Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, 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("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 15x^{5} + 16x^{4} + 49x^{3} - 53x^{2} - 44x + 48 \) |
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 | 1.5 | ||
Root | \(1.14366\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.65255 | 0.954103 | 0.477051 | − | 0.878875i | \(-0.341706\pi\) | ||||
0.477051 | + | 0.878875i | \(0.341706\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.725043 | 0.324249 | 0.162125 | − | 0.986770i | \(-0.448165\pi\) | ||||
0.162125 | + | 0.986770i | \(0.448165\pi\) | |||||||
\(6\) | 1.65255 | 0.674652 | ||||||||
\(7\) | 1.29978 | 0.491269 | 0.245635 | − | 0.969362i | \(-0.421004\pi\) | ||||
0.245635 | + | 0.969362i | \(0.421004\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.269065 | −0.0896884 | ||||||||
\(10\) | 0.725043 | 0.229279 | ||||||||
\(11\) | −3.71687 | −1.12068 | −0.560340 | − | 0.828263i | \(-0.689329\pi\) | ||||
−0.560340 | + | 0.828263i | \(0.689329\pi\) | |||||||
\(12\) | 1.65255 | 0.477051 | ||||||||
\(13\) | 2.30856 | 0.640280 | 0.320140 | − | 0.947370i | \(-0.396270\pi\) | ||||
0.320140 | + | 0.947370i | \(0.396270\pi\) | |||||||
\(14\) | 1.29978 | 0.347380 | ||||||||
\(15\) | 1.19817 | 0.309367 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.32982 | 1.53521 | 0.767603 | − | 0.640925i | \(-0.221449\pi\) | ||||
0.767603 | + | 0.640925i | \(0.221449\pi\) | |||||||
\(18\) | −0.269065 | −0.0634192 | ||||||||
\(19\) | 0.0212539 | 0.00487598 | 0.00243799 | − | 0.999997i | \(-0.499224\pi\) | ||||
0.00243799 | + | 0.999997i | \(0.499224\pi\) | |||||||
\(20\) | 0.725043 | 0.162125 | ||||||||
\(21\) | 2.14795 | 0.468721 | ||||||||
\(22\) | −3.71687 | −0.792440 | ||||||||
\(23\) | −1.30511 | −0.272134 | −0.136067 | − | 0.990700i | \(-0.543446\pi\) | ||||
−0.136067 | + | 0.990700i | \(0.543446\pi\) | |||||||
\(24\) | 1.65255 | 0.337326 | ||||||||
\(25\) | −4.47431 | −0.894863 | ||||||||
\(26\) | 2.30856 | 0.452747 | ||||||||
\(27\) | −5.40231 | −1.03967 | ||||||||
\(28\) | 1.29978 | 0.245635 | ||||||||
\(29\) | −2.06303 | −0.383095 | −0.191548 | − | 0.981483i | \(-0.561351\pi\) | ||||
−0.191548 | + | 0.981483i | \(0.561351\pi\) | |||||||
\(30\) | 1.19817 | 0.218755 | ||||||||
\(31\) | −5.82316 | −1.04587 | −0.522935 | − | 0.852372i | \(-0.675163\pi\) | ||||
−0.522935 | + | 0.852372i | \(0.675163\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.14233 | −1.06924 | ||||||||
\(34\) | 6.32982 | 1.08555 | ||||||||
\(35\) | 0.942394 | 0.159294 | ||||||||
\(36\) | −0.269065 | −0.0448442 | ||||||||
\(37\) | −7.25272 | −1.19234 | −0.596170 | − | 0.802858i | \(-0.703312\pi\) | ||||
−0.596170 | + | 0.802858i | \(0.703312\pi\) | |||||||
\(38\) | 0.0212539 | 0.00344784 | ||||||||
\(39\) | 3.81503 | 0.610893 | ||||||||
\(40\) | 0.725043 | 0.114639 | ||||||||
\(41\) | 8.77454 | 1.37035 | 0.685176 | − | 0.728377i | \(-0.259725\pi\) | ||||
0.685176 | + | 0.728377i | \(0.259725\pi\) | |||||||
\(42\) | 2.14795 | 0.331436 | ||||||||
\(43\) | 4.52327 | 0.689792 | 0.344896 | − | 0.938641i | \(-0.387914\pi\) | ||||
0.344896 | + | 0.938641i | \(0.387914\pi\) | |||||||
\(44\) | −3.71687 | −0.560340 | ||||||||
\(45\) | −0.195084 | −0.0290814 | ||||||||
\(46\) | −1.30511 | −0.192428 | ||||||||
\(47\) | 3.85502 | 0.562313 | 0.281156 | − | 0.959662i | \(-0.409282\pi\) | ||||
0.281156 | + | 0.959662i | \(0.409282\pi\) | |||||||
\(48\) | 1.65255 | 0.238526 | ||||||||
\(49\) | −5.31058 | −0.758654 | ||||||||
\(50\) | −4.47431 | −0.632763 | ||||||||
\(51\) | 10.4604 | 1.46474 | ||||||||
\(52\) | 2.30856 | 0.320140 | ||||||||
\(53\) | −6.86923 | −0.943562 | −0.471781 | − | 0.881716i | \(-0.656389\pi\) | ||||
−0.471781 | + | 0.881716i | \(0.656389\pi\) | |||||||
\(54\) | −5.40231 | −0.735161 | ||||||||
\(55\) | −2.69489 | −0.363379 | ||||||||
\(56\) | 1.29978 | 0.173690 | ||||||||
\(57\) | 0.0351232 | 0.00465218 | ||||||||
\(58\) | −2.06303 | −0.270889 | ||||||||
\(59\) | 7.84518 | 1.02136 | 0.510678 | − | 0.859772i | \(-0.329395\pi\) | ||||
0.510678 | + | 0.859772i | \(0.329395\pi\) | |||||||
\(60\) | 1.19817 | 0.154683 | ||||||||
\(61\) | 3.84958 | 0.492888 | 0.246444 | − | 0.969157i | \(-0.420738\pi\) | ||||
0.246444 | + | 0.969157i | \(0.420738\pi\) | |||||||
\(62\) | −5.82316 | −0.739542 | ||||||||
\(63\) | −0.349724 | −0.0440611 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.67381 | 0.207610 | ||||||||
\(66\) | −6.14233 | −0.756069 | ||||||||
\(67\) | −9.31541 | −1.13806 | −0.569029 | − | 0.822317i | \(-0.692681\pi\) | ||||
−0.569029 | + | 0.822317i | \(0.692681\pi\) | |||||||
\(68\) | 6.32982 | 0.767603 | ||||||||
\(69\) | −2.15676 | −0.259644 | ||||||||
\(70\) | 0.942394 | 0.112638 | ||||||||
\(71\) | −0.643097 | −0.0763215 | −0.0381608 | − | 0.999272i | \(-0.512150\pi\) | ||||
−0.0381608 | + | 0.999272i | \(0.512150\pi\) | |||||||
\(72\) | −0.269065 | −0.0317096 | ||||||||
\(73\) | −2.97920 | −0.348689 | −0.174345 | − | 0.984685i | \(-0.555781\pi\) | ||||
−0.174345 | + | 0.984685i | \(0.555781\pi\) | |||||||
\(74\) | −7.25272 | −0.843112 | ||||||||
\(75\) | −7.39404 | −0.853791 | ||||||||
\(76\) | 0.0212539 | 0.00243799 | ||||||||
\(77\) | −4.83110 | −0.550555 | ||||||||
\(78\) | 3.81503 | 0.431967 | ||||||||
\(79\) | 0.418245 | 0.0470563 | 0.0235281 | − | 0.999723i | \(-0.492510\pi\) | ||||
0.0235281 | + | 0.999723i | \(0.492510\pi\) | |||||||
\(80\) | 0.725043 | 0.0810623 | ||||||||
\(81\) | −8.12041 | −0.902268 | ||||||||
\(82\) | 8.77454 | 0.968985 | ||||||||
\(83\) | −15.6322 | −1.71585 | −0.857927 | − | 0.513771i | \(-0.828248\pi\) | ||||
−0.857927 | + | 0.513771i | \(0.828248\pi\) | |||||||
\(84\) | 2.14795 | 0.234361 | ||||||||
\(85\) | 4.58939 | 0.497789 | ||||||||
\(86\) | 4.52327 | 0.487757 | ||||||||
\(87\) | −3.40927 | −0.365512 | ||||||||
\(88\) | −3.71687 | −0.396220 | ||||||||
\(89\) | 10.3879 | 1.10111 | 0.550556 | − | 0.834798i | \(-0.314416\pi\) | ||||
0.550556 | + | 0.834798i | \(0.314416\pi\) | |||||||
\(90\) | −0.195084 | −0.0205636 | ||||||||
\(91\) | 3.00062 | 0.314550 | ||||||||
\(92\) | −1.30511 | −0.136067 | ||||||||
\(93\) | −9.62309 | −0.997868 | ||||||||
\(94\) | 3.85502 | 0.397615 | ||||||||
\(95\) | 0.0154100 | 0.00158103 | ||||||||
\(96\) | 1.65255 | 0.168663 | ||||||||
\(97\) | 5.07659 | 0.515450 | 0.257725 | − | 0.966218i | \(-0.417027\pi\) | ||||
0.257725 | + | 0.966218i | \(0.417027\pi\) | |||||||
\(98\) | −5.31058 | −0.536450 | ||||||||
\(99\) | 1.00008 | 0.100512 | ||||||||
\(100\) | −4.47431 | −0.447431 | ||||||||
\(101\) | 12.5321 | 1.24699 | 0.623495 | − | 0.781827i | \(-0.285712\pi\) | ||||
0.623495 | + | 0.781827i | \(0.285712\pi\) | |||||||
\(102\) | 10.4604 | 1.03573 | ||||||||
\(103\) | 5.43374 | 0.535403 | 0.267701 | − | 0.963502i | \(-0.413736\pi\) | ||||
0.267701 | + | 0.963502i | \(0.413736\pi\) | |||||||
\(104\) | 2.30856 | 0.226373 | ||||||||
\(105\) | 1.55736 | 0.151982 | ||||||||
\(106\) | −6.86923 | −0.667199 | ||||||||
\(107\) | −3.45500 | −0.334007 | −0.167004 | − | 0.985956i | \(-0.553409\pi\) | ||||
−0.167004 | + | 0.985956i | \(0.553409\pi\) | |||||||
\(108\) | −5.40231 | −0.519837 | ||||||||
\(109\) | −6.80801 | −0.652089 | −0.326044 | − | 0.945354i | \(-0.605716\pi\) | ||||
