Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,3,Mod(65,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.r (of order \(6\), degree \(2\), 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: | \(8.28340003655\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 38) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.65 |
Dual form | 304.3.r.a.145.1 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.72474 | − | 1.57313i | −0.908248 | − | 0.524377i | −0.0283812 | − | 0.999597i | \(-0.509035\pi\) |
−0.879867 | + | 0.475220i | \(0.842369\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | −0.811684 | − | 0.584096i | \(-0.801449\pi\) |
0.911684 | + | 0.410891i | \(0.134782\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.89898 | −0.985568 | −0.492784 | − | 0.870152i | \(-0.664021\pi\) | ||||
−0.492784 | + | 0.870152i | \(0.664021\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.449490 | + | 0.778539i | 0.0499433 | + | 0.0865043i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.8990 | 1.35445 | 0.677226 | − | 0.735775i | \(-0.263182\pi\) | ||||
0.677226 | + | 0.735775i | \(0.263182\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.8485 | + | 8.57277i | −1.14219 | + | 0.659444i | −0.946972 | − | 0.321316i | \(-0.895875\pi\) |
−0.195218 | + | 0.980760i | \(0.562541\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.72474 | + | 1.57313i | −0.181650 | + | 0.104875i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.05051 | − | 1.81954i | 0.0617947 | − | 0.107032i | −0.833473 | − | 0.552560i | \(-0.813651\pi\) |
0.895268 | + | 0.445529i | \(0.146984\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.3485 | + | 15.2385i | −0.597288 | + | 0.802027i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.7980 | + | 10.8530i | 0.895141 | + | 0.516810i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.5227 | + | 23.4220i | 0.587944 | + | 1.01835i | 0.994501 | + | 0.104723i | \(0.0333957\pi\) |
−0.406558 | + | 0.913625i | \(0.633271\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.0000 | + | 20.7846i | 0.480000 | + | 0.831384i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 25.4880i | 0.943998i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.54541 | + | 3.20164i | −0.191221 | + | 0.110401i | −0.592554 | − | 0.805531i | \(-0.701880\pi\) |
0.401333 | + | 0.915932i | \(0.368547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 31.1769i | − | 1.00571i | −0.864372 | − | 0.502853i | \(-0.832284\pi\) | ||
0.864372 | − | 0.502853i | \(-0.167716\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −40.5959 | − | 23.4381i | −1.23018 | − | 0.710244i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.44949 | + | 5.97469i | −0.0985568 | + | 0.170705i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 28.9199i | 0.781620i | 0.920471 | + | 0.390810i | \(0.127805\pi\) | ||||
−0.920471 | + | 0.390810i | \(0.872195\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 53.9444 | 1.38319 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 55.9393 | + | 32.2966i | 1.36437 | + | 0.787721i | 0.990202 | − | 0.139639i | \(-0.0445942\pi\) |
0.374170 | + | 0.927360i | \(0.377928\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −37.6691 | + | 65.2449i | −0.876026 | + | 1.51732i | −0.0203609 | + | 0.999793i | \(0.506482\pi\) |
−0.855665 | + | 0.517529i | \(0.826852\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.898979 | 0.0199773 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.77015 | − | 9.99420i | −0.122769 | − | 0.212642i | 0.798090 | − | 0.602539i | \(-0.205844\pi\) |
−0.920859 | + | 0.389896i | \(0.872511\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.40408 | −0.0286547 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.72474 | + | 3.30518i | −0.112250 | + | 0.0648075i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −69.2878 | + | 40.0033i | −1.30732 | + | 0.754779i | −0.981647 | − | 0.190705i | \(-0.938923\pi\) |
−0.325669 | + | 0.945484i | \(0.605589\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.44949 | − | 12.9029i | 0.135445 | − | 0.234598i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 54.8939 | − | 23.6684i | 0.963050 | − | 0.415235i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −50.9166 | − | 29.3967i | −0.862993 | − | 0.498249i | 0.00202049 | − | 0.999998i | \(-0.499357\pi\) |
−0.865013 | + | 0.501749i | \(0.832690\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.09592 | − | 1.89819i | −0.0179659 | − | 0.0311178i | 0.856903 | − | 0.515478i | \(-0.172386\pi\) |
−0.874869 | + | 0.484360i | \(0.839052\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.10102 | − | 5.37113i | −0.0492225 | − | 0.0852560i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.1455i | 0.263777i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 51.6589 | − | 29.8253i | 0.771029 | − | 0.445154i | −0.0622127 | − | 0.998063i | \(-0.519816\pi\) |
0.833241 | + | 0.552909i | \(0.186482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 85.0920i | − | 1.23322i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −87.5227 | − | 50.5313i | −1.23271 | − | 0.711708i | −0.265119 | − | 0.964216i | \(-0.585411\pi\) |
−0.967595 | + | 0.252508i | \(0.918745\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 63.6918 | − | 110.317i | 0.872491 | − | 1.51120i | 0.0130791 | − | 0.999914i | \(-0.495837\pi\) |
0.859412 | − | 0.511284i | \(-0.170830\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 75.5103i | − | 1.00680i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −102.788 | −1.33491 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.78036 | + | 3.33729i | 0.0731691 | + | 0.0422442i | 0.536138 | − | 0.844130i | \(-0.319883\pi\) |
−0.462969 | + | 0.886374i | \(0.653216\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 44.1413 | − | 76.4550i | 0.544955 | − | 0.943889i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.30306 | 0.0156995 | 0.00784977 | − | 0.999969i | \(-0.497501\pi\) | ||||
0.00784977 | + | 0.999969i | \(0.497501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.05051 | − | 1.81954i | −0.0123589 | − | 0.0214063i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20.1464 | 0.231568 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.84847 | − | 3.37662i | 0.0657131 | − | 0.0379395i | −0.466783 | − | 0.884372i | \(-0.654587\pi\) |
0.532497 | + | 0.846432i | \(0.321254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 102.439 | − | 59.1433i | 1.12571 | − | 0.649927i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −49.0454 | + | 84.9491i | −0.527370 | + | 0.913432i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.52270 | + | 17.4473i | 0.0791864 | + | 0.183656i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −114.152 | − | 65.9054i | −1.17682 | − | 0.679437i | −0.221543 | − | 0.975151i | \(-0.571109\pi\) |
−0.955277 | + | 0.295713i | \(0.904443\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.69694 | + | 11.5994i | 0.0676458 | + | 0.117166i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.24235 | − | 5.61591i | −0.0321024 | − | 0.0556031i | 0.849528 | − | 0.527544i | \(-0.176887\pi\) |
−0.881630 | + | 0.471941i | \(0.843554\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 80.0243i | 0.776935i | 0.921462 | + | 0.388467i | \(0.126995\pi\) | ||||
−0.921462 | + | 0.388467i | \(0.873005\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 18.7980 | − | 10.8530i | 0.179028 | − | 0.103362i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 80.0243i | 0.747890i | 0.927451 | + | 0.373945i | \(0.121995\pi\) | ||||
−0.927451 | + | 0.373945i | \(0.878005\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.2423 | − | 8.22282i | −0.130664 | − | 0.0754387i | 0.433243 | − | 0.901277i | \(-0.357369\pi\) |
