Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.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: | \(48.5490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.56155 | 0.901563 | 0.450781 | − | 0.892634i | \(-0.351145\pi\) | ||||
0.450781 | + | 0.892634i | \(0.351145\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.56155 | −0.590211 | −0.295106 | − | 0.955465i | \(-0.595355\pi\) | ||||
−0.295106 | + | 0.955465i | \(0.595355\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.68466 | 1.85399 | 0.926995 | − | 0.375073i | \(-0.122382\pi\) | ||||
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.56155 | 1.83395 | 0.916973 | − | 0.398949i | \(-0.130625\pi\) | ||||
0.916973 | + | 0.398949i | \(0.130625\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.43845 | −0.532113 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.68466 | 0.976819 | 0.488409 | − | 0.872615i | \(-0.337577\pi\) | ||||
0.488409 | + | 0.872615i | \(0.337577\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.56155 | −1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.68466 | −1.24131 | −0.620655 | − | 0.784084i | \(-0.713133\pi\) | ||||
−0.620655 | + | 0.784084i | \(0.713133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.12311 | −0.560926 | −0.280463 | − | 0.959865i | \(-0.590488\pi\) | ||||
−0.280463 | + | 0.959865i | \(0.590488\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.24621 | 1.08733 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.56155 | 0.263951 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.4384 | 1.67149 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.24621 | −0.663147 | −0.331573 | − | 0.943429i | \(-0.607579\pi\) | ||||
−0.331573 | + | 0.943429i | \(0.607579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.1231 | −1.69626 | −0.848129 | − | 0.529790i | \(-0.822271\pi\) | ||||
−0.848129 | + | 0.529790i | \(0.822271\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.561553 | 0.0837114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.2462 | 1.49456 | 0.747282 | − | 0.664507i | \(-0.231359\pi\) | ||||
0.747282 | + | 0.664507i | \(0.231359\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.56155 | −0.651650 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.8078 | 1.65342 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.438447 | 0.0602254 | 0.0301127 | − | 0.999547i | \(-0.490413\pi\) | ||||
0.0301127 | + | 0.999547i | \(0.490413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.56155 | −0.206833 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.56155 | −0.203297 | −0.101648 | − | 0.994820i | \(-0.532412\pi\) | ||||
−0.101648 | + | 0.994820i | \(0.532412\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.87689 | −0.368349 | −0.184174 | − | 0.982894i | \(-0.558961\pi\) | ||||
−0.184174 | + | 0.982894i | \(0.558961\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.876894 | 0.110478 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.68466 | −0.829130 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.56155 | 0.190774 | 0.0953870 | − | 0.995440i | \(-0.469591\pi\) | ||||
0.0953870 | + | 0.995440i | \(0.469591\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.31534 | 0.880664 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.24621 | 0.741289 | 0.370644 | − | 0.928775i | \(-0.379137\pi\) | ||||
0.370644 | + | 0.928775i | \(0.379137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6847 | 1.25054 | 0.625272 | − | 0.780407i | \(-0.284988\pi\) | ||||
0.625272 | + | 0.780407i | \(0.284988\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.56155 | 0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.24621 | −0.711822 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.12311 | −0.351377 | −0.175688 | − | 0.984446i | \(-0.556215\pi\) | ||||
−0.175688 | + | 0.984446i | \(0.556215\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.1231 | 1.22092 | 0.610460 | − | 0.792047i | \(-0.290985\pi\) | ||||
0.610460 | + | 0.792047i | \(0.290985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.56155 | −0.820166 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.4384 | −1.11912 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.4384 | −1.09425 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.87689 | −0.505710 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.24621 | −0.225753 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.36932 | −0.733274 | −0.366637 | − | 0.930364i | \(-0.619491\pi\) | ||||
−0.366637 | + | 0.930364i | \(0.619491\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2462 | 1.40372 | 0.701860 | − | 0.712314i | \(-0.252353\pi\) | ||||
0.701860 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.43845 | 0.237968 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.56155 | −0.924350 | −0.462175 | − | 0.886789i | \(-0.652931\pi\) | ||||
−0.462175 | + | 0.886789i | \(0.652931\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.56155 | −0.341135 | −0.170567 | − | 0.985346i | \(-0.554560\pi\) | ||||
−0.170567 | + | 0.985346i | \(0.554560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.36932 | 0.889296 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.1231 | 1.61081 | 0.805403 | − | 0.592727i | \(-0.201949\pi\) | ||||
0.805403 | + | 0.592727i | \(0.201949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.68466 | −0.436847 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.75379 | −0.347038 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.8078 | −1.08242 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.63068 | −0.597869 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.87689 | −0.432754 | −0.216377 | − | 0.976310i | \(-0.569424\pi\) | ||||
−0.216377 | + | 0.976310i | \(0.569424\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.3693 | −1.52928 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4924 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.56155 | 0.135404 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.56155 | 0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.80776 | 0.496191 | 0.248095 | − | 0.968736i | \(-0.420195\pi\) | ||||
