Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(251,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.b (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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.5 | ||
Root | \(1.14412 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.251 |
Dual form | 3150.2.b.a.251.2 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | − | 2.23607i | −0.534522 | − | 0.845154i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.41421i | − | 0.426401i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.39835i | 1.49723i | 0.663004 | + | 0.748616i | \(0.269281\pi\) | ||||
−0.663004 | + | 0.748616i | \(0.730719\pi\) | |||||||
\(14\) | 2.23607 | − | 1.41421i | 0.597614 | − | 0.377964i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.23607 | −0.542326 | −0.271163 | − | 0.962533i | \(-0.587408\pi\) | ||||
−0.271163 | + | 0.962533i | \(0.587408\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.30986i | − | 0.300502i | −0.988648 | − | 0.150251i | \(-0.951992\pi\) | ||
0.988648 | − | 0.150251i | \(-0.0480082\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.41421 | 0.301511 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | −0.994550 | − | 0.104257i | \(-0.966753\pi\) | ||
0.994550 | − | 0.104257i | \(-0.0332465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.39835 | −1.05870 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.41421 | + | 2.23607i | 0.267261 | + | 0.422577i | ||||
\(29\) | 9.24264i | 1.71632i | 0.513386 | + | 0.858158i | \(0.328391\pi\) | ||||
−0.513386 | + | 0.858158i | \(0.671609\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.56062i | − | 1.53753i | −0.639529 | − | 0.768767i | \(-0.720871\pi\) | ||
0.639529 | − | 0.768767i | \(-0.279129\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.23607i | − | 0.383482i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.82843 | 0.464991 | 0.232495 | − | 0.972598i | \(-0.425311\pi\) | ||||
0.232495 | + | 0.972598i | \(0.425311\pi\) | |||||||
\(38\) | 1.30986 | 0.212487 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.08849 | 0.638514 | 0.319257 | − | 0.947668i | \(-0.396567\pi\) | ||||
0.319257 | + | 0.947668i | \(0.396567\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.41421 | −0.978158 | −0.489079 | − | 0.872239i | \(-0.662667\pi\) | ||||
−0.489079 | + | 0.872239i | \(0.662667\pi\) | |||||||
\(44\) | 1.41421i | 0.213201i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 7.63441 | 1.11359 | 0.556797 | − | 0.830649i | \(-0.312030\pi\) | ||||
0.556797 | + | 0.830649i | \(0.312030\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | + | 6.32456i | −0.428571 | + | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 5.39835i | − | 0.748616i | ||||||
\(53\) | 6.07107i | 0.833925i | 0.908924 | + | 0.416963i | \(0.136905\pi\) | ||||
−0.908924 | + | 0.416963i | \(0.863095\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.23607 | + | 1.41421i | −0.298807 | + | 0.188982i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.24264 | −1.21362 | ||||||||
\(59\) | 11.7229 | 1.52619 | 0.763096 | − | 0.646285i | \(-0.223678\pi\) | ||||
0.763096 | + | 0.646285i | \(0.223678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.39835i | − | 0.691187i | −0.938384 | − | 0.345594i | \(-0.887678\pi\) | ||
0.938384 | − | 0.345594i | \(-0.112322\pi\) | |||||||
\(62\) | 8.56062 | 1.08720 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 2.23607 | 0.271163 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.34315i | 0.515437i | 0.966220 | + | 0.257718i | \(0.0829706\pi\) | ||||
−0.966220 | + | 0.257718i | \(0.917029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.01470i | 0.586926i | 0.955970 | + | 0.293463i | \(0.0948077\pi\) | ||||
−0.955970 | + | 0.293463i | \(0.905192\pi\) | |||||||
\(74\) | 2.82843i | 0.328798i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.30986i | 0.150251i | ||||||||
\(77\) | −3.16228 | + | 2.00000i | −0.360375 | + | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.07107 | 0.120505 | 0.0602523 | − | 0.998183i | \(-0.480809\pi\) | ||||
0.0602523 | + | 0.998183i | \(0.480809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.08849i | 0.451498i | ||||||||
\(83\) | 8.01806 | 0.880097 | 0.440048 | − | 0.897974i | \(-0.354961\pi\) | ||||
0.440048 | + | 0.897974i | \(0.354961\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 6.41421i | − | 0.691662i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.41421 | −0.150756 | ||||||||
\(89\) | 15.2688 | 1.61849 | 0.809246 | − | 0.587470i | \(-0.199876\pi\) | ||||
0.809246 | + | 0.587470i | \(0.199876\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0711 | − | 7.63441i | 1.26539 | − | 0.800304i | ||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.63441i | 0.787430i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.4311i | 1.87140i | 0.352803 | + | 0.935698i | \(0.385229\pi\) | ||||
−0.352803 | + | 0.935698i | \(0.614771\pi\) | |||||||
\(98\) | −6.32456 | − | 3.00000i | −0.638877 | − | 0.303046i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.78199 | −0.575330 | −0.287665 | − | 0.957731i | \(-0.592879\pi\) | ||||
−0.287665 | + | 0.957731i | \(0.592879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.8852i | 1.46668i | 0.679862 | + | 0.733340i | \(0.262040\pi\) | ||||
−0.679862 | + | 0.733340i | \(0.737960\pi\) | |||||||
\(104\) | 5.39835 | 0.529351 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.07107 | −0.589674 | ||||||||
\(107\) | − | 2.00000i | − | 0.193347i | −0.995316 | − | 0.0966736i | \(-0.969180\pi\) | ||
0.995316 | − | 0.0966736i | \(-0.0308203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.07107 | 0.677285 | 0.338643 | − | 0.940915i | \(-0.390032\pi\) | ||||
0.338643 | + | 0.940915i | \(0.390032\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.41421 | − | 2.23607i | −0.133631 | − | 0.211289i | ||||
\(113\) | 13.0711i | 1.22962i | 0.788674 | + | 0.614811i | \(0.210768\pi\) | ||||
−0.788674 | + | 0.614811i | \(0.789232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 9.24264i | − | 0.858158i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.7229i | 1.07918i | ||||||||
\(119\) | 3.16228 | + | 5.00000i | 0.289886 | + | 0.458349i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 5.39835 | 0.488743 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.56062i | 0.768767i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0000 | −0.887357 | −0.443678 | − | 0.896186i | \(-0.646327\pi\) | ||||
