Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.46840000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 11x^{4} + 8x^{3} + 31x^{2} - 15x - 9 \) |
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 | 1.6 | ||
Root | \(-2.38719\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.38719 | 1.68800 | 0.843999 | − | 0.536345i | \(-0.180195\pi\) | ||||
0.843999 | + | 0.536345i | \(0.180195\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.69868 | 1.84934 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.38719 | 0.974566 | ||||||||
\(7\) | 3.31671 | 1.25360 | 0.626799 | − | 0.779181i | \(-0.284365\pi\) | ||||
0.626799 | + | 0.779181i | \(0.284365\pi\) | |||||||
\(8\) | 4.05506 | 1.43368 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.36655 | −1.31656 | −0.658282 | − | 0.752771i | \(-0.728717\pi\) | ||||
−0.658282 | + | 0.752771i | \(0.728717\pi\) | |||||||
\(12\) | 3.69868 | 1.06772 | ||||||||
\(13\) | 5.85502 | 1.62389 | 0.811946 | − | 0.583733i | \(-0.198409\pi\) | ||||
0.811946 | + | 0.583733i | \(0.198409\pi\) | |||||||
\(14\) | 7.91762 | 2.11607 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.28286 | 0.570714 | ||||||||
\(17\) | 0.407830 | 0.0989132 | 0.0494566 | − | 0.998776i | \(-0.484251\pi\) | ||||
0.0494566 | + | 0.998776i | \(0.484251\pi\) | |||||||
\(18\) | 2.38719 | 0.562666 | ||||||||
\(19\) | −6.64447 | −1.52435 | −0.762173 | − | 0.647374i | \(-0.775867\pi\) | ||||
−0.762173 | + | 0.647374i | \(0.775867\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.31671 | 0.723766 | ||||||||
\(22\) | −10.4238 | −2.22236 | ||||||||
\(23\) | 4.61860 | 0.963045 | 0.481523 | − | 0.876434i | \(-0.340084\pi\) | ||||
0.481523 | + | 0.876434i | \(0.340084\pi\) | |||||||
\(24\) | 4.05506 | 0.827736 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 13.9771 | 2.74113 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 12.2674 | 2.31833 | ||||||||
\(29\) | 3.30132 | 0.613040 | 0.306520 | − | 0.951864i | \(-0.400835\pi\) | ||||
0.306520 | + | 0.951864i | \(0.400835\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.77495 | −1.57603 | −0.788014 | − | 0.615658i | \(-0.788890\pi\) | ||||
−0.788014 | + | 0.615658i | \(0.788890\pi\) | |||||||
\(32\) | −2.66052 | −0.470318 | ||||||||
\(33\) | −4.36655 | −0.760119 | ||||||||
\(34\) | 0.973567 | 0.166965 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.69868 | 0.616446 | ||||||||
\(37\) | 3.09911 | 0.509491 | 0.254745 | − | 0.967008i | \(-0.418008\pi\) | ||||
0.254745 | + | 0.967008i | \(0.418008\pi\) | |||||||
\(38\) | −15.8616 | −2.57309 | ||||||||
\(39\) | 5.85502 | 0.937554 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.89349 | 0.451888 | 0.225944 | − | 0.974140i | \(-0.427453\pi\) | ||||
0.225944 | + | 0.974140i | \(0.427453\pi\) | |||||||
\(42\) | 7.91762 | 1.22172 | ||||||||
\(43\) | 1.33270 | 0.203234 | 0.101617 | − | 0.994824i | \(-0.467598\pi\) | ||||
0.101617 | + | 0.994824i | \(0.467598\pi\) | |||||||
\(44\) | −16.1505 | −2.43477 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.0255 | 1.62562 | ||||||||
\(47\) | −11.0609 | −1.61339 | −0.806696 | − | 0.590967i | \(-0.798746\pi\) | ||||
−0.806696 | + | 0.590967i | \(0.798746\pi\) | |||||||
\(48\) | 2.28286 | 0.329502 | ||||||||
\(49\) | 4.00057 | 0.571510 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.407830 | 0.0571076 | ||||||||
\(52\) | 21.6558 | 3.00312 | ||||||||
\(53\) | 2.70021 | 0.370903 | 0.185451 | − | 0.982653i | \(-0.440625\pi\) | ||||
0.185451 | + | 0.982653i | \(0.440625\pi\) | |||||||
\(54\) | 2.38719 | 0.324855 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 13.4495 | 1.79726 | ||||||||
\(57\) | −6.64447 | −0.880081 | ||||||||
\(58\) | 7.88089 | 1.03481 | ||||||||
\(59\) | −5.80518 | −0.755770 | −0.377885 | − | 0.925852i | \(-0.623349\pi\) | ||||
−0.377885 | + | 0.925852i | \(0.623349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2366 | 1.43870 | 0.719352 | − | 0.694646i | \(-0.244439\pi\) | ||||
0.719352 | + | 0.694646i | \(0.244439\pi\) | |||||||
\(62\) | −20.9475 | −2.66033 | ||||||||
\(63\) | 3.31671 | 0.417866 | ||||||||
\(64\) | −10.9169 | −1.36461 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −10.4238 | −1.28308 | ||||||||
\(67\) | −0.0418484 | −0.00511260 | −0.00255630 | − | 0.999997i | \(-0.500814\pi\) | ||||
−0.00255630 | + | 0.999997i | \(0.500814\pi\) | |||||||
\(68\) | 1.50843 | 0.182924 | ||||||||
\(69\) | 4.61860 | 0.556014 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.2062 | −1.92332 | −0.961659 | − | 0.274250i | \(-0.911571\pi\) | ||||
−0.961659 | + | 0.274250i | \(0.911571\pi\) | |||||||
\(72\) | 4.05506 | 0.477894 | ||||||||
\(73\) | 5.35799 | 0.627105 | 0.313553 | − | 0.949571i | \(-0.398481\pi\) | ||||
0.313553 | + | 0.949571i | \(0.398481\pi\) | |||||||
\(74\) | 7.39817 | 0.860019 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −24.5757 | −2.81903 | ||||||||
\(77\) | −14.4826 | −1.65044 | ||||||||
\(78\) | 13.9771 | 1.58259 | ||||||||
\(79\) | −3.55370 | −0.399822 | −0.199911 | − | 0.979814i | \(-0.564065\pi\) | ||||
−0.199911 | + | 0.979814i | \(0.564065\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.90732 | 0.762786 | ||||||||
\(83\) | 4.98952 | 0.547671 | 0.273836 | − | 0.961776i | \(-0.411708\pi\) | ||||
0.273836 | + | 0.961776i | \(0.411708\pi\) | |||||||
\(84\) | 12.2674 | 1.33849 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.18140 | 0.343059 | ||||||||
\(87\) | 3.30132 | 0.353939 | ||||||||
\(88\) | −17.7066 | −1.88753 | ||||||||
\(89\) | −1.94025 | −0.205666 | −0.102833 | − | 0.994699i | \(-0.532791\pi\) | ||||
−0.102833 | + | 0.994699i | \(0.532791\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.4194 | 2.03571 | ||||||||
\(92\) | 17.0827 | 1.78100 | ||||||||
\(93\) | −8.77495 | −0.909920 | ||||||||
\(94\) | −26.4044 | −2.72340 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.66052 | −0.271538 | ||||||||
\(97\) | 5.99258 | 0.608454 | 0.304227 | − | 0.952600i | \(-0.401602\pi\) | ||||
0.304227 | + | 0.952600i | \(0.401602\pi\) | |||||||
\(98\) | 9.55012 | 0.964708 | ||||||||
\(99\) | −4.36655 | −0.438855 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.06181 | 0.503669 | 0.251834 | − | 0.967770i | \(-0.418966\pi\) | ||||
0.251834 | + | 0.967770i | \(0.418966\pi\) | |||||||
\(102\) | 0.973567 | 0.0963975 | ||||||||
\(103\) | 6.90359 | 0.680231 | 0.340115 | − | 0.940384i | \(-0.389534\pi\) | ||||
0.340115 | + | 0.940384i | \(0.389534\pi\) | |||||||
\(104\) | 23.7425 | 2.32814 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.44592 | 0.626083 | ||||||||
\(107\) | −17.2723 | −1.66978 | −0.834890 | − | 0.550417i | \(-0.814469\pi\) | ||||
−0.834890 | + | 0.550417i | \(0.814469\pi\) | |||||||
\(108\) | 3.69868 | 0.355905 | ||||||||
\(109\) | −6.54439 | −0.626839 | −0.313419 | − | 0.949615i | \(-0.601475\pi\) | ||||
−0.313419 | + | 0.949615i | \(0.601475\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.09911 | 0.294155 | ||||||||
