Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(3149,3150)]
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, 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("3150.3149");
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.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
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: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3149.1 | ||
Root | \(-1.14412 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.3149 |
Dual form | 3150.2.d.e.3149.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.23607 | − | 1.41421i | −0.845154 | − | 0.534522i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421i | 0.426401i | 0.977008 | + | 0.213201i | \(0.0683888\pi\) | ||||
−0.977008 | + | 0.213201i | \(0.931611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.39835 | −1.49723 | −0.748616 | − | 0.663004i | \(-0.769281\pi\) | ||||
−0.748616 | + | 0.663004i | \(0.769281\pi\) | |||||||
\(14\) | −2.23607 | − | 1.41421i | −0.597614 | − | 0.377964i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.23607i | − | 0.542326i | −0.962533 | − | 0.271163i | \(-0.912592\pi\) | ||
0.962533 | − | 0.271163i | \(-0.0874083\pi\) | |||||||
\(18\) | 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 | ||||||||
\(22\) | 1.41421i | 0.301511i | ||||||||
\(23\) | 1.00000 | 0.208514 | 0.104257 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104257 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.39835 | −1.05870 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.23607 | − | 1.41421i | −0.422577 | − | 0.267261i | ||||
\(29\) | 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 | \(0.279129\pi\) | ||||
−0.639529 | + | 0.768767i | \(0.720871\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.23607i | − | 0.383482i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.82843i | 0.464991i | 0.972598 | + | 0.232495i | \(0.0746890\pi\) | ||||
−0.972598 | + | 0.232495i | \(0.925311\pi\) | |||||||
\(38\) | − | 1.30986i | − | 0.212487i | ||||||
\(39\) | 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 | ||||||||
\(43\) | 6.41421i | 0.978158i | 0.872239 | + | 0.489079i | \(0.162667\pi\) | ||||
−0.872239 | + | 0.489079i | \(0.837333\pi\) | |||||||
\(44\) | 1.41421i | 0.213201i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 7.63441i | 1.11359i | 0.830649 | + | 0.556797i | \(0.187970\pi\) | ||||
−0.830649 | + | 0.556797i | \(0.812030\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | + | 6.32456i | 0.428571 | + | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.39835 | −0.748616 | ||||||||
\(53\) | −6.07107 | −0.833925 | −0.416963 | − | 0.908924i | \(-0.636905\pi\) | ||||
−0.416963 | + | 0.908924i | \(0.636905\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.23607 | − | 1.41421i | −0.298807 | − | 0.188982i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.24264i | 1.21362i | ||||||||
\(59\) | −11.7229 | −1.52619 | −0.763096 | − | 0.646285i | \(-0.776322\pi\) | ||||
−0.763096 | + | 0.646285i | \(0.776322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.39835i | 0.691187i | 0.938384 | + | 0.345594i | \(0.112322\pi\) | ||||
−0.938384 | + | 0.345594i | \(0.887678\pi\) | |||||||
\(62\) | 8.56062i | 1.08720i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | − | 2.23607i | − | 0.271163i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.34315i | − | 0.515437i | −0.966220 | − | 0.257718i | \(-0.917029\pi\) | ||
0.966220 | − | 0.257718i | \(-0.0829706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.01470 | −0.586926 | −0.293463 | − | 0.955970i | \(-0.594808\pi\) | ||||
−0.293463 | + | 0.955970i | \(0.594808\pi\) | |||||||
\(74\) | 2.82843i | 0.328798i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.30986i | − | 0.150251i | ||||||
\(77\) | 2.00000 | − | 3.16228i | 0.227921 | − | 0.360375i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.07107 | −0.120505 | −0.0602523 | − | 0.998183i | \(-0.519191\pi\) | ||||
−0.0602523 | + | 0.998183i | \(0.519191\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.08849 | 0.451498 | ||||||||
\(83\) | − | 8.01806i | − | 0.880097i | −0.897974 | − | 0.440048i | \(-0.854961\pi\) | ||
0.897974 | − | 0.440048i | \(-0.145039\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.41421i | 0.691662i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.41421i | 0.150756i | ||||||||
\(89\) | −15.2688 | −1.61849 | −0.809246 | − | 0.587470i | \(-0.800124\pi\) | ||||
−0.809246 | + | 0.587470i | \(0.800124\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0711 | + | 7.63441i | 1.26539 | + | 0.800304i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.63441i | 0.787430i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.4311 | 1.87140 | 0.935698 | − | 0.352803i | \(-0.114771\pi\) | ||||
0.935698 | + | 0.352803i | \(0.114771\pi\) | |||||||
\(98\) | 3.00000 | + | 6.32456i | 0.303046 | + | 0.638877i | ||||
\(99\) | 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 | ||||||||
\(103\) | −14.8852 | −1.46668 | −0.733340 | − | 0.679862i | \(-0.762040\pi\) | ||||
−0.733340 | + | 0.679862i | \(0.762040\pi\) | |||||||
\(104\) | −5.39835 | −0.529351 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.07107 | −0.589674 | ||||||||
\(107\) | −2.00000 | −0.193347 | −0.0966736 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966736 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.07107 | −0.677285 | −0.338643 | − | 0.940915i | \(-0.609968\pi\) | ||||
−0.338643 | + | 0.940915i | \(0.609968\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.23607 | − | 1.41421i | −0.211289 | − | 0.133631i | ||||
\(113\) | −13.0711 | −1.22962 | −0.614811 | − | 0.788674i | \(-0.710768\pi\) | ||||
