Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(440,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.o (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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 440.19 | ||
Character | \(\chi\) | \(=\) | 1323.440 |
Dual form | 1323.2.o.e.881.19 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28562 | + | 0.742253i | 0.909071 | + | 0.524852i | 0.880132 | − | 0.474729i | \(-0.157454\pi\) |
0.0289389 | + | 0.999581i | \(0.490787\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.101880 | + | 0.176462i | 0.0509401 | + | 0.0882308i | ||||
\(5\) | −0.154215 | − | 0.267109i | −0.0689672 | − | 0.119455i | 0.829480 | − | 0.558537i | \(-0.188637\pi\) |
−0.898447 | + | 0.439082i | \(0.855304\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.66653i | − | 0.942761i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 0.457868i | − | 0.144790i | ||||||
\(11\) | 2.73879 | + | 1.58124i | 0.825775 | + | 0.476761i | 0.852404 | − | 0.522884i | \(-0.175144\pi\) |
−0.0266288 | + | 0.999645i | \(0.508477\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00394 | + | 1.73432i | −0.833143 | + | 0.481015i | −0.854927 | − | 0.518748i | \(-0.826398\pi\) |
0.0217849 | + | 0.999763i | \(0.493065\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.18300 | − | 3.78107i | 0.545750 | − | 0.945267i | ||||
\(17\) | 4.88248 | 1.18418 | 0.592088 | − | 0.805873i | \(-0.298304\pi\) | ||||
0.592088 | + | 0.805873i | \(0.298304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.34116i | − | 1.22535i | −0.790336 | − | 0.612673i | \(-0.790094\pi\) | ||
0.790336 | − | 0.612673i | \(-0.209906\pi\) | |||||||
\(20\) | 0.0314230 | − | 0.0544262i | 0.00702639 | − | 0.0121701i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.34736 | + | 4.06575i | 0.500459 | + | 0.866820i | ||||
\(23\) | 5.17269 | − | 2.98645i | 1.07858 | − | 0.622719i | 0.148067 | − | 0.988977i | \(-0.452695\pi\) |
0.930513 | + | 0.366259i | \(0.119361\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.45244 | − | 4.24774i | 0.490487 | − | 0.849548i | ||||
\(26\) | −5.14923 | −1.00985 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.70372 | − | 1.56099i | −0.502069 | − | 0.289869i | 0.227499 | − | 0.973778i | \(-0.426945\pi\) |
−0.729567 | + | 0.683909i | \(0.760279\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.51414 | + | 3.76094i | −1.16997 | + | 0.675485i | −0.953674 | − | 0.300842i | \(-0.902732\pi\) |
−0.216300 | + | 0.976327i | \(0.569399\pi\) | |||||||
\(32\) | 0.994457 | − | 0.574150i | 0.175797 | − | 0.101496i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.27702 | + | 3.62404i | 1.07650 | + | 0.621518i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.8514 | 1.94835 | 0.974176 | − | 0.225788i | \(-0.0724957\pi\) | ||||
0.974176 | + | 0.225788i | \(0.0724957\pi\) | |||||||
\(38\) | 3.96450 | − | 6.86671i | 0.643126 | − | 1.11393i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.712254 | + | 0.411220i | −0.112617 | + | 0.0650196i | ||||
\(41\) | 2.58920 | + | 4.48462i | 0.404365 | + | 0.700380i | 0.994247 | − | 0.107109i | \(-0.0341593\pi\) |
−0.589883 | + | 0.807489i | \(0.700826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.75159 | − | 4.76589i | 0.419613 | − | 0.726792i | −0.576287 | − | 0.817247i | \(-0.695499\pi\) |
0.995900 | + | 0.0904557i | \(0.0288323\pi\) | |||||||
\(44\) | 0.644388i | 0.0971451i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.86682 | 1.30734 | ||||||||
\(47\) | 4.23198 | − | 7.33000i | 0.617298 | − | 1.06919i | −0.372679 | − | 0.927960i | \(-0.621561\pi\) |
0.989977 | − | 0.141231i | \(-0.0451059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.30580 | − | 3.64066i | 0.891775 | − | 0.514867i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.612084 | − | 0.353387i | −0.0848807 | − | 0.0490059i | ||||
\(53\) | 0.0855080i | 0.0117454i | 0.999983 | + | 0.00587272i | \(0.00186935\pi\) | ||||
−0.999983 | + | 0.00587272i | \(0.998131\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.975406i | − | 0.131524i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.31731 | − | 4.01369i | −0.304277 | − | 0.527024i | ||||
\(59\) | −1.04433 | − | 1.80884i | −0.135960 | − | 0.235490i | 0.790004 | − | 0.613102i | \(-0.210079\pi\) |
−0.925964 | + | 0.377612i | \(0.876745\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.69964 | − | 2.71334i | −0.601727 | − | 0.347407i | 0.167994 | − | 0.985788i | \(-0.446271\pi\) |
−0.769721 | + | 0.638381i | \(0.779604\pi\) | |||||||
\(62\) | −11.1663 | −1.41812 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.02734 | −0.878418 | ||||||||
\(65\) | 0.926507 | + | 0.534919i | 0.114919 | + | 0.0663485i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.0554134 | + | 0.0959787i | 0.00676982 | + | 0.0117257i | 0.869390 | − | 0.494126i | \(-0.164512\pi\) |
−0.862621 | + | 0.505851i | \(0.831178\pi\) | |||||||
\(68\) | 0.497429 | + | 0.861572i | 0.0603221 | + | 0.104481i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.78899i | 0.924384i | 0.886780 | + | 0.462192i | \(0.152937\pi\) | ||||
−0.886780 | + | 0.462192i | \(0.847063\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.61495i | − | 1.12534i | −0.826680 | − | 0.562672i | \(-0.809773\pi\) | ||
0.826680 | − | 0.562672i | \(-0.190227\pi\) | |||||||
\(74\) | 15.2364 | + | 8.79672i | 1.77119 | + | 1.02260i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.942510 | − | 0.544159i | 0.108113 | − | 0.0624193i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.56825 | + | 4.44834i | −0.288951 | + | 0.500477i | −0.973560 | − | 0.228433i | \(-0.926640\pi\) |
0.684609 | + | 0.728911i | \(0.259973\pi\) | |||||||
\(80\) | −1.34661 | −0.150556 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.68736i | 0.848927i | ||||||||
\(83\) | −4.42464 | + | 7.66370i | −0.485667 | + | 0.841201i | −0.999864 | − | 0.0164715i | \(-0.994757\pi\) |
0.514197 | + | 0.857672i | \(0.328090\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.752954 | − | 1.30416i | −0.0816694 | − | 0.141455i | ||||
\(86\) | 7.07500 | − | 4.08475i | 0.762917 | − | 0.440470i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.21642 | − | 7.30306i | 0.449472 | − | 0.778508i | ||||
\(89\) | 1.87377 | 0.198619 | 0.0993096 | − | 0.995057i | \(-0.468337\pi\) | ||||
0.0993096 | + | 0.995057i | \(0.468337\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.05399 | + | 0.608521i | 0.109886 | + | 0.0634427i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.8814 | − | 6.28240i | 1.12233 | − | 0.647980i | ||||
\(95\) | −1.42667 | + | 0.823689i | −0.146373 | + | 0.0845087i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9813 | + | 6.34007i | 1.11498 | + | 0.643736i | 0.940116 | − | 0.340855i | \(-0.110717\pi\) |
0.174868 | + | 0.984592i | \(0.444050\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.999418 | 0.0999418 | ||||||||
\(101\) | −3.68322 | + | 6.37952i | −0.366494 | + | 0.634786i | −0.989015 | − | 0.147817i | \(-0.952775\pi\) |
0.622521 | + | 0.782603i | \(0.286109\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.91120 | − | 3.99019i | 0.680981 | − | 0.393165i | −0.119244 | − | 0.992865i | \(-0.538047\pi\) |
0.800225 | + | 0.599700i | \(0.204714\pi\) | |||||||
\(104\) | 4.62463 | + | 8.01009i | 0.453482 | + | 0.785454i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0634686 | + | 0.109931i | −0.00616462 | + | 0.0106774i | ||||
\(107\) | 16.7694i | 1.62116i | 0.585625 | + | 0.810582i | \(0.300849\pi\) | ||||
−0.585625 | + | 0.810582i | \(0.699151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.86509 | −0.849122 | −0.424561 | − | 0.905399i | \(-0.639572\pi\) | ||||
−0.424561 | + | 0.905399i | \(0.639572\pi\) | |||||||
\(110\) | 0.723998 | − | 1.25400i | 0.0690305 | − | 0.119564i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.5621 | + | 7.83007i | −1.27581 | + | 0.736591i | −0.976076 | − | 0.217430i | \(-0.930233\pi\) |
