Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(4013,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4014.4013");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4013.6 | ||
Character | \(\chi\) | \(=\) | 4014.4013 |
Dual form | 4014.2.d.a.4013.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4014\mathbb{Z}\right)^\times\).
\(n\) | \(893\) | \(2233\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.31709 | −1.03624 | −0.518118 | − | 0.855309i | \(-0.673367\pi\) | ||||
−0.518118 | + | 0.855309i | \(0.673367\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.47546 | −0.935637 | −0.467819 | − | 0.883825i | \(-0.654960\pi\) | ||||
−0.467819 | + | 0.883825i | \(0.654960\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 2.31709i | − | 0.732729i | ||||||
\(11\) | −4.47607 | −1.34959 | −0.674793 | − | 0.738007i | \(-0.735767\pi\) | ||||
−0.674793 | + | 0.738007i | \(0.735767\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.18579i | 0.883580i | 0.897118 | + | 0.441790i | \(0.145656\pi\) | ||||
−0.897118 | + | 0.441790i | \(0.854344\pi\) | |||||||
\(14\) | − | 2.47546i | − | 0.661595i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.92873i | 1.68046i | 0.542227 | + | 0.840232i | \(0.317581\pi\) | ||||
−0.542227 | + | 0.840232i | \(0.682419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.20422 | −0.735098 | −0.367549 | − | 0.930004i | \(-0.619803\pi\) | ||||
−0.367549 | + | 0.930004i | \(0.619803\pi\) | |||||||
\(20\) | 2.31709 | 0.518118 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 4.47607i | − | 0.954301i | ||||||
\(23\) | −4.79334 | −0.999480 | −0.499740 | − | 0.866175i | \(-0.666571\pi\) | ||||
−0.499740 | + | 0.866175i | \(0.666571\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.368920 | 0.0737839 | ||||||||
\(26\) | −3.18579 | −0.624786 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.47546 | 0.467819 | ||||||||
\(29\) | 4.97704i | 0.924213i | 0.886824 | + | 0.462107i | \(0.152906\pi\) | ||||
−0.886824 | + | 0.462107i | \(0.847094\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.06904 | −0.551215 | −0.275608 | − | 0.961270i | \(-0.588879\pi\) | ||||
−0.275608 | + | 0.961270i | \(0.588879\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.92873 | −1.18827 | ||||||||
\(35\) | 5.73588 | 0.969540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.43114 | 0.235278 | 0.117639 | − | 0.993056i | \(-0.462467\pi\) | ||||
0.117639 | + | 0.993056i | \(0.462467\pi\) | |||||||
\(38\) | − | 3.20422i | − | 0.519793i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.31709i | 0.366365i | ||||||||
\(41\) | − | 5.12875i | − | 0.800976i | −0.916302 | − | 0.400488i | \(-0.868841\pi\) | ||
0.916302 | − | 0.400488i | \(-0.131159\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.70388 | 0.717335 | 0.358668 | − | 0.933465i | \(-0.383231\pi\) | ||||
0.358668 | + | 0.933465i | \(0.383231\pi\) | |||||||
\(44\) | 4.47607 | 0.674793 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 4.79334i | − | 0.706739i | ||||||
\(47\) | 5.15156i | 0.751432i | 0.926735 | + | 0.375716i | \(0.122603\pi\) | ||||
−0.926735 | + | 0.375716i | \(0.877397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.872083 | −0.124583 | ||||||||
\(50\) | 0.368920i | 0.0521731i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 3.18579i | − | 0.441790i | ||||||
\(53\) | 1.42456i | 0.195678i | 0.995202 | + | 0.0978391i | \(0.0311930\pi\) | ||||
−0.995202 | + | 0.0978391i | \(0.968807\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.3715 | 1.39849 | ||||||||
\(56\) | 2.47546i | 0.330798i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.97704 | −0.653518 | ||||||||
\(59\) | −7.24113 | −0.942715 | −0.471357 | − | 0.881942i | \(-0.656236\pi\) | ||||
−0.471357 | + | 0.881942i | \(0.656236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.09020i | 0.395659i | 0.980236 | + | 0.197830i | \(0.0633893\pi\) | ||||
−0.980236 | + | 0.197830i | \(0.936611\pi\) | |||||||
\(62\) | − | 3.06904i | − | 0.389768i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 7.38178i | − | 0.915597i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.492578i | − | 0.0601780i | −0.999547 | − | 0.0300890i | \(-0.990421\pi\) | ||
0.999547 | − | 0.0300890i | \(-0.00957907\pi\) | |||||||
\(68\) | − | 6.92873i | − | 0.840232i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.73588i | 0.685569i | ||||||||
\(71\) | −11.1458 | −1.32276 | −0.661382 | − | 0.750049i | \(-0.730030\pi\) | ||||
−0.661382 | + | 0.750049i | \(0.730030\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.2783 | 1.43707 | 0.718536 | − | 0.695490i | \(-0.244813\pi\) | ||||
0.718536 | + | 0.695490i | \(0.244813\pi\) | |||||||
\(74\) | 1.43114i | 0.166367i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.20422 | 0.367549 | ||||||||
\(77\) | 11.0803 | 1.26272 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.55115i | − | 0.849570i | −0.905294 | − | 0.424785i | \(-0.860350\pi\) | ||
0.905294 | − | 0.424785i | \(-0.139650\pi\) | |||||||
\(80\) | −2.31709 | −0.259059 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.12875 | 0.566376 | ||||||||
\(83\) | − | 5.70648i | − | 0.626368i | −0.949693 | − | 0.313184i | \(-0.898604\pi\) | ||
0.949693 | − | 0.313184i | \(-0.101396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 16.0545i | − | 1.74136i | ||||||
\(86\) | 4.70388i | 0.507233i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.47607i | 0.477150i | ||||||||
\(89\) | 10.7939i | 1.14415i | 0.820200 | + | 0.572077i | \(0.193862\pi\) | ||||
−0.820200 | + | 0.572077i | \(0.806138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 7.88632i | − | 0.826710i | ||||||
\(92\) | 4.79334 | 0.499740 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.15156 | −0.531342 | ||||||||
\(95\) | 7.42447 | 0.761734 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.87729i | − | 0.799817i | −0.916555 | − | 0.399909i | \(-0.869042\pi\) | ||
0.916555 | − | 0.399909i | \(-0.130958\pi\) | |||||||
\(98\) | − | 0.872083i | − | 0.0880937i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.368920 | −0.0368920 | ||||||||
\(101\) | − | 1.15442i | − | 0.114869i | −0.998349 | − | 0.0574343i | \(-0.981708\pi\) | ||
0.998349 | − | 0.0574343i | \(-0.0182920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.8044i | − | 1.16312i | −0.813504 | − | 0.581559i | \(-0.802443\pi\) | ||
0.813504 | − | 0.581559i | \(-0.197557\pi\) | |||||||
\(104\) | 3.18579 | 0.312393 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.42456 | −0.138365 | ||||||||
\(107\) | −15.3578 | −1.48470 | −0.742348 | − | 0.670014i | \(-0.766288\pi\) | ||||
−0.742348 | + | 0.670014i | \(0.766288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.03262 | 0.865168 | 0.432584 | − | 0.901594i | \(-0.357602\pi\) | ||||
0.432584 | + | 0.901594i | \(0.357602\pi\) | |||||||
