Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2004,2,Mod(1,2004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2004, 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("2004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2004.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: | \(16.0020205651\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.161121.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 3x^{2} + 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.07823\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2004.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.614948 | −0.275013 | −0.137507 | − | 0.990501i | \(-0.543909\pi\) | ||||
−0.137507 | + | 0.990501i | \(0.543909\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46328 | −1.30900 | −0.654499 | − | 0.756063i | \(-0.727120\pi\) | ||||
−0.654499 | + | 0.756063i | \(0.727120\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.80906 | 1.14847 | 0.574237 | − | 0.818689i | \(-0.305299\pi\) | ||||
0.574237 | + | 0.818689i | \(0.305299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.93060 | −0.812801 | −0.406401 | − | 0.913695i | \(-0.633216\pi\) | ||||
−0.406401 | + | 0.913695i | \(0.633216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.614948 | −0.158779 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.15646 | 0.765555 | 0.382778 | − | 0.923841i | \(-0.374968\pi\) | ||||
0.382778 | + | 0.923841i | \(0.374968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.58256 | −1.28073 | −0.640363 | − | 0.768072i | \(-0.721216\pi\) | ||||
−0.640363 | + | 0.768072i | \(0.721216\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.46328 | −0.755750 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.574360 | −0.119762 | −0.0598811 | − | 0.998206i | \(-0.519072\pi\) | ||||
−0.0598811 | + | 0.998206i | \(0.519072\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.62184 | −0.924368 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.25128 | −0.603748 | −0.301874 | − | 0.953348i | \(-0.597612\pi\) | ||||
−0.301874 | + | 0.953348i | \(0.597612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.74532 | −0.313468 | −0.156734 | − | 0.987641i | \(-0.550097\pi\) | ||||
−0.156734 | + | 0.987641i | \(0.550097\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.80906 | 0.663072 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.12974 | 0.359992 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.35964 | −0.716720 | −0.358360 | − | 0.933583i | \(-0.616664\pi\) | ||||
−0.358360 | + | 0.933583i | \(0.616664\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.93060 | −0.469271 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.51130 | −0.236026 | −0.118013 | − | 0.993012i | \(-0.537652\pi\) | ||||
−0.118013 | + | 0.993012i | \(0.537652\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.97984 | 1.52191 | 0.760956 | − | 0.648804i | \(-0.224730\pi\) | ||||
0.760956 | + | 0.648804i | \(0.224730\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.614948 | −0.0916711 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.29318 | −1.20968 | −0.604842 | − | 0.796345i | \(-0.706764\pi\) | ||||
−0.604842 | + | 0.796345i | \(0.706764\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.99433 | 0.713476 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.15646 | 0.441993 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.465048 | 0.0638792 | 0.0319396 | − | 0.999490i | \(-0.489832\pi\) | ||||
0.0319396 | + | 0.999490i | \(0.489832\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.34237 | −0.315845 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.58256 | −0.739428 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.58387 | −1.24771 | −0.623857 | − | 0.781539i | \(-0.714435\pi\) | ||||
−0.623857 | + | 0.781539i | \(0.714435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.22999 | −0.797668 | −0.398834 | − | 0.917023i | \(-0.630585\pi\) | ||||
−0.398834 | + | 0.917023i | \(0.630585\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.46328 | −0.436333 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.80217 | 0.223531 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.41132 | 0.416759 | 0.208380 | − | 0.978048i | \(-0.433181\pi\) | ||||
0.208380 | + | 0.978048i | \(0.433181\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.574360 | −0.0691448 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.58319 | −1.01864 | −0.509319 | − | 0.860578i | \(-0.670103\pi\) | ||||
−0.509319 | + | 0.860578i | \(0.670103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.90115 | −1.15884 | −0.579421 | − | 0.815028i | \(-0.696721\pi\) | ||||
−0.579421 | + | 0.815028i | \(0.696721\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.62184 | −0.533684 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.1918 | −1.50335 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2406 | 1.15216 | 0.576078 | − | 0.817395i | \(-0.304583\pi\) | ||||
0.576078 | + | 0.817395i | \(0.304583\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.39859 | −0.921865 | −0.460932 | − | 0.887435i | \(-0.652485\pi\) | ||||
−0.460932 | + | 0.887435i | \(0.652485\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.94106 | −0.210538 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.25128 | −0.348574 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.12992 | −0.755770 | −0.377885 | − | 0.925853i | \(-0.623348\pi\) | ||||
−0.377885 | + | 0.925853i | \(0.623348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.1495 | 1.06396 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.74532 | −0.180981 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.43299 | 0.352217 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.70410 | 0.477629 | 0.238815 | − | 0.971065i | \(-0.423241\pi\) | ||||
0.238815 | + | 0.971065i | \(0.423241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.80906 | 0.382825 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.74351 | −0.671004 | −0.335502 | − | 0.942039i | \(-0.608906\pi\) | ||||
−0.335502 | + | 0.942039i | \(0.608906\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.37572 | −0.332620 | −0.166310 | − | 0.986074i | \(-0.553185\pi\) | ||||
−0.166310 | + | 0.986074i | \(0.553185\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.12974 | 0.207841 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.87891 | −0.665010 | −0.332505 | − | 0.943102i | \(-0.607894\pi\) | ||||
