Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, 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("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.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: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 690) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-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 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 4.34017 | 1.64043 | 0.820216 | − | 0.572055i | \(-0.193853\pi\) | ||||
0.820216 | + | 0.572055i | \(0.193853\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.07838 | −0.325143 | −0.162572 | − | 0.986697i | \(-0.551979\pi\) | ||||
−0.162572 | + | 0.986697i | \(0.551979\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.34017 | −0.649047 | −0.324524 | − | 0.945878i | \(-0.605204\pi\) | ||||
−0.324524 | + | 0.945878i | \(0.605204\pi\) | |||||||
\(14\) | 4.34017 | 1.15996 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.921622 | 0.223526 | 0.111763 | − | 0.993735i | \(-0.464350\pi\) | ||||
0.111763 | + | 0.993735i | \(0.464350\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.34017 | 0.536873 | 0.268436 | − | 0.963297i | \(-0.413493\pi\) | ||||
0.268436 | + | 0.963297i | \(0.413493\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.34017 | −0.947103 | ||||||||
\(22\) | −1.07838 | −0.229911 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.34017 | −0.458946 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.34017 | 0.820216 | ||||||||
\(29\) | 10.4969 | 1.94923 | 0.974615 | − | 0.223886i | \(-0.0718743\pi\) | ||||
0.974615 | + | 0.223886i | \(0.0718743\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.07838 | 0.187721 | ||||||||
\(34\) | 0.921622 | 0.158057 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.58145 | 0.424388 | 0.212194 | − | 0.977228i | \(-0.431939\pi\) | ||||
0.212194 | + | 0.977228i | \(0.431939\pi\) | |||||||
\(38\) | 2.34017 | 0.379626 | ||||||||
\(39\) | 2.34017 | 0.374728 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.156755 | 0.0244811 | 0.0122405 | − | 0.999925i | \(-0.496104\pi\) | ||||
0.0122405 | + | 0.999925i | \(0.496104\pi\) | |||||||
\(42\) | −4.34017 | −0.669703 | ||||||||
\(43\) | 0.738205 | 0.112575 | 0.0562876 | − | 0.998415i | \(-0.482074\pi\) | ||||
0.0562876 | + | 0.998415i | \(0.482074\pi\) | |||||||
\(44\) | −1.07838 | −0.162572 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 6.83710 | 0.997294 | 0.498647 | − | 0.866805i | \(-0.333830\pi\) | ||||
0.498647 | + | 0.866805i | \(0.333830\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 11.8371 | 1.69101 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.921622 | −0.129053 | ||||||||
\(52\) | −2.34017 | −0.324524 | ||||||||
\(53\) | −0.340173 | −0.0467264 | −0.0233632 | − | 0.999727i | \(-0.507437\pi\) | ||||
−0.0233632 | + | 0.999727i | \(0.507437\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.34017 | 0.579980 | ||||||||
\(57\) | −2.34017 | −0.309963 | ||||||||
\(58\) | 10.4969 | 1.37831 | ||||||||
\(59\) | −8.83710 | −1.15049 | −0.575246 | − | 0.817980i | \(-0.695094\pi\) | ||||
−0.575246 | + | 0.817980i | \(0.695094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.5753 | −1.48207 | −0.741033 | − | 0.671469i | \(-0.765664\pi\) | ||||
−0.741033 | + | 0.671469i | \(0.765664\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 4.34017 | 0.546810 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.07838 | 0.132739 | ||||||||
\(67\) | 2.58145 | 0.315374 | 0.157687 | − | 0.987489i | \(-0.449596\pi\) | ||||
0.157687 | + | 0.987489i | \(0.449596\pi\) | |||||||
\(68\) | 0.921622 | 0.111763 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.1773 | 1.80121 | 0.900606 | − | 0.434637i | \(-0.143123\pi\) | ||||
0.900606 | + | 0.434637i | \(0.143123\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −4.68035 | −0.547793 | −0.273897 | − | 0.961759i | \(-0.588313\pi\) | ||||
−0.273897 | + | 0.961759i | \(0.588313\pi\) | |||||||
\(74\) | 2.58145 | 0.300087 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.34017 | 0.268436 | ||||||||
\(77\) | −4.68035 | −0.533375 | ||||||||
\(78\) | 2.34017 | 0.264972 | ||||||||
\(79\) | −11.9155 | −1.34060 | −0.670298 | − | 0.742092i | \(-0.733834\pi\) | ||||
−0.670298 | + | 0.742092i | \(0.733834\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.156755 | 0.0173107 | ||||||||
\(83\) | 11.4186 | 1.25335 | 0.626674 | − | 0.779281i | \(-0.284416\pi\) | ||||
0.626674 | + | 0.779281i | \(0.284416\pi\) | |||||||
\(84\) | −4.34017 | −0.473552 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.738205 | 0.0796027 | ||||||||
\(87\) | −10.4969 | −1.12539 | ||||||||
\(88\) | −1.07838 | −0.114955 | ||||||||
\(89\) | −4.68035 | −0.496116 | −0.248058 | − | 0.968745i | \(-0.579792\pi\) | ||||
−0.248058 | + | 0.968745i | \(0.579792\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.1568 | −1.06472 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 6.83710 | 0.705193 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 9.02052 | 0.915895 | 0.457947 | − | 0.888979i | \(-0.348585\pi\) | ||||
0.457947 | + | 0.888979i | \(0.348585\pi\) | |||||||
\(98\) | 11.8371 | 1.19573 | ||||||||
\(99\) | −1.07838 | −0.108381 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50307 | 0.149561 | 0.0747806 | − | 0.997200i | \(-0.476174\pi\) | ||||
0.0747806 | + | 0.997200i | \(0.476174\pi\) | |||||||
\(102\) | −0.921622 | −0.0912542 | ||||||||
\(103\) | −2.49693 | −0.246030 | −0.123015 | − | 0.992405i | \(-0.539256\pi\) | ||||
−0.123015 | + | 0.992405i | \(0.539256\pi\) | |||||||
\(104\) | −2.34017 | −0.229473 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.340173 | −0.0330405 | ||||||||
\(107\) | 9.57531 | 0.925680 | 0.462840 | − | 0.886442i | \(-0.346830\pi\) | ||||
0.462840 | + | 0.886442i | \(0.346830\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −9.78539 | −0.937270 | −0.468635 | − | 0.883392i | \(-0.655254\pi\) | ||||
−0.468635 | + | 0.883392i | \(0.655254\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.58145 | −0.245020 | ||||||||
\(112\) | 4.34017 | 0.410108 | ||||||||
\(113\) | 8.92162 | 0.839276 | 0.419638 | − | 0.907692i | \(-0.362157\pi\) | ||||
0.419638 | + | 0.907692i | \(0.362157\pi\) | |||||||
\(114\) | −2.34017 | −0.219177 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.4969 | 0.974615 | ||||||||
\(117\) | −2.34017 | −0.216349 | ||||||||
\(118\) | −8.83710 | −0.813521 | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.83710 | −0.894282 | ||||||||
\(122\) | −11.5753 | −1.04798 | ||||||||
\(123\) | −0.156755 | −0.0141342 | ||||||||
\(124\) | −4.00000 | −0.359211 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.34017 | 0.386653 | ||||||||
