Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,3,Mod(134,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.134");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.b (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: | \(5.14987699641\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1997017344.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 53x^{4} + 56x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 134.7 | ||
Root | \(-0.277334i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.134 |
Dual form | 189.3.b.c.134.2 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.27733i | 1.13867i | 0.822107 | + | 0.569334i | \(0.192799\pi\) | ||||
−0.822107 | + | 0.569334i | \(0.807201\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.18625 | −0.296563 | ||||||||
\(5\) | − 4.94527i | − 0.989054i | −0.869162 | − | 0.494527i | \(-0.835341\pi\) | ||||
0.869162 | − | 0.494527i | \(-0.164659\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575 | 0.377964 | ||||||||
\(8\) | 6.40785i | 0.800981i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11.2620 | 1.12620 | ||||||||
\(11\) | 20.1892i | 1.83538i | 0.397295 | + | 0.917691i | \(0.369949\pi\) | ||||
−0.397295 | + | 0.917691i | \(0.630051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25.8541 | 1.98877 | 0.994387 | − | 0.105803i | \(-0.0337414\pi\) | ||||
0.994387 | + | 0.105803i | \(0.0337414\pi\) | |||||||
\(14\) | 6.02526i | 0.430376i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.3378 | −1.20861 | ||||||||
\(17\) | 6.60531i | 0.388548i | 0.980947 | + | 0.194274i | \(0.0622351\pi\) | ||||
−0.980947 | + | 0.194274i | \(0.937765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.53147 | 0.291130 | 0.145565 | − | 0.989349i | \(-0.453500\pi\) | ||||
0.145565 | + | 0.989349i | \(0.453500\pi\) | |||||||
\(20\) | 5.86633i | 0.293317i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −45.9776 | −2.08989 | ||||||||
\(23\) | − 14.5333i | − 0.631884i | −0.948778 | − | 0.315942i | \(-0.897679\pi\) | ||||
0.948778 | − | 0.315942i | \(-0.102321\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.544307 | 0.0217723 | ||||||||
\(26\) | 58.8783i | 2.26455i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.13853 | −0.112090 | ||||||||
\(29\) | − 17.4877i | − 0.603025i | −0.953462 | − | 0.301512i | \(-0.902509\pi\) | ||||
0.953462 | − | 0.301512i | \(-0.0974914\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −45.3926 | −1.46428 | −0.732138 | − | 0.681156i | \(-0.761478\pi\) | ||||
−0.732138 | + | 0.681156i | \(0.761478\pi\) | |||||||
\(32\) | − 18.4073i | − 0.575228i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −15.0425 | −0.442427 | ||||||||
\(35\) | − 13.0840i | − 0.373827i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.8908 | 1.10516 | 0.552578 | − | 0.833461i | \(-0.313644\pi\) | ||||
0.552578 | + | 0.833461i | \(0.313644\pi\) | |||||||
\(38\) | 12.5970i | 0.331500i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 31.6885 | 0.792213 | ||||||||
\(41\) | − 30.4091i | − 0.741684i | −0.928696 | − | 0.370842i | \(-0.879069\pi\) | ||||
0.928696 | − | 0.370842i | \(-0.120931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −53.5305 | −1.24490 | −0.622448 | − | 0.782661i | \(-0.713862\pi\) | ||||
−0.622448 | + | 0.782661i | \(0.713862\pi\) | |||||||
\(44\) | − 23.9495i | − 0.544306i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 33.0973 | 0.719506 | ||||||||
\(47\) | − 27.8541i | − 0.592641i | −0.955089 | − | 0.296321i | \(-0.904240\pi\) | ||||
0.955089 | − | 0.296321i | \(-0.0957597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 1.23957i | 0.0247914i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −30.6694 | −0.589797 | ||||||||
\(53\) | 6.45594i | 0.121810i | 0.998144 | + | 0.0609051i | \(0.0193987\pi\) | ||||
−0.998144 | + | 0.0609051i | \(0.980601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 99.8411 | 1.81529 | ||||||||
\(56\) | 16.9536i | 0.302742i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 39.8254 | 0.686644 | ||||||||
\(59\) | 42.8050i | 0.725508i | 0.931885 | + | 0.362754i | \(0.118163\pi\) | ||||
−0.931885 | + | 0.362754i | \(0.881837\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35.5980 | 0.583574 | 0.291787 | − | 0.956483i | \(-0.405750\pi\) | ||||
0.291787 | + | 0.956483i | \(0.405750\pi\) | |||||||
\(62\) | − 103.374i | − 1.66732i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −35.4317 | −0.553621 | ||||||||
\(65\) | − 127.855i | − 1.96700i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −83.7309 | −1.24971 | −0.624857 | − | 0.780739i | \(-0.714843\pi\) | ||||
−0.624857 | + | 0.780739i | \(0.714843\pi\) | |||||||
\(68\) | − 7.83556i | − 0.115229i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 29.7965 | 0.425665 | ||||||||
\(71\) | − 113.821i | − 1.60311i | −0.597923 | − | 0.801554i | \(-0.704007\pi\) | ||||
0.597923 | − | 0.801554i | \(-0.295993\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25.5762 | −0.350358 | −0.175179 | − | 0.984537i | \(-0.556050\pi\) | ||||
−0.175179 | + | 0.984537i | \(0.556050\pi\) | |||||||
\(74\) | 93.1220i | 1.25840i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.56172 | −0.0863384 | ||||||||
\(77\) | 53.4156i | 0.693709i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 81.8944 | 1.03664 | 0.518319 | − | 0.855187i | \(-0.326558\pi\) | ||||
0.518319 | + | 0.855187i | \(0.326558\pi\) | |||||||
\(80\) | 95.6307i | 1.19538i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 69.2516 | 0.844532 | ||||||||
\(83\) | − 28.7852i | − 0.346810i | −0.984851 | − | 0.173405i | \(-0.944523\pi\) | ||||
0.984851 | − | 0.173405i | \(-0.0554769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 32.6651 | 0.384295 | ||||||||
\(86\) | − 121.907i | − 1.41752i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −129.369 | −1.47011 | ||||||||
\(89\) | − 5.92931i | − 0.0666214i | −0.999445 | − | 0.0333107i | \(-0.989395\pi\) | ||||
0.999445 | − | 0.0333107i | \(-0.0106051\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 68.4034 | 0.751686 | ||||||||
\(92\) | 17.2402i | 0.187393i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 63.4332 | 0.674821 | ||||||||
\(95\) | − 27.3546i | − 0.287944i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −94.4881 | −0.974104 | −0.487052 | − | 0.873373i | \(-0.661928\pi\) | ||||
−0.487052 | + | 0.873373i | \(0.661928\pi\) | |||||||
\(98\) | 15.9413i | 0.162667i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.645685 | −0.00645685 | ||||||||
\(101\) | − 123.052i | − 1.21834i | −0.793042 | − | 0.609168i | \(-0.791504\pi\) | ||||
0.793042 | − | 0.609168i | \(-0.208496\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −41.5755 | −0.403646 | −0.201823 | − | 0.979422i | \(-0.564687\pi\) | ||||
−0.201823 | + | 0.979422i | \(0.564687\pi\) | |||||||
\(104\) | 165.669i | 1.59297i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.7023 | −0.138701 | ||||||||
