Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(81,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.r (of order \(6\), degree \(2\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 737.12 | ||
Character | \(\chi\) | \(=\) | 1148.737 |
Dual form | 1148.2.r.a.81.12 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.507835 | + | 0.293199i | −0.293199 | + | 0.169278i | −0.639383 | − | 0.768888i | \(-0.720810\pi\) |
0.346185 | + | 0.938166i | \(0.387477\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.03735 | − | 1.79674i | 0.463916 | − | 0.803527i | −0.535236 | − | 0.844703i | \(-0.679777\pi\) |
0.999152 | + | 0.0411762i | \(0.0131105\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.44101 | − | 2.21889i | 0.544652 | − | 0.838662i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.32807 | + | 2.30028i | −0.442690 | + | 0.766761i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.222860 | − | 0.128668i | 0.0671949 | − | 0.0387950i | −0.466026 | − | 0.884771i | \(-0.654315\pi\) |
0.533221 | + | 0.845976i | \(0.320981\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.45553i | − | 0.958391i | −0.877708 | − | 0.479196i | \(-0.840928\pi\) | ||
0.877708 | − | 0.479196i | \(-0.159072\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.21660i | 0.314124i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.04528 | − | 2.33554i | 0.981123 | − | 0.566452i | 0.0785143 | − | 0.996913i | \(-0.474982\pi\) |
0.902609 | + | 0.430461i | \(0.141649\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.80286 | − | 1.04088i | −0.413604 | − | 0.238795i | 0.278733 | − | 0.960369i | \(-0.410086\pi\) |
−0.692337 | + | 0.721574i | \(0.743419\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0812217 | + | 1.54933i | −0.0177240 | + | 0.338092i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.62764 | + | 2.81916i | −0.339387 | + | 0.587836i | −0.984318 | − | 0.176406i | \(-0.943553\pi\) |
0.644931 | + | 0.764241i | \(0.276886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.347816 | + | 0.602435i | 0.0695633 | + | 0.120487i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.31674i | − | 0.638308i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.70628i | − | 0.688238i | −0.938926 | − | 0.344119i | \(-0.888178\pi\) | ||
0.938926 | − | 0.344119i | \(-0.111822\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.78319 | − | 4.82063i | −0.499876 | − | 0.865811i | 0.500124 | − | 0.865954i | \(-0.333288\pi\) |
−1.00000 | 0.000142943i | \(0.999954\pi\) | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0754508 | + | 0.130685i | −0.0131343 | + | 0.0227493i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.49194 | − | 4.89089i | −0.421214 | − | 0.826712i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.268952 | + | 0.465838i | −0.0442154 | + | 0.0765834i | −0.887286 | − | 0.461219i | \(-0.847412\pi\) |
0.843071 | + | 0.537803i | \(0.180745\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.01316 | + | 1.75484i | 0.162235 | + | 0.280999i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.37105 | + | 0.640121i | −0.994990 | + | 0.0999702i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.37720 | 1.27751 | 0.638756 | − | 0.769410i | \(-0.279450\pi\) | ||||
0.638756 | + | 0.769410i | \(0.279450\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.75534 | + | 4.77239i | 0.410742 | + | 0.711426i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.09770 | − | 4.09786i | −1.03531 | − | 0.597734i | −0.116805 | − | 0.993155i | \(-0.537265\pi\) |
−0.918500 | + | 0.395421i | \(0.870599\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.84695 | − | 6.39491i | −0.406708 | − | 0.913558i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.36955 | + | 2.37214i | −0.191776 | + | 0.332166i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.20381 | − | 3.00442i | 0.714798 | − | 0.412689i | −0.0980370 | − | 0.995183i | \(-0.531256\pi\) |
0.812835 | + | 0.582494i | \(0.197923\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.533896i | − | 0.0719905i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.22074 | 0.161691 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.959511 | + | 1.66192i | 0.124918 | + | 0.216364i | 0.921701 | − | 0.387902i | \(-0.126800\pi\) |
−0.796783 | + | 0.604265i | \(0.793467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.28053 | − | 7.41410i | 0.548066 | − | 0.949278i | −0.450341 | − | 0.892857i | \(-0.648698\pi\) |
0.998407 | − | 0.0564216i | \(-0.0179691\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.19031 | + | 6.26158i | 0.401941 | + | 0.788885i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.20869 | − | 3.58459i | −0.770093 | − | 0.444613i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.10708 | + | 4.10327i | −0.868268 | + | 0.501294i | −0.866772 | − | 0.498704i | \(-0.833809\pi\) |
−0.00149539 | + | 0.999999i | \(0.500476\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.90889i | − | 0.229803i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.57120i | − | 0.779858i | −0.920845 | − | 0.389929i | \(-0.872500\pi\) | ||
0.920845 | − | 0.389929i | \(-0.127500\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.75029 | + | 3.03159i | 0.204856 | + | 0.354820i | 0.950087 | − | 0.311986i | \(-0.100994\pi\) |
−0.745231 | + | 0.666806i | \(0.767661\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.353266 | − | 0.203958i | −0.0407917 | − | 0.0235511i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0356436 | − | 0.679915i | 0.00406197 | − | 0.0774835i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.43064 | − | 4.29008i | −0.836013 | − | 0.482672i | 0.0198941 | − | 0.999802i | \(-0.493667\pi\) |
−0.855907 | + | 0.517130i | \(0.827000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.01174 | − | 5.21649i | −0.334638 | − | 0.579610i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.65942 | 0.621202 | 0.310601 | − | 0.950540i | \(-0.399470\pi\) | ||||
0.310601 | + | 0.950540i | \(0.399470\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 9.69108i | − | 1.05115i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.08667 | + | 1.88218i | 0.116504 | + | 0.201790i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.91750 | + | 3.99382i | 0.733254 | + | 0.423344i | 0.819611 | − | 0.572920i | \(-0.194189\pi\) |
−0.0863576 | + | 0.996264i | \(0.527523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.66744 | − | 4.97947i | −0.803766 | − | 0.521990i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.82680 | + | 1.63206i | 0.293126 | + | 0.169236i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.74039 | + | 2.15951i | −0.383756 | + | 0.221561i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.39992i | 0.243675i | 0.992550 | + | 0.121838i | \(0.0388787\pi\) | ||||
−0.992550 | + | 0.121838i | \(0.961121\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.683522i | 0.0686965i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.9944 | − | 9.81172i | 1.69101 | − | 0.976303i | 0.737299 | − | 0.675567i | \(-0.236101\pi\) |
0.953707 | − | 0.300736i | \(-0.0972322\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.44694 | − | 16.3626i | 0.930834 | − | 1.61225i | 0.148936 | − | 0.988847i | \(-0.452415\pi\) |
0.781899 | − | 0.623406i | \(-0.214251\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.69949 | + | 1.75313i | 0.263444 | + | 0.171088i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.75048 | + | 8.22807i | −0.459246 | + | 0.795437i | −0.998921 | − | 0.0464359i | \(-0.985214\pi\) |
0.539675 | + | 0.841873i | \(0.318547\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.64417 | − | 5.56806i | 0.923743 | − | 0.533324i | 0.0389161 | − | 0.999242i | \(-0.487610\pi\) |
