.3431 | −1.69872 | −0.849359 | − | 0.527816i | \(-0.823011\pi\) | ||||
−0.849359 | + | 0.527816i | \(0.823011\pi\) | |||||||
\(174\) | 31.9465 | 2.42186 | ||||||||
\(175\) | −0.294903 | −0.0222926 | ||||||||
\(176\) | −71.4755 | −5.38767 | ||||||||
\(177\) | −34.8265 | −2.61772 | ||||||||
\(178\) | −31.0641 | −2.32835 | ||||||||
\(179\) | −18.2940 | −1.36736 | −0.683680 | − | 0.729782i | \(-0.739622\pi\) | ||||
−0.683680 | + | 0.729782i | \(0.739622\pi\) | |||||||
\(180\) | −78.6437 | −5.86175 | ||||||||
\(181\) | −12.2496 | −0.910504 | −0.455252 | − | 0.890363i | \(-0.650451\pi\) | ||||
−0.455252 | + | 0.890363i | \(0.650451\pi\) | |||||||
\(182\) | −1.56458 | −0.115974 | ||||||||
\(183\) | 9.55327 | 0.706198 | ||||||||
\(184\) | −36.6814 | −2.70419 | ||||||||
\(185\) | −19.3432 | −1.42214 | ||||||||
\(186\) | 32.0892 | 2.35289 | ||||||||
\(187\) | −11.8357 | −0.865514 | ||||||||
\(188\) | 22.0588 | 1.60880 | ||||||||
\(189\) | 3.28176 | 0.238713 | ||||||||
\(190\) | −20.6796 | −1.50025 | ||||||||
\(191\) | 4.85407 | 0.351228 | 0.175614 | − | 0.984459i | \(-0.443809\pi\) | ||||
0.175614 | + | 0.984459i | \(0.443809\pi\) | |||||||
\(192\) | 81.6010 | 5.88905 | ||||||||
\(193\) | −8.96655 | −0.645426 | −0.322713 | − | 0.946497i | \(-0.604595\pi\) | ||||
−0.322713 | + | 0.946497i | \(0.604595\pi\) | |||||||
\(194\) | 15.3545 | 1.10239 | ||||||||
\(195\) | −17.1257 | −1.22640 | ||||||||
\(196\) | −37.1480 | −2.65343 | ||||||||
\(197\) | −0.602301 | −0.0429122 | −0.0214561 | − | 0.999770i | \(-0.506830\pi\) | ||||
−0.0214561 | + | 0.999770i | \(0.506830\pi\) | |||||||
\(198\) | 108.690 | 7.72427 | ||||||||
\(199\) | −15.8168 | −1.12123 | −0.560613 | − | 0.828078i | \(-0.689434\pi\) | ||||
−0.560613 | + | 0.828078i | \(0.689434\pi\) | |||||||
\(200\) | 12.7232 | 0.899667 | ||||||||
\(201\) | 18.4059 | 1.29825 | ||||||||
\(202\) | 0.800519 | 0.0563243 | ||||||||
\(203\) | −0.753787 | −0.0529055 | ||||||||
\(204\) | 40.1597 | 2.81174 | ||||||||
\(205\) | 21.0003 | 1.46673 | ||||||||
\(206\) | 7.29928 | 0.508565 | ||||||||
\(207\) | 31.4826 | 2.18819 | ||||||||
\(208\) | 38.0983 | 2.64164 | ||||||||
\(209\) | 20.7933 | 1.43830 | ||||||||
\(210\) | 3.53562 | 0.243981 | ||||||||
\(211\) | −16.4907 | −1.13527 | −0.567633 | − | 0.823282i | \(-0.692141\pi\) | ||||
−0.567633 | + | 0.823282i | \(0.692141\pi\) | |||||||
\(212\) | −52.3439 | −3.59500 | ||||||||
\(213\) | −31.2777 | −2.14311 | ||||||||
\(214\) | −0.867182 | −0.0592794 | ||||||||
\(215\) | 10.5773 | 0.721366 | ||||||||
\(216\) | −141.588 | −9.63382 | ||||||||
\(217\) | −0.757153 | −0.0513989 | ||||||||
\(218\) | 10.8714 | 0.736307 | ||||||||
\(219\) | −18.8496 | −1.27374 | ||||||||
\(220\) | 52.2898 | 3.52538 | ||||||||
\(221\) | 6.30876 | 0.424373 | ||||||||
\(222\) | −90.7090 | −6.08799 | ||||||||
\(223\) | 22.1735 | 1.48484 | 0.742422 | − | 0.669932i | \(-0.233677\pi\) | ||||
0.742422 | + | 0.669932i | \(0.233677\pi\) | |||||||
\(224\) | −4.06844 | −0.271834 | ||||||||
\(225\) | −10.9200 | −0.727998 | ||||||||
\(226\) | −25.6500 | −1.70621 | ||||||||
\(227\) | −14.3168 | −0.950239 | −0.475119 | − | 0.879921i | \(-0.657595\pi\) | ||||
−0.475119 | + | 0.879921i | \(0.657595\pi\) | |||||||
\(228\) | −70.5534 | −4.67251 | ||||||||
\(229\) | −15.2184 | −1.00566 | −0.502832 | − | 0.864384i | \(-0.667708\pi\) | ||||
−0.502832 | + | 0.864384i | \(0.667708\pi\) | |||||||
\(230\) | 20.8182 | 1.37271 | ||||||||
\(231\) | −3.55506 | −0.233906 | ||||||||
\(232\) | 32.5212 | 2.13512 | ||||||||
\(233\) | 21.7843 | 1.42714 | 0.713568 | − | 0.700586i | \(-0.247078\pi\) | ||||
0.713568 | + | 0.700586i | \(0.247078\pi\) | |||||||
\(234\) | −57.9347 | −3.78731 | ||||||||
\(235\) | −7.83077 | −0.510823 | ||||||||
\(236\) | −56.6795 | −3.68952 | ||||||||
\(237\) | −35.9208 | −2.33331 | ||||||||
\(238\) | −1.30245 | −0.0844251 | ||||||||
\(239\) | −3.77638 | −0.244274 | −0.122137 | − | 0.992513i | \(-0.538975\pi\) | ||||
−0.122137 | + | 0.992513i | \(0.538975\pi\) | |||||||
\(240\) | −86.0944 | −5.55737 | ||||||||
\(241\) | 8.82310 | 0.568346 | 0.284173 | − | 0.958773i | \(-0.408281\pi\) | ||||
0.284173 | + | 0.958773i | \(0.408281\pi\) | |||||||
\(242\) | −42.4649 | −2.72975 | ||||||||
\(243\) | 45.0544 | 2.89024 | ||||||||
\(244\) | 15.5478 | 0.995346 | ||||||||
\(245\) | 13.1874 | 0.842511 | ||||||||
\(246\) | 98.4800 | 6.27885 | ||||||||
\(247\) | −11.0834 | −0.705218 | ||||||||
\(248\) | 32.6664 | 2.07432 | ||||||||
\(249\) | −28.1941 | −1.78673 | ||||||||
\(250\) | −32.9030 | −2.08097 | ||||||||
\(251\) | −5.13955 | −0.324406 | −0.162203 | − | 0.986757i | \(-0.551860\pi\) | ||||
−0.162203 | + | 0.986757i | \(0.551860\pi\) | |||||||
\(252\) | 8.70182 | 0.548163 | ||||||||
\(253\) | −20.9326 | −1.31602 | ||||||||
\(254\) | −54.5882 | −3.42517 | ||||||||
\(255\) | −14.2565 | −0.892776 | ||||||||
\(256\) | 27.7115 | 1.73197 | ||||||||
\(257\) | −23.8081 | −1.48511 | −0.742555 | − | 0.669785i | \(-0.766386\pi\) | ||||
−0.742555 | + | 0.669785i | \(0.766386\pi\) | |||||||
\(258\) | 49.6017 | 3.08807 | ||||||||
\(259\) | 2.14030 | 0.132992 | ||||||||
\(260\) | −27.8718 | −1.72854 | ||||||||
\(261\) | −27.9120 | −1.72771 | ||||||||
\(262\) | −1.86093 | −0.114968 | ||||||||
\(263\) | −14.7079 | −0.906927 | −0.453464 | − | 0.891275i | \(-0.649812\pi\) | ||||
−0.453464 | + | 0.891275i | \(0.649812\pi\) | |||||||
\(264\) | 153.379 | 9.43980 | ||||||||
\(265\) | 18.5819 | 1.14147 | ||||||||
\(266\) | 2.28817 | 0.140297 | ||||||||
\(267\) | 37.6234 | 2.30251 | ||||||||
\(268\) | 29.9552 | 1.82981 | ||||||||
\(269\) | −32.6396 | −1.99007 | −0.995036 | − | 0.0995109i | \(-0.968272\pi\) | ||||
−0.995036 | + | 0.0995109i | \(0.968272\pi\) | |||||||
\(270\) | 80.3566 | 4.89035 | ||||||||
\(271\) | 2.59250 | 0.157483 | 0.0787417 | − | 0.996895i | \(-0.474910\pi\) | ||||
