Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(5\) | 0.801938 | 0.358637 | 0.179319 | − | 0.983791i | \(-0.442611\pi\) | ||||
0.179319 | + | 0.983791i | \(0.442611\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.801938 | 0.253595 | ||||||||
\(11\) | −6.04892 | −1.82382 | −0.911909 | − | 0.410393i | \(-0.865391\pi\) | ||||
−0.911909 | + | 0.410393i | \(0.865391\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.801938 | 0.207059 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.85086 | −0.691434 | −0.345717 | − | 0.938339i | \(-0.612364\pi\) | ||||
−0.345717 | + | 0.938339i | \(0.612364\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.939001 | 0.215422 | 0.107711 | − | 0.994182i | \(-0.465648\pi\) | ||||
0.107711 | + | 0.994182i | \(0.465648\pi\) | |||||||
\(20\) | 0.801938 | 0.179319 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −6.04892 | −1.28963 | ||||||||
\(23\) | 0.911854 | 0.190135 | 0.0950674 | − | 0.995471i | \(-0.469693\pi\) | ||||
0.0950674 | + | 0.995471i | \(0.469693\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.35690 | −0.871379 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −3.35690 | −0.623360 | −0.311680 | − | 0.950187i | \(-0.600892\pi\) | ||||
−0.311680 | + | 0.950187i | \(0.600892\pi\) | |||||||
\(30\) | 0.801938 | 0.146413 | ||||||||
\(31\) | 2.15883 | 0.387738 | 0.193869 | − | 0.981027i | \(-0.437896\pi\) | ||||
0.193869 | + | 0.981027i | \(0.437896\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.04892 | −1.05298 | ||||||||
\(34\) | −2.85086 | −0.488918 | ||||||||
\(35\) | −0.801938 | −0.135552 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.91185 | −0.971903 | −0.485951 | − | 0.873986i | \(-0.661527\pi\) | ||||
−0.485951 | + | 0.873986i | \(0.661527\pi\) | |||||||
\(38\) | 0.939001 | 0.152326 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.801938 | 0.126797 | ||||||||
\(41\) | −1.19806 | −0.187106 | −0.0935529 | − | 0.995614i | \(-0.529822\pi\) | ||||
−0.0935529 | + | 0.995614i | \(0.529822\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 4.07606 | 0.621594 | 0.310797 | − | 0.950476i | \(-0.399404\pi\) | ||||
0.310797 | + | 0.950476i | \(0.399404\pi\) | |||||||
\(44\) | −6.04892 | −0.911909 | ||||||||
\(45\) | 0.801938 | 0.119546 | ||||||||
\(46\) | 0.911854 | 0.134446 | ||||||||
\(47\) | 1.27413 | 0.185850 | 0.0929252 | − | 0.995673i | \(-0.470378\pi\) | ||||
0.0929252 | + | 0.995673i | \(0.470378\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.35690 | −0.616158 | ||||||||
\(51\) | −2.85086 | −0.399200 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.15883 | 0.845981 | 0.422990 | − | 0.906134i | \(-0.360980\pi\) | ||||
0.422990 | + | 0.906134i | \(0.360980\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −4.85086 | −0.654089 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0.939001 | 0.124374 | ||||||||
\(58\) | −3.35690 | −0.440782 | ||||||||
\(59\) | −7.29590 | −0.949845 | −0.474922 | − | 0.880028i | \(-0.657524\pi\) | ||||
−0.474922 | + | 0.880028i | \(0.657524\pi\) | |||||||
\(60\) | 0.801938 | 0.103530 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 2.15883 | 0.274172 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.04892 | −0.744570 | ||||||||
\(67\) | 1.35690 | 0.165771 | 0.0828856 | − | 0.996559i | \(-0.473586\pi\) | ||||
0.0828856 | + | 0.996559i | \(0.473586\pi\) | |||||||
\(68\) | −2.85086 | −0.345717 | ||||||||
\(69\) | 0.911854 | 0.109774 | ||||||||
\(70\) | −0.801938 | −0.0958499 | ||||||||
\(71\) | −7.78017 | −0.923336 | −0.461668 | − | 0.887053i | \(-0.652749\pi\) | ||||
−0.461668 | + | 0.887053i | \(0.652749\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −14.4547 | −1.69180 | −0.845899 | − | 0.533343i | \(-0.820936\pi\) | ||||
−0.845899 | + | 0.533343i | \(0.820936\pi\) | |||||||
\(74\) | −5.91185 | −0.687239 | ||||||||
\(75\) | −4.35690 | −0.503091 | ||||||||
\(76\) | 0.939001 | 0.107711 | ||||||||
\(77\) | 6.04892 | 0.689338 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.131687 | 0.0148159 | 0.00740795 | − | 0.999973i | \(-0.497642\pi\) | ||||
0.00740795 | + | 0.999973i | \(0.497642\pi\) | |||||||
\(80\) | 0.801938 | 0.0896594 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.19806 | −0.132304 | ||||||||
\(83\) | −16.9148 | −1.85664 | −0.928322 | − | 0.371776i | \(-0.878749\pi\) | ||||
−0.928322 | + | 0.371776i | \(0.878749\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −2.28621 | −0.247974 | ||||||||
\(86\) | 4.07606 | 0.439533 | ||||||||
\(87\) | −3.35690 | −0.359897 | ||||||||
\(88\) | −6.04892 | −0.644817 | ||||||||
\(89\) | −12.7409 | −1.35054 | −0.675268 | − | 0.737572i | \(-0.735972\pi\) | ||||
−0.675268 | + | 0.737572i | \(0.735972\pi\) | |||||||
\(90\) | 0.801938 | 0.0845317 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.911854 | 0.0950674 | ||||||||
\(93\) | 2.15883 | 0.223861 | ||||||||
\(94\) | 1.27413 | 0.131416 | ||||||||
\(95\) | 0.753020 | 0.0772583 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −4.85623 | −0.493076 | −0.246538 | − | 0.969133i | \(-0.579293\pi\) | ||||
−0.246538 | + | 0.969133i | \(0.579293\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −6.04892 | −0.607939 | ||||||||
\(100\) | −4.35690 | −0.435690 | ||||||||
\(101\) | −4.92931 | −0.490485 | −0.245242 | − | 0.969462i | \(-0.578868\pi\) | ||||
−0.245242 | + | 0.969462i | \(0.578868\pi\) | |||||||
\(102\) | −2.85086 | −0.282277 | ||||||||
\(103\) | −0.170915 | −0.0168408 | −0.00842039 | − | 0.999965i | \(-0.502680\pi\) | ||||
−0.00842039 | + | 0.999965i | \(0.502680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.801938 | −0.0782611 | ||||||||
\(106\) | 6.15883 | 0.598199 | ||||||||
\(107\) | −6.30559 | −0.609584 | −0.304792 | − | 0.952419i | \(-0.598587\pi\) | ||||
−0.304792 | + | 0.952419i | \(0.598587\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 14.1739 | 1.35761 | 0.678807 | − | 0.734317i | \(-0.262497\pi\) | ||||
0.678807 | + | 0.734317i | \(0.262497\pi\) | |||||||
\(110\) | −4.85086 | −0.462511 | ||||||||
\(111\) | −5.91185 | −0.561128 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −0.198062 | −0.0186321 | −0.00931607 | − | 0.999957i | \(-0.502965\pi\) | ||||
−0.00931607 | + | 0.999957i | \(0.502965\pi\) | |||||||
\(114\) | 0.939001 | 0.0879455 | ||||||||
\(115\) | 0.731250 | 0.0681894 | ||||||||
\(116\) | −3.35690 | −0.311680 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.29590 | −0.671642 | ||||||||
\(119\) | 2.85086 | 0.261337 | ||||||||
\(120\) | 0.801938 | 0.0732066 | ||||||||
\(121\) | 25.5894 | 2.32631 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | −1.19806 | −0.108026 | ||||||||
\(124\) | 2.15883 | 0.193869 | ||||||||
\(125\) | −7.50365 | −0.671147 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −17.0465 | −1.51263 | −0.756317 | − | 0.654205i | \(-0.773003\pi\) | ||||
