Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
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 | 1.3 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.04892 | 0.396453 | 0.198227 | − | 0.980156i | \(-0.436482\pi\) | ||||
0.198227 | + | 0.980156i | \(0.436482\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.35690 | −0.409119 | −0.204560 | − | 0.978854i | \(-0.565576\pi\) | ||||
−0.204560 | + | 0.978854i | \(0.565576\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.04892 | −0.280335 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.08815 | −0.263914 | −0.131957 | − | 0.991255i | \(-0.542126\pi\) | ||||
−0.131957 | + | 0.991255i | \(0.542126\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.93900 | −0.674253 | −0.337127 | − | 0.941459i | \(-0.609455\pi\) | ||||
−0.337127 | + | 0.941459i | \(0.609455\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.04892 | 0.228893 | ||||||||
\(22\) | 1.35690 | 0.289291 | ||||||||
\(23\) | −0.692021 | −0.144296 | −0.0721482 | − | 0.997394i | \(-0.522985\pi\) | ||||
−0.0721482 | + | 0.997394i | \(0.522985\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.04892 | 0.198227 | ||||||||
\(29\) | −2.37867 | −0.441707 | −0.220854 | − | 0.975307i | \(-0.570884\pi\) | ||||
−0.220854 | + | 0.975307i | \(0.570884\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −9.85086 | −1.76927 | −0.884633 | − | 0.466288i | \(-0.845591\pi\) | ||||
−0.884633 | + | 0.466288i | \(0.845591\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.35690 | −0.236205 | ||||||||
\(34\) | 1.08815 | 0.186615 | ||||||||
\(35\) | 1.04892 | 0.177299 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.26875 | −1.52377 | −0.761887 | − | 0.647710i | \(-0.775727\pi\) | ||||
−0.761887 | + | 0.647710i | \(0.775727\pi\) | |||||||
\(38\) | 2.93900 | 0.476769 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −2.84117 | −0.443716 | −0.221858 | − | 0.975079i | \(-0.571212\pi\) | ||||
−0.221858 | + | 0.975079i | \(0.571212\pi\) | |||||||
\(42\) | −1.04892 | −0.161851 | ||||||||
\(43\) | −4.45473 | −0.679340 | −0.339670 | − | 0.940545i | \(-0.610315\pi\) | ||||
−0.339670 | + | 0.940545i | \(0.610315\pi\) | |||||||
\(44\) | −1.35690 | −0.204560 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0.692021 | 0.102033 | ||||||||
\(47\) | 3.31767 | 0.483931 | 0.241966 | − | 0.970285i | \(-0.422208\pi\) | ||||
0.241966 | + | 0.970285i | \(0.422208\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −5.89977 | −0.842825 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −1.08815 | −0.152371 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.664874 | 0.0913275 | 0.0456638 | − | 0.998957i | \(-0.485460\pi\) | ||||
0.0456638 | + | 0.998957i | \(0.485460\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.35690 | −0.182964 | ||||||||
\(56\) | −1.04892 | −0.140167 | ||||||||
\(57\) | −2.93900 | −0.389280 | ||||||||
\(58\) | 2.37867 | 0.312334 | ||||||||
\(59\) | 1.96077 | 0.255271 | 0.127635 | − | 0.991821i | \(-0.459261\pi\) | ||||
0.127635 | + | 0.991821i | \(0.459261\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 3.24698 | 0.415733 | 0.207867 | − | 0.978157i | \(-0.433348\pi\) | ||||
0.207867 | + | 0.978157i | \(0.433348\pi\) | |||||||
\(62\) | 9.85086 | 1.25106 | ||||||||
\(63\) | 1.04892 | 0.132151 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.35690 | 0.167022 | ||||||||
\(67\) | −6.91185 | −0.844417 | −0.422209 | − | 0.906499i | \(-0.638745\pi\) | ||||
−0.422209 | + | 0.906499i | \(0.638745\pi\) | |||||||
\(68\) | −1.08815 | −0.131957 | ||||||||
\(69\) | −0.692021 | −0.0833096 | ||||||||
\(70\) | −1.04892 | −0.125370 | ||||||||
\(71\) | −2.29590 | −0.272473 | −0.136236 | − | 0.990676i | \(-0.543501\pi\) | ||||
−0.136236 | + | 0.990676i | \(0.543501\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −3.36227 | −0.393524 | −0.196762 | − | 0.980451i | \(-0.563043\pi\) | ||||
−0.196762 | + | 0.980451i | \(0.563043\pi\) | |||||||
\(74\) | 9.26875 | 1.07747 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −2.93900 | −0.337127 | ||||||||
\(77\) | −1.42327 | −0.162197 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3230 | 1.38645 | 0.693225 | − | 0.720721i | \(-0.256189\pi\) | ||||
0.693225 | + | 0.720721i | \(0.256189\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.84117 | 0.313754 | ||||||||
\(83\) | −2.68664 | −0.294898 | −0.147449 | − | 0.989070i | \(-0.547106\pi\) | ||||
−0.147449 | + | 0.989070i | \(0.547106\pi\) | |||||||
\(84\) | 1.04892 | 0.114446 | ||||||||
\(85\) | −1.08815 | −0.118026 | ||||||||
\(86\) | 4.45473 | 0.480366 | ||||||||
\(87\) | −2.37867 | −0.255020 | ||||||||
\(88\) | 1.35690 | 0.144646 | ||||||||
\(89\) | −12.8877 | −1.36609 | −0.683046 | − | 0.730375i | \(-0.739345\pi\) | ||||
−0.683046 | + | 0.730375i | \(0.739345\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.692021 | −0.0721482 | ||||||||
\(93\) | −9.85086 | −1.02149 | ||||||||
\(94\) | −3.31767 | −0.342191 | ||||||||
\(95\) | −2.93900 | −0.301535 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −1.56704 | −0.159109 | −0.0795544 | − | 0.996831i | \(-0.525350\pi\) | ||||
−0.0795544 | + | 0.996831i | \(0.525350\pi\) | |||||||
\(98\) | 5.89977 | 0.595967 | ||||||||
\(99\) | −1.35690 | −0.136373 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.71379 | 0.469040 | 0.234520 | − | 0.972111i | \(-0.424648\pi\) | ||||
0.234520 | + | 0.972111i | \(0.424648\pi\) | |||||||
\(102\) | 1.08815 | 0.107743 | ||||||||
\(103\) | −12.1642 | −1.19858 | −0.599288 | − | 0.800534i | \(-0.704549\pi\) | ||||
−0.599288 | + | 0.800534i | \(0.704549\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.04892 | 0.102364 | ||||||||
\(106\) | −0.664874 | −0.0645783 | ||||||||
\(107\) | 1.83877 | 0.177761 | 0.0888805 | − | 0.996042i | \(-0.471671\pi\) | ||||
0.0888805 | + | 0.996042i | \(0.471671\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −16.2403 | −1.55554 | −0.777768 | − | 0.628551i | \(-0.783648\pi\) | ||||
−0.777768 | + | 0.628551i | \(0.783648\pi\) | |||||||
\(110\) | 1.35690 | 0.129375 | ||||||||
\(111\) | −9.26875 | −0.879751 | ||||||||
\(112\) | 1.04892 | 0.0991134 | ||||||||
\(113\) | 16.8267 | 1.58292 | 0.791461 | − | 0.611220i | \(-0.209321\pi\) | ||||
0.791461 | + | 0.611220i | \(0.209321\pi\) | |||||||
\(114\) | 2.93900 | 0.275263 | ||||||||
\(115\) | −0.692021 | −0.0645313 | ||||||||
\(116\) | −2.37867 | −0.220854 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.96077 | −0.180504 | ||||||||
\(119\) | −1.14138 | −0.104630 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −9.15883 | −0.832621 | ||||||||
\(122\) | −3.24698 | −0.293968 | ||||||||
\(123\) | −2.84117 | −0.256179 | ||||||||
\(124\) | −9.85086 | −0.884633 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.04892 | −0.0934450 | ||||||||
\(127\) | −5.06100 | −0.449091 | −0.224546 | − | 0.974464i | \(-0.572090\pi\) | ||||