0.248095 | + | 0.968736i | \(0.420195\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.4924 | −1.39887 | −0.699435 | − | 0.714697i | \(-0.746565\pi\) | ||||
−0.699435 | + | 0.714697i | \(0.746565\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.0000 | 1.34744 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 26.7386 | 2.23600 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.68466 | 0.555131 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.12311 | −0.587504 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.3693 | 0.931411 | 0.465705 | − | 0.884940i | \(-0.345801\pi\) | ||||
0.465705 | + | 0.884940i | \(0.345801\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.12311 | 0.254155 | 0.127077 | − | 0.991893i | \(-0.459440\pi\) | ||||
0.127077 | + | 0.991893i | \(0.459440\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.24621 | −0.343286 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.12311 | 0.250854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.75379 | 0.299585 | 0.149792 | − | 0.988717i | \(-0.452139\pi\) | ||||
0.149792 | + | 0.988717i | \(0.452139\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.684658 | 0.0542969 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.31534 | −0.576530 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.36932 | 0.733862 | 0.366931 | − | 0.930248i | \(-0.380409\pi\) | ||||
0.366931 | + | 0.930248i | \(0.380409\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.24621 | −0.486267 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3693 | −1.34408 | −0.672039 | − | 0.740516i | \(-0.734581\pi\) | ||||
−0.672039 | + | 0.740516i | \(0.734581\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.6847 | 2.43728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.561553 | 0.0429430 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.75379 | −0.285395 | −0.142698 | − | 0.989766i | \(-0.545578\pi\) | ||||
−0.142698 | + | 0.989766i | \(0.545578\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.56155 | −0.118042 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.43845 | −0.183285 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.75379 | −0.430058 | −0.215029 | − | 0.976608i | \(-0.568985\pi\) | ||||
−0.215029 | + | 0.976608i | \(0.568985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0000 | 1.33793 | 0.668965 | − | 0.743294i | \(-0.266738\pi\) | ||||
0.668965 | + | 0.743294i | \(0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.49242 | −0.332089 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | −0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.2462 | 2.21182 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.68466 | 0.631716 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.68466 | −0.628400 | −0.314200 | − | 0.949357i | \(-0.601736\pi\) | ||||
−0.314200 | + | 0.949357i | \(0.601736\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.4924 | 1.33111 | 0.665557 | − | 0.746347i | \(-0.268194\pi\) | ||||
0.665557 | + | 0.746347i | \(0.268194\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.4384 | −0.747513 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.75379 | 0.267446 | 0.133723 | − | 0.991019i | \(-0.457307\pi\) | ||||
0.133723 | + | 0.991019i | \(0.457307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.80776 | 0.269925 | 0.134963 | − | 0.990851i | \(-0.456909\pi\) | ||||
0.134963 | + | 0.990851i | \(0.456909\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.43845 | 0.171995 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.4384 | 0.732635 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.24621 | 0.296568 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.63068 | −0.182845 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.6847 | 1.42399 | 0.711995 | − | 0.702184i | \(-0.247792\pi\) | ||||
0.711995 | + | 0.702184i | \(0.247792\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.75379 | 0.668319 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.1231 | 0.758590 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.87689 | 0.331065 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.6847 | 1.12744 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 50.5464 | 3.40012 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.36932 | −0.0916962 | −0.0458481 | − | 0.998948i | \(-0.514599\pi\) | ||||
−0.0458481 | + | 0.998948i | \(0.514599\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.93087 | −0.194529 | −0.0972643 | − | 0.995259i | \(-0.531009\pi\) | ||||
−0.0972643 | + | 0.995259i | \(0.531009\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4924 | −1.22201 | −0.611007 | − | 0.791625i | \(-0.709235\pi\) | ||||
−0.611007 | + | 0.791625i | \(0.709235\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.75379 | −0.641752 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2462 | −0.668389 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.87689 | −0.316788 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.56155 | 0.359747 | 0.179873 | − | 0.983690i | \(-0.442431\pi\) | ||||
0.179873 | + | 0.983690i | \(0.442431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.8769 | 0.958305 | 0.479153 | − | 0.877732i | \(-0.340944\pi\) | ||||
0.479153 | + | 0.877732i | \(0.340944\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.75379 | 0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.56155 | 0.291427 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.68466 | −0.425335 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.3693 | 1.10074 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2462 | −0.646735 | −0.323368 | − | 0.946273i | \(-0.604815\pi\) | ||||
−0.323368 | + | 0.946273i | \(0.604815\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.7386 | 1.17809 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.8078 | −0.739431 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0000 | 0.873296 | 0.436648 | − | 0.899632i | \(-0.356166\pi\) | ||||
0.436648 | + | 0.899632i | \(0.356166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.36932 | −0.582181 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.75379 | 0.232354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.75379 | 0.354794 | 0.177397 | − | 0.984139i | \(-0.443232\pi\) | ||||