−0.443678 | + | 0.896186i | \(0.646327\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.6491 | 1.10516 | 0.552579 | − | 0.833461i | \(-0.313644\pi\) | ||||
0.552579 | + | 0.833461i | \(0.313644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.92893 | + | 1.85242i | −0.253971 | + | 0.160625i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.23607i | 0.191741i | ||||||||
\(137\) | 16.1421i | 1.37912i | 0.724231 | + | 0.689558i | \(0.242195\pi\) | ||||
−0.724231 | + | 0.689558i | \(0.757805\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.85242i | 0.157120i | 0.996909 | + | 0.0785601i | \(0.0250322\pi\) | ||||
−0.996909 | + | 0.0785601i | \(0.974968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.34315 | −0.364469 | ||||||||
\(143\) | 7.63441 | 0.638422 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.01470 | −0.415019 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.82843 | −0.232495 | ||||||||
\(149\) | − | 9.24264i | − | 0.757187i | −0.925563 | − | 0.378593i | \(-0.876408\pi\) | ||
0.925563 | − | 0.378593i | \(-0.123592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1421 | 1.15087 | 0.575435 | − | 0.817847i | \(-0.304833\pi\) | ||||
0.575435 | + | 0.817847i | \(0.304833\pi\) | |||||||
\(152\) | −1.30986 | −0.106244 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.00000 | − | 3.16228i | −0.161165 | − | 0.254824i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.85242i | 0.147839i | 0.997264 | + | 0.0739196i | \(0.0235508\pi\) | ||||
−0.997264 | + | 0.0739196i | \(0.976449\pi\) | |||||||
\(158\) | 1.07107i | 0.0852096i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.23607 | + | 1.41421i | −0.176227 | + | 0.111456i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0711 | −1.72874 | −0.864370 | − | 0.502857i | \(-0.832282\pi\) | ||||
−0.864370 | + | 0.502857i | \(0.832282\pi\) | |||||||
\(164\) | −4.08849 | −0.319257 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.01806i | 0.622322i | ||||||||
\(167\) | 5.78199 | 0.447424 | 0.223712 | − | 0.974655i | \(-0.428182\pi\) | ||||
0.223712 | + | 0.974655i | \(0.428182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16.1421 | −1.24170 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.41421 | 0.489079 | ||||||||
\(173\) | 16.5787 | 1.26045 | 0.630227 | − | 0.776411i | \(-0.282962\pi\) | ||||
0.630227 | + | 0.776411i | \(0.282962\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.41421i | − | 0.106600i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.2688i | 1.14445i | ||||||||
\(179\) | 11.3137i | 0.845626i | 0.906217 | + | 0.422813i | \(0.138957\pi\) | ||||
−0.906217 | + | 0.422813i | \(0.861043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.2688i | − | 1.13492i | −0.823400 | − | 0.567461i | \(-0.807926\pi\) | ||
0.823400 | − | 0.567461i | \(-0.192074\pi\) | |||||||
\(182\) | 7.63441 | + | 12.0711i | 0.565900 | + | 0.894767i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.16228i | 0.231249i | ||||||||
\(188\) | −7.63441 | −0.556797 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.6569i | 0.771103i | 0.922686 | + | 0.385551i | \(0.125989\pi\) | ||||
−0.922686 | + | 0.385551i | \(0.874011\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.48528 | 0.610784 | 0.305392 | − | 0.952227i | \(-0.401213\pi\) | ||||
0.305392 | + | 0.952227i | \(0.401213\pi\) | |||||||
\(194\) | −18.4311 | −1.32328 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | − | 6.32456i | 0.214286 | − | 0.451754i | ||||
\(197\) | − | 20.0711i | − | 1.43000i | −0.699122 | − | 0.715002i | \(-0.746426\pi\) | ||
0.699122 | − | 0.715002i | \(-0.253574\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.70484i | 0.262629i | 0.991341 | + | 0.131315i | \(0.0419198\pi\) | ||||
−0.991341 | + | 0.131315i | \(0.958080\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 5.78199i | − | 0.406820i | ||||||
\(203\) | 20.6672 | − | 13.0711i | 1.45055 | − | 0.917409i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.8852 | −1.03710 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.39835i | 0.374308i | ||||||||
\(209\) | −1.85242 | −0.128135 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.2132 | −1.80459 | −0.902296 | − | 0.431118i | \(-0.858119\pi\) | ||||
−0.902296 | + | 0.431118i | \(0.858119\pi\) | |||||||
\(212\) | − | 6.07107i | − | 0.416963i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.1421 | + | 12.1065i | −1.29945 | + | 0.821846i | ||||
\(218\) | 7.07107i | 0.478913i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.0711i | − | 0.811988i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.383649i | − | 0.0256910i | −0.999917 | − | 0.0128455i | \(-0.995911\pi\) | ||
0.999917 | − | 0.0128455i | \(-0.00408896\pi\) | |||||||
\(224\) | 2.23607 | − | 1.41421i | 0.149404 | − | 0.0944911i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.0711 | −0.869474 | ||||||||
\(227\) | 6.16564 | 0.409228 | 0.204614 | − | 0.978843i | \(-0.434406\pi\) | ||||
0.204614 | + | 0.978843i | \(0.434406\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.85242i | − | 0.122411i | −0.998125 | − | 0.0612057i | \(-0.980505\pi\) | ||
0.998125 | − | 0.0612057i | \(-0.0194946\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.24264 | 0.606809 | ||||||||
\(233\) | 8.92893i | 0.584954i | 0.956273 | + | 0.292477i | \(0.0944795\pi\) | ||||
−0.956273 | + | 0.292477i | \(0.905521\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.7229 | −0.763096 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.00000 | + | 3.16228i | −0.324102 | + | 0.204980i | ||||
\(239\) | 12.8284i | 0.829802i | 0.909867 | + | 0.414901i | \(0.136184\pi\) | ||||
−0.909867 | + | 0.414901i | \(0.863816\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.47214i | − | 0.288076i | −0.989572 | − | 0.144038i | \(-0.953991\pi\) | ||
0.989572 | − | 0.144038i | \(-0.0460087\pi\) | |||||||
\(242\) | 9.00000i | 0.578542i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.39835i | 0.345594i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.07107 | 0.449921 | ||||||||
\(248\) | −8.56062 | −0.543600 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.4902 | −0.788374 | −0.394187 | − | 0.919030i | \(-0.628974\pi\) | ||||
