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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.2 | ||
Root | \(2.24350 - 2.23726i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.m.604.15 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.88468i | − 1.44234i | −0.692758 | − | 0.721170i | \(-0.743604\pi\) | ||||
0.692758 | − | 0.721170i | \(-0.256396\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.32139 | −1.08035 | ||||||||
\(5\) | 0.441126 | 0.0882252 | 0.0441126 | − | 0.999027i | \(-0.485954\pi\) | ||||
0.0441126 | + | 0.999027i | \(0.485954\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.5820i | 1.51172i | 0.654736 | + | 0.755858i | \(0.272780\pi\) | ||||
−0.654736 | + | 0.755858i | \(0.727220\pi\) | |||||||
\(8\) | 0.927105i | 0.115888i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 1.27251i | − 0.127251i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.44736i | 0.495951i | 0.968766 | + | 0.247976i | \(0.0797653\pi\) | ||||
−0.968766 | + | 0.247976i | \(0.920235\pi\) | |||||||
\(14\) | 30.5257 | 2.18041 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14.6112 | −0.913197 | ||||||||
\(17\) | − 18.8981i | − 1.11165i | −0.831298 | − | 0.555827i | \(-0.812402\pi\) | ||||
0.831298 | − | 0.555827i | \(-0.187598\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 27.5450i | − 1.44974i | −0.688888 | − | 0.724868i | \(-0.741901\pi\) | ||||
0.688888 | − | 0.724868i | \(-0.258099\pi\) | |||||||
\(20\) | −1.90628 | −0.0953139 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.29263 | −0.273593 | −0.136796 | − | 0.990599i | \(-0.543681\pi\) | ||||
−0.136796 | + | 0.990599i | \(0.543681\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.8054 | −0.992216 | ||||||||
\(26\) | 18.5986 | 0.715331 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 45.7290i | − 1.63318i | ||||||||
\(29\) | 44.1676i | 1.52302i | 0.648153 | + | 0.761510i | \(0.275542\pi\) | ||||
−0.648153 | + | 0.761510i | \(0.724458\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −27.1033 | −0.874300 | −0.437150 | − | 0.899389i | \(-0.644012\pi\) | ||||
−0.437150 | + | 0.899389i | \(0.644012\pi\) | |||||||
\(32\) | 45.8569i | 1.43303i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −54.5151 | −1.60338 | ||||||||
\(35\) | 4.66800i | 0.133371i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.853144 | −0.0230579 | −0.0115290 | − | 0.999934i | \(-0.503670\pi\) | ||||
−0.0115290 | + | 0.999934i | \(0.503670\pi\) | |||||||
\(38\) | −79.4585 | −2.09101 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.408970i | 0.0102243i | ||||||||
\(41\) | 13.2319i | 0.322730i | 0.986895 | + | 0.161365i | \(0.0515897\pi\) | ||||
−0.986895 | + | 0.161365i | \(0.948410\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 68.8186i | 1.60043i | 0.599712 | + | 0.800216i | \(0.295282\pi\) | ||||
−0.599712 | + | 0.800216i | \(0.704718\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.1522i | 0.394614i | ||||||||
\(47\) | 16.1381 | 0.343363 | 0.171682 | − | 0.985152i | \(-0.445080\pi\) | ||||
0.171682 | + | 0.985152i | \(0.445080\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −62.9789 | −1.28528 | ||||||||
\(50\) | 71.5557i | 1.43111i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 27.8616i | − 0.535799i | ||||||||
\(53\) | −38.6822 | −0.729853 | −0.364926 | − | 0.931036i | \(-0.618906\pi\) | ||||
−0.364926 | + | 0.931036i | \(0.618906\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.81064 | −0.175190 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 127.409 | 2.19671 | ||||||||
\(59\) | −76.9113 | −1.30358 | −0.651791 | − | 0.758399i | \(-0.725982\pi\) | ||||
−0.651791 | + | 0.758399i | \(0.725982\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28.6652i | 0.469921i | 0.972005 | + | 0.234961i | \(0.0754961\pi\) | ||||
−0.972005 | + | 0.234961i | \(0.924504\pi\) | |||||||
\(62\) | 78.1844i | 1.26104i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 73.8381 | 1.15372 | ||||||||
\(65\) | 2.84410i | 0.0437554i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −78.0944 | −1.16559 | −0.582794 | − | 0.812620i | \(-0.698041\pi\) | ||||
−0.582794 | + | 0.812620i | \(0.698041\pi\) | |||||||
\(68\) | 81.6662i | 1.20097i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 13.4657 | 0.192367 | ||||||||
\(71\) | 27.1193 | 0.381963 | 0.190981 | − | 0.981594i | \(-0.438833\pi\) | ||||
0.190981 | + | 0.981594i | \(0.438833\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9807i | 0.177818i | 0.996040 | + | 0.0889092i | \(0.0283381\pi\) | ||||
−0.996040 | + | 0.0889092i | \(0.971662\pi\) | |||||||
\(74\) | 2.46105i | 0.0332574i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 119.033i | 1.56622i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 94.2544i | 1.19309i | 0.802578 | + | 0.596547i | \(0.203461\pi\) | ||||
−0.802578 | + | 0.596547i | \(0.796539\pi\) | |||||||
\(80\) | −6.44536 | −0.0805670 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 38.1699 | 0.465487 | ||||||||
\(83\) | − 115.975i | − 1.39729i | −0.715468 | − | 0.698645i | \(-0.753787\pi\) | ||||
0.715468 | − | 0.698645i | \(-0.246213\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 8.33646i | − 0.0980760i | ||||||||
\(86\) | 198.520 | 2.30837 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −65.2779 | −0.733460 | −0.366730 | − | 0.930327i | \(-0.619523\pi\) | ||||
−0.366730 | + | 0.930327i | \(0.619523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −68.2261 | −0.749737 | ||||||||
\(92\) | 27.1929 | 0.295575 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 46.5532i | − 0.495247i | ||||||||
\(95\) | − 12.1508i | − 0.127903i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −70.2994 | −0.724736 | −0.362368 | − | 0.932035i | \(-0.618032\pi\) | ||||
−0.362368 | + | 0.932035i | \(0.618032\pi\) | |||||||
\(98\) | 181.674i | 1.85382i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 107.194 | 1.07194 | ||||||||
\(101\) | 47.4114i | 0.469420i | 0.972065 | + | 0.234710i | \(0.0754141\pi\) | ||||
−0.972065 | + | 0.234710i | \(0.924586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −94.9775 | −0.922112 | −0.461056 | − | 0.887371i | \(-0.652529\pi\) | ||||
−0.461056 | + | 0.887371i | \(0.652529\pi\) | |||||||
\(104\) | −5.97739 | −0.0574749 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 111.586i | 1.05270i | ||||||||
\(107\) | 30.7567i | 0.287446i | 0.989618 | + | 0.143723i | \(0.0459074\pi\) | ||||
−0.989618 | + | 0.143723i | \(0.954093\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 79.2234i | − 0.726820i | −0.931629 | − | 0.363410i | \(-0.881612\pi\) | ||||
0.931629 | − | 0.363410i | \(-0.118388\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 154.615i | − 1.38049i | ||||||||