−0.224546 | + | 0.974464i | \(0.572090\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.45473 | −0.392217 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.81940 | 0.333702 | 0.166851 | − | 0.985982i | \(-0.446640\pi\) | ||||
0.166851 | + | 0.985982i | \(0.446640\pi\) | |||||||
\(132\) | −1.35690 | −0.118103 | ||||||||
\(133\) | −3.08277 | −0.267310 | ||||||||
\(134\) | 6.91185 | 0.597093 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 1.08815 | 0.0933077 | ||||||||
\(137\) | 8.59717 | 0.734506 | 0.367253 | − | 0.930121i | \(-0.380298\pi\) | ||||
0.367253 | + | 0.930121i | \(0.380298\pi\) | |||||||
\(138\) | 0.692021 | 0.0589088 | ||||||||
\(139\) | −2.38404 | −0.202212 | −0.101106 | − | 0.994876i | \(-0.532238\pi\) | ||||
−0.101106 | + | 0.994876i | \(0.532238\pi\) | |||||||
\(140\) | 1.04892 | 0.0886497 | ||||||||
\(141\) | 3.31767 | 0.279398 | ||||||||
\(142\) | 2.29590 | 0.192667 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.37867 | −0.197537 | ||||||||
\(146\) | 3.36227 | 0.278264 | ||||||||
\(147\) | −5.89977 | −0.486605 | ||||||||
\(148\) | −9.26875 | −0.761887 | ||||||||
\(149\) | 8.93900 | 0.732312 | 0.366156 | − | 0.930554i | \(-0.380674\pi\) | ||||
0.366156 | + | 0.930554i | \(0.380674\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 8.45473 | 0.688036 | 0.344018 | − | 0.938963i | \(-0.388212\pi\) | ||||
0.344018 | + | 0.938963i | \(0.388212\pi\) | |||||||
\(152\) | 2.93900 | 0.238384 | ||||||||
\(153\) | −1.08815 | −0.0879714 | ||||||||
\(154\) | 1.42327 | 0.114690 | ||||||||
\(155\) | −9.85086 | −0.791240 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.70410 | −0.215811 | −0.107905 | − | 0.994161i | \(-0.534414\pi\) | ||||
−0.107905 | + | 0.994161i | \(0.534414\pi\) | |||||||
\(158\) | −12.3230 | −0.980369 | ||||||||
\(159\) | 0.664874 | 0.0527280 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −0.725873 | −0.0572068 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 22.5284 | 1.76456 | 0.882280 | − | 0.470724i | \(-0.156007\pi\) | ||||
0.882280 | + | 0.470724i | \(0.156007\pi\) | |||||||
\(164\) | −2.84117 | −0.221858 | ||||||||
\(165\) | −1.35690 | −0.105634 | ||||||||
\(166\) | 2.68664 | 0.208524 | ||||||||
\(167\) | −12.2228 | −0.945830 | −0.472915 | − | 0.881108i | \(-0.656798\pi\) | ||||
−0.472915 | + | 0.881108i | \(0.656798\pi\) | |||||||
\(168\) | −1.04892 | −0.0809257 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.08815 | 0.0834570 | ||||||||
\(171\) | −2.93900 | −0.224751 | ||||||||
\(172\) | −4.45473 | −0.339670 | ||||||||
\(173\) | −11.7168 | −0.890810 | −0.445405 | − | 0.895329i | \(-0.646940\pi\) | ||||
−0.445405 | + | 0.895329i | \(0.646940\pi\) | |||||||
\(174\) | 2.37867 | 0.180326 | ||||||||
\(175\) | 1.04892 | 0.0792907 | ||||||||
\(176\) | −1.35690 | −0.102280 | ||||||||
\(177\) | 1.96077 | 0.147381 | ||||||||
\(178\) | 12.8877 | 0.965973 | ||||||||
\(179\) | 8.89738 | 0.665021 | 0.332511 | − | 0.943099i | \(-0.392104\pi\) | ||||
0.332511 | + | 0.943099i | \(0.392104\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 1.31229 | 0.0975418 | 0.0487709 | − | 0.998810i | \(-0.484470\pi\) | ||||
0.0487709 | + | 0.998810i | \(0.484470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.24698 | 0.240024 | ||||||||
\(184\) | 0.692021 | 0.0510165 | ||||||||
\(185\) | −9.26875 | −0.681452 | ||||||||
\(186\) | 9.85086 | 0.722300 | ||||||||
\(187\) | 1.47650 | 0.107972 | ||||||||
\(188\) | 3.31767 | 0.241966 | ||||||||
\(189\) | 1.04892 | 0.0762975 | ||||||||
\(190\) | 2.93900 | 0.213218 | ||||||||
\(191\) | 5.75063 | 0.416101 | 0.208050 | − | 0.978118i | \(-0.433288\pi\) | ||||
0.208050 | + | 0.978118i | \(0.433288\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −10.0339 | −0.722252 | −0.361126 | − | 0.932517i | \(-0.617608\pi\) | ||||
−0.361126 | + | 0.932517i | \(0.617608\pi\) | |||||||
\(194\) | 1.56704 | 0.112507 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.89977 | −0.421412 | ||||||||
\(197\) | −22.9071 | −1.63206 | −0.816031 | − | 0.578009i | \(-0.803830\pi\) | ||||
−0.816031 | + | 0.578009i | \(0.803830\pi\) | |||||||
\(198\) | 1.35690 | 0.0964304 | ||||||||
\(199\) | 27.0291 | 1.91604 | 0.958020 | − | 0.286702i | \(-0.0925589\pi\) | ||||
0.958020 | + | 0.286702i | \(0.0925589\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −6.91185 | −0.487525 | ||||||||
\(202\) | −4.71379 | −0.331661 | ||||||||
\(203\) | −2.49502 | −0.175116 | ||||||||
\(204\) | −1.08815 | −0.0761855 | ||||||||
\(205\) | −2.84117 | −0.198436 | ||||||||
\(206\) | 12.1642 | 0.847521 | ||||||||
\(207\) | −0.692021 | −0.0480988 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.98792 | 0.275850 | ||||||||
\(210\) | −1.04892 | −0.0723822 | ||||||||
\(211\) | 10.3720 | 0.714035 | 0.357018 | − | 0.934098i | \(-0.383794\pi\) | ||||
0.357018 | + | 0.934098i | \(0.383794\pi\) | |||||||
\(212\) | 0.664874 | 0.0456638 | ||||||||
\(213\) | −2.29590 | −0.157312 | ||||||||
\(214\) | −1.83877 | −0.125696 | ||||||||
\(215\) | −4.45473 | −0.303810 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −10.3327 | −0.701432 | ||||||||
\(218\) | 16.2403 | 1.09993 | ||||||||
\(219\) | −3.36227 | −0.227201 | ||||||||
\(220\) | −1.35690 | −0.0914819 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9.26875 | 0.622078 | ||||||||
\(223\) | −14.0532 | −0.941074 | −0.470537 | − | 0.882380i | \(-0.655940\pi\) | ||||
−0.470537 | + | 0.882380i | \(0.655940\pi\) | |||||||
\(224\) | −1.04892 | −0.0700837 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −16.8267 | −1.11929 | ||||||||
\(227\) | 1.93362 | 0.128339 | 0.0641696 | − | 0.997939i | \(-0.479560\pi\) | ||||
0.0641696 | + | 0.997939i | \(0.479560\pi\) | |||||||
\(228\) | −2.93900 | −0.194640 | ||||||||
\(229\) | 10.9148 | 0.721273 | 0.360636 | − | 0.932706i | \(-0.382560\pi\) | ||||
0.360636 | + | 0.932706i | \(0.382560\pi\) | |||||||
\(230\) | 0.692021 | 0.0456305 | ||||||||
\(231\) | −1.42327 | −0.0936444 | ||||||||
\(232\) | 2.37867 | 0.156167 | ||||||||
\(233\) | −21.6896 | −1.42093 | −0.710467 | − | 0.703730i | \(-0.751516\pi\) | ||||
−0.710467 | + | 0.703730i | \(0.751516\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.31767 | 0.216421 | ||||||||
\(236\) | 1.96077 | 0.127635 | ||||||||
\(237\) | 12.3230 | 0.800468 | ||||||||
\(238\) | 1.14138 | 0.0739844 | ||||||||
\(239\) | 27.2349 | 1.76168 | 0.880840 | − | 0.473415i | \(-0.156979\pi\) | ||||
0.880840 | + | 0.473415i | \(0.156979\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −8.21014 | −0.528862 | −0.264431 | − | 0.964405i | \(-0.585184\pi\) | ||||
−0.264431 | + | 0.964405i | \(0.585184\pi\) | |||||||
\(242\) | 9.15883 | 0.588752 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.24698 | 0.207867 | ||||||||
\(245\) | −5.89977 | −0.376923 | ||||||||
\(246\) | 2.84117 | 0.181146 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.85086 | 0.625530 | ||||||||