−0.326044 | + | 0.945354i | \(0.605716\pi\) | |||||||
\(110\) | −2.69489 | −0.256948 | ||||||||
\(111\) | −11.9855 | −1.13762 | ||||||||
\(112\) | 1.29978 | 0.122817 | ||||||||
\(113\) | 0.407582 | 0.0383421 | 0.0191710 | − | 0.999816i | \(-0.493897\pi\) | ||||
0.0191710 | + | 0.999816i | \(0.493897\pi\) | |||||||
\(114\) | 0.0351232 | 0.00328959 | ||||||||
\(115\) | −0.946259 | −0.0882391 | ||||||||
\(116\) | −2.06303 | −0.191548 | ||||||||
\(117\) | −0.621154 | −0.0574257 | ||||||||
\(118\) | 7.84518 | 0.722207 | ||||||||
\(119\) | 8.22735 | 0.754200 | ||||||||
\(120\) | 1.19817 | 0.109378 | ||||||||
\(121\) | 2.81514 | 0.255922 | ||||||||
\(122\) | 3.84958 | 0.348524 | ||||||||
\(123\) | 14.5004 | 1.30746 | ||||||||
\(124\) | −5.82316 | −0.522935 | ||||||||
\(125\) | −6.86928 | −0.614407 | ||||||||
\(126\) | −0.349724 | −0.0311559 | ||||||||
\(127\) | −9.52589 | −0.845286 | −0.422643 | − | 0.906296i | \(-0.638898\pi\) | ||||
−0.422643 | + | 0.906296i | \(0.638898\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 7.47495 | 0.658132 | ||||||||
\(130\) | 1.67381 | 0.146803 | ||||||||
\(131\) | −21.9325 | −1.91625 | −0.958127 | − | 0.286342i | \(-0.907561\pi\) | ||||
−0.958127 | + | 0.286342i | \(0.907561\pi\) | |||||||
\(132\) | −6.14233 | −0.534621 | ||||||||
\(133\) | 0.0276253 | 0.00239542 | ||||||||
\(134\) | −9.31541 | −0.804729 | ||||||||
\(135\) | −3.91690 | −0.337113 | ||||||||
\(136\) | 6.32982 | 0.542777 | ||||||||
\(137\) | −2.48849 | −0.212606 | −0.106303 | − | 0.994334i | \(-0.533901\pi\) | ||||
−0.106303 | + | 0.994334i | \(0.533901\pi\) | |||||||
\(138\) | −2.15676 | −0.183596 | ||||||||
\(139\) | 21.6244 | 1.83416 | 0.917078 | − | 0.398708i | \(-0.130541\pi\) | ||||
0.917078 | + | 0.398708i | \(0.130541\pi\) | |||||||
\(140\) | 0.942394 | 0.0796468 | ||||||||
\(141\) | 6.37063 | 0.536504 | ||||||||
\(142\) | −0.643097 | −0.0539675 | ||||||||
\(143\) | −8.58064 | −0.717549 | ||||||||
\(144\) | −0.269065 | −0.0224221 | ||||||||
\(145\) | −1.49579 | −0.124218 | ||||||||
\(146\) | −2.97920 | −0.246561 | ||||||||
\(147\) | −8.77602 | −0.723834 | ||||||||
\(148\) | −7.25272 | −0.596170 | ||||||||
\(149\) | 20.9106 | 1.71306 | 0.856532 | − | 0.516093i | \(-0.172614\pi\) | ||||
0.856532 | + | 0.516093i | \(0.172614\pi\) | |||||||
\(150\) | −7.39404 | −0.603721 | ||||||||
\(151\) | −2.07209 | −0.168624 | −0.0843120 | − | 0.996439i | \(-0.526869\pi\) | ||||
−0.0843120 | + | 0.996439i | \(0.526869\pi\) | |||||||
\(152\) | 0.0212539 | 0.00172392 | ||||||||
\(153\) | −1.70313 | −0.137690 | ||||||||
\(154\) | −4.83110 | −0.389301 | ||||||||
\(155\) | −4.22204 | −0.339123 | ||||||||
\(156\) | 3.81503 | 0.305447 | ||||||||
\(157\) | −2.60975 | −0.208281 | −0.104140 | − | 0.994563i | \(-0.533209\pi\) | ||||
−0.104140 | + | 0.994563i | \(0.533209\pi\) | |||||||
\(158\) | 0.418245 | 0.0332738 | ||||||||
\(159\) | −11.3518 | −0.900255 | ||||||||
\(160\) | 0.725043 | 0.0573197 | ||||||||
\(161\) | −1.69635 | −0.133691 | ||||||||
\(162\) | −8.12041 | −0.638000 | ||||||||
\(163\) | −6.63147 | −0.519417 | −0.259708 | − | 0.965687i | \(-0.583626\pi\) | ||||
−0.259708 | + | 0.965687i | \(0.583626\pi\) | |||||||
\(164\) | 8.77454 | 0.685176 | ||||||||
\(165\) | −4.45345 | −0.346701 | ||||||||
\(166\) | −15.6322 | −1.21329 | ||||||||
\(167\) | 22.6369 | 1.75170 | 0.875850 | − | 0.482584i | \(-0.160302\pi\) | ||||
0.875850 | + | 0.482584i | \(0.160302\pi\) | |||||||
\(168\) | 2.14795 | 0.165718 | ||||||||
\(169\) | −7.67053 | −0.590041 | ||||||||
\(170\) | 4.58939 | 0.351990 | ||||||||
\(171\) | −0.00571868 | −0.000437318 0 | ||||||||
\(172\) | 4.52327 | 0.344896 | ||||||||
\(173\) | 12.2456 | 0.931018 | 0.465509 | − | 0.885043i | \(-0.345871\pi\) | ||||
0.465509 | + | 0.885043i | \(0.345871\pi\) | |||||||
\(174\) | −3.40927 | −0.258456 | ||||||||
\(175\) | −5.81561 | −0.439619 | ||||||||
\(176\) | −3.71687 | −0.280170 | ||||||||
\(177\) | 12.9646 | 0.974478 | ||||||||
\(178\) | 10.3879 | 0.778603 | ||||||||
\(179\) | −18.0181 | −1.34673 | −0.673367 | − | 0.739308i | \(-0.735153\pi\) | ||||
−0.673367 | + | 0.739308i | \(0.735153\pi\) | |||||||
\(180\) | −0.195084 | −0.0145407 | ||||||||
\(181\) | 7.77690 | 0.578052 | 0.289026 | − | 0.957321i | \(-0.406669\pi\) | ||||
0.289026 | + | 0.957321i | \(0.406669\pi\) | |||||||
\(182\) | 3.00062 | 0.222421 | ||||||||
\(183\) | 6.36163 | 0.470266 | ||||||||
\(184\) | −1.30511 | −0.0962138 | ||||||||
\(185\) | −5.25854 | −0.386615 | ||||||||
\(186\) | −9.62309 | −0.705599 | ||||||||
\(187\) | −23.5271 | −1.72047 | ||||||||
\(188\) | 3.85502 | 0.281156 | ||||||||
\(189\) | −7.02179 | −0.510760 | ||||||||
\(190\) | 0.0154100 | 0.00111796 | ||||||||
\(191\) | 0.312243 | 0.0225931 | 0.0112965 | − | 0.999936i | \(-0.496404\pi\) | ||||
0.0112965 | + | 0.999936i | \(0.496404\pi\) | |||||||
\(192\) | 1.65255 | 0.119263 | ||||||||
\(193\) | −0.336949 | −0.0242541 | −0.0121271 | − | 0.999926i | \(-0.503860\pi\) | ||||
−0.0121271 | + | 0.999926i | \(0.503860\pi\) | |||||||
\(194\) | 5.07659 | 0.364478 | ||||||||
\(195\) | 2.76606 | 0.198082 | ||||||||
\(196\) | −5.31058 | −0.379327 | ||||||||
\(197\) | 26.8275 | 1.91138 | 0.955691 | − | 0.294370i | \(-0.0951099\pi\) | ||||
0.955691 | + | 0.294370i | \(0.0951099\pi\) | |||||||
\(198\) | 1.00008 | 0.0710726 | ||||||||
\(199\) | 4.03560 | 0.286076 | 0.143038 | − | 0.989717i | \(-0.454313\pi\) | ||||
0.143038 | + | 0.989717i | \(0.454313\pi\) | |||||||
\(200\) | −4.47431 | −0.316382 | ||||||||
\(201\) | −15.3942 | −1.08582 | ||||||||
\(202\) | 12.5321 | 0.881755 | ||||||||
\(203\) | −2.68148 | −0.188203 | ||||||||
\(204\) | 10.4604 | 0.732372 | ||||||||
\(205\) | 6.36192 | 0.444335 | ||||||||
\(206\) | 5.43374 | 0.378587 | ||||||||
\(207\) | 0.351159 | 0.0244072 | ||||||||
\(208\) | 2.30856 | 0.160070 | ||||||||
\(209\) | −0.0789980 | −0.00546440 | ||||||||
\(210\) | 1.55736 | 0.107468 | ||||||||
\(211\) | 9.22688 | 0.635205 | 0.317602 | − | 0.948224i | \(-0.397122\pi\) | ||||
0.317602 | + | 0.948224i | \(0.397122\pi\) | |||||||
\(212\) | −6.86923 | −0.471781 | ||||||||
\(213\) | −1.06275 | −0.0728186 | ||||||||
\(214\) | −3.45500 | −0.236179 | ||||||||
\(215\) | 3.27956 | 0.223664 | ||||||||
\(216\) | −5.40231 | −0.367580 | ||||||||
\(217\) | −7.56881 | −0.513804 | ||||||||
\(218\) | −6.80801 | −0.461096 | ||||||||
\(219\) | −4.92329 | −0.332685 | ||||||||
\(220\) | −2.69489 | −0.181690 | ||||||||
\(221\) | 14.6128 | 0.982963 | ||||||||
\(222\) | −11.9855 | −0.804415 | ||||||||
\(223\) | −9.44842 | −0.632713 | −0.316357 | − | 0.948640i | \(-0.602460\pi\) | ||||
−0.316357 | + | 0.948640i | \(0.602460\pi\) | |||||||
\(224\) | 1.29978 | 0.0868450 | ||||||||
\(225\) | 1.20388 | 0.0802588 | ||||||||
\(226\) | 0.407582 | 0.0271119 | ||||||||
\(227\) | 15.2061 | 1.00926 | 0.504632 | − | 0.863335i | \(-0.331628\pi\) | ||||
0.504632 | + | 0.863335i | \(0.331628\pi\) | |||||||
\(228\) | 0.0351232 | 0.00232609 | ||||||||
\(229\) | 28.6411 | 1.89266 | 0.946329 | − | 0.323205i | \(-0.104760\pi\) | ||||
0.946329 | + | 0.323205i | \(0.104760\pi\) | |||||||
\(230\) | −0.946259 | −0.0623945 | ||||||||
\(231\) | −7.98366 | −0.525286 | ||||||||
\(232\) | −2.06303 | −0.135445 | ||||||||