0.884827 | + | 0.465919i | \(0.154276\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 0.315425i | − | 0.0299388i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.9676 | 1.50211 | 0.751053 | − | 0.660242i | \(-0.229546\pi\) | ||||
0.751053 | + | 0.660242i | \(0.229546\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.37687 | + | 5.84890i | 0.314894 | + | 0.545413i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.94869 | + | 4.58918i | 0.734857 | + | 0.424270i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.646990 | − | 12.3416i | 0.0593095 | − | 1.13135i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.46689 | + | 9.46893i | −0.496990 | + | 0.860812i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.04776 | − | 2.19306i | 0.274807 | − | 0.197741i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8167 | 1.05692 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.9493 | −1.85895 | −0.929476 | − | 0.368883i | \(-0.879740\pi\) | ||||
−0.929476 | + | 0.368883i | \(0.879740\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.25423 | + | 2.45618i | −0.374564 | + | 0.216255i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.69535 | + | 9.86464i | −0.497605 | + | 0.861877i | −0.999996 | − | 0.00276326i | \(-0.999120\pi\) |
0.502391 | + | 0.864640i | \(0.332454\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.90755 | + | 2.50042i | −0.425539 | + | 0.216814i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.95933 | − | 3.44062i | −0.512897 | − | 0.296121i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0678 | − | 5.81267i | 0.860154 | − | 0.496610i | −0.00391012 | − | 0.999992i | \(-0.501245\pi\) |
0.864064 | + | 0.503382i | \(0.167911\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.426721 | 0.0361940 | 0.0180970 | − | 0.999836i | \(-0.494239\pi\) | ||||
0.0180970 | + | 0.999836i | \(0.494239\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.80594 | 0.404733 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.444617 | − | 0.770100i | −0.0371808 | − | 0.0643990i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.65922 | − | 3.84470i | −0.553018 | − | 0.319285i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.32076 | + | 2.41283i | 0.273892 | + | 0.199007i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.86303 | − | 3.38502i | −0.480318 | − | 0.277312i | 0.240231 | − | 0.970716i | \(-0.422777\pi\) |
−0.720549 | + | 0.693404i | \(0.756110\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.667476 | + | 0.385367i | −0.0543184 | + | 0.0313607i | −0.526913 | − | 0.849919i | \(-0.676651\pi\) |
0.472595 | + | 0.881280i | \(0.343317\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.4070i | 1.00305i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.5486 | −0.927603 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.6821 | + | 7.32204i | −1.01215 | + | 0.584363i | −0.911819 | − | 0.410592i | \(-0.865322\pi\) |
−0.100326 | + | 0.994955i | \(0.531989\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.76178 | + | 3.05150i | −0.139718 | + | 0.242000i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.90995 | + | 7.67401i | 0.308147 | + | 0.604797i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.29855 | + | 3.98120i | −0.180036 | + | 0.311832i | −0.941893 | − | 0.335914i | \(-0.890955\pi\) |
0.761856 | + | 0.647746i | \(0.224288\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.156537 | + | 0.271131i | 0.0121864 | + | 0.0211075i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.0661i | 1.47538i | 0.675141 | + | 0.737689i | \(0.264083\pi\) | ||||
−0.675141 | + | 0.737689i | \(0.735917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.05932 | 0.0814864 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.78864 | − | 2.76473i | 0.366197 | − | 0.211424i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.80164 | + | 13.5128i | −0.593147 | + | 1.02736i | 0.400658 | + | 0.916228i | \(0.368782\pi\) |
−0.993805 | + | 0.111134i | \(0.964552\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.83795 | + | 0.0963518i | 0.138936 | + | 0.00728351i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.974547 | − | 0.562655i | −0.0732514 | − | 0.0422917i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.8247 | + | 9.13642i | −1.18280 | + | 0.682888i | −0.956660 | − | 0.291207i | \(-0.905943\pi\) |
−0.226137 | + | 0.974095i | \(0.572610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.36252i | − | 0.547252i | −0.961836 | − | 0.273626i | \(-0.911777\pi\) | ||
0.961836 | − | 0.273626i | \(-0.0882230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.02018i | 0.371103i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.557994 | + | 0.966473i | 0.0410245 | + | 0.0710565i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.601020 | − | 1.04100i | 0.0439510 | − | 0.0761253i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.35949 | − | 4.77948i | −0.535324 | − | 0.347656i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0071 | + | 6.35493i | 0.796443 | + | 0.459826i | 0.842226 | − | 0.539125i | \(-0.181245\pi\) |
−0.0457831 | + | 0.998951i | \(0.514578\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.38830 | + | 3.11094i | −0.387859 | + | 0.223930i | −0.681232 | − | 0.732068i | \(-0.738555\pi\) |
0.293373 | + | 0.955998i | \(0.405222\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.20398 | 0.301053 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.53148 | 0.607843 | 0.303922 | − | 0.952697i | \(-0.401704\pi\) | ||||
0.303922 | + | 0.952697i | \(0.401704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.96960 | + | 4.60125i | −0.564950 | + | 0.326174i | −0.755130 | − | 0.655575i | \(-0.772426\pi\) |
0.190180 | + | 0.981749i | \(0.439093\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.40615 | − | 4.16757i | 0.169717 | − | 0.293958i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.22382 | − | 5.34080i | −0.577199 | − | 0.374851i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.45886 | + | 12.1111i | −0.381264 | + | 0.845879i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.32324 | − | 7.48808i | −0.300486 | − | 0.520457i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.535714 | −0.0370561 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.0849i | 1.72692i | 0.504420 | + | 0.863459i | \(0.331706\pi\) | ||||
−0.504420 | + | 0.863459i | \(0.668294\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.92667 | + | 3.33708i | 0.132013 | + | 0.228653i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.69008 | − | 15.0517i | 0.592658 | − | 1.02651i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.7071 | − | 0.770998i | −0.998381 | − | 0.0523388i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.77771 | − | 1.02636i | −0.120127 | − | 0.0693552i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.07053 | − | 13.9786i | −0.542882 | − | 0.940300i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2367 | 0.685499 | 0.342750 | − | 0.939427i | \(-0.388642\pi\) | ||||
0.342750 | + | 0.939427i | \(0.388642\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.84770 | −0.123180 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.3358 | + | 10.0088i | −1.15062 | + | 0.664309i | −0.949038 | − | 0.315163i | \(-0.897941\pi\) |
−0.201580 | + | 0.979472i | \(0.564608\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.29971 | + | 3.05979i | 0.350215 | + | 0.202197i | 0.664780 | − | 0.747039i | \(-0.268525\pi\) |
−0.314565 | + | 0.949236i | \(0.601859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.181249 | + | 0.355735i | 0.0119253 | + | 0.0234057i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.26585 | + | 5.34964i | 0.607026 | + | 0.350467i | 0.771801 | − | 0.635865i | \(-0.219356\pi\) |
