Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [580,2,Mod(1,580)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(580, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("580.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 580 = 2^{2} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 580.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: | \(4.63132331723\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.571993\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 580.1 |
$q$-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 | ||||||||
\(3\) | −2.67282 | −1.54316 | −0.771578 | − | 0.636135i | \(-0.780532\pi\) | ||||
−0.771578 | + | 0.636135i | \(0.780532\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.67282 | −1.76616 | −0.883081 | − | 0.469221i | \(-0.844535\pi\) | ||||
−0.883081 | + | 0.469221i | \(0.844535\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.14399 | 1.38133 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.672824 | −0.202864 | −0.101432 | − | 0.994842i | \(-0.532342\pi\) | ||||
−0.101432 | + | 0.994842i | \(0.532342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.14399 | −0.317285 | −0.158642 | − | 0.987336i | \(-0.550712\pi\) | ||||
−0.158642 | + | 0.987336i | \(0.550712\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.67282 | 0.690120 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.52884 | 0.855869 | 0.427934 | − | 0.903810i | \(-0.359241\pi\) | ||||
0.427934 | + | 0.903810i | \(0.359241\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.52884 | 1.26840 | 0.634201 | − | 0.773168i | \(-0.281329\pi\) | ||||
0.634201 | + | 0.773168i | \(0.281329\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.4896 | 2.72546 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.81681 | −0.795860 | −0.397930 | − | 0.917416i | \(-0.630271\pi\) | ||||
−0.397930 | + | 0.917416i | \(0.630271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.05767 | −0.588450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.52884 | −0.274587 | −0.137294 | − | 0.990530i | \(-0.543840\pi\) | ||||
−0.137294 | + | 0.990530i | \(0.543840\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.79834 | 0.313051 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.67282 | 0.789851 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.16246 | 1.17750 | 0.588750 | − | 0.808315i | \(-0.299620\pi\) | ||||
0.588750 | + | 0.808315i | \(0.299620\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.05767 | 0.489620 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.85601 | 0.446034 | 0.223017 | − | 0.974815i | \(-0.428409\pi\) | ||||
0.223017 | + | 0.974815i | \(0.428409\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.96080 | 1.36651 | 0.683254 | − | 0.730180i | \(-0.260564\pi\) | ||||
0.683254 | + | 0.730180i | \(0.260564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.14399 | −0.617749 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.67282 | −0.973331 | −0.486666 | − | 0.873588i | \(-0.661787\pi\) | ||||
−0.486666 | + | 0.873588i | \(0.661787\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.8353 | 2.11933 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.43196 | −1.32074 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4896 | 1.44086 | 0.720431 | − | 0.693527i | \(-0.243944\pi\) | ||||
0.720431 | + | 0.693527i | \(0.243944\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.672824 | 0.0907235 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.7776 | −1.95734 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.7776 | 1.40312 | 0.701562 | − | 0.712608i | \(-0.252486\pi\) | ||||
0.701562 | + | 0.712608i | \(0.252486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.4896 | −1.85521 | −0.927604 | − | 0.373566i | \(-0.878135\pi\) | ||||
−0.927604 | + | 0.373566i | \(0.878135\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −19.3641 | −2.43965 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.14399 | 0.141894 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.81681 | −0.954975 | −0.477488 | − | 0.878638i | \(-0.658452\pi\) | ||||
−0.477488 | + | 0.878638i | \(0.658452\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.2017 | 1.22814 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.48963 | 0.532822 | 0.266411 | − | 0.963860i | \(-0.414162\pi\) | ||||
0.266411 | + | 0.963860i | \(0.414162\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.96080 | −0.580617 | −0.290309 | − | 0.956933i | \(-0.593758\pi\) | ||||
−0.290309 | + | 0.956933i | \(0.593758\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.67282 | −0.308631 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.14399 | 0.358291 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.38485 | 0.268317 | 0.134158 | − | 0.990960i | \(-0.457167\pi\) | ||||
0.134158 | + | 0.990960i | \(0.457167\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.25934 | −0.473259 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.0185 | 1.53873 | 0.769364 | − | 0.638811i | \(-0.220573\pi\) | ||||
0.769364 | + | 0.638811i | \(0.220573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.52884 | −0.382756 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.67282 | 0.286557 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.63362 | −0.173163 | −0.0865817 | − | 0.996245i | \(-0.527594\pi\) | ||||
−0.0865817 | + | 0.996245i | \(0.527594\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.34565 | 0.560376 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.08631 | 0.423731 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.52884 | −0.567247 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.32718 | −0.947031 | −0.473516 | − | 0.880785i | \(-0.657015\pi\) | ||||
−0.473516 | + | 0.880785i | \(0.657015\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.78817 | −0.280222 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.3249 | −1.62439 | −0.812195 | − | 0.583386i | \(-0.801727\pi\) | ||||
−0.812195 | + | 0.583386i | \(0.801727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.5288 | −1.33304 | −0.666518 | − | 0.745489i | \(-0.732216\pi\) | ||||
−0.666518 | + | 0.745489i | \(0.732216\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.4896 | −1.21886 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.672824 | 0.0650443 | 0.0325222 | − | 0.999471i | \(-0.489646\pi\) | ||||
