Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.414214 | 0.185242 | 0.0926210 | − | 0.995701i | \(-0.470476\pi\) | ||||
0.0926210 | + | 0.995701i | \(0.470476\pi\) | |||||||
\(6\) | 1.41421 | 0.577350 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.585786 | 0.185242 | ||||||||
\(11\) | −5.65685 | −1.70561 | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 1.41421 | 0.377964 | ||||||||
\(15\) | 0.414214 | 0.106949 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.41421 | 0.333333 | ||||||||
\(19\) | −2.17157 | −0.498193 | −0.249096 | − | 0.968479i | \(-0.580134\pi\) | ||||
−0.249096 | + | 0.968479i | \(0.580134\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −8.00000 | −1.70561 | ||||||||
\(23\) | 1.24264 | 0.259108 | 0.129554 | − | 0.991572i | \(-0.458645\pi\) | ||||
0.129554 | + | 0.991572i | \(0.458645\pi\) | |||||||
\(24\) | −2.82843 | −0.577350 | ||||||||
\(25\) | −4.82843 | −0.965685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.82843 | 0.896616 | 0.448308 | − | 0.893879i | \(-0.352027\pi\) | ||||
0.448308 | + | 0.893879i | \(0.352027\pi\) | |||||||
\(30\) | 0.585786 | 0.106949 | ||||||||
\(31\) | −1.65685 | −0.297580 | −0.148790 | − | 0.988869i | \(-0.547538\pi\) | ||||
−0.148790 | + | 0.988869i | \(0.547538\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.65685 | −0.984732 | ||||||||
\(34\) | 1.41421 | 0.242536 | ||||||||
\(35\) | 0.414214 | 0.0700149 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.656854 | 0.107986 | 0.0539931 | − | 0.998541i | \(-0.482805\pi\) | ||||
0.0539931 | + | 0.998541i | \(0.482805\pi\) | |||||||
\(38\) | −3.07107 | −0.498193 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.17157 | −0.185242 | ||||||||
\(41\) | 7.65685 | 1.19580 | 0.597900 | − | 0.801571i | \(-0.296002\pi\) | ||||
0.597900 | + | 0.801571i | \(0.296002\pi\) | |||||||
\(42\) | 1.41421 | 0.218218 | ||||||||
\(43\) | −6.48528 | −0.988996 | −0.494498 | − | 0.869179i | \(-0.664648\pi\) | ||||
−0.494498 | + | 0.869179i | \(0.664648\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.414214 | 0.0617473 | ||||||||
\(46\) | 1.75736 | 0.259108 | ||||||||
\(47\) | −10.0711 | −1.46902 | −0.734508 | − | 0.678600i | \(-0.762587\pi\) | ||||
−0.734508 | + | 0.678600i | \(0.762587\pi\) | |||||||
\(48\) | −4.00000 | −0.577350 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −6.82843 | −0.965685 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.4142 | −1.70522 | −0.852612 | − | 0.522545i | \(-0.824983\pi\) | ||||
−0.852612 | + | 0.522545i | \(0.824983\pi\) | |||||||
\(54\) | 1.41421 | 0.192450 | ||||||||
\(55\) | −2.34315 | −0.315950 | ||||||||
\(56\) | −2.82843 | −0.377964 | ||||||||
\(57\) | −2.17157 | −0.287632 | ||||||||
\(58\) | 6.82843 | 0.896616 | ||||||||
\(59\) | −3.58579 | −0.466830 | −0.233415 | − | 0.972377i | \(-0.574990\pi\) | ||||
−0.233415 | + | 0.972377i | \(0.574990\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.656854 | −0.0841016 | −0.0420508 | − | 0.999115i | \(-0.513389\pi\) | ||||
−0.0420508 | + | 0.999115i | \(0.513389\pi\) | |||||||
\(62\) | −2.34315 | −0.297580 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.00000 | −0.984732 | ||||||||
\(67\) | −10.0000 | −1.22169 | −0.610847 | − | 0.791748i | \(-0.709171\pi\) | ||||
−0.610847 | + | 0.791748i | \(0.709171\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.24264 | 0.149596 | ||||||||
\(70\) | 0.585786 | 0.0700149 | ||||||||
\(71\) | −13.0711 | −1.55125 | −0.775625 | − | 0.631194i | \(-0.782565\pi\) | ||||
−0.775625 | + | 0.631194i | \(0.782565\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | −10.7279 | −1.25561 | −0.627804 | − | 0.778371i | \(-0.716046\pi\) | ||||
−0.627804 | + | 0.778371i | \(0.716046\pi\) | |||||||
\(74\) | 0.928932 | 0.107986 | ||||||||
\(75\) | −4.82843 | −0.557539 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.65685 | −0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | −1.65685 | −0.185242 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.8284 | 1.19580 | ||||||||
\(83\) | 5.41421 | 0.594287 | 0.297144 | − | 0.954833i | \(-0.403966\pi\) | ||||
0.297144 | + | 0.954833i | \(0.403966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.414214 | 0.0449278 | ||||||||
\(86\) | −9.17157 | −0.988996 | ||||||||
\(87\) | 4.82843 | 0.517662 | ||||||||
\(88\) | 16.0000 | 1.70561 | ||||||||
\(89\) | −6.34315 | −0.672372 | −0.336186 | − | 0.941796i | \(-0.609137\pi\) | ||||
−0.336186 | + | 0.941796i | \(0.609137\pi\) | |||||||
\(90\) | 0.585786 | 0.0617473 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.65685 | −0.171808 | ||||||||
\(94\) | −14.2426 | −1.46902 | ||||||||
\(95\) | −0.899495 | −0.0922862 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.4142 | 1.76815 | 0.884073 | − | 0.467349i | \(-0.154791\pi\) | ||||
0.884073 | + | 0.467349i | \(0.154791\pi\) | |||||||
\(98\) | −8.48528 | −0.857143 | ||||||||
\(99\) | −5.65685 | −0.568535 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.24264 | 0.422159 | 0.211079 | − | 0.977469i | \(-0.432302\pi\) | ||||
0.211079 | + | 0.977469i | \(0.432302\pi\) | |||||||
\(102\) | 1.41421 | 0.140028 | ||||||||
\(103\) | −2.24264 | −0.220974 | −0.110487 | − | 0.993878i | \(-0.535241\pi\) | ||||
−0.110487 | + | 0.993878i | \(0.535241\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.414214 | 0.0404231 | ||||||||
\(106\) | −17.5563 | −1.70522 | ||||||||
\(107\) | −3.41421 | −0.330064 | −0.165032 | − | 0.986288i | \(-0.552773\pi\) | ||||
−0.165032 | + | 0.986288i | \(0.552773\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.48528 | 0.812743 | 0.406371 | − | 0.913708i | \(-0.366794\pi\) | ||||
0.406371 | + | 0.913708i | \(0.366794\pi\) | |||||||
\(110\) | −3.31371 | −0.315950 | ||||||||
\(111\) | 0.656854 | 0.0623458 | ||||||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | −3.07107 | −0.287632 | ||||||||
\(115\) | 0.514719 | 0.0479978 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.07107 | −0.466830 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | −1.17157 | −0.106949 | ||||||||
\(121\) | 21.0000 | 1.90909 | ||||||||
\(122\) | −0.928932 | −0.0841016 | ||||||||
\(123\) | 7.65685 | 0.690395 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.07107 | −0.364127 | ||||||||
\(126\) | 1.41421 | 0.125988 | ||||||||
\(127\) | 20.2426 | 1.79624 | 0.898122 | − | 0.439746i | \(-0.144932\pi\) | ||||
0.898122 | + | 0.439746i | \(0.144932\pi\) | |||||||
\(128\) | 11.3137 | 1.00000 | ||||||||
\(129\) | −6.48528 | −0.570997 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.414214 | 0.0361900 | 0.0180950 | − | 0.999836i | \(-0.494240\pi\) | ||||