−0.164775 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.7256 | + | 8.50181i | −0.960590 | + | 0.554597i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.03139 | 0.326824 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.02006i | 0.583459i | 0.956501 | + | 0.291729i | \(0.0942307\pi\) | ||||
−0.956501 | + | 0.291729i | \(0.905769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.46522 | + | 16.3942i | 0.609708 | + | 1.05605i | 0.991288 | + | 0.131710i | \(0.0420468\pi\) |
−0.381580 | + | 0.924336i | \(0.624620\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.6761 | + | 6.74119i | 0.749021 | + | 0.432448i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.4433 | − | 1.51851i | −0.922747 | − | 0.0970141i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.59680 | + | 6.22983i | −0.228859 | + | 0.396395i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.87405 | + | 1.65933i | −0.182136 | + | 0.105156i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.9573 | 1.00721 | 0.503607 | − | 0.863933i | \(-0.332006\pi\) | ||||
0.503607 | + | 0.863933i | \(0.332006\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.837705i | 0.0526660i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.84141 | + | 4.92147i | 0.177936 | + | 0.308194i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.82462 | + | 1.63080i | 0.176195 | + | 0.101726i | 0.585504 | − | 0.810670i | \(-0.300897\pi\) |
−0.409309 | + | 0.912396i | \(0.634230\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.646081 | + | 1.26805i | 0.0401455 | + | 0.0787931i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.52549 | + | 4.92219i | 0.527714 | + | 0.304676i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.38300 | − | 3.10788i | 0.331930 | − | 0.191640i | −0.324768 | − | 0.945794i | \(-0.605286\pi\) |
0.656698 | + | 0.754154i | \(0.271953\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 12.4665i | − | 0.765812i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.68393 | −0.286652 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.71843 | + | 2.97641i | 0.104775 | + | 0.181475i | 0.913646 | − | 0.406510i | \(-0.133255\pi\) |
−0.808871 | + | 0.587986i | \(0.799921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.75999 | + | 6.51250i | −0.228403 | + | 0.395606i | −0.957335 | − | 0.288980i | \(-0.906684\pi\) |
0.728932 | + | 0.684586i | \(0.240017\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.35377 | + | 0.280664i | 0.324025 | + | 0.0169865i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.155029 | + | 0.0895059i | 0.00934859 | + | 0.00539741i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.4158 | − | 21.5047i | −0.745990 | − | 1.29209i | −0.949731 | − | 0.313068i | \(-0.898643\pi\) |
0.203740 | − | 0.979025i | \(-0.434690\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.7851 | 0.885160 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.569323i | − | 0.0339629i | −0.999856 | − | 0.0169815i | \(-0.994594\pi\) | ||
0.999856 | − | 0.0169815i | \(-0.00540563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.51558 | + | 7.82121i | 0.268423 | + | 0.464922i | 0.968455 | − | 0.249189i | \(-0.0801641\pi\) |
−0.700032 | + | 0.714112i | \(0.746831\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.26633 | − | 2.19335i | 0.0750111 | − | 0.129923i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.76041 | + | 15.0591i | −0.458083 | + | 0.888910i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.40950 | − | 4.17338i | 0.141735 | − | 0.245493i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.703654 | − | 1.21877i | −0.0412490 | − | 0.0714453i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.0084i | 1.34417i | 0.740475 | + | 0.672083i | \(0.234600\pi\) | ||||
−0.740475 | + | 0.672083i | \(0.765400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.98139 | 0.231806 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.426760 | − | 0.739170i | −0.0247631 | − | 0.0428910i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.74169 | + | 5.62437i | 0.563376 | + | 0.325265i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0717 | − | 18.5881i | 0.695799 | − | 1.07140i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.75357 | + | 9.96547i | −0.330534 | + | 0.572501i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.88081 | − | 15.3820i | −0.508514 | − | 0.880771i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.7547 | 1.75526 | 0.877631 | − | 0.479336i | \(-0.159123\pi\) | ||||
0.877631 | + | 0.479336i | \(0.159123\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.0793i | 0.630280i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.8312 | − | 7.98547i | 0.784298 | − | 0.452815i | −0.0536535 | − | 0.998560i | \(-0.517087\pi\) |
0.837951 | + | 0.545745i | \(0.183753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.8425 | − | 10.8787i | −1.06504 | − | 0.614902i | −0.138219 | − | 0.990402i | \(-0.544138\pi\) |
−0.926823 | + | 0.375500i | \(0.877471\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.5599 | + | 0.763283i | 0.820358 | + | 0.0430061i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.0409 | + | 11.5706i | 1.12561 | + | 0.649872i | 0.942827 | − | 0.333281i | \(-0.108156\pi\) |
0.182784 | + | 0.983153i | \(0.441489\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.476881 | − | 0.825981i | −0.0267002 | − | 0.0462461i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5.57133i | − | 0.310961i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.72409 | −0.541063 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.08173 | − | 1.20189i | 0.115474 | − | 0.0666688i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.26510 | + | 5.65531i | −0.180560 | + | 0.312739i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.3206 | + | 9.84394i | −1.06518 | + | 0.542714i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.36878 | − | 4.83172i | −0.459990 | − | 0.265575i | 0.252050 | − | 0.967714i | \(-0.418895\pi\) |
−0.712040 | + | 0.702139i | \(0.752229\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.714373 | − | 1.23733i | −0.0391474 | − | 0.0678053i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.0261i | 0.930235i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.60859 | −0.196572 | −0.0982862 | − | 0.995158i | \(-0.531336\pi\) | ||||
−0.0982862 | + | 0.995158i | \(0.531336\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.10891 | + | 4.68168i | −0.440416 | + | 0.254274i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.24053 | − | 0.716218i | −0.0671782 | − | 0.0387854i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.2921 | − | 2.89807i | −0.987681 | − | 0.156481i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.42978 | − | 1.98018i | −0.184653 | − | 0.106610i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.1457 | − | 15.6726i | 1.45726 | − | 0.841347i | 0.458380 | − | 0.888756i | \(-0.348430\pi\) |
0.998876 | + | 0.0474092i | \(0.0150965\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.9809 | 0.587792 | 0.293896 | − | 0.955837i | \(-0.405048\pi\) | ||||
0.293896 | + | 0.955837i | \(0.405048\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.4611 | −0.611748 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.88754 | − | 6.73342i | −0.206913 | − | 0.358384i | 0.743827 | − | 0.668372i | \(-0.233008\pi\) |
−0.950741 | + | 0.309988i | \(0.899675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.8067 | − | 6.81662i | −0.626637 | − | 0.361789i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.28997 | + | 6.45718i | 0.174124 | + | 0.341750i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.99511 | + | 5.18768i | −0.158076 | + | 0.273795i | −0.934175 | − | 0.356816i | \(-0.883862\pi\) |
