Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3100,3,Mod(1301,3100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3100.1301");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3100.d (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: | \(84.4688819517\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 620) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1301.15 | ||
Character | \(\chi\) | \(=\) | 3100.1301 |
Dual form | 3100.3.d.h.1301.16 |
$q$-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 \(\left(\mathbb{Z}/3100\mathbb{Z}\right)^\times\).
\(n\) | \(1551\) | \(1801\) | \(2977\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 4.48325i | − | 1.49442i | −0.664590 | − | 0.747208i | \(-0.731394\pi\) | ||
0.664590 | − | 0.747208i | \(-0.268606\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.21821 | −0.459744 | −0.229872 | − | 0.973221i | \(-0.573831\pi\) | ||||
−0.229872 | + | 0.973221i | \(0.573831\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.0995 | −1.23328 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.8341i | 1.71219i | 0.516819 | + | 0.856095i | \(0.327116\pi\) | ||||
−0.516819 | + | 0.856095i | \(0.672884\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.8796i | 1.06766i | 0.845591 | + | 0.533832i | \(0.179249\pi\) | ||||
−0.845591 | + | 0.533832i | \(0.820751\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 13.8252i | − | 0.813250i | −0.913595 | − | 0.406625i | \(-0.866706\pi\) | ||
0.913595 | − | 0.406625i | \(-0.133294\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.23431 | 0.433385 | 0.216692 | − | 0.976240i | \(-0.430473\pi\) | ||||
0.216692 | + | 0.976240i | \(0.430473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.4280i | 0.687049i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 21.0811i | − | 0.916571i | −0.888805 | − | 0.458286i | \(-0.848464\pi\) | ||
0.888805 | − | 0.458286i | \(-0.151536\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.41269i | 0.348618i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.1028i | 0.762167i | 0.924541 | + | 0.381083i | \(0.124449\pi\) | ||||
−0.924541 | + | 0.381083i | \(0.875551\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 30.4139 | − | 5.99969i | 0.981093 | − | 0.193538i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 84.4379 | 2.55872 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.01059i | − | 0.162448i | −0.996696 | − | 0.0812242i | \(-0.974117\pi\) | ||
0.996696 | − | 0.0812242i | \(-0.0258830\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 62.2259 | 1.59553 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 22.3665 | 0.545523 | 0.272762 | − | 0.962082i | \(-0.412063\pi\) | ||||
0.272762 | + | 0.962082i | \(0.412063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.93085i | 0.137927i | 0.997619 | + | 0.0689634i | \(0.0219692\pi\) | ||||
−0.997619 | + | 0.0689634i | \(0.978031\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −48.9623 | −1.04175 | −0.520876 | − | 0.853632i | \(-0.674395\pi\) | ||||
−0.520876 | + | 0.853632i | \(0.674395\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −38.6431 | −0.788635 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −61.9820 | −1.21533 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 52.0935i | − | 0.982896i | −0.870907 | − | 0.491448i | \(-0.836468\pi\) | ||
0.870907 | − | 0.491448i | \(-0.163532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 36.9165i | − | 0.647657i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −63.3369 | −1.07351 | −0.536754 | − | 0.843739i | \(-0.680350\pi\) | ||||
−0.536754 | + | 0.843739i | \(0.680350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 85.7365i | − | 1.40552i | −0.711428 | − | 0.702759i | \(-0.751951\pi\) | ||
0.711428 | − | 0.702759i | \(-0.248049\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 35.7206 | 0.566994 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −62.1709 | −0.927924 | −0.463962 | − | 0.885855i | \(-0.653573\pi\) | ||||
−0.463962 | + | 0.885855i | \(0.653573\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −94.5120 | −1.36974 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 52.1004 | 0.733808 | 0.366904 | − | 0.930259i | \(-0.380418\pi\) | ||||
0.366904 | + | 0.930259i | \(0.380418\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 62.7559i | − | 0.859670i | −0.902907 | − | 0.429835i | \(-0.858572\pi\) | ||
0.902907 | − | 0.429835i | \(-0.141428\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 60.6121i | − | 0.787170i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.84506i | 0.0866463i | 0.999061 | + | 0.0433231i | \(0.0137945\pi\) | ||||
−0.999061 | + | 0.0433231i | \(0.986205\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −57.6963 | −0.712300 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 109.459i | − | 1.31878i | −0.751799 | − | 0.659392i | \(-0.770814\pi\) | ||
0.751799 | − | 0.659392i | \(-0.229186\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 99.0926 | 1.13899 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 29.8993i | 0.335948i | 0.985791 | + | 0.167974i | \(0.0537224\pi\) | ||||
−0.985791 | + | 0.167974i | \(0.946278\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 44.6676i | − | 0.490853i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26.8981 | − | 136.353i | −0.289227 | − | 1.46616i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −139.038 | −1.43338 | −0.716689 | − | 0.697393i | \(-0.754343\pi\) | ||||
−0.716689 | + | 0.697393i | \(0.754343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 209.049i | − | 2.11161i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 76.4000 | 0.756436 | 0.378218 | − | 0.925717i | \(-0.376537\pi\) | ||||
0.378218 | + | 0.925717i | \(0.376537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 93.4551 | 0.907331 | 0.453665 | − | 0.891172i | \(-0.350116\pi\) | ||||