\(249\) | −2.68664 | −0.170259 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −6.57002 | −0.414696 | −0.207348 | − | 0.978267i | \(-0.566483\pi\) | ||||
−0.207348 | + | 0.978267i | \(0.566483\pi\) | |||||||
\(252\) | 1.04892 | 0.0660756 | ||||||||
\(253\) | 0.939001 | 0.0590345 | ||||||||
\(254\) | 5.06100 | 0.317555 | ||||||||
\(255\) | −1.08815 | −0.0681423 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.7657 | 0.858680 | 0.429340 | − | 0.903143i | \(-0.358746\pi\) | ||||
0.429340 | + | 0.903143i | \(0.358746\pi\) | |||||||
\(258\) | 4.45473 | 0.277339 | ||||||||
\(259\) | −9.72215 | −0.604105 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.37867 | −0.147236 | ||||||||
\(262\) | −3.81940 | −0.235963 | ||||||||
\(263\) | −9.54288 | −0.588439 | −0.294219 | − | 0.955738i | \(-0.595060\pi\) | ||||
−0.294219 | + | 0.955738i | \(0.595060\pi\) | |||||||
\(264\) | 1.35690 | 0.0835112 | ||||||||
\(265\) | 0.664874 | 0.0408429 | ||||||||
\(266\) | 3.08277 | 0.189017 | ||||||||
\(267\) | −12.8877 | −0.788714 | ||||||||
\(268\) | −6.91185 | −0.422209 | ||||||||
\(269\) | 9.07069 | 0.553050 | 0.276525 | − | 0.961007i | \(-0.410817\pi\) | ||||
0.276525 | + | 0.961007i | \(0.410817\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −17.5579 | −1.06657 | −0.533285 | − | 0.845936i | \(-0.679042\pi\) | ||||
−0.533285 | + | 0.845936i | \(0.679042\pi\) | |||||||
\(272\) | −1.08815 | −0.0659785 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.59717 | −0.519374 | ||||||||
\(275\) | −1.35690 | −0.0818239 | ||||||||
\(276\) | −0.692021 | −0.0416548 | ||||||||
\(277\) | 13.7071 | 0.823579 | 0.411790 | − | 0.911279i | \(-0.364904\pi\) | ||||
0.411790 | + | 0.911279i | \(0.364904\pi\) | |||||||
\(278\) | 2.38404 | 0.142985 | ||||||||
\(279\) | −9.85086 | −0.589755 | ||||||||
\(280\) | −1.04892 | −0.0626848 | ||||||||
\(281\) | 24.3696 | 1.45377 | 0.726883 | − | 0.686761i | \(-0.240968\pi\) | ||||
0.726883 | + | 0.686761i | \(0.240968\pi\) | |||||||
\(282\) | −3.31767 | −0.197564 | ||||||||
\(283\) | −17.1511 | −1.01952 | −0.509762 | − | 0.860315i | \(-0.670267\pi\) | ||||
−0.509762 | + | 0.860315i | \(0.670267\pi\) | |||||||
\(284\) | −2.29590 | −0.136236 | ||||||||
\(285\) | −2.93900 | −0.174091 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.98015 | −0.175913 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.8159 | −0.930349 | ||||||||
\(290\) | 2.37867 | 0.139680 | ||||||||
\(291\) | −1.56704 | −0.0918615 | ||||||||
\(292\) | −3.36227 | −0.196762 | ||||||||
\(293\) | 24.1172 | 1.40894 | 0.704471 | − | 0.709732i | \(-0.251184\pi\) | ||||
0.704471 | + | 0.709732i | \(0.251184\pi\) | |||||||
\(294\) | 5.89977 | 0.344082 | ||||||||
\(295\) | 1.96077 | 0.114161 | ||||||||
\(296\) | 9.26875 | 0.538735 | ||||||||
\(297\) | −1.35690 | −0.0787351 | ||||||||
\(298\) | −8.93900 | −0.517822 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −4.67264 | −0.269327 | ||||||||
\(302\) | −8.45473 | −0.486515 | ||||||||
\(303\) | 4.71379 | 0.270800 | ||||||||
\(304\) | −2.93900 | −0.168563 | ||||||||
\(305\) | 3.24698 | 0.185922 | ||||||||
\(306\) | 1.08815 | 0.0622052 | ||||||||
\(307\) | 17.2282 | 0.983265 | 0.491632 | − | 0.870803i | \(-0.336400\pi\) | ||||
0.491632 | + | 0.870803i | \(0.336400\pi\) | |||||||
\(308\) | −1.42327 | −0.0810984 | ||||||||
\(309\) | −12.1642 | −0.691998 | ||||||||
\(310\) | 9.85086 | 0.559491 | ||||||||
\(311\) | −25.9801 | −1.47320 | −0.736600 | − | 0.676329i | \(-0.763570\pi\) | ||||
−0.736600 | + | 0.676329i | \(0.763570\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.82669 | 0.442391 | 0.221195 | − | 0.975230i | \(-0.429004\pi\) | ||||
0.221195 | + | 0.975230i | \(0.429004\pi\) | |||||||
\(314\) | 2.70410 | 0.152601 | ||||||||
\(315\) | 1.04892 | 0.0590998 | ||||||||
\(316\) | 12.3230 | 0.693225 | ||||||||
\(317\) | −0.391813 | −0.0220064 | −0.0110032 | − | 0.999939i | \(-0.503502\pi\) | ||||
−0.0110032 | + | 0.999939i | \(0.503502\pi\) | |||||||
\(318\) | −0.664874 | −0.0372843 | ||||||||
\(319\) | 3.22760 | 0.180711 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 1.83877 | 0.102630 | ||||||||
\(322\) | 0.725873 | 0.0404513 | ||||||||
\(323\) | 3.19806 | 0.177945 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.5284 | −1.24773 | ||||||||
\(327\) | −16.2403 | −0.898089 | ||||||||
\(328\) | 2.84117 | 0.156877 | ||||||||
\(329\) | 3.47996 | 0.191856 | ||||||||
\(330\) | 1.35690 | 0.0746947 | ||||||||
\(331\) | −26.3424 | −1.44791 | −0.723955 | − | 0.689847i | \(-0.757678\pi\) | ||||
−0.723955 | + | 0.689847i | \(0.757678\pi\) | |||||||
\(332\) | −2.68664 | −0.147449 | ||||||||
\(333\) | −9.26875 | −0.507924 | ||||||||
\(334\) | 12.2228 | 0.668803 | ||||||||
\(335\) | −6.91185 | −0.377635 | ||||||||
\(336\) | 1.04892 | 0.0572231 | ||||||||
\(337\) | 14.8345 | 0.808085 | 0.404042 | − | 0.914740i | \(-0.367605\pi\) | ||||
0.404042 | + | 0.914740i | \(0.367605\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.8267 | 0.913900 | ||||||||
\(340\) | −1.08815 | −0.0590130 | ||||||||
\(341\) | 13.3666 | 0.723841 | ||||||||
\(342\) | 2.93900 | 0.158923 | ||||||||
\(343\) | −13.5308 | −0.730594 | ||||||||
\(344\) | 4.45473 | 0.240183 | ||||||||
\(345\) | −0.692021 | −0.0372572 | ||||||||
\(346\) | 11.7168 | 0.629898 | ||||||||
\(347\) | −0.636399 | −0.0341637 | −0.0170819 | − | 0.999854i | \(-0.505438\pi\) | ||||
−0.0170819 | + | 0.999854i | \(0.505438\pi\) | |||||||
\(348\) | −2.37867 | −0.127510 | ||||||||
\(349\) | −17.2784 | −0.924894 | −0.462447 | − | 0.886647i | \(-0.653028\pi\) | ||||
−0.462447 | + | 0.886647i | \(0.653028\pi\) | |||||||
\(350\) | −1.04892 | −0.0560670 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.35690 | 0.0723228 | ||||||||
\(353\) | 21.7614 | 1.15824 | 0.579121 | − | 0.815242i | \(-0.303396\pi\) | ||||
0.579121 | + | 0.815242i | \(0.303396\pi\) | |||||||
\(354\) | −1.96077 | −0.104214 | ||||||||
\(355\) | −2.29590 | −0.121854 | ||||||||
\(356\) | −12.8877 | −0.683046 | ||||||||
\(357\) | −1.14138 | −0.0604080 | ||||||||
\(358\) | −8.89738 | −0.470241 | ||||||||
\(359\) | 22.8412 | 1.20551 | 0.602755 | − | 0.797926i | \(-0.294070\pi\) | ||||
0.602755 | + | 0.797926i | \(0.294070\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −10.3623 | −0.545383 | ||||||||
\(362\) | −1.31229 | −0.0689725 | ||||||||
\(363\) | −9.15883 | −0.480714 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.36227 | −0.175989 | ||||||||
\(366\) | −3.24698 | −0.169722 | ||||||||
\(367\) | −7.78315 | −0.406277 | −0.203139 | − | 0.979150i | \(-0.565114\pi\) | ||||
−0.203139 | + | 0.979150i | \(0.565114\pi\) | |||||||
\(368\) | −0.692021 | −0.0360741 | ||||||||
\(369\) | −2.84117 | −0.147905 | ||||||||
\(370\) | 9.26875 | 0.481859 | ||||||||
\(371\) | 0.697398 | 0.0362071 | ||||||||
\(372\) | −9.85086 | −0.510743 | ||||||||
\(373\) | −30.5133 | −1.57992 | −0.789960 | − | 0.613158i | \(-0.789899\pi\) | ||||
