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 | 4013.5 | ||
Character | \(\chi\) | \(=\) | 4014.4013 |
Dual form | 4014.2.d.a.4013.6 |
$q$-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 | \(-0.854344\pi\) | ||
0.897118 | − | 0.441790i | \(-0.145656\pi\) | |||||||
\(14\) | 2.47546i | 0.661595i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.92873i | − | 1.68046i | −0.542227 | − | 0.840232i | \(-0.682419\pi\) | ||
0.542227 | − | 0.840232i | \(-0.317581\pi\) | |||||||
\(18\) | 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 | \(-0.847094\pi\) | ||
0.886824 | − | 0.462107i | \(-0.152906\pi\) | |||||||
\(30\) | 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 | \(0.131159\pi\) | ||||
−0.916302 | + | 0.400488i | \(0.868841\pi\) | |||||||
\(42\) | 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 | \(-0.877397\pi\) | ||
0.926735 | − | 0.375716i | \(-0.122603\pi\) | |||||||
\(48\) | 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 | \(-0.968807\pi\) | ||
0.995202 | − | 0.0978391i | \(-0.0311930\pi\) | |||||||
\(54\) | 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 | \(-0.936611\pi\) | ||
0.980236 | − | 0.197830i | \(-0.0633893\pi\) | |||||||
\(62\) | 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 | \(0.00957907\pi\) | ||||
−0.999547 | + | 0.0300890i | \(0.990421\pi\) | |||||||
\(68\) | 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 | \(0.139650\pi\) | ||||
−0.905294 | + | 0.424785i | \(0.860350\pi\) | |||||||
\(80\) | −2.31709 | −0.259059 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.12875 | 0.566376 | ||||||||
\(83\) | 5.70648i | 0.626368i | 0.949693 | + | 0.313184i | \(0.101396\pi\) | ||||
−0.949693 | + | 0.313184i | \(0.898604\pi\) | |||||||
\(84\) | 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 | \(-0.806138\pi\) | ||
0.820200 | − | 0.572077i | \(-0.193862\pi\) | |||||||
\(90\) | 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 | \(0.130958\pi\) | ||||
−0.916555 | + | 0.399909i | \(0.869042\pi\) | |||||||
\(98\) | 0.872083i | 0.0880937i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.368920 | −0.0368920 | ||||||||
\(101\) | 1.15442i | 0.114869i | 0.998349 | + | 0.0574343i | \(0.0182920\pi\) | ||||
−0.998349 | + | 0.0574343i | \(0.981708\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8044i | 1.16312i | 0.813504 | + | 0.581559i | \(0.197557\pi\) | ||||
−0.813504 | + | 0.581559i | \(0.802443\pi\) | |||||||
\(104\) | 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 | \(0.0788855\pi\) | ||||
−0.969448 | + | 0.245297i | \(0.921114\pi\) | |||||||
\(132\) | 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 | \(-0.860248\pi\) | ||
0.905159 | − | 0.425074i | \(-0.139752\pi\) | |||||||
\(152\) | − | 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 | \(0.161005\pi\) | ||||
−0.874782 | + | 0.484517i | \(0.838995\pi\) | |||||||
\(158\) | 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 | \(0.195661\pi\) | ||||
−0.816954 | + | 0.576703i | \(0.804339\pi\) | |||||||
\(164\) | − | 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 | \(-0.812207\pi\) | ||
0.830958 | − | 0.556335i | \(-0.187793\pi\) | |||||||
\(180\) | 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 | \(-0.918396\pi\) | ||
0.967318 | − | 0.253567i | \(-0.0816039\pi\) | |||||||
\(194\) | 7.87729 | 0.565556 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.872083 | 0.0622916 | ||||||||
\(197\) | − | 15.3685i | − | 1.09496i | −0.836819 | − | 0.547480i | \(-0.815587\pi\) | ||
0.836819 | − | 0.547480i | \(-0.184413\pi\) | |||||||
\(198\) | 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 | \(-0.891760\pi\) | ||
0.942739 | − | 0.333531i | \(-0.108240\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.88715i | 0.124706i | 0.998054 | + | 0.0623532i | \(0.0198605\pi\) | ||||
−0.998054 | + | 0.0623532i | \(0.980139\pi\) | |||||||
\(230\) | − | 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 | \(-0.916413\pi\) | ||