−0.299738 | + | 0.954022i | \(0.596899\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.59542 | − | 0.921114i | −0.148773 | − | 0.0858943i | ||||
\(116\) | − | 0.636138i | − | 0.0590639i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 3.10063i | − | 0.285437i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.499366 | − | 0.864928i | −0.0453969 | − | 0.0786298i | ||||
\(122\) | −4.02797 | − | 6.97664i | −0.364675 | − | 0.631635i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.32732 | − | 0.766330i | −0.119197 | − | 0.0688185i | ||||
\(125\) | −3.05497 | −0.273245 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.78064 | −0.601685 | −0.300842 | − | 0.953674i | \(-0.597268\pi\) | ||||
−0.300842 | + | 0.953674i | \(0.597268\pi\) | |||||||
\(128\) | −11.0234 | − | 6.36437i | −0.974341 | − | 0.562536i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.794091 | + | 1.37541i | 0.0696464 | + | 0.120631i | ||||
\(131\) | 9.77105 | + | 16.9240i | 0.853701 | + | 1.47865i | 0.877845 | + | 0.478944i | \(0.158980\pi\) |
−0.0241447 | + | 0.999708i | \(0.507686\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.164523i | 0.0142126i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 13.0193i | − | 1.11640i | ||||||
\(137\) | 1.37570 | + | 0.794262i | 0.117534 | + | 0.0678584i | 0.557615 | − | 0.830100i | \(-0.311717\pi\) |
−0.440080 | + | 0.897958i | \(0.645050\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.97274 | + | 2.29366i | −0.336963 | + | 0.194546i | −0.658928 | − | 0.752206i | \(-0.728990\pi\) |
0.321965 | + | 0.946752i | \(0.395657\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.78141 | + | 10.0137i | −0.485165 | + | 0.840330i | ||||
\(143\) | −10.9695 | −0.917318 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.962918i | 0.0799660i | ||||||||
\(146\) | 7.13673 | − | 12.3612i | 0.590640 | − | 1.02302i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.20742 | + | 2.09131i | 0.0992493 | + | 0.171905i | ||||
\(149\) | −8.42966 | + | 4.86686i | −0.690584 | + | 0.398709i | −0.803831 | − | 0.594858i | \(-0.797208\pi\) |
0.113247 | + | 0.993567i | \(0.463875\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.00916 | − | 5.21203i | 0.244882 | − | 0.424149i | −0.717216 | − | 0.696851i | \(-0.754584\pi\) |
0.962099 | + | 0.272702i | \(0.0879173\pi\) | |||||||
\(152\) | −14.2424 | −1.15521 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00916 | + | 1.15999i | 0.161380 | + | 0.0931726i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1600 | + | 8.17531i | −1.13009 | + | 0.652461i | −0.943959 | − | 0.330063i | \(-0.892930\pi\) |
−0.186136 | + | 0.982524i | \(0.559597\pi\) | |||||||
\(158\) | −6.60359 | + | 3.81258i | −0.525353 | + | 0.303313i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.306721 | − | 0.177086i | −0.0242484 | − | 0.0139998i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.46471 | −0.506355 | −0.253177 | − | 0.967420i | \(-0.581476\pi\) | ||||
−0.253177 | + | 0.967420i | \(0.581476\pi\) | |||||||
\(164\) | −0.527576 | + | 0.913788i | −0.0411968 | + | 0.0713549i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.3768 | + | 6.56841i | −0.883012 | + | 0.509807i | ||||
\(167\) | 1.33556 | + | 2.31325i | 0.103348 | + | 0.179005i | 0.913062 | − | 0.407820i | \(-0.133711\pi\) |
−0.809714 | + | 0.586825i | \(0.800378\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.484236 | + | 0.838722i | −0.0372489 | + | 0.0645171i | ||||
\(170\) | − | 2.23553i | − | 0.171457i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.12133 | 0.0855006 | ||||||||
\(173\) | 10.0983 | − | 17.4908i | 0.767760 | − | 1.32980i | −0.171015 | − | 0.985268i | \(-0.554705\pi\) |
0.938775 | − | 0.344531i | \(-0.111962\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.9575 | − | 6.90369i | 0.901334 | − | 0.520385i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.40896 | + | 1.39081i | 0.180559 | + | 0.104246i | ||||
\(179\) | − | 21.9622i | − | 1.64153i | −0.571266 | − | 0.820765i | \(-0.693548\pi\) | ||
0.571266 | − | 0.820765i | \(-0.306452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.50569i | − | 0.186246i | −0.995655 | − | 0.0931232i | \(-0.970315\pi\) | ||
0.995655 | − | 0.0931232i | \(-0.0296850\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.96347 | − | 13.7931i | −0.587075 | − | 1.01684i | ||||
\(185\) | −1.82766 | − | 3.16561i | −0.134372 | − | 0.232740i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.3721 | + | 7.72038i | 0.977864 | + | 0.564570i | ||||
\(188\) | 1.72462 | 0.125781 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.44554 | −0.177418 | ||||||||
\(191\) | 1.82276 | + | 1.05237i | 0.131891 | + | 0.0761470i | 0.564494 | − | 0.825437i | \(-0.309071\pi\) |
−0.432603 | + | 0.901584i | \(0.642405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.97730 | + | 5.15683i | 0.214311 | + | 0.371197i | 0.953059 | − | 0.302784i | \(-0.0979162\pi\) |
−0.738748 | + | 0.673981i | \(0.764583\pi\) | |||||||
\(194\) | 9.41187 | + | 16.3018i | 0.675733 | + | 1.17040i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.64511i | 0.544692i | 0.962199 | + | 0.272346i | \(0.0877995\pi\) | ||||
−0.962199 | + | 0.272346i | \(0.912200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.85193i | 0.485720i | 0.970061 | + | 0.242860i | \(0.0780856\pi\) | ||||
−0.970061 | + | 0.242860i | \(0.921914\pi\) | |||||||
\(200\) | −11.3267 | − | 6.53949i | −0.800921 | − | 0.462412i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.47044 | + | 5.46776i | −0.666338 | + | 0.384710i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.798588 | − | 1.38320i | 0.0557758 | − | 0.0966066i | ||||
\(206\) | 11.8469 | 0.825414 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.1441i | 1.05006i | ||||||||
\(209\) | 8.44565 | − | 14.6283i | 0.584198 | − | 1.01186i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.74784 | − | 4.75940i | −0.189169 | − | 0.327651i | 0.755804 | − | 0.654798i | \(-0.227246\pi\) |
−0.944974 | + | 0.327147i | \(0.893913\pi\) | |||||||
\(212\) | −0.0150889 | + | 0.00871157i | −0.00103631 | + | 0.000598313i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.4472 | + | 21.5591i | −0.850872 | + | 1.47375i | ||||
\(215\) | −1.69735 | −0.115758 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.3971 | − | 6.58015i | −0.771912 | − | 0.445664i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.172122 | − | 0.0993745i | 0.0116044 | − | 0.00669983i | ||||
\(221\) | −14.6667 | + | 8.46781i | −0.986588 | + | 0.569607i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.6080 | − | 10.1660i | −1.17912 | − | 0.680764i | −0.223307 | − | 0.974748i | \(-0.571685\pi\) |
−0.955810 | + | 0.293985i | \(0.905019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.2476 | −1.54641 | ||||||||
\(227\) | 0.161235 | − | 0.279268i | 0.0107016 | − | 0.0185356i | −0.860625 | − | 0.509239i | \(-0.829927\pi\) |
0.871327 | + | 0.490704i | \(0.163260\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.30171 | − | 1.32889i | 0.152101 | − | 0.0878157i | −0.422018 | − | 0.906588i | \(-0.638678\pi\) |
0.574119 | + | 0.818772i | \(0.305345\pi\) | |||||||
\(230\) | −1.36740 | − | 2.36841i | −0.0901637 | − | 0.156168i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.16244 | + | 7.20956i | −0.273278 | + | 0.473331i | ||||
\(233\) | 23.2575i | 1.52365i | 0.647785 | + | 0.761823i | \(0.275696\pi\) | ||||
−0.647785 | + | 0.761823i | \(0.724304\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.61055 | −0.170293 | ||||||||
\(236\) | 0.212793 | − | 0.368569i | 0.0138517 | − | 0.0239918i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.291265 | − | 0.168162i | 0.0188404 | − | 0.0108775i | −0.490550 | − | 0.871413i | \(-0.663204\pi\) |
0.509391 | + | 0.860535i | \(0.329871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.1846 | + | 11.0762i | 1.23579 | + | 0.713483i | 0.968231 | − | 0.250059i | \(-0.0804500\pi\) |