0.0787417 | + | 0.996895i | \(0.474910\pi\) | |||||||
\(272\) | 31.7154 | 1.92303 | ||||||||
\(273\) | 1.89494 | 0.114687 | ||||||||
\(274\) | −44.4205 | −2.68354 | ||||||||
\(275\) | 7.26063 | 0.437833 | ||||||||
\(276\) | 71.0262 | 4.27528 | ||||||||
\(277\) | 20.8916 | 1.25525 | 0.627626 | − | 0.778515i | \(-0.284027\pi\) | ||||
0.627626 | + | 0.778515i | \(0.284027\pi\) | |||||||
\(278\) | −45.3999 | −2.72290 | ||||||||
\(279\) | −28.0367 | −1.67851 | ||||||||
\(280\) | 3.59922 | 0.215095 | ||||||||
\(281\) | 3.10100 | 0.184990 | 0.0924952 | − | 0.995713i | \(-0.470516\pi\) | ||||
0.0924952 | + | 0.995713i | \(0.470516\pi\) | |||||||
\(282\) | −36.7220 | −2.18676 | ||||||||
\(283\) | −22.7565 | −1.35274 | −0.676368 | − | 0.736564i | \(-0.736447\pi\) | ||||
−0.676368 | + | 0.736564i | \(0.736447\pi\) | |||||||
\(284\) | −50.9039 | −3.02059 | ||||||||
\(285\) | 25.0461 | 1.48360 | ||||||||
\(286\) | 38.5205 | 2.27777 | ||||||||
\(287\) | −2.32366 | −0.137161 | ||||||||
\(288\) | −150.650 | −8.87716 | ||||||||
\(289\) | −11.7482 | −0.691071 | ||||||||
\(290\) | −18.4571 | −1.08384 | ||||||||
\(291\) | −18.5967 | −1.09016 | ||||||||
\(292\) | −30.6774 | −1.79526 | ||||||||
\(293\) | −30.8413 | −1.80177 | −0.900884 | − | 0.434059i | \(-0.857081\pi\) | ||||
−0.900884 | + | 0.434059i | \(0.857081\pi\) | |||||||
\(294\) | 61.8415 | 3.60667 | ||||||||
\(295\) | 20.1210 | 1.17149 | ||||||||
\(296\) | −92.3407 | −5.36720 | ||||||||
\(297\) | −80.7984 | −4.68840 | ||||||||
\(298\) | 14.2658 | 0.826394 | ||||||||
\(299\) | 11.1576 | 0.645263 | ||||||||
\(300\) | −24.6360 | −1.42236 | ||||||||
\(301\) | −1.17037 | −0.0674587 | ||||||||
\(302\) | 28.7580 | 1.65484 | ||||||||
\(303\) | −0.969551 | −0.0556993 | ||||||||
\(304\) | −55.7182 | −3.19566 | ||||||||
\(305\) | −5.51940 | −0.316040 | ||||||||
\(306\) | −48.2284 | −2.75703 | ||||||||
\(307\) | 25.6319 | 1.46289 | 0.731444 | − | 0.681901i | \(-0.238847\pi\) | ||||
0.731444 | + | 0.681901i | \(0.238847\pi\) | |||||||
\(308\) | −5.78580 | −0.329676 | ||||||||
\(309\) | −8.84055 | −0.502921 | ||||||||
\(310\) | −18.5395 | −1.05297 | ||||||||
\(311\) | 19.4166 | 1.10102 | 0.550508 | − | 0.834830i | \(-0.314434\pi\) | ||||
0.550508 | + | 0.834830i | \(0.314434\pi\) | |||||||
\(312\) | −81.7548 | −4.62846 | ||||||||
\(313\) | 15.6980 | 0.887304 | 0.443652 | − | 0.896199i | \(-0.353683\pi\) | ||||
0.443652 | + | 0.896199i | \(0.353683\pi\) | |||||||
\(314\) | −12.1188 | −0.683903 | ||||||||
\(315\) | −3.08911 | −0.174051 | ||||||||
\(316\) | −58.4605 | −3.28866 | ||||||||
\(317\) | −13.8845 | −0.779831 | −0.389915 | − | 0.920851i | \(-0.627496\pi\) | ||||
−0.389915 | + | 0.920851i | \(0.627496\pi\) | |||||||
\(318\) | 87.1386 | 4.88649 | ||||||||
\(319\) | 18.5585 | 1.03908 | ||||||||
\(320\) | −47.1449 | −2.63548 | ||||||||
\(321\) | 1.05029 | 0.0586215 | ||||||||
\(322\) | −2.30350 | −0.128369 | ||||||||
\(323\) | −9.22646 | −0.513374 | ||||||||
\(324\) | 149.709 | 8.31716 | ||||||||
\(325\) | −3.87011 | −0.214675 | ||||||||
\(326\) | −50.3488 | −2.78856 | ||||||||
\(327\) | −13.1670 | −0.728136 | ||||||||
\(328\) | 100.251 | 5.53546 | ||||||||
\(329\) | 0.866465 | 0.0477697 | ||||||||
\(330\) | −87.0484 | −4.79186 | ||||||||
\(331\) | −30.4171 | −1.67187 | −0.835937 | − | 0.548826i | \(-0.815075\pi\) | ||||
−0.835937 | + | 0.548826i | \(0.815075\pi\) | |||||||
\(332\) | −45.8854 | −2.51829 | ||||||||
\(333\) | 79.2534 | 4.34306 | ||||||||
\(334\) | 3.21439 | 0.175884 | ||||||||
\(335\) | −10.6340 | −0.580996 | ||||||||
\(336\) | 9.52624 | 0.519699 | ||||||||
\(337\) | −29.4203 | −1.60262 | −0.801312 | − | 0.598247i | \(-0.795864\pi\) | ||||
−0.801312 | + | 0.598247i | \(0.795864\pi\) | |||||||
\(338\) | 14.6887 | 0.798962 | ||||||||
\(339\) | 31.0661 | 1.68728 | ||||||||
\(340\) | −23.2022 | −1.25832 | ||||||||
\(341\) | 18.6414 | 1.00949 | ||||||||
\(342\) | 84.7287 | 4.58160 | ||||||||
\(343\) | −2.92757 | −0.158074 | ||||||||
\(344\) | 50.4939 | 2.72245 | ||||||||
\(345\) | −25.2140 | −1.35748 | ||||||||
\(346\) | 60.5348 | 3.25437 | ||||||||
\(347\) | 30.3090 | 1.62707 | 0.813536 | − | 0.581515i | \(-0.197540\pi\) | ||||
0.813536 | + | 0.581515i | \(0.197540\pi\) | |||||||
\(348\) | −62.9708 | −3.37559 | ||||||||
\(349\) | 9.41165 | 0.503794 | 0.251897 | − | 0.967754i | \(-0.418946\pi\) | ||||
0.251897 | + | 0.967754i | \(0.418946\pi\) | |||||||
\(350\) | 0.798987 | 0.0427077 | ||||||||
\(351\) | 43.0677 | 2.29878 | ||||||||
\(352\) | 100.167 | 5.33890 | ||||||||
\(353\) | −11.1145 | −0.591568 | −0.295784 | − | 0.955255i | \(-0.595581\pi\) | ||||
−0.295784 | + | 0.955255i | \(0.595581\pi\) | |||||||
\(354\) | 94.3563 | 5.01498 | ||||||||
\(355\) | 18.0707 | 0.959091 | ||||||||
\(356\) | 61.2315 | 3.24526 | ||||||||
\(357\) | 1.57746 | 0.0834882 | ||||||||
\(358\) | 49.5644 | 2.61956 | ||||||||
\(359\) | 34.8111 | 1.83726 | 0.918631 | − | 0.395117i | \(-0.129296\pi\) | ||||
0.918631 | + | 0.395117i | \(0.129296\pi\) | |||||||
\(360\) | 133.276 | 7.02424 | ||||||||
\(361\) | −2.79074 | −0.146881 | ||||||||
\(362\) | 33.1881 | 1.74433 | ||||||||
\(363\) | 51.4316 | 2.69946 | ||||||||
\(364\) | 3.08398 | 0.161645 | ||||||||
\(365\) | 10.8903 | 0.570026 | ||||||||
\(366\) | −25.8829 | −1.35292 | ||||||||
\(367\) | −18.8522 | −0.984078 | −0.492039 | − | 0.870573i | \(-0.663748\pi\) | ||||
−0.492039 | + | 0.870573i | \(0.663748\pi\) | |||||||
\(368\) | 56.0917 | 2.92398 | ||||||||
\(369\) | −86.0429 | −4.47922 | ||||||||
\(370\) | 52.4071 | 2.72451 | ||||||||
\(371\) | −2.05606 | −0.106745 | ||||||||
\(372\) | −63.2520 | −3.27946 | ||||||||
\(373\) | −36.6470 | −1.89751 | −0.948755 | − | 0.316012i | \(-0.897656\pi\) | ||||
−0.948755 | + | 0.316012i | \(0.897656\pi\) | |||||||