\(233\) | 3.14875 | 0.206281 | 0.103141 | − | 0.994667i | \(-0.467111\pi\) | ||||
0.103141 | + | 0.994667i | \(0.467111\pi\) | |||||||
\(234\) | −0.621154 | −0.0406061 | ||||||||
\(235\) | 2.79506 | 0.182329 | ||||||||
\(236\) | 7.84518 | 0.510678 | ||||||||
\(237\) | 0.691173 | 0.0448965 | ||||||||
\(238\) | 8.22735 | 0.533300 | ||||||||
\(239\) | 12.5059 | 0.808940 | 0.404470 | − | 0.914551i | \(-0.367456\pi\) | ||||
0.404470 | + | 0.914551i | \(0.367456\pi\) | |||||||
\(240\) | 1.19817 | 0.0773417 | ||||||||
\(241\) | 3.73027 | 0.240287 | 0.120144 | − | 0.992757i | \(-0.461664\pi\) | ||||
0.120144 | + | 0.992757i | \(0.461664\pi\) | |||||||
\(242\) | 2.81514 | 0.180964 | ||||||||
\(243\) | 2.78751 | 0.178819 | ||||||||
\(244\) | 3.84958 | 0.246444 | ||||||||
\(245\) | −3.85040 | −0.245993 | ||||||||
\(246\) | 14.5004 | 0.924511 | ||||||||
\(247\) | 0.0490660 | 0.00312199 | ||||||||
\(248\) | −5.82316 | −0.369771 | ||||||||
\(249\) | −25.8330 | −1.63710 | ||||||||
\(250\) | −6.86928 | −0.434452 | ||||||||
\(251\) | −26.2795 | −1.65875 | −0.829374 | − | 0.558694i | \(-0.811303\pi\) | ||||
−0.829374 | + | 0.558694i | \(0.811303\pi\) | |||||||
\(252\) | −0.349724 | −0.0220306 | ||||||||
\(253\) | 4.85092 | 0.304975 | ||||||||
\(254\) | −9.52589 | −0.597708 | ||||||||
\(255\) | 7.58421 | 0.474942 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.2237 | 1.76055 | 0.880273 | − | 0.474468i | \(-0.157359\pi\) | ||||
0.880273 | + | 0.474468i | \(0.157359\pi\) | |||||||
\(258\) | 7.47495 | 0.465370 | ||||||||
\(259\) | −9.42692 | −0.585760 | ||||||||
\(260\) | 1.67381 | 0.103805 | ||||||||
\(261\) | 0.555090 | 0.0343592 | ||||||||
\(262\) | −21.9325 | −1.35500 | ||||||||
\(263\) | 25.3865 | 1.56540 | 0.782701 | − | 0.622398i | \(-0.213842\pi\) | ||||
0.782701 | + | 0.622398i | \(0.213842\pi\) | |||||||
\(264\) | −6.14233 | −0.378034 | ||||||||
\(265\) | −4.98049 | −0.305949 | ||||||||
\(266\) | 0.0276253 | 0.00169382 | ||||||||
\(267\) | 17.1665 | 1.05057 | ||||||||
\(268\) | −9.31541 | −0.569029 | ||||||||
\(269\) | −1.00000 | −0.0609711 | ||||||||
\(270\) | −3.91690 | −0.238375 | ||||||||
\(271\) | −17.9078 | −1.08782 | −0.543911 | − | 0.839143i | \(-0.683057\pi\) | ||||
−0.543911 | + | 0.839143i | \(0.683057\pi\) | |||||||
\(272\) | 6.32982 | 0.383802 | ||||||||
\(273\) | 4.95868 | 0.300113 | ||||||||
\(274\) | −2.48849 | −0.150335 | ||||||||
\(275\) | 16.6304 | 1.00285 | ||||||||
\(276\) | −2.15676 | −0.129822 | ||||||||
\(277\) | −6.51988 | −0.391741 | −0.195871 | − | 0.980630i | \(-0.562753\pi\) | ||||
−0.195871 | + | 0.980630i | \(0.562753\pi\) | |||||||
\(278\) | 21.6244 | 1.29694 | ||||||||
\(279\) | 1.56681 | 0.0938024 | ||||||||
\(280\) | 0.942394 | 0.0563188 | ||||||||
\(281\) | −2.61394 | −0.155934 | −0.0779672 | − | 0.996956i | \(-0.524843\pi\) | ||||
−0.0779672 | + | 0.996956i | \(0.524843\pi\) | |||||||
\(282\) | 6.37063 | 0.379366 | ||||||||
\(283\) | −9.65338 | −0.573834 | −0.286917 | − | 0.957955i | \(-0.592630\pi\) | ||||
−0.286917 | + | 0.957955i | \(0.592630\pi\) | |||||||
\(284\) | −0.643097 | −0.0381608 | ||||||||
\(285\) | 0.0254658 | 0.00150847 | ||||||||
\(286\) | −8.58064 | −0.507384 | ||||||||
\(287\) | 11.4049 | 0.673212 | ||||||||
\(288\) | −0.269065 | −0.0158548 | ||||||||
\(289\) | 23.0666 | 1.35686 | ||||||||
\(290\) | −1.49579 | −0.0878356 | ||||||||
\(291\) | 8.38934 | 0.491792 | ||||||||
\(292\) | −2.97920 | −0.174345 | ||||||||
\(293\) | 2.04724 | 0.119601 | 0.0598005 | − | 0.998210i | \(-0.480954\pi\) | ||||
0.0598005 | + | 0.998210i | \(0.480954\pi\) | |||||||
\(294\) | −8.77602 | −0.511828 | ||||||||
\(295\) | 5.68809 | 0.331173 | ||||||||
\(296\) | −7.25272 | −0.421556 | ||||||||
\(297\) | 20.0797 | 1.16514 | ||||||||
\(298\) | 20.9106 | 1.21132 | ||||||||
\(299\) | −3.01293 | −0.174242 | ||||||||
\(300\) | −7.39404 | −0.426895 | ||||||||
\(301\) | 5.87924 | 0.338874 | ||||||||
\(302\) | −2.07209 | −0.119235 | ||||||||
\(303\) | 20.7100 | 1.18976 | ||||||||
\(304\) | 0.0212539 | 0.00121899 | ||||||||
\(305\) | 2.79111 | 0.159818 | ||||||||
\(306\) | −1.70313 | −0.0973616 | ||||||||
\(307\) | −18.6159 | −1.06246 | −0.531231 | − | 0.847227i | \(-0.678271\pi\) | ||||
−0.531231 | + | 0.847227i | \(0.678271\pi\) | |||||||
\(308\) | −4.83110 | −0.275278 | ||||||||
\(309\) | 8.97956 | 0.510829 | ||||||||
\(310\) | −4.22204 | −0.239796 | ||||||||
\(311\) | −9.88503 | −0.560529 | −0.280264 | − | 0.959923i | \(-0.590422\pi\) | ||||
−0.280264 | + | 0.959923i | \(0.590422\pi\) | |||||||
\(312\) | 3.81503 | 0.215983 | ||||||||
\(313\) | 17.4438 | 0.985983 | 0.492991 | − | 0.870034i | \(-0.335903\pi\) | ||||
0.492991 | + | 0.870034i | \(0.335903\pi\) | |||||||
\(314\) | −2.60975 | −0.147277 | ||||||||
\(315\) | −0.253565 | −0.0142868 | ||||||||
\(316\) | 0.418245 | 0.0235281 | ||||||||
\(317\) | 2.92828 | 0.164468 | 0.0822342 | − | 0.996613i | \(-0.473794\pi\) | ||||
0.0822342 | + | 0.996613i | \(0.473794\pi\) | |||||||
\(318\) | −11.3518 | −0.636576 | ||||||||
\(319\) | 7.66802 | 0.429327 | ||||||||
\(320\) | 0.725043 | 0.0405311 | ||||||||
\(321\) | −5.70957 | −0.318677 | ||||||||
\(322\) | −1.69635 | −0.0945338 | ||||||||
\(323\) | 0.134533 | 0.00748563 | ||||||||
\(324\) | −8.12041 | −0.451134 | ||||||||
\(325\) | −10.3292 | −0.572963 | ||||||||
\(326\) | −6.63147 | −0.367283 | ||||||||
\(327\) | −11.2506 | −0.622159 | ||||||||
\(328\) | 8.77454 | 0.484493 | ||||||||
\(329\) | 5.01067 | 0.276247 | ||||||||
\(330\) | −4.45345 | −0.245155 | ||||||||
\(331\) | 5.44140 | 0.299087 | 0.149543 | − | 0.988755i | \(-0.452220\pi\) | ||||
0.149543 | + | 0.988755i | \(0.452220\pi\) | |||||||
\(332\) | −15.6322 | −0.857927 | ||||||||
\(333\) | 1.95145 | 0.106939 | ||||||||
\(334\) | 22.6369 | 1.23864 | ||||||||
\(335\) | −6.75407 | −0.369014 | ||||||||
\(336\) | 2.14795 | 0.117180 | ||||||||
\(337\) | −3.73840 | −0.203644 | −0.101822 | − | 0.994803i | \(-0.532467\pi\) | ||||
−0.101822 | + | 0.994803i | \(0.532467\pi\) | |||||||
\(338\) | −7.67053 | −0.417222 | ||||||||
\(339\) | 0.673551 | 0.0365823 | ||||||||
\(340\) | 4.58939 | 0.248895 | ||||||||
\(341\) | 21.6439 | 1.17209 | ||||||||
\(342\) | −0.00571868 | −0.000309231 0 | ||||||||
\(343\) | −16.0010 | −0.863973 | ||||||||
\(344\) | 4.52327 | 0.243878 | ||||||||
\(345\) | −1.56374 | −0.0841892 | ||||||||
\(346\) | 12.2456 | 0.658329 | ||||||||
\(347\) | 10.8089 | 0.580252 | 0.290126 | − | 0.956988i | \(-0.406303\pi\) | ||||
0.290126 | + | 0.956988i | \(0.406303\pi\) | |||||||
\(348\) | −3.40927 | −0.182756 | ||||||||
\(349\) | 19.8978 | 1.06510 | 0.532552 | − | 0.846397i | \(-0.321233\pi\) | ||||
0.532552 | + | 0.846397i | \(0.321233\pi\) | |||||||
\(350\) | −5.81561 | −0.310857 | ||||||||
\(351\) | −12.4716 | −0.665683 | ||||||||
\(352\) | −3.71687 | −0.198110 | ||||||||
\(353\) | −11.8505 | −0.630736 | −0.315368 | − | 0.948969i | \(-0.602128\pi\) | ||||
−0.315368 | + | 0.948969i | \(0.602128\pi\) | |||||||
\(354\) | 12.9646 | 0.689060 | ||||||||
\(355\) | −0.466273 | −0.0247472 | ||||||||
\(356\) | 10.3879 | 0.550556 | ||||||||
\(357\) | 13.5961 | 0.719584 | ||||||||
\(358\) | −18.0181 | −0.952285 | ||||||||
\(359\) | 28.6632 | 1.51279 | 0.756393 | − | 0.654118i | \(-0.226960\pi\) | ||||
0.756393 | + | 0.654118i | \(0.226960\pi\) | |||||||