0.267558 | + | 0.963542i | \(0.413783\pi\) | |||||||
\(242\) | − | 1.48263i | − | 0.0953068i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1.10574i | − | 0.0707878i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.26331 | + | 16.0445i | 0.589410 | + | 1.02089i | ||||
\(248\) | 10.0287 | + | 17.3701i | 0.636820 | + | 1.10301i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.92753 | − | 2.26756i | −0.248399 | − | 0.143413i | ||||
\(251\) | 13.9800 | 0.882409 | 0.441205 | − | 0.897407i | \(-0.354551\pi\) | ||||
0.441205 | + | 0.897407i | \(0.354551\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.8892 | 1.18755 | ||||||||
\(254\) | −8.71734 | − | 5.03296i | −0.546974 | − | 0.315796i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.42061 | − | 4.19261i | −0.151288 | − | 0.262038i | ||||
\(257\) | −9.69064 | − | 16.7847i | −0.604486 | − | 1.04700i | −0.992133 | − | 0.125192i | \(-0.960045\pi\) |
0.387647 | − | 0.921808i | \(-0.373288\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.217991i | 0.0135192i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 29.0104i | 1.79227i | ||||||||
\(263\) | −4.40776 | − | 2.54482i | −0.271794 | − | 0.156920i | 0.357909 | − | 0.933757i | \(-0.383490\pi\) |
−0.629703 | + | 0.776836i | \(0.716823\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0228400 | − | 0.0131867i | 0.00140305 | − | 0.000810050i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.0112910 | + | 0.0195567i | −0.000689710 | + | 0.00119461i | ||||
\(269\) | −5.05601 | −0.308270 | −0.154135 | − | 0.988050i | \(-0.549259\pi\) | ||||
−0.154135 | + | 0.988050i | \(0.549259\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 31.3809i | − | 1.90626i | −0.302567 | − | 0.953128i | \(-0.597844\pi\) | ||
0.302567 | − | 0.953128i | \(-0.402156\pi\) | |||||||
\(272\) | 10.6585 | − | 18.4610i | 0.646265 | − | 1.11936i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.17909 | + | 2.04224i | 0.0712313 | + | 0.123376i | ||||
\(275\) | 13.4334 | − | 7.75577i | 0.810064 | − | 0.467691i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0279 | + | 22.5650i | −0.782771 | + | 1.35580i | 0.147551 | + | 0.989054i | \(0.452861\pi\) |
−0.930322 | + | 0.366744i | \(0.880473\pi\) | |||||||
\(278\) | −6.80991 | −0.408431 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.14335 | + | 2.39217i | 0.247172 | + | 0.142705i | 0.618469 | − | 0.785810i | \(-0.287753\pi\) |
−0.371297 | + | 0.928514i | \(0.621087\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.927241 | + | 0.535343i | −0.0551188 | + | 0.0318228i | −0.527306 | − | 0.849675i | \(-0.676798\pi\) |
0.472187 | + | 0.881498i | \(0.343465\pi\) | |||||||
\(284\) | −1.37446 | + | 0.793544i | −0.0815591 | + | 0.0470882i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.1026 | − | 8.14217i | −0.833907 | − | 0.481457i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.83866 | 0.402274 | ||||||||
\(290\) | −0.714729 | + | 1.23795i | −0.0419703 | + | 0.0726947i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.69667 | − | 0.979573i | 0.0992901 | − | 0.0573252i | ||||
\(293\) | −1.36267 | − | 2.36021i | −0.0796079 | − | 0.137885i | 0.823473 | − | 0.567356i | \(-0.192033\pi\) |
−0.903081 | + | 0.429471i | \(0.858700\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.322104 | + | 0.557900i | −0.0187536 | + | 0.0324822i | ||||
\(296\) | − | 31.6020i | − | 1.83683i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.4498 | −0.837054 | ||||||||
\(299\) | −10.3590 | + | 17.9422i | −0.599074 | + | 1.03763i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.73729 | − | 4.46713i | 0.445231 | − | 0.257054i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.1953 | − | 11.6598i | −1.15828 | − | 0.668733i | ||||
\(305\) | 1.67375i | 0.0958388i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.31294i | − | 0.474444i | −0.971455 | − | 0.237222i | \(-0.923763\pi\) | ||
0.971455 | − | 0.237222i | \(-0.0762369\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.72201 | + | 2.98261i | 0.0978037 | + | 0.169401i | ||||
\(311\) | 3.00023 | + | 5.19656i | 0.170128 | + | 0.294670i | 0.938464 | − | 0.345376i | \(-0.112249\pi\) |
−0.768337 | + | 0.640046i | \(0.778915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2410 | + | 5.91263i | 0.578854 | + | 0.334201i | 0.760678 | − | 0.649130i | \(-0.224867\pi\) |
−0.181824 | + | 0.983331i | \(0.558200\pi\) | |||||||
\(314\) | −24.2726 | −1.36978 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.04662 | −0.0588767 | ||||||||
\(317\) | −25.6726 | − | 14.8221i | −1.44192 | − | 0.832491i | −0.443940 | − | 0.896057i | \(-0.646420\pi\) |
−0.997978 | + | 0.0635652i | \(0.979753\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.93661 | − | 8.55046i | −0.276397 | − | 0.478734i | ||||
\(320\) | 1.08372 | + | 1.87707i | 0.0605821 | + | 0.104931i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 26.0781i | − | 1.45103i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.0133i | 0.943727i | ||||||||
\(326\) | −8.31116 | − | 4.79845i | −0.460313 | − | 0.265762i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.9584 | − | 6.90417i | 0.660291 | − | 0.381219i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.52504 | − | 14.7658i | 0.468579 | − | 0.811602i | −0.530776 | − | 0.847512i | \(-0.678100\pi\) |
0.999355 | + | 0.0359097i | \(0.0114329\pi\) | |||||||
\(332\) | −1.80313 | −0.0989598 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.96529i | 0.216971i | ||||||||
\(335\) | 0.0170912 | − | 0.0296028i | 0.000933791 | − | 0.00161737i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.1065 | + | 17.5050i | 0.550536 | + | 0.953556i | 0.998236 | + | 0.0593723i | \(0.0189099\pi\) |
−0.447700 | + | 0.894184i | \(0.647757\pi\) | |||||||
\(338\) | −1.24509 | + | 0.718852i | −0.0677239 | + | 0.0391004i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.153422 | − | 0.265735i | 0.00832049 | − | 0.0144115i | ||||
\(341\) | −23.7878 | −1.28818 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12.7084 | − | 7.33719i | −0.685191 | − | 0.395595i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.9652 | − | 14.9910i | 1.39590 | − | 0.805921i | ||||
\(347\) | −15.3128 | + | 8.84086i | −0.822036 | + | 0.474602i | −0.851118 | − | 0.524975i | \(-0.824075\pi\) |
0.0290824 | + | 0.999577i | \(0.490741\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.62628 | − | 2.09363i | −0.194110 | − | 0.112070i | 0.399795 | − | 0.916605i | \(-0.369081\pi\) |
−0.593905 | + | 0.804535i | \(0.702415\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.63148 | 0.193558 | ||||||||
\(353\) | −15.2477 | + | 26.4097i | −0.811551 | + | 1.40565i | 0.100227 | + | 0.994965i | \(0.468043\pi\) |
−0.911778 | + | 0.410684i | \(0.865290\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.08051 | − | 1.20118i | 0.110422 | − | 0.0637522i | ||||
\(356\) | 0.190900 | + | 0.330649i | 0.0101177 | + | 0.0175243i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.3015 | − | 28.2350i | 0.861561 | − | 1.49227i | ||||
\(359\) | − | 5.39131i | − | 0.284542i | −0.989828 | − | 0.142271i | \(-0.954559\pi\) | ||
0.989828 | − | 0.142271i | \(-0.0454405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.52801 | −0.501474 | ||||||||
\(362\) | 1.85986 | − | 3.22137i | 0.0977519 | − | 0.169311i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.56824 | + | 1.48277i | −0.134428 | + | 0.0776119i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3218 | + | 10.0007i | 0.904188 | + | 0.522033i | 0.878557 | − | 0.477638i | \(-0.158507\pi\) |
0.0256317 | + | 0.999671i | \(0.491840\pi\) | |||||||
\(368\) | − | 26.0777i | − | 1.35940i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 5.42636i | − | 0.282103i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0474 | + | 22.5988i | 0.675571 | + | 1.17012i | 0.976302 | + | 0.216414i | \(0.0694363\pi\) |
