Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3100,3,Mod(1301,3100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3100.1301");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3100.d (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: | \(84.4688819517\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 114 x^{18} + 5280 x^{16} + 128422 x^{14} + 1776819 x^{12} + 14249420 x^{10} + 65297060 x^{8} + \cdots + 20793600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 620) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1301.18 | ||
Root | \(4.37942i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3100.1301 |
Dual form | 3100.3.d.e.1301.3 |
$q$-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 \(\left(\mathbb{Z}/3100\mathbb{Z}\right)^\times\).
\(n\) | \(1551\) | \(1801\) | \(2977\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.37942i | 1.45981i | 0.683551 | + | 0.729903i | \(0.260435\pi\) | ||||
−0.683551 | + | 0.729903i | \(0.739565\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.17309 | 0.453299 | 0.226649 | − | 0.973976i | \(-0.427223\pi\) | ||||
0.226649 | + | 0.973976i | \(0.427223\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −10.1793 | −1.13103 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21.9048i | 1.99134i | 0.0929327 | + | 0.995672i | \(0.470376\pi\) | ||||
−0.0929327 | + | 0.995672i | \(0.529624\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 10.7062i | − | 0.823552i | −0.911285 | − | 0.411776i | \(-0.864909\pi\) | ||
0.911285 | − | 0.411776i | \(-0.135091\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 29.8794i | − | 1.75761i | −0.477177 | − | 0.878807i | \(-0.658340\pi\) | ||
0.477177 | − | 0.878807i | \(-0.341660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.6507 | 1.40267 | 0.701333 | − | 0.712834i | \(-0.252589\pi\) | ||||
0.701333 | + | 0.712834i | \(0.252589\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.8963i | 0.661728i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 9.73695i | − | 0.423346i | −0.977341 | − | 0.211673i | \(-0.932109\pi\) | ||
0.977341 | − | 0.211673i | \(-0.0678911\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.16467i | − | 0.191284i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 12.5940i | 0.434275i | 0.976141 | + | 0.217138i | \(0.0696720\pi\) | ||||
−0.976141 | + | 0.217138i | \(0.930328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −27.6074 | + | 14.1007i | −0.890562 | + | 0.454862i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −95.9302 | −2.90698 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 48.4755i | 1.31015i | 0.755564 | + | 0.655074i | \(0.227363\pi\) | ||||
−0.755564 | + | 0.655074i | \(0.772637\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 46.8868 | 1.20223 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −68.8299 | −1.67878 | −0.839390 | − | 0.543530i | \(-0.817087\pi\) | ||||
−0.839390 | + | 0.543530i | \(0.817087\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.0647i | 0.838713i | 0.907822 | + | 0.419357i | \(0.137744\pi\) | ||||
−0.907822 | + | 0.419357i | \(0.862256\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.79288 | 0.123253 | 0.0616264 | − | 0.998099i | \(-0.480371\pi\) | ||||
0.0616264 | + | 0.998099i | \(0.480371\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −38.9315 | −0.794520 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 130.855 | 2.56578 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.5038i | − | 0.217054i | −0.994094 | − | 0.108527i | \(-0.965387\pi\) | ||
0.994094 | − | 0.108527i | \(-0.0346133\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 116.714i | 2.04762i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 18.1346 | 0.307367 | 0.153683 | − | 0.988120i | \(-0.450886\pi\) | ||||
0.153683 | + | 0.988120i | \(0.450886\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 97.3036i | 1.59514i | 0.603226 | + | 0.797570i | \(0.293882\pi\) | ||||
−0.603226 | + | 0.797570i | \(0.706118\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −32.2999 | −0.512696 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −88.4233 | −1.31975 | −0.659875 | − | 0.751375i | \(-0.729391\pi\) | ||||
−0.659875 | + | 0.751375i | \(0.729391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 42.6422 | 0.618003 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 28.8155 | 0.405852 | 0.202926 | − | 0.979194i | \(-0.434955\pi\) | ||||
0.202926 | + | 0.979194i | \(0.434955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 27.2353i | − | 0.373087i | −0.982447 | − | 0.186543i | \(-0.940272\pi\) | ||
0.982447 | − | 0.186543i | \(-0.0597285\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 69.5059i | 0.902674i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 78.8596i | − | 0.998223i | −0.866538 | − | 0.499112i | \(-0.833660\pi\) | ||
0.866538 | − | 0.499112i | \(-0.166340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −68.9955 | −0.851796 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 37.4532i | 0.451243i | 0.974215 | + | 0.225621i | \(0.0724412\pi\) | ||||
−0.974215 | + | 0.225621i | \(0.927559\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −55.1543 | −0.633958 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 123.760i | 1.39056i | 0.718739 | + | 0.695280i | \(0.244720\pi\) | ||||
−0.718739 | + | 0.695280i | \(0.755280\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 33.9717i | − | 0.373315i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −61.7530 | − | 120.904i | −0.664010 | − | 1.30005i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −102.117 | −1.05275 | −0.526377 | − | 0.850251i | \(-0.676450\pi\) | ||||
−0.526377 | + | 0.850251i | \(0.676450\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 222.976i | − | 2.25228i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1447 | 0.120244 | 0.0601222 | − | 0.998191i | \(-0.480851\pi\) | ||||