\(110\) | 10.3715i | 0.988881i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.47546 | −0.233909 | ||||||||
\(113\) | −5.90600 | −0.555590 | −0.277795 | − | 0.960640i | \(-0.589604\pi\) | ||||
−0.277795 | + | 0.960640i | \(0.589604\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.1066 | 1.03570 | ||||||||
\(116\) | − | 4.97704i | − | 0.462107i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 7.24113i | − | 0.666600i | ||||||
\(119\) | − | 17.1518i | − | 1.57230i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.03519 | 0.821381 | ||||||||
\(122\) | −3.09020 | −0.279774 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.06904 | 0.275608 | ||||||||
\(125\) | 10.7306 | 0.959778 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.62356 | 0.765217 | 0.382609 | − | 0.923911i | \(-0.375026\pi\) | ||||
0.382609 | + | 0.923911i | \(0.375026\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.38178 | 0.647425 | ||||||||
\(131\) | − | 5.61511i | − | 0.490594i | −0.969448 | − | 0.245297i | \(-0.921114\pi\) | ||
0.969448 | − | 0.245297i | \(-0.0788855\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.93192 | 0.687785 | ||||||||
\(134\) | 0.492578 | 0.0425523 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.92873 | 0.594134 | ||||||||
\(137\) | 17.9442 | 1.53308 | 0.766539 | − | 0.642197i | \(-0.221977\pi\) | ||||
0.766539 | + | 0.642197i | \(0.221977\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.95347 | −0.335329 | −0.167665 | − | 0.985844i | \(-0.553623\pi\) | ||||
−0.167665 | + | 0.985844i | \(0.553623\pi\) | |||||||
\(140\) | −5.73588 | −0.484770 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 11.1458i | − | 0.935335i | ||||||
\(143\) | − | 14.2598i | − | 1.19247i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 11.5323i | − | 0.957703i | ||||||
\(146\) | 12.2783i | 1.01616i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.43114 | −0.117639 | ||||||||
\(149\) | 13.7892 | 1.12965 | 0.564827 | − | 0.825209i | \(-0.308943\pi\) | ||||
0.564827 | + | 0.825209i | \(0.308943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4468i | 0.850148i | 0.905159 | + | 0.425074i | \(0.139752\pi\) | ||||
−0.905159 | + | 0.425074i | \(0.860248\pi\) | |||||||
\(152\) | 3.20422i | 0.259896i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.0803i | 0.892879i | ||||||||
\(155\) | 7.11124 | 0.571189 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.1420i | − | 0.969034i | −0.874782 | − | 0.484517i | \(-0.838995\pi\) | ||
0.874782 | − | 0.484517i | \(-0.161005\pi\) | |||||||
\(158\) | 7.55115 | 0.600737 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 2.31709i | − | 0.183182i | ||||||
\(161\) | 11.8657 | 0.935151 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.7257i | − | 1.15341i | −0.816954 | − | 0.576703i | \(-0.804339\pi\) | ||
0.816954 | − | 0.576703i | \(-0.195661\pi\) | |||||||
\(164\) | 5.12875i | 0.400488i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.70648 | 0.442909 | ||||||||
\(167\) | 7.54710 | 0.584012 | 0.292006 | − | 0.956416i | \(-0.405677\pi\) | ||||
0.292006 | + | 0.956416i | \(0.405677\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.85072 | 0.219286 | ||||||||
\(170\) | 16.0545 | 1.23133 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.70388 | −0.358668 | ||||||||
\(173\) | −9.83355 | −0.747631 | −0.373815 | − | 0.927503i | \(-0.621951\pi\) | ||||
−0.373815 | + | 0.927503i | \(0.621951\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.913247 | −0.0690350 | ||||||||
\(176\) | −4.47607 | −0.337396 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.7939 | −0.809039 | ||||||||
\(179\) | 14.8865i | 1.11267i | 0.830958 | + | 0.556335i | \(0.187793\pi\) | ||||
−0.830958 | + | 0.556335i | \(0.812207\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.6535 | −0.940525 | −0.470262 | − | 0.882527i | \(-0.655841\pi\) | ||||
−0.470262 | + | 0.882527i | \(0.655841\pi\) | |||||||
\(182\) | 7.88632 | 0.584573 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.79334i | 0.353370i | ||||||||
\(185\) | −3.31608 | −0.243803 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 31.0135i | − | 2.26793i | ||||||
\(188\) | − | 5.15156i | − | 0.375716i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.42447i | 0.538628i | ||||||||
\(191\) | −23.5626 | −1.70493 | −0.852466 | − | 0.522783i | \(-0.824894\pi\) | ||||
−0.852466 | + | 0.522783i | \(0.824894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.04534i | 0.507135i | 0.967318 | + | 0.253567i | \(0.0816039\pi\) | ||||
−0.967318 | + | 0.253567i | \(0.918396\pi\) | |||||||
\(194\) | 7.87729 | 0.565556 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.872083 | 0.0622916 | ||||||||
\(197\) | 15.3685i | 1.09496i | 0.836819 | + | 0.547480i | \(0.184413\pi\) | ||||
−0.836819 | + | 0.547480i | \(0.815587\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.89975 | −0.347334 | −0.173667 | − | 0.984804i | \(-0.555562\pi\) | ||||
−0.173667 | + | 0.984804i | \(0.555562\pi\) | |||||||
\(200\) | − | 0.368920i | − | 0.0260866i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.15442 | 0.0812244 | ||||||||
\(203\) | − | 12.3205i | − | 0.864728i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.8838i | 0.830000i | ||||||||
\(206\) | 11.8044 | 0.822449 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.18579i | 0.220895i | ||||||||
\(209\) | 14.3423 | 0.992077 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.7020 | 1.56287 | 0.781434 | − | 0.623988i | \(-0.214489\pi\) | ||||
0.781434 | + | 0.623988i | \(0.214489\pi\) | |||||||
\(212\) | − | 1.42456i | − | 0.0978391i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 15.3578i | − | 1.04984i | ||||||
\(215\) | −10.8993 | −0.743328 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.59728 | 0.515737 | ||||||||
\(218\) | 9.03262i | 0.611766i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.3715 | −0.699244 | ||||||||
\(221\) | −22.0735 | −1.48483 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.80524 | + | 12.0610i | 0.589642 | + | 0.807664i | ||||
\(224\) | − | 2.47546i | − | 0.165399i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 5.90600i | − | 0.392861i | ||||||
\(227\) | 10.0503i | 0.667062i | 0.942739 | + | 0.333531i | \(0.108240\pi\) | ||||
−0.942739 | + | 0.333531i | \(0.891760\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.88715i | − | 0.124706i | −0.998054 | − | 0.0623532i | \(-0.980139\pi\) | ||
0.998054 | − | 0.0623532i | \(-0.0198605\pi\) | |||||||
\(230\) | 11.1066i | 0.732348i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.97704 | 0.326759 | ||||||||
\(233\) | −5.88159 | −0.385315 | −0.192658 | − | 0.981266i | \(-0.561711\pi\) | ||||
−0.192658 | + | 0.981266i | \(0.561711\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 11.9366i | − | 0.778660i | ||||||