−0.300730 | + | 0.953709i | \(0.597230\pi\) | |||||||
\(374\) | 11.4609 | + | 19.8509i | 0.592632 | + | 1.02647i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.5457 | − | 11.2847i | −1.00799 | − | 0.581964i | ||||
\(377\) | 10.8291 | 0.557726 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.5222 | 1.56782 | 0.783910 | − | 0.620875i | \(-0.213222\pi\) | ||||
0.783910 | + | 0.620875i | \(0.213222\pi\) | |||||||
\(380\) | −0.290699 | − | 0.167835i | −0.0149126 | − | 0.00860977i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.56225 | + | 2.70590i | 0.0799319 | + | 0.138446i | ||||
\(383\) | 11.3543 | + | 19.6662i | 0.580177 | + | 1.00490i | 0.995458 | + | 0.0952034i | \(0.0303501\pi\) |
−0.415280 | + | 0.909693i | \(0.636317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.83964i | 0.449926i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.58371i | 0.131168i | ||||||||
\(389\) | 3.89121 | + | 2.24659i | 0.197292 | + | 0.113907i | 0.595392 | − | 0.803436i | \(-0.296997\pi\) |
−0.398100 | + | 0.917342i | \(0.630330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.2556 | − | 14.5813i | 1.27723 | − | 0.737409i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.67461 | + | 9.82872i | −0.285883 | + | 0.495164i | ||||
\(395\) | 1.58425 | 0.0797125 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.65161i | 0.484400i | 0.970226 | + | 0.242200i | \(0.0778691\pi\) | ||||
−0.970226 | + | 0.242200i | \(0.922131\pi\) | |||||||
\(398\) | −5.08587 | + | 8.80898i | −0.254931 | + | 0.441554i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.7073 | − | 18.5457i | −0.535367 | − | 0.927283i | ||||
\(401\) | 17.2356 | − | 9.95098i | 0.860705 | − | 0.496928i | −0.00354346 | − | 0.999994i | \(-0.501128\pi\) |
0.864248 | + | 0.503066i | \(0.167795\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0454 | − | 22.5953i | 0.649837 | − | 1.12555i | ||||
\(404\) | −1.50099 | −0.0746769 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.4584 | + | 18.7398i | 1.60890 | + | 0.928900i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.10072 | − | 1.21285i | 0.103874 | − | 0.0599718i | −0.447163 | − | 0.894453i | \(-0.647566\pi\) |
0.551037 | + | 0.834481i | \(0.314232\pi\) | |||||||
\(410\) | 2.05336 | − | 1.18551i | 0.101408 | − | 0.0585482i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.40823 | + | 0.813042i | 0.0693785 | + | 0.0400557i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.72939 | 0.133981 | ||||||||
\(416\) | −1.99153 | + | 3.44942i | −0.0976426 | + | 0.169122i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 21.7158 | − | 12.5376i | 1.06216 | − | 0.613236i | ||||
\(419\) | −14.6878 | − | 25.4399i | −0.717544 | − | 1.24282i | −0.961970 | − | 0.273155i | \(-0.911933\pi\) |
0.244426 | − | 0.969668i | \(-0.421400\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.2078 | + | 31.5368i | −0.887392 | + | 1.53701i | −0.0444443 | + | 0.999012i | \(0.514152\pi\) |
−0.842948 | + | 0.537996i | \(0.819182\pi\) | |||||||
\(422\) | − | 8.15838i | − | 0.397144i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.228010 | 0.0110731 | ||||||||
\(425\) | 11.9740 | − | 20.7395i | 0.580823 | − | 1.00602i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.95916 | + | 1.70847i | −0.143037 | + | 0.0825822i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.18215 | − | 1.25986i | −0.105232 | − | 0.0607560i | ||||
\(431\) | 19.4520i | 0.936968i | 0.883472 | + | 0.468484i | \(0.155200\pi\) | ||||
−0.883472 | + | 0.468484i | \(0.844800\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.94623i | 0.477985i | 0.971021 | + | 0.238993i | \(0.0768172\pi\) | ||||
−0.971021 | + | 0.238993i | \(0.923183\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.903178 | − | 1.56435i | −0.0432544 | − | 0.0749188i | ||||
\(437\) | −15.9511 | − | 27.6282i | −0.763046 | − | 1.32163i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.38746 | − | 3.68780i | −0.304857 | − | 0.176009i | 0.339766 | − | 0.940510i | \(-0.389652\pi\) |
−0.644623 | + | 0.764501i | \(0.722986\pi\) | |||||||
\(440\) | −2.60095 | −0.123995 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −25.1411 | −1.19584 | ||||||||
\(443\) | −0.744629 | − | 0.429911i | −0.0353784 | − | 0.0204257i | 0.482207 | − | 0.876058i | \(-0.339835\pi\) |
−0.517585 | + | 0.855632i | \(0.673169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.288964 | − | 0.500501i | −0.0136982 | − | 0.0237260i | ||||
\(446\) | −15.0914 | − | 26.1392i | −0.714601 | − | 1.23772i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.6497i | 0.738556i | 0.929319 | + | 0.369278i | \(0.120395\pi\) | ||||
−0.929319 | + | 0.369278i | \(0.879605\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.3766i | 0.771142i | ||||||||
\(452\) | −2.76342 | − | 1.59546i | −0.129980 | − | 0.0750441i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.414575 | − | 0.239355i | 0.0194570 | − | 0.0112335i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.81559 | − | 4.87675i | 0.131708 | − | 0.228125i | −0.792627 | − | 0.609707i | \(-0.791287\pi\) |
0.924335 | + | 0.381582i | \(0.124621\pi\) | |||||||
\(458\) | 3.94550 | 0.184361 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 0.375373i | − | 0.0175019i | ||||||
\(461\) | −11.3342 | + | 19.6314i | −0.527886 | + | 0.914326i | 0.471585 | + | 0.881821i | \(0.343682\pi\) |
−0.999472 | + | 0.0325056i | \(0.989651\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0052 | − | 36.3821i | −0.976194 | − | 1.69082i | −0.675937 | − | 0.736960i | \(-0.736261\pi\) |
−0.300257 | − | 0.953858i | \(-0.597073\pi\) | |||||||
\(464\) | −11.8045 | + | 6.81531i | −0.548008 | + | 0.316393i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.2629 | + | 29.9003i | −0.799690 | + | 1.38510i | ||||
\(467\) | 24.8033 | 1.14776 | 0.573879 | − | 0.818940i | \(-0.305438\pi\) | ||||
0.573879 | + | 0.818940i | \(0.305438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.35617 | − | 1.93769i | −0.154809 | − | 0.0893788i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.82331 | + | 2.78474i | −0.222011 | + | 0.128178i | ||||
\(473\) | 15.0720 | − | 8.70184i | 0.693013 | − | 0.400111i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.6879 | − | 13.0989i | −1.04099 | − | 0.601017i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.499275 | 0.0228363 | ||||||||
\(479\) | 1.64647 | − | 2.85177i | 0.0752291 | − | 0.130301i | −0.825957 | − | 0.563733i | \(-0.809365\pi\) |
0.901186 | + | 0.433433i | \(0.142698\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.6008 | + | 20.5541i | −1.62326 | + | 0.937187i | ||||
\(482\) | 16.4427 | + | 28.4797i | 0.748946 | + | 1.29721i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.101751 | − | 0.176238i | 0.00462505 | − | 0.00801082i | ||||
\(485\) | − | 3.91094i | − | 0.177587i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.4448 | 0.473299 | 0.236650 | − | 0.971595i | \(-0.423951\pi\) | ||||
0.236650 | + | 0.971595i | \(0.423951\pi\) | |||||||
\(488\) | −7.23519 | + | 12.5317i | −0.327522 | + | 0.567284i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.2797 | − | 15.1726i | 1.18599 | − | 0.684731i | 0.228596 | − | 0.973521i | \(-0.426587\pi\) |
0.957392 | + | 0.288791i | \(0.0932532\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.2009 | − | 7.62153i | −0.594538 | − | 0.343257i | ||||
\(494\) | 27.5029i | 1.23741i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.8405i | 1.47458i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.984757 | − | 1.70565i | −0.0440838 | − | 0.0763554i | 0.843142 | − | 0.537692i | \(-0.180704\pi\) |
−0.887225 | + | 0.461336i | \(0.847370\pi\) | |||||||
\(500\) | −0.311241 | − | 0.539085i | −0.0139191 | − | 0.0241086i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.9730 | + | 10.3767i | 0.802173 | + | 0.463135i | ||||