−0.614811 | + | 0.788674i | \(0.710768\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.24264i | 0.858158i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.7229 | −1.07918 | ||||||||
\(119\) | −3.16228 | + | 5.00000i | −0.289886 | + | 0.458349i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 5.39835i | 0.488743i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.56062i | 0.768767i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.0000i | − | 0.887357i | −0.896186 | − | 0.443678i | \(-0.853673\pi\) | ||
0.896186 | − | 0.443678i | \(-0.146327\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 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 | ||||||||
\(133\) | −1.85242 | + | 2.92893i | −0.160625 | + | 0.253971i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 2.23607i | − | 0.191741i | ||||||
\(137\) | 16.1421 | 1.37912 | 0.689558 | − | 0.724231i | \(-0.257805\pi\) | ||||
0.689558 | + | 0.724231i | \(0.257805\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | − | 4.34315i | − | 0.364469i | ||||||
\(143\) | − | 7.63441i | − | 0.638422i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.01470 | −0.415019 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.82843i | 0.232495i | ||||||||
\(149\) | − | 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 | \(0.304833\pi\) | |||||||
\(152\) | − | 1.30986i | − | 0.106244i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | − | 3.16228i | 0.161165 | − | 0.254824i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.85242 | 0.147839 | 0.0739196 | − | 0.997264i | \(-0.476449\pi\) | ||||
0.0739196 | + | 0.997264i | \(0.476449\pi\) | |||||||
\(158\) | −1.07107 | −0.0852096 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.23607 | − | 1.41421i | −0.176227 | − | 0.111456i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.0711i | 1.72874i | 0.502857 | + | 0.864370i | \(0.332282\pi\) | ||||
−0.502857 | + | 0.864370i | \(0.667718\pi\) | |||||||
\(164\) | 4.08849 | 0.319257 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 8.01806i | − | 0.622322i | ||||||
\(167\) | 5.78199i | 0.447424i | 0.974655 | + | 0.223712i | \(0.0718175\pi\) | ||||
−0.974655 | + | 0.223712i | \(0.928182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.1421 | 1.24170 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.41421i | 0.489079i | ||||||||
\(173\) | − | 16.5787i | − | 1.26045i | −0.776411 | − | 0.630227i | \(-0.782962\pi\) | ||
0.776411 | − | 0.630227i | \(-0.217038\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.41421i | 0.106600i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.2688 | −1.14445 | ||||||||
\(179\) | 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 | \(0.192074\pi\) | ||||
−0.823400 | + | 0.567461i | \(0.807926\pi\) | |||||||
\(182\) | 12.0711 | + | 7.63441i | 0.894767 | + | 0.565900i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.16228 | 0.231249 | ||||||||
\(188\) | 7.63441i | 0.556797i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.6569i | − | 0.771103i | −0.922686 | − | 0.385551i | \(-0.874011\pi\) | ||
0.922686 | − | 0.385551i | \(-0.125989\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 8.48528i | − | 0.610784i | −0.952227 | − | 0.305392i | \(-0.901213\pi\) | ||
0.952227 | − | 0.305392i | \(-0.0987875\pi\) | |||||||
\(194\) | 18.4311 | 1.32328 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | + | 6.32456i | 0.214286 | + | 0.451754i | ||||
\(197\) | −20.0711 | −1.43000 | −0.715002 | − | 0.699122i | \(-0.753574\pi\) | ||||
−0.715002 | + | 0.699122i | \(0.753574\pi\) | |||||||
\(198\) | 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 | ||||||||
\(202\) | −5.78199 | −0.406820 | ||||||||
\(203\) | 13.0711 | − | 20.6672i | 0.917409 | − | 1.45055i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.8852 | −1.03710 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.39835 | −0.374308 | ||||||||
\(209\) | 1.85242 | 0.128135 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.2132 | −1.80459 | −0.902296 | − | 0.431118i | \(-0.858119\pi\) | ||||
−0.902296 | + | 0.431118i | \(0.858119\pi\) | |||||||
\(212\) | −6.07107 | −0.416963 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.00000 | −0.136717 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.1065 | − | 19.1421i | 0.821846 | − | 1.29945i | ||||
\(218\) | −7.07107 | −0.478913 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0711i | 0.811988i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.383649 | 0.0256910 | 0.0128455 | − | 0.999917i | \(-0.495911\pi\) | ||||
0.0128455 | + | 0.999917i | \(0.495911\pi\) | |||||||
\(224\) | −2.23607 | − | 1.41421i | −0.149404 | − | 0.0944911i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.0711 | −0.869474 | ||||||||
\(227\) | 6.16564i | 0.409228i | 0.978843 | + | 0.204614i | \(0.0655939\pi\) | ||||
−0.978843 | + | 0.204614i | \(0.934406\pi\) | |||||||
\(228\) | 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 | ||||||||
\(232\) | 9.24264i | 0.606809i | ||||||||
\(233\) | −8.92893 | −0.584954 | −0.292477 | − | 0.956273i | \(-0.594479\pi\) | ||||
−0.292477 | + | 0.956273i | \(0.594479\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.7229 | −0.763096 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.16228 | + | 5.00000i | −0.204980 | + | 0.324102i | ||||
\(239\) | 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 | \(0.0460087\pi\) | ||||
−0.989572 | + | 0.144038i | \(0.953991\pi\) | |||||||
\(242\) | 9.00000 | 0.578542 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.39835i | 0.345594i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.07107i | 0.449921i | ||||||||