\(112\) | 7.57157 | 0.715446 | ||||||||
\(113\) | 8.66993 | 0.815599 | 0.407799 | − | 0.913072i | \(-0.366296\pi\) | ||||
0.407799 | + | 0.913072i | \(0.366296\pi\) | |||||||
\(114\) | −15.8616 | −1.48558 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.2105 | 1.13372 | ||||||||
\(117\) | 5.85502 | 0.541297 | ||||||||
\(118\) | −13.8581 | −1.27574 | ||||||||
\(119\) | 1.35265 | 0.123998 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.06676 | 0.733342 | ||||||||
\(122\) | 26.8240 | 2.42853 | ||||||||
\(123\) | 2.89349 | 0.260898 | ||||||||
\(124\) | −32.4557 | −2.91461 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.91762 | 0.705358 | ||||||||
\(127\) | −3.24595 | −0.288031 | −0.144016 | − | 0.989575i | \(-0.546002\pi\) | ||||
−0.144016 | + | 0.989575i | \(0.546002\pi\) | |||||||
\(128\) | −20.7396 | −1.83314 | ||||||||
\(129\) | 1.33270 | 0.117337 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.40192 | −0.384598 | −0.192299 | − | 0.981336i | \(-0.561594\pi\) | ||||
−0.192299 | + | 0.981336i | \(0.561594\pi\) | |||||||
\(132\) | −16.1505 | −1.40572 | ||||||||
\(133\) | −22.0378 | −1.91092 | ||||||||
\(134\) | −0.0999001 | −0.00863005 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.65378 | 0.141810 | ||||||||
\(137\) | 1.06523 | 0.0910085 | 0.0455042 | − | 0.998964i | \(-0.485511\pi\) | ||||
0.0455042 | + | 0.998964i | \(0.485511\pi\) | |||||||
\(138\) | 11.0255 | 0.938551 | ||||||||
\(139\) | −3.77286 | −0.320010 | −0.160005 | − | 0.987116i | \(-0.551151\pi\) | ||||
−0.160005 | + | 0.987116i | \(0.551151\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.0609 | −0.931492 | ||||||||
\(142\) | −38.6872 | −3.24656 | ||||||||
\(143\) | −25.5663 | −2.13796 | ||||||||
\(144\) | 2.28286 | 0.190238 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.7905 | 1.05855 | ||||||||
\(147\) | 4.00057 | 0.329961 | ||||||||
\(148\) | 11.4626 | 0.942221 | ||||||||
\(149\) | −7.88089 | −0.645627 | −0.322814 | − | 0.946463i | \(-0.604629\pi\) | ||||
−0.322814 | + | 0.946463i | \(0.604629\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.46432 | 0.607437 | 0.303719 | − | 0.952762i | \(-0.401772\pi\) | ||||
0.303719 | + | 0.952762i | \(0.401772\pi\) | |||||||
\(152\) | −26.9437 | −2.18543 | ||||||||
\(153\) | 0.407830 | 0.0329711 | ||||||||
\(154\) | −34.5727 | −2.78595 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 21.6558 | 1.73385 | ||||||||
\(157\) | 0.268958 | 0.0214652 | 0.0107326 | − | 0.999942i | \(-0.496584\pi\) | ||||
0.0107326 | + | 0.999942i | \(0.496584\pi\) | |||||||
\(158\) | −8.48336 | −0.674900 | ||||||||
\(159\) | 2.70021 | 0.214141 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.3186 | 1.20727 | ||||||||
\(162\) | 2.38719 | 0.187555 | ||||||||
\(163\) | 10.3496 | 0.810645 | 0.405322 | − | 0.914174i | \(-0.367159\pi\) | ||||
0.405322 | + | 0.914174i | \(0.367159\pi\) | |||||||
\(164\) | 10.7021 | 0.835693 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.9109 | 0.924468 | ||||||||
\(167\) | −4.26896 | −0.330342 | −0.165171 | − | 0.986265i | \(-0.552818\pi\) | ||||
−0.165171 | + | 0.986265i | \(0.552818\pi\) | |||||||
\(168\) | 13.4495 | 1.03765 | ||||||||
\(169\) | 21.2813 | 1.63702 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.64447 | −0.508115 | ||||||||
\(172\) | 4.92921 | 0.375849 | ||||||||
\(173\) | −23.5031 | −1.78691 | −0.893454 | − | 0.449154i | \(-0.851725\pi\) | ||||
−0.893454 | + | 0.449154i | \(0.851725\pi\) | |||||||
\(174\) | 7.88089 | 0.597448 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.96820 | −0.751382 | ||||||||
\(177\) | −5.80518 | −0.436344 | ||||||||
\(178\) | −4.63175 | −0.347164 | ||||||||
\(179\) | 19.6897 | 1.47168 | 0.735840 | − | 0.677155i | \(-0.236788\pi\) | ||||
0.735840 | + | 0.677155i | \(0.236788\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.8221 | −0.953060 | −0.476530 | − | 0.879158i | \(-0.658106\pi\) | ||||
−0.476530 | + | 0.879158i | \(0.658106\pi\) | |||||||
\(182\) | 46.3578 | 3.43627 | ||||||||
\(183\) | 11.2366 | 0.830636 | ||||||||
\(184\) | 18.7287 | 1.38070 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −20.9475 | −1.53594 | ||||||||
\(187\) | −1.78081 | −0.130226 | ||||||||
\(188\) | −40.9105 | −2.98371 | ||||||||
\(189\) | 3.31671 | 0.241255 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.0583 | −1.37901 | −0.689507 | − | 0.724279i | \(-0.742173\pi\) | ||||
−0.689507 | + | 0.724279i | \(0.742173\pi\) | |||||||
\(192\) | −10.9169 | −0.787857 | ||||||||
\(193\) | 16.9842 | 1.22255 | 0.611275 | − | 0.791418i | \(-0.290657\pi\) | ||||
0.611275 | + | 0.791418i | \(0.290657\pi\) | |||||||
\(194\) | 14.3054 | 1.02707 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.7968 | 1.05692 | ||||||||
\(197\) | −0.469462 | −0.0334478 | −0.0167239 | − | 0.999860i | \(-0.505324\pi\) | ||||
−0.0167239 | + | 0.999860i | \(0.505324\pi\) | |||||||
\(198\) | −10.4238 | −0.740786 | ||||||||
\(199\) | 7.02491 | 0.497983 | 0.248991 | − | 0.968506i | \(-0.419901\pi\) | ||||
0.248991 | + | 0.968506i | \(0.419901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0418484 | −0.00295176 | ||||||||
\(202\) | 12.0835 | 0.850192 | ||||||||
\(203\) | 10.9495 | 0.768507 | ||||||||
\(204\) | 1.50843 | 0.105611 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.4802 | 1.14823 | ||||||||
\(207\) | 4.61860 | 0.321015 | ||||||||
\(208\) | 13.3662 | 0.926777 | ||||||||
\(209\) | 29.0134 | 2.00690 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.7531 | 1.08449 | 0.542243 | − | 0.840222i | \(-0.317575\pi\) | ||||
0.542243 | + | 0.840222i | \(0.317575\pi\) | |||||||
\(212\) | 9.98721 | 0.685925 | ||||||||
\(213\) | −16.2062 | −1.11043 | ||||||||
\(214\) | −41.2323 | −2.81859 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.05506 | 0.275912 | ||||||||
\(217\) | −29.1040 | −1.97571 | ||||||||
\(218\) | −15.6227 | −1.05810 | ||||||||
\(219\) | 5.35799 | 0.362059 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.38785 | 0.160624 | ||||||||
\(222\) | 7.39817 | 0.496532 | ||||||||
\(223\) | −2.27697 | −0.152477 | −0.0762385 | − | 0.997090i | \(-0.524291\pi\) | ||||
−0.0762385 | + | 0.997090i | \(0.524291\pi\) | |||||||
\(224\) | −8.82417 | −0.589590 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.6968 | 1.37673 | ||||||||
\(227\) | −20.2674 | −1.34520 | −0.672599 | − | 0.740007i | \(-0.734822\pi\) | ||||
−0.672599 | + | 0.740007i | \(0.734822\pi\) | |||||||
\(228\) | −24.5757 | −1.62757 | ||||||||
\(229\) | 19.6358 | 1.29757 | 0.648786 | − | 0.760971i | \(-0.275277\pi\) | ||||
0.648786 | + | 0.760971i | \(0.275277\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.4826 | −0.952884 | ||||||||
\(232\) | 13.3871 | 0.878905 | ||||||||
\(233\) | −17.1468 | −1.12333 | −0.561663 | − | 0.827366i | \(-0.689838\pi\) | ||||
−0.561663 | + | 0.827366i | \(0.689838\pi\) | |||||||
