Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,2,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.599");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.18279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.1 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.2.b.i.599.4 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | − 0.618034i | − 0.356822i | −0.983956 | − | 0.178411i | \(-0.942904\pi\) | ||||
0.983956 | − | 0.178411i | \(-0.0570957\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.618034 | −0.252311 | ||||||||
\(7\) | − 1.61803i | − 0.611559i | −0.952102 | − | 0.305780i | \(-0.901083\pi\) | ||||
0.952102 | − | 0.305780i | \(-0.0989171\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.61803 | 0.872678 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.85410 | 1.16206 | 0.581028 | − | 0.813884i | \(-0.302651\pi\) | ||||
0.581028 | + | 0.813884i | \(0.302651\pi\) | |||||||
\(12\) | 0.618034i | 0.178411i | ||||||||
\(13\) | 4.09017i | 1.13441i | 0.823577 | + | 0.567205i | \(0.191975\pi\) | ||||
−0.823577 | + | 0.567205i | \(0.808025\pi\) | |||||||
\(14\) | −1.61803 | −0.432438 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.09017i | 1.23455i | 0.786748 | + | 0.617274i | \(0.211763\pi\) | ||||
−0.786748 | + | 0.617274i | \(0.788237\pi\) | |||||||
\(18\) | − 2.61803i | − 0.617077i | ||||||||
\(19\) | 4.85410 | 1.11361 | 0.556804 | − | 0.830644i | \(-0.312028\pi\) | ||||
0.556804 | + | 0.830644i | \(0.312028\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | − 3.85410i | − 0.821697i | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0.618034 | 0.126156 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.09017 | 0.802148 | ||||||||
\(27\) | − 3.47214i | − 0.668213i | ||||||||
\(28\) | 1.61803i | 0.305780i | ||||||||
\(29\) | 4.76393 | 0.884640 | 0.442320 | − | 0.896857i | \(-0.354156\pi\) | ||||
0.442320 | + | 0.896857i | \(0.354156\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.09017 | −0.375406 | −0.187703 | − | 0.982226i | \(-0.560104\pi\) | ||||
−0.187703 | + | 0.982226i | \(0.560104\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 2.38197i | − 0.414647i | ||||||||
\(34\) | 5.09017 | 0.872957 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.61803 | −0.436339 | ||||||||
\(37\) | 2.47214i | 0.406417i | 0.979136 | + | 0.203208i | \(0.0651369\pi\) | ||||
−0.979136 | + | 0.203208i | \(0.934863\pi\) | |||||||
\(38\) | − 4.85410i | − 0.787439i | ||||||||
\(39\) | 2.52786 | 0.404782 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.3262 | −1.92503 | −0.962517 | − | 0.271220i | \(-0.912573\pi\) | ||||
−0.962517 | + | 0.271220i | \(0.912573\pi\) | |||||||
\(42\) | 1.00000i | 0.154303i | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | −3.85410 | −0.581028 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | − 9.70820i | − 1.41609i | −0.706169 | − | 0.708044i | \(-0.749578\pi\) | ||||
0.706169 | − | 0.708044i | \(-0.250422\pi\) | |||||||
\(48\) | − 0.618034i | − 0.0892055i | ||||||||
\(49\) | 4.38197 | 0.625995 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.14590 | 0.440514 | ||||||||
\(52\) | − 4.09017i | − 0.567205i | ||||||||
\(53\) | − 8.47214i | − 1.16374i | −0.813283 | − | 0.581869i | \(-0.802322\pi\) | ||||
0.813283 | − | 0.581869i | \(-0.197678\pi\) | |||||||
\(54\) | −3.47214 | −0.472498 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.61803 | 0.216219 | ||||||||
\(57\) | − 3.00000i | − 0.397360i | ||||||||
\(58\) | − 4.76393i | − 0.625535i | ||||||||
\(59\) | 11.7082 | 1.52428 | 0.762139 | − | 0.647413i | \(-0.224149\pi\) | ||||
0.762139 | + | 0.647413i | \(0.224149\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.32624 | 0.809992 | 0.404996 | − | 0.914319i | \(-0.367273\pi\) | ||||
0.404996 | + | 0.914319i | \(0.367273\pi\) | |||||||
\(62\) | 2.09017i | 0.265452i | ||||||||
\(63\) | − 4.23607i | − 0.533694i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.38197 | −0.293200 | ||||||||
\(67\) | − 5.52786i | − 0.675336i | −0.941265 | − | 0.337668i | \(-0.890362\pi\) | ||||
0.941265 | − | 0.337668i | \(-0.109638\pi\) | |||||||
\(68\) | − 5.09017i | − 0.617274i | ||||||||
\(69\) | 0.618034 | 0.0744025 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.09017 | 0.841448 | 0.420724 | − | 0.907189i | \(-0.361776\pi\) | ||||
0.420724 | + | 0.907189i | \(0.361776\pi\) | |||||||
\(72\) | 2.61803i | 0.308538i | ||||||||
\(73\) | − 1.23607i | − 0.144671i | −0.997380 | − | 0.0723354i | \(-0.976955\pi\) | ||||
0.997380 | − | 0.0723354i | \(-0.0230452\pi\) | |||||||
\(74\) | 2.47214 | 0.287380 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.85410 | −0.556804 | ||||||||
\(77\) | − 6.23607i | − 0.710666i | ||||||||
\(78\) | − 2.52786i | − 0.286224i | ||||||||
\(79\) | −10.4721 | −1.17821 | −0.589104 | − | 0.808057i | \(-0.700519\pi\) | ||||
−0.589104 | + | 0.808057i | \(0.700519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | 12.3262i | 1.36121i | ||||||||
\(83\) | 10.9443i | 1.20129i | 0.799516 | + | 0.600645i | \(0.205089\pi\) | ||||
−0.799516 | + | 0.600645i | \(0.794911\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2.94427i | − 0.315659i | ||||||||
\(88\) | 3.85410i | 0.410849i | ||||||||
\(89\) | 1.52786 | 0.161953 | 0.0809766 | − | 0.996716i | \(-0.474196\pi\) | ||||
0.0809766 | + | 0.996716i | \(0.474196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.61803 | 0.693758 | ||||||||
\(92\) | − 1.00000i | − 0.104257i | ||||||||
\(93\) | 1.29180i | 0.133953i | ||||||||
\(94\) | −9.70820 | −1.00132 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.618034 | −0.0630778 | ||||||||
\(97\) | − 14.6180i | − 1.48424i | −0.670269 | − | 0.742118i | \(-0.733821\pi\) | ||||
0.670269 | − | 0.742118i | \(-0.266179\pi\) | |||||||
\(98\) | − 4.38197i | − 0.442645i | ||||||||
\(99\) | 10.0902 | 1.01410 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.7082 | −1.36402 | −0.682009 | − | 0.731344i | \(-0.738893\pi\) | ||||
−0.682009 | + | 0.731344i | \(0.738893\pi\) | |||||||
\(102\) | − 3.14590i | − 0.311490i | ||||||||
\(103\) | − 3.56231i | − 0.351004i | −0.984479 | − | 0.175502i | \(-0.943845\pi\) | ||||
0.984479 | − | 0.175502i | \(-0.0561549\pi\) | |||||||
\(104\) | −4.09017 | −0.401074 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.47214 | −0.822887 | ||||||||
\(107\) | 4.18034i | 0.404129i | 0.979372 | + | 0.202064i | \(0.0647650\pi\) | ||||
−0.979372 | + | 0.202064i | \(0.935235\pi\) | |||||||
\(108\) | 3.47214i | 0.334106i | ||||||||
\(109\) | −8.56231 | −0.820120 | −0.410060 | − | 0.912059i | \(-0.634492\pi\) | ||||
−0.410060 | + | 0.912059i | \(0.634492\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.52786 | 0.145018 | ||||||||
\(112\) | − 1.61803i | − 0.152890i | ||||||||
\(113\) | 18.9443i | 1.78213i | 0.453878 | + | 0.891064i | \(0.350040\pi\) | ||||