\(248\) | 8.56062i | 0.543600i | ||||||||
\(249\) | 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 | ||||||||
\(253\) | 1.41421i | 0.0889108i | ||||||||
\(254\) | − | 10.0000i | − | 0.627456i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 16.7376i | − | 1.04406i | −0.852926 | − | 0.522031i | \(-0.825174\pi\) | ||
0.852926 | − | 0.522031i | \(-0.174826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | − | 6.32456i | 0.248548 | − | 0.392989i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.6491 | 0.781465 | ||||||||
\(263\) | −27.2843 | −1.68242 | −0.841210 | − | 0.540708i | \(-0.818156\pi\) | ||||
−0.841210 | + | 0.540708i | \(0.818156\pi\) | |||||||
\(264\) | 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 | \(-0.401092\pi\) | ||||
0.305751 | + | 0.952111i | \(0.401092\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.7410i | 1.19918i | 0.800308 | + | 0.599589i | \(0.204669\pi\) | ||||
−0.800308 | + | 0.599589i | \(0.795331\pi\) | |||||||
\(272\) | − | 2.23607i | − | 0.135582i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.1421 | 0.975182 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.2132i | − | 1.27458i | −0.770625 | − | 0.637289i | \(-0.780056\pi\) | ||
0.770625 | − | 0.637289i | \(-0.219944\pi\) | |||||||
\(278\) | 1.85242i | 0.111101i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.5147i | − | 0.686911i | −0.939169 | − | 0.343455i | \(-0.888403\pi\) | ||
0.939169 | − | 0.343455i | \(-0.111597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.30986 | −0.0778630 | −0.0389315 | − | 0.999242i | \(-0.512395\pi\) | ||||
−0.0389315 | + | 0.999242i | \(0.512395\pi\) | |||||||
\(284\) | − | 4.34315i | − | 0.257718i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 7.63441i | − | 0.451432i | ||||||
\(287\) | −9.14214 | − | 5.78199i | −0.539643 | − | 0.341300i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.0000 | 0.705882 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.01470 | −0.293463 | ||||||||
\(293\) | − | 25.2982i | − | 1.47794i | −0.673740 | − | 0.738969i | \(-0.735313\pi\) | ||
0.673740 | − | 0.738969i | \(-0.264687\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.82843i | 0.164399i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 9.24264i | − | 0.535412i | ||||||
\(299\) | −5.39835 | −0.312194 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.07107 | − | 14.3426i | 0.522848 | − | 0.826695i | ||||
\(302\) | 14.1421 | 0.813788 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 1.30986i | − | 0.0751255i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.5934 | −1.23240 | −0.616200 | − | 0.787590i | \(-0.711329\pi\) | ||||
−0.616200 | + | 0.787590i | \(0.711329\pi\) | |||||||
\(308\) | 2.00000 | − | 3.16228i | 0.113961 | − | 0.180187i | ||||
\(309\) | 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 | ||||||||
\(313\) | 10.2541 | 0.579598 | 0.289799 | − | 0.957088i | \(-0.406412\pi\) | ||||
0.289799 | + | 0.957088i | \(0.406412\pi\) | |||||||
\(314\) | 1.85242 | 0.104538 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.07107 | −0.0602523 | ||||||||
\(317\) | −15.9289 | −0.894658 | −0.447329 | − | 0.894369i | \(-0.647625\pi\) | ||||
−0.447329 | + | 0.894369i | \(0.647625\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.0711 | −0.731839 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.23607 | − | 1.41421i | −0.124611 | − | 0.0788110i | ||||
\(323\) | −2.92893 | −0.162970 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.0711i | 1.22240i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.08849 | 0.225749 | ||||||||
\(329\) | 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 | \(0.292546\pi\) | |||||||
\(332\) | − | 8.01806i | − | 0.440048i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.78199i | 0.316377i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.9706i | 1.19681i | 0.801193 | + | 0.598406i | \(0.204199\pi\) | ||||
−0.801193 | + | 0.598406i | \(0.795801\pi\) | |||||||
\(338\) | 16.1421 | 0.878016 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.1065 | −0.655606 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.23607 | − | 18.3848i | 0.120736 | − | 0.992685i | ||||
\(344\) | 6.41421i | 0.345831i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 16.5787i | − | 0.891276i | ||||||
\(347\) | 5.07107 | 0.272229 | 0.136115 | − | 0.990693i | \(-0.456538\pi\) | ||||
0.136115 | + | 0.990693i | \(0.456538\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | 1.41421i | 0.0753778i | ||||||||
\(353\) | − | 18.9737i | − | 1.00987i | −0.863158 | − | 0.504933i | \(-0.831517\pi\) | ||
0.863158 | − | 0.504933i | \(-0.168483\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.2688 | −0.809246 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.3137i | 0.597948i | ||||||||
\(359\) | − | 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 | ||||||||
\(362\) | 15.2688i | 0.802512i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.0711 | + | 7.63441i | 0.632696 | + | 0.400152i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.5967 | 1.28394 | 0.641970 | − | 0.766730i | \(-0.278117\pi\) | ||||
0.641970 | + | 0.766730i | \(0.278117\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.5753 | + | 8.58579i | 0.704796 | + | 0.445752i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.07107i | 0.366126i | 0.983101 | + | 0.183063i | \(0.0586012\pi\) | ||||
−0.983101 | + | 0.183063i | \(0.941399\pi\) | |||||||
\(374\) | 3.16228 | 0.163517 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.63441i | 0.393715i | ||||||||
\(377\) | − | 49.8950i | − | 2.56972i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.92893 | −0.407282 | −0.203641 | − | 0.979046i | \(-0.565278\pi\) | ||||