\(503\) | −17.3024 | −0.771477 | −0.385739 | − | 0.922608i | \(-0.626053\pi\) | ||||
−0.385739 | + | 0.922608i | \(0.626053\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.27203 | 0.101104 | ||||||||
\(506\) | 24.2843 | + | 14.0206i | 1.07957 | + | 0.623290i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.690813 | − | 1.19652i | −0.0306499 | − | 0.0530872i | ||||
\(509\) | −0.240892 | − | 0.417237i | −0.0106774 | − | 0.0184937i | 0.860637 | − | 0.509218i | \(-0.170065\pi\) |
−0.871315 | + | 0.490725i | \(0.836732\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.2707i | 0.807457i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 28.7717i | − | 1.26906i | ||||||
\(515\) | −2.13163 | − | 1.23070i | −0.0939307 | − | 0.0542309i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.1810 | − | 13.3835i | 1.01950 | − | 0.588607i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.42638 | − | 2.47056i | 0.0625508 | − | 0.108341i | ||||
\(521\) | 14.4154 | 0.631550 | 0.315775 | − | 0.948834i | \(-0.397735\pi\) | ||||
0.315775 | + | 0.948834i | \(0.397735\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.81956i | 0.298198i | 0.988822 | + | 0.149099i | \(0.0476374\pi\) | ||||
−0.988822 | + | 0.149099i | \(0.952363\pi\) | |||||||
\(524\) | −1.99095 | + | 3.44843i | −0.0869752 | + | 0.150645i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.77780 | − | 6.54334i | −0.164720 | − | 0.285303i | ||||
\(527\) | −31.8052 | + | 18.3627i | −1.38546 | + | 0.799893i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.33781 | − | 10.9774i | 0.275557 | − | 0.477278i | ||||
\(530\) | 0.0391514 | 0.00170063 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.5556 | − | 8.98102i | −0.673787 | − | 0.389011i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.47927 | − | 2.58611i | 0.193656 | − | 0.111807i | ||||
\(536\) | 0.255930 | − | 0.147761i | 0.0110545 | − | 0.00638232i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.50011 | − | 3.75284i | −0.280240 | − | 0.161796i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.8226 | −0.766252 | −0.383126 | − | 0.923696i | \(-0.625153\pi\) | ||||
−0.383126 | + | 0.923696i | \(0.625153\pi\) | |||||||
\(542\) | 23.2926 | − | 40.3440i | 1.00050 | − | 1.73292i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.85542 | − | 2.80328i | 0.208175 | − | 0.120190i | ||||
\(545\) | 1.36713 | + | 2.36795i | 0.0585616 | + | 0.101432i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.79325 | + | 11.7663i | −0.290458 | + | 0.503089i | −0.973918 | − | 0.226900i | \(-0.927141\pi\) |
0.683460 | + | 0.729988i | \(0.260474\pi\) | |||||||
\(548\) | 0.323678i | 0.0138268i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 23.0270 | 0.981874 | ||||||||
\(551\) | −8.33752 | + | 14.4410i | −0.355191 | + | 0.615208i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −33.4979 | + | 19.3400i | −1.42319 | + | 0.821678i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.809487 | − | 0.467357i | −0.0343299 | − | 0.0198204i | ||||
\(557\) | − | 7.21412i | − | 0.305672i | −0.988252 | − | 0.152836i | \(-0.951159\pi\) | ||
0.988252 | − | 0.152836i | \(-0.0488406\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.0886i | 0.807361i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.55119 | + | 6.15084i | 0.149798 | + | 0.259457i | ||||
\(563\) | −11.5472 | − | 20.0004i | −0.486657 | − | 0.842915i | 0.513225 | − | 0.858254i | \(-0.328451\pi\) |
−0.999882 | + | 0.0153392i | \(0.995117\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.18296 | + | 2.41504i | 0.175979 | + | 0.101601i | ||||
\(566\) | −1.58944 | −0.0668092 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.7696 | 0.871473 | ||||||||
\(569\) | 22.6039 | + | 13.0504i | 0.947605 | + | 0.547100i | 0.892336 | − | 0.451372i | \(-0.149065\pi\) |
0.0552688 | + | 0.998472i | \(0.482398\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.3318 | + | 21.3594i | 0.516071 | + | 0.893862i | 0.999826 | + | 0.0186582i | \(0.00593945\pi\) |
−0.483754 | + | 0.875204i | \(0.660727\pi\) | |||||||
\(572\) | −1.11758 | − | 1.93570i | −0.0467283 | − | 0.0809357i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 29.2963i | − | 1.22174i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19.3300i | − | 0.804719i | −0.915482 | − | 0.402360i | \(-0.868190\pi\) | ||
0.915482 | − | 0.402360i | \(-0.131810\pi\) | |||||||
\(578\) | 8.79192 | + | 5.07602i | 0.365696 | + | 0.211135i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.169918 | + | 0.0981022i | −0.00705546 | + | 0.00407347i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.135209 | + | 0.234188i | −0.00559977 | + | 0.00969908i | ||||
\(584\) | −25.6386 | −1.06093 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 4.04578i | − | 0.167130i | ||||||
\(587\) | 7.65692 | − | 13.2622i | 0.316035 | − | 0.547389i | −0.663622 | − | 0.748068i | \(-0.730982\pi\) |
0.979657 | + | 0.200679i | \(0.0643150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0878 | + | 34.7931i | 0.827703 | + | 1.43362i | ||||
\(590\) | −0.828207 | + | 0.478166i | −0.0340967 | + | 0.0196858i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25.8716 | − | 44.8108i | 1.06331 | − | 1.84171i | ||||
\(593\) | 39.2391 | 1.61136 | 0.805678 | − | 0.592354i | \(-0.201801\pi\) | ||||
0.805678 | + | 0.592354i | \(0.201801\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.71763 | − | 0.991674i | −0.0703569 | − | 0.0406206i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −26.6354 | + | 15.3779i | −1.08920 | + | 0.628851i | ||||
\(599\) | 29.7113 | − | 17.1538i | 1.21397 | − | 0.700887i | 0.250350 | − | 0.968155i | \(-0.419454\pi\) |
0.963622 | + | 0.267269i | \(0.0861211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0139 | + | 13.8644i | 0.979547 | + | 0.565541i | 0.902133 | − | 0.431458i | \(-0.142001\pi\) |
0.0774133 | + | 0.996999i | \(0.475334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.22630 | 0.0498973 | ||||||||
\(605\) | −0.154020 | + | 0.266770i | −0.00626180 | + | 0.0108458i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.0526 | − | 7.53592i | 0.529788 | − | 0.305873i | −0.211142 | − | 0.977455i | \(-0.567718\pi\) |
0.740930 | + | 0.671582i | \(0.234385\pi\) | |||||||
\(608\) | −3.06663 | − | 5.31156i | −0.124368 | − | 0.215412i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.24235 | + | 2.15181i | −0.0503012 | + | 0.0871243i | ||||
\(611\) | 29.3585i | 1.18772i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.65889 | 0.390119 | 0.195059 | − | 0.980791i | \(-0.437510\pi\) | ||||
0.195059 | + | 0.980791i | \(0.437510\pi\) | |||||||
\(614\) | 6.17031 | − | 10.6873i | 0.249013 | − | 0.431304i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.9761 | + | 9.22381i | −0.643174 | + | 0.371337i | −0.785836 | − | 0.618435i | \(-0.787767\pi\) |
0.142662 | + | 0.989771i | \(0.454434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.3519 | − | 16.9463i | −1.17975 | − | 0.681130i | −0.223795 | − | 0.974636i | \(-0.571845\pi\) |
−0.955957 | + | 0.293506i | \(0.905178\pi\) | |||||||
\(620\) | 0.472720i | 0.0189849i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.90774i | 0.357168i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.7911 | − | 20.4227i | −0.471642 | − | 0.816908i | ||||
\(626\) | 8.77733 | + | 15.2028i | 0.350813 | + | 0.607626i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.88526 | − | 1.66580i | −0.115134 | − | 0.0664728i | ||||
\(629\) | 57.8641 | 2.30719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.0134 | −0.398629 | −0.199314 | − | 0.979936i | \(-0.563871\pi\) | ||||
−0.199314 | + | 0.979936i | \(0.563871\pi\) | |||||||
\(632\) | 11.8616 | + | 6.84831i | 0.471830 | + | 0.272411i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.0035 | − | 38.1112i | −0.873870 | − | 1.51359i | ||||