\(236\) | 7.24113 | 0.471357 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.1518 | 1.11179 | ||||||||
\(239\) | 8.02633i | 0.519180i | 0.965719 | + | 0.259590i | \(0.0835875\pi\) | ||||
−0.965719 | + | 0.259590i | \(0.916413\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.93627 | −0.253557 | −0.126779 | − | 0.991931i | \(-0.540464\pi\) | ||||
−0.126779 | + | 0.991931i | \(0.540464\pi\) | |||||||
\(242\) | 9.03519i | 0.580804i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.09020i | − | 0.197830i | ||||||
\(245\) | 2.02070 | 0.129098 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 10.2080i | − | 0.649518i | ||||||
\(248\) | 3.06904i | 0.194884i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.7306i | 0.678665i | ||||||||
\(251\) | 13.6711i | 0.862909i | 0.902135 | + | 0.431455i | \(0.141999\pi\) | ||||
−0.902135 | + | 0.431455i | \(0.858001\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.4553 | 1.34888 | ||||||||
\(254\) | 8.62356i | 0.541090i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 25.0907i | − | 1.56511i | −0.622580 | − | 0.782556i | \(-0.713916\pi\) | ||
0.622580 | − | 0.782556i | \(-0.286084\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.54273 | −0.220135 | ||||||||
\(260\) | 7.38178i | 0.457799i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.61511 | 0.346902 | ||||||||
\(263\) | 21.4145 | 1.32047 | 0.660236 | − | 0.751058i | \(-0.270456\pi\) | ||||
0.660236 | + | 0.751058i | \(0.270456\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.30083i | − | 0.202769i | ||||||
\(266\) | 7.93192i | 0.486337i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.492578i | 0.0300890i | ||||||||
\(269\) | 11.5205 | 0.702415 | 0.351207 | − | 0.936298i | \(-0.385771\pi\) | ||||
0.351207 | + | 0.936298i | \(0.385771\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.80613i | − | 0.474188i | −0.971487 | − | 0.237094i | \(-0.923805\pi\) | ||
0.971487 | − | 0.237094i | \(-0.0761950\pi\) | |||||||
\(272\) | 6.92873i | 0.420116i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.9442i | 1.08405i | ||||||||
\(275\) | −1.65131 | −0.0995777 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.43334i | 0.326458i | 0.986588 | + | 0.163229i | \(0.0521909\pi\) | ||||
−0.986588 | + | 0.163229i | \(0.947809\pi\) | |||||||
\(278\) | − | 3.95347i | − | 0.237113i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 5.73588i | − | 0.342784i | ||||||
\(281\) | 6.21107i | 0.370521i | 0.982689 | + | 0.185261i | \(0.0593130\pi\) | ||||
−0.982689 | + | 0.185261i | \(0.940687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.88487 | −0.528150 | −0.264075 | − | 0.964502i | \(-0.585067\pi\) | ||||
−0.264075 | + | 0.964502i | \(0.585067\pi\) | |||||||
\(284\) | 11.1458 | 0.661382 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.2598 | 0.843202 | ||||||||
\(287\) | 12.6960i | 0.749423i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.0073 | −1.82396 | ||||||||
\(290\) | 11.5323 | 0.677198 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.2783 | −0.718536 | ||||||||
\(293\) | −18.8347 | −1.10033 | −0.550167 | − | 0.835055i | \(-0.685436\pi\) | ||||
−0.550167 | + | 0.835055i | \(0.685436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.7784 | 0.976875 | ||||||||
\(296\) | − | 1.43114i | − | 0.0831833i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.7892i | 0.798786i | ||||||||
\(299\) | − | 15.2706i | − | 0.883121i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.6443 | −0.671166 | ||||||||
\(302\) | −10.4468 | −0.601145 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.20422 | −0.183774 | ||||||||
\(305\) | − | 7.16028i | − | 0.409996i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.3097i | 1.33035i | 0.746686 | + | 0.665177i | \(0.231644\pi\) | ||||
−0.746686 | + | 0.665177i | \(0.768356\pi\) | |||||||
\(308\) | −11.0803 | −0.631361 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.11124i | 0.403891i | ||||||||
\(311\) | 4.23929 | 0.240388 | 0.120194 | − | 0.992750i | \(-0.461648\pi\) | ||||
0.120194 | + | 0.992750i | \(0.461648\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.91668i | 0.560524i | 0.959924 | + | 0.280262i | \(0.0904213\pi\) | ||||
−0.959924 | + | 0.280262i | \(0.909579\pi\) | |||||||
\(314\) | 12.1420 | 0.685211 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.55115i | 0.424785i | ||||||||
\(317\) | 10.4875i | 0.589037i | 0.955646 | + | 0.294518i | \(0.0951592\pi\) | ||||
−0.955646 | + | 0.294518i | \(0.904841\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 22.2776i | − | 1.24731i | ||||||
\(320\) | 2.31709 | 0.129529 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.8657i | 0.661251i | ||||||||
\(323\) | − | 22.2012i | − | 1.23531i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.17530i | 0.0651940i | ||||||||
\(326\) | 14.7257 | 0.815581 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.12875 | −0.283188 | ||||||||
\(329\) | − | 12.7525i | − | 0.703067i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.02817i | 0.331338i | 0.986181 | + | 0.165669i | \(0.0529783\pi\) | ||||
−0.986181 | + | 0.165669i | \(0.947022\pi\) | |||||||
\(332\) | 5.70648i | 0.313184i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.54710i | 0.412959i | ||||||||
\(335\) | 1.14135i | 0.0623586i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 18.3363i | − | 0.998840i | −0.866360 | − | 0.499420i | \(-0.833547\pi\) | ||
0.866360 | − | 0.499420i | \(-0.166453\pi\) | |||||||
\(338\) | 2.85072i | 0.155059i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.0545i | 0.870678i | ||||||||
\(341\) | 13.7372 | 0.743912 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4870 | 1.05220 | ||||||||
\(344\) | − | 4.70388i | − | 0.253616i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 9.83355i | − | 0.528655i | ||||||
\(347\) | − | 22.6952i | − | 1.21834i | −0.793039 | − | 0.609171i | \(-0.791502\pi\) | ||
0.793039 | − | 0.609171i | \(-0.208498\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2887 | −0.604271 | −0.302136 | − | 0.953265i | \(-0.597700\pi\) | ||||
−0.302136 | + | 0.953265i | \(0.597700\pi\) | |||||||
\(350\) | − | 0.913247i | − | 0.0488151i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.47607i | − | 0.238575i | ||||||
\(353\) | − | 21.2848i | − | 1.13288i | −0.824104 | − | 0.566438i | \(-0.808321\pi\) | ||
0.824104 | − | 0.566438i | \(-0.191679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.8259 | 1.37069 | ||||||||
\(356\) | − | 10.7939i | − | 0.572077i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.8865 | −0.786777 | ||||||||
\(359\) | 32.9135i | 1.73711i | 0.495596 | + | 0.868553i | \(0.334950\pi\) | ||||
−0.495596 | + | 0.868553i | \(0.665050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.73299 | −0.459631 | ||||||||
\(362\) | − | 12.6535i | − | 0.665052i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.88632i | 0.413355i | ||||||||