\(234\) | 13.9771 | 0.913709 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −21.4715 | −1.39768 | ||||||||
\(237\) | −3.55370 | −0.230838 | ||||||||
\(238\) | 3.22904 | 0.209308 | ||||||||
\(239\) | 21.7654 | 1.40789 | 0.703945 | − | 0.710255i | \(-0.251420\pi\) | ||||
0.703945 | + | 0.710255i | \(0.251420\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.90067 | 0.251264 | 0.125632 | − | 0.992077i | \(-0.459904\pi\) | ||||
0.125632 | + | 0.992077i | \(0.459904\pi\) | |||||||
\(242\) | 19.2569 | 1.23788 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 41.5607 | 2.66065 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.90732 | 0.440395 | ||||||||
\(247\) | −38.9035 | −2.47537 | ||||||||
\(248\) | −35.5830 | −2.25952 | ||||||||
\(249\) | 4.98952 | 0.316198 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.8389 | −1.37846 | −0.689230 | − | 0.724543i | \(-0.742051\pi\) | ||||
−0.689230 | + | 0.724543i | \(0.742051\pi\) | |||||||
\(252\) | 12.2674 | 0.772776 | ||||||||
\(253\) | −20.1674 | −1.26791 | ||||||||
\(254\) | −7.74869 | −0.486196 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.6757 | −1.72973 | ||||||||
\(257\) | 17.1453 | 1.06949 | 0.534747 | − | 0.845012i | \(-0.320407\pi\) | ||||
0.534747 | + | 0.845012i | \(0.320407\pi\) | |||||||
\(258\) | 3.18140 | 0.198065 | ||||||||
\(259\) | 10.2789 | 0.638697 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.30132 | 0.204347 | ||||||||
\(262\) | −10.5082 | −0.649201 | ||||||||
\(263\) | 17.6266 | 1.08690 | 0.543451 | − | 0.839441i | \(-0.317117\pi\) | ||||
0.543451 | + | 0.839441i | \(0.317117\pi\) | |||||||
\(264\) | −17.7066 | −1.08977 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −52.6084 | −3.22563 | ||||||||
\(267\) | −1.94025 | −0.118742 | ||||||||
\(268\) | −0.154784 | −0.00945492 | ||||||||
\(269\) | 1.94772 | 0.118755 | 0.0593773 | − | 0.998236i | \(-0.481088\pi\) | ||||
0.0593773 | + | 0.998236i | \(0.481088\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8707 | −0.842583 | −0.421292 | − | 0.906925i | \(-0.638423\pi\) | ||||
−0.421292 | + | 0.906925i | \(0.638423\pi\) | |||||||
\(272\) | 0.931016 | 0.0564512 | ||||||||
\(273\) | 19.4194 | 1.17532 | ||||||||
\(274\) | 2.54290 | 0.153622 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 17.0827 | 1.02826 | ||||||||
\(277\) | −26.4814 | −1.59111 | −0.795556 | − | 0.605880i | \(-0.792821\pi\) | ||||
−0.795556 | + | 0.605880i | \(0.792821\pi\) | |||||||
\(278\) | −9.00654 | −0.540177 | ||||||||
\(279\) | −8.77495 | −0.525342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.6050 | −1.28885 | −0.644425 | − | 0.764668i | \(-0.722903\pi\) | ||||
−0.644425 | + | 0.764668i | \(0.722903\pi\) | |||||||
\(282\) | −26.4044 | −1.57236 | ||||||||
\(283\) | −2.05287 | −0.122030 | −0.0610151 | − | 0.998137i | \(-0.519434\pi\) | ||||
−0.0610151 | + | 0.998137i | \(0.519434\pi\) | |||||||
\(284\) | −59.9413 | −3.55686 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −61.0315 | −3.60887 | ||||||||
\(287\) | 9.59688 | 0.566486 | ||||||||
\(288\) | −2.66052 | −0.156773 | ||||||||
\(289\) | −16.8337 | −0.990216 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.99258 | 0.351291 | ||||||||
\(292\) | 19.8175 | 1.15973 | ||||||||
\(293\) | 11.9787 | 0.699805 | 0.349902 | − | 0.936786i | \(-0.386215\pi\) | ||||
0.349902 | + | 0.936786i | \(0.386215\pi\) | |||||||
\(294\) | 9.55012 | 0.556974 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.5671 | 0.730447 | ||||||||
\(297\) | −4.36655 | −0.253373 | ||||||||
\(298\) | −18.8132 | −1.08982 | ||||||||
\(299\) | 27.0420 | 1.56388 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.42016 | 0.254774 | ||||||||
\(302\) | 17.8187 | 1.02535 | ||||||||
\(303\) | 5.06181 | 0.290793 | ||||||||
\(304\) | −15.1684 | −0.869965 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.973567 | 0.0556551 | ||||||||
\(307\) | 7.07969 | 0.404059 | 0.202030 | − | 0.979379i | \(-0.435246\pi\) | ||||
0.202030 | + | 0.979379i | \(0.435246\pi\) | |||||||
\(308\) | −53.5664 | −3.05223 | ||||||||
\(309\) | 6.90359 | 0.392732 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.4130 | −0.647171 | −0.323586 | − | 0.946199i | \(-0.604888\pi\) | ||||
−0.323586 | + | 0.946199i | \(0.604888\pi\) | |||||||
\(312\) | 23.7425 | 1.34415 | ||||||||
\(313\) | −11.9077 | −0.673064 | −0.336532 | − | 0.941672i | \(-0.609254\pi\) | ||||
−0.336532 | + | 0.941672i | \(0.609254\pi\) | |||||||
\(314\) | 0.642054 | 0.0362332 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.1440 | −0.739407 | ||||||||
\(317\) | −12.7719 | −0.717340 | −0.358670 | − | 0.933465i | \(-0.616770\pi\) | ||||
−0.358670 | + | 0.933465i | \(0.616770\pi\) | |||||||
\(318\) | 6.44592 | 0.361469 | ||||||||
\(319\) | −14.4154 | −0.807107 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.2723 | −0.964048 | ||||||||
\(322\) | 36.5683 | 2.03787 | ||||||||
\(323\) | −2.70981 | −0.150778 | ||||||||
\(324\) | 3.69868 | 0.205482 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.7065 | 1.36837 | ||||||||
\(327\) | −6.54439 | −0.361906 | ||||||||
\(328\) | 11.7333 | 0.647863 | ||||||||
\(329\) | −36.6857 | −2.02255 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.66041 | 0.476019 | 0.238010 | − | 0.971263i | \(-0.423505\pi\) | ||||
0.238010 | + | 0.971263i | \(0.423505\pi\) | |||||||
\(332\) | 18.4546 | 1.01283 | ||||||||
\(333\) | 3.09911 | 0.169830 | ||||||||
\(334\) | −10.1908 | −0.557617 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.57157 | 0.413063 | ||||||||
\(337\) | 15.2564 | 0.831069 | 0.415534 | − | 0.909577i | \(-0.363595\pi\) | ||||
0.415534 | + | 0.909577i | \(0.363595\pi\) | |||||||
\(338\) | 50.8025 | 2.76329 | ||||||||
\(339\) | 8.66993 | 0.470886 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 38.3163 | 2.07494 | ||||||||
\(342\) | −15.8616 | −0.857697 | ||||||||
\(343\) | −9.94824 | −0.537155 | ||||||||
\(344\) | 5.40416 | 0.291373 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −56.1064 | −3.01630 | ||||||||
\(347\) | 21.8540 | 1.17319 | 0.586593 | − | 0.809882i | \(-0.300469\pi\) | ||||
0.586593 | + | 0.809882i | \(0.300469\pi\) | |||||||
\(348\) | 12.2105 | 0.654553 | ||||||||
\(349\) | 7.29614 | 0.390553 | 0.195277 | − | 0.980748i | \(-0.437440\pi\) | ||||
0.195277 | + | 0.980748i | \(0.437440\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.85502 | 0.312518 | ||||||||
\(352\) | 11.6173 | 0.619203 | ||||||||
\(353\) | 30.5320 | 1.62506 | 0.812528 | − | 0.582923i | \(-0.198091\pi\) | ||||
0.812528 | + | 0.582923i | \(0.198091\pi\) | |||||||
\(354\) | −13.8581 | −0.736548 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.17637 | −0.380347 | ||||||||
\(357\) | 1.35265 | 0.0715900 | ||||||||
\(358\) | 47.0031 | 2.48419 | ||||||||
\(359\) | 3.06747 | 0.161895 | 0.0809473 | − | 0.996718i | \(-0.474205\pi\) | ||||
0.0809473 | + | 0.996718i | \(0.474205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.1489 | 1.32363 | ||||||||