−0.789960 | + | 0.613158i | \(0.789899\pi\) | |||||||
\(374\) | −1.47650 | −0.0763480 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −3.31767 | −0.171096 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.04892 | −0.0539505 | ||||||||
\(379\) | 6.41358 | 0.329444 | 0.164722 | − | 0.986340i | \(-0.447327\pi\) | ||||
0.164722 | + | 0.986340i | \(0.447327\pi\) | |||||||
\(380\) | −2.93900 | −0.150768 | ||||||||
\(381\) | −5.06100 | −0.259283 | ||||||||
\(382\) | −5.75063 | −0.294228 | ||||||||
\(383\) | 2.89440 | 0.147897 | 0.0739484 | − | 0.997262i | \(-0.476440\pi\) | ||||
0.0739484 | + | 0.997262i | \(0.476440\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −1.42327 | −0.0725366 | ||||||||
\(386\) | 10.0339 | 0.510710 | ||||||||
\(387\) | −4.45473 | −0.226447 | ||||||||
\(388\) | −1.56704 | −0.0795544 | ||||||||
\(389\) | −17.1250 | −0.868271 | −0.434136 | − | 0.900848i | \(-0.642946\pi\) | ||||
−0.434136 | + | 0.900848i | \(0.642946\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.753020 | 0.0380819 | ||||||||
\(392\) | 5.89977 | 0.297984 | ||||||||
\(393\) | 3.81940 | 0.192663 | ||||||||
\(394\) | 22.9071 | 1.15404 | ||||||||
\(395\) | 12.3230 | 0.620040 | ||||||||
\(396\) | −1.35690 | −0.0681866 | ||||||||
\(397\) | 25.0103 | 1.25523 | 0.627615 | − | 0.778524i | \(-0.284031\pi\) | ||||
0.627615 | + | 0.778524i | \(0.284031\pi\) | |||||||
\(398\) | −27.0291 | −1.35484 | ||||||||
\(399\) | −3.08277 | −0.154331 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −30.8689 | −1.54152 | −0.770760 | − | 0.637126i | \(-0.780123\pi\) | ||||
−0.770760 | + | 0.637126i | \(0.780123\pi\) | |||||||
\(402\) | 6.91185 | 0.344732 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.71379 | 0.234520 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 2.49502 | 0.123826 | ||||||||
\(407\) | 12.5767 | 0.623405 | ||||||||
\(408\) | 1.08815 | 0.0538713 | ||||||||
\(409\) | 11.0871 | 0.548221 | 0.274110 | − | 0.961698i | \(-0.411617\pi\) | ||||
0.274110 | + | 0.961698i | \(0.411617\pi\) | |||||||
\(410\) | 2.84117 | 0.140315 | ||||||||
\(411\) | 8.59717 | 0.424067 | ||||||||
\(412\) | −12.1642 | −0.599288 | ||||||||
\(413\) | 2.05669 | 0.101203 | ||||||||
\(414\) | 0.692021 | 0.0340110 | ||||||||
\(415\) | −2.68664 | −0.131882 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.38404 | −0.116747 | ||||||||
\(418\) | −3.98792 | −0.195055 | ||||||||
\(419\) | 17.5080 | 0.855320 | 0.427660 | − | 0.903940i | \(-0.359338\pi\) | ||||
0.427660 | + | 0.903940i | \(0.359338\pi\) | |||||||
\(420\) | 1.04892 | 0.0511819 | ||||||||
\(421\) | −16.1274 | −0.786000 | −0.393000 | − | 0.919538i | \(-0.628563\pi\) | ||||
−0.393000 | + | 0.919538i | \(0.628563\pi\) | |||||||
\(422\) | −10.3720 | −0.504899 | ||||||||
\(423\) | 3.31767 | 0.161310 | ||||||||
\(424\) | −0.664874 | −0.0322892 | ||||||||
\(425\) | −1.08815 | −0.0527828 | ||||||||
\(426\) | 2.29590 | 0.111237 | ||||||||
\(427\) | 3.40581 | 0.164819 | ||||||||
\(428\) | 1.83877 | 0.0888805 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.45473 | 0.214826 | ||||||||
\(431\) | 33.2905 | 1.60355 | 0.801774 | − | 0.597627i | \(-0.203890\pi\) | ||||
0.801774 | + | 0.597627i | \(0.203890\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −11.1056 | −0.533701 | −0.266851 | − | 0.963738i | \(-0.585983\pi\) | ||||
−0.266851 | + | 0.963738i | \(0.585983\pi\) | |||||||
\(434\) | 10.3327 | 0.495987 | ||||||||
\(435\) | −2.37867 | −0.114048 | ||||||||
\(436\) | −16.2403 | −0.777768 | ||||||||
\(437\) | 2.03385 | 0.0972923 | ||||||||
\(438\) | 3.36227 | 0.160656 | ||||||||
\(439\) | 12.6950 | 0.605900 | 0.302950 | − | 0.953007i | \(-0.402029\pi\) | ||||
0.302950 | + | 0.953007i | \(0.402029\pi\) | |||||||
\(440\) | 1.35690 | 0.0646875 | ||||||||
\(441\) | −5.89977 | −0.280942 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.90110 | −0.327881 | −0.163941 | − | 0.986470i | \(-0.552421\pi\) | ||||
−0.163941 | + | 0.986470i | \(0.552421\pi\) | |||||||
\(444\) | −9.26875 | −0.439875 | ||||||||
\(445\) | −12.8877 | −0.610935 | ||||||||
\(446\) | 14.0532 | 0.665440 | ||||||||
\(447\) | 8.93900 | 0.422800 | ||||||||
\(448\) | 1.04892 | 0.0495567 | ||||||||
\(449\) | 3.27652 | 0.154629 | 0.0773143 | − | 0.997007i | \(-0.475366\pi\) | ||||
0.0773143 | + | 0.997007i | \(0.475366\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 3.85517 | 0.181533 | ||||||||
\(452\) | 16.8267 | 0.791461 | ||||||||
\(453\) | 8.45473 | 0.397238 | ||||||||
\(454\) | −1.93362 | −0.0907495 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.93900 | 0.137631 | ||||||||
\(457\) | −1.40581 | −0.0657612 | −0.0328806 | − | 0.999459i | \(-0.510468\pi\) | ||||
−0.0328806 | + | 0.999459i | \(0.510468\pi\) | |||||||
\(458\) | −10.9148 | −0.510017 | ||||||||
\(459\) | −1.08815 | −0.0507903 | ||||||||
\(460\) | −0.692021 | −0.0322657 | ||||||||
\(461\) | −12.3773 | −0.576470 | −0.288235 | − | 0.957560i | \(-0.593068\pi\) | ||||
−0.288235 | + | 0.957560i | \(0.593068\pi\) | |||||||
\(462\) | 1.42327 | 0.0662166 | ||||||||
\(463\) | −31.7797 | −1.47693 | −0.738464 | − | 0.674293i | \(-0.764448\pi\) | ||||
−0.738464 | + | 0.674293i | \(0.764448\pi\) | |||||||
\(464\) | −2.37867 | −0.110427 | ||||||||
\(465\) | −9.85086 | −0.456822 | ||||||||
\(466\) | 21.6896 | 1.00475 | ||||||||
\(467\) | −36.2790 | −1.67879 | −0.839397 | − | 0.543519i | \(-0.817091\pi\) | ||||
−0.839397 | + | 0.543519i | \(0.817091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.24996 | −0.334772 | ||||||||
\(470\) | −3.31767 | −0.153033 | ||||||||
\(471\) | −2.70410 | −0.124598 | ||||||||
\(472\) | −1.96077 | −0.0902518 | ||||||||
\(473\) | 6.04461 | 0.277931 | ||||||||
\(474\) | −12.3230 | −0.566016 | ||||||||
\(475\) | −2.93900 | −0.134851 | ||||||||
\(476\) | −1.14138 | −0.0523148 | ||||||||
\(477\) | 0.664874 | 0.0304425 | ||||||||
\(478\) | −27.2349 | −1.24570 | ||||||||
\(479\) | 5.87933 | 0.268633 | 0.134317 | − | 0.990938i | \(-0.457116\pi\) | ||||
0.134317 | + | 0.990938i | \(0.457116\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 8.21014 | 0.373962 | ||||||||
\(483\) | −0.725873 | −0.0330284 | ||||||||
\(484\) | −9.15883 | −0.416311 | ||||||||
\(485\) | −1.56704 | −0.0711556 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −30.6243 | −1.38772 | −0.693860 | − | 0.720110i | \(-0.744091\pi\) | ||||
−0.693860 | + | 0.720110i | \(0.744091\pi\) | |||||||
\(488\) | −3.24698 | −0.146984 | ||||||||
\(489\) | 22.5284 | 1.01877 | ||||||||
\(490\) | 5.89977 | 0.266525 | ||||||||
\(491\) | 34.4456 | 1.55451 | 0.777255 | − | 0.629186i | \(-0.216612\pi\) | ||||
0.777255 | + | 0.629186i | \(0.216612\pi\) | |||||||
\(492\) | −2.84117 | −0.128090 | ||||||||
\(493\) | 2.58834 | 0.116573 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.35690 | −0.0609879 | ||||||||
\(496\) | −9.85086 | −0.442316 | ||||||||
\(497\) | −2.40821 | −0.108023 | ||||||||
