Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(209,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.209");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.h (of order \(2\), degree \(1\), not 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.976966189056.51 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 10x^{6} + 123x^{4} - 300x^{3} + 86x^{2} + 300x + 526 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.7 | ||
Root | \(2.37200 + 0.719687i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.209 |
Dual form | 224.3.h.d.209.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 4.11439 | 1.37146 | 0.685732 | − | 0.727854i | \(-0.259482\pi\) | ||||
0.685732 | + | 0.727854i | \(0.259482\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.10245 | −0.220489 | −0.110245 | − | 0.993904i | \(-0.535163\pi\) | ||||
−0.110245 | + | 0.993904i | \(0.535163\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.73205 | − | 5.92214i | 0.533150 | − | 0.846021i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.92820 | 0.880911 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 10.7436i | − | 0.976694i | −0.872650 | − | 0.488347i | \(-0.837600\pi\) | ||
0.872650 | − | 0.488347i | \(-0.162400\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.1502 | 1.01156 | 0.505778 | − | 0.862664i | \(-0.331206\pi\) | ||||
0.505778 | + | 0.862664i | \(0.331206\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.53590 | −0.302393 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 20.5149i | 1.20676i | 0.797454 | + | 0.603380i | \(0.206180\pi\) | ||||
−0.797454 | + | 0.603380i | \(0.793820\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24.3909 | 1.28373 | 0.641867 | − | 0.766816i | \(-0.278160\pi\) | ||||
0.641867 | + | 0.766816i | \(0.278160\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15.3551 | − | 24.3660i | 0.731196 | − | 1.16029i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16.7846 | −0.729766 | −0.364883 | − | 0.931053i | \(-0.618891\pi\) | ||||
−0.364883 | + | 0.931053i | \(0.618891\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.7846 | −0.951384 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.40979 | −0.163326 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.21478i | − | 0.145337i | −0.997356 | − | 0.0726686i | \(-0.976848\pi\) | ||
0.997356 | − | 0.0726686i | \(-0.0231515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 52.8741i | 1.70562i | 0.522224 | + | 0.852808i | \(0.325102\pi\) | ||||
−0.522224 | + | 0.852808i | \(0.674898\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 44.2035i | − | 1.33950i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.11439 | + | 6.52885i | −0.117554 | + | 0.186539i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.97227i | 0.269521i | 0.990878 | + | 0.134760i | \(0.0430265\pi\) | ||||
−0.990878 | + | 0.134760i | \(0.956974\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 54.1051 | 1.38731 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 23.6886i | 0.577770i | 0.957364 | + | 0.288885i | \(0.0932846\pi\) | ||||
−0.957364 | + | 0.288885i | \(0.906715\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 65.2331i | − | 1.51705i | −0.651644 | − | 0.758525i | \(-0.725920\pi\) | ||
0.651644 | − | 0.758525i | \(-0.274080\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.74043 | −0.194232 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 52.8741i | − | 1.12498i | −0.826804 | − | 0.562491i | \(-0.809843\pi\) | ||
0.826804 | − | 0.562491i | \(-0.190157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −21.1436 | − | 44.2035i | −0.431502 | − | 0.902112i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 84.4063i | 1.65503i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 47.1893i | 0.890364i | 0.895440 | + | 0.445182i | \(0.146861\pi\) | ||||
−0.895440 | + | 0.445182i | \(0.853139\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.8443i | 0.215351i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 100.354 | 1.76059 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −40.2577 | −0.682334 | −0.341167 | − | 0.940003i | \(-0.610822\pi\) | ||||
−0.341167 | + | 0.940003i | \(0.610822\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.10245 | −0.0180729 | −0.00903645 | − | 0.999959i | \(-0.502876\pi\) | ||||
−0.00903645 | + | 0.999959i | \(0.502876\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 29.5885 | − | 46.9520i | 0.469658 | − | 0.745269i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.4974 | −0.223037 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 65.2331i | 0.973629i | 0.873505 | + | 0.486815i | \(0.161841\pi\) | ||||
−0.873505 | + | 0.486815i | \(0.838159\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −69.0584 | −1.00085 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −113.033 | −1.59202 | −0.796009 | − | 0.605284i | \(-0.793059\pi\) | ||||
−0.796009 | + | 0.605284i | \(0.793059\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 91.5806i | 1.25453i | 0.778806 | + | 0.627265i | \(0.215826\pi\) | ||||
−0.778806 | + | 0.627265i | \(0.784174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −97.8592 | −1.30479 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −63.6253 | − | 40.0958i | −0.826303 | − | 0.520724i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −27.1769 | −0.344012 | −0.172006 | − | 0.985096i | \(-0.555025\pi\) | ||||
−0.172006 | + | 0.985096i | \(0.555025\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −89.4974 | −1.10491 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.34199 | −0.0282168 | −0.0141084 | − | 0.999900i | \(-0.504491\pi\) | ||||
−0.0141084 | + | 0.999900i | \(0.504491\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 22.6166i | − | 0.266078i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 17.3412i | − | 0.199325i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 50.5508i | 0.567987i | 0.958826 | + | 0.283993i | \(0.0916594\pi\) | ||||
−0.958826 | + | 0.283993i | \(0.908341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49.0773 | − | 77.8775i | 0.539311 | − | 0.855797i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 217.545i | 2.33919i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26.8897 | −0.283050 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 74.2394i | − | 0.765355i | −0.923882 | − | 0.382677i | \(-0.875002\pi\) | ||
0.923882 | − | 0.382677i | \(-0.124998\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 85.1777i | − | 0.860381i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −57.0898 | −0.565246 | −0.282623 | − | 0.959231i | \(-0.591204\pi\) | ||||
−0.282623 | + | 0.959231i | \(0.591204\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.3412i | 0.168362i | 0.996450 | + | 0.0841808i | \(0.0268273\pi\) | ||||
−0.996450 | + | 0.0841808i | \(0.973173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.9282 | + | 26.8622i | −0.161221 | + | 0.255831i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 102.037i | 0.953615i | 0.879008 | + | 0.476808i | \(0.158206\pi\) | ||||
−0.879008 | + | 0.476808i | \(0.841794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 116.279i | − | 1.06678i | −0.845869 | − | 0.533391i | \(-0.820917\pi\) | ||