0.0180950 | + | 0.999836i | \(0.494240\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.17157 | −0.188299 | ||||||||
\(134\) | −14.1421 | −1.22169 | ||||||||
\(135\) | 0.414214 | 0.0356498 | ||||||||
\(136\) | −2.82843 | −0.242536 | ||||||||
\(137\) | 18.5563 | 1.58538 | 0.792688 | − | 0.609628i | \(-0.208681\pi\) | ||||
0.792688 | + | 0.609628i | \(0.208681\pi\) | |||||||
\(138\) | 1.75736 | 0.149596 | ||||||||
\(139\) | 2.48528 | 0.210799 | 0.105399 | − | 0.994430i | \(-0.466388\pi\) | ||||
0.105399 | + | 0.994430i | \(0.466388\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.0711 | −0.848137 | ||||||||
\(142\) | −18.4853 | −1.55125 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.00000 | −0.333333 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | −15.1716 | −1.25561 | ||||||||
\(147\) | −6.00000 | −0.494872 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.0711 | −1.31659 | −0.658297 | − | 0.752759i | \(-0.728723\pi\) | ||||
−0.658297 | + | 0.752759i | \(0.728723\pi\) | |||||||
\(150\) | −6.82843 | −0.557539 | ||||||||
\(151\) | 0.514719 | 0.0418872 | 0.0209436 | − | 0.999781i | \(-0.493333\pi\) | ||||
0.0209436 | + | 0.999781i | \(0.493333\pi\) | |||||||
\(152\) | 6.14214 | 0.498193 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −8.00000 | −0.644658 | ||||||||
\(155\) | −0.686292 | −0.0551243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7279 | 0.856181 | 0.428091 | − | 0.903736i | \(-0.359186\pi\) | ||||
0.428091 | + | 0.903736i | \(0.359186\pi\) | |||||||
\(158\) | −1.41421 | −0.112509 | ||||||||
\(159\) | −12.4142 | −0.984511 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.24264 | 0.0979338 | ||||||||
\(162\) | 1.41421 | 0.111111 | ||||||||
\(163\) | −3.75736 | −0.294299 | −0.147150 | − | 0.989114i | \(-0.547010\pi\) | ||||
−0.147150 | + | 0.989114i | \(0.547010\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.34315 | −0.182414 | ||||||||
\(166\) | 7.65685 | 0.594287 | ||||||||
\(167\) | 10.0711 | 0.779323 | 0.389661 | − | 0.920958i | \(-0.372592\pi\) | ||||
0.389661 | + | 0.920958i | \(0.372592\pi\) | |||||||
\(168\) | −2.82843 | −0.218218 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0.585786 | 0.0449278 | ||||||||
\(171\) | −2.17157 | −0.166064 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.07107 | 0.385546 | 0.192773 | − | 0.981243i | \(-0.438252\pi\) | ||||
0.192773 | + | 0.981243i | \(0.438252\pi\) | |||||||
\(174\) | 6.82843 | 0.517662 | ||||||||
\(175\) | −4.82843 | −0.364995 | ||||||||
\(176\) | 22.6274 | 1.70561 | ||||||||
\(177\) | −3.58579 | −0.269524 | ||||||||
\(178\) | −8.97056 | −0.672372 | ||||||||
\(179\) | −10.2426 | −0.765571 | −0.382785 | − | 0.923837i | \(-0.625035\pi\) | ||||
−0.382785 | + | 0.923837i | \(0.625035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.585786 | 0.0435412 | 0.0217706 | − | 0.999763i | \(-0.493070\pi\) | ||||
0.0217706 | + | 0.999763i | \(0.493070\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.656854 | −0.0485561 | ||||||||
\(184\) | −3.51472 | −0.259108 | ||||||||
\(185\) | 0.272078 | 0.0200036 | ||||||||
\(186\) | −2.34315 | −0.171808 | ||||||||
\(187\) | −5.65685 | −0.413670 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −1.27208 | −0.0922862 | ||||||||
\(191\) | −19.5858 | −1.41718 | −0.708589 | − | 0.705622i | \(-0.750668\pi\) | ||||
−0.708589 | + | 0.705622i | \(0.750668\pi\) | |||||||
\(192\) | 8.00000 | 0.577350 | ||||||||
\(193\) | 15.4853 | 1.11465 | 0.557327 | − | 0.830293i | \(-0.311827\pi\) | ||||
0.557327 | + | 0.830293i | \(0.311827\pi\) | |||||||
\(194\) | 24.6274 | 1.76815 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.51472 | 0.250413 | 0.125207 | − | 0.992131i | \(-0.460041\pi\) | ||||
0.125207 | + | 0.992131i | \(0.460041\pi\) | |||||||
\(198\) | −8.00000 | −0.568535 | ||||||||
\(199\) | −1.82843 | −0.129614 | −0.0648069 | − | 0.997898i | \(-0.520643\pi\) | ||||
−0.0648069 | + | 0.997898i | \(0.520643\pi\) | |||||||
\(200\) | 13.6569 | 0.965685 | ||||||||
\(201\) | −10.0000 | −0.705346 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 4.82843 | 0.338889 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.17157 | 0.221512 | ||||||||
\(206\) | −3.17157 | −0.220974 | ||||||||
\(207\) | 1.24264 | 0.0863695 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.2843 | 0.849721 | ||||||||
\(210\) | 0.585786 | 0.0404231 | ||||||||
\(211\) | 13.9706 | 0.961773 | 0.480887 | − | 0.876783i | \(-0.340315\pi\) | ||||
0.480887 | + | 0.876783i | \(0.340315\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.0711 | −0.895615 | ||||||||
\(214\) | −4.82843 | −0.330064 | ||||||||
\(215\) | −2.68629 | −0.183204 | ||||||||
\(216\) | −2.82843 | −0.192450 | ||||||||
\(217\) | −1.65685 | −0.112475 | ||||||||
\(218\) | 12.0000 | 0.812743 | ||||||||
\(219\) | −10.7279 | −0.724926 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.928932 | 0.0623458 | ||||||||
\(223\) | −4.17157 | −0.279349 | −0.139675 | − | 0.990197i | \(-0.544606\pi\) | ||||
−0.139675 | + | 0.990197i | \(0.544606\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.82843 | −0.321895 | ||||||||
\(226\) | −16.9706 | −1.12887 | ||||||||
\(227\) | −18.8284 | −1.24969 | −0.624843 | − | 0.780750i | \(-0.714837\pi\) | ||||
−0.624843 | + | 0.780750i | \(0.714837\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.58579 | −0.170874 | −0.0854368 | − | 0.996344i | \(-0.527229\pi\) | ||||
−0.0854368 | + | 0.996344i | \(0.527229\pi\) | |||||||
\(230\) | 0.727922 | 0.0479978 | ||||||||
\(231\) | −5.65685 | −0.372194 | ||||||||
\(232\) | −13.6569 | −0.896616 | ||||||||
\(233\) | 24.3848 | 1.59750 | 0.798750 | − | 0.601663i | \(-0.205495\pi\) | ||||
0.798750 | + | 0.601663i | \(0.205495\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.17157 | −0.272123 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 1.41421 | 0.0916698 | ||||||||
\(239\) | −6.72792 | −0.435193 | −0.217597 | − | 0.976039i | \(-0.569822\pi\) | ||||
−0.217597 | + | 0.976039i | \(0.569822\pi\) | |||||||
\(240\) | −1.65685 | −0.106949 | ||||||||
\(241\) | −2.58579 | −0.166565 | −0.0832826 | − | 0.996526i | \(-0.526540\pi\) | ||||
−0.0832826 | + | 0.996526i | \(0.526540\pi\) | |||||||
\(242\) | 29.6985 | 1.90909 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.48528 | −0.158779 | ||||||||
\(246\) | 10.8284 | 0.690395 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.68629 | 0.297580 | ||||||||
\(249\) | 5.41421 | 0.343112 | ||||||||
\(250\) | −5.75736 | −0.364127 | ||||||||