−0.756317 | + | 0.654205i | \(0.773003\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.07606 | 0.358877 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.02715 | −0.264483 | −0.132242 | − | 0.991218i | \(-0.542217\pi\) | ||||
−0.132242 | + | 0.991218i | \(0.542217\pi\) | |||||||
\(132\) | −6.04892 | −0.526491 | ||||||||
\(133\) | −0.939001 | −0.0814217 | ||||||||
\(134\) | 1.35690 | 0.117218 | ||||||||
\(135\) | 0.801938 | 0.0690198 | ||||||||
\(136\) | −2.85086 | −0.244459 | ||||||||
\(137\) | 17.3817 | 1.48501 | 0.742507 | − | 0.669838i | \(-0.233636\pi\) | ||||
0.742507 | + | 0.669838i | \(0.233636\pi\) | |||||||
\(138\) | 0.911854 | 0.0776222 | ||||||||
\(139\) | 7.99330 | 0.677982 | 0.338991 | − | 0.940790i | \(-0.389914\pi\) | ||||
0.338991 | + | 0.940790i | \(0.389914\pi\) | |||||||
\(140\) | −0.801938 | −0.0677761 | ||||||||
\(141\) | 1.27413 | 0.107301 | ||||||||
\(142\) | −7.78017 | −0.652897 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.69202 | −0.223560 | ||||||||
\(146\) | −14.4547 | −1.19628 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −5.91185 | −0.485951 | ||||||||
\(149\) | −4.74333 | −0.388589 | −0.194294 | − | 0.980943i | \(-0.562242\pi\) | ||||
−0.194294 | + | 0.980943i | \(0.562242\pi\) | |||||||
\(150\) | −4.35690 | −0.355739 | ||||||||
\(151\) | 11.2687 | 0.917038 | 0.458519 | − | 0.888685i | \(-0.348380\pi\) | ||||
0.458519 | + | 0.888685i | \(0.348380\pi\) | |||||||
\(152\) | 0.939001 | 0.0761630 | ||||||||
\(153\) | −2.85086 | −0.230478 | ||||||||
\(154\) | 6.04892 | 0.487436 | ||||||||
\(155\) | 1.73125 | 0.139057 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.5797 | −1.72225 | −0.861124 | − | 0.508395i | \(-0.830239\pi\) | ||||
−0.861124 | + | 0.508395i | \(0.830239\pi\) | |||||||
\(158\) | 0.131687 | 0.0104764 | ||||||||
\(159\) | 6.15883 | 0.488427 | ||||||||
\(160\) | 0.801938 | 0.0633987 | ||||||||
\(161\) | −0.911854 | −0.0718642 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.25667 | 0.176756 | 0.0883780 | − | 0.996087i | \(-0.471832\pi\) | ||||
0.0883780 | + | 0.996087i | \(0.471832\pi\) | |||||||
\(164\) | −1.19806 | −0.0935529 | ||||||||
\(165\) | −4.85086 | −0.377639 | ||||||||
\(166\) | −16.9148 | −1.31285 | ||||||||
\(167\) | −0.302602 | −0.0234160 | −0.0117080 | − | 0.999931i | \(-0.503727\pi\) | ||||
−0.0117080 | + | 0.999931i | \(0.503727\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.28621 | −0.175344 | ||||||||
\(171\) | 0.939001 | 0.0718072 | ||||||||
\(172\) | 4.07606 | 0.310797 | ||||||||
\(173\) | 18.6896 | 1.42095 | 0.710473 | − | 0.703724i | \(-0.248481\pi\) | ||||
0.710473 | + | 0.703724i | \(0.248481\pi\) | |||||||
\(174\) | −3.35690 | −0.254486 | ||||||||
\(175\) | 4.35690 | 0.329350 | ||||||||
\(176\) | −6.04892 | −0.455954 | ||||||||
\(177\) | −7.29590 | −0.548393 | ||||||||
\(178\) | −12.7409 | −0.954974 | ||||||||
\(179\) | −22.5797 | −1.68769 | −0.843843 | − | 0.536589i | \(-0.819712\pi\) | ||||
−0.843843 | + | 0.536589i | \(0.819712\pi\) | |||||||
\(180\) | 0.801938 | 0.0597729 | ||||||||
\(181\) | 6.94331 | 0.516092 | 0.258046 | − | 0.966133i | \(-0.416921\pi\) | ||||
0.258046 | + | 0.966133i | \(0.416921\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 0.911854 | 0.0672228 | ||||||||
\(185\) | −4.74094 | −0.348561 | ||||||||
\(186\) | 2.15883 | 0.158293 | ||||||||
\(187\) | 17.2446 | 1.26105 | ||||||||
\(188\) | 1.27413 | 0.0929252 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0.753020 | 0.0546298 | ||||||||
\(191\) | 0.728857 | 0.0527383 | 0.0263691 | − | 0.999652i | \(-0.491605\pi\) | ||||
0.0263691 | + | 0.999652i | \(0.491605\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −14.0411 | −1.01070 | −0.505352 | − | 0.862913i | \(-0.668637\pi\) | ||||
−0.505352 | + | 0.862913i | \(0.668637\pi\) | |||||||
\(194\) | −4.85623 | −0.348657 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −7.94139 | −0.565801 | −0.282900 | − | 0.959149i | \(-0.591297\pi\) | ||||
−0.282900 | + | 0.959149i | \(0.591297\pi\) | |||||||
\(198\) | −6.04892 | −0.429878 | ||||||||
\(199\) | 8.00538 | 0.567486 | 0.283743 | − | 0.958900i | \(-0.408424\pi\) | ||||
0.283743 | + | 0.958900i | \(0.408424\pi\) | |||||||
\(200\) | −4.35690 | −0.308079 | ||||||||
\(201\) | 1.35690 | 0.0957081 | ||||||||
\(202\) | −4.92931 | −0.346825 | ||||||||
\(203\) | 3.35690 | 0.235608 | ||||||||
\(204\) | −2.85086 | −0.199600 | ||||||||
\(205\) | −0.960771 | −0.0671032 | ||||||||
\(206\) | −0.170915 | −0.0119082 | ||||||||
\(207\) | 0.911854 | 0.0633782 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.67994 | −0.392890 | ||||||||
\(210\) | −0.801938 | −0.0553390 | ||||||||
\(211\) | −16.2892 | −1.12139 | −0.560697 | − | 0.828021i | \(-0.689467\pi\) | ||||
−0.560697 | + | 0.828021i | \(0.689467\pi\) | |||||||
\(212\) | 6.15883 | 0.422990 | ||||||||
\(213\) | −7.78017 | −0.533088 | ||||||||
\(214\) | −6.30559 | −0.431041 | ||||||||
\(215\) | 3.26875 | 0.222927 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −2.15883 | −0.146551 | ||||||||
\(218\) | 14.1739 | 0.959978 | ||||||||
\(219\) | −14.4547 | −0.976760 | ||||||||
\(220\) | −4.85086 | −0.327045 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.91185 | −0.396778 | ||||||||
\(223\) | 17.6256 | 1.18030 | 0.590150 | − | 0.807293i | \(-0.299068\pi\) | ||||
0.590150 | + | 0.807293i | \(0.299068\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −4.35690 | −0.290460 | ||||||||
\(226\) | −0.198062 | −0.0131749 | ||||||||
\(227\) | −11.1914 | −0.742796 | −0.371398 | − | 0.928474i | \(-0.621122\pi\) | ||||
−0.371398 | + | 0.928474i | \(0.621122\pi\) | |||||||
\(228\) | 0.939001 | 0.0621869 | ||||||||
\(229\) | 25.4131 | 1.67935 | 0.839673 | − | 0.543093i | \(-0.182747\pi\) | ||||
0.839673 | + | 0.543093i | \(0.182747\pi\) | |||||||
\(230\) | 0.731250 | 0.0482172 | ||||||||
\(231\) | 6.04892 | 0.397990 | ||||||||
\(232\) | −3.35690 | −0.220391 | ||||||||
\(233\) | −4.20237 | −0.275307 | −0.137653 | − | 0.990480i | \(-0.543956\pi\) | ||||
−0.137653 | + | 0.990480i | \(0.543956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.02177 | 0.0666529 | ||||||||
\(236\) | −7.29590 | −0.474922 | ||||||||
\(237\) | 0.131687 | 0.00855396 | ||||||||
\(238\) | 2.85086 | 0.184793 | ||||||||
\(239\) | −20.3177 | −1.31424 | −0.657120 | − | 0.753786i | \(-0.728226\pi\) | ||||
−0.657120 | + | 0.753786i | \(0.728226\pi\) | |||||||
\(240\) | 0.801938 | 0.0517649 | ||||||||
\(241\) | −15.9433 | −1.02700 | −0.513500 | − | 0.858090i | \(-0.671651\pi\) | ||||
−0.513500 | + | 0.858090i | \(0.671651\pi\) | |||||||
\(242\) | 25.5894 | 1.64495 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 0.801938 | 0.0512339 | ||||||||
\(246\) | −1.19806 | −0.0763857 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.15883 | 0.137086 | ||||||||
\(249\) | −16.9148 | −1.07193 | ||||||||
\(250\) | −7.50365 | −0.474572 | ||||||||