\(365\) | −28.4501 | −1.48914 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.4416 | −0.910444 | −0.455222 | − | 0.890378i | \(-0.650440\pi\) | ||||
−0.455222 | + | 0.890378i | \(0.650440\pi\) | |||||||
\(368\) | −4.79334 | −0.249870 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 3.31608i | − | 0.172395i | ||||||
\(371\) | − | 3.52644i | − | 0.183084i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.833131i | 0.0431379i | 0.999767 | + | 0.0215689i | \(0.00686614\pi\) | ||||
−0.999767 | + | 0.0215689i | \(0.993134\pi\) | |||||||
\(374\) | 31.0135 | 1.60367 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.15156 | 0.265671 | ||||||||
\(377\) | −15.8558 | −0.816617 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3549 | 1.35376 | 0.676880 | − | 0.736093i | \(-0.263331\pi\) | ||||
0.676880 | + | 0.736093i | \(0.263331\pi\) | |||||||
\(380\) | −7.42447 | −0.380867 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 23.5626i | − | 1.20557i | ||||||
\(383\) | −22.1406 | −1.13133 | −0.565666 | − | 0.824634i | \(-0.691381\pi\) | ||||
−0.565666 | + | 0.824634i | \(0.691381\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.6742 | −1.30848 | ||||||||
\(386\) | −7.04534 | −0.358598 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.87729i | 0.399909i | ||||||||
\(389\) | 7.32613i | 0.371449i | 0.982602 | + | 0.185725i | \(0.0594633\pi\) | ||||
−0.982602 | + | 0.185725i | \(0.940537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 33.2118i | − | 1.67959i | ||||||
\(392\) | 0.872083i | 0.0440468i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.3685 | −0.774254 | ||||||||
\(395\) | 17.4967i | 0.880355i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.7523i | 0.790586i | 0.918555 | + | 0.395293i | \(0.129357\pi\) | ||||
−0.918555 | + | 0.395293i | \(0.870643\pi\) | |||||||
\(398\) | − | 4.89975i | − | 0.245602i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.368920 | 0.0184460 | ||||||||
\(401\) | − | 12.2999i | − | 0.614227i | −0.951673 | − | 0.307113i | \(-0.900637\pi\) | ||
0.951673 | − | 0.307113i | \(-0.0993631\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 9.77732i | − | 0.487043i | ||||||
\(404\) | 1.15442i | 0.0574343i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.3205 | 0.611455 | ||||||||
\(407\) | −6.40588 | −0.317527 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.6362i | − | 0.723715i | −0.932233 | − | 0.361857i | \(-0.882143\pi\) | ||
0.932233 | − | 0.361857i | \(-0.117857\pi\) | |||||||
\(410\) | −11.8838 | −0.586899 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.8044i | 0.581559i | ||||||||
\(413\) | 17.9252 | 0.882039 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.2224i | 0.649064i | ||||||||
\(416\) | −3.18579 | −0.156196 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.3423i | 0.701505i | ||||||||
\(419\) | − | 25.9262i | − | 1.26658i | −0.773916 | − | 0.633289i | \(-0.781705\pi\) | ||
0.773916 | − | 0.633289i | \(-0.218295\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.1612i | − | 1.08007i | −0.841642 | − | 0.540036i | \(-0.818411\pi\) | ||
0.841642 | − | 0.540036i | \(-0.181589\pi\) | |||||||
\(422\) | 22.7020i | 1.10511i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.42456 | 0.0691827 | ||||||||
\(425\) | 2.55614i | 0.123991i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 7.64967i | − | 0.370194i | ||||||
\(428\) | 15.3578 | 0.742348 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 10.8993i | − | 0.525613i | ||||||
\(431\) | 32.3460 | 1.55805 | 0.779026 | − | 0.626992i | \(-0.215714\pi\) | ||||
0.779026 | + | 0.626992i | \(0.215714\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.4500 | −1.65556 | −0.827780 | − | 0.561053i | \(-0.810397\pi\) | ||||
−0.827780 | + | 0.561053i | \(0.810397\pi\) | |||||||
\(434\) | 7.59728i | 0.364681i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.03262 | −0.432584 | ||||||||
\(437\) | 15.3589 | 0.734716 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.1050i | 0.768650i | 0.923198 | + | 0.384325i | \(0.125566\pi\) | ||||
−0.923198 | + | 0.384325i | \(0.874434\pi\) | |||||||
\(440\) | − | 10.3715i | − | 0.494440i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 22.0735i | − | 1.04993i | ||||||
\(443\) | 29.9702i | 1.42393i | 0.702215 | + | 0.711965i | \(0.252194\pi\) | ||||
−0.702215 | + | 0.711965i | \(0.747806\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 25.0105i | − | 1.18561i | ||||||
\(446\) | −12.0610 | + | 8.80524i | −0.571105 | + | 0.416940i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.47546 | 0.116955 | ||||||||
\(449\) | 31.4914 | 1.48617 | 0.743085 | − | 0.669197i | \(-0.233362\pi\) | ||||
0.743085 | + | 0.669197i | \(0.233362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.9566i | 1.08099i | ||||||||
\(452\) | 5.90600 | 0.277795 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.0503 | −0.471684 | ||||||||
\(455\) | 18.2733i | 0.856667i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.6715i | 0.592750i | 0.955072 | + | 0.296375i | \(0.0957778\pi\) | ||||
−0.955072 | + | 0.296375i | \(0.904222\pi\) | |||||||
\(458\) | 1.88715 | 0.0881807 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11.1066 | −0.517848 | ||||||||
\(461\) | − | 10.0712i | − | 0.469065i | −0.972108 | − | 0.234532i | \(-0.924644\pi\) | ||
0.972108 | − | 0.234532i | \(-0.0753559\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.2551 | −0.569541 | −0.284770 | − | 0.958596i | \(-0.591917\pi\) | ||||
−0.284770 | + | 0.958596i | \(0.591917\pi\) | |||||||
\(464\) | 4.97704i | 0.231053i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 5.88159i | − | 0.272459i | ||||||
\(467\) | −35.5860 | −1.64673 | −0.823363 | − | 0.567515i | \(-0.807905\pi\) | ||||
−0.823363 | + | 0.567515i | \(0.807905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.21936i | 0.0563048i | ||||||||
\(470\) | 11.9366 | 0.550596 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.24113i | 0.333300i | ||||||||
\(473\) | −21.0549 | −0.968105 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.18210 | −0.0542384 | ||||||||
\(476\) | 17.1518i | 0.786152i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.02633 | −0.367116 | ||||||||
\(479\) | 20.2002i | 0.922972i | 0.887147 | + | 0.461486i | \(0.152684\pi\) | ||||
−0.887147 | + | 0.461486i | \(0.847316\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.55931i | 0.207887i | ||||||||
\(482\) | − | 3.93627i | − | 0.179292i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.03519 | −0.410690 | ||||||||
\(485\) | 18.2524i | 0.828799i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.3808 | 0.651655 | 0.325827 | − | 0.945429i | \(-0.394357\pi\) | ||||
0.325827 | + | 0.945429i | \(0.394357\pi\) | |||||||