−0.394187 | + | 0.919030i | \(0.628974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.41421 | −0.0889108 | ||||||||
\(254\) | − | 10.0000i | − | 0.627456i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.7376 | −1.04406 | −0.522031 | − | 0.852926i | \(-0.674826\pi\) | ||||
−0.522031 | + | 0.852926i | \(0.674826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | − | 6.32456i | −0.248548 | − | 0.392989i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.6491i | 0.781465i | ||||||||
\(263\) | 27.2843i | 1.68242i | 0.540708 | + | 0.841210i | \(0.318156\pi\) | ||||
−0.540708 | + | 0.841210i | \(0.681844\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.85242 | − | 2.92893i | −0.113579 | − | 0.179584i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0294 | −0.611503 | −0.305751 | − | 0.952111i | \(-0.598908\pi\) | ||||
−0.305751 | + | 0.952111i | \(0.598908\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.7410i | − | 1.19918i | −0.800308 | − | 0.599589i | \(-0.795331\pi\) | ||
0.800308 | − | 0.599589i | \(-0.204669\pi\) | |||||||
\(272\) | −2.23607 | −0.135582 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.1421 | −0.975182 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.2132 | −1.27458 | −0.637289 | − | 0.770625i | \(-0.719944\pi\) | ||||
−0.637289 | + | 0.770625i | \(0.719944\pi\) | |||||||
\(278\) | −1.85242 | −0.111101 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.5147i | 0.686911i | 0.939169 | + | 0.343455i | \(0.111597\pi\) | ||||
−0.939169 | + | 0.343455i | \(0.888403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.30986i | 0.0778630i | 0.999242 | + | 0.0389315i | \(0.0123954\pi\) | ||||
−0.999242 | + | 0.0389315i | \(0.987605\pi\) | |||||||
\(284\) | − | 4.34315i | − | 0.257718i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.63441i | 0.451432i | ||||||||
\(287\) | −5.78199 | − | 9.14214i | −0.341300 | − | 0.539643i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0000 | −0.705882 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 5.01470i | − | 0.293463i | ||||||
\(293\) | 25.2982 | 1.47794 | 0.738969 | − | 0.673740i | \(-0.235313\pi\) | ||||
0.738969 | + | 0.673740i | \(0.235313\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 2.82843i | − | 0.164399i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.24264 | 0.535412 | ||||||||
\(299\) | 5.39835 | 0.312194 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.07107 | + | 14.3426i | 0.522848 | + | 0.826695i | ||||
\(302\) | 14.1421i | 0.813788i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 1.30986i | − | 0.0751255i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.5934i | − | 1.23240i | −0.787590 | − | 0.616200i | \(-0.788671\pi\) | ||
0.787590 | − | 0.616200i | \(-0.211329\pi\) | |||||||
\(308\) | 3.16228 | − | 2.00000i | 0.180187 | − | 0.113961i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.5377 | 1.73163 | 0.865816 | − | 0.500363i | \(-0.166800\pi\) | ||||
0.865816 | + | 0.500363i | \(0.166800\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10.2541i | − | 0.579598i | −0.957088 | − | 0.289799i | \(-0.906412\pi\) | ||
0.957088 | − | 0.289799i | \(-0.0935884\pi\) | |||||||
\(314\) | −1.85242 | −0.104538 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.07107 | −0.0602523 | ||||||||
\(317\) | − | 15.9289i | − | 0.894658i | −0.894369 | − | 0.447329i | \(-0.852375\pi\) | ||
0.894369 | − | 0.447329i | \(-0.147625\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.0711 | 0.731839 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.41421 | − | 2.23607i | −0.0788110 | − | 0.124611i | ||||
\(323\) | 2.92893i | 0.162970i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 22.0711i | − | 1.22240i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 4.08849i | − | 0.225749i | ||||||
\(329\) | −10.7967 | − | 17.0711i | −0.595241 | − | 0.941158i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.0711 | 1.21314 | 0.606568 | − | 0.795032i | \(-0.292546\pi\) | ||||
0.606568 | + | 0.795032i | \(0.292546\pi\) | |||||||
\(332\) | −8.01806 | −0.440048 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.78199i | 0.316377i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.9706 | 1.19681 | 0.598406 | − | 0.801193i | \(-0.295801\pi\) | ||||
0.598406 | + | 0.801193i | \(0.295801\pi\) | |||||||
\(338\) | − | 16.1421i | − | 0.878016i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.1065 | −0.655606 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3848 | − | 2.23607i | 0.992685 | − | 0.120736i | ||||
\(344\) | 6.41421i | 0.345831i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.5787i | 0.891276i | ||||||||
\(347\) | 5.07107i | 0.272229i | 0.990693 | + | 0.136115i | \(0.0434615\pi\) | ||||
−0.990693 | + | 0.136115i | \(0.956538\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.1393i | 1.34568i | 0.739790 | + | 0.672838i | \(0.234925\pi\) | ||||
−0.739790 | + | 0.672838i | \(0.765075\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.41421 | 0.0753778 | ||||||||
\(353\) | 18.9737 | 1.00987 | 0.504933 | − | 0.863158i | \(-0.331517\pi\) | ||||
0.504933 | + | 0.863158i | \(0.331517\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.2688 | −0.809246 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.3137 | −0.597948 | ||||||||
\(359\) | − | 6.31371i | − | 0.333225i | −0.986022 | − | 0.166612i | \(-0.946717\pi\) | ||
0.986022 | − | 0.166612i | \(-0.0532829\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.2843 | 0.909698 | ||||||||
\(362\) | 15.2688 | 0.802512 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.0711 | + | 7.63441i | −0.632696 | + | 0.400152i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.5967i | 1.28394i | 0.766730 | + | 0.641970i | \(0.221883\pi\) | ||||
−0.766730 | + | 0.641970i | \(0.778117\pi\) | |||||||
\(368\) | − | 1.00000i | − | 0.0521286i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.5753 | − | 8.58579i | 0.704796 | − | 0.445752i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.07107 | −0.366126 | −0.183063 | − | 0.983101i | \(-0.558601\pi\) | ||||
−0.183063 | + | 0.983101i | \(0.558601\pi\) | |||||||
\(374\) | −3.16228 | −0.163517 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 7.63441i | − | 0.393715i | ||||||