\(107\) | 2.53060i | 0.0236505i | 0.999930 | + | 0.0118252i | \(0.00376418\pi\) | ||||
−0.999930 | + | 0.0118252i | \(0.996236\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27.9757 | −0.256658 | −0.128329 | − | 0.991732i | \(-0.540961\pi\) | ||||
−0.128329 | + | 0.991732i | \(0.540961\pi\) | |||||||
\(110\) | 227.371i | 2.06701i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −51.1630 | −0.456813 | ||||||||
\(113\) | 183.509i | 1.62397i | 0.583678 | + | 0.811985i | \(0.301613\pi\) | ||||
−0.583678 | + | 0.811985i | \(0.698387\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −71.8713 | −0.624968 | ||||||||
\(116\) | 20.7448i | 0.178835i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −97.4812 | −0.826112 | ||||||||
\(119\) | 17.4760i | 0.146857i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −286.604 | −2.36863 | ||||||||
\(122\) | 81.0686i | 0.664497i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 53.8470 | 0.434250 | ||||||||
\(125\) | − 126.323i | − 1.01059i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −117.574 | −0.925780 | −0.462890 | − | 0.886416i | \(-0.653187\pi\) | ||||
−0.462890 | + | 0.886416i | \(0.653187\pi\) | |||||||
\(128\) | − 154.319i | − 1.20562i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 291.169 | 2.23976 | ||||||||
\(131\) | 175.442i | 1.33926i | 0.742697 | + | 0.669628i | \(0.233546\pi\) | ||||
−0.742697 | + | 0.669628i | \(0.766454\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.6349 | 0.110037 | ||||||||
\(134\) | − 190.683i | − 1.42301i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −42.3258 | −0.311219 | ||||||||
\(137\) | − 3.72691i | − 0.0272037i | −0.999907 | − | 0.0136019i | \(-0.995670\pi\) | ||||
0.999907 | − | 0.0136019i | \(-0.00432974\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 118.450 | 0.852159 | 0.426079 | − | 0.904686i | \(-0.359894\pi\) | ||||
0.426079 | + | 0.904686i | \(0.359894\pi\) | |||||||
\(140\) | 15.5209i | 0.110863i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 259.208 | 1.82541 | ||||||||
\(143\) | 521.973i | 3.65016i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −86.4815 | −0.596424 | ||||||||
\(146\) | − 58.2455i | − 0.398942i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −48.5068 | −0.327748 | ||||||||
\(149\) | − 208.169i | − 1.39711i | −0.715556 | − | 0.698555i | \(-0.753827\pi\) | ||||
0.715556 | − | 0.698555i | \(-0.246173\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 77.7758 | 0.515071 | 0.257536 | − | 0.966269i | \(-0.417090\pi\) | ||||
0.257536 | + | 0.966269i | \(0.417090\pi\) | |||||||
\(152\) | 35.4448i | 0.233190i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −121.645 | −0.789904 | ||||||||
\(155\) | 224.479i | 1.44825i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 113.687 | 0.724118 | 0.362059 | − | 0.932155i | \(-0.382074\pi\) | ||||
0.362059 | + | 0.932155i | \(0.382074\pi\) | |||||||
\(158\) | 186.501i | 1.18039i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −91.0290 | −0.568931 | ||||||||
\(161\) | − 38.4516i | − 0.238830i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −143.154 | −0.878243 | −0.439122 | − | 0.898428i | \(-0.644710\pi\) | ||||
−0.439122 | + | 0.898428i | \(0.644710\pi\) | |||||||
\(164\) | 36.0728i | 0.219956i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 65.5536 | 0.394901 | ||||||||
\(167\) | − 208.697i | − 1.24968i | −0.780752 | − | 0.624841i | \(-0.785164\pi\) | ||||
0.780752 | − | 0.624841i | \(-0.214836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 499.433 | 2.95522 | ||||||||
\(170\) | 74.3892i | 0.437584i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 63.5007 | 0.369190 | ||||||||
\(173\) | − 165.376i | − 0.955930i | −0.878379 | − | 0.477965i | \(-0.841375\pi\) | ||||
0.878379 | − | 0.477965i | \(-0.158625\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.44010 | 0.00822914 | ||||||||
\(176\) | − 390.415i | − 2.21827i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.5030 | 0.0758596 | ||||||||
\(179\) | 6.53386i | 0.0365020i | 0.999833 | + | 0.0182510i | \(0.00580980\pi\) | ||||
−0.999833 | + | 0.0182510i | \(0.994190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 47.6268 | 0.263132 | 0.131566 | − | 0.991307i | \(-0.458000\pi\) | ||||
0.131566 | + | 0.991307i | \(0.458000\pi\) | |||||||
\(182\) | 155.777i | 0.855920i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 93.1274 | 0.506127 | ||||||||
\(185\) | − 202.216i | − 1.09306i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −133.356 | −0.713134 | ||||||||
\(188\) | 33.0420i | 0.175755i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 62.2956 | 0.327872 | ||||||||
\(191\) | 59.7719i | 0.312942i | 0.987683 | + | 0.156471i | \(0.0500118\pi\) | ||||
−0.987683 | + | 0.156471i | \(0.949988\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −178.540 | −0.925079 | −0.462540 | − | 0.886599i | \(-0.653062\pi\) | ||||
−0.462540 | + | 0.886599i | \(0.653062\pi\) | |||||||
\(194\) | − 215.181i | − 1.10918i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.30376 | −0.0423661 | ||||||||
\(197\) | − 69.0446i | − 0.350480i | −0.984526 | − | 0.175240i | \(-0.943930\pi\) | ||||
0.984526 | − | 0.175240i | \(-0.0560702\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 360.982 | 1.81398 | 0.906989 | − | 0.421155i | \(-0.138375\pi\) | ||||
0.906989 | + | 0.421155i | \(0.138375\pi\) | |||||||
\(200\) | 3.48783i | 0.0174392i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 280.230 | 1.38728 | ||||||||
\(203\) | − 46.2681i | − 0.227922i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −150.381 | −0.733566 | ||||||||
\(206\) | − 94.6813i | − 0.459618i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −499.961 | −2.40366 | ||||||||
\(209\) | 111.676i | 0.534335i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −45.0507 | −0.213510 | −0.106755 | − | 0.994285i | \(-0.534046\pi\) | ||||
−0.106755 | + | 0.994285i | \(0.534046\pi\) | |||||||
\(212\) | − 7.65837i | − 0.0361244i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.76302 | −0.0269300 | ||||||||
\(215\) | 264.723i | 1.23127i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −120.097 | −0.553445 | ||||||||
\(218\) | − 63.7101i | − 0.292248i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −118.437 | −0.538348 | ||||||||
\(221\) | 170.774i | 0.772734i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −185.805 | −0.833209 | −0.416604 | − | 0.909088i | \(-0.636780\pi\) | ||||
−0.416604 | + | 0.909088i | \(0.636780\pi\) | |||||||
\(224\) | − 48.7011i | − 0.217416i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −417.910 | −1.84916 | ||||||||
\(227\) | − 199.040i | − 0.876827i | −0.898773 | − | 0.438414i | \(-0.855540\pi\) | ||||
0.898773 | − | 0.438414i | \(-0.144460\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −321.236 | −1.40278 | −0.701389 | − | 0.712779i | \(-0.747436\pi\) | ||||
−0.701389 | + | 0.712779i | \(0.747436\pi\) | |||||||