\(498\) | 2.68664 | 0.120391 | ||||||||
\(499\) | 10.0194 | 0.448529 | 0.224264 | − | 0.974528i | \(-0.428002\pi\) | ||||
0.224264 | + | 0.974528i | \(0.428002\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −12.2228 | −0.546075 | ||||||||
\(502\) | 6.57002 | 0.293235 | ||||||||
\(503\) | 8.27950 | 0.369165 | 0.184582 | − | 0.982817i | \(-0.440907\pi\) | ||||
0.184582 | + | 0.982817i | \(0.440907\pi\) | |||||||
\(504\) | −1.04892 | −0.0467225 | ||||||||
\(505\) | 4.71379 | 0.209761 | ||||||||
\(506\) | −0.939001 | −0.0417437 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.06100 | −0.224546 | ||||||||
\(509\) | 44.4607 | 1.97069 | 0.985343 | − | 0.170585i | \(-0.0545659\pi\) | ||||
0.985343 | + | 0.170585i | \(0.0545659\pi\) | |||||||
\(510\) | 1.08815 | 0.0481839 | ||||||||
\(511\) | −3.52675 | −0.156014 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.93900 | −0.129760 | ||||||||
\(514\) | −13.7657 | −0.607179 | ||||||||
\(515\) | −12.1642 | −0.536019 | ||||||||
\(516\) | −4.45473 | −0.196109 | ||||||||
\(517\) | −4.50173 | −0.197986 | ||||||||
\(518\) | 9.72215 | 0.427167 | ||||||||
\(519\) | −11.7168 | −0.514309 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.8461 | −1.57044 | −0.785222 | − | 0.619214i | \(-0.787451\pi\) | ||||
−0.785222 | + | 0.619214i | \(0.787451\pi\) | |||||||
\(522\) | 2.37867 | 0.104111 | ||||||||
\(523\) | −5.80433 | −0.253806 | −0.126903 | − | 0.991915i | \(-0.540504\pi\) | ||||
−0.126903 | + | 0.991915i | \(0.540504\pi\) | |||||||
\(524\) | 3.81940 | 0.166851 | ||||||||
\(525\) | 1.04892 | 0.0457785 | ||||||||
\(526\) | 9.54288 | 0.416089 | ||||||||
\(527\) | 10.7192 | 0.466934 | ||||||||
\(528\) | −1.35690 | −0.0590513 | ||||||||
\(529\) | −22.5211 | −0.979179 | ||||||||
\(530\) | −0.664874 | −0.0288803 | ||||||||
\(531\) | 1.96077 | 0.0850902 | ||||||||
\(532\) | −3.08277 | −0.133655 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 12.8877 | 0.557705 | ||||||||
\(535\) | 1.83877 | 0.0794971 | ||||||||
\(536\) | 6.91185 | 0.298547 | ||||||||
\(537\) | 8.89738 | 0.383950 | ||||||||
\(538\) | −9.07069 | −0.391065 | ||||||||
\(539\) | 8.00538 | 0.344816 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 23.2446 | 0.999363 | 0.499681 | − | 0.866209i | \(-0.333450\pi\) | ||||
0.499681 | + | 0.866209i | \(0.333450\pi\) | |||||||
\(542\) | 17.5579 | 0.754178 | ||||||||
\(543\) | 1.31229 | 0.0563158 | ||||||||
\(544\) | 1.08815 | 0.0466539 | ||||||||
\(545\) | −16.2403 | −0.695657 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.1588 | −0.690902 | −0.345451 | − | 0.938437i | \(-0.612274\pi\) | ||||
−0.345451 | + | 0.938437i | \(0.612274\pi\) | |||||||
\(548\) | 8.59717 | 0.367253 | ||||||||
\(549\) | 3.24698 | 0.138578 | ||||||||
\(550\) | 1.35690 | 0.0578582 | ||||||||
\(551\) | 6.99090 | 0.297822 | ||||||||
\(552\) | 0.692021 | 0.0294544 | ||||||||
\(553\) | 12.9259 | 0.549663 | ||||||||
\(554\) | −13.7071 | −0.582358 | ||||||||
\(555\) | −9.26875 | −0.393437 | ||||||||
\(556\) | −2.38404 | −0.101106 | ||||||||
\(557\) | −25.5937 | −1.08444 | −0.542220 | − | 0.840236i | \(-0.682416\pi\) | ||||
−0.542220 | + | 0.840236i | \(0.682416\pi\) | |||||||
\(558\) | 9.85086 | 0.417020 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.04892 | 0.0443248 | ||||||||
\(561\) | 1.47650 | 0.0623379 | ||||||||
\(562\) | −24.3696 | −1.02797 | ||||||||
\(563\) | −40.9232 | −1.72471 | −0.862354 | − | 0.506307i | \(-0.831010\pi\) | ||||
−0.862354 | + | 0.506307i | \(0.831010\pi\) | |||||||
\(564\) | 3.31767 | 0.139699 | ||||||||
\(565\) | 16.8267 | 0.707904 | ||||||||
\(566\) | 17.1511 | 0.720913 | ||||||||
\(567\) | 1.04892 | 0.0440504 | ||||||||
\(568\) | 2.29590 | 0.0963337 | ||||||||
\(569\) | −20.1946 | −0.846602 | −0.423301 | − | 0.905989i | \(-0.639129\pi\) | ||||
−0.423301 | + | 0.905989i | \(0.639129\pi\) | |||||||
\(570\) | 2.93900 | 0.123101 | ||||||||
\(571\) | 36.8756 | 1.54320 | 0.771598 | − | 0.636110i | \(-0.219458\pi\) | ||||
0.771598 | + | 0.636110i | \(0.219458\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.75063 | 0.240236 | ||||||||
\(574\) | 2.98015 | 0.124389 | ||||||||
\(575\) | −0.692021 | −0.0288593 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 5.07500 | 0.211275 | 0.105637 | − | 0.994405i | \(-0.466312\pi\) | ||||
0.105637 | + | 0.994405i | \(0.466312\pi\) | |||||||
\(578\) | 15.8159 | 0.657856 | ||||||||
\(579\) | −10.0339 | −0.416993 | ||||||||
\(580\) | −2.37867 | −0.0987687 | ||||||||
\(581\) | −2.81807 | −0.116913 | ||||||||
\(582\) | 1.56704 | 0.0649559 | ||||||||
\(583\) | −0.902165 | −0.0373639 | ||||||||
\(584\) | 3.36227 | 0.139132 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.1172 | −0.996273 | ||||||||
\(587\) | 10.5714 | 0.436326 | 0.218163 | − | 0.975912i | \(-0.429993\pi\) | ||||
0.218163 | + | 0.975912i | \(0.429993\pi\) | |||||||
\(588\) | −5.89977 | −0.243303 | ||||||||
\(589\) | 28.9517 | 1.19293 | ||||||||
\(590\) | −1.96077 | −0.0807237 | ||||||||
\(591\) | −22.9071 | −0.942271 | ||||||||
\(592\) | −9.26875 | −0.380943 | ||||||||
\(593\) | −38.4999 | −1.58100 | −0.790501 | − | 0.612460i | \(-0.790180\pi\) | ||||
−0.790501 | + | 0.612460i | \(0.790180\pi\) | |||||||
\(594\) | 1.35690 | 0.0556741 | ||||||||
\(595\) | −1.14138 | −0.0467918 | ||||||||
\(596\) | 8.93900 | 0.366156 | ||||||||
\(597\) | 27.0291 | 1.10623 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.332142 | −0.0135709 | −0.00678547 | − | 0.999977i | \(-0.502160\pi\) | ||||
−0.00678547 | + | 0.999977i | \(0.502160\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −7.04162 | −0.287234 | −0.143617 | − | 0.989633i | \(-0.545873\pi\) | ||||
−0.143617 | + | 0.989633i | \(0.545873\pi\) | |||||||
\(602\) | 4.67264 | 0.190443 | ||||||||
\(603\) | −6.91185 | −0.281472 | ||||||||
\(604\) | 8.45473 | 0.344018 | ||||||||
\(605\) | −9.15883 | −0.372360 | ||||||||
\(606\) | −4.71379 | −0.191485 | ||||||||
\(607\) | −29.4185 | −1.19406 | −0.597030 | − | 0.802219i | \(-0.703653\pi\) | ||||
−0.597030 | + | 0.802219i | \(0.703653\pi\) | |||||||
\(608\) | 2.93900 | 0.119192 | ||||||||
\(609\) | −2.49502 | −0.101103 | ||||||||
\(610\) | −3.24698 | −0.131466 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.08815 | −0.0439857 | ||||||||
\(613\) | −34.1987 | −1.38127 | −0.690635 | − | 0.723203i | \(-0.742669\pi\) | ||||
−0.690635 | + | 0.723203i | \(0.742669\pi\) | |||||||
\(614\) | −17.2282 | −0.695273 | ||||||||
\(615\) | −2.84117 | −0.114567 | ||||||||
\(616\) | 1.42327 | 0.0573452 | ||||||||
\(617\) | 34.1890 | 1.37640 | 0.688198 | − | 0.725523i | \(-0.258402\pi\) | ||||
0.688198 | + | 0.725523i | \(0.258402\pi\) | |||||||
\(618\) | 12.1642 | 0.489316 | ||||||||
\(619\) | −9.80061 | −0.393920 | −0.196960 | − | 0.980412i | \(-0.563107\pi\) | ||||
−0.196960 | + | 0.980412i | \(0.563107\pi\) | |||||||
\(620\) | −9.85086 | −0.395620 | ||||||||
\(621\) | −0.692021 | −0.0277699 | ||||||||
