Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.c (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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.79010463744.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 6x^{6} - 44x^{5} + 108x^{3} + 538x^{2} + 360x + 825 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.2 | ||
Root | \(-0.0586074 - 1.30099i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.i.604.8 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.11962i | − 1.55981i | −0.625897 | − | 0.779906i | \(-0.715267\pi\) | ||||
0.625897 | − | 0.779906i | \(-0.284733\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.73205 | −1.43301 | ||||||||
\(5\) | 6.02665 | 1.20533 | 0.602665 | − | 0.797994i | \(-0.294106\pi\) | ||||
0.602665 | + | 0.797994i | \(0.294106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.07107i | 1.01015i | 0.863075 | + | 0.505076i | \(0.168536\pi\) | ||||
−0.863075 | + | 0.505076i | \(0.831464\pi\) | |||||||
\(8\) | 5.40335i | 0.675418i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 18.8009i | − 1.88009i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.7303i | 1.28695i | 0.765468 | + | 0.643474i | \(0.222508\pi\) | ||||
−0.765468 | + | 0.643474i | \(0.777492\pi\) | |||||||
\(14\) | 22.0591 | 1.57565 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.07180 | −0.379487 | ||||||||
\(17\) | − 30.9723i | − 1.82190i | −0.412520 | − | 0.910949i | \(-0.635351\pi\) | ||||
0.412520 | − | 0.910949i | \(-0.364649\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.9802i | 1.73580i | 0.496740 | + | 0.867899i | \(0.334530\pi\) | ||||
−0.496740 | + | 0.867899i | \(0.665470\pi\) | |||||||
\(20\) | −34.5451 | −1.72725 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.54643 | 0.154192 | 0.0770962 | − | 0.997024i | \(-0.475435\pi\) | ||||
0.0770962 | + | 0.997024i | \(0.475435\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.3205 | 0.452820 | ||||||||
\(26\) | 52.1923 | 2.00740 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 40.5317i | − 1.44756i | ||||||||
\(29\) | − 4.17950i | − 0.144121i | −0.997400 | − | 0.0720604i | \(-0.977043\pi\) | ||||
0.997400 | − | 0.0720604i | \(-0.0229574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.0000 | 1.09677 | 0.548387 | − | 0.836225i | \(-0.315242\pi\) | ||||
0.548387 | + | 0.836225i | \(0.315242\pi\) | |||||||
\(32\) | 40.5551i | 1.26735i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −96.6218 | −2.84182 | ||||||||
\(35\) | 42.6148i | 1.21757i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 28.6603 | 0.774601 | 0.387301 | − | 0.921953i | \(-0.373408\pi\) | ||||
0.387301 | + | 0.921953i | \(0.373408\pi\) | |||||||
\(38\) | 102.886 | 2.70752 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 32.5641i | 0.814102i | ||||||||
\(41\) | 81.0502i | 1.97683i | 0.151762 | + | 0.988417i | \(0.451505\pi\) | ||||
−0.151762 | + | 0.988417i | \(0.548495\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 36.7423i | − 0.854473i | −0.904140 | − | 0.427237i | \(-0.859487\pi\) | ||||
0.904140 | − | 0.427237i | \(-0.140513\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 11.0635i | − 0.240511i | ||||||||
\(47\) | 52.0764 | 1.10801 | 0.554004 | − | 0.832514i | \(-0.313099\pi\) | ||||
0.554004 | + | 0.832514i | \(0.313099\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.0204082 | ||||||||
\(50\) | − 35.3157i | − 0.706314i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 95.8991i | − 1.84421i | ||||||||
\(53\) | 32.1808 | 0.607185 | 0.303592 | − | 0.952802i | \(-0.401814\pi\) | ||||
0.303592 | + | 0.952802i | \(0.401814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −38.2074 | −0.682276 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13.0385 | −0.224801 | ||||||||
\(59\) | 5.91071 | 0.100182 | 0.0500908 | − | 0.998745i | \(-0.484049\pi\) | ||||
0.0500908 | + | 0.998745i | \(0.484049\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35.0235i | 0.574156i | 0.957907 | + | 0.287078i | \(0.0926839\pi\) | ||||
−0.957907 | + | 0.287078i | \(0.907316\pi\) | |||||||
\(62\) | − 106.067i | − 1.71076i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 102.229 | 1.59734 | ||||||||
\(65\) | 100.828i | 1.55120i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 90.9808 | 1.35792 | 0.678961 | − | 0.734174i | \(-0.262431\pi\) | ||||
0.678961 | + | 0.734174i | \(0.262431\pi\) | |||||||
\(68\) | 177.535i | 2.61080i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 132.942 | 1.89918 | ||||||||
\(71\) | 98.4739 | 1.38696 | 0.693478 | − | 0.720477i | \(-0.256077\pi\) | ||||
0.693478 | + | 0.720477i | \(0.256077\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 47.0951i | 0.645138i | 0.946546 | + | 0.322569i | \(0.104547\pi\) | ||||
−0.946546 | + | 0.322569i | \(0.895453\pi\) | |||||||
\(74\) | − 89.4092i | − 1.20823i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 189.044i | − 2.48742i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 27.1203i | 0.343294i | 0.985158 | + | 0.171647i | \(0.0549089\pi\) | ||||
−0.985158 | + | 0.171647i | \(0.945091\pi\) | |||||||
\(80\) | −36.5926 | −0.457407 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 252.846 | 3.08349 | ||||||||
\(83\) | − 11.2547i | − 0.135598i | −0.997699 | − | 0.0677991i | \(-0.978402\pi\) | ||||
0.997699 | − | 0.0677991i | \(-0.0215977\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 186.659i | − 2.19599i | ||||||||
\(86\) | −114.622 | −1.33282 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −62.4300 | −0.701460 | −0.350730 | − | 0.936477i | \(-0.614067\pi\) | ||||
−0.350730 | + | 0.936477i | \(0.614067\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −118.301 | −1.30001 | ||||||||
\(92\) | −20.3283 | −0.220960 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 162.459i | − 1.72828i | ||||||||
\(95\) | 198.760i | 2.09221i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −110.622 | −1.14043 | −0.570215 | − | 0.821495i | \(-0.693140\pi\) | ||||
−0.570215 | + | 0.821495i | \(0.693140\pi\) | |||||||
\(98\) | 3.11962i | 0.0318329i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −64.8897 | −0.648897 | ||||||||
\(101\) | − 96.6483i | − 0.956914i | −0.878111 | − | 0.478457i | \(-0.841196\pi\) | ||||
0.878111 | − | 0.478457i | \(-0.158804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 57.5833 | 0.559061 | 0.279531 | − | 0.960137i | \(-0.409821\pi\) | ||||
0.279531 | + | 0.960137i | \(0.409821\pi\) | |||||||
\(104\) | −90.3997 | −0.869228 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 100.392i | − 0.947094i | ||||||||
