Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(1,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, 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("625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.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: | \(4.99065012633\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.14884000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 11x^{6} + 36x^{4} - 31x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.13370\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13370 | 0.801650 | 0.400825 | − | 0.916155i | \(-0.368724\pi\) | ||||
0.400825 | + | 0.916155i | \(0.368724\pi\) | |||||||
\(3\) | −2.60278 | −1.50272 | −0.751358 | − | 0.659895i | \(-0.770601\pi\) | ||||
−0.751358 | + | 0.659895i | \(0.770601\pi\) | |||||||
\(4\) | −0.714715 | −0.357358 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.95078 | −1.20465 | ||||||||
\(7\) | 0.407162 | 0.153893 | 0.0769463 | − | 0.997035i | \(-0.475483\pi\) | ||||
0.0769463 | + | 0.997035i | \(0.475483\pi\) | |||||||
\(8\) | −3.07768 | −1.08813 | ||||||||
\(9\) | 3.77447 | 1.25816 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 1.86025 | 0.537007 | ||||||||
\(13\) | −0.700668 | −0.194330 | −0.0971651 | − | 0.995268i | \(-0.530977\pi\) | ||||
−0.0971651 | + | 0.995268i | \(0.530977\pi\) | |||||||
\(14\) | 0.461601 | 0.123368 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.05975 | −0.514938 | ||||||||
\(17\) | 1.58273 | 0.383869 | 0.191934 | − | 0.981408i | \(-0.438524\pi\) | ||||
0.191934 | + | 0.981408i | \(0.438524\pi\) | |||||||
\(18\) | 4.27913 | 1.00860 | ||||||||
\(19\) | 4.95078 | 1.13579 | 0.567894 | − | 0.823102i | \(-0.307758\pi\) | ||||
0.567894 | + | 0.823102i | \(0.307758\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.05975 | −0.231257 | ||||||||
\(22\) | 2.26741 | 0.483413 | ||||||||
\(23\) | 1.20145 | 0.250519 | 0.125259 | − | 0.992124i | \(-0.460024\pi\) | ||||
0.125259 | + | 0.992124i | \(0.460024\pi\) | |||||||
\(24\) | 8.01054 | 1.63514 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.794350 | −0.155785 | ||||||||
\(27\) | −2.01577 | −0.387935 | ||||||||
\(28\) | −0.291004 | −0.0549947 | ||||||||
\(29\) | 5.50906 | 1.02301 | 0.511504 | − | 0.859281i | \(-0.329089\pi\) | ||||
0.511504 | + | 0.859281i | \(0.329089\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.20390 | 1.47346 | 0.736732 | − | 0.676185i | \(-0.236368\pi\) | ||||
0.736732 | + | 0.676185i | \(0.236368\pi\) | |||||||
\(32\) | 3.82022 | 0.675325 | ||||||||
\(33\) | −5.20556 | −0.906172 | ||||||||
\(34\) | 1.79435 | 0.307728 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.69767 | −0.449611 | ||||||||
\(37\) | −5.13532 | −0.844241 | −0.422121 | − | 0.906540i | \(-0.638714\pi\) | ||||
−0.422121 | + | 0.906540i | \(0.638714\pi\) | |||||||
\(38\) | 5.61272 | 0.910504 | ||||||||
\(39\) | 1.82368 | 0.292023 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.21619 | 1.12698 | 0.563489 | − | 0.826123i | \(-0.309459\pi\) | ||||
0.563489 | + | 0.826123i | \(0.309459\pi\) | |||||||
\(42\) | −1.20145 | −0.185387 | ||||||||
\(43\) | 9.16531 | 1.39770 | 0.698848 | − | 0.715270i | \(-0.253696\pi\) | ||||
0.698848 | + | 0.715270i | \(0.253696\pi\) | |||||||
\(44\) | −1.42943 | −0.215495 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.36208 | 0.200828 | ||||||||
\(47\) | −1.27323 | −0.185720 | −0.0928602 | − | 0.995679i | \(-0.529601\pi\) | ||||
−0.0928602 | + | 0.995679i | \(0.529601\pi\) | |||||||
\(48\) | 5.36108 | 0.773806 | ||||||||
\(49\) | −6.83422 | −0.976317 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.11950 | −0.576846 | ||||||||
\(52\) | 0.500778 | 0.0694454 | ||||||||
\(53\) | −5.07996 | −0.697786 | −0.348893 | − | 0.937162i | \(-0.613442\pi\) | ||||
−0.348893 | + | 0.937162i | \(0.613442\pi\) | |||||||
\(54\) | −2.28528 | −0.310988 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.25311 | −0.167454 | ||||||||
\(57\) | −12.8858 | −1.70677 | ||||||||
\(58\) | 6.24565 | 0.820094 | ||||||||
\(59\) | −6.49972 | −0.846191 | −0.423096 | − | 0.906085i | \(-0.639057\pi\) | ||||
−0.423096 | + | 0.906085i | \(0.639057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.42008 | −1.20612 | −0.603059 | − | 0.797697i | \(-0.706052\pi\) | ||||
−0.603059 | + | 0.797697i | \(0.706052\pi\) | |||||||
\(62\) | 9.30079 | 1.18120 | ||||||||
\(63\) | 1.53682 | 0.193621 | ||||||||
\(64\) | 8.45050 | 1.05631 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.90157 | −0.726433 | ||||||||
\(67\) | −3.08173 | −0.376493 | −0.188247 | − | 0.982122i | \(-0.560280\pi\) | ||||
−0.188247 | + | 0.982122i | \(0.560280\pi\) | |||||||
\(68\) | −1.13120 | −0.137178 | ||||||||
\(69\) | −3.12710 | −0.376458 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.86639 | 0.814891 | 0.407445 | − | 0.913230i | \(-0.366420\pi\) | ||||
0.407445 | + | 0.913230i | \(0.366420\pi\) | |||||||
\(72\) | −11.6166 | −1.36903 | ||||||||
\(73\) | 0.545146 | 0.0638045 | 0.0319022 | − | 0.999491i | \(-0.489843\pi\) | ||||
0.0319022 | + | 0.999491i | \(0.489843\pi\) | |||||||
\(74\) | −5.82193 | −0.676786 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.53840 | −0.405882 | ||||||||
\(77\) | 0.814323 | 0.0928007 | ||||||||
\(78\) | 2.06752 | 0.234100 | ||||||||
\(79\) | 5.48159 | 0.616727 | 0.308363 | − | 0.951269i | \(-0.400219\pi\) | ||||
0.308363 | + | 0.951269i | \(0.400219\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.07680 | −0.675200 | ||||||||
\(82\) | 8.18102 | 0.903442 | ||||||||
\(83\) | 0.974135 | 0.106925 | 0.0534626 | − | 0.998570i | \(-0.482974\pi\) | ||||
0.0534626 | + | 0.998570i | \(0.482974\pi\) | |||||||
\(84\) | 0.757421 | 0.0826414 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.3907 | 1.12046 | ||||||||
\(87\) | −14.3389 | −1.53729 | ||||||||
\(88\) | −6.15537 | −0.656164 | ||||||||
\(89\) | −2.26649 | −0.240247 | −0.120124 | − | 0.992759i | \(-0.538329\pi\) | ||||
−0.120124 | + | 0.992759i | \(0.538329\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.285285 | −0.0299060 | ||||||||
\(92\) | −0.858691 | −0.0895247 | ||||||||
\(93\) | −21.3529 | −2.21420 | ||||||||
\(94\) | −1.44347 | −0.148883 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.94319 | −1.01482 | ||||||||
\(97\) | 15.2185 | 1.54520 | 0.772600 | − | 0.634893i | \(-0.218956\pi\) | ||||
0.772600 | + | 0.634893i | \(0.218956\pi\) | |||||||
\(98\) | −7.74798 | −0.782664 | ||||||||
\(99\) | 7.54893 | 0.758696 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.3965 | 1.83052 | 0.915261 | − | 0.402861i | \(-0.131984\pi\) | ||||
0.915261 | + | 0.402861i | \(0.131984\pi\) | |||||||
\(102\) | −4.67030 | −0.462428 | ||||||||
\(103\) | 11.8842 | 1.17099 | 0.585495 | − | 0.810676i | \(-0.300900\pi\) | ||||
0.585495 | + | 0.810676i | \(0.300900\pi\) | |||||||
\(104\) | 2.15643 | 0.211456 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.75917 | −0.559380 | ||||||||
\(107\) | 0.754919 | 0.0729808 | 0.0364904 | − | 0.999334i | \(-0.488382\pi\) | ||||
0.0364904 | + | 0.999334i | \(0.488382\pi\) | |||||||
\(108\) | 1.44070 | 0.138631 | ||||||||
\(109\) | −9.15752 | −0.877131 | −0.438566 | − | 0.898699i | \(-0.644513\pi\) | ||||
