Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(53,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.n (of order \(5\), degree \(4\), 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: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 157.7 | ||
Character | \(\chi\) | \(=\) | 572.157 |
Dual form | 572.2.n.b.521.7 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.965759 | + | 2.97230i | 0.557581 | + | 1.71606i | 0.689028 | + | 0.724735i | \(0.258038\pi\) |
−0.131447 | + | 0.991323i | \(0.541962\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.96166 | + | 1.42523i | 0.877279 | + | 0.637381i | 0.932530 | − | 0.361092i | \(-0.117596\pi\) |
−0.0552511 | + | 0.998472i | \(0.517596\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.681960 | + | 2.09886i | −0.257757 | + | 0.793294i | 0.735517 | + | 0.677506i | \(0.236939\pi\) |
−0.993274 | + | 0.115788i | \(0.963061\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.47482 | + | 3.97769i | −1.82494 | + | 1.32590i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.402908 | − | 3.29206i | −0.121481 | − | 0.992594i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.809017 | − | 0.587785i | 0.224381 | − | 0.163022i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.34171 | + | 7.20705i | −0.604628 | + | 1.86085i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.69648 | + | 1.95911i | 0.653993 | + | 0.475154i | 0.864629 | − | 0.502411i | \(-0.167554\pi\) |
−0.210636 | + | 0.977565i | \(0.567554\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.295228 | − | 0.908620i | −0.0677300 | − | 0.208452i | 0.911463 | − | 0.411382i | \(-0.134954\pi\) |
−0.979193 | + | 0.202930i | \(0.934954\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.89704 | −1.50506 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.75510 | 0.574478 | 0.287239 | − | 0.957859i | \(-0.407263\pi\) | ||||
0.287239 | + | 0.957859i | \(0.407263\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.271738 | + | 0.836325i | 0.0543477 | + | 0.167265i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.52508 | − | 6.92038i | −1.83310 | − | 1.33183i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.70254 | − | 8.31758i | 0.501850 | − | 1.54454i | −0.304153 | − | 0.952623i | \(-0.598373\pi\) |
0.806003 | − | 0.591912i | \(-0.201627\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.33655 | + | 3.15069i | −0.778868 | + | 0.565881i | −0.904639 | − | 0.426179i | \(-0.859859\pi\) |
0.125771 | + | 0.992059i | \(0.459859\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.39588 | − | 4.37690i | 1.63561 | − | 0.761920i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.32912 | + | 3.14529i | −0.731755 | + | 0.531651i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.67674 | − | 5.16048i | 0.275655 | − | 0.848378i | −0.713391 | − | 0.700766i | \(-0.752841\pi\) |
0.989045 | − | 0.147611i | \(-0.0471585\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.52839 | + | 1.83698i | 0.404866 | + | 0.294153i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.06468 | − | 6.35442i | −0.322448 | − | 0.992394i | −0.972579 | − | 0.232572i | \(-0.925286\pi\) |
0.650131 | − | 0.759822i | \(-0.274714\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.04857 | 1.07490 | 0.537449 | − | 0.843297i | \(-0.319388\pi\) | ||||
0.537449 | + | 0.843297i | \(0.319388\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −16.4088 | −2.44608 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.50513 | + | 10.7877i | 0.511276 | + | 1.57355i | 0.789956 | + | 0.613163i | \(0.210103\pi\) |
−0.278680 | + | 0.960384i | \(0.589897\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.72298 | + | 1.25182i | 0.246141 | + | 0.178832i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.21891 | + | 9.90678i | −0.450737 | + | 1.38723i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.17380 | + | 3.03244i | −0.573315 | + | 0.416538i | −0.836308 | − | 0.548260i | \(-0.815290\pi\) |
0.262993 | + | 0.964798i | \(0.415290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.90157 | − | 7.03213i | 0.526087 | − | 0.948212i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.41557 | − | 1.75501i | 0.319950 | − | 0.232457i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.98434 | + | 12.2625i | −0.518717 | + | 1.59645i | 0.257700 | + | 0.966225i | \(0.417035\pi\) |
−0.776416 | + | 0.630220i | \(0.782965\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.131388 | + | 0.0954591i | 0.0168225 | + | 0.0122223i | 0.596165 | − | 0.802862i | \(-0.296691\pi\) |
−0.579342 | + | 0.815084i | \(0.696691\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.61500 | − | 14.2035i | −0.581435 | − | 1.78947i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.42474 | 0.300752 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.50821 | −0.672935 | −0.336467 | − | 0.941695i | \(-0.609232\pi\) | ||||
−0.336467 | + | 0.941695i | \(0.609232\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.66076 | + | 8.18898i | 0.320318 | + | 0.985838i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.78658 | − | 7.11036i | −1.16145 | − | 0.843845i | −0.171492 | − | 0.985186i | \(-0.554859\pi\) |
−0.989961 | + | 0.141340i | \(0.954859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.190697 | − | 0.586905i | 0.0223194 | − | 0.0686921i | −0.939276 | − | 0.343161i | \(-0.888502\pi\) |
0.961596 | + | 0.274469i | \(0.0885022\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.22337 | + | 1.61538i | −0.256733 | + | 0.186528i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.18434 | + | 1.39941i | 0.818731 | + | 0.159477i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.20582 | + | 5.23534i | −0.810719 | + | 0.589022i | −0.914039 | − | 0.405627i | \(-0.867053\pi\) |
0.103320 | + | 0.994648i | \(0.467053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.09691 | − | 15.6867i | 0.566323 | − | 1.74296i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.45763 | + | 1.05903i | 0.159995 | + | 0.116243i | 0.664902 | − | 0.746930i | \(-0.268473\pi\) |
−0.504907 | + | 0.863174i | \(0.668473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.49740 | + | 7.68619i | 0.270881 | + | 0.833685i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 27.3323 | 2.93033 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.18551 | 0.655663 | 0.327831 | − | 0.944736i | \(-0.393682\pi\) | ||||
0.327831 | + | 0.944736i | \(0.393682\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.681960 | + | 2.09886i | 0.0714889 | + | 0.220020i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.5529 | − | 9.84673i | −1.40537 | − | 1.02106i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.715852 | − | 2.20317i | 0.0734449 | − | 0.226040i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.314159 | − | 0.228250i | 0.0318980 | − | 0.0231753i | −0.571722 | − | 0.820447i | \(-0.693724\pi\) |
0.603620 | + | 0.797272i | \(0.293724\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.3007 | + | 16.4208i | 1.53777 | + | 1.65035i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.5551 | − | 9.84837i | 1.34878 | − | 0.979949i | 0.349714 | − | 0.936857i | \(-0.386279\pi\) |
0.999071 | − | 0.0430927i | \(-0.0137211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.13911 | − | 15.8166i | 0.506372 | − | 1.55845i | −0.292080 | − | 0.956394i | \(-0.594347\pi\) |
0.798452 | − | 0.602058i | \(-0.205653\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.5296 | − | 9.82985i | −1.32036 | − | 0.959295i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.13623 | + | 15.8077i | 0.496538 | + | 1.52819i | 0.814547 | + | 0.580098i | \(0.196986\pi\) |
−0.318009 | + | 0.948088i | \(0.603014\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.5350 | 1.20064 | 0.600318 | − | 0.799762i | \(-0.295041\pi\) | ||||