\(230\) | − 163.675i | − 0.711630i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 112.059 | 0.483011 | ||||||||
\(233\) | − 215.361i | − 0.924295i | −0.886803 | − | 0.462147i | \(-0.847079\pi\) | ||||
0.886803 | − | 0.462147i | \(-0.152921\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −137.746 | −0.586154 | ||||||||
\(236\) | − 50.7775i | − 0.215159i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −39.7987 | −0.167222 | ||||||||
\(239\) | 165.314i | 0.691691i | 0.938291 | + | 0.345846i | \(0.112408\pi\) | ||||
−0.938291 | + | 0.345846i | \(0.887592\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 251.336 | 1.04289 | 0.521443 | − | 0.853286i | \(-0.325394\pi\) | ||||
0.521443 | + | 0.853286i | \(0.325394\pi\) | |||||||
\(242\) | − 652.693i | − 2.69708i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −42.2282 | −0.173066 | ||||||||
\(245\) | − 34.6169i | − 0.141293i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 143.011 | 0.578992 | ||||||||
\(248\) | − 290.869i | − 1.17286i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 287.681 | 1.15072 | ||||||||
\(251\) | − 10.7301i | − 0.0427496i | −0.999772 | − | 0.0213748i | \(-0.993196\pi\) | ||||
0.999772 | − | 0.0213748i | \(-0.00680432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 293.417 | 1.15975 | ||||||||
\(254\) | − 267.755i | − 1.05415i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 209.709 | 0.819176 | ||||||||
\(257\) | 34.3713i | 0.133741i | 0.997762 | + | 0.0668703i | \(0.0213014\pi\) | ||||
−0.997762 | + | 0.0668703i | \(0.978699\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 108.187 | 0.417710 | ||||||||
\(260\) | 151.669i | 0.583341i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −399.541 | −1.52497 | ||||||||
\(263\) | 438.760i | 1.66829i | 0.551546 | + | 0.834144i | \(0.314038\pi\) | ||||
−0.551546 | + | 0.834144i | \(0.685962\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31.9264 | 0.120477 | ||||||||
\(266\) | 33.3286i | 0.125295i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 99.3259 | 0.370619 | ||||||||
\(269\) | 244.971i | 0.910673i | 0.890320 | + | 0.455336i | \(0.150481\pi\) | ||||
−0.890320 | + | 0.455336i | \(0.849519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 162.048 | 0.597962 | 0.298981 | − | 0.954259i | \(-0.403353\pi\) | ||||
0.298981 | + | 0.954259i | \(0.403353\pi\) | |||||||
\(272\) | − 127.732i | − 0.469604i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.48743 | 0.0309760 | ||||||||
\(275\) | 10.9891i | 0.0399604i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −282.791 | −1.02091 | −0.510453 | − | 0.859906i | \(-0.670522\pi\) | ||||
−0.510453 | + | 0.859906i | \(0.670522\pi\) | |||||||
\(278\) | 269.750i | 0.970325i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 83.8400 | 0.299428 | ||||||||
\(281\) | 68.2322i | 0.242819i | 0.992602 | + | 0.121410i | \(0.0387415\pi\) | ||||
−0.992602 | + | 0.121410i | \(0.961259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 194.706 | 0.688005 | 0.344003 | − | 0.938969i | \(-0.388217\pi\) | ||||
0.344003 | + | 0.938969i | \(0.388217\pi\) | |||||||
\(284\) | 135.020i | 0.475422i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1188.71 | −4.15632 | ||||||||
\(287\) | − 80.4548i | − 0.280330i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 245.370 | 0.849031 | ||||||||
\(290\) | − 196.947i | − 0.679128i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 30.3398 | 0.103903 | ||||||||
\(293\) | 233.076i | 0.795482i | 0.917498 | + | 0.397741i | \(0.130206\pi\) | ||||
−0.917498 | + | 0.397741i | \(0.869794\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 211.682 | 0.717567 | ||||||||
\(296\) | 262.022i | 0.885209i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 474.071 | 1.59084 | ||||||||
\(299\) | − 375.746i | − 1.25668i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −141.628 | −0.470526 | ||||||||
\(302\) | 177.121i | 0.586495i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −106.967 | −0.351864 | ||||||||
\(305\) | − 176.042i | − 0.577186i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 167.051 | 0.544140 | 0.272070 | − | 0.962277i | \(-0.412292\pi\) | ||||
0.272070 | + | 0.962277i | \(0.412292\pi\) | |||||||
\(308\) | − 63.3644i | − 0.205728i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −511.213 | −1.64907 | ||||||||
\(311\) | 194.748i | 0.626199i | 0.949720 | + | 0.313099i | \(0.101367\pi\) | ||||
−0.949720 | + | 0.313099i | \(0.898633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 328.297 | 1.04887 | 0.524436 | − | 0.851450i | \(-0.324276\pi\) | ||||
0.524436 | + | 0.851450i | \(0.324276\pi\) | |||||||
\(314\) | 258.902i | 0.824529i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −97.1474 | −0.307428 | ||||||||
\(317\) | 435.769i | 1.37467i | 0.726342 | + | 0.687333i | \(0.241219\pi\) | ||||
−0.726342 | + | 0.687333i | \(0.758781\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 353.063 | 1.10678 | ||||||||
\(320\) | 175.219i | 0.547561i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 87.5671 | 0.271948 | ||||||||
\(323\) | 36.5371i | 0.113118i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0725 | 0.0433001 | ||||||||
\(326\) | − 326.009i | − 1.00003i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 194.857 | 0.594075 | ||||||||
\(329\) | − 73.6951i | − 0.223997i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 441.180 | 1.33287 | 0.666436 | − | 0.745563i | \(-0.267819\pi\) | ||||
0.666436 | + | 0.745563i | \(0.267819\pi\) | |||||||
\(332\) | 34.1465i | 0.102851i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 475.273 | 1.42297 | ||||||||
\(335\) | 414.072i | 1.23603i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −226.991 | −0.673564 | −0.336782 | − | 0.941583i | \(-0.609339\pi\) | ||||
−0.336782 | + | 0.941583i | \(0.609339\pi\) | |||||||
\(338\) | 1137.38i | 3.36502i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −38.7490 | −0.113968 | ||||||||
\(341\) | − 916.440i | − 2.68751i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 0.0539949 | ||||||||
\(344\) | − 343.015i | − 0.997138i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 376.616 | 1.08849 | ||||||||
\(347\) | 127.698i | 0.368005i | 0.982926 | + | 0.184003i | \(0.0589055\pi\) | ||||
−0.982926 | + | 0.184003i | \(0.941095\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 68.5010 | 0.196278 | 0.0981390 | − | 0.995173i | \(-0.468711\pi\) | ||||
0.0981390 | + | 0.995173i | \(0.468711\pi\) | |||||||
\(350\) | 3.27959i | 0.00937026i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 371.628 | 1.05576 | ||||||||
\(353\) | 436.129i | 1.23549i | 0.786377 | + | 0.617747i | \(0.211954\pi\) | ||||
−0.786377 | + | 0.617747i | \(0.788046\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −562.874 | −1.58556 | ||||||||
\(356\) | 7.03365i | 0.0197574i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.8798 | −0.0415637 | ||||||||