0.965719 | − | 0.259590i | \(-0.0835875\pi\) | |||||||
\(240\) | 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 | \(-0.858001\pi\) | ||
0.902135 | − | 0.431455i | \(-0.141999\pi\) | |||||||
\(252\) | 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 | \(0.286084\pi\) | ||||
−0.622580 | + | 0.782556i | \(0.713916\pi\) | |||||||
\(258\) | 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 | \(0.0761950\pi\) | ||||
−0.971487 | + | 0.237094i | \(0.923805\pi\) | |||||||
\(272\) | − | 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 | \(-0.947809\pi\) | ||
0.986588 | − | 0.163229i | \(-0.0521909\pi\) | |||||||
\(278\) | 3.95347i | 0.237113i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.73588i | 0.342784i | ||||||||
\(281\) | − | 6.21107i | − | 0.370521i | −0.982689 | − | 0.185261i | \(-0.940687\pi\) | ||
0.982689 | − | 0.185261i | \(-0.0593130\pi\) | |||||||
\(282\) | 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 | \(-0.768356\pi\) | ||
0.746686 | − | 0.665177i | \(-0.231644\pi\) | |||||||
\(308\) | −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 | \(-0.909579\pi\) | ||
0.959924 | − | 0.280262i | \(-0.0904213\pi\) | |||||||
\(314\) | 12.1420 | 0.685211 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 7.55115i | − | 0.424785i | ||||||
\(317\) | − | 10.4875i | − | 0.589037i | −0.955646 | − | 0.294518i | \(-0.904841\pi\) | ||
0.955646 | − | 0.294518i | \(-0.0951592\pi\) | |||||||
\(318\) | 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 | \(-0.947022\pi\) | ||
0.986181 | − | 0.165669i | \(-0.0529783\pi\) | |||||||
\(332\) | − | 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 | \(0.166453\pi\) | ||||
−0.866360 | + | 0.499420i | \(0.833547\pi\) | |||||||
\(338\) | − | 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 | \(0.208498\pi\) | ||||
−0.793039 | + | 0.609171i | \(0.791502\pi\) | |||||||
\(348\) | 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 | \(0.191679\pi\) | ||||
−0.824104 | + | 0.566438i | \(0.808321\pi\) | |||||||
\(354\) | 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 | \(-0.665050\pi\) | ||
0.495596 | − | 0.868553i | \(-0.334950\pi\) | |||||||
\(360\) | 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 | \(-0.993134\pi\) | ||
0.999767 | − | 0.0215689i | \(-0.00686614\pi\) | |||||||
\(374\) | 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 | \(-0.940537\pi\) | ||
0.982602 | − | 0.185725i | \(-0.0594633\pi\) | |||||||
\(390\) | 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 | \(-0.870643\pi\) | ||
0.918555 | − | 0.395293i | \(-0.129357\pi\) | |||||||
\(398\) | 4.89975i | 0.245602i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.368920 | 0.0184460 | ||||||||
\(401\) | 12.2999i | 0.614227i | 0.951673 | + | 0.307113i | \(0.0993631\pi\) | ||||
−0.951673 | + | 0.307113i | \(0.900637\pi\) | |||||||
\(402\) | 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 | \(0.117857\pi\) | ||||
−0.932233 | + | 0.361857i | \(0.882143\pi\) | |||||||
\(410\) | −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 | \(0.218295\pi\) | ||||
−0.773916 | + | 0.633289i | \(0.781705\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.1612i | 1.08007i | 0.841642 | + | 0.540036i | \(0.181589\pi\) | ||||
−0.841642 | + | 0.540036i | \(0.818411\pi\) | |||||||
\(422\) | − | 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 | \(-0.874434\pi\) | ||
0.923198 | − | 0.384325i | \(-0.125566\pi\) | |||||||
\(440\) | 10.3715i | 0.494440i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.0735i | 1.04993i | ||||||||
\(443\) | − | 29.9702i | − | 1.42393i | −0.702215 | − | 0.711965i | \(-0.747806\pi\) | ||
0.702215 | − | 0.711965i | \(-0.252194\pi\) | |||||||
\(444\) | 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 | \(-0.904222\pi\) | ||
0.955072 | − | 0.296375i | \(-0.0957778\pi\) | |||||||
\(458\) | 1.88715 | 0.0881807 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11.1066 | −0.517848 | ||||||||