−0.563907 | + | 0.825838i | \(0.690702\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 45.4949 | − | 78.7995i | 0.409864 | − | 0.709905i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 132.843i | 1.17560i | 0.809006 | + | 0.587801i | \(0.200006\pi\) | ||||
−0.809006 | + | 0.587801i | \(0.799994\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.0454 | 0.235177 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.3485 | − | 7.70674i | −0.114089 | − | 0.0658696i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.24745 | + | 12.5529i | −0.0609029 | + | 0.105487i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 100.980 | 0.834542 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −101.614 | − | 176.000i | −0.826126 | − | 1.43089i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 49.0000 | 0.392000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −108.826 | + | 62.8306i | −0.856896 | + | 0.494729i | −0.862972 | − | 0.505253i | \(-0.831399\pi\) |
0.00607575 | + | 0.999982i | \(0.498066\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 205.278 | − | 118.517i | 1.59130 | − | 0.918737i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 53.6237 | − | 92.8790i | 0.409341 | − | 0.709000i | −0.585475 | − | 0.810691i | \(-0.699092\pi\) |
0.994816 | + | 0.101691i | \(0.0324252\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 78.2929 | − | 105.130i | 0.588668 | − | 0.790452i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 22.0732 | + | 12.7440i | 0.163505 | + | 0.0943998i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.05051 | + | 1.81954i | 0.00766796 | + | 0.0132813i | 0.869834 | − | 0.493345i | \(-0.164226\pi\) |
−0.862166 | + | 0.506626i | \(0.830893\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.8712 | − | 27.4897i | −0.114181 | − | 0.197767i | 0.803271 | − | 0.595614i | \(-0.203091\pi\) |
−0.917452 | + | 0.397846i | \(0.869758\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 36.3089i | 0.257510i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −221.227 | + | 127.725i | −1.54704 | + | 0.893185i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.40329i | 0.0441606i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.82577 | + | 2.20881i | 0.0260256 | + | 0.0150259i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −94.8383 | + | 164.265i | −0.636498 | + | 1.10245i | 0.349697 | + | 0.936863i | \(0.386284\pi\) |
−0.986196 | + | 0.165585i | \(0.947049\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2707i | 0.107753i | 0.998548 | + | 0.0538764i | \(0.0171577\pi\) | ||||
−0.998548 | + | 0.0538764i | \(0.982842\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.88877 | 0.0123449 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −27.0000 | − | 15.5885i | −0.174194 | − | 0.100571i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −135.076 | + | 233.958i | −0.860354 | + | 1.49018i | 0.0112344 | + | 0.999937i | \(0.496424\pi\) |
−0.871588 | + | 0.490239i | \(0.836909\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 251.722 | 1.58316 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −93.2929 | − | 161.588i | −0.579459 | − | 1.00365i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 156.697 | 0.961331 | 0.480665 | − | 0.876904i | \(-0.340395\pi\) | ||||
0.480665 | + | 0.876904i | \(0.340395\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −40.5959 | + | 23.4381i | −0.246036 | + | 0.142049i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 78.0834 | − | 45.0815i | 0.467565 | − | 0.269949i | −0.247655 | − | 0.968848i | \(-0.579660\pi\) |
0.715220 | + | 0.698899i | \(0.246326\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 62.4847 | − | 108.227i | 0.369732 | − | 0.640394i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.9648 | − | 1.98567i | −0.0992093 | − | 0.0116121i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −263.379 | − | 152.062i | −1.52242 | − | 0.878969i | −0.999649 | − | 0.0264959i | \(-0.991565\pi\) |
−0.522771 | − | 0.852473i | \(-0.675102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −82.7878 | − | 143.393i | −0.473073 | − | 0.819386i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 92.4898 | + | 160.197i | 0.522541 | + | 0.905068i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 315.198i | 1.76088i | 0.474156 | + | 0.880441i | \(0.342753\pi\) | ||||
−0.474156 | + | 0.880441i | \(0.657247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −27.8939 | + | 16.1045i | −0.154110 | + | 0.0889753i | −0.575072 | − | 0.818103i | \(-0.695026\pi\) |
0.420962 | + | 0.907078i | \(0.361693\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.89610i | 0.0376836i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.0454 | + | 14.4600i | 0.135381 | + | 0.0781620i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.6515 | − | 27.1092i | 0.0836980 | − | 0.144969i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 175.841i | − | 0.930375i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −280.252 | −1.46729 | −0.733644 | − | 0.679534i | \(-0.762182\pi\) | ||||
−0.733644 | + | 0.679534i | \(0.762182\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 42.0153 | + | 24.2575i | 0.217696 | + | 0.125687i | 0.604883 | − | 0.796314i | \(-0.293220\pi\) |
−0.387187 | + | 0.922001i | \(0.626553\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 26.9722 | − | 46.7172i | 0.138319 | − | 0.239575i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 251.909 | 1.27873 | 0.639363 | − | 0.768905i | \(-0.279198\pi\) | ||||
0.639363 | + | 0.768905i | \(0.279198\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 129.694 | + | 224.637i | 0.651729 | + | 1.12883i | 0.982703 | + | 0.185188i | \(0.0592895\pi\) |
−0.330974 | + | 0.943640i | \(0.607377\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −187.677 | −0.933714 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 38.2577 | − | 22.0881i | 0.188461 | − | 0.108808i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 55.9393 | − | 32.2966i | 0.272875 | − | 0.157544i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.1566 | + | 21.0559i | −0.0587277 | + | 0.101719i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −169.081 | + | 227.038i | −0.808998 | + | 1.08631i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −60.2503 | − | 34.7855i | −0.285546 | − | 0.164860i | 0.350385 | − | 0.936606i | \(-0.386051\pi\) |
−0.635932 | + | 0.771745i | \(0.719384\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 158.985 | + | 275.370i | 0.746407 | + | 1.29281i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 37.6691 | + | 65.2449i | 0.175205 | + | 0.303464i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 215.089i | 0.991193i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −347.088 | + | 200.391i | −1.58488 | + | 0.915029i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.0231i | 0.163001i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.47730 | + | 3.16232i | 0.0245619 | + | 0.0141808i | 0.512231 | − | 0.858848i | \(-0.328819\pi\) |
−0.487669 | + | 0.873029i | \(0.662153\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.7878 | + | 18.6849i | −0.0479456 | + | 0.0830442i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 55.7402i | 0.245552i | 0.992434 | + | 0.122776i | \(0.0391796\pi\) | ||||
−0.992434 | + | 0.122776i | \(0.960820\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −132.313 | −0.577787 | −0.288894 | − | 0.957361i | \(-0.593287\pi\) | ||||
−0.288894 | + | 0.957361i | \(0.593287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 280.070 | + | 161.699i | 1.21243 | + | 0.699994i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 111.859 | − | 193.745i | 0.480080 | − | 0.831523i | −0.519659 | − | 0.854374i | \(-0.673941\pi\) |
0.999739 | + | 0.0228507i | \(0.00727424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.5403 | −0.0491077 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.5000 | − | 18.1865i | −0.0443038 | − | 0.0767364i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 71.3235 | 0.298425 | 0.149212 | − | 0.988805i | \(-0.452326\pi\) | ||||