0.600318 | + | 0.799762i | \(0.295041\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.9578 | 1.60957 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.48061 | + | 7.63452i | 0.233356 | + | 0.718196i | 0.997335 | + | 0.0729549i | \(0.0232429\pi\) |
−0.763979 | + | 0.645241i | \(0.776757\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.40456 | + | 3.92664i | 0.503978 | + | 0.366161i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.09120 | + | 6.43604i | −0.193331 | + | 0.595012i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.95078 | + | 4.32350i | −0.545507 | + | 0.396334i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6753 | + | 2.65280i | −0.970485 | + | 0.241163i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.8933 | − | 12.2737i | 1.52321 | − | 1.10668i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.08753 | − | 9.50245i | 0.276157 | − | 0.849925i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.05492 | + | 5.12570i | 0.626023 | + | 0.454832i | 0.855020 | − | 0.518595i | \(-0.173545\pi\) |
−0.228997 | + | 0.973427i | \(0.573545\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.80722 | + | 20.9505i | 0.599342 | + | 1.84459i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5956 | −0.925745 | −0.462872 | − | 0.886425i | \(-0.653181\pi\) | ||||
−0.462872 | + | 0.886425i | \(0.653181\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.10840 | 0.182821 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.82183 | − | 27.1508i | −0.759262 | − | 2.33677i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.9916 | − | 8.71239i | −1.02451 | − | 0.744350i | −0.0573073 | − | 0.998357i | \(-0.518251\pi\) |
−0.967202 | + | 0.254007i | \(0.918251\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.13690 | − | 21.9651i | 0.605344 | − | 1.86306i | 0.110938 | − | 0.993827i | \(-0.464615\pi\) |
0.494407 | − | 0.869231i | \(-0.335385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28.6791 | + | 20.8366i | −2.41522 | + | 1.75476i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.26098 | − | 2.42651i | −0.189073 | − | 0.202915i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.1559 | − | 12.4645i | 1.42472 | − | 1.03512i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.05680 | + | 6.33018i | −0.169642 | + | 0.522105i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.66194 | − | 4.84019i | −0.545768 | − | 0.396523i | 0.280455 | − | 0.959867i | \(-0.409515\pi\) |
−0.826223 | + | 0.563344i | \(0.809515\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.74504 | − | 11.5260i | −0.304767 | − | 0.937976i | −0.979764 | − | 0.200156i | \(-0.935855\pi\) |
0.674997 | − | 0.737820i | \(-0.264145\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.5555 | −1.82350 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.9973 | −1.04397 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.66190 | − | 8.19248i | −0.212442 | − | 0.653831i | −0.999325 | − | 0.0367283i | \(-0.988306\pi\) |
0.786883 | − | 0.617102i | \(-0.211694\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.0442 | − | 9.47717i | −1.03447 | − | 0.751589i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.87887 | + | 5.78256i | −0.148076 | + | 0.455730i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7881 | − | 7.83800i | 0.844987 | − | 0.613919i | −0.0787720 | − | 0.996893i | \(-0.525100\pi\) |
0.923759 | + | 0.382973i | \(0.125100\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 24.6696 | + | 4.80528i | 1.92052 | + | 0.374091i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.4795 | − | 11.2465i | 1.19784 | − | 0.870280i | 0.203768 | − | 0.979019i | \(-0.434681\pi\) |
0.994070 | + | 0.108739i | \(0.0346812\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.309017 | − | 0.951057i | 0.0237705 | − | 0.0731582i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.23053 | + | 3.80020i | 0.399989 | + | 0.290609i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.77097 | + | 14.6835i | 0.362730 | + | 1.11637i | 0.951390 | + | 0.307987i | \(0.0996554\pi\) |
−0.588661 | + | 0.808380i | \(0.700345\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.94064 | −0.146699 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −40.2958 | −3.02882 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.00828 | + | 21.5693i | 0.523824 | + | 1.61216i | 0.766631 | + | 0.642089i | \(0.221932\pi\) |
−0.242807 | + | 0.970075i | \(0.578068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.99929 | + | 3.63220i | 0.371595 | + | 0.269979i | 0.757872 | − | 0.652403i | \(-0.226239\pi\) |
−0.386277 | + | 0.922383i | \(0.626239\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.156844 | + | 0.482715i | −0.0115942 | + | 0.0356833i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.6440 | − | 7.73335i | 0.782566 | − | 0.568567i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.36307 | − | 9.66632i | 0.392187 | − | 0.706871i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21.0206 | − | 15.2724i | 1.52902 | − | 1.11090i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.13163 | + | 6.56049i | −0.154240 | + | 0.474700i | −0.998083 | − | 0.0618889i | \(-0.980288\pi\) |
0.843844 | + | 0.536589i | \(0.180288\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.87632 | − | 7.17557i | −0.710913 | − | 0.516508i | 0.172555 | − | 0.985000i | \(-0.444798\pi\) |
−0.883468 | + | 0.468491i | \(0.844798\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.34171 | + | 7.20705i | 0.167694 | + | 0.516108i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.22791 | −0.443720 | −0.221860 | − | 0.975079i | \(-0.571213\pi\) | ||||
−0.221860 | + | 0.975079i | \(0.571213\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3142 | 0.802044 | 0.401022 | − | 0.916069i | \(-0.368655\pi\) | ||||
0.401022 | + | 0.916069i | \(0.368655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.31960 | − | 16.3720i | −0.375216 | − | 1.15479i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.6144 | + | 11.3445i | 1.09592 | + | 0.796229i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.00630 | − | 15.4078i | 0.349655 | − | 1.07613i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.0837 | + | 10.9589i | −1.04839 | + | 0.761699i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.87228 | + | 1.33800i | −0.198680 | + | 0.0925514i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.2684 | + | 14.7258i | −1.39533 | + | 1.01377i | −0.400075 | + | 0.916482i | \(0.631016\pi\) |
−0.995257 | + | 0.0972857i | \(0.968984\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.6827 | − | 35.9555i | 0.800483 | − | 2.46363i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.8269 | + | 10.0458i | 0.942985 | + | 0.685119i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.65549 | − | 11.2505i | −0.248151 | − | 0.763731i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.92863 | 0.130324 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.33303 | 0.224204 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.71554 | − | 17.5906i | −0.382741 | − | 1.17796i | −0.938106 | − | 0.346349i | \(-0.887421\pi\) |
0.555365 | − | 0.831607i | \(-0.312579\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.81436 | − | 3.49784i | −0.320957 | − | 0.233189i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.20541 | + | 9.86523i | −0.212750 | + | 0.654778i | 0.786555 | + | 0.617520i | \(0.211862\pi\) |
−0.999306 | + | 0.0372583i | \(0.988138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.98350 | + | 3.62072i | −0.329319 | + | 0.239264i | −0.740142 | − | 0.672451i | \(-0.765242\pi\) |
0.410823 | + | 0.911715i | \(0.365242\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.77887 | + | 22.7055i | 0.182836 | + | 1.49391i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.8903 | + | 11.5449i | −1.04100 | + | 0.756334i | −0.970481 | − | 0.241176i | \(-0.922467\pi\) |