\(488\) | 3.09020 | 0.139887 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.02070i | 0.0912858i | ||||||||
\(491\) | −14.5010 | −0.654423 | −0.327211 | − | 0.944951i | \(-0.606109\pi\) | ||||
−0.327211 | + | 0.944951i | \(0.606109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.4846 | −1.55311 | ||||||||
\(494\) | 10.2080 | 0.459279 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.06904 | −0.137804 | ||||||||
\(497\) | 27.5910 | 1.23763 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.662177 | 0.0296431 | 0.0148216 | − | 0.999890i | \(-0.495282\pi\) | ||||
0.0148216 | + | 0.999890i | \(0.495282\pi\) | |||||||
\(500\) | −10.7306 | −0.479889 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.6711 | −0.610169 | ||||||||
\(503\) | 0.806990 | 0.0359819 | 0.0179910 | − | 0.999838i | \(-0.494273\pi\) | ||||
0.0179910 | + | 0.999838i | \(0.494273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.67489i | 0.119031i | ||||||||
\(506\) | 21.4553i | 0.953805i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.62356 | −0.382609 | ||||||||
\(509\) | 38.7822i | 1.71899i | 0.511144 | + | 0.859495i | \(0.329222\pi\) | ||||
−0.511144 | + | 0.859495i | \(0.670778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.3946 | −1.34458 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.0907 | 1.10670 | ||||||||
\(515\) | 27.3518i | 1.20526i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 23.0587i | − | 1.01412i | ||||||
\(518\) | − | 3.54273i | − | 0.155659i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.38178 | −0.323713 | ||||||||
\(521\) | −12.2647 | −0.537326 | −0.268663 | − | 0.963234i | \(-0.586582\pi\) | ||||
−0.268663 | + | 0.963234i | \(0.586582\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.78942i | 0.165700i | 0.996562 | + | 0.0828498i | \(0.0264022\pi\) | ||||
−0.996562 | + | 0.0828498i | \(0.973598\pi\) | |||||||
\(524\) | 5.61511i | 0.245297i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.4145i | 0.933715i | ||||||||
\(527\) | − | 21.2645i | − | 0.926297i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.0239065 | −0.00103941 | ||||||||
\(530\) | 3.30083 | 0.143379 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.93192 | −0.343892 | ||||||||
\(533\) | 16.3391 | 0.707727 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.5855 | 1.53849 | ||||||||
\(536\) | −0.492578 | −0.0212761 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.5205i | 0.496682i | ||||||||
\(539\) | 3.90350 | 0.168136 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00406i | 0.344121i | 0.985086 | + | 0.172061i | \(0.0550425\pi\) | ||||
−0.985086 | + | 0.172061i | \(0.944957\pi\) | |||||||
\(542\) | 7.80613 | 0.335302 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.92873 | −0.297067 | ||||||||
\(545\) | −20.9294 | −0.896517 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.4378 | 1.38694 | 0.693469 | − | 0.720486i | \(-0.256081\pi\) | ||||
0.693469 | + | 0.720486i | \(0.256081\pi\) | |||||||
\(548\) | −17.9442 | −0.766539 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 1.65131i | − | 0.0704121i | ||||||
\(551\) | − | 15.9475i | − | 0.679387i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.6926i | 0.794889i | ||||||||
\(554\) | −5.43334 | −0.230841 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.95347 | 0.167665 | ||||||||
\(557\) | 36.7815 | 1.55848 | 0.779241 | − | 0.626725i | \(-0.215605\pi\) | ||||
0.779241 | + | 0.626725i | \(0.215605\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.9856i | 0.633823i | ||||||||
\(560\) | 5.73588 | 0.242385 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.21107 | −0.261998 | ||||||||
\(563\) | −8.32447 | −0.350835 | −0.175417 | − | 0.984494i | \(-0.556127\pi\) | ||||
−0.175417 | + | 0.984494i | \(0.556127\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.6848 | 0.575722 | ||||||||
\(566\) | − | 8.88487i | − | 0.373459i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.1458i | 0.467668i | ||||||||
\(569\) | −16.6911 | −0.699726 | −0.349863 | − | 0.936801i | \(-0.613772\pi\) | ||||
−0.349863 | + | 0.936801i | \(0.613772\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 12.1998i | − | 0.510546i | −0.966869 | − | 0.255273i | \(-0.917835\pi\) | ||
0.966869 | − | 0.255273i | \(-0.0821654\pi\) | |||||||
\(572\) | 14.2598i | 0.596234i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.6960 | −0.529922 | ||||||||
\(575\) | −1.76836 | −0.0737456 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.9535 | −1.70492 | −0.852459 | − | 0.522795i | \(-0.824889\pi\) | ||||
−0.852459 | + | 0.522795i | \(0.824889\pi\) | |||||||
\(578\) | − | 31.0073i | − | 1.28973i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.5323i | 0.478851i | ||||||||
\(581\) | 14.1262i | 0.586053i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.37642i | − | 0.264084i | ||||||
\(584\) | − | 12.2783i | − | 0.508082i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 18.8347i | − | 0.778054i | ||||||
\(587\) | −30.3885 | −1.25427 | −0.627133 | − | 0.778912i | \(-0.715772\pi\) | ||||
−0.627133 | + | 0.778912i | \(0.715772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.83386 | 0.405197 | ||||||||
\(590\) | 16.7784i | 0.690755i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.43114 | 0.0588195 | ||||||||
\(593\) | 28.9431 | 1.18855 | 0.594275 | − | 0.804262i | \(-0.297439\pi\) | ||||
0.594275 | + | 0.804262i | \(0.297439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 39.7424i | 1.62928i | ||||||||
\(596\) | −13.7892 | −0.564827 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.2706 | 0.624461 | ||||||||
\(599\) | − | 12.8836i | − | 0.526410i | −0.964740 | − | 0.263205i | \(-0.915220\pi\) | ||
0.964740 | − | 0.263205i | \(-0.0847796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.0957i | 1.30921i | 0.755971 | + | 0.654605i | \(0.227165\pi\) | ||||
−0.755971 | + | 0.654605i | \(0.772835\pi\) | |||||||
\(602\) | − | 11.6443i | − | 0.474586i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 10.4468i | − | 0.425074i | ||||||
\(605\) | −20.9354 | −0.851144 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.570165i | 0.0231423i | 0.999933 | + | 0.0115711i | \(0.00368329\pi\) | ||||
−0.999933 | + | 0.0115711i | \(0.996317\pi\) | |||||||
\(608\) | − | 3.20422i | − | 0.129948i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.16028 | 0.289911 | ||||||||
\(611\) | −16.4118 | −0.663950 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.5731i | 1.31561i | 0.753186 | + | 0.657807i | \(0.228516\pi\) | ||||
−0.753186 | + | 0.657807i | \(0.771484\pi\) | |||||||
\(614\) | −23.3097 | −0.940702 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 11.0803i | − | 0.446440i | ||||||
\(617\) | − | 17.8838i | − | 0.719973i | −0.932958 | − | 0.359986i | \(-0.882781\pi\) | ||