\(461\) | 10.0712i | 0.469065i | 0.972108 | + | 0.234532i | \(0.0753559\pi\) | ||||
−0.972108 | + | 0.234532i | \(0.924644\pi\) | |||||||
\(462\) | 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 | \(-0.847316\pi\) | ||
0.887147 | − | 0.461486i | \(-0.152684\pi\) | |||||||
\(480\) | 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 | \(-0.670778\pi\) | ||
0.511144 | − | 0.859495i | \(-0.329222\pi\) | |||||||
\(510\) | 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 | \(-0.973598\pi\) | ||
0.996562 | − | 0.0828498i | \(-0.0264022\pi\) | |||||||
\(524\) | − | 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 | \(-0.944957\pi\) | ||
0.985086 | − | 0.172061i | \(-0.0550425\pi\) | |||||||
\(542\) | 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 | \(0.0821654\pi\) | ||||
−0.966869 | + | 0.255273i | \(0.917835\pi\) | |||||||
\(572\) | − | 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 | \(0.0847796\pi\) | ||||
−0.964740 | + | 0.263205i | \(0.915220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 32.0957i | − | 1.30921i | −0.755971 | − | 0.654605i | \(-0.772835\pi\) | ||
0.755971 | − | 0.654605i | \(-0.227165\pi\) | |||||||
\(602\) | 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 | \(-0.996317\pi\) | ||
0.999933 | − | 0.0115711i | \(-0.00368329\pi\) | |||||||
\(608\) | 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 | \(-0.771484\pi\) | ||
0.753186 | − | 0.657807i | \(-0.228516\pi\) | |||||||
\(614\) | −23.3097 | −0.940702 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.0803i | 0.446440i | ||||||||
\(617\) | 17.8838i | 0.719973i | 0.932958 | + | 0.359986i | \(0.117219\pi\) | ||||
−0.932958 | + | 0.359986i | \(0.882781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 30.4967i | − | 1.22576i | −0.790174 | − | 0.612882i | \(-0.790010\pi\) | ||
0.790174 | − | 0.612882i | \(-0.209990\pi\) | |||||||
\(620\) | −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 | \(0.182123\pi\) | ||||
−0.840736 | + | 0.541445i | \(0.817877\pi\) | |||||||
\(632\) | −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 | \(0.315743\pi\) | ||||
−0.547070 | + | 0.837087i | \(0.684257\pi\) | |||||||
\(648\) | 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 | \(-0.997215\pi\) | ||
0.999962 | − | 0.00874770i | \(-0.00278452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 15.3311i | − | 0.596310i | −0.954517 | − | 0.298155i | \(-0.903629\pi\) | ||
0.954517 | − | 0.298155i | \(-0.0963713\pi\) | |||||||
\(662\) | −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 | \(0.0376742\pi\) | ||||
−0.993004 | + | 0.118081i | \(0.962326\pi\) | |||||||
\(678\) | 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 | \(0.254393\pi\) | ||||
−0.697280 | + | 0.716799i | \(0.745607\pi\) | |||||||
\(684\) | 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 | \(0.206842\pi\) | ||||
−0.796196 | + | 0.605038i | \(0.793158\pi\) | |||||||
\(692\) | 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 | \(-0.951172\pi\) | ||
0.988258 | − | 0.152797i | \(-0.0488281\pi\) | |||||||
\(702\) | 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 | \(0.175027\pi\) | ||||
−0.852596 | + | 0.522571i | \(0.824973\pi\) | |||||||
\(710\) | − | 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 | \(0.213177\pi\) | ||||
−0.783998 | + | 0.620763i | \(0.786823\pi\) | |||||||
\(720\) | 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 | \(0.0464908\pi\) | ||||
−0.989353 | + | 0.145536i | \(0.953509\pi\) | |||||||
\(740\) | 3.31608 | 0.121902 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.52644 | 0.129460 | ||||||||
\(743\) | 53.3888i | 1.95865i | 0.202304 | + | 0.979323i | \(0.435157\pi\) | ||||
−0.202304 | + | 0.979323i | \(0.564843\pi\) | |||||||
\(744\) | 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 | \(-0.880656\pi\) | ||
0.930533 | − | 0.366208i | \(-0.119344\pi\) | |||||||
\(758\) | − | 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 | \(-0.886121\pi\) | ||
0.936683 | − | 0.350178i | \(-0.113879\pi\) | |||||||