\(127\) | 17.1773 | 1.52424 | 0.762118 | − | 0.647438i | \(-0.224159\pi\) | ||||
0.762118 | + | 0.647438i | \(0.224159\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.738205 | −0.0649953 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.68035 | −0.583665 | −0.291832 | − | 0.956470i | \(-0.594265\pi\) | ||||
−0.291832 | + | 0.956470i | \(0.594265\pi\) | |||||||
\(132\) | 1.07838 | 0.0938607 | ||||||||
\(133\) | 10.1568 | 0.880702 | ||||||||
\(134\) | 2.58145 | 0.223003 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.921622 | 0.0790285 | ||||||||
\(137\) | 22.2823 | 1.90371 | 0.951853 | − | 0.306554i | \(-0.0991760\pi\) | ||||
0.951853 | + | 0.306554i | \(0.0991760\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −10.5236 | −0.892599 | −0.446300 | − | 0.894884i | \(-0.647258\pi\) | ||||
−0.446300 | + | 0.894884i | \(0.647258\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.83710 | −0.575788 | ||||||||
\(142\) | 15.1773 | 1.27365 | ||||||||
\(143\) | 2.52359 | 0.211033 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.68035 | −0.387348 | ||||||||
\(147\) | −11.8371 | −0.976308 | ||||||||
\(148\) | 2.58145 | 0.212194 | ||||||||
\(149\) | 6.92162 | 0.567041 | 0.283521 | − | 0.958966i | \(-0.408498\pi\) | ||||
0.283521 | + | 0.958966i | \(0.408498\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.15676 | 0.501030 | 0.250515 | − | 0.968113i | \(-0.419400\pi\) | ||||
0.250515 | + | 0.968113i | \(0.419400\pi\) | |||||||
\(152\) | 2.34017 | 0.189813 | ||||||||
\(153\) | 0.921622 | 0.0745087 | ||||||||
\(154\) | −4.68035 | −0.377153 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.34017 | 0.187364 | ||||||||
\(157\) | 2.89496 | 0.231043 | 0.115521 | − | 0.993305i | \(-0.463146\pi\) | ||||
0.115521 | + | 0.993305i | \(0.463146\pi\) | |||||||
\(158\) | −11.9155 | −0.947945 | ||||||||
\(159\) | 0.340173 | 0.0269775 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.34017 | 0.342054 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 6.52359 | 0.510967 | 0.255484 | − | 0.966813i | \(-0.417765\pi\) | ||||
0.255484 | + | 0.966813i | \(0.417765\pi\) | |||||||
\(164\) | 0.156755 | 0.0122405 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.4186 | 0.886251 | ||||||||
\(167\) | 5.47641 | 0.423777 | 0.211889 | − | 0.977294i | \(-0.432039\pi\) | ||||
0.211889 | + | 0.977294i | \(0.432039\pi\) | |||||||
\(168\) | −4.34017 | −0.334852 | ||||||||
\(169\) | −7.52359 | −0.578738 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.34017 | 0.178958 | ||||||||
\(172\) | 0.738205 | 0.0562876 | ||||||||
\(173\) | −15.6742 | −1.19169 | −0.595844 | − | 0.803100i | \(-0.703182\pi\) | ||||
−0.595844 | + | 0.803100i | \(0.703182\pi\) | |||||||
\(174\) | −10.4969 | −0.795770 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.07838 | −0.0812858 | ||||||||
\(177\) | 8.83710 | 0.664237 | ||||||||
\(178\) | −4.68035 | −0.350807 | ||||||||
\(179\) | 15.3607 | 1.14811 | 0.574056 | − | 0.818816i | \(-0.305369\pi\) | ||||
0.574056 | + | 0.818816i | \(0.305369\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.6163 | 1.60673 | 0.803365 | − | 0.595487i | \(-0.203041\pi\) | ||||
0.803365 | + | 0.595487i | \(0.203041\pi\) | |||||||
\(182\) | −10.1568 | −0.752869 | ||||||||
\(183\) | 11.5753 | 0.855671 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | −0.993857 | −0.0726780 | ||||||||
\(188\) | 6.83710 | 0.498647 | ||||||||
\(189\) | −4.34017 | −0.315701 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.36683 | 0.315973 | 0.157987 | − | 0.987441i | \(-0.449500\pi\) | ||||
0.157987 | + | 0.987441i | \(0.449500\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −8.68035 | −0.624825 | −0.312412 | − | 0.949947i | \(-0.601137\pi\) | ||||
−0.312412 | + | 0.949947i | \(0.601137\pi\) | |||||||
\(194\) | 9.02052 | 0.647636 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.8371 | 0.845507 | ||||||||
\(197\) | −22.6803 | −1.61591 | −0.807954 | − | 0.589246i | \(-0.799425\pi\) | ||||
−0.807954 | + | 0.589246i | \(0.799425\pi\) | |||||||
\(198\) | −1.07838 | −0.0766370 | ||||||||
\(199\) | −5.44521 | −0.386001 | −0.193000 | − | 0.981199i | \(-0.561822\pi\) | ||||
−0.193000 | + | 0.981199i | \(0.561822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.58145 | −0.182081 | ||||||||
\(202\) | 1.50307 | 0.105756 | ||||||||
\(203\) | 45.5585 | 3.19758 | ||||||||
\(204\) | −0.921622 | −0.0645265 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.49693 | −0.173969 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −2.34017 | −0.162262 | ||||||||
\(209\) | −2.52359 | −0.174560 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0410 | −1.51737 | −0.758684 | − | 0.651459i | \(-0.774157\pi\) | ||||
−0.758684 | + | 0.651459i | \(0.774157\pi\) | |||||||
\(212\) | −0.340173 | −0.0233632 | ||||||||
\(213\) | −15.1773 | −1.03993 | ||||||||
\(214\) | 9.57531 | 0.654554 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −17.3607 | −1.17852 | ||||||||
\(218\) | −9.78539 | −0.662750 | ||||||||
\(219\) | 4.68035 | 0.316268 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.15676 | −0.145079 | ||||||||
\(222\) | −2.58145 | −0.173256 | ||||||||
\(223\) | 21.1773 | 1.41814 | 0.709068 | − | 0.705141i | \(-0.249116\pi\) | ||||
0.709068 | + | 0.705141i | \(0.249116\pi\) | |||||||
\(224\) | 4.34017 | 0.289990 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.92162 | 0.593457 | ||||||||
\(227\) | −11.7854 | −0.782224 | −0.391112 | − | 0.920343i | \(-0.627909\pi\) | ||||
−0.391112 | + | 0.920343i | \(0.627909\pi\) | |||||||
\(228\) | −2.34017 | −0.154982 | ||||||||
\(229\) | 1.78539 | 0.117982 | 0.0589908 | − | 0.998259i | \(-0.481212\pi\) | ||||
0.0589908 | + | 0.998259i | \(0.481212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.68035 | 0.307944 | ||||||||
\(232\) | 10.4969 | 0.689157 | ||||||||
\(233\) | 18.3135 | 1.19976 | 0.599879 | − | 0.800091i | \(-0.295215\pi\) | ||||
0.599879 | + | 0.800091i | \(0.295215\pi\) | |||||||
\(234\) | −2.34017 | −0.152982 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.83710 | −0.575246 | ||||||||
\(237\) | 11.9155 | 0.773994 | ||||||||
\(238\) | 4.00000 | 0.259281 | ||||||||
\(239\) | −5.33403 | −0.345030 | −0.172515 | − | 0.985007i | \(-0.555189\pi\) | ||||
−0.172515 | + | 0.985007i | \(0.555189\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.1978 | 1.68755 | 0.843774 | − | 0.536698i | \(-0.180329\pi\) | ||||
0.843774 | + | 0.536698i | \(0.180329\pi\) | |||||||
\(242\) | −9.83710 | −0.632353 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.5753 | −0.741033 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.156755 | −0.00999437 | ||||||||
\(247\) | −5.47641 | −0.348456 | ||||||||