0.776099 | + | 0.630611i | \(0.217196\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.33313 | − | 12.7014i | −0.385954 | − | 0.668492i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 6.41154i | − | 0.336518i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.26263 | 0.380143 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.45073 | − | 9.44094i | −0.284526 | − | 0.492813i | 0.687968 | − | 0.725741i | \(-0.258503\pi\) |
−0.972494 | + | 0.232928i | \(0.925169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.98873 | − | 15.5053i | 0.363819 | − | 0.807176i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.832282 | − | 15.8761i | 0.0432100 | − | 0.824246i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.4469 | + | 25.0228i | −0.748033 | + | 1.29563i | 0.200731 | + | 0.979646i | \(0.435668\pi\) |
−0.948764 | + | 0.315985i | \(0.897665\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00094 | + | 3.46464i | −0.309887 | + | 0.178913i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.8071 | −0.659601 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.41610 | 0.226840 | 0.113420 | − | 0.993547i | \(-0.463819\pi\) | ||||
0.113420 | + | 0.993547i | \(0.463819\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.6388 | − | 6.14231i | 0.545042 | − | 0.314680i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.49960 | − | 4.32990i | −0.383212 | − | 0.221247i | 0.296003 | − | 0.955187i | \(-0.404346\pi\) |
−0.679215 | + | 0.733940i | \(0.737679\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.18466 | − | 0.769351i | −0.0603757 | − | 0.0392098i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.1255 | + | 19.2699i | −0.565541 | + | 0.979546i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.95320 | + | 3.38304i | 0.0990311 | + | 0.171527i | 0.911284 | − | 0.411779i | \(-0.135092\pi\) |
−0.812253 | + | 0.583306i | \(0.801759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.2057i | 0.768986i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.67947i | − | 0.336935i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.4163 | + | 8.90063i | −0.775680 | + | 0.447839i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.9795 | + | 10.3805i | 0.902366 | + | 0.520981i | 0.877967 | − | 0.478721i | \(-0.158899\pi\) |
0.0243990 | + | 0.999702i | \(0.492233\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.75910 | − | 2.70869i | 0.0880653 | − | 0.135604i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.74938 | + | 4.76207i | −0.137298 | + | 0.237807i | −0.926473 | − | 0.376362i | \(-0.877175\pi\) |
0.789175 | + | 0.614168i | \(0.210508\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.6578 | + | 9.61740i | −0.829786 | + | 0.479077i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.4969 | −0.620976 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.138422i | 0.00686134i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.94311 | − | 5.09762i | −0.145528 | − | 0.252061i | 0.784042 | − | 0.620708i | \(-0.213155\pi\) |
−0.929570 | + | 0.368646i | \(0.879821\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.40853 | + | 5.90375i | −0.168131 | + | 0.291211i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.07029 | + | 0.265803i | 0.249493 | + | 0.0130793i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.87079 | − | 10.1685i | 0.288186 | − | 0.499152i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.216704 | + | 0.125114i | −0.0106120 | + | 0.00612685i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.1932 | 0.839941 | 0.419971 | − | 0.907538i | \(-0.362040\pi\) | ||||
0.419971 | + | 0.907538i | \(0.362040\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.38887i | 0.408849i | 0.978882 | + | 0.204424i | \(0.0655322\pi\) | ||||
−0.978882 | + | 0.204424i | \(0.934468\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.8525 | − | 10.8845i | 0.916638 | − | 0.529221i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.81403 | + | 1.62468i | 0.136500 | + | 0.0788085i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2828 | − | 20.1819i | −0.497618 | − | 0.976669i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.451584 | + | 0.260722i | 0.0218027 | + | 0.0125878i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.02665 | + | 12.1705i | 0.338462 | + | 0.586233i | 0.984144 | − | 0.177374i | \(-0.0567601\pi\) |
−0.645682 | + | 0.763607i | \(0.723427\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3289 | 1.45751 | 0.728756 | − | 0.684773i | \(-0.240099\pi\) | ||||
0.728756 | + | 0.684773i | \(0.240099\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.50904 | 0.216192 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.86882 | − | 3.38837i | 0.280744 | − | 0.162088i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.3364 | − | 14.0506i | −1.16151 | − | 0.670600i | −0.209847 | − | 0.977734i | \(-0.567297\pi\) |
−0.951666 | + | 0.307134i | \(0.900630\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.4911 | + | 1.94408i | 0.880526 | + | 0.0925752i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.70957 | − | 2.96106i | 0.0812239 | − | 0.140684i | −0.822552 | − | 0.568690i | \(-0.807450\pi\) |
0.903776 | + | 0.428006i | \(0.140784\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.3517 | − | 8.28597i | 0.680337 | − | 0.392793i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.96993 | 0.187771 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.3383 | 1.47895 | 0.739473 | − | 0.673186i | \(-0.235075\pi\) | ||||
0.739473 | + | 0.673186i | \(0.235075\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.33749 | + | 0.962410i | −0.0629799 | + | 0.0453181i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.225978 | − | 0.391406i | 0.0106174 | − | 0.0183899i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.9006 | + | 8.61096i | −0.792313 | + | 0.403688i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.2715 | − | 20.9414i | −1.69671 | − | 0.979595i | −0.948845 | − | 0.315743i | \(-0.897746\pi\) |
−0.747864 | − | 0.663852i | \(-0.768921\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.74639 | − | 13.4171i | −0.361571 | − | 0.626259i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.9008 | 0.787147 | 0.393573 | − | 0.919293i | \(-0.371239\pi\) | ||||
0.393573 | + | 0.919293i | \(0.371239\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.2856i | − | 0.942750i | −0.881933 | − | 0.471375i | \(-0.843758\pi\) | ||
0.881933 | − | 0.471375i | \(-0.156242\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.86476 | − | 3.38602i | 0.271972 | − | 0.157023i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.31869 | + | 2.28403i | −0.0610215 | + | 0.105692i | −0.894922 | − | 0.446222i | \(-0.852769\pi\) |
0.833901 | + | 0.551914i | \(0.186102\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.13669 | + | 21.6827i | −0.0524873 | + | 1.00121i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.29362 | − | 7.43678i | 0.197840 | − | 0.342669i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.86694 | − | 1.07788i | 0.0858422 | − | 0.0495610i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.44814i | − | 0.0664453i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.9603i | 0.730772i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.408256 | + | 0.235707i | −0.0186537 | + | 0.0107697i | −0.509298 | − | 0.860590i | \(-0.670095\pi\) |
0.490644 | + | 0.871360i | \(0.336762\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.60972 | + | 0.929371i | 0.0733968 | + | 0.0423757i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.23562 | − | 2.75074i | −0.192727 | − | 0.125163i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.31204 | + | 2.48956i | 0.195800 | + | 0.113045i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.5814 | − | 18.3275i | −0.479487 | − | 0.830496i | 0.520236 | − | 0.854022i | \(-0.325844\pi\) |