\(360\) | −0.195084 | −0.0102818 | ||||||||
\(361\) | −18.9995 | −0.999976 | ||||||||
\(362\) | 7.77690 | 0.408745 | ||||||||
\(363\) | 4.65217 | 0.244176 | ||||||||
\(364\) | 3.00062 | 0.157275 | ||||||||
\(365\) | −2.16005 | −0.113062 | ||||||||
\(366\) | 6.36163 | 0.332528 | ||||||||
\(367\) | 13.1083 | 0.684246 | 0.342123 | − | 0.939655i | \(-0.388854\pi\) | ||||
0.342123 | + | 0.939655i | \(0.388854\pi\) | |||||||
\(368\) | −1.30511 | −0.0680335 | ||||||||
\(369\) | −2.36092 | −0.122905 | ||||||||
\(370\) | −5.25854 | −0.273378 | ||||||||
\(371\) | −8.92847 | −0.463543 | ||||||||
\(372\) | −9.62309 | −0.498934 | ||||||||
\(373\) | −17.2738 | −0.894406 | −0.447203 | − | 0.894432i | \(-0.647580\pi\) | ||||
−0.447203 | + | 0.894432i | \(0.647580\pi\) | |||||||
\(374\) | −23.5271 | −1.21656 | ||||||||
\(375\) | −11.3519 | −0.586208 | ||||||||
\(376\) | 3.85502 | 0.198808 | ||||||||
\(377\) | −4.76264 | −0.245288 | ||||||||
\(378\) | −7.02179 | −0.361162 | ||||||||
\(379\) | 6.30803 | 0.324022 | 0.162011 | − | 0.986789i | \(-0.448202\pi\) | ||||
0.162011 | + | 0.986789i | \(0.448202\pi\) | |||||||
\(380\) | 0.0154100 | 0.000790515 0 | ||||||||
\(381\) | −15.7421 | −0.806490 | ||||||||
\(382\) | 0.312243 | 0.0159757 | ||||||||
\(383\) | −28.2196 | −1.44196 | −0.720978 | − | 0.692958i | \(-0.756307\pi\) | ||||
−0.720978 | + | 0.692958i | \(0.756307\pi\) | |||||||
\(384\) | 1.65255 | 0.0843315 | ||||||||
\(385\) | −3.50276 | −0.178517 | ||||||||
\(386\) | −0.336949 | −0.0171502 | ||||||||
\(387\) | −1.21705 | −0.0618663 | ||||||||
\(388\) | 5.07659 | 0.257725 | ||||||||
\(389\) | −3.15029 | −0.159726 | −0.0798629 | − | 0.996806i | \(-0.525448\pi\) | ||||
−0.0798629 | + | 0.996806i | \(0.525448\pi\) | |||||||
\(390\) | 2.76606 | 0.140065 | ||||||||
\(391\) | −8.26110 | −0.417782 | ||||||||
\(392\) | −5.31058 | −0.268225 | ||||||||
\(393\) | −36.2447 | −1.82830 | ||||||||
\(394\) | 26.8275 | 1.35155 | ||||||||
\(395\) | 0.303246 | 0.0152579 | ||||||||
\(396\) | 1.00008 | 0.0502559 | ||||||||
\(397\) | 31.2926 | 1.57053 | 0.785265 | − | 0.619159i | \(-0.212527\pi\) | ||||
0.785265 | + | 0.619159i | \(0.212527\pi\) | |||||||
\(398\) | 4.03560 | 0.202286 | ||||||||
\(399\) | 0.0456523 | 0.00228547 | ||||||||
\(400\) | −4.47431 | −0.223716 | ||||||||
\(401\) | 0.744072 | 0.0371572 | 0.0185786 | − | 0.999827i | \(-0.494086\pi\) | ||||
0.0185786 | + | 0.999827i | \(0.494086\pi\) | |||||||
\(402\) | −15.3942 | −0.767794 | ||||||||
\(403\) | −13.4431 | −0.669651 | ||||||||
\(404\) | 12.5321 | 0.623495 | ||||||||
\(405\) | −5.88764 | −0.292559 | ||||||||
\(406\) | −2.68148 | −0.133080 | ||||||||
\(407\) | 26.9574 | 1.33623 | ||||||||
\(408\) | 10.4604 | 0.517865 | ||||||||
\(409\) | 3.60242 | 0.178128 | 0.0890641 | − | 0.996026i | \(-0.471612\pi\) | ||||
0.0890641 | + | 0.996026i | \(0.471612\pi\) | |||||||
\(410\) | 6.36192 | 0.314193 | ||||||||
\(411\) | −4.11237 | −0.202848 | ||||||||
\(412\) | 5.43374 | 0.267701 | ||||||||
\(413\) | 10.1970 | 0.501760 | ||||||||
\(414\) | 0.351159 | 0.0172585 | ||||||||
\(415\) | −11.3340 | −0.556364 | ||||||||
\(416\) | 2.30856 | 0.113187 | ||||||||
\(417\) | 35.7355 | 1.74997 | ||||||||
\(418\) | −0.0789980 | −0.00386392 | ||||||||
\(419\) | −17.1323 | −0.836966 | −0.418483 | − | 0.908225i | \(-0.637438\pi\) | ||||
−0.418483 | + | 0.908225i | \(0.637438\pi\) | |||||||
\(420\) | 1.55736 | 0.0759912 | ||||||||
\(421\) | 24.1651 | 1.17773 | 0.588866 | − | 0.808230i | \(-0.299574\pi\) | ||||
0.588866 | + | 0.808230i | \(0.299574\pi\) | |||||||
\(422\) | 9.22688 | 0.449158 | ||||||||
\(423\) | −1.03725 | −0.0504329 | ||||||||
\(424\) | −6.86923 | −0.333600 | ||||||||
\(425\) | −28.3216 | −1.37380 | ||||||||
\(426\) | −1.06275 | −0.0514905 | ||||||||
\(427\) | 5.00359 | 0.242141 | ||||||||
\(428\) | −3.45500 | −0.167004 | ||||||||
\(429\) | −14.1800 | −0.684615 | ||||||||
\(430\) | 3.27956 | 0.158155 | ||||||||
\(431\) | 16.8823 | 0.813193 | 0.406596 | − | 0.913608i | \(-0.366716\pi\) | ||||
0.406596 | + | 0.913608i | \(0.366716\pi\) | |||||||
\(432\) | −5.40231 | −0.259919 | ||||||||
\(433\) | −13.0644 | −0.627834 | −0.313917 | − | 0.949450i | \(-0.601641\pi\) | ||||
−0.313917 | + | 0.949450i | \(0.601641\pi\) | |||||||
\(434\) | −7.56881 | −0.363314 | ||||||||
\(435\) | −2.47187 | −0.118517 | ||||||||
\(436\) | −6.80801 | −0.326044 | ||||||||
\(437\) | −0.0277386 | −0.00132692 | ||||||||
\(438\) | −4.92329 | −0.235244 | ||||||||
\(439\) | 3.91599 | 0.186900 | 0.0934499 | − | 0.995624i | \(-0.470211\pi\) | ||||
0.0934499 | + | 0.995624i | \(0.470211\pi\) | |||||||
\(440\) | −2.69489 | −0.128474 | ||||||||
\(441\) | 1.42889 | 0.0680425 | ||||||||
\(442\) | 14.6128 | 0.695060 | ||||||||
\(443\) | 25.2673 | 1.20049 | 0.600243 | − | 0.799818i | \(-0.295071\pi\) | ||||
0.600243 | + | 0.799818i | \(0.295071\pi\) | |||||||
\(444\) | −11.9855 | −0.568808 | ||||||||
\(445\) | 7.53165 | 0.357034 | ||||||||
\(446\) | −9.44842 | −0.447396 | ||||||||
\(447\) | 34.5559 | 1.63444 | ||||||||
\(448\) | 1.29978 | 0.0614087 | ||||||||
\(449\) | 27.4706 | 1.29642 | 0.648210 | − | 0.761462i | \(-0.275518\pi\) | ||||
0.648210 | + | 0.761462i | \(0.275518\pi\) | |||||||
\(450\) | 1.20388 | 0.0567515 | ||||||||
\(451\) | −32.6138 | −1.53573 | ||||||||
\(452\) | 0.407582 | 0.0191710 | ||||||||
\(453\) | −3.42423 | −0.160885 | ||||||||
\(454\) | 15.2061 | 0.713657 | ||||||||
\(455\) | 2.17558 | 0.101993 | ||||||||
\(456\) | 0.0351232 | 0.00164479 | ||||||||
\(457\) | −14.5345 | −0.679896 | −0.339948 | − | 0.940444i | \(-0.610409\pi\) | ||||
−0.339948 | + | 0.940444i | \(0.610409\pi\) | |||||||
\(458\) | 28.6411 | 1.33831 | ||||||||
\(459\) | −34.1956 | −1.59611 | ||||||||
\(460\) | −0.946259 | −0.0441196 | ||||||||
\(461\) | −10.4630 | −0.487312 | −0.243656 | − | 0.969862i | \(-0.578347\pi\) | ||||
−0.243656 | + | 0.969862i | \(0.578347\pi\) | |||||||
\(462\) | −7.98366 | −0.371433 | ||||||||
\(463\) | −27.7519 | −1.28974 | −0.644871 | − | 0.764292i | \(-0.723089\pi\) | ||||
−0.644871 | + | 0.764292i | \(0.723089\pi\) | |||||||
\(464\) | −2.06303 | −0.0957738 | ||||||||
\(465\) | −6.97715 | −0.323558 | ||||||||
\(466\) | 3.14875 | 0.145863 | ||||||||
\(467\) | −12.3322 | −0.570665 | −0.285333 | − | 0.958429i | \(-0.592104\pi\) | ||||
−0.285333 | + | 0.958429i | \(0.592104\pi\) | |||||||
\(468\) | −0.621154 | −0.0287129 | ||||||||
\(469\) | −12.1080 | −0.559093 | ||||||||
\(470\) | 2.79506 | 0.128926 | ||||||||
\(471\) | −4.31276 | −0.198721 | ||||||||
\(472\) | 7.84518 | 0.361104 | ||||||||
\(473\) | −16.8124 | −0.773036 | ||||||||
\(474\) | 0.691173 | 0.0317466 | ||||||||
\(475\) | −0.0950965 | −0.00436333 | ||||||||
\(476\) | 8.22735 | 0.377100 | ||||||||
\(477\) | 1.84827 | 0.0846265 | ||||||||
\(478\) | 12.5059 | 0.572007 | ||||||||
\(479\) | −2.92366 | −0.133586 | −0.0667928 | − | 0.997767i | \(-0.521277\pi\) | ||||
−0.0667928 | + | 0.997767i | \(0.521277\pi\) | |||||||
\(480\) | 1.19817 | 0.0546888 | ||||||||
\(481\) | −16.7434 | −0.763432 | ||||||||
\(482\) | 3.73027 | 0.169909 | ||||||||
\(483\) | −2.80331 | −0.127555 | ||||||||
\(484\) | 2.81514 | 0.127961 | ||||||||
\(485\) | 3.68075 | 0.167134 | ||||||||
\(486\) | 2.78751 | 0.126444 | ||||||||