\(622\) | 25.9801 | 1.04171 | ||||||||
\(623\) | −13.5181 | −0.541592 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.82669 | −0.312818 | ||||||||
\(627\) | 3.98792 | 0.159262 | ||||||||
\(628\) | −2.70410 | −0.107905 | ||||||||
\(629\) | 10.0858 | 0.402145 | ||||||||
\(630\) | −1.04892 | −0.0417899 | ||||||||
\(631\) | −17.0968 | −0.680612 | −0.340306 | − | 0.940315i | \(-0.610531\pi\) | ||||
−0.340306 | + | 0.940315i | \(0.610531\pi\) | |||||||
\(632\) | −12.3230 | −0.490184 | ||||||||
\(633\) | 10.3720 | 0.412248 | ||||||||
\(634\) | 0.391813 | 0.0155609 | ||||||||
\(635\) | −5.06100 | −0.200840 | ||||||||
\(636\) | 0.664874 | 0.0263640 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.22760 | −0.127782 | ||||||||
\(639\) | −2.29590 | −0.0908243 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −14.7030 | −0.580735 | −0.290368 | − | 0.956915i | \(-0.593778\pi\) | ||||
−0.290368 | + | 0.956915i | \(0.593778\pi\) | |||||||
\(642\) | −1.83877 | −0.0725706 | ||||||||
\(643\) | −42.7036 | −1.68407 | −0.842033 | − | 0.539425i | \(-0.818641\pi\) | ||||
−0.842033 | + | 0.539425i | \(0.818641\pi\) | |||||||
\(644\) | −0.725873 | −0.0286034 | ||||||||
\(645\) | −4.45473 | −0.175405 | ||||||||
\(646\) | −3.19806 | −0.125826 | ||||||||
\(647\) | 41.7265 | 1.64044 | 0.820218 | − | 0.572051i | \(-0.193852\pi\) | ||||
0.820218 | + | 0.572051i | \(0.193852\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −2.66056 | −0.104436 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.3327 | −0.404972 | ||||||||
\(652\) | 22.5284 | 0.882280 | ||||||||
\(653\) | −28.2306 | −1.10475 | −0.552374 | − | 0.833596i | \(-0.686278\pi\) | ||||
−0.552374 | + | 0.833596i | \(0.686278\pi\) | |||||||
\(654\) | 16.2403 | 0.635045 | ||||||||
\(655\) | 3.81940 | 0.149236 | ||||||||
\(656\) | −2.84117 | −0.110929 | ||||||||
\(657\) | −3.36227 | −0.131175 | ||||||||
\(658\) | −3.47996 | −0.135663 | ||||||||
\(659\) | −38.7885 | −1.51099 | −0.755493 | − | 0.655156i | \(-0.772603\pi\) | ||||
−0.755493 | + | 0.655156i | \(0.772603\pi\) | |||||||
\(660\) | −1.35690 | −0.0528171 | ||||||||
\(661\) | −31.5733 | −1.22806 | −0.614029 | − | 0.789284i | \(-0.710452\pi\) | ||||
−0.614029 | + | 0.789284i | \(0.710452\pi\) | |||||||
\(662\) | 26.3424 | 1.02383 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.68664 | 0.104262 | ||||||||
\(665\) | −3.08277 | −0.119545 | ||||||||
\(666\) | 9.26875 | 0.359157 | ||||||||
\(667\) | 1.64609 | 0.0637368 | ||||||||
\(668\) | −12.2228 | −0.472915 | ||||||||
\(669\) | −14.0532 | −0.543329 | ||||||||
\(670\) | 6.91185 | 0.267028 | ||||||||
\(671\) | −4.40581 | −0.170085 | ||||||||
\(672\) | −1.04892 | −0.0404629 | ||||||||
\(673\) | −44.1400 | −1.70147 | −0.850737 | − | 0.525592i | \(-0.823844\pi\) | ||||
−0.850737 | + | 0.525592i | \(0.823844\pi\) | |||||||
\(674\) | −14.8345 | −0.571402 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.8431 | −0.877931 | −0.438966 | − | 0.898504i | \(-0.644655\pi\) | ||||
−0.438966 | + | 0.898504i | \(0.644655\pi\) | |||||||
\(678\) | −16.8267 | −0.646225 | ||||||||
\(679\) | −1.64370 | −0.0630792 | ||||||||
\(680\) | 1.08815 | 0.0417285 | ||||||||
\(681\) | 1.93362 | 0.0740966 | ||||||||
\(682\) | −13.3666 | −0.511833 | ||||||||
\(683\) | 13.6866 | 0.523705 | 0.261852 | − | 0.965108i | \(-0.415667\pi\) | ||||
0.261852 | + | 0.965108i | \(0.415667\pi\) | |||||||
\(684\) | −2.93900 | −0.112376 | ||||||||
\(685\) | 8.59717 | 0.328481 | ||||||||
\(686\) | 13.5308 | 0.516608 | ||||||||
\(687\) | 10.9148 | 0.416427 | ||||||||
\(688\) | −4.45473 | −0.169835 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.692021 | 0.0263448 | ||||||||
\(691\) | 24.0261 | 0.913995 | 0.456998 | − | 0.889468i | \(-0.348925\pi\) | ||||
0.456998 | + | 0.889468i | \(0.348925\pi\) | |||||||
\(692\) | −11.7168 | −0.445405 | ||||||||
\(693\) | −1.42327 | −0.0540656 | ||||||||
\(694\) | 0.636399 | 0.0241574 | ||||||||
\(695\) | −2.38404 | −0.0904319 | ||||||||
\(696\) | 2.37867 | 0.0901631 | ||||||||
\(697\) | 3.09160 | 0.117103 | ||||||||
\(698\) | 17.2784 | 0.653999 | ||||||||
\(699\) | −21.6896 | −0.820377 | ||||||||
\(700\) | 1.04892 | 0.0396453 | ||||||||
\(701\) | 50.5392 | 1.90884 | 0.954419 | − | 0.298471i | \(-0.0964765\pi\) | ||||
0.954419 | + | 0.298471i | \(0.0964765\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.2409 | 1.02741 | ||||||||
\(704\) | −1.35690 | −0.0511399 | ||||||||
\(705\) | 3.31767 | 0.124951 | ||||||||
\(706\) | −21.7614 | −0.819000 | ||||||||
\(707\) | 4.94438 | 0.185952 | ||||||||
\(708\) | 1.96077 | 0.0736903 | ||||||||
\(709\) | 12.1847 | 0.457604 | 0.228802 | − | 0.973473i | \(-0.426519\pi\) | ||||
0.228802 | + | 0.973473i | \(0.426519\pi\) | |||||||
\(710\) | 2.29590 | 0.0861635 | ||||||||
\(711\) | 12.3230 | 0.462150 | ||||||||
\(712\) | 12.8877 | 0.482987 | ||||||||
\(713\) | 6.81700 | 0.255299 | ||||||||
\(714\) | 1.14138 | 0.0427149 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.89738 | 0.332511 | ||||||||
\(717\) | 27.2349 | 1.01711 | ||||||||
\(718\) | −22.8412 | −0.852425 | ||||||||
\(719\) | −10.8401 | −0.404268 | −0.202134 | − | 0.979358i | \(-0.564788\pi\) | ||||
−0.202134 | + | 0.979358i | \(0.564788\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −12.7593 | −0.475179 | ||||||||
\(722\) | 10.3623 | 0.385644 | ||||||||
\(723\) | −8.21014 | −0.305339 | ||||||||
\(724\) | 1.31229 | 0.0487709 | ||||||||
\(725\) | −2.37867 | −0.0883414 | ||||||||
\(726\) | 9.15883 | 0.339916 | ||||||||
\(727\) | 33.2489 | 1.23313 | 0.616567 | − | 0.787303i | \(-0.288523\pi\) | ||||
0.616567 | + | 0.787303i | \(0.288523\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.36227 | 0.124443 | ||||||||
\(731\) | 4.84740 | 0.179287 | ||||||||
\(732\) | 3.24698 | 0.120012 | ||||||||
\(733\) | 8.59120 | 0.317323 | 0.158662 | − | 0.987333i | \(-0.449282\pi\) | ||||
0.158662 | + | 0.987333i | \(0.449282\pi\) | |||||||
\(734\) | 7.78315 | 0.287281 | ||||||||
\(735\) | −5.89977 | −0.217616 | ||||||||
\(736\) | 0.692021 | 0.0255082 | ||||||||
\(737\) | 9.37867 | 0.345468 | ||||||||
\(738\) | 2.84117 | 0.104585 | ||||||||
\(739\) | 38.4131 | 1.41305 | 0.706525 | − | 0.707689i | \(-0.250262\pi\) | ||||
0.706525 | + | 0.707689i | \(0.250262\pi\) | |||||||
\(740\) | −9.26875 | −0.340726 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.697398 | −0.0256023 | ||||||||
\(743\) | −21.7904 | −0.799414 | −0.399707 | − | 0.916643i | \(-0.630888\pi\) | ||||
−0.399707 | + | 0.916643i | \(0.630888\pi\) | |||||||
\(744\) | 9.85086 | 0.361150 | ||||||||
\(745\) | 8.93900 | 0.327500 | ||||||||
\(746\) | 30.5133 | 1.11717 | ||||||||
\(747\) | −2.68664 | −0.0982992 | ||||||||
\(748\) | 1.47650 | 0.0539862 | ||||||||
\(749\) | 1.92872 | 0.0704739 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 0.715120 | 0.0260951 | 0.0130475 | − | 0.999915i | \(-0.495847\pi\) | ||||
0.0130475 | + | 0.999915i | \(0.495847\pi\) | |||||||