0.932958 | − | 0.359986i | \(-0.117219\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.4967i | 1.22576i | 0.790174 | + | 0.612882i | \(0.209990\pi\) | ||||
−0.790174 | + | 0.612882i | \(0.790010\pi\) | |||||||
\(620\) | −7.11124 | −0.285594 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.23929i | 0.169980i | ||||||||
\(623\) | − | 26.7200i | − | 1.07051i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.7085 | −1.06834 | ||||||||
\(626\) | −9.91668 | −0.396350 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.1420i | 0.484517i | ||||||||
\(629\) | 9.91598i | 0.395376i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 27.2019i | − | 1.08289i | −0.840736 | − | 0.541445i | \(-0.817877\pi\) | ||
0.840736 | − | 0.541445i | \(-0.182123\pi\) | |||||||
\(632\) | −7.55115 | −0.300368 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.4875 | −0.416512 | ||||||||
\(635\) | −19.9816 | −0.792945 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.77828i | − | 0.110079i | ||||||
\(638\) | 22.2776 | 0.881978 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.31709i | 0.0915911i | ||||||||
\(641\) | 23.9546 | 0.946148 | 0.473074 | − | 0.881023i | \(-0.343144\pi\) | ||||
0.473074 | + | 0.881023i | \(0.343144\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.1127 | 0.753730 | 0.376865 | − | 0.926268i | \(-0.377002\pi\) | ||||
0.376865 | + | 0.926268i | \(0.377002\pi\) | |||||||
\(644\) | −11.8657 | −0.467575 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.2012 | 0.873493 | ||||||||
\(647\) | − | 42.5846i | − | 1.67417i | −0.547070 | − | 0.837087i | \(-0.684257\pi\) | ||
0.547070 | − | 0.837087i | \(-0.315743\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.4118 | 1.27227 | ||||||||
\(650\) | −1.17530 | −0.0460991 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.7257i | 0.576703i | ||||||||
\(653\) | −24.0328 | −0.940475 | −0.470237 | − | 0.882540i | \(-0.655832\pi\) | ||||
−0.470237 | + | 0.882540i | \(0.655832\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.0107i | 0.508371i | ||||||||
\(656\) | − | 5.12875i | − | 0.200244i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.7525 | 0.497144 | ||||||||
\(659\) | 0.449124i | 0.0174954i | 0.999962 | + | 0.00874770i | \(0.00278452\pi\) | ||||
−0.999962 | + | 0.00874770i | \(0.997215\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3311i | 0.596310i | 0.954517 | + | 0.298155i | \(0.0963713\pi\) | ||||
−0.954517 | + | 0.298155i | \(0.903629\pi\) | |||||||
\(662\) | −6.02817 | −0.234291 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.70648 | −0.221454 | ||||||||
\(665\) | −18.3790 | −0.712707 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 23.8566i | − | 0.923733i | ||||||
\(668\) | −7.54710 | −0.292006 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.14135 | −0.0440942 | ||||||||
\(671\) | − | 13.8319i | − | 0.533976i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.03508 | −0.309730 | −0.154865 | − | 0.987936i | \(-0.549494\pi\) | ||||
−0.154865 | + | 0.987936i | \(0.549494\pi\) | |||||||
\(674\) | 18.3363 | 0.706286 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.85072 | −0.109643 | ||||||||
\(677\) | − | 6.14474i | − | 0.236162i | −0.993004 | − | 0.118081i | \(-0.962326\pi\) | ||
0.993004 | − | 0.118081i | \(-0.0376742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.4999i | 0.748339i | ||||||||
\(680\) | −16.0545 | −0.615663 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.7372i | 0.526025i | ||||||||
\(683\) | − | 37.4660i | − | 1.43360i | −0.697280 | − | 0.716799i | \(-0.745607\pi\) | ||
0.697280 | − | 0.716799i | \(-0.254393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41.5784 | −1.58863 | ||||||||
\(686\) | 19.4870i | 0.744019i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.70388 | 0.179334 | ||||||||
\(689\) | −4.53835 | −0.172897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 31.8091i | − | 1.21008i | −0.796196 | − | 0.605038i | \(-0.793158\pi\) | ||
0.796196 | − | 0.605038i | \(-0.206842\pi\) | |||||||
\(692\) | 9.83355 | 0.373815 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.6952 | 0.861497 | ||||||||
\(695\) | 9.16056 | 0.347480 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.5357 | 1.34601 | ||||||||
\(698\) | − | 11.2887i | − | 0.427284i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.913247 | 0.0345175 | ||||||||
\(701\) | 8.09104i | 0.305594i | 0.988258 | + | 0.152797i | \(0.0488281\pi\) | ||||
−0.988258 | + | 0.152797i | \(0.951172\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.58568 | −0.172952 | ||||||||
\(704\) | 4.47607 | 0.168698 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.2848 | 0.801064 | ||||||||
\(707\) | 2.85771i | 0.107475i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 27.8290i | − | 1.04514i | −0.852596 | − | 0.522571i | \(-0.824973\pi\) | ||
0.852596 | − | 0.522571i | \(-0.175027\pi\) | |||||||
\(710\) | 25.8259i | 0.969228i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.7939 | 0.404519 | ||||||||
\(713\) | 14.7109 | 0.550929 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.0414i | 1.23568i | ||||||||
\(716\) | − | 14.8865i | − | 0.556335i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −32.9135 | −1.22832 | ||||||||
\(719\) | − | 33.2905i | − | 1.24153i | −0.783998 | − | 0.620763i | \(-0.786823\pi\) | ||
0.783998 | − | 0.620763i | \(-0.213177\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.2213i | 1.08826i | ||||||||
\(722\) | − | 8.73299i | − | 0.325008i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.6535 | 0.470262 | ||||||||
\(725\) | 1.83613i | 0.0681921i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.1927 | −0.934347 | −0.467174 | − | 0.884166i | \(-0.654728\pi\) | ||||
−0.467174 | + | 0.884166i | \(0.654728\pi\) | |||||||
\(728\) | −7.88632 | −0.292286 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 28.4501i | − | 1.05298i | ||||||
\(731\) | 32.5919i | 1.20546i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.2307 | 1.48596 | 0.742978 | − | 0.669316i | \(-0.233413\pi\) | ||||
0.742978 | + | 0.669316i | \(0.233413\pi\) | |||||||
\(734\) | − | 17.4416i | − | 0.643781i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 4.79334i | − | 0.176685i | ||||||
\(737\) | 2.20481i | 0.0812154i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 7.91269i | − | 0.291073i | −0.989353 | − | 0.145536i | \(-0.953509\pi\) | ||
0.989353 | − | 0.145536i | \(-0.0464908\pi\) | |||||||
\(740\) | 3.31608 | 0.121902 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.52644 | 0.129460 | ||||||||
\(743\) | − | 53.3888i | − | 1.95865i | −0.202304 | − | 0.979323i | \(-0.564843\pi\) | ||
0.202304 | − | 0.979323i | \(-0.435157\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.9508 | −1.17059 | ||||||||
\(746\) | −0.833131 | −0.0305031 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 31.0135i | 1.13397i | ||||||||