\(377\) | −49.8950 | −2.56972 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.92893 | 0.407282 | 0.203641 | − | 0.979046i | \(-0.434722\pi\) | ||||
0.203641 | + | 0.979046i | \(0.434722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.6569 | −0.545252 | ||||||||
\(383\) | −28.6852 | −1.46575 | −0.732874 | − | 0.680365i | \(-0.761821\pi\) | ||||
−0.732874 | + | 0.680365i | \(0.761821\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 18.4311i | − | 0.935698i | ||||||
\(389\) | − | 17.1716i | − | 0.870633i | −0.900277 | − | 0.435317i | \(-0.856636\pi\) | ||
0.900277 | − | 0.435317i | \(-0.143364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.23607i | 0.113083i | ||||||||
\(392\) | 6.32456 | + | 3.00000i | 0.319438 | + | 0.151523i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.0711 | 1.01117 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.6378i | 0.533895i | 0.963711 | + | 0.266947i | \(0.0860150\pi\) | ||||
−0.963711 | + | 0.266947i | \(0.913985\pi\) | |||||||
\(398\) | −3.70484 | −0.185707 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.7990i | 1.48809i | 0.668129 | + | 0.744045i | \(0.267095\pi\) | ||||
−0.668129 | + | 0.744045i | \(0.732905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 46.2132 | 2.30204 | ||||||||
\(404\) | 5.78199 | 0.287665 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.0711 | + | 20.6672i | 0.648706 | + | 1.02569i | ||||
\(407\) | − | 4.00000i | − | 0.198273i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.92957i | 0.194305i | 0.995270 | + | 0.0971525i | \(0.0309735\pi\) | ||||
−0.995270 | + | 0.0971525i | \(0.969027\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 14.8852i | − | 0.733340i | ||||||
\(413\) | −16.5787 | − | 26.2132i | −0.815784 | − | 1.28987i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.39835 | −0.264676 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1.85242i | − | 0.0906048i | ||||||
\(419\) | 15.4277 | 0.753694 | 0.376847 | − | 0.926275i | \(-0.377008\pi\) | ||||
0.376847 | + | 0.926275i | \(0.377008\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.3553 | −1.82059 | −0.910294 | − | 0.413963i | \(-0.864144\pi\) | ||||
−0.910294 | + | 0.413963i | \(0.864144\pi\) | |||||||
\(422\) | − | 26.2132i | − | 1.27604i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.07107 | 0.294837 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0711 | + | 7.63441i | −0.584160 | + | 0.369455i | ||||
\(428\) | 2.00000i | 0.0966736i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 34.7990i | − | 1.67621i | −0.545510 | − | 0.838104i | \(-0.683664\pi\) | ||
0.545510 | − | 0.838104i | \(-0.316336\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 35.0098i | − | 1.68246i | −0.540675 | − | 0.841232i | \(-0.681831\pi\) | ||
0.540675 | − | 0.841232i | \(-0.318169\pi\) | |||||||
\(434\) | −12.1065 | − | 19.1421i | −0.581133 | − | 0.918852i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.07107 | −0.338643 | ||||||||
\(437\) | −1.30986 | −0.0626590 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.56062i | 0.408576i | 0.978911 | + | 0.204288i | \(0.0654879\pi\) | ||||
−0.978911 | + | 0.204288i | \(0.934512\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0711 | 0.574162 | ||||||||
\(443\) | 8.92893i | 0.424226i | 0.977245 | + | 0.212113i | \(0.0680346\pi\) | ||||
−0.977245 | + | 0.212113i | \(0.931965\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.383649 | 0.0181663 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.41421 | + | 2.23607i | 0.0668153 | + | 0.105644i | ||||
\(449\) | 18.3848i | 0.867631i | 0.901002 | + | 0.433816i | \(0.142833\pi\) | ||||
−0.901002 | + | 0.433816i | \(0.857167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.78199i | − | 0.272263i | ||||||
\(452\) | − | 13.0711i | − | 0.614811i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.16564i | 0.289368i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.1716 | 0.569362 | 0.284681 | − | 0.958622i | \(-0.408112\pi\) | ||||
0.284681 | + | 0.958622i | \(0.408112\pi\) | |||||||
\(458\) | 1.85242 | 0.0865579 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.6148 | 1.51902 | 0.759512 | − | 0.650494i | \(-0.225438\pi\) | ||||
0.759512 | + | 0.650494i | \(0.225438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.2843 | −0.849742 | −0.424871 | − | 0.905254i | \(-0.639681\pi\) | ||||
−0.424871 | + | 0.905254i | \(0.639681\pi\) | |||||||
\(464\) | 9.24264i | 0.429079i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.92893 | −0.413625 | ||||||||
\(467\) | −10.6378 | −0.492258 | −0.246129 | − | 0.969237i | \(-0.579159\pi\) | ||||
−0.246129 | + | 0.969237i | \(0.579159\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 11.7229i | − | 0.539590i | ||||||
\(473\) | 9.07107i | 0.417088i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.16228 | − | 5.00000i | −0.144943 | − | 0.229175i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.8284 | −0.586759 | ||||||||
\(479\) | −2.07716 | −0.0949077 | −0.0474538 | − | 0.998873i | \(-0.515111\pi\) | ||||
−0.0474538 | + | 0.998873i | \(0.515111\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.2688i | 0.696199i | ||||||||
\(482\) | 4.47214 | 0.203700 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.00000 | −0.409091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.1005 | 0.457698 | 0.228849 | − | 0.973462i | \(-0.426504\pi\) | ||||
0.228849 | + | 0.973462i | \(0.426504\pi\) | |||||||
\(488\) | −5.39835 | −0.244372 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.4853i | 1.73682i | 0.495850 | + | 0.868408i | \(0.334857\pi\) | ||||
−0.495850 | + | 0.868408i | \(0.665143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 20.6672i | − | 0.930803i | ||||||
\(494\) | 7.07107i | 0.318142i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.56062i | − | 0.384383i | ||||||
\(497\) | 9.71157 | − | 6.14214i | 0.435623 | − | 0.275512i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.92893 | −0.354948 | −0.177474 | − | 0.984126i | \(-0.556793\pi\) | ||||
−0.177474 | + | 0.984126i | \(0.556793\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 12.4902i | − | 0.557465i | ||||||
\(503\) | −40.7918 | −1.81882 | −0.909408 | − | 0.415905i | \(-0.863465\pi\) | ||||
−0.909408 | + | 0.415905i | \(0.863465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 1.41421i | − | 0.0628695i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.0000 | 0.443678 | ||||||||