−0.999723 | + | 0.0235264i | \(0.992511\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.69573i | − | 0.121905i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.8212 | 1.30068 | 0.650342 | − | 0.759641i | \(-0.274626\pi\) | ||||
0.650342 | + | 0.759641i | \(0.274626\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.65616 | − | 14.9929i | −0.389854 | − | 0.675247i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.22811 | + | 0.709050i | 0.0551995 | + | 0.0318694i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.5808 | − | 9.46919i | −0.654037 | − | 0.424751i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.77029 | + | 2.75413i | 0.213547 | + | 0.123292i | 0.602959 | − | 0.797772i | \(-0.293988\pi\) |
−0.389412 | + | 0.921064i | \(0.627322\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.59015 | − | 9.68242i | −0.249749 | − | 0.432579i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.46515i | 0.199091i | 0.995033 | + | 0.0995455i | \(0.0317389\pi\) | ||||
−0.995033 | + | 0.0995455i | \(0.968261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 40.7127i | − | 1.81169i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.537961 | + | 0.310592i | −0.0238917 | + | 0.0137939i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.8708 | + | 13.7818i | 1.05805 | + | 0.610868i | 0.924893 | − | 0.380227i | \(-0.124154\pi\) |
0.133161 | + | 0.991094i | \(0.457487\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.24895 | + | 0.484863i | 0.409149 | + | 0.0214491i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.45234 | + | 5.97962i | −0.152424 | + | 0.264007i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.5995 | − | 33.9474i | −0.863659 | − | 1.49590i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.10906 | −0.0927563 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.14971i | − | 0.401628i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.68697 | + | 2.12868i | −0.161529 | + | 0.0932590i | −0.578586 | − | 0.815622i | \(-0.696395\pi\) |
0.417056 | + | 0.908881i | \(0.363062\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.22671 | − | 15.9811i | 0.403456 | − | 0.698806i | −0.590684 | − | 0.806903i | \(-0.701142\pi\) |
0.994140 | + | 0.108096i | \(0.0344755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.961624 | + | 0.489953i | −0.0419687 | + | 0.0213833i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.5176 | − | 13.0005i | −0.980881 | − | 0.566312i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.20156 | + | 10.7414i | 0.269633 | + | 0.467018i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.09719 | −0.221199 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.21196 | + | 22.0153i | 0.0958105 | + | 0.953590i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.85580 | + | 17.0707i | 0.426103 | + | 0.738033i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.35757 | − | 9.27959i | 0.231196 | − | 0.400444i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.45729 | − | 1.05886i | −0.0627701 | − | 0.0456082i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0566 | + | 26.0789i | −0.647335 | + | 1.12122i | 0.336421 | + | 0.941712i | \(0.390783\pi\) |
−0.983757 | + | 0.179506i | \(0.942550\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.15868 | + | 3.73894i | 0.0926378 | + | 0.160453i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 23.1041i | − | 0.989670i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20.8394i | − | 0.891028i | −0.895275 | − | 0.445514i | \(-0.853021\pi\) | ||
0.895275 | − | 0.445514i | \(-0.146979\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.3697 | + | 19.6929i | 0.485246 | + | 0.840471i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.85779 | + | 6.68190i | −0.164348 | + | 0.284658i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.2269 | + | 10.3057i | −0.860135 | + | 0.438244i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.566737 | − | 0.327206i | −0.0240567 | − | 0.0138891i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.1658 | + | 15.6842i | −1.15105 | + | 0.664561i | −0.949144 | − | 0.314843i | \(-0.898048\pi\) |
−0.201910 | + | 0.979404i | \(0.564715\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 28.9477i | − | 1.22436i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.704873i | 0.0297598i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.00473 | + | 1.15743i | −0.0844894 | + | 0.0487800i | −0.541649 | − | 0.840604i | \(-0.682200\pi\) |
0.457160 | + | 0.889384i | \(0.348867\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.5640 | − | 28.6897i | 0.696852 | − | 1.20698i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.9148 | − | 0.834311i | −0.668359 | − | 0.0350378i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.9287 | + | 34.5175i | −0.835454 | + | 1.44705i | 0.0582056 | + | 0.998305i | \(0.481462\pi\) |
−0.893660 | + | 0.448745i | \(0.851871\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.3747 | − | 19.2689i | 1.39669 | − | 0.806378i | 0.402643 | − | 0.915357i | \(-0.368092\pi\) |
0.994044 | + | 0.108980i | \(0.0347583\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.45302 | −0.311354 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.26448 | −0.0944355 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.5277 | + | 19.3572i | −1.39578 | + | 0.805851i | −0.993947 | − | 0.109864i | \(-0.964959\pi\) |
−0.401829 | + | 0.915715i | \(0.631625\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.82425 | − | 3.15969i | 0.0758131 | − | 0.131312i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.15531 | − | 12.5576i | 0.338339 | − | 0.520978i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.773148 | − | 1.33913i | 0.0320205 | − | 0.0554611i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.4911 | − | 9.52116i | 0.681824 | − | 0.393651i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 25.2840i | − | 1.04358i | −0.853074 | − | 0.521790i | \(-0.825264\pi\) | ||
0.853074 | − | 0.521790i | \(-0.174736\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.5879i | 0.477471i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.33258 | + | 2.50142i | −0.178219 | + | 0.102895i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.1142 | − | 9.88092i | −0.702798 | − | 0.405761i | 0.105591 | − | 0.994410i | \(-0.466327\pi\) |
−0.808389 | + | 0.588649i | \(0.799660\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.5034 | − | 13.9650i | −0.881555 | − | 0.572509i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.69816 | − | 4.67335i | 0.110428 | − | 0.191268i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.67447 | + | 9.82846i | 0.231852 | + | 0.401580i | 0.958353 | − | 0.285585i | \(-0.0921880\pi\) |
−0.726501 | + | 0.687166i | \(0.758855\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 32.4655i | − | 1.32429i | −0.749374 | − | 0.662147i | \(-0.769645\pi\) | ||
0.749374 | − | 0.662147i | \(-0.230355\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 21.7977i | − | 0.887672i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.3421 | + | 19.6452i | 0.461123 | + | 0.798689i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.98589 | − | 6.90377i | 0.161782 | − | 0.280215i | −0.773726 | − | 0.633521i | \(-0.781609\pi\) |
0.935508 | + | 0.353305i | \(0.114942\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.74226 | + | 0.301030i | 0.232688 | + | 0.0121984i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.1603 | + | 24.5263i | −0.572863 | + | 0.992227i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.40119 | + | 11.0872i | 0.258542 | + | 0.447807i | 0.965851 | − | 0.259096i | \(-0.0834247\pi\) |
−0.707310 | + | 0.706904i | \(0.750091\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.778769 | − | 7.75099i | −0.0314030 | − | 0.312550i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.07093 | −0.284665 | −0.142333 | − | 0.989819i | \(-0.545460\pi\) | ||||