0.149212 | + | 0.988805i | \(0.452326\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 120.727 | − | 69.7018i | 0.500942 | − | 0.289219i | −0.228160 | − | 0.973624i | \(-0.573271\pi\) |
0.729103 | + | 0.684405i | \(0.239938\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −41.8888 | + | 24.1845i | −0.172382 | + | 0.0995247i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.702041 | + | 1.21597i | −0.00286547 | + | 0.00496315i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 37.8712 | − | 323.556i | 0.153325 | − | 1.30994i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.55051 | − | 2.04989i | −0.0142591 | − | 0.00823248i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 120.038 | + | 207.912i | 0.478239 | + | 0.828334i | 0.999689 | − | 0.0249476i | \(-0.00794190\pi\) |
−0.521450 | + | 0.853282i | \(0.674609\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 201.474 | + | 348.964i | 0.796342 | + | 1.37930i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.61037i | 0.0259230i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.37857 | − | 4.83737i | 0.0326014 | − | 0.0188224i | −0.483611 | − | 0.875283i | \(-0.660675\pi\) |
0.516212 | + | 0.856461i | \(0.327342\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 199.518i | − | 0.770340i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.98521 | − | 2.87821i | −0.0191004 | − | 0.0110276i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −56.9620 | + | 98.6611i | −0.216586 | + | 0.375137i | −0.953762 | − | 0.300563i | \(-0.902825\pi\) |
0.737176 | + | 0.675700i | \(0.236159\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 80.0066i | 0.301912i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.2474 | −0.0795785 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −348.090 | − | 200.970i | −1.29402 | − | 0.747100i | −0.314652 | − | 0.949207i | \(-0.601888\pi\) |
−0.979364 | + | 0.202106i | \(0.935221\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 199.492 | − | 345.530i | 0.736133 | − | 1.27502i | −0.218091 | − | 0.975928i | \(-0.569983\pi\) |
0.954224 | − | 0.299092i | \(-0.0966836\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −372.161 | −1.36323 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 178.788 | + | 309.669i | 0.650137 | + | 1.12607i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 529.444 | 1.91135 | 0.955675 | − | 0.294424i | \(-0.0951278\pi\) | ||||
0.955675 | + | 0.294424i | \(0.0951278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.2724 | − | 14.0137i | 0.0869980 | − | 0.0502283i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 47.4092 | − | 27.3717i | 0.168716 | − | 0.0974082i | −0.413264 | − | 0.910611i | \(-0.635611\pi\) |
0.581980 | + | 0.813203i | \(0.302278\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −74.4671 | + | 128.981i | −0.263135 | + | 0.455762i | −0.967073 | − | 0.254498i | \(-0.918090\pi\) |
0.703939 | + | 0.710261i | \(0.251423\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.94949 | − | 59.3737i | 0.0243842 | − | 0.208329i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −385.924 | − | 222.813i | −1.34468 | − | 0.776353i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 142.293 | + | 246.458i | 0.492363 | + | 0.852797i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 207.356 | + | 359.151i | 0.712563 | + | 1.23420i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 145.685i | 0.497218i | 0.968604 | + | 0.248609i | \(0.0799734\pi\) | ||||
−0.968604 | + | 0.248609i | \(0.920027\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −50.9166 | + | 29.3967i | −0.172599 | + | 0.0996498i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 379.744i | 1.27860i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −401.583 | − | 231.854i | −1.34309 | − | 0.775431i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 259.879 | − | 450.123i | 0.863384 | − | 1.49542i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.4026i | 0.0673352i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.19184 | −0.00718635 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −98.0380 | − | 56.6023i | −0.319342 | − | 0.184372i | 0.331757 | − | 0.943365i | \(-0.392359\pi\) |
−0.651099 | + | 0.758993i | \(0.725692\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 125.889 | − | 218.046i | 0.407407 | − | 0.705650i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 105.666 | 0.339763 | 0.169882 | − | 0.985464i | \(-0.445661\pi\) | ||||
0.169882 | + | 0.985464i | \(0.445661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −124.121 | − | 214.984i | −0.396552 | − | 0.686849i | 0.596746 | − | 0.802431i | \(-0.296460\pi\) |
−0.993298 | + | 0.115582i | \(0.963127\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.20204 | −0.0196890 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −196.061 | + | 113.196i | −0.618488 | + | 0.357084i | −0.776280 | − | 0.630388i | \(-0.782896\pi\) |
0.157792 | + | 0.987472i | \(0.449562\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −82.6209 | + | 47.7012i | −0.259000 | + | 0.149534i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 125.889 | − | 218.046i | 0.392177 | − | 0.679270i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.8054 | + | 36.6572i | 0.0489330 | + | 0.113490i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −356.363 | − | 205.746i | −1.09650 | − | 0.633066i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.8712 | + | 44.8102i | 0.0791167 | + | 0.137034i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 39.8082 | + | 68.9498i | 0.120997 | + | 0.209574i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 293.328i | − | 0.886188i | −0.896475 | − | 0.443094i | \(-0.853881\pi\) | ||
0.896475 | − | 0.443094i | \(-0.146119\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.5153 | + | 12.9992i | −0.0676135 | + | 0.0390367i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 59.6506i | − | 0.178061i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −399.393 | − | 230.590i | −1.18514 | − | 0.684243i | −0.227945 | − | 0.973674i | \(-0.573201\pi\) |
−0.957199 | + | 0.289431i | \(0.906534\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 208.980 | − | 361.963i | 0.616459 | − | 1.06774i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 464.504i | − | 1.36218i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 347.737 | 1.01381 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −73.6918 | − | 42.5460i | −0.213600 | − | 0.123322i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 152.129 | − | 263.495i | 0.438412 | − | 0.759351i | −0.559156 | − | 0.829063i | \(-0.688875\pi\) |
0.997567 | + | 0.0697116i | \(0.0222079\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 50.4337 | 0.144509 | 0.0722545 | − | 0.997386i | \(-0.476981\pi\) | ||||
0.0722545 | + | 0.997386i | \(0.476981\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −218.502 | − | 378.457i | −0.622514 | − | 1.07823i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −316.817 | −0.897500 | −0.448750 | − | 0.893657i | \(-0.648131\pi\) | ||||
−0.448750 | + | 0.893657i | \(0.648131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −87.5227 | + | 50.5313i | −0.246543 | + | 0.142342i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 39.4949 | − | 22.8024i | 0.110630 | − | 0.0638722i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 74.7043 | − | 129.392i | 0.208090 | − | 0.360423i | −0.743023 | − | 0.669266i | \(-0.766609\pi\) |
0.951113 | + | 0.308844i | \(0.0999420\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −103.424 | − | 345.868i | −0.286494 | − | 0.958082i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −275.144 | − | 158.854i | −0.757971 | − | 0.437615i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −63.6918 | − | 110.317i | −0.174498 | − | 0.302240i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 117.038 | + | 202.716i | 0.318905 | + | 0.552359i | 0.980260 | − | 0.197714i | \(-0.0633517\pi\) |