\(509\) | −44.4966 | −1.97228 | −0.986139 | − | 0.165921i | \(-0.946940\pi\) | ||||
−0.986139 | + | 0.165921i | \(0.946940\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.2132 | − | 7.09185i | 0.496043 | − | 0.313725i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 16.7376i | − | 0.738264i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10.7967i | − | 0.474838i | ||||||
\(518\) | 6.32456 | − | 4.00000i | 0.277885 | − | 0.175750i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.85578 | −0.212736 | −0.106368 | − | 0.994327i | \(-0.533922\pi\) | ||||
−0.106368 | + | 0.994327i | \(0.533922\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 28.4605i | − | 1.24449i | −0.782822 | − | 0.622245i | \(-0.786221\pi\) | ||
0.782822 | − | 0.622245i | \(-0.213779\pi\) | |||||||
\(524\) | −12.6491 | −0.552579 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.2843 | −1.18965 | ||||||||
\(527\) | 19.1421i | 0.833845i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.0000 | 0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.92893 | − | 1.85242i | 0.126985 | − | 0.0803126i | ||||
\(533\) | 22.0711i | 0.956004i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 10.0294i | − | 0.432398i | ||||||
\(539\) | 8.94427 | + | 4.24264i | 0.385257 | + | 0.182743i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.07107 | −0.389996 | −0.194998 | − | 0.980804i | \(-0.562470\pi\) | ||||
−0.194998 | + | 0.980804i | \(0.562470\pi\) | |||||||
\(542\) | 19.7410 | 0.847947 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 2.23607i | − | 0.0958706i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.2132 | 1.12080 | 0.560398 | − | 0.828224i | \(-0.310648\pi\) | ||||
0.560398 | + | 0.828224i | \(0.310648\pi\) | |||||||
\(548\) | − | 16.1421i | − | 0.689558i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.1065 | 0.515756 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.51472 | − | 2.39498i | −0.0644124 | − | 0.101845i | ||||
\(554\) | − | 21.2132i | − | 0.901263i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 1.85242i | − | 0.0785601i | ||||||
\(557\) | − | 2.14214i | − | 0.0907652i | −0.998970 | − | 0.0453826i | \(-0.985549\pi\) | ||
0.998970 | − | 0.0453826i | \(-0.0144507\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.6261i | − | 1.46453i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.5147 | −0.485719 | ||||||||
\(563\) | −19.8999 | −0.838680 | −0.419340 | − | 0.907829i | \(-0.637738\pi\) | ||||
−0.419340 | + | 0.907829i | \(0.637738\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.30986 | −0.0550575 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.34315 | 0.182234 | ||||||||
\(569\) | − | 42.5269i | − | 1.78282i | −0.453197 | − | 0.891410i | \(-0.649717\pi\) | ||
0.453197 | − | 0.891410i | \(-0.350283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.21320 | 0.176317 | 0.0881585 | − | 0.996106i | \(-0.471902\pi\) | ||||
0.0881585 | + | 0.996106i | \(0.471902\pi\) | |||||||
\(572\) | −7.63441 | −0.319211 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.14214 | − | 5.78199i | 0.381585 | − | 0.241336i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.5015i | − | 0.603707i | −0.953354 | − | 0.301853i | \(-0.902395\pi\) | ||
0.953354 | − | 0.301853i | \(-0.0976053\pi\) | |||||||
\(578\) | − | 12.0000i | − | 0.499134i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.3393 | − | 17.9289i | −0.470431 | − | 0.743817i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.58579 | 0.355587 | ||||||||
\(584\) | 5.01470 | 0.207510 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.2982i | 1.04506i | ||||||||
\(587\) | 28.8441 | 1.19053 | 0.595263 | − | 0.803531i | \(-0.297048\pi\) | ||||
0.595263 | + | 0.803531i | \(0.297048\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.2132 | −0.462032 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.82843 | 0.116248 | ||||||||
\(593\) | 29.0031 | 1.19101 | 0.595506 | − | 0.803351i | \(-0.296951\pi\) | ||||
0.595506 | + | 0.803351i | \(0.296951\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.24264i | 0.378593i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.39835i | 0.220755i | ||||||||
\(599\) | 26.3137i | 1.07515i | 0.843216 | + | 0.537574i | \(0.180659\pi\) | ||||
−0.843216 | + | 0.537574i | \(0.819341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 5.78199i | − | 0.235852i | −0.993022 | − | 0.117926i | \(-0.962375\pi\) | ||
0.993022 | − | 0.117926i | \(-0.0376246\pi\) | |||||||
\(602\) | −14.3426 | + | 9.07107i | −0.584561 | + | 0.369709i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.1421 | −0.575435 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18.6558i | − | 0.757217i | −0.925557 | − | 0.378609i | \(-0.876403\pi\) | ||
0.925557 | − | 0.378609i | \(-0.123597\pi\) | |||||||
\(608\) | 1.30986 | 0.0531218 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 41.2132i | 1.66731i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.1421 | 1.78288 | 0.891442 | − | 0.453135i | \(-0.149694\pi\) | ||||
0.891442 | + | 0.453135i | \(0.149694\pi\) | |||||||
\(614\) | 21.5934 | 0.871438 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | + | 3.16228i | 0.0805823 | + | 0.127412i | ||||
\(617\) | − | 32.0000i | − | 1.28827i | −0.764911 | − | 0.644136i | \(-0.777217\pi\) | ||
0.764911 | − | 0.644136i | \(-0.222783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 45.0392i | − | 1.81028i | −0.425116 | − | 0.905139i | \(-0.639767\pi\) | ||
0.425116 | − | 0.905139i | \(-0.360233\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.5377i | 1.22445i | ||||||||
\(623\) | −21.5934 | − | 34.1421i | −0.865121 | − | 1.36788i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.2541 | 0.409837 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 1.85242i | − | 0.0739196i | ||||||
\(629\) | −6.32456 | −0.252177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.2843 | −1.84255 | −0.921274 | − | 0.388914i | \(-0.872850\pi\) | ||||
−0.921274 | + | 0.388914i | \(0.872850\pi\) | |||||||
\(632\) | − | 1.07107i | − | 0.0426048i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.9289 | 0.632619 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.1421 | − | 16.1950i | −1.35276 | − | 0.641671i | ||||