\(487\) | 10.1739 | 0.461025 | 0.230513 | − | 0.973069i | \(-0.425960\pi\) | ||||
0.230513 | + | 0.973069i | \(0.425960\pi\) | |||||||
\(488\) | 3.84958 | 0.174262 | ||||||||
\(489\) | −10.9589 | −0.495577 | ||||||||
\(490\) | −3.85040 | −0.173943 | ||||||||
\(491\) | −16.8181 | −0.758989 | −0.379494 | − | 0.925194i | \(-0.623902\pi\) | ||||
−0.379494 | + | 0.925194i | \(0.623902\pi\) | |||||||
\(492\) | 14.5004 | 0.653728 | ||||||||
\(493\) | −13.0586 | −0.588130 | ||||||||
\(494\) | 0.0490660 | 0.00220758 | ||||||||
\(495\) | 0.725101 | 0.0325909 | ||||||||
\(496\) | −5.82316 | −0.261468 | ||||||||
\(497\) | −0.835882 | −0.0374944 | ||||||||
\(498\) | −25.8330 | −1.15761 | ||||||||
\(499\) | −30.0514 | −1.34529 | −0.672643 | − | 0.739967i | \(-0.734841\pi\) | ||||
−0.672643 | + | 0.739967i | \(0.734841\pi\) | |||||||
\(500\) | −6.86928 | −0.307204 | ||||||||
\(501\) | 37.4088 | 1.67130 | ||||||||
\(502\) | −26.2795 | −1.17291 | ||||||||
\(503\) | −6.83648 | −0.304823 | −0.152412 | − | 0.988317i | \(-0.548704\pi\) | ||||
−0.152412 | + | 0.988317i | \(0.548704\pi\) | |||||||
\(504\) | −0.349724 | −0.0155780 | ||||||||
\(505\) | 9.08630 | 0.404335 | ||||||||
\(506\) | 4.85092 | 0.215650 | ||||||||
\(507\) | −12.6760 | −0.562960 | ||||||||
\(508\) | −9.52589 | −0.422643 | ||||||||
\(509\) | −16.9547 | −0.751502 | −0.375751 | − | 0.926721i | \(-0.622615\pi\) | ||||
−0.375751 | + | 0.926721i | \(0.622615\pi\) | |||||||
\(510\) | 7.58421 | 0.335835 | ||||||||
\(511\) | −3.87230 | −0.171300 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.114820 | −0.00506943 | ||||||||
\(514\) | 28.2237 | 1.24489 | ||||||||
\(515\) | 3.93970 | 0.173604 | ||||||||
\(516\) | 7.47495 | 0.329066 | ||||||||
\(517\) | −14.3286 | −0.630172 | ||||||||
\(518\) | −9.42692 | −0.414195 | ||||||||
\(519\) | 20.2366 | 0.888287 | ||||||||
\(520\) | 1.67381 | 0.0734013 | ||||||||
\(521\) | 37.1136 | 1.62597 | 0.812987 | − | 0.582282i | \(-0.197840\pi\) | ||||
0.812987 | + | 0.582282i | \(0.197840\pi\) | |||||||
\(522\) | 0.555090 | 0.0242956 | ||||||||
\(523\) | −9.80481 | −0.428734 | −0.214367 | − | 0.976753i | \(-0.568769\pi\) | ||||
−0.214367 | + | 0.976753i | \(0.568769\pi\) | |||||||
\(524\) | −21.9325 | −0.958127 | ||||||||
\(525\) | −9.61060 | −0.419441 | ||||||||
\(526\) | 25.3865 | 1.10691 | ||||||||
\(527\) | −36.8596 | −1.60563 | ||||||||
\(528\) | −6.14233 | −0.267311 | ||||||||
\(529\) | −21.2967 | −0.925943 | ||||||||
\(530\) | −4.98049 | −0.216339 | ||||||||
\(531\) | −2.11086 | −0.0916037 | ||||||||
\(532\) | 0.0276253 | 0.00119771 | ||||||||
\(533\) | 20.2566 | 0.877410 | ||||||||
\(534\) | 17.1665 | 0.742867 | ||||||||
\(535\) | −2.50502 | −0.108302 | ||||||||
\(536\) | −9.31541 | −0.402365 | ||||||||
\(537\) | −29.7758 | −1.28492 | ||||||||
\(538\) | −1.00000 | −0.0431131 | ||||||||
\(539\) | 19.7388 | 0.850208 | ||||||||
\(540\) | −3.91690 | −0.168557 | ||||||||
\(541\) | −15.4647 | −0.664878 | −0.332439 | − | 0.943125i | \(-0.607871\pi\) | ||||
−0.332439 | + | 0.943125i | \(0.607871\pi\) | |||||||
\(542\) | −17.9078 | −0.769206 | ||||||||
\(543\) | 12.8517 | 0.551521 | ||||||||
\(544\) | 6.32982 | 0.271389 | ||||||||
\(545\) | −4.93610 | −0.211439 | ||||||||
\(546\) | 4.95868 | 0.212212 | ||||||||
\(547\) | −31.5080 | −1.34719 | −0.673593 | − | 0.739103i | \(-0.735250\pi\) | ||||
−0.673593 | + | 0.739103i | \(0.735250\pi\) | |||||||
\(548\) | −2.48849 | −0.106303 | ||||||||
\(549\) | −1.03579 | −0.0442063 | ||||||||
\(550\) | 16.6304 | 0.709125 | ||||||||
\(551\) | −0.0438474 | −0.00186796 | ||||||||
\(552\) | −2.15676 | −0.0917979 | ||||||||
\(553\) | 0.543625 | 0.0231173 | ||||||||
\(554\) | −6.51988 | −0.277003 | ||||||||
\(555\) | −8.69001 | −0.368871 | ||||||||
\(556\) | 21.6244 | 0.917078 | ||||||||
\(557\) | −5.45649 | −0.231199 | −0.115599 | − | 0.993296i | \(-0.536879\pi\) | ||||
−0.115599 | + | 0.993296i | \(0.536879\pi\) | |||||||
\(558\) | 1.56681 | 0.0663283 | ||||||||
\(559\) | 10.4423 | 0.441660 | ||||||||
\(560\) | 0.942394 | 0.0398234 | ||||||||
\(561\) | −38.8798 | −1.64151 | ||||||||
\(562\) | −2.61394 | −0.110262 | ||||||||
\(563\) | −5.91106 | −0.249121 | −0.124561 | − | 0.992212i | \(-0.539752\pi\) | ||||
−0.124561 | + | 0.992212i | \(0.539752\pi\) | |||||||
\(564\) | 6.37063 | 0.268252 | ||||||||
\(565\) | 0.295514 | 0.0124324 | ||||||||
\(566\) | −9.65338 | −0.405762 | ||||||||
\(567\) | −10.5547 | −0.443256 | ||||||||
\(568\) | −0.643097 | −0.0269837 | ||||||||
\(569\) | 31.9474 | 1.33930 | 0.669652 | − | 0.742675i | \(-0.266443\pi\) | ||||
0.669652 | + | 0.742675i | \(0.266443\pi\) | |||||||
\(570\) | 0.0254658 | 0.00106665 | ||||||||
\(571\) | −13.7554 | −0.575647 | −0.287824 | − | 0.957683i | \(-0.592932\pi\) | ||||
−0.287824 | + | 0.957683i | \(0.592932\pi\) | |||||||
\(572\) | −8.58064 | −0.358774 | ||||||||
\(573\) | 0.515998 | 0.0215561 | ||||||||
\(574\) | 11.4049 | 0.476033 | ||||||||
\(575\) | 5.83946 | 0.243522 | ||||||||
\(576\) | −0.269065 | −0.0112110 | ||||||||
\(577\) | −2.93964 | −0.122379 | −0.0611893 | − | 0.998126i | \(-0.519489\pi\) | ||||
−0.0611893 | + | 0.998126i | \(0.519489\pi\) | |||||||
\(578\) | 23.0666 | 0.959444 | ||||||||
\(579\) | −0.556826 | −0.0231409 | ||||||||
\(580\) | −1.49579 | −0.0621091 | ||||||||
\(581\) | −20.3183 | −0.842947 | ||||||||
\(582\) | 8.38934 | 0.347749 | ||||||||
\(583\) | 25.5321 | 1.05743 | ||||||||
\(584\) | −2.97920 | −0.123280 | ||||||||
\(585\) | −0.450363 | −0.0186202 | ||||||||
\(586\) | 2.04724 | 0.0845707 | ||||||||
\(587\) | 15.2876 | 0.630989 | 0.315494 | − | 0.948927i | \(-0.397830\pi\) | ||||
0.315494 | + | 0.948927i | \(0.397830\pi\) | |||||||
\(588\) | −8.77602 | −0.361917 | ||||||||
\(589\) | −0.123765 | −0.00509964 | ||||||||
\(590\) | 5.68809 | 0.234175 | ||||||||
\(591\) | 44.3340 | 1.82366 | ||||||||
\(592\) | −7.25272 | −0.298085 | ||||||||
\(593\) | −33.5005 | −1.37570 | −0.687850 | − | 0.725853i | \(-0.741445\pi\) | ||||
−0.687850 | + | 0.725853i | \(0.741445\pi\) | |||||||
\(594\) | 20.0797 | 0.823879 | ||||||||
\(595\) | 5.96518 | 0.244549 | ||||||||
\(596\) | 20.9106 | 0.856532 | ||||||||
\(597\) | 6.66904 | 0.272946 | ||||||||
\(598\) | −3.01293 | −0.123208 | ||||||||
\(599\) | 0.150988 | 0.00616920 | 0.00308460 | − | 0.999995i | \(-0.499018\pi\) | ||||
0.00308460 | + | 0.999995i | \(0.499018\pi\) | |||||||
\(600\) | −7.39404 | −0.301861 | ||||||||
\(601\) | −34.9546 | −1.42583 | −0.712915 | − | 0.701251i | \(-0.752625\pi\) | ||||
−0.712915 | + | 0.701251i | \(0.752625\pi\) | |||||||
\(602\) | 5.87924 | 0.239620 | ||||||||
\(603\) | 2.50645 | 0.102071 | ||||||||
\(604\) | −2.07209 | −0.0843120 | ||||||||
\(605\) | 2.04110 | 0.0829824 | ||||||||
\(606\) | 20.7100 | 0.841285 | ||||||||
\(607\) | 10.5301 | 0.427404 | 0.213702 | − | 0.976899i | \(-0.431448\pi\) | ||||
0.213702 | + | 0.976899i | \(0.431448\pi\) | |||||||
\(608\) | 0.0212539 | 0.000861959 0 | ||||||||
\(609\) | −4.43129 | −0.179565 | ||||||||
\(610\) | 2.79111 | 0.113009 | ||||||||
\(611\) | 8.89957 | 0.360038 | ||||||||
\(612\) | −1.70313 | −0.0688451 | ||||||||
\(613\) | −20.2271 | −0.816965 | −0.408483 | − | 0.912766i | \(-0.633942\pi\) | ||||
−0.408483 | + | 0.912766i | \(0.633942\pi\) | |||||||
\(614\) | −18.6159 | −0.751275 | ||||||||
