Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,3,Mod(145,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cg (of order \(6\), degree \(2\), 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: | \(27.4660106475\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.577 |
Dual form | 1008.3.cg.a.145.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.50000 | + | 2.59808i | −0.900000 | + | 0.519615i | −0.877200 | − | 0.480125i | \(-0.840591\pi\) |
−0.0227998 | + | 0.999740i | \(0.507258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.50000 | + | 12.9904i | −0.681818 | + | 1.18094i | 0.292607 | + | 0.956233i | \(0.405477\pi\) |
−0.974425 | + | 0.224711i | \(0.927856\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 13.8564i | − | 1.06588i | −0.846154 | − | 0.532939i | \(-0.821088\pi\) | ||
0.846154 | − | 0.532939i | \(-0.178912\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −9.00000 | − | 5.19615i | −0.529412 | − | 0.305656i | 0.211365 | − | 0.977407i | \(-0.432209\pi\) |
−0.740777 | + | 0.671751i | \(0.765542\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.00000 | − | 5.19615i | 0.473684 | − | 0.273482i | −0.244096 | − | 0.969751i | \(-0.578491\pi\) |
0.717781 | + | 0.696269i | \(0.245158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | − | 1.73205i | 0.0400000 | − | 0.0692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.00000 | 0.310345 | 0.155172 | − | 0.987887i | \(-0.450407\pi\) | ||||
0.155172 | + | 0.987887i | \(0.450407\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.5000 | + | 6.06218i | 0.338710 | + | 0.195554i | 0.659701 | − | 0.751528i | \(-0.270683\pi\) |
−0.320992 | + | 0.947082i | \(0.604016\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 36.0000 | − | 5.19615i | 1.02857 | − | 0.148461i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | − | 8.66025i | −0.135135 | − | 0.234061i | 0.790514 | − | 0.612444i | \(-0.209814\pi\) |
−0.925649 | + | 0.378383i | \(0.876480\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3923i | 0.253471i | 0.991937 | + | 0.126735i | \(0.0404499\pi\) | ||||
−0.991937 | + | 0.126735i | \(0.959550\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 74.0000 | 1.72093 | 0.860465 | − | 0.509509i | \(-0.170173\pi\) | ||||
0.860465 | + | 0.509509i | \(0.170173\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 35.5000 | + | 33.7750i | 0.724490 | + | 0.689286i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 16.5000 | − | 28.5788i | 0.311321 | − | 0.539223i | −0.667328 | − | 0.744764i | \(-0.732562\pi\) |
0.978649 | + | 0.205541i | \(0.0658953\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 77.9423i | − | 1.41713i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.5000 | + | 7.79423i | 0.228814 | + | 0.132106i | 0.610025 | − | 0.792382i | \(-0.291160\pi\) |
−0.381211 | + | 0.924488i | \(0.624493\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 78.0000 | − | 45.0333i | 1.27869 | − | 0.738251i | 0.302081 | − | 0.953282i | \(-0.402319\pi\) |
0.976607 | + | 0.215031i | \(0.0689853\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 36.0000 | + | 62.3538i | 0.553846 | + | 0.959290i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −38.0000 | + | 65.8179i | −0.567164 | + | 0.982357i | 0.429681 | + | 0.902981i | \(0.358626\pi\) |
−0.996845 | + | 0.0793762i | \(0.974707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 84.0000 | 1.18310 | 0.591549 | − | 0.806269i | \(-0.298517\pi\) | ||||
0.591549 | + | 0.806269i | \(0.298517\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −54.0000 | − | 31.1769i | −0.739726 | − | 0.427081i | 0.0822437 | − | 0.996612i | \(-0.473791\pi\) |
−0.821970 | + | 0.569531i | \(0.807125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 82.5000 | − | 64.9519i | 1.07143 | − | 0.843531i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −21.5000 | − | 37.2391i | −0.272152 | − | 0.471381i | 0.697261 | − | 0.716818i | \(-0.254402\pi\) |
−0.969413 | + | 0.245437i | \(0.921069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 119.512i | − | 1.43990i | −0.694027 | − | 0.719949i | \(-0.744165\pi\) | ||
0.694027 | − | 0.719949i | \(-0.255835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 54.0000 | 0.635294 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 63.0000 | − | 36.3731i | 0.707865 | − | 0.408686i | −0.102405 | − | 0.994743i | \(-0.532654\pi\) |
0.810270 | + | 0.586057i | \(0.199320\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −36.0000 | + | 90.0666i | −0.395604 | + | 0.989743i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −27.0000 | + | 46.7654i | −0.284211 | + | 0.492267i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 185.329i | 1.91061i | 0.295618 | + | 0.955306i | \(0.404475\pi\) | ||||
−0.295618 | + | 0.955306i | \(0.595525\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 126.000 | + | 72.7461i | 1.24752 | + | 0.720259i | 0.970615 | − | 0.240637i | \(-0.0773564\pi\) |
0.276910 | + | 0.960896i | \(0.410690\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 60.0000 | − | 34.6410i | 0.582524 | − | 0.336321i | −0.179612 | − | 0.983738i | \(-0.557484\pi\) |
0.762136 | + | 0.647417i | \(0.224151\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −46.5000 | − | 80.5404i | −0.434579 | − | 0.752714i | 0.562682 | − | 0.826674i | \(-0.309770\pi\) |
−0.997261 | + | 0.0739599i | \(0.976436\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | − | 6.92820i | 0.0366972 | − | 0.0635615i | −0.847093 | − | 0.531444i | \(-0.821650\pi\) |
0.883791 | + | 0.467882i | \(0.154983\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −42.0000 | −0.371681 | −0.185841 | − | 0.982580i | \(-0.559501\pi\) | ||||