−0.0705235 | + | 0.997510i | \(0.522467\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.49904 | + | 26.1574i | −0.554416 | + | 1.70632i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −22.5201 | − | 16.3618i | −1.46284 | − | 1.06281i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.68203 | − | 14.4098i | −0.302856 | − | 0.932094i | −0.980469 | − | 0.196675i | \(-0.936986\pi\) |
0.677613 | − | 0.735419i | \(-0.263014\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.9436 | −0.898184 | −0.449092 | − | 0.893486i | \(-0.648252\pi\) | ||||
−0.449092 | + | 0.893486i | \(0.648252\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.2270 | 1.04096 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.59577 | + | 4.91128i | 0.101950 | + | 0.313770i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.772918 | − | 0.561558i | −0.0491796 | − | 0.0357311i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.74003 | + | 5.35527i | −0.110270 | + | 0.339377i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.6026 | + | 9.88286i | −0.858588 | + | 0.623801i | −0.927500 | − | 0.373822i | \(-0.878047\pi\) |
0.0689126 | + | 0.997623i | \(0.478047\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.11005 | − | 9.06996i | −0.0697884 | − | 0.570223i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.4338 | + | 14.8460i | −1.27961 | + | 0.929693i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.06083 | + | 12.4980i | −0.253308 | + | 0.779601i | 0.740850 | + | 0.671670i | \(0.234423\pi\) |
−0.994158 | + | 0.107931i | \(0.965577\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.68765 | + | 7.03849i | 0.601961 | + | 0.437350i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.2888 | + | 56.2872i | 1.13205 | + | 3.48409i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.18888 | −0.258297 | −0.129149 | − | 0.991625i | \(-0.541224\pi\) | ||||
−0.129149 | + | 0.991625i | \(0.541224\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.5095 | −0.768451 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.97371 | + | 18.3852i | 0.365585 | + | 1.12515i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.3164 | + | 9.67490i | 0.811913 | + | 0.589889i | 0.914385 | − | 0.404847i | \(-0.132675\pi\) |
−0.102472 | + | 0.994736i | \(0.532675\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.23748 | − | 19.1970i | 0.378900 | − | 1.16613i | −0.561910 | − | 0.827198i | \(-0.689933\pi\) |
0.940810 | − | 0.338935i | \(-0.110067\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.57983 | + | 4.05398i | −0.337706 | + | 0.245358i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.64375 | − | 1.23154i | 0.159424 | − | 0.0742647i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.6947 | − | 11.4028i | 0.943001 | − | 0.685130i | −0.00614026 | − | 0.999981i | \(-0.501955\pi\) |
0.949141 | + | 0.314851i | \(0.101955\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.2094 | − | 34.4989i | 0.671088 | − | 2.06540i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.29974 | + | 6.75666i | 0.554776 | + | 0.403069i | 0.829543 | − | 0.558442i | \(-0.188601\pi\) |
−0.274767 | + | 0.961511i | \(0.588601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.64458 | − | 17.3722i | −0.335535 | − | 1.03267i | −0.966458 | − | 0.256825i | \(-0.917323\pi\) |
0.630923 | − | 0.775846i | \(-0.282677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.23981 | 0.428849 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.7451 | 0.870373 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.82038 | − | 5.60256i | −0.107081 | − | 0.329562i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.981829 | + | 0.713340i | 0.0575558 | + | 0.0418168i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.45808 | − | 10.6429i | 0.202023 | − | 0.621763i | −0.797799 | − | 0.602923i | \(-0.794003\pi\) |
0.999823 | − | 0.0188403i | \(-0.00599740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.2928 | + | 18.3763i | −1.47260 | + | 1.06991i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.9446 | + | 34.1454i | −1.09928 | + | 1.98132i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.22892 | − | 1.61941i | 0.128902 | − | 0.0936527i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.80685 | + | 14.7940i | −0.277062 | + | 0.852709i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 42.3633 | + | 30.7787i | 2.43371 | + | 1.76819i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.121688 | + | 0.374516i | 0.00696781 | + | 0.0214447i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.7892 | −1.81430 | −0.907152 | − | 0.420804i | \(-0.861748\pi\) | ||||
−0.907152 | + | 0.420804i | \(0.861748\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 51.9747 | 2.95674 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.28383 | + | 7.02890i | 0.129504 | + | 0.398572i | 0.994695 | − | 0.102871i | \(-0.0328027\pi\) |
−0.865191 | + | 0.501443i | \(0.832803\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.2730 | + | 9.64343i | 0.750237 | + | 0.545079i | 0.895900 | − | 0.444255i | \(-0.146532\pi\) |
−0.145663 | + | 0.989334i | \(0.546532\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.1902 | − | 34.4398i | 0.630495 | − | 1.94046i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.317566 | − | 0.230725i | 0.0178363 | − | 0.0129588i | −0.578831 | − | 0.815447i | \(-0.696491\pi\) |
0.596668 | + | 0.802488i | \(0.296491\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.4709 | − | 5.54572i | −1.59406 | − | 0.310501i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.0248 | + | 30.5328i | −2.34560 | + | 1.70417i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.984007 | − | 3.02846i | 0.0547516 | − | 0.168508i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.711420 | + | 0.516877i | 0.0394625 | + | 0.0286712i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.1058 | + | 37.2578i | 0.669451 | + | 2.06036i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.0322 | −1.38007 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.6115 | 1.07795 | 0.538974 | − | 0.842323i | \(-0.318812\pi\) | ||||
0.538974 | + | 0.842323i | \(0.318812\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.3469 | + | 34.9223i | 0.621808 | + | 1.91373i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.8052 | − | 7.85044i | −0.590352 | − | 0.428916i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.26782 | − | 19.2904i | 0.341430 | − | 1.05081i | −0.622037 | − | 0.782988i | \(-0.713695\pi\) |
0.963467 | − | 0.267826i | \(-0.0863052\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.2964 | + | 14.7462i | −1.10235 | + | 0.800904i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.1195 | + | 13.0068i | 0.656307 | + | 0.704355i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.3002 | + | 11.8428i | −0.880126 | + | 0.639449i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.45166 | + | 19.8562i | −0.347345 | + | 1.06902i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.3532 | − | 15.5140i | −1.14630 | − | 0.832836i | −0.158316 | − | 0.987389i | \(-0.550606\pi\) |
−0.987985 | + | 0.154553i | \(0.950606\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.54209 | + | 4.74608i | 0.0825464 | + | 0.254052i | 0.983809 | − | 0.179222i | \(-0.0573582\pi\) |
−0.901262 | + | 0.433274i | \(0.857358\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.7736 | −0.628431 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.76581 | −0.466557 | −0.233278 | − | 0.972410i | \(-0.574945\pi\) | ||||
−0.233278 | + | 0.972410i | \(0.574945\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.06402 | − | 27.8962i | −0.481068 | − | 1.48058i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.5977 | − | 13.5121i | −0.984297 | − | 0.715134i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.678227 | − | 2.08737i | 0.0357955 | − | 0.110167i | −0.931562 | − | 0.363582i | \(-0.881554\pi\) |