0.845869 | − | 0.533391i | \(-0.179083\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 41.0298i | 0.369638i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3538 | 0.0916268 | 0.0458134 | − | 0.998950i | \(-0.485412\pi\) | ||||
0.0458134 | + | 0.998950i | \(0.485412\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.5041 | 0.160906 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 104.258 | 0.891091 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 121.492 | + | 76.5627i | 1.02094 | + | 0.643384i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.57437 | 0.0460692 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 97.4640i | 0.792391i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 53.7825 | 0.430260 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 111.636 | 0.879023 | 0.439511 | − | 0.898237i | \(-0.355152\pi\) | ||||
0.439511 | + | 0.898237i | \(0.355152\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 268.395i | − | 2.08058i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 77.5826 | 0.592234 | 0.296117 | − | 0.955152i | \(-0.404308\pi\) | ||||
0.296117 | + | 0.955152i | \(0.404308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 91.0282 | − | 144.447i | 0.684423 | − | 1.08607i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.86156 | 0.0360116 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 148.851 | 1.08651 | 0.543253 | − | 0.839569i | \(-0.317193\pi\) | ||||
0.543253 | + | 0.839569i | \(0.317193\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 62.5808 | 0.450222 | 0.225111 | − | 0.974333i | \(-0.427726\pi\) | ||||
0.225111 | + | 0.974333i | \(0.427726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 217.545i | − | 1.54287i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 141.281i | − | 0.987980i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.64657i | 0.0320453i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −86.9930 | − | 181.870i | −0.591789 | − | 1.23721i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 190.300i | 1.27718i | 0.769547 | + | 0.638590i | \(0.220482\pi\) | ||||
−0.769547 | + | 0.638590i | \(0.779518\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.3538 | −0.0685684 | −0.0342842 | − | 0.999412i | \(-0.510915\pi\) | ||||
−0.0342842 | + | 0.999412i | \(0.510915\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 162.646i | 1.06305i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 58.2909i | − | 0.376070i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 311.433 | 1.98365 | 0.991824 | − | 0.127610i | \(-0.0407306\pi\) | ||||
0.991824 | + | 0.127610i | \(0.0407306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 194.155i | 1.22110i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −62.6410 | + | 99.4009i | −0.389075 | + | 0.617397i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.65820i | 0.0469828i | 0.999724 | + | 0.0234914i | \(0.00747824\pi\) | ||||
−0.999724 | + | 0.0234914i | \(0.992522\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 48.7320i | 0.295346i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 135.784i | − | 0.813079i | −0.913633 | − | 0.406539i | \(-0.866735\pi\) | ||
0.913633 | − | 0.406539i | \(-0.133265\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.92820 | 0.0232438 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 193.376 | 1.13086 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −283.086 | −1.63633 | −0.818167 | − | 0.574980i | \(-0.805010\pi\) | ||||
−0.818167 | + | 0.574980i | \(0.805010\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −88.7654 | + | 140.856i | −0.507231 | + | 0.804891i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −165.636 | −0.935796 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 56.8036i | − | 0.317339i | −0.987332 | − | 0.158669i | \(-0.949280\pi\) | ||
0.987332 | − | 0.158669i | \(-0.0507204\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 171.976 | 0.950144 | 0.475072 | − | 0.879947i | \(-0.342422\pi\) | ||||
0.475072 | + | 0.879947i | \(0.342422\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.53590 | −0.0247863 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 10.9939i | − | 0.0594265i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 220.405 | 1.17863 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.4576 | + | 26.1154i | −0.0870770 | + | 0.138177i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −119.962 | −0.628071 | −0.314035 | − | 0.949411i | \(-0.601681\pi\) | ||||
−0.314035 | + | 0.949411i | \(0.601681\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.2154 | 0.0581108 | 0.0290554 | − | 0.999578i | \(-0.490750\pi\) | ||||
0.0290554 | + | 0.999578i | \(0.490750\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −59.6480 | −0.305887 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 207.986i | − | 1.05577i | −0.849317 | − | 0.527883i | \(-0.822986\pi\) | ||
0.849317 | − | 0.527883i | \(-0.177014\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 101.102i | − | 0.508048i | −0.967198 | − | 0.254024i | \(-0.918246\pi\) | ||
0.967198 | − | 0.254024i | \(-0.0817543\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 268.395i | 1.33530i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −24.9605 | − | 15.7298i | −0.122958 | − | 0.0774865i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 26.1154i | − | 0.127392i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −133.072 | −0.642859 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 262.047i | − | 1.25381i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 232.503i | − | 1.10191i | −0.834535 | − | 0.550955i | \(-0.814263\pi\) | ||
0.834535 | − | 0.550955i | \(-0.185737\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −465.063 | −2.18340 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 71.9161i | 0.334494i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 313.128 | + | 197.329i | 1.44299 | + | 0.909350i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 376.798i | 1.72054i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 269.776i | 1.22070i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 140.431i | − | 0.629734i | −0.949136 | − | 0.314867i | \(-0.898040\pi\) | ||
0.949136 | − | 0.314867i | \(-0.101960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −188.569 | −0.838085 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −180.738 | −0.796202 | −0.398101 | − | 0.917342i | \(-0.630331\pi\) | ||||
−0.398101 | + | 0.917342i | \(0.630331\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 153.630 | 0.670875 | 0.335437 | − | 0.942063i | \(-0.391116\pi\) | ||||
0.335437 | + | 0.942063i | \(0.391116\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −261.779 | − | 164.970i | −1.13324 | − | 0.714154i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 106.287 | 0.456168 | 0.228084 | − | 0.973641i | \(-0.426754\pi\) | ||||
0.228084 | + | 0.973641i | \(0.426754\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 58.2909i | 0.248046i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −111.816 | −0.471799 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 371.923 | 1.55616 | 0.778082 | − | 0.628163i | \(-0.216193\pi\) | ||||