\(251\) | 12.5563 | 0.792550 | 0.396275 | − | 0.918132i | \(-0.370303\pi\) | ||||
0.396275 | + | 0.918132i | \(0.370303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.02944 | −0.441937 | ||||||||
\(254\) | 28.6274 | 1.79624 | ||||||||
\(255\) | 0.414214 | 0.0259391 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.6274 | 1.28670 | 0.643351 | − | 0.765571i | \(-0.277543\pi\) | ||||
0.643351 | + | 0.765571i | \(0.277543\pi\) | |||||||
\(258\) | −9.17157 | −0.570997 | ||||||||
\(259\) | 0.656854 | 0.0408149 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.82843 | 0.298872 | ||||||||
\(262\) | 0.585786 | 0.0361900 | ||||||||
\(263\) | −24.3848 | −1.50363 | −0.751815 | − | 0.659374i | \(-0.770821\pi\) | ||||
−0.751815 | + | 0.659374i | \(0.770821\pi\) | |||||||
\(264\) | 16.0000 | 0.984732 | ||||||||
\(265\) | −5.14214 | −0.315879 | ||||||||
\(266\) | −3.07107 | −0.188299 | ||||||||
\(267\) | −6.34315 | −0.388194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4853 | −0.883183 | −0.441592 | − | 0.897216i | \(-0.645586\pi\) | ||||
−0.441592 | + | 0.897216i | \(0.645586\pi\) | |||||||
\(270\) | 0.585786 | 0.0356498 | ||||||||
\(271\) | 22.7279 | 1.38062 | 0.690311 | − | 0.723512i | \(-0.257474\pi\) | ||||
0.690311 | + | 0.723512i | \(0.257474\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 26.2426 | 1.58538 | ||||||||
\(275\) | 27.3137 | 1.64708 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.9706 | −1.01966 | −0.509831 | − | 0.860274i | \(-0.670292\pi\) | ||||
−0.509831 | + | 0.860274i | \(0.670292\pi\) | |||||||
\(278\) | 3.51472 | 0.210799 | ||||||||
\(279\) | −1.65685 | −0.0991933 | ||||||||
\(280\) | −1.17157 | −0.0700149 | ||||||||
\(281\) | −6.58579 | −0.392875 | −0.196438 | − | 0.980516i | \(-0.562937\pi\) | ||||
−0.196438 | + | 0.980516i | \(0.562937\pi\) | |||||||
\(282\) | −14.2426 | −0.848137 | ||||||||
\(283\) | 12.0000 | 0.713326 | 0.356663 | − | 0.934233i | \(-0.383914\pi\) | ||||
0.356663 | + | 0.934233i | \(0.383914\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.899495 | −0.0532815 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.65685 | 0.451970 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 2.82843 | 0.166091 | ||||||||
\(291\) | 17.4142 | 1.02084 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.8701 | 1.39450 | 0.697252 | − | 0.716826i | \(-0.254406\pi\) | ||||
0.697252 | + | 0.716826i | \(0.254406\pi\) | |||||||
\(294\) | −8.48528 | −0.494872 | ||||||||
\(295\) | −1.48528 | −0.0864764 | ||||||||
\(296\) | −1.85786 | −0.107986 | ||||||||
\(297\) | −5.65685 | −0.328244 | ||||||||
\(298\) | −22.7279 | −1.31659 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.48528 | −0.373805 | ||||||||
\(302\) | 0.727922 | 0.0418872 | ||||||||
\(303\) | 4.24264 | 0.243733 | ||||||||
\(304\) | 8.68629 | 0.498193 | ||||||||
\(305\) | −0.272078 | −0.0155791 | ||||||||
\(306\) | 1.41421 | 0.0808452 | ||||||||
\(307\) | 29.5563 | 1.68687 | 0.843435 | − | 0.537231i | \(-0.180530\pi\) | ||||
0.843435 | + | 0.537231i | \(0.180530\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.24264 | −0.127579 | ||||||||
\(310\) | −0.970563 | −0.0551243 | ||||||||
\(311\) | −13.7990 | −0.782469 | −0.391234 | − | 0.920291i | \(-0.627952\pi\) | ||||
−0.391234 | + | 0.920291i | \(0.627952\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.68629 | −0.264885 | −0.132442 | − | 0.991191i | \(-0.542282\pi\) | ||||
−0.132442 | + | 0.991191i | \(0.542282\pi\) | |||||||
\(314\) | 15.1716 | 0.856181 | ||||||||
\(315\) | 0.414214 | 0.0233383 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.7279 | −1.55736 | −0.778678 | − | 0.627424i | \(-0.784109\pi\) | ||||
−0.778678 | + | 0.627424i | \(0.784109\pi\) | |||||||
\(318\) | −17.5563 | −0.984511 | ||||||||
\(319\) | −27.3137 | −1.52927 | ||||||||
\(320\) | 3.31371 | 0.185242 | ||||||||
\(321\) | −3.41421 | −0.190563 | ||||||||
\(322\) | 1.75736 | 0.0979338 | ||||||||
\(323\) | −2.17157 | −0.120830 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.31371 | −0.294299 | ||||||||
\(327\) | 8.48528 | 0.469237 | ||||||||
\(328\) | −21.6569 | −1.19580 | ||||||||
\(329\) | −10.0711 | −0.555236 | ||||||||
\(330\) | −3.31371 | −0.182414 | ||||||||
\(331\) | −13.7574 | −0.756173 | −0.378086 | − | 0.925770i | \(-0.623418\pi\) | ||||
−0.378086 | + | 0.925770i | \(0.623418\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.656854 | 0.0359954 | ||||||||
\(334\) | 14.2426 | 0.779323 | ||||||||
\(335\) | −4.14214 | −0.226309 | ||||||||
\(336\) | −4.00000 | −0.218218 | ||||||||
\(337\) | −12.7279 | −0.693334 | −0.346667 | − | 0.937988i | \(-0.612687\pi\) | ||||
−0.346667 | + | 0.937988i | \(0.612687\pi\) | |||||||
\(338\) | −18.3848 | −1.00000 | ||||||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.37258 | 0.507554 | ||||||||
\(342\) | −3.07107 | −0.166064 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 18.3431 | 0.988996 | ||||||||
\(345\) | 0.514719 | 0.0277115 | ||||||||
\(346\) | 7.17157 | 0.385546 | ||||||||
\(347\) | −5.38478 | −0.289070 | −0.144535 | − | 0.989500i | \(-0.546169\pi\) | ||||
−0.144535 | + | 0.989500i | \(0.546169\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.24264 | −0.334161 | −0.167080 | − | 0.985943i | \(-0.553434\pi\) | ||||
−0.167080 | + | 0.985943i | \(0.553434\pi\) | |||||||
\(350\) | −6.82843 | −0.364995 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.72792 | 0.517765 | 0.258883 | − | 0.965909i | \(-0.416646\pi\) | ||||
0.258883 | + | 0.965909i | \(0.416646\pi\) | |||||||
\(354\) | −5.07107 | −0.269524 | ||||||||
\(355\) | −5.41421 | −0.287357 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.00000 | 0.0529256 | ||||||||
\(358\) | −14.4853 | −0.765571 | ||||||||
\(359\) | −15.6569 | −0.826337 | −0.413169 | − | 0.910655i | \(-0.635578\pi\) | ||||
−0.413169 | + | 0.910655i | \(0.635578\pi\) | |||||||
\(360\) | −1.17157 | −0.0617473 | ||||||||
\(361\) | −14.2843 | −0.751804 | ||||||||
\(362\) | 0.828427 | 0.0435412 | ||||||||
\(363\) | 21.0000 | 1.10221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.44365 | −0.232591 | ||||||||
\(366\) | −0.928932 | −0.0485561 | ||||||||
\(367\) | −23.5563 | −1.22963 | −0.614816 | − | 0.788671i | \(-0.710770\pi\) | ||||
−0.614816 | + | 0.788671i | \(0.710770\pi\) | |||||||
\(368\) | −4.97056 | −0.259108 | ||||||||
\(369\) | 7.65685 | 0.398600 | ||||||||
\(370\) | 0.384776 | 0.0200036 | ||||||||
\(371\) | −12.4142 | −0.644514 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.2426 | 0.737456 | 0.368728 | − | 0.929537i | \(-0.379793\pi\) | ||||