0.453665 | + | 0.891172i | \(0.350116\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 91.3976 | 0.854183 | 0.427091 | − | 0.904208i | \(-0.359538\pi\) | ||||
0.427091 | + | 0.904208i | \(0.359538\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −81.1782 | −0.744754 | −0.372377 | − | 0.928081i | \(-0.621457\pi\) | ||||
−0.372377 | + | 0.928081i | \(0.621457\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.9470 | −0.242765 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 197.874 | 1.75109 | 0.875547 | − | 0.483132i | \(-0.160501\pi\) | ||||
0.875547 | + | 0.483132i | \(0.160501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 154.057i | − | 1.31673i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 44.4925i | 0.373887i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −233.723 | −1.93159 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 100.274i | − | 0.815239i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 79.6437i | 0.627116i | 0.949569 | + | 0.313558i | \(0.101521\pi\) | ||||
−0.949569 | + | 0.313558i | \(0.898479\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 26.5895 | 0.206120 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −208.437 | −1.59112 | −0.795562 | − | 0.605872i | \(-0.792824\pi\) | ||||
−0.795562 | + | 0.605872i | \(0.792824\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26.4997 | −0.199246 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 198.811i | − | 1.45117i | −0.688130 | − | 0.725587i | \(-0.741568\pi\) | ||
0.688130 | − | 0.725587i | \(-0.258432\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 189.281i | − | 1.36174i | −0.732405 | − | 0.680869i | \(-0.761602\pi\) | ||
0.732405 | − | 0.680869i | \(-0.238398\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 219.510i | 1.55681i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −261.410 | −1.82804 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 173.247i | 1.17855i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −173.267 | −1.16286 | −0.581432 | − | 0.813595i | \(-0.697507\pi\) | ||||
−0.581432 | + | 0.813595i | \(0.697507\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 113.321i | − | 0.750469i | −0.926930 | − | 0.375234i | \(-0.877562\pi\) | ||
0.926930 | − | 0.375234i | \(-0.122438\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 153.454i | 1.00297i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.6060 | 0.0930320 | 0.0465160 | − | 0.998918i | \(-0.485188\pi\) | ||||
0.0465160 | + | 0.998918i | \(0.485188\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −233.548 | −1.46886 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 67.8435i | 0.421388i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −109.436 | −0.671385 | −0.335693 | − | 0.941972i | \(-0.608970\pi\) | ||||
−0.335693 | + | 0.941972i | \(0.608970\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 116.222i | − | 0.695942i | −0.937505 | − | 0.347971i | \(-0.886871\pi\) | ||
0.937505 | − | 0.347971i | \(-0.113129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.6442 | −0.139907 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −91.3969 | −0.534485 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −223.727 | −1.29322 | −0.646610 | − | 0.762821i | \(-0.723814\pi\) | ||||
−0.646610 | + | 0.762821i | \(0.723814\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 283.955i | 1.60427i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 40.8639i | − | 0.228290i | −0.993464 | − | 0.114145i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114145i | \(-0.0364128\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 108.105i | − | 0.597266i | −0.954368 | − | 0.298633i | \(-0.903469\pi\) | ||
0.954368 | − | 0.298633i | \(-0.0965306\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −384.378 | −2.10043 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 260.386 | 1.39244 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 30.2920i | − | 0.160275i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 152.194 | 0.796828 | 0.398414 | − | 0.917206i | \(-0.369561\pi\) | ||||
0.398414 | + | 0.917206i | \(0.369561\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 310.542 | 1.60903 | 0.804513 | − | 0.593935i | \(-0.202427\pi\) | ||||
0.804513 | + | 0.593935i | \(0.202427\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 101.199i | − | 0.513703i | −0.966451 | − | 0.256851i | \(-0.917315\pi\) | ||
0.966451 | − | 0.256851i | \(-0.0826851\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 341.297i | 1.71506i | 0.514433 | + | 0.857531i | \(0.328002\pi\) | ||||
−0.514433 | + | 0.857531i | \(0.671998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 278.728i | 1.38671i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 71.1316i | − | 0.350402i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 233.991i | 1.13039i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 155.086i | 0.742037i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 312.408 | 1.48061 | 0.740304 | − | 0.672272i | \(-0.234682\pi\) | ||||
0.740304 | + | 0.672272i | \(0.234682\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 233.579i | − | 1.09661i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −97.8782 | + | 19.3083i | −0.451052 | + | 0.0889782i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −281.351 | −1.28471 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 191.889 | 0.868277 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 276.398i | 1.23945i | 0.784819 | + | 0.619726i | \(0.212756\pi\) | ||||
−0.784819 | + | 0.619726i | \(0.787244\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 145.212 | 0.639702 | 0.319851 | − | 0.947468i | \(-0.396367\pi\) | ||||
0.319851 | + | 0.947468i | \(0.396367\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 88.1326i | − | 0.384859i | −0.981311 | − | 0.192429i | \(-0.938363\pi\) | ||