\(749\) | 38.0177 | 1.38914 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5434 | −0.749638 | −0.374819 | − | 0.927098i | \(-0.622295\pi\) | ||||
−0.374819 | + | 0.927098i | \(0.622295\pi\) | |||||||
\(752\) | 5.15156i | 0.187858i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 15.8558i | − | 0.577435i | ||||||
\(755\) | − | 24.2062i | − | 0.880953i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.1514i | 0.732416i | 0.930533 | + | 0.366208i | \(0.119344\pi\) | ||||
−0.930533 | + | 0.366208i | \(0.880656\pi\) | |||||||
\(758\) | 26.3549i | 0.957253i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 7.42447i | − | 0.269314i | ||||||
\(761\) | −38.5714 | −1.39821 | −0.699107 | − | 0.715018i | \(-0.746419\pi\) | ||||
−0.699107 | + | 0.715018i | \(0.746419\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.3599 | −0.809483 | ||||||||
\(764\) | 23.5626 | 0.852466 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 22.1406i | − | 0.799973i | ||||||
\(767\) | − | 23.0688i | − | 0.832964i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.2421 | 1.19874 | 0.599371 | − | 0.800471i | \(-0.295417\pi\) | ||||
0.599371 | + | 0.800471i | \(0.295417\pi\) | |||||||
\(770\) | − | 25.6742i | − | 0.925233i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 7.04534i | − | 0.253567i | ||||||
\(773\) | 38.5412 | 1.38623 | 0.693115 | − | 0.720827i | \(-0.256238\pi\) | ||||
0.693115 | + | 0.720827i | \(0.256238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.13223 | −0.0406708 | ||||||||
\(776\) | −7.87729 | −0.282778 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.32613 | −0.262654 | ||||||||
\(779\) | 16.4336i | 0.588796i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.8894 | 1.78518 | ||||||||
\(782\) | 33.2118 | 1.18765 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.872083 | −0.0311458 | ||||||||
\(785\) | 28.1341i | 1.00415i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.6474i | 0.700355i | 0.936683 | + | 0.350178i | \(0.113879\pi\) | ||||
−0.936683 | + | 0.350178i | \(0.886121\pi\) | |||||||
\(788\) | − | 15.3685i | − | 0.547480i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17.4967 | −0.622505 | ||||||||
\(791\) | 14.6201 | 0.519831 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.84474 | −0.349597 | ||||||||
\(794\) | −15.7523 | −0.559029 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.89975 | 0.173667 | ||||||||
\(797\) | − | 15.2579i | − | 0.540461i | −0.962796 | − | 0.270231i | \(-0.912900\pi\) | ||
0.962796 | − | 0.270231i | \(-0.0870999\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.6937 | −1.26275 | ||||||||
\(800\) | 0.368920i | 0.0130433i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.2999 | 0.434324 | ||||||||
\(803\) | −54.9587 | −1.93945 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.4940 | −0.969036 | ||||||||
\(806\) | 9.77732 | 0.344391 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.15442 | −0.0406122 | ||||||||
\(809\) | −32.5186 | −1.14329 | −0.571646 | − | 0.820500i | \(-0.693695\pi\) | ||||
−0.571646 | + | 0.820500i | \(0.693695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.3227i | 0.608283i | 0.952627 | + | 0.304142i | \(0.0983696\pi\) | ||||
−0.952627 | + | 0.304142i | \(0.901630\pi\) | |||||||
\(812\) | 12.3205i | 0.432364i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 6.40588i | − | 0.224526i | ||||||
\(815\) | 34.1208i | 1.19520i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.0723 | −0.527312 | ||||||||
\(818\) | 14.6362 | 0.511744 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 11.8838i | − | 0.415000i | ||||||
\(821\) | − | 27.0772i | − | 0.945000i | −0.881331 | − | 0.472500i | \(-0.843352\pi\) | ||
0.881331 | − | 0.472500i | \(-0.156648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.90080i | 0.101116i | 0.998721 | + | 0.0505578i | \(0.0160999\pi\) | ||||
−0.998721 | + | 0.0505578i | \(0.983900\pi\) | |||||||
\(824\) | −11.8044 | −0.411224 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.9252i | 0.623696i | ||||||||
\(827\) | 26.4616 | 0.920158 | 0.460079 | − | 0.887878i | \(-0.347821\pi\) | ||||
0.460079 | + | 0.887878i | \(0.347821\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.9299i | 0.414343i | 0.978305 | + | 0.207172i | \(0.0664258\pi\) | ||||
−0.978305 | + | 0.207172i | \(0.933574\pi\) | |||||||
\(830\) | −13.2224 | −0.458958 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 3.18579i | − | 0.110448i | ||||||
\(833\) | − | 6.04243i | − | 0.209358i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.4873 | −0.605174 | ||||||||
\(836\) | −14.3423 | −0.496039 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.9262 | 0.895605 | ||||||||
\(839\) | 10.2588 | 0.354175 | 0.177087 | − | 0.984195i | \(-0.443332\pi\) | ||||
0.177087 | + | 0.984195i | \(0.443332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.22905 | 0.145829 | ||||||||
\(842\) | 22.1612 | 0.763726 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.7020 | −0.781434 | ||||||||
\(845\) | −6.60537 | −0.227232 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.3663 | −0.768514 | ||||||||
\(848\) | 1.42456i | 0.0489195i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.55614 | −0.0876750 | ||||||||
\(851\) | −6.85993 | −0.235155 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 4.12570i | − | 0.141261i | −0.997503 | − | 0.0706306i | \(-0.977499\pi\) | ||
0.997503 | − | 0.0706306i | \(-0.0225012\pi\) | |||||||
\(854\) | 7.64967 | 0.261766 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.3578i | 0.524919i | ||||||||
\(857\) | − | 53.3902i | − | 1.82377i | −0.410442 | − | 0.911886i | \(-0.634626\pi\) | ||
0.410442 | − | 0.911886i | \(-0.365374\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.84229i | 0.0628582i | 0.999506 | + | 0.0314291i | \(0.0100058\pi\) | ||||
−0.999506 | + | 0.0314291i | \(0.989994\pi\) | |||||||
\(860\) | 10.8993 | 0.371664 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.3460i | 1.10171i | ||||||||
\(863\) | −22.2277 | −0.756640 | −0.378320 | − | 0.925675i | \(-0.623498\pi\) | ||||
−0.378320 | + | 0.925675i | \(0.623498\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.7852 | 0.774722 | ||||||||
\(866\) | − | 34.4500i | − | 1.17066i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.59728 | −0.257869 | ||||||||
\(869\) | 33.7994i | 1.14657i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.56925 | 0.0531721 | ||||||||
\(872\) | − | 9.03262i | − | 0.305883i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 15.3589i | 0.519522i | ||||||||
\(875\) | −26.5633 | −0.898004 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.6910i | 1.88055i | 0.340412 | + | 0.940277i | \(0.389434\pi\) | ||||
−0.340412 | + | 0.940277i | \(0.610566\pi\) | |||||||
\(878\) | −16.1050 | −0.543518 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.3715 | 0.349622 | ||||||||