\(638\) | 13.0711i | 0.517489i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 11.5147i | − | 0.454804i | −0.973801 | − | 0.227402i | \(-0.926977\pi\) | ||
0.973801 | − | 0.227402i | \(-0.0730231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.6705i | 0.933475i | 0.884396 | + | 0.466737i | \(0.154571\pi\) | ||||
−0.884396 | + | 0.466737i | \(0.845429\pi\) | |||||||
\(644\) | 2.23607 | − | 1.41421i | 0.0881134 | − | 0.0557278i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.92893 | −0.115237 | ||||||||
\(647\) | −43.4115 | −1.70668 | −0.853341 | − | 0.521353i | \(-0.825427\pi\) | ||||
−0.853341 | + | 0.521353i | \(0.825427\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 16.5787i | − | 0.650770i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.0711 | 0.864370 | ||||||||
\(653\) | − | 20.1421i | − | 0.788223i | −0.919063 | − | 0.394111i | \(-0.871052\pi\) | ||
0.919063 | − | 0.394111i | \(-0.128948\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.08849 | 0.159629 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17.0711 | − | 10.7967i | 0.665500 | − | 0.420899i | ||||
\(659\) | 11.6152i | 0.452465i | 0.974073 | + | 0.226232i | \(0.0726409\pi\) | ||||
−0.974073 | + | 0.226232i | \(0.927359\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.0392i | 1.75182i | 0.482473 | + | 0.875911i | \(0.339739\pi\) | ||||
−0.482473 | + | 0.875911i | \(0.660261\pi\) | |||||||
\(662\) | 22.0711i | 0.857816i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 8.01806i | − | 0.311161i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.24264 | 0.357876 | ||||||||
\(668\) | −5.78199 | −0.223712 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.63441 | −0.294723 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.79899 | −0.184987 | −0.0924937 | − | 0.995713i | \(-0.529484\pi\) | ||||
−0.0924937 | + | 0.995713i | \(0.529484\pi\) | |||||||
\(674\) | 21.9706i | 0.846274i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.1421 | 0.620851 | ||||||||
\(677\) | 3.92957 | 0.151026 | 0.0755129 | − | 0.997145i | \(-0.475941\pi\) | ||||
0.0755129 | + | 0.997145i | \(0.475941\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.2132 | − | 26.0655i | 1.58162 | − | 1.00030i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 12.1065i | − | 0.463584i | ||||||
\(683\) | − | 36.0000i | − | 1.37750i | −0.724998 | − | 0.688751i | \(-0.758159\pi\) | ||
0.724998 | − | 0.688751i | \(-0.241841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.23607 | + | 18.3848i | 0.0853735 | + | 0.701934i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.41421 | −0.244540 | ||||||||
\(689\) | −32.7737 | −1.24858 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.9326i | 1.25282i | 0.779495 | + | 0.626408i | \(0.215476\pi\) | ||||
−0.779495 | + | 0.626408i | \(0.784524\pi\) | |||||||
\(692\) | −16.5787 | −0.630227 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.07107 | −0.192495 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.14214 | −0.346283 | ||||||||
\(698\) | −25.1393 | −0.951537 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 11.8701i | − | 0.448326i | −0.974552 | − | 0.224163i | \(-0.928035\pi\) | ||
0.974552 | − | 0.224163i | \(-0.0719648\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.70484i | − | 0.139731i | ||||||
\(704\) | 1.41421i | 0.0533002i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.9737i | 0.714083i | ||||||||
\(707\) | 8.17697 | + | 12.9289i | 0.307527 | + | 0.486243i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.14214 | −0.155561 | −0.0777806 | − | 0.996971i | \(-0.524783\pi\) | ||||
−0.0777806 | + | 0.996971i | \(0.524783\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 15.2688i | − | 0.572223i | ||||||
\(713\) | −8.56062 | −0.320598 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 11.3137i | − | 0.422813i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.31371 | 0.235626 | ||||||||
\(719\) | 32.9326 | 1.22818 | 0.614090 | − | 0.789236i | \(-0.289523\pi\) | ||||
0.614090 | + | 0.789236i | \(0.289523\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.2843 | − | 21.0508i | 1.23957 | − | 0.783974i | ||||
\(722\) | 17.2843i | 0.643254i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.2688i | 0.567461i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.70820i | 0.248794i | 0.992233 | + | 0.124397i | \(0.0396996\pi\) | ||||
−0.992233 | + | 0.124397i | \(0.960300\pi\) | |||||||
\(728\) | −7.63441 | − | 12.0711i | −0.282950 | − | 0.447384i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.3426 | 0.530481 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 17.2802i | − | 0.638257i | −0.947711 | − | 0.319129i | \(-0.896610\pi\) | ||
0.947711 | − | 0.319129i | \(-0.103390\pi\) | |||||||
\(734\) | −24.5967 | −0.907883 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.3553 | 1.63164 | 0.815819 | − | 0.578308i | \(-0.196287\pi\) | ||||
0.815819 | + | 0.578308i | \(0.196287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.58579 | + | 13.5753i | 0.315194 | + | 0.498366i | ||||
\(743\) | 6.85786i | 0.251591i | 0.992056 | + | 0.125795i | \(0.0401483\pi\) | ||||
−0.992056 | + | 0.125795i | \(0.959852\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 7.07107i | − | 0.258890i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.16228i | − | 0.115624i | ||||||
\(749\) | −4.47214 | + | 2.82843i | −0.163408 | + | 0.103348i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.2132 | −0.409176 | −0.204588 | − | 0.978848i | \(-0.565585\pi\) | ||||
−0.204588 | + | 0.978848i | \(0.565585\pi\) | |||||||
\(752\) | 7.63441 | 0.278398 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 49.8950i | − | 1.81707i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.04163 | 0.146896 | 0.0734478 | − | 0.997299i | \(-0.476600\pi\) | ||||
0.0734478 | + | 0.997299i | \(0.476600\pi\) | |||||||
\(758\) | 7.92893i | 0.287992i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.3050 | 1.13480 | 0.567402 | − | 0.823441i | \(-0.307949\pi\) | ||||
0.567402 | + | 0.823441i | \(0.307949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0000 | − | 15.8114i | −0.362024 | − | 0.572411i | ||||
\(764\) | − | 10.6569i | − | 0.385551i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 28.6852i | − | 1.03644i | ||||||
\(767\) | 63.2843i | 2.28506i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 41.8769i | − | 1.51012i | −0.655656 | − | 0.755060i | \(-0.727608\pi\) | ||