0.967358 | + | 0.253415i | \(0.0815537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.6329 | − | 10.6314i | 0.770152 | − | 0.559548i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.1947 | − | 29.1683i | −0.954974 | − | 1.53094i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.21056 | − | 0.879520i | 0.0633634 | − | 0.0460362i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1831 | − | 34.4181i | 0.583753 | − | 1.79661i | −0.0204670 | − | 0.999791i | \(-0.506515\pi\) |
0.604220 | − | 0.796817i | \(-0.293485\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 36.5797 | + | 26.5767i | 1.90426 | + | 1.38353i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.51830 | − | 10.8282i | −0.182661 | − | 0.562173i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.6696 | −0.914896 | −0.457448 | − | 0.889236i | \(-0.651236\pi\) | ||||
−0.457448 | + | 0.889236i | \(0.651236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 31.2259 | 1.61250 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.70254 | − | 8.31758i | −0.139188 | − | 0.428377i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5800 | − | 10.5930i | −0.748926 | − | 0.544127i | 0.146568 | − | 0.989201i | \(-0.453177\pi\) |
−0.895494 | + | 0.445074i | \(0.853177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.42176 | + | 25.9195i | −0.431460 | + | 1.32790i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.38963 | + | 3.18925i | −0.224300 | + | 0.162963i | −0.694260 | − | 0.719724i | \(-0.744268\pi\) |
0.469960 | + | 0.882687i | \(0.344268\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.0987 | + | 12.9845i | 0.616608 | + | 0.661749i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −38.5897 | + | 28.0370i | −1.96162 | + | 1.42520i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.58539 | − | 17.1901i | 0.283191 | − | 0.871571i | −0.703745 | − | 0.710453i | \(-0.748490\pi\) |
0.986935 | − | 0.161118i | \(-0.0515100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.42908 | + | 5.39754i | 0.375705 | + | 0.272965i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.2328 | − | 31.4934i | −0.516178 | − | 1.58863i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.5969 | −1.08666 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.3394 | −0.920426 | −0.460213 | − | 0.887809i | \(-0.652227\pi\) | ||||
−0.460213 | + | 0.887809i | \(0.652227\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.03620 | + | 6.26679i | 0.101938 | + | 0.313732i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.90405 | + | 7.19571i | 0.494585 | + | 0.359337i | 0.806945 | − | 0.590627i | \(-0.201120\pi\) |
−0.312360 | + | 0.949964i | \(0.601120\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.65642 | + | 5.09792i | −0.0825119 | + | 0.253946i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 32.3555 | − | 23.5076i | 1.60776 | − | 1.16810i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.6642 | − | 3.44074i | −0.875581 | − | 0.170551i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.5690 | − | 10.5850i | 0.720392 | − | 0.523395i | −0.166117 | − | 0.986106i | \(-0.553123\pi\) |
0.886509 | + | 0.462711i | \(0.153123\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.3149 | − | 44.0566i | 0.706100 | − | 2.17315i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.0201 | − | 16.7251i | −1.13275 | − | 0.822989i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.35001 | + | 4.15490i | 0.0662693 | + | 0.203956i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 72.1795 | 3.53464 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.9915 | 0.536969 | 0.268484 | − | 0.963284i | \(-0.413477\pi\) | ||||
0.268484 | + | 0.963284i | \(0.413477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00857 | − | 18.4925i | −0.292840 | − | 0.901267i | −0.983939 | − | 0.178507i | \(-0.942873\pi\) |
0.691099 | − | 0.722760i | \(-0.257127\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −62.1001 | − | 45.1184i | −3.01941 | − | 2.19373i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.905713 | + | 2.78750i | −0.0439336 | + | 0.135214i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.289957 | + | 0.210666i | −0.0140320 | + | 0.0101948i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.02875 | − | 9.06374i | 0.242790 | − | 0.437602i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.5773 | + | 12.0441i | −0.798500 | + | 0.580144i | −0.910474 | − | 0.413567i | \(-0.864283\pi\) |
0.111974 | + | 0.993711i | \(0.464283\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0531 | + | 30.9402i | −0.483120 | + | 1.48689i | 0.351566 | + | 0.936163i | \(0.385649\pi\) |
−0.834686 | + | 0.550727i | \(0.814351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 53.6166 | + | 38.9548i | 2.57072 | + | 1.86774i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.813384 | − | 2.50334i | −0.0389094 | − | 0.119751i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.6025 | −0.935576 | −0.467788 | − | 0.883841i | \(-0.654949\pi\) | ||||
−0.467788 | + | 0.883841i | \(0.654949\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.4124 | −0.686304 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.27456 | − | 19.3111i | −0.298113 | − | 0.917499i | −0.982158 | − | 0.188059i | \(-0.939781\pi\) |
0.684044 | − | 0.729440i | \(-0.260219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.1338 | + | 8.81575i | 0.575199 | + | 0.417907i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.95265 | − | 24.4757i | 0.376147 | − | 1.15766i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.1975 | + | 12.4948i | −0.811602 | + | 0.589664i | −0.914295 | − | 0.405049i | \(-0.867254\pi\) |
0.102692 | + | 0.994713i | \(0.467254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.0873 | + | 9.35729i | −0.945873 | + | 0.440618i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 30.6420 | − | 22.2627i | 1.43969 | − | 1.04599i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.65358 | + | 5.08918i | −0.0775209 | + | 0.238585i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.4808 | + | 17.0598i | 1.09838 | + | 0.798023i | 0.980795 | − | 0.195039i | \(-0.0624835\pi\) |
0.117589 | + | 0.993062i | \(0.462483\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.1264 | − | 37.3213i | −0.566014 | − | 1.74201i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.9485 | −0.882520 | −0.441260 | − | 0.897379i | \(-0.645468\pi\) | ||||
−0.441260 | + | 0.897379i | \(0.645468\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.96519 | 0.277226 | 0.138613 | − | 0.990347i | \(-0.455736\pi\) | ||||
0.138613 | + | 0.990347i | \(0.455736\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.5522 | − | 38.6318i | −0.582095 | − | 1.79151i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.8733 | + | 14.4388i | 0.919626 | + | 0.668148i | 0.943431 | − | 0.331569i | \(-0.107578\pi\) |
−0.0238047 | + | 0.999717i | \(0.507578\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.75638 | − | 11.5609i | 0.173453 | − | 0.533835i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.7797 | − | 15.8239i | 1.00356 | − | 0.729127i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.83993 | − | 23.2043i | −0.130580 | − | 1.06694i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.679676 | − | 0.493814i | 0.0311857 | − | 0.0226577i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7887 | − | 33.2042i | 0.493980 | − | 1.52031i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0192 | − | 13.0917i | −0.823320 | − | 0.598177i | 0.0943417 | − | 0.995540i | \(-0.469925\pi\) |
−0.917662 | + | 0.397363i | \(0.869925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.67674 | − | 5.16048i | −0.0764529 | − | 0.235298i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.0020 | −0.864623 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.941580 | 0.0427549 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.56403 | − | 10.9690i | −0.161502 | − | 0.497051i | 0.837260 | − | 0.546805i | \(-0.184156\pi\) |