−0.332505 | + | 0.943102i | \(0.607894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.2964 | −1.17778 | −0.588891 | − | 0.808213i | \(-0.700435\pi\) | ||||
−0.588891 | + | 0.808213i | \(0.700435\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.35964 | −0.413798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.04942 | 0.475009 | 0.237505 | − | 0.971386i | \(-0.423671\pi\) | ||||
0.237505 | + | 0.971386i | \(0.423671\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.353202 | 0.0329362 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.93060 | −0.270934 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.9317 | −1.00211 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50891 | 0.318992 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.51130 | −0.136269 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.91693 | 0.529227 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.43089 | 0.748121 | 0.374060 | − | 0.927404i | \(-0.377965\pi\) | ||||
0.374060 | + | 0.927404i | \(0.377965\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.97984 | 0.878676 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.65327 | 0.668669 | 0.334335 | − | 0.942454i | \(-0.391488\pi\) | ||||
0.334335 | + | 0.942454i | \(0.391488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.3340 | 1.67647 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.614948 | −0.0529263 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.27810 | −0.450938 | −0.225469 | − | 0.974250i | \(-0.572391\pi\) | ||||
−0.225469 | + | 0.974250i | \(0.572391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.53478 | 0.469454 | 0.234727 | − | 0.972061i | \(-0.424580\pi\) | ||||
0.234727 | + | 0.972061i | \(0.424580\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.29318 | −0.698412 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.1628 | −0.933481 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.99937 | 0.166039 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.99433 | 0.411926 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.1803 | 1.07977 | 0.539886 | − | 0.841738i | \(-0.318467\pi\) | ||||
0.539886 | + | 0.841738i | \(0.318467\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.29363 | −0.186653 | −0.0933266 | − | 0.995636i | \(-0.529750\pi\) | ||||
−0.0933266 | + | 0.995636i | \(0.529750\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.15646 | 0.255185 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.07328 | 0.0862080 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.6203 | −1.16682 | −0.583412 | − | 0.812177i | \(-0.698283\pi\) | ||||
−0.583412 | + | 0.812177i | \(0.698283\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.465048 | 0.0368807 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.98917 | 0.156769 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6158 | 1.22312 | 0.611560 | − | 0.791198i | \(-0.290542\pi\) | ||||
0.611560 | + | 0.791198i | \(0.290542\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.34237 | −0.182353 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.41160 | −0.339354 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.58256 | −0.426909 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.8874 | 1.05584 | 0.527919 | − | 0.849295i | \(-0.322972\pi\) | ||||
0.527919 | + | 0.849295i | \(0.322972\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.0067 | 1.21000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.58387 | −0.720368 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.21586 | 0.240364 | 0.120182 | − | 0.992752i | \(-0.461652\pi\) | ||||
0.120182 | + | 0.992752i | \(0.461652\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.33183 | 0.544971 | 0.272485 | − | 0.962160i | \(-0.412154\pi\) | ||||
0.272485 | + | 0.962160i | \(0.412154\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.22999 | −0.460534 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.68095 | 0.197107 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0231 | 0.879220 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.46328 | −0.251917 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.33599 | 0.169026 | 0.0845130 | − | 0.996422i | \(-0.473067\pi\) | ||||
0.0845130 | + | 0.996422i | \(0.473067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.73301 | 0.700597 | 0.350299 | − | 0.936638i | \(-0.386080\pi\) | ||||
0.350299 | + | 0.936638i | \(0.386080\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.80217 | 0.129056 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.0432 | −1.35677 | −0.678386 | − | 0.734705i | \(-0.737320\pi\) | ||||
−0.678386 | + | 0.734705i | \(0.737320\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.26986 | 0.373570 | 0.186785 | − | 0.982401i | \(-0.440193\pi\) | ||||
0.186785 | + | 0.982401i | \(0.440193\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.41132 | 0.240616 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.2601 | 0.790305 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.929372 | 0.0649102 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.574360 | −0.0399208 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.2643 | −1.47088 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.49086 | −0.102635 | −0.0513176 | − | 0.998682i | \(-0.516342\pi\) | ||||
−0.0513176 | + | 0.998682i | \(0.516342\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.58319 | −0.588110 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.13709 | −0.418546 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.04453 | 0.410330 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.90115 | −0.669058 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.25032 | −0.622244 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.343506 | −0.0230029 | −0.0115014 | − | 0.999934i | \(-0.503661\pi\) | ||||
−0.0115014 | + | 0.999934i | \(0.503661\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.62184 | −0.308123 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.12470 | 0.539256 | 0.269628 | − | 0.962965i | \(-0.413099\pi\) | ||||
0.269628 | + | 0.962965i | \(0.413099\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.95619 | 0.393596 | 0.196798 | − | 0.980444i | \(-0.436946\pi\) | ||||
0.196798 | + | 0.980444i | \(0.436946\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.1918 | −0.867959 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.870260 | 0.0570126 | 0.0285063 | − | 0.999594i | \(-0.490925\pi\) | ||||