−0.142333 | + | 0.989819i | \(0.545460\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.72125 | − | 2.98130i | −0.0691830 | − | 0.119829i | 0.829359 | − | 0.558716i | \(-0.188706\pi\) |
−0.898542 | + | 0.438888i | \(0.855373\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.35043 | + | 5.39847i | 0.375220 | + | 0.216633i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.8301 | − | 9.59403i | 0.754411 | − | 0.384377i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.5190 | − | 18.2194i | 0.420759 | − | 0.728775i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.272054 | − | 0.157071i | 0.0108648 | − | 0.00627280i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.51259i | 0.100184i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.8212 | −1.14735 | −0.573677 | − | 0.819082i | \(-0.694483\pi\) | ||||
−0.573677 | + | 0.819082i | \(0.694483\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.35486 | − | 12.7390i | −0.292330 | − | 0.506330i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.7317 | + | 37.6405i | −0.862398 | + | 1.49372i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.0978 | + | 9.83773i | −0.875546 | + | 0.389785i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.1156 | + | 8.72701i | 0.597965 | + | 0.345235i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.8207 | − | 21.2585i | 1.45433 | − | 0.839658i | 0.455608 | − | 0.890180i | \(-0.349422\pi\) |
0.998723 | + | 0.0505221i | \(0.0160885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0505i | 0.711840i | 0.934516 | + | 0.355920i | \(0.115833\pi\) | ||||
−0.934516 | + | 0.355920i | \(0.884167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.1917i | 0.401297i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.4612 | + | 21.5834i | 0.489900 | + | 0.848531i | 0.999932 | − | 0.0116236i | \(-0.00370000\pi\) |
−0.510033 | + | 0.860155i | \(0.670367\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.427674 | + | 0.246918i | 0.0167877 | + | 0.00969236i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.69482 | − | 3.92055i | 0.301584 | − | 0.153659i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.739738 | + | 0.427088i | 0.0289482 | + | 0.0167133i | 0.514404 | − | 0.857548i | \(-0.328013\pi\) |
−0.485456 | + | 0.874261i | \(0.661346\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.8161 | + | 20.4661i | 0.461694 | + | 0.799678i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.29801 | −0.362750 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 8.38863i | − | 0.326775i | −0.986562 | − | 0.163387i | \(-0.947758\pi\) | ||
0.986562 | − | 0.163387i | \(-0.0522420\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.94238 | − | 6.82841i | −0.153341 | − | 0.265594i | 0.779113 | − | 0.626884i | \(-0.215670\pi\) |
−0.932454 | + | 0.361289i | \(0.882337\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.19699 | + | 4.73253i | 0.318345 | + | 0.183796i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.598227 | + | 11.4114i | −0.0231983 | + | 0.442515i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.4486 | + | 6.03249i | 0.404571 | + | 0.233579i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.19855 | + | 3.00138i | −0.200987 | + | 0.116040i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.20308i | − | 0.0850488i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.9646i | − | 1.42488i | −0.701733 | − | 0.712440i | \(-0.747590\pi\) | ||
0.701733 | − | 0.712440i | \(-0.252410\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.99812 | − | 1.15362i | 0.0769078 | − | 0.0444028i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.13106 | − | 1.95905i | 0.0434702 | − | 0.0752925i | −0.843472 | − | 0.537174i | \(-0.819492\pi\) |
0.886942 | + | 0.461881i | \(0.152825\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.32517 | + | 3.45833i | 0.204361 | + | 0.132718i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.86915 | − | 10.1657i | 0.224906 | − | 0.389549i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.13602 | − | 5.27469i | 0.349580 | − | 0.201830i | −0.314920 | − | 0.949118i | \(-0.601978\pi\) |
0.664500 | + | 0.747288i | \(0.268644\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 24.1191i | − | 0.921542i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.58850 | −0.136910 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.3819 | − | 17.9819i | −0.395517 | − | 0.685056i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.9468 | − | 10.9390i | −0.720772 | − | 0.416138i | 0.0942647 | − | 0.995547i | \(-0.469950\pi\) |
−0.815037 | + | 0.579409i | \(0.803283\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.51666 | + | 0.984965i | 0.0576132 | + | 0.0374157i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.442658 | − | 0.766706i | 0.0167910 | − | 0.0290828i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.2776 | + | 17.4693i | −0.919580 | + | 0.661697i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.27403 | −0.237306 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.8380 | 1.61797 | 0.808985 | − | 0.587830i | \(-0.200017\pi\) | ||||
0.808985 | + | 0.587830i | \(0.200017\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.969765 | − | 0.559894i | 0.0365754 | − | 0.0211168i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.98544 | − | 8.63503i | 0.187762 | − | 0.325214i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.71804 | − | 51.8476i | 0.102222 | − | 1.94993i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.4160 | − | 6.01368i | −0.391181 | − | 0.225848i | 0.291491 | − | 0.956574i | \(-0.405849\pi\) |
−0.682672 | + | 0.730725i | \(0.739182\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.7368 | − | 11.3951i | 0.740189 | − | 0.427348i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.1202 | 0.678606 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.84489 | −0.0689950 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.64467 | − | 4.58070i | −0.0987669 | − | 0.171069i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.3267 | + | 16.9318i | 1.09370 | + | 0.631449i | 0.934560 | − | 0.355807i | \(-0.115794\pi\) |
0.159142 | + | 0.987256i | \(0.449127\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.6936 | − | 44.5404i | −0.845154 | − | 1.65877i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.61354 | − | 5.55038i | −0.357531 | − | 0.206421i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.23279 | − | 1.28910i | 0.0829238 | − | 0.0478761i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.88181i | 0.292320i | 0.989261 | + | 0.146160i | \(0.0466914\pi\) | ||||
−0.989261 | + | 0.146160i | \(0.953309\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.1644 | 0.376460 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33.8881 | − | 19.5653i | 1.25340 | − | 0.723649i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.99235 | − | 10.3790i | 0.221332 | − | 0.383359i | −0.733880 | − | 0.679279i | \(-0.762293\pi\) |
0.955213 | + | 0.295920i | \(0.0956261\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.78002 | − | 3.46359i | 0.286970 | − | 0.127757i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.05592 | + | 1.82891i | −0.0388954 | + | 0.0673688i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.88348 | + | 6.72638i | 0.142856 | + | 0.247434i | 0.928571 | − | 0.371155i | \(-0.121038\pi\) |
−0.785715 | + | 0.618589i | \(0.787705\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 4.21830i | − | 0.154963i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.1316 | −0.775245 | −0.387622 | − | 0.921818i | \(-0.626704\pi\) | ||||