−0.185841 | + | 0.982580i | \(0.559501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 45.0000 | + | 57.1577i | 0.378151 | + | 0.480317i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −52.0000 | − | 90.0666i | −0.429752 | − | 0.744352i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 119.512i | − | 0.956092i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −35.0000 | −0.275591 | −0.137795 | − | 0.990461i | \(-0.544002\pi\) | ||||
−0.137795 | + | 0.990461i | \(0.544002\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 148.500 | − | 85.7365i | 1.13359 | − | 0.654477i | 0.188753 | − | 0.982025i | \(-0.439555\pi\) |
0.944835 | + | 0.327547i | \(0.106222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −72.0000 | + | 10.3923i | −0.541353 | + | 0.0781376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −48.0000 | + | 83.1384i | −0.350365 | + | 0.606850i | −0.986313 | − | 0.164882i | \(-0.947276\pi\) |
0.635948 | + | 0.771732i | \(0.280609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 183.597i | 1.32084i | 0.750894 | + | 0.660422i | \(0.229623\pi\) | ||||
−0.750894 | + | 0.660422i | \(0.770377\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 180.000 | + | 103.923i | 1.25874 | + | 0.726735i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −40.5000 | + | 23.3827i | −0.279310 | + | 0.161260i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −93.0000 | − | 161.081i | −0.624161 | − | 1.08108i | −0.988702 | − | 0.149892i | \(-0.952108\pi\) |
0.364541 | − | 0.931187i | \(-0.381226\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 39.5000 | − | 68.4160i | 0.261589 | − | 0.453086i | −0.705075 | − | 0.709133i | \(-0.749087\pi\) |
0.966664 | + | 0.256047i | \(0.0824200\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −63.0000 | −0.406452 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.0000 | − | 10.3923i | −0.114650 | − | 0.0661930i | 0.441579 | − | 0.897223i | \(-0.354419\pi\) |
−0.556228 | + | 0.831030i | \(0.687752\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −104.000 | − | 180.133i | −0.638037 | − | 1.10511i | −0.985863 | − | 0.167553i | \(-0.946413\pi\) |
0.347826 | − | 0.937559i | \(-0.386920\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 249.415i | − | 1.49350i | −0.665102 | − | 0.746752i | \(-0.731612\pi\) | ||
0.665102 | − | 0.746752i | \(-0.268388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −0.136095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 198.000 | − | 114.315i | 1.14451 | − | 0.660782i | 0.196966 | − | 0.980410i | \(-0.436891\pi\) |
0.947543 | + | 0.319628i | \(0.103558\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.0000 | + | 8.66025i | −0.0628571 | + | 0.0494872i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −45.0000 | + | 77.9423i | −0.251397 | + | 0.435432i | −0.963911 | − | 0.266226i | \(-0.914223\pi\) |
0.712514 | + | 0.701658i | \(0.247557\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.3923i | − | 0.0574160i | −0.999588 | − | 0.0287080i | \(-0.990861\pi\) | ||
0.999588 | − | 0.0287080i | \(-0.00913930\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 45.0000 | + | 25.9808i | 0.243243 | + | 0.140437i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 135.000 | − | 77.9423i | 0.721925 | − | 0.416804i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 156.000 | + | 270.200i | 0.816754 | + | 1.41466i | 0.908062 | + | 0.418837i | \(0.137562\pi\) |
−0.0913077 | + | 0.995823i | \(0.529105\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 92.5000 | − | 160.215i | 0.479275 | − | 0.830128i | −0.520443 | − | 0.853896i | \(-0.674233\pi\) |
0.999717 | + | 0.0237685i | \(0.00756646\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −330.000 | −1.67513 | −0.837563 | − | 0.546340i | \(-0.816021\pi\) | ||||
−0.837563 | + | 0.546340i | \(0.816021\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.00000 | − | 3.46410i | −0.0301508 | − | 0.0174075i | 0.484849 | − | 0.874598i | \(-0.338875\pi\) |
−0.515000 | + | 0.857190i | \(0.672208\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −58.5000 | − | 23.3827i | −0.288177 | − | 0.115186i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.0000 | − | 46.7654i | −0.131707 | − | 0.228124i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 155.885i | 0.745859i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 248.000 | 1.17536 | 0.587678 | − | 0.809095i | \(-0.300042\pi\) | ||||
0.587678 | + | 0.809095i | \(0.300042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −333.000 | + | 192.258i | −1.54884 | + | 0.894222i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −52.5000 | − | 66.6840i | −0.241935 | − | 0.307299i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −72.0000 | + | 124.708i | −0.325792 | + | 0.564288i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 192.258i | 0.862142i | 0.902318 | + | 0.431071i | \(0.141864\pi\) | ||||
−0.902318 | + | 0.431071i | \(0.858136\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −76.5000 | − | 44.1673i | −0.337004 | − | 0.194570i | 0.321942 | − | 0.946759i | \(-0.395664\pi\) |
−0.658947 | + | 0.752190i | \(0.728998\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 285.000 | − | 164.545i | 1.24454 | − | 0.718536i | 0.274526 | − | 0.961580i | \(-0.411479\pi\) |
0.970015 | + | 0.243043i | \(0.0781457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 135.000 | + | 233.827i | 0.579399 | + | 1.00355i | 0.995548 | + | 0.0942524i | \(0.0300461\pi\) |
−0.416149 | + | 0.909296i | \(0.636621\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −228.000 | −0.953975 | −0.476987 | − | 0.878910i | \(-0.658271\pi\) | ||||
−0.476987 | + | 0.878910i | \(0.658271\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 385.500 | + | 222.569i | 1.59959 | + | 0.923521i | 0.991567 | + | 0.129598i | \(0.0413687\pi\) |