−0.453878 | + | 0.891064i | \(0.649960\pi\) | |||||||
\(114\) | −3.00000 | −0.280976 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.76393 | −0.442320 | ||||||||
\(117\) | 10.7082i | 0.989974i | ||||||||
\(118\) | − 11.7082i | − 1.07783i | ||||||||
\(119\) | 8.23607 | 0.754999 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.85410 | 0.350373 | ||||||||
\(122\) | − 6.32624i | − 0.572751i | ||||||||
\(123\) | 7.61803i | 0.686895i | ||||||||
\(124\) | 2.09017 | 0.187703 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.23607 | −0.377379 | ||||||||
\(127\) | 6.18034i | 0.548416i | 0.961670 | + | 0.274208i | \(0.0884158\pi\) | ||||
−0.961670 | + | 0.274208i | \(0.911584\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.9443 | −1.30569 | −0.652844 | − | 0.757493i | \(-0.726424\pi\) | ||||
−0.652844 | + | 0.757493i | \(0.726424\pi\) | |||||||
\(132\) | 2.38197i | 0.207324i | ||||||||
\(133\) | − 7.85410i | − 0.681037i | ||||||||
\(134\) | −5.52786 | −0.477535 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.09017 | −0.436478 | ||||||||
\(137\) | − 5.32624i | − 0.455051i | −0.973772 | − | 0.227526i | \(-0.926936\pi\) | ||||
0.973772 | − | 0.227526i | \(-0.0730635\pi\) | |||||||
\(138\) | − 0.618034i | − 0.0526105i | ||||||||
\(139\) | −17.2361 | −1.46194 | −0.730972 | − | 0.682407i | \(-0.760933\pi\) | ||||
−0.730972 | + | 0.682407i | \(0.760933\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | − 7.09017i | − 0.594994i | ||||||||
\(143\) | 15.7639i | 1.31825i | ||||||||
\(144\) | 2.61803 | 0.218169 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.23607 | −0.102298 | ||||||||
\(147\) | − 2.70820i | − 0.223369i | ||||||||
\(148\) | − 2.47214i | − 0.203208i | ||||||||
\(149\) | 1.14590 | 0.0938756 | 0.0469378 | − | 0.998898i | \(-0.485054\pi\) | ||||
0.0469378 | + | 0.998898i | \(0.485054\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5623 | 1.42920 | 0.714600 | − | 0.699533i | \(-0.246609\pi\) | ||||
0.714600 | + | 0.699533i | \(0.246609\pi\) | |||||||
\(152\) | 4.85410i | 0.393720i | ||||||||
\(153\) | 13.3262i | 1.07736i | ||||||||
\(154\) | −6.23607 | −0.502517 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.52786 | −0.202391 | ||||||||
\(157\) | − 9.70820i | − 0.774799i | −0.921912 | − | 0.387400i | \(-0.873373\pi\) | ||||
0.921912 | − | 0.387400i | \(-0.126627\pi\) | |||||||
\(158\) | 10.4721i | 0.833118i | ||||||||
\(159\) | −5.23607 | −0.415247 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.61803 | 0.127519 | ||||||||
\(162\) | − 5.70820i | − 0.448479i | ||||||||
\(163\) | 3.61803i | 0.283386i | 0.989911 | + | 0.141693i | \(0.0452546\pi\) | ||||
−0.989911 | + | 0.141693i | \(0.954745\pi\) | |||||||
\(164\) | 12.3262 | 0.962517 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.9443 | 0.849440 | ||||||||
\(167\) | 8.00000i | 0.619059i | 0.950890 | + | 0.309529i | \(0.100171\pi\) | ||||
−0.950890 | + | 0.309529i | \(0.899829\pi\) | |||||||
\(168\) | − 1.00000i | − 0.0771517i | ||||||||
\(169\) | −3.72949 | −0.286884 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.7082 | 0.971821 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 21.5623i | − 1.63935i | −0.572828 | − | 0.819676i | \(-0.694154\pi\) | ||||
0.572828 | − | 0.819676i | \(-0.305846\pi\) | |||||||
\(174\) | −2.94427 | −0.223205 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.85410 | 0.290514 | ||||||||
\(177\) | − 7.23607i | − 0.543896i | ||||||||
\(178\) | − 1.52786i | − 0.114518i | ||||||||
\(179\) | 20.1803 | 1.50835 | 0.754175 | − | 0.656674i | \(-0.228037\pi\) | ||||
0.754175 | + | 0.656674i | \(0.228037\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.8541 | −1.40141 | −0.700707 | − | 0.713449i | \(-0.747132\pi\) | ||||
−0.700707 | + | 0.713449i | \(0.747132\pi\) | |||||||
\(182\) | − 6.61803i | − 0.490561i | ||||||||
\(183\) | − 3.90983i | − 0.289023i | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.29180 | 0.0947191 | ||||||||
\(187\) | 19.6180i | 1.43461i | ||||||||
\(188\) | 9.70820i | 0.708044i | ||||||||
\(189\) | −5.61803 | −0.408652 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.291796 | −0.0211136 | −0.0105568 | − | 0.999944i | \(-0.503360\pi\) | ||||
−0.0105568 | + | 0.999944i | \(0.503360\pi\) | |||||||
\(192\) | 0.618034i | 0.0446028i | ||||||||
\(193\) | 5.23607i | 0.376900i | 0.982083 | + | 0.188450i | \(0.0603464\pi\) | ||||
−0.982083 | + | 0.188450i | \(0.939654\pi\) | |||||||
\(194\) | −14.6180 | −1.04951 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.38197 | −0.312998 | ||||||||
\(197\) | 2.43769i | 0.173679i | 0.996222 | + | 0.0868393i | \(0.0276767\pi\) | ||||
−0.996222 | + | 0.0868393i | \(0.972323\pi\) | |||||||
\(198\) | − 10.0902i | − 0.717077i | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.41641 | −0.240975 | ||||||||
\(202\) | 13.7082i | 0.964506i | ||||||||
\(203\) | − 7.70820i | − 0.541010i | ||||||||
\(204\) | −3.14590 | −0.220257 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.56231 | −0.248198 | ||||||||
\(207\) | 2.61803i | 0.181966i | ||||||||
\(208\) | 4.09017i | 0.283602i | ||||||||
\(209\) | 18.7082 | 1.29407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | 8.47214i | 0.581869i | ||||||||
\(213\) | − 4.38197i | − 0.300247i | ||||||||
\(214\) | 4.18034 | 0.285762 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.47214 | 0.236249 | ||||||||
\(217\) | 3.38197i | 0.229583i | ||||||||
\(218\) | 8.56231i | 0.579913i | ||||||||
\(219\) | −0.763932 | −0.0516217 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.8197 | −1.40048 | ||||||||
\(222\) | − 1.52786i | − 0.102544i | ||||||||
\(223\) | − 3.05573i | − 0.204627i | −0.994752 | − | 0.102313i | \(-0.967376\pi\) | ||||
0.994752 | − | 0.102313i | \(-0.0326244\pi\) | |||||||
\(224\) | −1.61803 | −0.108109 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.9443 | 1.26015 | ||||||||
\(227\) | 23.2361i | 1.54223i | 0.636695 | + | 0.771116i | \(0.280301\pi\) | ||||
−0.636695 | + | 0.771116i | \(0.719699\pi\) | |||||||
\(228\) | 3.00000i | 0.198680i | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.85410 | −0.253581 | ||||||||
\(232\) | 4.76393i | 0.312767i | ||||||||
\(233\) | 19.7082i | 1.29113i | 0.763706 | + | 0.645564i | \(0.223378\pi\) | ||||
−0.763706 | + | 0.645564i | \(0.776622\pi\) | |||||||
\(234\) | 10.7082 | 0.700017 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.7082 | −0.762139 | ||||||||
\(237\) | 6.47214i | 0.420410i | ||||||||
\(238\) | − 8.23607i | − 0.533865i | ||||||||
\(239\) | −24.3607 | −1.57576 | −0.787881 | − | 0.615828i | \(-0.788822\pi\) | ||||
−0.787881 | + | 0.615828i | \(0.788822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | − 3.85410i | − 0.247751i | ||||||||
\(243\) | − 13.9443i | − 0.894525i | ||||||||
\(244\) | −6.32624 | −0.404996 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.61803 | 0.485708 | ||||||||
