Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.41108373504.15 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 4x^{6} + 20x^{5} + 20x^{4} - 28x^{3} + 4x^{2} + 12x + 33 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 363) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.4 | ||
Root | \(0.912245 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.j.604.5 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.124105i | − 0.0620523i | −0.999519 | − | 0.0310262i | \(-0.990122\pi\) | ||||
0.999519 | − | 0.0310262i | \(-0.00987752\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.98460 | 0.996150 | ||||||||
\(5\) | −4.55654 | −0.911308 | −0.455654 | − | 0.890157i | \(-0.650595\pi\) | ||||
−0.455654 | + | 0.890157i | \(0.650595\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.06958i | 0.724226i | 0.932134 | + | 0.362113i | \(0.117945\pi\) | ||||
−0.932134 | + | 0.362113i | \(0.882055\pi\) | |||||||
\(8\) | − 0.990926i | − 0.123866i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.565488i | 0.0565488i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.20664i | 0.554357i | 0.960818 | + | 0.277179i | \(0.0893994\pi\) | ||||
−0.960818 | + | 0.277179i | \(0.910601\pi\) | |||||||
\(14\) | 0.629159 | 0.0449399 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.8154 | 0.988463 | ||||||||
\(17\) | − 23.3204i | − 1.37179i | −0.727703 | − | 0.685893i | \(-0.759412\pi\) | ||||
0.727703 | − | 0.685893i | \(-0.240588\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 26.1041i | − 1.37390i | −0.726706 | − | 0.686949i | \(-0.758950\pi\) | ||||
0.726706 | − | 0.686949i | \(-0.241050\pi\) | |||||||
\(20\) | −18.1560 | −0.907799 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 41.1662 | 1.78983 | 0.894917 | − | 0.446233i | \(-0.147235\pi\) | ||||
0.894917 | + | 0.446233i | \(0.147235\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.23794 | −0.169518 | ||||||||
\(26\) | 0.894378 | 0.0343992 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 20.2003i | 0.721438i | ||||||||
\(29\) | 49.6430i | 1.71183i | 0.517118 | + | 0.855914i | \(0.327005\pi\) | ||||
−0.517118 | + | 0.855914i | \(0.672995\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.46048 | −0.305177 | −0.152588 | − | 0.988290i | \(-0.548761\pi\) | ||||
−0.152588 | + | 0.988290i | \(0.548761\pi\) | |||||||
\(32\) | − 5.92647i | − 0.185202i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.89417 | −0.0851225 | ||||||||
\(35\) | − 23.0998i | − 0.659993i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 49.5316 | 1.33869 | 0.669345 | − | 0.742951i | \(-0.266575\pi\) | ||||
0.669345 | + | 0.742951i | \(0.266575\pi\) | |||||||
\(38\) | −3.23964 | −0.0852536 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.51519i | 0.112880i | ||||||||
\(41\) | 69.5972i | 1.69749i | 0.528800 | + | 0.848747i | \(0.322642\pi\) | ||||
−0.528800 | + | 0.848747i | \(0.677358\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 47.5666i | 1.10620i | 0.833115 | + | 0.553100i | \(0.186555\pi\) | ||||
−0.833115 | + | 0.553100i | \(0.813445\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 5.10891i | − 0.111063i | ||||||||
\(47\) | −2.85744 | −0.0607966 | −0.0303983 | − | 0.999538i | \(-0.509678\pi\) | ||||
−0.0303983 | + | 0.999538i | \(0.509678\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.2993 | 0.475496 | ||||||||
\(50\) | 0.525948i | 0.0105190i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 28.7156i | 0.552223i | ||||||||
\(53\) | 18.6798 | 0.352449 | 0.176225 | − | 0.984350i | \(-0.443611\pi\) | ||||
0.176225 | + | 0.984350i | \(0.443611\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.02358 | 0.0897068 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.16093 | 0.106223 | ||||||||
\(59\) | 7.18782 | 0.121827 | 0.0609137 | − | 0.998143i | \(-0.480599\pi\) | ||||
0.0609137 | + | 0.998143i | \(0.480599\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 42.5499i | 0.697539i | 0.937208 | + | 0.348770i | \(0.113400\pi\) | ||||
−0.937208 | + | 0.348770i | \(0.886600\pi\) | |||||||
\(62\) | 1.17409i | 0.0189369i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 62.5262 | 0.976971 | ||||||||
\(65\) | − 32.8374i | − 0.505190i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 66.5772 | 0.993689 | 0.496845 | − | 0.867840i | \(-0.334492\pi\) | ||||
0.496845 | + | 0.867840i | \(0.334492\pi\) | |||||||
\(68\) | − 92.9223i | − 1.36650i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.86679 | −0.0409541 | ||||||||
\(71\) | 49.2289 | 0.693365 | 0.346683 | − | 0.937982i | \(-0.387308\pi\) | ||||
0.346683 | + | 0.937982i | \(0.387308\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 35.8561i | 0.491179i | 0.969374 | + | 0.245589i | \(0.0789815\pi\) | ||||
−0.969374 | + | 0.245589i | \(0.921018\pi\) | |||||||
\(74\) | − 6.14710i | − 0.0830689i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 104.014i | − 1.36861i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 105.196i | − 1.33160i | −0.746130 | − | 0.665800i | \(-0.768090\pi\) | ||||
0.746130 | − | 0.665800i | \(-0.231910\pi\) | |||||||
\(80\) | −72.0636 | −0.900795 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.63734 | 0.105333 | ||||||||
\(83\) | 127.287i | 1.53358i | 0.641898 | + | 0.766790i | \(0.278147\pi\) | ||||
−0.641898 | + | 0.766790i | \(0.721853\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 106.260i | 1.25012i | ||||||||
\(86\) | 5.90324 | 0.0686423 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 93.7491 | 1.05336 | 0.526680 | − | 0.850063i | \(-0.323436\pi\) | ||||
0.526680 | + | 0.850063i | \(0.323436\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −36.5347 | −0.401480 | ||||||||
\(92\) | 164.031 | 1.78294 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.354622i | 0.00377257i | ||||||||
\(95\) | 118.944i | 1.25204i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52.2081 | −0.538227 | −0.269114 | − | 0.963108i | \(-0.586731\pi\) | ||||
−0.269114 | + | 0.963108i | \(0.586731\pi\) | |||||||
\(98\) | − 2.89155i | − 0.0295056i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −16.8865 | −0.168865 | ||||||||
\(101\) | − 45.8271i | − 0.453734i | −0.973926 | − | 0.226867i | \(-0.927152\pi\) | ||||
0.973926 | − | 0.226867i | \(-0.0728482\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −50.3265 | −0.488606 | −0.244303 | − | 0.969699i | \(-0.578559\pi\) | ||||
−0.244303 | + | 0.969699i | \(0.578559\pi\) | |||||||
\(104\) | 7.14125 | 0.0686659 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 2.31825i | − 0.0218703i | ||||||||
\(107\) | 24.6692i | 0.230553i | 0.993333 | + | 0.115276i | \(0.0367754\pi\) | ||||