\(374\) | 32.0668 | 1.65813 | ||||||||
\(375\) | 39.8506 | 2.05788 | ||||||||
\(376\) | −37.3825 | −1.92786 | ||||||||
\(377\) | −9.89220 | −0.509474 | ||||||||
\(378\) | −8.89136 | −0.457322 | ||||||||
\(379\) | 32.8260 | 1.68616 | 0.843080 | − | 0.537789i | \(-0.180740\pi\) | ||||
0.843080 | + | 0.537789i | \(0.180740\pi\) | |||||||
\(380\) | 40.7622 | 2.09105 | ||||||||
\(381\) | 66.1147 | 3.38716 | ||||||||
\(382\) | −13.1512 | −0.672876 | ||||||||
\(383\) | 12.3381 | 0.630446 | 0.315223 | − | 0.949018i | \(-0.397921\pi\) | ||||
0.315223 | + | 0.949018i | \(0.397921\pi\) | |||||||
\(384\) | −93.8000 | −4.78671 | ||||||||
\(385\) | 2.05393 | 0.104678 | ||||||||
\(386\) | 24.2933 | 1.23650 | ||||||||
\(387\) | −43.3375 | −2.20297 | ||||||||
\(388\) | −30.2658 | −1.53651 | ||||||||
\(389\) | 9.17177 | 0.465027 | 0.232514 | − | 0.972593i | \(-0.425305\pi\) | ||||
0.232514 | + | 0.972593i | \(0.425305\pi\) | |||||||
\(390\) | 46.3991 | 2.34951 | ||||||||
\(391\) | 9.28830 | 0.469729 | ||||||||
\(392\) | 62.9539 | 3.17965 | ||||||||
\(393\) | 2.25387 | 0.113693 | ||||||||
\(394\) | 1.63183 | 0.0822104 | ||||||||
\(395\) | 20.7532 | 1.04421 | ||||||||
\(396\) | −214.242 | −10.7661 | ||||||||
\(397\) | 12.5377 | 0.629248 | 0.314624 | − | 0.949216i | \(-0.398122\pi\) | ||||
0.314624 | + | 0.949216i | \(0.398122\pi\) | |||||||
\(398\) | 42.8529 | 2.14802 | ||||||||
\(399\) | −2.77132 | −0.138740 | ||||||||
\(400\) | −19.4558 | −0.972790 | ||||||||
\(401\) | 23.7631 | 1.18667 | 0.593337 | − | 0.804954i | \(-0.297810\pi\) | ||||
0.593337 | + | 0.804954i | \(0.297810\pi\) | |||||||
\(402\) | −49.8674 | −2.48716 | ||||||||
\(403\) | −9.93638 | −0.494966 | ||||||||
\(404\) | −1.57793 | −0.0785049 | ||||||||
\(405\) | −53.1459 | −2.64084 | ||||||||
\(406\) | 2.04225 | 0.101355 | ||||||||
\(407\) | −52.6952 | −2.61200 | ||||||||
\(408\) | −68.0577 | −3.36936 | ||||||||
\(409\) | 16.2292 | 0.802481 | 0.401240 | − | 0.915973i | \(-0.368579\pi\) | ||||
0.401240 | + | 0.915973i | \(0.368579\pi\) | |||||||
\(410\) | −56.8967 | −2.80993 | ||||||||
\(411\) | 53.8000 | 2.65376 | ||||||||
\(412\) | −14.3879 | −0.708839 | ||||||||
\(413\) | −2.22636 | −0.109552 | ||||||||
\(414\) | −85.2965 | −4.19210 | ||||||||
\(415\) | 16.2891 | 0.799602 | ||||||||
\(416\) | −53.3915 | −2.61773 | ||||||||
\(417\) | 54.9862 | 2.69269 | ||||||||
\(418\) | −56.3357 | −2.75547 | ||||||||
\(419\) | 1.41667 | 0.0692089 | 0.0346045 | − | 0.999401i | \(-0.488983\pi\) | ||||
0.0346045 | + | 0.999401i | \(0.488983\pi\) | |||||||
\(420\) | −6.96917 | −0.340061 | ||||||||
\(421\) | −22.1382 | −1.07895 | −0.539475 | − | 0.842002i | \(-0.681377\pi\) | ||||
−0.539475 | + | 0.842002i | \(0.681377\pi\) | |||||||
\(422\) | 44.6786 | 2.17492 | ||||||||
\(423\) | 32.0843 | 1.55999 | ||||||||
\(424\) | 88.7061 | 4.30795 | ||||||||
\(425\) | −3.22172 | −0.156276 | ||||||||
\(426\) | 84.7413 | 4.10573 | ||||||||
\(427\) | 0.610714 | 0.0295545 | ||||||||
\(428\) | 1.70933 | 0.0826236 | ||||||||
\(429\) | −46.6542 | −2.25249 | ||||||||
\(430\) | −28.6573 | −1.38198 | ||||||||
\(431\) | −9.06906 | −0.436841 | −0.218421 | − | 0.975855i | \(-0.570090\pi\) | ||||
−0.218421 | + | 0.975855i | \(0.570090\pi\) | |||||||
\(432\) | 216.510 | 10.4168 | ||||||||
\(433\) | −18.0098 | −0.865496 | −0.432748 | − | 0.901515i | \(-0.642456\pi\) | ||||
−0.432748 | + | 0.901515i | \(0.642456\pi\) | |||||||
\(434\) | 2.05137 | 0.0984691 | ||||||||
\(435\) | 22.3543 | 1.07181 | ||||||||
\(436\) | −21.4290 | −1.02626 | ||||||||
\(437\) | −16.3179 | −0.780591 | ||||||||
\(438\) | 51.0696 | 2.44020 | ||||||||
\(439\) | −6.81076 | −0.325060 | −0.162530 | − | 0.986704i | \(-0.551965\pi\) | ||||
−0.162530 | + | 0.986704i | \(0.551965\pi\) | |||||||
\(440\) | −88.6143 | −4.22452 | ||||||||
\(441\) | −54.0315 | −2.57293 | ||||||||
\(442\) | −17.0925 | −0.813005 | ||||||||
\(443\) | −5.18584 | −0.246387 | −0.123193 | − | 0.992383i | \(-0.539314\pi\) | ||||
−0.123193 | + | 0.992383i | \(0.539314\pi\) | |||||||
\(444\) | 178.799 | 8.48545 | ||||||||
\(445\) | −21.7369 | −1.03043 | ||||||||
\(446\) | −60.0751 | −2.84464 | ||||||||
\(447\) | −17.2780 | −0.817223 | ||||||||
\(448\) | 5.21653 | 0.246458 | ||||||||
\(449\) | −9.34671 | −0.441099 | −0.220549 | − | 0.975376i | \(-0.570785\pi\) | ||||
−0.220549 | + | 0.975376i | \(0.570785\pi\) | |||||||
\(450\) | 29.5857 | 1.39468 | ||||||||
\(451\) | 57.2095 | 2.69389 | ||||||||
\(452\) | 50.5595 | 2.37812 | ||||||||
\(453\) | −34.8304 | −1.63647 | ||||||||
\(454\) | 38.7888 | 1.82045 | ||||||||
\(455\) | −1.09480 | −0.0513250 | ||||||||
\(456\) | 119.565 | 5.59916 | ||||||||
\(457\) | 27.7641 | 1.29875 | 0.649374 | − | 0.760469i | \(-0.275031\pi\) | ||||
0.649374 | + | 0.760469i | \(0.275031\pi\) | |||||||
\(458\) | 41.2317 | 1.92663 | ||||||||
\(459\) | 35.8522 | 1.67344 | ||||||||
\(460\) | −41.0353 | −1.91328 | ||||||||
\(461\) | −22.1977 | −1.03385 | −0.516924 | − | 0.856031i | \(-0.672923\pi\) | ||||
−0.516924 | + | 0.856031i | \(0.672923\pi\) | |||||||
\(462\) | 9.63180 | 0.448112 | ||||||||
\(463\) | −14.5578 | −0.676557 | −0.338278 | − | 0.941046i | \(-0.609845\pi\) | ||||
−0.338278 | + | 0.941046i | \(0.609845\pi\) | |||||||
\(464\) | −49.7300 | −2.30866 | ||||||||
\(465\) | 22.4542 | 1.04129 | ||||||||
\(466\) | −59.0206 | −2.73408 | ||||||||
\(467\) | 25.2113 | 1.16664 | 0.583320 | − | 0.812242i | \(-0.301753\pi\) | ||||
0.583320 | + | 0.812242i | \(0.301753\pi\) | |||||||
\(468\) | 114.197 | 5.27876 | ||||||||
\(469\) | 1.17663 | 0.0543320 | ||||||||
\(470\) | 21.2161 | 0.978625 | ||||||||
\(471\) | 14.6777 | 0.676313 | ||||||||
\(472\) | 96.0536 | 4.42122 | ||||||||
\(473\) | 28.8149 | 1.32491 | ||||||||
\(474\) | 97.3211 | 4.47011 | ||||||||
\(475\) | 5.65998 | 0.259698 | ||||||||
\(476\) | 2.56730 | 0.117672 | ||||||||