0.981311 | − | 0.192429i | \(-0.0616366\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −271.739 | −1.17636 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.1793 | −0.0823145 | −0.0411572 | − | 0.999153i | \(-0.513104\pi\) | ||||
−0.0411572 | + | 0.999153i | \(0.513104\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 30.6881 | 0.129486 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 419.216i | 1.75404i | 0.480453 | + | 0.877020i | \(0.340472\pi\) | ||||
−0.480453 | + | 0.877020i | \(0.659528\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 133.457i | − | 0.553764i | −0.960904 | − | 0.276882i | \(-0.910699\pi\) | ||
0.960904 | − | 0.276882i | \(-0.0893011\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 343.381i | 1.41309i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 114.289i | 0.462709i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −490.732 | −1.97081 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 231.713i | − | 0.923158i | −0.887099 | − | 0.461579i | \(-0.847283\pi\) | ||
0.887099 | − | 0.461579i | \(-0.152717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 397.044 | 1.56934 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 380.130 | 1.47910 | 0.739552 | − | 0.673099i | \(-0.235037\pi\) | ||||
0.739552 | + | 0.673099i | \(0.235037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.3433i | 0.0746847i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 245.331i | − | 0.939966i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 118.460i | 0.450417i | 0.974311 | + | 0.225208i | \(0.0723063\pi\) | ||||
−0.974311 | + | 0.225208i | \(0.927694\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 134.046 | 0.502046 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 345.117i | − | 1.28296i | −0.767138 | − | 0.641482i | \(-0.778320\pi\) | ||
0.767138 | − | 0.641482i | \(-0.221680\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 400.614i | − | 1.47828i | −0.673552 | − | 0.739140i | \(-0.735232\pi\) | ||
0.673552 | − | 0.739140i | \(-0.264768\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −200.256 | −0.733538 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 250.993i | − | 0.906110i | −0.891482 | − | 0.453055i | \(-0.850334\pi\) | ||
0.891482 | − | 0.453055i | \(-0.149666\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −337.580 | + | 66.5937i | −1.20996 | + | 0.238687i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −207.256 | −0.737565 | −0.368783 | − | 0.929516i | \(-0.620225\pi\) | ||||
−0.368783 | + | 0.929516i | \(0.620225\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −366.455 | −1.29489 | −0.647447 | − | 0.762111i | \(-0.724163\pi\) | ||||
−0.647447 | + | 0.762111i | \(0.724163\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −71.9800 | −0.250801 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 97.8626 | 0.338625 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 623.341i | 2.14206i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −219.593 | −0.749466 | −0.374733 | − | 0.927133i | \(-0.622266\pi\) | ||||
−0.374733 | + | 0.927133i | \(0.622266\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −177.280 | −0.596901 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 292.599 | 0.978590 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 19.0867i | − | 0.0634110i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 342.520i | − | 1.13043i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −435.216 | −1.41764 | −0.708821 | − | 0.705389i | \(-0.750772\pi\) | ||||
−0.708821 | + | 0.705389i | \(0.750772\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 418.982i | − | 1.35593i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −378.699 | −1.21768 | −0.608841 | − | 0.793292i | \(-0.708365\pi\) | ||||
−0.608841 | + | 0.793292i | \(0.708365\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 406.120i | 1.29751i | 0.760998 | + | 0.648755i | \(0.224710\pi\) | ||||
−0.760998 | + | 0.648755i | \(0.775290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 127.082 | 0.400891 | 0.200446 | − | 0.979705i | \(-0.435761\pi\) | ||||
0.200446 | + | 0.979705i | \(0.435761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −416.287 | −1.30497 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 409.758i | − | 1.27651i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 113.841i | − | 0.352450i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 363.942i | 1.11297i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 157.571 | 0.478940 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 84.9621i | − | 0.256683i | −0.991730 | − | 0.128342i | \(-0.959035\pi\) | ||
0.991730 | − | 0.128342i | \(-0.0409654\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 66.7147i | 0.200344i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 214.929i | − | 0.637771i | −0.947793 | − | 0.318886i | \(-0.896691\pi\) | ||
0.947793 | − | 0.318886i | \(-0.103309\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 887.117i | − | 2.61687i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 112.999 | + | 572.818i | 0.331374 | + | 1.67982i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 282.054 | 0.822315 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 441.126i | 1.27126i | 0.771996 | + | 0.635628i | \(0.219259\pi\) | ||||
−0.771996 | + | 0.635628i | \(0.780741\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −47.5681 | −0.136298 | −0.0681492 | − | 0.997675i | \(-0.521709\pi\) | ||||
−0.0681492 | + | 0.997675i | \(0.521709\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −130.645 | −0.372207 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 22.7511i | − | 0.0644508i | −0.999481 | − | 0.0322254i | \(-0.989741\pi\) | ||