\(248\) | −4.00000 | −0.254000 | ||||||||
\(249\) | −11.4186 | −0.723621 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.4329 | 1.73155 | 0.865775 | − | 0.500433i | \(-0.166826\pi\) | ||||
0.865775 | + | 0.500433i | \(0.166826\pi\) | |||||||
\(252\) | 4.34017 | 0.273405 | ||||||||
\(253\) | −1.07838 | −0.0677970 | ||||||||
\(254\) | 17.1773 | 1.07780 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.3135 | −0.643339 | −0.321670 | − | 0.946852i | \(-0.604244\pi\) | ||||
−0.321670 | + | 0.946852i | \(0.604244\pi\) | |||||||
\(258\) | −0.738205 | −0.0459586 | ||||||||
\(259\) | 11.2039 | 0.696179 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.4969 | 0.649744 | ||||||||
\(262\) | −6.68035 | −0.412713 | ||||||||
\(263\) | −20.9939 | −1.29454 | −0.647268 | − | 0.762262i | \(-0.724089\pi\) | ||||
−0.647268 | + | 0.762262i | \(0.724089\pi\) | |||||||
\(264\) | 1.07838 | 0.0663696 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.1568 | 0.622751 | ||||||||
\(267\) | 4.68035 | 0.286433 | ||||||||
\(268\) | 2.58145 | 0.157687 | ||||||||
\(269\) | 25.3874 | 1.54789 | 0.773947 | − | 0.633250i | \(-0.218280\pi\) | ||||
0.773947 | + | 0.633250i | \(0.218280\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.5646 | −1.97816 | −0.989080 | − | 0.147379i | \(-0.952916\pi\) | ||||
−0.989080 | + | 0.147379i | \(0.952916\pi\) | |||||||
\(272\) | 0.921622 | 0.0558816 | ||||||||
\(273\) | 10.1568 | 0.614715 | ||||||||
\(274\) | 22.2823 | 1.34612 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 15.7009 | 0.943374 | 0.471687 | − | 0.881766i | \(-0.343645\pi\) | ||||
0.471687 | + | 0.881766i | \(0.343645\pi\) | |||||||
\(278\) | −10.5236 | −0.631163 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.36069 | −0.558412 | −0.279206 | − | 0.960231i | \(-0.590071\pi\) | ||||
−0.279206 | + | 0.960231i | \(0.590071\pi\) | |||||||
\(282\) | −6.83710 | −0.407143 | ||||||||
\(283\) | −17.4186 | −1.03543 | −0.517713 | − | 0.855555i | \(-0.673216\pi\) | ||||
−0.517713 | + | 0.855555i | \(0.673216\pi\) | |||||||
\(284\) | 15.1773 | 0.900606 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.52359 | 0.149223 | ||||||||
\(287\) | 0.680346 | 0.0401596 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.1506 | −0.950036 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.02052 | −0.528792 | ||||||||
\(292\) | −4.68035 | −0.273897 | ||||||||
\(293\) | −16.3402 | −0.954603 | −0.477302 | − | 0.878740i | \(-0.658385\pi\) | ||||
−0.477302 | + | 0.878740i | \(0.658385\pi\) | |||||||
\(294\) | −11.8371 | −0.690354 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.58145 | 0.150044 | ||||||||
\(297\) | 1.07838 | 0.0625738 | ||||||||
\(298\) | 6.92162 | 0.400959 | ||||||||
\(299\) | −2.34017 | −0.135336 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.20394 | 0.184672 | ||||||||
\(302\) | 6.15676 | 0.354281 | ||||||||
\(303\) | −1.50307 | −0.0863492 | ||||||||
\(304\) | 2.34017 | 0.134218 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.921622 | 0.0526856 | ||||||||
\(307\) | −3.20394 | −0.182858 | −0.0914292 | − | 0.995812i | \(-0.529144\pi\) | ||||
−0.0914292 | + | 0.995812i | \(0.529144\pi\) | |||||||
\(308\) | −4.68035 | −0.266687 | ||||||||
\(309\) | 2.49693 | 0.142045 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.6537 | 0.717525 | 0.358762 | − | 0.933429i | \(-0.383199\pi\) | ||||
0.358762 | + | 0.933429i | \(0.383199\pi\) | |||||||
\(312\) | 2.34017 | 0.132486 | ||||||||
\(313\) | 33.2183 | 1.87761 | 0.938805 | − | 0.344449i | \(-0.111934\pi\) | ||||
0.938805 | + | 0.344449i | \(0.111934\pi\) | |||||||
\(314\) | 2.89496 | 0.163372 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.9155 | −0.670298 | ||||||||
\(317\) | −6.99386 | −0.392814 | −0.196407 | − | 0.980522i | \(-0.562927\pi\) | ||||
−0.196407 | + | 0.980522i | \(0.562927\pi\) | |||||||
\(318\) | 0.340173 | 0.0190760 | ||||||||
\(319\) | −11.3197 | −0.633779 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.57531 | −0.534441 | ||||||||
\(322\) | 4.34017 | 0.241868 | ||||||||
\(323\) | 2.15676 | 0.120005 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.52359 | 0.361308 | ||||||||
\(327\) | 9.78539 | 0.541133 | ||||||||
\(328\) | 0.156755 | 0.00865537 | ||||||||
\(329\) | 29.6742 | 1.63599 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.7275 | −1.63397 | −0.816986 | − | 0.576657i | \(-0.804357\pi\) | ||||
−0.816986 | + | 0.576657i | \(0.804357\pi\) | |||||||
\(332\) | 11.4186 | 0.626674 | ||||||||
\(333\) | 2.58145 | 0.141463 | ||||||||
\(334\) | 5.47641 | 0.299656 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.34017 | −0.236776 | ||||||||
\(337\) | 28.3402 | 1.54379 | 0.771894 | − | 0.635751i | \(-0.219310\pi\) | ||||
0.771894 | + | 0.635751i | \(0.219310\pi\) | |||||||
\(338\) | −7.52359 | −0.409229 | ||||||||
\(339\) | −8.92162 | −0.484556 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.31351 | 0.233590 | ||||||||
\(342\) | 2.34017 | 0.126542 | ||||||||
\(343\) | 20.9939 | 1.13356 | ||||||||
\(344\) | 0.738205 | 0.0398013 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.6742 | −0.842650 | ||||||||
\(347\) | −22.5236 | −1.20913 | −0.604565 | − | 0.796556i | \(-0.706653\pi\) | ||||
−0.604565 | + | 0.796556i | \(0.706653\pi\) | |||||||
\(348\) | −10.4969 | −0.562694 | ||||||||
\(349\) | 15.6742 | 0.839021 | 0.419510 | − | 0.907751i | \(-0.362202\pi\) | ||||
0.419510 | + | 0.907751i | \(0.362202\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.34017 | 0.124909 | ||||||||
\(352\) | −1.07838 | −0.0574777 | ||||||||
\(353\) | 26.3135 | 1.40053 | 0.700263 | − | 0.713885i | \(-0.253066\pi\) | ||||
0.700263 | + | 0.713885i | \(0.253066\pi\) | |||||||
\(354\) | 8.83710 | 0.469687 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.68035 | −0.248058 | ||||||||
\(357\) | −4.00000 | −0.211702 | ||||||||
\(358\) | 15.3607 | 0.811838 | ||||||||
\(359\) | −0.796064 | −0.0420146 | −0.0210073 | − | 0.999779i | \(-0.506687\pi\) | ||||
−0.0210073 | + | 0.999779i | \(0.506687\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.5236 | −0.711768 | ||||||||
\(362\) | 21.6163 | 1.13613 | ||||||||
\(363\) | 9.83710 | 0.516314 | ||||||||
\(364\) | −10.1568 | −0.532359 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.5753 | 0.605051 | ||||||||
\(367\) | 13.7009 | 0.715179 | 0.357590 | − | 0.933879i | \(-0.383599\pi\) | ||||
0.357590 | + | 0.933879i | \(0.383599\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0.156755 | 0.00816036 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.47641 | −0.0766514 | ||||||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | 4.25565 | 0.220349 | 0.110175 | − | 0.993912i | \(-0.464859\pi\) | ||||
0.110175 | + | 0.993912i | \(0.464859\pi\) | |||||||