\(107\) | 120.829i | 1.12925i | 0.825349 | + | 0.564623i | \(0.190979\pi\) | ||||
−0.825349 | + | 0.564623i | \(0.809021\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 22.8949i | 0.210045i | 0.994470 | + | 0.105022i | \(0.0334914\pi\) | ||||
−0.994470 | + | 0.105022i | \(0.966509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 42.9341i | − 0.383340i | ||||||||
\(113\) | −54.5566 | −0.482802 | −0.241401 | − | 0.970425i | \(-0.577607\pi\) | ||||
−0.241401 | + | 0.970425i | \(0.577607\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.3731 | 0.185853 | ||||||||
\(116\) | 23.9571i | 0.206527i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 18.4392i | − 0.156264i | ||||||||
\(119\) | 219.007 | 1.84039 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 109.260 | 0.895575 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −194.890 | −1.57169 | ||||||||
\(125\) | −82.4415 | −0.659532 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 156.950i | − 1.23583i | −0.786245 | − | 0.617915i | \(-0.787977\pi\) | ||||
0.786245 | − | 0.617915i | \(-0.212023\pi\) | |||||||
\(128\) | − 156.697i | − 1.22420i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 314.545 | 2.41958 | ||||||||
\(131\) | − 167.400i | − 1.27786i | −0.769264 | − | 0.638930i | \(-0.779377\pi\) | ||||
0.769264 | − | 0.638930i | \(-0.220623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −233.205 | −1.75342 | ||||||||
\(134\) | − 283.826i | − 2.11810i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 167.354 | 1.23054 | ||||||||
\(137\) | −132.818 | −0.969476 | −0.484738 | − | 0.874659i | \(-0.661085\pi\) | ||||
−0.484738 | + | 0.874659i | \(0.661085\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 52.1228i | 0.374984i | 0.982266 | + | 0.187492i | \(0.0600359\pi\) | ||||
−0.982266 | + | 0.187492i | \(0.939964\pi\) | |||||||
\(140\) | − 244.270i | − 1.74479i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 307.202i | − 2.16339i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 25.1884i | − 0.173713i | ||||||||
\(146\) | 146.919 | 1.00629 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −164.282 | −1.11001 | ||||||||
\(149\) | 75.7508i | 0.508395i | 0.967152 | + | 0.254197i | \(0.0818113\pi\) | ||||
−0.967152 | + | 0.254197i | \(0.918189\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 90.7127i | 0.600747i | 0.953822 | + | 0.300373i | \(0.0971113\pi\) | ||||
−0.953822 | + | 0.300373i | \(0.902889\pi\) | |||||||
\(152\) | −178.203 | −1.17239 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 204.906 | 1.32197 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 140.526 | 0.895067 | 0.447534 | − | 0.894267i | \(-0.352302\pi\) | ||||
0.447534 | + | 0.894267i | \(0.352302\pi\) | |||||||
\(158\) | 84.6050 | 0.535475 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 244.411i | 1.52757i | ||||||||
\(161\) | 25.0770i | 0.155758i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −34.9038 | −0.214134 | −0.107067 | − | 0.994252i | \(-0.534146\pi\) | ||||
−0.107067 | + | 0.994252i | \(0.534146\pi\) | |||||||
\(164\) | − 464.584i | − 2.83283i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −35.1103 | −0.211508 | ||||||||
\(167\) | − 220.089i | − 1.31790i | −0.752187 | − | 0.658950i | \(-0.771001\pi\) | ||||
0.752187 | − | 0.658950i | \(-0.228999\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −110.904 | −0.656236 | ||||||||
\(170\) | −582.306 | −3.42533 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 210.609i | 1.22447i | ||||||||
\(173\) | 116.262i | 0.672035i | 0.941856 | + | 0.336017i | \(0.109080\pi\) | ||||
−0.941856 | + | 0.336017i | \(0.890920\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 80.0481i | 0.457418i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 194.758i | 1.09415i | ||||||||
\(179\) | −336.797 | −1.88155 | −0.940773 | − | 0.339037i | \(-0.889899\pi\) | ||||
−0.940773 | + | 0.339037i | \(0.889899\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −108.660 | −0.600333 | −0.300166 | − | 0.953887i | \(-0.597042\pi\) | ||||
−0.300166 | + | 0.953887i | \(0.597042\pi\) | |||||||
\(182\) | 369.055i | 2.02778i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 19.1626i | 0.104144i | ||||||||
\(185\) | 172.725 | 0.933650 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −298.504 | −1.58779 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 620.056 | 3.26345 | ||||||||
\(191\) | −120.533 | −0.631063 | −0.315531 | − | 0.948915i | \(-0.602183\pi\) | ||||
−0.315531 | + | 0.948915i | \(0.602183\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 215.971i | − 1.11902i | −0.828823 | − | 0.559511i | \(-0.810989\pi\) | ||||
0.828823 | − | 0.559511i | \(-0.189011\pi\) | |||||||
\(194\) | 345.098i | 1.77886i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.73205 | 0.0292452 | ||||||||
\(197\) | 243.315i | 1.23510i | 0.786532 | + | 0.617550i | \(0.211875\pi\) | ||||
−0.786532 | + | 0.617550i | \(0.788125\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.02439 | 0.0101728 | 0.00508641 | − | 0.999987i | \(-0.498381\pi\) | ||||
0.00508641 | + | 0.999987i | \(0.498381\pi\) | |||||||
\(200\) | 61.1686i | 0.305843i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −301.506 | −1.49261 | ||||||||
\(203\) | 29.5535 | 0.145584 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 488.461i | 2.38274i | ||||||||
\(206\) | − 179.638i | − 0.872030i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 101.583i | − 0.488380i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 247.636i | 1.17363i | 0.809721 | + | 0.586815i | \(0.199619\pi\) | ||||
−0.809721 | + | 0.586815i | \(0.800381\pi\) | |||||||
\(212\) | −184.462 | −0.870103 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 376.942 | 1.76141 | ||||||||
\(215\) | − 221.433i | − 1.02992i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 240.416i | 1.10791i | ||||||||
\(218\) | 71.4233 | 0.327630 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 518.176 | 2.34469 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −263.205 | −1.18029 | −0.590146 | − | 0.807297i | \(-0.700930\pi\) | ||||
−0.590146 | + | 0.807297i | \(0.700930\pi\) | |||||||
\(224\) | −286.768 | −1.28021 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 170.196i | 0.753080i | ||||||||
\(227\) | 40.6151i | 0.178921i | 0.995990 | + | 0.0894606i | \(0.0285143\pi\) | ||||
−0.995990 | + | 0.0894606i | \(0.971486\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 71.0141 | 0.310105 | 0.155053 | − | 0.987906i | \(-0.450445\pi\) | ||||
0.155053 | + | 0.987906i | \(0.450445\pi\) | |||||||