−0.661355 | + | 0.750073i | \(0.730018\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 58.0679i | 0.157366i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 478.015 | − | 275.982i | 1.28845 | − | 0.743887i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 639.738i | − | 1.71512i | −0.514387 | − | 0.857558i | \(-0.671981\pi\) | ||
0.514387 | − | 0.857558i | \(-0.328019\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −133.512 | − | 77.0835i | −0.356033 | − | 0.205556i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 54.8939 | − | 95.0790i | 0.145607 | − | 0.252199i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 108.366i | − | 0.285927i | −0.989728 | − | 0.142963i | \(-0.954337\pi\) | ||
0.989728 | − | 0.142963i | \(-0.0456631\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 395.363 | 1.03770 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −215.552 | − | 124.449i | −0.562800 | − | 0.324933i | 0.191469 | − | 0.981499i | \(-0.438675\pi\) |
−0.754268 | + | 0.656566i | \(0.772008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −51.3939 | + | 89.0168i | −0.133491 | + | 0.231212i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −67.7276 | −0.175007 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 335.560 | + | 581.207i | 0.862623 | + | 1.49411i | 0.869389 | + | 0.494129i | \(0.164513\pi\) |
−0.00676592 | + | 0.999977i | \(0.502154\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 56.8230 | 0.145327 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −292.222 | + | 168.714i | −0.743567 | + | 0.429299i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.78036 | − | 3.33729i | 0.0146338 | − | 0.00844884i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 46.6816 | − | 80.8550i | 0.117586 | − | 0.203665i | −0.801225 | − | 0.598364i | \(-0.795818\pi\) |
0.918811 | + | 0.394699i | \(0.129151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −378.712 | + | 163.288i | −0.949152 | + | 0.409243i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 242.484 | + | 139.998i | 0.604699 | + | 0.349123i | 0.770888 | − | 0.636971i | \(-0.219813\pi\) |
−0.166189 | + | 0.986094i | \(0.553146\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 267.272 | + | 462.929i | 0.663207 | + | 1.14871i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −44.1413 | − | 76.4550i | −0.108991 | − | 0.188778i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 430.878i | 1.05867i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −555.833 | + | 320.910i | −1.35900 | + | 0.784621i | −0.989490 | − | 0.144604i | \(-0.953809\pi\) |
−0.369514 | + | 0.929225i | \(0.620476\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.61037i | − | 0.0160836i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 351.272 | + | 202.807i | 0.850539 | + | 0.491059i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.651531 | − | 1.12848i | 0.00156995 | − | 0.00271924i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 99.8698i | 0.239496i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −668.879 | −1.59637 | −0.798184 | − | 0.602413i | \(-0.794206\pi\) | ||||
−0.798184 | + | 0.602413i | \(0.794206\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 433.711 | + | 250.403i | 1.03019 | + | 0.594782i | 0.917040 | − | 0.398795i | \(-0.130572\pi\) |
0.113153 | + | 0.993578i | \(0.463905\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.18725 | − | 8.98458i | 0.0122630 | − | 0.0212401i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 50.4245 | 0.118646 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.56072 | + | 13.0955i | 0.0177066 | + | 0.0306687i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 803.716 | 1.87346 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −120.553 | + | 69.6015i | −0.279706 | + | 0.161488i | −0.633290 | − | 0.773914i | \(-0.718296\pi\) |
0.353584 | + | 0.935403i | \(0.384963\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 180.349 | − | 104.125i | 0.416510 | − | 0.240472i | −0.277073 | − | 0.960849i | \(-0.589364\pi\) |
0.693583 | + | 0.720377i | \(0.256031\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.0732 | − | 17.4473i | 0.0231568 | − | 0.0401088i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −510.379 | − | 59.7381i | −1.16791 | − | 0.136700i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −65.6748 | − | 37.9173i | −0.149601 | − | 0.0863721i | 0.423331 | − | 0.905975i | \(-0.360861\pi\) |
−0.572932 | + | 0.819603i | \(0.694194\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.631120 | − | 1.09313i | −0.00143111 | − | 0.00247876i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −227.628 | − | 394.264i | −0.513834 | − | 0.889986i | −0.999871 | − | 0.0160481i | \(-0.994892\pi\) |
0.486038 | − | 0.873938i | \(-0.338442\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 6.75323i | − | 0.0151758i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 516.820 | − | 298.386i | 1.15620 | − | 0.667531i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.44993i | 0.0188194i | 0.999956 | + | 0.00940972i | \(0.00299525\pi\) | ||||
−0.999956 | + | 0.00940972i | \(0.997005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 833.438 | + | 481.186i | 1.84798 | + | 1.06693i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.5959 | − | 44.3334i | 0.0565031 | − | 0.0978663i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 118.287i | − | 0.259971i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 208.424 | 0.456071 | 0.228036 | − | 0.973653i | \(-0.426770\pi\) | ||||
0.228036 | + | 0.973653i | \(0.426770\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 46.3763 | + | 26.7754i | 0.101038 | + | 0.0583341i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 308.808 | − | 534.871i | 0.669865 | − | 1.16024i | −0.308077 | − | 0.951361i | \(-0.599685\pi\) |
0.977942 | − | 0.208878i | \(-0.0669813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −640.958 | −1.38436 | −0.692179 | − | 0.721725i | \(-0.743349\pi\) | ||||
−0.692179 | + | 0.721725i | \(0.743349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 49.0454 | + | 84.9491i | 0.105474 | + | 0.182686i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −164.111 | −0.351416 | −0.175708 | − | 0.984442i | \(-0.556221\pi\) | ||||
−0.175708 | + | 0.984442i | \(0.556221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −356.394 | + | 205.764i | −0.759902 | + | 0.438729i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 736.093 | − | 424.983i | 1.56283 | − | 0.902300i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −561.232 | + | 972.082i | −1.18654 | + | 2.05514i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −452.908 | − | 53.0114i | −0.953491 | − | 0.111603i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −62.2883 | − | 35.9621i | −0.130583 | − | 0.0753923i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 401.401 | + | 695.247i | 0.837998 | + | 1.45146i | 0.891566 | + | 0.452892i | \(0.149608\pi\) |
−0.0535671 | + | 0.998564i | \(0.517059\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −247.924 | − | 429.417i | −0.515434 | − | 0.892759i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 587.048i | 1.21542i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −114.152 | + | 65.9054i | −0.235364 | + | 0.135887i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 454.391i | 0.933041i | 0.884510 | + | 0.466521i | \(0.154493\pi\) | ||||
−0.884510 | + | 0.466521i | \(0.845507\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −426.959 | − | 246.505i | −0.873127 | − | 0.504100i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 259.826 | − | 450.031i | 0.529177 | − | 0.916561i | −0.470244 | − | 0.882536i | \(-0.655834\pi\) |