0.0325222 | + | 0.999471i | \(0.489646\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5473 | 1.29760 | 0.648798 | − | 0.760960i | \(-0.275272\pi\) | ||||
0.648798 | + | 0.760960i | \(0.275272\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.1440 | −1.81707 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.0185 | 1.88318 | 0.941590 | − | 0.336762i | \(-0.109332\pi\) | ||||
0.941590 | + | 0.336762i | \(0.109332\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.81681 | 0.355919 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.74066 | −0.438275 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.4896 | −1.51160 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5473 | −0.958846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.63362 | −0.688300 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.03920 | −0.269686 | −0.134843 | − | 0.990867i | \(-0.543053\pi\) | ||||
−0.134843 | + | 0.990867i | \(0.543053\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −23.9506 | −2.10874 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.81681 | −0.333476 | −0.166738 | − | 0.986001i | \(-0.553323\pi\) | ||||
−0.166738 | + | 0.986001i | \(0.553323\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25.8353 | −2.24020 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.05767 | 0.263163 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.1048 | 1.37592 | 0.687962 | − | 0.725746i | \(-0.258505\pi\) | ||||
0.687962 | + | 0.725746i | \(0.258505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.05767 | 0.259349 | 0.129674 | − | 0.991557i | \(-0.458607\pi\) | ||||
0.129674 | + | 0.991557i | \(0.458607\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.8353 | 1.50200 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.769701 | 0.0643657 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −39.6521 | −3.27045 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0000 | 1.47462 | 0.737309 | − | 0.675556i | \(-0.236096\pi\) | ||||
0.737309 | + | 0.675556i | \(0.236096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.77761 | 0.551554 | 0.275777 | − | 0.961222i | \(-0.411065\pi\) | ||||
0.275777 | + | 0.961222i | \(0.411065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.6235 | 1.18224 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.52884 | 0.122799 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.96080 | 0.715149 | 0.357575 | − | 0.933885i | \(-0.383604\pi\) | ||||
0.357575 | + | 0.933885i | \(0.383604\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −28.0369 | −2.22347 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.8353 | 1.40562 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.30644 | −0.493959 | −0.246979 | − | 0.969021i | \(-0.579438\pi\) | ||||
−0.246979 | + | 0.969021i | \(0.579438\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.79834 | −0.140001 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.7961 | 0.990190 | 0.495095 | − | 0.868839i | \(-0.335133\pi\) | ||||
0.495095 | + | 0.868839i | \(0.335133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6913 | −0.899330 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.9114 | 1.75208 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.1233 | 1.37789 | 0.688943 | − | 0.724816i | \(-0.258075\pi\) | ||||
0.688943 | + | 0.724816i | \(0.258075\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.67282 | −0.353232 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −28.8066 | −2.16524 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.28797 | 0.469985 | 0.234993 | − | 0.971997i | \(-0.424493\pi\) | ||||
0.234993 | + | 0.971997i | \(0.424493\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.56804 | 0.339540 | 0.169770 | − | 0.985484i | \(-0.445698\pi\) | ||||
0.169770 | + | 0.985484i | \(0.445698\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 38.7282 | 2.86287 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.16246 | −0.526594 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.37429 | −0.173625 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.2880 | 1.03930 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6521 | 1.56669 | 0.783345 | − | 0.621587i | \(-0.213512\pi\) | ||||
0.783345 | + | 0.621587i | \(0.213512\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.2409 | −0.953098 | −0.476549 | − | 0.879148i | \(-0.658113\pi\) | ||||
−0.476549 | + | 0.879148i | \(0.658113\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.05767 | −0.218965 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.34565 | 0.523356 | 0.261678 | − | 0.965155i | \(-0.415724\pi\) | ||||
0.261678 | + | 0.965155i | \(0.415724\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7776 | 1.33111 | 0.665555 | − | 0.746349i | \(-0.268195\pi\) | ||||
0.665555 | + | 0.746349i | \(0.268195\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.8930 | 1.47368 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.67282 | 0.327968 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.85601 | −0.199473 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.8168 | −1.09934 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.71993 | −0.257313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.6521 | 1.21522 | 0.607610 | − | 0.794235i | \(-0.292128\pi\) | ||||
0.607610 | + | 0.794235i | \(0.292128\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.0000 | −0.822226 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.96080 | −0.611121 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.14399 | 0.484965 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.2593 | 0.895983 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.03694 | −0.271554 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.45043 | 0.498918 | 0.249459 | − | 0.968385i | \(-0.419747\pi\) | ||||
0.249459 | + | 0.968385i | \(0.419747\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.14399 | 0.276266 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.2201 | −1.60755 | −0.803773 | − | 0.594936i | \(-0.797178\pi\) | ||||
−0.803773 | + | 0.594936i | \(0.797178\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.40332 | −0.552898 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.287973 | −0.0188657 | −0.00943287 | − | 0.999956i | \(-0.503003\pi\) | ||||
−0.00943287 | + | 0.999956i | \(0.503003\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.67282 | 0.435287 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.37429 | −0.414054 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.51037 | 0.485805 | 0.242903 | − | 0.970051i | \(-0.421900\pi\) | ||||