−0.998761 | + | 0.0497542i | \(0.984156\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 33.7156 | + | 24.4958i | 1.52467 | + | 1.10774i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.44323 | − | 10.5972i | 0.155391 | − | 0.478244i | −0.842809 | − | 0.538212i | \(-0.819100\pi\) |
0.998200 | + | 0.0599680i | \(0.0190999\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.5824 | − | 17.1336i | 1.06210 | − | 0.771659i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.61125 | + | 54.0189i | 0.297154 | + | 2.42797i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.5977 | − | 15.6916i | 0.968789 | − | 0.703867i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.20731 | + | 12.9488i | −0.188345 | + | 0.579666i | −0.999990 | − | 0.00448468i | \(-0.998572\pi\) |
0.811645 | + | 0.584151i | \(0.198572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 48.3774 | + | 35.1482i | 2.16134 | + | 1.57031i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.47585 | + | 7.61987i | 0.110392 | + | 0.339753i | 0.990958 | − | 0.134171i | \(-0.0428371\pi\) |
−0.880566 | + | 0.473924i | \(0.842837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.6266 | 1.80786 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.12526 | 0.138798 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.285778 | + | 0.879533i | 0.0126669 | + | 0.0389846i | 0.957190 | − | 0.289460i | \(-0.0934756\pi\) |
−0.944523 | + | 0.328444i | \(0.893476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.10178 | + | 0.800492i | 0.0487400 | + | 0.0354117i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.47591 | + | 10.6978i | −0.153465 | + | 0.472318i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.6233 | − | 23.7023i | 1.43756 | − | 1.04445i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.1015 | − | 15.8856i | 1.49978 | − | 0.698646i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −39.0362 | + | 28.3615i | −1.71350 | + | 1.24493i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.796725 | + | 2.45207i | −0.0349051 | + | 0.107427i | −0.966991 | − | 0.254810i | \(-0.917987\pi\) |
0.932086 | + | 0.362237i | \(0.117987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.630466 | − | 0.458060i | −0.0275683 | − | 0.0200296i | 0.573916 | − | 0.818914i | \(-0.305424\pi\) |
−0.601484 | + | 0.798885i | \(0.705424\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.87419 | − | 5.76817i | −0.0817964 | − | 0.251744i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.8660 | −0.778254 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.4094 | −0.669975 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.9630 | − | 82.9836i | −1.17010 | − | 3.60118i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.40539 | − | 3.92725i | −0.234134 | − | 0.170108i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.4540 | + | 38.3295i | −0.538434 | + | 1.65713i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −57.3420 | + | 41.6614i | −2.47449 | + | 1.79782i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.42687 | − | 6.17654i | 0.147606 | − | 0.266042i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.3500 | + | 20.5975i | −1.21886 | + | 0.885554i | −0.996005 | − | 0.0892972i | \(-0.971538\pi\) |
−0.222856 | + | 0.974851i | \(0.571538\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.96787 | + | 18.3672i | −0.256106 | + | 0.788213i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.5894 | + | 17.8652i | 1.05329 | + | 0.765262i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.60928 | + | 26.4966i | 0.368106 | + | 1.13291i | 0.948013 | + | 0.318231i | \(0.103089\pi\) |
−0.579907 | + | 0.814683i | \(0.696911\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.09903 | −0.0469056 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.35538 | −0.355951 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.07414 | − | 18.6943i | −0.258299 | − | 0.794962i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 33.2654 | + | 24.1687i | 1.41204 | + | 1.02591i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.96360 | − | 15.2764i | 0.210314 | − | 0.647281i | −0.789139 | − | 0.614215i | \(-0.789473\pi\) |
0.999453 | − | 0.0330663i | \(-0.0105273\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.70241 | − | 4.14305i | 0.241186 | − | 0.175232i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 33.9106 | + | 6.60532i | 1.43171 | + | 0.278877i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.5731 | − | 12.7676i | 0.740619 | − | 0.538091i | −0.152286 | − | 0.988337i | \(-0.548663\pi\) |
0.892905 | + | 0.450245i | \(0.148663\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.01483 | + | 18.5117i | −0.253046 | + | 0.778795i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.4482 | + | 21.3954i | 1.23671 | + | 0.898522i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.2374 | + | 31.5074i | 0.429173 | + | 1.32086i | 0.898941 | + | 0.438069i | \(0.144337\pi\) |
−0.469768 | + | 0.882790i | \(0.655663\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.2494 | −1.22405 | −0.612026 | − | 0.790838i | \(-0.709645\pi\) | ||||
−0.612026 | + | 0.790838i | \(0.709645\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.5584 | −0.900615 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.748667 | + | 2.30416i | 0.0312216 | + | 0.0960901i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.1716 | − | 12.4759i | −0.714863 | − | 0.519378i | 0.169876 | − | 0.985465i | \(-0.445663\pi\) |
−0.884739 | + | 0.466087i | \(0.845663\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.7898 | − | 36.2852i | 0.489967 | − | 1.50796i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.21679 | + | 2.33714i | −0.133455 | + | 0.0969608i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.6646 | + | 12.5186i | 0.483100 | + | 0.518468i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.2750 | + | 9.64487i | −0.548855 | + | 0.398766i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.30781 | − | 10.1804i | 0.136528 | − | 0.420190i | −0.859297 | − | 0.511478i | \(-0.829098\pi\) |
0.995825 | + | 0.0912876i | \(0.0290983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.14305 | + | 3.01010i | 0.170711 | + | 0.124029i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.01465 | − | 18.5112i | −0.247410 | − | 0.761449i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.8443 | 0.527450 | 0.263725 | − | 0.964598i | \(-0.415049\pi\) | ||||
0.263725 | + | 0.964598i | \(0.415049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.8354 | −0.731178 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.9268 | + | 33.6292i | 0.447204 | + | 1.37635i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.0010 | + | 21.0704i | 1.18495 | + | 0.860915i | 0.992721 | − | 0.120436i | \(-0.0384292\pi\) |
0.192226 | + | 0.981351i | \(0.438429\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.5510 | − | 35.5502i | 0.471174 | − | 1.45012i | −0.379876 | − | 0.925038i | \(-0.624033\pi\) |
0.851049 | − | 0.525086i | \(-0.175967\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.1565 | − | 21.9100i | 1.22807 | − | 0.892242i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.7222 | − | 10.0109i | −1.00510 | − | 0.407001i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.599052 | − | 0.435237i | 0.0243148 | − | 0.0176657i | −0.575562 | − | 0.817758i | \(-0.695216\pi\) |
0.599876 | + | 0.800093i | \(0.295216\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.6396 | + | 57.3667i | −0.755313 | + | 2.32462i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.17656 | + | 6.66716i | 0.371244 | + | 0.269725i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.82410 | + | 21.0024i | 0.275623 | + | 0.848279i | 0.989054 | + | 0.147554i | \(0.0471400\pi\) |
−0.713431 | + | 0.700725i | \(0.752860\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 50.6315 | 2.04166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.3874 | −1.14283 | −0.571416 | − | 0.820661i | \(-0.693606\pi\) | ||||