−0.993333 | + | 0.115276i | \(0.963225\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 25.5067i | − 0.234006i | −0.993132 | − | 0.117003i | \(-0.962671\pi\) | ||||
0.993132 | − | 0.117003i | \(-0.0373288\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 80.1776i | 0.715871i | ||||||||
\(113\) | −73.9044 | −0.654021 | −0.327010 | − | 0.945021i | \(-0.606041\pi\) | ||||
−0.327010 | + | 0.945021i | \(0.606041\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −187.575 | −1.63109 | ||||||||
\(116\) | 197.807i | 1.70524i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 0.892042i | − 0.00755968i | ||||||||
\(119\) | 118.225 | 0.993483 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.28064 | 0.0432839 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −37.6962 | −0.304002 | ||||||||
\(125\) | 133.224 | 1.06579 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 175.883i | − 1.38490i | −0.721464 | − | 0.692452i | \(-0.756530\pi\) | ||||
0.721464 | − | 0.692452i | \(-0.243470\pi\) | |||||||
\(128\) | − 31.4657i | − 0.245826i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.07527 | −0.0313482 | ||||||||
\(131\) | − 124.649i | − 0.951521i | −0.879575 | − | 0.475760i | \(-0.842173\pi\) | ||||
0.879575 | − | 0.475760i | \(-0.157827\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 132.337 | 0.995013 | ||||||||
\(134\) | − 8.26254i | − 0.0616607i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −23.1087 | −0.169917 | ||||||||
\(137\) | 212.834 | 1.55353 | 0.776766 | − | 0.629790i | \(-0.216859\pi\) | ||||
0.776766 | + | 0.629790i | \(0.216859\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 135.725i | 0.976441i | 0.872720 | + | 0.488220i | \(0.162354\pi\) | ||||
−0.872720 | + | 0.488220i | \(0.837646\pi\) | |||||||
\(140\) | − 92.0433i | − 0.657452i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 6.10954i | − 0.0430249i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 226.200i | − 1.56000i | ||||||||
\(146\) | 4.44990 | 0.0304788 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 197.363 | 1.33354 | ||||||||
\(149\) | − 192.808i | − 1.29401i | −0.762485 | − | 0.647006i | \(-0.776021\pi\) | ||||
0.762485 | − | 0.647006i | \(-0.223979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 7.64995i | − 0.0506619i | −0.999679 | − | 0.0253310i | \(-0.991936\pi\) | ||||
0.999679 | − | 0.0253310i | \(-0.00806396\pi\) | |||||||
\(152\) | −25.8672 | −0.170179 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 43.1071 | 0.278110 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −45.0545 | −0.286971 | −0.143486 | − | 0.989652i | \(-0.545831\pi\) | ||||
−0.143486 | + | 0.989652i | \(0.545831\pi\) | |||||||
\(158\) | −13.0554 | −0.0826289 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 27.0042i | 0.168776i | ||||||||
\(161\) | 208.695i | 1.29624i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −186.553 | −1.14450 | −0.572248 | − | 0.820081i | \(-0.693928\pi\) | ||||
−0.572248 | + | 0.820081i | \(0.693928\pi\) | |||||||
\(164\) | 277.317i | 1.69096i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.7969 | 0.0951622 | ||||||||
\(167\) | 48.6198i | 0.291137i | 0.989348 | + | 0.145568i | \(0.0465011\pi\) | ||||
−0.989348 | + | 0.145568i | \(0.953499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 117.064 | 0.692688 | ||||||||
\(170\) | 13.1874 | 0.0775728 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 189.534i | 1.10194i | ||||||||
\(173\) | 17.1770i | 0.0992891i | 0.998767 | + | 0.0496445i | \(0.0158088\pi\) | ||||
−0.998767 | + | 0.0496445i | \(0.984191\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 21.4846i | − 0.122769i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 11.6347i | − 0.0653635i | ||||||||
\(179\) | 148.067 | 0.827190 | 0.413595 | − | 0.910461i | \(-0.364273\pi\) | ||||
0.413595 | + | 0.910461i | \(0.364273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −28.1792 | −0.155686 | −0.0778430 | − | 0.996966i | \(-0.524803\pi\) | ||||
−0.0778430 | + | 0.996966i | \(0.524803\pi\) | |||||||
\(182\) | 4.53413i | 0.0249128i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − 40.7926i | − 0.221699i | ||||||||
\(185\) | −225.693 | −1.21996 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −11.3858 | −0.0605625 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.7615 | 0.0776923 | ||||||||
\(191\) | −51.5509 | −0.269900 | −0.134950 | − | 0.990852i | \(-0.543087\pi\) | ||||
−0.134950 | + | 0.990852i | \(0.543087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 60.2956i | 0.312412i | 0.987724 | + | 0.156206i | \(0.0499264\pi\) | ||||
−0.987724 | + | 0.156206i | \(0.950074\pi\) | |||||||
\(194\) | 6.47926i | 0.0333983i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 92.8384 | 0.473665 | ||||||||
\(197\) | − 9.38629i | − 0.0476461i | −0.999716 | − | 0.0238231i | \(-0.992416\pi\) | ||||
0.999716 | − | 0.0238231i | \(-0.00758384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −174.756 | −0.878173 | −0.439086 | − | 0.898445i | \(-0.644698\pi\) | ||||
−0.439086 | + | 0.898445i | \(0.644698\pi\) | |||||||
\(200\) | 4.19948i | 0.0209974i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.68736 | −0.0281552 | ||||||||
\(203\) | −251.670 | −1.23975 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 317.123i | − 1.54694i | ||||||||
\(206\) | 6.24575i | 0.0303192i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 113.976i | 0.547962i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 360.511i | 1.70858i | 0.519794 | + | 0.854292i | \(0.326009\pi\) | ||||
−0.519794 | + | 0.854292i | \(0.673991\pi\) | |||||||
\(212\) | 74.4315 | 0.351092 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.06156 | 0.0143063 | ||||||||
\(215\) | − 216.739i | − 1.00809i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 47.9607i | − 0.221017i | ||||||||
\(218\) | −3.16550 | −0.0145206 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 168.062 | 0.760459 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 155.449 | 0.697082 | 0.348541 | − | 0.937293i | \(-0.386677\pi\) | ||||
0.348541 | + | 0.937293i | \(0.386677\pi\) | |||||||
\(224\) | 30.0447 | 0.134128 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.17187i | 0.0405835i | ||||||||
\(227\) | − 151.224i | − 0.666185i | −0.942894 | − | 0.333093i | \(-0.891908\pi\) | ||||
0.942894 | − | 0.333093i | \(-0.108092\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 307.605 | 1.34326 | 0.671628 | − | 0.740889i | \(-0.265596\pi\) | ||||
0.671628 | + | 0.740889i | \(0.265596\pi\) | |||||||
\(230\) | 23.2790i | 0.101213i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 49.1926 | 0.212037 | ||||||||
\(233\) | − 100.478i | − 0.431237i | −0.976478 | − | 0.215619i | \(-0.930823\pi\) | ||||