0.608018 | + | 0.793923i | \(0.291965\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −247.500 | − | 59.7558i | −1.01020 | − | 0.243901i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −72.0000 | − | 124.708i | −0.291498 | − | 0.504889i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.19615i | − | 0.0207018i | −0.999946 | − | 0.0103509i | \(-0.996705\pi\) | ||
0.999946 | − | 0.0103509i | \(-0.00329485\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −99.0000 | + | 57.1577i | −0.385214 | + | 0.222403i | −0.680084 | − | 0.733134i | \(-0.738057\pi\) |
0.294870 | + | 0.955537i | \(0.404724\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0000 | + | 69.2820i | 0.0386100 | + | 0.267498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −93.0000 | + | 161.081i | −0.353612 | + | 0.612474i | −0.986879 | − | 0.161459i | \(-0.948380\pi\) |
0.633267 | + | 0.773933i | \(0.281713\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 171.473i | 0.647068i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 292.500 | + | 168.875i | 1.08736 | + | 0.627788i | 0.932873 | − | 0.360207i | \(-0.117294\pi\) |
0.154488 | + | 0.987995i | \(0.450627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −79.5000 | + | 45.8993i | −0.293358 | + | 0.169370i | −0.639455 | − | 0.768828i | \(-0.720840\pi\) |
0.346097 | + | 0.938199i | \(0.387507\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.0000 | + | 25.9808i | 0.0545455 | + | 0.0944755i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −190.000 | + | 329.090i | −0.685921 | + | 1.18805i | 0.287226 | + | 0.957863i | \(0.407267\pi\) |
−0.973147 | + | 0.230186i | \(0.926066\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −300.000 | −1.06762 | −0.533808 | − | 0.845606i | \(-0.679239\pi\) | ||||
−0.533808 | + | 0.845606i | \(0.679239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −177.000 | − | 102.191i | −0.625442 | − | 0.361099i | 0.153543 | − | 0.988142i | \(-0.450932\pi\) |
−0.778985 | + | 0.627043i | \(0.784265\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.0000 | − | 67.5500i | 0.0940767 | − | 0.235366i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −90.5000 | − | 156.751i | −0.313149 | − | 0.542390i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 545.596i | − | 1.86210i | −0.364889 | − | 0.931051i | \(-0.618893\pi\) | ||
0.364889 | − | 0.931051i | \(-0.381107\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −81.0000 | −0.274576 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −481.000 | − | 192.258i | −1.59801 | − | 0.638730i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −234.000 | + | 405.300i | −0.767213 | + | 1.32885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 173.205i | − | 0.564186i | −0.959387 | − | 0.282093i | \(-0.908971\pi\) | ||
0.959387 | − | 0.282093i | \(-0.0910287\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −153.000 | − | 88.3346i | −0.491961 | − | 0.284034i | 0.233426 | − | 0.972374i | \(-0.425006\pi\) |
−0.725388 | + | 0.688340i | \(0.758340\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −184.500 | + | 106.521i | −0.589457 | + | 0.340323i | −0.764883 | − | 0.644170i | \(-0.777203\pi\) |
0.175426 | + | 0.984493i | \(0.443870\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 58.5000 | + | 101.325i | 0.184543 | + | 0.319637i | 0.943422 | − | 0.331594i | \(-0.107586\pi\) |
−0.758880 | + | 0.651231i | \(0.774253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −67.5000 | + | 116.913i | −0.211599 | + | 0.366500i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −108.000 | −0.334365 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.0000 | − | 13.8564i | −0.0738462 | − | 0.0426351i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | + | 34.6410i | 0.0604230 | + | 0.104656i | 0.894655 | − | 0.446759i | \(-0.147422\pi\) |
−0.834232 | + | 0.551414i | \(0.814088\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 394.908i | − | 1.17883i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 91.0000 | 0.270030 | 0.135015 | − | 0.990844i | \(-0.456892\pi\) | ||||
0.135015 | + | 0.990844i | \(0.456892\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −157.500 | + | 90.9327i | −0.461877 | + | 0.266665i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −143.000 | − | 311.769i | −0.416910 | − | 0.908948i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −105.000 | + | 181.865i | −0.302594 | + | 0.524108i | −0.976723 | − | 0.214506i | \(-0.931186\pi\) |
0.674129 | + | 0.738614i | \(0.264519\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 304.841i | − | 0.873470i | −0.899590 | − | 0.436735i | \(-0.856135\pi\) | ||
0.899590 | − | 0.436735i | \(-0.143865\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −342.000 | − | 197.454i | −0.968839 | − | 0.559359i | −0.0699566 | − | 0.997550i | \(-0.522286\pi\) |
−0.898882 | + | 0.438191i | \(0.855619\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −378.000 | + | 218.238i | −1.06479 | + | 0.614756i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −246.000 | − | 426.084i | −0.685237 | − | 1.18686i | −0.973362 | − | 0.229272i | \(-0.926365\pi\) |
0.288126 | − | 0.957593i | \(-0.406968\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −126.500 | + | 219.104i | −0.350416 | + | 0.606937i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 324.000 | 0.887671 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 283.500 | + | 163.679i | 0.772480 | + | 0.445991i | 0.833758 | − | 0.552129i | \(-0.186185\pi\) |
−0.0612789 | + | 0.998121i | \(0.519518\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −181.500 | + | 142.894i | −0.489218 | + | 0.385160i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −85.0000 | − | 147.224i | −0.227882 | − | 0.394703i | 0.729298 | − | 0.684196i | \(-0.239847\pi\) |
−0.957180 | + | 0.289493i | \(0.906513\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 124.708i | − | 0.330790i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −82.0000 | −0.216359 | −0.108179 | − | 0.994131i | \(-0.534502\pi\) | ||||