0.177397 | + | 0.984139i | \(0.443232\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.438447 | −0.0269336 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.12311 | 0.191131 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.0000 | 1.58525 | 0.792624 | − | 0.609711i | \(-0.208714\pi\) | ||||
0.792624 | + | 0.609711i | \(0.208714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.93087 | −0.421020 | −0.210510 | − | 0.977592i | \(-0.567513\pi\) | ||||
−0.210510 | + | 0.977592i | \(0.567513\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.3002 | −0.986532 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00000 | 0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.12311 | −0.548154 | −0.274077 | − | 0.961708i | \(-0.588372\pi\) | ||||
−0.274077 | + | 0.961708i | \(0.588372\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.75379 | 0.104997 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8769 | −0.765452 | −0.382726 | − | 0.923862i | \(-0.625015\pi\) | ||||
−0.382726 | + | 0.923862i | \(0.625015\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.56155 | 0.0924984 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.63068 | 0.391397 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.1771 | 2.36336 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.36932 | 0.549239 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.1771 | −1.35402 | −0.677010 | − | 0.735974i | \(-0.736725\pi\) | ||||
−0.677010 | + | 0.735974i | \(0.736725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.56155 | 0.0909171 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.2462 | −1.29086 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.3153 | 1.81101 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.3693 | 1.00115 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.5076 | −0.661093 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.87689 | 0.164730 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.492423 | −0.0281040 | −0.0140520 | − | 0.999901i | \(-0.504473\pi\) | ||||
−0.0140520 | + | 0.999901i | \(0.504473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.2462 | 1.26554 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.68466 | −0.492462 | −0.246231 | − | 0.969211i | \(-0.579192\pi\) | ||||
−0.246231 | + | 0.969211i | \(0.579192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.0540 | −1.81180 | −0.905899 | − | 0.423494i | \(-0.860803\pi\) | ||||
−0.905899 | + | 0.423494i | \(0.860803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.876894 | −0.0494074 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.0540 | 1.35101 | 0.675503 | − | 0.737357i | \(-0.263927\pi\) | ||||
0.675503 | + | 0.737357i | \(0.263927\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.7386 | −1.49708 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.9309 | −0.833360 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.56155 | −0.420736 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.68466 | 0.370798 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.56155 | −0.307555 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.0000 | −0.882109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.56155 | 0.0858307 | 0.0429154 | − | 0.999079i | \(-0.486335\pi\) | ||||
0.0429154 | + | 0.999079i | \(0.486335\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.36932 | −0.184637 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.56155 | −0.0853167 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0000 | −1.41631 | −0.708155 | − | 0.706057i | \(-0.750472\pi\) | ||||
−0.708155 | + | 0.706057i | \(0.750472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.7386 | 1.45224 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.4924 | −0.676503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0540 | 0.974823 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.31534 | −0.393845 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.3693 | −1.79136 | −0.895679 | − | 0.444700i | \(-0.853310\pi\) | ||||
−0.895679 | + | 0.444700i | \(0.853310\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.2462 | −1.08375 | −0.541877 | − | 0.840458i | \(-0.682286\pi\) | ||||
−0.541877 | + | 0.840458i | \(0.682286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −37.1771 | −1.98437 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.9309 | 1.32694 | 0.663468 | − | 0.748205i | \(-0.269084\pi\) | ||||
0.663468 | + | 0.748205i | \(0.269084\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.24621 | −0.331514 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.4384 | −0.975866 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.56155 | −0.293528 | −0.146764 | − | 0.989172i | \(-0.546886\pi\) | ||||
−0.146764 | + | 0.989172i | \(0.546886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.80776 | 0.409801 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.6847 | −0.559261 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2462 | 0.534848 | 0.267424 | − | 0.963579i | \(-0.413828\pi\) | ||||
0.267424 | + | 0.963579i | \(0.413828\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.38447 | 0.124131 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.684658 | −0.0355457 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.5616 | 1.42708 | 0.713542 | − | 0.700613i | \(-0.247090\pi\) | ||||
0.713542 | + | 0.700613i | \(0.247090\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.56155 | −0.0806382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −44.6847 | −2.30138 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.43845 | 0.330721 | 0.165360 | − | 0.986233i | \(-0.447121\pi\) | ||||
0.165360 | + | 0.986233i | \(0.447121\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.61553 | −0.390155 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.2462 | −1.54551 | −0.772755 | − | 0.634705i | \(-0.781122\pi\) | ||||
