Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,3,Mod(391,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.391");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.f (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(40.0545988610\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + \cdots + 101626561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.2 | ||
Root | \(0.848921 + 1.47037i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.391 |
Dual form | 1470.3.f.d.391.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − 2.23607i | − 0.447214i | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 3.16228i | 0.316228i | ||||||||
\(11\) | 19.9750 | 1.81591 | 0.907953 | − | 0.419071i | \(-0.137644\pi\) | ||||
0.907953 | + | 0.419071i | \(0.137644\pi\) | |||||||
\(12\) | − 3.46410i | − 0.288675i | ||||||||
\(13\) | − 3.49788i | − 0.269068i | −0.990909 | − | 0.134534i | \(-0.957046\pi\) | ||||
0.990909 | − | 0.134534i | \(-0.0429537\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.87298 | −0.258199 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 18.2422i | 1.07307i | 0.843877 | + | 0.536536i | \(0.180268\pi\) | ||||
−0.843877 | + | 0.536536i | \(0.819732\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | 24.6116i | 1.29535i | 0.761918 | + | 0.647673i | \(0.224258\pi\) | ||||
−0.761918 | + | 0.647673i | \(0.775742\pi\) | |||||||
\(20\) | − 4.47214i | − 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −28.2489 | −1.28404 | ||||||||
\(23\) | 25.1904 | 1.09523 | 0.547617 | − | 0.836729i | \(-0.315535\pi\) | ||||
0.547617 | + | 0.836729i | \(0.315535\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 4.94675i | 0.190260i | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −53.1223 | −1.83180 | −0.915902 | − | 0.401402i | \(-0.868523\pi\) | ||||
−0.915902 | + | 0.401402i | \(0.868523\pi\) | |||||||
\(30\) | 5.47723 | 0.182574 | ||||||||
\(31\) | 30.1312i | 0.971974i | 0.873966 | + | 0.485987i | \(0.161540\pi\) | ||||
−0.873966 | + | 0.485987i | \(0.838460\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | − 34.5977i | − 1.04841i | ||||||||
\(34\) | − 25.7984i | − 0.758777i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −46.7693 | −1.26403 | −0.632017 | − | 0.774954i | \(-0.717773\pi\) | ||||
−0.632017 | + | 0.774954i | \(0.717773\pi\) | |||||||
\(38\) | − 34.8060i | − 0.915948i | ||||||||
\(39\) | −6.05851 | −0.155346 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | 31.5250i | 0.768903i | 0.923145 | + | 0.384452i | \(0.125609\pi\) | ||||
−0.923145 | + | 0.384452i | \(0.874391\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64.4116 | 1.49794 | 0.748972 | − | 0.662602i | \(-0.230548\pi\) | ||||
0.748972 | + | 0.662602i | \(0.230548\pi\) | |||||||
\(44\) | 39.9499 | 0.907953 | ||||||||
\(45\) | 6.70820i | 0.149071i | ||||||||
\(46\) | −35.6246 | −0.774447 | ||||||||
\(47\) | 28.0626i | 0.597076i | 0.954398 | + | 0.298538i | \(0.0964990\pi\) | ||||
−0.954398 | + | 0.298538i | \(0.903501\pi\) | |||||||
\(48\) | − 6.92820i | − 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | 31.5965 | 0.619539 | ||||||||
\(52\) | − 6.99576i | − 0.134534i | ||||||||
\(53\) | −64.8748 | −1.22405 | −0.612027 | − | 0.790837i | \(-0.709646\pi\) | ||||
−0.612027 | + | 0.790837i | \(0.709646\pi\) | |||||||
\(54\) | − 7.34847i | − 0.136083i | ||||||||
\(55\) | − 44.6654i | − 0.812098i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 42.6285 | 0.747869 | ||||||||
\(58\) | 75.1263 | 1.29528 | ||||||||
\(59\) | 100.192i | 1.69816i | 0.528263 | + | 0.849081i | \(0.322844\pi\) | ||||
−0.528263 | + | 0.849081i | \(0.677156\pi\) | |||||||
\(60\) | −7.74597 | −0.129099 | ||||||||
\(61\) | − 8.02397i | − 0.131540i | −0.997835 | − | 0.0657702i | \(-0.979050\pi\) | ||||
0.997835 | − | 0.0657702i | \(-0.0209504\pi\) | |||||||
\(62\) | − 42.6119i | − 0.687289i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −7.82150 | −0.120331 | ||||||||
\(66\) | 48.9285i | 0.741341i | ||||||||
\(67\) | 16.2633 | 0.242736 | 0.121368 | − | 0.992608i | \(-0.461272\pi\) | ||||
0.121368 | + | 0.992608i | \(0.461272\pi\) | |||||||
\(68\) | 36.4845i | 0.536536i | ||||||||
\(69\) | − 43.6310i | − 0.632333i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −107.725 | −1.51725 | −0.758625 | − | 0.651528i | \(-0.774128\pi\) | ||||
−0.758625 | + | 0.651528i | \(0.774128\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | 51.6607i | 0.707681i | 0.935306 | + | 0.353840i | \(0.115124\pi\) | ||||
−0.935306 | + | 0.353840i | \(0.884876\pi\) | |||||||
\(74\) | 66.1417 | 0.893807 | ||||||||
\(75\) | 8.66025i | 0.115470i | ||||||||
\(76\) | 49.2232i | 0.647673i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.56803 | 0.109846 | ||||||||
\(79\) | −21.9755 | −0.278170 | −0.139085 | − | 0.990280i | \(-0.544416\pi\) | ||||
−0.139085 | + | 0.990280i | \(0.544416\pi\) | |||||||
\(80\) | − 8.94427i | − 0.111803i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − 44.5831i | − 0.543697i | ||||||||
\(83\) | − 0.417479i | − 0.00502987i | −0.999997 | − | 0.00251494i | \(-0.999199\pi\) | ||||
0.999997 | − | 0.00251494i | \(-0.000800530\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 40.7909 | 0.479893 | ||||||||
\(86\) | −91.0918 | −1.05921 | ||||||||
\(87\) | 92.0105i | 1.05759i | ||||||||
\(88\) | −56.4978 | −0.642020 | ||||||||
\(89\) | 111.210i | 1.24956i | 0.780803 | + | 0.624778i | \(0.214810\pi\) | ||||
−0.780803 | + | 0.624778i | \(0.785190\pi\) | |||||||
\(90\) | − 9.48683i | − 0.105409i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 50.3807 | 0.547617 | ||||||||
\(93\) | 52.1887 | 0.561169 | ||||||||
\(94\) | − 39.6865i | − 0.422197i | ||||||||
\(95\) | 55.0332 | 0.579297 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | − 74.2244i | − 0.765200i | −0.923914 | − | 0.382600i | \(-0.875029\pi\) | ||||
0.923914 | − | 0.382600i | \(-0.124971\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −59.9249 | −0.605302 | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | 87.5941i | 0.867268i | 0.901089 | + | 0.433634i | \(0.142769\pi\) | ||||
−0.901089 | + | 0.433634i | \(0.857231\pi\) | |||||||
\(102\) | −44.6842 | −0.438080 | ||||||||
\(103\) | − 139.041i | − 1.34991i | −0.737857 | − | 0.674957i | \(-0.764162\pi\) | ||||
0.737857 | − | 0.674957i | \(-0.235838\pi\) | |||||||
\(104\) | 9.89350i | 0.0951299i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 91.7469 | 0.865537 | ||||||||
\(107\) | 152.190 | 1.42234 | 0.711168 | − | 0.703023i | \(-0.248167\pi\) | ||||
0.711168 | + | 0.703023i | \(0.248167\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | 64.7554 | 0.594086 | 0.297043 | − | 0.954864i | \(-0.404000\pi\) | ||||
0.297043 | + | 0.954864i | \(0.404000\pi\) | |||||||
\(110\) | 63.1664i | 0.574240i | ||||||||
\(111\) | 81.0068i | 0.729791i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.25860 | 0.0288372 | 0.0144186 | − | 0.999896i | \(-0.495410\pi\) | ||||
0.0144186 | + | 0.999896i | \(0.495410\pi\) | |||||||
\(114\) | −60.2858 | −0.528823 | ||||||||
\(115\) | − 56.3274i | − 0.489803i | ||||||||
\(116\) | −106.245 | −0.915902 | ||||||||
\(117\) | 10.4936i | 0.0896893i | ||||||||