0.976478 | − | 0.215619i | \(-0.0691768\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.0200 | 0.0554045 | ||||||||
\(236\) | 28.6406 | 0.121358 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 14.6722i | − 0.0616480i | ||||||||
\(239\) | 460.051i | 1.92490i | 0.271457 | + | 0.962451i | \(0.412495\pi\) | ||||
−0.271457 | + | 0.962451i | \(0.587505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 251.848i | 1.04501i | 0.852635 | + | 0.522506i | \(0.175003\pi\) | ||||
−0.852635 | + | 0.522506i | \(0.824997\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 169.544i | 0.694853i | ||||||||
\(245\) | −106.164 | −0.433323 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 188.123 | 0.761630 | ||||||||
\(248\) | 9.37463i | 0.0378009i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 16.5337i | − 0.0661348i | ||||||||
\(251\) | 84.2374 | 0.335607 | 0.167804 | − | 0.985820i | \(-0.446333\pi\) | ||||
0.167804 | + | 0.985820i | \(0.446333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −21.8279 | −0.0859365 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 246.200 | 0.961717 | ||||||||
\(257\) | −495.580 | −1.92833 | −0.964163 | − | 0.265311i | \(-0.914526\pi\) | ||||
−0.964163 | + | 0.265311i | \(0.914526\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 251.104i | 0.969515i | ||||||||
\(260\) | − 130.844i | − 0.503245i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.4695 | −0.0590441 | ||||||||
\(263\) | − 303.296i | − 1.15322i | −0.817021 | − | 0.576608i | \(-0.804376\pi\) | ||||
0.817021 | − | 0.576608i | \(-0.195624\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −85.1153 | −0.321190 | ||||||||
\(266\) | − 16.4236i | − 0.0617429i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 265.283 | 0.989863 | ||||||||
\(269\) | −393.079 | −1.46126 | −0.730630 | − | 0.682774i | \(-0.760773\pi\) | ||||
−0.730630 | + | 0.682774i | \(0.760773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 121.331i | − 0.447717i | −0.974622 | − | 0.223859i | \(-0.928135\pi\) | ||||
0.974622 | − | 0.223859i | \(-0.0718654\pi\) | |||||||
\(272\) | − 368.821i | − 1.35596i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − 26.4137i | − 0.0964003i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 349.144i | − 1.26045i | −0.776414 | − | 0.630224i | \(-0.782963\pi\) | ||||
0.776414 | − | 0.630224i | \(-0.217037\pi\) | |||||||
\(278\) | 16.8441 | 0.0605904 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −22.8902 | −0.0817506 | ||||||||
\(281\) | − 214.011i | − 0.761607i | −0.924656 | − | 0.380803i | \(-0.875647\pi\) | ||||
0.924656 | − | 0.380803i | \(-0.124353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 130.356i | − 0.460621i | −0.973117 | − | 0.230310i | \(-0.926026\pi\) | ||||
0.973117 | − | 0.230310i | \(-0.0739741\pi\) | |||||||
\(284\) | 196.158 | 0.690696 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −352.829 | −1.22937 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −254.839 | −0.881796 | ||||||||
\(290\) | −28.0725 | −0.0968018 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 142.872i | 0.489288i | ||||||||
\(293\) | − 343.644i | − 1.17285i | −0.810005 | − | 0.586423i | \(-0.800536\pi\) | ||||
0.810005 | − | 0.586423i | \(-0.199464\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32.7516 | −0.111022 | ||||||||
\(296\) | − 49.0821i | − 0.165818i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23.9283 | −0.0802964 | ||||||||
\(299\) | 296.670i | 0.992207i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −241.143 | −0.801140 | ||||||||
\(302\) | −0.949395 | −0.00314369 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 412.847i | − 1.35805i | ||||||||
\(305\) | − 193.880i | − 0.635673i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 368.749i | − 1.20114i | −0.799573 | − | 0.600568i | \(-0.794941\pi\) | ||||
0.799573 | − | 0.600568i | \(-0.205059\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 5.34979i | − 0.0172574i | ||||||||
\(311\) | 143.959 | 0.462890 | 0.231445 | − | 0.972848i | \(-0.425655\pi\) | ||||
0.231445 | + | 0.972848i | \(0.425655\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −300.681 | −0.960642 | −0.480321 | − | 0.877093i | \(-0.659480\pi\) | ||||
−0.480321 | + | 0.877093i | \(0.659480\pi\) | |||||||
\(314\) | 5.59147i | 0.0178072i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − 419.165i | − 1.32647i | ||||||||
\(317\) | −198.224 | −0.625312 | −0.312656 | − | 0.949866i | \(-0.601219\pi\) | ||||
−0.312656 | + | 0.949866i | \(0.601219\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −284.903 | −0.890322 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 25.9001 | 0.0804350 | ||||||||
\(323\) | −608.756 | −1.88469 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 30.5413i | − 0.0939733i | ||||||||
\(326\) | 23.1521i | 0.0710186i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 68.9657 | 0.210261 | ||||||||
\(329\) | − 14.4860i | − 0.0440305i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −332.018 | −1.00307 | −0.501537 | − | 0.865136i | \(-0.667232\pi\) | ||||
−0.501537 | + | 0.865136i | \(0.667232\pi\) | |||||||
\(332\) | 507.188i | 1.52767i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.03395 | 0.0180657 | ||||||||
\(335\) | −303.362 | −0.905557 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 234.104i | 0.694671i | 0.937741 | + | 0.347335i | \(0.112913\pi\) | ||||
−0.937741 | + | 0.347335i | \(0.887087\pi\) | |||||||
\(338\) | − 14.5282i | − 0.0429829i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 423.404i | 1.24531i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 366.527i | 1.06859i | ||||||||
\(344\) | 47.1350 | 0.137020 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.13175 | 0.00616112 | ||||||||
\(347\) | − 57.6196i | − 0.166051i | −0.996547 | − | 0.0830254i | \(-0.973542\pi\) | ||||
0.996547 | − | 0.0830254i | \(-0.0264583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 611.166i | 1.75119i | 0.483045 | + | 0.875596i | \(0.339531\pi\) | ||||
−0.483045 | + | 0.875596i | \(0.660469\pi\) | |||||||
\(350\) | −2.66634 | −0.00761811 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −462.545 | −1.31032 | −0.655162 | − | 0.755488i | \(-0.727400\pi\) | ||||
−0.655162 | + | 0.755488i | \(0.727400\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −224.314 | −0.631869 | ||||||||
\(356\) | 373.553 | 1.04930 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 18.3758i | − 0.0513290i | ||||||||
\(359\) | − 598.189i | − 1.66626i | −0.553074 | − | 0.833132i | \(-0.686545\pi\) | ||||
0.553074 | − | 0.833132i | \(-0.313455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −320.422 | −0.887595 | ||||||||