\(113\) | 26.4704 | 0.234251 | 0.117126 | − | 0.993117i | \(-0.462632\pi\) | ||||
0.117126 | + | 0.993117i | \(0.462632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.77584 | −0.0241378 | ||||||||
\(116\) | − 190.865i | − 1.64539i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 221.865i | 1.88021i | ||||||||
\(119\) | 199.980 | 1.68051 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 82.6900 | 0.677787 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 117.124 | 0.944547 | ||||||||
\(125\) | −21.9705 | −0.175764 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 141.744i | 1.11609i | 0.829810 | + | 0.558046i | \(0.188449\pi\) | ||||
−0.829810 | + | 0.558046i | \(0.811551\pi\) | |||||||
\(128\) | − 29.5716i | − 0.231028i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.20433 | 0.0631102 | ||||||||
\(131\) | − 92.6286i | − 0.707088i | −0.935418 | − | 0.353544i | \(-0.884976\pi\) | ||||
0.935418 | − | 0.353544i | \(-0.115024\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 291.481 | 2.19159 | ||||||||
\(134\) | 225.277i | 1.68118i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.5206 | 0.128828 | ||||||||
\(137\) | 21.9256 | 0.160041 | 0.0800204 | − | 0.996793i | \(-0.474501\pi\) | ||||
0.0800204 | + | 0.996793i | \(0.474501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 189.655i | 1.36442i | 0.731154 | + | 0.682212i | \(0.238982\pi\) | ||||
−0.731154 | + | 0.682212i | \(0.761018\pi\) | |||||||
\(140\) | − 20.1722i | − 0.144087i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 78.2307i | − 0.550920i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.4835i | 0.134369i | ||||||||
\(146\) | 37.4453 | 0.256475 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.68677 | 0.0249106 | ||||||||
\(149\) | − 13.3105i | − 0.0893323i | −0.999002 | − | 0.0446661i | \(-0.985778\pi\) | ||||
0.999002 | − | 0.0446661i | \(-0.0142224\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 82.3554i | 0.545400i | 0.962099 | + | 0.272700i | \(0.0879167\pi\) | ||||
−0.962099 | + | 0.272700i | \(0.912083\pi\) | |||||||
\(152\) | 25.5371 | 0.168007 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.9560 | −0.0771353 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −92.4364 | −0.588767 | −0.294383 | − | 0.955687i | \(-0.595114\pi\) | ||||
−0.294383 | + | 0.955687i | \(0.595114\pi\) | |||||||
\(158\) | 271.894 | 1.72085 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 20.2287i | 0.126429i | ||||||||
\(161\) | − 66.5887i | − 0.413594i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 233.616 | 1.43322 | 0.716612 | − | 0.697472i | \(-0.245692\pi\) | ||||
0.716612 | + | 0.697472i | \(0.245692\pi\) | |||||||
\(164\) | − 57.1804i | − 0.348661i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −334.551 | −2.01537 | ||||||||
\(167\) | − 192.987i | − 1.15561i | −0.816175 | − | 0.577805i | \(-0.803910\pi\) | ||||
0.816175 | − | 0.577805i | \(-0.196090\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 127.431 | 0.754033 | ||||||||
\(170\) | −24.0480 | −0.141459 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 297.392i | − 1.72902i | ||||||||
\(173\) | − 88.1075i | − 0.509292i | −0.967034 | − | 0.254646i | \(-0.918041\pi\) | ||||
0.967034 | − | 0.254646i | \(-0.0819590\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 262.491i | − 1.49995i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 188.306i | 1.05790i | ||||||||
\(179\) | −317.289 | −1.77256 | −0.886282 | − | 0.463146i | \(-0.846720\pi\) | ||||
−0.886282 | + | 0.463146i | \(0.846720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.2796 | −0.0844179 | −0.0422089 | − | 0.999109i | \(-0.513440\pi\) | ||||
−0.0422089 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(182\) | 196.811i | 1.08138i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − 5.83393i | − 0.0317062i | ||||||||
\(185\) | −0.376344 | −0.00203429 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −69.7389 | −0.370952 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −35.0512 | −0.184480 | ||||||||
\(191\) | −20.4709 | −0.107178 | −0.0535888 | − | 0.998563i | \(-0.517066\pi\) | ||||
−0.0535888 | + | 0.998563i | \(0.517066\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 189.238i | − 0.980508i | −0.871580 | − | 0.490254i | \(-0.836904\pi\) | ||||
0.871580 | − | 0.490254i | \(-0.163096\pi\) | |||||||
\(194\) | 202.791i | 1.04532i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 272.156 | 1.38855 | ||||||||
\(197\) | − 380.855i | − 1.93327i | −0.256150 | − | 0.966637i | \(-0.582454\pi\) | ||||
0.256150 | − | 0.966637i | \(-0.417546\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 291.989 | 1.46728 | 0.733642 | − | 0.679537i | \(-0.237819\pi\) | ||||
0.733642 | + | 0.679537i | \(0.237819\pi\) | |||||||
\(200\) | − 22.9972i | − 0.114986i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 136.767 | 0.677064 | ||||||||
\(203\) | −467.382 | −2.30237 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.83696i | 0.0284730i | ||||||||
\(206\) | 273.980i | 1.33000i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 94.2034i | − 0.452901i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 33.3954i | − 0.158272i | −0.996864 | − | 0.0791359i | \(-0.974784\pi\) | ||||
0.996864 | − | 0.0791359i | \(-0.0252161\pi\) | |||||||
\(212\) | 167.161 | 0.788495 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 88.7232 | 0.414595 | ||||||||
\(215\) | 30.3577i | 0.141199i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 286.807i | − 1.32169i | ||||||||
\(218\) | −228.534 | −1.04832 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 121.843 | 0.551326 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −370.973 | −1.66356 | −0.831779 | − | 0.555107i | \(-0.812677\pi\) | ||||
−0.831779 | + | 0.555107i | \(0.812677\pi\) | |||||||
\(224\) | −485.259 | −2.16633 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 76.3587i | − 0.337871i | ||||||||
\(227\) | 114.155i | 0.502886i | 0.967872 | + | 0.251443i | \(0.0809050\pi\) | ||||
−0.967872 | + | 0.251443i | \(0.919095\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −53.6484 | −0.234272 | −0.117136 | − | 0.993116i | \(-0.537371\pi\) | ||||
−0.117136 | + | 0.993116i | \(0.537371\pi\) | |||||||
\(230\) | 8.00743i | 0.0348149i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −40.9480 | −0.176500 | ||||||||
\(233\) | 193.960i | 0.832446i | 0.909263 | + | 0.416223i | \(0.136646\pi\) | ||||
−0.909263 | + | 0.416223i | \(0.863354\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.11893 | 0.0302933 | ||||||||
\(236\) | 332.364 | 1.40832 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 576.879i | − 2.42386i | ||||||||