\(118\) | − 141.692i | − 1.20078i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.9545 | 0.0912871 | ||||||||
\(121\) | 278.000 | 2.29752 | ||||||||
\(122\) | 11.3476i | 0.0930131i | ||||||||
\(123\) | 54.6029 | 0.443926 | ||||||||
\(124\) | 60.2624i | 0.485987i | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −88.5772 | −0.697458 | −0.348729 | − | 0.937224i | \(-0.613387\pi\) | ||||
−0.348729 | + | 0.937224i | \(0.613387\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | − 111.564i | − 0.864839i | ||||||||
\(130\) | 11.0613 | 0.0850867 | ||||||||
\(131\) | 125.124i | 0.955146i | 0.878592 | + | 0.477573i | \(0.158483\pi\) | ||||
−0.878592 | + | 0.477573i | \(0.841517\pi\) | |||||||
\(132\) | − 69.1953i | − 0.524207i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −22.9998 | −0.171640 | ||||||||
\(135\) | 11.6190 | 0.0860663 | ||||||||
\(136\) | − 51.5968i | − 0.379388i | ||||||||
\(137\) | −38.9538 | −0.284334 | −0.142167 | − | 0.989843i | \(-0.545407\pi\) | ||||
−0.142167 | + | 0.989843i | \(0.545407\pi\) | |||||||
\(138\) | 61.7035i | 0.447127i | ||||||||
\(139\) | − 98.9454i | − 0.711837i | −0.934517 | − | 0.355919i | \(-0.884168\pi\) | ||||
0.934517 | − | 0.355919i | \(-0.115832\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 48.6058 | 0.344722 | ||||||||
\(142\) | 152.346 | 1.07286 | ||||||||
\(143\) | − 69.8701i | − 0.488602i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 118.785i | 0.819208i | ||||||||
\(146\) | − 73.0593i | − 0.500406i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −93.5385 | −0.632017 | ||||||||
\(149\) | −186.465 | −1.25144 | −0.625721 | − | 0.780047i | \(-0.715195\pi\) | ||||
−0.625721 | + | 0.780047i | \(0.715195\pi\) | |||||||
\(150\) | − 12.2474i | − 0.0816497i | ||||||||
\(151\) | 154.840 | 1.02543 | 0.512716 | − | 0.858558i | \(-0.328639\pi\) | ||||
0.512716 | + | 0.858558i | \(0.328639\pi\) | |||||||
\(152\) | − 69.6121i | − 0.457974i | ||||||||
\(153\) | − 54.7267i | − 0.357691i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 67.3754 | 0.434680 | ||||||||
\(156\) | −12.1170 | −0.0776732 | ||||||||
\(157\) | − 50.2037i | − 0.319769i | −0.987136 | − | 0.159885i | \(-0.948888\pi\) | ||||
0.987136 | − | 0.159885i | \(-0.0511122\pi\) | |||||||
\(158\) | 31.0780 | 0.196696 | ||||||||
\(159\) | 112.367i | 0.706708i | ||||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | −115.811 | −0.710496 | −0.355248 | − | 0.934772i | \(-0.615604\pi\) | ||||
−0.355248 | + | 0.934772i | \(0.615604\pi\) | |||||||
\(164\) | 63.0500i | 0.384452i | ||||||||
\(165\) | −77.3627 | −0.468865 | ||||||||
\(166\) | 0.590405i | 0.00355666i | ||||||||
\(167\) | 61.3210i | 0.367191i | 0.983002 | + | 0.183596i | \(0.0587737\pi\) | ||||
−0.983002 | + | 0.183596i | \(0.941226\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 156.765 | 0.927602 | ||||||||
\(170\) | −57.6870 | −0.339335 | ||||||||
\(171\) | − 73.8347i | − 0.431782i | ||||||||
\(172\) | 128.823 | 0.748972 | ||||||||
\(173\) | − 31.7016i | − 0.183246i | −0.995794 | − | 0.0916232i | \(-0.970794\pi\) | ||||
0.995794 | − | 0.0916232i | \(-0.0292055\pi\) | |||||||
\(174\) | − 130.123i | − 0.747831i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 79.8999 | 0.453977 | ||||||||
\(177\) | 173.537 | 0.980434 | ||||||||
\(178\) | − 157.275i | − 0.883569i | ||||||||
\(179\) | 131.894 | 0.736840 | 0.368420 | − | 0.929659i | \(-0.379899\pi\) | ||||
0.368420 | + | 0.929659i | \(0.379899\pi\) | |||||||
\(180\) | 13.4164i | 0.0745356i | ||||||||
\(181\) | − 55.1431i | − 0.304658i | −0.988330 | − | 0.152329i | \(-0.951323\pi\) | ||||
0.988330 | − | 0.152329i | \(-0.0486773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.8979 | −0.0759449 | ||||||||
\(184\) | −71.2491 | −0.387223 | ||||||||
\(185\) | 104.579i | 0.565293i | ||||||||
\(186\) | −73.8060 | −0.396807 | ||||||||
\(187\) | 364.388i | 1.94860i | ||||||||
\(188\) | 56.1252i | 0.298538i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −77.8287 | −0.409625 | ||||||||
\(191\) | 195.164 | 1.02180 | 0.510901 | − | 0.859639i | \(-0.329312\pi\) | ||||
0.510901 | + | 0.859639i | \(0.329312\pi\) | |||||||
\(192\) | − 13.8564i | − 0.0721688i | ||||||||
\(193\) | 348.760 | 1.80705 | 0.903523 | − | 0.428540i | \(-0.140972\pi\) | ||||
0.903523 | + | 0.428540i | \(0.140972\pi\) | |||||||
\(194\) | 104.969i | 0.541078i | ||||||||
\(195\) | 13.5472i | 0.0694730i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −56.3808 | −0.286197 | −0.143098 | − | 0.989708i | \(-0.545707\pi\) | ||||
−0.143098 | + | 0.989708i | \(0.545707\pi\) | |||||||
\(198\) | 84.7466 | 0.428013 | ||||||||
\(199\) | 171.308i | 0.860845i | 0.902628 | + | 0.430422i | \(0.141635\pi\) | ||||
−0.902628 | + | 0.430422i | \(0.858365\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | − 28.1689i | − 0.140144i | ||||||||
\(202\) | − 123.877i | − 0.613251i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 63.1930 | 0.309769 | ||||||||
\(205\) | 70.4921 | 0.343864 | ||||||||
\(206\) | 196.634i | 0.954533i | ||||||||
\(207\) | −75.5711 | −0.365078 | ||||||||
\(208\) | − 13.9915i | − 0.0672670i | ||||||||
\(209\) | 491.616i | 2.35223i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 162.038 | 0.767954 | 0.383977 | − | 0.923343i | \(-0.374554\pi\) | ||||
0.383977 | + | 0.923343i | \(0.374554\pi\) | |||||||
\(212\) | −129.750 | −0.612027 | ||||||||
\(213\) | 186.585i | 0.875984i | ||||||||
\(214\) | −215.229 | −1.00574 | ||||||||
\(215\) | − 144.029i | − 0.669901i | ||||||||
\(216\) | − 14.6969i | − 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −91.5779 | −0.420082 | ||||||||
\(219\) | 89.4789 | 0.408580 | ||||||||
\(220\) | − 89.3308i | − 0.406049i | ||||||||
\(221\) | 63.8092 | 0.288729 | ||||||||
\(222\) | − 114.561i | − 0.516040i | ||||||||
\(223\) | 365.329i | 1.63825i | 0.573618 | + | 0.819123i | \(0.305539\pi\) | ||||
−0.573618 | + | 0.819123i | \(0.694461\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | −4.60836 | −0.0203910 | ||||||||
\(227\) | 257.874i | 1.13601i | 0.823026 | + | 0.568004i | \(0.192284\pi\) | ||||
−0.823026 | + | 0.568004i | \(0.807716\pi\) | |||||||
\(228\) | 85.2570 | 0.373934 | ||||||||
\(229\) | 15.4308i | 0.0673832i | 0.999432 | + | 0.0336916i | \(0.0107264\pi\) | ||||
−0.999432 | + | 0.0336916i | \(0.989274\pi\) | |||||||
\(230\) | 79.6589i | 0.346343i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 150.253 | 0.647640 | ||||||||
\(233\) | −125.347 | −0.537969 | −0.268984 | − | 0.963145i | \(-0.586688\pi\) | ||||
−0.268984 | + | 0.963145i | \(0.586688\pi\) | |||||||
\(234\) | − 14.8403i | − 0.0634199i | ||||||||
\(235\) | 62.7499 | 0.267021 | ||||||||
\(236\) | 200.383i | 0.849081i | ||||||||
\(237\) | 38.0626i | 0.160602i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.62565 | −0.0151701 | −0.00758503 | − | 0.999971i | \(-0.502414\pi\) | ||||
−0.00758503 | + | 0.999971i | \(0.502414\pi\) | |||||||
\(240\) | −15.4919 | −0.0645497 | ||||||||
\(241\) | 96.6387i | 0.400990i | 0.979695 | + | 0.200495i | \(0.0642551\pi\) | ||||
−0.979695 | + | 0.200495i | \(0.935745\pi\) | |||||||