−0.772755 | + | 0.634705i | \(0.781122\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.24621 | 0.318336 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.24621 | 0.317513 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.12311 | −0.0569437 | −0.0284719 | − | 0.999595i | \(-0.509064\pi\) | ||||
−0.0284719 | + | 0.999595i | \(0.509064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.4233 | 1.79143 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.7538 | 1.29911 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.12311 | 0.157140 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.12311 | −0.0563671 | −0.0281835 | − | 0.999603i | \(-0.508972\pi\) | ||||
−0.0281835 | + | 0.999603i | \(0.508972\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.43845 | 0.122075 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.2462 | −1.01105 | −0.505524 | − | 0.862813i | \(-0.668701\pi\) | ||||
−0.505524 | + | 0.862813i | \(0.668701\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.8769 | −1.03995 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00000 | 0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.7386 | −1.22325 | −0.611623 | − | 0.791149i | \(-0.709483\pi\) | ||||
−0.611623 | + | 0.791149i | \(0.709483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.06913 | 0.447347 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.43845 | 0.119988 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.1231 | −0.546012 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.7538 | −1.26117 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.8617 | −1.65425 | −0.827127 | − | 0.562015i | \(-0.810026\pi\) | ||||
−0.827127 | + | 0.562015i | \(0.810026\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.93087 | −0.240316 | −0.120158 | − | 0.992755i | \(-0.538340\pi\) | ||||
−0.120158 | + | 0.992755i | \(0.538340\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.75379 | −0.279759 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.56155 | 0.366789 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.49242 | 0.217404 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 41.7538 | 2.01589 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.3693 | 1.89197 | 0.945984 | − | 0.324212i | \(-0.105099\pi\) | ||||
0.945984 | + | 0.324212i | \(0.105099\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.4384 | 0.500485 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.68466 | −0.224098 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.87689 | 0.232761 | 0.116381 | − | 0.993205i | \(-0.462871\pi\) | ||||
0.116381 | + | 0.993205i | \(0.462871\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.56155 | 0.121979 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.2462 | −0.676858 | −0.338429 | − | 0.940992i | \(-0.609895\pi\) | ||||
−0.338429 | + | 0.940992i | \(0.609895\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00000 | −0.0948091 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.7538 | 0.839725 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.7386 | 0.978717 | 0.489358 | − | 0.872083i | \(-0.337231\pi\) | ||||
0.489358 | + | 0.872083i | \(0.337231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.9848 | −0.799785 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.87689 | 0.229136 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.4384 | 0.489362 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.6847 | 0.874031 | 0.437016 | − | 0.899454i | \(-0.356035\pi\) | ||||
0.437016 | + | 0.899454i | \(0.356035\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −42.0540 | −1.96291 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.2462 | −0.942960 | −0.471480 | − | 0.881877i | \(-0.656280\pi\) | ||||
−0.471480 | + | 0.881877i | \(0.656280\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.7538 | 0.639193 | 0.319596 | − | 0.947554i | \(-0.396453\pi\) | ||||
0.319596 | + | 0.947554i | \(0.396453\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.87689 | 0.226161 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.75379 | 0.0811557 | 0.0405778 | − | 0.999176i | \(-0.487080\pi\) | ||||
0.0405778 | + | 0.999176i | \(0.487080\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.43845 | −0.112597 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.86174 | 0.270095 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −44.4924 | −2.04576 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.246211 | −0.0112732 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.0000 | −1.46212 | −0.731059 | − | 0.682315i | \(-0.760973\pi\) | ||||
−0.731059 | + | 0.682315i | \(0.760973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.1080 | 1.82877 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.4233 | −0.519778 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.00000 | −0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.6155 | −1.07012 | −0.535061 | − | 0.844814i | \(-0.679711\pi\) | ||||
−0.535061 | + | 0.844814i | \(0.679711\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.6307 | 0.661622 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.12311 | 0.321461 | 0.160731 | − | 0.986998i | \(-0.448615\pi\) | ||||
0.160731 | + | 0.986998i | \(0.448615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −50.5464 | −2.27650 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.24621 | 0.100960 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.75379 | −0.437517 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.1080 | −1.43735 | −0.718675 | − | 0.695347i | \(-0.755251\pi\) | ||||
−0.718675 | + | 0.695347i | \(0.755251\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.1231 | −1.21177 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.0540 | −1.34004 | −0.670020 | − | 0.742343i | \(-0.733715\pi\) | ||||
−0.670020 | + | 0.742343i | \(0.733715\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.36932 | 0.327930 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 49.4773 | 2.19736 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.4924 | 1.35155 | 0.675776 | − | 0.737107i | \(-0.263808\pi\) | ||||