\(359\) | 557.516i | 1.55297i | 0.630136 | + | 0.776485i | \(0.282999\pi\) | ||||
−0.630136 | + | 0.776485i | \(0.717001\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −330.403 | −0.915243 | ||||||||
\(362\) | 108.462i | 0.299619i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −81.1437 | −0.222922 | ||||||||
\(365\) | 126.481i | 0.346523i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −540.446 | −1.47260 | −0.736302 | − | 0.676653i | \(-0.763430\pi\) | ||||
−0.736302 | + | 0.676653i | \(0.763430\pi\) | |||||||
\(368\) | 281.043i | 0.763704i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 460.513 | 1.24463 | ||||||||
\(371\) | 17.0808i | 0.0460399i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −130.478 | −0.349807 | −0.174903 | − | 0.984586i | \(-0.555961\pi\) | ||||
−0.174903 | + | 0.984586i | \(0.555961\pi\) | |||||||
\(374\) | − 303.696i | − 0.812022i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 178.485 | 0.474694 | ||||||||
\(377\) | − 452.128i | − 1.19928i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −345.177 | −0.910757 | −0.455379 | − | 0.890298i | \(-0.650496\pi\) | ||||
−0.455379 | + | 0.890298i | \(0.650496\pi\) | |||||||
\(380\) | 32.4495i | 0.0853934i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −136.121 | −0.356337 | ||||||||
\(383\) | 105.528i | 0.275529i | 0.990465 | + | 0.137764i | \(0.0439917\pi\) | ||||
−0.990465 | + | 0.137764i | \(0.956008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 264.155 | 0.686116 | ||||||||
\(386\) | − 406.596i | − 1.05336i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 112.087 | 0.288883 | ||||||||
\(389\) | − 498.611i | − 1.28178i | −0.767634 | − | 0.640889i | \(-0.778566\pi\) | ||||
0.767634 | − | 0.640889i | \(-0.221434\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 95.9972 | 0.245517 | ||||||||
\(392\) | 44.8549i | 0.114426i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 157.238 | 0.399080 | ||||||||
\(395\) | − 404.990i | − 1.02529i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 119.497 | 0.301000 | 0.150500 | − | 0.988610i | \(-0.451912\pi\) | ||||
0.150500 | + | 0.988610i | \(0.451912\pi\) | |||||||
\(398\) | 822.076i | 2.06552i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.5257 | −0.0263143 | ||||||||
\(401\) | − 602.317i | − 1.50204i | −0.660280 | − | 0.751019i | \(-0.729563\pi\) | ||||
0.660280 | − | 0.751019i | \(-0.270437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1173.58 | −2.91212 | ||||||||
\(404\) | 145.970i | 0.361313i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 105.368 | 0.259527 | ||||||||
\(407\) | 825.552i | 2.02838i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −382.189 | −0.934447 | −0.467224 | − | 0.884139i | \(-0.654746\pi\) | ||||
−0.467224 | + | 0.884139i | \(0.654746\pi\) | |||||||
\(410\) | − 342.468i | − 0.835287i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 49.3190 | 0.119706 | ||||||||
\(413\) | 113.251i | 0.274216i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −142.351 | −0.343014 | ||||||||
\(416\) | − 475.903i | − 1.14400i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −254.324 | −0.608430 | ||||||||
\(419\) | − 101.655i | − 0.242612i | −0.992615 | − | 0.121306i | \(-0.961292\pi\) | ||||
0.992615 | − | 0.121306i | \(-0.0387083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −425.972 | −1.01181 | −0.505905 | − | 0.862589i | \(-0.668842\pi\) | ||||
−0.505905 | + | 0.862589i | \(0.668842\pi\) | |||||||
\(422\) | − 102.595i | − 0.243117i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −41.3687 | −0.0975676 | ||||||||
\(425\) | 3.59532i | 0.00845957i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 94.1835 | 0.220570 | ||||||||
\(428\) | − 3.00193i | − 0.00701385i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −602.863 | −1.40201 | ||||||||
\(431\) | 256.315i | 0.594698i | 0.954769 | + | 0.297349i | \(0.0961025\pi\) | ||||
−0.954769 | + | 0.297349i | \(0.903898\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 487.980 | 1.12697 | 0.563487 | − | 0.826125i | \(-0.309460\pi\) | ||||
0.563487 | + | 0.826125i | \(0.309460\pi\) | |||||||
\(434\) | − 273.502i | − 0.630189i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.1863 | 0.0761153 | ||||||||
\(437\) | − 80.3908i | − 0.183961i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −353.322 | −0.804833 | −0.402416 | − | 0.915457i | \(-0.631830\pi\) | ||||
−0.402416 | + | 0.915457i | \(0.631830\pi\) | |||||||
\(440\) | 639.766i | 1.45401i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −388.910 | −0.879887 | ||||||||
\(443\) | 14.5063i | 0.0327455i | 0.999866 | + | 0.0163728i | \(0.00521184\pi\) | ||||
−0.999866 | + | 0.0163728i | \(0.994788\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.3220 | −0.0658922 | ||||||||
\(446\) | − 423.141i | − 0.948747i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −93.7435 | −0.209249 | ||||||||
\(449\) | 848.396i | 1.88952i | 0.327759 | + | 0.944761i | \(0.393707\pi\) | ||||
−0.327759 | + | 0.944761i | \(0.606293\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 613.935 | 1.36127 | ||||||||
\(452\) | − 217.687i | − 0.481609i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 453.280 | 0.998415 | ||||||||
\(455\) | − 338.273i | − 0.743458i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 165.684 | 0.362546 | 0.181273 | − | 0.983433i | \(-0.441978\pi\) | ||||
0.181273 | + | 0.983433i | \(0.441978\pi\) | |||||||
\(458\) | − 731.562i | − 1.59730i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 85.2574 | 0.185342 | ||||||||
\(461\) | − 785.218i | − 1.70329i | −0.524117 | − | 0.851646i | \(-0.675605\pi\) | ||||
0.524117 | − | 0.851646i | \(-0.324395\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −575.009 | −1.24192 | −0.620960 | − | 0.783842i | \(-0.713257\pi\) | ||||
−0.620960 | + | 0.783842i | \(0.713257\pi\) | |||||||
\(464\) | 338.174i | 0.728824i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 490.448 | 1.05246 | ||||||||
\(467\) | − 773.867i | − 1.65710i | −0.559913 | − | 0.828551i | \(-0.689166\pi\) | ||||
0.559913 | − | 0.828551i | \(-0.310834\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −221.531 | −0.472348 | ||||||||
\(470\) | − 313.694i | − 0.667435i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −274.288 | −0.581118 | ||||||||
\(473\) | − 1080.74i | − 2.28486i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.01082 | 0.00633857 | ||||||||
\(476\) | − 20.7310i | − 0.0435524i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −376.476 | −0.787606 | ||||||||
\(479\) | − 489.868i | − 1.02269i | −0.859376 | − | 0.511345i | \(-0.829148\pi\) | ||||
0.859376 | − | 0.511345i | \(-0.170852\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1057.19 | 2.19791 | ||||||||
\(482\) | 572.376i | 1.18750i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 339.984 | 0.702447 | ||||||||