\(242\) | −393.151 | −1.62459 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | − 16.0479i | − 0.0657702i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −77.2202 | −0.313903 | ||||||||
\(247\) | 86.0884 | 0.348536 | ||||||||
\(248\) | − 85.2239i | − 0.343645i | ||||||||
\(249\) | −0.723095 | −0.00290400 | ||||||||
\(250\) | − 15.8114i | − 0.0632456i | ||||||||
\(251\) | 29.7311i | 0.118450i | 0.998245 | + | 0.0592252i | \(0.0188630\pi\) | ||||
−0.998245 | + | 0.0592252i | \(0.981137\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 503.177 | 1.98884 | ||||||||
\(254\) | 125.267 | 0.493178 | ||||||||
\(255\) | − 70.6519i | − 0.277066i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 441.623i | − 1.71838i | −0.511659 | − | 0.859189i | \(-0.670969\pi\) | ||||
0.511659 | − | 0.859189i | \(-0.329031\pi\) | |||||||
\(258\) | 157.776i | 0.611533i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −15.6430 | −0.0601654 | ||||||||
\(261\) | 159.367 | 0.610601 | ||||||||
\(262\) | − 176.952i | − 0.675390i | ||||||||
\(263\) | 343.047 | 1.30436 | 0.652180 | − | 0.758064i | \(-0.273855\pi\) | ||||
0.652180 | + | 0.758064i | \(0.273855\pi\) | |||||||
\(264\) | 97.8570i | 0.370670i | ||||||||
\(265\) | 145.065i | 0.547413i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 192.622 | 0.721431 | ||||||||
\(268\) | 32.5266 | 0.121368 | ||||||||
\(269\) | 463.351i | 1.72249i | 0.508186 | + | 0.861247i | \(0.330316\pi\) | ||||
−0.508186 | + | 0.861247i | \(0.669684\pi\) | |||||||
\(270\) | −16.4317 | −0.0608581 | ||||||||
\(271\) | − 244.581i | − 0.902515i | −0.892394 | − | 0.451257i | \(-0.850976\pi\) | ||||
0.892394 | − | 0.451257i | \(-0.149024\pi\) | |||||||
\(272\) | 72.9689i | 0.268268i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 55.0889 | 0.201054 | ||||||||
\(275\) | −99.8749 | −0.363181 | ||||||||
\(276\) | − 87.2620i | − 0.316167i | ||||||||
\(277\) | 141.018 | 0.509092 | 0.254546 | − | 0.967061i | \(-0.418074\pi\) | ||||
0.254546 | + | 0.967061i | \(0.418074\pi\) | |||||||
\(278\) | 139.930i | 0.503345i | ||||||||
\(279\) | − 90.3935i | − 0.323991i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 84.9953 | 0.302475 | 0.151237 | − | 0.988497i | \(-0.451674\pi\) | ||||
0.151237 | + | 0.988497i | \(0.451674\pi\) | |||||||
\(282\) | −68.7390 | −0.243755 | ||||||||
\(283\) | − 116.678i | − 0.412291i | −0.978521 | − | 0.206146i | \(-0.933908\pi\) | ||||
0.978521 | − | 0.206146i | \(-0.0660921\pi\) | |||||||
\(284\) | −215.449 | −0.758625 | ||||||||
\(285\) | − 95.3202i | − 0.334457i | ||||||||
\(286\) | 98.8112i | 0.345494i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −43.7791 | −0.151485 | ||||||||
\(290\) | − 167.987i | − 0.579267i | ||||||||
\(291\) | −128.560 | −0.441789 | ||||||||
\(292\) | 103.321i | 0.353840i | ||||||||
\(293\) | − 131.882i | − 0.450110i | −0.974346 | − | 0.225055i | \(-0.927744\pi\) | ||||
0.974346 | − | 0.225055i | \(-0.0722562\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 224.035 | 0.759441 | ||||||||
\(296\) | 132.283 | 0.446904 | ||||||||
\(297\) | 103.793i | 0.349471i | ||||||||
\(298\) | 263.701 | 0.884903 | ||||||||
\(299\) | − 88.1129i | − 0.294692i | ||||||||
\(300\) | 17.3205i | 0.0577350i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −218.977 | −0.725090 | ||||||||
\(303\) | 151.717 | 0.500717 | ||||||||
\(304\) | 98.4463i | 0.323837i | ||||||||
\(305\) | −17.9421 | −0.0588267 | ||||||||
\(306\) | 77.3952i | 0.252926i | ||||||||
\(307\) | − 429.871i | − 1.40023i | −0.714030 | − | 0.700115i | \(-0.753132\pi\) | ||||
0.714030 | − | 0.700115i | \(-0.246868\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −240.826 | −0.779373 | ||||||||
\(310\) | −95.2832 | −0.307365 | ||||||||
\(311\) | − 251.478i | − 0.808610i | −0.914624 | − | 0.404305i | \(-0.867513\pi\) | ||||
0.914624 | − | 0.404305i | \(-0.132487\pi\) | |||||||
\(312\) | 17.1361 | 0.0549232 | ||||||||
\(313\) | − 13.7033i | − 0.0437806i | −0.999760 | − | 0.0218903i | \(-0.993032\pi\) | ||||
0.999760 | − | 0.0218903i | \(-0.00696846\pi\) | |||||||
\(314\) | 70.9988i | 0.226111i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −43.9509 | −0.139085 | ||||||||
\(317\) | −32.9301 | −0.103881 | −0.0519403 | − | 0.998650i | \(-0.516541\pi\) | ||||
−0.0519403 | + | 0.998650i | \(0.516541\pi\) | |||||||
\(318\) | − 158.910i | − 0.499718i | ||||||||
\(319\) | −1061.12 | −3.32638 | ||||||||
\(320\) | − 17.8885i | − 0.0559017i | ||||||||
\(321\) | − 263.601i | − 0.821186i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −448.970 | −1.39000 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 17.4894i | 0.0538136i | ||||||||
\(326\) | 163.781 | 0.502397 | ||||||||
\(327\) | − 112.160i | − 0.342996i | ||||||||
\(328\) | − 89.1662i | − 0.271848i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 109.407 | 0.331538 | ||||||||
\(331\) | −417.881 | −1.26248 | −0.631240 | − | 0.775588i | \(-0.717454\pi\) | ||||
−0.631240 | + | 0.775588i | \(0.717454\pi\) | |||||||
\(332\) | − 0.834959i | − 0.00251494i | ||||||||
\(333\) | 140.308 | 0.421345 | ||||||||
\(334\) | − 86.7209i | − 0.259643i | ||||||||
\(335\) | − 36.3658i | − 0.108555i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −286.688 | −0.850705 | −0.425353 | − | 0.905028i | \(-0.639850\pi\) | ||||
−0.425353 | + | 0.905028i | \(0.639850\pi\) | |||||||
\(338\) | −221.699 | −0.655914 | ||||||||
\(339\) | − 5.64407i | − 0.0166492i | ||||||||
\(340\) | 81.5818 | 0.239946 | ||||||||
\(341\) | 601.870i | 1.76501i | ||||||||
\(342\) | 104.418i | 0.305316i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −182.184 | −0.529603 | ||||||||
\(345\) | −97.5619 | −0.282788 | ||||||||
\(346\) | 44.8329i | 0.129575i | ||||||||
\(347\) | 306.796 | 0.884137 | 0.442069 | − | 0.896981i | \(-0.354245\pi\) | ||||
0.442069 | + | 0.896981i | \(0.354245\pi\) | |||||||
\(348\) | 184.021i | 0.528796i | ||||||||
\(349\) | 340.162i | 0.974676i | 0.873214 | + | 0.487338i | \(0.162032\pi\) | ||||
−0.873214 | + | 0.487338i | \(0.837968\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.1755 | 0.0517821 | ||||||||
\(352\) | −112.996 | −0.321010 | ||||||||
\(353\) | − 375.002i | − 1.06233i | −0.847269 | − | 0.531165i | \(-0.821755\pi\) | ||||
0.847269 | − | 0.531165i | \(-0.178245\pi\) | |||||||
\(354\) | −245.418 | −0.693272 | ||||||||
\(355\) | 240.880i | 0.678534i | ||||||||
\(356\) | 222.421i | 0.624778i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −186.527 | −0.521025 | ||||||||
\(359\) | −329.501 | −0.917829 | −0.458915 | − | 0.888480i | \(-0.651762\pi\) | ||||
−0.458915 | + | 0.888480i | \(0.651762\pi\) | |||||||
\(360\) | − 18.9737i | − 0.0527046i | ||||||||
\(361\) | −244.730 | −0.677922 | ||||||||
\(362\) | 77.9841i | 0.215426i | ||||||||
\(363\) | − 481.509i | − 1.32647i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 115.517 | 0.316484 | ||||||||
\(366\) | 19.6546 | 0.0537012 | ||||||||
\(367\) | 27.1543i | 0.0739900i | 0.999315 | + | 0.0369950i | \(0.0117786\pi\) | ||||
−0.999315 | + | 0.0369950i | \(0.988221\pi\) | |||||||
\(368\) | 100.761 | 0.273808 | ||||||||
\(369\) | − 94.5751i | − 0.256301i | ||||||||
\(370\) | − 147.897i | − 0.399723i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 104.377 | 0.280585 | ||||||||