\(230\) | − 66.6759i | − 0.289895i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.5833 | 0.0973418 | ||||||||
\(233\) | − 292.125i | − 1.25375i | −0.779118 | − | 0.626877i | \(-0.784333\pi\) | ||||
0.779118 | − | 0.626877i | \(-0.215667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 313.846 | 1.33552 | ||||||||
\(236\) | −33.8805 | −0.143561 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 683.219i | − 2.87067i | ||||||||
\(239\) | − 343.159i | − 1.43581i | −0.696141 | − | 0.717905i | \(-0.745101\pi\) | ||||
0.696141 | − | 0.717905i | \(-0.254899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 305.294i | 1.26678i | 0.773832 | + | 0.633391i | \(0.218337\pi\) | ||||
−0.773832 | + | 0.633391i | \(0.781663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 200.757i | − 0.822773i | ||||||||
\(245\) | −6.02665 | −0.0245986 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −551.769 | −2.23388 | ||||||||
\(248\) | 183.714i | 0.740781i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 257.186i | 1.02875i | ||||||||
\(251\) | 448.251 | 1.78586 | 0.892931 | − | 0.450193i | \(-0.148645\pi\) | ||||
0.892931 | + | 0.450193i | \(0.148645\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −489.626 | −1.92766 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −79.9179 | −0.312179 | ||||||||
\(257\) | −240.865 | −0.937219 | −0.468609 | − | 0.883406i | \(-0.655245\pi\) | ||||
−0.468609 | + | 0.883406i | \(0.655245\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 202.659i | 0.782466i | ||||||||
\(260\) | − 577.950i | − 2.22289i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −522.224 | −1.99322 | ||||||||
\(263\) | 49.7939i | 0.189331i | 0.995509 | + | 0.0946653i | \(0.0301781\pi\) | ||||
−0.995509 | + | 0.0946653i | \(0.969822\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 193.942 | 0.731858 | ||||||||
\(266\) | 727.512i | 2.73501i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −521.506 | −1.94592 | ||||||||
\(269\) | 241.646 | 0.898311 | 0.449156 | − | 0.893454i | \(-0.351725\pi\) | ||||
0.449156 | + | 0.893454i | \(0.351725\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 312.338i | − 1.15254i | −0.817260 | − | 0.576270i | \(-0.804508\pi\) | ||||
0.817260 | − | 0.576270i | \(-0.195492\pi\) | |||||||
\(272\) | 188.057i | 0.691387i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 414.343i | 1.51220i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 278.088i | − 1.00393i | −0.864889 | − | 0.501963i | \(-0.832611\pi\) | ||||
0.864889 | − | 0.501963i | \(-0.167389\pi\) | |||||||
\(278\) | 162.604 | 0.584905 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −230.263 | −0.822367 | ||||||||
\(281\) | 181.878i | 0.647253i | 0.946185 | + | 0.323626i | \(0.104902\pi\) | ||||
−0.946185 | + | 0.323626i | \(0.895098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 254.422i | − 0.899019i | −0.893276 | − | 0.449510i | \(-0.851599\pi\) | ||||
0.893276 | − | 0.449510i | \(-0.148401\pi\) | |||||||
\(284\) | −564.458 | −1.98753 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −573.111 | −1.99690 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −670.281 | −2.31931 | ||||||||
\(290\) | −78.5783 | −0.270960 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 269.952i | − 0.924492i | ||||||||
\(293\) | 230.672i | 0.787277i | 0.919265 | + | 0.393638i | \(0.128784\pi\) | ||||
−0.919265 | + | 0.393638i | \(0.871216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.6218 | 0.120752 | ||||||||
\(296\) | 154.861i | 0.523180i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 236.314 | 0.793000 | ||||||||
\(299\) | 59.3329i | 0.198438i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 259.808 | 0.863148 | ||||||||
\(302\) | 282.990 | 0.937052 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 200.249i | − 0.658714i | ||||||||
\(305\) | 211.075i | 0.692048i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3.92541i | − 0.0127863i | −0.999980 | − | 0.00639317i | \(-0.997965\pi\) | ||||
0.999980 | − | 0.00639317i | \(-0.00203502\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 639.230i | − 2.06203i | ||||||||
\(311\) | 79.5824 | 0.255892 | 0.127946 | − | 0.991781i | \(-0.459162\pi\) | ||||
0.127946 | + | 0.991781i | \(0.459162\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 315.000 | 1.00639 | 0.503195 | − | 0.864173i | \(-0.332158\pi\) | ||||
0.503195 | + | 0.864173i | \(0.332158\pi\) | |||||||
\(314\) | − 438.387i | − 1.39614i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − 155.455i | − 0.491945i | ||||||||
\(317\) | −194.584 | −0.613828 | −0.306914 | − | 0.951737i | \(-0.599296\pi\) | ||||
−0.306914 | + | 0.951737i | \(0.599296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 616.101 | 1.92532 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 78.2309 | 0.242953 | ||||||||
\(323\) | 1021.47 | 3.16245 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 189.396i | 0.582756i | ||||||||
\(326\) | 108.887i | 0.334008i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −437.942 | −1.33519 | ||||||||
\(329\) | 368.236i | 1.11926i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 514.315 | 1.55382 | 0.776911 | − | 0.629610i | \(-0.216785\pi\) | ||||
0.776911 | + | 0.629610i | \(0.216785\pi\) | |||||||
\(332\) | 64.5122i | 0.194314i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −686.596 | −2.05568 | ||||||||
\(335\) | 548.309 | 1.63674 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 115.961i | 0.344098i | 0.985088 | + | 0.172049i | \(0.0550387\pi\) | ||||
−0.985088 | + | 0.172049i | \(0.944961\pi\) | |||||||
\(338\) | 345.978i | 1.02360i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1069.94i | 3.14688i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 339.411i | 0.989537i | ||||||||
\(344\) | 198.532 | 0.577127 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 362.694 | 1.04825 | ||||||||
\(347\) | − 135.144i | − 0.389463i | −0.980857 | − | 0.194732i | \(-0.937616\pi\) | ||||
0.980857 | − | 0.194732i | \(-0.0623836\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 144.902i | − 0.415191i | −0.978215 | − | 0.207595i | \(-0.933436\pi\) | ||||
0.978215 | − | 0.207595i | \(-0.0665637\pi\) | |||||||
\(350\) | 249.720 | 0.713485 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 579.562 | 1.64182 | 0.820910 | − | 0.571058i | \(-0.193467\pi\) | ||||
0.820910 | + | 0.571058i | \(0.193467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 593.468 | 1.67174 | ||||||||
\(356\) | 357.852 | 1.00520 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1050.68i | 2.93486i | ||||||||