\(477\) | −76.1339 | −3.48593 | ||||||||
\(478\) | 10.2314 | 0.467976 | ||||||||
\(479\) | −26.7187 | −1.22081 | −0.610404 | − | 0.792090i | \(-0.708993\pi\) | ||||
−0.610404 | + | 0.792090i | \(0.708993\pi\) | |||||||
\(480\) | 120.654 | 5.50707 | ||||||||
\(481\) | 28.0879 | 1.28070 | ||||||||
\(482\) | −23.9046 | −1.08883 | ||||||||
\(483\) | 2.78990 | 0.126945 | ||||||||
\(484\) | 83.7040 | 3.80473 | ||||||||
\(485\) | 10.7442 | 0.487870 | ||||||||
\(486\) | −122.067 | −5.53707 | ||||||||
\(487\) | 9.58729 | 0.434442 | 0.217221 | − | 0.976122i | \(-0.430301\pi\) | ||||
0.217221 | + | 0.976122i | \(0.430301\pi\) | |||||||
\(488\) | −26.3485 | −1.19274 | ||||||||
\(489\) | 60.9801 | 2.75762 | ||||||||
\(490\) | −35.7289 | −1.61407 | ||||||||
\(491\) | −19.3437 | −0.872969 | −0.436485 | − | 0.899712i | \(-0.643777\pi\) | ||||
−0.436485 | + | 0.899712i | \(0.643777\pi\) | |||||||
\(492\) | −194.117 | −8.75147 | ||||||||
\(493\) | −8.23487 | −0.370880 | ||||||||
\(494\) | 30.0284 | 1.35104 | ||||||||
\(495\) | 76.0551 | 3.41842 | ||||||||
\(496\) | −49.9521 | −2.24292 | ||||||||
\(497\) | −1.99950 | −0.0896896 | ||||||||
\(498\) | 76.3870 | 3.42298 | ||||||||
\(499\) | −0.905302 | −0.0405269 | −0.0202634 | − | 0.999795i | \(-0.506450\pi\) | ||||
−0.0202634 | + | 0.999795i | \(0.506450\pi\) | |||||||
\(500\) | 64.8562 | 2.90046 | ||||||||
\(501\) | −3.89312 | −0.173932 | ||||||||
\(502\) | 13.9247 | 0.621490 | ||||||||
\(503\) | 15.2979 | 0.682098 | 0.341049 | − | 0.940045i | \(-0.389218\pi\) | ||||
0.341049 | + | 0.940045i | \(0.389218\pi\) | |||||||
\(504\) | −14.7468 | −0.656874 | ||||||||
\(505\) | 0.560157 | 0.0249267 | ||||||||
\(506\) | 56.7132 | 2.52121 | ||||||||
\(507\) | −17.7903 | −0.790096 | ||||||||
\(508\) | 107.601 | 4.77400 | ||||||||
\(509\) | −14.8703 | −0.659114 | −0.329557 | − | 0.944136i | \(-0.606899\pi\) | ||||
−0.329557 | + | 0.944136i | \(0.606899\pi\) | |||||||
\(510\) | 38.6255 | 1.71036 | ||||||||
\(511\) | −1.20500 | −0.0533061 | ||||||||
\(512\) | −17.9087 | −0.791459 | ||||||||
\(513\) | −62.9859 | −2.78089 | ||||||||
\(514\) | 64.5039 | 2.84515 | ||||||||
\(515\) | 5.10762 | 0.225069 | ||||||||
\(516\) | −97.7715 | −4.30415 | ||||||||
\(517\) | −21.3327 | −0.938212 | ||||||||
\(518\) | −5.79878 | −0.254784 | ||||||||
\(519\) | −73.3169 | −3.21826 | ||||||||
\(520\) | 47.2338 | 2.07134 | ||||||||
\(521\) | −15.2271 | −0.667113 | −0.333556 | − | 0.942730i | \(-0.608249\pi\) | ||||
−0.333556 | + | 0.942730i | \(0.608249\pi\) | |||||||
\(522\) | 75.6226 | 3.30991 | ||||||||
\(523\) | −12.2771 | −0.536840 | −0.268420 | − | 0.963302i | \(-0.586502\pi\) | ||||
−0.268420 | + | 0.963302i | \(0.586502\pi\) | |||||||
\(524\) | 3.66813 | 0.160243 | ||||||||
\(525\) | −0.967696 | −0.0422337 | ||||||||
\(526\) | 39.8484 | 1.73747 | ||||||||
\(527\) | −8.27164 | −0.360318 | ||||||||
\(528\) | −234.540 | −10.2070 | ||||||||
\(529\) | −6.57275 | −0.285772 | ||||||||
\(530\) | −50.3443 | −2.18682 | ||||||||
\(531\) | −82.4400 | −3.57759 | ||||||||
\(532\) | −4.51028 | −0.195546 | ||||||||
\(533\) | −30.4942 | −1.32085 | ||||||||
\(534\) | −101.934 | −4.41111 | ||||||||
\(535\) | −0.606804 | −0.0262344 | ||||||||
\(536\) | −50.7644 | −2.19269 | ||||||||
\(537\) | −60.0301 | −2.59049 | ||||||||
\(538\) | 88.4313 | 3.81254 | ||||||||
\(539\) | 35.9253 | 1.54741 | ||||||||
\(540\) | −158.393 | −6.81617 | ||||||||
\(541\) | −34.0267 | −1.46292 | −0.731462 | − | 0.681882i | \(-0.761162\pi\) | ||||
−0.731462 | + | 0.681882i | \(0.761162\pi\) | |||||||
\(542\) | −7.02393 | −0.301704 | ||||||||
\(543\) | −40.1958 | −1.72497 | ||||||||
\(544\) | −44.4463 | −1.90562 | ||||||||
\(545\) | 7.60721 | 0.325857 | ||||||||
\(546\) | −5.13401 | −0.219715 | ||||||||
\(547\) | −37.5998 | −1.60765 | −0.803826 | − | 0.594865i | \(-0.797205\pi\) | ||||
−0.803826 | + | 0.594865i | \(0.797205\pi\) | |||||||
\(548\) | 87.5586 | 3.74032 | ||||||||
\(549\) | 22.6142 | 0.965149 | ||||||||
\(550\) | −19.6714 | −0.838791 | ||||||||
\(551\) | 14.4672 | 0.616323 | ||||||||
\(552\) | −120.367 | −5.12314 | ||||||||
\(553\) | −2.29632 | −0.0976494 | ||||||||
\(554\) | −56.6020 | −2.40479 | ||||||||
\(555\) | −63.4730 | −2.69428 | ||||||||
\(556\) | 89.4891 | 3.79518 | ||||||||
\(557\) | −6.86733 | −0.290978 | −0.145489 | − | 0.989360i | \(-0.546476\pi\) | ||||
−0.145489 | + | 0.989360i | \(0.546476\pi\) | |||||||
\(558\) | 75.9604 | 3.21566 | ||||||||
\(559\) | −15.3591 | −0.649621 | ||||||||
\(560\) | −5.50378 | −0.232577 | ||||||||
\(561\) | −38.8378 | −1.63973 | ||||||||
\(562\) | −8.40162 | −0.354401 | ||||||||
\(563\) | −0.799100 | −0.0336781 | −0.0168390 | − | 0.999858i | \(-0.505360\pi\) | ||||
−0.0168390 | + | 0.999858i | \(0.505360\pi\) | |||||||
\(564\) | 72.3838 | 3.04791 | ||||||||
\(565\) | −17.9484 | −0.755095 | ||||||||
\(566\) | 61.6548 | 2.59155 | ||||||||
\(567\) | 5.88053 | 0.246959 | ||||||||
\(568\) | 86.2657 | 3.61963 | ||||||||
\(569\) | 7.21890 | 0.302632 | 0.151316 | − | 0.988485i | \(-0.451649\pi\) | ||||
0.151316 | + | 0.988485i | \(0.451649\pi\) | |||||||
\(570\) | −67.8581 | −2.84226 | ||||||||
\(571\) | 18.7072 | 0.782871 | 0.391436 | − | 0.920205i | \(-0.371979\pi\) | ||||
0.391436 | + | 0.920205i | \(0.371979\pi\) | |||||||
\(572\) | −75.9290 | −3.17475 | ||||||||
\(573\) | 15.9282 | 0.665409 | ||||||||
\(574\) | 6.29555 | 0.262771 | ||||||||
\(575\) | −5.69791 | −0.237619 | ||||||||
\(576\) | 193.163 | 8.04845 | ||||||||
\(577\) | 4.96673 | 0.206768 | 0.103384 | − | 0.994642i | \(-0.467033\pi\) | ||||
0.103384 | + | 0.994642i | \(0.467033\pi\) | |||||||
\(578\) | 31.8297 | 1.32394 | ||||||||
\(579\) | −29.4229 | −1.22277 | ||||||||
\(580\) | 36.3813 | 1.51065 | ||||||||
\(581\) | −1.80237 | −0.0747750 | ||||||||
\(582\) | 50.3844 | 2.08850 | ||||||||