\(373\) | 127.498 | 0.341817 | 0.170908 | − | 0.985287i | \(-0.445330\pi\) | ||||
0.170908 | + | 0.985287i | \(0.445330\pi\) | |||||||
\(374\) | − 515.323i | − 1.37787i | ||||||||
\(375\) | 19.3649 | 0.0516398 | ||||||||
\(376\) | − 79.3730i | − 0.211098i | ||||||||
\(377\) | 185.816i | 0.492880i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 319.795 | 0.843785 | 0.421893 | − | 0.906646i | \(-0.361366\pi\) | ||||
0.421893 | + | 0.906646i | \(0.361366\pi\) | |||||||
\(380\) | 110.066 | 0.289648 | ||||||||
\(381\) | 153.420i | 0.402678i | ||||||||
\(382\) | −276.004 | −0.722524 | ||||||||
\(383\) | − 408.942i | − 1.06773i | −0.845568 | − | 0.533867i | \(-0.820738\pi\) | ||||
0.845568 | − | 0.533867i | \(-0.179262\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −493.221 | −1.27777 | ||||||||
\(387\) | −193.235 | −0.499315 | ||||||||
\(388\) | − 148.449i | − 0.382600i | ||||||||
\(389\) | 387.153 | 0.995252 | 0.497626 | − | 0.867392i | \(-0.334205\pi\) | ||||
0.497626 | + | 0.867392i | \(0.334205\pi\) | |||||||
\(390\) | − 19.1587i | − 0.0491248i | ||||||||
\(391\) | 459.529i | 1.17526i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 216.721 | 0.551454 | ||||||||
\(394\) | 79.7345 | 0.202372 | ||||||||
\(395\) | 49.1386i | 0.124402i | ||||||||
\(396\) | −119.850 | −0.302651 | ||||||||
\(397\) | − 30.1112i | − 0.0758468i | −0.999281 | − | 0.0379234i | \(-0.987926\pi\) | ||||
0.999281 | − | 0.0379234i | \(-0.0120743\pi\) | |||||||
\(398\) | − 242.266i | − 0.608709i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 136.770 | 0.341073 | 0.170537 | − | 0.985351i | \(-0.445450\pi\) | ||||
0.170537 | + | 0.985351i | \(0.445450\pi\) | |||||||
\(402\) | 39.8368i | 0.0990965i | ||||||||
\(403\) | 105.395 | 0.261527 | ||||||||
\(404\) | 175.188i | 0.433634i | ||||||||
\(405\) | − 20.1246i | − 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −934.215 | −2.29537 | ||||||||
\(408\) | −89.3683 | −0.219040 | ||||||||
\(409\) | − 492.870i | − 1.20506i | −0.798096 | − | 0.602531i | \(-0.794159\pi\) | ||||
0.798096 | − | 0.602531i | \(-0.205841\pi\) | |||||||
\(410\) | −99.6909 | −0.243148 | ||||||||
\(411\) | 67.4699i | 0.164160i | ||||||||
\(412\) | − 278.082i | − 0.674957i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 106.874 | 0.258149 | ||||||||
\(415\) | −0.933512 | −0.00224943 | ||||||||
\(416\) | 19.7870i | 0.0475649i | ||||||||
\(417\) | −171.378 | −0.410979 | ||||||||
\(418\) | − 695.250i | − 1.66328i | ||||||||
\(419\) | 311.640i | 0.743771i | 0.928279 | + | 0.371885i | \(0.121289\pi\) | ||||
−0.928279 | + | 0.371885i | \(0.878711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −539.935 | −1.28250 | −0.641252 | − | 0.767330i | \(-0.721585\pi\) | ||||
−0.641252 | + | 0.767330i | \(0.721585\pi\) | |||||||
\(422\) | −229.157 | −0.543025 | ||||||||
\(423\) | − 84.1878i | − 0.199025i | ||||||||
\(424\) | 183.494 | 0.432768 | ||||||||
\(425\) | − 91.2112i | − 0.214615i | ||||||||
\(426\) | − 263.871i | − 0.619414i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 304.380 | 0.711168 | ||||||||
\(429\) | −121.019 | −0.282095 | ||||||||
\(430\) | 203.687i | 0.473692i | ||||||||
\(431\) | −628.041 | −1.45717 | −0.728586 | − | 0.684954i | \(-0.759822\pi\) | ||||
−0.728586 | + | 0.684954i | \(0.759822\pi\) | |||||||
\(432\) | 20.7846i | 0.0481125i | ||||||||
\(433\) | − 706.789i | − 1.63231i | −0.577836 | − | 0.816153i | \(-0.696103\pi\) | ||||
0.577836 | − | 0.816153i | \(-0.303897\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 205.742 | 0.472970 | ||||||||
\(436\) | 129.511 | 0.297043 | ||||||||
\(437\) | 619.975i | 1.41871i | ||||||||
\(438\) | −126.542 | −0.288909 | ||||||||
\(439\) | − 651.773i | − 1.48468i | −0.670025 | − | 0.742338i | \(-0.733717\pi\) | ||||
0.670025 | − | 0.742338i | \(-0.266283\pi\) | |||||||
\(440\) | 126.333i | 0.287120i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −90.2398 | −0.204162 | ||||||||
\(443\) | −23.6258 | −0.0533314 | −0.0266657 | − | 0.999644i | \(-0.508489\pi\) | ||||
−0.0266657 | + | 0.999644i | \(0.508489\pi\) | |||||||
\(444\) | 162.014i | 0.364895i | ||||||||
\(445\) | 248.674 | 0.558818 | ||||||||
\(446\) | − 516.653i | − 1.15841i | ||||||||
\(447\) | 322.967i | 0.722520i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −55.1499 | −0.122828 | −0.0614141 | − | 0.998112i | \(-0.519561\pi\) | ||||
−0.0614141 | + | 0.998112i | \(0.519561\pi\) | |||||||
\(450\) | −21.2132 | −0.0471405 | ||||||||
\(451\) | 629.712i | 1.39626i | ||||||||
\(452\) | 6.51721 | 0.0144186 | ||||||||
\(453\) | − 268.191i | − 0.592034i | ||||||||
\(454\) | − 364.689i | − 0.803279i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −120.572 | −0.264411 | ||||||||
\(457\) | 350.773 | 0.767556 | 0.383778 | − | 0.923425i | \(-0.374623\pi\) | ||||
0.383778 | + | 0.923425i | \(0.374623\pi\) | |||||||
\(458\) | − 21.8224i | − 0.0476471i | ||||||||
\(459\) | −94.7894 | −0.206513 | ||||||||
\(460\) | − 112.655i | − 0.244902i | ||||||||
\(461\) | 471.598i | 1.02299i | 0.859287 | + | 0.511494i | \(0.170908\pi\) | ||||
−0.859287 | + | 0.511494i | \(0.829092\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 387.112 | 0.836094 | 0.418047 | − | 0.908425i | \(-0.362715\pi\) | ||||
0.418047 | + | 0.908425i | \(0.362715\pi\) | |||||||
\(464\) | −212.489 | −0.457951 | ||||||||
\(465\) | − 116.698i | − 0.250963i | ||||||||
\(466\) | 177.267 | 0.380402 | ||||||||
\(467\) | 293.346i | 0.628150i | 0.949398 | + | 0.314075i | \(0.101694\pi\) | ||||
−0.949398 | + | 0.314075i | \(0.898306\pi\) | |||||||
\(468\) | 20.9873i | 0.0448446i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −88.7417 | −0.188812 | ||||||||
\(471\) | −86.9554 | −0.184619 | ||||||||
\(472\) | − 283.384i | − 0.600391i | ||||||||
\(473\) | 1286.62 | 2.72013 | ||||||||
\(474\) | − 53.8287i | − 0.113563i | ||||||||
\(475\) | − 123.058i | − 0.259069i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 194.625 | 0.408018 | ||||||||
\(478\) | 5.12744 | 0.0107269 | ||||||||
\(479\) | − 763.032i | − 1.59297i | −0.604660 | − | 0.796484i | \(-0.706691\pi\) | ||||
0.604660 | − | 0.796484i | \(-0.293309\pi\) | |||||||
\(480\) | 21.9089 | 0.0456435 | ||||||||
\(481\) | 163.593i | 0.340111i | ||||||||
\(482\) | − 136.668i | − 0.283543i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 555.999 | 1.14876 | ||||||||
\(485\) | −165.971 | −0.342208 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | −223.889 | −0.459730 | −0.229865 | − | 0.973223i | \(-0.573828\pi\) | ||||
−0.229865 | + | 0.973223i | \(0.573828\pi\) | |||||||
\(488\) | 22.6952i | 0.0465066i | ||||||||
\(489\) | 200.590i | 0.410205i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −837.694 | −1.70610 | −0.853049 | − | 0.521830i | \(-0.825249\pi\) | ||||
−0.853049 | + | 0.521830i | \(0.825249\pi\) | |||||||
\(492\) | 109.206 | 0.221963 | ||||||||
\(493\) | − 969.070i | − 1.96566i | ||||||||
\(494\) | −121.747 | −0.246452 | ||||||||
\(495\) | 133.996i | 0.270699i | ||||||||
\(496\) | 120.525i | 0.242993i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.02261 | 0.00205344 | ||||||||
\(499\) | 174.647 | 0.349993 | 0.174997 | − | 0.984569i | \(-0.444009\pi\) | ||||