\(359\) | − 215.314i | − 0.599761i | −0.953977 | − | 0.299880i | \(-0.903053\pi\) | ||||
0.953977 | − | 0.299880i | \(-0.0969467\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −726.692 | −2.01300 | ||||||||
\(362\) | 338.979i | 0.936406i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 678.109 | 1.86294 | ||||||||
\(365\) | 283.826i | 0.777605i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 363.468 | 0.990376 | 0.495188 | − | 0.868786i | \(-0.335099\pi\) | ||||
0.495188 | + | 0.868786i | \(0.335099\pi\) | |||||||
\(368\) | −21.5332 | −0.0585141 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 538.838i | − 1.45632i | ||||||||
\(371\) | 227.552i | 0.613349i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 159.861i | 0.428581i | 0.976770 | + | 0.214290i | \(0.0687438\pi\) | ||||
−0.976770 | + | 0.214290i | \(0.931256\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 281.387i | 0.748369i | ||||||||
\(377\) | 69.9244 | 0.185476 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −260.711 | −0.687893 | −0.343946 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343946 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(380\) | − 1139.30i | − 2.99816i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 376.018i | 0.984339i | ||||||||
\(383\) | −275.874 | −0.720298 | −0.360149 | − | 0.932895i | \(-0.617274\pi\) | ||||
−0.360149 | + | 0.932895i | \(0.617274\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −673.749 | −1.74546 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 634.090 | 1.63425 | ||||||||
\(389\) | −127.023 | −0.326538 | −0.163269 | − | 0.986582i | \(-0.552204\pi\) | ||||
−0.163269 | + | 0.986582i | \(0.552204\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 109.841i | − 0.280923i | ||||||||
\(392\) | − 5.40335i | − 0.0137840i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 759.050 | 1.92652 | ||||||||
\(395\) | 163.444i | 0.413783i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 278.731 | 0.702092 | 0.351046 | − | 0.936358i | \(-0.385826\pi\) | ||||
0.351046 | + | 0.936358i | \(0.385826\pi\) | |||||||
\(398\) | − 6.31534i | − 0.0158677i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −68.7358 | −0.171840 | ||||||||
\(401\) | 529.997 | 1.32169 | 0.660845 | − | 0.750523i | \(-0.270198\pi\) | ||||
0.660845 | + | 0.750523i | \(0.270198\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 568.831i | 1.41149i | ||||||||
\(404\) | 553.993i | 1.37127i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − 92.1959i | − 0.227084i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 614.685i | 1.50290i | 0.659791 | + | 0.751449i | \(0.270645\pi\) | ||||
−0.659791 | + | 0.751449i | \(0.729355\pi\) | |||||||
\(410\) | 1523.81 | 3.71662 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −330.070 | −0.801142 | ||||||||
\(413\) | 41.7950i | 0.101199i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 67.8278i | − 0.163441i | ||||||||
\(416\) | −678.500 | −1.63101 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −166.235 | −0.396742 | −0.198371 | − | 0.980127i | \(-0.563565\pi\) | ||||
−0.198371 | + | 0.980127i | \(0.563565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −318.808 | −0.757263 | −0.378631 | − | 0.925548i | \(-0.623605\pi\) | ||||
−0.378631 | + | 0.925548i | \(0.623605\pi\) | |||||||
\(422\) | 772.531 | 1.83064 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 173.884i | 0.410104i | ||||||||
\(425\) | − 350.622i | − 0.824992i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −247.654 | −0.579985 | ||||||||
\(428\) | − 692.600i | − 1.61823i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −690.788 | −1.60648 | ||||||||
\(431\) | − 317.262i | − 0.736106i | −0.929805 | − | 0.368053i | \(-0.880024\pi\) | ||||
0.929805 | − | 0.368053i | \(-0.119976\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −260.429 | −0.601454 | −0.300727 | − | 0.953710i | \(-0.597229\pi\) | ||||
−0.300727 | + | 0.953710i | \(0.597229\pi\) | |||||||
\(434\) | 750.008 | 1.72813 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 131.235i | − 0.300997i | ||||||||
\(437\) | 116.962i | 0.267647i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 579.867i | 1.32088i | 0.750878 | + | 0.660441i | \(0.229631\pi\) | ||||
−0.750878 | + | 0.660441i | \(0.770369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 1616.51i | − 3.65727i | ||||||||
\(443\) | −115.550 | −0.260835 | −0.130417 | − | 0.991459i | \(-0.541632\pi\) | ||||
−0.130417 | + | 0.991459i | \(0.541632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −376.244 | −0.845491 | ||||||||
\(446\) | 821.101i | 1.84103i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 722.872i | 1.61355i | ||||||||
\(449\) | −659.609 | −1.46906 | −0.734531 | − | 0.678575i | \(-0.762598\pi\) | ||||
−0.734531 | + | 0.678575i | \(0.762598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 312.721 | 0.691861 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 126.704 | 0.279083 | ||||||||
\(455\) | −712.960 | −1.56695 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 305.121i | − 0.667661i | −0.942633 | − | 0.333830i | \(-0.891659\pi\) | ||||
0.942633 | − | 0.333830i | \(-0.108341\pi\) | |||||||
\(458\) | − 221.537i | − 0.483706i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −122.512 | −0.266329 | ||||||||
\(461\) | − 43.7347i | − 0.0948693i | −0.998874 | − | 0.0474346i | \(-0.984895\pi\) | ||||
0.998874 | − | 0.0474346i | \(-0.0151046\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −602.032 | −1.30028 | −0.650142 | − | 0.759812i | \(-0.725291\pi\) | ||||
−0.650142 | + | 0.759812i | \(0.725291\pi\) | |||||||
\(464\) | 25.3771i | 0.0546920i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −911.319 | −1.95562 | ||||||||
\(467\) | −461.278 | −0.987747 | −0.493873 | − | 0.869534i | \(-0.664419\pi\) | ||||
−0.493873 | + | 0.869534i | \(0.664419\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 643.331i | 1.37171i | ||||||||
\(470\) | − 979.082i | − 2.08315i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 31.9376i | 0.0676644i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 373.352i | 0.786005i | ||||||||
\(476\) | −1255.36 | −2.63731 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1070.53 | −2.23959 | ||||||||
\(479\) | − 522.797i | − 1.09143i | −0.837970 | − | 0.545717i | \(-0.816257\pi\) | ||||
0.837970 | − | 0.545717i | \(-0.183743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 479.495i | 0.996872i | ||||||||