0.778082 | + | 0.628163i | \(0.216193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.82024i | 0.0324491i | 0.999868 | + | 0.0162246i | \(0.00516467\pi\) | ||||
−0.999868 | + | 0.0162246i | \(0.994835\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −328.539 | −1.35201 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.3097 | + | 48.7320i | 0.0951416 | + | 0.198906i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 320.746 | 1.29857 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.63586 | −0.0386982 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −211.015 | −0.840699 | −0.420350 | − | 0.907362i | \(-0.638093\pi\) | ||||
−0.420350 | + | 0.907362i | \(0.638093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 180.328i | 0.712758i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 93.0536i | − | 0.364916i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 293.556i | − | 1.14224i | −0.820866 | − | 0.571121i | \(-0.806509\pi\) | ||
0.820866 | − | 0.571121i | \(-0.193491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 59.0572 | + | 37.2170i | 0.228020 | + | 0.143695i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 33.4156i | − | 0.128029i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −64.0385 | −0.243492 | −0.121746 | − | 0.992561i | \(-0.538849\pi\) | ||||
−0.121746 | + | 0.992561i | \(0.538849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 52.0237i | − | 0.196316i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 207.986i | 0.778973i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 333.798 | 1.24089 | 0.620443 | − | 0.784251i | \(-0.286953\pi\) | ||||
0.620443 | + | 0.784251i | \(0.286953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 142.131i | − | 0.524470i | −0.965004 | − | 0.262235i | \(-0.915540\pi\) | ||
0.965004 | − | 0.262235i | \(-0.0844596\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 201.923 | − | 320.418i | 0.739645 | − | 1.17369i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 255.533i | 0.929211i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 124.709i | 0.450212i | 0.974334 | + | 0.225106i | \(0.0722729\pi\) | ||||
−0.974334 | + | 0.225106i | \(0.927727\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 419.197i | 1.50250i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −297.138 | −1.05743 | −0.528716 | − | 0.848799i | \(-0.677326\pi\) | ||||
−0.528716 | + | 0.848799i | \(0.677326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −139.277 | −0.492146 | −0.246073 | − | 0.969251i | \(-0.579140\pi\) | ||||
−0.246073 | + | 0.969251i | \(0.579140\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −110.635 | −0.388192 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 140.287 | + | 88.4070i | 0.488806 | + | 0.308038i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −131.862 | −0.456268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 305.450i | − | 1.04966i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −372.695 | −1.27200 | −0.635998 | − | 0.771690i | \(-0.719411\pi\) | ||||
−0.635998 | + | 0.771690i | \(0.719411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 44.3820 | 0.150447 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 47.3772i | 0.159519i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −220.721 | −0.738198 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −386.320 | − | 243.453i | −1.28346 | − | 0.808815i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −234.890 | −0.775214 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.21539 | 0.00398489 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 358.543 | 1.16789 | 0.583946 | − | 0.811793i | \(-0.301508\pi\) | ||||
0.583946 | + | 0.811793i | \(0.301508\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 71.3486i | 0.230902i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 542.286i | 1.74369i | 0.489786 | + | 0.871843i | \(0.337075\pi\) | ||||
−0.489786 | + | 0.871843i | \(0.662925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 146.778i | − | 0.468939i | −0.972123 | − | 0.234470i | \(-0.924665\pi\) | ||
0.972123 | − | 0.234470i | \(-0.0753354\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −32.6197 | + | 51.7621i | −0.103555 | + | 0.164324i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 101.265i | − | 0.319449i | −0.987162 | − | 0.159725i | \(-0.948939\pi\) | ||
0.987162 | − | 0.159725i | \(-0.0510606\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.2820 | −0.141950 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 419.819i | 1.30785i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 500.378i | 1.54916i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −312.773 | −0.962378 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 478.418i | − | 1.46305i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −313.128 | − | 197.329i | −0.951757 | − | 0.599784i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 492.609i | − | 1.48824i | −0.668043 | − | 0.744122i | \(-0.732868\pi\) | ||
0.668043 | − | 0.744122i | \(-0.267132\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 79.0622i | 0.237424i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 71.9161i | − | 0.214675i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −137.626 | −0.408384 | −0.204192 | − | 0.978931i | \(-0.565457\pi\) | ||||
−0.204192 | + | 0.978931i | \(0.565457\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 42.5997 | 0.125663 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 568.060 | 1.66587 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −340.688 | − | 39.7542i | −0.993261 | − | 0.115902i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 76.1333 | 0.220676 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 385.999i | − | 1.11239i | −0.831052 | − | 0.556195i | \(-0.812261\pi\) | ||
0.831052 | − | 0.556195i | \(-0.187739\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 154.654 | 0.443133 | 0.221567 | − | 0.975145i | \(-0.428883\pi\) | ||||
0.221567 | + | 0.975145i | \(0.428883\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −57.9897 | −0.165213 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 536.789i | 1.52065i | 0.649543 | + | 0.760325i | \(0.274960\pi\) | ||||
−0.649543 | + | 0.760325i | \(0.725040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 124.613 | 0.351023 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 499.867 | + | 315.009i | 1.40019 | + | 0.882377i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −148.918 | −0.414813 | −0.207407 | − | 0.978255i | \(-0.566502\pi\) | ||||
−0.207407 | + | 0.978255i | \(0.566502\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 233.918 | 0.647972 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.9351 | 0.0631822 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 100.963i | − | 0.276611i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 351.927i | 0.958930i | 0.877561 | + | 0.479465i | \(0.159169\pi\) | ||||
