Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(199,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("900.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.f (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: | \(24.5232237924\) |
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: | \( x^{16} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.6 | ||
Root | \(0.422403 - 1.34966i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.199 |
Dual form | 900.3.f.f.199.5 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.696577 | + | 1.87477i | −0.348288 | + | 0.937387i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.02956 | − | 2.61185i | −0.757390 | − | 0.652962i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.46770 | −0.781100 | −0.390550 | − | 0.920582i | \(-0.627715\pi\) | ||||
−0.390550 | + | 0.920582i | \(0.627715\pi\) | |||||||
\(8\) | 7.00695 | − | 3.86039i | 0.875869 | − | 0.482549i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0403i | 1.00366i | 0.864965 | + | 0.501832i | \(0.167341\pi\) | ||||
−0.864965 | + | 0.501832i | \(0.832659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.1242i | 0.778784i | 0.921072 | + | 0.389392i | \(0.127315\pi\) | ||||
−0.921072 | + | 0.389392i | \(0.872685\pi\) | |||||||
\(14\) | 3.80867 | − | 10.2507i | 0.272048 | − | 0.732193i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.35649 | + | 15.8255i | 0.147280 | + | 0.989095i | ||||
\(17\) | − | 24.4146i | − | 1.43615i | −0.695964 | − | 0.718077i | \(-0.745023\pi\) | ||
0.695964 | − | 0.718077i | \(-0.254977\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23.7757i | 1.25135i | 0.780082 | + | 0.625677i | \(0.215177\pi\) | ||||
−0.780082 | + | 0.625677i | \(0.784823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −20.6981 | − | 7.69043i | −0.940823 | − | 0.349565i | ||||
\(23\) | 37.2526 | 1.61968 | 0.809838 | − | 0.586653i | \(-0.199555\pi\) | ||||
0.809838 | + | 0.586653i | \(0.199555\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −18.9806 | − | 7.05227i | −0.730022 | − | 0.271241i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.5647 | + | 14.2808i | 0.591598 | + | 0.510029i | ||||
\(29\) | −25.7726 | −0.888712 | −0.444356 | − | 0.895850i | \(-0.646567\pi\) | ||||
−0.444356 | + | 0.895850i | \(0.646567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.83647i | 0.156015i | 0.996953 | + | 0.0780076i | \(0.0248558\pi\) | ||||
−0.996953 | + | 0.0780076i | \(0.975144\pi\) | |||||||
\(32\) | −31.3108 | − | 6.60580i | −0.978461 | − | 0.206431i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 45.7719 | + | 17.0066i | 1.34623 | + | 0.500196i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 35.6493i | − | 0.963495i | −0.876310 | − | 0.481747i | \(-0.840002\pi\) | ||
0.876310 | − | 0.481747i | \(-0.159998\pi\) | |||||||
\(38\) | −44.5741 | − | 16.5616i | −1.17300 | − | 0.435832i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.30410 | 0.226929 | 0.113465 | − | 0.993542i | \(-0.463805\pi\) | ||||
0.113465 | + | 0.993542i | \(0.463805\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −70.0287 | −1.62857 | −0.814287 | − | 0.580462i | \(-0.802872\pi\) | ||||
−0.814287 | + | 0.580462i | \(0.802872\pi\) | |||||||
\(44\) | 28.8356 | − | 33.4473i | 0.655355 | − | 0.760166i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −25.9493 | + | 69.8401i | −0.564114 | + | 1.51826i | ||||
\(47\) | −38.0223 | −0.808984 | −0.404492 | − | 0.914542i | \(-0.632552\pi\) | ||||
−0.404492 | + | 0.914542i | \(0.632552\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.1043 | −0.389883 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 26.4428 | − | 30.6718i | 0.508516 | − | 0.589843i | ||||
\(53\) | − | 55.7762i | − | 1.05238i | −0.850366 | − | 0.526191i | \(-0.823620\pi\) | ||
0.850366 | − | 0.526191i | \(-0.176380\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −38.3119 | + | 21.1075i | −0.684141 | + | 0.376919i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 17.9526 | − | 48.3179i | 0.309528 | − | 0.833067i | ||||
\(59\) | − | 55.5411i | − | 0.941374i | −0.882300 | − | 0.470687i | \(-0.844006\pi\) | ||
0.882300 | − | 0.470687i | \(-0.155994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −82.2412 | −1.34822 | −0.674108 | − | 0.738633i | \(-0.735472\pi\) | ||||
−0.674108 | + | 0.738633i | \(0.735472\pi\) | |||||||
\(62\) | −9.06729 | − | 3.36897i | −0.146247 | − | 0.0543383i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 34.1947 | − | 54.0992i | 0.534293 | − | 0.845299i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −104.493 | −1.55960 | −0.779802 | − | 0.626026i | \(-0.784680\pi\) | ||||
−0.779802 | + | 0.626026i | \(0.784680\pi\) | |||||||
\(68\) | −63.7673 | + | 73.9656i | −0.937754 | + | 1.08773i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 76.7471i | 1.08094i | 0.841362 | + | 0.540472i | \(0.181754\pi\) | ||||
−0.841362 | + | 0.540472i | \(0.818246\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 93.5215i | − | 1.28112i | −0.767910 | − | 0.640558i | \(-0.778703\pi\) | ||
0.767910 | − | 0.640558i | \(-0.221297\pi\) | |||||||
\(74\) | 66.8344 | + | 24.8325i | 0.903168 | + | 0.335574i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 62.0986 | − | 72.0300i | 0.817087 | − | 0.947764i | ||||
\(77\) | − | 60.3651i | − | 0.783963i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 49.3762i | − | 0.625016i | −0.949915 | − | 0.312508i | \(-0.898831\pi\) | ||
0.949915 | − | 0.312508i | \(-0.101169\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.48102 | + | 17.4431i | −0.0790368 | + | 0.212721i | ||||
\(83\) | −72.3768 | −0.872010 | −0.436005 | − | 0.899944i | \(-0.643607\pi\) | ||||
−0.436005 | + | 0.899944i | \(0.643607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 48.7804 | − | 131.288i | 0.567214 | − | 1.52661i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 42.6199 | + | 77.3589i | 0.484318 | + | 0.879079i | ||||
\(89\) | 115.691 | 1.29990 | 0.649950 | − | 0.759977i | \(-0.274790\pi\) | ||||
0.649950 | + | 0.759977i | \(0.274790\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 55.3560i | − | 0.608308i | ||||||
\(92\) | −112.859 | − | 97.2980i | −1.22673 | − | 1.05759i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 26.4854 | − | 71.2832i | 0.281760 | − | 0.758332i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 72.9589i | 0.752154i | 0.926588 | + | 0.376077i | \(0.122727\pi\) | ||||
−0.926588 | + | 0.376077i | \(0.877273\pi\) | |||||||
\(98\) | 13.3076 | − | 35.8162i | 0.135792 | − | 0.365471i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −29.4092 | −0.291180 | −0.145590 | − | 0.989345i | \(-0.546508\pi\) | ||||
−0.145590 | + | 0.989345i | \(0.546508\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −28.1884 | −0.273673 | −0.136837 | − | 0.990594i | \(-0.543694\pi\) | ||||
−0.136837 | + | 0.990594i | \(0.543694\pi\) | |||||||
\(104\) | 39.0833 | + | 70.9397i | 0.375801 | + | 0.682112i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 104.568 | + | 38.8524i | 0.986490 | + | 0.366532i | ||||
\(107\) | −4.50700 | −0.0421215 | −0.0210607 | − | 0.999778i | \(-0.506704\pi\) | ||||
−0.0210607 | + | 0.999778i | \(0.506704\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −193.315 | −1.77353 | −0.886767 | − | 0.462217i | \(-0.847054\pi\) | ||||
