Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1672,2,Mod(1,1672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1672.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1672 = 2^{3} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1672.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: | \(13.3509872180\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.106392688.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 9x^{4} + 12x^{3} + 25x^{2} - 10x - 16 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.972165\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1672.1 |
$q$-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 | ||||||||
\(3\) | −0.0278351 | −0.0160706 | −0.00803531 | − | 0.999968i | \(-0.502558\pi\) | ||||
−0.00803531 | + | 0.999968i | \(0.502558\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.122408 | −0.0547424 | −0.0273712 | − | 0.999625i | \(-0.508714\pi\) | ||||
−0.0273712 | + | 0.999625i | \(0.508714\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.877592 | −0.331699 | −0.165849 | − | 0.986151i | \(-0.553037\pi\) | ||||
−0.165849 | + | 0.986151i | \(0.553037\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99923 | −0.999742 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.68436 | 0.467157 | 0.233579 | − | 0.972338i | \(-0.424956\pi\) | ||||
0.233579 | + | 0.972338i | \(0.424956\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.00340723 | 0.000879744 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.34040 | 1.53777 | 0.768886 | − | 0.639386i | \(-0.220811\pi\) | ||||
0.768886 | + | 0.639386i | \(0.220811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0244279 | 0.00533060 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.12835 | −1.27785 | −0.638925 | − | 0.769269i | \(-0.720621\pi\) | ||||
−0.638925 | + | 0.769269i | \(0.720621\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98502 | −0.997003 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.166989 | 0.0321371 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.64572 | 0.676994 | 0.338497 | − | 0.940968i | \(-0.390082\pi\) | ||||
0.338497 | + | 0.940968i | \(0.390082\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.00340723 | 0.000611957 0 | 0.000305979 | − | 1.00000i | \(-0.499903\pi\) | ||||
0.000305979 | 1.00000i | \(0.499903\pi\) | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0278351 | 0.00484547 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.107424 | 0.0181580 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.21050 | −1.34980 | −0.674899 | − | 0.737911i | \(-0.735813\pi\) | ||||
−0.674899 | + | 0.737911i | \(0.735813\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0468844 | −0.00750751 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.1723 | −1.74483 | −0.872414 | − | 0.488768i | \(-0.837446\pi\) | ||||
−0.872414 | + | 0.488768i | \(0.837446\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0339670 | 0.00517992 | 0.00258996 | − | 0.999997i | \(-0.499176\pi\) | ||||
0.00258996 | + | 0.999997i | \(0.499176\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.367128 | 0.0547282 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.10979 | −0.891205 | −0.445602 | − | 0.895231i | \(-0.647010\pi\) | ||||
−0.445602 | + | 0.895231i | \(0.647010\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.22983 | −0.889976 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.176486 | −0.0247130 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.24999 | 0.995862 | 0.497931 | − | 0.867217i | \(-0.334093\pi\) | ||||
0.497931 | + | 0.867217i | \(0.334093\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.122408 | 0.0165054 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0278351 | −0.00368685 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.2031 | −1.84909 | −0.924543 | − | 0.381077i | \(-0.875553\pi\) | ||||
−0.924543 | + | 0.381077i | \(0.875553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.05412 | −0.519077 | −0.259538 | − | 0.965733i | \(-0.583570\pi\) | ||||
−0.259538 | + | 0.965733i | \(0.583570\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.63210 | 0.331613 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.206179 | −0.0255733 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.58181 | −1.04843 | −0.524217 | − | 0.851585i | \(-0.675642\pi\) | ||||
−0.524217 | + | 0.851585i | \(0.675642\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.170583 | 0.0205358 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0136263 | 0.00161714 | 0.000808572 | − | 1.00000i | \(-0.499743\pi\) | ||||
0.000808572 | 1.00000i | \(0.499743\pi\) | ||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.73280 | 0.436891 | 0.218446 | − | 0.975849i | \(-0.429901\pi\) | ||||
0.218446 | + | 0.975849i | \(0.429901\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.138759 | 0.0160225 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.877592 | 0.100011 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.356156 | −0.0400707 | −0.0200353 | − | 0.999799i | \(-0.506378\pi\) | ||||
−0.0200353 | + | 0.999799i | \(0.506378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.99303 | 0.999225 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.5146 | −1.70294 | −0.851472 | − | 0.524400i | \(-0.824290\pi\) | ||||
−0.851472 | + | 0.524400i | \(0.824290\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.776113 | −0.0841813 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.101479 | −0.0108797 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.31740 | 0.563644 | 0.281822 | − | 0.959467i | \(-0.409061\pi\) | ||||
0.281822 | + | 0.959467i | \(0.409061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.47818 | −0.154956 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.48408e−5 0 | −9.83453e−6 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.122408 | −0.0125588 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.7120 | 1.69685 | 0.848424 | − | 0.529317i | \(-0.177552\pi\) | ||||
0.848424 | + | 0.529317i | \(0.177552\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.99923 | 0.301433 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.0126 | −1.09579 | −0.547896 | − | 0.836547i | \(-0.684571\pi\) | ||||
−0.547896 | + | 0.836547i | \(0.684571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.43605 | −0.634162 | −0.317081 | − | 0.948398i | \(-0.602703\pi\) | ||||