−0.877561 | + | 0.479465i | \(0.840831\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 187.808i | 0.508964i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 279.462 | + | 176.113i | 0.753267 | + | 0.474698i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 229.776i | − | 0.616021i | −0.951383 | − | 0.308010i | \(-0.900337\pi\) | ||
0.951383 | − | 0.308010i | \(-0.0996631\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 221.282 | 0.590085 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 55.4253i | − | 0.147017i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 219.556i | − | 0.579304i | −0.957132 | − | 0.289652i | \(-0.906460\pi\) | ||
0.957132 | − | 0.289652i | \(-0.0935396\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 459.313 | 1.20555 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 122.239i | − | 0.319162i | −0.987185 | − | 0.159581i | \(-0.948986\pi\) | ||
0.987185 | − | 0.159581i | \(-0.0510143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 70.1436 | + | 44.2035i | 0.182191 | + | 0.114814i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 517.182i | − | 1.33639i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 597.015i | − | 1.53474i | −0.641202 | − | 0.767372i | \(-0.721564\pi\) | ||
0.641202 | − | 0.767372i | \(-0.278436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 344.335i | − | 0.880652i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 319.205 | 0.812227 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.9611 | 0.0758509 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −277.969 | −0.700175 | −0.350087 | − | 0.936717i | \(-0.613848\pi\) | ||||
−0.350087 | + | 0.936717i | \(0.613848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 374.526 | − | 594.310i | 0.938661 | − | 1.48950i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 511.769 | 1.27623 | 0.638116 | − | 0.769940i | \(-0.279714\pi\) | ||||
0.638116 | + | 0.769940i | \(0.279714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 695.306i | 1.72533i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 98.6662 | 0.243620 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 107.138 | 0.263239 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 310.897i | 0.760140i | 0.924958 | + | 0.380070i | \(0.124100\pi\) | ||||
−0.924958 | + | 0.380070i | \(0.875900\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 612.432 | 1.49010 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −150.244 | + | 238.412i | −0.363786 | + | 0.577269i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.58192 | 0.00622150 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 257.482 | 0.617463 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 77.5826 | 0.185161 | 0.0925807 | − | 0.995705i | \(-0.470488\pi\) | ||||
0.0925807 | + | 0.995705i | \(0.470488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 305.450i | 0.725534i | 0.931880 | + | 0.362767i | \(0.118168\pi\) | ||||
−0.931880 | + | 0.362767i | \(0.881832\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 419.197i | − | 0.991009i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 487.939i | − | 1.14809i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.11439 | + | 6.52885i | −0.00963557 | + | 0.0152901i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 581.285i | − | 1.35498i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −66.5077 | −0.154310 | −0.0771551 | − | 0.997019i | \(-0.524584\pi\) | ||||
−0.0771551 | + | 0.997019i | \(0.524584\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 83.5325i | − | 0.192916i | −0.995337 | − | 0.0964579i | \(-0.969249\pi\) | ||
0.995337 | − | 0.0964579i | \(-0.0307513\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.1178i | 0.0439490i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −409.392 | −0.936825 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 507.604i | 1.15627i | 0.815940 | + | 0.578136i | \(0.196220\pi\) | ||||
−0.815940 | + | 0.578136i | \(0.803780\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −167.631 | − | 350.454i | −0.380115 | − | 0.794681i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 709.135i | − | 1.60076i | −0.599495 | − | 0.800378i | \(-0.704632\pi\) | ||
0.599495 | − | 0.800378i | \(-0.295368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 55.7296i | − | 0.125235i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 782.968i | 1.75161i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 224.564 | 0.500143 | 0.250071 | − | 0.968227i | \(-0.419546\pi\) | ||||
0.250071 | + | 0.968227i | \(0.419546\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 254.501 | 0.564305 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −42.5997 | −0.0940390 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −54.1051 | + | 85.8558i | −0.118912 | + | 0.188694i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −562.200 | −1.23020 | −0.615098 | − | 0.788450i | \(-0.710884\pi\) | ||||
−0.615098 | + | 0.788450i | \(0.710884\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 90.4664i | − | 0.197095i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 808.230 | 1.75321 | 0.876605 | − | 0.481211i | \(-0.159803\pi\) | ||||
0.876605 | + | 0.481211i | \(0.159803\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −545.069 | −1.17725 | −0.588627 | − | 0.808404i | \(-0.700331\pi\) | ||||
−0.588627 | + | 0.808404i | \(0.700331\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 239.832i | − | 0.515767i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 282.985 | 0.605965 | 0.302982 | − | 0.952996i | \(-0.402018\pi\) | ||||
0.302982 | + | 0.952996i | \(0.402018\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 386.320 | + | 243.453i | 0.823710 | + | 0.519090i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1281.36 | 2.72050 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −700.841 | −1.48169 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −580.129 | −1.22132 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 374.126i | 0.784332i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 335.436i | 0.700285i | 0.936697 | + | 0.350142i | \(0.113867\pi\) | ||||
−0.936697 | + | 0.350142i | \(0.886133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 131.138i | 0.272635i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −257.730 | + | 408.974i | −0.533602 | + | 0.846737i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 81.8450i | 0.168753i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −331.041 | −0.679755 | −0.339878 | − | 0.940470i | \(-0.610386\pi\) | ||||
−0.339878 | + | 0.940470i | \(0.610386\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.5088i | 0.0644352i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 189.529i | 0.386005i | 0.981198 | + | 0.193003i | \(0.0618226\pi\) | ||||
−0.981198 | + | 0.193003i | \(0.938177\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 86.4658 | 0.175387 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 93.9039i | 0.189705i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −421.846 | + | 669.400i | −0.848785 | + | 1.34688i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 139.556i | − | 0.279672i | −0.990175 | − | 0.139836i | \(-0.955342\pi\) | ||