0.675776 | + | 0.737107i | \(0.263808\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.6847 | −0.738086 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.56155 | 0.245549 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.2462 | −0.627763 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.9848 | 1.80251 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.86174 | −0.257302 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.12311 | 0.224447 | 0.112224 | − | 0.993683i | \(-0.464203\pi\) | ||||
0.112224 | + | 0.993683i | \(0.464203\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.3153 | −0.844601 | −0.422300 | − | 0.906456i | \(-0.638777\pi\) | ||||
−0.422300 | + | 0.906456i | \(0.638777\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.43845 | −0.106423 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.6155 | −1.02871 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.05398 | −0.0458250 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.876894 | 0.0380540 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.3845 | −1.22947 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.56155 | 0.413382 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.98485 | −0.387725 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.2462 | −0.785920 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.6155 | 1.78919 | 0.894596 | − | 0.446877i | \(-0.147464\pi\) | ||||
0.894596 | + | 0.446877i | \(0.147464\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.1080 | 1.20623 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.56155 | 0.152560 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4924 | −0.705165 | −0.352583 | − | 0.935781i | \(-0.614696\pi\) | ||||
−0.352583 | + | 0.935781i | \(0.614696\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.61553 | 0.0689491 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.68466 | 0.284776 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.87689 | 0.207387 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.36932 | −0.397705 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.61553 | 0.0684521 | 0.0342261 | − | 0.999414i | \(-0.489103\pi\) | ||||
0.0342261 | + | 0.999414i | \(0.489103\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −74.3542 | −3.14485 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 47.2311 | 1.99410 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.4924 | 1.03223 | 0.516116 | − | 0.856519i | \(-0.327377\pi\) | ||||
0.516116 | + | 0.856519i | \(0.327377\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.1231 | −0.720374 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.9309 | 0.459053 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.12311 | 0.214772 | 0.107386 | − | 0.994217i | \(-0.465752\pi\) | ||||
0.107386 | + | 0.994217i | \(0.465752\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.6155 | −0.820884 | −0.410442 | − | 0.911887i | \(-0.634626\pi\) | ||||
−0.410442 | + | 0.911887i | \(0.634626\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.5616 | −0.566542 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.68466 | 0.195364 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.6847 | −0.944375 | −0.472187 | − | 0.881498i | \(-0.656535\pi\) | ||||
−0.472187 | + | 0.881498i | \(0.656535\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.8769 | 1.20008 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.3693 | −0.720601 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.75379 | 0.0726345 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.75379 | 0.155200 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.3693 | 0.716908 | 0.358454 | − | 0.933547i | \(-0.383304\pi\) | ||||
0.358454 | + | 0.933547i | \(0.383304\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.12311 | 0.128685 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.86174 | 0.241120 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.2462 | 0.995673 | 0.497836 | − | 0.867271i | \(-0.334128\pi\) | ||||
0.497836 | + | 0.867271i | \(0.334128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.8078 | 0.484071 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.94602 | 0.243355 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −45.8617 | −1.87386 | −0.936930 | − | 0.349517i | \(-0.886346\pi\) | ||||
−0.936930 | + | 0.349517i | \(0.886346\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0000 | 0.734235 | 0.367118 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367118 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.876894 | −0.0357099 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00000 | −0.203279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.8769 | 0.522657 | 0.261329 | − | 0.965250i | \(-0.415839\pi\) | ||||
0.261329 | + | 0.965250i | \(0.415839\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.3002 | 0.660517 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 68.4924 | 2.77091 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.3693 | 0.782319 | 0.391160 | − | 0.920323i | \(-0.372074\pi\) | ||||
0.391160 | + | 0.920323i | \(0.372074\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.63068 | 0.267375 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.24621 | −0.170946 | −0.0854730 | − | 0.996340i | \(-0.527240\pi\) | ||||
−0.0854730 | + | 0.996340i | \(0.527240\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.0000 | −1.44696 | −0.723481 | − | 0.690344i | \(-0.757459\pi\) | ||||
−0.723481 | + | 0.690344i | \(0.757459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.0540 | −1.04551 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.12311 | −0.125125 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.24621 | −0.249450 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 45.3693 | 1.80899 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.4924 | −0.497315 | −0.248658 | − | 0.968591i | \(-0.579989\pi\) | ||||
−0.248658 | + | 0.968591i | \(0.579989\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.3002 | 1.28382 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.87689 | 0.193534 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.4924 | −1.20815 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.50758 | −0.138758 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.8617 | −1.41645 | −0.708227 | − | 0.705985i | \(-0.750505\pi\) | ||||