0.242903 | + | 0.970051i | \(0.421900\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.6706 | −1.39592 | −0.697962 | − | 0.716135i | \(-0.745909\pi\) | ||||
−0.697962 | + | 0.716135i | \(0.745909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.5575 | 1.31876 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.8353 | −0.947791 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.32492 | −0.402445 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −37.4689 | −2.37450 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.6728 | −0.799902 | −0.399951 | − | 0.916537i | \(-0.630973\pi\) | ||||
−0.399951 | + | 0.916537i | \(0.630973\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.56804 | 0.161451 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.43196 | 0.590652 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.9714 | 1.05864 | 0.529322 | − | 0.848421i | \(-0.322446\pi\) | ||||
0.529322 | + | 0.848421i | \(0.322446\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −33.4689 | −2.07966 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.14399 | −0.256506 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.90312 | 0.364002 | 0.182001 | − | 0.983298i | \(-0.441743\pi\) | ||||
0.182001 | + | 0.983298i | \(0.441743\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.4896 | −0.644373 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.36638 | 0.267218 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8560 | −0.905787 | −0.452894 | − | 0.891565i | \(-0.649608\pi\) | ||||
−0.452894 | + | 0.891565i | \(0.649608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.5944 | 1.37251 | 0.686257 | − | 0.727360i | \(-0.259253\pi\) | ||||
0.686257 | + | 0.727360i | \(0.259253\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.2880 | −0.864747 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.672824 | −0.0405728 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.4689 | 1.65045 | 0.825223 | − | 0.564807i | \(-0.191049\pi\) | ||||
0.825223 | + | 0.564807i | \(0.191049\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.33548 | −0.379295 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.5473 | 1.04678 | 0.523392 | − | 0.852092i | \(-0.324666\pi\) | ||||
0.523392 | + | 0.852092i | \(0.324666\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.5081 | 1.57574 | 0.787872 | − | 0.615839i | \(-0.211183\pi\) | ||||
0.787872 | + | 0.615839i | \(0.211183\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.7776 | 0.875350 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.3456 | −0.787769 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.54731 | −0.267489 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.9299 | 1.46142 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.7098 | −1.32672 | −0.663359 | − | 0.748301i | \(-0.730870\pi\) | ||||
−0.663359 | + | 0.748301i | \(0.730870\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.7776 | −0.627497 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.05728 | 0.119375 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.36638 | 0.252514 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −41.8722 | −2.41347 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 43.6336 | 2.50669 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.4896 | 0.829674 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9608 | 1.19630 | 0.598148 | − | 0.801386i | \(-0.295904\pi\) | ||||
0.598148 | + | 0.801386i | \(0.295904\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 36.1602 | 2.05708 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.4874 | −1.55867 | −0.779333 | − | 0.626610i | \(-0.784442\pi\) | ||||
−0.779333 | + | 0.626610i | \(0.784442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.8560 | −1.06580 | −0.532902 | − | 0.846177i | \(-0.678899\pi\) | ||||
−0.532902 | + | 0.846177i | \(0.678899\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 19.3641 | 1.09104 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.4504 | 1.65410 | 0.827050 | − | 0.562128i | \(-0.190017\pi\) | ||||
0.827050 | + | 0.562128i | \(0.190017\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.672824 | 0.0376709 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.79834 | −0.100374 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.5104 | 1.08559 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.14399 | −0.0634570 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −36.2096 | −2.00239 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.1809 | 1.71906 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.60724 | 0.198272 | 0.0991360 | − | 0.995074i | \(-0.468392\pi\) | ||||
0.0991360 | + | 0.995074i | \(0.468392\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 29.6811 | 1.62652 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.81681 | 0.427078 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.3064 | −0.997216 | −0.498608 | − | 0.866828i | \(-0.666155\pi\) | ||||
−0.498608 | + | 0.866828i | \(0.666155\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −53.5058 | −2.90604 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.02864 | 0.0557039 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −36.6129 | −1.97691 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.2017 | −0.549239 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.38485 | 0.342757 | 0.171378 | − | 0.985205i | \(-0.445178\pi\) | ||||
0.171378 | + | 0.985205i | \(0.445178\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.2672 | 0.924294 | 0.462147 | − | 0.886803i | \(-0.347079\pi\) | ||||
0.462147 | + | 0.886803i | \(0.347079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.49794 | 0.186706 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.91369 | −0.527652 | −0.263826 | − | 0.964570i | \(-0.584985\pi\) | ||||
−0.263826 | + | 0.964570i | \(0.584985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.48963 | −0.238285 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 44.0739 | 2.33264 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.81681 | −0.201444 | −0.100722 | − | 0.994915i | \(-0.532115\pi\) | ||||
−0.100722 | + | 0.994915i | \(0.532115\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.5680 | 0.608844 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.1911 | 1.47965 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.96080 | 0.259660 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.98153 | −0.416632 | −0.208316 | − | 0.978062i | \(-0.566798\pi\) | ||||