−0.317081 | + | 0.948398i | \(0.602703\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.00299016 | −0.000291810 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.58366 | 0.636467 | 0.318233 | − | 0.948012i | \(-0.396910\pi\) | ||||
0.318233 | + | 0.948012i | \(0.396910\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1528 | 1.35559 | 0.677794 | − | 0.735252i | \(-0.262936\pi\) | ||||
0.677794 | + | 0.735252i | \(0.262936\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.228540 | 0.0216921 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.82796 | 0.454176 | 0.227088 | − | 0.973874i | \(-0.427079\pi\) | ||||
0.227088 | + | 0.973874i | \(0.427079\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.750157 | 0.0699525 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.05178 | −0.467037 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.56428 | −0.510077 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.310984 | 0.0280405 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.22224 | 0.109321 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.05382 | 0.0935114 | 0.0467557 | − | 0.998906i | \(-0.485112\pi\) | ||||
0.0467557 | + | 0.998906i | \(0.485112\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.000945476 0 | −8.32445e−5 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.20418 | 0.804173 | 0.402086 | − | 0.915602i | \(-0.368285\pi\) | ||||
0.402086 | + | 0.915602i | \(0.368285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.877592 | −0.0760969 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0204408 | −0.00175926 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.50230 | −0.555529 | −0.277764 | − | 0.960649i | \(-0.589593\pi\) | ||||
−0.277764 | + | 0.960649i | \(0.589593\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.8310 | −1.00349 | −0.501747 | − | 0.865015i | \(-0.667309\pi\) | ||||
−0.501747 | + | 0.865015i | \(0.667309\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.170067 | 0.0143222 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.68436 | −0.140853 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.446264 | −0.0370602 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.173408 | 0.0143025 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.2102 | −1.49184 | −0.745921 | − | 0.666035i | \(-0.767990\pi\) | ||||
−0.745921 | + | 0.666035i | \(0.767990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.9002 | −1.21257 | −0.606283 | − | 0.795249i | \(-0.707340\pi\) | ||||
−0.606283 | + | 0.795249i | \(0.707340\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.0163 | −1.53738 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.000417071 0 | −3.35000e−5 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.8091 | 1.58094 | 0.790471 | − | 0.612500i | \(-0.209836\pi\) | ||||
0.790471 | + | 0.612500i | \(0.209836\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.201804 | −0.0160041 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.37820 | 0.423861 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.2833 | −1.35373 | −0.676865 | − | 0.736107i | \(-0.736662\pi\) | ||||
−0.676865 | + | 0.736107i | \(0.736662\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.00340723 | −0.000265253 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.9578 | −0.925320 | −0.462660 | − | 0.886536i | \(-0.653105\pi\) | ||||
−0.462660 | + | 0.886536i | \(0.653105\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1629 | −0.781764 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.99923 | −0.229356 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.0077 | −0.912930 | −0.456465 | − | 0.889741i | \(-0.650885\pi\) | ||||
−0.456465 | + | 0.889741i | \(0.650885\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.37481 | 0.330705 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.395345 | 0.0297160 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.4981 | 0.934153 | 0.467076 | − | 0.884217i | \(-0.345307\pi\) | ||||
0.467076 | + | 0.884217i | \(0.345307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.84332 | 0.360001 | 0.180001 | − | 0.983666i | \(-0.442390\pi\) | ||||
0.180001 | + | 0.983666i | \(0.442390\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.112847 | 0.00834189 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00503 | 0.0738911 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.34040 | −0.463656 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.146548 | −0.0106598 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.43667 | −0.682813 | −0.341407 | − | 0.939916i | \(-0.610903\pi\) | ||||
−0.341407 | + | 0.939916i | \(0.610903\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.7679 | 1.20698 | 0.603489 | − | 0.797371i | \(-0.293777\pi\) | ||||
0.603489 | + | 0.797371i | \(0.293777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.00573901 | 0.000410979 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.4397 | 1.88375 | 0.941875 | − | 0.335963i | \(-0.109062\pi\) | ||||
0.941875 | + | 0.335963i | \(0.109062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.2973 | 1.36795 | 0.683974 | − | 0.729506i | \(-0.260250\pi\) | ||||
0.683974 | + | 0.729506i | \(0.260250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.238876 | 0.0168490 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.19946 | −0.224558 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.36758 | 0.0955160 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.3803 | 1.27752 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.97964 | 0.687026 | 0.343513 | − | 0.939148i | \(-0.388383\pi\) | ||||
0.343513 | + | 0.939148i | \(0.388383\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.000379290 0 | −2.59885e−5 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.00415782 | −0.000283561 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.00299016 | −0.000202985 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.103903 | −0.00702112 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.6795 | 0.718382 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.2692 | 1.08947 | 0.544734 | − | 0.838609i | \(-0.316631\pi\) | ||||
0.544734 | + | 0.838609i | \(0.316631\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.9512 | 0.996746 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.1015 | −1.66605 | −0.833023 | − | 0.553238i | \(-0.813392\pi\) | ||||
−0.833023 | + | 0.553238i | \(0.813392\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.06007 | −0.202215 | −0.101107 | − | 0.994876i | \(-0.532239\pi\) | ||||