0.990175 | − | 0.139836i | \(-0.0446576\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 558.669i | − | 1.11511i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 243.628i | − | 0.484349i | −0.970233 | − | 0.242175i | \(-0.922139\pi\) | ||
0.970233 | − | 0.242175i | \(-0.0778607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 62.9385 | 0.124631 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.1622 | 0.0318780 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −542.704 | −1.06622 | −0.533108 | − | 0.846047i | \(-0.678976\pi\) | ||||
−0.533108 | + | 0.846047i | \(0.678976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 542.354 | + | 341.784i | 1.06136 | + | 0.668852i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −107.559 | −0.209666 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 19.1178i | − | 0.0371220i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −568.060 | −1.09876 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1164.73 | −2.24417 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 639.592i | − | 1.22762i | −0.789453 | − | 0.613812i | \(-0.789635\pi\) | ||
0.789453 | − | 0.613812i | \(-0.210365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −830.769 | −1.58847 | −0.794234 | − | 0.607612i | \(-0.792128\pi\) | ||||
−0.794234 | + | 0.607612i | \(0.792128\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −365.215 | + | 579.536i | −0.695648 | + | 1.10388i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1084.71 | −2.05827 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −247.277 | −0.467442 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −319.171 | −0.601076 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 311.510i | 0.584446i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 112.490i | − | 0.210262i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 233.712i | − | 0.435218i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −474.906 | + | 227.159i | −0.881087 | + | 0.421445i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 630.733i | − | 1.16587i | −0.812520 | − | 0.582933i | \(-0.801905\pi\) | ||
0.812520 | − | 0.582933i | \(-0.198095\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 707.577 | 1.30309 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 128.192i | 0.235214i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 561.588i | 1.02667i | 0.858188 | + | 0.513335i | \(0.171590\pi\) | ||||
−0.858188 | + | 0.513335i | \(0.828410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.74043 | −0.0159206 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 102.802i | − | 0.186574i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −101.426 | + | 160.946i | −0.183410 | + | 0.291041i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 45.2332i | − | 0.0815013i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 350.270i | − | 0.628850i | −0.949282 | − | 0.314425i | \(-0.898188\pi\) | ||
0.949282 | − | 0.314425i | \(-0.101812\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 857.830i | − | 1.53458i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 906.831 | 1.61645 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −196.562 | −0.349133 | −0.174567 | − | 0.984645i | \(-0.555852\pi\) | ||||
−0.174567 | + | 0.984645i | \(0.555852\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.4146 | −0.0202027 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −334.009 | + | 530.017i | −0.589081 | + | 0.934774i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 679.174 | 1.19363 | 0.596814 | − | 0.802380i | \(-0.296433\pi\) | ||||
0.596814 | + | 0.802380i | \(0.296433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 676.022i | 1.18393i | 0.805965 | + | 0.591963i | \(0.201647\pi\) | ||||
−0.805965 | + | 0.591963i | \(0.798353\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −493.568 | −0.861376 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 399.215 | 0.694288 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 104.047i | − | 0.180325i | −0.995927 | − | 0.0901624i | \(-0.971261\pi\) | ||
0.995927 | − | 0.0901624i | \(-0.0287386\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 46.1445 | 0.0796969 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.74043 | + | 13.8696i | −0.0150438 | + | 0.0238720i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 506.985 | 0.869613 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −114.939 | −0.196476 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1027.12 | 1.74978 | 0.874890 | − | 0.484322i | \(-0.160934\pi\) | ||||
0.874890 | + | 0.484322i | \(0.160934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1289.65i | 2.18956i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 855.735i | − | 1.44794i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1057.94i | 1.78404i | 0.451992 | + | 0.892022i | \(0.350713\pi\) | ||||
−0.451992 | + | 0.892022i | \(0.649287\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −133.939 | − | 84.4063i | −0.225107 | − | 0.141859i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 415.972i | − | 0.696770i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 650.295 | 1.08563 | 0.542817 | − | 0.839851i | \(-0.317358\pi\) | ||||
0.542817 | + | 0.839851i | \(0.317358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 779.794i | − | 1.29749i | −0.761004 | − | 0.648747i | \(-0.775293\pi\) | ||
0.761004 | − | 0.648747i | \(-0.224707\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 517.182i | 0.857681i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.14545 | −0.0101578 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 209.796i | − | 0.345627i | −0.984955 | − | 0.172814i | \(-0.944714\pi\) | ||
0.984955 | − | 0.172814i | \(-0.0552858\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −102.697 | − | 64.7184i | −0.168633 | − | 0.106270i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 695.306i | − | 1.13798i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1082.68i | 1.76620i | 0.469183 | + | 0.883101i | \(0.344549\pi\) | ||||
−0.469183 | + | 0.883101i | \(0.655451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 107.449i | − | 0.174714i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −435.902 | −0.706487 | −0.353243 | − | 0.935531i | \(-0.614921\pi\) | ||||
−0.353243 | + | 0.935531i | \(0.614921\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −560.717 | −0.905844 | −0.452922 | − | 0.891550i | \(-0.649618\pi\) | ||||
−0.452922 | + | 0.891550i | \(0.649618\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 74.0166 | 0.119189 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 299.369 | + | 188.658i | 0.480529 | + | 0.302822i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 535.323 | 0.856517 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1078.16i | − | 1.71956i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −204.580 | −0.325247 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −333.972 | −0.529274 | −0.264637 | − | 0.964348i | \(-0.585252\pi\) | ||||