−0.571416 | + | 0.820661i | \(0.693606\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.40162 | + | 19.7022i | 0.257303 | + | 0.791897i | 0.993367 | + | 0.114985i | \(0.0366821\pi\) |
−0.736064 | + | 0.676912i | \(0.763318\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.2425 | − | 19.0663i | −1.05308 | − | 0.765105i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.21827 | + | 12.9825i | −0.169001 | + | 0.520133i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1569 | − | 16.8245i | 0.926277 | − | 0.672980i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.75087 | − | 7.24509i | −0.269604 | − | 0.289341i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.6312 | − | 10.6302i | 0.583386 | − | 0.423855i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.44876 | − | 19.8472i | 0.256721 | − | 0.790106i | −0.736765 | − | 0.676149i | \(-0.763647\pi\) |
0.993486 | − | 0.113957i | \(-0.0363526\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −63.3439 | − | 46.0221i | −2.51769 | − | 1.82921i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.53404 | + | 20.1097i | 0.259296 | + | 0.798030i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.12973 | 0.0843828 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 81.8626 | 3.23843 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.2076 | − | 31.4159i | −0.403178 | − | 1.24085i | −0.922407 | − | 0.386218i | \(-0.873781\pi\) |
0.519230 | − | 0.854635i | \(-0.326219\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.8252 | + | 29.6612i | 1.60999 | + | 1.16973i | 0.863537 | + | 0.504286i | \(0.168244\pi\) |
0.746452 | + | 0.665439i | \(0.231756\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.5057 | + | 50.7994i | −0.649913 | + | 2.00023i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.84701 | + | 4.97465i | −0.269184 | + | 0.195573i | −0.714186 | − | 0.699956i | \(-0.753203\pi\) |
0.445002 | + | 0.895530i | \(0.353203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.9743 | + | 8.17601i | 1.64764 | + | 0.320936i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.9094 | − | 21.7304i | 1.17224 | − | 0.851683i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.63742 | + | 8.11714i | −0.103210 | + | 0.317648i | −0.989306 | − | 0.145853i | \(-0.953407\pi\) |
0.886096 | + | 0.463502i | \(0.153407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.7850 | − | 15.1012i | −0.812136 | − | 0.590052i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.29050 | + | 3.97174i | 0.0503470 | + | 0.154952i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.20657 | −0.358637 | −0.179318 | − | 0.983791i | \(-0.557389\pi\) | ||||
−0.179318 | + | 0.983791i | \(0.557389\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.95052 | −0.0758666 | −0.0379333 | − | 0.999280i | \(-0.512077\pi\) | ||||
−0.0379333 | + | 0.999280i | \(0.512077\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.21891 | + | 9.90678i | 0.125012 | + | 0.384747i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.13595 | + | 3.00494i | 0.160385 | + | 0.116527i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.44578 | − | 22.9158i | 0.288302 | − | 0.887302i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 46.7648 | − | 33.9766i | 1.80803 | − | 1.31361i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.261320 | − | 0.470999i | 0.0100881 | − | 0.0181827i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.5975 | + | 13.5118i | −0.716879 | + | 0.520843i | −0.885386 | − | 0.464857i | \(-0.846106\pi\) |
0.168506 | + | 0.985701i | \(0.446106\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.19935 | − | 9.84659i | 0.123143 | − | 0.378996i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.3580 | − | 19.1502i | −1.01302 | − | 0.736003i | −0.0481804 | − | 0.998839i | \(-0.515342\pi\) |
−0.964841 | + | 0.262836i | \(0.915342\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.264820 | + | 0.815033i | 0.0101629 | + | 0.0312781i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.4181 | −1.24226 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.2643 | −0.431017 | −0.215508 | − | 0.976502i | \(-0.569141\pi\) | ||||
−0.215508 | + | 0.976502i | \(0.569141\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.1062 | − | 34.1814i | −0.424347 | − | 1.30601i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.5747 | − | 11.3157i | −0.594213 | − | 0.431721i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.59425 | + | 4.90660i | −0.0607361 | + | 0.186926i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.07433 | − | 5.13980i | 0.269120 | − | 0.195527i | −0.445038 | − | 0.895512i | \(-0.646810\pi\) |
0.714158 | + | 0.699985i | \(0.246810\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −44.8994 | + | 20.9156i | −1.70559 | + | 0.794516i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 45.3054 | − | 32.9163i | 1.71853 | − | 1.24859i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.88164 | − | 21.1795i | 0.260661 | − | 0.802231i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −49.6612 | − | 36.0810i | −1.87836 | − | 1.36471i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.97550 | − | 12.2353i | −0.150153 | − | 0.462122i | 0.847485 | − | 0.530820i | \(-0.178116\pi\) |
−0.997638 | + | 0.0686971i | \(0.978116\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.18394 | −0.195516 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −85.9555 | −3.23727 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.4263 | + | 35.1665i | 0.429729 | + | 1.32257i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.4486 | + | 27.9345i | 1.44397 | + | 1.04910i | 0.987195 | + | 0.159521i | \(0.0509949\pi\) |
0.456773 | + | 0.889583i | \(0.349005\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.6261 | − | 57.3251i | 0.698531 | − | 2.14986i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.9476 | + | 8.68047i | −0.447443 | + | 0.325086i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.976947 | − | 7.98239i | −0.0365358 | − | 0.298525i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 38.3086 | − | 27.8328i | 1.43066 | − | 1.03944i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.27223 | − | 3.91553i | 0.0474462 | − | 0.146024i | −0.924527 | − | 0.381117i | \(-0.875539\pi\) |
0.971973 | + | 0.235093i | \(0.0755394\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.6920 | + | 21.5725i | 1.10579 | + | 0.803403i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.4661 | − | 41.4445i | −0.500810 | − | 1.54134i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.69058 | 0.285621 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.9974 | −1.22380 | −0.611902 | − | 0.790933i | \(-0.709596\pi\) | ||||
−0.611902 | + | 0.790933i | \(0.709596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.380588 | + | 1.17133i | 0.0140959 | + | 0.0433826i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.0063 | + | 13.8089i | 0.702975 | + | 0.510741i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.8641 | + | 33.4362i | −0.401274 | + | 1.23499i | 0.522693 | + | 0.852521i | \(0.324927\pi\) |
−0.923967 | + | 0.382473i | \(0.875073\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.0567 | + | 9.48623i | −0.481603 | + | 0.349905i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.21930 | + | 18.1334i | 0.0817490 | + | 0.667951i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.61152 | − | 5.53009i | 0.279994 | − | 0.203428i | −0.438921 | − | 0.898526i | \(-0.644639\pi\) |
0.718915 | + | 0.695098i | \(0.244639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.922666 | − | 2.83967i | 0.0338950 | − | 0.104318i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.2078 | − | 27.7596i | −1.40171 | − | 1.01840i | −0.994464 | − | 0.105082i | \(-0.966490\pi\) |