\(482\) | 952.403 | 1.97594 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −666.679 | −1.37460 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 222.750 | 0.457392 | 0.228696 | − | 0.973498i | \(-0.426554\pi\) | ||||
0.228696 | + | 0.973498i | \(0.426554\pi\) | |||||||
\(488\) | −189.244 | −0.387796 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.8009i | 0.0383691i | ||||||||
\(491\) | 394.952i | 0.804383i | 0.915555 | + | 0.402192i | \(0.131751\pi\) | ||||
−0.915555 | + | 0.402192i | \(0.868249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −129.449 | −0.262573 | ||||||||
\(494\) | 1721.31i | 3.48444i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −206.441 | −0.416212 | ||||||||
\(497\) | 696.316i | 1.40104i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −502.942 | −1.00790 | −0.503950 | − | 0.863733i | \(-0.668120\pi\) | ||||
−0.503950 | + | 0.863733i | \(0.668120\pi\) | |||||||
\(500\) | 472.559 | 0.945118 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 1398.38i | − 2.78561i | ||||||||
\(503\) | 51.3339i | 0.102056i | 0.998697 | + | 0.0510278i | \(0.0162497\pi\) | ||||
−0.998697 | + | 0.0510278i | \(0.983750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 582.466i | − 1.15340i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 899.648i | 1.77096i | ||||||||
\(509\) | 450.995 | 0.886041 | 0.443020 | − | 0.896512i | \(-0.353907\pi\) | ||||
0.443020 | + | 0.896512i | \(0.353907\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −333.013 | −0.651688 | ||||||||
\(512\) | − 377.474i | − 0.737255i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 751.409i | 1.46188i | ||||||||
\(515\) | 347.034 | 0.673853 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 632.219 | 1.22050 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −544.808 | −1.04771 | ||||||||
\(521\) | −10.6620 | −0.0204645 | −0.0102323 | − | 0.999948i | \(-0.503257\pi\) | ||||
−0.0102323 | + | 0.999948i | \(0.503257\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 829.309i | − 1.58568i | −0.609432 | − | 0.792839i | \(-0.708602\pi\) | ||||
0.609432 | − | 0.792839i | \(-0.291398\pi\) | |||||||
\(524\) | 959.544i | 1.83119i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 155.338 | 0.295320 | ||||||||
\(527\) | − 1053.06i | − 1.99821i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −516.423 | −0.976225 | ||||||||
\(530\) | − 605.027i | − 1.14156i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1336.74 | 2.51268 | ||||||||
\(533\) | −1356.00 | −2.54408 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 728.197i | 1.36112i | ||||||||
\(536\) | 491.601i | 0.917165i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 753.844i | − 1.40120i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 357.043i | − 0.659969i | −0.943986 | − | 0.329985i | \(-0.892956\pi\) | ||||
0.943986 | − | 0.329985i | \(-0.107044\pi\) | |||||||
\(542\) | −974.377 | −1.79774 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1256.08 | 2.30898 | ||||||||
\(545\) | 137.979i | 0.253173i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 331.461i | − 0.605961i | −0.952997 | − | 0.302981i | \(-0.902018\pi\) | ||||
0.952997 | − | 0.302981i | \(-0.0979818\pi\) | |||||||
\(548\) | 761.321 | 1.38927 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 137.841 | 0.250165 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −191.769 | −0.346780 | ||||||||
\(554\) | −867.529 | −1.56594 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 298.771i | − 0.537357i | ||||||||
\(557\) | − 499.064i | − 0.895985i | −0.894037 | − | 0.447993i | \(-0.852139\pi\) | ||||
0.894037 | − | 0.447993i | \(-0.147861\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 614.711 | 1.09966 | ||||||||
\(560\) | − 258.749i | − 0.462051i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 567.391 | 1.00959 | ||||||||
\(563\) | 902.615i | 1.60322i | 0.597845 | + | 0.801612i | \(0.296024\pi\) | ||||
−0.597845 | + | 0.801612i | \(0.703976\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −328.794 | −0.581935 | ||||||||
\(566\) | −793.702 | −1.40230 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 532.089i | 0.936776i | ||||||||
\(569\) | − 616.386i | − 1.08328i | −0.840611 | − | 0.541639i | \(-0.817804\pi\) | ||||
0.840611 | − | 0.541639i | \(-0.182196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 174.706i | 0.305965i | 0.988229 | + | 0.152983i | \(0.0488879\pi\) | ||||
−0.988229 | + | 0.152983i | \(0.951112\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1787.89i | 3.11479i | ||||||||
\(575\) | 40.1473 | 0.0698215 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 419.519 | 0.727069 | 0.363535 | − | 0.931581i | \(-0.381570\pi\) | ||||
0.363535 | + | 0.931581i | \(0.381570\pi\) | |||||||
\(578\) | 2091.02i | 3.61769i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 144.381i | 0.248933i | ||||||||
\(581\) | 79.5824 | 0.136975 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −254.471 | −0.435738 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 719.610 | 1.22800 | ||||||||
\(587\) | 460.452 | 0.784415 | 0.392208 | − | 0.919877i | \(-0.371711\pi\) | ||||
0.392208 | + | 0.919877i | \(0.371711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1121.33i | 1.90378i | ||||||||
\(590\) | − 111.127i | − 0.188350i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −174.019 | −0.293951 | ||||||||
\(593\) | − 329.636i | − 0.555879i | −0.960599 | − | 0.277940i | \(-0.910349\pi\) | ||||
0.960599 | − | 0.277940i | \(-0.0896515\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1319.88 | 2.21828 | ||||||||
\(596\) | − 434.207i | − 0.728536i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 185.096 | 0.309525 | ||||||||
\(599\) | −61.4259 | −0.102547 | −0.0512737 | − | 0.998685i | \(-0.516328\pi\) | ||||
−0.0512737 | + | 0.998685i | \(0.516328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 98.7003i | − 0.164227i | −0.996623 | − | 0.0821134i | \(-0.973833\pi\) | ||||
0.996623 | − | 0.0821134i | \(-0.0261670\pi\) | |||||||
\(602\) | − 810.502i | − 1.34635i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 519.970i | − 0.860878i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 945.864i | − 1.55826i | −0.626862 | − | 0.779130i | \(-0.715661\pi\) | ||||
0.626862 | − | 0.779130i | \(-0.284339\pi\) | |||||||
\(608\) | −1337.51 | −2.19986 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 658.473 | 1.07946 | ||||||||
\(611\) | 871.255i | 1.42595i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 140.320i | − 0.228907i | −0.993429 | − | 0.114453i | \(-0.963488\pi\) | ||||
0.993429 | − | 0.114453i | \(-0.0365116\pi\) | |||||||