0.999421 | − | 0.0340247i | \(-0.0108325\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4534i | 0.0272889i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.3939 | 0.0270583 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 603.817 | + | 348.614i | 1.21492 | + | 0.701437i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 221.543 | − | 383.724i | 0.443974 | − | 0.768986i | −0.554006 | − | 0.832513i | \(-0.686902\pi\) |
0.997980 | + | 0.0635269i | \(0.0202349\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −283.677 | −0.566221 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −120.841 | − | 209.302i | −0.240240 | − | 0.416107i | 0.720543 | − | 0.693410i | \(-0.243893\pi\) |
−0.960782 | + | 0.277303i | \(0.910559\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.48469 | −0.0128410 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −340.510 | + | 196.593i | −0.671617 | + | 0.387758i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 357.485 | − | 206.394i | 0.702329 | − | 0.405490i | −0.105886 | − | 0.994378i | \(-0.533768\pi\) |
0.808214 | + | 0.588889i | \(0.200434\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −439.409 | + | 761.078i | −0.859900 | + | 1.48939i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −388.398 | − | 289.249i | −0.757112 | − | 0.563839i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 69.3031 | + | 40.0121i | 0.134569 | + | 0.0776935i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −85.9694 | − | 148.903i | −0.166285 | − | 0.288014i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 478.426 | + | 828.659i | 0.921823 | + | 1.59664i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 888.839i | 1.70602i | 0.521891 | + | 0.853012i | \(0.325227\pi\) | ||||
−0.521891 | + | 0.853012i | \(0.674773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −132.856 | + | 76.7047i | −0.254027 | + | 0.146663i | −0.621607 | − | 0.783329i | \(-0.713520\pi\) |
0.367580 | + | 0.929992i | \(0.380187\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 520.944i | 0.992275i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −56.7276 | − | 32.7517i | −0.107642 | − | 0.0621474i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −101.227 | + | 175.330i | −0.191355 | + | 0.331437i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 52.8541i | − | 0.0995368i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1107.48 | −2.07783 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 69.3031 | + | 40.0121i | 0.129538 | + | 0.0747890i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 495.848 | − | 858.834i | 0.923367 | − | 1.59932i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.9194 | −0.0388115 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 446.424 | + | 773.229i | 0.825183 | + | 1.42926i | 0.901779 | + | 0.432197i | \(0.142261\pi\) |
−0.0765964 | + | 0.997062i | \(0.524405\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 101.338 | 0.186627 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.2423 | + | 8.22282i | −0.0261327 | + | 0.0150877i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 748.841 | − | 432.343i | 1.36900 | − | 0.790390i | 0.378196 | − | 0.925726i | \(-0.376545\pi\) |
0.990800 | + | 0.135336i | \(0.0432113\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.985208 | − | 1.70643i | 0.00179455 | − | 0.00310825i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.1436 | − | 120.838i | 0.0256690 | − | 0.219306i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −39.8786 | − | 23.0239i | −0.0721131 | − | 0.0416345i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −45.4949 | − | 78.7995i | −0.0819728 | − | 0.141981i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −374.853 | − | 649.265i | −0.672986 | − | 1.16565i | −0.977053 | − | 0.212995i | \(-0.931678\pi\) |
0.304068 | − | 0.952650i | \(-0.401655\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1291.71i | − | 2.31076i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −85.2929 | + | 49.2439i | −0.152037 | + | 0.0877787i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 162.777i | 0.289125i | 0.989496 | + | 0.144563i | \(0.0461775\pi\) | ||||
−0.989496 | + | 0.144563i | \(0.953823\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 115.045 | + | 66.4215i | 0.203620 | + | 0.117560i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −304.530 | + | 527.462i | −0.537090 | + | 0.930267i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 296.076i | − | 0.520345i | −0.965562 | − | 0.260173i | \(-0.916221\pi\) | ||
0.965562 | − | 0.260173i | \(-0.0837795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −274.758 | −0.481188 | −0.240594 | − | 0.970626i | \(-0.577342\pi\) | ||||
−0.240594 | + | 0.970626i | \(0.577342\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 763.615 | + | 440.873i | 1.33266 | + | 0.769413i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −324.545 | + | 562.128i | −0.564426 | + | 0.977614i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 524.595 | 0.909177 | 0.454588 | − | 0.890702i | \(-0.349786\pi\) | ||||
0.454588 | + | 0.890702i | \(0.349786\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −76.3207 | − | 132.191i | −0.131815 | − | 0.228310i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.98979 | −0.0154730 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1032.32 | + | 596.008i | −1.77070 | + | 1.02231i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.3485 | + | 7.70674i | −0.0228179 | + | 0.0131739i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −375.568 | + | 650.503i | −0.639809 | + | 1.10818i | 0.345665 | + | 0.938358i | \(0.387653\pi\) |
−0.985474 | + | 0.169824i | \(0.945680\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 475.090 | + | 353.810i | 0.806604 | + | 0.600697i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −686.388 | − | 396.286i | −1.16140 | − | 0.670535i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 285.030 | + | 493.687i | 0.480658 | + | 0.832524i | 0.999754 | − | 0.0221922i | \(-0.00706458\pi\) |
−0.519096 | + | 0.854716i | \(0.673731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.24745 | + | 12.5529i | 0.0121806 | + | 0.0210974i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 816.104i | − | 1.36701i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 341.447 | − | 197.134i | 0.570028 | − | 0.329106i | −0.187133 | − | 0.982335i | \(-0.559919\pi\) |
0.757160 | + | 0.653229i | \(0.226586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 241.665i | 0.402105i | 0.979580 | + | 0.201053i | \(0.0644362\pi\) | ||||
−0.979580 | + | 0.201053i | \(0.935564\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 46.4403 | + | 26.8123i | 0.0770154 | + | 0.0444649i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 50.4898 | − | 87.4509i | 0.0834542 | − | 0.144547i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 369.224i | − | 0.608276i | −0.952628 | − | 0.304138i | \(-0.901632\pi\) | ||
0.952628 | − | 0.304138i | \(-0.0983685\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −138.990 | −0.228226 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 171.356 | + | 98.9324i | 0.280451 | + | 0.161919i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −190.171 | + | 329.386i | −0.310230 | + | 0.537334i | −0.978412 | − | 0.206664i | \(-0.933739\pi\) |
0.668182 | + | 0.743998i | \(0.267073\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −203.227 | −0.330450 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −277.869 | − | 481.283i | −0.450355 | − | 0.780037i | 0.548053 | − | 0.836444i | \(-0.315369\pi\) |
−0.998408 | + | 0.0564062i | \(0.982036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 624.152 | 1.00832 | 0.504162 | − | 0.863609i | \(-0.331802\pi\) | ||||