\(485\) | 467.269i | 0.963442i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 750.641 | 1.54136 | 0.770678 | − | 0.637224i | \(-0.219918\pi\) | ||||
0.770678 | + | 0.637224i | \(0.219918\pi\) | |||||||
\(488\) | 228.107i | 0.467432i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 78.8342 | 0.160886 | ||||||||
\(491\) | 154.588i | 0.314843i | 0.987532 | + | 0.157421i | \(0.0503181\pi\) | ||||
−0.987532 | + | 0.157421i | \(0.949682\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 115.512 | 0.234304 | ||||||||
\(494\) | 325.684i | 0.659279i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 877.793 | 1.76974 | ||||||||
\(497\) | − 301.141i | − 0.605918i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −144.447 | −0.289473 | −0.144736 | − | 0.989470i | \(-0.546233\pi\) | ||||
−0.144736 | + | 0.989470i | \(0.546233\pi\) | |||||||
\(500\) | 149.851i | 0.299703i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.4361 | 0.0486775 | ||||||||
\(503\) | − 110.317i | − 0.219318i | −0.993969 | − | 0.109659i | \(-0.965024\pi\) | ||||
0.993969 | − | 0.109659i | \(-0.0349760\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −608.525 | −1.20500 | ||||||||
\(506\) | 668.208i | 1.32057i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 139.472 | 0.274552 | ||||||||
\(509\) | − 469.475i | − 0.922347i | −0.887310 | − | 0.461173i | \(-0.847429\pi\) | ||||
0.887310 | − | 0.461173i | \(-0.152571\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −67.6682 | −0.132423 | ||||||||
\(512\) | − 139.698i | − 0.272848i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −78.2750 | −0.152286 | ||||||||
\(515\) | 205.602i | 0.399227i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 562.353 | 1.08772 | ||||||||
\(518\) | 246.378i | 0.475632i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 819.277 | 1.57553 | ||||||||
\(521\) | − 470.639i | − 0.903338i | −0.892186 | − | 0.451669i | \(-0.850829\pi\) | ||||
0.892186 | − | 0.451669i | \(-0.149171\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5759 | 0.0259577 | 0.0129788 | − | 0.999916i | \(-0.495869\pi\) | ||||
0.0129788 | + | 0.999916i | \(0.495869\pi\) | |||||||
\(524\) | − 208.119i | − 0.397174i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −999.203 | −1.89963 | ||||||||
\(527\) | − 299.832i | − 0.568941i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 317.782 | 0.600722 | ||||||||
\(530\) | 72.7070i | 0.137183i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.3607 | −0.0326329 | ||||||||
\(533\) | − 786.198i | − 1.47504i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5145 | 0.0233916 | ||||||||
\(536\) | − 536.534i | − 1.00100i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −557.881 | −1.03695 | ||||||||
\(539\) | 141.324i | 0.262197i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7625 | 0.0291358 | 0.0145679 | − | 0.999894i | \(-0.495363\pi\) | ||||
0.0145679 | + | 0.999894i | \(0.495363\pi\) | |||||||
\(542\) | 369.037i | 0.680880i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 121.586 | 0.223503 | ||||||||
\(545\) | 138.348i | 0.253849i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 59.2428 | 0.108305 | 0.0541525 | − | 0.998533i | \(-0.482754\pi\) | ||||
0.0541525 | + | 0.998533i | \(0.482754\pi\) | |||||||
\(548\) | 4.42106i | 0.00806762i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −25.0259 | −0.0455016 | ||||||||
\(551\) | − 96.7328i | − 0.175559i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 216.672 | 0.391812 | ||||||||
\(554\) | − 644.010i | − 1.16247i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −140.512 | −0.252719 | ||||||||
\(557\) | 736.312i | 1.32192i | 0.750419 | + | 0.660962i | \(0.229852\pi\) | ||||
−0.750419 | + | 0.660962i | \(0.770148\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1383.98 | −2.47582 | ||||||||
\(560\) | 253.015i | 0.451813i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −155.388 | −0.276490 | ||||||||
\(563\) | 188.768i | 0.335290i | 0.985847 | + | 0.167645i | \(0.0536162\pi\) | ||||
−0.985847 | + | 0.167645i | \(0.946384\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 907.500 | 1.60619 | ||||||||
\(566\) | 443.410i | 0.783409i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 729.345 | 1.28406 | ||||||||
\(569\) | 804.768i | 1.41435i | 0.707036 | + | 0.707177i | \(0.250032\pi\) | ||||
−0.707036 | + | 0.707177i | \(0.749968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 563.341 | 0.986586 | 0.493293 | − | 0.869863i | \(-0.335793\pi\) | ||||
0.493293 | + | 0.869863i | \(0.335793\pi\) | |||||||
\(572\) | − 619.191i | − 1.08250i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 183.222 | 0.319203 | ||||||||
\(575\) | − 7.91059i | − 0.0137576i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −389.601 | −0.675218 | −0.337609 | − | 0.941286i | \(-0.609618\pi\) | ||||
−0.337609 | + | 0.941286i | \(0.609618\pi\) | |||||||
\(578\) | 558.789i | 0.966763i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 102.589 | 0.176877 | ||||||||
\(581\) | − 76.1585i | − 0.131082i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −130.340 | −0.223568 | ||||||||
\(584\) | − 163.888i | − 0.280630i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −530.793 | −0.905789 | ||||||||
\(587\) | − 894.933i | − 1.52459i | −0.647231 | − | 0.762294i | \(-0.724073\pi\) | ||||
0.647231 | − | 0.762294i | \(-0.275927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −251.088 | −0.426295 | ||||||||
\(590\) | 482.071i | 0.817069i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −790.738 | −1.33571 | ||||||||
\(593\) | 684.579i | 1.15443i | 0.816591 | + | 0.577217i | \(0.195861\pi\) | ||||
−0.816591 | + | 0.577217i | \(0.804139\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 86.4236 | 0.145250 | ||||||||
\(596\) | 246.941i | 0.414331i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 855.699 | 1.43093 | ||||||||
\(599\) | 159.478i | 0.266241i | 0.991100 | + | 0.133121i | \(0.0424998\pi\) | ||||
−0.991100 | + | 0.133121i | \(0.957500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −434.985 | −0.723769 | −0.361884 | − | 0.932223i | \(-0.617867\pi\) | ||||
−0.361884 | + | 0.932223i | \(0.617867\pi\) | |||||||
\(602\) | − 322.535i | − 0.535773i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −92.2616 | −0.152751 | ||||||||
\(605\) | 1417.33i | 2.34270i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 224.469 | 0.369800 | 0.184900 | − | 0.982757i | \(-0.440804\pi\) | ||||
0.184900 | + | 0.982757i | \(0.440804\pi\) | |||||||
\(608\) | − 101.819i | − 0.167466i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 400.906 | 0.657223 | ||||||||
\(611\) | − 720.143i | − 1.17863i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −550.312 | −0.897735 | −0.448868 | − | 0.893598i | \(-0.648173\pi\) | ||||
−0.448868 | + | 0.893598i | \(0.648173\pi\) | |||||||
\(614\) | 380.431i | 0.619595i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −342.279 | −0.555648 | ||||||||