−0.203641 | + | 0.979046i | \(0.565278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 10.6569i | − | 0.545252i | ||||||
\(383\) | 28.6852i | 1.46575i | 0.680365 | + | 0.732874i | \(0.261821\pi\) | ||||
−0.680365 | + | 0.732874i | \(0.738179\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 8.48528i | − | 0.431889i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.4311 | 0.935698 | ||||||||
\(389\) | − | 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 | ||||||
\(392\) | 3.00000 | + | 6.32456i | 0.151523 | + | 0.319438i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.0711 | −1.01117 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.6378 | 0.533895 | 0.266947 | − | 0.963711i | \(-0.413985\pi\) | ||||
0.266947 | + | 0.963711i | \(0.413985\pi\) | |||||||
\(398\) | 3.70484i | 0.185707i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 29.7990i | − | 1.48809i | −0.668129 | − | 0.744045i | \(-0.732905\pi\) | ||
0.668129 | − | 0.744045i | \(-0.267095\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 46.2132i | − | 2.30204i | ||||||
\(404\) | −5.78199 | −0.287665 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.0711 | − | 20.6672i | 0.648706 | − | 1.02569i | ||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 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 | ||||||||
\(412\) | −14.8852 | −0.733340 | ||||||||
\(413\) | 26.2132 | + | 16.5787i | 1.28987 | + | 0.815784i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.39835 | −0.264676 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.85242 | 0.0906048 | ||||||||
\(419\) | −15.4277 | −0.753694 | −0.376847 | − | 0.926275i | \(-0.622992\pi\) | ||||
−0.376847 | + | 0.926275i | \(0.622992\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.3553 | −1.82059 | −0.910294 | − | 0.413963i | \(-0.864144\pi\) | ||||
−0.910294 | + | 0.413963i | \(0.864144\pi\) | |||||||
\(422\) | −26.2132 | −1.27604 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.07107 | −0.294837 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.63441 | − | 12.0711i | 0.369455 | − | 0.584160i | ||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.7990i | 1.67621i | 0.545510 | + | 0.838104i | \(0.316336\pi\) | ||||
−0.545510 | + | 0.838104i | \(0.683664\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.0098 | 1.68246 | 0.841232 | − | 0.540675i | \(-0.181831\pi\) | ||||
0.841232 | + | 0.540675i | \(0.181831\pi\) | |||||||
\(434\) | 12.1065 | − | 19.1421i | 0.581133 | − | 0.918852i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.07107 | −0.338643 | ||||||||
\(437\) | − | 1.30986i | − | 0.0626590i | ||||||
\(438\) | 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 | ||||||||
\(442\) | 12.0711i | 0.574162i | ||||||||
\(443\) | −8.92893 | −0.424226 | −0.212113 | − | 0.977245i | \(-0.568035\pi\) | ||||
−0.212113 | + | 0.977245i | \(0.568035\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.383649 | 0.0181663 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.23607 | − | 1.41421i | −0.105644 | − | 0.0668153i | ||||
\(449\) | 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 | ||||||||
\(452\) | −13.0711 | −0.614811 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.16564i | 0.289368i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.1716i | 0.569362i | 0.958622 | + | 0.284681i | \(0.0918877\pi\) | ||||
−0.958622 | + | 0.284681i | \(0.908112\pi\) | |||||||
\(458\) | − | 1.85242i | − | 0.0865579i | ||||||
\(459\) | 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 | ||||||||
\(463\) | 18.2843i | 0.849742i | 0.905254 | + | 0.424871i | \(0.139681\pi\) | ||||
−0.905254 | + | 0.424871i | \(0.860319\pi\) | |||||||
\(464\) | 9.24264i | 0.429079i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.92893 | −0.413625 | ||||||||
\(467\) | − | 10.6378i | − | 0.492258i | −0.969237 | − | 0.246129i | \(-0.920841\pi\) | ||
0.969237 | − | 0.246129i | \(-0.0791586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.7229 | −0.539590 | ||||||||
\(473\) | −9.07107 | −0.417088 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.16228 | + | 5.00000i | −0.144943 | + | 0.229175i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.8284i | 0.586759i | ||||||||
\(479\) | 2.07716 | 0.0949077 | 0.0474538 | − | 0.998873i | \(-0.484889\pi\) | ||||
0.0474538 | + | 0.998873i | \(0.484889\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 15.2688i | − | 0.696199i | ||||||
\(482\) | 4.47214i | 0.203700i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.00000 | 0.409091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.1005i | 0.457698i | 0.973462 | + | 0.228849i | \(0.0734961\pi\) | ||||
−0.973462 | + | 0.228849i | \(0.926504\pi\) | |||||||
\(488\) | 5.39835i | 0.244372i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 38.4853i | − | 1.73682i | −0.495850 | − | 0.868408i | \(-0.665143\pi\) | ||
0.495850 | − | 0.868408i | \(-0.334857\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.6672 | 0.930803 | ||||||||
\(494\) | 7.07107i | 0.318142i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.56062i | 0.384383i | ||||||||
\(497\) | −6.14214 | + | 9.71157i | −0.275512 | + | 0.435623i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.92893 | 0.354948 | 0.177474 | − | 0.984126i | \(-0.443207\pi\) | ||||
0.177474 | + | 0.984126i | \(0.443207\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.4902 | −0.557465 | ||||||||
\(503\) | 40.7918i | 1.81882i | 0.415905 | + | 0.909408i | \(0.363465\pi\) | ||||
−0.415905 | + | 0.909408i | \(0.636535\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.41421i | 0.0628695i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 10.0000i | − | 0.443678i | ||||||