\(362\) | 3.49717i | 0.00966068i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −145.576 | −0.399934 | ||||||||
\(365\) | − 163.380i | − 0.447615i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −549.990 | −1.49861 | −0.749306 | − | 0.662224i | \(-0.769613\pi\) | ||||
−0.749306 | + | 0.662224i | \(0.769613\pi\) | |||||||
\(368\) | 651.060 | 1.76918 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 28.0095i | 0.0757013i | ||||||||
\(371\) | 94.6989i | 0.255253i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 394.767i | − 1.05836i | −0.848511 | − | 0.529178i | \(-0.822500\pi\) | ||||
0.848511 | − | 0.529178i | \(-0.177500\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.83151i | 0.00753062i | ||||||||
\(377\) | −357.760 | −0.948965 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 201.197 | 0.530864 | 0.265432 | − | 0.964130i | \(-0.414485\pi\) | ||||
0.265432 | + | 0.964130i | \(0.414485\pi\) | |||||||
\(380\) | 473.945i | 1.24722i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.39771i | 0.0167479i | ||||||||
\(383\) | 80.4688 | 0.210101 | 0.105051 | − | 0.994467i | \(-0.466500\pi\) | ||||
0.105051 | + | 0.994467i | \(0.466500\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.48296 | 0.0193859 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −208.028 | −0.536155 | ||||||||
\(389\) | −99.8895 | −0.256785 | −0.128393 | − | 0.991723i | \(-0.540982\pi\) | ||||
−0.128393 | + | 0.991723i | \(0.540982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 960.010i | − 2.45527i | ||||||||
\(392\) | − 23.0879i | − 0.0588977i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.16488 | −0.00295655 | ||||||||
\(395\) | 479.332i | 1.21350i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 195.426 | 0.492256 | 0.246128 | − | 0.969237i | \(-0.420842\pi\) | ||||
0.246128 | + | 0.969237i | \(0.420842\pi\) | |||||||
\(398\) | 21.6881i | 0.0544927i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −67.0248 | −0.167562 | ||||||||
\(401\) | 21.7160 | 0.0541547 | 0.0270773 | − | 0.999633i | \(-0.491380\pi\) | ||||
0.0270773 | + | 0.999633i | \(0.491380\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 68.1783i | − 0.169177i | ||||||||
\(404\) | − 182.603i | − 0.451987i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 31.2334i | 0.0769295i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 140.738i | 0.344103i | 0.985088 | + | 0.172052i | \(0.0550396\pi\) | ||||
−0.985088 | + | 0.172052i | \(0.944960\pi\) | |||||||
\(410\) | −39.3564 | −0.0959912 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −200.531 | −0.486725 | ||||||||
\(413\) | 36.4393i | 0.0882307i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 579.989i | − 1.39756i | ||||||||
\(416\) | 42.7100 | 0.102668 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −205.230 | −0.489810 | −0.244905 | − | 0.969547i | \(-0.578757\pi\) | ||||
−0.244905 | + | 0.969547i | \(0.578757\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 775.170 | 1.84126 | 0.920629 | − | 0.390439i | \(-0.127677\pi\) | ||||
0.920629 | + | 0.390439i | \(0.127677\pi\) | |||||||
\(422\) | 44.7411 | 0.106022 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 18.5103i | − 0.0436564i | ||||||||
\(425\) | 98.8303i | 0.232542i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −215.710 | −0.505176 | ||||||||
\(428\) | 98.2966i | 0.229665i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.8984 | −0.0625543 | ||||||||
\(431\) | − 54.6468i | − 0.126791i | −0.997988 | − | 0.0633954i | \(-0.979807\pi\) | ||||
0.997988 | − | 0.0633954i | \(-0.0201929\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −498.812 | −1.15199 | −0.575996 | − | 0.817453i | \(-0.695385\pi\) | ||||
−0.575996 | + | 0.817453i | \(0.695385\pi\) | |||||||
\(434\) | −5.95215 | −0.0137146 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 101.634i | − 0.233105i | ||||||||
\(437\) | − 1074.60i | − 2.45905i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 125.316i | − 0.285457i | −0.989762 | − | 0.142729i | \(-0.954412\pi\) | ||||
0.989762 | − | 0.142729i | \(-0.0455876\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 20.8572i | − 0.0471883i | ||||||||
\(443\) | 613.792 | 1.38553 | 0.692767 | − | 0.721161i | \(-0.256391\pi\) | ||||
0.692767 | + | 0.721161i | \(0.256391\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −427.172 | −0.959936 | ||||||||
\(446\) | − 19.2920i | − 0.0432556i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 316.982i | 0.707548i | ||||||||
\(449\) | −385.155 | −0.857806 | −0.428903 | − | 0.903351i | \(-0.641100\pi\) | ||||
−0.428903 | + | 0.903351i | \(0.641100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −294.479 | −0.651503 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.7676 | −0.0413383 | ||||||||
\(455\) | 166.472 | 0.365872 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 44.6202i | − 0.0976373i | −0.998808 | − | 0.0488186i | \(-0.984454\pi\) | ||||
0.998808 | − | 0.0488186i | \(-0.0155456\pi\) | |||||||
\(458\) | − 38.1753i | − 0.0833521i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −747.412 | −1.62481 | ||||||||
\(461\) | 392.409i | 0.851212i | 0.904909 | + | 0.425606i | \(0.139939\pi\) | ||||
−0.904909 | + | 0.425606i | \(0.860061\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −98.5450 | −0.212840 | −0.106420 | − | 0.994321i | \(-0.533939\pi\) | ||||
−0.106420 | + | 0.994321i | \(0.533939\pi\) | |||||||
\(464\) | 785.125i | 1.69208i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.4698 | −0.0267593 | ||||||||
\(467\) | −269.776 | −0.577679 | −0.288839 | − | 0.957378i | \(-0.593269\pi\) | ||||
−0.288839 | + | 0.957378i | \(0.593269\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 337.519i | 0.719656i | ||||||||
\(470\) | − 1.61585i | − 0.00343798i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 7.12260i | − 0.0150902i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 110.627i | 0.232900i | ||||||||
\(476\) | 471.077 | 0.989658 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 57.0945 | 0.119445 | ||||||||
\(479\) | − 408.366i | − 0.852539i | −0.904596 | − | 0.426270i | \(-0.859827\pi\) | ||||
0.904596 | − | 0.426270i | \(-0.140173\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 356.956i | 0.742113i | ||||||||
\(482\) | 31.2555 | 0.0648455 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 237.888 | 0.490491 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −494.516 | −1.01543 | −0.507717 | − | 0.861524i | \(-0.669510\pi\) | ||||
−0.507717 | + | 0.861524i | \(0.669510\pi\) | |||||||
\(488\) | 42.1638 | 0.0864012 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.1755i | 0.0268887i | ||||||||