\(617\) | 69.7803i | 0.113096i | 0.998400 | + | 0.0565481i | \(0.0180094\pi\) | ||||
−0.998400 | + | 0.0565481i | \(0.981991\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 74.8169 | 0.120867 | 0.0604337 | − | 0.998172i | \(-0.480752\pi\) | ||||
0.0604337 | + | 0.998172i | \(0.480752\pi\) | |||||||
\(620\) | − 266.288i | − 0.429497i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −443.506 | −0.713032 | ||||||||
\(623\) | − 15.6875i | − 0.0251805i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −611.096 | −0.977754 | ||||||||
\(626\) | 747.641i | 1.19432i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −134.861 | −0.214747 | ||||||||
\(629\) | 270.096i | 0.429406i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 576.881 | 0.914233 | 0.457116 | − | 0.889407i | \(-0.348882\pi\) | ||||
0.457116 | + | 0.889407i | \(0.348882\pi\) | |||||||
\(632\) | 524.767i | 0.830327i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −992.392 | −1.56529 | ||||||||
\(635\) | 581.435i | 0.915646i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 180.978 | 0.284111 | ||||||||
\(638\) | 804.043i | 1.26025i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −763.149 | −1.19242 | ||||||||
\(641\) | − 808.585i | − 1.26144i | −0.776009 | − | 0.630722i | \(-0.782759\pi\) | ||||
0.776009 | − | 0.630722i | \(-0.217241\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 911.869 | 1.41815 | 0.709074 | − | 0.705135i | \(-0.249113\pi\) | ||||
0.709074 | + | 0.705135i | \(0.249113\pi\) | |||||||
\(644\) | 45.6133i | 0.0708281i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −83.2072 | −0.128804 | ||||||||
\(647\) | − 1259.24i | − 1.94628i | −0.230210 | − | 0.973141i | \(-0.573941\pi\) | ||||
0.230210 | − | 0.973141i | \(-0.426059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −864.198 | −1.33158 | ||||||||
\(650\) | 32.0479i | 0.0493044i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 169.816 | 0.260454 | ||||||||
\(653\) | 159.535i | 0.244310i | 0.992511 | + | 0.122155i | \(0.0389806\pi\) | ||||
−0.992511 | + | 0.122155i | \(0.961019\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 867.610 | 1.32460 | ||||||||
\(656\) | 588.045i | 0.896410i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 167.828 | 0.255058 | ||||||||
\(659\) | 123.079i | 0.186767i | 0.995630 | + | 0.0933834i | \(0.0297682\pi\) | ||||
−0.995630 | + | 0.0933834i | \(0.970232\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −717.352 | −1.08525 | −0.542626 | − | 0.839974i | \(-0.682570\pi\) | ||||
−0.542626 | + | 0.839974i | \(0.682570\pi\) | |||||||
\(662\) | 1004.72i | 1.51770i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 184.451 | 0.277788 | ||||||||
\(665\) | − 72.3736i | − 0.108832i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −254.155 | −0.381042 | ||||||||
\(668\) | 247.567i | 0.370609i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −942.980 | −1.40743 | ||||||||
\(671\) | 718.696i | 1.07108i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 664.319 | 0.987101 | 0.493550 | − | 0.869717i | \(-0.335699\pi\) | ||||
0.493550 | + | 0.869717i | \(0.335699\pi\) | |||||||
\(674\) | − 516.935i | − 0.766966i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −592.453 | −0.876410 | ||||||||
\(677\) | − 468.775i | − 0.692429i | −0.938155 | − | 0.346215i | \(-0.887467\pi\) | ||||
0.938155 | − | 0.346215i | \(-0.112533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −249.992 | −0.368177 | ||||||||
\(680\) | 209.313i | 0.307813i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2087.04 | 3.06018 | ||||||||
\(683\) | 633.346i | 0.927300i | 0.886019 | + | 0.463650i | \(0.153460\pi\) | ||||
−0.886019 | + | 0.463650i | \(0.846540\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.4306 | −0.0269060 | ||||||||
\(686\) | 42.1768i | 0.0614822i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1035.16 | 1.50460 | ||||||||
\(689\) | 166.912i | 0.242253i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −640.635 | −0.927113 | −0.463557 | − | 0.886067i | \(-0.653427\pi\) | ||||
−0.463557 | + | 0.886067i | \(0.653427\pi\) | |||||||
\(692\) | 196.177i | 0.283493i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −290.811 | −0.419035 | ||||||||
\(695\) | − 585.768i | − 0.842831i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 200.861 | 0.288180 | ||||||||
\(698\) | 156.000i | 0.223495i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.70832 | −0.00244046 | ||||||||
\(701\) | 963.347i | 1.37425i | 0.726541 | + | 0.687123i | \(0.241127\pi\) | ||||
−0.726541 | + | 0.687123i | \(0.758873\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 226.186 | 0.321744 | ||||||||
\(704\) | − 715.338i | − 1.01611i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −993.212 | −1.40682 | ||||||||
\(707\) | − 325.565i | − 0.460487i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −235.904 | −0.332728 | −0.166364 | − | 0.986064i | \(-0.553203\pi\) | ||||
−0.166364 | + | 0.986064i | \(0.553203\pi\) | |||||||
\(710\) | − 1281.85i | − 1.80542i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 37.9941 | 0.0533625 | ||||||||
\(713\) | 659.706i | 0.925253i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2581.30 | 3.61021 | ||||||||
\(716\) | − 7.75081i | − 0.0108252i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1269.65 | −1.76832 | ||||||||
\(719\) | − 87.8999i | − 0.122253i | −0.998130 | − | 0.0611265i | \(-0.980531\pi\) | ||||
0.998130 | − | 0.0611265i | \(-0.0194693\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −109.998 | −0.152564 | ||||||||
\(722\) | − 752.438i | − 1.04216i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −56.4974 | −0.0780351 | ||||||||
\(725\) | − 9.51868i | − 0.0131292i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −878.296 | −1.20811 | −0.604055 | − | 0.796942i | \(-0.706449\pi\) | ||||
−0.604055 | + | 0.796942i | \(0.706449\pi\) | |||||||
\(728\) | 438.319i | 0.602086i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −288.040 | −0.394575 | ||||||||
\(731\) | − 353.586i | − 0.483702i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 162.061 | 0.221093 | 0.110547 | − | 0.993871i | \(-0.464740\pi\) | ||||
0.110547 | + | 0.993871i | \(0.464740\pi\) | |||||||
\(734\) | − 1230.78i | − 1.67681i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −267.519 | −0.363477 | ||||||||
\(737\) | − 1690.46i | − 2.29370i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.1893 | 0.0570897 | 0.0285449 | − | 0.999593i | \(-0.490913\pi\) | ||||
0.0285449 | + | 0.999593i | \(0.490913\pi\) | |||||||
\(740\) | 239.879i | 0.324161i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −38.8987 | −0.0524242 | ||||||||
\(743\) | 720.211i | 0.969328i | 0.874700 | + | 0.484664i | \(0.161058\pi\) | ||||
−0.874700 | + | 0.484664i | \(0.838942\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1029.45 | −1.38182 | ||||||||
\(746\) | − 297.142i | − 0.398313i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 158.194 | 0.211489 | ||||||||