\(615\) | 10.5134 | 0.423942 | ||||||||
\(616\) | −4.83110 | −0.194651 | ||||||||
\(617\) | 7.82969 | 0.315211 | 0.157606 | − | 0.987502i | \(-0.449622\pi\) | ||||
0.157606 | + | 0.987502i | \(0.449622\pi\) | |||||||
\(618\) | 8.97956 | 0.361211 | ||||||||
\(619\) | −23.6992 | −0.952549 | −0.476275 | − | 0.879297i | \(-0.658013\pi\) | ||||
−0.476275 | + | 0.879297i | \(0.658013\pi\) | |||||||
\(620\) | −4.22204 | −0.169561 | ||||||||
\(621\) | 7.05059 | 0.282931 | ||||||||
\(622\) | −9.88503 | −0.396354 | ||||||||
\(623\) | 13.5019 | 0.540942 | ||||||||
\(624\) | 3.81503 | 0.152723 | ||||||||
\(625\) | 17.3910 | 0.695642 | ||||||||
\(626\) | 17.4438 | 0.697195 | ||||||||
\(627\) | −0.130548 | −0.00521360 | ||||||||
\(628\) | −2.60975 | −0.104140 | ||||||||
\(629\) | −45.9084 | −1.83049 | ||||||||
\(630\) | −0.253565 | −0.0101023 | ||||||||
\(631\) | −31.8687 | −1.26867 | −0.634336 | − | 0.773058i | \(-0.718726\pi\) | ||||
−0.634336 | + | 0.773058i | \(0.718726\pi\) | |||||||
\(632\) | 0.418245 | 0.0166369 | ||||||||
\(633\) | 15.2479 | 0.606050 | ||||||||
\(634\) | 2.92828 | 0.116297 | ||||||||
\(635\) | −6.90668 | −0.274083 | ||||||||
\(636\) | −11.3518 | −0.450127 | ||||||||
\(637\) | −12.2598 | −0.485752 | ||||||||
\(638\) | 7.66802 | 0.303580 | ||||||||
\(639\) | 0.173035 | 0.00684515 | ||||||||
\(640\) | 0.725043 | 0.0286598 | ||||||||
\(641\) | 10.3578 | 0.409108 | 0.204554 | − | 0.978855i | \(-0.434426\pi\) | ||||
0.204554 | + | 0.978855i | \(0.434426\pi\) | |||||||
\(642\) | −5.70957 | −0.225339 | ||||||||
\(643\) | −21.9761 | −0.866653 | −0.433326 | − | 0.901237i | \(-0.642660\pi\) | ||||
−0.433326 | + | 0.901237i | \(0.642660\pi\) | |||||||
\(644\) | −1.69635 | −0.0668455 | ||||||||
\(645\) | 5.41966 | 0.213399 | ||||||||
\(646\) | 0.134533 | 0.00529314 | ||||||||
\(647\) | 9.10376 | 0.357906 | 0.178953 | − | 0.983858i | \(-0.442729\pi\) | ||||
0.178953 | + | 0.983858i | \(0.442729\pi\) | |||||||
\(648\) | −8.12041 | −0.319000 | ||||||||
\(649\) | −29.1595 | −1.14461 | ||||||||
\(650\) | −10.3292 | −0.405146 | ||||||||
\(651\) | −12.5079 | −0.490222 | ||||||||
\(652\) | −6.63147 | −0.259708 | ||||||||
\(653\) | 6.84892 | 0.268019 | 0.134010 | − | 0.990980i | \(-0.457215\pi\) | ||||
0.134010 | + | 0.990980i | \(0.457215\pi\) | |||||||
\(654\) | −11.2506 | −0.439933 | ||||||||
\(655\) | −15.9020 | −0.621344 | ||||||||
\(656\) | 8.77454 | 0.342588 | ||||||||
\(657\) | 0.801599 | 0.0312734 | ||||||||
\(658\) | 5.01067 | 0.195336 | ||||||||
\(659\) | −10.9102 | −0.424999 | −0.212500 | − | 0.977161i | \(-0.568160\pi\) | ||||
−0.212500 | + | 0.977161i | \(0.568160\pi\) | |||||||
\(660\) | −4.45345 | −0.173350 | ||||||||
\(661\) | −9.26687 | −0.360439 | −0.180220 | − | 0.983626i | \(-0.557681\pi\) | ||||
−0.180220 | + | 0.983626i | \(0.557681\pi\) | |||||||
\(662\) | 5.44140 | 0.211486 | ||||||||
\(663\) | 24.1484 | 0.937847 | ||||||||
\(664\) | −15.6322 | −0.606646 | ||||||||
\(665\) | 0.0200295 | 0.000776712 0 | ||||||||
\(666\) | 1.95145 | 0.0756173 | ||||||||
\(667\) | 2.69248 | 0.104253 | ||||||||
\(668\) | 22.6369 | 0.875850 | ||||||||
\(669\) | −15.6140 | −0.603673 | ||||||||
\(670\) | −6.75407 | −0.260933 | ||||||||
\(671\) | −14.3084 | −0.552369 | ||||||||
\(672\) | 2.14795 | 0.0828590 | ||||||||
\(673\) | −15.0272 | −0.579255 | −0.289627 | − | 0.957139i | \(-0.593531\pi\) | ||||
−0.289627 | + | 0.957139i | \(0.593531\pi\) | |||||||
\(674\) | −3.73840 | −0.143998 | ||||||||
\(675\) | 24.1716 | 0.930366 | ||||||||
\(676\) | −7.67053 | −0.295020 | ||||||||
\(677\) | −46.3947 | −1.78309 | −0.891547 | − | 0.452929i | \(-0.850379\pi\) | ||||
−0.891547 | + | 0.452929i | \(0.850379\pi\) | |||||||
\(678\) | 0.673551 | 0.0258676 | ||||||||
\(679\) | 6.59843 | 0.253225 | ||||||||
\(680\) | 4.58939 | 0.175995 | ||||||||
\(681\) | 25.1289 | 0.962941 | ||||||||
\(682\) | 21.6439 | 0.828790 | ||||||||
\(683\) | −34.2506 | −1.31056 | −0.655281 | − | 0.755385i | \(-0.727450\pi\) | ||||
−0.655281 | + | 0.755385i | \(0.727450\pi\) | |||||||
\(684\) | −0.00571868 | −0.000218659 0 | ||||||||
\(685\) | −1.80426 | −0.0689373 | ||||||||
\(686\) | −16.0010 | −0.610921 | ||||||||
\(687\) | 47.3310 | 1.80579 | ||||||||
\(688\) | 4.52327 | 0.172448 | ||||||||
\(689\) | −15.8581 | −0.604144 | ||||||||
\(690\) | −1.56374 | −0.0595307 | ||||||||
\(691\) | −1.19208 | −0.0453489 | −0.0226744 | − | 0.999743i | \(-0.507218\pi\) | ||||
−0.0226744 | + | 0.999743i | \(0.507218\pi\) | |||||||
\(692\) | 12.2456 | 0.465509 | ||||||||
\(693\) | 1.29988 | 0.0493784 | ||||||||
\(694\) | 10.8089 | 0.410300 | ||||||||
\(695\) | 15.6786 | 0.594723 | ||||||||
\(696\) | −3.40927 | −0.129228 | ||||||||
\(697\) | 55.5412 | 2.10377 | ||||||||
\(698\) | 19.8978 | 0.753142 | ||||||||
\(699\) | 5.20348 | 0.196814 | ||||||||
\(700\) | −5.81561 | −0.219809 | ||||||||
\(701\) | −24.6698 | −0.931767 | −0.465883 | − | 0.884846i | \(-0.654263\pi\) | ||||
−0.465883 | + | 0.884846i | \(0.654263\pi\) | |||||||
\(702\) | −12.4716 | −0.470709 | ||||||||
\(703\) | −0.154149 | −0.00581382 | ||||||||
\(704\) | −3.71687 | −0.140085 | ||||||||
\(705\) | 4.61898 | 0.173961 | ||||||||
\(706\) | −11.8505 | −0.445998 | ||||||||
\(707\) | 16.2889 | 0.612608 | ||||||||
\(708\) | 12.9646 | 0.487239 | ||||||||
\(709\) | 23.3891 | 0.878398 | 0.439199 | − | 0.898390i | \(-0.355262\pi\) | ||||
0.439199 | + | 0.898390i | \(0.355262\pi\) | |||||||
\(710\) | −0.466273 | −0.0174989 | ||||||||
\(711\) | −0.112535 | −0.00422040 | ||||||||
\(712\) | 10.3879 | 0.389302 | ||||||||
\(713\) | 7.59986 | 0.284617 | ||||||||
\(714\) | 13.5961 | 0.508823 | ||||||||
\(715\) | −6.22133 | −0.232665 | ||||||||
\(716\) | −18.0181 | −0.673367 | ||||||||
\(717\) | 20.6667 | 0.771812 | ||||||||
\(718\) | 28.6632 | 1.06970 | ||||||||
\(719\) | −1.52136 | −0.0567371 | −0.0283686 | − | 0.999598i | \(-0.509031\pi\) | ||||
−0.0283686 | + | 0.999598i | \(0.509031\pi\) | |||||||
\(720\) | −0.195084 | −0.00727034 | ||||||||
\(721\) | 7.06265 | 0.263027 | ||||||||
\(722\) | −18.9995 | −0.707090 | ||||||||
\(723\) | 6.16446 | 0.229259 | ||||||||
\(724\) | 7.77690 | 0.289026 | ||||||||
\(725\) | 9.23065 | 0.342818 | ||||||||
\(726\) | 4.65217 | 0.172658 | ||||||||
\(727\) | 36.3855 | 1.34946 | 0.674732 | − | 0.738063i | \(-0.264259\pi\) | ||||
0.674732 | + | 0.738063i | \(0.264259\pi\) | |||||||
\(728\) | 3.00062 | 0.111210 | ||||||||
\(729\) | 28.9677 | 1.07288 | ||||||||
\(730\) | −2.16005 | −0.0799470 | ||||||||
\(731\) | 28.6315 | 1.05897 | ||||||||
\(732\) | 6.36163 | 0.235133 | ||||||||
\(733\) | −18.7869 | −0.693908 | −0.346954 | − | 0.937882i | \(-0.612784\pi\) | ||||
−0.346954 | + | 0.937882i | \(0.612784\pi\) | |||||||
\(734\) | 13.1083 | 0.483835 | ||||||||
\(735\) | −6.36299 | −0.234703 | ||||||||
\(736\) | −1.30511 | −0.0481069 | ||||||||
\(737\) | 34.6242 | 1.27540 | ||||||||
\(738\) | −2.36092 | −0.0869067 | ||||||||
\(739\) | −38.7776 | −1.42646 | −0.713228 | − | 0.700932i | \(-0.752767\pi\) | ||||
−0.713228 | + | 0.700932i | \(0.752767\pi\) | |||||||
\(740\) | −5.25854 | −0.193308 | ||||||||
\(741\) | 0.0810841 | 0.00297870 | ||||||||
\(742\) | −8.92847 | −0.327774 | ||||||||
\(743\) | −6.80190 | −0.249537 | −0.124769 | − | 0.992186i | \(-0.539819\pi\) | ||||