0.0285063 | + | 0.999594i | \(0.490925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.09988 | 0.332679 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.2406 | 0.665197 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.0177 | 0.842046 | 0.421023 | − | 0.907050i | \(-0.361671\pi\) | ||||
0.421023 | + | 0.907050i | \(0.361671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.82934 | −0.182254 | −0.0911270 | − | 0.995839i | \(-0.529047\pi\) | ||||
−0.0911270 | + | 0.995839i | \(0.529047\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.07126 | −0.196215 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.3602 | 1.04098 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.39859 | −0.532239 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.4580 | −1.03882 | −0.519410 | − | 0.854525i | \(-0.673848\pi\) | ||||
−0.519410 | + | 0.854525i | \(0.673848\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.18777 | −0.137544 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.94106 | −0.121554 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.5773 | 1.53309 | 0.766545 | − | 0.642191i | \(-0.221974\pi\) | ||||
0.766545 | + | 0.642191i | \(0.221974\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.0987 | 0.938185 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.25128 | −0.201249 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.6483 | 1.51988 | 0.759939 | − | 0.649994i | \(-0.225229\pi\) | ||||
0.759939 | + | 0.649994i | \(0.225229\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.285980 | −0.0175676 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.12992 | −0.436344 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.52549 | −0.275924 | −0.137962 | − | 0.990438i | \(-0.544055\pi\) | ||||
−0.137962 | + | 0.990438i | \(0.544055\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.1048 | −1.34277 | −0.671385 | − | 0.741109i | \(-0.734300\pi\) | ||||
−0.671385 | + | 0.741109i | \(0.734300\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.1495 | 0.614275 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.6048 | −1.06161 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.4555 | −0.868548 | −0.434274 | − | 0.900781i | \(-0.642995\pi\) | ||||
−0.434274 | + | 0.900781i | \(0.642995\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.74532 | −0.104489 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.60180 | 0.214866 | 0.107433 | − | 0.994212i | \(-0.465737\pi\) | ||||
0.107433 | + | 0.994212i | \(0.465737\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.0928 | −1.31328 | −0.656639 | − | 0.754205i | \(-0.728023\pi\) | ||||
−0.656639 | + | 0.754205i | \(0.728023\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.43299 | 0.203352 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.23407 | 0.308957 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.03673 | −0.413926 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.70410 | 0.275759 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.403322 | −0.0235623 | −0.0117812 | − | 0.999931i | \(-0.503750\pi\) | ||||
−0.0117812 | + | 0.999931i | \(0.503750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.89358 | 0.343138 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.80906 | 0.221024 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.68322 | 0.0973430 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.5630 | −1.99218 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.74351 | −0.387404 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.83112 | 0.219369 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.5615 | 1.63009 | 0.815045 | − | 0.579397i | \(-0.196712\pi\) | ||||
0.815045 | + | 0.579397i | \(0.196712\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.37572 | −0.192038 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.0740 | −0.798061 | −0.399031 | − | 0.916938i | \(-0.630653\pi\) | ||||
−0.399031 | + | 0.916938i | \(0.630653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.3132 | 0.752504 | 0.376252 | − | 0.926517i | \(-0.377213\pi\) | ||||
0.376252 | + | 0.926517i | \(0.377213\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.12974 | 0.119997 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.0614 | −1.29526 | −0.647630 | − | 0.761955i | \(-0.724240\pi\) | ||||
−0.647630 | + | 0.761955i | \(0.724240\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.3843 | −0.693388 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.87891 | −0.383944 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.6211 | −0.980467 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.5447 | 0.751327 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.2964 | −0.679993 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 28.7216 | 1.58347 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.1825 | 1.71394 | 0.856972 | − | 0.515363i | \(-0.172343\pi\) | ||||
0.856972 | + | 0.515363i | \(0.172343\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.35964 | −0.238907 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.09779 | −0.114614 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.817442 | −0.0445289 | −0.0222645 | − | 0.999752i | \(-0.507088\pi\) | ||||
−0.0222645 | + | 0.999752i | \(0.507088\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.04942 | 0.274247 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.64802 | −0.360010 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.94619 | 0.375059 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.353202 | 0.0190157 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.97471 | −0.535471 | −0.267735 | − | 0.963492i | \(-0.586275\pi\) | ||||
−0.267735 | + | 0.963492i | \(0.586275\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.6700 | −0.731740 | −0.365870 | − | 0.930666i | \(-0.619229\pi\) | ||||
−0.365870 | + | 0.930666i | \(0.619229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.93060 | −0.156424 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.0887759 | −0.00472506 | −0.00236253 | − | 0.999997i | \(-0.500752\pi\) | ||||
−0.00236253 | + | 0.999997i | \(0.500752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.27822 | 0.280139 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.9317 | −0.578569 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.69628 | −0.353416 | −0.176708 | − | 0.984263i | \(-0.556545\pi\) | ||||