0.0601222 | + | 0.998191i | \(0.480851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −137.839 | −1.33825 | −0.669124 | − | 0.743151i | \(-0.733330\pi\) | ||||
−0.669124 | + | 0.743151i | \(0.733330\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −46.3858 | −0.433512 | −0.216756 | − | 0.976226i | \(-0.569548\pi\) | ||||
−0.216756 | + | 0.976226i | \(0.569548\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 89.8462 | 0.824277 | 0.412138 | − | 0.911121i | \(-0.364782\pi\) | ||||
0.412138 | + | 0.911121i | \(0.364782\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −212.295 | −1.91256 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 81.6265 | 0.722358 | 0.361179 | − | 0.932496i | \(-0.382374\pi\) | ||||
0.361179 | + | 0.932496i | \(0.382374\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 108.981i | 0.931465i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 94.8102i | − | 0.796724i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −358.820 | −2.96545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 301.435i | − | 2.45069i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 35.2926i | − | 0.277894i | −0.990300 | − | 0.138947i | \(-0.955628\pi\) | ||
0.990300 | − | 0.138947i | \(-0.0443718\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −157.942 | −1.22436 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 143.068 | 1.09212 | 0.546060 | − | 0.837746i | \(-0.316127\pi\) | ||||
0.546060 | + | 0.837746i | \(0.316127\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 84.5649 | 0.635827 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 76.9814i | − | 0.561908i | −0.959721 | − | 0.280954i | \(-0.909349\pi\) | ||
0.959721 | − | 0.280954i | \(-0.0906508\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 41.6873i | 0.299908i | 0.988693 | + | 0.149954i | \(0.0479126\pi\) | ||||
−0.988693 | + | 0.149954i | \(0.952087\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25.3694i | 0.179925i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 234.517 | 1.63998 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 170.497i | − | 1.15985i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −220.223 | −1.47801 | −0.739003 | − | 0.673702i | \(-0.764703\pi\) | ||||
−0.739003 | + | 0.673702i | \(0.764703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 292.506i | 1.93712i | 0.248771 | + | 0.968562i | \(0.419973\pi\) | ||||
−0.248771 | + | 0.968562i | \(0.580027\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 304.152i | 1.98792i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 230.414 | 1.46760 | 0.733802 | − | 0.679363i | \(-0.237744\pi\) | ||||
0.733802 | + | 0.679363i | \(0.237744\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 50.3801 | 0.316856 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 30.8962i | − | 0.191902i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 57.3892 | 0.352081 | 0.176040 | − | 0.984383i | \(-0.443671\pi\) | ||||
0.176040 | + | 0.984383i | \(0.443671\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 220.623i | 1.32110i | 0.750783 | + | 0.660549i | \(0.229677\pi\) | ||||
−0.750783 | + | 0.660549i | \(0.770323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 54.3778 | 0.321762 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −271.285 | −1.58646 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −189.101 | −1.09307 | −0.546534 | − | 0.837437i | \(-0.684053\pi\) | ||||
−0.546534 | + | 0.837437i | \(0.684053\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 79.4192i | 0.448696i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 189.267i | 1.05736i | 0.848823 | + | 0.528678i | \(0.177312\pi\) | ||||
−0.848823 | + | 0.528678i | \(0.822688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 135.389i | − | 0.748003i | −0.927428 | − | 0.374001i | \(-0.877986\pi\) | ||
0.927428 | − | 0.374001i | \(-0.122014\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −426.133 | −2.32860 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 654.503 | 3.50002 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 16.3880i | − | 0.0867088i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 170.416 | 0.892233 | 0.446116 | − | 0.894975i | \(-0.352807\pi\) | ||||
0.446116 | + | 0.894975i | \(0.352807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −231.933 | −1.20172 | −0.600862 | − | 0.799353i | \(-0.705176\pi\) | ||||
−0.600862 | + | 0.799353i | \(0.705176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 83.3134i | 0.422911i | 0.977388 | + | 0.211455i | \(0.0678203\pi\) | ||||
−0.977388 | + | 0.211455i | \(0.932180\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 213.014i | − | 1.07042i | −0.844718 | − | 0.535212i | \(-0.820232\pi\) | ||
0.844718 | − | 0.535212i | \(-0.179768\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 387.243i | − | 1.92658i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 39.9618i | 0.196856i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 99.1154i | 0.478818i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 583.777i | 2.79319i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −190.163 | −0.901247 | −0.450623 | − | 0.892714i | \(-0.648798\pi\) | ||||
−0.450623 | + | 0.892714i | \(0.648798\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 126.195i | 0.592465i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −87.6008 | + | 44.7429i | −0.403691 | + | 0.206188i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 119.275 | 0.544634 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −319.895 | −1.44749 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 41.5786i | 0.186451i | 0.995645 | + | 0.0932256i | \(0.0297178\pi\) | ||||
−0.995645 | + | 0.0932256i | \(0.970282\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −33.4102 | −0.147182 | −0.0735908 | − | 0.997289i | \(-0.523446\pi\) | ||||