\(251\) | 27.3207 | 1.72446 | 0.862232 | − | 0.506513i | \(-0.169066\pi\) | ||||
0.862232 | + | 0.506513i | \(0.169066\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −5.51573 | −0.346771 | ||||||||
\(254\) | −17.0465 | −1.06959 | ||||||||
\(255\) | −2.28621 | −0.143168 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.2446 | 1.57471 | 0.787357 | − | 0.616497i | \(-0.211449\pi\) | ||||
0.787357 | + | 0.616497i | \(0.211449\pi\) | |||||||
\(258\) | 4.07606 | 0.253765 | ||||||||
\(259\) | 5.91185 | 0.367345 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.35690 | −0.207787 | ||||||||
\(262\) | −3.02715 | −0.187018 | ||||||||
\(263\) | 11.8509 | 0.730755 | 0.365378 | − | 0.930859i | \(-0.380940\pi\) | ||||
0.365378 | + | 0.930859i | \(0.380940\pi\) | |||||||
\(264\) | −6.04892 | −0.372285 | ||||||||
\(265\) | 4.93900 | 0.303400 | ||||||||
\(266\) | −0.939001 | −0.0575738 | ||||||||
\(267\) | −12.7409 | −0.779733 | ||||||||
\(268\) | 1.35690 | 0.0828856 | ||||||||
\(269\) | 8.56465 | 0.522196 | 0.261098 | − | 0.965312i | \(-0.415915\pi\) | ||||
0.261098 | + | 0.965312i | \(0.415915\pi\) | |||||||
\(270\) | 0.801938 | 0.0488044 | ||||||||
\(271\) | −3.57971 | −0.217452 | −0.108726 | − | 0.994072i | \(-0.534677\pi\) | ||||
−0.108726 | + | 0.994072i | \(0.534677\pi\) | |||||||
\(272\) | −2.85086 | −0.172858 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.3817 | 1.05006 | ||||||||
\(275\) | 26.3545 | 1.58924 | ||||||||
\(276\) | 0.911854 | 0.0548872 | ||||||||
\(277\) | 12.1196 | 0.728196 | 0.364098 | − | 0.931361i | \(-0.381377\pi\) | ||||
0.364098 | + | 0.931361i | \(0.381377\pi\) | |||||||
\(278\) | 7.99330 | 0.479406 | ||||||||
\(279\) | 2.15883 | 0.129246 | ||||||||
\(280\) | −0.801938 | −0.0479249 | ||||||||
\(281\) | −28.4330 | −1.69617 | −0.848084 | − | 0.529862i | \(-0.822244\pi\) | ||||
−0.848084 | + | 0.529862i | \(0.822244\pi\) | |||||||
\(282\) | 1.27413 | 0.0758731 | ||||||||
\(283\) | −2.67994 | −0.159306 | −0.0796529 | − | 0.996823i | \(-0.525381\pi\) | ||||
−0.0796529 | + | 0.996823i | \(0.525381\pi\) | |||||||
\(284\) | −7.78017 | −0.461668 | ||||||||
\(285\) | 0.753020 | 0.0446051 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.19806 | 0.0707194 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −8.87263 | −0.521919 | ||||||||
\(290\) | −2.69202 | −0.158081 | ||||||||
\(291\) | −4.85623 | −0.284677 | ||||||||
\(292\) | −14.4547 | −0.845899 | ||||||||
\(293\) | −28.2271 | −1.64905 | −0.824523 | − | 0.565828i | \(-0.808557\pi\) | ||||
−0.824523 | + | 0.565828i | \(0.808557\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | −5.85086 | −0.340650 | ||||||||
\(296\) | −5.91185 | −0.343620 | ||||||||
\(297\) | −6.04892 | −0.350994 | ||||||||
\(298\) | −4.74333 | −0.274774 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.35690 | −0.251546 | ||||||||
\(301\) | −4.07606 | −0.234940 | ||||||||
\(302\) | 11.2687 | 0.648444 | ||||||||
\(303\) | −4.92931 | −0.283182 | ||||||||
\(304\) | 0.939001 | 0.0538554 | ||||||||
\(305\) | −0.801938 | −0.0459188 | ||||||||
\(306\) | −2.85086 | −0.162973 | ||||||||
\(307\) | 9.16959 | 0.523336 | 0.261668 | − | 0.965158i | \(-0.415727\pi\) | ||||
0.261668 | + | 0.965158i | \(0.415727\pi\) | |||||||
\(308\) | 6.04892 | 0.344669 | ||||||||
\(309\) | −0.170915 | −0.00972303 | ||||||||
\(310\) | 1.73125 | 0.0983284 | ||||||||
\(311\) | 26.2150 | 1.48652 | 0.743259 | − | 0.669003i | \(-0.233279\pi\) | ||||
0.743259 | + | 0.669003i | \(0.233279\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.1782 | 1.31011 | 0.655055 | − | 0.755581i | \(-0.272645\pi\) | ||||
0.655055 | + | 0.755581i | \(0.272645\pi\) | |||||||
\(314\) | −21.5797 | −1.21781 | ||||||||
\(315\) | −0.801938 | −0.0451841 | ||||||||
\(316\) | 0.131687 | 0.00740795 | ||||||||
\(317\) | 6.41252 | 0.360163 | 0.180081 | − | 0.983652i | \(-0.442364\pi\) | ||||
0.180081 | + | 0.983652i | \(0.442364\pi\) | |||||||
\(318\) | 6.15883 | 0.345370 | ||||||||
\(319\) | 20.3056 | 1.13689 | ||||||||
\(320\) | 0.801938 | 0.0448297 | ||||||||
\(321\) | −6.30559 | −0.351943 | ||||||||
\(322\) | −0.911854 | −0.0508156 | ||||||||
\(323\) | −2.67696 | −0.148950 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.25667 | 0.124985 | ||||||||
\(327\) | 14.1739 | 0.783818 | ||||||||
\(328\) | −1.19806 | −0.0661519 | ||||||||
\(329\) | −1.27413 | −0.0702449 | ||||||||
\(330\) | −4.85086 | −0.267031 | ||||||||
\(331\) | 31.2760 | 1.71909 | 0.859543 | − | 0.511063i | \(-0.170748\pi\) | ||||
0.859543 | + | 0.511063i | \(0.170748\pi\) | |||||||
\(332\) | −16.9148 | −0.928322 | ||||||||
\(333\) | −5.91185 | −0.323968 | ||||||||
\(334\) | −0.302602 | −0.0165576 | ||||||||
\(335\) | 1.08815 | 0.0594518 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 15.8635 | 0.864141 | 0.432071 | − | 0.901840i | \(-0.357783\pi\) | ||||
0.432071 | + | 0.901840i | \(0.357783\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.198062 | −0.0107573 | ||||||||
\(340\) | −2.28621 | −0.123987 | ||||||||
\(341\) | −13.0586 | −0.707163 | ||||||||
\(342\) | 0.939001 | 0.0507754 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 4.07606 | 0.219767 | ||||||||
\(345\) | 0.731250 | 0.0393692 | ||||||||
\(346\) | 18.6896 | 1.00476 | ||||||||
\(347\) | 19.9594 | 1.07148 | 0.535740 | − | 0.844383i | \(-0.320033\pi\) | ||||
0.535740 | + | 0.844383i | \(0.320033\pi\) | |||||||
\(348\) | −3.35690 | −0.179949 | ||||||||
\(349\) | −36.2127 | −1.93842 | −0.969209 | − | 0.246238i | \(-0.920806\pi\) | ||||
−0.969209 | + | 0.246238i | \(0.920806\pi\) | |||||||
\(350\) | 4.35690 | 0.232886 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.04892 | −0.322408 | ||||||||
\(353\) | 27.3793 | 1.45725 | 0.728625 | − | 0.684912i | \(-0.240160\pi\) | ||||
0.728625 | + | 0.684912i | \(0.240160\pi\) | |||||||
\(354\) | −7.29590 | −0.387773 | ||||||||
\(355\) | −6.23921 | −0.331143 | ||||||||
\(356\) | −12.7409 | −0.675268 | ||||||||
\(357\) | 2.85086 | 0.150883 | ||||||||
\(358\) | −22.5797 | −1.19337 | ||||||||
\(359\) | 23.2989 | 1.22967 | 0.614834 | − | 0.788657i | \(-0.289223\pi\) | ||||
0.614834 | + | 0.788657i | \(0.289223\pi\) | |||||||
\(360\) | 0.801938 | 0.0422658 | ||||||||
\(361\) | −18.1183 | −0.953594 | ||||||||
\(362\) | 6.94331 | 0.364932 | ||||||||
\(363\) | 25.5894 | 1.34310 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.5918 | −0.606742 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | 23.8780 | 1.24642 | 0.623211 | − | 0.782054i | \(-0.285828\pi\) | ||||
0.623211 | + | 0.782054i | \(0.285828\pi\) | |||||||
\(368\) | 0.911854 | 0.0475337 | ||||||||
\(369\) | −1.19806 | −0.0623686 | ||||||||
\(370\) | −4.74094 | −0.246470 | ||||||||
\(371\) | −6.15883 | −0.319751 | ||||||||
\(372\) | 2.15883 | 0.111930 | ||||||||
\(373\) | −20.0271 | −1.03697 | −0.518483 | − | 0.855088i | \(-0.673503\pi\) | ||||
−0.518483 | + | 0.855088i | \(0.673503\pi\) | |||||||