0.504162 | + | 0.863609i | \(0.331802\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −596.979 | + | 344.666i | −0.961319 | + | 0.555018i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −40.3485 | + | 23.2952i | −0.0647648 | + | 0.0373920i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −275.500 | + | 477.180i | −0.440800 | + | 0.763488i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 817.863 | − | 352.635i | 1.30441 | − | 0.562417i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 52.6209 | + | 30.3807i | 0.0836581 | + | 0.0483000i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.7247 | + | 74.0014i | 0.0677096 | + | 0.117276i | 0.897893 | − | 0.440214i | \(-0.145098\pi\) |
−0.830183 | + | 0.557491i | \(0.811764\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 109.444 | + | 189.563i | 0.172898 | + | 0.299468i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 125.661i | 0.197892i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.8485 | − | 12.0369i | 0.0327292 | − | 0.0188962i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 90.8531i | − | 0.142180i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 599.893 | + | 346.348i | 0.935870 | + | 0.540325i | 0.888663 | − | 0.458560i | \(-0.151635\pi\) |
0.0472069 | + | 0.998885i | \(0.484968\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −252.123 | + | 436.690i | −0.392105 | + | 0.679145i | −0.992727 | − | 0.120388i | \(-0.961586\pi\) |
0.600622 | + | 0.799533i | \(0.294920\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 237.034i | − | 0.367495i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 797.868 | 1.23318 | 0.616591 | − | 0.787284i | \(-0.288513\pi\) | ||||
0.616591 | + | 0.787284i | \(0.288513\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −758.605 | − | 437.981i | −1.16888 | − | 0.674855i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 338.363 | − | 586.062i | 0.519759 | − | 0.900249i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −651.383 | −0.997523 | −0.498762 | − | 0.866739i | \(-0.666212\pi\) | ||||
−0.498762 | + | 0.866739i | \(0.666212\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −53.6237 | − | 92.8790i | −0.0818683 | − | 0.141800i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 114.515 | 0.174300 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 395.082 | − | 228.101i | 0.599518 | − | 0.346132i | −0.169334 | − | 0.985559i | \(-0.554162\pi\) |
0.768852 | + | 0.639427i | \(0.220828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 495.696 | − | 286.190i | 0.749919 | − | 0.432966i | −0.0757457 | − | 0.997127i | \(-0.524134\pi\) |
0.825665 | + | 0.564161i | \(0.190800\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 56.6691 | − | 98.1538i | 0.0854738 | − | 0.148045i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −51.8990 | − | 120.369i | −0.0780436 | − | 0.181006i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −149.978 | − | 86.5897i | −0.224854 | − | 0.129820i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.94949 | − | 17.2330i | −0.0148722 | − | 0.0257594i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.3281 | − | 28.2810i | −0.0243339 | − | 0.0421476i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 914.574i | 1.35895i | 0.733698 | + | 0.679476i | \(0.237793\pi\) | ||||
−0.733698 | + | 0.679476i | \(0.762207\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −529.757 | + | 305.855i | −0.784825 | + | 0.453119i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 272.492i | 0.402500i | 0.979540 | + | 0.201250i | \(0.0645003\pi\) | ||||
−0.979540 | + | 0.201250i | \(0.935500\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 787.529 | + | 454.680i | 1.15984 | + | 0.669632i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 87.6867 | − | 151.878i | 0.128762 | − | 0.223022i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 164.842i | 0.241350i | 0.992692 | + | 0.120675i | \(0.0385058\pi\) | ||||
−0.992692 | + | 0.120675i | \(0.961494\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.10102 | 0.00306718 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 360.520 | + | 208.146i | 0.524774 | + | 0.302979i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 685.878 | − | 1187.98i | 0.995469 | − | 1.72420i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1040.21 | −1.50537 | −0.752685 | − | 0.658380i | \(-0.771242\pi\) | ||||
−0.752685 | + | 0.658380i | \(0.771242\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −46.2020 | − | 80.0243i | −0.0666696 | − | 0.115475i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.7423 | −0.0456724 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 117.530 | − | 67.8557i | 0.168622 | − | 0.0973540i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −609.573 | + | 351.937i | −0.872064 | + | 0.503486i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.8179 | − | 65.5024i | 0.0539484 | − | 0.0934414i | −0.837790 | − | 0.545993i | \(-0.816153\pi\) |
0.891738 | + | 0.452551i | \(0.149486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −440.697 | − | 328.197i | −0.626880 | − | 0.466852i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31.4444 | + | 18.1544i | 0.0446020 | + | 0.0257510i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.3689 | + | 38.7440i | 0.0316392 | + | 0.0548006i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 451.379 | + | 781.811i | 0.636641 | + | 1.10269i | 0.986165 | + | 0.165767i | \(0.0530101\pi\) |
−0.349524 | + | 0.936928i | \(0.613657\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.00031i | 0.00843926i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 730.226 | − | 421.596i | 1.02416 | − | 0.591299i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 255.451i | 0.357274i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −194.338 | − | 112.201i | −0.271044 | − | 0.156487i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 586.734 | − | 1016.25i | 0.816042 | − | 1.41343i | −0.0925359 | − | 0.995709i | \(-0.529497\pi\) |
0.908578 | − | 0.417716i | \(-0.137169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 552.086i | − | 0.765722i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −438.601 | −0.606640 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −133.090 | − | 76.8394i | −0.183572 | − | 0.105985i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 288.552 | − | 499.787i | 0.396908 | − | 0.687465i | −0.596434 | − | 0.802662i | \(-0.703416\pi\) |
0.993343 | + | 0.115197i | \(0.0367498\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −642.362 | −0.881155 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 79.1436 | + | 137.081i | 0.108268 | + | 0.187525i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −812.332 | −1.10823 | −0.554114 | − | 0.832441i | \(-0.686943\pi\) | ||||
−0.554114 | + | 0.832441i | \(0.686943\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.82577 | − | 2.20881i | 0.00520512 | − | 0.00300518i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 769.665 | − | 444.366i | 1.04432 | − | 0.602940i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −380.931 | + | 659.792i | −0.515469 | + | 0.892818i | 0.484370 | + | 0.874863i | \(0.339049\pi\) |
−0.999839 | + | 0.0179548i | \(0.994285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −612.186 | + | 822.032i | −0.826162 | + | 1.10936i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 118.810 | + | 68.5950i | 0.159906 | + | 0.0923216i | 0.577817 | − | 0.816166i | \(-0.303905\pi\) |
−0.417912 | + | 0.908488i | \(0.637238\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 94.8383 | + | 164.265i | 0.127300 | + | 0.220490i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.585713 | + | 1.01448i | 0.000784087 | + | 0.00135808i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 552.086i | − | 0.737097i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −95.0686 | + | 54.8879i | −0.126589 | + | 0.0730864i | −0.561957 | − | 0.827166i | \(-0.689952\pi\) |