−0.0735908 | + | 0.997289i | \(0.523446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 371.589i | − | 1.62266i | −0.584589 | − | 0.811330i | \(-0.698744\pi\) | ||
0.584589 | − | 0.811330i | \(-0.301256\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −304.395 | −1.31773 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −459.007 | −1.96999 | −0.984993 | − | 0.172595i | \(-0.944785\pi\) | ||||
−0.984993 | + | 0.172595i | \(0.944785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 345.359 | 1.45721 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 202.508i | − | 0.847315i | −0.905822 | − | 0.423658i | \(-0.860746\pi\) | ||
0.905822 | − | 0.423658i | \(-0.139254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 376.370i | − | 1.56170i | −0.624718 | − | 0.780851i | \(-0.714786\pi\) | ||
0.624718 | − | 0.780851i | \(-0.285214\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 348.642i | − | 1.43474i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 285.327i | − | 1.15517i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −164.023 | −0.658727 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 270.334i | 1.07703i | 0.842616 | + | 0.538515i | \(0.181014\pi\) | ||||
−0.842616 | + | 0.538515i | \(0.818986\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 213.286 | 0.843027 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 289.963 | 1.12826 | 0.564131 | − | 0.825686i | \(-0.309211\pi\) | ||||
0.564131 | + | 0.825686i | \(0.309211\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 153.817i | 0.593889i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 128.198i | − | 0.491180i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 264.996i | 1.00759i | 0.863824 | + | 0.503794i | \(0.168063\pi\) | ||||
−0.863824 | + | 0.503794i | \(0.831937\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −541.996 | −2.02995 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 258.522i | 0.961047i | 0.876982 | + | 0.480523i | \(0.159553\pi\) | ||||
−0.876982 | + | 0.480523i | \(0.840447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 357.865i | − | 1.32053i | −0.751031 | − | 0.660267i | \(-0.770443\pi\) | ||
0.751031 | − | 0.660267i | \(-0.229557\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 148.776 | 0.544968 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 95.7194i | 0.345558i | 0.984961 | + | 0.172779i | \(0.0552746\pi\) | ||||
−0.984961 | + | 0.172779i | \(0.944725\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 281.024 | − | 143.536i | 1.00726 | − | 0.514464i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 447.854 | 1.59379 | 0.796894 | − | 0.604119i | \(-0.206475\pi\) | ||||
0.796894 | + | 0.604119i | \(0.206475\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −172.581 | −0.609825 | −0.304913 | − | 0.952380i | \(-0.598627\pi\) | ||||
−0.304913 | + | 0.952380i | \(0.598627\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −218.404 | −0.760988 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −603.781 | −2.08921 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 447.214i | − | 1.53682i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −338.816 | −1.15637 | −0.578185 | − | 0.815906i | \(-0.696239\pi\) | ||||
−0.578185 | + | 0.815906i | \(0.696239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 113.131 | 0.380912 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −104.246 | −0.348647 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 114.436i | 0.380188i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 53.1866i | 0.175533i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 193.683 | 0.630890 | 0.315445 | − | 0.948944i | \(-0.397846\pi\) | ||||
0.315445 | + | 0.948944i | \(0.397846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 603.657i | − | 1.95358i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 76.4200 | 0.245724 | 0.122862 | − | 0.992424i | \(-0.460793\pi\) | ||||
0.122862 | + | 0.992424i | \(0.460793\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 70.1981i | − | 0.224275i | −0.993693 | − | 0.112138i | \(-0.964230\pi\) | ||
0.993693 | − | 0.112138i | \(-0.0357697\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 414.973 | 1.30906 | 0.654532 | − | 0.756034i | \(-0.272866\pi\) | ||||
0.654532 | + | 0.756034i | \(0.272866\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −275.869 | −0.864792 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 203.143i | − | 0.632844i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 796.307i | − | 2.46535i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 393.474i | 1.20328i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.3813 | 0.0558703 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 191.784i | 0.579409i | 0.957116 | + | 0.289705i | \(0.0935570\pi\) | ||||
−0.957116 | + | 0.289705i | \(0.906443\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 493.447i | − | 1.48182i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 612.613i | − | 1.81784i | −0.416968 | − | 0.908921i | \(-0.636907\pi\) | ||
0.416968 | − | 0.908921i | \(-0.363093\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 357.477i | 1.05450i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −308.873 | − | 604.735i | −0.905787 | − | 1.77342i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −279.015 | −0.813454 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 145.960i | − | 0.420634i | −0.977633 | − | 0.210317i | \(-0.932550\pi\) | ||
0.977633 | − | 0.210317i | \(-0.0674497\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 480.073 | 1.37557 | 0.687784 | − | 0.725915i | \(-0.258584\pi\) | ||||
0.687784 | + | 0.725915i | \(0.258584\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −55.2939 | −0.157532 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 150.889i | − | 0.427448i | −0.976894 | − | 0.213724i | \(-0.931441\pi\) | ||