0.368728 | + | 0.929537i | \(0.379793\pi\) | |||||||
\(374\) | −8.00000 | −0.413670 | ||||||||
\(375\) | −4.07107 | −0.210229 | ||||||||
\(376\) | 28.4853 | 1.46902 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.41421 | 0.0727393 | ||||||||
\(379\) | 38.4558 | 1.97534 | 0.987672 | − | 0.156538i | \(-0.0500332\pi\) | ||||
0.987672 | + | 0.156538i | \(0.0500332\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.2426 | 1.03706 | ||||||||
\(382\) | −27.6985 | −1.41718 | ||||||||
\(383\) | 13.7574 | 0.702968 | 0.351484 | − | 0.936194i | \(-0.385677\pi\) | ||||
0.351484 | + | 0.936194i | \(0.385677\pi\) | |||||||
\(384\) | 11.3137 | 0.577350 | ||||||||
\(385\) | −2.34315 | −0.119418 | ||||||||
\(386\) | 21.8995 | 1.11465 | ||||||||
\(387\) | −6.48528 | −0.329665 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.4142 | 0.882936 | 0.441468 | − | 0.897277i | \(-0.354458\pi\) | ||||
0.441468 | + | 0.897277i | \(0.354458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.24264 | 0.0628430 | ||||||||
\(392\) | 16.9706 | 0.857143 | ||||||||
\(393\) | 0.414214 | 0.0208943 | ||||||||
\(394\) | 4.97056 | 0.250413 | ||||||||
\(395\) | −0.414214 | −0.0208413 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.85786 | −0.394375 | −0.197187 | − | 0.980366i | \(-0.563181\pi\) | ||||
−0.197187 | + | 0.980366i | \(0.563181\pi\) | |||||||
\(398\) | −2.58579 | −0.129614 | ||||||||
\(399\) | −2.17157 | −0.108715 | ||||||||
\(400\) | 19.3137 | 0.965685 | ||||||||
\(401\) | 4.24264 | 0.211867 | 0.105934 | − | 0.994373i | \(-0.466217\pi\) | ||||
0.105934 | + | 0.994373i | \(0.466217\pi\) | |||||||
\(402\) | −14.1421 | −0.705346 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.414214 | 0.0205824 | ||||||||
\(406\) | 6.82843 | 0.338889 | ||||||||
\(407\) | −3.71573 | −0.184182 | ||||||||
\(408\) | −2.82843 | −0.140028 | ||||||||
\(409\) | 18.2843 | 0.904099 | 0.452050 | − | 0.891993i | \(-0.350693\pi\) | ||||
0.452050 | + | 0.891993i | \(0.350693\pi\) | |||||||
\(410\) | 4.48528 | 0.221512 | ||||||||
\(411\) | 18.5563 | 0.915317 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.58579 | −0.176445 | ||||||||
\(414\) | 1.75736 | 0.0863695 | ||||||||
\(415\) | 2.24264 | 0.110087 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.48528 | 0.121705 | ||||||||
\(418\) | 17.3726 | 0.849721 | ||||||||
\(419\) | 15.0711 | 0.736270 | 0.368135 | − | 0.929772i | \(-0.379996\pi\) | ||||
0.368135 | + | 0.929772i | \(0.379996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.9706 | 0.583410 | 0.291705 | − | 0.956508i | \(-0.405778\pi\) | ||||
0.291705 | + | 0.956508i | \(0.405778\pi\) | |||||||
\(422\) | 19.7574 | 0.961773 | ||||||||
\(423\) | −10.0711 | −0.489672 | ||||||||
\(424\) | 35.1127 | 1.70522 | ||||||||
\(425\) | −4.82843 | −0.234213 | ||||||||
\(426\) | −18.4853 | −0.895615 | ||||||||
\(427\) | −0.656854 | −0.0317874 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.79899 | −0.183204 | ||||||||
\(431\) | −39.7279 | −1.91363 | −0.956813 | − | 0.290703i | \(-0.906111\pi\) | ||||
−0.956813 | + | 0.290703i | \(0.906111\pi\) | |||||||
\(432\) | −4.00000 | −0.192450 | ||||||||
\(433\) | −25.6569 | −1.23299 | −0.616495 | − | 0.787359i | \(-0.711448\pi\) | ||||
−0.616495 | + | 0.787359i | \(0.711448\pi\) | |||||||
\(434\) | −2.34315 | −0.112475 | ||||||||
\(435\) | 2.00000 | 0.0958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.69848 | −0.129086 | ||||||||
\(438\) | −15.1716 | −0.724926 | ||||||||
\(439\) | 20.9289 | 0.998883 | 0.499442 | − | 0.866347i | \(-0.333538\pi\) | ||||
0.499442 | + | 0.866347i | \(0.333538\pi\) | |||||||
\(440\) | 6.62742 | 0.315950 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.4142 | −1.54005 | −0.770023 | − | 0.638016i | \(-0.779755\pi\) | ||||
−0.770023 | + | 0.638016i | \(0.779755\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.62742 | −0.124552 | ||||||||
\(446\) | −5.89949 | −0.279349 | ||||||||
\(447\) | −16.0711 | −0.760135 | ||||||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | −14.4853 | −0.683603 | −0.341801 | − | 0.939772i | \(-0.611037\pi\) | ||||
−0.341801 | + | 0.939772i | \(0.611037\pi\) | |||||||
\(450\) | −6.82843 | −0.321895 | ||||||||
\(451\) | −43.3137 | −2.03956 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.514719 | 0.0241836 | ||||||||
\(454\) | −26.6274 | −1.24969 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.14214 | 0.287632 | ||||||||
\(457\) | 16.4558 | 0.769772 | 0.384886 | − | 0.922964i | \(-0.374241\pi\) | ||||
0.384886 | + | 0.922964i | \(0.374241\pi\) | |||||||
\(458\) | −3.65685 | −0.170874 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.7990 | 1.48103 | 0.740513 | − | 0.672042i | \(-0.234582\pi\) | ||||
0.740513 | + | 0.672042i | \(0.234582\pi\) | |||||||
\(462\) | −8.00000 | −0.372194 | ||||||||
\(463\) | 10.2426 | 0.476016 | 0.238008 | − | 0.971263i | \(-0.423506\pi\) | ||||
0.238008 | + | 0.971263i | \(0.423506\pi\) | |||||||
\(464\) | −19.3137 | −0.896616 | ||||||||
\(465\) | −0.686292 | −0.0318260 | ||||||||
\(466\) | 34.4853 | 1.59750 | ||||||||
\(467\) | −13.4558 | −0.622662 | −0.311331 | − | 0.950302i | \(-0.600775\pi\) | ||||
−0.311331 | + | 0.950302i | \(0.600775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0000 | −0.461757 | ||||||||
\(470\) | −5.89949 | −0.272123 | ||||||||
\(471\) | 10.7279 | 0.494317 | ||||||||
\(472\) | 10.1421 | 0.466830 | ||||||||
\(473\) | 36.6863 | 1.68684 | ||||||||
\(474\) | −1.41421 | −0.0649570 | ||||||||
\(475\) | 10.4853 | 0.481098 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.4142 | −0.568408 | ||||||||
\(478\) | −9.51472 | −0.435193 | ||||||||
\(479\) | 34.8995 | 1.59460 | 0.797299 | − | 0.603584i | \(-0.206261\pi\) | ||||
0.797299 | + | 0.603584i | \(0.206261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −3.65685 | −0.166565 | ||||||||
\(483\) | 1.24264 | 0.0565421 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.21320 | 0.327535 | ||||||||
\(486\) | 1.41421 | 0.0641500 | ||||||||
\(487\) | 41.2132 | 1.86755 | 0.933774 | − | 0.357863i | \(-0.116494\pi\) | ||||
0.933774 | + | 0.357863i | \(0.116494\pi\) | |||||||
\(488\) | 1.85786 | 0.0841016 | ||||||||
\(489\) | −3.75736 | −0.169914 | ||||||||
\(490\) | −3.51472 | −0.158779 | ||||||||
\(491\) | −11.7990 | −0.532481 | −0.266240 | − | 0.963907i | \(-0.585782\pi\) | ||||
−0.266240 | + | 0.963907i | \(0.585782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.82843 | 0.217461 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.34315 | −0.105317 | ||||||||
\(496\) | 6.62742 | 0.297580 | ||||||||