−0.264637 | + | 0.964348i | \(0.585252\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 956.608i | − | 1.51123i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −123.073 | −0.193815 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −278.043 | − | 581.285i | −0.436488 | − | 0.912536i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −896.151 | −1.40243 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 670.354 | 1.04579 | 0.522897 | − | 0.852396i | \(-0.324851\pi\) | ||||
0.522897 | + | 0.852396i | \(0.324851\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −484.612 | −0.753673 | −0.376837 | − | 0.926280i | \(-0.622988\pi\) | ||||
−0.376837 | + | 0.926280i | \(0.622988\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 295.891i | 0.458746i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 975.878i | − | 1.50831i | −0.656695 | − | 0.754156i | \(-0.728046\pi\) | ||
0.656695 | − | 0.754156i | \(-0.271954\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 432.514i | 0.666431i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1288.33 | + | 811.888i | 1.97900 | + | 1.24714i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 813.541i | 1.24585i | 0.782281 | + | 0.622926i | \(0.214056\pi\) | ||||
−0.782281 | + | 0.622926i | \(0.785944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −85.5307 | −0.130581 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 726.070i | 1.10513i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 382.914i | − | 0.581053i | −0.956867 | − | 0.290527i | \(-0.906170\pi\) | ||
0.956867 | − | 0.290527i | \(-0.0938304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −537.587 | −0.813294 | −0.406647 | − | 0.913585i | \(-0.633302\pi\) | ||||
−0.406647 | + | 0.913585i | \(0.633302\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1109.96i | 1.67415i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −100.354 | + | 159.245i | −0.150908 | + | 0.239466i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 70.7434i | 0.106062i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 577.787i | − | 0.863657i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.8443i | 0.0176517i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.8616 | −0.0518002 | −0.0259001 | − | 0.999665i | \(-0.508245\pi\) | ||||
−0.0259001 | + | 0.999665i | \(0.508245\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 104.885 | 0.155385 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 799.093 | 1.18034 | 0.590172 | − | 0.807277i | \(-0.299060\pi\) | ||||
0.590172 | + | 0.807277i | \(0.299060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −439.656 | − | 277.065i | −0.647506 | − | 0.408049i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −743.626 | −1.09196 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 464.235i | − | 0.679700i | −0.940480 | − | 0.339850i | \(-0.889624\pi\) | ||
0.940480 | − | 0.339850i | \(-0.110376\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −164.101 | −0.239563 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 632.095 | 0.920080 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 620.550i | 0.900653i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −670.097 | −0.969750 | −0.484875 | − | 0.874584i | \(-0.661135\pi\) | ||||
−0.484875 | + | 0.874584i | \(0.661135\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −504.435 | − | 317.887i | −0.727900 | − | 0.458712i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −68.9921 | −0.0992692 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −485.969 | −0.697230 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 437.307 | 0.625618 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1239.37i | − | 1.76801i | −0.467478 | − | 0.884005i | \(-0.654837\pi\) | ||
0.467478 | − | 0.884005i | \(-0.345163\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 243.233i | 0.345993i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 239.832i | 0.340187i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −213.062 | + | 338.094i | −0.301361 | + | 0.478209i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1213.67i | − | 1.71181i | −0.517134 | − | 0.855904i | \(-0.673001\pi\) | ||
0.517134 | − | 0.855904i | \(-0.326999\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −215.464 | −0.303044 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 887.471i | − | 1.24470i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 155.755i | 0.217839i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1530.24 | 2.13422 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 295.652i | 0.411198i | 0.978636 | + | 0.205599i | \(0.0659143\pi\) | ||||
−0.978636 | + | 0.205599i | \(0.934086\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 102.697 | + | 64.7184i | 0.142437 | + | 0.0897620i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.1755i | 0.0445028i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 100.247i | 0.138272i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1349.79i | 1.85666i | 0.371755 | + | 0.928331i | \(0.378756\pi\) | ||||
−0.371755 | + | 0.928331i | \(0.621244\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −546.261 | −0.749330 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1338.25 | 1.83071 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 243.166 | 0.331741 | 0.165870 | − | 0.986148i | \(-0.446957\pi\) | ||||
0.165870 | + | 0.986148i | \(0.446957\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 95.9052 | + | 200.503i | 0.130483 | + | 0.272793i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 700.841 | 0.950938 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 177.903i | 0.240735i | 0.992729 | + | 0.120367i | \(0.0384072\pi\) | ||||
−0.992729 | + | 0.120367i | \(0.961593\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1319.67 | 1.78094 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −338.928 | −0.456162 | −0.228081 | − | 0.973642i | \(-0.573245\pi\) | ||||
−0.228081 | + | 0.973642i | \(0.573245\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 209.796i | − | 0.281605i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.5678 | −0.0248565 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 604.277 | + | 380.807i | 0.806778 | + | 0.508420i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 96.3229 | 0.128260 | 0.0641298 | − | 0.997942i | \(-0.479573\pi\) | ||||
0.0641298 | + | 0.997942i | \(0.479573\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −868.200 | −1.15299 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.4146 | 0.0151186 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 326.221i | − | 0.430939i | −0.976511 | − | 0.215470i | \(-0.930872\pi\) | ||
0.976511 | − | 0.215470i | \(-0.0691283\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 741.938i | 0.977521i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 93.5093i | − | 0.122877i | −0.998111 | − | 0.0614384i | \(-0.980431\pi\) | ||
0.998111 | − | 0.0614384i | \(-0.0195688\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −688.623 | − | 433.960i | −0.902520 | − | 0.568755i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 179.309i | − | 0.234391i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −529.397 | −0.690218 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 311.125i | − | 0.404584i | −0.979325 | − | 0.202292i | \(-0.935161\pi\) | ||