\(247\) | 19.8541i | 1.26329i | ||||||||
\(248\) | − 2.09017i | − 0.132726i | ||||||||
\(249\) | 6.76393 | 0.428647 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.8541 | 0.811344 | 0.405672 | − | 0.914019i | \(-0.367038\pi\) | ||||
0.405672 | + | 0.914019i | \(0.367038\pi\) | |||||||
\(252\) | 4.23607i | 0.266847i | ||||||||
\(253\) | 3.85410i | 0.242305i | ||||||||
\(254\) | 6.18034 | 0.387789 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 30.1803i | 1.88260i | 0.337574 | + | 0.941299i | \(0.390394\pi\) | ||||
−0.337574 | + | 0.941299i | \(0.609606\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.4721 | 0.772006 | ||||||||
\(262\) | 14.9443i | 0.923260i | ||||||||
\(263\) | − 21.7426i | − 1.34071i | −0.742041 | − | 0.670354i | \(-0.766142\pi\) | ||||
0.742041 | − | 0.670354i | \(-0.233858\pi\) | |||||||
\(264\) | 2.38197 | 0.146600 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.85410 | −0.481566 | ||||||||
\(267\) | − 0.944272i | − 0.0577885i | ||||||||
\(268\) | 5.52786i | 0.337668i | ||||||||
\(269\) | −8.18034 | −0.498764 | −0.249382 | − | 0.968405i | \(-0.580227\pi\) | ||||
−0.249382 | + | 0.968405i | \(0.580227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.6738 | −0.891368 | −0.445684 | − | 0.895190i | \(-0.647039\pi\) | ||||
−0.445684 | + | 0.895190i | \(0.647039\pi\) | |||||||
\(272\) | 5.09017i | 0.308637i | ||||||||
\(273\) | − 4.09017i | − 0.247548i | ||||||||
\(274\) | −5.32624 | −0.321770 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.618034 | −0.0372013 | ||||||||
\(277\) | − 2.58359i | − 0.155233i | −0.996983 | − | 0.0776165i | \(-0.975269\pi\) | ||||
0.996983 | − | 0.0776165i | \(-0.0247310\pi\) | |||||||
\(278\) | 17.2361i | 1.03375i | ||||||||
\(279\) | −5.47214 | −0.327608 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.2361 | 1.62477 | 0.812384 | − | 0.583123i | \(-0.198169\pi\) | ||||
0.812384 | + | 0.583123i | \(0.198169\pi\) | |||||||
\(282\) | 6.00000i | 0.357295i | ||||||||
\(283\) | − 9.05573i | − 0.538307i | −0.963097 | − | 0.269154i | \(-0.913256\pi\) | ||||
0.963097 | − | 0.269154i | \(-0.0867439\pi\) | |||||||
\(284\) | −7.09017 | −0.420724 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.7639 | 0.932141 | ||||||||
\(287\) | 19.9443i | 1.17727i | ||||||||
\(288\) | − 2.61803i | − 0.154269i | ||||||||
\(289\) | −8.90983 | −0.524108 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.03444 | −0.529608 | ||||||||
\(292\) | 1.23607i | 0.0723354i | ||||||||
\(293\) | 15.8885i | 0.928219i | 0.885778 | + | 0.464109i | \(0.153626\pi\) | ||||
−0.885778 | + | 0.464109i | \(0.846374\pi\) | |||||||
\(294\) | −2.70820 | −0.157946 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.47214 | −0.143690 | ||||||||
\(297\) | − 13.3820i | − 0.776500i | ||||||||
\(298\) | − 1.14590i | − 0.0663801i | ||||||||
\(299\) | −4.09017 | −0.236541 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 17.5623i | − 1.01060i | ||||||||
\(303\) | 8.47214i | 0.486711i | ||||||||
\(304\) | 4.85410 | 0.278402 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.3262 | 0.761810 | ||||||||
\(307\) | − 27.4508i | − 1.56670i | −0.621579 | − | 0.783351i | \(-0.713509\pi\) | ||||
0.621579 | − | 0.783351i | \(-0.286491\pi\) | |||||||
\(308\) | 6.23607i | 0.355333i | ||||||||
\(309\) | −2.20163 | −0.125246 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | 2.52786i | 0.143112i | ||||||||
\(313\) | − 11.7984i | − 0.666884i | −0.942771 | − | 0.333442i | \(-0.891790\pi\) | ||||
0.942771 | − | 0.333442i | \(-0.108210\pi\) | |||||||
\(314\) | −9.70820 | −0.547866 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4721 | 0.589104 | ||||||||
\(317\) | − 0.0901699i | − 0.00506445i | −0.999997 | − | 0.00253222i | \(-0.999194\pi\) | ||||
0.999997 | − | 0.00253222i | \(-0.000806033\pi\) | |||||||
\(318\) | 5.23607i | 0.293624i | ||||||||
\(319\) | 18.3607 | 1.02800 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.58359 | 0.144202 | ||||||||
\(322\) | − 1.61803i | − 0.0901695i | ||||||||
\(323\) | 24.7082i | 1.37480i | ||||||||
\(324\) | −5.70820 | −0.317122 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.61803 | 0.200384 | ||||||||
\(327\) | 5.29180i | 0.292637i | ||||||||
\(328\) | − 12.3262i | − 0.680603i | ||||||||
\(329\) | −15.7082 | −0.866021 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.7639 | 0.811499 | 0.405750 | − | 0.913984i | \(-0.367011\pi\) | ||||
0.405750 | + | 0.913984i | \(0.367011\pi\) | |||||||
\(332\) | − 10.9443i | − 0.600645i | ||||||||
\(333\) | 6.47214i | 0.354671i | ||||||||
\(334\) | 8.00000 | 0.437741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | − 29.3262i | − 1.59750i | −0.601662 | − | 0.798751i | \(-0.705494\pi\) | ||||
0.601662 | − | 0.798751i | \(-0.294506\pi\) | |||||||
\(338\) | 3.72949i | 0.202858i | ||||||||
\(339\) | 11.7082 | 0.635902 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.05573 | −0.436242 | ||||||||
\(342\) | − 12.7082i | − 0.687181i | ||||||||
\(343\) | − 18.4164i | − 0.994393i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.5623 | −1.15920 | ||||||||
\(347\) | 8.61803i | 0.462640i | 0.972878 | + | 0.231320i | \(0.0743045\pi\) | ||||
−0.972878 | + | 0.231320i | \(0.925696\pi\) | |||||||
\(348\) | 2.94427i | 0.157830i | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.2016 | 0.758027 | ||||||||
\(352\) | − 3.85410i | − 0.205424i | ||||||||
\(353\) | 24.0000i | 1.27739i | 0.769460 | + | 0.638696i | \(0.220526\pi\) | ||||
−0.769460 | + | 0.638696i | \(0.779474\pi\) | |||||||
\(354\) | −7.23607 | −0.384593 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.52786 | −0.0809766 | ||||||||
\(357\) | − 5.09017i | − 0.269400i | ||||||||
\(358\) | − 20.1803i | − 1.06656i | ||||||||
\(359\) | 18.3607 | 0.969040 | 0.484520 | − | 0.874780i | \(-0.338994\pi\) | ||||
0.484520 | + | 0.874780i | \(0.338994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.56231 | 0.240121 | ||||||||
\(362\) | 18.8541i | 0.990950i | ||||||||
\(363\) | − 2.38197i | − 0.125021i | ||||||||
\(364\) | −6.61803 | −0.346879 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.90983 | −0.204370 | ||||||||
\(367\) | 2.47214i | 0.129044i | 0.997916 | + | 0.0645222i | \(0.0205523\pi\) | ||||
−0.997916 | + | 0.0645222i | \(0.979448\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | −32.2705 | −1.67994 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.7082 | −0.711694 | ||||||||
\(372\) | − 1.29180i | − 0.0669765i | ||||||||
\(373\) | − 2.18034i | − 0.112894i | −0.998406 | − | 0.0564469i | \(-0.982023\pi\) | ||||
0.998406 | − | 0.0564469i | \(-0.0179771\pi\) | |||||||
\(374\) | 19.6180 | 1.01442 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.70820 | 0.500662 | ||||||||
\(377\) | 19.4853i | 1.00354i | ||||||||
\(378\) | 5.61803i | 0.288960i | ||||||||