\(497\) | −13.0711 | −0.586318 | ||||||||
\(498\) | 7.65685 | 0.343112 | ||||||||
\(499\) | −27.9411 | −1.25082 | −0.625408 | − | 0.780298i | \(-0.715068\pi\) | ||||
−0.625408 | + | 0.780298i | \(0.715068\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.0711 | 0.449942 | ||||||||
\(502\) | 17.7574 | 0.792550 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | −2.82843 | −0.125988 | ||||||||
\(505\) | 1.75736 | 0.0782015 | ||||||||
\(506\) | −9.94113 | −0.441937 | ||||||||
\(507\) | −13.0000 | −0.577350 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.3848 | 1.12516 | 0.562580 | − | 0.826743i | \(-0.309809\pi\) | ||||
0.562580 | + | 0.826743i | \(0.309809\pi\) | |||||||
\(510\) | 0.585786 | 0.0259391 | ||||||||
\(511\) | −10.7279 | −0.474575 | ||||||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | −2.17157 | −0.0958773 | ||||||||
\(514\) | 29.1716 | 1.28670 | ||||||||
\(515\) | −0.928932 | −0.0409336 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 56.9706 | 2.50556 | ||||||||
\(518\) | 0.928932 | 0.0408149 | ||||||||
\(519\) | 5.07107 | 0.222595 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.3137 | 0.495663 | 0.247831 | − | 0.968803i | \(-0.420282\pi\) | ||||
0.247831 | + | 0.968803i | \(0.420282\pi\) | |||||||
\(522\) | 6.82843 | 0.298872 | ||||||||
\(523\) | −27.4558 | −1.20056 | −0.600280 | − | 0.799790i | \(-0.704944\pi\) | ||||
−0.600280 | + | 0.799790i | \(0.704944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.82843 | −0.210730 | ||||||||
\(526\) | −34.4853 | −1.50363 | ||||||||
\(527\) | −1.65685 | −0.0721737 | ||||||||
\(528\) | 22.6274 | 0.984732 | ||||||||
\(529\) | −21.4558 | −0.932863 | ||||||||
\(530\) | −7.27208 | −0.315879 | ||||||||
\(531\) | −3.58579 | −0.155610 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.97056 | −0.388194 | ||||||||
\(535\) | −1.41421 | −0.0611418 | ||||||||
\(536\) | 28.2843 | 1.22169 | ||||||||
\(537\) | −10.2426 | −0.442003 | ||||||||
\(538\) | −20.4853 | −0.883183 | ||||||||
\(539\) | 33.9411 | 1.46195 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.27208 | −0.140678 | −0.0703388 | − | 0.997523i | \(-0.522408\pi\) | ||||
−0.0703388 | + | 0.997523i | \(0.522408\pi\) | |||||||
\(542\) | 32.1421 | 1.38062 | ||||||||
\(543\) | 0.585786 | 0.0251385 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.51472 | 0.150554 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.5563 | 1.86234 | 0.931168 | − | 0.364592i | \(-0.118791\pi\) | ||||
0.931168 | + | 0.364592i | \(0.118791\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.656854 | −0.0280339 | ||||||||
\(550\) | 38.6274 | 1.64708 | ||||||||
\(551\) | −10.4853 | −0.446688 | ||||||||
\(552\) | −3.51472 | −0.149596 | ||||||||
\(553\) | −1.00000 | −0.0425243 | ||||||||
\(554\) | −24.0000 | −1.01966 | ||||||||
\(555\) | 0.272078 | 0.0115491 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.1421 | −1.19242 | −0.596210 | − | 0.802828i | \(-0.703328\pi\) | ||||
−0.596210 | + | 0.802828i | \(0.703328\pi\) | |||||||
\(558\) | −2.34315 | −0.0991933 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.65685 | −0.0700149 | ||||||||
\(561\) | −5.65685 | −0.238833 | ||||||||
\(562\) | −9.31371 | −0.392875 | ||||||||
\(563\) | −34.5858 | −1.45762 | −0.728809 | − | 0.684718i | \(-0.759926\pi\) | ||||
−0.728809 | + | 0.684718i | \(0.759926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.97056 | −0.209113 | ||||||||
\(566\) | 16.9706 | 0.713326 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 36.9706 | 1.55125 | ||||||||
\(569\) | 38.3848 | 1.60917 | 0.804587 | − | 0.593835i | \(-0.202387\pi\) | ||||
0.804587 | + | 0.593835i | \(0.202387\pi\) | |||||||
\(570\) | −1.27208 | −0.0532815 | ||||||||
\(571\) | 20.6274 | 0.863231 | 0.431615 | − | 0.902058i | \(-0.357944\pi\) | ||||
0.431615 | + | 0.902058i | \(0.357944\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.5858 | −0.818208 | ||||||||
\(574\) | 10.8284 | 0.451970 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 8.00000 | 0.333333 | ||||||||
\(577\) | −6.72792 | −0.280087 | −0.140044 | − | 0.990145i | \(-0.544724\pi\) | ||||
−0.140044 | + | 0.990145i | \(0.544724\pi\) | |||||||
\(578\) | 1.41421 | 0.0588235 | ||||||||
\(579\) | 15.4853 | 0.643546 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.41421 | 0.224619 | ||||||||
\(582\) | 24.6274 | 1.02084 | ||||||||
\(583\) | 70.2254 | 2.90844 | ||||||||
\(584\) | 30.3431 | 1.25561 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.7574 | 1.39450 | ||||||||
\(587\) | −6.89949 | −0.284773 | −0.142386 | − | 0.989811i | \(-0.545478\pi\) | ||||
−0.142386 | + | 0.989811i | \(0.545478\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.59798 | 0.148252 | ||||||||
\(590\) | −2.10051 | −0.0864764 | ||||||||
\(591\) | 3.51472 | 0.144576 | ||||||||
\(592\) | −2.62742 | −0.107986 | ||||||||
\(593\) | −35.8995 | −1.47422 | −0.737108 | − | 0.675775i | \(-0.763809\pi\) | ||||
−0.737108 | + | 0.675775i | \(0.763809\pi\) | |||||||
\(594\) | −8.00000 | −0.328244 | ||||||||
\(595\) | 0.414214 | 0.0169811 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.82843 | −0.0748325 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.4437 | −0.671869 | −0.335935 | − | 0.941885i | \(-0.609052\pi\) | ||||
−0.335935 | + | 0.941885i | \(0.609052\pi\) | |||||||
\(600\) | 13.6569 | 0.557539 | ||||||||
\(601\) | 31.9706 | 1.30411 | 0.652053 | − | 0.758173i | \(-0.273908\pi\) | ||||
0.652053 | + | 0.758173i | \(0.273908\pi\) | |||||||
\(602\) | −9.17157 | −0.373805 | ||||||||
\(603\) | −10.0000 | −0.407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.69848 | 0.353644 | ||||||||
\(606\) | 6.00000 | 0.243733 | ||||||||
\(607\) | 22.0000 | 0.892952 | 0.446476 | − | 0.894795i | \(-0.352679\pi\) | ||||
0.446476 | + | 0.894795i | \(0.352679\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.82843 | 0.195658 | ||||||||
\(610\) | −0.384776 | −0.0155791 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.51472 | 0.0611789 | 0.0305895 | − | 0.999532i | \(-0.490262\pi\) | ||||
0.0305895 | + | 0.999532i | \(0.490262\pi\) | |||||||
\(614\) | 41.7990 | 1.68687 | ||||||||
\(615\) | 3.17157 | 0.127890 | ||||||||
\(616\) | 16.0000 | 0.644658 | ||||||||
\(617\) | −9.31371 | −0.374956 | −0.187478 | − | 0.982269i | \(-0.560031\pi\) | ||||
−0.187478 | + | 0.982269i | \(0.560031\pi\) | |||||||
\(618\) | −3.17157 | −0.127579 | ||||||||
\(619\) | 21.0000 | 0.844061 | 0.422031 | − | 0.906582i | \(-0.361317\pi\) | ||||
0.422031 | + | 0.906582i | \(0.361317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.24264 | 0.0498655 | ||||||||