−0.124769 | + | 0.992186i | \(0.539819\pi\) | |||||||
\(744\) | −9.62309 | −0.352800 | ||||||||
\(745\) | 15.1611 | 0.555460 | ||||||||
\(746\) | −17.2738 | −0.632441 | ||||||||
\(747\) | 4.20607 | 0.153892 | ||||||||
\(748\) | −23.5271 | −0.860237 | ||||||||
\(749\) | −4.49073 | −0.164088 | ||||||||
\(750\) | −11.3519 | −0.414511 | ||||||||
\(751\) | 10.5672 | 0.385601 | 0.192801 | − | 0.981238i | \(-0.438243\pi\) | ||||
0.192801 | + | 0.981238i | \(0.438243\pi\) | |||||||
\(752\) | 3.85502 | 0.140578 | ||||||||
\(753\) | −43.4283 | −1.58262 | ||||||||
\(754\) | −4.76264 | −0.173445 | ||||||||
\(755\) | −1.50235 | −0.0546762 | ||||||||
\(756\) | −7.02179 | −0.255380 | ||||||||
\(757\) | −22.6389 | −0.822825 | −0.411412 | − | 0.911449i | \(-0.634964\pi\) | ||||
−0.411412 | + | 0.911449i | \(0.634964\pi\) | |||||||
\(758\) | 6.30803 | 0.229118 | ||||||||
\(759\) | 8.01641 | 0.290977 | ||||||||
\(760\) | 0.0154100 | 0.000558979 0 | ||||||||
\(761\) | 1.83584 | 0.0665490 | 0.0332745 | − | 0.999446i | \(-0.489406\pi\) | ||||
0.0332745 | + | 0.999446i | \(0.489406\pi\) | |||||||
\(762\) | −15.7421 | −0.570274 | ||||||||
\(763\) | −8.84889 | −0.320351 | ||||||||
\(764\) | 0.312243 | 0.0112965 | ||||||||
\(765\) | −1.23484 | −0.0446459 | ||||||||
\(766\) | −28.2196 | −1.01962 | ||||||||
\(767\) | 18.1111 | 0.653954 | ||||||||
\(768\) | 1.65255 | 0.0596314 | ||||||||
\(769\) | 50.0137 | 1.80354 | 0.901770 | − | 0.432215i | \(-0.142268\pi\) | ||||
0.901770 | + | 0.432215i | \(0.142268\pi\) | |||||||
\(770\) | −3.50276 | −0.126231 | ||||||||
\(771\) | 46.6412 | 1.67974 | ||||||||
\(772\) | −0.336949 | −0.0121271 | ||||||||
\(773\) | 40.2988 | 1.44945 | 0.724724 | − | 0.689039i | \(-0.241967\pi\) | ||||
0.724724 | + | 0.689039i | \(0.241967\pi\) | |||||||
\(774\) | −1.21705 | −0.0437461 | ||||||||
\(775\) | 26.0546 | 0.935911 | ||||||||
\(776\) | 5.07659 | 0.182239 | ||||||||
\(777\) | −15.5785 | −0.558875 | ||||||||
\(778\) | −3.15029 | −0.112943 | ||||||||
\(779\) | 0.186493 | 0.00668180 | ||||||||
\(780\) | 2.76606 | 0.0990408 | ||||||||
\(781\) | 2.39031 | 0.0855319 | ||||||||
\(782\) | −8.26110 | −0.295416 | ||||||||
\(783\) | 11.1451 | 0.398294 | ||||||||
\(784\) | −5.31058 | −0.189664 | ||||||||
\(785\) | −1.89218 | −0.0675349 | ||||||||
\(786\) | −36.2447 | −1.29281 | ||||||||
\(787\) | 38.2500 | 1.36347 | 0.681733 | − | 0.731601i | \(-0.261227\pi\) | ||||
0.681733 | + | 0.731601i | \(0.261227\pi\) | |||||||
\(788\) | 26.8275 | 0.955691 | ||||||||
\(789\) | 41.9526 | 1.49355 | ||||||||
\(790\) | 0.303246 | 0.0107890 | ||||||||
\(791\) | 0.529765 | 0.0188363 | ||||||||
\(792\) | 1.00008 | 0.0355363 | ||||||||
\(793\) | 8.88700 | 0.315586 | ||||||||
\(794\) | 31.2926 | 1.11053 | ||||||||
\(795\) | −8.23053 | −0.291907 | ||||||||
\(796\) | 4.03560 | 0.143038 | ||||||||
\(797\) | −33.4247 | −1.18397 | −0.591983 | − | 0.805951i | \(-0.701655\pi\) | ||||
−0.591983 | + | 0.805951i | \(0.701655\pi\) | |||||||
\(798\) | 0.0456523 | 0.00161607 | ||||||||
\(799\) | 24.4016 | 0.863266 | ||||||||
\(800\) | −4.47431 | −0.158191 | ||||||||
\(801\) | −2.79501 | −0.0987569 | ||||||||
\(802\) | 0.744072 | 0.0262741 | ||||||||
\(803\) | 11.0733 | 0.390769 | ||||||||
\(804\) | −15.3942 | −0.542912 | ||||||||
\(805\) | −1.22993 | −0.0433492 | ||||||||
\(806\) | −13.4431 | −0.473514 | ||||||||
\(807\) | −1.65255 | −0.0581727 | ||||||||
\(808\) | 12.5321 | 0.440877 | ||||||||
\(809\) | −39.8841 | −1.40225 | −0.701125 | − | 0.713038i | \(-0.747319\pi\) | ||||
−0.701125 | + | 0.713038i | \(0.747319\pi\) | |||||||
\(810\) | −5.88764 | −0.206871 | ||||||||
\(811\) | 34.7237 | 1.21931 | 0.609657 | − | 0.792665i | \(-0.291307\pi\) | ||||
0.609657 | + | 0.792665i | \(0.291307\pi\) | |||||||
\(812\) | −2.68148 | −0.0941015 | ||||||||
\(813\) | −29.5936 | −1.03789 | ||||||||
\(814\) | 26.9574 | 0.944858 | ||||||||
\(815\) | −4.80810 | −0.168420 | ||||||||
\(816\) | 10.4604 | 0.366186 | ||||||||
\(817\) | 0.0961370 | 0.00336341 | ||||||||
\(818\) | 3.60242 | 0.125956 | ||||||||
\(819\) | −0.807361 | −0.0282115 | ||||||||
\(820\) | 6.36192 | 0.222168 | ||||||||
\(821\) | −48.5169 | −1.69325 | −0.846626 | − | 0.532189i | \(-0.821370\pi\) | ||||
−0.846626 | + | 0.532189i | \(0.821370\pi\) | |||||||
\(822\) | −4.11237 | −0.143435 | ||||||||
\(823\) | 19.5287 | 0.680728 | 0.340364 | − | 0.940294i | \(-0.389450\pi\) | ||||
0.340364 | + | 0.940294i | \(0.389450\pi\) | |||||||
\(824\) | 5.43374 | 0.189293 | ||||||||
\(825\) | 27.4827 | 0.956825 | ||||||||
\(826\) | 10.1970 | 0.354798 | ||||||||
\(827\) | 18.5400 | 0.644698 | 0.322349 | − | 0.946621i | \(-0.395528\pi\) | ||||
0.322349 | + | 0.946621i | \(0.395528\pi\) | |||||||
\(828\) | 0.351159 | 0.0122036 | ||||||||
\(829\) | −20.2344 | −0.702769 | −0.351385 | − | 0.936231i | \(-0.614289\pi\) | ||||
−0.351385 | + | 0.936231i | \(0.614289\pi\) | |||||||
\(830\) | −11.3340 | −0.393409 | ||||||||
\(831\) | −10.7744 | −0.373762 | ||||||||
\(832\) | 2.30856 | 0.0800351 | ||||||||
\(833\) | −33.6150 | −1.16469 | ||||||||
\(834\) | 35.7355 | 1.23742 | ||||||||
\(835\) | 16.4128 | 0.567987 | ||||||||
\(836\) | −0.0789980 | −0.00273220 | ||||||||
\(837\) | 31.4585 | 1.08737 | ||||||||
\(838\) | −17.1323 | −0.591824 | ||||||||
\(839\) | 46.3931 | 1.60167 | 0.800833 | − | 0.598887i | \(-0.204390\pi\) | ||||
0.800833 | + | 0.598887i | \(0.204390\pi\) | |||||||
\(840\) | 1.55736 | 0.0537339 | ||||||||
\(841\) | −24.7439 | −0.853238 | ||||||||
\(842\) | 24.1651 | 0.832783 | ||||||||
\(843\) | −4.31967 | −0.148777 | ||||||||
\(844\) | 9.22688 | 0.317602 | ||||||||
\(845\) | −5.56146 | −0.191320 | ||||||||
\(846\) | −1.03725 | −0.0356615 | ||||||||
\(847\) | 3.65905 | 0.125727 | ||||||||
\(848\) | −6.86923 | −0.235890 | ||||||||
\(849\) | −15.9527 | −0.547496 | ||||||||
\(850\) | −28.3216 | −0.971422 | ||||||||
\(851\) | 9.46559 | 0.324476 | ||||||||
\(852\) | −1.06275 | −0.0364093 | ||||||||
\(853\) | −0.133230 | −0.00456172 | −0.00228086 | − | 0.999997i | \(-0.500726\pi\) | ||||
−0.00228086 | + | 0.999997i | \(0.500726\pi\) | |||||||
\(854\) | 5.00359 | 0.171219 | ||||||||
\(855\) | −0.00414629 | −0.000141800 0 | ||||||||
\(856\) | −3.45500 | −0.118089 | ||||||||
\(857\) | −10.2942 | −0.351642 | −0.175821 | − | 0.984422i | \(-0.556258\pi\) | ||||
−0.175821 | + | 0.984422i | \(0.556258\pi\) | |||||||
\(858\) | −14.1800 | −0.484096 | ||||||||
\(859\) | 35.5814 | 1.21402 | 0.607011 | − | 0.794694i | \(-0.292368\pi\) | ||||
0.607011 | + | 0.794694i | \(0.292368\pi\) | |||||||
\(860\) | 3.27956 | 0.111832 | ||||||||
\(861\) | 18.8473 | 0.642313 | ||||||||
\(862\) | 16.8823 | 0.575014 | ||||||||
\(863\) | 17.9896 | 0.612372 | 0.306186 | − | 0.951972i | \(-0.400947\pi\) | ||||
0.306186 | + | 0.951972i | \(0.400947\pi\) | |||||||
\(864\) | −5.40231 | −0.183790 | ||||||||
\(865\) | 8.87861 | 0.301882 | ||||||||
\(866\) | −13.0644 | −0.443946 | ||||||||
\(867\) | 38.1188 | 1.29458 | ||||||||
\(868\) | −7.56881 | −0.256902 | ||||||||
\(869\) | −1.55456 | −0.0527350 | ||||||||
\(870\) | −2.47187 | −0.0838042 | ||||||||
\(871\) | −21.5052 | −0.728677 | ||||||||
\(872\) | −6.80801 | −0.230548 | ||||||||
\(873\) | −1.36593 | −0.0462298 | ||||||||
\(874\) | −0.0277386 | −0.000938273 0 | ||||||||