−0.708227 | + | 0.705985i | \(0.750505\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.61553 | 0.300327 | 0.150164 | − | 0.988661i | \(-0.452020\pi\) | ||||
0.150164 | + | 0.988661i | \(0.452020\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.3693 | 0.683916 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.56155 | −0.375903 | −0.187952 | − | 0.982178i | \(-0.560185\pi\) | ||||
−0.187952 | + | 0.982178i | \(0.560185\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.24621 | −0.245185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.61553 | 0.298476 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.12311 | −0.0439505 | −0.0219753 | − | 0.999759i | \(-0.506996\pi\) | ||||
−0.0219753 | + | 0.999759i | \(0.506996\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.4924 | −0.644412 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.9309 | −1.67235 | −0.836175 | − | 0.548463i | \(-0.815213\pi\) | ||||
−0.836175 | + | 0.548463i | \(0.815213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.80776 | −0.381478 | −0.190739 | − | 0.981641i | \(-0.561088\pi\) | ||||
−0.190739 | + | 0.981641i | \(0.561088\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 78.9309 | 3.06542 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.56155 | −0.0605544 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.3153 | −1.21253 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.13826 | −0.0826699 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.5076 | −0.444245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.36932 | −0.129878 | −0.0649388 | − | 0.997889i | \(-0.520685\pi\) | ||||
−0.0649388 | + | 0.997889i | \(0.520685\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.56155 | −0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.4384 | −1.40044 | −0.700222 | − | 0.713926i | \(-0.746915\pi\) | ||||
−0.700222 | + | 0.713926i | \(0.746915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.36932 | −0.359561 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.57671 | −0.175380 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.00000 | 0.153056 | 0.0765279 | − | 0.997067i | \(-0.475617\pi\) | ||||
0.0765279 | + | 0.997067i | \(0.475617\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.80776 | −0.221903 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.8769 | −1.10172 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.93087 | 0.111657 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.87689 | −0.337693 | −0.168846 | − | 0.985642i | \(-0.554004\pi\) | ||||
−0.168846 | + | 0.985642i | \(0.554004\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.50758 | 0.133242 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.4924 | 0.625593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.1080 | −1.21618 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.6155 | 0.590634 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.1231 | 1.09996 | 0.549982 | − | 0.835176i | \(-0.314634\pi\) | ||||
0.549982 | + | 0.835176i | \(0.314634\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | −0.226294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.0000 | −0.602595 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.5076 | 0.432787 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.0000 | −1.42712 | −0.713560 | − | 0.700594i | \(-0.752918\pi\) | ||||
−0.713560 | + | 0.700594i | \(0.752918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.75379 | 0.0657722 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.6307 | −0.547923 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.7386 | −0.999968 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.68466 | 0.324335 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.5616 | 1.10246 | 0.551230 | − | 0.834353i | \(-0.314159\pi\) | ||||
0.551230 | + | 0.834353i | \(0.314159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.2462 | −0.828492 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.2311 | 0.863972 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.68466 | −0.248262 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.6847 | 1.36056 | 0.680279 | − | 0.732953i | \(-0.261858\pi\) | ||||
0.680279 | + | 0.732953i | \(0.261858\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −84.1080 | −3.11084 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.1231 | 1.66666 | 0.833330 | − | 0.552776i | \(-0.186431\pi\) | ||||
0.833330 | + | 0.552776i | \(0.186431\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.12311 | 0.262740 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.24621 | 0.230082 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.8769 | 0.620827 | 0.310413 | − | 0.950602i | \(-0.399533\pi\) | ||||
0.310413 | + | 0.950602i | \(0.399533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.4384 | −0.383466 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.1231 | −0.995050 | −0.497525 | − | 0.867450i | \(-0.665758\pi\) | ||||
−0.497525 | + | 0.867450i | \(0.665758\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.3693 | −0.416540 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.24621 | −0.228537 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.9309 | 0.545562 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.1231 | 1.57358 | 0.786792 | − | 0.617218i | \(-0.211740\pi\) | ||||
0.786792 | + | 0.617218i | \(0.211740\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.0000 | −0.583072 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.12311 | −0.113661 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.50758 | −0.345559 | −0.172779 | − | 0.984961i | \(-0.555275\pi\) | ||||
−0.172779 | + | 0.984961i | \(0.555275\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.2614 | 1.06212 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.5464 | −1.03481 | −0.517403 | − | 0.855742i | \(-0.673101\pi\) | ||||