−0.101107 | + | 0.994876i | \(0.532239\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0244279 | −0.00160724 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.1783 | −1.45295 | −0.726473 | − | 0.687195i | \(-0.758842\pi\) | ||||
−0.726473 | + | 0.687195i | \(0.758842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.747885 | 0.0487866 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.00991364 | 0.000643960 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.9023 | 1.41674 | 0.708370 | − | 0.705842i | \(-0.249431\pi\) | ||||
0.708370 | + | 0.705842i | \(0.249431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.89608 | −0.186553 | −0.0932765 | − | 0.995640i | \(-0.529734\pi\) | ||||
−0.0932765 | + | 0.995640i | \(0.529734\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.751290 | −0.0481953 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.762579 | 0.0487194 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.68436 | 0.107173 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.431850 | 0.0273674 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.46432 | −0.471143 | −0.235572 | − | 0.971857i | \(-0.575696\pi\) | ||||
−0.235572 | + | 0.971857i | \(0.575696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.12835 | 0.385286 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0216032 | 0.00135285 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.24751 | 0.327331 | 0.163665 | − | 0.986516i | \(-0.447668\pi\) | ||||
0.163665 | + | 0.986516i | \(0.447668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.20547 | 0.447726 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.9343 | −0.676819 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.6240 | 1.14841 | 0.574204 | − | 0.818712i | \(-0.305312\pi\) | ||||
0.574204 | + | 0.818712i | \(0.305312\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.887454 | −0.0545158 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.148011 | −0.00905810 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0400 | −0.917005 | −0.458503 | − | 0.888693i | \(-0.651614\pi\) | ||||
−0.458503 | + | 0.888693i | \(0.651614\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.2895 | −1.71847 | −0.859234 | − | 0.511583i | \(-0.829059\pi\) | ||||
−0.859234 | + | 0.511583i | \(0.829059\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0411454 | 0.00249023 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.98502 | 0.300608 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.3581 | 1.34337 | 0.671685 | − | 0.740837i | \(-0.265571\pi\) | ||||
0.671685 | + | 0.740837i | \(0.265571\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.0102191 | −0.000611799 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.3487 | 0.736662 | 0.368331 | − | 0.929695i | \(-0.379929\pi\) | ||||
0.368331 | + | 0.929695i | \(0.379929\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.3996 | −0.737082 | −0.368541 | − | 0.929611i | \(-0.620143\pi\) | ||||
−0.368541 | + | 0.929611i | \(0.620143\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.00340723 | 0.000201827 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.80477 | 0.578757 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.2006 | 1.36474 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.465181 | −0.0272694 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.24377 | −0.423186 | −0.211593 | − | 0.977358i | \(-0.567865\pi\) | ||||
−0.211593 | + | 0.977358i | \(0.567865\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.73857 | 0.101223 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.166989 | −0.00968970 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.3224 | −0.596957 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0298092 | −0.00171817 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.306536 | 0.0176100 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.496255 | 0.0284155 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.1408 | −1.03535 | −0.517674 | − | 0.855578i | \(-0.673202\pi\) | ||||
−0.517674 | + | 0.855578i | \(0.673202\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.179148 | 0.0101914 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.59406 | 0.544029 | 0.272015 | − | 0.962293i | \(-0.412310\pi\) | ||||
0.272015 | + | 0.962293i | \(0.412310\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.2280 | 1.65207 | 0.826033 | − | 0.563622i | \(-0.190592\pi\) | ||||
0.826033 | + | 0.563622i | \(0.190592\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.322189 | −0.0181533 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.8728 | 0.723008 | 0.361504 | − | 0.932371i | \(-0.382263\pi\) | ||||
0.361504 | + | 0.932371i | \(0.382263\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.64572 | −0.204121 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.183257 | −0.0102284 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.34040 | 0.352789 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.39656 | −0.465758 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.393944 | −0.0217851 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.36191 | 0.295611 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.48289 | 0.466262 | 0.233131 | − | 0.972445i | \(-0.425103\pi\) | ||||
0.233131 | + | 0.972445i | \(0.425103\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.6251 | 1.34945 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.05048 | 0.0573938 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7212 | −0.747442 | −0.373721 | − | 0.927541i | \(-0.621918\pi\) | ||||
−0.373721 | + | 0.927541i | \(0.621918\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.134387 | −0.00729890 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.00340723 | −0.000184512 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.6104 | 0.626903 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0208807 | −0.00112418 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.8279 | −0.742318 | −0.371159 | − | 0.928569i | \(-0.621040\pi\) | ||||
−0.371159 | + | 0.928569i | \(0.621040\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.1644 | 1.61466 | 0.807331 | − | 0.590099i | \(-0.200911\pi\) | ||||
0.807331 | + | 0.590099i | \(0.200911\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.281270 | 0.0150131 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.9396 | −1.75320 | −0.876598 | − | 0.481223i | \(-0.840193\pi\) | ||||