0.976894 | − | 0.213724i | \(-0.0685594\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 415.214 | 1.16306 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −271.826 | −0.757174 | −0.378587 | − | 0.925566i | \(-0.623590\pi\) | ||||
−0.378587 | + | 0.925566i | \(0.623590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 349.257 | 0.967472 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 1571.42i | − | 4.32899i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 390.547i | − | 1.06416i | −0.846694 | − | 0.532080i | \(-0.821411\pi\) | ||
0.846694 | − | 0.532080i | \(-0.178589\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 700.641 | 1.89876 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 36.5027i | − | 0.0983901i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 246.577 | 0.661064 | 0.330532 | − | 0.943795i | \(-0.392772\pi\) | ||||
0.330532 | + | 0.943795i | \(0.392772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 134.833 | 0.357648 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −533.513 | −1.40769 | −0.703843 | − | 0.710356i | \(-0.748534\pi\) | ||||
−0.703843 | + | 0.710356i | \(0.748534\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 154.561 | 0.405672 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 52.7243i | − | 0.137661i | −0.997628 | − | 0.0688307i | \(-0.978073\pi\) | ||
0.997628 | − | 0.0688307i | \(-0.0219268\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 367.113i | − | 0.948613i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 143.777i | 0.369607i | 0.982775 | + | 0.184803i | \(0.0591649\pi\) | ||||
−0.982775 | + | 0.184803i | \(0.940835\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −290.935 | −0.744079 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 626.554i | 1.59428i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −332.656 | −0.837924 | −0.418962 | − | 0.908004i | \(-0.637606\pi\) | ||||
−0.418962 | + | 0.908004i | \(0.637606\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 370.345i | 0.928184i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 33.1046i | − | 0.0825551i | −0.999148 | − | 0.0412775i | \(-0.986857\pi\) | ||
0.999148 | − | 0.0412775i | \(-0.0131428\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 150.965 | + | 295.570i | 0.374603 | + | 0.733424i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1061.85 | −2.60896 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 168.197i | − | 0.411240i | −0.978632 | − | 0.205620i | \(-0.934079\pi\) | ||
0.978632 | − | 0.205620i | \(-0.0659210\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 337.134 | 0.820277 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 57.5429 | 0.139329 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −182.566 | −0.437808 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 269.033 | 0.642084 | 0.321042 | − | 0.947065i | \(-0.395967\pi\) | ||||
0.321042 | + | 0.947065i | \(0.395967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −514.900 | −1.22304 | −0.611521 | − | 0.791228i | \(-0.709442\pi\) | ||||
−0.611521 | + | 0.791228i | \(0.709442\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −58.9675 | −0.139403 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 308.753i | 0.723075i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1027.05i | 2.39405i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 179.927 | 0.417465 | 0.208733 | − | 0.977973i | \(-0.433066\pi\) | ||||
0.208733 | + | 0.977973i | \(0.433066\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 503.365i | 1.16251i | 0.813723 | + | 0.581253i | \(0.197437\pi\) | ||||
−0.813723 | + | 0.581253i | \(0.802563\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 259.496i | − | 0.593813i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −233.370 | −0.531595 | −0.265798 | − | 0.964029i | \(-0.585635\pi\) | ||||
−0.265798 | + | 0.964029i | \(0.585635\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 396.296 | 0.898629 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −583.212 | −1.31651 | −0.658253 | − | 0.752797i | \(-0.728704\pi\) | ||||
−0.658253 | + | 0.752797i | \(0.728704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 964.448i | − | 2.15760i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 152.533i | − | 0.339717i | −0.985468 | − | 0.169859i | \(-0.945669\pi\) | ||
0.985468 | − | 0.169859i | \(-0.0543311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1507.71i | − | 3.34303i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1281.01 | −2.82783 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 417.048i | − | 0.912578i | −0.889832 | − | 0.456289i | \(-0.849178\pi\) | ||
0.889832 | − | 0.456289i | \(-0.150822\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −154.317 | −0.336204 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 85.1724i | − | 0.184756i | −0.995724 | − | 0.0923779i | \(-0.970553\pi\) | ||
0.995724 | − | 0.0923779i | \(-0.0294468\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 661.319i | 1.42834i | 0.699975 | + | 0.714168i | \(0.253195\pi\) | ||||
−0.699975 | + | 0.714168i | \(0.746805\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 866.167 | 1.85475 | 0.927374 | − | 0.374136i | \(-0.122061\pi\) | ||||
0.927374 | + | 0.374136i | \(0.122061\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −280.575 | −0.598241 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1009.08i | 2.14242i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −789.989 | −1.67017 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 117.101i | 0.245495i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 396.326 | 0.827403 | 0.413702 | − | 0.910413i | \(-0.364236\pi\) | ||||