\(583\) | 50.6211 | 2.09651 | ||||||||
\(584\) | 51.9883 | 2.15129 | ||||||||
\(585\) | −40.5394 | −1.67610 | ||||||||
\(586\) | 83.5591 | 3.45179 | ||||||||
\(587\) | 26.1577 | 1.07964 | 0.539821 | − | 0.841780i | \(-0.318492\pi\) | ||||
0.539821 | + | 0.841780i | \(0.318492\pi\) | |||||||
\(588\) | −121.898 | −5.02698 | ||||||||
\(589\) | 14.5318 | 0.598773 | ||||||||
\(590\) | −54.5142 | −2.24432 | ||||||||
\(591\) | −1.97640 | −0.0812980 | ||||||||
\(592\) | 141.204 | 5.80343 | ||||||||
\(593\) | 1.93002 | 0.0792565 | 0.0396282 | − | 0.999214i | \(-0.487383\pi\) | ||||
0.0396282 | + | 0.999214i | \(0.487383\pi\) | |||||||
\(594\) | 218.909 | 8.98195 | ||||||||
\(595\) | −0.911378 | −0.0373629 | ||||||||
\(596\) | −28.1197 | −1.15183 | ||||||||
\(597\) | −51.9014 | −2.12418 | ||||||||
\(598\) | −30.2297 | −1.23618 | ||||||||
\(599\) | 42.7468 | 1.74659 | 0.873293 | − | 0.487195i | \(-0.161980\pi\) | ||||
0.873293 | + | 0.487195i | \(0.161980\pi\) | |||||||
\(600\) | 41.7500 | 1.70444 | ||||||||
\(601\) | −7.94266 | −0.323988 | −0.161994 | − | 0.986792i | \(-0.551792\pi\) | ||||
−0.161994 | + | 0.986792i | \(0.551792\pi\) | |||||||
\(602\) | 3.17090 | 0.129236 | ||||||||
\(603\) | 43.5697 | 1.77429 | ||||||||
\(604\) | −56.6859 | −2.30652 | ||||||||
\(605\) | −29.7145 | −1.20807 | ||||||||
\(606\) | 2.62683 | 0.106708 | ||||||||
\(607\) | −5.03411 | −0.204328 | −0.102164 | − | 0.994768i | \(-0.532577\pi\) | ||||
−0.102164 | + | 0.994768i | \(0.532577\pi\) | |||||||
\(608\) | 78.0843 | 3.16674 | ||||||||
\(609\) | −2.47348 | −0.100230 | ||||||||
\(610\) | 14.9538 | 0.605463 | ||||||||
\(611\) | 11.3709 | 0.460018 | ||||||||
\(612\) | 95.0645 | 3.84275 | ||||||||
\(613\) | 22.6503 | 0.914835 | 0.457418 | − | 0.889252i | \(-0.348774\pi\) | ||||
0.457418 | + | 0.889252i | \(0.348774\pi\) | |||||||
\(614\) | −69.4450 | −2.80257 | ||||||||
\(615\) | 68.9106 | 2.77874 | ||||||||
\(616\) | 9.80506 | 0.395057 | ||||||||
\(617\) | −31.8408 | −1.28186 | −0.640931 | − | 0.767598i | \(-0.721452\pi\) | ||||
−0.640931 | + | 0.767598i | \(0.721452\pi\) | |||||||
\(618\) | 23.9519 | 0.963487 | ||||||||
\(619\) | 32.3649 | 1.30086 | 0.650428 | − | 0.759568i | \(-0.274590\pi\) | ||||
0.650428 | + | 0.759568i | \(0.274590\pi\) | |||||||
\(620\) | 36.5438 | 1.46763 | ||||||||
\(621\) | 63.4080 | 2.54448 | ||||||||
\(622\) | −52.6059 | −2.10930 | ||||||||
\(623\) | 2.40516 | 0.0963607 | ||||||||
\(624\) | 125.016 | 5.00465 | ||||||||
\(625\) | −15.9945 | −0.639779 | ||||||||
\(626\) | −42.5310 | −1.69988 | ||||||||
\(627\) | 68.2311 | 2.72489 | ||||||||
\(628\) | 23.8877 | 0.953224 | ||||||||
\(629\) | 23.3821 | 0.932306 | ||||||||
\(630\) | 8.36939 | 0.333445 | ||||||||
\(631\) | −35.1277 | −1.39841 | −0.699206 | − | 0.714920i | \(-0.746463\pi\) | ||||
−0.699206 | + | 0.714920i | \(0.746463\pi\) | |||||||
\(632\) | 99.0718 | 3.94086 | ||||||||
\(633\) | −54.1126 | −2.15078 | ||||||||
\(634\) | 37.6176 | 1.49399 | ||||||||
\(635\) | −38.1977 | −1.51583 | ||||||||
\(636\) | −171.762 | −6.81080 | ||||||||
\(637\) | −19.1491 | −0.758717 | ||||||||
\(638\) | −50.2811 | −1.99065 | ||||||||
\(639\) | −74.0394 | −2.92895 | ||||||||
\(640\) | 54.1929 | 2.14216 | ||||||||
\(641\) | −1.04563 | −0.0413000 | −0.0206500 | − | 0.999787i | \(-0.506574\pi\) | ||||
−0.0206500 | + | 0.999787i | \(0.506574\pi\) | |||||||
\(642\) | −2.84558 | −0.112306 | ||||||||
\(643\) | −34.5026 | −1.36065 | −0.680324 | − | 0.732911i | \(-0.738161\pi\) | ||||
−0.680324 | + | 0.732911i | \(0.738161\pi\) | |||||||
\(644\) | 4.54051 | 0.178921 | ||||||||
\(645\) | 34.7084 | 1.36664 | ||||||||
\(646\) | 24.9975 | 0.983512 | ||||||||
\(647\) | 23.9717 | 0.942423 | 0.471212 | − | 0.882020i | \(-0.343817\pi\) | ||||
0.471212 | + | 0.882020i | \(0.343817\pi\) | |||||||
\(648\) | −253.708 | −9.96660 | ||||||||
\(649\) | 54.8139 | 2.15164 | ||||||||
\(650\) | 10.4854 | 0.411271 | ||||||||
\(651\) | −2.48453 | −0.0973763 | ||||||||
\(652\) | 99.2442 | 3.88670 | ||||||||
\(653\) | 38.0668 | 1.48967 | 0.744835 | − | 0.667249i | \(-0.232528\pi\) | ||||
0.744835 | + | 0.667249i | \(0.232528\pi\) | |||||||
\(654\) | 35.6736 | 1.39495 | ||||||||
\(655\) | −1.30217 | −0.0508800 | ||||||||
\(656\) | −153.300 | −5.98537 | ||||||||
\(657\) | −44.6200 | −1.74079 | ||||||||
\(658\) | −2.34753 | −0.0915164 | ||||||||
\(659\) | −23.5942 | −0.919098 | −0.459549 | − | 0.888152i | \(-0.651989\pi\) | ||||
−0.459549 | + | 0.888152i | \(0.651989\pi\) | |||||||
\(660\) | 171.584 | 6.67890 | ||||||||
\(661\) | 18.1139 | 0.704547 | 0.352274 | − | 0.935897i | \(-0.385409\pi\) | ||||
0.352274 | + | 0.935897i | \(0.385409\pi\) | |||||||
\(662\) | 82.4097 | 3.20294 | ||||||||
\(663\) | 20.7016 | 0.803983 | ||||||||
\(664\) | 77.7610 | 3.01771 | ||||||||
\(665\) | 1.60113 | 0.0620891 | ||||||||
\(666\) | −214.723 | −8.32035 | ||||||||
\(667\) | −14.5642 | −0.563926 | ||||||||
\(668\) | −6.33599 | −0.245147 | ||||||||
\(669\) | 72.7601 | 2.81307 | ||||||||
\(670\) | 28.8108 | 1.11306 | ||||||||
\(671\) | −15.0360 | −0.580460 | ||||||||
\(672\) | −13.3502 | −0.514995 | ||||||||
\(673\) | −23.9047 | −0.921457 | −0.460729 | − | 0.887541i | \(-0.652412\pi\) | ||||
−0.460729 | + | 0.887541i | \(0.652412\pi\) | |||||||
\(674\) | 79.7090 | 3.07027 | ||||||||
\(675\) | −21.9935 | −0.846532 | ||||||||
\(676\) | −28.9534 | −1.11359 | ||||||||
\(677\) | −10.0892 | −0.387758 | −0.193879 | − | 0.981025i | \(-0.562107\pi\) | ||||
−0.193879 | + | 0.981025i | \(0.562107\pi\) | |||||||
\(678\) | −84.1681 | −3.23246 | ||||||||
\(679\) | −1.18883 | −0.0456233 | ||||||||
\(680\) | 39.3203 | 1.50786 | ||||||||
\(681\) | −46.9792 | −1.80025 | ||||||||
\(682\) | −50.5057 | −1.93396 | ||||||||
\(683\) | 29.6675 | 1.13520 | 0.567598 | − | 0.823306i | \(-0.307873\pi\) | ||||