−0.876598 | + | 0.481223i | \(0.840193\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.00166796 | −8.85263e−5 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.154883 | 0.00819726 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.8135 | 1.89017 | 0.945083 | − | 0.326830i | \(-0.105980\pi\) | ||||
0.945083 | + | 0.326830i | \(0.105980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0278351 | −0.00146097 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.456923 | −0.0239165 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.6271 | 1.54652 | 0.773260 | − | 0.634089i | \(-0.218625\pi\) | ||||
0.773260 | + | 0.634089i | \(0.218625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 33.5084 | 1.74438 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.36253 | −0.330326 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.64878 | 0.188927 | 0.0944633 | − | 0.995528i | \(-0.469886\pi\) | ||||
0.0944633 | + | 0.995528i | \(0.469886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.0340213 | −0.00175685 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.14071 | 0.316263 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.07155 | 0.106408 | 0.0532041 | − | 0.998584i | \(-0.483057\pi\) | ||||
0.0532041 | + | 0.998584i | \(0.483057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.0293332 | −0.00150279 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.4545 | 0.738592 | 0.369296 | − | 0.929312i | \(-0.379599\pi\) | ||||
0.369296 | + | 0.929312i | \(0.379599\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.107424 | −0.00547483 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.101875 | −0.00517858 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.37041 | 0.322992 | 0.161496 | − | 0.986873i | \(-0.448368\pi\) | ||||
0.161496 | + | 0.986873i | \(0.448368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −38.8562 | −1.96504 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.256199 | −0.0129236 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.0435962 | 0.00219356 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.9040 | −0.697824 | −0.348912 | − | 0.937155i | \(-0.613449\pi\) | ||||
−0.348912 | + | 0.937155i | \(0.613449\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0244279 | 0.00122292 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.6324 | −1.28002 | −0.640011 | − | 0.768366i | \(-0.721070\pi\) | ||||
−0.640011 | + | 0.768366i | \(0.721070\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.00573901 | 0.000285880 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.10082 | −0.0547000 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.21050 | 0.406979 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.60766 | 0.128941 | 0.0644703 | − | 0.997920i | \(-0.479464\pi\) | ||||
0.0644703 | + | 0.997920i | \(0.479464\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.180992 | 0.00892769 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.4645 | 0.613340 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.89910 | 0.0932232 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.329318 | 0.0161268 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.20940 | −0.205643 | −0.102821 | − | 0.994700i | \(-0.532787\pi\) | ||||
−0.102821 | + | 0.994700i | \(0.532787\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.8223 | −1.69714 | −0.848568 | − | 0.529086i | \(-0.822535\pi\) | ||||
−0.848568 | + | 0.529086i | \(0.822535\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.3246 | 0.890974 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −31.6070 | −1.53316 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.55787 | 0.172177 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0468844 | 0.00226360 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.1564 | −1.01907 | −0.509535 | − | 0.860450i | \(-0.670182\pi\) | ||||
−0.509535 | + | 0.860450i | \(0.670182\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.66913 | 0.224384 | 0.112192 | − | 0.993687i | \(-0.464213\pi\) | ||||
0.112192 | + | 0.993687i | \(0.464213\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0124218 | 0.000595581 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.12835 | −0.293159 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.2453 | 1.72989 | 0.864947 | − | 0.501864i | \(-0.167352\pi\) | ||||
0.864947 | + | 0.501864i | \(0.167352\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.6847 | 0.889746 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.79016 | −0.275099 | −0.137549 | − | 0.990495i | \(-0.543923\pi\) | ||||
−0.137549 | + | 0.990495i | \(0.543923\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.650891 | −0.0308552 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.506884 | 0.0239748 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.4020 | −0.915635 | −0.457818 | − | 0.889046i | \(-0.651369\pi\) | ||||
−0.457818 | + | 0.889046i | \(0.651369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.1723 | 0.526085 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.414750 | 0.0194867 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.180941 | 0.00848263 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.6795 | 1.15446 | 0.577228 | − | 0.816583i | \(-0.304134\pi\) | ||||
0.577228 | + | 0.816583i | \(0.304134\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.05878 | 0.0494195 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.63779 | 0.169429 | 0.0847145 | − | 0.996405i | \(-0.473002\pi\) | ||||
0.0847145 | + | 0.996405i | \(0.473002\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1814 | 0.612592 | 0.306296 | − | 0.951936i | \(-0.400910\pi\) | ||||
0.306296 | + | 0.951936i | \(0.400910\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.16092e−5 0 | 5.38365e−7 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.6892 | −1.46640 | −0.733200 | − | 0.680013i | \(-0.761974\pi\) | ||||
−0.733200 | + | 0.680013i | \(0.761974\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.53133 | 0.347764 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.551390 | −0.0254067 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.0339670 | −0.00156180 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.98502 | −0.228728 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.7443 | −0.995605 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.2270 | 1.88371 | 0.941854 | − | 0.336022i | \(-0.109082\pi\) | ||||