−0.438566 | + | 0.898699i | \(0.644513\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.3661 | 1.26865 | ||||||||
\(112\) | −0.838652 | −0.0792452 | ||||||||
\(113\) | −12.8399 | −1.20788 | −0.603938 | − | 0.797032i | \(-0.706402\pi\) | ||||
−0.603938 | + | 0.797032i | \(0.706402\pi\) | |||||||
\(114\) | −14.6087 | −1.36823 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.93741 | −0.365579 | ||||||||
\(117\) | −2.64465 | −0.244498 | ||||||||
\(118\) | −7.36876 | −0.678349 | ||||||||
\(119\) | 0.644428 | 0.0590746 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −10.6796 | −0.966884 | ||||||||
\(123\) | −18.7821 | −1.69353 | ||||||||
\(124\) | −5.86345 | −0.526553 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.74230 | 0.155216 | ||||||||
\(127\) | 7.10517 | 0.630482 | 0.315241 | − | 0.949012i | \(-0.397915\pi\) | ||||
0.315241 | + | 0.949012i | \(0.397915\pi\) | |||||||
\(128\) | 1.93993 | 0.171467 | ||||||||
\(129\) | −23.8553 | −2.10034 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.39425 | 0.209187 | 0.104593 | − | 0.994515i | \(-0.466646\pi\) | ||||
0.104593 | + | 0.994515i | \(0.466646\pi\) | |||||||
\(132\) | 3.72049 | 0.323827 | ||||||||
\(133\) | 2.01577 | 0.174789 | ||||||||
\(134\) | −3.49377 | −0.301816 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.87115 | −0.417698 | ||||||||
\(137\) | 19.0193 | 1.62493 | 0.812466 | − | 0.583009i | \(-0.198125\pi\) | ||||
0.812466 | + | 0.583009i | \(0.198125\pi\) | |||||||
\(138\) | −3.54520 | −0.301788 | ||||||||
\(139\) | −6.73470 | −0.571230 | −0.285615 | − | 0.958344i | \(-0.592198\pi\) | ||||
−0.285615 | + | 0.958344i | \(0.592198\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.31395 | 0.279085 | ||||||||
\(142\) | 7.78445 | 0.653257 | ||||||||
\(143\) | −1.40134 | −0.117186 | ||||||||
\(144\) | −7.77447 | −0.647872 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.618034 | 0.0511489 | ||||||||
\(147\) | 17.7880 | 1.46713 | ||||||||
\(148\) | 3.67029 | 0.301696 | ||||||||
\(149\) | −0.720492 | −0.0590250 | −0.0295125 | − | 0.999564i | \(-0.509395\pi\) | ||||
−0.0295125 | + | 0.999564i | \(0.509395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5178 | −1.26282 | −0.631412 | − | 0.775447i | \(-0.717524\pi\) | ||||
−0.631412 | + | 0.775447i | \(0.717524\pi\) | |||||||
\(152\) | −15.2369 | −1.23588 | ||||||||
\(153\) | 5.97397 | 0.482967 | ||||||||
\(154\) | 0.923201 | 0.0743937 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.30341 | −0.104357 | ||||||||
\(157\) | −2.78418 | −0.222202 | −0.111101 | − | 0.993809i | \(-0.535438\pi\) | ||||
−0.111101 | + | 0.993809i | \(0.535438\pi\) | |||||||
\(158\) | 6.21450 | 0.494399 | ||||||||
\(159\) | 13.2220 | 1.04857 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.489182 | 0.0385530 | ||||||||
\(162\) | −6.88929 | −0.541274 | ||||||||
\(163\) | 24.2074 | 1.89607 | 0.948034 | − | 0.318170i | \(-0.103068\pi\) | ||||
0.948034 | + | 0.318170i | \(0.103068\pi\) | |||||||
\(164\) | −5.15752 | −0.402734 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.10438 | 0.0857165 | ||||||||
\(167\) | 19.0462 | 1.47384 | 0.736919 | − | 0.675982i | \(-0.236280\pi\) | ||||
0.736919 | + | 0.675982i | \(0.236280\pi\) | |||||||
\(168\) | 3.26158 | 0.251637 | ||||||||
\(169\) | −12.5091 | −0.962236 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.6866 | 1.42900 | ||||||||
\(172\) | −6.55058 | −0.499477 | ||||||||
\(173\) | 13.2470 | 1.00715 | 0.503577 | − | 0.863950i | \(-0.332017\pi\) | ||||
0.503577 | + | 0.863950i | \(0.332017\pi\) | |||||||
\(174\) | −16.2561 | −1.23237 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.11950 | −0.310519 | ||||||||
\(177\) | 16.9173 | 1.27159 | ||||||||
\(178\) | −2.56952 | −0.192594 | ||||||||
\(179\) | −12.2250 | −0.913737 | −0.456869 | − | 0.889534i | \(-0.651029\pi\) | ||||
−0.456869 | + | 0.889534i | \(0.651029\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9168 | 0.811439 | 0.405719 | − | 0.913998i | \(-0.367021\pi\) | ||||
0.405719 | + | 0.913998i | \(0.367021\pi\) | |||||||
\(182\) | −0.323429 | −0.0239741 | ||||||||
\(183\) | 24.5184 | 1.81245 | ||||||||
\(184\) | −3.69767 | −0.272596 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −24.2079 | −1.77501 | ||||||||
\(187\) | 3.16546 | 0.231482 | ||||||||
\(188\) | 0.910000 | 0.0663686 | ||||||||
\(189\) | −0.820743 | −0.0597003 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.56763 | 0.113430 | 0.0567148 | − | 0.998390i | \(-0.481937\pi\) | ||||
0.0567148 | + | 0.998390i | \(0.481937\pi\) | |||||||
\(192\) | −21.9948 | −1.58734 | ||||||||
\(193\) | −1.65786 | −0.119335 | −0.0596675 | − | 0.998218i | \(-0.519004\pi\) | ||||
−0.0596675 | + | 0.998218i | \(0.519004\pi\) | |||||||
\(194\) | 17.2532 | 1.23871 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.88452 | 0.348894 | ||||||||
\(197\) | −13.2831 | −0.946380 | −0.473190 | − | 0.880960i | \(-0.656898\pi\) | ||||
−0.473190 | + | 0.880960i | \(0.656898\pi\) | |||||||
\(198\) | 8.55826 | 0.608209 | ||||||||
\(199\) | 12.1025 | 0.857921 | 0.428960 | − | 0.903323i | \(-0.358880\pi\) | ||||
0.428960 | + | 0.903323i | \(0.358880\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.02107 | 0.565763 | ||||||||
\(202\) | 20.8562 | 1.46744 | ||||||||
\(203\) | 2.24308 | 0.157433 | ||||||||
\(204\) | 2.94427 | 0.206140 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.4732 | 0.938724 | ||||||||
\(207\) | 4.53482 | 0.315192 | ||||||||
\(208\) | 1.44320 | 0.100068 | ||||||||
\(209\) | 9.90157 | 0.684906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.70061 | −0.461289 | −0.230644 | − | 0.973038i | \(-0.574083\pi\) | ||||
−0.230644 | + | 0.973038i | \(0.574083\pi\) | |||||||
\(212\) | 3.63073 | 0.249359 | ||||||||
\(213\) | −17.8717 | −1.22455 | ||||||||
\(214\) | 0.855855 | 0.0585050 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.20390 | 0.422122 | ||||||||
\(217\) | 3.34031 | 0.226755 | ||||||||
\(218\) | −10.3819 | −0.703152 | ||||||||
\(219\) | −1.41889 | −0.0958800 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.10897 | −0.0745973 | ||||||||
\(222\) | 15.1532 | 1.01702 | ||||||||
\(223\) | 10.5917 | 0.709272 | 0.354636 | − | 0.935004i | \(-0.384605\pi\) | ||||
0.354636 | + | 0.935004i | \(0.384605\pi\) | |||||||
\(224\) | 1.55545 | 0.103928 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.5566 | −0.968293 | ||||||||
\(227\) | −19.6112 | −1.30164 | −0.650822 | − | 0.759231i | \(-0.725575\pi\) | ||||
−0.650822 | + | 0.759231i | \(0.725575\pi\) | |||||||
\(228\) | 9.20968 | 0.609926 | ||||||||
\(229\) | 8.83898 | 0.584096 | 0.292048 | − | 0.956404i | \(-0.405663\pi\) | ||||
0.292048 | + | 0.956404i | \(0.405663\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.11950 | −0.139453 | ||||||||
\(232\) | −16.9552 | −1.11316 | ||||||||
\(233\) | −11.0624 | −0.724723 | −0.362362 | − | 0.932038i | \(-0.618029\pi\) | ||||
−0.362362 | + | 0.932038i | \(0.618029\pi\) | |||||||
\(234\) | −2.99825 | −0.196002 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.64545 | 0.302393 | ||||||||
\(237\) | −14.2674 | −0.926765 | ||||||||
\(238\) | 0.730590 | 0.0473571 | ||||||||
\(239\) | 16.1055 | 1.04178 | 0.520888 | − | 0.853625i | \(-0.325601\pi\) | ||||