−0.176708 | + | 0.984263i | \(0.556545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.1650 | 0.640261 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.50891 | 0.184170 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.08870 | 0.318697 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.5833 | 1.38764 | 0.693819 | − | 0.720150i | \(-0.255927\pi\) | ||||
0.693819 | + | 0.720150i | \(0.255927\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.51130 | −0.0786752 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.61059 | −0.0836178 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.1865 | 1.30411 | 0.652053 | − | 0.758173i | \(-0.273908\pi\) | ||||
0.652053 | + | 0.758173i | \(0.273908\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.91693 | 0.305549 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.52820 | 0.490727 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.4647 | −0.794370 | −0.397185 | − | 0.917739i | \(-0.630013\pi\) | ||||
−0.397185 | + | 0.917739i | \(0.630013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.43089 | 0.431928 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.0700 | 1.53651 | 0.768253 | − | 0.640147i | \(-0.221126\pi\) | ||||
0.768253 | + | 0.640147i | \(0.221126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.11230 | 0.413441 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.97984 | 0.507304 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.8151 | −1.35958 | −0.679790 | − | 0.733407i | \(-0.737929\pi\) | ||||
−0.679790 | + | 0.733407i | \(0.737929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.81295 | −0.0916846 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.65327 | 0.386056 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.29743 | −0.316858 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.7692 | −0.540490 | −0.270245 | − | 0.962792i | \(-0.587105\pi\) | ||||
−0.270245 | + | 0.962792i | \(0.587105\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.3340 | 0.967910 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.6845 | 0.883121 | 0.441561 | − | 0.897231i | \(-0.354425\pi\) | ||||
0.441561 | + | 0.897231i | \(0.354425\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.11483 | 0.254788 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.614948 | −0.0305570 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.6061 | −0.823134 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.1733 | −0.997506 | −0.498753 | − | 0.866744i | \(-0.666209\pi\) | ||||
−0.498753 | + | 0.866744i | \(0.666209\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.27810 | −0.260349 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.1917 | 1.63325 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.16470 | 0.253525 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.53478 | 0.271039 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.91248 | 0.386550 | 0.193275 | − | 0.981145i | \(-0.438089\pi\) | ||||
0.193275 | + | 0.981145i | \(0.438089\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.95900 | 0.387898 | 0.193949 | − | 0.981012i | \(-0.437870\pi\) | ||||
0.193949 | + | 0.981012i | \(0.437870\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.29318 | −0.403228 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.5887 | −0.707654 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.5762 | 1.04415 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.1628 | −0.538945 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.43209 | 0.309823 | 0.154912 | − | 0.987928i | \(-0.450491\pi\) | ||||
0.154912 | + | 0.987928i | \(0.450491\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3350 | 1.21752 | 0.608761 | − | 0.793354i | \(-0.291667\pi\) | ||||
0.608761 | + | 0.793354i | \(0.291667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.99937 | 0.0958625 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.20640 | 0.153383 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.63416 | −0.268904 | −0.134452 | − | 0.990920i | \(-0.542927\pi\) | ||||
−0.134452 | + | 0.990920i | \(0.542927\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.99433 | 0.237825 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.5091 | 1.63958 | 0.819789 | − | 0.572666i | \(-0.194091\pi\) | ||||
0.819789 | + | 0.572666i | \(0.194091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.38453 | 0.207847 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.1803 | 0.623406 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.4839 | −1.76897 | −0.884487 | − | 0.466565i | \(-0.845491\pi\) | ||||
−0.884487 | + | 0.466565i | \(0.845491\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.75663 | −0.271069 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.29363 | −0.107764 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.24141 | −0.292602 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.87783 | 0.415287 | 0.207644 | − | 0.978205i | \(-0.433421\pi\) | ||||
0.207644 | + | 0.978205i | \(0.433421\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.15646 | 0.147331 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.67760 | 0.450731 | 0.225365 | − | 0.974274i | \(-0.427642\pi\) | ||||
0.225365 | + | 0.974274i | \(0.427642\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.66347 | 0.402626 | 0.201313 | − | 0.979527i | \(-0.435479\pi\) | ||||
0.201313 | + | 0.979527i | \(0.435479\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.07328 | 0.0497722 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.1541 | 1.44164 | 0.720819 | − | 0.693124i | \(-0.243766\pi\) | ||||
0.720819 | + | 0.693124i | \(0.243766\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.8144 | −0.545537 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.6203 | −0.673666 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 38.0138 | 1.74787 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.8017 | 1.18386 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.465048 | 0.0212931 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.78094 | 0.309829 | 0.154915 | − | 0.987928i | \(-0.450490\pi\) | ||||