\(379\) | −33.4508 | −1.71825 | −0.859127 | − | 0.511762i | \(-0.828993\pi\) | ||||
−0.859127 | + | 0.511762i | \(0.828993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.81966 | 0.195687 | ||||||||
\(382\) | 0.291796i | 0.0149296i | ||||||||
\(383\) | 17.8885i | 0.914062i | 0.889451 | + | 0.457031i | \(0.151087\pi\) | ||||
−0.889451 | + | 0.457031i | \(0.848913\pi\) | |||||||
\(384\) | 0.618034 | 0.0315389 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.23607 | 0.266509 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.6180i | 0.742118i | ||||||||
\(389\) | −5.67376 | −0.287671 | −0.143836 | − | 0.989602i | \(-0.545944\pi\) | ||||
−0.143836 | + | 0.989602i | \(0.545944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.09017 | −0.257421 | ||||||||
\(392\) | 4.38197i | 0.221323i | ||||||||
\(393\) | 9.23607i | 0.465898i | ||||||||
\(394\) | 2.43769 | 0.122809 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.0902 | −0.507050 | ||||||||
\(397\) | 8.32624i | 0.417882i | 0.977928 | + | 0.208941i | \(0.0670016\pi\) | ||||
−0.977928 | + | 0.208941i | \(0.932998\pi\) | |||||||
\(398\) | 2.00000i | 0.100251i | ||||||||
\(399\) | −4.85410 | −0.243009 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7082 | 0.584680 | 0.292340 | − | 0.956314i | \(-0.405566\pi\) | ||||
0.292340 | + | 0.956314i | \(0.405566\pi\) | |||||||
\(402\) | 3.41641i | 0.170395i | ||||||||
\(403\) | − 8.54915i | − 0.425864i | ||||||||
\(404\) | 13.7082 | 0.682009 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.70820 | −0.382552 | ||||||||
\(407\) | 9.52786i | 0.472279i | ||||||||
\(408\) | 3.14590i | 0.155745i | ||||||||
\(409\) | −21.2148 | −1.04900 | −0.524502 | − | 0.851409i | \(-0.675748\pi\) | ||||
−0.524502 | + | 0.851409i | \(0.675748\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.29180 | −0.162372 | ||||||||
\(412\) | 3.56231i | 0.175502i | ||||||||
\(413\) | − 18.9443i | − 0.932187i | ||||||||
\(414\) | 2.61803 | 0.128669 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.09017 | 0.200537 | ||||||||
\(417\) | 10.6525i | 0.521654i | ||||||||
\(418\) | − 18.7082i | − 0.915048i | ||||||||
\(419\) | −5.52786 | −0.270054 | −0.135027 | − | 0.990842i | \(-0.543112\pi\) | ||||
−0.135027 | + | 0.990842i | \(0.543112\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.7426 | −1.40083 | −0.700415 | − | 0.713735i | \(-0.747002\pi\) | ||||
−0.700415 | + | 0.713735i | \(0.747002\pi\) | |||||||
\(422\) | − 14.0000i | − 0.681509i | ||||||||
\(423\) | − 25.4164i | − 1.23579i | ||||||||
\(424\) | 8.47214 | 0.411443 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.38197 | −0.212307 | ||||||||
\(427\) | − 10.2361i | − 0.495358i | ||||||||
\(428\) | − 4.18034i | − 0.202064i | ||||||||
\(429\) | 9.74265 | 0.470379 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.6525 | 1.66915 | 0.834576 | − | 0.550894i | \(-0.185713\pi\) | ||||
0.834576 | + | 0.550894i | \(0.185713\pi\) | |||||||
\(432\) | − 3.47214i | − 0.167053i | ||||||||
\(433\) | − 29.5066i | − 1.41800i | −0.705211 | − | 0.708998i | \(-0.749148\pi\) | ||||
0.705211 | − | 0.708998i | \(-0.250852\pi\) | |||||||
\(434\) | 3.38197 | 0.162340 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.56231 | 0.410060 | ||||||||
\(437\) | 4.85410i | 0.232203i | ||||||||
\(438\) | 0.763932i | 0.0365021i | ||||||||
\(439\) | 15.6180 | 0.745408 | 0.372704 | − | 0.927950i | \(-0.378431\pi\) | ||||
0.372704 | + | 0.927950i | \(0.378431\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.4721 | 0.546292 | ||||||||
\(442\) | 20.8197i | 0.990290i | ||||||||
\(443\) | 13.9098i | 0.660876i | 0.943828 | + | 0.330438i | \(0.107196\pi\) | ||||
−0.943828 | + | 0.330438i | \(0.892804\pi\) | |||||||
\(444\) | −1.52786 | −0.0725092 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.05573 | −0.144693 | ||||||||
\(447\) | − 0.708204i | − 0.0334969i | ||||||||
\(448\) | 1.61803i | 0.0764449i | ||||||||
\(449\) | −18.5623 | −0.876009 | −0.438005 | − | 0.898973i | \(-0.644315\pi\) | ||||
−0.438005 | + | 0.898973i | \(0.644315\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −47.5066 | −2.23700 | ||||||||
\(452\) | − 18.9443i | − 0.891064i | ||||||||
\(453\) | − 10.8541i | − 0.509970i | ||||||||
\(454\) | 23.2361 | 1.09052 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.00000 | 0.140488 | ||||||||
\(457\) | − 33.7771i | − 1.58003i | −0.613090 | − | 0.790013i | \(-0.710074\pi\) | ||||
0.613090 | − | 0.790013i | \(-0.289926\pi\) | |||||||
\(458\) | 10.0000i | 0.467269i | ||||||||
\(459\) | 17.6738 | 0.824941 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.7639 | −1.61912 | −0.809559 | − | 0.587039i | \(-0.800294\pi\) | ||||
−0.809559 | + | 0.587039i | \(0.800294\pi\) | |||||||
\(462\) | 3.85410i | 0.179309i | ||||||||
\(463\) | 2.00000i | 0.0929479i | 0.998920 | + | 0.0464739i | \(0.0147984\pi\) | ||||
−0.998920 | + | 0.0464739i | \(0.985202\pi\) | |||||||
\(464\) | 4.76393 | 0.221160 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.7082 | 0.912965 | ||||||||
\(467\) | − 23.1246i | − 1.07008i | −0.844827 | − | 0.535040i | \(-0.820297\pi\) | ||||
0.844827 | − | 0.535040i | \(-0.179703\pi\) | |||||||
\(468\) | − 10.7082i | − 0.494987i | ||||||||
\(469\) | −8.94427 | −0.413008 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.00000 | −0.276465 | ||||||||
\(472\) | 11.7082i | 0.538914i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6.47214 | 0.297275 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.23607 | −0.377500 | ||||||||
\(477\) | − 22.1803i | − 1.01557i | ||||||||
\(478\) | 24.3607i | 1.11423i | ||||||||
\(479\) | −3.88854 | −0.177672 | −0.0888361 | − | 0.996046i | \(-0.528315\pi\) | ||||
−0.0888361 | + | 0.996046i | \(0.528315\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1115 | −0.461043 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.00000i | − 0.0455016i | ||||||||
\(484\) | −3.85410 | −0.175186 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.9443 | −0.632525 | ||||||||
\(487\) | 42.1803i | 1.91137i | 0.294385 | + | 0.955687i | \(0.404885\pi\) | ||||
−0.294385 | + | 0.955687i | \(0.595115\pi\) | |||||||
\(488\) | 6.32624i | 0.286375i | ||||||||
\(489\) | 2.23607 | 0.101118 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.1803 | −0.730209 | −0.365104 | − | 0.930967i | \(-0.618967\pi\) | ||||
−0.365104 | + | 0.930967i | \(0.618967\pi\) | |||||||
\(492\) | − 7.61803i | − 0.343447i | ||||||||
\(493\) | 24.2492i | 1.09213i | ||||||||
\(494\) | 19.8541 | 0.893278 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.09017 | −0.0938514 | ||||||||
\(497\) | − 11.4721i | − 0.514596i | ||||||||
\(498\) | − 6.76393i | − 0.303099i | ||||||||
\(499\) | 32.3607 | 1.44866 | 0.724331 | − | 0.689452i | \(-0.242149\pi\) | ||||
0.724331 | + | 0.689452i | \(0.242149\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.94427 | 0.220894 | ||||||||