\(509\) | 44.4966 | 1.97228 | 0.986139 | − | 0.165921i | \(-0.0530596\pi\) | ||||
0.986139 | + | 0.165921i | \(0.0530596\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.2132 | + | 7.09185i | 0.496043 | + | 0.313725i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 16.7376i | − | 0.738264i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.7967 | −0.474838 | ||||||||
\(518\) | 4.00000 | − | 6.32456i | 0.175750 | − | 0.277885i | ||||
\(519\) | 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 | ||||||||
\(523\) | 28.4605 | 1.24449 | 0.622245 | − | 0.782822i | \(-0.286221\pi\) | ||||
0.622245 | + | 0.782822i | \(0.286221\pi\) | |||||||
\(524\) | 12.6491 | 0.552579 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.2843 | −1.18965 | ||||||||
\(527\) | 19.1421 | 0.833845 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.85242 | + | 2.92893i | −0.0803126 | + | 0.126985i | ||||
\(533\) | −22.0711 | −0.956004 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.0294 | 0.432398 | ||||||||
\(539\) | −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 | \(0.562470\pi\) | |||||||
\(542\) | 19.7410i | 0.847947i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 2.23607i | − | 0.0958706i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.2132i | 1.12080i | 0.828224 | + | 0.560398i | \(0.189352\pi\) | ||||
−0.828224 | + | 0.560398i | \(0.810648\pi\) | |||||||
\(548\) | 16.1421 | 0.689558 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.1065 | 0.515756 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.39498 | + | 1.51472i | 0.101845 | + | 0.0644124i | ||||
\(554\) | − | 21.2132i | − | 0.901263i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.85242i | 0.0785601i | ||||||||
\(557\) | −2.14214 | −0.0907652 | −0.0453826 | − | 0.998970i | \(-0.514451\pi\) | ||||
−0.0453826 | + | 0.998970i | \(0.514451\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.6261i | − | 1.46453i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 11.5147i | − | 0.485719i | ||||||
\(563\) | 19.8999i | 0.838680i | 0.907829 | + | 0.419340i | \(0.137738\pi\) | ||||
−0.907829 | + | 0.419340i | \(0.862262\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.30986 | −0.0550575 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 4.34315i | − | 0.182234i | ||||||
\(569\) | − | 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 | \(0.471902\pi\) | |||||||
\(572\) | − | 7.63441i | − | 0.319211i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.14214 | − | 5.78199i | −0.381585 | − | 0.241336i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.5015 | −0.603707 | −0.301853 | − | 0.953354i | \(-0.597605\pi\) | ||||
−0.301853 | + | 0.953354i | \(0.597605\pi\) | |||||||
\(578\) | 12.0000 | 0.499134 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.3393 | + | 17.9289i | −0.470431 | + | 0.743817i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.58579i | − | 0.355587i | ||||||
\(584\) | −5.01470 | −0.207510 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 25.2982i | − | 1.04506i | ||||||
\(587\) | 28.8441i | 1.19053i | 0.803531 | + | 0.595263i | \(0.202952\pi\) | ||||
−0.803531 | + | 0.595263i | \(0.797048\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.2132 | 0.462032 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.82843i | 0.116248i | ||||||||
\(593\) | − | 29.0031i | − | 1.19101i | −0.803351 | − | 0.595506i | \(-0.796951\pi\) | ||
0.803351 | − | 0.595506i | \(-0.203049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 9.24264i | − | 0.378593i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.39835 | −0.220755 | ||||||||
\(599\) | 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 | \(0.0376246\pi\) | ||||
−0.993022 | + | 0.117926i | \(0.962375\pi\) | |||||||
\(602\) | 9.07107 | − | 14.3426i | 0.369709 | − | 0.584561i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.1421 | 0.575435 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.6558 | −0.757217 | −0.378609 | − | 0.925557i | \(-0.623597\pi\) | ||||
−0.378609 | + | 0.925557i | \(0.623597\pi\) | |||||||
\(608\) | − | 1.30986i | − | 0.0531218i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 41.2132i | − | 1.66731i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 44.1421i | − | 1.78288i | −0.453135 | − | 0.891442i | \(-0.649694\pi\) | ||
0.453135 | − | 0.891442i | \(-0.350306\pi\) | |||||||
\(614\) | −21.5934 | −0.871438 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | − | 3.16228i | 0.0805823 | − | 0.127412i | ||||
\(617\) | −32.0000 | −1.28827 | −0.644136 | − | 0.764911i | \(-0.722783\pi\) | ||||
−0.644136 | + | 0.764911i | \(0.722783\pi\) | |||||||
\(618\) | 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 | ||||||||
\(622\) | 30.5377 | 1.22445 | ||||||||
\(623\) | 34.1421 | + | 21.5934i | 1.36788 | + | 0.865121i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.2541 | 0.409837 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.85242 | 0.0739196 | ||||||||
\(629\) | 6.32456 | 0.252177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.2843 | −1.84255 | −0.921274 | − | 0.388914i | \(-0.872850\pi\) | ||||
−0.921274 | + | 0.388914i | \(0.872850\pi\) | |||||||
\(632\) | −1.07107 | −0.0426048 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.9289 | −0.632619 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.1950 | − | 34.1421i | −0.641671 | − | 1.35276i | ||||
\(638\) | −13.0711 | −0.517489 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.5147i | 0.454804i | 0.973801 | + | 0.227402i | \(0.0730231\pi\) | ||||
−0.973801 | + | 0.227402i | \(0.926977\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.6705 | −0.933475 | −0.466737 | − | 0.884396i | \(-0.654571\pi\) | ||||