−0.208316 | + | 0.978062i | \(0.566798\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.8353 | 0.616120 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −49.0162 | −2.54479 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.0369 | −1.34814 | −0.674071 | − | 0.738667i | \(-0.735456\pi\) | ||||
−0.674071 | + | 0.738667i | \(0.735456\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.67282 | 0.138024 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.14399 | 0.0589183 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8824 | 1.48359 | 0.741794 | − | 0.670627i | \(-0.233975\pi\) | ||||
0.741794 | + | 0.670627i | \(0.233975\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.12325 | 0.416167 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.0968776 | 0.00495021 | 0.00247511 | − | 0.999997i | \(-0.499212\pi\) | ||||
0.00247511 | + | 0.999997i | \(0.499212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.14399 | −0.160232 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 37.1334 | 1.88760 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.740665 | −0.0375532 | −0.0187766 | − | 0.999824i | \(-0.505977\pi\) | ||||
−0.0187766 | + | 0.999824i | \(0.505977\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.4689 | −0.681152 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.2017 | 0.514606 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.38485 | −0.119995 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.9216 | −1.20059 | −0.600295 | − | 0.799779i | \(-0.704950\pi\) | ||||
−0.600295 | + | 0.799779i | \(0.704950\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 69.0532 | 3.45698 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.54731 | −0.277019 | −0.138510 | − | 0.990361i | \(-0.544231\pi\) | ||||
−0.138510 | + | 0.990361i | \(0.544231\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.74897 | 0.0871224 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.25934 | 0.211648 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.81907 | −0.238872 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.8930 | −1.72535 | −0.862673 | − | 0.505762i | \(-0.831211\pi\) | ||||
−0.862673 | + | 0.505762i | \(0.831211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −43.0452 | −2.12327 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −50.3619 | −2.47814 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0185 | −0.688140 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.17262 | −0.400215 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.1233 | 0.592260 | 0.296130 | − | 0.955148i | \(-0.404304\pi\) | ||||
0.296130 | + | 0.955148i | \(0.404304\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0656 | 0.929200 | 0.464600 | − | 0.885521i | \(-0.346198\pi\) | ||||
0.464600 | + | 0.885521i | \(0.346198\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −27.6521 | −1.34449 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.52884 | 0.171174 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 67.7075 | 3.27660 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.05728 | −0.0993262 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.69129 | 0.129635 | 0.0648176 | − | 0.997897i | \(-0.479353\pi\) | ||||
0.0648176 | + | 0.997897i | \(0.479353\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.4874 | 0.840390 | 0.420195 | − | 0.907434i | \(-0.361962\pi\) | ||||
0.420195 | + | 0.907434i | \(0.361962\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.67282 | −0.128152 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.1025 | −1.00947 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.45269 | −0.212515 | −0.106258 | − | 0.994339i | \(-0.533887\pi\) | ||||
−0.106258 | + | 0.994339i | \(0.533887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 61.4772 | 2.92749 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.6151 | 0.551852 | 0.275926 | − | 0.961179i | \(-0.411015\pi\) | ||||
0.275926 | + | 0.961179i | \(0.411015\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.63362 | 0.0774410 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −48.1108 | −2.27556 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.91369 | −0.467856 | −0.233928 | − | 0.972254i | \(-0.575158\pi\) | ||||
−0.233928 | + | 0.972254i | \(0.575158\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.92159 | −0.0904843 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.1153 | −0.851133 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.34565 | −0.250608 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.6050 | 1.52520 | 0.762598 | − | 0.646872i | \(-0.223923\pi\) | ||||
0.762598 | + | 0.646872i | \(0.223923\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.7900 | −0.503636 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.23030 | 0.243599 | 0.121800 | − | 0.992555i | \(-0.461133\pi\) | ||||
0.121800 | + | 0.992555i | \(0.461133\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.0841 | −1.63049 | −0.815247 | − | 0.579113i | \(-0.803399\pi\) | ||||
−0.815247 | + | 0.579113i | \(0.803399\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.08631 | −0.189498 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.3641 | 0.988614 | 0.494307 | − | 0.869288i | \(-0.335422\pi\) | ||||
0.494307 | + | 0.869288i | \(0.335422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.5266 | 1.68664 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.9506 | −1.10359 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.02904 | −0.277215 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.52884 | 0.253680 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 43.4689 | 1.99030 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.03920 | 0.230247 | 0.115124 | − | 0.993351i | \(-0.463274\pi\) | ||||
0.115124 | + | 0.993351i | \(0.463274\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.19376 | −0.373603 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −47.6706 | −2.16909 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.32718 | 0.423525 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.8824 | 1.30879 | 0.654393 | − | 0.756155i | \(-0.272924\pi\) | ||||
0.654393 | + | 0.756155i | \(0.272924\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.8560 | 0.762255 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.16246 | 0.232978 | 0.116489 | − | 0.993192i | \(-0.462836\pi\) | ||||