0.999481 | − | 0.0322254i | \(-0.0102594\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 199.471 | 0.558743 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −207.050 | −0.576742 | −0.288371 | − | 0.957519i | \(-0.593114\pi\) | ||||
−0.288371 | + | 0.957519i | \(0.593114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −293.196 | −0.812178 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1047.84i | 2.88661i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 187.417i | − | 0.510672i | −0.966852 | − | 0.255336i | \(-0.917814\pi\) | ||
0.966852 | − | 0.255336i | \(-0.0821861\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −248.257 | −0.672783 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 167.648i | 0.451881i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 505.440 | 1.35507 | 0.677534 | − | 0.735491i | \(-0.263049\pi\) | ||||
0.677534 | + | 0.735491i | \(0.263049\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −306.779 | −0.813738 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.3655 | −0.0669274 | −0.0334637 | − | 0.999440i | \(-0.510654\pi\) | ||||
−0.0334637 | + | 0.999440i | \(0.510654\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 357.063 | 0.937173 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 98.1948i | 0.256383i | 0.991749 | + | 0.128192i | \(0.0409173\pi\) | ||||
−0.991749 | + | 0.128192i | \(0.959083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 65.8296i | − | 0.170102i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 513.777i | − | 1.32076i | −0.750931 | − | 0.660381i | \(-0.770395\pi\) | ||
0.750931 | − | 0.660381i | \(-0.229605\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −291.452 | −0.745401 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 934.476i | 2.37780i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −290.826 | −0.732559 | −0.366280 | − | 0.930505i | \(-0.619369\pi\) | ||||
−0.366280 | + | 0.930505i | \(0.619369\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 118.805i | 0.297757i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 51.0627i | − | 0.127338i | −0.997971 | − | 0.0636692i | \(-0.979720\pi\) | ||
0.997971 | − | 0.0636692i | \(-0.0202803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 83.2735 | + | 422.133i | 0.206634 | + | 1.04748i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 113.204 | 0.278142 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 772.380i | − | 1.88846i | −0.329286 | − | 0.944230i | \(-0.606808\pi\) | ||
0.329286 | − | 0.944230i | \(-0.393192\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −891.319 | −2.16866 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 203.832 | 0.493539 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −848.596 | −2.03500 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −636.613 | −1.51936 | −0.759682 | − | 0.650295i | \(-0.774645\pi\) | ||||
−0.759682 | + | 0.650295i | \(0.774645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 612.077 | 1.45387 | 0.726933 | − | 0.686709i | \(-0.240945\pi\) | ||||
0.726933 | + | 0.686709i | \(0.240945\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 543.459 | 1.28477 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 275.918i | 0.646179i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1171.97i | 2.73186i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −656.847 | −1.52401 | −0.762003 | − | 0.647573i | \(-0.775784\pi\) | ||||
−0.762003 | + | 0.647573i | \(0.775784\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 594.844i | − | 1.37377i | −0.726765 | − | 0.686887i | \(-0.758977\pi\) | ||
0.726765 | − | 0.686887i | \(-0.241023\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 173.589i | − | 0.397228i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −597.587 | −1.36125 | −0.680623 | − | 0.732634i | \(-0.738291\pi\) | ||||
−0.680623 | + | 0.732634i | \(0.738291\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 428.920 | 0.972608 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.1445 | 0.0793330 | 0.0396665 | − | 0.999213i | \(-0.487370\pi\) | ||||
0.0396665 | + | 0.999213i | \(0.487370\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 776.798i | 1.73780i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 56.6822i | − | 0.126241i | −0.998006 | − | 0.0631205i | \(-0.979895\pi\) | ||
0.998006 | − | 0.0631205i | \(-0.0201053\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 421.252i | 0.934040i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −508.045 | −1.12151 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 452.100i | − | 0.989279i | −0.869098 | − | 0.494639i | \(-0.835300\pi\) | ||
0.869098 | − | 0.494639i | \(-0.164700\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 130.133 | 0.283514 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 683.943i | − | 1.48361i | −0.670617 | − | 0.741804i | \(-0.733971\pi\) | ||
0.670617 | − | 0.741804i | \(-0.266029\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 543.501i | − | 1.17387i | −0.809634 | − | 0.586934i | \(-0.800335\pi\) | ||
0.809634 | − | 0.586934i | \(-0.199665\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.3448 | −0.0692608 | −0.0346304 | − | 0.999400i | \(-0.511025\pi\) | ||||
−0.0346304 | + | 0.999400i | \(0.511025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 200.079 | 0.426608 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 65.4825i | − | 0.139029i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −111.702 | −0.236157 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 578.213i | 1.21219i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −112.308 | −0.234463 | −0.117232 | − | 0.993105i | \(-0.537402\pi\) | ||||
−0.117232 | + | 0.993105i | \(0.537402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 83.4248 | 0.173440 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 304.160 | 0.629730 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 181.610i | − | 0.372916i | −0.982463 | − | 0.186458i | \(-0.940299\pi\) | ||