\(374\) | −0.993857 | −0.0513911 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.83710 | 0.352597 | ||||||||
\(377\) | −24.5646 | −1.26514 | ||||||||
\(378\) | −4.34017 | −0.223234 | ||||||||
\(379\) | −30.6537 | −1.57457 | −0.787287 | − | 0.616587i | \(-0.788515\pi\) | ||||
−0.787287 | + | 0.616587i | \(0.788515\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.1773 | −0.880018 | ||||||||
\(382\) | 4.36683 | 0.223427 | ||||||||
\(383\) | −20.8781 | −1.06682 | −0.533412 | − | 0.845856i | \(-0.679090\pi\) | ||||
−0.533412 | + | 0.845856i | \(0.679090\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.68035 | −0.441818 | ||||||||
\(387\) | 0.738205 | 0.0375251 | ||||||||
\(388\) | 9.02052 | 0.457947 | ||||||||
\(389\) | −16.9627 | −0.860041 | −0.430021 | − | 0.902819i | \(-0.641494\pi\) | ||||
−0.430021 | + | 0.902819i | \(0.641494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.921622 | 0.0466084 | ||||||||
\(392\) | 11.8371 | 0.597864 | ||||||||
\(393\) | 6.68035 | 0.336979 | ||||||||
\(394\) | −22.6803 | −1.14262 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.07838 | −0.0541905 | ||||||||
\(397\) | −16.4969 | −0.827957 | −0.413979 | − | 0.910287i | \(-0.635861\pi\) | ||||
−0.413979 | + | 0.910287i | \(0.635861\pi\) | |||||||
\(398\) | −5.44521 | −0.272944 | ||||||||
\(399\) | −10.1568 | −0.508474 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.2039 | −1.75800 | −0.879000 | − | 0.476821i | \(-0.841789\pi\) | ||||
−0.879000 | + | 0.476821i | \(0.841789\pi\) | |||||||
\(402\) | −2.58145 | −0.128751 | ||||||||
\(403\) | 9.36069 | 0.466289 | ||||||||
\(404\) | 1.50307 | 0.0747806 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 45.5585 | 2.26103 | ||||||||
\(407\) | −2.78378 | −0.137987 | ||||||||
\(408\) | −0.921622 | −0.0456271 | ||||||||
\(409\) | 11.3607 | 0.561750 | 0.280875 | − | 0.959744i | \(-0.409375\pi\) | ||||
0.280875 | + | 0.959744i | \(0.409375\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.2823 | −1.09911 | ||||||||
\(412\) | −2.49693 | −0.123015 | ||||||||
\(413\) | −38.3545 | −1.88730 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.34017 | −0.114736 | ||||||||
\(417\) | 10.5236 | 0.515342 | ||||||||
\(418\) | −2.52359 | −0.123433 | ||||||||
\(419\) | −18.1256 | −0.885491 | −0.442746 | − | 0.896647i | \(-0.645996\pi\) | ||||
−0.442746 | + | 0.896647i | \(0.645996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.58145 | 0.125812 | 0.0629061 | − | 0.998019i | \(-0.479963\pi\) | ||||
0.0629061 | + | 0.998019i | \(0.479963\pi\) | |||||||
\(422\) | −22.0410 | −1.07294 | ||||||||
\(423\) | 6.83710 | 0.332431 | ||||||||
\(424\) | −0.340173 | −0.0165203 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −15.1773 | −0.735341 | ||||||||
\(427\) | −50.2388 | −2.43123 | ||||||||
\(428\) | 9.57531 | 0.462840 | ||||||||
\(429\) | −2.52359 | −0.121840 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.9877 | −1.63713 | −0.818565 | − | 0.574414i | \(-0.805230\pi\) | ||||
−0.818565 | + | 0.574414i | \(0.805230\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −8.28685 | −0.398241 | −0.199120 | − | 0.979975i | \(-0.563808\pi\) | ||||
−0.199120 | + | 0.979975i | \(0.563808\pi\) | |||||||
\(434\) | −17.3607 | −0.833340 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.78539 | −0.468635 | ||||||||
\(437\) | 2.34017 | 0.111946 | ||||||||
\(438\) | 4.68035 | 0.223636 | ||||||||
\(439\) | −28.9939 | −1.38380 | −0.691901 | − | 0.721993i | \(-0.743226\pi\) | ||||
−0.691901 | + | 0.721993i | \(0.743226\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.8371 | 0.563671 | ||||||||
\(442\) | −2.15676 | −0.102586 | ||||||||
\(443\) | −3.20394 | −0.152224 | −0.0761118 | − | 0.997099i | \(-0.524251\pi\) | ||||
−0.0761118 | + | 0.997099i | \(0.524251\pi\) | |||||||
\(444\) | −2.58145 | −0.122510 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.1773 | 1.00277 | ||||||||
\(447\) | −6.92162 | −0.327381 | ||||||||
\(448\) | 4.34017 | 0.205054 | ||||||||
\(449\) | 28.1568 | 1.32880 | 0.664400 | − | 0.747377i | \(-0.268687\pi\) | ||||
0.664400 | + | 0.747377i | \(0.268687\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.169042 | −0.00795986 | ||||||||
\(452\) | 8.92162 | 0.419638 | ||||||||
\(453\) | −6.15676 | −0.289270 | ||||||||
\(454\) | −11.7854 | −0.553116 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.34017 | −0.109589 | ||||||||
\(457\) | −23.1773 | −1.08419 | −0.542094 | − | 0.840318i | \(-0.682368\pi\) | ||||
−0.542094 | + | 0.840318i | \(0.682368\pi\) | |||||||
\(458\) | 1.78539 | 0.0834256 | ||||||||
\(459\) | −0.921622 | −0.0430176 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −42.3279 | −1.97141 | −0.985703 | − | 0.168491i | \(-0.946110\pi\) | ||||
−0.985703 | + | 0.168491i | \(0.946110\pi\) | |||||||
\(462\) | 4.68035 | 0.217749 | ||||||||
\(463\) | −34.9048 | −1.62216 | −0.811082 | − | 0.584933i | \(-0.801121\pi\) | ||||
−0.811082 | + | 0.584933i | \(0.801121\pi\) | |||||||
\(464\) | 10.4969 | 0.487308 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.3135 | 0.848357 | ||||||||
\(467\) | −37.7731 | −1.74793 | −0.873965 | − | 0.485988i | \(-0.838460\pi\) | ||||
−0.873965 | + | 0.485988i | \(0.838460\pi\) | |||||||
\(468\) | −2.34017 | −0.108175 | ||||||||
\(469\) | 11.2039 | 0.517350 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.89496 | −0.133393 | ||||||||
\(472\) | −8.83710 | −0.406761 | ||||||||
\(473\) | −0.796064 | −0.0366030 | ||||||||
\(474\) | 11.9155 | 0.547296 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | −0.340173 | −0.0155755 | ||||||||
\(478\) | −5.33403 | −0.243973 | ||||||||
\(479\) | −28.1978 | −1.28839 | −0.644195 | − | 0.764861i | \(-0.722807\pi\) | ||||
−0.644195 | + | 0.764861i | \(0.722807\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.04104 | −0.275448 | ||||||||
\(482\) | 26.1978 | 1.19328 | ||||||||
\(483\) | −4.34017 | −0.197485 | ||||||||
\(484\) | −9.83710 | −0.447141 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 38.2245 | 1.73212 | 0.866058 | − | 0.499944i | \(-0.166646\pi\) | ||||
0.866058 | + | 0.499944i | \(0.166646\pi\) | |||||||
\(488\) | −11.5753 | −0.523989 | ||||||||
\(489\) | −6.52359 | −0.295007 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.3074 | 0.510294 | 0.255147 | − | 0.966902i | \(-0.417876\pi\) | ||||
0.255147 | + | 0.966902i | \(0.417876\pi\) | |||||||
\(492\) | −0.156755 | −0.00706708 | ||||||||
\(493\) | 9.67420 | 0.435704 | ||||||||
\(494\) | −5.47641 | −0.246395 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 65.8720 | 2.95476 | ||||||||
\(498\) | −11.4186 | −0.511677 | ||||||||
\(499\) | −2.47027 | −0.110584 | −0.0552922 | − | 0.998470i | \(-0.517609\pi\) | ||||