\(502\) | − 12.8541i | − 0.573707i | ||||||||
\(503\) | 20.6738i | 0.921797i | 0.887453 | + | 0.460899i | \(0.152473\pi\) | ||||
−0.887453 | + | 0.460899i | \(0.847527\pi\) | |||||||
\(504\) | 4.23607 | 0.188689 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.85410 | 0.171336 | ||||||||
\(507\) | 2.30495i | 0.102366i | ||||||||
\(508\) | − 6.18034i | − 0.274208i | ||||||||
\(509\) | −5.34752 | −0.237025 | −0.118512 | − | 0.992953i | \(-0.537813\pi\) | ||||
−0.118512 | + | 0.992953i | \(0.537813\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | −0.0884748 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 16.8541i | − 0.744127i | ||||||||
\(514\) | 30.1803 | 1.33120 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 37.4164i | − 1.64557i | ||||||||
\(518\) | − 4.00000i | − 0.175750i | ||||||||
\(519\) | −13.3262 | −0.584957 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.4721 | −1.07214 | −0.536072 | − | 0.844172i | \(-0.680092\pi\) | ||||
−0.536072 | + | 0.844172i | \(0.680092\pi\) | |||||||
\(522\) | − 12.4721i | − 0.545891i | ||||||||
\(523\) | − 26.0000i | − 1.13690i | −0.822718 | − | 0.568450i | \(-0.807543\pi\) | ||||
0.822718 | − | 0.568450i | \(-0.192457\pi\) | |||||||
\(524\) | 14.9443 | 0.652844 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.7426 | −0.948024 | ||||||||
\(527\) | − 10.6393i | − 0.463456i | ||||||||
\(528\) | − 2.38197i | − 0.103662i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.6525 | 1.33020 | ||||||||
\(532\) | 7.85410i | 0.340519i | ||||||||
\(533\) | − 50.4164i | − 2.18378i | ||||||||
\(534\) | −0.944272 | −0.0408626 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.52786 | 0.238767 | ||||||||
\(537\) | − 12.4721i | − 0.538212i | ||||||||
\(538\) | 8.18034i | 0.352679i | ||||||||
\(539\) | 16.8885 | 0.727441 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.8328 | −1.32561 | −0.662803 | − | 0.748794i | \(-0.730633\pi\) | ||||
−0.662803 | + | 0.748794i | \(0.730633\pi\) | |||||||
\(542\) | 14.6738i | 0.630292i | ||||||||
\(543\) | 11.6525i | 0.500056i | ||||||||
\(544\) | 5.09017 | 0.218239 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.09017 | −0.175043 | ||||||||
\(547\) | 36.9230i | 1.57871i | 0.613935 | + | 0.789356i | \(0.289586\pi\) | ||||
−0.613935 | + | 0.789356i | \(0.710414\pi\) | |||||||
\(548\) | 5.32624i | 0.227526i | ||||||||
\(549\) | 16.5623 | 0.706862 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.1246 | 0.985142 | ||||||||
\(552\) | 0.618034i | 0.0263053i | ||||||||
\(553\) | 16.9443i | 0.720544i | ||||||||
\(554\) | −2.58359 | −0.109766 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.2361 | 0.730972 | ||||||||
\(557\) | − 30.8328i | − 1.30643i | −0.757173 | − | 0.653214i | \(-0.773420\pi\) | ||||
0.757173 | − | 0.653214i | \(-0.226580\pi\) | |||||||
\(558\) | 5.47214i | 0.231654i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.1246 | 0.511902 | ||||||||
\(562\) | − 27.2361i | − 1.14888i | ||||||||
\(563\) | 21.8885i | 0.922492i | 0.887272 | + | 0.461246i | \(0.152597\pi\) | ||||
−0.887272 | + | 0.461246i | \(0.847403\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.05573 | −0.380641 | ||||||||
\(567\) | − 9.23607i | − 0.387878i | ||||||||
\(568\) | 7.09017i | 0.297497i | ||||||||
\(569\) | 2.00000 | 0.0838444 | 0.0419222 | − | 0.999121i | \(-0.486652\pi\) | ||||
0.0419222 | + | 0.999121i | \(0.486652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.9787 | −1.29642 | −0.648209 | − | 0.761462i | \(-0.724482\pi\) | ||||
−0.648209 | + | 0.761462i | \(0.724482\pi\) | |||||||
\(572\) | − 15.7639i | − 0.659123i | ||||||||
\(573\) | 0.180340i | 0.00753381i | ||||||||
\(574\) | 19.9443 | 0.832458 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.61803 | −0.109085 | ||||||||
\(577\) | 12.4721i | 0.519222i | 0.965713 | + | 0.259611i | \(0.0835943\pi\) | ||||
−0.965713 | + | 0.259611i | \(0.916406\pi\) | |||||||
\(578\) | 8.90983i | 0.370600i | ||||||||
\(579\) | 3.23607 | 0.134486 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.7082 | 0.734660 | ||||||||
\(582\) | 9.03444i | 0.374490i | ||||||||
\(583\) | − 32.6525i | − 1.35233i | ||||||||
\(584\) | 1.23607 | 0.0511489 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.8885 | 0.656350 | ||||||||
\(587\) | − 11.3820i | − 0.469784i | −0.972021 | − | 0.234892i | \(-0.924526\pi\) | ||||
0.972021 | − | 0.234892i | \(-0.0754737\pi\) | |||||||
\(588\) | 2.70820i | 0.111684i | ||||||||
\(589\) | −10.1459 | −0.418054 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.50658 | 0.0619723 | ||||||||
\(592\) | 2.47214i | 0.101604i | ||||||||
\(593\) | 34.7639i | 1.42758i | 0.700358 | + | 0.713792i | \(0.253024\pi\) | ||||
−0.700358 | + | 0.713792i | \(0.746976\pi\) | |||||||
\(594\) | −13.3820 | −0.549069 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.14590 | −0.0469378 | ||||||||
\(597\) | 1.23607i | 0.0505889i | ||||||||
\(598\) | 4.09017i | 0.167259i | ||||||||
\(599\) | 20.6180 | 0.842430 | 0.421215 | − | 0.906961i | \(-0.361604\pi\) | ||||
0.421215 | + | 0.906961i | \(0.361604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.270510 | 0.0110343 | 0.00551716 | − | 0.999985i | \(-0.498244\pi\) | ||||
0.00551716 | + | 0.999985i | \(0.498244\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 14.4721i | − 0.589351i | ||||||||
\(604\) | −17.5623 | −0.714600 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.47214 | 0.344157 | ||||||||
\(607\) | − 17.5279i | − 0.711434i | −0.934594 | − | 0.355717i | \(-0.884237\pi\) | ||||
0.934594 | − | 0.355717i | \(-0.115763\pi\) | |||||||
\(608\) | − 4.85410i | − 0.196860i | ||||||||
\(609\) | −4.76393 | −0.193044 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.7082 | 1.60642 | ||||||||
\(612\) | − 13.3262i | − 0.538681i | ||||||||
\(613\) | − 43.3050i | − 1.74907i | −0.484962 | − | 0.874535i | \(-0.661167\pi\) | ||||
0.484962 | − | 0.874535i | \(-0.338833\pi\) | |||||||
\(614\) | −27.4508 | −1.10783 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.23607 | 0.251258 | ||||||||
\(617\) | − 22.9098i | − 0.922315i | −0.887318 | − | 0.461158i | \(-0.847434\pi\) | ||||
0.887318 | − | 0.461158i | \(-0.152566\pi\) | |||||||
\(618\) | 2.20163i | 0.0885624i | ||||||||
\(619\) | −21.7984 | −0.876151 | −0.438075 | − | 0.898938i | \(-0.644340\pi\) | ||||
−0.438075 | + | 0.898938i | \(0.644340\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.47214 | 0.139332 | ||||||||
\(622\) | − 4.00000i | − 0.160385i | ||||||||
\(623\) | − 2.47214i | − 0.0990440i | ||||||||
\(624\) | 2.52786 | 0.101196 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.7984 | −0.471558 | ||||||||
\(627\) | − 11.5623i | − 0.461754i | ||||||||
\(628\) | 9.70820i | 0.387400i | ||||||||