0.174997 | + | 0.984569i | \(0.444009\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | 106.211 | 0.211998 | ||||||||
\(502\) | − 42.0461i | − 0.0837571i | ||||||||
\(503\) | 747.962i | 1.48700i | 0.668734 | + | 0.743501i | \(0.266836\pi\) | ||||
−0.668734 | + | 0.743501i | \(0.733164\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 195.866 | 0.387854 | ||||||||
\(506\) | −711.600 | −1.40632 | ||||||||
\(507\) | − 271.525i | − 0.535552i | ||||||||
\(508\) | −177.154 | −0.348729 | ||||||||
\(509\) | 234.429i | 0.460567i | 0.973124 | + | 0.230284i | \(0.0739654\pi\) | ||||
−0.973124 | + | 0.230284i | \(0.926035\pi\) | |||||||
\(510\) | 99.9168i | 0.195915i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −127.886 | −0.249290 | ||||||||
\(514\) | 624.549i | 1.21508i | ||||||||
\(515\) | −310.905 | −0.603700 | ||||||||
\(516\) | − 223.128i | − 0.432419i | ||||||||
\(517\) | 560.549i | 1.08423i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −54.9088 | −0.105797 | ||||||||
\(520\) | 22.1225 | 0.0425434 | ||||||||
\(521\) | 214.853i | 0.412386i | 0.978511 | + | 0.206193i | \(0.0661075\pi\) | ||||
−0.978511 | + | 0.206193i | \(0.933893\pi\) | |||||||
\(522\) | −225.379 | −0.431760 | ||||||||
\(523\) | − 925.040i | − 1.76872i | −0.466806 | − | 0.884360i | \(-0.654595\pi\) | ||||
0.466806 | − | 0.884360i | \(-0.345405\pi\) | |||||||
\(524\) | 250.248i | 0.477573i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −485.141 | −0.922321 | ||||||||
\(527\) | −549.660 | −1.04300 | ||||||||
\(528\) | − 138.391i | − 0.262104i | ||||||||
\(529\) | 105.555 | 0.199536 | ||||||||
\(530\) | − 205.152i | − 0.387080i | ||||||||
\(531\) | − 300.575i | − 0.566054i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 110.271 | 0.206887 | ||||||||
\(534\) | −272.409 | −0.510129 | ||||||||
\(535\) | − 340.307i | − 0.636088i | ||||||||
\(536\) | −45.9996 | −0.0858201 | ||||||||
\(537\) | − 228.448i | − 0.425415i | ||||||||
\(538\) | − 655.277i | − 1.21799i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 23.2379 | 0.0430331 | ||||||||
\(541\) | −114.312 | −0.211298 | −0.105649 | − | 0.994404i | \(-0.533692\pi\) | ||||
−0.105649 | + | 0.994404i | \(0.533692\pi\) | |||||||
\(542\) | 345.890i | 0.638174i | ||||||||
\(543\) | −95.5106 | −0.175894 | ||||||||
\(544\) | − 103.194i | − 0.189694i | ||||||||
\(545\) | − 144.797i | − 0.265683i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −57.7698 | −0.105612 | −0.0528060 | − | 0.998605i | \(-0.516817\pi\) | ||||
−0.0528060 | + | 0.998605i | \(0.516817\pi\) | |||||||
\(548\) | −77.9075 | −0.142167 | ||||||||
\(549\) | 24.0719i | 0.0438468i | ||||||||
\(550\) | 141.244 | 0.256808 | ||||||||
\(551\) | − 1307.42i | − 2.37282i | ||||||||
\(552\) | 123.407i | 0.223564i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −199.430 | −0.359982 | ||||||||
\(555\) | 181.137 | 0.326372 | ||||||||
\(556\) | − 197.891i | − 0.355919i | ||||||||
\(557\) | −406.152 | −0.729178 | −0.364589 | − | 0.931169i | \(-0.618790\pi\) | ||||
−0.364589 | + | 0.931169i | \(0.618790\pi\) | |||||||
\(558\) | 127.836i | 0.229096i | ||||||||
\(559\) | − 225.304i | − 0.403049i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 631.139 | 1.12502 | ||||||||
\(562\) | −120.202 | −0.213882 | ||||||||
\(563\) | − 428.292i | − 0.760731i | −0.924836 | − | 0.380366i | \(-0.875798\pi\) | ||||
0.924836 | − | 0.380366i | \(-0.124202\pi\) | |||||||
\(564\) | 97.2117 | 0.172361 | ||||||||
\(565\) | − 7.28646i | − 0.0128964i | ||||||||
\(566\) | 165.008i | 0.291534i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 304.691 | 0.536429 | ||||||||
\(569\) | −915.793 | −1.60948 | −0.804739 | − | 0.593628i | \(-0.797695\pi\) | ||||
−0.804739 | + | 0.593628i | \(0.797695\pi\) | |||||||
\(570\) | 134.803i | 0.236497i | ||||||||
\(571\) | −713.893 | −1.25025 | −0.625125 | − | 0.780524i | \(-0.714952\pi\) | ||||
−0.625125 | + | 0.780524i | \(0.714952\pi\) | |||||||
\(572\) | − 139.740i | − 0.244301i | ||||||||
\(573\) | − 338.035i | − 0.589938i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −125.952 | −0.219047 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | − 87.5946i | − 0.151810i | −0.997115 | − | 0.0759052i | \(-0.975815\pi\) | ||||
0.997115 | − | 0.0759052i | \(-0.0241846\pi\) | |||||||
\(578\) | 61.9130 | 0.107116 | ||||||||
\(579\) | − 604.070i | − 1.04330i | ||||||||
\(580\) | 237.570i | 0.409604i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 181.812 | 0.312392 | ||||||||
\(583\) | −1295.87 | −2.22277 | ||||||||
\(584\) | − 146.119i | − 0.250203i | ||||||||
\(585\) | 23.4645 | 0.0401103 | ||||||||
\(586\) | 186.510i | 0.318276i | ||||||||
\(587\) | 169.908i | 0.289452i | 0.989472 | + | 0.144726i | \(0.0462300\pi\) | ||||
−0.989472 | + | 0.144726i | \(0.953770\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −741.576 | −1.25904 | ||||||||
\(590\) | −316.833 | −0.537006 | ||||||||
\(591\) | 97.6544i | 0.165236i | ||||||||
\(592\) | −187.077 | −0.316009 | ||||||||
\(593\) | − 200.253i | − 0.337694i | −0.985642 | − | 0.168847i | \(-0.945996\pi\) | ||||
0.985642 | − | 0.168847i | \(-0.0540044\pi\) | |||||||
\(594\) | − 146.785i | − 0.247114i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −372.930 | −0.625721 | ||||||||
\(597\) | 296.714 | 0.497009 | ||||||||
\(598\) | 124.611i | 0.208379i | ||||||||
\(599\) | −700.402 | −1.16929 | −0.584643 | − | 0.811291i | \(-0.698765\pi\) | ||||
−0.584643 | + | 0.811291i | \(0.698765\pi\) | |||||||
\(600\) | − 24.4949i | − 0.0408248i | ||||||||
\(601\) | − 1039.21i | − 1.72914i | −0.502515 | − | 0.864569i | \(-0.667592\pi\) | ||||
0.502515 | − | 0.864569i | \(-0.332408\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −48.7899 | −0.0809119 | ||||||||
\(604\) | 309.681 | 0.512716 | ||||||||
\(605\) | − 621.626i | − 1.02748i | ||||||||
\(606\) | −214.561 | −0.354061 | ||||||||
\(607\) | − 61.1592i | − 0.100757i | −0.998730 | − | 0.0503783i | \(-0.983957\pi\) | ||||
0.998730 | − | 0.0503783i | \(-0.0160427\pi\) | |||||||
\(608\) | − 139.224i | − 0.228987i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.3740 | 0.0415967 | ||||||||
\(611\) | 98.1596 | 0.160654 | ||||||||
\(612\) | − 109.453i | − 0.178845i | ||||||||
\(613\) | −522.719 | −0.852722 | −0.426361 | − | 0.904553i | \(-0.640205\pi\) | ||||
−0.426361 | + | 0.904553i | \(0.640205\pi\) | |||||||
\(614\) | 607.929i | 0.990112i | ||||||||
\(615\) | − 122.096i | − 0.198530i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −608.200 | −0.985738 | −0.492869 | − | 0.870104i | \(-0.664052\pi\) | ||||
−0.492869 | + | 0.870104i | \(0.664052\pi\) | |||||||
\(618\) | 340.580 | 0.551100 | ||||||||
\(619\) | 1042.31i | 1.68387i | 0.539580 | + | 0.841934i | \(0.318583\pi\) | ||||
−0.539580 | + | 0.841934i | \(0.681417\pi\) | |||||||
\(620\) | 134.751 | 0.217340 | ||||||||
\(621\) | 130.893i | 0.210778i | ||||||||
\(622\) | 355.643i | 0.571774i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −24.2340 | −0.0388366 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 19.3794i | 0.0309576i | ||||||||
\(627\) | 851.503 | 1.35806 | ||||||||
\(628\) | − 100.407i | − 0.159885i | ||||||||