−0.886767 | + | 0.462217i | \(0.847054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.8846 | − | 86.5292i | −0.115041 | − | 0.772582i | ||||
\(113\) | − | 75.5727i | − | 0.668785i | −0.942434 | − | 0.334392i | \(-0.891469\pi\) | ||
0.942434 | − | 0.334392i | \(-0.108531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 78.0798 | + | 67.3142i | 0.673102 | + | 0.580295i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 104.127 | + | 38.6886i | 0.882432 | + | 0.327870i | ||||
\(119\) | 133.492i | 1.12178i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.888544 | −0.00734334 | ||||||||
\(122\) | 57.2873 | − | 154.184i | 0.469568 | − | 1.26380i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.6321 | − | 14.6524i | 0.101872 | − | 0.118164i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 131.306 | 1.03390 | 0.516951 | − | 0.856015i | \(-0.327067\pi\) | ||||
0.516951 | + | 0.856015i | \(0.327067\pi\) | |||||||
\(128\) | 77.6045 | + | 101.792i | 0.606285 | + | 0.795247i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 75.7533i | − | 0.578270i | −0.957288 | − | 0.289135i | \(-0.906632\pi\) | ||
0.957288 | − | 0.289135i | \(-0.0933676\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 129.999i | − | 0.977433i | ||||||
\(134\) | 72.7877 | − | 195.902i | 0.543192 | − | 1.46195i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −94.2500 | − | 171.072i | −0.693014 | − | 1.25788i | ||||
\(137\) | 66.7927i | 0.487538i | 0.969833 | + | 0.243769i | \(0.0783839\pi\) | ||||
−0.969833 | + | 0.243769i | \(0.921616\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 38.1214i | 0.274255i | 0.990553 | + | 0.137127i | \(0.0437869\pi\) | ||||
−0.990553 | + | 0.137127i | \(0.956213\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −143.884 | − | 53.4602i | −1.01326 | − | 0.376481i | ||||
\(143\) | −111.774 | −0.781638 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 175.332 | + | 65.1449i | 1.20090 | + | 0.446198i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −93.1106 | + | 108.002i | −0.629126 | + | 0.729742i | ||||
\(149\) | −126.717 | −0.850449 | −0.425225 | − | 0.905088i | \(-0.639805\pi\) | ||||
−0.425225 | + | 0.905088i | \(0.639805\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 68.4403i | 0.453247i | 0.973982 | + | 0.226623i | \(0.0727687\pi\) | ||||
−0.973982 | + | 0.226623i | \(0.927231\pi\) | |||||||
\(152\) | 91.7836 | + | 166.595i | 0.603840 | + | 1.09602i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 113.171 | + | 42.0489i | 0.734877 | + | 0.273045i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 25.5777i | − | 0.162915i | −0.996677 | − | 0.0814577i | \(-0.974042\pi\) | ||
0.996677 | − | 0.0814577i | \(-0.0259575\pi\) | |||||||
\(158\) | 92.5693 | + | 34.3943i | 0.585882 | + | 0.217686i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −203.686 | −1.26513 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 63.4771 | 0.389430 | 0.194715 | − | 0.980860i | \(-0.437622\pi\) | ||||
0.194715 | + | 0.980860i | \(0.437622\pi\) | |||||||
\(164\) | −28.1873 | − | 24.3009i | −0.171874 | − | 0.148176i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 50.4160 | − | 135.690i | 0.303711 | − | 0.817411i | ||||
\(167\) | 12.3771 | 0.0741144 | 0.0370572 | − | 0.999313i | \(-0.488202\pi\) | ||||
0.0370572 | + | 0.999313i | \(0.488202\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 66.5008 | 0.393496 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 212.156 | + | 182.904i | 1.23347 | + | 1.06340i | ||||
\(173\) | − | 59.3729i | − | 0.343196i | −0.985167 | − | 0.171598i | \(-0.945107\pi\) | ||
0.985167 | − | 0.171598i | \(-0.0548930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −174.719 | + | 26.0164i | −0.992720 | + | 0.147820i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −80.5877 | + | 216.895i | −0.452740 | + | 1.21851i | ||||
\(179\) | − | 252.782i | − | 1.41219i | −0.708118 | − | 0.706094i | \(-0.750455\pi\) | ||
0.708118 | − | 0.706094i | \(-0.249545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 125.373 | 0.692670 | 0.346335 | − | 0.938111i | \(-0.387426\pi\) | ||||
0.346335 | + | 0.938111i | \(0.387426\pi\) | |||||||
\(182\) | 103.780 | + | 38.5597i | 0.570220 | + | 0.211867i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 261.027 | − | 143.809i | 1.41862 | − | 0.781573i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 269.545 | 1.44142 | ||||||||
\(188\) | 115.191 | + | 99.3084i | 0.612717 | + | 0.528236i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 97.4640i | − | 0.510283i | −0.966904 | − | 0.255141i | \(-0.917878\pi\) | ||
0.966904 | − | 0.255141i | \(-0.0821220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 342.376i | − | 1.77397i | −0.461798 | − | 0.886985i | \(-0.652796\pi\) | ||
0.461798 | − | 0.886985i | \(-0.347204\pi\) | |||||||
\(194\) | −136.782 | − | 50.8215i | −0.705060 | − | 0.261966i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 57.8775 | + | 49.8974i | 0.295293 | + | 0.254579i | ||||
\(197\) | 74.4829i | 0.378086i | 0.981969 | + | 0.189043i | \(0.0605386\pi\) | ||||
−0.981969 | + | 0.189043i | \(0.939461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 178.027i | 0.894606i | 0.894382 | + | 0.447303i | \(0.147615\pi\) | ||||
−0.894382 | + | 0.447303i | \(0.852385\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.4858 | − | 55.1356i | 0.101415 | − | 0.272949i | ||||
\(203\) | 140.917 | 0.694173 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 19.6354 | − | 52.8468i | 0.0953172 | − | 0.256538i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −160.220 | + | 23.8575i | −0.770291 | + | 0.114700i | ||||
\(209\) | −262.491 | −1.25594 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 185.893i | 0.881008i | 0.897751 | + | 0.440504i | \(0.145200\pi\) | ||||
−0.897751 | + | 0.440504i | \(0.854800\pi\) | |||||||
\(212\) | −145.679 | + | 168.978i | −0.687166 | + | 0.797064i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.13947 | − | 8.44961i | 0.0146704 | − | 0.0394842i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 26.4444i | − | 0.121863i | ||||||
\(218\) | 134.659 | − | 362.422i | 0.617701 | − | 1.66249i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 247.178 | 1.11845 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 202.724 | 0.909074 | 0.454537 | − | 0.890728i | \(-0.349805\pi\) | ||||
0.454537 | + | 0.890728i | \(0.349805\pi\) | |||||||
\(224\) | 171.198 | + | 36.1186i | 0.764276 | + | 0.161244i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 141.682 | + | 52.6422i | 0.626910 | + | 0.232930i | ||||
\(227\) | 51.2708 | 0.225863 | 0.112931 | − | 0.993603i | \(-0.463976\pi\) | ||||
0.112931 | + | 0.993603i | \(0.463976\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −337.056 | −1.47186 | −0.735930 | − | 0.677058i | \(-0.763255\pi\) | ||||
−0.735930 | + | 0.677058i | \(0.763255\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −180.588 | + | 99.4925i | −0.778395 | + | 0.428847i | ||||
\(233\) | 80.2851i | 0.344571i | 0.985047 | + | 0.172286i | \(0.0551152\pi\) | ||||
−0.985047 | + | 0.172286i | \(0.944885\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −145.065 | + | 168.265i | −0.614682 | + | 0.712988i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −250.267 | − | 92.9873i | −1.05154 | − | 0.390703i | ||||