0.413702 | + | 0.910413i | \(0.364236\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 518.987 | 1.07898 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 135.308 | 0.280140 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 400.739i | 0.822873i | 0.911438 | + | 0.411436i | \(0.134973\pi\) | ||||
−0.911438 | + | 0.411436i | \(0.865027\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 251.331i | 0.513970i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.2174i | − | 0.0452493i | −0.999744 | − | 0.0226247i | \(-0.992798\pi\) | ||
0.999744 | − | 0.0226247i | \(-0.00720227\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 376.301 | 0.763288 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 91.4342 | 0.183972 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 224.526i | 0.449953i | 0.974364 | + | 0.224976i | \(0.0722305\pi\) | ||||
−0.974364 | + | 0.224976i | \(0.927770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −966.202 | −1.92855 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −120.740 | −0.240039 | −0.120020 | − | 0.992772i | \(-0.538296\pi\) | ||||
−0.120020 | + | 0.992772i | \(0.538296\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 238.143i | 0.469710i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 763.572i | 1.50014i | 0.661357 | + | 0.750071i | \(0.269981\pi\) | ||||
−0.661357 | + | 0.750071i | \(0.730019\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 86.4202i | − | 0.169120i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 137.642i | − | 0.268308i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 126.892i | 0.245439i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 828.151i | − | 1.59567i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 444.974 | 0.854077 | 0.427038 | − | 0.904234i | \(-0.359557\pi\) | ||||
0.427038 | + | 0.904234i | \(0.359557\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 499.676i | 0.955404i | 0.878522 | + | 0.477702i | \(0.158530\pi\) | ||||
−0.878522 | + | 0.477702i | \(0.841470\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 421.322 | + | 824.894i | 0.799472 | + | 1.56526i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 434.192 | 0.820778 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −184.598 | −0.347642 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 736.906i | 1.38256i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −828.877 | −1.54353 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 852.786i | − | 1.58216i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −347.974 | −0.643206 | −0.321603 | − | 0.946875i | \(-0.604222\pi\) | ||||
−0.321603 | + | 0.946875i | \(0.604222\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 592.923 | 1.09194 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 266.288 | 0.486815 | 0.243407 | − | 0.969924i | \(-0.421735\pi\) | ||||
0.243407 | + | 0.969924i | \(0.421735\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 990.483i | − | 1.80416i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 335.638i | 0.609143i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 250.229i | − | 0.452493i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 818.119i | 1.46880i | 0.678719 | + | 0.734398i | \(0.262535\pi\) | ||||
−0.678719 | + | 0.734398i | \(0.737465\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 386.115 | 0.690724 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2866.34i | 5.10935i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −577.339 | −1.02547 | −0.512734 | − | 0.858548i | \(-0.671367\pi\) | ||||
−0.512734 | + | 0.858548i | \(0.671367\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −218.929 | −0.386118 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 552.701i | 0.971355i | 0.874138 | + | 0.485677i | \(0.161427\pi\) | ||||
−0.874138 | + | 0.485677i | \(0.838573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 221.341i | − | 0.387637i | −0.981037 | − | 0.193818i | \(-0.937913\pi\) | ||
0.981037 | − | 0.193818i | \(-0.0620872\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 746.325i | 1.30249i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 320.225 | 0.554982 | 0.277491 | − | 0.960728i | \(-0.410497\pi\) | ||||
0.277491 | + | 0.960728i | \(0.410497\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 1015.73i | − | 1.75428i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 118.842i | 0.204548i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 251.989 | 0.432228 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 506.883i | − | 0.863515i | −0.901990 | − | 0.431757i | \(-0.857894\pi\) | ||
0.901990 | − | 0.431757i | \(-0.142106\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −735.756 | + | 375.793i | −1.24916 | + | 0.638020i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −364.864 | −0.617368 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 986.747 | 1.66399 | 0.831996 | − | 0.554782i | \(-0.187198\pi\) | ||||
0.831996 | + | 0.554782i | \(0.187198\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 932.880 | 1.56261 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 746.964 | 1.24702 | 0.623509 | − | 0.781816i | \(-0.285706\pi\) | ||||
0.623509 | + | 0.781816i | \(0.285706\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 368.950i | − | 0.613893i | −0.951727 | − | 0.306946i | \(-0.900693\pi\) | ||
0.951727 | − | 0.306946i | \(-0.0993073\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 900.088 | 1.49268 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −856.570 | −1.41115 | −0.705577 | − | 0.708634i | \(-0.749312\pi\) | ||||
−0.705577 | + | 0.708634i | \(0.749312\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −175.010 | −0.287372 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 62.0196i | − | 0.101505i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 357.438i | − | 0.583097i | −0.956556 | − | 0.291548i | \(-0.905830\pi\) | ||