−0.387622 | + | 0.921818i | \(0.626704\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1640 | + | 7.02289i | −0.445655 | + | 0.257299i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.51610 | + | 13.0183i | −0.275000 | + | 0.476314i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.4117 | + | 22.3976i | 0.416974 | + | 0.818389i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.1002 | + | 9.29546i | 0.587505 | + | 0.339196i | 0.764110 | − | 0.645086i | \(-0.223178\pi\) |
−0.176605 | + | 0.984282i | \(0.556512\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.10365 | + | 4.67865i | −0.295313 | + | 0.170499i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.59904i | 0.0581950i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 18.9035i | − | 0.687061i | −0.939142 | − | 0.343530i | \(-0.888377\pi\) | ||
0.939142 | − | 0.343530i | \(-0.111623\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.245614 | − | 0.425416i | −0.00891521 | − | 0.0154416i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.95049 | + | 3.37835i | −0.0707052 | + | 0.122465i | −0.899211 | − | 0.437516i | \(-0.855858\pi\) |
0.828505 | + | 0.559981i | \(0.189192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.54246 | − | 29.4230i | 0.0558408 | − | 1.06518i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.2922 | + | 12.8704i | 0.805977 | + | 0.465331i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.74282 | − | 3.31562i | 0.207361 | − | 0.119720i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.88478 | 0.248272 | 0.124136 | − | 0.992265i | \(-0.460384\pi\) | ||||
0.124136 | + | 0.992265i | \(0.460384\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.91259 | −0.0688802 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.73918 | + | 2.15882i | −0.134489 | + | 0.0776473i | −0.565735 | − | 0.824587i | \(-0.691407\pi\) |
0.431246 | + | 0.902234i | \(0.358074\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.93608 | − | 3.35339i | 0.0695460 | − | 0.120457i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.699894 | − | 0.454532i | −0.0251086 | − | 0.0163063i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.1524 | + | 5.47746i | 0.435405 | + | 0.196250i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.845506 | − | 1.46446i | −0.0302546 | − | 0.0524024i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.2928 | −0.439308 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.3820i | 1.08438i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.2446 | + | 31.6005i | 0.650349 | + | 1.12644i | 0.983038 | + | 0.183400i | \(0.0587105\pi\) |
−0.332690 | + | 0.943036i | \(0.607956\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.82245 | + | 3.15658i | −0.0648810 | + | 0.112377i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.0096 | − | 35.4304i | 0.818126 | − | 1.25976i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.6196 | − | 14.7915i | −0.909780 | − | 0.525262i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.65517 | + | 6.33093i | 0.129635 | + | 0.224535i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.4618 | −0.441419 | −0.220709 | − | 0.975340i | \(-0.570837\pi\) | ||||
−0.220709 | + | 0.975340i | \(0.570837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.2828 | −1.35435 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.3738 | + | 10.6081i | −0.649208 | + | 0.374820i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.780138 | + | 0.450413i | 0.0275305 | + | 0.0158947i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.8442 | + | 0.935457i | 0.628925 | + | 0.0329705i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.74536 | − | 1.00768i | −0.0614396 | − | 0.0354722i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.3793 | + | 18.6942i | −1.13840 | + | 0.657253i | −0.946033 | − | 0.324071i | \(-0.894948\pi\) |
−0.192363 | + | 0.981324i | \(0.561615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.01558 | 0.316580 | 0.158290 | − | 0.987393i | \(-0.449402\pi\) | ||||
0.158290 | + | 0.987393i | \(0.449402\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.40970i | − | 0.154655i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.76879 | + | 8.25979i | 0.167044 | + | 0.289328i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.1029 | − | 8.71967i | −0.528384 | − | 0.305063i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.6371 | − | 11.0242i | 0.756061 | − | 0.385217i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.55132 | + | 7.88312i | −0.158842 | + | 0.275123i | −0.934451 | − | 0.356091i | \(-0.884109\pi\) |
0.775609 | + | 0.631213i | \(0.217443\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.1005 | − | 6.40890i | 0.386941 | − | 0.223400i | −0.293893 | − | 0.955838i | \(-0.594951\pi\) |
0.680834 | + | 0.732438i | \(0.261618\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.104972 | −0.00365466 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.4173i | 1.82273i | 0.411602 | + | 0.911364i | \(0.364970\pi\) | ||||
−0.411602 | + | 0.911364i | \(0.635030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.7389 | − | 34.1888i | −0.685562 | − | 1.18743i | −0.973260 | − | 0.229707i | \(-0.926223\pi\) |
0.287698 | − | 0.957721i | \(-0.407110\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.6103 | + | 7.28056i | 0.437447 | + | 0.252560i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.4523 | − | 19.2200i | −0.916517 | − | 0.665933i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.2568 | + | 19.7782i | 1.18551 | + | 0.684452i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.9888 | + | 9.23114i | −0.552654 | + | 0.319075i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 37.7810i | − | 1.30435i | −0.758071 | − | 0.652173i | \(-0.773858\pi\) | ||
0.758071 | − | 0.652173i | \(-0.226142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.2635 | 0.526328 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.166925 | + | 0.289122i | 0.00574919 | + | 0.00995789i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.09889 | − | 1.90333i | 0.0378029 | − | 0.0654765i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.1327 | + | 25.7753i | 0.451243 | + | 0.885650i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.58633 | − | 2.64792i | −0.157403 | − | 0.0908764i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.875515 | − | 1.51644i | −0.0300123 | − | 0.0519828i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0326 | −0.480468 | −0.240234 | − | 0.970715i | \(-0.577224\pi\) | ||||
−0.240234 | + | 0.970715i | \(0.577224\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 11.4719i | − | 0.392332i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.29615 | − | 7.44115i | −0.146754 | − | 0.254185i | 0.783272 | − | 0.621679i | \(-0.213549\pi\) |
−0.930026 | + | 0.367494i | \(0.880216\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.19621 | − | 5.53600i | 0.109053 | − | 0.188886i | −0.806334 | − | 0.591461i | \(-0.798551\pi\) |
0.915387 | + | 0.402575i | \(0.131885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.474294 | − | 9.92287i | −0.0161639 | − | 0.338170i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.0029 | − | 22.5217i | 0.442623 | − | 0.766646i | −0.555260 | − | 0.831677i | \(-0.687381\pi\) |
0.997883 | + | 0.0650308i | \(0.0207146\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.1860 | + | 28.0350i | 0.550342 | + | 0.953220i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.82585i | 0.0959710i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.20799 | −0.0749010 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.1790 | + | 24.5587i | 0.480436 | + | 0.832140i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.52051 | − | 3.18727i | −0.186841 | − | 0.107873i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.0281 | − | 26.2200i | 0.575653 | − | 0.886398i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.5426 | − | 32.1168i | 0.626140 | − | 1.08451i | −0.362179 | − | 0.932109i | \(-0.617967\pi\) |