\(239\) | 330.808i | 1.38413i | 0.721834 | + | 0.692066i | \(0.243299\pi\) | ||||
−0.721834 | + | 0.692066i | \(0.756701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −359.914 | −1.49342 | −0.746710 | − | 0.665150i | \(-0.768368\pi\) | ||||
−0.746710 | + | 0.665150i | \(0.768368\pi\) | |||||||
\(242\) | 0.618939 | − | 1.66582i | 0.00255760 | − | 0.00688355i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 249.155 | + | 214.802i | 1.02113 | + | 0.880334i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −240.710 | −0.974534 | ||||||||
\(248\) | 18.6707 | + | 33.8889i | 0.0752850 | + | 0.136649i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 312.213i | − | 1.24388i | −0.783067 | − | 0.621938i | \(-0.786346\pi\) | ||
0.783067 | − | 0.621938i | \(-0.213654\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 411.280i | 1.62561i | ||||||||
\(254\) | −91.4645 | + | 246.169i | −0.360096 | + | 0.969167i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −244.894 | + | 74.5853i | −0.956617 | + | 0.291349i | ||||
\(257\) | 80.2592i | 0.312293i | 0.987734 | + | 0.156146i | \(0.0499072\pi\) | ||||
−0.987734 | + | 0.156146i | \(0.950093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 194.920i | 0.752586i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 142.020 | + | 52.7680i | 0.542063 | + | 0.201405i | ||||
\(263\) | −487.967 | −1.85539 | −0.927694 | − | 0.373342i | \(-0.878212\pi\) | ||||
−0.927694 | + | 0.373342i | \(0.878212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 243.718 | + | 90.5540i | 0.916233 | + | 0.340428i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 316.569 | + | 272.921i | 1.18123 | + | 1.01836i | ||||
\(269\) | −309.553 | −1.15076 | −0.575378 | − | 0.817888i | \(-0.695145\pi\) | ||||
−0.575378 | + | 0.817888i | \(0.695145\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 48.9693i | 0.180698i | 0.995910 | + | 0.0903492i | \(0.0287983\pi\) | ||||
−0.995910 | + | 0.0903492i | \(0.971202\pi\) | |||||||
\(272\) | 386.374 | − | 57.5327i | 1.42049 | − | 0.211517i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −125.221 | − | 46.5262i | −0.457012 | − | 0.169804i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 199.644i | 0.720736i | 0.932810 | + | 0.360368i | \(0.117349\pi\) | ||||
−0.932810 | + | 0.360368i | \(0.882651\pi\) | |||||||
\(278\) | −71.4690 | − | 26.5545i | −0.257083 | − | 0.0955197i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −61.1598 | −0.217650 | −0.108825 | − | 0.994061i | \(-0.534709\pi\) | ||||
−0.108825 | + | 0.994061i | \(0.534709\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −432.506 | −1.52829 | −0.764145 | − | 0.645044i | \(-0.776839\pi\) | ||||
−0.764145 | + | 0.645044i | \(0.776839\pi\) | |||||||
\(284\) | 200.452 | − | 232.510i | 0.705816 | − | 0.818697i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 77.8593 | − | 209.551i | 0.272235 | − | 0.732697i | ||||
\(287\) | −50.8720 | −0.177254 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −307.073 | −1.06254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −244.264 | + | 283.329i | −0.836521 | + | 0.970305i | ||||
\(293\) | 283.234i | 0.966668i | 0.875436 | + | 0.483334i | \(0.160574\pi\) | ||||
−0.875436 | + | 0.483334i | \(0.839426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −137.620 | − | 249.793i | −0.464933 | − | 0.843895i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 88.2681 | − | 237.566i | 0.296202 | − | 0.797200i | ||||
\(299\) | 377.152i | 1.26138i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 382.896 | 1.27208 | ||||||||
\(302\) | −128.310 | − | 47.6739i | −0.424868 | − | 0.157861i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −376.263 | + | 56.0272i | −1.23771 | + | 0.184300i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −100.077 | −0.325983 | −0.162992 | − | 0.986627i | \(-0.552114\pi\) | ||||
−0.162992 | + | 0.986627i | \(0.552114\pi\) | |||||||
\(308\) | −157.665 | + | 182.880i | −0.511898 | + | 0.593766i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 404.185i | 1.29963i | 0.760092 | + | 0.649815i | \(0.225154\pi\) | ||||
−0.760092 | + | 0.649815i | \(0.774846\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 128.579i | − | 0.410795i | −0.978679 | − | 0.205398i | \(-0.934151\pi\) | ||
0.978679 | − | 0.205398i | \(-0.0658487\pi\) | |||||||
\(314\) | 47.9525 | + | 17.8168i | 0.152715 | + | 0.0567415i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −128.963 | + | 149.588i | −0.408112 | + | 0.473381i | ||||
\(317\) | 85.9315i | 0.271077i | 0.990772 | + | 0.135539i | \(0.0432765\pi\) | ||||
−0.990772 | + | 0.135539i | \(0.956724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 284.538i | − | 0.891969i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 141.883 | − | 381.865i | 0.440630 | − | 1.18592i | ||||
\(323\) | 580.475 | 1.79714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −44.2167 | + | 119.005i | −0.135634 | + | 0.365047i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 65.1934 | − | 35.9175i | 0.198760 | − | 0.109505i | ||||
\(329\) | 207.894 | 0.631898 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 183.391i | 0.554052i | 0.960862 | + | 0.277026i | \(0.0893488\pi\) | ||||
−0.960862 | + | 0.277026i | \(0.910651\pi\) | |||||||
\(332\) | 219.270 | + | 189.037i | 0.660452 | + | 0.569390i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.62160 | + | 23.2043i | −0.0258132 | + | 0.0694739i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 168.130i | − | 0.498901i | −0.968388 | − | 0.249451i | \(-0.919750\pi\) | ||
0.968388 | − | 0.249451i | \(-0.0802500\pi\) | |||||||
\(338\) | −46.3229 | + | 124.674i | −0.137050 | + | 0.368858i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −53.3962 | −0.156587 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 372.374 | 1.08564 | ||||||||
\(344\) | −490.688 | + | 270.338i | −1.42642 | + | 0.785867i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 111.311 | + | 41.3578i | 0.321708 | + | 0.119531i | ||||
\(347\) | 137.414 | 0.396006 | 0.198003 | − | 0.980201i | \(-0.436554\pi\) | ||||
0.198003 | + | 0.980201i | \(0.436554\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.4893 | 0.0386513 | 0.0193256 | − | 0.999813i | \(-0.493848\pi\) | ||||
0.0193256 | + | 0.999813i | \(0.493848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 72.9301 | − | 345.681i | 0.207188 | − | 0.982047i | ||||
\(353\) | − | 243.547i | − | 0.689935i | −0.938615 | − | 0.344968i | \(-0.887890\pi\) | ||
0.938615 | − | 0.344968i | \(-0.112110\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −350.493 | − | 302.168i | −0.984532 | − | 0.848786i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 473.909 | + | 176.082i | 1.32377 | + | 0.491849i | ||||
\(359\) | 17.9166i | 0.0499068i | 0.999689 | + | 0.0249534i | \(0.00794374\pi\) | ||||
−0.999689 | + | 0.0249534i | \(0.992056\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −204.285 | −0.565887 | ||||||||
\(362\) | −87.3321 | + | 235.047i | −0.241249 | + | 0.649300i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −144.582 | + | 167.704i | −0.397202 | + | 0.460727i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −238.417 | −0.649637 | −0.324818 | − | 0.945776i | \(-0.605303\pi\) | ||||
−0.324818 | + | 0.945776i | \(0.605303\pi\) | |||||||