\(362\) | −30.6088 | −1.60876 | ||||||||
\(363\) | 8.06676 | 0.423395 | ||||||||
\(364\) | 71.8261 | 3.76471 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 26.8240 | 1.40211 | ||||||||
\(367\) | 31.6035 | 1.64969 | 0.824845 | − | 0.565358i | \(-0.191262\pi\) | ||||
0.824845 | + | 0.565358i | \(0.191262\pi\) | |||||||
\(368\) | 10.5436 | 0.549623 | ||||||||
\(369\) | 2.89349 | 0.150629 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.95582 | 0.464963 | ||||||||
\(372\) | −32.4557 | −1.68275 | ||||||||
\(373\) | 22.4904 | 1.16451 | 0.582254 | − | 0.813007i | \(-0.302171\pi\) | ||||
0.582254 | + | 0.813007i | \(0.302171\pi\) | |||||||
\(374\) | −4.25113 | −0.219821 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −44.8525 | −2.31309 | ||||||||
\(377\) | 19.3293 | 0.995511 | ||||||||
\(378\) | 7.91762 | 0.407238 | ||||||||
\(379\) | 30.1612 | 1.54928 | 0.774638 | − | 0.632404i | \(-0.217932\pi\) | ||||
0.774638 | + | 0.632404i | \(0.217932\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.24595 | −0.166295 | ||||||||
\(382\) | −45.4959 | −2.32777 | ||||||||
\(383\) | −16.7725 | −0.857034 | −0.428517 | − | 0.903534i | \(-0.640964\pi\) | ||||
−0.428517 | + | 0.903534i | \(0.640964\pi\) | |||||||
\(384\) | −20.7396 | −1.05836 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 40.5445 | 2.06366 | ||||||||
\(387\) | 1.33270 | 0.0677447 | ||||||||
\(388\) | 22.1646 | 1.12524 | ||||||||
\(389\) | 22.4835 | 1.13996 | 0.569980 | − | 0.821659i | \(-0.306951\pi\) | ||||
0.569980 | + | 0.821659i | \(0.306951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.88360 | 0.0952579 | ||||||||
\(392\) | 16.2226 | 0.819363 | ||||||||
\(393\) | −4.40192 | −0.222048 | ||||||||
\(394\) | −1.12069 | −0.0564598 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −16.1505 | −0.811591 | ||||||||
\(397\) | −3.65800 | −0.183590 | −0.0917948 | − | 0.995778i | \(-0.529260\pi\) | ||||
−0.0917948 | + | 0.995778i | \(0.529260\pi\) | |||||||
\(398\) | 16.7698 | 0.840594 | ||||||||
\(399\) | −22.0378 | −1.10327 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.3774 | −1.26729 | −0.633643 | − | 0.773626i | \(-0.718441\pi\) | ||||
−0.633643 | + | 0.773626i | \(0.718441\pi\) | |||||||
\(402\) | −0.0999001 | −0.00498256 | ||||||||
\(403\) | −51.3775 | −2.55930 | ||||||||
\(404\) | 18.7220 | 0.931454 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 26.1386 | 1.29724 | ||||||||
\(407\) | −13.5324 | −0.670777 | ||||||||
\(408\) | 1.65378 | 0.0818741 | ||||||||
\(409\) | −27.8011 | −1.37468 | −0.687339 | − | 0.726337i | \(-0.741221\pi\) | ||||
−0.687339 | + | 0.726337i | \(0.741221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.06523 | 0.0525438 | ||||||||
\(412\) | 25.5341 | 1.25798 | ||||||||
\(413\) | −19.2541 | −0.947433 | ||||||||
\(414\) | 11.0255 | 0.541873 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15.5774 | −0.763745 | ||||||||
\(417\) | −3.77286 | −0.184758 | ||||||||
\(418\) | 69.2605 | 3.38764 | ||||||||
\(419\) | −0.119817 | −0.00585344 | −0.00292672 | − | 0.999996i | \(-0.500932\pi\) | ||||
−0.00292672 | + | 0.999996i | \(0.500932\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0393633 | −0.00191845 | −0.000959225 | − | 1.00000i | \(-0.500305\pi\) | ||||
−0.000959225 | 1.00000i | \(0.500305\pi\) | ||||||||
\(422\) | 37.6056 | 1.83061 | ||||||||
\(423\) | −11.0609 | −0.537797 | ||||||||
\(424\) | 10.9495 | 0.531756 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −38.6872 | −1.87440 | ||||||||
\(427\) | 37.2687 | 1.80356 | ||||||||
\(428\) | −63.8848 | −3.08799 | ||||||||
\(429\) | −25.5663 | −1.23435 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.3869 | 0.789328 | 0.394664 | − | 0.918825i | \(-0.370861\pi\) | ||||
0.394664 | + | 0.918825i | \(0.370861\pi\) | |||||||
\(432\) | 2.28286 | 0.109834 | ||||||||
\(433\) | 17.5610 | 0.843930 | 0.421965 | − | 0.906612i | \(-0.361340\pi\) | ||||
0.421965 | + | 0.906612i | \(0.361340\pi\) | |||||||
\(434\) | −69.4767 | −3.33499 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24.2056 | −1.15924 | ||||||||
\(437\) | −30.6882 | −1.46801 | ||||||||
\(438\) | 12.7905 | 0.611156 | ||||||||
\(439\) | −31.1577 | −1.48708 | −0.743538 | − | 0.668694i | \(-0.766854\pi\) | ||||
−0.743538 | + | 0.668694i | \(0.766854\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.00057 | 0.190503 | ||||||||
\(442\) | 5.70026 | 0.271134 | ||||||||
\(443\) | 13.1787 | 0.626141 | 0.313071 | − | 0.949730i | \(-0.398642\pi\) | ||||
0.313071 | + | 0.949730i | \(0.398642\pi\) | |||||||
\(444\) | 11.4626 | 0.543991 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.43555 | −0.257381 | ||||||||
\(447\) | −7.88089 | −0.372753 | ||||||||
\(448\) | −36.2081 | −1.71067 | ||||||||
\(449\) | −29.2119 | −1.37859 | −0.689297 | − | 0.724479i | \(-0.742080\pi\) | ||||
−0.689297 | + | 0.724479i | \(0.742080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.6346 | −0.594939 | ||||||||
\(452\) | 32.0673 | 1.50832 | ||||||||
\(453\) | 7.46432 | 0.350704 | ||||||||
\(454\) | −48.3822 | −2.27069 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −26.9437 | −1.26176 | ||||||||
\(457\) | −35.8001 | −1.67466 | −0.837330 | − | 0.546698i | \(-0.815885\pi\) | ||||
−0.837330 | + | 0.546698i | \(0.815885\pi\) | |||||||
\(458\) | 46.8745 | 2.19030 | ||||||||
\(459\) | 0.407830 | 0.0190359 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.01315 | 0.280060 | 0.140030 | − | 0.990147i | \(-0.455280\pi\) | ||||
0.140030 | + | 0.990147i | \(0.455280\pi\) | |||||||
\(462\) | −34.5727 | −1.60847 | ||||||||
\(463\) | 41.2139 | 1.91537 | 0.957687 | − | 0.287813i | \(-0.0929281\pi\) | ||||
0.957687 | + | 0.287813i | \(0.0929281\pi\) | |||||||
\(464\) | 7.53644 | 0.349871 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −40.9328 | −1.89617 | ||||||||
\(467\) | 29.9663 | 1.38667 | 0.693337 | − | 0.720614i | \(-0.256140\pi\) | ||||
0.693337 | + | 0.720614i | \(0.256140\pi\) | |||||||
\(468\) | 21.6558 | 1.00104 | ||||||||
\(469\) | −0.138799 | −0.00640914 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.268958 | 0.0123929 | ||||||||
\(472\) | −23.5404 | −1.08353 | ||||||||
\(473\) | −5.81928 | −0.267571 | ||||||||
\(474\) | −8.48336 | −0.389653 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.00303 | 0.229313 | ||||||||
\(477\) | 2.70021 | 0.123634 | ||||||||
\(478\) | 51.9582 | 2.37651 | ||||||||
\(479\) | 8.33937 | 0.381036 | 0.190518 | − | 0.981684i | \(-0.438983\pi\) | ||||
0.190518 | + | 0.981684i | \(0.438983\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1454 | 0.827357 | ||||||||
\(482\) | 9.31165 | 0.424134 | ||||||||
\(483\) | 15.3186 | 0.697019 | ||||||||
\(484\) | 29.8363 | 1.35620 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.38719 | 0.108285 | ||||||||
\(487\) | 4.91110 | 0.222543 | 0.111272 | − | 0.993790i | \(-0.464508\pi\) | ||||
0.111272 | + | 0.993790i | \(0.464508\pi\) | |||||||