0.567598 | + | 0.823306i | \(0.307873\pi\) | |||||||
\(684\) | −167.011 | −6.38584 | ||||||||
\(685\) | −31.0829 | −1.18762 | ||||||||
\(686\) | 7.93172 | 0.302835 | ||||||||
\(687\) | −49.9379 | −1.90525 | ||||||||
\(688\) | −77.2132 | −2.94373 | ||||||||
\(689\) | −26.9824 | −1.02795 | ||||||||
\(690\) | 68.3128 | 2.60063 | ||||||||
\(691\) | −18.1269 | −0.689581 | −0.344790 | − | 0.938680i | \(-0.612050\pi\) | ||||
−0.344790 | + | 0.938680i | \(0.612050\pi\) | |||||||
\(692\) | −119.322 | −4.53594 | ||||||||
\(693\) | −8.41540 | −0.319675 | ||||||||
\(694\) | −82.1168 | −3.11711 | ||||||||
\(695\) | −31.7682 | −1.20504 | ||||||||
\(696\) | 106.715 | 4.04503 | ||||||||
\(697\) | −25.3852 | −0.961534 | ||||||||
\(698\) | −25.4992 | −0.965159 | ||||||||
\(699\) | 71.4830 | 2.70374 | ||||||||
\(700\) | −1.57491 | −0.0595260 | ||||||||
\(701\) | 4.53335 | 0.171222 | 0.0856112 | − | 0.996329i | \(-0.472716\pi\) | ||||
0.0856112 | + | 0.996329i | \(0.472716\pi\) | |||||||
\(702\) | −116.684 | −4.40397 | ||||||||
\(703\) | −41.0782 | −1.54929 | ||||||||
\(704\) | −128.433 | −4.84050 | ||||||||
\(705\) | −25.6959 | −0.967764 | ||||||||
\(706\) | 30.1129 | 1.13331 | ||||||||
\(707\) | −0.0619807 | −0.00233102 | ||||||||
\(708\) | −185.989 | −6.98988 | ||||||||
\(709\) | 30.4848 | 1.14488 | 0.572441 | − | 0.819946i | \(-0.305997\pi\) | ||||
0.572441 | + | 0.819946i | \(0.305997\pi\) | |||||||
\(710\) | −48.9592 | −1.83741 | ||||||||
\(711\) | −85.0304 | −3.18889 | ||||||||
\(712\) | −103.768 | −3.88885 | ||||||||
\(713\) | −14.6292 | −0.547868 | ||||||||
\(714\) | −4.27386 | −0.159945 | ||||||||
\(715\) | 26.9544 | 1.00804 | ||||||||
\(716\) | −97.6980 | −3.65115 | ||||||||
\(717\) | −12.3919 | −0.462782 | ||||||||
\(718\) | −94.3146 | −3.51979 | ||||||||
\(719\) | 21.6069 | 0.805802 | 0.402901 | − | 0.915243i | \(-0.368002\pi\) | ||||
0.402901 | + | 0.915243i | \(0.368002\pi\) | |||||||
\(720\) | −203.800 | −7.59516 | ||||||||
\(721\) | −0.565152 | −0.0210474 | ||||||||
\(722\) | 7.56102 | 0.281392 | ||||||||
\(723\) | 28.9522 | 1.07674 | ||||||||
\(724\) | −65.4181 | −2.43124 | ||||||||
\(725\) | 5.05168 | 0.187615 | ||||||||
\(726\) | −139.345 | −5.17157 | ||||||||
\(727\) | −24.8759 | −0.922597 | −0.461299 | − | 0.887245i | \(-0.652616\pi\) | ||||
−0.461299 | + | 0.887245i | \(0.652616\pi\) | |||||||
\(728\) | −5.22636 | −0.193702 | ||||||||
\(729\) | 63.7426 | 2.36084 | ||||||||
\(730\) | −29.5054 | −1.09204 | ||||||||
\(731\) | −12.7858 | −0.472902 | ||||||||
\(732\) | 51.0186 | 1.88570 | ||||||||
\(733\) | −40.7721 | −1.50595 | −0.752976 | − | 0.658048i | \(-0.771383\pi\) | ||||
−0.752976 | + | 0.658048i | \(0.771383\pi\) | |||||||
\(734\) | 51.0768 | 1.88528 | ||||||||
\(735\) | 43.2731 | 1.59615 | ||||||||
\(736\) | −78.6076 | −2.89752 | ||||||||
\(737\) | −28.9692 | −1.06710 | ||||||||
\(738\) | 233.118 | 8.58120 | ||||||||
\(739\) | 21.5673 | 0.793364 | 0.396682 | − | 0.917956i | \(-0.370162\pi\) | ||||
0.396682 | + | 0.917956i | \(0.370162\pi\) | |||||||
\(740\) | −103.301 | −3.79743 | ||||||||
\(741\) | −36.3690 | −1.33605 | ||||||||
\(742\) | 5.57053 | 0.204501 | ||||||||
\(743\) | 41.4941 | 1.52227 | 0.761136 | − | 0.648593i | \(-0.224642\pi\) | ||||
0.761136 | + | 0.648593i | \(0.224642\pi\) | |||||||
\(744\) | 107.192 | 3.92984 | ||||||||
\(745\) | 9.98237 | 0.365726 | ||||||||
\(746\) | 99.2886 | 3.63521 | ||||||||
\(747\) | −66.7401 | −2.44189 | ||||||||
\(748\) | −63.2079 | −2.31111 | ||||||||
\(749\) | 0.0671421 | 0.00245332 | ||||||||
\(750\) | −107.968 | −3.94244 | ||||||||
\(751\) | −2.04360 | −0.0745721 | −0.0372860 | − | 0.999305i | \(-0.511871\pi\) | ||||
−0.0372860 | + | 0.999305i | \(0.511871\pi\) | |||||||
\(752\) | 57.1638 | 2.08455 | ||||||||
\(753\) | −16.8650 | −0.614593 | ||||||||
\(754\) | 26.8012 | 0.976041 | ||||||||
\(755\) | 20.1232 | 0.732359 | ||||||||
\(756\) | 17.5260 | 0.637416 | ||||||||
\(757\) | −22.3884 | −0.813720 | −0.406860 | − | 0.913490i | \(-0.633376\pi\) | ||||
−0.406860 | + | 0.913490i | \(0.633376\pi\) | |||||||
\(758\) | −88.9363 | −3.23031 | ||||||||
\(759\) | −68.6884 | −2.49323 | ||||||||
\(760\) | −69.0787 | −2.50575 | ||||||||
\(761\) | −0.615377 | −0.0223074 | −0.0111537 | − | 0.999938i | \(-0.503550\pi\) | ||||
−0.0111537 | + | 0.999938i | \(0.503550\pi\) | |||||||
\(762\) | −179.126 | −6.48905 | ||||||||
\(763\) | −0.841728 | −0.0304726 | ||||||||
\(764\) | 25.9228 | 0.937855 | ||||||||
\(765\) | −33.7475 | −1.22014 | ||||||||
\(766\) | −33.4278 | −1.20780 | ||||||||
\(767\) | −29.2173 | −1.05498 | ||||||||
\(768\) | 90.9325 | 3.28125 | ||||||||
\(769\) | 52.3955 | 1.88943 | 0.944714 | − | 0.327894i | \(-0.106339\pi\) | ||||
0.944714 | + | 0.327894i | \(0.106339\pi\) | |||||||
\(770\) | −5.56477 | −0.200540 | ||||||||
\(771\) | −78.1242 | −2.81357 | ||||||||
\(772\) | −47.8853 | −1.72343 | ||||||||
\(773\) | 29.1928 | 1.04999 | 0.524997 | − | 0.851104i | \(-0.324067\pi\) | ||||
0.524997 | + | 0.851104i | \(0.324067\pi\) | |||||||
\(774\) | 117.415 | 4.22041 | ||||||||
\(775\) | 5.07425 | 0.182272 | ||||||||
\(776\) | 51.2907 | 1.84123 | ||||||||
\(777\) | 7.02321 | 0.251956 | ||||||||
\(778\) | −24.8493 | −0.890890 | ||||||||
\(779\) | 44.5973 | 1.59786 | ||||||||
\(780\) | −91.4588 | −3.27475 | ||||||||
\(781\) | 49.2284 | 1.76153 | ||||||||
\(782\) | −25.1650 | −0.899899 | ||||||||
\(783\) | −56.2166 | −2.00902 | ||||||||
\(784\) | −96.2665 | −3.43809 | ||||||||
\(785\) | −8.48004 | −0.302666 | ||||||||
\(786\) | −6.10645 | −0.217810 | ||||||||
\(787\) | 32.4773 | 1.15769 | 0.578845 | − | 0.815438i | \(-0.303504\pi\) | ||||
0.578845 | + | 0.815438i | \(0.303504\pi\) | |||||||
\(788\) | −3.21655 | −0.114585 | ||||||||
\(789\) | −48.2625 | −1.71819 | ||||||||
\(790\) | −56.2272 | −2.00047 | ||||||||