−0.407245 | − | 0.913319i | \(-0.633510\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.17008 | − | 18.9896i | −0.226054 | − | 0.695724i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.1927 | −0.446109 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.6808 | −1.34029 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.61945 | − | 23.4502i | −0.278038 | − | 0.855712i | −0.988400 | − | 0.151875i | \(-0.951469\pi\) |
0.710362 | − | 0.703836i | \(-0.248531\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −42.5116 | − | 30.8865i | −1.54921 | − | 1.12557i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.08074 | − | 27.9476i | 0.330482 | − | 1.01712i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.4016 | + | 17.0023i | −0.850547 | + | 0.617959i | −0.925297 | − | 0.379244i | \(-0.876184\pi\) |
0.0747496 | + | 0.997202i | \(0.476184\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.8866 | − | 12.0588i | 0.939624 | − | 0.437707i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.561785 | − | 0.408161i | 0.0203647 | − | 0.0147958i | −0.577556 | − | 0.816351i | \(-0.695994\pi\) |
0.597921 | + | 0.801555i | \(0.295994\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.54837 | + | 26.3092i | −0.309472 | + | 0.952456i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −44.2461 | − | 32.1467i | −1.59972 | − | 1.16227i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.98434 | + | 12.2625i | 0.143866 | + | 0.442774i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.04753 | 0.0738358 | 0.0369179 | − | 0.999318i | \(-0.488246\pi\) | ||||
0.0369179 | + | 0.999318i | \(0.488246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.0695 | −1.47908 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.6341 | + | 32.7283i | 0.382481 | + | 1.17716i | 0.938291 | + | 0.345847i | \(0.112408\pi\) |
−0.555810 | + | 0.831310i | \(0.687592\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.81341 | − | 2.77060i | −0.136982 | − | 0.0995230i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.5646 | + | 35.5921i | −0.414876 | + | 1.27686i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.16420 | + | 3.75201i | −0.185027 | + | 0.134430i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.4647 | + | 35.0828i | −0.696500 | + | 1.25536i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −83.3027 | + | 60.5230i | −2.97700 | + | 2.16291i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.45441 | − | 19.8646i | 0.230368 | − | 0.708999i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.0833 | − | 7.32594i | −0.359430 | − | 0.261141i | 0.393384 | − | 0.919374i | \(-0.371304\pi\) |
−0.752814 | + | 0.658233i | \(0.771304\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.04544 | − | 12.4506i | −0.144022 | − | 0.443253i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.7155 | −0.629889 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.162405 | 0.00576716 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.0811 | − | 37.1819i | −0.428474 | − | 1.31871i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.8870 | − | 13.7222i | −0.669013 | − | 0.486066i | 0.200682 | − | 0.979656i | \(-0.435684\pi\) |
−0.869695 | + | 0.493590i | \(0.835684\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.6827 | + | 35.9558i | −0.413305 | + | 1.27202i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.8646 | + | 24.6040i | −1.19655 | + | 0.869341i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.00896 | − | 0.391318i | −0.0708947 | − | 0.0138093i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.9272 | + | 8.66559i | −0.420377 | + | 0.305422i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.8963 | + | 48.9238i | −0.559577 | + | 1.72220i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.1435 | + | 18.2678i | 0.883998 | + | 0.642262i | 0.934306 | − | 0.356472i | \(-0.116020\pi\) |
−0.0503083 | + | 0.998734i | \(0.516020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.61212 | + | 20.3500i | 0.232183 | + | 0.714586i | 0.997483 | + | 0.0709117i | \(0.0225908\pi\) |
−0.765300 | + | 0.643674i | \(0.777409\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 63.0831 | 2.21242 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.3334 | 1.13259 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.08094 | − | 6.40447i | −0.0728028 | − | 0.224064i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.0822 | − | 8.77825i | −0.422187 | − | 0.306737i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.2585 | − | 34.6501i | 0.392925 | − | 1.20930i | −0.537641 | − | 0.843174i | \(-0.680684\pi\) |
0.930566 | − | 0.366124i | \(-0.119316\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.5713 | − | 14.2194i | 0.682212 | − | 0.495656i | −0.191879 | − | 0.981419i | \(-0.561458\pi\) |
0.874091 | + | 0.485763i | \(0.161458\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.21373 | + | 6.66863i | 0.216334 | + | 0.232172i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.7822 | + | 11.4665i | −0.548802 | + | 0.398728i | −0.827343 | − | 0.561696i | \(-0.810149\pi\) |
0.278542 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.35646 | + | 22.6408i | −0.255500 | + | 0.786349i | 0.738230 | + | 0.674549i | \(0.235662\pi\) |
−0.993731 | + | 0.111800i | \(0.964338\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 49.0499 | + | 35.6368i | 1.70152 | + | 1.23623i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.19354 | + | 6.75103i | 0.0760017 | + | 0.233909i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.3942 | 1.60554 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 63.1100 | 2.18140 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.11310 | + | 9.58112i | 0.107476 | + | 0.330777i | 0.990304 | − | 0.138920i | \(-0.0443631\pi\) |
−0.882828 | + | 0.469697i | \(0.844363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −38.4169 | − | 27.9115i | −1.32472 | − | 0.962465i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.1015 | + | 34.1669i | −0.382356 | + | 1.17677i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.96166 | − | 1.42523i | 0.0674830 | − | 0.0490293i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.71231 | − | 24.2151i | 0.0588357 | − | 0.832041i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 46.1841 | − | 33.5547i | 1.58504 | − | 1.15160i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.61959 | − | 14.2176i | 0.158358 | − | 0.487375i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.6624 | + | 30.2695i | 1.42649 | + | 1.03641i | 0.990656 | + | 0.136384i | \(0.0435480\pi\) |
0.435838 | + | 0.900025i | \(0.356452\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.84435 | + | 14.9094i | 0.165673 | + | 0.509890i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.19131 | −0.279810 | −0.139905 | − | 0.990165i | \(-0.544680\pi\) | ||||
−0.139905 | + | 0.990165i | \(0.544680\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.9106 | 0.576981 | 0.288491 | − | 0.957483i | \(-0.406847\pi\) | ||||
0.288491 | + | 0.957483i | \(0.406847\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.2402 | + | 43.8267i | 0.485304 | + | 1.49361i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.1759 | + | 11.0259i | 0.516593 | + | 0.375327i | 0.815319 | − | 0.579012i | \(-0.196562\pi\) |
−0.298726 | + | 0.954339i | \(0.596562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.5684 | + | 35.6037i | −0.393336 | + | 1.21056i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.8944 | − | 10.8214i | 0.505842 | − | 0.367515i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.1383 | + | 21.6127i | 0.683146 | + | 0.733159i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.45623 | + | 3.23764i | −0.150994 | + | 0.109703i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.812057 | + | 2.49926i | −0.0274840 | + | 0.0845870i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.8387 | + | 12.9606i | 0.603059 | + | 0.438148i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.1163 | + | 43.4456i | 0.476674 | + | 1.46705i | 0.843686 | + | 0.536837i | \(0.180381\pi\) |