0.154915 | + | 0.987928i | \(0.450490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.7763 | 0.582551 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.98917 | 0.0905104 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.89278 | −0.131354 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.19422 | 0.144744 | 0.0723719 | − | 0.997378i | \(-0.476943\pi\) | ||||
0.0723719 | + | 0.997378i | \(0.476943\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.6158 | 0.706169 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.1947 | 1.63344 | 0.816722 | − | 0.577031i | \(-0.195789\pi\) | ||||
0.816722 | + | 0.577031i | \(0.195789\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2626 | −0.462202 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.34237 | −0.105282 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.7260 | 1.33339 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.5019 | −0.873026 | −0.436513 | − | 0.899698i | \(-0.643787\pi\) | ||||
−0.436513 | + | 0.899698i | \(0.643787\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.7924 | −1.06085 | −0.530426 | − | 0.847731i | \(-0.677968\pi\) | ||||
−0.530426 | + | 0.847731i | \(0.677968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.14691 | 0.184535 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.41160 | −0.195926 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.6743 | −0.783399 | −0.391700 | − | 0.920093i | \(-0.628113\pi\) | ||||
−0.391700 | + | 0.920093i | \(0.628113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.2905 | 1.51692 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.58256 | −0.246476 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.07589 | 0.0914748 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.5892 | −1.38929 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.8874 | 0.609588 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.0601 | −1.79887 | −0.899437 | − | 0.437050i | \(-0.856023\pi\) | ||||
−0.899437 | + | 0.437050i | \(0.856023\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.50620 | 0.109588 | 0.0547942 | − | 0.998498i | \(-0.482550\pi\) | ||||
0.0547942 | + | 0.998498i | \(0.482550\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.0067 | 0.698591 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.50904 | −0.239977 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6701 | −0.985657 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.58387 | −0.415904 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.42902 | 0.191842 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.23018 | 0.182886 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.21586 | 0.138774 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.0237 | 0.819409 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.2521 | 1.55860 | 0.779299 | − | 0.626652i | \(-0.215575\pi\) | ||||
0.779299 | + | 0.626652i | \(0.215575\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.33183 | 0.314639 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.56165 | 0.323906 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.5354 | 0.450461 | 0.225230 | − | 0.974306i | \(-0.427686\pi\) | ||||
0.225230 | + | 0.974306i | \(0.427686\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.22999 | −0.265889 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.1505 | 0.773236 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.4660 | −1.50817 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.68095 | 0.113800 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.9650 | −0.761200 | −0.380600 | − | 0.924740i | \(-0.624283\pi\) | ||||
−0.380600 | + | 0.924740i | \(0.624283\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.2469 | −1.23701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0231 | 0.507618 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.50941 | −0.400774 | −0.200387 | − | 0.979717i | \(-0.564220\pi\) | ||||
−0.200387 | + | 0.979717i | \(0.564220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.10513 | −0.130634 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.46328 | −0.145444 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.4813 | −0.774778 | −0.387389 | − | 0.921916i | \(-0.626623\pi\) | ||||
−0.387389 | + | 0.921916i | \(0.626623\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.7478 | 0.533478 | 0.266739 | − | 0.963769i | \(-0.414054\pi\) | ||||
0.266739 | + | 0.963769i | \(0.414054\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.33599 | 0.0975872 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.65460 | 0.110704 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.1464 | −1.50480 | −0.752398 | − | 0.658709i | \(-0.771103\pi\) | ||||
−0.752398 | + | 0.658709i | \(0.771103\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.73301 | 0.404490 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.0867 | 1.20672 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.77139 | 0.0733636 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.80217 | 0.0745104 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.8985 | −1.85316 | −0.926580 | − | 0.376098i | \(-0.877266\pi\) | ||||
−0.926580 | + | 0.376098i | \(0.877266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.74334 | 0.401468 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.0432 | −0.783333 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.0796 | −0.988832 | −0.494416 | − | 0.869225i | \(-0.664618\pi\) | ||||
−0.494416 | + | 0.869225i | \(0.664618\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.72245 | 0.275594 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.26986 | 0.215681 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.07062 | 0.166321 | 0.0831604 | − | 0.996536i | \(-0.473499\pi\) | ||||
0.0831604 | + | 0.996536i | \(0.473499\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0899 | −0.533949 | −0.266974 | − | 0.963704i | \(-0.586024\pi\) | ||||
−0.266974 | + | 0.963704i | \(0.586024\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.41132 | 0.138920 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.15780 | −0.0877269 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.3314 | 1.19053 | 0.595263 | − | 0.803531i | \(-0.297048\pi\) | ||||
0.595263 | + | 0.803531i | \(0.297048\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.2601 | 0.456283 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.3040 | 0.983233 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.550896 | −0.0222505 | −0.0111252 | − | 0.999938i | \(-0.503541\pi\) | ||||