\(368\) | 87.7852 | + | 589.541i | 0.238547 | + | 1.60201i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 304.968i | 0.822016i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 181.271i | − | 0.485981i | −0.970029 | − | 0.242990i | \(-0.921872\pi\) | ||
0.970029 | − | 0.242990i | \(-0.0781283\pi\) | |||||||
\(374\) | −187.759 | + | 505.336i | −0.502029 | + | 1.35117i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −266.420 | + | 146.781i | −0.708564 | + | 0.390375i | ||||
\(377\) | − | 260.927i | − | 0.692114i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 306.206i | 0.807931i | 0.914774 | + | 0.403965i | \(0.132368\pi\) | ||||
−0.914774 | + | 0.403965i | \(0.867632\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 182.723 | + | 67.8912i | 0.478333 | + | 0.177726i | ||||
\(383\) | 144.027 | 0.376050 | 0.188025 | − | 0.982164i | \(-0.439791\pi\) | ||||
0.188025 | + | 0.982164i | \(0.439791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 641.878 | + | 238.491i | 1.66290 | + | 0.617853i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 190.558 | − | 221.034i | 0.491128 | − | 0.569674i | ||||
\(389\) | 14.0099 | 0.0360152 | 0.0180076 | − | 0.999838i | \(-0.494268\pi\) | ||||
0.0180076 | + | 0.999838i | \(0.494268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 909.506i | − | 2.32610i | ||||||
\(392\) | −133.863 | + | 73.7499i | −0.341486 | + | 0.188138i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −139.639 | − | 51.8831i | −0.354413 | − | 0.131683i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 39.1084i | − | 0.0985098i | −0.998786 | − | 0.0492549i | \(-0.984315\pi\) | ||
0.998786 | − | 0.0492549i | \(-0.0156847\pi\) | |||||||
\(398\) | −333.760 | − | 124.009i | −0.838592 | − | 0.311581i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 121.067 | 0.301913 | 0.150957 | − | 0.988540i | \(-0.451765\pi\) | ||||
0.150957 | + | 0.988540i | \(0.451765\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −48.9653 | −0.121502 | ||||||||
\(404\) | 89.0970 | + | 76.8124i | 0.220537 | + | 0.190130i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −98.1595 | + | 264.188i | −0.241772 | + | 0.650709i | ||||
\(407\) | 393.579 | 0.967026 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 541.795 | 1.32468 | 0.662342 | − | 0.749202i | \(-0.269563\pi\) | ||||
0.662342 | + | 0.749202i | \(0.269563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 85.3983 | + | 73.6237i | 0.207278 | + | 0.178698i | ||||
\(413\) | 303.682i | 0.735307i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 66.8784 | − | 316.996i | 0.160765 | − | 0.762009i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 182.845 | − | 492.112i | 0.437429 | − | 1.17730i | ||||
\(419\) | − | 687.825i | − | 1.64159i | −0.571224 | − | 0.820794i | \(-0.693531\pi\) | ||
0.571224 | − | 0.820794i | \(-0.306469\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −454.396 | −1.07932 | −0.539662 | − | 0.841882i | \(-0.681448\pi\) | ||||
−0.539662 | + | 0.841882i | \(0.681448\pi\) | |||||||
\(422\) | −348.507 | − | 129.489i | −0.825846 | − | 0.306845i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −215.318 | − | 390.821i | −0.507826 | − | 0.921749i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 449.670 | 1.05309 | ||||||||
\(428\) | 13.6542 | + | 11.7716i | 0.0319024 | + | 0.0275037i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 466.145i | 1.08154i | 0.841169 | + | 0.540772i | \(0.181868\pi\) | ||||
−0.841169 | + | 0.540772i | \(0.818132\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 457.094i | 1.05565i | 0.849355 | + | 0.527823i | \(0.176991\pi\) | ||||
−0.849355 | + | 0.527823i | \(0.823009\pi\) | |||||||
\(434\) | 49.5772 | + | 18.4205i | 0.114233 | + | 0.0424436i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 585.660 | + | 504.910i | 1.34326 | + | 1.15805i | ||||
\(437\) | 885.706i | 2.02679i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 777.467i | − | 1.77100i | −0.464644 | − | 0.885498i | \(-0.653818\pi\) | ||
0.464644 | − | 0.885498i | \(-0.346182\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −172.178 | + | 463.403i | −0.389544 | + | 1.04842i | ||||
\(443\) | 247.484 | 0.558654 | 0.279327 | − | 0.960196i | \(-0.409889\pi\) | ||||
0.279327 | + | 0.960196i | \(0.409889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −141.213 | + | 380.061i | −0.316620 | + | 0.852155i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −186.967 | + | 295.798i | −0.417336 | + | 0.660263i | ||||
\(449\) | 412.508 | 0.918726 | 0.459363 | − | 0.888249i | \(-0.348078\pi\) | ||||
0.459363 | + | 0.888249i | \(0.348078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 102.720i | 0.227761i | ||||||||
\(452\) | −197.384 | + | 228.952i | −0.436691 | + | 0.506531i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −35.7141 | + | 96.1213i | −0.0786654 | + | 0.211721i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 745.400i | 1.63107i | 0.578706 | + | 0.815537i | \(0.303558\pi\) | ||||
−0.578706 | + | 0.815537i | \(0.696442\pi\) | |||||||
\(458\) | 234.785 | − | 631.904i | 0.512631 | − | 1.37970i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −81.6151 | −0.177039 | −0.0885196 | − | 0.996074i | \(-0.528214\pi\) | ||||
−0.0885196 | + | 0.996074i | \(0.528214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −292.248 | −0.631205 | −0.315603 | − | 0.948891i | \(-0.602207\pi\) | ||||
−0.315603 | + | 0.948891i | \(0.602207\pi\) | |||||||
\(464\) | −60.7329 | − | 407.865i | −0.130890 | − | 0.879020i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −150.517 | − | 55.9248i | −0.322997 | − | 0.120010i | ||||
\(467\) | 51.4163 | 0.110099 | 0.0550495 | − | 0.998484i | \(-0.482468\pi\) | ||||
0.0550495 | + | 0.998484i | \(0.482468\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 571.339 | 1.21821 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −214.410 | − | 389.174i | −0.454259 | − | 0.824520i | ||||
\(473\) | − | 773.139i | − | 1.63454i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 348.660 | − | 404.422i | 0.732480 | − | 0.849625i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −620.190 | − | 230.433i | −1.29747 | − | 0.482077i | ||||
\(479\) | 122.593i | 0.255935i | 0.991778 | + | 0.127967i | \(0.0408453\pi\) | ||||
−0.991778 | + | 0.127967i | \(0.959155\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 360.920 | 0.750354 | ||||||||
\(482\) | 250.708 | − | 674.758i | 0.520141 | − | 1.39991i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.69190 | + | 2.32074i | 0.00556177 | + | 0.00479492i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 65.9859 | 0.135495 | 0.0677474 | − | 0.997703i | \(-0.478419\pi\) | ||||
0.0677474 | + | 0.997703i | \(0.478419\pi\) | |||||||
\(488\) | −576.260 | + | 317.483i | −1.18086 | + | 0.650580i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 361.163i | − | 0.735567i | −0.929911 | − | 0.367783i | \(-0.880117\pi\) | ||
0.929911 | − | 0.367783i | \(-0.119883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 629.229i | 1.27633i | ||||||||
\(494\) | 167.673 | − | 451.277i | 0.339419 | − | 0.913516i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −76.5396 | + | 11.3971i | −0.154314 | + | 0.0229780i | ||||