0.116489 | + | 0.993192i | \(0.462836\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.52884 | −0.158931 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.78817 | 0.125319 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.9793 | −0.941049 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.0946 | −1.21292 | −0.606461 | − | 0.795113i | \(-0.707411\pi\) | ||||
−0.606461 | + | 0.795113i | \(0.707411\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −34.2017 | −1.52802 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.7305 | 1.14727 | 0.573633 | − | 0.819112i | \(-0.305534\pi\) | ||||
0.573633 | + | 0.819112i | \(0.305534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.3249 | 0.726449 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.2488 | 1.38781 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.8353 | 0.524590 | 0.262295 | − | 0.964988i | \(-0.415521\pi\) | ||||
0.262295 | + | 0.964988i | \(0.415521\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.1809 | 1.02546 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.9054 | −0.746391 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.5288 | 0.596152 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.48963 | 0.197454 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −48.4403 | −2.12629 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.164719 | −0.00721646 | −0.00360823 | − | 0.999993i | \(-0.501149\pi\) | ||||
−0.00360823 | + | 0.999993i | \(0.501149\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.6072 | −0.507549 | −0.253775 | − | 0.967263i | \(-0.581672\pi\) | ||||
−0.253775 | + | 0.967263i | \(0.581672\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.4896 | 0.545092 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.39502 | −0.235011 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.43196 | −0.366607 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 44.6623 | 1.93818 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.26724 | −0.141520 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.672824 | −0.0290887 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.8066 | −0.725260 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.98153 | −0.429935 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.5922 | −1.53023 | −0.765113 | − | 0.643896i | \(-0.777317\pi\) | ||||
−0.765113 | + | 0.643896i | \(0.777317\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.2096 | −0.523963 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.5473 | −0.580303 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.3803 | −1.89757 | −0.948783 | − | 0.315929i | \(-0.897684\pi\) | ||||
−0.948783 | + | 0.315929i | \(0.897684\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −60.0448 | −2.56265 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.52884 | −0.235536 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.1440 | −0.473891 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.1440 | 0.812617 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.0739 | −1.10479 | −0.552393 | − | 0.833584i | \(-0.686285\pi\) | ||||
−0.552393 | + | 0.833584i | \(0.686285\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.2510 | −0.433572 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.34605 | 0.267930 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.4218 | −0.692096 | −0.346048 | − | 0.938217i | \(-0.612477\pi\) | ||||
−0.346048 | + | 0.938217i | \(0.612477\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.0185 | −0.842183 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.9031 | 0.835853 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.79834 | −0.326923 | −0.163462 | − | 0.986550i | \(-0.552266\pi\) | ||||
−0.163462 | + | 0.986550i | \(0.552266\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.3826 | −1.39702 | −0.698509 | − | 0.715601i | \(-0.746153\pi\) | ||||
−0.698509 | + | 0.715601i | \(0.746153\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −57.8722 | −2.41765 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.81681 | −0.159172 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.10478 | −0.337407 | −0.168703 | − | 0.985667i | \(-0.553958\pi\) | ||||
−0.168703 | + | 0.985667i | \(0.553958\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.3905 | 1.47078 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −65.5058 | −2.71764 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.05767 | −0.292299 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.74066 | 0.196002 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.5865 | 1.17989 | 0.589946 | − | 0.807443i | \(-0.299149\pi\) | ||||
0.589946 | + | 0.807443i | \(0.299149\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.45269 | −0.348287 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.6336 | −0.807619 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.4896 | 0.923539 | 0.461769 | − | 0.887000i | \(-0.347215\pi\) | ||||
0.461769 | + | 0.887000i | \(0.347215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.4896 | 0.676009 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −50.1892 | −2.05411 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.7305 | −1.29647 | −0.648237 | − | 0.761439i | \(-0.724493\pi\) | ||||
−0.648237 | + | 0.761439i | \(0.724493\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.56804 | 0.186334 | 0.0931671 | − | 0.995650i | \(-0.470301\pi\) | ||||
0.0931671 | + | 0.995650i | \(0.470301\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −32.3928 | −1.31914 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.5473 | 0.428809 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.7882 | −0.519056 | −0.259528 | − | 0.965736i | \(-0.583567\pi\) | ||||
−0.259528 | + | 0.965736i | \(0.583567\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.4896 | −0.506106 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.63362 | 0.308823 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.97927 | −0.281890 | −0.140945 | − | 0.990017i | \(-0.545014\pi\) | ||||
−0.140945 | + | 0.990017i | \(0.545014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.63362 | 0.307817 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.9193 | 1.24477 | 0.622383 | − | 0.782713i | \(-0.286165\pi\) | ||||