\(791\) | 1.98597 | 0.0706129 | ||||||||
\(792\) | 363.072 | 12.9012 | ||||||||
\(793\) | 8.01461 | 0.284607 | ||||||||
\(794\) | −33.9686 | −1.20550 | ||||||||
\(795\) | 60.9746 | 2.16255 | ||||||||
\(796\) | −84.4687 | −2.99391 | ||||||||
\(797\) | −6.58537 | −0.233266 | −0.116633 | − | 0.993175i | \(-0.537210\pi\) | ||||
−0.116633 | + | 0.993175i | \(0.537210\pi\) | |||||||
\(798\) | 7.50841 | 0.265795 | ||||||||
\(799\) | 9.46583 | 0.334877 | ||||||||
\(800\) | 27.2656 | 0.963986 | ||||||||
\(801\) | 89.0607 | 3.14681 | ||||||||
\(802\) | −64.3820 | −2.27341 | ||||||||
\(803\) | 29.6676 | 1.04695 | ||||||||
\(804\) | 98.2952 | 3.46660 | ||||||||
\(805\) | −1.61186 | −0.0568106 | ||||||||
\(806\) | 26.9209 | 0.948247 | ||||||||
\(807\) | −107.104 | −3.77023 | ||||||||
\(808\) | 2.67408 | 0.0940738 | ||||||||
\(809\) | −25.4573 | −0.895030 | −0.447515 | − | 0.894276i | \(-0.647691\pi\) | ||||
−0.447515 | + | 0.894276i | \(0.647691\pi\) | |||||||
\(810\) | 143.990 | 5.05928 | ||||||||
\(811\) | −1.06088 | −0.0372524 | −0.0186262 | − | 0.999827i | \(-0.505929\pi\) | ||||
−0.0186262 | + | 0.999827i | \(0.505929\pi\) | |||||||
\(812\) | −4.02555 | −0.141269 | ||||||||
\(813\) | 8.50706 | 0.298356 | ||||||||
\(814\) | 142.768 | 5.00403 | ||||||||
\(815\) | −35.2312 | −1.23410 | ||||||||
\(816\) | 104.071 | 3.64321 | ||||||||
\(817\) | 22.4625 | 0.785862 | ||||||||
\(818\) | −43.9701 | −1.53738 | ||||||||
\(819\) | 4.48563 | 0.156741 | ||||||||
\(820\) | 112.151 | 3.91648 | ||||||||
\(821\) | 38.7114 | 1.35104 | 0.675519 | − | 0.737342i | \(-0.263919\pi\) | ||||
0.675519 | + | 0.737342i | \(0.263919\pi\) | |||||||
\(822\) | −145.762 | −5.08402 | ||||||||
\(823\) | −9.58475 | −0.334103 | −0.167052 | − | 0.985948i | \(-0.553425\pi\) | ||||
−0.167052 | + | 0.985948i | \(0.553425\pi\) | |||||||
\(824\) | 24.3828 | 0.849414 | ||||||||
\(825\) | 23.8251 | 0.829483 | ||||||||
\(826\) | 6.03193 | 0.209878 | ||||||||
\(827\) | 21.5016 | 0.747684 | 0.373842 | − | 0.927492i | \(-0.378040\pi\) | ||||
0.373842 | + | 0.927492i | \(0.378040\pi\) | |||||||
\(828\) | 168.131 | 5.84295 | ||||||||
\(829\) | 12.3253 | 0.428076 | 0.214038 | − | 0.976825i | \(-0.431338\pi\) | ||||
0.214038 | + | 0.976825i | \(0.431338\pi\) | |||||||
\(830\) | −44.1325 | −1.53186 | ||||||||
\(831\) | 68.5537 | 2.37810 | ||||||||
\(832\) | 68.4582 | 2.37336 | ||||||||
\(833\) | −15.9409 | −0.552320 | ||||||||
\(834\) | −148.975 | −5.15859 | ||||||||
\(835\) | 2.24925 | 0.0778384 | ||||||||
\(836\) | 111.045 | 3.84057 | ||||||||
\(837\) | −56.4677 | −1.95181 | ||||||||
\(838\) | −3.83822 | −0.132589 | ||||||||
\(839\) | −39.2827 | −1.35619 | −0.678095 | − | 0.734975i | \(-0.737194\pi\) | ||||
−0.678095 | + | 0.734975i | \(0.737194\pi\) | |||||||
\(840\) | 11.8105 | 0.407501 | ||||||||
\(841\) | −16.0876 | −0.554746 | ||||||||
\(842\) | 59.9795 | 2.06703 | ||||||||
\(843\) | 10.1757 | 0.350468 | ||||||||
\(844\) | −88.0673 | −3.03140 | ||||||||
\(845\) | 10.2783 | 0.353586 | ||||||||
\(846\) | −86.9269 | −2.98861 | ||||||||
\(847\) | 3.28788 | 0.112973 | ||||||||
\(848\) | −135.646 | −4.65809 | ||||||||
\(849\) | −74.6734 | −2.56279 | ||||||||
\(850\) | 8.72867 | 0.299391 | ||||||||
\(851\) | 41.3535 | 1.41758 | ||||||||
\(852\) | −167.036 | −5.72257 | ||||||||
\(853\) | −47.0050 | −1.60942 | −0.804710 | − | 0.593668i | \(-0.797679\pi\) | ||||
−0.804710 | + | 0.593668i | \(0.797679\pi\) | |||||||
\(854\) | −1.65462 | −0.0566200 | ||||||||
\(855\) | 59.2883 | 2.02762 | ||||||||
\(856\) | −2.89676 | −0.0990093 | ||||||||
\(857\) | −6.82617 | −0.233177 | −0.116589 | − | 0.993180i | \(-0.537196\pi\) | ||||
−0.116589 | + | 0.993180i | \(0.537196\pi\) | |||||||
\(858\) | 126.401 | 4.31527 | ||||||||
\(859\) | 28.5434 | 0.973887 | 0.486943 | − | 0.873434i | \(-0.338112\pi\) | ||||
0.486943 | + | 0.873434i | \(0.338112\pi\) | |||||||
\(860\) | 56.4874 | 1.92620 | ||||||||
\(861\) | −7.62488 | −0.259855 | ||||||||
\(862\) | 24.5710 | 0.836892 | ||||||||
\(863\) | 3.32469 | 0.113174 | 0.0565870 | − | 0.998398i | \(-0.481978\pi\) | ||||
0.0565870 | + | 0.998398i | \(0.481978\pi\) | |||||||
\(864\) | −303.420 | −10.3226 | ||||||||
\(865\) | 42.3588 | 1.44024 | ||||||||
\(866\) | 48.7944 | 1.65810 | ||||||||
\(867\) | −38.5506 | −1.30925 | ||||||||
\(868\) | −4.04353 | −0.137246 | ||||||||
\(869\) | 56.5363 | 1.91786 | ||||||||
\(870\) | −60.5651 | −2.05335 | ||||||||
\(871\) | 15.4414 | 0.523211 | ||||||||
\(872\) | 36.3153 | 1.22979 | ||||||||
\(873\) | −44.0214 | −1.48990 | ||||||||
\(874\) | 44.2104 | 1.49544 | ||||||||
\(875\) | 2.54754 | 0.0861225 | ||||||||
\(876\) | −100.665 | −3.40115 | ||||||||
\(877\) | 2.00812 | 0.0678093 | 0.0339046 | − | 0.999425i | \(-0.489206\pi\) | ||||
0.0339046 | + | 0.999425i | \(0.489206\pi\) | |||||||
\(878\) | 18.4526 | 0.622744 | ||||||||
\(879\) | −101.203 | −3.41349 | ||||||||
\(880\) | 135.505 | 4.56788 | ||||||||
\(881\) | −50.4691 | −1.70035 | −0.850174 | − | 0.526501i | \(-0.823504\pi\) | ||||
−0.850174 | + | 0.526501i | \(0.823504\pi\) | |||||||
\(882\) | 146.389 | 4.92917 | ||||||||
\(883\) | 48.5004 | 1.63217 | 0.816085 | − | 0.577932i | \(-0.196140\pi\) | ||||
0.816085 | + | 0.577932i | \(0.196140\pi\) | |||||||
\(884\) | 33.6915 | 1.13317 | ||||||||
\(885\) | 66.0251 | 2.21941 | ||||||||
\(886\) | 14.0501 | 0.472023 | ||||||||
\(887\) | 4.20922 | 0.141332 | 0.0706659 | − | 0.997500i | \(-0.477488\pi\) | ||||
0.0706659 | + | 0.997500i | \(0.477488\pi\) | |||||||
\(888\) | −303.007 | −10.1683 | ||||||||
\(889\) | 4.22653 | 0.141753 | ||||||||
\(890\) | 58.8923 | 1.97407 | ||||||||
\(891\) | −144.781 | −4.85035 | ||||||||
\(892\) | 118.416 | 3.96486 | ||||||||
\(893\) | −16.6298 | −0.556495 | ||||||||
\(894\) | 46.8118 | 1.56562 | ||||||||
\(895\) | 34.6823 | 1.15930 | ||||||||