\(497\) | − | 419.630i | − | 0.844326i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 711.138i | 1.42513i | 0.701608 | + | 0.712564i | \(0.252466\pi\) | ||||
−0.701608 | + | 0.712564i | \(0.747534\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 585.328 | + | 217.480i | 1.16599 | + | 0.433227i | ||||
\(503\) | 353.756 | 0.703292 | 0.351646 | − | 0.936133i | \(-0.385622\pi\) | ||||
0.351646 | + | 0.936133i | \(0.385622\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −771.057 | − | 286.488i | −1.52383 | − | 0.566182i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −397.799 | − | 342.951i | −0.783068 | − | 0.675100i | ||||
\(509\) | 478.049 | 0.939192 | 0.469596 | − | 0.882881i | \(-0.344400\pi\) | ||||
0.469596 | + | 0.882881i | \(0.344400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 511.348i | 1.00068i | ||||||||
\(512\) | 30.7568 | − | 511.075i | 0.0600720 | − | 0.998194i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −150.468 | − | 55.9067i | −0.292739 | − | 0.108768i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 419.778i | − | 0.811949i | ||||||
\(518\) | −365.431 | − | 135.777i | −0.705464 | − | 0.262117i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.7365 | 0.0685921 | 0.0342960 | − | 0.999412i | \(-0.489081\pi\) | ||||
0.0342960 | + | 0.999412i | \(0.489081\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −733.562 | −1.40260 | −0.701302 | − | 0.712864i | \(-0.747398\pi\) | ||||
−0.701302 | + | 0.712864i | \(0.747398\pi\) | |||||||
\(524\) | −197.856 | + | 229.499i | −0.377588 | + | 0.437976i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 339.906 | − | 914.828i | 0.646210 | − | 1.73922i | ||||
\(527\) | 118.081 | 0.224062 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 858.753 | 1.62335 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −339.537 | + | 393.839i | −0.638227 | + | 0.740298i | ||||
\(533\) | 94.1965i | 0.176729i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −732.181 | + | 403.386i | −1.36601 | + | 0.752585i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 215.628 | − | 580.342i | 0.400795 | − | 1.07870i | ||||
\(539\) | − | 210.917i | − | 0.391312i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 608.939 | 1.12558 | 0.562790 | − | 0.826600i | \(-0.309728\pi\) | ||||
0.562790 | + | 0.826600i | \(0.309728\pi\) | |||||||
\(542\) | −91.8064 | − | 34.1109i | −0.169384 | − | 0.0629352i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −161.278 | + | 764.440i | −0.296467 | + | 1.40522i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −78.5868 | −0.143669 | −0.0718344 | − | 0.997417i | \(-0.522885\pi\) | ||||
−0.0718344 | + | 0.997417i | \(0.522885\pi\) | |||||||
\(548\) | 174.452 | − | 202.353i | 0.318344 | − | 0.369257i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 612.763i | − | 1.11209i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 269.974i | 0.488200i | ||||||||
\(554\) | −374.287 | − | 139.067i | −0.675609 | − | 0.251024i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 99.5673 | − | 115.491i | 0.179078 | − | 0.207718i | ||||
\(557\) | − | 928.488i | − | 1.66694i | −0.552561 | − | 0.833472i | \(-0.686349\pi\) | ||
0.552561 | − | 0.833472i | \(-0.313651\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 708.984i | − | 1.26831i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 42.6025 | − | 114.661i | 0.0758051 | − | 0.204023i | ||||
\(563\) | −447.978 | −0.795697 | −0.397849 | − | 0.917451i | \(-0.630243\pi\) | ||||
−0.397849 | + | 0.917451i | \(0.630243\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 301.274 | − | 810.852i | 0.532286 | − | 1.43260i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 296.274 | + | 537.763i | 0.521609 | + | 0.946766i | ||||
\(569\) | 571.441 | 1.00429 | 0.502145 | − | 0.864783i | \(-0.332544\pi\) | ||||
0.502145 | + | 0.864783i | \(0.332544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 990.801i | − | 1.73520i | −0.497260 | − | 0.867602i | \(-0.665660\pi\) | ||
0.497260 | − | 0.867602i | \(-0.334340\pi\) | |||||||
\(572\) | 338.627 | + | 291.937i | 0.592005 | + | 0.510380i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 35.4363 | − | 95.3736i | 0.0617357 | − | 0.166156i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 826.638i | − | 1.43265i | −0.697768 | − | 0.716324i | \(-0.745823\pi\) | ||
0.697768 | − | 0.716324i | \(-0.254177\pi\) | |||||||
\(578\) | 213.900 | − | 575.693i | 0.370069 | − | 0.996008i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 395.735 | 0.681127 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 615.787 | 1.05624 | ||||||||
\(584\) | −361.030 | − | 655.301i | −0.618202 | − | 1.12209i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −530.999 | − | 197.294i | −0.906142 | − | 0.336679i | ||||
\(587\) | −900.009 | −1.53323 | −0.766617 | − | 0.642104i | \(-0.778062\pi\) | ||||
−0.766617 | + | 0.642104i | \(0.778062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −114.991 | −0.195230 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 564.169 | − | 84.0071i | 0.952987 | − | 0.141904i | ||||
\(593\) | 704.088i | 1.18733i | 0.804711 | + | 0.593666i | \(0.202320\pi\) | ||||
−0.804711 | + | 0.593666i | \(0.797680\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 383.897 | + | 330.965i | 0.644122 | + | 0.555311i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −707.075 | − | 262.715i | −1.18240 | − | 0.439323i | ||||
\(599\) | − | 376.098i | − | 0.627876i | −0.949444 | − | 0.313938i | \(-0.898352\pi\) | ||
0.949444 | − | 0.313938i | \(-0.101648\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 430.191 | 0.715791 | 0.357896 | − | 0.933762i | \(-0.383494\pi\) | ||||
0.357896 | + | 0.933762i | \(0.383494\pi\) | |||||||
\(602\) | −266.716 | + | 717.844i | −0.443051 | + | 1.19243i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 178.756 | − | 207.344i | 0.295953 | − | 0.343285i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −93.4019 | −0.153875 | −0.0769373 | − | 0.997036i | \(-0.524514\pi\) | ||||
−0.0769373 | + | 0.997036i | \(0.524514\pi\) | |||||||
\(608\) | 157.058 | − | 744.436i | 0.258319 | − | 1.22440i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 384.944i | − | 0.630024i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 156.506i | − | 0.255312i | −0.991818 | − | 0.127656i | \(-0.959255\pi\) | ||
0.991818 | − | 0.127656i | \(-0.0407454\pi\) | |||||||
\(614\) | 69.7113 | − | 187.622i | 0.113536 | − | 0.305573i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −233.033 | − | 422.976i | −0.378301 | − | 0.686649i | ||||
\(617\) | − | 553.493i | − | 0.897072i | −0.893765 | − | 0.448536i | \(-0.851946\pi\) | ||
0.893765 | − | 0.448536i | \(-0.148054\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.4398i | 0.0233276i | 0.999932 | + | 0.0116638i | \(0.00371278\pi\) | ||||
−0.999932 | + | 0.0116638i | \(0.996287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −757.756 | − | 281.546i | −1.21826 | − | 0.452646i | ||||
\(623\) | −632.564 | −1.01535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 241.056 | + | 89.5651i | 0.385074 | + | 0.143075i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −66.8051 | + | 77.4893i | −0.106378 | + | 0.123391i | ||||
\(629\) | −870.364 | −1.38373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 352.389i | − | 0.558460i | −0.960224 | − | 0.279230i | \(-0.909921\pi\) | ||