0.941854 | + | 0.336022i | \(0.109082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.8294 | −0.630568 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.149703 | −0.00681171 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.04568 | −0.0928895 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.21468 | 0.145671 | 0.0728354 | − | 0.997344i | \(-0.476795\pi\) | ||||
0.0728354 | + | 0.997344i | \(0.476795\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.481082 | 0.0217553 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.92336 | −0.267317 | −0.133659 | − | 0.991027i | \(-0.542673\pi\) | ||||
−0.133659 | + | 0.991027i | \(0.542673\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.1153 | 1.04106 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.367128 | −0.0165012 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.0119583 | −0.000536404 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.8155 | −0.618468 | −0.309234 | − | 0.950986i | \(-0.600073\pi\) | ||||
−0.309234 | + | 0.950986i | \(0.600073\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.332846 | 0.0148705 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.8789 | 1.02012 | 0.510061 | − | 0.860138i | \(-0.329623\pi\) | ||||
0.510061 | + | 0.860138i | \(0.329623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.34802 | 0.0599862 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.282887 | 0.0125634 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.4761 | −1.66110 | −0.830549 | − | 0.556946i | \(-0.811973\pi\) | ||||
−0.830549 | + | 0.556946i | \(0.811973\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.27588 | −0.144916 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.166989 | 0.00737275 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.787821 | 0.0347156 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.10979 | 0.268708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.334237 | 0.0146714 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.4757 | 1.11611 | 0.558056 | − | 0.829803i | \(-0.311547\pi\) | ||||
0.558056 | + | 0.829803i | \(0.311547\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.3594 | 1.41498 | 0.707488 | − | 0.706725i | \(-0.249828\pi\) | ||||
0.707488 | + | 0.706725i | \(0.249828\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.121773 | −0.00531463 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.0216032 | 0.000941051 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.5567 | 0.632900 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 42.5983 | 1.84861 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.8183 | −0.815109 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.805891 | −0.0348417 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.347887 | −0.0150124 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.22983 | 0.268338 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.2211 | 0.783388 | 0.391694 | − | 0.920096i | \(-0.371889\pi\) | ||||
0.391694 | + | 0.920096i | \(0.371889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.134815 | −0.00578545 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.73241 | −0.0742081 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.5039 | −1.30425 | −0.652127 | − | 0.758110i | \(-0.726123\pi\) | ||||
−0.652127 | + | 0.758110i | \(0.726123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.1592 | 0.518943 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.64572 | 0.155313 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.312560 | 0.0132914 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.0279751 | −0.00118748 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.4094 | −0.949519 | −0.474759 | − | 0.880116i | \(-0.657465\pi\) | ||||
−0.474759 | + | 0.880116i | \(0.657465\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0572127 | 0.00241984 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.176486 | 0.00745124 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.7915 | −1.76130 | −0.880652 | − | 0.473764i | \(-0.842895\pi\) | ||||
−0.880652 | + | 0.473764i | \(0.842895\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.590979 | −0.0248627 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.89221 | −0.331442 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.4500 | −0.480009 | −0.240004 | − | 0.970772i | \(-0.577149\pi\) | ||||
−0.240004 | + | 0.970772i | \(0.577149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.39669 | 0.0584497 | 0.0292248 | − | 0.999573i | \(-0.490696\pi\) | ||||
0.0292248 | + | 0.999573i | \(0.490696\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.262671 | 0.0109732 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.5499 | 1.27402 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.85413 | −0.368602 | −0.184301 | − | 0.982870i | \(-0.559002\pi\) | ||||
−0.184301 | + | 0.982870i | \(0.559002\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.466736 | −0.0193969 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.6155 | 0.564864 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.24999 | −0.300264 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.618376 | 0.0255667 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.1705 | −0.419783 | −0.209891 | − | 0.977725i | \(-0.567311\pi\) | ||||
−0.209891 | + | 0.977725i | \(0.567311\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.00340723 | 0.000140393 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.735952 | −0.0302730 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.01632 | −0.205996 | −0.102998 | − | 0.994682i | \(-0.532843\pi\) | ||||
−0.102998 | + | 0.994682i | \(0.532843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.681111 | 0.0279228 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.537143 | −0.0219838 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.9408 | 1.14163 | 0.570816 | − | 0.821078i | \(-0.306627\pi\) | ||||
0.570816 | + | 0.821078i | \(0.306627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.9161 | −1.17951 | −0.589756 | − | 0.807581i | \(-0.700776\pi\) | ||||
−0.589756 | + | 0.807581i | \(0.700776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.7388 | 1.04816 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.122408 | −0.00497658 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.30116 | −0.133990 | −0.0669950 | − | 0.997753i | \(-0.521341\pi\) | ||||
−0.0669950 | + | 0.997753i | \(0.521341\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0890574 | 0.00360879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.2911 | −0.416333 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.7837 | −1.40490 | −0.702451 | − | 0.711732i | \(-0.747911\pi\) | ||||