−0.0552922 | + | 0.998470i | \(0.517609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.47641 | −0.244668 | ||||||||
\(502\) | 27.4329 | 1.22439 | ||||||||
\(503\) | −20.6270 | −0.919713 | −0.459857 | − | 0.887993i | \(-0.652099\pi\) | ||||
−0.459857 | + | 0.887993i | \(0.652099\pi\) | |||||||
\(504\) | 4.34017 | 0.193327 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.07838 | −0.0479397 | ||||||||
\(507\) | 7.52359 | 0.334134 | ||||||||
\(508\) | 17.1773 | 0.762118 | ||||||||
\(509\) | −32.2245 | −1.42832 | −0.714162 | − | 0.699981i | \(-0.753192\pi\) | ||||
−0.714162 | + | 0.699981i | \(0.753192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.3135 | −0.898617 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.34017 | −0.103321 | ||||||||
\(514\) | −10.3135 | −0.454909 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.738205 | −0.0324977 | ||||||||
\(517\) | −7.37298 | −0.324263 | ||||||||
\(518\) | 11.2039 | 0.492273 | ||||||||
\(519\) | 15.6742 | 0.688021 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.51745 | −0.154102 | −0.0770511 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770511 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(522\) | 10.4969 | 0.459438 | ||||||||
\(523\) | −35.9421 | −1.57164 | −0.785820 | − | 0.618455i | \(-0.787759\pi\) | ||||
−0.785820 | + | 0.618455i | \(0.787759\pi\) | |||||||
\(524\) | −6.68035 | −0.291832 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.9939 | −0.915376 | ||||||||
\(527\) | −3.68649 | −0.160586 | ||||||||
\(528\) | 1.07838 | 0.0469304 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.83710 | −0.383498 | ||||||||
\(532\) | 10.1568 | 0.440351 | ||||||||
\(533\) | −0.366835 | −0.0158894 | ||||||||
\(534\) | 4.68035 | 0.202538 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.58145 | 0.111502 | ||||||||
\(537\) | −15.3607 | −0.662863 | ||||||||
\(538\) | 25.3874 | 1.09453 | ||||||||
\(539\) | −12.7649 | −0.549822 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7275 | 1.36407 | 0.682036 | − | 0.731318i | \(-0.261095\pi\) | ||||
0.682036 | + | 0.731318i | \(0.261095\pi\) | |||||||
\(542\) | −32.5646 | −1.39877 | ||||||||
\(543\) | −21.6163 | −0.927646 | ||||||||
\(544\) | 0.921622 | 0.0395142 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.1568 | 0.434669 | ||||||||
\(547\) | −9.84324 | −0.420867 | −0.210433 | − | 0.977608i | \(-0.567488\pi\) | ||||
−0.210433 | + | 0.977608i | \(0.567488\pi\) | |||||||
\(548\) | 22.2823 | 0.951853 | ||||||||
\(549\) | −11.5753 | −0.494022 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.5646 | 1.04649 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −51.7152 | −2.19916 | ||||||||
\(554\) | 15.7009 | 0.667066 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.5236 | −0.446300 | ||||||||
\(557\) | 26.3279 | 1.11555 | 0.557774 | − | 0.829993i | \(-0.311656\pi\) | ||||
0.557774 | + | 0.829993i | \(0.311656\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | −1.72753 | −0.0730666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.993857 | 0.0419607 | ||||||||
\(562\) | −9.36069 | −0.394857 | ||||||||
\(563\) | −30.2557 | −1.27512 | −0.637562 | − | 0.770399i | \(-0.720057\pi\) | ||||
−0.637562 | + | 0.770399i | \(0.720057\pi\) | |||||||
\(564\) | −6.83710 | −0.287894 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.4186 | −0.732156 | ||||||||
\(567\) | 4.34017 | 0.182270 | ||||||||
\(568\) | 15.1773 | 0.636824 | ||||||||
\(569\) | 33.8720 | 1.41999 | 0.709994 | − | 0.704208i | \(-0.248698\pi\) | ||||
0.709994 | + | 0.704208i | \(0.248698\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.1650 | 1.47161 | 0.735804 | − | 0.677194i | \(-0.236804\pi\) | ||||
0.735804 | + | 0.677194i | \(0.236804\pi\) | |||||||
\(572\) | 2.52359 | 0.105517 | ||||||||
\(573\) | −4.36683 | −0.182427 | ||||||||
\(574\) | 0.680346 | 0.0283971 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −4.00000 | −0.166522 | −0.0832611 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832611 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(578\) | −16.1506 | −0.671777 | ||||||||
\(579\) | 8.68035 | 0.360743 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 49.5585 | 2.05603 | ||||||||
\(582\) | −9.02052 | −0.373913 | ||||||||
\(583\) | 0.366835 | 0.0151928 | ||||||||
\(584\) | −4.68035 | −0.193674 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.3402 | −0.675006 | ||||||||
\(587\) | 9.30737 | 0.384156 | 0.192078 | − | 0.981380i | \(-0.438477\pi\) | ||||
0.192078 | + | 0.981380i | \(0.438477\pi\) | |||||||
\(588\) | −11.8371 | −0.488154 | ||||||||
\(589\) | −9.36069 | −0.385701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.6803 | 0.932945 | ||||||||
\(592\) | 2.58145 | 0.106097 | ||||||||
\(593\) | 33.0349 | 1.35658 | 0.678290 | − | 0.734794i | \(-0.262721\pi\) | ||||
0.678290 | + | 0.734794i | \(0.262721\pi\) | |||||||
\(594\) | 1.07838 | 0.0442464 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.92162 | 0.283521 | ||||||||
\(597\) | 5.44521 | 0.222858 | ||||||||
\(598\) | −2.34017 | −0.0956968 | ||||||||
\(599\) | 13.6475 | 0.557623 | 0.278812 | − | 0.960346i | \(-0.410059\pi\) | ||||
0.278812 | + | 0.960346i | \(0.410059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.68649 | 0.0687933 | 0.0343967 | − | 0.999408i | \(-0.489049\pi\) | ||||
0.0343967 | + | 0.999408i | \(0.489049\pi\) | |||||||
\(602\) | 3.20394 | 0.130583 | ||||||||
\(603\) | 2.58145 | 0.105125 | ||||||||
\(604\) | 6.15676 | 0.250515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.50307 | −0.0610581 | ||||||||
\(607\) | −47.2183 | −1.91653 | −0.958266 | − | 0.285878i | \(-0.907715\pi\) | ||||
−0.958266 | + | 0.285878i | \(0.907715\pi\) | |||||||
\(608\) | 2.34017 | 0.0949065 | ||||||||
\(609\) | −45.5585 | −1.84612 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.0000 | −0.647291 | ||||||||
\(612\) | 0.921622 | 0.0372544 | ||||||||
\(613\) | −7.45959 | −0.301290 | −0.150645 | − | 0.988588i | \(-0.548135\pi\) | ||||
−0.150645 | + | 0.988588i | \(0.548135\pi\) | |||||||
\(614\) | −3.20394 | −0.129300 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.68035 | −0.188577 | ||||||||
\(617\) | 15.8120 | 0.636569 | 0.318285 | − | 0.947995i | \(-0.396893\pi\) | ||||
0.318285 | + | 0.947995i | \(0.396893\pi\) | |||||||
\(618\) | 2.49693 | 0.100441 | ||||||||
\(619\) | −26.3402 | −1.05870 | −0.529350 | − | 0.848403i | \(-0.677564\pi\) | ||||
−0.529350 | + | 0.848403i | \(0.677564\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 12.6537 | 0.507367 | ||||||||
\(623\) | −20.3135 | −0.813844 | ||||||||
\(624\) | 2.34017 | 0.0936819 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 33.2183 | 1.32767 | ||||||||
\(627\) | 2.52359 | 0.100782 | ||||||||