\(239\) | − 150.146i | − 0.628225i | −0.949386 | − | 0.314113i | \(-0.898293\pi\) | ||||
0.949386 | − | 0.314113i | \(-0.101707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 135.128i | 0.560696i | 0.959898 | + | 0.280348i | \(0.0904499\pi\) | ||||
−0.959898 | + | 0.280348i | \(0.909550\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 123.873i | − 0.507678i | ||||||||
\(245\) | −27.7817 | −0.113394 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 177.592 | 0.718998 | ||||||||
\(248\) | − 25.1276i | − 0.101321i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 63.3778i | 0.253511i | ||||||||
\(251\) | −235.203 | −0.937062 | −0.468531 | − | 0.883447i | \(-0.655217\pi\) | ||||
−0.468531 | + | 0.883447i | \(0.655217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 408.885 | 1.60978 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 210.048 | 0.820499 | ||||||||
\(257\) | 399.203 | 1.55332 | 0.776660 | − | 0.629921i | \(-0.216913\pi\) | ||||
0.776660 | + | 0.629921i | \(0.216913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9.02797i | − 0.0348570i | ||||||||
\(260\) | − 12.2905i | − 0.0472710i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −267.204 | −1.01986 | ||||||||
\(263\) | 281.116i | 1.06888i | 0.845206 | + | 0.534441i | \(0.179478\pi\) | ||||
−0.845206 | + | 0.534441i | \(0.820522\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.0637 | −0.0643914 | ||||||||
\(266\) | − 840.830i | − 3.16102i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 337.476 | 1.25924 | ||||||||
\(269\) | 444.987 | 1.65423 | 0.827114 | − | 0.562034i | \(-0.189981\pi\) | ||||
0.827114 | + | 0.562034i | \(0.189981\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 214.084i | 0.789979i | 0.918686 | + | 0.394990i | \(0.129252\pi\) | ||||
−0.918686 | + | 0.394990i | \(0.870748\pi\) | |||||||
\(272\) | 276.123i | 1.01516i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − 63.2483i | − 0.230833i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0389i | 0.0651226i | 0.999470 | + | 0.0325613i | \(0.0103664\pi\) | ||||
−0.999470 | + | 0.0325613i | \(0.989634\pi\) | |||||||
\(278\) | 547.094 | 1.96796 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.32773 | −0.0154562 | ||||||||
\(281\) | 200.710i | 0.714272i | 0.934052 | + | 0.357136i | \(0.116247\pi\) | ||||
−0.934052 | + | 0.357136i | \(0.883753\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 188.893i | 0.667467i | 0.942668 | + | 0.333733i | \(0.108309\pi\) | ||||
−0.942668 | + | 0.333733i | \(0.891691\pi\) | |||||||
\(284\) | −117.193 | −0.412652 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −140.021 | −0.487876 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −68.1392 | −0.235776 | ||||||||
\(290\) | 56.2036 | 0.193806 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 56.0949i | − 0.192106i | ||||||||
\(293\) | − 195.784i | − 0.668206i | −0.942537 | − | 0.334103i | \(-0.891567\pi\) | ||||
0.942537 | − | 0.334103i | \(-0.108433\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33.9276 | −0.115009 | ||||||||
\(296\) | − 0.790954i | − 0.00267214i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −38.3966 | −0.128848 | ||||||||
\(299\) | − 40.5709i | − 0.135689i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −728.239 | −2.41940 | ||||||||
\(302\) | 237.569 | 0.786653 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 402.464i | 1.32389i | ||||||||
\(305\) | 12.6450i | 0.0414589i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 115.995i | 0.377832i | 0.981993 | + | 0.188916i | \(0.0604974\pi\) | ||||
−0.981993 | + | 0.188916i | \(0.939503\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 34.4892i | 0.111255i | ||||||||
\(311\) | −273.924 | −0.880785 | −0.440392 | − | 0.897805i | \(-0.645161\pi\) | ||||
−0.440392 | + | 0.897805i | \(0.645161\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.03378 | 0.0288619 | 0.0144310 | − | 0.999896i | \(-0.495406\pi\) | ||||
0.0144310 | + | 0.999896i | \(0.495406\pi\) | |||||||
\(314\) | 266.649i | 0.849202i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − 407.310i | − 1.28896i | ||||||||
\(317\) | 162.560 | 0.512808 | 0.256404 | − | 0.966570i | \(-0.417462\pi\) | ||||
0.256404 | + | 0.966570i | \(0.417462\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 32.5719 | 0.101787 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −192.087 | −0.596544 | ||||||||
\(323\) | −520.548 | −1.61161 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 159.930i | − 0.492091i | ||||||||
\(326\) | − 673.907i | − 2.06720i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.2674 | −0.0374006 | ||||||||
\(329\) | 170.773i | 0.519068i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −448.559 | −1.35516 | −0.677581 | − | 0.735448i | \(-0.736972\pi\) | ||||
−0.677581 | + | 0.735448i | \(0.736972\pi\) | |||||||
\(332\) | 501.174i | 1.50956i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −556.705 | −1.66678 | ||||||||
\(335\) | −34.4495 | −0.102834 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 42.5410i | − 0.126234i | −0.998006 | − | 0.0631172i | \(-0.979896\pi\) | ||||
0.998006 | − | 0.0631172i | \(-0.0201042\pi\) | |||||||
\(338\) | − 367.599i | − 1.08757i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 36.0251i | 0.105956i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 147.925i | − 0.431269i | ||||||||
\(344\) | −63.8021 | −0.185471 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −254.162 | −0.734573 | ||||||||
\(347\) | 169.303i | 0.487904i | 0.969787 | + | 0.243952i | \(0.0784439\pi\) | ||||
−0.969787 | + | 0.243952i | \(0.921556\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 297.042i | − 0.851123i | −0.904929 | − | 0.425562i | \(-0.860077\pi\) | ||||
0.904929 | − | 0.425562i | \(-0.139923\pi\) | |||||||
\(350\) | −757.203 | −2.16344 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −639.289 | −1.81102 | −0.905509 | − | 0.424327i | \(-0.860511\pi\) | ||||
−0.905509 | + | 0.424327i | \(0.860511\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.9630 | 0.0336987 | ||||||||
\(356\) | 282.091 | 0.792392 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 915.277i | 2.55664i | ||||||||
\(359\) | − 383.235i | − 1.06751i | −0.845641 | − | 0.533753i | \(-0.820781\pi\) | ||||
0.845641 | − | 0.533753i | \(-0.179219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −397.726 | −1.10173 | ||||||||
\(362\) | 44.0769i | 0.121759i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 294.831 | 0.809976 | ||||||||
\(365\) | 5.72615i | 0.0156881i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 354.233 | 0.965211 | 0.482606 | − | 0.875838i | \(-0.339690\pi\) | ||||