\(614\) | −12.2458 | −0.0199443 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −564.302 | −0.914590 | −0.457295 | − | 0.889315i | \(-0.651182\pi\) | ||||
−0.457295 | + | 0.889315i | \(0.651182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −375.814 | −0.607131 | −0.303566 | − | 0.952811i | \(-0.598177\pi\) | ||||
−0.303566 | + | 0.952811i | \(0.598177\pi\) | |||||||
\(620\) | −1174.53 | −1.89441 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 248.267i | − 0.399143i | ||||||||
\(623\) | − 441.447i | − 0.708582i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −779.859 | −1.24777 | ||||||||
\(626\) | − 982.681i | − 1.56978i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −805.500 | −1.28264 | ||||||||
\(629\) | − 887.673i | − 1.41124i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 190.922 | 0.302570 | 0.151285 | − | 0.988490i | \(-0.451659\pi\) | ||||
0.151285 | + | 0.988490i | \(0.451659\pi\) | |||||||
\(632\) | −146.540 | −0.231867 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 607.027i | 0.957457i | ||||||||
\(635\) | − 945.886i | − 1.48958i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 16.7303i | − 0.0262642i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 944.358i | − 1.47556i | ||||||||
\(641\) | 335.793 | 0.523858 | 0.261929 | − | 0.965087i | \(-0.415641\pi\) | ||||
0.261929 | + | 0.965087i | \(0.415641\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 109.808 | 0.170774 | 0.0853870 | − | 0.996348i | \(-0.472787\pi\) | ||||
0.0853870 | + | 0.996348i | \(0.472787\pi\) | |||||||
\(644\) | − 143.743i | − 0.223203i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − 3186.60i | − 4.93282i | ||||||||
\(647\) | −393.200 | −0.607728 | −0.303864 | − | 0.952715i | \(-0.598277\pi\) | ||||
−0.303864 | + | 0.952715i | \(0.598277\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 590.844 | 0.908990 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 200.070 | 0.306856 | ||||||||
\(653\) | −187.135 | −0.286577 | −0.143288 | − | 0.989681i | \(-0.545768\pi\) | ||||
−0.143288 | + | 0.989681i | \(0.545768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1008.86i | − 1.54024i | ||||||||
\(656\) | − 492.120i | − 0.750183i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1148.76 | 1.74583 | ||||||||
\(659\) | − 353.157i | − 0.535899i | −0.963433 | − | 0.267949i | \(-0.913654\pi\) | ||||
0.963433 | − | 0.267949i | \(-0.0863460\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −580.885 | −0.878797 | −0.439398 | − | 0.898292i | \(-0.644808\pi\) | ||||
−0.439398 | + | 0.898292i | \(0.644808\pi\) | |||||||
\(662\) | − 1604.47i | − 2.42367i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 60.8128 | 0.0915855 | ||||||||
\(665\) | −1405.45 | −2.11345 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 14.8223i | − 0.0222223i | ||||||||
\(668\) | 1261.56i | 1.88857i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 1710.52i | − 2.55301i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 541.526i | 0.804644i | 0.915498 | + | 0.402322i | \(0.131797\pi\) | ||||
−0.915498 | + | 0.402322i | \(0.868203\pi\) | |||||||
\(674\) | 361.754 | 0.536727 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 635.706 | 0.940394 | ||||||||
\(677\) | 160.817i | 0.237543i | 0.992922 | + | 0.118771i | \(0.0378956\pi\) | ||||
−0.992922 | + | 0.118771i | \(0.962104\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 782.214i | − 1.15201i | ||||||||
\(680\) | 1008.58 | 1.48321 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.6486 | −0.0492659 | −0.0246329 | − | 0.999697i | \(-0.507842\pi\) | ||||
−0.0246329 | + | 0.999697i | \(0.507842\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −800.449 | −1.16854 | ||||||||
\(686\) | 1058.84 | 1.54349 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 223.092i | 0.324262i | ||||||||
\(689\) | 538.395i | 0.781415i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1000.13 | 1.44737 | 0.723686 | − | 0.690129i | \(-0.242446\pi\) | ||||
0.723686 | + | 0.690129i | \(0.242446\pi\) | |||||||
\(692\) | − 666.420i | − 0.963034i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −421.597 | −0.607489 | ||||||||
\(695\) | 314.126i | 0.451980i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2510.31 | 3.60159 | ||||||||
\(698\) | −452.038 | −0.647619 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − 458.840i | − 0.655485i | ||||||||
\(701\) | 161.581i | 0.230500i | 0.993337 | + | 0.115250i | \(0.0367669\pi\) | ||||
−0.993337 | + | 0.115250i | \(0.963233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 945.220i | 1.34455i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 1808.02i | − 2.56093i | ||||||||
\(707\) | 683.407 | 0.966629 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −646.820 | −0.912299 | −0.456150 | − | 0.889903i | \(-0.650772\pi\) | ||||
−0.456150 | + | 0.889903i | \(0.650772\pi\) | |||||||
\(710\) | − 1851.40i | − 2.60760i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 337.331i | − 0.473779i | ||||||||
\(713\) | 120.578 | 0.169114 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1930.54 | 2.69628 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −671.699 | −0.935514 | ||||||||
\(719\) | −1230.56 | −1.71148 | −0.855742 | − | 0.517403i | \(-0.826899\pi\) | ||||
−0.855742 | + | 0.517403i | \(0.826899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 407.175i | 0.564737i | ||||||||
\(722\) | 2267.01i | 3.13990i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 622.846 | 0.860285 | ||||||||
\(725\) | − 47.3141i | − 0.0652608i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 178.494 | 0.245521 | 0.122760 | − | 0.992436i | \(-0.460825\pi\) | ||||
0.122760 | + | 0.992436i | \(0.460825\pi\) | |||||||
\(728\) | − 639.223i | − 0.878053i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 885.429 | 1.21292 | ||||||||
\(731\) | −1137.99 | −1.55676 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 569.996i | − 0.777620i | −0.921318 | − | 0.388810i | \(-0.872886\pi\) | ||||
0.921318 | − | 0.388810i | \(-0.127114\pi\) | |||||||
\(734\) | − 1133.88i | − 1.54480i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 143.826i | 0.195415i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.9182i | 0.0499570i | 0.999688 | + | 0.0249785i | \(0.00795173\pi\) | ||||
−0.999688 | + | 0.0249785i | \(0.992048\pi\) | |||||||
\(740\) | −990.070 | −1.33793 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 709.878 | 0.956709 | ||||||||
\(743\) | 935.363i | 1.25890i | 0.777041 | + | 0.629450i | \(0.216720\pi\) | ||||