−0.108179 | + | 0.994131i | \(0.534502\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 189.000 | − | 109.119i | 0.493473 | − | 0.284907i | −0.232541 | − | 0.972587i | \(-0.574704\pi\) |
0.726014 | + | 0.687680i | \(0.241371\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −202.500 | + | 506.625i | −0.525974 | + | 1.31591i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 153.000 | − | 265.004i | 0.393316 | − | 0.681244i | −0.599568 | − | 0.800323i | \(-0.704661\pi\) |
0.992885 | + | 0.119080i | \(0.0379944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 193.500 | + | 111.717i | 0.489873 | + | 0.282829i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −222.000 | + | 128.172i | −0.559194 | + | 0.322851i | −0.752822 | − | 0.658224i | \(-0.771308\pi\) |
0.193628 | + | 0.981075i | \(0.437975\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 66.0000 | + | 114.315i | 0.164589 | + | 0.285076i | 0.936509 | − | 0.350643i | \(-0.114037\pi\) |
−0.771921 | + | 0.635719i | \(0.780704\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 84.0000 | − | 145.492i | 0.208437 | − | 0.361023i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 150.000 | 0.368550 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −313.500 | − | 180.999i | −0.766504 | − | 0.442541i | 0.0651223 | − | 0.997877i | \(-0.479256\pi\) |
−0.831626 | + | 0.555336i | \(0.812590\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −67.5000 | − | 85.7365i | −0.163438 | − | 0.207594i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 310.500 | + | 537.802i | 0.748193 | + | 1.29591i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 644.323i | 1.53776i | 0.639391 | + | 0.768882i | \(0.279187\pi\) | ||||
−0.639391 | + | 0.768882i | \(0.720813\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 752.000 | 1.78622 | 0.893112 | − | 0.449835i | \(-0.148517\pi\) | ||||
0.893112 | + | 0.449835i | \(0.148517\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.0000 | + | 10.3923i | −0.0423529 | + | 0.0244525i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −624.000 | + | 90.0666i | −1.46136 | + | 0.210929i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −81.0000 | + | 140.296i | −0.187935 | + | 0.325513i | −0.944562 | − | 0.328334i | \(-0.893513\pi\) |
0.756627 | + | 0.653847i | \(0.226846\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 339.482i | − | 0.784023i | −0.919960 | − | 0.392011i | \(-0.871779\pi\) | ||
0.919960 | − | 0.392011i | \(-0.128221\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −337.500 | + | 194.856i | −0.768793 | + | 0.443863i | −0.832444 | − | 0.554110i | \(-0.813059\pi\) |
0.0636511 | + | 0.997972i | \(0.479726\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 148.500 | + | 257.210i | 0.335214 | + | 0.580608i | 0.983526 | − | 0.180767i | \(-0.0578579\pi\) |
−0.648312 | + | 0.761375i | \(0.724525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −189.000 | + | 327.358i | −0.424719 | + | 0.735635i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 492.000 | 1.09577 | 0.547884 | − | 0.836554i | \(-0.315433\pi\) | ||||
0.547884 | + | 0.836554i | \(0.315433\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −135.000 | − | 77.9423i | −0.299335 | − | 0.172821i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −72.0000 | − | 498.831i | −0.158242 | − | 1.09633i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 221.500 | + | 383.649i | 0.484683 | + | 0.839495i | 0.999845 | − | 0.0175975i | \(-0.00560174\pi\) |
−0.515162 | + | 0.857093i | \(0.672268\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 415.692i | − | 0.901718i | −0.892595 | − | 0.450859i | \(-0.851118\pi\) | ||
0.892595 | − | 0.450859i | \(-0.148882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 82.0000 | 0.177106 | 0.0885529 | − | 0.996071i | \(-0.471776\pi\) | ||||
0.0885529 | + | 0.996071i | \(0.471776\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 234.000 | − | 135.100i | 0.501071 | − | 0.289293i | −0.228085 | − | 0.973641i | \(-0.573246\pi\) |
0.729156 | + | 0.684348i | \(0.239913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 418.000 | − | 329.090i | 0.891258 | − | 0.701684i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −555.000 | + | 961.288i | −1.17336 | + | 2.03232i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 20.7846i | − | 0.0437571i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 297.000 | + | 171.473i | 0.620042 | + | 0.357981i | 0.776885 | − | 0.629642i | \(-0.216798\pi\) |
−0.156844 | + | 0.987623i | \(0.550132\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −120.000 | + | 69.2820i | −0.249480 | + | 0.144037i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −481.500 | − | 833.982i | −0.992784 | − | 1.71955i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −158.500 | + | 274.530i | −0.325462 | + | 0.563717i | −0.981606 | − | 0.190919i | \(-0.938853\pi\) |
0.656144 | + | 0.754636i | \(0.272186\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.0000 | 0.0549898 | 0.0274949 | − | 0.999622i | \(-0.491247\pi\) | ||||
0.0274949 | + | 0.999622i | \(0.491247\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −81.0000 | − | 46.7654i | −0.164300 | − | 0.0948588i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −546.000 | − | 218.238i | −1.09859 | − | 0.439111i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −223.000 | − | 386.247i | −0.446894 | − | 0.774043i | 0.551288 | − | 0.834315i | \(-0.314136\pi\) |
−0.998182 | + | 0.0602721i | \(0.980803\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 488.438i | − | 0.971050i | −0.874223 | − | 0.485525i | \(-0.838628\pi\) | ||