0.622383 | + | 0.782713i | \(0.286165\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.7098 | −0.832396 | −0.416198 | − | 0.909274i | \(-0.636638\pi\) | ||||
−0.416198 | + | 0.909274i | \(0.636638\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.6706 | 0.468324 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.63362 | 0.305835 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.94272 | 0.397074 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.2751 | 1.00779 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.67508 | 0.385159 | 0.192580 | − | 0.981281i | \(-0.438315\pi\) | ||||
0.192580 | + | 0.981281i | \(0.438315\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −47.1809 | −1.87527 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.03920 | 0.120607 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.9714 | −0.672430 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.6050 | 0.736002 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.5058 | 0.928425 | 0.464213 | − | 0.885724i | \(-0.346337\pi\) | ||||
0.464213 | + | 0.885724i | \(0.346337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.6235 | 1.60203 | 0.801016 | − | 0.598643i | \(-0.204293\pi\) | ||||
0.801016 | + | 0.598643i | \(0.204293\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.9506 | 0.943055 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.2280 | −0.402106 | −0.201053 | − | 0.979580i | \(-0.564436\pi\) | ||||
−0.201053 | + | 0.979580i | \(0.564436\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.25143 | −0.284644 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.0946 | −0.748377 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.2280 | −1.10465 | −0.552324 | − | 0.833629i | \(-0.686259\pi\) | ||||
−0.552324 | + | 0.833629i | \(0.686259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.81681 | 0.149135 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.5575 | −0.802023 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.0471 | −0.586152 | −0.293076 | − | 0.956089i | \(-0.594679\pi\) | ||||
−0.293076 | + | 0.956089i | \(0.594679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.8767 | 0.539743 | 0.269871 | − | 0.962896i | \(-0.413019\pi\) | ||||
0.269871 | + | 0.962896i | \(0.413019\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.7900 | 0.419050 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.8353 | 1.00185 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.81681 | 0.147787 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.9137 | −0.769908 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.74897 | 0.376355 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.3456 | 0.591531 | 0.295766 | − | 0.955261i | \(-0.404425\pi\) | ||||
0.295766 | + | 0.955261i | \(0.404425\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.05767 | −0.117690 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −50.5530 | −1.94291 | −0.971454 | − | 0.237228i | \(-0.923761\pi\) | ||||
−0.971454 | + | 0.237228i | \(0.923761\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.5843 | 1.67261 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 64.7361 | 2.48069 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.6027 | 1.59188 | 0.795942 | − | 0.605373i | \(-0.206976\pi\) | ||||
0.795942 | + | 0.605373i | \(0.206976\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.1048 | −0.615332 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.34565 | −0.203949 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | −0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.6627 | −1.58492 | −0.792461 | − | 0.609922i | \(-0.791201\pi\) | ||||
−0.792461 | + | 0.609922i | \(0.791201\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.0286 | 0.494917 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.05767 | −0.115984 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.0784 | 0.381747 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.769701 | 0.0291128 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.8145 | −1.69262 | −0.846311 | − | 0.532689i | \(-0.821182\pi\) | ||||
−0.846311 | + | 0.532689i | \(0.821182\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.6001 | 1.49354 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.8353 | −0.671716 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 76.2835 | 2.86893 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.4320 | 0.880006 | 0.440003 | − | 0.897996i | \(-0.354977\pi\) | ||||
0.440003 | + | 0.897996i | \(0.354977\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.88279 | 0.370634 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.83528 | 0.218533 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.769701 | −0.0287852 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.0739 | −0.749673 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.3328 | 1.20581 | 0.602905 | − | 0.797813i | \(-0.294010\pi\) | ||||
0.602905 | + | 0.797813i | \(0.294010\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 63.2179 | 2.35436 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 57.9216 | 2.15413 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00000 | −0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.01847 | 0.149037 | 0.0745184 | − | 0.997220i | \(-0.476258\pi\) | ||||
0.0745184 | + | 0.997220i | \(0.476258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.1685 | −1.56180 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.6212 | 1.16955 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.49189 | −0.128976 | −0.0644880 | − | 0.997918i | \(-0.520541\pi\) | ||||
−0.0644880 | + | 0.997918i | \(0.520541\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 39.6521 | 1.46259 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.25934 | 0.193730 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.4090 | −1.67040 | −0.835198 | − | 0.549949i | \(-0.814647\pi\) | ||||
−0.835198 | + | 0.549949i | \(0.814647\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.9054 | 0.621035 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.6683 | 1.49198 | 0.745988 | − | 0.665960i | \(-0.231978\pi\) | ||||
0.745988 | + | 0.665960i | \(0.231978\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | −0.659469 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 58.0924 | 2.12549 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.14399 | −0.114879 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.0268 | 1.78901 | 0.894506 | − | 0.447055i | \(-0.147527\pi\) | ||||