\(622\) | −19.5147 | −0.782469 | ||||||||
\(623\) | −6.34315 | −0.254133 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.4558 | 0.898234 | ||||||||
\(626\) | −6.62742 | −0.264885 | ||||||||
\(627\) | 12.2843 | 0.490587 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.656854 | 0.0261905 | ||||||||
\(630\) | 0.585786 | 0.0233383 | ||||||||
\(631\) | 24.0000 | 0.955425 | 0.477712 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477712 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(632\) | 2.82843 | 0.112509 | ||||||||
\(633\) | 13.9706 | 0.555280 | ||||||||
\(634\) | −39.2132 | −1.55736 | ||||||||
\(635\) | 8.38478 | 0.332740 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −38.6274 | −1.52927 | ||||||||
\(639\) | −13.0711 | −0.517083 | ||||||||
\(640\) | 4.68629 | 0.185242 | ||||||||
\(641\) | 6.55635 | 0.258960 | 0.129480 | − | 0.991582i | \(-0.458669\pi\) | ||||
0.129480 | + | 0.991582i | \(0.458669\pi\) | |||||||
\(642\) | −4.82843 | −0.190563 | ||||||||
\(643\) | −33.2132 | −1.30980 | −0.654900 | − | 0.755715i | \(-0.727289\pi\) | ||||
−0.654900 | + | 0.755715i | \(0.727289\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.68629 | −0.105773 | ||||||||
\(646\) | −3.07107 | −0.120830 | ||||||||
\(647\) | −1.58579 | −0.0623437 | −0.0311718 | − | 0.999514i | \(-0.509924\pi\) | ||||
−0.0311718 | + | 0.999514i | \(0.509924\pi\) | |||||||
\(648\) | −2.82843 | −0.111111 | ||||||||
\(649\) | 20.2843 | 0.796227 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.65685 | −0.0649372 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.0711 | −1.25504 | −0.627519 | − | 0.778601i | \(-0.715930\pi\) | ||||
−0.627519 | + | 0.778601i | \(0.715930\pi\) | |||||||
\(654\) | 12.0000 | 0.469237 | ||||||||
\(655\) | 0.171573 | 0.00670391 | ||||||||
\(656\) | −30.6274 | −1.19580 | ||||||||
\(657\) | −10.7279 | −0.418536 | ||||||||
\(658\) | −14.2426 | −0.555236 | ||||||||
\(659\) | 3.72792 | 0.145219 | 0.0726096 | − | 0.997360i | \(-0.476867\pi\) | ||||
0.0726096 | + | 0.997360i | \(0.476867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.6985 | 1.77747 | 0.888733 | − | 0.458426i | \(-0.151587\pi\) | ||||
0.888733 | + | 0.458426i | \(0.151587\pi\) | |||||||
\(662\) | −19.4558 | −0.756173 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.3137 | −0.594287 | ||||||||
\(665\) | −0.899495 | −0.0348809 | ||||||||
\(666\) | 0.928932 | 0.0359954 | ||||||||
\(667\) | 6.00000 | 0.232321 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.17157 | −0.161282 | ||||||||
\(670\) | −5.85786 | −0.226309 | ||||||||
\(671\) | 3.71573 | 0.143444 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.9706 | 0.654167 | 0.327084 | − | 0.944995i | \(-0.393934\pi\) | ||||
0.327084 | + | 0.944995i | \(0.393934\pi\) | |||||||
\(674\) | −18.0000 | −0.693334 | ||||||||
\(675\) | −4.82843 | −0.185846 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.5858 | −0.829609 | −0.414805 | − | 0.909911i | \(-0.636150\pi\) | ||||
−0.414805 | + | 0.909911i | \(0.636150\pi\) | |||||||
\(678\) | −16.9706 | −0.651751 | ||||||||
\(679\) | 17.4142 | 0.668296 | ||||||||
\(680\) | −1.17157 | −0.0449278 | ||||||||
\(681\) | −18.8284 | −0.721507 | ||||||||
\(682\) | 13.2548 | 0.507554 | ||||||||
\(683\) | 25.8701 | 0.989890 | 0.494945 | − | 0.868924i | \(-0.335188\pi\) | ||||
0.494945 | + | 0.868924i | \(0.335188\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.68629 | 0.293678 | ||||||||
\(686\) | −18.3848 | −0.701934 | ||||||||
\(687\) | −2.58579 | −0.0986539 | ||||||||
\(688\) | 25.9411 | 0.988996 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.727922 | 0.0277115 | ||||||||
\(691\) | −25.4853 | −0.969506 | −0.484753 | − | 0.874651i | \(-0.661090\pi\) | ||||
−0.484753 | + | 0.874651i | \(0.661090\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.65685 | −0.214886 | ||||||||
\(694\) | −7.61522 | −0.289070 | ||||||||
\(695\) | 1.02944 | 0.0390488 | ||||||||
\(696\) | −13.6569 | −0.517662 | ||||||||
\(697\) | 7.65685 | 0.290024 | ||||||||
\(698\) | −8.82843 | −0.334161 | ||||||||
\(699\) | 24.3848 | 0.922317 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.4142 | −0.393339 | −0.196670 | − | 0.980470i | \(-0.563013\pi\) | ||||
−0.196670 | + | 0.980470i | \(0.563013\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.42641 | −0.0537980 | ||||||||
\(704\) | −45.2548 | −1.70561 | ||||||||
\(705\) | −4.17157 | −0.157111 | ||||||||
\(706\) | 13.7574 | 0.517765 | ||||||||
\(707\) | 4.24264 | 0.159561 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.7990 | −1.68246 | −0.841231 | − | 0.540676i | \(-0.818168\pi\) | ||||
−0.841231 | + | 0.540676i | \(0.818168\pi\) | |||||||
\(710\) | −7.65685 | −0.287357 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | 17.9411 | 0.672372 | ||||||||
\(713\) | −2.05887 | −0.0771055 | ||||||||
\(714\) | 1.41421 | 0.0529256 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.72792 | −0.251259 | ||||||||
\(718\) | −22.1421 | −0.826337 | ||||||||
\(719\) | 15.3137 | 0.571105 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(720\) | −1.65685 | −0.0617473 | ||||||||
\(721\) | −2.24264 | −0.0835203 | ||||||||
\(722\) | −20.2010 | −0.751804 | ||||||||
\(723\) | −2.58579 | −0.0961664 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.3137 | −0.865849 | ||||||||
\(726\) | 29.6985 | 1.10221 | ||||||||
\(727\) | 5.00000 | 0.185440 | 0.0927199 | − | 0.995692i | \(-0.470444\pi\) | ||||
0.0927199 | + | 0.995692i | \(0.470444\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.28427 | −0.232591 | ||||||||
\(731\) | −6.48528 | −0.239867 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.2843 | −1.52487 | −0.762435 | − | 0.647065i | \(-0.775996\pi\) | ||||
−0.762435 | + | 0.647065i | \(0.775996\pi\) | |||||||
\(734\) | −33.3137 | −1.22963 | ||||||||
\(735\) | −2.48528 | −0.0916710 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 56.5685 | 2.08373 | ||||||||
\(738\) | 10.8284 | 0.398600 | ||||||||
\(739\) | 3.37258 | 0.124062 | 0.0620312 | − | 0.998074i | \(-0.480242\pi\) | ||||
0.0620312 | + | 0.998074i | \(0.480242\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.5563 | −0.644514 | ||||||||
\(743\) | −42.2132 | −1.54865 | −0.774326 | − | 0.632787i | \(-0.781911\pi\) | ||||
−0.774326 | + | 0.632787i | \(0.781911\pi\) | |||||||
\(744\) | 4.68629 | 0.171808 | ||||||||
\(745\) | −6.65685 | −0.243888 | ||||||||
\(746\) | 20.1421 | 0.737456 | ||||||||
\(747\) | 5.41421 | 0.198096 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.41421 | −0.124753 | ||||||||