0.482606 | + | 0.875838i | \(0.339690\pi\) | |||||||
\(368\) | 91.9426 | 0.249844 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.08563i | 0.00293414i | ||||||||
\(371\) | − 409.335i | − 1.10333i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 185.060i | − 0.496140i | −0.968742 | − | 0.248070i | \(-0.920204\pi\) | ||||
0.968742 | − | 0.248070i | \(-0.0797962\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.9617i | 0.0397918i | ||||||||
\(377\) | −284.764 | −0.755343 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −252.585 | −0.666452 | −0.333226 | − | 0.942847i | \(-0.608137\pi\) | ||||
−0.333226 | + | 0.942847i | \(0.608137\pi\) | |||||||
\(380\) | 52.5084i | 0.138180i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 59.0521i | 0.154587i | ||||||||
\(383\) | 251.069 | 0.655532 | 0.327766 | − | 0.944759i | \(-0.393704\pi\) | ||||
0.327766 | + | 0.944759i | \(0.393704\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −545.891 | −1.41423 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 303.791 | 0.782966 | ||||||||
\(389\) | 150.224 | 0.386180 | 0.193090 | − | 0.981181i | \(-0.438149\pi\) | ||||
0.193090 | + | 0.981181i | \(0.438149\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 118.919i | 0.304141i | ||||||||
\(392\) | − 58.3881i | − 0.148949i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1098.65 | −2.78844 | ||||||||
\(395\) | 41.5781i | 0.105261i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −516.245 | −1.30036 | −0.650182 | − | 0.759778i | \(-0.725307\pi\) | ||||
−0.650182 | + | 0.759778i | \(0.725307\pi\) | |||||||
\(398\) | − 842.296i | − 2.11632i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 362.436 | 0.906089 | ||||||||
\(401\) | 16.6182 | 0.0414418 | 0.0207209 | − | 0.999785i | \(-0.493404\pi\) | ||||
0.0207209 | + | 0.999785i | \(0.493404\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 174.745i | − 0.433610i | ||||||||
\(404\) | − 204.883i | − 0.507137i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1348.25i | 3.32081i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 405.773i | − 0.992109i | −0.868291 | − | 0.496054i | \(-0.834782\pi\) | ||||
0.868291 | − | 0.496054i | \(-0.165218\pi\) | |||||||
\(410\) | 16.8378 | 0.0410677 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 410.435 | 0.996201 | ||||||||
\(413\) | − 813.876i | − 1.97065i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 51.1597i | − 0.123276i | ||||||||
\(416\) | −295.656 | −0.710713 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 628.759 | 1.50062 | 0.750309 | − | 0.661087i | \(-0.229905\pi\) | ||||
0.750309 | + | 0.661087i | \(0.229905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 605.034 | 1.43713 | 0.718567 | − | 0.695458i | \(-0.244798\pi\) | ||||
0.718567 | + | 0.695458i | \(0.244798\pi\) | |||||||
\(422\) | −96.3350 | −0.228282 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 35.8625i | − 0.0845813i | ||||||||
\(425\) | 468.776i | 1.10300i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −303.335 | −0.710387 | ||||||||
\(428\) | − 132.912i | − 0.310541i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 87.5723 | 0.203656 | ||||||||
\(431\) | 726.164i | 1.68484i | 0.538825 | + | 0.842418i | \(0.318868\pi\) | ||||
−0.538825 | + | 0.842418i | \(0.681132\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −234.892 | −0.542475 | −0.271238 | − | 0.962512i | \(-0.587433\pi\) | ||||
−0.271238 | + | 0.962512i | \(0.587433\pi\) | |||||||
\(434\) | −827.348 | −1.90633 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 342.355i | 0.785218i | ||||||||
\(437\) | 173.330i | 0.396637i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 142.495i | − 0.324589i | −0.986742 | − | 0.162295i | \(-0.948111\pi\) | ||||
0.986742 | − | 0.162295i | \(-0.0518895\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 351.479i | − 0.795201i | ||||||||
\(443\) | −390.409 | −0.881285 | −0.440643 | − | 0.897683i | \(-0.645249\pi\) | ||||
−0.440643 | + | 0.897683i | \(0.645249\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.7958 | −0.0647097 | ||||||||
\(446\) | 1070.14i | 2.39942i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 781.355i | 1.74410i | ||||||||
\(449\) | −716.748 | −1.59632 | −0.798160 | − | 0.602445i | \(-0.794193\pi\) | ||||
−0.798160 | + | 0.602445i | \(0.794193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −114.389 | −0.253073 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 329.301 | 0.725332 | ||||||||
\(455\) | −30.0963 | −0.0661457 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 190.455i | − 0.416752i | −0.978049 | − | 0.208376i | \(-0.933182\pi\) | ||||
0.978049 | − | 0.208376i | \(-0.0668177\pi\) | |||||||
\(458\) | 154.758i | 0.337901i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.9955 | 0.0260772 | ||||||||
\(461\) | − 857.726i | − 1.86058i | −0.366828 | − | 0.930289i | \(-0.619556\pi\) | ||||
0.366828 | − | 0.930289i | \(-0.380444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.4807 | −0.0723126 | −0.0361563 | − | 0.999346i | \(-0.511511\pi\) | ||||
−0.0361563 | + | 0.999346i | \(0.511511\pi\) | |||||||
\(464\) | − 645.339i | − 1.39082i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 559.513 | 1.20067 | ||||||||
\(467\) | 263.349 | 0.563916 | 0.281958 | − | 0.959427i | \(-0.409016\pi\) | ||||
0.281958 | + | 0.959427i | \(0.409016\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 826.396i | − 1.76204i | ||||||||
\(470\) | − 20.5358i | − 0.0436933i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 71.3049i | − 0.151070i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 683.264i | 1.43845i | ||||||||
\(476\) | −864.192 | −1.81553 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −433.123 | −0.906115 | ||||||||
\(479\) | − 615.130i | − 1.28420i | −0.766622 | − | 0.642098i | \(-0.778064\pi\) | ||||
0.766622 | − | 0.642098i | \(-0.221936\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 5.50053i | − 0.0114356i | ||||||||
\(482\) | 389.801 | 0.808715 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.0109 | −0.0639400 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 298.390 | 0.612710 | 0.306355 | − | 0.951917i | \(-0.400891\pi\) | ||||
0.306355 | + | 0.951917i | \(0.400891\pi\) | |||||||
\(488\) | −26.5757 | −0.0544583 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 80.1412i | 0.163554i | ||||||||
\(491\) | − 465.746i | − 0.948567i | −0.880372 | − | 0.474284i | \(-0.842707\pi\) | ||||
0.880372 | − | 0.474284i | \(-0.157293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 834.684 | 1.69307 | ||||||||
\(494\) | − 512.298i | − 1.03704i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 396.010 | 0.798408 | ||||||||