\(374\) | 17.2446 | 0.891696 | ||||||||
\(375\) | −7.50365 | −0.387487 | ||||||||
\(376\) | 1.27413 | 0.0657081 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −0.295897 | −0.0151992 | −0.00759960 | − | 0.999971i | \(-0.502419\pi\) | ||||
−0.00759960 | + | 0.999971i | \(0.502419\pi\) | |||||||
\(380\) | 0.753020 | 0.0386291 | ||||||||
\(381\) | −17.0465 | −0.873320 | ||||||||
\(382\) | 0.728857 | 0.0372916 | ||||||||
\(383\) | −22.2282 | −1.13581 | −0.567904 | − | 0.823095i | \(-0.692245\pi\) | ||||
−0.567904 | + | 0.823095i | \(0.692245\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 4.85086 | 0.247222 | ||||||||
\(386\) | −14.0411 | −0.714676 | ||||||||
\(387\) | 4.07606 | 0.207198 | ||||||||
\(388\) | −4.85623 | −0.246538 | ||||||||
\(389\) | 31.5840 | 1.60137 | 0.800687 | − | 0.599083i | \(-0.204468\pi\) | ||||
0.800687 | + | 0.599083i | \(0.204468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.59956 | −0.131466 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −3.02715 | −0.152699 | ||||||||
\(394\) | −7.94139 | −0.400082 | ||||||||
\(395\) | 0.105604 | 0.00531353 | ||||||||
\(396\) | −6.04892 | −0.303970 | ||||||||
\(397\) | 11.6267 | 0.583528 | 0.291764 | − | 0.956490i | \(-0.405758\pi\) | ||||
0.291764 | + | 0.956490i | \(0.405758\pi\) | |||||||
\(398\) | 8.00538 | 0.401273 | ||||||||
\(399\) | −0.939001 | −0.0470089 | ||||||||
\(400\) | −4.35690 | −0.217845 | ||||||||
\(401\) | −6.49827 | −0.324508 | −0.162254 | − | 0.986749i | \(-0.551876\pi\) | ||||
−0.162254 | + | 0.986749i | \(0.551876\pi\) | |||||||
\(402\) | 1.35690 | 0.0676758 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4.92931 | −0.245242 | ||||||||
\(405\) | 0.801938 | 0.0398486 | ||||||||
\(406\) | 3.35690 | 0.166600 | ||||||||
\(407\) | 35.7603 | 1.77257 | ||||||||
\(408\) | −2.85086 | −0.141138 | ||||||||
\(409\) | −35.8122 | −1.77080 | −0.885400 | − | 0.464830i | \(-0.846116\pi\) | ||||
−0.885400 | + | 0.464830i | \(0.846116\pi\) | |||||||
\(410\) | −0.960771 | −0.0474491 | ||||||||
\(411\) | 17.3817 | 0.857374 | ||||||||
\(412\) | −0.170915 | −0.00842039 | ||||||||
\(413\) | 7.29590 | 0.359008 | ||||||||
\(414\) | 0.911854 | 0.0448152 | ||||||||
\(415\) | −13.5646 | −0.665862 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.99330 | 0.391433 | ||||||||
\(418\) | −5.67994 | −0.277815 | ||||||||
\(419\) | −1.96376 | −0.0959357 | −0.0479679 | − | 0.998849i | \(-0.515275\pi\) | ||||
−0.0479679 | + | 0.998849i | \(0.515275\pi\) | |||||||
\(420\) | −0.801938 | −0.0391306 | ||||||||
\(421\) | 8.76271 | 0.427068 | 0.213534 | − | 0.976936i | \(-0.431503\pi\) | ||||
0.213534 | + | 0.976936i | \(0.431503\pi\) | |||||||
\(422\) | −16.2892 | −0.792945 | ||||||||
\(423\) | 1.27413 | 0.0619502 | ||||||||
\(424\) | 6.15883 | 0.299099 | ||||||||
\(425\) | 12.4209 | 0.602501 | ||||||||
\(426\) | −7.78017 | −0.376950 | ||||||||
\(427\) | 1.00000 | 0.0483934 | ||||||||
\(428\) | −6.30559 | −0.304792 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.26875 | 0.157633 | ||||||||
\(431\) | 33.5023 | 1.61375 | 0.806875 | − | 0.590722i | \(-0.201157\pi\) | ||||
0.806875 | + | 0.590722i | \(0.201157\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −0.928247 | −0.0446087 | −0.0223044 | − | 0.999751i | \(-0.507100\pi\) | ||||
−0.0223044 | + | 0.999751i | \(0.507100\pi\) | |||||||
\(434\) | −2.15883 | −0.103627 | ||||||||
\(435\) | −2.69202 | −0.129073 | ||||||||
\(436\) | 14.1739 | 0.678807 | ||||||||
\(437\) | 0.856232 | 0.0409591 | ||||||||
\(438\) | −14.4547 | −0.690674 | ||||||||
\(439\) | −2.32736 | −0.111079 | −0.0555393 | − | 0.998457i | \(-0.517688\pi\) | ||||
−0.0555393 | + | 0.998457i | \(0.517688\pi\) | |||||||
\(440\) | −4.85086 | −0.231255 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.8984 | −0.897892 | −0.448946 | − | 0.893559i | \(-0.648200\pi\) | ||||
−0.448946 | + | 0.893559i | \(0.648200\pi\) | |||||||
\(444\) | −5.91185 | −0.280564 | ||||||||
\(445\) | −10.2174 | −0.484353 | ||||||||
\(446\) | 17.6256 | 0.834599 | ||||||||
\(447\) | −4.74333 | −0.224352 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −2.64012 | −0.124595 | −0.0622975 | − | 0.998058i | \(-0.519843\pi\) | ||||
−0.0622975 | + | 0.998058i | \(0.519843\pi\) | |||||||
\(450\) | −4.35690 | −0.205386 | ||||||||
\(451\) | 7.24698 | 0.341247 | ||||||||
\(452\) | −0.198062 | −0.00931607 | ||||||||
\(453\) | 11.2687 | 0.529452 | ||||||||
\(454\) | −11.1914 | −0.525236 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.939001 | 0.0439728 | ||||||||
\(457\) | 1.25368 | 0.0586449 | 0.0293224 | − | 0.999570i | \(-0.490665\pi\) | ||||
0.0293224 | + | 0.999570i | \(0.490665\pi\) | |||||||
\(458\) | 25.4131 | 1.18748 | ||||||||
\(459\) | −2.85086 | −0.133067 | ||||||||
\(460\) | 0.731250 | 0.0340947 | ||||||||
\(461\) | 22.4198 | 1.04419 | 0.522097 | − | 0.852886i | \(-0.325150\pi\) | ||||
0.522097 | + | 0.852886i | \(0.325150\pi\) | |||||||
\(462\) | 6.04892 | 0.281421 | ||||||||
\(463\) | −8.94975 | −0.415930 | −0.207965 | − | 0.978136i | \(-0.566684\pi\) | ||||
−0.207965 | + | 0.978136i | \(0.566684\pi\) | |||||||
\(464\) | −3.35690 | −0.155840 | ||||||||
\(465\) | 1.73125 | 0.0802848 | ||||||||
\(466\) | −4.20237 | −0.194671 | ||||||||
\(467\) | 9.62996 | 0.445621 | 0.222811 | − | 0.974862i | \(-0.428477\pi\) | ||||
0.222811 | + | 0.974862i | \(0.428477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.35690 | −0.0626556 | ||||||||
\(470\) | 1.02177 | 0.0471307 | ||||||||
\(471\) | −21.5797 | −0.994341 | ||||||||
\(472\) | −7.29590 | −0.335821 | ||||||||
\(473\) | −24.6558 | −1.13367 | ||||||||
\(474\) | 0.131687 | 0.00604856 | ||||||||
\(475\) | −4.09113 | −0.187714 | ||||||||
\(476\) | 2.85086 | 0.130669 | ||||||||
\(477\) | 6.15883 | 0.281994 | ||||||||
\(478\) | −20.3177 | −0.929308 | ||||||||
\(479\) | 16.0586 | 0.733736 | 0.366868 | − | 0.930273i | \(-0.380430\pi\) | ||||
0.366868 | + | 0.930273i | \(0.380430\pi\) | |||||||
\(480\) | 0.801938 | 0.0366033 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −15.9433 | −0.726198 | ||||||||
\(483\) | −0.911854 | −0.0414908 | ||||||||
\(484\) | 25.5894 | 1.16315 | ||||||||
\(485\) | −3.89440 | −0.176835 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −30.4295 | −1.37889 | −0.689446 | − | 0.724337i | \(-0.742146\pi\) | ||||
−0.689446 | + | 0.724337i | \(0.742146\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | 2.25667 | 0.102050 | ||||||||
\(490\) | 0.801938 | 0.0362279 | ||||||||
\(491\) | −22.4413 | −1.01276 | −0.506381 | − | 0.862310i | \(-0.669017\pi\) | ||||
−0.506381 | + | 0.862310i | \(0.669017\pi\) | |||||||
\(492\) | −1.19806 | −0.0540128 | ||||||||
\(493\) | 9.57002 | 0.431012 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.85086 | −0.218030 | ||||||||
\(496\) | 2.15883 | 0.0969345 | ||||||||
\(497\) | 7.78017 | 0.348988 | ||||||||