\(629\) | −12.5836 | −0.501741 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0689 | −0.639692 | −0.319846 | − | 0.947470i | \(-0.603631\pi\) | ||||
−0.319846 | + | 0.947470i | \(0.603631\pi\) | |||||||
\(632\) | − 10.4721i | − 0.416559i | ||||||||
\(633\) | − 8.65248i | − 0.343905i | ||||||||
\(634\) | −0.0901699 | −0.00358111 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.23607 | 0.207624 | ||||||||
\(637\) | 17.9230i | 0.710135i | ||||||||
\(638\) | − 18.3607i | − 0.726906i | ||||||||
\(639\) | 18.5623 | 0.734313 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.3607 | −1.75214 | −0.876071 | − | 0.482183i | \(-0.839844\pi\) | ||||
−0.876071 | + | 0.482183i | \(0.839844\pi\) | |||||||
\(642\) | − 2.58359i | − 0.101966i | ||||||||
\(643\) | − 21.7082i | − 0.856088i | −0.903758 | − | 0.428044i | \(-0.859203\pi\) | ||||
0.903758 | − | 0.428044i | \(-0.140797\pi\) | |||||||
\(644\) | −1.61803 | −0.0637595 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.7082 | 0.972131 | ||||||||
\(647\) | − 44.2492i | − 1.73962i | −0.493390 | − | 0.869808i | \(-0.664242\pi\) | ||||
0.493390 | − | 0.869808i | \(-0.335758\pi\) | |||||||
\(648\) | 5.70820i | 0.224239i | ||||||||
\(649\) | 45.1246 | 1.77130 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.09017 | 0.0819202 | ||||||||
\(652\) | − 3.61803i | − 0.141693i | ||||||||
\(653\) | 21.0344i | 0.823141i | 0.911378 | + | 0.411571i | \(0.135020\pi\) | ||||
−0.911378 | + | 0.411571i | \(0.864980\pi\) | |||||||
\(654\) | 5.29180 | 0.206926 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.3262 | −0.481259 | ||||||||
\(657\) | − 3.23607i | − 0.126251i | ||||||||
\(658\) | 15.7082i | 0.612370i | ||||||||
\(659\) | −34.2492 | −1.33416 | −0.667080 | − | 0.744986i | \(-0.732456\pi\) | ||||
−0.667080 | + | 0.744986i | \(0.732456\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.3262 | 1.33514 | 0.667568 | − | 0.744549i | \(-0.267335\pi\) | ||||
0.667568 | + | 0.744549i | \(0.267335\pi\) | |||||||
\(662\) | − 14.7639i | − 0.573817i | ||||||||
\(663\) | 12.8673i | 0.499723i | ||||||||
\(664\) | −10.9443 | −0.424720 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.47214 | 0.250790 | ||||||||
\(667\) | 4.76393i | 0.184460i | ||||||||
\(668\) | − 8.00000i | − 0.309529i | ||||||||
\(669\) | −1.88854 | −0.0730153 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.3820 | 0.941255 | ||||||||
\(672\) | 1.00000i | 0.0385758i | ||||||||
\(673\) | 6.94427i | 0.267682i | 0.991003 | + | 0.133841i | \(0.0427311\pi\) | ||||
−0.991003 | + | 0.133841i | \(0.957269\pi\) | |||||||
\(674\) | −29.3262 | −1.12960 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.72949 | 0.143442 | ||||||||
\(677\) | 33.0557i | 1.27043i | 0.772333 | + | 0.635217i | \(0.219090\pi\) | ||||
−0.772333 | + | 0.635217i | \(0.780910\pi\) | |||||||
\(678\) | − 11.7082i | − 0.449651i | ||||||||
\(679\) | −23.6525 | −0.907699 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.3607 | 0.550302 | ||||||||
\(682\) | 8.05573i | 0.308470i | ||||||||
\(683\) | − 11.4377i | − 0.437651i | −0.975764 | − | 0.218826i | \(-0.929777\pi\) | ||||
0.975764 | − | 0.218826i | \(-0.0702226\pi\) | |||||||
\(684\) | −12.7082 | −0.485910 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.4164 | −0.703142 | ||||||||
\(687\) | 6.18034i | 0.235795i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.6525 | 1.32015 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.7639 | −0.942064 | −0.471032 | − | 0.882116i | \(-0.656118\pi\) | ||||
−0.471032 | + | 0.882116i | \(0.656118\pi\) | |||||||
\(692\) | 21.5623i | 0.819676i | ||||||||
\(693\) | − 16.3262i | − 0.620182i | ||||||||
\(694\) | 8.61803 | 0.327136 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.94427 | 0.111602 | ||||||||
\(697\) | − 62.7426i | − 2.37655i | ||||||||
\(698\) | − 2.00000i | − 0.0757011i | ||||||||
\(699\) | 12.1803 | 0.460703 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.3394 | −1.82575 | −0.912877 | − | 0.408235i | \(-0.866144\pi\) | ||||
−0.912877 | + | 0.408235i | \(0.866144\pi\) | |||||||
\(702\) | − 14.2016i | − 0.536006i | ||||||||
\(703\) | 12.0000i | 0.452589i | ||||||||
\(704\) | −3.85410 | −0.145257 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | 22.1803i | 0.834178i | ||||||||
\(708\) | 7.23607i | 0.271948i | ||||||||
\(709\) | 14.9098 | 0.559950 | 0.279975 | − | 0.960007i | \(-0.409674\pi\) | ||||
0.279975 | + | 0.960007i | \(0.409674\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27.4164 | −1.02820 | ||||||||
\(712\) | 1.52786i | 0.0572591i | ||||||||
\(713\) | − 2.09017i | − 0.0782775i | ||||||||
\(714\) | −5.09017 | −0.190495 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20.1803 | −0.754175 | ||||||||
\(717\) | 15.0557i | 0.562266i | ||||||||
\(718\) | − 18.3607i | − 0.685214i | ||||||||
\(719\) | −1.72949 | −0.0644991 | −0.0322495 | − | 0.999480i | \(-0.510267\pi\) | ||||
−0.0322495 | + | 0.999480i | \(0.510267\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.76393 | −0.214660 | ||||||||
\(722\) | − 4.56231i | − 0.169791i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.8541 | 0.700707 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.38197 | −0.0884031 | ||||||||
\(727\) | − 52.7984i | − 1.95818i | −0.203420 | − | 0.979092i | \(-0.565206\pi\) | ||||
0.203420 | − | 0.979092i | \(-0.434794\pi\) | |||||||
\(728\) | 6.61803i | 0.245281i | ||||||||
\(729\) | 8.50658 | 0.315058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 3.90983i | 0.144511i | ||||||||
\(733\) | − 2.58359i | − 0.0954272i | −0.998861 | − | 0.0477136i | \(-0.984807\pi\) | ||||
0.998861 | − | 0.0477136i | \(-0.0151935\pi\) | |||||||
\(734\) | 2.47214 | 0.0912482 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | − 21.3050i | − 0.784778i | ||||||||
\(738\) | 32.2705i | 1.18789i | ||||||||
\(739\) | −21.8885 | −0.805183 | −0.402592 | − | 0.915380i | \(-0.631890\pi\) | ||||
−0.402592 | + | 0.915380i | \(0.631890\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.2705 | 0.450768 | ||||||||
\(742\) | 13.7082i | 0.503244i | ||||||||
\(743\) | − 44.6312i | − 1.63736i | −0.574250 | − | 0.818680i | \(-0.694706\pi\) | ||||
0.574250 | − | 0.818680i | \(-0.305294\pi\) | |||||||
\(744\) | −1.29180 | −0.0473595 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.18034 | −0.0798279 | ||||||||
\(747\) | 28.6525i | 1.04834i | ||||||||
\(748\) | − 19.6180i | − 0.717306i | ||||||||
\(749\) | 6.76393 | 0.247149 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.0132 | 1.05871 | 0.529353 | − | 0.848402i | \(-0.322435\pi\) | ||||
0.529353 | + | 0.848402i | \(0.322435\pi\) | |||||||
\(752\) | − 9.70820i | − 0.354022i | ||||||||
\(753\) | − 7.94427i | − 0.289505i | ||||||||
\(754\) | 19.4853 | 0.709612 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.61803 | 0.204326 | ||||||||
\(757\) | − 17.8885i | − 0.650170i | −0.945685 | − | 0.325085i | \(-0.894607\pi\) | ||||