\(749\) | 6.69534i | 0.00893904i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1309.52 | 1.74370 | 0.871850 | − | 0.489773i | \(-0.162920\pi\) | ||||
0.871850 | + | 0.489773i | \(0.162920\pi\) | |||||||
\(752\) | 538.638i | 0.716274i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1029.65 | 1.36558 | ||||||||
\(755\) | − 384.622i | − 0.509433i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −695.235 | −0.918409 | −0.459204 | − | 0.888331i | \(-0.651865\pi\) | ||||
−0.459204 | + | 0.888331i | \(0.651865\pi\) | |||||||
\(758\) | − 786.083i | − 1.03705i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 175.284 | 0.230637 | ||||||||
\(761\) | 1060.27i | 1.39325i | 0.717434 | + | 0.696626i | \(0.245316\pi\) | ||||
−0.717434 | + | 0.696626i | \(0.754684\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −74.0169 | −0.0970077 | ||||||||
\(764\) | − 70.9045i | − 0.0928070i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −240.322 | −0.313736 | ||||||||
\(767\) | 1106.68i | 1.44287i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1255.65 | −1.63283 | −0.816415 | − | 0.577466i | \(-0.804042\pi\) | ||||
−0.816415 | + | 0.577466i | \(0.804042\pi\) | |||||||
\(770\) | 601.568i | 0.781258i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 211.794 | 0.274344 | ||||||||
\(773\) | 1182.69i | 1.53000i | 0.644033 | + | 0.764998i | \(0.277260\pi\) | ||||
−0.644033 | + | 0.764998i | \(0.722740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.7075 | −0.0318806 | ||||||||
\(776\) | − 605.465i | − 0.780239i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1135.50 | 1.45952 | ||||||||
\(779\) | − 168.207i | − 0.215927i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2297.95 | 2.94231 | ||||||||
\(782\) | 218.618i | 0.279562i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −135.365 | −0.172659 | ||||||||
\(785\) | − 562.211i | − 0.716192i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 630.329 | 0.800927 | 0.400463 | − | 0.916313i | \(-0.368849\pi\) | ||||
0.400463 | + | 0.916313i | \(0.368849\pi\) | |||||||
\(788\) | 81.9043i | 0.103939i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 922.297 | 1.16746 | ||||||||
\(791\) | 485.518i | 0.613803i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 920.354 | 1.16060 | ||||||||
\(794\) | 272.135i | 0.342739i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −428.215 | −0.537958 | ||||||||
\(797\) | 273.631i | 0.343326i | 0.985156 | + | 0.171663i | \(0.0549140\pi\) | ||||
−0.985156 | + | 0.171663i | \(0.945086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 183.985 | 0.230269 | ||||||||
\(800\) | − 10.0192i | − 0.0125240i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1371.68 | 1.71032 | ||||||||
\(803\) | − 516.363i | − 0.643042i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −190.154 | −0.236216 | ||||||||
\(806\) | − 2672.64i | − 3.31593i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 788.497 | 0.975863 | ||||||||
\(809\) | 182.061i | 0.225044i | 0.993649 | + | 0.112522i | \(0.0358929\pi\) | ||||
−0.993649 | + | 0.112522i | \(0.964107\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 98.8163 | 0.121845 | 0.0609225 | − | 0.998142i | \(-0.480596\pi\) | ||||
0.0609225 | + | 0.998142i | \(0.480596\pi\) | |||||||
\(812\) | 54.8857i | 0.0675932i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1880.06 | −2.30965 | ||||||||
\(815\) | 707.933i | 0.868630i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −296.103 | −0.362427 | ||||||||
\(818\) | − 870.372i | − 1.06402i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 178.390 | 0.217548 | ||||||||
\(821\) | − 566.107i | − 0.689534i | −0.938688 | − | 0.344767i | \(-0.887958\pi\) | ||||
0.938688 | − | 0.344767i | \(-0.112042\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 452.893 | 0.550296 | 0.275148 | − | 0.961402i | \(-0.411273\pi\) | ||||
0.275148 | + | 0.961402i | \(0.411273\pi\) | |||||||
\(824\) | − 266.409i | − 0.323312i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −257.911 | −0.312241 | ||||||||
\(827\) | − 1268.79i | − 1.53421i | −0.641521 | − | 0.767105i | \(-0.721696\pi\) | ||||
0.641521 | − | 0.767105i | \(-0.278304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1017.98 | 1.22797 | 0.613983 | − | 0.789319i | \(-0.289566\pi\) | ||||
0.613983 | + | 0.789319i | \(0.289566\pi\) | |||||||
\(830\) | − 324.180i | − 0.390578i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −916.054 | −1.10103 | ||||||||
\(833\) | 46.2372i | 0.0555068i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1032.06 | −1.23600 | ||||||||
\(836\) | − 132.476i | − 0.158464i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 231.501 | 0.276255 | ||||||||
\(839\) | − 1175.45i | − 1.40101i | −0.713646 | − | 0.700507i | \(-0.752957\pi\) | ||||
0.713646 | − | 0.700507i | \(-0.247043\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 535.180 | 0.636361 | ||||||||
\(842\) | − 970.082i | − 1.15212i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 53.4414 | 0.0633192 | ||||||||
\(845\) | − 2469.83i | − 2.92287i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −758.283 | −0.895257 | ||||||||
\(848\) | − 124.844i | − 0.147221i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.18774 | −0.00963263 | ||||||||
\(851\) | − 594.279i | − 0.698331i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1058.27 | 1.24065 | 0.620323 | − | 0.784346i | \(-0.287001\pi\) | ||||
0.620323 | + | 0.784346i | \(0.287001\pi\) | |||||||
\(854\) | 214.487i | 0.251156i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.2157 | −0.0189436 | ||||||||
\(857\) | 1392.71i | 1.62510i | 0.582888 | + | 0.812552i | \(0.301923\pi\) | ||||
−0.582888 | + | 0.812552i | \(0.698077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −748.263 | −0.871086 | −0.435543 | − | 0.900168i | \(-0.643444\pi\) | ||||
−0.435543 | + | 0.900168i | \(0.643444\pi\) | |||||||
\(860\) | − 314.028i | − 0.365149i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −583.714 | −0.677163 | ||||||||
\(863\) | 908.810i | 1.05308i | 0.850150 | + | 0.526541i | \(0.176511\pi\) | ||||
−0.850150 | + | 0.526541i | \(0.823489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −817.829 | −0.945467 | ||||||||
\(866\) | 1111.29i | 1.28325i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 142.466 | 0.164131 | ||||||||
\(869\) | 1653.38i | 1.90263i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2164.78 | −2.48540 | ||||||||
\(872\) | − 179.264i | − 0.205578i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 183.077 | 0.209470 | ||||||||
\(875\) | − 334.221i | − 0.381966i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −587.685 | −0.670108 | −0.335054 | − | 0.942199i | \(-0.608755\pi\) | ||||
−0.335054 | + | 0.942199i | \(0.608755\pi\) | |||||||
\(878\) | − 804.631i | − 0.916437i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1930.71 | −2.19399 | ||||||||