\(750\) | −5.75736 | −0.210229 | ||||||||
\(751\) | −32.2843 | −1.17807 | −0.589035 | − | 0.808108i | \(-0.700492\pi\) | ||||
−0.589035 | + | 0.808108i | \(0.700492\pi\) | |||||||
\(752\) | 40.2843 | 1.46902 | ||||||||
\(753\) | 12.5563 | 0.457579 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.213203 | 0.00775927 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.9706 | −0.435078 | −0.217539 | − | 0.976052i | \(-0.569803\pi\) | ||||
−0.217539 | + | 0.976052i | \(0.569803\pi\) | |||||||
\(758\) | 54.3848 | 1.97534 | ||||||||
\(759\) | −7.02944 | −0.255152 | ||||||||
\(760\) | 2.54416 | 0.0922862 | ||||||||
\(761\) | −3.55635 | −0.128918 | −0.0644588 | − | 0.997920i | \(-0.520532\pi\) | ||||
−0.0644588 | + | 0.997920i | \(0.520532\pi\) | |||||||
\(762\) | 28.6274 | 1.03706 | ||||||||
\(763\) | 8.48528 | 0.307188 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.414214 | 0.0149759 | ||||||||
\(766\) | 19.4558 | 0.702968 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.4853 | 1.45994 | 0.729968 | − | 0.683481i | \(-0.239535\pi\) | ||||
0.729968 | + | 0.683481i | \(0.239535\pi\) | |||||||
\(770\) | −3.31371 | −0.119418 | ||||||||
\(771\) | 20.6274 | 0.742878 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.6569 | −0.635073 | −0.317536 | − | 0.948246i | \(-0.602856\pi\) | ||||
−0.317536 | + | 0.948246i | \(0.602856\pi\) | |||||||
\(774\) | −9.17157 | −0.329665 | ||||||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | −49.2548 | −1.76815 | ||||||||
\(777\) | 0.656854 | 0.0235645 | ||||||||
\(778\) | 24.6274 | 0.882936 | ||||||||
\(779\) | −16.6274 | −0.595739 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 73.9411 | 2.64582 | ||||||||
\(782\) | 1.75736 | 0.0628430 | ||||||||
\(783\) | 4.82843 | 0.172554 | ||||||||
\(784\) | 24.0000 | 0.857143 | ||||||||
\(785\) | 4.44365 | 0.158601 | ||||||||
\(786\) | 0.585786 | 0.0208943 | ||||||||
\(787\) | −3.27208 | −0.116637 | −0.0583185 | − | 0.998298i | \(-0.518574\pi\) | ||||
−0.0583185 | + | 0.998298i | \(0.518574\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.3848 | −0.868121 | ||||||||
\(790\) | −0.585786 | −0.0208413 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 16.0000 | 0.568535 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −11.1127 | −0.394375 | ||||||||
\(795\) | −5.14214 | −0.182373 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.5858 | −1.18967 | −0.594835 | − | 0.803848i | \(-0.702783\pi\) | ||||
−0.594835 | + | 0.803848i | \(0.702783\pi\) | |||||||
\(798\) | −3.07107 | −0.108715 | ||||||||
\(799\) | −10.0711 | −0.356289 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.34315 | −0.224124 | ||||||||
\(802\) | 6.00000 | 0.211867 | ||||||||
\(803\) | 60.6863 | 2.14157 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.514719 | 0.0181414 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.4853 | −0.509906 | ||||||||
\(808\) | −12.0000 | −0.422159 | ||||||||
\(809\) | −3.65685 | −0.128568 | −0.0642841 | − | 0.997932i | \(-0.520476\pi\) | ||||
−0.0642841 | + | 0.997932i | \(0.520476\pi\) | |||||||
\(810\) | 0.585786 | 0.0205824 | ||||||||
\(811\) | 2.72792 | 0.0957903 | 0.0478951 | − | 0.998852i | \(-0.484749\pi\) | ||||
0.0478951 | + | 0.998852i | \(0.484749\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.7279 | 0.797103 | ||||||||
\(814\) | −5.25483 | −0.184182 | ||||||||
\(815\) | −1.55635 | −0.0545165 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | 14.0833 | 0.492711 | ||||||||
\(818\) | 25.8579 | 0.904099 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.1127 | −1.50464 | −0.752322 | − | 0.658796i | \(-0.771066\pi\) | ||||
−0.752322 | + | 0.658796i | \(0.771066\pi\) | |||||||
\(822\) | 26.2426 | 0.915317 | ||||||||
\(823\) | −31.4853 | −1.09751 | −0.548754 | − | 0.835984i | \(-0.684898\pi\) | ||||
−0.548754 | + | 0.835984i | \(0.684898\pi\) | |||||||
\(824\) | 6.34315 | 0.220974 | ||||||||
\(825\) | 27.3137 | 0.950941 | ||||||||
\(826\) | −5.07107 | −0.176445 | ||||||||
\(827\) | 19.7574 | 0.687031 | 0.343515 | − | 0.939147i | \(-0.388382\pi\) | ||||
0.343515 | + | 0.939147i | \(0.388382\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.3137 | −0.740256 | −0.370128 | − | 0.928981i | \(-0.620686\pi\) | ||||
−0.370128 | + | 0.928981i | \(0.620686\pi\) | |||||||
\(830\) | 3.17157 | 0.110087 | ||||||||
\(831\) | −16.9706 | −0.588702 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.00000 | −0.207888 | ||||||||
\(834\) | 3.51472 | 0.121705 | ||||||||
\(835\) | 4.17157 | 0.144363 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.65685 | −0.0572693 | ||||||||
\(838\) | 21.3137 | 0.736270 | ||||||||
\(839\) | 47.5269 | 1.64081 | 0.820406 | − | 0.571782i | \(-0.193748\pi\) | ||||
0.820406 | + | 0.571782i | \(0.193748\pi\) | |||||||
\(840\) | −1.17157 | −0.0404231 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | 16.9289 | 0.583410 | ||||||||
\(843\) | −6.58579 | −0.226827 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.38478 | −0.185242 | ||||||||
\(846\) | −14.2426 | −0.489672 | ||||||||
\(847\) | 21.0000 | 0.721569 | ||||||||
\(848\) | 49.6569 | 1.70522 | ||||||||
\(849\) | 12.0000 | 0.411839 | ||||||||
\(850\) | −6.82843 | −0.234213 | ||||||||
\(851\) | 0.816234 | 0.0279801 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0294 | 0.343401 | 0.171701 | − | 0.985149i | \(-0.445074\pi\) | ||||
0.171701 | + | 0.985149i | \(0.445074\pi\) | |||||||
\(854\) | −0.928932 | −0.0317874 | ||||||||
\(855\) | −0.899495 | −0.0307621 | ||||||||
\(856\) | 9.65685 | 0.330064 | ||||||||
\(857\) | 9.31371 | 0.318150 | 0.159075 | − | 0.987266i | \(-0.449149\pi\) | ||||
0.159075 | + | 0.987266i | \(0.449149\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.4558 | −0.732064 | −0.366032 | − | 0.930602i | \(-0.619284\pi\) | ||||
−0.366032 | + | 0.930602i | \(0.619284\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.65685 | 0.260945 | ||||||||
\(862\) | −56.1838 | −1.91363 | ||||||||
\(863\) | −30.6274 | −1.04257 | −0.521285 | − | 0.853383i | \(-0.674547\pi\) | ||||
−0.521285 | + | 0.853383i | \(0.674547\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.10051 | 0.0714193 | ||||||||
\(866\) | −36.2843 | −1.23299 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.65685 | 0.191896 | ||||||||
\(870\) | 2.82843 | 0.0958927 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −24.0000 | −0.812743 | ||||||||
\(873\) | 17.4142 | 0.589382 | ||||||||
\(874\) | −3.81623 | −0.129086 | ||||||||