0.979325 | − | 0.202292i | \(-0.0648390\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1207.80i | − | 1.56654i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 192.295 | 0.248765 | 0.124382 | − | 0.992234i | \(-0.460305\pi\) | ||||
0.124382 | + | 0.992234i | \(0.460305\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1257.59i | − | 1.62270i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 242.985 | + | 153.125i | 0.312721 | + | 0.197073i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 577.787i | 0.741703i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1214.39i | 1.55491i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.5863i | 0.0237373i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −343.338 | −0.437374 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 58.4877 | 0.0743172 | 0.0371586 | − | 0.999309i | \(-0.488169\pi\) | ||||
0.0371586 | + | 0.999309i | \(0.488169\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −263.479 | −0.333941 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.6410 | − | 61.3169i | 0.0488508 | − | 0.0775182i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.4974 | −0.0182817 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 214.046i | − | 0.269240i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −195.523 | −0.245324 | −0.122662 | − | 0.992449i | \(-0.539143\pi\) | ||||
−0.122662 | + | 0.992449i | \(0.539143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1084.71 | 1.35758 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 400.777i | 0.500346i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 983.909 | 1.22529 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 69.0584 | − | 109.584i | 0.0857869 | − | 0.136130i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1373.38 | 1.70183 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 557.184 | 0.688732 | 0.344366 | − | 0.938835i | \(-0.388094\pi\) | ||||
0.344366 | + | 0.938835i | \(0.388094\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 460.284 | 0.567552 | 0.283776 | − | 0.958891i | \(-0.408413\pi\) | ||||
0.283776 | + | 0.958891i | \(0.408413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 584.784i | − | 0.719292i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 8.44276i | − | 0.0103592i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1591.10i | − | 1.94749i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 389.095 | − | 617.429i | 0.475085 | − | 0.753881i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 130.053i | 0.158408i | 0.996858 | + | 0.0792040i | \(0.0252378\pi\) | ||||
−0.996858 | + | 0.0792040i | \(0.974762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 967.233 | 1.17525 | 0.587627 | − | 0.809132i | \(-0.300062\pi\) | ||||
0.587627 | + | 0.809132i | \(0.300062\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1051.36i | 1.27438i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 138.014i | − | 0.166885i | −0.996513 | − | 0.0834424i | \(-0.973409\pi\) | ||
0.996513 | − | 0.0834424i | \(-0.0265915\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1134.08 | −1.36801 | −0.684004 | − | 0.729478i | \(-0.739763\pi\) | ||||
−0.684004 | + | 0.729478i | \(0.739763\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 513.101i | 0.617450i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 906.831 | − | 433.759i | 1.08863 | − | 0.520719i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 149.695i | 0.179275i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 233.164i | − | 0.278571i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1023.26i | − | 1.21961i | −0.792550 | − | 0.609807i | \(-0.791247\pi\) | ||
0.792550 | − | 0.609807i | \(-0.208753\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 823.236 | 0.978877 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1222.54 | −1.45023 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.33064 | −0.00512501 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.8038 | − | 33.0122i | 0.0245618 | − | 0.0389755i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −573.041 | −0.674960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 167.381i | − | 0.196687i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.0002 | −0.0586169 | −0.0293084 | − | 0.999570i | \(-0.509331\pi\) | ||||
−0.0293084 | + | 0.999570i | \(0.509331\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −213.187 | −0.249342 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 307.496i | 0.358805i | 0.983776 | + | 0.179402i | \(0.0574164\pi\) | ||||
−0.983776 | + | 0.179402i | \(0.942584\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1360.72 | 1.58408 | 0.792039 | − | 0.610470i | \(-0.209019\pi\) | ||||
0.792039 | + | 0.610470i | \(0.209019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 577.196 | + | 363.741i | 0.670379 | + | 0.422463i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −940.403 | −1.08969 | −0.544845 | − | 0.838537i | \(-0.683412\pi\) | ||||
−0.544845 | + | 0.838537i | \(0.683412\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 312.087 | 0.360795 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −542.530 | −0.625755 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 291.979i | 0.335994i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 857.830i | 0.984880i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 588.585i | − | 0.674210i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 200.719 | − | 318.508i | 0.229393 | − | 0.364009i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 418.946i | 0.477704i | 0.971056 | + | 0.238852i | \(0.0767711\pi\) | ||||
−0.971056 | + | 0.238852i | \(0.923229\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1533.41 | −1.74450 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 855.735i | 0.971322i | 0.874147 | + | 0.485661i | \(0.161421\pi\) | ||||
−0.874147 | + | 0.485661i | \(0.838579\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1056.84i | 1.19688i | 0.801168 | + | 0.598439i | \(0.204212\pi\) | ||||
−0.801168 | + | 0.598439i | \(0.795788\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 182.605 | 0.206333 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 885.315i | − | 0.998100i | −0.866573 | − | 0.499050i | \(-0.833682\pi\) | ||
0.866573 | − | 0.499050i | \(-0.166318\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 416.631 | − | 661.124i | 0.468651 | − | 0.743671i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 961.527i | 1.07916i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1289.65i | − | 1.44418i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62.6230i | 0.0699698i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −908.133 | −1.01241 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 222.853 | 0.247890 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −968.084 | −1.07446 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1589.47 | − | 1001.66i | −1.76021 | − | 1.10926i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −189.595 | −0.209497 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 790.234i | 0.871262i | 0.900125 | + | 0.435631i | \(0.143475\pi\) | ||||