\(788\) | 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 | \(0.0870999\pi\) | ||||
−0.962796 | + | 0.270231i | \(0.912900\pi\) | |||||||
\(798\) | 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 | \(-0.901630\pi\) | ||
0.952627 | − | 0.304142i | \(-0.0983696\pi\) | |||||||
\(812\) | − | 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 | \(0.156648\pi\) | ||||
−0.881331 | + | 0.472500i | \(0.843352\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.90080i | − | 0.101116i | −0.998721 | − | 0.0505578i | \(-0.983900\pi\) | ||
0.998721 | − | 0.0505578i | \(-0.0160999\pi\) | |||||||
\(824\) | −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 | \(-0.933574\pi\) | ||
0.978305 | − | 0.207172i | \(-0.0664258\pi\) | |||||||
\(830\) | −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 | \(0.0225012\pi\) | ||||
−0.997503 | + | 0.0706306i | \(0.977499\pi\) | |||||||
\(854\) | 7.64967 | 0.261766 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 15.3578i | − | 0.524919i | ||||||
\(857\) | 53.3902i | 1.82377i | 0.410442 | + | 0.911886i | \(0.365374\pi\) | ||||
−0.410442 | + | 0.911886i | \(0.634626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.84229i | − | 0.0628582i | −0.999506 | − | 0.0314291i | \(-0.989994\pi\) | ||
0.999506 | − | 0.0314291i | \(-0.0100058\pi\) | |||||||
\(860\) | 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 | \(-0.610566\pi\) | ||
0.340412 | − | 0.940277i | \(-0.389434\pi\) | |||||||
\(878\) | −16.1050 | −0.543518 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.3715 | 0.349622 | ||||||||
\(881\) | 35.2348i | 1.18709i | 0.804801 | + | 0.593545i | \(0.202272\pi\) | ||||
−0.804801 | + | 0.593545i | \(0.797728\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 51.3102i | − | 1.72673i | −0.504583 | − | 0.863363i | \(-0.668354\pi\) | ||
0.504583 | − | 0.863363i | \(-0.331646\pi\) | |||||||
\(884\) | 22.0735 | 0.742413 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.9702 | −1.00687 | ||||||||
\(887\) | − | 43.5073i | − | 1.46083i | −0.683003 | − | 0.730416i | \(-0.739326\pi\) | ||
0.683003 | − | 0.730416i | \(-0.260674\pi\) | |||||||
\(888\) | 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 | \(0.0208992\pi\) | ||||
−0.997845 | + | 0.0656095i | \(0.979101\pi\) | |||||||
\(912\) | 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 | \(-0.956002\pi\) | ||
0.990462 | − | 0.137784i | \(-0.0439979\pi\) | |||||||
\(920\) | 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 | \(0.174464\pi\) | ||||
−0.853519 | + | 0.521061i | \(0.825536\pi\) | |||||||
\(930\) | 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 | \(0.0235874\pi\) | ||||
−0.997256 | + | 0.0740343i | \(0.976413\pi\) | |||||||
\(938\) | −1.21936 | −0.0398135 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 11.9366i | − | 0.389330i | ||||||
\(941\) | − | 30.0482i | − | 0.979542i | −0.871851 | − | 0.489771i | \(-0.837080\pi\) | ||
0.871851 | − | 0.489771i | \(-0.162920\pi\) | |||||||
\(942\) | 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 | \(0.144522\pi\) | ||||
−0.898687 | + | 0.438590i | \(0.855478\pi\) | |||||||
\(948\) | 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 | \(-0.961726\pi\) | ||
0.992780 | − | 0.119953i | \(-0.0382744\pi\) | |||||||
\(968\) | 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 | \(0.246378\pi\) | ||||
−0.715106 | + | 0.699016i | \(0.753622\pi\) | |||||||
\(992\) | 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.4013.5 | ✓ | 72 | |
3.2 | odd | 2 | inner | 4014.2.d.a.4013.32 | yes | 72 | |
223.222 | odd | 2 | inner | 4014.2.d.a.4013.31 | yes | 72 | |
669.668 | even | 2 | inner | 4014.2.d.a.4013.6 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4014.2.d.a.4013.5 | ✓ | 72 | 1.1 | even | 1 | trivial | |
4014.2.d.a.4013.6 | yes | 72 | 669.668 | even | 2 | inner | |
4014.2.d.a.4013.31 | yes | 72 | 223.222 | odd | 2 | inner | |
4014.2.d.a.4013.32 | yes | 72 | 3.2 | odd | 2 | inner |