0.960224 | − | 0.279230i | \(-0.0900793\pi\) | |||||||
\(632\) | −190.612 | − | 345.977i | −0.301601 | − | 0.547432i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −161.102 | − | 59.8579i | −0.254104 | − | 0.0944130i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 193.415i | − | 0.303634i | ||||||
\(638\) | 533.445 | + | 198.203i | 0.836120 | + | 0.310662i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 545.742 | 0.851391 | 0.425696 | − | 0.904866i | \(-0.360029\pi\) | ||||
0.425696 | + | 0.904866i | \(0.360029\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 757.447 | 1.17799 | 0.588995 | − | 0.808137i | \(-0.299524\pi\) | ||||
0.588995 | + | 0.808137i | \(0.299524\pi\) | |||||||
\(644\) | 617.079 | + | 531.997i | 0.958197 | + | 0.826082i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −404.345 | + | 1088.26i | −0.625922 | + | 1.68461i | ||||
\(647\) | −1161.36 | −1.79500 | −0.897499 | − | 0.441016i | \(-0.854618\pi\) | ||||
−0.897499 | + | 0.441016i | \(0.854618\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 613.191 | 0.944824 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −192.308 | − | 165.793i | −0.294950 | − | 0.254283i | ||||
\(653\) | 621.231i | 0.951348i | 0.879622 | + | 0.475674i | \(0.157796\pi\) | ||||
−0.879622 | + | 0.475674i | \(0.842204\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 21.9250 | + | 147.242i | 0.0334223 | + | 0.224455i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −144.814 | + | 389.755i | −0.220083 | + | 0.592333i | ||||
\(659\) | − | 736.047i | − | 1.11692i | −0.829533 | − | 0.558458i | \(-0.811393\pi\) | ||
0.829533 | − | 0.558458i | \(-0.188607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 383.845 | 0.580704 | 0.290352 | − | 0.956920i | \(-0.406228\pi\) | ||||
0.290352 | + | 0.956920i | \(0.406228\pi\) | |||||||
\(662\) | −343.817 | − | 127.746i | −0.519362 | − | 0.192970i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −507.141 | + | 279.403i | −0.763766 | + | 0.420788i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −960.096 | −1.43942 | ||||||||
\(668\) | −37.4972 | − | 32.3271i | −0.0561335 | − | 0.0483939i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 907.968i | − | 1.35316i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 984.464i | 1.46280i | 0.681949 | + | 0.731400i | \(0.261133\pi\) | ||||
−0.681949 | + | 0.731400i | \(0.738867\pi\) | |||||||
\(674\) | 315.205 | + | 117.115i | 0.467664 | + | 0.173761i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −201.468 | − | 173.690i | −0.298030 | − | 0.256938i | ||||
\(677\) | 673.154i | 0.994319i | 0.867659 | + | 0.497160i | \(0.165624\pi\) | ||||
−0.867659 | + | 0.497160i | \(0.834376\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 398.918i | − | 0.587507i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 37.1945 | − | 100.106i | 0.0545374 | − | 0.146783i | ||||
\(683\) | −291.192 | −0.426343 | −0.213171 | − | 0.977015i | \(-0.568379\pi\) | ||||
−0.213171 | + | 0.977015i | \(0.568379\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −259.387 | + | 698.117i | −0.378115 | + | 1.01766i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −165.022 | − | 1108.24i | −0.239857 | − | 1.61081i | ||||
\(689\) | 564.689 | 0.819578 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 943.693i | 1.36569i | 0.730563 | + | 0.682846i | \(0.239258\pi\) | ||||
−0.730563 | + | 0.682846i | \(0.760742\pi\) | |||||||
\(692\) | −155.073 | + | 179.874i | −0.224094 | + | 0.259933i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −95.7193 | + | 257.620i | −0.137924 | + | 0.371211i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 227.156i | − | 0.325905i | ||||||
\(698\) | −9.39633 | + | 25.2894i | −0.0134618 | + | 0.0362312i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −885.681 | −1.26345 | −0.631727 | − | 0.775191i | \(-0.717654\pi\) | ||||
−0.631727 | + | 0.775191i | \(0.717654\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 847.588 | 1.20567 | ||||||||
\(704\) | 597.272 | + | 377.521i | 0.848397 | + | 0.536251i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 456.596 | + | 169.649i | 0.646737 | + | 0.240296i | ||||
\(707\) | 160.801 | 0.227441 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 286.183 | 0.403644 | 0.201822 | − | 0.979422i | \(-0.435314\pi\) | ||||
0.201822 | + | 0.979422i | \(0.435314\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 810.642 | − | 446.613i | 1.13854 | − | 0.627266i | ||||
\(713\) | 180.171i | 0.252694i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −660.228 | + | 765.818i | −0.922106 | + | 1.06958i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.5895 | − | 12.4803i | −0.0467820 | − | 0.0173820i | ||||
\(719\) | 666.163i | 0.926513i | 0.886224 | + | 0.463257i | \(0.153319\pi\) | ||||
−0.886224 | + | 0.463257i | \(0.846681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 154.125 | 0.213766 | ||||||||
\(722\) | 142.300 | − | 382.989i | 0.197092 | − | 0.530455i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −379.826 | − | 327.456i | −0.524622 | − | 0.452287i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 856.270 | 1.17781 | 0.588907 | − | 0.808201i | \(-0.299559\pi\) | ||||
0.588907 | + | 0.808201i | \(0.299559\pi\) | |||||||
\(728\) | −213.696 | − | 387.877i | −0.293538 | − | 0.532798i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1709.72i | 2.33888i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 769.487i | − | 1.04978i | −0.851171 | − | 0.524889i | \(-0.824107\pi\) | ||
0.851171 | − | 0.524889i | \(-0.175893\pi\) | |||||||
\(734\) | 166.076 | − | 446.978i | 0.226261 | − | 0.608961i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1166.41 | − | 246.083i | −1.58479 | − | 0.334352i | ||||
\(737\) | − | 1153.64i | − | 1.56532i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1156.70i | − | 1.56522i | −0.622511 | − | 0.782611i | \(-0.713887\pi\) | ||
0.622511 | − | 0.782611i | \(-0.286113\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −571.746 | − | 212.433i | −0.770547 | − | 0.286298i | ||||
\(743\) | −426.794 | −0.574421 | −0.287210 | − | 0.957868i | \(-0.592728\pi\) | ||||
−0.287210 | + | 0.957868i | \(0.592728\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 339.842 | + | 126.269i | 0.455552 | + | 0.169261i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −816.603 | − | 704.011i | −1.09172 | − | 0.941191i | ||||
\(749\) | 24.6429 | 0.0329011 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1222.03i | 1.62721i | 0.581420 | + | 0.813604i | \(0.302497\pi\) | ||||
−0.581420 | + | 0.813604i | \(0.697503\pi\) | |||||||
\(752\) | −89.5990 | − | 601.722i | −0.119148 | − | 0.800162i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 489.179 | + | 181.756i | 0.648779 | + | 0.241055i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1312.95i | 1.73442i | 0.497945 | + | 0.867209i | \(0.334088\pi\) | ||||
−0.497945 | + | 0.867209i | \(0.665912\pi\) | |||||||
\(758\) | −574.067 | − | 213.296i | −0.757344 | − | 0.281393i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 189.584 | 0.249124 | 0.124562 | − | 0.992212i | \(-0.460247\pi\) | ||||
0.124562 | + | 0.992212i | \(0.460247\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1056.99 | 1.38531 | ||||||||