−0.777041 | + | 0.629450i | \(0.783280\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 456.524i | 0.612783i | ||||||||
\(746\) | 498.705 | 0.668505 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −854.393 | −1.14071 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −944.053 | −1.25706 | −0.628530 | − | 0.777785i | \(-0.716343\pi\) | ||||
−0.628530 | + | 0.777785i | \(0.716343\pi\) | |||||||
\(752\) | −316.197 | −0.420475 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 218.138i | − 0.289308i | ||||||||
\(755\) | 546.694i | 0.724098i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −228.205 | −0.301460 | −0.150730 | − | 0.988575i | \(-0.548162\pi\) | ||||
−0.150730 | + | 0.988575i | \(0.548162\pi\) | |||||||
\(758\) | 813.322i | 1.07298i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1073.97 | −1.41312 | ||||||||
\(761\) | − 438.687i | − 0.576461i | −0.957561 | − | 0.288231i | \(-0.906933\pi\) | ||||
0.957561 | − | 0.288231i | \(-0.0930670\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −161.891 | −0.212177 | ||||||||
\(764\) | 690.901 | 0.904321 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 860.623i | 1.12353i | ||||||||
\(767\) | 98.8881i | 0.128928i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 113.000i | 0.146945i | 0.997297 | + | 0.0734723i | \(0.0234080\pi\) | ||||
−0.997297 | + | 0.0734723i | \(0.976592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1237.96i | 1.60357i | ||||||||
\(773\) | −1020.56 | −1.32026 | −0.660129 | − | 0.751152i | \(-0.729498\pi\) | ||||
−0.660129 | + | 0.751152i | \(0.729498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 384.897 | 0.496642 | ||||||||
\(776\) | − 597.728i | − 0.770268i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 396.265i | 0.509338i | ||||||||
\(779\) | −2673.05 | −3.43139 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −342.662 | −0.438187 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.07180 | 0.00774464 | ||||||||
\(785\) | 846.899 | 1.07885 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 776.158i | − 0.986224i | −0.869966 | − | 0.493112i | \(-0.835859\pi\) | ||||
0.869966 | − | 0.493112i | \(-0.164141\pi\) | |||||||
\(788\) | − 1394.69i | − 1.76991i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 509.885 | 0.645424 | ||||||||
\(791\) | − 385.773i | − 0.487703i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −585.955 | −0.738909 | ||||||||
\(794\) | − 869.535i | − 1.09513i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.6039 | −0.0145778 | ||||||||
\(797\) | 1228.97 | 1.54200 | 0.770999 | − | 0.636836i | \(-0.219757\pi\) | ||||
0.770999 | + | 0.636836i | \(0.219757\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1612.92i | − 2.01868i | ||||||||
\(800\) | 459.104i | 0.573880i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 1653.39i | − 2.06159i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 151.130i | 0.187740i | ||||||||
\(806\) | 1774.54 | 2.20166 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 522.224 | 0.646317 | ||||||||
\(809\) | − 223.073i | − 0.275739i | −0.990450 | − | 0.137870i | \(-0.955975\pi\) | ||||
0.990450 | − | 0.137870i | \(-0.0440255\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 197.930i | − 0.244057i | −0.992527 | − | 0.122028i | \(-0.961060\pi\) | ||||
0.992527 | − | 0.122028i | \(-0.0389399\pi\) | |||||||
\(812\) | −169.402 | −0.208624 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −210.353 | −0.258102 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1211.77 | 1.48319 | ||||||||
\(818\) | 1917.59 | 2.34424 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 2799.88i | − 3.41449i | ||||||||
\(821\) | − 1165.08i | − 1.41910i | −0.704656 | − | 0.709549i | \(-0.748899\pi\) | ||||
0.704656 | − | 0.709549i | \(-0.251101\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −253.468 | −0.307980 | −0.153990 | − | 0.988072i | \(-0.549212\pi\) | ||||
−0.153990 | + | 0.988072i | \(0.549212\pi\) | |||||||
\(824\) | 311.143i | 0.377600i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 130.385 | 0.157851 | ||||||||
\(827\) | 816.785i | 0.987648i | 0.869562 | + | 0.493824i | \(0.164401\pi\) | ||||
−0.869562 | + | 0.493824i | \(0.835599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 522.454 | 0.630222 | 0.315111 | − | 0.949055i | \(-0.397958\pi\) | ||||
0.315111 | + | 0.949055i | \(0.397958\pi\) | |||||||
\(830\) | −211.597 | −0.254937 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1710.33i | 2.05569i | ||||||||
\(833\) | 30.9723i | 0.0371816i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1326.40i | − 1.58850i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 518.590i | 0.618843i | ||||||||
\(839\) | 1008.38 | 1.20189 | 0.600943 | − | 0.799292i | \(-0.294792\pi\) | ||||
0.600943 | + | 0.799292i | \(0.294792\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 823.532 | 0.979229 | ||||||||
\(842\) | 994.560i | 1.18119i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − 1419.46i | − 1.68183i | ||||||||
\(845\) | −668.378 | −0.790980 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −195.395 | −0.230419 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1093.81 | −1.28683 | ||||||||
\(851\) | 101.641 | 0.119438 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1379.14i | 1.61682i | 0.588623 | + | 0.808408i | \(0.299670\pi\) | ||||
−0.588623 | + | 0.808408i | \(0.700330\pi\) | |||||||
\(854\) | 772.586i | 0.904668i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −652.883 | −0.762714 | ||||||||
\(857\) | − 992.620i | − 1.15825i | −0.815239 | − | 0.579125i | \(-0.803394\pi\) | ||||
0.815239 | − | 0.579125i | \(-0.196606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −768.301 | −0.894414 | −0.447207 | − | 0.894431i | \(-0.647581\pi\) | ||||
−0.447207 | + | 0.894431i | \(0.647581\pi\) | |||||||
\(860\) | 1269.27i | 1.47589i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −989.737 | −1.14819 | ||||||||
\(863\) | 758.006 | 0.878338 | 0.439169 | − | 0.898404i | \(-0.355273\pi\) | ||||
0.439169 | + | 0.898404i | \(0.355273\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 700.670i | 0.810023i | ||||||||
\(866\) | 812.442i | 0.938154i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 1378.08i | − 1.58765i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1522.14i | 1.74757i | ||||||||
\(872\) | −123.709 | −0.141868 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 364.877 | 0.417479 | ||||||||
\(875\) | − 582.949i | − 0.666228i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1483.59i | 1.69166i | 0.533451 | + | 0.845831i | \(0.320895\pi\) | ||||