\(491\) | 37.3031i | 0.0759738i | 0.999278 | + | 0.0379869i | \(0.0120945\pi\) | ||||
−0.999278 | + | 0.0379869i | \(0.987905\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1157.69 | 2.34826 | ||||||||
\(494\) | − 23.3469i | − 0.0472609i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −149.621 | −0.301656 | ||||||||
\(497\) | 249.570i | 0.502154i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 202.446 | 0.405703 | 0.202851 | − | 0.979210i | \(-0.434979\pi\) | ||||
0.202851 | + | 0.979210i | \(0.434979\pi\) | |||||||
\(500\) | 530.844 | 1.06169 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 10.4543i | − 0.0208252i | ||||||||
\(503\) | 369.829i | 0.735247i | 0.929975 | + | 0.367623i | \(0.119828\pi\) | ||||
−0.929975 | + | 0.367623i | \(0.880172\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 208.813i | 0.413491i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 700.822i | − 1.37957i | ||||||||
\(509\) | −76.0419 | −0.149395 | −0.0746974 | − | 0.997206i | \(-0.523799\pi\) | ||||
−0.0746974 | + | 0.997206i | \(0.523799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −181.775 | −0.355725 | ||||||||
\(512\) | − 156.417i | − 0.305502i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 61.5038i | 0.119657i | ||||||||
\(515\) | 229.315 | 0.445271 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 31.1632 | 0.0601607 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −32.5394 | −0.0625758 | ||||||||
\(521\) | 339.649 | 0.651918 | 0.325959 | − | 0.945384i | \(-0.394313\pi\) | ||||
0.325959 | + | 0.945384i | \(0.394313\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 102.616i | − 0.196207i | −0.995176 | − | 0.0981035i | \(-0.968722\pi\) | ||||
0.995176 | − | 0.0981035i | \(-0.0312776\pi\) | |||||||
\(524\) | − 496.677i | − 0.947857i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −37.6404 | −0.0715597 | ||||||||
\(527\) | 220.622i | 0.418637i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1165.65 | 2.20350 | ||||||||
\(530\) | 10.5632i | 0.0199306i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 527.309 | 0.991182 | ||||||||
\(533\) | −501.562 | −0.941018 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 112.406i | − 0.210105i | ||||||||
\(536\) | − 65.9730i | − 0.123084i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 48.7829i | 0.0906745i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 431.271i | 0.797173i | 0.917131 | + | 0.398587i | \(0.130499\pi\) | ||||
−0.917131 | + | 0.398587i | \(0.869501\pi\) | |||||||
\(542\) | −15.0578 | −0.0277819 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −138.207 | −0.254058 | ||||||||
\(545\) | 116.222i | 0.213252i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 518.823i | 0.948488i | 0.880393 | + | 0.474244i | \(0.157279\pi\) | ||||
−0.880393 | + | 0.474244i | \(0.842721\pi\) | |||||||
\(548\) | 848.057 | 1.54755 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1295.88 | 2.35188 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 533.302 | 0.964380 | ||||||||
\(554\) | −43.3304 | −0.0782137 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 540.811i | 0.972681i | ||||||||
\(557\) | 487.784i | 0.875734i | 0.899040 | + | 0.437867i | \(0.144266\pi\) | ||||
−0.899040 | + | 0.437867i | \(0.855734\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −342.796 | −0.613230 | ||||||||
\(560\) | − 365.332i | − 0.652379i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26.5598 | −0.0472595 | ||||||||
\(563\) | − 203.073i | − 0.360697i | −0.983603 | − | 0.180349i | \(-0.942277\pi\) | ||||
0.983603 | − | 0.180349i | \(-0.0577226\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 336.748 | 0.596014 | ||||||||
\(566\) | −16.1777 | −0.0285826 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 48.7822i | − 0.0858842i | ||||||||
\(569\) | 728.660i | 1.28060i | 0.768126 | + | 0.640299i | \(0.221189\pi\) | ||||
−0.768126 | + | 0.640299i | \(0.778811\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 384.133i | 0.672738i | 0.941730 | + | 0.336369i | \(0.109199\pi\) | ||||
−0.941730 | + | 0.336369i | \(0.890801\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 43.7877i | 0.0762852i | ||||||||
\(575\) | −174.460 | −0.303408 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 523.738 | 0.907691 | 0.453846 | − | 0.891080i | \(-0.350052\pi\) | ||||
0.453846 | + | 0.891080i | \(0.350052\pi\) | |||||||
\(578\) | 31.6267i | 0.0547175i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 901.318i | − 1.55400i | ||||||||
\(581\) | −645.293 | −1.11066 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 35.5307 | 0.0608402 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −42.6478 | −0.0727779 | ||||||||
\(587\) | −645.790 | −1.10015 | −0.550077 | − | 0.835114i | \(-0.685402\pi\) | ||||
−0.550077 | + | 0.835114i | \(0.685402\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 246.957i | 0.419282i | ||||||||
\(590\) | 4.06463i | 0.00688920i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 783.362 | 1.32325 | ||||||||
\(593\) | − 640.096i | − 1.07942i | −0.841851 | − | 0.539710i | \(-0.818534\pi\) | ||||
0.841851 | − | 0.539710i | \(-0.181466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −538.695 | −0.905369 | ||||||||
\(596\) | − 768.261i | − 1.28903i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 36.8181 | 0.0615688 | ||||||||
\(599\) | 126.085 | 0.210493 | 0.105247 | − | 0.994446i | \(-0.466437\pi\) | ||||
0.105247 | + | 0.994446i | \(0.466437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 1070.82i | − 1.78174i | −0.454260 | − | 0.890869i | \(-0.650096\pi\) | ||||
0.454260 | − | 0.890869i | \(-0.349904\pi\) | |||||||
\(602\) | 29.9270i | 0.0497126i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 30.4820i | − 0.0504669i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 175.511i | − 0.289145i | −0.989494 | − | 0.144572i | \(-0.953819\pi\) | ||||
0.989494 | − | 0.144572i | \(-0.0461807\pi\) | |||||||
\(608\) | −154.705 | −0.254449 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.0615 | −0.0394450 | ||||||||
\(611\) | − 20.5926i | − 0.0337031i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 175.385i | − 0.286109i | −0.989715 | − | 0.143055i | \(-0.954308\pi\) | ||||
0.989715 | − | 0.143055i | \(-0.0456924\pi\) | |||||||
\(614\) | −45.7635 | −0.0745333 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −377.991 | −0.612627 | −0.306313 | − | 0.951931i | \(-0.599096\pi\) | ||||
−0.306313 | + | 0.951931i | \(0.599096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 866.149 | 1.39927 | 0.699636 | − | 0.714500i | \(-0.253346\pi\) | ||||
0.699636 | + | 0.714500i | \(0.253346\pi\) | |||||||