−0.702451 | + | 0.711732i | \(0.747911\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0380668 | −0.00153500 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.452766 | −0.0182277 | −0.00911383 | − | 0.999958i | \(-0.502901\pi\) | ||||
−0.00911383 | + | 0.999958i | \(0.502901\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.7171 | 1.23462 | 0.617312 | − | 0.786718i | \(-0.288222\pi\) | ||||
0.617312 | + | 0.786718i | \(0.288222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.02337 | −0.0410664 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.66651 | −0.186960 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7755 | 0.991019 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0278351 | 0.00111163 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.0578 | −2.07568 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0741 | 0.600092 | 0.300046 | − | 0.953925i | \(-0.402998\pi\) | ||||
0.300046 | + | 0.953925i | \(0.402998\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.277784 | −0.0110409 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.128996 | −0.00511904 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.4933 | −0.415759 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0408683 | −0.00161673 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.2312 | 1.39155 | 0.695774 | − | 0.718261i | \(-0.255061\pi\) | ||||
0.695774 | + | 0.718261i | \(0.255061\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.1788 | 1.03239 | 0.516195 | − | 0.856471i | \(-0.327348\pi\) | ||||
0.516195 | + | 0.856471i | \(0.327348\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.000115733 0 | 4.55700e−6 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.2822 | −0.954633 | −0.477316 | − | 0.878732i | \(-0.658390\pi\) | ||||
−0.477316 | + | 0.878732i | \(0.658390\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.2031 | 0.557520 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.32315e−5 0 | 3.26210e−6 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −50.2439 | −1.96620 | −0.983098 | − | 0.183078i | \(-0.941394\pi\) | ||||
−0.983098 | + | 0.183078i | \(0.941394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.12666 | −0.0440223 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.1955 | −0.436779 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.25601 | 0.360563 | 0.180281 | − | 0.983615i | \(-0.442299\pi\) | ||||
0.180281 | + | 0.983615i | \(0.442299\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.8800 | 0.889927 | 0.444964 | − | 0.895549i | \(-0.353217\pi\) | ||||
0.444964 | + | 0.895549i | \(0.353217\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.297266 | −0.0115448 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.107424 | 0.00416572 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.3423 | −0.865096 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.452856 | −0.0175084 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.05412 | 0.156508 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.5307 | −1.63944 | −0.819718 | − | 0.572767i | \(-0.805870\pi\) | ||||
−0.819718 | + | 0.572767i | \(0.805870\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.832444 | −0.0320408 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.8688 | 1.14795 | 0.573976 | − | 0.818872i | \(-0.305400\pi\) | ||||
0.573976 | + | 0.818872i | \(0.305400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.6663 | −0.562842 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.698704 | 0.0267744 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.1162 | −1.72632 | −0.863162 | − | 0.504928i | \(-0.831519\pi\) | ||||
−0.863162 | + | 0.504928i | \(0.831519\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.795931 | 0.0304109 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.0851773 | 0.00324972 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.2116 | 0.465224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.2491 | −0.542062 | −0.271031 | − | 0.962571i | \(-0.587365\pi\) | ||||
−0.271031 | + | 0.962571i | \(0.587365\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.63210 | −0.0999851 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.44821 | 0.0549336 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −70.8371 | −2.68315 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.617335 | 0.0233497 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.86294 | 0.183671 | 0.0918354 | − | 0.995774i | \(-0.470727\pi\) | ||||
0.0918354 | + | 0.995774i | \(0.470727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.21050 | −0.309665 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0208175 | −0.000784032 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.66454 | 0.363473 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.0524 | −0.940863 | −0.470432 | − | 0.882436i | \(-0.655902\pi\) | ||||
−0.470432 | + | 0.882436i | \(0.655902\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.06819 | 0.0400603 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.0208807 | −0.000781989 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.206179 | 0.00771064 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.609652 | −0.0227679 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.9734 | −1.71452 | −0.857260 | − | 0.514884i | \(-0.827835\pi\) | ||||
−0.857260 | + | 0.514884i | \(0.827835\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.64822 | 0.210351 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.0806128 | 0.00299802 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.1740 | −0.674965 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.4967 | 0.982709 | 0.491354 | − | 0.870960i | \(-0.336502\pi\) | ||||
0.491354 | + | 0.870960i | \(0.336502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9582 | −0.998451 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.215364 | 0.00796554 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.180886 | −0.00668116 | −0.00334058 | − | 0.999994i | \(-0.501063\pi\) | ||||
−0.00334058 | + | 0.999994i | \(0.501063\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.0212265 | −0.000782951 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.58181 | 0.316115 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.3719 | 1.66903 | 0.834516 | − | 0.550984i | \(-0.185747\pi\) | ||||