0.894506 | + | 0.447055i | \(0.147527\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.8722 | 1.23437 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.77761 | −0.246662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.7260 | −1.88001 | −0.940006 | − | 0.341157i | \(-0.889181\pi\) | ||||
−0.940006 | + | 0.341157i | \(0.889181\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.86392 | −0.249144 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.2307 | 1.24086 | 0.620431 | − | 0.784261i | \(-0.286958\pi\) | ||||
0.620431 | + | 0.784261i | \(0.286958\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −63.3042 | −2.29177 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.6235 | −0.528712 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.3294 | −0.445190 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.5971 | 0.814871 | 0.407436 | − | 0.913234i | \(-0.366423\pi\) | ||||
0.407436 | + | 0.913234i | \(0.366423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45.3615 | −1.63365 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.8538 | 0.498285 | 0.249142 | − | 0.968467i | \(-0.419851\pi\) | ||||
0.249142 | + | 0.968467i | \(0.419851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.52884 | −0.0549175 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 89.4565 | 3.20923 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.7904 | 0.565751 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.02073 | −0.108090 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.05767 | 0.109272 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.96080 | −0.319825 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0969 | 0.716376 | 0.358188 | − | 0.933649i | \(-0.383395\pi\) | ||||
0.358188 | + | 0.933649i | \(0.383395\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.7780 | −0.561712 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −93.5428 | −3.32600 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.5759 | 0.588629 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.0369 | 0.994368 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.6890 | 1.54754 | 0.773772 | − | 0.633464i | \(-0.218367\pi\) | ||||
0.773772 | + | 0.633464i | \(0.218367\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.5473 | −0.833044 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.76970 | −0.239196 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.33774 | 0.117786 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.8353 | −0.628611 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.7075 | 1.39777 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.4403 | −0.648325 | −0.324163 | − | 0.946001i | \(-0.605082\pi\) | ||||
−0.324163 | + | 0.946001i | \(0.605082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.0577 | 0.528746 | 0.264373 | − | 0.964420i | \(-0.414835\pi\) | ||||
0.264373 | + | 0.964420i | \(0.414835\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −60.3909 | −2.11800 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.30644 | 0.220905 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.5428 | 1.73328 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22.1523 | 0.774064 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.9793 | 1.77919 | 0.889594 | − | 0.456751i | \(-0.150987\pi\) | ||||
0.889594 | + | 0.456751i | \(0.150987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.84545 | −0.0991861 | −0.0495930 | − | 0.998770i | \(-0.515792\pi\) | ||||
−0.0495930 | + | 0.998770i | \(0.515792\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.79834 | 0.0626101 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.0761 | −0.524249 | −0.262124 | − | 0.965034i | \(-0.584423\pi\) | ||||
−0.262124 | + | 0.965034i | \(0.584423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.6992 | −1.20515 | −0.602577 | − | 0.798061i | \(-0.705859\pi\) | ||||
−0.602577 | + | 0.798061i | \(0.705859\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −73.4195 | −2.54690 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 52.3513 | 1.81386 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.7961 | −0.442827 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.67469 | 0.161581 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.7882 | −0.510544 | −0.255272 | − | 0.966869i | \(-0.582165\pi\) | ||||
−0.255272 | + | 0.966869i | \(0.582165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −46.9009 | −1.61535 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.6913 | 0.402193 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 49.2857 | 1.69348 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −70.8515 | −2.43162 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.3377 | −0.937126 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.7753 | 1.22492 | 0.612462 | − | 0.790500i | \(-0.290179\pi\) | ||||
0.612462 | + | 0.790500i | \(0.290179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.9114 | −0.783554 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.4112 | −0.423959 | −0.211980 | − | 0.977274i | \(-0.567991\pi\) | ||||
−0.211980 | + | 0.977274i | \(0.567991\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0599353 | −0.00204497 | −0.00102248 | − | 0.999999i | \(-0.500325\pi\) | ||||
−0.00102248 | + | 0.999999i | \(0.500325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.6706 | 1.21565 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.5530 | −1.51660 | −0.758300 | − | 0.651906i | \(-0.773970\pi\) | ||||
−0.758300 | + | 0.651906i | \(0.773970\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.1233 | −0.616209 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.1542 | 0.412777 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.60458 | −0.0544318 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.94233 | 0.302999 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38.6517 | −1.30816 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.67282 | 0.157970 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.9137 | 1.01011 | 0.505057 | − | 0.863086i | \(-0.331472\pi\) | ||||
0.505057 | + | 0.863086i | \(0.331472\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 60.6992 | 2.04733 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.2386 | −1.08615 | −0.543073 | − | 0.839685i | \(-0.682739\pi\) | ||||
−0.543073 | + | 0.839685i | \(0.682739\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.7098 | 1.23538 | 0.617691 | − | 0.786421i | \(-0.288068\pi\) | ||||