\(620\) | 171.764 | 0.277039 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 17.8659i | − 0.0287234i | ||||||||
\(623\) | 475.269i | 0.762872i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −501.091 | −0.801746 | ||||||||
\(626\) | 37.3159i | 0.0596101i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −179.524 | −0.285866 | ||||||||
\(629\) | − 1155.09i | − 1.83640i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −437.321 | −0.693060 | −0.346530 | − | 0.938039i | \(-0.612640\pi\) | ||||
−0.346530 | + | 0.938039i | \(0.612640\pi\) | |||||||
\(632\) | −104.242 | −0.164940 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.6005i | 0.0388021i | ||||||||
\(635\) | 801.417i | 1.26207i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 167.910i | 0.263595i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 143.375i | 0.224023i | ||||||||
\(641\) | −928.077 | −1.44786 | −0.723929 | − | 0.689875i | \(-0.757666\pi\) | ||||
−0.723929 | + | 0.689875i | \(0.757666\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 616.947 | 0.959482 | 0.479741 | − | 0.877410i | \(-0.340731\pi\) | ||||
0.479741 | + | 0.877410i | \(0.340731\pi\) | |||||||
\(644\) | 831.567i | 1.29125i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 75.5495i | 0.116950i | ||||||||
\(647\) | −473.750 | −0.732226 | −0.366113 | − | 0.930570i | \(-0.619312\pi\) | ||||
−0.366113 | + | 0.930570i | \(0.619312\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.79032 | −0.00583126 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −743.338 | −1.14009 | ||||||||
\(653\) | 489.445 | 0.749532 | 0.374766 | − | 0.927119i | \(-0.377723\pi\) | ||||
0.374766 | + | 0.927119i | \(0.377723\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 567.969i | 0.867128i | ||||||||
\(656\) | 1100.71i | 1.67791i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.79779 | −0.00273220 | ||||||||
\(659\) | − 597.704i | − 0.906986i | −0.891260 | − | 0.453493i | \(-0.850178\pi\) | ||||
0.891260 | − | 0.453493i | \(-0.149822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −510.846 | −0.772838 | −0.386419 | − | 0.922323i | \(-0.626288\pi\) | ||||
−0.386419 | + | 0.922323i | \(0.626288\pi\) | |||||||
\(662\) | 41.2049i | 0.0622431i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 126.132 | 0.189958 | ||||||||
\(665\) | −602.998 | −0.906763 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2043.61i | 3.06389i | ||||||||
\(668\) | 193.731i | 0.290016i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 37.6486i | 0.0561919i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 236.608i | − 0.351572i | −0.984428 | − | 0.175786i | \(-0.943753\pi\) | ||||
0.984428 | − | 0.175786i | \(-0.0562467\pi\) | |||||||
\(674\) | 29.0534 | 0.0431059 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 466.454 | 0.690021 | ||||||||
\(677\) | − 1252.79i | − 1.85050i | −0.379353 | − | 0.925252i | \(-0.623853\pi\) | ||||
0.379353 | − | 0.925252i | \(-0.376147\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 264.673i | − 0.389799i | ||||||||
\(680\) | 105.296 | 0.154847 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 144.720 | 0.211888 | 0.105944 | − | 0.994372i | \(-0.466213\pi\) | ||||
0.105944 | + | 0.994372i | \(0.466213\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −969.786 | −1.41575 | ||||||||
\(686\) | 45.4878 | 0.0663087 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 752.286i | 1.09344i | ||||||||
\(689\) | 134.619i | 0.195383i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1115.11 | 1.61376 | 0.806882 | − | 0.590712i | \(-0.201153\pi\) | ||||
0.806882 | + | 0.590712i | \(0.201153\pi\) | |||||||
\(692\) | 68.4435i | 0.0989068i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.15087 | −0.0103038 | ||||||||
\(695\) | − 618.438i | − 0.889838i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1623.03 | 2.32860 | ||||||||
\(698\) | 75.8485 | 0.108665 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − 85.6075i | − 0.122296i | ||||||||
\(701\) | 422.309i | 0.602437i | 0.953555 | + | 0.301219i | \(0.0973934\pi\) | ||||
−0.953555 | + | 0.301219i | \(0.902607\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1292.97i | − 1.83922i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 57.4039i | 0.0813087i | ||||||||
\(707\) | 232.324 | 0.328606 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 406.871 | 0.573865 | 0.286933 | − | 0.957951i | \(-0.407364\pi\) | ||||
0.286933 | + | 0.957951i | \(0.407364\pi\) | |||||||
\(710\) | 27.8384i | 0.0392090i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 92.8984i | − 0.130475i | ||||||||
\(713\) | −389.452 | −0.546216 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 589.987 | 0.824005 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −74.2380 | −0.103396 | ||||||||
\(719\) | −192.781 | −0.268123 | −0.134062 | − | 0.990973i | \(-0.542802\pi\) | ||||
−0.134062 | + | 0.990973i | \(0.542802\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 255.134i | − 0.353862i | ||||||||
\(722\) | 39.7659i | 0.0550774i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −112.283 | −0.155087 | ||||||||
\(725\) | − 210.384i | − 0.290185i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 778.698 | 1.07111 | 0.535556 | − | 0.844500i | \(-0.320102\pi\) | ||||
0.535556 | + | 0.844500i | \(0.320102\pi\) | |||||||
\(728\) | 36.2032i | 0.0497296i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20.2762 | −0.0277756 | ||||||||
\(731\) | 1109.27 | 1.51747 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 66.1405i | 0.0902325i | 0.998982 | + | 0.0451163i | \(0.0143658\pi\) | ||||
−0.998982 | + | 0.0451163i | \(0.985634\pi\) | |||||||
\(734\) | 68.2564i | 0.0929923i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 243.970i | − 0.331481i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 515.469i | − 0.697522i | −0.937212 | − | 0.348761i | \(-0.886603\pi\) | ||||
0.937212 | − | 0.348761i | \(-0.113397\pi\) | |||||||
\(740\) | −899.294 | −1.21526 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.7526 | 0.0158390 | ||||||||
\(743\) | 586.425i | 0.789266i | 0.918839 | + | 0.394633i | \(0.129128\pi\) | ||||
−0.918839 | + | 0.394633i | \(0.870872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 878.536i | 1.17924i | ||||||||
\(746\) | −48.9924 | −0.0656735 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −125.062 | −0.166972 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −975.919 | −1.29949 | −0.649746 | − | 0.760151i | \(-0.725125\pi\) | ||||
−0.649746 | + | 0.760151i | \(0.725125\pi\) | |||||||
\(752\) | −45.1916 | −0.0600952 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 44.3996i | 0.0588855i | ||||||||