\(497\) | 286.977i | 0.577419i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 545.872 | 1.09393 | 0.546965 | − | 0.837155i | \(-0.315783\pi\) | ||||
0.546965 | + | 0.837155i | \(0.315783\pi\) | |||||||
\(500\) | 94.9429 | 0.189886 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 678.484i | 1.35156i | ||||||||
\(503\) | − 625.729i | − 1.24399i | −0.783020 | − | 0.621997i | \(-0.786322\pi\) | ||||
0.783020 | − | 0.621997i | \(-0.213678\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.9144i | 0.0414147i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 612.529i | − 1.20577i | ||||||||
\(509\) | 208.095 | 0.408830 | 0.204415 | − | 0.978884i | \(-0.434471\pi\) | ||||
0.204415 | + | 0.978884i | \(0.434471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −137.362 | −0.268811 | ||||||||
\(512\) | − 724.207i | − 1.41447i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 1151.57i | − 2.24042i | ||||||||
\(515\) | −41.8971 | −0.0813535 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −26.0428 | −0.0502757 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.63678 | −0.00507073 | ||||||||
\(521\) | −315.168 | −0.604929 | −0.302464 | − | 0.953161i | \(-0.597809\pi\) | ||||
−0.302464 | + | 0.953161i | \(0.597809\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 472.827i | − 0.904067i | −0.892001 | − | 0.452034i | \(-0.850699\pi\) | ||||
0.892001 | − | 0.452034i | \(-0.149301\pi\) | |||||||
\(524\) | 400.284i | 0.763901i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 810.930 | 1.54169 | ||||||||
\(527\) | 512.201i | 0.971919i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −489.403 | −0.925147 | ||||||||
\(530\) | 49.2234i | 0.0928744i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1259.60 | −2.36768 | ||||||||
\(533\) | −85.3112 | −0.160058 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.5676i | 0.0253600i | ||||||||
\(536\) | − 72.4017i | − 0.135078i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 1283.65i | − 2.38596i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1746i | 0.0262008i | 0.999914 | + | 0.0131004i | \(0.00417010\pi\) | ||||
−0.999914 | + | 0.0131004i | \(0.995830\pi\) | |||||||
\(542\) | 617.565 | 1.13942 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 866.610 | 1.59303 | ||||||||
\(545\) | − 34.9475i | − 0.0641239i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 640.079i | 1.17016i | 0.810975 | + | 0.585081i | \(0.198937\pi\) | ||||
−0.810975 | + | 0.585081i | \(0.801063\pi\) | |||||||
\(548\) | −94.7490 | −0.172900 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1216.59 | 2.20798 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −997.401 | −1.80362 | ||||||||
\(554\) | 52.0366 | 0.0939289 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 819.573i | − 1.47405i | ||||||||
\(557\) | 570.143i | 1.02360i | 0.859106 | + | 0.511798i | \(0.171020\pi\) | ||||
−0.859106 | + | 0.511798i | \(0.828980\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −443.699 | −0.793736 | ||||||||
\(560\) | − 68.2049i | − 0.121794i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 578.986 | 1.03022 | ||||||||
\(563\) | − 235.923i | − 0.419046i | −0.977804 | − | 0.209523i | \(-0.932809\pi\) | ||||
0.977804 | − | 0.209523i | \(-0.0671910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.6768 | 0.0206669 | ||||||||
\(566\) | 544.896 | 0.962715 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.1425i | 0.0442649i | ||||||||
\(569\) | − 396.044i | − 0.696035i | −0.937488 | − | 0.348018i | \(-0.886855\pi\) | ||||
0.937488 | − | 0.348018i | \(-0.113145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 67.0903i | − 0.117496i | −0.998273 | − | 0.0587481i | \(-0.981289\pi\) | ||||
0.998273 | − | 0.0587481i | \(-0.0187109\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 403.915i | 0.703684i | ||||||||
\(575\) | 156.091 | 0.271463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −160.995 | −0.279020 | −0.139510 | − | 0.990221i | \(-0.544553\pi\) | ||||
−0.139510 | + | 0.990221i | \(0.544553\pi\) | |||||||
\(578\) | 196.560i | 0.340069i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 84.1957i | − 0.145165i | ||||||||
\(581\) | 1227.25 | 2.11231 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −12.0345 | −0.0206071 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −564.776 | −0.963781 | ||||||||
\(587\) | 607.600 | 1.03509 | 0.517547 | − | 0.855655i | \(-0.326845\pi\) | ||||
0.517547 | + | 0.855655i | \(0.326845\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 746.559i | 1.26750i | ||||||||
\(590\) | 97.8703i | 0.165882i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.4654 | 0.0210564 | ||||||||
\(593\) | 691.234i | 1.16566i | 0.812596 | + | 0.582828i | \(0.198054\pi\) | ||||
−0.812596 | + | 0.582828i | \(0.801946\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 88.2165 | 0.148263 | ||||||||
\(596\) | 57.5199i | 0.0965099i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −117.034 | −0.195709 | ||||||||
\(599\) | −241.924 | −0.403880 | −0.201940 | − | 0.979398i | \(-0.564725\pi\) | ||||
−0.201940 | + | 0.979398i | \(0.564725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 63.6092i | − 0.105839i | −0.998599 | − | 0.0529194i | \(-0.983147\pi\) | ||||
0.998599 | − | 0.0529194i | \(-0.0168527\pi\) | |||||||
\(602\) | 2100.74i | 3.48960i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 355.890i | − 0.589222i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 515.315i | 0.848953i | 0.905439 | + | 0.424477i | \(0.139542\pi\) | ||||
−0.905439 | + | 0.424477i | \(0.860458\pi\) | |||||||
\(608\) | 1263.13 | 2.07751 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.4767 | 0.0597979 | ||||||||
\(611\) | 104.048i | 0.170291i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.8301i | 0.0633443i | 0.999498 | + | 0.0316722i | \(0.0100833\pi\) | ||||
−0.999498 | + | 0.0316722i | \(0.989917\pi\) | |||||||
\(614\) | 334.607 | 0.544963 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −636.272 | −1.03124 | −0.515618 | − | 0.856819i | \(-0.672438\pi\) | ||||
−0.515618 | + | 0.856819i | \(0.672438\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.7230 | −0.0690193 | −0.0345097 | − | 0.999404i | \(-0.510987\pi\) | ||||
−0.0345097 | + | 0.999404i | \(0.510987\pi\) | |||||||
\(620\) | 51.6664 | 0.0833329 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 790.184i | 1.27039i | ||||||||
\(623\) | − 690.772i | − 1.10878i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 610.443 | 0.976710 | ||||||||
\(626\) | − 26.0596i | − 0.0416287i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 399.454 | 0.636072 | ||||||||