\(628\) | 2.89496 | 0.115521 | ||||||||
\(629\) | 2.37912 | 0.0948618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.4391 | −0.574810 | −0.287405 | − | 0.957809i | \(-0.592793\pi\) | ||||
−0.287405 | + | 0.957809i | \(0.592793\pi\) | |||||||
\(632\) | −11.9155 | −0.473972 | ||||||||
\(633\) | 22.0410 | 0.876053 | ||||||||
\(634\) | −6.99386 | −0.277762 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.340173 | 0.0134887 | ||||||||
\(637\) | −27.7009 | −1.09755 | ||||||||
\(638\) | −11.3197 | −0.448149 | ||||||||
\(639\) | 15.1773 | 0.600404 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.78992 | −0.228688 | −0.114344 | − | 0.993441i | \(-0.536477\pi\) | ||||
−0.114344 | + | 0.993441i | \(0.536477\pi\) | |||||||
\(642\) | −9.57531 | −0.377907 | ||||||||
\(643\) | 23.4063 | 0.923053 | 0.461526 | − | 0.887126i | \(-0.347302\pi\) | ||||
0.461526 | + | 0.887126i | \(0.347302\pi\) | |||||||
\(644\) | 4.34017 | 0.171027 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.15676 | 0.0848564 | ||||||||
\(647\) | 25.9877 | 1.02168 | 0.510841 | − | 0.859675i | \(-0.329334\pi\) | ||||
0.510841 | + | 0.859675i | \(0.329334\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 9.52973 | 0.374075 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.3607 | 0.680419 | ||||||||
\(652\) | 6.52359 | 0.255484 | ||||||||
\(653\) | −0.325797 | −0.0127494 | −0.00637471 | − | 0.999980i | \(-0.502029\pi\) | ||||
−0.00637471 | + | 0.999980i | \(0.502029\pi\) | |||||||
\(654\) | 9.78539 | 0.382639 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.156755 | 0.00612027 | ||||||||
\(657\) | −4.68035 | −0.182598 | ||||||||
\(658\) | 29.6742 | 1.15682 | ||||||||
\(659\) | −3.11942 | −0.121515 | −0.0607576 | − | 0.998153i | \(-0.519352\pi\) | ||||
−0.0607576 | + | 0.998153i | \(0.519352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.1399 | 0.938935 | 0.469467 | − | 0.882950i | \(-0.344446\pi\) | ||||
0.469467 | + | 0.882950i | \(0.344446\pi\) | |||||||
\(662\) | −29.7275 | −1.15539 | ||||||||
\(663\) | 2.15676 | 0.0837614 | ||||||||
\(664\) | 11.4186 | 0.443126 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.58145 | 0.100029 | ||||||||
\(667\) | 10.4969 | 0.406443 | ||||||||
\(668\) | 5.47641 | 0.211889 | ||||||||
\(669\) | −21.1773 | −0.818761 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.4826 | 0.481884 | ||||||||
\(672\) | −4.34017 | −0.167426 | ||||||||
\(673\) | −45.6742 | −1.76061 | −0.880306 | − | 0.474407i | \(-0.842662\pi\) | ||||
−0.880306 | + | 0.474407i | \(0.842662\pi\) | |||||||
\(674\) | 28.3402 | 1.09162 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.52359 | −0.289369 | ||||||||
\(677\) | 9.38735 | 0.360785 | 0.180393 | − | 0.983595i | \(-0.442263\pi\) | ||||
0.180393 | + | 0.983595i | \(0.442263\pi\) | |||||||
\(678\) | −8.92162 | −0.342633 | ||||||||
\(679\) | 39.1506 | 1.50246 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.7854 | 0.451617 | ||||||||
\(682\) | 4.31351 | 0.165173 | ||||||||
\(683\) | 20.9939 | 0.803308 | 0.401654 | − | 0.915792i | \(-0.368436\pi\) | ||||
0.401654 | + | 0.915792i | \(0.368436\pi\) | |||||||
\(684\) | 2.34017 | 0.0894788 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.9939 | 0.801549 | ||||||||
\(687\) | −1.78539 | −0.0681167 | ||||||||
\(688\) | 0.738205 | 0.0281438 | ||||||||
\(689\) | 0.796064 | 0.0303276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.1445 | −1.67933 | −0.839667 | − | 0.543101i | \(-0.817250\pi\) | ||||
−0.839667 | + | 0.543101i | \(0.817250\pi\) | |||||||
\(692\) | −15.6742 | −0.595844 | ||||||||
\(693\) | −4.68035 | −0.177792 | ||||||||
\(694\) | −22.5236 | −0.854984 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10.4969 | −0.397885 | ||||||||
\(697\) | 0.144469 | 0.00547217 | ||||||||
\(698\) | 15.6742 | 0.593277 | ||||||||
\(699\) | −18.3135 | −0.692681 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.7998 | −1.04998 | −0.524991 | − | 0.851108i | \(-0.675931\pi\) | ||||
−0.524991 | + | 0.851108i | \(0.675931\pi\) | |||||||
\(702\) | 2.34017 | 0.0883241 | ||||||||
\(703\) | 6.04104 | 0.227842 | ||||||||
\(704\) | −1.07838 | −0.0406429 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.3135 | 0.990322 | ||||||||
\(707\) | 6.52359 | 0.245345 | ||||||||
\(708\) | 8.83710 | 0.332119 | ||||||||
\(709\) | 4.30898 | 0.161827 | 0.0809135 | − | 0.996721i | \(-0.474216\pi\) | ||||
0.0809135 | + | 0.996721i | \(0.474216\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.9155 | −0.446865 | ||||||||
\(712\) | −4.68035 | −0.175403 | ||||||||
\(713\) | −4.00000 | −0.149801 | ||||||||
\(714\) | −4.00000 | −0.149696 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.3607 | 0.574056 | ||||||||
\(717\) | 5.33403 | 0.199203 | ||||||||
\(718\) | −0.796064 | −0.0297088 | ||||||||
\(719\) | 15.9733 | 0.595705 | 0.297852 | − | 0.954612i | \(-0.403730\pi\) | ||||
0.297852 | + | 0.954612i | \(0.403730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8371 | −0.403595 | ||||||||
\(722\) | −13.5236 | −0.503296 | ||||||||
\(723\) | −26.1978 | −0.974306 | ||||||||
\(724\) | 21.6163 | 0.803365 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.83710 | 0.365089 | ||||||||
\(727\) | −0.340173 | −0.0126163 | −0.00630816 | − | 0.999980i | \(-0.502008\pi\) | ||||
−0.00630816 | + | 0.999980i | \(0.502008\pi\) | |||||||
\(728\) | −10.1568 | −0.376434 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.680346 | 0.0251635 | ||||||||
\(732\) | 11.5753 | 0.427836 | ||||||||
\(733\) | −19.2618 | −0.711451 | −0.355725 | − | 0.934591i | \(-0.615766\pi\) | ||||
−0.355725 | + | 0.934591i | \(0.615766\pi\) | |||||||
\(734\) | 13.7009 | 0.505708 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −2.78378 | −0.102542 | ||||||||
\(738\) | 0.156755 | 0.00577025 | ||||||||
\(739\) | 25.5585 | 0.940184 | 0.470092 | − | 0.882617i | \(-0.344221\pi\) | ||||
0.470092 | + | 0.882617i | \(0.344221\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.47641 | 0.201181 | ||||||||
\(742\) | −1.47641 | −0.0542007 | ||||||||
\(743\) | −36.8781 | −1.35293 | −0.676464 | − | 0.736476i | \(-0.736489\pi\) | ||||
−0.676464 | + | 0.736476i | \(0.736489\pi\) | |||||||
\(744\) | 4.00000 | 0.146647 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.25565 | 0.155810 | ||||||||
\(747\) | 11.4186 | 0.417783 | ||||||||
\(748\) | −0.993857 | −0.0363390 | ||||||||
\(749\) | 41.5585 | 1.51851 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.1256 | 0.661411 | 0.330706 | − | 0.943734i | \(-0.392713\pi\) | ||||
0.330706 | + | 0.943734i | \(0.392713\pi\) | |||||||
\(752\) | 6.83710 | 0.249323 | ||||||||
\(753\) | −27.4329 | −0.999711 | ||||||||
\(754\) | −24.5646 | −0.894591 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.34017 | −0.157851 | ||||||||