0.988319 | − | 0.152398i | \(-0.0486997\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.74604 | − | 11.6845i | −0.227538 | − | 0.394108i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.5556 | 0.423008 | 0.211504 | − | 0.977377i | \(-0.432164\pi\) | ||||
0.211504 | + | 0.977377i | \(0.432164\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.7251i | 1.57242i | 0.617957 | + | 0.786212i | \(0.287960\pi\) | ||||
−0.617957 | + | 0.786212i | \(0.712040\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.02189 | + | 1.16734i | −0.0679650 | + | 0.0392396i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.2765 | − | 24.9857i | −1.45308 | − | 0.838937i | −0.454426 | − | 0.890784i | \(-0.650156\pi\) |
−0.998655 | + | 0.0518476i | \(0.983489\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.1883 | + | 46.4843i | −1.01248 | + | 1.55903i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.34240 | − | 0.775032i | −0.0449719 | − | 0.0259646i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.53077 | + | 14.7757i | 0.285471 | + | 0.494451i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.9106i | 1.26721i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.59622 | −0.220242 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.8666 | + | 10.3153i | −0.595884 | + | 0.344034i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.0339 | − | 24.3074i | 0.467537 | − | 0.809797i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.680410 | + | 12.9791i | −0.0226426 | + | 0.431917i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.2285 | − | 7.63750i | −0.439731 | − | 0.253879i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.14774 | + | 10.6482i | 0.204132 | + | 0.353568i | 0.949856 | − | 0.312688i | \(-0.101229\pi\) |
−0.745724 | + | 0.666255i | \(0.767896\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 52.1226i | 1.72880i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.78973 | 0.258085 | 0.129043 | − | 0.991639i | \(-0.458810\pi\) | ||||
0.129043 | + | 0.991639i | \(0.458810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.26126 | − | 0.728188i | 0.0417416 | − | 0.0240995i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.01997 | + | 5.20768i | 0.298191 | + | 0.172161i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.6815 | + | 26.8524i | 0.451802 | + | 0.886746i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.8463 | − | 15.4997i | −0.885576 | − | 0.511288i | −0.0130835 | − | 0.999914i | \(-0.504165\pi\) |
−0.872493 | + | 0.488627i | \(0.837498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.6183 | + | 9.01723i | −0.514641 | + | 0.297128i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.7070 | −0.747409 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.374183 | −0.0123031 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.0924 | + | 43.4613i | 0.824142 | + | 1.42746i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.7331 | − | 8.50615i | −0.483377 | − | 0.279078i | 0.238446 | − | 0.971156i | \(-0.423362\pi\) |
−0.721823 | + | 0.692078i | \(0.756695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.52368 | + | 14.4925i | −0.0499367 | + | 0.474971i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.68266 | + | 8.11060i | −0.153303 | + | 0.265529i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.24694 | − | 2.15976i | −0.0407791 | − | 0.0706316i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.2023i | 1.24802i | 0.781418 | + | 0.624008i | \(0.214497\pi\) | ||||
−0.781418 | + | 0.624008i | \(0.785503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.7585 | 0.416358 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.07502 | − | 12.2543i | −0.230639 | − | 0.399478i | 0.727357 | − | 0.686259i | \(-0.240748\pi\) |
−0.957996 | + | 0.286781i | \(0.907415\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.56519 | − | 19.0029i | 0.278921 | − | 0.618819i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.2218 | + | 8.26511i | −0.527696 | + | 0.268864i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.1438 | − | 19.3015i | 0.362123 | − | 0.627216i | −0.626187 | − | 0.779673i | \(-0.715385\pi\) |
0.988310 | + | 0.152457i | \(0.0487186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4757 | − | 6.04817i | 0.340057 | − | 0.196332i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.5700 | −0.440037 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.2735 | −0.527151 | −0.263576 | − | 0.964639i | \(-0.584902\pi\) | ||||
−0.263576 | + | 0.964639i | \(0.584902\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.8363 | − | 13.1845i | 0.738966 | − | 0.426642i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.484353 | + | 0.279641i | 0.0156569 | + | 0.00903952i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.61022 | − | 30.7156i | 0.0519968 | − | 0.991858i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.00767448 | − | 0.0132926i | 0.000247564 | − | 0.000428793i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.6179 | − | 21.8549i | −0.406607 | − | 0.704264i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.9085i | 0.415540i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.3396i | 0.461130i | 0.973057 | + | 0.230565i | \(0.0740574\pi\) | ||||
−0.973057 | + | 0.230565i | \(0.925943\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.93823 | − | 2.85109i | 0.158639 | − | 0.0915901i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.6839 | − | 11.9419i | −0.663779 | − | 0.383233i | 0.129937 | − | 0.991522i | \(-0.458523\pi\) |
−0.793715 | + | 0.608289i | \(0.791856\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.614911 | − | 0.946847i | 0.0197131 | − | 0.0303545i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.704784 | + | 1.22072i | −0.0225712 | + | 0.0390944i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.3035 | + | 7.68080i | −0.425618 | + | 0.245730i | −0.697478 | − | 0.716606i | \(-0.745694\pi\) |
0.271860 | + | 0.962337i | \(0.412361\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.05551 | 0.0656945 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.5791i | 0.944387i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.42677 | + | 7.66738i | 0.141192 | + | 0.244552i | 0.927946 | − | 0.372715i | \(-0.121573\pi\) |
−0.786754 | + | 0.617267i | \(0.788240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.85012 | − | 15.3289i | 0.281988 | − | 0.488418i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.92543 | − | 10.6639i | 0.220439 | − | 0.339435i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.6351 | + | 23.6167i | −0.433571 | + | 0.750966i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.9929 | + | 13.2750i | −0.730394 | + | 0.421693i | −0.818566 | − | 0.574412i | \(-0.805231\pi\) |
0.0881722 | + | 0.996105i | \(0.471897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.66661 | 0.179824 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.0924i | 0.605270i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.26235 | − | 1.88352i | 0.103320 | − | 0.0596517i | −0.447450 | − | 0.894309i | \(-0.647668\pi\) |
0.550770 | + | 0.834657i | \(0.314334\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.54507 | + | 0.892044i | 0.0488837 | + | 0.0282230i |
(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 | 1148.2.r.a.737.12 | yes | 56 | |
7.4 | even | 3 | inner | 1148.2.r.a.81.17 | yes | 56 | |
41.40 | even | 2 | inner | 1148.2.r.a.737.17 | yes | 56 | |
287.81 | even | 6 | inner | 1148.2.r.a.81.12 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.r.a.81.12 | ✓ | 56 | 287.81 | even | 6 | inner | |
1148.2.r.a.81.17 | yes | 56 | 7.4 | even | 3 | inner | |
1148.2.r.a.737.12 | yes | 56 | 1.1 | even | 1 | trivial | |
1148.2.r.a.737.17 | yes | 56 | 41.40 | even | 2 | inner |