0.982463 | − | 0.186458i | \(-0.0597008\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 490.628i | 1.00333i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 107.169i | − | 0.218267i | −0.994027 | − | 0.109134i | \(-0.965192\pi\) | ||
0.994027 | − | 0.109134i | \(-0.0348076\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 305.577 | 0.619832 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −167.670 | −0.337364 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 654.047i | 1.31072i | 0.755318 | + | 0.655358i | \(0.227482\pi\) | ||||
−0.755318 | + | 0.655358i | \(0.772518\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −521.054 | −1.04003 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −393.697 | −0.782697 | −0.391349 | − | 0.920242i | \(-0.627991\pi\) | ||||
−0.391349 | + | 0.920242i | \(0.627991\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 106.003i | 0.209079i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 414.968i | 0.815262i | 0.913147 | + | 0.407631i | \(0.133645\pi\) | ||||
−0.913147 | + | 0.407631i | \(0.866355\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 201.962i | 0.395229i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 77.5070i | 0.151086i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 922.161i | − | 1.78368i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1003.02i | 1.93261i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 795.823 | 1.52749 | 0.763746 | − | 0.645517i | \(-0.223358\pi\) | ||||
0.763746 | + | 0.645517i | \(0.223358\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.2497i | 0.0693111i | 0.999399 | + | 0.0346556i | \(0.0110334\pi\) | ||||
−0.999399 | + | 0.0346556i | \(0.988967\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −82.9472 | − | 420.479i | −0.157395 | − | 0.797873i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 84.5855 | 0.159897 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 703.010 | 1.32394 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 310.438i | 0.582436i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −183.203 | −0.341160 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 727.808i | − | 1.35029i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −519.820 | −0.960850 | −0.480425 | − | 0.877036i | \(-0.659518\pi\) | ||||
−0.480425 | + | 0.877036i | \(0.659518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −484.662 | −0.892564 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −733.365 | −1.34070 | −0.670352 | − | 0.742043i | \(-0.733857\pi\) | ||||
−0.670352 | + | 0.742043i | \(0.733857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 951.635i | 1.73340i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 182.002i | 0.330312i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 22.0288i | − | 0.0398351i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 407.005i | − | 0.730708i | −0.930869 | − | 0.365354i | \(-0.880948\pi\) | ||
0.930869 | − | 0.365354i | \(-0.119052\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −82.3180 | −0.147259 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1167.37i | − | 2.08088i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −515.750 | −0.916074 | −0.458037 | − | 0.888933i | \(-0.651447\pi\) | ||||
−0.458037 | + | 0.888933i | \(0.651447\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 185.679 | 0.327476 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 722.033i | 1.26895i | 0.772943 | + | 0.634476i | \(0.218784\pi\) | ||||
−0.772943 | + | 0.634476i | \(0.781216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 191.199i | − | 0.334849i | −0.985885 | − | 0.167424i | \(-0.946455\pi\) | ||
0.985885 | − | 0.167424i | \(-0.0535450\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 682.325i | − | 1.19079i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −304.057 | −0.526961 | −0.263481 | − | 0.964665i | \(-0.584870\pi\) | ||||
−0.263481 | + | 0.964665i | \(0.584870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 1392.24i | − | 2.40455i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 352.262i | 0.606304i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 981.134 | 1.68291 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 615.500i | 1.04855i | 0.851548 | + | 0.524276i | \(0.175664\pi\) | ||||
−0.851548 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 250.437 | − | 49.4033i | 0.425191 | − | 0.0838766i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −453.702 | −0.767686 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 70.1322 | 0.118267 | 0.0591334 | − | 0.998250i | \(-0.481166\pi\) | ||||
0.0591334 | + | 0.998250i | \(0.481166\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1530.12 | 2.56302 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1031.52 | 1.72207 | 0.861037 | − | 0.508543i | \(-0.169816\pi\) | ||||
0.861037 | + | 0.508543i | \(0.169816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 910.252i | 1.51456i | 0.653089 | + | 0.757281i | \(0.273473\pi\) | ||||
−0.653089 | + | 0.757281i | \(0.726527\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 690.068 | 1.14439 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −971.049 | −1.59975 | −0.799875 | − | 0.600166i | \(-0.795101\pi\) | ||||
−0.799875 | + | 0.600166i | \(0.795101\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −318.901 | −0.523646 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 679.579i | − | 1.11224i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1069.36i | − | 1.74446i | −0.489094 | − | 0.872231i | \(-0.662672\pi\) | ||
0.489094 | − | 0.872231i | \(-0.337328\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 893.953 | 1.44887 | 0.724435 | − | 0.689343i | \(-0.242101\pi\) | ||||