−0.466737 | + | 0.884396i | \(0.654571\pi\) | |||||||
\(644\) | −2.23607 | − | 1.41421i | −0.0881134 | − | 0.0557278i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.92893 | −0.115237 | ||||||||
\(647\) | − | 43.4115i | − | 1.70668i | −0.521353 | − | 0.853341i | \(-0.674573\pi\) | ||
0.521353 | − | 0.853341i | \(-0.325427\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 16.5787i | − | 0.650770i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.0711i | 0.864370i | ||||||||
\(653\) | 20.1421 | 0.788223 | 0.394111 | − | 0.919063i | \(-0.371052\pi\) | ||||
0.394111 | + | 0.919063i | \(0.371052\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.08849 | 0.159629 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.7967 | − | 17.0711i | 0.420899 | − | 0.665500i | ||||
\(659\) | 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 | \(-0.660261\pi\) | ||
0.482473 | − | 0.875911i | \(-0.339739\pi\) | |||||||
\(662\) | 22.0711 | 0.857816 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 8.01806i | − | 0.311161i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.24264i | 0.357876i | ||||||||
\(668\) | 5.78199i | 0.223712i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.63441 | −0.294723 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.79899i | 0.184987i | 0.995713 | + | 0.0924937i | \(0.0294838\pi\) | ||||
−0.995713 | + | 0.0924937i | \(0.970516\pi\) | |||||||
\(674\) | 21.9706i | 0.846274i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.1421 | 0.620851 | ||||||||
\(677\) | 3.92957i | 0.151026i | 0.997145 | + | 0.0755129i | \(0.0240594\pi\) | ||||
−0.997145 | + | 0.0755129i | \(0.975941\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.2132 | − | 26.0655i | −1.58162 | − | 1.00030i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.1065 | −0.463584 | ||||||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.23607 | − | 18.3848i | 0.0853735 | − | 0.701934i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.41421i | 0.244540i | ||||||||
\(689\) | 32.7737 | 1.24858 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 32.9326i | − | 1.25282i | −0.779495 | − | 0.626408i | \(-0.784524\pi\) | ||
0.779495 | − | 0.626408i | \(-0.215476\pi\) | |||||||
\(692\) | − | 16.5787i | − | 0.630227i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.07107 | 0.192495 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 9.14214i | − | 0.346283i | ||||||
\(698\) | 25.1393i | 0.951537i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.8701i | 0.448326i | 0.974552 | + | 0.224163i | \(0.0719648\pi\) | ||||
−0.974552 | + | 0.224163i | \(0.928035\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.70484 | 0.139731 | ||||||||
\(704\) | 1.41421i | 0.0533002i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 18.9737i | − | 0.714083i | ||||||
\(707\) | 12.9289 | + | 8.17697i | 0.486243 | + | 0.307527i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.14214 | 0.155561 | 0.0777806 | − | 0.996971i | \(-0.475217\pi\) | ||||
0.0777806 | + | 0.996971i | \(0.475217\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.2688 | −0.572223 | ||||||||
\(713\) | 8.56062i | 0.320598i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.3137i | 0.422813i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 6.31371i | − | 0.235626i | ||||||
\(719\) | −32.9326 | −1.22818 | −0.614090 | − | 0.789236i | \(-0.710477\pi\) | ||||
−0.614090 | + | 0.789236i | \(0.710477\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.2843 | + | 21.0508i | 1.23957 | + | 0.783974i | ||||
\(722\) | 17.2843 | 0.643254 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.2688i | 0.567461i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.70820 | 0.248794 | 0.124397 | − | 0.992233i | \(-0.460300\pi\) | ||||
0.124397 | + | 0.992233i | \(0.460300\pi\) | |||||||
\(728\) | 12.0711 | + | 7.63441i | 0.447384 | + | 0.282950i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.3426 | 0.530481 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.2802 | 0.638257 | 0.319129 | − | 0.947711i | \(-0.396610\pi\) | ||||
0.319129 | + | 0.947711i | \(0.396610\pi\) | |||||||
\(734\) | 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 | \(-0.803713\pi\) | ||||
−0.815819 | + | 0.578308i | \(0.803713\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.5753 | + | 8.58579i | 0.498366 | + | 0.315194i | ||||
\(743\) | −6.85786 | −0.251591 | −0.125795 | − | 0.992056i | \(-0.540148\pi\) | ||||
−0.125795 | + | 0.992056i | \(0.540148\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.07107i | 0.258890i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.16228 | 0.115624 | ||||||||
\(749\) | 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 | \(0.565585\pi\) | |||||||
\(752\) | 7.63441i | 0.278398i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 49.8950i | − | 1.81707i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.04163i | 0.146896i | 0.997299 | + | 0.0734478i | \(0.0234002\pi\) | ||||
−0.997299 | + | 0.0734478i | \(0.976600\pi\) | |||||||
\(758\) | −7.92893 | −0.287992 | ||||||||
\(759\) | 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 | ||||||||
\(763\) | 15.8114 | + | 10.0000i | 0.572411 | + | 0.362024i | ||||
\(764\) | − | 10.6569i | − | 0.385551i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.6852i | 1.03644i | ||||||||
\(767\) | 63.2843 | 2.28506 | ||||||||
\(768\) | 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 | ||||||||
\(772\) | − | 8.48528i | − | 0.305392i | ||||||
\(773\) | 36.3196i | 1.30633i | 0.757217 | + | 0.653163i | \(0.226559\pi\) | ||||