\(488\) | 45.5653 | 2.06264 | ||||||||
\(489\) | 10.3496 | 0.468026 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.33484 | 0.195629 | 0.0978144 | − | 0.995205i | \(-0.468815\pi\) | ||||
0.0978144 | + | 0.995205i | \(0.468815\pi\) | |||||||
\(492\) | 10.7021 | 0.482488 | ||||||||
\(493\) | 1.34638 | 0.0606378 | ||||||||
\(494\) | −92.8701 | −4.17842 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.0319 | −0.899461 | ||||||||
\(497\) | −53.7511 | −2.41107 | ||||||||
\(498\) | 11.9109 | 0.533742 | ||||||||
\(499\) | 36.1803 | 1.61965 | 0.809826 | − | 0.586671i | \(-0.199562\pi\) | ||||
0.809826 | + | 0.586671i | \(0.199562\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.26896 | −0.190723 | ||||||||
\(502\) | −52.1336 | −2.32684 | ||||||||
\(503\) | 37.3990 | 1.66754 | 0.833769 | − | 0.552113i | \(-0.186178\pi\) | ||||
0.833769 | + | 0.552113i | \(0.186178\pi\) | |||||||
\(504\) | 13.4495 | 0.599087 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −48.1433 | −2.14023 | ||||||||
\(507\) | 21.2813 | 0.945135 | ||||||||
\(508\) | −12.0057 | −0.532667 | ||||||||
\(509\) | −26.2959 | −1.16555 | −0.582773 | − | 0.812635i | \(-0.698032\pi\) | ||||
−0.582773 | + | 0.812635i | \(0.698032\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.7709 | 0.786138 | ||||||||
\(512\) | −24.5878 | −1.08664 | ||||||||
\(513\) | −6.64447 | −0.293360 | ||||||||
\(514\) | 40.9291 | 1.80530 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.92921 | 0.216996 | ||||||||
\(517\) | 48.2978 | 2.12413 | ||||||||
\(518\) | 24.5376 | 1.07812 | ||||||||
\(519\) | −23.5031 | −1.03167 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.02231 | 0.307653 | 0.153826 | − | 0.988098i | \(-0.450840\pi\) | ||||
0.153826 | + | 0.988098i | \(0.450840\pi\) | |||||||
\(522\) | 7.88089 | 0.344937 | ||||||||
\(523\) | −13.0796 | −0.571933 | −0.285967 | − | 0.958240i | \(-0.592315\pi\) | ||||
−0.285967 | + | 0.958240i | \(0.592315\pi\) | |||||||
\(524\) | −16.2813 | −0.711252 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 42.0780 | 1.83469 | ||||||||
\(527\) | −3.57869 | −0.155890 | ||||||||
\(528\) | −9.96820 | −0.433810 | ||||||||
\(529\) | −1.66851 | −0.0725437 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.80518 | −0.251923 | ||||||||
\(532\) | −81.5106 | −3.53393 | ||||||||
\(533\) | 16.9415 | 0.733817 | ||||||||
\(534\) | −4.63175 | −0.200436 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.169698 | −0.00732984 | ||||||||
\(537\) | 19.6897 | 0.849675 | ||||||||
\(538\) | 4.64958 | 0.200458 | ||||||||
\(539\) | −17.4687 | −0.752430 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.08066 | −0.0894546 | −0.0447273 | − | 0.998999i | \(-0.514242\pi\) | ||||
−0.0447273 | + | 0.998999i | \(0.514242\pi\) | |||||||
\(542\) | −33.1119 | −1.42228 | ||||||||
\(543\) | −12.8221 | −0.550249 | ||||||||
\(544\) | −1.08504 | −0.0465206 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 46.3578 | 1.98393 | ||||||||
\(547\) | 36.9553 | 1.58009 | 0.790046 | − | 0.613047i | \(-0.210056\pi\) | ||||
0.790046 | + | 0.613047i | \(0.210056\pi\) | |||||||
\(548\) | 3.93993 | 0.168305 | ||||||||
\(549\) | 11.2366 | 0.479568 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.9355 | −0.934485 | ||||||||
\(552\) | 18.7287 | 0.797148 | ||||||||
\(553\) | −11.7866 | −0.501217 | ||||||||
\(554\) | −63.2161 | −2.68579 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.9546 | −0.591807 | ||||||||
\(557\) | 2.67455 | 0.113324 | 0.0566621 | − | 0.998393i | \(-0.481954\pi\) | ||||
0.0566621 | + | 0.998393i | \(0.481954\pi\) | |||||||
\(558\) | −20.9475 | −0.886777 | ||||||||
\(559\) | 7.80296 | 0.330030 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.78081 | −0.0751858 | ||||||||
\(562\) | −51.5754 | −2.17557 | ||||||||
\(563\) | −13.8746 | −0.584745 | −0.292372 | − | 0.956305i | \(-0.594445\pi\) | ||||
−0.292372 | + | 0.956305i | \(0.594445\pi\) | |||||||
\(564\) | −40.9105 | −1.72264 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.90058 | −0.205987 | ||||||||
\(567\) | 3.31671 | 0.139289 | ||||||||
\(568\) | −65.7170 | −2.75742 | ||||||||
\(569\) | 33.3404 | 1.39770 | 0.698852 | − | 0.715266i | \(-0.253695\pi\) | ||||
0.698852 | + | 0.715266i | \(0.253695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3794 | 1.48058 | 0.740291 | − | 0.672287i | \(-0.234688\pi\) | ||||
0.740291 | + | 0.672287i | \(0.234688\pi\) | |||||||
\(572\) | −94.5613 | −3.95381 | ||||||||
\(573\) | −19.0583 | −0.796174 | ||||||||
\(574\) | 22.9096 | 0.956227 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10.9169 | −0.454870 | ||||||||
\(577\) | −16.6041 | −0.691239 | −0.345620 | − | 0.938375i | \(-0.612331\pi\) | ||||
−0.345620 | + | 0.938375i | \(0.612331\pi\) | |||||||
\(578\) | −40.1852 | −1.67148 | ||||||||
\(579\) | 16.9842 | 0.705839 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.5488 | 0.686560 | ||||||||
\(582\) | 14.3054 | 0.592979 | ||||||||
\(583\) | −11.7906 | −0.488317 | ||||||||
\(584\) | 21.7270 | 0.899069 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.5955 | 1.18127 | ||||||||
\(587\) | 26.9696 | 1.11315 | 0.556576 | − | 0.830796i | \(-0.312115\pi\) | ||||
0.556576 | + | 0.830796i | \(0.312115\pi\) | |||||||
\(588\) | 14.7968 | 0.610210 | ||||||||
\(589\) | 58.3049 | 2.40241 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.469462 | −0.0193111 | ||||||||
\(592\) | 7.07482 | 0.290773 | ||||||||
\(593\) | −12.7895 | −0.525201 | −0.262600 | − | 0.964905i | \(-0.584580\pi\) | ||||
−0.262600 | + | 0.964905i | \(0.584580\pi\) | |||||||
\(594\) | −10.4238 | −0.427693 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −29.1489 | −1.19398 | ||||||||
\(597\) | 7.02491 | 0.287511 | ||||||||
\(598\) | 64.5545 | 2.63983 | ||||||||
\(599\) | 31.1978 | 1.27471 | 0.637354 | − | 0.770571i | \(-0.280029\pi\) | ||||
0.637354 | + | 0.770571i | \(0.280029\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2310 | 0.784450 | 0.392225 | − | 0.919869i | \(-0.371705\pi\) | ||||
0.392225 | + | 0.919869i | \(0.371705\pi\) | |||||||
\(602\) | 10.5518 | 0.430058 | ||||||||
\(603\) | −0.0418484 | −0.00170420 | ||||||||
\(604\) | 27.6081 | 1.12336 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.0835 | 0.490858 | ||||||||
\(607\) | 8.01104 | 0.325158 | 0.162579 | − | 0.986696i | \(-0.448019\pi\) | ||||
0.162579 | + | 0.986696i | \(0.448019\pi\) | |||||||
\(608\) | 17.6777 | 0.716926 | ||||||||
\(609\) | 10.9495 | 0.443698 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −64.7616 | −2.61997 | ||||||||
\(612\) | 1.50843 | 0.0609747 | ||||||||
\(613\) | −11.3203 | −0.457224 | −0.228612 | − | 0.973518i | \(-0.573419\pi\) | ||||
−0.228612 | + | 0.973518i | \(0.573419\pi\) | |||||||
\(614\) | 16.9006 | 0.682052 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −58.7278 | −2.36621 | ||||||||
\(617\) | 9.71325 | 0.391041 | 0.195520 | − | 0.980700i | \(-0.437360\pi\) | ||||