−0.0111252 | + | 0.999938i | \(0.503541\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.929372 | 0.0374759 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47.2384 | −1.90175 | −0.950874 | − | 0.309578i | \(-0.899812\pi\) | ||||
−0.950874 | + | 0.309578i | \(0.899812\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.51048 | −0.100905 | −0.0504524 | − | 0.998726i | \(-0.516066\pi\) | ||||
−0.0504524 | + | 0.998726i | \(0.516066\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.574360 | −0.0230483 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.6929 | 0.989301 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.4706 | 0.778823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.2643 | −0.849214 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.7610 | −0.548689 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.8135 | 1.70438 | 0.852190 | − | 0.523233i | \(-0.175274\pi\) | ||||
0.852190 | + | 0.523233i | \(0.175274\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.49086 | −0.0592564 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.18456 | −0.205743 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.6364 | −0.579915 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.58319 | −0.339546 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.7594 | −1.53090 | −0.765452 | − | 0.643493i | \(-0.777485\pi\) | ||||
−0.765452 | + | 0.643493i | \(0.777485\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.1097 | 1.18741 | 0.593705 | − | 0.804682i | \(-0.297664\pi\) | ||||
0.593705 | + | 0.804682i | \(0.297664\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.13709 | −0.241648 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.3050 | 0.562389 | 0.281195 | − | 0.959651i | \(-0.409269\pi\) | ||||
0.281195 | + | 0.959651i | \(0.409269\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.5055 | −1.43297 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.04453 | 0.236904 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.0547 | 0.823933 | 0.411966 | − | 0.911199i | \(-0.364842\pi\) | ||||
0.411966 | + | 0.911199i | \(0.364842\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.70637 | −0.183893 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.90115 | −0.386281 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.02197 | −0.156674 | −0.0783368 | − | 0.996927i | \(-0.524961\pi\) | ||||
−0.0783368 | + | 0.996927i | \(0.524961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5974 | 0.762252 | 0.381126 | − | 0.924523i | \(-0.375536\pi\) | ||||
0.381126 | + | 0.924523i | \(0.375536\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.25032 | −0.359253 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.8894 | −0.461051 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.86741 | 0.0723062 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.343506 | −0.0132807 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.7304 | −0.916101 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.6277 | −0.718046 | −0.359023 | − | 0.933329i | \(-0.616890\pi\) | ||||
−0.359023 | + | 0.933329i | \(0.616890\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.62184 | −0.177895 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.2425 | −0.739549 | −0.369774 | − | 0.929122i | \(-0.620565\pi\) | ||||
−0.369774 | + | 0.929122i | \(0.620565\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.2916 | −0.625216 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.12470 | 0.311339 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.3752 | 1.39186 | 0.695929 | − | 0.718111i | \(-0.254993\pi\) | ||||
0.695929 | + | 0.718111i | \(0.254993\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.24576 | 0.124014 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.95619 | 0.227243 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.36287 | −0.0519211 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.4677 | −1.19709 | −0.598543 | − | 0.801091i | \(-0.704254\pi\) | ||||
−0.598543 | + | 0.801091i | \(0.704254\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.1918 | −0.501117 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.40360 | −0.129106 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.77037 | −0.180691 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.870260 | 0.0329162 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.1706 | −1.44168 | −0.720841 | − | 0.693100i | \(-0.756244\pi\) | ||||
−0.720841 | + | 0.693100i | \(0.756244\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.3379 | 0.917922 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.09988 | 0.192072 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.3547 | 0.878343 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0061 | 0.450900 | 0.225450 | − | 0.974255i | \(-0.427615\pi\) | ||||
0.225450 | + | 0.974255i | \(0.427615\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.2406 | 0.384052 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.00244 | 0.0375417 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.86455 | 0.256720 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.0177 | 0.486155 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.4358 | 0.687539 | 0.343769 | − | 0.939054i | \(-0.388296\pi\) | ||||
0.343769 | + | 0.939054i | \(0.388296\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.6911 | 0.435399 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.82934 | −0.105224 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.0269 | 0.558085 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.4468 | −0.535802 | −0.267901 | − | 0.963446i | \(-0.586330\pi\) | ||||
−0.267901 | + | 0.963446i | \(0.586330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.5010 | 1.16511 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.5104 | 1.64403 | 0.822014 | − | 0.569467i | \(-0.192850\pi\) | ||||
0.822014 | + | 0.569467i | \(0.192850\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.07126 | −0.113285 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9939 | 0.478637 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.3056 | 1.07802 | 0.539011 | − | 0.842298i | \(-0.318798\pi\) | ||||
0.539011 | + | 0.842298i | \(0.318798\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.3602 | 0.601008 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.42691 | 0.345840 | 0.172920 | − | 0.984936i | \(-0.444680\pi\) | ||||