\(764\) | −254.561 | + | 295.273i | −0.333195 | + | 0.386483i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −100.326 | + | 270.019i | −0.130974 | + | 0.352505i | ||||
\(767\) | 562.308 | 0.733127 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −254.995 | −0.331594 | −0.165797 | − | 0.986160i | \(-0.553020\pi\) | ||||
−0.165797 | + | 0.986160i | \(0.553020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −894.235 | + | 1037.25i | −1.15834 | + | 1.34359i | ||||
\(773\) | − | 23.2536i | − | 0.0300823i | −0.999887 | − | 0.0150411i | \(-0.995212\pi\) | ||
0.999887 | − | 0.0150411i | \(-0.00478793\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 281.650 | + | 511.220i | 0.362951 | + | 0.658788i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.75897 | + | 26.2654i | −0.0125437 | + | 0.0337602i | ||||
\(779\) | 221.212i | 0.283969i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −847.312 | −1.08491 | ||||||||
\(782\) | 1705.12 | + | 633.541i | 2.18046 | + | 0.810155i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −45.0189 | − | 302.335i | −0.0574221 | − | 0.385631i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −220.593 | −0.280296 | −0.140148 | − | 0.990131i | \(-0.544758\pi\) | ||||
−0.140148 | + | 0.990131i | \(0.544758\pi\) | |||||||
\(788\) | 194.538 | − | 225.651i | 0.246876 | − | 0.286359i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 413.209i | 0.522388i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 832.625i | − | 1.04997i | ||||||
\(794\) | 73.3194 | + | 27.2420i | 0.0923418 | + | 0.0343098i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 464.979 | − | 539.343i | 0.584144 | − | 0.677566i | ||||
\(797\) | 1010.38i | 1.26773i | 0.773442 | + | 0.633867i | \(0.218533\pi\) | ||||
−0.773442 | + | 0.633867i | \(0.781467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 928.298i | 1.16183i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −84.3327 | + | 226.974i | −0.105153 | + | 0.283010i | ||||
\(803\) | 1032.51 | 1.28581 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 34.1081 | − | 91.7990i | 0.0423178 | − | 0.113894i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −206.069 | + | 113.531i | −0.255036 | + | 0.140509i | ||||
\(809\) | 1410.37 | 1.74335 | 0.871674 | − | 0.490086i | \(-0.163035\pi\) | ||||
0.871674 | + | 0.490086i | \(0.163035\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 950.157i | 1.17159i | 0.810460 | + | 0.585793i | \(0.199217\pi\) | ||||
−0.810460 | + | 0.585793i | \(0.800783\pi\) | |||||||
\(812\) | −426.917 | − | 368.054i | −0.525760 | − | 0.453269i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −274.158 | + | 737.873i | −0.336804 | + | 0.906478i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1664.98i | − | 2.03792i | ||||||
\(818\) | −377.402 | + | 1015.74i | −0.461372 | + | 1.24174i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −77.3347 | −0.0941957 | −0.0470979 | − | 0.998890i | \(-0.514997\pi\) | ||||
−0.0470979 | + | 0.998890i | \(0.514997\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1260.16 | −1.53118 | −0.765591 | − | 0.643328i | \(-0.777553\pi\) | ||||
−0.765591 | + | 0.643328i | \(0.777553\pi\) | |||||||
\(824\) | −197.514 | + | 108.818i | −0.239702 | + | 0.132061i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −569.335 | − | 211.538i | −0.689268 | − | 0.256099i | ||||
\(827\) | −438.047 | −0.529681 | −0.264841 | − | 0.964292i | \(-0.585319\pi\) | ||||
−0.264841 | + | 0.964292i | \(0.585319\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −361.388 | −0.435933 | −0.217966 | − | 0.975956i | \(-0.569942\pi\) | ||||
−0.217966 | + | 0.975956i | \(0.569942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 547.710 | + | 346.194i | 0.658305 | + | 0.416098i | ||||
\(833\) | 466.423i | 0.559931i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 795.234 | + | 685.588i | 0.951237 | + | 0.820082i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1289.52 | + | 479.123i | 1.53880 | + | 0.571746i | ||||
\(839\) | 785.017i | 0.935658i | 0.883819 | + | 0.467829i | \(0.154964\pi\) | ||||
−0.883819 | + | 0.467829i | \(0.845036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −176.771 | −0.210192 | ||||||||
\(842\) | 316.521 | − | 851.890i | 0.375916 | − | 1.01175i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 485.524 | − | 563.173i | 0.575265 | − | 0.667267i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.85829 | 0.00573588 | ||||||||
\(848\) | 882.688 | − | 131.436i | 1.04091 | − | 0.154995i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1328.03i | − | 1.56055i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1113.79i | 1.30573i | 0.757474 | + | 0.652865i | \(0.226433\pi\) | ||||
−0.757474 | + | 0.652865i | \(0.773567\pi\) | |||||||
\(854\) | −313.230 | + | 843.030i | −0.366780 | + | 0.987155i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.5803 | + | 17.3988i | −0.0368929 | + | 0.0203257i | ||||
\(857\) | − | 306.591i | − | 0.357749i | −0.983872 | − | 0.178875i | \(-0.942754\pi\) | ||
0.983872 | − | 0.178875i | \(-0.0572456\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 204.542i | − | 0.238116i | −0.992887 | − | 0.119058i | \(-0.962013\pi\) | ||
0.992887 | − | 0.119058i | \(-0.0379875\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −873.918 | − | 324.706i | −1.01383 | − | 0.376689i | ||||
\(863\) | −654.384 | −0.758266 | −0.379133 | − | 0.925342i | \(-0.623778\pi\) | ||||
−0.379133 | + | 0.925342i | \(0.623778\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −856.949 | − | 318.401i | −0.989549 | − | 0.367669i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −69.0687 | + | 80.1149i | −0.0795722 | + | 0.0922982i | ||||
\(869\) | 545.129 | 0.627306 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1057.91i | − | 1.21459i | ||||||
\(872\) | −1354.55 | + | 746.272i | −1.55338 | + | 0.855817i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1660.50 | − | 616.963i | −1.89989 | − | 0.705907i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 604.453i | 0.689228i | 0.938744 | + | 0.344614i | \(0.111990\pi\) | ||||
−0.938744 | + | 0.344614i | \(0.888010\pi\) | |||||||
\(878\) | 1457.58 | + | 541.565i | 1.66011 | + | 0.616817i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1436.81 | −1.63089 | −0.815445 | − | 0.578834i | \(-0.803508\pi\) | ||||
−0.815445 | + | 0.578834i | \(0.803508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −120.993 | −0.137025 | −0.0685123 | − | 0.997650i | \(-0.521825\pi\) | ||||
−0.0685123 | + | 0.997650i | \(0.521825\pi\) | |||||||
\(884\) | −748.841 | − | 645.592i | −0.847105 | − | 0.730307i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −172.392 | + | 463.977i | −0.194573 | + | 0.523676i | ||||
\(887\) | 286.448 | 0.322941 | 0.161470 | − | 0.986878i | \(-0.448376\pi\) | ||||
0.161470 | + | 0.986878i | \(0.448376\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −717.940 | −0.807582 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −614.164 | − | 529.483i | −0.688524 | − | 0.593591i | ||||
\(893\) | − | 904.007i | − | 1.01233i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −424.318 | − | 556.566i | −0.473569 | − | 0.621168i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −287.344 | + | 773.360i | −0.319982 | + | 0.861203i | ||||