\(635\) | 1.04568 | + | 1.81117i | 0.0414965 | + | 0.0718741i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 14.6569i | − | 0.580271i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.92594i | 0.155186i | ||||||||
\(641\) | 34.7673 | + | 20.0729i | 1.37323 | + | 0.792833i | 0.991333 | − | 0.131373i | \(-0.0419387\pi\) |
0.381894 | + | 0.924206i | \(0.375272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.0552 | + | 17.3524i | −1.18526 | + | 0.684311i | −0.957226 | − | 0.289342i | \(-0.906564\pi\) |
−0.228036 | + | 0.973653i | \(0.573230\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.3566 | − | 33.5266i | 0.761575 | − | 1.31909i | ||||
\(647\) | −14.3693 | −0.564916 | −0.282458 | − | 0.959280i | \(-0.591150\pi\) | ||||
−0.282458 | + | 0.959280i | \(0.591150\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.60535i | − | 0.259283i | ||||||
\(650\) | −12.6282 | + | 21.8726i | −0.495317 | + | 0.857915i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.658626 | − | 1.14077i | −0.0257938 | − | 0.0446761i | ||||
\(653\) | 0.971455 | − | 0.560870i | 0.0380160 | − | 0.0219485i | −0.480872 | − | 0.876791i | \(-0.659680\pi\) |
0.518888 | + | 0.854843i | \(0.326346\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.01369 | − | 5.21987i | 0.117755 | − | 0.203957i | ||||
\(656\) | 22.6089 | 0.882729 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.45240 | + | 3.14795i | 0.212395 | + | 0.122627i | 0.602424 | − | 0.798176i | \(-0.294202\pi\) |
−0.390029 | + | 0.920803i | \(0.627535\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.6913 | − | 21.7611i | 1.46602 | − | 0.846409i | 0.466745 | − | 0.884392i | \(-0.345427\pi\) |
0.999278 | + | 0.0379828i | \(0.0120932\pi\) | |||||||
\(662\) | 21.9199 | − | 12.6555i | 0.851943 | − | 0.491869i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.4355 | + | 11.7984i | 0.793051 | + | 0.457868i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.6474 | −0.722028 | ||||||||
\(668\) | −0.272134 | + | 0.471349i | −0.0105292 | + | 0.0182370i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.0439456 | − | 0.0253720i | 0.00169776 | − | 0.000980205i | ||||
\(671\) | −8.58086 | − | 14.8625i | −0.331261 | − | 0.573760i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.6052 | + | 20.1008i | −0.447347 | + | 0.774827i | −0.998212 | − | 0.0597668i | \(-0.980964\pi\) |
0.550866 | + | 0.834594i | \(0.314298\pi\) | |||||||
\(674\) | 30.0063i | 1.15580i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.197336 | −0.00758986 | ||||||||
\(677\) | −22.8213 | + | 39.5276i | −0.877093 | + | 1.51917i | −0.0225758 | + | 0.999745i | \(0.507187\pi\) |
−0.854517 | + | 0.519424i | \(0.826147\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.47757 | + | 2.00778i | −0.133359 | + | 0.0769947i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −30.5821 | − | 17.6566i | −1.17105 | − | 0.676104i | ||||
\(683\) | 4.40243i | 0.168454i | 0.996447 | + | 0.0842272i | \(0.0268421\pi\) | ||||
−0.996447 | + | 0.0842272i | \(0.973158\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.489950i | − | 0.0187200i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.0134 | − | 20.8079i | −0.458008 | − | 0.793294i | ||||
\(689\) | −0.148299 | − | 0.256861i | −0.00564973 | − | 0.00978562i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.08070 | − | 4.66539i | −0.307404 | − | 0.177480i | 0.338360 | − | 0.941017i | \(-0.390128\pi\) |
−0.645764 | + | 0.763537i | \(0.723461\pi\) | |||||||
\(692\) | 4.11527 | 0.156439 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.2486 | −0.996385 | ||||||||
\(695\) | 1.22531 | + | 0.707436i | 0.0464788 | + | 0.0268346i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.6417 | + | 21.8961i | 0.478839 | + | 0.829374i | ||||
\(698\) | −3.10802 | − | 5.38324i | −0.117640 | − | 0.203759i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.9051i | 0.865116i | 0.901606 | + | 0.432558i | \(0.142389\pi\) | ||||
−0.901606 | + | 0.432558i | \(0.857611\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 63.3001i | − | 2.38741i | ||||||
\(704\) | −19.2464 | − | 11.1119i | −0.725376 | − | 0.418796i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −39.2054 | + | 22.6353i | −1.47552 | + | 0.851889i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.78180 | + | 4.81822i | −0.104473 | + | 0.180952i | −0.913523 | − | 0.406788i | \(-0.866649\pi\) |
0.809050 | + | 0.587740i | \(0.199982\pi\) | |||||||
\(710\) | 3.56633 | 0.133842 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 4.99647i | − | 0.187250i | ||||||
\(713\) | −22.4637 | + | 38.9083i | −0.841274 | + | 1.45713i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.69167 | + | 2.93006i | 0.0632649 | + | 0.109578i | ||||
\(716\) | 3.87548 | − | 2.23751i | 0.144834 | − | 0.0836197i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.00172 | − | 6.93118i | 0.149343 | − | 0.258669i | ||||
\(719\) | −19.9978 | −0.745790 | −0.372895 | − | 0.927873i | \(-0.621635\pi\) | ||||
−0.372895 | + | 0.927873i | \(0.621635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.2494 | − | 7.07220i | −0.455876 | − | 0.263200i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.442158 | − | 0.255280i | 0.0164327 | − | 0.00948741i | ||||
\(725\) | −13.2614 | + | 7.65648i | −0.492516 | + | 0.284354i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.0380 | + | 14.4557i | 0.928610 | + | 0.536133i | 0.886372 | − | 0.462975i | \(-0.153218\pi\) |
0.0422381 | + | 0.999108i | \(0.486551\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.40237 | −0.162939 | ||||||||
\(731\) | 13.4346 | − | 23.2694i | 0.496896 | − | 0.860650i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.5498 | + | 15.9059i | −1.01757 | + | 0.587496i | −0.913400 | − | 0.407063i | \(-0.866553\pi\) |
−0.104173 | + | 0.994559i | \(0.533220\pi\) | |||||||
\(734\) | 14.8461 | + | 25.7143i | 0.547981 | + | 0.949131i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.42935 | − | 5.93980i | 0.126407 | − | 0.218944i | ||||
\(737\) | 0.350487i | 0.0129104i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.7871 | 0.838236 | 0.419118 | − | 0.907932i | \(-0.362339\pi\) | ||||
0.419118 | + | 0.907932i | \(0.362339\pi\) | |||||||
\(740\) | 0.372405 | − | 0.645025i | 0.0136899 | − | 0.0237116i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.8554 | + | 6.84471i | −0.434932 | + | 0.251108i | −0.701446 | − | 0.712723i | \(-0.747462\pi\) |
0.266513 | + | 0.963831i | \(0.414128\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.59997 | + | 1.50109i | 0.0952554 | + | 0.0549957i | ||||
\(746\) | 38.7380i | 1.41830i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.14621i | 0.115037i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.2030 | − | 17.6721i | −0.372312 | − | 0.644864i | 0.617608 | − | 0.786486i | \(-0.288102\pi\) |
−0.989921 | + | 0.141622i | \(0.954768\pi\) | |||||||
\(752\) | −18.4768 | − | 32.0028i | −0.673781 | − | 1.16702i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.9221 | + | 8.03793i | 0.507013 | + | 0.292724i | ||||
\(755\) | −1.85624 | −0.0675554 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.02306 | −0.146221 | −0.0731104 | − | 0.997324i | \(-0.523293\pi\) | ||||
−0.0731104 | + | 0.997324i | \(0.523293\pi\) | |||||||
\(758\) | 39.2400 | + | 22.6552i | 1.42526 | + | 0.822874i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.19639 | + | 3.80426i | 0.0796715 | + | 0.137995i | ||||
\(761\) | −22.9595 | − | 39.7670i | −0.832280 | − | 1.44155i | −0.896226 | − | 0.443598i | \(-0.853702\pi\) |
0.0639453 | − | 0.997953i | \(-0.479632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.428864i | 0.0155157i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.7111i | 1.21803i | ||||||||
\(767\) | 6.27422 | + | 3.62242i | 0.226549 | + | 0.130798i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.22983 | − | 3.01944i | 0.188592 | − | 0.108884i | −0.402731 | − | 0.915318i | \(-0.631939\pi\) |