0.172920 | + | 0.984936i | \(0.444680\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.10520 | −0.296951 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.39859 | −0.307288 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.8236 | 0.870496 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.0724 | 1.17034 | 0.585170 | − | 0.810911i | \(-0.301028\pi\) | ||||
0.585170 | + | 0.810911i | \(0.301028\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.4580 | −0.599763 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.41047 | 0.0513321 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.9811 | −0.653533 | −0.326767 | − | 0.945105i | \(-0.605959\pi\) | ||||
−0.326767 | + | 0.945105i | \(0.605959\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.18777 | −0.0794110 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.0598 | 1.23467 | 0.617333 | − | 0.786702i | \(-0.288213\pi\) | ||||
0.617333 | + | 0.786702i | \(0.288213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.5859 | 1.54171 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.94106 | −0.0701793 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.0865 | 1.01414 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.20670 | 0.0435147 | 0.0217574 | − | 0.999763i | \(-0.493074\pi\) | ||||
0.0217574 | + | 0.999763i | \(0.493074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.5773 | 0.885129 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.9957 | −0.575327 | −0.287663 | − | 0.957732i | \(-0.592878\pi\) | ||||
−0.287663 | + | 0.957732i | \(0.592878\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.06658 | 0.289760 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.0987 | 0.541661 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.43693 | 0.302284 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.6938 | −1.16988 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.25128 | −0.116191 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.99070 | 0.320892 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.7244 | −1.16650 | −0.583250 | − | 0.812292i | \(-0.698219\pi\) | ||||
−0.583250 | + | 0.812292i | \(0.698219\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.6483 | 0.877502 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.4876 | −0.621786 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.2576 | 0.648346 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.285980 | −0.0101427 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.2345 | −1.10638 | −0.553191 | − | 0.833054i | \(-0.686590\pi\) | ||||
−0.553191 | + | 0.833054i | \(0.686590\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.1771 | −0.926080 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.12992 | −0.251923 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.7140 | −1.33090 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.22324 | −0.0431135 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.52549 | −0.159305 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.8880 | −1.64849 | −0.824247 | − | 0.566230i | \(-0.808401\pi\) | ||||
−0.824247 | + | 0.566230i | \(0.808401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.2325 | −1.41275 | −0.706377 | − | 0.707836i | \(-0.749672\pi\) | ||||
−0.706377 | + | 0.707836i | \(0.749672\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.1048 | −0.775248 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.60288 | −0.336374 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −55.7130 | −1.94915 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.1495 | 0.354652 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.3186 | 1.37223 | 0.686115 | − | 0.727494i | \(-0.259315\pi\) | ||||
0.686115 | + | 0.727494i | \(0.259315\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.64345 | −0.161860 | −0.0809302 | − | 0.996720i | \(-0.525789\pi\) | ||||
−0.0809302 | + | 0.996720i | \(0.525789\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.6048 | −0.612922 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.5624 | 0.680251 | 0.340125 | − | 0.940380i | \(-0.389530\pi\) | ||||
0.340125 | + | 0.940380i | \(0.389530\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.01629 | 0.104760 | 0.0523801 | − | 0.998627i | \(-0.483319\pi\) | ||||
0.0523801 | + | 0.998627i | \(0.483319\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.4555 | −0.501457 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.7644 | 0.546205 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.614948 | 0.0212812 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.74532 | −0.0603270 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.4908 | −0.880041 | −0.440020 | − | 0.897988i | \(-0.645029\pi\) | ||||
−0.440020 | + | 0.897988i | \(0.645029\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4292 | −0.635489 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.60180 | 0.124053 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.71291 | 0.0933268 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.1523 | −0.417559 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.0928 | −0.758222 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.50400 | 0.0858360 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.8504 | 0.782382 | 0.391191 | − | 0.920310i | \(-0.372063\pi\) | ||||
0.391191 | + | 0.920310i | \(0.372063\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.43299 | 0.117406 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.9103 | 0.475167 | 0.237584 | − | 0.971367i | \(-0.423645\pi\) | ||||
0.237584 | + | 0.971367i | \(0.423645\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.0864 | −1.12889 | −0.564447 | − | 0.825469i | \(-0.690910\pi\) | ||||
−0.564447 | + | 0.825469i | \(0.690910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.23407 | 0.178377 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.6677 | −1.65667 | −0.828334 | − | 0.560234i | \(-0.810711\pi\) | ||||
−0.828334 | + | 0.560234i | \(0.810711\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.54002 | −0.290369 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.03673 | −0.238980 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.0069 | 1.32322 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.99721 | −0.338742 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.70410 | 0.159210 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.4920 | −0.692757 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.5965 | 0.729264 | 0.364632 | − | 0.931152i | \(-0.381195\pi\) | ||||