0.874223 | − | 0.485525i | \(-0.161372\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −756.000 | −1.49703 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −85.5000 | + | 49.3634i | −0.167976 | + | 0.0969812i | −0.581631 | − | 0.813453i | \(-0.697585\pi\) |
0.413655 | + | 0.910434i | \(0.364252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 270.000 | + | 342.946i | 0.528376 | + | 0.671127i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −180.000 | + | 311.769i | −0.349515 | + | 0.605377i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 783.000 | + | 452.065i | 1.50288 | + | 0.867688i | 0.999994 | + | 0.00333410i | \(0.00106128\pi\) |
0.502885 | + | 0.864354i | \(0.332272\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 606.000 | − | 349.874i | 1.15870 | − | 0.668976i | 0.207708 | − | 0.978191i | \(-0.433400\pi\) |
0.950992 | + | 0.309215i | \(0.100066\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −63.0000 | − | 109.119i | −0.119545 | − | 0.207057i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 264.500 | − | 458.127i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 144.000 | 0.270169 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 418.500 | + | 241.621i | 0.782243 | + | 0.451628i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −705.000 | + | 207.846i | −1.30798 | + | 0.385614i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.0000 | − | 64.0859i | −0.0683919 | − | 0.118458i | 0.829802 | − | 0.558058i | \(-0.188453\pi\) |
−0.898194 | + | 0.439600i | \(0.855120\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 41.5692i | 0.0762738i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 934.000 | 1.70750 | 0.853748 | − | 0.520687i | \(-0.174324\pi\) | ||||
0.853748 | + | 0.520687i | \(0.174324\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 81.0000 | − | 46.7654i | 0.147005 | − | 0.0848736i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.0000 | + | 297.913i | 0.0777577 | + | 0.538721i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 421.500 | − | 730.059i | 0.756732 | − | 1.31070i | −0.187776 | − | 0.982212i | \(-0.560128\pi\) |
0.944508 | − | 0.328487i | \(-0.106539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1025.37i | − | 1.83430i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 823.500 | + | 475.448i | 1.46270 | + | 0.844490i | 0.999135 | − | 0.0415731i | \(-0.0132369\pi\) |
0.463564 | + | 0.886063i | \(0.346570\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 189.000 | − | 109.119i | 0.334513 | − | 0.193131i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 111.000 | + | 192.258i | 0.195079 | + | 0.337887i | 0.946926 | − | 0.321450i | \(-0.104170\pi\) |
−0.751847 | + | 0.659337i | \(0.770837\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 220.000 | − | 381.051i | 0.385289 | − | 0.667340i | −0.606520 | − | 0.795068i | \(-0.707435\pi\) |
0.991809 | + | 0.127728i | \(0.0407684\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 568.500 | + | 328.224i | 0.985269 | + | 0.568845i | 0.903857 | − | 0.427835i | \(-0.140724\pi\) |
0.0814120 | + | 0.996681i | \(0.474057\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −310.500 | + | 776.825i | −0.534423 | + | 1.33705i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 247.500 | + | 428.683i | 0.424528 | + | 0.735305i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1054.82i | − | 1.79697i | −0.439008 | − | 0.898483i | \(-0.644670\pi\) | ||
0.439008 | − | 0.898483i | \(-0.355330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 126.000 | 0.213922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −612.000 | + | 353.338i | −1.03204 | + | 0.595849i | −0.917569 | − | 0.397578i | \(-0.869851\pi\) |
−0.114472 | + | 0.993426i | \(0.536518\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −351.000 | − | 140.296i | −0.589916 | − | 0.235792i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −258.000 | + | 446.869i | −0.430718 | + | 0.746025i | −0.996935 | − | 0.0782307i | \(-0.975073\pi\) |
0.566217 | + | 0.824256i | \(0.308406\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 247.683i | − | 0.412119i | −0.978540 | − | 0.206059i | \(-0.933936\pi\) | ||
0.978540 | − | 0.206059i | \(-0.0660640\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 468.000 | + | 270.200i | 0.773554 | + | 0.446611i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 562.500 | − | 324.760i | 0.926689 | − | 0.535024i | 0.0409259 | − | 0.999162i | \(-0.486969\pi\) |
0.885763 | + | 0.464138i | \(0.153636\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 446.000 | − | 772.495i | 0.727569 | − | 1.26019i | −0.230338 | − | 0.973111i | \(-0.573983\pi\) |
0.957908 | − | 0.287076i | \(-0.0926834\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1224.00 | 1.98379 | 0.991896 | − | 0.127050i | \(-0.0405510\pi\) | ||||
0.991896 | + | 0.127050i | \(0.0405510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 348.000 | + | 200.918i | 0.562197 | + | 0.324585i | 0.754027 | − | 0.656844i | \(-0.228109\pi\) |
−0.191830 | + | 0.981428i | \(0.561442\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −504.000 | + | 72.7461i | −0.808989 | + | 0.116767i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 335.500 | + | 581.103i | 0.536800 | + | 0.929765i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 103.923i | 0.165219i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1115.00 | −1.76704 | −0.883518 | − | 0.468397i | \(-0.844832\pi\) | ||||
−0.883518 | + | 0.468397i | \(0.844832\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 157.500 | − | 90.9327i | 0.248031 | − | 0.143201i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 468.000 | − | 491.902i | 0.734694 | − | 0.772217i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −192.000 | + | 332.554i | −0.299532 | + | 0.518805i | −0.976029 | − | 0.217641i | \(-0.930164\pi\) |