\(498\) | −16.9148 | −0.757972 | ||||||||
\(499\) | 37.9909 | 1.70071 | 0.850353 | − | 0.526212i | \(-0.176388\pi\) | ||||
0.850353 | + | 0.526212i | \(0.176388\pi\) | |||||||
\(500\) | −7.50365 | −0.335573 | ||||||||
\(501\) | −0.302602 | −0.0135192 | ||||||||
\(502\) | 27.3207 | 1.21938 | ||||||||
\(503\) | 26.6950 | 1.19027 | 0.595136 | − | 0.803625i | \(-0.297098\pi\) | ||||
0.595136 | + | 0.803625i | \(0.297098\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −3.95300 | −0.175906 | ||||||||
\(506\) | −5.51573 | −0.245204 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.0465 | −0.756317 | ||||||||
\(509\) | −42.2693 | −1.87356 | −0.936778 | − | 0.349925i | \(-0.886207\pi\) | ||||
−0.936778 | + | 0.349925i | \(0.886207\pi\) | |||||||
\(510\) | −2.28621 | −0.101235 | ||||||||
\(511\) | 14.4547 | 0.639440 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.939001 | 0.0414579 | ||||||||
\(514\) | 25.2446 | 1.11349 | ||||||||
\(515\) | −0.137063 | −0.00603973 | ||||||||
\(516\) | 4.07606 | 0.179439 | ||||||||
\(517\) | −7.70709 | −0.338957 | ||||||||
\(518\) | 5.91185 | 0.259752 | ||||||||
\(519\) | 18.6896 | 0.820384 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.2760 | −0.537823 | −0.268912 | − | 0.963165i | \(-0.586664\pi\) | ||||
−0.268912 | + | 0.963165i | \(0.586664\pi\) | |||||||
\(522\) | −3.35690 | −0.146927 | ||||||||
\(523\) | −2.23921 | −0.0979138 | −0.0489569 | − | 0.998801i | \(-0.515590\pi\) | ||||
−0.0489569 | + | 0.998801i | \(0.515590\pi\) | |||||||
\(524\) | −3.02715 | −0.132242 | ||||||||
\(525\) | 4.35690 | 0.190151 | ||||||||
\(526\) | 11.8509 | 0.516722 | ||||||||
\(527\) | −6.15452 | −0.268095 | ||||||||
\(528\) | −6.04892 | −0.263245 | ||||||||
\(529\) | −22.1685 | −0.963849 | ||||||||
\(530\) | 4.93900 | 0.214536 | ||||||||
\(531\) | −7.29590 | −0.316615 | ||||||||
\(532\) | −0.939001 | −0.0407109 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −12.7409 | −0.551354 | ||||||||
\(535\) | −5.05669 | −0.218620 | ||||||||
\(536\) | 1.35690 | 0.0586090 | ||||||||
\(537\) | −22.5797 | −0.974387 | ||||||||
\(538\) | 8.56465 | 0.369248 | ||||||||
\(539\) | −6.04892 | −0.260545 | ||||||||
\(540\) | 0.801938 | 0.0345099 | ||||||||
\(541\) | −10.0519 | −0.432165 | −0.216082 | − | 0.976375i | \(-0.569328\pi\) | ||||
−0.216082 | + | 0.976375i | \(0.569328\pi\) | |||||||
\(542\) | −3.57971 | −0.153762 | ||||||||
\(543\) | 6.94331 | 0.297966 | ||||||||
\(544\) | −2.85086 | −0.122229 | ||||||||
\(545\) | 11.3666 | 0.486891 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.8745 | 1.79043 | 0.895213 | − | 0.445638i | \(-0.147023\pi\) | ||||
0.895213 | + | 0.445638i | \(0.147023\pi\) | |||||||
\(548\) | 17.3817 | 0.742507 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 26.3545 | 1.12376 | ||||||||
\(551\) | −3.15213 | −0.134285 | ||||||||
\(552\) | 0.911854 | 0.0388111 | ||||||||
\(553\) | −0.131687 | −0.00559988 | ||||||||
\(554\) | 12.1196 | 0.514913 | ||||||||
\(555\) | −4.74094 | −0.201242 | ||||||||
\(556\) | 7.99330 | 0.338991 | ||||||||
\(557\) | 34.0847 | 1.44421 | 0.722107 | − | 0.691781i | \(-0.243174\pi\) | ||||
0.722107 | + | 0.691781i | \(0.243174\pi\) | |||||||
\(558\) | 2.15883 | 0.0913907 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.801938 | −0.0338881 | ||||||||
\(561\) | 17.2446 | 0.728067 | ||||||||
\(562\) | −28.4330 | −1.19937 | ||||||||
\(563\) | −7.10513 | −0.299446 | −0.149723 | − | 0.988728i | \(-0.547838\pi\) | ||||
−0.149723 | + | 0.988728i | \(0.547838\pi\) | |||||||
\(564\) | 1.27413 | 0.0536504 | ||||||||
\(565\) | −0.158834 | −0.00668218 | ||||||||
\(566\) | −2.67994 | −0.112646 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −7.78017 | −0.326449 | ||||||||
\(569\) | −17.2959 | −0.725082 | −0.362541 | − | 0.931968i | \(-0.618091\pi\) | ||||
−0.362541 | + | 0.931968i | \(0.618091\pi\) | |||||||
\(570\) | 0.753020 | 0.0315406 | ||||||||
\(571\) | −1.25800 | −0.0526455 | −0.0263228 | − | 0.999653i | \(-0.508380\pi\) | ||||
−0.0263228 | + | 0.999653i | \(0.508380\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.728857 | 0.0304484 | ||||||||
\(574\) | 1.19806 | 0.0500062 | ||||||||
\(575\) | −3.97285 | −0.165679 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 35.1062 | 1.46149 | 0.730745 | − | 0.682651i | \(-0.239173\pi\) | ||||
0.730745 | + | 0.682651i | \(0.239173\pi\) | |||||||
\(578\) | −8.87263 | −0.369053 | ||||||||
\(579\) | −14.0411 | −0.583530 | ||||||||
\(580\) | −2.69202 | −0.111780 | ||||||||
\(581\) | 16.9148 | 0.701746 | ||||||||
\(582\) | −4.85623 | −0.201297 | ||||||||
\(583\) | −37.2543 | −1.54291 | ||||||||
\(584\) | −14.4547 | −0.598141 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.2271 | −1.16605 | ||||||||
\(587\) | −10.0532 | −0.414941 | −0.207471 | − | 0.978241i | \(-0.566523\pi\) | ||||
−0.207471 | + | 0.978241i | \(0.566523\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | 2.02715 | 0.0835271 | ||||||||
\(590\) | −5.85086 | −0.240876 | ||||||||
\(591\) | −7.94139 | −0.326665 | ||||||||
\(592\) | −5.91185 | −0.242976 | ||||||||
\(593\) | −23.2808 | −0.956029 | −0.478015 | − | 0.878352i | \(-0.658643\pi\) | ||||
−0.478015 | + | 0.878352i | \(0.658643\pi\) | |||||||
\(594\) | −6.04892 | −0.248190 | ||||||||
\(595\) | 2.28621 | 0.0937254 | ||||||||
\(596\) | −4.74333 | −0.194294 | ||||||||
\(597\) | 8.00538 | 0.327638 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0285 | −0.491470 | −0.245735 | − | 0.969337i | \(-0.579029\pi\) | ||||
−0.245735 | + | 0.969337i | \(0.579029\pi\) | |||||||
\(600\) | −4.35690 | −0.177870 | ||||||||
\(601\) | 8.67935 | 0.354038 | 0.177019 | − | 0.984207i | \(-0.443355\pi\) | ||||
0.177019 | + | 0.984207i | \(0.443355\pi\) | |||||||
\(602\) | −4.07606 | −0.166128 | ||||||||
\(603\) | 1.35690 | 0.0552571 | ||||||||
\(604\) | 11.2687 | 0.458519 | ||||||||
\(605\) | 20.5211 | 0.834302 | ||||||||
\(606\) | −4.92931 | −0.200240 | ||||||||
\(607\) | 38.6862 | 1.57022 | 0.785112 | − | 0.619354i | \(-0.212606\pi\) | ||||
0.785112 | + | 0.619354i | \(0.212606\pi\) | |||||||
\(608\) | 0.939001 | 0.0380815 | ||||||||
\(609\) | 3.35690 | 0.136028 | ||||||||
\(610\) | −0.801938 | −0.0324695 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.85086 | −0.115239 | ||||||||
\(613\) | −28.6601 | −1.15757 | −0.578785 | − | 0.815480i | \(-0.696473\pi\) | ||||
−0.578785 | + | 0.815480i | \(0.696473\pi\) | |||||||
\(614\) | 9.16959 | 0.370054 | ||||||||
\(615\) | −0.960771 | −0.0387420 | ||||||||
\(616\) | 6.04892 | 0.243718 | ||||||||
\(617\) | −37.8756 | −1.52481 | −0.762407 | − | 0.647097i | \(-0.775983\pi\) | ||||
−0.762407 | + | 0.647097i | \(0.775983\pi\) | |||||||
\(618\) | −0.170915 | −0.00687522 | ||||||||
\(619\) | −11.6256 | −0.467274 | −0.233637 | − | 0.972324i | \(-0.575063\pi\) | ||||
−0.233637 | + | 0.972324i | \(0.575063\pi\) | |||||||
\(620\) | 1.73125 | 0.0695287 | ||||||||