−0.533451 | + | 0.845831i | \(0.679105\pi\) | |||||||
\(878\) | 1808.97 | 2.06033 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −277.110 | −0.314540 | −0.157270 | − | 0.987556i | \(-0.550269\pi\) | ||||
−0.157270 | + | 0.987556i | \(0.550269\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1747.60 | 1.97916 | 0.989582 | − | 0.143969i | \(-0.0459865\pi\) | ||||
0.989582 | + | 0.143969i | \(0.0459865\pi\) | |||||||
\(884\) | −2970.21 | −3.35997 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 360.472i | 0.406853i | ||||||||
\(887\) | − 1682.19i | − 1.89650i | −0.317529 | − | 0.948249i | \(-0.602853\pi\) | ||||
0.317529 | − | 0.948249i | \(-0.397147\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1109.81 | 1.24838 | ||||||||
\(890\) | 1173.74i | 1.31881i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1508.70 | 1.69137 | ||||||||
\(893\) | 1717.49i | 1.92328i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2029.76 | −2.26788 | ||||||||
\(896\) | 1108.02 | 1.23662 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2057.73i | 2.29146i | ||||||||
\(899\) | − 142.103i | − 0.158068i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 996.711i | − 1.10623i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 294.788i | − 0.326093i | ||||||||
\(905\) | −654.857 | −0.723599 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1243.80 | −1.37134 | −0.685668 | − | 0.727915i | \(-0.740490\pi\) | ||||
−0.685668 | + | 0.727915i | \(0.740490\pi\) | |||||||
\(908\) | − 232.808i | − 0.256396i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2224.17i | 2.44414i | ||||||||
\(911\) | 1164.80 | 1.27860 | 0.639300 | − | 0.768958i | \(-0.279224\pi\) | ||||
0.639300 | + | 0.768958i | \(0.279224\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −951.863 | −1.04143 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −407.056 | −0.444385 | ||||||||
\(917\) | 1183.70 | 1.29083 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 853.559i | − 0.928791i | −0.885628 | − | 0.464396i | \(-0.846272\pi\) | ||||
0.885628 | − | 0.464396i | \(-0.153728\pi\) | |||||||
\(920\) | 115.486i | 0.125528i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −136.436 | −0.147978 | ||||||||
\(923\) | 1647.50i | 1.78494i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 324.449 | 0.350755 | ||||||||
\(926\) | 1878.11i | 2.02820i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 169.500 | 0.182651 | ||||||||
\(929\) | 1411.51 | 1.51939 | 0.759694 | − | 0.650281i | \(-0.225349\pi\) | ||||
0.759694 | + | 0.650281i | \(0.225349\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 32.9802i | − 0.0354245i | ||||||||
\(932\) | 1674.47i | 1.79665i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1439.01i | 1.54070i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1181.80i | − 1.26126i | −0.776085 | − | 0.630628i | \(-0.782797\pi\) | ||||
0.776085 | − | 0.630628i | \(-0.217203\pi\) | |||||||
\(938\) | 2006.95 | 2.13961 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1798.98 | −1.91381 | ||||||||
\(941\) | − 1345.84i | − 1.43022i | −0.699012 | − | 0.715110i | \(-0.746377\pi\) | ||||
0.699012 | − | 0.715110i | \(-0.253623\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 287.439i | 0.304813i | ||||||||
\(944\) | −35.8886 | −0.0380176 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1244.85 | 1.31452 | 0.657260 | − | 0.753664i | \(-0.271715\pi\) | ||||
0.657260 | + | 0.753664i | \(0.271715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −787.917 | −0.830260 | ||||||||
\(950\) | 1164.72 | 1.22602 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1183.37i | 1.24304i | ||||||||
\(953\) | − 425.793i | − 0.446792i | −0.974728 | − | 0.223396i | \(-0.928286\pi\) | ||||
0.974728 | − | 0.223396i | \(-0.0717143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −726.410 | −0.760639 | ||||||||
\(956\) | 1967.00i | 2.05753i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1630.93 | −1.70243 | ||||||||
\(959\) | − 939.166i | − 0.979318i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 195.000 | 0.202914 | ||||||||
\(962\) | 1495.85 | 1.55493 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 1749.96i | − 1.81531i | ||||||||
\(965\) | − 1301.58i | − 1.34879i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1096.76i | − 1.13419i | −0.823653 | − | 0.567093i | \(-0.808068\pi\) | ||||
0.823653 | − | 0.567093i | \(-0.191932\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2079.79i | 2.14411i | ||||||||
\(971\) | −947.691 | −0.975995 | −0.487998 | − | 0.872845i | \(-0.662273\pi\) | ||||
−0.487998 | + | 0.872845i | \(0.662273\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −368.564 | −0.378791 | ||||||||
\(974\) | − 694.896i | − 0.713445i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 212.656i | − 0.217885i | ||||||||
\(977\) | −228.201 | −0.233573 | −0.116787 | − | 0.993157i | \(-0.537259\pi\) | ||||
−0.116787 | + | 0.993157i | \(0.537259\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 34.5451 | 0.0352501 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1232.10 | 1.25469 | ||||||||
\(983\) | 1677.50 | 1.70651 | 0.853253 | − | 0.521497i | \(-0.174626\pi\) | ||||
0.853253 | + | 0.521497i | \(0.174626\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1466.37i | 1.48870i | ||||||||
\(986\) | 403.831i | 0.409565i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3162.77 | 3.20118 | ||||||||
\(989\) | − 130.304i | − 0.131753i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −122.603 | −0.123716 | −0.0618580 | − | 0.998085i | \(-0.519703\pi\) | ||||
−0.0618580 | + | 0.998085i | \(0.519703\pi\) | |||||||
\(992\) | 1378.87i | 1.38999i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2172.24 | 2.18536 | ||||||||
\(995\) | 12.2003 | 0.0122616 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1052.25i | 1.05542i | 0.849425 | + | 0.527709i | \(0.176949\pi\) | ||||
−0.849425 | + | 0.527709i | \(0.823051\pi\) | |||||||
\(998\) | 1568.99i | 1.57213i | ||||||||
\(999\) | 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 | 1089.3.c.i.604.2 | yes | 8 | |
3.2 | odd | 2 | inner | 1089.3.c.i.604.7 | yes | 8 | |
11.10 | odd | 2 | inner | 1089.3.c.i.604.8 | yes | 8 | |
33.32 | even | 2 | inner | 1089.3.c.i.604.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1089.3.c.i.604.1 | ✓ | 8 | 33.32 | even | 2 | inner | |
1089.3.c.i.604.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1089.3.c.i.604.7 | yes | 8 | 3.2 | odd | 2 | inner | |
1089.3.c.i.604.8 | yes | 8 | 11.10 | odd | 2 | inner |