0.724435 | + | 0.689343i | \(0.242101\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 461.336i | − | 0.745292i | −0.927973 | − | 0.372646i | \(-0.878450\pi\) | ||
0.927973 | − | 0.372646i | \(-0.121550\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 198.430 | 0.319534 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 96.2223i | − | 0.154450i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 695.288 | 1.10891 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −83.0979 | −0.132111 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 452.521i | 0.717149i | 0.933501 | + | 0.358574i | \(0.116737\pi\) | ||||
−0.933501 | + | 0.358574i | \(0.883263\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1400.60i | − | 2.21264i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 536.352i | − | 0.841997i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −578.289 | −0.904991 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 755.215i | 1.17818i | 0.808067 | + | 0.589091i | \(0.200514\pi\) | ||||
−0.808067 | + | 0.589091i | \(0.799486\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 547.824i | − | 0.851981i | −0.904728 | − | 0.425990i | \(-0.859926\pi\) | ||
0.904728 | − | 0.425990i | \(-0.140074\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1239.70i | − | 1.91607i | −0.286645 | − | 0.958037i | \(-0.592540\pi\) | ||
0.286645 | − | 0.958037i | \(-0.407460\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1192.89i | − | 1.83805i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 86.5638 | + | 438.813i | 0.132970 | + | 0.674059i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1138.13 | −1.74292 | −0.871459 | − | 0.490468i | \(-0.836826\pi\) | ||||
−0.871459 | + | 0.490468i | \(0.836826\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 696.561i | 1.06021i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −211.476 | −0.320905 | −0.160453 | − | 0.987044i | \(-0.551295\pi\) | ||||
−0.160453 | + | 0.987044i | \(0.551295\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 354.893 | 0.536903 | 0.268452 | − | 0.963293i | \(-0.413488\pi\) | ||||
0.268452 | + | 0.963293i | \(0.413488\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 860.288i | − | 1.29757i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 465.953 | 0.698580 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1239.16 | 1.85226 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1614.77 | 2.40651 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 383.163i | 0.569336i | 0.958626 | + | 0.284668i | \(0.0918834\pi\) | ||||
−0.958626 | + | 0.284668i | \(0.908117\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 657.100i | 0.970605i | 0.874346 | + | 0.485303i | \(0.161291\pi\) | ||||
−0.874346 | + | 0.485303i | \(0.838709\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 447.453 | 0.658988 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 651.023i | − | 0.955981i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 165.392 | 0.242155 | 0.121077 | − | 0.992643i | \(-0.461365\pi\) | ||||
0.121077 | + | 0.992643i | \(0.461365\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −395.121 | −0.575139 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 723.039 | 1.04940 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1003.97 | −1.45292 | −0.726461 | − | 0.687208i | \(-0.758836\pi\) | ||||
−0.726461 | + | 0.687208i | \(0.758836\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 672.765i | 0.970801i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 309.222i | − | 0.443647i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 85.9854i | 0.123012i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1237.18 | 1.76488 | 0.882438 | − | 0.470428i | \(-0.155901\pi\) | ||||
0.882438 | + | 0.470428i | \(0.155901\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 49.4930i | − | 0.0704026i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −245.871 | −0.347767 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 592.687i | − | 0.835947i | −0.908459 | − | 0.417974i | \(-0.862740\pi\) | ||
0.908459 | − | 0.417974i | \(-0.137260\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 75.9769i | − | 0.106859i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −126.480 | − | 641.159i | −0.177392 | − | 0.899241i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1879.45 | 2.62127 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1146.24i | − | 1.59422i | −0.603835 | − | 0.797110i | \(-0.706361\pi\) | ||
0.603835 | − | 0.797110i | \(-0.293639\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −300.758 | −0.417140 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −598.322 | −0.827554 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 704.034 | 0.968410 | 0.484205 | − | 0.874954i | \(-0.339109\pi\) | ||||
0.484205 | + | 0.874954i | \(0.339109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1020.20 | 1.39945 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 81.9955 | 0.112169 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −555.219 | −0.757461 | −0.378730 | − | 0.925507i | \(-0.623639\pi\) | ||||
−0.378730 | + | 0.925507i | \(0.623639\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1170.93i | − | 1.58878i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 900.377i | 1.21837i | 0.793027 | + | 0.609186i | \(0.208504\pi\) | ||||
−0.793027 | + | 0.609186i | \(0.791496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 512.387 | 0.691480 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 102.316i | − | 0.137706i | −0.997627 | − | 0.0688532i | \(-0.978066\pi\) | ||
0.997627 | − | 0.0688532i | \(-0.0219340\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1214.94i | 1.62643i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −294.137 | −0.392706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 546.187 | 0.727280 | 0.363640 | − | 0.931540i | \(-0.381534\pi\) | ||||