0.834516 | + | 0.550984i | \(0.185747\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0468844 | −0.00172234 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.6104 | −1.78334 | −0.891672 | − | 0.452683i | \(-0.850467\pi\) | ||||
−0.891672 | + | 0.452683i | \(0.850467\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.22907 | 0.0816669 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 46.5317 | 1.70250 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.77777 | −0.211115 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.6401 | 1.59245 | 0.796225 | − | 0.605000i | \(-0.206827\pi\) | ||||
0.796225 | + | 0.605000i | \(0.206827\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.207770 | 0.00757157 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.82390 | 0.0663787 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.0661 | 1.45623 | 0.728114 | − | 0.685456i | \(-0.240397\pi\) | ||||
0.728114 | + | 0.685456i | \(0.240397\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.170583 | −0.00619179 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.0137 | 0.870494 | 0.435247 | − | 0.900311i | \(-0.356661\pi\) | ||||
0.435247 | + | 0.900311i | \(0.356661\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.4204 | −0.449647 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.32774 | 0.0841596 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.9231 | −0.863814 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.8574 | 1.11275 | 0.556374 | − | 0.830932i | \(-0.312192\pi\) | ||||
0.556374 | + | 0.830932i | \(0.312192\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.146065 | −0.00526041 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.0873 | −0.650554 | −0.325277 | − | 0.945619i | \(-0.605458\pi\) | ||||
−0.325277 | + | 0.945619i | \(0.605458\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0169851 | −0.000610123 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.200565 | −0.00719523 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.1723 | −0.400291 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0136263 | −0.000487587 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.608797 | 0.0217566 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.42479 | −0.0865445 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.3431 | −1.58066 | −0.790330 | − | 0.612681i | \(-0.790091\pi\) | ||||
−0.790330 | + | 0.612681i | \(0.790091\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.518403 | −0.0184556 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.23698 | −0.150650 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.82860 | −0.242491 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0247024 | 0.000876103 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.4047 | −0.403976 | −0.201988 | − | 0.979388i | \(-0.564740\pi\) | ||||
−0.201988 | + | 0.979388i | \(0.564740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.7385 | −1.37047 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.9481 | −0.563498 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.73280 | −0.131728 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.658332 | −0.0232032 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.418641 | 0.0147368 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.4641 | −0.403057 | −0.201528 | − | 0.979483i | \(-0.564591\pi\) | ||||
−0.201528 | + | 0.979483i | \(0.564591\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.7845 | −1.18633 | −0.593167 | − | 0.805080i | \(-0.702122\pi\) | ||||
−0.593167 | + | 0.805080i | \(0.702122\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.787443 | 0.0276168 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.11560 | 0.0741064 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0339670 | 0.00118836 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.43340 | 0.154916 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.9537 | 0.521889 | 0.260944 | − | 0.965354i | \(-0.415966\pi\) | ||||
0.260944 | + | 0.965354i | \(0.415966\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.9606 | −0.660925 | −0.330462 | − | 0.943819i | \(-0.607205\pi\) | ||||
−0.330462 | + | 0.943819i | \(0.607205\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.138759 | −0.00483095 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.1451 | 0.978699 | 0.489350 | − | 0.872088i | \(-0.337234\pi\) | ||||
0.489350 | + | 0.872088i | \(0.337234\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.4452 | 1.09214 | 0.546069 | − | 0.837740i | \(-0.316124\pi\) | ||||
0.546069 | + | 0.837740i | \(0.316124\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.622342 | −0.0215888 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.4996 | −1.36858 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.46372 | 0.0506542 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.000568971 0 | 1.96665e−5 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.6194 | 1.71305 | 0.856526 | − | 0.516104i | \(-0.172618\pi\) | ||||
0.856526 | + | 0.516104i | \(0.172618\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.7087 | −0.541679 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.343728 | −0.0118386 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.24402 | 0.0427956 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.877592 | −0.0301544 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.345146 | 0.0118454 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50.3168 | 1.72484 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.9643 | −0.957478 | −0.478739 | − | 0.877957i | \(-0.658906\pi\) | ||||
−0.478739 | + | 0.877957i | \(0.658906\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.367128 | 0.0125555 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.38737 | −0.0473916 | −0.0236958 | − | 0.999719i | \(-0.507543\pi\) | ||||
−0.0236958 | + | 0.999719i | \(0.507543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3432 | 0.625864 | 0.312932 | − | 0.949776i | \(-0.398689\pi\) | ||||
0.312932 | + | 0.949776i | \(0.398689\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.272917 | −0.00930098 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.2423 | −1.54006 | −0.770032 | − | 0.638005i | \(-0.779760\pi\) | ||||
−0.770032 | + | 0.638005i | \(0.779760\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.46984 | 0.0499760 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.645793 | −0.0219323 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.356156 | 0.0120818 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4549 | −0.489784 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −50.1231 | −1.69641 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.07263 | −0.0362615 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.8202 | −1.44593 | −0.722967 | − | 0.690882i | \(-0.757222\pi\) | ||||