\(621\) | 0.911854 | 0.0365914 | ||||||||
\(622\) | 26.2150 | 1.05113 | ||||||||
\(623\) | 12.7409 | 0.510455 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.7670 | 0.630681 | ||||||||
\(626\) | 23.1782 | 0.926388 | ||||||||
\(627\) | −5.67994 | −0.226835 | ||||||||
\(628\) | −21.5797 | −0.861124 | ||||||||
\(629\) | 16.8538 | 0.672007 | ||||||||
\(630\) | −0.801938 | −0.0319500 | ||||||||
\(631\) | 38.0853 | 1.51615 | 0.758076 | − | 0.652167i | \(-0.226140\pi\) | ||||
0.758076 | + | 0.652167i | \(0.226140\pi\) | |||||||
\(632\) | 0.131687 | 0.00523821 | ||||||||
\(633\) | −16.2892 | −0.647437 | ||||||||
\(634\) | 6.41252 | 0.254674 | ||||||||
\(635\) | −13.6703 | −0.542487 | ||||||||
\(636\) | 6.15883 | 0.244214 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.3056 | 0.803906 | ||||||||
\(639\) | −7.78017 | −0.307779 | ||||||||
\(640\) | 0.801938 | 0.0316994 | ||||||||
\(641\) | −42.6359 | −1.68402 | −0.842009 | − | 0.539464i | \(-0.818627\pi\) | ||||
−0.842009 | + | 0.539464i | \(0.818627\pi\) | |||||||
\(642\) | −6.30559 | −0.248862 | ||||||||
\(643\) | 8.86161 | 0.349468 | 0.174734 | − | 0.984616i | \(-0.444093\pi\) | ||||
0.174734 | + | 0.984616i | \(0.444093\pi\) | |||||||
\(644\) | −0.911854 | −0.0359321 | ||||||||
\(645\) | 3.26875 | 0.128707 | ||||||||
\(646\) | −2.67696 | −0.105323 | ||||||||
\(647\) | 6.01102 | 0.236317 | 0.118159 | − | 0.992995i | \(-0.462301\pi\) | ||||
0.118159 | + | 0.992995i | \(0.462301\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 44.1323 | 1.73234 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.15883 | −0.0846114 | ||||||||
\(652\) | 2.25667 | 0.0883780 | ||||||||
\(653\) | −41.9221 | −1.64054 | −0.820270 | − | 0.571977i | \(-0.806177\pi\) | ||||
−0.820270 | + | 0.571977i | \(0.806177\pi\) | |||||||
\(654\) | 14.1739 | 0.554243 | ||||||||
\(655\) | −2.42758 | −0.0948535 | ||||||||
\(656\) | −1.19806 | −0.0467765 | ||||||||
\(657\) | −14.4547 | −0.563933 | ||||||||
\(658\) | −1.27413 | −0.0496706 | ||||||||
\(659\) | 18.1957 | 0.708803 | 0.354401 | − | 0.935093i | \(-0.384685\pi\) | ||||
0.354401 | + | 0.935093i | \(0.384685\pi\) | |||||||
\(660\) | −4.85086 | −0.188819 | ||||||||
\(661\) | −28.6980 | −1.11622 | −0.558111 | − | 0.829766i | \(-0.688474\pi\) | ||||
−0.558111 | + | 0.829766i | \(0.688474\pi\) | |||||||
\(662\) | 31.2760 | 1.21558 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.9148 | −0.656423 | ||||||||
\(665\) | −0.753020 | −0.0292009 | ||||||||
\(666\) | −5.91185 | −0.229080 | ||||||||
\(667\) | −3.06100 | −0.118522 | ||||||||
\(668\) | −0.302602 | −0.0117080 | ||||||||
\(669\) | 17.6256 | 0.681447 | ||||||||
\(670\) | 1.08815 | 0.0420387 | ||||||||
\(671\) | 6.04892 | 0.233516 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −36.2301 | −1.39657 | −0.698284 | − | 0.715821i | \(-0.746053\pi\) | ||||
−0.698284 | + | 0.715821i | \(0.746053\pi\) | |||||||
\(674\) | 15.8635 | 0.611040 | ||||||||
\(675\) | −4.35690 | −0.167697 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.3045 | −1.04940 | −0.524699 | − | 0.851288i | \(-0.675822\pi\) | ||||
−0.524699 | + | 0.851288i | \(0.675822\pi\) | |||||||
\(678\) | −0.198062 | −0.00760654 | ||||||||
\(679\) | 4.85623 | 0.186365 | ||||||||
\(680\) | −2.28621 | −0.0876721 | ||||||||
\(681\) | −11.1914 | −0.428854 | ||||||||
\(682\) | −13.0586 | −0.500040 | ||||||||
\(683\) | −0.800610 | −0.0306345 | −0.0153172 | − | 0.999883i | \(-0.504876\pi\) | ||||
−0.0153172 | + | 0.999883i | \(0.504876\pi\) | |||||||
\(684\) | 0.939001 | 0.0359036 | ||||||||
\(685\) | 13.9390 | 0.532582 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 25.4131 | 0.969571 | ||||||||
\(688\) | 4.07606 | 0.155398 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.731250 | 0.0278382 | ||||||||
\(691\) | 26.7168 | 1.01635 | 0.508177 | − | 0.861253i | \(-0.330320\pi\) | ||||
0.508177 | + | 0.861253i | \(0.330320\pi\) | |||||||
\(692\) | 18.6896 | 0.710473 | ||||||||
\(693\) | 6.04892 | 0.229779 | ||||||||
\(694\) | 19.9594 | 0.757650 | ||||||||
\(695\) | 6.41013 | 0.243150 | ||||||||
\(696\) | −3.35690 | −0.127243 | ||||||||
\(697\) | 3.41550 | 0.129371 | ||||||||
\(698\) | −36.2127 | −1.37067 | ||||||||
\(699\) | −4.20237 | −0.158948 | ||||||||
\(700\) | 4.35690 | 0.164675 | ||||||||
\(701\) | −11.8062 | −0.445916 | −0.222958 | − | 0.974828i | \(-0.571571\pi\) | ||||
−0.222958 | + | 0.974828i | \(0.571571\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.55124 | −0.209369 | ||||||||
\(704\) | −6.04892 | −0.227977 | ||||||||
\(705\) | 1.02177 | 0.0384821 | ||||||||
\(706\) | 27.3793 | 1.03043 | ||||||||
\(707\) | 4.92931 | 0.185386 | ||||||||
\(708\) | −7.29590 | −0.274197 | ||||||||
\(709\) | −34.9734 | −1.31346 | −0.656728 | − | 0.754128i | \(-0.728060\pi\) | ||||
−0.656728 | + | 0.754128i | \(0.728060\pi\) | |||||||
\(710\) | −6.23921 | −0.234153 | ||||||||
\(711\) | 0.131687 | 0.00493863 | ||||||||
\(712\) | −12.7409 | −0.477487 | ||||||||
\(713\) | 1.96854 | 0.0737224 | ||||||||
\(714\) | 2.85086 | 0.106691 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.5797 | −0.843843 | ||||||||
\(717\) | −20.3177 | −0.758777 | ||||||||
\(718\) | 23.2989 | 0.869507 | ||||||||
\(719\) | −19.6310 | −0.732114 | −0.366057 | − | 0.930593i | \(-0.619292\pi\) | ||||
−0.366057 | + | 0.930593i | \(0.619292\pi\) | |||||||
\(720\) | 0.801938 | 0.0298865 | ||||||||
\(721\) | 0.170915 | 0.00636521 | ||||||||
\(722\) | −18.1183 | −0.674292 | ||||||||
\(723\) | −15.9433 | −0.592938 | ||||||||
\(724\) | 6.94331 | 0.258046 | ||||||||
\(725\) | 14.6256 | 0.543183 | ||||||||
\(726\) | 25.5894 | 0.949712 | ||||||||
\(727\) | −24.4523 | −0.906887 | −0.453444 | − | 0.891285i | \(-0.649805\pi\) | ||||
−0.453444 | + | 0.891285i | \(0.649805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −11.5918 | −0.429032 | ||||||||
\(731\) | −11.6203 | −0.429791 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | 38.0441 | 1.40519 | 0.702596 | − | 0.711589i | \(-0.252024\pi\) | ||||
0.702596 | + | 0.711589i | \(0.252024\pi\) | |||||||
\(734\) | 23.8780 | 0.881353 | ||||||||
\(735\) | 0.801938 | 0.0295799 | ||||||||
\(736\) | 0.911854 | 0.0336114 | ||||||||
\(737\) | −8.20775 | −0.302336 | ||||||||
\(738\) | −1.19806 | −0.0441013 | ||||||||
\(739\) | 23.3045 | 0.857271 | 0.428635 | − | 0.903478i | \(-0.358995\pi\) | ||||
0.428635 | + | 0.903478i | \(0.358995\pi\) | |||||||
\(740\) | −4.74094 | −0.174280 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.15883 | −0.226098 | ||||||||
\(743\) | −20.5714 | −0.754690 | −0.377345 | − | 0.926073i | \(-0.623163\pi\) | ||||
−0.377345 | + | 0.926073i | \(0.623163\pi\) | |||||||
\(744\) | 2.15883 | 0.0791467 | ||||||||
\(745\) | −3.80386 | −0.139363 | ||||||||
\(746\) | −20.0271 | −0.733246 | ||||||||
\(747\) | −16.9148 | −0.618882 | ||||||||
\(748\) | 17.2446 | 0.630525 | ||||||||
\(749\) | 6.30559 | 0.230401 | ||||||||