0.364632 | + | 0.931152i | \(0.381195\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.403322 | −0.0136037 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.38305 | −0.0465960 | −0.0232980 | − | 0.999729i | \(-0.507417\pi\) | ||||
−0.0232980 | + | 0.999729i | \(0.507417\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.0085 | −0.807951 | −0.403976 | − | 0.914770i | \(-0.632372\pi\) | ||||
−0.403976 | + | 0.914770i | \(0.632372\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.89358 | 0.198111 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.6184 | −1.29668 | −0.648339 | − | 0.761352i | \(-0.724536\pi\) | ||||
−0.648339 | + | 0.761352i | \(0.724536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.1986 | −0.979289 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.80906 | 0.127608 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.2972 | 1.54928 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.97759 | −0.0661034 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.68322 | 0.0562010 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.67452 | 0.189256 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.46791 | 0.0489030 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −34.5630 | −1.15019 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.50870 | −0.149874 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.3349 | 1.10687 | 0.553433 | − | 0.832893i | \(-0.313317\pi\) | ||||
0.553433 | + | 0.832893i | \(0.313317\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.74351 | −0.223668 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.7100 | −0.354838 | −0.177419 | − | 0.984135i | \(-0.556775\pi\) | ||||
−0.177419 | + | 0.984135i | \(0.556775\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.9907 | −1.05874 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.83112 | 0.126653 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.5054 | −0.875287 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.1186 | −1.85118 | −0.925591 | − | 0.378525i | \(-0.876431\pi\) | ||||
−0.925591 | + | 0.378525i | \(0.876431\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.5615 | 0.941133 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.1539 | 0.827950 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.1495 | 0.662513 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.37572 | −0.110873 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.8268 | 0.978587 | 0.489293 | − | 0.872119i | \(-0.337255\pi\) | ||||
0.489293 | + | 0.872119i | \(0.337255\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.8812 | −0.913768 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.0740 | −0.460761 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.39361 | −0.241797 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.8975 | 0.780696 | 0.390348 | − | 0.920667i | \(-0.372355\pi\) | ||||
0.390348 | + | 0.920667i | \(0.372355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.3132 | 0.434458 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.7999 | 0.515061 | 0.257530 | − | 0.966270i | \(-0.417091\pi\) | ||||
0.257530 | + | 0.966270i | \(0.417091\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.868031 | 0.0282670 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.12974 | 0.0692805 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.5289 | −1.64197 | −0.820985 | − | 0.570950i | \(-0.806575\pi\) | ||||
−0.820985 | + | 0.570950i | \(0.806575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.0163 | 0.941909 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.0614 | −0.747818 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.2502 | −0.461609 | −0.230804 | − | 0.973000i | \(-0.574136\pi\) | ||||
−0.230804 | + | 0.973000i | \(0.574136\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.43651 | −0.0464844 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.3843 | −0.400328 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.2795 | 0.590277 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.9539 | −0.901738 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.87891 | −0.221670 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.98530 | −0.192673 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.5040 | 0.820152 | 0.410076 | − | 0.912051i | \(-0.365502\pi\) | ||||
0.410076 | + | 0.912051i | \(0.365502\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.6211 | −0.566073 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.48205 | −0.208019 | −0.104009 | − | 0.994576i | \(-0.533167\pi\) | ||||
−0.104009 | + | 0.994576i | \(0.533167\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.1685 | −0.614514 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.5447 | 0.433779 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.9008 | −0.572698 | −0.286349 | − | 0.958125i | \(-0.592442\pi\) | ||||
−0.286349 | + | 0.958125i | \(0.592442\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.1582 | −0.867981 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.2964 | −0.392594 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54.4682 | −1.73727 | −0.868634 | − | 0.495455i | \(-0.835001\pi\) | ||||
−0.868634 | + | 0.495455i | \(0.835001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.7106 | 0.373130 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.7216 | 0.914220 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.73202 | −0.182268 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.3981 | −1.25152 | −0.625760 | − | 0.780016i | \(-0.715211\pi\) | ||||
−0.625760 | + | 0.780016i | \(0.715211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.1825 | 0.989546 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.24069 | −0.102737 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.2166 | 0.450245 | 0.225122 | − | 0.974331i | \(-0.427722\pi\) | ||||
0.225122 | + | 0.974331i | \(0.427722\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.35964 | −0.137933 |
(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 | 2004.2.a.b.1.4 | ✓ | 5 | |
3.2 | odd | 2 | 6012.2.a.f.1.2 | 5 | |||
4.3 | odd | 2 | 8016.2.a.q.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.b.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
6012.2.a.f.1.2 | 5 | 3.2 | odd | 2 | |||
8016.2.a.q.1.4 | 5 | 4.3 | odd | 2 |