\(629\) | − 853.176i | − 1.35640i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −235.274 | −0.372859 | −0.186430 | − | 0.982468i | \(-0.559692\pi\) | ||||
−0.186430 | + | 0.982468i | \(0.559692\pi\) | |||||||
\(632\) | 62.1560 | 0.0983481 | ||||||||
\(633\) | − 280.658i | − 0.443378i | ||||||||
\(634\) | 46.5703 | 0.0734547 | ||||||||
\(635\) | 198.065i | 0.311913i | ||||||||
\(636\) | 224.733i | 0.353354i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1500.65 | 2.35211 | ||||||||
\(639\) | 323.174 | 0.505750 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | −116.980 | −0.182496 | −0.0912481 | − | 0.995828i | \(-0.529086\pi\) | ||||
−0.0912481 | + | 0.995828i | \(0.529086\pi\) | |||||||
\(642\) | 372.788i | 0.580666i | ||||||||
\(643\) | 874.209i | 1.35958i | 0.733408 | + | 0.679789i | \(0.237929\pi\) | ||||
−0.733408 | + | 0.679789i | \(0.762071\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −249.465 | −0.386768 | ||||||||
\(646\) | 634.940 | 0.982879 | ||||||||
\(647\) | − 11.6838i | − 0.0180584i | −0.999959 | − | 0.00902920i | \(-0.997126\pi\) | ||||
0.999959 | − | 0.00902920i | \(-0.00287412\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | 2001.32i | 3.08370i | ||||||||
\(650\) | − 24.7338i | − 0.0380519i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −231.622 | −0.355248 | ||||||||
\(653\) | 638.135 | 0.977236 | 0.488618 | − | 0.872498i | \(-0.337501\pi\) | ||||
0.488618 | + | 0.872498i | \(0.337501\pi\) | |||||||
\(654\) | 158.618i | 0.242535i | ||||||||
\(655\) | 279.786 | 0.427154 | ||||||||
\(656\) | 126.100i | 0.192226i | ||||||||
\(657\) | − 154.982i | − 0.235894i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 870.363 | 1.32073 | 0.660367 | − | 0.750943i | \(-0.270401\pi\) | ||||
0.660367 | + | 0.750943i | \(0.270401\pi\) | |||||||
\(660\) | −154.725 | −0.234433 | ||||||||
\(661\) | 482.170i | 0.729455i | 0.931114 | + | 0.364728i | \(0.118838\pi\) | ||||
−0.931114 | + | 0.364728i | \(0.881162\pi\) | |||||||
\(662\) | 590.973 | 0.892708 | ||||||||
\(663\) | − 110.521i | − 0.166698i | ||||||||
\(664\) | 1.18081i | 0.00177833i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −198.425 | −0.297936 | ||||||||
\(667\) | −1338.17 | −2.00625 | ||||||||
\(668\) | 122.642i | 0.183596i | ||||||||
\(669\) | 632.768 | 0.945842 | ||||||||
\(670\) | 51.4291i | 0.0767598i | ||||||||
\(671\) | − 160.279i | − 0.238865i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −399.323 | −0.593347 | −0.296674 | − | 0.954979i | \(-0.595877\pi\) | ||||
−0.296674 | + | 0.954979i | \(0.595877\pi\) | |||||||
\(674\) | 405.438 | 0.601539 | ||||||||
\(675\) | − 25.9808i | − 0.0384900i | ||||||||
\(676\) | 313.530 | 0.463801 | ||||||||
\(677\) | − 141.341i | − 0.208776i | −0.994537 | − | 0.104388i | \(-0.966712\pi\) | ||||
0.994537 | − | 0.104388i | \(-0.0332884\pi\) | |||||||
\(678\) | 7.98191i | 0.0117727i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −115.374 | −0.169668 | ||||||||
\(681\) | 446.650 | 0.655874 | ||||||||
\(682\) | − 851.172i | − 1.24805i | ||||||||
\(683\) | 988.175 | 1.44682 | 0.723408 | − | 0.690421i | \(-0.242575\pi\) | ||||
0.723408 | + | 0.690421i | \(0.242575\pi\) | |||||||
\(684\) | − 147.669i | − 0.215891i | ||||||||
\(685\) | 87.1032i | 0.127158i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.7268 | 0.0389037 | ||||||||
\(688\) | 257.646 | 0.374486 | ||||||||
\(689\) | 226.925i | 0.329353i | ||||||||
\(690\) | 137.973 | 0.199961 | ||||||||
\(691\) | − 350.831i | − 0.507715i | −0.967242 | − | 0.253857i | \(-0.918301\pi\) | ||||
0.967242 | − | 0.253857i | \(-0.0816994\pi\) | |||||||
\(692\) | − 63.4033i | − 0.0916232i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −433.875 | −0.625180 | ||||||||
\(695\) | −221.249 | −0.318343 | ||||||||
\(696\) | − 260.245i | − 0.373915i | ||||||||
\(697\) | −575.087 | −0.825089 | ||||||||
\(698\) | − 481.061i | − 0.689200i | ||||||||
\(699\) | 217.107i | 0.310597i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 307.500 | 0.438659 | 0.219330 | − | 0.975651i | \(-0.429613\pi\) | ||||
0.219330 | + | 0.975651i | \(0.429613\pi\) | |||||||
\(702\) | −25.7041 | −0.0366155 | ||||||||
\(703\) | − 1151.07i | − 1.63736i | ||||||||
\(704\) | 159.800 | 0.226988 | ||||||||
\(705\) | − 108.686i | − 0.154164i | ||||||||
\(706\) | 530.333i | 0.751180i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 347.074 | 0.490217 | ||||||||
\(709\) | −98.1423 | −0.138424 | −0.0692118 | − | 0.997602i | \(-0.522048\pi\) | ||||
−0.0692118 | + | 0.997602i | \(0.522048\pi\) | |||||||
\(710\) | − 340.655i | − 0.479796i | ||||||||
\(711\) | 65.9264 | 0.0927235 | ||||||||
\(712\) | − 314.551i | − 0.441784i | ||||||||
\(713\) | 759.016i | 1.06454i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −156.234 | −0.218510 | ||||||||
\(716\) | 263.789 | 0.368420 | ||||||||
\(717\) | 6.27980i | 0.00875844i | ||||||||
\(718\) | 465.984 | 0.649003 | ||||||||
\(719\) | − 707.069i | − 0.983406i | −0.870763 | − | 0.491703i | \(-0.836375\pi\) | ||||
0.870763 | − | 0.491703i | \(-0.163625\pi\) | |||||||
\(720\) | 26.8328i | 0.0372678i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 346.100 | 0.479363 | ||||||||
\(723\) | 167.383 | 0.231512 | ||||||||
\(724\) | − 110.286i | − 0.152329i | ||||||||
\(725\) | 265.612 | 0.366361 | ||||||||
\(726\) | 680.957i | 0.937957i | ||||||||
\(727\) | 1353.85i | 1.86225i | 0.364705 | + | 0.931123i | \(0.381170\pi\) | ||||
−0.364705 | + | 0.931123i | \(0.618830\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −163.365 | −0.223788 | ||||||||
\(731\) | 1175.01i | 1.60740i | ||||||||
\(732\) | −27.7958 | −0.0379725 | ||||||||
\(733\) | 553.033i | 0.754479i | 0.926116 | + | 0.377240i | \(0.123127\pi\) | ||||
−0.926116 | + | 0.377240i | \(0.876873\pi\) | |||||||
\(734\) | − 38.4020i | − 0.0523188i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −142.498 | −0.193612 | ||||||||
\(737\) | 324.859 | 0.440786 | ||||||||
\(738\) | 133.749i | 0.181232i | ||||||||
\(739\) | 933.479 | 1.26316 | 0.631582 | − | 0.775309i | \(-0.282406\pi\) | ||||
0.631582 | + | 0.775309i | \(0.282406\pi\) | |||||||
\(740\) | 209.159i | 0.282647i | ||||||||
\(741\) | − 149.110i | − 0.201227i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 554.921 | 0.746865 | 0.373432 | − | 0.927657i | \(-0.378181\pi\) | ||||
0.373432 | + | 0.927657i | \(0.378181\pi\) | |||||||
\(744\) | −147.612 | −0.198403 | ||||||||
\(745\) | 416.948i | 0.559662i | ||||||||
\(746\) | −180.309 | −0.241701 | ||||||||
\(747\) | 1.25244i | 0.00167662i | ||||||||
\(748\) | 728.776i | 0.974300i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −27.3861 | −0.0365148 | ||||||||
\(751\) | 727.948 | 0.969305 | 0.484652 | − | 0.874707i | \(-0.338946\pi\) | ||||
0.484652 | + | 0.874707i | \(0.338946\pi\) | |||||||
\(752\) | 112.250i | 0.149269i | ||||||||
\(753\) | 51.4957 | 0.0683874 | ||||||||
\(754\) | − 262.783i | − 0.348518i | ||||||||
\(755\) | − 346.233i | − 0.458587i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 667.167 | 0.881330 | 0.440665 | − | 0.897672i | \(-0.354743\pi\) | ||||
0.440665 | + | 0.897672i | \(0.354743\pi\) | |||||||
\(758\) | −452.258 | −0.596646 | ||||||||