0.655656 | − | 0.755060i | \(-0.272392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.48528 | −0.305392 | ||||||||
\(773\) | −36.3196 | −1.30633 | −0.653163 | − | 0.757217i | \(-0.726559\pi\) | ||||
−0.653163 | + | 0.757217i | \(0.726559\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18.4311 | 0.661638 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.1716 | 0.615631 | ||||||||
\(779\) | − | 5.35534i | − | 0.191875i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.14214 | 0.219783 | ||||||||
\(782\) | −2.23607 | −0.0799616 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00000 | + | 6.32456i | −0.107143 | + | 0.225877i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 46.5738i | − | 1.66018i | −0.557632 | − | 0.830088i | \(-0.688290\pi\) | ||
0.557632 | − | 0.830088i | \(-0.311710\pi\) | |||||||
\(788\) | 20.0711i | 0.715002i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.2278 | − | 18.4853i | 1.03922 | − | 0.657261i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.1421 | 1.03487 | ||||||||
\(794\) | −10.6378 | −0.377521 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 3.70484i | − | 0.131315i | ||||||
\(797\) | 42.6442 | 1.51054 | 0.755268 | − | 0.655417i | \(-0.227507\pi\) | ||||
0.755268 | + | 0.655417i | \(0.227507\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.0711 | −0.603931 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −29.7990 | −1.05224 | ||||||||
\(803\) | 7.09185 | 0.250266 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 46.2132i | 1.62779i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.78199i | 0.203410i | ||||||||
\(809\) | − | 0.100505i | − | 0.00353357i | −0.999998 | − | 0.00176678i | \(-0.999438\pi\) | ||
0.999998 | − | 0.00176678i | \(-0.000562385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.1096i | 1.44355i | 0.692126 | + | 0.721777i | \(0.256674\pi\) | ||||
−0.692126 | + | 0.721777i | \(0.743326\pi\) | |||||||
\(812\) | −20.6672 | + | 13.0711i | −0.725276 | + | 0.458705i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.00000 | 0.140200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.40171i | 0.293939i | ||||||||
\(818\) | −3.92957 | −0.137394 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.9411i | 0.835551i | 0.908550 | + | 0.417776i | \(0.137190\pi\) | ||||
−0.908550 | + | 0.417776i | \(0.862810\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.92893 | 0.102096 | 0.0510481 | − | 0.998696i | \(-0.483744\pi\) | ||||
0.0510481 | + | 0.998696i | \(0.483744\pi\) | |||||||
\(824\) | 14.8852 | 0.518550 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.2132 | − | 16.5787i | 0.912074 | − | 0.576846i | ||||
\(827\) | − | 54.4264i | − | 1.89259i | −0.323302 | − | 0.946296i | \(-0.604793\pi\) | ||
0.323302 | − | 0.946296i | \(-0.395207\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.7590i | 0.964111i | 0.876141 | + | 0.482055i | \(0.160110\pi\) | ||||
−0.876141 | + | 0.482055i | \(0.839890\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.39835i | − | 0.187154i | ||||||
\(833\) | 6.70820 | − | 14.1421i | 0.232425 | − | 0.489996i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.85242 | 0.0640673 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.4277i | 0.532942i | ||||||||
\(839\) | −9.71157 | −0.335281 | −0.167640 | − | 0.985848i | \(-0.553615\pi\) | ||||
−0.167640 | + | 0.985848i | \(0.553615\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −56.4264 | −1.94574 | ||||||||
\(842\) | − | 37.3553i | − | 1.28735i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 26.2132 | 0.902296 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.7279 | − | 20.1246i | −0.437337 | − | 0.691490i | ||||
\(848\) | 6.07107i | 0.208481i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.82843i | − | 0.0969572i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 22.5196i | − | 0.771056i | −0.922696 | − | 0.385528i | \(-0.874019\pi\) | ||
0.922696 | − | 0.385528i | \(-0.125981\pi\) | |||||||
\(854\) | −7.63441 | − | 12.0711i | −0.261244 | − | 0.413063i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.00000 | −0.0683586 | ||||||||
\(857\) | 17.8885 | 0.611061 | 0.305531 | − | 0.952182i | \(-0.401166\pi\) | ||||
0.305531 | + | 0.952182i | \(0.401166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 15.2688i | − | 0.520966i | −0.965478 | − | 0.260483i | \(-0.916118\pi\) | ||
0.965478 | − | 0.260483i | \(-0.0838817\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34.7990 | 1.18526 | ||||||||
\(863\) | − | 48.1421i | − | 1.63878i | −0.573238 | − | 0.819389i | \(-0.694313\pi\) | ||
0.573238 | − | 0.819389i | \(-0.305687\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.0098 | 1.18968 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 19.1421 | − | 12.1065i | 0.649726 | − | 0.410923i | ||||
\(869\) | − | 1.51472i | − | 0.0513833i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 7.07107i | − | 0.239457i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.30986i | − | 0.0443066i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.1421 | 1.15290 | 0.576449 | − | 0.817133i | \(-0.304438\pi\) | ||||
0.576449 | + | 0.817133i | \(0.304438\pi\) | |||||||
\(878\) | −8.56062 | −0.288907 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.5900 | 0.626314 | 0.313157 | − | 0.949701i | \(-0.398613\pi\) | ||||
0.313157 | + | 0.949701i | \(0.398613\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.0122 | −1.54843 | −0.774217 | − | 0.632920i | \(-0.781856\pi\) | ||||
−0.774217 | + | 0.632920i | \(0.781856\pi\) | |||||||
\(884\) | 12.0711i | 0.405994i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.92893 | −0.299973 | ||||||||
\(887\) | 34.2425 | 1.14975 | 0.574875 | − | 0.818241i | \(-0.305051\pi\) | ||||
0.574875 | + | 0.818241i | \(0.305051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.1421 | + | 22.3607i | 0.474312 | + | 0.749953i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.383649i | 0.0128455i | ||||||||
\(893\) | − | 10.0000i | − | 0.334637i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.23607 | + | 1.41421i | −0.0747018 | + | 0.0472456i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.3848 | −0.613508 | ||||||||
\(899\) | 79.1228 | 2.63889 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 13.5753i | − | 0.452259i | ||||||