−0.517403 | + | 0.855742i | \(0.673101\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.56155 | 0.201342 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.24621 | 0.153522 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.4384 | −0.376910 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.5616 | 1.13814 | 0.569069 | − | 0.822290i | \(-0.307304\pi\) | ||||
0.569069 | + | 0.822290i | \(0.307304\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.8617 | 0.787331 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.80776 | 0.352761 | 0.176380 | − | 0.984322i | \(-0.443561\pi\) | ||||
0.176380 | + | 0.984322i | \(0.443561\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.12311 | −0.112185 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.6307 | −0.524873 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.24621 | 0.152136 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.9848 | 0.894028 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 37.1771 | 1.32860 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.75379 | −0.133978 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.8078 | 1.13382 | 0.566912 | − | 0.823778i | \(-0.308138\pi\) | ||||
0.566912 | + | 0.823778i | \(0.308138\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.98485 | 0.319869 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.7386 | −0.950716 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.2311 | −0.682915 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.684658 | −0.0242823 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.3002 | −1.49835 | −0.749175 | − | 0.662372i | \(-0.769550\pi\) | ||||
−0.749175 | + | 0.662372i | \(0.769550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 77.4773 | 2.74095 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.12311 | −0.0396830 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.7386 | 1.50821 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.31534 | 0.257832 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 40.6004 | 1.42920 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.43845 | −0.296680 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.192236 | −0.00675032 | −0.00337516 | − | 0.999994i | \(-0.501074\pi\) | ||||
−0.00337516 | + | 0.999994i | \(0.501074\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.8229 | −0.379576 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.36932 | −0.328193 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.1231 | 0.389148 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.86174 | 0.204826 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.36932 | −0.257191 | −0.128595 | − | 0.991697i | \(-0.541047\pi\) | ||||
−0.128595 | + | 0.991697i | \(0.541047\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.5616 | 1.16988 | 0.584941 | − | 0.811076i | \(-0.301118\pi\) | ||||
0.584941 | + | 0.811076i | \(0.301118\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.24621 | 0.217465 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.43845 | −0.223887 | −0.111943 | − | 0.993715i | \(-0.535708\pi\) | ||||
−0.111943 | + | 0.993715i | \(0.535708\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.0540 | −0.557578 | −0.278789 | − | 0.960352i | \(-0.589933\pi\) | ||||
−0.278789 | + | 0.960352i | \(0.589933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.2462 | −0.494196 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.4924 | −1.19509 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.3693 | 0.601090 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.3693 | 0.600371 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.4924 | 0.431286 | 0.215643 | − | 0.976472i | \(-0.430815\pi\) | ||||
0.215643 | + | 0.976472i | \(0.430815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6847 | 0.540850 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.12311 | 0.107565 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.6847 | −1.08999 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.80776 | −0.268278 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.1080 | −0.690103 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.1080 | 0.963528 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.7386 | −0.847035 | −0.423517 | − | 0.905888i | \(-0.639205\pi\) | ||||
−0.423517 | + | 0.905888i | \(0.639205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.561553 | −0.0192047 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.3693 | 1.34483 | 0.672415 | − | 0.740174i | \(-0.265257\pi\) | ||||
0.672415 | + | 0.740174i | \(0.265257\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.9848 | 0.443037 | 0.221519 | − | 0.975156i | \(-0.428899\pi\) | ||||
0.221519 | + | 0.975156i | \(0.428899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.3542 | 0.352869 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.2462 | 0.484947 | 0.242473 | − | 0.970158i | \(-0.422041\pi\) | ||||
0.242473 | + | 0.970158i | \(0.422041\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.75379 | 0.127633 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 62.7386 | 2.13072 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.4924 | −0.423776 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.4384 | 0.353693 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.36932 | −0.114034 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.56155 | 0.0527901 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.9309 | −0.841856 | −0.420928 | − | 0.907094i | \(-0.638295\pi\) | ||||
−0.420928 | + | 0.907094i | \(0.638295\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −36.1922 | −1.22073 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.9848 | −0.774379 | −0.387190 | − | 0.922000i | \(-0.626554\pi\) | ||||
−0.387190 | + | 0.922000i | \(0.626554\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.6155 | −1.60239 | −0.801195 | − | 0.598403i | \(-0.795802\pi\) | ||||
−0.801195 | + | 0.598403i | \(0.795802\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.43845 | 0.0819675 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.49242 | 0.150841 | 0.0754204 | − | 0.997152i | \(-0.475970\pi\) | ||||