\(759\) | − 871.528i | − 1.14826i | ||||||||
\(760\) | −155.657 | −0.204812 | ||||||||
\(761\) | 727.532i | 0.956021i | 0.878354 | + | 0.478010i | \(0.158642\pi\) | ||||
−0.878354 | + | 0.478010i | \(0.841358\pi\) | |||||||
\(762\) | − 216.969i | − 0.284736i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 390.329 | 0.510901 | ||||||||
\(765\) | −122.373 | −0.159964 | ||||||||
\(766\) | 578.332i | 0.755003i | ||||||||
\(767\) | 350.458 | 0.456921 | ||||||||
\(768\) | − 27.7128i | − 0.0360844i | ||||||||
\(769\) | − 1374.28i | − 1.78709i | −0.448969 | − | 0.893547i | \(-0.648209\pi\) | ||||
0.448969 | − | 0.893547i | \(-0.351791\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −764.913 | −0.992106 | ||||||||
\(772\) | 697.520 | 0.903523 | ||||||||
\(773\) | 92.6712i | 0.119885i | 0.998202 | + | 0.0599425i | \(0.0190917\pi\) | ||||
−0.998202 | + | 0.0599425i | \(0.980908\pi\) | |||||||
\(774\) | 273.275 | 0.353069 | ||||||||
\(775\) | − 150.656i | − 0.194395i | ||||||||
\(776\) | 209.938i | 0.270539i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −547.517 | −0.703749 | ||||||||
\(779\) | −775.881 | −0.995996 | ||||||||
\(780\) | 27.0945i | 0.0347365i | ||||||||
\(781\) | −2151.80 | −2.75518 | ||||||||
\(782\) | − 649.872i | − 0.831038i | ||||||||
\(783\) | − 276.032i | − 0.352531i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −112.259 | −0.143005 | ||||||||
\(786\) | −306.490 | −0.389937 | ||||||||
\(787\) | 836.226i | 1.06255i | 0.847200 | + | 0.531275i | \(0.178287\pi\) | ||||
−0.847200 | + | 0.531275i | \(0.821713\pi\) | |||||||
\(788\) | −112.762 | −0.143098 | ||||||||
\(789\) | − 594.174i | − 0.753072i | ||||||||
\(790\) | − 69.4925i | − 0.0879652i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 169.493 | 0.214007 | ||||||||
\(793\) | −28.0669 | −0.0353933 | ||||||||
\(794\) | 42.5836i | 0.0536318i | ||||||||
\(795\) | 251.259 | 0.316049 | ||||||||
\(796\) | 342.616i | 0.430422i | ||||||||
\(797\) | 130.279i | 0.163462i | 0.996654 | + | 0.0817310i | \(0.0260448\pi\) | ||||
−0.996654 | + | 0.0817310i | \(0.973955\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −511.924 | −0.640706 | ||||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | − 333.631i | − 0.416518i | ||||||||
\(802\) | −193.423 | −0.241175 | ||||||||
\(803\) | 1031.92i | 1.28508i | ||||||||
\(804\) | − 56.3377i | − 0.0700718i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −149.052 | −0.184927 | ||||||||
\(807\) | 802.548 | 0.994483 | ||||||||
\(808\) | − 247.753i | − 0.306626i | ||||||||
\(809\) | 621.564 | 0.768311 | 0.384156 | − | 0.923268i | \(-0.374493\pi\) | ||||
0.384156 | + | 0.923268i | \(0.374493\pi\) | |||||||
\(810\) | 28.4605i | 0.0351364i | ||||||||
\(811\) | − 445.846i | − 0.549748i | −0.961480 | − | 0.274874i | \(-0.911364\pi\) | ||||
0.961480 | − | 0.274874i | \(-0.0886361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −423.627 | −0.521067 | ||||||||
\(814\) | 1321.18 | 1.62307 | ||||||||
\(815\) | 258.961i | 0.317743i | ||||||||
\(816\) | 126.386 | 0.154885 | ||||||||
\(817\) | 1585.27i | 1.94036i | ||||||||
\(818\) | 697.023i | 0.852107i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 140.984 | 0.171932 | ||||||||
\(821\) | 1257.24 | 1.53136 | 0.765678 | − | 0.643224i | \(-0.222403\pi\) | ||||
0.765678 | + | 0.643224i | \(0.222403\pi\) | |||||||
\(822\) | − 95.4168i | − 0.116079i | ||||||||
\(823\) | 120.342 | 0.146223 | 0.0731117 | − | 0.997324i | \(-0.476707\pi\) | ||||
0.0731117 | + | 0.997324i | \(0.476707\pi\) | |||||||
\(824\) | 393.268i | 0.477267i | ||||||||
\(825\) | 172.988i | 0.209683i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 151.053 | 0.182652 | 0.0913258 | − | 0.995821i | \(-0.470890\pi\) | ||||
0.0913258 | + | 0.995821i | \(0.470890\pi\) | |||||||
\(828\) | −151.142 | −0.182539 | ||||||||
\(829\) | 251.308i | 0.303147i | 0.988446 | + | 0.151573i | \(0.0484340\pi\) | ||||
−0.988446 | + | 0.151573i | \(0.951566\pi\) | |||||||
\(830\) | 1.32019 | 0.00159058 | ||||||||
\(831\) | − 244.251i | − 0.293924i | ||||||||
\(832\) | − 27.9831i | − 0.0336335i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 242.366 | 0.290606 | ||||||||
\(835\) | 137.118 | 0.164213 | ||||||||
\(836\) | 983.231i | 1.17611i | ||||||||
\(837\) | −156.566 | −0.187056 | ||||||||
\(838\) | − 440.725i | − 0.525925i | ||||||||
\(839\) | 499.592i | 0.595461i | 0.954650 | + | 0.297730i | \(0.0962297\pi\) | ||||
−0.954650 | + | 0.297730i | \(0.903770\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1980.98 | 2.35550 | ||||||||
\(842\) | 763.583 | 0.906868 | ||||||||
\(843\) | − 147.216i | − 0.174634i | ||||||||
\(844\) | 324.076 | 0.383977 | ||||||||
\(845\) | − 350.537i | − 0.414836i | ||||||||
\(846\) | 119.059i | 0.140732i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −259.499 | −0.306013 | ||||||||
\(849\) | −202.093 | −0.238037 | ||||||||
\(850\) | 128.992i | 0.151755i | ||||||||
\(851\) | −1178.14 | −1.38441 | ||||||||
\(852\) | 373.169i | 0.437992i | ||||||||
\(853\) | − 1265.99i | − 1.48416i | −0.670310 | − | 0.742082i | \(-0.733839\pi\) | ||||
0.670310 | − | 0.742082i | \(-0.266161\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −165.100 | −0.193099 | ||||||||
\(856\) | −430.458 | −0.502871 | ||||||||
\(857\) | 369.620i | 0.431295i | 0.976471 | + | 0.215648i | \(0.0691862\pi\) | ||||
−0.976471 | + | 0.215648i | \(0.930814\pi\) | |||||||
\(858\) | 171.146 | 0.199471 | ||||||||
\(859\) | 1258.03i | 1.46453i | 0.681021 | + | 0.732264i | \(0.261536\pi\) | ||||
−0.681021 | + | 0.732264i | \(0.738464\pi\) | |||||||
\(860\) | − 288.057i | − 0.334951i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 888.184 | 1.03038 | ||||||||
\(863\) | −236.666 | −0.274236 | −0.137118 | − | 0.990555i | \(-0.543784\pi\) | ||||
−0.137118 | + | 0.990555i | \(0.543784\pi\) | |||||||
\(864\) | − 29.3939i | − 0.0340207i | ||||||||
\(865\) | −70.8870 | −0.0819503 | ||||||||
\(866\) | 999.550i | 1.15421i | ||||||||
\(867\) | 75.8277i | 0.0874598i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −438.959 | −0.505132 | ||||||||
\(870\) | −290.963 | −0.334440 | ||||||||
\(871\) | − 56.8871i | − 0.0653124i | ||||||||
\(872\) | −183.156 | −0.210041 | ||||||||
\(873\) | 222.673i | 0.255067i | ||||||||
\(874\) | − 876.777i | − 1.00318i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 178.958 | 0.204290 | ||||||||
\(877\) | 805.531 | 0.918508 | 0.459254 | − | 0.888305i | \(-0.348117\pi\) | ||||
0.459254 | + | 0.888305i | \(0.348117\pi\) | |||||||
\(878\) | 921.746i | 1.04982i | ||||||||
\(879\) | −228.427 | −0.259871 | ||||||||
\(880\) | − 178.662i | − 0.203025i | ||||||||
\(881\) | − 763.260i | − 0.866356i | −0.901308 | − | 0.433178i | \(-0.857392\pi\) | ||||
0.901308 | − | 0.433178i | \(-0.142608\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 574.986 | 0.651173 | 0.325587 | − | 0.945512i | \(-0.394438\pi\) | ||||
0.325587 | + | 0.945512i | \(0.394438\pi\) | |||||||
\(884\) | 127.618 | 0.144365 | ||||||||
\(885\) | − 388.040i | − 0.438464i | ||||||||
\(886\) | 33.4119 | 0.0377110 | ||||||||
\(887\) | 383.502i | 0.432358i | 0.976354 | + | 0.216179i | \(0.0693595\pi\) | ||||