−0.900125 | + | 0.435631i | \(0.856525\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −452.620 | −0.497931 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1360.17 | 1.49305 | 0.746525 | − | 0.665357i | \(-0.231721\pi\) | ||||
0.746525 | + | 0.665357i | \(0.231721\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.1615i | 0.0275591i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.00059 | 0.00546513 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 289.542 | − | 459.455i | 0.315749 | − | 0.501042i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 927.121 | 1.00884 | 0.504418 | − | 0.863460i | \(-0.331707\pi\) | ||||
0.504418 | + | 0.863460i | \(0.331707\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1475.18 | 1.60172 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1486.41 | −1.61041 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 237.187i | − | 0.256418i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 137.485i | 0.148312i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 907.531i | 0.976890i | 0.872595 | + | 0.488445i | \(0.162436\pi\) | ||||
−0.872595 | + | 0.488445i | \(0.837564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −515.712 | − | 1078.16i | −0.553934 | − | 1.15807i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2231.18i | 2.39140i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −242.985 | −0.259877 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1376.66i | 1.46922i | 0.678492 | + | 0.734608i | \(0.262634\pi\) | ||||
−0.678492 | + | 0.734608i | \(0.737366\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 603.902i | − | 0.643133i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1266.59 | −1.34601 | −0.673004 | − | 0.739639i | \(-0.734996\pi\) | ||||
−0.673004 | + | 0.739639i | \(0.734996\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 397.604i | − | 0.421637i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.1436 | − | 28.7909i | 0.0191996 | − | 0.0304665i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1058.05i | 1.11727i | 0.829414 | + | 0.558635i | \(0.188675\pi\) | ||||
−0.829414 | + | 0.558635i | \(0.811325\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1204.31i | 1.26903i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 416.646i | − | 0.438113i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1151.72 | −1.20852 | −0.604262 | − | 0.796786i | \(-0.706532\pi\) | ||||
−0.604262 | + | 0.796786i | \(0.706532\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 132.251 | 0.138483 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −186.308 | −0.194679 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 555.520 | − | 881.519i | 0.579271 | − | 0.919206i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1834.67 | −1.90913 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 808.969i | 0.840050i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.3644 | −0.0128128 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1443.46 | −1.49272 | −0.746361 | − | 0.665542i | \(-0.768201\pi\) | ||||
−0.746361 | + | 0.665542i | \(0.768201\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2058.75i | 2.12461i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1604.91 | −1.65284 | −0.826420 | − | 0.563054i | \(-0.809626\pi\) | ||||
−0.826420 | + | 0.563054i | \(0.809626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 233.555 | − | 370.613i | 0.240036 | − | 0.380897i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1286.87 | −1.31987 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1239.07 | 1.26824 | 0.634118 | − | 0.773236i | \(-0.281363\pi\) | ||||
0.634118 | + | 0.773236i | \(0.281363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 543.099 | 0.554749 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 921.885i | − | 0.939741i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1584.98i | 1.61239i | 0.591651 | + | 0.806194i | \(0.298476\pi\) | ||||
−0.591651 | + | 0.806194i | \(0.701524\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 229.293i | 0.232785i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1288.33 | − | 811.888i | −1.30530 | − | 0.822581i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1094.91i | 1.10709i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1479.12 | −1.49255 | −0.746274 | − | 0.665639i | \(-0.768159\pi\) | ||||
−0.746274 | + | 0.665639i | \(0.768159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2026.79i | − | 2.04107i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 111.459i | 0.112019i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 599.409 | 0.601213 | 0.300606 | − | 0.953748i | \(-0.402811\pi\) | ||||
0.300606 | + | 0.953748i | \(0.402811\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 43.9756i | − | 0.0440196i |
(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 | 224.3.h.d.209.7 | 8 | ||
3.2 | odd | 2 | 2016.3.l.f.433.5 | 8 | |||
4.3 | odd | 2 | 56.3.h.d.13.7 | yes | 8 | ||
7.6 | odd | 2 | inner | 224.3.h.d.209.2 | 8 | ||
8.3 | odd | 2 | 56.3.h.d.13.6 | yes | 8 | ||
8.5 | even | 2 | inner | 224.3.h.d.209.1 | 8 | ||
12.11 | even | 2 | 504.3.l.f.181.2 | 8 | |||
21.20 | even | 2 | 2016.3.l.f.433.4 | 8 | |||
24.5 | odd | 2 | 2016.3.l.f.433.3 | 8 | |||
24.11 | even | 2 | 504.3.l.f.181.3 | 8 | |||
28.3 | even | 6 | 392.3.j.d.117.1 | 16 | |||
28.11 | odd | 6 | 392.3.j.d.117.2 | 16 | |||
28.19 | even | 6 | 392.3.j.d.325.5 | 16 | |||
28.23 | odd | 6 | 392.3.j.d.325.6 | 16 | |||
28.27 | even | 2 | 56.3.h.d.13.8 | yes | 8 | ||
56.3 | even | 6 | 392.3.j.d.117.6 | 16 | |||
56.11 | odd | 6 | 392.3.j.d.117.5 | 16 | |||
56.13 | odd | 2 | inner | 224.3.h.d.209.8 | 8 | ||
56.19 | even | 6 | 392.3.j.d.325.2 | 16 | |||
56.27 | even | 2 | 56.3.h.d.13.5 | ✓ | 8 | ||
56.51 | odd | 6 | 392.3.j.d.325.1 | 16 | |||
84.83 | odd | 2 | 504.3.l.f.181.1 | 8 | |||
168.83 | odd | 2 | 504.3.l.f.181.4 | 8 | |||
168.125 | even | 2 | 2016.3.l.f.433.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.h.d.13.5 | ✓ | 8 | 56.27 | even | 2 | ||
56.3.h.d.13.6 | yes | 8 | 8.3 | odd | 2 | ||
56.3.h.d.13.7 | yes | 8 | 4.3 | odd | 2 | ||
56.3.h.d.13.8 | yes | 8 | 28.27 | even | 2 | ||
224.3.h.d.209.1 | 8 | 8.5 | even | 2 | inner | ||
224.3.h.d.209.2 | 8 | 7.6 | odd | 2 | inner | ||
224.3.h.d.209.7 | 8 | 1.1 | even | 1 | trivial | ||
224.3.h.d.209.8 | 8 | 56.13 | odd | 2 | inner | ||
392.3.j.d.117.1 | 16 | 28.3 | even | 6 | |||
392.3.j.d.117.2 | 16 | 28.11 | odd | 6 | |||
392.3.j.d.117.5 | 16 | 56.11 | odd | 6 | |||
392.3.j.d.117.6 | 16 | 56.3 | even | 6 | |||
392.3.j.d.325.1 | 16 | 56.51 | odd | 6 | |||
392.3.j.d.325.2 | 16 | 56.19 | even | 6 | |||
392.3.j.d.325.5 | 16 | 28.19 | even | 6 | |||
392.3.j.d.325.6 | 16 | 28.23 | odd | 6 | |||
504.3.l.f.181.1 | 8 | 84.83 | odd | 2 | |||
504.3.l.f.181.2 | 8 | 12.11 | even | 2 | |||
504.3.l.f.181.3 | 8 | 24.11 | even | 2 | |||
504.3.l.f.181.4 | 8 | 168.83 | odd | 2 | |||
2016.3.l.f.433.3 | 8 | 24.5 | odd | 2 | |||
2016.3.l.f.433.4 | 8 | 21.20 | even | 2 | |||
2016.3.l.f.433.5 | 8 | 3.2 | odd | 2 | |||
2016.3.l.f.433.6 | 8 | 168.125 | even | 2 |