0.676497 | + | 0.736445i | \(0.263497\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.92820i | 0.0107748i | 0.999985 | + | 0.00538741i | \(0.00171487\pi\) | ||||
−0.999985 | + | 0.00538741i | \(0.998285\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 774.000 | + | 446.869i | 1.19629 | + | 0.690679i | 0.959726 | − | 0.280937i | \(-0.0906452\pi\) |
0.236564 | + | 0.971616i | \(0.423979\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −202.500 | + | 116.913i | −0.312018 | + | 0.180144i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.5000 | + | 64.9519i | 0.0574273 | + | 0.0994669i | 0.893310 | − | 0.449441i | \(-0.148377\pi\) |
−0.835883 | + | 0.548908i | \(0.815044\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −445.500 | + | 771.629i | −0.680153 | + | 1.17806i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 642.000 | 0.974203 | 0.487102 | − | 0.873345i | \(-0.338054\pi\) | ||||
0.487102 | + | 0.873345i | \(0.338054\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −243.000 | − | 140.296i | −0.367625 | − | 0.212248i | 0.304795 | − | 0.952418i | \(-0.401412\pi\) |
−0.672420 | + | 0.740170i | \(0.734745\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 297.000 | − | 233.827i | 0.446617 | − | 0.351619i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1351.00i | 2.01341i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.0000 | 0.0193165 | 0.00965825 | − | 0.999953i | \(-0.496926\pi\) | ||||
0.00965825 | + | 0.999953i | \(0.496926\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1093.50 | − | 631.333i | 1.61521 | − | 0.932544i | 0.627079 | − | 0.778955i | \(-0.284250\pi\) |
0.988135 | − | 0.153589i | \(-0.0490832\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 481.500 | − | 1204.64i | 0.709131 | − | 1.77414i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 484.500 | − | 839.179i | 0.709370 | − | 1.22867i | −0.255721 | − | 0.966751i | \(-0.582313\pi\) |
0.965091 | − | 0.261915i | \(-0.0843540\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 498.831i | − | 0.728220i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −396.000 | − | 228.631i | −0.574746 | − | 0.331830i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 87.0000 | − | 50.2295i | 0.125904 | − | 0.0726910i | −0.435725 | − | 0.900080i | \(-0.643508\pi\) |
0.561629 | + | 0.827389i | \(0.310175\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −477.000 | − | 826.188i | −0.686331 | − | 1.18876i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.0000 | − | 93.5307i | 0.0774749 | − | 0.134190i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −597.000 | −0.851641 | −0.425820 | − | 0.904808i | \(-0.640014\pi\) | ||||
−0.425820 | + | 0.904808i | \(0.640014\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −90.0000 | − | 51.9615i | −0.128023 | − | 0.0739140i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −630.000 | − | 800.207i | −0.891089 | − | 1.13184i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 415.000 | + | 718.801i | 0.585331 | + | 1.01382i | 0.994834 | + | 0.101515i | \(0.0323689\pi\) |
−0.409503 | + | 0.912309i | \(0.634298\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1080.00 | −1.51049 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 297.000 | − | 171.473i | 0.413074 | − | 0.238488i | −0.279036 | − | 0.960281i | \(-0.590015\pi\) |
0.692110 | + | 0.721792i | \(0.256681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −480.000 | + | 69.2820i | −0.665742 | + | 0.0960916i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.00000 | − | 15.5885i | 0.0124138 | − | 0.0215013i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 50.2295i | − | 0.0690914i | −0.999403 | − | 0.0345457i | \(-0.989002\pi\) | ||
0.999403 | − | 0.0345457i | \(-0.0109984\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −666.000 | − | 384.515i | −0.911081 | − | 0.526013i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −159.000 | + | 91.7987i | −0.216917 | + | 0.125237i | −0.604522 | − | 0.796589i | \(-0.706636\pi\) |
0.387605 | + | 0.921826i | \(0.373302\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −570.000 | − | 987.269i | −0.773406 | − | 1.33958i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −167.000 | + | 289.252i | −0.225981 | + | 0.391411i | −0.956613 | − | 0.291361i | \(-0.905892\pi\) |
0.730632 | + | 0.682771i | \(0.239225\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 84.0000 | 0.113055 | 0.0565276 | − | 0.998401i | \(-0.481997\pi\) | ||||
0.0565276 | + | 0.998401i | \(0.481997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 837.000 | + | 483.242i | 1.12349 | + | 0.648647i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 93.0000 | + | 644.323i | 0.124166 | + | 0.860244i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −179.500 | − | 310.903i | −0.239015 | − | 0.413986i | 0.721417 | − | 0.692501i | \(-0.243491\pi\) |
−0.960432 | + | 0.278515i | \(0.910158\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 410.496i | 0.543703i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −80.0000 | −0.105680 | −0.0528402 | − | 0.998603i | \(-0.516827\pi\) | ||||
−0.0528402 | + | 0.998603i | \(0.516827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 702.000 | − | 405.300i | 0.922470 | − | 0.532589i | 0.0380481 | − | 0.999276i | \(-0.487886\pi\) |
0.884422 | + | 0.466687i | \(0.154553\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.0000 | + | 34.6410i | −0.0576671 | + | 0.0454011i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 108.000 | − | 187.061i | 0.140808 | − | 0.243887i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 774.227i | − | 1.00680i | −0.864054 | − | 0.503398i | \(-0.832083\pi\) | ||
0.864054 | − | 0.503398i | \(-0.167917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 630.000 | + | 363.731i | 0.815006 | + | 0.470544i | 0.848691 | − | 0.528888i | \(-0.177391\pi\) |