0.520888 | + | 0.853625i | \(0.325601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.98873 | 0.385768 | 0.192884 | − | 0.981222i | \(-0.438216\pi\) | ||||
0.192884 | + | 0.981222i | \(0.438216\pi\) | |||||||
\(242\) | −7.93593 | −0.510141 | ||||||||
\(243\) | 21.8639 | 1.40257 | ||||||||
\(244\) | 6.73268 | 0.431015 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −21.2934 | −1.35762 | ||||||||
\(247\) | −3.46885 | −0.220718 | ||||||||
\(248\) | −25.2490 | −1.60331 | ||||||||
\(249\) | −2.53546 | −0.160678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.73176 | 0.235547 | 0.117773 | − | 0.993041i | \(-0.462424\pi\) | ||||
0.117773 | + | 0.993041i | \(0.462424\pi\) | |||||||
\(252\) | −1.09839 | −0.0691919 | ||||||||
\(253\) | 2.40289 | 0.151068 | ||||||||
\(254\) | 8.05516 | 0.505426 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.7017 | −0.918856 | ||||||||
\(257\) | 23.5935 | 1.47172 | 0.735862 | − | 0.677132i | \(-0.236777\pi\) | ||||
0.735862 | + | 0.677132i | \(0.236777\pi\) | |||||||
\(258\) | −27.0448 | −1.68374 | ||||||||
\(259\) | −2.09090 | −0.129922 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.7938 | 1.28710 | ||||||||
\(262\) | 2.71438 | 0.167695 | ||||||||
\(263\) | 6.64126 | 0.409518 | 0.204759 | − | 0.978812i | \(-0.434359\pi\) | ||||
0.204759 | + | 0.978812i | \(0.434359\pi\) | |||||||
\(264\) | 16.0211 | 0.986029 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.28528 | 0.140120 | ||||||||
\(267\) | 5.89917 | 0.361023 | ||||||||
\(268\) | 2.20256 | 0.134543 | ||||||||
\(269\) | −13.0439 | −0.795300 | −0.397650 | − | 0.917537i | \(-0.630174\pi\) | ||||
−0.397650 | + | 0.917537i | \(0.630174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.8488 | −0.719762 | −0.359881 | − | 0.932998i | \(-0.617183\pi\) | ||||
−0.359881 | + | 0.932998i | \(0.617183\pi\) | |||||||
\(272\) | −3.26004 | −0.197669 | ||||||||
\(273\) | 0.742534 | 0.0449402 | ||||||||
\(274\) | 21.5623 | 1.30263 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.23498 | 0.134530 | ||||||||
\(277\) | −16.9559 | −1.01878 | −0.509390 | − | 0.860536i | \(-0.670129\pi\) | ||||
−0.509390 | + | 0.860536i | \(0.670129\pi\) | |||||||
\(278\) | −7.63516 | −0.457926 | ||||||||
\(279\) | 30.9653 | 1.85385 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.07498 | −0.302748 | −0.151374 | − | 0.988477i | \(-0.548370\pi\) | ||||
−0.151374 | + | 0.988477i | \(0.548370\pi\) | |||||||
\(282\) | 3.75704 | 0.223728 | ||||||||
\(283\) | −11.8248 | −0.702914 | −0.351457 | − | 0.936204i | \(-0.614314\pi\) | ||||
−0.351457 | + | 0.936204i | \(0.614314\pi\) | |||||||
\(284\) | −4.90751 | −0.291207 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.58870 | −0.0939418 | ||||||||
\(287\) | 2.93815 | 0.173434 | ||||||||
\(288\) | 14.4193 | 0.849665 | ||||||||
\(289\) | −14.4950 | −0.852645 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −39.6103 | −2.32200 | ||||||||
\(292\) | −0.389624 | −0.0228010 | ||||||||
\(293\) | 19.4348 | 1.13540 | 0.567698 | − | 0.823237i | \(-0.307834\pi\) | ||||
0.567698 | + | 0.823237i | \(0.307834\pi\) | |||||||
\(294\) | 20.1663 | 1.17612 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15.8049 | 0.918640 | ||||||||
\(297\) | −4.03154 | −0.233934 | ||||||||
\(298\) | −0.816825 | −0.0473174 | ||||||||
\(299\) | −0.841814 | −0.0486834 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.73176 | 0.215095 | ||||||||
\(302\) | −17.5926 | −1.01234 | ||||||||
\(303\) | −47.8821 | −2.75076 | ||||||||
\(304\) | −10.1974 | −0.584860 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.77271 | 0.387170 | ||||||||
\(307\) | −25.4169 | −1.45062 | −0.725310 | − | 0.688423i | \(-0.758303\pi\) | ||||
−0.725310 | + | 0.688423i | \(0.758303\pi\) | |||||||
\(308\) | −0.582009 | −0.0331630 | ||||||||
\(309\) | −30.9321 | −1.75967 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.8578 | 0.899212 | 0.449606 | − | 0.893227i | \(-0.351564\pi\) | ||||
0.449606 | + | 0.893227i | \(0.351564\pi\) | |||||||
\(312\) | −5.61272 | −0.317758 | ||||||||
\(313\) | −7.01644 | −0.396592 | −0.198296 | − | 0.980142i | \(-0.563541\pi\) | ||||
−0.198296 | + | 0.980142i | \(0.563541\pi\) | |||||||
\(314\) | −3.15643 | −0.178128 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.91777 | −0.220392 | ||||||||
\(317\) | −13.0337 | −0.732044 | −0.366022 | − | 0.930606i | \(-0.619280\pi\) | ||||
−0.366022 | + | 0.930606i | \(0.619280\pi\) | |||||||
\(318\) | 14.9899 | 0.840590 | ||||||||
\(319\) | 11.0181 | 0.616897 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.96489 | −0.109669 | ||||||||
\(322\) | 0.554588 | 0.0309060 | ||||||||
\(323\) | 7.83576 | 0.435994 | ||||||||
\(324\) | 4.34318 | 0.241288 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 27.4440 | 1.51998 | ||||||||
\(327\) | 23.8350 | 1.31808 | ||||||||
\(328\) | −22.2091 | −1.22629 | ||||||||
\(329\) | −0.518412 | −0.0285810 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6439 | −0.969794 | −0.484897 | − | 0.874571i | \(-0.661143\pi\) | ||||
−0.484897 | + | 0.874571i | \(0.661143\pi\) | |||||||
\(332\) | −0.696229 | −0.0382105 | ||||||||
\(333\) | −19.3831 | −1.06219 | ||||||||
\(334\) | 21.5927 | 1.18150 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.18283 | 0.119083 | ||||||||
\(337\) | −24.8495 | −1.35364 | −0.676819 | − | 0.736149i | \(-0.736642\pi\) | ||||
−0.676819 | + | 0.736149i | \(0.736642\pi\) | |||||||
\(338\) | −14.1816 | −0.771376 | ||||||||
\(339\) | 33.4194 | 1.81509 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.4078 | 0.888532 | ||||||||
\(342\) | 21.1850 | 1.14556 | ||||||||
\(343\) | −5.63276 | −0.304141 | ||||||||
\(344\) | −28.2079 | −1.52087 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.0182 | 0.807385 | ||||||||
\(347\) | −13.2775 | −0.712773 | −0.356386 | − | 0.934339i | \(-0.615991\pi\) | ||||
−0.356386 | + | 0.934339i | \(0.615991\pi\) | |||||||
\(348\) | 10.2482 | 0.549362 | ||||||||
\(349\) | −18.1283 | −0.970385 | −0.485192 | − | 0.874407i | \(-0.661250\pi\) | ||||
−0.485192 | + | 0.874407i | \(0.661250\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41238 | 0.0753875 | ||||||||
\(352\) | 7.64044 | 0.407237 | ||||||||
\(353\) | 17.7042 | 0.942302 | 0.471151 | − | 0.882053i | \(-0.343839\pi\) | ||||
0.471151 | + | 0.882053i | \(0.343839\pi\) | |||||||
\(354\) | 19.1793 | 1.01937 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.61989 | 0.0858541 | ||||||||
\(357\) | −1.67730 | −0.0887723 | ||||||||
\(358\) | −13.8595 | −0.732497 | ||||||||
\(359\) | 32.5443 | 1.71762 | 0.858812 | − | 0.512290i | \(-0.171203\pi\) | ||||
0.858812 | + | 0.512290i | \(0.171203\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.51025 | 0.290013 | ||||||||
\(362\) | 12.3764 | 0.650490 | ||||||||
\(363\) | 18.2195 | 0.956274 | ||||||||
\(364\) | 0.203897 | 0.0106871 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 27.7966 | 1.45295 | ||||||||
\(367\) | −32.9481 | −1.71988 | −0.859939 | − | 0.510397i | \(-0.829499\pi\) | ||||
−0.859939 | + | 0.510397i | \(0.829499\pi\) | |||||||
\(368\) | −2.47468 | −0.129002 | ||||||||
\(369\) | 27.2373 | 1.41791 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.06837 | −0.107384 | ||||||||
\(372\) | 15.2613 | 0.791260 | ||||||||