−0.976354 | + | 0.216179i | \(0.930641\pi\) | |||||||
\(888\) | − 229.122i | − 0.258020i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −351.678 | −0.395144 | ||||||||
\(891\) | 179.775 | 0.201767 | ||||||||
\(892\) | 730.658i | 0.819123i | ||||||||
\(893\) | −690.665 | −0.773421 | ||||||||
\(894\) | − 456.744i | − 0.510899i | ||||||||
\(895\) | − 294.925i | − 0.329525i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −152.616 | −0.170141 | ||||||||
\(898\) | 77.9937 | 0.0868526 | ||||||||
\(899\) | − 1600.64i | − 1.78046i | ||||||||
\(900\) | 30.0000 | 0.0333333 | ||||||||
\(901\) | − 1183.46i | − 1.31350i | ||||||||
\(902\) | − 890.547i | − 0.987302i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.21672 | −0.0101955 | ||||||||
\(905\) | −123.304 | −0.136247 | ||||||||
\(906\) | 379.280i | 0.418631i | ||||||||
\(907\) | −1162.44 | −1.28163 | −0.640816 | − | 0.767695i | \(-0.721404\pi\) | ||||
−0.640816 | + | 0.767695i | \(0.721404\pi\) | |||||||
\(908\) | 515.747i | 0.568004i | ||||||||
\(909\) | − 262.782i | − 0.289089i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1070.03 | 1.17457 | 0.587284 | − | 0.809381i | \(-0.300197\pi\) | ||||
0.587284 | + | 0.809381i | \(0.300197\pi\) | |||||||
\(912\) | 170.514 | 0.186967 | ||||||||
\(913\) | − 8.33914i | − 0.00913378i | ||||||||
\(914\) | −496.068 | −0.542744 | ||||||||
\(915\) | 31.0767i | 0.0339636i | ||||||||
\(916\) | 30.8615i | 0.0336916i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 134.053 | 0.146027 | ||||||||
\(919\) | 1166.72 | 1.26955 | 0.634777 | − | 0.772695i | \(-0.281092\pi\) | ||||
0.634777 | + | 0.772695i | \(0.281092\pi\) | |||||||
\(920\) | 159.318i | 0.173172i | ||||||||
\(921\) | −744.558 | −0.808423 | ||||||||
\(922\) | − 666.940i | − 0.723362i | ||||||||
\(923\) | 376.808i | 0.408243i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 233.846 | 0.252807 | ||||||||
\(926\) | −547.458 | −0.591208 | ||||||||
\(927\) | 417.123i | 0.449971i | ||||||||
\(928\) | 300.505 | 0.323820 | ||||||||
\(929\) | − 224.387i | − 0.241536i | −0.992681 | − | 0.120768i | \(-0.961464\pi\) | ||||
0.992681 | − | 0.120768i | \(-0.0385358\pi\) | |||||||
\(930\) | 165.035i | 0.177457i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −250.694 | −0.268984 | ||||||||
\(933\) | −435.572 | −0.466851 | ||||||||
\(934\) | − 414.854i | − 0.444169i | ||||||||
\(935\) | 814.797 | 0.871440 | ||||||||
\(936\) | − 29.6805i | − 0.0317100i | ||||||||
\(937\) | 644.185i | 0.687497i | 0.939062 | + | 0.343749i | \(0.111697\pi\) | ||||
−0.939062 | + | 0.343749i | \(0.888303\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.7349 | −0.0252767 | ||||||||
\(940\) | 125.500 | 0.133510 | ||||||||
\(941\) | − 307.262i | − 0.326527i | −0.986582 | − | 0.163264i | \(-0.947798\pi\) | ||||
0.986582 | − | 0.163264i | \(-0.0522021\pi\) | |||||||
\(942\) | 122.974 | 0.130545 | ||||||||
\(943\) | 794.127i | 0.842128i | ||||||||
\(944\) | 400.766i | 0.424540i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1819.56 | −1.92342 | ||||||||
\(947\) | −981.511 | −1.03644 | −0.518221 | − | 0.855247i | \(-0.673406\pi\) | ||||
−0.518221 | + | 0.855247i | \(0.673406\pi\) | |||||||
\(948\) | 76.1252i | 0.0803009i | ||||||||
\(949\) | 180.703 | 0.190414 | ||||||||
\(950\) | 174.030i | 0.183190i | ||||||||
\(951\) | 57.0367i | 0.0599755i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1258.67 | 1.32075 | 0.660375 | − | 0.750936i | \(-0.270397\pi\) | ||||
0.660375 | + | 0.750936i | \(0.270397\pi\) | |||||||
\(954\) | −275.241 | −0.288512 | ||||||||
\(955\) | − 436.401i | − 0.456964i | ||||||||
\(956\) | −7.25129 | −0.00758503 | ||||||||
\(957\) | 1837.91i | 1.92049i | ||||||||
\(958\) | 1079.09i | 1.12640i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −30.9839 | −0.0322749 | ||||||||
\(961\) | 53.1118 | 0.0552673 | ||||||||
\(962\) | − 231.356i | − 0.240495i | ||||||||
\(963\) | −456.570 | −0.474112 | ||||||||
\(964\) | 193.277i | 0.200495i | ||||||||
\(965\) | − 779.851i | − 0.808135i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −992.744 | −1.02662 | −0.513311 | − | 0.858202i | \(-0.671581\pi\) | ||||
−0.513311 | + | 0.858202i | \(0.671581\pi\) | |||||||
\(968\) | −786.301 | −0.812295 | ||||||||
\(969\) | 777.639i | 0.802517i | ||||||||
\(970\) | 234.718 | 0.241978 | ||||||||
\(971\) | 357.573i | 0.368253i | 0.982903 | + | 0.184126i | \(0.0589455\pi\) | ||||
−0.982903 | + | 0.184126i | \(0.941054\pi\) | |||||||
\(972\) | − 31.1769i | − 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 316.626 | 0.325078 | ||||||||
\(975\) | 30.2925 | 0.0310693 | ||||||||
\(976\) | − 32.0959i | − 0.0328851i | ||||||||
\(977\) | −877.346 | −0.898000 | −0.449000 | − | 0.893532i | \(-0.648220\pi\) | ||||
−0.449000 | + | 0.893532i | \(0.648220\pi\) | |||||||
\(978\) | − 283.677i | − 0.290059i | ||||||||
\(979\) | 2221.43i | 2.26908i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −194.266 | −0.198029 | ||||||||
\(982\) | 1184.68 | 1.20639 | ||||||||
\(983\) | − 1440.21i | − 1.46511i | −0.680705 | − | 0.732557i | \(-0.738327\pi\) | ||||
0.680705 | − | 0.732557i | \(-0.261673\pi\) | |||||||
\(984\) | −154.440 | −0.156952 | ||||||||
\(985\) | 126.071i | 0.127991i | ||||||||
\(986\) | 1370.47i | 1.38993i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 172.177 | 0.174268 | ||||||||
\(989\) | 1622.55 | 1.64060 | ||||||||
\(990\) | − 189.499i | − 0.191413i | ||||||||
\(991\) | 1154.36 | 1.16485 | 0.582423 | − | 0.812886i | \(-0.302105\pi\) | ||||
0.582423 | + | 0.812886i | \(0.302105\pi\) | |||||||
\(992\) | − 170.448i | − 0.171822i | ||||||||
\(993\) | 723.791i | 0.728893i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 383.057 | 0.384981 | ||||||||
\(996\) | −1.44619 | −0.00145200 | ||||||||
\(997\) | 1624.90i | 1.62979i | 0.579608 | + | 0.814896i | \(0.303206\pi\) | ||||
−0.579608 | + | 0.814896i | \(0.696794\pi\) | |||||||
\(998\) | −246.988 | −0.247483 | ||||||||
\(999\) | − 243.020i | − 0.243264i |
(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 | 1470.3.f.d.391.2 | 16 | ||
7.4 | even | 3 | 210.3.o.b.61.7 | yes | 16 | ||
7.5 | odd | 6 | 210.3.o.b.31.7 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 1470.3.f.d.391.8 | 16 | ||
21.5 | even | 6 | 630.3.v.c.451.1 | 16 | |||
21.11 | odd | 6 | 630.3.v.c.271.1 | 16 | |||
35.4 | even | 6 | 1050.3.p.i.901.4 | 16 | |||
35.12 | even | 12 | 1050.3.q.e.199.1 | 32 | |||
35.18 | odd | 12 | 1050.3.q.e.649.1 | 32 | |||
35.19 | odd | 6 | 1050.3.p.i.451.4 | 16 | |||
35.32 | odd | 12 | 1050.3.q.e.649.10 | 32 | |||
35.33 | even | 12 | 1050.3.q.e.199.10 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.7 | ✓ | 16 | 7.5 | odd | 6 | ||
210.3.o.b.61.7 | yes | 16 | 7.4 | even | 3 | ||
630.3.v.c.271.1 | 16 | 21.11 | odd | 6 | |||
630.3.v.c.451.1 | 16 | 21.5 | even | 6 | |||
1050.3.p.i.451.4 | 16 | 35.19 | odd | 6 | |||
1050.3.p.i.901.4 | 16 | 35.4 | even | 6 | |||
1050.3.q.e.199.1 | 32 | 35.12 | even | 12 | |||
1050.3.q.e.199.10 | 32 | 35.33 | even | 12 | |||
1050.3.q.e.649.1 | 32 | 35.18 | odd | 12 | |||
1050.3.q.e.649.10 | 32 | 35.32 | odd | 12 | |||
1470.3.f.d.391.2 | 16 | 1.1 | even | 1 | trivial | ||
1470.3.f.d.391.8 | 16 | 7.6 | odd | 2 | inner |