−0.0336850 | + | 0.999433i | \(0.510724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.0000 | − | 12.1244i | 0.0270968 | − | 0.0156443i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 54.0000 | + | 93.5307i | 0.0693196 | + | 0.120065i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −630.000 | + | 1091.19i | −0.806658 | + | 1.39717i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 108.000 | 0.137580 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1236.00 | + | 713.605i | 1.57052 | + | 0.906741i | 0.996105 | + | 0.0881773i | \(0.0281042\pi\) |
0.574416 | + | 0.818563i | \(0.305229\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 273.000 | + | 109.119i | 0.345133 | + | 0.137951i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −624.000 | − | 1080.80i | −0.786885 | − | 1.36293i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 607.950i | − | 0.762798i | −0.924411 | − | 0.381399i | \(-0.875442\pi\) | ||
0.924411 | − | 0.381399i | \(-0.124558\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 810.000 | − | 467.654i | 1.00872 | − | 0.582383i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −84.0000 | + | 145.492i | −0.103832 | + | 0.179842i | −0.913260 | − | 0.407376i | \(-0.866444\pi\) |
0.809428 | + | 0.587218i | \(0.199777\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 353.338i | − | 0.435682i | −0.975984 | − | 0.217841i | \(-0.930099\pi\) | ||
0.975984 | − | 0.217841i | \(-0.0699015\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 936.000 | + | 540.400i | 1.14847 | + | 0.663067i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 666.000 | − | 384.515i | 0.815177 | − | 0.470643i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 142.500 | + | 246.817i | 0.173569 | + | 0.300630i | 0.939665 | − | 0.342096i | \(-0.111137\pi\) |
−0.766096 | + | 0.642726i | \(0.777803\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −137.000 | + | 237.291i | −0.166464 | + | 0.288324i | −0.937174 | − | 0.348862i | \(-0.886568\pi\) |
0.770710 | + | 0.637186i | \(0.219902\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 429.000 | 0.518742 | 0.259371 | − | 0.965778i | \(-0.416485\pi\) | ||||
0.259371 | + | 0.965778i | \(0.416485\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −819.000 | − | 472.850i | −0.987937 | − | 0.570386i | −0.0832802 | − | 0.996526i | \(-0.526540\pi\) |
−0.904657 | + | 0.426140i | \(0.859873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −144.000 | − | 488.438i | −0.172869 | − | 0.586361i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 648.000 | + | 1122.37i | 0.776048 | + | 1.34415i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 259.808i | 0.309663i | 0.987941 | + | 0.154832i | \(0.0494835\pi\) | ||||
−0.987941 | + | 0.154832i | \(0.950516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −760.000 | −0.903686 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 103.500 | − | 59.7558i | 0.122485 | − | 0.0707169i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 104.000 | + | 720.533i | 0.122786 | + | 0.850688i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 997.661i | 1.16959i | 0.811181 | + | 0.584796i | \(0.198825\pi\) | ||||
−0.811181 | + | 0.584796i | \(0.801175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −378.000 | − | 218.238i | −0.441074 | − | 0.254654i | 0.262979 | − | 0.964801i | \(-0.415295\pi\) |
−0.704053 | + | 0.710148i | \(0.748628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 393.000 | − | 226.899i | 0.457509 | − | 0.264143i | −0.253487 | − | 0.967339i | \(-0.581578\pi\) |
0.710996 | + | 0.703196i | \(0.248244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 195.000 | + | 337.750i | 0.225956 | + | 0.391367i | 0.956606 | − | 0.291385i | \(-0.0941161\pi\) |
−0.730650 | + | 0.682752i | \(0.760783\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −594.000 | + | 1028.84i | −0.686705 | + | 1.18941i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 645.000 | 0.742232 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 912.000 | + | 526.543i | 1.04707 | + | 0.604527i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −310.500 | + | 776.825i | −0.354857 | + | 0.887800i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 272.000 | + | 471.118i | 0.310148 | + | 0.537192i | 0.978394 | − | 0.206748i | \(-0.0662880\pi\) |
−0.668246 | + | 0.743940i | \(0.732955\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 187.061i | 0.212329i | 0.994349 | + | 0.106164i | \(0.0338569\pi\) | ||||
−0.994349 | + | 0.106164i | \(0.966143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −322.000 | −0.364666 | −0.182333 | − | 0.983237i | \(-0.558365\pi\) | ||||
−0.182333 | + | 0.983237i | \(0.558365\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 612.000 | − | 353.338i | 0.689966 | − | 0.398352i | −0.113633 | − | 0.993523i | \(-0.536249\pi\) |
0.803599 | + | 0.595171i | \(0.202916\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 227.500 | + | 90.9327i | 0.255906 | + | 0.102286i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 467.654i | − | 0.522518i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 94.5000 | + | 54.5596i | 0.105117 | + | 0.0606892i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −297.000 | + | 171.473i | −0.329634 | + | 0.190314i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.0000 | + | 46.7654i | 0.0298343 | + | 0.0516744i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −550.000 | + | 952.628i | −0.606395 | + | 1.05031i | 0.385435 | + | 0.922735i | \(0.374052\pi\) |
−0.991829 | + | 0.127571i | \(0.959282\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 900.000 | 0.987925 | 0.493963 | − | 0.869483i | \(-0.335548\pi\) | ||||