\(750\) | −7.50365 | −0.273994 | ||||||||
\(751\) | −8.68366 | −0.316871 | −0.158436 | − | 0.987369i | \(-0.550645\pi\) | ||||
−0.158436 | + | 0.987369i | \(0.550645\pi\) | |||||||
\(752\) | 1.27413 | 0.0464626 | ||||||||
\(753\) | 27.3207 | 0.995620 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.03684 | 0.328884 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 32.4969 | 1.18112 | 0.590561 | − | 0.806993i | \(-0.298907\pi\) | ||||
0.590561 | + | 0.806993i | \(0.298907\pi\) | |||||||
\(758\) | −0.295897 | −0.0107475 | ||||||||
\(759\) | −5.51573 | −0.200208 | ||||||||
\(760\) | 0.753020 | 0.0273149 | ||||||||
\(761\) | 12.6243 | 0.457631 | 0.228816 | − | 0.973470i | \(-0.426515\pi\) | ||||
0.228816 | + | 0.973470i | \(0.426515\pi\) | |||||||
\(762\) | −17.0465 | −0.617530 | ||||||||
\(763\) | −14.1739 | −0.513130 | ||||||||
\(764\) | 0.728857 | 0.0263691 | ||||||||
\(765\) | −2.28621 | −0.0826580 | ||||||||
\(766\) | −22.2282 | −0.803137 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 15.0271 | 0.541893 | 0.270946 | − | 0.962594i | \(-0.412663\pi\) | ||||
0.270946 | + | 0.962594i | \(0.412663\pi\) | |||||||
\(770\) | 4.85086 | 0.174813 | ||||||||
\(771\) | 25.2446 | 0.909162 | ||||||||
\(772\) | −14.0411 | −0.505352 | ||||||||
\(773\) | −44.7096 | −1.60809 | −0.804046 | − | 0.594567i | \(-0.797324\pi\) | ||||
−0.804046 | + | 0.594567i | \(0.797324\pi\) | |||||||
\(774\) | 4.07606 | 0.146511 | ||||||||
\(775\) | −9.40581 | −0.337867 | ||||||||
\(776\) | −4.85623 | −0.174329 | ||||||||
\(777\) | 5.91185 | 0.212087 | ||||||||
\(778\) | 31.5840 | 1.13234 | ||||||||
\(779\) | −1.12498 | −0.0403067 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.0616 | 1.68400 | ||||||||
\(782\) | −2.59956 | −0.0929602 | ||||||||
\(783\) | −3.35690 | −0.119966 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −17.3056 | −0.617663 | ||||||||
\(786\) | −3.02715 | −0.107975 | ||||||||
\(787\) | 33.0140 | 1.17682 | 0.588411 | − | 0.808562i | \(-0.299754\pi\) | ||||
0.588411 | + | 0.808562i | \(0.299754\pi\) | |||||||
\(788\) | −7.94139 | −0.282900 | ||||||||
\(789\) | 11.8509 | 0.421902 | ||||||||
\(790\) | 0.105604 | 0.00375724 | ||||||||
\(791\) | 0.198062 | 0.00704228 | ||||||||
\(792\) | −6.04892 | −0.214939 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11.6267 | 0.412617 | ||||||||
\(795\) | 4.93900 | 0.175168 | ||||||||
\(796\) | 8.00538 | 0.283743 | ||||||||
\(797\) | −32.4644 | −1.14995 | −0.574974 | − | 0.818171i | \(-0.694988\pi\) | ||||
−0.574974 | + | 0.818171i | \(0.694988\pi\) | |||||||
\(798\) | −0.939001 | −0.0332403 | ||||||||
\(799\) | −3.63235 | −0.128503 | ||||||||
\(800\) | −4.35690 | −0.154040 | ||||||||
\(801\) | −12.7409 | −0.450179 | ||||||||
\(802\) | −6.49827 | −0.229462 | ||||||||
\(803\) | 87.4355 | 3.08553 | ||||||||
\(804\) | 1.35690 | 0.0478540 | ||||||||
\(805\) | −0.731250 | −0.0257732 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.56465 | 0.301490 | ||||||||
\(808\) | −4.92931 | −0.173413 | ||||||||
\(809\) | 33.2597 | 1.16935 | 0.584674 | − | 0.811269i | \(-0.301223\pi\) | ||||
0.584674 | + | 0.811269i | \(0.301223\pi\) | |||||||
\(810\) | 0.801938 | 0.0281772 | ||||||||
\(811\) | 0.508434 | 0.0178535 | 0.00892676 | − | 0.999960i | \(-0.497158\pi\) | ||||
0.00892676 | + | 0.999960i | \(0.497158\pi\) | |||||||
\(812\) | 3.35690 | 0.117804 | ||||||||
\(813\) | −3.57971 | −0.125546 | ||||||||
\(814\) | 35.7603 | 1.25340 | ||||||||
\(815\) | 1.80971 | 0.0633913 | ||||||||
\(816\) | −2.85086 | −0.0997999 | ||||||||
\(817\) | 3.82743 | 0.133905 | ||||||||
\(818\) | −35.8122 | −1.25214 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.960771 | −0.0335516 | ||||||||
\(821\) | 24.8713 | 0.868014 | 0.434007 | − | 0.900909i | \(-0.357099\pi\) | ||||
0.434007 | + | 0.900909i | \(0.357099\pi\) | |||||||
\(822\) | 17.3817 | 0.606255 | ||||||||
\(823\) | −43.8001 | −1.52678 | −0.763388 | − | 0.645940i | \(-0.776466\pi\) | ||||
−0.763388 | + | 0.645940i | \(0.776466\pi\) | |||||||
\(824\) | −0.170915 | −0.00595411 | ||||||||
\(825\) | 26.3545 | 0.917546 | ||||||||
\(826\) | 7.29590 | 0.253857 | ||||||||
\(827\) | −36.3900 | −1.26540 | −0.632702 | − | 0.774395i | \(-0.718054\pi\) | ||||
−0.632702 | + | 0.774395i | \(0.718054\pi\) | |||||||
\(828\) | 0.911854 | 0.0316891 | ||||||||
\(829\) | −29.1976 | −1.01407 | −0.507037 | − | 0.861924i | \(-0.669259\pi\) | ||||
−0.507037 | + | 0.861924i | \(0.669259\pi\) | |||||||
\(830\) | −13.5646 | −0.470836 | ||||||||
\(831\) | 12.1196 | 0.420424 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.85086 | −0.0987763 | ||||||||
\(834\) | 7.99330 | 0.276785 | ||||||||
\(835\) | −0.242668 | −0.00839786 | ||||||||
\(836\) | −5.67994 | −0.196445 | ||||||||
\(837\) | 2.15883 | 0.0746202 | ||||||||
\(838\) | −1.96376 | −0.0678368 | ||||||||
\(839\) | 13.2446 | 0.457254 | 0.228627 | − | 0.973514i | \(-0.426576\pi\) | ||||
0.228627 | + | 0.973514i | \(0.426576\pi\) | |||||||
\(840\) | −0.801938 | −0.0276695 | ||||||||
\(841\) | −17.7313 | −0.611422 | ||||||||
\(842\) | 8.76271 | 0.301983 | ||||||||
\(843\) | −28.4330 | −0.979283 | ||||||||
\(844\) | −16.2892 | −0.560697 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.27413 | 0.0438054 | ||||||||
\(847\) | −25.5894 | −0.879262 | ||||||||
\(848\) | 6.15883 | 0.211495 | ||||||||
\(849\) | −2.67994 | −0.0919753 | ||||||||
\(850\) | 12.4209 | 0.426033 | ||||||||
\(851\) | −5.39075 | −0.184792 | ||||||||
\(852\) | −7.78017 | −0.266544 | ||||||||
\(853\) | 56.7047 | 1.94153 | 0.970766 | − | 0.240028i | \(-0.0771568\pi\) | ||||
0.970766 | + | 0.240028i | \(0.0771568\pi\) | |||||||
\(854\) | 1.00000 | 0.0342193 | ||||||||
\(855\) | 0.753020 | 0.0257528 | ||||||||
\(856\) | −6.30559 | −0.215520 | ||||||||
\(857\) | 21.0737 | 0.719863 | 0.359931 | − | 0.932979i | \(-0.382800\pi\) | ||||
0.359931 | + | 0.932979i | \(0.382800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4494 | 0.561245 | 0.280622 | − | 0.959818i | \(-0.409459\pi\) | ||||
0.280622 | + | 0.959818i | \(0.409459\pi\) | |||||||
\(860\) | 3.26875 | 0.111463 | ||||||||
\(861\) | 1.19806 | 0.0408299 | ||||||||
\(862\) | 33.5023 | 1.14109 | ||||||||
\(863\) | −46.0743 | −1.56839 | −0.784193 | − | 0.620517i | \(-0.786923\pi\) | ||||
−0.784193 | + | 0.620517i | \(0.786923\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 14.9879 | 0.509605 | ||||||||
\(866\) | −0.928247 | −0.0315431 | ||||||||
\(867\) | −8.87263 | −0.301330 | ||||||||
\(868\) | −2.15883 | −0.0732756 | ||||||||
\(869\) | −0.796561 | −0.0270215 | ||||||||
\(870\) | −2.69202 | −0.0912681 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 14.1739 | 0.479989 | ||||||||
\(873\) | −4.85623 | −0.164359 | ||||||||
\(874\) | 0.856232 | 0.0289625 | ||||||||
\(875\) | 7.50365 | 0.253670 | ||||||||
\(876\) | −14.4547 | −0.488380 | ||||||||