\(896\) | −5.99637 | −0.200325 | ||||||||
\(897\) | 36.6128 | 1.22246 | ||||||||
\(898\) | 25.3233 | 0.845048 | ||||||||
\(899\) | 12.9700 | 0.432575 | ||||||||
\(900\) | −58.3174 | −1.94391 | ||||||||
\(901\) | −22.4618 | −0.748310 | ||||||||
\(902\) | −154.999 | −5.16090 | ||||||||
\(903\) | −3.84044 | −0.127802 | ||||||||
\(904\) | −85.6821 | −2.84975 | ||||||||
\(905\) | 23.2231 | 0.771962 | ||||||||
\(906\) | 94.3668 | 3.13513 | ||||||||
\(907\) | 5.84708 | 0.194149 | 0.0970745 | − | 0.995277i | \(-0.469051\pi\) | ||||
0.0970745 | + | 0.995277i | \(0.469051\pi\) | |||||||
\(908\) | −76.4579 | −2.53734 | ||||||||
\(909\) | −2.29509 | −0.0761232 | ||||||||
\(910\) | 2.96617 | 0.0983275 | ||||||||
\(911\) | 35.3269 | 1.17043 | 0.585216 | − | 0.810877i | \(-0.301010\pi\) | ||||
0.585216 | + | 0.810877i | \(0.301010\pi\) | |||||||
\(912\) | −182.834 | −6.05424 | ||||||||
\(913\) | 44.3751 | 1.46860 | ||||||||
\(914\) | −75.2218 | −2.48812 | ||||||||
\(915\) | −18.1114 | −0.598744 | ||||||||
\(916\) | −81.2731 | −2.68534 | ||||||||
\(917\) | 0.144083 | 0.00475806 | ||||||||
\(918\) | −97.1351 | −3.20594 | ||||||||
\(919\) | −36.4202 | −1.20139 | −0.600696 | − | 0.799477i | \(-0.705110\pi\) | ||||
−0.600696 | + | 0.799477i | \(0.705110\pi\) | |||||||
\(920\) | 69.5417 | 2.29272 | ||||||||
\(921\) | 84.1086 | 2.77147 | ||||||||
\(922\) | 60.1407 | 1.98063 | ||||||||
\(923\) | −26.2400 | −0.863702 | ||||||||
\(924\) | −18.9856 | −0.624579 | ||||||||
\(925\) | −14.3438 | −0.471620 | ||||||||
\(926\) | 39.4417 | 1.29613 | ||||||||
\(927\) | −20.9270 | −0.687334 | ||||||||
\(928\) | 69.6923 | 2.28776 | ||||||||
\(929\) | 5.15251 | 0.169048 | 0.0845242 | − | 0.996421i | \(-0.473063\pi\) | ||||
0.0845242 | + | 0.996421i | \(0.473063\pi\) | |||||||
\(930\) | −60.8356 | −1.99488 | ||||||||
\(931\) | 28.0053 | 0.917838 | ||||||||
\(932\) | 116.337 | 3.81076 | ||||||||
\(933\) | 63.7138 | 2.08590 | ||||||||
\(934\) | −68.3056 | −2.23503 | ||||||||
\(935\) | 22.4385 | 0.733818 | ||||||||
\(936\) | −193.527 | −6.32563 | ||||||||
\(937\) | −26.8558 | −0.877341 | −0.438671 | − | 0.898648i | \(-0.644551\pi\) | ||||
−0.438671 | + | 0.898648i | \(0.644551\pi\) | |||||||
\(938\) | −3.18788 | −0.104088 | ||||||||
\(939\) | 51.5115 | 1.68102 | ||||||||
\(940\) | −41.8197 | −1.36401 | ||||||||
\(941\) | 18.9305 | 0.617118 | 0.308559 | − | 0.951205i | \(-0.400153\pi\) | ||||
0.308559 | + | 0.951205i | \(0.400153\pi\) | |||||||
\(942\) | −39.7667 | −1.29567 | ||||||||
\(943\) | −44.8962 | −1.46202 | ||||||||
\(944\) | −146.881 | −4.78057 | ||||||||
\(945\) | −6.22167 | −0.202391 | ||||||||
\(946\) | −78.0688 | −2.53824 | ||||||||
\(947\) | 21.6729 | 0.704274 | 0.352137 | − | 0.935948i | \(-0.385455\pi\) | ||||
0.352137 | + | 0.935948i | \(0.385455\pi\) | |||||||
\(948\) | −191.833 | −6.23044 | ||||||||
\(949\) | −15.8136 | −0.513332 | ||||||||
\(950\) | −15.3347 | −0.497524 | ||||||||
\(951\) | −45.5607 | −1.47741 | ||||||||
\(952\) | −4.35074 | −0.141008 | ||||||||
\(953\) | 46.3982 | 1.50299 | 0.751493 | − | 0.659741i | \(-0.229334\pi\) | ||||
0.751493 | + | 0.659741i | \(0.229334\pi\) | |||||||
\(954\) | 206.271 | 6.67828 | ||||||||
\(955\) | −9.20248 | −0.297785 | ||||||||
\(956\) | −20.1675 | −0.652264 | ||||||||
\(957\) | 60.8981 | 1.96856 | ||||||||
\(958\) | 72.3896 | 2.33880 | ||||||||
\(959\) | 3.43928 | 0.111060 | ||||||||
\(960\) | −154.702 | −4.99297 | ||||||||
\(961\) | −17.9720 | −0.579743 | ||||||||
\(962\) | −76.0993 | −2.45354 | ||||||||
\(963\) | 2.48621 | 0.0801170 | ||||||||
\(964\) | 47.1192 | 1.51761 | ||||||||
\(965\) | 16.9990 | 0.547219 | ||||||||
\(966\) | −7.55873 | −0.243198 | ||||||||
\(967\) | −22.2626 | −0.715916 | −0.357958 | − | 0.933738i | \(-0.616527\pi\) | ||||
−0.357958 | + | 0.933738i | \(0.616527\pi\) | |||||||
\(968\) | −141.851 | −4.55927 | ||||||||
\(969\) | −30.2758 | −0.972598 | ||||||||
\(970\) | −29.1095 | −0.934651 | ||||||||
\(971\) | 34.7524 | 1.11526 | 0.557629 | − | 0.830091i | \(-0.311711\pi\) | ||||
0.557629 | + | 0.830091i | \(0.311711\pi\) | |||||||
\(972\) | 240.610 | 7.71757 | ||||||||
\(973\) | 3.51511 | 0.112689 | ||||||||
\(974\) | −25.9751 | −0.832295 | ||||||||
\(975\) | −12.6994 | −0.406706 | ||||||||
\(976\) | 40.2910 | 1.28968 | ||||||||
\(977\) | 47.6648 | 1.52493 | 0.762465 | − | 0.647029i | \(-0.223989\pi\) | ||||
0.762465 | + | 0.647029i | \(0.223989\pi\) | |||||||
\(978\) | −165.215 | −5.28299 | ||||||||
\(979\) | −59.2160 | −1.89255 | ||||||||
\(980\) | 70.4263 | 2.24969 | ||||||||
\(981\) | −31.1684 | −0.995130 | ||||||||
\(982\) | 52.4084 | 1.67242 | ||||||||
\(983\) | −10.7104 | −0.341609 | −0.170805 | − | 0.985305i | \(-0.554637\pi\) | ||||
−0.170805 | + | 0.985305i | \(0.554637\pi\) | |||||||
\(984\) | 328.966 | 10.4870 | ||||||||
\(985\) | 1.14186 | 0.0363827 | ||||||||
\(986\) | 22.3109 | 0.710524 | ||||||||
\(987\) | 2.84322 | 0.0905008 | ||||||||
\(988\) | −59.1900 | −1.88308 | ||||||||
\(989\) | −22.6130 | −0.719052 | ||||||||
\(990\) | −206.058 | −6.54895 | ||||||||
\(991\) | 12.9717 | 0.412060 | 0.206030 | − | 0.978546i | \(-0.433946\pi\) | ||||
0.206030 | + | 0.978546i | \(0.433946\pi\) | |||||||
\(992\) | 70.0036 | 2.22262 | ||||||||
\(993\) | −99.8107 | −3.16740 | ||||||||
\(994\) | 5.41728 | 0.171826 | ||||||||
\(995\) | 29.9860 | 0.950620 | ||||||||
\(996\) | −150.569 | −4.77095 | ||||||||
\(997\) | −33.2909 | −1.05433 | −0.527167 | − | 0.849762i | \(-0.676746\pi\) | ||||
−0.527167 | + | 0.849762i | \(0.676746\pi\) | |||||||
\(998\) | 2.45276 | 0.0776406 | ||||||||
\(999\) | 159.622 | 5.05020 |
(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 | 6043.2.a.b.1.12 | ✓ | 243 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6043.2.a.b.1.12 | ✓ | 243 | 1.1 | even | 1 | trivial |