\(757\) | −17.4186 | −0.633088 | −0.316544 | − | 0.948578i | \(-0.602522\pi\) | ||||
−0.316544 | + | 0.948578i | \(0.602522\pi\) | |||||||
\(758\) | −30.6537 | −1.11339 | ||||||||
\(759\) | 1.07838 | 0.0391426 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.4140 | −0.848757 | −0.424379 | − | 0.905485i | \(-0.639507\pi\) | ||||
−0.424379 | + | 0.905485i | \(0.639507\pi\) | |||||||
\(762\) | −17.1773 | −0.622267 | ||||||||
\(763\) | −42.4703 | −1.53753 | ||||||||
\(764\) | 4.36683 | 0.157987 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.8781 | −0.754358 | ||||||||
\(767\) | 20.6803 | 0.746724 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −29.7152 | −1.07156 | −0.535779 | − | 0.844358i | \(-0.679982\pi\) | ||||
−0.535779 | + | 0.844358i | \(0.679982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3135 | 0.371432 | ||||||||
\(772\) | −8.68035 | −0.312412 | ||||||||
\(773\) | 15.3463 | 0.551969 | 0.275984 | − | 0.961162i | \(-0.410996\pi\) | ||||
0.275984 | + | 0.961162i | \(0.410996\pi\) | |||||||
\(774\) | 0.738205 | 0.0265342 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.02052 | 0.323818 | ||||||||
\(777\) | −11.2039 | −0.401939 | ||||||||
\(778\) | −16.9627 | −0.608141 | ||||||||
\(779\) | 0.366835 | 0.0131432 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.3668 | −0.585651 | ||||||||
\(782\) | 0.921622 | 0.0329571 | ||||||||
\(783\) | −10.4969 | −0.375130 | ||||||||
\(784\) | 11.8371 | 0.422754 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.68035 | 0.238280 | ||||||||
\(787\) | −22.8950 | −0.816117 | −0.408059 | − | 0.912956i | \(-0.633794\pi\) | ||||
−0.408059 | + | 0.912956i | \(0.633794\pi\) | |||||||
\(788\) | −22.6803 | −0.807954 | ||||||||
\(789\) | 20.9939 | 0.747401 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.7214 | 1.37677 | ||||||||
\(792\) | −1.07838 | −0.0383185 | ||||||||
\(793\) | 27.0882 | 0.961931 | ||||||||
\(794\) | −16.4969 | −0.585454 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.44521 | −0.193000 | ||||||||
\(797\) | −7.60650 | −0.269436 | −0.134718 | − | 0.990884i | \(-0.543013\pi\) | ||||
−0.134718 | + | 0.990884i | \(0.543013\pi\) | |||||||
\(798\) | −10.1568 | −0.359545 | ||||||||
\(799\) | 6.30122 | 0.222921 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.68035 | −0.165372 | ||||||||
\(802\) | −35.2039 | −1.24309 | ||||||||
\(803\) | 5.04718 | 0.178111 | ||||||||
\(804\) | −2.58145 | −0.0910407 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.36069 | 0.329716 | ||||||||
\(807\) | −25.3874 | −0.893677 | ||||||||
\(808\) | 1.50307 | 0.0528779 | ||||||||
\(809\) | 43.7275 | 1.53738 | 0.768689 | − | 0.639623i | \(-0.220909\pi\) | ||||
0.768689 | + | 0.639623i | \(0.220909\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.79606 | −0.168413 | −0.0842063 | − | 0.996448i | \(-0.526835\pi\) | ||||
−0.0842063 | + | 0.996448i | \(0.526835\pi\) | |||||||
\(812\) | 45.5585 | 1.59879 | ||||||||
\(813\) | 32.5646 | 1.14209 | ||||||||
\(814\) | −2.78378 | −0.0975713 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.921622 | −0.0322632 | ||||||||
\(817\) | 1.72753 | 0.0604385 | ||||||||
\(818\) | 11.3607 | 0.397217 | ||||||||
\(819\) | −10.1568 | −0.354906 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.2245 | −0.426636 | −0.213318 | − | 0.976983i | \(-0.568427\pi\) | ||||
−0.213318 | + | 0.976983i | \(0.568427\pi\) | |||||||
\(822\) | −22.2823 | −0.777185 | ||||||||
\(823\) | −37.5441 | −1.30871 | −0.654353 | − | 0.756189i | \(-0.727059\pi\) | ||||
−0.654353 | + | 0.756189i | \(0.727059\pi\) | |||||||
\(824\) | −2.49693 | −0.0869846 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −38.3545 | −1.33453 | ||||||||
\(827\) | −38.3090 | −1.33213 | −0.666067 | − | 0.745892i | \(-0.732023\pi\) | ||||
−0.666067 | + | 0.745892i | \(0.732023\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −31.4140 | −1.09105 | −0.545527 | − | 0.838093i | \(-0.683670\pi\) | ||||
−0.545527 | + | 0.838093i | \(0.683670\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.7009 | −0.544657 | ||||||||
\(832\) | −2.34017 | −0.0811309 | ||||||||
\(833\) | 10.9093 | 0.377986 | ||||||||
\(834\) | 10.5236 | 0.364402 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.52359 | −0.0872802 | ||||||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | −18.1256 | −0.626137 | ||||||||
\(839\) | 23.1506 | 0.799248 | 0.399624 | − | 0.916679i | \(-0.369141\pi\) | ||||
0.399624 | + | 0.916679i | \(0.369141\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 81.1855 | 2.79950 | ||||||||
\(842\) | 2.58145 | 0.0889626 | ||||||||
\(843\) | 9.36069 | 0.322399 | ||||||||
\(844\) | −22.0410 | −0.758684 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.83710 | 0.235064 | ||||||||
\(847\) | −42.6947 | −1.46701 | ||||||||
\(848\) | −0.340173 | −0.0116816 | ||||||||
\(849\) | 17.4186 | 0.597803 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.58145 | 0.0884909 | ||||||||
\(852\) | −15.1773 | −0.519965 | ||||||||
\(853\) | −32.4969 | −1.11267 | −0.556337 | − | 0.830957i | \(-0.687794\pi\) | ||||
−0.556337 | + | 0.830957i | \(0.687794\pi\) | |||||||
\(854\) | −50.2388 | −1.71914 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.57531 | 0.327277 | ||||||||
\(857\) | 37.8310 | 1.29228 | 0.646140 | − | 0.763219i | \(-0.276382\pi\) | ||||
0.646140 | + | 0.763219i | \(0.276382\pi\) | |||||||
\(858\) | −2.52359 | −0.0861540 | ||||||||
\(859\) | −28.1978 | −0.962096 | −0.481048 | − | 0.876694i | \(-0.659744\pi\) | ||||
−0.481048 | + | 0.876694i | \(0.659744\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.680346 | −0.0231861 | ||||||||
\(862\) | −33.9877 | −1.15763 | ||||||||
\(863\) | 32.0288 | 1.09027 | 0.545136 | − | 0.838348i | \(-0.316478\pi\) | ||||
0.545136 | + | 0.838348i | \(0.316478\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.28685 | −0.281599 | ||||||||
\(867\) | 16.1506 | 0.548504 | ||||||||
\(868\) | −17.3607 | −0.589260 | ||||||||
\(869\) | 12.8494 | 0.435886 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.04104 | −0.204693 | ||||||||
\(872\) | −9.78539 | −0.331375 | ||||||||
\(873\) | 9.02052 | 0.305298 | ||||||||
\(874\) | 2.34017 | 0.0791575 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.68035 | 0.158134 | ||||||||
\(877\) | 27.7009 | 0.935392 | 0.467696 | − | 0.883889i | \(-0.345084\pi\) | ||||
0.467696 | + | 0.883889i | \(0.345084\pi\) | |||||||
\(878\) | −28.9939 | −0.978495 | ||||||||
\(879\) | 16.3402 | 0.551140 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.3135 | 0.414853 | 0.207426 | − | 0.978251i | \(-0.433491\pi\) | ||||
0.207426 | + | 0.978251i | \(0.433491\pi\) | |||||||
\(882\) | 11.8371 | 0.398576 | ||||||||