\(752\) | 3.31767 | 0.120983 | ||||||||
\(753\) | −6.57002 | −0.239425 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.45473 | 0.307699 | ||||||||
\(756\) | 1.04892 | 0.0381488 | ||||||||
\(757\) | 29.7894 | 1.08271 | 0.541357 | − | 0.840793i | \(-0.317911\pi\) | ||||
0.541357 | + | 0.840793i | \(0.317911\pi\) | |||||||
\(758\) | −6.41358 | −0.232952 | ||||||||
\(759\) | 0.939001 | 0.0340836 | ||||||||
\(760\) | 2.93900 | 0.106609 | ||||||||
\(761\) | −28.4112 | −1.02990 | −0.514952 | − | 0.857219i | \(-0.672190\pi\) | ||||
−0.514952 | + | 0.857219i | \(0.672190\pi\) | |||||||
\(762\) | 5.06100 | 0.183341 | ||||||||
\(763\) | −17.0347 | −0.616698 | ||||||||
\(764\) | 5.75063 | 0.208050 | ||||||||
\(765\) | −1.08815 | −0.0393420 | ||||||||
\(766\) | −2.89440 | −0.104579 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −16.6200 | −0.599333 | −0.299666 | − | 0.954044i | \(-0.596875\pi\) | ||||
−0.299666 | + | 0.954044i | \(0.596875\pi\) | |||||||
\(770\) | 1.42327 | 0.0512911 | ||||||||
\(771\) | 13.7657 | 0.495759 | ||||||||
\(772\) | −10.0339 | −0.361126 | ||||||||
\(773\) | 10.8388 | 0.389844 | 0.194922 | − | 0.980819i | \(-0.437555\pi\) | ||||
0.194922 | + | 0.980819i | \(0.437555\pi\) | |||||||
\(774\) | 4.45473 | 0.160122 | ||||||||
\(775\) | −9.85086 | −0.353853 | ||||||||
\(776\) | 1.56704 | 0.0562534 | ||||||||
\(777\) | −9.72215 | −0.348780 | ||||||||
\(778\) | 17.1250 | 0.613960 | ||||||||
\(779\) | 8.35019 | 0.299177 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.11529 | 0.111474 | ||||||||
\(782\) | −0.753020 | −0.0269280 | ||||||||
\(783\) | −2.37867 | −0.0850066 | ||||||||
\(784\) | −5.89977 | −0.210706 | ||||||||
\(785\) | −2.70410 | −0.0965136 | ||||||||
\(786\) | −3.81940 | −0.136233 | ||||||||
\(787\) | 4.55974 | 0.162537 | 0.0812687 | − | 0.996692i | \(-0.474103\pi\) | ||||
0.0812687 | + | 0.996692i | \(0.474103\pi\) | |||||||
\(788\) | −22.9071 | −0.816031 | ||||||||
\(789\) | −9.54288 | −0.339735 | ||||||||
\(790\) | −12.3230 | −0.438434 | ||||||||
\(791\) | 17.6498 | 0.627555 | ||||||||
\(792\) | 1.35690 | 0.0482152 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −25.0103 | −0.887582 | ||||||||
\(795\) | 0.664874 | 0.0235807 | ||||||||
\(796\) | 27.0291 | 0.958020 | ||||||||
\(797\) | −13.6601 | −0.483865 | −0.241933 | − | 0.970293i | \(-0.577781\pi\) | ||||
−0.241933 | + | 0.970293i | \(0.577781\pi\) | |||||||
\(798\) | 3.08277 | 0.109129 | ||||||||
\(799\) | −3.61011 | −0.127716 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −12.8877 | −0.455364 | ||||||||
\(802\) | 30.8689 | 1.09002 | ||||||||
\(803\) | 4.56225 | 0.160998 | ||||||||
\(804\) | −6.91185 | −0.243762 | ||||||||
\(805\) | −0.725873 | −0.0255837 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.07069 | 0.319303 | ||||||||
\(808\) | −4.71379 | −0.165831 | ||||||||
\(809\) | 30.2857 | 1.06479 | 0.532395 | − | 0.846496i | \(-0.321292\pi\) | ||||
0.532395 | + | 0.846496i | \(0.321292\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 26.5327 | 0.931690 | 0.465845 | − | 0.884866i | \(-0.345751\pi\) | ||||
0.465845 | + | 0.884866i | \(0.345751\pi\) | |||||||
\(812\) | −2.49502 | −0.0875582 | ||||||||
\(813\) | −17.5579 | −0.615784 | ||||||||
\(814\) | −12.5767 | −0.440814 | ||||||||
\(815\) | 22.5284 | 0.789136 | ||||||||
\(816\) | −1.08815 | −0.0380927 | ||||||||
\(817\) | 13.0925 | 0.458047 | ||||||||
\(818\) | −11.0871 | −0.387651 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.84117 | −0.0992178 | ||||||||
\(821\) | 48.5370 | 1.69395 | 0.846977 | − | 0.531630i | \(-0.178420\pi\) | ||||
0.846977 | + | 0.531630i | \(0.178420\pi\) | |||||||
\(822\) | −8.59717 | −0.299861 | ||||||||
\(823\) | −41.2650 | −1.43841 | −0.719204 | − | 0.694799i | \(-0.755493\pi\) | ||||
−0.719204 | + | 0.694799i | \(0.755493\pi\) | |||||||
\(824\) | 12.1642 | 0.423760 | ||||||||
\(825\) | −1.35690 | −0.0472411 | ||||||||
\(826\) | −2.05669 | −0.0715613 | ||||||||
\(827\) | 22.9004 | 0.796324 | 0.398162 | − | 0.917315i | \(-0.369648\pi\) | ||||
0.398162 | + | 0.917315i | \(0.369648\pi\) | |||||||
\(828\) | −0.692021 | −0.0240494 | ||||||||
\(829\) | 13.9782 | 0.485484 | 0.242742 | − | 0.970091i | \(-0.421953\pi\) | ||||
0.242742 | + | 0.970091i | \(0.421953\pi\) | |||||||
\(830\) | 2.68664 | 0.0932548 | ||||||||
\(831\) | 13.7071 | 0.475494 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.41981 | 0.222433 | ||||||||
\(834\) | 2.38404 | 0.0825527 | ||||||||
\(835\) | −12.2228 | −0.422988 | ||||||||
\(836\) | 3.98792 | 0.137925 | ||||||||
\(837\) | −9.85086 | −0.340495 | ||||||||
\(838\) | −17.5080 | −0.604802 | ||||||||
\(839\) | −1.35258 | −0.0466964 | −0.0233482 | − | 0.999727i | \(-0.507433\pi\) | ||||
−0.0233482 | + | 0.999727i | \(0.507433\pi\) | |||||||
\(840\) | −1.04892 | −0.0361911 | ||||||||
\(841\) | −23.3419 | −0.804895 | ||||||||
\(842\) | 16.1274 | 0.555786 | ||||||||
\(843\) | 24.3696 | 0.839333 | ||||||||
\(844\) | 10.3720 | 0.357018 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.31767 | −0.114064 | ||||||||
\(847\) | −9.60686 | −0.330096 | ||||||||
\(848\) | 0.664874 | 0.0228319 | ||||||||
\(849\) | −17.1511 | −0.588623 | ||||||||
\(850\) | 1.08815 | 0.0373231 | ||||||||
\(851\) | 6.41417 | 0.219875 | ||||||||
\(852\) | −2.29590 | −0.0786561 | ||||||||
\(853\) | −18.0887 | −0.619347 | −0.309673 | − | 0.950843i | \(-0.600220\pi\) | ||||
−0.309673 | + | 0.950843i | \(0.600220\pi\) | |||||||
\(854\) | −3.40581 | −0.116545 | ||||||||
\(855\) | −2.93900 | −0.100512 | ||||||||
\(856\) | −1.83877 | −0.0628480 | ||||||||
\(857\) | −8.47889 | −0.289633 | −0.144817 | − | 0.989458i | \(-0.546259\pi\) | ||||
−0.144817 | + | 0.989458i | \(0.546259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.8968 | 0.678870 | 0.339435 | − | 0.940630i | \(-0.389764\pi\) | ||||
0.339435 | + | 0.940630i | \(0.389764\pi\) | |||||||
\(860\) | −4.45473 | −0.151905 | ||||||||
\(861\) | −2.98015 | −0.101563 | ||||||||
\(862\) | −33.2905 | −1.13388 | ||||||||
\(863\) | 16.0989 | 0.548013 | 0.274006 | − | 0.961728i | \(-0.411651\pi\) | ||||
0.274006 | + | 0.961728i | \(0.411651\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −11.7168 | −0.398382 | ||||||||
\(866\) | 11.1056 | 0.377384 | ||||||||
\(867\) | −15.8159 | −0.537137 | ||||||||
\(868\) | −10.3327 | −0.350716 | ||||||||
\(869\) | −16.7211 | −0.567224 | ||||||||
\(870\) | 2.37867 | 0.0806443 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 16.2403 | 0.549965 | ||||||||
\(873\) | −1.56704 | −0.0530363 | ||||||||
\(874\) | −2.03385 | −0.0687961 | ||||||||
\(875\) | 1.04892 | 0.0354599 | ||||||||
\(876\) | −3.36227 | −0.113601 | ||||||||
\(877\) | −7.14377 | −0.241228 | −0.120614 | − | 0.992699i | \(-0.538486\pi\) | ||||
−0.120614 | + | 0.992699i | \(0.538486\pi\) | |||||||
\(878\) | −12.6950 | −0.428436 | ||||||||
\(879\) | 24.1172 | 0.813453 | ||||||||