\(373\) | −3.46648 | −0.179487 | −0.0897436 | − | 0.995965i | \(-0.528605\pi\) | ||||
−0.0897436 | + | 0.995965i | \(0.528605\pi\) | |||||||
\(374\) | 3.58870 | 0.185567 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.91861 | 0.202087 | ||||||||
\(377\) | −3.86002 | −0.198801 | ||||||||
\(378\) | −0.930480 | −0.0478587 | ||||||||
\(379\) | −1.92863 | −0.0990670 | −0.0495335 | − | 0.998772i | \(-0.515773\pi\) | ||||
−0.0495335 | + | 0.998772i | \(0.515773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.4932 | −0.947436 | ||||||||
\(382\) | 1.77723 | 0.0909309 | ||||||||
\(383\) | 4.93003 | 0.251913 | 0.125956 | − | 0.992036i | \(-0.459800\pi\) | ||||
0.125956 | + | 0.992036i | \(0.459800\pi\) | |||||||
\(384\) | −5.04922 | −0.257667 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.87952 | −0.0956649 | ||||||||
\(387\) | 34.5942 | 1.75852 | ||||||||
\(388\) | −10.8769 | −0.552189 | ||||||||
\(389\) | 13.3860 | 0.678697 | 0.339348 | − | 0.940661i | \(-0.389793\pi\) | ||||
0.339348 | + | 0.940661i | \(0.389793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.90157 | 0.0961663 | ||||||||
\(392\) | 21.0336 | 1.06236 | ||||||||
\(393\) | −6.23172 | −0.314349 | ||||||||
\(394\) | −15.0591 | −0.758666 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.39534 | −0.271126 | ||||||||
\(397\) | −2.13887 | −0.107347 | −0.0536733 | − | 0.998559i | \(-0.517093\pi\) | ||||
−0.0536733 | + | 0.998559i | \(0.517093\pi\) | |||||||
\(398\) | 13.7206 | 0.687752 | ||||||||
\(399\) | −5.24660 | −0.262659 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.8213 | −1.33939 | −0.669696 | − | 0.742635i | \(-0.733576\pi\) | ||||
−0.669696 | + | 0.742635i | \(0.733576\pi\) | |||||||
\(402\) | 9.09352 | 0.453544 | ||||||||
\(403\) | −5.74821 | −0.286339 | ||||||||
\(404\) | −13.1483 | −0.654151 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.54299 | 0.126206 | ||||||||
\(407\) | −10.2706 | −0.509097 | ||||||||
\(408\) | 12.6785 | 0.627681 | ||||||||
\(409\) | 13.9982 | 0.692169 | 0.346084 | − | 0.938203i | \(-0.387511\pi\) | ||||
0.346084 | + | 0.938203i | \(0.387511\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −49.5032 | −2.44181 | ||||||||
\(412\) | −8.49385 | −0.418462 | ||||||||
\(413\) | −2.64644 | −0.130223 | ||||||||
\(414\) | 5.14114 | 0.252673 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.67670 | −0.131236 | ||||||||
\(417\) | 17.5290 | 0.858397 | ||||||||
\(418\) | 11.2254 | 0.549055 | ||||||||
\(419\) | 30.9020 | 1.50966 | 0.754831 | − | 0.655919i | \(-0.227719\pi\) | ||||
0.754831 | + | 0.655919i | \(0.227719\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.23974 | −0.401581 | −0.200790 | − | 0.979634i | \(-0.564351\pi\) | ||||
−0.200790 | + | 0.979634i | \(0.564351\pi\) | |||||||
\(422\) | −7.59651 | −0.369792 | ||||||||
\(423\) | −4.80578 | −0.233665 | ||||||||
\(424\) | 15.6345 | 0.759279 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −20.2612 | −0.981660 | ||||||||
\(427\) | −3.83550 | −0.185613 | ||||||||
\(428\) | −0.539552 | −0.0260802 | ||||||||
\(429\) | 3.64737 | 0.176097 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.1482 | 1.30768 | 0.653841 | − | 0.756632i | \(-0.273157\pi\) | ||||
0.653841 | + | 0.756632i | \(0.273157\pi\) | |||||||
\(432\) | 4.15198 | 0.199762 | ||||||||
\(433\) | 21.4905 | 1.03277 | 0.516383 | − | 0.856357i | \(-0.327278\pi\) | ||||
0.516383 | + | 0.856357i | \(0.327278\pi\) | |||||||
\(434\) | 3.78692 | 0.181778 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.54502 | 0.313449 | ||||||||
\(437\) | 5.94810 | 0.284536 | ||||||||
\(438\) | −1.60861 | −0.0768622 | ||||||||
\(439\) | −25.7956 | −1.23116 | −0.615578 | − | 0.788076i | \(-0.711078\pi\) | ||||
−0.615578 | + | 0.788076i | \(0.711078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.7955 | −1.22836 | ||||||||
\(442\) | −1.25724 | −0.0598009 | ||||||||
\(443\) | 3.18479 | 0.151314 | 0.0756570 | − | 0.997134i | \(-0.475895\pi\) | ||||
0.0756570 | + | 0.997134i | \(0.475895\pi\) | |||||||
\(444\) | −9.55296 | −0.453363 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.0078 | 0.568588 | ||||||||
\(447\) | 1.87528 | 0.0886978 | ||||||||
\(448\) | 3.44072 | 0.162559 | ||||||||
\(449\) | 36.0785 | 1.70265 | 0.851325 | − | 0.524639i | \(-0.175800\pi\) | ||||
0.851325 | + | 0.524639i | \(0.175800\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.4324 | 0.679594 | ||||||||
\(452\) | 9.17686 | 0.431643 | ||||||||
\(453\) | 40.3896 | 1.89767 | ||||||||
\(454\) | −22.2333 | −1.04346 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 39.6584 | 1.85718 | ||||||||
\(457\) | 25.5245 | 1.19399 | 0.596994 | − | 0.802246i | \(-0.296362\pi\) | ||||
0.596994 | + | 0.802246i | \(0.296362\pi\) | |||||||
\(458\) | 10.0208 | 0.468241 | ||||||||
\(459\) | −3.19042 | −0.148916 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.6392 | −0.774963 | −0.387482 | − | 0.921877i | \(-0.626655\pi\) | ||||
−0.387482 | + | 0.921877i | \(0.626655\pi\) | |||||||
\(462\) | −2.40289 | −0.111793 | ||||||||
\(463\) | 17.8178 | 0.828062 | 0.414031 | − | 0.910263i | \(-0.364120\pi\) | ||||
0.414031 | + | 0.910263i | \(0.364120\pi\) | |||||||
\(464\) | −11.3473 | −0.526786 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.5415 | −0.580974 | ||||||||
\(467\) | −14.2480 | −0.659321 | −0.329660 | − | 0.944100i | \(-0.606934\pi\) | ||||
−0.329660 | + | 0.944100i | \(0.606934\pi\) | |||||||
\(468\) | 1.89017 | 0.0873731 | ||||||||
\(469\) | −1.25476 | −0.0579395 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.24660 | 0.333906 | ||||||||
\(472\) | 20.0041 | 0.920762 | ||||||||
\(473\) | 18.3306 | 0.842843 | ||||||||
\(474\) | −16.1750 | −0.742941 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.460582 | −0.0211107 | ||||||||
\(477\) | −19.1742 | −0.877924 | ||||||||
\(478\) | 18.2588 | 0.835139 | ||||||||
\(479\) | 2.90864 | 0.132899 | 0.0664496 | − | 0.997790i | \(-0.478833\pi\) | ||||
0.0664496 | + | 0.997790i | \(0.478833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.59815 | 0.164062 | ||||||||
\(482\) | 6.78945 | 0.309251 | ||||||||
\(483\) | −1.27323 | −0.0579342 | ||||||||
\(484\) | 5.00301 | 0.227409 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 24.7872 | 1.12437 | ||||||||
\(487\) | −17.0652 | −0.773298 | −0.386649 | − | 0.922227i | \(-0.626368\pi\) | ||||
−0.386649 | + | 0.922227i | \(0.626368\pi\) | |||||||
\(488\) | 28.9920 | 1.31241 | ||||||||
\(489\) | −63.0065 | −2.84925 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.7768 | 1.38894 | 0.694470 | − | 0.719522i | \(-0.255639\pi\) | ||||
0.694470 | + | 0.719522i | \(0.255639\pi\) | |||||||
\(492\) | 13.4239 | 0.605195 | ||||||||
\(493\) | 8.71937 | 0.392701 | ||||||||
\(494\) | −3.93265 | −0.176938 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.8980 | −0.758742 | ||||||||
\(497\) | 2.79573 | 0.125406 | ||||||||
\(498\) | −2.87446 | −0.128808 | ||||||||
\(499\) | −11.8824 | −0.531927 | −0.265964 | − | 0.963983i | \(-0.585690\pi\) | ||||
−0.265964 | + | 0.963983i | \(0.585690\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −49.5730 | −2.21476 | ||||||||
\(502\) | 4.23071 | 0.188826 | ||||||||
\(503\) | −2.97823 | −0.132793 | −0.0663964 | − | 0.997793i | \(-0.521150\pi\) | ||||