−0.757217 | + | 0.653163i | \(0.773441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18.4311 | 0.661638 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 17.1716i | − | 0.615631i | ||||||
\(779\) | − | 5.35534i | − | 0.191875i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.14214 | 0.219783 | ||||||||
\(782\) | − | 2.23607i | − | 0.0799616i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | + | 6.32456i | 0.107143 | + | 0.225877i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.5738 | −1.66018 | −0.830088 | − | 0.557632i | \(-0.811710\pi\) | ||||
−0.830088 | + | 0.557632i | \(0.811710\pi\) | |||||||
\(788\) | −20.0711 | −0.715002 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.2278 | + | 18.4853i | 1.03922 | + | 0.657261i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 29.1421i | − | 1.03487i | ||||||
\(794\) | 10.6378 | 0.377521 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.70484i | 0.131315i | ||||||||
\(797\) | 42.6442i | 1.51054i | 0.655417 | + | 0.755268i | \(0.272493\pi\) | ||||
−0.655417 | + | 0.755268i | \(0.727507\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.0711 | 0.603931 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 29.7990i | − | 1.05224i | ||||||
\(803\) | − | 7.09185i | − | 0.250266i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 46.2132i | − | 1.62779i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.78199 | −0.203410 | ||||||||
\(809\) | − | 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 | \(-0.743326\pi\) | ||
0.692126 | − | 0.721777i | \(-0.256674\pi\) | |||||||
\(812\) | 13.0711 | − | 20.6672i | 0.458705 | − | 0.725276i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.00000 | −0.140200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.40171 | 0.293939 | ||||||||
\(818\) | 3.92957i | 0.137394i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 23.9411i | − | 0.835551i | −0.908550 | − | 0.417776i | \(-0.862810\pi\) | ||
0.908550 | − | 0.417776i | \(-0.137190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.92893i | − | 0.102096i | −0.998696 | − | 0.0510481i | \(-0.983744\pi\) | ||
0.998696 | − | 0.0510481i | \(-0.0162562\pi\) | |||||||
\(824\) | −14.8852 | −0.518550 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.2132 | + | 16.5787i | 0.912074 | + | 0.576846i | ||||
\(827\) | −54.4264 | −1.89259 | −0.946296 | − | 0.323302i | \(-0.895207\pi\) | ||||
−0.946296 | + | 0.323302i | \(0.895207\pi\) | |||||||
\(828\) | 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 | ||||||||
\(832\) | −5.39835 | −0.187154 | ||||||||
\(833\) | 14.1421 | − | 6.70820i | 0.489996 | − | 0.232425i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.85242 | 0.0640673 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.4277 | −0.532942 | ||||||||
\(839\) | 9.71157 | 0.335281 | 0.167640 | − | 0.985848i | \(-0.446385\pi\) | ||||
0.167640 | + | 0.985848i | \(0.446385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −56.4264 | −1.94574 | ||||||||
\(842\) | −37.3553 | −1.28735 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −26.2132 | −0.902296 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.1246 | − | 12.7279i | −0.691490 | − | 0.437337i | ||||
\(848\) | −6.07107 | −0.208481 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.82843i | 0.0969572i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.5196 | 0.771056 | 0.385528 | − | 0.922696i | \(-0.374019\pi\) | ||||
0.385528 | + | 0.922696i | \(0.374019\pi\) | |||||||
\(854\) | 7.63441 | − | 12.0711i | 0.261244 | − | 0.413063i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.00000 | −0.0683586 | ||||||||
\(857\) | 17.8885i | 0.611061i | 0.952182 | + | 0.305531i | \(0.0988338\pi\) | ||||
−0.952182 | + | 0.305531i | \(0.901166\pi\) | |||||||
\(858\) | 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 | ||||||||
\(862\) | 34.7990i | 1.18526i | ||||||||
\(863\) | 48.1421 | 1.63878 | 0.819389 | − | 0.573238i | \(-0.194313\pi\) | ||||
0.819389 | + | 0.573238i | \(0.194313\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.0098 | 1.18968 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.1065 | − | 19.1421i | 0.410923 | − | 0.649726i | ||||
\(869\) | − | 1.51472i | − | 0.0513833i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −7.07107 | −0.239457 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.30986i | − | 0.0443066i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.1421i | 1.15290i | 0.817133 | + | 0.576449i | \(0.195562\pi\) | ||||
−0.817133 | + | 0.576449i | \(0.804438\pi\) | |||||||
\(878\) | 8.56062i | 0.288907i | ||||||||
\(879\) | 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 | ||||||||
\(883\) | 46.0122i | 1.54843i | 0.632920 | + | 0.774217i | \(0.281856\pi\) | ||||
−0.632920 | + | 0.774217i | \(0.718144\pi\) | |||||||
\(884\) | 12.0711i | 0.405994i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.92893 | −0.299973 | ||||||||
\(887\) | 34.2425i | 1.14975i | 0.818241 | + | 0.574875i | \(0.194949\pi\) | ||||
−0.818241 | + | 0.574875i | \(0.805051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.1421 | + | 22.3607i | −0.474312 | + | 0.749953i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.383649 | 0.0128455 | ||||||||
\(893\) | 10.0000 | 0.334637 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.23607 | − | 1.41421i | −0.0747018 | − | 0.0472456i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.3848i | 0.613508i | ||||||||
\(899\) | −79.1228 | −2.63889 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5753i | 0.452259i | ||||||||
\(902\) | 5.78199i | 0.192519i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.0711 | −0.434737 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 4.89949i | − | 0.162685i | −0.996686 | − | 0.0813425i | \(-0.974079\pi\) | ||