\(875\) | −8.92853 | −0.301839 | ||||||||
\(876\) | −4.92329 | −0.166343 | ||||||||
\(877\) | 47.6131 | 1.60778 | 0.803890 | − | 0.594778i | \(-0.202760\pi\) | ||||
0.803890 | + | 0.594778i | \(0.202760\pi\) | |||||||
\(878\) | 3.91599 | 0.132158 | ||||||||
\(879\) | 3.38318 | 0.114112 | ||||||||
\(880\) | −2.69489 | −0.0908448 | ||||||||
\(881\) | −15.7287 | −0.529914 | −0.264957 | − | 0.964260i | \(-0.585358\pi\) | ||||
−0.264957 | + | 0.964260i | \(0.585358\pi\) | |||||||
\(882\) | 1.42889 | 0.0481133 | ||||||||
\(883\) | −20.9111 | −0.703713 | −0.351856 | − | 0.936054i | \(-0.614449\pi\) | ||||
−0.351856 | + | 0.936054i | \(0.614449\pi\) | |||||||
\(884\) | 14.6128 | 0.491481 | ||||||||
\(885\) | 9.39988 | 0.315973 | ||||||||
\(886\) | 25.2673 | 0.848871 | ||||||||
\(887\) | 3.47543 | 0.116694 | 0.0583468 | − | 0.998296i | \(-0.481417\pi\) | ||||
0.0583468 | + | 0.998296i | \(0.481417\pi\) | |||||||
\(888\) | −11.9855 | −0.402208 | ||||||||
\(889\) | −12.3815 | −0.415263 | ||||||||
\(890\) | 7.53165 | 0.252461 | ||||||||
\(891\) | 30.1825 | 1.01115 | ||||||||
\(892\) | −9.44842 | −0.316357 | ||||||||
\(893\) | 0.0819342 | 0.00274182 | ||||||||
\(894\) | 34.5559 | 1.15572 | ||||||||
\(895\) | −13.0639 | −0.436677 | ||||||||
\(896\) | 1.29978 | 0.0434225 | ||||||||
\(897\) | −4.97902 | −0.166245 | ||||||||
\(898\) | 27.4706 | 0.916707 | ||||||||
\(899\) | 12.0134 | 0.400668 | ||||||||
\(900\) | 1.20388 | 0.0401294 | ||||||||
\(901\) | −43.4810 | −1.44856 | ||||||||
\(902\) | −32.6138 | −1.08592 | ||||||||
\(903\) | 9.71576 | 0.323320 | ||||||||
\(904\) | 0.407582 | 0.0135560 | ||||||||
\(905\) | 5.63859 | 0.187433 | ||||||||
\(906\) | −3.42423 | −0.113763 | ||||||||
\(907\) | 5.99370 | 0.199018 | 0.0995088 | − | 0.995037i | \(-0.468273\pi\) | ||||
0.0995088 | + | 0.995037i | \(0.468273\pi\) | |||||||
\(908\) | 15.2061 | 0.504632 | ||||||||
\(909\) | −3.37195 | −0.111840 | ||||||||
\(910\) | 2.17558 | 0.0721196 | ||||||||
\(911\) | 3.66404 | 0.121395 | 0.0606976 | − | 0.998156i | \(-0.480667\pi\) | ||||
0.0606976 | + | 0.998156i | \(0.480667\pi\) | |||||||
\(912\) | 0.0351232 | 0.00116305 | ||||||||
\(913\) | 58.1028 | 1.92292 | ||||||||
\(914\) | −14.5345 | −0.480759 | ||||||||
\(915\) | 4.61246 | 0.152483 | ||||||||
\(916\) | 28.6411 | 0.946329 | ||||||||
\(917\) | −28.5074 | −0.941397 | ||||||||
\(918\) | −34.1956 | −1.12862 | ||||||||
\(919\) | 44.8323 | 1.47888 | 0.739441 | − | 0.673222i | \(-0.235090\pi\) | ||||
0.739441 | + | 0.673222i | \(0.235090\pi\) | |||||||
\(920\) | −0.946259 | −0.0311972 | ||||||||
\(921\) | −30.7637 | −1.01370 | ||||||||
\(922\) | −10.4630 | −0.344581 | ||||||||
\(923\) | −1.48463 | −0.0488672 | ||||||||
\(924\) | −7.98366 | −0.262643 | ||||||||
\(925\) | 32.4510 | 1.06698 | ||||||||
\(926\) | −27.7519 | −0.911985 | ||||||||
\(927\) | −1.46203 | −0.0480194 | ||||||||
\(928\) | −2.06303 | −0.0677223 | ||||||||
\(929\) | −35.1823 | −1.15429 | −0.577146 | − | 0.816641i | \(-0.695834\pi\) | ||||
−0.577146 | + | 0.816641i | \(0.695834\pi\) | |||||||
\(930\) | −6.97715 | −0.228790 | ||||||||
\(931\) | −0.112870 | −0.00369918 | ||||||||
\(932\) | 3.14875 | 0.103141 | ||||||||
\(933\) | −16.3355 | −0.534802 | ||||||||
\(934\) | −12.3322 | −0.403521 | ||||||||
\(935\) | −17.0582 | −0.557862 | ||||||||
\(936\) | −0.621154 | −0.0203031 | ||||||||
\(937\) | 37.7329 | 1.23268 | 0.616339 | − | 0.787481i | \(-0.288615\pi\) | ||||
0.616339 | + | 0.787481i | \(0.288615\pi\) | |||||||
\(938\) | −12.1080 | −0.395339 | ||||||||
\(939\) | 28.8268 | 0.940729 | ||||||||
\(940\) | 2.79506 | 0.0911647 | ||||||||
\(941\) | −31.0321 | −1.01162 | −0.505809 | − | 0.862646i | \(-0.668806\pi\) | ||||
−0.505809 | + | 0.862646i | \(0.668806\pi\) | |||||||
\(942\) | −4.31276 | −0.140517 | ||||||||
\(943\) | −11.4517 | −0.372919 | ||||||||
\(944\) | 7.84518 | 0.255339 | ||||||||
\(945\) | −5.09110 | −0.165613 | ||||||||
\(946\) | −16.8124 | −0.546619 | ||||||||
\(947\) | 19.5388 | 0.634924 | 0.317462 | − | 0.948271i | \(-0.397169\pi\) | ||||
0.317462 | + | 0.948271i | \(0.397169\pi\) | |||||||
\(948\) | 0.691173 | 0.0224482 | ||||||||
\(949\) | −6.87768 | −0.223259 | ||||||||
\(950\) | −0.0950965 | −0.00308534 | ||||||||
\(951\) | 4.83914 | 0.156920 | ||||||||
\(952\) | 8.22735 | 0.266650 | ||||||||
\(953\) | 15.9894 | 0.517948 | 0.258974 | − | 0.965884i | \(-0.416616\pi\) | ||||
0.258974 | + | 0.965884i | \(0.416616\pi\) | |||||||
\(954\) | 1.84827 | 0.0598400 | ||||||||
\(955\) | 0.226389 | 0.00732579 | ||||||||
\(956\) | 12.5059 | 0.404470 | ||||||||
\(957\) | 12.6718 | 0.409622 | ||||||||
\(958\) | −2.92366 | −0.0944592 | ||||||||
\(959\) | −3.23448 | −0.104447 | ||||||||
\(960\) | 1.19817 | 0.0386709 | ||||||||
\(961\) | 2.90921 | 0.0938456 | ||||||||
\(962\) | −16.7434 | −0.539828 | ||||||||
\(963\) | 0.929619 | 0.0299566 | ||||||||
\(964\) | 3.73027 | 0.120144 | ||||||||
\(965\) | −0.244302 | −0.00786437 | ||||||||
\(966\) | −2.80331 | −0.0901950 | ||||||||
\(967\) | 38.1787 | 1.22774 | 0.613872 | − | 0.789406i | \(-0.289611\pi\) | ||||
0.613872 | + | 0.789406i | \(0.289611\pi\) | |||||||
\(968\) | 2.81514 | 0.0904820 | ||||||||
\(969\) | 0.222323 | 0.00714206 | ||||||||
\(970\) | 3.68075 | 0.118182 | ||||||||
\(971\) | 2.16411 | 0.0694497 | 0.0347248 | − | 0.999397i | \(-0.488945\pi\) | ||||
0.0347248 | + | 0.999397i | \(0.488945\pi\) | |||||||
\(972\) | 2.78751 | 0.0894093 | ||||||||
\(973\) | 28.1069 | 0.901064 | ||||||||
\(974\) | 10.1739 | 0.325994 | ||||||||
\(975\) | −17.0696 | −0.546665 | ||||||||
\(976\) | 3.84958 | 0.123222 | ||||||||
\(977\) | −14.7297 | −0.471243 | −0.235622 | − | 0.971845i | \(-0.575713\pi\) | ||||
−0.235622 | + | 0.971845i | \(0.575713\pi\) | |||||||
\(978\) | −10.9589 | −0.350426 | ||||||||
\(979\) | −38.6104 | −1.23399 | ||||||||
\(980\) | −3.85040 | −0.122996 | ||||||||
\(981\) | 1.83180 | 0.0584848 | ||||||||
\(982\) | −16.8181 | −0.536686 | ||||||||
\(983\) | 36.4217 | 1.16167 | 0.580836 | − | 0.814020i | \(-0.302726\pi\) | ||||
0.580836 | + | 0.814020i | \(0.302726\pi\) | |||||||
\(984\) | 14.5004 | 0.462256 | ||||||||
\(985\) | 19.4511 | 0.619764 | ||||||||
\(986\) | −13.0586 | −0.415871 | ||||||||
\(987\) | 8.28040 | 0.263568 | ||||||||
\(988\) | 0.0490660 | 0.00156100 | ||||||||
\(989\) | −5.90336 | −0.187716 | ||||||||
\(990\) | 0.725101 | 0.0230452 | ||||||||
\(991\) | −24.5429 | −0.779632 | −0.389816 | − | 0.920893i | \(-0.627461\pi\) | ||||
−0.389816 | + | 0.920893i | \(0.627461\pi\) | |||||||
\(992\) | −5.82316 | −0.184886 | ||||||||
\(993\) | 8.99221 | 0.285359 | ||||||||
\(994\) | −0.835882 | −0.0265126 | ||||||||
\(995\) | 2.92598 | 0.0927598 | ||||||||
\(996\) | −25.8330 | −0.818551 | ||||||||
\(997\) | −52.7413 | −1.67033 | −0.835167 | − | 0.549996i | \(-0.814629\pi\) | ||||
−0.835167 | + | 0.549996i | \(0.814629\pi\) | |||||||
\(998\) | −30.0514 | −0.951260 | ||||||||
\(999\) | 39.1814 | 1.23965 |
(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 | 538.2.a.e.1.5 | ✓ | 7 | |
3.2 | odd | 2 | 4842.2.a.n.1.4 | 7 | |||
4.3 | odd | 2 | 4304.2.a.h.1.3 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.e.1.5 | ✓ | 7 | 1.1 | even | 1 | trivial | |
4304.2.a.h.1.3 | 7 | 4.3 | odd | 2 | |||
4842.2.a.n.1.4 | 7 | 3.2 | odd | 2 |