\(880\) | −1.35690 | −0.0457410 | ||||||||
\(881\) | 42.5786 | 1.43451 | 0.717256 | − | 0.696810i | \(-0.245398\pi\) | ||||
0.717256 | + | 0.696810i | \(0.245398\pi\) | |||||||
\(882\) | 5.89977 | 0.198656 | ||||||||
\(883\) | −38.3997 | −1.29225 | −0.646126 | − | 0.763230i | \(-0.723612\pi\) | ||||
−0.646126 | + | 0.763230i | \(0.723612\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.96077 | 0.0659106 | ||||||||
\(886\) | 6.90110 | 0.231847 | ||||||||
\(887\) | 57.1943 | 1.92040 | 0.960199 | − | 0.279317i | \(-0.0901079\pi\) | ||||
0.960199 | + | 0.279317i | \(0.0901079\pi\) | |||||||
\(888\) | 9.26875 | 0.311039 | ||||||||
\(889\) | −5.30857 | −0.178044 | ||||||||
\(890\) | 12.8877 | 0.431996 | ||||||||
\(891\) | −1.35690 | −0.0454577 | ||||||||
\(892\) | −14.0532 | −0.470537 | ||||||||
\(893\) | −9.75063 | −0.326292 | ||||||||
\(894\) | −8.93900 | −0.298965 | ||||||||
\(895\) | 8.89738 | 0.297407 | ||||||||
\(896\) | −1.04892 | −0.0350419 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.27652 | −0.109339 | ||||||||
\(899\) | 23.4319 | 0.781497 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −0.723480 | −0.0241026 | ||||||||
\(902\) | −3.85517 | −0.128363 | ||||||||
\(903\) | −4.67264 | −0.155496 | ||||||||
\(904\) | −16.8267 | −0.559647 | ||||||||
\(905\) | 1.31229 | 0.0436220 | ||||||||
\(906\) | −8.45473 | −0.280890 | ||||||||
\(907\) | 1.07415 | 0.0356664 | 0.0178332 | − | 0.999841i | \(-0.494323\pi\) | ||||
0.0178332 | + | 0.999841i | \(0.494323\pi\) | |||||||
\(908\) | 1.93362 | 0.0641696 | ||||||||
\(909\) | 4.71379 | 0.156347 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.9904 | −1.68939 | −0.844694 | − | 0.535249i | \(-0.820218\pi\) | ||||
−0.844694 | + | 0.535249i | \(0.820218\pi\) | |||||||
\(912\) | −2.93900 | −0.0973201 | ||||||||
\(913\) | 3.64550 | 0.120648 | ||||||||
\(914\) | 1.40581 | 0.0465002 | ||||||||
\(915\) | 3.24698 | 0.107342 | ||||||||
\(916\) | 10.9148 | 0.360636 | ||||||||
\(917\) | 4.00623 | 0.132297 | ||||||||
\(918\) | 1.08815 | 0.0359142 | ||||||||
\(919\) | 7.82344 | 0.258072 | 0.129036 | − | 0.991640i | \(-0.458812\pi\) | ||||
0.129036 | + | 0.991640i | \(0.458812\pi\) | |||||||
\(920\) | 0.692021 | 0.0228153 | ||||||||
\(921\) | 17.2282 | 0.567688 | ||||||||
\(922\) | 12.3773 | 0.407626 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.42327 | −0.0468222 | ||||||||
\(925\) | −9.26875 | −0.304755 | ||||||||
\(926\) | 31.7797 | 1.04435 | ||||||||
\(927\) | −12.1642 | −0.399525 | ||||||||
\(928\) | 2.37867 | 0.0780835 | ||||||||
\(929\) | 19.5007 | 0.639796 | 0.319898 | − | 0.947452i | \(-0.396351\pi\) | ||||
0.319898 | + | 0.947452i | \(0.396351\pi\) | |||||||
\(930\) | 9.85086 | 0.323022 | ||||||||
\(931\) | 17.3394 | 0.568277 | ||||||||
\(932\) | −21.6896 | −0.710467 | ||||||||
\(933\) | −25.9801 | −0.850552 | ||||||||
\(934\) | 36.2790 | 1.18709 | ||||||||
\(935\) | 1.47650 | 0.0482867 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.0968 | −1.04856 | −0.524278 | − | 0.851547i | \(-0.675665\pi\) | ||||
−0.524278 | + | 0.851547i | \(0.675665\pi\) | |||||||
\(938\) | 7.24996 | 0.236720 | ||||||||
\(939\) | 7.82669 | 0.255414 | ||||||||
\(940\) | 3.31767 | 0.108210 | ||||||||
\(941\) | −35.9181 | −1.17090 | −0.585448 | − | 0.810710i | \(-0.699081\pi\) | ||||
−0.585448 | + | 0.810710i | \(0.699081\pi\) | |||||||
\(942\) | 2.70410 | 0.0881044 | ||||||||
\(943\) | 1.96615 | 0.0640266 | ||||||||
\(944\) | 1.96077 | 0.0638177 | ||||||||
\(945\) | 1.04892 | 0.0341213 | ||||||||
\(946\) | −6.04461 | −0.196527 | ||||||||
\(947\) | −20.7700 | −0.674934 | −0.337467 | − | 0.941337i | \(-0.609570\pi\) | ||||
−0.337467 | + | 0.941337i | \(0.609570\pi\) | |||||||
\(948\) | 12.3230 | 0.400234 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.93900 | 0.0953538 | ||||||||
\(951\) | −0.391813 | −0.0127054 | ||||||||
\(952\) | 1.14138 | 0.0369922 | ||||||||
\(953\) | −11.7855 | −0.381771 | −0.190886 | − | 0.981612i | \(-0.561136\pi\) | ||||
−0.190886 | + | 0.981612i | \(0.561136\pi\) | |||||||
\(954\) | −0.664874 | −0.0215261 | ||||||||
\(955\) | 5.75063 | 0.186086 | ||||||||
\(956\) | 27.2349 | 0.880840 | ||||||||
\(957\) | 3.22760 | 0.104334 | ||||||||
\(958\) | −5.87933 | −0.189953 | ||||||||
\(959\) | 9.01772 | 0.291197 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 66.0393 | 2.13030 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.83877 | 0.0592536 | ||||||||
\(964\) | −8.21014 | −0.264431 | ||||||||
\(965\) | −10.0339 | −0.323001 | ||||||||
\(966\) | 0.725873 | 0.0233546 | ||||||||
\(967\) | 52.0116 | 1.67258 | 0.836290 | − | 0.548287i | \(-0.184720\pi\) | ||||
0.836290 | + | 0.548287i | \(0.184720\pi\) | |||||||
\(968\) | 9.15883 | 0.294376 | ||||||||
\(969\) | 3.19806 | 0.102737 | ||||||||
\(970\) | 1.56704 | 0.0503146 | ||||||||
\(971\) | −17.7144 | −0.568482 | −0.284241 | − | 0.958753i | \(-0.591742\pi\) | ||||
−0.284241 | + | 0.958753i | \(0.591742\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −2.50066 | −0.0801676 | ||||||||
\(974\) | 30.6243 | 0.981266 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.24698 | 0.103933 | ||||||||
\(977\) | 8.16959 | 0.261368 | 0.130684 | − | 0.991424i | \(-0.458283\pi\) | ||||
0.130684 | + | 0.991424i | \(0.458283\pi\) | |||||||
\(978\) | −22.5284 | −0.720379 | ||||||||
\(979\) | 17.4873 | 0.558895 | ||||||||
\(980\) | −5.89977 | −0.188461 | ||||||||
\(981\) | −16.2403 | −0.518512 | ||||||||
\(982\) | −34.4456 | −1.09920 | ||||||||
\(983\) | −57.0256 | −1.81883 | −0.909417 | − | 0.415885i | \(-0.863472\pi\) | ||||
−0.909417 | + | 0.415885i | \(0.863472\pi\) | |||||||
\(984\) | 2.84117 | 0.0905731 | ||||||||
\(985\) | −22.9071 | −0.729880 | ||||||||
\(986\) | −2.58834 | −0.0824294 | ||||||||
\(987\) | 3.47996 | 0.110768 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.08277 | 0.0980264 | ||||||||
\(990\) | 1.35690 | 0.0431250 | ||||||||
\(991\) | 37.2416 | 1.18302 | 0.591509 | − | 0.806298i | \(-0.298532\pi\) | ||||
0.591509 | + | 0.806298i | \(0.298532\pi\) | |||||||
\(992\) | 9.85086 | 0.312765 | ||||||||
\(993\) | −26.3424 | −0.835951 | ||||||||
\(994\) | 2.40821 | 0.0763837 | ||||||||
\(995\) | 27.0291 | 0.856879 | ||||||||
\(996\) | −2.68664 | −0.0851296 | ||||||||
\(997\) | −9.00059 | −0.285052 | −0.142526 | − | 0.989791i | \(-0.545522\pi\) | ||||
−0.142526 | + | 0.989791i | \(0.545522\pi\) | |||||||
\(998\) | −10.0194 | −0.317158 | ||||||||
\(999\) | −9.26875 | −0.293250 |
(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 | 5070.2.a.bp.1.3 | ✓ | 3 | |
13.5 | odd | 4 | 5070.2.b.z.1351.6 | 6 | |||
13.8 | odd | 4 | 5070.2.b.z.1351.1 | 6 | |||
13.12 | even | 2 | 5070.2.a.bw.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bp.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5070.2.a.bw.1.1 | yes | 3 | 13.12 | even | 2 | ||
5070.2.b.z.1351.1 | 6 | 13.8 | odd | 4 | |||
5070.2.b.z.1351.6 | 6 | 13.5 | odd | 4 |