\(902\) | 5.78199 | 0.192519 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.0711 | 0.434737 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.89949 | −0.162685 | −0.0813425 | − | 0.996686i | \(-0.525921\pi\) | ||||
−0.0813425 | + | 0.996686i | \(0.525921\pi\) | |||||||
\(908\) | −6.16564 | −0.204614 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.6274i | 1.90928i | 0.297760 | + | 0.954641i | \(0.403760\pi\) | ||||
−0.297760 | + | 0.954641i | \(0.596240\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 11.3393i | − | 0.375274i | ||||||
\(914\) | 12.1716i | 0.402600i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.85242i | 0.0612057i | ||||||||
\(917\) | −17.8885 | − | 28.2843i | −0.590732 | − | 0.934029i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.07107 | −0.233253 | −0.116627 | − | 0.993176i | \(-0.537208\pi\) | ||||
−0.116627 | + | 0.993176i | \(0.537208\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.6148i | 1.07411i | ||||||||
\(923\) | −23.4458 | −0.771728 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 18.2843i | − | 0.600858i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.24264 | −0.303405 | ||||||||
\(929\) | −50.6623 | −1.66218 | −0.831088 | − | 0.556142i | \(-0.812281\pi\) | ||||
−0.831088 | + | 0.556142i | \(0.812281\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.28427 | + | 3.92957i | 0.271506 | + | 0.128787i | ||||
\(932\) | − | 8.92893i | − | 0.292477i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 10.6378i | − | 0.348079i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.5377i | 0.997622i | 0.866711 | + | 0.498811i | \(0.166230\pi\) | ||||
−0.866711 | + | 0.498811i | \(0.833770\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.2719 | −1.44322 | −0.721611 | − | 0.692299i | \(-0.756598\pi\) | ||||
−0.721611 | + | 0.692299i | \(0.756598\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.08849i | − | 0.133139i | ||||||
\(944\) | 11.7229 | 0.381548 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.07107 | −0.294926 | ||||||||
\(947\) | 37.3553i | 1.21389i | 0.794746 | + | 0.606943i | \(0.207604\pi\) | ||||
−0.794746 | + | 0.606943i | \(0.792396\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.0711 | −0.878764 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.00000 | − | 3.16228i | 0.162051 | − | 0.102490i | ||||
\(953\) | 36.0000i | 1.16615i | 0.812417 | + | 0.583077i | \(0.198151\pi\) | ||||
−0.812417 | + | 0.583077i | \(0.801849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 12.8284i | − | 0.414901i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 2.07716i | − | 0.0671098i | ||||||
\(959\) | 36.0949 | − | 22.8284i | 1.16557 | − | 0.737168i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −42.2843 | −1.36401 | ||||||||
\(962\) | −15.2688 | −0.492287 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.47214i | 0.144038i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.4975 | 1.59173 | 0.795866 | − | 0.605473i | \(-0.207016\pi\) | ||||
0.795866 | + | 0.605473i | \(0.207016\pi\) | |||||||
\(968\) | − | 9.00000i | − | 0.289271i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52.8983 | −1.69759 | −0.848794 | − | 0.528723i | \(-0.822671\pi\) | ||||
−0.848794 | + | 0.528723i | \(0.822671\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.14214 | − | 2.61972i | 0.132791 | − | 0.0839843i | ||||
\(974\) | 10.1005i | 0.323641i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 5.39835i | − | 0.172797i | ||||||
\(977\) | − | 12.0000i | − | 0.383914i | −0.981403 | − | 0.191957i | \(-0.938517\pi\) | ||
0.981403 | − | 0.191957i | \(-0.0614834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 21.5934i | − | 0.690127i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −38.4853 | −1.22811 | ||||||||
\(983\) | −6.32456 | −0.201722 | −0.100861 | − | 0.994901i | \(-0.532160\pi\) | ||||
−0.100861 | + | 0.994901i | \(0.532160\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 20.6672 | 0.658177 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.07107 | −0.224961 | ||||||||
\(989\) | 6.41421i | 0.203960i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.3553 | 1.44076 | 0.720380 | − | 0.693580i | \(-0.243967\pi\) | ||||
0.720380 | + | 0.693580i | \(0.243967\pi\) | |||||||
\(992\) | 8.56062 | 0.271800 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.14214 | + | 9.71157i | 0.194817 | + | 0.308032i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.7967i | 0.341935i | 0.985277 | + | 0.170967i | \(0.0546893\pi\) | ||||
−0.985277 | + | 0.170967i | \(0.945311\pi\) | |||||||
\(998\) | − | 7.92893i | − | 0.250986i | ||||||
\(999\) | 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 | 3150.2.b.a.251.5 | yes | 8 | |
3.2 | odd | 2 | inner | 3150.2.b.a.251.1 | ✓ | 8 | |
5.2 | odd | 4 | 3150.2.d.b.3149.6 | 8 | |||
5.3 | odd | 4 | 3150.2.d.e.3149.3 | 8 | |||
5.4 | even | 2 | 3150.2.b.d.251.4 | yes | 8 | ||
7.6 | odd | 2 | inner | 3150.2.b.a.251.6 | yes | 8 | |
15.2 | even | 4 | 3150.2.d.e.3149.6 | 8 | |||
15.8 | even | 4 | 3150.2.d.b.3149.3 | 8 | |||
15.14 | odd | 2 | 3150.2.b.d.251.8 | yes | 8 | ||
21.20 | even | 2 | inner | 3150.2.b.a.251.2 | yes | 8 | |
35.13 | even | 4 | 3150.2.d.e.3149.8 | 8 | |||
35.27 | even | 4 | 3150.2.d.b.3149.1 | 8 | |||
35.34 | odd | 2 | 3150.2.b.d.251.3 | yes | 8 | ||
105.62 | odd | 4 | 3150.2.d.e.3149.1 | 8 | |||
105.83 | odd | 4 | 3150.2.d.b.3149.8 | 8 | |||
105.104 | even | 2 | 3150.2.b.d.251.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.b.a.251.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
3150.2.b.a.251.2 | yes | 8 | 21.20 | even | 2 | inner | |
3150.2.b.a.251.5 | yes | 8 | 1.1 | even | 1 | trivial | |
3150.2.b.a.251.6 | yes | 8 | 7.6 | odd | 2 | inner | |
3150.2.b.d.251.3 | yes | 8 | 35.34 | odd | 2 | ||
3150.2.b.d.251.4 | yes | 8 | 5.4 | even | 2 | ||
3150.2.b.d.251.7 | yes | 8 | 105.104 | even | 2 | ||
3150.2.b.d.251.8 | yes | 8 | 15.14 | odd | 2 | ||
3150.2.d.b.3149.1 | 8 | 35.27 | even | 4 | |||
3150.2.d.b.3149.3 | 8 | 15.8 | even | 4 | |||
3150.2.d.b.3149.6 | 8 | 5.2 | odd | 4 | |||
3150.2.d.b.3149.8 | 8 | 105.83 | odd | 4 | |||
3150.2.d.e.3149.1 | 8 | 105.62 | odd | 4 | |||
3150.2.d.e.3149.3 | 8 | 5.3 | odd | 4 | |||
3150.2.d.e.3149.6 | 8 | 15.2 | even | 4 | |||
3150.2.d.e.3149.8 | 8 | 35.13 | even | 4 |