−0.0663964 | + | 0.997793i | \(0.521150\pi\) | |||||||
\(504\) | −4.72984 | −0.210684 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.72417 | 0.121104 | ||||||||
\(507\) | 32.5584 | 1.44597 | ||||||||
\(508\) | −5.07817 | −0.225308 | ||||||||
\(509\) | −36.7159 | −1.62740 | −0.813702 | − | 0.581282i | \(-0.802551\pi\) | ||||
−0.813702 | + | 0.581282i | \(0.802551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.221962 | 0.00981904 | ||||||||
\(512\) | −20.5472 | −0.908068 | ||||||||
\(513\) | −9.97963 | −0.440612 | ||||||||
\(514\) | 26.7481 | 1.17981 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 17.0497 | 0.750573 | ||||||||
\(517\) | −2.54647 | −0.111994 | ||||||||
\(518\) | −2.37047 | −0.104152 | ||||||||
\(519\) | −34.4792 | −1.51347 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.50039 | 0.109544 | 0.0547720 | − | 0.998499i | \(-0.482557\pi\) | ||||
0.0547720 | + | 0.998499i | \(0.482557\pi\) | |||||||
\(522\) | 23.5740 | 1.03181 | ||||||||
\(523\) | −42.1258 | −1.84203 | −0.921017 | − | 0.389523i | \(-0.872640\pi\) | ||||
−0.921017 | + | 0.389523i | \(0.872640\pi\) | |||||||
\(524\) | −1.71121 | −0.0747545 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.52922 | 0.328290 | ||||||||
\(527\) | 12.9846 | 0.565617 | ||||||||
\(528\) | 10.7222 | 0.466622 | ||||||||
\(529\) | −21.5565 | −0.937240 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.5330 | −1.06464 | ||||||||
\(532\) | −1.44070 | −0.0624623 | ||||||||
\(533\) | −5.05615 | −0.219006 | ||||||||
\(534\) | 6.68791 | 0.289414 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.48459 | 0.409672 | ||||||||
\(537\) | 31.8189 | 1.37309 | ||||||||
\(538\) | −14.7879 | −0.637552 | ||||||||
\(539\) | −13.6684 | −0.588741 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.3492 | −1.17583 | −0.587916 | − | 0.808922i | \(-0.700052\pi\) | ||||
−0.587916 | + | 0.808922i | \(0.700052\pi\) | |||||||
\(542\) | −13.4330 | −0.576997 | ||||||||
\(543\) | −28.4140 | −1.21936 | ||||||||
\(544\) | 6.04638 | 0.259236 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.841814 | 0.0360263 | ||||||||
\(547\) | −20.3392 | −0.869640 | −0.434820 | − | 0.900517i | \(-0.643188\pi\) | ||||
−0.434820 | + | 0.900517i | \(0.643188\pi\) | |||||||
\(548\) | −13.5934 | −0.580682 | ||||||||
\(549\) | −35.5558 | −1.51748 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.2742 | 1.16192 | ||||||||
\(552\) | 9.62422 | 0.409634 | ||||||||
\(553\) | 2.23189 | 0.0949097 | ||||||||
\(554\) | −19.2229 | −0.816705 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.81339 | 0.204133 | ||||||||
\(557\) | −28.2605 | −1.19744 | −0.598718 | − | 0.800960i | \(-0.704323\pi\) | ||||
−0.598718 | + | 0.800960i | \(0.704323\pi\) | |||||||
\(558\) | 35.1055 | 1.48614 | ||||||||
\(559\) | −6.42184 | −0.271615 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.23901 | −0.347851 | ||||||||
\(562\) | −5.75353 | −0.242698 | ||||||||
\(563\) | −12.9254 | −0.544742 | −0.272371 | − | 0.962192i | \(-0.587808\pi\) | ||||
−0.272371 | + | 0.962192i | \(0.587808\pi\) | |||||||
\(564\) | −2.36853 | −0.0997331 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.4059 | −0.563491 | ||||||||
\(567\) | −2.47424 | −0.103908 | ||||||||
\(568\) | −21.1326 | −0.886703 | ||||||||
\(569\) | −3.08443 | −0.129306 | −0.0646531 | − | 0.997908i | \(-0.520594\pi\) | ||||
−0.0646531 | + | 0.997908i | \(0.520594\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.12766 | −0.172737 | −0.0863687 | − | 0.996263i | \(-0.527526\pi\) | ||||
−0.0863687 | + | 0.996263i | \(0.527526\pi\) | |||||||
\(572\) | 1.00156 | 0.0418771 | ||||||||
\(573\) | −4.08019 | −0.170453 | ||||||||
\(574\) | 3.33100 | 0.139033 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 31.8961 | 1.32901 | ||||||||
\(577\) | −6.35570 | −0.264591 | −0.132296 | − | 0.991210i | \(-0.542235\pi\) | ||||
−0.132296 | + | 0.991210i | \(0.542235\pi\) | |||||||
\(578\) | −16.4330 | −0.683522 | ||||||||
\(579\) | 4.31503 | 0.179327 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.396630 | 0.0164550 | ||||||||
\(582\) | −44.9063 | −1.86143 | ||||||||
\(583\) | −10.1599 | −0.420781 | ||||||||
\(584\) | −1.67779 | −0.0694273 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.0334 | 0.910190 | ||||||||
\(587\) | 21.1040 | 0.871054 | 0.435527 | − | 0.900176i | \(-0.356562\pi\) | ||||
0.435527 | + | 0.900176i | \(0.356562\pi\) | |||||||
\(588\) | −12.7133 | −0.524289 | ||||||||
\(589\) | 40.6157 | 1.67354 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.5729 | 1.42214 | ||||||||
\(592\) | 10.5775 | 0.434732 | ||||||||
\(593\) | −21.6529 | −0.889177 | −0.444589 | − | 0.895735i | \(-0.646650\pi\) | ||||
−0.444589 | + | 0.895735i | \(0.646650\pi\) | |||||||
\(594\) | −4.57057 | −0.187533 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.514946 | 0.0210930 | ||||||||
\(597\) | −31.5000 | −1.28921 | ||||||||
\(598\) | −0.954368 | −0.0390270 | ||||||||
\(599\) | −3.38501 | −0.138308 | −0.0691539 | − | 0.997606i | \(-0.522030\pi\) | ||||
−0.0691539 | + | 0.997606i | \(0.522030\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.8265 | 1.17586 | 0.587928 | − | 0.808913i | \(-0.299944\pi\) | ||||
0.587928 | + | 0.808913i | \(0.299944\pi\) | |||||||
\(602\) | 4.23071 | 0.172431 | ||||||||
\(603\) | −11.6319 | −0.473687 | ||||||||
\(604\) | 11.0908 | 0.451280 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −54.2842 | −2.20514 | ||||||||
\(607\) | 15.6708 | 0.636059 | 0.318029 | − | 0.948081i | \(-0.396979\pi\) | ||||
0.318029 | + | 0.948081i | \(0.396979\pi\) | |||||||
\(608\) | 18.9131 | 0.767026 | ||||||||
\(609\) | −5.83824 | −0.236578 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.892114 | 0.0360911 | ||||||||
\(612\) | −4.26969 | −0.172592 | ||||||||
\(613\) | −38.2005 | −1.54290 | −0.771451 | − | 0.636288i | \(-0.780469\pi\) | ||||
−0.771451 | + | 0.636288i | \(0.780469\pi\) | |||||||
\(614\) | −28.8153 | −1.16289 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.50623 | −0.100979 | ||||||||
\(617\) | 13.2318 | 0.532691 | 0.266346 | − | 0.963878i | \(-0.414184\pi\) | ||||
0.266346 | + | 0.963878i | \(0.414184\pi\) | |||||||
\(618\) | −35.0678 | −1.41064 | ||||||||
\(619\) | 6.04463 | 0.242954 | 0.121477 | − | 0.992594i | \(-0.461237\pi\) | ||||
0.121477 | + | 0.992594i | \(0.461237\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.42184 | −0.0971849 | ||||||||
\(622\) | 17.9780 | 0.720853 | ||||||||
\(623\) | −0.922826 | −0.0369722 | ||||||||
\(624\) | −3.75634 | −0.150374 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.95456 | −0.317928 | ||||||||
\(627\) | −25.7716 | −1.02922 | ||||||||
\(628\) | 1.98989 | 0.0794054 | ||||||||
\(629\) | −8.12783 | −0.324078 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.7855 | −1.50422 | −0.752108 | − | 0.659040i | \(-0.770963\pi\) | ||||
−0.752108 | + | 0.659040i | \(0.770963\pi\) | |||||||
\(632\) | −16.8706 | −0.671076 | ||||||||
\(633\) | 17.4402 | 0.693186 | ||||||||
\(634\) | −14.7763 | −0.586843 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.44998 | −0.374716 | ||||||||
\(637\) | 4.78852 | 0.189728 | ||||||||
\(638\) | 12.4913 | 0.494535 | ||||||||