\(881\) | − | 35.2348i | − | 1.18709i | −0.804801 | − | 0.593545i | \(-0.797728\pi\) | ||
0.804801 | − | 0.593545i | \(-0.202272\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.3102i | 1.72673i | 0.504583 | + | 0.863363i | \(0.331646\pi\) | ||||
−0.504583 | + | 0.863363i | \(0.668354\pi\) | |||||||
\(884\) | 22.0735 | 0.742413 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.9702 | −1.00687 | ||||||||
\(887\) | 43.5073i | 1.46083i | 0.683003 | + | 0.730416i | \(0.260674\pi\) | ||||
−0.683003 | + | 0.730416i | \(0.739326\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.3473 | −0.715966 | ||||||||
\(890\) | 25.0105 | 0.838355 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.80524 | − | 12.0610i | −0.294821 | − | 0.403832i | ||||
\(893\) | − | 16.5067i | − | 0.552376i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 34.4934i | − | 1.15299i | ||||||
\(896\) | 2.47546i | 0.0826994i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.4914i | 1.05088i | ||||||||
\(899\) | − | 15.2747i | − | 0.509440i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.87038 | −0.328830 | ||||||||
\(902\) | −22.9566 | −0.764372 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.90600i | 0.196431i | ||||||||
\(905\) | 29.3193 | 0.974605 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.03310 | 0.233530 | 0.116765 | − | 0.993160i | \(-0.462748\pi\) | ||||
0.116765 | + | 0.993160i | \(0.462748\pi\) | |||||||
\(908\) | − | 10.0503i | − | 0.333531i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −18.2733 | −0.605755 | ||||||||
\(911\) | − | 3.96055i | − | 0.131219i | −0.997845 | − | 0.0656095i | \(-0.979101\pi\) | ||
0.997845 | − | 0.0656095i | \(-0.0208992\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.5426i | 0.845336i | ||||||||
\(914\) | −12.6715 | −0.419137 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.88715i | 0.0623532i | ||||||||
\(917\) | 13.9000i | 0.459018i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.35383i | 0.275567i | 0.990462 | + | 0.137784i | \(0.0439979\pi\) | ||||
−0.990462 | + | 0.137784i | \(0.956002\pi\) | |||||||
\(920\) | − | 11.1066i | − | 0.366174i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.0712 | 0.331679 | ||||||||
\(923\) | − | 35.5082i | − | 1.16877i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.527975 | 0.0173597 | ||||||||
\(926\) | − | 12.2551i | − | 0.402726i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.97704 | −0.163379 | ||||||||
\(929\) | − | 31.7634i | − | 1.04212i | −0.853519 | − | 0.521061i | \(-0.825536\pi\) | ||
0.853519 | − | 0.521061i | \(-0.174464\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.79434 | 0.0915809 | ||||||||
\(932\) | 5.88159 | 0.192658 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 35.5860i | − | 1.16441i | ||||||
\(935\) | 71.8611i | 2.35011i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.53245i | − | 0.148069i | −0.997256 | − | 0.0740343i | \(-0.976413\pi\) | ||
0.997256 | − | 0.0740343i | \(-0.0235874\pi\) | |||||||
\(938\) | −1.21936 | −0.0398135 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11.9366i | 0.389330i | ||||||||
\(941\) | 30.0482i | 0.979542i | 0.871851 | + | 0.489771i | \(0.162920\pi\) | ||||
−0.871851 | + | 0.489771i | \(0.837080\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.5838i | 0.800560i | ||||||||
\(944\) | −7.24113 | −0.235679 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 21.0549i | − | 0.684554i | ||||||
\(947\) | − | 26.9938i | − | 0.877180i | −0.898687 | − | 0.438590i | \(-0.855478\pi\) | ||
0.898687 | − | 0.438590i | \(-0.144522\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.1163i | 1.26977i | ||||||||
\(950\) | − | 1.18210i | − | 0.0383523i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.1518 | −0.555894 | ||||||||
\(953\) | −25.5880 | −0.828875 | −0.414438 | − | 0.910078i | \(-0.636022\pi\) | ||||
−0.414438 | + | 0.910078i | \(0.636022\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.5968 | 1.76671 | ||||||||
\(956\) | − | 8.02633i | − | 0.259590i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.2002 | −0.652640 | ||||||||
\(959\) | −44.4203 | −1.43441 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.5810 | −0.696162 | ||||||||
\(962\) | −4.55931 | −0.146998 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.93627 | 0.126779 | ||||||||
\(965\) | − | 16.3247i | − | 0.525511i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.46027i | 0.239906i | 0.992780 | + | 0.119953i | \(0.0382744\pi\) | ||||
−0.992780 | + | 0.119953i | \(0.961726\pi\) | |||||||
\(968\) | − | 9.03519i | − | 0.290402i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.2524 | −0.586050 | ||||||||
\(971\) | 32.0804 | 1.02951 | 0.514755 | − | 0.857337i | \(-0.327883\pi\) | ||||
0.514755 | + | 0.857337i | \(0.327883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.78667 | 0.313746 | ||||||||
\(974\) | 14.3808i | 0.460789i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.09020i | 0.0989149i | ||||||||
\(977\) | −47.8549 | −1.53101 | −0.765507 | − | 0.643428i | \(-0.777512\pi\) | ||||
−0.765507 | + | 0.643428i | \(0.777512\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 48.3143i | − | 1.54413i | ||||||
\(980\) | −2.02070 | −0.0645488 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 14.5010i | − | 0.462747i | ||||||
\(983\) | 9.92674 | 0.316614 | 0.158307 | − | 0.987390i | \(-0.449396\pi\) | ||||
0.158307 | + | 0.987390i | \(0.449396\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 35.6102i | − | 1.13464i | ||||||
\(986\) | − | 34.4846i | − | 1.09821i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.2080i | 0.324759i | ||||||||
\(989\) | −22.5473 | −0.716962 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 44.0103i | − | 1.39803i | −0.715106 | − | 0.699016i | \(-0.753622\pi\) | ||
0.715106 | − | 0.699016i | \(-0.246378\pi\) | |||||||
\(992\) | − | 3.06904i | − | 0.0974420i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 27.5910i | 0.875134i | ||||||||
\(995\) | 11.3532 | 0.359920 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.3977 | 0.994375 | 0.497188 | − | 0.867643i | \(-0.334366\pi\) | ||||
0.497188 | + | 0.867643i | \(0.334366\pi\) | |||||||
\(998\) | 0.662177i | 0.0209609i | ||||||||
\(999\) | 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 | 4014.2.d.a.4013.6 | yes | 72 | |
3.2 | odd | 2 | inner | 4014.2.d.a.4013.31 | yes | 72 | |
223.222 | odd | 2 | inner | 4014.2.d.a.4013.32 | yes | 72 | |
669.668 | even | 2 | inner | 4014.2.d.a.4013.5 | ✓ | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4014.2.d.a.4013.5 | ✓ | 72 | 669.668 | even | 2 | inner | |
4014.2.d.a.4013.6 | yes | 72 | 1.1 | even | 1 | trivial | |
4014.2.d.a.4013.31 | yes | 72 | 3.2 | odd | 2 | inner | |
4014.2.d.a.4013.32 | yes | 72 | 223.222 | odd | 2 | inner |