\(883\) | 7.15061 | 0.240637 | 0.120319 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120319 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(884\) | −2.15676 | −0.0725395 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.20394 | −0.107638 | ||||||||
\(887\) | 9.19165 | 0.308625 | 0.154313 | − | 0.988022i | \(-0.450684\pi\) | ||||
0.154313 | + | 0.988022i | \(0.450684\pi\) | |||||||
\(888\) | −2.58145 | −0.0866278 | ||||||||
\(889\) | 74.5523 | 2.50041 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.07838 | −0.0361270 | ||||||||
\(892\) | 21.1773 | 0.709068 | ||||||||
\(893\) | 16.0000 | 0.535420 | ||||||||
\(894\) | −6.92162 | −0.231494 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.34017 | 0.144995 | ||||||||
\(897\) | 2.34017 | 0.0781361 | ||||||||
\(898\) | 28.1568 | 0.939603 | ||||||||
\(899\) | −41.9877 | −1.40037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.313511 | −0.0104446 | ||||||||
\(902\) | −0.169042 | −0.00562847 | ||||||||
\(903\) | −3.20394 | −0.106620 | ||||||||
\(904\) | 8.92162 | 0.296729 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.15676 | −0.204545 | ||||||||
\(907\) | −14.0989 | −0.468146 | −0.234073 | − | 0.972219i | \(-0.575206\pi\) | ||||
−0.234073 | + | 0.972219i | \(0.575206\pi\) | |||||||
\(908\) | −11.7854 | −0.391112 | ||||||||
\(909\) | 1.50307 | 0.0498537 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.9939 | −0.695558 | −0.347779 | − | 0.937577i | \(-0.613064\pi\) | ||||
−0.347779 | + | 0.937577i | \(0.613064\pi\) | |||||||
\(912\) | −2.34017 | −0.0774909 | ||||||||
\(913\) | −12.3135 | −0.407518 | ||||||||
\(914\) | −23.1773 | −0.766636 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.78539 | 0.0589908 | ||||||||
\(917\) | −28.9939 | −0.957462 | ||||||||
\(918\) | −0.921622 | −0.0304181 | ||||||||
\(919\) | −1.92777 | −0.0635911 | −0.0317956 | − | 0.999494i | \(-0.510123\pi\) | ||||
−0.0317956 | + | 0.999494i | \(0.510123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.20394 | 0.105573 | ||||||||
\(922\) | −42.3279 | −1.39399 | ||||||||
\(923\) | −35.5174 | −1.16907 | ||||||||
\(924\) | 4.68035 | 0.153972 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −34.9048 | −1.14704 | ||||||||
\(927\) | −2.49693 | −0.0820099 | ||||||||
\(928\) | 10.4969 | 0.344579 | ||||||||
\(929\) | 18.5646 | 0.609086 | 0.304543 | − | 0.952499i | \(-0.401496\pi\) | ||||
0.304543 | + | 0.952499i | \(0.401496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.7009 | 0.907859 | ||||||||
\(932\) | 18.3135 | 0.599879 | ||||||||
\(933\) | −12.6537 | −0.414263 | ||||||||
\(934\) | −37.7731 | −1.23597 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.34017 | −0.0764909 | ||||||||
\(937\) | 22.3279 | 0.729420 | 0.364710 | − | 0.931121i | \(-0.381168\pi\) | ||||
0.364710 | + | 0.931121i | \(0.381168\pi\) | |||||||
\(938\) | 11.2039 | 0.365821 | ||||||||
\(939\) | −33.2183 | −1.08404 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0661 | −0.360744 | −0.180372 | − | 0.983598i | \(-0.557730\pi\) | ||||
−0.180372 | + | 0.983598i | \(0.557730\pi\) | |||||||
\(942\) | −2.89496 | −0.0943229 | ||||||||
\(943\) | 0.156755 | 0.00510466 | ||||||||
\(944\) | −8.83710 | −0.287623 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.796064 | −0.0258823 | ||||||||
\(947\) | 8.05332 | 0.261698 | 0.130849 | − | 0.991402i | \(-0.458230\pi\) | ||||
0.130849 | + | 0.991402i | \(0.458230\pi\) | |||||||
\(948\) | 11.9155 | 0.386997 | ||||||||
\(949\) | 10.9528 | 0.355544 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.99386 | 0.226791 | ||||||||
\(952\) | 4.00000 | 0.129641 | ||||||||
\(953\) | 39.5897 | 1.28244 | 0.641218 | − | 0.767359i | \(-0.278430\pi\) | ||||
0.641218 | + | 0.767359i | \(0.278430\pi\) | |||||||
\(954\) | −0.340173 | −0.0110135 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.33403 | −0.172515 | ||||||||
\(957\) | 11.3197 | 0.365912 | ||||||||
\(958\) | −28.1978 | −0.911029 | ||||||||
\(959\) | 96.7091 | 3.12290 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −6.04104 | −0.194771 | ||||||||
\(963\) | 9.57531 | 0.308560 | ||||||||
\(964\) | 26.1978 | 0.843774 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.34017 | −0.139643 | ||||||||
\(967\) | 48.2655 | 1.55211 | 0.776057 | − | 0.630663i | \(-0.217217\pi\) | ||||
0.776057 | + | 0.630663i | \(0.217217\pi\) | |||||||
\(968\) | −9.83710 | −0.316176 | ||||||||
\(969\) | −2.15676 | −0.0692850 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0722 | 0.579966 | 0.289983 | − | 0.957032i | \(-0.406350\pi\) | ||||
0.289983 | + | 0.957032i | \(0.406350\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −45.6742 | −1.46425 | ||||||||
\(974\) | 38.2245 | 1.22479 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.5753 | −0.370517 | ||||||||
\(977\) | −45.9442 | −1.46989 | −0.734943 | − | 0.678129i | \(-0.762791\pi\) | ||||
−0.734943 | + | 0.678129i | \(0.762791\pi\) | |||||||
\(978\) | −6.52359 | −0.208601 | ||||||||
\(979\) | 5.04718 | 0.161309 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.78539 | −0.312423 | ||||||||
\(982\) | 11.3074 | 0.360833 | ||||||||
\(983\) | 1.78992 | 0.0570896 | 0.0285448 | − | 0.999593i | \(-0.490913\pi\) | ||||
0.0285448 | + | 0.999593i | \(0.490913\pi\) | |||||||
\(984\) | −0.156755 | −0.00499718 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.67420 | 0.308089 | ||||||||
\(987\) | −29.6742 | −0.944540 | ||||||||
\(988\) | −5.47641 | −0.174228 | ||||||||
\(989\) | 0.738205 | 0.0234735 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.68649 | 0.244169 | 0.122085 | − | 0.992520i | \(-0.461042\pi\) | ||||
0.122085 | + | 0.992520i | \(0.461042\pi\) | |||||||
\(992\) | −4.00000 | −0.127000 | ||||||||
\(993\) | 29.7275 | 0.943375 | ||||||||
\(994\) | 65.8720 | 2.08933 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.4186 | −0.361811 | ||||||||
\(997\) | −21.4908 | −0.680620 | −0.340310 | − | 0.940313i | \(-0.610532\pi\) | ||||
−0.340310 | + | 0.940313i | \(0.610532\pi\) | |||||||
\(998\) | −2.47027 | −0.0781949 | ||||||||
\(999\) | −2.58145 | −0.0816734 |
(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 | 3450.2.a.bt.1.3 | 3 | ||
5.2 | odd | 4 | 690.2.d.c.139.5 | yes | 6 | ||
5.3 | odd | 4 | 690.2.d.c.139.2 | ✓ | 6 | ||
5.4 | even | 2 | 3450.2.a.bo.1.1 | 3 | |||
15.2 | even | 4 | 2070.2.d.e.829.2 | 6 | |||
15.8 | even | 4 | 2070.2.d.e.829.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.c.139.2 | ✓ | 6 | 5.3 | odd | 4 | ||
690.2.d.c.139.5 | yes | 6 | 5.2 | odd | 4 | ||
2070.2.d.e.829.2 | 6 | 15.2 | even | 4 | |||
2070.2.d.e.829.5 | 6 | 15.8 | even | 4 | |||
3450.2.a.bo.1.1 | 3 | 5.4 | even | 2 | |||
3450.2.a.bt.1.3 | 3 | 1.1 | even | 1 | trivial |