0.956556 | − | 0.291548i | \(-0.0941704\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 227.390 | 0.368541 | 0.184270 | − | 0.982876i | \(-0.441008\pi\) | ||||
0.184270 | + | 0.982876i | \(0.441008\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.8294i | − | 0.0223416i | −0.999938 | − | 0.0111708i | \(-0.996444\pi\) | ||
0.999938 | − | 0.0111708i | \(-0.00355585\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −50.2881 | −0.0809793 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 392.701i | 0.630339i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2556.60 | −4.07752 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1448.42 | 2.30274 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 229.859i | 0.364277i | 0.983273 | + | 0.182139i | \(0.0583019\pi\) | ||||
−0.983273 | + | 0.182139i | \(0.941698\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 832.804i | − | 1.31565i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 416.808i | 0.654329i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −293.322 | −0.459032 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 186.314i | − | 0.290662i | −0.989383 | − | 0.145331i | \(-0.953575\pi\) | ||
0.989383 | − | 0.145331i | \(-0.0464246\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 187.737i | − | 0.291971i | −0.989287 | − | 0.145985i | \(-0.953365\pi\) | ||
0.989287 | − | 0.145985i | \(-0.0466352\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 185.216i | 0.286268i | 0.989703 | + | 0.143134i | \(0.0457180\pi\) | ||||
−0.989703 | + | 0.143134i | \(0.954282\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 397.236i | 0.612073i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −195.948 | − | 383.641i | −0.300995 | − | 0.589310i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −527.549 | −0.807885 | −0.403942 | − | 0.914784i | \(-0.632360\pi\) | ||||
−0.403942 | + | 0.914784i | \(0.632360\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 277.237i | 0.421974i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3222 | −0.0156634 | −0.00783171 | − | 0.999969i | \(-0.502493\pi\) | ||||
−0.00783171 | + | 0.999969i | \(0.502493\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 480.618 | 0.727108 | 0.363554 | − | 0.931573i | \(-0.381563\pi\) | ||||
0.363554 | + | 0.931573i | \(0.381563\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1400.95i | − | 2.11305i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 122.627 | 0.183849 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −182.090 | −0.272183 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2131.41 | −3.17647 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1149.20i | − | 1.70758i | −0.520620 | − | 0.853788i | \(-0.674299\pi\) | ||
0.520620 | − | 0.853788i | \(-0.325701\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 905.301i | 1.33722i | 0.743611 | + | 0.668612i | \(0.233111\pi\) | ||||
−0.743611 | + | 0.668612i | \(0.766889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −324.027 | −0.477212 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 146.317i | − | 0.214856i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 360.313 | 0.527544 | 0.263772 | − | 0.964585i | \(-0.415033\pi\) | ||||
0.263772 | + | 0.964585i | \(0.415033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1627.34 | 2.36877 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −123.162 | −0.178755 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −258.880 | −0.374645 | −0.187323 | − | 0.982298i | \(-0.559981\pi\) | ||||
−0.187323 | + | 0.982298i | \(0.559981\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 707.522i | − | 1.02095i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2056.60i | 2.95065i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 2010.18i | − | 2.87580i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 628.260 | 0.896234 | 0.448117 | − | 0.893975i | \(-0.352095\pi\) | ||||
0.448117 | + | 0.893975i | \(0.352095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1291.90i | 1.83770i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.5362 | 0.0545066 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1407.10i | 1.98463i | 0.123751 | + | 0.992313i | \(0.460507\pi\) | ||||
−0.123751 | + | 0.992313i | \(0.539493\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 802.736i | 1.12902i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 137.298 | + | 268.812i | 0.192564 | + | 0.377016i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 886.869 | 1.23692 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 743.741i | − | 1.03441i | −0.855862 | − | 0.517205i | \(-0.826972\pi\) | ||
0.855862 | − | 0.517205i | \(-0.173028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −437.377 | −0.606626 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1648.28 | 2.27978 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1319.89 | 1.81553 | 0.907766 | − | 0.419477i | \(-0.137787\pi\) | ||||
0.907766 | + | 0.419477i | \(0.137787\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 905.890 | 1.24265 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1077.59 | 1.47413 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 266.946 | 0.364183 | 0.182091 | − | 0.983282i | \(-0.441713\pi\) | ||||
0.182091 | + | 0.983282i | \(0.441713\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1936.89i | − | 2.62808i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 714.076i | 0.966273i | 0.875545 | + | 0.483136i | \(0.160502\pi\) | ||||
−0.875545 | + | 0.483136i | \(0.839498\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1249.56 | 1.68632 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 74.8223i | − | 0.100703i | −0.998732 | − | 0.0503515i | \(-0.983966\pi\) | ||