\(881\) | 1218.08i | 1.38261i | 0.722565 | + | 0.691303i | \(0.242963\pi\) | ||||
−0.722565 | + | 0.691303i | \(0.757037\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −635.067 | −0.719215 | −0.359607 | − | 0.933104i | \(-0.617089\pi\) | ||||
−0.359607 | + | 0.933104i | \(0.617089\pi\) | |||||||
\(884\) | − 202.581i | − 0.229164i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −33.0356 | −0.0372862 | ||||||||
\(887\) | 603.102i | 0.679935i | 0.940437 | + | 0.339967i | \(0.110416\pi\) | ||||
−0.940437 | + | 0.339967i | \(0.889584\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −311.072 | −0.349912 | ||||||||
\(890\) | − 66.7760i | − 0.0750293i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 220.412 | 0.247099 | ||||||||
\(893\) | − 154.074i | − 0.172536i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.3117 | 0.0361025 | ||||||||
\(896\) | − 408.290i | − 0.455680i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1932.08 | −2.15154 | ||||||||
\(899\) | 793.812i | 0.882995i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.6435 | −0.0473291 | ||||||||
\(902\) | 1398.13i | 1.55004i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1175.89 | −1.30077 | ||||||||
\(905\) | − 235.527i | − 0.260251i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 275.919 | 0.304210 | 0.152105 | − | 0.988364i | \(-0.451395\pi\) | ||||
0.152105 | + | 0.988364i | \(0.451395\pi\) | |||||||
\(908\) | 236.111i | 0.260035i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 770.362 | 0.846551 | ||||||||
\(911\) | − 515.110i | − 0.565434i | −0.959203 | − | 0.282717i | \(-0.908764\pi\) | ||||
0.959203 | − | 0.282717i | \(-0.0912357\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 581.151 | 0.636529 | ||||||||
\(914\) | 377.317i | 0.412819i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 381.067 | 0.416012 | ||||||||
\(917\) | 464.177i | 0.506191i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −245.344 | −0.266968 | −0.133484 | − | 0.991051i | \(-0.542616\pi\) | ||||
−0.133484 | + | 0.991051i | \(0.542616\pi\) | |||||||
\(920\) | − 460.540i | − 0.500587i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1788.20 | 1.93948 | ||||||||
\(923\) | − 2942.73i | − 3.18822i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.2571 | 0.0240618 | ||||||||
\(926\) | − 1309.49i | − 1.41413i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −321.901 | −0.346876 | ||||||||
\(929\) | 903.534i | 0.972587i | 0.873795 | + | 0.486294i | \(0.161651\pi\) | ||||
−0.873795 | + | 0.486294i | \(0.838349\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.7203 | 0.0415900 | ||||||||
\(932\) | 255.472i | 0.274112i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1762.35 | 1.88689 | ||||||||
\(935\) | 659.481i | 0.705328i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1413.35 | −1.50837 | −0.754187 | − | 0.656660i | \(-0.771969\pi\) | ||||
−0.754187 | + | 0.656660i | \(0.771969\pi\) | |||||||
\(938\) | − 504.500i | − 0.537847i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 163.402 | 0.173832 | ||||||||
\(941\) | − 581.423i | − 0.617878i | −0.951082 | − | 0.308939i | \(-0.900026\pi\) | ||||
0.951082 | − | 0.308939i | \(-0.0999739\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −441.945 | −0.468659 | ||||||||
\(944\) | − 827.755i | − 0.876859i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2461.20 | 2.60170 | ||||||||
\(947\) | − 957.202i | − 1.01077i | −0.862893 | − | 0.505386i | \(-0.831350\pi\) | ||||
0.862893 | − | 0.505386i | \(-0.168650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −661.248 | −0.696784 | ||||||||
\(950\) | 6.85664i | 0.00721752i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −111.984 | −0.117630 | ||||||||
\(953\) | 1060.55i | 1.11285i | 0.830898 | + | 0.556425i | \(0.187827\pi\) | ||||
−0.830898 | + | 0.556425i | \(0.812173\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 295.588 | 0.309517 | ||||||||
\(956\) | − 196.104i | − 0.205130i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1115.59 | 1.16450 | ||||||||
\(959\) | − 9.86048i | − 0.0102820i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1099.49 | 1.14411 | ||||||||
\(962\) | 2407.58i | 2.50268i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −298.147 | −0.309282 | ||||||||
\(965\) | 882.930i | 0.914953i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1651.29 | −1.70764 | −0.853821 | − | 0.520567i | \(-0.825720\pi\) | ||||
−0.853821 | + | 0.520567i | \(0.825720\pi\) | |||||||
\(968\) | − 1836.51i | − 1.89723i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1064.13 | −1.09704 | ||||||||
\(971\) | 1166.15i | 1.20098i | 0.799633 | + | 0.600490i | \(0.205028\pi\) | ||||
−0.799633 | + | 0.600490i | \(0.794972\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 313.389 | 0.322086 | ||||||||
\(974\) | 1709.46i | 1.75509i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −688.388 | −0.705316 | ||||||||
\(977\) | 11.4573i | 0.0117271i | 0.999983 | + | 0.00586353i | \(0.00186643\pi\) | ||||
−0.999983 | + | 0.00586353i | \(0.998134\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 119.708 | 0.122276 | ||||||||
\(980\) | 41.0643i | 0.0419024i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −352.048 | −0.358501 | ||||||||
\(983\) | 1270.31i | 1.29228i | 0.763221 | + | 0.646138i | \(0.223617\pi\) | ||||
−0.763221 | + | 0.646138i | \(0.776383\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −341.444 | −0.346644 | ||||||||
\(986\) | 263.059i | 0.266794i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −169.647 | −0.171708 | ||||||||
\(989\) | 777.977i | 0.786630i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 107.860 | 0.108839 | 0.0544196 | − | 0.998518i | \(-0.482669\pi\) | ||||
0.0544196 | + | 0.998518i | \(0.482669\pi\) | |||||||
\(992\) | 835.554i | 0.842292i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 685.799 | 0.689939 | ||||||||
\(995\) | − 1785.15i | − 1.79412i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −208.773 | −0.209402 | −0.104701 | − | 0.994504i | \(-0.533388\pi\) | ||||
−0.104701 | + | 0.994504i | \(0.533388\pi\) | |||||||
\(998\) | − 328.954i | − 0.329613i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 189.3.b.c.134.7 | yes | 8 | |
3.2 | odd | 2 | inner | 189.3.b.c.134.2 | ✓ | 8 | |
4.3 | odd | 2 | 3024.3.d.j.1457.3 | 8 | |||
9.2 | odd | 6 | 567.3.r.e.134.2 | 16 | |||
9.4 | even | 3 | 567.3.r.e.512.2 | 16 | |||
9.5 | odd | 6 | 567.3.r.e.512.7 | 16 | |||
9.7 | even | 3 | 567.3.r.e.134.7 | 16 | |||
12.11 | even | 2 | 3024.3.d.j.1457.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.3.b.c.134.2 | ✓ | 8 | 3.2 | odd | 2 | inner | |
189.3.b.c.134.7 | yes | 8 | 1.1 | even | 1 | trivial | |
567.3.r.e.134.2 | 16 | 9.2 | odd | 6 | |||
567.3.r.e.134.7 | 16 | 9.7 | even | 3 | |||
567.3.r.e.512.2 | 16 | 9.4 | even | 3 | |||
567.3.r.e.512.7 | 16 | 9.5 | odd | 6 | |||
3024.3.d.j.1457.3 | 8 | 4.3 | odd | 2 | |||
3024.3.d.j.1457.6 | 8 | 12.11 | even | 2 |