0.195520 | + | 0.980700i | \(0.437360\pi\) | |||||||
\(618\) | 16.4802 | 0.662930 | ||||||||
\(619\) | 20.4652 | 0.822567 | 0.411284 | − | 0.911507i | \(-0.365081\pi\) | ||||
0.411284 | + | 0.911507i | \(0.365081\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.61860 | 0.185338 | ||||||||
\(622\) | −27.2450 | −1.09242 | ||||||||
\(623\) | −6.43526 | −0.257823 | ||||||||
\(624\) | 13.3662 | 0.535075 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −28.4260 | −1.13613 | ||||||||
\(627\) | 29.0134 | 1.15868 | ||||||||
\(628\) | 0.994789 | 0.0396964 | ||||||||
\(629\) | 1.26391 | 0.0503954 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.46405 | 0.0980924 | 0.0490462 | − | 0.998797i | \(-0.484382\pi\) | ||||
0.0490462 | + | 0.998797i | \(0.484382\pi\) | |||||||
\(632\) | −14.4105 | −0.573218 | ||||||||
\(633\) | 15.7531 | 0.626128 | ||||||||
\(634\) | −30.4889 | −1.21087 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.98721 | 0.396019 | ||||||||
\(637\) | 23.4234 | 0.928070 | ||||||||
\(638\) | −34.4123 | −1.36240 | ||||||||
\(639\) | −16.2062 | −0.641106 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.7217 | 1.25293 | 0.626465 | − | 0.779449i | \(-0.284501\pi\) | ||||
0.626465 | + | 0.779449i | \(0.284501\pi\) | |||||||
\(642\) | −41.2323 | −1.62731 | ||||||||
\(643\) | 11.5574 | 0.455779 | 0.227889 | − | 0.973687i | \(-0.426818\pi\) | ||||
0.227889 | + | 0.973687i | \(0.426818\pi\) | |||||||
\(644\) | 56.6584 | 2.23266 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.46883 | −0.254513 | ||||||||
\(647\) | −6.06222 | −0.238330 | −0.119165 | − | 0.992874i | \(-0.538022\pi\) | ||||
−0.119165 | + | 0.992874i | \(0.538022\pi\) | |||||||
\(648\) | 4.05506 | 0.159298 | ||||||||
\(649\) | 25.3486 | 0.995021 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.1040 | −1.14067 | ||||||||
\(652\) | 38.2799 | 1.49916 | ||||||||
\(653\) | −26.3569 | −1.03143 | −0.515713 | − | 0.856762i | \(-0.672473\pi\) | ||||
−0.515713 | + | 0.856762i | \(0.672473\pi\) | |||||||
\(654\) | −15.6227 | −0.610896 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.60543 | 0.257899 | ||||||||
\(657\) | 5.35799 | 0.209035 | ||||||||
\(658\) | −87.5756 | −3.41405 | ||||||||
\(659\) | 16.2879 | 0.634487 | 0.317243 | − | 0.948344i | \(-0.397243\pi\) | ||||
0.317243 | + | 0.948344i | \(0.397243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.4308 | −0.794665 | −0.397332 | − | 0.917675i | \(-0.630064\pi\) | ||||
−0.397332 | + | 0.917675i | \(0.630064\pi\) | |||||||
\(662\) | 20.6740 | 0.803519 | ||||||||
\(663\) | 2.38785 | 0.0927365 | ||||||||
\(664\) | 20.2328 | 0.785186 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.39817 | 0.286673 | ||||||||
\(667\) | 15.2475 | 0.590386 | ||||||||
\(668\) | −15.7895 | −0.610914 | ||||||||
\(669\) | −2.27697 | −0.0880326 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49.0653 | −1.89415 | ||||||||
\(672\) | −8.82417 | −0.340400 | ||||||||
\(673\) | 20.7479 | 0.799772 | 0.399886 | − | 0.916565i | \(-0.369050\pi\) | ||||
0.399886 | + | 0.916565i | \(0.369050\pi\) | |||||||
\(674\) | 36.4199 | 1.40284 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 78.7126 | 3.02741 | ||||||||
\(677\) | −20.1892 | −0.775935 | −0.387967 | − | 0.921673i | \(-0.626823\pi\) | ||||
−0.387967 | + | 0.921673i | \(0.626823\pi\) | |||||||
\(678\) | 20.6968 | 0.794855 | ||||||||
\(679\) | 19.8756 | 0.762757 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.2674 | −0.776650 | ||||||||
\(682\) | 91.4682 | 3.50250 | ||||||||
\(683\) | 6.69431 | 0.256151 | 0.128075 | − | 0.991764i | \(-0.459120\pi\) | ||||
0.128075 | + | 0.991764i | \(0.459120\pi\) | |||||||
\(684\) | −24.5757 | −0.939677 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −23.7484 | −0.906716 | ||||||||
\(687\) | 19.6358 | 0.749154 | ||||||||
\(688\) | 3.04235 | 0.115989 | ||||||||
\(689\) | 15.8098 | 0.602306 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.86690 | −0.299271 | −0.149635 | − | 0.988741i | \(-0.547810\pi\) | ||||
−0.149635 | + | 0.988741i | \(0.547810\pi\) | |||||||
\(692\) | −86.9304 | −3.30460 | ||||||||
\(693\) | −14.4826 | −0.550148 | ||||||||
\(694\) | 52.1697 | 1.98034 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 13.3871 | 0.507436 | ||||||||
\(697\) | 1.18005 | 0.0446977 | ||||||||
\(698\) | 17.4173 | 0.659254 | ||||||||
\(699\) | −17.1468 | −0.648553 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.5944 | 0.437916 | 0.218958 | − | 0.975734i | \(-0.429734\pi\) | ||||
0.218958 | + | 0.975734i | \(0.429734\pi\) | |||||||
\(702\) | 13.9771 | 0.527530 | ||||||||
\(703\) | −20.5919 | −0.776640 | ||||||||
\(704\) | 47.6691 | 1.79660 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 72.8857 | 2.74309 | ||||||||
\(707\) | 16.7885 | 0.631398 | ||||||||
\(708\) | −21.4715 | −0.806948 | ||||||||
\(709\) | 37.6176 | 1.41276 | 0.706379 | − | 0.707834i | \(-0.250327\pi\) | ||||
0.706379 | + | 0.707834i | \(0.250327\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.55370 | −0.133274 | ||||||||
\(712\) | −7.86785 | −0.294860 | ||||||||
\(713\) | −40.5280 | −1.51779 | ||||||||
\(714\) | 3.22904 | 0.120844 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 72.8260 | 2.72163 | ||||||||
\(717\) | 21.7654 | 0.812845 | ||||||||
\(718\) | 7.32263 | 0.273278 | ||||||||
\(719\) | −21.0855 | −0.786355 | −0.393177 | − | 0.919463i | \(-0.628624\pi\) | ||||
−0.393177 | + | 0.919463i | \(0.628624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.8972 | 0.852737 | ||||||||
\(722\) | 60.0353 | 2.23428 | ||||||||
\(723\) | 3.90067 | 0.145068 | ||||||||
\(724\) | −47.4248 | −1.76253 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 19.2569 | 0.714690 | ||||||||
\(727\) | −26.1113 | −0.968416 | −0.484208 | − | 0.874953i | \(-0.660892\pi\) | ||||
−0.484208 | + | 0.874953i | \(0.660892\pi\) | |||||||
\(728\) | 78.7470 | 2.91856 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.543513 | 0.0201025 | ||||||||
\(732\) | 41.5607 | 1.53613 | ||||||||
\(733\) | −13.4461 | −0.496642 | −0.248321 | − | 0.968678i | \(-0.579879\pi\) | ||||
−0.248321 | + | 0.968678i | \(0.579879\pi\) | |||||||
\(734\) | 75.4436 | 2.78468 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.2879 | −0.452937 | ||||||||
\(737\) | 0.182733 | 0.00673106 | ||||||||
\(738\) | 6.90732 | 0.254262 | ||||||||
\(739\) | −53.9014 | −1.98279 | −0.991397 | − | 0.130887i | \(-0.958218\pi\) | ||||
−0.991397 | + | 0.130887i | \(0.958218\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −38.9035 | −1.42916 | ||||||||
\(742\) | 21.3793 | 0.784857 | ||||||||
\(743\) | −4.33521 | −0.159043 | −0.0795216 | − | 0.996833i | \(-0.525339\pi\) | ||||
−0.0795216 | + | 0.996833i | \(0.525339\pi\) | |||||||
\(744\) | −35.5830 | −1.30454 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 53.6888 | 1.96569 | ||||||||
\(747\) | 4.98952 | 0.182557 | ||||||||
\(748\) | −6.58664 | −0.240831 | ||||||||