0.998732 | − | 0.0503515i | \(-0.0160342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 381.247i | − | 0.510371i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −147.186 | −0.196511 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −131.577 | −0.175202 | −0.0876009 | − | 0.996156i | \(-0.527920\pi\) | ||||
−0.0876009 | + | 0.996156i | \(0.527920\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1183.91 | −1.57225 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 368.843i | − | 0.487244i | −0.969870 | − | 0.243622i | \(-0.921664\pi\) | ||
0.969870 | − | 0.243622i | \(-0.0783356\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 934.068i | 1.23066i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 514.706i | 0.676355i | 0.941082 | + | 0.338178i | \(0.109810\pi\) | ||||
−0.941082 | + | 0.338178i | \(0.890190\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 285.090 | 0.373644 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 194.153i | − | 0.253133i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −782.294 | −1.01729 | −0.508644 | − | 0.860977i | \(-0.669853\pi\) | ||||
−0.508644 | + | 0.860977i | \(0.669853\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1269.87i | 1.64704i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1068.37i | 1.38211i | 0.722800 | + | 0.691057i | \(0.242855\pi\) | ||||
−0.722800 | + | 0.691057i | \(0.757145\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −673.630 | −0.866962 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1834.36 | −2.35477 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 631.197i | 0.808191i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 65.0437 | 0.0830699 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 742.554i | 0.943525i | 0.881726 | + | 0.471763i | \(0.156382\pi\) | ||||
−0.881726 | + | 0.471763i | \(0.843618\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1160.53 | −1.47088 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 259.008 | 0.327444 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1041.75 | 1.31368 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1232.92i | 1.54695i | 0.633830 | + | 0.773473i | \(0.281482\pi\) | ||||
−0.633830 | + | 0.773473i | \(0.718518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 173.088i | − | 0.216631i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1259.79i | − | 1.57277i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 596.584 | 0.742944 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1132.17 | −1.40294 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 707.180i | − | 0.874141i | −0.899427 | − | 0.437071i | \(-0.856016\pi\) | ||
0.899427 | − | 0.437071i | \(-0.143984\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 198.481 | 0.244736 | 0.122368 | − | 0.992485i | \(-0.460951\pi\) | ||||
0.122368 | + | 0.992485i | \(0.460951\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1567.24 | 1.92772 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 961.147i | 1.17643i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 345.808i | 0.422232i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 372.466i | 0.453673i | 0.973933 | + | 0.226837i | \(0.0728384\pi\) | ||||
−0.973933 | + | 0.226837i | \(0.927162\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 795.950i | 0.967132i | 0.875308 | + | 0.483566i | \(0.160659\pi\) | ||||
−0.875308 | + | 0.483566i | \(0.839341\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 359.898i | 0.435185i | 0.976040 | + | 0.217592i | \(0.0698203\pi\) | ||||
−0.976040 | + | 0.217592i | \(0.930180\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 249.911i | 0.301461i | 0.988575 | + | 0.150730i | \(0.0481626\pi\) | ||||
−0.988575 | + | 0.150730i | \(0.951837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −419.195 | −0.504447 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1163.25i | 1.39646i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 72.8256 | + | 142.583i | 0.0870078 | + | 0.170350i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.73361 | 0.00206628 | 0.00103314 | − | 0.999999i | \(-0.499671\pi\) | ||||
0.00103314 | + | 0.999999i | \(0.499671\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 682.392 | 0.811405 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1961.34i | 2.32662i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1138.57 | −1.34424 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 755.802i | − | 0.890227i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 472.004 | 0.554646 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −898.359 | −1.05318 | −0.526588 | − | 0.850121i | \(-0.676529\pi\) | ||||
−0.526588 | + | 0.850121i | \(0.676529\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1426.13 | −1.66410 | −0.832048 | − | 0.554704i | \(-0.812832\pi\) | ||||
−0.832048 | + | 0.554704i | \(0.812832\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 166.412i | − | 0.193728i | −0.995298 | − | 0.0968638i | \(-0.969119\pi\) | ||
0.995298 | − | 0.0968638i | \(-0.0308811\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 956.481i | − | 1.11090i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 679.129i | − | 0.786940i | −0.919337 | − | 0.393470i | \(-0.871274\pi\) | ||
0.919337 | − | 0.393470i | \(-0.128726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2644.21i | − | 3.04984i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1727.40 | 1.98781 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 946.676i | 1.08688i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1039.48 | 1.19070 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1330.13 | −1.51668 | −0.758342 | − | 0.651857i | \(-0.773990\pi\) | ||||
−0.758342 | + | 0.651857i | \(0.773990\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1483.82i | − | 1.68808i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 372.975i | 0.423354i | 0.977340 | + | 0.211677i | \(0.0678926\pi\) | ||||