0.617691 | + | 0.786421i | \(0.288068\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.8066 | 0.968325 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.63588 | −0.0885042 | −0.0442521 | − | 0.999020i | \(-0.514090\pi\) | ||||
−0.0442521 | + | 0.999020i | \(0.514090\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.2017 | 0.476308 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.86578 | 0.0960073 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.8930 | −1.23458 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.28797 | −0.210184 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.6706 | −0.389669 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.52884 | 0.0509896 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.0162 | 1.23319 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 111.917 | 3.72437 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.56804 | −0.151847 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.0185 | 0.531885 | 0.265942 | − | 0.963989i | \(-0.414317\pi\) | ||||
0.265942 | + | 0.963989i | \(0.414317\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −67.6502 | −2.24382 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.9480 | 1.25727 | 0.628636 | − | 0.777700i | \(-0.283613\pi\) | ||||
0.628636 | + | 0.777700i | \(0.283613\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.43196 | −0.312152 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −38.7282 | −1.28032 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.8353 | 0.588973 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.58425 | −0.250181 | −0.125091 | − | 0.992145i | \(-0.539922\pi\) | ||||
−0.125091 | + | 0.992145i | \(0.539922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −56.0245 | −1.84607 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.13608 | −0.169056 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.16246 | 0.235500 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −56.0633 | −1.84136 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.4033 | 0.866265 | 0.433132 | − | 0.901330i | \(-0.357408\pi\) | ||||
0.433132 | + | 0.901330i | \(0.357408\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 82.0219 | 2.68816 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 73.4689 | 2.40526 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.37429 | 0.0776474 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.6050 | 1.45718 | 0.728591 | − | 0.684949i | \(-0.240176\pi\) | ||||
0.728591 | + | 0.684949i | \(0.240176\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 50.3988 | 1.64470 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.26724 | −0.302103 | −0.151052 | − | 0.988526i | \(-0.548266\pi\) | ||||
−0.151052 | + | 0.988526i | \(0.548266\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.9009 | −0.354981 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.2880 | −0.464788 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.4218 | −0.923584 | −0.461792 | − | 0.886988i | \(-0.652793\pi\) | ||||
−0.461792 | + | 0.886988i | \(0.652793\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.67508 | 0.184221 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −78.7158 | −2.55254 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.2100 | 1.78843 | 0.894213 | − | 0.447642i | \(-0.147736\pi\) | ||||
0.894213 | + | 0.447642i | \(0.147736\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.6521 | −0.700645 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.79834 | −0.0581320 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −75.2548 | −2.43010 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6627 | −0.924602 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.78817 | 0.0898476 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.2409 | 0.426238 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.1496 | −1.09818 | −0.549089 | − | 0.835764i | \(-0.685025\pi\) | ||||
−0.549089 | + | 0.835764i | \(0.685025\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −52.1478 | −1.67523 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.4090 | −1.32888 | −0.664438 | − | 0.747343i | \(-0.731329\pi\) | ||||
−0.664438 | + | 0.747343i | \(0.731329\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.2880 | −0.458051 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.05767 | 0.0979239 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.9506 | −0.446320 | −0.223160 | − | 0.974782i | \(-0.571637\pi\) | ||||
−0.223160 | + | 0.974782i | \(0.571637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.09914 | 0.0351286 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 56.1399 | 1.79241 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.6521 | −1.26471 | −0.632353 | − | 0.774681i | \(-0.717911\pi\) | ||||
−0.632353 | + | 0.774681i | \(0.717911\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.34565 | −0.234052 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −83.3411 | −2.65278 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.2017 | −1.08755 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.93442 | 0.0932149 | 0.0466075 | − | 0.998913i | \(-0.485159\pi\) | ||||
0.0466075 | + | 0.998913i | \(0.485159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.64153 | −0.305965 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.7776 | −0.595290 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.9977 | 0.411643 | 0.205821 | − | 0.978590i | \(-0.434013\pi\) | ||||
0.205821 | + | 0.978590i | \(0.434013\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.9005 | −0.692900 |
(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 | 580.2.a.c.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 5220.2.a.x.1.1 | 3 | |||
4.3 | odd | 2 | 2320.2.a.m.1.3 | 3 | |||
5.2 | odd | 4 | 2900.2.c.f.349.5 | 6 | |||
5.3 | odd | 4 | 2900.2.c.f.349.2 | 6 | |||
5.4 | even | 2 | 2900.2.a.g.1.3 | 3 | |||
8.3 | odd | 2 | 9280.2.a.bw.1.1 | 3 | |||
8.5 | even | 2 | 9280.2.a.bk.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
580.2.a.c.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2320.2.a.m.1.3 | 3 | 4.3 | odd | 2 | |||
2900.2.a.g.1.3 | 3 | 5.4 | even | 2 | |||
2900.2.c.f.349.2 | 6 | 5.3 | odd | 4 | |||
2900.2.c.f.349.5 | 6 | 5.2 | odd | 4 | |||
5220.2.a.x.1.1 | 3 | 3.2 | odd | 2 | |||
9280.2.a.bk.1.3 | 3 | 8.5 | even | 2 | |||
9280.2.a.bw.1.1 | 3 | 8.3 | odd | 2 |