\(749\) | −57.2873 | −2.09323 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.87653 | −0.104966 | −0.0524831 | − | 0.998622i | \(-0.516714\pi\) | ||||
−0.0524831 | + | 0.998622i | \(0.516714\pi\) | |||||||
\(752\) | −25.2503 | −0.920785 | ||||||||
\(753\) | −21.8389 | −0.795854 | ||||||||
\(754\) | 46.1428 | 1.68042 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.2674 | 0.446162 | ||||||||
\(757\) | 16.0480 | 0.583275 | 0.291637 | − | 0.956529i | \(-0.405800\pi\) | ||||
0.291637 | + | 0.956529i | \(0.405800\pi\) | |||||||
\(758\) | 72.0005 | 2.61518 | ||||||||
\(759\) | −20.1674 | −0.732029 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.5182 | −1.57753 | −0.788767 | − | 0.614692i | \(-0.789280\pi\) | ||||
−0.788767 | + | 0.614692i | \(0.789280\pi\) | |||||||
\(762\) | −7.74869 | −0.280706 | ||||||||
\(763\) | −21.7058 | −0.785804 | ||||||||
\(764\) | −70.4907 | −2.55026 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40.0391 | −1.44667 | ||||||||
\(767\) | −33.9895 | −1.22729 | ||||||||
\(768\) | −27.6757 | −0.998659 | ||||||||
\(769\) | −25.9575 | −0.936052 | −0.468026 | − | 0.883715i | \(-0.655035\pi\) | ||||
−0.468026 | + | 0.883715i | \(0.655035\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.1453 | 0.617473 | ||||||||
\(772\) | 62.8191 | 2.26091 | ||||||||
\(773\) | 52.9965 | 1.90615 | 0.953076 | − | 0.302731i | \(-0.0978984\pi\) | ||||
0.953076 | + | 0.302731i | \(0.0978984\pi\) | |||||||
\(774\) | 3.18140 | 0.114353 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.3003 | 0.872329 | ||||||||
\(777\) | 10.2789 | 0.368752 | ||||||||
\(778\) | 53.6724 | 1.92425 | ||||||||
\(779\) | −19.2257 | −0.688833 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 70.7650 | 2.53217 | ||||||||
\(782\) | 4.49652 | 0.160795 | ||||||||
\(783\) | 3.30132 | 0.117980 | ||||||||
\(784\) | 9.13272 | 0.326169 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.5082 | −0.374816 | ||||||||
\(787\) | 13.1832 | 0.469929 | 0.234964 | − | 0.972004i | \(-0.424503\pi\) | ||||
0.234964 | + | 0.972004i | \(0.424503\pi\) | |||||||
\(788\) | −1.73639 | −0.0618562 | ||||||||
\(789\) | 17.6266 | 0.627523 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.7557 | 1.02243 | ||||||||
\(792\) | −17.7066 | −0.629178 | ||||||||
\(793\) | 65.7908 | 2.33630 | ||||||||
\(794\) | −8.73233 | −0.309899 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.9829 | 0.920939 | ||||||||
\(797\) | −15.6197 | −0.553280 | −0.276640 | − | 0.960974i | \(-0.589221\pi\) | ||||
−0.276640 | + | 0.960974i | \(0.589221\pi\) | |||||||
\(798\) | −52.6084 | −1.86232 | ||||||||
\(799\) | −4.51095 | −0.159586 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.94025 | −0.0685555 | ||||||||
\(802\) | −60.5806 | −2.13918 | ||||||||
\(803\) | −23.3959 | −0.825625 | ||||||||
\(804\) | −0.154784 | −0.00545880 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −122.648 | −4.32009 | ||||||||
\(807\) | 1.94772 | 0.0685630 | ||||||||
\(808\) | 20.5259 | 0.722100 | ||||||||
\(809\) | 11.7683 | 0.413750 | 0.206875 | − | 0.978367i | \(-0.433671\pi\) | ||||
0.206875 | + | 0.978367i | \(0.433671\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.3050 | −1.34507 | −0.672536 | − | 0.740065i | \(-0.734795\pi\) | ||||
−0.672536 | + | 0.740065i | \(0.734795\pi\) | |||||||
\(812\) | 40.4988 | 1.42123 | ||||||||
\(813\) | −13.8707 | −0.486466 | ||||||||
\(814\) | −32.3045 | −1.13227 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.931016 | 0.0325921 | ||||||||
\(817\) | −8.85505 | −0.309799 | ||||||||
\(818\) | −66.3666 | −2.32045 | ||||||||
\(819\) | 19.4194 | 0.678569 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.4713 | 0.784254 | 0.392127 | − | 0.919911i | \(-0.371739\pi\) | ||||
0.392127 | + | 0.919911i | \(0.371739\pi\) | |||||||
\(822\) | 2.54290 | 0.0886938 | ||||||||
\(823\) | −19.8645 | −0.692434 | −0.346217 | − | 0.938155i | \(-0.612534\pi\) | ||||
−0.346217 | + | 0.938155i | \(0.612534\pi\) | |||||||
\(824\) | 27.9945 | 0.975235 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −45.9632 | −1.59927 | ||||||||
\(827\) | −21.4039 | −0.744288 | −0.372144 | − | 0.928175i | \(-0.621377\pi\) | ||||
−0.372144 | + | 0.928175i | \(0.621377\pi\) | |||||||
\(828\) | 17.0827 | 0.593666 | ||||||||
\(829\) | −24.6676 | −0.856743 | −0.428371 | − | 0.903603i | \(-0.640912\pi\) | ||||
−0.428371 | + | 0.903603i | \(0.640912\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.4814 | −0.918629 | ||||||||
\(832\) | −63.9185 | −2.21598 | ||||||||
\(833\) | 1.63155 | 0.0565299 | ||||||||
\(834\) | −9.00654 | −0.311871 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 107.311 | 3.71143 | ||||||||
\(837\) | −8.77495 | −0.303307 | ||||||||
\(838\) | −0.286026 | −0.00988060 | ||||||||
\(839\) | −4.60054 | −0.158828 | −0.0794142 | − | 0.996842i | \(-0.525305\pi\) | ||||
−0.0794142 | + | 0.996842i | \(0.525305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1013 | −0.624182 | ||||||||
\(842\) | −0.0939677 | −0.00323834 | ||||||||
\(843\) | −21.6050 | −0.744117 | ||||||||
\(844\) | 58.2655 | 2.00558 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −26.4044 | −0.907801 | ||||||||
\(847\) | 26.7551 | 0.919317 | ||||||||
\(848\) | 6.16419 | 0.211679 | ||||||||
\(849\) | −2.05287 | −0.0704542 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.3136 | 0.490663 | ||||||||
\(852\) | −59.9413 | −2.05356 | ||||||||
\(853\) | 27.1689 | 0.930245 | 0.465122 | − | 0.885246i | \(-0.346010\pi\) | ||||
0.465122 | + | 0.885246i | \(0.346010\pi\) | |||||||
\(854\) | 88.9674 | 3.04440 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −70.0404 | −2.39393 | ||||||||
\(857\) | −7.66692 | −0.261897 | −0.130949 | − | 0.991389i | \(-0.541802\pi\) | ||||
−0.130949 | + | 0.991389i | \(0.541802\pi\) | |||||||
\(858\) | −61.0315 | −2.08358 | ||||||||
\(859\) | 9.09944 | 0.310469 | 0.155234 | − | 0.987878i | \(-0.450387\pi\) | ||||
0.155234 | + | 0.987878i | \(0.450387\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.59688 | 0.327061 | ||||||||
\(862\) | 39.1186 | 1.33238 | ||||||||
\(863\) | −21.7471 | −0.740279 | −0.370140 | − | 0.928976i | \(-0.620690\pi\) | ||||
−0.370140 | + | 0.928976i | \(0.620690\pi\) | |||||||
\(864\) | −2.66052 | −0.0905127 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 41.9216 | 1.42455 | ||||||||
\(867\) | −16.8337 | −0.571702 | ||||||||
\(868\) | −107.646 | −3.65375 | ||||||||
\(869\) | 15.5174 | 0.526392 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.245023 | −0.00830230 | ||||||||
\(872\) | −26.5379 | −0.898687 | ||||||||
\(873\) | 5.99258 | 0.202818 | ||||||||
\(874\) | −73.2585 | −2.47800 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.8175 | 0.669570 | ||||||||
\(877\) | 20.9781 | 0.708379 | 0.354190 | − | 0.935174i | \(-0.384757\pi\) | ||||
0.354190 | + | 0.935174i | \(0.384757\pi\) | |||||||
\(878\) | −74.3794 | −2.51018 | ||||||||