0.996686 | − | 0.0813425i | \(-0.0259208\pi\) | |||||||
\(908\) | 6.16564i | 0.204614i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 57.6274i | − | 1.90928i | −0.297760 | − | 0.954641i | \(-0.596240\pi\) | ||
0.297760 | − | 0.954641i | \(-0.403760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.3393 | 0.375274 | ||||||||
\(914\) | 12.1716i | 0.402600i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 1.85242i | − | 0.0612057i | ||||||
\(917\) | −28.2843 | − | 17.8885i | −0.934029 | − | 0.590732i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.07107 | 0.233253 | 0.116627 | − | 0.993176i | \(-0.462792\pi\) | ||||
0.116627 | + | 0.993176i | \(0.462792\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.6148 | 1.07411 | ||||||||
\(923\) | 23.4458i | 0.771728i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.2843i | 0.600858i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.24264i | 0.303405i | ||||||||
\(929\) | 50.6623 | 1.66218 | 0.831088 | − | 0.556142i | \(-0.187719\pi\) | ||||
0.831088 | + | 0.556142i | \(0.187719\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.28427 | − | 3.92957i | 0.271506 | − | 0.128787i | ||||
\(932\) | −8.92893 | −0.292477 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 10.6378i | − | 0.348079i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.5377 | 0.997622 | 0.498811 | − | 0.866711i | \(-0.333770\pi\) | ||||
0.498811 | + | 0.866711i | \(0.333770\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 4.08849 | 0.133139 | ||||||||
\(944\) | −11.7229 | −0.381548 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.07107 | −0.294926 | ||||||||
\(947\) | 37.3553 | 1.21389 | 0.606943 | − | 0.794746i | \(-0.292396\pi\) | ||||
0.606943 | + | 0.794746i | \(0.292396\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.0711 | 0.878764 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.16228 | + | 5.00000i | −0.102490 | + | 0.162051i | ||||
\(953\) | −36.0000 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.8284i | 0.414901i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.07716 | 0.0671098 | ||||||||
\(959\) | −36.0949 | − | 22.8284i | −1.16557 | − | 0.737168i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −42.2843 | −1.36401 | ||||||||
\(962\) | − | 15.2688i | − | 0.492287i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.47214i | 0.144038i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.4975i | 1.59173i | 0.605473 | + | 0.795866i | \(0.292984\pi\) | ||||
−0.605473 | + | 0.795866i | \(0.707016\pi\) | |||||||
\(968\) | 9.00000 | 0.289271 | ||||||||
\(969\) | 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 | ||||||||
\(973\) | 2.61972 | − | 4.14214i | 0.0839843 | − | 0.132791i | ||||
\(974\) | 10.1005i | 0.323641i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.39835i | 0.172797i | ||||||||
\(977\) | −12.0000 | −0.383914 | −0.191957 | − | 0.981403i | \(-0.561483\pi\) | ||||
−0.191957 | + | 0.981403i | \(0.561483\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 21.5934i | − | 0.690127i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 38.4853i | − | 1.22811i | ||||||
\(983\) | 6.32456i | 0.201722i | 0.994901 | + | 0.100861i | \(0.0321597\pi\) | ||||
−0.994901 | + | 0.100861i | \(0.967840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 20.6672 | 0.658177 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.07107i | 0.224961i | ||||||||
\(989\) | 6.41421i | 0.203960i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.3553 | 1.44076 | 0.720380 | − | 0.693580i | \(-0.243967\pi\) | ||||
0.720380 | + | 0.693580i | \(0.243967\pi\) | |||||||
\(992\) | 8.56062i | 0.271800i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.14214 | + | 9.71157i | −0.194817 | + | 0.308032i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.7967 | 0.341935 | 0.170967 | − | 0.985277i | \(-0.445311\pi\) | ||||
0.170967 | + | 0.985277i | \(0.445311\pi\) | |||||||
\(998\) | 7.92893 | 0.250986 | ||||||||
\(999\) | 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.d.e.3149.1 | 8 | ||
3.2 | odd | 2 | 3150.2.d.b.3149.1 | 8 | |||
5.2 | odd | 4 | 3150.2.b.d.251.7 | yes | 8 | ||
5.3 | odd | 4 | 3150.2.b.a.251.2 | yes | 8 | ||
5.4 | even | 2 | 3150.2.d.b.3149.8 | 8 | |||
7.6 | odd | 2 | inner | 3150.2.d.e.3149.6 | 8 | ||
15.2 | even | 4 | 3150.2.b.d.251.3 | yes | 8 | ||
15.8 | even | 4 | 3150.2.b.a.251.6 | yes | 8 | ||
15.14 | odd | 2 | inner | 3150.2.d.e.3149.8 | 8 | ||
21.20 | even | 2 | 3150.2.d.b.3149.6 | 8 | |||
35.13 | even | 4 | 3150.2.b.a.251.1 | ✓ | 8 | ||
35.27 | even | 4 | 3150.2.b.d.251.8 | yes | 8 | ||
35.34 | odd | 2 | 3150.2.d.b.3149.3 | 8 | |||
105.62 | odd | 4 | 3150.2.b.d.251.4 | yes | 8 | ||
105.83 | odd | 4 | 3150.2.b.a.251.5 | yes | 8 | ||
105.104 | even | 2 | inner | 3150.2.d.e.3149.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.b.a.251.1 | ✓ | 8 | 35.13 | even | 4 | ||
3150.2.b.a.251.2 | yes | 8 | 5.3 | odd | 4 | ||
3150.2.b.a.251.5 | yes | 8 | 105.83 | odd | 4 | ||
3150.2.b.a.251.6 | yes | 8 | 15.8 | even | 4 | ||
3150.2.b.d.251.3 | yes | 8 | 15.2 | even | 4 | ||
3150.2.b.d.251.4 | yes | 8 | 105.62 | odd | 4 | ||
3150.2.b.d.251.7 | yes | 8 | 5.2 | odd | 4 | ||
3150.2.b.d.251.8 | yes | 8 | 35.27 | even | 4 | ||
3150.2.d.b.3149.1 | 8 | 3.2 | odd | 2 | |||
3150.2.d.b.3149.3 | 8 | 35.34 | odd | 2 | |||
3150.2.d.b.3149.6 | 8 | 21.20 | even | 2 | |||
3150.2.d.b.3149.8 | 8 | 5.4 | even | 2 | |||
3150.2.d.e.3149.1 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.d.e.3149.3 | 8 | 105.104 | even | 2 | inner | ||
3150.2.d.e.3149.6 | 8 | 7.6 | odd | 2 | inner | ||
3150.2.d.e.3149.8 | 8 | 15.14 | odd | 2 | inner |