0.945685 | − | 0.325085i | \(-0.105393\pi\) | |||||||
\(758\) | 33.4508i | 1.21499i | ||||||||
\(759\) | 2.38197 | 0.0864599 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.8673 | −1.30019 | −0.650094 | − | 0.759854i | \(-0.725270\pi\) | ||||
−0.650094 | + | 0.759854i | \(0.725270\pi\) | |||||||
\(762\) | − 3.81966i | − 0.138372i | ||||||||
\(763\) | 13.8541i | 0.501552i | ||||||||
\(764\) | 0.291796 | 0.0105568 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.8885 | 0.646339 | ||||||||
\(767\) | 47.8885i | 1.72916i | ||||||||
\(768\) | − 0.618034i | − 0.0223014i | ||||||||
\(769\) | 33.4164 | 1.20503 | 0.602513 | − | 0.798109i | \(-0.294166\pi\) | ||||
0.602513 | + | 0.798109i | \(0.294166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.6525 | 0.671753 | ||||||||
\(772\) | − 5.23607i | − 0.188450i | ||||||||
\(773\) | 11.0557i | 0.397647i | 0.980035 | + | 0.198823i | \(0.0637120\pi\) | ||||
−0.980035 | + | 0.198823i | \(0.936288\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.6180 | 0.524757 | ||||||||
\(777\) | − 2.47214i | − 0.0886874i | ||||||||
\(778\) | 5.67376i | 0.203414i | ||||||||
\(779\) | −59.8328 | −2.14373 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.3262 | 0.977810 | ||||||||
\(782\) | 5.09017i | 0.182024i | ||||||||
\(783\) | − 16.5410i | − 0.591128i | ||||||||
\(784\) | 4.38197 | 0.156499 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.23607 | 0.329440 | ||||||||
\(787\) | 43.1246i | 1.53723i | 0.639714 | + | 0.768613i | \(0.279053\pi\) | ||||
−0.639714 | + | 0.768613i | \(0.720947\pi\) | |||||||
\(788\) | − 2.43769i | − 0.0868393i | ||||||||
\(789\) | −13.4377 | −0.478395 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.6525 | 1.08988 | ||||||||
\(792\) | 10.0902i | 0.358539i | ||||||||
\(793\) | 25.8754i | 0.918862i | ||||||||
\(794\) | 8.32624 | 0.295487 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | 0.0708881 | ||||||||
\(797\) | − 0.291796i | − 0.0103359i | −0.999987 | − | 0.00516797i | \(-0.998355\pi\) | ||||
0.999987 | − | 0.00516797i | \(-0.00164502\pi\) | |||||||
\(798\) | 4.85410i | 0.171833i | ||||||||
\(799\) | 49.4164 | 1.74823 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.00000 | 0.141333 | ||||||||
\(802\) | − 11.7082i | − 0.413431i | ||||||||
\(803\) | − 4.76393i | − 0.168116i | ||||||||
\(804\) | 3.41641 | 0.120487 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.54915 | −0.301131 | ||||||||
\(807\) | 5.05573i | 0.177970i | ||||||||
\(808\) | − 13.7082i | − 0.482253i | ||||||||
\(809\) | 4.25735 | 0.149681 | 0.0748403 | − | 0.997196i | \(-0.476155\pi\) | ||||
0.0748403 | + | 0.997196i | \(0.476155\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.1803 | 1.55138 | 0.775691 | − | 0.631113i | \(-0.217402\pi\) | ||||
0.775691 | + | 0.631113i | \(0.217402\pi\) | |||||||
\(812\) | 7.70820i | 0.270505i | ||||||||
\(813\) | 9.06888i | 0.318060i | ||||||||
\(814\) | 9.52786 | 0.333951 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.14590 | 0.110128 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 21.2148i | 0.741757i | ||||||||
\(819\) | 17.3262 | 0.605428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.9443 | −1.77797 | −0.888984 | − | 0.457939i | \(-0.848588\pi\) | ||||
−0.888984 | + | 0.457939i | \(0.848588\pi\) | |||||||
\(822\) | 3.29180i | 0.114815i | ||||||||
\(823\) | − 1.41641i | − 0.0493729i | −0.999695 | − | 0.0246864i | \(-0.992141\pi\) | ||||
0.999695 | − | 0.0246864i | \(-0.00785874\pi\) | |||||||
\(824\) | 3.56231 | 0.124099 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.9443 | −0.659156 | ||||||||
\(827\) | − 8.29180i | − 0.288334i | −0.989553 | − | 0.144167i | \(-0.953950\pi\) | ||||
0.989553 | − | 0.144167i | \(-0.0460502\pi\) | |||||||
\(828\) | − 2.61803i | − 0.0909830i | ||||||||
\(829\) | −1.05573 | −0.0366670 | −0.0183335 | − | 0.999832i | \(-0.505836\pi\) | ||||
−0.0183335 | + | 0.999832i | \(0.505836\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.59675 | −0.0553906 | ||||||||
\(832\) | − 4.09017i | − 0.141801i | ||||||||
\(833\) | 22.3050i | 0.772821i | ||||||||
\(834\) | 10.6525 | 0.368865 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18.7082 | −0.647037 | ||||||||
\(837\) | 7.25735i | 0.250851i | ||||||||
\(838\) | 5.52786i | 0.190957i | ||||||||
\(839\) | 43.0132 | 1.48498 | 0.742490 | − | 0.669858i | \(-0.233645\pi\) | ||||
0.742490 | + | 0.669858i | \(0.233645\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.30495 | −0.217412 | ||||||||
\(842\) | 28.7426i | 0.990537i | ||||||||
\(843\) | − 16.8328i | − 0.579753i | ||||||||
\(844\) | −14.0000 | −0.481900 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −25.4164 | −0.873834 | ||||||||
\(847\) | − 6.23607i | − 0.214274i | ||||||||
\(848\) | − 8.47214i | − 0.290934i | ||||||||
\(849\) | −5.59675 | −0.192080 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.47214 | −0.0847437 | ||||||||
\(852\) | 4.38197i | 0.150124i | ||||||||
\(853\) | 13.7984i | 0.472447i | 0.971699 | + | 0.236224i | \(0.0759098\pi\) | ||||
−0.971699 | + | 0.236224i | \(0.924090\pi\) | |||||||
\(854\) | −10.2361 | −0.350271 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.18034 | −0.142881 | ||||||||
\(857\) | 33.4164i | 1.14148i | 0.821130 | + | 0.570741i | \(0.193344\pi\) | ||||
−0.821130 | + | 0.570741i | \(0.806656\pi\) | |||||||
\(858\) | − 9.74265i | − 0.332608i | ||||||||
\(859\) | −34.0689 | −1.16242 | −0.581208 | − | 0.813755i | \(-0.697420\pi\) | ||||
−0.581208 | + | 0.813755i | \(0.697420\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.3262 | 0.420077 | ||||||||
\(862\) | − 34.6525i | − 1.18027i | ||||||||
\(863\) | 37.2361i | 1.26753i | 0.773525 | + | 0.633765i | \(0.218491\pi\) | ||||
−0.773525 | + | 0.633765i | \(0.781509\pi\) | |||||||
\(864\) | −3.47214 | −0.118124 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −29.5066 | −1.00267 | ||||||||
\(867\) | 5.50658i | 0.187013i | ||||||||
\(868\) | − 3.38197i | − 0.114791i | ||||||||
\(869\) | −40.3607 | −1.36914 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.6099 | 0.766107 | ||||||||
\(872\) | − 8.56231i | − 0.289956i | ||||||||
\(873\) | − 38.2705i | − 1.29526i | ||||||||
\(874\) | 4.85410 | 0.164192 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.763932 | 0.0258109 | ||||||||
\(877\) | 23.7426i | 0.801732i | 0.916137 | + | 0.400866i | \(0.131291\pi\) | ||||
−0.916137 | + | 0.400866i | \(0.868709\pi\) | |||||||
\(878\) | − 15.6180i | − 0.527083i | ||||||||
\(879\) | 9.81966 | 0.331209 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.4164 | 1.19321 | 0.596605 | − | 0.802535i | \(-0.296516\pi\) | ||||
0.596605 | + | 0.802535i | \(0.296516\pi\) | |||||||
\(882\) | − 11.4721i | − 0.386287i | ||||||||
\(883\) | − 4.56231i | − 0.153534i | −0.997049 | − | 0.0767669i | \(-0.975540\pi\) | ||||