0.435368 | + | 0.900253i | \(0.356618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 755.343i | − | 1.00311i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.0908 | + | 8.13534i | 0.0186633 | + | 0.0107753i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −133.257 | + | 230.808i | −0.176033 | + | 0.304898i | −0.940518 | − | 0.339743i | \(-0.889660\pi\) |
0.764485 | + | 0.644641i | \(0.222993\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1267.78i | − | 1.67033i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1227.85 | 1.61346 | 0.806732 | − | 0.590918i | \(-0.201234\pi\) | ||||
0.806732 | + | 0.590918i | \(0.201234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 98.2577 | + | 56.7291i | 0.128778 | + | 0.0743500i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.944387 | − | 1.63573i | 0.00123449 | − | 0.00213820i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1008.04 | 1.31427 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −334.115 | − | 578.705i | −0.434480 | − | 0.752542i | 0.562773 | − | 0.826612i | \(-0.309735\pi\) |
−0.997253 | + | 0.0740698i | \(0.976401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.4393 | −0.0394803 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −492.591 | + | 284.397i | −0.637246 | + | 0.367914i | −0.783553 | − | 0.621325i | \(-0.786595\pi\) |
0.146307 | + | 0.989239i | \(0.453261\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 648.000 | − | 374.123i | 0.836129 | − | 0.482739i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −313.868 | + | 543.636i | −0.403949 | + | 0.699660i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1126.98 | + | 485.915i | −1.44670 | + | 0.623768i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1304.00 | − | 752.864i | −1.66965 | − | 0.963975i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −81.6033 | − | 141.341i | −0.104219 | − | 0.180512i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 135.076 | + | 233.958i | 0.172071 | + | 0.298035i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 460.132i | 0.584665i | 0.956317 | + | 0.292333i | \(0.0944315\pi\) | ||||
−0.956317 | + | 0.292333i | \(0.905569\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 310.414 | − | 179.217i | 0.393427 | − | 0.227145i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 916.481i | − | 1.15864i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.5454 | + | 18.7901i | 0.0410409 | + | 0.0236950i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 125.861 | − | 217.998i | 0.158316 | − | 0.274211i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1211.02i | − | 1.51947i | −0.650234 | − | 0.759734i | \(-0.725329\pi\) | ||
0.650234 | − | 0.759734i | \(-0.274671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.2464 | −0.0303460 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.25765 | + | 3.03551i | 0.00656386 | + | 0.00378965i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 948.943 | − | 1643.62i | 1.18175 | − | 2.04685i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −186.586 | −0.231783 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 632.305 | + | 1095.18i | 0.783525 | + | 1.35711i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 914.089 | 1.12990 | 0.564950 | − | 0.825125i | \(-0.308896\pi\) | ||||
0.564950 | + | 0.825125i | \(0.308896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 403.234 | − | 232.808i | 0.497206 | − | 0.287062i | −0.230353 | − | 0.973107i | \(-0.573988\pi\) |
0.727559 | + | 0.686045i | \(0.240655\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1087.13 | + | 627.655i | −1.33718 | + | 0.772023i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 78.3485 | − | 135.704i | 0.0961331 | − | 0.166507i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −566.747 | − | 1314.45i | −0.693693 | − | 1.60887i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 92.0908 | + | 53.1687i | 0.112443 | + | 0.0649190i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.5556 | + | 84.1008i | 0.0591420 | + | 0.102437i | 0.894081 | − | 0.447906i | \(-0.147830\pi\) |
−0.834938 | + | 0.550343i | \(0.814497\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −562.052 | − | 973.502i | −0.682930 | − | 1.18287i | −0.974082 | − | 0.226193i | \(-0.927372\pi\) |
0.291152 | − | 0.956677i | \(-0.405961\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1125.03i | − | 1.36367i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 56.8722 | − | 32.8352i | 0.0687693 | − | 0.0397040i | −0.465221 | − | 0.885195i | \(-0.654025\pi\) |
0.533990 | + | 0.845491i | \(0.320692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 276.987i | 0.334121i | 0.985947 | + | 0.167061i | \(0.0534276\pi\) | ||||
−0.985947 | + | 0.167061i | \(0.946572\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1442.60 | − | 832.885i | −1.73598 | − | 1.00227i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.47500 | + | 2.55478i | −0.00177071 | + | 0.00306696i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 90.1630i | − | 0.107980i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 794.636 | 0.949386 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 159.598 | + | 92.1438i | 0.190224 | + | 0.109826i | 0.592087 | − | 0.805874i | \(-0.298304\pi\) |
−0.401864 | + | 0.915700i | \(0.631637\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −399.999 | + | 692.819i | −0.475623 | + | 0.823803i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −172.237 | −0.204315 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −62.4847 | − | 108.227i | −0.0739464 | − | 0.128079i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −696.656 | −0.822498 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 405.808 | − | 234.293i | 0.477983 | − | 0.275964i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −677.363 | + | 391.076i | −0.795962 | + | 0.459549i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 640.620 | − | 1109.59i | 0.751020 | − | 1.30081i | −0.196308 | − | 0.980542i | \(-0.562895\pi\) |
0.947329 | − | 0.320263i | \(-0.103771\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.2020 | + | 13.6991i | −0.0119322 | + | 0.0160224i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 90.2265 | + | 52.0923i | 0.105282 | + | 0.0607845i | 0.551716 | − | 0.834032i | \(-0.313973\pi\) |
−0.446435 | + | 0.894816i | \(0.647306\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −374.183 | − | 648.105i | −0.435604 | − | 0.754487i | 0.561741 | − | 0.827313i | \(-0.310132\pi\) |
−0.997345 | + | 0.0728256i | \(0.976798\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 701.030 | + | 1214.22i | 0.814204 | + | 1.41024i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.3495i | 0.0224212i | 0.999937 | + | 0.0112106i | \(0.00356852\pi\) | ||||
−0.999937 | + | 0.0112106i | \(0.996431\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −263.379 | + | 152.062i | −0.304484 | + | 0.175794i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 895.382i | − | 1.03274i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 86.1214 | + | 49.7222i | 0.0991041 | + | 0.0572178i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −511.371 | + | 885.720i | −0.587108 | + | 1.01690i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 118.495i | − | 0.135733i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −338.050 | −0.386343 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −303.060 | − | 174.972i | −0.345564 | − | 0.199512i | 0.317166 | − | 0.948370i | \(-0.397269\pi\) |
−0.662730 | + | 0.748859i | \(0.730602\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 229.182 | − | 396.954i | 0.260730 | − | 0.451598i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −449.707 | −0.510451 | −0.255225 | − | 0.966882i | \(-0.582150\pi\) | ||||