−0.367012 | + | 0.930216i | \(0.619619\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 34.9735 | 1.17963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.8104 | 1.07172 | 0.535859 | − | 0.844307i | \(-0.319988\pi\) | ||||
0.535859 | + | 0.844307i | \(0.319988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.65717 | − | 11.2556i | −0.123073 | − | 0.378781i | 0.870472 | − | 0.492218i | \(-0.163814\pi\) |
−0.993545 | + | 0.113437i | \(0.963814\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −79.0465 | − | 57.4307i | −2.65712 | − | 1.93051i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.85106 | − | 8.77466i | 0.0957292 | − | 0.294624i | −0.891714 | − | 0.452600i | \(-0.850497\pi\) |
0.987443 | + | 0.157975i | \(0.0504967\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.5693 | + | 11.3118i | −0.522177 | + | 0.379384i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −53.6951 | − | 10.4591i | −1.79885 | − | 0.350391i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.76710 | − | 6.36967i | 0.293380 | − | 0.213153i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.9933 | + | 52.2999i | −0.568022 | + | 1.74819i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.96596 | + | 5.06107i | 0.232587 | + | 0.168984i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.4864 | + | 44.5845i | 0.483148 | + | 1.48698i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.1955 | −0.572864 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −48.6143 | −1.61778 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.63019 | + | 14.2502i | 0.153913 | + | 0.473694i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.4122 | + | 18.4630i | 0.843798 | + | 0.613055i | 0.923429 | − | 0.383769i | \(-0.125374\pi\) |
−0.0796308 | + | 0.996824i | \(0.525374\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −35.0381 | + | 107.836i | −1.16214 | + | 3.57670i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.0572 | − | 12.3928i | 0.565132 | − | 0.410592i | −0.268202 | − | 0.963363i | \(-0.586429\pi\) |
0.833334 | + | 0.552770i | \(0.186429\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.89910 | − | 5.22529i | 0.0959461 | − | 0.172932i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.995652 | + | 0.723384i | −0.0329152 | + | 0.0239143i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.22580 | − | 22.2387i | 0.238617 | − | 0.734387i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.97985 | − | 5.07116i | −0.230244 | − | 0.167282i | 0.466682 | − | 0.884425i | \(-0.345449\pi\) |
−0.696926 | + | 0.717143i | \(0.745449\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.7007 | − | 94.4869i | −1.01162 | − | 3.11345i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.0969 | −0.398173 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.77147 | 0.156885 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.7777 | + | 107.035i | 1.14225 | + | 3.51548i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.9618 | − | 26.8543i | −1.21268 | − | 0.881062i | −0.217207 | − | 0.976126i | \(-0.569695\pi\) |
−0.995471 | + | 0.0950634i | \(0.969695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.628755 | − | 1.93511i | 0.0206066 | − | 0.0634207i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.6864 | + | 13.5764i | −0.611764 | + | 0.444473i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.2972 | − | 11.3184i | 0.794603 | − | 0.370152i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.0413 | − | 18.1936i | 0.818064 | − | 0.594358i | −0.0980935 | − | 0.995177i | \(-0.531274\pi\) |
0.916157 | + | 0.400819i | \(0.131274\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.8446 | + | 48.7647i | −0.517069 | + | 1.59138i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.7496 | − | 10.7162i | −0.480824 | − | 0.349339i | 0.320821 | − | 0.947140i | \(-0.396041\pi\) |
−0.801645 | + | 0.597801i | \(0.796041\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.68839 | − | 17.5071i | −0.185240 | − | 0.570109i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 63.0018 | 2.04945 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.3499 | 1.24620 | 0.623102 | − | 0.782141i | \(-0.285872\pi\) | ||||
0.623102 | + | 0.782141i | \(0.285872\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.190697 | − | 0.586905i | −0.00619029 | − | 0.0190518i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.992476 | + | 0.721076i | 0.0321832 | + | 0.0233825i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.23863 | + | 25.3559i | −0.266876 | + | 0.821359i | 0.724380 | + | 0.689401i | \(0.242126\pi\) |
−0.991255 | + | 0.131957i | \(0.957874\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.5317 | + | 9.83137i | −0.437876 | + | 0.318136i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.0124 | − | 89.9797i | −0.355981 | − | 2.90863i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.4639 | − | 19.2271i | 0.854562 | − | 0.620876i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.700685 | + | 2.15649i | −0.0226028 | + | 0.0695641i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −90.9980 | − | 66.1139i | −2.93237 | − | 2.13049i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.14713 | − | 28.1520i | −0.294457 | − | 0.906244i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.1213 | −0.389796 | −0.194898 | − | 0.980824i | \(-0.562438\pi\) | ||||
−0.194898 | + | 0.980824i | \(0.562438\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.95180 | 0.319698 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.79043 | + | 30.1318i | 0.314190 | + | 0.966977i | 0.976087 | + | 0.217382i | \(0.0697517\pi\) |
−0.661897 | + | 0.749595i | \(0.730248\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.2346 | + | 29.9587i | 1.32192 | + | 0.960432i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.849253 | + | 2.61373i | −0.0271979 | + | 0.0837064i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.4034 | + | 32.2609i | −1.42059 | + | 1.03212i | −0.428916 | + | 0.903344i | \(0.641104\pi\) |
−0.991674 | + | 0.128775i | \(0.958896\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.49219 | − | 20.3631i | −0.0796508 | − | 0.650807i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −68.6269 | + | 49.8604i | −2.19109 | + | 1.59192i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.857177 | + | 2.63812i | −0.0273397 | + | 0.0841430i | −0.963795 | − | 0.266643i | \(-0.914086\pi\) |
0.936456 | + | 0.350786i | \(0.114086\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.2170 | − | 8.87618i | −0.389266 | − | 0.282819i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.1751 | − | 74.4032i | −0.769501 | − | 2.36828i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.4195 | 0.617505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.7848 | 0.469655 | 0.234828 | − | 0.972037i | \(-0.424547\pi\) | ||||
0.234828 | + | 0.972037i | \(0.424547\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.9400 | + | 58.2913i | 0.601043 | + | 1.84982i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.1946 | + | 16.1253i | 0.703616 | + | 0.511207i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.4241 | − | 38.2374i | 0.393474 | − | 1.21099i | −0.536669 | − | 0.843793i | \(-0.680318\pi\) |
0.930143 | − | 0.367196i | \(-0.119682\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −51.6836 | + | 37.5503i | −1.63520 | + | 1.18804i |
(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 | 572.2.n.b.157.7 | ✓ | 28 | |
11.2 | odd | 10 | 6292.2.a.y.1.14 | 14 | |||
11.4 | even | 5 | inner | 572.2.n.b.521.7 | yes | 28 | |
11.9 | even | 5 | 6292.2.a.z.1.14 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.n.b.157.7 | ✓ | 28 | 1.1 | even | 1 | trivial | |
572.2.n.b.521.7 | yes | 28 | 11.4 | even | 5 | inner | |
6292.2.a.y.1.14 | 14 | 11.2 | odd | 10 | |||
6292.2.a.z.1.14 | 14 | 11.9 | even | 5 |