0.591323 | + | 0.806434i | \(0.298606\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.606656 | + | 1.05076i | −0.0218340 | + | 0.0378176i | ||||
\(773\) | 38.2314 | 1.37509 | 0.687545 | − | 0.726142i | \(-0.258689\pi\) | ||||
0.687545 | + | 0.726142i | \(0.258689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.8938i | 1.32527i | ||||||||
\(776\) | 16.9060 | − | 29.2820i | 0.606889 | − | 1.05116i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.33508 | + | 5.77653i | 0.119568 | + | 0.207098i | ||||
\(779\) | 23.9531 | − | 13.8293i | 0.858209 | − | 0.495487i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3163 | + | 21.3324i | −0.440711 | + | 0.763333i | ||||
\(782\) | 43.2921 | 1.54812 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.36739 | + | 2.52152i | 0.155879 | + | 0.0899968i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.7875 | + | 24.1260i | −1.48957 | + | 0.860001i | −0.999929 | − | 0.0119261i | \(-0.996204\pi\) |
−0.489636 | + | 0.871927i | \(0.662870\pi\) | |||||||
\(788\) | −1.34907 | + | 0.778886i | −0.0480586 | + | 0.0277467i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.03675 | + | 1.17592i | 0.0724643 | + | 0.0418373i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.8232 | 0.668432 | ||||||||
\(794\) | −7.16394 | + | 12.4083i | −0.254239 | + | 0.440354i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.20910 | + | 0.698076i | −0.0428555 | + | 0.0247426i | ||||
\(797\) | −12.6517 | − | 21.9133i | −0.448145 | − | 0.776209i | 0.550121 | − | 0.835085i | \(-0.314582\pi\) |
−0.998265 | + | 0.0588759i | \(0.981248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.6626 | − | 35.7886i | 0.730989 | − | 1.26611i | ||||
\(800\) | − | 5.63227i | − | 0.199131i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29.5446 | 1.04326 | ||||||||
\(803\) | 15.2035 | − | 26.3333i | 0.536521 | − | 0.929282i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 33.5428 | − | 19.3660i | 1.18150 | − | 0.682137i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.0112 | + | 9.82141i | 0.598451 | + | 0.345516i | ||||
\(809\) | 11.1541i | 0.392158i | 0.980588 | + | 0.196079i | \(0.0628209\pi\) | ||||
−0.980588 | + | 0.196079i | \(0.937179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.90097i | 0.0667520i | 0.999443 | + | 0.0333760i | \(0.0106259\pi\) | ||||
−0.999443 | + | 0.0333760i | \(0.989374\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 27.8194 | + | 48.1847i | 0.975070 | + | 1.68887i | ||||
\(815\) | 0.996957 | + | 1.72678i | 0.0349219 | + | 0.0604865i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.4554 | − | 14.6967i | −0.890572 | − | 0.514172i | ||||
\(818\) | 3.60098 | 0.125905 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.325441 | 0.0113649 | ||||||||
\(821\) | 8.79955 | + | 5.08042i | 0.307106 | + | 0.177308i | 0.645631 | − | 0.763650i | \(-0.276594\pi\) |
−0.338524 | + | 0.940958i | \(0.609928\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.9763 | − | 27.6717i | −0.556898 | − | 0.964576i | −0.997753 | − | 0.0669975i | \(-0.978658\pi\) |
0.440855 | − | 0.897578i | \(-0.354675\pi\) | |||||||
\(824\) | −10.6399 | − | 18.4289i | −0.370660 | − | 0.642002i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.7400i | − | 0.477787i | −0.971046 | − | 0.238894i | \(-0.923215\pi\) | ||
0.971046 | − | 0.238894i | \(-0.0767847\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.9078i | 0.621962i | 0.950416 | + | 0.310981i | \(0.100658\pi\) | ||||
−0.950416 | + | 0.310981i | \(0.899342\pi\) | |||||||
\(830\) | 3.50896 | + | 2.02590i | 0.121798 | + | 0.0703200i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 21.1097 | − | 12.1877i | 0.731848 | − | 0.422532i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.411927 | − | 0.713478i | 0.0142553 | − | 0.0246909i | ||||
\(836\) | 3.44178 | 0.119036 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 43.6082i | − | 1.50642i | ||||||
\(839\) | −27.5601 | + | 47.7356i | −0.951482 | + | 1.64802i | −0.209261 | + | 0.977860i | \(0.567106\pi\) |
−0.742221 | + | 0.670155i | \(0.766227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.62659 | − | 16.6737i | −0.331951 | − | 0.574957i | ||||
\(842\) | −46.8165 | + | 27.0295i | −1.61340 | + | 0.931499i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.559902 | − | 0.969778i | 0.0192726 | − | 0.0333811i | ||||
\(845\) | 0.298707 | 0.0102758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.323312 | + | 0.186664i | 0.0111026 | + | 0.00641007i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.7880 | − | 17.7755i | 1.05602 | − | 0.609693i | ||||
\(851\) | 61.3034 | − | 35.3936i | 2.10145 | − | 1.21328i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.07425 | + | 1.19757i | 0.0710209 | + | 0.0410039i | 0.535090 | − | 0.844795i | \(-0.320278\pi\) |
−0.464069 | + | 0.885799i | \(0.653611\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44.7162 | 1.52837 | ||||||||
\(857\) | 15.2461 | − | 26.4070i | 0.520796 | − | 0.902046i | −0.478911 | − | 0.877863i | \(-0.658968\pi\) |
0.999708 | − | 0.0241822i | \(-0.00769820\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.9437 | − | 22.4841i | 1.32874 | − | 0.767149i | 0.343636 | − | 0.939103i | \(-0.388341\pi\) |
0.985105 | + | 0.171954i | \(0.0550079\pi\) | |||||||
\(860\) | −0.172926 | − | 0.299517i | −0.00589674 | − | 0.0102134i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.4383 | + | 25.0078i | −0.491770 | + | 0.851770i | ||||
\(863\) | − | 52.5198i | − | 1.78779i | −0.448272 | − | 0.893897i | \(-0.647960\pi\) | ||
0.448272 | − | 0.893897i | \(-0.352040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.22926 | −0.211801 | ||||||||
\(866\) | −7.38262 | + | 12.7871i | −0.250872 | + | 0.434523i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.0678 | + | 8.12203i | −0.477217 | + | 0.275521i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.332917 | − | 0.192209i | −0.0112804 | − | 0.00651277i | ||||
\(872\) | 23.6390i | 0.800519i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 47.3591i | − | 1.60195i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.683876 | − | 1.18451i | −0.0230929 | − | 0.0399980i | 0.854248 | − | 0.519866i | \(-0.174018\pi\) |
−0.877341 | + | 0.479868i | \(0.840685\pi\) | |||||||
\(878\) | −5.47457 | − | 9.48224i | −0.184758 | − | 0.320010i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.68808 | − | 2.12931i | −0.124325 | − | 0.0717791i | ||||
\(881\) | −20.7141 | −0.697876 | −0.348938 | − | 0.937146i | \(-0.613458\pi\) | ||||
−0.348938 | + | 0.937146i | \(0.613458\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.3561 | −0.483120 | −0.241560 | − | 0.970386i | \(-0.577659\pi\) | ||||
−0.241560 | + | 0.970386i | \(0.577659\pi\) | |||||||
\(884\) | −2.98849 | − | 1.72541i | −0.100514 | − | 0.0580317i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.638206 | − | 1.10541i | −0.0214410 | − | 0.0371368i | ||||
\(887\) | 22.0913 | + | 38.2633i | 0.741754 | + | 1.28475i | 0.951696 | + | 0.307041i | \(0.0993390\pi\) |
−0.209943 | + | 0.977714i | \(0.567328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 0.857939i | − | 0.0287582i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 4.14284i | − | 0.138713i | ||||||
\(893\) | −39.1507 | − | 22.6037i | −1.31013 | − | 0.756404i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.86629 | + | 3.38691i | −0.196089 | + | 0.113212i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.6161 | + | 20.1196i | −0.387633 | + | 0.671400i | ||||
\(899\) | 23.4832 | 0.783209 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.417492i | 0.0139087i | ||||||||
\(902\) | −12.1556 | + | 21.0540i | −0.404736 | + | 0.701023i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.8791 | + | 36.1637i | 0.694429 | + | 1.20279i | ||||