\(629\) | 16.1228i | 0.0256325i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 584.880 | 0.926910 | 0.463455 | − | 0.886120i | \(-0.346610\pi\) | ||||
0.463455 | + | 0.886120i | \(0.346610\pi\) | |||||||
\(632\) | −87.3838 | −0.138265 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − 468.934i | − 0.739643i | ||||||||
\(635\) | 62.5268i | 0.0984674i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 406.048i | − 0.637438i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 13.0448i | − 0.0203825i | ||||||||
\(641\) | 205.562 | 0.320689 | 0.160345 | − | 0.987061i | \(-0.448739\pi\) | ||||
0.160345 | + | 0.987061i | \(0.448739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 120.317 | 0.187118 | 0.0935592 | − | 0.995614i | \(-0.470176\pi\) | ||||
0.0935592 | + | 0.995614i | \(0.470176\pi\) | |||||||
\(644\) | 287.756i | 0.446826i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1501.62i | 2.32448i | ||||||||
\(647\) | 583.513 | 0.901874 | 0.450937 | − | 0.892556i | \(-0.351090\pi\) | ||||
0.450937 | + | 0.892556i | \(0.351090\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −461.346 | −0.709763 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1009.54 | −1.54838 | ||||||||
\(653\) | 438.744 | 0.671890 | 0.335945 | − | 0.941882i | \(-0.390944\pi\) | ||||
0.335945 | + | 0.941882i | \(0.390944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 40.8609i | − 0.0623830i | ||||||||
\(656\) | − 193.334i | − 0.294716i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 492.627 | 0.748673 | ||||||||
\(659\) | 598.225i | 0.907777i | 0.891058 | + | 0.453888i | \(0.149964\pi\) | ||||
−0.891058 | + | 0.453888i | \(0.850036\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 811.159 | 1.22717 | 0.613585 | − | 0.789629i | \(-0.289727\pi\) | ||||
0.613585 | + | 0.789629i | \(0.289727\pi\) | |||||||
\(662\) | 1293.95i | 1.95461i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 107.521 | 0.161929 | ||||||||
\(665\) | 128.580 | 0.193353 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 277.930i | − 0.416687i | ||||||||
\(668\) | 833.971i | 1.24846i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 99.3758i | 0.148322i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 933.510i | − 1.38709i | −0.720414 | − | 0.693544i | \(-0.756048\pi\) | ||||
0.720414 | − | 0.693544i | \(-0.243952\pi\) | |||||||
\(674\) | −122.717 | −0.182073 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −550.681 | −0.814617 | ||||||||
\(677\) | 795.030i | 1.17434i | 0.809463 | + | 0.587171i | \(0.199758\pi\) | ||||
−0.809463 | + | 0.587171i | \(0.800242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 743.908i | − 1.09559i | ||||||||
\(680\) | 7.72878 | 0.0113658 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −364.827 | −0.534154 | −0.267077 | − | 0.963675i | \(-0.586058\pi\) | ||||
−0.267077 | + | 0.963675i | \(0.586058\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.67195 | 0.0141196 | ||||||||
\(686\) | −426.717 | −0.622036 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 1005.52i | − 1.46151i | ||||||||
\(689\) | − 249.398i | − 0.361971i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 882.970 | 1.27781 | 0.638907 | − | 0.769284i | \(-0.279387\pi\) | ||||
0.638907 | + | 0.769284i | \(0.279387\pi\) | |||||||
\(692\) | 380.747i | 0.550212i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 488.384 | 0.703724 | ||||||||
\(695\) | 83.6618i | 0.120377i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 250.059 | 0.358765 | ||||||||
\(698\) | −856.872 | −1.22761 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1134.33i | 1.62047i | ||||||||
\(701\) | 1100.51i | 1.56991i | 0.619553 | + | 0.784955i | \(0.287314\pi\) | ||||
−0.619553 | + | 0.784955i | \(0.712686\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.4998i | 0.0334279i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1844.15i | 2.61211i | ||||||||
\(707\) | −501.708 | −0.709630 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1390.19 | 1.96077 | 0.980384 | − | 0.197094i | \(-0.0631506\pi\) | ||||
0.980384 | + | 0.197094i | \(0.0631506\pi\) | |||||||
\(710\) | − 34.5096i | − 0.0486051i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 60.5195i | − 0.0849993i | ||||||||
\(713\) | 170.551 | 0.239202 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1371.13 | 1.91498 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1105.51 | −1.53971 | ||||||||
\(719\) | 59.7926 | 0.0831607 | 0.0415804 | − | 0.999135i | \(-0.486761\pi\) | ||||
0.0415804 | + | 0.999135i | \(0.486761\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 1005.05i | − 1.39397i | ||||||||
\(722\) | 1147.31i | 1.58907i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 66.0293 | 0.0912006 | ||||||||
\(725\) | − 1095.59i | − 1.51116i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1173.95 | −1.61479 | −0.807396 | − | 0.590010i | \(-0.799124\pi\) | ||||
−0.807396 | + | 0.590010i | \(0.799124\pi\) | |||||||
\(728\) | − 63.2528i | − 0.0868857i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.5181 | 0.0226276 | ||||||||
\(731\) | 1300.54 | 1.77913 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 576.624i | − 0.786663i | −0.919397 | − | 0.393331i | \(-0.871323\pi\) | ||||
0.919397 | − | 0.393331i | \(-0.128677\pi\) | |||||||
\(734\) | − 1021.85i | − 1.39216i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 288.561i | − 0.392066i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 171.619i | 0.232231i | 0.993236 | + | 0.116116i | \(0.0370443\pi\) | ||||
−0.993236 | + | 0.116116i | \(0.962956\pi\) | |||||||
\(740\) | 1.62633 | 0.00219774 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1180.80 | −1.59138 | ||||||||
\(743\) | 251.057i | 0.337896i | 0.985625 | + | 0.168948i | \(0.0540370\pi\) | ||||
−0.985625 | + | 0.168948i | \(0.945963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 5.87162i | − 0.00788136i | ||||||||
\(746\) | −533.839 | −0.715602 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −325.468 | −0.434536 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 403.716 | 0.537571 | 0.268786 | − | 0.963200i | \(-0.413378\pi\) | ||||
0.268786 | + | 0.963200i | \(0.413378\pi\) | |||||||
\(752\) | −235.796 | −0.313558 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 821.455i | 1.08946i | ||||||||
\(755\) | 36.3291i | 0.0481181i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1080.23 | 1.42699 | 0.713494 | − | 0.700662i | \(-0.247112\pi\) | ||||
0.713494 | + | 0.700662i | \(0.247112\pi\) | |||||||
\(758\) | 728.628i | 0.961250i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.2651 | 0.0148225 | ||||||||
\(761\) | − 1359.77i | − 1.78682i | −0.449238 | − | 0.893412i | \(-0.648305\pi\) | ||||