0.997049 | − | 0.0767669i | \(-0.0244597\pi\) | |||||||
\(884\) | 20.8197 | 0.700241 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.9098 | 0.467310 | ||||||||
\(887\) | 58.8328i | 1.97541i | 0.156321 | + | 0.987706i | \(0.450037\pi\) | ||||
−0.156321 | + | 0.987706i | \(0.549963\pi\) | |||||||
\(888\) | 1.52786i | 0.0512718i | ||||||||
\(889\) | 10.0000 | 0.335389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.0000 | 0.737028 | ||||||||
\(892\) | 3.05573i | 0.102313i | ||||||||
\(893\) | − 47.1246i | − 1.57697i | ||||||||
\(894\) | −0.708204 | −0.0236859 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.61803 | 0.0540547 | ||||||||
\(897\) | 2.52786i | 0.0844029i | ||||||||
\(898\) | 18.5623i | 0.619432i | ||||||||
\(899\) | −9.95743 | −0.332099 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.1246 | 1.43669 | ||||||||
\(902\) | 47.5066i | 1.58180i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.9443 | −0.630077 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.8541 | −0.360603 | ||||||||
\(907\) | 33.1246i | 1.09988i | 0.835203 | + | 0.549942i | \(0.185350\pi\) | ||||
−0.835203 | + | 0.549942i | \(0.814650\pi\) | |||||||
\(908\) | − 23.2361i | − 0.771116i | ||||||||
\(909\) | −35.8885 | −1.19035 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.0689 | −0.731175 | −0.365587 | − | 0.930777i | \(-0.619132\pi\) | ||||
−0.365587 | + | 0.930777i | \(0.619132\pi\) | |||||||
\(912\) | − 3.00000i | − 0.0993399i | ||||||||
\(913\) | 42.1803i | 1.39597i | ||||||||
\(914\) | −33.7771 | −1.11725 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | 24.1803i | 0.798505i | ||||||||
\(918\) | − 17.6738i | − 0.583321i | ||||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.9656 | −0.559034 | ||||||||
\(922\) | 34.7639i | 1.14489i | ||||||||
\(923\) | 29.0000i | 0.954547i | ||||||||
\(924\) | 3.85410 | 0.126791 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.00000 | 0.0657241 | ||||||||
\(927\) | − 9.32624i | − 0.306314i | ||||||||
\(928\) | − 4.76393i | − 0.156384i | ||||||||
\(929\) | 12.4721 | 0.409198 | 0.204599 | − | 0.978846i | \(-0.434411\pi\) | ||||
0.204599 | + | 0.978846i | \(0.434411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.2705 | 0.697113 | ||||||||
\(932\) | − 19.7082i | − 0.645564i | ||||||||
\(933\) | − 2.47214i | − 0.0809341i | ||||||||
\(934\) | −23.1246 | −0.756660 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.7082 | −0.350009 | ||||||||
\(937\) | 12.2016i | 0.398610i | 0.979938 | + | 0.199305i | \(0.0638684\pi\) | ||||
−0.979938 | + | 0.199305i | \(0.936132\pi\) | |||||||
\(938\) | 8.94427i | 0.292041i | ||||||||
\(939\) | −7.29180 | −0.237959 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −60.5066 | −1.97246 | −0.986229 | − | 0.165385i | \(-0.947113\pi\) | ||||
−0.986229 | + | 0.165385i | \(0.947113\pi\) | |||||||
\(942\) | 6.00000i | 0.195491i | ||||||||
\(943\) | − 12.3262i | − 0.401398i | ||||||||
\(944\) | 11.7082 | 0.381070 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 5.68692i | − 0.184800i | −0.995722 | − | 0.0924000i | \(-0.970546\pi\) | ||||
0.995722 | − | 0.0924000i | \(-0.0294538\pi\) | |||||||
\(948\) | − 6.47214i | − 0.210205i | ||||||||
\(949\) | 5.05573 | 0.164116 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.0557281 | −0.00180711 | ||||||||
\(952\) | 8.23607i | 0.266932i | ||||||||
\(953\) | − 20.7984i | − 0.673725i | −0.941554 | − | 0.336863i | \(-0.890634\pi\) | ||||
0.941554 | − | 0.336863i | \(-0.109366\pi\) | |||||||
\(954\) | −22.1803 | −0.718115 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 24.3607 | 0.787881 | ||||||||
\(957\) | − 11.3475i | − 0.366813i | ||||||||
\(958\) | 3.88854i | 0.125633i | ||||||||
\(959\) | −8.61803 | −0.278291 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.6312 | −0.859071 | ||||||||
\(962\) | 10.1115i | 0.326006i | ||||||||
\(963\) | 10.9443i | 0.352674i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.00000 | −0.0321745 | ||||||||
\(967\) | − 50.5410i | − 1.62529i | −0.582759 | − | 0.812645i | \(-0.698027\pi\) | ||||
0.582759 | − | 0.812645i | \(-0.301973\pi\) | |||||||
\(968\) | 3.85410i | 0.123876i | ||||||||
\(969\) | 15.2705 | 0.490559 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.729490 | 0.0234105 | 0.0117052 | − | 0.999931i | \(-0.496274\pi\) | ||||
0.0117052 | + | 0.999931i | \(0.496274\pi\) | |||||||
\(972\) | 13.9443i | 0.447263i | ||||||||
\(973\) | 27.8885i | 0.894066i | ||||||||
\(974\) | 42.1803 | 1.35155 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.32624 | 0.202498 | ||||||||
\(977\) | 3.43769i | 0.109982i | 0.998487 | + | 0.0549908i | \(0.0175129\pi\) | ||||
−0.998487 | + | 0.0549908i | \(0.982487\pi\) | |||||||
\(978\) | − 2.23607i | − 0.0715016i | ||||||||
\(979\) | 5.88854 | 0.188199 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.4164 | −0.715701 | ||||||||
\(982\) | 16.1803i | 0.516335i | ||||||||
\(983\) | 19.2705i | 0.614634i | 0.951607 | + | 0.307317i | \(0.0994312\pi\) | ||||
−0.951607 | + | 0.307317i | \(0.900569\pi\) | |||||||
\(984\) | −7.61803 | −0.242854 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 24.2492 | 0.772253 | ||||||||
\(987\) | 9.70820i | 0.309016i | ||||||||
\(988\) | − 19.8541i | − 0.631643i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.5066 | −0.333752 | −0.166876 | − | 0.985978i | \(-0.553368\pi\) | ||||
−0.166876 | + | 0.985978i | \(0.553368\pi\) | |||||||
\(992\) | 2.09017i | 0.0663630i | ||||||||
\(993\) | − 9.12461i | − 0.289561i | ||||||||
\(994\) | −11.4721 | −0.363874 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.76393 | −0.214323 | ||||||||
\(997\) | 41.1935i | 1.30461i | 0.757956 | + | 0.652306i | \(0.226198\pi\) | ||||
−0.757956 | + | 0.652306i | \(0.773802\pi\) | |||||||
\(998\) | − 32.3607i | − 1.02436i | ||||||||
\(999\) | 8.58359 | 0.271573 |
(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 | 1150.2.b.i.599.1 | 4 | ||
5.2 | odd | 4 | 230.2.a.c.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1150.2.a.j.1.2 | 2 | |||
5.4 | even | 2 | inner | 1150.2.b.i.599.4 | 4 | ||
15.2 | even | 4 | 2070.2.a.u.1.2 | 2 | |||
20.3 | even | 4 | 9200.2.a.bu.1.1 | 2 | |||
20.7 | even | 4 | 1840.2.a.l.1.2 | 2 | |||
40.27 | even | 4 | 7360.2.a.bn.1.1 | 2 | |||
40.37 | odd | 4 | 7360.2.a.bh.1.2 | 2 | |||
115.22 | even | 4 | 5290.2.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.c.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
1150.2.a.j.1.2 | 2 | 5.3 | odd | 4 | |||
1150.2.b.i.599.1 | 4 | 1.1 | even | 1 | trivial | ||
1150.2.b.i.599.4 | 4 | 5.4 | even | 2 | inner | ||
1840.2.a.l.1.2 | 2 | 20.7 | even | 4 | |||
2070.2.a.u.1.2 | 2 | 15.2 | even | 4 | |||
5290.2.a.o.1.1 | 2 | 115.22 | even | 4 | |||
7360.2.a.bh.1.2 | 2 | 40.37 | odd | 4 | |||
7360.2.a.bn.1.1 | 2 | 40.27 | even | 4 | |||
9200.2.a.bu.1.1 | 2 | 20.3 | even | 4 |