−0.255225 | + | 0.966882i | \(0.582150\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 557.532 | + | 965.674i | 0.631406 | + | 1.09363i | 0.987264 | + | 0.159088i | \(0.0508553\pi\) |
−0.355858 | + | 0.934540i | \(0.615811\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 184.980 | 0.209016 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −818.675 | + | 472.662i | −0.922970 | + | 0.532877i | −0.884581 | − | 0.466386i | \(-0.845556\pi\) |
−0.0383889 | + | 0.999263i | \(0.512223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 750.787 | − | 433.467i | 0.844529 | − | 0.487589i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 657.661 | − | 1139.10i | 0.738115 | − | 1.27845i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 217.779 | + | 25.4903i | 0.243874 | + | 0.0285446i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 272.969 | + | 157.599i | 0.304994 | + | 0.176088i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 729.474 | + | 1263.49i | 0.813237 | + | 1.40857i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 99.8173 | + | 172.889i | 0.111032 | + | 0.192312i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 168.096i | 0.186566i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1416.21 | + | 817.647i | −1.56833 | + | 0.905478i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.2091i | 0.0355901i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −617.886 | − | 356.737i | −0.681241 | − | 0.393315i | 0.119081 | − | 0.992885i | \(-0.462005\pi\) |
−0.800323 | + | 0.599570i | \(0.795338\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.91480 | − | 5.04859i | 0.00320660 | − | 0.00555400i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1490.37i | 1.63597i | 0.575242 | + | 0.817984i | \(0.304908\pi\) | ||||
−0.575242 | + | 0.817984i | \(0.695092\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.4143 | 0.0212643 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.97219 | + | 3.44805i | 0.00652699 | + | 0.00376836i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −369.949 | + | 640.770i | −0.403434 | + | 0.698768i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 543.666 | 0.591585 | 0.295792 | − | 0.955252i | \(-0.404416\pi\) | ||||
0.295792 | + | 0.955252i | \(0.404416\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 178.086 | + | 308.454i | 0.193361 | + | 0.334912i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1732.77 | 1.87732 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −601.090 | + | 347.039i | −0.649827 | + | 0.375178i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −62.3020 | + | 35.9701i | −0.0672082 | + | 0.0388027i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.2582 | + | 97.4420i | −0.0605578 | + | 0.104889i | −0.894715 | − | 0.446638i | \(-0.852621\pi\) |
0.834157 | + | 0.551527i | \(0.185955\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.9342 | − | 21.3961i | 0.0171151 | − | 0.0229819i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −287.914 | − | 166.227i | −0.308589 | − | 0.178164i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.6515 | − | 27.1092i | −0.0167396 | − | 0.0289938i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 125.894 | + | 218.055i | 0.134358 | + | 0.232716i | 0.925352 | − | 0.379109i | \(-0.123769\pi\) |
−0.790994 | + | 0.611824i | \(0.790436\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 781.034i | 0.831773i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.6520 | + | 10.7688i | −0.0198215 | + | 0.0114440i | −0.509878 | − | 0.860247i | \(-0.670309\pi\) |
0.490057 | + | 0.871691i | \(0.336976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1746.95i | 1.85254i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −152.283 | − | 87.9204i | −0.161146 | − | 0.0930375i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 314.735 | − | 545.137i | 0.332349 | − | 0.575646i | −0.650623 | − | 0.759401i | \(-0.725492\pi\) |
0.982972 | + | 0.183755i | \(0.0588253\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2184.06i | 2.30143i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 712.287 | 0.748988 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −420.863 | − | 242.986i | −0.441619 | − | 0.254969i | 0.262665 | − | 0.964887i | \(-0.415399\pi\) |
−0.704284 | + | 0.709918i | \(0.748732\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −140.126 | + | 242.705i | −0.146729 | + | 0.254142i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 300.161 | 0.313648 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.24745 | − | 12.5529i | −0.00755730 | − | 0.0130896i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0000 | −0.0114464 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −62.3020 | + | 35.9701i | −0.0646958 | + | 0.0373521i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 42.0153 | − | 24.2575i | 0.0435392 | − | 0.0251374i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 216.372 | − | 374.767i | 0.223756 | − | 0.387556i | −0.732190 | − | 0.681101i | \(-0.761502\pi\) |
0.955945 | + | 0.293545i | \(0.0948349\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.6010 | − | 124.745i | 0.0150681 | − | 0.128736i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1058.42 | + | 611.077i | 1.09003 | + | 0.629327i | 0.933584 | − | 0.358360i | \(-0.116664\pi\) |
0.156443 | + | 0.987687i | \(0.449997\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 109.495 | + | 189.651i | 0.112533 | + | 0.194913i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 647.333 | + | 1121.21i | 0.663931 | + | 1.14996i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 867.932i | − | 0.888365i | −0.895936 | − | 0.444182i | \(-0.853494\pi\) | ||
0.895936 | − | 0.444182i | \(-0.146506\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 87.1362 | − | 50.3081i | 0.0890053 | − | 0.0513873i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 14.7843i | − | 0.0150706i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −930.158 | − | 537.027i | −0.946245 | − | 0.546315i | −0.0543322 | − | 0.998523i | \(-0.517303\pi\) |
−0.891912 | + | 0.452208i | \(0.850636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 125.955 | − | 218.160i | 0.127873 | − | 0.221482i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 250.494i | − | 0.253793i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2037.55 | −2.06022 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1527.57 | + | 881.941i | 1.54144 | + | 0.889951i | 0.998748 | + | 0.0500189i | \(0.0159282\pi\) |
0.542692 | + | 0.839932i | \(0.317405\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −461.444 | + | 799.244i | −0.464697 | + | 0.804878i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 259.388 | 0.260692 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.6214 | + | 20.1289i | 0.0116564 | + | 0.0201895i | 0.871795 | − | 0.489871i | \(-0.162956\pi\) |
−0.860138 | + | 0.510061i | \(0.829623\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −737.110 | −0.737848 |
(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 | 304.3.r.a.65.1 | 4 | ||
4.3 | odd | 2 | 38.3.d.a.27.1 | ✓ | 4 | ||
12.11 | even | 2 | 342.3.m.a.217.2 | 4 | |||
19.12 | odd | 6 | inner | 304.3.r.a.145.1 | 4 | ||
76.11 | odd | 6 | 722.3.b.b.721.3 | 4 | |||
76.27 | even | 6 | 722.3.b.b.721.2 | 4 | |||
76.31 | even | 6 | 38.3.d.a.31.1 | yes | 4 | ||
228.107 | odd | 6 | 342.3.m.a.145.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.3.d.a.27.1 | ✓ | 4 | 4.3 | odd | 2 | ||
38.3.d.a.31.1 | yes | 4 | 76.31 | even | 6 | ||
304.3.r.a.65.1 | 4 | 1.1 | even | 1 | trivial | ||
304.3.r.a.145.1 | 4 | 19.12 | odd | 6 | inner | ||
342.3.m.a.145.2 | 4 | 228.107 | odd | 6 | |||
342.3.m.a.217.2 | 4 | 12.11 | even | 2 | |||
722.3.b.b.721.2 | 4 | 76.27 | even | 6 | |||
722.3.b.b.721.3 | 4 | 76.11 | odd | 6 |