0.449238 | − | 0.893412i | \(-0.351695\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 838.342 | 1.09875 | ||||||||
\(764\) | 88.4628 | 0.115789 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 724.254i | − 0.945501i | ||||||||
\(767\) | − 495.875i | − 0.646513i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 925.077i | 1.20296i | 0.798888 | + | 0.601480i | \(0.205422\pi\) | ||||
−0.798888 | + | 0.601480i | \(0.794578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 817.771i | 1.05929i | ||||||||
\(773\) | −363.454 | −0.470186 | −0.235093 | − | 0.971973i | \(-0.575540\pi\) | ||||
−0.235093 | + | 0.971973i | \(0.575540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 672.308 | 0.867494 | ||||||||
\(776\) | − 65.1749i | − 0.0839883i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 433.348i | − 0.557003i | ||||||||
\(779\) | 364.474 | 0.467874 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 343.043 | 0.438674 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 920.195 | 1.17372 | ||||||||
\(785\) | −40.7761 | −0.0519441 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 112.181i | − 0.142542i | −0.997457 | − | 0.0712712i | \(-0.977294\pi\) | ||||
0.997457 | − | 0.0712712i | \(-0.0227056\pi\) | |||||||
\(788\) | 1645.82i | 2.08861i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 119.940 | 0.151822 | ||||||||
\(791\) | 280.110i | 0.354122i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −184.815 | −0.233058 | ||||||||
\(794\) | 1489.20i | 1.87557i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1261.80 | −1.58518 | ||||||||
\(797\) | −1444.35 | −1.81224 | −0.906120 | − | 0.423021i | \(-0.860969\pi\) | ||||
−0.906120 | + | 0.423021i | \(0.860969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 304.979i | − 0.381701i | ||||||||
\(800\) | − 1137.50i | − 1.42188i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 47.9381i | − 0.0597732i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 29.3740i | − 0.0364895i | ||||||||
\(806\) | −504.083 | −0.625413 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −43.9554 | −0.0544002 | ||||||||
\(809\) | − 593.021i | − 0.733029i | −0.930412 | − | 0.366515i | \(-0.880551\pi\) | ||||
0.930412 | − | 0.366515i | \(-0.119449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 432.443i | 0.533222i | 0.963804 | + | 0.266611i | \(0.0859038\pi\) | ||||
−0.963804 | + | 0.266611i | \(0.914096\pi\) | |||||||
\(812\) | 2019.74 | 2.48736 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 103.054 | 0.126447 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1895.61 | 2.32020 | ||||||||
\(818\) | −1170.52 | −1.43096 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 25.2238i | − 0.0307607i | ||||||||
\(821\) | − 583.606i | − 0.710848i | −0.934705 | − | 0.355424i | \(-0.884337\pi\) | ||||
0.934705 | − | 0.355424i | \(-0.115663\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.274319 | 0.000333316 0 | 0.000166658 | − | 1.00000i | \(-0.499947\pi\) | ||||
0.000166658 | 1.00000i | \(0.499947\pi\) | ||||||||
\(824\) | − 88.0541i | − 0.106862i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2347.77 | −2.84234 | ||||||||
\(827\) | 1481.38i | 1.79127i | 0.444789 | + | 0.895635i | \(0.353279\pi\) | ||||
−0.444789 | + | 0.895635i | \(0.646721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −707.744 | −0.853732 | −0.426866 | − | 0.904315i | \(-0.640382\pi\) | ||||
−0.426866 | + | 0.904315i | \(0.640382\pi\) | |||||||
\(830\) | −147.579 | −0.177806 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 476.061i | 0.572189i | ||||||||
\(833\) | 1190.18i | 1.42879i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 85.1315i | − 0.101954i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 1813.77i | − 2.16440i | ||||||||
\(839\) | 1350.18 | 1.60927 | 0.804636 | − | 0.593768i | \(-0.202360\pi\) | ||||
0.804636 | + | 0.593768i | \(0.202360\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1109.77 | −1.31959 | ||||||||
\(842\) | − 1745.33i | − 2.07284i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 144.314i | 0.170989i | ||||||||
\(845\) | 56.2134 | 0.0665247 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 565.192 | 0.666499 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1352.27 | 1.59090 | ||||||||
\(851\) | 5.36852 | 0.00630848 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 427.682i | − 0.501386i | −0.968067 | − | 0.250693i | \(-0.919341\pi\) | ||||
0.968067 | − | 0.250693i | \(-0.0806585\pi\) | |||||||
\(854\) | 875.026i | 1.02462i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.5147 | −0.0333116 | ||||||||
\(857\) | − 281.918i | − 0.328959i | −0.986380 | − | 0.164480i | \(-0.947405\pi\) | ||||
0.986380 | − | 0.164480i | \(-0.0525945\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1367.66 | 1.59215 | 0.796075 | − | 0.605198i | \(-0.206906\pi\) | ||||
0.796075 | + | 0.605198i | \(0.206906\pi\) | |||||||
\(860\) | − 131.187i | − 0.152543i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2094.75 | 2.43011 | ||||||||
\(863\) | −1144.02 | −1.32564 | −0.662818 | − | 0.748780i | \(-0.730640\pi\) | ||||
−0.662818 | + | 0.748780i | \(0.730640\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 38.8665i | − 0.0449324i | ||||||||
\(866\) | 677.588i | 0.782434i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1239.41i | 1.42789i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 503.503i | − 0.578075i | ||||||||
\(872\) | 73.4484 | 0.0842298 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 500.003 | 0.572086 | ||||||||
\(875\) | − 232.492i | − 0.265705i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 445.784i | 0.508306i | 0.967164 | + | 0.254153i | \(0.0817966\pi\) | ||||
−0.967164 | + | 0.254153i | \(0.918203\pi\) | |||||||
\(878\) | −411.052 | −0.468168 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1122.27 | −1.27386 | −0.636931 | − | 0.770921i | \(-0.719796\pi\) | ||||
−0.636931 | + | 0.770921i | \(0.719796\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.40671 | −0.00952063 | −0.00476031 | − | 0.999989i | \(-0.501515\pi\) | ||||
−0.00476031 | + | 0.999989i | \(0.501515\pi\) | |||||||
\(884\) | −526.532 | −0.595624 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1126.21i | 1.27111i | ||||||||
\(887\) | 1330.63i | 1.50014i | 0.661356 | + | 0.750072i | \(0.269981\pi\) | ||||
−0.661356 | + | 0.750072i | \(0.730019\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1499.93 | −1.68721 | ||||||||
\(890\) | 83.0667i | 0.0933334i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1603.12 | 1.79722 | ||||||||
\(893\) | − 444.523i | − 0.497786i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −139.964 | −0.156385 | ||||||||