0.363640 | + | 0.931540i | \(0.381534\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1038.83 | −1.37958 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 481.444i | − | 0.635989i | −0.948093 | − | 0.317995i | \(-0.896991\pi\) | ||
0.948093 | − | 0.317995i | \(-0.103009\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1780.05i | − | 2.34525i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1306.55i | 1.71689i | 0.512909 | + | 0.858443i | \(0.328568\pi\) | ||||
−0.512909 | + | 0.858443i | \(0.671432\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 261.249 | 0.342397 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 879.094i | − | 1.14615i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −112.257 | −0.145977 | −0.0729886 | − | 0.997333i | \(-0.523254\pi\) | ||||
−0.0729886 | + | 0.997333i | \(0.523254\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1704.22i | − | 2.21040i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1245.77i | − | 1.61161i | −0.592184 | − | 0.805803i | \(-0.701734\pi\) | ||
0.592184 | − | 0.805803i | \(-0.298266\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 86.7210 | 0.111610 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 184.172 | 0.236422 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 981.263i | 1.25642i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −208.047 | −0.265705 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 426.534i | − | 0.541975i | −0.962583 | − | 0.270987i | \(-0.912650\pi\) | ||
0.962583 | − | 0.270987i | \(-0.0873501\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 531.084 | 0.673110 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −636.799 | −0.805056 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1189.99 | 1.50062 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1469.49i | 1.84378i | 0.387449 | + | 0.921891i | \(0.373356\pi\) | ||||
−0.387449 | + | 0.921891i | \(0.626644\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 676.916i | 0.847205i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 331.868i | − | 0.414318i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1181.95 | 1.47192 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1547.25 | −1.91728 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 678.065i | − | 0.838152i | −0.907951 | − | 0.419076i | \(-0.862354\pi\) | ||
0.907951 | − | 0.419076i | \(-0.137646\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1545.06 | −1.90513 | −0.952565 | − | 0.304337i | \(-0.901565\pi\) | ||||
−0.952565 | + | 0.304337i | \(0.901565\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1796.05 | −2.20917 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.8365i | 0.0597754i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 495.789i | 0.605359i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 464.590i | 0.565883i | 0.959137 | + | 0.282941i | \(0.0913102\pi\) | ||||
−0.959137 | + | 0.282941i | \(0.908690\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 890.360i | − | 1.08185i | −0.841072 | − | 0.540924i | \(-0.818075\pi\) | ||
0.841072 | − | 0.540924i | \(-0.181925\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1517.24i | 1.83464i | 0.398155 | + | 0.917318i | \(0.369651\pi\) | ||||
−0.398155 | + | 0.917318i | \(0.630349\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 591.726i | 0.713783i | 0.934146 | + | 0.356892i | \(0.116163\pi\) | ||||
−0.934146 | + | 0.356892i | \(0.883837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1125.26 | −1.35411 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 534.251i | 0.641357i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 56.4732 | + | 286.277i | 0.0674710 | + | 0.342027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 805.910 | 0.960560 | 0.480280 | − | 0.877115i | \(-0.340535\pi\) | ||||
0.480280 | + | 0.877115i | \(0.340535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 352.464 | 0.419102 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 929.180i | 1.10223i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 752.169 | 0.888040 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1642.91i | 1.93511i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −126.710 | −0.148896 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1180.58 | −1.38403 | −0.692016 | − | 0.721882i | \(-0.743277\pi\) | ||||
−0.692016 | + | 0.721882i | \(0.743277\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 210.998 | 0.246205 | 0.123102 | − | 0.992394i | \(-0.460716\pi\) | ||||
0.123102 | + | 0.992394i | \(0.460716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1516.76i | 1.76573i | 0.469629 | + | 0.882864i | \(0.344388\pi\) | ||||
−0.469629 | + | 0.882864i | \(0.655612\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 322.704i | 0.374802i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 723.205i | − | 0.838013i | −0.907983 | − | 0.419006i | \(-0.862378\pi\) | ||
0.907983 | − | 0.419006i | \(-0.137622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 438.743i | − | 0.506047i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −128.920 | −0.148355 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 862.910i | − | 0.990711i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1543.25 | 1.76776 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 373.676 | 0.426085 | 0.213042 | − | 0.977043i | \(-0.431663\pi\) | ||||
0.213042 | + | 0.977043i | \(0.431663\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 984.492i | 1.12001i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1679.49i | − | 1.90634i | −0.302432 | − | 0.953171i | \(-0.597798\pi\) | ||
0.302432 | − | 0.953171i | \(-0.402202\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 779.936i | 0.883280i | 0.897192 | + | 0.441640i | \(0.145603\pi\) | ||||