\(755\) | 34.8573i | 0.0461686i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1018.99 | −1.34609 | −0.673047 | − | 0.739600i | \(-0.735015\pi\) | ||||
−0.673047 | + | 0.739600i | \(0.735015\pi\) | |||||||
\(758\) | − 24.9695i | − 0.0329413i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 117.865 | 0.155085 | ||||||||
\(761\) | − 636.194i | − 0.835998i | −0.908448 | − | 0.417999i | \(-0.862732\pi\) | ||||
0.908448 | − | 0.417999i | \(-0.137268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 129.308 | 0.169474 | ||||||||
\(764\) | −205.410 | −0.268861 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 9.98655i | − 0.0130373i | ||||||||
\(767\) | 51.8001i | 0.0675359i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1120.79i | 1.45747i | 0.684796 | + | 0.728735i | \(0.259891\pi\) | ||||
−0.684796 | + | 0.728735i | \(0.740109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 240.254i | 0.311209i | ||||||||
\(773\) | −411.320 | −0.532108 | −0.266054 | − | 0.963958i | \(-0.585720\pi\) | ||||
−0.266054 | + | 0.963958i | \(0.585720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.0929 | 0.0517328 | ||||||||
\(776\) | 51.7343i | 0.0666679i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.3968i | 0.0159341i | ||||||||
\(779\) | 1816.77 | 2.33218 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −119.142 | −0.152355 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 368.488 | 0.470011 | ||||||||
\(785\) | 205.292 | 0.261519 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 98.1176i | 0.124673i | 0.998055 | + | 0.0623365i | \(0.0198552\pi\) | ||||
−0.998055 | + | 0.0623365i | \(0.980145\pi\) | |||||||
\(788\) | − 37.4006i | − 0.0474627i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 59.4873 | 0.0753004 | ||||||||
\(791\) | − 374.664i | − 0.473659i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −306.642 | −0.386686 | ||||||||
\(794\) | − 24.2532i | − 0.0305456i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −696.334 | −0.874791 | ||||||||
\(797\) | 27.5903 | 0.0346178 | 0.0173089 | − | 0.999850i | \(-0.494490\pi\) | ||||
0.0173089 | + | 0.999850i | \(0.494490\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 66.6366i | 0.0833999i | ||||||||
\(800\) | 25.1160i | 0.0313950i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 2.69506i | − 0.00336042i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 950.929i | − 1.18128i | ||||||||
\(806\) | −8.46125 | −0.0104978 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −45.4113 | −0.0562021 | ||||||||
\(809\) | 1113.72i | 1.37666i | 0.725398 | + | 0.688330i | \(0.241656\pi\) | ||||
−0.725398 | + | 0.688330i | \(0.758344\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1459.55i | − 1.79969i | −0.436211 | − | 0.899844i | \(-0.643680\pi\) | ||||
0.436211 | − | 0.899844i | \(-0.356320\pi\) | |||||||
\(812\) | −1002.80 | −1.23498 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 850.035 | 1.04299 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1241.68 | 1.51981 | ||||||||
\(818\) | 17.4663 | 0.0213524 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 1263.61i | − 1.54098i | ||||||||
\(821\) | 1130.31i | 1.37675i | 0.725355 | + | 0.688375i | \(0.241676\pi\) | ||||
−0.725355 | + | 0.688375i | \(0.758324\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −980.288 | −1.19112 | −0.595558 | − | 0.803313i | \(-0.703069\pi\) | ||||
−0.595558 | + | 0.803313i | \(0.703069\pi\) | |||||||
\(824\) | 49.8698i | 0.0605216i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.52228 | 0.00547492 | ||||||||
\(827\) | 1041.92i | 1.25988i | 0.776643 | + | 0.629942i | \(0.216921\pi\) | ||||
−0.776643 | + | 0.629942i | \(0.783079\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.3982 | 0.0547626 | 0.0273813 | − | 0.999625i | \(-0.491283\pi\) | ||||
0.0273813 | + | 0.999625i | \(0.491283\pi\) | |||||||
\(830\) | −71.9793 | −0.0867221 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 450.604i | 0.541591i | ||||||||
\(833\) | − 543.348i | − 0.652279i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 221.538i | − 0.265315i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.4701i | 0.0303939i | ||||||||
\(839\) | 896.214 | 1.06819 | 0.534096 | − | 0.845424i | \(-0.320652\pi\) | ||||
0.534096 | + | 0.845424i | \(0.320652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1623.43 | −1.93036 | ||||||||
\(842\) | − 96.2022i | − 0.114254i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1436.49i | 1.70200i | ||||||||
\(845\) | −533.408 | −0.631252 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 295.429 | 0.348383 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.2653 | 0.0144298 | ||||||||
\(851\) | 2039.02 | 2.39603 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 522.189i | 0.612180i | 0.952003 | + | 0.306090i | \(0.0990208\pi\) | ||||
−0.952003 | + | 0.306090i | \(0.900979\pi\) | |||||||
\(854\) | 26.7707i | 0.0313474i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.4453 | 0.0285576 | ||||||||
\(857\) | − 116.799i | − 0.136288i | −0.997675 | − | 0.0681442i | \(-0.978292\pi\) | ||||
0.997675 | − | 0.0681442i | \(-0.0217078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1359.69 | 1.58287 | 0.791436 | − | 0.611251i | \(-0.209334\pi\) | ||||
0.791436 | + | 0.611251i | \(0.209334\pi\) | |||||||
\(860\) | − 863.619i | − 1.00421i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.78193 | −0.00786766 | ||||||||
\(863\) | 1194.91 | 1.38460 | 0.692298 | − | 0.721612i | \(-0.256598\pi\) | ||||
0.692298 | + | 0.721612i | \(0.256598\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 78.2677i | − 0.0904829i | ||||||||
\(866\) | 61.9049i | 0.0714837i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 191.104i | − 0.220166i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 479.798i | 0.550859i | ||||||||
\(872\) | −25.2752 | −0.0289854 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −133.363 | −0.152590 | ||||||||
\(875\) | 675.390i | 0.771874i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 564.773i | − 0.643983i | −0.946743 | − | 0.321992i | \(-0.895648\pi\) | ||||
0.946743 | − | 0.321992i | \(-0.104352\pi\) | |||||||
\(878\) | −15.5523 | −0.0177133 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1276.50 | 1.44892 | 0.724462 | − | 0.689315i | \(-0.242088\pi\) | ||||
0.724462 | + | 0.689315i | \(0.242088\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1357.43 | −1.53730 | −0.768649 | − | 0.639671i | \(-0.779071\pi\) | ||||
−0.768649 | + | 0.639671i | \(0.779071\pi\) | |||||||
\(884\) | 669.658 | 0.757531 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 76.1744i | − 0.0859756i | ||||||||