\(896\) | 312.927 | 0.349249 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2067.59i | 2.30244i | ||||||||
\(899\) | − 1197.09i | − 1.33158i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 731.021i | 0.811344i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.5409i | 0.0271470i | ||||||||
\(905\) | −6.74025 | −0.00744779 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.0706 | 0.0397691 | 0.0198846 | − | 0.999802i | \(-0.493670\pi\) | ||||
0.0198846 | + | 0.999802i | \(0.493670\pi\) | |||||||
\(908\) | − 493.308i | − 0.543291i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 86.8183i | 0.0954047i | ||||||||
\(911\) | −1506.82 | −1.65403 | −0.827014 | − | 0.562182i | \(-0.809962\pi\) | ||||
−0.827014 | + | 0.562182i | \(0.809962\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −549.403 | −0.601098 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 231.835 | 0.253095 | ||||||||
\(917\) | 980.197 | 1.06892 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 449.899i | − 0.489553i | −0.969580 | − | 0.244776i | \(-0.921285\pi\) | ||||
0.969580 | − | 0.244776i | \(-0.0787145\pi\) | |||||||
\(920\) | − 2.57350i | − 0.00279728i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2474.27 | −2.68359 | ||||||||
\(923\) | 174.848i | 0.189435i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.1626 | 0.0228785 | ||||||||
\(926\) | 96.5813i | 0.104299i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2025.39 | −2.18253 | ||||||||
\(929\) | 184.104 | 0.198175 | 0.0990874 | − | 0.995079i | \(-0.468408\pi\) | ||||
0.0990874 | + | 0.995079i | \(0.468408\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1734.75i | 1.86332i | ||||||||
\(932\) | − 838.176i | − 0.899331i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 759.677i | − 0.813359i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 397.162i | − 0.423866i | −0.977284 | − | 0.211933i | \(-0.932024\pi\) | ||||
0.977284 | − | 0.211933i | \(-0.0679758\pi\) | |||||||
\(938\) | −2383.89 | −2.54146 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30.7637 | −0.0327273 | ||||||||
\(941\) | − 964.377i | − 1.02484i | −0.858734 | − | 0.512421i | \(-0.828749\pi\) | ||||
0.858734 | − | 0.512421i | \(-0.171251\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 83.2637i | − 0.0882967i | ||||||||
\(944\) | 1123.76 | 1.19043 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −154.326 | −0.162963 | −0.0814815 | − | 0.996675i | \(-0.525965\pi\) | ||||
−0.0814815 | + | 0.996675i | \(0.525965\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −83.6916 | −0.0881893 | ||||||||
\(950\) | 1971.00 | 2.07474 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 185.403i | 0.194751i | ||||||||
\(953\) | − 697.639i | − 0.732045i | −0.930606 | − | 0.366022i | \(-0.880719\pi\) | ||||
0.930606 | − | 0.366022i | \(-0.119281\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.03026 | −0.00945577 | ||||||||
\(956\) | 648.838i | 0.678701i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1774.45 | −1.85225 | ||||||||
\(959\) | 232.017i | 0.241936i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −226.412 | −0.235600 | ||||||||
\(962\) | −15.8673 | −0.0164940 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 583.940i | − 0.605747i | ||||||||
\(965\) | − 83.4778i | − 0.0865055i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1569.06i | 1.62260i | 0.584627 | + | 0.811302i | \(0.301241\pi\) | ||||
−0.584627 | + | 0.811302i | \(0.698759\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 89.4565i | 0.0922232i | ||||||||
\(971\) | 1239.12 | 1.27613 | 0.638066 | − | 0.769982i | \(-0.279735\pi\) | ||||
0.638066 | + | 0.769982i | \(0.279735\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2006.93 | −2.06262 | ||||||||
\(974\) | − 860.760i | − 0.883737i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 418.832i | − 0.429131i | ||||||||
\(977\) | −71.3624 | −0.0730423 | −0.0365212 | − | 0.999333i | \(-0.511628\pi\) | ||||
−0.0365212 | + | 0.999333i | \(0.511628\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 120.055 | 0.122505 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1343.53 | −1.36816 | ||||||||
\(983\) | 294.338 | 0.299428 | 0.149714 | − | 0.988729i | \(-0.452165\pi\) | ||||
0.149714 | + | 0.988729i | \(0.452165\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 168.005i | − 0.170564i | ||||||||
\(986\) | − 2407.80i | − 2.44199i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −767.446 | −0.776767 | ||||||||
\(989\) | − 433.050i | − 0.437867i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1230.78 | 1.24195 | 0.620977 | − | 0.783829i | \(-0.286736\pi\) | ||||
0.620977 | + | 0.783829i | \(0.286736\pi\) | |||||||
\(992\) | − 1242.87i | − 1.25290i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 827.838 | 0.832835 | ||||||||
\(995\) | 128.804 | 0.129451 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 161.251i | − 0.161736i | −0.996725 | − | 0.0808679i | \(-0.974231\pi\) | ||||
0.996725 | − | 0.0808679i | \(-0.0257692\pi\) | |||||||
\(998\) | − 1574.67i | − 1.57782i | ||||||||
\(999\) | 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.m.604.2 | 16 | ||
3.2 | odd | 2 | 363.3.c.e.241.15 | 16 | |||
11.6 | odd | 10 | 99.3.k.c.19.1 | 16 | |||
11.9 | even | 5 | 99.3.k.c.73.1 | 16 | |||
11.10 | odd | 2 | inner | 1089.3.c.m.604.15 | 16 | ||
33.2 | even | 10 | 363.3.g.f.40.1 | 16 | |||
33.5 | odd | 10 | 363.3.g.f.118.1 | 16 | |||
33.8 | even | 10 | 363.3.g.a.112.1 | 16 | |||
33.14 | odd | 10 | 363.3.g.g.112.4 | 16 | |||
33.17 | even | 10 | 33.3.g.a.19.4 | yes | 16 | ||
33.20 | odd | 10 | 33.3.g.a.7.4 | ✓ | 16 | ||
33.26 | odd | 10 | 363.3.g.a.94.1 | 16 | |||
33.29 | even | 10 | 363.3.g.g.94.4 | 16 | |||
33.32 | even | 2 | 363.3.c.e.241.2 | 16 | |||
132.83 | odd | 10 | 528.3.bf.b.481.4 | 16 | |||
132.119 | even | 10 | 528.3.bf.b.337.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.7.4 | ✓ | 16 | 33.20 | odd | 10 | ||
33.3.g.a.19.4 | yes | 16 | 33.17 | even | 10 | ||
99.3.k.c.19.1 | 16 | 11.6 | odd | 10 | |||
99.3.k.c.73.1 | 16 | 11.9 | even | 5 | |||
363.3.c.e.241.2 | 16 | 33.32 | even | 2 | |||
363.3.c.e.241.15 | 16 | 3.2 | odd | 2 | |||
363.3.g.a.94.1 | 16 | 33.26 | odd | 10 | |||
363.3.g.a.112.1 | 16 | 33.8 | even | 10 | |||
363.3.g.f.40.1 | 16 | 33.2 | even | 10 | |||
363.3.g.f.118.1 | 16 | 33.5 | odd | 10 | |||
363.3.g.g.94.4 | 16 | 33.29 | even | 10 | |||
363.3.g.g.112.4 | 16 | 33.14 | odd | 10 | |||
528.3.bf.b.337.4 | 16 | 132.119 | even | 10 | |||
528.3.bf.b.481.4 | 16 | 132.83 | odd | 10 | |||
1089.3.c.m.604.2 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.c.m.604.15 | 16 | 11.10 | odd | 2 | inner |