−0.897192 | + | 0.441640i | \(0.854397\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1197.60 | 1.35017 | 0.675084 | − | 0.737741i | \(-0.264107\pi\) | ||||
0.675084 | + | 0.737741i | \(0.264107\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 256.310i | − | 0.288313i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1086.66i | − | 1.21959i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −403.171 | −0.451479 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1311.79i | − | 1.46242i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 132.610 | + | 672.233i | 0.147509 | + | 0.747756i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −720.205 | −0.799340 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −85.5706 | −0.0947625 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 214.969 | 0.237012 | 0.118506 | − | 0.992953i | \(-0.462190\pi\) | ||||
0.118506 | + | 0.992953i | \(0.462190\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −848.004 | −0.932898 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 137.331i | 0.150748i | 0.997155 | + | 0.0753740i | \(0.0240151\pi\) | ||||
−0.997155 | + | 0.0753740i | \(0.975985\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2061.56 | 2.25801 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 670.795 | 0.731510 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1155.05 | 1.25686 | 0.628430 | − | 0.777866i | \(-0.283698\pi\) | ||||
0.628430 | + | 0.777866i | \(0.283698\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1951.18i | 2.11855i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 723.134i | 0.783460i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1037.31 | −1.11899 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 342.449i | 0.368621i | 0.982868 | + | 0.184311i | \(0.0590052\pi\) | ||||
−0.982868 | + | 0.184311i | \(0.940995\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −318.199 | −0.341782 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1697.80i | 1.81972i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −535.787 | −0.571812 | −0.285906 | − | 0.958258i | \(-0.592294\pi\) | ||||
−0.285906 | + | 0.958258i | \(0.592294\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1820.74 | 1.93902 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 106.745i | − | 0.113438i | −0.998390 | − | 0.0567189i | \(-0.981936\pi\) | ||
0.998390 | − | 0.0567189i | \(-0.0180639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 471.511i | − | 0.500011i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 863.638i | − | 0.911973i | −0.889987 | − | 0.455986i | \(-0.849287\pi\) | ||
0.889987 | − | 0.455986i | \(-0.150713\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 871.029 | 0.917839 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 569.742i | − | 0.599098i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 974.470i | − | 1.02253i | −0.859423 | − | 0.511265i | \(-0.829177\pi\) | ||
0.859423 | − | 0.511265i | \(-0.170823\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1866.32i | 1.95018i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 639.815i | 0.667169i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 889.007 | − | 364.948i | 0.925086 | − | 0.379758i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1014.47 | −1.05345 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 241.654i | − | 0.249900i | −0.992163 | − | 0.124950i | \(-0.960123\pi\) | ||
0.992163 | − | 0.124950i | \(-0.0398771\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −510.379 | −0.526707 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1713.55 | 1.76473 | 0.882364 | − | 0.470568i | \(-0.155951\pi\) | ||||
0.882364 | + | 0.470568i | \(0.155951\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 609.148i | 0.626051i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.2146 | −0.0217140 | −0.0108570 | − | 0.999941i | \(-0.503456\pi\) | ||||
−0.0108570 | + | 0.999941i | \(0.503456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −563.127 | −0.575206 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 901.040 | 0.918491 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 84.5958i | − | 0.0860588i | −0.999074 | − | 0.0430294i | \(-0.986299\pi\) | ||
0.999074 | − | 0.0430294i | \(-0.0137009\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 706.431i | − | 0.715735i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 125.029 | 0.126420 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1065.20i | 1.07487i | 0.843304 | + | 0.537437i | \(0.180607\pi\) | ||||
−0.843304 | + | 0.537437i | \(0.819393\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −380.906 | −0.383591 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −926.931 | −0.929720 | −0.464860 | − | 0.885384i | \(-0.653895\pi\) | ||||
−0.464860 | + | 0.885384i | \(0.653895\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 56.5758 | 0.0566325 |
(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 | 3100.3.d.h.1301.15 | 24 | ||
5.2 | odd | 4 | 620.3.f.c.309.3 | ✓ | 24 | ||
5.3 | odd | 4 | 620.3.f.c.309.22 | yes | 24 | ||
5.4 | even | 2 | inner | 3100.3.d.h.1301.10 | 24 | ||
31.30 | odd | 2 | inner | 3100.3.d.h.1301.16 | 24 | ||
155.92 | even | 4 | 620.3.f.c.309.21 | yes | 24 | ||
155.123 | even | 4 | 620.3.f.c.309.4 | yes | 24 | ||
155.154 | odd | 2 | inner | 3100.3.d.h.1301.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
620.3.f.c.309.3 | ✓ | 24 | 5.2 | odd | 4 | ||
620.3.f.c.309.4 | yes | 24 | 155.123 | even | 4 | ||
620.3.f.c.309.21 | yes | 24 | 155.92 | even | 4 | ||
620.3.f.c.309.22 | yes | 24 | 5.3 | odd | 4 | ||
3100.3.d.h.1301.9 | 24 | 155.154 | odd | 2 | inner | ||
3100.3.d.h.1301.10 | 24 | 5.4 | even | 2 | inner | ||
3100.3.d.h.1301.15 | 24 | 1.1 | even | 1 | trivial | ||
3100.3.d.h.1301.16 | 24 | 31.30 | odd | 2 | inner |