−0.722967 | + | 0.690882i | \(0.757222\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.201631 | 0.00680086 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.4911 | −1.09465 | −0.547326 | − | 0.836920i | \(-0.684354\pi\) | ||||
−0.547326 | + | 0.836920i | \(0.684354\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.0319 | 0.438558 | 0.219279 | − | 0.975662i | \(-0.429630\pi\) | ||||
0.219279 | + | 0.975662i | \(0.429630\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0483933 | −0.00162672 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.6956 | −1.33285 | −0.666424 | − | 0.745573i | \(-0.732176\pi\) | ||||
−0.666424 | + | 0.745573i | \(0.732176\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.924824 | −0.0310176 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.99303 | −0.301278 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.10979 | −0.204456 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.52986 | −0.0511377 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.287324 | 0.00959347 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.0124218 | 0.000414291 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.9678 | 1.53141 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.000829742 0 | 2.76121e−5 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.592860 | −0.0197073 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.181821 | −0.00603727 | −0.00301863 | − | 0.999995i | \(-0.500961\pi\) | ||||
−0.00301863 | + | 0.999995i | \(0.500961\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33.0292 | 1.09551 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.9193 | −1.05753 | −0.528767 | − | 0.848767i | \(-0.677345\pi\) | ||||
−0.528767 | + | 0.848767i | \(0.677345\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.5146 | 0.513457 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0138133 | −0.000456655 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.07751 | −0.266743 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.8673 | 0.952246 | 0.476123 | − | 0.879379i | \(-0.342042\pi\) | ||||
0.476123 | + | 0.879379i | \(0.342042\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.504950 | 0.0166387 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.0229516 | 0.000755461 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.9295 | 1.34575 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.3031 | 0.633999 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.5258 | 0.804666 | 0.402333 | − | 0.915493i | \(-0.368199\pi\) | ||||
0.402333 | + | 0.915493i | \(0.368199\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.22983 | −0.204174 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.267052 | −0.00874289 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.776113 | 0.0253816 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.6373 | −0.347506 | −0.173753 | − | 0.984789i | \(-0.555589\pi\) | ||||
−0.173753 | + | 0.984789i | \(0.555589\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.813566 | −0.0265497 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.41861 | 0.0462453 | 0.0231226 | − | 0.999733i | \(-0.492639\pi\) | ||||
0.0231226 | + | 0.999733i | \(0.492639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 68.4681 | 2.22963 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0179387 | 0.000583544 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.25867 | −0.170884 | −0.0854418 | − | 0.996343i | \(-0.527230\pi\) | ||||
−0.0854418 | + | 0.996343i | \(0.527230\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.28738 | 0.204097 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.358316 | −0.0116192 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.5273 | −1.66913 | −0.834567 | − | 0.550906i | \(-0.814282\pi\) | ||||
−0.834567 | + | 0.550906i | \(0.814282\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.15512 | 0.0373788 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.101479 | 0.00328036 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.70636 | 0.184268 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.7459 | −0.636302 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.05252 | −0.0660728 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.8627 | 1.53916 | 0.769581 | − | 0.638550i | \(-0.220465\pi\) | ||||
0.769581 | + | 0.638550i | \(0.220465\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.176486 | −0.00566954 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.48025 | 0.240053 | 0.120026 | − | 0.992771i | \(-0.461702\pi\) | ||||
0.120026 | + | 0.992771i | \(0.461702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.3828 | 0.332857 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.233719 | 0.00748501 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.0292 | −0.416841 | −0.208420 | − | 0.978039i | \(-0.566832\pi\) | ||||
−0.208420 | + | 0.978039i | \(0.566832\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.31740 | −0.169945 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.4473 | −1.35524 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.1827 | 1.53679 | 0.768394 | − | 0.639977i | \(-0.221056\pi\) | ||||
0.768394 | + | 0.639977i | \(0.221056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.23642 | −0.103121 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.149249 | −0.00475066 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.208162 | −0.00661916 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.1756 | −1.72095 | −0.860473 | − | 0.509496i | \(-0.829832\pi\) | ||||
−0.860473 | + | 0.509496i | \(0.829832\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.236122 | −0.00749312 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.36214 | −0.0748848 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.3227 | −0.548617 | −0.274308 | − | 0.961642i | \(-0.588449\pi\) | ||||
−0.274308 | + | 0.961642i | \(0.588449\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.37106 | −0.0433786 |
(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 | 1672.2.a.i.1.4 | ✓ | 6 | |
4.3 | odd | 2 | 3344.2.a.z.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.i.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
3344.2.a.z.1.3 | 6 | 4.3 | odd | 2 |