0.493963 | + | 0.869483i | \(0.335548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1552.50 | + | 896.336i | 1.70044 | + | 0.981748i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1188.00 | + | 171.473i | −1.29553 | + | 0.186993i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −859.000 | − | 1487.83i | −0.934712 | − | 1.61897i | −0.775147 | − | 0.631781i | \(-0.782324\pi\) |
−0.159564 | − | 0.987188i | \(-0.551009\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1163.94i | − | 1.26104i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0000 | −0.0216216 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1287.00 | − | 743.050i | 1.38536 | − | 0.799838i | 0.392573 | − | 0.919721i | \(-0.371585\pi\) |
0.992788 | + | 0.119883i | \(0.0382519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 495.000 | + | 119.512i | 0.531686 | + | 0.128369i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −405.000 | + | 701.481i | −0.433155 | + | 0.750247i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 957.824i | − | 1.02222i | −0.859514 | − | 0.511112i | \(-0.829234\pi\) | ||
0.859514 | − | 0.511112i | \(-0.170766\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −310.500 | − | 179.267i | −0.329968 | − | 0.190507i | 0.325859 | − | 0.945418i | \(-0.394347\pi\) |
−0.655827 | + | 0.754911i | \(0.727680\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −81.0000 | − | 140.296i | −0.0855333 | − | 0.148148i | 0.820085 | − | 0.572242i | \(-0.193926\pi\) |
−0.905618 | + | 0.424094i | \(0.860593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −432.000 | + | 748.246i | −0.455216 | + | 0.788457i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 954.000 | 1.00105 | 0.500525 | − | 0.865722i | \(-0.333140\pi\) | ||||
0.500525 | + | 0.865722i | \(0.333140\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1404.00 | − | 810.600i | −1.47016 | − | 0.848796i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 528.000 | − | 415.692i | 0.550574 | − | 0.433464i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −407.000 | − | 704.945i | −0.423517 | − | 0.733553i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 961.288i | 0.996154i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 751.000 | 0.776629 | 0.388314 | − | 0.921527i | \(-0.373057\pi\) | ||||
0.388314 | + | 0.921527i | \(0.373057\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −247.500 | + | 142.894i | −0.254892 | + | 0.147162i | −0.622002 | − | 0.783016i | \(-0.713680\pi\) |
0.367110 | + | 0.930177i | \(0.380347\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 477.000 | − | 1193.38i | 0.490236 | − | 1.22650i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.00000 | + | 15.5885i | −0.00921187 | + | 0.0159554i | −0.870595 | − | 0.492001i | \(-0.836266\pi\) |
0.861383 | + | 0.507957i | \(0.169599\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1091.19i | 1.11460i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −855.000 | − | 493.634i | −0.869786 | − | 0.502171i | −0.00250913 | − | 0.999997i | \(-0.500799\pi\) |
−0.867277 | + | 0.497825i | \(0.834132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1485.00 | − | 857.365i | 1.50761 | − | 0.870421i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 351.500 | − | 608.816i | 0.354692 | − | 0.614345i | −0.632373 | − | 0.774664i | \(-0.717919\pi\) |
0.987065 | + | 0.160319i | \(0.0512523\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.0000 | 0.0361809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 186.000 | + | 107.387i | 0.186560 | + | 0.107710i | 0.590371 | − | 0.807132i | \(-0.298981\pi\) |
−0.403811 | + | 0.914842i | \(0.632315\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1008.3.cg.a.577.1 | 2 | ||
3.2 | odd | 2 | 336.3.bh.d.241.1 | 2 | |||
4.3 | odd | 2 | 63.3.m.d.10.1 | 2 | |||
7.5 | odd | 6 | inner | 1008.3.cg.a.145.1 | 2 | ||
12.11 | even | 2 | 21.3.f.a.10.1 | ✓ | 2 | ||
21.5 | even | 6 | 336.3.bh.d.145.1 | 2 | |||
21.11 | odd | 6 | 2352.3.f.a.97.1 | 2 | |||
21.17 | even | 6 | 2352.3.f.a.97.2 | 2 | |||
28.3 | even | 6 | 441.3.d.a.244.2 | 2 | |||
28.11 | odd | 6 | 441.3.d.a.244.1 | 2 | |||
28.19 | even | 6 | 63.3.m.d.19.1 | 2 | |||
28.23 | odd | 6 | 441.3.m.g.19.1 | 2 | |||
28.27 | even | 2 | 441.3.m.g.325.1 | 2 | |||
60.23 | odd | 4 | 525.3.s.e.199.1 | 4 | |||
60.47 | odd | 4 | 525.3.s.e.199.2 | 4 | |||
60.59 | even | 2 | 525.3.o.h.451.1 | 2 | |||
84.11 | even | 6 | 147.3.d.c.97.2 | 2 | |||
84.23 | even | 6 | 147.3.f.a.19.1 | 2 | |||
84.47 | odd | 6 | 21.3.f.a.19.1 | yes | 2 | ||
84.59 | odd | 6 | 147.3.d.c.97.1 | 2 | |||
84.83 | odd | 2 | 147.3.f.a.31.1 | 2 | |||
420.47 | even | 12 | 525.3.s.e.124.1 | 4 | |||
420.299 | odd | 6 | 525.3.o.h.376.1 | 2 | |||
420.383 | even | 12 | 525.3.s.e.124.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.f.a.10.1 | ✓ | 2 | 12.11 | even | 2 | ||
21.3.f.a.19.1 | yes | 2 | 84.47 | odd | 6 | ||
63.3.m.d.10.1 | 2 | 4.3 | odd | 2 | |||
63.3.m.d.19.1 | 2 | 28.19 | even | 6 | |||
147.3.d.c.97.1 | 2 | 84.59 | odd | 6 | |||
147.3.d.c.97.2 | 2 | 84.11 | even | 6 | |||
147.3.f.a.19.1 | 2 | 84.23 | even | 6 | |||
147.3.f.a.31.1 | 2 | 84.83 | odd | 2 | |||
336.3.bh.d.145.1 | 2 | 21.5 | even | 6 | |||
336.3.bh.d.241.1 | 2 | 3.2 | odd | 2 | |||
441.3.d.a.244.1 | 2 | 28.11 | odd | 6 | |||
441.3.d.a.244.2 | 2 | 28.3 | even | 6 | |||
441.3.m.g.19.1 | 2 | 28.23 | odd | 6 | |||
441.3.m.g.325.1 | 2 | 28.27 | even | 2 | |||
525.3.o.h.376.1 | 2 | 420.299 | odd | 6 | |||
525.3.o.h.451.1 | 2 | 60.59 | even | 2 | |||
525.3.s.e.124.1 | 4 | 420.47 | even | 12 | |||
525.3.s.e.124.2 | 4 | 420.383 | even | 12 | |||
525.3.s.e.199.1 | 4 | 60.23 | odd | 4 | |||
525.3.s.e.199.2 | 4 | 60.47 | odd | 4 | |||
1008.3.cg.a.145.1 | 2 | 7.5 | odd | 6 | inner | ||
1008.3.cg.a.577.1 | 2 | 1.1 | even | 1 | trivial | ||
2352.3.f.a.97.1 | 2 | 21.11 | odd | 6 | |||
2352.3.f.a.97.2 | 2 | 21.17 | even | 6 |