\(905\) | −0.669292 | + | 0.386416i | −0.0222480 | + | 0.0128449i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.18075 | − | 12.4374i | 0.238433 | − | 0.412978i | −0.721832 | − | 0.692068i | \(-0.756700\pi\) |
0.960265 | + | 0.279091i | \(0.0900330\pi\) | |||||||
\(908\) | 0.0657067 | 0.00218055 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.6920 | + | 24.0709i | 1.38132 | + | 0.797505i | 0.992316 | − | 0.123732i | \(-0.0394863\pi\) |
0.389003 | + | 0.921237i | \(0.372820\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.2363 | + | 13.9928i | −0.802104 | + | 0.463095i | ||||
\(914\) | 7.23957 | − | 4.17977i | 0.239464 | − | 0.138254i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.468997 | + | 0.270776i | 0.0154961 | + | 0.00894668i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.0641 | 0.760816 | 0.380408 | − | 0.924819i | \(-0.375784\pi\) | ||||
0.380408 | + | 0.924819i | \(0.375784\pi\) | |||||||
\(920\) | −2.45618 | + | 4.25423i | −0.0809778 | + | 0.140258i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29.1430 | + | 16.8257i | −0.959773 | + | 0.554125i | ||||
\(923\) | −13.5086 | − | 23.3977i | −0.444642 | − | 0.770143i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.0647 | − | 50.3416i | 0.955642 | − | 1.65522i | ||||
\(926\) | − | 62.3647i | − | 2.04943i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.58498 | −0.117683 | ||||||||
\(929\) | −18.7804 | + | 32.5286i | −0.616165 | + | 1.06723i | 0.374014 | + | 0.927423i | \(0.377981\pi\) |
−0.990179 | + | 0.139806i | \(0.955352\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.10405 | + | 2.36947i | −0.134433 | + | 0.0776147i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31.8876 | + | 18.4103i | 1.04339 | + | 0.602403i | ||||
\(935\) | − | 4.76240i | − | 0.155747i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 18.9436i | − | 0.618859i | −0.950922 | − | 0.309430i | \(-0.899862\pi\) | ||
0.950922 | − | 0.309430i | \(-0.100138\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.265963 | − | 0.460661i | −0.00867475 | − | 0.0150251i | ||||
\(941\) | 27.7551 | + | 48.0733i | 0.904792 | + | 1.56714i | 0.821197 | + | 0.570645i | \(0.193307\pi\) |
0.0835947 | + | 0.996500i | \(0.473360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.7862 | + | 15.4650i | 0.872280 | + | 0.503611i | ||||
\(944\) | −9.11911 | −0.296802 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.8359 | 0.839997 | ||||||||
\(947\) | −16.3036 | − | 9.41290i | −0.529797 | − | 0.305878i | 0.211137 | − | 0.977456i | \(-0.432283\pi\) |
−0.740934 | + | 0.671578i | \(0.765617\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.6754 | + | 28.8827i | 0.541308 | + | 0.937573i | ||||
\(950\) | −19.4453 | − | 33.6803i | −0.630890 | − | 1.09273i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 35.0089i | − | 1.13405i | −0.823701 | − | 0.567024i | \(-0.808095\pi\) | ||
0.823701 | − | 0.567024i | \(-0.191905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.649168i | − | 0.0210066i | ||||||
\(956\) | 0.0593482 | + | 0.0342647i | 0.00191946 | + | 0.00110820i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.23347 | − | 2.44420i | 0.136777 | − | 0.0789684i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.7893 | − | 22.1518i | 0.412559 | − | 0.714573i | ||||
\(962\) | −61.0255 | −1.96754 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.51380i | 0.145380i | ||||||||
\(965\) | 0.918291 | − | 1.59053i | 0.0295608 | − | 0.0512008i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.47001 | − | 12.9384i | −0.240219 | − | 0.416072i | 0.720557 | − | 0.693395i | \(-0.243886\pi\) |
−0.960777 | + | 0.277323i | \(0.910553\pi\) | |||||||
\(968\) | −2.30636 | + | 1.33158i | −0.0741291 | + | 0.0427985i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.90291 | − | 5.02799i | 0.0932069 | − | 0.161439i | ||||
\(971\) | −30.3564 | −0.974182 | −0.487091 | − | 0.873351i | \(-0.661942\pi\) | ||||
−0.487091 | + | 0.873351i | \(0.661942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 13.4280 | + | 7.75269i | 0.430262 | + | 0.248412i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.5186 | + | 11.8464i | −0.656785 | + | 0.379195i | ||||
\(977\) | −47.1306 | + | 27.2109i | −1.50784 | + | 0.870554i | −0.507885 | + | 0.861425i | \(0.669572\pi\) |
−0.999958 | + | 0.00912839i | \(0.997094\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.13186 | + | 2.96288i | 0.164015 | + | 0.0946940i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 45.0477 | 1.43753 | ||||||||
\(983\) | −13.1343 | + | 22.7493i | −0.418920 | + | 0.725590i | −0.995831 | − | 0.0912165i | \(-0.970924\pi\) |
0.576911 | + | 0.816807i | \(0.304258\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.04208 | − | 1.17899i | 0.0650660 | − | 0.0375659i | ||||
\(986\) | −11.3142 | − | 19.5968i | −0.360318 | − | 0.624089i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.88750 | + | 3.26924i | −0.0600492 | + | 0.104008i | ||||
\(989\) | − | 32.8700i | − | 1.04520i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.4942 | −1.03221 | −0.516106 | − | 0.856525i | \(-0.672619\pi\) | ||||
−0.516106 | + | 0.856525i | \(0.672619\pi\) | |||||||
\(992\) | −4.31869 | + | 7.48019i | −0.137118 | + | 0.237496i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.83021 | − | 1.05667i | 0.0580216 | − | 0.0334988i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.8691 | + | 18.3996i | 1.00931 | + | 0.582723i | 0.910988 | − | 0.412433i | \(-0.135321\pi\) |
0.0983170 | + | 0.995155i | \(0.468654\pi\) | |||||||
\(998\) | − | 2.92376i | − | 0.0925499i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1323.2.o.e.440.19 | 48 | ||
3.2 | odd | 2 | 441.2.o.e.146.6 | yes | 48 | ||
7.2 | even | 3 | 1323.2.i.d.521.13 | 48 | |||
7.3 | odd | 6 | 1323.2.s.d.656.6 | 48 | |||
7.4 | even | 3 | 1323.2.s.d.656.5 | 48 | |||
7.5 | odd | 6 | 1323.2.i.d.521.5 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.o.e.440.20 | 48 | ||
9.4 | even | 3 | 441.2.o.e.293.5 | yes | 48 | ||
9.5 | odd | 6 | inner | 1323.2.o.e.881.20 | 48 | ||
21.2 | odd | 6 | 441.2.i.d.227.20 | 48 | |||
21.5 | even | 6 | 441.2.i.d.227.19 | 48 | |||
21.11 | odd | 6 | 441.2.s.d.362.19 | 48 | |||
21.17 | even | 6 | 441.2.s.d.362.20 | 48 | |||
21.20 | even | 2 | 441.2.o.e.146.5 | ✓ | 48 | ||
63.4 | even | 3 | 441.2.i.d.68.5 | 48 | |||
63.5 | even | 6 | 1323.2.s.d.962.5 | 48 | |||
63.13 | odd | 6 | 441.2.o.e.293.6 | yes | 48 | ||
63.23 | odd | 6 | 1323.2.s.d.962.6 | 48 | |||
63.31 | odd | 6 | 441.2.i.d.68.6 | 48 | |||
63.32 | odd | 6 | 1323.2.i.d.1097.5 | 48 | |||
63.40 | odd | 6 | 441.2.s.d.374.19 | 48 | |||
63.41 | even | 6 | inner | 1323.2.o.e.881.19 | 48 | ||
63.58 | even | 3 | 441.2.s.d.374.20 | 48 | |||
63.59 | even | 6 | 1323.2.i.d.1097.13 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.5 | 48 | 63.4 | even | 3 | |||
441.2.i.d.68.6 | 48 | 63.31 | odd | 6 | |||
441.2.i.d.227.19 | 48 | 21.5 | even | 6 | |||
441.2.i.d.227.20 | 48 | 21.2 | odd | 6 | |||
441.2.o.e.146.5 | ✓ | 48 | 21.20 | even | 2 | ||
441.2.o.e.146.6 | yes | 48 | 3.2 | odd | 2 | ||
441.2.o.e.293.5 | yes | 48 | 9.4 | even | 3 | ||
441.2.o.e.293.6 | yes | 48 | 63.13 | odd | 6 | ||
441.2.s.d.362.19 | 48 | 21.11 | odd | 6 | |||
441.2.s.d.362.20 | 48 | 21.17 | even | 6 | |||
441.2.s.d.374.19 | 48 | 63.40 | odd | 6 | |||
441.2.s.d.374.20 | 48 | 63.58 | even | 3 | |||
1323.2.i.d.521.5 | 48 | 7.5 | odd | 6 | |||
1323.2.i.d.521.13 | 48 | 7.2 | even | 3 | |||
1323.2.i.d.1097.5 | 48 | 63.32 | odd | 6 | |||
1323.2.i.d.1097.13 | 48 | 63.59 | even | 6 | |||
1323.2.o.e.440.19 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.o.e.440.20 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.o.e.881.19 | 48 | 63.41 | even | 6 | inner | ||
1323.2.o.e.881.20 | 48 | 9.5 | odd | 6 | inner | ||
1323.2.s.d.656.5 | 48 | 7.4 | even | 3 | |||
1323.2.s.d.656.6 | 48 | 7.3 | odd | 6 | |||
1323.2.s.d.962.5 | 48 | 63.5 | even | 6 | |||
1323.2.s.d.962.6 | 48 | 63.23 | odd | 6 |