\(639\) | 25.9170 | 1.02526 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.8570 | −0.823802 | −0.411901 | − | 0.911229i | \(-0.635135\pi\) | ||||
−0.411901 | + | 0.911229i | \(0.635135\pi\) | |||||||
\(642\) | −2.22760 | −0.0879164 | ||||||||
\(643\) | −37.5552 | −1.48103 | −0.740516 | − | 0.672039i | \(-0.765419\pi\) | ||||
−0.740516 | + | 0.672039i | \(0.765419\pi\) | |||||||
\(644\) | −0.349626 | −0.0137772 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.88344 | 0.349514 | ||||||||
\(647\) | −27.4003 | −1.07722 | −0.538608 | − | 0.842557i | \(-0.681049\pi\) | ||||
−0.538608 | + | 0.842557i | \(0.681049\pi\) | |||||||
\(648\) | 18.7025 | 0.734702 | ||||||||
\(649\) | −12.9994 | −0.510272 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.69410 | −0.340749 | ||||||||
\(652\) | −17.3014 | −0.677574 | ||||||||
\(653\) | 23.0461 | 0.901864 | 0.450932 | − | 0.892558i | \(-0.351092\pi\) | ||||
0.450932 | + | 0.892558i | \(0.351092\pi\) | |||||||
\(654\) | 27.0218 | 1.05664 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −14.8636 | −0.580324 | ||||||||
\(657\) | 2.05763 | 0.0802760 | ||||||||
\(658\) | −0.587726 | −0.0229119 | ||||||||
\(659\) | 20.4837 | 0.797931 | 0.398966 | − | 0.916966i | \(-0.369369\pi\) | ||||
0.398966 | + | 0.916966i | \(0.369369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.9900 | 0.544147 | 0.272074 | − | 0.962276i | \(-0.412291\pi\) | ||||
0.272074 | + | 0.962276i | \(0.412291\pi\) | |||||||
\(662\) | −20.0029 | −0.777436 | ||||||||
\(663\) | 2.88640 | 0.112099 | ||||||||
\(664\) | −2.99808 | −0.116348 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.9747 | −0.851502 | ||||||||
\(667\) | 6.61884 | 0.256283 | ||||||||
\(668\) | −13.6126 | −0.526687 | ||||||||
\(669\) | −27.5678 | −1.06583 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.8402 | −0.727317 | ||||||||
\(672\) | −4.04848 | −0.156174 | ||||||||
\(673\) | 7.84572 | 0.302430 | 0.151215 | − | 0.988501i | \(-0.451681\pi\) | ||||
0.151215 | + | 0.988501i | \(0.451681\pi\) | |||||||
\(674\) | −28.1720 | −1.08514 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.94042 | 0.343862 | ||||||||
\(677\) | 14.3983 | 0.553371 | 0.276686 | − | 0.960960i | \(-0.410764\pi\) | ||||
0.276686 | + | 0.960960i | \(0.410764\pi\) | |||||||
\(678\) | 37.8877 | 1.45507 | ||||||||
\(679\) | 6.19637 | 0.237795 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 51.0437 | 1.95600 | ||||||||
\(682\) | 18.6016 | 0.712291 | ||||||||
\(683\) | −12.6740 | −0.484956 | −0.242478 | − | 0.970157i | \(-0.577960\pi\) | ||||
−0.242478 | + | 0.970157i | \(0.577960\pi\) | |||||||
\(684\) | −13.3556 | −0.510663 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.38589 | −0.243814 | ||||||||
\(687\) | −23.0059 | −0.877731 | ||||||||
\(688\) | −18.8783 | −0.719727 | ||||||||
\(689\) | 3.55937 | 0.135601 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.74530 | 0.218562 | 0.109281 | − | 0.994011i | \(-0.465145\pi\) | ||||
0.109281 | + | 0.994011i | \(0.465145\pi\) | |||||||
\(692\) | −9.46787 | −0.359914 | ||||||||
\(693\) | 3.07364 | 0.116758 | ||||||||
\(694\) | −15.0527 | −0.571394 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 44.1306 | 1.67276 | ||||||||
\(697\) | 11.4213 | 0.432612 | ||||||||
\(698\) | −20.5521 | −0.777909 | ||||||||
\(699\) | 28.7931 | 1.08905 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.5834 | −1.15512 | −0.577560 | − | 0.816348i | \(-0.695995\pi\) | ||||
−0.577560 | + | 0.816348i | \(0.695995\pi\) | |||||||
\(702\) | 1.60123 | 0.0604344 | ||||||||
\(703\) | −25.4238 | −0.958879 | ||||||||
\(704\) | 16.9010 | 0.636980 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.0714 | 0.755396 | ||||||||
\(707\) | 7.49036 | 0.281704 | ||||||||
\(708\) | −12.0911 | −0.454411 | ||||||||
\(709\) | −27.0696 | −1.01662 | −0.508310 | − | 0.861174i | \(-0.669730\pi\) | ||||
−0.508310 | + | 0.861174i | \(0.669730\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.6901 | 0.775938 | ||||||||
\(712\) | 6.97553 | 0.261419 | ||||||||
\(713\) | 9.85653 | 0.369130 | ||||||||
\(714\) | −1.90157 | −0.0711643 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.73737 | 0.326531 | ||||||||
\(717\) | −41.9190 | −1.56549 | ||||||||
\(718\) | 36.8957 | 1.37693 | ||||||||
\(719\) | −16.7066 | −0.623052 | −0.311526 | − | 0.950238i | \(-0.600840\pi\) | ||||
−0.311526 | + | 0.950238i | \(0.600840\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.83881 | 0.180207 | ||||||||
\(722\) | 6.24700 | 0.232489 | ||||||||
\(723\) | −15.5874 | −0.579700 | ||||||||
\(724\) | −7.80240 | −0.289974 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.6555 | 0.766597 | ||||||||
\(727\) | 11.7006 | 0.433951 | 0.216975 | − | 0.976177i | \(-0.430381\pi\) | ||||
0.216975 | + | 0.976177i | \(0.430381\pi\) | |||||||
\(728\) | 0.878017 | 0.0325415 | ||||||||
\(729\) | −38.6765 | −1.43246 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.5062 | 0.536532 | ||||||||
\(732\) | −17.5237 | −0.647694 | ||||||||
\(733\) | 34.1078 | 1.25980 | 0.629901 | − | 0.776676i | \(-0.283096\pi\) | ||||
0.629901 | + | 0.776676i | \(0.283096\pi\) | |||||||
\(734\) | −37.3534 | −1.37874 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.58978 | 0.169182 | ||||||||
\(737\) | −6.16346 | −0.227034 | ||||||||
\(738\) | 30.8790 | 1.13667 | ||||||||
\(739\) | 5.74517 | 0.211340 | 0.105670 | − | 0.994401i | \(-0.466301\pi\) | ||||
0.105670 | + | 0.994401i | \(0.466301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.02866 | 0.331676 | ||||||||
\(742\) | −2.34491 | −0.0860845 | ||||||||
\(743\) | 36.4348 | 1.33666 | 0.668332 | − | 0.743863i | \(-0.267009\pi\) | ||||
0.668332 | + | 0.743863i | \(0.267009\pi\) | |||||||
\(744\) | 65.7176 | 2.40932 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.92996 | −0.143886 | ||||||||
\(747\) | 3.67684 | 0.134528 | ||||||||
\(748\) | −2.26240 | −0.0827217 | ||||||||
\(749\) | 0.307374 | 0.0112312 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.48912 | 0.0543387 | 0.0271693 | − | 0.999631i | \(-0.491351\pi\) | ||||
0.0271693 | + | 0.999631i | \(0.491351\pi\) | |||||||
\(752\) | 2.62255 | 0.0956345 | ||||||||
\(753\) | −9.71296 | −0.353960 | ||||||||
\(754\) | −4.37612 | −0.159369 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.586598 | 0.0213344 | ||||||||
\(757\) | −5.53316 | −0.201106 | −0.100553 | − | 0.994932i | \(-0.532061\pi\) | ||||
−0.100553 | + | 0.994932i | \(0.532061\pi\) | |||||||
\(758\) | −2.18649 | −0.0794171 | ||||||||
\(759\) | −6.25420 | −0.227013 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.6697 | −0.676776 | −0.338388 | − | 0.941007i | \(-0.609882\pi\) | ||||
−0.338388 | + | 0.941007i | \(0.609882\pi\) | |||||||
\(762\) | −20.9658 | −0.759512 | ||||||||
\(763\) | −3.72859 | −0.134984 | ||||||||
\(764\) | −1.12041 | −0.0405349 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.58920 | 0.201946 | ||||||||
\(767\) | 4.55414 | 0.164441 | ||||||||
\(768\) | 38.2653 | 1.38078 | ||||||||
\(769\) | −13.1433 | −0.473960 | −0.236980 | − | 0.971515i | \(-0.576158\pi\) | ||||
−0.236980 | + | 0.971515i | \(0.576158\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −61.4088 | −2.21158 | ||||||||
\(772\) | 1.18489 | 0.0426453 | ||||||||