\(875\) | −4.07107 | −0.137627 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.7279 | −1.44282 | −0.721410 | − | 0.692509i | \(-0.756506\pi\) | ||||
−0.721410 | + | 0.692509i | \(0.756506\pi\) | |||||||
\(878\) | 29.5980 | 0.998883 | ||||||||
\(879\) | 23.8701 | 0.805117 | ||||||||
\(880\) | 9.37258 | 0.315950 | ||||||||
\(881\) | 33.9411 | 1.14351 | 0.571753 | − | 0.820426i | \(-0.306264\pi\) | ||||
0.571753 | + | 0.820426i | \(0.306264\pi\) | |||||||
\(882\) | −8.48528 | −0.285714 | ||||||||
\(883\) | −25.0294 | −0.842308 | −0.421154 | − | 0.906989i | \(-0.638375\pi\) | ||||
−0.421154 | + | 0.906989i | \(0.638375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.48528 | −0.0499272 | ||||||||
\(886\) | −45.8406 | −1.54005 | ||||||||
\(887\) | 24.4142 | 0.819749 | 0.409875 | − | 0.912142i | \(-0.365572\pi\) | ||||
0.409875 | + | 0.912142i | \(0.365572\pi\) | |||||||
\(888\) | −1.85786 | −0.0623458 | ||||||||
\(889\) | 20.2426 | 0.678916 | ||||||||
\(890\) | −3.71573 | −0.124552 | ||||||||
\(891\) | −5.65685 | −0.189512 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.8701 | 0.731854 | ||||||||
\(894\) | −22.7279 | −0.760135 | ||||||||
\(895\) | −4.24264 | −0.141816 | ||||||||
\(896\) | 11.3137 | 0.377964 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.4853 | −0.683603 | ||||||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.4142 | −0.413577 | ||||||||
\(902\) | −61.2548 | −2.03956 | ||||||||
\(903\) | −6.48528 | −0.215817 | ||||||||
\(904\) | 33.9411 | 1.12887 | ||||||||
\(905\) | 0.242641 | 0.00806565 | ||||||||
\(906\) | 0.727922 | 0.0241836 | ||||||||
\(907\) | −22.1005 | −0.733835 | −0.366918 | − | 0.930253i | \(-0.619587\pi\) | ||||
−0.366918 | + | 0.930253i | \(0.619587\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.24264 | 0.140720 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.3137 | −1.10373 | −0.551866 | − | 0.833933i | \(-0.686084\pi\) | ||||
−0.551866 | + | 0.833933i | \(0.686084\pi\) | |||||||
\(912\) | 8.68629 | 0.287632 | ||||||||
\(913\) | −30.6274 | −1.01362 | ||||||||
\(914\) | 23.2721 | 0.769772 | ||||||||
\(915\) | −0.272078 | −0.00899462 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.414214 | 0.0136785 | ||||||||
\(918\) | 1.41421 | 0.0466760 | ||||||||
\(919\) | 6.97056 | 0.229938 | 0.114969 | − | 0.993369i | \(-0.463323\pi\) | ||||
0.114969 | + | 0.993369i | \(0.463323\pi\) | |||||||
\(920\) | −1.45584 | −0.0479978 | ||||||||
\(921\) | 29.5563 | 0.973915 | ||||||||
\(922\) | 44.9706 | 1.48103 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.17157 | −0.104281 | ||||||||
\(926\) | 14.4853 | 0.476016 | ||||||||
\(927\) | −2.24264 | −0.0736580 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.9289 | −0.949127 | −0.474564 | − | 0.880221i | \(-0.657394\pi\) | ||||
−0.474564 | + | 0.880221i | \(0.657394\pi\) | |||||||
\(930\) | −0.970563 | −0.0318260 | ||||||||
\(931\) | 13.0294 | 0.427023 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.7990 | −0.451759 | ||||||||
\(934\) | −19.0294 | −0.622662 | ||||||||
\(935\) | −2.34315 | −0.0766291 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.2721 | 0.760266 | 0.380133 | − | 0.924932i | \(-0.375878\pi\) | ||||
0.380133 | + | 0.924932i | \(0.375878\pi\) | |||||||
\(938\) | −14.1421 | −0.461757 | ||||||||
\(939\) | −4.68629 | −0.152931 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.4975 | 1.64617 | 0.823085 | − | 0.567918i | \(-0.192251\pi\) | ||||
0.823085 | + | 0.567918i | \(0.192251\pi\) | |||||||
\(942\) | 15.1716 | 0.494317 | ||||||||
\(943\) | 9.51472 | 0.309842 | ||||||||
\(944\) | 14.3431 | 0.466830 | ||||||||
\(945\) | 0.414214 | 0.0134744 | ||||||||
\(946\) | 51.8823 | 1.68684 | ||||||||
\(947\) | 6.68629 | 0.217275 | 0.108638 | − | 0.994081i | \(-0.465351\pi\) | ||||
0.108638 | + | 0.994081i | \(0.465351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 14.8284 | 0.481098 | ||||||||
\(951\) | −27.7279 | −0.899139 | ||||||||
\(952\) | −2.82843 | −0.0916698 | ||||||||
\(953\) | 12.3431 | 0.399834 | 0.199917 | − | 0.979813i | \(-0.435933\pi\) | ||||
0.199917 | + | 0.979813i | \(0.435933\pi\) | |||||||
\(954\) | −17.5563 | −0.568408 | ||||||||
\(955\) | −8.11270 | −0.262521 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −27.3137 | −0.882927 | ||||||||
\(958\) | 49.3553 | 1.59460 | ||||||||
\(959\) | 18.5563 | 0.599216 | ||||||||
\(960\) | 3.31371 | 0.106949 | ||||||||
\(961\) | −28.2548 | −0.911446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.41421 | −0.110021 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.41421 | 0.206481 | ||||||||
\(966\) | 1.75736 | 0.0565421 | ||||||||
\(967\) | −34.3137 | −1.10345 | −0.551727 | − | 0.834025i | \(-0.686031\pi\) | ||||
−0.551727 | + | 0.834025i | \(0.686031\pi\) | |||||||
\(968\) | −59.3970 | −1.90909 | ||||||||
\(969\) | −2.17157 | −0.0697610 | ||||||||
\(970\) | 10.2010 | 0.327535 | ||||||||
\(971\) | −48.2843 | −1.54952 | −0.774758 | − | 0.632258i | \(-0.782128\pi\) | ||||
−0.774758 | + | 0.632258i | \(0.782128\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.48528 | 0.0796745 | ||||||||
\(974\) | 58.2843 | 1.86755 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.62742 | 0.0841016 | ||||||||
\(977\) | −28.4142 | −0.909051 | −0.454526 | − | 0.890734i | \(-0.650191\pi\) | ||||
−0.454526 | + | 0.890734i | \(0.650191\pi\) | |||||||
\(978\) | −5.31371 | −0.169914 | ||||||||
\(979\) | 35.8823 | 1.14680 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.48528 | 0.270914 | ||||||||
\(982\) | −16.6863 | −0.532481 | ||||||||
\(983\) | 11.2721 | 0.359523 | 0.179762 | − | 0.983710i | \(-0.442467\pi\) | ||||
0.179762 | + | 0.983710i | \(0.442467\pi\) | |||||||
\(984\) | −21.6569 | −0.690395 | ||||||||
\(985\) | 1.45584 | 0.0463871 | ||||||||
\(986\) | 6.82843 | 0.217461 | ||||||||
\(987\) | −10.0711 | −0.320566 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.05887 | −0.256257 | ||||||||
\(990\) | −3.31371 | −0.105317 | ||||||||
\(991\) | −25.4853 | −0.809567 | −0.404783 | − | 0.914413i | \(-0.632653\pi\) | ||||
−0.404783 | + | 0.914413i | \(0.632653\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.7574 | −0.436577 | ||||||||
\(994\) | −18.4853 | −0.586318 | ||||||||
\(995\) | −0.757359 | −0.0240099 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.4853 | 1.34552 | 0.672761 | − | 0.739860i | \(-0.265108\pi\) | ||||
0.672761 | + | 0.739860i | \(0.265108\pi\) | |||||||
\(998\) | −39.5147 | −1.25082 | ||||||||
\(999\) | 0.656854 | 0.0207819 |
(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 | 4029.2.a.c.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |