Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.44400625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 11x^{4} - x^{3} + 29x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.141689\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.141689 | 0.100190 | 0.0500948 | − | 0.998744i | \(-0.484048\pi\) | ||||
0.0500948 | + | 0.998744i | \(0.484048\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.97992 | −0.989962 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.858311 | −0.324411 | −0.162205 | − | 0.986757i | \(-0.551861\pi\) | ||||
−0.162205 | + | 0.986757i | \(0.551861\pi\) | |||||||
\(8\) | −0.563913 | −0.199374 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.67993 | 1.10954 | 0.554770 | − | 0.832004i | \(-0.312806\pi\) | ||||
0.554770 | + | 0.832004i | \(0.312806\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.58134 | 1.27064 | 0.635318 | − | 0.772251i | \(-0.280869\pi\) | ||||
0.635318 | + | 0.772251i | \(0.280869\pi\) | |||||||
\(14\) | −0.121614 | −0.0325026 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.87995 | 0.969987 | ||||||||
\(17\) | 5.30702 | 1.28714 | 0.643571 | − | 0.765387i | \(-0.277452\pi\) | ||||
0.643571 | + | 0.765387i | \(0.277452\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.36870 | 1.46108 | 0.730540 | − | 0.682870i | \(-0.239268\pi\) | ||||
0.730540 | + | 0.682870i | \(0.239268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.521407 | 0.111164 | ||||||||
\(23\) | −3.42379 | −0.713909 | −0.356954 | − | 0.934122i | \(-0.616185\pi\) | ||||
−0.356954 | + | 0.934122i | \(0.616185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.649128 | 0.127304 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.69939 | 0.321154 | ||||||||
\(29\) | −3.73405 | −0.693396 | −0.346698 | − | 0.937977i | \(-0.612697\pi\) | ||||
−0.346698 | + | 0.937977i | \(0.612697\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25290 | 0.225028 | 0.112514 | − | 0.993650i | \(-0.464110\pi\) | ||||
0.112514 | + | 0.993650i | \(0.464110\pi\) | |||||||
\(32\) | 1.67757 | 0.296556 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.751949 | 0.128958 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.45067 | −1.22488 | −0.612441 | − | 0.790516i | \(-0.709812\pi\) | ||||
−0.612441 | + | 0.790516i | \(0.709812\pi\) | |||||||
\(38\) | 0.902378 | 0.146385 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.53168 | 0.395381 | 0.197691 | − | 0.980264i | \(-0.436656\pi\) | ||||
0.197691 | + | 0.980264i | \(0.436656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.37972 | −0.515402 | −0.257701 | − | 0.966225i | \(-0.582965\pi\) | ||||
−0.257701 | + | 0.966225i | \(0.582965\pi\) | |||||||
\(44\) | −7.28598 | −1.09840 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.485114 | −0.0715262 | ||||||||
\(47\) | 8.49937 | 1.23976 | 0.619880 | − | 0.784696i | \(-0.287181\pi\) | ||||
0.619880 | + | 0.784696i | \(0.287181\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.26330 | −0.894758 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.07071 | −1.25788 | ||||||||
\(53\) | 2.34827 | 0.322560 | 0.161280 | − | 0.986909i | \(-0.448438\pi\) | ||||
0.161280 | + | 0.986909i | \(0.448438\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.484013 | 0.0646789 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.529076 | −0.0694710 | ||||||||
\(59\) | −13.1264 | −1.70891 | −0.854455 | − | 0.519525i | \(-0.826109\pi\) | ||||
−0.854455 | + | 0.519525i | \(0.826109\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3476 | 1.32488 | 0.662439 | − | 0.749116i | \(-0.269521\pi\) | ||||
0.662439 | + | 0.749116i | \(0.269521\pi\) | |||||||
\(62\) | 0.177523 | 0.0225454 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.52220 | −0.940275 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.34649 | 0.408838 | 0.204419 | − | 0.978883i | \(-0.434469\pi\) | ||||
0.204419 | + | 0.978883i | \(0.434469\pi\) | |||||||
\(68\) | −10.5075 | −1.27422 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.32289 | 0.513032 | 0.256516 | − | 0.966540i | \(-0.417425\pi\) | ||||
0.256516 | + | 0.966540i | \(0.417425\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.08007 | −1.06274 | −0.531371 | − | 0.847139i | \(-0.678323\pi\) | ||||
−0.531371 | + | 0.847139i | \(0.678323\pi\) | |||||||
\(74\) | −1.05568 | −0.122721 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.6095 | −1.44641 | ||||||||
\(77\) | −3.15852 | −0.359947 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.24730 | −0.365350 | −0.182675 | − | 0.983173i | \(-0.558476\pi\) | ||||
−0.182675 | + | 0.983173i | \(0.558476\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.358712 | 0.0396131 | ||||||||
\(83\) | 7.39269 | 0.811453 | 0.405727 | − | 0.913994i | \(-0.367019\pi\) | ||||
0.405727 | + | 0.913994i | \(0.367019\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.478870 | −0.0516379 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.07516 | −0.221213 | ||||||||
\(89\) | 15.4975 | 1.64273 | 0.821367 | − | 0.570400i | \(-0.193212\pi\) | ||||
0.821367 | + | 0.570400i | \(0.193212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.93221 | −0.412208 | ||||||||
\(92\) | 6.77883 | 0.706742 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.20427 | 0.124211 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0386 | −1.01926 | −0.509631 | − | 0.860393i | \(-0.670218\pi\) | ||||
−0.509631 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(98\) | −0.887444 | −0.0896454 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.714616 | 0.0711070 | 0.0355535 | − | 0.999368i | \(-0.488681\pi\) | ||||
0.0355535 | + | 0.999368i | \(0.488681\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.780764 | 0.0769310 | 0.0384655 | − | 0.999260i | \(-0.487753\pi\) | ||||
0.0384655 | + | 0.999260i | \(0.487753\pi\) | |||||||
\(104\) | −2.58348 | −0.253331 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.332725 | 0.0323171 | ||||||||
\(107\) | −11.9601 | −1.15623 | −0.578113 | − | 0.815957i | \(-0.696211\pi\) | ||||
−0.578113 | + | 0.815957i | \(0.696211\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.43384 | 0.233119 | 0.116560 | − | 0.993184i | \(-0.462813\pi\) | ||||
0.116560 | + | 0.993184i | \(0.462813\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.33020 | −0.314674 | ||||||||
\(113\) | 16.0354 | 1.50848 | 0.754240 | − | 0.656599i | \(-0.228006\pi\) | ||||
0.754240 | + | 0.656599i | \(0.228006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.39313 | 0.686435 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.85987 | −0.171215 | ||||||||
\(119\) | −4.55507 | −0.417563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.54188 | 0.231080 | ||||||||
\(122\) | 1.46615 | 0.132739 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.48065 | −0.222769 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.83848 | −0.340610 | −0.170305 | − | 0.985391i | \(-0.554475\pi\) | ||||
−0.170305 | + | 0.985391i | \(0.554475\pi\) | |||||||
\(128\) | −4.42097 | −0.390762 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.4495 | 1.08771 | 0.543857 | − | 0.839178i | \(-0.316963\pi\) | ||||
0.543857 | + | 0.839178i | \(0.316963\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.46632 | −0.473990 | ||||||||
\(134\) | 0.474162 | 0.0409613 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.99270 | −0.256622 | ||||||||
\(137\) | 11.8589 | 1.01317 | 0.506587 | − | 0.862189i | \(-0.330907\pi\) | ||||
0.506587 | + | 0.862189i | \(0.330907\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.66089 | −0.395332 | −0.197666 | − | 0.980269i | \(-0.563336\pi\) | ||||
−0.197666 | + | 0.980269i | \(0.563336\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.612508 | 0.0514005 | ||||||||
\(143\) | 16.8590 | 1.40982 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.28655 | −0.106476 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.7518 | 1.21259 | ||||||||
\(149\) | 11.5480 | 0.946053 | 0.473026 | − | 0.881048i | \(-0.343162\pi\) | ||||
0.473026 | + | 0.881048i | \(0.343162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.4694 | 1.99129 | 0.995646 | − | 0.0932103i | \(-0.0297129\pi\) | ||||
0.995646 | + | 0.0932103i | \(0.0297129\pi\) | |||||||
\(152\) | −3.59140 | −0.291301 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.447529 | −0.0360629 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.3660 | −1.78500 | −0.892501 | − | 0.451045i | \(-0.851052\pi\) | ||||
−0.892501 | + | 0.451045i | \(0.851052\pi\) | |||||||
\(158\) | −0.460109 | −0.0366043 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.93867 | 0.231600 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.813450 | −0.0637143 | −0.0318572 | − | 0.999492i | \(-0.510142\pi\) | ||||
−0.0318572 | + | 0.999492i | \(0.510142\pi\) | |||||||
\(164\) | −5.01253 | −0.391413 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.04747 | 0.0812992 | ||||||||
\(167\) | 25.1660 | 1.94740 | 0.973700 | − | 0.227833i | \(-0.0731639\pi\) | ||||
0.973700 | + | 0.227833i | \(0.0731639\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.98869 | 0.614515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.69158 | 0.510229 | ||||||||
\(173\) | −0.410945 | −0.0312436 | −0.0156218 | − | 0.999878i | \(-0.504973\pi\) | ||||
−0.0156218 | + | 0.999878i | \(0.504973\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.2779 | 1.07624 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.19584 | 0.164585 | ||||||||
\(179\) | 14.8502 | 1.10996 | 0.554978 | − | 0.831865i | \(-0.312727\pi\) | ||||
0.554978 | + | 0.831865i | \(0.312727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.739223 | 0.0549460 | 0.0274730 | − | 0.999623i | \(-0.491254\pi\) | ||||
0.0274730 | + | 0.999623i | \(0.491254\pi\) | |||||||
\(182\) | −0.557153 | −0.0412990 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.93072 | 0.142334 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.5295 | 1.42814 | ||||||||
\(188\) | −16.8281 | −1.22732 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.72506 | 0.197179 | 0.0985893 | − | 0.995128i | \(-0.468567\pi\) | ||||
0.0985893 | + | 0.995128i | \(0.468567\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.2040 | 1.02243 | 0.511215 | − | 0.859453i | \(-0.329196\pi\) | ||||
0.511215 | + | 0.859453i | \(0.329196\pi\) | |||||||
\(194\) | −1.42236 | −0.102120 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.4009 | 0.885776 | ||||||||
\(197\) | 5.54591 | 0.395130 | 0.197565 | − | 0.980290i | \(-0.436697\pi\) | ||||
0.197565 | + | 0.980290i | \(0.436697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.96371 | 0.422756 | 0.211378 | − | 0.977404i | \(-0.432205\pi\) | ||||
0.211378 | + | 0.977404i | \(0.432205\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.101254 | 0.00712418 | ||||||||
\(203\) | 3.20497 | 0.224945 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.110626 | 0.00770768 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.7754 | 1.23250 | ||||||||
\(209\) | 23.4364 | 1.62113 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.7183 | −0.944407 | −0.472204 | − | 0.881490i | \(-0.656541\pi\) | ||||
−0.472204 | + | 0.881490i | \(0.656541\pi\) | |||||||
\(212\) | −4.64940 | −0.319322 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.69462 | −0.115842 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.07538 | −0.0730014 | ||||||||
\(218\) | 0.344849 | 0.0233561 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.3133 | 1.63549 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.24170 | 0.217081 | 0.108540 | − | 0.994092i | \(-0.465382\pi\) | ||||
0.108540 | + | 0.994092i | \(0.465382\pi\) | |||||||
\(224\) | −1.43988 | −0.0962060 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.27204 | 0.151134 | ||||||||
\(227\) | −13.1799 | −0.874779 | −0.437390 | − | 0.899272i | \(-0.644097\pi\) | ||||
−0.437390 | + | 0.899272i | \(0.644097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.83810 | 0.385793 | 0.192896 | − | 0.981219i | \(-0.438212\pi\) | ||||
0.192896 | + | 0.981219i | \(0.438212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.10568 | 0.138245 | ||||||||
\(233\) | −9.33453 | −0.611526 | −0.305763 | − | 0.952108i | \(-0.598911\pi\) | ||||
−0.305763 | + | 0.952108i | \(0.598911\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 25.9893 | 1.69176 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.645406 | −0.0418354 | ||||||||
\(239\) | −17.1502 | −1.10935 | −0.554676 | − | 0.832066i | \(-0.687158\pi\) | ||||
−0.554676 | + | 0.832066i | \(0.687158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.22073 | 0.465128 | 0.232564 | − | 0.972581i | \(-0.425289\pi\) | ||||
0.232564 | + | 0.972581i | \(0.425289\pi\) | |||||||
\(242\) | 0.360157 | 0.0231518 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20.4875 | −1.31158 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.1772 | 1.85650 | ||||||||
\(248\) | −0.706527 | −0.0448645 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.75708 | 0.363383 | 0.181692 | − | 0.983356i | \(-0.441843\pi\) | ||||
0.181692 | + | 0.983356i | \(0.441843\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.5993 | −0.792110 | ||||||||
\(254\) | −0.543872 | −0.0341256 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.4180 | 0.901125 | ||||||||
\(257\) | −26.9602 | −1.68173 | −0.840867 | − | 0.541242i | \(-0.817954\pi\) | ||||
−0.840867 | + | 0.541242i | \(0.817954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.39499 | 0.397365 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.76396 | 0.108978 | ||||||||
\(263\) | −20.6673 | −1.27440 | −0.637200 | − | 0.770699i | \(-0.719907\pi\) | ||||
−0.637200 | + | 0.770699i | \(0.719907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.774520 | −0.0474889 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.62579 | −0.404734 | ||||||||
\(269\) | 13.7435 | 0.837958 | 0.418979 | − | 0.907996i | \(-0.362388\pi\) | ||||
0.418979 | + | 0.907996i | \(0.362388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.34392 | 0.203128 | 0.101564 | − | 0.994829i | \(-0.467615\pi\) | ||||
0.101564 | + | 0.994829i | \(0.467615\pi\) | |||||||
\(272\) | 20.5910 | 1.24851 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.68028 | 0.101510 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.90947 | 0.535318 | 0.267659 | − | 0.963514i | \(-0.413750\pi\) | ||||
0.267659 | + | 0.963514i | \(0.413750\pi\) | |||||||
\(278\) | −0.660400 | −0.0396081 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.4913 | 1.34172 | 0.670859 | − | 0.741585i | \(-0.265926\pi\) | ||||
0.670859 | + | 0.741585i | \(0.265926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.30694 | 0.0776894 | 0.0388447 | − | 0.999245i | \(-0.487632\pi\) | ||||
0.0388447 | + | 0.999245i | \(0.487632\pi\) | |||||||
\(284\) | −8.55899 | −0.507883 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.38874 | 0.141249 | ||||||||
\(287\) | −2.17296 | −0.128266 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.1645 | 0.656733 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.9779 | 1.05207 | ||||||||
\(293\) | −1.97058 | −0.115123 | −0.0575613 | − | 0.998342i | \(-0.518332\pi\) | ||||
−0.0575613 | + | 0.998342i | \(0.518332\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.20153 | 0.244209 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.63624 | 0.0947847 | ||||||||
\(299\) | −15.6855 | −0.907118 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.90085 | 0.167202 | ||||||||
\(302\) | 3.46706 | 0.199507 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 24.7102 | 1.41723 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2544 | −0.870617 | −0.435308 | − | 0.900281i | \(-0.643361\pi\) | ||||
−0.435308 | + | 0.900281i | \(0.643361\pi\) | |||||||
\(308\) | 6.25363 | 0.356334 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.7452 | −1.00624 | −0.503120 | − | 0.864217i | \(-0.667815\pi\) | ||||
−0.503120 | + | 0.864217i | \(0.667815\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.3869 | −1.54800 | −0.773999 | − | 0.633187i | \(-0.781747\pi\) | ||||
−0.773999 | + | 0.633187i | \(0.781747\pi\) | |||||||
\(314\) | −3.16903 | −0.178839 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.42941 | 0.361683 | ||||||||
\(317\) | −8.64563 | −0.485587 | −0.242793 | − | 0.970078i | \(-0.578064\pi\) | ||||
−0.242793 | + | 0.970078i | \(0.578064\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.7410 | −0.769350 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.416379 | 0.0232039 | ||||||||
\(323\) | 33.7988 | 1.88062 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.115257 | −0.00638351 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.42765 | −0.0788286 | ||||||||
\(329\) | −7.29510 | −0.402192 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.96260 | 0.272769 | 0.136385 | − | 0.990656i | \(-0.456452\pi\) | ||||
0.136385 | + | 0.990656i | \(0.456452\pi\) | |||||||
\(332\) | −14.6370 | −0.803308 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.56575 | 0.195109 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.30529 | −0.397945 | −0.198972 | − | 0.980005i | \(-0.563760\pi\) | ||||
−0.198972 | + | 0.980005i | \(0.563760\pi\) | |||||||
\(338\) | 1.13191 | 0.0615680 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.61058 | 0.249677 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.3840 | 0.614680 | ||||||||
\(344\) | 1.90587 | 0.102758 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0582266 | −0.00313028 | ||||||||
\(347\) | −15.9374 | −0.855565 | −0.427783 | − | 0.903882i | \(-0.640705\pi\) | ||||
−0.427783 | + | 0.903882i | \(0.640705\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5844 | 0.887743 | 0.443871 | − | 0.896091i | \(-0.353605\pi\) | ||||
0.443871 | + | 0.896091i | \(0.353605\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.17336 | 0.329041 | ||||||||
\(353\) | −12.9691 | −0.690277 | −0.345138 | − | 0.938552i | \(-0.612168\pi\) | ||||
−0.345138 | + | 0.938552i | \(0.612168\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −30.6839 | −1.62624 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.10412 | 0.111206 | ||||||||
\(359\) | 13.4920 | 0.712082 | 0.356041 | − | 0.934470i | \(-0.384126\pi\) | ||||
0.356041 | + | 0.934470i | \(0.384126\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.5603 | 1.13475 | ||||||||
\(362\) | 0.104740 | 0.00550502 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.78549 | 0.408070 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.57463 | 0.238794 | 0.119397 | − | 0.992847i | \(-0.461904\pi\) | ||||
0.119397 | + | 0.992847i | \(0.461904\pi\) | |||||||
\(368\) | −13.2841 | −0.692482 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.01555 | −0.104642 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.7463 | −1.07420 | −0.537101 | − | 0.843518i | \(-0.680481\pi\) | ||||
−0.537101 | + | 0.843518i | \(0.680481\pi\) | |||||||
\(374\) | 2.76712 | 0.143084 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.79291 | −0.247175 | ||||||||
\(377\) | −17.1070 | −0.881053 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.78163 | −0.296982 | −0.148491 | − | 0.988914i | \(-0.547442\pi\) | ||||
−0.148491 | + | 0.988914i | \(0.547442\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.386113 | 0.0197553 | ||||||||
\(383\) | −25.8124 | −1.31895 | −0.659476 | − | 0.751726i | \(-0.729222\pi\) | ||||
−0.659476 | + | 0.751726i | \(0.729222\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.01256 | 0.102437 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.8756 | 1.00903 | ||||||||
\(389\) | 15.7046 | 0.796254 | 0.398127 | − | 0.917330i | \(-0.369660\pi\) | ||||
0.398127 | + | 0.917330i | \(0.369660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.1701 | −0.918901 | ||||||||
\(392\) | 3.53196 | 0.178391 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.785797 | 0.0395879 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.6040 | −0.983895 | −0.491948 | − | 0.870625i | \(-0.663715\pi\) | ||||
−0.491948 | + | 0.870625i | \(0.663715\pi\) | |||||||
\(398\) | 0.844995 | 0.0423558 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.4239 | 0.720297 | 0.360148 | − | 0.932895i | \(-0.382726\pi\) | ||||
0.360148 | + | 0.932895i | \(0.382726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.73996 | 0.285928 | ||||||||
\(404\) | −1.41489 | −0.0703932 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.454111 | 0.0225372 | ||||||||
\(407\) | −27.4179 | −1.35906 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.8742 | −1.37829 | −0.689146 | − | 0.724622i | \(-0.742014\pi\) | ||||
−0.689146 | + | 0.724622i | \(0.742014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.54585 | −0.0761588 | ||||||||
\(413\) | 11.2665 | 0.554389 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.68554 | 0.376815 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.32069 | 0.162420 | ||||||||
\(419\) | 36.2881 | 1.77279 | 0.886396 | − | 0.462928i | \(-0.153201\pi\) | ||||
0.886396 | + | 0.462928i | \(0.153201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.37600 | −0.164536 | −0.0822681 | − | 0.996610i | \(-0.526216\pi\) | ||||
−0.0822681 | + | 0.996610i | \(0.526216\pi\) | |||||||
\(422\) | −1.94374 | −0.0946198 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.32422 | −0.0643099 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.88148 | −0.429805 | ||||||||
\(428\) | 23.6801 | 1.14462 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.6625 | 1.23612 | 0.618059 | − | 0.786131i | \(-0.287919\pi\) | ||||
0.618059 | + | 0.786131i | \(0.287919\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.8070 | −1.91300 | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||||
−0.956501 | + | 0.291730i | \(0.905769\pi\) | |||||||
\(434\) | −0.152370 | −0.00731398 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.81882 | −0.230779 | ||||||||
\(437\) | −21.8051 | −1.04308 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.9180 | 1.61882 | 0.809408 | − | 0.587247i | \(-0.199788\pi\) | ||||
0.809408 | + | 0.587247i | \(0.199788\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.44494 | 0.163859 | ||||||||
\(443\) | 28.9300 | 1.37451 | 0.687253 | − | 0.726418i | \(-0.258816\pi\) | ||||
0.687253 | + | 0.726418i | \(0.258816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.459315 | 0.0217492 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.45638 | 0.305035 | ||||||||
\(449\) | 10.2089 | 0.481788 | 0.240894 | − | 0.970551i | \(-0.422559\pi\) | ||||
0.240894 | + | 0.970551i | \(0.422559\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.31639 | 0.438692 | ||||||||
\(452\) | −31.7488 | −1.49334 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.86745 | −0.0876438 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.4952 | 1.52006 | 0.760030 | − | 0.649888i | \(-0.225184\pi\) | ||||
0.760030 | + | 0.649888i | \(0.225184\pi\) | |||||||
\(458\) | 0.827198 | 0.0386524 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.700568 | 0.0326287 | 0.0163144 | − | 0.999867i | \(-0.494807\pi\) | ||||
0.0163144 | + | 0.999867i | \(0.494807\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.17126 | 0.100907 | 0.0504535 | − | 0.998726i | \(-0.483933\pi\) | ||||
0.0504535 | + | 0.998726i | \(0.483933\pi\) | |||||||
\(464\) | −14.4879 | −0.672585 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.32261 | −0.0612685 | ||||||||
\(467\) | 3.87710 | 0.179411 | 0.0897053 | − | 0.995968i | \(-0.471407\pi\) | ||||
0.0897053 | + | 0.995968i | \(0.471407\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.87232 | −0.132632 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.40215 | 0.340711 | ||||||||
\(473\) | −12.4371 | −0.571859 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.01870 | 0.413371 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.43000 | −0.111146 | ||||||||
\(479\) | 21.9994 | 1.00518 | 0.502588 | − | 0.864526i | \(-0.332381\pi\) | ||||
0.502588 | + | 0.864526i | \(0.332381\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.1341 | −1.55638 | ||||||||
\(482\) | 1.02310 | 0.0466010 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.03272 | −0.228760 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.3997 | 1.28692 | 0.643458 | − | 0.765482i | \(-0.277499\pi\) | ||||
0.643458 | + | 0.765482i | \(0.277499\pi\) | |||||||
\(488\) | −5.83517 | −0.264146 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0468 | 0.633925 | 0.316963 | − | 0.948438i | \(-0.397337\pi\) | ||||
0.316963 | + | 0.948438i | \(0.397337\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.8167 | −0.892498 | ||||||||
\(494\) | 4.13410 | 0.186002 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.86119 | 0.218274 | ||||||||
\(497\) | −3.71038 | −0.166433 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0842 | 0.585731 | 0.292866 | − | 0.956154i | \(-0.405391\pi\) | ||||
0.292866 | + | 0.956154i | \(0.405391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.815717 | 0.0364072 | ||||||||
\(503\) | −12.3044 | −0.548625 | −0.274312 | − | 0.961641i | \(-0.588450\pi\) | ||||
−0.274312 | + | 0.961641i | \(0.588450\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.78519 | −0.0793612 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.59990 | 0.337191 | ||||||||
\(509\) | −0.0783897 | −0.00347456 | −0.00173728 | − | 0.999998i | \(-0.500553\pi\) | ||||
−0.00173728 | + | 0.999998i | \(0.500553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.79352 | 0.344765 | ||||||||
\(512\) | 10.8848 | 0.481045 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.81998 | −0.168492 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.2771 | 1.37556 | ||||||||
\(518\) | 0.906103 | 0.0398119 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.1194 | −0.793824 | −0.396912 | − | 0.917857i | \(-0.629918\pi\) | ||||
−0.396912 | + | 0.917857i | \(0.629918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.6303 | 0.508558 | 0.254279 | − | 0.967131i | \(-0.418162\pi\) | ||||
0.254279 | + | 0.967131i | \(0.418162\pi\) | |||||||
\(524\) | −24.6490 | −1.07680 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.92834 | −0.127682 | ||||||||
\(527\) | 6.64917 | 0.289642 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2777 | −0.490335 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.8229 | 0.469232 | ||||||||
\(533\) | 11.5985 | 0.502386 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.88713 | −0.0815115 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.94732 | 0.0839547 | ||||||||
\(539\) | −23.0485 | −0.992770 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.2716 | 1.25848 | 0.629242 | − | 0.777209i | \(-0.283365\pi\) | ||||
0.629242 | + | 0.777209i | \(0.283365\pi\) | |||||||
\(542\) | 0.473798 | 0.0203514 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.90292 | 0.381710 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0675 | 0.515971 | 0.257985 | − | 0.966149i | \(-0.416941\pi\) | ||||
0.257985 | + | 0.966149i | \(0.416941\pi\) | |||||||
\(548\) | −23.4797 | −1.00300 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.7810 | −1.01311 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.78719 | 0.118524 | ||||||||
\(554\) | 1.26238 | 0.0536333 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.22821 | 0.391363 | ||||||||
\(557\) | 41.4154 | 1.75483 | 0.877413 | − | 0.479737i | \(-0.159268\pi\) | ||||
0.877413 | + | 0.479737i | \(0.159268\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.4836 | −0.654888 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.18678 | 0.134426 | ||||||||
\(563\) | 32.1467 | 1.35482 | 0.677411 | − | 0.735604i | \(-0.263102\pi\) | ||||
0.677411 | + | 0.735604i | \(0.263102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.185179 | 0.00778367 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.43773 | −0.102285 | ||||||||
\(569\) | −21.1080 | −0.884893 | −0.442446 | − | 0.896795i | \(-0.645889\pi\) | ||||
−0.442446 | + | 0.896795i | \(0.645889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.7493 | −1.03573 | −0.517863 | − | 0.855464i | \(-0.673272\pi\) | ||||
−0.517863 | + | 0.855464i | \(0.673272\pi\) | |||||||
\(572\) | −33.3796 | −1.39567 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.307886 | −0.0128509 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7710 | −0.781448 | −0.390724 | − | 0.920508i | \(-0.627775\pi\) | ||||
−0.390724 | + | 0.920508i | \(0.627775\pi\) | |||||||
\(578\) | 1.58189 | 0.0657979 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.34522 | −0.263244 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.64147 | 0.357893 | ||||||||
\(584\) | 5.12037 | 0.211883 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.279211 | −0.0115341 | ||||||||
\(587\) | −14.7572 | −0.609095 | −0.304547 | − | 0.952497i | \(-0.598505\pi\) | ||||
−0.304547 | + | 0.952497i | \(0.598505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.97935 | 0.328783 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −28.9082 | −1.18812 | ||||||||
\(593\) | −8.01859 | −0.329284 | −0.164642 | − | 0.986353i | \(-0.552647\pi\) | ||||
−0.164642 | + | 0.986353i | \(0.552647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.8643 | −0.936556 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.22247 | −0.0908838 | ||||||||
\(599\) | 1.28951 | 0.0526878 | 0.0263439 | − | 0.999653i | \(-0.491614\pi\) | ||||
0.0263439 | + | 0.999653i | \(0.491614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.8813 | −0.688603 | −0.344302 | − | 0.938859i | \(-0.611884\pi\) | ||||
−0.344302 | + | 0.938859i | \(0.611884\pi\) | |||||||
\(602\) | 0.411020 | 0.0167519 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −48.4476 | −1.97130 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.499318 | −0.0202667 | −0.0101334 | − | 0.999949i | \(-0.503226\pi\) | ||||
−0.0101334 | + | 0.999949i | \(0.503226\pi\) | |||||||
\(608\) | 10.6840 | 0.433292 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.9385 | 1.57528 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.4241 | 1.10765 | 0.553825 | − | 0.832633i | \(-0.313168\pi\) | ||||
0.553825 | + | 0.832633i | \(0.313168\pi\) | |||||||
\(614\) | −2.16139 | −0.0872267 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.78113 | 0.0717639 | ||||||||
\(617\) | 28.3205 | 1.14014 | 0.570070 | − | 0.821596i | \(-0.306916\pi\) | ||||
0.570070 | + | 0.821596i | \(0.306916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.371804 | −0.0149440 | −0.00747202 | − | 0.999972i | \(-0.502378\pi\) | ||||
−0.00747202 | + | 0.999972i | \(0.502378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.51431 | −0.100815 | ||||||||
\(623\) | −13.3017 | −0.532921 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.88043 | −0.155093 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 44.2830 | 1.76709 | ||||||||
\(629\) | −39.5409 | −1.57660 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.4507 | 0.654892 | 0.327446 | − | 0.944870i | \(-0.393812\pi\) | ||||
0.327446 | + | 0.944870i | \(0.393812\pi\) | |||||||
\(632\) | 1.83120 | 0.0728411 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.22499 | −0.0486508 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.6943 | −1.13691 | ||||||||
\(638\) | −1.94696 | −0.0770809 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.02604 | 0.0800239 | 0.0400119 | − | 0.999199i | \(-0.487260\pi\) | ||||
0.0400119 | + | 0.999199i | \(0.487260\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.2034 | −1.30941 | −0.654706 | − | 0.755883i | \(-0.727208\pi\) | ||||
−0.654706 | + | 0.755883i | \(0.727208\pi\) | |||||||
\(644\) | −5.81834 | −0.229275 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.78894 | 0.188418 | ||||||||
\(647\) | 40.5797 | 1.59535 | 0.797677 | − | 0.603085i | \(-0.206062\pi\) | ||||
0.797677 | + | 0.603085i | \(0.206062\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.3042 | −1.89611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.61057 | 0.0630748 | ||||||||
\(653\) | 9.29712 | 0.363824 | 0.181912 | − | 0.983315i | \(-0.441771\pi\) | ||||
0.181912 | + | 0.983315i | \(0.441771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.82277 | 0.383515 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.03364 | −0.0402954 | ||||||||
\(659\) | 3.47563 | 0.135391 | 0.0676957 | − | 0.997706i | \(-0.478435\pi\) | ||||
0.0676957 | + | 0.997706i | \(0.478435\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.07303 | 0.158422 | 0.0792112 | − | 0.996858i | \(-0.474760\pi\) | ||||
0.0792112 | + | 0.996858i | \(0.474760\pi\) | |||||||
\(662\) | 0.703148 | 0.0273286 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.16884 | −0.161782 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.7846 | 0.495021 | ||||||||
\(668\) | −49.8267 | −1.92785 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.0785 | 1.47001 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.3843 | 0.824305 | 0.412153 | − | 0.911115i | \(-0.364777\pi\) | ||||
0.412153 | + | 0.911115i | \(0.364777\pi\) | |||||||
\(674\) | −1.03508 | −0.0398699 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.8170 | −0.608346 | ||||||||
\(677\) | 20.3257 | 0.781181 | 0.390590 | − | 0.920565i | \(-0.372271\pi\) | ||||
0.390590 | + | 0.920565i | \(0.372271\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.61621 | 0.330660 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.653271 | 0.0250150 | ||||||||
\(683\) | 18.9591 | 0.725449 | 0.362725 | − | 0.931896i | \(-0.381847\pi\) | ||||
0.362725 | + | 0.931896i | \(0.381847\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.61300 | 0.0615845 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.1131 | −0.499933 | ||||||||
\(689\) | 10.7582 | 0.409856 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.8195 | 0.563762 | 0.281881 | − | 0.959449i | \(-0.409042\pi\) | ||||
0.281881 | + | 0.959449i | \(0.409042\pi\) | |||||||
\(692\) | 0.813641 | 0.0309300 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.25816 | −0.0857187 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.4357 | 0.508912 | ||||||||
\(698\) | 2.34984 | 0.0889426 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.3996 | −1.18595 | −0.592973 | − | 0.805222i | \(-0.702046\pi\) | ||||
−0.592973 | + | 0.805222i | \(0.702046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −47.4511 | −1.78965 | ||||||||
\(704\) | −27.6812 | −1.04327 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.83759 | −0.0691586 | ||||||||
\(707\) | −0.613363 | −0.0230679 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.3324 | 0.951379 | 0.475690 | − | 0.879613i | \(-0.342199\pi\) | ||||
0.475690 | + | 0.879613i | \(0.342199\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.73926 | −0.327518 | ||||||||
\(713\) | −4.28966 | −0.160649 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −29.4023 | −1.09881 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.91168 | 0.0713432 | ||||||||
\(719\) | 4.12711 | 0.153915 | 0.0769575 | − | 0.997034i | \(-0.475479\pi\) | ||||
0.0769575 | + | 0.997034i | \(0.475479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.670138 | −0.0249572 | ||||||||
\(722\) | 3.05487 | 0.113691 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.46361 | −0.0543945 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.0039 | 0.853168 | 0.426584 | − | 0.904448i | \(-0.359717\pi\) | ||||
0.426584 | + | 0.904448i | \(0.359717\pi\) | |||||||
\(728\) | 2.21743 | 0.0821834 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.9362 | −0.663396 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.35692 | −0.345606 | −0.172803 | − | 0.984956i | \(-0.555282\pi\) | ||||
−0.172803 | + | 0.984956i | \(0.555282\pi\) | |||||||
\(734\) | 0.648176 | 0.0239246 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.74366 | −0.211714 | ||||||||
\(737\) | 12.3148 | 0.453623 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.1754 | −1.73538 | −0.867688 | − | 0.497109i | \(-0.834395\pi\) | ||||
−0.867688 | + | 0.497109i | \(0.834395\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.285582 | −0.0104840 | ||||||||
\(743\) | −2.39450 | −0.0878455 | −0.0439228 | − | 0.999035i | \(-0.513986\pi\) | ||||
−0.0439228 | + | 0.999035i | \(0.513986\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.93953 | −0.107624 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −38.6668 | −1.41380 | ||||||||
\(749\) | 10.2655 | 0.375092 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.21632 | −0.263327 | −0.131664 | − | 0.991294i | \(-0.542032\pi\) | ||||
−0.131664 | + | 0.991294i | \(0.542032\pi\) | |||||||
\(752\) | 32.9771 | 1.20255 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.42388 | −0.0882724 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.3742 | 0.486094 | 0.243047 | − | 0.970015i | \(-0.421853\pi\) | ||||
0.243047 | + | 0.970015i | \(0.421853\pi\) | |||||||
\(758\) | −0.819196 | −0.0297545 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.7541 | −0.788584 | −0.394292 | − | 0.918985i | \(-0.629010\pi\) | ||||
−0.394292 | + | 0.918985i | \(0.629010\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.08899 | −0.0756265 | ||||||||
\(764\) | −5.39542 | −0.195199 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.65735 | −0.132145 | ||||||||
\(767\) | −60.1365 | −2.17140 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.2003 | 0.512077 | 0.256038 | − | 0.966667i | \(-0.417583\pi\) | ||||
0.256038 | + | 0.966667i | \(0.417583\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −28.1229 | −1.01217 | ||||||||
\(773\) | −22.8365 | −0.821373 | −0.410687 | − | 0.911777i | \(-0.634711\pi\) | ||||
−0.410687 | + | 0.911777i | \(0.634711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.66089 | 0.203214 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.22517 | 0.0797763 | ||||||||
\(779\) | 16.1235 | 0.577684 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.9079 | 0.569230 | ||||||||
\(782\) | −2.57451 | −0.0920644 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −24.3013 | −0.867903 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.4761 | −1.37153 | −0.685763 | − | 0.727825i | \(-0.740531\pi\) | ||||
−0.685763 | + | 0.727825i | \(0.740531\pi\) | |||||||
\(788\) | −10.9805 | −0.391163 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.7633 | −0.489367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 47.4060 | 1.68344 | ||||||||
\(794\) | −2.77768 | −0.0985760 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.8077 | −0.418512 | ||||||||
\(797\) | 1.86739 | 0.0661464 | 0.0330732 | − | 0.999453i | \(-0.489471\pi\) | ||||
0.0330732 | + | 0.999453i | \(0.489471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.1063 | 1.59575 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.04372 | 0.0721662 | ||||||||
\(803\) | −33.4140 | −1.17916 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.813293 | 0.0286470 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.402982 | −0.0141768 | ||||||||
\(809\) | −35.1514 | −1.23586 | −0.617929 | − | 0.786234i | \(-0.712028\pi\) | ||||
−0.617929 | + | 0.786234i | \(0.712028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.59158 | −0.231462 | −0.115731 | − | 0.993281i | \(-0.536921\pi\) | ||||
−0.115731 | + | 0.993281i | \(0.536921\pi\) | |||||||
\(812\) | −6.34561 | −0.222687 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.88483 | −0.136163 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.5244 | −0.753044 | ||||||||
\(818\) | −3.94949 | −0.138091 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.25743 | −0.183486 | −0.0917428 | − | 0.995783i | \(-0.529244\pi\) | ||||
−0.0917428 | + | 0.995783i | \(0.529244\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.1919 | −0.773560 | −0.386780 | − | 0.922172i | \(-0.626413\pi\) | ||||
−0.386780 | + | 0.922172i | \(0.626413\pi\) | |||||||
\(824\) | −0.440283 | −0.0153380 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.59635 | 0.0555440 | ||||||||
\(827\) | 6.56256 | 0.228203 | 0.114101 | − | 0.993469i | \(-0.463601\pi\) | ||||
0.114101 | + | 0.993469i | \(0.463601\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.0574 | 0.870279 | 0.435140 | − | 0.900363i | \(-0.356699\pi\) | ||||
0.435140 | + | 0.900363i | \(0.356699\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −34.4618 | −1.19475 | ||||||||
\(833\) | −33.2395 | −1.15168 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −46.4022 | −1.60485 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.14165 | 0.177615 | ||||||||
\(839\) | 42.1485 | 1.45513 | 0.727564 | − | 0.686040i | \(-0.240652\pi\) | ||||
0.727564 | + | 0.686040i | \(0.240652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.0569 | −0.519203 | ||||||||
\(842\) | −0.478344 | −0.0164848 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 27.1612 | 0.934927 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.18172 | −0.0749648 | ||||||||
\(848\) | 9.11117 | 0.312879 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.5095 | 0.874454 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.2473 | 1.48076 | 0.740379 | − | 0.672189i | \(-0.234646\pi\) | ||||
0.740379 | + | 0.672189i | \(0.234646\pi\) | |||||||
\(854\) | −1.25841 | −0.0430620 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.74446 | 0.230521 | ||||||||
\(857\) | 39.2430 | 1.34052 | 0.670258 | − | 0.742128i | \(-0.266183\pi\) | ||||
0.670258 | + | 0.742128i | \(0.266183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.6092 | 1.79500 | 0.897501 | − | 0.441013i | \(-0.145381\pi\) | ||||
0.897501 | + | 0.441013i | \(0.145381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.63611 | 0.123846 | ||||||||
\(863\) | 42.8744 | 1.45946 | 0.729731 | − | 0.683735i | \(-0.239645\pi\) | ||||
0.729731 | + | 0.683735i | \(0.239645\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.64023 | −0.191663 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.12917 | 0.0722686 | ||||||||
\(869\) | −11.9498 | −0.405371 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.3314 | 0.519484 | ||||||||
\(872\) | −1.37247 | −0.0464778 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.08955 | −0.104506 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.390314 | −0.0131800 | −0.00658999 | − | 0.999978i | \(-0.502098\pi\) | ||||
−0.00658999 | + | 0.999978i | \(0.502098\pi\) | |||||||
\(878\) | 4.80582 | 0.162188 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.7002 | −1.50599 | −0.752994 | − | 0.658028i | \(-0.771391\pi\) | ||||
−0.752994 | + | 0.658028i | \(0.771391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.7567 | 1.10235 | 0.551175 | − | 0.834390i | \(-0.314180\pi\) | ||||
0.551175 | + | 0.834390i | \(0.314180\pi\) | |||||||
\(884\) | −48.1384 | −1.61907 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.09908 | 0.137711 | ||||||||
\(887\) | 15.7130 | 0.527591 | 0.263796 | − | 0.964579i | \(-0.415026\pi\) | ||||
0.263796 | + | 0.964579i | \(0.415026\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.29461 | 0.110498 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.41833 | −0.214902 | ||||||||
\(893\) | 54.1299 | 1.81139 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.79456 | 0.126767 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.44649 | 0.0482701 | ||||||||
\(899\) | −4.67839 | −0.156033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.4623 | 0.415180 | ||||||||
\(902\) | 1.32003 | 0.0439523 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.04256 | −0.300751 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.50466 | −0.0499613 | −0.0249806 | − | 0.999688i | \(-0.507952\pi\) | ||||
−0.0249806 | + | 0.999688i | \(0.507952\pi\) | |||||||
\(908\) | 26.0952 | 0.865998 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.4509 | −0.379386 | −0.189693 | − | 0.981843i | \(-0.560749\pi\) | ||||
−0.189693 | + | 0.981843i | \(0.560749\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.2046 | 0.900340 | ||||||||
\(914\) | 4.60422 | 0.152294 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.5590 | −0.381920 | ||||||||
\(917\) | −10.6855 | −0.352866 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.8001 | −0.719119 | −0.359559 | − | 0.933122i | \(-0.617073\pi\) | ||||
−0.359559 | + | 0.933122i | \(0.617073\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.0992632 | 0.00326906 | ||||||||
\(923\) | 19.8046 | 0.651877 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.307645 | 0.0101098 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.26415 | −0.205631 | ||||||||
\(929\) | 30.7507 | 1.00890 | 0.504449 | − | 0.863442i | \(-0.331696\pi\) | ||||
0.504449 | + | 0.863442i | \(0.331696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39.8891 | −1.30731 | ||||||||
\(932\) | 18.4817 | 0.605387 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.549344 | 0.0179751 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.81060 | −0.124487 | −0.0622435 | − | 0.998061i | \(-0.519826\pi\) | ||||
−0.0622435 | + | 0.998061i | \(0.519826\pi\) | |||||||
\(938\) | −0.406978 | −0.0132883 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.7043 | 0.674939 | 0.337470 | − | 0.941336i | \(-0.390429\pi\) | ||||
0.337470 | + | 0.941336i | \(0.390429\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.66792 | −0.282266 | ||||||||
\(944\) | −50.9297 | −1.65762 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.76221 | −0.0572944 | ||||||||
\(947\) | −15.6833 | −0.509639 | −0.254819 | − | 0.966989i | \(-0.582016\pi\) | ||||
−0.254819 | + | 0.966989i | \(0.582016\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.5989 | −1.35036 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.56867 | 0.0832509 | ||||||||
\(953\) | 7.75207 | 0.251114 | 0.125557 | − | 0.992086i | \(-0.459928\pi\) | ||||
0.125557 | + | 0.992086i | \(0.459928\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 33.9560 | 1.09822 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.11708 | 0.100708 | ||||||||
\(959\) | −10.1786 | −0.328685 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4302 | −0.949363 | ||||||||
\(962\) | −4.83644 | −0.155933 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.2965 | −0.460459 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.4273 | −1.55732 | −0.778659 | − | 0.627447i | \(-0.784100\pi\) | ||||
−0.778659 | + | 0.627447i | \(0.784100\pi\) | |||||||
\(968\) | −1.43340 | −0.0460712 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.3350 | −0.813039 | −0.406520 | − | 0.913642i | \(-0.633258\pi\) | ||||
−0.406520 | + | 0.913642i | \(0.633258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.00049 | 0.128250 | ||||||||
\(974\) | 4.02394 | 0.128936 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 40.1483 | 1.28511 | ||||||||
\(977\) | 1.16885 | 0.0373948 | 0.0186974 | − | 0.999825i | \(-0.494048\pi\) | ||||
0.0186974 | + | 0.999825i | \(0.494048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57.0298 | 1.82268 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.99029 | 0.0635127 | ||||||||
\(983\) | 23.9943 | 0.765299 | 0.382649 | − | 0.923894i | \(-0.375012\pi\) | ||||
0.382649 | + | 0.923894i | \(0.375012\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.80782 | −0.0894190 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −57.7686 | −1.83786 | ||||||||
\(989\) | 11.5714 | 0.367950 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.6726 | −1.16494 | −0.582472 | − | 0.812851i | \(-0.697914\pi\) | ||||
−0.582472 | + | 0.812851i | \(0.697914\pi\) | |||||||
\(992\) | 2.10183 | 0.0667333 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.525722 | −0.0166749 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57.0203 | −1.80585 | −0.902925 | − | 0.429798i | \(-0.858585\pi\) | ||||
−0.902925 | + | 0.429798i | \(0.858585\pi\) | |||||||
\(998\) | 1.85390 | 0.0586842 | ||||||||
\(999\) | 0 | 0 |
(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 | 5625.2.a.p.1.4 | 6 | ||
3.2 | odd | 2 | 1875.2.a.j.1.3 | 6 | |||
5.4 | even | 2 | 5625.2.a.q.1.3 | 6 | |||
15.2 | even | 4 | 1875.2.b.f.1249.6 | 12 | |||
15.8 | even | 4 | 1875.2.b.f.1249.7 | 12 | |||
15.14 | odd | 2 | 1875.2.a.k.1.4 | 6 | |||
25.6 | even | 5 | 225.2.h.d.136.2 | 12 | |||
25.21 | even | 5 | 225.2.h.d.91.2 | 12 | |||
75.8 | even | 20 | 375.2.i.d.199.3 | 24 | |||
75.17 | even | 20 | 375.2.i.d.199.4 | 24 | |||
75.29 | odd | 10 | 375.2.g.c.76.2 | 12 | |||
75.44 | odd | 10 | 375.2.g.c.301.2 | 12 | |||
75.47 | even | 20 | 375.2.i.d.49.3 | 24 | |||
75.53 | even | 20 | 375.2.i.d.49.4 | 24 | |||
75.56 | odd | 10 | 75.2.g.c.61.2 | yes | 12 | ||
75.71 | odd | 10 | 75.2.g.c.16.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.2 | ✓ | 12 | 75.71 | odd | 10 | ||
75.2.g.c.61.2 | yes | 12 | 75.56 | odd | 10 | ||
225.2.h.d.91.2 | 12 | 25.21 | even | 5 | |||
225.2.h.d.136.2 | 12 | 25.6 | even | 5 | |||
375.2.g.c.76.2 | 12 | 75.29 | odd | 10 | |||
375.2.g.c.301.2 | 12 | 75.44 | odd | 10 | |||
375.2.i.d.49.3 | 24 | 75.47 | even | 20 | |||
375.2.i.d.49.4 | 24 | 75.53 | even | 20 | |||
375.2.i.d.199.3 | 24 | 75.8 | even | 20 | |||
375.2.i.d.199.4 | 24 | 75.17 | even | 20 | |||
1875.2.a.j.1.3 | 6 | 3.2 | odd | 2 | |||
1875.2.a.k.1.4 | 6 | 15.14 | odd | 2 | |||
1875.2.b.f.1249.6 | 12 | 15.2 | even | 4 | |||
1875.2.b.f.1249.7 | 12 | 15.8 | even | 4 | |||
5625.2.a.p.1.4 | 6 | 1.1 | even | 1 | trivial | ||
5625.2.a.q.1.3 | 6 | 5.4 | even | 2 |