\(773\) | 27.9736 | 1.00614 | 0.503070 | − | 0.864246i | \(-0.332204\pi\) | ||||
0.503070 | + | 0.864246i | \(0.332204\pi\) | |||||||
\(774\) | 39.2195 | 1.40972 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −46.8376 | −1.68137 | ||||||||
\(777\) | 5.44217 | 0.195237 | ||||||||
\(778\) | 15.1758 | 0.544077 | ||||||||
\(779\) | 35.7258 | 1.28001 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.7328 | 0.491398 | ||||||||
\(782\) | 2.15581 | 0.0770917 | ||||||||
\(783\) | −11.1050 | −0.396860 | ||||||||
\(784\) | 14.0768 | 0.502743 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.06492 | −0.251998 | ||||||||
\(787\) | 33.3670 | 1.18940 | 0.594702 | − | 0.803946i | \(-0.297270\pi\) | ||||
0.594702 | + | 0.803946i | \(0.297270\pi\) | |||||||
\(788\) | 9.49362 | 0.338196 | ||||||||
\(789\) | −17.2857 | −0.615389 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.22791 | −0.185883 | ||||||||
\(792\) | −23.2332 | −0.825557 | ||||||||
\(793\) | 6.60035 | 0.234385 | ||||||||
\(794\) | −2.42484 | −0.0860544 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.64981 | −0.306584 | ||||||||
\(797\) | 37.3986 | 1.32473 | 0.662364 | − | 0.749183i | \(-0.269553\pi\) | ||||
0.662364 | + | 0.749183i | \(0.269553\pi\) | |||||||
\(798\) | −5.94810 | −0.210560 | ||||||||
\(799\) | −2.01519 | −0.0712923 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.55478 | −0.302268 | ||||||||
\(802\) | −30.4074 | −1.07372 | ||||||||
\(803\) | 1.09029 | 0.0384756 | ||||||||
\(804\) | −5.73278 | −0.202180 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.51676 | −0.229543 | ||||||||
\(807\) | 33.9504 | 1.19511 | ||||||||
\(808\) | −56.6187 | −1.99184 | ||||||||
\(809\) | 33.6017 | 1.18137 | 0.590687 | − | 0.806901i | \(-0.298857\pi\) | ||||
0.590687 | + | 0.806901i | \(0.298857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.0056 | −1.33456 | −0.667278 | − | 0.744809i | \(-0.732541\pi\) | ||||
−0.667278 | + | 0.744809i | \(0.732541\pi\) | |||||||
\(812\) | −1.60316 | −0.0562600 | ||||||||
\(813\) | 30.8398 | 1.08160 | ||||||||
\(814\) | −11.6439 | −0.408117 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.48516 | 0.297040 | ||||||||
\(817\) | 45.3755 | 1.58749 | ||||||||
\(818\) | 15.8699 | 0.554877 | ||||||||
\(819\) | −1.07680 | −0.0376264 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.9332 | 0.870176 | 0.435088 | − | 0.900388i | \(-0.356717\pi\) | ||||
0.435088 | + | 0.900388i | \(0.356717\pi\) | |||||||
\(822\) | −56.1220 | −1.95748 | ||||||||
\(823\) | −25.4606 | −0.887499 | −0.443750 | − | 0.896151i | \(-0.646352\pi\) | ||||
−0.443750 | + | 0.896151i | \(0.646352\pi\) | |||||||
\(824\) | −36.5760 | −1.27418 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.00027 | −0.104393 | ||||||||
\(827\) | −32.3387 | −1.12453 | −0.562263 | − | 0.826958i | \(-0.690069\pi\) | ||||
−0.562263 | + | 0.826958i | \(0.690069\pi\) | |||||||
\(828\) | −3.24110 | −0.112636 | ||||||||
\(829\) | 24.9812 | 0.867633 | 0.433816 | − | 0.901001i | \(-0.357167\pi\) | ||||
0.433816 | + | 0.901001i | \(0.357167\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 44.1324 | 1.53094 | ||||||||
\(832\) | −5.92099 | −0.205273 | ||||||||
\(833\) | −10.8167 | −0.374778 | ||||||||
\(834\) | 19.8726 | 0.688133 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.07680 | −0.244756 | ||||||||
\(837\) | −16.5372 | −0.571608 | ||||||||
\(838\) | 35.0337 | 1.21022 | ||||||||
\(839\) | 19.3526 | 0.668125 | 0.334062 | − | 0.942551i | \(-0.391580\pi\) | ||||
0.334062 | + | 0.942551i | \(0.391580\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.34980 | 0.0465447 | ||||||||
\(842\) | −9.34143 | −0.321927 | ||||||||
\(843\) | 13.2091 | 0.454944 | ||||||||
\(844\) | 4.78903 | 0.164845 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.44833 | −0.187318 | ||||||||
\(847\) | −2.85013 | −0.0979317 | ||||||||
\(848\) | 10.4635 | 0.359317 | ||||||||
\(849\) | 30.7775 | 1.05628 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.16980 | −0.211498 | ||||||||
\(852\) | 12.7732 | 0.437602 | ||||||||
\(853\) | −26.7876 | −0.917190 | −0.458595 | − | 0.888645i | \(-0.651647\pi\) | ||||
−0.458595 | + | 0.888645i | \(0.651647\pi\) | |||||||
\(854\) | −4.34832 | −0.148796 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.32340 | −0.0794122 | ||||||||
\(857\) | 47.5186 | 1.62320 | 0.811602 | − | 0.584210i | \(-0.198596\pi\) | ||||
0.811602 | + | 0.584210i | \(0.198596\pi\) | |||||||
\(858\) | 4.13504 | 0.141168 | ||||||||
\(859\) | 11.5290 | 0.393365 | 0.196682 | − | 0.980467i | \(-0.436983\pi\) | ||||
0.196682 | + | 0.980467i | \(0.436983\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.64737 | −0.260622 | ||||||||
\(862\) | 30.7780 | 1.04830 | ||||||||
\(863\) | −18.0057 | −0.612922 | −0.306461 | − | 0.951883i | \(-0.599145\pi\) | ||||
−0.306461 | + | 0.951883i | \(0.599145\pi\) | |||||||
\(864\) | −7.70067 | −0.261982 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 24.3639 | 0.827917 | ||||||||
\(867\) | 37.7272 | 1.28128 | ||||||||
\(868\) | −2.38737 | −0.0810327 | ||||||||
\(869\) | 10.9632 | 0.371900 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.15927 | 0.0731641 | ||||||||
\(872\) | 28.1839 | 0.954429 | ||||||||
\(873\) | 57.4415 | 1.94410 | ||||||||
\(874\) | 6.74338 | 0.228098 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.01411 | 0.0342635 | ||||||||
\(877\) | 17.0973 | 0.577335 | 0.288668 | − | 0.957429i | \(-0.406788\pi\) | ||||
0.288668 | + | 0.957429i | \(0.406788\pi\) | |||||||
\(878\) | −29.2446 | −0.986957 | ||||||||
\(879\) | −50.5846 | −1.70618 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.0291 | −1.28123 | −0.640617 | − | 0.767861i | \(-0.721321\pi\) | ||||
−0.640617 | + | 0.767861i | \(0.721321\pi\) | |||||||
\(882\) | −29.2445 | −0.984714 | ||||||||
\(883\) | 36.8494 | 1.24008 | 0.620040 | − | 0.784570i | \(-0.287116\pi\) | ||||
0.620040 | + | 0.784570i | \(0.287116\pi\) | |||||||
\(884\) | 0.792597 | 0.0266579 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.61061 | 0.121301 | ||||||||
\(887\) | −29.8738 | −1.00306 | −0.501532 | − | 0.865139i | \(-0.667230\pi\) | ||||
−0.501532 | + | 0.865139i | \(0.667230\pi\) | |||||||
\(888\) | −41.1366 | −1.38046 | ||||||||
\(889\) | 2.89295 | 0.0970265 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.1536 | −0.407161 | ||||||||
\(892\) | −7.57004 | −0.253464 | ||||||||
\(893\) | −6.30351 | −0.210939 | ||||||||
\(894\) | 2.12602 | 0.0711046 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.789866 | 0.0263876 | ||||||||
\(897\) | 2.19106 | 0.0731573 | ||||||||
\(898\) | 40.9023 | 1.36493 | ||||||||
\(899\) | 45.1958 | 1.50736 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.04022 | −0.267859 | ||||||||
\(902\) | 16.3620 | 0.544796 | ||||||||
\(903\) | −9.71296 | −0.323227 | ||||||||
\(904\) | 39.5171 | 1.31432 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 45.7898 | 1.52126 | ||||||||
\(907\) | −43.4897 | −1.44405 | −0.722026 | − | 0.691866i | \(-0.756789\pi\) | ||||
−0.722026 | + | 0.691866i | \(0.756789\pi\) | |||||||
\(908\) | 14.0164 | 0.465152 | ||||||||
\(909\) | 69.4371 | 2.30308 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.3690 | −0.807383 | −0.403691 | − | 0.914895i | \(-0.632273\pi\) | ||||