0.0754204 | + | 0.997152i | \(0.475970\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.61553 | 0.255417 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.0000 | −0.938035 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.2462 | −0.342876 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.75379 | 0.192328 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 48.9006 | 1.63274 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.8769 | 0.696283 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.31534 | 0.110450 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.1231 | 0.902600 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0000 | −0.598340 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.1771 | 0.835991 | 0.417996 | − | 0.908449i | \(-0.362733\pi\) | ||||
0.417996 | + | 0.908449i | \(0.362733\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.13826 | 0.137257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.4924 | 0.943996 | 0.471998 | − | 0.881600i | \(-0.343533\pi\) | ||||
0.471998 | + | 0.881600i | \(0.343533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.4924 | 1.47248 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.49242 | 0.148515 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.7538 | −0.850465 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.9309 | 1.02032 | 0.510158 | − | 0.860081i | \(-0.329587\pi\) | ||||
0.510158 | + | 0.860081i | \(0.329587\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.768944 | −0.0253376 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.7538 | 1.37434 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.3002 | 1.12535 | 0.562676 | − | 0.826677i | \(-0.309772\pi\) | ||||
0.562676 | + | 0.826677i | \(0.309772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.56155 | 0.149499 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.5616 | −0.443985 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30.2462 | −0.989157 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.4384 | 1.19039 | 0.595196 | − | 0.803580i | \(-0.297074\pi\) | ||||
0.595196 | + | 0.803580i | \(0.297074\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −50.0540 | −1.63345 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.1922 | −1.11464 | −0.557318 | − | 0.830299i | \(-0.688169\pi\) | ||||
−0.557318 | + | 0.830299i | \(0.688169\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.8920 | −0.647774 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.68466 | −0.282512 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.7538 | −0.576921 | −0.288460 | − | 0.957492i | \(-0.593143\pi\) | ||||
−0.288460 | + | 0.957492i | \(0.593143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 71.4233 | 2.31850 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37.5616 | 1.21802 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.1080 | −0.975292 | −0.487646 | − | 0.873041i | \(-0.662144\pi\) | ||||
−0.487646 | + | 0.873041i | \(0.662144\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.68466 | 0.281029 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −41.7538 | −1.34971 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.06913 | −0.292857 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.2462 | −0.685362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.36932 | 0.173024 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.4924 | −0.595292 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.4924 | 1.55941 | 0.779706 | − | 0.626146i | \(-0.215369\pi\) | ||||
0.779706 | + | 0.626146i | \(0.215369\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.8078 | −0.379320 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.5076 | −0.754394 | −0.377197 | − | 0.926133i | \(-0.623112\pi\) | ||||
−0.377197 | + | 0.926133i | \(0.623112\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.7538 | 0.825629 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.4384 | 0.334298 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.7386 | −0.663488 | −0.331744 | − | 0.943370i | \(-0.607637\pi\) | ||||
−0.331744 | + | 0.943370i | \(0.607637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000 | 0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.1231 | −0.865093 | −0.432546 | − | 0.901612i | \(-0.642385\pi\) | ||||
−0.432546 | + | 0.901612i | \(0.642385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.75379 | −0.119606 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.9848 | −0.795276 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −52.1080 | −1.65694 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1231 | −0.353337 | −0.176669 | − | 0.984270i | \(-0.556532\pi\) | ||||
−0.176669 | + | 0.984270i | \(0.556532\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.43845 | 0.0773818 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.80776 | −0.120714 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.7386 | −1.03684 | −0.518421 | − | 0.855125i | \(-0.673480\pi\) | ||||
−0.518421 | + | 0.855125i | \(0.673480\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −33.3693 | −1.05576 |
(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 | 6080.2.a.bb.1.2 | 2 | ||
4.3 | odd | 2 | 6080.2.a.bh.1.1 | 2 | |||
8.3 | odd | 2 | 190.2.a.d.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 1520.2.a.n.1.1 | 2 | |||
24.11 | even | 2 | 1710.2.a.w.1.2 | 2 | |||
40.3 | even | 4 | 950.2.b.f.799.4 | 4 | |||
40.19 | odd | 2 | 950.2.a.h.1.1 | 2 | |||
40.27 | even | 4 | 950.2.b.f.799.1 | 4 | |||
40.29 | even | 2 | 7600.2.a.y.1.2 | 2 | |||
56.27 | even | 2 | 9310.2.a.bc.1.1 | 2 | |||
120.59 | even | 2 | 8550.2.a.br.1.1 | 2 | |||
152.75 | even | 2 | 3610.2.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.a.d.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
950.2.a.h.1.1 | 2 | 40.19 | odd | 2 | |||
950.2.b.f.799.1 | 4 | 40.27 | even | 4 | |||
950.2.b.f.799.4 | 4 | 40.3 | even | 4 | |||
1520.2.a.n.1.1 | 2 | 8.5 | even | 2 | |||
1710.2.a.w.1.2 | 2 | 24.11 | even | 2 | |||
3610.2.a.t.1.1 | 2 | 152.75 | even | 2 | |||
6080.2.a.bb.1.2 | 2 | 1.1 | even | 1 | trivial | ||
6080.2.a.bh.1.1 | 2 | 4.3 | odd | 2 | |||
7600.2.a.y.1.2 | 2 | 40.29 | even | 2 | |||
8550.2.a.br.1.1 | 2 | 120.59 | even | 2 | |||
9310.2.a.bc.1.1 | 2 | 56.27 | even | 2 |