\(879\) | 11.9787 | 0.404032 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.6001 | 1.36785 | 0.683927 | − | 0.729551i | \(-0.260271\pi\) | ||||
0.683927 | + | 0.729551i | \(0.260271\pi\) | |||||||
\(882\) | 9.55012 | 0.321569 | ||||||||
\(883\) | 44.2689 | 1.48977 | 0.744883 | − | 0.667195i | \(-0.232505\pi\) | ||||
0.744883 | + | 0.667195i | \(0.232505\pi\) | |||||||
\(884\) | 8.83189 | 0.297049 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.4602 | 1.05693 | ||||||||
\(887\) | −21.2137 | −0.712285 | −0.356142 | − | 0.934432i | \(-0.615908\pi\) | ||||
−0.356142 | + | 0.934432i | \(0.615908\pi\) | |||||||
\(888\) | 12.5671 | 0.421724 | ||||||||
\(889\) | −10.7659 | −0.361076 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.36655 | −0.146285 | ||||||||
\(892\) | −8.42177 | −0.281982 | ||||||||
\(893\) | 73.4935 | 2.45937 | ||||||||
\(894\) | −18.8132 | −0.629207 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −68.7873 | −2.29802 | ||||||||
\(897\) | 27.0420 | 0.902907 | ||||||||
\(898\) | −69.7343 | −2.32706 | ||||||||
\(899\) | −28.9689 | −0.966168 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.10123 | 0.0366872 | ||||||||
\(902\) | −30.1612 | −1.00426 | ||||||||
\(903\) | 4.42016 | 0.147094 | ||||||||
\(904\) | 35.1571 | 1.16931 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.8187 | 0.591988 | ||||||||
\(907\) | 42.8598 | 1.42314 | 0.711568 | − | 0.702617i | \(-0.247985\pi\) | ||||
0.711568 | + | 0.702617i | \(0.247985\pi\) | |||||||
\(908\) | −74.9627 | −2.48772 | ||||||||
\(909\) | 5.06181 | 0.167890 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.6870 | 1.74560 | 0.872800 | − | 0.488078i | \(-0.162302\pi\) | ||||
0.872800 | + | 0.488078i | \(0.162302\pi\) | |||||||
\(912\) | −15.1684 | −0.502274 | ||||||||
\(913\) | −21.7870 | −0.721045 | ||||||||
\(914\) | −85.4617 | −2.82682 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 72.6266 | 2.39965 | ||||||||
\(917\) | −14.5999 | −0.482131 | ||||||||
\(918\) | 0.973567 | 0.0321325 | ||||||||
\(919\) | −17.5655 | −0.579434 | −0.289717 | − | 0.957112i | \(-0.593561\pi\) | ||||
−0.289717 | + | 0.957112i | \(0.593561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.07969 | 0.233284 | ||||||||
\(922\) | 14.3545 | 0.472741 | ||||||||
\(923\) | −94.8874 | −3.12326 | ||||||||
\(924\) | −53.5664 | −1.76221 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 98.3855 | 3.23315 | ||||||||
\(927\) | 6.90359 | 0.226744 | ||||||||
\(928\) | −8.78323 | −0.288324 | ||||||||
\(929\) | −58.2546 | −1.91127 | −0.955636 | − | 0.294550i | \(-0.904830\pi\) | ||||
−0.955636 | + | 0.294550i | \(0.904830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.5816 | −0.871178 | ||||||||
\(932\) | −63.4206 | −2.07741 | ||||||||
\(933\) | −11.4130 | −0.373644 | ||||||||
\(934\) | 71.5352 | 2.34070 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 23.7425 | 0.776048 | ||||||||
\(937\) | −21.6766 | −0.708142 | −0.354071 | − | 0.935218i | \(-0.615203\pi\) | ||||
−0.354071 | + | 0.935218i | \(0.615203\pi\) | |||||||
\(938\) | −0.331340 | −0.0108186 | ||||||||
\(939\) | −11.9077 | −0.388594 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.9457 | −1.36739 | −0.683695 | − | 0.729768i | \(-0.739628\pi\) | ||||
−0.683695 | + | 0.729768i | \(0.739628\pi\) | |||||||
\(942\) | 0.642054 | 0.0209193 | ||||||||
\(943\) | 13.3639 | 0.435188 | ||||||||
\(944\) | −13.2524 | −0.431329 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.8917 | −0.451659 | ||||||||
\(947\) | 40.0301 | 1.30080 | 0.650401 | − | 0.759591i | \(-0.274601\pi\) | ||||
0.650401 | + | 0.759591i | \(0.274601\pi\) | |||||||
\(948\) | −13.1440 | −0.426897 | ||||||||
\(949\) | 31.3712 | 1.01835 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.7719 | −0.414156 | ||||||||
\(952\) | 5.48510 | 0.177773 | ||||||||
\(953\) | 33.1969 | 1.07535 | 0.537677 | − | 0.843151i | \(-0.319302\pi\) | ||||
0.537677 | + | 0.843151i | \(0.319302\pi\) | |||||||
\(954\) | 6.44592 | 0.208694 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 80.5033 | 2.60366 | ||||||||
\(957\) | −14.4154 | −0.465984 | ||||||||
\(958\) | 19.9077 | 0.643187 | ||||||||
\(959\) | 3.53305 | 0.114088 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.9997 | 1.48386 | ||||||||
\(962\) | 43.3164 | 1.39658 | ||||||||
\(963\) | −17.2723 | −0.556593 | ||||||||
\(964\) | 14.4273 | 0.464673 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 36.5683 | 1.17657 | ||||||||
\(967\) | −20.5477 | −0.660770 | −0.330385 | − | 0.943846i | \(-0.607179\pi\) | ||||
−0.330385 | + | 0.943846i | \(0.607179\pi\) | |||||||
\(968\) | 32.7112 | 1.05138 | ||||||||
\(969\) | −2.70981 | −0.0870517 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.4201 | 0.655312 | 0.327656 | − | 0.944797i | \(-0.393741\pi\) | ||||
0.327656 | + | 0.944797i | \(0.393741\pi\) | |||||||
\(972\) | 3.69868 | 0.118635 | ||||||||
\(973\) | −12.5135 | −0.401164 | ||||||||
\(974\) | 11.7237 | 0.375653 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25.6516 | 0.821088 | ||||||||
\(977\) | 27.7767 | 0.888655 | 0.444327 | − | 0.895864i | \(-0.353443\pi\) | ||||
0.444327 | + | 0.895864i | \(0.353443\pi\) | |||||||
\(978\) | 24.7065 | 0.790027 | ||||||||
\(979\) | 8.47221 | 0.270773 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.54439 | −0.208946 | ||||||||
\(982\) | 10.3481 | 0.330221 | ||||||||
\(983\) | 15.7171 | 0.501298 | 0.250649 | − | 0.968078i | \(-0.419356\pi\) | ||||
0.250649 | + | 0.968078i | \(0.419356\pi\) | |||||||
\(984\) | 11.7333 | 0.374044 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.21406 | 0.102357 | ||||||||
\(987\) | −36.6857 | −1.16772 | ||||||||
\(988\) | −143.891 | −4.57780 | ||||||||
\(989\) | 6.15519 | 0.195724 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.18035 | −0.196325 | −0.0981627 | − | 0.995170i | \(-0.531297\pi\) | ||||
−0.0981627 | + | 0.995170i | \(0.531297\pi\) | |||||||
\(992\) | 23.3459 | 0.741233 | ||||||||
\(993\) | 8.66041 | 0.274830 | ||||||||
\(994\) | −128.314 | −4.06988 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 18.4546 | 0.584757 | ||||||||
\(997\) | 60.9412 | 1.93003 | 0.965014 | − | 0.262200i | \(-0.0844479\pi\) | ||||
0.965014 | + | 0.262200i | \(0.0844479\pi\) | |||||||
\(998\) | 86.3692 | 2.73397 | ||||||||
\(999\) | 3.09911 | 0.0980515 |
(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 | 1875.2.a.i.1.6 | ✓ | 6 | |
3.2 | odd | 2 | 5625.2.a.r.1.1 | 6 | |||
5.2 | odd | 4 | 1875.2.b.e.1249.11 | 12 | |||
5.3 | odd | 4 | 1875.2.b.e.1249.2 | 12 | |||
5.4 | even | 2 | 1875.2.a.l.1.1 | yes | 6 | ||
15.14 | odd | 2 | 5625.2.a.o.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.i.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1875.2.a.l.1.1 | yes | 6 | 5.4 | even | 2 | ||
1875.2.b.e.1249.2 | 12 | 5.3 | odd | 4 | |||
1875.2.b.e.1249.11 | 12 | 5.2 | odd | 4 | |||
5625.2.a.o.1.6 | 6 | 15.14 | odd | 2 | |||
5625.2.a.r.1.1 | 6 | 3.2 | odd | 2 |