−0.403691 | + | 0.914895i | \(0.632273\pi\) | |||||||
\(912\) | 26.5416 | 0.878879 | ||||||||
\(913\) | 1.94827 | 0.0644783 | ||||||||
\(914\) | 28.9373 | 0.957160 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.31735 | −0.208731 | ||||||||
\(917\) | 0.974848 | 0.0321923 | ||||||||
\(918\) | −3.61699 | −0.119379 | ||||||||
\(919\) | 45.5143 | 1.50138 | 0.750690 | − | 0.660655i | \(-0.229721\pi\) | ||||
0.750690 | + | 0.660655i | \(0.229721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 66.1546 | 2.17987 | ||||||||
\(922\) | −18.8639 | −0.621249 | ||||||||
\(923\) | −4.81106 | −0.158358 | ||||||||
\(924\) | 1.51484 | 0.0498346 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20.2001 | 0.663816 | ||||||||
\(927\) | 44.8567 | 1.47329 | ||||||||
\(928\) | 21.0458 | 0.690863 | ||||||||
\(929\) | 9.03795 | 0.296525 | 0.148263 | − | 0.988948i | \(-0.452632\pi\) | ||||
0.148263 | + | 0.988948i | \(0.452632\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.8347 | −1.10889 | ||||||||
\(932\) | 7.90648 | 0.258985 | ||||||||
\(933\) | −41.2743 | −1.35126 | ||||||||
\(934\) | −16.1531 | −0.528545 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.13939 | 0.266044 | ||||||||
\(937\) | 33.3272 | 1.08875 | 0.544376 | − | 0.838841i | \(-0.316766\pi\) | ||||
0.544376 | + | 0.838841i | \(0.316766\pi\) | |||||||
\(938\) | −1.42253 | −0.0464472 | ||||||||
\(939\) | 18.2622 | 0.595966 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.3010 | −0.955186 | −0.477593 | − | 0.878581i | \(-0.658491\pi\) | ||||
−0.477593 | + | 0.878581i | \(0.658491\pi\) | |||||||
\(942\) | 8.21550 | 0.267676 | ||||||||
\(943\) | 8.66985 | 0.282329 | ||||||||
\(944\) | 13.3878 | 0.435736 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.7815 | 0.675665 | ||||||||
\(947\) | 56.8456 | 1.84723 | 0.923617 | − | 0.383317i | \(-0.125218\pi\) | ||||
0.923617 | + | 0.383317i | \(0.125218\pi\) | |||||||
\(948\) | 10.1971 | 0.331187 | ||||||||
\(949\) | −0.381966 | −0.0123991 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.9238 | 1.10005 | ||||||||
\(952\) | −1.98334 | −0.0642806 | ||||||||
\(953\) | 19.0368 | 0.616663 | 0.308331 | − | 0.951279i | \(-0.400229\pi\) | ||||
0.308331 | + | 0.951279i | \(0.400229\pi\) | |||||||
\(954\) | −21.7378 | −0.703788 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.5108 | −0.372286 | ||||||||
\(957\) | −28.6778 | −0.927021 | ||||||||
\(958\) | 3.29754 | 0.106539 | ||||||||
\(959\) | 7.74394 | 0.250065 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.3039 | 1.17109 | ||||||||
\(962\) | 4.07924 | 0.131520 | ||||||||
\(963\) | 2.84942 | 0.0918212 | ||||||||
\(964\) | −4.28024 | −0.137857 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.44347 | −0.0464429 | ||||||||
\(967\) | −14.7105 | −0.473059 | −0.236529 | − | 0.971624i | \(-0.576010\pi\) | ||||
−0.236529 | + | 0.971624i | \(0.576010\pi\) | |||||||
\(968\) | 21.5438 | 0.692443 | ||||||||
\(969\) | −20.3948 | −0.655174 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.8453 | −1.24661 | −0.623303 | − | 0.781980i | \(-0.714210\pi\) | ||||
−0.623303 | + | 0.781980i | \(0.714210\pi\) | |||||||
\(972\) | −15.6264 | −0.501218 | ||||||||
\(973\) | −2.74211 | −0.0879081 | ||||||||
\(974\) | −19.3469 | −0.619914 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.4030 | 0.621076 | ||||||||
\(977\) | 58.4544 | 1.87012 | 0.935060 | − | 0.354489i | \(-0.115345\pi\) | ||||
0.935060 | + | 0.354489i | \(0.115345\pi\) | |||||||
\(978\) | −71.4307 | −2.28410 | ||||||||
\(979\) | −4.53297 | −0.144874 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.5647 | −1.10357 | ||||||||
\(982\) | 34.8918 | 1.11344 | ||||||||
\(983\) | −28.1595 | −0.898147 | −0.449074 | − | 0.893495i | \(-0.648246\pi\) | ||||
−0.449074 | + | 0.893495i | \(0.648246\pi\) | |||||||
\(984\) | 57.8055 | 1.84277 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.88519 | 0.314809 | ||||||||
\(987\) | 1.34931 | 0.0429491 | ||||||||
\(988\) | 2.47924 | 0.0788752 | ||||||||
\(989\) | 11.0116 | 0.350149 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.3437 | 1.24979 | 0.624897 | − | 0.780707i | \(-0.285141\pi\) | ||||
0.624897 | + | 0.780707i | \(0.285141\pi\) | |||||||
\(992\) | 31.3407 | 0.995067 | ||||||||
\(993\) | 45.9231 | 1.45733 | ||||||||
\(994\) | 3.16953 | 0.100531 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.81213 | 0.0574195 | ||||||||
\(997\) | −43.1178 | −1.36555 | −0.682777 | − | 0.730627i | \(-0.739228\pi\) | ||||
−0.682777 | + | 0.730627i | \(0.739228\pi\) | |||||||
\(998\) | −13.4711 | −0.426419 | ||||||||
\(999\) | 10.3516 | 0.327511 |
(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 | 625.2.a.f.1.6 | 8 | ||
3.2 | odd | 2 | 5625.2.a.x.1.3 | 8 | |||
4.3 | odd | 2 | 10000.2.a.bj.1.8 | 8 | |||
5.2 | odd | 4 | 625.2.b.c.624.6 | 8 | |||
5.3 | odd | 4 | 625.2.b.c.624.3 | 8 | |||
5.4 | even | 2 | inner | 625.2.a.f.1.3 | 8 | ||
15.14 | odd | 2 | 5625.2.a.x.1.6 | 8 | |||
20.19 | odd | 2 | 10000.2.a.bj.1.1 | 8 | |||
25.2 | odd | 20 | 625.2.e.i.124.2 | 8 | |||
25.3 | odd | 20 | 125.2.e.b.49.1 | 8 | |||
25.4 | even | 10 | 125.2.d.b.76.3 | 16 | |||
25.6 | even | 5 | 125.2.d.b.51.2 | 16 | |||
25.8 | odd | 20 | 25.2.e.a.14.2 | yes | 8 | ||
25.9 | even | 10 | 625.2.d.o.126.2 | 16 | |||
25.11 | even | 5 | 625.2.d.o.501.3 | 16 | |||
25.12 | odd | 20 | 625.2.e.a.499.1 | 8 | |||
25.13 | odd | 20 | 625.2.e.i.499.2 | 8 | |||
25.14 | even | 10 | 625.2.d.o.501.2 | 16 | |||
25.16 | even | 5 | 625.2.d.o.126.3 | 16 | |||
25.17 | odd | 20 | 125.2.e.b.74.1 | 8 | |||
25.19 | even | 10 | 125.2.d.b.51.3 | 16 | |||
25.21 | even | 5 | 125.2.d.b.76.2 | 16 | |||
25.22 | odd | 20 | 25.2.e.a.9.2 | ✓ | 8 | ||
25.23 | odd | 20 | 625.2.e.a.124.1 | 8 | |||
75.8 | even | 20 | 225.2.m.a.64.1 | 8 | |||
75.47 | even | 20 | 225.2.m.a.109.1 | 8 | |||
100.47 | even | 20 | 400.2.y.c.209.2 | 8 | |||
100.83 | even | 20 | 400.2.y.c.289.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.e.a.9.2 | ✓ | 8 | 25.22 | odd | 20 | ||
25.2.e.a.14.2 | yes | 8 | 25.8 | odd | 20 | ||
125.2.d.b.51.2 | 16 | 25.6 | even | 5 | |||
125.2.d.b.51.3 | 16 | 25.19 | even | 10 | |||
125.2.d.b.76.2 | 16 | 25.21 | even | 5 | |||
125.2.d.b.76.3 | 16 | 25.4 | even | 10 | |||
125.2.e.b.49.1 | 8 | 25.3 | odd | 20 | |||
125.2.e.b.74.1 | 8 | 25.17 | odd | 20 | |||
225.2.m.a.64.1 | 8 | 75.8 | even | 20 | |||
225.2.m.a.109.1 | 8 | 75.47 | even | 20 | |||
400.2.y.c.209.2 | 8 | 100.47 | even | 20 | |||
400.2.y.c.289.2 | 8 | 100.83 | even | 20 | |||
625.2.a.f.1.3 | 8 | 5.4 | even | 2 | inner | ||
625.2.a.f.1.6 | 8 | 1.1 | even | 1 | trivial | ||
625.2.b.c.624.3 | 8 | 5.3 | odd | 4 | |||
625.2.b.c.624.6 | 8 | 5.2 | odd | 4 | |||
625.2.d.o.126.2 | 16 | 25.9 | even | 10 | |||
625.2.d.o.126.3 | 16 | 25.16 | even | 5 | |||
625.2.d.o.501.2 | 16 | 25.14 | even | 10 | |||
625.2.d.o.501.3 | 16 | 25.11 | even | 5 | |||
625.2.e.a.124.1 | 8 | 25.23 | odd | 20 | |||
625.2.e.a.499.1 | 8 | 25.12 | odd | 20 | |||
625.2.e.i.124.2 | 8 | 25.2 | odd | 20 | |||
625.2.e.i.499.2 | 8 | 25.13 | odd | 20 | |||
5625.2.a.x.1.3 | 8 | 3.2 | odd | 2 | |||
5625.2.a.x.1.6 | 8 | 15.14 | odd | 2 | |||
10000.2.a.bj.1.1 | 8 | 20.19 | odd | 2 | |||
10000.2.a.bj.1.8 | 8 | 4.3 | odd | 2 |