\(887\) | 710.054i | 0.800512i | 0.916403 | + | 0.400256i | \(0.131079\pi\) | ||||
−0.916403 | + | 0.400256i | \(0.868921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 891.653 | 1.00298 | ||||||||
\(890\) | 53.0140i | 0.0595663i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 619.403 | 0.694398 | ||||||||
\(893\) | 74.5908i | 0.0835284i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −674.673 | −0.753825 | ||||||||
\(896\) | 159.518 | 0.178033 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 47.7995i | 0.0532288i | ||||||||
\(899\) | − 469.647i | − 0.522410i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 435.620i | − 0.483485i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 73.2337i | 0.0810108i | ||||||||
\(905\) | 128.400 | 0.141878 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 462.174 | 0.509564 | 0.254782 | − | 0.966999i | \(-0.417996\pi\) | ||||
0.254782 | + | 0.966999i | \(0.417996\pi\) | |||||||
\(908\) | − 602.567i | − 0.663620i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − 20.6599i | − 0.0227032i | ||||||||
\(911\) | 1419.86 | 1.55857 | 0.779286 | − | 0.626668i | \(-0.215582\pi\) | ||||
0.779286 | + | 0.626668i | \(0.215582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −5.53758 | −0.00605862 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1225.68 | 1.33808 | ||||||||
\(917\) | 631.920 | 0.689116 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1235.25i | − 1.34413i | −0.740493 | − | 0.672064i | \(-0.765408\pi\) | ||||
0.740493 | − | 0.672064i | \(-0.234592\pi\) | |||||||
\(920\) | 185.873i | 0.202036i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 48.6997 | 0.0528197 | ||||||||
\(923\) | 354.775i | 0.384372i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −209.912 | −0.226932 | ||||||||
\(926\) | 12.2299i | 0.0132072i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 294.208 | 0.317034 | ||||||||
\(929\) | 97.7349 | 0.105204 | 0.0526022 | − | 0.998616i | \(-0.483248\pi\) | ||||
0.0526022 | + | 0.998616i | \(0.483248\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 608.207i | − 0.653283i | ||||||||
\(932\) | − 400.366i | − 0.429577i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.4805i | 0.0358463i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 523.196i | − 0.558374i | −0.960237 | − | 0.279187i | \(-0.909935\pi\) | ||||
0.960237 | − | 0.279187i | \(-0.0900649\pi\) | |||||||
\(938\) | 41.8876 | 0.0446563 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 51.8797 | 0.0551911 | ||||||||
\(941\) | 86.4170i | 0.0918353i | 0.998945 | + | 0.0459177i | \(0.0146212\pi\) | ||||
−0.998945 | + | 0.0459177i | \(0.985379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2865.05i | 3.03823i | ||||||||
\(944\) | 113.678 | 0.120422 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.94234 | −0.00627491 | −0.00313746 | − | 0.999995i | \(-0.500999\pi\) | ||||
−0.00313746 | + | 0.999995i | \(0.500999\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −258.402 | −0.272289 | ||||||||
\(950\) | 13.7294 | 0.0144520 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 117.152i | − 0.123059i | ||||||||
\(953\) | − 1251.07i | − 1.31277i | −0.754426 | − | 0.656386i | \(-0.772084\pi\) | ||||
0.754426 | − | 0.656386i | \(-0.227916\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 234.894 | 0.245962 | ||||||||
\(956\) | 1833.12i | 1.91749i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −50.6802 | −0.0529020 | ||||||||
\(959\) | 1078.98i | 1.12511i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −871.499 | −0.906867 | ||||||||
\(962\) | 44.2999 | 0.0460498 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1003.51i | 1.04099i | ||||||||
\(965\) | − 274.739i | − 0.284704i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 4.40274i | − 0.00455299i | −0.999997 | − | 0.00227650i | \(-0.999275\pi\) | ||||
0.999997 | − | 0.00227650i | \(-0.000724632\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − 29.5230i | − 0.0304361i | ||||||||
\(971\) | 332.226 | 0.342148 | 0.171074 | − | 0.985258i | \(-0.445276\pi\) | ||||
0.171074 | + | 0.985258i | \(0.445276\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −688.071 | −0.707164 | ||||||||
\(974\) | 61.3718i | 0.0630100i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 672.944i | 0.689492i | ||||||||
\(977\) | −865.872 | −0.886256 | −0.443128 | − | 0.896458i | \(-0.646131\pi\) | ||||
−0.443128 | + | 0.896458i | \(0.646131\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −423.022 | −0.431655 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.62949 | 0.00471435 | ||||||||
\(983\) | −53.4433 | −0.0543676 | −0.0271838 | − | 0.999630i | \(-0.508654\pi\) | ||||
−0.0271838 | + | 0.999630i | \(0.508654\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.7690i | 0.0434203i | ||||||||
\(986\) | − 143.675i | − 0.145715i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 749.593 | 0.758698 | ||||||||
\(989\) | 1958.14i | 1.97992i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −624.037 | −0.629704 | −0.314852 | − | 0.949141i | \(-0.601955\pi\) | ||||
−0.314852 | + | 0.949141i | \(0.601955\pi\) | |||||||
\(992\) | 56.0672i | 0.0565194i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 30.9728 | 0.0311598 | ||||||||
\(995\) | 796.284 | 0.800286 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1255.44i | − 1.25922i | −0.776912 | − | 0.629609i | \(-0.783215\pi\) | ||||
0.776912 | − | 0.629609i | \(-0.216785\pi\) | |||||||
\(998\) | − 25.1245i | − 0.0251748i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1089.3.c.j.604.4 | 8 | ||
3.2 | odd | 2 | 363.3.c.d.241.5 | yes | 8 | ||
11.10 | odd | 2 | inner | 1089.3.c.j.604.5 | 8 | ||
33.2 | even | 10 | 363.3.g.h.40.4 | 32 | |||
33.5 | odd | 10 | 363.3.g.h.118.4 | 32 | |||
33.8 | even | 10 | 363.3.g.h.112.4 | 32 | |||
33.14 | odd | 10 | 363.3.g.h.112.5 | 32 | |||
33.17 | even | 10 | 363.3.g.h.118.5 | 32 | |||
33.20 | odd | 10 | 363.3.g.h.40.5 | 32 | |||
33.26 | odd | 10 | 363.3.g.h.94.4 | 32 | |||
33.29 | even | 10 | 363.3.g.h.94.5 | 32 | |||
33.32 | even | 2 | 363.3.c.d.241.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.3.c.d.241.4 | ✓ | 8 | 33.32 | even | 2 | ||
363.3.c.d.241.5 | yes | 8 | 3.2 | odd | 2 | ||
363.3.g.h.40.4 | 32 | 33.2 | even | 10 | |||
363.3.g.h.40.5 | 32 | 33.20 | odd | 10 | |||
363.3.g.h.94.4 | 32 | 33.26 | odd | 10 | |||
363.3.g.h.94.5 | 32 | 33.29 | even | 10 | |||
363.3.g.h.112.4 | 32 | 33.8 | even | 10 | |||
363.3.g.h.112.5 | 32 | 33.14 | odd | 10 | |||
363.3.g.h.118.4 | 32 | 33.5 | odd | 10 | |||
363.3.g.h.118.5 | 32 | 33.17 | even | 10 | |||
1089.3.c.j.604.4 | 8 | 1.1 | even | 1 | trivial | ||
1089.3.c.j.604.5 | 8 | 11.10 | odd | 2 | inner |