−0.977340 | + | 0.211677i | \(0.932107\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1286.13i | 1.45655i | 0.685285 | + | 0.728275i | \(0.259678\pi\) | ||||
−0.685285 | + | 0.728275i | \(0.740322\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1114.04 | −1.25596 | −0.627979 | − | 0.778230i | \(-0.716118\pi\) | ||||
−0.627979 | + | 0.778230i | \(0.716118\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 111.986i | − | 0.125969i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1511.33i | − | 1.69622i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 154.384 | 0.172882 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 456.535i | − | 0.508957i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −177.584 | − | 347.687i | −0.197535 | − | 0.386749i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −343.728 | −0.381496 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −501.165 | −0.555000 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −964.204 | −1.06307 | −0.531535 | − | 0.847036i | \(-0.678385\pi\) | ||||
−0.531535 | + | 0.847036i | \(0.678385\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −123.624 | −0.136000 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 326.462i | − | 0.358355i | −0.983817 | − | 0.179178i | \(-0.942656\pi\) | ||
0.983817 | − | 0.179178i | \(-0.0573437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −820.404 | −0.898580 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 453.967 | 0.495057 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1233.96 | −1.34272 | −0.671361 | − | 0.741130i | \(-0.734290\pi\) | ||||
−0.671361 | + | 0.741130i | \(0.734290\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 848.220i | 0.920978i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 308.504i | − | 0.334240i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1403.11 | 1.51360 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 997.308i | 1.07353i | 0.843732 | + | 0.536764i | \(0.180353\pi\) | ||||
−0.843732 | + | 0.536764i | \(0.819647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1037.55 | −1.11445 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 334.675i | 0.358709i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −788.023 | −0.841006 | −0.420503 | − | 0.907291i | \(-0.638146\pi\) | ||||
−0.420503 | + | 0.907291i | \(0.638146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 307.427 | 0.327398 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1138.15i | 1.20951i | 0.796413 | + | 0.604754i | \(0.206728\pi\) | ||||
−0.796413 | + | 0.604754i | \(0.793272\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 670.194i | 0.710704i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 339.643i | − | 0.358651i | −0.983790 | − | 0.179326i | \(-0.942608\pi\) | ||
0.983790 | − | 0.179326i | \(-0.0573916\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −291.586 | −0.307256 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1817.34i | 1.91098i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1516.62i | − | 1.59141i | −0.605682 | − | 0.795706i | \(-0.707100\pi\) | ||
0.605682 | − | 0.795706i | \(-0.292900\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1208.14i | − | 1.26243i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 244.269i | − | 0.254712i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 563.339 | − | 778.569i | 0.586201 | − | 0.810166i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 472.176 | 0.490317 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 232.357i | 0.240286i | 0.992757 | + | 0.120143i | \(0.0383354\pi\) | ||||
−0.992757 | + | 0.120143i | \(0.961665\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3487.36 | 3.59893 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −98.8188 | −0.101770 | −0.0508850 | − | 0.998705i | \(-0.516204\pi\) | ||||
−0.0508850 | + | 0.998705i | \(0.516204\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 132.277i | 0.135948i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 866.051 | 0.886439 | 0.443220 | − | 0.896413i | \(-0.353836\pi\) | ||||
0.443220 | + | 0.896413i | \(0.353836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2710.94 | −2.76909 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −914.572 | −0.932285 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1190.98i | 1.21157i | 0.795627 | + | 0.605787i | \(0.207142\pi\) | ||||
−0.795627 | + | 0.605787i | \(0.792858\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 80.4995i | 0.0815598i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 351.160 | 0.355066 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 109.095i | − | 0.110086i | −0.998484 | − | 0.0550429i | \(-0.982470\pi\) | ||
0.998484 | − | 0.0550429i | \(-0.0175296\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −839.904 | −0.845825 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −102.381 | −0.102689 | −0.0513447 | − | 0.998681i | \(-0.516351\pi\) | ||||
−0.0513447 | + | 0.998681i | \(0.516351\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 250.360 | 0.250611 |
(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 | 3100.3.d.e.1301.18 | 20 | ||
5.2 | odd | 4 | 3100.3.f.c.1549.35 | 40 | |||
5.3 | odd | 4 | 3100.3.f.c.1549.6 | 40 | |||
5.4 | even | 2 | 620.3.d.a.61.3 | ✓ | 20 | ||
31.30 | odd | 2 | inner | 3100.3.d.e.1301.3 | 20 | ||
155.92 | even | 4 | 3100.3.f.c.1549.5 | 40 | |||
155.123 | even | 4 | 3100.3.f.c.1549.36 | 40 | |||
155.154 | odd | 2 | 620.3.d.a.61.18 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
620.3.d.a.61.3 | ✓ | 20 | 5.4 | even | 2 | ||
620.3.d.a.61.18 | yes | 20 | 155.154 | odd | 2 | ||
3100.3.d.e.1301.3 | 20 | 31.30 | odd | 2 | inner | ||
3100.3.d.e.1301.18 | 20 | 1.1 | even | 1 | trivial | ||
3100.3.f.c.1549.5 | 40 | 155.92 | even | 4 | |||
3100.3.f.c.1549.6 | 40 | 5.3 | odd | 4 | |||
3100.3.f.c.1549.35 | 40 | 5.2 | odd | 4 | |||
3100.3.f.c.1549.36 | 40 | 155.123 | even | 4 |