\(877\) | 9.46548 | 0.319627 | 0.159813 | − | 0.987147i | \(-0.448911\pi\) | ||||
0.159813 | + | 0.987147i | \(0.448911\pi\) | |||||||
\(878\) | −2.32736 | −0.0785445 | ||||||||
\(879\) | −28.2271 | −0.952077 | ||||||||
\(880\) | −4.85086 | −0.163522 | ||||||||
\(881\) | −20.3840 | −0.686756 | −0.343378 | − | 0.939197i | \(-0.611571\pi\) | ||||
−0.343378 | + | 0.939197i | \(0.611571\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −28.4446 | −0.957236 | −0.478618 | − | 0.878023i | \(-0.658862\pi\) | ||||
−0.478618 | + | 0.878023i | \(0.658862\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.85086 | −0.196674 | ||||||||
\(886\) | −18.8984 | −0.634906 | ||||||||
\(887\) | −30.2881 | −1.01698 | −0.508488 | − | 0.861069i | \(-0.669795\pi\) | ||||
−0.508488 | + | 0.861069i | \(0.669795\pi\) | |||||||
\(888\) | −5.91185 | −0.198389 | ||||||||
\(889\) | 17.0465 | 0.571722 | ||||||||
\(890\) | −10.2174 | −0.342489 | ||||||||
\(891\) | −6.04892 | −0.202646 | ||||||||
\(892\) | 17.6256 | 0.590150 | ||||||||
\(893\) | 1.19641 | 0.0400362 | ||||||||
\(894\) | −4.74333 | −0.158641 | ||||||||
\(895\) | −18.1075 | −0.605268 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.64012 | −0.0881020 | ||||||||
\(899\) | −7.24698 | −0.241700 | ||||||||
\(900\) | −4.35690 | −0.145230 | ||||||||
\(901\) | −17.5579 | −0.584940 | ||||||||
\(902\) | 7.24698 | 0.241298 | ||||||||
\(903\) | −4.07606 | −0.135643 | ||||||||
\(904\) | −0.198062 | −0.00658745 | ||||||||
\(905\) | 5.56810 | 0.185090 | ||||||||
\(906\) | 11.2687 | 0.374379 | ||||||||
\(907\) | 59.5478 | 1.97725 | 0.988626 | − | 0.150396i | \(-0.0480550\pi\) | ||||
0.988626 | + | 0.150396i | \(0.0480550\pi\) | |||||||
\(908\) | −11.1914 | −0.371398 | ||||||||
\(909\) | −4.92931 | −0.163495 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.9957 | 0.861276 | 0.430638 | − | 0.902525i | \(-0.358289\pi\) | ||||
0.430638 | + | 0.902525i | \(0.358289\pi\) | |||||||
\(912\) | 0.939001 | 0.0310934 | ||||||||
\(913\) | 102.316 | 3.38618 | ||||||||
\(914\) | 1.25368 | 0.0414682 | ||||||||
\(915\) | −0.801938 | −0.0265112 | ||||||||
\(916\) | 25.4131 | 0.839673 | ||||||||
\(917\) | 3.02715 | 0.0999652 | ||||||||
\(918\) | −2.85086 | −0.0940922 | ||||||||
\(919\) | 17.6088 | 0.580860 | 0.290430 | − | 0.956896i | \(-0.406202\pi\) | ||||
0.290430 | + | 0.956896i | \(0.406202\pi\) | |||||||
\(920\) | 0.731250 | 0.0241086 | ||||||||
\(921\) | 9.16959 | 0.302148 | ||||||||
\(922\) | 22.4198 | 0.738357 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 6.04892 | 0.198995 | ||||||||
\(925\) | 25.7573 | 0.846896 | ||||||||
\(926\) | −8.94975 | −0.294107 | ||||||||
\(927\) | −0.170915 | −0.00561359 | ||||||||
\(928\) | −3.35690 | −0.110196 | ||||||||
\(929\) | −15.6324 | −0.512881 | −0.256440 | − | 0.966560i | \(-0.582550\pi\) | ||||
−0.256440 | + | 0.966560i | \(0.582550\pi\) | |||||||
\(930\) | 1.73125 | 0.0567699 | ||||||||
\(931\) | 0.939001 | 0.0307745 | ||||||||
\(932\) | −4.20237 | −0.137653 | ||||||||
\(933\) | 26.2150 | 0.858242 | ||||||||
\(934\) | 9.62996 | 0.315102 | ||||||||
\(935\) | 13.8291 | 0.452259 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.1849 | 1.05144 | 0.525718 | − | 0.850659i | \(-0.323797\pi\) | ||||
0.525718 | + | 0.850659i | \(0.323797\pi\) | |||||||
\(938\) | −1.35690 | −0.0443042 | ||||||||
\(939\) | 23.1782 | 0.756392 | ||||||||
\(940\) | 1.02177 | 0.0333265 | ||||||||
\(941\) | 48.9952 | 1.59720 | 0.798599 | − | 0.601863i | \(-0.205575\pi\) | ||||
0.798599 | + | 0.601863i | \(0.205575\pi\) | |||||||
\(942\) | −21.5797 | −0.703105 | ||||||||
\(943\) | −1.09246 | −0.0355753 | ||||||||
\(944\) | −7.29590 | −0.237461 | ||||||||
\(945\) | −0.801938 | −0.0260870 | ||||||||
\(946\) | −24.6558 | −0.801628 | ||||||||
\(947\) | 7.05190 | 0.229156 | 0.114578 | − | 0.993414i | \(-0.463448\pi\) | ||||
0.114578 | + | 0.993414i | \(0.463448\pi\) | |||||||
\(948\) | 0.131687 | 0.00427698 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.09113 | −0.132734 | ||||||||
\(951\) | 6.41252 | 0.207940 | ||||||||
\(952\) | 2.85086 | 0.0923967 | ||||||||
\(953\) | 6.99164 | 0.226481 | 0.113241 | − | 0.993568i | \(-0.463877\pi\) | ||||
0.113241 | + | 0.993568i | \(0.463877\pi\) | |||||||
\(954\) | 6.15883 | 0.199400 | ||||||||
\(955\) | 0.584498 | 0.0189139 | ||||||||
\(956\) | −20.3177 | −0.657120 | ||||||||
\(957\) | 20.3056 | 0.656386 | ||||||||
\(958\) | 16.0586 | 0.518830 | ||||||||
\(959\) | −17.3817 | −0.561283 | ||||||||
\(960\) | 0.801938 | 0.0258824 | ||||||||
\(961\) | −26.3394 | −0.849659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.30559 | −0.203195 | ||||||||
\(964\) | −15.9433 | −0.513500 | ||||||||
\(965\) | −11.2601 | −0.362476 | ||||||||
\(966\) | −0.911854 | −0.0293384 | ||||||||
\(967\) | −9.68473 | −0.311440 | −0.155720 | − | 0.987801i | \(-0.549770\pi\) | ||||
−0.155720 | + | 0.987801i | \(0.549770\pi\) | |||||||
\(968\) | 25.5894 | 0.822474 | ||||||||
\(969\) | −2.67696 | −0.0859962 | ||||||||
\(970\) | −3.89440 | −0.125042 | ||||||||
\(971\) | −42.8340 | −1.37461 | −0.687304 | − | 0.726370i | \(-0.741206\pi\) | ||||
−0.687304 | + | 0.726370i | \(0.741206\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −7.99330 | −0.256253 | ||||||||
\(974\) | −30.4295 | −0.975024 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | −37.3510 | −1.19497 | −0.597483 | − | 0.801882i | \(-0.703832\pi\) | ||||
−0.597483 | + | 0.801882i | \(0.703832\pi\) | |||||||
\(978\) | 2.25667 | 0.0721603 | ||||||||
\(979\) | 77.0689 | 2.46313 | ||||||||
\(980\) | 0.801938 | 0.0256170 | ||||||||
\(981\) | 14.1739 | 0.452538 | ||||||||
\(982\) | −22.4413 | −0.716131 | ||||||||
\(983\) | −5.61058 | −0.178950 | −0.0894749 | − | 0.995989i | \(-0.528519\pi\) | ||||
−0.0894749 | + | 0.995989i | \(0.528519\pi\) | |||||||
\(984\) | −1.19806 | −0.0381928 | ||||||||
\(985\) | −6.36850 | −0.202917 | ||||||||
\(986\) | 9.57002 | 0.304772 | ||||||||
\(987\) | −1.27413 | −0.0405559 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.71678 | 0.118187 | ||||||||
\(990\) | −4.85086 | −0.154170 | ||||||||
\(991\) | 8.12605 | 0.258132 | 0.129066 | − | 0.991636i | \(-0.458802\pi\) | ||||
0.129066 | + | 0.991636i | \(0.458802\pi\) | |||||||
\(992\) | 2.15883 | 0.0685430 | ||||||||
\(993\) | 31.2760 | 0.992515 | ||||||||
\(994\) | 7.78017 | 0.246772 | ||||||||
\(995\) | 6.41981 | 0.203522 | ||||||||
\(996\) | −16.9148 | −0.535967 | ||||||||
\(997\) | 7.72050 | 0.244511 | 0.122255 | − | 0.992499i | \(-0.460987\pi\) | ||||
0.122255 | + | 0.992499i | \(0.460987\pi\) | |||||||
\(998\) | 37.9909 | 1.20258 | ||||||||
\(999\) | −5.91185 | −0.187043 |
(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 | 7098.2.a.cm.1.3 | yes | 3 | |
13.12 | even | 2 | 7098.2.a.cf.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cf.1.1 | ✓ | 3 | 13.12 | even | 2 | ||
7098.2.a.cm.1.3 | yes | 3 | 1.1 | even | 1 | trivial |