\(899\) | − | 124.649i | − | 0.138652i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1361.75 | −1.51138 | ||||||||
\(902\) | −192.577 | − | 71.5525i | −0.213500 | − | 0.0793265i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −291.740 | − | 529.534i | −0.322721 | − | 0.585768i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 234.706 | 0.258772 | 0.129386 | − | 0.991594i | \(-0.458699\pi\) | ||||
0.129386 | + | 0.991594i | \(0.458699\pi\) | |||||||
\(908\) | −155.328 | − | 133.912i | −0.171066 | − | 0.147480i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 491.244i | − | 0.539236i | −0.962967 | − | 0.269618i | \(-0.913103\pi\) | ||
0.962967 | − | 0.269618i | \(-0.0868974\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 799.063i | − | 0.875206i | ||||||
\(914\) | −1397.46 | − | 519.229i | −1.52895 | − | 0.568084i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1021.13 | + | 880.339i | 1.11477 | + | 0.961069i | ||||
\(917\) | 414.197i | 0.451687i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 356.091i | 0.387477i | 0.981053 | + | 0.193738i | \(0.0620613\pi\) | ||||
−0.981053 | + | 0.193738i | \(0.937939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 56.8511 | − | 153.010i | 0.0616607 | − | 0.165954i | ||||
\(923\) | −777.002 | −0.841822 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 203.573 | − | 547.899i | 0.219841 | − | 0.591684i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 806.961 | + | 170.249i | 0.869570 | + | 0.183458i | ||||
\(929\) | −916.019 | −0.986027 | −0.493014 | − | 0.870022i | \(-0.664105\pi\) | ||||
−0.493014 | + | 0.870022i | \(0.664105\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 454.217i | − | 0.487881i | ||||||
\(932\) | 209.693 | − | 243.229i | 0.224992 | − | 0.260975i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −35.8154 | + | 96.3939i | −0.0383462 | + | 0.103205i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 143.818i | − | 0.153488i | −0.997051 | − | 0.0767440i | \(-0.975548\pi\) | ||
0.997051 | − | 0.0767440i | \(-0.0244524\pi\) | |||||||
\(938\) | −397.981 | + | 1071.13i | −0.424287 | + | 1.14193i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1488.04 | 1.58133 | 0.790667 | − | 0.612246i | \(-0.209734\pi\) | ||||
0.790667 | + | 0.612246i | \(0.209734\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 346.602 | 0.367552 | ||||||||
\(944\) | 878.966 | − | 130.882i | 0.931108 | − | 0.138646i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1449.46 | + | 538.551i | 1.53220 | + | 0.569292i | ||||
\(947\) | 1095.51 | 1.15682 | 0.578411 | − | 0.815745i | \(-0.303673\pi\) | ||||
0.578411 | + | 0.815745i | \(0.303673\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 946.829 | 0.997713 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 515.331 | + | 935.370i | 0.541314 | + | 0.982532i | ||||
\(953\) | − | 1277.86i | − | 1.34089i | −0.741961 | − | 0.670443i | \(-0.766104\pi\) | ||
0.741961 | − | 0.670443i | \(-0.233896\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 864.020 | − | 1002.20i | 0.903786 | − | 1.04833i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −229.834 | − | 85.3953i | −0.239910 | − | 0.0891392i | ||||
\(959\) | − | 365.202i | − | 0.380816i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 937.609 | 0.975659 | ||||||||
\(962\) | −251.409 | + | 676.644i | −0.261339 | + | 0.703372i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1090.38 | + | 940.041i | 1.13110 | + | 0.975146i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −237.958 | −0.246079 | −0.123039 | − | 0.992402i | \(-0.539264\pi\) | ||||
−0.123039 | + | 0.992402i | \(0.539264\pi\) | |||||||
\(968\) | −6.22598 | + | 3.43013i | −0.00643180 | + | 0.00354352i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1602.10i | 1.64995i | 0.565169 | + | 0.824975i | \(0.308811\pi\) | ||||
−0.565169 | + | 0.824975i | \(0.691189\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 208.436i | − | 0.214220i | ||||||
\(974\) | −45.9643 | + | 123.709i | −0.0471912 | + | 0.127011i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −193.800 | − | 1301.51i | −0.198566 | − | 1.33351i | ||||
\(977\) | 918.977i | 0.940611i | 0.882504 | + | 0.470305i | \(0.155856\pi\) | ||||
−0.882504 | + | 0.470305i | \(0.844144\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1277.27i | 1.30466i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 677.100 | + | 251.578i | 0.689511 | + | 0.256189i | ||||
\(983\) | 1162.30 | 1.18240 | 0.591200 | − | 0.806525i | \(-0.298654\pi\) | ||||
0.591200 | + | 0.806525i | \(0.298654\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1179.66 | − | 438.306i | −1.19641 | − | 0.444530i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 729.245 | + | 628.698i | 0.738103 | + | 0.636334i | ||||
\(989\) | −2608.75 | −2.63776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 491.614i | − | 0.496079i | −0.968750 | − | 0.248040i | \(-0.920214\pi\) | ||
0.968750 | − | 0.248040i | \(-0.0797863\pi\) | |||||||
\(992\) | 31.9488 | − | 151.434i | 0.0322064 | − | 0.152655i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 786.712 | + | 292.305i | 0.791461 | + | 0.294069i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1262.51i | 1.26630i | 0.774027 | + | 0.633152i | \(0.218239\pi\) | ||||
−0.774027 | + | 0.633152i | \(0.781761\pi\) | |||||||
\(998\) | −1333.22 | − | 495.363i | −1.33590 | − | 0.496355i | ||||
\(999\) | 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 | 900.3.f.f.199.6 | 16 | ||
3.2 | odd | 2 | 300.3.f.b.199.11 | 16 | |||
4.3 | odd | 2 | inner | 900.3.f.f.199.12 | 16 | ||
5.2 | odd | 4 | 180.3.c.b.91.1 | 8 | |||
5.3 | odd | 4 | 900.3.c.u.451.8 | 8 | |||
5.4 | even | 2 | inner | 900.3.f.f.199.11 | 16 | ||
12.11 | even | 2 | 300.3.f.b.199.5 | 16 | |||
15.2 | even | 4 | 60.3.c.a.31.8 | yes | 8 | ||
15.8 | even | 4 | 300.3.c.d.151.1 | 8 | |||
15.14 | odd | 2 | 300.3.f.b.199.6 | 16 | |||
20.3 | even | 4 | 900.3.c.u.451.7 | 8 | |||
20.7 | even | 4 | 180.3.c.b.91.2 | 8 | |||
20.19 | odd | 2 | inner | 900.3.f.f.199.5 | 16 | ||
40.27 | even | 4 | 2880.3.e.j.2431.3 | 8 | |||
40.37 | odd | 4 | 2880.3.e.j.2431.2 | 8 | |||
60.23 | odd | 4 | 300.3.c.d.151.2 | 8 | |||
60.47 | odd | 4 | 60.3.c.a.31.7 | ✓ | 8 | ||
60.59 | even | 2 | 300.3.f.b.199.12 | 16 | |||
120.77 | even | 4 | 960.3.e.c.511.3 | 8 | |||
120.107 | odd | 4 | 960.3.e.c.511.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.7 | ✓ | 8 | 60.47 | odd | 4 | ||
60.3.c.a.31.8 | yes | 8 | 15.2 | even | 4 | ||
180.3.c.b.91.1 | 8 | 5.2 | odd | 4 | |||
180.3.c.b.91.2 | 8 | 20.7 | even | 4 | |||
300.3.c.d.151.1 | 8 | 15.8 | even | 4 | |||
300.3.c.d.151.2 | 8 | 60.23 | odd | 4 | |||
300.3.f.b.199.5 | 16 | 12.11 | even | 2 | |||
300.3.f.b.199.6 | 16 | 15.14 | odd | 2 | |||
300.3.f.b.199.11 | 16 | 3.2 | odd | 2 | |||
300.3.f.b.199.12 | 16 | 60.59 | even | 2 | |||
900.3.c.u.451.7 | 8 | 20.3 | even | 4 | |||
900.3.c.u.451.8 | 8 | 5.3 | odd | 4 | |||
900.3.f.f.199.5 | 16 | 20.19 | odd | 2 | inner | ||
900.3.f.f.199.6 | 16 | 1.1 | even | 1 | trivial | ||
900.3.f.f.199.11 | 16 | 5.4 | even | 2 | inner | ||
900.3.f.f.199.12 | 16 | 4.3 | odd | 2 | inner | ||
960.3.e.c.511.3 | 8 | 120.77 | even | 4 | |||
960.3.e.c.511.8 | 8 | 120.107 | odd | 4 | |||
2880.3.e.j.2431.2 | 8 | 40.37 | odd | 4 | |||
2880.3.e.j.2431.3 | 8 | 40.27 | even | 4 |